LMFDB - Embedded newform 1764.2.b.f.1567.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1567,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1764.1567");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.b (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:	no
Analytic conductor:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.2048.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 4x^{2} + 2 $ x^4 + 4*x^2 + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 7 $
Twist minimal:	no (minimal twist has level 196)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			1567.1
Root			$-1.84776i$ of defining polynomial
Character	$\chi$	$=$	1764.1567
Dual form			1764.2.b.f.1567.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +2.00000 q^{4} -2.93015i q^{5} -2.82843 q^{8} +O(q^{10})$	$q-1.41421 q^{2} +2.00000 q^{4} -2.93015i q^{5} -2.82843 q^{8} +4.14386i q^{10} -7.07401i q^{13} +4.00000 q^{16} +1.21371i q^{17} -5.86030i q^{20} -3.58579 q^{25} +10.0042i q^{26} +4.24264 q^{29} -5.65685 q^{32} -1.71644i q^{34} -7.07107 q^{37} +8.28772i q^{40} -11.2179i q^{41} +5.07107 q^{50} -14.1480i q^{52} -4.00000 q^{53} -6.00000 q^{58} -4.64659i q^{61} +8.00000 q^{64} -20.7279 q^{65} +2.42742i q^{68} +17.0782i q^{73} +10.0000 q^{74} -11.7206i q^{80} +15.8645i q^{82} +3.55635 q^{85} +15.3617i q^{89} +0.502734i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{4}+O(q^{10}) $ 4 * q + 8 * q^4	$ 4 q + 8 q^{4} + 16 q^{16} - 20 q^{25} - 8 q^{50} - 16 q^{53} - 24 q^{58} + 32 q^{64} - 32 q^{65} + 40 q^{74} - 48 q^{85}+O(q^{100}) $ 4 * q + 8 * q^4 + 16 * q^16 - 20 * q^25 - 8 * q^50 - 16 * q^53 - 24 * q^58 + 32 * q^64 - 32 * q^65 + 40 * q^74 - 48 * q^85

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.41421	−1.00000
$2$	−1.41421	−1.00000
$3$	0	0
$3$	0	0
$4$	2.00000	1.00000
$5$	− 2.93015i	− 1.31040i	−0.755454	−	0.655202i	$-0.772584\pi$
$5$	− 2.93015i	− 1.31040i	0.755454	−	0.655202i	$-0.227416\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	−2.82843	−1.00000
$9$	0	0
$10$	4.14386i	1.31040i
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	0	0
$13$	− 7.07401i	− 1.96198i	−0.194064	−	0.980989i	$-0.562167\pi$
$13$	− 7.07401i	− 1.96198i	0.194064	−	0.980989i	$-0.437833\pi$
$14$	0	0
$15$	0	0
$16$	4.00000	1.00000
$17$	1.21371i	0.294368i	0.989109	+	0.147184i	$0.0470209\pi$
$17$	1.21371i	0.294368i	−0.989109	+	0.147184i	$0.952979\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	− 5.86030i	− 1.31040i
$21$	0	0
$22$	0	0
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	0	0
$25$	−3.58579	−0.717157
$26$	10.0042i	1.96198i
$27$	0	0
$28$	0	0
$29$	4.24264	0.787839	0.393919	−	0.919145i	$-0.371119\pi$
$29$	4.24264	0.787839	0.393919	+	0.919145i	$0.371119\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−5.65685	−1.00000
$33$	0	0
$34$	− 1.71644i	− 0.294368i
$35$	0	0
$36$	0	0
$37$	−7.07107	−1.16248	−0.581238	−	0.813733i	$-0.697432\pi$
$37$	−7.07107	−1.16248	−0.581238	+	0.813733i	$0.697432\pi$
$38$	0	0
$39$	0	0
$40$	8.28772i	1.31040i
$41$	− 11.2179i	− 1.75194i	−0.482368	−	0.875969i	$-0.660223\pi$
$41$	− 11.2179i	− 1.75194i	0.482368	−	0.875969i	$-0.339777\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	0	0
$50$	5.07107	0.717157
$51$	0	0
$52$	− 14.1480i	− 1.96198i
$53$	−4.00000	−0.549442	−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000	−0.549442	−0.274721	+	0.961524i	$0.588586\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	−6.00000	−0.787839
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	− 4.64659i	− 0.594935i	−0.954732	−	0.297468i	$-0.903858\pi$
$61$	− 4.64659i	− 0.594935i	0.954732	−	0.297468i	$-0.0961421\pi$
$62$	0	0
$63$	0	0
$64$	8.00000	1.00000
$65$	−20.7279	−2.57098
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	2.42742i	0.294368i
$69$	0	0
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	0	0
$73$	17.0782i	1.99885i	0.0339219	+	0.999424i	$0.489200\pi$
$73$	17.0782i	1.99885i	−0.0339219	+	0.999424i	$0.510800\pi$
$74$	10.0000	1.16248
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	− 11.7206i	− 1.31040i
$81$	0	0
$82$	15.8645i	1.75194i
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	3.55635	0.385740
$86$	0	0
$87$	0	0
$88$	0	0
$89$	15.3617i	1.62834i	0.580626	+	0.814170i	$0.302808\pi$
$89$	15.3617i	1.62834i	−0.580626	+	0.814170i	$0.697192\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0.502734i	0.0510450i	0.999674	+	0.0255225i	$0.00812494\pi$
$97$	0.502734i	0.0510450i	−0.999674	+	0.0255225i	$0.991875\pi$
$98$	0	0
$99$	0	0
$100$	−7.17157	−0.717157
$101$	− 9.50143i	− 0.945427i	−0.881216	−	0.472714i	$-0.843274\pi$
$101$	− 9.50143i	− 0.945427i	0.881216	−	0.472714i	$-0.156726\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	20.0083i	1.96198i
$105$	0	0
$106$	5.65685	0.549442
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	0	0
$109$	−18.3848	−1.76094	−0.880471	−	0.474100i	$-0.842774\pi$
$109$	−18.3848	−1.76094	−0.880471	+	0.474100i	$0.842774\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	−16.0000	−1.50515	−0.752577	−	0.658505i	$-0.771189\pi$
$113$	−16.0000	−1.50515	−0.752577	+	0.658505i	$0.771189\pi$
$114$	0	0
$115$	0	0
$116$	8.48528	0.787839
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	11.0000	1.00000
$122$	6.57128i	0.594935i
$123$	0	0
$124$	0	0
$125$	− 4.14386i	− 0.370638i
$126$	0	0
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	−11.3137	−1.00000
$129$	0	0
$130$	29.3137	2.57098
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	− 3.43289i	− 0.294368i
$137$	−21.2132	−1.81237	−0.906183	−	0.422885i	$-0.861017\pi$
$137$	−21.2132	−1.81237	−0.906183	+	0.422885i	$0.861017\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	− 12.4316i	− 1.03239i
$146$	− 24.1522i	− 1.99885i
$147$	0	0
$148$	−14.1421	−1.16248
$149$	20.0000	1.63846	0.819232	−	0.573462i	$-0.194400\pi$
$149$	20.0000	1.63846	0.819232	+	0.573462i	$0.194400\pi$
$150$	0	0
$151$	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
$157$	− 19.5056i	− 1.55672i	−0.627821	−	0.778358i	$-0.716053\pi$
$157$	− 19.5056i	− 1.55672i	0.627821	−	0.778358i	$-0.283947\pi$
$158$	0	0
$159$	0	0
$160$	16.5754i	1.31040i
$161$	0	0
$162$	0	0
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	− 22.4357i	− 1.75194i
$165$	0	0
$166$	0	0
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	−37.0416	−2.84936
$170$	−5.02944	−0.385740
$171$	0	0
$172$	0	0
$173$	− 13.6453i	− 1.03743i	−0.854947	−	0.518716i	$-0.826410\pi$
$173$	− 13.6453i	− 1.03743i	0.854947	−	0.518716i	$-0.173590\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	0	0
$178$	− 21.7248i	− 1.62834i
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	− 25.3659i	− 1.88543i	−0.333596	−	0.942716i	$-0.608262\pi$
$181$	− 25.3659i	− 1.88543i	0.333596	−	0.942716i	$-0.391738\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	20.7193i	1.52331i
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	0	0
$193$	−24.0000	−1.72756	−0.863779	−	0.503871i	$-0.831909\pi$
$193$	−24.0000	−1.72756	−0.863779	+	0.503871i	$0.831909\pi$
$194$	− 0.710974i	− 0.0510450i
$195$	0	0
$196$	0	0
$197$	−2.00000	−0.142494	−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000	−0.142494	−0.0712470	+	0.997459i	$0.522698\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	10.1421	0.717157
$201$	0	0
$202$	13.4370i	0.945427i
$203$	0	0
$204$	0	0
$205$	−32.8701	−2.29574
$206$	0	0
$207$	0	0
$208$	− 28.2960i	− 1.96198i
$209$	0	0
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	−8.00000	−0.549442
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	26.0000	1.76094
$219$	0	0
$220$	0	0
$221$	8.58579	0.577542
$222$	0	0
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	0	0
$225$	0	0
$226$	22.6274	1.50515
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	0	0
$229$	− 7.78498i	− 0.514446i	−0.966352	−	0.257223i	$-0.917192\pi$
$229$	− 7.78498i	− 0.514446i	0.966352	−	0.257223i	$-0.0828075\pi$
$230$	0	0
$231$	0	0
$232$	−12.0000	−0.787839
$233$	7.07107	0.463241	0.231621	−	0.972806i	$-0.425597\pi$
$233$	7.07107	0.463241	0.231621	+	0.972806i	$0.425597\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0	0
$241$	24.6549i	1.58816i	0.607811	+	0.794081i	$0.292048\pi$
$241$	24.6549i	1.58816i	−0.607811	+	0.794081i	$0.707952\pi$
$242$	−15.5563	−1.00000
$243$	0	0
$244$	− 9.29319i	− 0.594935i
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	5.86030i	0.370638i
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	16.0000	1.00000
$257$	− 28.7988i	− 1.79642i	−0.439568	−	0.898209i	$-0.644869\pi$
$257$	− 28.7988i	− 1.79642i	0.439568	−	0.898209i	$-0.355131\pi$
$258$	0	0
$259$	0	0
$260$	−41.4558	−2.57098
$261$	0	0
$262$	0	0
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	11.7206i	0.719991i
$266$	0	0
$267$	0	0
$268$	0	0
$269$	16.3672i	0.997926i	0.866623	+	0.498963i	$0.166286\pi$
$269$	16.3672i	0.997926i	−0.866623	+	0.498963i	$0.833714\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	4.85483i	0.294368i
$273$	0	0
$274$	30.0000	1.81237
$275$	0	0
$276$	0	0
$277$	18.0000	1.08152	0.540758	−	0.841178i	$-0.318138\pi$
$277$	18.0000	1.08152	0.540758	+	0.841178i	$0.318138\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	−15.5563	−0.928014	−0.464007	−	0.885832i	$-0.653589\pi$
$281$	−15.5563	−0.928014	−0.464007	+	0.885832i	$0.653589\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	15.5269	0.913348
$290$	17.5809i	1.03239i
$291$	0	0
$292$	34.1563i	1.99885i
$293$	32.9426i	1.92453i	0.272115	+	0.962265i	$0.412277\pi$
$293$	32.9426i	1.92453i	−0.272115	+	0.962265i	$0.587723\pi$
$294$	0	0
$295$	0	0
$296$	20.0000	1.16248
$297$	0	0
$298$	−28.2843	−1.63846
$299$	0	0
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	−13.6152	−0.779605
$306$	0	0
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	− 12.2233i	− 0.690904i	−0.938436	−	0.345452i	$-0.887726\pi$
$313$	− 12.2233i	− 0.690904i	0.938436	−	0.345452i	$-0.112274\pi$
$314$	27.5851i	1.55672i
$315$	0	0
$316$	0	0
$317$	−22.0000	−1.23564	−0.617822	−	0.786318i	$-0.711985\pi$
$317$	−22.0000	−1.23564	−0.617822	+	0.786318i	$0.711985\pi$
$318$	0	0
$319$	0	0
$320$	− 23.4412i	− 1.31040i
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	25.3659i	1.40705i
$326$	0	0
$327$	0	0
$328$	31.7289i	1.75194i
$329$	0	0
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	35.3553	1.92593	0.962964	−	0.269630i	$-0.0869014\pi$
$337$	35.3553	1.92593	0.962964	+	0.269630i	$0.0869014\pi$
$338$	52.3848	2.84936
$339$	0	0
$340$	7.11270	0.385740
$341$	0	0
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	19.2974i	1.03743i
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	37.0865i	1.98519i	0.121452	+	0.992597i	$0.461245\pi$
$349$	37.0865i	1.98519i	−0.121452	+	0.992597i	$0.538755\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	− 27.7933i	− 1.47929i	−0.672998	−	0.739644i	$-0.734994\pi$
$353$	− 27.7933i	− 1.47929i	0.672998	−	0.739644i	$-0.265006\pi$
$354$	0	0
$355$	0	0
$356$	30.7235i	1.62834i
$357$	0	0
$358$	0	0
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	35.8728i	1.88543i
$363$	0	0
$364$	0	0
$365$	50.0416	2.61930
$366$	0	0
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	0	0
$369$	0	0
$370$	− 29.3015i	− 1.52331i
$371$	0	0
$372$	0	0
$373$	36.0000	1.86401	0.932005	−	0.362446i	$-0.118058\pi$
$373$	36.0000	1.86401	0.932005	+	0.362446i	$0.118058\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	− 30.0125i	− 1.54572i
$378$	0	0
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	0	0
$386$	33.9411	1.72756
$387$	0	0
$388$	1.00547i	0.0510450i
$389$	38.1838	1.93599	0.967997	−	0.250962i	$-0.0807470\pi$
$389$	38.1838	1.93599	0.967997	+	0.250962i	$0.0807470\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	2.82843	0.142494
$395$	0	0
$396$	0	0
$397$	− 30.5152i	− 1.53152i	−0.643129	−	0.765758i	$-0.722364\pi$
$397$	− 30.5152i	− 1.53152i	0.643129	−	0.765758i	$-0.277636\pi$
$398$	0	0
$399$	0	0
$400$	−14.3431	−0.717157
$401$	26.8701	1.34183	0.670913	−	0.741536i	$-0.265902\pi$
$401$	26.8701	1.34183	0.670913	+	0.741536i	$0.265902\pi$
$402$	0	0
$403$	0	0
$404$	− 19.0029i	− 0.945427i
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	− 34.6591i	− 1.71378i	−0.515498	−	0.856891i	$-0.672393\pi$
$409$	− 34.6591i	− 1.71378i	0.515498	−	0.856891i	$-0.327607\pi$
$410$	46.4853	2.29574
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	40.0166i	1.96198i
$417$	0	0
$418$	0	0
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	30.0000	1.46211	0.731055	−	0.682318i	$-0.239028\pi$
$421$	30.0000	1.46211	0.731055	+	0.682318i	$0.239028\pi$
$422$	0	0
$423$	0	0
$424$	11.3137	0.549442
$425$	− 4.35210i	− 0.211108i
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0	0
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	0	0
$433$	− 22.2275i	− 1.06819i	−0.845426	−	0.534093i	$-0.820653\pi$
$433$	− 22.2275i	− 1.06819i	0.845426	−	0.534093i	$-0.179347\pi$
$434$	0	0
$435$	0	0
$436$	−36.7696	−1.76094
$437$	0	0
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	0	0
$442$	−12.1421	−0.577542
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	0	0
$445$	45.0122	2.13378
$446$	0	0
$447$	0	0
$448$	0	0
$449$	40.0000	1.88772	0.943858	−	0.330350i	$-0.107167\pi$
$449$	40.0000	1.88772	0.943858	+	0.330350i	$0.107167\pi$
$450$	0	0
$451$	0	0
$452$	−32.0000	−1.50515
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	8.00000	0.374224	0.187112	−	0.982339i	$-0.440087\pi$
$457$	8.00000	0.374224	0.187112	+	0.982339i	$0.440087\pi$
$458$	11.0096i	0.514446i
$459$	0	0
$460$	0	0
$461$	3.93562i	0.183300i	0.995791	+	0.0916501i	$0.0292141\pi$
$461$	3.93562i	0.183300i	−0.995791	+	0.0916501i	$0.970786\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	16.9706	0.787839
$465$	0	0
$466$	−10.0000	−0.463241
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	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		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	50.0208i	2.28075i
$482$	− 34.8673i	− 1.58816i
$483$	0	0
$484$	22.0000	1.00000
$485$	1.47309	0.0668895
$486$	0	0
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	13.1426i	0.594935i
$489$	0	0
$490$	0	0
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	5.14933i	0.231914i
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	− 8.28772i	− 0.370638i
$501$	0	0
$502$	0	0
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	−27.8406	−1.23889
$506$	0	0
$507$	0	0
$508$	0	0
$509$	26.0769i	1.15584i	0.816095	+	0.577918i	$0.196135\pi$
$509$	26.0769i	1.15584i	−0.816095	+	0.577918i	$0.803865\pi$
$510$	0	0
$511$	0	0
$512$	−22.6274	−1.00000
$513$	0	0
$514$	40.7276i	1.79642i
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	58.6274	2.57098
$521$	45.3742i	1.98788i	0.109922	+	0.993940i	$0.464940\pi$
$521$	45.3742i	1.98788i	−0.109922	+	0.993940i	$0.535060\pi$
$522$	0	0
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	23.0000	1.00000
$530$	− 16.5754i	− 0.719991i
$531$	0	0
$532$	0	0
$533$	−79.3553	−3.43726
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	− 23.1467i	− 0.997926i
$539$	0	0
$540$	0	0
$541$	−20.0000	−0.859867	−0.429934	−	0.902861i	$-0.641463\pi$
$541$	−20.0000	−0.859867	−0.429934	+	0.902861i	$0.641463\pi$
$542$	0	0
$543$	0	0
$544$	− 6.86577i	− 0.294368i
$545$	53.8702i	2.30754i
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	−42.4264	−1.81237
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	−25.4558	−1.08152
$555$	0	0
$556$	0	0
$557$	38.0000	1.61011	0.805056	−	0.593199i	$-0.202135\pi$
$557$	38.0000	1.61011	0.805056	+	0.593199i	$0.202135\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	22.0000	0.928014
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	0	0
$565$	46.8824i	1.97236i
$566$	0	0
$567$	0	0
$568$	0	0
$569$	46.6690	1.95647	0.978234	−	0.207504i	$-0.0665341\pi$
$569$	46.6690	1.95647	0.978234	+	0.207504i	$0.0665341\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	20.2166i	0.841627i	0.907147	+	0.420813i	$0.138255\pi$
$577$	20.2166i	0.841627i	−0.907147	+	0.420813i	$0.861745\pi$
$578$	−21.9584	−0.913348
$579$	0	0
$580$	− 24.8632i	− 1.03239i
$581$	0	0
$582$	0	0
$583$	0	0
$584$	− 48.3044i	− 1.99885i
$585$	0	0
$586$	− 46.5879i	− 1.92453i
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	−28.2843	−1.16248
$593$	− 36.3755i	− 1.49376i	−0.664957	−	0.746882i	$-0.731550\pi$
$593$	− 36.3755i	− 1.49376i	0.664957	−	0.746882i	$-0.268450\pi$
$594$	0	0
$595$	0	0
$596$	40.0000	1.63846
$597$	0	0
$598$	0	0
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	0	0
$601$	− 40.5194i	− 1.65282i	−0.563069	−	0.826410i	$-0.690379\pi$
$601$	− 40.5194i	− 1.65282i	0.563069	−	0.826410i	$-0.309621\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	− 32.2317i	− 1.31040i
$606$	0	0
$607$	0	0		−	1.00000i	$-0.5\pi$
$607$	0	0			1.00000i	$0.5\pi$
$608$	0	0
$609$	0	0
$610$	19.2548	0.779605
$611$	0	0
$612$	0	0
$613$	1.41421	0.0571195	0.0285598	−	0.999592i	$-0.490908\pi$
$613$	1.41421	0.0571195	0.0285598	+	0.999592i	$0.490908\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	4.24264	0.170802	0.0854011	−	0.996347i	$-0.472783\pi$
$617$	4.24264	0.170802	0.0854011	+	0.996347i	$0.472783\pi$
$618$	0	0
$619$	0	0		−	1.00000i	$-0.5\pi$
$619$	0	0			1.00000i	$0.5\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−30.0711	−1.20284
$626$	17.2864i	0.690904i
$627$	0	0
$628$	− 39.0112i	− 1.55672i
$629$	− 8.58221i	− 0.342195i
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	0	0
$634$	31.1127	1.23564
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	33.1509i	1.31040i
$641$	−41.0122	−1.61988	−0.809942	−	0.586510i	$-0.800502\pi$
$641$	−41.0122	−1.61988	−0.809942	+	0.586510i	$0.800502\pi$
$642$	0	0
$643$	0	0		−	1.00000i	$-0.5\pi$
$643$	0	0			1.00000i	$0.5\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	0	0
$649$	0	0
$650$	− 35.8728i	− 1.40705i
$651$	0	0
$652$	0	0
$653$	−12.7279	−0.498082	−0.249041	−	0.968493i	$-0.580115\pi$
$653$	−12.7279	−0.498082	−0.249041	+	0.968493i	$0.580115\pi$
$654$	0	0
$655$	0	0
$656$	− 44.8715i	− 1.75194i
$657$	0	0
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	− 30.2207i	− 1.17545i	−0.809061	−	0.587725i	$-0.800024\pi$
$661$	− 30.2207i	− 1.17545i	0.809061	−	0.587725i	$-0.199976\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	15.5563	0.599653	0.299827	−	0.953994i	$-0.403071\pi$
$673$	15.5563	0.599653	0.299827	+	0.953994i	$0.403071\pi$
$674$	−50.0000	−1.92593
$675$	0	0
$676$	−74.0833	−2.84936
$677$	48.8071i	1.87581i	0.346893	+	0.937905i	$0.387237\pi$
$677$	48.8071i	1.87581i	−0.346893	+	0.937905i	$0.612763\pi$
$678$	0	0
$679$	0	0
$680$	−10.0589	−0.385740
$681$	0	0
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	62.1579i	2.37493i
$686$	0	0
$687$	0	0
$688$	0	0
$689$	28.2960i	1.07799i
$690$	0	0
$691$	0	0		−	1.00000i	$-0.5\pi$
$691$	0	0			1.00000i	$0.5\pi$
$692$	− 27.2906i	− 1.03743i
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	13.6152	0.515713
$698$	− 52.4482i	− 1.98519i
$699$	0	0
$700$	0	0
$701$	43.8406	1.65584	0.827919	−	0.560848i	$-0.189525\pi$
$701$	43.8406	1.65584	0.827919	+	0.560848i	$0.189525\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	39.3057i	1.47929i
$707$	0	0
$708$	0	0
$709$	52.3259	1.96514	0.982570	−	0.185892i	$-0.0595174\pi$
$709$	52.3259	1.96514	0.982570	+	0.185892i	$0.0595174\pi$
$710$	0	0
$711$	0	0
$712$	− 43.4495i	− 1.62834i
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	0	0
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	0	0
$722$	26.8701	1.00000
$723$	0	0
$724$	− 50.7318i	− 1.88543i
$725$	−15.2132	−0.565004
$726$	0	0
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	0	0
$729$	0	0
$730$	−70.7696	−2.61930
$731$	0	0
$732$	0	0
$733$	24.3604i	0.899773i	0.893086	+	0.449886i	$0.148536\pi$
$733$	24.3604i	0.899773i	−0.893086	+	0.449886i	$0.851464\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	41.4386i	1.52331i
$741$	0	0
$742$	0	0
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	− 58.6030i	− 2.14705i
$746$	−50.9117	−1.86401
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	0	0
$753$	0	0
$754$	42.4441i	1.54572i
$755$	0	0
$756$	0	0
$757$	−24.0416	−0.873808	−0.436904	−	0.899508i	$-0.643925\pi$
$757$	−24.0416	−0.873808	−0.436904	+	0.899508i	$0.643925\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	19.8001i	0.717753i	0.933385	+	0.358876i	$0.116840\pi$
$761$	19.8001i	0.717753i	−0.933385	+	0.358876i	$0.883160\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	55.3784i	1.99700i	0.0547934	+	0.998498i	$0.482550\pi$
$769$	55.3784i	1.99700i	−0.0547934	+	0.998498i	$0.517450\pi$
$770$	0	0
$771$	0	0
$772$	−48.0000	−1.72756
$773$	− 53.6619i	− 1.93009i	−0.262092	−	0.965043i	$-0.584412\pi$
$773$	− 53.6619i	− 1.93009i	0.262092	−	0.965043i	$-0.415588\pi$
$774$	0	0
$775$	0	0
$776$	− 1.42195i	− 0.0510450i
$777$	0	0
$778$	−54.0000	−1.93599
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	0	0
$785$	−57.1543	−2.03993
$786$	0	0
$787$	0	0		−	1.00000i	$-0.5\pi$
$787$	0	0			1.00000i	$0.5\pi$
$788$	−4.00000	−0.142494
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−32.8701	−1.16725
$794$	43.1550i	1.53152i
$795$	0	0
$796$	0	0
$797$	− 40.2249i	− 1.42484i	−0.701754	−	0.712419i	$-0.747599\pi$
$797$	− 40.2249i	− 1.42484i	0.701754	−	0.712419i	$-0.252401\pi$
$798$	0	0
$799$	0	0
$800$	20.2843	0.717157
$801$	0	0
$802$	−38.0000	−1.34183
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	26.8741i	0.945427i
$809$	10.0000	0.351581	0.175791	−	0.984428i	$-0.443752\pi$
$809$	10.0000	0.351581	0.175791	+	0.984428i	$0.443752\pi$
$810$	0	0
$811$	0	0		−	1.00000i	$-0.5\pi$
$811$	0	0			1.00000i	$0.5\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	49.0153i	1.71378i
$819$	0	0
$820$	−65.7401	−2.29574
$821$	−50.0000	−1.74501	−0.872506	−	0.488603i	$-0.837507\pi$
$821$	−50.0000	−1.74501	−0.872506	+	0.488603i	$0.837507\pi$
$822$	0	0
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0	0
$829$	− 42.2358i	− 1.46691i	−0.679738	−	0.733455i	$-0.737906\pi$
$829$	− 42.2358i	− 1.46691i	0.679738	−	0.733455i	$-0.262094\pi$
$830$	0	0
$831$	0	0
$832$	− 56.5921i	− 1.96198i
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	−11.0000	−0.379310
$842$	−42.4264	−1.46211
$843$	0	0
$844$	0	0
$845$	108.538i	3.73381i
$846$	0	0
$847$	0	0
$848$	−16.0000	−0.549442
$849$	0	0
$850$	6.15480i	0.211108i
$851$	0	0
$852$	0	0
$853$	15.6562i	0.536059i	0.963411	+	0.268029i	$0.0863725\pi$
$853$	15.6562i	0.536059i	−0.963411	+	0.268029i	$0.913628\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	− 50.5235i	− 1.72585i	−0.505331	−	0.862926i	$-0.668630\pi$
$857$	− 50.5235i	− 1.72585i	0.505331	−	0.862926i	$-0.331370\pi$
$858$	0	0
$859$	0	0		−	1.00000i	$-0.5\pi$
$859$	0	0			1.00000i	$0.5\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	−39.9828	−1.35945
$866$	31.4344i	1.06819i
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	52.0000	1.76094
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	32.5269	1.09836	0.549178	−	0.835705i	$-0.314941\pi$
$877$	32.5269	1.09836	0.549178	+	0.835705i	$0.314941\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	− 33.9481i	− 1.14374i	−0.820344	−	0.571870i	$-0.806218\pi$
$881$	− 33.9481i	− 1.14374i	0.820344	−	0.571870i	$-0.193782\pi$
$882$	0	0
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	17.1716	0.577542
$885$	0	0
$886$	0	0
$887$	0	0		−	1.00000i	$-0.5\pi$
$887$	0	0			1.00000i	$0.5\pi$
$888$	0	0
$889$	0	0
$890$	−63.6569	−2.13378
$891$	0	0
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	−56.5685	−1.88772
$899$	0	0
$900$	0	0
$901$	− 4.85483i	− 0.161738i
$902$	0	0
$903$	0	0
$904$	45.2548	1.50515
$905$	−74.3259	−2.47068
$906$	0	0
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	0	0
$914$	−11.3137	−0.374224
$915$	0	0
$916$	− 15.5700i	− 0.514446i
$917$	0	0
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0	0
$922$	− 5.56581i	− 0.183300i
$923$	0	0
$924$	0	0
$925$	25.3553	0.833678
$926$	0	0
$927$	0	0
$928$	−24.0000	−0.787839
$929$	− 57.8058i	− 1.89655i	−0.317455	−	0.948273i	$-0.602828\pi$
$929$	− 57.8058i	− 1.89655i	0.317455	−	0.948273i	$-0.397172\pi$
$930$	0	0
$931$	0	0
$932$	14.1421	0.463241
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	− 29.8042i	− 0.973662i	−0.873496	−	0.486831i	$-0.838153\pi$
$937$	− 29.8042i	− 0.973662i	0.873496	−	0.486831i	$-0.161847\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	− 61.2387i	− 1.99632i	−0.0606025	−	0.998162i	$-0.519302\pi$
$941$	− 61.2387i	− 1.99632i	0.0606025	−	0.998162i	$-0.480698\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	120.811	3.92170
$950$	0	0
$951$	0	0
$952$	0	0
$953$	26.0000	0.842223	0.421111	−	0.907009i	$-0.361640\pi$
$953$	26.0000	0.842223	0.421111	+	0.907009i	$0.361640\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−31.0000	−1.00000
$962$	− 70.7401i	− 2.28075i
$963$	0	0
$964$	49.3098i	1.58816i
$965$	70.3236i	2.26380i
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	−31.1127	−1.00000
$969$	0	0
$970$	−2.08326	−0.0668895
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	− 18.5864i	− 0.594935i
$977$	38.1838	1.22161	0.610803	−	0.791782i	$-0.290847\pi$
$977$	38.1838	1.22161	0.610803	+	0.791782i	$0.290847\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	0	0
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	0	0
$985$	5.86030i	0.186725i
$986$	− 7.28225i	− 0.231914i
$987$	0	0
$988$	0	0
$989$	0	0
$990$	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
$996$	0	0
$997$	12.6398i	0.400307i	0.979765	+	0.200154i	$0.0641441\pi$
$997$	12.6398i	0.400307i	−0.979765	+	0.200154i	$0.935856\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.b.f.1567.1		4
3.2	odd	2		196.2.d.a.195.4	yes	4
4.3	odd	2	CM	1764.2.b.f.1567.1		4
7.6	odd	2	inner	1764.2.b.f.1567.2		4
12.11	even	2		196.2.d.a.195.4	yes	4
21.2	odd	6		196.2.f.c.31.2		8
21.5	even	6		196.2.f.c.31.1		8
21.11	odd	6		196.2.f.c.19.1		8
21.17	even	6		196.2.f.c.19.2		8
21.20	even	2		196.2.d.a.195.3	✓	4
24.5	odd	2		3136.2.f.c.3135.2		4
24.11	even	2		3136.2.f.c.3135.2		4
28.27	even	2	inner	1764.2.b.f.1567.2		4
84.11	even	6		196.2.f.c.19.1		8
84.23	even	6		196.2.f.c.31.2		8
84.47	odd	6		196.2.f.c.31.1		8
84.59	odd	6		196.2.f.c.19.2		8
84.83	odd	2		196.2.d.a.195.3	✓	4
168.83	odd	2		3136.2.f.c.3135.3		4
168.125	even	2		3136.2.f.c.3135.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.2.d.a.195.3	✓	4	21.20	even	2
196.2.d.a.195.3	✓	4	84.83	odd	2
196.2.d.a.195.4	yes	4	3.2	odd	2
196.2.d.a.195.4	yes	4	12.11	even	2
196.2.f.c.19.1		8	21.11	odd	6
196.2.f.c.19.1		8	84.11	even	6
196.2.f.c.19.2		8	21.17	even	6
196.2.f.c.19.2		8	84.59	odd	6
196.2.f.c.31.1		8	21.5	even	6
196.2.f.c.31.1		8	84.47	odd	6
196.2.f.c.31.2		8	21.2	odd	6
196.2.f.c.31.2		8	84.23	even	6
1764.2.b.f.1567.1		4	1.1	even	1	trivial
1764.2.b.f.1567.1		4	4.3	odd	2	CM
1764.2.b.f.1567.2		4	7.6	odd	2	inner
1764.2.b.f.1567.2		4	28.27	even	2	inner
3136.2.f.c.3135.2		4	24.5	odd	2
3136.2.f.c.3135.2		4	24.11	even	2
3136.2.f.c.3135.3		4	168.83	odd	2
3136.2.f.c.3135.3		4	168.125	even	2

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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +2.00000 q^{4} -2.93015i q^{5} -2.82843 q^{8} +O(q^{10})\)	\(q-1.41421 q^{2} +2.00000 q^{4} -2.93015i q^{5} -2.82843 q^{8} +4.14386i q^{10} -7.07401i q^{13} +4.00000 q^{16} +1.21371i q^{17} -5.86030i q^{20} -3.58579 q^{25} +10.0042i q^{26} +4.24264 q^{29} -5.65685 q^{32} -1.71644i q^{34} -7.07107 q^{37} +8.28772i q^{40} -11.2179i q^{41} +5.07107 q^{50} -14.1480i q^{52} -4.00000 q^{53} -6.00000 q^{58} -4.64659i q^{61} +8.00000 q^{64} -20.7279 q^{65} +2.42742i q^{68} +17.0782i q^{73} +10.0000 q^{74} -11.7206i q^{80} +15.8645i q^{82} +3.55635 q^{85} +15.3617i q^{89} +0.502734i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4}+O(q^{10}) \) 4 * q + 8 * q^4	\( 4 q + 8 q^{4} + 16 q^{16} - 20 q^{25} - 8 q^{50} - 16 q^{53} - 24 q^{58} + 32 q^{64} - 32 q^{65} + 40 q^{74} - 48 q^{85}+O(q^{100}) \) 4 * q + 8 * q^4 + 16 * q^16 - 20 * q^25 - 8 * q^50 - 16 * q^53 - 24 * q^58 + 32 * q^64 - 32 * q^65 + 40 * q^74 - 48 * q^85

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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