OPINION OF THE COURT

ALDISERT, Circuit Judge.

Appellants Matthew Nestor and William Moyer appeal from final judgments entered by the United States District Court for the Middle District of Pennsylvania after a jury found Nestor guilty on Count Two of the indictment and Moyer guilty on Count Five. Count Two of the indictment charged Nestor with knowingly falsifying police reports with the intent to impede, obstruct, or influence the investigation into a matter within the jurisdiction of the Federal Bureau of Investigation ("FBI"), in violation of 18 U.S.C. § 1519. Count Five charged Moyer with knowingly making a false material statement in a matter within the FBI's jurisdiction, in violation of 18 U.S.C. § 1001.

Nestor now challenges both the indictment and his conviction. First, he contends that the District Court: (1) exceeded its discretion by denying, in relevant part, his motion for a bill of particulars; (2) erred by refusing to dismiss Count Two because it was duplicitous; and (3) exceeded its discretion by refusing to enforce the bill of particulars it did order. Nestor also contends (4) that the government presented insufficient evidence to support his conviction; and (5) that 18 U.S.C. § 1519 is unconstitutionally vague. Moyer argues that the evidence was insufficient to support his conviction under § 1001. For the reasons that follow, we will affirm.

I.

A.

In the late evening of July 12, 2008, in Shenandoah, Pennsylvania, teenagers Brandon Piekarsky, Derrick Donchak, Brian Scully, Colin Walsh, Ben Lawson, and Josh Redmond encountered Luis Ramirez, a Hispanic man, in a local park. After some of the teenagers shouted racially derogatory comments at Ramirez and told him to "go back to Mexico," a violent fight ensued. App. 00765. Walsh knocked Ramirez down and Piekarsky kicked their victim in the head while he was on the ground. The fight ended with Ramirez lying unconscious in the street.

Arielle Garcia witnessed part of the incident. She recognized the teenagers as students from Shenandoah High School and heard Scully shouting "racial" things to Ramirez about his ancestry. App. 00767. She saw Scully and Ramirez "interlock" and later saw "some[one]" kick Ramirez in the head "really hard" after he fell. App. 00675. After the teenagers fled the scene toward the park, Garcia phoned 911.

At the same time, Francis Ney saw approximately four "younger individuals" run in front of his moving car. App. 00977. He heard a female shouting and saw Ramirez lying in the street. Ney called 911 and reported seeing the teenagers in the park. Ney tried to revive Ramirez but eventually ran to the park with a man referred to as "Mexican Jesse," who confronted Piekarsky, Scully, Donchak, Walsh, Lawson and Redmond. According to some, "Mexican Jesse" brandished a gun.1 Officer Robert Senape of the West Mahanoy Police Department arrived at the scene and requested an ambulance. Lieutenant William Moyer and Officer Jason Hayes of the Shenandoah Police Department—both defendants below—arrived shortly thereafter. In the meantime, the police dispatch system reported a man chasing people in the park, so Lieutenant Moyer and Officer Hayes left to respond.

Moments later, Ney again called 911 to report that the teenagers who had beaten Ramirez were near the baseball field and urged the dispatcher to send police to the area. Ney was speaking with the dispatcher when Lieutenant Moyer and Officer Hayes arrived. While still on the phone with the 911 dispatcher, Ney told the officers that approximately five teenagers were running through the field on the back side of the school. When one of the officers asked who the teenagers were, Ney responded that they were a bunch of 16- to 17-year-old kids. Ney told the officers that he saw the teenagers who were beating Ramirez and that they fled when he stopped them to ask what they were doing. Ney told the police that Donchak remained in the park while the others ran away. Throughout this conversation—which was recorded on the 911 call—the dispatcher repeatedly asked if Ney was speaking with the police. After the dispatcher's third inquiry, Ney responded in the affirmative and the dispatcher terminated the call.

Ney and Donchak were placed in the police cruiser, and Lieutenant Moyer drove to Donchak's home, where the teenagers had gathered. After speaking with them, the officers looked "shocked" and "confused," and released the pair from the police car. App. 00989. But moments later, when Lieutenant Moyer and Officer Hayes saw Ney on their way back to the scene, they arrested him based on Piekarsky's assertion that Ney had a gun. Officer Charles Kovalewski of the Mahanoy City Police Department arrived while Lieutenant Moyer was handcuffing Ney, who kept saying "it wasn't him." App. 00957. Lieutenant Moyer told Ney to "shut up" and placed him in the rear seat of the police car. App. 00958. Officer Kovalewski also got into the car. At no point did Kovalewski hear Ney say anything about a man with a gun. The officers then drove back to the scene of the assault. Once there, Officer Hayes—who was romantically involved with Piekarsky's mother, Tammy—took Piekarsky toward the park and spoke with him privately.

Lieutenant Moyer telephoned Matthew Nestor, the Chief of Police, who was off-duty at a bar, and briefed him on the incident. Chief Nestor then called Piekarsky's mother.2 Other officers remained at the park and eventually found a BB gun. At the police station, Garcia and Ney provided statements, during which Garcia never identified who kicked Ramirez in the head. Officer Hayes interviewed Ney about the gun but did not ask what Ney knew about the assault.

The next day, July 13, 2008, detectives from the District Attorney's office arrived at the station. They, along with Lieutenant Moyer, interviewed Scully, who relayed "the cover story [the teenagers] made up" the night before. App. 00774. Later that day, District Attorney ("D.A.") James Goodman was briefed about the assault, and he instructed his detectives to continue to assist the police with their investigation.

Ramirez died on July 14. The cause of death was ruled a homicide. Phone records indicate that on the afternoon of July 15— immediately after learning the cause of death—Chief Nestor placed six telephone calls to Tammy Piekarsky.

By July 21, D.A. Goodman decided to take over the investigation because (1) the romantic relationship between Tammy Piekarsky and Officer Hayes created a conflict of interest, and (2) some of the suspects were "trying to protect the kicker." App. 01365. On July 23, D.A. Goodman contacted the Pennsylvania State Police and the State Attorney General's Office about a possible cover-up involving the Shenandoah Police Department.3 Two days later, on July 25, the D.A.'s office filed criminal complaints against the teenagers.

On July 28, the D.A.'s office contacted Chief Nestor because D.A. Goodman had not yet received any investigative reports from Officer Hayes. In fact, the only reports D.A. Goodman received from the police department were (1) a July 20 report from Chief Nestor regarding his investigative steps in the Ramirez assault, and (2) a one-page report from Lieutenant Moyer about "an individual who brought a BB gun to the scene after the assault" on Ramirez, but nothing regarding the assault itself. App. 01367. Chief Nestor's July 20 report did not: (1) identify the teenaged suspects; (2) include any of his contacts with Ms. Piekarsky; or (3) include his conversation with Borough Manager Palubinsky about the conflict of interest.

On August 1, D.A. Goodman sent a formal memorandum to Chief Nestor, Lieutenant Moyer and Officer Hayes, requesting additional information from Nestor and reports from Moyer and Hayes on their involvement in the investigation. They complied with this request. Lieutenant Moyer's report indicated that eyewitness Garcia told him at the scene that Scully had kicked Ramirez in the head. Officer Hayes's report—which Chief Nestor reviewed and incorporated into his August 1 report—also indicated that Garcia identified Scully as the kicker. This was the first time the D.A.'s office heard from the Shenandoah Police Department that someone had identified Scully as the kicker, even though Lieutenant Moyer briefed the D.A.'s office about the incident on the morning of July 13. In his August 1 report, Nestor stated that he was the one who: (1) contacted the D.A.'s office about a possible conflict of interest, and (2) requested that the D.A.'s office take over the case.4

The FBI became involved by the end of July 2008, after media reports revealed that the assault may have been racially motivated. As part of the investigation, FBI Special Agent Adam Aichele interviewed Lieutenant Moyer on June 2, 2009. At that time, Lieutenant Moyer stated that when he initially encountered Ney in the park on the night of the assault, Ney said someone had a gun, and, upon hearing this information, Moyer instructed Ney to get into the police car. Lieutenant Moyer also stated that Ney never identified Ramirez's assailants. When Special Agent Aichele interviewed Lieutenant Moyer again on June 11, 2009, Moyer reiterated the same sequence of events. Special Agent Aichele questioned Moyer's account and played the 911 recording for Moyer, in which Ney does not mention a man with a gun but does identify Ramirez's assailants. After hearing the recording, Lieutenant Moyer said, "That's not what he told me." App. 01674. Special Agent Aichele played the recording several more times for Moyer, who denied that Ney was speaking to him when Ney stated in the 911 call, "There they go," claiming that Ney must have been speaking to the dispatcher. Lieutenant Moyer then changed his story, stating that Ney must have told him about the gun after he put Ney in the police cruiser.

B.

On December 10, 2009, a federal grand jury returned a five-count indictment against Chief Nestor, Lieutenant Moyer and Officer Hayes, charging each with conspiring to falsify documents with the intent to obstruct an investigation of a matter within the jurisdiction of an agency of the United States, in violation of 18 U.S.C. § 371 (Count One), and with the substantive offense of falsifying documents in violation of 18 U.S.C. § 1519 (Count Two). The indictment additionally charged Lieutenant Moyer with two counts of obstruction of justice in violation of 18 U.S.C. § 1512 (Counts Three and Four) and one count of making false statements in violation of 18 U.S.C. § 1001 (Count Five).

Chief Nestor moved to dismiss Counts One and Two of the indictment and also moved for a bill of particulars seeking (1) the agency and matter within the federal government's jurisdiction and (2) the reports and/or statements alleged to be false in Count Two. The District Court denied the motion to dismiss and granted Chief Nestor's motion for a bill of particulars with respect to the "federal investigation or matter under the jurisdiction of a United States agency [Nestor] is alleged to have contemplated at the time of the alleged obstructive acts." App. 00287. In response, the government informed Chief Nestor that the matter within the FBI's jurisdiction was the racially motivated killing of Ramirez. The Court denied Chief Nestor's motion with respect to reports and/or statements pertaining to Count Two, concluding that the indictment specifically identified the reports at issue, the investigation to which they pertained, their subject matter, authors, and relevant dates.

Defendants pleaded not guilty and proceeded to trial. At the close of the government's case-in-chief, defendants moved for judgments of acquittal on sufficiency grounds. The Court denied the motions. On January 27, 2011, after a two-week trial, the jury convicted Moyer of making false statements (Count Five) and Nestor of falsifying documents (Count Two). Defendants were acquitted on all other counts. After the verdict, the Court denied defendants' motions for judgments of acquittal and new trials. Lieutenant Moyer was sentenced to three months' imprisonment on Count Five, followed by one year of supervised release; Chief Nestor was sentenced to thirteen months' imprisonment on Count Two, followed by two years of supervised release. Defendants timely appealed.5

II.

We first consider Nestor's substantive challenges to Count Two of the indictment. He contends that the District Court (1) exceeded its discretion by denying the requested bill of particulars relating to the alleged false statements; (2) erred by refusing to dismiss Count Two because it was duplicitous; and (3) exceeded its discretion by failing to enforce the bill of particulars it did order. We address each of these contentions in turn.

A.

First, Nestor contends that the District Court exceeded its discretion by denying the requested bill of particulars relating to the alleged false statements. The sufficiency of an indictment is a question of law over which we exercise plenary review. See United States v. Hodge, 211 F.3d 74, 76 (3d Cir.2000). A district court's denial of a motion for a bill of particulars is reviewed for an abuse of discretion. See United States v. Urban, 404 F.3d 754, 771 (3d Cir.2005).

For an indictment to be sufficient, it must contain all the elements of a crime and adequately apprise the defendant of what he must be prepared to meet. See Russell v. United States, 369 U.S. 749, 763-766, 82 S.Ct. 1038, 8 L.Ed.2d 240 (1962). "[W]hen the indictment itself is too vague and indefinite for such purposes," a bill of particulars is warranted. United States v. Addonizio, 451 F.2d 49, 64 (3d Cir.1971) (internal quotation marks and citation omitted). "The purpose of the bill of particulars is to inform the defendant of the nature of the charges brought against him to adequately prepare his defense, to avoid surprise during the trial and to protect him against a second prosecution for an inadequately described offense." Id. at 63-64 (quoting United States v. Tucker, 262 F.Supp. 305, 308 (S.D.N.Y.1966)). The decision to grant a motion for a bill of particulars is a "discretionary matter with the trial court," and a denial of such a motion "does not amount to an abuse of discretion unless the deprivation of the information sought leads to the defendant's inability to adequately prepare his case, to avoid surprise at trial, or to avoid the later risk of double jeopardy." Id. at 64.

Nestor contends that Count Two of the indictment was insufficient because it failed to identify the false statements underlying his conviction. See Virgin Islands v. Pemberton, 813 F.2d 626, 632 (3d Cir.1987). Nestor asserts he was prejudiced by this because, without knowing which statements were allegedly false, he was unable to properly prepare for trial. Therefore, Nestor contends, the District Court exceeded its discretion by denying his motion for a bill of particulars.

We conclude that the indictment here was sufficiently detailed such that a bill of particulars was not necessary. When an indictment merely quotes the language of a statute and that statute contains generalities, the indictment must factually define those generalities, descending into particulars. See Russell, 369 U.S. at 765, 82 S.Ct. 1038. Tracking the language of § 1519, Count Two charged Nestor with aiding and abetting others in falsifying documents while acting in relation to and in contemplation of a matter within federal jurisdiction, and doing so with the intent to impede, obstruct, and influence an investigation into that matter. The indictment, however, did more than just set forth the offense in the words of the statute. Count Two explained that the falsified documents were "official police reports" created between July 12, 2008, and March 30, 2009. App. 00053. Because Count Two incorporated Count One (charging conspiracy to violate § 1519), Nestor also knew which specific police reports were being investigated and which federal matter was at issue: the racially motivated assault of Ramirez.

Although the government did not identify every omission or inclusion that rendered false the documents identified in the indictment, and thus "did not, at the pre-trial stage, weave the information at its command into the warp of a fully integrated trial theory for the benefit of the defendant[]," the government was not "required to do so." Addonizio, 451 F.2d at 64 (citation omitted). Rule 7(c) of the Federal Rules of Criminal Procedure requires an indictment to be "concise" and contain "essential facts," but does not require the indictment to include every fact to be alleged by the government. Moreover, we agree with the District Court's assessment that the specificity with which the government identified the reports at issue made it "highly unlikely that [Nestor would] be unfairly surprised with an unfamiliar police report at trial." App. 00288. Because the indictment here was sufficiently detailed, we conclude that the District Court did not exceed its discretion by declining Nestor's request for a bill of particulars.

B.

Nestor asserts that Count Two of the indictment should be dismissed altogether because it alleged multiple false statements in multiple police reports in a single count and was, therefore, duplicitous. "Duplicity is the joining of two or more distinct offenses in a single count, so that a general verdict does not reveal exactly which crimes the jury found the defendant had committed." United States v. Gomberg, 715 F.2d 843, 845 (3d Cir.1983) (citation omitted), overruled on other grounds by Garrett v. United States, 471 U.S. 773, 105 S.Ct. 2407, 85 L.Ed.2d 764 (1985). Whether an indictment is duplicitous is a question of law subject to de novo review. See United States v. Haddy, 134 F.3d 542, 547 (3d Cir.1998).

Our analysis begins by ascertaining "the allowable unit of prosecution to decide whether the indictment properly charges a violation of the pertinent statute." United States v. Root, 585 F.3d 145, 150 (3d Cir.2009) (citation omitted). To do so, we discern "[c]ongressional intent by examining the language of the statute." Id. (citation omitted). The statute states:

18 U.S.C. § 1519. The statute is silent as to whether each falsified document—or even each falsified statement—is required to be charged separately or whether multiple statements or documents may be combined in one count.

The question of whether each falsified entry in a single document must be charged separately was recently considered in United States v. Schmeltz, 667 F.3d 685 (6th Cir.2011), in which the government charged a defendant with one count of obstruction for multiple falsified entries in a single document. The court held that "[t]he `falsifies' clause of § 1519 was ... intended to punish the falsification of a document, rather than specific statements or omissions within a document. Accordingly, [the defendant] could violate § 1519 once—and no more than once—by falsifying [a single] ... report with his omissions." Id. at 688. We agree with the rationale of the Court of Appeals for the Sixth Circuit and conclude that the statute does not require the government to charge separate counts for each false entry in a document.

Section 1519 does not explain in ipsis verbis whether each falsified document must be charged separately. The statute criminalizes the falsifying of "any record." The word "any" is defined as "[a]n indeterminate derivative of one ... in which the idea of unity ... is subordinated to that of indifference as to the particular one or ones that may be selected." Oxford English Dictionary (3d ed. 2009) (online version Dec. 2011). Courts have consistently rejected duplicity arguments when the statute employs "any" as a signifier regarding the "allowable unit of prosecution." See e.g., Root, 585 F.3d at 150-151 (explaining that multiple years of tax evasion may be combined in one count for violation of 26 U.S.C. § 7201, which criminalizes any willful "attempts in any manner to evade or defeat any tax imposed by this title...." (emphases added)); United States v. Brimberry, 744 F.2d 580, 583 (7th Cir.1984) ("We find that these separate actions of the defendant were in furtherance of the sole object of destroying all Stix records in Miller's possession, and ... these actions constituted a continuing course of conduct."); United States v. Berardi, 675 F.2d 894, 898 (7th Cir.1982) (concluding that an indictment may combine three separate attempts to influence a witness's testimony into one count of obstructing justice by "threats or force, or by any threatening letter" in violation of 18 U.S.C. § 1503).

Interpretation of the word "record" permits this reading as well. "Record" is defined as "anything preserving information and constituting a piece of evidence about past events." Oxford English Dictionary (3d ed. 2009) (online version Dec. 2011). Thus, the "record" concerning the investigation into the Ramirez assault could fairly be interpreted as the collection of official police reports. Because Count Two alleges a continuing course, between July 12, 2008, and March 30, 2009, of falsifying the "record" to obstruct a single federal investigation—and identifies multiple reports that were created to that singular end—the indictment is not duplicitous. See Berardi, 675 F.2d at 898 (holding that an indictment is not duplicitous when it is "fairly interpreted" to set forth a "continuing course of conduct, during a discrete period of time" to obstruct justice with facts that support such a theory); see also Rule 7(c)(1) (allowing a single count to allege "that the defendant committed [the offense] by one or more specified means").

But our inquiry is not yet finished. Because the government has discretion to draw "[t]he line between multiple offenses and multiple means to the commission of a single continuing offense," Berardi, 675 F.2d at 898, we must also "examine the concerns traditionally associated with charging in one count what could be several independent charges." Root, 585 F.3d at 154 (internal quotation marks and citation omitted). These concerns include: (1) avoiding doubt that a general verdict may mask a finding of guilt as to one crime but not another; (2) avoiding risk that the jury was not unanimous as to any one of the crimes charged; (3) providing the defendant adequate notice; (4) supplying an adequate basis for sentencing; and (5) protecting against double jeopardy. See id. (citation omitted).

Nestor argues that Count Two's duplicity prejudiced him because the jurors may have relied on different acts in concluding that he was guilty of obstructing justice. We disagree. Nestor was convicted of knowingly falsifying the record with the intent to obstruct a matter within the jurisdiction of the FBI. The jury instructions were crystal clear that if the jury found Nestor "guilty of an offense[,] every [juror] must agree that the government has overcome the presumption of innocence with evidence that proves each element of that offense beyond a reasonable doubt." App. 02626. At trial, following the reading of the verdict, the jury was polled and the verdict was affirmed individually by each juror. Thus, every juror agreed that between July 12, 2008, and March 30, 2009, Nestor engaged in a continuing course of conduct of using the official police reports to knowingly falsify the record of the Ramirez investigation, with the intent to obstruct a matter within the jurisdiction of the FBI. Given this, we conclude that Count Two of the indictment "may fairly be read to charge but a single scheme and is therefore not duplicitous." Root, 585 F.3d at 150 (quoting United States v. Shorter, 809 F.2d 54, 57 (D.C.Cir.1987)).

C.

Nestor contends also that the District Court exceeded its discretion in refusing to enforce the bill of particulars that it did order.6 In response to the Court's order, the government informed Nestor that "the matter within the jurisdiction of the [FBI was] the racially motivated killing of" Ramirez. App. 00302. Nestor asserts that this response was inadequate and required further enforcement. We disagree.

First, the FBI clearly has jurisdiction to investigate racially motivated killings under several statutes, including 18 U.S.C. § 241, § 245, and 42 U.S.C. § 3631. Second, that the government did not identify a specific criminal statute over which it had jurisdiction is of no consequence. The plain language of 18 U.S.C. § 1519 criminalizes a defendant's efforts to obstruct "the investigation or proper administration of any matter" within the jurisdiction of the FBI, "or in relation to or contemplation of any such matter." Indeed, § 1519 covers efforts to obstruct investigations that do not result in the filing of charges. See, e.g., United States v. Gray, 642 F.3d 371, 379 (2d Cir. 2011) ("[Section] 1519 does not require the existence or likelihood of a federal investigation."). Thus, if the statute does not require the existence of a federal investigation before criminal liability may attach, it certainly does not require the government to identify a specific federal statute that is the focus of the investigation. Therefore, because the FBI unquestionably has jurisdiction to investigate racially motivated killings, and because Nestor was informed that the racially motivated killing of Ramirez was the federal matter at issue in Count Two, the District Court did not exceed its discretion by denying a request for additional information. We therefore reject Nestor's three challenges to the indictment.

III.

Nestor raises several challenges to the sufficiency of evidence to support his conviction on Count Two for obstructing justice in violation of 18 U.S.C. § 1519. For the reasons that follow, we conclude that these contentions do not carry the day.

Count Two of the indictment charged Nestor with knowingly falsifying police reports with the intent to impede, obstruct, or influence the investigation into the racially motivated assault of Ramirez. Nestor contends that the evidence was insufficient to prove his guilt on Count Two. Sufficiency of the evidence is a question of law, subject to plenary review. See United States v. Silveus, 542 F.3d 993, 1002 (3d Cir.2008). We review "the evidence in the light most favorable to the Government," afford "deference to a jury's findings," and draw "all reasonable inferences in favor of the jury verdict." United States v. Riley, 621 F.3d 312, 329 (3d Cir.2010) (internal quotation marks and citation omitted). We will overturn the verdict "only when the record contains no evidence, regardless of how it is weighted, from which the jury could find guilt beyond a reasonable doubt." Id. (internal quotation marks and citation omitted).

Nestor asserts that the evidence was insufficient to convict him because the government failed to prove: (1) that he knowingly falsified documents; (2) that he knew the "matter" at issue was within the FBI's jurisdiction; (3) that he intended to obstruct an FBI investigation; and (4) that he acted in "contemplation of" such a matter. To resolve these challenges, we must first consider what proof is required to establish a violation of § 1519.

A.

The parties agree that the government must prove that Nestor knowingly falsified a record or document. The government presented evidence from which a reasonable juror could conclude not only that Nestor had a motive to falsify police reports,7 but that he did, in fact, knowingly falsify reports and aided and abetted others in doing so as well. The jury learned that on August 1, 2008, as part of the D.A.'s investigation into a possible police cover-up of the Ramirez assault, the D.A. formally directed Nestor, Moyer and Hayes to prepare reports of their investigative efforts. The jury learned that Hayes's report—which Nestor reviewed and incorporated into his own report— falsely indicated that eyewitness Garcia identified Scully as the one who kicked the victim in the head. The jury also heard evidence from which it could reasonably infer that Nestor—who was present at Garcia's interview—knew the information in the report about Garcia identifying the kicker was false. App. 01997. Moreover, none of the police reports included any mention of racial motivation for the assault. Nestor's own July 20 report did not: (1) identify the teenaged suspects then known to him; (2) include any of his contacts with Ms. Piekarsky; or (3) include his conversation with Palubinsky about the conflict of interest. Nestor's August 1 report, moreover, falsely stated that he was the person who (1) contacted the D.A.'s office about a possible conflict of interest; and (2) requested that the D.A.'s office take over the case. In these respects, the reverse was true.

Nestor contends that, like other obstruction of justice statutes, § 1519 does not criminalize the omissions in his report because there is no proof that he had a contemporaneous duty to disclose the specific information alleged to have been omitted. See United States v. Curran, 20 F.3d 560, 566 (3d Cir.1994) ("[T]o convict under a section 1001 concealment charge, the government must show that a defendant had a legal duty to disclose the facts at the time he was alleged to have concealed them."). Furthermore, Nestor contends, none of the omissions or false representations may be considered material.

These arguments fail. It borders on the ridiculous to assert that a Chief of Police would not have a duty to disclose the identity of suspects in his official police reports or, conversely, that withholding the names of suspects—known to him—in those official police reports would be deemed acceptable. Furthermore, although one court has concluded that material omissions may support a conviction under § 1519, see United States v. Lanham, 617 F.3d 873, 887 (6th Cir.2010), we refuse to require such a conclusion, because materiality is not an express element of § 1519, as it is in 18 U.S.C. § 1001. Nestor's reliance on Curran, therefore, is misplaced, because that case involved § 1001.8

From all of this evidence, we conclude that a reasonable juror could find that Nestor knowingly falsified documents. There was sufficient evidence to prove that he knowingly (1) endorsed false information contained in his subordinate's report, (2) omitted information from his own report, and (3) produced false information in his report, all with the intent to impede the investigation into the racially motivated assault.

B.

Nestor maintains that the knowledge requirement of § 1519 necessitates that the government prove Nestor knew the "matter" at issue was within the jurisdiction of the FBI. We decline to read such a requirement into the statute. See Bates v. United States, 522 U.S. 23, 29, 118 S.Ct. 285, 139 L.Ed.2d 215 (1997) ("[W]e ordinarily resist reading words or elements into a statute that do not appear on its face.").

The most natural reading of § 1519, which we accept, is to interpret "knowingly" as modifying its surrounding verbs only: "alters, destroys, mutilates, conceals, covers up, falsifies, or makes a false entry." 18 U.S.C. § 1519; see also United States v. Yielding, 657 F.3d 688, 714 (8th Cir.2011). Although the Supreme Court has occasionally interpreted "knowingly" more broadly when scienter is not otherwise expressed in the criminal statute, see, e.g., United States v. X-Citement Video, Inc., 513 U.S. 64, 69-70, 115 S.Ct. 464, 130 L.Ed.2d 372 (1994), that "concern[] [is] not present here," because § 1519 expressly "requires proof that an accused knowingly falsified a document, with intent to impede, obstruct, or interfere with the investigation or proper administration of a matter," Yielding, 657 F.3d at 714. "By the plain terms of § 1519, knowledge of a pending federal investigation or proceeding is not an element of the obstruction crime." Gray, 642 F.3d at 378.

Indeed, "[i]t is well settled that mens rea requirements typically do not extend to the jurisdictional elements of a crime—that `the existence of the fact that confers federal jurisdiction need not be one in the mind of the actor at the time he perpetrates the act made criminal by the federal statute.'" United States v. Cooper, 482 F.3d 658, 664 (4th Cir.2007) (quoting United States v. Feola, 420 U.S. 671, 677 n. 9, 95 S.Ct. 1255, 43 L.Ed.2d 541 (1975)). The government therefore need not prove that Nestor actually knew that the "matter" at issue was within the jurisdiction of the federal government when he falsified documents.9 It need only prove that he knowingly falsified them. To that end, we conclude that there was sufficient evidence for a reasonable juror to find that he did so.

C.

Nestor contends also that the government did not prove a sufficient "nexus" between his conduct and the federal investigation, as required by United States v. Aguilar, 515 U.S. 593, 115 S.Ct. 2357, 132 L.Ed.2d 520 (1995), and Arthur Andersen LLP v. United States, 544 U.S. 696, 125 S.Ct. 2129, 161 L.Ed.2d 1008 (2005). We conclude that proof of such a nexus is not required. The text of § 1519 requires only proof that Nestor knowingly falsified documents and did so with the intent to "impede, obstruct, or influence the investigation or proper administration of any matter" that happens to be within federal jurisdiction.

In reliance upon Aguilar and Arthur Andersen, Nestor argues that the government must prove that he intended to impede a specific federal investigation. In Aguilar, the Court held that the defendant's act of lying to investigators was not sufficiently connected to a grand jury proceeding to uphold his conviction under the general obstruction statute, 18 U.S.C. § 1503. See 515 U.S. at 600-601, 115 S.Ct. 2357. Extending the reasoning of Aguilar to § 1512(b)(2), the Court in Arthur Andersen held that the government was required to prove a "nexus" between the defendant's attempts to persuade another to destroy documents and a pending or foreseeable official proceeding. 544 U.S. at 708, 125 S.Ct. 2129 (reasoning that a knowingly corrupt persuader "cannot be someone who persuades others to shred documents under a document retention policy when he does not have in contemplation any particular official proceeding in which those documents might be material").

We decline to extend the reasoning of §§ 1503 and 1512(b)(2), because "the language of § 1519 is materially different from [those] statutes." Yielding, 657 F.3d at 712; see also United States v. Kernell, 667 F.3d 746, 753-55 (6th Cir.2012). Section 1503 forbids "corruptly endeavor[ing]" to obstruct justice, and § 1512(b)(2) prohibits the "knowingly corrupt[t] persua[sion]" to obstruct justice. Thus, in both Aguilar and Arthur Andersen, the Court was "required to discern the substance of an intent requirement from statutory terms that appeared to imply one, but did not speak directly to its content." Yielding, 657 F.3d at 713. By contrast, the statute at issue here speaks "more directly to the requisite intent and describe[s] its scope more precisely." Id. "That the accused's intent must be wrongful is evident from the nature of the acts prohibited, such as knowing falsification of documents, and the requisite intent to influence, obstruct, or impede an investigation." Id. (citation omitted). Nestor's argument, therefore, conflicts with the plain meaning of the statute. "The words of the statute are unambiguous, and thus, `judicial inquiry is complete.'" Gray, 642 F.3d at 377 (quoting Conn. Nat'l Bank v. Germain, 503 U.S. 249, 254, 112 S.Ct. 1146, 117 L.Ed.2d 391 (1992)). Therefore, "[i]t is sufficient that the `matter' [under investigation] is within the jurisdiction of a federal agency as a factual matter." Yielding, 657 F.3d at 714 (citation omitted). We accept the analysis of the Court of Appeals for the Eighth Circuit in this respect.

The legislative history further confirms this interpretation. The Senate considered the intent requirement to be independent of the jurisdiction requirement, explaining that § 1519 "is meant to apply broadly to any acts to destroy or fabricate physical evidence so long as they are done with the intent to obstruct, impede or influence the investigation or proper administration of any matter, and such matter is within the jurisdiction of an agency of the United States." S.Rep. No. 107-146, at 14 (2002) (emphases added). The Senate Report goes on to clarify: "[t]his statute is specifically meant not to include any technical requirement, which some courts have read into other obstruction of justice statutes, to tie the obstructive conduct to a pending or imminent proceeding or matter." Id. at 14-15; see also 148 Cong. Rec. S7419 (daily ed. July 26, 2002) (statement of Sen. Patrick Leahy) ("The fact that a matter is within the jurisdiction of a federal agency is intended to be a jurisdictional matter, and not in any way linked to the intent of the defendant.").

Thus, we conclude that the government was required only to prove that (1) Nestor intended to impede an investigation into "any matter" and (2) the matter at issue was ultimately proven to be within the federal government's jurisdiction. It was not required to prove that Nestor intended to obstruct or impede a specific federal investigation.

D.

Nestor contends also that no reasonable juror could have found that he acted in "contemplation of" a specific federal investigation at the time he prepared his reports in July and August of 2008. Again, Nestor's argument is based upon a misguided reading of § 1519.

The statute expressly criminalizes the knowing falsification of any record "with the intent to impede, obstruct, or influence the investigation or proper administration of any matter within the jurisdiction of" the federal government. 18 U.S.C. § 1519. To ensure that the statute is applied "broadly," criminal liability "also extends to acts done in contemplation of such federal matters, so that the timing of the act in relation to the beginning of the matter or investigation is also not a bar to prosecution." S.Rep. No. 107-146, at 13 (2002) (emphasis added); see also Gray, 642 F.3d at 379 ("[Section] 1519 does not require the existence or likelihood of a federal investigation."). In analyzing the intent requirement of § 1519, we examined the statute's use of "any matter" and concluded that a defendant need not intend to obstruct or impede a specific federal investigation; the government must prove only that (1) a defendant intended to impede the investigation of "any matter" and (2) the matter at issue was ultimately proven to be within the federal government's jurisdiction. See supra Part III.C. The in "contemplation of" clause of § 1519 refers to the same "matter." Thus, the same analysis is required.

Looking to the evidence presented at trial, we conclude that a reasonable juror could have found that Nestor acted in "contemplation of" an investigation into the racially motivated assault on Ramirez, which was within the jurisdiction of the FBI. The government presented evidence that D.A. Goodman took over the investigation because he determined that the "coverup was more than just the [teenaged] boys." App. 01455. As part of the D.A.'s investigation, Goodman directed Nestor to prepare the police reports at issue. Moreover, there was evidence that, by the end of July 2008, it was well-reported by local news outlets that the FBI was investigating the Ramirez assault. We conclude that this evidence was sufficient to prove Nestor knowingly falsified documents in "contemplation of" an investigation of a "matter," which was proven to be within the jurisdiction of the federal government.

IV.

Finally, Nestor challenges the constitutionality of § 1519, arguing it is too vague. We apply de novo review to this challenge. See United States v. Weatherly, 525 F.3d 265, 273 (3d Cir.2008). "It is well established that vagueness challenges to statutes which do not involve First Amendment freedoms must be examined in the light of the facts of the case at hand." United States v. Mazurie, 419 U.S. 544, 550, 95 S.Ct. 710, 42 L.Ed.2d 706 (1975) (citation omitted).

A.

A statute is unconstitutionally vague only if it "fails to provide people of ordinary intelligence a reasonable opportunity to understand what conduct it prohibits" or "authorizes ... arbitrary and discriminatory enforcement." United States v. Amirnazmi, 645 F.3d 564, 588 (3d Cir. 2011) (internal quotation marks and citation omitted). In criminal cases, because "vagueness attacks are based on lack of notice, they may be overcome in any specific case where reasonable persons would know their conduct puts [them] at risk of punishment under the statute." San Filippo v. Bongiovanni, 961 F.2d 1125, 1136 (3d Cir.1992) (alteration in original) (internal quotation marks and citation omitted). Criminal statutes, therefore, need only give "`fair warning' that certain conduct is prohibited" to withstand a constitutional challenge. Id. (quoting Colten v. Kentucky, 407 U.S. 104, 110, 92 S.Ct. 1953, 32 L.Ed.2d 584 (1972)).

The focus of our inquiry is the meaning of the statute in light of common understanding and practice. See Robinson v. Napolitano, 554 F.3d 358, 365 (3d Cir.2009). In looking at the language of the statute, § 1519 "rather plainly criminalizes the conduct of an individual who (1) knowingly (2) makes a false entry in a record or document (3) with the intent to impede or influence a federal investigation." United States v. Hunt, 526 F.3d 739, 743 (11th Cir.2008). As a law enforcement officer, Nestor cannot credibly argue that the statute was unconstitutionally vague as applied to him. Any person of ordinary intelligence—let alone a chief of police—would comprehend that this statute prohibits a police officer from knowingly writing a false report with the intent to impede an ongoing, or future, investigation. See id. ("A person of ordinary intelligence would understand a police report to be a `record' or `document,' and would also read the language `any matter within the jurisdiction of [a] department ... of the United States' to include an FBI investigation."). Nestor's conduct, therefore, falls plainly within the prohibitions of the statute, and as such, the statute's "plain text" put Nestor "on notice [that] his conduct was unlawful." Id.

Section 1519's scienter requirement, moreover, eliminates any concerns regarding statutory vagueness. Scienter requirements in criminal statutes "alleviate vagueness concerns" because a mens rea element makes it less likely that a defendant will be convicted for an action committed by mistake. Gonzales v. Carhart, 550 U.S. 124, 149, 127 S.Ct. 1610, 167 L.Ed.2d 480 (2007) (citation omitted). Because a defendant will be convicted for violating § 1519 "only for an act knowingly done with the purpose of doing that which the statute prohibits, the accused cannot be said to suffer from lack of warning or knowledge that the act which he does is a violation of law." Screws v. United States, 325 U.S. 91, 102, 65 S.Ct. 1031, 89 L.Ed. 1495 (1945). Here, by the express language of the statute, no liability will be imposed for knowingly falsifying documents without an "intent to impede, obstruct, or influence a matter." 18 U.S.C. § 1519; see also Kernell, 667 F.3d at 753 ("[T]he construction creates the needed specific intent and avoids [defendant's] concern that `the statute would forbid innocent conduct.'" (quoting Yielding, 657 F.3d at 711)).

B.

Nestor contends also that applying § 1519 to his actions would require a Procrustean stretching of that statute's language, because his actions were not done in "contemplation of" an FBI investigation. Specifically, Nestor asserts that the "contemplation of" clause is too vague because it does not specify what a defendant must know to trigger criminal liability.

We have already concluded that it was enough that the government prove that Nestor acted in "contemplation of" an investigation into the racially motivated assault on Ramirez, which was within the jurisdiction of the FBI. Although this interpretation makes criminal liability very broad under § 1519, this "is consistent with the legislative history and other cases to consider the question." Kernell, 667 F.3d at 755; see also Gray, 642 F.3d at 379 ("[Section] 1519 does not require the existence or likelihood of a federal investigation."); S.Rep. No. 107-146, at 14 (2002) (explaining that § 1519 "is meant to apply broadly to any acts to destroy or fabricate physical evidence" (emphasis added)).

"Moreover, even if this element is potentially vague as it relates to hypothetical defendants," it is clearly not vague as it relates to Nestor. Kernell, 667 F.3d at 755. As previously discussed, the government presented sufficient evidence to prove that when Nestor falsified the police reports, he contemplated an investigation into a matter within the jurisdiction of the FBI, intending to impede that investigation. See supra, Part III.D. Thus, we conclude that the statute is not vague "in the light of the facts of the case at hand." Mazurie, 419 U.S. at 550, 95 S.Ct. 710 (citation omitted).10

Because § 1519 clearly expresses the elements that the government must prove to secure a conviction under the statute, we reject Nestor's challenges to its constitutionality.

V.

We now turn to review Moyer's conviction on Count Five, for knowingly making a false material statement in a matter within the FBI's jurisdiction in violation of 18 U.S.C. § 1001.11 Specifically, the indictment alleged that, in conversations with the FBI on June 2 and 11, 2009, Moyer falsely stated that (1) an eyewitness warned that there was a man with a gun in the park and (2) the same eyewitness never identified anyone involved in the assault on Ramirez.

To establish a violation of § 1001, the government was required to prove each of the following five elements: (1) that Moyer made a statement or representation; (2) that the statement or representation was false; (3) that the false statement was made knowingly and willfully; (4) that the statement or representation was material; and (5) that the statement or representation was made in a matter within the jurisdiction of the federal government.12 See United States v. Barr, 963 F.2d 641, 645 (3d Cir.1992). Moyer contends that the government's evidence was insufficient to prove three of the required five elements: (1) that the statements were false; (2) that they were made knowingly and willfully; and (3) that they were material. For the reasons that follow, we conclude that the evidence was sufficient to support Moyer's conviction.

A.

First, we agree with the government that there was sufficient evidence that Moyer made false statements. Based on the evidence presented at trial, a reasonable juror could find that Moyer falsely stated that the eyewitness, Francis Ney, did not identify Ramirez's assailants. Indeed, the 911 call recorded this identification. The recording indicates that, after being asked who the teenagers were, Ney told the officers that a bunch of 16- to 17year-old kids, who had beaten up Ramirez, began running when Ney asked what they were doing. This evidence is more than sufficient to support the jury's finding that Moyer falsely stated to the FBI that Ney did not identify the suspects. See United States v. McKanry, 628 F.3d 1010, 1018 (8th Cir.2011) (upholding defendant's false statement conviction where defendant's statement was "directly contradicted by [trial] evidence").

The jury's finding that Moyer falsely stated that Ney reported seeing a man with a gun is equally well supported. There is no mention of a man with a gun whatsoever in the 911 recording. Moreover, Officer Hayes's written report makes no mention of Ney informing the officers about such a man. Ney even testified that immediately after the 911 call ended, he got into the police cruiser and did "not remember" having a conversation with anyone while in the cruiser. App. 01027. Furthermore, Moyer confirmed that there were no conversations while Ney was in it. Ney also testified that it was only after one of the teenagers told police that Ney had a gun—and immediately before the police arrested him—that he realized the police were even concerned about a man with a gun. Thus, the jury could reasonably conclude that Ney never actually informed the police—either during the recorded 911 call or immediately after—that there was a man with a gun. Although Moyer testified that Ney did, in fact, mention a man with a gun, it was the jury's duty—and not ours—to "weigh evidence [and] determine the credibility of witnesses...." United States v. Beckett, 208 F.3d 140, 151 (3d Cir.2000) (citing United States v. Casper, 956 F.2d 416, 421 (3d Cir.1992)). Based on the 911 recording, Hayes's written report, and Ney's testimony, the evidence was sufficient to support a finding that Moyer's statements to the FBI were false. See McKanry, 628 F.3d at 1018 (holding that the "evidence adequately supports the jury's verdict" when defendant's "denial was directly contradicted by evidence, including [defendant's] recorded admission").

B.

We also agree that there was sufficient evidence that Moyer acted "deliberately and with knowledge" that his representations were false and that he was aware "at least in a general sense, that his conduct was unlawful." United States v. Starnes, 583 F.3d 196, 212 (3d Cir.2009). When questioned on June 2 and June 11, 2009, Moyer told the FBI that, immediately upon his arrival at the scene, Ney warned of someone in the park with a gun. The jury also heard testimony that, when confronted with the 911 recording in which Ney did not mention a gun and did identify the participants, Moyer changed his original statement so it would no longer conflict with the recording. Moyer's efforts to conform his statement to the recording are sufficient to support the jury's finding that Moyer deliberately changed his statement and knew that both his original and changed statements were false. See id. at 212-213. The government, moreover, presented evidence that no gunman was ever mentioned, as Ney testified at trial that he had no recollection of ever mentioning that anyone had a gun in the park that night. Furthermore, the jury also heard sufficient evidence to conclude that Moyer knew his actions were unlawful; as a certified law enforcement officer, Moyer received training that made him aware that, "at least in a general sense," obstructing a criminal investigation by lying to a federal law enforcement officer is unlawful. Id. at 212. All of this evidence was sufficient to prove that Moyer's actions were knowing and willful.

C.

Finally, we conclude that there was sufficient evidence to support a finding of materiality. Courts have recognized that "a frequent aim of false statements made to federal investigators is to cast suspicion away from the declarant." United States v. Lupton, 620 F.3d 790, 806 (7th Cir.2010). "When statements are aimed at misdirecting agents and their investigation, even if they miss spectacularly or stand absolutely no chance of succeeding, they satisfy the materiality requirement of 18 U.S.C. § 1001." Id. at 806-807.

Although the government was not required to show actual reliance on Moyer's statements, it was required to prove that Moyer's statements had a "natural tendency to influence" or were "capable of influencing" the FBI. United States v. Gaudin, 515 U.S. 506, 509, 115 S.Ct. 2310, 132 L.Ed.2d 444 (1995) (internal quotation marks and citation omitted); see also McBane, 433 F.3d at 352 (explaining that false statements that could cause the FBI "to re-direct their investigation ... question their informant differently or more fully, or perhaps close their investigation altogether" were material). Count Five focused on Moyer's efforts to obstruct the investigation, and specifically, his actions to focus attention away from Piekarsky. His statements to the FBI that Ney mentioned a man with a gun but did not identify Ramirez's assailants, if taken as true, could have explained Moyer's actions on the night of the assault with respect to his protection of the teenaged suspects. If believed and acted upon, Moyer's false statements could have refocused the FBI's investigation. For this reason, Moyer's statements were material, because they were "of a type capable of influencing a reasonable decisionmaker." McBane, 433 F.3d at 351.

Thus, we conclude that Moyer's conviction was sufficiently supported by evidence that he knowingly and willfully made materially false statements to the FBI and we will therefore affirm his conviction.

VI.

For the foregoing reasons, we will AFFIRM the judgments of the District Court.