LMFDB - Embedded newform 9702.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9702,2,Mod(1,9702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9702, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9702.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9702.a (trivial)

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:	$77.4708600410$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 66)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	9702.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} -4.00000 q^{5} -1.00000 q^{8} +O(q^{10})$

$q-1.00000 q^{2} +1.00000 q^{4} -4.00000 q^{5} -1.00000 q^{8} +4.00000 q^{10} -1.00000 q^{11} -4.00000 q^{13} +1.00000 q^{16} -2.00000 q^{17} -4.00000 q^{20} +1.00000 q^{22} +6.00000 q^{23} +11.0000 q^{25} +4.00000 q^{26} -10.0000 q^{29} +8.00000 q^{31} -1.00000 q^{32} +2.00000 q^{34} -2.00000 q^{37} +4.00000 q^{40} +2.00000 q^{41} +4.00000 q^{43} -1.00000 q^{44} -6.00000 q^{46} -2.00000 q^{47} -11.0000 q^{50} -4.00000 q^{52} -4.00000 q^{53} +4.00000 q^{55} +10.0000 q^{58} +8.00000 q^{61} -8.00000 q^{62} +1.00000 q^{64} +16.0000 q^{65} -12.0000 q^{67} -2.00000 q^{68} -2.00000 q^{71} +6.00000 q^{73} +2.00000 q^{74} +10.0000 q^{79} -4.00000 q^{80} -2.00000 q^{82} +4.00000 q^{83} +8.00000 q^{85} -4.00000 q^{86} +1.00000 q^{88} +10.0000 q^{89} +6.00000 q^{92} +2.00000 q^{94} +2.00000 q^{97} +O(q^{100})$

Display 100 coefficients 10 coefficients

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	−0.707107
$2$	−1.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	−4.00000	−1.78885	−0.894427	−	0.447214i	$-0.852416\pi$
$5$	−4.00000	−1.78885	−0.894427	+	0.447214i	$0.852416\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	0	0
$10$	4.00000	1.26491
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0	0
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	−4.00000	−0.894427
$21$	0	0
$22$	1.00000	0.213201
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	0	0
$25$	11.0000	2.20000
$26$	4.00000	0.784465
$27$	0	0
$28$	0	0
$29$	−10.0000	−1.85695	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−10.0000	−1.85695	−0.928477	+	0.371391i	$0.878881\pi$
$30$	0	0
$31$	8.00000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	2.00000	0.342997
$35$	0	0
$36$	0	0
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	0	0
$39$	0	0
$40$	4.00000	0.632456
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	0	0
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	−6.00000	−0.884652
$47$	−2.00000	−0.291730	−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000	−0.291730	−0.145865	+	0.989305i	$0.546597\pi$
$48$	0	0
$49$	0	0
$50$	−11.0000	−1.55563
$51$	0	0
$52$	−4.00000	−0.554700
$53$	−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
$55$	4.00000	0.539360
$56$	0	0
$57$	0	0
$58$	10.0000	1.31306
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	8.00000	1.02430	0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000	1.02430	0.512148	+	0.858898i	$0.328850\pi$
$62$	−8.00000	−1.01600
$63$	0	0
$64$	1.00000	0.125000
$65$	16.0000	1.98456
$66$	0	0
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	−2.00000	−0.242536
$69$	0	0
$70$	0	0
$71$	−2.00000	−0.237356	−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000	−0.237356	−0.118678	+	0.992933i	$0.537866\pi$
$72$	0	0
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	2.00000	0.232495
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	10.0000	1.12509	0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000	1.12509	0.562544	+	0.826767i	$0.309823\pi$
$80$	−4.00000	−0.447214
$81$	0	0
$82$	−2.00000	−0.220863
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	0	0
$85$	8.00000	0.867722
$86$	−4.00000	−0.431331
$87$	0	0
$88$	1.00000	0.106600
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	0	0
$91$	0	0
$92$	6.00000	0.625543
$93$	0	0
$94$	2.00000	0.206284
$95$	0	0
$96$	0	0
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	0	0
$99$	0	0
$100$	11.0000	1.10000
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	0	0
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	4.00000	0.392232
$105$	0	0
$106$	4.00000	0.388514
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	0	0
$109$	20.0000	1.91565	0.957826	−	0.287348i	$-0.0927736\pi$
$109$	20.0000	1.91565	0.957826	+	0.287348i	$0.0927736\pi$
$110$	−4.00000	−0.381385
$111$	0	0
$112$	0	0
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	0	0
$115$	−24.0000	−2.23801
$116$	−10.0000	−0.928477
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	1.00000	0.0909091
$122$	−8.00000	−0.724286
$123$	0	0
$124$	8.00000	0.718421
$125$	−24.0000	−2.14663
$126$	0	0
$127$	−22.0000	−1.95218	−0.976092	−	0.217357i	$-0.930256\pi$
$127$	−22.0000	−1.95218	−0.976092	+	0.217357i	$0.930256\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	−16.0000	−1.40329
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	0	0
$133$	0	0
$134$	12.0000	1.03664
$135$	0	0
$136$	2.00000	0.171499
$137$	2.00000	0.170872	0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000	0.170872	0.0854358	+	0.996344i	$0.472772\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	0	0
$142$	2.00000	0.167836
$143$	4.00000	0.334497
$144$	0	0
$145$	40.0000	3.32182
$146$	−6.00000	−0.496564
$147$	0	0
$148$	−2.00000	−0.164399
$149$	10.0000	0.819232	0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000	0.819232	0.409616	+	0.912258i	$0.365663\pi$
$150$	0	0
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	−32.0000	−2.57030
$156$	0	0
$157$	−18.0000	−1.43656	−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000	−1.43656	−0.718278	+	0.695756i	$0.755069\pi$
$158$	−10.0000	−0.795557
$159$	0	0
$160$	4.00000	0.316228
$161$	0	0
$162$	0	0
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	2.00000	0.156174
$165$	0	0
$166$	−4.00000	−0.310460
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	−8.00000	−0.613572
$171$	0	0
$172$	4.00000	0.304997
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	0	0
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	0	0
$178$	−10.0000	−0.749532
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	0	0
$183$	0	0
$184$	−6.00000	−0.442326
$185$	8.00000	0.588172
$186$	0	0
$187$	2.00000	0.146254
$188$	−2.00000	−0.145865
$189$	0	0
$190$	0	0
$191$	−22.0000	−1.59186	−0.795932	−	0.605386i	$-0.793019\pi$
$191$	−22.0000	−1.59186	−0.795932	+	0.605386i	$0.793019\pi$
$192$	0	0
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	−2.00000	−0.143592
$195$	0	0
$196$	0	0
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	0	0
$199$	−20.0000	−1.41776	−0.708881	−	0.705328i	$-0.750800\pi$
$199$	−20.0000	−1.41776	−0.708881	+	0.705328i	$0.750800\pi$
$200$	−11.0000	−0.777817
$201$	0	0
$202$	−2.00000	−0.140720
$203$	0	0
$204$	0	0
$205$	−8.00000	−0.558744
$206$	4.00000	0.278693
$207$	0	0
$208$	−4.00000	−0.277350
$209$	0	0
$210$	0	0
$211$	12.0000	0.826114	0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000	0.826114	0.413057	+	0.910705i	$0.364461\pi$
$212$	−4.00000	−0.274721
$213$	0	0
$214$	−12.0000	−0.820303
$215$	−16.0000	−1.09119
$216$	0	0
$217$	0	0
$218$	−20.0000	−1.35457
$219$	0	0
$220$	4.00000	0.269680
$221$	8.00000	0.538138
$222$	0	0
$223$	16.0000	1.07144	0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000	1.07144	0.535720	+	0.844396i	$0.320040\pi$
$224$	0	0
$225$	0	0
$226$	−6.00000	−0.399114
$227$	−12.0000	−0.796468	−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000	−0.796468	−0.398234	+	0.917284i	$0.630377\pi$
$228$	0	0
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	24.0000	1.58251
$231$	0	0
$232$	10.0000	0.656532
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	0	0
$235$	8.00000	0.521862
$236$	0	0
$237$	0	0
$238$	0	0
$239$	20.0000	1.29369	0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000	1.29369	0.646846	+	0.762620i	$0.276088\pi$
$240$	0	0
$241$	18.0000	1.15948	0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000	1.15948	0.579741	+	0.814801i	$0.303154\pi$
$242$	−1.00000	−0.0642824
$243$	0	0
$244$	8.00000	0.512148
$245$	0	0
$246$	0	0
$247$	0	0
$248$	−8.00000	−0.508001
$249$	0	0
$250$	24.0000	1.51789
$251$	−8.00000	−0.504956	−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000	−0.504956	−0.252478	+	0.967603i	$0.581245\pi$
$252$	0	0
$253$	−6.00000	−0.377217
$254$	22.0000	1.38040
$255$	0	0
$256$	1.00000	0.0625000
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	0	0
$259$	0	0
$260$	16.0000	0.992278
$261$	0	0
$262$	−12.0000	−0.741362
$263$	16.0000	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$264$	0	0
$265$	16.0000	0.982872
$266$	0	0
$267$	0	0
$268$	−12.0000	−0.733017
$269$	−20.0000	−1.21942	−0.609711	−	0.792624i	$-0.708714\pi$
$269$	−20.0000	−1.21942	−0.609711	+	0.792624i	$0.708714\pi$
$270$	0	0
$271$	−22.0000	−1.33640	−0.668202	−	0.743980i	$-0.732936\pi$
$271$	−22.0000	−1.33640	−0.668202	+	0.743980i	$0.732936\pi$
$272$	−2.00000	−0.121268
$273$	0	0
$274$	−2.00000	−0.120824
$275$	−11.0000	−0.663325
$276$	0	0
$277$	8.00000	0.480673	0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000	0.480673	0.240337	+	0.970690i	$0.422742\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	−22.0000	−1.31241	−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000	−1.31241	−0.656205	+	0.754583i	$0.727839\pi$
$282$	0	0
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	−2.00000	−0.118678
$285$	0	0
$286$	−4.00000	−0.236525
$287$	0	0
$288$	0	0
$289$	−13.0000	−0.764706
$290$	−40.0000	−2.34888
$291$	0	0
$292$	6.00000	0.351123
$293$	14.0000	0.817889	0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000	0.817889	0.408944	+	0.912559i	$0.365897\pi$
$294$	0	0
$295$	0	0
$296$	2.00000	0.116248
$297$	0	0
$298$	−10.0000	−0.579284
$299$	−24.0000	−1.38796
$300$	0	0
$301$	0	0
$302$	−2.00000	−0.115087
$303$	0	0
$304$	0	0
$305$	−32.0000	−1.83231
$306$	0	0
$307$	−8.00000	−0.456584	−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000	−0.456584	−0.228292	+	0.973593i	$0.573314\pi$
$308$	0	0
$309$	0	0
$310$	32.0000	1.81748
$311$	2.00000	0.113410	0.0567048	−	0.998391i	$-0.481941\pi$
$311$	2.00000	0.113410	0.0567048	+	0.998391i	$0.481941\pi$
$312$	0	0
$313$	6.00000	0.339140	0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000	0.339140	0.169570	+	0.985518i	$0.445762\pi$
$314$	18.0000	1.01580
$315$	0	0
$316$	10.0000	0.562544
$317$	32.0000	1.79730	0.898650	−	0.438667i	$-0.144549\pi$
$317$	32.0000	1.79730	0.898650	+	0.438667i	$0.144549\pi$
$318$	0	0
$319$	10.0000	0.559893
$320$	−4.00000	−0.223607
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	−44.0000	−2.44068
$326$	−4.00000	−0.221540
$327$	0	0
$328$	−2.00000	−0.110432
$329$	0	0
$330$	0	0
$331$	−28.0000	−1.53902	−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000	−1.53902	−0.769510	+	0.638635i	$0.779499\pi$
$332$	4.00000	0.219529
$333$	0	0
$334$	12.0000	0.656611
$335$	48.0000	2.62252
$336$	0	0
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	−3.00000	−0.163178
$339$	0	0
$340$	8.00000	0.433861
$341$	−8.00000	−0.433224
$342$	0	0
$343$	0	0
$344$	−4.00000	−0.215666
$345$	0	0
$346$	6.00000	0.322562
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	0	0
$349$	20.0000	1.07058	0.535288	−	0.844670i	$-0.320203\pi$
$349$	20.0000	1.07058	0.535288	+	0.844670i	$0.320203\pi$
$350$	0	0
$351$	0	0
$352$	1.00000	0.0533002
$353$	−6.00000	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$354$	0	0
$355$	8.00000	0.424596
$356$	10.0000	0.529999
$357$	0	0
$358$	0	0
$359$	20.0000	1.05556	0.527780	−	0.849381i	$-0.323025\pi$
$359$	20.0000	1.05556	0.527780	+	0.849381i	$0.323025\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	2.00000	0.105118
$363$	0	0
$364$	0	0
$365$	−24.0000	−1.25622
$366$	0	0
$367$	−8.00000	−0.417597	−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000	−0.417597	−0.208798	+	0.977959i	$0.566955\pi$
$368$	6.00000	0.312772
$369$	0	0
$370$	−8.00000	−0.415900
$371$	0	0
$372$	0	0
$373$	4.00000	0.207112	0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000	0.207112	0.103556	+	0.994624i	$0.466978\pi$
$374$	−2.00000	−0.103418
$375$	0	0
$376$	2.00000	0.103142
$377$	40.0000	2.06010
$378$	0	0
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	0	0
$381$	0	0
$382$	22.0000	1.12562
$383$	−6.00000	−0.306586	−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000	−0.306586	−0.153293	+	0.988181i	$0.548988\pi$
$384$	0	0
$385$	0	0
$386$	−14.0000	−0.712581
$387$	0	0
$388$	2.00000	0.101535
$389$	20.0000	1.01404	0.507020	−	0.861934i	$-0.330747\pi$
$389$	20.0000	1.01404	0.507020	+	0.861934i	$0.330747\pi$
$390$	0	0
$391$	−12.0000	−0.606866
$392$	0	0
$393$	0	0
$394$	18.0000	0.906827
$395$	−40.0000	−2.01262
$396$	0	0
$397$	−18.0000	−0.903394	−0.451697	−	0.892171i	$-0.649181\pi$
$397$	−18.0000	−0.903394	−0.451697	+	0.892171i	$0.649181\pi$
$398$	20.0000	1.00251
$399$	0	0
$400$	11.0000	0.550000
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	0	0
$403$	−32.0000	−1.59403
$404$	2.00000	0.0995037
$405$	0	0
$406$	0	0
$407$	2.00000	0.0991363
$408$	0	0
$409$	10.0000	0.494468	0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000	0.494468	0.247234	+	0.968956i	$0.420478\pi$
$410$	8.00000	0.395092
$411$	0	0
$412$	−4.00000	−0.197066
$413$	0	0
$414$	0	0
$415$	−16.0000	−0.785409
$416$	4.00000	0.196116
$417$	0	0
$418$	0	0
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	−18.0000	−0.877266	−0.438633	−	0.898666i	$-0.644537\pi$
$421$	−18.0000	−0.877266	−0.438633	+	0.898666i	$0.644537\pi$
$422$	−12.0000	−0.584151
$423$	0	0
$424$	4.00000	0.194257
$425$	−22.0000	−1.06716
$426$	0	0
$427$	0	0
$428$	12.0000	0.580042
$429$	0	0
$430$	16.0000	0.771589
$431$	−32.0000	−1.54139	−0.770693	−	0.637207i	$-0.780090\pi$
$431$	−32.0000	−1.54139	−0.770693	+	0.637207i	$0.780090\pi$
$432$	0	0
$433$	6.00000	0.288342	0.144171	−	0.989553i	$-0.453949\pi$
$433$	6.00000	0.288342	0.144171	+	0.989553i	$0.453949\pi$
$434$	0	0
$435$	0	0
$436$	20.0000	0.957826
$437$	0	0
$438$	0	0
$439$	−10.0000	−0.477274	−0.238637	−	0.971109i	$-0.576701\pi$
$439$	−10.0000	−0.477274	−0.238637	+	0.971109i	$0.576701\pi$
$440$	−4.00000	−0.190693
$441$	0	0
$442$	−8.00000	−0.380521
$443$	−24.0000	−1.14027	−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000	−1.14027	−0.570137	+	0.821549i	$0.693110\pi$
$444$	0	0
$445$	−40.0000	−1.89618
$446$	−16.0000	−0.757622
$447$	0	0
$448$	0	0
$449$	−30.0000	−1.41579	−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000	−1.41579	−0.707894	+	0.706319i	$0.750354\pi$
$450$	0	0
$451$	−2.00000	−0.0941763
$452$	6.00000	0.282216
$453$	0	0
$454$	12.0000	0.563188
$455$	0	0
$456$	0	0
$457$	−2.00000	−0.0935561	−0.0467780	−	0.998905i	$-0.514895\pi$
$457$	−2.00000	−0.0935561	−0.0467780	+	0.998905i	$0.514895\pi$
$458$	10.0000	0.467269
$459$	0	0
$460$	−24.0000	−1.11901
$461$	−18.0000	−0.838344	−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000	−0.838344	−0.419172	+	0.907907i	$0.637680\pi$
$462$	0	0
$463$	4.00000	0.185896	0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000	0.185896	0.0929479	+	0.995671i	$0.470371\pi$
$464$	−10.0000	−0.464238
$465$	0	0
$466$	−6.00000	−0.277945
$467$	28.0000	1.29569	0.647843	−	0.761774i	$-0.275671\pi$
$467$	28.0000	1.29569	0.647843	+	0.761774i	$0.275671\pi$
$468$	0	0
$469$	0	0
$470$	−8.00000	−0.369012
$471$	0	0
$472$	0	0
$473$	−4.00000	−0.183920
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	−20.0000	−0.914779
$479$	40.0000	1.82765	0.913823	−	0.406112i	$-0.133116\pi$
$479$	40.0000	1.82765	0.913823	+	0.406112i	$0.133116\pi$
$480$	0	0
$481$	8.00000	0.364769
$482$	−18.0000	−0.819878
$483$	0	0
$484$	1.00000	0.0454545
$485$	−8.00000	−0.363261
$486$	0	0
$487$	28.0000	1.26880	0.634401	−	0.773004i	$-0.281247\pi$
$487$	28.0000	1.26880	0.634401	+	0.773004i	$0.281247\pi$
$488$	−8.00000	−0.362143
$489$	0	0
$490$	0	0
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	0	0
$493$	20.0000	0.900755
$494$	0	0
$495$	0	0
$496$	8.00000	0.359211
$497$	0	0
$498$	0	0
$499$	−20.0000	−0.895323	−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000	−0.895323	−0.447661	+	0.894203i	$0.647743\pi$
$500$	−24.0000	−1.07331
$501$	0	0
$502$	8.00000	0.357057
$503$	4.00000	0.178351	0.0891756	−	0.996016i	$-0.471577\pi$
$503$	4.00000	0.178351	0.0891756	+	0.996016i	$0.471577\pi$
$504$	0	0
$505$	−8.00000	−0.355995
$506$	6.00000	0.266733
$507$	0	0
$508$	−22.0000	−0.976092
$509$	−20.0000	−0.886484	−0.443242	−	0.896402i	$-0.646172\pi$
$509$	−20.0000	−0.886484	−0.443242	+	0.896402i	$0.646172\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−18.0000	−0.793946
$515$	16.0000	0.705044
$516$	0	0
$517$	2.00000	0.0879599
$518$	0	0
$519$	0	0
$520$	−16.0000	−0.701646
$521$	−18.0000	−0.788594	−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000	−0.788594	−0.394297	+	0.918983i	$0.629012\pi$
$522$	0	0
$523$	−44.0000	−1.92399	−0.961993	−	0.273075i	$-0.911959\pi$
$523$	−44.0000	−1.92399	−0.961993	+	0.273075i	$0.911959\pi$
$524$	12.0000	0.524222
$525$	0	0
$526$	−16.0000	−0.697633
$527$	−16.0000	−0.696971
$528$	0	0
$529$	13.0000	0.565217
$530$	−16.0000	−0.694996
$531$	0	0
$532$	0	0
$533$	−8.00000	−0.346518
$534$	0	0
$535$	−48.0000	−2.07522
$536$	12.0000	0.518321
$537$	0	0
$538$	20.0000	0.862261
$539$	0	0
$540$	0	0
$541$	12.0000	0.515920	0.257960	−	0.966156i	$-0.416950\pi$
$541$	12.0000	0.515920	0.257960	+	0.966156i	$0.416950\pi$
$542$	22.0000	0.944981
$543$	0	0
$544$	2.00000	0.0857493
$545$	−80.0000	−3.42682
$546$	0	0
$547$	−32.0000	−1.36822	−0.684111	−	0.729378i	$-0.739809\pi$
$547$	−32.0000	−1.36822	−0.684111	+	0.729378i	$0.739809\pi$
$548$	2.00000	0.0854358
$549$	0	0
$550$	11.0000	0.469042
$551$	0	0
$552$	0	0
$553$	0	0
$554$	−8.00000	−0.339887
$555$	0	0
$556$	0	0
$557$	−38.0000	−1.61011	−0.805056	−	0.593199i	$-0.797865\pi$
$557$	−38.0000	−1.61011	−0.805056	+	0.593199i	$0.797865\pi$
$558$	0	0
$559$	−16.0000	−0.676728
$560$	0	0
$561$	0	0
$562$	22.0000	0.928014
$563$	−36.0000	−1.51722	−0.758610	−	0.651546i	$-0.774121\pi$
$563$	−36.0000	−1.51722	−0.758610	+	0.651546i	$0.774121\pi$
$564$	0	0
$565$	−24.0000	−1.00969
$566$	4.00000	0.168133
$567$	0	0
$568$	2.00000	0.0839181
$569$	10.0000	0.419222	0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000	0.419222	0.209611	+	0.977785i	$0.432780\pi$
$570$	0	0
$571$	32.0000	1.33916	0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000	1.33916	0.669579	+	0.742741i	$0.266474\pi$
$572$	4.00000	0.167248
$573$	0	0
$574$	0	0
$575$	66.0000	2.75239
$576$	0	0
$577$	2.00000	0.0832611	0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000	0.0832611	0.0416305	+	0.999133i	$0.486745\pi$
$578$	13.0000	0.540729
$579$	0	0
$580$	40.0000	1.66091
$581$	0	0
$582$	0	0
$583$	4.00000	0.165663
$584$	−6.00000	−0.248282
$585$	0	0
$586$	−14.0000	−0.578335
$587$	8.00000	0.330195	0.165098	−	0.986277i	$-0.447206\pi$
$587$	8.00000	0.330195	0.165098	+	0.986277i	$0.447206\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	−2.00000	−0.0821995
$593$	14.0000	0.574911	0.287456	−	0.957794i	$-0.407191\pi$
$593$	14.0000	0.574911	0.287456	+	0.957794i	$0.407191\pi$
$594$	0	0
$595$	0	0
$596$	10.0000	0.409616
$597$	0	0
$598$	24.0000	0.981433
$599$	30.0000	1.22577	0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000	1.22577	0.612883	+	0.790173i	$0.290010\pi$
$600$	0	0
$601$	−42.0000	−1.71322	−0.856608	−	0.515968i	$-0.827432\pi$
$601$	−42.0000	−1.71322	−0.856608	+	0.515968i	$0.827432\pi$
$602$	0	0
$603$	0	0
$604$	2.00000	0.0813788
$605$	−4.00000	−0.162623
$606$	0	0
$607$	22.0000	0.892952	0.446476	−	0.894795i	$-0.352679\pi$
$607$	22.0000	0.892952	0.446476	+	0.894795i	$0.352679\pi$
$608$	0	0
$609$	0	0
$610$	32.0000	1.29564
$611$	8.00000	0.323645
$612$	0	0
$613$	−16.0000	−0.646234	−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000	−0.646234	−0.323117	+	0.946359i	$0.604731\pi$
$614$	8.00000	0.322854
$615$	0	0
$616$	0	0
$617$	22.0000	0.885687	0.442843	−	0.896599i	$-0.353970\pi$
$617$	22.0000	0.885687	0.442843	+	0.896599i	$0.353970\pi$
$618$	0	0
$619$	20.0000	0.803868	0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000	0.803868	0.401934	+	0.915669i	$0.368338\pi$
$620$	−32.0000	−1.28515
$621$	0	0
$622$	−2.00000	−0.0801927
$623$	0	0
$624$	0	0
$625$	41.0000	1.64000
$626$	−6.00000	−0.239808
$627$	0	0
$628$	−18.0000	−0.718278
$629$	4.00000	0.159490
$630$	0	0
$631$	−48.0000	−1.91085	−0.955425	−	0.295234i	$-0.904602\pi$
$631$	−48.0000	−1.91085	−0.955425	+	0.295234i	$0.904602\pi$
$632$	−10.0000	−0.397779
$633$	0	0
$634$	−32.0000	−1.27088
$635$	88.0000	3.49217
$636$	0	0
$637$	0	0
$638$	−10.0000	−0.395904
$639$	0	0
$640$	4.00000	0.158114
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	0	0
$643$	−44.0000	−1.73519	−0.867595	−	0.497271i	$-0.834335\pi$
$643$	−44.0000	−1.73519	−0.867595	+	0.497271i	$0.834335\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−22.0000	−0.864909	−0.432455	−	0.901656i	$-0.642352\pi$
$647$	−22.0000	−0.864909	−0.432455	+	0.901656i	$0.642352\pi$
$648$	0	0
$649$	0	0
$650$	44.0000	1.72582
$651$	0	0
$652$	4.00000	0.156652
$653$	−24.0000	−0.939193	−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000	−0.939193	−0.469596	+	0.882881i	$0.655601\pi$
$654$	0	0
$655$	−48.0000	−1.87552
$656$	2.00000	0.0780869
$657$	0	0
$658$	0	0
$659$	20.0000	0.779089	0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000	0.779089	0.389545	+	0.921008i	$0.372632\pi$
$660$	0	0
$661$	−42.0000	−1.63361	−0.816805	−	0.576913i	$-0.804257\pi$
$661$	−42.0000	−1.63361	−0.816805	+	0.576913i	$0.804257\pi$
$662$	28.0000	1.08825
$663$	0	0
$664$	−4.00000	−0.155230
$665$	0	0
$666$	0	0
$667$	−60.0000	−2.32321
$668$	−12.0000	−0.464294
$669$	0	0
$670$	−48.0000	−1.85440
$671$	−8.00000	−0.308837
$672$	0	0
$673$	14.0000	0.539660	0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000	0.539660	0.269830	+	0.962908i	$0.413032\pi$
$674$	22.0000	0.847408
$675$	0	0
$676$	3.00000	0.115385
$677$	−22.0000	−0.845529	−0.422764	−	0.906240i	$-0.638940\pi$
$677$	−22.0000	−0.845529	−0.422764	+	0.906240i	$0.638940\pi$
$678$	0	0
$679$	0	0
$680$	−8.00000	−0.306786
$681$	0	0
$682$	8.00000	0.306336
$683$	16.0000	0.612223	0.306111	−	0.951996i	$-0.400972\pi$
$683$	16.0000	0.612223	0.306111	+	0.951996i	$0.400972\pi$
$684$	0	0
$685$	−8.00000	−0.305664
$686$	0	0
$687$	0	0
$688$	4.00000	0.152499
$689$	16.0000	0.609551
$690$	0	0
$691$	−52.0000	−1.97817	−0.989087	−	0.147335i	$-0.952930\pi$
$691$	−52.0000	−1.97817	−0.989087	+	0.147335i	$0.952930\pi$
$692$	−6.00000	−0.228086
$693$	0	0
$694$	−12.0000	−0.455514
$695$	0	0
$696$	0	0
$697$	−4.00000	−0.151511
$698$	−20.0000	−0.757011
$699$	0	0
$700$	0	0
$701$	18.0000	0.679851	0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000	0.679851	0.339925	+	0.940452i	$0.389598\pi$
$702$	0	0
$703$	0	0
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	6.00000	0.225813
$707$	0	0
$708$	0	0
$709$	10.0000	0.375558	0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000	0.375558	0.187779	+	0.982211i	$0.439871\pi$
$710$	−8.00000	−0.300235
$711$	0	0
$712$	−10.0000	−0.374766
$713$	48.0000	1.79761
$714$	0	0
$715$	−16.0000	−0.598366
$716$	0	0
$717$	0	0
$718$	−20.0000	−0.746393
$719$	10.0000	0.372937	0.186469	−	0.982461i	$-0.440296\pi$
$719$	10.0000	0.372937	0.186469	+	0.982461i	$0.440296\pi$
$720$	0	0
$721$	0	0
$722$	19.0000	0.707107
$723$	0	0
$724$	−2.00000	−0.0743294
$725$	−110.000	−4.08530
$726$	0	0
$727$	−28.0000	−1.03846	−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000	−1.03846	−0.519231	+	0.854634i	$0.673782\pi$
$728$	0	0
$729$	0	0
$730$	24.0000	0.888280
$731$	−8.00000	−0.295891
$732$	0	0
$733$	−4.00000	−0.147743	−0.0738717	−	0.997268i	$-0.523536\pi$
$733$	−4.00000	−0.147743	−0.0738717	+	0.997268i	$0.523536\pi$
$734$	8.00000	0.295285
$735$	0	0
$736$	−6.00000	−0.221163
$737$	12.0000	0.442026
$738$	0	0
$739$	20.0000	0.735712	0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000	0.735712	0.367856	+	0.929883i	$0.380092\pi$
$740$	8.00000	0.294086
$741$	0	0
$742$	0	0
$743$	−44.0000	−1.61420	−0.807102	−	0.590412i	$-0.798965\pi$
$743$	−44.0000	−1.61420	−0.807102	+	0.590412i	$0.798965\pi$
$744$	0	0
$745$	−40.0000	−1.46549
$746$	−4.00000	−0.146450
$747$	0	0
$748$	2.00000	0.0731272
$749$	0	0
$750$	0	0
$751$	−8.00000	−0.291924	−0.145962	−	0.989290i	$-0.546628\pi$
$751$	−8.00000	−0.291924	−0.145962	+	0.989290i	$0.546628\pi$
$752$	−2.00000	−0.0729325
$753$	0	0
$754$	−40.0000	−1.45671
$755$	−8.00000	−0.291150
$756$	0	0
$757$	−42.0000	−1.52652	−0.763258	−	0.646094i	$-0.776401\pi$
$757$	−42.0000	−1.52652	−0.763258	+	0.646094i	$0.776401\pi$
$758$	20.0000	0.726433
$759$	0	0
$760$	0	0
$761$	22.0000	0.797499	0.398750	−	0.917060i	$-0.369444\pi$
$761$	22.0000	0.797499	0.398750	+	0.917060i	$0.369444\pi$
$762$	0	0
$763$	0	0
$764$	−22.0000	−0.795932
$765$	0	0
$766$	6.00000	0.216789
$767$	0	0
$768$	0	0
$769$	50.0000	1.80305	0.901523	−	0.432731i	$-0.142450\pi$
$769$	50.0000	1.80305	0.901523	+	0.432731i	$0.142450\pi$
$770$	0	0
$771$	0	0
$772$	14.0000	0.503871
$773$	4.00000	0.143870	0.0719350	−	0.997409i	$-0.477083\pi$
$773$	4.00000	0.143870	0.0719350	+	0.997409i	$0.477083\pi$
$774$	0	0
$775$	88.0000	3.16105
$776$	−2.00000	−0.0717958
$777$	0	0
$778$	−20.0000	−0.717035
$779$	0	0
$780$	0	0
$781$	2.00000	0.0715656
$782$	12.0000	0.429119
$783$	0	0
$784$	0	0
$785$	72.0000	2.56979
$786$	0	0
$787$	52.0000	1.85360	0.926800	−	0.375555i	$-0.122548\pi$
$787$	52.0000	1.85360	0.926800	+	0.375555i	$0.122548\pi$
$788$	−18.0000	−0.641223
$789$	0	0
$790$	40.0000	1.42314
$791$	0	0
$792$	0	0
$793$	−32.0000	−1.13635
$794$	18.0000	0.638796
$795$	0	0
$796$	−20.0000	−0.708881
$797$	28.0000	0.991811	0.495905	−	0.868377i	$-0.334836\pi$
$797$	28.0000	0.991811	0.495905	+	0.868377i	$0.334836\pi$
$798$	0	0
$799$	4.00000	0.141510
$800$	−11.0000	−0.388909
$801$	0	0
$802$	−18.0000	−0.635602
$803$	−6.00000	−0.211735
$804$	0	0
$805$	0	0
$806$	32.0000	1.12715
$807$	0	0
$808$	−2.00000	−0.0703598
$809$	−10.0000	−0.351581	−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−10.0000	−0.351581	−0.175791	+	0.984428i	$0.556248\pi$
$810$	0	0
$811$	−12.0000	−0.421377	−0.210688	−	0.977553i	$-0.567571\pi$
$811$	−12.0000	−0.421377	−0.210688	+	0.977553i	$0.567571\pi$
$812$	0	0
$813$	0	0
$814$	−2.00000	−0.0701000
$815$	−16.0000	−0.560456
$816$	0	0
$817$	0	0
$818$	−10.0000	−0.349642
$819$	0	0
$820$	−8.00000	−0.279372
$821$	38.0000	1.32621	0.663105	−	0.748527i	$-0.269238\pi$
$821$	38.0000	1.32621	0.663105	+	0.748527i	$0.269238\pi$
$822$	0	0
$823$	24.0000	0.836587	0.418294	−	0.908312i	$-0.362628\pi$
$823$	24.0000	0.836587	0.418294	+	0.908312i	$0.362628\pi$
$824$	4.00000	0.139347
$825$	0	0
$826$	0	0
$827$	12.0000	0.417281	0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000	0.417281	0.208640	+	0.977992i	$0.433096\pi$
$828$	0	0
$829$	−30.0000	−1.04194	−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000	−1.04194	−0.520972	+	0.853574i	$0.674430\pi$
$830$	16.0000	0.555368
$831$	0	0
$832$	−4.00000	−0.138675
$833$	0	0
$834$	0	0
$835$	48.0000	1.66111
$836$	0	0
$837$	0	0
$838$	0	0
$839$	30.0000	1.03572	0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000	1.03572	0.517858	+	0.855467i	$0.326730\pi$
$840$	0	0
$841$	71.0000	2.44828
$842$	18.0000	0.620321
$843$	0	0
$844$	12.0000	0.413057
$845$	−12.0000	−0.412813
$846$	0	0
$847$	0	0
$848$	−4.00000	−0.137361
$849$	0	0
$850$	22.0000	0.754594
$851$	−12.0000	−0.411355
$852$	0	0
$853$	−24.0000	−0.821744	−0.410872	−	0.911693i	$-0.634776\pi$
$853$	−24.0000	−0.821744	−0.410872	+	0.911693i	$0.634776\pi$
$854$	0	0
$855$	0	0
$856$	−12.0000	−0.410152
$857$	−22.0000	−0.751506	−0.375753	−	0.926720i	$-0.622616\pi$
$857$	−22.0000	−0.751506	−0.375753	+	0.926720i	$0.622616\pi$
$858$	0	0
$859$	20.0000	0.682391	0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000	0.682391	0.341196	+	0.939992i	$0.389168\pi$
$860$	−16.0000	−0.545595
$861$	0	0
$862$	32.0000	1.08992
$863$	−54.0000	−1.83818	−0.919091	−	0.394046i	$-0.871075\pi$
$863$	−54.0000	−1.83818	−0.919091	+	0.394046i	$0.871075\pi$
$864$	0	0
$865$	24.0000	0.816024
$866$	−6.00000	−0.203888
$867$	0	0
$868$	0	0
$869$	−10.0000	−0.339227
$870$	0	0
$871$	48.0000	1.62642
$872$	−20.0000	−0.677285
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	28.0000	0.945493	0.472746	−	0.881199i	$-0.343263\pi$
$877$	28.0000	0.945493	0.472746	+	0.881199i	$0.343263\pi$
$878$	10.0000	0.337484
$879$	0	0
$880$	4.00000	0.134840
$881$	−38.0000	−1.28025	−0.640126	−	0.768270i	$-0.721118\pi$
$881$	−38.0000	−1.28025	−0.640126	+	0.768270i	$0.721118\pi$
$882$	0	0
$883$	44.0000	1.48072	0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000	1.48072	0.740359	+	0.672212i	$0.234656\pi$
$884$	8.00000	0.269069
$885$	0	0
$886$	24.0000	0.806296
$887$	−12.0000	−0.402921	−0.201460	−	0.979497i	$-0.564569\pi$
$887$	−12.0000	−0.402921	−0.201460	+	0.979497i	$0.564569\pi$
$888$	0	0
$889$	0	0
$890$	40.0000	1.34080
$891$	0	0
$892$	16.0000	0.535720
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	30.0000	1.00111
$899$	−80.0000	−2.66815
$900$	0	0
$901$	8.00000	0.266519
$902$	2.00000	0.0665927
$903$	0	0
$904$	−6.00000	−0.199557
$905$	8.00000	0.265929
$906$	0	0
$907$	−12.0000	−0.398453	−0.199227	−	0.979953i	$-0.563843\pi$
$907$	−12.0000	−0.398453	−0.199227	+	0.979953i	$0.563843\pi$
$908$	−12.0000	−0.398234
$909$	0	0
$910$	0	0
$911$	−2.00000	−0.0662630	−0.0331315	−	0.999451i	$-0.510548\pi$
$911$	−2.00000	−0.0662630	−0.0331315	+	0.999451i	$0.510548\pi$
$912$	0	0
$913$	−4.00000	−0.132381
$914$	2.00000	0.0661541
$915$	0	0
$916$	−10.0000	−0.330409
$917$	0	0
$918$	0	0
$919$	−10.0000	−0.329870	−0.164935	−	0.986304i	$-0.552741\pi$
$919$	−10.0000	−0.329870	−0.164935	+	0.986304i	$0.552741\pi$
$920$	24.0000	0.791257
$921$	0	0
$922$	18.0000	0.592798
$923$	8.00000	0.263323
$924$	0	0
$925$	−22.0000	−0.723356
$926$	−4.00000	−0.131448
$927$	0	0
$928$	10.0000	0.328266
$929$	30.0000	0.984268	0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000	0.984268	0.492134	+	0.870519i	$0.336217\pi$
$930$	0	0
$931$	0	0
$932$	6.00000	0.196537
$933$	0	0
$934$	−28.0000	−0.916188
$935$	−8.00000	−0.261628
$936$	0	0
$937$	−58.0000	−1.89478	−0.947389	−	0.320085i	$-0.896288\pi$
$937$	−58.0000	−1.89478	−0.947389	+	0.320085i	$0.896288\pi$
$938$	0	0
$939$	0	0
$940$	8.00000	0.260931
$941$	42.0000	1.36916	0.684580	−	0.728937i	$-0.259985\pi$
$941$	42.0000	1.36916	0.684580	+	0.728937i	$0.259985\pi$
$942$	0	0
$943$	12.0000	0.390774
$944$	0	0
$945$	0	0
$946$	4.00000	0.130051
$947$	−28.0000	−0.909878	−0.454939	−	0.890523i	$-0.650339\pi$
$947$	−28.0000	−0.909878	−0.454939	+	0.890523i	$0.650339\pi$
$948$	0	0
$949$	−24.0000	−0.779073
$950$	0	0
$951$	0	0
$952$	0	0
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	0	0
$955$	88.0000	2.84761
$956$	20.0000	0.646846
$957$	0	0
$958$	−40.0000	−1.29234
$959$	0	0
$960$	0	0
$961$	33.0000	1.06452
$962$	−8.00000	−0.257930
$963$	0	0
$964$	18.0000	0.579741
$965$	−56.0000	−1.80270
$966$	0	0
$967$	−22.0000	−0.707472	−0.353736	−	0.935345i	$-0.615089\pi$
$967$	−22.0000	−0.707472	−0.353736	+	0.935345i	$0.615089\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	8.00000	0.256865
$971$	32.0000	1.02693	0.513464	−	0.858111i	$-0.328362\pi$
$971$	32.0000	1.02693	0.513464	+	0.858111i	$0.328362\pi$
$972$	0	0
$973$	0	0
$974$	−28.0000	−0.897178
$975$	0	0
$976$	8.00000	0.256074
$977$	−38.0000	−1.21573	−0.607864	−	0.794041i	$-0.707973\pi$
$977$	−38.0000	−1.21573	−0.607864	+	0.794041i	$0.707973\pi$
$978$	0	0
$979$	−10.0000	−0.319601
$980$	0	0
$981$	0	0
$982$	12.0000	0.382935
$983$	−46.0000	−1.46717	−0.733586	−	0.679597i	$-0.762155\pi$
$983$	−46.0000	−1.46717	−0.733586	+	0.679597i	$0.762155\pi$
$984$	0	0
$985$	72.0000	2.29411
$986$	−20.0000	−0.636930
$987$	0	0
$988$	0	0
$989$	24.0000	0.763156
$990$	0	0
$991$	−8.00000	−0.254128	−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000	−0.254128	−0.127064	+	0.991894i	$0.540555\pi$
$992$	−8.00000	−0.254000
$993$	0	0
$994$	0	0
$995$	80.0000	2.53617
$996$	0	0
$997$	52.0000	1.64686	0.823428	−	0.567420i	$-0.192059\pi$
$997$	52.0000	1.64686	0.823428	+	0.567420i	$0.192059\pi$
$998$	20.0000	0.633089
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9702.2.a.a.1.1		1
3.2	odd	2		3234.2.a.s.1.1		1
7.6	odd	2		198.2.a.c.1.1		1
21.20	even	2		66.2.a.c.1.1	✓	1
28.27	even	2		1584.2.a.s.1.1		1
35.13	even	4		4950.2.c.d.199.2		2
35.27	even	4		4950.2.c.d.199.1		2
35.34	odd	2		4950.2.a.bo.1.1		1
56.13	odd	2		6336.2.a.c.1.1		1
56.27	even	2		6336.2.a.d.1.1		1
63.13	odd	6		1782.2.e.n.1189.1		2
63.20	even	6		1782.2.e.l.595.1		2
63.34	odd	6		1782.2.e.n.595.1		2
63.41	even	6		1782.2.e.l.1189.1		2
77.76	even	2		2178.2.a.m.1.1		1
84.83	odd	2		528.2.a.a.1.1		1
105.62	odd	4		1650.2.c.m.199.2		2
105.83	odd	4		1650.2.c.m.199.1		2
105.104	even	2		1650.2.a.c.1.1		1
168.83	odd	2		2112.2.a.bd.1.1		1
168.125	even	2		2112.2.a.n.1.1		1
231.20	even	10		726.2.e.e.565.1		4
231.41	odd	10		726.2.e.m.493.1		4
231.62	odd	10		726.2.e.m.511.1		4
231.83	odd	10		726.2.e.m.487.1		4
231.104	even	10		726.2.e.e.487.1		4
231.125	even	10		726.2.e.e.511.1		4
231.146	even	10		726.2.e.e.493.1		4
231.167	odd	10		726.2.e.m.565.1		4
231.230	odd	2		726.2.a.d.1.1		1
924.923	even	2		5808.2.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.a.c.1.1	✓	1	21.20	even	2
198.2.a.c.1.1		1	7.6	odd	2
528.2.a.a.1.1		1	84.83	odd	2
726.2.a.d.1.1		1	231.230	odd	2
726.2.e.e.487.1		4	231.104	even	10
726.2.e.e.493.1		4	231.146	even	10
726.2.e.e.511.1		4	231.125	even	10
726.2.e.e.565.1		4	231.20	even	10
726.2.e.m.487.1		4	231.83	odd	10
726.2.e.m.493.1		4	231.41	odd	10
726.2.e.m.511.1		4	231.62	odd	10
726.2.e.m.565.1		4	231.167	odd	10
1584.2.a.s.1.1		1	28.27	even	2
1650.2.a.c.1.1		1	105.104	even	2
1650.2.c.m.199.1		2	105.83	odd	4
1650.2.c.m.199.2		2	105.62	odd	4
1782.2.e.l.595.1		2	63.20	even	6
1782.2.e.l.1189.1		2	63.41	even	6
1782.2.e.n.595.1		2	63.34	odd	6
1782.2.e.n.1189.1		2	63.13	odd	6
2112.2.a.n.1.1		1	168.125	even	2
2112.2.a.bd.1.1		1	168.83	odd	2
2178.2.a.m.1.1		1	77.76	even	2
3234.2.a.s.1.1		1	3.2	odd	2
4950.2.a.bo.1.1		1	35.34	odd	2
4950.2.c.d.199.1		2	35.27	even	4
4950.2.c.d.199.2		2	35.13	even	4
5808.2.a.b.1.1		1	924.923	even	2
6336.2.a.c.1.1		1	56.13	odd	2
6336.2.a.d.1.1		1	56.27	even	2
9702.2.a.a.1.1		1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9702.a (trivial)

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