LMFDB - Embedded newform 3630.2.a.n.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:	no (minimal twist has level 330)
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)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{12} -2.00000 q^{13} +1.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{18} -8.00000 q^{19} -1.00000 q^{20} +4.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} -1.00000 q^{27} -2.00000 q^{29} +1.00000 q^{30} +8.00000 q^{31} +1.00000 q^{32} +2.00000 q^{34} +1.00000 q^{36} -2.00000 q^{37} -8.00000 q^{38} +2.00000 q^{39} -1.00000 q^{40} -6.00000 q^{41} -8.00000 q^{43} -1.00000 q^{45} +4.00000 q^{46} -4.00000 q^{47} -1.00000 q^{48} -7.00000 q^{49} +1.00000 q^{50} -2.00000 q^{51} -2.00000 q^{52} +2.00000 q^{53} -1.00000 q^{54} +8.00000 q^{57} -2.00000 q^{58} +4.00000 q^{59} +1.00000 q^{60} +6.00000 q^{61} +8.00000 q^{62} +1.00000 q^{64} +2.00000 q^{65} -12.0000 q^{67} +2.00000 q^{68} -4.00000 q^{69} -12.0000 q^{71} +1.00000 q^{72} -2.00000 q^{73} -2.00000 q^{74} -1.00000 q^{75} -8.00000 q^{76} +2.00000 q^{78} -1.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} -4.00000 q^{83} -2.00000 q^{85} -8.00000 q^{86} +2.00000 q^{87} -6.00000 q^{89} -1.00000 q^{90} +4.00000 q^{92} -8.00000 q^{93} -4.00000 q^{94} +8.00000 q^{95} -1.00000 q^{96} -14.0000 q^{97} -7.00000 q^{98} +O(q^{100})\)

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
$7$	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
$11$	0	0
$11$	0	0
$12$	−1.00000	−0.288675
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	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
$19$	−8.00000	−1.83533	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−8.00000	−1.83533	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	0	0
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−2.00000	−0.392232
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	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
$33$	0	0
$34$	2.00000	0.342997
$35$	0	0
$36$	1.00000	0.166667
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	−8.00000	−1.29777
$39$	2.00000	0.320256
$40$	−1.00000	−0.158114
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	4.00000	0.589768
$47$	−4.00000	−0.583460	−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000	−0.583460	−0.291730	+	0.956501i	$0.594231\pi$
$48$	−1.00000	−0.144338
$49$	−7.00000	−1.00000
$50$	1.00000	0.141421
$51$	−2.00000	−0.280056
$52$	−2.00000	−0.277350
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	0	0
$57$	8.00000	1.05963
$58$	−2.00000	−0.262613
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	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
$65$	2.00000	0.248069
$66$	0	0
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	2.00000	0.242536
$69$	−4.00000	−0.481543
$70$	0	0
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	1.00000	0.117851
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	−2.00000	−0.232495
$75$	−1.00000	−0.115470
$76$	−8.00000	−0.917663
$77$	0	0
$78$	2.00000	0.226455
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−6.00000	−0.662589
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	0	0
$85$	−2.00000	−0.216930
$86$	−8.00000	−0.862662
$87$	2.00000	0.214423
$88$	0	0
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	−1.00000	−0.105409
$91$	0	0
$92$	4.00000	0.417029
$93$	−8.00000	−0.829561
$94$	−4.00000	−0.412568
$95$	8.00000	0.820783
$96$	−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
$99$	0	0
$100$	1.00000	0.100000
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	−2.00000	−0.198030
$103$	16.0000	1.57653	0.788263	−	0.615338i	$-0.210980\pi$
$103$	16.0000	1.57653	0.788263	+	0.615338i	$0.210980\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	2.00000	0.194257
$107$	−20.0000	−1.93347	−0.966736	−	0.255774i	$-0.917670\pi$
$107$	−20.0000	−1.93347	−0.966736	+	0.255774i	$0.917670\pi$
$108$	−1.00000	−0.0962250
$109$	6.00000	0.574696	0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000	0.574696	0.287348	+	0.957826i	$0.407226\pi$
$110$	0	0
$111$	2.00000	0.189832
$112$	0	0
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	8.00000	0.749269
$115$	−4.00000	−0.373002
$116$	−2.00000	−0.185695
$117$	−2.00000	−0.184900
$118$	4.00000	0.368230
$119$	0	0
$120$	1.00000	0.0912871
$121$	0	0
$122$	6.00000	0.543214
$123$	6.00000	0.541002
$124$	8.00000	0.718421
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	1.00000	0.0883883
$129$	8.00000	0.704361
$130$	2.00000	0.175412
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	0	0
$133$	0	0
$134$	−12.0000	−1.03664
$135$	1.00000	0.0860663
$136$	2.00000	0.171499
$137$	2.00000	0.170872	0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000	0.170872	0.0854358	+	0.996344i	$0.472772\pi$
$138$	−4.00000	−0.340503
$139$	−16.0000	−1.35710	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000	−1.35710	−0.678551	+	0.734553i	$0.737392\pi$
$140$	0	0
$141$	4.00000	0.336861
$142$	−12.0000	−1.00702
$143$	0	0
$144$	1.00000	0.0833333
$145$	2.00000	0.166091
$146$	−2.00000	−0.165521
$147$	7.00000	0.577350
$148$	−2.00000	−0.164399
$149$	−10.0000	−0.819232	−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000	−0.819232	−0.409616	+	0.912258i	$0.634337\pi$
$150$	−1.00000	−0.0816497
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	−8.00000	−0.648886
$153$	2.00000	0.161690
$154$	0	0
$155$	−8.00000	−0.642575
$156$	2.00000	0.160128
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	0	0
$159$	−2.00000	−0.158610
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	1.00000	0.0785674
$163$	20.0000	1.56652	0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000	1.56652	0.783260	+	0.621694i	$0.213555\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	−4.00000	−0.310460
$167$	−16.0000	−1.23812	−0.619059	−	0.785345i	$-0.712486\pi$
$167$	−16.0000	−1.23812	−0.619059	+	0.785345i	$0.712486\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	−2.00000	−0.153393
$171$	−8.00000	−0.611775
$172$	−8.00000	−0.609994
$173$	−18.0000	−1.36851	−0.684257	−	0.729241i	$-0.739873\pi$
$173$	−18.0000	−1.36851	−0.684257	+	0.729241i	$0.739873\pi$
$174$	2.00000	0.151620
$175$	0	0
$176$	0	0
$177$	−4.00000	−0.300658
$178$	−6.00000	−0.449719
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	−1.00000	−0.0745356
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	0	0
$183$	−6.00000	−0.443533
$184$	4.00000	0.294884
$185$	2.00000	0.147043
$186$	−8.00000	−0.586588
$187$	0	0
$188$	−4.00000	−0.291730
$189$	0	0
$190$	8.00000	0.580381
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	−1.00000	−0.0721688
$193$	22.0000	1.58359	0.791797	−	0.610784i	$-0.209146\pi$
$193$	22.0000	1.58359	0.791797	+	0.610784i	$0.209146\pi$
$194$	−14.0000	−1.00514
$195$	−2.00000	−0.143223
$196$	−7.00000	−0.500000
$197$	−10.0000	−0.712470	−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000	−0.712470	−0.356235	+	0.934396i	$0.615940\pi$
$198$	0	0
$199$	−24.0000	−1.70131	−0.850657	−	0.525720i	$-0.823796\pi$
$199$	−24.0000	−1.70131	−0.850657	+	0.525720i	$0.823796\pi$
$200$	1.00000	0.0707107
$201$	12.0000	0.846415
$202$	6.00000	0.422159
$203$	0	0
$204$	−2.00000	−0.140028
$205$	6.00000	0.419058
$206$	16.0000	1.11477
$207$	4.00000	0.278019
$208$	−2.00000	−0.138675
$209$	0	0
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	2.00000	0.137361
$213$	12.0000	0.822226
$214$	−20.0000	−1.36717
$215$	8.00000	0.545595
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	6.00000	0.406371
$219$	2.00000	0.135147
$220$	0	0
$221$	−4.00000	−0.269069
$222$	2.00000	0.134231
$223$	−16.0000	−1.07144	−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000	−1.07144	−0.535720	+	0.844396i	$0.679960\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	2.00000	0.133038
$227$	−12.0000	−0.796468	−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000	−0.796468	−0.398234	+	0.917284i	$0.630377\pi$
$228$	8.00000	0.529813
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	−4.00000	−0.263752
$231$	0	0
$232$	−2.00000	−0.131306
$233$	18.0000	1.17922	0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000	1.17922	0.589610	+	0.807688i	$0.299282\pi$
$234$	−2.00000	−0.130744
$235$	4.00000	0.260931
$236$	4.00000	0.260378
$237$	0	0
$238$	0	0
$239$	−16.0000	−1.03495	−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000	−1.03495	−0.517477	+	0.855697i	$0.673129\pi$
$240$	1.00000	0.0645497
$241$	−18.0000	−1.15948	−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000	−1.15948	−0.579741	+	0.814801i	$0.696846\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	6.00000	0.384111
$245$	7.00000	0.447214
$246$	6.00000	0.382546
$247$	16.0000	1.01806
$248$	8.00000	0.508001
$249$	4.00000	0.253490
$250$	−1.00000	−0.0632456
$251$	−20.0000	−1.26239	−0.631194	−	0.775625i	$-0.717435\pi$
$251$	−20.0000	−1.26239	−0.631194	+	0.775625i	$0.717435\pi$
$252$	0	0
$253$	0	0
$254$	16.0000	1.00393
$255$	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
$260$	2.00000	0.124035
$261$	−2.00000	−0.123797
$262$	−12.0000	−0.741362
$263$	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
$265$	−2.00000	−0.122859
$266$	0	0
$267$	6.00000	0.367194
$268$	−12.0000	−0.733017
$269$	−22.0000	−1.34136	−0.670682	−	0.741745i	$-0.733998\pi$
$269$	−22.0000	−1.34136	−0.670682	+	0.741745i	$0.733998\pi$
$270$	1.00000	0.0608581
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	2.00000	0.121268
$273$	0	0
$274$	2.00000	0.120824
$275$	0	0
$276$	−4.00000	−0.240772
$277$	14.0000	0.841178	0.420589	−	0.907251i	$-0.361823\pi$
$277$	14.0000	0.841178	0.420589	+	0.907251i	$0.361823\pi$
$278$	−16.0000	−0.959616
$279$	8.00000	0.478947
$280$	0	0
$281$	10.0000	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$282$	4.00000	0.238197
$283$	8.00000	0.475551	0.237775	−	0.971320i	$-0.423582\pi$
$283$	8.00000	0.475551	0.237775	+	0.971320i	$0.423582\pi$
$284$	−12.0000	−0.712069
$285$	−8.00000	−0.473879
$286$	0	0
$287$	0	0
$288$	1.00000	0.0589256
$289$	−13.0000	−0.764706
$290$	2.00000	0.117444
$291$	14.0000	0.820695
$292$	−2.00000	−0.117041
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	7.00000	0.408248
$295$	−4.00000	−0.232889
$296$	−2.00000	−0.116248
$297$	0	0
$298$	−10.0000	−0.579284
$299$	−8.00000	−0.462652
$300$	−1.00000	−0.0577350
$301$	0	0
$302$	8.00000	0.460348
$303$	−6.00000	−0.344691
$304$	−8.00000	−0.458831
$305$	−6.00000	−0.343559
$306$	2.00000	0.114332
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	0	0
$309$	−16.0000	−0.910208
$310$	−8.00000	−0.454369
$311$	−20.0000	−1.13410	−0.567048	−	0.823685i	$-0.691915\pi$
$311$	−20.0000	−1.13410	−0.567048	+	0.823685i	$0.691915\pi$
$312$	2.00000	0.113228
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	−2.00000	−0.112867
$315$	0	0
$316$	0	0
$317$	−6.00000	−0.336994	−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000	−0.336994	−0.168497	+	0.985702i	$0.553891\pi$
$318$	−2.00000	−0.112154
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	20.0000	1.11629
$322$	0	0
$323$	−16.0000	−0.890264
$324$	1.00000	0.0555556
$325$	−2.00000	−0.110940
$326$	20.0000	1.10770
$327$	−6.00000	−0.331801
$328$	−6.00000	−0.331295
$329$	0	0
$330$	0	0
$331$	−12.0000	−0.659580	−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000	−0.659580	−0.329790	+	0.944054i	$0.606978\pi$
$332$	−4.00000	−0.219529
$333$	−2.00000	−0.109599
$334$	−16.0000	−0.875481
$335$	12.0000	0.655630
$336$	0	0
$337$	−10.0000	−0.544735	−0.272367	−	0.962193i	$-0.587807\pi$
$337$	−10.0000	−0.544735	−0.272367	+	0.962193i	$0.587807\pi$
$338$	−9.00000	−0.489535
$339$	−2.00000	−0.108625
$340$	−2.00000	−0.108465
$341$	0	0
$342$	−8.00000	−0.432590
$343$	0	0
$344$	−8.00000	−0.431331
$345$	4.00000	0.215353
$346$	−18.0000	−0.967686
$347$	20.0000	1.07366	0.536828	−	0.843692i	$-0.319622\pi$
$347$	20.0000	1.07366	0.536828	+	0.843692i	$0.319622\pi$
$348$	2.00000	0.107211
$349$	30.0000	1.60586	0.802932	−	0.596071i	$-0.203272\pi$
$349$	30.0000	1.60586	0.802932	+	0.596071i	$0.203272\pi$
$350$	0	0
$351$	2.00000	0.106752
$352$	0	0
$353$	26.0000	1.38384	0.691920	−	0.721974i	$-0.256765\pi$
$353$	26.0000	1.38384	0.691920	+	0.721974i	$0.256765\pi$
$354$	−4.00000	−0.212598
$355$	12.0000	0.636894
$356$	−6.00000	−0.317999
$357$	0	0
$358$	−12.0000	−0.634220
$359$	32.0000	1.68890	0.844448	−	0.535638i	$-0.179929\pi$
$359$	32.0000	1.68890	0.844448	+	0.535638i	$0.179929\pi$
$360$	−1.00000	−0.0527046
$361$	45.0000	2.36842
$362$	−2.00000	−0.105118
$363$	0	0
$364$	0	0
$365$	2.00000	0.104685
$366$	−6.00000	−0.313625
$367$	16.0000	0.835193	0.417597	−	0.908633i	$-0.362873\pi$
$367$	16.0000	0.835193	0.417597	+	0.908633i	$0.362873\pi$
$368$	4.00000	0.208514
$369$	−6.00000	−0.312348
$370$	2.00000	0.103975
$371$	0	0
$372$	−8.00000	−0.414781
$373$	−2.00000	−0.103556	−0.0517780	−	0.998659i	$-0.516489\pi$
$373$	−2.00000	−0.103556	−0.0517780	+	0.998659i	$0.516489\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	−4.00000	−0.206284
$377$	4.00000	0.206010
$378$	0	0
$379$	36.0000	1.84920	0.924598	−	0.380945i	$-0.124401\pi$
$379$	36.0000	1.84920	0.924598	+	0.380945i	$0.124401\pi$
$380$	8.00000	0.410391
$381$	−16.0000	−0.819705
$382$	−12.0000	−0.613973
$383$	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
$386$	22.0000	1.11977
$387$	−8.00000	−0.406663
$388$	−14.0000	−0.710742
$389$	−22.0000	−1.11544	−0.557722	−	0.830028i	$-0.688325\pi$
$389$	−22.0000	−1.11544	−0.557722	+	0.830028i	$0.688325\pi$
$390$	−2.00000	−0.101274
$391$	8.00000	0.404577
$392$	−7.00000	−0.353553
$393$	12.0000	0.605320
$394$	−10.0000	−0.503793
$395$	0	0
$396$	0	0
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	−24.0000	−1.20301
$399$	0	0
$400$	1.00000	0.0500000
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	12.0000	0.598506
$403$	−16.0000	−0.797017
$404$	6.00000	0.298511
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	0	0
$408$	−2.00000	−0.0990148
$409$	−26.0000	−1.28562	−0.642809	−	0.766027i	$-0.722231\pi$
$409$	−26.0000	−1.28562	−0.642809	+	0.766027i	$0.722231\pi$
$410$	6.00000	0.296319
$411$	−2.00000	−0.0986527
$412$	16.0000	0.788263
$413$	0	0
$414$	4.00000	0.196589
$415$	4.00000	0.196352
$416$	−2.00000	−0.0980581
$417$	16.0000	0.783523
$418$	0	0
$419$	4.00000	0.195413	0.0977064	−	0.995215i	$-0.468849\pi$
$419$	4.00000	0.195413	0.0977064	+	0.995215i	$0.468849\pi$
$420$	0	0
$421$	38.0000	1.85201	0.926003	−	0.377515i	$-0.123221\pi$
$421$	38.0000	1.85201	0.926003	+	0.377515i	$0.123221\pi$
$422$	0	0
$423$	−4.00000	−0.194487
$424$	2.00000	0.0971286
$425$	2.00000	0.0970143
$426$	12.0000	0.581402
$427$	0	0
$428$	−20.0000	−0.966736
$429$	0	0
$430$	8.00000	0.385794
$431$	24.0000	1.15604	0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000	1.15604	0.578020	+	0.816023i	$0.303826\pi$
$432$	−1.00000	−0.0481125
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	0	0
$435$	−2.00000	−0.0958927
$436$	6.00000	0.287348
$437$	−32.0000	−1.53077
$438$	2.00000	0.0955637
$439$	16.0000	0.763638	0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000	0.763638	0.381819	+	0.924237i	$0.375298\pi$
$440$	0	0
$441$	−7.00000	−0.333333
$442$	−4.00000	−0.190261
$443$	−28.0000	−1.33032	−0.665160	−	0.746701i	$-0.731637\pi$
$443$	−28.0000	−1.33032	−0.665160	+	0.746701i	$0.731637\pi$
$444$	2.00000	0.0949158
$445$	6.00000	0.284427
$446$	−16.0000	−0.757622
$447$	10.0000	0.472984
$448$	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
$451$	0	0
$452$	2.00000	0.0940721
$453$	−8.00000	−0.375873
$454$	−12.0000	−0.563188
$455$	0	0
$456$	8.00000	0.374634
$457$	38.0000	1.77757	0.888783	−	0.458329i	$-0.151552\pi$
$457$	38.0000	1.77757	0.888783	+	0.458329i	$0.151552\pi$
$458$	14.0000	0.654177
$459$	−2.00000	−0.0933520
$460$	−4.00000	−0.186501
$461$	−18.0000	−0.838344	−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000	−0.838344	−0.419172	+	0.907907i	$0.637680\pi$
$462$	0	0
$463$	8.00000	0.371792	0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000	0.371792	0.185896	+	0.982569i	$0.440481\pi$
$464$	−2.00000	−0.0928477
$465$	8.00000	0.370991
$466$	18.0000	0.833834
$467$	36.0000	1.66588	0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000	1.66588	0.832941	+	0.553362i	$0.186655\pi$
$468$	−2.00000	−0.0924500
$469$	0	0
$470$	4.00000	0.184506
$471$	2.00000	0.0921551
$472$	4.00000	0.184115
$473$	0	0
$474$	0	0
$475$	−8.00000	−0.367065
$476$	0	0
$477$	2.00000	0.0915737
$478$	−16.0000	−0.731823
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	1.00000	0.0456435
$481$	4.00000	0.182384
$482$	−18.0000	−0.819878
$483$	0	0
$484$	0	0
$485$	14.0000	0.635707
$486$	−1.00000	−0.0453609
$487$	8.00000	0.362515	0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000	0.362515	0.181257	+	0.983436i	$0.441983\pi$
$488$	6.00000	0.271607
$489$	−20.0000	−0.904431
$490$	7.00000	0.316228
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	6.00000	0.270501
$493$	−4.00000	−0.180151
$494$	16.0000	0.719874
$495$	0	0
$496$	8.00000	0.359211
$497$	0	0
$498$	4.00000	0.179244
$499$	4.00000	0.179065	0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000	0.179065	0.0895323	+	0.995984i	$0.471463\pi$
$500$	−1.00000	−0.0447214
$501$	16.0000	0.714827
$502$	−20.0000	−0.892644
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	−6.00000	−0.266996
$506$	0	0
$507$	9.00000	0.399704
$508$	16.0000	0.709885
$509$	−22.0000	−0.975133	−0.487566	−	0.873086i	$-0.662115\pi$
$509$	−22.0000	−0.975133	−0.487566	+	0.873086i	$0.662115\pi$
$510$	2.00000	0.0885615
$511$	0	0
$512$	1.00000	0.0441942
$513$	8.00000	0.353209
$514$	26.0000	1.14681
$515$	−16.0000	−0.705044
$516$	8.00000	0.352180
$517$	0	0
$518$	0	0
$519$	18.0000	0.790112
$520$	2.00000	0.0877058
$521$	−38.0000	−1.66481	−0.832405	−	0.554168i	$-0.813037\pi$
$521$	−38.0000	−1.66481	−0.832405	+	0.554168i	$0.813037\pi$
$522$	−2.00000	−0.0875376
$523$	−24.0000	−1.04945	−0.524723	−	0.851273i	$-0.675831\pi$
$523$	−24.0000	−1.04945	−0.524723	+	0.851273i	$0.675831\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	24.0000	1.04645
$527$	16.0000	0.696971
$528$	0	0
$529$	−7.00000	−0.304348
$530$	−2.00000	−0.0868744
$531$	4.00000	0.173585
$532$	0	0
$533$	12.0000	0.519778
$534$	6.00000	0.259645
$535$	20.0000	0.864675
$536$	−12.0000	−0.518321
$537$	12.0000	0.517838
$538$	−22.0000	−0.948487
$539$	0	0
$540$	1.00000	0.0430331
$541$	−26.0000	−1.11783	−0.558914	−	0.829226i	$-0.688782\pi$
$541$	−26.0000	−1.11783	−0.558914	+	0.829226i	$0.688782\pi$
$542$	0	0
$543$	2.00000	0.0858282
$544$	2.00000	0.0857493
$545$	−6.00000	−0.257012
$546$	0	0
$547$	−8.00000	−0.342055	−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000	−0.342055	−0.171028	+	0.985266i	$0.554709\pi$
$548$	2.00000	0.0854358
$549$	6.00000	0.256074
$550$	0	0
$551$	16.0000	0.681623
$552$	−4.00000	−0.170251
$553$	0	0
$554$	14.0000	0.594803
$555$	−2.00000	−0.0848953
$556$	−16.0000	−0.678551
$557$	46.0000	1.94908	0.974541	−	0.224208i	$-0.0719796\pi$
$557$	46.0000	1.94908	0.974541	+	0.224208i	$0.0719796\pi$
$558$	8.00000	0.338667
$559$	16.0000	0.676728
$560$	0	0
$561$	0	0
$562$	10.0000	0.421825
$563$	−4.00000	−0.168580	−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000	−0.168580	−0.0842900	+	0.996441i	$0.526862\pi$
$564$	4.00000	0.168430
$565$	−2.00000	−0.0841406
$566$	8.00000	0.336265
$567$	0	0
$568$	−12.0000	−0.503509
$569$	−14.0000	−0.586911	−0.293455	−	0.955973i	$-0.594805\pi$
$569$	−14.0000	−0.586911	−0.293455	+	0.955973i	$0.594805\pi$
$570$	−8.00000	−0.335083
$571$	40.0000	1.67395	0.836974	−	0.547243i	$-0.184323\pi$
$571$	40.0000	1.67395	0.836974	+	0.547243i	$0.184323\pi$
$572$	0	0
$573$	12.0000	0.501307
$574$	0	0
$575$	4.00000	0.166812
$576$	1.00000	0.0416667
$577$	18.0000	0.749350	0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000	0.749350	0.374675	+	0.927156i	$0.377754\pi$
$578$	−13.0000	−0.540729
$579$	−22.0000	−0.914289
$580$	2.00000	0.0830455
$581$	0	0
$582$	14.0000	0.580319
$583$	0	0
$584$	−2.00000	−0.0827606
$585$	2.00000	0.0826898
$586$	6.00000	0.247858
$587$	−12.0000	−0.495293	−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000	−0.495293	−0.247647	+	0.968850i	$0.579657\pi$
$588$	7.00000	0.288675
$589$	−64.0000	−2.63707
$590$	−4.00000	−0.164677
$591$	10.0000	0.411345
$592$	−2.00000	−0.0821995
$593$	26.0000	1.06769	0.533846	−	0.845582i	$-0.320746\pi$
$593$	26.0000	1.06769	0.533846	+	0.845582i	$0.320746\pi$
$594$	0	0
$595$	0	0
$596$	−10.0000	−0.409616
$597$	24.0000	0.982255
$598$	−8.00000	−0.327144
$599$	−36.0000	−1.47092	−0.735460	−	0.677568i	$-0.763034\pi$
$599$	−36.0000	−1.47092	−0.735460	+	0.677568i	$0.763034\pi$
$600$	−1.00000	−0.0408248
$601$	22.0000	0.897399	0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000	0.897399	0.448699	+	0.893683i	$0.351887\pi$
$602$	0	0
$603$	−12.0000	−0.488678
$604$	8.00000	0.325515
$605$	0	0
$606$	−6.00000	−0.243733
$607$	−16.0000	−0.649420	−0.324710	−	0.945814i	$-0.605267\pi$
$607$	−16.0000	−0.649420	−0.324710	+	0.945814i	$0.605267\pi$
$608$	−8.00000	−0.324443
$609$	0	0
$610$	−6.00000	−0.242933
$611$	8.00000	0.323645
$612$	2.00000	0.0808452
$613$	38.0000	1.53481	0.767403	−	0.641165i	$-0.221549\pi$
$613$	38.0000	1.53481	0.767403	+	0.641165i	$0.221549\pi$
$614$	0	0
$615$	−6.00000	−0.241943
$616$	0	0
$617$	42.0000	1.69086	0.845428	−	0.534089i	$-0.179345\pi$
$617$	42.0000	1.69086	0.845428	+	0.534089i	$0.179345\pi$
$618$	−16.0000	−0.643614
$619$	−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
$621$	−4.00000	−0.160514
$622$	−20.0000	−0.801927
$623$	0	0
$624$	2.00000	0.0800641
$625$	1.00000	0.0400000
$626$	−6.00000	−0.239808
$627$	0	0
$628$	−2.00000	−0.0798087
$629$	−4.00000	−0.159490
$630$	0	0
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	0	0
$633$	0	0
$634$	−6.00000	−0.238290
$635$	−16.0000	−0.634941
$636$	−2.00000	−0.0793052
$637$	14.0000	0.554700
$638$	0	0
$639$	−12.0000	−0.474713
$640$	−1.00000	−0.0395285
$641$	42.0000	1.65890	0.829450	−	0.558581i	$-0.188654\pi$
$641$	42.0000	1.65890	0.829450	+	0.558581i	$0.188654\pi$
$642$	20.0000	0.789337
$643$	−20.0000	−0.788723	−0.394362	−	0.918955i	$-0.629034\pi$
$643$	−20.0000	−0.788723	−0.394362	+	0.918955i	$0.629034\pi$
$644$	0	0
$645$	−8.00000	−0.315000
$646$	−16.0000	−0.629512
$647$	−44.0000	−1.72982	−0.864909	−	0.501928i	$-0.832624\pi$
$647$	−44.0000	−1.72982	−0.864909	+	0.501928i	$0.832624\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	−2.00000	−0.0784465
$651$	0	0
$652$	20.0000	0.783260
$653$	−30.0000	−1.17399	−0.586995	−	0.809590i	$-0.699689\pi$
$653$	−30.0000	−1.17399	−0.586995	+	0.809590i	$0.699689\pi$
$654$	−6.00000	−0.234619
$655$	12.0000	0.468879
$656$	−6.00000	−0.234261
$657$	−2.00000	−0.0780274
$658$	0	0
$659$	−4.00000	−0.155818	−0.0779089	−	0.996960i	$-0.524824\pi$
$659$	−4.00000	−0.155818	−0.0779089	+	0.996960i	$0.524824\pi$
$660$	0	0
$661$	14.0000	0.544537	0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000	0.544537	0.272268	+	0.962221i	$0.412226\pi$
$662$	−12.0000	−0.466393
$663$	4.00000	0.155347
$664$	−4.00000	−0.155230
$665$	0	0
$666$	−2.00000	−0.0774984
$667$	−8.00000	−0.309761
$668$	−16.0000	−0.619059
$669$	16.0000	0.618596
$670$	12.0000	0.463600
$671$	0	0
$672$	0	0
$673$	6.00000	0.231283	0.115642	−	0.993291i	$-0.463108\pi$
$673$	6.00000	0.231283	0.115642	+	0.993291i	$0.463108\pi$
$674$	−10.0000	−0.385186
$675$	−1.00000	−0.0384900
$676$	−9.00000	−0.346154
$677$	38.0000	1.46046	0.730229	−	0.683202i	$-0.239413\pi$
$677$	38.0000	1.46046	0.730229	+	0.683202i	$0.239413\pi$
$678$	−2.00000	−0.0768095
$679$	0	0
$680$	−2.00000	−0.0766965
$681$	12.0000	0.459841
$682$	0	0
$683$	−4.00000	−0.153056	−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000	−0.153056	−0.0765279	+	0.997067i	$0.524383\pi$
$684$	−8.00000	−0.305888
$685$	−2.00000	−0.0764161
$686$	0	0
$687$	−14.0000	−0.534133
$688$	−8.00000	−0.304997
$689$	−4.00000	−0.152388
$690$	4.00000	0.152277
$691$	20.0000	0.760836	0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000	0.760836	0.380418	+	0.924815i	$0.375780\pi$
$692$	−18.0000	−0.684257
$693$	0	0
$694$	20.0000	0.759190
$695$	16.0000	0.606915
$696$	2.00000	0.0758098
$697$	−12.0000	−0.454532
$698$	30.0000	1.13552
$699$	−18.0000	−0.680823
$700$	0	0
$701$	46.0000	1.73740	0.868698	−	0.495342i	$-0.164957\pi$
$701$	46.0000	1.73740	0.868698	+	0.495342i	$0.164957\pi$
$702$	2.00000	0.0754851
$703$	16.0000	0.603451
$704$	0	0
$705$	−4.00000	−0.150649
$706$	26.0000	0.978523
$707$	0	0
$708$	−4.00000	−0.150329
$709$	46.0000	1.72757	0.863783	−	0.503864i	$-0.168089\pi$
$709$	46.0000	1.72757	0.863783	+	0.503864i	$0.168089\pi$
$710$	12.0000	0.450352
$711$	0	0
$712$	−6.00000	−0.224860
$713$	32.0000	1.19841
$714$	0	0
$715$	0	0
$716$	−12.0000	−0.448461
$717$	16.0000	0.597531
$718$	32.0000	1.19423
$719$	−36.0000	−1.34257	−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000	−1.34257	−0.671287	+	0.741198i	$0.734258\pi$
$720$	−1.00000	−0.0372678
$721$	0	0
$722$	45.0000	1.67473
$723$	18.0000	0.669427
$724$	−2.00000	−0.0743294
$725$	−2.00000	−0.0742781
$726$	0	0
$727$	−40.0000	−1.48352	−0.741759	−	0.670667i	$-0.766008\pi$
$727$	−40.0000	−1.48352	−0.741759	+	0.670667i	$0.766008\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	2.00000	0.0740233
$731$	−16.0000	−0.591781
$732$	−6.00000	−0.221766
$733$	14.0000	0.517102	0.258551	−	0.965998i	$-0.416755\pi$
$733$	14.0000	0.517102	0.258551	+	0.965998i	$0.416755\pi$
$734$	16.0000	0.590571
$735$	−7.00000	−0.258199
$736$	4.00000	0.147442
$737$	0	0
$738$	−6.00000	−0.220863
$739$	−24.0000	−0.882854	−0.441427	−	0.897297i	$-0.645528\pi$
$739$	−24.0000	−0.882854	−0.441427	+	0.897297i	$0.645528\pi$
$740$	2.00000	0.0735215
$741$	−16.0000	−0.587775
$742$	0	0
$743$	8.00000	0.293492	0.146746	−	0.989174i	$-0.453120\pi$
$743$	8.00000	0.293492	0.146746	+	0.989174i	$0.453120\pi$
$744$	−8.00000	−0.293294
$745$	10.0000	0.366372
$746$	−2.00000	−0.0732252
$747$	−4.00000	−0.146352
$748$	0	0
$749$	0	0
$750$	1.00000	0.0365148
$751$	−40.0000	−1.45962	−0.729810	−	0.683650i	$-0.760392\pi$
$751$	−40.0000	−1.45962	−0.729810	+	0.683650i	$0.760392\pi$
$752$	−4.00000	−0.145865
$753$	20.0000	0.728841
$754$	4.00000	0.145671
$755$	−8.00000	−0.291150
$756$	0	0
$757$	−34.0000	−1.23575	−0.617876	−	0.786276i	$-0.712006\pi$
$757$	−34.0000	−1.23575	−0.617876	+	0.786276i	$0.712006\pi$
$758$	36.0000	1.30758
$759$	0	0
$760$	8.00000	0.290191
$761$	−30.0000	−1.08750	−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000	−1.08750	−0.543750	+	0.839248i	$0.682996\pi$
$762$	−16.0000	−0.579619
$763$	0	0
$764$	−12.0000	−0.434145
$765$	−2.00000	−0.0723102
$766$	12.0000	0.433578
$767$	−8.00000	−0.288863
$768$	−1.00000	−0.0360844
$769$	−10.0000	−0.360609	−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000	−0.360609	−0.180305	+	0.983611i	$0.557708\pi$
$770$	0	0
$771$	−26.0000	−0.936367
$772$	22.0000	0.791797
$773$	34.0000	1.22290	0.611448	−	0.791285i	$-0.290588\pi$
$773$	34.0000	1.22290	0.611448	+	0.791285i	$0.290588\pi$
$774$	−8.00000	−0.287554
$775$	8.00000	0.287368
$776$	−14.0000	−0.502571
$777$	0	0
$778$	−22.0000	−0.788738
$779$	48.0000	1.71978
$780$	−2.00000	−0.0716115
$781$	0	0
$782$	8.00000	0.286079
$783$	2.00000	0.0714742
$784$	−7.00000	−0.250000
$785$	2.00000	0.0713831
$786$	12.0000	0.428026
$787$	32.0000	1.14068	0.570338	−	0.821410i	$-0.306812\pi$
$787$	32.0000	1.14068	0.570338	+	0.821410i	$0.306812\pi$
$788$	−10.0000	−0.356235
$789$	−24.0000	−0.854423
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−12.0000	−0.426132
$794$	−2.00000	−0.0709773
$795$	2.00000	0.0709327
$796$	−24.0000	−0.850657
$797$	−30.0000	−1.06265	−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000	−1.06265	−0.531327	+	0.847167i	$0.678307\pi$
$798$	0	0
$799$	−8.00000	−0.283020
$800$	1.00000	0.0353553
$801$	−6.00000	−0.212000
$802$	18.0000	0.635602
$803$	0	0
$804$	12.0000	0.423207
$805$	0	0
$806$	−16.0000	−0.563576
$807$	22.0000	0.774437
$808$	6.00000	0.211079
$809$	−30.0000	−1.05474	−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000	−1.05474	−0.527372	+	0.849635i	$0.676823\pi$
$810$	−1.00000	−0.0351364
$811$	8.00000	0.280918	0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000	0.280918	0.140459	+	0.990086i	$0.455142\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	−20.0000	−0.700569
$816$	−2.00000	−0.0700140
$817$	64.0000	2.23908
$818$	−26.0000	−0.909069
$819$	0	0
$820$	6.00000	0.209529
$821$	−10.0000	−0.349002	−0.174501	−	0.984657i	$-0.555831\pi$
$821$	−10.0000	−0.349002	−0.174501	+	0.984657i	$0.555831\pi$
$822$	−2.00000	−0.0697580
$823$	−24.0000	−0.836587	−0.418294	−	0.908312i	$-0.637372\pi$
$823$	−24.0000	−0.836587	−0.418294	+	0.908312i	$0.637372\pi$
$824$	16.0000	0.557386
$825$	0	0
$826$	0	0
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	4.00000	0.139010
$829$	−2.00000	−0.0694629	−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000	−0.0694629	−0.0347314	+	0.999397i	$0.511058\pi$
$830$	4.00000	0.138842
$831$	−14.0000	−0.485655
$832$	−2.00000	−0.0693375
$833$	−14.0000	−0.485071
$834$	16.0000	0.554035
$835$	16.0000	0.553703
$836$	0	0
$837$	−8.00000	−0.276520
$838$	4.00000	0.138178
$839$	−12.0000	−0.414286	−0.207143	−	0.978311i	$-0.566417\pi$
$839$	−12.0000	−0.414286	−0.207143	+	0.978311i	$0.566417\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	38.0000	1.30957
$843$	−10.0000	−0.344418
$844$	0	0
$845$	9.00000	0.309609
$846$	−4.00000	−0.137523
$847$	0	0
$848$	2.00000	0.0686803
$849$	−8.00000	−0.274559
$850$	2.00000	0.0685994
$851$	−8.00000	−0.274236
$852$	12.0000	0.411113
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	0	0
$855$	8.00000	0.273594
$856$	−20.0000	−0.683586
$857$	42.0000	1.43469	0.717346	−	0.696717i	$-0.245357\pi$
$857$	42.0000	1.43469	0.717346	+	0.696717i	$0.245357\pi$
$858$	0	0
$859$	4.00000	0.136478	0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000	0.136478	0.0682391	+	0.997669i	$0.478262\pi$
$860$	8.00000	0.272798
$861$	0	0
$862$	24.0000	0.817443
$863$	4.00000	0.136162	0.0680808	−	0.997680i	$-0.478312\pi$
$863$	4.00000	0.136162	0.0680808	+	0.997680i	$0.478312\pi$
$864$	−1.00000	−0.0340207
$865$	18.0000	0.612018
$866$	2.00000	0.0679628
$867$	13.0000	0.441503
$868$	0	0
$869$	0	0
$870$	−2.00000	−0.0678064
$871$	24.0000	0.813209
$872$	6.00000	0.203186
$873$	−14.0000	−0.473828
$874$	−32.0000	−1.08242
$875$	0	0
$876$	2.00000	0.0675737
$877$	22.0000	0.742887	0.371444	−	0.928456i	$-0.378863\pi$
$877$	22.0000	0.742887	0.371444	+	0.928456i	$0.378863\pi$
$878$	16.0000	0.539974
$879$	−6.00000	−0.202375
$880$	0	0
$881$	58.0000	1.95407	0.977035	−	0.213080i	$-0.0683494\pi$
$881$	58.0000	1.95407	0.977035	+	0.213080i	$0.0683494\pi$
$882$	−7.00000	−0.235702
$883$	4.00000	0.134611	0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000	0.134611	0.0673054	+	0.997732i	$0.478560\pi$
$884$	−4.00000	−0.134535
$885$	4.00000	0.134459
$886$	−28.0000	−0.940678
$887$	−40.0000	−1.34307	−0.671534	−	0.740973i	$-0.734364\pi$
$887$	−40.0000	−1.34307	−0.671534	+	0.740973i	$0.734364\pi$
$888$	2.00000	0.0671156
$889$	0	0
$890$	6.00000	0.201120
$891$	0	0
$892$	−16.0000	−0.535720
$893$	32.0000	1.07084
$894$	10.0000	0.334450
$895$	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
$901$	4.00000	0.133259
$902$	0	0
$903$	0	0
$904$	2.00000	0.0665190
$905$	2.00000	0.0664822
$906$	−8.00000	−0.265782
$907$	52.0000	1.72663	0.863316	−	0.504664i	$-0.168384\pi$
$907$	52.0000	1.72663	0.863316	+	0.504664i	$0.168384\pi$
$908$	−12.0000	−0.398234
$909$	6.00000	0.199007
$910$	0	0
$911$	−20.0000	−0.662630	−0.331315	−	0.943520i	$-0.607492\pi$
$911$	−20.0000	−0.662630	−0.331315	+	0.943520i	$0.607492\pi$
$912$	8.00000	0.264906
$913$	0	0
$914$	38.0000	1.25693
$915$	6.00000	0.198354
$916$	14.0000	0.462573
$917$	0	0
$918$	−2.00000	−0.0660098
$919$	−56.0000	−1.84727	−0.923635	−	0.383274i	$-0.874797\pi$
$919$	−56.0000	−1.84727	−0.923635	+	0.383274i	$0.874797\pi$
$920$	−4.00000	−0.131876
$921$	0	0
$922$	−18.0000	−0.592798
$923$	24.0000	0.789970
$924$	0	0
$925$	−2.00000	−0.0657596
$926$	8.00000	0.262896
$927$	16.0000	0.525509
$928$	−2.00000	−0.0656532
$929$	50.0000	1.64045	0.820223	−	0.572043i	$-0.193849\pi$
$929$	50.0000	1.64045	0.820223	+	0.572043i	$0.193849\pi$
$930$	8.00000	0.262330
$931$	56.0000	1.83533
$932$	18.0000	0.589610
$933$	20.0000	0.654771
$934$	36.0000	1.17796
$935$	0	0
$936$	−2.00000	−0.0653720
$937$	54.0000	1.76410	0.882052	−	0.471153i	$-0.156162\pi$
$937$	54.0000	1.76410	0.882052	+	0.471153i	$0.156162\pi$
$938$	0	0
$939$	6.00000	0.195803
$940$	4.00000	0.130466
$941$	−50.0000	−1.62995	−0.814977	−	0.579494i	$-0.803250\pi$
$941$	−50.0000	−1.62995	−0.814977	+	0.579494i	$0.803250\pi$
$942$	2.00000	0.0651635
$943$	−24.0000	−0.781548
$944$	4.00000	0.130189
$945$	0	0
$946$	0	0
$947$	28.0000	0.909878	0.454939	−	0.890523i	$-0.349661\pi$
$947$	28.0000	0.909878	0.454939	+	0.890523i	$0.349661\pi$
$948$	0	0
$949$	4.00000	0.129845
$950$	−8.00000	−0.259554
$951$	6.00000	0.194563
$952$	0	0
$953$	−38.0000	−1.23094	−0.615470	−	0.788160i	$-0.711034\pi$
$953$	−38.0000	−1.23094	−0.615470	+	0.788160i	$0.711034\pi$
$954$	2.00000	0.0647524
$955$	12.0000	0.388311
$956$	−16.0000	−0.517477
$957$	0	0
$958$	−24.0000	−0.775405
$959$	0	0
$960$	1.00000	0.0322749
$961$	33.0000	1.06452
$962$	4.00000	0.128965
$963$	−20.0000	−0.644491
$964$	−18.0000	−0.579741
$965$	−22.0000	−0.708205
$966$	0	0
$967$	8.00000	0.257263	0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000	0.257263	0.128631	+	0.991692i	$0.458942\pi$
$968$	0	0
$969$	16.0000	0.513994
$970$	14.0000	0.449513
$971$	36.0000	1.15529	0.577647	−	0.816286i	$-0.303971\pi$
$971$	36.0000	1.15529	0.577647	+	0.816286i	$0.303971\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	8.00000	0.256337
$975$	2.00000	0.0640513
$976$	6.00000	0.192055
$977$	−38.0000	−1.21573	−0.607864	−	0.794041i	$-0.707973\pi$
$977$	−38.0000	−1.21573	−0.607864	+	0.794041i	$0.707973\pi$
$978$	−20.0000	−0.639529
$979$	0	0
$980$	7.00000	0.223607
$981$	6.00000	0.191565
$982$	12.0000	0.382935
$983$	4.00000	0.127580	0.0637901	−	0.997963i	$-0.479681\pi$
$983$	4.00000	0.127580	0.0637901	+	0.997963i	$0.479681\pi$
$984$	6.00000	0.191273
$985$	10.0000	0.318626
$986$	−4.00000	−0.127386
$987$	0	0
$988$	16.0000	0.509028
$989$	−32.0000	−1.01754
$990$	0	0
$991$	40.0000	1.27064	0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000	1.27064	0.635321	+	0.772248i	$0.280868\pi$
$992$	8.00000	0.254000
$993$	12.0000	0.380808
$994$	0	0
$995$	24.0000	0.760851
$996$	4.00000	0.126745
$997$	−2.00000	−0.0633406	−0.0316703	−	0.999498i	$-0.510083\pi$
$997$	−2.00000	−0.0633406	−0.0316703	+	0.999498i	$0.510083\pi$
$998$	4.00000	0.126618
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3630.2.a.n.1.1		1
11.10	odd	2		330.2.a.a.1.1	✓	1
33.32	even	2		990.2.a.j.1.1		1
44.43	even	2		2640.2.a.n.1.1		1
55.32	even	4		1650.2.c.l.199.1		2
55.43	even	4		1650.2.c.l.199.2		2
55.54	odd	2		1650.2.a.r.1.1		1
132.131	odd	2		7920.2.a.bb.1.1		1
165.32	odd	4		4950.2.c.g.199.2		2
165.98	odd	4		4950.2.c.g.199.1		2
165.164	even	2		4950.2.a.k.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.a.a.1.1	✓	1	11.10	odd	2
990.2.a.j.1.1		1	33.32	even	2
1650.2.a.r.1.1		1	55.54	odd	2
1650.2.c.l.199.1		2	55.32	even	4
1650.2.c.l.199.2		2	55.43	even	4
2640.2.a.n.1.1		1	44.43	even	2
3630.2.a.n.1.1		1	1.1	even	1	trivial
4950.2.a.k.1.1		1	165.164	even	2
4950.2.c.g.199.1		2	165.98	odd	4
4950.2.c.g.199.2		2	165.32	odd	4
7920.2.a.bb.1.1		1	132.131	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

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