LMFDB - Embedded newform 9450.2.a.bu.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:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	9450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} -1.00000 q^{8} +3.00000 q^{11} -1.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} -4.00000 q^{19} -3.00000 q^{22} +3.00000 q^{23} +1.00000 q^{26} +1.00000 q^{28} -6.00000 q^{29} -4.00000 q^{31} -1.00000 q^{32} -1.00000 q^{37} +4.00000 q^{38} -6.00000 q^{41} +8.00000 q^{43} +3.00000 q^{44} -3.00000 q^{46} +3.00000 q^{47} +1.00000 q^{49} -1.00000 q^{52} +12.0000 q^{53} -1.00000 q^{56} +6.00000 q^{58} -3.00000 q^{59} -7.00000 q^{61} +4.00000 q^{62} +1.00000 q^{64} -4.00000 q^{67} +3.00000 q^{71} -10.0000 q^{73} +1.00000 q^{74} -4.00000 q^{76} +3.00000 q^{77} -10.0000 q^{79} +6.00000 q^{82} -12.0000 q^{83} -8.00000 q^{86} -3.00000 q^{88} -6.00000 q^{89} -1.00000 q^{91} +3.00000 q^{92} -3.00000 q^{94} -13.0000 q^{97} -1.00000 q^{98} +O(q^{100})$

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	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	0	0
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	0	0
$21$	0	0
$22$	−3.00000	−0.639602
$23$	3.00000	0.625543	0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000	0.625543	0.312772	+	0.949828i	$0.398743\pi$
$24$	0	0
$25$	0	0
$26$	1.00000	0.196116
$27$	0	0
$28$	1.00000	0.188982
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	0	0
$35$	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	$0.526194\pi$
$38$	4.00000	0.648886
$39$	0	0
$40$	0	0
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	3.00000	0.452267
$45$	0	0
$46$	−3.00000	−0.442326
$47$	3.00000	0.437595	0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000	0.437595	0.218797	+	0.975770i	$0.429787\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	−1.00000	−0.138675
$53$	12.0000	1.64833	0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000	1.64833	0.824163	+	0.566352i	$0.191646\pi$
$54$	0	0
$55$	0	0
$56$	−1.00000	−0.133631
$57$	0	0
$58$	6.00000	0.787839
$59$	−3.00000	−0.390567	−0.195283	−	0.980747i	$-0.562563\pi$
$59$	−3.00000	−0.390567	−0.195283	+	0.980747i	$0.562563\pi$
$60$	0	0
$61$	−7.00000	−0.896258	−0.448129	−	0.893969i	$-0.647910\pi$
$61$	−7.00000	−0.896258	−0.448129	+	0.893969i	$0.647910\pi$
$62$	4.00000	0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	0	0
$69$	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
$73$	−10.0000	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	−4.00000	−0.458831
$77$	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
$82$	6.00000	0.662589
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	0	0
$85$	0	0
$86$	−8.00000	−0.862662
$87$	0	0
$88$	−3.00000	−0.319801
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	0	0
$91$	−1.00000	−0.104828
$92$	3.00000	0.312772
$93$	0	0
$94$	−3.00000	−0.309426
$95$	0	0
$96$	0	0
$97$	−13.0000	−1.31995	−0.659975	−	0.751288i	$-0.729433\pi$
$97$	−13.0000	−1.31995	−0.659975	+	0.751288i	$0.729433\pi$
$98$	−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
$103$	−10.0000	−0.985329	−0.492665	−	0.870219i	$-0.663977\pi$
$103$	−10.0000	−0.985329	−0.492665	+	0.870219i	$0.663977\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	−12.0000	−1.16554
$107$	−3.00000	−0.290021	−0.145010	−	0.989430i	$-0.546322\pi$
$107$	−3.00000	−0.290021	−0.145010	+	0.989430i	$0.546322\pi$
$108$	0	0
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	0	0
$111$	0	0
$112$	1.00000	0.0944911
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	0	0
$115$	0	0
$116$	−6.00000	−0.557086
$117$	0	0
$118$	3.00000	0.276172
$119$	0	0
$120$	0	0
$121$	−2.00000	−0.181818
$122$	7.00000	0.633750
$123$	0	0
$124$	−4.00000	−0.359211
$125$	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
$131$	9.00000	0.786334	0.393167	−	0.919467i	$-0.371379\pi$
$131$	9.00000	0.786334	0.393167	+	0.919467i	$0.371379\pi$
$132$	0	0
$133$	−4.00000	−0.346844
$134$	4.00000	0.345547
$135$	0	0
$136$	0	0
$137$	18.0000	1.53784	0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000	1.53784	0.768922	+	0.639343i	$0.220793\pi$
$138$	0	0
$139$	2.00000	0.169638	0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000	0.169638	0.0848189	+	0.996396i	$0.472969\pi$
$140$	0	0
$141$	0	0
$142$	−3.00000	−0.251754
$143$	−3.00000	−0.250873
$144$	0	0
$145$	0	0
$146$	10.0000	0.827606
$147$	0	0
$148$	−1.00000	−0.0821995
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	4.00000	0.324443
$153$	0	0
$154$	−3.00000	−0.241747
$155$	0	0
$156$	0	0
$157$	−10.0000	−0.798087	−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000	−0.798087	−0.399043	+	0.916932i	$0.630658\pi$
$158$	10.0000	0.795557
$159$	0	0
$160$	0	0
$161$	3.00000	0.236433
$162$	0	0
$163$	14.0000	1.09656	0.548282	−	0.836293i	$-0.315282\pi$
$163$	14.0000	1.09656	0.548282	+	0.836293i	$0.315282\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	12.0000	0.931381
$167$	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
$169$	−12.0000	−0.923077
$170$	0	0
$171$	0	0
$172$	8.00000	0.609994
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	0	0
$175$	0	0
$176$	3.00000	0.226134
$177$	0	0
$178$	6.00000	0.449719
$179$	3.00000	0.224231	0.112115	−	0.993695i	$-0.464237\pi$
$179$	3.00000	0.224231	0.112115	+	0.993695i	$0.464237\pi$
$180$	0	0
$181$	−25.0000	−1.85824	−0.929118	−	0.369784i	$-0.879432\pi$
$181$	−25.0000	−1.85824	−0.929118	+	0.369784i	$0.879432\pi$
$182$	1.00000	0.0741249
$183$	0	0
$184$	−3.00000	−0.221163
$185$	0	0
$186$	0	0
$187$	0	0
$188$	3.00000	0.218797
$189$	0	0
$190$	0	0
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	0	0
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	13.0000	0.933346
$195$	0	0
$196$	1.00000	0.0714286
$197$	−12.0000	−0.854965	−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000	−0.854965	−0.427482	+	0.904024i	$0.640599\pi$
$198$	0	0
$199$	−10.0000	−0.708881	−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000	−0.708881	−0.354441	+	0.935079i	$0.615329\pi$
$200$	0	0
$201$	0	0
$202$	−12.0000	−0.844317
$203$	−6.00000	−0.421117
$204$	0	0
$205$	0	0
$206$	10.0000	0.696733
$207$	0	0
$208$	−1.00000	−0.0693375
$209$	−12.0000	−0.830057
$210$	0	0
$211$	2.00000	0.137686	0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000	0.137686	0.0688428	+	0.997628i	$0.478069\pi$
$212$	12.0000	0.824163
$213$	0	0
$214$	3.00000	0.205076
$215$	0	0
$216$	0	0
$217$	−4.00000	−0.271538
$218$	10.0000	0.677285
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	0	0
$227$	−3.00000	−0.199117	−0.0995585	−	0.995032i	$-0.531743\pi$
$227$	−3.00000	−0.199117	−0.0995585	+	0.995032i	$0.531743\pi$
$228$	0	0
$229$	−13.0000	−0.859064	−0.429532	−	0.903052i	$-0.641321\pi$
$229$	−13.0000	−0.859064	−0.429532	+	0.903052i	$0.641321\pi$
$230$	0	0
$231$	0	0
$232$	6.00000	0.393919
$233$	−24.0000	−1.57229	−0.786146	−	0.618041i	$-0.787927\pi$
$233$	−24.0000	−1.57229	−0.786146	+	0.618041i	$0.787927\pi$
$234$	0	0
$235$	0	0
$236$	−3.00000	−0.195283
$237$	0	0
$238$	0	0
$239$	−15.0000	−0.970269	−0.485135	−	0.874439i	$-0.661229\pi$
$239$	−15.0000	−0.970269	−0.485135	+	0.874439i	$0.661229\pi$
$240$	0	0
$241$	11.0000	0.708572	0.354286	−	0.935137i	$-0.384724\pi$
$241$	11.0000	0.708572	0.354286	+	0.935137i	$0.384724\pi$
$242$	2.00000	0.128565
$243$	0	0
$244$	−7.00000	−0.448129
$245$	0	0
$246$	0	0
$247$	4.00000	0.254514
$248$	4.00000	0.254000
$249$	0	0
$250$	0	0
$251$	9.00000	0.568075	0.284037	−	0.958813i	$-0.408326\pi$
$251$	9.00000	0.568075	0.284037	+	0.958813i	$0.408326\pi$
$252$	0	0
$253$	9.00000	0.565825
$254$	−8.00000	−0.501965
$255$	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
$259$	−1.00000	−0.0621370
$260$	0	0
$261$	0	0
$262$	−9.00000	−0.556022
$263$	−9.00000	−0.554964	−0.277482	−	0.960731i	$-0.589500\pi$
$263$	−9.00000	−0.554964	−0.277482	+	0.960731i	$0.589500\pi$
$264$	0	0
$265$	0	0
$266$	4.00000	0.245256
$267$	0	0
$268$	−4.00000	−0.244339
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	0	0
$271$	2.00000	0.121491	0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000	0.121491	0.0607457	+	0.998153i	$0.480652\pi$
$272$	0	0
$273$	0	0
$274$	−18.0000	−1.08742
$275$	0	0
$276$	0	0
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	−2.00000	−0.119952
$279$	0	0
$280$	0	0
$281$	12.0000	0.715860	0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000	0.715860	0.357930	+	0.933748i	$0.383483\pi$
$282$	0	0
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	3.00000	0.178017
$285$	0	0
$286$	3.00000	0.177394
$287$	−6.00000	−0.354169
$288$	0	0
$289$	−17.0000	−1.00000
$290$	0	0
$291$	0	0
$292$	−10.0000	−0.585206
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	0	0
$295$	0	0
$296$	1.00000	0.0581238
$297$	0	0
$298$	0	0
$299$	−3.00000	−0.173494
$300$	0	0
$301$	8.00000	0.461112
$302$	−2.00000	−0.115087
$303$	0	0
$304$	−4.00000	−0.229416
$305$	0	0
$306$	0	0
$307$	2.00000	0.114146	0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000	0.114146	0.0570730	+	0.998370i	$0.481823\pi$
$308$	3.00000	0.170941
$309$	0	0
$310$	0	0
$311$	−3.00000	−0.170114	−0.0850572	−	0.996376i	$-0.527107\pi$
$311$	−3.00000	−0.170114	−0.0850572	+	0.996376i	$0.527107\pi$
$312$	0	0
$313$	26.0000	1.46961	0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000	1.46961	0.734803	+	0.678280i	$0.237274\pi$
$314$	10.0000	0.564333
$315$	0	0
$316$	−10.0000	−0.562544
$317$	30.0000	1.68497	0.842484	−	0.538721i	$-0.181092\pi$
$317$	30.0000	1.68497	0.842484	+	0.538721i	$0.181092\pi$
$318$	0	0
$319$	−18.0000	−1.00781
$320$	0	0
$321$	0	0
$322$	−3.00000	−0.167183
$323$	0	0
$324$	0	0
$325$	0	0
$326$	−14.0000	−0.775388
$327$	0	0
$328$	6.00000	0.331295
$329$	3.00000	0.165395
$330$	0	0
$331$	−10.0000	−0.549650	−0.274825	−	0.961494i	$-0.588620\pi$
$331$	−10.0000	−0.549650	−0.274825	+	0.961494i	$0.588620\pi$
$332$	−12.0000	−0.658586
$333$	0	0
$334$	−3.00000	−0.164153
$335$	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
$341$	−12.0000	−0.649836
$342$	0	0
$343$	1.00000	0.0539949
$344$	−8.00000	−0.431331
$345$	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
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	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
$356$	−6.00000	−0.317999
$357$	0	0
$358$	−3.00000	−0.158555
$359$	9.00000	0.475002	0.237501	−	0.971387i	$-0.423672\pi$
$359$	9.00000	0.475002	0.237501	+	0.971387i	$0.423672\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	25.0000	1.31397
$363$	0	0
$364$	−1.00000	−0.0524142
$365$	0	0
$366$	0	0
$367$	−10.0000	−0.521996	−0.260998	−	0.965339i	$-0.584052\pi$
$367$	−10.0000	−0.521996	−0.260998	+	0.965339i	$0.584052\pi$
$368$	3.00000	0.156386
$369$	0	0
$370$	0	0
$371$	12.0000	0.623009
$372$	0	0
$373$	26.0000	1.34623	0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000	1.34623	0.673114	+	0.739538i	$0.264956\pi$
$374$	0	0
$375$	0	0
$376$	−3.00000	−0.154713
$377$	6.00000	0.309016
$378$	0	0
$379$	8.00000	0.410932	0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000	0.410932	0.205466	+	0.978664i	$0.434129\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	15.0000	0.766464	0.383232	−	0.923652i	$-0.374811\pi$
$383$	15.0000	0.766464	0.383232	+	0.923652i	$0.374811\pi$
$384$	0	0
$385$	0	0
$386$	−14.0000	−0.712581
$387$	0	0
$388$	−13.0000	−0.659975
$389$	−12.0000	−0.608424	−0.304212	−	0.952604i	$-0.598393\pi$
$389$	−12.0000	−0.608424	−0.304212	+	0.952604i	$0.598393\pi$
$390$	0	0
$391$	0	0
$392$	−1.00000	−0.0505076
$393$	0	0
$394$	12.0000	0.604551
$395$	0	0
$396$	0	0
$397$	−7.00000	−0.351320	−0.175660	−	0.984451i	$-0.556206\pi$
$397$	−7.00000	−0.351320	−0.175660	+	0.984451i	$0.556206\pi$
$398$	10.0000	0.501255
$399$	0	0
$400$	0	0
$401$	12.0000	0.599251	0.299626	−	0.954057i	$-0.403138\pi$
$401$	12.0000	0.599251	0.299626	+	0.954057i	$0.403138\pi$
$402$	0	0
$403$	4.00000	0.199254
$404$	12.0000	0.597022
$405$	0	0
$406$	6.00000	0.297775
$407$	−3.00000	−0.148704
$408$	0	0
$409$	11.0000	0.543915	0.271957	−	0.962309i	$-0.412329\pi$
$409$	11.0000	0.543915	0.271957	+	0.962309i	$0.412329\pi$
$410$	0	0
$411$	0	0
$412$	−10.0000	−0.492665
$413$	−3.00000	−0.147620
$414$	0	0
$415$	0	0
$416$	1.00000	0.0490290
$417$	0	0
$418$	12.0000	0.586939
$419$	−12.0000	−0.586238	−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000	−0.586238	−0.293119	+	0.956076i	$0.594693\pi$
$420$	0	0
$421$	−7.00000	−0.341159	−0.170580	−	0.985344i	$-0.554564\pi$
$421$	−7.00000	−0.341159	−0.170580	+	0.985344i	$0.554564\pi$
$422$	−2.00000	−0.0973585
$423$	0	0
$424$	−12.0000	−0.582772
$425$	0	0
$426$	0	0
$427$	−7.00000	−0.338754
$428$	−3.00000	−0.145010
$429$	0	0
$430$	0	0
$431$	9.00000	0.433515	0.216757	−	0.976226i	$-0.430452\pi$
$431$	9.00000	0.433515	0.216757	+	0.976226i	$0.430452\pi$
$432$	0	0
$433$	−7.00000	−0.336399	−0.168199	−	0.985753i	$-0.553795\pi$
$433$	−7.00000	−0.336399	−0.168199	+	0.985753i	$0.553795\pi$
$434$	4.00000	0.192006
$435$	0	0
$436$	−10.0000	−0.478913
$437$	−12.0000	−0.574038
$438$	0	0
$439$	−40.0000	−1.90910	−0.954548	−	0.298057i	$-0.903661\pi$
$439$	−40.0000	−1.90910	−0.954548	+	0.298057i	$0.903661\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	15.0000	0.712672	0.356336	−	0.934358i	$-0.384026\pi$
$443$	15.0000	0.712672	0.356336	+	0.934358i	$0.384026\pi$
$444$	0	0
$445$	0	0
$446$	−8.00000	−0.378811
$447$	0	0
$448$	1.00000	0.0472456
$449$	−24.0000	−1.13263	−0.566315	−	0.824189i	$-0.691631\pi$
$449$	−24.0000	−1.13263	−0.566315	+	0.824189i	$0.691631\pi$
$450$	0	0
$451$	−18.0000	−0.847587
$452$	0	0
$453$	0	0
$454$	3.00000	0.140797
$455$	0	0
$456$	0	0
$457$	29.0000	1.35656	0.678281	−	0.734802i	$-0.262725\pi$
$457$	29.0000	1.35656	0.678281	+	0.734802i	$0.262725\pi$
$458$	13.0000	0.607450
$459$	0	0
$460$	0	0
$461$	30.0000	1.39724	0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000	1.39724	0.698620	+	0.715493i	$0.253798\pi$
$462$	0	0
$463$	14.0000	0.650635	0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000	0.650635	0.325318	+	0.945605i	$0.394529\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	24.0000	1.11178
$467$	−27.0000	−1.24941	−0.624705	−	0.780860i	$-0.714781\pi$
$467$	−27.0000	−1.24941	−0.624705	+	0.780860i	$0.714781\pi$
$468$	0	0
$469$	−4.00000	−0.184703
$470$	0	0
$471$	0	0
$472$	3.00000	0.138086
$473$	24.0000	1.10352
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	15.0000	0.686084
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	0	0
$481$	1.00000	0.0455961
$482$	−11.0000	−0.501036
$483$	0	0
$484$	−2.00000	−0.0909091
$485$	0	0
$486$	0	0
$487$	2.00000	0.0906287	0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000	0.0906287	0.0453143	+	0.998973i	$0.485571\pi$
$488$	7.00000	0.316875
$489$	0	0
$490$	0	0
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	0	0
$493$	0	0
$494$	−4.00000	−0.179969
$495$	0	0
$496$	−4.00000	−0.179605
$497$	3.00000	0.134568
$498$	0	0
$499$	8.00000	0.358129	0.179065	−	0.983837i	$-0.442693\pi$
$499$	8.00000	0.358129	0.179065	+	0.983837i	$0.442693\pi$
$500$	0	0
$501$	0	0
$502$	−9.00000	−0.401690
$503$	−24.0000	−1.07011	−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000	−1.07011	−0.535054	+	0.844818i	$0.679709\pi$
$504$	0	0
$505$	0	0
$506$	−9.00000	−0.400099
$507$	0	0
$508$	8.00000	0.354943
$509$	24.0000	1.06378	0.531891	−	0.846813i	$-0.321482\pi$
$509$	24.0000	1.06378	0.531891	+	0.846813i	$0.321482\pi$
$510$	0	0
$511$	−10.0000	−0.442374
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−12.0000	−0.529297
$515$	0	0
$516$	0	0
$517$	9.00000	0.395820
$518$	1.00000	0.0439375
$519$	0	0
$520$	0	0
$521$	−12.0000	−0.525730	−0.262865	−	0.964833i	$-0.584667\pi$
$521$	−12.0000	−0.525730	−0.262865	+	0.964833i	$0.584667\pi$
$522$	0	0
$523$	−34.0000	−1.48672	−0.743358	−	0.668894i	$-0.766768\pi$
$523$	−34.0000	−1.48672	−0.743358	+	0.668894i	$0.766768\pi$
$524$	9.00000	0.393167
$525$	0	0
$526$	9.00000	0.392419
$527$	0	0
$528$	0	0
$529$	−14.0000	−0.608696
$530$	0	0
$531$	0	0
$532$	−4.00000	−0.173422
$533$	6.00000	0.259889
$534$	0	0
$535$	0	0
$536$	4.00000	0.172774
$537$	0	0
$538$	6.00000	0.258678
$539$	3.00000	0.129219
$540$	0	0
$541$	−43.0000	−1.84871	−0.924357	−	0.381528i	$-0.875398\pi$
$541$	−43.0000	−1.84871	−0.924357	+	0.381528i	$0.875398\pi$
$542$	−2.00000	−0.0859074
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−46.0000	−1.96682	−0.983409	−	0.181402i	$-0.941936\pi$
$547$	−46.0000	−1.96682	−0.983409	+	0.181402i	$0.941936\pi$
$548$	18.0000	0.768922
$549$	0	0
$550$	0	0
$551$	24.0000	1.02243
$552$	0	0
$553$	−10.0000	−0.425243
$554$	10.0000	0.424859
$555$	0	0
$556$	2.00000	0.0848189
$557$	−24.0000	−1.01691	−0.508456	−	0.861088i	$-0.669784\pi$
$557$	−24.0000	−1.01691	−0.508456	+	0.861088i	$0.669784\pi$
$558$	0	0
$559$	−8.00000	−0.338364
$560$	0	0
$561$	0	0
$562$	−12.0000	−0.506189
$563$	−33.0000	−1.39078	−0.695392	−	0.718631i	$-0.744769\pi$
$563$	−33.0000	−1.39078	−0.695392	+	0.718631i	$0.744769\pi$
$564$	0	0
$565$	0	0
$566$	−14.0000	−0.588464
$567$	0	0
$568$	−3.00000	−0.125877
$569$	−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
$571$	32.0000	1.33916	0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000	1.33916	0.669579	+	0.742741i	$0.266474\pi$
$572$	−3.00000	−0.125436
$573$	0	0
$574$	6.00000	0.250435
$575$	0	0
$576$	0	0
$577$	−43.0000	−1.79011	−0.895057	−	0.445952i	$-0.852865\pi$
$577$	−43.0000	−1.79011	−0.895057	+	0.445952i	$0.852865\pi$
$578$	17.0000	0.707107
$579$	0	0
$580$	0	0
$581$	−12.0000	−0.497844
$582$	0	0
$583$	36.0000	1.49097
$584$	10.0000	0.413803
$585$	0	0
$586$	6.00000	0.247858
$587$	36.0000	1.48588	0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000	1.48588	0.742940	+	0.669359i	$0.233431\pi$
$588$	0	0
$589$	16.0000	0.659269
$590$	0	0
$591$	0	0
$592$	−1.00000	−0.0410997
$593$	−30.0000	−1.23195	−0.615976	−	0.787765i	$-0.711238\pi$
$593$	−30.0000	−1.23195	−0.615976	+	0.787765i	$0.711238\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	3.00000	0.122679
$599$	24.0000	0.980613	0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000	0.980613	0.490307	+	0.871550i	$0.336885\pi$
$600$	0	0
$601$	5.00000	0.203954	0.101977	−	0.994787i	$-0.467483\pi$
$601$	5.00000	0.203954	0.101977	+	0.994787i	$0.467483\pi$
$602$	−8.00000	−0.326056
$603$	0	0
$604$	2.00000	0.0813788
$605$	0	0
$606$	0	0
$607$	8.00000	0.324710	0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000	0.324710	0.162355	+	0.986732i	$0.448091\pi$
$608$	4.00000	0.162221
$609$	0	0
$610$	0	0
$611$	−3.00000	−0.121367
$612$	0	0
$613$	11.0000	0.444286	0.222143	−	0.975014i	$-0.428695\pi$
$613$	11.0000	0.444286	0.222143	+	0.975014i	$0.428695\pi$
$614$	−2.00000	−0.0807134
$615$	0	0
$616$	−3.00000	−0.120873
$617$	12.0000	0.483102	0.241551	−	0.970388i	$-0.422344\pi$
$617$	12.0000	0.483102	0.241551	+	0.970388i	$0.422344\pi$
$618$	0	0
$619$	−28.0000	−1.12542	−0.562708	−	0.826656i	$-0.690240\pi$
$619$	−28.0000	−1.12542	−0.562708	+	0.826656i	$0.690240\pi$
$620$	0	0
$621$	0	0
$622$	3.00000	0.120289
$623$	−6.00000	−0.240385
$624$	0	0
$625$	0	0
$626$	−26.0000	−1.03917
$627$	0	0
$628$	−10.0000	−0.399043
$629$	0	0
$630$	0	0
$631$	−4.00000	−0.159237	−0.0796187	−	0.996825i	$-0.525370\pi$
$631$	−4.00000	−0.159237	−0.0796187	+	0.996825i	$0.525370\pi$
$632$	10.0000	0.397779
$633$	0	0
$634$	−30.0000	−1.19145
$635$	0	0
$636$	0	0
$637$	−1.00000	−0.0396214
$638$	18.0000	0.712627
$639$	0	0
$640$	0	0
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	0	0
$643$	32.0000	1.26196	0.630978	−	0.775800i	$-0.282654\pi$
$643$	32.0000	1.26196	0.630978	+	0.775800i	$0.282654\pi$
$644$	3.00000	0.118217
$645$	0	0
$646$	0	0
$647$	−21.0000	−0.825595	−0.412798	−	0.910823i	$-0.635448\pi$
$647$	−21.0000	−0.825595	−0.412798	+	0.910823i	$0.635448\pi$
$648$	0	0
$649$	−9.00000	−0.353281
$650$	0	0
$651$	0	0
$652$	14.0000	0.548282
$653$	−36.0000	−1.40879	−0.704394	−	0.709809i	$-0.748781\pi$
$653$	−36.0000	−1.40879	−0.704394	+	0.709809i	$0.748781\pi$
$654$	0	0
$655$	0	0
$656$	−6.00000	−0.234261
$657$	0	0
$658$	−3.00000	−0.116952
$659$	−36.0000	−1.40236	−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000	−1.40236	−0.701180	+	0.712984i	$0.747343\pi$
$660$	0	0
$661$	29.0000	1.12797	0.563985	−	0.825785i	$-0.309268\pi$
$661$	29.0000	1.12797	0.563985	+	0.825785i	$0.309268\pi$
$662$	10.0000	0.388661
$663$	0	0
$664$	12.0000	0.465690
$665$	0	0
$666$	0	0
$667$	−18.0000	−0.696963
$668$	3.00000	0.116073
$669$	0	0
$670$	0	0
$671$	−21.0000	−0.810696
$672$	0	0
$673$	−1.00000	−0.0385472	−0.0192736	−	0.999814i	$-0.506135\pi$
$673$	−1.00000	−0.0385472	−0.0192736	+	0.999814i	$0.506135\pi$
$674$	22.0000	0.847408
$675$	0	0
$676$	−12.0000	−0.461538
$677$	−12.0000	−0.461197	−0.230599	−	0.973049i	$-0.574068\pi$
$677$	−12.0000	−0.461197	−0.230599	+	0.973049i	$0.574068\pi$
$678$	0	0
$679$	−13.0000	−0.498894
$680$	0	0
$681$	0	0
$682$	12.0000	0.459504
$683$	−15.0000	−0.573959	−0.286980	−	0.957937i	$-0.592651\pi$
$683$	−15.0000	−0.573959	−0.286980	+	0.957937i	$0.592651\pi$
$684$	0	0
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	0	0
$688$	8.00000	0.304997
$689$	−12.0000	−0.457164
$690$	0	0
$691$	2.00000	0.0760836	0.0380418	−	0.999276i	$-0.487888\pi$
$691$	2.00000	0.0760836	0.0380418	+	0.999276i	$0.487888\pi$
$692$	6.00000	0.228086
$693$	0	0
$694$	12.0000	0.455514
$695$	0	0
$696$	0	0
$697$	0	0
$698$	10.0000	0.378506
$699$	0	0
$700$	0	0
$701$	−48.0000	−1.81293	−0.906467	−	0.422276i	$-0.861231\pi$
$701$	−48.0000	−1.81293	−0.906467	+	0.422276i	$0.861231\pi$
$702$	0	0
$703$	4.00000	0.150863
$704$	3.00000	0.113067
$705$	0	0
$706$	6.00000	0.225813
$707$	12.0000	0.451306
$708$	0	0
$709$	41.0000	1.53979	0.769894	−	0.638172i	$-0.220309\pi$
$709$	41.0000	1.53979	0.769894	+	0.638172i	$0.220309\pi$
$710$	0	0
$711$	0	0
$712$	6.00000	0.224860
$713$	−12.0000	−0.449404
$714$	0	0
$715$	0	0
$716$	3.00000	0.112115
$717$	0	0
$718$	−9.00000	−0.335877
$719$	39.0000	1.45445	0.727227	−	0.686397i	$-0.240809\pi$
$719$	39.0000	1.45445	0.727227	+	0.686397i	$0.240809\pi$
$720$	0	0
$721$	−10.0000	−0.372419
$722$	3.00000	0.111648
$723$	0	0
$724$	−25.0000	−0.929118
$725$	0	0
$726$	0	0
$727$	−16.0000	−0.593407	−0.296704	−	0.954970i	$-0.595887\pi$
$727$	−16.0000	−0.593407	−0.296704	+	0.954970i	$0.595887\pi$
$728$	1.00000	0.0370625
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	11.0000	0.406294	0.203147	−	0.979148i	$-0.434883\pi$
$733$	11.0000	0.406294	0.203147	+	0.979148i	$0.434883\pi$
$734$	10.0000	0.369107
$735$	0	0
$736$	−3.00000	−0.110581
$737$	−12.0000	−0.442026
$738$	0	0
$739$	−46.0000	−1.69214	−0.846069	−	0.533074i	$-0.821037\pi$
$739$	−46.0000	−1.69214	−0.846069	+	0.533074i	$0.821037\pi$
$740$	0	0
$741$	0	0
$742$	−12.0000	−0.440534
$743$	3.00000	0.110059	0.0550297	−	0.998485i	$-0.482475\pi$
$743$	3.00000	0.110059	0.0550297	+	0.998485i	$0.482475\pi$
$744$	0	0
$745$	0	0
$746$	−26.0000	−0.951928
$747$	0	0
$748$	0	0
$749$	−3.00000	−0.109618
$750$	0	0
$751$	26.0000	0.948753	0.474377	−	0.880322i	$-0.342673\pi$
$751$	26.0000	0.948753	0.474377	+	0.880322i	$0.342673\pi$
$752$	3.00000	0.109399
$753$	0	0
$754$	−6.00000	−0.218507
$755$	0	0
$756$	0	0
$757$	5.00000	0.181728	0.0908640	−	0.995863i	$-0.471037\pi$
$757$	5.00000	0.181728	0.0908640	+	0.995863i	$0.471037\pi$
$758$	−8.00000	−0.290573
$759$	0	0
$760$	0	0
$761$	54.0000	1.95750	0.978749	−	0.205061i	$-0.0657392\pi$
$761$	54.0000	1.95750	0.978749	+	0.205061i	$0.0657392\pi$
$762$	0	0
$763$	−10.0000	−0.362024
$764$	0	0
$765$	0	0
$766$	−15.0000	−0.541972
$767$	3.00000	0.108324
$768$	0	0
$769$	14.0000	0.504853	0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000	0.504853	0.252426	+	0.967616i	$0.418771\pi$
$770$	0	0
$771$	0	0
$772$	14.0000	0.503871
$773$	6.00000	0.215805	0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000	0.215805	0.107903	+	0.994161i	$0.465587\pi$
$774$	0	0
$775$	0	0
$776$	13.0000	0.466673
$777$	0	0
$778$	12.0000	0.430221
$779$	24.0000	0.859889
$780$	0	0
$781$	9.00000	0.322045
$782$	0	0
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	−28.0000	−0.998092	−0.499046	−	0.866575i	$-0.666316\pi$
$787$	−28.0000	−0.998092	−0.499046	+	0.866575i	$0.666316\pi$
$788$	−12.0000	−0.427482
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	7.00000	0.248577
$794$	7.00000	0.248421
$795$	0	0
$796$	−10.0000	−0.354441
$797$	−18.0000	−0.637593	−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000	−0.637593	−0.318796	+	0.947823i	$0.603279\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	−12.0000	−0.423735
$803$	−30.0000	−1.05868
$804$	0	0
$805$	0	0
$806$	−4.00000	−0.140894
$807$	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
$811$	−16.0000	−0.561836	−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000	−0.561836	−0.280918	+	0.959732i	$0.590639\pi$
$812$	−6.00000	−0.210559
$813$	0	0
$814$	3.00000	0.105150
$815$	0	0
$816$	0	0
$817$	−32.0000	−1.11954
$818$	−11.0000	−0.384606
$819$	0	0
$820$	0	0
$821$	18.0000	0.628204	0.314102	−	0.949389i	$-0.398297\pi$
$821$	18.0000	0.628204	0.314102	+	0.949389i	$0.398297\pi$
$822$	0	0
$823$	−34.0000	−1.18517	−0.592583	−	0.805510i	$-0.701892\pi$
$823$	−34.0000	−1.18517	−0.592583	+	0.805510i	$0.701892\pi$
$824$	10.0000	0.348367
$825$	0	0
$826$	3.00000	0.104383
$827$	−33.0000	−1.14752	−0.573761	−	0.819023i	$-0.694516\pi$
$827$	−33.0000	−1.14752	−0.573761	+	0.819023i	$0.694516\pi$
$828$	0	0
$829$	−25.0000	−0.868286	−0.434143	−	0.900844i	$-0.642949\pi$
$829$	−25.0000	−0.868286	−0.434143	+	0.900844i	$0.642949\pi$
$830$	0	0
$831$	0	0
$832$	−1.00000	−0.0346688
$833$	0	0
$834$	0	0
$835$	0	0
$836$	−12.0000	−0.415029
$837$	0	0
$838$	12.0000	0.414533
$839$	51.0000	1.76072	0.880358	−	0.474310i	$-0.157302\pi$
$839$	51.0000	1.76072	0.880358	+	0.474310i	$0.157302\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	7.00000	0.241236
$843$	0	0
$844$	2.00000	0.0688428
$845$	0	0
$846$	0	0
$847$	−2.00000	−0.0687208
$848$	12.0000	0.412082
$849$	0	0
$850$	0	0
$851$	−3.00000	−0.102839
$852$	0	0
$853$	17.0000	0.582069	0.291034	−	0.956713i	$-0.406001\pi$
$853$	17.0000	0.582069	0.291034	+	0.956713i	$0.406001\pi$
$854$	7.00000	0.239535
$855$	0	0
$856$	3.00000	0.102538
$857$	36.0000	1.22974	0.614868	−	0.788630i	$-0.289209\pi$
$857$	36.0000	1.22974	0.614868	+	0.788630i	$0.289209\pi$
$858$	0	0
$859$	14.0000	0.477674	0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000	0.477674	0.238837	+	0.971060i	$0.423234\pi$
$860$	0	0
$861$	0	0
$862$	−9.00000	−0.306541
$863$	0	0		−	1.00000i	$-0.5\pi$
$863$	0	0			1.00000i	$0.5\pi$
$864$	0	0
$865$	0	0
$866$	7.00000	0.237870
$867$	0	0
$868$	−4.00000	−0.135769
$869$	−30.0000	−1.01768
$870$	0	0
$871$	4.00000	0.135535
$872$	10.0000	0.338643
$873$	0	0
$874$	12.0000	0.405906
$875$	0	0
$876$	0	0
$877$	−13.0000	−0.438979	−0.219489	−	0.975615i	$-0.570439\pi$
$877$	−13.0000	−0.438979	−0.219489	+	0.975615i	$0.570439\pi$
$878$	40.0000	1.34993
$879$	0	0
$880$	0	0
$881$	12.0000	0.404290	0.202145	−	0.979356i	$-0.435209\pi$
$881$	12.0000	0.404290	0.202145	+	0.979356i	$0.435209\pi$
$882$	0	0
$883$	14.0000	0.471138	0.235569	−	0.971858i	$-0.424305\pi$
$883$	14.0000	0.471138	0.235569	+	0.971858i	$0.424305\pi$
$884$	0	0
$885$	0	0
$886$	−15.0000	−0.503935
$887$	−27.0000	−0.906571	−0.453286	−	0.891365i	$-0.649748\pi$
$887$	−27.0000	−0.906571	−0.453286	+	0.891365i	$0.649748\pi$
$888$	0	0
$889$	8.00000	0.268311
$890$	0	0
$891$	0	0
$892$	8.00000	0.267860
$893$	−12.0000	−0.401565
$894$	0	0
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	24.0000	0.800890
$899$	24.0000	0.800445
$900$	0	0
$901$	0	0
$902$	18.0000	0.599334
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	44.0000	1.46100	0.730498	−	0.682915i	$-0.239288\pi$
$907$	44.0000	1.46100	0.730498	+	0.682915i	$0.239288\pi$
$908$	−3.00000	−0.0995585
$909$	0	0
$910$	0	0
$911$	9.00000	0.298183	0.149092	−	0.988823i	$-0.452365\pi$
$911$	9.00000	0.298183	0.149092	+	0.988823i	$0.452365\pi$
$912$	0	0
$913$	−36.0000	−1.19143
$914$	−29.0000	−0.959235
$915$	0	0
$916$	−13.0000	−0.429532
$917$	9.00000	0.297206
$918$	0	0
$919$	38.0000	1.25350	0.626752	−	0.779219i	$-0.284384\pi$
$919$	38.0000	1.25350	0.626752	+	0.779219i	$0.284384\pi$
$920$	0	0
$921$	0	0
$922$	−30.0000	−0.987997
$923$	−3.00000	−0.0987462
$924$	0	0
$925$	0	0
$926$	−14.0000	−0.460069
$927$	0	0
$928$	6.00000	0.196960
$929$	−24.0000	−0.787414	−0.393707	−	0.919236i	$-0.628808\pi$
$929$	−24.0000	−0.787414	−0.393707	+	0.919236i	$0.628808\pi$
$930$	0	0
$931$	−4.00000	−0.131095
$932$	−24.0000	−0.786146
$933$	0	0
$934$	27.0000	0.883467
$935$	0	0
$936$	0	0
$937$	29.0000	0.947389	0.473694	−	0.880689i	$-0.342920\pi$
$937$	29.0000	0.947389	0.473694	+	0.880689i	$0.342920\pi$
$938$	4.00000	0.130605
$939$	0	0
$940$	0	0
$941$	0	0		−	1.00000i	$-0.5\pi$
$941$	0	0			1.00000i	$0.5\pi$
$942$	0	0
$943$	−18.0000	−0.586161
$944$	−3.00000	−0.0976417
$945$	0	0
$946$	−24.0000	−0.780307
$947$	−36.0000	−1.16984	−0.584921	−	0.811090i	$-0.698875\pi$
$947$	−36.0000	−1.16984	−0.584921	+	0.811090i	$0.698875\pi$
$948$	0	0
$949$	10.0000	0.324614
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−24.0000	−0.777436	−0.388718	−	0.921357i	$-0.627082\pi$
$953$	−24.0000	−0.777436	−0.388718	+	0.921357i	$0.627082\pi$
$954$	0	0
$955$	0	0
$956$	−15.0000	−0.485135
$957$	0	0
$958$	24.0000	0.775405
$959$	18.0000	0.581250
$960$	0	0
$961$	−15.0000	−0.483871
$962$	−1.00000	−0.0322413
$963$	0	0
$964$	11.0000	0.354286
$965$	0	0
$966$	0	0
$967$	8.00000	0.257263	0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000	0.257263	0.128631	+	0.991692i	$0.458942\pi$
$968$	2.00000	0.0642824
$969$	0	0
$970$	0	0
$971$	−27.0000	−0.866471	−0.433236	−	0.901281i	$-0.642628\pi$
$971$	−27.0000	−0.866471	−0.433236	+	0.901281i	$0.642628\pi$
$972$	0	0
$973$	2.00000	0.0641171
$974$	−2.00000	−0.0640841
$975$	0	0
$976$	−7.00000	−0.224065
$977$	−54.0000	−1.72761	−0.863807	−	0.503824i	$-0.831926\pi$
$977$	−54.0000	−1.72761	−0.863807	+	0.503824i	$0.831926\pi$
$978$	0	0
$979$	−18.0000	−0.575282
$980$	0	0
$981$	0	0
$982$	12.0000	0.382935
$983$	39.0000	1.24391	0.621953	−	0.783054i	$-0.286339\pi$
$983$	39.0000	1.24391	0.621953	+	0.783054i	$0.286339\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	4.00000	0.127257
$989$	24.0000	0.763156
$990$	0	0
$991$	2.00000	0.0635321	0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000	0.0635321	0.0317660	+	0.999495i	$0.489887\pi$
$992$	4.00000	0.127000
$993$	0	0
$994$	−3.00000	−0.0951542
$995$	0	0
$996$	0	0
$997$	17.0000	0.538395	0.269198	−	0.963085i	$-0.413241\pi$
$997$	17.0000	0.538395	0.269198	+	0.963085i	$0.413241\pi$
$998$	−8.00000	−0.253236
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9450.2.a.bu.1.1	yes	1
3.2	odd	2		9450.2.a.df.1.1	yes	1
5.4	even	2		9450.2.a.ct.1.1	yes	1
15.14	odd	2		9450.2.a.g.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9450.2.a.g.1.1	✓	1	15.14	odd	2
9450.2.a.bu.1.1	yes	1	1.1	even	1	trivial
9450.2.a.ct.1.1	yes	1	5.4	even	2
9450.2.a.df.1.1	yes	1	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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