LMFDB - Embedded newform 7410.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7410,2,Mod(1,7410)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7410, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("7410.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7410 = 2 \cdot 3 \cdot 5 \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7410.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:	$59.1691478978$
Analytic rank:	$1$
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	$\chi$	$=$	7410.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -4.00000 q^{11} +1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{18} -1.00000 q^{19} -1.00000 q^{20} -4.00000 q^{22} -8.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -1.00000 q^{26} +1.00000 q^{27} +2.00000 q^{29} -1.00000 q^{30} +8.00000 q^{31} +1.00000 q^{32} -4.00000 q^{33} +2.00000 q^{34} +1.00000 q^{36} -6.00000 q^{37} -1.00000 q^{38} -1.00000 q^{39} -1.00000 q^{40} +2.00000 q^{41} -8.00000 q^{43} -4.00000 q^{44} -1.00000 q^{45} -8.00000 q^{46} +4.00000 q^{47} +1.00000 q^{48} -7.00000 q^{49} +1.00000 q^{50} +2.00000 q^{51} -1.00000 q^{52} -6.00000 q^{53} +1.00000 q^{54} +4.00000 q^{55} -1.00000 q^{57} +2.00000 q^{58} -1.00000 q^{60} +6.00000 q^{61} +8.00000 q^{62} +1.00000 q^{64} +1.00000 q^{65} -4.00000 q^{66} -16.0000 q^{67} +2.00000 q^{68} -8.00000 q^{69} +1.00000 q^{72} -10.0000 q^{73} -6.00000 q^{74} +1.00000 q^{75} -1.00000 q^{76} -1.00000 q^{78} -4.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +2.00000 q^{82} +4.00000 q^{83} -2.00000 q^{85} -8.00000 q^{86} +2.00000 q^{87} -4.00000 q^{88} +18.0000 q^{89} -1.00000 q^{90} -8.00000 q^{92} +8.00000 q^{93} +4.00000 q^{94} +1.00000 q^{95} +1.00000 q^{96} -14.0000 q^{97} -7.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)

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
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.00000	0.408248
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−1.00000	−0.223607
$21$	0	0
$22$	−4.00000	−0.852803
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	0	0
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	−1.00000	−0.182574
$31$	8.00000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	1.00000	0.176777
$33$	−4.00000	−0.696311
$34$	2.00000	0.342997
$35$	0	0
$36$	1.00000	0.166667
$37$	−6.00000	−0.986394	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000	−0.986394	−0.493197	+	0.869918i	$0.664172\pi$
$38$	−1.00000	−0.162221
$39$	−1.00000	−0.160128
$40$	−1.00000	−0.158114
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	0	0
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	−4.00000	−0.603023
$45$	−1.00000	−0.149071
$46$	−8.00000	−1.17954
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	1.00000	0.144338
$49$	−7.00000	−1.00000
$50$	1.00000	0.141421
$51$	2.00000	0.280056
$52$	−1.00000	−0.138675
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	1.00000	0.136083
$55$	4.00000	0.539360
$56$	0	0
$57$	−1.00000	−0.132453
$58$	2.00000	0.262613
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	−1.00000	−0.129099
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	8.00000	1.01600
$63$	0	0
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	−4.00000	−0.492366
$67$	−16.0000	−1.95471	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−16.0000	−1.95471	−0.977356	+	0.211604i	$0.932131\pi$
$68$	2.00000	0.242536
$69$	−8.00000	−0.963087
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	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
$75$	1.00000	0.115470
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−1.00000	−0.113228
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	2.00000	0.220863
$83$	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
$85$	−2.00000	−0.216930
$86$	−8.00000	−0.862662
$87$	2.00000	0.214423
$88$	−4.00000	−0.426401
$89$	18.0000	1.90800	0.953998	−	0.299813i	$-0.0969242\pi$
$89$	18.0000	1.90800	0.953998	+	0.299813i	$0.0969242\pi$
$90$	−1.00000	−0.105409
$91$	0	0
$92$	−8.00000	−0.834058
$93$	8.00000	0.829561
$94$	4.00000	0.412568
$95$	1.00000	0.102598
$96$	1.00000	0.102062
$97$	−14.0000	−1.42148	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000	−1.42148	−0.710742	+	0.703452i	$0.751641\pi$
$98$	−7.00000	−0.707107
$99$	−4.00000	−0.402015
$100$	1.00000	0.100000
$101$	−14.0000	−1.39305	−0.696526	−	0.717532i	$-0.745272\pi$
$101$	−14.0000	−1.39305	−0.696526	+	0.717532i	$0.745272\pi$
$102$	2.00000	0.198030
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	−1.00000	−0.0980581
$105$	0	0
$106$	−6.00000	−0.582772
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	1.00000	0.0962250
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	4.00000	0.381385
$111$	−6.00000	−0.569495
$112$	0	0
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	−1.00000	−0.0936586
$115$	8.00000	0.746004
$116$	2.00000	0.185695
$117$	−1.00000	−0.0924500
$118$	0	0
$119$	0	0
$120$	−1.00000	−0.0912871
$121$	5.00000	0.454545
$122$	6.00000	0.543214
$123$	2.00000	0.180334
$124$	8.00000	0.718421
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	1.00000	0.0883883
$129$	−8.00000	−0.704361
$130$	1.00000	0.0877058
$131$	8.00000	0.698963	0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000	0.698963	0.349482	+	0.936943i	$0.386358\pi$
$132$	−4.00000	−0.348155
$133$	0	0
$134$	−16.0000	−1.38219
$135$	−1.00000	−0.0860663
$136$	2.00000	0.171499
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	−8.00000	−0.681005
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	0	0
$141$	4.00000	0.336861
$142$	0	0
$143$	4.00000	0.334497
$144$	1.00000	0.0833333
$145$	−2.00000	−0.166091
$146$	−10.0000	−0.827606
$147$	−7.00000	−0.577350
$148$	−6.00000	−0.493197
$149$	−22.0000	−1.80231	−0.901155	−	0.433497i	$-0.857280\pi$
$149$	−22.0000	−1.80231	−0.901155	+	0.433497i	$0.857280\pi$
$150$	1.00000	0.0816497
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	−1.00000	−0.0811107
$153$	2.00000	0.161690
$154$	0	0
$155$	−8.00000	−0.642575
$156$	−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	$0.369342\pi$
$158$	−4.00000	−0.318223
$159$	−6.00000	−0.475831
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	1.00000	0.0785674
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	2.00000	0.156174
$165$	4.00000	0.311400
$166$	4.00000	0.310460
$167$	24.0000	1.85718	0.928588	−	0.371113i	$-0.121024\pi$
$167$	24.0000	1.85718	0.928588	+	0.371113i	$0.121024\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−2.00000	−0.153393
$171$	−1.00000	−0.0764719
$172$	−8.00000	−0.609994
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	2.00000	0.151620
$175$	0	0
$176$	−4.00000	−0.301511
$177$	0	0
$178$	18.0000	1.34916
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	−1.00000	−0.0745356
$181$	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
$183$	6.00000	0.443533
$184$	−8.00000	−0.589768
$185$	6.00000	0.441129
$186$	8.00000	0.586588
$187$	−8.00000	−0.585018
$188$	4.00000	0.291730
$189$	0	0
$190$	1.00000	0.0725476
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	1.00000	0.0721688
$193$	2.00000	0.143963	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000	0.143963	0.0719816	+	0.997406i	$0.477068\pi$
$194$	−14.0000	−1.00514
$195$	1.00000	0.0716115
$196$	−7.00000	−0.500000
$197$	−14.0000	−0.997459	−0.498729	−	0.866758i	$-0.666200\pi$
$197$	−14.0000	−0.997459	−0.498729	+	0.866758i	$0.666200\pi$
$198$	−4.00000	−0.284268
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	1.00000	0.0707107
$201$	−16.0000	−1.12855
$202$	−14.0000	−0.985037
$203$	0	0
$204$	2.00000	0.140028
$205$	−2.00000	−0.139686
$206$	−8.00000	−0.557386
$207$	−8.00000	−0.556038
$208$	−1.00000	−0.0693375
$209$	4.00000	0.276686
$210$	0	0
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	−6.00000	−0.412082
$213$	0	0
$214$	4.00000	0.273434
$215$	8.00000	0.545595
$216$	1.00000	0.0680414
$217$	0	0
$218$	−10.0000	−0.677285
$219$	−10.0000	−0.675737
$220$	4.00000	0.269680
$221$	−2.00000	−0.134535
$222$	−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	$0.320040\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	−6.00000	−0.399114
$227$	−20.0000	−1.32745	−0.663723	−	0.747978i	$-0.731025\pi$
$227$	−20.0000	−1.32745	−0.663723	+	0.747978i	$0.731025\pi$
$228$	−1.00000	−0.0662266
$229$	−6.00000	−0.396491	−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000	−0.396491	−0.198246	+	0.980152i	$0.563524\pi$
$230$	8.00000	0.527504
$231$	0	0
$232$	2.00000	0.131306
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	−1.00000	−0.0653720
$235$	−4.00000	−0.260931
$236$	0	0
$237$	−4.00000	−0.259828
$238$	0	0
$239$	16.0000	1.03495	0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000	1.03495	0.517477	+	0.855697i	$0.326871\pi$
$240$	−1.00000	−0.0645497
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	5.00000	0.321412
$243$	1.00000	0.0641500
$244$	6.00000	0.384111
$245$	7.00000	0.447214
$246$	2.00000	0.127515
$247$	1.00000	0.0636285
$248$	8.00000	0.508001
$249$	4.00000	0.253490
$250$	−1.00000	−0.0632456
$251$	8.00000	0.504956	0.252478	−	0.967603i	$-0.418755\pi$
$251$	8.00000	0.504956	0.252478	+	0.967603i	$0.418755\pi$
$252$	0	0
$253$	32.0000	2.01182
$254$	−8.00000	−0.501965
$255$	−2.00000	−0.125245
$256$	1.00000	0.0625000
$257$	26.0000	1.62184	0.810918	−	0.585160i	$-0.198968\pi$
$257$	26.0000	1.62184	0.810918	+	0.585160i	$0.198968\pi$
$258$	−8.00000	−0.498058
$259$	0	0
$260$	1.00000	0.0620174
$261$	2.00000	0.123797
$262$	8.00000	0.494242
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	−4.00000	−0.246183
$265$	6.00000	0.368577
$266$	0	0
$267$	18.0000	1.10158
$268$	−16.0000	−0.977356
$269$	−14.0000	−0.853595	−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−14.0000	−0.853595	−0.426798	+	0.904347i	$0.640358\pi$
$270$	−1.00000	−0.0608581
$271$	12.0000	0.728948	0.364474	−	0.931214i	$-0.381249\pi$
$271$	12.0000	0.728948	0.364474	+	0.931214i	$0.381249\pi$
$272$	2.00000	0.121268
$273$	0	0
$274$	−6.00000	−0.362473
$275$	−4.00000	−0.241209
$276$	−8.00000	−0.481543
$277$	−14.0000	−0.841178	−0.420589	−	0.907251i	$-0.638177\pi$
$277$	−14.0000	−0.841178	−0.420589	+	0.907251i	$0.638177\pi$
$278$	−4.00000	−0.239904
$279$	8.00000	0.478947
$280$	0	0
$281$	−14.0000	−0.835170	−0.417585	−	0.908638i	$-0.637123\pi$
$281$	−14.0000	−0.835170	−0.417585	+	0.908638i	$0.637123\pi$
$282$	4.00000	0.238197
$283$	24.0000	1.42665	0.713326	−	0.700832i	$-0.247188\pi$
$283$	24.0000	1.42665	0.713326	+	0.700832i	$0.247188\pi$
$284$	0	0
$285$	1.00000	0.0592349
$286$	4.00000	0.236525
$287$	0	0
$288$	1.00000	0.0589256
$289$	−13.0000	−0.764706
$290$	−2.00000	−0.117444
$291$	−14.0000	−0.820695
$292$	−10.0000	−0.585206
$293$	−2.00000	−0.116841	−0.0584206	−	0.998292i	$-0.518606\pi$
$293$	−2.00000	−0.116841	−0.0584206	+	0.998292i	$0.518606\pi$
$294$	−7.00000	−0.408248
$295$	0	0
$296$	−6.00000	−0.348743
$297$	−4.00000	−0.232104
$298$	−22.0000	−1.27443
$299$	8.00000	0.462652
$300$	1.00000	0.0577350
$301$	0	0
$302$	−8.00000	−0.460348
$303$	−14.0000	−0.804279
$304$	−1.00000	−0.0573539
$305$	−6.00000	−0.343559
$306$	2.00000	0.114332
$307$	−16.0000	−0.913168	−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000	−0.913168	−0.456584	+	0.889680i	$0.650927\pi$
$308$	0	0
$309$	−8.00000	−0.455104
$310$	−8.00000	−0.454369
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	−1.00000	−0.0566139
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	10.0000	0.564333
$315$	0	0
$316$	−4.00000	−0.225018
$317$	6.00000	0.336994	0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000	0.336994	0.168497	+	0.985702i	$0.446109\pi$
$318$	−6.00000	−0.336463
$319$	−8.00000	−0.447914
$320$	−1.00000	−0.0559017
$321$	4.00000	0.223258
$322$	0	0
$323$	−2.00000	−0.111283
$324$	1.00000	0.0555556
$325$	−1.00000	−0.0554700
$326$	−4.00000	−0.221540
$327$	−10.0000	−0.553001
$328$	2.00000	0.110432
$329$	0	0
$330$	4.00000	0.220193
$331$	−20.0000	−1.09930	−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000	−1.09930	−0.549650	+	0.835395i	$0.685239\pi$
$332$	4.00000	0.219529
$333$	−6.00000	−0.328798
$334$	24.0000	1.31322
$335$	16.0000	0.874173
$336$	0	0
$337$	14.0000	0.762629	0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000	0.762629	0.381314	+	0.924445i	$0.375472\pi$
$338$	1.00000	0.0543928
$339$	−6.00000	−0.325875
$340$	−2.00000	−0.108465
$341$	−32.0000	−1.73290
$342$	−1.00000	−0.0540738
$343$	0	0
$344$	−8.00000	−0.431331
$345$	8.00000	0.430706
$346$	−6.00000	−0.322562
$347$	4.00000	0.214731	0.107366	−	0.994220i	$-0.465758\pi$
$347$	4.00000	0.214731	0.107366	+	0.994220i	$0.465758\pi$
$348$	2.00000	0.107211
$349$	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
$352$	−4.00000	−0.213201
$353$	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
$356$	18.0000	0.953998
$357$	0	0
$358$	12.0000	0.634220
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	−1.00000	−0.0527046
$361$	1.00000	0.0526316
$362$	2.00000	0.105118
$363$	5.00000	0.262432
$364$	0	0
$365$	10.0000	0.523424
$366$	6.00000	0.313625
$367$	24.0000	1.25279	0.626395	−	0.779506i	$-0.284530\pi$
$367$	24.0000	1.25279	0.626395	+	0.779506i	$0.284530\pi$
$368$	−8.00000	−0.417029
$369$	2.00000	0.104116
$370$	6.00000	0.311925
$371$	0	0
$372$	8.00000	0.414781
$373$	−22.0000	−1.13912	−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000	−1.13912	−0.569558	+	0.821951i	$0.692886\pi$
$374$	−8.00000	−0.413670
$375$	−1.00000	−0.0516398
$376$	4.00000	0.206284
$377$	−2.00000	−0.103005
$378$	0	0
$379$	−28.0000	−1.43826	−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000	−1.43826	−0.719132	+	0.694874i	$0.755460\pi$
$380$	1.00000	0.0512989
$381$	−8.00000	−0.409852
$382$	0	0
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	2.00000	0.101797
$387$	−8.00000	−0.406663
$388$	−14.0000	−0.710742
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	1.00000	0.0506370
$391$	−16.0000	−0.809155
$392$	−7.00000	−0.353553
$393$	8.00000	0.403547
$394$	−14.0000	−0.705310
$395$	4.00000	0.201262
$396$	−4.00000	−0.201008
$397$	18.0000	0.903394	0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000	0.903394	0.451697	+	0.892171i	$0.350819\pi$
$398$	−16.0000	−0.802008
$399$	0	0
$400$	1.00000	0.0500000
$401$	−30.0000	−1.49813	−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000	−1.49813	−0.749064	+	0.662497i	$0.769497\pi$
$402$	−16.0000	−0.798007
$403$	−8.00000	−0.398508
$404$	−14.0000	−0.696526
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	24.0000	1.18964
$408$	2.00000	0.0990148
$409$	26.0000	1.28562	0.642809	−	0.766027i	$-0.277769\pi$
$409$	26.0000	1.28562	0.642809	+	0.766027i	$0.277769\pi$
$410$	−2.00000	−0.0987730
$411$	−6.00000	−0.295958
$412$	−8.00000	−0.394132
$413$	0	0
$414$	−8.00000	−0.393179
$415$	−4.00000	−0.196352
$416$	−1.00000	−0.0490290
$417$	−4.00000	−0.195881
$418$	4.00000	0.195646
$419$	40.0000	1.95413	0.977064	−	0.212946i	$-0.0683059\pi$
$419$	40.0000	1.95413	0.977064	+	0.212946i	$0.0683059\pi$
$420$	0	0
$421$	−2.00000	−0.0974740	−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000	−0.0974740	−0.0487370	+	0.998812i	$0.515520\pi$
$422$	20.0000	0.973585
$423$	4.00000	0.194487
$424$	−6.00000	−0.291386
$425$	2.00000	0.0970143
$426$	0	0
$427$	0	0
$428$	4.00000	0.193347
$429$	4.00000	0.193122
$430$	8.00000	0.385794
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	1.00000	0.0481125
$433$	−18.0000	−0.865025	−0.432512	−	0.901628i	$-0.642373\pi$
$433$	−18.0000	−0.865025	−0.432512	+	0.901628i	$0.642373\pi$
$434$	0	0
$435$	−2.00000	−0.0958927
$436$	−10.0000	−0.478913
$437$	8.00000	0.382692
$438$	−10.0000	−0.477818
$439$	28.0000	1.33637	0.668184	−	0.743996i	$-0.267072\pi$
$439$	28.0000	1.33637	0.668184	+	0.743996i	$0.267072\pi$
$440$	4.00000	0.190693
$441$	−7.00000	−0.333333
$442$	−2.00000	−0.0951303
$443$	20.0000	0.950229	0.475114	−	0.879924i	$-0.342407\pi$
$443$	20.0000	0.950229	0.475114	+	0.879924i	$0.342407\pi$
$444$	−6.00000	−0.284747
$445$	−18.0000	−0.853282
$446$	16.0000	0.757622
$447$	−22.0000	−1.04056
$448$	0	0
$449$	10.0000	0.471929	0.235965	−	0.971762i	$-0.424175\pi$
$449$	10.0000	0.471929	0.235965	+	0.971762i	$0.424175\pi$
$450$	1.00000	0.0471405
$451$	−8.00000	−0.376705
$452$	−6.00000	−0.282216
$453$	−8.00000	−0.375873
$454$	−20.0000	−0.938647
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	−6.00000	−0.280362
$459$	2.00000	0.0933520
$460$	8.00000	0.373002
$461$	−14.0000	−0.652045	−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000	−0.652045	−0.326023	+	0.945362i	$0.605709\pi$
$462$	0	0
$463$	−16.0000	−0.743583	−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000	−0.743583	−0.371792	+	0.928316i	$0.621256\pi$
$464$	2.00000	0.0928477
$465$	−8.00000	−0.370991
$466$	−6.00000	−0.277945
$467$	28.0000	1.29569	0.647843	−	0.761774i	$-0.275671\pi$
$467$	28.0000	1.29569	0.647843	+	0.761774i	$0.275671\pi$
$468$	−1.00000	−0.0462250
$469$	0	0
$470$	−4.00000	−0.184506
$471$	10.0000	0.460776
$472$	0	0
$473$	32.0000	1.47136
$474$	−4.00000	−0.183726
$475$	−1.00000	−0.0458831
$476$	0	0
$477$	−6.00000	−0.274721
$478$	16.0000	0.731823
$479$	−16.0000	−0.731059	−0.365529	−	0.930800i	$-0.619112\pi$
$479$	−16.0000	−0.731059	−0.365529	+	0.930800i	$0.619112\pi$
$480$	−1.00000	−0.0456435
$481$	6.00000	0.273576
$482$	−14.0000	−0.637683
$483$	0	0
$484$	5.00000	0.227273
$485$	14.0000	0.635707
$486$	1.00000	0.0453609
$487$	16.0000	0.725029	0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000	0.725029	0.362515	+	0.931978i	$0.381918\pi$
$488$	6.00000	0.271607
$489$	−4.00000	−0.180886
$490$	7.00000	0.316228
$491$	8.00000	0.361035	0.180517	−	0.983572i	$-0.442223\pi$
$491$	8.00000	0.361035	0.180517	+	0.983572i	$0.442223\pi$
$492$	2.00000	0.0901670
$493$	4.00000	0.180151
$494$	1.00000	0.0449921
$495$	4.00000	0.179787
$496$	8.00000	0.359211
$497$	0	0
$498$	4.00000	0.179244
$499$	20.0000	0.895323	0.447661	−	0.894203i	$-0.352257\pi$
$499$	20.0000	0.895323	0.447661	+	0.894203i	$0.352257\pi$
$500$	−1.00000	−0.0447214
$501$	24.0000	1.07224
$502$	8.00000	0.357057
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	14.0000	0.622992
$506$	32.0000	1.42257
$507$	1.00000	0.0444116
$508$	−8.00000	−0.354943
$509$	2.00000	0.0886484	0.0443242	−	0.999017i	$-0.485887\pi$
$509$	2.00000	0.0886484	0.0443242	+	0.999017i	$0.485887\pi$
$510$	−2.00000	−0.0885615
$511$	0	0
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	26.0000	1.14681
$515$	8.00000	0.352522
$516$	−8.00000	−0.352180
$517$	−16.0000	−0.703679
$518$	0	0
$519$	−6.00000	−0.263371
$520$	1.00000	0.0438529
$521$	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
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	8.00000	0.349482
$525$	0	0
$526$	24.0000	1.04645
$527$	16.0000	0.696971
$528$	−4.00000	−0.174078
$529$	41.0000	1.78261
$530$	6.00000	0.260623
$531$	0	0
$532$	0	0
$533$	−2.00000	−0.0866296
$534$	18.0000	0.778936
$535$	−4.00000	−0.172935
$536$	−16.0000	−0.691095
$537$	12.0000	0.517838
$538$	−14.0000	−0.603583
$539$	28.0000	1.20605
$540$	−1.00000	−0.0430331
$541$	10.0000	0.429934	0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000	0.429934	0.214967	+	0.976621i	$0.431036\pi$
$542$	12.0000	0.515444
$543$	2.00000	0.0858282
$544$	2.00000	0.0857493
$545$	10.0000	0.428353
$546$	0	0
$547$	−36.0000	−1.53925	−0.769624	−	0.638497i	$-0.779557\pi$
$547$	−36.0000	−1.53925	−0.769624	+	0.638497i	$0.779557\pi$
$548$	−6.00000	−0.256307
$549$	6.00000	0.256074
$550$	−4.00000	−0.170561
$551$	−2.00000	−0.0852029
$552$	−8.00000	−0.340503
$553$	0	0
$554$	−14.0000	−0.594803
$555$	6.00000	0.254686
$556$	−4.00000	−0.169638
$557$	2.00000	0.0847427	0.0423714	−	0.999102i	$-0.486509\pi$
$557$	2.00000	0.0847427	0.0423714	+	0.999102i	$0.486509\pi$
$558$	8.00000	0.338667
$559$	8.00000	0.338364
$560$	0	0
$561$	−8.00000	−0.337760
$562$	−14.0000	−0.590554
$563$	−12.0000	−0.505740	−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000	−0.505740	−0.252870	+	0.967500i	$0.581374\pi$
$564$	4.00000	0.168430
$565$	6.00000	0.252422
$566$	24.0000	1.00880
$567$	0	0
$568$	0	0
$569$	−2.00000	−0.0838444	−0.0419222	−	0.999121i	$-0.513348\pi$
$569$	−2.00000	−0.0838444	−0.0419222	+	0.999121i	$0.513348\pi$
$570$	1.00000	0.0418854
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	4.00000	0.167248
$573$	0	0
$574$	0	0
$575$	−8.00000	−0.333623
$576$	1.00000	0.0416667
$577$	−34.0000	−1.41544	−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000	−1.41544	−0.707719	+	0.706494i	$0.750276\pi$
$578$	−13.0000	−0.540729
$579$	2.00000	0.0831172
$580$	−2.00000	−0.0830455
$581$	0	0
$582$	−14.0000	−0.580319
$583$	24.0000	0.993978
$584$	−10.0000	−0.413803
$585$	1.00000	0.0413449
$586$	−2.00000	−0.0826192
$587$	−28.0000	−1.15568	−0.577842	−	0.816149i	$-0.696105\pi$
$587$	−28.0000	−1.15568	−0.577842	+	0.816149i	$0.696105\pi$
$588$	−7.00000	−0.288675
$589$	−8.00000	−0.329634
$590$	0	0
$591$	−14.0000	−0.575883
$592$	−6.00000	−0.246598
$593$	−6.00000	−0.246390	−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000	−0.246390	−0.123195	+	0.992382i	$0.539314\pi$
$594$	−4.00000	−0.164122
$595$	0	0
$596$	−22.0000	−0.901155
$597$	−16.0000	−0.654836
$598$	8.00000	0.327144
$599$	−8.00000	−0.326871	−0.163436	−	0.986554i	$-0.552258\pi$
$599$	−8.00000	−0.326871	−0.163436	+	0.986554i	$0.552258\pi$
$600$	1.00000	0.0408248
$601$	2.00000	0.0815817	0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000	0.0815817	0.0407909	+	0.999168i	$0.487012\pi$
$602$	0	0
$603$	−16.0000	−0.651570
$604$	−8.00000	−0.325515
$605$	−5.00000	−0.203279
$606$	−14.0000	−0.568711
$607$	32.0000	1.29884	0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000	1.29884	0.649420	+	0.760430i	$0.275012\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	−6.00000	−0.242933
$611$	−4.00000	−0.161823
$612$	2.00000	0.0808452
$613$	−38.0000	−1.53481	−0.767403	−	0.641165i	$-0.778451\pi$
$613$	−38.0000	−1.53481	−0.767403	+	0.641165i	$0.778451\pi$
$614$	−16.0000	−0.645707
$615$	−2.00000	−0.0806478
$616$	0	0
$617$	10.0000	0.402585	0.201292	−	0.979531i	$-0.435486\pi$
$617$	10.0000	0.402585	0.201292	+	0.979531i	$0.435486\pi$
$618$	−8.00000	−0.321807
$619$	−20.0000	−0.803868	−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000	−0.803868	−0.401934	+	0.915669i	$0.631662\pi$
$620$	−8.00000	−0.321288
$621$	−8.00000	−0.321029
$622$	0	0
$623$	0	0
$624$	−1.00000	−0.0400320
$625$	1.00000	0.0400000
$626$	−6.00000	−0.239808
$627$	4.00000	0.159745
$628$	10.0000	0.399043
$629$	−12.0000	−0.478471
$630$	0	0
$631$	−20.0000	−0.796187	−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000	−0.796187	−0.398094	+	0.917345i	$0.630328\pi$
$632$	−4.00000	−0.159111
$633$	20.0000	0.794929
$634$	6.00000	0.238290
$635$	8.00000	0.317470
$636$	−6.00000	−0.237915
$637$	7.00000	0.277350
$638$	−8.00000	−0.316723
$639$	0	0
$640$	−1.00000	−0.0395285
$641$	14.0000	0.552967	0.276483	−	0.961019i	$-0.410831\pi$
$641$	14.0000	0.552967	0.276483	+	0.961019i	$0.410831\pi$
$642$	4.00000	0.157867
$643$	−44.0000	−1.73519	−0.867595	−	0.497271i	$-0.834335\pi$
$643$	−44.0000	−1.73519	−0.867595	+	0.497271i	$0.834335\pi$
$644$	0	0
$645$	8.00000	0.315000
$646$	−2.00000	−0.0786889
$647$	−24.0000	−0.943537	−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000	−0.943537	−0.471769	+	0.881722i	$0.656384\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	−1.00000	−0.0392232
$651$	0	0
$652$	−4.00000	−0.156652
$653$	14.0000	0.547862	0.273931	−	0.961749i	$-0.411676\pi$
$653$	14.0000	0.547862	0.273931	+	0.961749i	$0.411676\pi$
$654$	−10.0000	−0.391031
$655$	−8.00000	−0.312586
$656$	2.00000	0.0780869
$657$	−10.0000	−0.390137
$658$	0	0
$659$	−36.0000	−1.40236	−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000	−1.40236	−0.701180	+	0.712984i	$0.747343\pi$
$660$	4.00000	0.155700
$661$	6.00000	0.233373	0.116686	−	0.993169i	$-0.462773\pi$
$661$	6.00000	0.233373	0.116686	+	0.993169i	$0.462773\pi$
$662$	−20.0000	−0.777322
$663$	−2.00000	−0.0776736
$664$	4.00000	0.155230
$665$	0	0
$666$	−6.00000	−0.232495
$667$	−16.0000	−0.619522
$668$	24.0000	0.928588
$669$	16.0000	0.618596
$670$	16.0000	0.618134
$671$	−24.0000	−0.926510
$672$	0	0
$673$	−18.0000	−0.693849	−0.346925	−	0.937893i	$-0.612774\pi$
$673$	−18.0000	−0.693849	−0.346925	+	0.937893i	$0.612774\pi$
$674$	14.0000	0.539260
$675$	1.00000	0.0384900
$676$	1.00000	0.0384615
$677$	18.0000	0.691796	0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000	0.691796	0.345898	+	0.938272i	$0.387574\pi$
$678$	−6.00000	−0.230429
$679$	0	0
$680$	−2.00000	−0.0766965
$681$	−20.0000	−0.766402
$682$	−32.0000	−1.22534
$683$	−52.0000	−1.98972	−0.994862	−	0.101237i	$-0.967720\pi$
$683$	−52.0000	−1.98972	−0.994862	+	0.101237i	$0.967720\pi$
$684$	−1.00000	−0.0382360
$685$	6.00000	0.229248
$686$	0	0
$687$	−6.00000	−0.228914
$688$	−8.00000	−0.304997
$689$	6.00000	0.228582
$690$	8.00000	0.304555
$691$	12.0000	0.456502	0.228251	−	0.973602i	$-0.426699\pi$
$691$	12.0000	0.456502	0.228251	+	0.973602i	$0.426699\pi$
$692$	−6.00000	−0.228086
$693$	0	0
$694$	4.00000	0.151838
$695$	4.00000	0.151729
$696$	2.00000	0.0758098
$697$	4.00000	0.151511
$698$	26.0000	0.984115
$699$	−6.00000	−0.226941
$700$	0	0
$701$	34.0000	1.28416	0.642081	−	0.766637i	$-0.278071\pi$
$701$	34.0000	1.28416	0.642081	+	0.766637i	$0.278071\pi$
$702$	−1.00000	−0.0377426
$703$	6.00000	0.226294
$704$	−4.00000	−0.150756
$705$	−4.00000	−0.150649
$706$	18.0000	0.677439
$707$	0	0
$708$	0	0
$709$	10.0000	0.375558	0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000	0.375558	0.187779	+	0.982211i	$0.439871\pi$
$710$	0	0
$711$	−4.00000	−0.150012
$712$	18.0000	0.674579
$713$	−64.0000	−2.39682
$714$	0	0
$715$	−4.00000	−0.149592
$716$	12.0000	0.448461
$717$	16.0000	0.597531
$718$	0	0
$719$	16.0000	0.596699	0.298350	−	0.954457i	$-0.403564\pi$
$719$	16.0000	0.596699	0.298350	+	0.954457i	$0.403564\pi$
$720$	−1.00000	−0.0372678
$721$	0	0
$722$	1.00000	0.0372161
$723$	−14.0000	−0.520666
$724$	2.00000	0.0743294
$725$	2.00000	0.0742781
$726$	5.00000	0.185567
$727$	40.0000	1.48352	0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000	1.48352	0.741759	+	0.670667i	$0.233992\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	10.0000	0.370117
$731$	−16.0000	−0.591781
$732$	6.00000	0.221766
$733$	18.0000	0.664845	0.332423	−	0.943131i	$-0.392134\pi$
$733$	18.0000	0.664845	0.332423	+	0.943131i	$0.392134\pi$
$734$	24.0000	0.885856
$735$	7.00000	0.258199
$736$	−8.00000	−0.294884
$737$	64.0000	2.35747
$738$	2.00000	0.0736210
$739$	12.0000	0.441427	0.220714	−	0.975339i	$-0.429161\pi$
$739$	12.0000	0.441427	0.220714	+	0.975339i	$0.429161\pi$
$740$	6.00000	0.220564
$741$	1.00000	0.0367359
$742$	0	0
$743$	−16.0000	−0.586983	−0.293492	−	0.955962i	$-0.594817\pi$
$743$	−16.0000	−0.586983	−0.293492	+	0.955962i	$0.594817\pi$
$744$	8.00000	0.293294
$745$	22.0000	0.806018
$746$	−22.0000	−0.805477
$747$	4.00000	0.146352
$748$	−8.00000	−0.292509
$749$	0	0
$750$	−1.00000	−0.0365148
$751$	−4.00000	−0.145962	−0.0729810	−	0.997333i	$-0.523251\pi$
$751$	−4.00000	−0.145962	−0.0729810	+	0.997333i	$0.523251\pi$
$752$	4.00000	0.145865
$753$	8.00000	0.291536
$754$	−2.00000	−0.0728357
$755$	8.00000	0.291150
$756$	0	0
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	−28.0000	−1.01701
$759$	32.0000	1.16153
$760$	1.00000	0.0362738
$761$	−34.0000	−1.23250	−0.616250	−	0.787551i	$-0.711349\pi$
$761$	−34.0000	−1.23250	−0.616250	+	0.787551i	$0.711349\pi$
$762$	−8.00000	−0.289809
$763$	0	0
$764$	0	0
$765$	−2.00000	−0.0723102
$766$	−24.0000	−0.867155
$767$	0	0
$768$	1.00000	0.0360844
$769$	2.00000	0.0721218	0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000	0.0721218	0.0360609	+	0.999350i	$0.488519\pi$
$770$	0	0
$771$	26.0000	0.936367
$772$	2.00000	0.0719816
$773$	6.00000	0.215805	0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000	0.215805	0.107903	+	0.994161i	$0.465587\pi$
$774$	−8.00000	−0.287554
$775$	8.00000	0.287368
$776$	−14.0000	−0.502571
$777$	0	0
$778$	−6.00000	−0.215110
$779$	−2.00000	−0.0716574
$780$	1.00000	0.0358057
$781$	0	0
$782$	−16.0000	−0.572159
$783$	2.00000	0.0714742
$784$	−7.00000	−0.250000
$785$	−10.0000	−0.356915
$786$	8.00000	0.285351
$787$	−32.0000	−1.14068	−0.570338	−	0.821410i	$-0.693188\pi$
$787$	−32.0000	−1.14068	−0.570338	+	0.821410i	$0.693188\pi$
$788$	−14.0000	−0.498729
$789$	24.0000	0.854423
$790$	4.00000	0.142314
$791$	0	0
$792$	−4.00000	−0.142134
$793$	−6.00000	−0.213066
$794$	18.0000	0.638796
$795$	6.00000	0.212798
$796$	−16.0000	−0.567105
$797$	18.0000	0.637593	0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000	0.637593	0.318796	+	0.947823i	$0.396721\pi$
$798$	0	0
$799$	8.00000	0.283020
$800$	1.00000	0.0353553
$801$	18.0000	0.635999
$802$	−30.0000	−1.05934
$803$	40.0000	1.41157
$804$	−16.0000	−0.564276
$805$	0	0
$806$	−8.00000	−0.281788
$807$	−14.0000	−0.492823
$808$	−14.0000	−0.492518
$809$	−6.00000	−0.210949	−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000	−0.210949	−0.105474	+	0.994422i	$0.533636\pi$
$810$	−1.00000	−0.0351364
$811$	−28.0000	−0.983213	−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000	−0.983213	−0.491606	+	0.870817i	$0.663590\pi$
$812$	0	0
$813$	12.0000	0.420858
$814$	24.0000	0.841200
$815$	4.00000	0.140114
$816$	2.00000	0.0700140
$817$	8.00000	0.279885
$818$	26.0000	0.909069
$819$	0	0
$820$	−2.00000	−0.0698430
$821$	42.0000	1.46581	0.732905	−	0.680331i	$-0.238164\pi$
$821$	42.0000	1.46581	0.732905	+	0.680331i	$0.238164\pi$
$822$	−6.00000	−0.209274
$823$	24.0000	0.836587	0.418294	−	0.908312i	$-0.362628\pi$
$823$	24.0000	0.836587	0.418294	+	0.908312i	$0.362628\pi$
$824$	−8.00000	−0.278693
$825$	−4.00000	−0.139262
$826$	0	0
$827$	28.0000	0.973655	0.486828	−	0.873498i	$-0.338154\pi$
$827$	28.0000	0.973655	0.486828	+	0.873498i	$0.338154\pi$
$828$	−8.00000	−0.278019
$829$	34.0000	1.18087	0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000	1.18087	0.590434	+	0.807086i	$0.298956\pi$
$830$	−4.00000	−0.138842
$831$	−14.0000	−0.485655
$832$	−1.00000	−0.0346688
$833$	−14.0000	−0.485071
$834$	−4.00000	−0.138509
$835$	−24.0000	−0.830554
$836$	4.00000	0.138343
$837$	8.00000	0.276520
$838$	40.0000	1.38178
$839$	8.00000	0.276191	0.138095	−	0.990419i	$-0.455902\pi$
$839$	8.00000	0.276191	0.138095	+	0.990419i	$0.455902\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	−2.00000	−0.0689246
$843$	−14.0000	−0.482186
$844$	20.0000	0.688428
$845$	−1.00000	−0.0344010
$846$	4.00000	0.137523
$847$	0	0
$848$	−6.00000	−0.206041
$849$	24.0000	0.823678
$850$	2.00000	0.0685994
$851$	48.0000	1.64542
$852$	0	0
$853$	10.0000	0.342393	0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000	0.342393	0.171197	+	0.985237i	$0.445237\pi$
$854$	0	0
$855$	1.00000	0.0341993
$856$	4.00000	0.136717
$857$	−14.0000	−0.478231	−0.239115	−	0.970991i	$-0.576857\pi$
$857$	−14.0000	−0.478231	−0.239115	+	0.970991i	$0.576857\pi$
$858$	4.00000	0.136558
$859$	44.0000	1.50126	0.750630	−	0.660722i	$-0.229750\pi$
$859$	44.0000	1.50126	0.750630	+	0.660722i	$0.229750\pi$
$860$	8.00000	0.272798
$861$	0	0
$862$	0	0
$863$	−24.0000	−0.816970	−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000	−0.816970	−0.408485	+	0.912765i	$0.633943\pi$
$864$	1.00000	0.0340207
$865$	6.00000	0.204006
$866$	−18.0000	−0.611665
$867$	−13.0000	−0.441503
$868$	0	0
$869$	16.0000	0.542763
$870$	−2.00000	−0.0678064
$871$	16.0000	0.542139
$872$	−10.0000	−0.338643
$873$	−14.0000	−0.473828
$874$	8.00000	0.270604
$875$	0	0
$876$	−10.0000	−0.337869
$877$	42.0000	1.41824	0.709120	−	0.705088i	$-0.249093\pi$
$877$	42.0000	1.41824	0.709120	+	0.705088i	$0.249093\pi$
$878$	28.0000	0.944954
$879$	−2.00000	−0.0674583
$880$	4.00000	0.134840
$881$	2.00000	0.0673817	0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000	0.0673817	0.0336909	+	0.999432i	$0.489274\pi$
$882$	−7.00000	−0.235702
$883$	−32.0000	−1.07689	−0.538443	−	0.842662i	$-0.680987\pi$
$883$	−32.0000	−1.07689	−0.538443	+	0.842662i	$0.680987\pi$
$884$	−2.00000	−0.0672673
$885$	0	0
$886$	20.0000	0.671913
$887$	20.0000	0.671534	0.335767	−	0.941945i	$-0.391004\pi$
$887$	20.0000	0.671534	0.335767	+	0.941945i	$0.391004\pi$
$888$	−6.00000	−0.201347
$889$	0	0
$890$	−18.0000	−0.603361
$891$	−4.00000	−0.134005
$892$	16.0000	0.535720
$893$	−4.00000	−0.133855
$894$	−22.0000	−0.735790
$895$	−12.0000	−0.401116
$896$	0	0
$897$	8.00000	0.267112
$898$	10.0000	0.333704
$899$	16.0000	0.533630
$900$	1.00000	0.0333333
$901$	−12.0000	−0.399778
$902$	−8.00000	−0.266371
$903$	0	0
$904$	−6.00000	−0.199557
$905$	−2.00000	−0.0664822
$906$	−8.00000	−0.265782
$907$	36.0000	1.19536	0.597680	−	0.801735i	$-0.296089\pi$
$907$	36.0000	1.19536	0.597680	+	0.801735i	$0.296089\pi$
$908$	−20.0000	−0.663723
$909$	−14.0000	−0.464351
$910$	0	0
$911$	−8.00000	−0.265052	−0.132526	−	0.991180i	$-0.542309\pi$
$911$	−8.00000	−0.265052	−0.132526	+	0.991180i	$0.542309\pi$
$912$	−1.00000	−0.0331133
$913$	−16.0000	−0.529523
$914$	−10.0000	−0.330771
$915$	−6.00000	−0.198354
$916$	−6.00000	−0.198246
$917$	0	0
$918$	2.00000	0.0660098
$919$	56.0000	1.84727	0.923635	−	0.383274i	$-0.125203\pi$
$919$	56.0000	1.84727	0.923635	+	0.383274i	$0.125203\pi$
$920$	8.00000	0.263752
$921$	−16.0000	−0.527218
$922$	−14.0000	−0.461065
$923$	0	0
$924$	0	0
$925$	−6.00000	−0.197279
$926$	−16.0000	−0.525793
$927$	−8.00000	−0.262754
$928$	2.00000	0.0656532
$929$	−18.0000	−0.590561	−0.295280	−	0.955411i	$-0.595413\pi$
$929$	−18.0000	−0.590561	−0.295280	+	0.955411i	$0.595413\pi$
$930$	−8.00000	−0.262330
$931$	7.00000	0.229416
$932$	−6.00000	−0.196537
$933$	0	0
$934$	28.0000	0.916188
$935$	8.00000	0.261628
$936$	−1.00000	−0.0326860
$937$	18.0000	0.588034	0.294017	−	0.955800i	$-0.405008\pi$
$937$	18.0000	0.588034	0.294017	+	0.955800i	$0.405008\pi$
$938$	0	0
$939$	−6.00000	−0.195803
$940$	−4.00000	−0.130466
$941$	−30.0000	−0.977972	−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000	−0.977972	−0.488986	+	0.872292i	$0.662633\pi$
$942$	10.0000	0.325818
$943$	−16.0000	−0.521032
$944$	0	0
$945$	0	0
$946$	32.0000	1.04041
$947$	−4.00000	−0.129983	−0.0649913	−	0.997886i	$-0.520702\pi$
$947$	−4.00000	−0.129983	−0.0649913	+	0.997886i	$0.520702\pi$
$948$	−4.00000	−0.129914
$949$	10.0000	0.324614
$950$	−1.00000	−0.0324443
$951$	6.00000	0.194563
$952$	0	0
$953$	42.0000	1.36051	0.680257	−	0.732974i	$-0.261868\pi$
$953$	42.0000	1.36051	0.680257	+	0.732974i	$0.261868\pi$
$954$	−6.00000	−0.194257
$955$	0	0
$956$	16.0000	0.517477
$957$	−8.00000	−0.258603
$958$	−16.0000	−0.516937
$959$	0	0
$960$	−1.00000	−0.0322749
$961$	33.0000	1.06452
$962$	6.00000	0.193448
$963$	4.00000	0.128898
$964$	−14.0000	−0.450910
$965$	−2.00000	−0.0643823
$966$	0	0
$967$	−24.0000	−0.771788	−0.385894	−	0.922543i	$-0.626107\pi$
$967$	−24.0000	−0.771788	−0.385894	+	0.922543i	$0.626107\pi$
$968$	5.00000	0.160706
$969$	−2.00000	−0.0642493
$970$	14.0000	0.449513
$971$	12.0000	0.385098	0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000	0.385098	0.192549	+	0.981287i	$0.438325\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	16.0000	0.512673
$975$	−1.00000	−0.0320256
$976$	6.00000	0.192055
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	−4.00000	−0.127906
$979$	−72.0000	−2.30113
$980$	7.00000	0.223607
$981$	−10.0000	−0.319275
$982$	8.00000	0.255290
$983$	16.0000	0.510321	0.255160	−	0.966899i	$-0.417872\pi$
$983$	16.0000	0.510321	0.255160	+	0.966899i	$0.417872\pi$
$984$	2.00000	0.0637577
$985$	14.0000	0.446077
$986$	4.00000	0.127386
$987$	0	0
$988$	1.00000	0.0318142
$989$	64.0000	2.03508
$990$	4.00000	0.127128
$991$	52.0000	1.65183	0.825917	−	0.563791i	$-0.190658\pi$
$991$	52.0000	1.65183	0.825917	+	0.563791i	$0.190658\pi$
$992$	8.00000	0.254000
$993$	−20.0000	−0.634681
$994$	0	0
$995$	16.0000	0.507234
$996$	4.00000	0.126745
$997$	18.0000	0.570066	0.285033	−	0.958518i	$-0.407995\pi$
$997$	18.0000	0.570066	0.285033	+	0.958518i	$0.407995\pi$
$998$	20.0000	0.633089
$999$	−6.00000	−0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7410.2.a.u.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7410.2.a.u.1.1	✓	1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 7410 = 2 \cdot 3 \cdot 5 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7410.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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