LMFDB - Embedded newform 9450.2.a.dx.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)

$f(q)$

$=$

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

$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} +1.00000 q^{8} +4.00000 q^{11} +6.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} +4.00000 q^{17} +4.00000 q^{22} +4.00000 q^{23} +6.00000 q^{26} +1.00000 q^{28} -3.00000 q^{29} +7.00000 q^{31} +1.00000 q^{32} +4.00000 q^{34} -1.00000 q^{37} +7.00000 q^{41} -10.0000 q^{43} +4.00000 q^{44} +4.00000 q^{46} -13.0000 q^{47} +1.00000 q^{49} +6.00000 q^{52} +6.00000 q^{53} +1.00000 q^{56} -3.00000 q^{58} +5.00000 q^{59} -7.00000 q^{61} +7.00000 q^{62} +1.00000 q^{64} +4.00000 q^{67} +4.00000 q^{68} +3.00000 q^{71} -7.00000 q^{73} -1.00000 q^{74} +4.00000 q^{77} +12.0000 q^{79} +7.00000 q^{82} -2.00000 q^{83} -10.0000 q^{86} +4.00000 q^{88} -14.0000 q^{89} +6.00000 q^{91} +4.00000 q^{92} -13.0000 q^{94} +10.0000 q^{97} +1.00000 q^{98} +O(q^{100})$

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
$11$	4.00000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	0	0
$13$	6.00000	1.66410	0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000	1.66410	0.832050	+	0.554700i	$0.187167\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	0	0
$22$	4.00000	0.852803
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	0	0
$25$	0	0
$26$	6.00000	1.17670
$27$	0	0
$28$	1.00000	0.188982
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	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
$34$	4.00000	0.685994
$35$	0	0
$36$	0	0
$37$	−1.00000	−0.164399	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000	−0.164399	−0.0821995	+	0.996616i	$0.526194\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	7.00000	1.09322	0.546608	−	0.837389i	$-0.315919\pi$
$41$	7.00000	1.09322	0.546608	+	0.837389i	$0.315919\pi$
$42$	0	0
$43$	−10.0000	−1.52499	−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000	−1.52499	−0.762493	+	0.646997i	$0.776025\pi$
$44$	4.00000	0.603023
$45$	0	0
$46$	4.00000	0.589768
$47$	−13.0000	−1.89624	−0.948122	−	0.317905i	$-0.897021\pi$
$47$	−13.0000	−1.89624	−0.948122	+	0.317905i	$0.897021\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	6.00000	0.832050
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	0	0
$55$	0	0
$56$	1.00000	0.133631
$57$	0	0
$58$	−3.00000	−0.393919
$59$	5.00000	0.650945	0.325472	−	0.945552i	$-0.394477\pi$
$59$	5.00000	0.650945	0.325472	+	0.945552i	$0.394477\pi$
$60$	0	0
$61$	−7.00000	−0.896258	−0.448129	−	0.893969i	$-0.647910\pi$
$61$	−7.00000	−0.896258	−0.448129	+	0.893969i	$0.647910\pi$
$62$	7.00000	0.889001
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	4.00000	0.485071
$69$	0	0
$70$	0	0
$71$	3.00000	0.356034	0.178017	−	0.984027i	$-0.443032\pi$
$71$	3.00000	0.356034	0.178017	+	0.984027i	$0.443032\pi$
$72$	0	0
$73$	−7.00000	−0.819288	−0.409644	−	0.912245i	$-0.634347\pi$
$73$	−7.00000	−0.819288	−0.409644	+	0.912245i	$0.634347\pi$
$74$	−1.00000	−0.116248
$75$	0	0
$76$	0	0
$77$	4.00000	0.455842
$78$	0	0
$79$	12.0000	1.35011	0.675053	−	0.737769i	$-0.264121\pi$
$79$	12.0000	1.35011	0.675053	+	0.737769i	$0.264121\pi$
$80$	0	0
$81$	0	0
$82$	7.00000	0.773021
$83$	−2.00000	−0.219529	−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000	−0.219529	−0.109764	+	0.993958i	$0.535010\pi$
$84$	0	0
$85$	0	0
$86$	−10.0000	−1.07833
$87$	0	0
$88$	4.00000	0.426401
$89$	−14.0000	−1.48400	−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000	−1.48400	−0.741999	+	0.670402i	$0.766122\pi$
$90$	0	0
$91$	6.00000	0.628971
$92$	4.00000	0.417029
$93$	0	0
$94$	−13.0000	−1.34085
$95$	0	0
$96$	0	0
$97$	10.0000	1.01535	0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000	1.01535	0.507673	+	0.861550i	$0.330506\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	0	0
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	0	0
$103$	−14.0000	−1.37946	−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000	−1.37946	−0.689730	+	0.724066i	$0.742271\pi$
$104$	6.00000	0.588348
$105$	0	0
$106$	6.00000	0.582772
$107$	9.00000	0.870063	0.435031	−	0.900415i	$-0.356737\pi$
$107$	9.00000	0.870063	0.435031	+	0.900415i	$0.356737\pi$
$108$	0	0
$109$	−20.0000	−1.91565	−0.957826	−	0.287348i	$-0.907226\pi$
$109$	−20.0000	−1.91565	−0.957826	+	0.287348i	$0.907226\pi$
$110$	0	0
$111$	0	0
$112$	1.00000	0.0944911
$113$	3.00000	0.282216	0.141108	−	0.989994i	$-0.454933\pi$
$113$	3.00000	0.282216	0.141108	+	0.989994i	$0.454933\pi$
$114$	0	0
$115$	0	0
$116$	−3.00000	−0.278543
$117$	0	0
$118$	5.00000	0.460287
$119$	4.00000	0.366679
$120$	0	0
$121$	5.00000	0.454545
$122$	−7.00000	−0.633750
$123$	0	0
$124$	7.00000	0.628619
$125$	0	0
$126$	0	0
$127$	−7.00000	−0.621150	−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000	−0.621150	−0.310575	+	0.950549i	$0.600522\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	0	0
$131$	−15.0000	−1.31056	−0.655278	−	0.755388i	$-0.727449\pi$
$131$	−15.0000	−1.31056	−0.655278	+	0.755388i	$0.727449\pi$
$132$	0	0
$133$	0	0
$134$	4.00000	0.345547
$135$	0	0
$136$	4.00000	0.342997
$137$	15.0000	1.28154	0.640768	−	0.767734i	$-0.278616\pi$
$137$	15.0000	1.28154	0.640768	+	0.767734i	$0.278616\pi$
$138$	0	0
$139$	−14.0000	−1.18746	−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000	−1.18746	−0.593732	+	0.804663i	$0.702346\pi$
$140$	0	0
$141$	0	0
$142$	3.00000	0.251754
$143$	24.0000	2.00698
$144$	0	0
$145$	0	0
$146$	−7.00000	−0.579324
$147$	0	0
$148$	−1.00000	−0.0821995
$149$	−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
$151$	−14.0000	−1.13930	−0.569652	−	0.821886i	$-0.692922\pi$
$151$	−14.0000	−1.13930	−0.569652	+	0.821886i	$0.692922\pi$
$152$	0	0
$153$	0	0
$154$	4.00000	0.322329
$155$	0	0
$156$	0	0
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	12.0000	0.954669
$159$	0	0
$160$	0	0
$161$	4.00000	0.315244
$162$	0	0
$163$	−14.0000	−1.09656	−0.548282	−	0.836293i	$-0.684718\pi$
$163$	−14.0000	−1.09656	−0.548282	+	0.836293i	$0.684718\pi$
$164$	7.00000	0.546608
$165$	0	0
$166$	−2.00000	−0.155230
$167$	3.00000	0.232147	0.116073	−	0.993241i	$-0.462969\pi$
$167$	3.00000	0.232147	0.116073	+	0.993241i	$0.462969\pi$
$168$	0	0
$169$	23.0000	1.76923
$170$	0	0
$171$	0	0
$172$	−10.0000	−0.762493
$173$	17.0000	1.29249	0.646243	−	0.763132i	$-0.276339\pi$
$173$	17.0000	1.29249	0.646243	+	0.763132i	$0.276339\pi$
$174$	0	0
$175$	0	0
$176$	4.00000	0.301511
$177$	0	0
$178$	−14.0000	−1.04934
$179$	−16.0000	−1.19590	−0.597948	−	0.801535i	$-0.704017\pi$
$179$	−16.0000	−1.19590	−0.597948	+	0.801535i	$0.704017\pi$
$180$	0	0
$181$	23.0000	1.70958	0.854788	−	0.518977i	$-0.173687\pi$
$181$	23.0000	1.70958	0.854788	+	0.518977i	$0.173687\pi$
$182$	6.00000	0.444750
$183$	0	0
$184$	4.00000	0.294884
$185$	0	0
$186$	0	0
$187$	16.0000	1.17004
$188$	−13.0000	−0.948122
$189$	0	0
$190$	0	0
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	0	0
$193$	2.00000	0.143963	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000	0.143963	0.0719816	+	0.997406i	$0.477068\pi$
$194$	10.0000	0.717958
$195$	0	0
$196$	1.00000	0.0714286
$197$	8.00000	0.569976	0.284988	−	0.958531i	$-0.408010\pi$
$197$	8.00000	0.569976	0.284988	+	0.958531i	$0.408010\pi$
$198$	0	0
$199$	24.0000	1.70131	0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000	1.70131	0.850657	+	0.525720i	$0.176204\pi$
$200$	0	0
$201$	0	0
$202$	−10.0000	−0.703598
$203$	−3.00000	−0.210559
$204$	0	0
$205$	0	0
$206$	−14.0000	−0.975426
$207$	0	0
$208$	6.00000	0.416025
$209$	0	0
$210$	0	0
$211$	−15.0000	−1.03264	−0.516321	−	0.856395i	$-0.672699\pi$
$211$	−15.0000	−1.03264	−0.516321	+	0.856395i	$0.672699\pi$
$212$	6.00000	0.412082
$213$	0	0
$214$	9.00000	0.615227
$215$	0	0
$216$	0	0
$217$	7.00000	0.475191
$218$	−20.0000	−1.35457
$219$	0	0
$220$	0	0
$221$	24.0000	1.61441
$222$	0	0
$223$	−4.00000	−0.267860	−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000	−0.267860	−0.133930	+	0.990991i	$0.542760\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	3.00000	0.199557
$227$	16.0000	1.06196	0.530979	−	0.847385i	$-0.321824\pi$
$227$	16.0000	1.06196	0.530979	+	0.847385i	$0.321824\pi$
$228$	0	0
$229$	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
$231$	0	0
$232$	−3.00000	−0.196960
$233$	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
$236$	5.00000	0.325472
$237$	0	0
$238$	4.00000	0.259281
$239$	13.0000	0.840900	0.420450	−	0.907316i	$-0.361872\pi$
$239$	13.0000	0.840900	0.420450	+	0.907316i	$0.361872\pi$
$240$	0	0
$241$	−2.00000	−0.128831	−0.0644157	−	0.997923i	$-0.520518\pi$
$241$	−2.00000	−0.128831	−0.0644157	+	0.997923i	$0.520518\pi$
$242$	5.00000	0.321412
$243$	0	0
$244$	−7.00000	−0.448129
$245$	0	0
$246$	0	0
$247$	0	0
$248$	7.00000	0.444500
$249$	0	0
$250$	0	0
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	0	0
$253$	16.0000	1.00591
$254$	−7.00000	−0.439219
$255$	0	0
$256$	1.00000	0.0625000
$257$	−24.0000	−1.49708	−0.748539	−	0.663090i	$-0.769245\pi$
$257$	−24.0000	−1.49708	−0.748539	+	0.663090i	$0.769245\pi$
$258$	0	0
$259$	−1.00000	−0.0621370
$260$	0	0
$261$	0	0
$262$	−15.0000	−0.926703
$263$	16.0000	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	4.00000	0.244339
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	0	0
$271$	−11.0000	−0.668202	−0.334101	−	0.942537i	$-0.608433\pi$
$271$	−11.0000	−0.668202	−0.334101	+	0.942537i	$0.608433\pi$
$272$	4.00000	0.242536
$273$	0	0
$274$	15.0000	0.906183
$275$	0	0
$276$	0	0
$277$	2.00000	0.120168	0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000	0.120168	0.0600842	+	0.998193i	$0.480863\pi$
$278$	−14.0000	−0.839664
$279$	0	0
$280$	0	0
$281$	−24.0000	−1.43172	−0.715860	−	0.698244i	$-0.753965\pi$
$281$	−24.0000	−1.43172	−0.715860	+	0.698244i	$0.753965\pi$
$282$	0	0
$283$	7.00000	0.416107	0.208053	−	0.978117i	$-0.433287\pi$
$283$	7.00000	0.416107	0.208053	+	0.978117i	$0.433287\pi$
$284$	3.00000	0.178017
$285$	0	0
$286$	24.0000	1.41915
$287$	7.00000	0.413197
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	0	0
$292$	−7.00000	−0.409644
$293$	15.0000	0.876309	0.438155	−	0.898900i	$-0.355632\pi$
$293$	15.0000	0.876309	0.438155	+	0.898900i	$0.355632\pi$
$294$	0	0
$295$	0	0
$296$	−1.00000	−0.0581238
$297$	0	0
$298$	−10.0000	−0.579284
$299$	24.0000	1.38796
$300$	0	0
$301$	−10.0000	−0.576390
$302$	−14.0000	−0.805609
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−12.0000	−0.684876	−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000	−0.684876	−0.342438	+	0.939540i	$0.611253\pi$
$308$	4.00000	0.227921
$309$	0	0
$310$	0	0
$311$	30.0000	1.70114	0.850572	−	0.525859i	$-0.176256\pi$
$311$	30.0000	1.70114	0.850572	+	0.525859i	$0.176256\pi$
$312$	0	0
$313$	26.0000	1.46961	0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000	1.46961	0.734803	+	0.678280i	$0.237274\pi$
$314$	−14.0000	−0.790066
$315$	0	0
$316$	12.0000	0.675053
$317$	−14.0000	−0.786318	−0.393159	−	0.919470i	$-0.628618\pi$
$317$	−14.0000	−0.786318	−0.393159	+	0.919470i	$0.628618\pi$
$318$	0	0
$319$	−12.0000	−0.671871
$320$	0	0
$321$	0	0
$322$	4.00000	0.222911
$323$	0	0
$324$	0	0
$325$	0	0
$326$	−14.0000	−0.775388
$327$	0	0
$328$	7.00000	0.386510
$329$	−13.0000	−0.716713
$330$	0	0
$331$	−35.0000	−1.92377	−0.961887	−	0.273447i	$-0.911836\pi$
$331$	−35.0000	−1.92377	−0.961887	+	0.273447i	$0.911836\pi$
$332$	−2.00000	−0.109764
$333$	0	0
$334$	3.00000	0.164153
$335$	0	0
$336$	0	0
$337$	−16.0000	−0.871576	−0.435788	−	0.900049i	$-0.643530\pi$
$337$	−16.0000	−0.871576	−0.435788	+	0.900049i	$0.643530\pi$
$338$	23.0000	1.25104
$339$	0	0
$340$	0	0
$341$	28.0000	1.51629
$342$	0	0
$343$	1.00000	0.0539949
$344$	−10.0000	−0.539164
$345$	0	0
$346$	17.0000	0.913926
$347$	27.0000	1.44944	0.724718	−	0.689046i	$-0.241970\pi$
$347$	27.0000	1.44944	0.724718	+	0.689046i	$0.241970\pi$
$348$	0	0
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	0	0
$351$	0	0
$352$	4.00000	0.213201
$353$	32.0000	1.70319	0.851594	−	0.524202i	$-0.175636\pi$
$353$	32.0000	1.70319	0.851594	+	0.524202i	$0.175636\pi$
$354$	0	0
$355$	0	0
$356$	−14.0000	−0.741999
$357$	0	0
$358$	−16.0000	−0.845626
$359$	12.0000	0.633336	0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000	0.633336	0.316668	+	0.948536i	$0.397436\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	23.0000	1.20885
$363$	0	0
$364$	6.00000	0.314485
$365$	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	$0.483377\pi$
$368$	4.00000	0.208514
$369$	0	0
$370$	0	0
$371$	6.00000	0.311504
$372$	0	0
$373$	3.00000	0.155334	0.0776671	−	0.996979i	$-0.475253\pi$
$373$	3.00000	0.155334	0.0776671	+	0.996979i	$0.475253\pi$
$374$	16.0000	0.827340
$375$	0	0
$376$	−13.0000	−0.670424
$377$	−18.0000	−0.927047
$378$	0	0
$379$	−1.00000	−0.0513665	−0.0256833	−	0.999670i	$-0.508176\pi$
$379$	−1.00000	−0.0513665	−0.0256833	+	0.999670i	$0.508176\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	8.00000	0.408781	0.204390	−	0.978889i	$-0.434479\pi$
$383$	8.00000	0.408781	0.204390	+	0.978889i	$0.434479\pi$
$384$	0	0
$385$	0	0
$386$	2.00000	0.101797
$387$	0	0
$388$	10.0000	0.507673
$389$	−23.0000	−1.16615	−0.583073	−	0.812420i	$-0.698150\pi$
$389$	−23.0000	−1.16615	−0.583073	+	0.812420i	$0.698150\pi$
$390$	0	0
$391$	16.0000	0.809155
$392$	1.00000	0.0505076
$393$	0	0
$394$	8.00000	0.403034
$395$	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	$0.385733\pi$
$398$	24.0000	1.20301
$399$	0	0
$400$	0	0
$401$	−16.0000	−0.799002	−0.399501	−	0.916733i	$-0.630817\pi$
$401$	−16.0000	−0.799002	−0.399501	+	0.916733i	$0.630817\pi$
$402$	0	0
$403$	42.0000	2.09217
$404$	−10.0000	−0.497519
$405$	0	0
$406$	−3.00000	−0.148888
$407$	−4.00000	−0.198273
$408$	0	0
$409$	20.0000	0.988936	0.494468	−	0.869196i	$-0.335363\pi$
$409$	20.0000	0.988936	0.494468	+	0.869196i	$0.335363\pi$
$410$	0	0
$411$	0	0
$412$	−14.0000	−0.689730
$413$	5.00000	0.246034
$414$	0	0
$415$	0	0
$416$	6.00000	0.294174
$417$	0	0
$418$	0	0
$419$	25.0000	1.22133	0.610665	−	0.791889i	$-0.290902\pi$
$419$	25.0000	1.22133	0.610665	+	0.791889i	$0.290902\pi$
$420$	0	0
$421$	−20.0000	−0.974740	−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000	−0.974740	−0.487370	+	0.873195i	$0.662044\pi$
$422$	−15.0000	−0.730189
$423$	0	0
$424$	6.00000	0.291386
$425$	0	0
$426$	0	0
$427$	−7.00000	−0.338754
$428$	9.00000	0.435031
$429$	0	0
$430$	0	0
$431$	−11.0000	−0.529851	−0.264926	−	0.964269i	$-0.585347\pi$
$431$	−11.0000	−0.529851	−0.264926	+	0.964269i	$0.585347\pi$
$432$	0	0
$433$	29.0000	1.39365	0.696826	−	0.717241i	$-0.254595\pi$
$433$	29.0000	1.39365	0.696826	+	0.717241i	$0.254595\pi$
$434$	7.00000	0.336011
$435$	0	0
$436$	−20.0000	−0.957826
$437$	0	0
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	0	0
$442$	24.0000	1.14156
$443$	9.00000	0.427603	0.213801	−	0.976877i	$-0.431415\pi$
$443$	9.00000	0.427603	0.213801	+	0.976877i	$0.431415\pi$
$444$	0	0
$445$	0	0
$446$	−4.00000	−0.189405
$447$	0	0
$448$	1.00000	0.0472456
$449$	−36.0000	−1.69895	−0.849473	−	0.527633i	$-0.823080\pi$
$449$	−36.0000	−1.69895	−0.849473	+	0.527633i	$0.823080\pi$
$450$	0	0
$451$	28.0000	1.31847
$452$	3.00000	0.141108
$453$	0	0
$454$	16.0000	0.750917
$455$	0	0
$456$	0	0
$457$	8.00000	0.374224	0.187112	−	0.982339i	$-0.440087\pi$
$457$	8.00000	0.374224	0.187112	+	0.982339i	$0.440087\pi$
$458$	14.0000	0.654177
$459$	0	0
$460$	0	0
$461$	36.0000	1.67669	0.838344	−	0.545142i	$-0.183524\pi$
$461$	36.0000	1.67669	0.838344	+	0.545142i	$0.183524\pi$
$462$	0	0
$463$	−33.0000	−1.53364	−0.766820	−	0.641862i	$-0.778162\pi$
$463$	−33.0000	−1.53364	−0.766820	+	0.641862i	$0.778162\pi$
$464$	−3.00000	−0.139272
$465$	0	0
$466$	11.0000	0.509565
$467$	−18.0000	−0.832941	−0.416470	−	0.909149i	$-0.636733\pi$
$467$	−18.0000	−0.832941	−0.416470	+	0.909149i	$0.636733\pi$
$468$	0	0
$469$	4.00000	0.184703
$470$	0	0
$471$	0	0
$472$	5.00000	0.230144
$473$	−40.0000	−1.83920
$474$	0	0
$475$	0	0
$476$	4.00000	0.183340
$477$	0	0
$478$	13.0000	0.594606
$479$	4.00000	0.182765	0.0913823	−	0.995816i	$-0.470871\pi$
$479$	4.00000	0.182765	0.0913823	+	0.995816i	$0.470871\pi$
$480$	0	0
$481$	−6.00000	−0.273576
$482$	−2.00000	−0.0910975
$483$	0	0
$484$	5.00000	0.227273
$485$	0	0
$486$	0	0
$487$	−21.0000	−0.951601	−0.475800	−	0.879553i	$-0.657842\pi$
$487$	−21.0000	−0.951601	−0.475800	+	0.879553i	$0.657842\pi$
$488$	−7.00000	−0.316875
$489$	0	0
$490$	0	0
$491$	30.0000	1.35388	0.676941	−	0.736038i	$-0.263305\pi$
$491$	30.0000	1.35388	0.676941	+	0.736038i	$0.263305\pi$
$492$	0	0
$493$	−12.0000	−0.540453
$494$	0	0
$495$	0	0
$496$	7.00000	0.314309
$497$	3.00000	0.134568
$498$	0	0
$499$	9.00000	0.402895	0.201448	−	0.979499i	$-0.435435\pi$
$499$	9.00000	0.402895	0.201448	+	0.979499i	$0.435435\pi$
$500$	0	0
$501$	0	0
$502$	−12.0000	−0.535586
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	0	0
$506$	16.0000	0.711287
$507$	0	0
$508$	−7.00000	−0.310575
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	−7.00000	−0.309662
$512$	1.00000	0.0441942
$513$	0	0
$514$	−24.0000	−1.05859
$515$	0	0
$516$	0	0
$517$	−52.0000	−2.28696
$518$	−1.00000	−0.0439375
$519$	0	0
$520$	0	0
$521$	38.0000	1.66481	0.832405	−	0.554168i	$-0.186963\pi$
$521$	38.0000	1.66481	0.832405	+	0.554168i	$0.186963\pi$
$522$	0	0
$523$	28.0000	1.22435	0.612177	−	0.790721i	$-0.290294\pi$
$523$	28.0000	1.22435	0.612177	+	0.790721i	$0.290294\pi$
$524$	−15.0000	−0.655278
$525$	0	0
$526$	16.0000	0.697633
$527$	28.0000	1.21970
$528$	0	0
$529$	−7.00000	−0.304348
$530$	0	0
$531$	0	0
$532$	0	0
$533$	42.0000	1.81922
$534$	0	0
$535$	0	0
$536$	4.00000	0.172774
$537$	0	0
$538$	0	0
$539$	4.00000	0.172292
$540$	0	0
$541$	−32.0000	−1.37579	−0.687894	−	0.725811i	$-0.741464\pi$
$541$	−32.0000	−1.37579	−0.687894	+	0.725811i	$0.741464\pi$
$542$	−11.0000	−0.472490
$543$	0	0
$544$	4.00000	0.171499
$545$	0	0
$546$	0	0
$547$	32.0000	1.36822	0.684111	−	0.729378i	$-0.260191\pi$
$547$	32.0000	1.36822	0.684111	+	0.729378i	$0.260191\pi$
$548$	15.0000	0.640768
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	12.0000	0.510292
$554$	2.00000	0.0849719
$555$	0	0
$556$	−14.0000	−0.593732
$557$	12.0000	0.508456	0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000	0.508456	0.254228	+	0.967144i	$0.418179\pi$
$558$	0	0
$559$	−60.0000	−2.53773
$560$	0	0
$561$	0	0
$562$	−24.0000	−1.01238
$563$	−10.0000	−0.421450	−0.210725	−	0.977545i	$-0.567582\pi$
$563$	−10.0000	−0.421450	−0.210725	+	0.977545i	$0.567582\pi$
$564$	0	0
$565$	0	0
$566$	7.00000	0.294232
$567$	0	0
$568$	3.00000	0.125877
$569$	−20.0000	−0.838444	−0.419222	−	0.907884i	$-0.637697\pi$
$569$	−20.0000	−0.838444	−0.419222	+	0.907884i	$0.637697\pi$
$570$	0	0
$571$	19.0000	0.795125	0.397563	−	0.917575i	$-0.369856\pi$
$571$	19.0000	0.795125	0.397563	+	0.917575i	$0.369856\pi$
$572$	24.0000	1.00349
$573$	0	0
$574$	7.00000	0.292174
$575$	0	0
$576$	0	0
$577$	11.0000	0.457936	0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000	0.457936	0.228968	+	0.973434i	$0.426465\pi$
$578$	−1.00000	−0.0415945
$579$	0	0
$580$	0	0
$581$	−2.00000	−0.0829740
$582$	0	0
$583$	24.0000	0.993978
$584$	−7.00000	−0.289662
$585$	0	0
$586$	15.0000	0.619644
$587$	−18.0000	−0.742940	−0.371470	−	0.928445i	$-0.621146\pi$
$587$	−18.0000	−0.742940	−0.371470	+	0.928445i	$0.621146\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	−1.00000	−0.0410997
$593$	30.0000	1.23195	0.615976	−	0.787765i	$-0.288762\pi$
$593$	30.0000	1.23195	0.615976	+	0.787765i	$0.288762\pi$
$594$	0	0
$595$	0	0
$596$	−10.0000	−0.409616
$597$	0	0
$598$	24.0000	0.981433
$599$	15.0000	0.612883	0.306442	−	0.951889i	$-0.400862\pi$
$599$	15.0000	0.612883	0.306442	+	0.951889i	$0.400862\pi$
$600$	0	0
$601$	44.0000	1.79480	0.897399	−	0.441221i	$-0.145454\pi$
$601$	44.0000	1.79480	0.897399	+	0.441221i	$0.145454\pi$
$602$	−10.0000	−0.407570
$603$	0	0
$604$	−14.0000	−0.569652
$605$	0	0
$606$	0	0
$607$	−14.0000	−0.568242	−0.284121	−	0.958788i	$-0.591702\pi$
$607$	−14.0000	−0.568242	−0.284121	+	0.958788i	$0.591702\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−78.0000	−3.15554
$612$	0	0
$613$	−22.0000	−0.888572	−0.444286	−	0.895885i	$-0.646543\pi$
$613$	−22.0000	−0.888572	−0.444286	+	0.895885i	$0.646543\pi$
$614$	−12.0000	−0.484281
$615$	0	0
$616$	4.00000	0.161165
$617$	31.0000	1.24801	0.624007	−	0.781419i	$-0.285504\pi$
$617$	31.0000	1.24801	0.624007	+	0.781419i	$0.285504\pi$
$618$	0	0
$619$	−40.0000	−1.60774	−0.803868	−	0.594808i	$-0.797228\pi$
$619$	−40.0000	−1.60774	−0.803868	+	0.594808i	$0.797228\pi$
$620$	0	0
$621$	0	0
$622$	30.0000	1.20289
$623$	−14.0000	−0.560898
$624$	0	0
$625$	0	0
$626$	26.0000	1.03917
$627$	0	0
$628$	−14.0000	−0.558661
$629$	−4.00000	−0.159490
$630$	0	0
$631$	−40.0000	−1.59237	−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000	−1.59237	−0.796187	+	0.605050i	$0.793153\pi$
$632$	12.0000	0.477334
$633$	0	0
$634$	−14.0000	−0.556011
$635$	0	0
$636$	0	0
$637$	6.00000	0.237729
$638$	−12.0000	−0.475085
$639$	0	0
$640$	0	0
$641$	−26.0000	−1.02694	−0.513469	−	0.858108i	$-0.671640\pi$
$641$	−26.0000	−1.02694	−0.513469	+	0.858108i	$0.671640\pi$
$642$	0	0
$643$	39.0000	1.53801	0.769005	−	0.639243i	$-0.220752\pi$
$643$	39.0000	1.53801	0.769005	+	0.639243i	$0.220752\pi$
$644$	4.00000	0.157622
$645$	0	0
$646$	0	0
$647$	−33.0000	−1.29736	−0.648682	−	0.761060i	$-0.724679\pi$
$647$	−33.0000	−1.29736	−0.648682	+	0.761060i	$0.724679\pi$
$648$	0	0
$649$	20.0000	0.785069
$650$	0	0
$651$	0	0
$652$	−14.0000	−0.548282
$653$	−14.0000	−0.547862	−0.273931	−	0.961749i	$-0.588324\pi$
$653$	−14.0000	−0.547862	−0.273931	+	0.961749i	$0.588324\pi$
$654$	0	0
$655$	0	0
$656$	7.00000	0.273304
$657$	0	0
$658$	−13.0000	−0.506793
$659$	26.0000	1.01282	0.506408	−	0.862294i	$-0.330973\pi$
$659$	26.0000	1.01282	0.506408	+	0.862294i	$0.330973\pi$
$660$	0	0
$661$	−19.0000	−0.739014	−0.369507	−	0.929228i	$-0.620473\pi$
$661$	−19.0000	−0.739014	−0.369507	+	0.929228i	$0.620473\pi$
$662$	−35.0000	−1.36031
$663$	0	0
$664$	−2.00000	−0.0776151
$665$	0	0
$666$	0	0
$667$	−12.0000	−0.464642
$668$	3.00000	0.116073
$669$	0	0
$670$	0	0
$671$	−28.0000	−1.08093
$672$	0	0
$673$	−36.0000	−1.38770	−0.693849	−	0.720121i	$-0.744086\pi$
$673$	−36.0000	−1.38770	−0.693849	+	0.720121i	$0.744086\pi$
$674$	−16.0000	−0.616297
$675$	0	0
$676$	23.0000	0.884615
$677$	−29.0000	−1.11456	−0.557280	−	0.830324i	$-0.688155\pi$
$677$	−29.0000	−1.11456	−0.557280	+	0.830324i	$0.688155\pi$
$678$	0	0
$679$	10.0000	0.383765
$680$	0	0
$681$	0	0
$682$	28.0000	1.07218
$683$	1.00000	0.0382639	0.0191320	−	0.999817i	$-0.493910\pi$
$683$	1.00000	0.0382639	0.0191320	+	0.999817i	$0.493910\pi$
$684$	0	0
$685$	0	0
$686$	1.00000	0.0381802
$687$	0	0
$688$	−10.0000	−0.381246
$689$	36.0000	1.37149
$690$	0	0
$691$	−38.0000	−1.44559	−0.722794	−	0.691063i	$-0.757142\pi$
$691$	−38.0000	−1.44559	−0.722794	+	0.691063i	$0.757142\pi$
$692$	17.0000	0.646243
$693$	0	0
$694$	27.0000	1.02491
$695$	0	0
$696$	0	0
$697$	28.0000	1.06058
$698$	−2.00000	−0.0757011
$699$	0	0
$700$	0	0
$701$	−35.0000	−1.32193	−0.660966	−	0.750416i	$-0.729853\pi$
$701$	−35.0000	−1.32193	−0.660966	+	0.750416i	$0.729853\pi$
$702$	0	0
$703$	0	0
$704$	4.00000	0.150756
$705$	0	0
$706$	32.0000	1.20434
$707$	−10.0000	−0.376089
$708$	0	0
$709$	48.0000	1.80268	0.901339	−	0.433114i	$-0.142585\pi$
$709$	48.0000	1.80268	0.901339	+	0.433114i	$0.142585\pi$
$710$	0	0
$711$	0	0
$712$	−14.0000	−0.524672
$713$	28.0000	1.04861
$714$	0	0
$715$	0	0
$716$	−16.0000	−0.597948
$717$	0	0
$718$	12.0000	0.447836
$719$	−2.00000	−0.0745874	−0.0372937	−	0.999304i	$-0.511874\pi$
$719$	−2.00000	−0.0745874	−0.0372937	+	0.999304i	$0.511874\pi$
$720$	0	0
$721$	−14.0000	−0.521387
$722$	−19.0000	−0.707107
$723$	0	0
$724$	23.0000	0.854788
$725$	0	0
$726$	0	0
$727$	6.00000	0.222528	0.111264	−	0.993791i	$-0.464510\pi$
$727$	6.00000	0.222528	0.111264	+	0.993791i	$0.464510\pi$
$728$	6.00000	0.222375
$729$	0	0
$730$	0	0
$731$	−40.0000	−1.47945
$732$	0	0
$733$	−44.0000	−1.62518	−0.812589	−	0.582838i	$-0.801942\pi$
$733$	−44.0000	−1.62518	−0.812589	+	0.582838i	$0.801942\pi$
$734$	2.00000	0.0738213
$735$	0	0
$736$	4.00000	0.147442
$737$	16.0000	0.589368
$738$	0	0
$739$	13.0000	0.478213	0.239106	−	0.970993i	$-0.423146\pi$
$739$	13.0000	0.478213	0.239106	+	0.970993i	$0.423146\pi$
$740$	0	0
$741$	0	0
$742$	6.00000	0.220267
$743$	18.0000	0.660356	0.330178	−	0.943919i	$-0.392891\pi$
$743$	18.0000	0.660356	0.330178	+	0.943919i	$0.392891\pi$
$744$	0	0
$745$	0	0
$746$	3.00000	0.109838
$747$	0	0
$748$	16.0000	0.585018
$749$	9.00000	0.328853
$750$	0	0
$751$	−22.0000	−0.802791	−0.401396	−	0.915905i	$-0.631475\pi$
$751$	−22.0000	−0.802791	−0.401396	+	0.915905i	$0.631475\pi$
$752$	−13.0000	−0.474061
$753$	0	0
$754$	−18.0000	−0.655521
$755$	0	0
$756$	0	0
$757$	−19.0000	−0.690567	−0.345283	−	0.938498i	$-0.612217\pi$
$757$	−19.0000	−0.690567	−0.345283	+	0.938498i	$0.612217\pi$
$758$	−1.00000	−0.0363216
$759$	0	0
$760$	0	0
$761$	−3.00000	−0.108750	−0.0543750	−	0.998521i	$-0.517317\pi$
$761$	−3.00000	−0.108750	−0.0543750	+	0.998521i	$0.517317\pi$
$762$	0	0
$763$	−20.0000	−0.724049
$764$	0	0
$765$	0	0
$766$	8.00000	0.289052
$767$	30.0000	1.08324
$768$	0	0
$769$	−12.0000	−0.432731	−0.216366	−	0.976312i	$-0.569420\pi$
$769$	−12.0000	−0.432731	−0.216366	+	0.976312i	$0.569420\pi$
$770$	0	0
$771$	0	0
$772$	2.00000	0.0719816
$773$	−27.0000	−0.971123	−0.485561	−	0.874203i	$-0.661385\pi$
$773$	−27.0000	−0.971123	−0.485561	+	0.874203i	$0.661385\pi$
$774$	0	0
$775$	0	0
$776$	10.0000	0.358979
$777$	0	0
$778$	−23.0000	−0.824590
$779$	0	0
$780$	0	0
$781$	12.0000	0.429394
$782$	16.0000	0.572159
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	−7.00000	−0.249523	−0.124762	−	0.992187i	$-0.539817\pi$
$787$	−7.00000	−0.249523	−0.124762	+	0.992187i	$0.539817\pi$
$788$	8.00000	0.284988
$789$	0	0
$790$	0	0
$791$	3.00000	0.106668
$792$	0	0
$793$	−42.0000	−1.49146
$794$	14.0000	0.496841
$795$	0	0
$796$	24.0000	0.850657
$797$	37.0000	1.31061	0.655304	−	0.755366i	$-0.272541\pi$
$797$	37.0000	1.31061	0.655304	+	0.755366i	$0.272541\pi$
$798$	0	0
$799$	−52.0000	−1.83963
$800$	0	0
$801$	0	0
$802$	−16.0000	−0.564980
$803$	−28.0000	−0.988099
$804$	0	0
$805$	0	0
$806$	42.0000	1.47939
$807$	0	0
$808$	−10.0000	−0.351799
$809$	−18.0000	−0.632846	−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000	−0.632846	−0.316423	+	0.948618i	$0.602482\pi$
$810$	0	0
$811$	−14.0000	−0.491606	−0.245803	−	0.969320i	$-0.579052\pi$
$811$	−14.0000	−0.491606	−0.245803	+	0.969320i	$0.579052\pi$
$812$	−3.00000	−0.105279
$813$	0	0
$814$	−4.00000	−0.140200
$815$	0	0
$816$	0	0
$817$	0	0
$818$	20.0000	0.699284
$819$	0	0
$820$	0	0
$821$	2.00000	0.0698005	0.0349002	−	0.999391i	$-0.488889\pi$
$821$	2.00000	0.0698005	0.0349002	+	0.999391i	$0.488889\pi$
$822$	0	0
$823$	−51.0000	−1.77775	−0.888874	−	0.458151i	$-0.848512\pi$
$823$	−51.0000	−1.77775	−0.888874	+	0.458151i	$0.848512\pi$
$824$	−14.0000	−0.487713
$825$	0	0
$826$	5.00000	0.173972
$827$	25.0000	0.869335	0.434668	−	0.900591i	$-0.356866\pi$
$827$	25.0000	0.869335	0.434668	+	0.900591i	$0.356866\pi$
$828$	0	0
$829$	6.00000	0.208389	0.104194	−	0.994557i	$-0.466774\pi$
$829$	6.00000	0.208389	0.104194	+	0.994557i	$0.466774\pi$
$830$	0	0
$831$	0	0
$832$	6.00000	0.208013
$833$	4.00000	0.138592
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	25.0000	0.863611
$839$	−4.00000	−0.138095	−0.0690477	−	0.997613i	$-0.521996\pi$
$839$	−4.00000	−0.138095	−0.0690477	+	0.997613i	$0.521996\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	−20.0000	−0.689246
$843$	0	0
$844$	−15.0000	−0.516321
$845$	0	0
$846$	0	0
$847$	5.00000	0.171802
$848$	6.00000	0.206041
$849$	0	0
$850$	0	0
$851$	−4.00000	−0.137118
$852$	0	0
$853$	16.0000	0.547830	0.273915	−	0.961754i	$-0.411681\pi$
$853$	16.0000	0.547830	0.273915	+	0.961754i	$0.411681\pi$
$854$	−7.00000	−0.239535
$855$	0	0
$856$	9.00000	0.307614
$857$	0	0		−	1.00000i	$-0.5\pi$
$857$	0	0			1.00000i	$0.5\pi$
$858$	0	0
$859$	−40.0000	−1.36478	−0.682391	−	0.730987i	$-0.739060\pi$
$859$	−40.0000	−1.36478	−0.682391	+	0.730987i	$0.739060\pi$
$860$	0	0
$861$	0	0
$862$	−11.0000	−0.374661
$863$	6.00000	0.204242	0.102121	−	0.994772i	$-0.467437\pi$
$863$	6.00000	0.204242	0.102121	+	0.994772i	$0.467437\pi$
$864$	0	0
$865$	0	0
$866$	29.0000	0.985460
$867$	0	0
$868$	7.00000	0.237595
$869$	48.0000	1.62829
$870$	0	0
$871$	24.0000	0.813209
$872$	−20.0000	−0.677285
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	49.0000	1.65461	0.827306	−	0.561751i	$-0.189872\pi$
$877$	49.0000	1.65461	0.827306	+	0.561751i	$0.189872\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	−33.0000	−1.11180	−0.555899	−	0.831250i	$-0.687626\pi$
$881$	−33.0000	−1.11180	−0.555899	+	0.831250i	$0.687626\pi$
$882$	0	0
$883$	−54.0000	−1.81724	−0.908622	−	0.417619i	$-0.862865\pi$
$883$	−54.0000	−1.81724	−0.908622	+	0.417619i	$0.862865\pi$
$884$	24.0000	0.807207
$885$	0	0
$886$	9.00000	0.302361
$887$	39.0000	1.30949	0.654746	−	0.755849i	$-0.272776\pi$
$887$	39.0000	1.30949	0.654746	+	0.755849i	$0.272776\pi$
$888$	0	0
$889$	−7.00000	−0.234772
$890$	0	0
$891$	0	0
$892$	−4.00000	−0.133930
$893$	0	0
$894$	0	0
$895$	0	0
$896$	1.00000	0.0334077
$897$	0	0
$898$	−36.0000	−1.20134
$899$	−21.0000	−0.700389
$900$	0	0
$901$	24.0000	0.799556
$902$	28.0000	0.932298
$903$	0	0
$904$	3.00000	0.0997785
$905$	0	0
$906$	0	0
$907$	−24.0000	−0.796907	−0.398453	−	0.917189i	$-0.630453\pi$
$907$	−24.0000	−0.796907	−0.398453	+	0.917189i	$0.630453\pi$
$908$	16.0000	0.530979
$909$	0	0
$910$	0	0
$911$	−9.00000	−0.298183	−0.149092	−	0.988823i	$-0.547635\pi$
$911$	−9.00000	−0.298183	−0.149092	+	0.988823i	$0.547635\pi$
$912$	0	0
$913$	−8.00000	−0.264761
$914$	8.00000	0.264616
$915$	0	0
$916$	14.0000	0.462573
$917$	−15.0000	−0.495344
$918$	0	0
$919$	18.0000	0.593765	0.296883	−	0.954914i	$-0.404053\pi$
$919$	18.0000	0.593765	0.296883	+	0.954914i	$0.404053\pi$
$920$	0	0
$921$	0	0
$922$	36.0000	1.18560
$923$	18.0000	0.592477
$924$	0	0
$925$	0	0
$926$	−33.0000	−1.08445
$927$	0	0
$928$	−3.00000	−0.0984798
$929$	42.0000	1.37798	0.688988	−	0.724773i	$-0.258055\pi$
$929$	42.0000	1.37798	0.688988	+	0.724773i	$0.258055\pi$
$930$	0	0
$931$	0	0
$932$	11.0000	0.360317
$933$	0	0
$934$	−18.0000	−0.588978
$935$	0	0
$936$	0	0
$937$	−23.0000	−0.751377	−0.375689	−	0.926746i	$-0.622594\pi$
$937$	−23.0000	−0.751377	−0.375689	+	0.926746i	$0.622594\pi$
$938$	4.00000	0.130605
$939$	0	0
$940$	0	0
$941$	40.0000	1.30396	0.651981	−	0.758235i	$-0.273938\pi$
$941$	40.0000	1.30396	0.651981	+	0.758235i	$0.273938\pi$
$942$	0	0
$943$	28.0000	0.911805
$944$	5.00000	0.162736
$945$	0	0
$946$	−40.0000	−1.30051
$947$	12.0000	0.389948	0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000	0.389948	0.194974	+	0.980808i	$0.437538\pi$
$948$	0	0
$949$	−42.0000	−1.36338
$950$	0	0
$951$	0	0
$952$	4.00000	0.129641
$953$	38.0000	1.23094	0.615470	−	0.788160i	$-0.288966\pi$
$953$	38.0000	1.23094	0.615470	+	0.788160i	$0.288966\pi$
$954$	0	0
$955$	0	0
$956$	13.0000	0.420450
$957$	0	0
$958$	4.00000	0.129234
$959$	15.0000	0.484375
$960$	0	0
$961$	18.0000	0.580645
$962$	−6.00000	−0.193448
$963$	0	0
$964$	−2.00000	−0.0644157
$965$	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	$0.654409\pi$
$968$	5.00000	0.160706
$969$	0	0
$970$	0	0
$971$	−33.0000	−1.05902	−0.529510	−	0.848304i	$-0.677624\pi$
$971$	−33.0000	−1.05902	−0.529510	+	0.848304i	$0.677624\pi$
$972$	0	0
$973$	−14.0000	−0.448819
$974$	−21.0000	−0.672883
$975$	0	0
$976$	−7.00000	−0.224065
$977$	−18.0000	−0.575871	−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000	−0.575871	−0.287936	+	0.957650i	$0.592969\pi$
$978$	0	0
$979$	−56.0000	−1.78977
$980$	0	0
$981$	0	0
$982$	30.0000	0.957338
$983$	−52.0000	−1.65854	−0.829271	−	0.558846i	$-0.811244\pi$
$983$	−52.0000	−1.65854	−0.829271	+	0.558846i	$0.811244\pi$
$984$	0	0
$985$	0	0
$986$	−12.0000	−0.382158
$987$	0	0
$988$	0	0
$989$	−40.0000	−1.27193
$990$	0	0
$991$	−2.00000	−0.0635321	−0.0317660	−	0.999495i	$-0.510113\pi$
$991$	−2.00000	−0.0635321	−0.0317660	+	0.999495i	$0.510113\pi$
$992$	7.00000	0.222250
$993$	0	0
$994$	3.00000	0.0951542
$995$	0	0
$996$	0	0
$997$	−12.0000	−0.380044	−0.190022	−	0.981780i	$-0.560856\pi$
$997$	−12.0000	−0.380044	−0.190022	+	0.981780i	$0.560856\pi$
$998$	9.00000	0.284890
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9450.2.a.dx.1.1		1
3.2	odd	2		9450.2.a.be.1.1		1
5.2	odd	4		1890.2.g.k.379.2	yes	2
5.3	odd	4		1890.2.g.k.379.1	yes	2
5.4	even	2		9450.2.a.w.1.1		1
15.2	even	4		1890.2.g.a.379.1	✓	2
15.8	even	4		1890.2.g.a.379.2	yes	2
15.14	odd	2		9450.2.a.cc.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.g.a.379.1	✓	2	15.2	even	4
1890.2.g.a.379.2	yes	2	15.8	even	4
1890.2.g.k.379.1	yes	2	5.3	odd	4
1890.2.g.k.379.2	yes	2	5.2	odd	4
9450.2.a.w.1.1		1	5.4	even	2
9450.2.a.be.1.1		1	3.2	odd	2
9450.2.a.cc.1.1		1	15.14	odd	2
9450.2.a.dx.1.1		1	1.1	even	1	trivial

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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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