LMFDB - Embedded newform 5265.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5265,2,Mod(1,5265)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5265, 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("5265.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5265 = 3^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5265.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:	$42.0412366642$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 585)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5265.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{4} -1.00000 q^{5} +2.00000 q^{7} +3.00000 q^{8} +O(q^{10})$

$q-1.00000 q^{2} -1.00000 q^{4} -1.00000 q^{5} +2.00000 q^{7} +3.00000 q^{8} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{13} -2.00000 q^{14} -1.00000 q^{16} +2.00000 q^{17} -3.00000 q^{19} +1.00000 q^{20} +1.00000 q^{22} +1.00000 q^{25} +1.00000 q^{26} -2.00000 q^{28} +5.00000 q^{29} -1.00000 q^{31} -5.00000 q^{32} -2.00000 q^{34} -2.00000 q^{35} -5.00000 q^{37} +3.00000 q^{38} -3.00000 q^{40} -8.00000 q^{43} +1.00000 q^{44} -2.00000 q^{47} -3.00000 q^{49} -1.00000 q^{50} +1.00000 q^{52} +14.0000 q^{53} +1.00000 q^{55} +6.00000 q^{56} -5.00000 q^{58} -9.00000 q^{59} -1.00000 q^{61} +1.00000 q^{62} +7.00000 q^{64} +1.00000 q^{65} +14.0000 q^{67} -2.00000 q^{68} +2.00000 q^{70} +6.00000 q^{73} +5.00000 q^{74} +3.00000 q^{76} -2.00000 q^{77} -12.0000 q^{79} +1.00000 q^{80} -10.0000 q^{83} -2.00000 q^{85} +8.00000 q^{86} -3.00000 q^{88} +2.00000 q^{89} -2.00000 q^{91} +2.00000 q^{94} +3.00000 q^{95} +1.00000 q^{97} +3.00000 q^{98} +O(q^{100})$

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	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	0	0
$3$	0	0
$4$	−1.00000	−0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	2.00000	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	3.00000	1.06066
$9$	0	0
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−2.00000	−0.534522
$15$	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
$19$	−3.00000	−0.688247	−0.344124	−	0.938924i	$-0.611824\pi$
$19$	−3.00000	−0.688247	−0.344124	+	0.938924i	$0.611824\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	1.00000	0.213201
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	0	0
$28$	−2.00000	−0.377964
$29$	5.00000	0.928477	0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000	0.928477	0.464238	+	0.885710i	$0.346328\pi$
$30$	0	0
$31$	−1.00000	−0.179605	−0.0898027	−	0.995960i	$-0.528624\pi$
$31$	−1.00000	−0.179605	−0.0898027	+	0.995960i	$0.528624\pi$
$32$	−5.00000	−0.883883
$33$	0	0
$34$	−2.00000	−0.342997
$35$	−2.00000	−0.338062
$36$	0	0
$37$	−5.00000	−0.821995	−0.410997	−	0.911636i	$-0.634819\pi$
$37$	−5.00000	−0.821995	−0.410997	+	0.911636i	$0.634819\pi$
$38$	3.00000	0.486664
$39$	0	0
$40$	−3.00000	−0.474342
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	1.00000	0.150756
$45$	0	0
$46$	0	0
$47$	−2.00000	−0.291730	−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000	−0.291730	−0.145865	+	0.989305i	$0.546597\pi$
$48$	0	0
$49$	−3.00000	−0.428571
$50$	−1.00000	−0.141421
$51$	0	0
$52$	1.00000	0.138675
$53$	14.0000	1.92305	0.961524	−	0.274721i	$-0.0885855\pi$
$53$	14.0000	1.92305	0.961524	+	0.274721i	$0.0885855\pi$
$54$	0	0
$55$	1.00000	0.134840
$56$	6.00000	0.801784
$57$	0	0
$58$	−5.00000	−0.656532
$59$	−9.00000	−1.17170	−0.585850	−	0.810419i	$-0.699239\pi$
$59$	−9.00000	−1.17170	−0.585850	+	0.810419i	$0.699239\pi$
$60$	0	0
$61$	−1.00000	−0.128037	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	−1.00000	−0.128037	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	1.00000	0.127000
$63$	0	0
$64$	7.00000	0.875000
$65$	1.00000	0.124035
$66$	0	0
$67$	14.0000	1.71037	0.855186	−	0.518321i	$-0.173443\pi$
$67$	14.0000	1.71037	0.855186	+	0.518321i	$0.173443\pi$
$68$	−2.00000	−0.242536
$69$	0	0
$70$	2.00000	0.239046
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	5.00000	0.581238
$75$	0	0
$76$	3.00000	0.344124
$77$	−2.00000	−0.227921
$78$	0	0
$79$	−12.0000	−1.35011	−0.675053	−	0.737769i	$-0.735879\pi$
$79$	−12.0000	−1.35011	−0.675053	+	0.737769i	$0.735879\pi$
$80$	1.00000	0.111803
$81$	0	0
$82$	0	0
$83$	−10.0000	−1.09764	−0.548821	−	0.835940i	$-0.684923\pi$
$83$	−10.0000	−1.09764	−0.548821	+	0.835940i	$0.684923\pi$
$84$	0	0
$85$	−2.00000	−0.216930
$86$	8.00000	0.862662
$87$	0	0
$88$	−3.00000	−0.319801
$89$	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
$91$	−2.00000	−0.209657
$92$	0	0
$93$	0	0
$94$	2.00000	0.206284
$95$	3.00000	0.307794
$96$	0	0
$97$	1.00000	0.101535	0.0507673	−	0.998711i	$-0.483833\pi$
$97$	1.00000	0.101535	0.0507673	+	0.998711i	$0.483833\pi$
$98$	3.00000	0.303046
$99$	0	0
$100$	−1.00000	−0.100000
$101$	3.00000	0.298511	0.149256	−	0.988799i	$-0.452312\pi$
$101$	3.00000	0.298511	0.149256	+	0.988799i	$0.452312\pi$
$102$	0	0
$103$	−1.00000	−0.0985329	−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000	−0.0985329	−0.0492665	+	0.998786i	$0.515688\pi$
$104$	−3.00000	−0.294174
$105$	0	0
$106$	−14.0000	−1.35980
$107$	19.0000	1.83680	0.918400	−	0.395654i	$-0.129482\pi$
$107$	19.0000	1.83680	0.918400	+	0.395654i	$0.129482\pi$
$108$	0	0
$109$	−14.0000	−1.34096	−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000	−1.34096	−0.670478	+	0.741929i	$0.733911\pi$
$110$	−1.00000	−0.0953463
$111$	0	0
$112$	−2.00000	−0.188982
$113$	10.0000	0.940721	0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000	0.940721	0.470360	+	0.882474i	$0.344124\pi$
$114$	0	0
$115$	0	0
$116$	−5.00000	−0.464238
$117$	0	0
$118$	9.00000	0.828517
$119$	4.00000	0.366679
$120$	0	0
$121$	−10.0000	−0.909091
$122$	1.00000	0.0905357
$123$	0	0
$124$	1.00000	0.0898027
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	3.00000	0.265165
$129$	0	0
$130$	−1.00000	−0.0877058
$131$	−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
$133$	−6.00000	−0.520266
$134$	−14.0000	−1.20942
$135$	0	0
$136$	6.00000	0.514496
$137$	−5.00000	−0.427179	−0.213589	−	0.976924i	$-0.568515\pi$
$137$	−5.00000	−0.427179	−0.213589	+	0.976924i	$0.568515\pi$
$138$	0	0
$139$	12.0000	1.01783	0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000	1.01783	0.508913	+	0.860818i	$0.330047\pi$
$140$	2.00000	0.169031
$141$	0	0
$142$	0	0
$143$	1.00000	0.0836242
$144$	0	0
$145$	−5.00000	−0.415227
$146$	−6.00000	−0.496564
$147$	0	0
$148$	5.00000	0.410997
$149$	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
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	−9.00000	−0.729996
$153$	0	0
$154$	2.00000	0.161165
$155$	1.00000	0.0803219
$156$	0	0
$157$	−6.00000	−0.478852	−0.239426	−	0.970915i	$-0.576959\pi$
$157$	−6.00000	−0.478852	−0.239426	+	0.970915i	$0.576959\pi$
$158$	12.0000	0.954669
$159$	0	0
$160$	5.00000	0.395285
$161$	0	0
$162$	0	0
$163$	−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
$166$	10.0000	0.776151
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	2.00000	0.153393
$171$	0	0
$172$	8.00000	0.609994
$173$	12.0000	0.912343	0.456172	−	0.889892i	$-0.349220\pi$
$173$	12.0000	0.912343	0.456172	+	0.889892i	$0.349220\pi$
$174$	0	0
$175$	2.00000	0.151186
$176$	1.00000	0.0753778
$177$	0	0
$178$	−2.00000	−0.149906
$179$	−18.0000	−1.34538	−0.672692	−	0.739923i	$-0.734862\pi$
$179$	−18.0000	−1.34538	−0.672692	+	0.739923i	$0.734862\pi$
$180$	0	0
$181$	17.0000	1.26360	0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000	1.26360	0.631800	+	0.775131i	$0.282316\pi$
$182$	2.00000	0.148250
$183$	0	0
$184$	0	0
$185$	5.00000	0.367607
$186$	0	0
$187$	−2.00000	−0.146254
$188$	2.00000	0.145865
$189$	0	0
$190$	−3.00000	−0.217643
$191$	18.0000	1.30243	0.651217	−	0.758891i	$-0.274259\pi$
$191$	18.0000	1.30243	0.651217	+	0.758891i	$0.274259\pi$
$192$	0	0
$193$	13.0000	0.935760	0.467880	−	0.883792i	$-0.345018\pi$
$193$	13.0000	0.935760	0.467880	+	0.883792i	$0.345018\pi$
$194$	−1.00000	−0.0717958
$195$	0	0
$196$	3.00000	0.214286
$197$	15.0000	1.06871	0.534353	−	0.845262i	$-0.320555\pi$
$197$	15.0000	1.06871	0.534353	+	0.845262i	$0.320555\pi$
$198$	0	0
$199$	−22.0000	−1.55954	−0.779769	−	0.626067i	$-0.784664\pi$
$199$	−22.0000	−1.55954	−0.779769	+	0.626067i	$0.784664\pi$
$200$	3.00000	0.212132
$201$	0	0
$202$	−3.00000	−0.211079
$203$	10.0000	0.701862
$204$	0	0
$205$	0	0
$206$	1.00000	0.0696733
$207$	0	0
$208$	1.00000	0.0693375
$209$	3.00000	0.207514
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	−14.0000	−0.961524
$213$	0	0
$214$	−19.0000	−1.29881
$215$	8.00000	0.545595
$216$	0	0
$217$	−2.00000	−0.135769
$218$	14.0000	0.948200
$219$	0	0
$220$	−1.00000	−0.0674200
$221$	−2.00000	−0.134535
$222$	0	0
$223$	−26.0000	−1.74109	−0.870544	−	0.492090i	$-0.836233\pi$
$223$	−26.0000	−1.74109	−0.870544	+	0.492090i	$0.836233\pi$
$224$	−10.0000	−0.668153
$225$	0	0
$226$	−10.0000	−0.665190
$227$	−26.0000	−1.72568	−0.862840	−	0.505477i	$-0.831317\pi$
$227$	−26.0000	−1.72568	−0.862840	+	0.505477i	$0.831317\pi$
$228$	0	0
$229$	−16.0000	−1.05731	−0.528655	−	0.848837i	$-0.677303\pi$
$229$	−16.0000	−1.05731	−0.528655	+	0.848837i	$0.677303\pi$
$230$	0	0
$231$	0	0
$232$	15.0000	0.984798
$233$	−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
$235$	2.00000	0.130466
$236$	9.00000	0.585850
$237$	0	0
$238$	−4.00000	−0.259281
$239$	15.0000	0.970269	0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000	0.970269	0.485135	+	0.874439i	$0.338771\pi$
$240$	0	0
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	10.0000	0.642824
$243$	0	0
$244$	1.00000	0.0640184
$245$	3.00000	0.191663
$246$	0	0
$247$	3.00000	0.190885
$248$	−3.00000	−0.190500
$249$	0	0
$250$	1.00000	0.0632456
$251$	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
$254$	8.00000	0.501965
$255$	0	0
$256$	−17.0000	−1.06250
$257$	−28.0000	−1.74659	−0.873296	−	0.487190i	$-0.838022\pi$
$257$	−28.0000	−1.74659	−0.873296	+	0.487190i	$0.838022\pi$
$258$	0	0
$259$	−10.0000	−0.621370
$260$	−1.00000	−0.0620174
$261$	0	0
$262$	4.00000	0.247121
$263$	−16.0000	−0.986602	−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000	−0.986602	−0.493301	+	0.869859i	$0.664210\pi$
$264$	0	0
$265$	−14.0000	−0.860013
$266$	6.00000	0.367884
$267$	0	0
$268$	−14.0000	−0.855186
$269$	3.00000	0.182913	0.0914566	−	0.995809i	$-0.470848\pi$
$269$	3.00000	0.182913	0.0914566	+	0.995809i	$0.470848\pi$
$270$	0	0
$271$	−7.00000	−0.425220	−0.212610	−	0.977137i	$-0.568196\pi$
$271$	−7.00000	−0.425220	−0.212610	+	0.977137i	$0.568196\pi$
$272$	−2.00000	−0.121268
$273$	0	0
$274$	5.00000	0.302061
$275$	−1.00000	−0.0603023
$276$	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
$280$	−6.00000	−0.358569
$281$	−12.0000	−0.715860	−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000	−0.715860	−0.357930	+	0.933748i	$0.616517\pi$
$282$	0	0
$283$	−25.0000	−1.48610	−0.743048	−	0.669238i	$-0.766621\pi$
$283$	−25.0000	−1.48610	−0.743048	+	0.669238i	$0.766621\pi$
$284$	0	0
$285$	0	0
$286$	−1.00000	−0.0591312
$287$	0	0
$288$	0	0
$289$	−13.0000	−0.764706
$290$	5.00000	0.293610
$291$	0	0
$292$	−6.00000	−0.351123
$293$	1.00000	0.0584206	0.0292103	−	0.999573i	$-0.490701\pi$
$293$	1.00000	0.0584206	0.0292103	+	0.999573i	$0.490701\pi$
$294$	0	0
$295$	9.00000	0.524000
$296$	−15.0000	−0.871857
$297$	0	0
$298$	−6.00000	−0.347571
$299$	0	0
$300$	0	0
$301$	−16.0000	−0.922225
$302$	8.00000	0.460348
$303$	0	0
$304$	3.00000	0.172062
$305$	1.00000	0.0572598
$306$	0	0
$307$	2.00000	0.114146	0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000	0.114146	0.0570730	+	0.998370i	$0.481823\pi$
$308$	2.00000	0.113961
$309$	0	0
$310$	−1.00000	−0.0567962
$311$	−4.00000	−0.226819	−0.113410	−	0.993548i	$-0.536177\pi$
$311$	−4.00000	−0.226819	−0.113410	+	0.993548i	$0.536177\pi$
$312$	0	0
$313$	−28.0000	−1.58265	−0.791327	−	0.611393i	$-0.790609\pi$
$313$	−28.0000	−1.58265	−0.791327	+	0.611393i	$0.790609\pi$
$314$	6.00000	0.338600
$315$	0	0
$316$	12.0000	0.675053
$317$	−27.0000	−1.51647	−0.758236	−	0.651981i	$-0.773938\pi$
$317$	−27.0000	−1.51647	−0.758236	+	0.651981i	$0.773938\pi$
$318$	0	0
$319$	−5.00000	−0.279946
$320$	−7.00000	−0.391312
$321$	0	0
$322$	0	0
$323$	−6.00000	−0.333849
$324$	0	0
$325$	−1.00000	−0.0554700
$326$	12.0000	0.664619
$327$	0	0
$328$	0	0
$329$	−4.00000	−0.220527
$330$	0	0
$331$	27.0000	1.48405	0.742027	−	0.670370i	$-0.233865\pi$
$331$	27.0000	1.48405	0.742027	+	0.670370i	$0.233865\pi$
$332$	10.0000	0.548821
$333$	0	0
$334$	0	0
$335$	−14.0000	−0.764902
$336$	0	0
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	−1.00000	−0.0543928
$339$	0	0
$340$	2.00000	0.108465
$341$	1.00000	0.0541530
$342$	0	0
$343$	−20.0000	−1.07990
$344$	−24.0000	−1.29399
$345$	0	0
$346$	−12.0000	−0.645124
$347$	17.0000	0.912608	0.456304	−	0.889824i	$-0.349173\pi$
$347$	17.0000	0.912608	0.456304	+	0.889824i	$0.349173\pi$
$348$	0	0
$349$	12.0000	0.642345	0.321173	−	0.947021i	$-0.395923\pi$
$349$	12.0000	0.642345	0.321173	+	0.947021i	$0.395923\pi$
$350$	−2.00000	−0.106904
$351$	0	0
$352$	5.00000	0.266501
$353$	−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
$356$	−2.00000	−0.106000
$357$	0	0
$358$	18.0000	0.951330
$359$	−31.0000	−1.63612	−0.818059	−	0.575135i	$-0.804950\pi$
$359$	−31.0000	−1.63612	−0.818059	+	0.575135i	$0.804950\pi$
$360$	0	0
$361$	−10.0000	−0.526316
$362$	−17.0000	−0.893500
$363$	0	0
$364$	2.00000	0.104828
$365$	−6.00000	−0.314054
$366$	0	0
$367$	25.0000	1.30499	0.652495	−	0.757793i	$-0.273722\pi$
$367$	25.0000	1.30499	0.652495	+	0.757793i	$0.273722\pi$
$368$	0	0
$369$	0	0
$370$	−5.00000	−0.259938
$371$	28.0000	1.45369
$372$	0	0
$373$	−20.0000	−1.03556	−0.517780	−	0.855514i	$-0.673242\pi$
$373$	−20.0000	−1.03556	−0.517780	+	0.855514i	$0.673242\pi$
$374$	2.00000	0.103418
$375$	0	0
$376$	−6.00000	−0.309426
$377$	−5.00000	−0.257513
$378$	0	0
$379$	−23.0000	−1.18143	−0.590715	−	0.806880i	$-0.701154\pi$
$379$	−23.0000	−1.18143	−0.590715	+	0.806880i	$0.701154\pi$
$380$	−3.00000	−0.153897
$381$	0	0
$382$	−18.0000	−0.920960
$383$	−12.0000	−0.613171	−0.306586	−	0.951843i	$-0.599187\pi$
$383$	−12.0000	−0.613171	−0.306586	+	0.951843i	$0.599187\pi$
$384$	0	0
$385$	2.00000	0.101929
$386$	−13.0000	−0.661683
$387$	0	0
$388$	−1.00000	−0.0507673
$389$	−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
$392$	−9.00000	−0.454569
$393$	0	0
$394$	−15.0000	−0.755689
$395$	12.0000	0.603786
$396$	0	0
$397$	−30.0000	−1.50566	−0.752828	−	0.658217i	$-0.771311\pi$
$397$	−30.0000	−1.50566	−0.752828	+	0.658217i	$0.771311\pi$
$398$	22.0000	1.10276
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	28.0000	1.39825	0.699127	−	0.714998i	$-0.253572\pi$
$401$	28.0000	1.39825	0.699127	+	0.714998i	$0.253572\pi$
$402$	0	0
$403$	1.00000	0.0498135
$404$	−3.00000	−0.149256
$405$	0	0
$406$	−10.0000	−0.496292
$407$	5.00000	0.247841
$408$	0	0
$409$	0	0		−	1.00000i	$-0.5\pi$
$409$	0	0			1.00000i	$0.5\pi$
$410$	0	0
$411$	0	0
$412$	1.00000	0.0492665
$413$	−18.0000	−0.885722
$414$	0	0
$415$	10.0000	0.490881
$416$	5.00000	0.245145
$417$	0	0
$418$	−3.00000	−0.146735
$419$	20.0000	0.977064	0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000	0.977064	0.488532	+	0.872546i	$0.337533\pi$
$420$	0	0
$421$	10.0000	0.487370	0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000	0.487370	0.243685	+	0.969854i	$0.421644\pi$
$422$	0	0
$423$	0	0
$424$	42.0000	2.03970
$425$	2.00000	0.0970143
$426$	0	0
$427$	−2.00000	−0.0967868
$428$	−19.0000	−0.918400
$429$	0	0
$430$	−8.00000	−0.385794
$431$	17.0000	0.818861	0.409431	−	0.912341i	$-0.365727\pi$
$431$	17.0000	0.818861	0.409431	+	0.912341i	$0.365727\pi$
$432$	0	0
$433$	−38.0000	−1.82616	−0.913082	−	0.407777i	$-0.866304\pi$
$433$	−38.0000	−1.82616	−0.913082	+	0.407777i	$0.866304\pi$
$434$	2.00000	0.0960031
$435$	0	0
$436$	14.0000	0.670478
$437$	0	0
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	3.00000	0.143019
$441$	0	0
$442$	2.00000	0.0951303
$443$	−7.00000	−0.332580	−0.166290	−	0.986077i	$-0.553179\pi$
$443$	−7.00000	−0.332580	−0.166290	+	0.986077i	$0.553179\pi$
$444$	0	0
$445$	−2.00000	−0.0948091
$446$	26.0000	1.23114
$447$	0	0
$448$	14.0000	0.661438
$449$	−30.0000	−1.41579	−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000	−1.41579	−0.707894	+	0.706319i	$0.750354\pi$
$450$	0	0
$451$	0	0
$452$	−10.0000	−0.470360
$453$	0	0
$454$	26.0000	1.22024
$455$	2.00000	0.0937614
$456$	0	0
$457$	26.0000	1.21623	0.608114	−	0.793849i	$-0.291926\pi$
$457$	26.0000	1.21623	0.608114	+	0.793849i	$0.291926\pi$
$458$	16.0000	0.747631
$459$	0	0
$460$	0	0
$461$	−26.0000	−1.21094	−0.605470	−	0.795868i	$-0.707015\pi$
$461$	−26.0000	−1.21094	−0.605470	+	0.795868i	$0.707015\pi$
$462$	0	0
$463$	−6.00000	−0.278844	−0.139422	−	0.990233i	$-0.544524\pi$
$463$	−6.00000	−0.278844	−0.139422	+	0.990233i	$0.544524\pi$
$464$	−5.00000	−0.232119
$465$	0	0
$466$	14.0000	0.648537
$467$	−28.0000	−1.29569	−0.647843	−	0.761774i	$-0.724329\pi$
$467$	−28.0000	−1.29569	−0.647843	+	0.761774i	$0.724329\pi$
$468$	0	0
$469$	28.0000	1.29292
$470$	−2.00000	−0.0922531
$471$	0	0
$472$	−27.0000	−1.24278
$473$	8.00000	0.367840
$474$	0	0
$475$	−3.00000	−0.137649
$476$	−4.00000	−0.183340
$477$	0	0
$478$	−15.0000	−0.686084
$479$	15.0000	0.685367	0.342684	−	0.939451i	$-0.388664\pi$
$479$	15.0000	0.685367	0.342684	+	0.939451i	$0.388664\pi$
$480$	0	0
$481$	5.00000	0.227980
$482$	−10.0000	−0.455488
$483$	0	0
$484$	10.0000	0.454545
$485$	−1.00000	−0.0454077
$486$	0	0
$487$	−34.0000	−1.54069	−0.770344	−	0.637629i	$-0.779915\pi$
$487$	−34.0000	−1.54069	−0.770344	+	0.637629i	$0.779915\pi$
$488$	−3.00000	−0.135804
$489$	0	0
$490$	−3.00000	−0.135526
$491$	−6.00000	−0.270776	−0.135388	−	0.990793i	$-0.543228\pi$
$491$	−6.00000	−0.270776	−0.135388	+	0.990793i	$0.543228\pi$
$492$	0	0
$493$	10.0000	0.450377
$494$	−3.00000	−0.134976
$495$	0	0
$496$	1.00000	0.0449013
$497$	0	0
$498$	0	0
$499$	28.0000	1.25345	0.626726	−	0.779240i	$-0.284395\pi$
$499$	28.0000	1.25345	0.626726	+	0.779240i	$0.284395\pi$
$500$	1.00000	0.0447214
$501$	0	0
$502$	−12.0000	−0.535586
$503$	−9.00000	−0.401290	−0.200645	−	0.979664i	$-0.564304\pi$
$503$	−9.00000	−0.401290	−0.200645	+	0.979664i	$0.564304\pi$
$504$	0	0
$505$	−3.00000	−0.133498
$506$	0	0
$507$	0	0
$508$	8.00000	0.354943
$509$	−24.0000	−1.06378	−0.531891	−	0.846813i	$-0.678518\pi$
$509$	−24.0000	−1.06378	−0.531891	+	0.846813i	$0.678518\pi$
$510$	0	0
$511$	12.0000	0.530849
$512$	11.0000	0.486136
$513$	0	0
$514$	28.0000	1.23503
$515$	1.00000	0.0440653
$516$	0	0
$517$	2.00000	0.0879599
$518$	10.0000	0.439375
$519$	0	0
$520$	3.00000	0.131559
$521$	6.00000	0.262865	0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000	0.262865	0.131432	+	0.991325i	$0.458042\pi$
$522$	0	0
$523$	−15.0000	−0.655904	−0.327952	−	0.944694i	$-0.606358\pi$
$523$	−15.0000	−0.655904	−0.327952	+	0.944694i	$0.606358\pi$
$524$	4.00000	0.174741
$525$	0	0
$526$	16.0000	0.697633
$527$	−2.00000	−0.0871214
$528$	0	0
$529$	−23.0000	−1.00000
$530$	14.0000	0.608121
$531$	0	0
$532$	6.00000	0.260133
$533$	0	0
$534$	0	0
$535$	−19.0000	−0.821442
$536$	42.0000	1.81412
$537$	0	0
$538$	−3.00000	−0.129339
$539$	3.00000	0.129219
$540$	0	0
$541$	32.0000	1.37579	0.687894	−	0.725811i	$-0.258536\pi$
$541$	32.0000	1.37579	0.687894	+	0.725811i	$0.258536\pi$
$542$	7.00000	0.300676
$543$	0	0
$544$	−10.0000	−0.428746
$545$	14.0000	0.599694
$546$	0	0
$547$	−15.0000	−0.641354	−0.320677	−	0.947189i	$-0.603910\pi$
$547$	−15.0000	−0.641354	−0.320677	+	0.947189i	$0.603910\pi$
$548$	5.00000	0.213589
$549$	0	0
$550$	1.00000	0.0426401
$551$	−15.0000	−0.639021
$552$	0	0
$553$	−24.0000	−1.02058
$554$	−10.0000	−0.424859
$555$	0	0
$556$	−12.0000	−0.508913
$557$	−5.00000	−0.211857	−0.105928	−	0.994374i	$-0.533781\pi$
$557$	−5.00000	−0.211857	−0.105928	+	0.994374i	$0.533781\pi$
$558$	0	0
$559$	8.00000	0.338364
$560$	2.00000	0.0845154
$561$	0	0
$562$	12.0000	0.506189
$563$	−19.0000	−0.800755	−0.400377	−	0.916350i	$-0.631121\pi$
$563$	−19.0000	−0.800755	−0.400377	+	0.916350i	$0.631121\pi$
$564$	0	0
$565$	−10.0000	−0.420703
$566$	25.0000	1.05083
$567$	0	0
$568$	0	0
$569$	−11.0000	−0.461144	−0.230572	−	0.973055i	$-0.574060\pi$
$569$	−11.0000	−0.461144	−0.230572	+	0.973055i	$0.574060\pi$
$570$	0	0
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	−1.00000	−0.0418121
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	11.0000	0.457936	0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000	0.457936	0.228968	+	0.973434i	$0.426465\pi$
$578$	13.0000	0.540729
$579$	0	0
$580$	5.00000	0.207614
$581$	−20.0000	−0.829740
$582$	0	0
$583$	−14.0000	−0.579821
$584$	18.0000	0.744845
$585$	0	0
$586$	−1.00000	−0.0413096
$587$	−14.0000	−0.577842	−0.288921	−	0.957353i	$-0.593296\pi$
$587$	−14.0000	−0.577842	−0.288921	+	0.957353i	$0.593296\pi$
$588$	0	0
$589$	3.00000	0.123613
$590$	−9.00000	−0.370524
$591$	0	0
$592$	5.00000	0.205499
$593$	−31.0000	−1.27302	−0.636509	−	0.771270i	$-0.719622\pi$
$593$	−31.0000	−1.27302	−0.636509	+	0.771270i	$0.719622\pi$
$594$	0	0
$595$	−4.00000	−0.163984
$596$	−6.00000	−0.245770
$597$	0	0
$598$	0	0
$599$	14.0000	0.572024	0.286012	−	0.958226i	$-0.407670\pi$
$599$	14.0000	0.572024	0.286012	+	0.958226i	$0.407670\pi$
$600$	0	0
$601$	−17.0000	−0.693444	−0.346722	−	0.937968i	$-0.612705\pi$
$601$	−17.0000	−0.693444	−0.346722	+	0.937968i	$0.612705\pi$
$602$	16.0000	0.652111
$603$	0	0
$604$	8.00000	0.325515
$605$	10.0000	0.406558
$606$	0	0
$607$	−8.00000	−0.324710	−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000	−0.324710	−0.162355	+	0.986732i	$0.551909\pi$
$608$	15.0000	0.608330
$609$	0	0
$610$	−1.00000	−0.0404888
$611$	2.00000	0.0809113
$612$	0	0
$613$	30.0000	1.21169	0.605844	−	0.795583i	$-0.292835\pi$
$613$	30.0000	1.21169	0.605844	+	0.795583i	$0.292835\pi$
$614$	−2.00000	−0.0807134
$615$	0	0
$616$	−6.00000	−0.241747
$617$	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
$619$	−11.0000	−0.442127	−0.221064	−	0.975259i	$-0.570953\pi$
$619$	−11.0000	−0.442127	−0.221064	+	0.975259i	$0.570953\pi$
$620$	−1.00000	−0.0401610
$621$	0	0
$622$	4.00000	0.160385
$623$	4.00000	0.160257
$624$	0	0
$625$	1.00000	0.0400000
$626$	28.0000	1.11911
$627$	0	0
$628$	6.00000	0.239426
$629$	−10.0000	−0.398726
$630$	0	0
$631$	−5.00000	−0.199047	−0.0995234	−	0.995035i	$-0.531732\pi$
$631$	−5.00000	−0.199047	−0.0995234	+	0.995035i	$0.531732\pi$
$632$	−36.0000	−1.43200
$633$	0	0
$634$	27.0000	1.07231
$635$	8.00000	0.317470
$636$	0	0
$637$	3.00000	0.118864
$638$	5.00000	0.197952
$639$	0	0
$640$	−3.00000	−0.118585
$641$	17.0000	0.671460	0.335730	−	0.941958i	$-0.391017\pi$
$641$	17.0000	0.671460	0.335730	+	0.941958i	$0.391017\pi$
$642$	0	0
$643$	32.0000	1.26196	0.630978	−	0.775800i	$-0.282654\pi$
$643$	32.0000	1.26196	0.630978	+	0.775800i	$0.282654\pi$
$644$	0	0
$645$	0	0
$646$	6.00000	0.236067
$647$	41.0000	1.61188	0.805938	−	0.592000i	$-0.201661\pi$
$647$	41.0000	1.61188	0.805938	+	0.592000i	$0.201661\pi$
$648$	0	0
$649$	9.00000	0.353281
$650$	1.00000	0.0392232
$651$	0	0
$652$	12.0000	0.469956
$653$	48.0000	1.87839	0.939193	−	0.343391i	$-0.111576\pi$
$653$	48.0000	1.87839	0.939193	+	0.343391i	$0.111576\pi$
$654$	0	0
$655$	4.00000	0.156293
$656$	0	0
$657$	0	0
$658$	4.00000	0.155936
$659$	−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
$661$	38.0000	1.47803	0.739014	−	0.673690i	$-0.235292\pi$
$661$	38.0000	1.47803	0.739014	+	0.673690i	$0.235292\pi$
$662$	−27.0000	−1.04938
$663$	0	0
$664$	−30.0000	−1.16423
$665$	6.00000	0.232670
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	14.0000	0.540867
$671$	1.00000	0.0386046
$672$	0	0
$673$	24.0000	0.925132	0.462566	−	0.886585i	$-0.346929\pi$
$673$	24.0000	0.925132	0.462566	+	0.886585i	$0.346929\pi$
$674$	22.0000	0.847408
$675$	0	0
$676$	−1.00000	−0.0384615
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	0	0
$679$	2.00000	0.0767530
$680$	−6.00000	−0.230089
$681$	0	0
$682$	−1.00000	−0.0382920
$683$	−20.0000	−0.765279	−0.382639	−	0.923898i	$-0.624985\pi$
$683$	−20.0000	−0.765279	−0.382639	+	0.923898i	$0.624985\pi$
$684$	0	0
$685$	5.00000	0.191040
$686$	20.0000	0.763604
$687$	0	0
$688$	8.00000	0.304997
$689$	−14.0000	−0.533358
$690$	0	0
$691$	1.00000	0.0380418	0.0190209	−	0.999819i	$-0.493945\pi$
$691$	1.00000	0.0380418	0.0190209	+	0.999819i	$0.493945\pi$
$692$	−12.0000	−0.456172
$693$	0	0
$694$	−17.0000	−0.645311
$695$	−12.0000	−0.455186
$696$	0	0
$697$	0	0
$698$	−12.0000	−0.454207
$699$	0	0
$700$	−2.00000	−0.0755929
$701$	−5.00000	−0.188847	−0.0944237	−	0.995532i	$-0.530101\pi$
$701$	−5.00000	−0.188847	−0.0944237	+	0.995532i	$0.530101\pi$
$702$	0	0
$703$	15.0000	0.565736
$704$	−7.00000	−0.263822
$705$	0	0
$706$	3.00000	0.112906
$707$	6.00000	0.225653
$708$	0	0
$709$	4.00000	0.150223	0.0751116	−	0.997175i	$-0.476069\pi$
$709$	4.00000	0.150223	0.0751116	+	0.997175i	$0.476069\pi$
$710$	0	0
$711$	0	0
$712$	6.00000	0.224860
$713$	0	0
$714$	0	0
$715$	−1.00000	−0.0373979
$716$	18.0000	0.672692
$717$	0	0
$718$	31.0000	1.15691
$719$	−2.00000	−0.0745874	−0.0372937	−	0.999304i	$-0.511874\pi$
$719$	−2.00000	−0.0745874	−0.0372937	+	0.999304i	$0.511874\pi$
$720$	0	0
$721$	−2.00000	−0.0744839
$722$	10.0000	0.372161
$723$	0	0
$724$	−17.0000	−0.631800
$725$	5.00000	0.185695
$726$	0	0
$727$	48.0000	1.78022	0.890111	−	0.455744i	$-0.150627\pi$
$727$	48.0000	1.78022	0.890111	+	0.455744i	$0.150627\pi$
$728$	−6.00000	−0.222375
$729$	0	0
$730$	6.00000	0.222070
$731$	−16.0000	−0.591781
$732$	0	0
$733$	13.0000	0.480166	0.240083	−	0.970752i	$-0.422825\pi$
$733$	13.0000	0.480166	0.240083	+	0.970752i	$0.422825\pi$
$734$	−25.0000	−0.922767
$735$	0	0
$736$	0	0
$737$	−14.0000	−0.515697
$738$	0	0
$739$	9.00000	0.331070	0.165535	−	0.986204i	$-0.447065\pi$
$739$	9.00000	0.331070	0.165535	+	0.986204i	$0.447065\pi$
$740$	−5.00000	−0.183804
$741$	0	0
$742$	−28.0000	−1.02791
$743$	−48.0000	−1.76095	−0.880475	−	0.474093i	$-0.842776\pi$
$743$	−48.0000	−1.76095	−0.880475	+	0.474093i	$0.842776\pi$
$744$	0	0
$745$	−6.00000	−0.219823
$746$	20.0000	0.732252
$747$	0	0
$748$	2.00000	0.0731272
$749$	38.0000	1.38849
$750$	0	0
$751$	2.00000	0.0729810	0.0364905	−	0.999334i	$-0.488382\pi$
$751$	2.00000	0.0729810	0.0364905	+	0.999334i	$0.488382\pi$
$752$	2.00000	0.0729325
$753$	0	0
$754$	5.00000	0.182089
$755$	8.00000	0.291150
$756$	0	0
$757$	−16.0000	−0.581530	−0.290765	−	0.956795i	$-0.593910\pi$
$757$	−16.0000	−0.581530	−0.290765	+	0.956795i	$0.593910\pi$
$758$	23.0000	0.835398
$759$	0	0
$760$	9.00000	0.326464
$761$	−36.0000	−1.30500	−0.652499	−	0.757789i	$-0.726280\pi$
$761$	−36.0000	−1.30500	−0.652499	+	0.757789i	$0.726280\pi$
$762$	0	0
$763$	−28.0000	−1.01367
$764$	−18.0000	−0.651217
$765$	0	0
$766$	12.0000	0.433578
$767$	9.00000	0.324971
$768$	0	0
$769$	−40.0000	−1.44244	−0.721218	−	0.692708i	$-0.756418\pi$
$769$	−40.0000	−1.44244	−0.721218	+	0.692708i	$0.756418\pi$
$770$	−2.00000	−0.0720750
$771$	0	0
$772$	−13.0000	−0.467880
$773$	31.0000	1.11499	0.557496	−	0.830179i	$-0.311762\pi$
$773$	31.0000	1.11499	0.557496	+	0.830179i	$0.311762\pi$
$774$	0	0
$775$	−1.00000	−0.0359211
$776$	3.00000	0.107694
$777$	0	0
$778$	22.0000	0.788738
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	3.00000	0.107143
$785$	6.00000	0.214149
$786$	0	0
$787$	38.0000	1.35455	0.677277	−	0.735728i	$-0.263160\pi$
$787$	38.0000	1.35455	0.677277	+	0.735728i	$0.263160\pi$
$788$	−15.0000	−0.534353
$789$	0	0
$790$	−12.0000	−0.426941
$791$	20.0000	0.711118
$792$	0	0
$793$	1.00000	0.0355110
$794$	30.0000	1.06466
$795$	0	0
$796$	22.0000	0.779769
$797$	−42.0000	−1.48772	−0.743858	−	0.668338i	$-0.767006\pi$
$797$	−42.0000	−1.48772	−0.743858	+	0.668338i	$0.767006\pi$
$798$	0	0
$799$	−4.00000	−0.141510
$800$	−5.00000	−0.176777
$801$	0	0
$802$	−28.0000	−0.988714
$803$	−6.00000	−0.211735
$804$	0	0
$805$	0	0
$806$	−1.00000	−0.0352235
$807$	0	0
$808$	9.00000	0.316619
$809$	−5.00000	−0.175791	−0.0878953	−	0.996130i	$-0.528014\pi$
$809$	−5.00000	−0.175791	−0.0878953	+	0.996130i	$0.528014\pi$
$810$	0	0
$811$	−36.0000	−1.26413	−0.632065	−	0.774915i	$-0.717793\pi$
$811$	−36.0000	−1.26413	−0.632065	+	0.774915i	$0.717793\pi$
$812$	−10.0000	−0.350931
$813$	0	0
$814$	−5.00000	−0.175250
$815$	12.0000	0.420342
$816$	0	0
$817$	24.0000	0.839654
$818$	0	0
$819$	0	0
$820$	0	0
$821$	32.0000	1.11681	0.558404	−	0.829569i	$-0.311414\pi$
$821$	32.0000	1.11681	0.558404	+	0.829569i	$0.311414\pi$
$822$	0	0
$823$	11.0000	0.383436	0.191718	−	0.981450i	$-0.438594\pi$
$823$	11.0000	0.383436	0.191718	+	0.981450i	$0.438594\pi$
$824$	−3.00000	−0.104510
$825$	0	0
$826$	18.0000	0.626300
$827$	−44.0000	−1.53003	−0.765015	−	0.644013i	$-0.777268\pi$
$827$	−44.0000	−1.53003	−0.765015	+	0.644013i	$0.777268\pi$
$828$	0	0
$829$	34.0000	1.18087	0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000	1.18087	0.590434	+	0.807086i	$0.298956\pi$
$830$	−10.0000	−0.347105
$831$	0	0
$832$	−7.00000	−0.242681
$833$	−6.00000	−0.207888
$834$	0	0
$835$	0	0
$836$	−3.00000	−0.103757
$837$	0	0
$838$	−20.0000	−0.690889
$839$	5.00000	0.172619	0.0863096	−	0.996268i	$-0.472493\pi$
$839$	5.00000	0.172619	0.0863096	+	0.996268i	$0.472493\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	−10.0000	−0.344623
$843$	0	0
$844$	0	0
$845$	−1.00000	−0.0344010
$846$	0	0
$847$	−20.0000	−0.687208
$848$	−14.0000	−0.480762
$849$	0	0
$850$	−2.00000	−0.0685994
$851$	0	0
$852$	0	0
$853$	−54.0000	−1.84892	−0.924462	−	0.381273i	$-0.875486\pi$
$853$	−54.0000	−1.84892	−0.924462	+	0.381273i	$0.875486\pi$
$854$	2.00000	0.0684386
$855$	0	0
$856$	57.0000	1.94822
$857$	24.0000	0.819824	0.409912	−	0.912125i	$-0.365559\pi$
$857$	24.0000	0.819824	0.409912	+	0.912125i	$0.365559\pi$
$858$	0	0
$859$	28.0000	0.955348	0.477674	−	0.878537i	$-0.341480\pi$
$859$	28.0000	0.955348	0.477674	+	0.878537i	$0.341480\pi$
$860$	−8.00000	−0.272798
$861$	0	0
$862$	−17.0000	−0.579022
$863$	−30.0000	−1.02121	−0.510606	−	0.859815i	$-0.670579\pi$
$863$	−30.0000	−1.02121	−0.510606	+	0.859815i	$0.670579\pi$
$864$	0	0
$865$	−12.0000	−0.408012
$866$	38.0000	1.29129
$867$	0	0
$868$	2.00000	0.0678844
$869$	12.0000	0.407072
$870$	0	0
$871$	−14.0000	−0.474372
$872$	−42.0000	−1.42230
$873$	0	0
$874$	0	0
$875$	−2.00000	−0.0676123
$876$	0	0
$877$	15.0000	0.506514	0.253257	−	0.967399i	$-0.418498\pi$
$877$	15.0000	0.506514	0.253257	+	0.967399i	$0.418498\pi$
$878$	0	0
$879$	0	0
$880$	−1.00000	−0.0337100
$881$	23.0000	0.774890	0.387445	−	0.921893i	$-0.373358\pi$
$881$	23.0000	0.774890	0.387445	+	0.921893i	$0.373358\pi$
$882$	0	0
$883$	47.0000	1.58168	0.790838	−	0.612026i	$-0.209645\pi$
$883$	47.0000	1.58168	0.790838	+	0.612026i	$0.209645\pi$
$884$	2.00000	0.0672673
$885$	0	0
$886$	7.00000	0.235170
$887$	−23.0000	−0.772264	−0.386132	−	0.922443i	$-0.626189\pi$
$887$	−23.0000	−0.772264	−0.386132	+	0.922443i	$0.626189\pi$
$888$	0	0
$889$	−16.0000	−0.536623
$890$	2.00000	0.0670402
$891$	0	0
$892$	26.0000	0.870544
$893$	6.00000	0.200782
$894$	0	0
$895$	18.0000	0.601674
$896$	6.00000	0.200446
$897$	0	0
$898$	30.0000	1.00111
$899$	−5.00000	−0.166759
$900$	0	0
$901$	28.0000	0.932815
$902$	0	0
$903$	0	0
$904$	30.0000	0.997785
$905$	−17.0000	−0.565099
$906$	0	0
$907$	−1.00000	−0.0332045	−0.0166022	−	0.999862i	$-0.505285\pi$
$907$	−1.00000	−0.0332045	−0.0166022	+	0.999862i	$0.505285\pi$
$908$	26.0000	0.862840
$909$	0	0
$910$	−2.00000	−0.0662994
$911$	42.0000	1.39152	0.695761	−	0.718273i	$-0.255067\pi$
$911$	42.0000	1.39152	0.695761	+	0.718273i	$0.255067\pi$
$912$	0	0
$913$	10.0000	0.330952
$914$	−26.0000	−0.860004
$915$	0	0
$916$	16.0000	0.528655
$917$	−8.00000	−0.264183
$918$	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
$922$	26.0000	0.856264
$923$	0	0
$924$	0	0
$925$	−5.00000	−0.164399
$926$	6.00000	0.197172
$927$	0	0
$928$	−25.0000	−0.820665
$929$	−56.0000	−1.83730	−0.918650	−	0.395072i	$-0.870720\pi$
$929$	−56.0000	−1.83730	−0.918650	+	0.395072i	$0.870720\pi$
$930$	0	0
$931$	9.00000	0.294963
$932$	14.0000	0.458585
$933$	0	0
$934$	28.0000	0.916188
$935$	2.00000	0.0654070
$936$	0	0
$937$	60.0000	1.96011	0.980057	−	0.198715i	$-0.0636769\pi$
$937$	60.0000	1.96011	0.980057	+	0.198715i	$0.0636769\pi$
$938$	−28.0000	−0.914232
$939$	0	0
$940$	−2.00000	−0.0652328
$941$	−36.0000	−1.17357	−0.586783	−	0.809744i	$-0.699606\pi$
$941$	−36.0000	−1.17357	−0.586783	+	0.809744i	$0.699606\pi$
$942$	0	0
$943$	0	0
$944$	9.00000	0.292925
$945$	0	0
$946$	−8.00000	−0.260102
$947$	24.0000	0.779895	0.389948	−	0.920837i	$-0.372493\pi$
$947$	24.0000	0.779895	0.389948	+	0.920837i	$0.372493\pi$
$948$	0	0
$949$	−6.00000	−0.194768
$950$	3.00000	0.0973329
$951$	0	0
$952$	12.0000	0.388922
$953$	−48.0000	−1.55487	−0.777436	−	0.628962i	$-0.783480\pi$
$953$	−48.0000	−1.55487	−0.777436	+	0.628962i	$0.783480\pi$
$954$	0	0
$955$	−18.0000	−0.582466
$956$	−15.0000	−0.485135
$957$	0	0
$958$	−15.0000	−0.484628
$959$	−10.0000	−0.322917
$960$	0	0
$961$	−30.0000	−0.967742
$962$	−5.00000	−0.161206
$963$	0	0
$964$	−10.0000	−0.322078
$965$	−13.0000	−0.418485
$966$	0	0
$967$	−50.0000	−1.60789	−0.803946	−	0.594703i	$-0.797270\pi$
$967$	−50.0000	−1.60789	−0.803946	+	0.594703i	$0.797270\pi$
$968$	−30.0000	−0.964237
$969$	0	0
$970$	1.00000	0.0321081
$971$	50.0000	1.60458	0.802288	−	0.596937i	$-0.203616\pi$
$971$	50.0000	1.60458	0.802288	+	0.596937i	$0.203616\pi$
$972$	0	0
$973$	24.0000	0.769405
$974$	34.0000	1.08943
$975$	0	0
$976$	1.00000	0.0320092
$977$	−9.00000	−0.287936	−0.143968	−	0.989582i	$-0.545986\pi$
$977$	−9.00000	−0.287936	−0.143968	+	0.989582i	$0.545986\pi$
$978$	0	0
$979$	−2.00000	−0.0639203
$980$	−3.00000	−0.0958315
$981$	0	0
$982$	6.00000	0.191468
$983$	−4.00000	−0.127580	−0.0637901	−	0.997963i	$-0.520319\pi$
$983$	−4.00000	−0.127580	−0.0637901	+	0.997963i	$0.520319\pi$
$984$	0	0
$985$	−15.0000	−0.477940
$986$	−10.0000	−0.318465
$987$	0	0
$988$	−3.00000	−0.0954427
$989$	0	0
$990$	0	0
$991$	−18.0000	−0.571789	−0.285894	−	0.958261i	$-0.592291\pi$
$991$	−18.0000	−0.571789	−0.285894	+	0.958261i	$0.592291\pi$
$992$	5.00000	0.158750
$993$	0	0
$994$	0	0
$995$	22.0000	0.697447
$996$	0	0
$997$	−40.0000	−1.26681	−0.633406	−	0.773819i	$-0.718344\pi$
$997$	−40.0000	−1.26681	−0.633406	+	0.773819i	$0.718344\pi$
$998$	−28.0000	−0.886325
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5265.2.a.e.1.1		1
3.2	odd	2		5265.2.a.m.1.1		1
9.2	odd	6		1755.2.i.b.1171.1		2
9.4	even	3		585.2.i.b.196.1	✓	2
9.5	odd	6		1755.2.i.b.586.1		2
9.7	even	3		585.2.i.b.391.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.b.196.1	✓	2	9.4	even	3
585.2.i.b.391.1	yes	2	9.7	even	3
1755.2.i.b.586.1		2	9.5	odd	6
1755.2.i.b.1171.1		2	9.2	odd	6
5265.2.a.e.1.1		1	1.1	even	1	trivial
5265.2.a.m.1.1		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:	\( N \)	\(=\)	\( 5265 = 3^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5265.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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