LMFDB - Embedded newform 3630.2.a.i.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)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{12} +4.00000 q^{13} -2.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +6.00000 q^{17} -1.00000 q^{18} -2.00000 q^{19} -1.00000 q^{20} +2.00000 q^{21} +4.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} -4.00000 q^{26} +1.00000 q^{27} +2.00000 q^{28} +2.00000 q^{29} +1.00000 q^{30} -8.00000 q^{31} -1.00000 q^{32} -6.00000 q^{34} -2.00000 q^{35} +1.00000 q^{36} +10.0000 q^{37} +2.00000 q^{38} +4.00000 q^{39} +1.00000 q^{40} -2.00000 q^{41} -2.00000 q^{42} +6.00000 q^{43} -1.00000 q^{45} -4.00000 q^{46} -8.00000 q^{47} +1.00000 q^{48} -3.00000 q^{49} -1.00000 q^{50} +6.00000 q^{51} +4.00000 q^{52} -10.0000 q^{53} -1.00000 q^{54} -2.00000 q^{56} -2.00000 q^{57} -2.00000 q^{58} -1.00000 q^{60} +12.0000 q^{61} +8.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} -4.00000 q^{65} -4.00000 q^{67} +6.00000 q^{68} +4.00000 q^{69} +2.00000 q^{70} -8.00000 q^{71} -1.00000 q^{72} +8.00000 q^{73} -10.0000 q^{74} +1.00000 q^{75} -2.00000 q^{76} -4.00000 q^{78} +6.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +2.00000 q^{82} -8.00000 q^{83} +2.00000 q^{84} -6.00000 q^{85} -6.00000 q^{86} +2.00000 q^{87} -6.00000 q^{89} +1.00000 q^{90} +8.00000 q^{91} +4.00000 q^{92} -8.00000 q^{93} +8.00000 q^{94} +2.00000 q^{95} -1.00000 q^{96} +10.0000 q^{97} +3.00000 q^{98} +O(q^{100})\)

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
$7$	2.00000	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	−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
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	−2.00000	−0.534522
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	−1.00000	−0.235702
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	−1.00000	−0.223607
$21$	2.00000	0.436436
$22$	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
$26$	−4.00000	−0.784465
$27$	1.00000	0.192450
$28$	2.00000	0.377964
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	1.00000	0.182574
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−6.00000	−1.02899
$35$	−2.00000	−0.338062
$36$	1.00000	0.166667
$37$	10.0000	1.64399	0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000	1.64399	0.821995	+	0.569495i	$0.192861\pi$
$38$	2.00000	0.324443
$39$	4.00000	0.640513
$40$	1.00000	0.158114
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	−2.00000	−0.308607
$43$	6.00000	0.914991	0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000	0.914991	0.457496	+	0.889212i	$0.348747\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	−4.00000	−0.589768
$47$	−8.00000	−1.16692	−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000	−1.16692	−0.583460	+	0.812142i	$0.698301\pi$
$48$	1.00000	0.144338
$49$	−3.00000	−0.428571
$50$	−1.00000	−0.141421
$51$	6.00000	0.840168
$52$	4.00000	0.554700
$53$	−10.0000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−2.00000	−0.267261
$57$	−2.00000	−0.264906
$58$	−2.00000	−0.262613
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	−1.00000	−0.129099
$61$	12.0000	1.53644	0.768221	−	0.640184i	$-0.221142\pi$
$61$	12.0000	1.53644	0.768221	+	0.640184i	$0.221142\pi$
$62$	8.00000	1.01600
$63$	2.00000	0.251976
$64$	1.00000	0.125000
$65$	−4.00000	−0.496139
$66$	0	0
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	6.00000	0.727607
$69$	4.00000	0.481543
$70$	2.00000	0.239046
$71$	−8.00000	−0.949425	−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000	−0.949425	−0.474713	+	0.880141i	$0.657448\pi$
$72$	−1.00000	−0.117851
$73$	8.00000	0.936329	0.468165	−	0.883641i	$-0.344915\pi$
$73$	8.00000	0.936329	0.468165	+	0.883641i	$0.344915\pi$
$74$	−10.0000	−1.16248
$75$	1.00000	0.115470
$76$	−2.00000	−0.229416
$77$	0	0
$78$	−4.00000	−0.452911
$79$	6.00000	0.675053	0.337526	−	0.941316i	$-0.390410\pi$
$79$	6.00000	0.675053	0.337526	+	0.941316i	$0.390410\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	2.00000	0.220863
$83$	−8.00000	−0.878114	−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000	−0.878114	−0.439057	+	0.898459i	$0.644687\pi$
$84$	2.00000	0.218218
$85$	−6.00000	−0.650791
$86$	−6.00000	−0.646997
$87$	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
$92$	4.00000	0.417029
$93$	−8.00000	−0.829561
$94$	8.00000	0.825137
$95$	2.00000	0.205196
$96$	−1.00000	−0.102062
$97$	10.0000	1.01535	0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000	1.01535	0.507673	+	0.861550i	$0.330506\pi$
$98$	3.00000	0.303046
$99$	0	0
$100$	1.00000	0.100000
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	−6.00000	−0.594089
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	−4.00000	−0.392232
$105$	−2.00000	−0.195180
$106$	10.0000	0.971286
$107$	−16.0000	−1.54678	−0.773389	−	0.633932i	$-0.781440\pi$
$107$	−16.0000	−1.54678	−0.773389	+	0.633932i	$0.781440\pi$
$108$	1.00000	0.0962250
$109$	16.0000	1.53252	0.766261	−	0.642529i	$-0.222115\pi$
$109$	16.0000	1.53252	0.766261	+	0.642529i	$0.222115\pi$
$110$	0	0
$111$	10.0000	0.949158
$112$	2.00000	0.188982
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	2.00000	0.187317
$115$	−4.00000	−0.373002
$116$	2.00000	0.185695
$117$	4.00000	0.369800
$118$	0	0
$119$	12.0000	1.10004
$120$	1.00000	0.0912871
$121$	0	0
$122$	−12.0000	−1.08643
$123$	−2.00000	−0.180334
$124$	−8.00000	−0.718421
$125$	−1.00000	−0.0894427
$126$	−2.00000	−0.178174
$127$	−14.0000	−1.24230	−0.621150	−	0.783692i	$-0.713334\pi$
$127$	−14.0000	−1.24230	−0.621150	+	0.783692i	$0.713334\pi$
$128$	−1.00000	−0.0883883
$129$	6.00000	0.528271
$130$	4.00000	0.350823
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	−4.00000	−0.346844
$134$	4.00000	0.345547
$135$	−1.00000	−0.0860663
$136$	−6.00000	−0.514496
$137$	−2.00000	−0.170872	−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000	−0.170872	−0.0854358	+	0.996344i	$0.527228\pi$
$138$	−4.00000	−0.340503
$139$	−2.00000	−0.169638	−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000	−0.169638	−0.0848189	+	0.996396i	$0.527031\pi$
$140$	−2.00000	−0.169031
$141$	−8.00000	−0.673722
$142$	8.00000	0.671345
$143$	0	0
$144$	1.00000	0.0833333
$145$	−2.00000	−0.166091
$146$	−8.00000	−0.662085
$147$	−3.00000	−0.247436
$148$	10.0000	0.821995
$149$	14.0000	1.14692	0.573462	−	0.819232i	$-0.305600\pi$
$149$	14.0000	1.14692	0.573462	+	0.819232i	$0.305600\pi$
$150$	−1.00000	−0.0816497
$151$	6.00000	0.488273	0.244137	−	0.969741i	$-0.421495\pi$
$151$	6.00000	0.488273	0.244137	+	0.969741i	$0.421495\pi$
$152$	2.00000	0.162221
$153$	6.00000	0.485071
$154$	0	0
$155$	8.00000	0.642575
$156$	4.00000	0.320256
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	−6.00000	−0.477334
$159$	−10.0000	−0.793052
$160$	1.00000	0.0790569
$161$	8.00000	0.630488
$162$	−1.00000	−0.0785674
$163$	12.0000	0.939913	0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000	0.939913	0.469956	+	0.882690i	$0.344270\pi$
$164$	−2.00000	−0.156174
$165$	0	0
$166$	8.00000	0.620920
$167$	8.00000	0.619059	0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000	0.619059	0.309529	+	0.950890i	$0.399829\pi$
$168$	−2.00000	−0.154303
$169$	3.00000	0.230769
$170$	6.00000	0.460179
$171$	−2.00000	−0.152944
$172$	6.00000	0.457496
$173$	−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
$175$	2.00000	0.151186
$176$	0	0
$177$	0	0
$178$	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
$183$	12.0000	0.887066
$184$	−4.00000	−0.294884
$185$	−10.0000	−0.735215
$186$	8.00000	0.586588
$187$	0	0
$188$	−8.00000	−0.583460
$189$	2.00000	0.145479
$190$	−2.00000	−0.145095
$191$	16.0000	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$192$	1.00000	0.0721688
$193$	−12.0000	−0.863779	−0.431889	−	0.901927i	$-0.642153\pi$
$193$	−12.0000	−0.863779	−0.431889	+	0.901927i	$0.642153\pi$
$194$	−10.0000	−0.717958
$195$	−4.00000	−0.286446
$196$	−3.00000	−0.214286
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	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
$201$	−4.00000	−0.282138
$202$	−10.0000	−0.703598
$203$	4.00000	0.280745
$204$	6.00000	0.420084
$205$	2.00000	0.139686
$206$	−8.00000	−0.557386
$207$	4.00000	0.278019
$208$	4.00000	0.277350
$209$	0	0
$210$	2.00000	0.138013
$211$	14.0000	0.963800	0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000	0.963800	0.481900	+	0.876226i	$0.339947\pi$
$212$	−10.0000	−0.686803
$213$	−8.00000	−0.548151
$214$	16.0000	1.09374
$215$	−6.00000	−0.409197
$216$	−1.00000	−0.0680414
$217$	−16.0000	−1.08615
$218$	−16.0000	−1.08366
$219$	8.00000	0.540590
$220$	0	0
$221$	24.0000	1.61441
$222$	−10.0000	−0.671156
$223$	−16.0000	−1.07144	−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000	−1.07144	−0.535720	+	0.844396i	$0.679960\pi$
$224$	−2.00000	−0.133631
$225$	1.00000	0.0666667
$226$	−6.00000	−0.399114
$227$	24.0000	1.59294	0.796468	−	0.604681i	$-0.206699\pi$
$227$	24.0000	1.59294	0.796468	+	0.604681i	$0.206699\pi$
$228$	−2.00000	−0.132453
$229$	−22.0000	−1.45380	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000	−1.45380	−0.726900	+	0.686743i	$0.759040\pi$
$230$	4.00000	0.263752
$231$	0	0
$232$	−2.00000	−0.131306
$233$	26.0000	1.70332	0.851658	−	0.524097i	$-0.175597\pi$
$233$	26.0000	1.70332	0.851658	+	0.524097i	$0.175597\pi$
$234$	−4.00000	−0.261488
$235$	8.00000	0.521862
$236$	0	0
$237$	6.00000	0.389742
$238$	−12.0000	−0.777844
$239$	−20.0000	−1.29369	−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000	−1.29369	−0.646846	+	0.762620i	$0.723912\pi$
$240$	−1.00000	−0.0645497
$241$	12.0000	0.772988	0.386494	−	0.922292i	$-0.373686\pi$
$241$	12.0000	0.772988	0.386494	+	0.922292i	$0.373686\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	12.0000	0.768221
$245$	3.00000	0.191663
$246$	2.00000	0.127515
$247$	−8.00000	−0.509028
$248$	8.00000	0.508001
$249$	−8.00000	−0.506979
$250$	1.00000	0.0632456
$251$	20.0000	1.26239	0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000	1.26239	0.631194	+	0.775625i	$0.282565\pi$
$252$	2.00000	0.125988
$253$	0	0
$254$	14.0000	0.878438
$255$	−6.00000	−0.375735
$256$	1.00000	0.0625000
$257$	2.00000	0.124757	0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000	0.124757	0.0623783	+	0.998053i	$0.480131\pi$
$258$	−6.00000	−0.373544
$259$	20.0000	1.24274
$260$	−4.00000	−0.248069
$261$	2.00000	0.123797
$262$	0	0
$263$	16.0000	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$264$	0	0
$265$	10.0000	0.614295
$266$	4.00000	0.245256
$267$	−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
$271$	10.0000	0.607457	0.303728	−	0.952759i	$-0.401768\pi$
$271$	10.0000	0.607457	0.303728	+	0.952759i	$0.401768\pi$
$272$	6.00000	0.363803
$273$	8.00000	0.484182
$274$	2.00000	0.120824
$275$	0	0
$276$	4.00000	0.240772
$277$	−28.0000	−1.68236	−0.841178	−	0.540758i	$-0.818138\pi$
$277$	−28.0000	−1.68236	−0.841178	+	0.540758i	$0.818138\pi$
$278$	2.00000	0.119952
$279$	−8.00000	−0.478947
$280$	2.00000	0.119523
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	8.00000	0.476393
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	−8.00000	−0.474713
$285$	2.00000	0.118470
$286$	0	0
$287$	−4.00000	−0.236113
$288$	−1.00000	−0.0589256
$289$	19.0000	1.11765
$290$	2.00000	0.117444
$291$	10.0000	0.586210
$292$	8.00000	0.468165
$293$	−14.0000	−0.817889	−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000	−0.817889	−0.408944	+	0.912559i	$0.634103\pi$
$294$	3.00000	0.174964
$295$	0	0
$296$	−10.0000	−0.581238
$297$	0	0
$298$	−14.0000	−0.810998
$299$	16.0000	0.925304
$300$	1.00000	0.0577350
$301$	12.0000	0.691669
$302$	−6.00000	−0.345261
$303$	10.0000	0.574485
$304$	−2.00000	−0.114708
$305$	−12.0000	−0.687118
$306$	−6.00000	−0.342997
$307$	2.00000	0.114146	0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000	0.114146	0.0570730	+	0.998370i	$0.481823\pi$
$308$	0	0
$309$	8.00000	0.455104
$310$	−8.00000	−0.454369
$311$	20.0000	1.13410	0.567048	−	0.823685i	$-0.308085\pi$
$311$	20.0000	1.13410	0.567048	+	0.823685i	$0.308085\pi$
$312$	−4.00000	−0.226455
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	−18.0000	−1.01580
$315$	−2.00000	−0.112687
$316$	6.00000	0.337526
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	10.0000	0.560772
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−16.0000	−0.893033
$322$	−8.00000	−0.445823
$323$	−12.0000	−0.667698
$324$	1.00000	0.0555556
$325$	4.00000	0.221880
$326$	−12.0000	−0.664619
$327$	16.0000	0.884802
$328$	2.00000	0.110432
$329$	−16.0000	−0.882109
$330$	0	0
$331$	−12.0000	−0.659580	−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000	−0.659580	−0.329790	+	0.944054i	$0.606978\pi$
$332$	−8.00000	−0.439057
$333$	10.0000	0.547997
$334$	−8.00000	−0.437741
$335$	4.00000	0.218543
$336$	2.00000	0.109109
$337$	32.0000	1.74315	0.871576	−	0.490261i	$-0.163099\pi$
$337$	32.0000	1.74315	0.871576	+	0.490261i	$0.163099\pi$
$338$	−3.00000	−0.163178
$339$	6.00000	0.325875
$340$	−6.00000	−0.325396
$341$	0	0
$342$	2.00000	0.108148
$343$	−20.0000	−1.07990
$344$	−6.00000	−0.323498
$345$	−4.00000	−0.215353
$346$	18.0000	0.967686
$347$	−32.0000	−1.71785	−0.858925	−	0.512101i	$-0.828867\pi$
$347$	−32.0000	−1.71785	−0.858925	+	0.512101i	$0.828867\pi$
$348$	2.00000	0.107211
$349$	−20.0000	−1.07058	−0.535288	−	0.844670i	$-0.679797\pi$
$349$	−20.0000	−1.07058	−0.535288	+	0.844670i	$0.679797\pi$
$350$	−2.00000	−0.106904
$351$	4.00000	0.213504
$352$	0	0
$353$	18.0000	0.958043	0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	0	0
$355$	8.00000	0.424596
$356$	−6.00000	−0.317999
$357$	12.0000	0.635107
$358$	−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
$361$	−15.0000	−0.789474
$362$	−6.00000	−0.315353
$363$	0	0
$364$	8.00000	0.419314
$365$	−8.00000	−0.418739
$366$	−12.0000	−0.627250
$367$	−8.00000	−0.417597	−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000	−0.417597	−0.208798	+	0.977959i	$0.566955\pi$
$368$	4.00000	0.208514
$369$	−2.00000	−0.104116
$370$	10.0000	0.519875
$371$	−20.0000	−1.03835
$372$	−8.00000	−0.414781
$373$	16.0000	0.828449	0.414224	−	0.910175i	$-0.364053\pi$
$373$	16.0000	0.828449	0.414224	+	0.910175i	$0.364053\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	8.00000	0.412568
$377$	8.00000	0.412021
$378$	−2.00000	−0.102869
$379$	12.0000	0.616399	0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000	0.616399	0.308199	+	0.951322i	$0.400274\pi$
$380$	2.00000	0.102598
$381$	−14.0000	−0.717242
$382$	−16.0000	−0.818631
$383$	36.0000	1.83951	0.919757	−	0.392488i	$-0.128386\pi$
$383$	36.0000	1.83951	0.919757	+	0.392488i	$0.128386\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	12.0000	0.610784
$387$	6.00000	0.304997
$388$	10.0000	0.507673
$389$	−22.0000	−1.11544	−0.557722	−	0.830028i	$-0.688325\pi$
$389$	−22.0000	−1.11544	−0.557722	+	0.830028i	$0.688325\pi$
$390$	4.00000	0.202548
$391$	24.0000	1.21373
$392$	3.00000	0.151523
$393$	0	0
$394$	18.0000	0.906827
$395$	−6.00000	−0.301893
$396$	0	0
$397$	−34.0000	−1.70641	−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000	−1.70641	−0.853206	+	0.521575i	$0.825345\pi$
$398$	16.0000	0.802008
$399$	−4.00000	−0.200250
$400$	1.00000	0.0500000
$401$	6.00000	0.299626	0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000	0.299626	0.149813	+	0.988714i	$0.452133\pi$
$402$	4.00000	0.199502
$403$	−32.0000	−1.59403
$404$	10.0000	0.497519
$405$	−1.00000	−0.0496904
$406$	−4.00000	−0.198517
$407$	0	0
$408$	−6.00000	−0.297044
$409$	−12.0000	−0.593362	−0.296681	−	0.954977i	$-0.595880\pi$
$409$	−12.0000	−0.593362	−0.296681	+	0.954977i	$0.595880\pi$
$410$	−2.00000	−0.0987730
$411$	−2.00000	−0.0986527
$412$	8.00000	0.394132
$413$	0	0
$414$	−4.00000	−0.196589
$415$	8.00000	0.392705
$416$	−4.00000	−0.196116
$417$	−2.00000	−0.0979404
$418$	0	0
$419$	4.00000	0.195413	0.0977064	−	0.995215i	$-0.468849\pi$
$419$	4.00000	0.195413	0.0977064	+	0.995215i	$0.468849\pi$
$420$	−2.00000	−0.0975900
$421$	26.0000	1.26716	0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000	1.26716	0.633581	+	0.773676i	$0.281584\pi$
$422$	−14.0000	−0.681509
$423$	−8.00000	−0.388973
$424$	10.0000	0.485643
$425$	6.00000	0.291043
$426$	8.00000	0.387601
$427$	24.0000	1.16144
$428$	−16.0000	−0.773389
$429$	0	0
$430$	6.00000	0.289346
$431$	28.0000	1.34871	0.674356	−	0.738406i	$-0.264421\pi$
$431$	28.0000	1.34871	0.674356	+	0.738406i	$0.264421\pi$
$432$	1.00000	0.0481125
$433$	34.0000	1.63394	0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000	1.63394	0.816968	+	0.576683i	$0.195653\pi$
$434$	16.0000	0.768025
$435$	−2.00000	−0.0958927
$436$	16.0000	0.766261
$437$	−8.00000	−0.382692
$438$	−8.00000	−0.382255
$439$	34.0000	1.62273	0.811366	−	0.584539i	$-0.198725\pi$
$439$	34.0000	1.62273	0.811366	+	0.584539i	$0.198725\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	−24.0000	−1.14156
$443$	−32.0000	−1.52037	−0.760183	−	0.649709i	$-0.774891\pi$
$443$	−32.0000	−1.52037	−0.760183	+	0.649709i	$0.774891\pi$
$444$	10.0000	0.474579
$445$	6.00000	0.284427
$446$	16.0000	0.757622
$447$	14.0000	0.662177
$448$	2.00000	0.0944911
$449$	18.0000	0.849473	0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000	0.849473	0.424736	+	0.905317i	$0.360367\pi$
$450$	−1.00000	−0.0471405
$451$	0	0
$452$	6.00000	0.282216
$453$	6.00000	0.281905
$454$	−24.0000	−1.12638
$455$	−8.00000	−0.375046
$456$	2.00000	0.0936586
$457$	−32.0000	−1.49690	−0.748448	−	0.663193i	$-0.769201\pi$
$457$	−32.0000	−1.49690	−0.748448	+	0.663193i	$0.769201\pi$
$458$	22.0000	1.02799
$459$	6.00000	0.280056
$460$	−4.00000	−0.186501
$461$	−2.00000	−0.0931493	−0.0465746	−	0.998915i	$-0.514831\pi$
$461$	−2.00000	−0.0931493	−0.0465746	+	0.998915i	$0.514831\pi$
$462$	0	0
$463$	24.0000	1.11537	0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000	1.11537	0.557687	+	0.830051i	$0.311689\pi$
$464$	2.00000	0.0928477
$465$	8.00000	0.370991
$466$	−26.0000	−1.20443
$467$	−32.0000	−1.48078	−0.740392	−	0.672176i	$-0.765360\pi$
$467$	−32.0000	−1.48078	−0.740392	+	0.672176i	$0.765360\pi$
$468$	4.00000	0.184900
$469$	−8.00000	−0.369406
$470$	−8.00000	−0.369012
$471$	18.0000	0.829396
$472$	0	0
$473$	0	0
$474$	−6.00000	−0.275589
$475$	−2.00000	−0.0917663
$476$	12.0000	0.550019
$477$	−10.0000	−0.457869
$478$	20.0000	0.914779
$479$	36.0000	1.64488	0.822441	−	0.568850i	$-0.192612\pi$
$479$	36.0000	1.64488	0.822441	+	0.568850i	$0.192612\pi$
$480$	1.00000	0.0456435
$481$	40.0000	1.82384
$482$	−12.0000	−0.546585
$483$	8.00000	0.364013
$484$	0	0
$485$	−10.0000	−0.454077
$486$	−1.00000	−0.0453609
$487$	−32.0000	−1.45006	−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000	−1.45006	−0.725029	+	0.688718i	$0.758174\pi$
$488$	−12.0000	−0.543214
$489$	12.0000	0.542659
$490$	−3.00000	−0.135526
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	−2.00000	−0.0901670
$493$	12.0000	0.540453
$494$	8.00000	0.359937
$495$	0	0
$496$	−8.00000	−0.359211
$497$	−16.0000	−0.717698
$498$	8.00000	0.358489
$499$	−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
$501$	8.00000	0.357414
$502$	−20.0000	−0.892644
$503$	24.0000	1.07011	0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000	1.07011	0.535054	+	0.844818i	$0.320291\pi$
$504$	−2.00000	−0.0890871
$505$	−10.0000	−0.444994
$506$	0	0
$507$	3.00000	0.133235
$508$	−14.0000	−0.621150
$509$	−2.00000	−0.0886484	−0.0443242	−	0.999017i	$-0.514113\pi$
$509$	−2.00000	−0.0886484	−0.0443242	+	0.999017i	$0.514113\pi$
$510$	6.00000	0.265684
$511$	16.0000	0.707798
$512$	−1.00000	−0.0441942
$513$	−2.00000	−0.0883022
$514$	−2.00000	−0.0882162
$515$	−8.00000	−0.352522
$516$	6.00000	0.264135
$517$	0	0
$518$	−20.0000	−0.878750
$519$	−18.0000	−0.790112
$520$	4.00000	0.175412
$521$	6.00000	0.262865	0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000	0.262865	0.131432	+	0.991325i	$0.458042\pi$
$522$	−2.00000	−0.0875376
$523$	30.0000	1.31181	0.655904	−	0.754844i	$-0.272288\pi$
$523$	30.0000	1.31181	0.655904	+	0.754844i	$0.272288\pi$
$524$	0	0
$525$	2.00000	0.0872872
$526$	−16.0000	−0.697633
$527$	−48.0000	−2.09091
$528$	0	0
$529$	−7.00000	−0.304348
$530$	−10.0000	−0.434372
$531$	0	0
$532$	−4.00000	−0.173422
$533$	−8.00000	−0.346518
$534$	6.00000	0.259645
$535$	16.0000	0.691740
$536$	4.00000	0.172774
$537$	12.0000	0.517838
$538$	10.0000	0.431131
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	−16.0000	−0.687894	−0.343947	−	0.938989i	$-0.611764\pi$
$541$	−16.0000	−0.687894	−0.343947	+	0.938989i	$0.611764\pi$
$542$	−10.0000	−0.429537
$543$	6.00000	0.257485
$544$	−6.00000	−0.257248
$545$	−16.0000	−0.685365
$546$	−8.00000	−0.342368
$547$	14.0000	0.598597	0.299298	−	0.954160i	$-0.403247\pi$
$547$	14.0000	0.598597	0.299298	+	0.954160i	$0.403247\pi$
$548$	−2.00000	−0.0854358
$549$	12.0000	0.512148
$550$	0	0
$551$	−4.00000	−0.170406
$552$	−4.00000	−0.170251
$553$	12.0000	0.510292
$554$	28.0000	1.18961
$555$	−10.0000	−0.424476
$556$	−2.00000	−0.0848189
$557$	−14.0000	−0.593199	−0.296600	−	0.955002i	$-0.595853\pi$
$557$	−14.0000	−0.593199	−0.296600	+	0.955002i	$0.595853\pi$
$558$	8.00000	0.338667
$559$	24.0000	1.01509
$560$	−2.00000	−0.0845154
$561$	0	0
$562$	18.0000	0.759284
$563$	12.0000	0.505740	0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000	0.505740	0.252870	+	0.967500i	$0.418626\pi$
$564$	−8.00000	−0.336861
$565$	−6.00000	−0.252422
$566$	−14.0000	−0.588464
$567$	2.00000	0.0839921
$568$	8.00000	0.335673
$569$	42.0000	1.76073	0.880366	−	0.474295i	$-0.157297\pi$
$569$	42.0000	1.76073	0.880366	+	0.474295i	$0.157297\pi$
$570$	−2.00000	−0.0837708
$571$	−46.0000	−1.92504	−0.962520	−	0.271211i	$-0.912576\pi$
$571$	−46.0000	−1.92504	−0.962520	+	0.271211i	$0.912576\pi$
$572$	0	0
$573$	16.0000	0.668410
$574$	4.00000	0.166957
$575$	4.00000	0.166812
$576$	1.00000	0.0416667
$577$	−18.0000	−0.749350	−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000	−0.749350	−0.374675	+	0.927156i	$0.622246\pi$
$578$	−19.0000	−0.790296
$579$	−12.0000	−0.498703
$580$	−2.00000	−0.0830455
$581$	−16.0000	−0.663792
$582$	−10.0000	−0.414513
$583$	0	0
$584$	−8.00000	−0.331042
$585$	−4.00000	−0.165380
$586$	14.0000	0.578335
$587$	16.0000	0.660391	0.330195	−	0.943913i	$-0.392885\pi$
$587$	16.0000	0.660391	0.330195	+	0.943913i	$0.392885\pi$
$588$	−3.00000	−0.123718
$589$	16.0000	0.659269
$590$	0	0
$591$	−18.0000	−0.740421
$592$	10.0000	0.410997
$593$	−22.0000	−0.903432	−0.451716	−	0.892162i	$-0.649188\pi$
$593$	−22.0000	−0.903432	−0.451716	+	0.892162i	$0.649188\pi$
$594$	0	0
$595$	−12.0000	−0.491952
$596$	14.0000	0.573462
$597$	−16.0000	−0.654836
$598$	−16.0000	−0.654289
$599$	−20.0000	−0.817178	−0.408589	−	0.912719i	$-0.633979\pi$
$599$	−20.0000	−0.817178	−0.408589	+	0.912719i	$0.633979\pi$
$600$	−1.00000	−0.0408248
$601$	−8.00000	−0.326327	−0.163163	−	0.986599i	$-0.552170\pi$
$601$	−8.00000	−0.326327	−0.163163	+	0.986599i	$0.552170\pi$
$602$	−12.0000	−0.489083
$603$	−4.00000	−0.162893
$604$	6.00000	0.244137
$605$	0	0
$606$	−10.0000	−0.406222
$607$	−38.0000	−1.54237	−0.771186	−	0.636610i	$-0.780336\pi$
$607$	−38.0000	−1.54237	−0.771186	+	0.636610i	$0.780336\pi$
$608$	2.00000	0.0811107
$609$	4.00000	0.162088
$610$	12.0000	0.485866
$611$	−32.0000	−1.29458
$612$	6.00000	0.242536
$613$	32.0000	1.29247	0.646234	−	0.763139i	$-0.276343\pi$
$613$	32.0000	1.29247	0.646234	+	0.763139i	$0.276343\pi$
$614$	−2.00000	−0.0807134
$615$	2.00000	0.0806478
$616$	0	0
$617$	30.0000	1.20775	0.603877	−	0.797077i	$-0.293622\pi$
$617$	30.0000	1.20775	0.603877	+	0.797077i	$0.293622\pi$
$618$	−8.00000	−0.321807
$619$	−12.0000	−0.482321	−0.241160	−	0.970485i	$-0.577528\pi$
$619$	−12.0000	−0.482321	−0.241160	+	0.970485i	$0.577528\pi$
$620$	8.00000	0.321288
$621$	4.00000	0.160514
$622$	−20.0000	−0.801927
$623$	−12.0000	−0.480770
$624$	4.00000	0.160128
$625$	1.00000	0.0400000
$626$	10.0000	0.399680
$627$	0	0
$628$	18.0000	0.718278
$629$	60.0000	2.39236
$630$	2.00000	0.0796819
$631$	16.0000	0.636950	0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000	0.636950	0.318475	+	0.947931i	$0.396829\pi$
$632$	−6.00000	−0.238667
$633$	14.0000	0.556450
$634$	−18.0000	−0.714871
$635$	14.0000	0.555573
$636$	−10.0000	−0.396526
$637$	−12.0000	−0.475457
$638$	0	0
$639$	−8.00000	−0.316475
$640$	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	$0.188654\pi$
$642$	16.0000	0.631470
$643$	−36.0000	−1.41970	−0.709851	−	0.704352i	$-0.751238\pi$
$643$	−36.0000	−1.41970	−0.709851	+	0.704352i	$0.751238\pi$
$644$	8.00000	0.315244
$645$	−6.00000	−0.236250
$646$	12.0000	0.472134
$647$	12.0000	0.471769	0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000	0.471769	0.235884	+	0.971781i	$0.424201\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	−4.00000	−0.156893
$651$	−16.0000	−0.627089
$652$	12.0000	0.469956
$653$	−10.0000	−0.391330	−0.195665	−	0.980671i	$-0.562687\pi$
$653$	−10.0000	−0.391330	−0.195665	+	0.980671i	$0.562687\pi$
$654$	−16.0000	−0.625650
$655$	0	0
$656$	−2.00000	−0.0780869
$657$	8.00000	0.312110
$658$	16.0000	0.623745
$659$	−40.0000	−1.55818	−0.779089	−	0.626913i	$-0.784318\pi$
$659$	−40.0000	−1.55818	−0.779089	+	0.626913i	$0.784318\pi$
$660$	0	0
$661$	10.0000	0.388955	0.194477	−	0.980907i	$-0.437699\pi$
$661$	10.0000	0.388955	0.194477	+	0.980907i	$0.437699\pi$
$662$	12.0000	0.466393
$663$	24.0000	0.932083
$664$	8.00000	0.310460
$665$	4.00000	0.155113
$666$	−10.0000	−0.387492
$667$	8.00000	0.309761
$668$	8.00000	0.309529
$669$	−16.0000	−0.618596
$670$	−4.00000	−0.154533
$671$	0	0
$672$	−2.00000	−0.0771517
$673$	36.0000	1.38770	0.693849	−	0.720121i	$-0.255914\pi$
$673$	36.0000	1.38770	0.693849	+	0.720121i	$0.255914\pi$
$674$	−32.0000	−1.23259
$675$	1.00000	0.0384900
$676$	3.00000	0.115385
$677$	−18.0000	−0.691796	−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000	−0.691796	−0.345898	+	0.938272i	$0.612426\pi$
$678$	−6.00000	−0.230429
$679$	20.0000	0.767530
$680$	6.00000	0.230089
$681$	24.0000	0.919682
$682$	0	0
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	−2.00000	−0.0764719
$685$	2.00000	0.0764161
$686$	20.0000	0.763604
$687$	−22.0000	−0.839352
$688$	6.00000	0.228748
$689$	−40.0000	−1.52388
$690$	4.00000	0.152277
$691$	−4.00000	−0.152167	−0.0760836	−	0.997101i	$-0.524242\pi$
$691$	−4.00000	−0.152167	−0.0760836	+	0.997101i	$0.524242\pi$
$692$	−18.0000	−0.684257
$693$	0	0
$694$	32.0000	1.21470
$695$	2.00000	0.0758643
$696$	−2.00000	−0.0758098
$697$	−12.0000	−0.454532
$698$	20.0000	0.757011
$699$	26.0000	0.983410
$700$	2.00000	0.0755929
$701$	6.00000	0.226617	0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000	0.226617	0.113308	+	0.993560i	$0.463855\pi$
$702$	−4.00000	−0.150970
$703$	−20.0000	−0.754314
$704$	0	0
$705$	8.00000	0.301297
$706$	−18.0000	−0.677439
$707$	20.0000	0.752177
$708$	0	0
$709$	−38.0000	−1.42712	−0.713560	−	0.700594i	$-0.752918\pi$
$709$	−38.0000	−1.42712	−0.713560	+	0.700594i	$0.752918\pi$
$710$	−8.00000	−0.300235
$711$	6.00000	0.225018
$712$	6.00000	0.224860
$713$	−32.0000	−1.19841
$714$	−12.0000	−0.449089
$715$	0	0
$716$	12.0000	0.448461
$717$	−20.0000	−0.746914
$718$	24.0000	0.895672
$719$	−24.0000	−0.895049	−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000	−0.895049	−0.447524	+	0.894272i	$0.647694\pi$
$720$	−1.00000	−0.0372678
$721$	16.0000	0.595871
$722$	15.0000	0.558242
$723$	12.0000	0.446285
$724$	6.00000	0.222988
$725$	2.00000	0.0742781
$726$	0	0
$727$	−8.00000	−0.296704	−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000	−0.296704	−0.148352	+	0.988935i	$0.547397\pi$
$728$	−8.00000	−0.296500
$729$	1.00000	0.0370370
$730$	8.00000	0.296093
$731$	36.0000	1.33151
$732$	12.0000	0.443533
$733$	4.00000	0.147743	0.0738717	−	0.997268i	$-0.476464\pi$
$733$	4.00000	0.147743	0.0738717	+	0.997268i	$0.476464\pi$
$734$	8.00000	0.295285
$735$	3.00000	0.110657
$736$	−4.00000	−0.147442
$737$	0	0
$738$	2.00000	0.0736210
$739$	26.0000	0.956425	0.478213	−	0.878244i	$-0.341285\pi$
$739$	26.0000	0.956425	0.478213	+	0.878244i	$0.341285\pi$
$740$	−10.0000	−0.367607
$741$	−8.00000	−0.293887
$742$	20.0000	0.734223
$743$	−4.00000	−0.146746	−0.0733729	−	0.997305i	$-0.523376\pi$
$743$	−4.00000	−0.146746	−0.0733729	+	0.997305i	$0.523376\pi$
$744$	8.00000	0.293294
$745$	−14.0000	−0.512920
$746$	−16.0000	−0.585802
$747$	−8.00000	−0.292705
$748$	0	0
$749$	−32.0000	−1.16925
$750$	1.00000	0.0365148
$751$	−32.0000	−1.16770	−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000	−1.16770	−0.583848	+	0.811863i	$0.698454\pi$
$752$	−8.00000	−0.291730
$753$	20.0000	0.728841
$754$	−8.00000	−0.291343
$755$	−6.00000	−0.218362
$756$	2.00000	0.0727393
$757$	−54.0000	−1.96266	−0.981332	−	0.192323i	$-0.938398\pi$
$757$	−54.0000	−1.96266	−0.981332	+	0.192323i	$0.938398\pi$
$758$	−12.0000	−0.435860
$759$	0	0
$760$	−2.00000	−0.0725476
$761$	−22.0000	−0.797499	−0.398750	−	0.917060i	$-0.630556\pi$
$761$	−22.0000	−0.797499	−0.398750	+	0.917060i	$0.630556\pi$
$762$	14.0000	0.507166
$763$	32.0000	1.15848
$764$	16.0000	0.578860
$765$	−6.00000	−0.216930
$766$	−36.0000	−1.30073
$767$	0	0
$768$	1.00000	0.0360844
$769$	8.00000	0.288487	0.144244	−	0.989542i	$-0.453925\pi$
$769$	8.00000	0.288487	0.144244	+	0.989542i	$0.453925\pi$
$770$	0	0
$771$	2.00000	0.0720282
$772$	−12.0000	−0.431889
$773$	−42.0000	−1.51064	−0.755318	−	0.655359i	$-0.772517\pi$
$773$	−42.0000	−1.51064	−0.755318	+	0.655359i	$0.772517\pi$
$774$	−6.00000	−0.215666
$775$	−8.00000	−0.287368
$776$	−10.0000	−0.358979
$777$	20.0000	0.717496
$778$	22.0000	0.788738
$779$	4.00000	0.143315
$780$	−4.00000	−0.143223
$781$	0	0
$782$	−24.0000	−0.858238
$783$	2.00000	0.0714742
$784$	−3.00000	−0.107143
$785$	−18.0000	−0.642448
$786$	0	0
$787$	−42.0000	−1.49714	−0.748569	−	0.663057i	$-0.769259\pi$
$787$	−42.0000	−1.49714	−0.748569	+	0.663057i	$0.769259\pi$
$788$	−18.0000	−0.641223
$789$	16.0000	0.569615
$790$	6.00000	0.213470
$791$	12.0000	0.426671
$792$	0	0
$793$	48.0000	1.70453
$794$	34.0000	1.20661
$795$	10.0000	0.354663
$796$	−16.0000	−0.567105
$797$	42.0000	1.48772	0.743858	−	0.668338i	$-0.232994\pi$
$797$	42.0000	1.48772	0.743858	+	0.668338i	$0.232994\pi$
$798$	4.00000	0.141598
$799$	−48.0000	−1.69812
$800$	−1.00000	−0.0353553
$801$	−6.00000	−0.212000
$802$	−6.00000	−0.211867
$803$	0	0
$804$	−4.00000	−0.141069
$805$	−8.00000	−0.281963
$806$	32.0000	1.12715
$807$	−10.0000	−0.352017
$808$	−10.0000	−0.351799
$809$	−6.00000	−0.210949	−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000	−0.210949	−0.105474	+	0.994422i	$0.533636\pi$
$810$	1.00000	0.0351364
$811$	−10.0000	−0.351147	−0.175574	−	0.984466i	$-0.556178\pi$
$811$	−10.0000	−0.351147	−0.175574	+	0.984466i	$0.556178\pi$
$812$	4.00000	0.140372
$813$	10.0000	0.350715
$814$	0	0
$815$	−12.0000	−0.420342
$816$	6.00000	0.210042
$817$	−12.0000	−0.419827
$818$	12.0000	0.419570
$819$	8.00000	0.279543
$820$	2.00000	0.0698430
$821$	−22.0000	−0.767805	−0.383903	−	0.923374i	$-0.625420\pi$
$821$	−22.0000	−0.767805	−0.383903	+	0.923374i	$0.625420\pi$
$822$	2.00000	0.0697580
$823$	−40.0000	−1.39431	−0.697156	−	0.716919i	$-0.745552\pi$
$823$	−40.0000	−1.39431	−0.697156	+	0.716919i	$0.745552\pi$
$824$	−8.00000	−0.278693
$825$	0	0
$826$	0	0
$827$	−48.0000	−1.66912	−0.834562	−	0.550914i	$-0.814279\pi$
$827$	−48.0000	−1.66912	−0.834562	+	0.550914i	$0.814279\pi$
$828$	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	$0.511058\pi$
$830$	−8.00000	−0.277684
$831$	−28.0000	−0.971309
$832$	4.00000	0.138675
$833$	−18.0000	−0.623663
$834$	2.00000	0.0692543
$835$	−8.00000	−0.276851
$836$	0	0
$837$	−8.00000	−0.276520
$838$	−4.00000	−0.138178
$839$	−4.00000	−0.138095	−0.0690477	−	0.997613i	$-0.521996\pi$
$839$	−4.00000	−0.138095	−0.0690477	+	0.997613i	$0.521996\pi$
$840$	2.00000	0.0690066
$841$	−25.0000	−0.862069
$842$	−26.0000	−0.896019
$843$	−18.0000	−0.619953
$844$	14.0000	0.481900
$845$	−3.00000	−0.103203
$846$	8.00000	0.275046
$847$	0	0
$848$	−10.0000	−0.343401
$849$	14.0000	0.480479
$850$	−6.00000	−0.205798
$851$	40.0000	1.37118
$852$	−8.00000	−0.274075
$853$	16.0000	0.547830	0.273915	−	0.961754i	$-0.411681\pi$
$853$	16.0000	0.547830	0.273915	+	0.961754i	$0.411681\pi$
$854$	−24.0000	−0.821263
$855$	2.00000	0.0683986
$856$	16.0000	0.546869
$857$	−10.0000	−0.341593	−0.170797	−	0.985306i	$-0.554634\pi$
$857$	−10.0000	−0.341593	−0.170797	+	0.985306i	$0.554634\pi$
$858$	0	0
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	−6.00000	−0.204598
$861$	−4.00000	−0.136320
$862$	−28.0000	−0.953684
$863$	28.0000	0.953131	0.476566	−	0.879139i	$-0.341881\pi$
$863$	28.0000	0.953131	0.476566	+	0.879139i	$0.341881\pi$
$864$	−1.00000	−0.0340207
$865$	18.0000	0.612018
$866$	−34.0000	−1.15537
$867$	19.0000	0.645274
$868$	−16.0000	−0.543075
$869$	0	0
$870$	2.00000	0.0678064
$871$	−16.0000	−0.542139
$872$	−16.0000	−0.541828
$873$	10.0000	0.338449
$874$	8.00000	0.270604
$875$	−2.00000	−0.0676123
$876$	8.00000	0.270295
$877$	8.00000	0.270141	0.135070	−	0.990836i	$-0.456874\pi$
$877$	8.00000	0.270141	0.135070	+	0.990836i	$0.456874\pi$
$878$	−34.0000	−1.14744
$879$	−14.0000	−0.472208
$880$	0	0
$881$	46.0000	1.54978	0.774890	−	0.632096i	$-0.217805\pi$
$881$	46.0000	1.54978	0.774890	+	0.632096i	$0.217805\pi$
$882$	3.00000	0.101015
$883$	−20.0000	−0.673054	−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000	−0.673054	−0.336527	+	0.941674i	$0.609252\pi$
$884$	24.0000	0.807207
$885$	0	0
$886$	32.0000	1.07506
$887$	44.0000	1.47738	0.738688	−	0.674048i	$-0.235446\pi$
$887$	44.0000	1.47738	0.738688	+	0.674048i	$0.235446\pi$
$888$	−10.0000	−0.335578
$889$	−28.0000	−0.939090
$890$	−6.00000	−0.201120
$891$	0	0
$892$	−16.0000	−0.535720
$893$	16.0000	0.535420
$894$	−14.0000	−0.468230
$895$	−12.0000	−0.401116
$896$	−2.00000	−0.0668153
$897$	16.0000	0.534224
$898$	−18.0000	−0.600668
$899$	−16.0000	−0.533630
$900$	1.00000	0.0333333
$901$	−60.0000	−1.99889
$902$	0	0
$903$	12.0000	0.399335
$904$	−6.00000	−0.199557
$905$	−6.00000	−0.199447
$906$	−6.00000	−0.199337
$907$	−12.0000	−0.398453	−0.199227	−	0.979953i	$-0.563843\pi$
$907$	−12.0000	−0.398453	−0.199227	+	0.979953i	$0.563843\pi$
$908$	24.0000	0.796468
$909$	10.0000	0.331679
$910$	8.00000	0.265197
$911$	16.0000	0.530104	0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000	0.530104	0.265052	+	0.964234i	$0.414611\pi$
$912$	−2.00000	−0.0662266
$913$	0	0
$914$	32.0000	1.05847
$915$	−12.0000	−0.396708
$916$	−22.0000	−0.726900
$917$	0	0
$918$	−6.00000	−0.198030
$919$	−46.0000	−1.51740	−0.758700	−	0.651440i	$-0.774165\pi$
$919$	−46.0000	−1.51740	−0.758700	+	0.651440i	$0.774165\pi$
$920$	4.00000	0.131876
$921$	2.00000	0.0659022
$922$	2.00000	0.0658665
$923$	−32.0000	−1.05329
$924$	0	0
$925$	10.0000	0.328798
$926$	−24.0000	−0.788689
$927$	8.00000	0.262754
$928$	−2.00000	−0.0656532
$929$	14.0000	0.459325	0.229663	−	0.973270i	$-0.426238\pi$
$929$	14.0000	0.459325	0.229663	+	0.973270i	$0.426238\pi$
$930$	−8.00000	−0.262330
$931$	6.00000	0.196642
$932$	26.0000	0.851658
$933$	20.0000	0.654771
$934$	32.0000	1.04707
$935$	0	0
$936$	−4.00000	−0.130744
$937$	−52.0000	−1.69877	−0.849383	−	0.527777i	$-0.823026\pi$
$937$	−52.0000	−1.69877	−0.849383	+	0.527777i	$0.823026\pi$
$938$	8.00000	0.261209
$939$	−10.0000	−0.326338
$940$	8.00000	0.260931
$941$	−46.0000	−1.49956	−0.749779	−	0.661689i	$-0.769840\pi$
$941$	−46.0000	−1.49956	−0.749779	+	0.661689i	$0.769840\pi$
$942$	−18.0000	−0.586472
$943$	−8.00000	−0.260516
$944$	0	0
$945$	−2.00000	−0.0650600
$946$	0	0
$947$	−28.0000	−0.909878	−0.454939	−	0.890523i	$-0.650339\pi$
$947$	−28.0000	−0.909878	−0.454939	+	0.890523i	$0.650339\pi$
$948$	6.00000	0.194871
$949$	32.0000	1.03876
$950$	2.00000	0.0648886
$951$	18.0000	0.583690
$952$	−12.0000	−0.388922
$953$	−10.0000	−0.323932	−0.161966	−	0.986796i	$-0.551783\pi$
$953$	−10.0000	−0.323932	−0.161966	+	0.986796i	$0.551783\pi$
$954$	10.0000	0.323762
$955$	−16.0000	−0.517748
$956$	−20.0000	−0.646846
$957$	0	0
$958$	−36.0000	−1.16311
$959$	−4.00000	−0.129167
$960$	−1.00000	−0.0322749
$961$	33.0000	1.06452
$962$	−40.0000	−1.28965
$963$	−16.0000	−0.515593
$964$	12.0000	0.386494
$965$	12.0000	0.386294
$966$	−8.00000	−0.257396
$967$	34.0000	1.09337	0.546683	−	0.837340i	$-0.315890\pi$
$967$	34.0000	1.09337	0.546683	+	0.837340i	$0.315890\pi$
$968$	0	0
$969$	−12.0000	−0.385496
$970$	10.0000	0.321081
$971$	−32.0000	−1.02693	−0.513464	−	0.858111i	$-0.671638\pi$
$971$	−32.0000	−1.02693	−0.513464	+	0.858111i	$0.671638\pi$
$972$	1.00000	0.0320750
$973$	−4.00000	−0.128234
$974$	32.0000	1.02535
$975$	4.00000	0.128103
$976$	12.0000	0.384111
$977$	−18.0000	−0.575871	−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000	−0.575871	−0.287936	+	0.957650i	$0.592969\pi$
$978$	−12.0000	−0.383718
$979$	0	0
$980$	3.00000	0.0958315
$981$	16.0000	0.510841
$982$	12.0000	0.382935
$983$	−36.0000	−1.14822	−0.574111	−	0.818778i	$-0.694652\pi$
$983$	−36.0000	−1.14822	−0.574111	+	0.818778i	$0.694652\pi$
$984$	2.00000	0.0637577
$985$	18.0000	0.573528
$986$	−12.0000	−0.382158
$987$	−16.0000	−0.509286
$988$	−8.00000	−0.254514
$989$	24.0000	0.763156
$990$	0	0
$991$	−16.0000	−0.508257	−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000	−0.508257	−0.254128	+	0.967170i	$0.581789\pi$
$992$	8.00000	0.254000
$993$	−12.0000	−0.380808
$994$	16.0000	0.507489
$995$	16.0000	0.507234
$996$	−8.00000	−0.253490
$997$	−48.0000	−1.52018	−0.760088	−	0.649821i	$-0.774844\pi$
$997$	−48.0000	−1.52018	−0.760088	+	0.649821i	$0.774844\pi$
$998$	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.i.1.1	✓	1
11.10	odd	2		3630.2.a.t.1.1	yes	1

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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