LMFDB - Embedded newform 5265.2.a.d.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)

$f(q)$

$=$

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

$q-1.00000 q^{2} -1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{7} +3.00000 q^{8} +1.00000 q^{10} +2.00000 q^{11} -1.00000 q^{13} +1.00000 q^{14} -1.00000 q^{16} -4.00000 q^{17} +1.00000 q^{20} -2.00000 q^{22} -3.00000 q^{23} +1.00000 q^{25} +1.00000 q^{26} +1.00000 q^{28} -1.00000 q^{29} +8.00000 q^{31} -5.00000 q^{32} +4.00000 q^{34} +1.00000 q^{35} +4.00000 q^{37} -3.00000 q^{40} +9.00000 q^{41} -8.00000 q^{43} -2.00000 q^{44} +3.00000 q^{46} +13.0000 q^{47} -6.00000 q^{49} -1.00000 q^{50} +1.00000 q^{52} -10.0000 q^{53} -2.00000 q^{55} -3.00000 q^{56} +1.00000 q^{58} +6.00000 q^{59} -1.00000 q^{61} -8.00000 q^{62} +7.00000 q^{64} +1.00000 q^{65} -1.00000 q^{67} +4.00000 q^{68} -1.00000 q^{70} -6.00000 q^{71} -12.0000 q^{73} -4.00000 q^{74} -2.00000 q^{77} -6.00000 q^{79} +1.00000 q^{80} -9.00000 q^{82} +11.0000 q^{83} +4.00000 q^{85} +8.00000 q^{86} +6.00000 q^{88} +5.00000 q^{89} +1.00000 q^{91} +3.00000 q^{92} -13.0000 q^{94} -2.00000 q^{97} +6.00000 q^{98} +O(q^{100})$

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
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	3.00000	1.06066
$9$	0	0
$10$	1.00000	0.316228
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	1.00000	0.267261
$15$	0	0
$16$	−1.00000	−0.250000
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	−2.00000	−0.426401
$23$	−3.00000	−0.625543	−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000	−0.625543	−0.312772	+	0.949828i	$0.601257\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	0	0
$28$	1.00000	0.188982
$29$	−1.00000	−0.185695	−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000	−0.185695	−0.0928477	+	0.995680i	$0.529597\pi$
$30$	0	0
$31$	8.00000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	−5.00000	−0.883883
$33$	0	0
$34$	4.00000	0.685994
$35$	1.00000	0.169031
$36$	0	0
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	0	0
$39$	0	0
$40$	−3.00000	−0.474342
$41$	9.00000	1.40556	0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000	1.40556	0.702782	+	0.711405i	$0.251941\pi$
$42$	0	0
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	−2.00000	−0.301511
$45$	0	0
$46$	3.00000	0.442326
$47$	13.0000	1.89624	0.948122	−	0.317905i	$-0.102979\pi$
$47$	13.0000	1.89624	0.948122	+	0.317905i	$0.102979\pi$
$48$	0	0
$49$	−6.00000	−0.857143
$50$	−1.00000	−0.141421
$51$	0	0
$52$	1.00000	0.138675
$53$	−10.0000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	0	0
$55$	−2.00000	−0.269680
$56$	−3.00000	−0.400892
$57$	0	0
$58$	1.00000	0.131306
$59$	6.00000	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$60$	0	0
$61$	−1.00000	−0.128037	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	−1.00000	−0.128037	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	−8.00000	−1.01600
$63$	0	0
$64$	7.00000	0.875000
$65$	1.00000	0.124035
$66$	0	0
$67$	−1.00000	−0.122169	−0.0610847	−	0.998133i	$-0.519456\pi$
$67$	−1.00000	−0.122169	−0.0610847	+	0.998133i	$0.519456\pi$
$68$	4.00000	0.485071
$69$	0	0
$70$	−1.00000	−0.119523
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	0	0
$73$	−12.0000	−1.40449	−0.702247	−	0.711934i	$-0.747820\pi$
$73$	−12.0000	−1.40449	−0.702247	+	0.711934i	$0.747820\pi$
$74$	−4.00000	−0.464991
$75$	0	0
$76$	0	0
$77$	−2.00000	−0.227921
$78$	0	0
$79$	−6.00000	−0.675053	−0.337526	−	0.941316i	$-0.609590\pi$
$79$	−6.00000	−0.675053	−0.337526	+	0.941316i	$0.609590\pi$
$80$	1.00000	0.111803
$81$	0	0
$82$	−9.00000	−0.993884
$83$	11.0000	1.20741	0.603703	−	0.797209i	$-0.293691\pi$
$83$	11.0000	1.20741	0.603703	+	0.797209i	$0.293691\pi$
$84$	0	0
$85$	4.00000	0.433861
$86$	8.00000	0.862662
$87$	0	0
$88$	6.00000	0.639602
$89$	5.00000	0.529999	0.264999	−	0.964249i	$-0.414628\pi$
$89$	5.00000	0.529999	0.264999	+	0.964249i	$0.414628\pi$
$90$	0	0
$91$	1.00000	0.104828
$92$	3.00000	0.312772
$93$	0	0
$94$	−13.0000	−1.34085
$95$	0	0
$96$	0	0
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	6.00000	0.606092
$99$	0	0
$100$	−1.00000	−0.100000
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	0	0
$103$	−16.0000	−1.57653	−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000	−1.57653	−0.788263	+	0.615338i	$0.789020\pi$
$104$	−3.00000	−0.294174
$105$	0	0
$106$	10.0000	0.971286
$107$	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
$109$	1.00000	0.0957826	0.0478913	−	0.998853i	$-0.484750\pi$
$109$	1.00000	0.0957826	0.0478913	+	0.998853i	$0.484750\pi$
$110$	2.00000	0.190693
$111$	0	0
$112$	1.00000	0.0944911
$113$	4.00000	0.376288	0.188144	−	0.982141i	$-0.439753\pi$
$113$	4.00000	0.376288	0.188144	+	0.982141i	$0.439753\pi$
$114$	0	0
$115$	3.00000	0.279751
$116$	1.00000	0.0928477
$117$	0	0
$118$	−6.00000	−0.552345
$119$	4.00000	0.366679
$120$	0	0
$121$	−7.00000	−0.636364
$122$	1.00000	0.0905357
$123$	0	0
$124$	−8.00000	−0.718421
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	13.0000	1.15356	0.576782	−	0.816898i	$-0.304308\pi$
$127$	13.0000	1.15356	0.576782	+	0.816898i	$0.304308\pi$
$128$	3.00000	0.265165
$129$	0	0
$130$	−1.00000	−0.0877058
$131$	14.0000	1.22319	0.611593	−	0.791173i	$-0.290529\pi$
$131$	14.0000	1.22319	0.611593	+	0.791173i	$0.290529\pi$
$132$	0	0
$133$	0	0
$134$	1.00000	0.0863868
$135$	0	0
$136$	−12.0000	−1.02899
$137$	16.0000	1.36697	0.683486	−	0.729964i	$-0.260463\pi$
$137$	16.0000	1.36697	0.683486	+	0.729964i	$0.260463\pi$
$138$	0	0
$139$	−12.0000	−1.01783	−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000	−1.01783	−0.508913	+	0.860818i	$0.669953\pi$
$140$	−1.00000	−0.0845154
$141$	0	0
$142$	6.00000	0.503509
$143$	−2.00000	−0.167248
$144$	0	0
$145$	1.00000	0.0830455
$146$	12.0000	0.993127
$147$	0	0
$148$	−4.00000	−0.328798
$149$	−3.00000	−0.245770	−0.122885	−	0.992421i	$-0.539215\pi$
$149$	−3.00000	−0.245770	−0.122885	+	0.992421i	$0.539215\pi$
$150$	0	0
$151$	10.0000	0.813788	0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000	0.813788	0.406894	+	0.913475i	$0.366612\pi$
$152$	0	0
$153$	0	0
$154$	2.00000	0.161165
$155$	−8.00000	−0.642575
$156$	0	0
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	6.00000	0.477334
$159$	0	0
$160$	5.00000	0.395285
$161$	3.00000	0.236433
$162$	0	0
$163$	−12.0000	−0.939913	−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000	−0.939913	−0.469956	+	0.882690i	$0.655730\pi$
$164$	−9.00000	−0.702782
$165$	0	0
$166$	−11.0000	−0.853766
$167$	−3.00000	−0.232147	−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000	−0.232147	−0.116073	+	0.993241i	$0.537031\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−4.00000	−0.306786
$171$	0	0
$172$	8.00000	0.609994
$173$	−12.0000	−0.912343	−0.456172	−	0.889892i	$-0.650780\pi$
$173$	−12.0000	−0.912343	−0.456172	+	0.889892i	$0.650780\pi$
$174$	0	0
$175$	−1.00000	−0.0755929
$176$	−2.00000	−0.150756
$177$	0	0
$178$	−5.00000	−0.374766
$179$	6.00000	0.448461	0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000	0.448461	0.224231	+	0.974536i	$0.428013\pi$
$180$	0	0
$181$	−7.00000	−0.520306	−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000	−0.520306	−0.260153	+	0.965567i	$0.583773\pi$
$182$	−1.00000	−0.0741249
$183$	0	0
$184$	−9.00000	−0.663489
$185$	−4.00000	−0.294086
$186$	0	0
$187$	−8.00000	−0.585018
$188$	−13.0000	−0.948122
$189$	0	0
$190$	0	0
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	0	0
$193$	−2.00000	−0.143963	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000	−0.143963	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	2.00000	0.143592
$195$	0	0
$196$	6.00000	0.428571
$197$	−24.0000	−1.70993	−0.854965	−	0.518686i	$-0.826421\pi$
$197$	−24.0000	−1.70993	−0.854965	+	0.518686i	$0.826421\pi$
$198$	0	0
$199$	20.0000	1.41776	0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000	1.41776	0.708881	+	0.705328i	$0.249200\pi$
$200$	3.00000	0.212132
$201$	0	0
$202$	−6.00000	−0.422159
$203$	1.00000	0.0701862
$204$	0	0
$205$	−9.00000	−0.628587
$206$	16.0000	1.11477
$207$	0	0
$208$	1.00000	0.0693375
$209$	0	0
$210$	0	0
$211$	6.00000	0.413057	0.206529	−	0.978441i	$-0.433783\pi$
$211$	6.00000	0.413057	0.206529	+	0.978441i	$0.433783\pi$
$212$	10.0000	0.686803
$213$	0	0
$214$	−13.0000	−0.888662
$215$	8.00000	0.545595
$216$	0	0
$217$	−8.00000	−0.543075
$218$	−1.00000	−0.0677285
$219$	0	0
$220$	2.00000	0.134840
$221$	4.00000	0.269069
$222$	0	0
$223$	−17.0000	−1.13840	−0.569202	−	0.822198i	$-0.692748\pi$
$223$	−17.0000	−1.13840	−0.569202	+	0.822198i	$0.692748\pi$
$224$	5.00000	0.334077
$225$	0	0
$226$	−4.00000	−0.266076
$227$	4.00000	0.265489	0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000	0.265489	0.132745	+	0.991150i	$0.457621\pi$
$228$	0	0
$229$	−13.0000	−0.859064	−0.429532	−	0.903052i	$-0.641321\pi$
$229$	−13.0000	−0.859064	−0.429532	+	0.903052i	$0.641321\pi$
$230$	−3.00000	−0.197814
$231$	0	0
$232$	−3.00000	−0.196960
$233$	4.00000	0.262049	0.131024	−	0.991379i	$-0.458173\pi$
$233$	4.00000	0.262049	0.131024	+	0.991379i	$0.458173\pi$
$234$	0	0
$235$	−13.0000	−0.848026
$236$	−6.00000	−0.390567
$237$	0	0
$238$	−4.00000	−0.259281
$239$	−24.0000	−1.55243	−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000	−1.55243	−0.776215	+	0.630468i	$0.782863\pi$
$240$	0	0
$241$	−23.0000	−1.48156	−0.740780	−	0.671748i	$-0.765544\pi$
$241$	−23.0000	−1.48156	−0.740780	+	0.671748i	$0.765544\pi$
$242$	7.00000	0.449977
$243$	0	0
$244$	1.00000	0.0640184
$245$	6.00000	0.383326
$246$	0	0
$247$	0	0
$248$	24.0000	1.52400
$249$	0	0
$250$	1.00000	0.0632456
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	−6.00000	−0.377217
$254$	−13.0000	−0.815693
$255$	0	0
$256$	−17.0000	−1.06250
$257$	−22.0000	−1.37232	−0.686161	−	0.727450i	$-0.740706\pi$
$257$	−22.0000	−1.37232	−0.686161	+	0.727450i	$0.740706\pi$
$258$	0	0
$259$	−4.00000	−0.248548
$260$	−1.00000	−0.0620174
$261$	0	0
$262$	−14.0000	−0.864923
$263$	−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
$265$	10.0000	0.614295
$266$	0	0
$267$	0	0
$268$	1.00000	0.0610847
$269$	9.00000	0.548740	0.274370	−	0.961624i	$-0.411531\pi$
$269$	9.00000	0.548740	0.274370	+	0.961624i	$0.411531\pi$
$270$	0	0
$271$	−4.00000	−0.242983	−0.121491	−	0.992592i	$-0.538768\pi$
$271$	−4.00000	−0.242983	−0.121491	+	0.992592i	$0.538768\pi$
$272$	4.00000	0.242536
$273$	0	0
$274$	−16.0000	−0.966595
$275$	2.00000	0.120605
$276$	0	0
$277$	−20.0000	−1.20168	−0.600842	−	0.799368i	$-0.705168\pi$
$277$	−20.0000	−1.20168	−0.600842	+	0.799368i	$0.705168\pi$
$278$	12.0000	0.719712
$279$	0	0
$280$	3.00000	0.179284
$281$	−27.0000	−1.61068	−0.805342	−	0.592810i	$-0.798019\pi$
$281$	−27.0000	−1.61068	−0.805342	+	0.592810i	$0.798019\pi$
$282$	0	0
$283$	−13.0000	−0.772770	−0.386385	−	0.922338i	$-0.626276\pi$
$283$	−13.0000	−0.772770	−0.386385	+	0.922338i	$0.626276\pi$
$284$	6.00000	0.356034
$285$	0	0
$286$	2.00000	0.118262
$287$	−9.00000	−0.531253
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	−1.00000	−0.0587220
$291$	0	0
$292$	12.0000	0.702247
$293$	4.00000	0.233682	0.116841	−	0.993151i	$-0.462723\pi$
$293$	4.00000	0.233682	0.116841	+	0.993151i	$0.462723\pi$
$294$	0	0
$295$	−6.00000	−0.349334
$296$	12.0000	0.697486
$297$	0	0
$298$	3.00000	0.173785
$299$	3.00000	0.173494
$300$	0	0
$301$	8.00000	0.461112
$302$	−10.0000	−0.575435
$303$	0	0
$304$	0	0
$305$	1.00000	0.0572598
$306$	0	0
$307$	−19.0000	−1.08439	−0.542194	−	0.840254i	$-0.682406\pi$
$307$	−19.0000	−1.08439	−0.542194	+	0.840254i	$0.682406\pi$
$308$	2.00000	0.113961
$309$	0	0
$310$	8.00000	0.454369
$311$	−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
$313$	14.0000	0.791327	0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000	0.791327	0.395663	+	0.918396i	$0.370515\pi$
$314$	−18.0000	−1.01580
$315$	0	0
$316$	6.00000	0.337526
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	0	0
$319$	−2.00000	−0.111979
$320$	−7.00000	−0.391312
$321$	0	0
$322$	−3.00000	−0.167183
$323$	0	0
$324$	0	0
$325$	−1.00000	−0.0554700
$326$	12.0000	0.664619
$327$	0	0
$328$	27.0000	1.49083
$329$	−13.0000	−0.716713
$330$	0	0
$331$	−18.0000	−0.989369	−0.494685	−	0.869072i	$-0.664716\pi$
$331$	−18.0000	−0.989369	−0.494685	+	0.869072i	$0.664716\pi$
$332$	−11.0000	−0.603703
$333$	0	0
$334$	3.00000	0.164153
$335$	1.00000	0.0546358
$336$	0	0
$337$	20.0000	1.08947	0.544735	−	0.838608i	$-0.316630\pi$
$337$	20.0000	1.08947	0.544735	+	0.838608i	$0.316630\pi$
$338$	−1.00000	−0.0543928
$339$	0	0
$340$	−4.00000	−0.216930
$341$	16.0000	0.866449
$342$	0	0
$343$	13.0000	0.701934
$344$	−24.0000	−1.29399
$345$	0	0
$346$	12.0000	0.645124
$347$	−28.0000	−1.50312	−0.751559	−	0.659665i	$-0.770698\pi$
$347$	−28.0000	−1.50312	−0.751559	+	0.659665i	$0.770698\pi$
$348$	0	0
$349$	−9.00000	−0.481759	−0.240879	−	0.970555i	$-0.577436\pi$
$349$	−9.00000	−0.481759	−0.240879	+	0.970555i	$0.577436\pi$
$350$	1.00000	0.0534522
$351$	0	0
$352$	−10.0000	−0.533002
$353$	0	0		−	1.00000i	$-0.5\pi$
$353$	0	0			1.00000i	$0.5\pi$
$354$	0	0
$355$	6.00000	0.318447
$356$	−5.00000	−0.264999
$357$	0	0
$358$	−6.00000	−0.317110
$359$	8.00000	0.422224	0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000	0.422224	0.211112	+	0.977462i	$0.432292\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	7.00000	0.367912
$363$	0	0
$364$	−1.00000	−0.0524142
$365$	12.0000	0.628109
$366$	0	0
$367$	−32.0000	−1.67039	−0.835193	−	0.549957i	$-0.814644\pi$
$367$	−32.0000	−1.67039	−0.835193	+	0.549957i	$0.814644\pi$
$368$	3.00000	0.156386
$369$	0	0
$370$	4.00000	0.207950
$371$	10.0000	0.519174
$372$	0	0
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	8.00000	0.413670
$375$	0	0
$376$	39.0000	2.01127
$377$	1.00000	0.0515026
$378$	0	0
$379$	−26.0000	−1.33553	−0.667765	−	0.744372i	$-0.732749\pi$
$379$	−26.0000	−1.33553	−0.667765	+	0.744372i	$0.732749\pi$
$380$	0	0
$381$	0	0
$382$	12.0000	0.613973
$383$	−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
$386$	2.00000	0.101797
$387$	0	0
$388$	2.00000	0.101535
$389$	−31.0000	−1.57176	−0.785881	−	0.618378i	$-0.787790\pi$
$389$	−31.0000	−1.57176	−0.785881	+	0.618378i	$0.787790\pi$
$390$	0	0
$391$	12.0000	0.606866
$392$	−18.0000	−0.909137
$393$	0	0
$394$	24.0000	1.20910
$395$	6.00000	0.301893
$396$	0	0
$397$	18.0000	0.903394	0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000	0.903394	0.451697	+	0.892171i	$0.350819\pi$
$398$	−20.0000	−1.00251
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	22.0000	1.09863	0.549314	−	0.835616i	$-0.314889\pi$
$401$	22.0000	1.09863	0.549314	+	0.835616i	$0.314889\pi$
$402$	0	0
$403$	−8.00000	−0.398508
$404$	−6.00000	−0.298511
$405$	0	0
$406$	−1.00000	−0.0496292
$407$	8.00000	0.396545
$408$	0	0
$409$	30.0000	1.48340	0.741702	−	0.670729i	$-0.234019\pi$
$409$	30.0000	1.48340	0.741702	+	0.670729i	$0.234019\pi$
$410$	9.00000	0.444478
$411$	0	0
$412$	16.0000	0.788263
$413$	−6.00000	−0.295241
$414$	0	0
$415$	−11.0000	−0.539969
$416$	5.00000	0.245145
$417$	0	0
$418$	0	0
$419$	−10.0000	−0.488532	−0.244266	−	0.969708i	$-0.578547\pi$
$419$	−10.0000	−0.488532	−0.244266	+	0.969708i	$0.578547\pi$
$420$	0	0
$421$	−14.0000	−0.682318	−0.341159	−	0.940006i	$-0.610819\pi$
$421$	−14.0000	−0.682318	−0.341159	+	0.940006i	$0.610819\pi$
$422$	−6.00000	−0.292075
$423$	0	0
$424$	−30.0000	−1.45693
$425$	−4.00000	−0.194029
$426$	0	0
$427$	1.00000	0.0483934
$428$	−13.0000	−0.628379
$429$	0	0
$430$	−8.00000	−0.385794
$431$	26.0000	1.25238	0.626188	−	0.779672i	$-0.284614\pi$
$431$	26.0000	1.25238	0.626188	+	0.779672i	$0.284614\pi$
$432$	0	0
$433$	−32.0000	−1.53782	−0.768911	−	0.639356i	$-0.779201\pi$
$433$	−32.0000	−1.53782	−0.768911	+	0.639356i	$0.779201\pi$
$434$	8.00000	0.384012
$435$	0	0
$436$	−1.00000	−0.0478913
$437$	0	0
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	−6.00000	−0.286039
$441$	0	0
$442$	−4.00000	−0.190261
$443$	17.0000	0.807694	0.403847	−	0.914826i	$-0.367673\pi$
$443$	17.0000	0.807694	0.403847	+	0.914826i	$0.367673\pi$
$444$	0	0
$445$	−5.00000	−0.237023
$446$	17.0000	0.804973
$447$	0	0
$448$	−7.00000	−0.330719
$449$	6.00000	0.283158	0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000	0.283158	0.141579	+	0.989927i	$0.454782\pi$
$450$	0	0
$451$	18.0000	0.847587
$452$	−4.00000	−0.188144
$453$	0	0
$454$	−4.00000	−0.187729
$455$	−1.00000	−0.0468807
$456$	0	0
$457$	−16.0000	−0.748448	−0.374224	−	0.927338i	$-0.622091\pi$
$457$	−16.0000	−0.748448	−0.374224	+	0.927338i	$0.622091\pi$
$458$	13.0000	0.607450
$459$	0	0
$460$	−3.00000	−0.139876
$461$	13.0000	0.605470	0.302735	−	0.953075i	$-0.402100\pi$
$461$	13.0000	0.605470	0.302735	+	0.953075i	$0.402100\pi$
$462$	0	0
$463$	−36.0000	−1.67306	−0.836531	−	0.547920i	$-0.815420\pi$
$463$	−36.0000	−1.67306	−0.836531	+	0.547920i	$0.815420\pi$
$464$	1.00000	0.0464238
$465$	0	0
$466$	−4.00000	−0.185296
$467$	−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
$469$	1.00000	0.0461757
$470$	13.0000	0.599645
$471$	0	0
$472$	18.0000	0.828517
$473$	−16.0000	−0.735681
$474$	0	0
$475$	0	0
$476$	−4.00000	−0.183340
$477$	0	0
$478$	24.0000	1.09773
$479$	6.00000	0.274147	0.137073	−	0.990561i	$-0.456230\pi$
$479$	6.00000	0.274147	0.137073	+	0.990561i	$0.456230\pi$
$480$	0	0
$481$	−4.00000	−0.182384
$482$	23.0000	1.04762
$483$	0	0
$484$	7.00000	0.318182
$485$	2.00000	0.0908153
$486$	0	0
$487$	−16.0000	−0.725029	−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000	−0.725029	−0.362515	+	0.931978i	$0.618082\pi$
$488$	−3.00000	−0.135804
$489$	0	0
$490$	−6.00000	−0.271052
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	0	0
$493$	4.00000	0.180151
$494$	0	0
$495$	0	0
$496$	−8.00000	−0.359211
$497$	6.00000	0.269137
$498$	0	0
$499$	−20.0000	−0.895323	−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000	−0.895323	−0.447661	+	0.894203i	$0.647743\pi$
$500$	1.00000	0.0447214
$501$	0	0
$502$	0	0
$503$	39.0000	1.73892	0.869462	−	0.494000i	$-0.164466\pi$
$503$	39.0000	1.73892	0.869462	+	0.494000i	$0.164466\pi$
$504$	0	0
$505$	−6.00000	−0.266996
$506$	6.00000	0.266733
$507$	0	0
$508$	−13.0000	−0.576782
$509$	15.0000	0.664863	0.332432	−	0.943127i	$-0.392131\pi$
$509$	15.0000	0.664863	0.332432	+	0.943127i	$0.392131\pi$
$510$	0	0
$511$	12.0000	0.530849
$512$	11.0000	0.486136
$513$	0	0
$514$	22.0000	0.970378
$515$	16.0000	0.705044
$516$	0	0
$517$	26.0000	1.14348
$518$	4.00000	0.175750
$519$	0	0
$520$	3.00000	0.131559
$521$	3.00000	0.131432	0.0657162	−	0.997838i	$-0.479067\pi$
$521$	3.00000	0.131432	0.0657162	+	0.997838i	$0.479067\pi$
$522$	0	0
$523$	21.0000	0.918266	0.459133	−	0.888368i	$-0.348160\pi$
$523$	21.0000	0.918266	0.459133	+	0.888368i	$0.348160\pi$
$524$	−14.0000	−0.611593
$525$	0	0
$526$	16.0000	0.697633
$527$	−32.0000	−1.39394
$528$	0	0
$529$	−14.0000	−0.608696
$530$	−10.0000	−0.434372
$531$	0	0
$532$	0	0
$533$	−9.00000	−0.389833
$534$	0	0
$535$	−13.0000	−0.562039
$536$	−3.00000	−0.129580
$537$	0	0
$538$	−9.00000	−0.388018
$539$	−12.0000	−0.516877
$540$	0	0
$541$	5.00000	0.214967	0.107483	−	0.994207i	$-0.465721\pi$
$541$	5.00000	0.214967	0.107483	+	0.994207i	$0.465721\pi$
$542$	4.00000	0.171815
$543$	0	0
$544$	20.0000	0.857493
$545$	−1.00000	−0.0428353
$546$	0	0
$547$	45.0000	1.92406	0.962031	−	0.272942i	$-0.0879967\pi$
$547$	45.0000	1.92406	0.962031	+	0.272942i	$0.0879967\pi$
$548$	−16.0000	−0.683486
$549$	0	0
$550$	−2.00000	−0.0852803
$551$	0	0
$552$	0	0
$553$	6.00000	0.255146
$554$	20.0000	0.849719
$555$	0	0
$556$	12.0000	0.508913
$557$	22.0000	0.932170	0.466085	−	0.884740i	$-0.345664\pi$
$557$	22.0000	0.932170	0.466085	+	0.884740i	$0.345664\pi$
$558$	0	0
$559$	8.00000	0.338364
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	27.0000	1.13893
$563$	−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
$565$	−4.00000	−0.168281
$566$	13.0000	0.546431
$567$	0	0
$568$	−18.0000	−0.755263
$569$	−38.0000	−1.59304	−0.796521	−	0.604610i	$-0.793329\pi$
$569$	−38.0000	−1.59304	−0.796521	+	0.604610i	$0.793329\pi$
$570$	0	0
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	2.00000	0.0836242
$573$	0	0
$574$	9.00000	0.375653
$575$	−3.00000	−0.125109
$576$	0	0
$577$	−34.0000	−1.41544	−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000	−1.41544	−0.707719	+	0.706494i	$0.750276\pi$
$578$	1.00000	0.0415945
$579$	0	0
$580$	−1.00000	−0.0415227
$581$	−11.0000	−0.456357
$582$	0	0
$583$	−20.0000	−0.828315
$584$	−36.0000	−1.48969
$585$	0	0
$586$	−4.00000	−0.165238
$587$	37.0000	1.52715	0.763577	−	0.645717i	$-0.223441\pi$
$587$	37.0000	1.52715	0.763577	+	0.645717i	$0.223441\pi$
$588$	0	0
$589$	0	0
$590$	6.00000	0.247016
$591$	0	0
$592$	−4.00000	−0.164399
$593$	−4.00000	−0.164260	−0.0821302	−	0.996622i	$-0.526172\pi$
$593$	−4.00000	−0.164260	−0.0821302	+	0.996622i	$0.526172\pi$
$594$	0	0
$595$	−4.00000	−0.163984
$596$	3.00000	0.122885
$597$	0	0
$598$	−3.00000	−0.122679
$599$	26.0000	1.06233	0.531166	−	0.847268i	$-0.321754\pi$
$599$	26.0000	1.06233	0.531166	+	0.847268i	$0.321754\pi$
$600$	0	0
$601$	10.0000	0.407909	0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000	0.407909	0.203954	+	0.978980i	$0.434621\pi$
$602$	−8.00000	−0.326056
$603$	0	0
$604$	−10.0000	−0.406894
$605$	7.00000	0.284590
$606$	0	0
$607$	−23.0000	−0.933541	−0.466771	−	0.884378i	$-0.654583\pi$
$607$	−23.0000	−0.933541	−0.466771	+	0.884378i	$0.654583\pi$
$608$	0	0
$609$	0	0
$610$	−1.00000	−0.0404888
$611$	−13.0000	−0.525924
$612$	0	0
$613$	24.0000	0.969351	0.484675	−	0.874694i	$-0.338938\pi$
$613$	24.0000	0.969351	0.484675	+	0.874694i	$0.338938\pi$
$614$	19.0000	0.766778
$615$	0	0
$616$	−6.00000	−0.241747
$617$	−48.0000	−1.93241	−0.966204	−	0.257780i	$-0.917009\pi$
$617$	−48.0000	−1.93241	−0.966204	+	0.257780i	$0.917009\pi$
$618$	0	0
$619$	40.0000	1.60774	0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000	1.60774	0.803868	+	0.594808i	$0.202772\pi$
$620$	8.00000	0.321288
$621$	0	0
$622$	4.00000	0.160385
$623$	−5.00000	−0.200321
$624$	0	0
$625$	1.00000	0.0400000
$626$	−14.0000	−0.559553
$627$	0	0
$628$	−18.0000	−0.718278
$629$	−16.0000	−0.637962
$630$	0	0
$631$	4.00000	0.159237	0.0796187	−	0.996825i	$-0.474630\pi$
$631$	4.00000	0.159237	0.0796187	+	0.996825i	$0.474630\pi$
$632$	−18.0000	−0.716002
$633$	0	0
$634$	18.0000	0.714871
$635$	−13.0000	−0.515889
$636$	0	0
$637$	6.00000	0.237729
$638$	2.00000	0.0791808
$639$	0	0
$640$	−3.00000	−0.118585
$641$	41.0000	1.61940	0.809701	−	0.586842i	$-0.199629\pi$
$641$	41.0000	1.61940	0.809701	+	0.586842i	$0.199629\pi$
$642$	0	0
$643$	−19.0000	−0.749287	−0.374643	−	0.927169i	$-0.622235\pi$
$643$	−19.0000	−0.749287	−0.374643	+	0.927169i	$0.622235\pi$
$644$	−3.00000	−0.118217
$645$	0	0
$646$	0	0
$647$	−7.00000	−0.275198	−0.137599	−	0.990488i	$-0.543939\pi$
$647$	−7.00000	−0.275198	−0.137599	+	0.990488i	$0.543939\pi$
$648$	0	0
$649$	12.0000	0.471041
$650$	1.00000	0.0392232
$651$	0	0
$652$	12.0000	0.469956
$653$	−36.0000	−1.40879	−0.704394	−	0.709809i	$-0.748781\pi$
$653$	−36.0000	−1.40879	−0.704394	+	0.709809i	$0.748781\pi$
$654$	0	0
$655$	−14.0000	−0.547025
$656$	−9.00000	−0.351391
$657$	0	0
$658$	13.0000	0.506793
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	0	0
$661$	26.0000	1.01128	0.505641	−	0.862744i	$-0.331256\pi$
$661$	26.0000	1.01128	0.505641	+	0.862744i	$0.331256\pi$
$662$	18.0000	0.699590
$663$	0	0
$664$	33.0000	1.28065
$665$	0	0
$666$	0	0
$667$	3.00000	0.116160
$668$	3.00000	0.116073
$669$	0	0
$670$	−1.00000	−0.0386334
$671$	−2.00000	−0.0772091
$672$	0	0
$673$	18.0000	0.693849	0.346925	−	0.937893i	$-0.387226\pi$
$673$	18.0000	0.693849	0.346925	+	0.937893i	$0.387226\pi$
$674$	−20.0000	−0.770371
$675$	0	0
$676$	−1.00000	−0.0384615
$677$	−42.0000	−1.61419	−0.807096	−	0.590421i	$-0.798962\pi$
$677$	−42.0000	−1.61419	−0.807096	+	0.590421i	$0.798962\pi$
$678$	0	0
$679$	2.00000	0.0767530
$680$	12.0000	0.460179
$681$	0	0
$682$	−16.0000	−0.612672
$683$	4.00000	0.153056	0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000	0.153056	0.0765279	+	0.997067i	$0.475617\pi$
$684$	0	0
$685$	−16.0000	−0.611329
$686$	−13.0000	−0.496342
$687$	0	0
$688$	8.00000	0.304997
$689$	10.0000	0.380970
$690$	0	0
$691$	−50.0000	−1.90209	−0.951045	−	0.309053i	$-0.899988\pi$
$691$	−50.0000	−1.90209	−0.951045	+	0.309053i	$0.899988\pi$
$692$	12.0000	0.456172
$693$	0	0
$694$	28.0000	1.06287
$695$	12.0000	0.455186
$696$	0	0
$697$	−36.0000	−1.36360
$698$	9.00000	0.340655
$699$	0	0
$700$	1.00000	0.0377964
$701$	7.00000	0.264386	0.132193	−	0.991224i	$-0.457798\pi$
$701$	7.00000	0.264386	0.132193	+	0.991224i	$0.457798\pi$
$702$	0	0
$703$	0	0
$704$	14.0000	0.527645
$705$	0	0
$706$	0	0
$707$	−6.00000	−0.225653
$708$	0	0
$709$	43.0000	1.61490	0.807449	−	0.589937i	$-0.200847\pi$
$709$	43.0000	1.61490	0.807449	+	0.589937i	$0.200847\pi$
$710$	−6.00000	−0.225176
$711$	0	0
$712$	15.0000	0.562149
$713$	−24.0000	−0.898807
$714$	0	0
$715$	2.00000	0.0747958
$716$	−6.00000	−0.224231
$717$	0	0
$718$	−8.00000	−0.298557
$719$	−26.0000	−0.969636	−0.484818	−	0.874615i	$-0.661114\pi$
$719$	−26.0000	−0.969636	−0.484818	+	0.874615i	$0.661114\pi$
$720$	0	0
$721$	16.0000	0.595871
$722$	19.0000	0.707107
$723$	0	0
$724$	7.00000	0.260153
$725$	−1.00000	−0.0371391
$726$	0	0
$727$	33.0000	1.22390	0.611951	−	0.790896i	$-0.290385\pi$
$727$	33.0000	1.22390	0.611951	+	0.790896i	$0.290385\pi$
$728$	3.00000	0.111187
$729$	0	0
$730$	−12.0000	−0.444140
$731$	32.0000	1.18356
$732$	0	0
$733$	−14.0000	−0.517102	−0.258551	−	0.965998i	$-0.583245\pi$
$733$	−14.0000	−0.517102	−0.258551	+	0.965998i	$0.583245\pi$
$734$	32.0000	1.18114
$735$	0	0
$736$	15.0000	0.552907
$737$	−2.00000	−0.0736709
$738$	0	0
$739$	6.00000	0.220714	0.110357	−	0.993892i	$-0.464801\pi$
$739$	6.00000	0.220714	0.110357	+	0.993892i	$0.464801\pi$
$740$	4.00000	0.147043
$741$	0	0
$742$	−10.0000	−0.367112
$743$	33.0000	1.21065	0.605326	−	0.795977i	$-0.293043\pi$
$743$	33.0000	1.21065	0.605326	+	0.795977i	$0.293043\pi$
$744$	0	0
$745$	3.00000	0.109911
$746$	14.0000	0.512576
$747$	0	0
$748$	8.00000	0.292509
$749$	−13.0000	−0.475010
$750$	0	0
$751$	−22.0000	−0.802791	−0.401396	−	0.915905i	$-0.631475\pi$
$751$	−22.0000	−0.802791	−0.401396	+	0.915905i	$0.631475\pi$
$752$	−13.0000	−0.474061
$753$	0	0
$754$	−1.00000	−0.0364179
$755$	−10.0000	−0.363937
$756$	0	0
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	26.0000	0.944363
$759$	0	0
$760$	0	0
$761$	27.0000	0.978749	0.489375	−	0.872074i	$-0.337225\pi$
$761$	27.0000	0.978749	0.489375	+	0.872074i	$0.337225\pi$
$762$	0	0
$763$	−1.00000	−0.0362024
$764$	12.0000	0.434145
$765$	0	0
$766$	12.0000	0.433578
$767$	−6.00000	−0.216647
$768$	0	0
$769$	17.0000	0.613036	0.306518	−	0.951865i	$-0.400836\pi$
$769$	17.0000	0.613036	0.306518	+	0.951865i	$0.400836\pi$
$770$	−2.00000	−0.0720750
$771$	0	0
$772$	2.00000	0.0719816
$773$	−8.00000	−0.287740	−0.143870	−	0.989597i	$-0.545955\pi$
$773$	−8.00000	−0.287740	−0.143870	+	0.989597i	$0.545955\pi$
$774$	0	0
$775$	8.00000	0.287368
$776$	−6.00000	−0.215387
$777$	0	0
$778$	31.0000	1.11140
$779$	0	0
$780$	0	0
$781$	−12.0000	−0.429394
$782$	−12.0000	−0.429119
$783$	0	0
$784$	6.00000	0.214286
$785$	−18.0000	−0.642448
$786$	0	0
$787$	−28.0000	−0.998092	−0.499046	−	0.866575i	$-0.666316\pi$
$787$	−28.0000	−0.998092	−0.499046	+	0.866575i	$0.666316\pi$
$788$	24.0000	0.854965
$789$	0	0
$790$	−6.00000	−0.213470
$791$	−4.00000	−0.142224
$792$	0	0
$793$	1.00000	0.0355110
$794$	−18.0000	−0.638796
$795$	0	0
$796$	−20.0000	−0.708881
$797$	30.0000	1.06265	0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000	1.06265	0.531327	+	0.847167i	$0.321693\pi$
$798$	0	0
$799$	−52.0000	−1.83963
$800$	−5.00000	−0.176777
$801$	0	0
$802$	−22.0000	−0.776847
$803$	−24.0000	−0.846942
$804$	0	0
$805$	−3.00000	−0.105736
$806$	8.00000	0.281788
$807$	0	0
$808$	18.0000	0.633238
$809$	34.0000	1.19538	0.597688	−	0.801729i	$-0.296086\pi$
$809$	34.0000	1.19538	0.597688	+	0.801729i	$0.296086\pi$
$810$	0	0
$811$	54.0000	1.89620	0.948098	−	0.317978i	$-0.103004\pi$
$811$	54.0000	1.89620	0.948098	+	0.317978i	$0.103004\pi$
$812$	−1.00000	−0.0350931
$813$	0	0
$814$	−8.00000	−0.280400
$815$	12.0000	0.420342
$816$	0	0
$817$	0	0
$818$	−30.0000	−1.04893
$819$	0	0
$820$	9.00000	0.314294
$821$	−37.0000	−1.29131	−0.645654	−	0.763630i	$-0.723415\pi$
$821$	−37.0000	−1.29131	−0.645654	+	0.763630i	$0.723415\pi$
$822$	0	0
$823$	−37.0000	−1.28974	−0.644869	−	0.764293i	$-0.723088\pi$
$823$	−37.0000	−1.28974	−0.644869	+	0.764293i	$0.723088\pi$
$824$	−48.0000	−1.67216
$825$	0	0
$826$	6.00000	0.208767
$827$	−41.0000	−1.42571	−0.712855	−	0.701312i	$-0.752598\pi$
$827$	−41.0000	−1.42571	−0.712855	+	0.701312i	$0.752598\pi$
$828$	0	0
$829$	−11.0000	−0.382046	−0.191023	−	0.981586i	$-0.561180\pi$
$829$	−11.0000	−0.382046	−0.191023	+	0.981586i	$0.561180\pi$
$830$	11.0000	0.381816
$831$	0	0
$832$	−7.00000	−0.242681
$833$	24.0000	0.831551
$834$	0	0
$835$	3.00000	0.103819
$836$	0	0
$837$	0	0
$838$	10.0000	0.345444
$839$	−28.0000	−0.966667	−0.483334	−	0.875436i	$-0.660574\pi$
$839$	−28.0000	−0.966667	−0.483334	+	0.875436i	$0.660574\pi$
$840$	0	0
$841$	−28.0000	−0.965517
$842$	14.0000	0.482472
$843$	0	0
$844$	−6.00000	−0.206529
$845$	−1.00000	−0.0344010
$846$	0	0
$847$	7.00000	0.240523
$848$	10.0000	0.343401
$849$	0	0
$850$	4.00000	0.137199
$851$	−12.0000	−0.411355
$852$	0	0
$853$	42.0000	1.43805	0.719026	−	0.694983i	$-0.244588\pi$
$853$	42.0000	1.43805	0.719026	+	0.694983i	$0.244588\pi$
$854$	−1.00000	−0.0342193
$855$	0	0
$856$	39.0000	1.33299
$857$	−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
$859$	−14.0000	−0.477674	−0.238837	−	0.971060i	$-0.576766\pi$
$859$	−14.0000	−0.477674	−0.238837	+	0.971060i	$0.576766\pi$
$860$	−8.00000	−0.272798
$861$	0	0
$862$	−26.0000	−0.885564
$863$	27.0000	0.919091	0.459545	−	0.888154i	$-0.348012\pi$
$863$	27.0000	0.919091	0.459545	+	0.888154i	$0.348012\pi$
$864$	0	0
$865$	12.0000	0.408012
$866$	32.0000	1.08740
$867$	0	0
$868$	8.00000	0.271538
$869$	−12.0000	−0.407072
$870$	0	0
$871$	1.00000	0.0338837
$872$	3.00000	0.101593
$873$	0	0
$874$	0	0
$875$	1.00000	0.0338062
$876$	0	0
$877$	−18.0000	−0.607817	−0.303908	−	0.952701i	$-0.598292\pi$
$877$	−18.0000	−0.607817	−0.303908	+	0.952701i	$0.598292\pi$
$878$	0	0
$879$	0	0
$880$	2.00000	0.0674200
$881$	−43.0000	−1.44871	−0.724353	−	0.689429i	$-0.757862\pi$
$881$	−43.0000	−1.44871	−0.724353	+	0.689429i	$0.757862\pi$
$882$	0	0
$883$	−7.00000	−0.235569	−0.117784	−	0.993039i	$-0.537579\pi$
$883$	−7.00000	−0.235569	−0.117784	+	0.993039i	$0.537579\pi$
$884$	−4.00000	−0.134535
$885$	0	0
$886$	−17.0000	−0.571126
$887$	−20.0000	−0.671534	−0.335767	−	0.941945i	$-0.608996\pi$
$887$	−20.0000	−0.671534	−0.335767	+	0.941945i	$0.608996\pi$
$888$	0	0
$889$	−13.0000	−0.436006
$890$	5.00000	0.167600
$891$	0	0
$892$	17.0000	0.569202
$893$	0	0
$894$	0	0
$895$	−6.00000	−0.200558
$896$	−3.00000	−0.100223
$897$	0	0
$898$	−6.00000	−0.200223
$899$	−8.00000	−0.266815
$900$	0	0
$901$	40.0000	1.33259
$902$	−18.0000	−0.599334
$903$	0	0
$904$	12.0000	0.399114
$905$	7.00000	0.232688
$906$	0	0
$907$	−13.0000	−0.431658	−0.215829	−	0.976431i	$-0.569245\pi$
$907$	−13.0000	−0.431658	−0.215829	+	0.976431i	$0.569245\pi$
$908$	−4.00000	−0.132745
$909$	0	0
$910$	1.00000	0.0331497
$911$	30.0000	0.993944	0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000	0.993944	0.496972	+	0.867766i	$0.334445\pi$
$912$	0	0
$913$	22.0000	0.728094
$914$	16.0000	0.529233
$915$	0	0
$916$	13.0000	0.429532
$917$	−14.0000	−0.462321
$918$	0	0
$919$	−10.0000	−0.329870	−0.164935	−	0.986304i	$-0.552741\pi$
$919$	−10.0000	−0.329870	−0.164935	+	0.986304i	$0.552741\pi$
$920$	9.00000	0.296721
$921$	0	0
$922$	−13.0000	−0.428132
$923$	6.00000	0.197492
$924$	0	0
$925$	4.00000	0.131519
$926$	36.0000	1.18303
$927$	0	0
$928$	5.00000	0.164133
$929$	−26.0000	−0.853032	−0.426516	−	0.904480i	$-0.640259\pi$
$929$	−26.0000	−0.853032	−0.426516	+	0.904480i	$0.640259\pi$
$930$	0	0
$931$	0	0
$932$	−4.00000	−0.131024
$933$	0	0
$934$	28.0000	0.916188
$935$	8.00000	0.261628
$936$	0	0
$937$	0	0		−	1.00000i	$-0.5\pi$
$937$	0	0			1.00000i	$0.5\pi$
$938$	−1.00000	−0.0326512
$939$	0	0
$940$	13.0000	0.424013
$941$	−3.00000	−0.0977972	−0.0488986	−	0.998804i	$-0.515571\pi$
$941$	−3.00000	−0.0977972	−0.0488986	+	0.998804i	$0.515571\pi$
$942$	0	0
$943$	−27.0000	−0.879241
$944$	−6.00000	−0.195283
$945$	0	0
$946$	16.0000	0.520205
$947$	3.00000	0.0974869	0.0487435	−	0.998811i	$-0.484478\pi$
$947$	3.00000	0.0974869	0.0487435	+	0.998811i	$0.484478\pi$
$948$	0	0
$949$	12.0000	0.389536
$950$	0	0
$951$	0	0
$952$	12.0000	0.388922
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	0	0
$955$	12.0000	0.388311
$956$	24.0000	0.776215
$957$	0	0
$958$	−6.00000	−0.193851
$959$	−16.0000	−0.516667
$960$	0	0
$961$	33.0000	1.06452
$962$	4.00000	0.128965
$963$	0	0
$964$	23.0000	0.740780
$965$	2.00000	0.0643823
$966$	0	0
$967$	43.0000	1.38279	0.691393	−	0.722478i	$-0.256997\pi$
$967$	43.0000	1.38279	0.691393	+	0.722478i	$0.256997\pi$
$968$	−21.0000	−0.674966
$969$	0	0
$970$	−2.00000	−0.0642161
$971$	8.00000	0.256732	0.128366	−	0.991727i	$-0.459027\pi$
$971$	8.00000	0.256732	0.128366	+	0.991727i	$0.459027\pi$
$972$	0	0
$973$	12.0000	0.384702
$974$	16.0000	0.512673
$975$	0	0
$976$	1.00000	0.0320092
$977$	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
$979$	10.0000	0.319601
$980$	−6.00000	−0.191663
$981$	0	0
$982$	0	0
$983$	−31.0000	−0.988746	−0.494373	−	0.869250i	$-0.664602\pi$
$983$	−31.0000	−0.988746	−0.494373	+	0.869250i	$0.664602\pi$
$984$	0	0
$985$	24.0000	0.764704
$986$	−4.00000	−0.127386
$987$	0	0
$988$	0	0
$989$	24.0000	0.763156
$990$	0	0
$991$	30.0000	0.952981	0.476491	−	0.879180i	$-0.341909\pi$
$991$	30.0000	0.952981	0.476491	+	0.879180i	$0.341909\pi$
$992$	−40.0000	−1.27000
$993$	0	0
$994$	−6.00000	−0.190308
$995$	−20.0000	−0.634043
$996$	0	0
$997$	50.0000	1.58352	0.791758	−	0.610835i	$-0.209166\pi$
$997$	50.0000	1.58352	0.791758	+	0.610835i	$0.209166\pi$
$998$	20.0000	0.633089
$999$	0	0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.c.196.1	✓	2	9.4	even	3
585.2.i.c.391.1	yes	2	9.7	even	3
1755.2.i.c.586.1		2	9.5	odd	6
1755.2.i.c.1171.1		2	9.2	odd	6
5265.2.a.d.1.1		1	1.1	even	1	trivial
5265.2.a.l.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)

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L-functions

Modular forms

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Fields

Representations

Groups

Database

Properties

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