LMFDB - Embedded newform 2925.2.a.p.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2925,2,Mod(1,2925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2925, 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("2925.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2925 = 3^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2925.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:	$23.3562425912$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2925.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -1.00000 q^{4} +4.00000 q^{7} -3.00000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} -1.00000 q^{4} +4.00000 q^{7} -3.00000 q^{8} -4.00000 q^{11} -1.00000 q^{13} +4.00000 q^{14} -1.00000 q^{16} +2.00000 q^{17} -4.00000 q^{22} -1.00000 q^{26} -4.00000 q^{28} +10.0000 q^{29} +4.00000 q^{31} +5.00000 q^{32} +2.00000 q^{34} +2.00000 q^{37} -6.00000 q^{41} +12.0000 q^{43} +4.00000 q^{44} +9.00000 q^{49} +1.00000 q^{52} +6.00000 q^{53} -12.0000 q^{56} +10.0000 q^{58} -12.0000 q^{59} -2.00000 q^{61} +4.00000 q^{62} +7.00000 q^{64} +8.00000 q^{67} -2.00000 q^{68} -2.00000 q^{73} +2.00000 q^{74} -16.0000 q^{77} +8.00000 q^{79} -6.00000 q^{82} +4.00000 q^{83} +12.0000 q^{86} +12.0000 q^{88} +2.00000 q^{89} -4.00000 q^{91} -10.0000 q^{97} +9.00000 q^{98} +O(q^{100})$

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	0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000	0.707107	0.353553	+	0.935414i	$0.384973\pi$
$3$	0	0
$3$	0	0
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	4.00000	1.51186	0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000	1.51186	0.755929	+	0.654654i	$0.227186\pi$
$8$	−3.00000	−1.06066
$9$	0	0
$10$	0	0
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	4.00000	1.06904
$15$	0	0
$16$	−1.00000	−0.250000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	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
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	0	0
$26$	−1.00000	−0.196116
$27$	0	0
$28$	−4.00000	−0.755929
$29$	10.0000	1.85695	0.928477	−	0.371391i	$-0.121119\pi$
$29$	10.0000	1.85695	0.928477	+	0.371391i	$0.121119\pi$
$30$	0	0
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	5.00000	0.883883
$33$	0	0
$34$	2.00000	0.342997
$35$	0	0
$36$	0	0
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	0	0
$39$	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
$43$	12.0000	1.82998	0.914991	−	0.403473i	$-0.132197\pi$
$43$	12.0000	1.82998	0.914991	+	0.403473i	$0.132197\pi$
$44$	4.00000	0.603023
$45$	0	0
$46$	0	0
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	9.00000	1.28571
$50$	0	0
$51$	0	0
$52$	1.00000	0.138675
$53$	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
$56$	−12.0000	−1.60357
$57$	0	0
$58$	10.0000	1.31306
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	0	0
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	4.00000	0.508001
$63$	0	0
$64$	7.00000	0.875000
$65$	0	0
$66$	0	0
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	−2.00000	−0.242536
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	2.00000	0.232495
$75$	0	0
$76$	0	0
$77$	−16.0000	−1.82337
$78$	0	0
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	0	0
$81$	0	0
$82$	−6.00000	−0.662589
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	0	0
$85$	0	0
$86$	12.0000	1.29399
$87$	0	0
$88$	12.0000	1.27920
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	0	0
$91$	−4.00000	−0.419314
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−10.0000	−1.01535	−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000	−1.01535	−0.507673	+	0.861550i	$0.669494\pi$
$98$	9.00000	0.909137
$99$	0	0
$100$	0	0
$101$	18.0000	1.79107	0.895533	−	0.444994i	$-0.146794\pi$
$101$	18.0000	1.79107	0.895533	+	0.444994i	$0.146794\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	3.00000	0.294174
$105$	0	0
$106$	6.00000	0.582772
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	0	0
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	0	0
$111$	0	0
$112$	−4.00000	−0.377964
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	0	0
$115$	0	0
$116$	−10.0000	−0.928477
$117$	0	0
$118$	−12.0000	−1.10469
$119$	8.00000	0.733359
$120$	0	0
$121$	5.00000	0.454545
$122$	−2.00000	−0.181071
$123$	0	0
$124$	−4.00000	−0.359211
$125$	0	0
$126$	0	0
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	−3.00000	−0.265165
$129$	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
$133$	0	0
$134$	8.00000	0.691095
$135$	0	0
$136$	−6.00000	−0.514496
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	0	0
$139$	12.0000	1.01783	0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000	1.01783	0.508913	+	0.860818i	$0.330047\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	4.00000	0.334497
$144$	0	0
$145$	0	0
$146$	−2.00000	−0.165521
$147$	0	0
$148$	−2.00000	−0.164399
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	0	0
$151$	4.00000	0.325515	0.162758	−	0.986666i	$-0.447961\pi$
$151$	4.00000	0.325515	0.162758	+	0.986666i	$0.447961\pi$
$152$	0	0
$153$	0	0
$154$	−16.0000	−1.28932
$155$	0	0
$156$	0	0
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	8.00000	0.636446
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−8.00000	−0.626608	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	−8.00000	−0.626608	−0.313304	+	0.949653i	$0.601436\pi$
$164$	6.00000	0.468521
$165$	0	0
$166$	4.00000	0.310460
$167$	−8.00000	−0.619059	−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000	−0.619059	−0.309529	+	0.950890i	$0.600171\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0	0
$171$	0	0
$172$	−12.0000	−0.914991
$173$	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
$176$	4.00000	0.301511
$177$	0	0
$178$	2.00000	0.149906
$179$	−4.00000	−0.298974	−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000	−0.298974	−0.149487	+	0.988764i	$0.547762\pi$
$180$	0	0
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	−4.00000	−0.296500
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−8.00000	−0.585018
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−8.00000	−0.578860	−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000	−0.578860	−0.289430	+	0.957199i	$0.593466\pi$
$192$	0	0
$193$	−18.0000	−1.29567	−0.647834	−	0.761781i	$-0.724325\pi$
$193$	−18.0000	−1.29567	−0.647834	+	0.761781i	$0.724325\pi$
$194$	−10.0000	−0.717958
$195$	0	0
$196$	−9.00000	−0.642857
$197$	18.0000	1.28245	0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000	1.28245	0.641223	+	0.767354i	$0.278427\pi$
$198$	0	0
$199$	8.00000	0.567105	0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000	0.567105	0.283552	+	0.958957i	$0.408487\pi$
$200$	0	0
$201$	0	0
$202$	18.0000	1.26648
$203$	40.0000	2.80745
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	1.00000	0.0693375
$209$	0	0
$210$	0	0
$211$	−20.0000	−1.37686	−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000	−1.37686	−0.688428	+	0.725304i	$0.741699\pi$
$212$	−6.00000	−0.412082
$213$	0	0
$214$	12.0000	0.820303
$215$	0	0
$216$	0	0
$217$	16.0000	1.08615
$218$	−2.00000	−0.135457
$219$	0	0
$220$	0	0
$221$	−2.00000	−0.134535
$222$	0	0
$223$	−4.00000	−0.267860	−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000	−0.267860	−0.133930	+	0.990991i	$0.542760\pi$
$224$	20.0000	1.33631
$225$	0	0
$226$	−6.00000	−0.399114
$227$	−20.0000	−1.32745	−0.663723	−	0.747978i	$-0.731025\pi$
$227$	−20.0000	−1.32745	−0.663723	+	0.747978i	$0.731025\pi$
$228$	0	0
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	0	0
$231$	0	0
$232$	−30.0000	−1.96960
$233$	−14.0000	−0.917170	−0.458585	−	0.888650i	$-0.651644\pi$
$233$	−14.0000	−0.917170	−0.458585	+	0.888650i	$0.651644\pi$
$234$	0	0
$235$	0	0
$236$	12.0000	0.781133
$237$	0	0
$238$	8.00000	0.518563
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	0	0
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	5.00000	0.321412
$243$	0	0
$244$	2.00000	0.128037
$245$	0	0
$246$	0	0
$247$	0	0
$248$	−12.0000	−0.762001
$249$	0	0
$250$	0	0
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	0	0
$253$	0	0
$254$	16.0000	1.00393
$255$	0	0
$256$	−17.0000	−1.06250
$257$	26.0000	1.62184	0.810918	−	0.585160i	$-0.198968\pi$
$257$	26.0000	1.62184	0.810918	+	0.585160i	$0.198968\pi$
$258$	0	0
$259$	8.00000	0.497096
$260$	0	0
$261$	0	0
$262$	−4.00000	−0.247121
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	−8.00000	−0.488678
$269$	−22.0000	−1.34136	−0.670682	−	0.741745i	$-0.733998\pi$
$269$	−22.0000	−1.34136	−0.670682	+	0.741745i	$0.733998\pi$
$270$	0	0
$271$	−12.0000	−0.728948	−0.364474	−	0.931214i	$-0.618751\pi$
$271$	−12.0000	−0.728948	−0.364474	+	0.931214i	$0.618751\pi$
$272$	−2.00000	−0.121268
$273$	0	0
$274$	6.00000	0.362473
$275$	0	0
$276$	0	0
$277$	10.0000	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$278$	12.0000	0.719712
$279$	0	0
$280$	0	0
$281$	10.0000	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$282$	0	0
$283$	−12.0000	−0.713326	−0.356663	−	0.934233i	$-0.616086\pi$
$283$	−12.0000	−0.713326	−0.356663	+	0.934233i	$0.616086\pi$
$284$	0	0
$285$	0	0
$286$	4.00000	0.236525
$287$	−24.0000	−1.41668
$288$	0	0
$289$	−13.0000	−0.764706
$290$	0	0
$291$	0	0
$292$	2.00000	0.117041
$293$	−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
$296$	−6.00000	−0.348743
$297$	0	0
$298$	6.00000	0.347571
$299$	0	0
$300$	0	0
$301$	48.0000	2.76667
$302$	4.00000	0.230174
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	16.0000	0.913168	0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000	0.913168	0.456584	+	0.889680i	$0.349073\pi$
$308$	16.0000	0.911685
$309$	0	0
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	6.00000	0.339140	0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000	0.339140	0.169570	+	0.985518i	$0.445762\pi$
$314$	18.0000	1.01580
$315$	0	0
$316$	−8.00000	−0.450035
$317$	26.0000	1.46031	0.730153	−	0.683284i	$-0.239449\pi$
$317$	26.0000	1.46031	0.730153	+	0.683284i	$0.239449\pi$
$318$	0	0
$319$	−40.0000	−2.23957
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	0	0
$326$	−8.00000	−0.443079
$327$	0	0
$328$	18.0000	0.993884
$329$	0	0
$330$	0	0
$331$	−16.0000	−0.879440	−0.439720	−	0.898135i	$-0.644922\pi$
$331$	−16.0000	−0.879440	−0.439720	+	0.898135i	$0.644922\pi$
$332$	−4.00000	−0.219529
$333$	0	0
$334$	−8.00000	−0.437741
$335$	0	0
$336$	0	0
$337$	−18.0000	−0.980522	−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000	−0.980522	−0.490261	+	0.871576i	$0.663099\pi$
$338$	1.00000	0.0543928
$339$	0	0
$340$	0	0
$341$	−16.0000	−0.866449
$342$	0	0
$343$	8.00000	0.431959
$344$	−36.0000	−1.94099
$345$	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
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	0	0
$351$	0	0
$352$	−20.0000	−1.06600
$353$	−2.00000	−0.106449	−0.0532246	−	0.998583i	$-0.516950\pi$
$353$	−2.00000	−0.106449	−0.0532246	+	0.998583i	$0.516950\pi$
$354$	0	0
$355$	0	0
$356$	−2.00000	−0.106000
$357$	0	0
$358$	−4.00000	−0.211407
$359$	−24.0000	−1.26667	−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000	−1.26667	−0.633336	+	0.773877i	$0.718315\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	−10.0000	−0.525588
$363$	0	0
$364$	4.00000	0.209657
$365$	0	0
$366$	0	0
$367$	−16.0000	−0.835193	−0.417597	−	0.908633i	$-0.637127\pi$
$367$	−16.0000	−0.835193	−0.417597	+	0.908633i	$0.637127\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	24.0000	1.24602
$372$	0	0
$373$	26.0000	1.34623	0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000	1.34623	0.673114	+	0.739538i	$0.264956\pi$
$374$	−8.00000	−0.413670
$375$	0	0
$376$	0	0
$377$	−10.0000	−0.515026
$378$	0	0
$379$	−24.0000	−1.23280	−0.616399	−	0.787434i	$-0.711409\pi$
$379$	−24.0000	−1.23280	−0.616399	+	0.787434i	$0.711409\pi$
$380$	0	0
$381$	0	0
$382$	−8.00000	−0.409316
$383$	−16.0000	−0.817562	−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000	−0.817562	−0.408781	+	0.912633i	$0.634046\pi$
$384$	0	0
$385$	0	0
$386$	−18.0000	−0.916176
$387$	0	0
$388$	10.0000	0.507673
$389$	−22.0000	−1.11544	−0.557722	−	0.830028i	$-0.688325\pi$
$389$	−22.0000	−1.11544	−0.557722	+	0.830028i	$0.688325\pi$
$390$	0	0
$391$	0	0
$392$	−27.0000	−1.36371
$393$	0	0
$394$	18.0000	0.906827
$395$	0	0
$396$	0	0
$397$	−38.0000	−1.90717	−0.953583	−	0.301131i	$-0.902636\pi$
$397$	−38.0000	−1.90717	−0.953583	+	0.301131i	$0.902636\pi$
$398$	8.00000	0.401004
$399$	0	0
$400$	0	0
$401$	−22.0000	−1.09863	−0.549314	−	0.835616i	$-0.685111\pi$
$401$	−22.0000	−1.09863	−0.549314	+	0.835616i	$0.685111\pi$
$402$	0	0
$403$	−4.00000	−0.199254
$404$	−18.0000	−0.895533
$405$	0	0
$406$	40.0000	1.98517
$407$	−8.00000	−0.396545
$408$	0	0
$409$	34.0000	1.68119	0.840596	−	0.541663i	$-0.182205\pi$
$409$	34.0000	1.68119	0.840596	+	0.541663i	$0.182205\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	−48.0000	−2.36193
$414$	0	0
$415$	0	0
$416$	−5.00000	−0.245145
$417$	0	0
$418$	0	0
$419$	−4.00000	−0.195413	−0.0977064	−	0.995215i	$-0.531151\pi$
$419$	−4.00000	−0.195413	−0.0977064	+	0.995215i	$0.531151\pi$
$420$	0	0
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	−20.0000	−0.973585
$423$	0	0
$424$	−18.0000	−0.874157
$425$	0	0
$426$	0	0
$427$	−8.00000	−0.387147
$428$	−12.0000	−0.580042
$429$	0	0
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	0	0
$433$	−34.0000	−1.63394	−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000	−1.63394	−0.816968	+	0.576683i	$0.804347\pi$
$434$	16.0000	0.768025
$435$	0	0
$436$	2.00000	0.0957826
$437$	0	0
$438$	0	0
$439$	32.0000	1.52728	0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000	1.52728	0.763638	+	0.645644i	$0.223411\pi$
$440$	0	0
$441$	0	0
$442$	−2.00000	−0.0951303
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	0	0
$445$	0	0
$446$	−4.00000	−0.189405
$447$	0	0
$448$	28.0000	1.32288
$449$	−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
$451$	24.0000	1.13012
$452$	6.00000	0.282216
$453$	0	0
$454$	−20.0000	−0.938647
$455$	0	0
$456$	0	0
$457$	−2.00000	−0.0935561	−0.0467780	−	0.998905i	$-0.514895\pi$
$457$	−2.00000	−0.0935561	−0.0467780	+	0.998905i	$0.514895\pi$
$458$	−10.0000	−0.467269
$459$	0	0
$460$	0	0
$461$	38.0000	1.76984	0.884918	−	0.465746i	$-0.154214\pi$
$461$	38.0000	1.76984	0.884918	+	0.465746i	$0.154214\pi$
$462$	0	0
$463$	−4.00000	−0.185896	−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000	−0.185896	−0.0929479	+	0.995671i	$0.529629\pi$
$464$	−10.0000	−0.464238
$465$	0	0
$466$	−14.0000	−0.648537
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	0	0
$469$	32.0000	1.47762
$470$	0	0
$471$	0	0
$472$	36.0000	1.65703
$473$	−48.0000	−2.20704
$474$	0	0
$475$	0	0
$476$	−8.00000	−0.366679
$477$	0	0
$478$	24.0000	1.09773
$479$	24.0000	1.09659	0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000	1.09659	0.548294	+	0.836286i	$0.315277\pi$
$480$	0	0
$481$	−2.00000	−0.0911922
$482$	10.0000	0.455488
$483$	0	0
$484$	−5.00000	−0.227273
$485$	0	0
$486$	0	0
$487$	−12.0000	−0.543772	−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000	−0.543772	−0.271886	+	0.962329i	$0.587647\pi$
$488$	6.00000	0.271607
$489$	0	0
$490$	0	0
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	0	0
$493$	20.0000	0.900755
$494$	0	0
$495$	0	0
$496$	−4.00000	−0.179605
$497$	0	0
$498$	0	0
$499$	−24.0000	−1.07439	−0.537194	−	0.843459i	$-0.680516\pi$
$499$	−24.0000	−1.07439	−0.537194	+	0.843459i	$0.680516\pi$
$500$	0	0
$501$	0	0
$502$	12.0000	0.535586
$503$	−8.00000	−0.356702	−0.178351	−	0.983967i	$-0.557076\pi$
$503$	−8.00000	−0.356702	−0.178351	+	0.983967i	$0.557076\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	−16.0000	−0.709885
$509$	−10.0000	−0.443242	−0.221621	−	0.975133i	$-0.571135\pi$
$509$	−10.0000	−0.443242	−0.221621	+	0.975133i	$0.571135\pi$
$510$	0	0
$511$	−8.00000	−0.353899
$512$	−11.0000	−0.486136
$513$	0	0
$514$	26.0000	1.14681
$515$	0	0
$516$	0	0
$517$	0	0
$518$	8.00000	0.351500
$519$	0	0
$520$	0	0
$521$	−18.0000	−0.788594	−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000	−0.788594	−0.394297	+	0.918983i	$0.629012\pi$
$522$	0	0
$523$	−44.0000	−1.92399	−0.961993	−	0.273075i	$-0.911959\pi$
$523$	−44.0000	−1.92399	−0.961993	+	0.273075i	$0.911959\pi$
$524$	4.00000	0.174741
$525$	0	0
$526$	24.0000	1.04645
$527$	8.00000	0.348485
$528$	0	0
$529$	−23.0000	−1.00000
$530$	0	0
$531$	0	0
$532$	0	0
$533$	6.00000	0.259889
$534$	0	0
$535$	0	0
$536$	−24.0000	−1.03664
$537$	0	0
$538$	−22.0000	−0.948487
$539$	−36.0000	−1.55063
$540$	0	0
$541$	30.0000	1.28980	0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000	1.28980	0.644900	+	0.764267i	$0.276899\pi$
$542$	−12.0000	−0.515444
$543$	0	0
$544$	10.0000	0.428746
$545$	0	0
$546$	0	0
$547$	−4.00000	−0.171028	−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000	−0.171028	−0.0855138	+	0.996337i	$0.527253\pi$
$548$	−6.00000	−0.256307
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	32.0000	1.36078
$554$	10.0000	0.424859
$555$	0	0
$556$	−12.0000	−0.508913
$557$	18.0000	0.762684	0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000	0.762684	0.381342	+	0.924434i	$0.375462\pi$
$558$	0	0
$559$	−12.0000	−0.507546
$560$	0	0
$561$	0	0
$562$	10.0000	0.421825
$563$	−12.0000	−0.505740	−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000	−0.505740	−0.252870	+	0.967500i	$0.581374\pi$
$564$	0	0
$565$	0	0
$566$	−12.0000	−0.504398
$567$	0	0
$568$	0	0
$569$	−34.0000	−1.42535	−0.712677	−	0.701492i	$-0.752517\pi$
$569$	−34.0000	−1.42535	−0.712677	+	0.701492i	$0.752517\pi$
$570$	0	0
$571$	−4.00000	−0.167395	−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000	−0.167395	−0.0836974	+	0.996491i	$0.526673\pi$
$572$	−4.00000	−0.167248
$573$	0	0
$574$	−24.0000	−1.00174
$575$	0	0
$576$	0	0
$577$	46.0000	1.91501	0.957503	−	0.288425i	$-0.0931316\pi$
$577$	46.0000	1.91501	0.957503	+	0.288425i	$0.0931316\pi$
$578$	−13.0000	−0.540729
$579$	0	0
$580$	0	0
$581$	16.0000	0.663792
$582$	0	0
$583$	−24.0000	−0.993978
$584$	6.00000	0.248282
$585$	0	0
$586$	−6.00000	−0.247858
$587$	28.0000	1.15568	0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000	1.15568	0.577842	+	0.816149i	$0.303895\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	−2.00000	−0.0821995
$593$	−26.0000	−1.06769	−0.533846	−	0.845582i	$-0.679254\pi$
$593$	−26.0000	−1.06769	−0.533846	+	0.845582i	$0.679254\pi$
$594$	0	0
$595$	0	0
$596$	−6.00000	−0.245770
$597$	0	0
$598$	0	0
$599$	40.0000	1.63436	0.817178	−	0.576386i	$-0.195537\pi$
$599$	40.0000	1.63436	0.817178	+	0.576386i	$0.195537\pi$
$600$	0	0
$601$	−38.0000	−1.55005	−0.775026	−	0.631929i	$-0.782263\pi$
$601$	−38.0000	−1.55005	−0.775026	+	0.631929i	$0.782263\pi$
$602$	48.0000	1.95633
$603$	0	0
$604$	−4.00000	−0.162758
$605$	0	0
$606$	0	0
$607$	16.0000	0.649420	0.324710	−	0.945814i	$-0.394733\pi$
$607$	16.0000	0.649420	0.324710	+	0.945814i	$0.394733\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	2.00000	0.0807792	0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000	0.0807792	0.0403896	+	0.999184i	$0.487140\pi$
$614$	16.0000	0.645707
$615$	0	0
$616$	48.0000	1.93398
$617$	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
$619$	24.0000	0.964641	0.482321	−	0.875995i	$-0.339794\pi$
$619$	24.0000	0.964641	0.482321	+	0.875995i	$0.339794\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	8.00000	0.320513
$624$	0	0
$625$	0	0
$626$	6.00000	0.239808
$627$	0	0
$628$	−18.0000	−0.718278
$629$	4.00000	0.159490
$630$	0	0
$631$	20.0000	0.796187	0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000	0.796187	0.398094	+	0.917345i	$0.369672\pi$
$632$	−24.0000	−0.954669
$633$	0	0
$634$	26.0000	1.03259
$635$	0	0
$636$	0	0
$637$	−9.00000	−0.356593
$638$	−40.0000	−1.58362
$639$	0	0
$640$	0	0
$641$	−2.00000	−0.0789953	−0.0394976	−	0.999220i	$-0.512576\pi$
$641$	−2.00000	−0.0789953	−0.0394976	+	0.999220i	$0.512576\pi$
$642$	0	0
$643$	40.0000	1.57745	0.788723	−	0.614749i	$-0.210743\pi$
$643$	40.0000	1.57745	0.788723	+	0.614749i	$0.210743\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−8.00000	−0.314512	−0.157256	−	0.987558i	$-0.550265\pi$
$647$	−8.00000	−0.314512	−0.157256	+	0.987558i	$0.550265\pi$
$648$	0	0
$649$	48.0000	1.88416
$650$	0	0
$651$	0	0
$652$	8.00000	0.313304
$653$	6.00000	0.234798	0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000	0.234798	0.117399	+	0.993085i	$0.462544\pi$
$654$	0	0
$655$	0	0
$656$	6.00000	0.234261
$657$	0	0
$658$	0	0
$659$	−28.0000	−1.09073	−0.545363	−	0.838200i	$-0.683608\pi$
$659$	−28.0000	−1.09073	−0.545363	+	0.838200i	$0.683608\pi$
$660$	0	0
$661$	30.0000	1.16686	0.583432	−	0.812162i	$-0.301709\pi$
$661$	30.0000	1.16686	0.583432	+	0.812162i	$0.301709\pi$
$662$	−16.0000	−0.621858
$663$	0	0
$664$	−12.0000	−0.465690
$665$	0	0
$666$	0	0
$667$	0	0
$668$	8.00000	0.309529
$669$	0	0
$670$	0	0
$671$	8.00000	0.308837
$672$	0	0
$673$	14.0000	0.539660	0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000	0.539660	0.269830	+	0.962908i	$0.413032\pi$
$674$	−18.0000	−0.693334
$675$	0	0
$676$	−1.00000	−0.0384615
$677$	22.0000	0.845529	0.422764	−	0.906240i	$-0.361060\pi$
$677$	22.0000	0.845529	0.422764	+	0.906240i	$0.361060\pi$
$678$	0	0
$679$	−40.0000	−1.53506
$680$	0	0
$681$	0	0
$682$	−16.0000	−0.612672
$683$	−12.0000	−0.459167	−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000	−0.459167	−0.229584	+	0.973289i	$0.573736\pi$
$684$	0	0
$685$	0	0
$686$	8.00000	0.305441
$687$	0	0
$688$	−12.0000	−0.457496
$689$	−6.00000	−0.228582
$690$	0	0
$691$	−24.0000	−0.913003	−0.456502	−	0.889723i	$-0.650898\pi$
$691$	−24.0000	−0.913003	−0.456502	+	0.889723i	$0.650898\pi$
$692$	−6.00000	−0.228086
$693$	0	0
$694$	−12.0000	−0.455514
$695$	0	0
$696$	0	0
$697$	−12.0000	−0.454532
$698$	−26.0000	−0.984115
$699$	0	0
$700$	0	0
$701$	34.0000	1.28416	0.642081	−	0.766637i	$-0.278071\pi$
$701$	34.0000	1.28416	0.642081	+	0.766637i	$0.278071\pi$
$702$	0	0
$703$	0	0
$704$	−28.0000	−1.05529
$705$	0	0
$706$	−2.00000	−0.0752710
$707$	72.0000	2.70784
$708$	0	0
$709$	−26.0000	−0.976450	−0.488225	−	0.872718i	$-0.662356\pi$
$709$	−26.0000	−0.976450	−0.488225	+	0.872718i	$0.662356\pi$
$710$	0	0
$711$	0	0
$712$	−6.00000	−0.224860
$713$	0	0
$714$	0	0
$715$	0	0
$716$	4.00000	0.149487
$717$	0	0
$718$	−24.0000	−0.895672
$719$	24.0000	0.895049	0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000	0.895049	0.447524	+	0.894272i	$0.352306\pi$
$720$	0	0
$721$	0	0
$722$	−19.0000	−0.707107
$723$	0	0
$724$	10.0000	0.371647
$725$	0	0
$726$	0	0
$727$	−8.00000	−0.296704	−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000	−0.296704	−0.148352	+	0.988935i	$0.547397\pi$
$728$	12.0000	0.444750
$729$	0	0
$730$	0	0
$731$	24.0000	0.887672
$732$	0	0
$733$	−30.0000	−1.10808	−0.554038	−	0.832492i	$-0.686914\pi$
$733$	−30.0000	−1.10808	−0.554038	+	0.832492i	$0.686914\pi$
$734$	−16.0000	−0.590571
$735$	0	0
$736$	0	0
$737$	−32.0000	−1.17874
$738$	0	0
$739$	32.0000	1.17714	0.588570	−	0.808447i	$-0.299691\pi$
$739$	32.0000	1.17714	0.588570	+	0.808447i	$0.299691\pi$
$740$	0	0
$741$	0	0
$742$	24.0000	0.881068
$743$	48.0000	1.76095	0.880475	−	0.474093i	$-0.157224\pi$
$743$	48.0000	1.76095	0.880475	+	0.474093i	$0.157224\pi$
$744$	0	0
$745$	0	0
$746$	26.0000	0.951928
$747$	0	0
$748$	8.00000	0.292509
$749$	48.0000	1.75388
$750$	0	0
$751$	8.00000	0.291924	0.145962	−	0.989290i	$-0.453372\pi$
$751$	8.00000	0.291924	0.145962	+	0.989290i	$0.453372\pi$
$752$	0	0
$753$	0	0
$754$	−10.0000	−0.364179
$755$	0	0
$756$	0	0
$757$	−22.0000	−0.799604	−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000	−0.799604	−0.399802	+	0.916602i	$0.630921\pi$
$758$	−24.0000	−0.871719
$759$	0	0
$760$	0	0
$761$	10.0000	0.362500	0.181250	−	0.983437i	$-0.441986\pi$
$761$	10.0000	0.362500	0.181250	+	0.983437i	$0.441986\pi$
$762$	0	0
$763$	−8.00000	−0.289619
$764$	8.00000	0.289430
$765$	0	0
$766$	−16.0000	−0.578103
$767$	12.0000	0.433295
$768$	0	0
$769$	−30.0000	−1.08183	−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000	−1.08183	−0.540914	+	0.841078i	$0.681921\pi$
$770$	0	0
$771$	0	0
$772$	18.0000	0.647834
$773$	10.0000	0.359675	0.179838	−	0.983696i	$-0.442443\pi$
$773$	10.0000	0.359675	0.179838	+	0.983696i	$0.442443\pi$
$774$	0	0
$775$	0	0
$776$	30.0000	1.07694
$777$	0	0
$778$	−22.0000	−0.788738
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	−9.00000	−0.321429
$785$	0	0
$786$	0	0
$787$	32.0000	1.14068	0.570338	−	0.821410i	$-0.306812\pi$
$787$	32.0000	1.14068	0.570338	+	0.821410i	$0.306812\pi$
$788$	−18.0000	−0.641223
$789$	0	0
$790$	0	0
$791$	−24.0000	−0.853342
$792$	0	0
$793$	2.00000	0.0710221
$794$	−38.0000	−1.34857
$795$	0	0
$796$	−8.00000	−0.283552
$797$	46.0000	1.62940	0.814702	−	0.579880i	$-0.196901\pi$
$797$	46.0000	1.62940	0.814702	+	0.579880i	$0.196901\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	−22.0000	−0.776847
$803$	8.00000	0.282314
$804$	0	0
$805$	0	0
$806$	−4.00000	−0.140894
$807$	0	0
$808$	−54.0000	−1.89971
$809$	30.0000	1.05474	0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000	1.05474	0.527372	+	0.849635i	$0.323177\pi$
$810$	0	0
$811$	8.00000	0.280918	0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000	0.280918	0.140459	+	0.990086i	$0.455142\pi$
$812$	−40.0000	−1.40372
$813$	0	0
$814$	−8.00000	−0.280400
$815$	0	0
$816$	0	0
$817$	0	0
$818$	34.0000	1.18878
$819$	0	0
$820$	0	0
$821$	22.0000	0.767805	0.383903	−	0.923374i	$-0.374580\pi$
$821$	22.0000	0.767805	0.383903	+	0.923374i	$0.374580\pi$
$822$	0	0
$823$	0	0		−	1.00000i	$-0.5\pi$
$823$	0	0			1.00000i	$0.5\pi$
$824$	0	0
$825$	0	0
$826$	−48.0000	−1.67013
$827$	4.00000	0.139094	0.0695468	−	0.997579i	$-0.477845\pi$
$827$	4.00000	0.139094	0.0695468	+	0.997579i	$0.477845\pi$
$828$	0	0
$829$	−34.0000	−1.18087	−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000	−1.18087	−0.590434	+	0.807086i	$0.701044\pi$
$830$	0	0
$831$	0	0
$832$	−7.00000	−0.242681
$833$	18.0000	0.623663
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	−4.00000	−0.138178
$839$	−48.0000	−1.65714	−0.828572	−	0.559883i	$-0.810846\pi$
$839$	−48.0000	−1.65714	−0.828572	+	0.559883i	$0.810846\pi$
$840$	0	0
$841$	71.0000	2.44828
$842$	−10.0000	−0.344623
$843$	0	0
$844$	20.0000	0.688428
$845$	0	0
$846$	0	0
$847$	20.0000	0.687208
$848$	−6.00000	−0.206041
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	−30.0000	−1.02718	−0.513590	−	0.858036i	$-0.671685\pi$
$853$	−30.0000	−1.02718	−0.513590	+	0.858036i	$0.671685\pi$
$854$	−8.00000	−0.273754
$855$	0	0
$856$	−36.0000	−1.23045
$857$	−46.0000	−1.57133	−0.785665	−	0.618652i	$-0.787679\pi$
$857$	−46.0000	−1.57133	−0.785665	+	0.618652i	$0.787679\pi$
$858$	0	0
$859$	−44.0000	−1.50126	−0.750630	−	0.660722i	$-0.770250\pi$
$859$	−44.0000	−1.50126	−0.750630	+	0.660722i	$0.770250\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	16.0000	0.544646	0.272323	−	0.962206i	$-0.412208\pi$
$863$	16.0000	0.544646	0.272323	+	0.962206i	$0.412208\pi$
$864$	0	0
$865$	0	0
$866$	−34.0000	−1.15537
$867$	0	0
$868$	−16.0000	−0.543075
$869$	−32.0000	−1.08553
$870$	0	0
$871$	−8.00000	−0.271070
$872$	6.00000	0.203186
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	10.0000	0.337676	0.168838	−	0.985644i	$-0.445999\pi$
$877$	10.0000	0.337676	0.168838	+	0.985644i	$0.445999\pi$
$878$	32.0000	1.07995
$879$	0	0
$880$	0	0
$881$	−58.0000	−1.95407	−0.977035	−	0.213080i	$-0.931651\pi$
$881$	−58.0000	−1.95407	−0.977035	+	0.213080i	$0.931651\pi$
$882$	0	0
$883$	44.0000	1.48072	0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000	1.48072	0.740359	+	0.672212i	$0.234656\pi$
$884$	2.00000	0.0672673
$885$	0	0
$886$	−4.00000	−0.134383
$887$	−48.0000	−1.61168	−0.805841	−	0.592132i	$-0.798286\pi$
$887$	−48.0000	−1.61168	−0.805841	+	0.592132i	$0.798286\pi$
$888$	0	0
$889$	64.0000	2.14649
$890$	0	0
$891$	0	0
$892$	4.00000	0.133930
$893$	0	0
$894$	0	0
$895$	0	0
$896$	−12.0000	−0.400892
$897$	0	0
$898$	−22.0000	−0.734150
$899$	40.0000	1.33407
$900$	0	0
$901$	12.0000	0.399778
$902$	24.0000	0.799113
$903$	0	0
$904$	18.0000	0.598671
$905$	0	0
$906$	0	0
$907$	−12.0000	−0.398453	−0.199227	−	0.979953i	$-0.563843\pi$
$907$	−12.0000	−0.398453	−0.199227	+	0.979953i	$0.563843\pi$
$908$	20.0000	0.663723
$909$	0	0
$910$	0	0
$911$	40.0000	1.32526	0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000	1.32526	0.662630	+	0.748947i	$0.269440\pi$
$912$	0	0
$913$	−16.0000	−0.529523
$914$	−2.00000	−0.0661541
$915$	0	0
$916$	10.0000	0.330409
$917$	−16.0000	−0.528367
$918$	0	0
$919$	−48.0000	−1.58337	−0.791687	−	0.610927i	$-0.790797\pi$
$919$	−48.0000	−1.58337	−0.791687	+	0.610927i	$0.790797\pi$
$920$	0	0
$921$	0	0
$922$	38.0000	1.25146
$923$	0	0
$924$	0	0
$925$	0	0
$926$	−4.00000	−0.131448
$927$	0	0
$928$	50.0000	1.64133
$929$	−30.0000	−0.984268	−0.492134	−	0.870519i	$-0.663783\pi$
$929$	−30.0000	−0.984268	−0.492134	+	0.870519i	$0.663783\pi$
$930$	0	0
$931$	0	0
$932$	14.0000	0.458585
$933$	0	0
$934$	12.0000	0.392652
$935$	0	0
$936$	0	0
$937$	−26.0000	−0.849383	−0.424691	−	0.905338i	$-0.639617\pi$
$937$	−26.0000	−0.849383	−0.424691	+	0.905338i	$0.639617\pi$
$938$	32.0000	1.04484
$939$	0	0
$940$	0	0
$941$	14.0000	0.456387	0.228193	−	0.973616i	$-0.426718\pi$
$941$	14.0000	0.456387	0.228193	+	0.973616i	$0.426718\pi$
$942$	0	0
$943$	0	0
$944$	12.0000	0.390567
$945$	0	0
$946$	−48.0000	−1.56061
$947$	−60.0000	−1.94974	−0.974869	−	0.222779i	$-0.928487\pi$
$947$	−60.0000	−1.94974	−0.974869	+	0.222779i	$0.928487\pi$
$948$	0	0
$949$	2.00000	0.0649227
$950$	0	0
$951$	0	0
$952$	−24.0000	−0.777844
$953$	−30.0000	−0.971795	−0.485898	−	0.874016i	$-0.661507\pi$
$953$	−30.0000	−0.971795	−0.485898	+	0.874016i	$0.661507\pi$
$954$	0	0
$955$	0	0
$956$	−24.0000	−0.776215
$957$	0	0
$958$	24.0000	0.775405
$959$	24.0000	0.775000
$960$	0	0
$961$	−15.0000	−0.483871
$962$	−2.00000	−0.0644826
$963$	0	0
$964$	−10.0000	−0.322078
$965$	0	0
$966$	0	0
$967$	52.0000	1.67221	0.836104	−	0.548572i	$-0.184828\pi$
$967$	52.0000	1.67221	0.836104	+	0.548572i	$0.184828\pi$
$968$	−15.0000	−0.482118
$969$	0	0
$970$	0	0
$971$	60.0000	1.92549	0.962746	−	0.270408i	$-0.0871586\pi$
$971$	60.0000	1.92549	0.962746	+	0.270408i	$0.0871586\pi$
$972$	0	0
$973$	48.0000	1.53881
$974$	−12.0000	−0.384505
$975$	0	0
$976$	2.00000	0.0640184
$977$	−42.0000	−1.34370	−0.671850	−	0.740688i	$-0.734500\pi$
$977$	−42.0000	−1.34370	−0.671850	+	0.740688i	$0.734500\pi$
$978$	0	0
$979$	−8.00000	−0.255681
$980$	0	0
$981$	0	0
$982$	12.0000	0.382935
$983$	16.0000	0.510321	0.255160	−	0.966899i	$-0.417872\pi$
$983$	16.0000	0.510321	0.255160	+	0.966899i	$0.417872\pi$
$984$	0	0
$985$	0	0
$986$	20.0000	0.636930
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	16.0000	0.508257	0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000	0.508257	0.254128	+	0.967170i	$0.418211\pi$
$992$	20.0000	0.635001
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	26.0000	0.823428	0.411714	−	0.911313i	$-0.364930\pi$
$997$	26.0000	0.823428	0.411714	+	0.911313i	$0.364930\pi$
$998$	−24.0000	−0.759707
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2925.2.a.p.1.1		1
3.2	odd	2		975.2.a.f.1.1		1
5.2	odd	4		2925.2.c.e.2224.2		2
5.3	odd	4		2925.2.c.e.2224.1		2
5.4	even	2		117.2.a.a.1.1		1
15.2	even	4		975.2.c.f.274.1		2
15.8	even	4		975.2.c.f.274.2		2
15.14	odd	2		39.2.a.a.1.1	✓	1
20.19	odd	2		1872.2.a.h.1.1		1
35.34	odd	2		5733.2.a.e.1.1		1
40.19	odd	2		7488.2.a.by.1.1		1
40.29	even	2		7488.2.a.bl.1.1		1
45.4	even	6		1053.2.e.d.703.1		2
45.14	odd	6		1053.2.e.b.703.1		2
45.29	odd	6		1053.2.e.b.352.1		2
45.34	even	6		1053.2.e.d.352.1		2
60.59	even	2		624.2.a.i.1.1		1
65.34	odd	4		1521.2.b.b.1351.1		2
65.44	odd	4		1521.2.b.b.1351.2		2
65.64	even	2		1521.2.a.e.1.1		1
105.104	even	2		1911.2.a.f.1.1		1
120.29	odd	2		2496.2.a.q.1.1		1
120.59	even	2		2496.2.a.e.1.1		1
165.164	even	2		4719.2.a.c.1.1		1
195.29	odd	6		507.2.e.a.22.1		2
195.44	even	4		507.2.b.a.337.1		2
195.59	even	12		507.2.j.e.361.2		4
195.74	odd	6		507.2.e.a.484.1		2
195.89	even	12		507.2.j.e.316.1		4
195.119	even	12		507.2.j.e.316.2		4
195.134	odd	6		507.2.e.b.484.1		2
195.149	even	12		507.2.j.e.361.1		4
195.164	even	4		507.2.b.a.337.2		2
195.179	odd	6		507.2.e.b.22.1		2
195.194	odd	2		507.2.a.a.1.1		1
780.779	even	2		8112.2.a.s.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.a.a.1.1	✓	1	15.14	odd	2
117.2.a.a.1.1		1	5.4	even	2
507.2.a.a.1.1		1	195.194	odd	2
507.2.b.a.337.1		2	195.44	even	4
507.2.b.a.337.2		2	195.164	even	4
507.2.e.a.22.1		2	195.29	odd	6
507.2.e.a.484.1		2	195.74	odd	6
507.2.e.b.22.1		2	195.179	odd	6
507.2.e.b.484.1		2	195.134	odd	6
507.2.j.e.316.1		4	195.89	even	12
507.2.j.e.316.2		4	195.119	even	12
507.2.j.e.361.1		4	195.149	even	12
507.2.j.e.361.2		4	195.59	even	12
624.2.a.i.1.1		1	60.59	even	2
975.2.a.f.1.1		1	3.2	odd	2
975.2.c.f.274.1		2	15.2	even	4
975.2.c.f.274.2		2	15.8	even	4
1053.2.e.b.352.1		2	45.29	odd	6
1053.2.e.b.703.1		2	45.14	odd	6
1053.2.e.d.352.1		2	45.34	even	6
1053.2.e.d.703.1		2	45.4	even	6
1521.2.a.e.1.1		1	65.64	even	2
1521.2.b.b.1351.1		2	65.34	odd	4
1521.2.b.b.1351.2		2	65.44	odd	4
1872.2.a.h.1.1		1	20.19	odd	2
1911.2.a.f.1.1		1	105.104	even	2
2496.2.a.e.1.1		1	120.59	even	2
2496.2.a.q.1.1		1	120.29	odd	2
2925.2.a.p.1.1		1	1.1	even	1	trivial
2925.2.c.e.2224.1		2	5.3	odd	4
2925.2.c.e.2224.2		2	5.2	odd	4
4719.2.a.c.1.1		1	165.164	even	2
5733.2.a.e.1.1		1	35.34	odd	2
7488.2.a.bl.1.1		1	40.29	even	2
7488.2.a.by.1.1		1	40.19	odd	2
8112.2.a.s.1.1		1	780.779	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:	\( N \)	\(=\)	\( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2925.a (trivial)

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