LMFDB - Embedded newform 3630.2.a.s.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:	$0$
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)

$f(q)$

$=$

$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} +2.00000 q^{13} +4.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{18} +8.00000 q^{19} +1.00000 q^{20} -4.00000 q^{21} -1.00000 q^{24} +1.00000 q^{25} +2.00000 q^{26} -1.00000 q^{27} +4.00000 q^{28} -2.00000 q^{29} -1.00000 q^{30} -8.00000 q^{31} +1.00000 q^{32} +2.00000 q^{34} +4.00000 q^{35} +1.00000 q^{36} -10.0000 q^{37} +8.00000 q^{38} -2.00000 q^{39} +1.00000 q^{40} +10.0000 q^{41} -4.00000 q^{42} +1.00000 q^{45} -1.00000 q^{48} +9.00000 q^{49} +1.00000 q^{50} -2.00000 q^{51} +2.00000 q^{52} +14.0000 q^{53} -1.00000 q^{54} +4.00000 q^{56} -8.00000 q^{57} -2.00000 q^{58} -4.00000 q^{59} -1.00000 q^{60} -14.0000 q^{61} -8.00000 q^{62} +4.00000 q^{63} +1.00000 q^{64} +2.00000 q^{65} -4.00000 q^{67} +2.00000 q^{68} +4.00000 q^{70} +8.00000 q^{71} +1.00000 q^{72} -10.0000 q^{73} -10.0000 q^{74} -1.00000 q^{75} +8.00000 q^{76} -2.00000 q^{78} -12.0000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +10.0000 q^{82} -4.00000 q^{83} -4.00000 q^{84} +2.00000 q^{85} +2.00000 q^{87} -6.00000 q^{89} +1.00000 q^{90} +8.00000 q^{91} +8.00000 q^{93} +8.00000 q^{95} -1.00000 q^{96} -14.0000 q^{97} +9.00000 q^{98} +O(q^{100})\)

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
$7$	4.00000	1.51186	0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000	1.51186	0.755929	+	0.654654i	$0.227186\pi$
$8$	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	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	4.00000	1.06904
$15$	−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	$-0.130073\pi$
$19$	8.00000	1.83533	0.917663	+	0.397360i	$0.130073\pi$
$20$	1.00000	0.223607
$21$	−4.00000	−0.872872
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	2.00000	0.392232
$27$	−1.00000	−0.192450
$28$	4.00000	0.755929
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	−1.00000	−0.182574
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	2.00000	0.342997
$35$	4.00000	0.676123
$36$	1.00000	0.166667
$37$	−10.0000	−1.64399	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000	−1.64399	−0.821995	+	0.569495i	$0.807139\pi$
$38$	8.00000	1.29777
$39$	−2.00000	−0.320256
$40$	1.00000	0.158114
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	−4.00000	−0.617213
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	0	0
$45$	1.00000	0.149071
$46$	0	0
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	−1.00000	−0.144338
$49$	9.00000	1.28571
$50$	1.00000	0.141421
$51$	−2.00000	−0.280056
$52$	2.00000	0.277350
$53$	14.0000	1.92305	0.961524	−	0.274721i	$-0.0885855\pi$
$53$	14.0000	1.92305	0.961524	+	0.274721i	$0.0885855\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	4.00000	0.534522
$57$	−8.00000	−1.05963
$58$	−2.00000	−0.262613
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	−1.00000	−0.129099
$61$	−14.0000	−1.79252	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000	−1.79252	−0.896258	+	0.443533i	$0.853725\pi$
$62$	−8.00000	−1.01600
$63$	4.00000	0.503953
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	0	0
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	2.00000	0.242536
$69$	0	0
$70$	4.00000	0.478091
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	1.00000	0.117851
$73$	−10.0000	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$74$	−10.0000	−1.16248
$75$	−1.00000	−0.115470
$76$	8.00000	0.917663
$77$	0	0
$78$	−2.00000	−0.226455
$79$	−12.0000	−1.35011	−0.675053	−	0.737769i	$-0.735879\pi$
$79$	−12.0000	−1.35011	−0.675053	+	0.737769i	$0.735879\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	10.0000	1.10432
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	−4.00000	−0.436436
$85$	2.00000	0.216930
$86$	0	0
$87$	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
$91$	8.00000	0.838628
$92$	0	0
$93$	8.00000	0.829561
$94$	0	0
$95$	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	$0.751641\pi$
$98$	9.00000	0.909137
$99$	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
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	2.00000	0.196116
$105$	−4.00000	−0.390360
$106$	14.0000	1.35980
$107$	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	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	0	0
$111$	10.0000	0.949158
$112$	4.00000	0.377964
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	−8.00000	−0.749269
$115$	0	0
$116$	−2.00000	−0.185695
$117$	2.00000	0.184900
$118$	−4.00000	−0.368230
$119$	8.00000	0.733359
$120$	−1.00000	−0.0912871
$121$	0	0
$122$	−14.0000	−1.26750
$123$	−10.0000	−0.901670
$124$	−8.00000	−0.718421
$125$	1.00000	0.0894427
$126$	4.00000	0.356348
$127$	12.0000	1.06483	0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000	1.06483	0.532414	+	0.846484i	$0.321285\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	2.00000	0.175412
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	0	0
$133$	32.0000	2.77475
$134$	−4.00000	−0.345547
$135$	−1.00000	−0.0860663
$136$	2.00000	0.171499
$137$	18.0000	1.53784	0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000	1.53784	0.768922	+	0.639343i	$0.220793\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	4.00000	0.338062
$141$	0	0
$142$	8.00000	0.671345
$143$	0	0
$144$	1.00000	0.0833333
$145$	−2.00000	−0.166091
$146$	−10.0000	−0.827606
$147$	−9.00000	−0.742307
$148$	−10.0000	−0.821995
$149$	−2.00000	−0.163846	−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000	−0.163846	−0.0819232	+	0.996639i	$0.526106\pi$
$150$	−1.00000	−0.0816497
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	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	$0.525431\pi$
$158$	−12.0000	−0.954669
$159$	−14.0000	−1.11027
$160$	1.00000	0.0790569
$161$	0	0
$162$	1.00000	0.0785674
$163$	−12.0000	−0.939913	−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000	−0.939913	−0.469956	+	0.882690i	$0.655730\pi$
$164$	10.0000	0.780869
$165$	0	0
$166$	−4.00000	−0.310460
$167$	−24.0000	−1.85718	−0.928588	−	0.371113i	$-0.878976\pi$
$167$	−24.0000	−1.85718	−0.928588	+	0.371113i	$0.878976\pi$
$168$	−4.00000	−0.308607
$169$	−9.00000	−0.692308
$170$	2.00000	0.153393
$171$	8.00000	0.611775
$172$	0	0
$173$	22.0000	1.67263	0.836315	−	0.548250i	$-0.184706\pi$
$173$	22.0000	1.67263	0.836315	+	0.548250i	$0.184706\pi$
$174$	2.00000	0.151620
$175$	4.00000	0.302372
$176$	0	0
$177$	4.00000	0.300658
$178$	−6.00000	−0.449719
$179$	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
$181$	6.00000	0.445976	0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000	0.445976	0.222988	+	0.974821i	$0.428419\pi$
$182$	8.00000	0.592999
$183$	14.0000	1.03491
$184$	0	0
$185$	−10.0000	−0.735215
$186$	8.00000	0.586588
$187$	0	0
$188$	0	0
$189$	−4.00000	−0.290957
$190$	8.00000	0.580381
$191$	−16.0000	−1.15772	−0.578860	−	0.815427i	$-0.696502\pi$
$191$	−16.0000	−1.15772	−0.578860	+	0.815427i	$0.696502\pi$
$192$	−1.00000	−0.0721688
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	−14.0000	−1.00514
$195$	−2.00000	−0.143223
$196$	9.00000	0.642857
$197$	−2.00000	−0.142494	−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000	−0.142494	−0.0712470	+	0.997459i	$0.522698\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	1.00000	0.0707107
$201$	4.00000	0.282138
$202$	6.00000	0.422159
$203$	−8.00000	−0.561490
$204$	−2.00000	−0.140028
$205$	10.0000	0.698430
$206$	8.00000	0.557386
$207$	0	0
$208$	2.00000	0.138675
$209$	0	0
$210$	−4.00000	−0.276026
$211$	24.0000	1.65223	0.826114	−	0.563503i	$-0.190547\pi$
$211$	24.0000	1.65223	0.826114	+	0.563503i	$0.190547\pi$
$212$	14.0000	0.961524
$213$	−8.00000	−0.548151
$214$	4.00000	0.273434
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	−32.0000	−2.17230
$218$	10.0000	0.677285
$219$	10.0000	0.675737
$220$	0	0
$221$	4.00000	0.269069
$222$	10.0000	0.671156
$223$	16.0000	1.07144	0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000	1.07144	0.535720	+	0.844396i	$0.320040\pi$
$224$	4.00000	0.267261
$225$	1.00000	0.0666667
$226$	−6.00000	−0.399114
$227$	−4.00000	−0.265489	−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000	−0.265489	−0.132745	+	0.991150i	$0.542379\pi$
$228$	−8.00000	−0.529813
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	0	0
$231$	0	0
$232$	−2.00000	−0.131306
$233$	2.00000	0.131024	0.0655122	−	0.997852i	$-0.479132\pi$
$233$	2.00000	0.131024	0.0655122	+	0.997852i	$0.479132\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	−4.00000	−0.260378
$237$	12.0000	0.779484
$238$	8.00000	0.518563
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	−1.00000	−0.0645497
$241$	−26.0000	−1.67481	−0.837404	−	0.546585i	$-0.815928\pi$
$241$	−26.0000	−1.67481	−0.837404	+	0.546585i	$0.815928\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	−14.0000	−0.896258
$245$	9.00000	0.574989
$246$	−10.0000	−0.637577
$247$	16.0000	1.01806
$248$	−8.00000	−0.508001
$249$	4.00000	0.253490
$250$	1.00000	0.0632456
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	4.00000	0.251976
$253$	0	0
$254$	12.0000	0.752947
$255$	−2.00000	−0.125245
$256$	1.00000	0.0625000
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	0	0
$259$	−40.0000	−2.48548
$260$	2.00000	0.124035
$261$	−2.00000	−0.123797
$262$	12.0000	0.741362
$263$	−8.00000	−0.493301	−0.246651	−	0.969104i	$-0.579330\pi$
$263$	−8.00000	−0.493301	−0.246651	+	0.969104i	$0.579330\pi$
$264$	0	0
$265$	14.0000	0.860013
$266$	32.0000	1.96205
$267$	6.00000	0.367194
$268$	−4.00000	−0.244339
$269$	−10.0000	−0.609711	−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000	−0.609711	−0.304855	+	0.952399i	$0.598608\pi$
$270$	−1.00000	−0.0608581
$271$	28.0000	1.70088	0.850439	−	0.526073i	$-0.176336\pi$
$271$	28.0000	1.70088	0.850439	+	0.526073i	$0.176336\pi$
$272$	2.00000	0.121268
$273$	−8.00000	−0.484182
$274$	18.0000	1.08742
$275$	0	0
$276$	0	0
$277$	10.0000	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$278$	0	0
$279$	−8.00000	−0.478947
$280$	4.00000	0.239046
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	0	0
$283$	16.0000	0.951101	0.475551	−	0.879688i	$-0.342249\pi$
$283$	16.0000	0.951101	0.475551	+	0.879688i	$0.342249\pi$
$284$	8.00000	0.474713
$285$	−8.00000	−0.473879
$286$	0	0
$287$	40.0000	2.36113
$288$	1.00000	0.0589256
$289$	−13.0000	−0.764706
$290$	−2.00000	−0.117444
$291$	14.0000	0.820695
$292$	−10.0000	−0.585206
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	−9.00000	−0.524891
$295$	−4.00000	−0.232889
$296$	−10.0000	−0.581238
$297$	0	0
$298$	−2.00000	−0.115857
$299$	0	0
$300$	−1.00000	−0.0577350
$301$	0	0
$302$	−4.00000	−0.230174
$303$	−6.00000	−0.344691
$304$	8.00000	0.458831
$305$	−14.0000	−0.801638
$306$	2.00000	0.114332
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	0	0
$309$	−8.00000	−0.455104
$310$	−8.00000	−0.454369
$311$	32.0000	1.81455	0.907277	−	0.420534i	$-0.138157\pi$
$311$	32.0000	1.81455	0.907277	+	0.420534i	$0.138157\pi$
$312$	−2.00000	−0.113228
$313$	−22.0000	−1.24351	−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000	−1.24351	−0.621757	+	0.783210i	$0.713581\pi$
$314$	−2.00000	−0.112867
$315$	4.00000	0.225374
$316$	−12.0000	−0.675053
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	−14.0000	−0.785081
$319$	0	0
$320$	1.00000	0.0559017
$321$	−4.00000	−0.223258
$322$	0	0
$323$	16.0000	0.890264
$324$	1.00000	0.0555556
$325$	2.00000	0.110940
$326$	−12.0000	−0.664619
$327$	−10.0000	−0.553001
$328$	10.0000	0.552158
$329$	0	0
$330$	0	0
$331$	12.0000	0.659580	0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000	0.659580	0.329790	+	0.944054i	$0.393022\pi$
$332$	−4.00000	−0.219529
$333$	−10.0000	−0.547997
$334$	−24.0000	−1.31322
$335$	−4.00000	−0.218543
$336$	−4.00000	−0.218218
$337$	−2.00000	−0.108947	−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000	−0.108947	−0.0544735	+	0.998515i	$0.517348\pi$
$338$	−9.00000	−0.489535
$339$	6.00000	0.325875
$340$	2.00000	0.108465
$341$	0	0
$342$	8.00000	0.432590
$343$	8.00000	0.431959
$344$	0	0
$345$	0	0
$346$	22.0000	1.18273
$347$	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
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	4.00000	0.213809
$351$	−2.00000	−0.106752
$352$	0	0
$353$	−14.0000	−0.745145	−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000	−0.745145	−0.372572	+	0.928003i	$0.621524\pi$
$354$	4.00000	0.212598
$355$	8.00000	0.424596
$356$	−6.00000	−0.317999
$357$	−8.00000	−0.423405
$358$	12.0000	0.634220
$359$	−24.0000	−1.26667	−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000	−1.26667	−0.633336	+	0.773877i	$0.718315\pi$
$360$	1.00000	0.0527046
$361$	45.0000	2.36842
$362$	6.00000	0.315353
$363$	0	0
$364$	8.00000	0.419314
$365$	−10.0000	−0.523424
$366$	14.0000	0.731792
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	0	0
$369$	10.0000	0.520579
$370$	−10.0000	−0.519875
$371$	56.0000	2.90738
$372$	8.00000	0.414781
$373$	34.0000	1.76045	0.880227	−	0.474554i	$-0.157390\pi$
$373$	34.0000	1.76045	0.880227	+	0.474554i	$0.157390\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	0	0
$377$	−4.00000	−0.206010
$378$	−4.00000	−0.205738
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	8.00000	0.410391
$381$	−12.0000	−0.614779
$382$	−16.0000	−0.818631
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−10.0000	−0.508987
$387$	0	0
$388$	−14.0000	−0.710742
$389$	22.0000	1.11544	0.557722	−	0.830028i	$-0.311675\pi$
$389$	22.0000	1.11544	0.557722	+	0.830028i	$0.311675\pi$
$390$	−2.00000	−0.101274
$391$	0	0
$392$	9.00000	0.454569
$393$	−12.0000	−0.605320
$394$	−2.00000	−0.100759
$395$	−12.0000	−0.603786
$396$	0	0
$397$	−18.0000	−0.903394	−0.451697	−	0.892171i	$-0.649181\pi$
$397$	−18.0000	−0.903394	−0.451697	+	0.892171i	$0.649181\pi$
$398$	0	0
$399$	−32.0000	−1.60200
$400$	1.00000	0.0500000
$401$	−38.0000	−1.89763	−0.948815	−	0.315833i	$-0.897716\pi$
$401$	−38.0000	−1.89763	−0.948815	+	0.315833i	$0.897716\pi$
$402$	4.00000	0.199502
$403$	−16.0000	−0.797017
$404$	6.00000	0.298511
$405$	1.00000	0.0496904
$406$	−8.00000	−0.397033
$407$	0	0
$408$	−2.00000	−0.0990148
$409$	14.0000	0.692255	0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000	0.692255	0.346128	+	0.938187i	$0.387496\pi$
$410$	10.0000	0.493865
$411$	−18.0000	−0.887875
$412$	8.00000	0.394132
$413$	−16.0000	−0.787309
$414$	0	0
$415$	−4.00000	−0.196352
$416$	2.00000	0.0980581
$417$	0	0
$418$	0	0
$419$	−36.0000	−1.75872	−0.879358	−	0.476162i	$-0.842028\pi$
$419$	−36.0000	−1.75872	−0.879358	+	0.476162i	$0.842028\pi$
$420$	−4.00000	−0.195180
$421$	−26.0000	−1.26716	−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000	−1.26716	−0.633581	+	0.773676i	$0.718416\pi$
$422$	24.0000	1.16830
$423$	0	0
$424$	14.0000	0.679900
$425$	2.00000	0.0970143
$426$	−8.00000	−0.387601
$427$	−56.0000	−2.71003
$428$	4.00000	0.193347
$429$	0	0
$430$	0	0
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	−1.00000	−0.0481125
$433$	−14.0000	−0.672797	−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000	−0.672797	−0.336399	+	0.941720i	$0.609209\pi$
$434$	−32.0000	−1.53605
$435$	2.00000	0.0958927
$436$	10.0000	0.478913
$437$	0	0
$438$	10.0000	0.477818
$439$	4.00000	0.190910	0.0954548	−	0.995434i	$-0.469569\pi$
$439$	4.00000	0.190910	0.0954548	+	0.995434i	$0.469569\pi$
$440$	0	0
$441$	9.00000	0.428571
$442$	4.00000	0.190261
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	10.0000	0.474579
$445$	−6.00000	−0.284427
$446$	16.0000	0.757622
$447$	2.00000	0.0945968
$448$	4.00000	0.188982
$449$	−14.0000	−0.660701	−0.330350	−	0.943858i	$-0.607167\pi$
$449$	−14.0000	−0.660701	−0.330350	+	0.943858i	$0.607167\pi$
$450$	1.00000	0.0471405
$451$	0	0
$452$	−6.00000	−0.282216
$453$	4.00000	0.187936
$454$	−4.00000	−0.187729
$455$	8.00000	0.375046
$456$	−8.00000	−0.374634
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	−10.0000	−0.467269
$459$	−2.00000	−0.0933520
$460$	0	0
$461$	−26.0000	−1.21094	−0.605470	−	0.795868i	$-0.707015\pi$
$461$	−26.0000	−1.21094	−0.605470	+	0.795868i	$0.707015\pi$
$462$	0	0
$463$	32.0000	1.48717	0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000	1.48717	0.743583	+	0.668644i	$0.233125\pi$
$464$	−2.00000	−0.0928477
$465$	8.00000	0.370991
$466$	2.00000	0.0926482
$467$	20.0000	0.925490	0.462745	−	0.886492i	$-0.346865\pi$
$467$	20.0000	0.925490	0.462745	+	0.886492i	$0.346865\pi$
$468$	2.00000	0.0924500
$469$	−16.0000	−0.738811
$470$	0	0
$471$	2.00000	0.0921551
$472$	−4.00000	−0.184115
$473$	0	0
$474$	12.0000	0.551178
$475$	8.00000	0.367065
$476$	8.00000	0.366679
$477$	14.0000	0.641016
$478$	24.0000	1.09773
$479$	−40.0000	−1.82765	−0.913823	−	0.406112i	$-0.866884\pi$
$479$	−40.0000	−1.82765	−0.913823	+	0.406112i	$0.866884\pi$
$480$	−1.00000	−0.0456435
$481$	−20.0000	−0.911922
$482$	−26.0000	−1.18427
$483$	0	0
$484$	0	0
$485$	−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	$0.381918\pi$
$488$	−14.0000	−0.633750
$489$	12.0000	0.542659
$490$	9.00000	0.406579
$491$	−20.0000	−0.902587	−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000	−0.902587	−0.451294	+	0.892375i	$0.649037\pi$
$492$	−10.0000	−0.450835
$493$	−4.00000	−0.180151
$494$	16.0000	0.719874
$495$	0	0
$496$	−8.00000	−0.359211
$497$	32.0000	1.43540
$498$	4.00000	0.179244
$499$	−4.00000	−0.179065	−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000	−0.179065	−0.0895323	+	0.995984i	$0.528537\pi$
$500$	1.00000	0.0447214
$501$	24.0000	1.07224
$502$	−12.0000	−0.535586
$503$	−24.0000	−1.07011	−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000	−1.07011	−0.535054	+	0.844818i	$0.679709\pi$
$504$	4.00000	0.178174
$505$	6.00000	0.266996
$506$	0	0
$507$	9.00000	0.399704
$508$	12.0000	0.532414
$509$	−42.0000	−1.86162	−0.930809	−	0.365507i	$-0.880896\pi$
$509$	−42.0000	−1.86162	−0.930809	+	0.365507i	$0.880896\pi$
$510$	−2.00000	−0.0885615
$511$	−40.0000	−1.76950
$512$	1.00000	0.0441942
$513$	−8.00000	−0.353209
$514$	18.0000	0.793946
$515$	8.00000	0.352522
$516$	0	0
$517$	0	0
$518$	−40.0000	−1.75750
$519$	−22.0000	−0.965693
$520$	2.00000	0.0877058
$521$	2.00000	0.0876216	0.0438108	−	0.999040i	$-0.486050\pi$
$521$	2.00000	0.0876216	0.0438108	+	0.999040i	$0.486050\pi$
$522$	−2.00000	−0.0875376
$523$	32.0000	1.39926	0.699631	−	0.714504i	$-0.253348\pi$
$523$	32.0000	1.39926	0.699631	+	0.714504i	$0.253348\pi$
$524$	12.0000	0.524222
$525$	−4.00000	−0.174574
$526$	−8.00000	−0.348817
$527$	−16.0000	−0.696971
$528$	0	0
$529$	−23.0000	−1.00000
$530$	14.0000	0.608121
$531$	−4.00000	−0.173585
$532$	32.0000	1.38738
$533$	20.0000	0.866296
$534$	6.00000	0.259645
$535$	4.00000	0.172935
$536$	−4.00000	−0.172774
$537$	−12.0000	−0.517838
$538$	−10.0000	−0.431131
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	−38.0000	−1.63375	−0.816874	−	0.576816i	$-0.804295\pi$
$541$	−38.0000	−1.63375	−0.816874	+	0.576816i	$0.804295\pi$
$542$	28.0000	1.20270
$543$	−6.00000	−0.257485
$544$	2.00000	0.0857493
$545$	10.0000	0.428353
$546$	−8.00000	−0.342368
$547$	−8.00000	−0.342055	−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000	−0.342055	−0.171028	+	0.985266i	$0.554709\pi$
$548$	18.0000	0.768922
$549$	−14.0000	−0.597505
$550$	0	0
$551$	−16.0000	−0.681623
$552$	0	0
$553$	−48.0000	−2.04117
$554$	10.0000	0.424859
$555$	10.0000	0.424476
$556$	0	0
$557$	−34.0000	−1.44063	−0.720313	−	0.693649i	$-0.756002\pi$
$557$	−34.0000	−1.44063	−0.720313	+	0.693649i	$0.756002\pi$
$558$	−8.00000	−0.338667
$559$	0	0
$560$	4.00000	0.169031
$561$	0	0
$562$	−6.00000	−0.253095
$563$	36.0000	1.51722	0.758610	−	0.651546i	$-0.225879\pi$
$563$	36.0000	1.51722	0.758610	+	0.651546i	$0.225879\pi$
$564$	0	0
$565$	−6.00000	−0.252422
$566$	16.0000	0.672530
$567$	4.00000	0.167984
$568$	8.00000	0.335673
$569$	18.0000	0.754599	0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000	0.754599	0.377300	+	0.926091i	$0.376853\pi$
$570$	−8.00000	−0.335083
$571$	−8.00000	−0.334790	−0.167395	−	0.985890i	$-0.553535\pi$
$571$	−8.00000	−0.334790	−0.167395	+	0.985890i	$0.553535\pi$
$572$	0	0
$573$	16.0000	0.668410
$574$	40.0000	1.66957
$575$	0	0
$576$	1.00000	0.0416667
$577$	−14.0000	−0.582828	−0.291414	−	0.956597i	$-0.594126\pi$
$577$	−14.0000	−0.582828	−0.291414	+	0.956597i	$0.594126\pi$
$578$	−13.0000	−0.540729
$579$	10.0000	0.415586
$580$	−2.00000	−0.0830455
$581$	−16.0000	−0.663792
$582$	14.0000	0.580319
$583$	0	0
$584$	−10.0000	−0.413803
$585$	2.00000	0.0826898
$586$	6.00000	0.247858
$587$	44.0000	1.81607	0.908037	−	0.418890i	$-0.137581\pi$
$587$	44.0000	1.81607	0.908037	+	0.418890i	$0.137581\pi$
$588$	−9.00000	−0.371154
$589$	−64.0000	−2.63707
$590$	−4.00000	−0.164677
$591$	2.00000	0.0822690
$592$	−10.0000	−0.410997
$593$	42.0000	1.72473	0.862367	−	0.506284i	$-0.168981\pi$
$593$	42.0000	1.72473	0.862367	+	0.506284i	$0.168981\pi$
$594$	0	0
$595$	8.00000	0.327968
$596$	−2.00000	−0.0819232
$597$	0	0
$598$	0	0
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	−1.00000	−0.0408248
$601$	−10.0000	−0.407909	−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000	−0.407909	−0.203954	+	0.978980i	$0.565379\pi$
$602$	0	0
$603$	−4.00000	−0.162893
$604$	−4.00000	−0.162758
$605$	0	0
$606$	−6.00000	−0.243733
$607$	12.0000	0.487065	0.243532	−	0.969893i	$-0.421694\pi$
$607$	12.0000	0.487065	0.243532	+	0.969893i	$0.421694\pi$
$608$	8.00000	0.324443
$609$	8.00000	0.324176
$610$	−14.0000	−0.566843
$611$	0	0
$612$	2.00000	0.0808452
$613$	2.00000	0.0807792	0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000	0.0807792	0.0403896	+	0.999184i	$0.487140\pi$
$614$	0	0
$615$	−10.0000	−0.403239
$616$	0	0
$617$	−30.0000	−1.20775	−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000	−1.20775	−0.603877	+	0.797077i	$0.706378\pi$
$618$	−8.00000	−0.321807
$619$	−4.00000	−0.160774	−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000	−0.160774	−0.0803868	+	0.996764i	$0.525616\pi$
$620$	−8.00000	−0.321288
$621$	0	0
$622$	32.0000	1.28308
$623$	−24.0000	−0.961540
$624$	−2.00000	−0.0800641
$625$	1.00000	0.0400000
$626$	−22.0000	−0.879297
$627$	0	0
$628$	−2.00000	−0.0798087
$629$	−20.0000	−0.797452
$630$	4.00000	0.159364
$631$	−32.0000	−1.27390	−0.636950	−	0.770905i	$-0.719804\pi$
$631$	−32.0000	−1.27390	−0.636950	+	0.770905i	$0.719804\pi$
$632$	−12.0000	−0.477334
$633$	−24.0000	−0.953914
$634$	−18.0000	−0.714871
$635$	12.0000	0.476205
$636$	−14.0000	−0.555136
$637$	18.0000	0.713186
$638$	0	0
$639$	8.00000	0.316475
$640$	1.00000	0.0395285
$641$	34.0000	1.34292	0.671460	−	0.741041i	$-0.265668\pi$
$641$	34.0000	1.34292	0.671460	+	0.741041i	$0.265668\pi$
$642$	−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
$645$	0	0
$646$	16.0000	0.629512
$647$	16.0000	0.629025	0.314512	−	0.949253i	$-0.398159\pi$
$647$	16.0000	0.629025	0.314512	+	0.949253i	$0.398159\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	2.00000	0.0784465
$651$	32.0000	1.25418
$652$	−12.0000	−0.469956
$653$	22.0000	0.860927	0.430463	−	0.902608i	$-0.358350\pi$
$653$	22.0000	0.860927	0.430463	+	0.902608i	$0.358350\pi$
$654$	−10.0000	−0.391031
$655$	12.0000	0.468879
$656$	10.0000	0.390434
$657$	−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	$0.747343\pi$
$660$	0	0
$661$	−10.0000	−0.388955	−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000	−0.388955	−0.194477	+	0.980907i	$0.562301\pi$
$662$	12.0000	0.466393
$663$	−4.00000	−0.155347
$664$	−4.00000	−0.155230
$665$	32.0000	1.24091
$666$	−10.0000	−0.387492
$667$	0	0
$668$	−24.0000	−0.928588
$669$	−16.0000	−0.618596
$670$	−4.00000	−0.154533
$671$	0	0
$672$	−4.00000	−0.154303
$673$	−10.0000	−0.385472	−0.192736	−	0.981251i	$-0.561736\pi$
$673$	−10.0000	−0.385472	−0.192736	+	0.981251i	$0.561736\pi$
$674$	−2.00000	−0.0770371
$675$	−1.00000	−0.0384900
$676$	−9.00000	−0.346154
$677$	46.0000	1.76792	0.883962	−	0.467559i	$-0.154866\pi$
$677$	46.0000	1.76792	0.883962	+	0.467559i	$0.154866\pi$
$678$	6.00000	0.230429
$679$	−56.0000	−2.14908
$680$	2.00000	0.0766965
$681$	4.00000	0.153280
$682$	0	0
$683$	−12.0000	−0.459167	−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000	−0.459167	−0.229584	+	0.973289i	$0.573736\pi$
$684$	8.00000	0.305888
$685$	18.0000	0.687745
$686$	8.00000	0.305441
$687$	10.0000	0.381524
$688$	0	0
$689$	28.0000	1.06672
$690$	0	0
$691$	36.0000	1.36950	0.684752	−	0.728776i	$-0.259910\pi$
$691$	36.0000	1.36950	0.684752	+	0.728776i	$0.259910\pi$
$692$	22.0000	0.836315
$693$	0	0
$694$	4.00000	0.151838
$695$	0	0
$696$	2.00000	0.0758098
$697$	20.0000	0.757554
$698$	2.00000	0.0757011
$699$	−2.00000	−0.0756469
$700$	4.00000	0.151186
$701$	6.00000	0.226617	0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000	0.226617	0.113308	+	0.993560i	$0.463855\pi$
$702$	−2.00000	−0.0754851
$703$	−80.0000	−3.01726
$704$	0	0
$705$	0	0
$706$	−14.0000	−0.526897
$707$	24.0000	0.902613
$708$	4.00000	0.150329
$709$	−10.0000	−0.375558	−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000	−0.375558	−0.187779	+	0.982211i	$0.560129\pi$
$710$	8.00000	0.300235
$711$	−12.0000	−0.450035
$712$	−6.00000	−0.224860
$713$	0	0
$714$	−8.00000	−0.299392
$715$	0	0
$716$	12.0000	0.448461
$717$	−24.0000	−0.896296
$718$	−24.0000	−0.895672
$719$	−16.0000	−0.596699	−0.298350	−	0.954457i	$-0.596436\pi$
$719$	−16.0000	−0.596699	−0.298350	+	0.954457i	$0.596436\pi$
$720$	1.00000	0.0372678
$721$	32.0000	1.19174
$722$	45.0000	1.67473
$723$	26.0000	0.966950
$724$	6.00000	0.222988
$725$	−2.00000	−0.0742781
$726$	0	0
$727$	16.0000	0.593407	0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000	0.593407	0.296704	+	0.954970i	$0.404113\pi$
$728$	8.00000	0.296500
$729$	1.00000	0.0370370
$730$	−10.0000	−0.370117
$731$	0	0
$732$	14.0000	0.517455
$733$	−14.0000	−0.517102	−0.258551	−	0.965998i	$-0.583245\pi$
$733$	−14.0000	−0.517102	−0.258551	+	0.965998i	$0.583245\pi$
$734$	0	0
$735$	−9.00000	−0.331970
$736$	0	0
$737$	0	0
$738$	10.0000	0.368105
$739$	−16.0000	−0.588570	−0.294285	−	0.955718i	$-0.595081\pi$
$739$	−16.0000	−0.588570	−0.294285	+	0.955718i	$0.595081\pi$
$740$	−10.0000	−0.367607
$741$	−16.0000	−0.587775
$742$	56.0000	2.05582
$743$	32.0000	1.17397	0.586983	−	0.809599i	$-0.300316\pi$
$743$	32.0000	1.17397	0.586983	+	0.809599i	$0.300316\pi$
$744$	8.00000	0.293294
$745$	−2.00000	−0.0732743
$746$	34.0000	1.24483
$747$	−4.00000	−0.146352
$748$	0	0
$749$	16.0000	0.584627
$750$	−1.00000	−0.0365148
$751$	8.00000	0.291924	0.145962	−	0.989290i	$-0.453372\pi$
$751$	8.00000	0.291924	0.145962	+	0.989290i	$0.453372\pi$
$752$	0	0
$753$	12.0000	0.437304
$754$	−4.00000	−0.145671
$755$	−4.00000	−0.145575
$756$	−4.00000	−0.145479
$757$	−42.0000	−1.52652	−0.763258	−	0.646094i	$-0.776401\pi$
$757$	−42.0000	−1.52652	−0.763258	+	0.646094i	$0.776401\pi$
$758$	−20.0000	−0.726433
$759$	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	$0.682996\pi$
$762$	−12.0000	−0.434714
$763$	40.0000	1.44810
$764$	−16.0000	−0.578860
$765$	2.00000	0.0723102
$766$	24.0000	0.867155
$767$	−8.00000	−0.288863
$768$	−1.00000	−0.0360844
$769$	−34.0000	−1.22607	−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000	−1.22607	−0.613036	+	0.790055i	$0.710052\pi$
$770$	0	0
$771$	−18.0000	−0.648254
$772$	−10.0000	−0.359908
$773$	14.0000	0.503545	0.251773	−	0.967786i	$-0.418987\pi$
$773$	14.0000	0.503545	0.251773	+	0.967786i	$0.418987\pi$
$774$	0	0
$775$	−8.00000	−0.287368
$776$	−14.0000	−0.502571
$777$	40.0000	1.43499
$778$	22.0000	0.788738
$779$	80.0000	2.86630
$780$	−2.00000	−0.0716115
$781$	0	0
$782$	0	0
$783$	2.00000	0.0714742
$784$	9.00000	0.321429
$785$	−2.00000	−0.0713831
$786$	−12.0000	−0.428026
$787$	40.0000	1.42585	0.712923	−	0.701242i	$-0.247371\pi$
$787$	40.0000	1.42585	0.712923	+	0.701242i	$0.247371\pi$
$788$	−2.00000	−0.0712470
$789$	8.00000	0.284808
$790$	−12.0000	−0.426941
$791$	−24.0000	−0.853342
$792$	0	0
$793$	−28.0000	−0.994309
$794$	−18.0000	−0.638796
$795$	−14.0000	−0.496529
$796$	0	0
$797$	−34.0000	−1.20434	−0.602171	−	0.798367i	$-0.705697\pi$
$797$	−34.0000	−1.20434	−0.602171	+	0.798367i	$0.705697\pi$
$798$	−32.0000	−1.13279
$799$	0	0
$800$	1.00000	0.0353553
$801$	−6.00000	−0.212000
$802$	−38.0000	−1.34183
$803$	0	0
$804$	4.00000	0.141069
$805$	0	0
$806$	−16.0000	−0.563576
$807$	10.0000	0.352017
$808$	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
$811$	0	0		−	1.00000i	$-0.5\pi$
$811$	0	0			1.00000i	$0.5\pi$
$812$	−8.00000	−0.280745
$813$	−28.0000	−0.982003
$814$	0	0
$815$	−12.0000	−0.420342
$816$	−2.00000	−0.0700140
$817$	0	0
$818$	14.0000	0.489499
$819$	8.00000	0.279543
$820$	10.0000	0.349215
$821$	−26.0000	−0.907406	−0.453703	−	0.891153i	$-0.649897\pi$
$821$	−26.0000	−0.907406	−0.453703	+	0.891153i	$0.649897\pi$
$822$	−18.0000	−0.627822
$823$	−24.0000	−0.836587	−0.418294	−	0.908312i	$-0.637372\pi$
$823$	−24.0000	−0.836587	−0.418294	+	0.908312i	$0.637372\pi$
$824$	8.00000	0.278693
$825$	0	0
$826$	−16.0000	−0.556711
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	0	0
$829$	−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
$831$	−10.0000	−0.346896
$832$	2.00000	0.0693375
$833$	18.0000	0.623663
$834$	0	0
$835$	−24.0000	−0.830554
$836$	0	0
$837$	8.00000	0.276520
$838$	−36.0000	−1.24360
$839$	−16.0000	−0.552381	−0.276191	−	0.961103i	$-0.589072\pi$
$839$	−16.0000	−0.552381	−0.276191	+	0.961103i	$0.589072\pi$
$840$	−4.00000	−0.138013
$841$	−25.0000	−0.862069
$842$	−26.0000	−0.896019
$843$	6.00000	0.206651
$844$	24.0000	0.826114
$845$	−9.00000	−0.309609
$846$	0	0
$847$	0	0
$848$	14.0000	0.480762
$849$	−16.0000	−0.549119
$850$	2.00000	0.0685994
$851$	0	0
$852$	−8.00000	−0.274075
$853$	−14.0000	−0.479351	−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000	−0.479351	−0.239675	+	0.970853i	$0.577041\pi$
$854$	−56.0000	−1.91628
$855$	8.00000	0.273594
$856$	4.00000	0.136717
$857$	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
$859$	28.0000	0.955348	0.477674	−	0.878537i	$-0.341480\pi$
$859$	28.0000	0.955348	0.477674	+	0.878537i	$0.341480\pi$
$860$	0	0
$861$	−40.0000	−1.36320
$862$	−24.0000	−0.817443
$863$	−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
$865$	22.0000	0.748022
$866$	−14.0000	−0.475739
$867$	13.0000	0.441503
$868$	−32.0000	−1.08615
$869$	0	0
$870$	2.00000	0.0678064
$871$	−8.00000	−0.271070
$872$	10.0000	0.338643
$873$	−14.0000	−0.473828
$874$	0	0
$875$	4.00000	0.135225
$876$	10.0000	0.337869
$877$	−6.00000	−0.202606	−0.101303	−	0.994856i	$-0.532301\pi$
$877$	−6.00000	−0.202606	−0.101303	+	0.994856i	$0.532301\pi$
$878$	4.00000	0.134993
$879$	−6.00000	−0.202375
$880$	0	0
$881$	−54.0000	−1.81931	−0.909653	−	0.415369i	$-0.863653\pi$
$881$	−54.0000	−1.81931	−0.909653	+	0.415369i	$0.863653\pi$
$882$	9.00000	0.303046
$883$	−4.00000	−0.134611	−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000	−0.134611	−0.0673054	+	0.997732i	$0.521440\pi$
$884$	4.00000	0.134535
$885$	4.00000	0.134459
$886$	−4.00000	−0.134383
$887$	48.0000	1.61168	0.805841	−	0.592132i	$-0.201714\pi$
$887$	48.0000	1.61168	0.805841	+	0.592132i	$0.201714\pi$
$888$	10.0000	0.335578
$889$	48.0000	1.60987
$890$	−6.00000	−0.201120
$891$	0	0
$892$	16.0000	0.535720
$893$	0	0
$894$	2.00000	0.0668900
$895$	12.0000	0.401116
$896$	4.00000	0.133631
$897$	0	0
$898$	−14.0000	−0.467186
$899$	16.0000	0.533630
$900$	1.00000	0.0333333
$901$	28.0000	0.932815
$902$	0	0
$903$	0	0
$904$	−6.00000	−0.199557
$905$	6.00000	0.199447
$906$	4.00000	0.132891
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	−4.00000	−0.132745
$909$	6.00000	0.199007
$910$	8.00000	0.265197
$911$	−16.0000	−0.530104	−0.265052	−	0.964234i	$-0.585389\pi$
$911$	−16.0000	−0.530104	−0.265052	+	0.964234i	$0.585389\pi$
$912$	−8.00000	−0.264906
$913$	0	0
$914$	−10.0000	−0.330771
$915$	14.0000	0.462826
$916$	−10.0000	−0.330409
$917$	48.0000	1.58510
$918$	−2.00000	−0.0660098
$919$	20.0000	0.659739	0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000	0.659739	0.329870	+	0.944027i	$0.392995\pi$
$920$	0	0
$921$	0	0
$922$	−26.0000	−0.856264
$923$	16.0000	0.526646
$924$	0	0
$925$	−10.0000	−0.328798
$926$	32.0000	1.05159
$927$	8.00000	0.262754
$928$	−2.00000	−0.0656532
$929$	−6.00000	−0.196854	−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000	−0.196854	−0.0984268	+	0.995144i	$0.531381\pi$
$930$	8.00000	0.262330
$931$	72.0000	2.35970
$932$	2.00000	0.0655122
$933$	−32.0000	−1.04763
$934$	20.0000	0.654420
$935$	0	0
$936$	2.00000	0.0653720
$937$	14.0000	0.457360	0.228680	−	0.973502i	$-0.426559\pi$
$937$	14.0000	0.457360	0.228680	+	0.973502i	$0.426559\pi$
$938$	−16.0000	−0.522419
$939$	22.0000	0.717943
$940$	0	0
$941$	30.0000	0.977972	0.488986	−	0.872292i	$-0.337367\pi$
$941$	30.0000	0.977972	0.488986	+	0.872292i	$0.337367\pi$
$942$	2.00000	0.0651635
$943$	0	0
$944$	−4.00000	−0.130189
$945$	−4.00000	−0.130120
$946$	0	0
$947$	−36.0000	−1.16984	−0.584921	−	0.811090i	$-0.698875\pi$
$947$	−36.0000	−1.16984	−0.584921	+	0.811090i	$0.698875\pi$
$948$	12.0000	0.389742
$949$	−20.0000	−0.649227
$950$	8.00000	0.259554
$951$	18.0000	0.583690
$952$	8.00000	0.259281
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	14.0000	0.453267
$955$	−16.0000	−0.517748
$956$	24.0000	0.776215
$957$	0	0
$958$	−40.0000	−1.29234
$959$	72.0000	2.32500
$960$	−1.00000	−0.0322749
$961$	33.0000	1.06452
$962$	−20.0000	−0.644826
$963$	4.00000	0.128898
$964$	−26.0000	−0.837404
$965$	−10.0000	−0.321911
$966$	0	0
$967$	−60.0000	−1.92947	−0.964735	−	0.263223i	$-0.915214\pi$
$967$	−60.0000	−1.92947	−0.964735	+	0.263223i	$0.915214\pi$
$968$	0	0
$969$	−16.0000	−0.513994
$970$	−14.0000	−0.449513
$971$	−36.0000	−1.15529	−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000	−1.15529	−0.577647	+	0.816286i	$0.696029\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	16.0000	0.512673
$975$	−2.00000	−0.0640513
$976$	−14.0000	−0.448129
$977$	−54.0000	−1.72761	−0.863807	−	0.503824i	$-0.831926\pi$
$977$	−54.0000	−1.72761	−0.863807	+	0.503824i	$0.831926\pi$
$978$	12.0000	0.383718
$979$	0	0
$980$	9.00000	0.287494
$981$	10.0000	0.319275
$982$	−20.0000	−0.638226
$983$	−32.0000	−1.02064	−0.510321	−	0.859984i	$-0.670473\pi$
$983$	−32.0000	−1.02064	−0.510321	+	0.859984i	$0.670473\pi$
$984$	−10.0000	−0.318788
$985$	−2.00000	−0.0637253
$986$	−4.00000	−0.127386
$987$	0	0
$988$	16.0000	0.509028
$989$	0	0
$990$	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
$994$	32.0000	1.01498
$995$	0	0
$996$	4.00000	0.126745
$997$	−14.0000	−0.443384	−0.221692	−	0.975117i	$-0.571158\pi$
$997$	−14.0000	−0.443384	−0.221692	+	0.975117i	$0.571158\pi$
$998$	−4.00000	−0.126618
$999$	10.0000	0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3630.2.a.s.1.1		1
11.10	odd	2		330.2.a.b.1.1	✓	1
33.32	even	2		990.2.a.h.1.1		1
44.43	even	2		2640.2.a.v.1.1		1
55.32	even	4		1650.2.c.j.199.1		2
55.43	even	4		1650.2.c.j.199.2		2
55.54	odd	2		1650.2.a.t.1.1		1
132.131	odd	2		7920.2.a.r.1.1		1
165.32	odd	4		4950.2.c.o.199.2		2
165.98	odd	4		4950.2.c.o.199.1		2
165.164	even	2		4950.2.a.t.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.a.b.1.1	✓	1	11.10	odd	2
990.2.a.h.1.1		1	33.32	even	2
1650.2.a.t.1.1		1	55.54	odd	2
1650.2.c.j.199.1		2	55.32	even	4
1650.2.c.j.199.2		2	55.43	even	4
2640.2.a.v.1.1		1	44.43	even	2
3630.2.a.s.1.1		1	1.1	even	1	trivial
4950.2.a.t.1.1		1	165.164	even	2
4950.2.c.o.199.1		2	165.98	odd	4
4950.2.c.o.199.2		2	165.32	odd	4
7920.2.a.r.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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