LMFDB - Embedded newform 7938.2.a.m.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:	$1$
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)

$f(q)$

$=$

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

$q-1.00000 q^{2} +1.00000 q^{4} +3.00000 q^{5} -1.00000 q^{8} -3.00000 q^{10} -3.00000 q^{11} -1.00000 q^{13} +1.00000 q^{16} +3.00000 q^{17} -7.00000 q^{19} +3.00000 q^{20} +3.00000 q^{22} -9.00000 q^{23} +4.00000 q^{25} +1.00000 q^{26} +3.00000 q^{29} +8.00000 q^{31} -1.00000 q^{32} -3.00000 q^{34} -1.00000 q^{37} +7.00000 q^{38} -3.00000 q^{40} +3.00000 q^{41} -1.00000 q^{43} -3.00000 q^{44} +9.00000 q^{46} -4.00000 q^{50} -1.00000 q^{52} +3.00000 q^{53} -9.00000 q^{55} -3.00000 q^{58} +2.00000 q^{61} -8.00000 q^{62} +1.00000 q^{64} -3.00000 q^{65} -4.00000 q^{67} +3.00000 q^{68} +12.0000 q^{71} +11.0000 q^{73} +1.00000 q^{74} -7.00000 q^{76} -16.0000 q^{79} +3.00000 q^{80} -3.00000 q^{82} -9.00000 q^{83} +9.00000 q^{85} +1.00000 q^{86} +3.00000 q^{88} +3.00000 q^{89} -9.00000 q^{92} -21.0000 q^{95} -1.00000 q^{97} +O(q^{100})$

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	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	0	0
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	3.00000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	0	0
$19$	−7.00000	−1.60591	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−7.00000	−1.60591	−0.802955	+	0.596040i	$0.796740\pi$
$20$	3.00000	0.670820
$21$	0	0
$22$	3.00000	0.639602
$23$	−9.00000	−1.87663	−0.938315	−	0.345782i	$-0.887614\pi$
$23$	−9.00000	−1.87663	−0.938315	+	0.345782i	$0.887614\pi$
$24$	0	0
$25$	4.00000	0.800000
$26$	1.00000	0.196116
$27$	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
$31$	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
$34$	−3.00000	−0.514496
$35$	0	0
$36$	0	0
$37$	−1.00000	−0.164399	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000	−0.164399	−0.0821995	+	0.996616i	$0.526194\pi$
$38$	7.00000	1.13555
$39$	0	0
$40$	−3.00000	−0.474342
$41$	3.00000	0.468521	0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000	0.468521	0.234261	+	0.972174i	$0.424733\pi$
$42$	0	0
$43$	−1.00000	−0.152499	−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000	−0.152499	−0.0762493	+	0.997089i	$0.524294\pi$
$44$	−3.00000	−0.452267
$45$	0	0
$46$	9.00000	1.32698
$47$	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
$52$	−1.00000	−0.138675
$53$	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
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−8.00000	−1.01600
$63$	0	0
$64$	1.00000	0.125000
$65$	−3.00000	−0.372104
$66$	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
$71$	12.0000	1.42414	0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000	1.42414	0.712069	+	0.702109i	$0.247758\pi$
$72$	0	0
$73$	11.0000	1.28745	0.643726	−	0.765256i	$-0.277388\pi$
$73$	11.0000	1.28745	0.643726	+	0.765256i	$0.277388\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	−7.00000	−0.802955
$77$	0	0
$78$	0	0
$79$	−16.0000	−1.80014	−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000	−1.80014	−0.900070	+	0.435745i	$0.856485\pi$
$80$	3.00000	0.335410
$81$	0	0
$82$	−3.00000	−0.331295
$83$	−9.00000	−0.987878	−0.493939	−	0.869496i	$-0.664443\pi$
$83$	−9.00000	−0.987878	−0.493939	+	0.869496i	$0.664443\pi$
$84$	0	0
$85$	9.00000	0.976187
$86$	1.00000	0.107833
$87$	0	0
$88$	3.00000	0.319801
$89$	3.00000	0.317999	0.159000	−	0.987279i	$-0.449173\pi$
$89$	3.00000	0.317999	0.159000	+	0.987279i	$0.449173\pi$
$90$	0	0
$91$	0	0
$92$	−9.00000	−0.938315
$93$	0	0
$94$	0	0
$95$	−21.0000	−2.15455
$96$	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
$103$	−13.0000	−1.28093	−0.640464	−	0.767988i	$-0.721258\pi$
$103$	−13.0000	−1.28093	−0.640464	+	0.767988i	$0.721258\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	−3.00000	−0.291386
$107$	9.00000	0.870063	0.435031	−	0.900415i	$-0.356737\pi$
$107$	9.00000	0.870063	0.435031	+	0.900415i	$0.356737\pi$
$108$	0	0
$109$	−13.0000	−1.24517	−0.622587	−	0.782551i	$-0.713918\pi$
$109$	−13.0000	−1.24517	−0.622587	+	0.782551i	$0.713918\pi$
$110$	9.00000	0.858116
$111$	0	0
$112$	0	0
$113$	−9.00000	−0.846649	−0.423324	−	0.905978i	$-0.639137\pi$
$113$	−9.00000	−0.846649	−0.423324	+	0.905978i	$0.639137\pi$
$114$	0	0
$115$	−27.0000	−2.51776
$116$	3.00000	0.278543
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−2.00000	−0.181818
$122$	−2.00000	−0.181071
$123$	0	0
$124$	8.00000	0.718421
$125$	−3.00000	−0.268328
$126$	0	0
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	3.00000	0.263117
$131$	15.0000	1.31056	0.655278	−	0.755388i	$-0.272551\pi$
$131$	15.0000	1.31056	0.655278	+	0.755388i	$0.272551\pi$
$132$	0	0
$133$	0	0
$134$	4.00000	0.345547
$135$	0	0
$136$	−3.00000	−0.257248
$137$	−9.00000	−0.768922	−0.384461	−	0.923141i	$-0.625613\pi$
$137$	−9.00000	−0.768922	−0.384461	+	0.923141i	$0.625613\pi$
$138$	0	0
$139$	−7.00000	−0.593732	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	−7.00000	−0.593732	−0.296866	+	0.954919i	$0.595942\pi$
$140$	0	0
$141$	0	0
$142$	−12.0000	−1.00702
$143$	3.00000	0.250873
$144$	0	0
$145$	9.00000	0.747409
$146$	−11.0000	−0.910366
$147$	0	0
$148$	−1.00000	−0.0821995
$149$	−9.00000	−0.737309	−0.368654	−	0.929567i	$-0.620181\pi$
$149$	−9.00000	−0.737309	−0.368654	+	0.929567i	$0.620181\pi$
$150$	0	0
$151$	−7.00000	−0.569652	−0.284826	−	0.958579i	$-0.591936\pi$
$151$	−7.00000	−0.569652	−0.284826	+	0.958579i	$0.591936\pi$
$152$	7.00000	0.567775
$153$	0	0
$154$	0	0
$155$	24.0000	1.92773
$156$	0	0
$157$	−22.0000	−1.75579	−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000	−1.75579	−0.877896	+	0.478852i	$0.841053\pi$
$158$	16.0000	1.27289
$159$	0	0
$160$	−3.00000	−0.237171
$161$	0	0
$162$	0	0
$163$	−19.0000	−1.48819	−0.744097	−	0.668071i	$-0.767120\pi$
$163$	−19.0000	−1.48819	−0.744097	+	0.668071i	$0.767120\pi$
$164$	3.00000	0.234261
$165$	0	0
$166$	9.00000	0.698535
$167$	−15.0000	−1.16073	−0.580367	−	0.814355i	$-0.697091\pi$
$167$	−15.0000	−1.16073	−0.580367	+	0.814355i	$0.697091\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	−9.00000	−0.690268
$171$	0	0
$172$	−1.00000	−0.0762493
$173$	−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
$178$	−3.00000	−0.224860
$179$	−21.0000	−1.56961	−0.784807	−	0.619740i	$-0.787238\pi$
$179$	−21.0000	−1.56961	−0.784807	+	0.619740i	$0.787238\pi$
$180$	0	0
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	0	0
$183$	0	0
$184$	9.00000	0.663489
$185$	−3.00000	−0.220564
$186$	0	0
$187$	−9.00000	−0.658145
$188$	0	0
$189$	0	0
$190$	21.0000	1.52350
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	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
$197$	18.0000	1.28245	0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000	1.28245	0.641223	+	0.767354i	$0.278427\pi$
$198$	0	0
$199$	−25.0000	−1.77220	−0.886102	−	0.463491i	$-0.846597\pi$
$199$	−25.0000	−1.77220	−0.886102	+	0.463491i	$0.846597\pi$
$200$	−4.00000	−0.282843
$201$	0	0
$202$	−3.00000	−0.211079
$203$	0	0
$204$	0	0
$205$	9.00000	0.628587
$206$	13.0000	0.905753
$207$	0	0
$208$	−1.00000	−0.0693375
$209$	21.0000	1.45260
$210$	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
$214$	−9.00000	−0.615227
$215$	−3.00000	−0.204598
$216$	0	0
$217$	0	0
$218$	13.0000	0.880471
$219$	0	0
$220$	−9.00000	−0.606780
$221$	−3.00000	−0.201802
$222$	0	0
$223$	−1.00000	−0.0669650	−0.0334825	−	0.999439i	$-0.510660\pi$
$223$	−1.00000	−0.0669650	−0.0334825	+	0.999439i	$0.510660\pi$
$224$	0	0
$225$	0	0
$226$	9.00000	0.598671
$227$	−3.00000	−0.199117	−0.0995585	−	0.995032i	$-0.531743\pi$
$227$	−3.00000	−0.199117	−0.0995585	+	0.995032i	$0.531743\pi$
$228$	0	0
$229$	−13.0000	−0.859064	−0.429532	−	0.903052i	$-0.641321\pi$
$229$	−13.0000	−0.859064	−0.429532	+	0.903052i	$0.641321\pi$
$230$	27.0000	1.78033
$231$	0	0
$232$	−3.00000	−0.196960
$233$	3.00000	0.196537	0.0982683	−	0.995160i	$-0.468670\pi$
$233$	3.00000	0.196537	0.0982683	+	0.995160i	$0.468670\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	−3.00000	−0.194054	−0.0970269	−	0.995282i	$-0.530933\pi$
$239$	−3.00000	−0.194054	−0.0970269	+	0.995282i	$0.530933\pi$
$240$	0	0
$241$	−13.0000	−0.837404	−0.418702	−	0.908124i	$-0.637515\pi$
$241$	−13.0000	−0.837404	−0.418702	+	0.908124i	$0.637515\pi$
$242$	2.00000	0.128565
$243$	0	0
$244$	2.00000	0.128037
$245$	0	0
$246$	0	0
$247$	7.00000	0.445399
$248$	−8.00000	−0.508001
$249$	0	0
$250$	3.00000	0.189737
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	0	0
$253$	27.0000	1.69748
$254$	4.00000	0.250982
$255$	0	0
$256$	1.00000	0.0625000
$257$	−21.0000	−1.30994	−0.654972	−	0.755653i	$-0.727320\pi$
$257$	−21.0000	−1.30994	−0.654972	+	0.755653i	$0.727320\pi$
$258$	0	0
$259$	0	0
$260$	−3.00000	−0.186052
$261$	0	0
$262$	−15.0000	−0.926703
$263$	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
$269$	15.0000	0.914566	0.457283	−	0.889321i	$-0.348823\pi$
$269$	15.0000	0.914566	0.457283	+	0.889321i	$0.348823\pi$
$270$	0	0
$271$	5.00000	0.303728	0.151864	−	0.988401i	$-0.451472\pi$
$271$	5.00000	0.303728	0.151864	+	0.988401i	$0.451472\pi$
$272$	3.00000	0.181902
$273$	0	0
$274$	9.00000	0.543710
$275$	−12.0000	−0.723627
$276$	0	0
$277$	−1.00000	−0.0600842	−0.0300421	−	0.999549i	$-0.509564\pi$
$277$	−1.00000	−0.0600842	−0.0300421	+	0.999549i	$0.509564\pi$
$278$	7.00000	0.419832
$279$	0	0
$280$	0	0
$281$	−21.0000	−1.25275	−0.626377	−	0.779520i	$-0.715463\pi$
$281$	−21.0000	−1.25275	−0.626377	+	0.779520i	$0.715463\pi$
$282$	0	0
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	12.0000	0.712069
$285$	0	0
$286$	−3.00000	−0.177394
$287$	0	0
$288$	0	0
$289$	−8.00000	−0.470588
$290$	−9.00000	−0.528498
$291$	0	0
$292$	11.0000	0.643726
$293$	−9.00000	−0.525786	−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000	−0.525786	−0.262893	+	0.964825i	$0.584677\pi$
$294$	0	0
$295$	0	0
$296$	1.00000	0.0581238
$297$	0	0
$298$	9.00000	0.521356
$299$	9.00000	0.520483
$300$	0	0
$301$	0	0
$302$	7.00000	0.402805
$303$	0	0
$304$	−7.00000	−0.401478
$305$	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
$310$	−24.0000	−1.36311
$311$	−24.0000	−1.36092	−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000	−1.36092	−0.680458	+	0.732787i	$0.738219\pi$
$312$	0	0
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	22.0000	1.24153
$315$	0	0
$316$	−16.0000	−0.900070
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	0	0
$319$	−9.00000	−0.503903
$320$	3.00000	0.167705
$321$	0	0
$322$	0	0
$323$	−21.0000	−1.16847
$324$	0	0
$325$	−4.00000	−0.221880
$326$	19.0000	1.05231
$327$	0	0
$328$	−3.00000	−0.165647
$329$	0	0
$330$	0	0
$331$	8.00000	0.439720	0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000	0.439720	0.219860	+	0.975531i	$0.429440\pi$
$332$	−9.00000	−0.493939
$333$	0	0
$334$	15.0000	0.820763
$335$	−12.0000	−0.655630
$336$	0	0
$337$	−13.0000	−0.708155	−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000	−0.708155	−0.354078	+	0.935216i	$0.615205\pi$
$338$	12.0000	0.652714
$339$	0	0
$340$	9.00000	0.488094
$341$	−24.0000	−1.29967
$342$	0	0
$343$	0	0
$344$	1.00000	0.0539164
$345$	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
$349$	23.0000	1.23116	0.615581	−	0.788074i	$-0.288921\pi$
$349$	23.0000	1.23116	0.615581	+	0.788074i	$0.288921\pi$
$350$	0	0
$351$	0	0
$352$	3.00000	0.159901
$353$	3.00000	0.159674	0.0798369	−	0.996808i	$-0.474560\pi$
$353$	3.00000	0.159674	0.0798369	+	0.996808i	$0.474560\pi$
$354$	0	0
$355$	36.0000	1.91068
$356$	3.00000	0.159000
$357$	0	0
$358$	21.0000	1.10988
$359$	9.00000	0.475002	0.237501	−	0.971387i	$-0.423672\pi$
$359$	9.00000	0.475002	0.237501	+	0.971387i	$0.423672\pi$
$360$	0	0
$361$	30.0000	1.57895
$362$	−2.00000	−0.105118
$363$	0	0
$364$	0	0
$365$	33.0000	1.72730
$366$	0	0
$367$	17.0000	0.887393	0.443696	−	0.896177i	$-0.353667\pi$
$367$	17.0000	0.887393	0.443696	+	0.896177i	$0.353667\pi$
$368$	−9.00000	−0.469157
$369$	0	0
$370$	3.00000	0.155963
$371$	0	0
$372$	0	0
$373$	−13.0000	−0.673114	−0.336557	−	0.941663i	$-0.609263\pi$
$373$	−13.0000	−0.673114	−0.336557	+	0.941663i	$0.609263\pi$
$374$	9.00000	0.465379
$375$	0	0
$376$	0	0
$377$	−3.00000	−0.154508
$378$	0	0
$379$	−28.0000	−1.43826	−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000	−1.43826	−0.719132	+	0.694874i	$0.755460\pi$
$380$	−21.0000	−1.07728
$381$	0	0
$382$	0	0
$383$	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
$389$	27.0000	1.36895	0.684477	−	0.729034i	$-0.260031\pi$
$389$	27.0000	1.36895	0.684477	+	0.729034i	$0.260031\pi$
$390$	0	0
$391$	−27.0000	−1.36545
$392$	0	0
$393$	0	0
$394$	−18.0000	−0.906827
$395$	−48.0000	−2.41514
$396$	0	0
$397$	−13.0000	−0.652451	−0.326226	−	0.945292i	$-0.605777\pi$
$397$	−13.0000	−0.652451	−0.326226	+	0.945292i	$0.605777\pi$
$398$	25.0000	1.25314
$399$	0	0
$400$	4.00000	0.200000
$401$	27.0000	1.34832	0.674158	−	0.738587i	$-0.264507\pi$
$401$	27.0000	1.34832	0.674158	+	0.738587i	$0.264507\pi$
$402$	0	0
$403$	−8.00000	−0.398508
$404$	3.00000	0.149256
$405$	0	0
$406$	0	0
$407$	3.00000	0.148704
$408$	0	0
$409$	−34.0000	−1.68119	−0.840596	−	0.541663i	$-0.817795\pi$
$409$	−34.0000	−1.68119	−0.840596	+	0.541663i	$0.817795\pi$
$410$	−9.00000	−0.444478
$411$	0	0
$412$	−13.0000	−0.640464
$413$	0	0
$414$	0	0
$415$	−27.0000	−1.32538
$416$	1.00000	0.0490290
$417$	0	0
$418$	−21.0000	−1.02714
$419$	9.00000	0.439679	0.219839	−	0.975536i	$-0.429447\pi$
$419$	9.00000	0.439679	0.219839	+	0.975536i	$0.429447\pi$
$420$	0	0
$421$	35.0000	1.70580	0.852898	−	0.522078i	$-0.174843\pi$
$421$	35.0000	1.70580	0.852898	+	0.522078i	$0.174843\pi$
$422$	−5.00000	−0.243396
$423$	0	0
$424$	−3.00000	−0.145693
$425$	12.0000	0.582086
$426$	0	0
$427$	0	0
$428$	9.00000	0.435031
$429$	0	0
$430$	3.00000	0.144673
$431$	27.0000	1.30054	0.650272	−	0.759701i	$-0.274655\pi$
$431$	27.0000	1.30054	0.650272	+	0.759701i	$0.274655\pi$
$432$	0	0
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	0	0
$435$	0	0
$436$	−13.0000	−0.622587
$437$	63.0000	3.01370
$438$	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
$442$	3.00000	0.142695
$443$	36.0000	1.71041	0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000	1.71041	0.855206	+	0.518289i	$0.173431\pi$
$444$	0	0
$445$	9.00000	0.426641
$446$	1.00000	0.0473514
$447$	0	0
$448$	0	0
$449$	6.00000	0.283158	0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000	0.283158	0.141579	+	0.989927i	$0.454782\pi$
$450$	0	0
$451$	−9.00000	−0.423793
$452$	−9.00000	−0.423324
$453$	0	0
$454$	3.00000	0.140797
$455$	0	0
$456$	0	0
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	13.0000	0.607450
$459$	0	0
$460$	−27.0000	−1.25888
$461$	−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
$463$	41.0000	1.90543	0.952716	−	0.303863i	$-0.0982765\pi$
$463$	41.0000	1.90543	0.952716	+	0.303863i	$0.0982765\pi$
$464$	3.00000	0.139272
$465$	0	0
$466$	−3.00000	−0.138972
$467$	−3.00000	−0.138823	−0.0694117	−	0.997588i	$-0.522112\pi$
$467$	−3.00000	−0.138823	−0.0694117	+	0.997588i	$0.522112\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	3.00000	0.137940
$474$	0	0
$475$	−28.0000	−1.28473
$476$	0	0
$477$	0	0
$478$	3.00000	0.137217
$479$	−3.00000	−0.137073	−0.0685367	−	0.997649i	$-0.521833\pi$
$479$	−3.00000	−0.137073	−0.0685367	+	0.997649i	$0.521833\pi$
$480$	0	0
$481$	1.00000	0.0455961
$482$	13.0000	0.592134
$483$	0	0
$484$	−2.00000	−0.0909091
$485$	−3.00000	−0.136223
$486$	0	0
$487$	−25.0000	−1.13286	−0.566429	−	0.824110i	$-0.691675\pi$
$487$	−25.0000	−1.13286	−0.566429	+	0.824110i	$0.691675\pi$
$488$	−2.00000	−0.0905357
$489$	0	0
$490$	0	0
$491$	21.0000	0.947717	0.473858	−	0.880601i	$-0.342861\pi$
$491$	21.0000	0.947717	0.473858	+	0.880601i	$0.342861\pi$
$492$	0	0
$493$	9.00000	0.405340
$494$	−7.00000	−0.314945
$495$	0	0
$496$	8.00000	0.359211
$497$	0	0
$498$	0	0
$499$	−25.0000	−1.11915	−0.559577	−	0.828778i	$-0.689036\pi$
$499$	−25.0000	−1.11915	−0.559577	+	0.828778i	$0.689036\pi$
$500$	−3.00000	−0.134164
$501$	0	0
$502$	−12.0000	−0.535586
$503$	−24.0000	−1.07011	−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000	−1.07011	−0.535054	+	0.844818i	$0.679709\pi$
$504$	0	0
$505$	9.00000	0.400495
$506$	−27.0000	−1.20030
$507$	0	0
$508$	−4.00000	−0.177471
$509$	−9.00000	−0.398918	−0.199459	−	0.979906i	$-0.563918\pi$
$509$	−9.00000	−0.398918	−0.199459	+	0.979906i	$0.563918\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	21.0000	0.926270
$515$	−39.0000	−1.71855
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	3.00000	0.131559
$521$	3.00000	0.131432	0.0657162	−	0.997838i	$-0.479067\pi$
$521$	3.00000	0.131432	0.0657162	+	0.997838i	$0.479067\pi$
$522$	0	0
$523$	−7.00000	−0.306089	−0.153044	−	0.988219i	$-0.548908\pi$
$523$	−7.00000	−0.306089	−0.153044	+	0.988219i	$0.548908\pi$
$524$	15.0000	0.655278
$525$	0	0
$526$	−9.00000	−0.392419
$527$	24.0000	1.04546
$528$	0	0
$529$	58.0000	2.52174
$530$	−9.00000	−0.390935
$531$	0	0
$532$	0	0
$533$	−3.00000	−0.129944
$534$	0	0
$535$	27.0000	1.16731
$536$	4.00000	0.172774
$537$	0	0
$538$	−15.0000	−0.646696
$539$	0	0
$540$	0	0
$541$	11.0000	0.472927	0.236463	−	0.971640i	$-0.424012\pi$
$541$	11.0000	0.472927	0.236463	+	0.971640i	$0.424012\pi$
$542$	−5.00000	−0.214768
$543$	0	0
$544$	−3.00000	−0.128624
$545$	−39.0000	−1.67058
$546$	0	0
$547$	11.0000	0.470326	0.235163	−	0.971956i	$-0.424438\pi$
$547$	11.0000	0.470326	0.235163	+	0.971956i	$0.424438\pi$
$548$	−9.00000	−0.384461
$549$	0	0
$550$	12.0000	0.511682
$551$	−21.0000	−0.894630
$552$	0	0
$553$	0	0
$554$	1.00000	0.0424859
$555$	0	0
$556$	−7.00000	−0.296866
$557$	−9.00000	−0.381342	−0.190671	−	0.981654i	$-0.561066\pi$
$557$	−9.00000	−0.381342	−0.190671	+	0.981654i	$0.561066\pi$
$558$	0	0
$559$	1.00000	0.0422955
$560$	0	0
$561$	0	0
$562$	21.0000	0.885832
$563$	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
$565$	−27.0000	−1.13590
$566$	4.00000	0.168133
$567$	0	0
$568$	−12.0000	−0.503509
$569$	−18.0000	−0.754599	−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000	−0.754599	−0.377300	+	0.926091i	$0.623147\pi$
$570$	0	0
$571$	32.0000	1.33916	0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000	1.33916	0.669579	+	0.742741i	$0.266474\pi$
$572$	3.00000	0.125436
$573$	0	0
$574$	0	0
$575$	−36.0000	−1.50130
$576$	0	0
$577$	−25.0000	−1.04076	−0.520382	−	0.853934i	$-0.674210\pi$
$577$	−25.0000	−1.04076	−0.520382	+	0.853934i	$0.674210\pi$
$578$	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
$586$	9.00000	0.371787
$587$	3.00000	0.123823	0.0619116	−	0.998082i	$-0.480280\pi$
$587$	3.00000	0.123823	0.0619116	+	0.998082i	$0.480280\pi$
$588$	0	0
$589$	−56.0000	−2.30744
$590$	0	0
$591$	0	0
$592$	−1.00000	−0.0410997
$593$	39.0000	1.60154	0.800769	−	0.598973i	$-0.204424\pi$
$593$	39.0000	1.60154	0.800769	+	0.598973i	$0.204424\pi$
$594$	0	0
$595$	0	0
$596$	−9.00000	−0.368654
$597$	0	0
$598$	−9.00000	−0.368037
$599$	−24.0000	−0.980613	−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000	−0.980613	−0.490307	+	0.871550i	$0.663115\pi$
$600$	0	0
$601$	−25.0000	−1.01977	−0.509886	−	0.860242i	$-0.670312\pi$
$601$	−25.0000	−1.01977	−0.509886	+	0.860242i	$0.670312\pi$
$602$	0	0
$603$	0	0
$604$	−7.00000	−0.284826
$605$	−6.00000	−0.243935
$606$	0	0
$607$	−13.0000	−0.527654	−0.263827	−	0.964570i	$-0.584985\pi$
$607$	−13.0000	−0.527654	−0.263827	+	0.964570i	$0.584985\pi$
$608$	7.00000	0.283887
$609$	0	0
$610$	−6.00000	−0.242933
$611$	0	0
$612$	0	0
$613$	23.0000	0.928961	0.464481	−	0.885583i	$-0.346241\pi$
$613$	23.0000	0.928961	0.464481	+	0.885583i	$0.346241\pi$
$614$	28.0000	1.12999
$615$	0	0
$616$	0	0
$617$	−45.0000	−1.81163	−0.905816	−	0.423672i	$-0.860741\pi$
$617$	−45.0000	−1.81163	−0.905816	+	0.423672i	$0.860741\pi$
$618$	0	0
$619$	17.0000	0.683288	0.341644	−	0.939829i	$-0.389016\pi$
$619$	17.0000	0.683288	0.341644	+	0.939829i	$0.389016\pi$
$620$	24.0000	0.963863
$621$	0	0
$622$	24.0000	0.962312
$623$	0	0
$624$	0	0
$625$	−29.0000	−1.16000
$626$	10.0000	0.399680
$627$	0	0
$628$	−22.0000	−0.877896
$629$	−3.00000	−0.119618
$630$	0	0
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	16.0000	0.636446
$633$	0	0
$634$	−18.0000	−0.714871
$635$	−12.0000	−0.476205
$636$	0	0
$637$	0	0
$638$	9.00000	0.356313
$639$	0	0
$640$	−3.00000	−0.118585
$641$	−33.0000	−1.30342	−0.651711	−	0.758468i	$-0.725948\pi$
$641$	−33.0000	−1.30342	−0.651711	+	0.758468i	$0.725948\pi$
$642$	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
$646$	21.0000	0.826234
$647$	−21.0000	−0.825595	−0.412798	−	0.910823i	$-0.635448\pi$
$647$	−21.0000	−0.825595	−0.412798	+	0.910823i	$0.635448\pi$
$648$	0	0
$649$	0	0
$650$	4.00000	0.156893
$651$	0	0
$652$	−19.0000	−0.744097
$653$	15.0000	0.586995	0.293498	−	0.955960i	$-0.405181\pi$
$653$	15.0000	0.586995	0.293498	+	0.955960i	$0.405181\pi$
$654$	0	0
$655$	45.0000	1.75830
$656$	3.00000	0.117130
$657$	0	0
$658$	0	0
$659$	3.00000	0.116863	0.0584317	−	0.998291i	$-0.481390\pi$
$659$	3.00000	0.116863	0.0584317	+	0.998291i	$0.481390\pi$
$660$	0	0
$661$	−22.0000	−0.855701	−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000	−0.855701	−0.427850	+	0.903850i	$0.640729\pi$
$662$	−8.00000	−0.310929
$663$	0	0
$664$	9.00000	0.349268
$665$	0	0
$666$	0	0
$667$	−27.0000	−1.04544
$668$	−15.0000	−0.580367
$669$	0	0
$670$	12.0000	0.463600
$671$	−6.00000	−0.231627
$672$	0	0
$673$	35.0000	1.34915	0.674575	−	0.738206i	$-0.264327\pi$
$673$	35.0000	1.34915	0.674575	+	0.738206i	$0.264327\pi$
$674$	13.0000	0.500741
$675$	0	0
$676$	−12.0000	−0.461538
$677$	−30.0000	−1.15299	−0.576497	−	0.817099i	$-0.695581\pi$
$677$	−30.0000	−1.15299	−0.576497	+	0.817099i	$0.695581\pi$
$678$	0	0
$679$	0	0
$680$	−9.00000	−0.345134
$681$	0	0
$682$	24.0000	0.919007
$683$	−9.00000	−0.344375	−0.172188	−	0.985064i	$-0.555084\pi$
$683$	−9.00000	−0.344375	−0.172188	+	0.985064i	$0.555084\pi$
$684$	0	0
$685$	−27.0000	−1.03162
$686$	0	0
$687$	0	0
$688$	−1.00000	−0.0381246
$689$	−3.00000	−0.114291
$690$	0	0
$691$	44.0000	1.67384	0.836919	−	0.547326i	$-0.184354\pi$
$691$	44.0000	1.67384	0.836919	+	0.547326i	$0.184354\pi$
$692$	−6.00000	−0.228086
$693$	0	0
$694$	−12.0000	−0.455514
$695$	−21.0000	−0.796575
$696$	0	0
$697$	9.00000	0.340899
$698$	−23.0000	−0.870563
$699$	0	0
$700$	0	0
$701$	−18.0000	−0.679851	−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000	−0.679851	−0.339925	+	0.940452i	$0.610402\pi$
$702$	0	0
$703$	7.00000	0.264010
$704$	−3.00000	−0.113067
$705$	0	0
$706$	−3.00000	−0.112906
$707$	0	0
$708$	0	0
$709$	26.0000	0.976450	0.488225	−	0.872718i	$-0.337644\pi$
$709$	26.0000	0.976450	0.488225	+	0.872718i	$0.337644\pi$
$710$	−36.0000	−1.35106
$711$	0	0
$712$	−3.00000	−0.112430
$713$	−72.0000	−2.69642
$714$	0	0
$715$	9.00000	0.336581
$716$	−21.0000	−0.784807
$717$	0	0
$718$	−9.00000	−0.335877
$719$	−15.0000	−0.559406	−0.279703	−	0.960087i	$-0.590236\pi$
$719$	−15.0000	−0.559406	−0.279703	+	0.960087i	$0.590236\pi$
$720$	0	0
$721$	0	0
$722$	−30.0000	−1.11648
$723$	0	0
$724$	2.00000	0.0743294
$725$	12.0000	0.445669
$726$	0	0
$727$	−13.0000	−0.482143	−0.241072	−	0.970507i	$-0.577499\pi$
$727$	−13.0000	−0.482143	−0.241072	+	0.970507i	$0.577499\pi$
$728$	0	0
$729$	0	0
$730$	−33.0000	−1.22138
$731$	−3.00000	−0.110959
$732$	0	0
$733$	−1.00000	−0.0369358	−0.0184679	−	0.999829i	$-0.505879\pi$
$733$	−1.00000	−0.0369358	−0.0184679	+	0.999829i	$0.505879\pi$
$734$	−17.0000	−0.627481
$735$	0	0
$736$	9.00000	0.331744
$737$	12.0000	0.442026
$738$	0	0
$739$	23.0000	0.846069	0.423034	−	0.906114i	$-0.360965\pi$
$739$	23.0000	0.846069	0.423034	+	0.906114i	$0.360965\pi$
$740$	−3.00000	−0.110282
$741$	0	0
$742$	0	0
$743$	21.0000	0.770415	0.385208	−	0.922830i	$-0.374130\pi$
$743$	21.0000	0.770415	0.385208	+	0.922830i	$0.374130\pi$
$744$	0	0
$745$	−27.0000	−0.989203
$746$	13.0000	0.475964
$747$	0	0
$748$	−9.00000	−0.329073
$749$	0	0
$750$	0	0
$751$	−13.0000	−0.474377	−0.237188	−	0.971464i	$-0.576226\pi$
$751$	−13.0000	−0.474377	−0.237188	+	0.971464i	$0.576226\pi$
$752$	0	0
$753$	0	0
$754$	3.00000	0.109254
$755$	−21.0000	−0.764268
$756$	0	0
$757$	−22.0000	−0.799604	−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000	−0.799604	−0.399802	+	0.916602i	$0.630921\pi$
$758$	28.0000	1.01701
$759$	0	0
$760$	21.0000	0.761750
$761$	−45.0000	−1.63125	−0.815624	−	0.578582i	$-0.803606\pi$
$761$	−45.0000	−1.63125	−0.815624	+	0.578582i	$0.803606\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	−15.0000	−0.541972
$767$	0	0
$768$	0	0
$769$	23.0000	0.829401	0.414701	−	0.909958i	$-0.363886\pi$
$769$	23.0000	0.829401	0.414701	+	0.909958i	$0.363886\pi$
$770$	0	0
$771$	0	0
$772$	14.0000	0.503871
$773$	27.0000	0.971123	0.485561	−	0.874203i	$-0.338615\pi$
$773$	27.0000	0.971123	0.485561	+	0.874203i	$0.338615\pi$
$774$	0	0
$775$	32.0000	1.14947
$776$	1.00000	0.0358979
$777$	0	0
$778$	−27.0000	−0.967997
$779$	−21.0000	−0.752403
$780$	0	0
$781$	−36.0000	−1.28818
$782$	27.0000	0.965518
$783$	0	0
$784$	0	0
$785$	−66.0000	−2.35564
$786$	0	0
$787$	−28.0000	−0.998092	−0.499046	−	0.866575i	$-0.666316\pi$
$787$	−28.0000	−0.998092	−0.499046	+	0.866575i	$0.666316\pi$
$788$	18.0000	0.641223
$789$	0	0
$790$	48.0000	1.70776
$791$	0	0
$792$	0	0
$793$	−2.00000	−0.0710221
$794$	13.0000	0.461353
$795$	0	0
$796$	−25.0000	−0.886102
$797$	−21.0000	−0.743858	−0.371929	−	0.928261i	$-0.621304\pi$
$797$	−21.0000	−0.743858	−0.371929	+	0.928261i	$0.621304\pi$
$798$	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
$806$	8.00000	0.281788
$807$	0	0
$808$	−3.00000	−0.105540
$809$	−33.0000	−1.16022	−0.580109	−	0.814539i	$-0.696990\pi$
$809$	−33.0000	−1.16022	−0.580109	+	0.814539i	$0.696990\pi$
$810$	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
$814$	−3.00000	−0.105150
$815$	−57.0000	−1.99662
$816$	0	0
$817$	7.00000	0.244899
$818$	34.0000	1.18878
$819$	0	0
$820$	9.00000	0.314294
$821$	−42.0000	−1.46581	−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000	−1.46581	−0.732905	+	0.680331i	$0.761836\pi$
$822$	0	0
$823$	−40.0000	−1.39431	−0.697156	−	0.716919i	$-0.745552\pi$
$823$	−40.0000	−1.39431	−0.697156	+	0.716919i	$0.745552\pi$
$824$	13.0000	0.452876
$825$	0	0
$826$	0	0
$827$	36.0000	1.25184	0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000	1.25184	0.625921	+	0.779886i	$0.284723\pi$
$828$	0	0
$829$	11.0000	0.382046	0.191023	−	0.981586i	$-0.438820\pi$
$829$	11.0000	0.382046	0.191023	+	0.981586i	$0.438820\pi$
$830$	27.0000	0.937184
$831$	0	0
$832$	−1.00000	−0.0346688
$833$	0	0
$834$	0	0
$835$	−45.0000	−1.55729
$836$	21.0000	0.726300
$837$	0	0
$838$	−9.00000	−0.310900
$839$	15.0000	0.517858	0.258929	−	0.965896i	$-0.416631\pi$
$839$	15.0000	0.517858	0.258929	+	0.965896i	$0.416631\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	−35.0000	−1.20618
$843$	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
$851$	9.00000	0.308516
$852$	0	0
$853$	−1.00000	−0.0342393	−0.0171197	−	0.999853i	$-0.505450\pi$
$853$	−1.00000	−0.0342393	−0.0171197	+	0.999853i	$0.505450\pi$
$854$	0	0
$855$	0	0
$856$	−9.00000	−0.307614
$857$	3.00000	0.102478	0.0512390	−	0.998686i	$-0.483683\pi$
$857$	3.00000	0.102478	0.0512390	+	0.998686i	$0.483683\pi$
$858$	0	0
$859$	−25.0000	−0.852989	−0.426494	−	0.904490i	$-0.640252\pi$
$859$	−25.0000	−0.852989	−0.426494	+	0.904490i	$0.640252\pi$
$860$	−3.00000	−0.102299
$861$	0	0
$862$	−27.0000	−0.919624
$863$	−51.0000	−1.73606	−0.868030	−	0.496512i	$-0.834614\pi$
$863$	−51.0000	−1.73606	−0.868030	+	0.496512i	$0.834614\pi$
$864$	0	0
$865$	−18.0000	−0.612018
$866$	−2.00000	−0.0679628
$867$	0	0
$868$	0	0
$869$	48.0000	1.62829
$870$	0	0
$871$	4.00000	0.135535
$872$	13.0000	0.440236
$873$	0	0
$874$	−63.0000	−2.13101
$875$	0	0
$876$	0	0
$877$	47.0000	1.58708	0.793539	−	0.608520i	$-0.208236\pi$
$877$	47.0000	1.58708	0.793539	+	0.608520i	$0.208236\pi$
$878$	−8.00000	−0.269987
$879$	0	0
$880$	−9.00000	−0.303390
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	0	0
$883$	20.0000	0.673054	0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000	0.673054	0.336527	+	0.941674i	$0.390748\pi$
$884$	−3.00000	−0.100901
$885$	0	0
$886$	−36.0000	−1.20944
$887$	−33.0000	−1.10803	−0.554016	−	0.832506i	$-0.686905\pi$
$887$	−33.0000	−1.10803	−0.554016	+	0.832506i	$0.686905\pi$
$888$	0	0
$889$	0	0
$890$	−9.00000	−0.301681
$891$	0	0
$892$	−1.00000	−0.0334825
$893$	0	0
$894$	0	0
$895$	−63.0000	−2.10586
$896$	0	0
$897$	0	0
$898$	−6.00000	−0.200223
$899$	24.0000	0.800445
$900$	0	0
$901$	9.00000	0.299833
$902$	9.00000	0.299667
$903$	0	0
$904$	9.00000	0.299336
$905$	6.00000	0.199447
$906$	0	0
$907$	−43.0000	−1.42779	−0.713896	−	0.700252i	$-0.753071\pi$
$907$	−43.0000	−1.42779	−0.713896	+	0.700252i	$0.753071\pi$
$908$	−3.00000	−0.0995585
$909$	0	0
$910$	0	0
$911$	39.0000	1.29213	0.646064	−	0.763283i	$-0.276414\pi$
$911$	39.0000	1.29213	0.646064	+	0.763283i	$0.276414\pi$
$912$	0	0
$913$	27.0000	0.893570
$914$	10.0000	0.330771
$915$	0	0
$916$	−13.0000	−0.429532
$917$	0	0
$918$	0	0
$919$	53.0000	1.74831	0.874154	−	0.485648i	$-0.161416\pi$
$919$	53.0000	1.74831	0.874154	+	0.485648i	$0.161416\pi$
$920$	27.0000	0.890164
$921$	0	0
$922$	9.00000	0.296399
$923$	−12.0000	−0.394985
$924$	0	0
$925$	−4.00000	−0.131519
$926$	−41.0000	−1.34734
$927$	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
$932$	3.00000	0.0982683
$933$	0	0
$934$	3.00000	0.0981630
$935$	−27.0000	−0.882994
$936$	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
$940$	0	0
$941$	−6.00000	−0.195594	−0.0977972	−	0.995206i	$-0.531180\pi$
$941$	−6.00000	−0.195594	−0.0977972	+	0.995206i	$0.531180\pi$
$942$	0	0
$943$	−27.0000	−0.879241
$944$	0	0
$945$	0	0
$946$	−3.00000	−0.0975384
$947$	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
$949$	−11.0000	−0.357075
$950$	28.0000	0.908440
$951$	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
$955$	0	0
$956$	−3.00000	−0.0970269
$957$	0	0
$958$	3.00000	0.0969256
$959$	0	0
$960$	0	0
$961$	33.0000	1.06452
$962$	−1.00000	−0.0322413
$963$	0	0
$964$	−13.0000	−0.418702
$965$	42.0000	1.35203
$966$	0	0
$967$	41.0000	1.31847	0.659236	−	0.751936i	$-0.270880\pi$
$967$	41.0000	1.31847	0.659236	+	0.751936i	$0.270880\pi$
$968$	2.00000	0.0642824
$969$	0	0
$970$	3.00000	0.0963242
$971$	33.0000	1.05902	0.529510	−	0.848304i	$-0.322376\pi$
$971$	33.0000	1.05902	0.529510	+	0.848304i	$0.322376\pi$
$972$	0	0
$973$	0	0
$974$	25.0000	0.801052
$975$	0	0
$976$	2.00000	0.0640184
$977$	−30.0000	−0.959785	−0.479893	−	0.877327i	$-0.659324\pi$
$977$	−30.0000	−0.959785	−0.479893	+	0.877327i	$0.659324\pi$
$978$	0	0
$979$	−9.00000	−0.287641
$980$	0	0
$981$	0	0
$982$	−21.0000	−0.670137
$983$	−15.0000	−0.478426	−0.239213	−	0.970967i	$-0.576889\pi$
$983$	−15.0000	−0.478426	−0.239213	+	0.970967i	$0.576889\pi$
$984$	0	0
$985$	54.0000	1.72058
$986$	−9.00000	−0.286618
$987$	0	0
$988$	7.00000	0.222700
$989$	9.00000	0.286183
$990$	0	0
$991$	−25.0000	−0.794151	−0.397076	−	0.917786i	$-0.629975\pi$
$991$	−25.0000	−0.794151	−0.397076	+	0.917786i	$0.629975\pi$
$992$	−8.00000	−0.254000
$993$	0	0
$994$	0	0
$995$	−75.0000	−2.37766
$996$	0	0
$997$	−13.0000	−0.411714	−0.205857	−	0.978582i	$-0.565998\pi$
$997$	−13.0000	−0.411714	−0.205857	+	0.978582i	$0.565998\pi$
$998$	25.0000	0.791361
$999$	0	0

Twists

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

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