LMFDB - Embedded newform 9450.2.a.i.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:	no (minimal twist has level 1890)
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)

$f(q)$

$=$

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

$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} -1.00000 q^{8} -3.00000 q^{11} +5.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -4.00000 q^{17} +1.00000 q^{19} +3.00000 q^{22} -8.00000 q^{23} -5.00000 q^{26} -1.00000 q^{28} -10.0000 q^{29} -8.00000 q^{31} -1.00000 q^{32} +4.00000 q^{34} -4.00000 q^{37} -1.00000 q^{38} -9.00000 q^{41} +1.00000 q^{43} -3.00000 q^{44} +8.00000 q^{46} +13.0000 q^{47} +1.00000 q^{49} +5.00000 q^{52} +3.00000 q^{53} +1.00000 q^{56} +10.0000 q^{58} +14.0000 q^{59} +6.00000 q^{61} +8.00000 q^{62} +1.00000 q^{64} -11.0000 q^{67} -4.00000 q^{68} +7.00000 q^{73} +4.00000 q^{74} +1.00000 q^{76} +3.00000 q^{77} -10.0000 q^{79} +9.00000 q^{82} +15.0000 q^{83} -1.00000 q^{86} +3.00000 q^{88} +11.0000 q^{89} -5.00000 q^{91} -8.00000 q^{92} -13.0000 q^{94} +18.0000 q^{97} -1.00000 q^{98} +O(q^{100})$

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
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	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
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	0	0
$19$	1.00000	0.229416	0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000	0.229416	0.114708	+	0.993399i	$0.463407\pi$
$20$	0	0
$21$	0	0
$22$	3.00000	0.639602
$23$	−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
$29$	−10.0000	−1.85695	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−10.0000	−1.85695	−0.928477	+	0.371391i	$0.878881\pi$
$30$	0	0
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	4.00000	0.685994
$35$	0	0
$36$	0	0
$37$	−4.00000	−0.657596	−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000	−0.657596	−0.328798	+	0.944400i	$0.606644\pi$
$38$	−1.00000	−0.162221
$39$	0	0
$40$	0	0
$41$	−9.00000	−1.40556	−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000	−1.40556	−0.702782	+	0.711405i	$0.748059\pi$
$42$	0	0
$43$	1.00000	0.152499	0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000	0.152499	0.0762493	+	0.997089i	$0.475706\pi$
$44$	−3.00000	−0.452267
$45$	0	0
$46$	8.00000	1.17954
$47$	13.0000	1.89624	0.948122	−	0.317905i	$-0.102979\pi$
$47$	13.0000	1.89624	0.948122	+	0.317905i	$0.102979\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	5.00000	0.693375
$53$	3.00000	0.412082	0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000	0.412082	0.206041	+	0.978543i	$0.433942\pi$
$54$	0	0
$55$	0	0
$56$	1.00000	0.133631
$57$	0	0
$58$	10.0000	1.31306
$59$	14.0000	1.82264	0.911322	−	0.411693i	$-0.135063\pi$
$59$	14.0000	1.82264	0.911322	+	0.411693i	$0.135063\pi$
$60$	0	0
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	8.00000	1.01600
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	−11.0000	−1.34386	−0.671932	−	0.740613i	$-0.734535\pi$
$67$	−11.0000	−1.34386	−0.671932	+	0.740613i	$0.734535\pi$
$68$	−4.00000	−0.485071
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	7.00000	0.819288	0.409644	−	0.912245i	$-0.365653\pi$
$73$	7.00000	0.819288	0.409644	+	0.912245i	$0.365653\pi$
$74$	4.00000	0.464991
$75$	0	0
$76$	1.00000	0.114708
$77$	3.00000	0.341882
$78$	0	0
$79$	−10.0000	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$80$	0	0
$81$	0	0
$82$	9.00000	0.993884
$83$	15.0000	1.64646	0.823232	−	0.567705i	$-0.192169\pi$
$83$	15.0000	1.64646	0.823232	+	0.567705i	$0.192169\pi$
$84$	0	0
$85$	0	0
$86$	−1.00000	−0.107833
$87$	0	0
$88$	3.00000	0.319801
$89$	11.0000	1.16600	0.582999	−	0.812473i	$-0.301879\pi$
$89$	11.0000	1.16600	0.582999	+	0.812473i	$0.301879\pi$
$90$	0	0
$91$	−5.00000	−0.524142
$92$	−8.00000	−0.834058
$93$	0	0
$94$	−13.0000	−1.34085
$95$	0	0
$96$	0	0
$97$	18.0000	1.82762	0.913812	−	0.406138i	$-0.133125\pi$
$97$	18.0000	1.82762	0.913812	+	0.406138i	$0.133125\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	0	0
$101$	3.00000	0.298511	0.149256	−	0.988799i	$-0.452312\pi$
$101$	3.00000	0.298511	0.149256	+	0.988799i	$0.452312\pi$
$102$	0	0
$103$	14.0000	1.37946	0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000	1.37946	0.689730	+	0.724066i	$0.257729\pi$
$104$	−5.00000	−0.490290
$105$	0	0
$106$	−3.00000	−0.291386
$107$	10.0000	0.966736	0.483368	−	0.875417i	$-0.339413\pi$
$107$	10.0000	0.966736	0.483368	+	0.875417i	$0.339413\pi$
$108$	0	0
$109$	5.00000	0.478913	0.239457	−	0.970907i	$-0.423031\pi$
$109$	5.00000	0.478913	0.239457	+	0.970907i	$0.423031\pi$
$110$	0	0
$111$	0	0
$112$	−1.00000	−0.0944911
$113$	−17.0000	−1.59923	−0.799613	−	0.600516i	$-0.794962\pi$
$113$	−17.0000	−1.59923	−0.799613	+	0.600516i	$0.794962\pi$
$114$	0	0
$115$	0	0
$116$	−10.0000	−0.928477
$117$	0	0
$118$	−14.0000	−1.28880
$119$	4.00000	0.366679
$120$	0	0
$121$	−2.00000	−0.181818
$122$	−6.00000	−0.543214
$123$	0	0
$124$	−8.00000	−0.718421
$125$	0	0
$126$	0	0
$127$	17.0000	1.50851	0.754253	−	0.656584i	$-0.227999\pi$
$127$	17.0000	1.50851	0.754253	+	0.656584i	$0.227999\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	0	0
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	0	0
$133$	−1.00000	−0.0867110
$134$	11.0000	0.950255
$135$	0	0
$136$	4.00000	0.342997
$137$	−7.00000	−0.598050	−0.299025	−	0.954245i	$-0.596661\pi$
$137$	−7.00000	−0.598050	−0.299025	+	0.954245i	$0.596661\pi$
$138$	0	0
$139$	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
$141$	0	0
$142$	0	0
$143$	−15.0000	−1.25436
$144$	0	0
$145$	0	0
$146$	−7.00000	−0.579324
$147$	0	0
$148$	−4.00000	−0.328798
$149$	−12.0000	−0.983078	−0.491539	−	0.870855i	$-0.663566\pi$
$149$	−12.0000	−0.983078	−0.491539	+	0.870855i	$0.663566\pi$
$150$	0	0
$151$	−6.00000	−0.488273	−0.244137	−	0.969741i	$-0.578505\pi$
$151$	−6.00000	−0.488273	−0.244137	+	0.969741i	$0.578505\pi$
$152$	−1.00000	−0.0811107
$153$	0	0
$154$	−3.00000	−0.241747
$155$	0	0
$156$	0	0
$157$	−18.0000	−1.43656	−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000	−1.43656	−0.718278	+	0.695756i	$0.755069\pi$
$158$	10.0000	0.795557
$159$	0	0
$160$	0	0
$161$	8.00000	0.630488
$162$	0	0
$163$	12.0000	0.939913	0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000	0.939913	0.469956	+	0.882690i	$0.344270\pi$
$164$	−9.00000	−0.702782
$165$	0	0
$166$	−15.0000	−1.16423
$167$	−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
$172$	1.00000	0.0762493
$173$	−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
$176$	−3.00000	−0.226134
$177$	0	0
$178$	−11.0000	−0.824485
$179$	−5.00000	−0.373718	−0.186859	−	0.982387i	$-0.559831\pi$
$179$	−5.00000	−0.373718	−0.186859	+	0.982387i	$0.559831\pi$
$180$	0	0
$181$	−22.0000	−1.63525	−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000	−1.63525	−0.817624	+	0.575753i	$0.804709\pi$
$182$	5.00000	0.370625
$183$	0	0
$184$	8.00000	0.589768
$185$	0	0
$186$	0	0
$187$	12.0000	0.877527
$188$	13.0000	0.948122
$189$	0	0
$190$	0	0
$191$	−5.00000	−0.361787	−0.180894	−	0.983503i	$-0.557899\pi$
$191$	−5.00000	−0.361787	−0.180894	+	0.983503i	$0.557899\pi$
$192$	0	0
$193$	10.0000	0.719816	0.359908	−	0.932988i	$-0.382808\pi$
$193$	10.0000	0.719816	0.359908	+	0.932988i	$0.382808\pi$
$194$	−18.0000	−1.29232
$195$	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
$199$	−3.00000	−0.212664	−0.106332	−	0.994331i	$-0.533911\pi$
$199$	−3.00000	−0.212664	−0.106332	+	0.994331i	$0.533911\pi$
$200$	0	0
$201$	0	0
$202$	−3.00000	−0.211079
$203$	10.0000	0.701862
$204$	0	0
$205$	0	0
$206$	−14.0000	−0.975426
$207$	0	0
$208$	5.00000	0.346688
$209$	−3.00000	−0.207514
$210$	0	0
$211$	6.00000	0.413057	0.206529	−	0.978441i	$-0.433783\pi$
$211$	6.00000	0.413057	0.206529	+	0.978441i	$0.433783\pi$
$212$	3.00000	0.206041
$213$	0	0
$214$	−10.0000	−0.683586
$215$	0	0
$216$	0	0
$217$	8.00000	0.543075
$218$	−5.00000	−0.338643
$219$	0	0
$220$	0	0
$221$	−20.0000	−1.34535
$222$	0	0
$223$	26.0000	1.74109	0.870544	−	0.492090i	$-0.163767\pi$
$223$	26.0000	1.74109	0.870544	+	0.492090i	$0.163767\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	17.0000	1.13082
$227$	−9.00000	−0.597351	−0.298675	−	0.954355i	$-0.596545\pi$
$227$	−9.00000	−0.597351	−0.298675	+	0.954355i	$0.596545\pi$
$228$	0	0
$229$	−2.00000	−0.132164	−0.0660819	−	0.997814i	$-0.521050\pi$
$229$	−2.00000	−0.132164	−0.0660819	+	0.997814i	$0.521050\pi$
$230$	0	0
$231$	0	0
$232$	10.0000	0.656532
$233$	11.0000	0.720634	0.360317	−	0.932830i	$-0.382669\pi$
$233$	11.0000	0.720634	0.360317	+	0.932830i	$0.382669\pi$
$234$	0	0
$235$	0	0
$236$	14.0000	0.911322
$237$	0	0
$238$	−4.00000	−0.259281
$239$	−4.00000	−0.258738	−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000	−0.258738	−0.129369	+	0.991596i	$0.541295\pi$
$240$	0	0
$241$	6.00000	0.386494	0.193247	−	0.981150i	$-0.438098\pi$
$241$	6.00000	0.386494	0.193247	+	0.981150i	$0.438098\pi$
$242$	2.00000	0.128565
$243$	0	0
$244$	6.00000	0.384111
$245$	0	0
$246$	0	0
$247$	5.00000	0.318142
$248$	8.00000	0.508001
$249$	0	0
$250$	0	0
$251$	8.00000	0.504956	0.252478	−	0.967603i	$-0.418755\pi$
$251$	8.00000	0.504956	0.252478	+	0.967603i	$0.418755\pi$
$252$	0	0
$253$	24.0000	1.50887
$254$	−17.0000	−1.06667
$255$	0	0
$256$	1.00000	0.0625000
$257$	12.0000	0.748539	0.374270	−	0.927320i	$-0.377893\pi$
$257$	12.0000	0.748539	0.374270	+	0.927320i	$0.377893\pi$
$258$	0	0
$259$	4.00000	0.248548
$260$	0	0
$261$	0	0
$262$	4.00000	0.247121
$263$	12.0000	0.739952	0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000	0.739952	0.369976	+	0.929041i	$0.379366\pi$
$264$	0	0
$265$	0	0
$266$	1.00000	0.0613139
$267$	0	0
$268$	−11.0000	−0.671932
$269$	−10.0000	−0.609711	−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000	−0.609711	−0.304855	+	0.952399i	$0.598608\pi$
$270$	0	0
$271$	15.0000	0.911185	0.455593	−	0.890188i	$-0.349427\pi$
$271$	15.0000	0.911185	0.455593	+	0.890188i	$0.349427\pi$
$272$	−4.00000	−0.242536
$273$	0	0
$274$	7.00000	0.422885
$275$	0	0
$276$	0	0
$277$	8.00000	0.480673	0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000	0.480673	0.240337	+	0.970690i	$0.422742\pi$
$278$	−4.00000	−0.239904
$279$	0	0
$280$	0	0
$281$	30.0000	1.78965	0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000	1.78965	0.894825	+	0.446417i	$0.147300\pi$
$282$	0	0
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	0	0
$285$	0	0
$286$	15.0000	0.886969
$287$	9.00000	0.531253
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	0	0
$292$	7.00000	0.409644
$293$	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
$298$	12.0000	0.695141
$299$	−40.0000	−2.31326
$300$	0	0
$301$	−1.00000	−0.0576390
$302$	6.00000	0.345261
$303$	0	0
$304$	1.00000	0.0573539
$305$	0	0
$306$	0	0
$307$	10.0000	0.570730	0.285365	−	0.958419i	$-0.407885\pi$
$307$	10.0000	0.570730	0.285365	+	0.958419i	$0.407885\pi$
$308$	3.00000	0.170941
$309$	0	0
$310$	0	0
$311$	18.0000	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$312$	0	0
$313$	25.0000	1.41308	0.706542	−	0.707671i	$-0.250254\pi$
$313$	25.0000	1.41308	0.706542	+	0.707671i	$0.250254\pi$
$314$	18.0000	1.01580
$315$	0	0
$316$	−10.0000	−0.562544
$317$	−13.0000	−0.730153	−0.365076	−	0.930978i	$-0.618957\pi$
$317$	−13.0000	−0.730153	−0.365076	+	0.930978i	$0.618957\pi$
$318$	0	0
$319$	30.0000	1.67968
$320$	0	0
$321$	0	0
$322$	−8.00000	−0.445823
$323$	−4.00000	−0.222566
$324$	0	0
$325$	0	0
$326$	−12.0000	−0.664619
$327$	0	0
$328$	9.00000	0.496942
$329$	−13.0000	−0.716713
$330$	0	0
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	15.0000	0.823232
$333$	0	0
$334$	12.0000	0.656611
$335$	0	0
$336$	0	0
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	−12.0000	−0.652714
$339$	0	0
$340$	0	0
$341$	24.0000	1.29967
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	−1.00000	−0.0539164
$345$	0	0
$346$	6.00000	0.322562
$347$	−12.0000	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	0	0
$349$	−24.0000	−1.28469	−0.642345	−	0.766415i	$-0.722038\pi$
$349$	−24.0000	−1.28469	−0.642345	+	0.766415i	$0.722038\pi$
$350$	0	0
$351$	0	0
$352$	3.00000	0.159901
$353$	−6.00000	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$354$	0	0
$355$	0	0
$356$	11.0000	0.582999
$357$	0	0
$358$	5.00000	0.264258
$359$	13.0000	0.686114	0.343057	−	0.939315i	$-0.388538\pi$
$359$	13.0000	0.686114	0.343057	+	0.939315i	$0.388538\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	22.0000	1.15629
$363$	0	0
$364$	−5.00000	−0.262071
$365$	0	0
$366$	0	0
$367$	2.00000	0.104399	0.0521996	−	0.998637i	$-0.483377\pi$
$367$	2.00000	0.104399	0.0521996	+	0.998637i	$0.483377\pi$
$368$	−8.00000	−0.417029
$369$	0	0
$370$	0	0
$371$	−3.00000	−0.155752
$372$	0	0
$373$	10.0000	0.517780	0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000	0.517780	0.258890	+	0.965907i	$0.416643\pi$
$374$	−12.0000	−0.620505
$375$	0	0
$376$	−13.0000	−0.670424
$377$	−50.0000	−2.57513
$378$	0	0
$379$	−14.0000	−0.719132	−0.359566	−	0.933120i	$-0.617075\pi$
$379$	−14.0000	−0.719132	−0.359566	+	0.933120i	$0.617075\pi$
$380$	0	0
$381$	0	0
$382$	5.00000	0.255822
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	0	0
$385$	0	0
$386$	−10.0000	−0.508987
$387$	0	0
$388$	18.0000	0.913812
$389$	−18.0000	−0.912636	−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000	−0.912636	−0.456318	+	0.889817i	$0.650832\pi$
$390$	0	0
$391$	32.0000	1.61831
$392$	−1.00000	−0.0505076
$393$	0	0
$394$	−5.00000	−0.251896
$395$	0	0
$396$	0	0
$397$	14.0000	0.702640	0.351320	−	0.936255i	$-0.385733\pi$
$397$	14.0000	0.702640	0.351320	+	0.936255i	$0.385733\pi$
$398$	3.00000	0.150376
$399$	0	0
$400$	0	0
$401$	6.00000	0.299626	0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000	0.299626	0.149813	+	0.988714i	$0.452133\pi$
$402$	0	0
$403$	−40.0000	−1.99254
$404$	3.00000	0.149256
$405$	0	0
$406$	−10.0000	−0.496292
$407$	12.0000	0.594818
$408$	0	0
$409$	−26.0000	−1.28562	−0.642809	−	0.766027i	$-0.722231\pi$
$409$	−26.0000	−1.28562	−0.642809	+	0.766027i	$0.722231\pi$
$410$	0	0
$411$	0	0
$412$	14.0000	0.689730
$413$	−14.0000	−0.688895
$414$	0	0
$415$	0	0
$416$	−5.00000	−0.245145
$417$	0	0
$418$	3.00000	0.146735
$419$	26.0000	1.27018	0.635092	−	0.772437i	$-0.280962\pi$
$419$	26.0000	1.27018	0.635092	+	0.772437i	$0.280962\pi$
$420$	0	0
$421$	1.00000	0.0487370	0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000	0.0487370	0.0243685	+	0.999703i	$0.492242\pi$
$422$	−6.00000	−0.292075
$423$	0	0
$424$	−3.00000	−0.145693
$425$	0	0
$426$	0	0
$427$	−6.00000	−0.290360
$428$	10.0000	0.483368
$429$	0	0
$430$	0	0
$431$	11.0000	0.529851	0.264926	−	0.964269i	$-0.414653\pi$
$431$	11.0000	0.529851	0.264926	+	0.964269i	$0.414653\pi$
$432$	0	0
$433$	5.00000	0.240285	0.120142	−	0.992757i	$-0.461665\pi$
$433$	5.00000	0.240285	0.120142	+	0.992757i	$0.461665\pi$
$434$	−8.00000	−0.384012
$435$	0	0
$436$	5.00000	0.239457
$437$	−8.00000	−0.382692
$438$	0	0
$439$	−1.00000	−0.0477274	−0.0238637	−	0.999715i	$-0.507597\pi$
$439$	−1.00000	−0.0477274	−0.0238637	+	0.999715i	$0.507597\pi$
$440$	0	0
$441$	0	0
$442$	20.0000	0.951303
$443$	−12.0000	−0.570137	−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000	−0.570137	−0.285069	+	0.958507i	$0.592016\pi$
$444$	0	0
$445$	0	0
$446$	−26.0000	−1.23114
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	−22.0000	−1.03824	−0.519122	−	0.854700i	$-0.673741\pi$
$449$	−22.0000	−1.03824	−0.519122	+	0.854700i	$0.673741\pi$
$450$	0	0
$451$	27.0000	1.27138
$452$	−17.0000	−0.799613
$453$	0	0
$454$	9.00000	0.422391
$455$	0	0
$456$	0	0
$457$	−38.0000	−1.77757	−0.888783	−	0.458329i	$-0.848448\pi$
$457$	−38.0000	−1.77757	−0.888783	+	0.458329i	$0.848448\pi$
$458$	2.00000	0.0934539
$459$	0	0
$460$	0	0
$461$	7.00000	0.326023	0.163011	−	0.986624i	$-0.447879\pi$
$461$	7.00000	0.326023	0.163011	+	0.986624i	$0.447879\pi$
$462$	0	0
$463$	11.0000	0.511213	0.255607	−	0.966781i	$-0.417725\pi$
$463$	11.0000	0.511213	0.255607	+	0.966781i	$0.417725\pi$
$464$	−10.0000	−0.464238
$465$	0	0
$466$	−11.0000	−0.509565
$467$	−4.00000	−0.185098	−0.0925490	−	0.995708i	$-0.529501\pi$
$467$	−4.00000	−0.185098	−0.0925490	+	0.995708i	$0.529501\pi$
$468$	0	0
$469$	11.0000	0.507933
$470$	0	0
$471$	0	0
$472$	−14.0000	−0.644402
$473$	−3.00000	−0.137940
$474$	0	0
$475$	0	0
$476$	4.00000	0.183340
$477$	0	0
$478$	4.00000	0.182956
$479$	6.00000	0.274147	0.137073	−	0.990561i	$-0.456230\pi$
$479$	6.00000	0.274147	0.137073	+	0.990561i	$0.456230\pi$
$480$	0	0
$481$	−20.0000	−0.911922
$482$	−6.00000	−0.273293
$483$	0	0
$484$	−2.00000	−0.0909091
$485$	0	0
$486$	0	0
$487$	−7.00000	−0.317200	−0.158600	−	0.987343i	$-0.550698\pi$
$487$	−7.00000	−0.317200	−0.158600	+	0.987343i	$0.550698\pi$
$488$	−6.00000	−0.271607
$489$	0	0
$490$	0	0
$491$	36.0000	1.62466	0.812329	−	0.583200i	$-0.198200\pi$
$491$	36.0000	1.62466	0.812329	+	0.583200i	$0.198200\pi$
$492$	0	0
$493$	40.0000	1.80151
$494$	−5.00000	−0.224961
$495$	0	0
$496$	−8.00000	−0.359211
$497$	0	0
$498$	0	0
$499$	40.0000	1.79065	0.895323	−	0.445418i	$-0.146945\pi$
$499$	40.0000	1.79065	0.895323	+	0.445418i	$0.146945\pi$
$500$	0	0
$501$	0	0
$502$	−8.00000	−0.357057
$503$	35.0000	1.56057	0.780286	−	0.625422i	$-0.215073\pi$
$503$	35.0000	1.56057	0.780286	+	0.625422i	$0.215073\pi$
$504$	0	0
$505$	0	0
$506$	−24.0000	−1.06693
$507$	0	0
$508$	17.0000	0.754253
$509$	26.0000	1.15243	0.576215	−	0.817298i	$-0.304529\pi$
$509$	26.0000	1.15243	0.576215	+	0.817298i	$0.304529\pi$
$510$	0	0
$511$	−7.00000	−0.309662
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−12.0000	−0.529297
$515$	0	0
$516$	0	0
$517$	−39.0000	−1.71522
$518$	−4.00000	−0.175750
$519$	0	0
$520$	0	0
$521$	27.0000	1.18289	0.591446	−	0.806345i	$-0.298557\pi$
$521$	27.0000	1.18289	0.591446	+	0.806345i	$0.298557\pi$
$522$	0	0
$523$	−4.00000	−0.174908	−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000	−0.174908	−0.0874539	+	0.996169i	$0.527873\pi$
$524$	−4.00000	−0.174741
$525$	0	0
$526$	−12.0000	−0.523225
$527$	32.0000	1.39394
$528$	0	0
$529$	41.0000	1.78261
$530$	0	0
$531$	0	0
$532$	−1.00000	−0.0433555
$533$	−45.0000	−1.94917
$534$	0	0
$535$	0	0
$536$	11.0000	0.475128
$537$	0	0
$538$	10.0000	0.431131
$539$	−3.00000	−0.129219
$540$	0	0
$541$	35.0000	1.50477	0.752384	−	0.658725i	$-0.228904\pi$
$541$	35.0000	1.50477	0.752384	+	0.658725i	$0.228904\pi$
$542$	−15.0000	−0.644305
$543$	0	0
$544$	4.00000	0.171499
$545$	0	0
$546$	0	0
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	−7.00000	−0.299025
$549$	0	0
$550$	0	0
$551$	−10.0000	−0.426014
$552$	0	0
$553$	10.0000	0.425243
$554$	−8.00000	−0.339887
$555$	0	0
$556$	4.00000	0.169638
$557$	−2.00000	−0.0847427	−0.0423714	−	0.999102i	$-0.513491\pi$
$557$	−2.00000	−0.0847427	−0.0423714	+	0.999102i	$0.513491\pi$
$558$	0	0
$559$	5.00000	0.211477
$560$	0	0
$561$	0	0
$562$	−30.0000	−1.26547
$563$	19.0000	0.800755	0.400377	−	0.916350i	$-0.368879\pi$
$563$	19.0000	0.800755	0.400377	+	0.916350i	$0.368879\pi$
$564$	0	0
$565$	0	0
$566$	−4.00000	−0.168133
$567$	0	0
$568$	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
$571$	−34.0000	−1.42286	−0.711428	−	0.702759i	$-0.751951\pi$
$571$	−34.0000	−1.42286	−0.711428	+	0.702759i	$0.751951\pi$
$572$	−15.0000	−0.627182
$573$	0	0
$574$	−9.00000	−0.375653
$575$	0	0
$576$	0	0
$577$	13.0000	0.541197	0.270599	−	0.962692i	$-0.412778\pi$
$577$	13.0000	0.541197	0.270599	+	0.962692i	$0.412778\pi$
$578$	1.00000	0.0415945
$579$	0	0
$580$	0	0
$581$	−15.0000	−0.622305
$582$	0	0
$583$	−9.00000	−0.372742
$584$	−7.00000	−0.289662
$585$	0	0
$586$	−6.00000	−0.247858
$587$	−28.0000	−1.15568	−0.577842	−	0.816149i	$-0.696105\pi$
$587$	−28.0000	−1.15568	−0.577842	+	0.816149i	$0.696105\pi$
$588$	0	0
$589$	−8.00000	−0.329634
$590$	0	0
$591$	0	0
$592$	−4.00000	−0.164399
$593$	6.00000	0.246390	0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000	0.246390	0.123195	+	0.992382i	$0.460686\pi$
$594$	0	0
$595$	0	0
$596$	−12.0000	−0.491539
$597$	0	0
$598$	40.0000	1.63572
$599$	−3.00000	−0.122577	−0.0612883	−	0.998120i	$-0.519521\pi$
$599$	−3.00000	−0.122577	−0.0612883	+	0.998120i	$0.519521\pi$
$600$	0	0
$601$	−28.0000	−1.14214	−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000	−1.14214	−0.571072	+	0.820900i	$0.693472\pi$
$602$	1.00000	0.0407570
$603$	0	0
$604$	−6.00000	−0.244137
$605$	0	0
$606$	0	0
$607$	4.00000	0.162355	0.0811775	−	0.996700i	$-0.474132\pi$
$607$	4.00000	0.162355	0.0811775	+	0.996700i	$0.474132\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	0	0
$611$	65.0000	2.62962
$612$	0	0
$613$	36.0000	1.45403	0.727013	−	0.686624i	$-0.240908\pi$
$613$	36.0000	1.45403	0.727013	+	0.686624i	$0.240908\pi$
$614$	−10.0000	−0.403567
$615$	0	0
$616$	−3.00000	−0.120873
$617$	22.0000	0.885687	0.442843	−	0.896599i	$-0.353970\pi$
$617$	22.0000	0.885687	0.442843	+	0.896599i	$0.353970\pi$
$618$	0	0
$619$	7.00000	0.281354	0.140677	−	0.990056i	$-0.455072\pi$
$619$	7.00000	0.281354	0.140677	+	0.990056i	$0.455072\pi$
$620$	0	0
$621$	0	0
$622$	−18.0000	−0.721734
$623$	−11.0000	−0.440706
$624$	0	0
$625$	0	0
$626$	−25.0000	−0.999201
$627$	0	0
$628$	−18.0000	−0.718278
$629$	16.0000	0.637962
$630$	0	0
$631$	−30.0000	−1.19428	−0.597141	−	0.802137i	$-0.703697\pi$
$631$	−30.0000	−1.19428	−0.597141	+	0.802137i	$0.703697\pi$
$632$	10.0000	0.397779
$633$	0	0
$634$	13.0000	0.516296
$635$	0	0
$636$	0	0
$637$	5.00000	0.198107
$638$	−30.0000	−1.18771
$639$	0	0
$640$	0	0
$641$	−14.0000	−0.552967	−0.276483	−	0.961019i	$-0.589169\pi$
$641$	−14.0000	−0.552967	−0.276483	+	0.961019i	$0.589169\pi$
$642$	0	0
$643$	−10.0000	−0.394362	−0.197181	−	0.980367i	$-0.563179\pi$
$643$	−10.0000	−0.394362	−0.197181	+	0.980367i	$0.563179\pi$
$644$	8.00000	0.315244
$645$	0	0
$646$	4.00000	0.157378
$647$	−3.00000	−0.117942	−0.0589711	−	0.998260i	$-0.518782\pi$
$647$	−3.00000	−0.117942	−0.0589711	+	0.998260i	$0.518782\pi$
$648$	0	0
$649$	−42.0000	−1.64864
$650$	0	0
$651$	0	0
$652$	12.0000	0.469956
$653$	−30.0000	−1.17399	−0.586995	−	0.809590i	$-0.699689\pi$
$653$	−30.0000	−1.17399	−0.586995	+	0.809590i	$0.699689\pi$
$654$	0	0
$655$	0	0
$656$	−9.00000	−0.351391
$657$	0	0
$658$	13.0000	0.506793
$659$	−12.0000	−0.467454	−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000	−0.467454	−0.233727	+	0.972302i	$0.575092\pi$
$660$	0	0
$661$	−32.0000	−1.24466	−0.622328	−	0.782757i	$-0.713813\pi$
$661$	−32.0000	−1.24466	−0.622328	+	0.782757i	$0.713813\pi$
$662$	−20.0000	−0.777322
$663$	0	0
$664$	−15.0000	−0.582113
$665$	0	0
$666$	0	0
$667$	80.0000	3.09761
$668$	−12.0000	−0.464294
$669$	0	0
$670$	0	0
$671$	−18.0000	−0.694882
$672$	0	0
$673$	4.00000	0.154189	0.0770943	−	0.997024i	$-0.475436\pi$
$673$	4.00000	0.154189	0.0770943	+	0.997024i	$0.475436\pi$
$674$	22.0000	0.847408
$675$	0	0
$676$	12.0000	0.461538
$677$	−4.00000	−0.153732	−0.0768662	−	0.997041i	$-0.524491\pi$
$677$	−4.00000	−0.153732	−0.0768662	+	0.997041i	$0.524491\pi$
$678$	0	0
$679$	−18.0000	−0.690777
$680$	0	0
$681$	0	0
$682$	−24.0000	−0.919007
$683$	20.0000	0.765279	0.382639	−	0.923898i	$-0.375015\pi$
$683$	20.0000	0.765279	0.382639	+	0.923898i	$0.375015\pi$
$684$	0	0
$685$	0	0
$686$	1.00000	0.0381802
$687$	0	0
$688$	1.00000	0.0381246
$689$	15.0000	0.571454
$690$	0	0
$691$	25.0000	0.951045	0.475522	−	0.879704i	$-0.342259\pi$
$691$	25.0000	0.951045	0.475522	+	0.879704i	$0.342259\pi$
$692$	−6.00000	−0.228086
$693$	0	0
$694$	12.0000	0.455514
$695$	0	0
$696$	0	0
$697$	36.0000	1.36360
$698$	24.0000	0.908413
$699$	0	0
$700$	0	0
$701$	−40.0000	−1.51078	−0.755390	−	0.655276i	$-0.772552\pi$
$701$	−40.0000	−1.51078	−0.755390	+	0.655276i	$0.772552\pi$
$702$	0	0
$703$	−4.00000	−0.150863
$704$	−3.00000	−0.113067
$705$	0	0
$706$	6.00000	0.225813
$707$	−3.00000	−0.112827
$708$	0	0
$709$	27.0000	1.01401	0.507003	−	0.861944i	$-0.330753\pi$
$709$	27.0000	1.01401	0.507003	+	0.861944i	$0.330753\pi$
$710$	0	0
$711$	0	0
$712$	−11.0000	−0.412242
$713$	64.0000	2.39682
$714$	0	0
$715$	0	0
$716$	−5.00000	−0.186859
$717$	0	0
$718$	−13.0000	−0.485156
$719$	14.0000	0.522112	0.261056	−	0.965324i	$-0.415929\pi$
$719$	14.0000	0.522112	0.261056	+	0.965324i	$0.415929\pi$
$720$	0	0
$721$	−14.0000	−0.521387
$722$	18.0000	0.669891
$723$	0	0
$724$	−22.0000	−0.817624
$725$	0	0
$726$	0	0
$727$	2.00000	0.0741759	0.0370879	−	0.999312i	$-0.488192\pi$
$727$	2.00000	0.0741759	0.0370879	+	0.999312i	$0.488192\pi$
$728$	5.00000	0.185312
$729$	0	0
$730$	0	0
$731$	−4.00000	−0.147945
$732$	0	0
$733$	−11.0000	−0.406294	−0.203147	−	0.979148i	$-0.565117\pi$
$733$	−11.0000	−0.406294	−0.203147	+	0.979148i	$0.565117\pi$
$734$	−2.00000	−0.0738213
$735$	0	0
$736$	8.00000	0.294884
$737$	33.0000	1.21557
$738$	0	0
$739$	−44.0000	−1.61857	−0.809283	−	0.587419i	$-0.800144\pi$
$739$	−44.0000	−1.61857	−0.809283	+	0.587419i	$0.800144\pi$
$740$	0	0
$741$	0	0
$742$	3.00000	0.110133
$743$	−18.0000	−0.660356	−0.330178	−	0.943919i	$-0.607109\pi$
$743$	−18.0000	−0.660356	−0.330178	+	0.943919i	$0.607109\pi$
$744$	0	0
$745$	0	0
$746$	−10.0000	−0.366126
$747$	0	0
$748$	12.0000	0.438763
$749$	−10.0000	−0.365392
$750$	0	0
$751$	10.0000	0.364905	0.182453	−	0.983215i	$-0.441596\pi$
$751$	10.0000	0.364905	0.182453	+	0.983215i	$0.441596\pi$
$752$	13.0000	0.474061
$753$	0	0
$754$	50.0000	1.82089
$755$	0	0
$756$	0	0
$757$	−24.0000	−0.872295	−0.436147	−	0.899875i	$-0.643657\pi$
$757$	−24.0000	−0.872295	−0.436147	+	0.899875i	$0.643657\pi$
$758$	14.0000	0.508503
$759$	0	0
$760$	0	0
$761$	−14.0000	−0.507500	−0.253750	−	0.967270i	$-0.581664\pi$
$761$	−14.0000	−0.507500	−0.253750	+	0.967270i	$0.581664\pi$
$762$	0	0
$763$	−5.00000	−0.181012
$764$	−5.00000	−0.180894
$765$	0	0
$766$	−24.0000	−0.867155
$767$	70.0000	2.52755
$768$	0	0
$769$	−26.0000	−0.937584	−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000	−0.937584	−0.468792	+	0.883309i	$0.655311\pi$
$770$	0	0
$771$	0	0
$772$	10.0000	0.359908
$773$	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
$776$	−18.0000	−0.646162
$777$	0	0
$778$	18.0000	0.645331
$779$	−9.00000	−0.322458
$780$	0	0
$781$	0	0
$782$	−32.0000	−1.14432
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	18.0000	0.641631	0.320815	−	0.947142i	$-0.396043\pi$
$787$	18.0000	0.641631	0.320815	+	0.947142i	$0.396043\pi$
$788$	5.00000	0.178118
$789$	0	0
$790$	0	0
$791$	17.0000	0.604450
$792$	0	0
$793$	30.0000	1.06533
$794$	−14.0000	−0.496841
$795$	0	0
$796$	−3.00000	−0.106332
$797$	8.00000	0.283375	0.141687	−	0.989911i	$-0.454747\pi$
$797$	8.00000	0.283375	0.141687	+	0.989911i	$0.454747\pi$
$798$	0	0
$799$	−52.0000	−1.83963
$800$	0	0
$801$	0	0
$802$	−6.00000	−0.211867
$803$	−21.0000	−0.741074
$804$	0	0
$805$	0	0
$806$	40.0000	1.40894
$807$	0	0
$808$	−3.00000	−0.105540
$809$	28.0000	0.984428	0.492214	−	0.870474i	$-0.336188\pi$
$809$	28.0000	0.984428	0.492214	+	0.870474i	$0.336188\pi$
$810$	0	0
$811$	21.0000	0.737410	0.368705	−	0.929547i	$-0.379801\pi$
$811$	21.0000	0.737410	0.368705	+	0.929547i	$0.379801\pi$
$812$	10.0000	0.350931
$813$	0	0
$814$	−12.0000	−0.420600
$815$	0	0
$816$	0	0
$817$	1.00000	0.0349856
$818$	26.0000	0.909069
$819$	0	0
$820$	0	0
$821$	6.00000	0.209401	0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000	0.209401	0.104701	+	0.994504i	$0.466612\pi$
$822$	0	0
$823$	−33.0000	−1.15031	−0.575154	−	0.818045i	$-0.695058\pi$
$823$	−33.0000	−1.15031	−0.575154	+	0.818045i	$0.695058\pi$
$824$	−14.0000	−0.487713
$825$	0	0
$826$	14.0000	0.487122
$827$	−26.0000	−0.904109	−0.452054	−	0.891990i	$-0.649309\pi$
$827$	−26.0000	−0.904109	−0.452054	+	0.891990i	$0.649309\pi$
$828$	0	0
$829$	−2.00000	−0.0694629	−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000	−0.0694629	−0.0347314	+	0.999397i	$0.511058\pi$
$830$	0	0
$831$	0	0
$832$	5.00000	0.173344
$833$	−4.00000	−0.138592
$834$	0	0
$835$	0	0
$836$	−3.00000	−0.103757
$837$	0	0
$838$	−26.0000	−0.898155
$839$	26.0000	0.897620	0.448810	−	0.893627i	$-0.351848\pi$
$839$	26.0000	0.897620	0.448810	+	0.893627i	$0.351848\pi$
$840$	0	0
$841$	71.0000	2.44828
$842$	−1.00000	−0.0344623
$843$	0	0
$844$	6.00000	0.206529
$845$	0	0
$846$	0	0
$847$	2.00000	0.0687208
$848$	3.00000	0.103020
$849$	0	0
$850$	0	0
$851$	32.0000	1.09695
$852$	0	0
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	6.00000	0.205316
$855$	0	0
$856$	−10.0000	−0.341793
$857$	52.0000	1.77629	0.888143	−	0.459567i	$-0.151995\pi$
$857$	52.0000	1.77629	0.888143	+	0.459567i	$0.151995\pi$
$858$	0	0
$859$	−15.0000	−0.511793	−0.255897	−	0.966704i	$-0.582371\pi$
$859$	−15.0000	−0.511793	−0.255897	+	0.966704i	$0.582371\pi$
$860$	0	0
$861$	0	0
$862$	−11.0000	−0.374661
$863$	−22.0000	−0.748889	−0.374444	−	0.927249i	$-0.622167\pi$
$863$	−22.0000	−0.748889	−0.374444	+	0.927249i	$0.622167\pi$
$864$	0	0
$865$	0	0
$866$	−5.00000	−0.169907
$867$	0	0
$868$	8.00000	0.271538
$869$	30.0000	1.01768
$870$	0	0
$871$	−55.0000	−1.86360
$872$	−5.00000	−0.169321
$873$	0	0
$874$	8.00000	0.270604
$875$	0	0
$876$	0	0
$877$	14.0000	0.472746	0.236373	−	0.971662i	$-0.424041\pi$
$877$	14.0000	0.472746	0.236373	+	0.971662i	$0.424041\pi$
$878$	1.00000	0.0337484
$879$	0	0
$880$	0	0
$881$	30.0000	1.01073	0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000	1.01073	0.505363	+	0.862907i	$0.331359\pi$
$882$	0	0
$883$	−52.0000	−1.74994	−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000	−1.74994	−0.874970	+	0.484178i	$0.839119\pi$
$884$	−20.0000	−0.672673
$885$	0	0
$886$	12.0000	0.403148
$887$	21.0000	0.705111	0.352555	−	0.935791i	$-0.385313\pi$
$887$	21.0000	0.705111	0.352555	+	0.935791i	$0.385313\pi$
$888$	0	0
$889$	−17.0000	−0.570162
$890$	0	0
$891$	0	0
$892$	26.0000	0.870544
$893$	13.0000	0.435028
$894$	0	0
$895$	0	0
$896$	1.00000	0.0334077
$897$	0	0
$898$	22.0000	0.734150
$899$	80.0000	2.66815
$900$	0	0
$901$	−12.0000	−0.399778
$902$	−27.0000	−0.899002
$903$	0	0
$904$	17.0000	0.565412
$905$	0	0
$906$	0	0
$907$	37.0000	1.22856	0.614282	−	0.789086i	$-0.289446\pi$
$907$	37.0000	1.22856	0.614282	+	0.789086i	$0.289446\pi$
$908$	−9.00000	−0.298675
$909$	0	0
$910$	0	0
$911$	−43.0000	−1.42465	−0.712327	−	0.701848i	$-0.752359\pi$
$911$	−43.0000	−1.42465	−0.712327	+	0.701848i	$0.752359\pi$
$912$	0	0
$913$	−45.0000	−1.48928
$914$	38.0000	1.25693
$915$	0	0
$916$	−2.00000	−0.0660819
$917$	4.00000	0.132092
$918$	0	0
$919$	14.0000	0.461817	0.230909	−	0.972975i	$-0.425830\pi$
$919$	14.0000	0.461817	0.230909	+	0.972975i	$0.425830\pi$
$920$	0	0
$921$	0	0
$922$	−7.00000	−0.230533
$923$	0	0
$924$	0	0
$925$	0	0
$926$	−11.0000	−0.361482
$927$	0	0
$928$	10.0000	0.328266
$929$	−15.0000	−0.492134	−0.246067	−	0.969253i	$-0.579138\pi$
$929$	−15.0000	−0.492134	−0.246067	+	0.969253i	$0.579138\pi$
$930$	0	0
$931$	1.00000	0.0327737
$932$	11.0000	0.360317
$933$	0	0
$934$	4.00000	0.130884
$935$	0	0
$936$	0	0
$937$	47.0000	1.53542	0.767712	−	0.640796i	$-0.221395\pi$
$937$	47.0000	1.53542	0.767712	+	0.640796i	$0.221395\pi$
$938$	−11.0000	−0.359163
$939$	0	0
$940$	0	0
$941$	−7.00000	−0.228193	−0.114097	−	0.993470i	$-0.536397\pi$
$941$	−7.00000	−0.228193	−0.114097	+	0.993470i	$0.536397\pi$
$942$	0	0
$943$	72.0000	2.34464
$944$	14.0000	0.455661
$945$	0	0
$946$	3.00000	0.0975384
$947$	−42.0000	−1.36482	−0.682408	−	0.730971i	$-0.739067\pi$
$947$	−42.0000	−1.36482	−0.682408	+	0.730971i	$0.739067\pi$
$948$	0	0
$949$	35.0000	1.13615
$950$	0	0
$951$	0	0
$952$	−4.00000	−0.129641
$953$	−42.0000	−1.36051	−0.680257	−	0.732974i	$-0.738132\pi$
$953$	−42.0000	−1.36051	−0.680257	+	0.732974i	$0.738132\pi$
$954$	0	0
$955$	0	0
$956$	−4.00000	−0.129369
$957$	0	0
$958$	−6.00000	−0.193851
$959$	7.00000	0.226042
$960$	0	0
$961$	33.0000	1.06452
$962$	20.0000	0.644826
$963$	0	0
$964$	6.00000	0.193247
$965$	0	0
$966$	0	0
$967$	−29.0000	−0.932577	−0.466289	−	0.884633i	$-0.654409\pi$
$967$	−29.0000	−0.932577	−0.466289	+	0.884633i	$0.654409\pi$
$968$	2.00000	0.0642824
$969$	0	0
$970$	0	0
$971$	42.0000	1.34784	0.673922	−	0.738802i	$-0.264608\pi$
$971$	42.0000	1.34784	0.673922	+	0.738802i	$0.264608\pi$
$972$	0	0
$973$	−4.00000	−0.128234
$974$	7.00000	0.224294
$975$	0	0
$976$	6.00000	0.192055
$977$	−33.0000	−1.05576	−0.527882	−	0.849318i	$-0.677014\pi$
$977$	−33.0000	−1.05576	−0.527882	+	0.849318i	$0.677014\pi$
$978$	0	0
$979$	−33.0000	−1.05468
$980$	0	0
$981$	0	0
$982$	−36.0000	−1.14881
$983$	−16.0000	−0.510321	−0.255160	−	0.966899i	$-0.582128\pi$
$983$	−16.0000	−0.510321	−0.255160	+	0.966899i	$0.582128\pi$
$984$	0	0
$985$	0	0
$986$	−40.0000	−1.27386
$987$	0	0
$988$	5.00000	0.159071
$989$	−8.00000	−0.254385
$990$	0	0
$991$	52.0000	1.65183	0.825917	−	0.563791i	$-0.190658\pi$
$991$	52.0000	1.65183	0.825917	+	0.563791i	$0.190658\pi$
$992$	8.00000	0.254000
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	14.0000	0.443384	0.221692	−	0.975117i	$-0.428842\pi$
$997$	14.0000	0.443384	0.221692	+	0.975117i	$0.428842\pi$
$998$	−40.0000	−1.26618
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9450.2.a.i.1.1		1
3.2	odd	2		9450.2.a.cv.1.1		1
5.2	odd	4		1890.2.g.g.379.1	yes	2
5.3	odd	4		1890.2.g.g.379.2	yes	2
5.4	even	2		9450.2.a.de.1.1		1
15.2	even	4		1890.2.g.e.379.2	yes	2
15.8	even	4		1890.2.g.e.379.1	✓	2
15.14	odd	2		9450.2.a.bt.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.g.e.379.1	✓	2	15.8	even	4
1890.2.g.e.379.2	yes	2	15.2	even	4
1890.2.g.g.379.1	yes	2	5.2	odd	4
1890.2.g.g.379.2	yes	2	5.3	odd	4
9450.2.a.i.1.1		1	1.1	even	1	trivial
9450.2.a.bt.1.1		1	15.14	odd	2
9450.2.a.cv.1.1		1	3.2	odd	2
9450.2.a.de.1.1		1	5.4	even	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:	\( N \)	\(=\)	\( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9450.a (trivial)

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