LMFDB - Embedded newform 9702.2.a.bg.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:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1386)
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)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} -2.00000 q^{5} +1.00000 q^{8} -2.00000 q^{10} -1.00000 q^{11} +2.00000 q^{13} +1.00000 q^{16} -3.00000 q^{17} +7.00000 q^{19} -2.00000 q^{20} -1.00000 q^{22} -7.00000 q^{23} -1.00000 q^{25} +2.00000 q^{26} -5.00000 q^{29} +2.00000 q^{31} +1.00000 q^{32} -3.00000 q^{34} +3.00000 q^{37} +7.00000 q^{38} -2.00000 q^{40} +6.00000 q^{41} +11.0000 q^{43} -1.00000 q^{44} -7.00000 q^{46} -7.00000 q^{47} -1.00000 q^{50} +2.00000 q^{52} -4.00000 q^{53} +2.00000 q^{55} -5.00000 q^{58} +11.0000 q^{59} +10.0000 q^{61} +2.00000 q^{62} +1.00000 q^{64} -4.00000 q^{65} -4.00000 q^{67} -3.00000 q^{68} -5.00000 q^{71} -8.00000 q^{73} +3.00000 q^{74} +7.00000 q^{76} -8.00000 q^{79} -2.00000 q^{80} +6.00000 q^{82} +14.0000 q^{83} +6.00000 q^{85} +11.0000 q^{86} -1.00000 q^{88} +2.00000 q^{89} -7.00000 q^{92} -7.00000 q^{94} -14.0000 q^{95} +15.0000 q^{97} +O(q^{100})$

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
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	0	0
$10$	−2.00000	−0.632456
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0	0
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	0	0
$19$	7.00000	1.60591	0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000	1.60591	0.802955	+	0.596040i	$0.203260\pi$
$20$	−2.00000	−0.447214
$21$	0	0
$22$	−1.00000	−0.213201
$23$	−7.00000	−1.45960	−0.729800	−	0.683660i	$-0.760387\pi$
$23$	−7.00000	−1.45960	−0.729800	+	0.683660i	$0.760387\pi$
$24$	0	0
$25$	−1.00000	−0.200000
$26$	2.00000	0.392232
$27$	0	0
$28$	0	0
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−3.00000	−0.514496
$35$	0	0
$36$	0	0
$37$	3.00000	0.493197	0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000	0.493197	0.246598	+	0.969118i	$0.420687\pi$
$38$	7.00000	1.13555
$39$	0	0
$40$	−2.00000	−0.316228
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	0	0
$43$	11.0000	1.67748	0.838742	−	0.544529i	$-0.183292\pi$
$43$	11.0000	1.67748	0.838742	+	0.544529i	$0.183292\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	−7.00000	−1.03209
$47$	−7.00000	−1.02105	−0.510527	−	0.859861i	$-0.670550\pi$
$47$	−7.00000	−1.02105	−0.510527	+	0.859861i	$0.670550\pi$
$48$	0	0
$49$	0	0
$50$	−1.00000	−0.141421
$51$	0	0
$52$	2.00000	0.277350
$53$	−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
$55$	2.00000	0.269680
$56$	0	0
$57$	0	0
$58$	−5.00000	−0.656532
$59$	11.0000	1.43208	0.716039	−	0.698060i	$-0.245953\pi$
$59$	11.0000	1.43208	0.716039	+	0.698060i	$0.245953\pi$
$60$	0	0
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	2.00000	0.254000
$63$	0	0
$64$	1.00000	0.125000
$65$	−4.00000	−0.496139
$66$	0	0
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	−3.00000	−0.363803
$69$	0	0
$70$	0	0
$71$	−5.00000	−0.593391	−0.296695	−	0.954972i	$-0.595885\pi$
$71$	−5.00000	−0.593391	−0.296695	+	0.954972i	$0.595885\pi$
$72$	0	0
$73$	−8.00000	−0.936329	−0.468165	−	0.883641i	$-0.655085\pi$
$73$	−8.00000	−0.936329	−0.468165	+	0.883641i	$0.655085\pi$
$74$	3.00000	0.348743
$75$	0	0
$76$	7.00000	0.802955
$77$	0	0
$78$	0	0
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	−2.00000	−0.223607
$81$	0	0
$82$	6.00000	0.662589
$83$	14.0000	1.53670	0.768350	−	0.640030i	$-0.221078\pi$
$83$	14.0000	1.53670	0.768350	+	0.640030i	$0.221078\pi$
$84$	0	0
$85$	6.00000	0.650791
$86$	11.0000	1.18616
$87$	0	0
$88$	−1.00000	−0.106600
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	0	0
$91$	0	0
$92$	−7.00000	−0.729800
$93$	0	0
$94$	−7.00000	−0.721995
$95$	−14.0000	−1.43637
$96$	0	0
$97$	15.0000	1.52302	0.761510	−	0.648154i	$-0.224459\pi$
$97$	15.0000	1.52302	0.761510	+	0.648154i	$0.224459\pi$
$98$	0	0
$99$	0	0
$100$	−1.00000	−0.100000
$101$	3.00000	0.298511	0.149256	−	0.988799i	$-0.452312\pi$
$101$	3.00000	0.298511	0.149256	+	0.988799i	$0.452312\pi$
$102$	0	0
$103$	−10.0000	−0.985329	−0.492665	−	0.870219i	$-0.663977\pi$
$103$	−10.0000	−0.985329	−0.492665	+	0.870219i	$0.663977\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	−4.00000	−0.388514
$107$	18.0000	1.74013	0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000	1.74013	0.870063	+	0.492941i	$0.164078\pi$
$108$	0	0
$109$	4.00000	0.383131	0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000	0.383131	0.191565	+	0.981480i	$0.438644\pi$
$110$	2.00000	0.190693
$111$	0	0
$112$	0	0
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	0	0
$115$	14.0000	1.30551
$116$	−5.00000	−0.464238
$117$	0	0
$118$	11.0000	1.01263
$119$	0	0
$120$	0	0
$121$	1.00000	0.0909091
$122$	10.0000	0.905357
$123$	0	0
$124$	2.00000	0.179605
$125$	12.0000	1.07331
$126$	0	0
$127$	−19.0000	−1.68598	−0.842989	−	0.537931i	$-0.819206\pi$
$127$	−19.0000	−1.68598	−0.842989	+	0.537931i	$0.819206\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	−4.00000	−0.350823
$131$	−8.00000	−0.698963	−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000	−0.698963	−0.349482	+	0.936943i	$0.613642\pi$
$132$	0	0
$133$	0	0
$134$	−4.00000	−0.345547
$135$	0	0
$136$	−3.00000	−0.257248
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	0	0
$139$	17.0000	1.44192	0.720961	−	0.692976i	$-0.243701\pi$
$139$	17.0000	1.44192	0.720961	+	0.692976i	$0.243701\pi$
$140$	0	0
$141$	0	0
$142$	−5.00000	−0.419591
$143$	−2.00000	−0.167248
$144$	0	0
$145$	10.0000	0.830455
$146$	−8.00000	−0.662085
$147$	0	0
$148$	3.00000	0.246598
$149$	17.0000	1.39269	0.696347	−	0.717705i	$-0.254807\pi$
$149$	17.0000	1.39269	0.696347	+	0.717705i	$0.254807\pi$
$150$	0	0
$151$	−5.00000	−0.406894	−0.203447	−	0.979086i	$-0.565214\pi$
$151$	−5.00000	−0.406894	−0.203447	+	0.979086i	$0.565214\pi$
$152$	7.00000	0.567775
$153$	0	0
$154$	0	0
$155$	−4.00000	−0.321288
$156$	0	0
$157$	1.00000	0.0798087	0.0399043	−	0.999204i	$-0.487295\pi$
$157$	1.00000	0.0798087	0.0399043	+	0.999204i	$0.487295\pi$
$158$	−8.00000	−0.636446
$159$	0	0
$160$	−2.00000	−0.158114
$161$	0	0
$162$	0	0
$163$	6.00000	0.469956	0.234978	−	0.972001i	$-0.424498\pi$
$163$	6.00000	0.469956	0.234978	+	0.972001i	$0.424498\pi$
$164$	6.00000	0.468521
$165$	0	0
$166$	14.0000	1.08661
$167$	−10.0000	−0.773823	−0.386912	−	0.922117i	$-0.626458\pi$
$167$	−10.0000	−0.773823	−0.386912	+	0.922117i	$0.626458\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	6.00000	0.460179
$171$	0	0
$172$	11.0000	0.838742
$173$	14.0000	1.06440	0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000	1.06440	0.532200	+	0.846619i	$0.321365\pi$
$174$	0	0
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	0	0
$178$	2.00000	0.149906
$179$	−9.00000	−0.672692	−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000	−0.672692	−0.336346	+	0.941739i	$0.609191\pi$
$180$	0	0
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	0	0
$183$	0	0
$184$	−7.00000	−0.516047
$185$	−6.00000	−0.441129
$186$	0	0
$187$	3.00000	0.219382
$188$	−7.00000	−0.510527
$189$	0	0
$190$	−14.0000	−1.01567
$191$	−8.00000	−0.578860	−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000	−0.578860	−0.289430	+	0.957199i	$0.593466\pi$
$192$	0	0
$193$	24.0000	1.72756	0.863779	−	0.503871i	$-0.168091\pi$
$193$	24.0000	1.72756	0.863779	+	0.503871i	$0.168091\pi$
$194$	15.0000	1.07694
$195$	0	0
$196$	0	0
$197$	15.0000	1.06871	0.534353	−	0.845262i	$-0.320555\pi$
$197$	15.0000	1.06871	0.534353	+	0.845262i	$0.320555\pi$
$198$	0	0
$199$	10.0000	0.708881	0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000	0.708881	0.354441	+	0.935079i	$0.384671\pi$
$200$	−1.00000	−0.0707107
$201$	0	0
$202$	3.00000	0.211079
$203$	0	0
$204$	0	0
$205$	−12.0000	−0.838116
$206$	−10.0000	−0.696733
$207$	0	0
$208$	2.00000	0.138675
$209$	−7.00000	−0.484200
$210$	0	0
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	−4.00000	−0.274721
$213$	0	0
$214$	18.0000	1.23045
$215$	−22.0000	−1.50039
$216$	0	0
$217$	0	0
$218$	4.00000	0.270914
$219$	0	0
$220$	2.00000	0.134840
$221$	−6.00000	−0.403604
$222$	0	0
$223$	−14.0000	−0.937509	−0.468755	−	0.883328i	$-0.655297\pi$
$223$	−14.0000	−0.937509	−0.468755	+	0.883328i	$0.655297\pi$
$224$	0	0
$225$	0	0
$226$	2.00000	0.133038
$227$	10.0000	0.663723	0.331862	−	0.943328i	$-0.392323\pi$
$227$	10.0000	0.663723	0.331862	+	0.943328i	$0.392323\pi$
$228$	0	0
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	14.0000	0.923133
$231$	0	0
$232$	−5.00000	−0.328266
$233$	−9.00000	−0.589610	−0.294805	−	0.955557i	$-0.595255\pi$
$233$	−9.00000	−0.589610	−0.294805	+	0.955557i	$0.595255\pi$
$234$	0	0
$235$	14.0000	0.913259
$236$	11.0000	0.716039
$237$	0	0
$238$	0	0
$239$	−10.0000	−0.646846	−0.323423	−	0.946254i	$-0.604834\pi$
$239$	−10.0000	−0.646846	−0.323423	+	0.946254i	$0.604834\pi$
$240$	0	0
$241$	−4.00000	−0.257663	−0.128831	−	0.991667i	$-0.541123\pi$
$241$	−4.00000	−0.257663	−0.128831	+	0.991667i	$0.541123\pi$
$242$	1.00000	0.0642824
$243$	0	0
$244$	10.0000	0.640184
$245$	0	0
$246$	0	0
$247$	14.0000	0.890799
$248$	2.00000	0.127000
$249$	0	0
$250$	12.0000	0.758947
$251$	5.00000	0.315597	0.157799	−	0.987471i	$-0.449560\pi$
$251$	5.00000	0.315597	0.157799	+	0.987471i	$0.449560\pi$
$252$	0	0
$253$	7.00000	0.440086
$254$	−19.0000	−1.19217
$255$	0	0
$256$	1.00000	0.0625000
$257$	−14.0000	−0.873296	−0.436648	−	0.899632i	$-0.643834\pi$
$257$	−14.0000	−0.873296	−0.436648	+	0.899632i	$0.643834\pi$
$258$	0	0
$259$	0	0
$260$	−4.00000	−0.248069
$261$	0	0
$262$	−8.00000	−0.494242
$263$	30.0000	1.84988	0.924940	−	0.380114i	$-0.124115\pi$
$263$	30.0000	1.84988	0.924940	+	0.380114i	$0.124115\pi$
$264$	0	0
$265$	8.00000	0.491436
$266$	0	0
$267$	0	0
$268$	−4.00000	−0.244339
$269$	−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
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	−3.00000	−0.181902
$273$	0	0
$274$	6.00000	0.362473
$275$	1.00000	0.0603023
$276$	0	0
$277$	24.0000	1.44202	0.721010	−	0.692925i	$-0.243678\pi$
$277$	24.0000	1.44202	0.721010	+	0.692925i	$0.243678\pi$
$278$	17.0000	1.01959
$279$	0	0
$280$	0	0
$281$	3.00000	0.178965	0.0894825	−	0.995988i	$-0.471479\pi$
$281$	3.00000	0.178965	0.0894825	+	0.995988i	$0.471479\pi$
$282$	0	0
$283$	24.0000	1.42665	0.713326	−	0.700832i	$-0.247188\pi$
$283$	24.0000	1.42665	0.713326	+	0.700832i	$0.247188\pi$
$284$	−5.00000	−0.296695
$285$	0	0
$286$	−2.00000	−0.118262
$287$	0	0
$288$	0	0
$289$	−8.00000	−0.470588
$290$	10.0000	0.587220
$291$	0	0
$292$	−8.00000	−0.468165
$293$	−3.00000	−0.175262	−0.0876309	−	0.996153i	$-0.527930\pi$
$293$	−3.00000	−0.175262	−0.0876309	+	0.996153i	$0.527930\pi$
$294$	0	0
$295$	−22.0000	−1.28089
$296$	3.00000	0.174371
$297$	0	0
$298$	17.0000	0.984784
$299$	−14.0000	−0.809641
$300$	0	0
$301$	0	0
$302$	−5.00000	−0.287718
$303$	0	0
$304$	7.00000	0.401478
$305$	−20.0000	−1.14520
$306$	0	0
$307$	28.0000	1.59804	0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000	1.59804	0.799022	+	0.601302i	$0.205351\pi$
$308$	0	0
$309$	0	0
$310$	−4.00000	−0.227185
$311$	27.0000	1.53103	0.765515	−	0.643418i	$-0.222484\pi$
$311$	27.0000	1.53103	0.765515	+	0.643418i	$0.222484\pi$
$312$	0	0
$313$	15.0000	0.847850	0.423925	−	0.905697i	$-0.360652\pi$
$313$	15.0000	0.847850	0.423925	+	0.905697i	$0.360652\pi$
$314$	1.00000	0.0564333
$315$	0	0
$316$	−8.00000	−0.450035
$317$	30.0000	1.68497	0.842484	−	0.538721i	$-0.181092\pi$
$317$	30.0000	1.68497	0.842484	+	0.538721i	$0.181092\pi$
$318$	0	0
$319$	5.00000	0.279946
$320$	−2.00000	−0.111803
$321$	0	0
$322$	0	0
$323$	−21.0000	−1.16847
$324$	0	0
$325$	−2.00000	−0.110940
$326$	6.00000	0.332309
$327$	0	0
$328$	6.00000	0.331295
$329$	0	0
$330$	0	0
$331$	−14.0000	−0.769510	−0.384755	−	0.923019i	$-0.625714\pi$
$331$	−14.0000	−0.769510	−0.384755	+	0.923019i	$0.625714\pi$
$332$	14.0000	0.768350
$333$	0	0
$334$	−10.0000	−0.547176
$335$	8.00000	0.437087
$336$	0	0
$337$	8.00000	0.435788	0.217894	−	0.975972i	$-0.430081\pi$
$337$	8.00000	0.435788	0.217894	+	0.975972i	$0.430081\pi$
$338$	−9.00000	−0.489535
$339$	0	0
$340$	6.00000	0.325396
$341$	−2.00000	−0.108306
$342$	0	0
$343$	0	0
$344$	11.0000	0.593080
$345$	0	0
$346$	14.0000	0.752645
$347$	24.0000	1.28839	0.644194	−	0.764862i	$-0.277193\pi$
$347$	24.0000	1.28839	0.644194	+	0.764862i	$0.277193\pi$
$348$	0	0
$349$	8.00000	0.428230	0.214115	−	0.976808i	$-0.431313\pi$
$349$	8.00000	0.428230	0.214115	+	0.976808i	$0.431313\pi$
$350$	0	0
$351$	0	0
$352$	−1.00000	−0.0533002
$353$	10.0000	0.532246	0.266123	−	0.963939i	$-0.414257\pi$
$353$	10.0000	0.532246	0.266123	+	0.963939i	$0.414257\pi$
$354$	0	0
$355$	10.0000	0.530745
$356$	2.00000	0.106000
$357$	0	0
$358$	−9.00000	−0.475665
$359$	−18.0000	−0.950004	−0.475002	−	0.879985i	$-0.657553\pi$
$359$	−18.0000	−0.950004	−0.475002	+	0.879985i	$0.657553\pi$
$360$	0	0
$361$	30.0000	1.57895
$362$	−10.0000	−0.525588
$363$	0	0
$364$	0	0
$365$	16.0000	0.837478
$366$	0	0
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	−7.00000	−0.364900
$369$	0	0
$370$	−6.00000	−0.311925
$371$	0	0
$372$	0	0
$373$	−22.0000	−1.13912	−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000	−1.13912	−0.569558	+	0.821951i	$0.692886\pi$
$374$	3.00000	0.155126
$375$	0	0
$376$	−7.00000	−0.360997
$377$	−10.0000	−0.515026
$378$	0	0
$379$	−16.0000	−0.821865	−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000	−0.821865	−0.410932	+	0.911666i	$0.634797\pi$
$380$	−14.0000	−0.718185
$381$	0	0
$382$	−8.00000	−0.409316
$383$	31.0000	1.58403	0.792013	−	0.610504i	$-0.209033\pi$
$383$	31.0000	1.58403	0.792013	+	0.610504i	$0.209033\pi$
$384$	0	0
$385$	0	0
$386$	24.0000	1.22157
$387$	0	0
$388$	15.0000	0.761510
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	0	0
$391$	21.0000	1.06202
$392$	0	0
$393$	0	0
$394$	15.0000	0.755689
$395$	16.0000	0.805047
$396$	0	0
$397$	−3.00000	−0.150566	−0.0752828	−	0.997162i	$-0.523986\pi$
$397$	−3.00000	−0.150566	−0.0752828	+	0.997162i	$0.523986\pi$
$398$	10.0000	0.501255
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	32.0000	1.59800	0.799002	−	0.601329i	$-0.205362\pi$
$401$	32.0000	1.59800	0.799002	+	0.601329i	$0.205362\pi$
$402$	0	0
$403$	4.00000	0.199254
$404$	3.00000	0.149256
$405$	0	0
$406$	0	0
$407$	−3.00000	−0.148704
$408$	0	0
$409$	32.0000	1.58230	0.791149	−	0.611623i	$-0.209483\pi$
$409$	32.0000	1.58230	0.791149	+	0.611623i	$0.209483\pi$
$410$	−12.0000	−0.592638
$411$	0	0
$412$	−10.0000	−0.492665
$413$	0	0
$414$	0	0
$415$	−28.0000	−1.37447
$416$	2.00000	0.0980581
$417$	0	0
$418$	−7.00000	−0.342381
$419$	3.00000	0.146560	0.0732798	−	0.997311i	$-0.476653\pi$
$419$	3.00000	0.146560	0.0732798	+	0.997311i	$0.476653\pi$
$420$	0	0
$421$	−17.0000	−0.828529	−0.414265	−	0.910156i	$-0.635961\pi$
$421$	−17.0000	−0.828529	−0.414265	+	0.910156i	$0.635961\pi$
$422$	20.0000	0.973585
$423$	0	0
$424$	−4.00000	−0.194257
$425$	3.00000	0.145521
$426$	0	0
$427$	0	0
$428$	18.0000	0.870063
$429$	0	0
$430$	−22.0000	−1.06093
$431$	40.0000	1.92673	0.963366	−	0.268190i	$-0.0864254\pi$
$431$	40.0000	1.92673	0.963366	+	0.268190i	$0.0864254\pi$
$432$	0	0
$433$	5.00000	0.240285	0.120142	−	0.992757i	$-0.461665\pi$
$433$	5.00000	0.240285	0.120142	+	0.992757i	$0.461665\pi$
$434$	0	0
$435$	0	0
$436$	4.00000	0.191565
$437$	−49.0000	−2.34399
$438$	0	0
$439$	5.00000	0.238637	0.119318	−	0.992856i	$-0.461929\pi$
$439$	5.00000	0.238637	0.119318	+	0.992856i	$0.461929\pi$
$440$	2.00000	0.0953463
$441$	0	0
$442$	−6.00000	−0.285391
$443$	41.0000	1.94797	0.973984	−	0.226615i	$-0.0727659\pi$
$443$	41.0000	1.94797	0.973984	+	0.226615i	$0.0727659\pi$
$444$	0	0
$445$	−4.00000	−0.189618
$446$	−14.0000	−0.662919
$447$	0	0
$448$	0	0
$449$	−36.0000	−1.69895	−0.849473	−	0.527633i	$-0.823080\pi$
$449$	−36.0000	−1.69895	−0.849473	+	0.527633i	$0.823080\pi$
$450$	0	0
$451$	−6.00000	−0.282529
$452$	2.00000	0.0940721
$453$	0	0
$454$	10.0000	0.469323
$455$	0	0
$456$	0	0
$457$	40.0000	1.87112	0.935561	−	0.353166i	$-0.114895\pi$
$457$	40.0000	1.87112	0.935561	+	0.353166i	$0.114895\pi$
$458$	−10.0000	−0.467269
$459$	0	0
$460$	14.0000	0.652753
$461$	13.0000	0.605470	0.302735	−	0.953075i	$-0.402100\pi$
$461$	13.0000	0.605470	0.302735	+	0.953075i	$0.402100\pi$
$462$	0	0
$463$	−24.0000	−1.11537	−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000	−1.11537	−0.557687	+	0.830051i	$0.688311\pi$
$464$	−5.00000	−0.232119
$465$	0	0
$466$	−9.00000	−0.416917
$467$	13.0000	0.601568	0.300784	−	0.953692i	$-0.402752\pi$
$467$	13.0000	0.601568	0.300784	+	0.953692i	$0.402752\pi$
$468$	0	0
$469$	0	0
$470$	14.0000	0.645772
$471$	0	0
$472$	11.0000	0.506316
$473$	−11.0000	−0.505781
$474$	0	0
$475$	−7.00000	−0.321182
$476$	0	0
$477$	0	0
$478$	−10.0000	−0.457389
$479$	18.0000	0.822441	0.411220	−	0.911536i	$-0.365103\pi$
$479$	18.0000	0.822441	0.411220	+	0.911536i	$0.365103\pi$
$480$	0	0
$481$	6.00000	0.273576
$482$	−4.00000	−0.182195
$483$	0	0
$484$	1.00000	0.0454545
$485$	−30.0000	−1.36223
$486$	0	0
$487$	18.0000	0.815658	0.407829	−	0.913058i	$-0.366286\pi$
$487$	18.0000	0.815658	0.407829	+	0.913058i	$0.366286\pi$
$488$	10.0000	0.452679
$489$	0	0
$490$	0	0
$491$	−26.0000	−1.17336	−0.586682	−	0.809818i	$-0.699566\pi$
$491$	−26.0000	−1.17336	−0.586682	+	0.809818i	$0.699566\pi$
$492$	0	0
$493$	15.0000	0.675566
$494$	14.0000	0.629890
$495$	0	0
$496$	2.00000	0.0898027
$497$	0	0
$498$	0	0
$499$	−40.0000	−1.79065	−0.895323	−	0.445418i	$-0.853055\pi$
$499$	−40.0000	−1.79065	−0.895323	+	0.445418i	$0.853055\pi$
$500$	12.0000	0.536656
$501$	0	0
$502$	5.00000	0.223161
$503$	−30.0000	−1.33763	−0.668817	−	0.743427i	$-0.733199\pi$
$503$	−30.0000	−1.33763	−0.668817	+	0.743427i	$0.733199\pi$
$504$	0	0
$505$	−6.00000	−0.266996
$506$	7.00000	0.311188
$507$	0	0
$508$	−19.0000	−0.842989
$509$	4.00000	0.177297	0.0886484	−	0.996063i	$-0.471745\pi$
$509$	4.00000	0.177297	0.0886484	+	0.996063i	$0.471745\pi$
$510$	0	0
$511$	0	0
$512$	1.00000	0.0441942
$513$	0	0
$514$	−14.0000	−0.617514
$515$	20.0000	0.881305
$516$	0	0
$517$	7.00000	0.307860
$518$	0	0
$519$	0	0
$520$	−4.00000	−0.175412
$521$	−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
$523$	−20.0000	−0.874539	−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000	−0.874539	−0.437269	+	0.899331i	$0.644054\pi$
$524$	−8.00000	−0.349482
$525$	0	0
$526$	30.0000	1.30806
$527$	−6.00000	−0.261364
$528$	0	0
$529$	26.0000	1.13043
$530$	8.00000	0.347498
$531$	0	0
$532$	0	0
$533$	12.0000	0.519778
$534$	0	0
$535$	−36.0000	−1.55642
$536$	−4.00000	−0.172774
$537$	0	0
$538$	−20.0000	−0.862261
$539$	0	0
$540$	0	0
$541$	16.0000	0.687894	0.343947	−	0.938989i	$-0.388236\pi$
$541$	16.0000	0.687894	0.343947	+	0.938989i	$0.388236\pi$
$542$	8.00000	0.343629
$543$	0	0
$544$	−3.00000	−0.128624
$545$	−8.00000	−0.342682
$546$	0	0
$547$	−11.0000	−0.470326	−0.235163	−	0.971956i	$-0.575562\pi$
$547$	−11.0000	−0.470326	−0.235163	+	0.971956i	$0.575562\pi$
$548$	6.00000	0.256307
$549$	0	0
$550$	1.00000	0.0426401
$551$	−35.0000	−1.49105
$552$	0	0
$553$	0	0
$554$	24.0000	1.01966
$555$	0	0
$556$	17.0000	0.720961
$557$	9.00000	0.381342	0.190671	−	0.981654i	$-0.438934\pi$
$557$	9.00000	0.381342	0.190671	+	0.981654i	$0.438934\pi$
$558$	0	0
$559$	22.0000	0.930501
$560$	0	0
$561$	0	0
$562$	3.00000	0.126547
$563$	−42.0000	−1.77009	−0.885044	−	0.465506i	$-0.845872\pi$
$563$	−42.0000	−1.77009	−0.885044	+	0.465506i	$0.845872\pi$
$564$	0	0
$565$	−4.00000	−0.168281
$566$	24.0000	1.00880
$567$	0	0
$568$	−5.00000	−0.209795
$569$	13.0000	0.544988	0.272494	−	0.962157i	$-0.412151\pi$
$569$	13.0000	0.544988	0.272494	+	0.962157i	$0.412151\pi$
$570$	0	0
$571$	−43.0000	−1.79949	−0.899747	−	0.436412i	$-0.856249\pi$
$571$	−43.0000	−1.79949	−0.899747	+	0.436412i	$0.856249\pi$
$572$	−2.00000	−0.0836242
$573$	0	0
$574$	0	0
$575$	7.00000	0.291920
$576$	0	0
$577$	−18.0000	−0.749350	−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000	−0.749350	−0.374675	+	0.927156i	$0.622246\pi$
$578$	−8.00000	−0.332756
$579$	0	0
$580$	10.0000	0.415227
$581$	0	0
$582$	0	0
$583$	4.00000	0.165663
$584$	−8.00000	−0.331042
$585$	0	0
$586$	−3.00000	−0.123929
$587$	−12.0000	−0.495293	−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000	−0.495293	−0.247647	+	0.968850i	$0.579657\pi$
$588$	0	0
$589$	14.0000	0.576860
$590$	−22.0000	−0.905726
$591$	0	0
$592$	3.00000	0.123299
$593$	−21.0000	−0.862367	−0.431183	−	0.902264i	$-0.641904\pi$
$593$	−21.0000	−0.862367	−0.431183	+	0.902264i	$0.641904\pi$
$594$	0	0
$595$	0	0
$596$	17.0000	0.696347
$597$	0	0
$598$	−14.0000	−0.572503
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	0	0		−	1.00000i	$-0.5\pi$
$601$	0	0			1.00000i	$0.5\pi$
$602$	0	0
$603$	0	0
$604$	−5.00000	−0.203447
$605$	−2.00000	−0.0813116
$606$	0	0
$607$	36.0000	1.46119	0.730597	−	0.682808i	$-0.239242\pi$
$607$	36.0000	1.46119	0.730597	+	0.682808i	$0.239242\pi$
$608$	7.00000	0.283887
$609$	0	0
$610$	−20.0000	−0.809776
$611$	−14.0000	−0.566379
$612$	0	0
$613$	2.00000	0.0807792	0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000	0.0807792	0.0403896	+	0.999184i	$0.487140\pi$
$614$	28.0000	1.12999
$615$	0	0
$616$	0	0
$617$	−20.0000	−0.805170	−0.402585	−	0.915383i	$-0.631888\pi$
$617$	−20.0000	−0.805170	−0.402585	+	0.915383i	$0.631888\pi$
$618$	0	0
$619$	−26.0000	−1.04503	−0.522514	−	0.852631i	$-0.675006\pi$
$619$	−26.0000	−1.04503	−0.522514	+	0.852631i	$0.675006\pi$
$620$	−4.00000	−0.160644
$621$	0	0
$622$	27.0000	1.08260
$623$	0	0
$624$	0	0
$625$	−19.0000	−0.760000
$626$	15.0000	0.599521
$627$	0	0
$628$	1.00000	0.0399043
$629$	−9.00000	−0.358854
$630$	0	0
$631$	−10.0000	−0.398094	−0.199047	−	0.979990i	$-0.563785\pi$
$631$	−10.0000	−0.398094	−0.199047	+	0.979990i	$0.563785\pi$
$632$	−8.00000	−0.318223
$633$	0	0
$634$	30.0000	1.19145
$635$	38.0000	1.50798
$636$	0	0
$637$	0	0
$638$	5.00000	0.197952
$639$	0	0
$640$	−2.00000	−0.0790569
$641$	−12.0000	−0.473972	−0.236986	−	0.971513i	$-0.576159\pi$
$641$	−12.0000	−0.473972	−0.236986	+	0.971513i	$0.576159\pi$
$642$	0	0
$643$	40.0000	1.57745	0.788723	−	0.614749i	$-0.210743\pi$
$643$	40.0000	1.57745	0.788723	+	0.614749i	$0.210743\pi$
$644$	0	0
$645$	0	0
$646$	−21.0000	−0.826234
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	0	0
$649$	−11.0000	−0.431788
$650$	−2.00000	−0.0784465
$651$	0	0
$652$	6.00000	0.234978
$653$	−10.0000	−0.391330	−0.195665	−	0.980671i	$-0.562687\pi$
$653$	−10.0000	−0.391330	−0.195665	+	0.980671i	$0.562687\pi$
$654$	0	0
$655$	16.0000	0.625172
$656$	6.00000	0.234261
$657$	0	0
$658$	0	0
$659$	−20.0000	−0.779089	−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000	−0.779089	−0.389545	+	0.921008i	$0.627368\pi$
$660$	0	0
$661$	−11.0000	−0.427850	−0.213925	−	0.976850i	$-0.568625\pi$
$661$	−11.0000	−0.427850	−0.213925	+	0.976850i	$0.568625\pi$
$662$	−14.0000	−0.544125
$663$	0	0
$664$	14.0000	0.543305
$665$	0	0
$666$	0	0
$667$	35.0000	1.35521
$668$	−10.0000	−0.386912
$669$	0	0
$670$	8.00000	0.309067
$671$	−10.0000	−0.386046
$672$	0	0
$673$	−10.0000	−0.385472	−0.192736	−	0.981251i	$-0.561736\pi$
$673$	−10.0000	−0.385472	−0.192736	+	0.981251i	$0.561736\pi$
$674$	8.00000	0.308148
$675$	0	0
$676$	−9.00000	−0.346154
$677$	−21.0000	−0.807096	−0.403548	−	0.914959i	$-0.632223\pi$
$677$	−21.0000	−0.807096	−0.403548	+	0.914959i	$0.632223\pi$
$678$	0	0
$679$	0	0
$680$	6.00000	0.230089
$681$	0	0
$682$	−2.00000	−0.0765840
$683$	39.0000	1.49229	0.746147	−	0.665782i	$-0.231902\pi$
$683$	39.0000	1.49229	0.746147	+	0.665782i	$0.231902\pi$
$684$	0	0
$685$	−12.0000	−0.458496
$686$	0	0
$687$	0	0
$688$	11.0000	0.419371
$689$	−8.00000	−0.304776
$690$	0	0
$691$	18.0000	0.684752	0.342376	−	0.939563i	$-0.388768\pi$
$691$	18.0000	0.684752	0.342376	+	0.939563i	$0.388768\pi$
$692$	14.0000	0.532200
$693$	0	0
$694$	24.0000	0.911028
$695$	−34.0000	−1.28969
$696$	0	0
$697$	−18.0000	−0.681799
$698$	8.00000	0.302804
$699$	0	0
$700$	0	0
$701$	−27.0000	−1.01978	−0.509888	−	0.860241i	$-0.670313\pi$
$701$	−27.0000	−1.01978	−0.509888	+	0.860241i	$0.670313\pi$
$702$	0	0
$703$	21.0000	0.792030
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	10.0000	0.376355
$707$	0	0
$708$	0	0
$709$	−31.0000	−1.16423	−0.582115	−	0.813107i	$-0.697775\pi$
$709$	−31.0000	−1.16423	−0.582115	+	0.813107i	$0.697775\pi$
$710$	10.0000	0.375293
$711$	0	0
$712$	2.00000	0.0749532
$713$	−14.0000	−0.524304
$714$	0	0
$715$	4.00000	0.149592
$716$	−9.00000	−0.336346
$717$	0	0
$718$	−18.0000	−0.671754
$719$	9.00000	0.335643	0.167822	−	0.985817i	$-0.446327\pi$
$719$	9.00000	0.335643	0.167822	+	0.985817i	$0.446327\pi$
$720$	0	0
$721$	0	0
$722$	30.0000	1.11648
$723$	0	0
$724$	−10.0000	−0.371647
$725$	5.00000	0.185695
$726$	0	0
$727$	−14.0000	−0.519231	−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000	−0.519231	−0.259616	+	0.965712i	$0.583596\pi$
$728$	0	0
$729$	0	0
$730$	16.0000	0.592187
$731$	−33.0000	−1.22055
$732$	0	0
$733$	22.0000	0.812589	0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000	0.812589	0.406294	+	0.913742i	$0.366821\pi$
$734$	0	0
$735$	0	0
$736$	−7.00000	−0.258023
$737$	4.00000	0.147342
$738$	0	0
$739$	20.0000	0.735712	0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000	0.735712	0.367856	+	0.929883i	$0.380092\pi$
$740$	−6.00000	−0.220564
$741$	0	0
$742$	0	0
$743$	−4.00000	−0.146746	−0.0733729	−	0.997305i	$-0.523376\pi$
$743$	−4.00000	−0.146746	−0.0733729	+	0.997305i	$0.523376\pi$
$744$	0	0
$745$	−34.0000	−1.24566
$746$	−22.0000	−0.805477
$747$	0	0
$748$	3.00000	0.109691
$749$	0	0
$750$	0	0
$751$	−40.0000	−1.45962	−0.729810	−	0.683650i	$-0.760392\pi$
$751$	−40.0000	−1.45962	−0.729810	+	0.683650i	$0.760392\pi$
$752$	−7.00000	−0.255264
$753$	0	0
$754$	−10.0000	−0.364179
$755$	10.0000	0.363937
$756$	0	0
$757$	15.0000	0.545184	0.272592	−	0.962130i	$-0.412119\pi$
$757$	15.0000	0.545184	0.272592	+	0.962130i	$0.412119\pi$
$758$	−16.0000	−0.581146
$759$	0	0
$760$	−14.0000	−0.507833
$761$	−30.0000	−1.08750	−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000	−1.08750	−0.543750	+	0.839248i	$0.682996\pi$
$762$	0	0
$763$	0	0
$764$	−8.00000	−0.289430
$765$	0	0
$766$	31.0000	1.12008
$767$	22.0000	0.794374
$768$	0	0
$769$	28.0000	1.00971	0.504853	−	0.863205i	$-0.331547\pi$
$769$	28.0000	1.00971	0.504853	+	0.863205i	$0.331547\pi$
$770$	0	0
$771$	0	0
$772$	24.0000	0.863779
$773$	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
$775$	−2.00000	−0.0718421
$776$	15.0000	0.538469
$777$	0	0
$778$	−6.00000	−0.215110
$779$	42.0000	1.50481
$780$	0	0
$781$	5.00000	0.178914
$782$	21.0000	0.750958
$783$	0	0
$784$	0	0
$785$	−2.00000	−0.0713831
$786$	0	0
$787$	−37.0000	−1.31891	−0.659454	−	0.751745i	$-0.729212\pi$
$787$	−37.0000	−1.31891	−0.659454	+	0.751745i	$0.729212\pi$
$788$	15.0000	0.534353
$789$	0	0
$790$	16.0000	0.569254
$791$	0	0
$792$	0	0
$793$	20.0000	0.710221
$794$	−3.00000	−0.106466
$795$	0	0
$796$	10.0000	0.354441
$797$	−50.0000	−1.77109	−0.885545	−	0.464553i	$-0.846215\pi$
$797$	−50.0000	−1.77109	−0.885545	+	0.464553i	$0.846215\pi$
$798$	0	0
$799$	21.0000	0.742927
$800$	−1.00000	−0.0353553
$801$	0	0
$802$	32.0000	1.12996
$803$	8.00000	0.282314
$804$	0	0
$805$	0	0
$806$	4.00000	0.140894
$807$	0	0
$808$	3.00000	0.105540
$809$	−14.0000	−0.492214	−0.246107	−	0.969243i	$-0.579151\pi$
$809$	−14.0000	−0.492214	−0.246107	+	0.969243i	$0.579151\pi$
$810$	0	0
$811$	−28.0000	−0.983213	−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000	−0.983213	−0.491606	+	0.870817i	$0.663590\pi$
$812$	0	0
$813$	0	0
$814$	−3.00000	−0.105150
$815$	−12.0000	−0.420342
$816$	0	0
$817$	77.0000	2.69389
$818$	32.0000	1.11885
$819$	0	0
$820$	−12.0000	−0.419058
$821$	50.0000	1.74501	0.872506	−	0.488603i	$-0.162493\pi$
$821$	50.0000	1.74501	0.872506	+	0.488603i	$0.162493\pi$
$822$	0	0
$823$	−4.00000	−0.139431	−0.0697156	−	0.997567i	$-0.522209\pi$
$823$	−4.00000	−0.139431	−0.0697156	+	0.997567i	$0.522209\pi$
$824$	−10.0000	−0.348367
$825$	0	0
$826$	0	0
$827$	−10.0000	−0.347734	−0.173867	−	0.984769i	$-0.555626\pi$
$827$	−10.0000	−0.347734	−0.173867	+	0.984769i	$0.555626\pi$
$828$	0	0
$829$	−17.0000	−0.590434	−0.295217	−	0.955430i	$-0.595392\pi$
$829$	−17.0000	−0.590434	−0.295217	+	0.955430i	$0.595392\pi$
$830$	−28.0000	−0.971894
$831$	0	0
$832$	2.00000	0.0693375
$833$	0	0
$834$	0	0
$835$	20.0000	0.692129
$836$	−7.00000	−0.242100
$837$	0	0
$838$	3.00000	0.103633
$839$	24.0000	0.828572	0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000	0.828572	0.414286	+	0.910147i	$0.364031\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	−17.0000	−0.585859
$843$	0	0
$844$	20.0000	0.688428
$845$	18.0000	0.619219
$846$	0	0
$847$	0	0
$848$	−4.00000	−0.137361
$849$	0	0
$850$	3.00000	0.102899
$851$	−21.0000	−0.719871
$852$	0	0
$853$	46.0000	1.57501	0.787505	−	0.616308i	$-0.211372\pi$
$853$	46.0000	1.57501	0.787505	+	0.616308i	$0.211372\pi$
$854$	0	0
$855$	0	0
$856$	18.0000	0.615227
$857$	21.0000	0.717346	0.358673	−	0.933463i	$-0.383229\pi$
$857$	21.0000	0.717346	0.358673	+	0.933463i	$0.383229\pi$
$858$	0	0
$859$	−22.0000	−0.750630	−0.375315	−	0.926897i	$-0.622466\pi$
$859$	−22.0000	−0.750630	−0.375315	+	0.926897i	$0.622466\pi$
$860$	−22.0000	−0.750194
$861$	0	0
$862$	40.0000	1.36241
$863$	−28.0000	−0.953131	−0.476566	−	0.879139i	$-0.658119\pi$
$863$	−28.0000	−0.953131	−0.476566	+	0.879139i	$0.658119\pi$
$864$	0	0
$865$	−28.0000	−0.952029
$866$	5.00000	0.169907
$867$	0	0
$868$	0	0
$869$	8.00000	0.271381
$870$	0	0
$871$	−8.00000	−0.271070
$872$	4.00000	0.135457
$873$	0	0
$874$	−49.0000	−1.65745
$875$	0	0
$876$	0	0
$877$	26.0000	0.877958	0.438979	−	0.898497i	$-0.355340\pi$
$877$	26.0000	0.877958	0.438979	+	0.898497i	$0.355340\pi$
$878$	5.00000	0.168742
$879$	0	0
$880$	2.00000	0.0674200
$881$	36.0000	1.21287	0.606435	−	0.795133i	$-0.292599\pi$
$881$	36.0000	1.21287	0.606435	+	0.795133i	$0.292599\pi$
$882$	0	0
$883$	8.00000	0.269221	0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000	0.269221	0.134611	+	0.990899i	$0.457022\pi$
$884$	−6.00000	−0.201802
$885$	0	0
$886$	41.0000	1.37742
$887$	−20.0000	−0.671534	−0.335767	−	0.941945i	$-0.608996\pi$
$887$	−20.0000	−0.671534	−0.335767	+	0.941945i	$0.608996\pi$
$888$	0	0
$889$	0	0
$890$	−4.00000	−0.134080
$891$	0	0
$892$	−14.0000	−0.468755
$893$	−49.0000	−1.63972
$894$	0	0
$895$	18.0000	0.601674
$896$	0	0
$897$	0	0
$898$	−36.0000	−1.20134
$899$	−10.0000	−0.333519
$900$	0	0
$901$	12.0000	0.399778
$902$	−6.00000	−0.199778
$903$	0	0
$904$	2.00000	0.0665190
$905$	20.0000	0.664822
$906$	0	0
$907$	−24.0000	−0.796907	−0.398453	−	0.917189i	$-0.630453\pi$
$907$	−24.0000	−0.796907	−0.398453	+	0.917189i	$0.630453\pi$
$908$	10.0000	0.331862
$909$	0	0
$910$	0	0
$911$	13.0000	0.430709	0.215355	−	0.976536i	$-0.430909\pi$
$911$	13.0000	0.430709	0.215355	+	0.976536i	$0.430909\pi$
$912$	0	0
$913$	−14.0000	−0.463332
$914$	40.0000	1.32308
$915$	0	0
$916$	−10.0000	−0.330409
$917$	0	0
$918$	0	0
$919$	43.0000	1.41844	0.709220	−	0.704988i	$-0.249047\pi$
$919$	43.0000	1.41844	0.709220	+	0.704988i	$0.249047\pi$
$920$	14.0000	0.461566
$921$	0	0
$922$	13.0000	0.428132
$923$	−10.0000	−0.329154
$924$	0	0
$925$	−3.00000	−0.0986394
$926$	−24.0000	−0.788689
$927$	0	0
$928$	−5.00000	−0.164133
$929$	4.00000	0.131236	0.0656179	−	0.997845i	$-0.479098\pi$
$929$	4.00000	0.131236	0.0656179	+	0.997845i	$0.479098\pi$
$930$	0	0
$931$	0	0
$932$	−9.00000	−0.294805
$933$	0	0
$934$	13.0000	0.425373
$935$	−6.00000	−0.196221
$936$	0	0
$937$	26.0000	0.849383	0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000	0.849383	0.424691	+	0.905338i	$0.360383\pi$
$938$	0	0
$939$	0	0
$940$	14.0000	0.456630
$941$	15.0000	0.488986	0.244493	−	0.969651i	$-0.421378\pi$
$941$	15.0000	0.488986	0.244493	+	0.969651i	$0.421378\pi$
$942$	0	0
$943$	−42.0000	−1.36771
$944$	11.0000	0.358020
$945$	0	0
$946$	−11.0000	−0.357641
$947$	−27.0000	−0.877382	−0.438691	−	0.898638i	$-0.644558\pi$
$947$	−27.0000	−0.877382	−0.438691	+	0.898638i	$0.644558\pi$
$948$	0	0
$949$	−16.0000	−0.519382
$950$	−7.00000	−0.227110
$951$	0	0
$952$	0	0
$953$	−10.0000	−0.323932	−0.161966	−	0.986796i	$-0.551783\pi$
$953$	−10.0000	−0.323932	−0.161966	+	0.986796i	$0.551783\pi$
$954$	0	0
$955$	16.0000	0.517748
$956$	−10.0000	−0.323423
$957$	0	0
$958$	18.0000	0.581554
$959$	0	0
$960$	0	0
$961$	−27.0000	−0.870968
$962$	6.00000	0.193448
$963$	0	0
$964$	−4.00000	−0.128831
$965$	−48.0000	−1.54517
$966$	0	0
$967$	−3.00000	−0.0964735	−0.0482367	−	0.998836i	$-0.515360\pi$
$967$	−3.00000	−0.0964735	−0.0482367	+	0.998836i	$0.515360\pi$
$968$	1.00000	0.0321412
$969$	0	0
$970$	−30.0000	−0.963242
$971$	−36.0000	−1.15529	−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000	−1.15529	−0.577647	+	0.816286i	$0.696029\pi$
$972$	0	0
$973$	0	0
$974$	18.0000	0.576757
$975$	0	0
$976$	10.0000	0.320092
$977$	−44.0000	−1.40768	−0.703842	−	0.710356i	$-0.748534\pi$
$977$	−44.0000	−1.40768	−0.703842	+	0.710356i	$0.748534\pi$
$978$	0	0
$979$	−2.00000	−0.0639203
$980$	0	0
$981$	0	0
$982$	−26.0000	−0.829693
$983$	49.0000	1.56286	0.781429	−	0.623995i	$-0.214491\pi$
$983$	49.0000	1.56286	0.781429	+	0.623995i	$0.214491\pi$
$984$	0	0
$985$	−30.0000	−0.955879
$986$	15.0000	0.477697
$987$	0	0
$988$	14.0000	0.445399
$989$	−77.0000	−2.44846
$990$	0	0
$991$	8.00000	0.254128	0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000	0.254128	0.127064	+	0.991894i	$0.459445\pi$
$992$	2.00000	0.0635001
$993$	0	0
$994$	0	0
$995$	−20.0000	−0.634043
$996$	0	0
$997$	30.0000	0.950110	0.475055	−	0.879956i	$-0.342428\pi$
$997$	30.0000	0.950110	0.475055	+	0.879956i	$0.342428\pi$
$998$	−40.0000	−1.26618
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9702.2.a.bg.1.1		1
3.2	odd	2		9702.2.a.w.1.1		1
7.2	even	3		1386.2.k.i.991.1	yes	2
7.4	even	3		1386.2.k.i.793.1	✓	2
7.6	odd	2		9702.2.a.bx.1.1		1
21.2	odd	6		1386.2.k.k.991.1	yes	2
21.11	odd	6		1386.2.k.k.793.1	yes	2
21.20	even	2		9702.2.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.k.i.793.1	✓	2	7.4	even	3
1386.2.k.i.991.1	yes	2	7.2	even	3
1386.2.k.k.793.1	yes	2	21.11	odd	6
1386.2.k.k.991.1	yes	2	21.2	odd	6
9702.2.a.j.1.1		1	21.20	even	2
9702.2.a.w.1.1		1	3.2	odd	2
9702.2.a.bg.1.1		1	1.1	even	1	trivial
9702.2.a.bx.1.1		1	7.6	odd	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:	\( N \)	\(=\)	\( 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9702.a (trivial)

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