LMFDB - Embedded newform 9450.2.a.bi.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9450,2,Mod(1,9450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9450, 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("9450.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9450.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:	$75.4586299101$
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	$\chi$	$=$	9450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} -1.00000 q^{8} -2.00000 q^{11} +5.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} +6.00000 q^{17} +6.00000 q^{19} +2.00000 q^{22} -8.00000 q^{23} -5.00000 q^{26} +1.00000 q^{28} +5.00000 q^{29} +7.00000 q^{31} -1.00000 q^{32} -6.00000 q^{34} +4.00000 q^{37} -6.00000 q^{38} -1.00000 q^{41} +4.00000 q^{43} -2.00000 q^{44} +8.00000 q^{46} -2.00000 q^{47} +1.00000 q^{49} +5.00000 q^{52} +13.0000 q^{53} -1.00000 q^{56} -5.00000 q^{58} -4.00000 q^{59} -9.00000 q^{61} -7.00000 q^{62} +1.00000 q^{64} -9.00000 q^{67} +6.00000 q^{68} +15.0000 q^{71} -12.0000 q^{73} -4.00000 q^{74} +6.00000 q^{76} -2.00000 q^{77} +10.0000 q^{79} +1.00000 q^{82} +5.00000 q^{83} -4.00000 q^{86} +2.00000 q^{88} -11.0000 q^{89} +5.00000 q^{91} -8.00000 q^{92} +2.00000 q^{94} -8.00000 q^{97} -1.00000 q^{98} +O(q^{100})$

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
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	0	0
$10$	0	0
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	0	0
$13$	5.00000	1.38675	0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000	1.38675	0.693375	+	0.720577i	$0.256123\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	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	$0.240633\pi$
$18$	0	0
$19$	6.00000	1.37649	0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000	1.37649	0.688247	+	0.725476i	$0.258380\pi$
$20$	0	0
$21$	0	0
$22$	2.00000	0.426401
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	0	0
$25$	0	0
$26$	−5.00000	−0.980581
$27$	0	0
$28$	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
$31$	7.00000	1.25724	0.628619	−	0.777714i	$-0.283621\pi$
$31$	7.00000	1.25724	0.628619	+	0.777714i	$0.283621\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−6.00000	−1.02899
$35$	0	0
$36$	0	0
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	−6.00000	−0.973329
$39$	0	0
$40$	0	0
$41$	−1.00000	−0.156174	−0.0780869	−	0.996947i	$-0.524881\pi$
$41$	−1.00000	−0.156174	−0.0780869	+	0.996947i	$0.524881\pi$
$42$	0	0
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−2.00000	−0.301511
$45$	0	0
$46$	8.00000	1.17954
$47$	−2.00000	−0.291730	−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000	−0.291730	−0.145865	+	0.989305i	$0.546597\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	5.00000	0.693375
$53$	13.0000	1.78569	0.892844	−	0.450367i	$-0.148707\pi$
$53$	13.0000	1.78569	0.892844	+	0.450367i	$0.148707\pi$
$54$	0	0
$55$	0	0
$56$	−1.00000	−0.133631
$57$	0	0
$58$	−5.00000	−0.656532
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	0	0
$61$	−9.00000	−1.15233	−0.576166	−	0.817333i	$-0.695452\pi$
$61$	−9.00000	−1.15233	−0.576166	+	0.817333i	$0.695452\pi$
$62$	−7.00000	−0.889001
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	−9.00000	−1.09952	−0.549762	−	0.835321i	$-0.685282\pi$
$67$	−9.00000	−1.09952	−0.549762	+	0.835321i	$0.685282\pi$
$68$	6.00000	0.727607
$69$	0	0
$70$	0	0
$71$	15.0000	1.78017	0.890086	−	0.455792i	$-0.150644\pi$
$71$	15.0000	1.78017	0.890086	+	0.455792i	$0.150644\pi$
$72$	0	0
$73$	−12.0000	−1.40449	−0.702247	−	0.711934i	$-0.747820\pi$
$73$	−12.0000	−1.40449	−0.702247	+	0.711934i	$0.747820\pi$
$74$	−4.00000	−0.464991
$75$	0	0
$76$	6.00000	0.688247
$77$	−2.00000	−0.227921
$78$	0	0
$79$	10.0000	1.12509	0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000	1.12509	0.562544	+	0.826767i	$0.309823\pi$
$80$	0	0
$81$	0	0
$82$	1.00000	0.110432
$83$	5.00000	0.548821	0.274411	−	0.961613i	$-0.411517\pi$
$83$	5.00000	0.548821	0.274411	+	0.961613i	$0.411517\pi$
$84$	0	0
$85$	0	0
$86$	−4.00000	−0.431331
$87$	0	0
$88$	2.00000	0.213201
$89$	−11.0000	−1.16600	−0.582999	−	0.812473i	$-0.698121\pi$
$89$	−11.0000	−1.16600	−0.582999	+	0.812473i	$0.698121\pi$
$90$	0	0
$91$	5.00000	0.524142
$92$	−8.00000	−0.834058
$93$	0	0
$94$	2.00000	0.206284
$95$	0	0
$96$	0	0
$97$	−8.00000	−0.812277	−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000	−0.812277	−0.406138	+	0.913812i	$0.633125\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	0	0
$101$	12.0000	1.19404	0.597022	−	0.802225i	$-0.296350\pi$
$101$	12.0000	1.19404	0.597022	+	0.802225i	$0.296350\pi$
$102$	0	0
$103$	16.0000	1.57653	0.788263	−	0.615338i	$-0.210980\pi$
$103$	16.0000	1.57653	0.788263	+	0.615338i	$0.210980\pi$
$104$	−5.00000	−0.490290
$105$	0	0
$106$	−13.0000	−1.26267
$107$	−10.0000	−0.966736	−0.483368	−	0.875417i	$-0.660587\pi$
$107$	−10.0000	−0.966736	−0.483368	+	0.875417i	$0.660587\pi$
$108$	0	0
$109$	0	0		−	1.00000i	$-0.5\pi$
$109$	0	0			1.00000i	$0.5\pi$
$110$	0	0
$111$	0	0
$112$	1.00000	0.0944911
$113$	−12.0000	−1.12887	−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000	−1.12887	−0.564433	+	0.825479i	$0.690905\pi$
$114$	0	0
$115$	0	0
$116$	5.00000	0.464238
$117$	0	0
$118$	4.00000	0.368230
$119$	6.00000	0.550019
$120$	0	0
$121$	−7.00000	−0.636364
$122$	9.00000	0.814822
$123$	0	0
$124$	7.00000	0.628619
$125$	0	0
$126$	0	0
$127$	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
$129$	0	0
$130$	0	0
$131$	−1.00000	−0.0873704	−0.0436852	−	0.999045i	$-0.513910\pi$
$131$	−1.00000	−0.0873704	−0.0436852	+	0.999045i	$0.513910\pi$
$132$	0	0
$133$	6.00000	0.520266
$134$	9.00000	0.777482
$135$	0	0
$136$	−6.00000	−0.514496
$137$	−12.0000	−1.02523	−0.512615	−	0.858619i	$-0.671323\pi$
$137$	−12.0000	−1.02523	−0.512615	+	0.858619i	$0.671323\pi$
$138$	0	0
$139$	14.0000	1.18746	0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000	1.18746	0.593732	+	0.804663i	$0.297654\pi$
$140$	0	0
$141$	0	0
$142$	−15.0000	−1.25877
$143$	−10.0000	−0.836242
$144$	0	0
$145$	0	0
$146$	12.0000	0.993127
$147$	0	0
$148$	4.00000	0.328798
$149$	−18.0000	−1.47462	−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000	−1.47462	−0.737309	+	0.675556i	$0.763904\pi$
$150$	0	0
$151$	24.0000	1.95309	0.976546	−	0.215308i	$-0.0690756\pi$
$151$	24.0000	1.95309	0.976546	+	0.215308i	$0.0690756\pi$
$152$	−6.00000	−0.486664
$153$	0	0
$154$	2.00000	0.161165
$155$	0	0
$156$	0	0
$157$	−17.0000	−1.35675	−0.678374	−	0.734717i	$-0.737315\pi$
$157$	−17.0000	−1.35675	−0.678374	+	0.734717i	$0.737315\pi$
$158$	−10.0000	−0.795557
$159$	0	0
$160$	0	0
$161$	−8.00000	−0.630488
$162$	0	0
$163$	−7.00000	−0.548282	−0.274141	−	0.961689i	$-0.588394\pi$
$163$	−7.00000	−0.548282	−0.274141	+	0.961689i	$0.588394\pi$
$164$	−1.00000	−0.0780869
$165$	0	0
$166$	−5.00000	−0.388075
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	0	0
$169$	12.0000	0.923077
$170$	0	0
$171$	0	0
$172$	4.00000	0.304997
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	0	0
$175$	0	0
$176$	−2.00000	−0.150756
$177$	0	0
$178$	11.0000	0.824485
$179$	10.0000	0.747435	0.373718	−	0.927543i	$-0.378083\pi$
$179$	10.0000	0.747435	0.373718	+	0.927543i	$0.378083\pi$
$180$	0	0
$181$	3.00000	0.222988	0.111494	−	0.993765i	$-0.464436\pi$
$181$	3.00000	0.222988	0.111494	+	0.993765i	$0.464436\pi$
$182$	−5.00000	−0.370625
$183$	0	0
$184$	8.00000	0.589768
$185$	0	0
$186$	0	0
$187$	−12.0000	−0.877527
$188$	−2.00000	−0.145865
$189$	0	0
$190$	0	0
$191$	15.0000	1.08536	0.542681	−	0.839939i	$-0.317409\pi$
$191$	15.0000	1.08536	0.542681	+	0.839939i	$0.317409\pi$
$192$	0	0
$193$	−25.0000	−1.79954	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−25.0000	−1.79954	−0.899770	+	0.436365i	$0.856266\pi$
$194$	8.00000	0.574367
$195$	0	0
$196$	1.00000	0.0714286
$197$	5.00000	0.356235	0.178118	−	0.984009i	$-0.442999\pi$
$197$	5.00000	0.356235	0.178118	+	0.984009i	$0.442999\pi$
$198$	0	0
$199$	27.0000	1.91398	0.956990	−	0.290122i	$-0.0936959\pi$
$199$	27.0000	1.91398	0.956990	+	0.290122i	$0.0936959\pi$
$200$	0	0
$201$	0	0
$202$	−12.0000	−0.844317
$203$	5.00000	0.350931
$204$	0	0
$205$	0	0
$206$	−16.0000	−1.11477
$207$	0	0
$208$	5.00000	0.346688
$209$	−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	$0.543966\pi$
$212$	13.0000	0.892844
$213$	0	0
$214$	10.0000	0.683586
$215$	0	0
$216$	0	0
$217$	7.00000	0.475191
$218$	0	0
$219$	0	0
$220$	0	0
$221$	30.0000	2.01802
$222$	0	0
$223$	−21.0000	−1.40626	−0.703132	−	0.711059i	$-0.748216\pi$
$223$	−21.0000	−1.40626	−0.703132	+	0.711059i	$0.748216\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	12.0000	0.798228
$227$	−19.0000	−1.26107	−0.630537	−	0.776159i	$-0.717165\pi$
$227$	−19.0000	−1.26107	−0.630537	+	0.776159i	$0.717165\pi$
$228$	0	0
$229$	−22.0000	−1.45380	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000	−1.45380	−0.726900	+	0.686743i	$0.759040\pi$
$230$	0	0
$231$	0	0
$232$	−5.00000	−0.328266
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	0	0
$235$	0	0
$236$	−4.00000	−0.260378
$237$	0	0
$238$	−6.00000	−0.388922
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	0	0
$241$	16.0000	1.03065	0.515325	−	0.856995i	$-0.327671\pi$
$241$	16.0000	1.03065	0.515325	+	0.856995i	$0.327671\pi$
$242$	7.00000	0.449977
$243$	0	0
$244$	−9.00000	−0.576166
$245$	0	0
$246$	0	0
$247$	30.0000	1.90885
$248$	−7.00000	−0.444500
$249$	0	0
$250$	0	0
$251$	−13.0000	−0.820553	−0.410276	−	0.911961i	$-0.634568\pi$
$251$	−13.0000	−0.820553	−0.410276	+	0.911961i	$0.634568\pi$
$252$	0	0
$253$	16.0000	1.00591
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	7.00000	0.436648	0.218324	−	0.975876i	$-0.429941\pi$
$257$	7.00000	0.436648	0.218324	+	0.975876i	$0.429941\pi$
$258$	0	0
$259$	4.00000	0.248548
$260$	0	0
$261$	0	0
$262$	1.00000	0.0617802
$263$	27.0000	1.66489	0.832446	−	0.554107i	$-0.186940\pi$
$263$	27.0000	1.66489	0.832446	+	0.554107i	$0.186940\pi$
$264$	0	0
$265$	0	0
$266$	−6.00000	−0.367884
$267$	0	0
$268$	−9.00000	−0.549762
$269$	−20.0000	−1.21942	−0.609711	−	0.792624i	$-0.708714\pi$
$269$	−20.0000	−1.21942	−0.609711	+	0.792624i	$0.708714\pi$
$270$	0	0
$271$	5.00000	0.303728	0.151864	−	0.988401i	$-0.451472\pi$
$271$	5.00000	0.303728	0.151864	+	0.988401i	$0.451472\pi$
$272$	6.00000	0.363803
$273$	0	0
$274$	12.0000	0.724947
$275$	0	0
$276$	0	0
$277$	−8.00000	−0.480673	−0.240337	−	0.970690i	$-0.577258\pi$
$277$	−8.00000	−0.480673	−0.240337	+	0.970690i	$0.577258\pi$
$278$	−14.0000	−0.839664
$279$	0	0
$280$	0	0
$281$	10.0000	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$282$	0	0
$283$	26.0000	1.54554	0.772770	−	0.634686i	$-0.218871\pi$
$283$	26.0000	1.54554	0.772770	+	0.634686i	$0.218871\pi$
$284$	15.0000	0.890086
$285$	0	0
$286$	10.0000	0.591312
$287$	−1.00000	−0.0590281
$288$	0	0
$289$	19.0000	1.11765
$290$	0	0
$291$	0	0
$292$	−12.0000	−0.702247
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	0	0
$295$	0	0
$296$	−4.00000	−0.232495
$297$	0	0
$298$	18.0000	1.04271
$299$	−40.0000	−2.31326
$300$	0	0
$301$	4.00000	0.230556
$302$	−24.0000	−1.38104
$303$	0	0
$304$	6.00000	0.344124
$305$	0	0
$306$	0	0
$307$	−20.0000	−1.14146	−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000	−1.14146	−0.570730	+	0.821138i	$0.693340\pi$
$308$	−2.00000	−0.113961
$309$	0	0
$310$	0	0
$311$	−18.0000	−1.02069	−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000	−1.02069	−0.510343	+	0.859971i	$0.670482\pi$
$312$	0	0
$313$	30.0000	1.69570	0.847850	−	0.530236i	$-0.177897\pi$
$313$	30.0000	1.69570	0.847850	+	0.530236i	$0.177897\pi$
$314$	17.0000	0.959366
$315$	0	0
$316$	10.0000	0.562544
$317$	−3.00000	−0.168497	−0.0842484	−	0.996445i	$-0.526849\pi$
$317$	−3.00000	−0.168497	−0.0842484	+	0.996445i	$0.526849\pi$
$318$	0	0
$319$	−10.0000	−0.559893
$320$	0	0
$321$	0	0
$322$	8.00000	0.445823
$323$	36.0000	2.00309
$324$	0	0
$325$	0	0
$326$	7.00000	0.387694
$327$	0	0
$328$	1.00000	0.0552158
$329$	−2.00000	−0.110264
$330$	0	0
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	5.00000	0.274411
$333$	0	0
$334$	12.0000	0.656611
$335$	0	0
$336$	0	0
$337$	−18.0000	−0.980522	−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000	−0.980522	−0.490261	+	0.871576i	$0.663099\pi$
$338$	−12.0000	−0.652714
$339$	0	0
$340$	0	0
$341$	−14.0000	−0.758143
$342$	0	0
$343$	1.00000	0.0539949
$344$	−4.00000	−0.215666
$345$	0	0
$346$	6.00000	0.322562
$347$	8.00000	0.429463	0.214731	−	0.976673i	$-0.431112\pi$
$347$	8.00000	0.429463	0.214731	+	0.976673i	$0.431112\pi$
$348$	0	0
$349$	21.0000	1.12410	0.562052	−	0.827102i	$-0.310012\pi$
$349$	21.0000	1.12410	0.562052	+	0.827102i	$0.310012\pi$
$350$	0	0
$351$	0	0
$352$	2.00000	0.106600
$353$	9.00000	0.479022	0.239511	−	0.970894i	$-0.423013\pi$
$353$	9.00000	0.479022	0.239511	+	0.970894i	$0.423013\pi$
$354$	0	0
$355$	0	0
$356$	−11.0000	−0.582999
$357$	0	0
$358$	−10.0000	−0.528516
$359$	17.0000	0.897226	0.448613	−	0.893726i	$-0.351918\pi$
$359$	17.0000	0.897226	0.448613	+	0.893726i	$0.351918\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	−3.00000	−0.157676
$363$	0	0
$364$	5.00000	0.262071
$365$	0	0
$366$	0	0
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	−8.00000	−0.417029
$369$	0	0
$370$	0	0
$371$	13.0000	0.674926
$372$	0	0
$373$	30.0000	1.55334	0.776671	−	0.629907i	$-0.216907\pi$
$373$	30.0000	1.55334	0.776671	+	0.629907i	$0.216907\pi$
$374$	12.0000	0.620505
$375$	0	0
$376$	2.00000	0.103142
$377$	25.0000	1.28757
$378$	0	0
$379$	11.0000	0.565032	0.282516	−	0.959263i	$-0.408831\pi$
$379$	11.0000	0.565032	0.282516	+	0.959263i	$0.408831\pi$
$380$	0	0
$381$	0	0
$382$	−15.0000	−0.767467
$383$	14.0000	0.715367	0.357683	−	0.933843i	$-0.383567\pi$
$383$	14.0000	0.715367	0.357683	+	0.933843i	$0.383567\pi$
$384$	0	0
$385$	0	0
$386$	25.0000	1.27247
$387$	0	0
$388$	−8.00000	−0.406138
$389$	−22.0000	−1.11544	−0.557722	−	0.830028i	$-0.688325\pi$
$389$	−22.0000	−1.11544	−0.557722	+	0.830028i	$0.688325\pi$
$390$	0	0
$391$	−48.0000	−2.42746
$392$	−1.00000	−0.0505076
$393$	0	0
$394$	−5.00000	−0.251896
$395$	0	0
$396$	0	0
$397$	−29.0000	−1.45547	−0.727734	−	0.685859i	$-0.759427\pi$
$397$	−29.0000	−1.45547	−0.727734	+	0.685859i	$0.759427\pi$
$398$	−27.0000	−1.35339
$399$	0	0
$400$	0	0
$401$	14.0000	0.699127	0.349563	−	0.936913i	$-0.386330\pi$
$401$	14.0000	0.699127	0.349563	+	0.936913i	$0.386330\pi$
$402$	0	0
$403$	35.0000	1.74347
$404$	12.0000	0.597022
$405$	0	0
$406$	−5.00000	−0.248146
$407$	−8.00000	−0.396545
$408$	0	0
$409$	−16.0000	−0.791149	−0.395575	−	0.918434i	$-0.629455\pi$
$409$	−16.0000	−0.791149	−0.395575	+	0.918434i	$0.629455\pi$
$410$	0	0
$411$	0	0
$412$	16.0000	0.788263
$413$	−4.00000	−0.196827
$414$	0	0
$415$	0	0
$416$	−5.00000	−0.245145
$417$	0	0
$418$	12.0000	0.586939
$419$	−1.00000	−0.0488532	−0.0244266	−	0.999702i	$-0.507776\pi$
$419$	−1.00000	−0.0488532	−0.0244266	+	0.999702i	$0.507776\pi$
$420$	0	0
$421$	−14.0000	−0.682318	−0.341159	−	0.940006i	$-0.610819\pi$
$421$	−14.0000	−0.682318	−0.341159	+	0.940006i	$0.610819\pi$
$422$	4.00000	0.194717
$423$	0	0
$424$	−13.0000	−0.631336
$425$	0	0
$426$	0	0
$427$	−9.00000	−0.435541
$428$	−10.0000	−0.483368
$429$	0	0
$430$	0	0
$431$	−21.0000	−1.01153	−0.505767	−	0.862670i	$-0.668791\pi$
$431$	−21.0000	−1.01153	−0.505767	+	0.862670i	$0.668791\pi$
$432$	0	0
$433$	20.0000	0.961139	0.480569	−	0.876957i	$-0.340430\pi$
$433$	20.0000	0.961139	0.480569	+	0.876957i	$0.340430\pi$
$434$	−7.00000	−0.336011
$435$	0	0
$436$	0	0
$437$	−48.0000	−2.29615
$438$	0	0
$439$	−16.0000	−0.763638	−0.381819	−	0.924237i	$-0.624702\pi$
$439$	−16.0000	−0.763638	−0.381819	+	0.924237i	$0.624702\pi$
$440$	0	0
$441$	0	0
$442$	−30.0000	−1.42695
$443$	−2.00000	−0.0950229	−0.0475114	−	0.998871i	$-0.515129\pi$
$443$	−2.00000	−0.0950229	−0.0475114	+	0.998871i	$0.515129\pi$
$444$	0	0
$445$	0	0
$446$	21.0000	0.994379
$447$	0	0
$448$	1.00000	0.0472456
$449$	−8.00000	−0.377543	−0.188772	−	0.982021i	$-0.560451\pi$
$449$	−8.00000	−0.377543	−0.188772	+	0.982021i	$0.560451\pi$
$450$	0	0
$451$	2.00000	0.0941763
$452$	−12.0000	−0.564433
$453$	0	0
$454$	19.0000	0.891714
$455$	0	0
$456$	0	0
$457$	−42.0000	−1.96468	−0.982339	−	0.187112i	$-0.940087\pi$
$457$	−42.0000	−1.96468	−0.982339	+	0.187112i	$0.940087\pi$
$458$	22.0000	1.02799
$459$	0	0
$460$	0	0
$461$	18.0000	0.838344	0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000	0.838344	0.419172	+	0.907907i	$0.362320\pi$
$462$	0	0
$463$	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
$466$	−6.00000	−0.277945
$467$	21.0000	0.971764	0.485882	−	0.874024i	$-0.338498\pi$
$467$	21.0000	0.971764	0.485882	+	0.874024i	$0.338498\pi$
$468$	0	0
$469$	−9.00000	−0.415581
$470$	0	0
$471$	0	0
$472$	4.00000	0.184115
$473$	−8.00000	−0.367840
$474$	0	0
$475$	0	0
$476$	6.00000	0.275010
$477$	0	0
$478$	−24.0000	−1.09773
$479$	−16.0000	−0.731059	−0.365529	−	0.930800i	$-0.619112\pi$
$479$	−16.0000	−0.731059	−0.365529	+	0.930800i	$0.619112\pi$
$480$	0	0
$481$	20.0000	0.911922
$482$	−16.0000	−0.728780
$483$	0	0
$484$	−7.00000	−0.318182
$485$	0	0
$486$	0	0
$487$	−8.00000	−0.362515	−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000	−0.362515	−0.181257	+	0.983436i	$0.558017\pi$
$488$	9.00000	0.407411
$489$	0	0
$490$	0	0
$491$	−26.0000	−1.17336	−0.586682	−	0.809818i	$-0.699566\pi$
$491$	−26.0000	−1.17336	−0.586682	+	0.809818i	$0.699566\pi$
$492$	0	0
$493$	30.0000	1.35113
$494$	−30.0000	−1.34976
$495$	0	0
$496$	7.00000	0.314309
$497$	15.0000	0.672842
$498$	0	0
$499$	25.0000	1.11915	0.559577	−	0.828778i	$-0.310964\pi$
$499$	25.0000	1.11915	0.559577	+	0.828778i	$0.310964\pi$
$500$	0	0
$501$	0	0
$502$	13.0000	0.580218
$503$	−30.0000	−1.33763	−0.668817	−	0.743427i	$-0.733199\pi$
$503$	−30.0000	−1.33763	−0.668817	+	0.743427i	$0.733199\pi$
$504$	0	0
$505$	0	0
$506$	−16.0000	−0.711287
$507$	0	0
$508$	8.00000	0.354943
$509$	−26.0000	−1.15243	−0.576215	−	0.817298i	$-0.695471\pi$
$509$	−26.0000	−1.15243	−0.576215	+	0.817298i	$0.695471\pi$
$510$	0	0
$511$	−12.0000	−0.530849
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−7.00000	−0.308757
$515$	0	0
$516$	0	0
$517$	4.00000	0.175920
$518$	−4.00000	−0.175750
$519$	0	0
$520$	0	0
$521$	33.0000	1.44576	0.722878	−	0.690976i	$-0.242819\pi$
$521$	33.0000	1.44576	0.722878	+	0.690976i	$0.242819\pi$
$522$	0	0
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	−1.00000	−0.0436852
$525$	0	0
$526$	−27.0000	−1.17726
$527$	42.0000	1.82955
$528$	0	0
$529$	41.0000	1.78261
$530$	0	0
$531$	0	0
$532$	6.00000	0.260133
$533$	−5.00000	−0.216574
$534$	0	0
$535$	0	0
$536$	9.00000	0.388741
$537$	0	0
$538$	20.0000	0.862261
$539$	−2.00000	−0.0861461
$540$	0	0
$541$	−10.0000	−0.429934	−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000	−0.429934	−0.214967	+	0.976621i	$0.568964\pi$
$542$	−5.00000	−0.214768
$543$	0	0
$544$	−6.00000	−0.257248
$545$	0	0
$546$	0	0
$547$	−13.0000	−0.555840	−0.277920	−	0.960604i	$-0.589645\pi$
$547$	−13.0000	−0.555840	−0.277920	+	0.960604i	$0.589645\pi$
$548$	−12.0000	−0.512615
$549$	0	0
$550$	0	0
$551$	30.0000	1.27804
$552$	0	0
$553$	10.0000	0.425243
$554$	8.00000	0.339887
$555$	0	0
$556$	14.0000	0.593732
$557$	3.00000	0.127114	0.0635570	−	0.997978i	$-0.479756\pi$
$557$	3.00000	0.127114	0.0635570	+	0.997978i	$0.479756\pi$
$558$	0	0
$559$	20.0000	0.845910
$560$	0	0
$561$	0	0
$562$	−10.0000	−0.421825
$563$	4.00000	0.168580	0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000	0.168580	0.0842900	+	0.996441i	$0.473138\pi$
$564$	0	0
$565$	0	0
$566$	−26.0000	−1.09286
$567$	0	0
$568$	−15.0000	−0.629386
$569$	−18.0000	−0.754599	−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000	−0.754599	−0.377300	+	0.926091i	$0.623147\pi$
$570$	0	0
$571$	1.00000	0.0418487	0.0209243	−	0.999781i	$-0.493339\pi$
$571$	1.00000	0.0418487	0.0209243	+	0.999781i	$0.493339\pi$
$572$	−10.0000	−0.418121
$573$	0	0
$574$	1.00000	0.0417392
$575$	0	0
$576$	0	0
$577$	32.0000	1.33218	0.666089	−	0.745873i	$-0.267967\pi$
$577$	32.0000	1.33218	0.666089	+	0.745873i	$0.267967\pi$
$578$	−19.0000	−0.790296
$579$	0	0
$580$	0	0
$581$	5.00000	0.207435
$582$	0	0
$583$	−26.0000	−1.07681
$584$	12.0000	0.496564
$585$	0	0
$586$	−6.00000	−0.247858
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	0	0
$589$	42.0000	1.73058
$590$	0	0
$591$	0	0
$592$	4.00000	0.164399
$593$	−14.0000	−0.574911	−0.287456	−	0.957794i	$-0.592809\pi$
$593$	−14.0000	−0.574911	−0.287456	+	0.957794i	$0.592809\pi$
$594$	0	0
$595$	0	0
$596$	−18.0000	−0.737309
$597$	0	0
$598$	40.0000	1.63572
$599$	13.0000	0.531166	0.265583	−	0.964088i	$-0.414436\pi$
$599$	13.0000	0.531166	0.265583	+	0.964088i	$0.414436\pi$
$600$	0	0
$601$	−8.00000	−0.326327	−0.163163	−	0.986599i	$-0.552170\pi$
$601$	−8.00000	−0.326327	−0.163163	+	0.986599i	$0.552170\pi$
$602$	−4.00000	−0.163028
$603$	0	0
$604$	24.0000	0.976546
$605$	0	0
$606$	0	0
$607$	−29.0000	−1.17707	−0.588537	−	0.808470i	$-0.700296\pi$
$607$	−29.0000	−1.17707	−0.588537	+	0.808470i	$0.700296\pi$
$608$	−6.00000	−0.243332
$609$	0	0
$610$	0	0
$611$	−10.0000	−0.404557
$612$	0	0
$613$	−16.0000	−0.646234	−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000	−0.646234	−0.323117	+	0.946359i	$0.604731\pi$
$614$	20.0000	0.807134
$615$	0	0
$616$	2.00000	0.0805823
$617$	−8.00000	−0.322068	−0.161034	−	0.986949i	$-0.551483\pi$
$617$	−8.00000	−0.322068	−0.161034	+	0.986949i	$0.551483\pi$
$618$	0	0
$619$	2.00000	0.0803868	0.0401934	−	0.999192i	$-0.487203\pi$
$619$	2.00000	0.0803868	0.0401934	+	0.999192i	$0.487203\pi$
$620$	0	0
$621$	0	0
$622$	18.0000	0.721734
$623$	−11.0000	−0.440706
$624$	0	0
$625$	0	0
$626$	−30.0000	−1.19904
$627$	0	0
$628$	−17.0000	−0.678374
$629$	24.0000	0.956943
$630$	0	0
$631$	40.0000	1.59237	0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000	1.59237	0.796187	+	0.605050i	$0.206847\pi$
$632$	−10.0000	−0.397779
$633$	0	0
$634$	3.00000	0.119145
$635$	0	0
$636$	0	0
$637$	5.00000	0.198107
$638$	10.0000	0.395904
$639$	0	0
$640$	0	0
$641$	−36.0000	−1.42191	−0.710957	−	0.703235i	$-0.751738\pi$
$641$	−36.0000	−1.42191	−0.710957	+	0.703235i	$0.751738\pi$
$642$	0	0
$643$	−20.0000	−0.788723	−0.394362	−	0.918955i	$-0.629034\pi$
$643$	−20.0000	−0.788723	−0.394362	+	0.918955i	$0.629034\pi$
$644$	−8.00000	−0.315244
$645$	0	0
$646$	−36.0000	−1.41640
$647$	22.0000	0.864909	0.432455	−	0.901656i	$-0.357648\pi$
$647$	22.0000	0.864909	0.432455	+	0.901656i	$0.357648\pi$
$648$	0	0
$649$	8.00000	0.314027
$650$	0	0
$651$	0	0
$652$	−7.00000	−0.274141
$653$	25.0000	0.978326	0.489163	−	0.872192i	$-0.337302\pi$
$653$	25.0000	0.978326	0.489163	+	0.872192i	$0.337302\pi$
$654$	0	0
$655$	0	0
$656$	−1.00000	−0.0390434
$657$	0	0
$658$	2.00000	0.0779681
$659$	12.0000	0.467454	0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000	0.467454	0.233727	+	0.972302i	$0.424908\pi$
$660$	0	0
$661$	18.0000	0.700119	0.350059	−	0.936727i	$-0.386161\pi$
$661$	18.0000	0.700119	0.350059	+	0.936727i	$0.386161\pi$
$662$	−20.0000	−0.777322
$663$	0	0
$664$	−5.00000	−0.194038
$665$	0	0
$666$	0	0
$667$	−40.0000	−1.54881
$668$	−12.0000	−0.464294
$669$	0	0
$670$	0	0
$671$	18.0000	0.694882
$672$	0	0
$673$	−19.0000	−0.732396	−0.366198	−	0.930537i	$-0.619341\pi$
$673$	−19.0000	−0.732396	−0.366198	+	0.930537i	$0.619341\pi$
$674$	18.0000	0.693334
$675$	0	0
$676$	12.0000	0.461538
$677$	−34.0000	−1.30673	−0.653363	−	0.757045i	$-0.726642\pi$
$677$	−34.0000	−1.30673	−0.653363	+	0.757045i	$0.726642\pi$
$678$	0	0
$679$	−8.00000	−0.307012
$680$	0	0
$681$	0	0
$682$	14.0000	0.536088
$683$	40.0000	1.53056	0.765279	−	0.643699i	$-0.222601\pi$
$683$	40.0000	1.53056	0.765279	+	0.643699i	$0.222601\pi$
$684$	0	0
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	0	0
$688$	4.00000	0.152499
$689$	65.0000	2.47630
$690$	0	0
$691$	0	0		−	1.00000i	$-0.5\pi$
$691$	0	0			1.00000i	$0.5\pi$
$692$	−6.00000	−0.228086
$693$	0	0
$694$	−8.00000	−0.303676
$695$	0	0
$696$	0	0
$697$	−6.00000	−0.227266
$698$	−21.0000	−0.794862
$699$	0	0
$700$	0	0
$701$	−15.0000	−0.566542	−0.283271	−	0.959040i	$-0.591420\pi$
$701$	−15.0000	−0.566542	−0.283271	+	0.959040i	$0.591420\pi$
$702$	0	0
$703$	24.0000	0.905177
$704$	−2.00000	−0.0753778
$705$	0	0
$706$	−9.00000	−0.338719
$707$	12.0000	0.451306
$708$	0	0
$709$	2.00000	0.0751116	0.0375558	−	0.999295i	$-0.488043\pi$
$709$	2.00000	0.0751116	0.0375558	+	0.999295i	$0.488043\pi$
$710$	0	0
$711$	0	0
$712$	11.0000	0.412242
$713$	−56.0000	−2.09722
$714$	0	0
$715$	0	0
$716$	10.0000	0.373718
$717$	0	0
$718$	−17.0000	−0.634434
$719$	16.0000	0.596699	0.298350	−	0.954457i	$-0.403564\pi$
$719$	16.0000	0.596699	0.298350	+	0.954457i	$0.403564\pi$
$720$	0	0
$721$	16.0000	0.595871
$722$	−17.0000	−0.632674
$723$	0	0
$724$	3.00000	0.111494
$725$	0	0
$726$	0	0
$727$	13.0000	0.482143	0.241072	−	0.970507i	$-0.422501\pi$
$727$	13.0000	0.482143	0.241072	+	0.970507i	$0.422501\pi$
$728$	−5.00000	−0.185312
$729$	0	0
$730$	0	0
$731$	24.0000	0.887672
$732$	0	0
$733$	−14.0000	−0.517102	−0.258551	−	0.965998i	$-0.583245\pi$
$733$	−14.0000	−0.517102	−0.258551	+	0.965998i	$0.583245\pi$
$734$	−8.00000	−0.295285
$735$	0	0
$736$	8.00000	0.294884
$737$	18.0000	0.663039
$738$	0	0
$739$	11.0000	0.404642	0.202321	−	0.979319i	$-0.435152\pi$
$739$	11.0000	0.404642	0.202321	+	0.979319i	$0.435152\pi$
$740$	0	0
$741$	0	0
$742$	−13.0000	−0.477245
$743$	37.0000	1.35740	0.678699	−	0.734416i	$-0.262544\pi$
$743$	37.0000	1.35740	0.678699	+	0.734416i	$0.262544\pi$
$744$	0	0
$745$	0	0
$746$	−30.0000	−1.09838
$747$	0	0
$748$	−12.0000	−0.438763
$749$	−10.0000	−0.365392
$750$	0	0
$751$	−40.0000	−1.45962	−0.729810	−	0.683650i	$-0.760392\pi$
$751$	−40.0000	−1.45962	−0.729810	+	0.683650i	$0.760392\pi$
$752$	−2.00000	−0.0729325
$753$	0	0
$754$	−25.0000	−0.910446
$755$	0	0
$756$	0	0
$757$	34.0000	1.23575	0.617876	−	0.786276i	$-0.287994\pi$
$757$	34.0000	1.23575	0.617876	+	0.786276i	$0.287994\pi$
$758$	−11.0000	−0.399538
$759$	0	0
$760$	0	0
$761$	−21.0000	−0.761249	−0.380625	−	0.924730i	$-0.624291\pi$
$761$	−21.0000	−0.761249	−0.380625	+	0.924730i	$0.624291\pi$
$762$	0	0
$763$	0	0
$764$	15.0000	0.542681
$765$	0	0
$766$	−14.0000	−0.505841
$767$	−20.0000	−0.722158
$768$	0	0
$769$	34.0000	1.22607	0.613036	−	0.790055i	$-0.289948\pi$
$769$	34.0000	1.22607	0.613036	+	0.790055i	$0.289948\pi$
$770$	0	0
$771$	0	0
$772$	−25.0000	−0.899770
$773$	42.0000	1.51064	0.755318	−	0.655359i	$-0.227483\pi$
$773$	42.0000	1.51064	0.755318	+	0.655359i	$0.227483\pi$
$774$	0	0
$775$	0	0
$776$	8.00000	0.287183
$777$	0	0
$778$	22.0000	0.788738
$779$	−6.00000	−0.214972
$780$	0	0
$781$	−30.0000	−1.07348
$782$	48.0000	1.71648
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	32.0000	1.14068	0.570338	−	0.821410i	$-0.306812\pi$
$787$	32.0000	1.14068	0.570338	+	0.821410i	$0.306812\pi$
$788$	5.00000	0.178118
$789$	0	0
$790$	0	0
$791$	−12.0000	−0.426671
$792$	0	0
$793$	−45.0000	−1.59800
$794$	29.0000	1.02917
$795$	0	0
$796$	27.0000	0.956990
$797$	48.0000	1.70025	0.850124	−	0.526583i	$-0.176527\pi$
$797$	48.0000	1.70025	0.850124	+	0.526583i	$0.176527\pi$
$798$	0	0
$799$	−12.0000	−0.424529
$800$	0	0
$801$	0	0
$802$	−14.0000	−0.494357
$803$	24.0000	0.846942
$804$	0	0
$805$	0	0
$806$	−35.0000	−1.23282
$807$	0	0
$808$	−12.0000	−0.422159
$809$	12.0000	0.421898	0.210949	−	0.977497i	$-0.432345\pi$
$809$	12.0000	0.421898	0.210949	+	0.977497i	$0.432345\pi$
$810$	0	0
$811$	6.00000	0.210688	0.105344	−	0.994436i	$-0.466406\pi$
$811$	6.00000	0.210688	0.105344	+	0.994436i	$0.466406\pi$
$812$	5.00000	0.175466
$813$	0	0
$814$	8.00000	0.280400
$815$	0	0
$816$	0	0
$817$	24.0000	0.839654
$818$	16.0000	0.559427
$819$	0	0
$820$	0	0
$821$	39.0000	1.36111	0.680555	−	0.732697i	$-0.261739\pi$
$821$	39.0000	1.36111	0.680555	+	0.732697i	$0.261739\pi$
$822$	0	0
$823$	18.0000	0.627441	0.313720	−	0.949515i	$-0.398425\pi$
$823$	18.0000	0.627441	0.313720	+	0.949515i	$0.398425\pi$
$824$	−16.0000	−0.557386
$825$	0	0
$826$	4.00000	0.139178
$827$	44.0000	1.53003	0.765015	−	0.644013i	$-0.222732\pi$
$827$	44.0000	1.53003	0.765015	+	0.644013i	$0.222732\pi$
$828$	0	0
$829$	13.0000	0.451509	0.225754	−	0.974184i	$-0.427515\pi$
$829$	13.0000	0.451509	0.225754	+	0.974184i	$0.427515\pi$
$830$	0	0
$831$	0	0
$832$	5.00000	0.173344
$833$	6.00000	0.207888
$834$	0	0
$835$	0	0
$836$	−12.0000	−0.415029
$837$	0	0
$838$	1.00000	0.0345444
$839$	−56.0000	−1.93333	−0.966667	−	0.256036i	$-0.917584\pi$
$839$	−56.0000	−1.93333	−0.966667	+	0.256036i	$0.917584\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	14.0000	0.482472
$843$	0	0
$844$	−4.00000	−0.137686
$845$	0	0
$846$	0	0
$847$	−7.00000	−0.240523
$848$	13.0000	0.446422
$849$	0	0
$850$	0	0
$851$	−32.0000	−1.09695
$852$	0	0
$853$	26.0000	0.890223	0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000	0.890223	0.445112	+	0.895475i	$0.353164\pi$
$854$	9.00000	0.307974
$855$	0	0
$856$	10.0000	0.341793
$857$	−23.0000	−0.785665	−0.392833	−	0.919610i	$-0.628505\pi$
$857$	−23.0000	−0.785665	−0.392833	+	0.919610i	$0.628505\pi$
$858$	0	0
$859$	30.0000	1.02359	0.511793	−	0.859109i	$-0.328981\pi$
$859$	30.0000	1.02359	0.511793	+	0.859109i	$0.328981\pi$
$860$	0	0
$861$	0	0
$862$	21.0000	0.715263
$863$	13.0000	0.442525	0.221263	−	0.975214i	$-0.428982\pi$
$863$	13.0000	0.442525	0.221263	+	0.975214i	$0.428982\pi$
$864$	0	0
$865$	0	0
$866$	−20.0000	−0.679628
$867$	0	0
$868$	7.00000	0.237595
$869$	−20.0000	−0.678454
$870$	0	0
$871$	−45.0000	−1.52477
$872$	0	0
$873$	0	0
$874$	48.0000	1.62362
$875$	0	0
$876$	0	0
$877$	−44.0000	−1.48577	−0.742887	−	0.669417i	$-0.766544\pi$
$877$	−44.0000	−1.48577	−0.742887	+	0.669417i	$0.766544\pi$
$878$	16.0000	0.539974
$879$	0	0
$880$	0	0
$881$	35.0000	1.17918	0.589590	−	0.807703i	$-0.299289\pi$
$881$	35.0000	1.17918	0.589590	+	0.807703i	$0.299289\pi$
$882$	0	0
$883$	12.0000	0.403832	0.201916	−	0.979403i	$-0.435283\pi$
$883$	12.0000	0.403832	0.201916	+	0.979403i	$0.435283\pi$
$884$	30.0000	1.00901
$885$	0	0
$886$	2.00000	0.0671913
$887$	56.0000	1.88030	0.940148	−	0.340766i	$-0.110687\pi$
$887$	56.0000	1.88030	0.940148	+	0.340766i	$0.110687\pi$
$888$	0	0
$889$	8.00000	0.268311
$890$	0	0
$891$	0	0
$892$	−21.0000	−0.703132
$893$	−12.0000	−0.401565
$894$	0	0
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	8.00000	0.266963
$899$	35.0000	1.16732
$900$	0	0
$901$	78.0000	2.59856
$902$	−2.00000	−0.0665927
$903$	0	0
$904$	12.0000	0.399114
$905$	0	0
$906$	0	0
$907$	−17.0000	−0.564476	−0.282238	−	0.959344i	$-0.591077\pi$
$907$	−17.0000	−0.564476	−0.282238	+	0.959344i	$0.591077\pi$
$908$	−19.0000	−0.630537
$909$	0	0
$910$	0	0
$911$	53.0000	1.75597	0.877984	−	0.478690i	$-0.158888\pi$
$911$	53.0000	1.75597	0.877984	+	0.478690i	$0.158888\pi$
$912$	0	0
$913$	−10.0000	−0.330952
$914$	42.0000	1.38924
$915$	0	0
$916$	−22.0000	−0.726900
$917$	−1.00000	−0.0330229
$918$	0	0
$919$	−6.00000	−0.197922	−0.0989609	−	0.995091i	$-0.531552\pi$
$919$	−6.00000	−0.197922	−0.0989609	+	0.995091i	$0.531552\pi$
$920$	0	0
$921$	0	0
$922$	−18.0000	−0.592798
$923$	75.0000	2.46866
$924$	0	0
$925$	0	0
$926$	−4.00000	−0.131448
$927$	0	0
$928$	−5.00000	−0.164133
$929$	15.0000	0.492134	0.246067	−	0.969253i	$-0.420862\pi$
$929$	15.0000	0.492134	0.246067	+	0.969253i	$0.420862\pi$
$930$	0	0
$931$	6.00000	0.196642
$932$	6.00000	0.196537
$933$	0	0
$934$	−21.0000	−0.687141
$935$	0	0
$936$	0	0
$937$	18.0000	0.588034	0.294017	−	0.955800i	$-0.405008\pi$
$937$	18.0000	0.588034	0.294017	+	0.955800i	$0.405008\pi$
$938$	9.00000	0.293860
$939$	0	0
$940$	0	0
$941$	42.0000	1.36916	0.684580	−	0.728937i	$-0.259985\pi$
$941$	42.0000	1.36916	0.684580	+	0.728937i	$0.259985\pi$
$942$	0	0
$943$	8.00000	0.260516
$944$	−4.00000	−0.130189
$945$	0	0
$946$	8.00000	0.260102
$947$	−32.0000	−1.03986	−0.519930	−	0.854209i	$-0.674042\pi$
$947$	−32.0000	−1.03986	−0.519930	+	0.854209i	$0.674042\pi$
$948$	0	0
$949$	−60.0000	−1.94768
$950$	0	0
$951$	0	0
$952$	−6.00000	−0.194461
$953$	58.0000	1.87880	0.939402	−	0.342817i	$-0.111381\pi$
$953$	58.0000	1.87880	0.939402	+	0.342817i	$0.111381\pi$
$954$	0	0
$955$	0	0
$956$	24.0000	0.776215
$957$	0	0
$958$	16.0000	0.516937
$959$	−12.0000	−0.387500
$960$	0	0
$961$	18.0000	0.580645
$962$	−20.0000	−0.644826
$963$	0	0
$964$	16.0000	0.515325
$965$	0	0
$966$	0	0
$967$	14.0000	0.450210	0.225105	−	0.974335i	$-0.427728\pi$
$967$	14.0000	0.450210	0.225105	+	0.974335i	$0.427728\pi$
$968$	7.00000	0.224989
$969$	0	0
$970$	0	0
$971$	3.00000	0.0962746	0.0481373	−	0.998841i	$-0.484672\pi$
$971$	3.00000	0.0962746	0.0481373	+	0.998841i	$0.484672\pi$
$972$	0	0
$973$	14.0000	0.448819
$974$	8.00000	0.256337
$975$	0	0
$976$	−9.00000	−0.288083
$977$	42.0000	1.34370	0.671850	−	0.740688i	$-0.265500\pi$
$977$	42.0000	1.34370	0.671850	+	0.740688i	$0.265500\pi$
$978$	0	0
$979$	22.0000	0.703123
$980$	0	0
$981$	0	0
$982$	26.0000	0.829693
$983$	4.00000	0.127580	0.0637901	−	0.997963i	$-0.479681\pi$
$983$	4.00000	0.127580	0.0637901	+	0.997963i	$0.479681\pi$
$984$	0	0
$985$	0	0
$986$	−30.0000	−0.955395
$987$	0	0
$988$	30.0000	0.954427
$989$	−32.0000	−1.01754
$990$	0	0
$991$	22.0000	0.698853	0.349427	−	0.936964i	$-0.386376\pi$
$991$	22.0000	0.698853	0.349427	+	0.936964i	$0.386376\pi$
$992$	−7.00000	−0.222250
$993$	0	0
$994$	−15.0000	−0.475771
$995$	0	0
$996$	0	0
$997$	−59.0000	−1.86855	−0.934274	−	0.356555i	$-0.883951\pi$
$997$	−59.0000	−1.86855	−0.934274	+	0.356555i	$0.883951\pi$
$998$	−25.0000	−0.791361
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9450.2.a.bi.1.1	yes	1
3.2	odd	2		9450.2.a.du.1.1	yes	1
5.4	even	2		9450.2.a.cg.1.1	yes	1
15.14	odd	2		9450.2.a.s.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9450.2.a.s.1.1	✓	1	15.14	odd	2
9450.2.a.bi.1.1	yes	1	1.1	even	1	trivial
9450.2.a.cg.1.1	yes	1	5.4	even	2
9450.2.a.du.1.1	yes	1	3.2	odd	2

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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:	\( N \)	\(=\)	\( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9450.a (trivial)

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