LMFDB - Embedded newform 5025.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5025,2,Mod(1,5025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5025, 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("5025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5025 = 3 \cdot 5^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5025.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:	$40.1248270157$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 201)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} +1.00000 q^{3} +2.00000 q^{4} +2.00000 q^{6} +1.00000 q^{9} +O(q^{10})$

$q+2.00000 q^{2} +1.00000 q^{3} +2.00000 q^{4} +2.00000 q^{6} +1.00000 q^{9} -6.00000 q^{11} +2.00000 q^{12} -4.00000 q^{13} -4.00000 q^{16} +7.00000 q^{17} +2.00000 q^{18} -5.00000 q^{19} -12.0000 q^{22} +1.00000 q^{23} -8.00000 q^{26} +1.00000 q^{27} +1.00000 q^{29} -4.00000 q^{31} -8.00000 q^{32} -6.00000 q^{33} +14.0000 q^{34} +2.00000 q^{36} -3.00000 q^{37} -10.0000 q^{38} -4.00000 q^{39} +6.00000 q^{43} -12.0000 q^{44} +2.00000 q^{46} -9.00000 q^{47} -4.00000 q^{48} -7.00000 q^{49} +7.00000 q^{51} -8.00000 q^{52} -10.0000 q^{53} +2.00000 q^{54} -5.00000 q^{57} +2.00000 q^{58} +3.00000 q^{59} +2.00000 q^{61} -8.00000 q^{62} -8.00000 q^{64} -12.0000 q^{66} +1.00000 q^{67} +14.0000 q^{68} +1.00000 q^{69} -16.0000 q^{71} +7.00000 q^{73} -6.00000 q^{74} -10.0000 q^{76} -8.00000 q^{78} +8.00000 q^{79} +1.00000 q^{81} +4.00000 q^{83} +12.0000 q^{86} +1.00000 q^{87} -15.0000 q^{89} +2.00000 q^{92} -4.00000 q^{93} -18.0000 q^{94} -8.00000 q^{96} -4.00000 q^{97} -14.0000 q^{98} -6.00000 q^{99} +O(q^{100})$

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 $

$2$	2.00000	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$2$	2.00000	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.00000	1.00000
$5$	0	0
$5$	0	0
$6$	2.00000	0.816497
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	−6.00000	−1.80907	−0.904534	−	0.426401i	$-0.859781\pi$
$11$	−6.00000	−1.80907	−0.904534	+	0.426401i	$0.859781\pi$
$12$	2.00000	0.577350
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	0	0
$15$	0	0
$16$	−4.00000	−1.00000
$17$	7.00000	1.69775	0.848875	−	0.528594i	$-0.177281\pi$
$17$	7.00000	1.69775	0.848875	+	0.528594i	$0.177281\pi$
$18$	2.00000	0.471405
$19$	−5.00000	−1.14708	−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000	−1.14708	−0.573539	+	0.819178i	$0.694430\pi$
$20$	0	0
$21$	0	0
$22$	−12.0000	−2.55841
$23$	1.00000	0.208514	0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000	0.208514	0.104257	+	0.994550i	$0.466753\pi$
$24$	0	0
$25$	0	0
$26$	−8.00000	−1.56893
$27$	1.00000	0.192450
$28$	0	0
$29$	1.00000	0.185695	0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000	0.185695	0.0928477	+	0.995680i	$0.470403\pi$
$30$	0	0
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	−8.00000	−1.41421
$33$	−6.00000	−1.04447
$34$	14.0000	2.40098
$35$	0	0
$36$	2.00000	0.333333
$37$	−3.00000	−0.493197	−0.246598	−	0.969118i	$-0.579313\pi$
$37$	−3.00000	−0.493197	−0.246598	+	0.969118i	$0.579313\pi$
$38$	−10.0000	−1.62221
$39$	−4.00000	−0.640513
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	6.00000	0.914991	0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000	0.914991	0.457496	+	0.889212i	$0.348747\pi$
$44$	−12.0000	−1.80907
$45$	0	0
$46$	2.00000	0.294884
$47$	−9.00000	−1.31278	−0.656392	−	0.754420i	$-0.727918\pi$
$47$	−9.00000	−1.31278	−0.656392	+	0.754420i	$0.727918\pi$
$48$	−4.00000	−0.577350
$49$	−7.00000	−1.00000
$50$	0	0
$51$	7.00000	0.980196
$52$	−8.00000	−1.10940
$53$	−10.0000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	2.00000	0.272166
$55$	0	0
$56$	0	0
$57$	−5.00000	−0.662266
$58$	2.00000	0.262613
$59$	3.00000	0.390567	0.195283	−	0.980747i	$-0.437437\pi$
$59$	3.00000	0.390567	0.195283	+	0.980747i	$0.437437\pi$
$60$	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
$64$	−8.00000	−1.00000
$65$	0	0
$66$	−12.0000	−1.47710
$67$	1.00000	0.122169
$67$	1.00000	0.122169
$68$	14.0000	1.69775
$69$	1.00000	0.120386
$70$	0	0
$71$	−16.0000	−1.89885	−0.949425	−	0.313993i	$-0.898333\pi$
$71$	−16.0000	−1.89885	−0.949425	+	0.313993i	$0.898333\pi$
$72$	0	0
$73$	7.00000	0.819288	0.409644	−	0.912245i	$-0.365653\pi$
$73$	7.00000	0.819288	0.409644	+	0.912245i	$0.365653\pi$
$74$	−6.00000	−0.697486
$75$	0	0
$76$	−10.0000	−1.14708
$77$	0	0
$78$	−8.00000	−0.905822
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	0	0
$85$	0	0
$86$	12.0000	1.29399
$87$	1.00000	0.107211
$88$	0	0
$89$	−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
$92$	2.00000	0.208514
$93$	−4.00000	−0.414781
$94$	−18.0000	−1.85656
$95$	0	0
$96$	−8.00000	−0.816497
$97$	−4.00000	−0.406138	−0.203069	−	0.979164i	$-0.565092\pi$
$97$	−4.00000	−0.406138	−0.203069	+	0.979164i	$0.565092\pi$
$98$	−14.0000	−1.41421
$99$	−6.00000	−0.603023
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	14.0000	1.38621
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	0	0
$105$	0	0
$106$	−20.0000	−1.94257
$107$	−7.00000	−0.676716	−0.338358	−	0.941018i	$-0.609871\pi$
$107$	−7.00000	−0.676716	−0.338358	+	0.941018i	$0.609871\pi$
$108$	2.00000	0.192450
$109$	4.00000	0.383131	0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000	0.383131	0.191565	+	0.981480i	$0.438644\pi$
$110$	0	0
$111$	−3.00000	−0.284747
$112$	0	0
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	−10.0000	−0.936586
$115$	0	0
$116$	2.00000	0.185695
$117$	−4.00000	−0.369800
$118$	6.00000	0.552345
$119$	0	0
$120$	0	0
$121$	25.0000	2.27273
$122$	4.00000	0.362143
$123$	0	0
$124$	−8.00000	−0.718421
$125$	0	0
$126$	0	0
$127$	9.00000	0.798621	0.399310	−	0.916816i	$-0.369250\pi$
$127$	9.00000	0.798621	0.399310	+	0.916816i	$0.369250\pi$
$128$	0	0
$129$	6.00000	0.528271
$130$	0	0
$131$	4.00000	0.349482	0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000	0.349482	0.174741	+	0.984614i	$0.444091\pi$
$132$	−12.0000	−1.04447
$133$	0	0
$134$	2.00000	0.172774
$135$	0	0
$136$	0	0
$137$	−14.0000	−1.19610	−0.598050	−	0.801459i	$-0.704058\pi$
$137$	−14.0000	−1.19610	−0.598050	+	0.801459i	$0.704058\pi$
$138$	2.00000	0.170251
$139$	2.00000	0.169638	0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000	0.169638	0.0848189	+	0.996396i	$0.472969\pi$
$140$	0	0
$141$	−9.00000	−0.757937
$142$	−32.0000	−2.68538
$143$	24.0000	2.00698
$144$	−4.00000	−0.333333
$145$	0	0
$146$	14.0000	1.15865
$147$	−7.00000	−0.577350
$148$	−6.00000	−0.493197
$149$	19.0000	1.55654	0.778270	−	0.627929i	$-0.216097\pi$
$149$	19.0000	1.55654	0.778270	+	0.627929i	$0.216097\pi$
$150$	0	0
$151$	−21.0000	−1.70896	−0.854478	−	0.519488i	$-0.826123\pi$
$151$	−21.0000	−1.70896	−0.854478	+	0.519488i	$0.826123\pi$
$152$	0	0
$153$	7.00000	0.565916
$154$	0	0
$155$	0	0
$156$	−8.00000	−0.640513
$157$	−17.0000	−1.35675	−0.678374	−	0.734717i	$-0.737315\pi$
$157$	−17.0000	−1.35675	−0.678374	+	0.734717i	$0.737315\pi$
$158$	16.0000	1.27289
$159$	−10.0000	−0.793052
$160$	0	0
$161$	0	0
$162$	2.00000	0.157135
$163$	13.0000	1.01824	0.509119	−	0.860696i	$-0.329971\pi$
$163$	13.0000	1.01824	0.509119	+	0.860696i	$0.329971\pi$
$164$	0	0
$165$	0	0
$166$	8.00000	0.620920
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	0	0
$171$	−5.00000	−0.382360
$172$	12.0000	0.914991
$173$	11.0000	0.836315	0.418157	−	0.908375i	$-0.362676\pi$
$173$	11.0000	0.836315	0.418157	+	0.908375i	$0.362676\pi$
$174$	2.00000	0.151620
$175$	0	0
$176$	24.0000	1.80907
$177$	3.00000	0.225494
$178$	−30.0000	−2.24860
$179$	26.0000	1.94333	0.971666	−	0.236360i	$-0.0759544\pi$
$179$	26.0000	1.94333	0.971666	+	0.236360i	$0.0759544\pi$
$180$	0	0
$181$	23.0000	1.70958	0.854788	−	0.518977i	$-0.173687\pi$
$181$	23.0000	1.70958	0.854788	+	0.518977i	$0.173687\pi$
$182$	0	0
$183$	2.00000	0.147844
$184$	0	0
$185$	0	0
$186$	−8.00000	−0.586588
$187$	−42.0000	−3.07134
$188$	−18.0000	−1.31278
$189$	0	0
$190$	0	0
$191$	−24.0000	−1.73658	−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000	−1.73658	−0.868290	+	0.496058i	$0.834780\pi$
$192$	−8.00000	−0.577350
$193$	15.0000	1.07972	0.539862	−	0.841754i	$-0.318476\pi$
$193$	15.0000	1.07972	0.539862	+	0.841754i	$0.318476\pi$
$194$	−8.00000	−0.574367
$195$	0	0
$196$	−14.0000	−1.00000
$197$	22.0000	1.56744	0.783718	−	0.621117i	$-0.213321\pi$
$197$	22.0000	1.56744	0.783718	+	0.621117i	$0.213321\pi$
$198$	−12.0000	−0.852803
$199$	7.00000	0.496217	0.248108	−	0.968732i	$-0.420191\pi$
$199$	7.00000	0.496217	0.248108	+	0.968732i	$0.420191\pi$
$200$	0	0
$201$	1.00000	0.0705346
$202$	0	0
$203$	0	0
$204$	14.0000	0.980196
$205$	0	0
$206$	−8.00000	−0.557386
$207$	1.00000	0.0695048
$208$	16.0000	1.10940
$209$	30.0000	2.07514
$210$	0	0
$211$	−20.0000	−1.37686	−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000	−1.37686	−0.688428	+	0.725304i	$0.741699\pi$
$212$	−20.0000	−1.37361
$213$	−16.0000	−1.09630
$214$	−14.0000	−0.957020
$215$	0	0
$216$	0	0
$217$	0	0
$218$	8.00000	0.541828
$219$	7.00000	0.473016
$220$	0	0
$221$	−28.0000	−1.88348
$222$	−6.00000	−0.402694
$223$	−15.0000	−1.00447	−0.502237	−	0.864730i	$-0.667490\pi$
$223$	−15.0000	−1.00447	−0.502237	+	0.864730i	$0.667490\pi$
$224$	0	0
$225$	0	0
$226$	−12.0000	−0.798228
$227$	19.0000	1.26107	0.630537	−	0.776159i	$-0.282835\pi$
$227$	19.0000	1.26107	0.630537	+	0.776159i	$0.282835\pi$
$228$	−10.0000	−0.662266
$229$	−18.0000	−1.18947	−0.594737	−	0.803921i	$-0.702744\pi$
$229$	−18.0000	−1.18947	−0.594737	+	0.803921i	$0.702744\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	16.0000	1.04819	0.524097	−	0.851658i	$-0.324403\pi$
$233$	16.0000	1.04819	0.524097	+	0.851658i	$0.324403\pi$
$234$	−8.00000	−0.522976
$235$	0	0
$236$	6.00000	0.390567
$237$	8.00000	0.519656
$238$	0	0
$239$	16.0000	1.03495	0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000	1.03495	0.517477	+	0.855697i	$0.326871\pi$
$240$	0	0
$241$	17.0000	1.09507	0.547533	−	0.836784i	$-0.315567\pi$
$241$	17.0000	1.09507	0.547533	+	0.836784i	$0.315567\pi$
$242$	50.0000	3.21412
$243$	1.00000	0.0641500
$244$	4.00000	0.256074
$245$	0	0
$246$	0	0
$247$	20.0000	1.27257
$248$	0	0
$249$	4.00000	0.253490
$250$	0	0
$251$	−2.00000	−0.126239	−0.0631194	−	0.998006i	$-0.520105\pi$
$251$	−2.00000	−0.126239	−0.0631194	+	0.998006i	$0.520105\pi$
$252$	0	0
$253$	−6.00000	−0.377217
$254$	18.0000	1.12942
$255$	0	0
$256$	16.0000	1.00000
$257$	19.0000	1.18519	0.592594	−	0.805502i	$-0.298104\pi$
$257$	19.0000	1.18519	0.592594	+	0.805502i	$0.298104\pi$
$258$	12.0000	0.747087
$259$	0	0
$260$	0	0
$261$	1.00000	0.0618984
$262$	8.00000	0.494242
$263$	8.00000	0.493301	0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000	0.493301	0.246651	+	0.969104i	$0.420670\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−15.0000	−0.917985
$268$	2.00000	0.122169
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	0	0
$271$	−22.0000	−1.33640	−0.668202	−	0.743980i	$-0.732936\pi$
$271$	−22.0000	−1.33640	−0.668202	+	0.743980i	$0.732936\pi$
$272$	−28.0000	−1.69775
$273$	0	0
$274$	−28.0000	−1.69154
$275$	0	0
$276$	2.00000	0.120386
$277$	2.00000	0.120168	0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000	0.120168	0.0600842	+	0.998193i	$0.480863\pi$
$278$	4.00000	0.239904
$279$	−4.00000	−0.239474
$280$	0	0
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	−18.0000	−1.07188
$283$	19.0000	1.12943	0.564716	−	0.825285i	$-0.308986\pi$
$283$	19.0000	1.12943	0.564716	+	0.825285i	$0.308986\pi$
$284$	−32.0000	−1.89885
$285$	0	0
$286$	48.0000	2.83830
$287$	0	0
$288$	−8.00000	−0.471405
$289$	32.0000	1.88235
$290$	0	0
$291$	−4.00000	−0.234484
$292$	14.0000	0.819288
$293$	10.0000	0.584206	0.292103	−	0.956387i	$-0.405645\pi$
$293$	10.0000	0.584206	0.292103	+	0.956387i	$0.405645\pi$
$294$	−14.0000	−0.816497
$295$	0	0
$296$	0	0
$297$	−6.00000	−0.348155
$298$	38.0000	2.20128
$299$	−4.00000	−0.231326
$300$	0	0
$301$	0	0
$302$	−42.0000	−2.41683
$303$	0	0
$304$	20.0000	1.14708
$305$	0	0
$306$	14.0000	0.800327
$307$	−23.0000	−1.31268	−0.656340	−	0.754466i	$-0.727896\pi$
$307$	−23.0000	−1.31268	−0.656340	+	0.754466i	$0.727896\pi$
$308$	0	0
$309$	−4.00000	−0.227552
$310$	0	0
$311$	26.0000	1.47432	0.737162	−	0.675716i	$-0.236165\pi$
$311$	26.0000	1.47432	0.737162	+	0.675716i	$0.236165\pi$
$312$	0	0
$313$	18.0000	1.01742	0.508710	−	0.860938i	$-0.330123\pi$
$313$	18.0000	1.01742	0.508710	+	0.860938i	$0.330123\pi$
$314$	−34.0000	−1.91873
$315$	0	0
$316$	16.0000	0.900070
$317$	14.0000	0.786318	0.393159	−	0.919470i	$-0.371382\pi$
$317$	14.0000	0.786318	0.393159	+	0.919470i	$0.371382\pi$
$318$	−20.0000	−1.12154
$319$	−6.00000	−0.335936
$320$	0	0
$321$	−7.00000	−0.390702
$322$	0	0
$323$	−35.0000	−1.94745
$324$	2.00000	0.111111
$325$	0	0
$326$	26.0000	1.44001
$327$	4.00000	0.221201
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−4.00000	−0.219860	−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000	−0.219860	−0.109930	+	0.993939i	$0.535063\pi$
$332$	8.00000	0.439057
$333$	−3.00000	−0.164399
$334$	−24.0000	−1.31322
$335$	0	0
$336$	0	0
$337$	−2.00000	−0.108947	−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000	−0.108947	−0.0544735	+	0.998515i	$0.517348\pi$
$338$	6.00000	0.326357
$339$	−6.00000	−0.325875
$340$	0	0
$341$	24.0000	1.29967
$342$	−10.0000	−0.540738
$343$	0	0
$344$	0	0
$345$	0	0
$346$	22.0000	1.18273
$347$	6.00000	0.322097	0.161048	−	0.986947i	$-0.448512\pi$
$347$	6.00000	0.322097	0.161048	+	0.986947i	$0.448512\pi$
$348$	2.00000	0.107211
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	0	0
$351$	−4.00000	−0.213504
$352$	48.0000	2.55841
$353$	0	0		−	1.00000i	$-0.5\pi$
$353$	0	0			1.00000i	$0.5\pi$
$354$	6.00000	0.318896
$355$	0	0
$356$	−30.0000	−1.59000
$357$	0	0
$358$	52.0000	2.74829
$359$	5.00000	0.263890	0.131945	−	0.991257i	$-0.457878\pi$
$359$	5.00000	0.263890	0.131945	+	0.991257i	$0.457878\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	46.0000	2.41771
$363$	25.0000	1.31216
$364$	0	0
$365$	0	0
$366$	4.00000	0.209083
$367$	−28.0000	−1.46159	−0.730794	−	0.682598i	$-0.760850\pi$
$367$	−28.0000	−1.46159	−0.730794	+	0.682598i	$0.760850\pi$
$368$	−4.00000	−0.208514
$369$	0	0
$370$	0	0
$371$	0	0
$372$	−8.00000	−0.414781
$373$	−8.00000	−0.414224	−0.207112	−	0.978317i	$-0.566407\pi$
$373$	−8.00000	−0.414224	−0.207112	+	0.978317i	$0.566407\pi$
$374$	−84.0000	−4.34354
$375$	0	0
$376$	0	0
$377$	−4.00000	−0.206010
$378$	0	0
$379$	−10.0000	−0.513665	−0.256833	−	0.966456i	$-0.582679\pi$
$379$	−10.0000	−0.513665	−0.256833	+	0.966456i	$0.582679\pi$
$380$	0	0
$381$	9.00000	0.461084
$382$	−48.0000	−2.45589
$383$	−12.0000	−0.613171	−0.306586	−	0.951843i	$-0.599187\pi$
$383$	−12.0000	−0.613171	−0.306586	+	0.951843i	$0.599187\pi$
$384$	0	0
$385$	0	0
$386$	30.0000	1.52696
$387$	6.00000	0.304997
$388$	−8.00000	−0.406138
$389$	−10.0000	−0.507020	−0.253510	−	0.967333i	$-0.581585\pi$
$389$	−10.0000	−0.507020	−0.253510	+	0.967333i	$0.581585\pi$
$390$	0	0
$391$	7.00000	0.354005
$392$	0	0
$393$	4.00000	0.201773
$394$	44.0000	2.21669
$395$	0	0
$396$	−12.0000	−0.603023
$397$	−29.0000	−1.45547	−0.727734	−	0.685859i	$-0.759427\pi$
$397$	−29.0000	−1.45547	−0.727734	+	0.685859i	$0.759427\pi$
$398$	14.0000	0.701757
$399$	0	0
$400$	0	0
$401$	−30.0000	−1.49813	−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000	−1.49813	−0.749064	+	0.662497i	$0.769497\pi$
$402$	2.00000	0.0997509
$403$	16.0000	0.797017
$404$	0	0
$405$	0	0
$406$	0	0
$407$	18.0000	0.892227
$408$	0	0
$409$	−32.0000	−1.58230	−0.791149	−	0.611623i	$-0.790517\pi$
$409$	−32.0000	−1.58230	−0.791149	+	0.611623i	$0.790517\pi$
$410$	0	0
$411$	−14.0000	−0.690569
$412$	−8.00000	−0.394132
$413$	0	0
$414$	2.00000	0.0982946
$415$	0	0
$416$	32.0000	1.56893
$417$	2.00000	0.0979404
$418$	60.0000	2.93470
$419$	−7.00000	−0.341972	−0.170986	−	0.985273i	$-0.554695\pi$
$419$	−7.00000	−0.341972	−0.170986	+	0.985273i	$0.554695\pi$
$420$	0	0
$421$	19.0000	0.926003	0.463002	−	0.886357i	$-0.346772\pi$
$421$	19.0000	0.926003	0.463002	+	0.886357i	$0.346772\pi$
$422$	−40.0000	−1.94717
$423$	−9.00000	−0.437595
$424$	0	0
$425$	0	0
$426$	−32.0000	−1.55041
$427$	0	0
$428$	−14.0000	−0.676716
$429$	24.0000	1.15873
$430$	0	0
$431$	5.00000	0.240842	0.120421	−	0.992723i	$-0.461576\pi$
$431$	5.00000	0.240842	0.120421	+	0.992723i	$0.461576\pi$
$432$	−4.00000	−0.192450
$433$	−20.0000	−0.961139	−0.480569	−	0.876957i	$-0.659570\pi$
$433$	−20.0000	−0.961139	−0.480569	+	0.876957i	$0.659570\pi$
$434$	0	0
$435$	0	0
$436$	8.00000	0.383131
$437$	−5.00000	−0.239182
$438$	14.0000	0.668946
$439$	−29.0000	−1.38409	−0.692047	−	0.721852i	$-0.743291\pi$
$439$	−29.0000	−1.38409	−0.692047	+	0.721852i	$0.743291\pi$
$440$	0	0
$441$	−7.00000	−0.333333
$442$	−56.0000	−2.66365
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	−6.00000	−0.284747
$445$	0	0
$446$	−30.0000	−1.42054
$447$	19.0000	0.898669
$448$	0	0
$449$	−27.0000	−1.27421	−0.637104	−	0.770778i	$-0.719868\pi$
$449$	−27.0000	−1.27421	−0.637104	+	0.770778i	$0.719868\pi$
$450$	0	0
$451$	0	0
$452$	−12.0000	−0.564433
$453$	−21.0000	−0.986666
$454$	38.0000	1.78343
$455$	0	0
$456$	0	0
$457$	35.0000	1.63723	0.818615	−	0.574342i	$-0.194742\pi$
$457$	35.0000	1.63723	0.818615	+	0.574342i	$0.194742\pi$
$458$	−36.0000	−1.68217
$459$	7.00000	0.326732
$460$	0	0
$461$	−21.0000	−0.978068	−0.489034	−	0.872265i	$-0.662651\pi$
$461$	−21.0000	−0.978068	−0.489034	+	0.872265i	$0.662651\pi$
$462$	0	0
$463$	−28.0000	−1.30127	−0.650635	−	0.759390i	$-0.725497\pi$
$463$	−28.0000	−1.30127	−0.650635	+	0.759390i	$0.725497\pi$
$464$	−4.00000	−0.185695
$465$	0	0
$466$	32.0000	1.48237
$467$	−12.0000	−0.555294	−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000	−0.555294	−0.277647	+	0.960683i	$0.589555\pi$
$468$	−8.00000	−0.369800
$469$	0	0
$470$	0	0
$471$	−17.0000	−0.783319
$472$	0	0
$473$	−36.0000	−1.65528
$474$	16.0000	0.734904
$475$	0	0
$476$	0	0
$477$	−10.0000	−0.457869
$478$	32.0000	1.46365
$479$	−35.0000	−1.59919	−0.799595	−	0.600539i	$-0.794953\pi$
$479$	−35.0000	−1.59919	−0.799595	+	0.600539i	$0.794953\pi$
$480$	0	0
$481$	12.0000	0.547153
$482$	34.0000	1.54866
$483$	0	0
$484$	50.0000	2.27273
$485$	0	0
$486$	2.00000	0.0907218
$487$	−4.00000	−0.181257	−0.0906287	−	0.995885i	$-0.528888\pi$
$487$	−4.00000	−0.181257	−0.0906287	+	0.995885i	$0.528888\pi$
$488$	0	0
$489$	13.0000	0.587880
$490$	0	0
$491$	5.00000	0.225647	0.112823	−	0.993615i	$-0.464011\pi$
$491$	5.00000	0.225647	0.112823	+	0.993615i	$0.464011\pi$
$492$	0	0
$493$	7.00000	0.315264
$494$	40.0000	1.79969
$495$	0	0
$496$	16.0000	0.718421
$497$	0	0
$498$	8.00000	0.358489
$499$	−30.0000	−1.34298	−0.671492	−	0.741012i	$-0.734346\pi$
$499$	−30.0000	−1.34298	−0.671492	+	0.741012i	$0.734346\pi$
$500$	0	0
$501$	−12.0000	−0.536120
$502$	−4.00000	−0.178529
$503$	8.00000	0.356702	0.178351	−	0.983967i	$-0.442924\pi$
$503$	8.00000	0.356702	0.178351	+	0.983967i	$0.442924\pi$
$504$	0	0
$505$	0	0
$506$	−12.0000	−0.533465
$507$	3.00000	0.133235
$508$	18.0000	0.798621
$509$	15.0000	0.664863	0.332432	−	0.943127i	$-0.392131\pi$
$509$	15.0000	0.664863	0.332432	+	0.943127i	$0.392131\pi$
$510$	0	0
$511$	0	0
$512$	32.0000	1.41421
$513$	−5.00000	−0.220755
$514$	38.0000	1.67611
$515$	0	0
$516$	12.0000	0.528271
$517$	54.0000	2.37492
$518$	0	0
$519$	11.0000	0.482846
$520$	0	0
$521$	30.0000	1.31432	0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000	1.31432	0.657162	+	0.753749i	$0.271757\pi$
$522$	2.00000	0.0875376
$523$	−41.0000	−1.79280	−0.896402	−	0.443241i	$-0.853829\pi$
$523$	−41.0000	−1.79280	−0.896402	+	0.443241i	$0.853829\pi$
$524$	8.00000	0.349482
$525$	0	0
$526$	16.0000	0.697633
$527$	−28.0000	−1.21970
$528$	24.0000	1.04447
$529$	−22.0000	−0.956522
$530$	0	0
$531$	3.00000	0.130189
$532$	0	0
$533$	0	0
$534$	−30.0000	−1.29823
$535$	0	0
$536$	0	0
$537$	26.0000	1.12198
$538$	−12.0000	−0.517357
$539$	42.0000	1.80907
$540$	0	0
$541$	−40.0000	−1.71973	−0.859867	−	0.510518i	$-0.829454\pi$
$541$	−40.0000	−1.71973	−0.859867	+	0.510518i	$0.829454\pi$
$542$	−44.0000	−1.88996
$543$	23.0000	0.987024
$544$	−56.0000	−2.40098
$545$	0	0
$546$	0	0
$547$	2.00000	0.0855138	0.0427569	−	0.999086i	$-0.486386\pi$
$547$	2.00000	0.0855138	0.0427569	+	0.999086i	$0.486386\pi$
$548$	−28.0000	−1.19610
$549$	2.00000	0.0853579
$550$	0	0
$551$	−5.00000	−0.213007
$552$	0	0
$553$	0	0
$554$	4.00000	0.169944
$555$	0	0
$556$	4.00000	0.169638
$557$	14.0000	0.593199	0.296600	−	0.955002i	$-0.404147\pi$
$557$	14.0000	0.593199	0.296600	+	0.955002i	$0.404147\pi$
$558$	−8.00000	−0.338667
$559$	−24.0000	−1.01509
$560$	0	0
$561$	−42.0000	−1.77324
$562$	−36.0000	−1.51857
$563$	−8.00000	−0.337160	−0.168580	−	0.985688i	$-0.553918\pi$
$563$	−8.00000	−0.337160	−0.168580	+	0.985688i	$0.553918\pi$
$564$	−18.0000	−0.757937
$565$	0	0
$566$	38.0000	1.59726
$567$	0	0
$568$	0	0
$569$	15.0000	0.628833	0.314416	−	0.949285i	$-0.398191\pi$
$569$	15.0000	0.628833	0.314416	+	0.949285i	$0.398191\pi$
$570$	0	0
$571$	−7.00000	−0.292941	−0.146470	−	0.989215i	$-0.546791\pi$
$571$	−7.00000	−0.292941	−0.146470	+	0.989215i	$0.546791\pi$
$572$	48.0000	2.00698
$573$	−24.0000	−1.00261
$574$	0	0
$575$	0	0
$576$	−8.00000	−0.333333
$577$	12.0000	0.499567	0.249783	−	0.968302i	$-0.419641\pi$
$577$	12.0000	0.499567	0.249783	+	0.968302i	$0.419641\pi$
$578$	64.0000	2.66205
$579$	15.0000	0.623379
$580$	0	0
$581$	0	0
$582$	−8.00000	−0.331611
$583$	60.0000	2.48495
$584$	0	0
$585$	0	0
$586$	20.0000	0.826192
$587$	24.0000	0.990586	0.495293	−	0.868726i	$-0.335061\pi$
$587$	24.0000	0.990586	0.495293	+	0.868726i	$0.335061\pi$
$588$	−14.0000	−0.577350
$589$	20.0000	0.824086
$590$	0	0
$591$	22.0000	0.904959
$592$	12.0000	0.493197
$593$	6.00000	0.246390	0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000	0.246390	0.123195	+	0.992382i	$0.460686\pi$
$594$	−12.0000	−0.492366
$595$	0	0
$596$	38.0000	1.55654
$597$	7.00000	0.286491
$598$	−8.00000	−0.327144
$599$	−6.00000	−0.245153	−0.122577	−	0.992459i	$-0.539116\pi$
$599$	−6.00000	−0.245153	−0.122577	+	0.992459i	$0.539116\pi$
$600$	0	0
$601$	−45.0000	−1.83559	−0.917794	−	0.397057i	$-0.870032\pi$
$601$	−45.0000	−1.83559	−0.917794	+	0.397057i	$0.870032\pi$
$602$	0	0
$603$	1.00000	0.0407231
$604$	−42.0000	−1.70896
$605$	0	0
$606$	0	0
$607$	−8.00000	−0.324710	−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000	−0.324710	−0.162355	+	0.986732i	$0.551909\pi$
$608$	40.0000	1.62221
$609$	0	0
$610$	0	0
$611$	36.0000	1.45640
$612$	14.0000	0.565916
$613$	33.0000	1.33286	0.666429	−	0.745569i	$-0.267822\pi$
$613$	33.0000	1.33286	0.666429	+	0.745569i	$0.267822\pi$
$614$	−46.0000	−1.85641
$615$	0	0
$616$	0	0
$617$	39.0000	1.57008	0.785040	−	0.619445i	$-0.212642\pi$
$617$	39.0000	1.57008	0.785040	+	0.619445i	$0.212642\pi$
$618$	−8.00000	−0.321807
$619$	20.0000	0.803868	0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000	0.803868	0.401934	+	0.915669i	$0.368338\pi$
$620$	0	0
$621$	1.00000	0.0401286
$622$	52.0000	2.08501
$623$	0	0
$624$	16.0000	0.640513
$625$	0	0
$626$	36.0000	1.43885
$627$	30.0000	1.19808
$628$	−34.0000	−1.35675
$629$	−21.0000	−0.837325
$630$	0	0
$631$	−6.00000	−0.238856	−0.119428	−	0.992843i	$-0.538106\pi$
$631$	−6.00000	−0.238856	−0.119428	+	0.992843i	$0.538106\pi$
$632$	0	0
$633$	−20.0000	−0.794929
$634$	28.0000	1.11202
$635$	0	0
$636$	−20.0000	−0.793052
$637$	28.0000	1.10940
$638$	−12.0000	−0.475085
$639$	−16.0000	−0.632950
$640$	0	0
$641$	0	0		−	1.00000i	$-0.5\pi$
$641$	0	0			1.00000i	$0.5\pi$
$642$	−14.0000	−0.552536
$643$	−36.0000	−1.41970	−0.709851	−	0.704352i	$-0.751238\pi$
$643$	−36.0000	−1.41970	−0.709851	+	0.704352i	$0.751238\pi$
$644$	0	0
$645$	0	0
$646$	−70.0000	−2.75411
$647$	−18.0000	−0.707653	−0.353827	−	0.935311i	$-0.615120\pi$
$647$	−18.0000	−0.707653	−0.353827	+	0.935311i	$0.615120\pi$
$648$	0	0
$649$	−18.0000	−0.706562
$650$	0	0
$651$	0	0
$652$	26.0000	1.01824
$653$	−10.0000	−0.391330	−0.195665	−	0.980671i	$-0.562687\pi$
$653$	−10.0000	−0.391330	−0.195665	+	0.980671i	$0.562687\pi$
$654$	8.00000	0.312825
$655$	0	0
$656$	0	0
$657$	7.00000	0.273096
$658$	0	0
$659$	33.0000	1.28550	0.642749	−	0.766077i	$-0.277794\pi$
$659$	33.0000	1.28550	0.642749	+	0.766077i	$0.277794\pi$
$660$	0	0
$661$	−12.0000	−0.466746	−0.233373	−	0.972387i	$-0.574976\pi$
$661$	−12.0000	−0.466746	−0.233373	+	0.972387i	$0.574976\pi$
$662$	−8.00000	−0.310929
$663$	−28.0000	−1.08743
$664$	0	0
$665$	0	0
$666$	−6.00000	−0.232495
$667$	1.00000	0.0387202
$668$	−24.0000	−0.928588
$669$	−15.0000	−0.579934
$670$	0	0
$671$	−12.0000	−0.463255
$672$	0	0
$673$	0	0		−	1.00000i	$-0.5\pi$
$673$	0	0			1.00000i	$0.5\pi$
$674$	−4.00000	−0.154074
$675$	0	0
$676$	6.00000	0.230769
$677$	30.0000	1.15299	0.576497	−	0.817099i	$-0.304419\pi$
$677$	30.0000	1.15299	0.576497	+	0.817099i	$0.304419\pi$
$678$	−12.0000	−0.460857
$679$	0	0
$680$	0	0
$681$	19.0000	0.728082
$682$	48.0000	1.83801
$683$	14.0000	0.535695	0.267848	−	0.963461i	$-0.413688\pi$
$683$	14.0000	0.535695	0.267848	+	0.963461i	$0.413688\pi$
$684$	−10.0000	−0.382360
$685$	0	0
$686$	0	0
$687$	−18.0000	−0.686743
$688$	−24.0000	−0.914991
$689$	40.0000	1.52388
$690$	0	0
$691$	−5.00000	−0.190209	−0.0951045	−	0.995467i	$-0.530319\pi$
$691$	−5.00000	−0.190209	−0.0951045	+	0.995467i	$0.530319\pi$
$692$	22.0000	0.836315
$693$	0	0
$694$	12.0000	0.455514
$695$	0	0
$696$	0	0
$697$	0	0
$698$	28.0000	1.05982
$699$	16.0000	0.605176
$700$	0	0
$701$	14.0000	0.528773	0.264386	−	0.964417i	$-0.414831\pi$
$701$	14.0000	0.528773	0.264386	+	0.964417i	$0.414831\pi$
$702$	−8.00000	−0.301941
$703$	15.0000	0.565736
$704$	48.0000	1.80907
$705$	0	0
$706$	0	0
$707$	0	0
$708$	6.00000	0.225494
$709$	−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
$711$	8.00000	0.300023
$712$	0	0
$713$	−4.00000	−0.149801
$714$	0	0
$715$	0	0
$716$	52.0000	1.94333
$717$	16.0000	0.597531
$718$	10.0000	0.373197
$719$	−1.00000	−0.0372937	−0.0186469	−	0.999826i	$-0.505936\pi$
$719$	−1.00000	−0.0372937	−0.0186469	+	0.999826i	$0.505936\pi$
$720$	0	0
$721$	0	0
$722$	12.0000	0.446594
$723$	17.0000	0.632237
$724$	46.0000	1.70958
$725$	0	0
$726$	50.0000	1.85567
$727$	−2.00000	−0.0741759	−0.0370879	−	0.999312i	$-0.511808\pi$
$727$	−2.00000	−0.0741759	−0.0370879	+	0.999312i	$0.511808\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	42.0000	1.55343
$732$	4.00000	0.147844
$733$	−34.0000	−1.25582	−0.627909	−	0.778287i	$-0.716089\pi$
$733$	−34.0000	−1.25582	−0.627909	+	0.778287i	$0.716089\pi$
$734$	−56.0000	−2.06700
$735$	0	0
$736$	−8.00000	−0.294884
$737$	−6.00000	−0.221013
$738$	0	0
$739$	44.0000	1.61857	0.809283	−	0.587419i	$-0.199856\pi$
$739$	44.0000	1.61857	0.809283	+	0.587419i	$0.199856\pi$
$740$	0	0
$741$	20.0000	0.734718
$742$	0	0
$743$	−40.0000	−1.46746	−0.733729	−	0.679442i	$-0.762222\pi$
$743$	−40.0000	−1.46746	−0.733729	+	0.679442i	$0.762222\pi$
$744$	0	0
$745$	0	0
$746$	−16.0000	−0.585802
$747$	4.00000	0.146352
$748$	−84.0000	−3.07134
$749$	0	0
$750$	0	0
$751$	−49.0000	−1.78804	−0.894018	−	0.448032i	$-0.852125\pi$
$751$	−49.0000	−1.78804	−0.894018	+	0.448032i	$0.852125\pi$
$752$	36.0000	1.31278
$753$	−2.00000	−0.0728841
$754$	−8.00000	−0.291343
$755$	0	0
$756$	0	0
$757$	−50.0000	−1.81728	−0.908640	−	0.417579i	$-0.862879\pi$
$757$	−50.0000	−1.81728	−0.908640	+	0.417579i	$0.862879\pi$
$758$	−20.0000	−0.726433
$759$	−6.00000	−0.217786
$760$	0	0
$761$	−3.00000	−0.108750	−0.0543750	−	0.998521i	$-0.517317\pi$
$761$	−3.00000	−0.108750	−0.0543750	+	0.998521i	$0.517317\pi$
$762$	18.0000	0.652071
$763$	0	0
$764$	−48.0000	−1.73658
$765$	0	0
$766$	−24.0000	−0.867155
$767$	−12.0000	−0.433295
$768$	16.0000	0.577350
$769$	34.0000	1.22607	0.613036	−	0.790055i	$-0.289948\pi$
$769$	34.0000	1.22607	0.613036	+	0.790055i	$0.289948\pi$
$770$	0	0
$771$	19.0000	0.684268
$772$	30.0000	1.07972
$773$	33.0000	1.18693	0.593464	−	0.804861i	$-0.297760\pi$
$773$	33.0000	1.18693	0.593464	+	0.804861i	$0.297760\pi$
$774$	12.0000	0.431331
$775$	0	0
$776$	0	0
$777$	0	0
$778$	−20.0000	−0.717035
$779$	0	0
$780$	0	0
$781$	96.0000	3.43515
$782$	14.0000	0.500639
$783$	1.00000	0.0357371
$784$	28.0000	1.00000
$785$	0	0
$786$	8.00000	0.285351
$787$	4.00000	0.142585	0.0712923	−	0.997455i	$-0.477288\pi$
$787$	4.00000	0.142585	0.0712923	+	0.997455i	$0.477288\pi$
$788$	44.0000	1.56744
$789$	8.00000	0.284808
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−8.00000	−0.284088
$794$	−58.0000	−2.05834
$795$	0	0
$796$	14.0000	0.496217
$797$	−34.0000	−1.20434	−0.602171	−	0.798367i	$-0.705697\pi$
$797$	−34.0000	−1.20434	−0.602171	+	0.798367i	$0.705697\pi$
$798$	0	0
$799$	−63.0000	−2.22878
$800$	0	0
$801$	−15.0000	−0.529999
$802$	−60.0000	−2.11867
$803$	−42.0000	−1.48215
$804$	2.00000	0.0705346
$805$	0	0
$806$	32.0000	1.12715
$807$	−6.00000	−0.211210
$808$	0	0
$809$	−20.0000	−0.703163	−0.351581	−	0.936157i	$-0.614356\pi$
$809$	−20.0000	−0.703163	−0.351581	+	0.936157i	$0.614356\pi$
$810$	0	0
$811$	−2.00000	−0.0702295	−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000	−0.0702295	−0.0351147	+	0.999383i	$0.511180\pi$
$812$	0	0
$813$	−22.0000	−0.771574
$814$	36.0000	1.26180
$815$	0	0
$816$	−28.0000	−0.980196
$817$	−30.0000	−1.04957
$818$	−64.0000	−2.23771
$819$	0	0
$820$	0	0
$821$	−27.0000	−0.942306	−0.471153	−	0.882051i	$-0.656162\pi$
$821$	−27.0000	−0.942306	−0.471153	+	0.882051i	$0.656162\pi$
$822$	−28.0000	−0.976612
$823$	17.0000	0.592583	0.296291	−	0.955098i	$-0.404250\pi$
$823$	17.0000	0.592583	0.296291	+	0.955098i	$0.404250\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	21.0000	0.730242	0.365121	−	0.930960i	$-0.381028\pi$
$827$	21.0000	0.730242	0.365121	+	0.930960i	$0.381028\pi$
$828$	2.00000	0.0695048
$829$	45.0000	1.56291	0.781457	−	0.623959i	$-0.214477\pi$
$829$	45.0000	1.56291	0.781457	+	0.623959i	$0.214477\pi$
$830$	0	0
$831$	2.00000	0.0693792
$832$	32.0000	1.10940
$833$	−49.0000	−1.69775
$834$	4.00000	0.138509
$835$	0	0
$836$	60.0000	2.07514
$837$	−4.00000	−0.138260
$838$	−14.0000	−0.483622
$839$	47.0000	1.62262	0.811310	−	0.584616i	$-0.198755\pi$
$839$	47.0000	1.62262	0.811310	+	0.584616i	$0.198755\pi$
$840$	0	0
$841$	−28.0000	−0.965517
$842$	38.0000	1.30957
$843$	−18.0000	−0.619953
$844$	−40.0000	−1.37686
$845$	0	0
$846$	−18.0000	−0.618853
$847$	0	0
$848$	40.0000	1.37361
$849$	19.0000	0.652078
$850$	0	0
$851$	−3.00000	−0.102839
$852$	−32.0000	−1.09630
$853$	11.0000	0.376633	0.188316	−	0.982108i	$-0.439697\pi$
$853$	11.0000	0.376633	0.188316	+	0.982108i	$0.439697\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	48.0000	1.63965	0.819824	−	0.572615i	$-0.194071\pi$
$857$	48.0000	1.63965	0.819824	+	0.572615i	$0.194071\pi$
$858$	48.0000	1.63869
$859$	20.0000	0.682391	0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000	0.682391	0.341196	+	0.939992i	$0.389168\pi$
$860$	0	0
$861$	0	0
$862$	10.0000	0.340601
$863$	−3.00000	−0.102121	−0.0510606	−	0.998696i	$-0.516260\pi$
$863$	−3.00000	−0.102121	−0.0510606	+	0.998696i	$0.516260\pi$
$864$	−8.00000	−0.272166
$865$	0	0
$866$	−40.0000	−1.35926
$867$	32.0000	1.08678
$868$	0	0
$869$	−48.0000	−1.62829
$870$	0	0
$871$	−4.00000	−0.135535
$872$	0	0
$873$	−4.00000	−0.135379
$874$	−10.0000	−0.338255
$875$	0	0
$876$	14.0000	0.473016
$877$	19.0000	0.641584	0.320792	−	0.947150i	$-0.396051\pi$
$877$	19.0000	0.641584	0.320792	+	0.947150i	$0.396051\pi$
$878$	−58.0000	−1.95741
$879$	10.0000	0.337292
$880$	0	0
$881$	21.0000	0.707508	0.353754	−	0.935339i	$-0.384905\pi$
$881$	21.0000	0.707508	0.353754	+	0.935339i	$0.384905\pi$
$882$	−14.0000	−0.471405
$883$	20.0000	0.673054	0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000	0.673054	0.336527	+	0.941674i	$0.390748\pi$
$884$	−56.0000	−1.88348
$885$	0	0
$886$	−8.00000	−0.268765
$887$	37.0000	1.24234	0.621169	−	0.783676i	$-0.286658\pi$
$887$	37.0000	1.24234	0.621169	+	0.783676i	$0.286658\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−6.00000	−0.201008
$892$	−30.0000	−1.00447
$893$	45.0000	1.50587
$894$	38.0000	1.27091
$895$	0	0
$896$	0	0
$897$	−4.00000	−0.133556
$898$	−54.0000	−1.80200
$899$	−4.00000	−0.133407
$900$	0	0
$901$	−70.0000	−2.33204
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	−42.0000	−1.39536
$907$	−37.0000	−1.22856	−0.614282	−	0.789086i	$-0.710554\pi$
$907$	−37.0000	−1.22856	−0.614282	+	0.789086i	$0.710554\pi$
$908$	38.0000	1.26107
$909$	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	$0.547635\pi$
$912$	20.0000	0.662266
$913$	−24.0000	−0.794284
$914$	70.0000	2.31539
$915$	0	0
$916$	−36.0000	−1.18947
$917$	0	0
$918$	14.0000	0.462069
$919$	42.0000	1.38545	0.692726	−	0.721201i	$-0.256409\pi$
$919$	42.0000	1.38545	0.692726	+	0.721201i	$0.256409\pi$
$920$	0	0
$921$	−23.0000	−0.757876
$922$	−42.0000	−1.38320
$923$	64.0000	2.10659
$924$	0	0
$925$	0	0
$926$	−56.0000	−1.84027
$927$	−4.00000	−0.131377
$928$	−8.00000	−0.262613
$929$	−20.0000	−0.656179	−0.328089	−	0.944647i	$-0.606405\pi$
$929$	−20.0000	−0.656179	−0.328089	+	0.944647i	$0.606405\pi$
$930$	0	0
$931$	35.0000	1.14708
$932$	32.0000	1.04819
$933$	26.0000	0.851202
$934$	−24.0000	−0.785304
$935$	0	0
$936$	0	0
$937$	−8.00000	−0.261349	−0.130674	−	0.991425i	$-0.541714\pi$
$937$	−8.00000	−0.261349	−0.130674	+	0.991425i	$0.541714\pi$
$938$	0	0
$939$	18.0000	0.587408
$940$	0	0
$941$	−10.0000	−0.325991	−0.162995	−	0.986627i	$-0.552116\pi$
$941$	−10.0000	−0.325991	−0.162995	+	0.986627i	$0.552116\pi$
$942$	−34.0000	−1.10778
$943$	0	0
$944$	−12.0000	−0.390567
$945$	0	0
$946$	−72.0000	−2.34092
$947$	−47.0000	−1.52729	−0.763647	−	0.645634i	$-0.776593\pi$
$947$	−47.0000	−1.52729	−0.763647	+	0.645634i	$0.776593\pi$
$948$	16.0000	0.519656
$949$	−28.0000	−0.908918
$950$	0	0
$951$	14.0000	0.453981
$952$	0	0
$953$	−11.0000	−0.356325	−0.178162	−	0.984001i	$-0.557015\pi$
$953$	−11.0000	−0.356325	−0.178162	+	0.984001i	$0.557015\pi$
$954$	−20.0000	−0.647524
$955$	0	0
$956$	32.0000	1.03495
$957$	−6.00000	−0.193952
$958$	−70.0000	−2.26160
$959$	0	0
$960$	0	0
$961$	−15.0000	−0.483871
$962$	24.0000	0.773791
$963$	−7.00000	−0.225572
$964$	34.0000	1.09507
$965$	0	0
$966$	0	0
$967$	48.0000	1.54358	0.771788	−	0.635880i	$-0.219363\pi$
$967$	48.0000	1.54358	0.771788	+	0.635880i	$0.219363\pi$
$968$	0	0
$969$	−35.0000	−1.12436
$970$	0	0
$971$	55.0000	1.76503	0.882517	−	0.470281i	$-0.155847\pi$
$971$	55.0000	1.76503	0.882517	+	0.470281i	$0.155847\pi$
$972$	2.00000	0.0641500
$973$	0	0
$974$	−8.00000	−0.256337
$975$	0	0
$976$	−8.00000	−0.256074
$977$	−29.0000	−0.927792	−0.463896	−	0.885890i	$-0.653549\pi$
$977$	−29.0000	−0.927792	−0.463896	+	0.885890i	$0.653549\pi$
$978$	26.0000	0.831388
$979$	90.0000	2.87641
$980$	0	0
$981$	4.00000	0.127710
$982$	10.0000	0.319113
$983$	−56.0000	−1.78612	−0.893061	−	0.449935i	$-0.851447\pi$
$983$	−56.0000	−1.78612	−0.893061	+	0.449935i	$0.851447\pi$
$984$	0	0
$985$	0	0
$986$	14.0000	0.445851
$987$	0	0
$988$	40.0000	1.27257
$989$	6.00000	0.190789
$990$	0	0
$991$	46.0000	1.46124	0.730619	−	0.682785i	$-0.239232\pi$
$991$	46.0000	1.46124	0.730619	+	0.682785i	$0.239232\pi$
$992$	32.0000	1.01600
$993$	−4.00000	−0.126936
$994$	0	0
$995$	0	0
$996$	8.00000	0.253490
$997$	−30.0000	−0.950110	−0.475055	−	0.879956i	$-0.657572\pi$
$997$	−30.0000	−0.950110	−0.475055	+	0.879956i	$0.657572\pi$
$998$	−60.0000	−1.89927
$999$	−3.00000	−0.0949158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5025.2.a.i.1.1		1
5.4	even	2		201.2.a.a.1.1	✓	1
15.14	odd	2		603.2.a.f.1.1		1
20.19	odd	2		3216.2.a.j.1.1		1
35.34	odd	2		9849.2.a.b.1.1		1
60.59	even	2		9648.2.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.a.a.1.1	✓	1	5.4	even	2
603.2.a.f.1.1		1	15.14	odd	2
3216.2.a.j.1.1		1	20.19	odd	2
5025.2.a.i.1.1		1	1.1	even	1	trivial
9648.2.a.j.1.1		1	60.59	even	2
9849.2.a.b.1.1		1	35.34	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:	\( N \)	\(=\)	\( 5025 = 3 \cdot 5^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5025.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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