LMFDB - Embedded newform 627.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [627,2,Mod(1,627)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(627, 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("627.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 627 = 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	627.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:	$5.00662020673$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	627.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{3} -2.00000 q^{4} +2.00000 q^{7} +1.00000 q^{9} +O(q^{10})$

$q+1.00000 q^{3} -2.00000 q^{4} +2.00000 q^{7} +1.00000 q^{9} +1.00000 q^{11} -2.00000 q^{12} -1.00000 q^{13} +4.00000 q^{16} +3.00000 q^{17} +1.00000 q^{19} +2.00000 q^{21} +6.00000 q^{23} -5.00000 q^{25} +1.00000 q^{27} -4.00000 q^{28} +8.00000 q^{31} +1.00000 q^{33} -2.00000 q^{36} +2.00000 q^{37} -1.00000 q^{39} +6.00000 q^{41} +8.00000 q^{43} -2.00000 q^{44} -6.00000 q^{47} +4.00000 q^{48} -3.00000 q^{49} +3.00000 q^{51} +2.00000 q^{52} +9.00000 q^{53} +1.00000 q^{57} +3.00000 q^{59} -10.0000 q^{61} +2.00000 q^{63} -8.00000 q^{64} -10.0000 q^{67} -6.00000 q^{68} +6.00000 q^{69} -3.00000 q^{71} -4.00000 q^{73} -5.00000 q^{75} -2.00000 q^{76} +2.00000 q^{77} -13.0000 q^{79} +1.00000 q^{81} -3.00000 q^{83} -4.00000 q^{84} +15.0000 q^{89} -2.00000 q^{91} -12.0000 q^{92} +8.00000 q^{93} -10.0000 q^{97} +1.00000 q^{99} +O(q^{100})$

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 $

$2$	0	0		−	1.00000i	$-0.5\pi$
$2$	0	0			1.00000i	$0.5\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−2.00000	−1.00000
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	2.00000	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.00000	−0.577350
$13$	−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
$16$	4.00000	1.00000
$17$	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
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	2.00000	0.436436
$22$	0	0
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	0	0
$25$	−5.00000	−1.00000
$26$	0	0
$27$	1.00000	0.192450
$28$	−4.00000	−0.755929
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	8.00000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	0	0
$33$	1.00000	0.174078
$34$	0	0
$35$	0	0
$36$	−2.00000	−0.333333
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	0	0
$39$	−1.00000	−0.160128
$40$	0	0
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	0	0
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	−2.00000	−0.301511
$45$	0	0
$46$	0	0
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	4.00000	0.577350
$49$	−3.00000	−0.428571
$50$	0	0
$51$	3.00000	0.420084
$52$	2.00000	0.277350
$53$	9.00000	1.23625	0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000	1.23625	0.618123	+	0.786082i	$0.287894\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	1.00000	0.132453
$58$	0	0
$59$	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
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	0	0
$63$	2.00000	0.251976
$64$	−8.00000	−1.00000
$65$	0	0
$66$	0	0
$67$	−10.0000	−1.22169	−0.610847	−	0.791748i	$-0.709171\pi$
$67$	−10.0000	−1.22169	−0.610847	+	0.791748i	$0.709171\pi$
$68$	−6.00000	−0.727607
$69$	6.00000	0.722315
$70$	0	0
$71$	−3.00000	−0.356034	−0.178017	−	0.984027i	$-0.556968\pi$
$71$	−3.00000	−0.356034	−0.178017	+	0.984027i	$0.556968\pi$
$72$	0	0
$73$	−4.00000	−0.468165	−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000	−0.468165	−0.234082	+	0.972217i	$0.575209\pi$
$74$	0	0
$75$	−5.00000	−0.577350
$76$	−2.00000	−0.229416
$77$	2.00000	0.227921
$78$	0	0
$79$	−13.0000	−1.46261	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	−13.0000	−1.46261	−0.731307	+	0.682048i	$0.761089\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	−3.00000	−0.329293	−0.164646	−	0.986353i	$-0.552648\pi$
$83$	−3.00000	−0.329293	−0.164646	+	0.986353i	$0.552648\pi$
$84$	−4.00000	−0.436436
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	15.0000	1.59000	0.794998	−	0.606612i	$-0.207472\pi$
$89$	15.0000	1.59000	0.794998	+	0.606612i	$0.207472\pi$
$90$	0	0
$91$	−2.00000	−0.209657
$92$	−12.0000	−1.25109
$93$	8.00000	0.829561
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−10.0000	−1.01535	−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000	−1.01535	−0.507673	+	0.861550i	$0.669494\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	10.0000	1.00000
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	0	0
$103$	−10.0000	−0.985329	−0.492665	−	0.870219i	$-0.663977\pi$
$103$	−10.0000	−0.985329	−0.492665	+	0.870219i	$0.663977\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	18.0000	1.74013	0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000	1.74013	0.870063	+	0.492941i	$0.164078\pi$
$108$	−2.00000	−0.192450
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	0	0
$111$	2.00000	0.189832
$112$	8.00000	0.755929
$113$	−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
$115$	0	0
$116$	0	0
$117$	−1.00000	−0.0924500
$118$	0	0
$119$	6.00000	0.550019
$120$	0	0
$121$	1.00000	0.0909091
$122$	0	0
$123$	6.00000	0.541002
$124$	−16.0000	−1.43684
$125$	0	0
$126$	0	0
$127$	−7.00000	−0.621150	−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000	−0.621150	−0.310575	+	0.950549i	$0.600522\pi$
$128$	0	0
$129$	8.00000	0.704361
$130$	0	0
$131$	21.0000	1.83478	0.917389	−	0.397991i	$-0.130293\pi$
$131$	21.0000	1.83478	0.917389	+	0.397991i	$0.130293\pi$
$132$	−2.00000	−0.174078
$133$	2.00000	0.173422
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	0	0
$139$	−16.0000	−1.35710	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000	−1.35710	−0.678551	+	0.734553i	$0.737392\pi$
$140$	0	0
$141$	−6.00000	−0.505291
$142$	0	0
$143$	−1.00000	−0.0836242
$144$	4.00000	0.333333
$145$	0	0
$146$	0	0
$147$	−3.00000	−0.247436
$148$	−4.00000	−0.328798
$149$	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
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	0	0
$153$	3.00000	0.242536
$154$	0	0
$155$	0	0
$156$	2.00000	0.160128
$157$	11.0000	0.877896	0.438948	−	0.898513i	$-0.355351\pi$
$157$	11.0000	0.877896	0.438948	+	0.898513i	$0.355351\pi$
$158$	0	0
$159$	9.00000	0.713746
$160$	0	0
$161$	12.0000	0.945732
$162$	0	0
$163$	−19.0000	−1.48819	−0.744097	−	0.668071i	$-0.767120\pi$
$163$	−19.0000	−1.48819	−0.744097	+	0.668071i	$0.767120\pi$
$164$	−12.0000	−0.937043
$165$	0	0
$166$	0	0
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	1.00000	0.0764719
$172$	−16.0000	−1.21999
$173$	−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
$175$	−10.0000	−0.755929
$176$	4.00000	0.301511
$177$	3.00000	0.225494
$178$	0	0
$179$	−15.0000	−1.12115	−0.560576	−	0.828103i	$-0.689420\pi$
$179$	−15.0000	−1.12115	−0.560576	+	0.828103i	$0.689420\pi$
$180$	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
$183$	−10.0000	−0.739221
$184$	0	0
$185$	0	0
$186$	0	0
$187$	3.00000	0.219382
$188$	12.0000	0.875190
$189$	2.00000	0.145479
$190$	0	0
$191$	−6.00000	−0.434145	−0.217072	−	0.976156i	$-0.569651\pi$
$191$	−6.00000	−0.434145	−0.217072	+	0.976156i	$0.569651\pi$
$192$	−8.00000	−0.577350
$193$	5.00000	0.359908	0.179954	−	0.983675i	$-0.442405\pi$
$193$	5.00000	0.359908	0.179954	+	0.983675i	$0.442405\pi$
$194$	0	0
$195$	0	0
$196$	6.00000	0.428571
$197$	15.0000	1.06871	0.534353	−	0.845262i	$-0.320555\pi$
$197$	15.0000	1.06871	0.534353	+	0.845262i	$0.320555\pi$
$198$	0	0
$199$	11.0000	0.779769	0.389885	−	0.920864i	$-0.372515\pi$
$199$	11.0000	0.779769	0.389885	+	0.920864i	$0.372515\pi$
$200$	0	0
$201$	−10.0000	−0.705346
$202$	0	0
$203$	0	0
$204$	−6.00000	−0.420084
$205$	0	0
$206$	0	0
$207$	6.00000	0.417029
$208$	−4.00000	−0.277350
$209$	1.00000	0.0691714
$210$	0	0
$211$	23.0000	1.58339	0.791693	−	0.610920i	$-0.209200\pi$
$211$	23.0000	1.58339	0.791693	+	0.610920i	$0.209200\pi$
$212$	−18.0000	−1.23625
$213$	−3.00000	−0.205557
$214$	0	0
$215$	0	0
$216$	0	0
$217$	16.0000	1.08615
$218$	0	0
$219$	−4.00000	−0.270295
$220$	0	0
$221$	−3.00000	−0.201802
$222$	0	0
$223$	2.00000	0.133930	0.0669650	−	0.997755i	$-0.478668\pi$
$223$	2.00000	0.133930	0.0669650	+	0.997755i	$0.478668\pi$
$224$	0	0
$225$	−5.00000	−0.333333
$226$	0	0
$227$	−18.0000	−1.19470	−0.597351	−	0.801980i	$-0.703780\pi$
$227$	−18.0000	−1.19470	−0.597351	+	0.801980i	$0.703780\pi$
$228$	−2.00000	−0.132453
$229$	−13.0000	−0.859064	−0.429532	−	0.903052i	$-0.641321\pi$
$229$	−13.0000	−0.859064	−0.429532	+	0.903052i	$0.641321\pi$
$230$	0	0
$231$	2.00000	0.131590
$232$	0	0
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	0	0
$235$	0	0
$236$	−6.00000	−0.390567
$237$	−13.0000	−0.844441
$238$	0	0
$239$	−24.0000	−1.55243	−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000	−1.55243	−0.776215	+	0.630468i	$0.782863\pi$
$240$	0	0
$241$	5.00000	0.322078	0.161039	−	0.986948i	$-0.448515\pi$
$241$	5.00000	0.322078	0.161039	+	0.986948i	$0.448515\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	20.0000	1.28037
$245$	0	0
$246$	0	0
$247$	−1.00000	−0.0636285
$248$	0	0
$249$	−3.00000	−0.190117
$250$	0	0
$251$	−6.00000	−0.378717	−0.189358	−	0.981908i	$-0.560641\pi$
$251$	−6.00000	−0.378717	−0.189358	+	0.981908i	$0.560641\pi$
$252$	−4.00000	−0.251976
$253$	6.00000	0.377217
$254$	0	0
$255$	0	0
$256$	16.0000	1.00000
$257$	−30.0000	−1.87135	−0.935674	−	0.352865i	$-0.885208\pi$
$257$	−30.0000	−1.87135	−0.935674	+	0.352865i	$0.885208\pi$
$258$	0	0
$259$	4.00000	0.248548
$260$	0	0
$261$	0	0
$262$	0	0
$263$	21.0000	1.29492	0.647458	−	0.762101i	$-0.275832\pi$
$263$	21.0000	1.29492	0.647458	+	0.762101i	$0.275832\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	15.0000	0.917985
$268$	20.0000	1.22169
$269$	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
$271$	2.00000	0.121491	0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000	0.121491	0.0607457	+	0.998153i	$0.480652\pi$
$272$	12.0000	0.727607
$273$	−2.00000	−0.121046
$274$	0	0
$275$	−5.00000	−0.301511
$276$	−12.0000	−0.722315
$277$	26.0000	1.56219	0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000	1.56219	0.781094	+	0.624413i	$0.214662\pi$
$278$	0	0
$279$	8.00000	0.478947
$280$	0	0
$281$	24.0000	1.43172	0.715860	−	0.698244i	$-0.246035\pi$
$281$	24.0000	1.43172	0.715860	+	0.698244i	$0.246035\pi$
$282$	0	0
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	6.00000	0.356034
$285$	0	0
$286$	0	0
$287$	12.0000	0.708338
$288$	0	0
$289$	−8.00000	−0.470588
$290$	0	0
$291$	−10.0000	−0.586210
$292$	8.00000	0.468165
$293$	30.0000	1.75262	0.876309	−	0.481749i	$-0.159998\pi$
$293$	30.0000	1.75262	0.876309	+	0.481749i	$0.159998\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	1.00000	0.0580259
$298$	0	0
$299$	−6.00000	−0.346989
$300$	10.0000	0.577350
$301$	16.0000	0.922225
$302$	0	0
$303$	−6.00000	−0.344691
$304$	4.00000	0.229416
$305$	0	0
$306$	0	0
$307$	−7.00000	−0.399511	−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000	−0.399511	−0.199756	+	0.979846i	$0.564015\pi$
$308$	−4.00000	−0.227921
$309$	−10.0000	−0.568880
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	−1.00000	−0.0565233	−0.0282617	−	0.999601i	$-0.508997\pi$
$313$	−1.00000	−0.0565233	−0.0282617	+	0.999601i	$0.508997\pi$
$314$	0	0
$315$	0	0
$316$	26.0000	1.46261
$317$	6.00000	0.336994	0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000	0.336994	0.168497	+	0.985702i	$0.446109\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	18.0000	1.00466
$322$	0	0
$323$	3.00000	0.166924
$324$	−2.00000	−0.111111
$325$	5.00000	0.277350
$326$	0	0
$327$	2.00000	0.110600
$328$	0	0
$329$	−12.0000	−0.661581
$330$	0	0
$331$	−4.00000	−0.219860	−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000	−0.219860	−0.109930	+	0.993939i	$0.535063\pi$
$332$	6.00000	0.329293
$333$	2.00000	0.109599
$334$	0	0
$335$	0	0
$336$	8.00000	0.436436
$337$	14.0000	0.762629	0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000	0.762629	0.381314	+	0.924445i	$0.375472\pi$
$338$	0	0
$339$	−15.0000	−0.814688
$340$	0	0
$341$	8.00000	0.433224
$342$	0	0
$343$	−20.0000	−1.07990
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−3.00000	−0.161048	−0.0805242	−	0.996753i	$-0.525659\pi$
$347$	−3.00000	−0.161048	−0.0805242	+	0.996753i	$0.525659\pi$
$348$	0	0
$349$	26.0000	1.39175	0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000	1.39175	0.695874	+	0.718164i	$0.255017\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	0	0
$353$	18.0000	0.958043	0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	0	0
$355$	0	0
$356$	−30.0000	−1.59000
$357$	6.00000	0.317554
$358$	0	0
$359$	−9.00000	−0.475002	−0.237501	−	0.971387i	$-0.576328\pi$
$359$	−9.00000	−0.475002	−0.237501	+	0.971387i	$0.576328\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	0	0
$363$	1.00000	0.0524864
$364$	4.00000	0.209657
$365$	0	0
$366$	0	0
$367$	−7.00000	−0.365397	−0.182699	−	0.983169i	$-0.558483\pi$
$367$	−7.00000	−0.365397	−0.182699	+	0.983169i	$0.558483\pi$
$368$	24.0000	1.25109
$369$	6.00000	0.312348
$370$	0	0
$371$	18.0000	0.934513
$372$	−16.0000	−0.829561
$373$	14.0000	0.724893	0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000	0.724893	0.362446	+	0.932005i	$0.381942\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	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
$381$	−7.00000	−0.358621
$382$	0	0
$383$	−27.0000	−1.37964	−0.689818	−	0.723983i	$-0.742309\pi$
$383$	−27.0000	−1.37964	−0.689818	+	0.723983i	$0.742309\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	8.00000	0.406663
$388$	20.0000	1.01535
$389$	−12.0000	−0.608424	−0.304212	−	0.952604i	$-0.598393\pi$
$389$	−12.0000	−0.608424	−0.304212	+	0.952604i	$0.598393\pi$
$390$	0	0
$391$	18.0000	0.910299
$392$	0	0
$393$	21.0000	1.05931
$394$	0	0
$395$	0	0
$396$	−2.00000	−0.100504
$397$	−1.00000	−0.0501886	−0.0250943	−	0.999685i	$-0.507989\pi$
$397$	−1.00000	−0.0501886	−0.0250943	+	0.999685i	$0.507989\pi$
$398$	0	0
$399$	2.00000	0.100125
$400$	−20.0000	−1.00000
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	0	0
$403$	−8.00000	−0.398508
$404$	12.0000	0.597022
$405$	0	0
$406$	0	0
$407$	2.00000	0.0991363
$408$	0	0
$409$	5.00000	0.247234	0.123617	−	0.992330i	$-0.460551\pi$
$409$	5.00000	0.247234	0.123617	+	0.992330i	$0.460551\pi$
$410$	0	0
$411$	−18.0000	−0.887875
$412$	20.0000	0.985329
$413$	6.00000	0.295241
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−16.0000	−0.783523
$418$	0	0
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	8.00000	0.389896	0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000	0.389896	0.194948	+	0.980814i	$0.437546\pi$
$422$	0	0
$423$	−6.00000	−0.291730
$424$	0	0
$425$	−15.0000	−0.727607
$426$	0	0
$427$	−20.0000	−0.967868
$428$	−36.0000	−1.74013
$429$	−1.00000	−0.0482805
$430$	0	0
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	4.00000	0.192450
$433$	−10.0000	−0.480569	−0.240285	−	0.970702i	$-0.577241\pi$
$433$	−10.0000	−0.480569	−0.240285	+	0.970702i	$0.577241\pi$
$434$	0	0
$435$	0	0
$436$	−4.00000	−0.191565
$437$	6.00000	0.287019
$438$	0	0
$439$	−7.00000	−0.334092	−0.167046	−	0.985949i	$-0.553423\pi$
$439$	−7.00000	−0.334092	−0.167046	+	0.985949i	$0.553423\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	0	0
$443$	−6.00000	−0.285069	−0.142534	−	0.989790i	$-0.545525\pi$
$443$	−6.00000	−0.285069	−0.142534	+	0.989790i	$0.545525\pi$
$444$	−4.00000	−0.189832
$445$	0	0
$446$	0	0
$447$	3.00000	0.141895
$448$	−16.0000	−0.755929
$449$	9.00000	0.424736	0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000	0.424736	0.212368	+	0.977190i	$0.431882\pi$
$450$	0	0
$451$	6.00000	0.282529
$452$	30.0000	1.41108
$453$	8.00000	0.375873
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−28.0000	−1.30978	−0.654892	−	0.755722i	$-0.727286\pi$
$457$	−28.0000	−1.30978	−0.654892	+	0.755722i	$0.727286\pi$
$458$	0	0
$459$	3.00000	0.140028
$460$	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
$463$	−19.0000	−0.883005	−0.441502	−	0.897260i	$-0.645554\pi$
$463$	−19.0000	−0.883005	−0.441502	+	0.897260i	$0.645554\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−6.00000	−0.277647	−0.138823	−	0.990317i	$-0.544332\pi$
$467$	−6.00000	−0.277647	−0.138823	+	0.990317i	$0.544332\pi$
$468$	2.00000	0.0924500
$469$	−20.0000	−0.923514
$470$	0	0
$471$	11.0000	0.506853
$472$	0	0
$473$	8.00000	0.367840
$474$	0	0
$475$	−5.00000	−0.229416
$476$	−12.0000	−0.550019
$477$	9.00000	0.412082
$478$	0	0
$479$	−27.0000	−1.23366	−0.616831	−	0.787096i	$-0.711584\pi$
$479$	−27.0000	−1.23366	−0.616831	+	0.787096i	$0.711584\pi$
$480$	0	0
$481$	−2.00000	−0.0911922
$482$	0	0
$483$	12.0000	0.546019
$484$	−2.00000	−0.0909091
$485$	0	0
$486$	0	0
$487$	38.0000	1.72194	0.860972	−	0.508652i	$-0.169856\pi$
$487$	38.0000	1.72194	0.860972	+	0.508652i	$0.169856\pi$
$488$	0	0
$489$	−19.0000	−0.859210
$490$	0	0
$491$	−33.0000	−1.48927	−0.744635	−	0.667472i	$-0.767376\pi$
$491$	−33.0000	−1.48927	−0.744635	+	0.667472i	$0.767376\pi$
$492$	−12.0000	−0.541002
$493$	0	0
$494$	0	0
$495$	0	0
$496$	32.0000	1.43684
$497$	−6.00000	−0.269137
$498$	0	0
$499$	−19.0000	−0.850557	−0.425278	−	0.905063i	$-0.639824\pi$
$499$	−19.0000	−0.850557	−0.425278	+	0.905063i	$0.639824\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	24.0000	1.07011	0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000	1.07011	0.535054	+	0.844818i	$0.320291\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−12.0000	−0.532939
$508$	14.0000	0.621150
$509$	−30.0000	−1.32973	−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000	−1.32973	−0.664863	+	0.746965i	$0.731510\pi$
$510$	0	0
$511$	−8.00000	−0.353899
$512$	0	0
$513$	1.00000	0.0441511
$514$	0	0
$515$	0	0
$516$	−16.0000	−0.704361
$517$	−6.00000	−0.263880
$518$	0	0
$519$	−6.00000	−0.263371
$520$	0	0
$521$	−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
$523$	−25.0000	−1.09317	−0.546587	−	0.837402i	$-0.684073\pi$
$523$	−25.0000	−1.09317	−0.546587	+	0.837402i	$0.684073\pi$
$524$	−42.0000	−1.83478
$525$	−10.0000	−0.436436
$526$	0	0
$527$	24.0000	1.04546
$528$	4.00000	0.174078
$529$	13.0000	0.565217
$530$	0	0
$531$	3.00000	0.130189
$532$	−4.00000	−0.173422
$533$	−6.00000	−0.259889
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−15.0000	−0.647298
$538$	0	0
$539$	−3.00000	−0.129219
$540$	0	0
$541$	32.0000	1.37579	0.687894	−	0.725811i	$-0.258536\pi$
$541$	32.0000	1.37579	0.687894	+	0.725811i	$0.258536\pi$
$542$	0	0
$543$	2.00000	0.0858282
$544$	0	0
$545$	0	0
$546$	0	0
$547$	20.0000	0.855138	0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000	0.855138	0.427569	+	0.903983i	$0.359370\pi$
$548$	36.0000	1.53784
$549$	−10.0000	−0.426790
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−26.0000	−1.10563
$554$	0	0
$555$	0	0
$556$	32.0000	1.35710
$557$	18.0000	0.762684	0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000	0.762684	0.381342	+	0.924434i	$0.375462\pi$
$558$	0	0
$559$	−8.00000	−0.338364
$560$	0	0
$561$	3.00000	0.126660
$562$	0	0
$563$	−36.0000	−1.51722	−0.758610	−	0.651546i	$-0.774121\pi$
$563$	−36.0000	−1.51722	−0.758610	+	0.651546i	$0.774121\pi$
$564$	12.0000	0.505291
$565$	0	0
$566$	0	0
$567$	2.00000	0.0839921
$568$	0	0
$569$	−36.0000	−1.50920	−0.754599	−	0.656186i	$-0.772169\pi$
$569$	−36.0000	−1.50920	−0.754599	+	0.656186i	$0.772169\pi$
$570$	0	0
$571$	−34.0000	−1.42286	−0.711428	−	0.702759i	$-0.751951\pi$
$571$	−34.0000	−1.42286	−0.711428	+	0.702759i	$0.751951\pi$
$572$	2.00000	0.0836242
$573$	−6.00000	−0.250654
$574$	0	0
$575$	−30.0000	−1.25109
$576$	−8.00000	−0.333333
$577$	−7.00000	−0.291414	−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000	−0.291414	−0.145707	+	0.989328i	$0.546546\pi$
$578$	0	0
$579$	5.00000	0.207793
$580$	0	0
$581$	−6.00000	−0.248922
$582$	0	0
$583$	9.00000	0.372742
$584$	0	0
$585$	0	0
$586$	0	0
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	6.00000	0.247436
$589$	8.00000	0.329634
$590$	0	0
$591$	15.0000	0.617018
$592$	8.00000	0.328798
$593$	15.0000	0.615976	0.307988	−	0.951390i	$-0.400344\pi$
$593$	15.0000	0.615976	0.307988	+	0.951390i	$0.400344\pi$
$594$	0	0
$595$	0	0
$596$	−6.00000	−0.245770
$597$	11.0000	0.450200
$598$	0	0
$599$	15.0000	0.612883	0.306442	−	0.951889i	$-0.400862\pi$
$599$	15.0000	0.612883	0.306442	+	0.951889i	$0.400862\pi$
$600$	0	0
$601$	14.0000	0.571072	0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000	0.571072	0.285536	+	0.958368i	$0.407828\pi$
$602$	0	0
$603$	−10.0000	−0.407231
$604$	−16.0000	−0.651031
$605$	0	0
$606$	0	0
$607$	−16.0000	−0.649420	−0.324710	−	0.945814i	$-0.605267\pi$
$607$	−16.0000	−0.649420	−0.324710	+	0.945814i	$0.605267\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	6.00000	0.242734
$612$	−6.00000	−0.242536
$613$	20.0000	0.807792	0.403896	−	0.914805i	$-0.367656\pi$
$613$	20.0000	0.807792	0.403896	+	0.914805i	$0.367656\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	0	0
$619$	−25.0000	−1.00483	−0.502417	−	0.864625i	$-0.667556\pi$
$619$	−25.0000	−1.00483	−0.502417	+	0.864625i	$0.667556\pi$
$620$	0	0
$621$	6.00000	0.240772
$622$	0	0
$623$	30.0000	1.20192
$624$	−4.00000	−0.160128
$625$	25.0000	1.00000
$626$	0	0
$627$	1.00000	0.0399362
$628$	−22.0000	−0.877896
$629$	6.00000	0.239236
$630$	0	0
$631$	−40.0000	−1.59237	−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000	−1.59237	−0.796187	+	0.605050i	$0.793153\pi$
$632$	0	0
$633$	23.0000	0.914168
$634$	0	0
$635$	0	0
$636$	−18.0000	−0.713746
$637$	3.00000	0.118864
$638$	0	0
$639$	−3.00000	−0.118678
$640$	0	0
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	0	0
$643$	44.0000	1.73519	0.867595	−	0.497271i	$-0.165665\pi$
$643$	44.0000	1.73519	0.867595	+	0.497271i	$0.165665\pi$
$644$	−24.0000	−0.945732
$645$	0	0
$646$	0	0
$647$	−12.0000	−0.471769	−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000	−0.471769	−0.235884	+	0.971781i	$0.575799\pi$
$648$	0	0
$649$	3.00000	0.117760
$650$	0	0
$651$	16.0000	0.627089
$652$	38.0000	1.48819
$653$	30.0000	1.17399	0.586995	−	0.809590i	$-0.300311\pi$
$653$	30.0000	1.17399	0.586995	+	0.809590i	$0.300311\pi$
$654$	0	0
$655$	0	0
$656$	24.0000	0.937043
$657$	−4.00000	−0.156055
$658$	0	0
$659$	30.0000	1.16863	0.584317	−	0.811525i	$-0.301362\pi$
$659$	30.0000	1.16863	0.584317	+	0.811525i	$0.301362\pi$
$660$	0	0
$661$	−4.00000	−0.155582	−0.0777910	−	0.996970i	$-0.524787\pi$
$661$	−4.00000	−0.155582	−0.0777910	+	0.996970i	$0.524787\pi$
$662$	0	0
$663$	−3.00000	−0.116510
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	2.00000	0.0773245
$670$	0	0
$671$	−10.0000	−0.386046
$672$	0	0
$673$	11.0000	0.424019	0.212009	−	0.977268i	$-0.431999\pi$
$673$	11.0000	0.424019	0.212009	+	0.977268i	$0.431999\pi$
$674$	0	0
$675$	−5.00000	−0.192450
$676$	24.0000	0.923077
$677$	−36.0000	−1.38359	−0.691796	−	0.722093i	$-0.743180\pi$
$677$	−36.0000	−1.38359	−0.691796	+	0.722093i	$0.743180\pi$
$678$	0	0
$679$	−20.0000	−0.767530
$680$	0	0
$681$	−18.0000	−0.689761
$682$	0	0
$683$	−3.00000	−0.114792	−0.0573959	−	0.998351i	$-0.518280\pi$
$683$	−3.00000	−0.114792	−0.0573959	+	0.998351i	$0.518280\pi$
$684$	−2.00000	−0.0764719
$685$	0	0
$686$	0	0
$687$	−13.0000	−0.495981
$688$	32.0000	1.21999
$689$	−9.00000	−0.342873
$690$	0	0
$691$	−28.0000	−1.06517	−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000	−1.06517	−0.532585	+	0.846376i	$0.678779\pi$
$692$	12.0000	0.456172
$693$	2.00000	0.0759737
$694$	0	0
$695$	0	0
$696$	0	0
$697$	18.0000	0.681799
$698$	0	0
$699$	−6.00000	−0.226941
$700$	20.0000	0.755929
$701$	−45.0000	−1.69963	−0.849813	−	0.527084i	$-0.823285\pi$
$701$	−45.0000	−1.69963	−0.849813	+	0.527084i	$0.823285\pi$
$702$	0	0
$703$	2.00000	0.0754314
$704$	−8.00000	−0.301511
$705$	0	0
$706$	0	0
$707$	−12.0000	−0.451306
$708$	−6.00000	−0.225494
$709$	−49.0000	−1.84023	−0.920117	−	0.391644i	$-0.871906\pi$
$709$	−49.0000	−1.84023	−0.920117	+	0.391644i	$0.871906\pi$
$710$	0	0
$711$	−13.0000	−0.487538
$712$	0	0
$713$	48.0000	1.79761
$714$	0	0
$715$	0	0
$716$	30.0000	1.12115
$717$	−24.0000	−0.896296
$718$	0	0
$719$	12.0000	0.447524	0.223762	−	0.974644i	$-0.428166\pi$
$719$	12.0000	0.447524	0.223762	+	0.974644i	$0.428166\pi$
$720$	0	0
$721$	−20.0000	−0.744839
$722$	0	0
$723$	5.00000	0.185952
$724$	−4.00000	−0.148659
$725$	0	0
$726$	0	0
$727$	−28.0000	−1.03846	−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000	−1.03846	−0.519231	+	0.854634i	$0.673782\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	24.0000	0.887672
$732$	20.0000	0.739221
$733$	−4.00000	−0.147743	−0.0738717	−	0.997268i	$-0.523536\pi$
$733$	−4.00000	−0.147743	−0.0738717	+	0.997268i	$0.523536\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−10.0000	−0.368355
$738$	0	0
$739$	−4.00000	−0.147142	−0.0735712	−	0.997290i	$-0.523440\pi$
$739$	−4.00000	−0.147142	−0.0735712	+	0.997290i	$0.523440\pi$
$740$	0	0
$741$	−1.00000	−0.0367359
$742$	0	0
$743$	−18.0000	−0.660356	−0.330178	−	0.943919i	$-0.607109\pi$
$743$	−18.0000	−0.660356	−0.330178	+	0.943919i	$0.607109\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−3.00000	−0.109764
$748$	−6.00000	−0.219382
$749$	36.0000	1.31541
$750$	0	0
$751$	−34.0000	−1.24068	−0.620339	−	0.784334i	$-0.713005\pi$
$751$	−34.0000	−1.24068	−0.620339	+	0.784334i	$0.713005\pi$
$752$	−24.0000	−0.875190
$753$	−6.00000	−0.218652
$754$	0	0
$755$	0	0
$756$	−4.00000	−0.145479
$757$	35.0000	1.27210	0.636048	−	0.771649i	$-0.280568\pi$
$757$	35.0000	1.27210	0.636048	+	0.771649i	$0.280568\pi$
$758$	0	0
$759$	6.00000	0.217786
$760$	0	0
$761$	−42.0000	−1.52250	−0.761249	−	0.648459i	$-0.775414\pi$
$761$	−42.0000	−1.52250	−0.761249	+	0.648459i	$0.775414\pi$
$762$	0	0
$763$	4.00000	0.144810
$764$	12.0000	0.434145
$765$	0	0
$766$	0	0
$767$	−3.00000	−0.108324
$768$	16.0000	0.577350
$769$	20.0000	0.721218	0.360609	−	0.932717i	$-0.382569\pi$
$769$	20.0000	0.721218	0.360609	+	0.932717i	$0.382569\pi$
$770$	0	0
$771$	−30.0000	−1.08042
$772$	−10.0000	−0.359908
$773$	39.0000	1.40273	0.701366	−	0.712801i	$-0.252574\pi$
$773$	39.0000	1.40273	0.701366	+	0.712801i	$0.252574\pi$
$774$	0	0
$775$	−40.0000	−1.43684
$776$	0	0
$777$	4.00000	0.143499
$778$	0	0
$779$	6.00000	0.214972
$780$	0	0
$781$	−3.00000	−0.107348
$782$	0	0
$783$	0	0
$784$	−12.0000	−0.428571
$785$	0	0
$786$	0	0
$787$	53.0000	1.88925	0.944623	−	0.328158i	$-0.106428\pi$
$787$	53.0000	1.88925	0.944623	+	0.328158i	$0.106428\pi$
$788$	−30.0000	−1.06871
$789$	21.0000	0.747620
$790$	0	0
$791$	−30.0000	−1.06668
$792$	0	0
$793$	10.0000	0.355110
$794$	0	0
$795$	0	0
$796$	−22.0000	−0.779769
$797$	6.00000	0.212531	0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000	0.212531	0.106265	+	0.994338i	$0.466111\pi$
$798$	0	0
$799$	−18.0000	−0.636794
$800$	0	0
$801$	15.0000	0.529999
$802$	0	0
$803$	−4.00000	−0.141157
$804$	20.0000	0.705346
$805$	0	0
$806$	0	0
$807$	15.0000	0.528025
$808$	0	0
$809$	−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
$811$	−7.00000	−0.245803	−0.122902	−	0.992419i	$-0.539220\pi$
$811$	−7.00000	−0.245803	−0.122902	+	0.992419i	$0.539220\pi$
$812$	0	0
$813$	2.00000	0.0701431
$814$	0	0
$815$	0	0
$816$	12.0000	0.420084
$817$	8.00000	0.279885
$818$	0	0
$819$	−2.00000	−0.0698857
$820$	0	0
$821$	−15.0000	−0.523504	−0.261752	−	0.965135i	$-0.584300\pi$
$821$	−15.0000	−0.523504	−0.261752	+	0.965135i	$0.584300\pi$
$822$	0	0
$823$	−40.0000	−1.39431	−0.697156	−	0.716919i	$-0.745552\pi$
$823$	−40.0000	−1.39431	−0.697156	+	0.716919i	$0.745552\pi$
$824$	0	0
$825$	−5.00000	−0.174078
$826$	0	0
$827$	−6.00000	−0.208640	−0.104320	−	0.994544i	$-0.533267\pi$
$827$	−6.00000	−0.208640	−0.104320	+	0.994544i	$0.533267\pi$
$828$	−12.0000	−0.417029
$829$	20.0000	0.694629	0.347314	−	0.937749i	$-0.387094\pi$
$829$	20.0000	0.694629	0.347314	+	0.937749i	$0.387094\pi$
$830$	0	0
$831$	26.0000	0.901930
$832$	8.00000	0.277350
$833$	−9.00000	−0.311832
$834$	0	0
$835$	0	0
$836$	−2.00000	−0.0691714
$837$	8.00000	0.276520
$838$	0	0
$839$	12.0000	0.414286	0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000	0.414286	0.207143	+	0.978311i	$0.433583\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	0	0
$843$	24.0000	0.826604
$844$	−46.0000	−1.58339
$845$	0	0
$846$	0	0
$847$	2.00000	0.0687208
$848$	36.0000	1.23625
$849$	−4.00000	−0.137280
$850$	0	0
$851$	12.0000	0.411355
$852$	6.00000	0.205557
$853$	−16.0000	−0.547830	−0.273915	−	0.961754i	$-0.588319\pi$
$853$	−16.0000	−0.547830	−0.273915	+	0.961754i	$0.588319\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	42.0000	1.43469	0.717346	−	0.696717i	$-0.245357\pi$
$857$	42.0000	1.43469	0.717346	+	0.696717i	$0.245357\pi$
$858$	0	0
$859$	−13.0000	−0.443554	−0.221777	−	0.975097i	$-0.571186\pi$
$859$	−13.0000	−0.443554	−0.221777	+	0.975097i	$0.571186\pi$
$860$	0	0
$861$	12.0000	0.408959
$862$	0	0
$863$	−12.0000	−0.408485	−0.204242	−	0.978920i	$-0.565473\pi$
$863$	−12.0000	−0.408485	−0.204242	+	0.978920i	$0.565473\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−8.00000	−0.271694
$868$	−32.0000	−1.08615
$869$	−13.0000	−0.440995
$870$	0	0
$871$	10.0000	0.338837
$872$	0	0
$873$	−10.0000	−0.338449
$874$	0	0
$875$	0	0
$876$	8.00000	0.270295
$877$	41.0000	1.38447	0.692236	−	0.721671i	$-0.256626\pi$
$877$	41.0000	1.38447	0.692236	+	0.721671i	$0.256626\pi$
$878$	0	0
$879$	30.0000	1.01187
$880$	0	0
$881$	54.0000	1.81931	0.909653	−	0.415369i	$-0.136347\pi$
$881$	54.0000	1.81931	0.909653	+	0.415369i	$0.136347\pi$
$882$	0	0
$883$	8.00000	0.269221	0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000	0.269221	0.134611	+	0.990899i	$0.457022\pi$
$884$	6.00000	0.201802
$885$	0	0
$886$	0	0
$887$	36.0000	1.20876	0.604381	−	0.796696i	$-0.293421\pi$
$887$	36.0000	1.20876	0.604381	+	0.796696i	$0.293421\pi$
$888$	0	0
$889$	−14.0000	−0.469545
$890$	0	0
$891$	1.00000	0.0335013
$892$	−4.00000	−0.133930
$893$	−6.00000	−0.200782
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−6.00000	−0.200334
$898$	0	0
$899$	0	0
$900$	10.0000	0.333333
$901$	27.0000	0.899500
$902$	0	0
$903$	16.0000	0.532447
$904$	0	0
$905$	0	0
$906$	0	0
$907$	8.00000	0.265636	0.132818	−	0.991140i	$-0.457597\pi$
$907$	8.00000	0.265636	0.132818	+	0.991140i	$0.457597\pi$
$908$	36.0000	1.19470
$909$	−6.00000	−0.199007
$910$	0	0
$911$	24.0000	0.795155	0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000	0.795155	0.397578	+	0.917568i	$0.369851\pi$
$912$	4.00000	0.132453
$913$	−3.00000	−0.0992855
$914$	0	0
$915$	0	0
$916$	26.0000	0.859064
$917$	42.0000	1.38696
$918$	0	0
$919$	−46.0000	−1.51740	−0.758700	−	0.651440i	$-0.774165\pi$
$919$	−46.0000	−1.51740	−0.758700	+	0.651440i	$0.774165\pi$
$920$	0	0
$921$	−7.00000	−0.230658
$922$	0	0
$923$	3.00000	0.0987462
$924$	−4.00000	−0.131590
$925$	−10.0000	−0.328798
$926$	0	0
$927$	−10.0000	−0.328443
$928$	0	0
$929$	60.0000	1.96854	0.984268	−	0.176682i	$-0.0565363\pi$
$929$	60.0000	1.96854	0.984268	+	0.176682i	$0.0565363\pi$
$930$	0	0
$931$	−3.00000	−0.0983210
$932$	12.0000	0.393073
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	8.00000	0.261349	0.130674	−	0.991425i	$-0.458286\pi$
$937$	8.00000	0.261349	0.130674	+	0.991425i	$0.458286\pi$
$938$	0	0
$939$	−1.00000	−0.0326338
$940$	0	0
$941$	−30.0000	−0.977972	−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000	−0.977972	−0.488986	+	0.872292i	$0.662633\pi$
$942$	0	0
$943$	36.0000	1.17232
$944$	12.0000	0.390567
$945$	0	0
$946$	0	0
$947$	−42.0000	−1.36482	−0.682408	−	0.730971i	$-0.739067\pi$
$947$	−42.0000	−1.36482	−0.682408	+	0.730971i	$0.739067\pi$
$948$	26.0000	0.844441
$949$	4.00000	0.129845
$950$	0	0
$951$	6.00000	0.194563
$952$	0	0
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	0	0
$955$	0	0
$956$	48.0000	1.55243
$957$	0	0
$958$	0	0
$959$	−36.0000	−1.16250
$960$	0	0
$961$	33.0000	1.06452
$962$	0	0
$963$	18.0000	0.580042
$964$	−10.0000	−0.322078
$965$	0	0
$966$	0	0
$967$	−22.0000	−0.707472	−0.353736	−	0.935345i	$-0.615089\pi$
$967$	−22.0000	−0.707472	−0.353736	+	0.935345i	$0.615089\pi$
$968$	0	0
$969$	3.00000	0.0963739
$970$	0	0
$971$	−9.00000	−0.288824	−0.144412	−	0.989518i	$-0.546129\pi$
$971$	−9.00000	−0.288824	−0.144412	+	0.989518i	$0.546129\pi$
$972$	−2.00000	−0.0641500
$973$	−32.0000	−1.02587
$974$	0	0
$975$	5.00000	0.160128
$976$	−40.0000	−1.28037
$977$	−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
$979$	15.0000	0.479402
$980$	0	0
$981$	2.00000	0.0638551
$982$	0	0
$983$	24.0000	0.765481	0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000	0.765481	0.382741	+	0.923856i	$0.374980\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	−12.0000	−0.381964
$988$	2.00000	0.0636285
$989$	48.0000	1.52631
$990$	0	0
$991$	−4.00000	−0.127064	−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000	−0.127064	−0.0635321	+	0.997980i	$0.520237\pi$
$992$	0	0
$993$	−4.00000	−0.126936
$994$	0	0
$995$	0	0
$996$	6.00000	0.190117
$997$	38.0000	1.20347	0.601736	−	0.798695i	$-0.294476\pi$
$997$	38.0000	1.20347	0.601736	+	0.798695i	$0.294476\pi$
$998$	0	0
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	627.2.a.a.1.1	✓	1
3.2	odd	2		1881.2.a.b.1.1		1
11.10	odd	2		6897.2.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.a.a.1.1	✓	1	1.1	even	1	trivial
1881.2.a.b.1.1		1	3.2	odd	2
6897.2.a.b.1.1		1	11.10	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:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.a (trivial)

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