LMFDB - Embedded newform 20.3.d.b.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,3,Mod(19,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, 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("20.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	20.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:	$0.544960528721$
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			19.1
Character	$\chi$	$=$	20.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} -4.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -8.00000 q^{6} +4.00000 q^{7} +8.00000 q^{8} +7.00000 q^{9} +O(q^{10})$

$q+2.00000 q^{2} -4.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -8.00000 q^{6} +4.00000 q^{7} +8.00000 q^{8} +7.00000 q^{9} -10.0000 q^{10} -16.0000 q^{12} +8.00000 q^{14} +20.0000 q^{15} +16.0000 q^{16} +14.0000 q^{18} -20.0000 q^{20} -16.0000 q^{21} -44.0000 q^{23} -32.0000 q^{24} +25.0000 q^{25} +8.00000 q^{27} +16.0000 q^{28} -22.0000 q^{29} +40.0000 q^{30} +32.0000 q^{32} -20.0000 q^{35} +28.0000 q^{36} -40.0000 q^{40} +62.0000 q^{41} -32.0000 q^{42} +76.0000 q^{43} -35.0000 q^{45} -88.0000 q^{46} +4.00000 q^{47} -64.0000 q^{48} -33.0000 q^{49} +50.0000 q^{50} +16.0000 q^{54} +32.0000 q^{56} -44.0000 q^{58} +80.0000 q^{60} -58.0000 q^{61} +28.0000 q^{63} +64.0000 q^{64} -116.000 q^{67} +176.000 q^{69} -40.0000 q^{70} +56.0000 q^{72} -100.000 q^{75} -80.0000 q^{80} -95.0000 q^{81} +124.000 q^{82} +76.0000 q^{83} -64.0000 q^{84} +152.000 q^{86} +88.0000 q^{87} -142.000 q^{89} -70.0000 q^{90} -176.000 q^{92} +8.00000 q^{94} -128.000 q^{96} -66.0000 q^{98} +O(q^{100})$

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$-1$

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 $

$2$	2.00000	1.00000
$2$	2.00000	1.00000
$3$	−4.00000	−1.33333	−0.666667	−	0.745356i	$-0.732280\pi$
$3$	−4.00000	−1.33333	−0.666667	+	0.745356i	$0.732280\pi$
$4$	4.00000	1.00000
$5$	−5.00000	−1.00000
$5$	−5.00000	−1.00000
$6$	−8.00000	−1.33333
$7$	4.00000	0.571429	0.285714	−	0.958315i	$-0.407769\pi$
$7$	4.00000	0.571429	0.285714	+	0.958315i	$0.407769\pi$
$8$	8.00000	1.00000
$9$	7.00000	0.777778
$10$	−10.0000	−1.00000
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	−16.0000	−1.33333
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	8.00000	0.571429
$15$	20.0000	1.33333
$16$	16.0000	1.00000
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	14.0000	0.777778
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	−20.0000	−1.00000
$21$	−16.0000	−0.761905
$22$	0	0
$23$	−44.0000	−1.91304	−0.956522	−	0.291661i	$-0.905792\pi$
$23$	−44.0000	−1.91304	−0.956522	+	0.291661i	$0.905792\pi$
$24$	−32.0000	−1.33333
$25$	25.0000	1.00000
$26$	0	0
$27$	8.00000	0.296296
$28$	16.0000	0.571429
$29$	−22.0000	−0.758621	−0.379310	−	0.925270i	$-0.623839\pi$
$29$	−22.0000	−0.758621	−0.379310	+	0.925270i	$0.623839\pi$
$30$	40.0000	1.33333
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	32.0000	1.00000
$33$	0	0
$34$	0	0
$35$	−20.0000	−0.571429
$36$	28.0000	0.777778
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	0	0
$40$	−40.0000	−1.00000
$41$	62.0000	1.51220	0.756098	−	0.654459i	$-0.227104\pi$
$41$	62.0000	1.51220	0.756098	+	0.654459i	$0.227104\pi$
$42$	−32.0000	−0.761905
$43$	76.0000	1.76744	0.883721	−	0.468014i	$-0.155030\pi$
$43$	76.0000	1.76744	0.883721	+	0.468014i	$0.155030\pi$
$44$	0	0
$45$	−35.0000	−0.777778
$46$	−88.0000	−1.91304
$47$	4.00000	0.0851064	0.0425532	−	0.999094i	$-0.486451\pi$
$47$	4.00000	0.0851064	0.0425532	+	0.999094i	$0.486451\pi$
$48$	−64.0000	−1.33333
$49$	−33.0000	−0.673469
$50$	50.0000	1.00000
$51$	0	0
$52$	0	0
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	16.0000	0.296296
$55$	0	0
$56$	32.0000	0.571429
$57$	0	0
$58$	−44.0000	−0.758621
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	80.0000	1.33333
$61$	−58.0000	−0.950820	−0.475410	−	0.879764i	$-0.657700\pi$
$61$	−58.0000	−0.950820	−0.475410	+	0.879764i	$0.657700\pi$
$62$	0	0
$63$	28.0000	0.444444
$64$	64.0000	1.00000
$65$	0	0
$66$	0	0
$67$	−116.000	−1.73134	−0.865672	−	0.500612i	$-0.833108\pi$
$67$	−116.000	−1.73134	−0.865672	+	0.500612i	$0.833108\pi$
$68$	0	0
$69$	176.000	2.55072
$70$	−40.0000	−0.571429
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	56.0000	0.777778
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0	0
$75$	−100.000	−1.33333
$76$	0	0
$77$	0	0
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	−80.0000	−1.00000
$81$	−95.0000	−1.17284
$82$	124.000	1.51220
$83$	76.0000	0.915663	0.457831	−	0.889039i	$-0.348626\pi$
$83$	76.0000	0.915663	0.457831	+	0.889039i	$0.348626\pi$
$84$	−64.0000	−0.761905
$85$	0	0
$86$	152.000	1.76744
$87$	88.0000	1.01149
$88$	0	0
$89$	−142.000	−1.59551	−0.797753	−	0.602985i	$-0.793978\pi$
$89$	−142.000	−1.59551	−0.797753	+	0.602985i	$0.793978\pi$
$90$	−70.0000	−0.777778
$91$	0	0
$92$	−176.000	−1.91304
$93$	0	0
$94$	8.00000	0.0851064
$95$	0	0
$96$	−128.000	−1.33333
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	−66.0000	−0.673469
$99$	0	0
$100$	100.000	1.00000
$101$	122.000	1.20792	0.603960	−	0.797014i	$-0.293589\pi$
$101$	122.000	1.20792	0.603960	+	0.797014i	$0.293589\pi$
$102$	0	0
$103$	−44.0000	−0.427184	−0.213592	−	0.976923i	$-0.568516\pi$
$103$	−44.0000	−0.427184	−0.213592	+	0.976923i	$0.568516\pi$
$104$	0	0
$105$	80.0000	0.761905
$106$	0	0
$107$	124.000	1.15888	0.579439	−	0.815015i	$-0.303272\pi$
$107$	124.000	1.15888	0.579439	+	0.815015i	$0.303272\pi$
$108$	32.0000	0.296296
$109$	38.0000	0.348624	0.174312	−	0.984690i	$-0.444230\pi$
$109$	38.0000	0.348624	0.174312	+	0.984690i	$0.444230\pi$
$110$	0	0
$111$	0	0
$112$	64.0000	0.571429
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	220.000	1.91304
$116$	−88.0000	−0.758621
$117$	0	0
$118$	0	0
$119$	0	0
$120$	160.000	1.33333
$121$	121.000	1.00000
$122$	−116.000	−0.950820
$123$	−248.000	−2.01626
$124$	0	0
$125$	−125.000	−1.00000
$126$	56.0000	0.444444
$127$	−236.000	−1.85827	−0.929134	−	0.369744i	$-0.879446\pi$
$127$	−236.000	−1.85827	−0.929134	+	0.369744i	$0.879446\pi$
$128$	128.000	1.00000
$129$	−304.000	−2.35659
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	0	0
$134$	−232.000	−1.73134
$135$	−40.0000	−0.296296
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	352.000	2.55072
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	−80.0000	−0.571429
$141$	−16.0000	−0.113475
$142$	0	0
$143$	0	0
$144$	112.000	0.777778
$145$	110.000	0.758621
$146$	0	0
$147$	132.000	0.897959
$148$	0	0
$149$	278.000	1.86577	0.932886	−	0.360172i	$-0.117282\pi$
$149$	278.000	1.86577	0.932886	+	0.360172i	$0.117282\pi$
$150$	−200.000	−1.33333
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	0	0
$159$	0	0
$160$	−160.000	−1.00000
$161$	−176.000	−1.09317
$162$	−190.000	−1.17284
$163$	−164.000	−1.00613	−0.503067	−	0.864247i	$-0.667795\pi$
$163$	−164.000	−1.00613	−0.503067	+	0.864247i	$0.667795\pi$
$164$	248.000	1.51220
$165$	0	0
$166$	152.000	0.915663
$167$	244.000	1.46108	0.730539	−	0.682871i	$-0.239269\pi$
$167$	244.000	1.46108	0.730539	+	0.682871i	$0.239269\pi$
$168$	−128.000	−0.761905
$169$	169.000	1.00000
$170$	0	0
$171$	0	0
$172$	304.000	1.76744
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	176.000	1.01149
$175$	100.000	0.571429
$176$	0	0
$177$	0	0
$178$	−284.000	−1.59551
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	−140.000	−0.777778
$181$	−358.000	−1.97790	−0.988950	−	0.148248i	$-0.952637\pi$
$181$	−358.000	−1.97790	−0.988950	+	0.148248i	$0.952637\pi$
$182$	0	0
$183$	232.000	1.26776
$184$	−352.000	−1.91304
$185$	0	0
$186$	0	0
$187$	0	0
$188$	16.0000	0.0851064
$189$	32.0000	0.169312
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	−256.000	−1.33333
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	0	0
$196$	−132.000	−0.673469
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	0	0
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	200.000	1.00000
$201$	464.000	2.30846
$202$	244.000	1.20792
$203$	−88.0000	−0.433498
$204$	0	0
$205$	−310.000	−1.51220
$206$	−88.0000	−0.427184
$207$	−308.000	−1.48792
$208$	0	0
$209$	0	0
$210$	160.000	0.761905
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	0	0
$213$	0	0
$214$	248.000	1.15888
$215$	−380.000	−1.76744
$216$	64.0000	0.296296
$217$	0	0
$218$	76.0000	0.348624
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	436.000	1.95516	0.977578	−	0.210571i	$-0.0675325\pi$
$223$	436.000	1.95516	0.977578	+	0.210571i	$0.0675325\pi$
$224$	128.000	0.571429
$225$	175.000	0.777778
$226$	0	0
$227$	−356.000	−1.56828	−0.784141	−	0.620583i	$-0.786896\pi$
$227$	−356.000	−1.56828	−0.784141	+	0.620583i	$0.786896\pi$
$228$	0	0
$229$	−262.000	−1.14410	−0.572052	−	0.820217i	$-0.693853\pi$
$229$	−262.000	−1.14410	−0.572052	+	0.820217i	$0.693853\pi$
$230$	440.000	1.91304
$231$	0	0
$232$	−176.000	−0.758621
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	−20.0000	−0.0851064
$236$	0	0
$237$	0	0
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	320.000	1.33333
$241$	302.000	1.25311	0.626556	−	0.779376i	$-0.284464\pi$
$241$	302.000	1.25311	0.626556	+	0.779376i	$0.284464\pi$
$242$	242.000	1.00000
$243$	308.000	1.26749
$244$	−232.000	−0.950820
$245$	165.000	0.673469
$246$	−496.000	−2.01626
$247$	0	0
$248$	0	0
$249$	−304.000	−1.22088
$250$	−250.000	−1.00000
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	112.000	0.444444
$253$	0	0
$254$	−472.000	−1.85827
$255$	0	0
$256$	256.000	1.00000
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	−608.000	−2.35659
$259$	0	0
$260$	0	0
$261$	−154.000	−0.590038
$262$	0	0
$263$	−284.000	−1.07985	−0.539924	−	0.841714i	$-0.681547\pi$
$263$	−284.000	−1.07985	−0.539924	+	0.841714i	$0.681547\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	568.000	2.12734
$268$	−464.000	−1.73134
$269$	38.0000	0.141264	0.0706320	−	0.997502i	$-0.477498\pi$
$269$	38.0000	0.141264	0.0706320	+	0.997502i	$0.477498\pi$
$270$	−80.0000	−0.296296
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	704.000	2.55072
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0	0
$279$	0	0
$280$	−160.000	−0.571429
$281$	−418.000	−1.48754	−0.743772	−	0.668433i	$-0.766965\pi$
$281$	−418.000	−1.48754	−0.743772	+	0.668433i	$0.766965\pi$
$282$	−32.0000	−0.113475
$283$	316.000	1.11661	0.558304	−	0.829637i	$-0.311452\pi$
$283$	316.000	1.11661	0.558304	+	0.829637i	$0.311452\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	248.000	0.864111
$288$	224.000	0.777778
$289$	289.000	1.00000
$290$	220.000	0.758621
$291$	0	0
$292$	0	0
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	264.000	0.897959
$295$	0	0
$296$	0	0
$297$	0	0
$298$	556.000	1.86577
$299$	0	0
$300$	−400.000	−1.33333
$301$	304.000	1.00997
$302$	0	0
$303$	−488.000	−1.61056
$304$	0	0
$305$	290.000	0.950820
$306$	0	0
$307$	−596.000	−1.94137	−0.970684	−	0.240359i	$-0.922735\pi$
$307$	−596.000	−1.94137	−0.970684	+	0.240359i	$0.922735\pi$
$308$	0	0
$309$	176.000	0.569579
$310$	0	0
$311$	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
$315$	−140.000	−0.444444
$316$	0	0
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	0	0
$320$	−320.000	−1.00000
$321$	−496.000	−1.54517
$322$	−352.000	−1.09317
$323$	0	0
$324$	−380.000	−1.17284
$325$	0	0
$326$	−328.000	−1.00613
$327$	−152.000	−0.464832
$328$	496.000	1.51220
$329$	16.0000	0.0486322
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	304.000	0.915663
$333$	0	0
$334$	488.000	1.46108
$335$	580.000	1.73134
$336$	−256.000	−0.761905
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	338.000	1.00000
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−328.000	−0.956268
$344$	608.000	1.76744
$345$	−880.000	−2.55072
$346$	0	0
$347$	−116.000	−0.334294	−0.167147	−	0.985932i	$-0.553455\pi$
$347$	−116.000	−0.334294	−0.167147	+	0.985932i	$0.553455\pi$
$348$	352.000	1.01149
$349$	−22.0000	−0.0630372	−0.0315186	−	0.999503i	$-0.510034\pi$
$349$	−22.0000	−0.0630372	−0.0315186	+	0.999503i	$0.510034\pi$
$350$	200.000	0.571429
$351$	0	0
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	−568.000	−1.59551
$357$	0	0
$358$	0	0
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	−280.000	−0.777778
$361$	361.000	1.00000
$362$	−716.000	−1.97790
$363$	−484.000	−1.33333
$364$	0	0
$365$	0	0
$366$	464.000	1.26776
$367$	724.000	1.97275	0.986376	−	0.164506i	$-0.0526031\pi$
$367$	724.000	1.97275	0.986376	+	0.164506i	$0.0526031\pi$
$368$	−704.000	−1.91304
$369$	434.000	1.17615
$370$	0	0
$371$	0	0
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	500.000	1.33333
$376$	32.0000	0.0851064
$377$	0	0
$378$	64.0000	0.169312
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	0	0
$381$	944.000	2.47769
$382$	0	0
$383$	−44.0000	−0.114883	−0.0574413	−	0.998349i	$-0.518294\pi$
$383$	−44.0000	−0.114883	−0.0574413	+	0.998349i	$0.518294\pi$
$384$	−512.000	−1.33333
$385$	0	0
$386$	0	0
$387$	532.000	1.37468
$388$	0	0
$389$	−202.000	−0.519280	−0.259640	−	0.965705i	$-0.583604\pi$
$389$	−202.000	−0.519280	−0.259640	+	0.965705i	$0.583604\pi$
$390$	0	0
$391$	0	0
$392$	−264.000	−0.673469
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	0	0
$399$	0	0
$400$	400.000	1.00000
$401$	−478.000	−1.19202	−0.596010	−	0.802977i	$-0.703248\pi$
$401$	−478.000	−1.19202	−0.596010	+	0.802977i	$0.703248\pi$
$402$	928.000	2.30846
$403$	0	0
$404$	488.000	1.20792
$405$	475.000	1.17284
$406$	−176.000	−0.433498
$407$	0	0
$408$	0	0
$409$	−802.000	−1.96088	−0.980440	−	0.196818i	$-0.936939\pi$
$409$	−802.000	−1.96088	−0.980440	+	0.196818i	$0.936939\pi$
$410$	−620.000	−1.51220
$411$	0	0
$412$	−176.000	−0.427184
$413$	0	0
$414$	−616.000	−1.48792
$415$	−380.000	−0.915663
$416$	0	0
$417$	0	0
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	320.000	0.761905
$421$	−778.000	−1.84798	−0.923990	−	0.382415i	$-0.875092\pi$
$421$	−778.000	−1.84798	−0.923990	+	0.382415i	$0.875092\pi$
$422$	0	0
$423$	28.0000	0.0661939
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−232.000	−0.543326
$428$	496.000	1.15888
$429$	0	0
$430$	−760.000	−1.76744
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	128.000	0.296296
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	−440.000	−1.01149
$436$	152.000	0.348624
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	−231.000	−0.523810
$442$	0	0
$443$	796.000	1.79684	0.898420	−	0.439138i	$-0.144716\pi$
$443$	796.000	1.79684	0.898420	+	0.439138i	$0.144716\pi$
$444$	0	0
$445$	710.000	1.59551
$446$	872.000	1.95516
$447$	−1112.00	−2.48770
$448$	256.000	0.571429
$449$	398.000	0.886414	0.443207	−	0.896419i	$-0.353841\pi$
$449$	398.000	0.886414	0.443207	+	0.896419i	$0.353841\pi$
$450$	350.000	0.777778
$451$	0	0
$452$	0	0
$453$	0	0
$454$	−712.000	−1.56828
$455$	0	0
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	−524.000	−1.14410
$459$	0	0
$460$	880.000	1.91304
$461$	842.000	1.82646	0.913232	−	0.407440i	$-0.133578\pi$
$461$	842.000	1.82646	0.913232	+	0.407440i	$0.133578\pi$
$462$	0	0
$463$	−764.000	−1.65011	−0.825054	−	0.565054i	$-0.808855\pi$
$463$	−764.000	−1.65011	−0.825054	+	0.565054i	$0.808855\pi$
$464$	−352.000	−0.758621
$465$	0	0
$466$	0	0
$467$	124.000	0.265525	0.132762	−	0.991148i	$-0.457615\pi$
$467$	124.000	0.265525	0.132762	+	0.991148i	$0.457615\pi$
$468$	0	0
$469$	−464.000	−0.989339
$470$	−40.0000	−0.0851064
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	0	0
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	640.000	1.33333
$481$	0	0
$482$	604.000	1.25311
$483$	704.000	1.45756
$484$	484.000	1.00000
$485$	0	0
$486$	616.000	1.26749
$487$	484.000	0.993840	0.496920	−	0.867796i	$-0.334464\pi$
$487$	484.000	0.993840	0.496920	+	0.867796i	$0.334464\pi$
$488$	−464.000	−0.950820
$489$	656.000	1.34151
$490$	330.000	0.673469
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	−992.000	−2.01626
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	−608.000	−1.22088
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	−500.000	−1.00000
$501$	−976.000	−1.94810
$502$	0	0
$503$	916.000	1.82107	0.910537	−	0.413428i	$-0.135669\pi$
$503$	916.000	1.82107	0.910537	+	0.413428i	$0.135669\pi$
$504$	224.000	0.444444
$505$	−610.000	−1.20792
$506$	0	0
$507$	−676.000	−1.33333
$508$	−944.000	−1.85827
$509$	−982.000	−1.92927	−0.964637	−	0.263584i	$-0.915095\pi$
$509$	−982.000	−1.92927	−0.964637	+	0.263584i	$0.915095\pi$
$510$	0	0
$511$	0	0
$512$	512.000	1.00000
$513$	0	0
$514$	0	0
$515$	220.000	0.427184
$516$	−1216.00	−2.35659
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	722.000	1.38580	0.692898	−	0.721035i	$-0.256333\pi$
$521$	722.000	1.38580	0.692898	+	0.721035i	$0.256333\pi$
$522$	−308.000	−0.590038
$523$	−164.000	−0.313576	−0.156788	−	0.987632i	$-0.550114\pi$
$523$	−164.000	−0.313576	−0.156788	+	0.987632i	$0.550114\pi$
$524$	0	0
$525$	−400.000	−0.761905
$526$	−568.000	−1.07985
$527$	0	0
$528$	0	0
$529$	1407.00	2.65974
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	1136.00	2.12734
$535$	−620.000	−1.15888
$536$	−928.000	−1.73134
$537$	0	0
$538$	76.0000	0.141264
$539$	0	0
$540$	−160.000	−0.296296
$541$	362.000	0.669131	0.334566	−	0.942372i	$-0.391410\pi$
$541$	362.000	0.669131	0.334566	+	0.942372i	$0.391410\pi$
$542$	0	0
$543$	1432.00	2.63720
$544$	0	0
$545$	−190.000	−0.348624
$546$	0	0
$547$	1084.00	1.98172	0.990859	−	0.134900i	$-0.0430713\pi$
$547$	1084.00	1.98172	0.990859	+	0.134900i	$0.0430713\pi$
$548$	0	0
$549$	−406.000	−0.739526
$550$	0	0
$551$	0	0
$552$	1408.00	2.55072
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	0	0
$560$	−320.000	−0.571429
$561$	0	0
$562$	−836.000	−1.48754
$563$	−1124.00	−1.99645	−0.998224	−	0.0595755i	$-0.981025\pi$
$563$	−1124.00	−1.99645	−0.998224	+	0.0595755i	$0.981025\pi$
$564$	−64.0000	−0.113475
$565$	0	0
$566$	632.000	1.11661
$567$	−380.000	−0.670194
$568$	0	0
$569$	158.000	0.277680	0.138840	−	0.990315i	$-0.455663\pi$
$569$	158.000	0.277680	0.138840	+	0.990315i	$0.455663\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	496.000	0.864111
$575$	−1100.00	−1.91304
$576$	448.000	0.777778
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	578.000	1.00000
$579$	0	0
$580$	440.000	0.758621
$581$	304.000	0.523236
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−1076.00	−1.83305	−0.916525	−	0.399978i	$-0.869018\pi$
$587$	−1076.00	−1.83305	−0.916525	+	0.399978i	$0.869018\pi$
$588$	528.000	0.897959
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	0	0
$595$	0	0
$596$	1112.00	1.86577
$597$	0	0
$598$	0	0
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	−800.000	−1.33333
$601$	−418.000	−0.695507	−0.347754	−	0.937586i	$-0.613055\pi$
$601$	−418.000	−0.695507	−0.347754	+	0.937586i	$0.613055\pi$
$602$	608.000	1.00997
$603$	−812.000	−1.34660
$604$	0	0
$605$	−605.000	−1.00000
$606$	−976.000	−1.61056
$607$	964.000	1.58814	0.794069	−	0.607827i	$-0.207959\pi$
$607$	964.000	1.58814	0.794069	+	0.607827i	$0.207959\pi$
$608$	0	0
$609$	352.000	0.577997
$610$	580.000	0.950820
$611$	0	0
$612$	0	0
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	−1192.00	−1.94137
$615$	1240.00	2.01626
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	352.000	0.569579
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	−352.000	−0.566828
$622$	0	0
$623$	−568.000	−0.911717
$624$	0	0
$625$	625.000	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	−280.000	−0.444444
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	1180.00	1.85827
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	−640.000	−1.00000
$641$	−1138.00	−1.77535	−0.887676	−	0.460470i	$-0.847681\pi$
$641$	−1138.00	−1.77535	−0.887676	+	0.460470i	$0.847681\pi$
$642$	−992.000	−1.54517
$643$	−404.000	−0.628305	−0.314152	−	0.949373i	$-0.601720\pi$
$643$	−404.000	−0.628305	−0.314152	+	0.949373i	$0.601720\pi$
$644$	−704.000	−1.09317
$645$	1520.00	2.35659
$646$	0	0
$647$	−956.000	−1.47759	−0.738794	−	0.673931i	$-0.764605\pi$
$647$	−956.000	−1.47759	−0.738794	+	0.673931i	$0.764605\pi$
$648$	−760.000	−1.17284
$649$	0	0
$650$	0	0
$651$	0	0
$652$	−656.000	−1.00613
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	−304.000	−0.464832
$655$	0	0
$656$	992.000	1.51220
$657$	0	0
$658$	32.0000	0.0486322
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	−298.000	−0.450832	−0.225416	−	0.974263i	$-0.572374\pi$
$661$	−298.000	−0.450832	−0.225416	+	0.974263i	$0.572374\pi$
$662$	0	0
$663$	0	0
$664$	608.000	0.915663
$665$	0	0
$666$	0	0
$667$	968.000	1.45127
$668$	976.000	1.46108
$669$	−1744.00	−2.60688
$670$	1160.00	1.73134
$671$	0	0
$672$	−512.000	−0.761905
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	200.000	0.296296
$676$	676.000	1.00000
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	1424.00	2.09104
$682$	0	0
$683$	556.000	0.814056	0.407028	−	0.913416i	$-0.366565\pi$
$683$	556.000	0.814056	0.407028	+	0.913416i	$0.366565\pi$
$684$	0	0
$685$	0	0
$686$	−656.000	−0.956268
$687$	1048.00	1.52547
$688$	1216.00	1.76744
$689$	0	0
$690$	−1760.00	−2.55072
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	0	0
$694$	−232.000	−0.334294
$695$	0	0
$696$	704.000	1.01149
$697$	0	0
$698$	−44.0000	−0.0630372
$699$	0	0
$700$	400.000	0.571429
$701$	902.000	1.28673	0.643367	−	0.765558i	$-0.277537\pi$
$701$	902.000	1.28673	0.643367	+	0.765558i	$0.277537\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	80.0000	0.113475
$706$	0	0
$707$	488.000	0.690240
$708$	0	0
$709$	698.000	0.984485	0.492243	−	0.870458i	$-0.336177\pi$
$709$	698.000	0.984485	0.492243	+	0.870458i	$0.336177\pi$
$710$	0	0
$711$	0	0
$712$	−1136.00	−1.59551
$713$	0	0
$714$	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			$\pi$
$720$	−560.000	−0.777778
$721$	−176.000	−0.244105
$722$	722.000	1.00000
$723$	−1208.00	−1.67082
$724$	−1432.00	−1.97790
$725$	−550.000	−0.758621
$726$	−968.000	−1.33333
$727$	−1436.00	−1.97524	−0.987620	−	0.156863i	$-0.949862\pi$
$727$	−1436.00	−1.97524	−0.987620	+	0.156863i	$0.949862\pi$
$728$	0	0
$729$	−377.000	−0.517147
$730$	0	0
$731$	0	0
$732$	928.000	1.26776
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	1448.00	1.97275
$735$	−660.000	−0.897959
$736$	−1408.00	−1.91304
$737$	0	0
$738$	868.000	1.17615
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	−764.000	−1.02826	−0.514132	−	0.857711i	$-0.671886\pi$
$743$	−764.000	−1.02826	−0.514132	+	0.857711i	$0.671886\pi$
$744$	0	0
$745$	−1390.00	−1.86577
$746$	0	0
$747$	532.000	0.712182
$748$	0	0
$749$	496.000	0.662216
$750$	1000.00	1.33333
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	64.0000	0.0851064
$753$	0	0
$754$	0	0
$755$	0	0
$756$	128.000	0.169312
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	242.000	0.318003	0.159001	−	0.987278i	$-0.449173\pi$
$761$	242.000	0.318003	0.159001	+	0.987278i	$0.449173\pi$
$762$	1888.00	2.47769
$763$	152.000	0.199214
$764$	0	0
$765$	0	0
$766$	−88.0000	−0.114883
$767$	0	0
$768$	−1024.00	−1.33333
$769$	−1342.00	−1.74512	−0.872562	−	0.488504i	$-0.837543\pi$
$769$	−1342.00	−1.74512	−0.872562	+	0.488504i	$0.837543\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	1064.00	1.37468
$775$	0	0
$776$	0	0
$777$	0	0
$778$	−404.000	−0.519280
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	−176.000	−0.224777
$784$	−528.000	−0.673469
$785$	0	0
$786$	0	0
$787$	−116.000	−0.147395	−0.0736976	−	0.997281i	$-0.523480\pi$
$787$	−116.000	−0.147395	−0.0736976	+	0.997281i	$0.523480\pi$
$788$	0	0
$789$	1136.00	1.43980
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	800.000	1.00000
$801$	−994.000	−1.24095
$802$	−956.000	−1.19202
$803$	0	0
$804$	1856.00	2.30846
$805$	880.000	1.09317
$806$	0	0
$807$	−152.000	−0.188352
$808$	976.000	1.20792
$809$	1298.00	1.60445	0.802225	−	0.597022i	$-0.203649\pi$
$809$	1298.00	1.60445	0.802225	+	0.597022i	$0.203649\pi$
$810$	950.000	1.17284
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	−352.000	−0.433498
$813$	0	0
$814$	0	0
$815$	820.000	1.00613
$816$	0	0
$817$	0	0
$818$	−1604.00	−1.96088
$819$	0	0
$820$	−1240.00	−1.51220
$821$	662.000	0.806334	0.403167	−	0.915126i	$-0.367909\pi$
$821$	662.000	0.806334	0.403167	+	0.915126i	$0.367909\pi$
$822$	0	0
$823$	1396.00	1.69623	0.848117	−	0.529810i	$-0.177737\pi$
$823$	1396.00	1.69623	0.848117	+	0.529810i	$0.177737\pi$
$824$	−352.000	−0.427184
$825$	0	0
$826$	0	0
$827$	−596.000	−0.720677	−0.360339	−	0.932822i	$-0.617339\pi$
$827$	−596.000	−0.720677	−0.360339	+	0.932822i	$0.617339\pi$
$828$	−1232.00	−1.48792
$829$	1478.00	1.78287	0.891435	−	0.453148i	$-0.149699\pi$
$829$	1478.00	1.78287	0.891435	+	0.453148i	$0.149699\pi$
$830$	−760.000	−0.915663
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	−1220.00	−1.46108
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	640.000	0.761905
$841$	−357.000	−0.424495
$842$	−1556.00	−1.84798
$843$	1672.00	1.98339
$844$	0	0
$845$	−845.000	−1.00000
$846$	56.0000	0.0661939
$847$	484.000	0.571429
$848$	0	0
$849$	−1264.00	−1.48881
$850$	0	0
$851$	0	0
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	−464.000	−0.543326
$855$	0	0
$856$	992.000	1.15888
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	−1520.00	−1.76744
$861$	−992.000	−1.15215
$862$	0	0
$863$	1636.00	1.89571	0.947856	−	0.318698i	$-0.103246\pi$
$863$	1636.00	1.89571	0.947856	+	0.318698i	$0.103246\pi$
$864$	256.000	0.296296
$865$	0	0
$866$	0	0
$867$	−1156.00	−1.33333
$868$	0	0
$869$	0	0
$870$	−880.000	−1.01149
$871$	0	0
$872$	304.000	0.348624
$873$	0	0
$874$	0	0
$875$	−500.000	−0.571429
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	−1618.00	−1.83655	−0.918275	−	0.395944i	$-0.870417\pi$
$881$	−1618.00	−1.83655	−0.918275	+	0.395944i	$0.870417\pi$
$882$	−462.000	−0.523810
$883$	1276.00	1.44507	0.722537	−	0.691332i	$-0.242976\pi$
$883$	1276.00	1.44507	0.722537	+	0.691332i	$0.242976\pi$
$884$	0	0
$885$	0	0
$886$	1592.00	1.79684
$887$	964.000	1.08681	0.543405	−	0.839471i	$-0.317135\pi$
$887$	964.000	1.08681	0.543405	+	0.839471i	$0.317135\pi$
$888$	0	0
$889$	−944.000	−1.06187
$890$	1420.00	1.59551
$891$	0	0
$892$	1744.00	1.95516
$893$	0	0
$894$	−2224.00	−2.48770
$895$	0	0
$896$	512.000	0.571429
$897$	0	0
$898$	796.000	0.886414
$899$	0	0
$900$	700.000	0.777778
$901$	0	0
$902$	0	0
$903$	−1216.00	−1.34662
$904$	0	0
$905$	1790.00	1.97790
$906$	0	0
$907$	−1796.00	−1.98015	−0.990077	−	0.140525i	$-0.955121\pi$
$907$	−1796.00	−1.98015	−0.990077	+	0.140525i	$0.955121\pi$
$908$	−1424.00	−1.56828
$909$	854.000	0.939494
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	−1160.00	−1.26776
$916$	−1048.00	−1.14410
$917$	0	0
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	1760.00	1.91304
$921$	2384.00	2.58849
$922$	1684.00	1.82646
$923$	0	0
$924$	0	0
$925$	0	0
$926$	−1528.00	−1.65011
$927$	−308.000	−0.332255
$928$	−704.000	−0.758621
$929$	−562.000	−0.604952	−0.302476	−	0.953157i	$-0.597813\pi$
$929$	−562.000	−0.604952	−0.302476	+	0.953157i	$0.597813\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	248.000	0.265525
$935$	0	0
$936$	0	0
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	−928.000	−0.989339
$939$	0	0
$940$	−80.0000	−0.0851064
$941$	−118.000	−0.125399	−0.0626993	−	0.998032i	$-0.519971\pi$
$941$	−118.000	−0.125399	−0.0626993	+	0.998032i	$0.519971\pi$
$942$	0	0
$943$	−2728.00	−2.89290
$944$	0	0
$945$	−160.000	−0.169312
$946$	0	0
$947$	1804.00	1.90496	0.952482	−	0.304596i	$-0.0985216\pi$
$947$	1804.00	1.90496	0.952482	+	0.304596i	$0.0985216\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	1280.00	1.33333
$961$	961.000	1.00000
$962$	0	0
$963$	868.000	0.901350
$964$	1208.00	1.25311
$965$	0	0
$966$	1408.00	1.45756
$967$	244.000	0.252327	0.126163	−	0.992009i	$-0.459734\pi$
$967$	244.000	0.252327	0.126163	+	0.992009i	$0.459734\pi$
$968$	968.000	1.00000
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	1232.00	1.26749
$973$	0	0
$974$	968.000	0.993840
$975$	0	0
$976$	−928.000	−0.950820
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	1312.00	1.34151
$979$	0	0
$980$	660.000	0.673469
$981$	266.000	0.271152
$982$	0	0
$983$	−284.000	−0.288911	−0.144456	−	0.989511i	$-0.546143\pi$
$983$	−284.000	−0.288911	−0.144456	+	0.989511i	$0.546143\pi$
$984$	−1984.00	−2.01626
$985$	0	0
$986$	0	0
$987$	−64.0000	−0.0648430
$988$	0	0
$989$	−3344.00	−3.38119
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	−1216.00	−1.22088
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.3.d.b.19.1	yes	1
3.2	odd	2		180.3.f.a.19.1		1
4.3	odd	2		20.3.d.a.19.1	✓	1
5.2	odd	4		100.3.b.c.51.2		2
5.3	odd	4		100.3.b.c.51.1		2
5.4	even	2		20.3.d.a.19.1	✓	1
8.3	odd	2		320.3.h.a.319.1		1
8.5	even	2		320.3.h.b.319.1		1
12.11	even	2		180.3.f.b.19.1		1
15.2	even	4		900.3.c.h.451.1		2
15.8	even	4		900.3.c.h.451.2		2
15.14	odd	2		180.3.f.b.19.1		1
16.3	odd	4		1280.3.e.c.639.2		2
16.5	even	4		1280.3.e.b.639.2		2
16.11	odd	4		1280.3.e.c.639.1		2
16.13	even	4		1280.3.e.b.639.1		2
20.3	even	4		100.3.b.c.51.2		2
20.7	even	4		100.3.b.c.51.1		2
20.19	odd	2	CM	20.3.d.b.19.1	yes	1
40.3	even	4		1600.3.b.f.1151.1		2
40.13	odd	4		1600.3.b.f.1151.2		2
40.19	odd	2		320.3.h.b.319.1		1
40.27	even	4		1600.3.b.f.1151.2		2
40.29	even	2		320.3.h.a.319.1		1
40.37	odd	4		1600.3.b.f.1151.1		2
60.23	odd	4		900.3.c.h.451.1		2
60.47	odd	4		900.3.c.h.451.2		2
60.59	even	2		180.3.f.a.19.1		1
80.19	odd	4		1280.3.e.b.639.1		2
80.29	even	4		1280.3.e.c.639.2		2
80.59	odd	4		1280.3.e.b.639.2		2
80.69	even	4		1280.3.e.c.639.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.3.d.a.19.1	✓	1	4.3	odd	2
20.3.d.a.19.1	✓	1	5.4	even	2
20.3.d.b.19.1	yes	1	1.1	even	1	trivial
20.3.d.b.19.1	yes	1	20.19	odd	2	CM
100.3.b.c.51.1		2	5.3	odd	4
100.3.b.c.51.1		2	20.7	even	4
100.3.b.c.51.2		2	5.2	odd	4
100.3.b.c.51.2		2	20.3	even	4
180.3.f.a.19.1		1	3.2	odd	2
180.3.f.a.19.1		1	60.59	even	2
180.3.f.b.19.1		1	12.11	even	2
180.3.f.b.19.1		1	15.14	odd	2
320.3.h.a.319.1		1	8.3	odd	2
320.3.h.a.319.1		1	40.29	even	2
320.3.h.b.319.1		1	8.5	even	2
320.3.h.b.319.1		1	40.19	odd	2
900.3.c.h.451.1		2	15.2	even	4
900.3.c.h.451.1		2	60.23	odd	4
900.3.c.h.451.2		2	15.8	even	4
900.3.c.h.451.2		2	60.47	odd	4
1280.3.e.b.639.1		2	16.13	even	4
1280.3.e.b.639.1		2	80.19	odd	4
1280.3.e.b.639.2		2	16.5	even	4
1280.3.e.b.639.2		2	80.59	odd	4
1280.3.e.c.639.1		2	16.11	odd	4
1280.3.e.c.639.1		2	80.69	even	4
1280.3.e.c.639.2		2	16.3	odd	4
1280.3.e.c.639.2		2	80.29	even	4
1600.3.b.f.1151.1		2	40.3	even	4
1600.3.b.f.1151.1		2	40.37	odd	4
1600.3.b.f.1151.2		2	40.13	odd	4
1600.3.b.f.1151.2		2	40.27	even	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:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	20.d (of order \(2\), degree \(1\), minimal)

\(n\)	\(11\)	\(17\)
\(\chi(n)\)	\(-1\)	\(-1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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