LMFDB - Embedded newform 1950.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(1,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, 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("1950.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.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:	$15.5708283941$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1950.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{11} +1.00000 q^{12} -1.00000 q^{13} +4.00000 q^{14} +1.00000 q^{16} -4.00000 q^{17} -1.00000 q^{18} +2.00000 q^{19} -4.00000 q^{21} -2.00000 q^{22} +6.00000 q^{23} -1.00000 q^{24} +1.00000 q^{26} +1.00000 q^{27} -4.00000 q^{28} -2.00000 q^{29} -4.00000 q^{31} -1.00000 q^{32} +2.00000 q^{33} +4.00000 q^{34} +1.00000 q^{36} +6.00000 q^{37} -2.00000 q^{38} -1.00000 q^{39} -6.00000 q^{41} +4.00000 q^{42} -8.00000 q^{43} +2.00000 q^{44} -6.00000 q^{46} -8.00000 q^{47} +1.00000 q^{48} +9.00000 q^{49} -4.00000 q^{51} -1.00000 q^{52} -10.0000 q^{53} -1.00000 q^{54} +4.00000 q^{56} +2.00000 q^{57} +2.00000 q^{58} -14.0000 q^{59} +10.0000 q^{61} +4.00000 q^{62} -4.00000 q^{63} +1.00000 q^{64} -2.00000 q^{66} -4.00000 q^{67} -4.00000 q^{68} +6.00000 q^{69} +8.00000 q^{71} -1.00000 q^{72} -10.0000 q^{73} -6.00000 q^{74} +2.00000 q^{76} -8.00000 q^{77} +1.00000 q^{78} -8.00000 q^{79} +1.00000 q^{81} +6.00000 q^{82} -12.0000 q^{83} -4.00000 q^{84} +8.00000 q^{86} -2.00000 q^{87} -2.00000 q^{88} -18.0000 q^{89} +4.00000 q^{91} +6.00000 q^{92} -4.00000 q^{93} +8.00000 q^{94} -1.00000 q^{96} -6.00000 q^{97} -9.00000 q^{98} +2.00000 q^{99} +O(q^{100})\)

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	−4.00000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	4.00000	1.06904
$15$	0	0
$16$	1.00000	0.250000
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	−1.00000	−0.235702
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	0	0
$21$	−4.00000	−0.872872
$22$	−2.00000	−0.426401
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	−4.00000	−0.755929
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	0	0
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	−1.00000	−0.176777
$33$	2.00000	0.348155
$34$	4.00000	0.685994
$35$	0	0
$36$	1.00000	0.166667
$37$	6.00000	0.986394	0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000	0.986394	0.493197	+	0.869918i	$0.335828\pi$
$38$	−2.00000	−0.324443
$39$	−1.00000	−0.160128
$40$	0	0
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	4.00000	0.617213
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	−6.00000	−0.884652
$47$	−8.00000	−1.16692	−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000	−1.16692	−0.583460	+	0.812142i	$0.698301\pi$
$48$	1.00000	0.144338
$49$	9.00000	1.28571
$50$	0	0
$51$	−4.00000	−0.560112
$52$	−1.00000	−0.138675
$53$	−10.0000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	4.00000	0.534522
$57$	2.00000	0.264906
$58$	2.00000	0.262613
$59$	−14.0000	−1.82264	−0.911322	−	0.411693i	$-0.864937\pi$
$59$	−14.0000	−1.82264	−0.911322	+	0.411693i	$0.864937\pi$
$60$	0	0
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	4.00000	0.508001
$63$	−4.00000	−0.503953
$64$	1.00000	0.125000
$65$	0	0
$66$	−2.00000	−0.246183
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	−4.00000	−0.485071
$69$	6.00000	0.722315
$70$	0	0
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	−1.00000	−0.117851
$73$	−10.0000	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$74$	−6.00000	−0.697486
$75$	0	0
$76$	2.00000	0.229416
$77$	−8.00000	−0.911685
$78$	1.00000	0.113228
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	6.00000	0.662589
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	−4.00000	−0.436436
$85$	0	0
$86$	8.00000	0.862662
$87$	−2.00000	−0.214423
$88$	−2.00000	−0.213201
$89$	−18.0000	−1.90800	−0.953998	−	0.299813i	$-0.903076\pi$
$89$	−18.0000	−1.90800	−0.953998	+	0.299813i	$0.903076\pi$
$90$	0	0
$91$	4.00000	0.419314
$92$	6.00000	0.625543
$93$	−4.00000	−0.414781
$94$	8.00000	0.825137
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−6.00000	−0.609208	−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000	−0.609208	−0.304604	+	0.952479i	$0.598524\pi$
$98$	−9.00000	−0.909137
$99$	2.00000	0.201008
$100$	0	0
$101$	−14.0000	−1.39305	−0.696526	−	0.717532i	$-0.745272\pi$
$101$	−14.0000	−1.39305	−0.696526	+	0.717532i	$0.745272\pi$
$102$	4.00000	0.396059
$103$	−6.00000	−0.591198	−0.295599	−	0.955312i	$-0.595519\pi$
$103$	−6.00000	−0.591198	−0.295599	+	0.955312i	$0.595519\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	10.0000	0.971286
$107$	8.00000	0.773389	0.386695	−	0.922208i	$-0.373617\pi$
$107$	8.00000	0.773389	0.386695	+	0.922208i	$0.373617\pi$
$108$	1.00000	0.0962250
$109$	12.0000	1.14939	0.574696	−	0.818367i	$-0.305120\pi$
$109$	12.0000	1.14939	0.574696	+	0.818367i	$0.305120\pi$
$110$	0	0
$111$	6.00000	0.569495
$112$	−4.00000	−0.377964
$113$	12.0000	1.12887	0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000	1.12887	0.564433	+	0.825479i	$0.309095\pi$
$114$	−2.00000	−0.187317
$115$	0	0
$116$	−2.00000	−0.185695
$117$	−1.00000	−0.0924500
$118$	14.0000	1.28880
$119$	16.0000	1.46672
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−10.0000	−0.905357
$123$	−6.00000	−0.541002
$124$	−4.00000	−0.359211
$125$	0	0
$126$	4.00000	0.356348
$127$	18.0000	1.59724	0.798621	−	0.601834i	$-0.205563\pi$
$127$	18.0000	1.59724	0.798621	+	0.601834i	$0.205563\pi$
$128$	−1.00000	−0.0883883
$129$	−8.00000	−0.704361
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	2.00000	0.174078
$133$	−8.00000	−0.693688
$134$	4.00000	0.345547
$135$	0	0
$136$	4.00000	0.342997
$137$	−2.00000	−0.170872	−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000	−0.170872	−0.0854358	+	0.996344i	$0.527228\pi$
$138$	−6.00000	−0.510754
$139$	16.0000	1.35710	0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000	1.35710	0.678551	+	0.734553i	$0.262608\pi$
$140$	0	0
$141$	−8.00000	−0.673722
$142$	−8.00000	−0.671345
$143$	−2.00000	−0.167248
$144$	1.00000	0.0833333
$145$	0	0
$146$	10.0000	0.827606
$147$	9.00000	0.742307
$148$	6.00000	0.493197
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	−2.00000	−0.162221
$153$	−4.00000	−0.323381
$154$	8.00000	0.644658
$155$	0	0
$156$	−1.00000	−0.0800641
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	8.00000	0.636446
$159$	−10.0000	−0.793052
$160$	0	0
$161$	−24.0000	−1.89146
$162$	−1.00000	−0.0785674
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	12.0000	0.931381
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	4.00000	0.308607
$169$	1.00000	0.0769231
$170$	0	0
$171$	2.00000	0.152944
$172$	−8.00000	−0.609994
$173$	−10.0000	−0.760286	−0.380143	−	0.924928i	$-0.624125\pi$
$173$	−10.0000	−0.760286	−0.380143	+	0.924928i	$0.624125\pi$
$174$	2.00000	0.151620
$175$	0	0
$176$	2.00000	0.150756
$177$	−14.0000	−1.05230
$178$	18.0000	1.34916
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	6.00000	0.445976	0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000	0.445976	0.222988	+	0.974821i	$0.428419\pi$
$182$	−4.00000	−0.296500
$183$	10.0000	0.739221
$184$	−6.00000	−0.442326
$185$	0	0
$186$	4.00000	0.293294
$187$	−8.00000	−0.585018
$188$	−8.00000	−0.583460
$189$	−4.00000	−0.290957
$190$	0	0
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	1.00000	0.0721688
$193$	−6.00000	−0.431889	−0.215945	−	0.976406i	$-0.569283\pi$
$193$	−6.00000	−0.431889	−0.215945	+	0.976406i	$0.569283\pi$
$194$	6.00000	0.430775
$195$	0	0
$196$	9.00000	0.642857
$197$	−26.0000	−1.85242	−0.926212	−	0.377004i	$-0.876954\pi$
$197$	−26.0000	−1.85242	−0.926212	+	0.377004i	$0.876954\pi$
$198$	−2.00000	−0.142134
$199$	24.0000	1.70131	0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000	1.70131	0.850657	+	0.525720i	$0.176204\pi$
$200$	0	0
$201$	−4.00000	−0.282138
$202$	14.0000	0.985037
$203$	8.00000	0.561490
$204$	−4.00000	−0.280056
$205$	0	0
$206$	6.00000	0.418040
$207$	6.00000	0.417029
$208$	−1.00000	−0.0693375
$209$	4.00000	0.276686
$210$	0	0
$211$	−28.0000	−1.92760	−0.963800	−	0.266627i	$-0.914091\pi$
$211$	−28.0000	−1.92760	−0.963800	+	0.266627i	$0.914091\pi$
$212$	−10.0000	−0.686803
$213$	8.00000	0.548151
$214$	−8.00000	−0.546869
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	16.0000	1.08615
$218$	−12.0000	−0.812743
$219$	−10.0000	−0.675737
$220$	0	0
$221$	4.00000	0.269069
$222$	−6.00000	−0.402694
$223$	16.0000	1.07144	0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000	1.07144	0.535720	+	0.844396i	$0.320040\pi$
$224$	4.00000	0.267261
$225$	0	0
$226$	−12.0000	−0.798228
$227$	−12.0000	−0.796468	−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000	−0.796468	−0.398234	+	0.917284i	$0.630377\pi$
$228$	2.00000	0.132453
$229$	−16.0000	−1.05731	−0.528655	−	0.848837i	$-0.677303\pi$
$229$	−16.0000	−1.05731	−0.528655	+	0.848837i	$0.677303\pi$
$230$	0	0
$231$	−8.00000	−0.526361
$232$	2.00000	0.131306
$233$	4.00000	0.262049	0.131024	−	0.991379i	$-0.458173\pi$
$233$	4.00000	0.262049	0.131024	+	0.991379i	$0.458173\pi$
$234$	1.00000	0.0653720
$235$	0	0
$236$	−14.0000	−0.911322
$237$	−8.00000	−0.519656
$238$	−16.0000	−1.03713
$239$	−12.0000	−0.776215	−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000	−0.776215	−0.388108	+	0.921614i	$0.626871\pi$
$240$	0	0
$241$	−30.0000	−1.93247	−0.966235	−	0.257663i	$-0.917048\pi$
$241$	−30.0000	−1.93247	−0.966235	+	0.257663i	$0.917048\pi$
$242$	7.00000	0.449977
$243$	1.00000	0.0641500
$244$	10.0000	0.640184
$245$	0	0
$246$	6.00000	0.382546
$247$	−2.00000	−0.127257
$248$	4.00000	0.254000
$249$	−12.0000	−0.760469
$250$	0	0
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	−4.00000	−0.251976
$253$	12.0000	0.754434
$254$	−18.0000	−1.12942
$255$	0	0
$256$	1.00000	0.0625000
$257$	12.0000	0.748539	0.374270	−	0.927320i	$-0.377893\pi$
$257$	12.0000	0.748539	0.374270	+	0.927320i	$0.377893\pi$
$258$	8.00000	0.498058
$259$	−24.0000	−1.49129
$260$	0	0
$261$	−2.00000	−0.123797
$262$	0	0
$263$	10.0000	0.616626	0.308313	−	0.951285i	$-0.400236\pi$
$263$	10.0000	0.616626	0.308313	+	0.951285i	$0.400236\pi$
$264$	−2.00000	−0.123091
$265$	0	0
$266$	8.00000	0.490511
$267$	−18.0000	−1.10158
$268$	−4.00000	−0.244339
$269$	−14.0000	−0.853595	−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−14.0000	−0.853595	−0.426798	+	0.904347i	$0.640358\pi$
$270$	0	0
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	−4.00000	−0.242536
$273$	4.00000	0.242091
$274$	2.00000	0.120824
$275$	0	0
$276$	6.00000	0.361158
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	−16.0000	−0.959616
$279$	−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	$0.680403\pi$
$282$	8.00000	0.476393
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	8.00000	0.474713
$285$	0	0
$286$	2.00000	0.118262
$287$	24.0000	1.41668
$288$	−1.00000	−0.0589256
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	−6.00000	−0.351726
$292$	−10.0000	−0.585206
$293$	14.0000	0.817889	0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000	0.817889	0.408944	+	0.912559i	$0.365897\pi$
$294$	−9.00000	−0.524891
$295$	0	0
$296$	−6.00000	−0.348743
$297$	2.00000	0.116052
$298$	0	0
$299$	−6.00000	−0.346989
$300$	0	0
$301$	32.0000	1.84445
$302$	−8.00000	−0.460348
$303$	−14.0000	−0.804279
$304$	2.00000	0.114708
$305$	0	0
$306$	4.00000	0.228665
$307$	−28.0000	−1.59804	−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000	−1.59804	−0.799022	+	0.601302i	$0.794649\pi$
$308$	−8.00000	−0.455842
$309$	−6.00000	−0.341328
$310$	0	0
$311$	8.00000	0.453638	0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000	0.453638	0.226819	+	0.973937i	$0.427167\pi$
$312$	1.00000	0.0566139
$313$	−8.00000	−0.452187	−0.226093	−	0.974106i	$-0.572595\pi$
$313$	−8.00000	−0.452187	−0.226093	+	0.974106i	$0.572595\pi$
$314$	−10.0000	−0.564333
$315$	0	0
$316$	−8.00000	−0.450035
$317$	30.0000	1.68497	0.842484	−	0.538721i	$-0.181092\pi$
$317$	30.0000	1.68497	0.842484	+	0.538721i	$0.181092\pi$
$318$	10.0000	0.560772
$319$	−4.00000	−0.223957
$320$	0	0
$321$	8.00000	0.446516
$322$	24.0000	1.33747
$323$	−8.00000	−0.445132
$324$	1.00000	0.0555556
$325$	0	0
$326$	−4.00000	−0.221540
$327$	12.0000	0.663602
$328$	6.00000	0.331295
$329$	32.0000	1.76422
$330$	0	0
$331$	18.0000	0.989369	0.494685	−	0.869072i	$-0.335284\pi$
$331$	18.0000	0.989369	0.494685	+	0.869072i	$0.335284\pi$
$332$	−12.0000	−0.658586
$333$	6.00000	0.328798
$334$	0	0
$335$	0	0
$336$	−4.00000	−0.218218
$337$	32.0000	1.74315	0.871576	−	0.490261i	$-0.163099\pi$
$337$	32.0000	1.74315	0.871576	+	0.490261i	$0.163099\pi$
$338$	−1.00000	−0.0543928
$339$	12.0000	0.651751
$340$	0	0
$341$	−8.00000	−0.433224
$342$	−2.00000	−0.108148
$343$	−8.00000	−0.431959
$344$	8.00000	0.431331
$345$	0	0
$346$	10.0000	0.537603
$347$	24.0000	1.28839	0.644194	−	0.764862i	$-0.277193\pi$
$347$	24.0000	1.28839	0.644194	+	0.764862i	$0.277193\pi$
$348$	−2.00000	−0.107211
$349$	−28.0000	−1.49881	−0.749403	−	0.662114i	$-0.769659\pi$
$349$	−28.0000	−1.49881	−0.749403	+	0.662114i	$0.769659\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	−2.00000	−0.106600
$353$	26.0000	1.38384	0.691920	−	0.721974i	$-0.256765\pi$
$353$	26.0000	1.38384	0.691920	+	0.721974i	$0.256765\pi$
$354$	14.0000	0.744092
$355$	0	0
$356$	−18.0000	−0.953998
$357$	16.0000	0.846810
$358$	0	0
$359$	20.0000	1.05556	0.527780	−	0.849381i	$-0.323025\pi$
$359$	20.0000	1.05556	0.527780	+	0.849381i	$0.323025\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	−6.00000	−0.315353
$363$	−7.00000	−0.367405
$364$	4.00000	0.209657
$365$	0	0
$366$	−10.0000	−0.522708
$367$	−22.0000	−1.14839	−0.574195	−	0.818718i	$-0.694685\pi$
$367$	−22.0000	−1.14839	−0.574195	+	0.818718i	$0.694685\pi$
$368$	6.00000	0.312772
$369$	−6.00000	−0.312348
$370$	0	0
$371$	40.0000	2.07670
$372$	−4.00000	−0.207390
$373$	2.00000	0.103556	0.0517780	−	0.998659i	$-0.483511\pi$
$373$	2.00000	0.103556	0.0517780	+	0.998659i	$0.483511\pi$
$374$	8.00000	0.413670
$375$	0	0
$376$	8.00000	0.412568
$377$	2.00000	0.103005
$378$	4.00000	0.205738
$379$	26.0000	1.33553	0.667765	−	0.744372i	$-0.267251\pi$
$379$	26.0000	1.33553	0.667765	+	0.744372i	$0.267251\pi$
$380$	0	0
$381$	18.0000	0.922168
$382$	0	0
$383$	12.0000	0.613171	0.306586	−	0.951843i	$-0.400813\pi$
$383$	12.0000	0.613171	0.306586	+	0.951843i	$0.400813\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	6.00000	0.305392
$387$	−8.00000	−0.406663
$388$	−6.00000	−0.304604
$389$	−26.0000	−1.31825	−0.659126	−	0.752032i	$-0.729074\pi$
$389$	−26.0000	−1.31825	−0.659126	+	0.752032i	$0.729074\pi$
$390$	0	0
$391$	−24.0000	−1.21373
$392$	−9.00000	−0.454569
$393$	0	0
$394$	26.0000	1.30986
$395$	0	0
$396$	2.00000	0.100504
$397$	−6.00000	−0.301131	−0.150566	−	0.988600i	$-0.548110\pi$
$397$	−6.00000	−0.301131	−0.150566	+	0.988600i	$0.548110\pi$
$398$	−24.0000	−1.20301
$399$	−8.00000	−0.400501
$400$	0	0
$401$	−18.0000	−0.898877	−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000	−0.898877	−0.449439	+	0.893311i	$0.648376\pi$
$402$	4.00000	0.199502
$403$	4.00000	0.199254
$404$	−14.0000	−0.696526
$405$	0	0
$406$	−8.00000	−0.397033
$407$	12.0000	0.594818
$408$	4.00000	0.198030
$409$	−2.00000	−0.0988936	−0.0494468	−	0.998777i	$-0.515746\pi$
$409$	−2.00000	−0.0988936	−0.0494468	+	0.998777i	$0.515746\pi$
$410$	0	0
$411$	−2.00000	−0.0986527
$412$	−6.00000	−0.295599
$413$	56.0000	2.75558
$414$	−6.00000	−0.294884
$415$	0	0
$416$	1.00000	0.0490290
$417$	16.0000	0.783523
$418$	−4.00000	−0.195646
$419$	16.0000	0.781651	0.390826	−	0.920465i	$-0.372190\pi$
$419$	16.0000	0.781651	0.390826	+	0.920465i	$0.372190\pi$
$420$	0	0
$421$	28.0000	1.36464	0.682318	−	0.731055i	$-0.260972\pi$
$421$	28.0000	1.36464	0.682318	+	0.731055i	$0.260972\pi$
$422$	28.0000	1.36302
$423$	−8.00000	−0.388973
$424$	10.0000	0.485643
$425$	0	0
$426$	−8.00000	−0.387601
$427$	−40.0000	−1.93574
$428$	8.00000	0.386695
$429$	−2.00000	−0.0965609
$430$	0	0
$431$	−8.00000	−0.385346	−0.192673	−	0.981263i	$-0.561716\pi$
$431$	−8.00000	−0.385346	−0.192673	+	0.981263i	$0.561716\pi$
$432$	1.00000	0.0481125
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	−16.0000	−0.768025
$435$	0	0
$436$	12.0000	0.574696
$437$	12.0000	0.574038
$438$	10.0000	0.477818
$439$	32.0000	1.52728	0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000	1.52728	0.763638	+	0.645644i	$0.223411\pi$
$440$	0	0
$441$	9.00000	0.428571
$442$	−4.00000	−0.190261
$443$	−8.00000	−0.380091	−0.190046	−	0.981775i	$-0.560864\pi$
$443$	−8.00000	−0.380091	−0.190046	+	0.981775i	$0.560864\pi$
$444$	6.00000	0.284747
$445$	0	0
$446$	−16.0000	−0.757622
$447$	0	0
$448$	−4.00000	−0.188982
$449$	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
$451$	−12.0000	−0.565058
$452$	12.0000	0.564433
$453$	8.00000	0.375873
$454$	12.0000	0.563188
$455$	0	0
$456$	−2.00000	−0.0936586
$457$	26.0000	1.21623	0.608114	−	0.793849i	$-0.291926\pi$
$457$	26.0000	1.21623	0.608114	+	0.793849i	$0.291926\pi$
$458$	16.0000	0.747631
$459$	−4.00000	−0.186704
$460$	0	0
$461$	−4.00000	−0.186299	−0.0931493	−	0.995652i	$-0.529693\pi$
$461$	−4.00000	−0.186299	−0.0931493	+	0.995652i	$0.529693\pi$
$462$	8.00000	0.372194
$463$	36.0000	1.67306	0.836531	−	0.547920i	$-0.184580\pi$
$463$	36.0000	1.67306	0.836531	+	0.547920i	$0.184580\pi$
$464$	−2.00000	−0.0928477
$465$	0	0
$466$	−4.00000	−0.185296
$467$	16.0000	0.740392	0.370196	−	0.928954i	$-0.379291\pi$
$467$	16.0000	0.740392	0.370196	+	0.928954i	$0.379291\pi$
$468$	−1.00000	−0.0462250
$469$	16.0000	0.738811
$470$	0	0
$471$	10.0000	0.460776
$472$	14.0000	0.644402
$473$	−16.0000	−0.735681
$474$	8.00000	0.367452
$475$	0	0
$476$	16.0000	0.733359
$477$	−10.0000	−0.457869
$478$	12.0000	0.548867
$479$	−12.0000	−0.548294	−0.274147	−	0.961688i	$-0.588395\pi$
$479$	−12.0000	−0.548294	−0.274147	+	0.961688i	$0.588395\pi$
$480$	0	0
$481$	−6.00000	−0.273576
$482$	30.0000	1.36646
$483$	−24.0000	−1.09204
$484$	−7.00000	−0.318182
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	40.0000	1.81257	0.906287	−	0.422664i	$-0.138905\pi$
$487$	40.0000	1.81257	0.906287	+	0.422664i	$0.138905\pi$
$488$	−10.0000	−0.452679
$489$	4.00000	0.180886
$490$	0	0
$491$	8.00000	0.361035	0.180517	−	0.983572i	$-0.442223\pi$
$491$	8.00000	0.361035	0.180517	+	0.983572i	$0.442223\pi$
$492$	−6.00000	−0.270501
$493$	8.00000	0.360302
$494$	2.00000	0.0899843
$495$	0	0
$496$	−4.00000	−0.179605
$497$	−32.0000	−1.43540
$498$	12.0000	0.537733
$499$	30.0000	1.34298	0.671492	−	0.741012i	$-0.265654\pi$
$499$	30.0000	1.34298	0.671492	+	0.741012i	$0.265654\pi$
$500$	0	0
$501$	0	0
$502$	12.0000	0.535586
$503$	−18.0000	−0.802580	−0.401290	−	0.915951i	$-0.631438\pi$
$503$	−18.0000	−0.802580	−0.401290	+	0.915951i	$0.631438\pi$
$504$	4.00000	0.178174
$505$	0	0
$506$	−12.0000	−0.533465
$507$	1.00000	0.0444116
$508$	18.0000	0.798621
$509$	−16.0000	−0.709188	−0.354594	−	0.935020i	$-0.615381\pi$
$509$	−16.0000	−0.709188	−0.354594	+	0.935020i	$0.615381\pi$
$510$	0	0
$511$	40.0000	1.76950
$512$	−1.00000	−0.0441942
$513$	2.00000	0.0883022
$514$	−12.0000	−0.529297
$515$	0	0
$516$	−8.00000	−0.352180
$517$	−16.0000	−0.703679
$518$	24.0000	1.05450
$519$	−10.0000	−0.438951
$520$	0	0
$521$	38.0000	1.66481	0.832405	−	0.554168i	$-0.186963\pi$
$521$	38.0000	1.66481	0.832405	+	0.554168i	$0.186963\pi$
$522$	2.00000	0.0875376
$523$	−8.00000	−0.349816	−0.174908	−	0.984585i	$-0.555963\pi$
$523$	−8.00000	−0.349816	−0.174908	+	0.984585i	$0.555963\pi$
$524$	0	0
$525$	0	0
$526$	−10.0000	−0.436021
$527$	16.0000	0.696971
$528$	2.00000	0.0870388
$529$	13.0000	0.565217
$530$	0	0
$531$	−14.0000	−0.607548
$532$	−8.00000	−0.346844
$533$	6.00000	0.259889
$534$	18.0000	0.778936
$535$	0	0
$536$	4.00000	0.172774
$537$	0	0
$538$	14.0000	0.603583
$539$	18.0000	0.775315
$540$	0	0
$541$	−8.00000	−0.343947	−0.171973	−	0.985102i	$-0.555014\pi$
$541$	−8.00000	−0.343947	−0.171973	+	0.985102i	$0.555014\pi$
$542$	−16.0000	−0.687259
$543$	6.00000	0.257485
$544$	4.00000	0.171499
$545$	0	0
$546$	−4.00000	−0.171184
$547$	−44.0000	−1.88130	−0.940652	−	0.339372i	$-0.889785\pi$
$547$	−44.0000	−1.88130	−0.940652	+	0.339372i	$0.889785\pi$
$548$	−2.00000	−0.0854358
$549$	10.0000	0.426790
$550$	0	0
$551$	−4.00000	−0.170406
$552$	−6.00000	−0.255377
$553$	32.0000	1.36078
$554$	2.00000	0.0849719
$555$	0	0
$556$	16.0000	0.678551
$557$	−14.0000	−0.593199	−0.296600	−	0.955002i	$-0.595853\pi$
$557$	−14.0000	−0.593199	−0.296600	+	0.955002i	$0.595853\pi$
$558$	4.00000	0.169334
$559$	8.00000	0.338364
$560$	0	0
$561$	−8.00000	−0.337760
$562$	18.0000	0.759284
$563$	16.0000	0.674320	0.337160	−	0.941447i	$-0.390534\pi$
$563$	16.0000	0.674320	0.337160	+	0.941447i	$0.390534\pi$
$564$	−8.00000	−0.336861
$565$	0	0
$566$	−4.00000	−0.168133
$567$	−4.00000	−0.167984
$568$	−8.00000	−0.335673
$569$	−42.0000	−1.76073	−0.880366	−	0.474295i	$-0.842703\pi$
$569$	−42.0000	−1.76073	−0.880366	+	0.474295i	$0.842703\pi$
$570$	0	0
$571$	−36.0000	−1.50655	−0.753277	−	0.657704i	$-0.771528\pi$
$571$	−36.0000	−1.50655	−0.753277	+	0.657704i	$0.771528\pi$
$572$	−2.00000	−0.0836242
$573$	0	0
$574$	−24.0000	−1.00174
$575$	0	0
$576$	1.00000	0.0416667
$577$	−26.0000	−1.08239	−0.541197	−	0.840896i	$-0.682029\pi$
$577$	−26.0000	−1.08239	−0.541197	+	0.840896i	$0.682029\pi$
$578$	1.00000	0.0415945
$579$	−6.00000	−0.249351
$580$	0	0
$581$	48.0000	1.99138
$582$	6.00000	0.248708
$583$	−20.0000	−0.828315
$584$	10.0000	0.413803
$585$	0	0
$586$	−14.0000	−0.578335
$587$	−36.0000	−1.48588	−0.742940	−	0.669359i	$-0.766569\pi$
$587$	−36.0000	−1.48588	−0.742940	+	0.669359i	$0.766569\pi$
$588$	9.00000	0.371154
$589$	−8.00000	−0.329634
$590$	0	0
$591$	−26.0000	−1.06950
$592$	6.00000	0.246598
$593$	−14.0000	−0.574911	−0.287456	−	0.957794i	$-0.592809\pi$
$593$	−14.0000	−0.574911	−0.287456	+	0.957794i	$0.592809\pi$
$594$	−2.00000	−0.0820610
$595$	0	0
$596$	0	0
$597$	24.0000	0.982255
$598$	6.00000	0.245358
$599$	−16.0000	−0.653742	−0.326871	−	0.945069i	$-0.605994\pi$
$599$	−16.0000	−0.653742	−0.326871	+	0.945069i	$0.605994\pi$
$600$	0	0
$601$	−10.0000	−0.407909	−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000	−0.407909	−0.203954	+	0.978980i	$0.565379\pi$
$602$	−32.0000	−1.30422
$603$	−4.00000	−0.162893
$604$	8.00000	0.325515
$605$	0	0
$606$	14.0000	0.568711
$607$	−18.0000	−0.730597	−0.365299	−	0.930890i	$-0.619033\pi$
$607$	−18.0000	−0.730597	−0.365299	+	0.930890i	$0.619033\pi$
$608$	−2.00000	−0.0811107
$609$	8.00000	0.324176
$610$	0	0
$611$	8.00000	0.323645
$612$	−4.00000	−0.161690
$613$	−26.0000	−1.05013	−0.525065	−	0.851062i	$-0.675959\pi$
$613$	−26.0000	−1.05013	−0.525065	+	0.851062i	$0.675959\pi$
$614$	28.0000	1.12999
$615$	0	0
$616$	8.00000	0.322329
$617$	34.0000	1.36879	0.684394	−	0.729112i	$-0.260067\pi$
$617$	34.0000	1.36879	0.684394	+	0.729112i	$0.260067\pi$
$618$	6.00000	0.241355
$619$	42.0000	1.68812	0.844061	−	0.536247i	$-0.180158\pi$
$619$	42.0000	1.68812	0.844061	+	0.536247i	$0.180158\pi$
$620$	0	0
$621$	6.00000	0.240772
$622$	−8.00000	−0.320771
$623$	72.0000	2.88462
$624$	−1.00000	−0.0400320
$625$	0	0
$626$	8.00000	0.319744
$627$	4.00000	0.159745
$628$	10.0000	0.399043
$629$	−24.0000	−0.956943
$630$	0	0
$631$	−32.0000	−1.27390	−0.636950	−	0.770905i	$-0.719804\pi$
$631$	−32.0000	−1.27390	−0.636950	+	0.770905i	$0.719804\pi$
$632$	8.00000	0.318223
$633$	−28.0000	−1.11290
$634$	−30.0000	−1.19145
$635$	0	0
$636$	−10.0000	−0.396526
$637$	−9.00000	−0.356593
$638$	4.00000	0.158362
$639$	8.00000	0.316475
$640$	0	0
$641$	−2.00000	−0.0789953	−0.0394976	−	0.999220i	$-0.512576\pi$
$641$	−2.00000	−0.0789953	−0.0394976	+	0.999220i	$0.512576\pi$
$642$	−8.00000	−0.315735
$643$	20.0000	0.788723	0.394362	−	0.918955i	$-0.370966\pi$
$643$	20.0000	0.788723	0.394362	+	0.918955i	$0.370966\pi$
$644$	−24.0000	−0.945732
$645$	0	0
$646$	8.00000	0.314756
$647$	6.00000	0.235884	0.117942	−	0.993020i	$-0.462370\pi$
$647$	6.00000	0.235884	0.117942	+	0.993020i	$0.462370\pi$
$648$	−1.00000	−0.0392837
$649$	−28.0000	−1.09910
$650$	0	0
$651$	16.0000	0.627089
$652$	4.00000	0.156652
$653$	26.0000	1.01746	0.508729	−	0.860927i	$-0.330115\pi$
$653$	26.0000	1.01746	0.508729	+	0.860927i	$0.330115\pi$
$654$	−12.0000	−0.469237
$655$	0	0
$656$	−6.00000	−0.234261
$657$	−10.0000	−0.390137
$658$	−32.0000	−1.24749
$659$	40.0000	1.55818	0.779089	−	0.626913i	$-0.215682\pi$
$659$	40.0000	1.55818	0.779089	+	0.626913i	$0.215682\pi$
$660$	0	0
$661$	24.0000	0.933492	0.466746	−	0.884391i	$-0.345426\pi$
$661$	24.0000	0.933492	0.466746	+	0.884391i	$0.345426\pi$
$662$	−18.0000	−0.699590
$663$	4.00000	0.155347
$664$	12.0000	0.465690
$665$	0	0
$666$	−6.00000	−0.232495
$667$	−12.0000	−0.464642
$668$	0	0
$669$	16.0000	0.618596
$670$	0	0
$671$	20.0000	0.772091
$672$	4.00000	0.154303
$673$	−12.0000	−0.462566	−0.231283	−	0.972887i	$-0.574292\pi$
$673$	−12.0000	−0.462566	−0.231283	+	0.972887i	$0.574292\pi$
$674$	−32.0000	−1.23259
$675$	0	0
$676$	1.00000	0.0384615
$677$	−22.0000	−0.845529	−0.422764	−	0.906240i	$-0.638940\pi$
$677$	−22.0000	−0.845529	−0.422764	+	0.906240i	$0.638940\pi$
$678$	−12.0000	−0.460857
$679$	24.0000	0.921035
$680$	0	0
$681$	−12.0000	−0.459841
$682$	8.00000	0.306336
$683$	−12.0000	−0.459167	−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000	−0.459167	−0.229584	+	0.973289i	$0.573736\pi$
$684$	2.00000	0.0764719
$685$	0	0
$686$	8.00000	0.305441
$687$	−16.0000	−0.610438
$688$	−8.00000	−0.304997
$689$	10.0000	0.380970
$690$	0	0
$691$	2.00000	0.0760836	0.0380418	−	0.999276i	$-0.487888\pi$
$691$	2.00000	0.0760836	0.0380418	+	0.999276i	$0.487888\pi$
$692$	−10.0000	−0.380143
$693$	−8.00000	−0.303895
$694$	−24.0000	−0.911028
$695$	0	0
$696$	2.00000	0.0758098
$697$	24.0000	0.909065
$698$	28.0000	1.05982
$699$	4.00000	0.151294
$700$	0	0
$701$	−30.0000	−1.13308	−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000	−1.13308	−0.566542	+	0.824033i	$0.691719\pi$
$702$	1.00000	0.0377426
$703$	12.0000	0.452589
$704$	2.00000	0.0753778
$705$	0	0
$706$	−26.0000	−0.978523
$707$	56.0000	2.10610
$708$	−14.0000	−0.526152
$709$	−32.0000	−1.20179	−0.600893	−	0.799330i	$-0.705188\pi$
$709$	−32.0000	−1.20179	−0.600893	+	0.799330i	$0.705188\pi$
$710$	0	0
$711$	−8.00000	−0.300023
$712$	18.0000	0.674579
$713$	−24.0000	−0.898807
$714$	−16.0000	−0.598785
$715$	0	0
$716$	0	0
$717$	−12.0000	−0.448148
$718$	−20.0000	−0.746393
$719$	24.0000	0.895049	0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000	0.895049	0.447524	+	0.894272i	$0.352306\pi$
$720$	0	0
$721$	24.0000	0.893807
$722$	15.0000	0.558242
$723$	−30.0000	−1.11571
$724$	6.00000	0.222988
$725$	0	0
$726$	7.00000	0.259794
$727$	−14.0000	−0.519231	−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000	−0.519231	−0.259616	+	0.965712i	$0.583596\pi$
$728$	−4.00000	−0.148250
$729$	1.00000	0.0370370
$730$	0	0
$731$	32.0000	1.18356
$732$	10.0000	0.369611
$733$	2.00000	0.0738717	0.0369358	−	0.999318i	$-0.488240\pi$
$733$	2.00000	0.0738717	0.0369358	+	0.999318i	$0.488240\pi$
$734$	22.0000	0.812035
$735$	0	0
$736$	−6.00000	−0.221163
$737$	−8.00000	−0.294684
$738$	6.00000	0.220863
$739$	−2.00000	−0.0735712	−0.0367856	−	0.999323i	$-0.511712\pi$
$739$	−2.00000	−0.0735712	−0.0367856	+	0.999323i	$0.511712\pi$
$740$	0	0
$741$	−2.00000	−0.0734718
$742$	−40.0000	−1.46845
$743$	4.00000	0.146746	0.0733729	−	0.997305i	$-0.476624\pi$
$743$	4.00000	0.146746	0.0733729	+	0.997305i	$0.476624\pi$
$744$	4.00000	0.146647
$745$	0	0
$746$	−2.00000	−0.0732252
$747$	−12.0000	−0.439057
$748$	−8.00000	−0.292509
$749$	−32.0000	−1.16925
$750$	0	0
$751$	48.0000	1.75154	0.875772	−	0.482724i	$-0.160353\pi$
$751$	48.0000	1.75154	0.875772	+	0.482724i	$0.160353\pi$
$752$	−8.00000	−0.291730
$753$	−12.0000	−0.437304
$754$	−2.00000	−0.0728357
$755$	0	0
$756$	−4.00000	−0.145479
$757$	22.0000	0.799604	0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000	0.799604	0.399802	+	0.916602i	$0.369079\pi$
$758$	−26.0000	−0.944363
$759$	12.0000	0.435572
$760$	0	0
$761$	14.0000	0.507500	0.253750	−	0.967270i	$-0.418336\pi$
$761$	14.0000	0.507500	0.253750	+	0.967270i	$0.418336\pi$
$762$	−18.0000	−0.652071
$763$	−48.0000	−1.73772
$764$	0	0
$765$	0	0
$766$	−12.0000	−0.433578
$767$	14.0000	0.505511
$768$	1.00000	0.0360844
$769$	−22.0000	−0.793340	−0.396670	−	0.917961i	$-0.629834\pi$
$769$	−22.0000	−0.793340	−0.396670	+	0.917961i	$0.629834\pi$
$770$	0	0
$771$	12.0000	0.432169
$772$	−6.00000	−0.215945
$773$	−14.0000	−0.503545	−0.251773	−	0.967786i	$-0.581013\pi$
$773$	−14.0000	−0.503545	−0.251773	+	0.967786i	$0.581013\pi$
$774$	8.00000	0.287554
$775$	0	0
$776$	6.00000	0.215387
$777$	−24.0000	−0.860995
$778$	26.0000	0.932145
$779$	−12.0000	−0.429945
$780$	0	0
$781$	16.0000	0.572525
$782$	24.0000	0.858238
$783$	−2.00000	−0.0714742
$784$	9.00000	0.321429
$785$	0	0
$786$	0	0
$787$	28.0000	0.998092	0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000	0.998092	0.499046	+	0.866575i	$0.333684\pi$
$788$	−26.0000	−0.926212
$789$	10.0000	0.356009
$790$	0	0
$791$	−48.0000	−1.70668
$792$	−2.00000	−0.0710669
$793$	−10.0000	−0.355110
$794$	6.00000	0.212932
$795$	0	0
$796$	24.0000	0.850657
$797$	−34.0000	−1.20434	−0.602171	−	0.798367i	$-0.705697\pi$
$797$	−34.0000	−1.20434	−0.602171	+	0.798367i	$0.705697\pi$
$798$	8.00000	0.283197
$799$	32.0000	1.13208
$800$	0	0
$801$	−18.0000	−0.635999
$802$	18.0000	0.635602
$803$	−20.0000	−0.705785
$804$	−4.00000	−0.141069
$805$	0	0
$806$	−4.00000	−0.140894
$807$	−14.0000	−0.492823
$808$	14.0000	0.492518
$809$	14.0000	0.492214	0.246107	−	0.969243i	$-0.420849\pi$
$809$	14.0000	0.492214	0.246107	+	0.969243i	$0.420849\pi$
$810$	0	0
$811$	−2.00000	−0.0702295	−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000	−0.0702295	−0.0351147	+	0.999383i	$0.511180\pi$
$812$	8.00000	0.280745
$813$	16.0000	0.561144
$814$	−12.0000	−0.420600
$815$	0	0
$816$	−4.00000	−0.140028
$817$	−16.0000	−0.559769
$818$	2.00000	0.0699284
$819$	4.00000	0.139771
$820$	0	0
$821$	−12.0000	−0.418803	−0.209401	−	0.977830i	$-0.567152\pi$
$821$	−12.0000	−0.418803	−0.209401	+	0.977830i	$0.567152\pi$
$822$	2.00000	0.0697580
$823$	−26.0000	−0.906303	−0.453152	−	0.891434i	$-0.649700\pi$
$823$	−26.0000	−0.906303	−0.453152	+	0.891434i	$0.649700\pi$
$824$	6.00000	0.209020
$825$	0	0
$826$	−56.0000	−1.94849
$827$	12.0000	0.417281	0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000	0.417281	0.208640	+	0.977992i	$0.433096\pi$
$828$	6.00000	0.208514
$829$	42.0000	1.45872	0.729360	−	0.684130i	$-0.239818\pi$
$829$	42.0000	1.45872	0.729360	+	0.684130i	$0.239818\pi$
$830$	0	0
$831$	−2.00000	−0.0693792
$832$	−1.00000	−0.0346688
$833$	−36.0000	−1.24733
$834$	−16.0000	−0.554035
$835$	0	0
$836$	4.00000	0.138343
$837$	−4.00000	−0.138260
$838$	−16.0000	−0.552711
$839$	16.0000	0.552381	0.276191	−	0.961103i	$-0.410928\pi$
$839$	16.0000	0.552381	0.276191	+	0.961103i	$0.410928\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	−28.0000	−0.964944
$843$	−18.0000	−0.619953
$844$	−28.0000	−0.963800
$845$	0	0
$846$	8.00000	0.275046
$847$	28.0000	0.962091
$848$	−10.0000	−0.343401
$849$	4.00000	0.137280
$850$	0	0
$851$	36.0000	1.23406
$852$	8.00000	0.274075
$853$	42.0000	1.43805	0.719026	−	0.694983i	$-0.244588\pi$
$853$	42.0000	1.43805	0.719026	+	0.694983i	$0.244588\pi$
$854$	40.0000	1.36877
$855$	0	0
$856$	−8.00000	−0.273434
$857$	40.0000	1.36637	0.683187	−	0.730243i	$-0.260593\pi$
$857$	40.0000	1.36637	0.683187	+	0.730243i	$0.260593\pi$
$858$	2.00000	0.0682789
$859$	−4.00000	−0.136478	−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000	−0.136478	−0.0682391	+	0.997669i	$0.521738\pi$
$860$	0	0
$861$	24.0000	0.817918
$862$	8.00000	0.272481
$863$	24.0000	0.816970	0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000	0.816970	0.408485	+	0.912765i	$0.366057\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	0	0
$867$	−1.00000	−0.0339618
$868$	16.0000	0.543075
$869$	−16.0000	−0.542763
$870$	0	0
$871$	4.00000	0.135535
$872$	−12.0000	−0.406371
$873$	−6.00000	−0.203069
$874$	−12.0000	−0.405906
$875$	0	0
$876$	−10.0000	−0.337869
$877$	30.0000	1.01303	0.506514	−	0.862232i	$-0.330934\pi$
$877$	30.0000	1.01303	0.506514	+	0.862232i	$0.330934\pi$
$878$	−32.0000	−1.07995
$879$	14.0000	0.472208
$880$	0	0
$881$	−46.0000	−1.54978	−0.774890	−	0.632096i	$-0.782195\pi$
$881$	−46.0000	−1.54978	−0.774890	+	0.632096i	$0.782195\pi$
$882$	−9.00000	−0.303046
$883$	−48.0000	−1.61533	−0.807664	−	0.589643i	$-0.799269\pi$
$883$	−48.0000	−1.61533	−0.807664	+	0.589643i	$0.799269\pi$
$884$	4.00000	0.134535
$885$	0	0
$886$	8.00000	0.268765
$887$	6.00000	0.201460	0.100730	−	0.994914i	$-0.467882\pi$
$887$	6.00000	0.201460	0.100730	+	0.994914i	$0.467882\pi$
$888$	−6.00000	−0.201347
$889$	−72.0000	−2.41480
$890$	0	0
$891$	2.00000	0.0670025
$892$	16.0000	0.535720
$893$	−16.0000	−0.535420
$894$	0	0
$895$	0	0
$896$	4.00000	0.133631
$897$	−6.00000	−0.200334
$898$	−6.00000	−0.200223
$899$	8.00000	0.266815
$900$	0	0
$901$	40.0000	1.33259
$902$	12.0000	0.399556
$903$	32.0000	1.06489
$904$	−12.0000	−0.399114
$905$	0	0
$906$	−8.00000	−0.265782
$907$	32.0000	1.06254	0.531271	−	0.847202i	$-0.321714\pi$
$907$	32.0000	1.06254	0.531271	+	0.847202i	$0.321714\pi$
$908$	−12.0000	−0.398234
$909$	−14.0000	−0.464351
$910$	0	0
$911$	−32.0000	−1.06021	−0.530104	−	0.847933i	$-0.677847\pi$
$911$	−32.0000	−1.06021	−0.530104	+	0.847933i	$0.677847\pi$
$912$	2.00000	0.0662266
$913$	−24.0000	−0.794284
$914$	−26.0000	−0.860004
$915$	0	0
$916$	−16.0000	−0.528655
$917$	0	0
$918$	4.00000	0.132020
$919$	−24.0000	−0.791687	−0.395843	−	0.918318i	$-0.629548\pi$
$919$	−24.0000	−0.791687	−0.395843	+	0.918318i	$0.629548\pi$
$920$	0	0
$921$	−28.0000	−0.922631
$922$	4.00000	0.131733
$923$	−8.00000	−0.263323
$924$	−8.00000	−0.263181
$925$	0	0
$926$	−36.0000	−1.18303
$927$	−6.00000	−0.197066
$928$	2.00000	0.0656532
$929$	46.0000	1.50921	0.754606	−	0.656179i	$-0.227828\pi$
$929$	46.0000	1.50921	0.754606	+	0.656179i	$0.227828\pi$
$930$	0	0
$931$	18.0000	0.589926
$932$	4.00000	0.131024
$933$	8.00000	0.261908
$934$	−16.0000	−0.523536
$935$	0	0
$936$	1.00000	0.0326860
$937$	−16.0000	−0.522697	−0.261349	−	0.965244i	$-0.584167\pi$
$937$	−16.0000	−0.522697	−0.261349	+	0.965244i	$0.584167\pi$
$938$	−16.0000	−0.522419
$939$	−8.00000	−0.261070
$940$	0	0
$941$	40.0000	1.30396	0.651981	−	0.758235i	$-0.273938\pi$
$941$	40.0000	1.30396	0.651981	+	0.758235i	$0.273938\pi$
$942$	−10.0000	−0.325818
$943$	−36.0000	−1.17232
$944$	−14.0000	−0.455661
$945$	0	0
$946$	16.0000	0.520205
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	−8.00000	−0.259828
$949$	10.0000	0.324614
$950$	0	0
$951$	30.0000	0.972817
$952$	−16.0000	−0.518563
$953$	48.0000	1.55487	0.777436	−	0.628962i	$-0.216520\pi$
$953$	48.0000	1.55487	0.777436	+	0.628962i	$0.216520\pi$
$954$	10.0000	0.323762
$955$	0	0
$956$	−12.0000	−0.388108
$957$	−4.00000	−0.129302
$958$	12.0000	0.387702
$959$	8.00000	0.258333
$960$	0	0
$961$	−15.0000	−0.483871
$962$	6.00000	0.193448
$963$	8.00000	0.257796
$964$	−30.0000	−0.966235
$965$	0	0
$966$	24.0000	0.772187
$967$	28.0000	0.900419	0.450210	−	0.892923i	$-0.351349\pi$
$967$	28.0000	0.900419	0.450210	+	0.892923i	$0.351349\pi$
$968$	7.00000	0.224989
$969$	−8.00000	−0.256997
$970$	0	0
$971$	−28.0000	−0.898563	−0.449281	−	0.893390i	$-0.648320\pi$
$971$	−28.0000	−0.898563	−0.449281	+	0.893390i	$0.648320\pi$
$972$	1.00000	0.0320750
$973$	−64.0000	−2.05175
$974$	−40.0000	−1.28168
$975$	0	0
$976$	10.0000	0.320092
$977$	−42.0000	−1.34370	−0.671850	−	0.740688i	$-0.734500\pi$
$977$	−42.0000	−1.34370	−0.671850	+	0.740688i	$0.734500\pi$
$978$	−4.00000	−0.127906
$979$	−36.0000	−1.15056
$980$	0	0
$981$	12.0000	0.383131
$982$	−8.00000	−0.255290
$983$	−4.00000	−0.127580	−0.0637901	−	0.997963i	$-0.520319\pi$
$983$	−4.00000	−0.127580	−0.0637901	+	0.997963i	$0.520319\pi$
$984$	6.00000	0.191273
$985$	0	0
$986$	−8.00000	−0.254772
$987$	32.0000	1.01857
$988$	−2.00000	−0.0636285
$989$	−48.0000	−1.52631
$990$	0	0
$991$	32.0000	1.01651	0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000	1.01651	0.508257	+	0.861206i	$0.330290\pi$
$992$	4.00000	0.127000
$993$	18.0000	0.571213
$994$	32.0000	1.01498
$995$	0	0
$996$	−12.0000	−0.380235
$997$	−38.0000	−1.20347	−0.601736	−	0.798695i	$-0.705524\pi$
$997$	−38.0000	−1.20347	−0.601736	+	0.798695i	$0.705524\pi$
$998$	−30.0000	−0.949633
$999$	6.00000	0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.a.g.1.1		1
3.2	odd	2		5850.2.a.bd.1.1		1
5.2	odd	4		390.2.e.b.79.1	✓	2
5.3	odd	4		390.2.e.b.79.2	yes	2
5.4	even	2		1950.2.a.u.1.1		1
15.2	even	4		1170.2.e.b.469.2		2
15.8	even	4		1170.2.e.b.469.1		2
15.14	odd	2		5850.2.a.x.1.1		1
20.3	even	4		3120.2.l.h.1249.1		2
20.7	even	4		3120.2.l.h.1249.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.e.b.79.1	✓	2	5.2	odd	4
390.2.e.b.79.2	yes	2	5.3	odd	4
1170.2.e.b.469.1		2	15.8	even	4
1170.2.e.b.469.2		2	15.2	even	4
1950.2.a.g.1.1		1	1.1	even	1	trivial
1950.2.a.u.1.1		1	5.4	even	2
3120.2.l.h.1249.1		2	20.3	even	4
3120.2.l.h.1249.2		2	20.7	even	4
5850.2.a.x.1.1		1	15.14	odd	2
5850.2.a.bd.1.1		1	3.2	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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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