LMFDB - Embedded newform 1150.2.a.f.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1150,2,Mod(1,1150)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1150.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1150, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1150.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,1,-2,1,0,-2,-1,1,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$9.18279623245$
Analytic rank:	$1$
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	$\chi$	$=$	1150.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q+1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} -2.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +5.00000 q^{11} -2.00000 q^{12} -7.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} +1.00000 q^{18} -7.00000 q^{19} +2.00000 q^{21} +5.00000 q^{22} +1.00000 q^{23} -2.00000 q^{24} -7.00000 q^{26} +4.00000 q^{27} -1.00000 q^{28} +5.00000 q^{29} -10.0000 q^{31} +1.00000 q^{32} -10.0000 q^{33} +1.00000 q^{36} -2.00000 q^{37} -7.00000 q^{38} +14.0000 q^{39} +3.00000 q^{41} +2.00000 q^{42} -9.00000 q^{43} +5.00000 q^{44} +1.00000 q^{46} -8.00000 q^{47} -2.00000 q^{48} -6.00000 q^{49} -7.00000 q^{52} -4.00000 q^{53} +4.00000 q^{54} -1.00000 q^{56} +14.0000 q^{57} +5.00000 q^{58} -2.00000 q^{59} -6.00000 q^{61} -10.0000 q^{62} -1.00000 q^{63} +1.00000 q^{64} -10.0000 q^{66} -8.00000 q^{67} -2.00000 q^{69} -2.00000 q^{71} +1.00000 q^{72} +7.00000 q^{73} -2.00000 q^{74} -7.00000 q^{76} -5.00000 q^{77} +14.0000 q^{78} +1.00000 q^{79} -11.0000 q^{81} +3.00000 q^{82} -17.0000 q^{83} +2.00000 q^{84} -9.00000 q^{86} -10.0000 q^{87} +5.00000 q^{88} +6.00000 q^{89} +7.00000 q^{91} +1.00000 q^{92} +20.0000 q^{93} -8.00000 q^{94} -2.00000 q^{96} -4.00000 q^{97} -6.00000 q^{98} +5.00000 q^{99} +O(q^{100})\)

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
$3$	−2.00000	−1.15470	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−2.00000	−0.816497
$7$	−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
$10$	0	0
$11$	5.00000	1.50756	0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000	1.50756	0.753778	+	0.657129i	$0.228229\pi$
$12$	−2.00000	−0.577350
$13$	−7.00000	−1.94145	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−7.00000	−1.94145	−0.970725	+	0.240192i	$0.922790\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	1.00000	0.235702
$19$	−7.00000	−1.60591	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−7.00000	−1.60591	−0.802955	+	0.596040i	$0.796740\pi$
$20$	0	0
$21$	2.00000	0.436436
$22$	5.00000	1.06600
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.00000	−0.408248
$25$	0	0
$26$	−7.00000	−1.37281
$27$	4.00000	0.769800
$28$	−1.00000	−0.188982
$29$	5.00000	0.928477	0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000	0.928477	0.464238	+	0.885710i	$0.346328\pi$
$30$	0	0
$31$	−10.0000	−1.79605	−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−10.0000	−1.79605	−0.898027	+	0.439941i	$0.854999\pi$
$32$	1.00000	0.176777
$33$	−10.0000	−1.74078
$34$	0	0
$35$	0	0
$36$	1.00000	0.166667
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	−7.00000	−1.13555
$39$	14.0000	2.24179
$40$	0	0
$41$	3.00000	0.468521	0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000	0.468521	0.234261	+	0.972174i	$0.424733\pi$
$42$	2.00000	0.308607
$43$	−9.00000	−1.37249	−0.686244	−	0.727372i	$-0.740742\pi$
$43$	−9.00000	−1.37249	−0.686244	+	0.727372i	$0.740742\pi$
$44$	5.00000	0.753778
$45$	0	0
$46$	1.00000	0.147442
$47$	−8.00000	−1.16692	−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000	−1.16692	−0.583460	+	0.812142i	$0.698301\pi$
$48$	−2.00000	−0.288675
$49$	−6.00000	−0.857143
$50$	0	0
$51$	0	0
$52$	−7.00000	−0.970725
$53$	−4.00000	−0.549442	−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000	−0.549442	−0.274721	+	0.961524i	$0.588586\pi$
$54$	4.00000	0.544331
$55$	0	0
$56$	−1.00000	−0.133631
$57$	14.0000	1.85435
$58$	5.00000	0.656532
$59$	−2.00000	−0.260378	−0.130189	−	0.991489i	$-0.541558\pi$
$59$	−2.00000	−0.260378	−0.130189	+	0.991489i	$0.541558\pi$
$60$	0	0
$61$	−6.00000	−0.768221	−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000	−0.768221	−0.384111	+	0.923287i	$0.625492\pi$
$62$	−10.0000	−1.27000
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−10.0000	−1.23091
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	0	0
$69$	−2.00000	−0.240772
$70$	0	0
$71$	−2.00000	−0.237356	−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000	−0.237356	−0.118678	+	0.992933i	$0.537866\pi$
$72$	1.00000	0.117851
$73$	7.00000	0.819288	0.409644	−	0.912245i	$-0.365653\pi$
$73$	7.00000	0.819288	0.409644	+	0.912245i	$0.365653\pi$
$74$	−2.00000	−0.232495
$75$	0	0
$76$	−7.00000	−0.802955
$77$	−5.00000	−0.569803
$78$	14.0000	1.58519
$79$	1.00000	0.112509	0.0562544	−	0.998416i	$-0.482084\pi$
$79$	1.00000	0.112509	0.0562544	+	0.998416i	$0.482084\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	3.00000	0.331295
$83$	−17.0000	−1.86599	−0.932996	−	0.359886i	$-0.882816\pi$
$83$	−17.0000	−1.86599	−0.932996	+	0.359886i	$0.882816\pi$
$84$	2.00000	0.218218
$85$	0	0
$86$	−9.00000	−0.970495
$87$	−10.0000	−1.07211
$88$	5.00000	0.533002
$89$	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
$91$	7.00000	0.733799
$92$	1.00000	0.104257
$93$	20.0000	2.07390
$94$	−8.00000	−0.825137
$95$	0	0
$96$	−2.00000	−0.204124
$97$	−4.00000	−0.406138	−0.203069	−	0.979164i	$-0.565092\pi$
$97$	−4.00000	−0.406138	−0.203069	+	0.979164i	$0.565092\pi$
$98$	−6.00000	−0.606092
$99$	5.00000	0.502519
$100$	0	0
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	0	0
$103$	5.00000	0.492665	0.246332	−	0.969185i	$-0.420775\pi$
$103$	5.00000	0.492665	0.246332	+	0.969185i	$0.420775\pi$
$104$	−7.00000	−0.686406
$105$	0	0
$106$	−4.00000	−0.388514
$107$	16.0000	1.54678	0.773389	−	0.633932i	$-0.218560\pi$
$107$	16.0000	1.54678	0.773389	+	0.633932i	$0.218560\pi$
$108$	4.00000	0.384900
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	0	0
$111$	4.00000	0.379663
$112$	−1.00000	−0.0944911
$113$	16.0000	1.50515	0.752577	−	0.658505i	$-0.228811\pi$
$113$	16.0000	1.50515	0.752577	+	0.658505i	$0.228811\pi$
$114$	14.0000	1.31122
$115$	0	0
$116$	5.00000	0.464238
$117$	−7.00000	−0.647150
$118$	−2.00000	−0.184115
$119$	0	0
$120$	0	0
$121$	14.0000	1.27273
$122$	−6.00000	−0.543214
$123$	−6.00000	−0.541002
$124$	−10.0000	−0.898027
$125$	0	0
$126$	−1.00000	−0.0890871
$127$	10.0000	0.887357	0.443678	−	0.896186i	$-0.353673\pi$
$127$	10.0000	0.887357	0.443678	+	0.896186i	$0.353673\pi$
$128$	1.00000	0.0883883
$129$	18.0000	1.58481
$130$	0	0
$131$	10.0000	0.873704	0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000	0.873704	0.436852	+	0.899533i	$0.356093\pi$
$132$	−10.0000	−0.870388
$133$	7.00000	0.606977
$134$	−8.00000	−0.691095
$135$	0	0
$136$	0	0
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	−2.00000	−0.170251
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	0	0
$141$	16.0000	1.34744
$142$	−2.00000	−0.167836
$143$	−35.0000	−2.92685
$144$	1.00000	0.0833333
$145$	0	0
$146$	7.00000	0.579324
$147$	12.0000	0.989743
$148$	−2.00000	−0.164399
$149$	−10.0000	−0.819232	−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000	−0.819232	−0.409616	+	0.912258i	$0.634337\pi$
$150$	0	0
$151$	−22.0000	−1.79033	−0.895167	−	0.445730i	$-0.852944\pi$
$151$	−22.0000	−1.79033	−0.895167	+	0.445730i	$0.852944\pi$
$152$	−7.00000	−0.567775
$153$	0	0
$154$	−5.00000	−0.402911
$155$	0	0
$156$	14.0000	1.12090
$157$	8.00000	0.638470	0.319235	−	0.947676i	$-0.396574\pi$
$157$	8.00000	0.638470	0.319235	+	0.947676i	$0.396574\pi$
$158$	1.00000	0.0795557
$159$	8.00000	0.634441
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	−11.0000	−0.864242
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	3.00000	0.234261
$165$	0	0
$166$	−17.0000	−1.31946
$167$	14.0000	1.08335	0.541676	−	0.840587i	$-0.317790\pi$
$167$	14.0000	1.08335	0.541676	+	0.840587i	$0.317790\pi$
$168$	2.00000	0.154303
$169$	36.0000	2.76923
$170$	0	0
$171$	−7.00000	−0.535303
$172$	−9.00000	−0.686244
$173$	−1.00000	−0.0760286	−0.0380143	−	0.999277i	$-0.512103\pi$
$173$	−1.00000	−0.0760286	−0.0380143	+	0.999277i	$0.512103\pi$
$174$	−10.0000	−0.758098
$175$	0	0
$176$	5.00000	0.376889
$177$	4.00000	0.300658
$178$	6.00000	0.449719
$179$	−4.00000	−0.298974	−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000	−0.298974	−0.149487	+	0.988764i	$0.547762\pi$
$180$	0	0
$181$	16.0000	1.18927	0.594635	−	0.803996i	$-0.297296\pi$
$181$	16.0000	1.18927	0.594635	+	0.803996i	$0.297296\pi$
$182$	7.00000	0.518875
$183$	12.0000	0.887066
$184$	1.00000	0.0737210
$185$	0	0
$186$	20.0000	1.46647
$187$	0	0
$188$	−8.00000	−0.583460
$189$	−4.00000	−0.290957
$190$	0	0
$191$	−13.0000	−0.940647	−0.470323	−	0.882494i	$-0.655863\pi$
$191$	−13.0000	−0.940647	−0.470323	+	0.882494i	$0.655863\pi$
$192$	−2.00000	−0.144338
$193$	22.0000	1.58359	0.791797	−	0.610784i	$-0.209146\pi$
$193$	22.0000	1.58359	0.791797	+	0.610784i	$0.209146\pi$
$194$	−4.00000	−0.287183
$195$	0	0
$196$	−6.00000	−0.428571
$197$	−5.00000	−0.356235	−0.178118	−	0.984009i	$-0.557001\pi$
$197$	−5.00000	−0.356235	−0.178118	+	0.984009i	$0.557001\pi$
$198$	5.00000	0.355335
$199$	−23.0000	−1.63043	−0.815213	−	0.579161i	$-0.803380\pi$
$199$	−23.0000	−1.63043	−0.815213	+	0.579161i	$0.803380\pi$
$200$	0	0
$201$	16.0000	1.12855
$202$	10.0000	0.703598
$203$	−5.00000	−0.350931
$204$	0	0
$205$	0	0
$206$	5.00000	0.348367
$207$	1.00000	0.0695048
$208$	−7.00000	−0.485363
$209$	−35.0000	−2.42100
$210$	0	0
$211$	−14.0000	−0.963800	−0.481900	−	0.876226i	$-0.660053\pi$
$211$	−14.0000	−0.963800	−0.481900	+	0.876226i	$0.660053\pi$
$212$	−4.00000	−0.274721
$213$	4.00000	0.274075
$214$	16.0000	1.09374
$215$	0	0
$216$	4.00000	0.272166
$217$	10.0000	0.678844
$218$	−2.00000	−0.135457
$219$	−14.0000	−0.946032
$220$	0	0
$221$	0	0
$222$	4.00000	0.268462
$223$	4.00000	0.267860	0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000	0.267860	0.133930	+	0.990991i	$0.457240\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	16.0000	1.06430
$227$	−20.0000	−1.32745	−0.663723	−	0.747978i	$-0.731025\pi$
$227$	−20.0000	−1.32745	−0.663723	+	0.747978i	$0.731025\pi$
$228$	14.0000	0.927173
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	0	0
$231$	10.0000	0.657952
$232$	5.00000	0.328266
$233$	9.00000	0.589610	0.294805	−	0.955557i	$-0.404745\pi$
$233$	9.00000	0.589610	0.294805	+	0.955557i	$0.404745\pi$
$234$	−7.00000	−0.457604
$235$	0	0
$236$	−2.00000	−0.130189
$237$	−2.00000	−0.129914
$238$	0	0
$239$	−16.0000	−1.03495	−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000	−1.03495	−0.517477	+	0.855697i	$0.673129\pi$
$240$	0	0
$241$	16.0000	1.03065	0.515325	−	0.856995i	$-0.327671\pi$
$241$	16.0000	1.03065	0.515325	+	0.856995i	$0.327671\pi$
$242$	14.0000	0.899954
$243$	10.0000	0.641500
$244$	−6.00000	−0.384111
$245$	0	0
$246$	−6.00000	−0.382546
$247$	49.0000	3.11780
$248$	−10.0000	−0.635001
$249$	34.0000	2.15466
$250$	0	0
$251$	28.0000	1.76734	0.883672	−	0.468106i	$-0.155064\pi$
$251$	28.0000	1.76734	0.883672	+	0.468106i	$0.155064\pi$
$252$	−1.00000	−0.0629941
$253$	5.00000	0.314347
$254$	10.0000	0.627456
$255$	0	0
$256$	1.00000	0.0625000
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	18.0000	1.12063
$259$	2.00000	0.124274
$260$	0	0
$261$	5.00000	0.309492
$262$	10.0000	0.617802
$263$	8.00000	0.493301	0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000	0.493301	0.246651	+	0.969104i	$0.420670\pi$
$264$	−10.0000	−0.615457
$265$	0	0
$266$	7.00000	0.429198
$267$	−12.0000	−0.734388
$268$	−8.00000	−0.488678
$269$	−15.0000	−0.914566	−0.457283	−	0.889321i	$-0.651177\pi$
$269$	−15.0000	−0.914566	−0.457283	+	0.889321i	$0.651177\pi$
$270$	0	0
$271$	−20.0000	−1.21491	−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000	−1.21491	−0.607457	+	0.794353i	$0.707810\pi$
$272$	0	0
$273$	−14.0000	−0.847319
$274$	−6.00000	−0.362473
$275$	0	0
$276$	−2.00000	−0.120386
$277$	−9.00000	−0.540758	−0.270379	−	0.962754i	$-0.587149\pi$
$277$	−9.00000	−0.540758	−0.270379	+	0.962754i	$0.587149\pi$
$278$	4.00000	0.239904
$279$	−10.0000	−0.598684
$280$	0	0
$281$	8.00000	0.477240	0.238620	−	0.971113i	$-0.423305\pi$
$281$	8.00000	0.477240	0.238620	+	0.971113i	$0.423305\pi$
$282$	16.0000	0.952786
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	−2.00000	−0.118678
$285$	0	0
$286$	−35.0000	−2.06959
$287$	−3.00000	−0.177084
$288$	1.00000	0.0589256
$289$	−17.0000	−1.00000
$290$	0	0
$291$	8.00000	0.468968
$292$	7.00000	0.409644
$293$	16.0000	0.934730	0.467365	−	0.884064i	$-0.345203\pi$
$293$	16.0000	0.934730	0.467365	+	0.884064i	$0.345203\pi$
$294$	12.0000	0.699854
$295$	0	0
$296$	−2.00000	−0.116248
$297$	20.0000	1.16052
$298$	−10.0000	−0.579284
$299$	−7.00000	−0.404820
$300$	0	0
$301$	9.00000	0.518751
$302$	−22.0000	−1.26596
$303$	−20.0000	−1.14897
$304$	−7.00000	−0.401478
$305$	0	0
$306$	0	0
$307$	−4.00000	−0.228292	−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000	−0.228292	−0.114146	+	0.993464i	$0.536413\pi$
$308$	−5.00000	−0.284901
$309$	−10.0000	−0.568880
$310$	0	0
$311$	34.0000	1.92796	0.963982	−	0.265969i	$-0.0856919\pi$
$311$	34.0000	1.92796	0.963982	+	0.265969i	$0.0856919\pi$
$312$	14.0000	0.792594
$313$	34.0000	1.92179	0.960897	−	0.276907i	$-0.0893093\pi$
$313$	34.0000	1.92179	0.960897	+	0.276907i	$0.0893093\pi$
$314$	8.00000	0.451466
$315$	0	0
$316$	1.00000	0.0562544
$317$	−21.0000	−1.17948	−0.589739	−	0.807594i	$-0.700769\pi$
$317$	−21.0000	−1.17948	−0.589739	+	0.807594i	$0.700769\pi$
$318$	8.00000	0.448618
$319$	25.0000	1.39973
$320$	0	0
$321$	−32.0000	−1.78607
$322$	−1.00000	−0.0557278
$323$	0	0
$324$	−11.0000	−0.611111
$325$	0	0
$326$	−4.00000	−0.221540
$327$	4.00000	0.221201
$328$	3.00000	0.165647
$329$	8.00000	0.441054
$330$	0	0
$331$	−30.0000	−1.64895	−0.824475	−	0.565899i	$-0.808529\pi$
$331$	−30.0000	−1.64895	−0.824475	+	0.565899i	$0.808529\pi$
$332$	−17.0000	−0.932996
$333$	−2.00000	−0.109599
$334$	14.0000	0.766046
$335$	0	0
$336$	2.00000	0.109109
$337$	−16.0000	−0.871576	−0.435788	−	0.900049i	$-0.643530\pi$
$337$	−16.0000	−0.871576	−0.435788	+	0.900049i	$0.643530\pi$
$338$	36.0000	1.95814
$339$	−32.0000	−1.73800
$340$	0	0
$341$	−50.0000	−2.70765
$342$	−7.00000	−0.378517
$343$	13.0000	0.701934
$344$	−9.00000	−0.485247
$345$	0	0
$346$	−1.00000	−0.0537603
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	−10.0000	−0.536056
$349$	−27.0000	−1.44528	−0.722638	−	0.691226i	$-0.757071\pi$
$349$	−27.0000	−1.44528	−0.722638	+	0.691226i	$0.757071\pi$
$350$	0	0
$351$	−28.0000	−1.49453
$352$	5.00000	0.266501
$353$	−5.00000	−0.266123	−0.133062	−	0.991108i	$-0.542481\pi$
$353$	−5.00000	−0.266123	−0.133062	+	0.991108i	$0.542481\pi$
$354$	4.00000	0.212598
$355$	0	0
$356$	6.00000	0.317999
$357$	0	0
$358$	−4.00000	−0.211407
$359$	−31.0000	−1.63612	−0.818059	−	0.575135i	$-0.804950\pi$
$359$	−31.0000	−1.63612	−0.818059	+	0.575135i	$0.804950\pi$
$360$	0	0
$361$	30.0000	1.57895
$362$	16.0000	0.840941
$363$	−28.0000	−1.46962
$364$	7.00000	0.366900
$365$	0	0
$366$	12.0000	0.627250
$367$	3.00000	0.156599	0.0782994	−	0.996930i	$-0.475051\pi$
$367$	3.00000	0.156599	0.0782994	+	0.996930i	$0.475051\pi$
$368$	1.00000	0.0521286
$369$	3.00000	0.156174
$370$	0	0
$371$	4.00000	0.207670
$372$	20.0000	1.03695
$373$	−24.0000	−1.24267	−0.621336	−	0.783544i	$-0.713410\pi$
$373$	−24.0000	−1.24267	−0.621336	+	0.783544i	$0.713410\pi$
$374$	0	0
$375$	0	0
$376$	−8.00000	−0.412568
$377$	−35.0000	−1.80259
$378$	−4.00000	−0.205738
$379$	−4.00000	−0.205466	−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000	−0.205466	−0.102733	+	0.994709i	$0.532759\pi$
$380$	0	0
$381$	−20.0000	−1.02463
$382$	−13.0000	−0.665138
$383$	27.0000	1.37964	0.689818	−	0.723983i	$-0.257691\pi$
$383$	27.0000	1.37964	0.689818	+	0.723983i	$0.257691\pi$
$384$	−2.00000	−0.102062
$385$	0	0
$386$	22.0000	1.11977
$387$	−9.00000	−0.457496
$388$	−4.00000	−0.203069
$389$	−8.00000	−0.405616	−0.202808	−	0.979219i	$-0.565007\pi$
$389$	−8.00000	−0.405616	−0.202808	+	0.979219i	$0.565007\pi$
$390$	0	0
$391$	0	0
$392$	−6.00000	−0.303046
$393$	−20.0000	−1.00887
$394$	−5.00000	−0.251896
$395$	0	0
$396$	5.00000	0.251259
$397$	−26.0000	−1.30490	−0.652451	−	0.757831i	$-0.726259\pi$
$397$	−26.0000	−1.30490	−0.652451	+	0.757831i	$0.726259\pi$
$398$	−23.0000	−1.15289
$399$	−14.0000	−0.700877
$400$	0	0
$401$	2.00000	0.0998752	0.0499376	−	0.998752i	$-0.484098\pi$
$401$	2.00000	0.0998752	0.0499376	+	0.998752i	$0.484098\pi$
$402$	16.0000	0.798007
$403$	70.0000	3.48695
$404$	10.0000	0.497519
$405$	0	0
$406$	−5.00000	−0.248146
$407$	−10.0000	−0.495682
$408$	0	0
$409$	−19.0000	−0.939490	−0.469745	−	0.882802i	$-0.655654\pi$
$409$	−19.0000	−0.939490	−0.469745	+	0.882802i	$0.655654\pi$
$410$	0	0
$411$	12.0000	0.591916
$412$	5.00000	0.246332
$413$	2.00000	0.0984136
$414$	1.00000	0.0491473
$415$	0	0
$416$	−7.00000	−0.343203
$417$	−8.00000	−0.391762
$418$	−35.0000	−1.71191
$419$	3.00000	0.146560	0.0732798	−	0.997311i	$-0.476653\pi$
$419$	3.00000	0.146560	0.0732798	+	0.997311i	$0.476653\pi$
$420$	0	0
$421$	−30.0000	−1.46211	−0.731055	−	0.682318i	$-0.760972\pi$
$421$	−30.0000	−1.46211	−0.731055	+	0.682318i	$0.760972\pi$
$422$	−14.0000	−0.681509
$423$	−8.00000	−0.388973
$424$	−4.00000	−0.194257
$425$	0	0
$426$	4.00000	0.193801
$427$	6.00000	0.290360
$428$	16.0000	0.773389
$429$	70.0000	3.37963
$430$	0	0
$431$	8.00000	0.385346	0.192673	−	0.981263i	$-0.438284\pi$
$431$	8.00000	0.385346	0.192673	+	0.981263i	$0.438284\pi$
$432$	4.00000	0.192450
$433$	−14.0000	−0.672797	−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000	−0.672797	−0.336399	+	0.941720i	$0.609209\pi$
$434$	10.0000	0.480015
$435$	0	0
$436$	−2.00000	−0.0957826
$437$	−7.00000	−0.334855
$438$	−14.0000	−0.668946
$439$	−8.00000	−0.381819	−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000	−0.381819	−0.190910	+	0.981608i	$0.561144\pi$
$440$	0	0
$441$	−6.00000	−0.285714
$442$	0	0
$443$	−26.0000	−1.23530	−0.617649	−	0.786454i	$-0.711915\pi$
$443$	−26.0000	−1.23530	−0.617649	+	0.786454i	$0.711915\pi$
$444$	4.00000	0.189832
$445$	0	0
$446$	4.00000	0.189405
$447$	20.0000	0.945968
$448$	−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	$0.249646\pi$
$450$	0	0
$451$	15.0000	0.706322
$452$	16.0000	0.752577
$453$	44.0000	2.06730
$454$	−20.0000	−0.938647
$455$	0	0
$456$	14.0000	0.655610
$457$	−16.0000	−0.748448	−0.374224	−	0.927338i	$-0.622091\pi$
$457$	−16.0000	−0.748448	−0.374224	+	0.927338i	$0.622091\pi$
$458$	14.0000	0.654177
$459$	0	0
$460$	0	0
$461$	−3.00000	−0.139724	−0.0698620	−	0.997557i	$-0.522256\pi$
$461$	−3.00000	−0.139724	−0.0698620	+	0.997557i	$0.522256\pi$
$462$	10.0000	0.465242
$463$	4.00000	0.185896	0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000	0.185896	0.0929479	+	0.995671i	$0.470371\pi$
$464$	5.00000	0.232119
$465$	0	0
$466$	9.00000	0.416917
$467$	−3.00000	−0.138823	−0.0694117	−	0.997588i	$-0.522112\pi$
$467$	−3.00000	−0.138823	−0.0694117	+	0.997588i	$0.522112\pi$
$468$	−7.00000	−0.323575
$469$	8.00000	0.369406
$470$	0	0
$471$	−16.0000	−0.737241
$472$	−2.00000	−0.0920575
$473$	−45.0000	−2.06910
$474$	−2.00000	−0.0918630
$475$	0	0
$476$	0	0
$477$	−4.00000	−0.183147
$478$	−16.0000	−0.731823
$479$	27.0000	1.23366	0.616831	−	0.787096i	$-0.288416\pi$
$479$	27.0000	1.23366	0.616831	+	0.787096i	$0.288416\pi$
$480$	0	0
$481$	14.0000	0.638345
$482$	16.0000	0.728780
$483$	2.00000	0.0910032
$484$	14.0000	0.636364
$485$	0	0
$486$	10.0000	0.453609
$487$	−8.00000	−0.362515	−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000	−0.362515	−0.181257	+	0.983436i	$0.558017\pi$
$488$	−6.00000	−0.271607
$489$	8.00000	0.361773
$490$	0	0
$491$	−6.00000	−0.270776	−0.135388	−	0.990793i	$-0.543228\pi$
$491$	−6.00000	−0.270776	−0.135388	+	0.990793i	$0.543228\pi$
$492$	−6.00000	−0.270501
$493$	0	0
$494$	49.0000	2.20461
$495$	0	0
$496$	−10.0000	−0.449013
$497$	2.00000	0.0897123
$498$	34.0000	1.52358
$499$	−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
$501$	−28.0000	−1.25095
$502$	28.0000	1.24970
$503$	9.00000	0.401290	0.200645	−	0.979664i	$-0.435696\pi$
$503$	9.00000	0.401290	0.200645	+	0.979664i	$0.435696\pi$
$504$	−1.00000	−0.0445435
$505$	0	0
$506$	5.00000	0.222277
$507$	−72.0000	−3.19763
$508$	10.0000	0.443678
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	0	0
$511$	−7.00000	−0.309662
$512$	1.00000	0.0441942
$513$	−28.0000	−1.23623
$514$	18.0000	0.793946
$515$	0	0
$516$	18.0000	0.792406
$517$	−40.0000	−1.75920
$518$	2.00000	0.0878750
$519$	2.00000	0.0877903
$520$	0	0
$521$	30.0000	1.31432	0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000	1.31432	0.657162	+	0.753749i	$0.271757\pi$
$522$	5.00000	0.218844
$523$	−7.00000	−0.306089	−0.153044	−	0.988219i	$-0.548908\pi$
$523$	−7.00000	−0.306089	−0.153044	+	0.988219i	$0.548908\pi$
$524$	10.0000	0.436852
$525$	0	0
$526$	8.00000	0.348817
$527$	0	0
$528$	−10.0000	−0.435194
$529$	1.00000	0.0434783
$530$	0	0
$531$	−2.00000	−0.0867926
$532$	7.00000	0.303488
$533$	−21.0000	−0.909611
$534$	−12.0000	−0.519291
$535$	0	0
$536$	−8.00000	−0.345547
$537$	8.00000	0.345225
$538$	−15.0000	−0.646696
$539$	−30.0000	−1.29219
$540$	0	0
$541$	−11.0000	−0.472927	−0.236463	−	0.971640i	$-0.575988\pi$
$541$	−11.0000	−0.472927	−0.236463	+	0.971640i	$0.575988\pi$
$542$	−20.0000	−0.859074
$543$	−32.0000	−1.37325
$544$	0	0
$545$	0	0
$546$	−14.0000	−0.599145
$547$	−16.0000	−0.684111	−0.342055	−	0.939680i	$-0.611123\pi$
$547$	−16.0000	−0.684111	−0.342055	+	0.939680i	$0.611123\pi$
$548$	−6.00000	−0.256307
$549$	−6.00000	−0.256074
$550$	0	0
$551$	−35.0000	−1.49105
$552$	−2.00000	−0.0851257
$553$	−1.00000	−0.0425243
$554$	−9.00000	−0.382373
$555$	0	0
$556$	4.00000	0.169638
$557$	38.0000	1.61011	0.805056	−	0.593199i	$-0.202135\pi$
$557$	38.0000	1.61011	0.805056	+	0.593199i	$0.202135\pi$
$558$	−10.0000	−0.423334
$559$	63.0000	2.66462
$560$	0	0
$561$	0	0
$562$	8.00000	0.337460
$563$	15.0000	0.632175	0.316087	−	0.948730i	$-0.397631\pi$
$563$	15.0000	0.632175	0.316087	+	0.948730i	$0.397631\pi$
$564$	16.0000	0.673722
$565$	0	0
$566$	4.00000	0.168133
$567$	11.0000	0.461957
$568$	−2.00000	−0.0839181
$569$	−32.0000	−1.34151	−0.670755	−	0.741679i	$-0.734030\pi$
$569$	−32.0000	−1.34151	−0.670755	+	0.741679i	$0.734030\pi$
$570$	0	0
$571$	−12.0000	−0.502184	−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000	−0.502184	−0.251092	+	0.967963i	$0.580790\pi$
$572$	−35.0000	−1.46342
$573$	26.0000	1.08617
$574$	−3.00000	−0.125218
$575$	0	0
$576$	1.00000	0.0416667
$577$	−17.0000	−0.707719	−0.353860	−	0.935299i	$-0.615131\pi$
$577$	−17.0000	−0.707719	−0.353860	+	0.935299i	$0.615131\pi$
$578$	−17.0000	−0.707107
$579$	−44.0000	−1.82858
$580$	0	0
$581$	17.0000	0.705279
$582$	8.00000	0.331611
$583$	−20.0000	−0.828315
$584$	7.00000	0.289662
$585$	0	0
$586$	16.0000	0.660954
$587$	−18.0000	−0.742940	−0.371470	−	0.928445i	$-0.621146\pi$
$587$	−18.0000	−0.742940	−0.371470	+	0.928445i	$0.621146\pi$
$588$	12.0000	0.494872
$589$	70.0000	2.88430
$590$	0	0
$591$	10.0000	0.411345
$592$	−2.00000	−0.0821995
$593$	−15.0000	−0.615976	−0.307988	−	0.951390i	$-0.599656\pi$
$593$	−15.0000	−0.615976	−0.307988	+	0.951390i	$0.599656\pi$
$594$	20.0000	0.820610
$595$	0	0
$596$	−10.0000	−0.409616
$597$	46.0000	1.88265
$598$	−7.00000	−0.286251
$599$	2.00000	0.0817178	0.0408589	−	0.999165i	$-0.486991\pi$
$599$	2.00000	0.0817178	0.0408589	+	0.999165i	$0.486991\pi$
$600$	0	0
$601$	10.0000	0.407909	0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000	0.407909	0.203954	+	0.978980i	$0.434621\pi$
$602$	9.00000	0.366813
$603$	−8.00000	−0.325785
$604$	−22.0000	−0.895167
$605$	0	0
$606$	−20.0000	−0.812444
$607$	48.0000	1.94826	0.974130	−	0.225989i	$-0.0725612\pi$
$607$	48.0000	1.94826	0.974130	+	0.225989i	$0.0725612\pi$
$608$	−7.00000	−0.283887
$609$	10.0000	0.405220
$610$	0	0
$611$	56.0000	2.26552
$612$	0	0
$613$	14.0000	0.565455	0.282727	−	0.959200i	$-0.408761\pi$
$613$	14.0000	0.565455	0.282727	+	0.959200i	$0.408761\pi$
$614$	−4.00000	−0.161427
$615$	0	0
$616$	−5.00000	−0.201456
$617$	−48.0000	−1.93241	−0.966204	−	0.257780i	$-0.917009\pi$
$617$	−48.0000	−1.93241	−0.966204	+	0.257780i	$0.917009\pi$
$618$	−10.0000	−0.402259
$619$	40.0000	1.60774	0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000	1.60774	0.803868	+	0.594808i	$0.202772\pi$
$620$	0	0
$621$	4.00000	0.160514
$622$	34.0000	1.36328
$623$	−6.00000	−0.240385
$624$	14.0000	0.560449
$625$	0	0
$626$	34.0000	1.35891
$627$	70.0000	2.79553
$628$	8.00000	0.319235
$629$	0	0
$630$	0	0
$631$	−5.00000	−0.199047	−0.0995234	−	0.995035i	$-0.531732\pi$
$631$	−5.00000	−0.199047	−0.0995234	+	0.995035i	$0.531732\pi$
$632$	1.00000	0.0397779
$633$	28.0000	1.11290
$634$	−21.0000	−0.834017
$635$	0	0
$636$	8.00000	0.317221
$637$	42.0000	1.66410
$638$	25.0000	0.989759
$639$	−2.00000	−0.0791188
$640$	0	0
$641$	−24.0000	−0.947943	−0.473972	−	0.880540i	$-0.657180\pi$
$641$	−24.0000	−0.947943	−0.473972	+	0.880540i	$0.657180\pi$
$642$	−32.0000	−1.26294
$643$	−37.0000	−1.45914	−0.729569	−	0.683907i	$-0.760279\pi$
$643$	−37.0000	−1.45914	−0.729569	+	0.683907i	$0.760279\pi$
$644$	−1.00000	−0.0394055
$645$	0	0
$646$	0	0
$647$	28.0000	1.10079	0.550397	−	0.834903i	$-0.314476\pi$
$647$	28.0000	1.10079	0.550397	+	0.834903i	$0.314476\pi$
$648$	−11.0000	−0.432121
$649$	−10.0000	−0.392534
$650$	0	0
$651$	−20.0000	−0.783862
$652$	−4.00000	−0.156652
$653$	33.0000	1.29139	0.645695	−	0.763596i	$-0.276568\pi$
$653$	33.0000	1.29139	0.645695	+	0.763596i	$0.276568\pi$
$654$	4.00000	0.156412
$655$	0	0
$656$	3.00000	0.117130
$657$	7.00000	0.273096
$658$	8.00000	0.311872
$659$	27.0000	1.05177	0.525885	−	0.850555i	$-0.323734\pi$
$659$	27.0000	1.05177	0.525885	+	0.850555i	$0.323734\pi$
$660$	0	0
$661$	−16.0000	−0.622328	−0.311164	−	0.950356i	$-0.600719\pi$
$661$	−16.0000	−0.622328	−0.311164	+	0.950356i	$0.600719\pi$
$662$	−30.0000	−1.16598
$663$	0	0
$664$	−17.0000	−0.659728
$665$	0	0
$666$	−2.00000	−0.0774984
$667$	5.00000	0.193601
$668$	14.0000	0.541676
$669$	−8.00000	−0.309298
$670$	0	0
$671$	−30.0000	−1.15814
$672$	2.00000	0.0771517
$673$	1.00000	0.0385472	0.0192736	−	0.999814i	$-0.493865\pi$
$673$	1.00000	0.0385472	0.0192736	+	0.999814i	$0.493865\pi$
$674$	−16.0000	−0.616297
$675$	0	0
$676$	36.0000	1.38462
$677$	−22.0000	−0.845529	−0.422764	−	0.906240i	$-0.638940\pi$
$677$	−22.0000	−0.845529	−0.422764	+	0.906240i	$0.638940\pi$
$678$	−32.0000	−1.22895
$679$	4.00000	0.153506
$680$	0	0
$681$	40.0000	1.53280
$682$	−50.0000	−1.91460
$683$	−6.00000	−0.229584	−0.114792	−	0.993390i	$-0.536620\pi$
$683$	−6.00000	−0.229584	−0.114792	+	0.993390i	$0.536620\pi$
$684$	−7.00000	−0.267652
$685$	0	0
$686$	13.0000	0.496342
$687$	−28.0000	−1.06827
$688$	−9.00000	−0.343122
$689$	28.0000	1.06672
$690$	0	0
$691$	−28.0000	−1.06517	−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000	−1.06517	−0.532585	+	0.846376i	$0.678779\pi$
$692$	−1.00000	−0.0380143
$693$	−5.00000	−0.189934
$694$	12.0000	0.455514
$695$	0	0
$696$	−10.0000	−0.379049
$697$	0	0
$698$	−27.0000	−1.02197
$699$	−18.0000	−0.680823
$700$	0	0
$701$	12.0000	0.453234	0.226617	−	0.973984i	$-0.427233\pi$
$701$	12.0000	0.453234	0.226617	+	0.973984i	$0.427233\pi$
$702$	−28.0000	−1.05679
$703$	14.0000	0.528020
$704$	5.00000	0.188445
$705$	0	0
$706$	−5.00000	−0.188177
$707$	−10.0000	−0.376089
$708$	4.00000	0.150329
$709$	34.0000	1.27690	0.638448	−	0.769665i	$-0.279577\pi$
$709$	34.0000	1.27690	0.638448	+	0.769665i	$0.279577\pi$
$710$	0	0
$711$	1.00000	0.0375029
$712$	6.00000	0.224860
$713$	−10.0000	−0.374503
$714$	0	0
$715$	0	0
$716$	−4.00000	−0.149487
$717$	32.0000	1.19506
$718$	−31.0000	−1.15691
$719$	−50.0000	−1.86469	−0.932343	−	0.361576i	$-0.882239\pi$
$719$	−50.0000	−1.86469	−0.932343	+	0.361576i	$0.882239\pi$
$720$	0	0
$721$	−5.00000	−0.186210
$722$	30.0000	1.11648
$723$	−32.0000	−1.19009
$724$	16.0000	0.594635
$725$	0	0
$726$	−28.0000	−1.03918
$727$	−32.0000	−1.18681	−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000	−1.18681	−0.593407	+	0.804902i	$0.702218\pi$
$728$	7.00000	0.259437
$729$	13.0000	0.481481
$730$	0	0
$731$	0	0
$732$	12.0000	0.443533
$733$	−2.00000	−0.0738717	−0.0369358	−	0.999318i	$-0.511760\pi$
$733$	−2.00000	−0.0738717	−0.0369358	+	0.999318i	$0.511760\pi$
$734$	3.00000	0.110732
$735$	0	0
$736$	1.00000	0.0368605
$737$	−40.0000	−1.47342
$738$	3.00000	0.110432
$739$	2.00000	0.0735712	0.0367856	−	0.999323i	$-0.488288\pi$
$739$	2.00000	0.0735712	0.0367856	+	0.999323i	$0.488288\pi$
$740$	0	0
$741$	−98.0000	−3.60012
$742$	4.00000	0.146845
$743$	7.00000	0.256805	0.128403	−	0.991722i	$-0.459015\pi$
$743$	7.00000	0.256805	0.128403	+	0.991722i	$0.459015\pi$
$744$	20.0000	0.733236
$745$	0	0
$746$	−24.0000	−0.878702
$747$	−17.0000	−0.621997
$748$	0	0
$749$	−16.0000	−0.584627
$750$	0	0
$751$	−1.00000	−0.0364905	−0.0182453	−	0.999834i	$-0.505808\pi$
$751$	−1.00000	−0.0364905	−0.0182453	+	0.999834i	$0.505808\pi$
$752$	−8.00000	−0.291730
$753$	−56.0000	−2.04075
$754$	−35.0000	−1.27462
$755$	0	0
$756$	−4.00000	−0.145479
$757$	−10.0000	−0.363456	−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000	−0.363456	−0.181728	+	0.983349i	$0.558169\pi$
$758$	−4.00000	−0.145287
$759$	−10.0000	−0.362977
$760$	0	0
$761$	−15.0000	−0.543750	−0.271875	−	0.962333i	$-0.587644\pi$
$761$	−15.0000	−0.543750	−0.271875	+	0.962333i	$0.587644\pi$
$762$	−20.0000	−0.724524
$763$	2.00000	0.0724049
$764$	−13.0000	−0.470323
$765$	0	0
$766$	27.0000	0.975550
$767$	14.0000	0.505511
$768$	−2.00000	−0.0721688
$769$	50.0000	1.80305	0.901523	−	0.432731i	$-0.142450\pi$
$769$	50.0000	1.80305	0.901523	+	0.432731i	$0.142450\pi$
$770$	0	0
$771$	−36.0000	−1.29651
$772$	22.0000	0.791797
$773$	−18.0000	−0.647415	−0.323708	−	0.946157i	$-0.604929\pi$
$773$	−18.0000	−0.647415	−0.323708	+	0.946157i	$0.604929\pi$
$774$	−9.00000	−0.323498
$775$	0	0
$776$	−4.00000	−0.143592
$777$	−4.00000	−0.143499
$778$	−8.00000	−0.286814
$779$	−21.0000	−0.752403
$780$	0	0
$781$	−10.0000	−0.357828
$782$	0	0
$783$	20.0000	0.714742
$784$	−6.00000	−0.214286
$785$	0	0
$786$	−20.0000	−0.713376
$787$	−47.0000	−1.67537	−0.837685	−	0.546154i	$-0.816091\pi$
$787$	−47.0000	−1.67537	−0.837685	+	0.546154i	$0.816091\pi$
$788$	−5.00000	−0.178118
$789$	−16.0000	−0.569615
$790$	0	0
$791$	−16.0000	−0.568895
$792$	5.00000	0.177667
$793$	42.0000	1.49146
$794$	−26.0000	−0.922705
$795$	0	0
$796$	−23.0000	−0.815213
$797$	−30.0000	−1.06265	−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000	−1.06265	−0.531327	+	0.847167i	$0.678307\pi$
$798$	−14.0000	−0.495595
$799$	0	0
$800$	0	0
$801$	6.00000	0.212000
$802$	2.00000	0.0706225
$803$	35.0000	1.23512
$804$	16.0000	0.564276
$805$	0	0
$806$	70.0000	2.46564
$807$	30.0000	1.05605
$808$	10.0000	0.351799
$809$	−15.0000	−0.527372	−0.263686	−	0.964609i	$-0.584938\pi$
$809$	−15.0000	−0.527372	−0.263686	+	0.964609i	$0.584938\pi$
$810$	0	0
$811$	−24.0000	−0.842754	−0.421377	−	0.906886i	$-0.638453\pi$
$811$	−24.0000	−0.842754	−0.421377	+	0.906886i	$0.638453\pi$
$812$	−5.00000	−0.175466
$813$	40.0000	1.40286
$814$	−10.0000	−0.350500
$815$	0	0
$816$	0	0
$817$	63.0000	2.20409
$818$	−19.0000	−0.664319
$819$	7.00000	0.244600
$820$	0	0
$821$	15.0000	0.523504	0.261752	−	0.965135i	$-0.415700\pi$
$821$	15.0000	0.523504	0.261752	+	0.965135i	$0.415700\pi$
$822$	12.0000	0.418548
$823$	24.0000	0.836587	0.418294	−	0.908312i	$-0.362628\pi$
$823$	24.0000	0.836587	0.418294	+	0.908312i	$0.362628\pi$
$824$	5.00000	0.174183
$825$	0	0
$826$	2.00000	0.0695889
$827$	9.00000	0.312961	0.156480	−	0.987681i	$-0.449985\pi$
$827$	9.00000	0.312961	0.156480	+	0.987681i	$0.449985\pi$
$828$	1.00000	0.0347524
$829$	37.0000	1.28506	0.642532	−	0.766259i	$-0.277884\pi$
$829$	37.0000	1.28506	0.642532	+	0.766259i	$0.277884\pi$
$830$	0	0
$831$	18.0000	0.624413
$832$	−7.00000	−0.242681
$833$	0	0
$834$	−8.00000	−0.277017
$835$	0	0
$836$	−35.0000	−1.21050
$837$	−40.0000	−1.38260
$838$	3.00000	0.103633
$839$	−21.0000	−0.725001	−0.362500	−	0.931984i	$-0.618077\pi$
$839$	−21.0000	−0.725001	−0.362500	+	0.931984i	$0.618077\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	−30.0000	−1.03387
$843$	−16.0000	−0.551069
$844$	−14.0000	−0.481900
$845$	0	0
$846$	−8.00000	−0.275046
$847$	−14.0000	−0.481046
$848$	−4.00000	−0.137361
$849$	−8.00000	−0.274559
$850$	0	0
$851$	−2.00000	−0.0685591
$852$	4.00000	0.137038
$853$	−23.0000	−0.787505	−0.393753	−	0.919216i	$-0.628823\pi$
$853$	−23.0000	−0.787505	−0.393753	+	0.919216i	$0.628823\pi$
$854$	6.00000	0.205316
$855$	0	0
$856$	16.0000	0.546869
$857$	6.00000	0.204956	0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000	0.204956	0.102478	+	0.994735i	$0.467323\pi$
$858$	70.0000	2.38976
$859$	−22.0000	−0.750630	−0.375315	−	0.926897i	$-0.622466\pi$
$859$	−22.0000	−0.750630	−0.375315	+	0.926897i	$0.622466\pi$
$860$	0	0
$861$	6.00000	0.204479
$862$	8.00000	0.272481
$863$	−12.0000	−0.408485	−0.204242	−	0.978920i	$-0.565473\pi$
$863$	−12.0000	−0.408485	−0.204242	+	0.978920i	$0.565473\pi$
$864$	4.00000	0.136083
$865$	0	0
$866$	−14.0000	−0.475739
$867$	34.0000	1.15470
$868$	10.0000	0.339422
$869$	5.00000	0.169613
$870$	0	0
$871$	56.0000	1.89749
$872$	−2.00000	−0.0677285
$873$	−4.00000	−0.135379
$874$	−7.00000	−0.236779
$875$	0	0
$876$	−14.0000	−0.473016
$877$	−38.0000	−1.28317	−0.641584	−	0.767052i	$-0.721723\pi$
$877$	−38.0000	−1.28317	−0.641584	+	0.767052i	$0.721723\pi$
$878$	−8.00000	−0.269987
$879$	−32.0000	−1.07933
$880$	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
$883$	40.0000	1.34611	0.673054	−	0.739594i	$-0.264982\pi$
$883$	40.0000	1.34611	0.673054	+	0.739594i	$0.264982\pi$
$884$	0	0
$885$	0	0
$886$	−26.0000	−0.873487
$887$	48.0000	1.61168	0.805841	−	0.592132i	$-0.201714\pi$
$887$	48.0000	1.61168	0.805841	+	0.592132i	$0.201714\pi$
$888$	4.00000	0.134231
$889$	−10.0000	−0.335389
$890$	0	0
$891$	−55.0000	−1.84257
$892$	4.00000	0.133930
$893$	56.0000	1.87397
$894$	20.0000	0.668900
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	14.0000	0.467446
$898$	30.0000	1.00111
$899$	−50.0000	−1.66759
$900$	0	0
$901$	0	0
$902$	15.0000	0.499445
$903$	−18.0000	−0.599002
$904$	16.0000	0.532152
$905$	0	0
$906$	44.0000	1.46180
$907$	41.0000	1.36138	0.680691	−	0.732570i	$-0.261680\pi$
$907$	41.0000	1.36138	0.680691	+	0.732570i	$0.261680\pi$
$908$	−20.0000	−0.663723
$909$	10.0000	0.331679
$910$	0	0
$911$	33.0000	1.09334	0.546669	−	0.837349i	$-0.315895\pi$
$911$	33.0000	1.09334	0.546669	+	0.837349i	$0.315895\pi$
$912$	14.0000	0.463586
$913$	−85.0000	−2.81309
$914$	−16.0000	−0.529233
$915$	0	0
$916$	14.0000	0.462573
$917$	−10.0000	−0.330229
$918$	0	0
$919$	−16.0000	−0.527791	−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000	−0.527791	−0.263896	+	0.964551i	$0.585007\pi$
$920$	0	0
$921$	8.00000	0.263609
$922$	−3.00000	−0.0987997
$923$	14.0000	0.460816
$924$	10.0000	0.328976
$925$	0	0
$926$	4.00000	0.131448
$927$	5.00000	0.164222
$928$	5.00000	0.164133
$929$	−45.0000	−1.47640	−0.738201	−	0.674581i	$-0.764324\pi$
$929$	−45.0000	−1.47640	−0.738201	+	0.674581i	$0.764324\pi$
$930$	0	0
$931$	42.0000	1.37649
$932$	9.00000	0.294805
$933$	−68.0000	−2.22622
$934$	−3.00000	−0.0981630
$935$	0	0
$936$	−7.00000	−0.228802
$937$	36.0000	1.17607	0.588034	−	0.808836i	$-0.299902\pi$
$937$	36.0000	1.17607	0.588034	+	0.808836i	$0.299902\pi$
$938$	8.00000	0.261209
$939$	−68.0000	−2.21910
$940$	0	0
$941$	32.0000	1.04317	0.521585	−	0.853199i	$-0.325341\pi$
$941$	32.0000	1.04317	0.521585	+	0.853199i	$0.325341\pi$
$942$	−16.0000	−0.521308
$943$	3.00000	0.0976934
$944$	−2.00000	−0.0650945
$945$	0	0
$946$	−45.0000	−1.46308
$947$	−34.0000	−1.10485	−0.552426	−	0.833562i	$-0.686298\pi$
$947$	−34.0000	−1.10485	−0.552426	+	0.833562i	$0.686298\pi$
$948$	−2.00000	−0.0649570
$949$	−49.0000	−1.59061
$950$	0	0
$951$	42.0000	1.36194
$952$	0	0
$953$	46.0000	1.49009	0.745043	−	0.667016i	$-0.232429\pi$
$953$	46.0000	1.49009	0.745043	+	0.667016i	$0.232429\pi$
$954$	−4.00000	−0.129505
$955$	0	0
$956$	−16.0000	−0.517477
$957$	−50.0000	−1.61627
$958$	27.0000	0.872330
$959$	6.00000	0.193750
$960$	0	0
$961$	69.0000	2.22581
$962$	14.0000	0.451378
$963$	16.0000	0.515593
$964$	16.0000	0.515325
$965$	0	0
$966$	2.00000	0.0643489
$967$	8.00000	0.257263	0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000	0.257263	0.128631	+	0.991692i	$0.458942\pi$
$968$	14.0000	0.449977
$969$	0	0
$970$	0	0
$971$	39.0000	1.25157	0.625785	−	0.779996i	$-0.284779\pi$
$971$	39.0000	1.25157	0.625785	+	0.779996i	$0.284779\pi$
$972$	10.0000	0.320750
$973$	−4.00000	−0.128234
$974$	−8.00000	−0.256337
$975$	0	0
$976$	−6.00000	−0.192055
$977$	44.0000	1.40768	0.703842	−	0.710356i	$-0.251466\pi$
$977$	44.0000	1.40768	0.703842	+	0.710356i	$0.251466\pi$
$978$	8.00000	0.255812
$979$	30.0000	0.958804
$980$	0	0
$981$	−2.00000	−0.0638551
$982$	−6.00000	−0.191468
$983$	−51.0000	−1.62665	−0.813324	−	0.581811i	$-0.802344\pi$
$983$	−51.0000	−1.62665	−0.813324	+	0.581811i	$0.802344\pi$
$984$	−6.00000	−0.191273
$985$	0	0
$986$	0	0
$987$	−16.0000	−0.509286
$988$	49.0000	1.55890
$989$	−9.00000	−0.286183
$990$	0	0
$991$	4.00000	0.127064	0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000	0.127064	0.0635321	+	0.997980i	$0.479763\pi$
$992$	−10.0000	−0.317500
$993$	60.0000	1.90404
$994$	2.00000	0.0634361
$995$	0	0
$996$	34.0000	1.07733
$997$	−25.0000	−0.791758	−0.395879	−	0.918303i	$-0.629560\pi$
$997$	−25.0000	−0.791758	−0.395879	+	0.918303i	$0.629560\pi$
$998$	−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	1150.2.a.f.1.1	yes	1
4.3	odd	2		9200.2.a.be.1.1		1
5.2	odd	4		1150.2.b.b.599.2		2
5.3	odd	4		1150.2.b.b.599.1		2
5.4	even	2		1150.2.a.c.1.1	✓	1
20.19	odd	2		9200.2.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1150.2.a.c.1.1	✓	1	5.4	even	2
1150.2.a.f.1.1	yes	1	1.1	even	1	trivial
1150.2.b.b.599.1		2	5.3	odd	4
1150.2.b.b.599.2		2	5.2	odd	4
9200.2.a.e.1.1		1	20.19	odd	2
9200.2.a.be.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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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