Among the issues on this appeal from convictions for drug and firearm crimes is a challenge to a conviction for using a firearm in relation to a drug trafficking crime. When the firearm, as here, is a machine gun, this conviction carries a mandatory 30-year sentence to run consecutively to any other sentence. The record reveals that this weapon was in defendant’s girlfriend’s apartment, less than a block away from where he sold heroin on the street. Moreover, when defendant was arrested in the apartment in which the machine gun had been placed he possessed drug records and a commercial amount of heroin. It would be naive to think the machine gun’s location was a coincidence, unrelated to defendant’s drug trafficking activities. More likely, the presence of the machine gun facilitated his possession and distribution of heroin.
Eight defendants — Steven Ramos, Raul Rodriguez, Johnny Davila, Leonardo Mas, Luis Rosario, Antonio Sanchez, Edwin Mendoza, Hector Colon — are appellants before us on this appeal. They were charged, along with 25 other defendants, in a 37-count indictment with an assortment of violations of federal narcotics and firearms laws for their *44activities occurring over a two-year period from late 1988 to January 1991. Alejandro who had pled guilty successfully moved to have his appeal severed without prejudice and has withdrawn from the instant appeal. Appellants were members of a heroin distribution organization headed by Steven Ramos.
Before the case went to the jury, the district court granted appellant Johnny Davila’s motion to dismiss a heroin possession count and several other counts alleging firearms violations. After a three-month jury trial in the Southern District of New York, before United States District Court Judge Robert J. Ward, the remaining appellants were convicted on all counts.
Following the verdicts, the trial court dismissed several counts that charged Ramos and Rodriguez with firearms violations. All the appellants who went to trial were convicted of conspiracy to violate the narcotics laws of the United States, in violation of 21 U.S.C. § 846. In addition, appellants were convicted of the following: Ramos — engaging in a continuing criminal enterprise, in violation of 21 U.S.C. §§ 848(a) and (c); Ramos and Da-vila — maintaining premises for the purpose of manufacturing narcotics, in violation of 21 U.S.C. §§ 812 and 856(a)(1) and 18 U.S.C. § 2; Ramos, Rosario, Mas and Colon — possession with intent to distribute and distributing heroin, in violation of 21 U.S.C. §§ 812, 841(a)(1), 841(b)(1)(C) and 18 U.S.C. § 2; and Mas and Colon — possessing and using machine guns in relation to a drug trafficking crime, in violation of 18 U.S.C. § 924(c) and 18 U.S.C. § 2. Appellants were sentenced to terms of imprisonment ranging from 151 months (over 12 years) for Sanchez to 595 months (nearly 50 years) for Mas.
The 21 issues appellants raise on appeal include a challenge to a wiretap application, denial of pretrial motions to suppress evidence, admissibility of expert testimony to interpret narcotics transaction records, and various aspects of their sentences. Most of these issues are without merit and warrant no discussion. Four issues do require some analysis: (1) whether there was sufficient evidence to convict Colon of using a machine gun in relation to a drug trafficking crime, in violation of § 924(c); (2) whether it was error for the trial court to admit evidence of Davi-la’s prior state weapons possession conviction; (3) whether the trial court should have held an evidentiary hearing to determine whether Ramos’ Ninth Amendment or Due Process rights were violated; and (4) whether the trial court, over Sanchez’ objection, should have given the jury an Allen charge.
On January 26, 1995 we issued an opinion affirming the convictions as to all appellants, except Colon’s § 924(c) conviction which a divided panel reversed. Shortly thereafter we determined sua sponte to reconsider Colon’s § 924(c) conviction, withdrew our original opinion, and requested additional briefing. We now affirm the convictions of all appellants, and vacate our earlier January 26, 1995 opinion.
BACKGROUND
Appellants’ arrests followed an investigation beginning in 1989 of heroin trafficking by the Ramos organization. The investigation, conducted by the New York Drug Enforcement Task Force (Task Force), made up of local, state and federal law enforcement officers, revealed that the Ramos organization sold heroin in the Bronx and Manhattan, New York, Paterson, New Jersey, and in a New York State prison.
The government’s proof at trial included the testimony of four former members of the Ramos organization and three undercover officers who purchased heroin from it. Other proof consisted of 130 tape-recorded conversations obtained from a court-authorized wiretap of Steven Ramos’ home telephone, surveillance videotapes and photographs of appellants and their associates, narcotics, narcotics paraphernalia, drug records, firearms, ammunition and bulletproof vests seized from appellants during the Task Force’s investigation and at the time of their arrests.
This evidence established that from late 1988 or early 1989 until his arrest on January 9, 1991, Ramos was the supervisor of a narcotics conspiracy that distributed massive amounts of heroin under the brand names “Pure Energy,” “Absolute,” and “Eternity.” *45After the heroin was processed and packaged at a cutting mill, it was distributed to street spots for sale. Each street spot was run by an owner who was responsible for selling heroin in that geographic area. The spot owners, who received the heroin on consignment, kept a percentage of the sales proceeds and remitted the remainder to Ramos. Spot owners usually maintained a “stash” apartment, close to the street selling spot, where heroin could easily be stored and retrieved and where weapons used to protect the selling spot were available.
The remaining appellants were members of the Ramos conspiracy and held various positions within his organization. Rodriguez obtained pure heroin from suppliers and delivered it to the heroin cutting mill where it was processed and packaged for street distribution. Davila was in charge of operating the heroin cutting mill. Rosario assisted Ramos in numerous tasks, acted as his bodyguard and driver and was involved with the smuggling of heroin into a New York state prison. Mas ran the organization’s principal street outlet at 162nd Street and Melrose Avenue in the Bronx. Appellants Mendoza and Sanchez served the organization in various capacities. Colon, in addition to selling heroin at the 162nd Street spot, maintained records of the outlet’s heroin transactions and cash receipts. By the end of 1990, he developed his own street selling spot at 157th Street and Melrose Avenue.
The evidence also demonstrated that in the course of its heroin trafficking operation the Ramos organization accumulated a number of machine guns, semi-automatic weapons and other firearms that were used to protect its operations. The drug ring carried out two shootings: one targeting a co-conspirator suspected of stealing from the organization (carried out by Mendoza, aided by Colon), and the second targeting two persons who had robbed one of the organization’s “stash” houses of heroin and money (carried out again by Mendoza, with Mas, Colon and others engaging in an armed search for the robbers). This brief background of the organization’s activities will be supplemented in the following discussion by those facts that pertain to the specific issues to which they relate.
DISCUSSION
I Conviction for Violation of 18 U.S.C. § 924(c)
A. Proof at Trial
We turn to the first issue. Colon contends the evidence presented at trial was insufficient to establish beyond a reasonable doubt that he used a machine gun during and in relation to a drug trafficking crime. In the early morning hours of January 9, 1991 the Task Force went to 428 East 157th Street, Colon’s building, to execute an arrest warrant for him. The officers investigated apartment 8D, where Colon lived with his parents, and apartments 4B and 2B. Upon knocking on the door of apartment 2B and identifying themselves, the police officers heard a male voice say “just a minute.” The police officers then heard objects being moved around inside the apartment. After a second knock by police, and several seconds of hesitation, Colon opened the door and was promptly arrested. Apartment 2B is located two floors below Colon’s own apartment and is leased by Denise Colon, who is his girlfriend, but not related to him.
While the police officers were attempting to gain entry into apartment 2B, an officer stationed outside the building saw a second-floor window thrown open and several objects hurled out. Among the items jettisoned were a loaded machine gun, a box of “Absolute” heroin, and a drug record with the name “Hec” written on it. Several officers identified the open window as belonging to apartment 2B. While being transported to the Drug Enforcement Administration headquarters for processing, Colon volunteered that his girlfriend had thrown the gun out the window. No evidence was presented that connected Denise Colon with the Ramos organization.
The machine gun was unique because it was manufactured without a serial number, similar to other machine guns that Ramos had purchased from co-conspirator turned government witness, Moisés Serrano. Rafael Brillon, another co-conspirator turned gov*46ernment witness, testified that he had given Colon a machine gun at the direction of Mas, and that Colon kept it in apartment 2B at 428 East 157th Street — the apartment where he was arrested — less than one block from the street spot where he sold heroin. Further, the jury heard testimony about Colon’s participation in armed searches for individuals who stole from the Ramos organization, and the shooting of one such individual. Finally, Serraúo, who obtained the machine gun for Ramos, testified on behalf of the government that while he and Colon were in custody subsequent to their January 9, 1991 arrest, Colon told him that he had thrown the machine gun out of the window when the officers stormed the apartment.
As a result of this proof, in addition to his other convictions, Colon was convicted of using a machine gun in relation to a drug trafficking crime, namely, the conspiracy to violate federal narcotics laws (distribution of and possession with intent to distribute heroin), in violation of 18 U.S.C. § 924(c) and 18 U.S.C. § 2. He was sentenced to a mandatory 360-months’ sentence for using a machine gun during and in relation to a drug trafficking crime, that sentence to run consecutively to a 151 months’ sentence on the narcotics convictions.
B. Tests for Sufficiency of Proof
A defendant challenging the sufficiency of the evidence supporting his conviction after a jury trial shoulders a heavy burden. See United States v. Jones, 30 F.3d 276, 281 (2d Cir.), cert. denied, — U.S. -, 115 S.Ct. 602, 130 L.Ed.2d 513 (1994). In reviewing such a claim, the evidence is viewed in the light most favorable to the government, see Glosser v. United States, 315 U.S. 60, 80, 62 S.Ct. 457, 469, 86 L.Ed. 680 (1942), and the jury verdict must be sustained if “any rational trier of fact could have found the essential elements of a crime beyond a reasonable doubt,” Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 2789, 61 L.Ed.2d 560 (1979) (emphasis in original).
In order to convict a defendant for violating 18 U.S.C. § 924(c)(1), the government must prove beyond a reasonable doubt that “during and in relation to ... [a] drug trafficking crime ... [the defendant] use[d] or carrie[d] a firearm_” 18 U.S.C. § 924(c)(1) (1988 & Supp. IV 1993). Section 924(c)(2) defines a drug trafficking crime as “any felony punishable under the Controlled Substances Act (21 U.S.C. 801 et seq.)_” Conspiracy to distribute and possess with intent to distribute heroin is a proper underlying drug trafficking crime upon which to base a § 924(e) conviction. See United States v. Meggett, 875 F.2d 24, 27 (2d Cir.), cert. denied, 493 U.S. 858, 110 S.Ct. 166, 107 L.Ed.2d 123 (1989); see also United States v. Diaz, 864 F.2d 544, 547-48 (7th Cir.1988), cert. denied, 490 U.S. 1070, 109 S.Ct. 2075, 104 L.Ed.2d 639 (1989); United States v. Torres, 862 F.2d 1025, 1026, 1030-32 (3d Cir.1988). If the firearm is a machine gun, the defendant shall be sentenced to a 30-year term of imprisonment to run consecutively to any other term of imprisonment, including that imposed for commission of the underlying drug trafficking crime. See § 924(c)(1).
Use of a firearm “in relation to” a drug trafficking crime requires the government to demonstrate a nexus between the firearm and the underlying drug trafficking crime. See Smith v. United States, — U.S. -, -, 113 S.Ct. 2050, 2058-59, 124 L.Ed.2d 138 (1993). The phrase “in relation to” requires at a minimum “that the firearm must have some purpose or effect with respect to the drug trafficking crime; its presence or involvement cannot be the result of accident or coincidence.” Id. at -, 113 S.Ct. at 2059. To be used in relation to a drug trafficking crime the firearm need not actually have been fired or even exhibited during a drug offense, see United States v. Taylor, 18 F.3d 55, 58 (2d Cir.), cert. denied, — U.S. -, 114 S.Ct. 2720, 129 L.Ed.2d 845 (1994), but the proof must show that the firearm was an integral part of the underlying drug crime and facilitated or had the potential to facilitate that offense, see Smith, — U.S. at -, 113 S.Ct. at 2059; see also Taylor, 18 F.3d at 58; United States v. Medina, 944 F.2d 60, 66 (2d Cir.1991), cert. denied, 503 U.S. 949, 112 S.Ct. 1508, 117 L.Ed.2d 646 (1992).
*47C. Test Applied to this Case
The availability of a gun to facilitate a narcotics offense poses a fact question for the jury. See United States v. Reyes-Mercado, 22 F.3d 363, 367 (1st Cir.1994). Facilitation may be found based on reasonable inferences derived from circumstantial evidence. See United States v. Fermin, 32 F.3d 674, 678 (2d Cir.1994), cert. denied, — U.S. -, 115 S.Ct. 1145, 130 L.Ed.2d 1104 (1995). We have ruled that a jury may find the presence of guns facilitated a drug crime when firearms are located in a place where drug transactions have occurred or where drugs are manufactured or stored. See, e.g., id. (defendant “engaged in numerous narcotics transactions from the office where the gun was found”); Taylor, 18 F.3d at 57, 59 (machine gun found in apartment where drug transactions occurred); United States v. Lindsay, 985 F.2d 666, 672 (2d Cir.) (five firearms located in house and one outside house where drug business conducted), cert. denied, — U.S. -, 114 S.Ct. 103, 126 L.Ed.2d 70 (1993); United States v. Torres, 901 F.2d 205, 218 (2d Cir.) (sufficient evidence to conclude that apartment was used for narcotics trafficking on a continuing basis and therefore firearm on premises was used in relation to drug trafficking), cert. denied, 498 U.S. 906, 111 S.Ct. 273, 112 L.Ed.2d 229 (1990); Meggett, 875 F.2d at 29 (sufficient evidence to conclude five firearms were on hand to protect apartment as a storage and processing point for large quantities of narcotics).
Colon contends the evidence was insufficient to establish a nexus between his possession of the machine gun and his drug trafficking crime, principally because there was no proof that the apartment where he was found and from which the machine gun was thrown out was used as a drug processing or storage site, or that drug transactions had occurred there. We think this contention unpersuasive. The statute has no such requirement and our cases do not preclude upholding a conviction under § 924(c) where a more modest quantity of narcotics is recovered with the firearm and other evidence links the weapon with a defendant’s drug trafficking crime. Such is the case here. Defendant’s conviction was for using a firearm in relation to a conspiracy to distribute and possess with the intent to distribute heroin. An integral part and object of that conspiracy was his possession of the box of “Absolute” heroin found in his girlfriend’s apartment on January 9,1991. Possession of that heroin was as much a part of the conspiracy as its actual distribution. See Meggett, 875 F.2d at 29 (conviction upheld where use of firearm occurred with a preliminary stage of the conspiracy as distinct from the ultimate object).
Further, the evidence before the jury showed defendant’s involvement with the Ramos organization and its use of guns, including those of the type Colon threw from the apartment window, to obtain retribution against those who had stolen either drugs or money from it. The proof revealed Colon’s possession of the loaded machine gun, together with a quantity of heroin and a drug record in his girlfriend’s apartment, less than a block from the street site where he was selling heroin. Under these circumstances, a rational jury could conclude that the “presence of [the firearm] constituted ‘use’ to protect [Colon’s] possession of the narcotics,” see id., or, in other words, the machine gun facilitated Colon’s drug trafficking activities. As a consequence, his § 924(e) conviction must stand.
II Evidence of Davila’s Prior Conviction
Next, we consider Davila’s most meritorious argument. He asserts the district court erred when it improperly admitted evidence of his prior state weapons possession conviction. In the early hours of November 12, 1990, Davila, who was driving appellant Edwin Ruiz’ car, was stopped by New York City Police officers for a traffic violation. A semi-automatic handgun was discovered on the floor of the ear. The weapon belonged to Ruiz; Davila was unaware of its presence. Davila had borrowed Ruiz’ ear in order to go to work at the organization’s heroin cutting mill.
Later that same morning the Task Force intercepted a lengthy telephone conversation between Ramos and Rodriguez in which they discussed the fact that Davila had been arrested while driving Ruiz’ car and that a *48weapon had been found. This intercepted communication was replete with references to the heroin conspiracy. It contained references to the organization’s heroin supplier, an apartment where a weapons “stash” was located, arrangements Ramos was going to make for Davila’s bail and legal representation, and a discussion about how much cash the organization had at various locations. Critical to the argument now being raised, at four separate times during the conversation, Ramos and Rodriguez made references to Davila’s prior state arrest for possession of a weapon, his being on probation or parole for that charge, and his previous jail experience.
Before trial, transcripts of this conversation, along with other intercepted conversations the government intended to introduce at trial, were given to defense counsel. As a result, certain tapes and transcripts were redacted in order to accommodate defense objections or requests. Davila never requested that any portion of this intercepted conversation that referred to his prior arrest be redacted.
At trial, when the government sought to introduce the tape recording of the Ramos-Rodriguez conversation, Davila objected on the grounds that the conversation as a whole was not relevant and any probative value was substantially outweighed by its prejudicial impact. The district court ruled, pursuant to Fed.R.Evid. 403, that the conversation was relevant and not outweighed by any danger of unfair prejudice, and that it was admissible under Rule 404(b) as evidence supporting the existence of a plan. After the tape was played for the jury, Davila renewed his objection to the tape and any testimony concerning the details of the pre-November 12 arrest. It was not until the next morning that he specifically objected on hearsay grounds to the tape references regarding his prior weapons arrest.
Federal Rule of Evidence 103(a)(1) requires a timely objection or motion to strike proof being offered at trial, and that such objection state the specific ground of objection, if it is not apparent from the context. Upon reviewing Davila’s original objection to the admission of the subject tape recording, it is plain that defense counsel made no objection specific enough to alert the trial court that he was challenging the fleeting references to Davila’s pre-November 12,1990 arrest. Hence, the only basis on which appellant may now succeed on this issue is if it may be said that the receipt of the unredact-ed tape was plain error. See Fed.R.Crim.P. 52(b) (“Plain errors or defects affecting substantial rights may be noticed although they were not brought to the attention of the court.”).
Plain error analysis is used sparingly, see United States v. Scarpa, 913 F.2d 993, 1021 (2d Cir.1990), to correct particularly egregious errors or to redress a miscarriage of justice. See United States v. Frady, 456 U.S. 152, 163, 102 S.Ct. 1584, 1592, 71 L.Ed.2d 816 (1982). Although the trial court properly ruled that the substance of the conversation between Ramos and Rodriguez was relevant as evidence supporting the existence of a plan, pursuant to Fed.R.Evid. 404(b), the snippets of conversation relating to Davila’s prior arrest for possession of a weapon were not relevant to the charges in the indictment and should have been redacted before the jury heard the tape.
Yet admitting this tape into evidence did not amount to plain error. The jury heard the conversation once, did not receive a copy of the transcript, and the government did not question any witness about Davila’s prior weapons arrest or refer to it during its summation. Further, the evidence of Davila’s guilt was overwhelming. Even had defense counsel specifically objected to the offensive material in a timely fashion and preserved the issue for appeal, admitting the references to Davila’s prior weapons arrest would be harmless error since we can conclude with fair assurance that the evidence did not substantially influence the jury. See United States v. Rea, 958 F.2d 1206, 1220 (2d Cir.1992); see also Kotteakos v. United States, 328 U.S. 750, 764-65, 66 S.Ct. 1239, 1247-48, 90 L.Ed. 1557 (1946).
Hence, it follows that Davila’s convictions of conspiracy and of maintaining premises for the purpose of manufacturing narcotics were not influenced by the fleeting reference to his prior weapons conviction and should therefore be affirmed.
*49III Choice of Forum
The third issue for analysis is Ramos’ insistence that the district court improperly denied his motion for an evidentiary hearing to determine whether his Ninth Amendment or Due Process rights were violated because of New York State involvement in his federal prosecution. Specifically, he complains that his constitutional rights were violated because New York prosecutors dismissed the state prosecutions of Edwin Ruiz and Edward Ramos for possession of machine guns and handguns following their December 6, 1990 arrests. Their prosecution on these charges was then joined to the federal indictment of the Ramos organization.
During the course of the conspiracy, Ramos, as its leader, maintained a large arsenal of firearms stored at 66 Caryl Avenue in Yonkers, New York. On December 5, 1990 Task Force members executed a search warrant in a second-floor apartment at 66 Caryl Avenue without recovering any weapons. Later that evening, electronic surveillance of Ramos’ telephone recorded a conversation during which Ramos ordered Ruiz to remove the firearms from a third-floor apartment at 66 Caryl Avenue and store them in Ramos’ car for safekeeping. When Ruiz and Edward Ramos were later observed by Task Force members loading weapons into the trunk of Steven Ramos’ automobile, the officers followed the vehicle and, when it ran a traffic light, stopped it. Upon opening the trunk the officers found boxes containing 12 machine guns and 16 handguns. Ruiz and Edward Ramos were arrested and charged in state court with New York firearms violations. Although the weapons were found in Steven Ramos’ vehicle, he was not charged with any state law violations.
A month later, after Ruiz and Edward Ramos were indicted on federal firearms charges, state prosecutors dismissed the state firearms charges against them. In Counts 13 through 15 of the second superseding federal indictment, Steven Ramos was charged with using and carrying firearms during and in relation to drug trafficking crimes based on the weapons found in his car during the December 6, 1990 arrest of Ruiz and Edward Ramos.
Before trial, Steven Ramos moved the district court to dismiss the indictment upon the grounds that his constitutional rights had been violated by the joint and combined actions of the New York and federal law enforcement agencies. He declared that the Task Force’s choice to prosecute him for violations of federal law in federal court, in light of the involvement of state prosecutors and local police in the stop, search and seizure of his automobile, was deliberate and made with the intent to deprive him of rights provided by the New York Constitution. He requested an evidentiary hearing to be held in the event an issue of fact was raised regarding this issue.
During argument on Ramos’ constitutional claims, defense counsel pointed out that by choosing a federal forum to prosecute Edward Ramos and Ruiz, the government was able to rely upon electronic surveillance obtained pursuant to a federal wiretap to justify the seizure of his auto by New York City police on December 6, 1990. Ramos provided no authority supporting his position that the guns seized from his auto would have been suppressed in state court for lack of probable cause. He relied instead upon the fact that the Bronx County Assistant District Attorney who commenced the prosecution against Ruiz and Edward Ramos in state court was also involved in the federal proceedings and that this amounted to a denial of his constitutional rights.
The issue as Judge Ward correctly saw it is whether this combined state and federal action against Edward Ramos and Ruiz denied Steven Ramos his constitutional rights. The district judge found it unnecessary to conduct an evidentiary hearing because Ramos failed to raise an issue of fact and lacked the requisite standing. Accordingly, he denied the motion to dismiss, relying on United States v. Pforzheimer, 826 F.2d 200 (2d Cir.1987), for the proposition that federal, not state, law should be applied in resolving search and seizure questions in federal prosecutions even though the search and seizure was conducted by local law enforcement officers.
*50It is clear that whether or not to file what charges, against whom, and when to file, are questions to be determined exclusively within the discretionary authority of district attorneys in state court and United States attorneys in federal court. See United States v. Davis, 906 F.2d 829, 834 (2d Cir.1990) (federal prosecution properly initiated even though based on evidence suppressed in state court). It was not error to refuse to hold an evidentiary hearing on Ramos’ allegations of constitutional violations, as Ramos failed to raise an issue of fact to demonstrate that the prosecution of Edward Ramos and Ruiz was transferred in bad faith to federal court with the intent of denying Ramos his rights guaranteed by the New York Constitution. That the Task Force intended from the outset to preserve its ability to turn its investigation over to federal prosecutors is shown by the fact that in October 1990 it had applied to the United States District Court for the Southern District of New York for a wiretap of Ramos’ telephone.
Unless it can be shown that the decision to drop state charges and initiate federal prosecution is based on suspect characteristics of the defendant or is otherwise done in bad faith, there is no due process violation. United States v. Nance, 962 F.2d 860, 865 (9th Cir.1992) (per curiam); United States v. Parson, 955 F.2d 858, 873 n. 22 (3d Cir.1992) (no due process violation where under a federal-state agreement drug cases referred to the U.S. Attorney for federal prosecution); United States v. Carter, 953 F.2d 1449, 1461-62 (5th Cir.) (no due process violation where task force members referred prosecution either to state district attorney or the U.S. Attorney; even where prosecution had been referred to state court, defendant could still be prosecuted in federal court for the same conduct), cert. denied, 504 U.S. 990, 112 S.Ct. 2980, 119 L.Ed.2d 598 (1992); United States v. Allen, 954 F.2d 1160, 1165-66 (6th Cir.1992) (absent improper motive, even when the crime was investigated solely by state officials, no due process violation when defendant was prosecuted in federal court); see also United States v. Andersen, 940 F.2d 593, 595-97 (10th Cir.1991); United States v. Turpin, 920 F.2d 1377, 1387-88 (8th Cir.1990), cert. denied, 499 U.S. 953, 111 S.Ct. 1428, 113 L.Ed.2d 480 (1991).
While defendants often raise this due process claim in the context of their receipt of harsher sentences under the federal Sentencing Guidelines, see, e.g., Nance, 962 F.2d at 864; Parson, 955 F.2d at 873 n. 22; Carter 953 F.2d at 1462; Allen, 954 F.2d at 1165; Andersen, 940 F.2d at 596; Turpin, 920 F.2d at 1387-88, the same fundamental rationales — prosecutorial discretion and dual sovereignty — still apply. See Davis, 906 F.2d at 834. Under that analysis, absent improper motive, there are no grounds for finding a due process violation or a Ninth Amendment violation implicating unenumerated rights “retained by the people.” U.S. Const, amend. IX.
Moreover, the application of federal law in a federal forum does not implicate the Ninth Amendment. See Allen, 954 F.2d at 1167-68 (holding defendant’s Ninth Amendment rights not violated by applying federal law to suppression claims when defendant prosecuted in federal court based on a state investigation). Consequently, the Ninth Amendment and due process arguments Ramos raises afford him no grounds for overturning his convictions.
IV The Allen Charge
We pass to the only remaining point requiring discussion. Sanchez asserts the district court erred when it delivered a supplemental jury charge pursuant to Allen v. United States, 164 U.S. 492, 17 S.Ct. 154, 41 L.Ed. 528 (1896), over defense objection, which Sanchez believes improperly coerced the jury into rendering a guilty verdict against him. Sanchez was charged in a single count of conspiracy to violate the narcotics laws of the United States.
After hearing lengthy trial testimony, the jury began its deliberations on June 12,1992. Several times during the course of deliberations, the jury requested Sanchez’ testimony read back and asked to view all the evidence where he was referred to or depicted. Material regarding other defendants was also requested. On June 25 the jury sent a note to Judge Ward advising him that it was unable *51to reach a unanimous decision on one count against one defendant, after having “spent several days in trying to reach unanimity.” When the trial judge asked whether further deliberations could bring about unanimity, the jury responded that while it could “give the Court no guarantee of a unanimous verdict on the one count[, it was] willing to continue its deliberations.” The trial judge told the jury it could report its verdicts on the other defendants and return the following Monday to resume deliberations on the one count. When the jury returned to the courtroom, it reported it had been unable to reach a verdict on defendant Sanchez, but had found all the other defendants guilty on all counts submitted to it.
The jury continued deliberations on June 29, the eleventh day of its deliberations. In the early afternoon of that day it sent a note: “[T]he jury regrets to inform you that we have exhausted all avenues of discussion on the remaining count and cannot reach unanimity.” The defense moved for a mistrial and the government informed the court that while it was not requesting an Allen charge it had no objection to such a charge. Over defense objection, the court delivered an Allen charge at approximately 3:00 P.M. on June 29. Although Sanchez’ counsel objected to the giving of the charge, he did not object to its language. An hour later the jury reached a unanimous verdict convicting Sanchez on the conspiracy count for which he was later sentenced to 151 months imprisonment.
Sanchez characterizes the jury as a “model jury,” one which was capable of deliberating on 16 counts against nine separate defendants tried jointly. He contends therefore that the jury was acting in the same highly competent manner when it deadlocked on the charge against him and that the Allen charge improperly coerced this jury into an “abandonment of reason.”
The use of a supplemental charge “has long been sanctioned” by the Supreme Court, Lowenfield v. Phelps, 484 U.S. 231, 237, 108 S.Ct. 546, 550, 98 L.Ed.2d 568 (1988), and all of the Courts of Appeals, see id. at 238 n. 1, 108 S.Ct. at 551 n. 1 (collecting cases); see also United States v. Hynes, 424 F.2d 754, 757 (2d Cir.) (“This Court has consistently reaffirmed its approval of the supplementary charge to encourage a verdict in the face of an apparent deadlock”), cert. denied, 399 U.S. 933, 90 S.Ct. 2270, 26 L.Ed.2d 804 (1970).
An Allen charge simply repeats those precepts that a trial court almost invariably uses to guide the jurors’ deliberations in its original charge. The emphasis of such a charge is that a verdict works in the best interests of the prosecution and the defendant. See Hynes, 424 F.2d at 757. Whether an Allen charge was appropriate in a given case hinges on whether it tends to coerce undecided jurors into reaching a verdict. Coercion may be found when jurors are encouraged to abandon, without any principled reason, doubts that any juror conscientiously holds as to a defendant’s guilt. See United States v. Robinson, 560 F.2d 507, 517 (2d Cir.1977) (en banc), cert. denied, 435 U.S. 905, 98 S.Ct. 1451, 55 L.Ed.2d 496 (1978). At the same time, such a charge is helpful and not coercive when it only expresses encouragement to the jurors to reach a verdict, if possible, to avoid the expense and delay of a new trial. See United States v. Bermudez, 526 F.2d 89, 100 (2d Cir.1975), cert. denied, 425 U.S. 970, 96 S.Ct. 2166, 48 L.Ed.2d 793 (1976).
Sanchez maintains that the Allen charge was patently coercive because the jury reached a verdict after only an hour of further deliberations following that charge. The length of time it takes a jury to reach a verdict after an Allen charge has been delivered is not a factor logically to be considered in determining whether the charge should have been given in the first place. In Hynes, for example, the jury returned a verdict five minutes after the Allen charge was given. 424 F.2d at 758. The appropriate question instead is whether the district court instructed the jury as to the “necessity on the part of each juror to adhere to his [or her] own judgment.” Id.
The supplemental charge here was given after the jury had deliberated for 11 days in an exceedingly complex, multi-defendant trial. We agree with Sanchez that this jury *52was particularly conscientious in its deliberation and very articulate in its communications with the court. But unlike Sanchez, we think these traits aided this jury in understanding and appreciating the supplemental instruction. During the course of delivering it the district judge stated at least twice that no juror was to abandon his or her conscientious judgment simply to reach a unanimous verdict.
This language could not have “coerce[d] undecided jurors into reaching a verdict by abandoning without reason conscientiously held doubts.” Robinson, 560 F.2d at 517. Further, we have approved essentially the same instruction in Hynes, 424 F.2d at 756 n. 2, holding that it was “couched in the fairest possible language,” id. at 757. We did not then, and do not now, take exception to the district court’s quoting directly from Allen v. United States. Thus, it follows that the district court did not abuse its discretion in delivering this supplemental charge, and that the charge was not coercive.
Sanchez further insists that the jury should have been instructed that the majority had an obligation to review its position, and that the charge was erroneous because it did not reiterate that the burden of proof was on the government to prove Sanchez guilty beyond a reasonable doubt. Because Sanchez specifically approved the language of the charge before the court delivered it, we review this issue only for plain error.
We have never held that the trial court must specifically inform the jury that the majority must consider the arguments and the opinions of those in the minority. The brief language used by the trial court, other than the entire quote from Allen, was directed to each juror, not just those designated the majority or the minority. All jurors were instructed to consider the views of the other jurors without abandoning their own conscientious opinions. With respect to the district court’s not repeating its instruction that the government must prove its case beyond a reasonable doubt, we review the “legal sufficiency of supplemental instructions ... in light of the jury instructions as a whole.” United States v. Tillem, 906 F.2d 814, 826 (2d Cir.1990). In its general instructions, and then again when instructing on the conspiracy count, the trial court properly charged the jury that in order to convict the defendants, the government must prove all elements of the crime charged beyond a reasonable doubt. We therefore find no error in the supplemental charge as given.
CONCLUSION
In accordance with the above discussion, convictions of all the defendants on appeal are affirmed.