LMFDB - Embedded newform 3850.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3850,2,Mod(1,3850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3850, 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("3850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3850.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:	$30.7424047782$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	3850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$

$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} -1.00000 q^{11} -1.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} +6.00000 q^{17} +3.00000 q^{18} +1.00000 q^{19} +1.00000 q^{22} +1.00000 q^{23} +1.00000 q^{26} -1.00000 q^{28} -5.00000 q^{29} -7.00000 q^{31} -1.00000 q^{32} -6.00000 q^{34} -3.00000 q^{36} +8.00000 q^{37} -1.00000 q^{38} +3.00000 q^{43} -1.00000 q^{44} -1.00000 q^{46} +1.00000 q^{49} -1.00000 q^{52} -12.0000 q^{53} +1.00000 q^{56} +5.00000 q^{58} -6.00000 q^{61} +7.00000 q^{62} +3.00000 q^{63} +1.00000 q^{64} +8.00000 q^{67} +6.00000 q^{68} +1.00000 q^{71} +3.00000 q^{72} -16.0000 q^{73} -8.00000 q^{74} +1.00000 q^{76} +1.00000 q^{77} -6.00000 q^{79} +9.00000 q^{81} +13.0000 q^{83} -3.00000 q^{86} +1.00000 q^{88} +9.00000 q^{89} +1.00000 q^{91} +1.00000 q^{92} +13.0000 q^{97} -1.00000 q^{98} +3.00000 q^{99} +O(q^{100})$

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		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	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
$9$	−3.00000	−1.00000
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	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
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	3.00000	0.707107
$19$	1.00000	0.229416	0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000	0.229416	0.114708	+	0.993399i	$0.463407\pi$
$20$	0	0
$21$	0	0
$22$	1.00000	0.213201
$23$	1.00000	0.208514	0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000	0.208514	0.104257	+	0.994550i	$0.466753\pi$
$24$	0	0
$25$	0	0
$26$	1.00000	0.196116
$27$	0	0
$28$	−1.00000	−0.188982
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	0	0
$31$	−7.00000	−1.25724	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000	−1.25724	−0.628619	+	0.777714i	$0.716379\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−6.00000	−1.02899
$35$	0	0
$36$	−3.00000	−0.500000
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	−1.00000	−0.162221
$39$	0	0
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	3.00000	0.457496	0.228748	−	0.973486i	$-0.426537\pi$
$43$	3.00000	0.457496	0.228748	+	0.973486i	$0.426537\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	−1.00000	−0.147442
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	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	$-0.808354\pi$
$53$	−12.0000	−1.64833	−0.824163	+	0.566352i	$0.808354\pi$
$54$	0	0
$55$	0	0
$56$	1.00000	0.133631
$57$	0	0
$58$	5.00000	0.656532
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	−6.00000	−0.768221	−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000	−0.768221	−0.384111	+	0.923287i	$0.625492\pi$
$62$	7.00000	0.889001
$63$	3.00000	0.377964
$64$	1.00000	0.125000
$65$	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	$0.337479\pi$
$68$	6.00000	0.727607
$69$	0	0
$70$	0	0
$71$	1.00000	0.118678	0.0593391	−	0.998238i	$-0.481101\pi$
$71$	1.00000	0.118678	0.0593391	+	0.998238i	$0.481101\pi$
$72$	3.00000	0.353553
$73$	−16.0000	−1.87266	−0.936329	−	0.351123i	$-0.885800\pi$
$73$	−16.0000	−1.87266	−0.936329	+	0.351123i	$0.885800\pi$
$74$	−8.00000	−0.929981
$75$	0	0
$76$	1.00000	0.114708
$77$	1.00000	0.113961
$78$	0	0
$79$	−6.00000	−0.675053	−0.337526	−	0.941316i	$-0.609590\pi$
$79$	−6.00000	−0.675053	−0.337526	+	0.941316i	$0.609590\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	0	0
$83$	13.0000	1.42694	0.713468	−	0.700688i	$-0.247124\pi$
$83$	13.0000	1.42694	0.713468	+	0.700688i	$0.247124\pi$
$84$	0	0
$85$	0	0
$86$	−3.00000	−0.323498
$87$	0	0
$88$	1.00000	0.106600
$89$	9.00000	0.953998	0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000	0.953998	0.476999	+	0.878904i	$0.341725\pi$
$90$	0	0
$91$	1.00000	0.104828
$92$	1.00000	0.104257
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	13.0000	1.31995	0.659975	−	0.751288i	$-0.270567\pi$
$97$	13.0000	1.31995	0.659975	+	0.751288i	$0.270567\pi$
$98$	−1.00000	−0.101015
$99$	3.00000	0.301511
$100$	0	0
$101$	−3.00000	−0.298511	−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000	−0.298511	−0.149256	+	0.988799i	$0.547688\pi$
$102$	0	0
$103$	9.00000	0.886796	0.443398	−	0.896325i	$-0.353773\pi$
$103$	9.00000	0.886796	0.443398	+	0.896325i	$0.353773\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	12.0000	1.16554
$107$	13.0000	1.25676	0.628379	−	0.777908i	$-0.283719\pi$
$107$	13.0000	1.25676	0.628379	+	0.777908i	$0.283719\pi$
$108$	0	0
$109$	9.00000	0.862044	0.431022	−	0.902342i	$-0.358153\pi$
$109$	9.00000	0.862044	0.431022	+	0.902342i	$0.358153\pi$
$110$	0	0
$111$	0	0
$112$	−1.00000	−0.0944911
$113$	18.0000	1.69330	0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000	1.69330	0.846649	+	0.532152i	$0.178617\pi$
$114$	0	0
$115$	0	0
$116$	−5.00000	−0.464238
$117$	3.00000	0.277350
$118$	0	0
$119$	−6.00000	−0.550019
$120$	0	0
$121$	1.00000	0.0909091
$122$	6.00000	0.543214
$123$	0	0
$124$	−7.00000	−0.628619
$125$	0	0
$126$	−3.00000	−0.267261
$127$	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
$131$	5.00000	0.436852	0.218426	−	0.975854i	$-0.429908\pi$
$131$	5.00000	0.436852	0.218426	+	0.975854i	$0.429908\pi$
$132$	0	0
$133$	−1.00000	−0.0867110
$134$	−8.00000	−0.691095
$135$	0	0
$136$	−6.00000	−0.514496
$137$	7.00000	0.598050	0.299025	−	0.954245i	$-0.403339\pi$
$137$	7.00000	0.598050	0.299025	+	0.954245i	$0.403339\pi$
$138$	0	0
$139$	7.00000	0.593732	0.296866	−	0.954919i	$-0.404058\pi$
$139$	7.00000	0.593732	0.296866	+	0.954919i	$0.404058\pi$
$140$	0	0
$141$	0	0
$142$	−1.00000	−0.0839181
$143$	1.00000	0.0836242
$144$	−3.00000	−0.250000
$145$	0	0
$146$	16.0000	1.32417
$147$	0	0
$148$	8.00000	0.657596
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	0	0
$151$	22.0000	1.79033	0.895167	−	0.445730i	$-0.147056\pi$
$151$	22.0000	1.79033	0.895167	+	0.445730i	$0.147056\pi$
$152$	−1.00000	−0.0811107
$153$	−18.0000	−1.45521
$154$	−1.00000	−0.0805823
$155$	0	0
$156$	0	0
$157$	−12.0000	−0.957704	−0.478852	−	0.877896i	$-0.658947\pi$
$157$	−12.0000	−0.957704	−0.478852	+	0.877896i	$0.658947\pi$
$158$	6.00000	0.477334
$159$	0	0
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	−9.00000	−0.707107
$163$	−12.0000	−0.939913	−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000	−0.939913	−0.469956	+	0.882690i	$0.655730\pi$
$164$	0	0
$165$	0	0
$166$	−13.0000	−1.00900
$167$	2.00000	0.154765	0.0773823	−	0.997001i	$-0.475344\pi$
$167$	2.00000	0.154765	0.0773823	+	0.997001i	$0.475344\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	−3.00000	−0.229416
$172$	3.00000	0.228748
$173$	−1.00000	−0.0760286	−0.0380143	−	0.999277i	$-0.512103\pi$
$173$	−1.00000	−0.0760286	−0.0380143	+	0.999277i	$0.512103\pi$
$174$	0	0
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	0	0
$178$	−9.00000	−0.674579
$179$	−2.00000	−0.149487	−0.0747435	−	0.997203i	$-0.523814\pi$
$179$	−2.00000	−0.149487	−0.0747435	+	0.997203i	$0.523814\pi$
$180$	0	0
$181$	20.0000	1.48659	0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000	1.48659	0.743294	+	0.668965i	$0.233262\pi$
$182$	−1.00000	−0.0741249
$183$	0	0
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	0	0
$187$	−6.00000	−0.438763
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−15.0000	−1.08536	−0.542681	−	0.839939i	$-0.682591\pi$
$191$	−15.0000	−1.08536	−0.542681	+	0.839939i	$0.682591\pi$
$192$	0	0
$193$	4.00000	0.287926	0.143963	−	0.989583i	$-0.454015\pi$
$193$	4.00000	0.287926	0.143963	+	0.989583i	$0.454015\pi$
$194$	−13.0000	−0.933346
$195$	0	0
$196$	1.00000	0.0714286
$197$	19.0000	1.35369	0.676847	−	0.736124i	$-0.263346\pi$
$197$	19.0000	1.35369	0.676847	+	0.736124i	$0.263346\pi$
$198$	−3.00000	−0.213201
$199$	−5.00000	−0.354441	−0.177220	−	0.984171i	$-0.556711\pi$
$199$	−5.00000	−0.354441	−0.177220	+	0.984171i	$0.556711\pi$
$200$	0	0
$201$	0	0
$202$	3.00000	0.211079
$203$	5.00000	0.350931
$204$	0	0
$205$	0	0
$206$	−9.00000	−0.627060
$207$	−3.00000	−0.208514
$208$	−1.00000	−0.0693375
$209$	−1.00000	−0.0691714
$210$	0	0
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	−12.0000	−0.824163
$213$	0	0
$214$	−13.0000	−0.888662
$215$	0	0
$216$	0	0
$217$	7.00000	0.475191
$218$	−9.00000	−0.609557
$219$	0	0
$220$	0	0
$221$	−6.00000	−0.403604
$222$	0	0
$223$	−24.0000	−1.60716	−0.803579	−	0.595198i	$-0.797074\pi$
$223$	−24.0000	−1.60716	−0.803579	+	0.595198i	$0.797074\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	−18.0000	−1.19734
$227$	9.00000	0.597351	0.298675	−	0.954355i	$-0.403455\pi$
$227$	9.00000	0.597351	0.298675	+	0.954355i	$0.403455\pi$
$228$	0	0
$229$	−22.0000	−1.45380	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000	−1.45380	−0.726900	+	0.686743i	$0.759040\pi$
$230$	0	0
$231$	0	0
$232$	5.00000	0.328266
$233$	−4.00000	−0.262049	−0.131024	−	0.991379i	$-0.541827\pi$
$233$	−4.00000	−0.262049	−0.131024	+	0.991379i	$0.541827\pi$
$234$	−3.00000	−0.196116
$235$	0	0
$236$	0	0
$237$	0	0
$238$	6.00000	0.388922
$239$	−2.00000	−0.129369	−0.0646846	−	0.997906i	$-0.520604\pi$
$239$	−2.00000	−0.129369	−0.0646846	+	0.997906i	$0.520604\pi$
$240$	0	0
$241$	2.00000	0.128831	0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000	0.128831	0.0644157	+	0.997923i	$0.479482\pi$
$242$	−1.00000	−0.0642824
$243$	0	0
$244$	−6.00000	−0.384111
$245$	0	0
$246$	0	0
$247$	−1.00000	−0.0636285
$248$	7.00000	0.444500
$249$	0	0
$250$	0	0
$251$	6.00000	0.378717	0.189358	−	0.981908i	$-0.439359\pi$
$251$	6.00000	0.378717	0.189358	+	0.981908i	$0.439359\pi$
$252$	3.00000	0.188982
$253$	−1.00000	−0.0628695
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	21.0000	1.30994	0.654972	−	0.755653i	$-0.272680\pi$
$257$	21.0000	1.30994	0.654972	+	0.755653i	$0.272680\pi$
$258$	0	0
$259$	−8.00000	−0.497096
$260$	0	0
$261$	15.0000	0.928477
$262$	−5.00000	−0.308901
$263$	6.00000	0.369976	0.184988	−	0.982741i	$-0.440775\pi$
$263$	6.00000	0.369976	0.184988	+	0.982741i	$0.440775\pi$
$264$	0	0
$265$	0	0
$266$	1.00000	0.0613139
$267$	0	0
$268$	8.00000	0.488678
$269$	12.0000	0.731653	0.365826	−	0.930683i	$-0.380786\pi$
$269$	12.0000	0.731653	0.365826	+	0.930683i	$0.380786\pi$
$270$	0	0
$271$	24.0000	1.45790	0.728948	−	0.684569i	$-0.240010\pi$
$271$	24.0000	1.45790	0.728948	+	0.684569i	$0.240010\pi$
$272$	6.00000	0.363803
$273$	0	0
$274$	−7.00000	−0.422885
$275$	0	0
$276$	0	0
$277$	22.0000	1.32185	0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000	1.32185	0.660926	+	0.750451i	$0.270164\pi$
$278$	−7.00000	−0.419832
$279$	21.0000	1.25724
$280$	0	0
$281$	18.0000	1.07379	0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000	1.07379	0.536895	+	0.843649i	$0.319597\pi$
$282$	0	0
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	1.00000	0.0593391
$285$	0	0
$286$	−1.00000	−0.0591312
$287$	0	0
$288$	3.00000	0.176777
$289$	19.0000	1.11765
$290$	0	0
$291$	0	0
$292$	−16.0000	−0.936329
$293$	26.0000	1.51894	0.759468	−	0.650545i	$-0.225459\pi$
$293$	26.0000	1.51894	0.759468	+	0.650545i	$0.225459\pi$
$294$	0	0
$295$	0	0
$296$	−8.00000	−0.464991
$297$	0	0
$298$	6.00000	0.347571
$299$	−1.00000	−0.0578315
$300$	0	0
$301$	−3.00000	−0.172917
$302$	−22.0000	−1.26596
$303$	0	0
$304$	1.00000	0.0573539
$305$	0	0
$306$	18.0000	1.02899
$307$	−8.00000	−0.456584	−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000	−0.456584	−0.228292	+	0.973593i	$0.573314\pi$
$308$	1.00000	0.0569803
$309$	0	0
$310$	0	0
$311$	15.0000	0.850572	0.425286	−	0.905059i	$-0.360174\pi$
$311$	15.0000	0.850572	0.425286	+	0.905059i	$0.360174\pi$
$312$	0	0
$313$	6.00000	0.339140	0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000	0.339140	0.169570	+	0.985518i	$0.445762\pi$
$314$	12.0000	0.677199
$315$	0	0
$316$	−6.00000	−0.337526
$317$	−6.00000	−0.336994	−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000	−0.336994	−0.168497	+	0.985702i	$0.553891\pi$
$318$	0	0
$319$	5.00000	0.279946
$320$	0	0
$321$	0	0
$322$	1.00000	0.0557278
$323$	6.00000	0.333849
$324$	9.00000	0.500000
$325$	0	0
$326$	12.0000	0.664619
$327$	0	0
$328$	0	0
$329$	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	$0.644922\pi$
$332$	13.0000	0.713468
$333$	−24.0000	−1.31519
$334$	−2.00000	−0.109435
$335$	0	0
$336$	0	0
$337$	−8.00000	−0.435788	−0.217894	−	0.975972i	$-0.569919\pi$
$337$	−8.00000	−0.435788	−0.217894	+	0.975972i	$0.569919\pi$
$338$	12.0000	0.652714
$339$	0	0
$340$	0	0
$341$	7.00000	0.379071
$342$	3.00000	0.162221
$343$	−1.00000	−0.0539949
$344$	−3.00000	−0.161749
$345$	0	0
$346$	1.00000	0.0537603
$347$	24.0000	1.28839	0.644194	−	0.764862i	$-0.277193\pi$
$347$	24.0000	1.28839	0.644194	+	0.764862i	$0.277193\pi$
$348$	0	0
$349$	5.00000	0.267644	0.133822	−	0.991005i	$-0.457275\pi$
$349$	5.00000	0.267644	0.133822	+	0.991005i	$0.457275\pi$
$350$	0	0
$351$	0	0
$352$	1.00000	0.0533002
$353$	−3.00000	−0.159674	−0.0798369	−	0.996808i	$-0.525440\pi$
$353$	−3.00000	−0.159674	−0.0798369	+	0.996808i	$0.525440\pi$
$354$	0	0
$355$	0	0
$356$	9.00000	0.476999
$357$	0	0
$358$	2.00000	0.105703
$359$	−12.0000	−0.633336	−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000	−0.633336	−0.316668	+	0.948536i	$0.602564\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	−20.0000	−1.05118
$363$	0	0
$364$	1.00000	0.0524142
$365$	0	0
$366$	0	0
$367$	−3.00000	−0.156599	−0.0782994	−	0.996930i	$-0.524949\pi$
$367$	−3.00000	−0.156599	−0.0782994	+	0.996930i	$0.524949\pi$
$368$	1.00000	0.0521286
$369$	0	0
$370$	0	0
$371$	12.0000	0.623009
$372$	0	0
$373$	18.0000	0.932005	0.466002	−	0.884783i	$-0.345694\pi$
$373$	18.0000	0.932005	0.466002	+	0.884783i	$0.345694\pi$
$374$	6.00000	0.310253
$375$	0	0
$376$	0	0
$377$	5.00000	0.257513
$378$	0	0
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	0	0
$381$	0	0
$382$	15.0000	0.767467
$383$	13.0000	0.664269	0.332134	−	0.943232i	$-0.392231\pi$
$383$	13.0000	0.664269	0.332134	+	0.943232i	$0.392231\pi$
$384$	0	0
$385$	0	0
$386$	−4.00000	−0.203595
$387$	−9.00000	−0.457496
$388$	13.0000	0.659975
$389$	14.0000	0.709828	0.354914	−	0.934899i	$-0.384510\pi$
$389$	14.0000	0.709828	0.354914	+	0.934899i	$0.384510\pi$
$390$	0	0
$391$	6.00000	0.303433
$392$	−1.00000	−0.0505076
$393$	0	0
$394$	−19.0000	−0.957206
$395$	0	0
$396$	3.00000	0.150756
$397$	−22.0000	−1.10415	−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000	−1.10415	−0.552074	+	0.833795i	$0.686163\pi$
$398$	5.00000	0.250627
$399$	0	0
$400$	0	0
$401$	−1.00000	−0.0499376	−0.0249688	−	0.999688i	$-0.507949\pi$
$401$	−1.00000	−0.0499376	−0.0249688	+	0.999688i	$0.507949\pi$
$402$	0	0
$403$	7.00000	0.348695
$404$	−3.00000	−0.149256
$405$	0	0
$406$	−5.00000	−0.248146
$407$	−8.00000	−0.396545
$408$	0	0
$409$	−14.0000	−0.692255	−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000	−0.692255	−0.346128	+	0.938187i	$0.612504\pi$
$410$	0	0
$411$	0	0
$412$	9.00000	0.443398
$413$	0	0
$414$	3.00000	0.147442
$415$	0	0
$416$	1.00000	0.0490290
$417$	0	0
$418$	1.00000	0.0489116
$419$	30.0000	1.46560	0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000	1.46560	0.732798	+	0.680446i	$0.238214\pi$
$420$	0	0
$421$	−40.0000	−1.94948	−0.974740	−	0.223341i	$-0.928304\pi$
$421$	−40.0000	−1.94948	−0.974740	+	0.223341i	$0.928304\pi$
$422$	−20.0000	−0.973585
$423$	0	0
$424$	12.0000	0.582772
$425$	0	0
$426$	0	0
$427$	6.00000	0.290360
$428$	13.0000	0.628379
$429$	0	0
$430$	0	0
$431$	4.00000	0.192673	0.0963366	−	0.995349i	$-0.469287\pi$
$431$	4.00000	0.192673	0.0963366	+	0.995349i	$0.469287\pi$
$432$	0	0
$433$	−19.0000	−0.913082	−0.456541	−	0.889702i	$-0.650912\pi$
$433$	−19.0000	−0.913082	−0.456541	+	0.889702i	$0.650912\pi$
$434$	−7.00000	−0.336011
$435$	0	0
$436$	9.00000	0.431022
$437$	1.00000	0.0478365
$438$	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
$441$	−3.00000	−0.142857
$442$	6.00000	0.285391
$443$	−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
$446$	24.0000	1.13643
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	29.0000	1.36859	0.684297	−	0.729203i	$-0.260109\pi$
$449$	29.0000	1.36859	0.684297	+	0.729203i	$0.260109\pi$
$450$	0	0
$451$	0	0
$452$	18.0000	0.846649
$453$	0	0
$454$	−9.00000	−0.422391
$455$	0	0
$456$	0	0
$457$	−26.0000	−1.21623	−0.608114	−	0.793849i	$-0.708074\pi$
$457$	−26.0000	−1.21623	−0.608114	+	0.793849i	$0.708074\pi$
$458$	22.0000	1.02799
$459$	0	0
$460$	0	0
$461$	−18.0000	−0.838344	−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000	−0.838344	−0.419172	+	0.907907i	$0.637680\pi$
$462$	0	0
$463$	25.0000	1.16185	0.580924	−	0.813958i	$-0.302691\pi$
$463$	25.0000	1.16185	0.580924	+	0.813958i	$0.302691\pi$
$464$	−5.00000	−0.232119
$465$	0	0
$466$	4.00000	0.185296
$467$	30.0000	1.38823	0.694117	−	0.719862i	$-0.255795\pi$
$467$	30.0000	1.38823	0.694117	+	0.719862i	$0.255795\pi$
$468$	3.00000	0.138675
$469$	−8.00000	−0.369406
$470$	0	0
$471$	0	0
$472$	0	0
$473$	−3.00000	−0.137940
$474$	0	0
$475$	0	0
$476$	−6.00000	−0.275010
$477$	36.0000	1.64833
$478$	2.00000	0.0914779
$479$	42.0000	1.91903	0.959514	−	0.281659i	$-0.0908848\pi$
$479$	42.0000	1.91903	0.959514	+	0.281659i	$0.0908848\pi$
$480$	0	0
$481$	−8.00000	−0.364769
$482$	−2.00000	−0.0910975
$483$	0	0
$484$	1.00000	0.0454545
$485$	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	$0.657842\pi$
$488$	6.00000	0.271607
$489$	0	0
$490$	0	0
$491$	19.0000	0.857458	0.428729	−	0.903433i	$-0.358962\pi$
$491$	19.0000	0.857458	0.428729	+	0.903433i	$0.358962\pi$
$492$	0	0
$493$	−30.0000	−1.35113
$494$	1.00000	0.0449921
$495$	0	0
$496$	−7.00000	−0.314309
$497$	−1.00000	−0.0448561
$498$	0	0
$499$	−6.00000	−0.268597	−0.134298	−	0.990941i	$-0.542878\pi$
$499$	−6.00000	−0.268597	−0.134298	+	0.990941i	$0.542878\pi$
$500$	0	0
$501$	0	0
$502$	−6.00000	−0.267793
$503$	−18.0000	−0.802580	−0.401290	−	0.915951i	$-0.631438\pi$
$503$	−18.0000	−0.802580	−0.401290	+	0.915951i	$0.631438\pi$
$504$	−3.00000	−0.133631
$505$	0	0
$506$	1.00000	0.0444554
$507$	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
$511$	16.0000	0.707798
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−21.0000	−0.926270
$515$	0	0
$516$	0	0
$517$	0	0
$518$	8.00000	0.351500
$519$	0	0
$520$	0	0
$521$	−23.0000	−1.00765	−0.503824	−	0.863806i	$-0.668074\pi$
$521$	−23.0000	−1.00765	−0.503824	+	0.863806i	$0.668074\pi$
$522$	−15.0000	−0.656532
$523$	31.0000	1.35554	0.677768	−	0.735276i	$-0.262948\pi$
$523$	31.0000	1.35554	0.677768	+	0.735276i	$0.262948\pi$
$524$	5.00000	0.218426
$525$	0	0
$526$	−6.00000	−0.261612
$527$	−42.0000	−1.82955
$528$	0	0
$529$	−22.0000	−0.956522
$530$	0	0
$531$	0	0
$532$	−1.00000	−0.0433555
$533$	0	0
$534$	0	0
$535$	0	0
$536$	−8.00000	−0.345547
$537$	0	0
$538$	−12.0000	−0.517357
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	1.00000	0.0429934	0.0214967	−	0.999769i	$-0.493157\pi$
$541$	1.00000	0.0429934	0.0214967	+	0.999769i	$0.493157\pi$
$542$	−24.0000	−1.03089
$543$	0	0
$544$	−6.00000	−0.257248
$545$	0	0
$546$	0	0
$547$	−27.0000	−1.15444	−0.577218	−	0.816590i	$-0.695862\pi$
$547$	−27.0000	−1.15444	−0.577218	+	0.816590i	$0.695862\pi$
$548$	7.00000	0.299025
$549$	18.0000	0.768221
$550$	0	0
$551$	−5.00000	−0.213007
$552$	0	0
$553$	6.00000	0.255146
$554$	−22.0000	−0.934690
$555$	0	0
$556$	7.00000	0.296866
$557$	15.0000	0.635570	0.317785	−	0.948163i	$-0.397061\pi$
$557$	15.0000	0.635570	0.317785	+	0.948163i	$0.397061\pi$
$558$	−21.0000	−0.889001
$559$	−3.00000	−0.126886
$560$	0	0
$561$	0	0
$562$	−18.0000	−0.759284
$563$	−4.00000	−0.168580	−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000	−0.168580	−0.0842900	+	0.996441i	$0.526862\pi$
$564$	0	0
$565$	0	0
$566$	4.00000	0.168133
$567$	−9.00000	−0.377964
$568$	−1.00000	−0.0419591
$569$	−22.0000	−0.922288	−0.461144	−	0.887325i	$-0.652561\pi$
$569$	−22.0000	−0.922288	−0.461144	+	0.887325i	$0.652561\pi$
$570$	0	0
$571$	15.0000	0.627730	0.313865	−	0.949468i	$-0.398376\pi$
$571$	15.0000	0.627730	0.313865	+	0.949468i	$0.398376\pi$
$572$	1.00000	0.0418121
$573$	0	0
$574$	0	0
$575$	0	0
$576$	−3.00000	−0.125000
$577$	−34.0000	−1.41544	−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000	−1.41544	−0.707719	+	0.706494i	$0.750276\pi$
$578$	−19.0000	−0.790296
$579$	0	0
$580$	0	0
$581$	−13.0000	−0.539331
$582$	0	0
$583$	12.0000	0.496989
$584$	16.0000	0.662085
$585$	0	0
$586$	−26.0000	−1.07405
$587$	44.0000	1.81607	0.908037	−	0.418890i	$-0.137581\pi$
$587$	44.0000	1.81607	0.908037	+	0.418890i	$0.137581\pi$
$588$	0	0
$589$	−7.00000	−0.288430
$590$	0	0
$591$	0	0
$592$	8.00000	0.328798
$593$	0	0		−	1.00000i	$-0.5\pi$
$593$	0	0			1.00000i	$0.5\pi$
$594$	0	0
$595$	0	0
$596$	−6.00000	−0.245770
$597$	0	0
$598$	1.00000	0.0408930
$599$	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
$601$	32.0000	1.30531	0.652654	−	0.757656i	$-0.273656\pi$
$601$	32.0000	1.30531	0.652654	+	0.757656i	$0.273656\pi$
$602$	3.00000	0.122271
$603$	−24.0000	−0.977356
$604$	22.0000	0.895167
$605$	0	0
$606$	0	0
$607$	−22.0000	−0.892952	−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000	−0.892952	−0.446476	+	0.894795i	$0.647321\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	0	0
$611$	0	0
$612$	−18.0000	−0.727607
$613$	−2.00000	−0.0807792	−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000	−0.0807792	−0.0403896	+	0.999184i	$0.512860\pi$
$614$	8.00000	0.322854
$615$	0	0
$616$	−1.00000	−0.0402911
$617$	9.00000	0.362326	0.181163	−	0.983453i	$-0.442014\pi$
$617$	9.00000	0.362326	0.181163	+	0.983453i	$0.442014\pi$
$618$	0	0
$619$	46.0000	1.84890	0.924448	−	0.381308i	$-0.124526\pi$
$619$	46.0000	1.84890	0.924448	+	0.381308i	$0.124526\pi$
$620$	0	0
$621$	0	0
$622$	−15.0000	−0.601445
$623$	−9.00000	−0.360577
$624$	0	0
$625$	0	0
$626$	−6.00000	−0.239808
$627$	0	0
$628$	−12.0000	−0.478852
$629$	48.0000	1.91389
$630$	0	0
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	6.00000	0.238667
$633$	0	0
$634$	6.00000	0.238290
$635$	0	0
$636$	0	0
$637$	−1.00000	−0.0396214
$638$	−5.00000	−0.197952
$639$	−3.00000	−0.118678
$640$	0	0
$641$	−11.0000	−0.434474	−0.217237	−	0.976119i	$-0.569704\pi$
$641$	−11.0000	−0.434474	−0.217237	+	0.976119i	$0.569704\pi$
$642$	0	0
$643$	−22.0000	−0.867595	−0.433798	−	0.901010i	$-0.642827\pi$
$643$	−22.0000	−0.867595	−0.433798	+	0.901010i	$0.642827\pi$
$644$	−1.00000	−0.0394055
$645$	0	0
$646$	−6.00000	−0.236067
$647$	−40.0000	−1.57256	−0.786281	−	0.617869i	$-0.787996\pi$
$647$	−40.0000	−1.57256	−0.786281	+	0.617869i	$0.787996\pi$
$648$	−9.00000	−0.353553
$649$	0	0
$650$	0	0
$651$	0	0
$652$	−12.0000	−0.469956
$653$	−24.0000	−0.939193	−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000	−0.939193	−0.469596	+	0.882881i	$0.655601\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	48.0000	1.87266
$658$	0	0
$659$	−19.0000	−0.740135	−0.370067	−	0.929005i	$-0.620665\pi$
$659$	−19.0000	−0.740135	−0.370067	+	0.929005i	$0.620665\pi$
$660$	0	0
$661$	14.0000	0.544537	0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000	0.544537	0.272268	+	0.962221i	$0.412226\pi$
$662$	16.0000	0.621858
$663$	0	0
$664$	−13.0000	−0.504498
$665$	0	0
$666$	24.0000	0.929981
$667$	−5.00000	−0.193601
$668$	2.00000	0.0773823
$669$	0	0
$670$	0	0
$671$	6.00000	0.231627
$672$	0	0
$673$	28.0000	1.07932	0.539660	−	0.841883i	$-0.318553\pi$
$673$	28.0000	1.07932	0.539660	+	0.841883i	$0.318553\pi$
$674$	8.00000	0.308148
$675$	0	0
$676$	−12.0000	−0.461538
$677$	−37.0000	−1.42203	−0.711013	−	0.703179i	$-0.751763\pi$
$677$	−37.0000	−1.42203	−0.711013	+	0.703179i	$0.751763\pi$
$678$	0	0
$679$	−13.0000	−0.498894
$680$	0	0
$681$	0	0
$682$	−7.00000	−0.268044
$683$	−30.0000	−1.14792	−0.573959	−	0.818884i	$-0.694593\pi$
$683$	−30.0000	−1.14792	−0.573959	+	0.818884i	$0.694593\pi$
$684$	−3.00000	−0.114708
$685$	0	0
$686$	1.00000	0.0381802
$687$	0	0
$688$	3.00000	0.114374
$689$	12.0000	0.457164
$690$	0	0
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	−1.00000	−0.0380143
$693$	−3.00000	−0.113961
$694$	−24.0000	−0.911028
$695$	0	0
$696$	0	0
$697$	0	0
$698$	−5.00000	−0.189253
$699$	0	0
$700$	0	0
$701$	−15.0000	−0.566542	−0.283271	−	0.959040i	$-0.591420\pi$
$701$	−15.0000	−0.566542	−0.283271	+	0.959040i	$0.591420\pi$
$702$	0	0
$703$	8.00000	0.301726
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	3.00000	0.112906
$707$	3.00000	0.112827
$708$	0	0
$709$	−22.0000	−0.826227	−0.413114	−	0.910679i	$-0.635559\pi$
$709$	−22.0000	−0.826227	−0.413114	+	0.910679i	$0.635559\pi$
$710$	0	0
$711$	18.0000	0.675053
$712$	−9.00000	−0.337289
$713$	−7.00000	−0.262152
$714$	0	0
$715$	0	0
$716$	−2.00000	−0.0747435
$717$	0	0
$718$	12.0000	0.447836
$719$	−40.0000	−1.49175	−0.745874	−	0.666087i	$-0.767968\pi$
$719$	−40.0000	−1.49175	−0.745874	+	0.666087i	$0.767968\pi$
$720$	0	0
$721$	−9.00000	−0.335178
$722$	18.0000	0.669891
$723$	0	0
$724$	20.0000	0.743294
$725$	0	0
$726$	0	0
$727$	13.0000	0.482143	0.241072	−	0.970507i	$-0.422501\pi$
$727$	13.0000	0.482143	0.241072	+	0.970507i	$0.422501\pi$
$728$	−1.00000	−0.0370625
$729$	−27.0000	−1.00000
$730$	0	0
$731$	18.0000	0.665754
$732$	0	0
$733$	23.0000	0.849524	0.424762	−	0.905305i	$-0.360358\pi$
$733$	23.0000	0.849524	0.424762	+	0.905305i	$0.360358\pi$
$734$	3.00000	0.110732
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	−8.00000	−0.294684
$738$	0	0
$739$	12.0000	0.441427	0.220714	−	0.975339i	$-0.429161\pi$
$739$	12.0000	0.441427	0.220714	+	0.975339i	$0.429161\pi$
$740$	0	0
$741$	0	0
$742$	−12.0000	−0.440534
$743$	16.0000	0.586983	0.293492	−	0.955962i	$-0.405183\pi$
$743$	16.0000	0.586983	0.293492	+	0.955962i	$0.405183\pi$
$744$	0	0
$745$	0	0
$746$	−18.0000	−0.659027
$747$	−39.0000	−1.42694
$748$	−6.00000	−0.219382
$749$	−13.0000	−0.475010
$750$	0	0
$751$	−11.0000	−0.401396	−0.200698	−	0.979653i	$-0.564321\pi$
$751$	−11.0000	−0.401396	−0.200698	+	0.979653i	$0.564321\pi$
$752$	0	0
$753$	0	0
$754$	−5.00000	−0.182089
$755$	0	0
$756$	0	0
$757$	−44.0000	−1.59921	−0.799604	−	0.600528i	$-0.794957\pi$
$757$	−44.0000	−1.59921	−0.799604	+	0.600528i	$0.794957\pi$
$758$	20.0000	0.726433
$759$	0	0
$760$	0	0
$761$	−22.0000	−0.797499	−0.398750	−	0.917060i	$-0.630556\pi$
$761$	−22.0000	−0.797499	−0.398750	+	0.917060i	$0.630556\pi$
$762$	0	0
$763$	−9.00000	−0.325822
$764$	−15.0000	−0.542681
$765$	0	0
$766$	−13.0000	−0.469709
$767$	0	0
$768$	0	0
$769$	52.0000	1.87517	0.937584	−	0.347759i	$-0.113057\pi$
$769$	52.0000	1.87517	0.937584	+	0.347759i	$0.113057\pi$
$770$	0	0
$771$	0	0
$772$	4.00000	0.143963
$773$	−36.0000	−1.29483	−0.647415	−	0.762138i	$-0.724150\pi$
$773$	−36.0000	−1.29483	−0.647415	+	0.762138i	$0.724150\pi$
$774$	9.00000	0.323498
$775$	0	0
$776$	−13.0000	−0.466673
$777$	0	0
$778$	−14.0000	−0.501924
$779$	0	0
$780$	0	0
$781$	−1.00000	−0.0357828
$782$	−6.00000	−0.214560
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	4.00000	0.142585	0.0712923	−	0.997455i	$-0.477288\pi$
$787$	4.00000	0.142585	0.0712923	+	0.997455i	$0.477288\pi$
$788$	19.0000	0.676847
$789$	0	0
$790$	0	0
$791$	−18.0000	−0.640006
$792$	−3.00000	−0.106600
$793$	6.00000	0.213066
$794$	22.0000	0.780751
$795$	0	0
$796$	−5.00000	−0.177220
$797$	14.0000	0.495905	0.247953	−	0.968772i	$-0.420242\pi$
$797$	14.0000	0.495905	0.247953	+	0.968772i	$0.420242\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	−27.0000	−0.953998
$802$	1.00000	0.0353112
$803$	16.0000	0.564628
$804$	0	0
$805$	0	0
$806$	−7.00000	−0.246564
$807$	0	0
$808$	3.00000	0.105540
$809$	−48.0000	−1.68759	−0.843795	−	0.536666i	$-0.819684\pi$
$809$	−48.0000	−1.68759	−0.843795	+	0.536666i	$0.819684\pi$
$810$	0	0
$811$	4.00000	0.140459	0.0702295	−	0.997531i	$-0.477627\pi$
$811$	4.00000	0.140459	0.0702295	+	0.997531i	$0.477627\pi$
$812$	5.00000	0.175466
$813$	0	0
$814$	8.00000	0.280400
$815$	0	0
$816$	0	0
$817$	3.00000	0.104957
$818$	14.0000	0.489499
$819$	−3.00000	−0.104828
$820$	0	0
$821$	−9.00000	−0.314102	−0.157051	−	0.987590i	$-0.550199\pi$
$821$	−9.00000	−0.314102	−0.157051	+	0.987590i	$0.550199\pi$
$822$	0	0
$823$	−16.0000	−0.557725	−0.278862	−	0.960331i	$-0.589957\pi$
$823$	−16.0000	−0.557725	−0.278862	+	0.960331i	$0.589957\pi$
$824$	−9.00000	−0.313530
$825$	0	0
$826$	0	0
$827$	47.0000	1.63435	0.817175	−	0.576390i	$-0.195539\pi$
$827$	47.0000	1.63435	0.817175	+	0.576390i	$0.195539\pi$
$828$	−3.00000	−0.104257
$829$	−30.0000	−1.04194	−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000	−1.04194	−0.520972	+	0.853574i	$0.674430\pi$
$830$	0	0
$831$	0	0
$832$	−1.00000	−0.0346688
$833$	6.00000	0.207888
$834$	0	0
$835$	0	0
$836$	−1.00000	−0.0345857
$837$	0	0
$838$	−30.0000	−1.03633
$839$	48.0000	1.65714	0.828572	−	0.559883i	$-0.189154\pi$
$839$	48.0000	1.65714	0.828572	+	0.559883i	$0.189154\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	40.0000	1.37849
$843$	0	0
$844$	20.0000	0.688428
$845$	0	0
$846$	0	0
$847$	−1.00000	−0.0343604
$848$	−12.0000	−0.412082
$849$	0	0
$850$	0	0
$851$	8.00000	0.274236
$852$	0	0
$853$	−22.0000	−0.753266	−0.376633	−	0.926363i	$-0.622918\pi$
$853$	−22.0000	−0.753266	−0.376633	+	0.926363i	$0.622918\pi$
$854$	−6.00000	−0.205316
$855$	0	0
$856$	−13.0000	−0.444331
$857$	−42.0000	−1.43469	−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000	−1.43469	−0.717346	+	0.696717i	$0.754643\pi$
$858$	0	0
$859$	20.0000	0.682391	0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000	0.682391	0.341196	+	0.939992i	$0.389168\pi$
$860$	0	0
$861$	0	0
$862$	−4.00000	−0.136241
$863$	15.0000	0.510606	0.255303	−	0.966861i	$-0.417825\pi$
$863$	15.0000	0.510606	0.255303	+	0.966861i	$0.417825\pi$
$864$	0	0
$865$	0	0
$866$	19.0000	0.645646
$867$	0	0
$868$	7.00000	0.237595
$869$	6.00000	0.203536
$870$	0	0
$871$	−8.00000	−0.271070
$872$	−9.00000	−0.304778
$873$	−39.0000	−1.31995
$874$	−1.00000	−0.0338255
$875$	0	0
$876$	0	0
$877$	−21.0000	−0.709120	−0.354560	−	0.935033i	$-0.615369\pi$
$877$	−21.0000	−0.709120	−0.354560	+	0.935033i	$0.615369\pi$
$878$	−32.0000	−1.07995
$879$	0	0
$880$	0	0
$881$	−25.0000	−0.842271	−0.421136	−	0.906998i	$-0.638368\pi$
$881$	−25.0000	−0.842271	−0.421136	+	0.906998i	$0.638368\pi$
$882$	3.00000	0.101015
$883$	−36.0000	−1.21150	−0.605748	−	0.795656i	$-0.707126\pi$
$883$	−36.0000	−1.21150	−0.605748	+	0.795656i	$0.707126\pi$
$884$	−6.00000	−0.201802
$885$	0	0
$886$	4.00000	0.134383
$887$	−26.0000	−0.872995	−0.436497	−	0.899706i	$-0.643781\pi$
$887$	−26.0000	−0.872995	−0.436497	+	0.899706i	$0.643781\pi$
$888$	0	0
$889$	−8.00000	−0.268311
$890$	0	0
$891$	−9.00000	−0.301511
$892$	−24.0000	−0.803579
$893$	0	0
$894$	0	0
$895$	0	0
$896$	1.00000	0.0334077
$897$	0	0
$898$	−29.0000	−0.967743
$899$	35.0000	1.16732
$900$	0	0
$901$	−72.0000	−2.39867
$902$	0	0
$903$	0	0
$904$	−18.0000	−0.598671
$905$	0	0
$906$	0	0
$907$	−32.0000	−1.06254	−0.531271	−	0.847202i	$-0.678286\pi$
$907$	−32.0000	−1.06254	−0.531271	+	0.847202i	$0.678286\pi$
$908$	9.00000	0.298675
$909$	9.00000	0.298511
$910$	0	0
$911$	−48.0000	−1.59031	−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000	−1.59031	−0.795155	+	0.606406i	$0.792611\pi$
$912$	0	0
$913$	−13.0000	−0.430237
$914$	26.0000	0.860004
$915$	0	0
$916$	−22.0000	−0.726900
$917$	−5.00000	−0.165115
$918$	0	0
$919$	−16.0000	−0.527791	−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000	−0.527791	−0.263896	+	0.964551i	$0.585007\pi$
$920$	0	0
$921$	0	0
$922$	18.0000	0.592798
$923$	−1.00000	−0.0329154
$924$	0	0
$925$	0	0
$926$	−25.0000	−0.821551
$927$	−27.0000	−0.886796
$928$	5.00000	0.164133
$929$	9.00000	0.295280	0.147640	−	0.989041i	$-0.452832\pi$
$929$	9.00000	0.295280	0.147640	+	0.989041i	$0.452832\pi$
$930$	0	0
$931$	1.00000	0.0327737
$932$	−4.00000	−0.131024
$933$	0	0
$934$	−30.0000	−0.981630
$935$	0	0
$936$	−3.00000	−0.0980581
$937$	52.0000	1.69877	0.849383	−	0.527777i	$-0.176974\pi$
$937$	52.0000	1.69877	0.849383	+	0.527777i	$0.176974\pi$
$938$	8.00000	0.261209
$939$	0	0
$940$	0	0
$941$	−14.0000	−0.456387	−0.228193	−	0.973616i	$-0.573282\pi$
$941$	−14.0000	−0.456387	−0.228193	+	0.973616i	$0.573282\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	3.00000	0.0975384
$947$	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
$949$	16.0000	0.519382
$950$	0	0
$951$	0	0
$952$	6.00000	0.194461
$953$	56.0000	1.81402	0.907009	−	0.421111i	$-0.138360\pi$
$953$	56.0000	1.81402	0.907009	+	0.421111i	$0.138360\pi$
$954$	−36.0000	−1.16554
$955$	0	0
$956$	−2.00000	−0.0646846
$957$	0	0
$958$	−42.0000	−1.35696
$959$	−7.00000	−0.226042
$960$	0	0
$961$	18.0000	0.580645
$962$	8.00000	0.257930
$963$	−39.0000	−1.25676
$964$	2.00000	0.0644157
$965$	0	0
$966$	0	0
$967$	−4.00000	−0.128631	−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000	−0.128631	−0.0643157	+	0.997930i	$0.520486\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	0	0
$971$	−54.0000	−1.73294	−0.866471	−	0.499227i	$-0.833617\pi$
$971$	−54.0000	−1.73294	−0.866471	+	0.499227i	$0.833617\pi$
$972$	0	0
$973$	−7.00000	−0.224410
$974$	21.0000	0.672883
$975$	0	0
$976$	−6.00000	−0.192055
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	0	0
$979$	−9.00000	−0.287641
$980$	0	0
$981$	−27.0000	−0.862044
$982$	−19.0000	−0.606314
$983$	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
$986$	30.0000	0.955395
$987$	0	0
$988$	−1.00000	−0.0318142
$989$	3.00000	0.0953945
$990$	0	0
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	7.00000	0.222250
$993$	0	0
$994$	1.00000	0.0317181
$995$	0	0
$996$	0	0
$997$	42.0000	1.33015	0.665077	−	0.746775i	$-0.268399\pi$
$997$	42.0000	1.33015	0.665077	+	0.746775i	$0.268399\pi$
$998$	6.00000	0.189927
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3850.2.a.c.1.1	✓	1
5.2	odd	4		3850.2.c.i.1849.1		2
5.3	odd	4		3850.2.c.i.1849.2		2
5.4	even	2		3850.2.a.w.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3850.2.a.c.1.1	✓	1	1.1	even	1	trivial
3850.2.a.w.1.1	yes	1	5.4	even	2
3850.2.c.i.1849.1		2	5.2	odd	4
3850.2.c.i.1849.2		2	5.3	odd	4

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:	\( N \)	\(=\)	\( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3850.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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