LMFDB - Embedded newform 3630.2.a.u.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:	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)

$f(q)$

$=$

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

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{12} +5.00000 q^{13} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -3.00000 q^{17} +1.00000 q^{18} +5.00000 q^{19} -1.00000 q^{20} -1.00000 q^{21} +1.00000 q^{24} +1.00000 q^{25} +5.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} -3.00000 q^{29} -1.00000 q^{30} +2.00000 q^{31} +1.00000 q^{32} -3.00000 q^{34} +1.00000 q^{35} +1.00000 q^{36} +5.00000 q^{37} +5.00000 q^{38} +5.00000 q^{39} -1.00000 q^{40} +6.00000 q^{41} -1.00000 q^{42} +2.00000 q^{43} -1.00000 q^{45} -6.00000 q^{47} +1.00000 q^{48} -6.00000 q^{49} +1.00000 q^{50} -3.00000 q^{51} +5.00000 q^{52} +1.00000 q^{54} -1.00000 q^{56} +5.00000 q^{57} -3.00000 q^{58} -1.00000 q^{60} +8.00000 q^{61} +2.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} -5.00000 q^{65} +2.00000 q^{67} -3.00000 q^{68} +1.00000 q^{70} +9.00000 q^{71} +1.00000 q^{72} +14.0000 q^{73} +5.00000 q^{74} +1.00000 q^{75} +5.00000 q^{76} +5.00000 q^{78} +14.0000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} -3.00000 q^{83} -1.00000 q^{84} +3.00000 q^{85} +2.00000 q^{86} -3.00000 q^{87} -12.0000 q^{89} -1.00000 q^{90} -5.00000 q^{91} +2.00000 q^{93} -6.00000 q^{94} -5.00000 q^{95} +1.00000 q^{96} -10.0000 q^{97} -6.00000 q^{98} +O(q^{100})\)

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
$13$	5.00000	1.38675	0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000	1.38675	0.693375	+	0.720577i	$0.256123\pi$
$14$	−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
$19$	5.00000	1.14708	0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000	1.14708	0.573539	+	0.819178i	$0.305570\pi$
$20$	−1.00000	−0.223607
$21$	−1.00000	−0.218218
$22$	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
$26$	5.00000	0.980581
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	−1.00000	−0.182574
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−3.00000	−0.514496
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	5.00000	0.821995	0.410997	−	0.911636i	$-0.365181\pi$
$37$	5.00000	0.821995	0.410997	+	0.911636i	$0.365181\pi$
$38$	5.00000	0.811107
$39$	5.00000	0.800641
$40$	−1.00000	−0.158114
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	−1.00000	−0.154303
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	1.00000	0.144338
$49$	−6.00000	−0.857143
$50$	1.00000	0.141421
$51$	−3.00000	−0.420084
$52$	5.00000	0.693375
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−1.00000	−0.133631
$57$	5.00000	0.662266
$58$	−3.00000	−0.393919
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	−1.00000	−0.129099
$61$	8.00000	1.02430	0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000	1.02430	0.512148	+	0.858898i	$0.328850\pi$
$62$	2.00000	0.254000
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	−5.00000	−0.620174
$66$	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
$69$	0	0
$70$	1.00000	0.119523
$71$	9.00000	1.06810	0.534052	−	0.845452i	$-0.320669\pi$
$71$	9.00000	1.06810	0.534052	+	0.845452i	$0.320669\pi$
$72$	1.00000	0.117851
$73$	14.0000	1.63858	0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000	1.63858	0.819288	+	0.573382i	$0.194369\pi$
$74$	5.00000	0.581238
$75$	1.00000	0.115470
$76$	5.00000	0.573539
$77$	0	0
$78$	5.00000	0.566139
$79$	14.0000	1.57512	0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000	1.57512	0.787562	+	0.616236i	$0.211343\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	6.00000	0.662589
$83$	−3.00000	−0.329293	−0.164646	−	0.986353i	$-0.552648\pi$
$83$	−3.00000	−0.329293	−0.164646	+	0.986353i	$0.552648\pi$
$84$	−1.00000	−0.109109
$85$	3.00000	0.325396
$86$	2.00000	0.215666
$87$	−3.00000	−0.321634
$88$	0	0
$89$	−12.0000	−1.27200	−0.635999	−	0.771690i	$-0.719412\pi$
$89$	−12.0000	−1.27200	−0.635999	+	0.771690i	$0.719412\pi$
$90$	−1.00000	−0.105409
$91$	−5.00000	−0.524142
$92$	0	0
$93$	2.00000	0.207390
$94$	−6.00000	−0.618853
$95$	−5.00000	−0.512989
$96$	1.00000	0.102062
$97$	−10.0000	−1.01535	−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000	−1.01535	−0.507673	+	0.861550i	$0.669494\pi$
$98$	−6.00000	−0.606092
$99$	0	0
$100$	1.00000	0.100000
$101$	15.0000	1.49256	0.746278	−	0.665635i	$-0.231839\pi$
$101$	15.0000	1.49256	0.746278	+	0.665635i	$0.231839\pi$
$102$	−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	$0.515688\pi$
$104$	5.00000	0.490290
$105$	1.00000	0.0975900
$106$	0	0
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	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
$111$	5.00000	0.474579
$112$	−1.00000	−0.0944911
$113$	18.0000	1.69330	0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000	1.69330	0.846649	+	0.532152i	$0.178617\pi$
$114$	5.00000	0.468293
$115$	0	0
$116$	−3.00000	−0.278543
$117$	5.00000	0.462250
$118$	0	0
$119$	3.00000	0.275010
$120$	−1.00000	−0.0912871
$121$	0	0
$122$	8.00000	0.724286
$123$	6.00000	0.541002
$124$	2.00000	0.179605
$125$	−1.00000	−0.0894427
$126$	−1.00000	−0.0890871
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	1.00000	0.0883883
$129$	2.00000	0.176090
$130$	−5.00000	−0.438529
$131$	−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
$133$	−5.00000	−0.433555
$134$	2.00000	0.172774
$135$	−1.00000	−0.0860663
$136$	−3.00000	−0.257248
$137$	15.0000	1.28154	0.640768	−	0.767734i	$-0.278616\pi$
$137$	15.0000	1.28154	0.640768	+	0.767734i	$0.278616\pi$
$138$	0	0
$139$	23.0000	1.95083	0.975417	−	0.220366i	$-0.0707252\pi$
$139$	23.0000	1.95083	0.975417	+	0.220366i	$0.0707252\pi$
$140$	1.00000	0.0845154
$141$	−6.00000	−0.505291
$142$	9.00000	0.755263
$143$	0	0
$144$	1.00000	0.0833333
$145$	3.00000	0.249136
$146$	14.0000	1.15865
$147$	−6.00000	−0.494872
$148$	5.00000	0.410997
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	1.00000	0.0816497
$151$	20.0000	1.62758	0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000	1.62758	0.813788	+	0.581161i	$0.197401\pi$
$152$	5.00000	0.405554
$153$	−3.00000	−0.242536
$154$	0	0
$155$	−2.00000	−0.160644
$156$	5.00000	0.400320
$157$	−13.0000	−1.03751	−0.518756	−	0.854922i	$-0.673605\pi$
$157$	−13.0000	−1.03751	−0.518756	+	0.854922i	$0.673605\pi$
$158$	14.0000	1.11378
$159$	0	0
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	1.00000	0.0785674
$163$	−16.0000	−1.25322	−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000	−1.25322	−0.626608	+	0.779334i	$0.715557\pi$
$164$	6.00000	0.468521
$165$	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
$171$	5.00000	0.382360
$172$	2.00000	0.152499
$173$	12.0000	0.912343	0.456172	−	0.889892i	$-0.349220\pi$
$173$	12.0000	0.912343	0.456172	+	0.889892i	$0.349220\pi$
$174$	−3.00000	−0.227429
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	0	0
$178$	−12.0000	−0.899438
$179$	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
$181$	−16.0000	−1.18927	−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000	−1.18927	−0.594635	+	0.803996i	$0.702704\pi$
$182$	−5.00000	−0.370625
$183$	8.00000	0.591377
$184$	0	0
$185$	−5.00000	−0.367607
$186$	2.00000	0.146647
$187$	0	0
$188$	−6.00000	−0.437595
$189$	−1.00000	−0.0727393
$190$	−5.00000	−0.362738
$191$	−21.0000	−1.51951	−0.759753	−	0.650211i	$-0.774680\pi$
$191$	−21.0000	−1.51951	−0.759753	+	0.650211i	$0.774680\pi$
$192$	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	$0.545985\pi$
$194$	−10.0000	−0.717958
$195$	−5.00000	−0.358057
$196$	−6.00000	−0.428571
$197$	−24.0000	−1.70993	−0.854965	−	0.518686i	$-0.826421\pi$
$197$	−24.0000	−1.70993	−0.854965	+	0.518686i	$0.826421\pi$
$198$	0	0
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	1.00000	0.0707107
$201$	2.00000	0.141069
$202$	15.0000	1.05540
$203$	3.00000	0.210559
$204$	−3.00000	−0.210042
$205$	−6.00000	−0.419058
$206$	−1.00000	−0.0696733
$207$	0	0
$208$	5.00000	0.346688
$209$	0	0
$210$	1.00000	0.0690066
$211$	5.00000	0.344214	0.172107	−	0.985078i	$-0.444942\pi$
$211$	5.00000	0.344214	0.172107	+	0.985078i	$0.444942\pi$
$212$	0	0
$213$	9.00000	0.616670
$214$	0	0
$215$	−2.00000	−0.136399
$216$	1.00000	0.0680414
$217$	−2.00000	−0.135769
$218$	−16.0000	−1.08366
$219$	14.0000	0.946032
$220$	0	0
$221$	−15.0000	−1.00901
$222$	5.00000	0.335578
$223$	5.00000	0.334825	0.167412	−	0.985887i	$-0.446459\pi$
$223$	5.00000	0.334825	0.167412	+	0.985887i	$0.446459\pi$
$224$	−1.00000	−0.0668153
$225$	1.00000	0.0666667
$226$	18.0000	1.19734
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	5.00000	0.331133
$229$	20.0000	1.32164	0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000	1.32164	0.660819	+	0.750546i	$0.270209\pi$
$230$	0	0
$231$	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	$0.437031\pi$
$234$	5.00000	0.326860
$235$	6.00000	0.391397
$236$	0	0
$237$	14.0000	0.909398
$238$	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
$241$	−7.00000	−0.450910	−0.225455	−	0.974254i	$-0.572387\pi$
$241$	−7.00000	−0.450910	−0.225455	+	0.974254i	$0.572387\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	8.00000	0.512148
$245$	6.00000	0.383326
$246$	6.00000	0.382546
$247$	25.0000	1.59071
$248$	2.00000	0.127000
$249$	−3.00000	−0.190117
$250$	−1.00000	−0.0632456
$251$	−24.0000	−1.51487	−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000	−1.51487	−0.757433	+	0.652913i	$0.773547\pi$
$252$	−1.00000	−0.0629941
$253$	0	0
$254$	−4.00000	−0.250982
$255$	3.00000	0.187867
$256$	1.00000	0.0625000
$257$	−27.0000	−1.68421	−0.842107	−	0.539311i	$-0.818685\pi$
$257$	−27.0000	−1.68421	−0.842107	+	0.539311i	$0.818685\pi$
$258$	2.00000	0.124515
$259$	−5.00000	−0.310685
$260$	−5.00000	−0.310087
$261$	−3.00000	−0.185695
$262$	−12.0000	−0.741362
$263$	18.0000	1.10993	0.554964	−	0.831875i	$-0.312732\pi$
$263$	18.0000	1.10993	0.554964	+	0.831875i	$0.312732\pi$
$264$	0	0
$265$	0	0
$266$	−5.00000	−0.306570
$267$	−12.0000	−0.734388
$268$	2.00000	0.122169
$269$	15.0000	0.914566	0.457283	−	0.889321i	$-0.348823\pi$
$269$	15.0000	0.914566	0.457283	+	0.889321i	$0.348823\pi$
$270$	−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
$273$	−5.00000	−0.302614
$274$	15.0000	0.906183
$275$	0	0
$276$	0	0
$277$	−22.0000	−1.32185	−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000	−1.32185	−0.660926	+	0.750451i	$0.729836\pi$
$278$	23.0000	1.37945
$279$	2.00000	0.119737
$280$	1.00000	0.0597614
$281$	0	0		−	1.00000i	$-0.5\pi$
$281$	0	0			1.00000i	$0.5\pi$
$282$	−6.00000	−0.357295
$283$	−16.0000	−0.951101	−0.475551	−	0.879688i	$-0.657751\pi$
$283$	−16.0000	−0.951101	−0.475551	+	0.879688i	$0.657751\pi$
$284$	9.00000	0.534052
$285$	−5.00000	−0.296174
$286$	0	0
$287$	−6.00000	−0.354169
$288$	1.00000	0.0589256
$289$	−8.00000	−0.470588
$290$	3.00000	0.176166
$291$	−10.0000	−0.586210
$292$	14.0000	0.819288
$293$	−12.0000	−0.701047	−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000	−0.701047	−0.350524	+	0.936554i	$0.613996\pi$
$294$	−6.00000	−0.349927
$295$	0	0
$296$	5.00000	0.290619
$297$	0	0
$298$	−6.00000	−0.347571
$299$	0	0
$300$	1.00000	0.0577350
$301$	−2.00000	−0.115278
$302$	20.0000	1.15087
$303$	15.0000	0.861727
$304$	5.00000	0.286770
$305$	−8.00000	−0.458079
$306$	−3.00000	−0.171499
$307$	−22.0000	−1.25561	−0.627803	−	0.778372i	$-0.716046\pi$
$307$	−22.0000	−1.25561	−0.627803	+	0.778372i	$0.716046\pi$
$308$	0	0
$309$	−1.00000	−0.0568880
$310$	−2.00000	−0.113592
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	5.00000	0.283069
$313$	−34.0000	−1.92179	−0.960897	−	0.276907i	$-0.910691\pi$
$313$	−34.0000	−1.92179	−0.960897	+	0.276907i	$0.910691\pi$
$314$	−13.0000	−0.733632
$315$	1.00000	0.0563436
$316$	14.0000	0.787562
$317$	−12.0000	−0.673987	−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000	−0.673987	−0.336994	+	0.941507i	$0.609410\pi$
$318$	0	0
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	0	0
$322$	0	0
$323$	−15.0000	−0.834622
$324$	1.00000	0.0555556
$325$	5.00000	0.277350
$326$	−16.0000	−0.886158
$327$	−16.0000	−0.884802
$328$	6.00000	0.331295
$329$	6.00000	0.330791
$330$	0	0
$331$	−13.0000	−0.714545	−0.357272	−	0.934000i	$-0.616293\pi$
$331$	−13.0000	−0.714545	−0.357272	+	0.934000i	$0.616293\pi$
$332$	−3.00000	−0.164646
$333$	5.00000	0.273998
$334$	12.0000	0.656611
$335$	−2.00000	−0.109272
$336$	−1.00000	−0.0545545
$337$	14.0000	0.762629	0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000	0.762629	0.381314	+	0.924445i	$0.375472\pi$
$338$	12.0000	0.652714
$339$	18.0000	0.977626
$340$	3.00000	0.162698
$341$	0	0
$342$	5.00000	0.270369
$343$	13.0000	0.701934
$344$	2.00000	0.107833
$345$	0	0
$346$	12.0000	0.645124
$347$	−21.0000	−1.12734	−0.563670	−	0.826000i	$-0.690611\pi$
$347$	−21.0000	−1.12734	−0.563670	+	0.826000i	$0.690611\pi$
$348$	−3.00000	−0.160817
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	−1.00000	−0.0534522
$351$	5.00000	0.266880
$352$	0	0
$353$	−18.0000	−0.958043	−0.479022	−	0.877803i	$-0.659008\pi$
$353$	−18.0000	−0.958043	−0.479022	+	0.877803i	$0.659008\pi$
$354$	0	0
$355$	−9.00000	−0.477670
$356$	−12.0000	−0.635999
$357$	3.00000	0.158777
$358$	12.0000	0.634220
$359$	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
$361$	6.00000	0.315789
$362$	−16.0000	−0.840941
$363$	0	0
$364$	−5.00000	−0.262071
$365$	−14.0000	−0.732793
$366$	8.00000	0.418167
$367$	23.0000	1.20059	0.600295	−	0.799779i	$-0.295050\pi$
$367$	23.0000	1.20059	0.600295	+	0.799779i	$0.295050\pi$
$368$	0	0
$369$	6.00000	0.312348
$370$	−5.00000	−0.259938
$371$	0	0
$372$	2.00000	0.103695
$373$	−13.0000	−0.673114	−0.336557	−	0.941663i	$-0.609263\pi$
$373$	−13.0000	−0.673114	−0.336557	+	0.941663i	$0.609263\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	−6.00000	−0.309426
$377$	−15.0000	−0.772539
$378$	−1.00000	−0.0514344
$379$	5.00000	0.256833	0.128416	−	0.991720i	$-0.459011\pi$
$379$	5.00000	0.256833	0.128416	+	0.991720i	$0.459011\pi$
$380$	−5.00000	−0.256495
$381$	−4.00000	−0.204926
$382$	−21.0000	−1.07445
$383$	−6.00000	−0.306586	−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000	−0.306586	−0.153293	+	0.988181i	$0.548988\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−4.00000	−0.203595
$387$	2.00000	0.101666
$388$	−10.0000	−0.507673
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	−5.00000	−0.253185
$391$	0	0
$392$	−6.00000	−0.303046
$393$	−12.0000	−0.605320
$394$	−24.0000	−1.20910
$395$	−14.0000	−0.704416
$396$	0	0
$397$	29.0000	1.45547	0.727734	−	0.685859i	$-0.240573\pi$
$397$	29.0000	1.45547	0.727734	+	0.685859i	$0.240573\pi$
$398$	−16.0000	−0.802008
$399$	−5.00000	−0.250313
$400$	1.00000	0.0500000
$401$	−30.0000	−1.49813	−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000	−1.49813	−0.749064	+	0.662497i	$0.769497\pi$
$402$	2.00000	0.0997509
$403$	10.0000	0.498135
$404$	15.0000	0.746278
$405$	−1.00000	−0.0496904
$406$	3.00000	0.148888
$407$	0	0
$408$	−3.00000	−0.148522
$409$	14.0000	0.692255	0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000	0.692255	0.346128	+	0.938187i	$0.387496\pi$
$410$	−6.00000	−0.296319
$411$	15.0000	0.739895
$412$	−1.00000	−0.0492665
$413$	0	0
$414$	0	0
$415$	3.00000	0.147264
$416$	5.00000	0.245145
$417$	23.0000	1.12631
$418$	0	0
$419$	−30.0000	−1.46560	−0.732798	−	0.680446i	$-0.761786\pi$
$419$	−30.0000	−1.46560	−0.732798	+	0.680446i	$0.761786\pi$
$420$	1.00000	0.0487950
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	5.00000	0.243396
$423$	−6.00000	−0.291730
$424$	0	0
$425$	−3.00000	−0.145521
$426$	9.00000	0.436051
$427$	−8.00000	−0.387147
$428$	0	0
$429$	0	0
$430$	−2.00000	−0.0964486
$431$	−15.0000	−0.722525	−0.361262	−	0.932464i	$-0.617654\pi$
$431$	−15.0000	−0.722525	−0.361262	+	0.932464i	$0.617654\pi$
$432$	1.00000	0.0481125
$433$	−16.0000	−0.768911	−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000	−0.768911	−0.384455	+	0.923144i	$0.625611\pi$
$434$	−2.00000	−0.0960031
$435$	3.00000	0.143839
$436$	−16.0000	−0.766261
$437$	0	0
$438$	14.0000	0.668946
$439$	26.0000	1.24091	0.620456	−	0.784241i	$-0.286947\pi$
$439$	26.0000	1.24091	0.620456	+	0.784241i	$0.286947\pi$
$440$	0	0
$441$	−6.00000	−0.285714
$442$	−15.0000	−0.713477
$443$	−9.00000	−0.427603	−0.213801	−	0.976877i	$-0.568585\pi$
$443$	−9.00000	−0.427603	−0.213801	+	0.976877i	$0.568585\pi$
$444$	5.00000	0.237289
$445$	12.0000	0.568855
$446$	5.00000	0.236757
$447$	−6.00000	−0.283790
$448$	−1.00000	−0.0472456
$449$	30.0000	1.41579	0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000	1.41579	0.707894	+	0.706319i	$0.249646\pi$
$450$	1.00000	0.0471405
$451$	0	0
$452$	18.0000	0.846649
$453$	20.0000	0.939682
$454$	0	0
$455$	5.00000	0.234404
$456$	5.00000	0.234146
$457$	8.00000	0.374224	0.187112	−	0.982339i	$-0.440087\pi$
$457$	8.00000	0.374224	0.187112	+	0.982339i	$0.440087\pi$
$458$	20.0000	0.934539
$459$	−3.00000	−0.140028
$460$	0	0
$461$	−3.00000	−0.139724	−0.0698620	−	0.997557i	$-0.522256\pi$
$461$	−3.00000	−0.139724	−0.0698620	+	0.997557i	$0.522256\pi$
$462$	0	0
$463$	32.0000	1.48717	0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000	1.48717	0.743583	+	0.668644i	$0.233125\pi$
$464$	−3.00000	−0.139272
$465$	−2.00000	−0.0927478
$466$	6.00000	0.277945
$467$	33.0000	1.52706	0.763529	−	0.645774i	$-0.223465\pi$
$467$	33.0000	1.52706	0.763529	+	0.645774i	$0.223465\pi$
$468$	5.00000	0.231125
$469$	−2.00000	−0.0923514
$470$	6.00000	0.276759
$471$	−13.0000	−0.599008
$472$	0	0
$473$	0	0
$474$	14.0000	0.643041
$475$	5.00000	0.229416
$476$	3.00000	0.137505
$477$	0	0
$478$	−21.0000	−0.960518
$479$	−21.0000	−0.959514	−0.479757	−	0.877401i	$-0.659275\pi$
$479$	−21.0000	−0.959514	−0.479757	+	0.877401i	$0.659275\pi$
$480$	−1.00000	−0.0456435
$481$	25.0000	1.13990
$482$	−7.00000	−0.318841
$483$	0	0
$484$	0	0
$485$	10.0000	0.454077
$486$	1.00000	0.0453609
$487$	−25.0000	−1.13286	−0.566429	−	0.824110i	$-0.691675\pi$
$487$	−25.0000	−1.13286	−0.566429	+	0.824110i	$0.691675\pi$
$488$	8.00000	0.362143
$489$	−16.0000	−0.723545
$490$	6.00000	0.271052
$491$	18.0000	0.812329	0.406164	−	0.913800i	$-0.366866\pi$
$491$	18.0000	0.812329	0.406164	+	0.913800i	$0.366866\pi$
$492$	6.00000	0.270501
$493$	9.00000	0.405340
$494$	25.0000	1.12480
$495$	0	0
$496$	2.00000	0.0898027
$497$	−9.00000	−0.403705
$498$	−3.00000	−0.134433
$499$	5.00000	0.223831	0.111915	−	0.993718i	$-0.464301\pi$
$499$	5.00000	0.223831	0.111915	+	0.993718i	$0.464301\pi$
$500$	−1.00000	−0.0447214
$501$	12.0000	0.536120
$502$	−24.0000	−1.07117
$503$	−24.0000	−1.07011	−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000	−1.07011	−0.535054	+	0.844818i	$0.679709\pi$
$504$	−1.00000	−0.0445435
$505$	−15.0000	−0.667491
$506$	0	0
$507$	12.0000	0.532939
$508$	−4.00000	−0.177471
$509$	18.0000	0.797836	0.398918	−	0.916987i	$-0.369386\pi$
$509$	18.0000	0.797836	0.398918	+	0.916987i	$0.369386\pi$
$510$	3.00000	0.132842
$511$	−14.0000	−0.619324
$512$	1.00000	0.0441942
$513$	5.00000	0.220755
$514$	−27.0000	−1.19092
$515$	1.00000	0.0440653
$516$	2.00000	0.0880451
$517$	0	0
$518$	−5.00000	−0.219687
$519$	12.0000	0.526742
$520$	−5.00000	−0.219265
$521$	−36.0000	−1.57719	−0.788594	−	0.614914i	$-0.789191\pi$
$521$	−36.0000	−1.57719	−0.788594	+	0.614914i	$0.789191\pi$
$522$	−3.00000	−0.131306
$523$	−16.0000	−0.699631	−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000	−0.699631	−0.349816	+	0.936819i	$0.613756\pi$
$524$	−12.0000	−0.524222
$525$	−1.00000	−0.0436436
$526$	18.0000	0.784837
$527$	−6.00000	−0.261364
$528$	0	0
$529$	−23.0000	−1.00000
$530$	0	0
$531$	0	0
$532$	−5.00000	−0.216777
$533$	30.0000	1.29944
$534$	−12.0000	−0.519291
$535$	0	0
$536$	2.00000	0.0863868
$537$	12.0000	0.517838
$538$	15.0000	0.646696
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	−10.0000	−0.429934	−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000	−0.429934	−0.214967	+	0.976621i	$0.568964\pi$
$542$	2.00000	0.0859074
$543$	−16.0000	−0.686626
$544$	−3.00000	−0.128624
$545$	16.0000	0.685365
$546$	−5.00000	−0.213980
$547$	−46.0000	−1.96682	−0.983409	−	0.181402i	$-0.941936\pi$
$547$	−46.0000	−1.96682	−0.983409	+	0.181402i	$0.941936\pi$
$548$	15.0000	0.640768
$549$	8.00000	0.341432
$550$	0	0
$551$	−15.0000	−0.639021
$552$	0	0
$553$	−14.0000	−0.595341
$554$	−22.0000	−0.934690
$555$	−5.00000	−0.212238
$556$	23.0000	0.975417
$557$	−6.00000	−0.254228	−0.127114	−	0.991888i	$-0.540571\pi$
$557$	−6.00000	−0.254228	−0.127114	+	0.991888i	$0.540571\pi$
$558$	2.00000	0.0846668
$559$	10.0000	0.422955
$560$	1.00000	0.0422577
$561$	0	0
$562$	0	0
$563$	−9.00000	−0.379305	−0.189652	−	0.981851i	$-0.560736\pi$
$563$	−9.00000	−0.379305	−0.189652	+	0.981851i	$0.560736\pi$
$564$	−6.00000	−0.252646
$565$	−18.0000	−0.757266
$566$	−16.0000	−0.672530
$567$	−1.00000	−0.0419961
$568$	9.00000	0.377632
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	−5.00000	−0.209427
$571$	32.0000	1.33916	0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000	1.33916	0.669579	+	0.742741i	$0.266474\pi$
$572$	0	0
$573$	−21.0000	−0.877288
$574$	−6.00000	−0.250435
$575$	0	0
$576$	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
$582$	−10.0000	−0.414513
$583$	0	0
$584$	14.0000	0.579324
$585$	−5.00000	−0.206725
$586$	−12.0000	−0.495715
$587$	−33.0000	−1.36206	−0.681028	−	0.732257i	$-0.738467\pi$
$587$	−33.0000	−1.36206	−0.681028	+	0.732257i	$0.738467\pi$
$588$	−6.00000	−0.247436
$589$	10.0000	0.412043
$590$	0	0
$591$	−24.0000	−0.987228
$592$	5.00000	0.205499
$593$	30.0000	1.23195	0.615976	−	0.787765i	$-0.288762\pi$
$593$	30.0000	1.23195	0.615976	+	0.787765i	$0.288762\pi$
$594$	0	0
$595$	−3.00000	−0.122988
$596$	−6.00000	−0.245770
$597$	−16.0000	−0.654836
$598$	0	0
$599$	−24.0000	−0.980613	−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000	−0.980613	−0.490307	+	0.871550i	$0.663115\pi$
$600$	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	$0.565379\pi$
$602$	−2.00000	−0.0815139
$603$	2.00000	0.0814463
$604$	20.0000	0.813788
$605$	0	0
$606$	15.0000	0.609333
$607$	5.00000	0.202944	0.101472	−	0.994838i	$-0.467645\pi$
$607$	5.00000	0.202944	0.101472	+	0.994838i	$0.467645\pi$
$608$	5.00000	0.202777
$609$	3.00000	0.121566
$610$	−8.00000	−0.323911
$611$	−30.0000	−1.21367
$612$	−3.00000	−0.121268
$613$	5.00000	0.201948	0.100974	−	0.994889i	$-0.467804\pi$
$613$	5.00000	0.201948	0.100974	+	0.994889i	$0.467804\pi$
$614$	−22.0000	−0.887848
$615$	−6.00000	−0.241943
$616$	0	0
$617$	15.0000	0.603877	0.301939	−	0.953327i	$-0.402366\pi$
$617$	15.0000	0.603877	0.301939	+	0.953327i	$0.402366\pi$
$618$	−1.00000	−0.0402259
$619$	29.0000	1.16561	0.582804	−	0.812613i	$-0.301955\pi$
$619$	29.0000	1.16561	0.582804	+	0.812613i	$0.301955\pi$
$620$	−2.00000	−0.0803219
$621$	0	0
$622$	0	0
$623$	12.0000	0.480770
$624$	5.00000	0.200160
$625$	1.00000	0.0400000
$626$	−34.0000	−1.35891
$627$	0	0
$628$	−13.0000	−0.518756
$629$	−15.0000	−0.598089
$630$	1.00000	0.0398410
$631$	−4.00000	−0.159237	−0.0796187	−	0.996825i	$-0.525370\pi$
$631$	−4.00000	−0.159237	−0.0796187	+	0.996825i	$0.525370\pi$
$632$	14.0000	0.556890
$633$	5.00000	0.198732
$634$	−12.0000	−0.476581
$635$	4.00000	0.158735
$636$	0	0
$637$	−30.0000	−1.18864
$638$	0	0
$639$	9.00000	0.356034
$640$	−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	$0.188654\pi$
$642$	0	0
$643$	−16.0000	−0.630978	−0.315489	−	0.948929i	$-0.602169\pi$
$643$	−16.0000	−0.630978	−0.315489	+	0.948929i	$0.602169\pi$
$644$	0	0
$645$	−2.00000	−0.0787499
$646$	−15.0000	−0.590167
$647$	36.0000	1.41531	0.707653	−	0.706560i	$-0.249754\pi$
$647$	36.0000	1.41531	0.707653	+	0.706560i	$0.249754\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	5.00000	0.196116
$651$	−2.00000	−0.0783862
$652$	−16.0000	−0.626608
$653$	−30.0000	−1.17399	−0.586995	−	0.809590i	$-0.699689\pi$
$653$	−30.0000	−1.17399	−0.586995	+	0.809590i	$0.699689\pi$
$654$	−16.0000	−0.625650
$655$	12.0000	0.468879
$656$	6.00000	0.234261
$657$	14.0000	0.546192
$658$	6.00000	0.233904
$659$	18.0000	0.701180	0.350590	−	0.936529i	$-0.385981\pi$
$659$	18.0000	0.701180	0.350590	+	0.936529i	$0.385981\pi$
$660$	0	0
$661$	26.0000	1.01128	0.505641	−	0.862744i	$-0.331256\pi$
$661$	26.0000	1.01128	0.505641	+	0.862744i	$0.331256\pi$
$662$	−13.0000	−0.505259
$663$	−15.0000	−0.582552
$664$	−3.00000	−0.116423
$665$	5.00000	0.193892
$666$	5.00000	0.193746
$667$	0	0
$668$	12.0000	0.464294
$669$	5.00000	0.193311
$670$	−2.00000	−0.0772667
$671$	0	0
$672$	−1.00000	−0.0385758
$673$	32.0000	1.23351	0.616755	−	0.787155i	$-0.288447\pi$
$673$	32.0000	1.23351	0.616755	+	0.787155i	$0.288447\pi$
$674$	14.0000	0.539260
$675$	1.00000	0.0384900
$676$	12.0000	0.461538
$677$	30.0000	1.15299	0.576497	−	0.817099i	$-0.304419\pi$
$677$	30.0000	1.15299	0.576497	+	0.817099i	$0.304419\pi$
$678$	18.0000	0.691286
$679$	10.0000	0.383765
$680$	3.00000	0.115045
$681$	0	0
$682$	0	0
$683$	33.0000	1.26271	0.631355	−	0.775494i	$-0.282499\pi$
$683$	33.0000	1.26271	0.631355	+	0.775494i	$0.282499\pi$
$684$	5.00000	0.191180
$685$	−15.0000	−0.573121
$686$	13.0000	0.496342
$687$	20.0000	0.763048
$688$	2.00000	0.0762493
$689$	0	0
$690$	0	0
$691$	29.0000	1.10321	0.551606	−	0.834105i	$-0.314015\pi$
$691$	29.0000	1.10321	0.551606	+	0.834105i	$0.314015\pi$
$692$	12.0000	0.456172
$693$	0	0
$694$	−21.0000	−0.797149
$695$	−23.0000	−0.872440
$696$	−3.00000	−0.113715
$697$	−18.0000	−0.681799
$698$	2.00000	0.0757011
$699$	6.00000	0.226941
$700$	−1.00000	−0.0377964
$701$	−3.00000	−0.113308	−0.0566542	−	0.998394i	$-0.518043\pi$
$701$	−3.00000	−0.113308	−0.0566542	+	0.998394i	$0.518043\pi$
$702$	5.00000	0.188713
$703$	25.0000	0.942893
$704$	0	0
$705$	6.00000	0.225973
$706$	−18.0000	−0.677439
$707$	−15.0000	−0.564133
$708$	0	0
$709$	−46.0000	−1.72757	−0.863783	−	0.503864i	$-0.831911\pi$
$709$	−46.0000	−1.72757	−0.863783	+	0.503864i	$0.831911\pi$
$710$	−9.00000	−0.337764
$711$	14.0000	0.525041
$712$	−12.0000	−0.449719
$713$	0	0
$714$	3.00000	0.112272
$715$	0	0
$716$	12.0000	0.448461
$717$	−21.0000	−0.784259
$718$	24.0000	0.895672
$719$	−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
$721$	1.00000	0.0372419
$722$	6.00000	0.223297
$723$	−7.00000	−0.260333
$724$	−16.0000	−0.594635
$725$	−3.00000	−0.111417
$726$	0	0
$727$	53.0000	1.96566	0.982831	−	0.184510i	$-0.0590699\pi$
$727$	53.0000	1.96566	0.982831	+	0.184510i	$0.0590699\pi$
$728$	−5.00000	−0.185312
$729$	1.00000	0.0370370
$730$	−14.0000	−0.518163
$731$	−6.00000	−0.221918
$732$	8.00000	0.295689
$733$	−22.0000	−0.812589	−0.406294	−	0.913742i	$-0.633179\pi$
$733$	−22.0000	−0.812589	−0.406294	+	0.913742i	$0.633179\pi$
$734$	23.0000	0.848945
$735$	6.00000	0.221313
$736$	0	0
$737$	0	0
$738$	6.00000	0.220863
$739$	−25.0000	−0.919640	−0.459820	−	0.888012i	$-0.652086\pi$
$739$	−25.0000	−0.919640	−0.459820	+	0.888012i	$0.652086\pi$
$740$	−5.00000	−0.183804
$741$	25.0000	0.918398
$742$	0	0
$743$	−36.0000	−1.32071	−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000	−1.32071	−0.660356	+	0.750953i	$0.729595\pi$
$744$	2.00000	0.0733236
$745$	6.00000	0.219823
$746$	−13.0000	−0.475964
$747$	−3.00000	−0.109764
$748$	0	0
$749$	0	0
$750$	−1.00000	−0.0365148
$751$	−22.0000	−0.802791	−0.401396	−	0.915905i	$-0.631475\pi$
$751$	−22.0000	−0.802791	−0.401396	+	0.915905i	$0.631475\pi$
$752$	−6.00000	−0.218797
$753$	−24.0000	−0.874609
$754$	−15.0000	−0.546268
$755$	−20.0000	−0.727875
$756$	−1.00000	−0.0363696
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	5.00000	0.181608
$759$	0	0
$760$	−5.00000	−0.181369
$761$	−12.0000	−0.435000	−0.217500	−	0.976060i	$-0.569790\pi$
$761$	−12.0000	−0.435000	−0.217500	+	0.976060i	$0.569790\pi$
$762$	−4.00000	−0.144905
$763$	16.0000	0.579239
$764$	−21.0000	−0.759753
$765$	3.00000	0.108465
$766$	−6.00000	−0.216789
$767$	0	0
$768$	1.00000	0.0360844
$769$	−1.00000	−0.0360609	−0.0180305	−	0.999837i	$-0.505740\pi$
$769$	−1.00000	−0.0360609	−0.0180305	+	0.999837i	$0.505740\pi$
$770$	0	0
$771$	−27.0000	−0.972381
$772$	−4.00000	−0.143963
$773$	24.0000	0.863220	0.431610	−	0.902060i	$-0.357946\pi$
$773$	24.0000	0.863220	0.431610	+	0.902060i	$0.357946\pi$
$774$	2.00000	0.0718885
$775$	2.00000	0.0718421
$776$	−10.0000	−0.358979
$777$	−5.00000	−0.179374
$778$	6.00000	0.215110
$779$	30.0000	1.07486
$780$	−5.00000	−0.179029
$781$	0	0
$782$	0	0
$783$	−3.00000	−0.107211
$784$	−6.00000	−0.214286
$785$	13.0000	0.463990
$786$	−12.0000	−0.428026
$787$	−28.0000	−0.998092	−0.499046	−	0.866575i	$-0.666316\pi$
$787$	−28.0000	−0.998092	−0.499046	+	0.866575i	$0.666316\pi$
$788$	−24.0000	−0.854965
$789$	18.0000	0.640817
$790$	−14.0000	−0.498098
$791$	−18.0000	−0.640006
$792$	0	0
$793$	40.0000	1.42044
$794$	29.0000	1.02917
$795$	0	0
$796$	−16.0000	−0.567105
$797$	−12.0000	−0.425062	−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000	−0.425062	−0.212531	+	0.977154i	$0.568171\pi$
$798$	−5.00000	−0.176998
$799$	18.0000	0.636794
$800$	1.00000	0.0353553
$801$	−12.0000	−0.423999
$802$	−30.0000	−1.05934
$803$	0	0
$804$	2.00000	0.0705346
$805$	0	0
$806$	10.0000	0.352235
$807$	15.0000	0.528025
$808$	15.0000	0.527698
$809$	−18.0000	−0.632846	−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000	−0.632846	−0.316423	+	0.948618i	$0.602482\pi$
$810$	−1.00000	−0.0351364
$811$	29.0000	1.01833	0.509164	−	0.860670i	$-0.329955\pi$
$811$	29.0000	1.01833	0.509164	+	0.860670i	$0.329955\pi$
$812$	3.00000	0.105279
$813$	2.00000	0.0701431
$814$	0	0
$815$	16.0000	0.560456
$816$	−3.00000	−0.105021
$817$	10.0000	0.349856
$818$	14.0000	0.489499
$819$	−5.00000	−0.174714
$820$	−6.00000	−0.209529
$821$	−18.0000	−0.628204	−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000	−0.628204	−0.314102	+	0.949389i	$0.601703\pi$
$822$	15.0000	0.523185
$823$	41.0000	1.42917	0.714585	−	0.699549i	$-0.246616\pi$
$823$	41.0000	1.42917	0.714585	+	0.699549i	$0.246616\pi$
$824$	−1.00000	−0.0348367
$825$	0	0
$826$	0	0
$827$	−33.0000	−1.14752	−0.573761	−	0.819023i	$-0.694516\pi$
$827$	−33.0000	−1.14752	−0.573761	+	0.819023i	$0.694516\pi$
$828$	0	0
$829$	44.0000	1.52818	0.764092	−	0.645108i	$-0.223188\pi$
$829$	44.0000	1.52818	0.764092	+	0.645108i	$0.223188\pi$
$830$	3.00000	0.104132
$831$	−22.0000	−0.763172
$832$	5.00000	0.173344
$833$	18.0000	0.623663
$834$	23.0000	0.796425
$835$	−12.0000	−0.415277
$836$	0	0
$837$	2.00000	0.0691301
$838$	−30.0000	−1.03633
$839$	45.0000	1.55357	0.776786	−	0.629764i	$-0.216849\pi$
$839$	45.0000	1.55357	0.776786	+	0.629764i	$0.216849\pi$
$840$	1.00000	0.0345033
$841$	−20.0000	−0.689655
$842$	−10.0000	−0.344623
$843$	0	0
$844$	5.00000	0.172107
$845$	−12.0000	−0.412813
$846$	−6.00000	−0.206284
$847$	0	0
$848$	0	0
$849$	−16.0000	−0.549119
$850$	−3.00000	−0.102899
$851$	0	0
$852$	9.00000	0.308335
$853$	−31.0000	−1.06142	−0.530710	−	0.847554i	$-0.678075\pi$
$853$	−31.0000	−1.06142	−0.530710	+	0.847554i	$0.678075\pi$
$854$	−8.00000	−0.273754
$855$	−5.00000	−0.170996
$856$	0	0
$857$	−39.0000	−1.33221	−0.666107	−	0.745856i	$-0.732041\pi$
$857$	−39.0000	−1.33221	−0.666107	+	0.745856i	$0.732041\pi$
$858$	0	0
$859$	44.0000	1.50126	0.750630	−	0.660722i	$-0.229750\pi$
$859$	44.0000	1.50126	0.750630	+	0.660722i	$0.229750\pi$
$860$	−2.00000	−0.0681994
$861$	−6.00000	−0.204479
$862$	−15.0000	−0.510902
$863$	42.0000	1.42970	0.714848	−	0.699280i	$-0.246496\pi$
$863$	42.0000	1.42970	0.714848	+	0.699280i	$0.246496\pi$
$864$	1.00000	0.0340207
$865$	−12.0000	−0.408012
$866$	−16.0000	−0.543702
$867$	−8.00000	−0.271694
$868$	−2.00000	−0.0678844
$869$	0	0
$870$	3.00000	0.101710
$871$	10.0000	0.338837
$872$	−16.0000	−0.541828
$873$	−10.0000	−0.338449
$874$	0	0
$875$	1.00000	0.0338062
$876$	14.0000	0.473016
$877$	−25.0000	−0.844190	−0.422095	−	0.906552i	$-0.638705\pi$
$877$	−25.0000	−0.844190	−0.422095	+	0.906552i	$0.638705\pi$
$878$	26.0000	0.877457
$879$	−12.0000	−0.404750
$880$	0	0
$881$	−6.00000	−0.202145	−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000	−0.202145	−0.101073	+	0.994879i	$0.532227\pi$
$882$	−6.00000	−0.202031
$883$	2.00000	0.0673054	0.0336527	−	0.999434i	$-0.489286\pi$
$883$	2.00000	0.0673054	0.0336527	+	0.999434i	$0.489286\pi$
$884$	−15.0000	−0.504505
$885$	0	0
$886$	−9.00000	−0.302361
$887$	−48.0000	−1.61168	−0.805841	−	0.592132i	$-0.798286\pi$
$887$	−48.0000	−1.61168	−0.805841	+	0.592132i	$0.798286\pi$
$888$	5.00000	0.167789
$889$	4.00000	0.134156
$890$	12.0000	0.402241
$891$	0	0
$892$	5.00000	0.167412
$893$	−30.0000	−1.00391
$894$	−6.00000	−0.200670
$895$	−12.0000	−0.401116
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	30.0000	1.00111
$899$	−6.00000	−0.200111
$900$	1.00000	0.0333333
$901$	0	0
$902$	0	0
$903$	−2.00000	−0.0665558
$904$	18.0000	0.598671
$905$	16.0000	0.531858
$906$	20.0000	0.664455
$907$	−22.0000	−0.730498	−0.365249	−	0.930910i	$-0.619016\pi$
$907$	−22.0000	−0.730498	−0.365249	+	0.930910i	$0.619016\pi$
$908$	0	0
$909$	15.0000	0.497519
$910$	5.00000	0.165748
$911$	−15.0000	−0.496972	−0.248486	−	0.968635i	$-0.579933\pi$
$911$	−15.0000	−0.496972	−0.248486	+	0.968635i	$0.579933\pi$
$912$	5.00000	0.165567
$913$	0	0
$914$	8.00000	0.264616
$915$	−8.00000	−0.264472
$916$	20.0000	0.660819
$917$	12.0000	0.396275
$918$	−3.00000	−0.0990148
$919$	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
$921$	−22.0000	−0.724925
$922$	−3.00000	−0.0987997
$923$	45.0000	1.48119
$924$	0	0
$925$	5.00000	0.164399
$926$	32.0000	1.05159
$927$	−1.00000	−0.0328443
$928$	−3.00000	−0.0984798
$929$	−24.0000	−0.787414	−0.393707	−	0.919236i	$-0.628808\pi$
$929$	−24.0000	−0.787414	−0.393707	+	0.919236i	$0.628808\pi$
$930$	−2.00000	−0.0655826
$931$	−30.0000	−0.983210
$932$	6.00000	0.196537
$933$	0	0
$934$	33.0000	1.07979
$935$	0	0
$936$	5.00000	0.163430
$937$	2.00000	0.0653372	0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000	0.0653372	0.0326686	+	0.999466i	$0.489599\pi$
$938$	−2.00000	−0.0653023
$939$	−34.0000	−1.10955
$940$	6.00000	0.195698
$941$	−3.00000	−0.0977972	−0.0488986	−	0.998804i	$-0.515571\pi$
$941$	−3.00000	−0.0977972	−0.0488986	+	0.998804i	$0.515571\pi$
$942$	−13.0000	−0.423563
$943$	0	0
$944$	0	0
$945$	1.00000	0.0325300
$946$	0	0
$947$	27.0000	0.877382	0.438691	−	0.898638i	$-0.355442\pi$
$947$	27.0000	0.877382	0.438691	+	0.898638i	$0.355442\pi$
$948$	14.0000	0.454699
$949$	70.0000	2.27230
$950$	5.00000	0.162221
$951$	−12.0000	−0.389127
$952$	3.00000	0.0972306
$953$	−42.0000	−1.36051	−0.680257	−	0.732974i	$-0.738132\pi$
$953$	−42.0000	−1.36051	−0.680257	+	0.732974i	$0.738132\pi$
$954$	0	0
$955$	21.0000	0.679544
$956$	−21.0000	−0.679189
$957$	0	0
$958$	−21.0000	−0.678479
$959$	−15.0000	−0.484375
$960$	−1.00000	−0.0322749
$961$	−27.0000	−0.870968
$962$	25.0000	0.806032
$963$	0	0
$964$	−7.00000	−0.225455
$965$	4.00000	0.128765
$966$	0	0
$967$	−40.0000	−1.28631	−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000	−1.28631	−0.643157	+	0.765735i	$0.722376\pi$
$968$	0	0
$969$	−15.0000	−0.481869
$970$	10.0000	0.321081
$971$	−60.0000	−1.92549	−0.962746	−	0.270408i	$-0.912841\pi$
$971$	−60.0000	−1.92549	−0.962746	+	0.270408i	$0.912841\pi$
$972$	1.00000	0.0320750
$973$	−23.0000	−0.737346
$974$	−25.0000	−0.801052
$975$	5.00000	0.160128
$976$	8.00000	0.256074
$977$	−54.0000	−1.72761	−0.863807	−	0.503824i	$-0.831926\pi$
$977$	−54.0000	−1.72761	−0.863807	+	0.503824i	$0.831926\pi$
$978$	−16.0000	−0.511624
$979$	0	0
$980$	6.00000	0.191663
$981$	−16.0000	−0.510841
$982$	18.0000	0.574403
$983$	42.0000	1.33959	0.669796	−	0.742545i	$-0.266382\pi$
$983$	42.0000	1.33959	0.669796	+	0.742545i	$0.266382\pi$
$984$	6.00000	0.191273
$985$	24.0000	0.764704
$986$	9.00000	0.286618
$987$	6.00000	0.190982
$988$	25.0000	0.795356
$989$	0	0
$990$	0	0
$991$	50.0000	1.58830	0.794151	−	0.607720i	$-0.207916\pi$
$991$	50.0000	1.58830	0.794151	+	0.607720i	$0.207916\pi$
$992$	2.00000	0.0635001
$993$	−13.0000	−0.412543
$994$	−9.00000	−0.285463
$995$	16.0000	0.507234
$996$	−3.00000	−0.0950586
$997$	23.0000	0.728417	0.364209	−	0.931317i	$-0.381339\pi$
$997$	23.0000	0.728417	0.364209	+	0.931317i	$0.381339\pi$
$998$	5.00000	0.158272
$999$	5.00000	0.158193

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3630.2.a.h.1.1	✓	1	11.10	odd	2
3630.2.a.u.1.1	yes	1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3630.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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