LMFDB - Embedded newform 15.3.d.a.14.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,3,Mod(14,15)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("15.14");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	15.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$0.408720396540$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			14.1
Character	$\chi$	$=$	15.14

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +3.00000 q^{3} -3.00000 q^{4} -5.00000 q^{5} -3.00000 q^{6} +7.00000 q^{8} +9.00000 q^{9} +O(q^{10})$

$q-1.00000 q^{2} +3.00000 q^{3} -3.00000 q^{4} -5.00000 q^{5} -3.00000 q^{6} +7.00000 q^{8} +9.00000 q^{9} +5.00000 q^{10} -9.00000 q^{12} -15.0000 q^{15} +5.00000 q^{16} +14.0000 q^{17} -9.00000 q^{18} -22.0000 q^{19} +15.0000 q^{20} -34.0000 q^{23} +21.0000 q^{24} +25.0000 q^{25} +27.0000 q^{27} +15.0000 q^{30} +2.00000 q^{31} -33.0000 q^{32} -14.0000 q^{34} -27.0000 q^{36} +22.0000 q^{38} -35.0000 q^{40} -45.0000 q^{45} +34.0000 q^{46} +14.0000 q^{47} +15.0000 q^{48} +49.0000 q^{49} -25.0000 q^{50} +42.0000 q^{51} +86.0000 q^{53} -27.0000 q^{54} -66.0000 q^{57} +45.0000 q^{60} -118.000 q^{61} -2.00000 q^{62} +13.0000 q^{64} -42.0000 q^{68} -102.000 q^{69} +63.0000 q^{72} +75.0000 q^{75} +66.0000 q^{76} +98.0000 q^{79} -25.0000 q^{80} +81.0000 q^{81} -154.000 q^{83} -70.0000 q^{85} +45.0000 q^{90} +102.000 q^{92} +6.00000 q^{93} -14.0000 q^{94} +110.000 q^{95} -99.0000 q^{96} -49.0000 q^{98} +O(q^{100})$

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.500000	−0.250000	−	0.968246i	$-0.580431\pi$
$2$	−1.00000	−0.500000	−0.250000	+	0.968246i	$0.580431\pi$
$3$	3.00000	1.00000
$3$	3.00000	1.00000
$4$	−3.00000	−0.750000
$5$	−5.00000	−1.00000
$5$	−5.00000	−1.00000
$6$	−3.00000	−0.500000
$7$	0	0	1.00000			$0$
$7$	0	0	−1.00000			$\pi$
$8$	7.00000	0.875000
$9$	9.00000	1.00000
$10$	5.00000	0.500000
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	−9.00000	−0.750000
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	0	0
$15$	−15.0000	−1.00000
$16$	5.00000	0.312500
$17$	14.0000	0.823529	0.411765	−	0.911290i	$-0.364913\pi$
$17$	14.0000	0.823529	0.411765	+	0.911290i	$0.364913\pi$
$18$	−9.00000	−0.500000
$19$	−22.0000	−1.15789	−0.578947	−	0.815365i	$-0.696536\pi$
$19$	−22.0000	−1.15789	−0.578947	+	0.815365i	$0.696536\pi$
$20$	15.0000	0.750000
$21$	0	0
$22$	0	0
$23$	−34.0000	−1.47826	−0.739130	−	0.673562i	$-0.764763\pi$
$23$	−34.0000	−1.47826	−0.739130	+	0.673562i	$0.764763\pi$
$24$	21.0000	0.875000
$25$	25.0000	1.00000
$26$	0	0
$27$	27.0000	1.00000
$28$	0	0
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	15.0000	0.500000
$31$	2.00000	0.0645161	0.0322581	−	0.999480i	$-0.489730\pi$
$31$	2.00000	0.0645161	0.0322581	+	0.999480i	$0.489730\pi$
$32$	−33.0000	−1.03125
$33$	0	0
$34$	−14.0000	−0.411765
$35$	0	0
$36$	−27.0000	−0.750000
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	22.0000	0.578947
$39$	0	0
$40$	−35.0000	−0.875000
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	0	0
$45$	−45.0000	−1.00000
$46$	34.0000	0.739130
$47$	14.0000	0.297872	0.148936	−	0.988847i	$-0.452415\pi$
$47$	14.0000	0.297872	0.148936	+	0.988847i	$0.452415\pi$
$48$	15.0000	0.312500
$49$	49.0000	1.00000
$50$	−25.0000	−0.500000
$51$	42.0000	0.823529
$52$	0	0
$53$	86.0000	1.62264	0.811321	−	0.584601i	$-0.198749\pi$
$53$	86.0000	1.62264	0.811321	+	0.584601i	$0.198749\pi$
$54$	−27.0000	−0.500000
$55$	0	0
$56$	0	0
$57$	−66.0000	−1.15789
$58$	0	0
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	45.0000	0.750000
$61$	−118.000	−1.93443	−0.967213	−	0.253966i	$-0.918265\pi$
$61$	−118.000	−1.93443	−0.967213	+	0.253966i	$0.918265\pi$
$62$	−2.00000	−0.0322581
$63$	0	0
$64$	13.0000	0.203125
$65$	0	0
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	−42.0000	−0.617647
$69$	−102.000	−1.47826
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	63.0000	0.875000
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0	0
$75$	75.0000	1.00000
$76$	66.0000	0.868421
$77$	0	0
$78$	0	0
$79$	98.0000	1.24051	0.620253	−	0.784402i	$-0.287030\pi$
$79$	98.0000	1.24051	0.620253	+	0.784402i	$0.287030\pi$
$80$	−25.0000	−0.312500
$81$	81.0000	1.00000
$82$	0	0
$83$	−154.000	−1.85542	−0.927711	−	0.373300i	$-0.878226\pi$
$83$	−154.000	−1.85542	−0.927711	+	0.373300i	$0.878226\pi$
$84$	0	0
$85$	−70.0000	−0.823529
$86$	0	0
$87$	0	0
$88$	0	0
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	45.0000	0.500000
$91$	0	0
$92$	102.000	1.10870
$93$	6.00000	0.0645161
$94$	−14.0000	−0.148936
$95$	110.000	1.15789
$96$	−99.0000	−1.03125
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	−49.0000	−0.500000
$99$	0	0
$100$	−75.0000	−0.750000
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	−42.0000	−0.411765
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	0	0
$105$	0	0
$106$	−86.0000	−0.811321
$107$	−106.000	−0.990654	−0.495327	−	0.868707i	$-0.664952\pi$
$107$	−106.000	−0.990654	−0.495327	+	0.868707i	$0.664952\pi$
$108$	−81.0000	−0.750000
$109$	−22.0000	−0.201835	−0.100917	−	0.994895i	$-0.532178\pi$
$109$	−22.0000	−0.201835	−0.100917	+	0.994895i	$0.532178\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	206.000	1.82301	0.911504	−	0.411290i	$-0.134922\pi$
$113$	206.000	1.82301	0.911504	+	0.411290i	$0.134922\pi$
$114$	66.0000	0.578947
$115$	170.000	1.47826
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	−105.000	−0.875000
$121$	121.000	1.00000
$122$	118.000	0.967213
$123$	0	0
$124$	−6.00000	−0.0483871
$125$	−125.000	−1.00000
$126$	0	0
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	119.000	0.929688
$129$	0	0
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	−135.000	−1.00000
$136$	98.0000	0.720588
$137$	−226.000	−1.64964	−0.824818	−	0.565399i	$-0.808722\pi$
$137$	−226.000	−1.64964	−0.824818	+	0.565399i	$0.808722\pi$
$138$	102.000	0.739130
$139$	−262.000	−1.88489	−0.942446	−	0.334358i	$-0.891480\pi$
$139$	−262.000	−1.88489	−0.942446	+	0.334358i	$0.891480\pi$
$140$	0	0
$141$	42.0000	0.297872
$142$	0	0
$143$	0	0
$144$	45.0000	0.312500
$145$	0	0
$146$	0	0
$147$	147.000	1.00000
$148$	0	0
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	−75.0000	−0.500000
$151$	−238.000	−1.57616	−0.788079	−	0.615574i	$-0.788924\pi$
$151$	−238.000	−1.57616	−0.788079	+	0.615574i	$0.788924\pi$
$152$	−154.000	−1.01316
$153$	126.000	0.823529
$154$	0	0
$155$	−10.0000	−0.0645161
$156$	0	0
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	−98.0000	−0.620253
$159$	258.000	1.62264
$160$	165.000	1.03125
$161$	0	0
$162$	−81.0000	−0.500000
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	0	0
$165$	0	0
$166$	154.000	0.927711
$167$	254.000	1.52096	0.760479	−	0.649362i	$-0.224964\pi$
$167$	254.000	1.52096	0.760479	+	0.649362i	$0.224964\pi$
$168$	0	0
$169$	169.000	1.00000
$170$	70.0000	0.411765
$171$	−198.000	−1.15789
$172$	0	0
$173$	−154.000	−0.890173	−0.445087	−	0.895487i	$-0.646827\pi$
$173$	−154.000	−0.890173	−0.445087	+	0.895487i	$0.646827\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	0	0
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	135.000	0.750000
$181$	122.000	0.674033	0.337017	−	0.941499i	$-0.390582\pi$
$181$	122.000	0.674033	0.337017	+	0.941499i	$0.390582\pi$
$182$	0	0
$183$	−354.000	−1.93443
$184$	−238.000	−1.29348
$185$	0	0
$186$	−6.00000	−0.0322581
$187$	0	0
$188$	−42.0000	−0.223404
$189$	0	0
$190$	−110.000	−0.578947
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	39.0000	0.203125
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	0	0
$196$	−147.000	−0.750000
$197$	374.000	1.89848	0.949239	−	0.314557i	$-0.101856\pi$
$197$	374.000	1.89848	0.949239	+	0.314557i	$0.101856\pi$
$198$	0	0
$199$	−142.000	−0.713568	−0.356784	−	0.934187i	$-0.616127\pi$
$199$	−142.000	−0.713568	−0.356784	+	0.934187i	$0.616127\pi$
$200$	175.000	0.875000
$201$	0	0
$202$	0	0
$203$	0	0
$204$	−126.000	−0.617647
$205$	0	0
$206$	0	0
$207$	−306.000	−1.47826
$208$	0	0
$209$	0	0
$210$	0	0
$211$	362.000	1.71564	0.857820	−	0.513950i	$-0.171818\pi$
$211$	362.000	1.71564	0.857820	+	0.513950i	$0.171818\pi$
$212$	−258.000	−1.21698
$213$	0	0
$214$	106.000	0.495327
$215$	0	0
$216$	189.000	0.875000
$217$	0	0
$218$	22.0000	0.100917
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	0	0
$225$	225.000	1.00000
$226$	−206.000	−0.911504
$227$	134.000	0.590308	0.295154	−	0.955450i	$-0.404629\pi$
$227$	134.000	0.590308	0.295154	+	0.955450i	$0.404629\pi$
$228$	198.000	0.868421
$229$	218.000	0.951965	0.475983	−	0.879455i	$-0.342093\pi$
$229$	218.000	0.951965	0.475983	+	0.879455i	$0.342093\pi$
$230$	−170.000	−0.739130
$231$	0	0
$232$	0	0
$233$	−34.0000	−0.145923	−0.0729614	−	0.997335i	$-0.523245\pi$
$233$	−34.0000	−0.145923	−0.0729614	+	0.997335i	$0.523245\pi$
$234$	0	0
$235$	−70.0000	−0.297872
$236$	0	0
$237$	294.000	1.24051
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	−75.0000	−0.312500
$241$	−478.000	−1.98340	−0.991701	−	0.128564i	$-0.958963\pi$
$241$	−478.000	−1.98340	−0.991701	+	0.128564i	$0.958963\pi$
$242$	−121.000	−0.500000
$243$	243.000	1.00000
$244$	354.000	1.45082
$245$	−245.000	−1.00000
$246$	0	0
$247$	0	0
$248$	14.0000	0.0564516
$249$	−462.000	−1.85542
$250$	125.000	0.500000
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	−210.000	−0.823529
$256$	−171.000	−0.667969
$257$	−466.000	−1.81323	−0.906615	−	0.421959i	$-0.861343\pi$
$257$	−466.000	−1.81323	−0.906615	+	0.421959i	$0.861343\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	446.000	1.69582	0.847909	−	0.530142i	$-0.177861\pi$
$263$	446.000	1.69582	0.847909	+	0.530142i	$0.177861\pi$
$264$	0	0
$265$	−430.000	−1.62264
$266$	0	0
$267$	0	0
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	135.000	0.500000
$271$	482.000	1.77860	0.889299	−	0.457326i	$-0.151193\pi$
$271$	482.000	1.77860	0.889299	+	0.457326i	$0.151193\pi$
$272$	70.0000	0.257353
$273$	0	0
$274$	226.000	0.824818
$275$	0	0
$276$	306.000	1.10870
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	262.000	0.942446
$279$	18.0000	0.0645161
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	−42.0000	−0.148936
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0	0
$285$	330.000	1.15789
$286$	0	0
$287$	0	0
$288$	−297.000	−1.03125
$289$	−93.0000	−0.321799
$290$	0	0
$291$	0	0
$292$	0	0
$293$	−394.000	−1.34471	−0.672355	−	0.740229i	$-0.734717\pi$
$293$	−394.000	−1.34471	−0.672355	+	0.740229i	$0.734717\pi$
$294$	−147.000	−0.500000
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	−225.000	−0.750000
$301$	0	0
$302$	238.000	0.788079
$303$	0	0
$304$	−110.000	−0.361842
$305$	590.000	1.93443
$306$	−126.000	−0.411765
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	0	0
$309$	0	0
$310$	10.0000	0.0322581
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	0	0
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	0	0
$315$	0	0
$316$	−294.000	−0.930380
$317$	134.000	0.422713	0.211356	−	0.977409i	$-0.432212\pi$
$317$	134.000	0.422713	0.211356	+	0.977409i	$0.432212\pi$
$318$	−258.000	−0.811321
$319$	0	0
$320$	−65.0000	−0.203125
$321$	−318.000	−0.990654
$322$	0	0
$323$	−308.000	−0.953560
$324$	−243.000	−0.750000
$325$	0	0
$326$	0	0
$327$	−66.0000	−0.201835
$328$	0	0
$329$	0	0
$330$	0	0
$331$	122.000	0.368580	0.184290	−	0.982872i	$-0.441001\pi$
$331$	122.000	0.368580	0.184290	+	0.982872i	$0.441001\pi$
$332$	462.000	1.39157
$333$	0	0
$334$	−254.000	−0.760479
$335$	0	0
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	−169.000	−0.500000
$339$	618.000	1.82301
$340$	210.000	0.617647
$341$	0	0
$342$	198.000	0.578947
$343$	0	0
$344$	0	0
$345$	510.000	1.47826
$346$	154.000	0.445087
$347$	−586.000	−1.68876	−0.844380	−	0.535744i	$-0.820031\pi$
$347$	−586.000	−1.68876	−0.844380	+	0.535744i	$0.820031\pi$
$348$	0	0
$349$	458.000	1.31232	0.656160	−	0.754621i	$-0.272179\pi$
$349$	458.000	1.31232	0.656160	+	0.754621i	$0.272179\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	−274.000	−0.776204	−0.388102	−	0.921616i	$-0.626869\pi$
$353$	−274.000	−0.776204	−0.388102	+	0.921616i	$0.626869\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	−315.000	−0.875000
$361$	123.000	0.340720
$362$	−122.000	−0.337017
$363$	363.000	1.00000
$364$	0	0
$365$	0	0
$366$	354.000	0.967213
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	−170.000	−0.461957
$369$	0	0
$370$	0	0
$371$	0	0
$372$	−18.0000	−0.0483871
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	−375.000	−1.00000
$376$	98.0000	0.260638
$377$	0	0
$378$	0	0
$379$	−742.000	−1.95778	−0.978892	−	0.204379i	$-0.934482\pi$
$379$	−742.000	−1.95778	−0.978892	+	0.204379i	$0.934482\pi$
$380$	−330.000	−0.868421
$381$	0	0
$382$	0	0
$383$	686.000	1.79112	0.895561	−	0.444938i	$-0.146774\pi$
$383$	686.000	1.79112	0.895561	+	0.444938i	$0.146774\pi$
$384$	357.000	0.929688
$385$	0	0
$386$	0	0
$387$	0	0
$388$	0	0
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	0	0
$391$	−476.000	−1.21739
$392$	343.000	0.875000
$393$	0	0
$394$	−374.000	−0.949239
$395$	−490.000	−1.24051
$396$	0	0
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	142.000	0.356784
$399$	0	0
$400$	125.000	0.312500
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	−405.000	−1.00000
$406$	0	0
$407$	0	0
$408$	294.000	0.720588
$409$	−142.000	−0.347188	−0.173594	−	0.984817i	$-0.555538\pi$
$409$	−142.000	−0.347188	−0.173594	+	0.984817i	$0.555538\pi$
$410$	0	0
$411$	−678.000	−1.64964
$412$	0	0
$413$	0	0
$414$	306.000	0.739130
$415$	770.000	1.85542
$416$	0	0
$417$	−786.000	−1.88489
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	602.000	1.42993	0.714964	−	0.699161i	$-0.246443\pi$
$421$	602.000	1.42993	0.714964	+	0.699161i	$0.246443\pi$
$422$	−362.000	−0.857820
$423$	126.000	0.297872
$424$	602.000	1.41981
$425$	350.000	0.823529
$426$	0	0
$427$	0	0
$428$	318.000	0.742991
$429$	0	0
$430$	0	0
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	135.000	0.312500
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	66.0000	0.151376
$437$	748.000	1.71167
$438$	0	0
$439$	−622.000	−1.41686	−0.708428	−	0.705783i	$-0.750595\pi$
$439$	−622.000	−1.41686	−0.708428	+	0.705783i	$0.750595\pi$
$440$	0	0
$441$	441.000	1.00000
$442$	0	0
$443$	566.000	1.27765	0.638826	−	0.769351i	$-0.279420\pi$
$443$	566.000	1.27765	0.638826	+	0.769351i	$0.279420\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	−225.000	−0.500000
$451$	0	0
$452$	−618.000	−1.36726
$453$	−714.000	−1.57616
$454$	−134.000	−0.295154
$455$	0	0
$456$	−462.000	−1.01316
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	−218.000	−0.475983
$459$	378.000	0.823529
$460$	−510.000	−1.10870
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	0	0
$465$	−30.0000	−0.0645161
$466$	34.0000	0.0729614
$467$	−346.000	−0.740899	−0.370450	−	0.928853i	$-0.620796\pi$
$467$	−346.000	−0.740899	−0.370450	+	0.928853i	$0.620796\pi$
$468$	0	0
$469$	0	0
$470$	70.0000	0.148936
$471$	0	0
$472$	0	0
$473$	0	0
$474$	−294.000	−0.620253
$475$	−550.000	−1.15789
$476$	0	0
$477$	774.000	1.62264
$478$	0	0
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	495.000	1.03125
$481$	0	0
$482$	478.000	0.991701
$483$	0	0
$484$	−363.000	−0.750000
$485$	0	0
$486$	−243.000	−0.500000
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	−826.000	−1.69262
$489$	0	0
$490$	245.000	0.500000
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	10.0000	0.0201613
$497$	0	0
$498$	462.000	0.927711
$499$	938.000	1.87976	0.939880	−	0.341506i	$-0.110937\pi$
$499$	938.000	1.87976	0.939880	+	0.341506i	$0.110937\pi$
$500$	375.000	0.750000
$501$	762.000	1.52096
$502$	0	0
$503$	−994.000	−1.97614	−0.988072	−	0.153995i	$-0.950786\pi$
$503$	−994.000	−1.97614	−0.988072	+	0.153995i	$0.950786\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	507.000	1.00000
$508$	0	0
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	210.000	0.411765
$511$	0	0
$512$	−305.000	−0.595703
$513$	−594.000	−1.15789
$514$	466.000	0.906615
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	−462.000	−0.890173
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	0	0
$526$	−446.000	−0.847909
$527$	28.0000	0.0531309
$528$	0	0
$529$	627.000	1.18526
$530$	430.000	0.811321
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	530.000	0.990654
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	405.000	0.750000
$541$	−1078.00	−1.99261	−0.996303	−	0.0859072i	$-0.972621\pi$
$541$	−1078.00	−1.99261	−0.996303	+	0.0859072i	$0.972621\pi$
$542$	−482.000	−0.889299
$543$	366.000	0.674033
$544$	−462.000	−0.849265
$545$	110.000	0.201835
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	678.000	1.23723
$549$	−1062.00	−1.93443
$550$	0	0
$551$	0	0
$552$	−714.000	−1.29348
$553$	0	0
$554$	0	0
$555$	0	0
$556$	786.000	1.41367
$557$	614.000	1.10233	0.551167	−	0.834395i	$-0.314183\pi$
$557$	614.000	1.10233	0.551167	+	0.834395i	$0.314183\pi$
$558$	−18.0000	−0.0322581
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	−154.000	−0.273535	−0.136767	−	0.990603i	$-0.543671\pi$
$563$	−154.000	−0.273535	−0.136767	+	0.990603i	$0.543671\pi$
$564$	−126.000	−0.223404
$565$	−1030.00	−1.82301
$566$	0	0
$567$	0	0
$568$	0	0
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	−330.000	−0.578947
$571$	−358.000	−0.626970	−0.313485	−	0.949593i	$-0.601497\pi$
$571$	−358.000	−0.626970	−0.313485	+	0.949593i	$0.601497\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	−850.000	−1.47826
$576$	117.000	0.203125
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	93.0000	0.160900
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	394.000	0.672355
$587$	854.000	1.45486	0.727428	−	0.686184i	$-0.240716\pi$
$587$	854.000	1.45486	0.727428	+	0.686184i	$0.240716\pi$
$588$	−441.000	−0.750000
$589$	−44.0000	−0.0747029
$590$	0	0
$591$	1122.00	1.89848
$592$	0	0
$593$	1166.00	1.96627	0.983137	−	0.182873i	$-0.0585396\pi$
$593$	1166.00	1.96627	0.983137	+	0.182873i	$0.0585396\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−426.000	−0.713568
$598$	0	0
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	525.000	0.875000
$601$	242.000	0.402662	0.201331	−	0.979523i	$-0.435473\pi$
$601$	242.000	0.402662	0.201331	+	0.979523i	$0.435473\pi$
$602$	0	0
$603$	0	0
$604$	714.000	1.18212
$605$	−605.000	−1.00000
$606$	0	0
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	726.000	1.19408
$609$	0	0
$610$	−590.000	−0.967213
$611$	0	0
$612$	−378.000	−0.617647
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−1186.00	−1.92220	−0.961102	−	0.276193i	$-0.910927\pi$
$617$	−1186.00	−1.92220	−0.961102	+	0.276193i	$0.910927\pi$
$618$	0	0
$619$	698.000	1.12763	0.563813	−	0.825903i	$-0.309334\pi$
$619$	698.000	1.12763	0.563813	+	0.825903i	$0.309334\pi$
$620$	30.0000	0.0483871
$621$	−918.000	−1.47826
$622$	0	0
$623$	0	0
$624$	0	0
$625$	625.000	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	−238.000	−0.377179	−0.188590	−	0.982056i	$-0.560392\pi$
$631$	−238.000	−0.377179	−0.188590	+	0.982056i	$0.560392\pi$
$632$	686.000	1.08544
$633$	1086.00	1.71564
$634$	−134.000	−0.211356
$635$	0	0
$636$	−774.000	−1.21698
$637$	0	0
$638$	0	0
$639$	0	0
$640$	−595.000	−0.929688
$641$	0	0	1.00000			$0$
$641$	0	0	−1.00000			$\pi$
$642$	318.000	0.495327
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	0	0
$645$	0	0
$646$	308.000	0.476780
$647$	−706.000	−1.09119	−0.545595	−	0.838049i	$-0.683696\pi$
$647$	−706.000	−1.09119	−0.545595	+	0.838049i	$0.683696\pi$
$648$	567.000	0.875000
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−1114.00	−1.70597	−0.852986	−	0.521933i	$-0.825211\pi$
$653$	−1114.00	−1.70597	−0.852986	+	0.521933i	$0.825211\pi$
$654$	66.0000	0.100917
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	−838.000	−1.26778	−0.633888	−	0.773425i	$-0.718542\pi$
$661$	−838.000	−1.26778	−0.633888	+	0.773425i	$0.718542\pi$
$662$	−122.000	−0.184290
$663$	0	0
$664$	−1078.00	−1.62349
$665$	0	0
$666$	0	0
$667$	0	0
$668$	−762.000	−1.14072
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	675.000	1.00000
$676$	−507.000	−0.750000
$677$	374.000	0.552437	0.276219	−	0.961095i	$-0.410919\pi$
$677$	374.000	0.552437	0.276219	+	0.961095i	$0.410919\pi$
$678$	−618.000	−0.911504
$679$	0	0
$680$	−490.000	−0.720588
$681$	402.000	0.590308
$682$	0	0
$683$	86.0000	0.125915	0.0629575	−	0.998016i	$-0.479947\pi$
$683$	86.0000	0.125915	0.0629575	+	0.998016i	$0.479947\pi$
$684$	594.000	0.868421
$685$	1130.00	1.64964
$686$	0	0
$687$	654.000	0.951965
$688$	0	0
$689$	0	0
$690$	−510.000	−0.739130
$691$	1322.00	1.91317	0.956585	−	0.291455i	$-0.0941392\pi$
$691$	1322.00	1.91317	0.956585	+	0.291455i	$0.0941392\pi$
$692$	462.000	0.667630
$693$	0	0
$694$	586.000	0.844380
$695$	1310.00	1.88489
$696$	0	0
$697$	0	0
$698$	−458.000	−0.656160
$699$	−102.000	−0.145923
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	−210.000	−0.297872
$706$	274.000	0.388102
$707$	0	0
$708$	0	0
$709$	−742.000	−1.04654	−0.523272	−	0.852166i	$-0.675289\pi$
$709$	−742.000	−1.04654	−0.523272	+	0.852166i	$0.675289\pi$
$710$	0	0
$711$	882.000	1.24051
$712$	0	0
$713$	−68.0000	−0.0953717
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	−225.000	−0.312500
$721$	0	0
$722$	−123.000	−0.170360
$723$	−1434.00	−1.98340
$724$	−366.000	−0.505525
$725$	0	0
$726$	−363.000	−0.500000
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	729.000	1.00000
$730$	0	0
$731$	0	0
$732$	1062.00	1.45082
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	−735.000	−1.00000
$736$	1122.00	1.52446
$737$	0	0
$738$	0	0
$739$	−1462.00	−1.97835	−0.989175	−	0.146744i	$-0.953121\pi$
$739$	−1462.00	−1.97835	−0.989175	+	0.146744i	$0.953121\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	−514.000	−0.691790	−0.345895	−	0.938273i	$-0.612425\pi$
$743$	−514.000	−0.691790	−0.345895	+	0.938273i	$0.612425\pi$
$744$	42.0000	0.0564516
$745$	0	0
$746$	0	0
$747$	−1386.00	−1.85542
$748$	0	0
$749$	0	0
$750$	375.000	0.500000
$751$	−1438.00	−1.91478	−0.957390	−	0.288798i	$-0.906745\pi$
$751$	−1438.00	−1.91478	−0.957390	+	0.288798i	$0.906745\pi$
$752$	70.0000	0.0930851
$753$	0	0
$754$	0	0
$755$	1190.00	1.57616
$756$	0	0
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	742.000	0.978892
$759$	0	0
$760$	770.000	1.01316
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	−630.000	−0.823529
$766$	−686.000	−0.895561
$767$	0	0
$768$	−513.000	−0.667969
$769$	578.000	0.751625	0.375813	−	0.926696i	$-0.377364\pi$
$769$	578.000	0.751625	0.375813	+	0.926696i	$0.377364\pi$
$770$	0	0
$771$	−1398.00	−1.81323
$772$	0	0
$773$	1526.00	1.97413	0.987063	−	0.160330i	$-0.0512560\pi$
$773$	1526.00	1.97413	0.987063	+	0.160330i	$0.0512560\pi$
$774$	0	0
$775$	50.0000	0.0645161
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	0	0
$782$	476.000	0.608696
$783$	0	0
$784$	245.000	0.312500
$785$	0	0
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	−1122.00	−1.42386
$789$	1338.00	1.69582
$790$	490.000	0.620253
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	−1290.00	−1.62264
$796$	426.000	0.535176
$797$	−826.000	−1.03639	−0.518193	−	0.855264i	$-0.673395\pi$
$797$	−826.000	−1.03639	−0.518193	+	0.855264i	$0.673395\pi$
$798$	0	0
$799$	196.000	0.245307
$800$	−825.000	−1.03125
$801$	0	0
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	405.000	0.500000
$811$	1082.00	1.33416	0.667078	−	0.744988i	$-0.267545\pi$
$811$	1082.00	1.33416	0.667078	+	0.744988i	$0.267545\pi$
$812$	0	0
$813$	1446.00	1.77860
$814$	0	0
$815$	0	0
$816$	210.000	0.257353
$817$	0	0
$818$	142.000	0.173594
$819$	0	0
$820$	0	0
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	678.000	0.824818
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	374.000	0.452237	0.226119	−	0.974100i	$-0.427396\pi$
$827$	374.000	0.452237	0.226119	+	0.974100i	$0.427396\pi$
$828$	918.000	1.10870
$829$	−502.000	−0.605549	−0.302774	−	0.953062i	$-0.597913\pi$
$829$	−502.000	−0.605549	−0.302774	+	0.953062i	$0.597913\pi$
$830$	−770.000	−0.927711
$831$	0	0
$832$	0	0
$833$	686.000	0.823529
$834$	786.000	0.942446
$835$	−1270.00	−1.52096
$836$	0	0
$837$	54.0000	0.0645161
$838$	0	0
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	841.000	1.00000
$842$	−602.000	−0.714964
$843$	0	0
$844$	−1086.00	−1.28673
$845$	−845.000	−1.00000
$846$	−126.000	−0.148936
$847$	0	0
$848$	430.000	0.507075
$849$	0	0
$850$	−350.000	−0.411765
$851$	0	0
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	990.000	1.15789
$856$	−742.000	−0.866822
$857$	−1666.00	−1.94399	−0.971995	−	0.235000i	$-0.924491\pi$
$857$	−1666.00	−1.94399	−0.971995	+	0.235000i	$0.924491\pi$
$858$	0	0
$859$	218.000	0.253783	0.126892	−	0.991917i	$-0.459500\pi$
$859$	218.000	0.253783	0.126892	+	0.991917i	$0.459500\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−274.000	−0.317497	−0.158749	−	0.987319i	$-0.550746\pi$
$863$	−274.000	−0.317497	−0.158749	+	0.987319i	$0.550746\pi$
$864$	−891.000	−1.03125
$865$	770.000	0.890173
$866$	0	0
$867$	−279.000	−0.321799
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	−154.000	−0.176606
$873$	0	0
$874$	−748.000	−0.855835
$875$	0	0
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	622.000	0.708428
$879$	−1182.00	−1.34471
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	−441.000	−0.500000
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0	0
$885$	0	0
$886$	−566.000	−0.638826
$887$	1694.00	1.90981	0.954904	−	0.296914i	$-0.0959575\pi$
$887$	1694.00	1.90981	0.954904	+	0.296914i	$0.0959575\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	0	0
$892$	0	0
$893$	−308.000	−0.344905
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	−675.000	−0.750000
$901$	1204.00	1.33629
$902$	0	0
$903$	0	0
$904$	1442.00	1.59513
$905$	−610.000	−0.674033
$906$	714.000	0.788079
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	−402.000	−0.442731
$909$	0	0
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	−330.000	−0.361842
$913$	0	0
$914$	0	0
$915$	1770.00	1.93443
$916$	−654.000	−0.713974
$917$	0	0
$918$	−378.000	−0.411765
$919$	1298.00	1.41240	0.706202	−	0.708010i	$-0.250407\pi$
$919$	1298.00	1.41240	0.706202	+	0.708010i	$0.250407\pi$
$920$	1190.00	1.29348
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	0	0
$928$	0	0
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	30.0000	0.0322581
$931$	−1078.00	−1.15789
$932$	102.000	0.109442
$933$	0	0
$934$	346.000	0.370450
$935$	0	0
$936$	0	0
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	0	0
$939$	0	0
$940$	210.000	0.223404
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0	0
$947$	1574.00	1.66209	0.831045	−	0.556205i	$-0.187743\pi$
$947$	1574.00	1.66209	0.831045	+	0.556205i	$0.187743\pi$
$948$	−882.000	−0.930380
$949$	0	0
$950$	550.000	0.578947
$951$	402.000	0.422713
$952$	0	0
$953$	−1474.00	−1.54669	−0.773347	−	0.633983i	$-0.781419\pi$
$953$	−1474.00	−1.54669	−0.773347	+	0.633983i	$0.781419\pi$
$954$	−774.000	−0.811321
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	−195.000	−0.203125
$961$	−957.000	−0.995838
$962$	0	0
$963$	−954.000	−0.990654
$964$	1434.00	1.48755
$965$	0	0
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	847.000	0.875000
$969$	−924.000	−0.953560
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	−729.000	−0.750000
$973$	0	0
$974$	0	0
$975$	0	0
$976$	−590.000	−0.604508
$977$	1934.00	1.97953	0.989765	−	0.142710i	$-0.0455815\pi$
$977$	1934.00	1.97953	0.989765	+	0.142710i	$0.0455815\pi$
$978$	0	0
$979$	0	0
$980$	735.000	0.750000
$981$	−198.000	−0.201835
$982$	0	0
$983$	−1954.00	−1.98779	−0.993896	−	0.110319i	$-0.964813\pi$
$983$	−1954.00	−1.98779	−0.993896	+	0.110319i	$0.964813\pi$
$984$	0	0
$985$	−1870.00	−1.89848
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	−958.000	−0.966700	−0.483350	−	0.875427i	$-0.660580\pi$
$991$	−958.000	−0.966700	−0.483350	+	0.875427i	$0.660580\pi$
$992$	−66.0000	−0.0665323
$993$	366.000	0.368580
$994$	0	0
$995$	710.000	0.713568
$996$	1386.00	1.39157
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	−938.000	−0.939880
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.3.d.a.14.1	✓	1
3.2	odd	2		15.3.d.b.14.1	yes	1
4.3	odd	2		240.3.c.a.209.1		1
5.2	odd	4		75.3.c.d.26.1		2
5.3	odd	4		75.3.c.d.26.2		2
5.4	even	2		15.3.d.b.14.1	yes	1
8.3	odd	2		960.3.c.d.449.1		1
8.5	even	2		960.3.c.b.449.1		1
9.2	odd	6		405.3.h.a.134.1		2
9.4	even	3		405.3.h.b.269.1		2
9.5	odd	6		405.3.h.a.269.1		2
9.7	even	3		405.3.h.b.134.1		2
12.11	even	2		240.3.c.b.209.1		1
15.2	even	4		75.3.c.d.26.2		2
15.8	even	4		75.3.c.d.26.1		2
15.14	odd	2	CM	15.3.d.a.14.1	✓	1
20.3	even	4		1200.3.l.l.401.1		2
20.7	even	4		1200.3.l.l.401.2		2
20.19	odd	2		240.3.c.b.209.1		1
24.5	odd	2		960.3.c.c.449.1		1
24.11	even	2		960.3.c.a.449.1		1
40.19	odd	2		960.3.c.a.449.1		1
40.29	even	2		960.3.c.c.449.1		1
45.4	even	6		405.3.h.a.269.1		2
45.14	odd	6		405.3.h.b.269.1		2
45.29	odd	6		405.3.h.b.134.1		2
45.34	even	6		405.3.h.a.134.1		2
60.23	odd	4		1200.3.l.l.401.2		2
60.47	odd	4		1200.3.l.l.401.1		2
60.59	even	2		240.3.c.a.209.1		1
120.29	odd	2		960.3.c.b.449.1		1
120.59	even	2		960.3.c.d.449.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.3.d.a.14.1	✓	1	1.1	even	1	trivial
15.3.d.a.14.1	✓	1	15.14	odd	2	CM
15.3.d.b.14.1	yes	1	3.2	odd	2
15.3.d.b.14.1	yes	1	5.4	even	2
75.3.c.d.26.1		2	5.2	odd	4
75.3.c.d.26.1		2	15.8	even	4
75.3.c.d.26.2		2	5.3	odd	4
75.3.c.d.26.2		2	15.2	even	4
240.3.c.a.209.1		1	4.3	odd	2
240.3.c.a.209.1		1	60.59	even	2
240.3.c.b.209.1		1	12.11	even	2
240.3.c.b.209.1		1	20.19	odd	2
405.3.h.a.134.1		2	9.2	odd	6
405.3.h.a.134.1		2	45.34	even	6
405.3.h.a.269.1		2	9.5	odd	6
405.3.h.a.269.1		2	45.4	even	6
405.3.h.b.134.1		2	9.7	even	3
405.3.h.b.134.1		2	45.29	odd	6
405.3.h.b.269.1		2	9.4	even	3
405.3.h.b.269.1		2	45.14	odd	6
960.3.c.a.449.1		1	24.11	even	2
960.3.c.a.449.1		1	40.19	odd	2
960.3.c.b.449.1		1	8.5	even	2
960.3.c.b.449.1		1	120.29	odd	2
960.3.c.c.449.1		1	24.5	odd	2
960.3.c.c.449.1		1	40.29	even	2
960.3.c.d.449.1		1	8.3	odd	2
960.3.c.d.449.1		1	120.59	even	2
1200.3.l.l.401.1		2	20.3	even	4
1200.3.l.l.401.1		2	60.47	odd	4
1200.3.l.l.401.2		2	20.7	even	4
1200.3.l.l.401.2		2	60.23	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	15.d (of order \(2\), degree \(1\), minimal)

\(n\)	\(7\)	\(11\)
\(\chi(n)\)	\(-1\)	\(-1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more