LMFDB - Embedded newform 3630.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3630,2,Mod(1,3630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3630, 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("3630.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3630.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:	$28.9856959337$
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	$\chi$	$=$	3630.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -3.00000 q^{17} -1.00000 q^{18} -1.00000 q^{19} -1.00000 q^{20} -1.00000 q^{21} +6.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} +3.00000 q^{29} +1.00000 q^{30} -4.00000 q^{31} -1.00000 q^{32} +3.00000 q^{34} +1.00000 q^{35} +1.00000 q^{36} -1.00000 q^{37} +1.00000 q^{38} -1.00000 q^{39} +1.00000 q^{40} +1.00000 q^{42} -4.00000 q^{43} -1.00000 q^{45} -6.00000 q^{46} +6.00000 q^{47} +1.00000 q^{48} -6.00000 q^{49} -1.00000 q^{50} -3.00000 q^{51} -1.00000 q^{52} +6.00000 q^{53} -1.00000 q^{54} +1.00000 q^{56} -1.00000 q^{57} -3.00000 q^{58} -6.00000 q^{59} -1.00000 q^{60} -10.0000 q^{61} +4.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} +1.00000 q^{65} +2.00000 q^{67} -3.00000 q^{68} +6.00000 q^{69} -1.00000 q^{70} -15.0000 q^{71} -1.00000 q^{72} -4.00000 q^{73} +1.00000 q^{74} +1.00000 q^{75} -1.00000 q^{76} +1.00000 q^{78} -10.0000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +3.00000 q^{83} -1.00000 q^{84} +3.00000 q^{85} +4.00000 q^{86} +3.00000 q^{87} +12.0000 q^{89} +1.00000 q^{90} +1.00000 q^{91} +6.00000 q^{92} -4.00000 q^{93} -6.00000 q^{94} +1.00000 q^{95} -1.00000 q^{96} +8.00000 q^{97} +6.00000 q^{98} +O(q^{100})\)

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
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	1.00000	0.267261
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000	−0.229416	−0.114708	+	0.993399i	$0.536593\pi$
$20$	−1.00000	−0.223607
$21$	−1.00000	−0.218218
$22$	0	0
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	1.00000	0.182574
$31$	−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
$33$	0	0
$34$	3.00000	0.514496
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	−1.00000	−0.164399	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000	−0.164399	−0.0821995	+	0.996616i	$0.526194\pi$
$38$	1.00000	0.162221
$39$	−1.00000	−0.160128
$40$	1.00000	0.158114
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	1.00000	0.154303
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	−6.00000	−0.884652
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	1.00000	0.144338
$49$	−6.00000	−0.857143
$50$	−1.00000	−0.141421
$51$	−3.00000	−0.420084
$52$	−1.00000	−0.138675
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	1.00000	0.133631
$57$	−1.00000	−0.132453
$58$	−3.00000	−0.393919
$59$	−6.00000	−0.781133	−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000	−0.781133	−0.390567	+	0.920575i	$0.627721\pi$
$60$	−1.00000	−0.129099
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	4.00000	0.508001
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	0	0
$67$	2.00000	0.244339	0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000	0.244339	0.122169	+	0.992509i	$0.461015\pi$
$68$	−3.00000	−0.363803
$69$	6.00000	0.722315
$70$	−1.00000	−0.119523
$71$	−15.0000	−1.78017	−0.890086	−	0.455792i	$-0.849356\pi$
$71$	−15.0000	−1.78017	−0.890086	+	0.455792i	$0.849356\pi$
$72$	−1.00000	−0.117851
$73$	−4.00000	−0.468165	−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000	−0.468165	−0.234082	+	0.972217i	$0.575209\pi$
$74$	1.00000	0.116248
$75$	1.00000	0.115470
$76$	−1.00000	−0.114708
$77$	0	0
$78$	1.00000	0.113228
$79$	−10.0000	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	0	0
$83$	3.00000	0.329293	0.164646	−	0.986353i	$-0.447352\pi$
$83$	3.00000	0.329293	0.164646	+	0.986353i	$0.447352\pi$
$84$	−1.00000	−0.109109
$85$	3.00000	0.325396
$86$	4.00000	0.431331
$87$	3.00000	0.321634
$88$	0	0
$89$	12.0000	1.27200	0.635999	−	0.771690i	$-0.280588\pi$
$89$	12.0000	1.27200	0.635999	+	0.771690i	$0.280588\pi$
$90$	1.00000	0.105409
$91$	1.00000	0.104828
$92$	6.00000	0.625543
$93$	−4.00000	−0.414781
$94$	−6.00000	−0.618853
$95$	1.00000	0.102598
$96$	−1.00000	−0.102062
$97$	8.00000	0.812277	0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000	0.812277	0.406138	+	0.913812i	$0.366875\pi$
$98$	6.00000	0.606092
$99$	0	0
$100$	1.00000	0.100000
$101$	−3.00000	−0.298511	−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000	−0.298511	−0.149256	+	0.988799i	$0.547688\pi$
$102$	3.00000	0.297044
$103$	−1.00000	−0.0985329	−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000	−0.0985329	−0.0492665	+	0.998786i	$0.515688\pi$
$104$	1.00000	0.0980581
$105$	1.00000	0.0975900
$106$	−6.00000	−0.582772
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	1.00000	0.0962250
$109$	−16.0000	−1.53252	−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000	−1.53252	−0.766261	+	0.642529i	$0.777885\pi$
$110$	0	0
$111$	−1.00000	−0.0949158
$112$	−1.00000	−0.0944911
$113$	−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
$115$	−6.00000	−0.559503
$116$	3.00000	0.278543
$117$	−1.00000	−0.0924500
$118$	6.00000	0.552345
$119$	3.00000	0.275010
$120$	1.00000	0.0912871
$121$	0	0
$122$	10.0000	0.905357
$123$	0	0
$124$	−4.00000	−0.359211
$125$	−1.00000	−0.0894427
$126$	1.00000	0.0890871
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	−1.00000	−0.0883883
$129$	−4.00000	−0.352180
$130$	−1.00000	−0.0877058
$131$	−6.00000	−0.524222	−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000	−0.524222	−0.262111	+	0.965038i	$0.584419\pi$
$132$	0	0
$133$	1.00000	0.0867110
$134$	−2.00000	−0.172774
$135$	−1.00000	−0.0860663
$136$	3.00000	0.257248
$137$	−21.0000	−1.79415	−0.897076	−	0.441877i	$-0.854313\pi$
$137$	−21.0000	−1.79415	−0.897076	+	0.441877i	$0.854313\pi$
$138$	−6.00000	−0.510754
$139$	5.00000	0.424094	0.212047	−	0.977259i	$-0.431987\pi$
$139$	5.00000	0.424094	0.212047	+	0.977259i	$0.431987\pi$
$140$	1.00000	0.0845154
$141$	6.00000	0.505291
$142$	15.0000	1.25877
$143$	0	0
$144$	1.00000	0.0833333
$145$	−3.00000	−0.249136
$146$	4.00000	0.331042
$147$	−6.00000	−0.494872
$148$	−1.00000	−0.0821995
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	−1.00000	−0.0816497
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	1.00000	0.0811107
$153$	−3.00000	−0.242536
$154$	0	0
$155$	4.00000	0.321288
$156$	−1.00000	−0.0800641
$157$	−7.00000	−0.558661	−0.279330	−	0.960195i	$-0.590112\pi$
$157$	−7.00000	−0.558661	−0.279330	+	0.960195i	$0.590112\pi$
$158$	10.0000	0.795557
$159$	6.00000	0.475831
$160$	1.00000	0.0790569
$161$	−6.00000	−0.472866
$162$	−1.00000	−0.0785674
$163$	14.0000	1.09656	0.548282	−	0.836293i	$-0.315282\pi$
$163$	14.0000	1.09656	0.548282	+	0.836293i	$0.315282\pi$
$164$	0	0
$165$	0	0
$166$	−3.00000	−0.232845
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	1.00000	0.0771517
$169$	−12.0000	−0.923077
$170$	−3.00000	−0.230089
$171$	−1.00000	−0.0764719
$172$	−4.00000	−0.304997
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	−3.00000	−0.227429
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−6.00000	−0.450988
$178$	−12.0000	−0.899438
$179$	−18.0000	−1.34538	−0.672692	−	0.739923i	$-0.734862\pi$
$179$	−18.0000	−1.34538	−0.672692	+	0.739923i	$0.734862\pi$
$180$	−1.00000	−0.0745356
$181$	−22.0000	−1.63525	−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000	−1.63525	−0.817624	+	0.575753i	$0.804709\pi$
$182$	−1.00000	−0.0741249
$183$	−10.0000	−0.739221
$184$	−6.00000	−0.442326
$185$	1.00000	0.0735215
$186$	4.00000	0.293294
$187$	0	0
$188$	6.00000	0.437595
$189$	−1.00000	−0.0727393
$190$	−1.00000	−0.0725476
$191$	−9.00000	−0.651217	−0.325609	−	0.945505i	$-0.605569\pi$
$191$	−9.00000	−0.651217	−0.325609	+	0.945505i	$0.605569\pi$
$192$	1.00000	0.0721688
$193$	−4.00000	−0.287926	−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000	−0.287926	−0.143963	+	0.989583i	$0.545985\pi$
$194$	−8.00000	−0.574367
$195$	1.00000	0.0716115
$196$	−6.00000	−0.428571
$197$	12.0000	0.854965	0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000	0.854965	0.427482	+	0.904024i	$0.359401\pi$
$198$	0	0
$199$	20.0000	1.41776	0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000	1.41776	0.708881	+	0.705328i	$0.249200\pi$
$200$	−1.00000	−0.0707107
$201$	2.00000	0.141069
$202$	3.00000	0.211079
$203$	−3.00000	−0.210559
$204$	−3.00000	−0.210042
$205$	0	0
$206$	1.00000	0.0696733
$207$	6.00000	0.417029
$208$	−1.00000	−0.0693375
$209$	0	0
$210$	−1.00000	−0.0690066
$211$	−13.0000	−0.894957	−0.447478	−	0.894295i	$-0.647678\pi$
$211$	−13.0000	−0.894957	−0.447478	+	0.894295i	$0.647678\pi$
$212$	6.00000	0.412082
$213$	−15.0000	−1.02778
$214$	12.0000	0.820303
$215$	4.00000	0.272798
$216$	−1.00000	−0.0680414
$217$	4.00000	0.271538
$218$	16.0000	1.08366
$219$	−4.00000	−0.270295
$220$	0	0
$221$	3.00000	0.201802
$222$	1.00000	0.0671156
$223$	−19.0000	−1.27233	−0.636167	−	0.771551i	$-0.719481\pi$
$223$	−19.0000	−1.27233	−0.636167	+	0.771551i	$0.719481\pi$
$224$	1.00000	0.0668153
$225$	1.00000	0.0666667
$226$	6.00000	0.399114
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	−1.00000	−0.0662266
$229$	8.00000	0.528655	0.264327	−	0.964433i	$-0.414850\pi$
$229$	8.00000	0.528655	0.264327	+	0.964433i	$0.414850\pi$
$230$	6.00000	0.395628
$231$	0	0
$232$	−3.00000	−0.196960
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	1.00000	0.0653720
$235$	−6.00000	−0.391397
$236$	−6.00000	−0.390567
$237$	−10.0000	−0.649570
$238$	−3.00000	−0.194461
$239$	−21.0000	−1.35838	−0.679189	−	0.733964i	$-0.737668\pi$
$239$	−21.0000	−1.35838	−0.679189	+	0.733964i	$0.737668\pi$
$240$	−1.00000	−0.0645497
$241$	−19.0000	−1.22390	−0.611949	−	0.790897i	$-0.709614\pi$
$241$	−19.0000	−1.22390	−0.611949	+	0.790897i	$0.709614\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	−10.0000	−0.640184
$245$	6.00000	0.383326
$246$	0	0
$247$	1.00000	0.0636285
$248$	4.00000	0.254000
$249$	3.00000	0.190117
$250$	1.00000	0.0632456
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	−1.00000	−0.0629941
$253$	0	0
$254$	16.0000	1.00393
$255$	3.00000	0.187867
$256$	1.00000	0.0625000
$257$	−3.00000	−0.187135	−0.0935674	−	0.995613i	$-0.529827\pi$
$257$	−3.00000	−0.187135	−0.0935674	+	0.995613i	$0.529827\pi$
$258$	4.00000	0.249029
$259$	1.00000	0.0621370
$260$	1.00000	0.0620174
$261$	3.00000	0.185695
$262$	6.00000	0.370681
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	0	0
$265$	−6.00000	−0.368577
$266$	−1.00000	−0.0613139
$267$	12.0000	0.734388
$268$	2.00000	0.122169
$269$	9.00000	0.548740	0.274370	−	0.961624i	$-0.411531\pi$
$269$	9.00000	0.548740	0.274370	+	0.961624i	$0.411531\pi$
$270$	1.00000	0.0608581
$271$	2.00000	0.121491	0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000	0.121491	0.0607457	+	0.998153i	$0.480652\pi$
$272$	−3.00000	−0.181902
$273$	1.00000	0.0605228
$274$	21.0000	1.26866
$275$	0	0
$276$	6.00000	0.361158
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	−5.00000	−0.299880
$279$	−4.00000	−0.239474
$280$	−1.00000	−0.0597614
$281$	30.0000	1.78965	0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000	1.78965	0.894825	+	0.446417i	$0.147300\pi$
$282$	−6.00000	−0.357295
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	−15.0000	−0.890086
$285$	1.00000	0.0592349
$286$	0	0
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−8.00000	−0.470588
$290$	3.00000	0.176166
$291$	8.00000	0.468968
$292$	−4.00000	−0.234082
$293$	−24.0000	−1.40209	−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000	−1.40209	−0.701047	+	0.713115i	$0.747284\pi$
$294$	6.00000	0.349927
$295$	6.00000	0.349334
$296$	1.00000	0.0581238
$297$	0	0
$298$	−18.0000	−1.04271
$299$	−6.00000	−0.346989
$300$	1.00000	0.0577350
$301$	4.00000	0.230556
$302$	−2.00000	−0.115087
$303$	−3.00000	−0.172345
$304$	−1.00000	−0.0573539
$305$	10.0000	0.572598
$306$	3.00000	0.171499
$307$	32.0000	1.82634	0.913168	−	0.407583i	$-0.133628\pi$
$307$	32.0000	1.82634	0.913168	+	0.407583i	$0.133628\pi$
$308$	0	0
$309$	−1.00000	−0.0568880
$310$	−4.00000	−0.227185
$311$	−24.0000	−1.36092	−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000	−1.36092	−0.680458	+	0.732787i	$0.738219\pi$
$312$	1.00000	0.0566139
$313$	8.00000	0.452187	0.226093	−	0.974106i	$-0.427405\pi$
$313$	8.00000	0.452187	0.226093	+	0.974106i	$0.427405\pi$
$314$	7.00000	0.395033
$315$	1.00000	0.0563436
$316$	−10.0000	−0.562544
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	−6.00000	−0.336463
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−12.0000	−0.669775
$322$	6.00000	0.334367
$323$	3.00000	0.166924
$324$	1.00000	0.0555556
$325$	−1.00000	−0.0554700
$326$	−14.0000	−0.775388
$327$	−16.0000	−0.884802
$328$	0	0
$329$	−6.00000	−0.330791
$330$	0	0
$331$	−19.0000	−1.04433	−0.522167	−	0.852843i	$-0.674876\pi$
$331$	−19.0000	−1.04433	−0.522167	+	0.852843i	$0.674876\pi$
$332$	3.00000	0.164646
$333$	−1.00000	−0.0547997
$334$	−12.0000	−0.656611
$335$	−2.00000	−0.109272
$336$	−1.00000	−0.0545545
$337$	32.0000	1.74315	0.871576	−	0.490261i	$-0.163099\pi$
$337$	32.0000	1.74315	0.871576	+	0.490261i	$0.163099\pi$
$338$	12.0000	0.652714
$339$	−6.00000	−0.325875
$340$	3.00000	0.162698
$341$	0	0
$342$	1.00000	0.0540738
$343$	13.0000	0.701934
$344$	4.00000	0.215666
$345$	−6.00000	−0.323029
$346$	6.00000	0.322562
$347$	−3.00000	−0.161048	−0.0805242	−	0.996753i	$-0.525659\pi$
$347$	−3.00000	−0.161048	−0.0805242	+	0.996753i	$0.525659\pi$
$348$	3.00000	0.160817
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	1.00000	0.0534522
$351$	−1.00000	−0.0533761
$352$	0	0
$353$	6.00000	0.319348	0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000	0.319348	0.159674	+	0.987170i	$0.448956\pi$
$354$	6.00000	0.318896
$355$	15.0000	0.796117
$356$	12.0000	0.635999
$357$	3.00000	0.158777
$358$	18.0000	0.951330
$359$	24.0000	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$360$	1.00000	0.0527046
$361$	−18.0000	−0.947368
$362$	22.0000	1.15629
$363$	0	0
$364$	1.00000	0.0524142
$365$	4.00000	0.209370
$366$	10.0000	0.522708
$367$	−13.0000	−0.678594	−0.339297	−	0.940679i	$-0.610189\pi$
$367$	−13.0000	−0.678594	−0.339297	+	0.940679i	$0.610189\pi$
$368$	6.00000	0.312772
$369$	0	0
$370$	−1.00000	−0.0519875
$371$	−6.00000	−0.311504
$372$	−4.00000	−0.207390
$373$	−31.0000	−1.60512	−0.802560	−	0.596572i	$-0.796529\pi$
$373$	−31.0000	−1.60512	−0.802560	+	0.596572i	$0.796529\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	−6.00000	−0.309426
$377$	−3.00000	−0.154508
$378$	1.00000	0.0514344
$379$	11.0000	0.565032	0.282516	−	0.959263i	$-0.408831\pi$
$379$	11.0000	0.565032	0.282516	+	0.959263i	$0.408831\pi$
$380$	1.00000	0.0512989
$381$	−16.0000	−0.819705
$382$	9.00000	0.460480
$383$	−18.0000	−0.919757	−0.459879	−	0.887982i	$-0.652107\pi$
$383$	−18.0000	−0.919757	−0.459879	+	0.887982i	$0.652107\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	4.00000	0.203595
$387$	−4.00000	−0.203331
$388$	8.00000	0.406138
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	−1.00000	−0.0506370
$391$	−18.0000	−0.910299
$392$	6.00000	0.303046
$393$	−6.00000	−0.302660
$394$	−12.0000	−0.604551
$395$	10.0000	0.503155
$396$	0	0
$397$	−25.0000	−1.25471	−0.627357	−	0.778732i	$-0.715863\pi$
$397$	−25.0000	−1.25471	−0.627357	+	0.778732i	$0.715863\pi$
$398$	−20.0000	−1.00251
$399$	1.00000	0.0500626
$400$	1.00000	0.0500000
$401$	−24.0000	−1.19850	−0.599251	−	0.800561i	$-0.704535\pi$
$401$	−24.0000	−1.19850	−0.599251	+	0.800561i	$0.704535\pi$
$402$	−2.00000	−0.0997509
$403$	4.00000	0.199254
$404$	−3.00000	−0.149256
$405$	−1.00000	−0.0496904
$406$	3.00000	0.148888
$407$	0	0
$408$	3.00000	0.148522
$409$	−22.0000	−1.08783	−0.543915	−	0.839140i	$-0.683059\pi$
$409$	−22.0000	−1.08783	−0.543915	+	0.839140i	$0.683059\pi$
$410$	0	0
$411$	−21.0000	−1.03585
$412$	−1.00000	−0.0492665
$413$	6.00000	0.295241
$414$	−6.00000	−0.294884
$415$	−3.00000	−0.147264
$416$	1.00000	0.0490290
$417$	5.00000	0.244851
$418$	0	0
$419$	−6.00000	−0.293119	−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000	−0.293119	−0.146560	+	0.989202i	$0.546820\pi$
$420$	1.00000	0.0487950
$421$	8.00000	0.389896	0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000	0.389896	0.194948	+	0.980814i	$0.437546\pi$
$422$	13.0000	0.632830
$423$	6.00000	0.291730
$424$	−6.00000	−0.291386
$425$	−3.00000	−0.145521
$426$	15.0000	0.726752
$427$	10.0000	0.483934
$428$	−12.0000	−0.580042
$429$	0	0
$430$	−4.00000	−0.192897
$431$	21.0000	1.01153	0.505767	−	0.862670i	$-0.331209\pi$
$431$	21.0000	1.01153	0.505767	+	0.862670i	$0.331209\pi$
$432$	1.00000	0.0481125
$433$	−28.0000	−1.34559	−0.672797	−	0.739827i	$-0.734907\pi$
$433$	−28.0000	−1.34559	−0.672797	+	0.739827i	$0.734907\pi$
$434$	−4.00000	−0.192006
$435$	−3.00000	−0.143839
$436$	−16.0000	−0.766261
$437$	−6.00000	−0.287019
$438$	4.00000	0.191127
$439$	−10.0000	−0.477274	−0.238637	−	0.971109i	$-0.576701\pi$
$439$	−10.0000	−0.477274	−0.238637	+	0.971109i	$0.576701\pi$
$440$	0	0
$441$	−6.00000	−0.285714
$442$	−3.00000	−0.142695
$443$	−27.0000	−1.28281	−0.641404	−	0.767203i	$-0.721648\pi$
$443$	−27.0000	−1.28281	−0.641404	+	0.767203i	$0.721648\pi$
$444$	−1.00000	−0.0474579
$445$	−12.0000	−0.568855
$446$	19.0000	0.899676
$447$	18.0000	0.851371
$448$	−1.00000	−0.0472456
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	−1.00000	−0.0471405
$451$	0	0
$452$	−6.00000	−0.282216
$453$	2.00000	0.0939682
$454$	−12.0000	−0.563188
$455$	−1.00000	−0.0468807
$456$	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	$0.575146\pi$
$458$	−8.00000	−0.373815
$459$	−3.00000	−0.140028
$460$	−6.00000	−0.279751
$461$	−9.00000	−0.419172	−0.209586	−	0.977790i	$-0.567212\pi$
$461$	−9.00000	−0.419172	−0.209586	+	0.977790i	$0.567212\pi$
$462$	0	0
$463$	−4.00000	−0.185896	−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000	−0.185896	−0.0929479	+	0.995671i	$0.529629\pi$
$464$	3.00000	0.139272
$465$	4.00000	0.185496
$466$	−6.00000	−0.277945
$467$	−9.00000	−0.416470	−0.208235	−	0.978079i	$-0.566772\pi$
$467$	−9.00000	−0.416470	−0.208235	+	0.978079i	$0.566772\pi$
$468$	−1.00000	−0.0462250
$469$	−2.00000	−0.0923514
$470$	6.00000	0.276759
$471$	−7.00000	−0.322543
$472$	6.00000	0.276172
$473$	0	0
$474$	10.0000	0.459315
$475$	−1.00000	−0.0458831
$476$	3.00000	0.137505
$477$	6.00000	0.274721
$478$	21.0000	0.960518
$479$	15.0000	0.685367	0.342684	−	0.939451i	$-0.388664\pi$
$479$	15.0000	0.685367	0.342684	+	0.939451i	$0.388664\pi$
$480$	1.00000	0.0456435
$481$	1.00000	0.0455961
$482$	19.0000	0.865426
$483$	−6.00000	−0.273009
$484$	0	0
$485$	−8.00000	−0.363261
$486$	−1.00000	−0.0453609
$487$	23.0000	1.04223	0.521115	−	0.853487i	$-0.325516\pi$
$487$	23.0000	1.04223	0.521115	+	0.853487i	$0.325516\pi$
$488$	10.0000	0.452679
$489$	14.0000	0.633102
$490$	−6.00000	−0.271052
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	0	0
$493$	−9.00000	−0.405340
$494$	−1.00000	−0.0449921
$495$	0	0
$496$	−4.00000	−0.179605
$497$	15.0000	0.672842
$498$	−3.00000	−0.134433
$499$	−13.0000	−0.581960	−0.290980	−	0.956729i	$-0.593981\pi$
$499$	−13.0000	−0.581960	−0.290980	+	0.956729i	$0.593981\pi$
$500$	−1.00000	−0.0447214
$501$	12.0000	0.536120
$502$	0	0
$503$	−42.0000	−1.87269	−0.936344	−	0.351085i	$-0.885813\pi$
$503$	−42.0000	−1.87269	−0.936344	+	0.351085i	$0.885813\pi$
$504$	1.00000	0.0445435
$505$	3.00000	0.133498
$506$	0	0
$507$	−12.0000	−0.532939
$508$	−16.0000	−0.709885
$509$	−6.00000	−0.265945	−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000	−0.265945	−0.132973	+	0.991120i	$0.542452\pi$
$510$	−3.00000	−0.132842
$511$	4.00000	0.176950
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	3.00000	0.132324
$515$	1.00000	0.0440653
$516$	−4.00000	−0.176090
$517$	0	0
$518$	−1.00000	−0.0439375
$519$	−6.00000	−0.263371
$520$	−1.00000	−0.0438529
$521$	−18.0000	−0.788594	−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000	−0.788594	−0.394297	+	0.918983i	$0.629012\pi$
$522$	−3.00000	−0.131306
$523$	−34.0000	−1.48672	−0.743358	−	0.668894i	$-0.766768\pi$
$523$	−34.0000	−1.48672	−0.743358	+	0.668894i	$0.766768\pi$
$524$	−6.00000	−0.262111
$525$	−1.00000	−0.0436436
$526$	−24.0000	−1.04645
$527$	12.0000	0.522728
$528$	0	0
$529$	13.0000	0.565217
$530$	6.00000	0.260623
$531$	−6.00000	−0.260378
$532$	1.00000	0.0433555
$533$	0	0
$534$	−12.0000	−0.519291
$535$	12.0000	0.518805
$536$	−2.00000	−0.0863868
$537$	−18.0000	−0.776757
$538$	−9.00000	−0.388018
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	20.0000	0.859867	0.429934	−	0.902861i	$-0.358537\pi$
$541$	20.0000	0.859867	0.429934	+	0.902861i	$0.358537\pi$
$542$	−2.00000	−0.0859074
$543$	−22.0000	−0.944110
$544$	3.00000	0.128624
$545$	16.0000	0.685365
$546$	−1.00000	−0.0427960
$547$	26.0000	1.11168	0.555840	−	0.831289i	$-0.312397\pi$
$547$	26.0000	1.11168	0.555840	+	0.831289i	$0.312397\pi$
$548$	−21.0000	−0.897076
$549$	−10.0000	−0.426790
$550$	0	0
$551$	−3.00000	−0.127804
$552$	−6.00000	−0.255377
$553$	10.0000	0.425243
$554$	10.0000	0.424859
$555$	1.00000	0.0424476
$556$	5.00000	0.212047
$557$	30.0000	1.27114	0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000	1.27114	0.635570	+	0.772043i	$0.280765\pi$
$558$	4.00000	0.169334
$559$	4.00000	0.169182
$560$	1.00000	0.0422577
$561$	0	0
$562$	−30.0000	−1.26547
$563$	9.00000	0.379305	0.189652	−	0.981851i	$-0.439264\pi$
$563$	9.00000	0.379305	0.189652	+	0.981851i	$0.439264\pi$
$564$	6.00000	0.252646
$565$	6.00000	0.252422
$566$	4.00000	0.168133
$567$	−1.00000	−0.0419961
$568$	15.0000	0.629386
$569$	−24.0000	−1.00613	−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000	−1.00613	−0.503066	+	0.864248i	$0.667795\pi$
$570$	−1.00000	−0.0418854
$571$	−4.00000	−0.167395	−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000	−0.167395	−0.0836974	+	0.996491i	$0.526673\pi$
$572$	0	0
$573$	−9.00000	−0.375980
$574$	0	0
$575$	6.00000	0.250217
$576$	1.00000	0.0416667
$577$	2.00000	0.0832611	0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000	0.0832611	0.0416305	+	0.999133i	$0.486745\pi$
$578$	8.00000	0.332756
$579$	−4.00000	−0.166234
$580$	−3.00000	−0.124568
$581$	−3.00000	−0.124461
$582$	−8.00000	−0.331611
$583$	0	0
$584$	4.00000	0.165521
$585$	1.00000	0.0413449
$586$	24.0000	0.991431
$587$	33.0000	1.36206	0.681028	−	0.732257i	$-0.261533\pi$
$587$	33.0000	1.36206	0.681028	+	0.732257i	$0.261533\pi$
$588$	−6.00000	−0.247436
$589$	4.00000	0.164817
$590$	−6.00000	−0.247016
$591$	12.0000	0.493614
$592$	−1.00000	−0.0410997
$593$	−6.00000	−0.246390	−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000	−0.246390	−0.123195	+	0.992382i	$0.539314\pi$
$594$	0	0
$595$	−3.00000	−0.122988
$596$	18.0000	0.737309
$597$	20.0000	0.818546
$598$	6.00000	0.245358
$599$	36.0000	1.47092	0.735460	−	0.677568i	$-0.236966\pi$
$599$	36.0000	1.47092	0.735460	+	0.677568i	$0.236966\pi$
$600$	−1.00000	−0.0408248
$601$	−22.0000	−0.897399	−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000	−0.897399	−0.448699	+	0.893683i	$0.648113\pi$
$602$	−4.00000	−0.163028
$603$	2.00000	0.0814463
$604$	2.00000	0.0813788
$605$	0	0
$606$	3.00000	0.121867
$607$	41.0000	1.66414	0.832069	−	0.554672i	$-0.187156\pi$
$607$	41.0000	1.66414	0.832069	+	0.554672i	$0.187156\pi$
$608$	1.00000	0.0405554
$609$	−3.00000	−0.121566
$610$	−10.0000	−0.404888
$611$	−6.00000	−0.242734
$612$	−3.00000	−0.121268
$613$	23.0000	0.928961	0.464481	−	0.885583i	$-0.346241\pi$
$613$	23.0000	0.928961	0.464481	+	0.885583i	$0.346241\pi$
$614$	−32.0000	−1.29141
$615$	0	0
$616$	0	0
$617$	−45.0000	−1.81163	−0.905816	−	0.423672i	$-0.860741\pi$
$617$	−45.0000	−1.81163	−0.905816	+	0.423672i	$0.860741\pi$
$618$	1.00000	0.0402259
$619$	−25.0000	−1.00483	−0.502417	−	0.864625i	$-0.667556\pi$
$619$	−25.0000	−1.00483	−0.502417	+	0.864625i	$0.667556\pi$
$620$	4.00000	0.160644
$621$	6.00000	0.240772
$622$	24.0000	0.962312
$623$	−12.0000	−0.480770
$624$	−1.00000	−0.0400320
$625$	1.00000	0.0400000
$626$	−8.00000	−0.319744
$627$	0	0
$628$	−7.00000	−0.279330
$629$	3.00000	0.119618
$630$	−1.00000	−0.0398410
$631$	38.0000	1.51276	0.756378	−	0.654135i	$-0.226967\pi$
$631$	38.0000	1.51276	0.756378	+	0.654135i	$0.226967\pi$
$632$	10.0000	0.397779
$633$	−13.0000	−0.516704
$634$	−18.0000	−0.714871
$635$	16.0000	0.634941
$636$	6.00000	0.237915
$637$	6.00000	0.237729
$638$	0	0
$639$	−15.0000	−0.593391
$640$	1.00000	0.0395285
$641$	−18.0000	−0.710957	−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000	−0.710957	−0.355479	+	0.934684i	$0.615682\pi$
$642$	12.0000	0.473602
$643$	20.0000	0.788723	0.394362	−	0.918955i	$-0.370966\pi$
$643$	20.0000	0.788723	0.394362	+	0.918955i	$0.370966\pi$
$644$	−6.00000	−0.236433
$645$	4.00000	0.157500
$646$	−3.00000	−0.118033
$647$	24.0000	0.943537	0.471769	−	0.881722i	$-0.343616\pi$
$647$	24.0000	0.943537	0.471769	+	0.881722i	$0.343616\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	1.00000	0.0392232
$651$	4.00000	0.156772
$652$	14.0000	0.548282
$653$	36.0000	1.40879	0.704394	−	0.709809i	$-0.251219\pi$
$653$	36.0000	1.40879	0.704394	+	0.709809i	$0.251219\pi$
$654$	16.0000	0.625650
$655$	6.00000	0.234439
$656$	0	0
$657$	−4.00000	−0.156055
$658$	6.00000	0.233904
$659$	−42.0000	−1.63609	−0.818044	−	0.575156i	$-0.804941\pi$
$659$	−42.0000	−1.63609	−0.818044	+	0.575156i	$0.804941\pi$
$660$	0	0
$661$	8.00000	0.311164	0.155582	−	0.987823i	$-0.450275\pi$
$661$	8.00000	0.311164	0.155582	+	0.987823i	$0.450275\pi$
$662$	19.0000	0.738456
$663$	3.00000	0.116510
$664$	−3.00000	−0.116423
$665$	−1.00000	−0.0387783
$666$	1.00000	0.0387492
$667$	18.0000	0.696963
$668$	12.0000	0.464294
$669$	−19.0000	−0.734582
$670$	2.00000	0.0772667
$671$	0	0
$672$	1.00000	0.0385758
$673$	44.0000	1.69608	0.848038	−	0.529936i	$-0.177784\pi$
$673$	44.0000	1.69608	0.848038	+	0.529936i	$0.177784\pi$
$674$	−32.0000	−1.23259
$675$	1.00000	0.0384900
$676$	−12.0000	−0.461538
$677$	12.0000	0.461197	0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000	0.461197	0.230599	+	0.973049i	$0.425932\pi$
$678$	6.00000	0.230429
$679$	−8.00000	−0.307012
$680$	−3.00000	−0.115045
$681$	12.0000	0.459841
$682$	0	0
$683$	15.0000	0.573959	0.286980	−	0.957937i	$-0.407349\pi$
$683$	15.0000	0.573959	0.286980	+	0.957937i	$0.407349\pi$
$684$	−1.00000	−0.0382360
$685$	21.0000	0.802369
$686$	−13.0000	−0.496342
$687$	8.00000	0.305219
$688$	−4.00000	−0.152499
$689$	−6.00000	−0.228582
$690$	6.00000	0.228416
$691$	−37.0000	−1.40755	−0.703773	−	0.710425i	$-0.748503\pi$
$691$	−37.0000	−1.40755	−0.703773	+	0.710425i	$0.748503\pi$
$692$	−6.00000	−0.228086
$693$	0	0
$694$	3.00000	0.113878
$695$	−5.00000	−0.189661
$696$	−3.00000	−0.113715
$697$	0	0
$698$	−14.0000	−0.529908
$699$	6.00000	0.226941
$700$	−1.00000	−0.0377964
$701$	−9.00000	−0.339925	−0.169963	−	0.985451i	$-0.554365\pi$
$701$	−9.00000	−0.339925	−0.169963	+	0.985451i	$0.554365\pi$
$702$	1.00000	0.0377426
$703$	1.00000	0.0377157
$704$	0	0
$705$	−6.00000	−0.225973
$706$	−6.00000	−0.225813
$707$	3.00000	0.112827
$708$	−6.00000	−0.225494
$709$	32.0000	1.20179	0.600893	−	0.799330i	$-0.294812\pi$
$709$	32.0000	1.20179	0.600893	+	0.799330i	$0.294812\pi$
$710$	−15.0000	−0.562940
$711$	−10.0000	−0.375029
$712$	−12.0000	−0.449719
$713$	−24.0000	−0.898807
$714$	−3.00000	−0.112272
$715$	0	0
$716$	−18.0000	−0.672692
$717$	−21.0000	−0.784259
$718$	−24.0000	−0.895672
$719$	24.0000	0.895049	0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000	0.895049	0.447524	+	0.894272i	$0.352306\pi$
$720$	−1.00000	−0.0372678
$721$	1.00000	0.0372419
$722$	18.0000	0.669891
$723$	−19.0000	−0.706618
$724$	−22.0000	−0.817624
$725$	3.00000	0.111417
$726$	0	0
$727$	17.0000	0.630495	0.315248	−	0.949009i	$-0.397912\pi$
$727$	17.0000	0.630495	0.315248	+	0.949009i	$0.397912\pi$
$728$	−1.00000	−0.0370625
$729$	1.00000	0.0370370
$730$	−4.00000	−0.148047
$731$	12.0000	0.443836
$732$	−10.0000	−0.369611
$733$	14.0000	0.517102	0.258551	−	0.965998i	$-0.416755\pi$
$733$	14.0000	0.517102	0.258551	+	0.965998i	$0.416755\pi$
$734$	13.0000	0.479839
$735$	6.00000	0.221313
$736$	−6.00000	−0.221163
$737$	0	0
$738$	0	0
$739$	5.00000	0.183928	0.0919640	−	0.995762i	$-0.470686\pi$
$739$	5.00000	0.183928	0.0919640	+	0.995762i	$0.470686\pi$
$740$	1.00000	0.0367607
$741$	1.00000	0.0367359
$742$	6.00000	0.220267
$743$	18.0000	0.660356	0.330178	−	0.943919i	$-0.392891\pi$
$743$	18.0000	0.660356	0.330178	+	0.943919i	$0.392891\pi$
$744$	4.00000	0.146647
$745$	−18.0000	−0.659469
$746$	31.0000	1.13499
$747$	3.00000	0.109764
$748$	0	0
$749$	12.0000	0.438470
$750$	1.00000	0.0365148
$751$	20.0000	0.729810	0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000	0.729810	0.364905	+	0.931045i	$0.381101\pi$
$752$	6.00000	0.218797
$753$	0	0
$754$	3.00000	0.109254
$755$	−2.00000	−0.0727875
$756$	−1.00000	−0.0363696
$757$	38.0000	1.38113	0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000	1.38113	0.690567	+	0.723269i	$0.257361\pi$
$758$	−11.0000	−0.399538
$759$	0	0
$760$	−1.00000	−0.0362738
$761$	36.0000	1.30500	0.652499	−	0.757789i	$-0.273720\pi$
$761$	36.0000	1.30500	0.652499	+	0.757789i	$0.273720\pi$
$762$	16.0000	0.579619
$763$	16.0000	0.579239
$764$	−9.00000	−0.325609
$765$	3.00000	0.108465
$766$	18.0000	0.650366
$767$	6.00000	0.216647
$768$	1.00000	0.0360844
$769$	−49.0000	−1.76699	−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−49.0000	−1.76699	−0.883493	+	0.468445i	$0.844814\pi$
$770$	0	0
$771$	−3.00000	−0.108042
$772$	−4.00000	−0.143963
$773$	18.0000	0.647415	0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000	0.647415	0.323708	+	0.946157i	$0.395071\pi$
$774$	4.00000	0.143777
$775$	−4.00000	−0.143684
$776$	−8.00000	−0.287183
$777$	1.00000	0.0358748
$778$	−18.0000	−0.645331
$779$	0	0
$780$	1.00000	0.0358057
$781$	0	0
$782$	18.0000	0.643679
$783$	3.00000	0.107211
$784$	−6.00000	−0.214286
$785$	7.00000	0.249841
$786$	6.00000	0.214013
$787$	−46.0000	−1.63972	−0.819861	−	0.572562i	$-0.805950\pi$
$787$	−46.0000	−1.63972	−0.819861	+	0.572562i	$0.805950\pi$
$788$	12.0000	0.427482
$789$	24.0000	0.854423
$790$	−10.0000	−0.355784
$791$	6.00000	0.213335
$792$	0	0
$793$	10.0000	0.355110
$794$	25.0000	0.887217
$795$	−6.00000	−0.212798
$796$	20.0000	0.708881
$797$	−42.0000	−1.48772	−0.743858	−	0.668338i	$-0.767006\pi$
$797$	−42.0000	−1.48772	−0.743858	+	0.668338i	$0.767006\pi$
$798$	−1.00000	−0.0353996
$799$	−18.0000	−0.636794
$800$	−1.00000	−0.0353553
$801$	12.0000	0.423999
$802$	24.0000	0.847469
$803$	0	0
$804$	2.00000	0.0705346
$805$	6.00000	0.211472
$806$	−4.00000	−0.140894
$807$	9.00000	0.316815
$808$	3.00000	0.105540
$809$	24.0000	0.843795	0.421898	−	0.906644i	$-0.361364\pi$
$809$	24.0000	0.843795	0.421898	+	0.906644i	$0.361364\pi$
$810$	1.00000	0.0351364
$811$	11.0000	0.386262	0.193131	−	0.981173i	$-0.438136\pi$
$811$	11.0000	0.386262	0.193131	+	0.981173i	$0.438136\pi$
$812$	−3.00000	−0.105279
$813$	2.00000	0.0701431
$814$	0	0
$815$	−14.0000	−0.490399
$816$	−3.00000	−0.105021
$817$	4.00000	0.139942
$818$	22.0000	0.769212
$819$	1.00000	0.0349428
$820$	0	0
$821$	6.00000	0.209401	0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000	0.209401	0.104701	+	0.994504i	$0.466612\pi$
$822$	21.0000	0.732459
$823$	−31.0000	−1.08059	−0.540296	−	0.841475i	$-0.681688\pi$
$823$	−31.0000	−1.08059	−0.540296	+	0.841475i	$0.681688\pi$
$824$	1.00000	0.0348367
$825$	0	0
$826$	−6.00000	−0.208767
$827$	21.0000	0.730242	0.365121	−	0.930960i	$-0.381028\pi$
$827$	21.0000	0.730242	0.365121	+	0.930960i	$0.381028\pi$
$828$	6.00000	0.208514
$829$	14.0000	0.486240	0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000	0.486240	0.243120	+	0.969996i	$0.421829\pi$
$830$	3.00000	0.104132
$831$	−10.0000	−0.346896
$832$	−1.00000	−0.0346688
$833$	18.0000	0.623663
$834$	−5.00000	−0.173136
$835$	−12.0000	−0.415277
$836$	0	0
$837$	−4.00000	−0.138260
$838$	6.00000	0.207267
$839$	−27.0000	−0.932144	−0.466072	−	0.884747i	$-0.654331\pi$
$839$	−27.0000	−0.932144	−0.466072	+	0.884747i	$0.654331\pi$
$840$	−1.00000	−0.0345033
$841$	−20.0000	−0.689655
$842$	−8.00000	−0.275698
$843$	30.0000	1.03325
$844$	−13.0000	−0.447478
$845$	12.0000	0.412813
$846$	−6.00000	−0.206284
$847$	0	0
$848$	6.00000	0.206041
$849$	−4.00000	−0.137280
$850$	3.00000	0.102899
$851$	−6.00000	−0.205677
$852$	−15.0000	−0.513892
$853$	23.0000	0.787505	0.393753	−	0.919216i	$-0.371177\pi$
$853$	23.0000	0.787505	0.393753	+	0.919216i	$0.371177\pi$
$854$	−10.0000	−0.342193
$855$	1.00000	0.0341993
$856$	12.0000	0.410152
$857$	21.0000	0.717346	0.358673	−	0.933463i	$-0.383229\pi$
$857$	21.0000	0.717346	0.358673	+	0.933463i	$0.383229\pi$
$858$	0	0
$859$	20.0000	0.682391	0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000	0.682391	0.341196	+	0.939992i	$0.389168\pi$
$860$	4.00000	0.136399
$861$	0	0
$862$	−21.0000	−0.715263
$863$	30.0000	1.02121	0.510606	−	0.859815i	$-0.329421\pi$
$863$	30.0000	1.02121	0.510606	+	0.859815i	$0.329421\pi$
$864$	−1.00000	−0.0340207
$865$	6.00000	0.204006
$866$	28.0000	0.951479
$867$	−8.00000	−0.271694
$868$	4.00000	0.135769
$869$	0	0
$870$	3.00000	0.101710
$871$	−2.00000	−0.0677674
$872$	16.0000	0.541828
$873$	8.00000	0.270759
$874$	6.00000	0.202953
$875$	1.00000	0.0338062
$876$	−4.00000	−0.135147
$877$	53.0000	1.78968	0.894841	−	0.446384i	$-0.147289\pi$
$877$	53.0000	1.78968	0.894841	+	0.446384i	$0.147289\pi$
$878$	10.0000	0.337484
$879$	−24.0000	−0.809500
$880$	0	0
$881$	−12.0000	−0.404290	−0.202145	−	0.979356i	$-0.564791\pi$
$881$	−12.0000	−0.404290	−0.202145	+	0.979356i	$0.564791\pi$
$882$	6.00000	0.202031
$883$	20.0000	0.673054	0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000	0.673054	0.336527	+	0.941674i	$0.390748\pi$
$884$	3.00000	0.100901
$885$	6.00000	0.201688
$886$	27.0000	0.907083
$887$	36.0000	1.20876	0.604381	−	0.796696i	$-0.293421\pi$
$887$	36.0000	1.20876	0.604381	+	0.796696i	$0.293421\pi$
$888$	1.00000	0.0335578
$889$	16.0000	0.536623
$890$	12.0000	0.402241
$891$	0	0
$892$	−19.0000	−0.636167
$893$	−6.00000	−0.200782
$894$	−18.0000	−0.602010
$895$	18.0000	0.601674
$896$	1.00000	0.0334077
$897$	−6.00000	−0.200334
$898$	6.00000	0.200223
$899$	−12.0000	−0.400222
$900$	1.00000	0.0333333
$901$	−18.0000	−0.599667
$902$	0	0
$903$	4.00000	0.133112
$904$	6.00000	0.199557
$905$	22.0000	0.731305
$906$	−2.00000	−0.0664455
$907$	38.0000	1.26177	0.630885	−	0.775877i	$-0.282692\pi$
$907$	38.0000	1.26177	0.630885	+	0.775877i	$0.282692\pi$
$908$	12.0000	0.398234
$909$	−3.00000	−0.0995037
$910$	1.00000	0.0331497
$911$	9.00000	0.298183	0.149092	−	0.988823i	$-0.452365\pi$
$911$	9.00000	0.298183	0.149092	+	0.988823i	$0.452365\pi$
$912$	−1.00000	−0.0331133
$913$	0	0
$914$	10.0000	0.330771
$915$	10.0000	0.330590
$916$	8.00000	0.264327
$917$	6.00000	0.198137
$918$	3.00000	0.0990148
$919$	2.00000	0.0659739	0.0329870	−	0.999456i	$-0.489498\pi$
$919$	2.00000	0.0659739	0.0329870	+	0.999456i	$0.489498\pi$
$920$	6.00000	0.197814
$921$	32.0000	1.05444
$922$	9.00000	0.296399
$923$	15.0000	0.493731
$924$	0	0
$925$	−1.00000	−0.0328798
$926$	4.00000	0.131448
$927$	−1.00000	−0.0328443
$928$	−3.00000	−0.0984798
$929$	−6.00000	−0.196854	−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000	−0.196854	−0.0984268	+	0.995144i	$0.531381\pi$
$930$	−4.00000	−0.131165
$931$	6.00000	0.196642
$932$	6.00000	0.196537
$933$	−24.0000	−0.785725
$934$	9.00000	0.294489
$935$	0	0
$936$	1.00000	0.0326860
$937$	38.0000	1.24141	0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000	1.24141	0.620703	+	0.784046i	$0.286847\pi$
$938$	2.00000	0.0653023
$939$	8.00000	0.261070
$940$	−6.00000	−0.195698
$941$	27.0000	0.880175	0.440087	−	0.897955i	$-0.354947\pi$
$941$	27.0000	0.880175	0.440087	+	0.897955i	$0.354947\pi$
$942$	7.00000	0.228072
$943$	0	0
$944$	−6.00000	−0.195283
$945$	1.00000	0.0325300
$946$	0	0
$947$	−15.0000	−0.487435	−0.243717	−	0.969846i	$-0.578367\pi$
$947$	−15.0000	−0.487435	−0.243717	+	0.969846i	$0.578367\pi$
$948$	−10.0000	−0.324785
$949$	4.00000	0.129845
$950$	1.00000	0.0324443
$951$	18.0000	0.583690
$952$	−3.00000	−0.0972306
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	−6.00000	−0.194257
$955$	9.00000	0.291233
$956$	−21.0000	−0.679189
$957$	0	0
$958$	−15.0000	−0.484628
$959$	21.0000	0.678125
$960$	−1.00000	−0.0322749
$961$	−15.0000	−0.483871
$962$	−1.00000	−0.0322413
$963$	−12.0000	−0.386695
$964$	−19.0000	−0.611949
$965$	4.00000	0.128765
$966$	6.00000	0.193047
$967$	32.0000	1.02905	0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000	1.02905	0.514525	+	0.857475i	$0.327968\pi$
$968$	0	0
$969$	3.00000	0.0963739
$970$	8.00000	0.256865
$971$	−48.0000	−1.54039	−0.770197	−	0.637806i	$-0.779842\pi$
$971$	−48.0000	−1.54039	−0.770197	+	0.637806i	$0.779842\pi$
$972$	1.00000	0.0320750
$973$	−5.00000	−0.160293
$974$	−23.0000	−0.736968
$975$	−1.00000	−0.0320256
$976$	−10.0000	−0.320092
$977$	−54.0000	−1.72761	−0.863807	−	0.503824i	$-0.831926\pi$
$977$	−54.0000	−1.72761	−0.863807	+	0.503824i	$0.831926\pi$
$978$	−14.0000	−0.447671
$979$	0	0
$980$	6.00000	0.191663
$981$	−16.0000	−0.510841
$982$	−12.0000	−0.382935
$983$	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
$985$	−12.0000	−0.382352
$986$	9.00000	0.286618
$987$	−6.00000	−0.190982
$988$	1.00000	0.0318142
$989$	−24.0000	−0.763156
$990$	0	0
$991$	14.0000	0.444725	0.222362	−	0.974964i	$-0.428623\pi$
$991$	14.0000	0.444725	0.222362	+	0.974964i	$0.428623\pi$
$992$	4.00000	0.127000
$993$	−19.0000	−0.602947
$994$	−15.0000	−0.475771
$995$	−20.0000	−0.634043
$996$	3.00000	0.0950586
$997$	−31.0000	−0.981780	−0.490890	−	0.871222i	$-0.663328\pi$
$997$	−31.0000	−0.981780	−0.490890	+	0.871222i	$0.663328\pi$
$998$	13.0000	0.411508
$999$	−1.00000	−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3630.2.a.g.1.1	✓	1
11.10	odd	2		3630.2.a.v.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3630.2.a.g.1.1	✓	1	1.1	even	1	trivial
3630.2.a.v.1.1	yes	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:	\( N \)	\(=\)	\( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3630.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more