LMFDB - Embedded newform 966.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(1,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, 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("966.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.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:	$7.71354883526$
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	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +6.00000 q^{11} +1.00000 q^{12} +2.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} -6.00000 q^{17} -1.00000 q^{18} +2.00000 q^{19} +1.00000 q^{21} -6.00000 q^{22} +1.00000 q^{23} -1.00000 q^{24} -5.00000 q^{25} -2.00000 q^{26} +1.00000 q^{27} +1.00000 q^{28} -6.00000 q^{29} +8.00000 q^{31} -1.00000 q^{32} +6.00000 q^{33} +6.00000 q^{34} +1.00000 q^{36} +8.00000 q^{37} -2.00000 q^{38} +2.00000 q^{39} +6.00000 q^{41} -1.00000 q^{42} +2.00000 q^{43} +6.00000 q^{44} -1.00000 q^{46} +1.00000 q^{48} +1.00000 q^{49} +5.00000 q^{50} -6.00000 q^{51} +2.00000 q^{52} -12.0000 q^{53} -1.00000 q^{54} -1.00000 q^{56} +2.00000 q^{57} +6.00000 q^{58} +8.00000 q^{61} -8.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} -6.00000 q^{66} -10.0000 q^{67} -6.00000 q^{68} +1.00000 q^{69} -1.00000 q^{72} +14.0000 q^{73} -8.00000 q^{74} -5.00000 q^{75} +2.00000 q^{76} +6.00000 q^{77} -2.00000 q^{78} +8.00000 q^{79} +1.00000 q^{81} -6.00000 q^{82} +6.00000 q^{83} +1.00000 q^{84} -2.00000 q^{86} -6.00000 q^{87} -6.00000 q^{88} +6.00000 q^{89} +2.00000 q^{91} +1.00000 q^{92} +8.00000 q^{93} -1.00000 q^{96} -10.0000 q^{97} -1.00000 q^{98} +6.00000 q^{99} +O(q^{100})\)

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
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	6.00000	1.80907	0.904534	−	0.426401i	$-0.140219\pi$
$11$	6.00000	1.80907	0.904534	+	0.426401i	$0.140219\pi$
$12$	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	$0.410544\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	−1.00000	−0.235702
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	0	0
$21$	1.00000	0.218218
$22$	−6.00000	−1.27920
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	−5.00000	−1.00000
$26$	−2.00000	−0.392232
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	8.00000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	−1.00000	−0.176777
$33$	6.00000	1.04447
$34$	6.00000	1.02899
$35$	0	0
$36$	1.00000	0.166667
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	−2.00000	−0.324443
$39$	2.00000	0.320256
$40$	0	0
$41$	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	$0.451268\pi$
$44$	6.00000	0.904534
$45$	0	0
$46$	−1.00000	−0.147442
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	5.00000	0.707107
$51$	−6.00000	−0.840168
$52$	2.00000	0.277350
$53$	−12.0000	−1.64833	−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000	−1.64833	−0.824163	+	0.566352i	$0.808354\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−1.00000	−0.133631
$57$	2.00000	0.264906
$58$	6.00000	0.787839
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	8.00000	1.02430	0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000	1.02430	0.512148	+	0.858898i	$0.328850\pi$
$62$	−8.00000	−1.01600
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−6.00000	−0.738549
$67$	−10.0000	−1.22169	−0.610847	−	0.791748i	$-0.709171\pi$
$67$	−10.0000	−1.22169	−0.610847	+	0.791748i	$0.709171\pi$
$68$	−6.00000	−0.727607
$69$	1.00000	0.120386
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	−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	$0.194369\pi$
$74$	−8.00000	−0.929981
$75$	−5.00000	−0.577350
$76$	2.00000	0.229416
$77$	6.00000	0.683763
$78$	−2.00000	−0.226455
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−6.00000	−0.662589
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	1.00000	0.109109
$85$	0	0
$86$	−2.00000	−0.215666
$87$	−6.00000	−0.643268
$88$	−6.00000	−0.639602
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	0	0
$91$	2.00000	0.209657
$92$	1.00000	0.104257
$93$	8.00000	0.829561
$94$	0	0
$95$	0	0
$96$	−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	$0.669494\pi$
$98$	−1.00000	−0.101015
$99$	6.00000	0.603023
$100$	−5.00000	−0.500000
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	6.00000	0.594089
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	12.0000	1.16554
$107$	−6.00000	−0.580042	−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000	−0.580042	−0.290021	+	0.957020i	$0.593662\pi$
$108$	1.00000	0.0962250
$109$	−4.00000	−0.383131	−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000	−0.383131	−0.191565	+	0.981480i	$0.561356\pi$
$110$	0	0
$111$	8.00000	0.759326
$112$	1.00000	0.0944911
$113$	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
$115$	0	0
$116$	−6.00000	−0.557086
$117$	2.00000	0.184900
$118$	0	0
$119$	−6.00000	−0.550019
$120$	0	0
$121$	25.0000	2.27273
$122$	−8.00000	−0.724286
$123$	6.00000	0.541002
$124$	8.00000	0.718421
$125$	0	0
$126$	−1.00000	−0.0890871
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−1.00000	−0.0883883
$129$	2.00000	0.176090
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	6.00000	0.522233
$133$	2.00000	0.173422
$134$	10.0000	0.863868
$135$	0	0
$136$	6.00000	0.514496
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	−1.00000	−0.0851257
$139$	−16.0000	−1.35710	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000	−1.35710	−0.678551	+	0.734553i	$0.737392\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	12.0000	1.00349
$144$	1.00000	0.0833333
$145$	0	0
$146$	−14.0000	−1.15865
$147$	1.00000	0.0824786
$148$	8.00000	0.657596
$149$	12.0000	0.983078	0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000	0.983078	0.491539	+	0.870855i	$0.336434\pi$
$150$	5.00000	0.408248
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	−2.00000	−0.162221
$153$	−6.00000	−0.485071
$154$	−6.00000	−0.483494
$155$	0	0
$156$	2.00000	0.160128
$157$	−4.00000	−0.319235	−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000	−0.319235	−0.159617	+	0.987179i	$0.551026\pi$
$158$	−8.00000	−0.636446
$159$	−12.0000	−0.951662
$160$	0	0
$161$	1.00000	0.0788110
$162$	−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
$166$	−6.00000	−0.465690
$167$	24.0000	1.85718	0.928588	−	0.371113i	$-0.121024\pi$
$167$	24.0000	1.85718	0.928588	+	0.371113i	$0.121024\pi$
$168$	−1.00000	−0.0771517
$169$	−9.00000	−0.692308
$170$	0	0
$171$	2.00000	0.152944
$172$	2.00000	0.152499
$173$	−18.0000	−1.36851	−0.684257	−	0.729241i	$-0.739873\pi$
$173$	−18.0000	−1.36851	−0.684257	+	0.729241i	$0.739873\pi$
$174$	6.00000	0.454859
$175$	−5.00000	−0.377964
$176$	6.00000	0.452267
$177$	0	0
$178$	−6.00000	−0.449719
$179$	−24.0000	−1.79384	−0.896922	−	0.442189i	$-0.854202\pi$
$179$	−24.0000	−1.79384	−0.896922	+	0.442189i	$0.854202\pi$
$180$	0	0
$181$	8.00000	0.594635	0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000	0.594635	0.297318	+	0.954779i	$0.403908\pi$
$182$	−2.00000	−0.148250
$183$	8.00000	0.591377
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	−8.00000	−0.586588
$187$	−36.0000	−2.63258
$188$	0	0
$189$	1.00000	0.0727393
$190$	0	0
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	1.00000	0.0721688
$193$	−22.0000	−1.58359	−0.791797	−	0.610784i	$-0.790854\pi$
$193$	−22.0000	−1.58359	−0.791797	+	0.610784i	$0.790854\pi$
$194$	10.0000	0.717958
$195$	0	0
$196$	1.00000	0.0714286
$197$	−6.00000	−0.427482	−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000	−0.427482	−0.213741	+	0.976890i	$0.568565\pi$
$198$	−6.00000	−0.426401
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	5.00000	0.353553
$201$	−10.0000	−0.705346
$202$	6.00000	0.422159
$203$	−6.00000	−0.421117
$204$	−6.00000	−0.420084
$205$	0	0
$206$	4.00000	0.278693
$207$	1.00000	0.0695048
$208$	2.00000	0.138675
$209$	12.0000	0.830057
$210$	0	0
$211$	−4.00000	−0.275371	−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000	−0.275371	−0.137686	+	0.990476i	$0.543966\pi$
$212$	−12.0000	−0.824163
$213$	0	0
$214$	6.00000	0.410152
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	8.00000	0.543075
$218$	4.00000	0.270914
$219$	14.0000	0.946032
$220$	0	0
$221$	−12.0000	−0.807207
$222$	−8.00000	−0.536925
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	−1.00000	−0.0668153
$225$	−5.00000	−0.333333
$226$	−6.00000	−0.399114
$227$	18.0000	1.19470	0.597351	−	0.801980i	$-0.296220\pi$
$227$	18.0000	1.19470	0.597351	+	0.801980i	$0.296220\pi$
$228$	2.00000	0.132453
$229$	8.00000	0.528655	0.264327	−	0.964433i	$-0.414850\pi$
$229$	8.00000	0.528655	0.264327	+	0.964433i	$0.414850\pi$
$230$	0	0
$231$	6.00000	0.394771
$232$	6.00000	0.393919
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	−2.00000	−0.130744
$235$	0	0
$236$	0	0
$237$	8.00000	0.519656
$238$	6.00000	0.388922
$239$	−24.0000	−1.55243	−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000	−1.55243	−0.776215	+	0.630468i	$0.782863\pi$
$240$	0	0
$241$	−10.0000	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$242$	−25.0000	−1.60706
$243$	1.00000	0.0641500
$244$	8.00000	0.512148
$245$	0	0
$246$	−6.00000	−0.382546
$247$	4.00000	0.254514
$248$	−8.00000	−0.508001
$249$	6.00000	0.380235
$250$	0	0
$251$	6.00000	0.378717	0.189358	−	0.981908i	$-0.439359\pi$
$251$	6.00000	0.378717	0.189358	+	0.981908i	$0.439359\pi$
$252$	1.00000	0.0629941
$253$	6.00000	0.377217
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	−18.0000	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	−2.00000	−0.124515
$259$	8.00000	0.497096
$260$	0	0
$261$	−6.00000	−0.371391
$262$	0	0
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	−6.00000	−0.369274
$265$	0	0
$266$	−2.00000	−0.122628
$267$	6.00000	0.367194
$268$	−10.0000	−0.610847
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	0	0
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	−6.00000	−0.363803
$273$	2.00000	0.121046
$274$	6.00000	0.362473
$275$	−30.0000	−1.80907
$276$	1.00000	0.0601929
$277$	26.0000	1.56219	0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000	1.56219	0.781094	+	0.624413i	$0.214662\pi$
$278$	16.0000	0.959616
$279$	8.00000	0.478947
$280$	0	0
$281$	6.00000	0.357930	0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000	0.357930	0.178965	+	0.983855i	$0.442725\pi$
$282$	0	0
$283$	−10.0000	−0.594438	−0.297219	−	0.954809i	$-0.596059\pi$
$283$	−10.0000	−0.594438	−0.297219	+	0.954809i	$0.596059\pi$
$284$	0	0
$285$	0	0
$286$	−12.0000	−0.709575
$287$	6.00000	0.354169
$288$	−1.00000	−0.0589256
$289$	19.0000	1.11765
$290$	0	0
$291$	−10.0000	−0.586210
$292$	14.0000	0.819288
$293$	24.0000	1.40209	0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000	1.40209	0.701047	+	0.713115i	$0.252716\pi$
$294$	−1.00000	−0.0583212
$295$	0	0
$296$	−8.00000	−0.464991
$297$	6.00000	0.348155
$298$	−12.0000	−0.695141
$299$	2.00000	0.115663
$300$	−5.00000	−0.288675
$301$	2.00000	0.115278
$302$	−8.00000	−0.460348
$303$	−6.00000	−0.344691
$304$	2.00000	0.114708
$305$	0	0
$306$	6.00000	0.342997
$307$	−4.00000	−0.228292	−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000	−0.228292	−0.114146	+	0.993464i	$0.536413\pi$
$308$	6.00000	0.341882
$309$	−4.00000	−0.227552
$310$	0	0
$311$	−24.0000	−1.36092	−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000	−1.36092	−0.680458	+	0.732787i	$0.738219\pi$
$312$	−2.00000	−0.113228
$313$	−34.0000	−1.92179	−0.960897	−	0.276907i	$-0.910691\pi$
$313$	−34.0000	−1.92179	−0.960897	+	0.276907i	$0.910691\pi$
$314$	4.00000	0.225733
$315$	0	0
$316$	8.00000	0.450035
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	12.0000	0.672927
$319$	−36.0000	−2.01561
$320$	0	0
$321$	−6.00000	−0.334887
$322$	−1.00000	−0.0557278
$323$	−12.0000	−0.667698
$324$	1.00000	0.0555556
$325$	−10.0000	−0.554700
$326$	16.0000	0.886158
$327$	−4.00000	−0.221201
$328$	−6.00000	−0.331295
$329$	0	0
$330$	0	0
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	6.00000	0.329293
$333$	8.00000	0.438397
$334$	−24.0000	−1.31322
$335$	0	0
$336$	1.00000	0.0545545
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	9.00000	0.489535
$339$	6.00000	0.325875
$340$	0	0
$341$	48.0000	2.59935
$342$	−2.00000	−0.108148
$343$	1.00000	0.0539949
$344$	−2.00000	−0.107833
$345$	0	0
$346$	18.0000	0.967686
$347$	−24.0000	−1.28839	−0.644194	−	0.764862i	$-0.722807\pi$
$347$	−24.0000	−1.28839	−0.644194	+	0.764862i	$0.722807\pi$
$348$	−6.00000	−0.321634
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	5.00000	0.267261
$351$	2.00000	0.106752
$352$	−6.00000	−0.319801
$353$	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
$355$	0	0
$356$	6.00000	0.317999
$357$	−6.00000	−0.317554
$358$	24.0000	1.26844
$359$	36.0000	1.90001	0.950004	−	0.312239i	$-0.101079\pi$
$359$	36.0000	1.90001	0.950004	+	0.312239i	$0.101079\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	−8.00000	−0.420471
$363$	25.0000	1.31216
$364$	2.00000	0.104828
$365$	0	0
$366$	−8.00000	−0.418167
$367$	−16.0000	−0.835193	−0.417597	−	0.908633i	$-0.637127\pi$
$367$	−16.0000	−0.835193	−0.417597	+	0.908633i	$0.637127\pi$
$368$	1.00000	0.0521286
$369$	6.00000	0.312348
$370$	0	0
$371$	−12.0000	−0.623009
$372$	8.00000	0.414781
$373$	−16.0000	−0.828449	−0.414224	−	0.910175i	$-0.635947\pi$
$373$	−16.0000	−0.828449	−0.414224	+	0.910175i	$0.635947\pi$
$374$	36.0000	1.86152
$375$	0	0
$376$	0	0
$377$	−12.0000	−0.618031
$378$	−1.00000	−0.0514344
$379$	−10.0000	−0.513665	−0.256833	−	0.966456i	$-0.582679\pi$
$379$	−10.0000	−0.513665	−0.256833	+	0.966456i	$0.582679\pi$
$380$	0	0
$381$	8.00000	0.409852
$382$	12.0000	0.613973
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	22.0000	1.11977
$387$	2.00000	0.101666
$388$	−10.0000	−0.507673
$389$	24.0000	1.21685	0.608424	−	0.793612i	$-0.291802\pi$
$389$	24.0000	1.21685	0.608424	+	0.793612i	$0.291802\pi$
$390$	0	0
$391$	−6.00000	−0.303433
$392$	−1.00000	−0.0505076
$393$	0	0
$394$	6.00000	0.302276
$395$	0	0
$396$	6.00000	0.301511
$397$	26.0000	1.30490	0.652451	−	0.757831i	$-0.273741\pi$
$397$	26.0000	1.30490	0.652451	+	0.757831i	$0.273741\pi$
$398$	16.0000	0.802008
$399$	2.00000	0.100125
$400$	−5.00000	−0.250000
$401$	−30.0000	−1.49813	−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000	−1.49813	−0.749064	+	0.662497i	$0.769497\pi$
$402$	10.0000	0.498755
$403$	16.0000	0.797017
$404$	−6.00000	−0.298511
$405$	0	0
$406$	6.00000	0.297775
$407$	48.0000	2.37927
$408$	6.00000	0.297044
$409$	−22.0000	−1.08783	−0.543915	−	0.839140i	$-0.683059\pi$
$409$	−22.0000	−1.08783	−0.543915	+	0.839140i	$0.683059\pi$
$410$	0	0
$411$	−6.00000	−0.295958
$412$	−4.00000	−0.197066
$413$	0	0
$414$	−1.00000	−0.0491473
$415$	0	0
$416$	−2.00000	−0.0980581
$417$	−16.0000	−0.783523
$418$	−12.0000	−0.586939
$419$	−18.0000	−0.879358	−0.439679	−	0.898155i	$-0.644908\pi$
$419$	−18.0000	−0.879358	−0.439679	+	0.898155i	$0.644908\pi$
$420$	0	0
$421$	8.00000	0.389896	0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000	0.389896	0.194948	+	0.980814i	$0.437546\pi$
$422$	4.00000	0.194717
$423$	0	0
$424$	12.0000	0.582772
$425$	30.0000	1.45521
$426$	0	0
$427$	8.00000	0.387147
$428$	−6.00000	−0.290021
$429$	12.0000	0.579365
$430$	0	0
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	1.00000	0.0481125
$433$	38.0000	1.82616	0.913082	−	0.407777i	$-0.133696\pi$
$433$	38.0000	1.82616	0.913082	+	0.407777i	$0.133696\pi$
$434$	−8.00000	−0.384012
$435$	0	0
$436$	−4.00000	−0.191565
$437$	2.00000	0.0956730
$438$	−14.0000	−0.668946
$439$	8.00000	0.381819	0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000	0.381819	0.190910	+	0.981608i	$0.438856\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	12.0000	0.570782
$443$	0	0		−	1.00000i	$-0.5\pi$
$443$	0	0			1.00000i	$0.5\pi$
$444$	8.00000	0.379663
$445$	0	0
$446$	−8.00000	−0.378811
$447$	12.0000	0.567581
$448$	1.00000	0.0472456
$449$	6.00000	0.283158	0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000	0.283158	0.141579	+	0.989927i	$0.454782\pi$
$450$	5.00000	0.235702
$451$	36.0000	1.69517
$452$	6.00000	0.282216
$453$	8.00000	0.375873
$454$	−18.0000	−0.844782
$455$	0	0
$456$	−2.00000	−0.0936586
$457$	−34.0000	−1.59045	−0.795226	−	0.606313i	$-0.792648\pi$
$457$	−34.0000	−1.59045	−0.795226	+	0.606313i	$0.792648\pi$
$458$	−8.00000	−0.373815
$459$	−6.00000	−0.280056
$460$	0	0
$461$	30.0000	1.39724	0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000	1.39724	0.698620	+	0.715493i	$0.253798\pi$
$462$	−6.00000	−0.279145
$463$	−16.0000	−0.743583	−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000	−0.743583	−0.371792	+	0.928316i	$0.621256\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	6.00000	0.277945
$467$	30.0000	1.38823	0.694117	−	0.719862i	$-0.255795\pi$
$467$	30.0000	1.38823	0.694117	+	0.719862i	$0.255795\pi$
$468$	2.00000	0.0924500
$469$	−10.0000	−0.461757
$470$	0	0
$471$	−4.00000	−0.184310
$472$	0	0
$473$	12.0000	0.551761
$474$	−8.00000	−0.367452
$475$	−10.0000	−0.458831
$476$	−6.00000	−0.275010
$477$	−12.0000	−0.549442
$478$	24.0000	1.09773
$479$	24.0000	1.09659	0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000	1.09659	0.548294	+	0.836286i	$0.315277\pi$
$480$	0	0
$481$	16.0000	0.729537
$482$	10.0000	0.455488
$483$	1.00000	0.0455016
$484$	25.0000	1.13636
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	−40.0000	−1.81257	−0.906287	−	0.422664i	$-0.861095\pi$
$487$	−40.0000	−1.81257	−0.906287	+	0.422664i	$0.861095\pi$
$488$	−8.00000	−0.362143
$489$	−16.0000	−0.723545
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	6.00000	0.270501
$493$	36.0000	1.62136
$494$	−4.00000	−0.179969
$495$	0	0
$496$	8.00000	0.359211
$497$	0	0
$498$	−6.00000	−0.268866
$499$	−16.0000	−0.716258	−0.358129	−	0.933672i	$-0.616585\pi$
$499$	−16.0000	−0.716258	−0.358129	+	0.933672i	$0.616585\pi$
$500$	0	0
$501$	24.0000	1.07224
$502$	−6.00000	−0.267793
$503$	12.0000	0.535054	0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000	0.535054	0.267527	+	0.963550i	$0.413794\pi$
$504$	−1.00000	−0.0445435
$505$	0	0
$506$	−6.00000	−0.266733
$507$	−9.00000	−0.399704
$508$	8.00000	0.354943
$509$	−42.0000	−1.86162	−0.930809	−	0.365507i	$-0.880896\pi$
$509$	−42.0000	−1.86162	−0.930809	+	0.365507i	$0.880896\pi$
$510$	0	0
$511$	14.0000	0.619324
$512$	−1.00000	−0.0441942
$513$	2.00000	0.0883022
$514$	18.0000	0.793946
$515$	0	0
$516$	2.00000	0.0880451
$517$	0	0
$518$	−8.00000	−0.351500
$519$	−18.0000	−0.790112
$520$	0	0
$521$	42.0000	1.84005	0.920027	−	0.391856i	$-0.128167\pi$
$521$	42.0000	1.84005	0.920027	+	0.391856i	$0.128167\pi$
$522$	6.00000	0.262613
$523$	26.0000	1.13690	0.568450	−	0.822718i	$-0.307543\pi$
$523$	26.0000	1.13690	0.568450	+	0.822718i	$0.307543\pi$
$524$	0	0
$525$	−5.00000	−0.218218
$526$	24.0000	1.04645
$527$	−48.0000	−2.09091
$528$	6.00000	0.261116
$529$	1.00000	0.0434783
$530$	0	0
$531$	0	0
$532$	2.00000	0.0867110
$533$	12.0000	0.519778
$534$	−6.00000	−0.259645
$535$	0	0
$536$	10.0000	0.431934
$537$	−24.0000	−1.03568
$538$	18.0000	0.776035
$539$	6.00000	0.258438
$540$	0	0
$541$	26.0000	1.11783	0.558914	−	0.829226i	$-0.311218\pi$
$541$	26.0000	1.11783	0.558914	+	0.829226i	$0.311218\pi$
$542$	16.0000	0.687259
$543$	8.00000	0.343313
$544$	6.00000	0.257248
$545$	0	0
$546$	−2.00000	−0.0855921
$547$	−28.0000	−1.19719	−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000	−1.19719	−0.598597	+	0.801050i	$0.704275\pi$
$548$	−6.00000	−0.256307
$549$	8.00000	0.341432
$550$	30.0000	1.27920
$551$	−12.0000	−0.511217
$552$	−1.00000	−0.0425628
$553$	8.00000	0.340195
$554$	−26.0000	−1.10463
$555$	0	0
$556$	−16.0000	−0.678551
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	−8.00000	−0.338667
$559$	4.00000	0.169182
$560$	0	0
$561$	−36.0000	−1.51992
$562$	−6.00000	−0.253095
$563$	18.0000	0.758610	0.379305	−	0.925272i	$-0.376163\pi$
$563$	18.0000	0.758610	0.379305	+	0.925272i	$0.376163\pi$
$564$	0	0
$565$	0	0
$566$	10.0000	0.420331
$567$	1.00000	0.0419961
$568$	0	0
$569$	18.0000	0.754599	0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000	0.754599	0.377300	+	0.926091i	$0.376853\pi$
$570$	0	0
$571$	−10.0000	−0.418487	−0.209243	−	0.977864i	$-0.567100\pi$
$571$	−10.0000	−0.418487	−0.209243	+	0.977864i	$0.567100\pi$
$572$	12.0000	0.501745
$573$	−12.0000	−0.501307
$574$	−6.00000	−0.250435
$575$	−5.00000	−0.208514
$576$	1.00000	0.0416667
$577$	−10.0000	−0.416305	−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000	−0.416305	−0.208153	+	0.978096i	$0.566745\pi$
$578$	−19.0000	−0.790296
$579$	−22.0000	−0.914289
$580$	0	0
$581$	6.00000	0.248922
$582$	10.0000	0.414513
$583$	−72.0000	−2.98194
$584$	−14.0000	−0.579324
$585$	0	0
$586$	−24.0000	−0.991431
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	1.00000	0.0412393
$589$	16.0000	0.659269
$590$	0	0
$591$	−6.00000	−0.246807
$592$	8.00000	0.328798
$593$	30.0000	1.23195	0.615976	−	0.787765i	$-0.288762\pi$
$593$	30.0000	1.23195	0.615976	+	0.787765i	$0.288762\pi$
$594$	−6.00000	−0.246183
$595$	0	0
$596$	12.0000	0.491539
$597$	−16.0000	−0.654836
$598$	−2.00000	−0.0817861
$599$	24.0000	0.980613	0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000	0.980613	0.490307	+	0.871550i	$0.336885\pi$
$600$	5.00000	0.204124
$601$	14.0000	0.571072	0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000	0.571072	0.285536	+	0.958368i	$0.407828\pi$
$602$	−2.00000	−0.0815139
$603$	−10.0000	−0.407231
$604$	8.00000	0.325515
$605$	0	0
$606$	6.00000	0.243733
$607$	−40.0000	−1.62355	−0.811775	−	0.583970i	$-0.801498\pi$
$607$	−40.0000	−1.62355	−0.811775	+	0.583970i	$0.801498\pi$
$608$	−2.00000	−0.0811107
$609$	−6.00000	−0.243132
$610$	0	0
$611$	0	0
$612$	−6.00000	−0.242536
$613$	20.0000	0.807792	0.403896	−	0.914805i	$-0.367656\pi$
$613$	20.0000	0.807792	0.403896	+	0.914805i	$0.367656\pi$
$614$	4.00000	0.161427
$615$	0	0
$616$	−6.00000	−0.241747
$617$	6.00000	0.241551	0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000	0.241551	0.120775	+	0.992680i	$0.461462\pi$
$618$	4.00000	0.160904
$619$	38.0000	1.52735	0.763674	−	0.645601i	$-0.223393\pi$
$619$	38.0000	1.52735	0.763674	+	0.645601i	$0.223393\pi$
$620$	0	0
$621$	1.00000	0.0401286
$622$	24.0000	0.962312
$623$	6.00000	0.240385
$624$	2.00000	0.0800641
$625$	25.0000	1.00000
$626$	34.0000	1.35891
$627$	12.0000	0.479234
$628$	−4.00000	−0.159617
$629$	−48.0000	−1.91389
$630$	0	0
$631$	20.0000	0.796187	0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000	0.796187	0.398094	+	0.917345i	$0.369672\pi$
$632$	−8.00000	−0.318223
$633$	−4.00000	−0.158986
$634$	−18.0000	−0.714871
$635$	0	0
$636$	−12.0000	−0.475831
$637$	2.00000	0.0792429
$638$	36.0000	1.42525
$639$	0	0
$640$	0	0
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	6.00000	0.236801
$643$	−34.0000	−1.34083	−0.670415	−	0.741987i	$-0.733884\pi$
$643$	−34.0000	−1.34083	−0.670415	+	0.741987i	$0.733884\pi$
$644$	1.00000	0.0394055
$645$	0	0
$646$	12.0000	0.472134
$647$	−24.0000	−0.943537	−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000	−0.943537	−0.471769	+	0.881722i	$0.656384\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	10.0000	0.392232
$651$	8.00000	0.313545
$652$	−16.0000	−0.626608
$653$	6.00000	0.234798	0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000	0.234798	0.117399	+	0.993085i	$0.462544\pi$
$654$	4.00000	0.156412
$655$	0	0
$656$	6.00000	0.234261
$657$	14.0000	0.546192
$658$	0	0
$659$	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
$661$	8.00000	0.311164	0.155582	−	0.987823i	$-0.450275\pi$
$661$	8.00000	0.311164	0.155582	+	0.987823i	$0.450275\pi$
$662$	−20.0000	−0.777322
$663$	−12.0000	−0.466041
$664$	−6.00000	−0.232845
$665$	0	0
$666$	−8.00000	−0.309994
$667$	−6.00000	−0.232321
$668$	24.0000	0.928588
$669$	8.00000	0.309298
$670$	0	0
$671$	48.0000	1.85302
$672$	−1.00000	−0.0385758
$673$	14.0000	0.539660	0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000	0.539660	0.269830	+	0.962908i	$0.413032\pi$
$674$	22.0000	0.847408
$675$	−5.00000	−0.192450
$676$	−9.00000	−0.346154
$677$	24.0000	0.922395	0.461197	−	0.887298i	$-0.347420\pi$
$677$	24.0000	0.922395	0.461197	+	0.887298i	$0.347420\pi$
$678$	−6.00000	−0.230429
$679$	−10.0000	−0.383765
$680$	0	0
$681$	18.0000	0.689761
$682$	−48.0000	−1.83801
$683$	−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
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	8.00000	0.305219
$688$	2.00000	0.0762493
$689$	−24.0000	−0.914327
$690$	0	0
$691$	8.00000	0.304334	0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000	0.304334	0.152167	+	0.988355i	$0.451375\pi$
$692$	−18.0000	−0.684257
$693$	6.00000	0.227921
$694$	24.0000	0.911028
$695$	0	0
$696$	6.00000	0.227429
$697$	−36.0000	−1.36360
$698$	10.0000	0.378506
$699$	−6.00000	−0.226941
$700$	−5.00000	−0.188982
$701$	0	0		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	−2.00000	−0.0754851
$703$	16.0000	0.603451
$704$	6.00000	0.226134
$705$	0	0
$706$	−18.0000	−0.677439
$707$	−6.00000	−0.225653
$708$	0	0
$709$	8.00000	0.300446	0.150223	−	0.988652i	$-0.452001\pi$
$709$	8.00000	0.300446	0.150223	+	0.988652i	$0.452001\pi$
$710$	0	0
$711$	8.00000	0.300023
$712$	−6.00000	−0.224860
$713$	8.00000	0.299602
$714$	6.00000	0.224544
$715$	0	0
$716$	−24.0000	−0.896922
$717$	−24.0000	−0.896296
$718$	−36.0000	−1.34351
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	−4.00000	−0.148968
$722$	15.0000	0.558242
$723$	−10.0000	−0.371904
$724$	8.00000	0.297318
$725$	30.0000	1.11417
$726$	−25.0000	−0.927837
$727$	8.00000	0.296704	0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000	0.296704	0.148352	+	0.988935i	$0.452603\pi$
$728$	−2.00000	−0.0741249
$729$	1.00000	0.0370370
$730$	0	0
$731$	−12.0000	−0.443836
$732$	8.00000	0.295689
$733$	20.0000	0.738717	0.369358	−	0.929287i	$-0.379577\pi$
$733$	20.0000	0.738717	0.369358	+	0.929287i	$0.379577\pi$
$734$	16.0000	0.590571
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	−60.0000	−2.21013
$738$	−6.00000	−0.220863
$739$	8.00000	0.294285	0.147142	−	0.989115i	$-0.452992\pi$
$739$	8.00000	0.294285	0.147142	+	0.989115i	$0.452992\pi$
$740$	0	0
$741$	4.00000	0.146944
$742$	12.0000	0.440534
$743$	−48.0000	−1.76095	−0.880475	−	0.474093i	$-0.842776\pi$
$743$	−48.0000	−1.76095	−0.880475	+	0.474093i	$0.842776\pi$
$744$	−8.00000	−0.293294
$745$	0	0
$746$	16.0000	0.585802
$747$	6.00000	0.219529
$748$	−36.0000	−1.31629
$749$	−6.00000	−0.219235
$750$	0	0
$751$	20.0000	0.729810	0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000	0.729810	0.364905	+	0.931045i	$0.381101\pi$
$752$	0	0
$753$	6.00000	0.218652
$754$	12.0000	0.437014
$755$	0	0
$756$	1.00000	0.0363696
$757$	−52.0000	−1.88997	−0.944986	−	0.327111i	$-0.893925\pi$
$757$	−52.0000	−1.88997	−0.944986	+	0.327111i	$0.893925\pi$
$758$	10.0000	0.363216
$759$	6.00000	0.217786
$760$	0	0
$761$	−6.00000	−0.217500	−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000	−0.217500	−0.108750	+	0.994069i	$0.534685\pi$
$762$	−8.00000	−0.289809
$763$	−4.00000	−0.144810
$764$	−12.0000	−0.434145
$765$	0	0
$766$	0	0
$767$	0	0
$768$	1.00000	0.0360844
$769$	−10.0000	−0.360609	−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000	−0.360609	−0.180305	+	0.983611i	$0.557708\pi$
$770$	0	0
$771$	−18.0000	−0.648254
$772$	−22.0000	−0.791797
$773$	−36.0000	−1.29483	−0.647415	−	0.762138i	$-0.724150\pi$
$773$	−36.0000	−1.29483	−0.647415	+	0.762138i	$0.724150\pi$
$774$	−2.00000	−0.0718885
$775$	−40.0000	−1.43684
$776$	10.0000	0.358979
$777$	8.00000	0.286998
$778$	−24.0000	−0.860442
$779$	12.0000	0.429945
$780$	0	0
$781$	0	0
$782$	6.00000	0.214560
$783$	−6.00000	−0.214423
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	14.0000	0.499046	0.249523	−	0.968369i	$-0.419726\pi$
$787$	14.0000	0.499046	0.249523	+	0.968369i	$0.419726\pi$
$788$	−6.00000	−0.213741
$789$	−24.0000	−0.854423
$790$	0	0
$791$	6.00000	0.213335
$792$	−6.00000	−0.213201
$793$	16.0000	0.568177
$794$	−26.0000	−0.922705
$795$	0	0
$796$	−16.0000	−0.567105
$797$	12.0000	0.425062	0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000	0.425062	0.212531	+	0.977154i	$0.431829\pi$
$798$	−2.00000	−0.0707992
$799$	0	0
$800$	5.00000	0.176777
$801$	6.00000	0.212000
$802$	30.0000	1.05934
$803$	84.0000	2.96430
$804$	−10.0000	−0.352673
$805$	0	0
$806$	−16.0000	−0.563576
$807$	−18.0000	−0.633630
$808$	6.00000	0.211079
$809$	−6.00000	−0.210949	−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000	−0.210949	−0.105474	+	0.994422i	$0.533636\pi$
$810$	0	0
$811$	−16.0000	−0.561836	−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000	−0.561836	−0.280918	+	0.959732i	$0.590639\pi$
$812$	−6.00000	−0.210559
$813$	−16.0000	−0.561144
$814$	−48.0000	−1.68240
$815$	0	0
$816$	−6.00000	−0.210042
$817$	4.00000	0.139942
$818$	22.0000	0.769212
$819$	2.00000	0.0698857
$820$	0	0
$821$	−42.0000	−1.46581	−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000	−1.46581	−0.732905	+	0.680331i	$0.761836\pi$
$822$	6.00000	0.209274
$823$	−40.0000	−1.39431	−0.697156	−	0.716919i	$-0.745552\pi$
$823$	−40.0000	−1.39431	−0.697156	+	0.716919i	$0.745552\pi$
$824$	4.00000	0.139347
$825$	−30.0000	−1.04447
$826$	0	0
$827$	−30.0000	−1.04320	−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000	−1.04320	−0.521601	+	0.853189i	$0.674665\pi$
$828$	1.00000	0.0347524
$829$	38.0000	1.31979	0.659897	−	0.751356i	$-0.270600\pi$
$829$	38.0000	1.31979	0.659897	+	0.751356i	$0.270600\pi$
$830$	0	0
$831$	26.0000	0.901930
$832$	2.00000	0.0693375
$833$	−6.00000	−0.207888
$834$	16.0000	0.554035
$835$	0	0
$836$	12.0000	0.415029
$837$	8.00000	0.276520
$838$	18.0000	0.621800
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−8.00000	−0.275698
$843$	6.00000	0.206651
$844$	−4.00000	−0.137686
$845$	0	0
$846$	0	0
$847$	25.0000	0.859010
$848$	−12.0000	−0.412082
$849$	−10.0000	−0.343199
$850$	−30.0000	−1.02899
$851$	8.00000	0.274236
$852$	0	0
$853$	−22.0000	−0.753266	−0.376633	−	0.926363i	$-0.622918\pi$
$853$	−22.0000	−0.753266	−0.376633	+	0.926363i	$0.622918\pi$
$854$	−8.00000	−0.273754
$855$	0	0
$856$	6.00000	0.205076
$857$	−54.0000	−1.84460	−0.922302	−	0.386469i	$-0.873695\pi$
$857$	−54.0000	−1.84460	−0.922302	+	0.386469i	$0.873695\pi$
$858$	−12.0000	−0.409673
$859$	−4.00000	−0.136478	−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000	−0.136478	−0.0682391	+	0.997669i	$0.521738\pi$
$860$	0	0
$861$	6.00000	0.204479
$862$	−12.0000	−0.408722
$863$	24.0000	0.816970	0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000	0.816970	0.408485	+	0.912765i	$0.366057\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	−38.0000	−1.29129
$867$	19.0000	0.645274
$868$	8.00000	0.271538
$869$	48.0000	1.62829
$870$	0	0
$871$	−20.0000	−0.677674
$872$	4.00000	0.135457
$873$	−10.0000	−0.338449
$874$	−2.00000	−0.0676510
$875$	0	0
$876$	14.0000	0.473016
$877$	50.0000	1.68838	0.844190	−	0.536044i	$-0.180082\pi$
$877$	50.0000	1.68838	0.844190	+	0.536044i	$0.180082\pi$
$878$	−8.00000	−0.269987
$879$	24.0000	0.809500
$880$	0	0
$881$	54.0000	1.81931	0.909653	−	0.415369i	$-0.136347\pi$
$881$	54.0000	1.81931	0.909653	+	0.415369i	$0.136347\pi$
$882$	−1.00000	−0.0336718
$883$	−52.0000	−1.74994	−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000	−1.74994	−0.874970	+	0.484178i	$0.839119\pi$
$884$	−12.0000	−0.403604
$885$	0	0
$886$	0	0
$887$	24.0000	0.805841	0.402921	−	0.915235i	$-0.367995\pi$
$887$	24.0000	0.805841	0.402921	+	0.915235i	$0.367995\pi$
$888$	−8.00000	−0.268462
$889$	8.00000	0.268311
$890$	0	0
$891$	6.00000	0.201008
$892$	8.00000	0.267860
$893$	0	0
$894$	−12.0000	−0.401340
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	2.00000	0.0667781
$898$	−6.00000	−0.200223
$899$	−48.0000	−1.60089
$900$	−5.00000	−0.166667
$901$	72.0000	2.39867
$902$	−36.0000	−1.19867
$903$	2.00000	0.0665558
$904$	−6.00000	−0.199557
$905$	0	0
$906$	−8.00000	−0.265782
$907$	2.00000	0.0664089	0.0332045	−	0.999449i	$-0.489429\pi$
$907$	2.00000	0.0664089	0.0332045	+	0.999449i	$0.489429\pi$
$908$	18.0000	0.597351
$909$	−6.00000	−0.199007
$910$	0	0
$911$	12.0000	0.397578	0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000	0.397578	0.198789	+	0.980042i	$0.436299\pi$
$912$	2.00000	0.0662266
$913$	36.0000	1.19143
$914$	34.0000	1.12462
$915$	0	0
$916$	8.00000	0.264327
$917$	0	0
$918$	6.00000	0.198030
$919$	32.0000	1.05558	0.527791	−	0.849374i	$-0.323020\pi$
$919$	32.0000	1.05558	0.527791	+	0.849374i	$0.323020\pi$
$920$	0	0
$921$	−4.00000	−0.131804
$922$	−30.0000	−0.987997
$923$	0	0
$924$	6.00000	0.197386
$925$	−40.0000	−1.31519
$926$	16.0000	0.525793
$927$	−4.00000	−0.131377
$928$	6.00000	0.196960
$929$	30.0000	0.984268	0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000	0.984268	0.492134	+	0.870519i	$0.336217\pi$
$930$	0	0
$931$	2.00000	0.0655474
$932$	−6.00000	−0.196537
$933$	−24.0000	−0.785725
$934$	−30.0000	−0.981630
$935$	0	0
$936$	−2.00000	−0.0653720
$937$	−46.0000	−1.50275	−0.751377	−	0.659873i	$-0.770610\pi$
$937$	−46.0000	−1.50275	−0.751377	+	0.659873i	$0.770610\pi$
$938$	10.0000	0.326512
$939$	−34.0000	−1.10955
$940$	0	0
$941$	−48.0000	−1.56476	−0.782378	−	0.622804i	$-0.785993\pi$
$941$	−48.0000	−1.56476	−0.782378	+	0.622804i	$0.785993\pi$
$942$	4.00000	0.130327
$943$	6.00000	0.195387
$944$	0	0
$945$	0	0
$946$	−12.0000	−0.390154
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	8.00000	0.259828
$949$	28.0000	0.908918
$950$	10.0000	0.324443
$951$	18.0000	0.583690
$952$	6.00000	0.194461
$953$	42.0000	1.36051	0.680257	−	0.732974i	$-0.261868\pi$
$953$	42.0000	1.36051	0.680257	+	0.732974i	$0.261868\pi$
$954$	12.0000	0.388514
$955$	0	0
$956$	−24.0000	−0.776215
$957$	−36.0000	−1.16371
$958$	−24.0000	−0.775405
$959$	−6.00000	−0.193750
$960$	0	0
$961$	33.0000	1.06452
$962$	−16.0000	−0.515861
$963$	−6.00000	−0.193347
$964$	−10.0000	−0.322078
$965$	0	0
$966$	−1.00000	−0.0321745
$967$	−40.0000	−1.28631	−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000	−1.28631	−0.643157	+	0.765735i	$0.722376\pi$
$968$	−25.0000	−0.803530
$969$	−12.0000	−0.385496
$970$	0	0
$971$	18.0000	0.577647	0.288824	−	0.957382i	$-0.406736\pi$
$971$	18.0000	0.577647	0.288824	+	0.957382i	$0.406736\pi$
$972$	1.00000	0.0320750
$973$	−16.0000	−0.512936
$974$	40.0000	1.28168
$975$	−10.0000	−0.320256
$976$	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
$979$	36.0000	1.15056
$980$	0	0
$981$	−4.00000	−0.127710
$982$	0	0
$983$	60.0000	1.91370	0.956851	−	0.290578i	$-0.0938475\pi$
$983$	60.0000	1.91370	0.956851	+	0.290578i	$0.0938475\pi$
$984$	−6.00000	−0.191273
$985$	0	0
$986$	−36.0000	−1.14647
$987$	0	0
$988$	4.00000	0.127257
$989$	2.00000	0.0635963
$990$	0	0
$991$	8.00000	0.254128	0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000	0.254128	0.127064	+	0.991894i	$0.459445\pi$
$992$	−8.00000	−0.254000
$993$	20.0000	0.634681
$994$	0	0
$995$	0	0
$996$	6.00000	0.190117
$997$	14.0000	0.443384	0.221692	−	0.975117i	$-0.428842\pi$
$997$	14.0000	0.443384	0.221692	+	0.975117i	$0.428842\pi$
$998$	16.0000	0.506471
$999$	8.00000	0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.a.f.1.1	✓	1
3.2	odd	2		2898.2.a.o.1.1		1
4.3	odd	2		7728.2.a.c.1.1		1
7.6	odd	2		6762.2.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.a.f.1.1	✓	1	1.1	even	1	trivial
2898.2.a.o.1.1		1	3.2	odd	2
6762.2.a.h.1.1		1	7.6	odd	2
7728.2.a.c.1.1		1	4.3	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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