LMFDB - Embedded newform 7938.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7938,2,Mod(1,7938)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7938, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("7938.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7938 = 2 \cdot 3^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7938.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:	$63.3852491245$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	7938.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} +3.00000 q^{5} -1.00000 q^{8} +O(q^{10})$

$q-1.00000 q^{2} +1.00000 q^{4} +3.00000 q^{5} -1.00000 q^{8} -3.00000 q^{10} +3.00000 q^{11} +5.00000 q^{13} +1.00000 q^{16} -3.00000 q^{17} +5.00000 q^{19} +3.00000 q^{20} -3.00000 q^{22} +3.00000 q^{23} +4.00000 q^{25} -5.00000 q^{26} +3.00000 q^{29} -4.00000 q^{31} -1.00000 q^{32} +3.00000 q^{34} -7.00000 q^{37} -5.00000 q^{38} -3.00000 q^{40} +9.00000 q^{41} +11.0000 q^{43} +3.00000 q^{44} -3.00000 q^{46} -4.00000 q^{50} +5.00000 q^{52} +3.00000 q^{53} +9.00000 q^{55} -3.00000 q^{58} -12.0000 q^{59} +2.00000 q^{61} +4.00000 q^{62} +1.00000 q^{64} +15.0000 q^{65} -4.00000 q^{67} -3.00000 q^{68} +11.0000 q^{73} +7.00000 q^{74} +5.00000 q^{76} +8.00000 q^{79} +3.00000 q^{80} -9.00000 q^{82} -3.00000 q^{83} -9.00000 q^{85} -11.0000 q^{86} -3.00000 q^{88} -15.0000 q^{89} +3.00000 q^{92} +15.0000 q^{95} -1.00000 q^{97} +O(q^{100})$

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
$5$	3.00000	1.34164	0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000	1.34164	0.670820	+	0.741620i	$0.265942\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	0	0
$10$	−3.00000	−0.948683
$11$	3.00000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	0	0
$13$	5.00000	1.38675	0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000	1.38675	0.693375	+	0.720577i	$0.256123\pi$
$14$	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
$19$	5.00000	1.14708	0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000	1.14708	0.573539	+	0.819178i	$0.305570\pi$
$20$	3.00000	0.670820
$21$	0	0
$22$	−3.00000	−0.639602
$23$	3.00000	0.625543	0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000	0.625543	0.312772	+	0.949828i	$0.398743\pi$
$24$	0	0
$25$	4.00000	0.800000
$26$	−5.00000	−0.980581
$27$	0	0
$28$	0	0
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	0	0
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	3.00000	0.514496
$35$	0	0
$36$	0	0
$37$	−7.00000	−1.15079	−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000	−1.15079	−0.575396	+	0.817875i	$0.695152\pi$
$38$	−5.00000	−0.811107
$39$	0	0
$40$	−3.00000	−0.474342
$41$	9.00000	1.40556	0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000	1.40556	0.702782	+	0.711405i	$0.251941\pi$
$42$	0	0
$43$	11.0000	1.67748	0.838742	−	0.544529i	$-0.183292\pi$
$43$	11.0000	1.67748	0.838742	+	0.544529i	$0.183292\pi$
$44$	3.00000	0.452267
$45$	0	0
$46$	−3.00000	−0.442326
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	0	0
$50$	−4.00000	−0.565685
$51$	0	0
$52$	5.00000	0.693375
$53$	3.00000	0.412082	0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000	0.412082	0.206041	+	0.978543i	$0.433942\pi$
$54$	0	0
$55$	9.00000	1.21356
$56$	0	0
$57$	0	0
$58$	−3.00000	−0.393919
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	4.00000	0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	15.0000	1.86052
$66$	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
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	11.0000	1.28745	0.643726	−	0.765256i	$-0.277388\pi$
$73$	11.0000	1.28745	0.643726	+	0.765256i	$0.277388\pi$
$74$	7.00000	0.813733
$75$	0	0
$76$	5.00000	0.573539
$77$	0	0
$78$	0	0
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	3.00000	0.335410
$81$	0	0
$82$	−9.00000	−0.993884
$83$	−3.00000	−0.329293	−0.164646	−	0.986353i	$-0.552648\pi$
$83$	−3.00000	−0.329293	−0.164646	+	0.986353i	$0.552648\pi$
$84$	0	0
$85$	−9.00000	−0.976187
$86$	−11.0000	−1.18616
$87$	0	0
$88$	−3.00000	−0.319801
$89$	−15.0000	−1.59000	−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000	−1.59000	−0.794998	+	0.606612i	$0.792528\pi$
$90$	0	0
$91$	0	0
$92$	3.00000	0.312772
$93$	0	0
$94$	0	0
$95$	15.0000	1.53897
$96$	0	0
$97$	−1.00000	−0.101535	−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000	−0.101535	−0.0507673	+	0.998711i	$0.516167\pi$
$98$	0	0
$99$	0	0
$100$	4.00000	0.400000
$101$	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
$103$	5.00000	0.492665	0.246332	−	0.969185i	$-0.420775\pi$
$103$	5.00000	0.492665	0.246332	+	0.969185i	$0.420775\pi$
$104$	−5.00000	−0.490290
$105$	0	0
$106$	−3.00000	−0.291386
$107$	15.0000	1.45010	0.725052	−	0.688694i	$-0.241816\pi$
$107$	15.0000	1.45010	0.725052	+	0.688694i	$0.241816\pi$
$108$	0	0
$109$	−7.00000	−0.670478	−0.335239	−	0.942133i	$-0.608817\pi$
$109$	−7.00000	−0.670478	−0.335239	+	0.942133i	$0.608817\pi$
$110$	−9.00000	−0.858116
$111$	0	0
$112$	0	0
$113$	−15.0000	−1.41108	−0.705541	−	0.708669i	$-0.749296\pi$
$113$	−15.0000	−1.41108	−0.705541	+	0.708669i	$0.749296\pi$
$114$	0	0
$115$	9.00000	0.839254
$116$	3.00000	0.278543
$117$	0	0
$118$	12.0000	1.10469
$119$	0	0
$120$	0	0
$121$	−2.00000	−0.181818
$122$	−2.00000	−0.181071
$123$	0	0
$124$	−4.00000	−0.359211
$125$	−3.00000	−0.268328
$126$	0	0
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	−15.0000	−1.31559
$131$	−3.00000	−0.262111	−0.131056	−	0.991375i	$-0.541837\pi$
$131$	−3.00000	−0.262111	−0.131056	+	0.991375i	$0.541837\pi$
$132$	0	0
$133$	0	0
$134$	4.00000	0.345547
$135$	0	0
$136$	3.00000	0.257248
$137$	−3.00000	−0.256307	−0.128154	−	0.991754i	$-0.540905\pi$
$137$	−3.00000	−0.256307	−0.128154	+	0.991754i	$0.540905\pi$
$138$	0	0
$139$	5.00000	0.424094	0.212047	−	0.977259i	$-0.431987\pi$
$139$	5.00000	0.424094	0.212047	+	0.977259i	$0.431987\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	15.0000	1.25436
$144$	0	0
$145$	9.00000	0.747409
$146$	−11.0000	−0.910366
$147$	0	0
$148$	−7.00000	−0.575396
$149$	3.00000	0.245770	0.122885	−	0.992421i	$-0.460785\pi$
$149$	3.00000	0.245770	0.122885	+	0.992421i	$0.460785\pi$
$150$	0	0
$151$	11.0000	0.895167	0.447584	−	0.894242i	$-0.352285\pi$
$151$	11.0000	0.895167	0.447584	+	0.894242i	$0.352285\pi$
$152$	−5.00000	−0.405554
$153$	0	0
$154$	0	0
$155$	−12.0000	−0.963863
$156$	0	0
$157$	14.0000	1.11732	0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000	1.11732	0.558661	+	0.829396i	$0.311315\pi$
$158$	−8.00000	−0.636446
$159$	0	0
$160$	−3.00000	−0.237171
$161$	0	0
$162$	0	0
$163$	17.0000	1.33154	0.665771	−	0.746156i	$-0.268103\pi$
$163$	17.0000	1.33154	0.665771	+	0.746156i	$0.268103\pi$
$164$	9.00000	0.702782
$165$	0	0
$166$	3.00000	0.232845
$167$	−3.00000	−0.232147	−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000	−0.232147	−0.116073	+	0.993241i	$0.537031\pi$
$168$	0	0
$169$	12.0000	0.923077
$170$	9.00000	0.690268
$171$	0	0
$172$	11.0000	0.838742
$173$	−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
$176$	3.00000	0.226134
$177$	0	0
$178$	15.0000	1.12430
$179$	−3.00000	−0.224231	−0.112115	−	0.993695i	$-0.535763\pi$
$179$	−3.00000	−0.224231	−0.112115	+	0.993695i	$0.535763\pi$
$180$	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
$184$	−3.00000	−0.221163
$185$	−21.0000	−1.54395
$186$	0	0
$187$	−9.00000	−0.658145
$188$	0	0
$189$	0	0
$190$	−15.0000	−1.08821
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	0	0
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	1.00000	0.0717958
$195$	0	0
$196$	0	0
$197$	6.00000	0.427482	0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000	0.427482	0.213741	+	0.976890i	$0.431435\pi$
$198$	0	0
$199$	−7.00000	−0.496217	−0.248108	−	0.968732i	$-0.579809\pi$
$199$	−7.00000	−0.496217	−0.248108	+	0.968732i	$0.579809\pi$
$200$	−4.00000	−0.282843
$201$	0	0
$202$	−3.00000	−0.211079
$203$	0	0
$204$	0	0
$205$	27.0000	1.88576
$206$	−5.00000	−0.348367
$207$	0	0
$208$	5.00000	0.346688
$209$	15.0000	1.03757
$210$	0	0
$211$	5.00000	0.344214	0.172107	−	0.985078i	$-0.444942\pi$
$211$	5.00000	0.344214	0.172107	+	0.985078i	$0.444942\pi$
$212$	3.00000	0.206041
$213$	0	0
$214$	−15.0000	−1.02538
$215$	33.0000	2.25058
$216$	0	0
$217$	0	0
$218$	7.00000	0.474100
$219$	0	0
$220$	9.00000	0.606780
$221$	−15.0000	−1.00901
$222$	0	0
$223$	17.0000	1.13840	0.569202	−	0.822198i	$-0.307252\pi$
$223$	17.0000	1.13840	0.569202	+	0.822198i	$0.307252\pi$
$224$	0	0
$225$	0	0
$226$	15.0000	0.997785
$227$	−9.00000	−0.597351	−0.298675	−	0.954355i	$-0.596545\pi$
$227$	−9.00000	−0.597351	−0.298675	+	0.954355i	$0.596545\pi$
$228$	0	0
$229$	17.0000	1.12339	0.561696	−	0.827344i	$-0.310149\pi$
$229$	17.0000	1.12339	0.561696	+	0.827344i	$0.310149\pi$
$230$	−9.00000	−0.593442
$231$	0	0
$232$	−3.00000	−0.196960
$233$	−27.0000	−1.76883	−0.884414	−	0.466702i	$-0.845442\pi$
$233$	−27.0000	−1.76883	−0.884414	+	0.466702i	$0.845442\pi$
$234$	0	0
$235$	0	0
$236$	−12.0000	−0.781133
$237$	0	0
$238$	0	0
$239$	−27.0000	−1.74648	−0.873242	−	0.487286i	$-0.837987\pi$
$239$	−27.0000	−1.74648	−0.873242	+	0.487286i	$0.837987\pi$
$240$	0	0
$241$	23.0000	1.48156	0.740780	−	0.671748i	$-0.234456\pi$
$241$	23.0000	1.48156	0.740780	+	0.671748i	$0.234456\pi$
$242$	2.00000	0.128565
$243$	0	0
$244$	2.00000	0.128037
$245$	0	0
$246$	0	0
$247$	25.0000	1.59071
$248$	4.00000	0.254000
$249$	0	0
$250$	3.00000	0.189737
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	0	0
$253$	9.00000	0.565825
$254$	16.0000	1.00393
$255$	0	0
$256$	1.00000	0.0625000
$257$	−15.0000	−0.935674	−0.467837	−	0.883815i	$-0.654967\pi$
$257$	−15.0000	−0.935674	−0.467837	+	0.883815i	$0.654967\pi$
$258$	0	0
$259$	0	0
$260$	15.0000	0.930261
$261$	0	0
$262$	3.00000	0.185341
$263$	9.00000	0.554964	0.277482	−	0.960731i	$-0.410500\pi$
$263$	9.00000	0.554964	0.277482	+	0.960731i	$0.410500\pi$
$264$	0	0
$265$	9.00000	0.552866
$266$	0	0
$267$	0	0
$268$	−4.00000	−0.244339
$269$	−21.0000	−1.28039	−0.640196	−	0.768211i	$-0.721147\pi$
$269$	−21.0000	−1.28039	−0.640196	+	0.768211i	$0.721147\pi$
$270$	0	0
$271$	−13.0000	−0.789694	−0.394847	−	0.918747i	$-0.629202\pi$
$271$	−13.0000	−0.789694	−0.394847	+	0.918747i	$0.629202\pi$
$272$	−3.00000	−0.181902
$273$	0	0
$274$	3.00000	0.181237
$275$	12.0000	0.723627
$276$	0	0
$277$	−7.00000	−0.420589	−0.210295	−	0.977638i	$-0.567442\pi$
$277$	−7.00000	−0.420589	−0.210295	+	0.977638i	$0.567442\pi$
$278$	−5.00000	−0.299880
$279$	0	0
$280$	0	0
$281$	−3.00000	−0.178965	−0.0894825	−	0.995988i	$-0.528521\pi$
$281$	−3.00000	−0.178965	−0.0894825	+	0.995988i	$0.528521\pi$
$282$	0	0
$283$	8.00000	0.475551	0.237775	−	0.971320i	$-0.423582\pi$
$283$	8.00000	0.475551	0.237775	+	0.971320i	$0.423582\pi$
$284$	0	0
$285$	0	0
$286$	−15.0000	−0.886969
$287$	0	0
$288$	0	0
$289$	−8.00000	−0.470588
$290$	−9.00000	−0.528498
$291$	0	0
$292$	11.0000	0.643726
$293$	27.0000	1.57736	0.788678	−	0.614806i	$-0.210766\pi$
$293$	27.0000	1.57736	0.788678	+	0.614806i	$0.210766\pi$
$294$	0	0
$295$	−36.0000	−2.09600
$296$	7.00000	0.406867
$297$	0	0
$298$	−3.00000	−0.173785
$299$	15.0000	0.867472
$300$	0	0
$301$	0	0
$302$	−11.0000	−0.632979
$303$	0	0
$304$	5.00000	0.286770
$305$	6.00000	0.343559
$306$	0	0
$307$	−28.0000	−1.59804	−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000	−1.59804	−0.799022	+	0.601302i	$0.794649\pi$
$308$	0	0
$309$	0	0
$310$	12.0000	0.681554
$311$	24.0000	1.36092	0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000	1.36092	0.680458	+	0.732787i	$0.261781\pi$
$312$	0	0
$313$	14.0000	0.791327	0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000	0.791327	0.395663	+	0.918396i	$0.370515\pi$
$314$	−14.0000	−0.790066
$315$	0	0
$316$	8.00000	0.450035
$317$	−30.0000	−1.68497	−0.842484	−	0.538721i	$-0.818908\pi$
$317$	−30.0000	−1.68497	−0.842484	+	0.538721i	$0.818908\pi$
$318$	0	0
$319$	9.00000	0.503903
$320$	3.00000	0.167705
$321$	0	0
$322$	0	0
$323$	−15.0000	−0.834622
$324$	0	0
$325$	20.0000	1.10940
$326$	−17.0000	−0.941543
$327$	0	0
$328$	−9.00000	−0.496942
$329$	0	0
$330$	0	0
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	−3.00000	−0.164646
$333$	0	0
$334$	3.00000	0.164153
$335$	−12.0000	−0.655630
$336$	0	0
$337$	−25.0000	−1.36184	−0.680918	−	0.732359i	$-0.738419\pi$
$337$	−25.0000	−1.36184	−0.680918	+	0.732359i	$0.738419\pi$
$338$	−12.0000	−0.652714
$339$	0	0
$340$	−9.00000	−0.488094
$341$	−12.0000	−0.649836
$342$	0	0
$343$	0	0
$344$	−11.0000	−0.593080
$345$	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
$349$	5.00000	0.267644	0.133822	−	0.991005i	$-0.457275\pi$
$349$	5.00000	0.267644	0.133822	+	0.991005i	$0.457275\pi$
$350$	0	0
$351$	0	0
$352$	−3.00000	−0.159901
$353$	9.00000	0.479022	0.239511	−	0.970894i	$-0.423013\pi$
$353$	9.00000	0.479022	0.239511	+	0.970894i	$0.423013\pi$
$354$	0	0
$355$	0	0
$356$	−15.0000	−0.794998
$357$	0	0
$358$	3.00000	0.158555
$359$	−15.0000	−0.791670	−0.395835	−	0.918322i	$-0.629545\pi$
$359$	−15.0000	−0.791670	−0.395835	+	0.918322i	$0.629545\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	10.0000	0.525588
$363$	0	0
$364$	0	0
$365$	33.0000	1.72730
$366$	0	0
$367$	−1.00000	−0.0521996	−0.0260998	−	0.999659i	$-0.508309\pi$
$367$	−1.00000	−0.0521996	−0.0260998	+	0.999659i	$0.508309\pi$
$368$	3.00000	0.156386
$369$	0	0
$370$	21.0000	1.09174
$371$	0	0
$372$	0	0
$373$	17.0000	0.880227	0.440113	−	0.897942i	$-0.354938\pi$
$373$	17.0000	0.880227	0.440113	+	0.897942i	$0.354938\pi$
$374$	9.00000	0.465379
$375$	0	0
$376$	0	0
$377$	15.0000	0.772539
$378$	0	0
$379$	−16.0000	−0.821865	−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000	−0.821865	−0.410932	+	0.911666i	$0.634797\pi$
$380$	15.0000	0.769484
$381$	0	0
$382$	12.0000	0.613973
$383$	15.0000	0.766464	0.383232	−	0.923652i	$-0.374811\pi$
$383$	15.0000	0.766464	0.383232	+	0.923652i	$0.374811\pi$
$384$	0	0
$385$	0	0
$386$	−14.0000	−0.712581
$387$	0	0
$388$	−1.00000	−0.0507673
$389$	−9.00000	−0.456318	−0.228159	−	0.973624i	$-0.573271\pi$
$389$	−9.00000	−0.456318	−0.228159	+	0.973624i	$0.573271\pi$
$390$	0	0
$391$	−9.00000	−0.455150
$392$	0	0
$393$	0	0
$394$	−6.00000	−0.302276
$395$	24.0000	1.20757
$396$	0	0
$397$	29.0000	1.45547	0.727734	−	0.685859i	$-0.240573\pi$
$397$	29.0000	1.45547	0.727734	+	0.685859i	$0.240573\pi$
$398$	7.00000	0.350878
$399$	0	0
$400$	4.00000	0.200000
$401$	−27.0000	−1.34832	−0.674158	−	0.738587i	$-0.735493\pi$
$401$	−27.0000	−1.34832	−0.674158	+	0.738587i	$0.735493\pi$
$402$	0	0
$403$	−20.0000	−0.996271
$404$	3.00000	0.149256
$405$	0	0
$406$	0	0
$407$	−21.0000	−1.04093
$408$	0	0
$409$	−22.0000	−1.08783	−0.543915	−	0.839140i	$-0.683059\pi$
$409$	−22.0000	−1.08783	−0.543915	+	0.839140i	$0.683059\pi$
$410$	−27.0000	−1.33343
$411$	0	0
$412$	5.00000	0.246332
$413$	0	0
$414$	0	0
$415$	−9.00000	−0.441793
$416$	−5.00000	−0.245145
$417$	0	0
$418$	−15.0000	−0.733674
$419$	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
$421$	−31.0000	−1.51085	−0.755424	−	0.655237i	$-0.772569\pi$
$421$	−31.0000	−1.51085	−0.755424	+	0.655237i	$0.772569\pi$
$422$	−5.00000	−0.243396
$423$	0	0
$424$	−3.00000	−0.145693
$425$	−12.0000	−0.582086
$426$	0	0
$427$	0	0
$428$	15.0000	0.725052
$429$	0	0
$430$	−33.0000	−1.59140
$431$	3.00000	0.144505	0.0722525	−	0.997386i	$-0.476981\pi$
$431$	3.00000	0.144505	0.0722525	+	0.997386i	$0.476981\pi$
$432$	0	0
$433$	14.0000	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$434$	0	0
$435$	0	0
$436$	−7.00000	−0.335239
$437$	15.0000	0.717547
$438$	0	0
$439$	8.00000	0.381819	0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000	0.381819	0.190910	+	0.981608i	$0.438856\pi$
$440$	−9.00000	−0.429058
$441$	0	0
$442$	15.0000	0.713477
$443$	0	0		−	1.00000i	$-0.5\pi$
$443$	0	0			1.00000i	$0.5\pi$
$444$	0	0
$445$	−45.0000	−2.13320
$446$	−17.0000	−0.804973
$447$	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
$451$	27.0000	1.27138
$452$	−15.0000	−0.705541
$453$	0	0
$454$	9.00000	0.422391
$455$	0	0
$456$	0	0
$457$	−34.0000	−1.59045	−0.795226	−	0.606313i	$-0.792648\pi$
$457$	−34.0000	−1.59045	−0.795226	+	0.606313i	$0.792648\pi$
$458$	−17.0000	−0.794358
$459$	0	0
$460$	9.00000	0.419627
$461$	−9.00000	−0.419172	−0.209586	−	0.977790i	$-0.567212\pi$
$461$	−9.00000	−0.419172	−0.209586	+	0.977790i	$0.567212\pi$
$462$	0	0
$463$	35.0000	1.62659	0.813294	−	0.581853i	$-0.197672\pi$
$463$	35.0000	1.62659	0.813294	+	0.581853i	$0.197672\pi$
$464$	3.00000	0.139272
$465$	0	0
$466$	27.0000	1.25075
$467$	3.00000	0.138823	0.0694117	−	0.997588i	$-0.477888\pi$
$467$	3.00000	0.138823	0.0694117	+	0.997588i	$0.477888\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	12.0000	0.552345
$473$	33.0000	1.51734
$474$	0	0
$475$	20.0000	0.917663
$476$	0	0
$477$	0	0
$478$	27.0000	1.23495
$479$	9.00000	0.411220	0.205610	−	0.978634i	$-0.434082\pi$
$479$	9.00000	0.411220	0.205610	+	0.978634i	$0.434082\pi$
$480$	0	0
$481$	−35.0000	−1.59586
$482$	−23.0000	−1.04762
$483$	0	0
$484$	−2.00000	−0.0909091
$485$	−3.00000	−0.136223
$486$	0	0
$487$	−31.0000	−1.40474	−0.702372	−	0.711810i	$-0.747876\pi$
$487$	−31.0000	−1.40474	−0.702372	+	0.711810i	$0.747876\pi$
$488$	−2.00000	−0.0905357
$489$	0	0
$490$	0	0
$491$	39.0000	1.76005	0.880023	−	0.474932i	$-0.157527\pi$
$491$	39.0000	1.76005	0.880023	+	0.474932i	$0.157527\pi$
$492$	0	0
$493$	−9.00000	−0.405340
$494$	−25.0000	−1.12480
$495$	0	0
$496$	−4.00000	−0.179605
$497$	0	0
$498$	0	0
$499$	11.0000	0.492428	0.246214	−	0.969216i	$-0.420813\pi$
$499$	11.0000	0.492428	0.246214	+	0.969216i	$0.420813\pi$
$500$	−3.00000	−0.134164
$501$	0	0
$502$	12.0000	0.535586
$503$	12.0000	0.535054	0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000	0.535054	0.267527	+	0.963550i	$0.413794\pi$
$504$	0	0
$505$	9.00000	0.400495
$506$	−9.00000	−0.400099
$507$	0	0
$508$	−16.0000	−0.709885
$509$	27.0000	1.19675	0.598377	−	0.801215i	$-0.295813\pi$
$509$	27.0000	1.19675	0.598377	+	0.801215i	$0.295813\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	15.0000	0.661622
$515$	15.0000	0.660979
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	−15.0000	−0.657794
$521$	−3.00000	−0.131432	−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000	−0.131432	−0.0657162	+	0.997838i	$0.520933\pi$
$522$	0	0
$523$	−7.00000	−0.306089	−0.153044	−	0.988219i	$-0.548908\pi$
$523$	−7.00000	−0.306089	−0.153044	+	0.988219i	$0.548908\pi$
$524$	−3.00000	−0.131056
$525$	0	0
$526$	−9.00000	−0.392419
$527$	12.0000	0.522728
$528$	0	0
$529$	−14.0000	−0.608696
$530$	−9.00000	−0.390935
$531$	0	0
$532$	0	0
$533$	45.0000	1.94917
$534$	0	0
$535$	45.0000	1.94552
$536$	4.00000	0.172774
$537$	0	0
$538$	21.0000	0.905374
$539$	0	0
$540$	0	0
$541$	17.0000	0.730887	0.365444	−	0.930834i	$-0.380917\pi$
$541$	17.0000	0.730887	0.365444	+	0.930834i	$0.380917\pi$
$542$	13.0000	0.558398
$543$	0	0
$544$	3.00000	0.128624
$545$	−21.0000	−0.899541
$546$	0	0
$547$	11.0000	0.470326	0.235163	−	0.971956i	$-0.424438\pi$
$547$	11.0000	0.470326	0.235163	+	0.971956i	$0.424438\pi$
$548$	−3.00000	−0.128154
$549$	0	0
$550$	−12.0000	−0.511682
$551$	15.0000	0.639021
$552$	0	0
$553$	0	0
$554$	7.00000	0.297402
$555$	0	0
$556$	5.00000	0.212047
$557$	3.00000	0.127114	0.0635570	−	0.997978i	$-0.479756\pi$
$557$	3.00000	0.127114	0.0635570	+	0.997978i	$0.479756\pi$
$558$	0	0
$559$	55.0000	2.32625
$560$	0	0
$561$	0	0
$562$	3.00000	0.126547
$563$	12.0000	0.505740	0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000	0.505740	0.252870	+	0.967500i	$0.418626\pi$
$564$	0	0
$565$	−45.0000	−1.89316
$566$	−8.00000	−0.336265
$567$	0	0
$568$	0	0
$569$	−30.0000	−1.25767	−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000	−1.25767	−0.628833	+	0.777541i	$0.716467\pi$
$570$	0	0
$571$	20.0000	0.836974	0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000	0.836974	0.418487	+	0.908223i	$0.362561\pi$
$572$	15.0000	0.627182
$573$	0	0
$574$	0	0
$575$	12.0000	0.500435
$576$	0	0
$577$	11.0000	0.457936	0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000	0.457936	0.228968	+	0.973434i	$0.426465\pi$
$578$	8.00000	0.332756
$579$	0	0
$580$	9.00000	0.373705
$581$	0	0
$582$	0	0
$583$	9.00000	0.372742
$584$	−11.0000	−0.455183
$585$	0	0
$586$	−27.0000	−1.11536
$587$	33.0000	1.36206	0.681028	−	0.732257i	$-0.261533\pi$
$587$	33.0000	1.36206	0.681028	+	0.732257i	$0.261533\pi$
$588$	0	0
$589$	−20.0000	−0.824086
$590$	36.0000	1.48210
$591$	0	0
$592$	−7.00000	−0.287698
$593$	21.0000	0.862367	0.431183	−	0.902264i	$-0.358096\pi$
$593$	21.0000	0.862367	0.431183	+	0.902264i	$0.358096\pi$
$594$	0	0
$595$	0	0
$596$	3.00000	0.122885
$597$	0	0
$598$	−15.0000	−0.613396
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	−1.00000	−0.0407909	−0.0203954	−	0.999792i	$-0.506493\pi$
$601$	−1.00000	−0.0407909	−0.0203954	+	0.999792i	$0.506493\pi$
$602$	0	0
$603$	0	0
$604$	11.0000	0.447584
$605$	−6.00000	−0.243935
$606$	0	0
$607$	−43.0000	−1.74532	−0.872658	−	0.488332i	$-0.837606\pi$
$607$	−43.0000	−1.74532	−0.872658	+	0.488332i	$0.837606\pi$
$608$	−5.00000	−0.202777
$609$	0	0
$610$	−6.00000	−0.242933
$611$	0	0
$612$	0	0
$613$	−31.0000	−1.25208	−0.626039	−	0.779792i	$-0.715325\pi$
$613$	−31.0000	−1.25208	−0.626039	+	0.779792i	$0.715325\pi$
$614$	28.0000	1.12999
$615$	0	0
$616$	0	0
$617$	−3.00000	−0.120775	−0.0603877	−	0.998175i	$-0.519234\pi$
$617$	−3.00000	−0.120775	−0.0603877	+	0.998175i	$0.519234\pi$
$618$	0	0
$619$	−19.0000	−0.763674	−0.381837	−	0.924230i	$-0.624709\pi$
$619$	−19.0000	−0.763674	−0.381837	+	0.924230i	$0.624709\pi$
$620$	−12.0000	−0.481932
$621$	0	0
$622$	−24.0000	−0.962312
$623$	0	0
$624$	0	0
$625$	−29.0000	−1.16000
$626$	−14.0000	−0.559553
$627$	0	0
$628$	14.0000	0.558661
$629$	21.0000	0.837325
$630$	0	0
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	−8.00000	−0.318223
$633$	0	0
$634$	30.0000	1.19145
$635$	−48.0000	−1.90482
$636$	0	0
$637$	0	0
$638$	−9.00000	−0.356313
$639$	0	0
$640$	−3.00000	−0.118585
$641$	45.0000	1.77739	0.888697	−	0.458496i	$-0.151612\pi$
$641$	45.0000	1.77739	0.888697	+	0.458496i	$0.151612\pi$
$642$	0	0
$643$	29.0000	1.14365	0.571824	−	0.820376i	$-0.306236\pi$
$643$	29.0000	1.14365	0.571824	+	0.820376i	$0.306236\pi$
$644$	0	0
$645$	0	0
$646$	15.0000	0.590167
$647$	3.00000	0.117942	0.0589711	−	0.998260i	$-0.481218\pi$
$647$	3.00000	0.117942	0.0589711	+	0.998260i	$0.481218\pi$
$648$	0	0
$649$	−36.0000	−1.41312
$650$	−20.0000	−0.784465
$651$	0	0
$652$	17.0000	0.665771
$653$	−9.00000	−0.352197	−0.176099	−	0.984373i	$-0.556348\pi$
$653$	−9.00000	−0.352197	−0.176099	+	0.984373i	$0.556348\pi$
$654$	0	0
$655$	−9.00000	−0.351659
$656$	9.00000	0.351391
$657$	0	0
$658$	0	0
$659$	−39.0000	−1.51922	−0.759612	−	0.650376i	$-0.774611\pi$
$659$	−39.0000	−1.51922	−0.759612	+	0.650376i	$0.774611\pi$
$660$	0	0
$661$	14.0000	0.544537	0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000	0.544537	0.272268	+	0.962221i	$0.412226\pi$
$662$	−20.0000	−0.777322
$663$	0	0
$664$	3.00000	0.116423
$665$	0	0
$666$	0	0
$667$	9.00000	0.348481
$668$	−3.00000	−0.116073
$669$	0	0
$670$	12.0000	0.463600
$671$	6.00000	0.231627
$672$	0	0
$673$	11.0000	0.424019	0.212009	−	0.977268i	$-0.431999\pi$
$673$	11.0000	0.424019	0.212009	+	0.977268i	$0.431999\pi$
$674$	25.0000	0.962964
$675$	0	0
$676$	12.0000	0.461538
$677$	−6.00000	−0.230599	−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000	−0.230599	−0.115299	+	0.993331i	$0.536783\pi$
$678$	0	0
$679$	0	0
$680$	9.00000	0.345134
$681$	0	0
$682$	12.0000	0.459504
$683$	33.0000	1.26271	0.631355	−	0.775494i	$-0.282499\pi$
$683$	33.0000	1.26271	0.631355	+	0.775494i	$0.282499\pi$
$684$	0	0
$685$	−9.00000	−0.343872
$686$	0	0
$687$	0	0
$688$	11.0000	0.419371
$689$	15.0000	0.571454
$690$	0	0
$691$	20.0000	0.760836	0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000	0.760836	0.380418	+	0.924815i	$0.375780\pi$
$692$	−6.00000	−0.228086
$693$	0	0
$694$	−12.0000	−0.455514
$695$	15.0000	0.568982
$696$	0	0
$697$	−27.0000	−1.02270
$698$	−5.00000	−0.189253
$699$	0	0
$700$	0	0
$701$	−6.00000	−0.226617	−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000	−0.226617	−0.113308	+	0.993560i	$0.536145\pi$
$702$	0	0
$703$	−35.0000	−1.32005
$704$	3.00000	0.113067
$705$	0	0
$706$	−9.00000	−0.338719
$707$	0	0
$708$	0	0
$709$	−10.0000	−0.375558	−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000	−0.375558	−0.187779	+	0.982211i	$0.560129\pi$
$710$	0	0
$711$	0	0
$712$	15.0000	0.562149
$713$	−12.0000	−0.449404
$714$	0	0
$715$	45.0000	1.68290
$716$	−3.00000	−0.112115
$717$	0	0
$718$	15.0000	0.559795
$719$	−39.0000	−1.45445	−0.727227	−	0.686397i	$-0.759191\pi$
$719$	−39.0000	−1.45445	−0.727227	+	0.686397i	$0.759191\pi$
$720$	0	0
$721$	0	0
$722$	−6.00000	−0.223297
$723$	0	0
$724$	−10.0000	−0.371647
$725$	12.0000	0.445669
$726$	0	0
$727$	5.00000	0.185440	0.0927199	−	0.995692i	$-0.470444\pi$
$727$	5.00000	0.185440	0.0927199	+	0.995692i	$0.470444\pi$
$728$	0	0
$729$	0	0
$730$	−33.0000	−1.22138
$731$	−33.0000	−1.22055
$732$	0	0
$733$	41.0000	1.51437	0.757185	−	0.653201i	$-0.226574\pi$
$733$	41.0000	1.51437	0.757185	+	0.653201i	$0.226574\pi$
$734$	1.00000	0.0369107
$735$	0	0
$736$	−3.00000	−0.110581
$737$	−12.0000	−0.442026
$738$	0	0
$739$	47.0000	1.72892	0.864461	−	0.502699i	$-0.167660\pi$
$739$	47.0000	1.72892	0.864461	+	0.502699i	$0.167660\pi$
$740$	−21.0000	−0.771975
$741$	0	0
$742$	0	0
$743$	−3.00000	−0.110059	−0.0550297	−	0.998485i	$-0.517525\pi$
$743$	−3.00000	−0.110059	−0.0550297	+	0.998485i	$0.517525\pi$
$744$	0	0
$745$	9.00000	0.329734
$746$	−17.0000	−0.622414
$747$	0	0
$748$	−9.00000	−0.329073
$749$	0	0
$750$	0	0
$751$	29.0000	1.05823	0.529113	−	0.848552i	$-0.322525\pi$
$751$	29.0000	1.05823	0.529113	+	0.848552i	$0.322525\pi$
$752$	0	0
$753$	0	0
$754$	−15.0000	−0.546268
$755$	33.0000	1.20099
$756$	0	0
$757$	14.0000	0.508839	0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000	0.508839	0.254419	+	0.967094i	$0.418116\pi$
$758$	16.0000	0.581146
$759$	0	0
$760$	−15.0000	−0.544107
$761$	−3.00000	−0.108750	−0.0543750	−	0.998521i	$-0.517317\pi$
$761$	−3.00000	−0.108750	−0.0543750	+	0.998521i	$0.517317\pi$
$762$	0	0
$763$	0	0
$764$	−12.0000	−0.434145
$765$	0	0
$766$	−15.0000	−0.541972
$767$	−60.0000	−2.16647
$768$	0	0
$769$	−1.00000	−0.0360609	−0.0180305	−	0.999837i	$-0.505740\pi$
$769$	−1.00000	−0.0360609	−0.0180305	+	0.999837i	$0.505740\pi$
$770$	0	0
$771$	0	0
$772$	14.0000	0.503871
$773$	−21.0000	−0.755318	−0.377659	−	0.925945i	$-0.623271\pi$
$773$	−21.0000	−0.755318	−0.377659	+	0.925945i	$0.623271\pi$
$774$	0	0
$775$	−16.0000	−0.574737
$776$	1.00000	0.0358979
$777$	0	0
$778$	9.00000	0.322666
$779$	45.0000	1.61229
$780$	0	0
$781$	0	0
$782$	9.00000	0.321839
$783$	0	0
$784$	0	0
$785$	42.0000	1.49904
$786$	0	0
$787$	44.0000	1.56843	0.784215	−	0.620489i	$-0.213066\pi$
$787$	44.0000	1.56843	0.784215	+	0.620489i	$0.213066\pi$
$788$	6.00000	0.213741
$789$	0	0
$790$	−24.0000	−0.853882
$791$	0	0
$792$	0	0
$793$	10.0000	0.355110
$794$	−29.0000	−1.02917
$795$	0	0
$796$	−7.00000	−0.248108
$797$	27.0000	0.956389	0.478195	−	0.878254i	$-0.341291\pi$
$797$	27.0000	0.956389	0.478195	+	0.878254i	$0.341291\pi$
$798$	0	0
$799$	0	0
$800$	−4.00000	−0.141421
$801$	0	0
$802$	27.0000	0.953403
$803$	33.0000	1.16454
$804$	0	0
$805$	0	0
$806$	20.0000	0.704470
$807$	0	0
$808$	−3.00000	−0.105540
$809$	−39.0000	−1.37117	−0.685583	−	0.727994i	$-0.740453\pi$
$809$	−39.0000	−1.37117	−0.685583	+	0.727994i	$0.740453\pi$
$810$	0	0
$811$	20.0000	0.702295	0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000	0.702295	0.351147	+	0.936320i	$0.385792\pi$
$812$	0	0
$813$	0	0
$814$	21.0000	0.736050
$815$	51.0000	1.78645
$816$	0	0
$817$	55.0000	1.92421
$818$	22.0000	0.769212
$819$	0	0
$820$	27.0000	0.942881
$821$	54.0000	1.88461	0.942306	−	0.334751i	$-0.108652\pi$
$821$	54.0000	1.88461	0.942306	+	0.334751i	$0.108652\pi$
$822$	0	0
$823$	−40.0000	−1.39431	−0.697156	−	0.716919i	$-0.745552\pi$
$823$	−40.0000	−1.39431	−0.697156	+	0.716919i	$0.745552\pi$
$824$	−5.00000	−0.174183
$825$	0	0
$826$	0	0
$827$	24.0000	0.834562	0.417281	−	0.908778i	$-0.362983\pi$
$827$	24.0000	0.834562	0.417281	+	0.908778i	$0.362983\pi$
$828$	0	0
$829$	41.0000	1.42399	0.711994	−	0.702185i	$-0.247792\pi$
$829$	41.0000	1.42399	0.711994	+	0.702185i	$0.247792\pi$
$830$	9.00000	0.312395
$831$	0	0
$832$	5.00000	0.173344
$833$	0	0
$834$	0	0
$835$	−9.00000	−0.311458
$836$	15.0000	0.518786
$837$	0	0
$838$	−3.00000	−0.103633
$839$	39.0000	1.34643	0.673215	−	0.739447i	$-0.264913\pi$
$839$	39.0000	1.34643	0.673215	+	0.739447i	$0.264913\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	31.0000	1.06833
$843$	0	0
$844$	5.00000	0.172107
$845$	36.0000	1.23844
$846$	0	0
$847$	0	0
$848$	3.00000	0.103020
$849$	0	0
$850$	12.0000	0.411597
$851$	−21.0000	−0.719871
$852$	0	0
$853$	17.0000	0.582069	0.291034	−	0.956713i	$-0.406001\pi$
$853$	17.0000	0.582069	0.291034	+	0.956713i	$0.406001\pi$
$854$	0	0
$855$	0	0
$856$	−15.0000	−0.512689
$857$	33.0000	1.12726	0.563629	−	0.826028i	$-0.309405\pi$
$857$	33.0000	1.12726	0.563629	+	0.826028i	$0.309405\pi$
$858$	0	0
$859$	11.0000	0.375315	0.187658	−	0.982235i	$-0.439910\pi$
$859$	11.0000	0.375315	0.187658	+	0.982235i	$0.439910\pi$
$860$	33.0000	1.12529
$861$	0	0
$862$	−3.00000	−0.102180
$863$	−15.0000	−0.510606	−0.255303	−	0.966861i	$-0.582175\pi$
$863$	−15.0000	−0.510606	−0.255303	+	0.966861i	$0.582175\pi$
$864$	0	0
$865$	−18.0000	−0.612018
$866$	−14.0000	−0.475739
$867$	0	0
$868$	0	0
$869$	24.0000	0.814144
$870$	0	0
$871$	−20.0000	−0.677674
$872$	7.00000	0.237050
$873$	0	0
$874$	−15.0000	−0.507383
$875$	0	0
$876$	0	0
$877$	−43.0000	−1.45201	−0.726003	−	0.687691i	$-0.758624\pi$
$877$	−43.0000	−1.45201	−0.726003	+	0.687691i	$0.758624\pi$
$878$	−8.00000	−0.269987
$879$	0	0
$880$	9.00000	0.303390
$881$	−6.00000	−0.202145	−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000	−0.202145	−0.101073	+	0.994879i	$0.532227\pi$
$882$	0	0
$883$	−4.00000	−0.134611	−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000	−0.134611	−0.0673054	+	0.997732i	$0.521440\pi$
$884$	−15.0000	−0.504505
$885$	0	0
$886$	0	0
$887$	39.0000	1.30949	0.654746	−	0.755849i	$-0.272776\pi$
$887$	39.0000	1.30949	0.654746	+	0.755849i	$0.272776\pi$
$888$	0	0
$889$	0	0
$890$	45.0000	1.50840
$891$	0	0
$892$	17.0000	0.569202
$893$	0	0
$894$	0	0
$895$	−9.00000	−0.300837
$896$	0	0
$897$	0	0
$898$	30.0000	1.00111
$899$	−12.0000	−0.400222
$900$	0	0
$901$	−9.00000	−0.299833
$902$	−27.0000	−0.899002
$903$	0	0
$904$	15.0000	0.498893
$905$	−30.0000	−0.997234
$906$	0	0
$907$	17.0000	0.564476	0.282238	−	0.959344i	$-0.408923\pi$
$907$	17.0000	0.564476	0.282238	+	0.959344i	$0.408923\pi$
$908$	−9.00000	−0.298675
$909$	0	0
$910$	0	0
$911$	−9.00000	−0.298183	−0.149092	−	0.988823i	$-0.547635\pi$
$911$	−9.00000	−0.298183	−0.149092	+	0.988823i	$0.547635\pi$
$912$	0	0
$913$	−9.00000	−0.297857
$914$	34.0000	1.12462
$915$	0	0
$916$	17.0000	0.561696
$917$	0	0
$918$	0	0
$919$	−1.00000	−0.0329870	−0.0164935	−	0.999864i	$-0.505250\pi$
$919$	−1.00000	−0.0329870	−0.0164935	+	0.999864i	$0.505250\pi$
$920$	−9.00000	−0.296721
$921$	0	0
$922$	9.00000	0.296399
$923$	0	0
$924$	0	0
$925$	−28.0000	−0.920634
$926$	−35.0000	−1.15017
$927$	0	0
$928$	−3.00000	−0.0984798
$929$	18.0000	0.590561	0.295280	−	0.955411i	$-0.404587\pi$
$929$	18.0000	0.590561	0.295280	+	0.955411i	$0.404587\pi$
$930$	0	0
$931$	0	0
$932$	−27.0000	−0.884414
$933$	0	0
$934$	−3.00000	−0.0981630
$935$	−27.0000	−0.882994
$936$	0	0
$937$	−34.0000	−1.11073	−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000	−1.11073	−0.555366	+	0.831606i	$0.687422\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	−54.0000	−1.76035	−0.880175	−	0.474650i	$-0.842575\pi$
$941$	−54.0000	−1.76035	−0.880175	+	0.474650i	$0.842575\pi$
$942$	0	0
$943$	27.0000	0.879241
$944$	−12.0000	−0.390567
$945$	0	0
$946$	−33.0000	−1.07292
$947$	12.0000	0.389948	0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000	0.389948	0.194974	+	0.980808i	$0.437538\pi$
$948$	0	0
$949$	55.0000	1.78538
$950$	−20.0000	−0.648886
$951$	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
$955$	−36.0000	−1.16493
$956$	−27.0000	−0.873242
$957$	0	0
$958$	−9.00000	−0.290777
$959$	0	0
$960$	0	0
$961$	−15.0000	−0.483871
$962$	35.0000	1.12845
$963$	0	0
$964$	23.0000	0.740780
$965$	42.0000	1.35203
$966$	0	0
$967$	−49.0000	−1.57573	−0.787867	−	0.615846i	$-0.788815\pi$
$967$	−49.0000	−1.57573	−0.787867	+	0.615846i	$0.788815\pi$
$968$	2.00000	0.0642824
$969$	0	0
$970$	3.00000	0.0963242
$971$	27.0000	0.866471	0.433236	−	0.901281i	$-0.357372\pi$
$971$	27.0000	0.866471	0.433236	+	0.901281i	$0.357372\pi$
$972$	0	0
$973$	0	0
$974$	31.0000	0.993304
$975$	0	0
$976$	2.00000	0.0640184
$977$	−6.00000	−0.191957	−0.0959785	−	0.995383i	$-0.530598\pi$
$977$	−6.00000	−0.191957	−0.0959785	+	0.995383i	$0.530598\pi$
$978$	0	0
$979$	−45.0000	−1.43821
$980$	0	0
$981$	0	0
$982$	−39.0000	−1.24454
$983$	21.0000	0.669796	0.334898	−	0.942254i	$-0.391298\pi$
$983$	21.0000	0.669796	0.334898	+	0.942254i	$0.391298\pi$
$984$	0	0
$985$	18.0000	0.573528
$986$	9.00000	0.286618
$987$	0	0
$988$	25.0000	0.795356
$989$	33.0000	1.04934
$990$	0	0
$991$	29.0000	0.921215	0.460608	−	0.887604i	$-0.347632\pi$
$991$	29.0000	0.921215	0.460608	+	0.887604i	$0.347632\pi$
$992$	4.00000	0.127000
$993$	0	0
$994$	0	0
$995$	−21.0000	−0.665745
$996$	0	0
$997$	41.0000	1.29848	0.649242	−	0.760582i	$-0.275086\pi$
$997$	41.0000	1.29848	0.649242	+	0.760582i	$0.275086\pi$
$998$	−11.0000	−0.348199
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7938.2.a.o.1.1		1
3.2	odd	2		7938.2.a.r.1.1		1
7.2	even	3		1134.2.g.f.487.1		2
7.4	even	3		1134.2.g.f.163.1		2
7.6	odd	2		7938.2.a.c.1.1		1
9.2	odd	6		882.2.f.e.589.1		2
9.4	even	3		2646.2.f.e.883.1		2
9.5	odd	6		882.2.f.e.295.1		2
9.7	even	3		2646.2.f.e.1765.1		2
21.2	odd	6		1134.2.g.d.487.1		2
21.11	odd	6		1134.2.g.d.163.1		2
21.20	even	2		7938.2.a.bd.1.1		1
63.2	odd	6		126.2.h.a.67.1	yes	2
63.4	even	3		378.2.h.b.289.1		2
63.5	even	6		882.2.e.h.655.1		2
63.11	odd	6		126.2.e.b.121.1	yes	2
63.13	odd	6		2646.2.f.i.883.1		2
63.16	even	3		378.2.h.b.361.1		2
63.20	even	6		882.2.f.a.589.1		2
63.23	odd	6		126.2.e.b.25.1	✓	2
63.25	even	3		378.2.e.a.37.1		2
63.31	odd	6		2646.2.h.f.667.1		2
63.32	odd	6		126.2.h.a.79.1	yes	2
63.34	odd	6		2646.2.f.i.1765.1		2
63.38	even	6		882.2.e.h.373.1		2
63.40	odd	6		2646.2.e.e.2125.1		2
63.41	even	6		882.2.f.a.295.1		2
63.47	even	6		882.2.h.e.67.1		2
63.52	odd	6		2646.2.e.e.1549.1		2
63.58	even	3		378.2.e.a.235.1		2
63.59	even	6		882.2.h.e.79.1		2
63.61	odd	6		2646.2.h.f.361.1		2
252.11	even	6		1008.2.q.e.625.1		2
252.23	even	6		1008.2.q.e.529.1		2
252.67	odd	6		3024.2.t.f.289.1		2
252.79	odd	6		3024.2.t.f.1873.1		2
252.95	even	6		1008.2.t.c.961.1		2
252.151	odd	6		3024.2.q.a.2305.1		2
252.191	even	6		1008.2.t.c.193.1		2
252.247	odd	6		3024.2.q.a.2881.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.b.25.1	✓	2	63.23	odd	6
126.2.e.b.121.1	yes	2	63.11	odd	6
126.2.h.a.67.1	yes	2	63.2	odd	6
126.2.h.a.79.1	yes	2	63.32	odd	6
378.2.e.a.37.1		2	63.25	even	3
378.2.e.a.235.1		2	63.58	even	3
378.2.h.b.289.1		2	63.4	even	3
378.2.h.b.361.1		2	63.16	even	3
882.2.e.h.373.1		2	63.38	even	6
882.2.e.h.655.1		2	63.5	even	6
882.2.f.a.295.1		2	63.41	even	6
882.2.f.a.589.1		2	63.20	even	6
882.2.f.e.295.1		2	9.5	odd	6
882.2.f.e.589.1		2	9.2	odd	6
882.2.h.e.67.1		2	63.47	even	6
882.2.h.e.79.1		2	63.59	even	6
1008.2.q.e.529.1		2	252.23	even	6
1008.2.q.e.625.1		2	252.11	even	6
1008.2.t.c.193.1		2	252.191	even	6
1008.2.t.c.961.1		2	252.95	even	6
1134.2.g.d.163.1		2	21.11	odd	6
1134.2.g.d.487.1		2	21.2	odd	6
1134.2.g.f.163.1		2	7.4	even	3
1134.2.g.f.487.1		2	7.2	even	3
2646.2.e.e.1549.1		2	63.52	odd	6
2646.2.e.e.2125.1		2	63.40	odd	6
2646.2.f.e.883.1		2	9.4	even	3
2646.2.f.e.1765.1		2	9.7	even	3
2646.2.f.i.883.1		2	63.13	odd	6
2646.2.f.i.1765.1		2	63.34	odd	6
2646.2.h.f.361.1		2	63.61	odd	6
2646.2.h.f.667.1		2	63.31	odd	6
3024.2.q.a.2305.1		2	252.151	odd	6
3024.2.q.a.2881.1		2	252.247	odd	6
3024.2.t.f.289.1		2	252.67	odd	6
3024.2.t.f.1873.1		2	252.79	odd	6
7938.2.a.c.1.1		1	7.6	odd	2
7938.2.a.o.1.1		1	1.1	even	1	trivial
7938.2.a.r.1.1		1	3.2	odd	2
7938.2.a.bd.1.1		1	21.20	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:	\( N \)	\(=\)	\( 7938 = 2 \cdot 3^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7938.a (trivial)

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