LMFDB - Embedded newform 1617.2.c.a.538.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,2,Mod(538,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1617.538");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1617.c (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$12.9118100068$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			538.10
Character	$\chi$	$=$	1617.538
Dual form			1617.2.c.a.538.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.07576i q^{2} +1.00000i q^{3} +0.842743 q^{4} -3.36307i q^{5} +1.07576 q^{6} -3.05811i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.07576i q^{2} +1.00000i q^{3} +0.842743 q^{4} -3.36307i q^{5} +1.07576 q^{6} -3.05811i q^{8} -1.00000 q^{9} -3.61785 q^{10} +(-3.27999 + 0.491622i) q^{11} +0.842743i q^{12} +4.53855 q^{13} +3.36307 q^{15} -1.60430 q^{16} +1.76157 q^{17} +1.07576i q^{18} +7.04969 q^{19} -2.83420i q^{20} +(0.528867 + 3.52847i) q^{22} +3.35161 q^{23} +3.05811 q^{24} -6.31022 q^{25} -4.88239i q^{26} -1.00000i q^{27} -3.85686i q^{29} -3.61785i q^{30} +3.22070i q^{31} -4.39037i q^{32} +(-0.491622 - 3.27999i) q^{33} -1.89502i q^{34} -0.842743 q^{36} -9.04886 q^{37} -7.58377i q^{38} +4.53855i q^{39} -10.2846 q^{40} -6.67488 q^{41} -10.7063i q^{43} +(-2.76418 + 0.414311i) q^{44} +3.36307i q^{45} -3.60552i q^{46} -5.21495i q^{47} -1.60430i q^{48} +6.78828i q^{50} +1.76157i q^{51} +3.82483 q^{52} -11.0581 q^{53} -1.07576 q^{54} +(1.65336 + 11.0308i) q^{55} +7.04969i q^{57} -4.14906 q^{58} -4.52604i q^{59} +2.83420 q^{60} +3.44862 q^{61} +3.46470 q^{62} -7.93158 q^{64} -15.2635i q^{65} +(-3.52847 + 0.528867i) q^{66} +0.302543 q^{67} +1.48455 q^{68} +3.35161i q^{69} +2.04994 q^{71} +3.05811i q^{72} +10.1578 q^{73} +9.73439i q^{74} -6.31022i q^{75} +5.94108 q^{76} +4.88239 q^{78} +0.790546i q^{79} +5.39537i q^{80} +1.00000 q^{81} +7.18056i q^{82} -1.19239 q^{83} -5.92426i q^{85} -11.5174 q^{86} +3.85686 q^{87} +(1.50343 + 10.0305i) q^{88} +8.59780i q^{89} +3.61785 q^{90} +2.82454 q^{92} -3.22070 q^{93} -5.61003 q^{94} -23.7086i q^{95} +4.39037 q^{96} +5.01177i q^{97} +(3.27999 - 0.491622i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 24 q^{4} - 32 q^{9}+O(q^{10}) $ 32 * q - 24 * q^4 - 32 * q^9	$ 32 q - 24 q^{4} - 32 q^{9} - 4 q^{11} + 8 q^{15} + 40 q^{16} + 8 q^{22} - 48 q^{23} + 24 q^{36} + 64 q^{37} + 56 q^{44} - 72 q^{53} - 24 q^{58} + 8 q^{64} - 40 q^{67} + 72 q^{71} - 48 q^{78} + 32 q^{81} - 128 q^{86} - 48 q^{88} - 16 q^{92} - 32 q^{93} + 4 q^{99}+O(q^{100}) $ 32 * q - 24 * q^4 - 32 * q^9 - 4 * q^11 + 8 * q^15 + 40 * q^16 + 8 * q^22 - 48 * q^23 + 24 * q^36 + 64 * q^37 + 56 * q^44 - 72 * q^53 - 24 * q^58 + 8 * q^64 - 40 * q^67 + 72 * q^71 - 48 * q^78 + 32 * q^81 - 128 * q^86 - 48 * q^88 - 16 * q^92 - 32 * q^93 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1617\mathbb{Z}\right)^\times$.

$n$	$199$	$442$	$1079$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	1.07576i		−	0.760676i	−0.924847	−	0.380338i	$-0.875808\pi$
$2$		−	1.07576i		−	0.760676i	0.924847	−	0.380338i	$-0.124192\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.842743			0.421371
$5$		−	3.36307i		−	1.50401i	−0.659158	−	0.752005i	$-0.729087\pi$
$5$		−	3.36307i		−	1.50401i	0.659158	−	0.752005i	$-0.270913\pi$
$6$	1.07576			0.439177
$7$		0			0
$7$		0			0
$8$		−	3.05811i		−	1.08120i
$9$	−1.00000			−0.333333
$10$	−3.61785			−1.14406
$11$	−3.27999	+	0.491622i	−0.988953	+	0.148230i
$11$	−3.27999	+	0.491622i	−0.988953	+	0.148230i
$12$			0.842743i			0.243279i
$13$	4.53855			1.25877			0.629384	−	0.777094i	$-0.283307\pi$
$13$	4.53855			1.25877			0.629384	+	0.777094i	$0.283307\pi$
$14$		0			0
$15$	3.36307			0.868340
$16$	−1.60430			−0.401075
$17$	1.76157			0.427242			0.213621	−	0.976917i	$-0.431474\pi$
$17$	1.76157			0.427242			0.213621	+	0.976917i	$0.431474\pi$
$18$			1.07576i			0.253559i
$19$	7.04969			1.61731			0.808655	−	0.588283i	$-0.200196\pi$
$19$	7.04969			1.61731			0.808655	+	0.588283i	$0.200196\pi$
$20$		−	2.83420i		−	0.633746i
$21$		0			0
$22$	0.528867	+	3.52847i	0.112755	+	0.752273i
$23$	3.35161			0.698859			0.349429	−	0.936963i	$-0.386375\pi$
$23$	3.35161			0.698859			0.349429	+	0.936963i	$0.386375\pi$
$24$	3.05811			0.624233
$25$	−6.31022			−1.26204
$26$		−	4.88239i		−	0.957515i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$		−	3.85686i		−	0.716202i	−0.933683	−	0.358101i	$-0.883424\pi$
$29$		−	3.85686i		−	0.716202i	0.933683	−	0.358101i	$-0.116576\pi$
$30$		−	3.61785i		−	0.660526i
$31$			3.22070i			0.578455i	0.957260	+	0.289228i	$0.0933985\pi$
$31$			3.22070i			0.578455i	−0.957260	+	0.289228i	$0.906602\pi$
$32$		−	4.39037i		−	0.776115i
$33$	−0.491622	−	3.27999i	−0.0855805	−	0.570972i
$34$		−	1.89502i		−	0.324993i
$35$		0			0
$36$	−0.842743			−0.140457
$37$	−9.04886			−1.48762			−0.743812	−	0.668389i	$-0.766984\pi$
$37$	−9.04886			−1.48762			−0.743812	+	0.668389i	$0.766984\pi$
$38$		−	7.58377i		−	1.23025i
$39$			4.53855i			0.726750i
$40$	−10.2846			−1.62614
$41$	−6.67488			−1.04244			−0.521220	−	0.853422i	$-0.674523\pi$
$41$	−6.67488			−1.04244			−0.521220	+	0.853422i	$0.674523\pi$
$42$		0			0
$43$		−	10.7063i		−	1.63269i	−0.577564	−	0.816345i	$-0.695997\pi$
$43$		−	10.7063i		−	1.63269i	0.577564	−	0.816345i	$-0.304003\pi$
$44$	−2.76418	+	0.414311i	−0.416716	+	0.0624598i
$45$			3.36307i			0.501336i
$46$		−	3.60552i		−	0.531605i
$47$		−	5.21495i		−	0.760679i	−0.924847	−	0.380339i	$-0.875807\pi$
$47$		−	5.21495i		−	0.760679i	0.924847	−	0.380339i	$-0.124193\pi$
$48$		−	1.60430i		−	0.231561i
$49$		0			0
$50$			6.78828i			0.960008i
$51$			1.76157i			0.246669i
$52$	3.82483			0.530409
$53$	−11.0581			−1.51894			−0.759470	−	0.650542i	$-0.774542\pi$
$53$	−11.0581			−1.51894			−0.759470	+	0.650542i	$0.774542\pi$
$54$	−1.07576			−0.146392
$55$	1.65336	+	11.0308i	0.222939	+	1.48739i
$56$		0			0
$57$			7.04969i			0.933755i
$58$	−4.14906			−0.544798
$59$		−	4.52604i		−	0.589240i	−0.955615	−	0.294620i	$-0.904807\pi$
$59$		−	4.52604i		−	0.589240i	0.955615	−	0.294620i	$-0.0951930\pi$
$60$	2.83420			0.365894
$61$	3.44862			0.441550			0.220775	−	0.975325i	$-0.429141\pi$
$61$	3.44862			0.441550			0.220775	+	0.975325i	$0.429141\pi$
$62$	3.46470			0.440017
$63$		0			0
$64$	−7.93158			−0.991448
$65$		−	15.2635i		−	1.89320i
$66$	−3.52847	+	0.528867i	−0.434325	+	0.0650991i
$67$	0.302543			0.0369615			0.0184808	−	0.999829i	$-0.494117\pi$
$67$	0.302543			0.0369615			0.0184808	+	0.999829i	$0.494117\pi$
$68$	1.48455			0.180028
$69$			3.35161i			0.403486i
$70$		0			0
$71$	2.04994			0.243284			0.121642	−	0.992574i	$-0.461184\pi$
$71$	2.04994			0.243284			0.121642	+	0.992574i	$0.461184\pi$
$72$			3.05811i			0.360401i
$73$	10.1578			1.18888			0.594440	−	0.804140i	$-0.297374\pi$
$73$	10.1578			1.18888			0.594440	+	0.804140i	$0.297374\pi$
$74$			9.73439i			1.13160i
$75$		−	6.31022i		−	0.728642i
$76$	5.94108			0.681488
$77$		0			0
$78$	4.88239			0.552822
$79$			0.790546i			0.0889434i	0.999011	+	0.0444717i	$0.0141605\pi$
$79$			0.790546i			0.0889434i	−0.999011	+	0.0444717i	$0.985840\pi$
$80$			5.39537i			0.603221i
$81$	1.00000			0.111111
$82$			7.18056i			0.792960i
$83$	−1.19239			−0.130882			−0.0654408	−	0.997856i	$-0.520845\pi$
$83$	−1.19239			−0.130882			−0.0654408	+	0.997856i	$0.520845\pi$
$84$		0			0
$85$		−	5.92426i		−	0.642577i
$86$	−11.5174			−1.24195
$87$	3.85686			0.413499
$88$	1.50343	+	10.0305i	0.160267	+	1.06926i
$89$			8.59780i			0.911365i	0.890142	+	0.455682i	$0.150605\pi$
$89$			8.59780i			0.911365i	−0.890142	+	0.455682i	$0.849395\pi$
$90$	3.61785			0.381355
$91$		0			0
$92$	2.82454			0.294479
$93$	−3.22070			−0.333971
$94$	−5.61003			−0.578630
$95$		−	23.7086i		−	2.43245i
$96$	4.39037			0.448090
$97$			5.01177i			0.508868i	0.967090	+	0.254434i	$0.0818891\pi$
$97$			5.01177i			0.508868i	−0.967090	+	0.254434i	$0.918111\pi$
$98$		0			0
$99$	3.27999	−	0.491622i	0.329651	−	0.0494099i
$100$	−5.31789			−0.531789
$101$	−11.1382			−1.10829			−0.554144	−	0.832421i	$-0.686954\pi$
$101$	−11.1382			−1.10829			−0.554144	+	0.832421i	$0.686954\pi$
$102$	1.89502			0.187635
$103$		−	7.77131i		−	0.765730i	−0.923804	−	0.382865i	$-0.874937\pi$
$103$		−	7.77131i		−	0.765730i	0.923804	−	0.382865i	$-0.125063\pi$
$104$		−	13.8794i		−	1.36098i
$105$		0			0
$106$			11.8958i			1.15542i
$107$			17.4321i			1.68523i	0.538520	+	0.842613i	$0.318984\pi$
$107$			17.4321i			1.68523i	−0.538520	+	0.842613i	$0.681016\pi$
$108$		−	0.842743i		−	0.0810929i
$109$			11.9884i			1.14828i	0.818756	+	0.574142i	$0.194664\pi$
$109$			11.9884i			1.14828i	−0.818756	+	0.574142i	$0.805336\pi$
$110$	11.8665	−	1.77862i	1.13143	−	0.169584i
$111$		−	9.04886i		−	0.858880i
$112$		0			0
$113$	3.78756			0.356304			0.178152	−	0.984003i	$-0.442988\pi$
$113$	3.78756			0.356304			0.178152	+	0.984003i	$0.442988\pi$
$114$	7.58377			0.710285
$115$		−	11.2717i		−	1.05109i
$116$		−	3.25034i		−	0.301787i
$117$	−4.53855			−0.419589
$118$	−4.86892			−0.448221
$119$		0			0
$120$		−	10.2846i		−	0.938853i
$121$	10.5166	−	3.22503i	0.956056	−	0.293185i
$122$		−	3.70988i		−	0.335877i
$123$		−	6.67488i		−	0.601853i
$124$			2.71422i			0.243745i
$125$			4.40637i			0.394117i
$126$		0			0
$127$			2.54037i			0.225421i	0.993628	+	0.112711i	$0.0359533\pi$
$127$			2.54037i			0.225421i	−0.993628	+	0.112711i	$0.964047\pi$
$128$		−	0.248273i		−	0.0219445i
$129$	10.7063			0.942635
$130$	−16.4198			−1.44011
$131$	2.81643			0.246073			0.123036	−	0.992402i	$-0.460737\pi$
$131$	2.81643			0.246073			0.123036	+	0.992402i	$0.460737\pi$
$132$	−0.414311	−	2.76418i	−0.0360612	−	0.240591i
$133$		0			0
$134$		−	0.325464i		−	0.0281158i
$135$	−3.36307			−0.289447
$136$		−	5.38705i		−	0.461936i
$137$	12.3683			1.05669			0.528347	−	0.849028i	$-0.322812\pi$
$137$	12.3683			1.05669			0.528347	+	0.849028i	$0.322812\pi$
$138$	3.60552			0.306922
$139$	−12.6203			−1.07044			−0.535220	−	0.844712i	$-0.679771\pi$
$139$	−12.6203			−1.07044			−0.535220	+	0.844712i	$0.679771\pi$
$140$		0			0
$141$	5.21495			0.439178
$142$		−	2.20525i		−	0.185060i
$143$	−14.8864	+	2.23125i	−1.24486	+	0.186587i
$144$	1.60430			0.133692
$145$	−12.9709			−1.07717
$146$		−	10.9273i		−	0.904352i
$147$		0			0
$148$	−7.62586			−0.626842
$149$			2.67275i			0.218960i	0.993989	+	0.109480i	$0.0349186\pi$
$149$			2.67275i			0.218960i	−0.993989	+	0.109480i	$0.965081\pi$
$150$	−6.78828			−0.554261
$151$		−	9.16166i		−	0.745565i	−0.927919	−	0.372783i	$-0.878404\pi$
$151$		−	9.16166i		−	0.745565i	0.927919	−	0.372783i	$-0.121596\pi$
$152$		−	21.5587i		−	1.74864i
$153$	−1.76157			−0.142414
$154$		0			0
$155$	10.8314			0.870003
$156$			3.82483i			0.306232i
$157$		−	0.879280i		−	0.0701742i	−0.999384	−	0.0350871i	$-0.988829\pi$
$157$		−	0.879280i		−	0.0701742i	0.999384	−	0.0350871i	$-0.0111709\pi$
$158$	0.850437			0.0676572
$159$		−	11.0581i		−	0.876961i
$160$	−14.7651			−1.16728
$161$		0			0
$162$		−	1.07576i		−	0.0845196i
$163$	−10.2998			−0.806745			−0.403373	−	0.915036i	$-0.632162\pi$
$163$	−10.2998			−0.806745			−0.403373	+	0.915036i	$0.632162\pi$
$164$	−5.62520			−0.439254
$165$	−11.0308	+	1.65336i	−0.858748	+	0.128714i
$166$			1.28272i			0.0995586i
$167$	16.1423			1.24913			0.624563	−	0.780974i	$-0.285277\pi$
$167$	16.1423			1.24913			0.624563	+	0.780974i	$0.285277\pi$
$168$		0			0
$169$	7.59847			0.584497
$170$	−6.37308			−0.488793
$171$	−7.04969			−0.539104
$172$		−	9.02263i		−	0.687969i
$173$	9.31647			0.708318			0.354159	−	0.935185i	$-0.384767\pi$
$173$	9.31647			0.708318			0.354159	+	0.935185i	$0.384767\pi$
$174$		−	4.14906i		−	0.314539i
$175$		0			0
$176$	5.26208	−	0.788710i	0.396644	−	0.0594512i
$177$	4.52604			0.340198
$178$	9.24916			0.693254
$179$	18.9548			1.41675			0.708373	−	0.705839i	$-0.249430\pi$
$179$	18.9548			1.41675			0.708373	+	0.705839i	$0.249430\pi$
$180$			2.83420i			0.211249i
$181$		−	10.7034i		−	0.795578i	−0.917477	−	0.397789i	$-0.869778\pi$
$181$		−	10.7034i		−	0.795578i	0.917477	−	0.397789i	$-0.130222\pi$
$182$		0			0
$183$			3.44862i			0.254929i
$184$		−	10.2496i		−	0.755608i
$185$			30.4319i			2.23740i
$186$			3.46470i			0.254044i
$187$	−5.77791	+	0.866025i	−0.422523	+	0.0633300i
$188$		−	4.39486i		−	0.320528i
$189$		0			0
$190$	−25.5047			−1.85031
$191$	19.4034			1.40398			0.701989	−	0.712188i	$-0.252296\pi$
$191$	19.4034			1.40398			0.701989	+	0.712188i	$0.252296\pi$
$192$		−	7.93158i		−	0.572413i
$193$		−	0.704389i		−	0.0507030i	−0.999679	−	0.0253515i	$-0.991929\pi$
$193$		−	0.704389i		−	0.0507030i	0.999679	−	0.0253515i	$-0.00807051\pi$
$194$	5.39145			0.387084
$195$	15.2635			1.09304
$196$		0			0
$197$			19.8657i			1.41537i	0.706527	+	0.707686i	$0.250261\pi$
$197$			19.8657i			1.41537i	−0.706527	+	0.707686i	$0.749739\pi$
$198$	−0.528867	−	3.52847i	−0.0375850	−	0.250758i
$199$		−	15.4117i		−	1.09250i	−0.837621	−	0.546252i	$-0.816054\pi$
$199$		−	15.4117i		−	1.09250i	0.837621	−	0.546252i	$-0.183946\pi$
$200$			19.2973i			1.36453i
$201$			0.302543i			0.0213398i
$202$			11.9820i			0.843048i
$203$		0			0
$204$			1.48455i			0.103939i
$205$			22.4481i			1.56784i
$206$	−8.36006			−0.582473
$207$	−3.35161			−0.232953
$208$	−7.28120			−0.504860
$209$	−23.1229	+	3.46579i	−1.59944	+	0.239734i
$210$		0			0
$211$			19.8619i			1.36735i	0.729787	+	0.683675i	$0.239619\pi$
$211$			19.8619i			1.36735i	−0.729787	+	0.683675i	$0.760381\pi$
$212$	−9.31910			−0.640038
$213$			2.04994i			0.140460i
$214$	18.7527			1.28191
$215$	−36.0059			−2.45558
$216$	−3.05811			−0.208078
$217$		0			0
$218$	12.8967			0.873473
$219$			10.1578i			0.686400i
$220$	1.39336	+	9.29614i	0.0939401	+	0.626745i
$221$	7.99496			0.537799
$222$	−9.73439			−0.653330
$223$		−	3.03619i		−	0.203318i	−0.994819	−	0.101659i	$-0.967585\pi$
$223$		−	3.03619i		−	0.203318i	0.994819	−	0.101659i	$-0.0324151\pi$
$224$		0			0
$225$	6.31022			0.420682
$226$		−	4.07451i		−	0.271032i
$227$	17.7873			1.18058			0.590291	−	0.807190i	$-0.299013\pi$
$227$	17.7873			1.18058			0.590291	+	0.807190i	$0.299013\pi$
$228$			5.94108i			0.393457i
$229$			26.6141i			1.75871i	0.476167	+	0.879355i	$0.342026\pi$
$229$			26.6141i			1.75871i	−0.476167	+	0.879355i	$0.657974\pi$
$230$	−12.1256			−0.799539
$231$		0			0
$232$	−11.7947			−0.774360
$233$		−	6.83301i		−	0.447646i	−0.974630	−	0.223823i	$-0.928146\pi$
$233$		−	6.83301i		−	0.447646i	0.974630	−	0.223823i	$-0.0718537\pi$
$234$			4.88239i			0.319172i
$235$	−17.5382			−1.14407
$236$		−	3.81428i		−	0.248289i
$237$	−0.790546			−0.0513515
$238$		0			0
$239$		−	5.63815i		−	0.364701i	−0.983234	−	0.182351i	$-0.941629\pi$
$239$		−	5.63815i		−	0.364701i	0.983234	−	0.182351i	$-0.0583706\pi$
$240$	−5.39537			−0.348270
$241$	27.4430			1.76776			0.883879	−	0.467716i	$-0.154923\pi$
$241$	27.4430			1.76776			0.883879	+	0.467716i	$0.154923\pi$
$242$	−3.46935	−	11.3133i	−0.223019	−	0.727249i
$243$			1.00000i			0.0641500i
$244$	2.90630			0.186057
$245$		0			0
$246$	−7.18056			−0.457816
$247$	31.9954			2.03582
$248$	9.84925			0.625428
$249$		−	1.19239i		−	0.0755645i
$250$	4.74019			0.299796
$251$			13.5227i			0.853545i	0.904359	+	0.426773i	$0.140350\pi$
$251$			13.5227i			0.853545i	−0.904359	+	0.426773i	$0.859650\pi$
$252$		0			0
$253$	−10.9932	+	1.64773i	−0.691138	+	0.103592i
$254$	2.73282			0.171473
$255$	5.92426			0.370992
$256$	−16.1302			−1.00814
$257$			11.9597i			0.746027i	0.927826	+	0.373013i	$0.121675\pi$
$257$			11.9597i			0.746027i	−0.927826	+	0.373013i	$0.878325\pi$
$258$		−	11.5174i		−	0.717040i
$259$		0			0
$260$		−	12.8632i		−	0.797740i
$261$			3.85686i			0.238734i
$262$		−	3.02980i		−	0.187182i
$263$			3.70706i			0.228587i	0.993447	+	0.114294i	$0.0364605\pi$
$263$			3.70706i			0.228587i	−0.993447	+	0.114294i	$0.963540\pi$
$264$	−10.0305	+	1.50343i	−0.617337	+	0.0925299i
$265$			37.1890i			2.28450i
$266$		0			0
$267$	−8.59780			−0.526177
$268$	0.254966			0.0155745
$269$		−	4.14265i		−	0.252582i	−0.991993	−	0.126291i	$-0.959693\pi$
$269$		−	4.14265i		−	0.252582i	0.991993	−	0.126291i	$-0.0403073\pi$
$270$			3.61785i			0.220175i
$271$	28.7634			1.74725			0.873627	−	0.486597i	$-0.161762\pi$
$271$	28.7634			1.74725			0.873627	+	0.486597i	$0.161762\pi$
$272$	−2.82608			−0.171356
$273$		0			0
$274$		−	13.3053i		−	0.803803i
$275$	20.6974	−	3.10225i	1.24810	−	0.187073i
$276$			2.82454i			0.170017i
$277$		−	11.7521i		−	0.706115i	−0.935602	−	0.353058i	$-0.885142\pi$
$277$		−	11.7521i		−	0.706115i	0.935602	−	0.353058i	$-0.114858\pi$
$278$			13.5764i			0.814259i
$279$		−	3.22070i		−	0.192818i
$280$		0			0
$281$			9.06116i			0.540543i	0.962784	+	0.270272i	$0.0871135\pi$
$281$			9.06116i			0.540543i	−0.962784	+	0.270272i	$0.912887\pi$
$282$		−	5.61003i		−	0.334072i
$283$	−14.3501			−0.853024			−0.426512	−	0.904482i	$-0.640258\pi$
$283$	−14.3501			−0.853024			−0.426512	+	0.904482i	$0.640258\pi$
$284$	1.72758			0.102513
$285$	23.7086			1.40438
$286$	2.40029	+	16.0142i	0.141932	+	0.946938i
$287$		0			0
$288$			4.39037i			0.258705i
$289$	−13.8969			−0.817464
$290$			13.9536i			0.819381i
$291$	−5.01177			−0.293795
$292$	8.56040			0.500960
$293$	16.0376			0.936929			0.468464	−	0.883482i	$-0.344807\pi$
$293$	16.0376			0.936929			0.468464	+	0.883482i	$0.344807\pi$
$294$		0			0
$295$	−15.2214			−0.886222
$296$			27.6724i			1.60842i
$297$	0.491622	+	3.27999i	0.0285268	+	0.190324i
$298$	2.87523			0.166558
$299$	15.2114			0.879701
$300$		−	5.31789i		−	0.307029i
$301$		0			0
$302$	−9.85574			−0.567134
$303$		−	11.1382i		−	0.639870i
$304$	−11.3098			−0.648663
$305$		−	11.5979i		−	0.664096i
$306$			1.89502i			0.108331i
$307$	7.44188			0.424730			0.212365	−	0.977190i	$-0.431883\pi$
$307$	7.44188			0.424730			0.212365	+	0.977190i	$0.431883\pi$
$308$		0			0
$309$	7.77131			0.442094
$310$		−	11.6520i		−	0.661790i
$311$		−	15.7420i		−	0.892649i	−0.894871	−	0.446325i	$-0.852733\pi$
$311$		−	15.7420i		−	0.892649i	0.894871	−	0.446325i	$-0.147267\pi$
$312$	13.8794			0.785765
$313$			31.4543i			1.77790i	0.458002	+	0.888951i	$0.348565\pi$
$313$			31.4543i			1.77790i	−0.458002	+	0.888951i	$0.651435\pi$
$314$	−0.945893			−0.0533799
$315$		0			0
$316$			0.666227i			0.0374782i
$317$	−7.32612			−0.411476			−0.205738	−	0.978607i	$-0.565959\pi$
$317$	−7.32612			−0.411476			−0.205738	+	0.978607i	$0.565959\pi$
$318$	−11.8958			−0.667084
$319$	1.89612	+	12.6505i	0.106162	+	0.708290i
$320$			26.6744i			1.49115i
$321$	−17.4321			−0.972965
$322$		0			0
$323$	12.4185			0.690984
$324$	0.842743			0.0468190
$325$	−28.6393			−1.58862
$326$			11.0801i			0.613672i
$327$	−11.9884			−0.662962
$328$			20.4125i			1.12709i
$329$		0			0
$330$	1.77862	+	11.8665i	0.0979096	+	0.653229i
$331$	8.78604			0.482925			0.241462	−	0.970410i	$-0.422373\pi$
$331$	8.78604			0.482925			0.241462	+	0.970410i	$0.422373\pi$
$332$	−1.00488			−0.0551498
$333$	9.04886			0.495874
$334$		−	17.3652i		−	0.950181i
$335$		−	1.01747i		−	0.0555905i
$336$		0			0
$337$		−	25.4066i		−	1.38398i	−0.721905	−	0.691992i	$-0.756733\pi$
$337$		−	25.4066i		−	1.38398i	0.721905	−	0.691992i	$-0.243267\pi$
$338$		−	8.17412i		−	0.444613i
$339$			3.78756i			0.205712i
$340$		−	4.99263i		−	0.270763i
$341$	−1.58337	−	10.5639i	−0.0857443	−	0.572065i
$342$			7.58377i			0.410083i
$343$		0			0
$344$	−32.7409			−1.76527
$345$	11.2717			0.606847
$346$		−	10.0223i		−	0.538801i
$347$			1.62171i			0.0870578i	0.999052	+	0.0435289i	$0.0138601\pi$
$347$			1.62171i			0.0870578i	−0.999052	+	0.0435289i	$0.986140\pi$
$348$	3.25034			0.174237
$349$	7.14543			0.382486			0.191243	−	0.981543i	$-0.438748\pi$
$349$	7.14543			0.382486			0.191243	+	0.981543i	$0.438748\pi$
$350$		0			0
$351$		−	4.53855i		−	0.242250i
$352$	2.15841	+	14.4004i	0.115043	+	0.767542i
$353$			19.8267i			1.05527i	0.849472	+	0.527634i	$0.176921\pi$
$353$			19.8267i			1.05527i	−0.849472	+	0.527634i	$0.823079\pi$
$354$		−	4.86892i		−	0.258780i
$355$		−	6.89410i		−	0.365901i
$356$			7.24573i			0.384023i
$357$		0			0
$358$		−	20.3907i		−	1.07768i
$359$		−	14.9904i		−	0.791161i	−0.918431	−	0.395580i	$-0.870543\pi$
$359$		−	14.9904i		−	0.791161i	0.918431	−	0.395580i	$-0.129457\pi$
$360$	10.2846			0.542047
$361$	30.6982			1.61569
$362$	−11.5143			−0.605178
$363$	3.22503	+	10.5166i	0.169270	+	0.551979i
$364$		0			0
$365$		−	34.1613i		−	1.78809i
$366$	3.70988			0.193919
$367$		−	14.3471i		−	0.748915i	−0.927244	−	0.374457i	$-0.877829\pi$
$367$		−	14.3471i		−	0.748915i	0.927244	−	0.374457i	$-0.122171\pi$
$368$	−5.37698			−0.280295
$369$	6.67488			0.347480
$370$	32.7374			1.70194
$371$		0			0
$372$	−2.71422			−0.140726
$373$			0.969570i			0.0502024i	0.999685	+	0.0251012i	$0.00799081\pi$
$373$			0.969570i			0.0502024i	−0.999685	+	0.0251012i	$0.992009\pi$
$374$	0.931634	+	6.21564i	0.0481737	+	0.321403i
$375$	−4.40637			−0.227544
$376$	−15.9479			−0.822449
$377$		−	17.5046i		−	0.901532i
$378$		0			0
$379$	−28.4006			−1.45884			−0.729421	−	0.684065i	$-0.760211\pi$
$379$	−28.4006			−1.45884			−0.729421	+	0.684065i	$0.760211\pi$
$380$		−	19.9802i		−	1.02496i
$381$	−2.54037			−0.130147
$382$		−	20.8733i		−	1.06797i
$383$			10.6537i			0.544376i	0.962244	+	0.272188i	$0.0877473\pi$
$383$			10.6537i			0.544376i	−0.962244	+	0.272188i	$0.912253\pi$
$384$	0.248273			0.0126697
$385$		0			0
$386$	−0.757753			−0.0385686
$387$			10.7063i			0.544230i
$388$			4.22363i			0.214422i
$389$	−9.26567			−0.469788			−0.234894	−	0.972021i	$-0.575474\pi$
$389$	−9.26567			−0.469788			−0.234894	+	0.972021i	$0.575474\pi$
$390$		−	16.4198i		−	0.831449i
$391$	5.90408			0.298582
$392$		0			0
$393$			2.81643i			0.142070i
$394$	21.3707			1.07664
$395$	2.65866			0.133772
$396$	2.76418	−	0.414311i	0.138905	−	0.0208199i
$397$			25.2340i			1.26646i	0.773964	+	0.633230i	$0.218271\pi$
$397$			25.2340i			1.26646i	−0.773964	+	0.633230i	$0.781729\pi$
$398$	−16.5792			−0.831041
$399$		0			0
$400$	10.1235			0.506174
$401$	−26.3304			−1.31488			−0.657440	−	0.753507i	$-0.728361\pi$
$401$	−26.3304			−1.31488			−0.657440	+	0.753507i	$0.728361\pi$
$402$	0.325464			0.0162326
$403$			14.6173i			0.728141i
$404$	−9.38659			−0.467000
$405$		−	3.36307i		−	0.167112i
$406$		0			0
$407$	29.6801	−	4.44862i	1.47119	−	0.220510i
$408$	5.38705			0.266699
$409$	−34.7204			−1.71681			−0.858406	−	0.512971i	$-0.828545\pi$
$409$	−34.7204			−1.71681			−0.858406	+	0.512971i	$0.828545\pi$
$410$	24.1487			1.19262
$411$			12.3683i			0.610083i
$412$		−	6.54921i		−	0.322657i
$413$		0			0
$414$			3.60552i			0.177202i
$415$			4.01008i			0.196847i
$416$		−	19.9259i		−	0.976949i
$417$		−	12.6203i		−	0.618019i
$418$	3.72835	+	24.8747i	0.182360	+	1.21666i
$419$			9.71143i			0.474434i	0.971457	+	0.237217i	$0.0762353\pi$
$419$			9.71143i			0.474434i	−0.971457	+	0.237217i	$0.923765\pi$
$420$		0			0
$421$	6.61647			0.322467			0.161233	−	0.986916i	$-0.448453\pi$
$421$	6.61647			0.322467			0.161233	+	0.986916i	$0.448453\pi$
$422$	21.3666			1.04011
$423$			5.21495i			0.253560i
$424$			33.8167i			1.64228i
$425$	−11.1159			−0.539199
$426$	2.20525			0.106845
$427$		0			0
$428$			14.6908i			0.710106i
$429$	−2.23125	−	14.8864i	−0.107726	−	0.718722i
$430$			38.7337i			1.86790i
$431$			33.0175i			1.59040i	0.606350	+	0.795198i	$0.292633\pi$
$431$			33.0175i			1.59040i	−0.606350	+	0.795198i	$0.707367\pi$
$432$			1.60430i			0.0771869i
$433$		−	1.62159i		−	0.0779289i	−0.999241	−	0.0389644i	$-0.987594\pi$
$433$		−	1.62159i		−	0.0779289i	0.999241	−	0.0389644i	$-0.0124059\pi$
$434$		0			0
$435$		−	12.9709i		−	0.621907i
$436$			10.1032i			0.483854i
$437$	23.6278			1.13027
$438$	10.9273			0.522128
$439$	−8.65604			−0.413130			−0.206565	−	0.978433i	$-0.566229\pi$
$439$	−8.65604			−0.413130			−0.206565	+	0.978433i	$0.566229\pi$
$440$	33.7334	−	5.05615i	1.60818	−	0.241042i
$441$		0			0
$442$		−	8.60065i		−	0.409091i
$443$	29.2958			1.39189			0.695944	−	0.718096i	$-0.254986\pi$
$443$	29.2958			1.39189			0.695944	+	0.718096i	$0.254986\pi$
$444$		−	7.62586i		−	0.361907i
$445$	28.9150			1.37070
$446$	−3.26621			−0.154659
$447$	−2.67275			−0.126417
$448$		0			0
$449$	−11.3704			−0.536601			−0.268301	−	0.963335i	$-0.586462\pi$
$449$	−11.3704			−0.536601			−0.268301	+	0.963335i	$0.586462\pi$
$450$		−	6.78828i		−	0.320003i
$451$	21.8935	−	3.28152i	1.03092	−	0.154521i
$452$	3.19194			0.150136
$453$	9.16166			0.430452
$454$		−	19.1348i		−	0.898041i
$455$		0			0
$456$	21.5587			1.00958
$457$		−	2.37954i		−	0.111310i	−0.998450	−	0.0556550i	$-0.982275\pi$
$457$		−	2.37954i		−	0.111310i	0.998450	−	0.0556550i	$-0.0177247\pi$
$458$	28.6304			1.33781
$459$		−	1.76157i		−	0.0822228i
$460$		−	9.49913i		−	0.442899i
$461$	−3.88940			−0.181147			−0.0905737	−	0.995890i	$-0.528870\pi$
$461$	−3.88940			−0.181147			−0.0905737	+	0.995890i	$0.528870\pi$
$462$		0			0
$463$	42.6876			1.98386			0.991931	−	0.126776i	$-0.0404630\pi$
$463$	42.6876			1.98386			0.991931	+	0.126776i	$0.0404630\pi$
$464$			6.18757i			0.287250i
$465$			10.8314i			0.502296i
$466$	−7.35068			−0.340514
$467$		−	3.37916i		−	0.156369i	−0.996939	−	0.0781845i	$-0.975088\pi$
$467$		−	3.37916i		−	0.156369i	0.996939	−	0.0781845i	$-0.0249123\pi$
$468$	−3.82483			−0.176803
$469$		0			0
$470$			18.8669i			0.870266i
$471$	0.879280			0.0405151
$472$	−13.8411			−0.637088
$473$	5.26344	+	35.1164i	0.242013	+	1.61465i
$474$			0.850437i			0.0390619i
$475$	−44.4851			−2.04112
$476$		0			0
$477$	11.0581			0.506314
$478$	−6.06529			−0.277420
$479$	−0.405542			−0.0185297			−0.00926483	−	0.999957i	$-0.502949\pi$
$479$	−0.405542			−0.0185297			−0.00926483	+	0.999957i	$0.502949\pi$
$480$		−	14.7651i		−	0.673932i
$481$	−41.0687			−1.87257
$482$		−	29.5220i		−	1.34469i
$483$		0			0
$484$	8.86280	−	2.71787i	0.402854	−	0.123540i
$485$	16.8549			0.765342
$486$	1.07576			0.0487974
$487$	9.73550			0.441158			0.220579	−	0.975369i	$-0.429205\pi$
$487$	9.73550			0.441158			0.220579	+	0.975369i	$0.429205\pi$
$488$		−	10.5462i		−	0.477406i
$489$		−	10.2998i		−	0.465775i
$490$		0			0
$491$		−	8.22678i		−	0.371270i	−0.982619	−	0.185635i	$-0.940566\pi$
$491$		−	8.22678i		−	0.371270i	0.982619	−	0.185635i	$-0.0594341\pi$
$492$		−	5.62520i		−	0.253604i
$493$		−	6.79412i		−	0.305992i
$494$		−	34.4193i		−	1.54860i
$495$	−1.65336	−	11.0308i	−0.0743130	−	0.495798i
$496$		−	5.16697i		−	0.232004i
$497$		0			0
$498$	−1.28272			−0.0574802
$499$	7.63186			0.341649			0.170824	−	0.985301i	$-0.445357\pi$
$499$	7.63186			0.341649			0.170824	+	0.985301i	$0.445357\pi$
$500$			3.71343i			0.166070i
$501$			16.1423i			0.721184i
$502$	14.5472			0.649272
$503$	29.4681			1.31392			0.656959	−	0.753927i	$-0.271843\pi$
$503$	29.4681			1.31392			0.656959	+	0.753927i	$0.271843\pi$
$504$		0			0
$505$			37.4584i			1.66687i
$506$	1.77256	+	11.8261i	0.0787997	+	0.525733i
$507$			7.59847i			0.337460i
$508$			2.14088i			0.0949860i
$509$			0.374844i			0.0166147i	0.999965	+	0.00830734i	$0.00264434\pi$
$509$			0.374844i			0.0166147i	−0.999965	+	0.00830734i	$0.997356\pi$
$510$		−	6.37308i		−	0.282205i
$511$		0			0
$512$			16.8557i			0.744924i
$513$		−	7.04969i		−	0.311252i
$514$	12.8658			0.567485
$515$	−26.1354			−1.15166
$516$	9.02263			0.397199
$517$	2.56379	+	17.1050i	0.112755	+	0.752276i
$518$		0			0
$519$			9.31647i			0.408947i
$520$	−46.6773			−2.04693
$521$			15.2477i			0.668014i	0.942571	+	0.334007i	$0.108401\pi$
$521$			15.2477i			0.668014i	−0.942571	+	0.334007i	$0.891599\pi$
$522$	4.14906			0.181599
$523$	12.3999			0.542208			0.271104	−	0.962550i	$-0.412611\pi$
$523$	12.3999			0.542208			0.271104	+	0.962550i	$0.412611\pi$
$524$	2.37353			0.103688
$525$		0			0
$526$	3.98790			0.173881
$527$			5.67348i			0.247141i
$528$	0.788710	+	5.26208i	0.0343242	+	0.229003i
$529$	−11.7667			−0.511597
$530$	40.0064			1.73777
$531$			4.52604i			0.196413i
$532$		0			0
$533$	−30.2943			−1.31219
$534$			9.24916i			0.400250i
$535$	58.6254			2.53460
$536$		−	0.925209i		−	0.0399630i
$537$			18.9548i			0.817958i
$538$	−4.45650			−0.192133
$539$		0			0
$540$	−2.83420			−0.121965
$541$		−	15.2368i		−	0.655081i	−0.944837	−	0.327541i	$-0.893780\pi$
$541$		−	15.2368i		−	0.655081i	0.944837	−	0.327541i	$-0.106220\pi$
$542$		−	30.9425i		−	1.32909i
$543$	10.7034			0.459327
$544$		−	7.73393i		−	0.331589i
$545$	40.3179			1.72703
$546$		0			0
$547$		−	22.3874i		−	0.957217i	−0.878028	−	0.478609i	$-0.841141\pi$
$547$		−	22.3874i		−	0.957217i	0.878028	−	0.478609i	$-0.158859\pi$
$548$	10.4233			0.445261
$549$	−3.44862			−0.147183
$550$	−3.33727	−	22.2655i	−0.142302	−	0.949402i
$551$		−	27.1897i		−	1.15832i
$552$	10.2496			0.436251
$553$		0			0
$554$	−12.6424			−0.537125
$555$	−30.4319			−1.29176
$556$	−10.6357			−0.451053
$557$			0.216973i			0.00919343i	0.999989	+	0.00459671i	$0.00146318\pi$
$557$			0.216973i			0.00919343i	−0.999989	+	0.00459671i	$0.998537\pi$
$558$	−3.46470			−0.146672
$559$		−	48.5910i		−	2.05518i
$560$		0			0
$561$	−0.866025	−	5.77791i	−0.0365636	−	0.243944i
$562$	9.74762			0.411179
$563$	−22.9828			−0.968611			−0.484305	−	0.874899i	$-0.660928\pi$
$563$	−22.9828			−0.968611			−0.484305	+	0.874899i	$0.660928\pi$
$564$	4.39486			0.185057
$565$		−	12.7378i		−	0.535885i
$566$			15.4372i			0.648875i
$567$		0			0
$568$		−	6.26895i		−	0.263039i
$569$		−	1.40956i		−	0.0590919i	−0.999563	−	0.0295459i	$-0.990594\pi$
$569$		−	1.40956i		−	0.0590919i	0.999563	−	0.0295459i	$-0.00940614\pi$
$570$		−	25.5047i		−	1.06828i
$571$		−	15.2582i		−	0.638537i	−0.947664	−	0.319269i	$-0.896563\pi$
$571$		−	15.2582i		−	0.638537i	0.947664	−	0.319269i	$-0.103437\pi$
$572$	−12.5454	+	1.88037i	−0.524549	+	0.0786224i
$573$			19.4034i			0.810587i
$574$		0			0
$575$	−21.1494			−0.881991
$576$	7.93158			0.330483
$577$			29.2008i			1.21564i	0.794073	+	0.607822i	$0.207957\pi$
$577$			29.2008i			1.21564i	−0.794073	+	0.607822i	$0.792043\pi$
$578$			14.9497i			0.621826i
$579$	0.704389			0.0292734
$580$	−10.9311			−0.453890
$581$		0			0
$582$			5.39145i			0.223483i
$583$	36.2703	−	5.43639i	1.50216	−	0.225152i
$584$		−	31.0636i		−	1.28542i
$585$			15.2635i			0.631066i
$586$		−	17.2526i		−	0.712700i
$587$			33.0528i			1.36424i	0.731242	+	0.682118i	$0.238941\pi$
$587$			33.0528i			1.36424i	−0.731242	+	0.682118i	$0.761059\pi$
$588$		0			0
$589$			22.7050i			0.935542i
$590$			16.3745i			0.674128i
$591$	−19.8657			−0.817166
$592$	14.5171			0.596649
$593$	−3.84578			−0.157927			−0.0789635	−	0.996878i	$-0.525161\pi$
$593$	−3.84578			−0.157927			−0.0789635	+	0.996878i	$0.525161\pi$
$594$	3.52847	−	0.528867i	0.144775	−	0.0216997i
$595$		0			0
$596$			2.25244i			0.0922634i
$597$	15.4117			0.630757
$598$		−	16.3639i		−	0.669168i
$599$	−43.1790			−1.76425			−0.882123	−	0.471020i	$-0.843886\pi$
$599$	−43.1790			−1.76425			−0.882123	+	0.471020i	$0.843886\pi$
$600$	−19.2973			−0.787810
$601$	−22.7863			−0.929472			−0.464736	−	0.885449i	$-0.653851\pi$
$601$	−22.7863			−0.929472			−0.464736	+	0.885449i	$0.653851\pi$
$602$		0			0
$603$	−0.302543			−0.0123205
$604$		−	7.72092i		−	0.314160i
$605$	−10.8460	−	35.3681i	−0.440952	−	1.43792i
$606$	−11.9820			−0.486734
$607$	11.5584			0.469141			0.234571	−	0.972099i	$-0.424632\pi$
$607$	11.5584			0.469141			0.234571	+	0.972099i	$0.424632\pi$
$608$		−	30.9508i		−	1.25522i
$609$		0			0
$610$	−12.4766			−0.505162
$611$		−	23.6683i		−	0.957518i
$612$	−1.48455			−0.0600092
$613$		−	33.0465i		−	1.33473i	−0.744729	−	0.667367i	$-0.767421\pi$
$613$		−	33.0465i		−	1.33473i	0.744729	−	0.667367i	$-0.232579\pi$
$614$		−	8.00566i		−	0.323082i
$615$	−22.4481			−0.905193
$616$		0			0
$617$	20.7120			0.833835			0.416917	−	0.908944i	$-0.363110\pi$
$617$	20.7120			0.833835			0.416917	+	0.908944i	$0.363110\pi$
$618$		−	8.36006i		−	0.336291i
$619$		−	22.2820i		−	0.895588i	−0.894137	−	0.447794i	$-0.852210\pi$
$619$		−	22.2820i		−	0.895588i	0.894137	−	0.447794i	$-0.147790\pi$
$620$	9.12812			0.366594
$621$		−	3.35161i		−	0.134495i
$622$	−16.9346			−0.679017
$623$		0			0
$624$		−	7.28120i		−	0.291481i
$625$	−16.7322			−0.669288
$626$	33.8373			1.35241
$627$	−3.46579	−	23.1229i	−0.138410	−	0.923439i
$628$		−	0.741007i		−	0.0295694i
$629$	−15.9402			−0.635576
$630$		0			0
$631$	2.65495			0.105692			0.0528459	−	0.998603i	$-0.483171\pi$
$631$	2.65495			0.105692			0.0528459	+	0.998603i	$0.483171\pi$
$632$	2.41757			0.0961659
$633$	−19.8619			−0.789439
$634$			7.88114i			0.313000i
$635$	8.54343			0.339036
$636$		−	9.31910i		−	0.369526i
$637$		0			0
$638$	13.6088	−	2.03977i	0.538779	−	0.0807552i
$639$	−2.04994			−0.0810945
$640$	−0.834960			−0.0330047
$641$	10.3321			0.408092			0.204046	−	0.978961i	$-0.434591\pi$
$641$	10.3321			0.408092			0.204046	+	0.978961i	$0.434591\pi$
$642$			18.7527i			0.740112i
$643$			22.8722i			0.901993i	0.892526	+	0.450996i	$0.148931\pi$
$643$			22.8722i			0.901993i	−0.892526	+	0.450996i	$0.851069\pi$
$644$		0			0
$645$		−	36.0059i		−	1.41773i
$646$		−	13.3593i		−	0.525615i
$647$			25.3961i			0.998423i	0.866480	+	0.499211i	$0.166377\pi$
$647$			25.3961i			0.998423i	−0.866480	+	0.499211i	$0.833623\pi$
$648$		−	3.05811i		−	0.120134i
$649$	2.22510	+	14.8453i	0.0873429	+	0.582730i
$650$			30.8090i			1.20843i
$651$		0			0
$652$	−8.68011			−0.339939
$653$	−25.6740			−1.00470			−0.502350	−	0.864664i	$-0.667531\pi$
$653$	−25.6740			−1.00470			−0.502350	+	0.864664i	$0.667531\pi$
$654$			12.8967i			0.504300i
$655$		−	9.47185i		−	0.370096i
$656$	10.7085			0.418097
$657$	−10.1578			−0.396293
$658$		0			0
$659$			2.65060i			0.103253i	0.998666	+	0.0516264i	$0.0164405\pi$
$659$			2.65060i			0.103253i	−0.998666	+	0.0516264i	$0.983559\pi$
$660$	−9.29614	+	1.39336i	−0.361852	+	0.0542363i
$661$			29.1612i			1.13424i	0.823636	+	0.567119i	$0.191942\pi$
$661$			29.1612i			1.13424i	−0.823636	+	0.567119i	$0.808058\pi$
$662$		−	9.45167i		−	0.367349i
$663$			7.99496i			0.310498i
$664$			3.64645i			0.141510i
$665$		0			0
$666$		−	9.73439i		−	0.377200i
$667$		−	12.9267i		−	0.500524i
$668$	13.6038			0.526346
$669$	3.03619			0.117386
$670$	−1.09456			−0.0422864
$671$	−11.3114	+	1.69542i	−0.436673	+	0.0654509i
$672$		0			0
$673$			3.32912i			0.128328i	0.997939	+	0.0641641i	$0.0204381\pi$
$673$			3.32912i			0.128328i	−0.997939	+	0.0641641i	$0.979562\pi$
$674$	−27.3313			−1.05276
$675$			6.31022i			0.242881i
$676$	6.40355			0.246290
$677$	21.2709			0.817508			0.408754	−	0.912645i	$-0.365963\pi$
$677$	21.2709			0.817508			0.408754	+	0.912645i	$0.365963\pi$
$678$	4.07451			0.156480
$679$		0			0
$680$	−18.1170			−0.694756
$681$			17.7873i			0.681610i
$682$	−11.3642	+	1.70333i	−0.435157	+	0.0652237i
$683$	−49.3456			−1.88816			−0.944078	−	0.329722i	$-0.893045\pi$
$683$	−49.3456			−1.88816			−0.944078	+	0.329722i	$0.893045\pi$
$684$	−5.94108			−0.227163
$685$		−	41.5954i		−	1.58928i
$686$		0			0
$687$	−26.6141			−1.01539
$688$			17.1761i			0.654831i
$689$	−50.1876			−1.91199
$690$		−	12.1256i		−	0.461614i
$691$			19.1487i			0.728450i	0.931311	+	0.364225i	$0.118666\pi$
$691$			19.1487i			0.728450i	−0.931311	+	0.364225i	$0.881334\pi$
$692$	7.85138			0.298465
$693$		0			0
$694$	1.74457			0.0662228
$695$			42.4430i			1.60995i
$696$		−	11.7947i		−	0.447077i
$697$	−11.7582			−0.445375
$698$		−	7.68676i		−	0.290948i
$699$	6.83301			0.258448
$700$		0			0
$701$		−	14.4372i		−	0.545286i	−0.962115	−	0.272643i	$-0.912102\pi$
$701$		−	14.4372i		−	0.545286i	0.962115	−	0.272643i	$-0.0878978\pi$
$702$	−4.88239			−0.184274
$703$	−63.7917			−2.40595
$704$	26.0155	−	3.89934i	0.980495	−	0.146962i
$705$		−	17.5382i		−	0.660528i
$706$	21.3287			0.802717
$707$		0			0
$708$	3.81428			0.143350
$709$	−22.2635			−0.836123			−0.418061	−	0.908419i	$-0.637290\pi$
$709$	−22.2635			−0.836123			−0.418061	+	0.908419i	$0.637290\pi$
$710$	−7.41639			−0.278332
$711$		−	0.790546i		−	0.0296478i
$712$	26.2930			0.985371
$713$			10.7945i			0.404259i
$714$		0			0
$715$	7.50386	+	50.0639i	0.280628	+	1.87229i
$716$	15.9740			0.596976
$717$	5.63815			0.210560
$718$	−16.1260			−0.601817
$719$			3.74664i			0.139726i	0.997557	+	0.0698630i	$0.0222562\pi$
$719$			3.74664i			0.139726i	−0.997557	+	0.0698630i	$0.977744\pi$
$720$		−	5.39537i		−	0.201074i
$721$		0			0
$722$		−	33.0238i		−	1.22902i
$723$			27.4430i			1.02062i
$724$		−	9.02022i		−	0.335234i
$725$			24.3377i			0.903878i
$726$	11.3133	−	3.46935i	0.419878	−	0.128760i
$727$			5.54411i			0.205620i	0.994701	+	0.102810i	$0.0327833\pi$
$727$			5.54411i			0.205620i	−0.994701	+	0.102810i	$0.967217\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−36.7494			−1.36015
$731$		−	18.8598i		−	0.697555i
$732$			2.90630i			0.107420i
$733$	5.89454			0.217720			0.108860	−	0.994057i	$-0.465280\pi$
$733$	5.89454			0.217720			0.108860	+	0.994057i	$0.465280\pi$
$734$	−15.4341			−0.569682
$735$		0			0
$736$		−	14.7148i		−	0.542395i
$737$	−0.992338	+	0.148737i	−0.0365532	+	0.00547880i
$738$		−	7.18056i		−	0.264320i
$739$			33.8088i			1.24368i	0.783146	+	0.621838i	$0.213614\pi$
$739$			33.8088i			1.24368i	−0.783146	+	0.621838i	$0.786386\pi$
$740$			25.6463i			0.942776i
$741$			31.9954i			1.17538i
$742$		0			0
$743$			42.0798i			1.54376i	0.635770	+	0.771879i	$0.280683\pi$
$743$			42.0798i			1.54376i	−0.635770	+	0.771879i	$0.719317\pi$
$744$			9.84925i			0.361091i
$745$	8.98863			0.329318
$746$	1.04302			0.0381878
$747$	1.19239			0.0436272
$748$	−4.86929	+	0.729836i	−0.178039	+	0.0266855i
$749$		0			0
$750$			4.74019i			0.173087i
$751$	−36.7220			−1.34001			−0.670003	−	0.742358i	$-0.733707\pi$
$751$	−36.7220			−1.34001			−0.670003	+	0.742358i	$0.733707\pi$
$752$			8.36634i			0.305089i
$753$	−13.5227			−0.492795
$754$	−18.8307			−0.685774
$755$	−30.8113			−1.12134
$756$		0			0
$757$	7.77963			0.282755			0.141378	−	0.989956i	$-0.454847\pi$
$757$	7.77963			0.282755			0.141378	+	0.989956i	$0.454847\pi$
$758$			30.5522i			1.10971i
$759$	−1.64773	−	10.9932i	−0.0598087	−	0.399029i
$760$	−72.5034			−2.62997
$761$	−35.3289			−1.28067			−0.640336	−	0.768095i	$-0.721205\pi$
$761$	−35.3289			−1.28067			−0.640336	+	0.768095i	$0.721205\pi$
$762$			2.73282i			0.0989998i
$763$		0			0
$764$	16.3520			0.591596
$765$			5.92426i			0.214192i
$766$	11.4608			0.414094
$767$		−	20.5417i		−	0.741716i
$768$		−	16.1302i		−	0.582050i
$769$	22.2058			0.800761			0.400380	−	0.916349i	$-0.368878\pi$
$769$	22.2058			0.800761			0.400380	+	0.916349i	$0.368878\pi$
$770$		0			0
$771$	−11.9597			−0.430719
$772$		−	0.593619i		−	0.0213648i
$773$		−	7.90241i		−	0.284230i	−0.989850	−	0.142115i	$-0.954610\pi$
$773$		−	7.90241i		−	0.284230i	0.989850	−	0.142115i	$-0.0453903\pi$
$774$	11.5174			0.413983
$775$		−	20.3234i		−	0.730037i
$776$	15.3265			0.550190
$777$		0			0
$778$			9.96763i			0.357357i
$779$	−47.0558			−1.68595
$780$	12.8632			0.460575
$781$	−6.72379	+	1.00780i	−0.240596	+	0.0360619i
$782$		−	6.35136i		−	0.227124i
$783$	−3.85686			−0.137833
$784$		0			0
$785$	−2.95708			−0.105543
$786$	3.02980			0.108069
$787$	35.0401			1.24905			0.624523	−	0.781006i	$-0.285293\pi$
$787$	35.0401			1.24905			0.624523	+	0.781006i	$0.285293\pi$
$788$			16.7417i			0.596397i
$789$	−3.70706			−0.131975
$790$		−	2.86008i		−	0.101757i
$791$		0			0
$792$	−1.50343	−	10.0305i	−0.0534222	−	0.356420i
$793$	15.6517			0.555810
$794$	27.1457			0.963366
$795$	−37.1890			−1.31896
$796$		−	12.9881i		−	0.460349i
$797$		−	14.1495i		−	0.501200i	−0.968091	−	0.250600i	$-0.919372\pi$
$797$		−	14.1495i		−	0.501200i	0.968091	−	0.250600i	$-0.0806279\pi$
$798$		0			0
$799$		−	9.18648i		−	0.324994i
$800$			27.7042i			0.979492i
$801$		−	8.59780i		−	0.303788i
$802$			28.3252i			1.00020i
$803$	−33.3174	+	4.99380i	−1.17575	+	0.176227i
$804$			0.254966i			0.00899196i
$805$		0			0
$806$	15.7247			0.553880
$807$	4.14265			0.145828
$808$			34.0616i			1.19828i
$809$		−	17.8452i		−	0.627402i	−0.949522	−	0.313701i	$-0.898431\pi$
$809$		−	17.8452i		−	0.627402i	0.949522	−	0.313701i	$-0.101569\pi$
$810$	−3.61785			−0.127118
$811$	7.04619			0.247425			0.123713	−	0.992318i	$-0.460520\pi$
$811$	7.04619			0.247425			0.123713	+	0.992318i	$0.460520\pi$
$812$		0			0
$813$			28.7634i			1.00878i
$814$	−4.78565	−	31.9287i	−0.167737	−	1.11910i
$815$			34.6390i			1.21335i
$816$		−	2.82608i		−	0.0989326i
$817$		−	75.4759i		−	2.64057i
$818$			37.3507i			1.30594i
$819$		0			0
$820$			18.9179i			0.660643i
$821$		−	19.1916i		−	0.669793i	−0.942255	−	0.334896i	$-0.891299\pi$
$821$		−	19.1916i		−	0.669793i	0.942255	−	0.334896i	$-0.108701\pi$
$822$	13.3053			0.464076
$823$	46.3496			1.61565			0.807823	−	0.589425i	$-0.200646\pi$
$823$	46.3496			1.61565			0.807823	+	0.589425i	$0.200646\pi$
$824$	−23.7655			−0.827910
$825$	3.10225	+	20.6974i	0.108006	+	0.720592i
$826$		0			0
$827$			15.7698i			0.548370i	0.961677	+	0.274185i	$0.0884081\pi$
$827$			15.7698i			0.548370i	−0.961677	+	0.274185i	$0.911592\pi$
$828$	−2.82454			−0.0981596
$829$			7.95804i			0.276394i	0.990405	+	0.138197i	$0.0441307\pi$
$829$			7.95804i			0.276394i	−0.990405	+	0.138197i	$0.955869\pi$
$830$	4.31388			0.149737
$831$	11.7521			0.407676
$832$	−35.9979			−1.24800
$833$		0			0
$834$	−13.5764			−0.470113
$835$		−	54.2876i		−	1.87870i
$836$	−19.4866	+	2.92077i	−0.673960	+	0.101017i
$837$	3.22070			0.111324
$838$	10.4472			0.360891
$839$		−	38.9532i		−	1.34481i	−0.740182	−	0.672406i	$-0.765261\pi$
$839$		−	38.9532i		−	1.34481i	0.740182	−	0.672406i	$-0.234739\pi$
$840$		0			0
$841$	14.1246			0.487055
$842$		−	7.11772i		−	0.245293i
$843$	−9.06116			−0.312083
$844$			16.7385i			0.576162i
$845$		−	25.5542i		−	0.879090i
$846$	5.61003			0.192877
$847$		0			0
$848$	17.7404			0.609209
$849$		−	14.3501i		−	0.492493i
$850$			11.9580i			0.410156i
$851$	−30.3282			−1.03964
$852$			1.72758i			0.0591857i
$853$	−3.09036			−0.105812			−0.0529060	−	0.998599i	$-0.516848\pi$
$853$	−3.09036			−0.105812			−0.0529060	+	0.998599i	$0.516848\pi$
$854$		0			0
$855$			23.7086i			0.810817i
$856$	53.3092			1.82207
$857$	42.5265			1.45268			0.726339	−	0.687337i	$-0.241220\pi$
$857$	42.5265			1.45268			0.726339	+	0.687337i	$0.241220\pi$
$858$	−16.0142	+	2.40029i	−0.546715	+	0.0819446i
$859$		−	46.1194i		−	1.57357i	−0.617226	−	0.786786i	$-0.711743\pi$
$859$		−	46.1194i		−	1.57357i	0.617226	−	0.786786i	$-0.288257\pi$
$860$	−30.3437			−1.03471
$861$		0			0
$862$	35.5189			1.20978
$863$	−43.8734			−1.49347			−0.746734	−	0.665122i	$-0.768379\pi$
$863$	−43.8734			−1.49347			−0.746734	+	0.665122i	$0.768379\pi$
$864$	−4.39037			−0.149363
$865$		−	31.3319i		−	1.06532i
$866$	−1.74444			−0.0592787
$867$		−	13.8969i		−	0.471963i
$868$		0			0
$869$	−0.388650	−	2.59298i	−0.0131841	−	0.0879609i
$870$	−13.9536			−0.473070
$871$	1.37311			0.0465260
$872$	36.6619			1.24153
$873$		−	5.01177i		−	0.169623i
$874$		−	25.4178i		−	0.859771i
$875$		0			0
$876$			8.56040i			0.289229i
$877$			49.9573i			1.68694i	0.537179	+	0.843468i	$0.319490\pi$
$877$			49.9573i			1.68694i	−0.537179	+	0.843468i	$0.680510\pi$
$878$			9.31181i			0.314259i
$879$			16.0376i			0.540936i
$880$	−2.65248	−	17.6967i	−0.0894152	−	0.596557i
$881$			35.8354i			1.20732i	0.797240	+	0.603662i	$0.206292\pi$
$881$			35.8354i			1.20732i	−0.797240	+	0.603662i	$0.793708\pi$
$882$		0			0
$883$	−33.7068			−1.13432			−0.567162	−	0.823606i	$-0.691959\pi$
$883$	−33.7068			−1.13432			−0.567162	+	0.823606i	$0.691959\pi$
$884$	6.73769			0.226613
$885$		−	15.2214i		−	0.511661i
$886$		−	31.5153i		−	1.05878i
$887$	−17.1279			−0.575099			−0.287550	−	0.957766i	$-0.592841\pi$
$887$	−17.1279			−0.575099			−0.287550	+	0.957766i	$0.592841\pi$
$888$	−27.6724			−0.928624
$889$		0			0
$890$		−	31.1056i		−	1.04266i
$891$	−3.27999	+	0.491622i	−0.109884	+	0.0164700i
$892$		−	2.55873i		−	0.0856725i
$893$		−	36.7638i		−	1.23025i
$894$			2.87523i			0.0961621i
$895$		−	63.7461i		−	2.13080i
$896$		0			0
$897$			15.2114i			0.507896i
$898$			12.2318i			0.408180i
$899$	12.4218			0.414291
$900$	5.31789			0.177263
$901$	−19.4795			−0.648956
$902$	−3.53012	−	23.5521i	−0.117540	−	0.784200i
$903$		0			0
$904$		−	11.5828i		−	0.385237i
$905$	−35.9963			−1.19656
$906$		−	9.85574i		−	0.327435i
$907$	−34.2931			−1.13868			−0.569341	−	0.822101i	$-0.692802\pi$
$907$	−34.2931			−1.13868			−0.569341	+	0.822101i	$0.692802\pi$
$908$	14.9901			0.497464
$909$	11.1382			0.369429
$910$		0			0
$911$	32.4545			1.07526			0.537632	−	0.843179i	$-0.319319\pi$
$911$	32.4545			1.07526			0.537632	+	0.843179i	$0.319319\pi$
$912$		−	11.3098i		−	0.374506i
$913$	3.91102	−	0.586205i	0.129436	−	0.0194006i
$914$	−2.55981			−0.0846709
$915$	11.5979			0.383416
$916$			22.4288i			0.741070i
$917$		0			0
$918$	−1.89502			−0.0625450
$919$			28.4257i			0.937678i	0.883284	+	0.468839i	$0.155327\pi$
$919$			28.4257i			0.937678i	−0.883284	+	0.468839i	$0.844673\pi$
$920$	−34.4700			−1.13644
$921$			7.44188i			0.245218i
$922$			4.18406i			0.137795i
$923$	9.30378			0.306238
$924$		0			0
$925$	57.1003			1.87745
$926$		−	45.9216i		−	1.50908i
$927$			7.77131i			0.255243i
$928$	−16.9331			−0.555855
$929$		−	54.8690i		−	1.80019i	−0.435691	−	0.900097i	$-0.643496\pi$
$929$		−	54.8690i		−	1.80019i	0.435691	−	0.900097i	$-0.356504\pi$
$930$	11.6520			0.382085
$931$		0			0
$932$		−	5.75847i		−	0.188625i
$933$	15.7420			0.515371
$934$	−3.63517			−0.118946
$935$	2.91250	+	19.4315i	0.0952490	+	0.635478i
$936$			13.8794i			0.453662i
$937$	57.2963			1.87179			0.935894	−	0.352282i	$-0.114594\pi$
$937$	57.2963			1.87179			0.935894	+	0.352282i	$0.114594\pi$
$938$		0			0
$939$	−31.4543			−1.02647
$940$	−14.7802			−0.482077
$941$	−37.9434			−1.23692			−0.618460	−	0.785816i	$-0.712243\pi$
$941$	−37.9434			−1.23692			−0.618460	+	0.785816i	$0.712243\pi$
$942$		−	0.945893i		−	0.0308189i
$943$	−22.3716			−0.728518
$944$			7.26112i			0.236329i
$945$		0			0
$946$	37.7768	−	5.66220i	1.22823	−	0.184094i
$947$	−0.380424			−0.0123621			−0.00618106	−	0.999981i	$-0.501968\pi$
$947$	−0.380424			−0.0123621			−0.00618106	+	0.999981i	$0.501968\pi$
$948$	−0.666227			−0.0216380
$949$	46.1017			1.49652
$950$			47.8553i			1.55263i
$951$		−	7.32612i		−	0.237566i
$952$		0			0
$953$			56.1107i			1.81760i	0.417229	+	0.908801i	$0.363001\pi$
$953$			56.1107i			1.81760i	−0.417229	+	0.908801i	$0.636999\pi$
$954$		−	11.8958i		−	0.385141i
$955$		−	65.2548i		−	2.11160i
$956$		−	4.75151i		−	0.153675i
$957$	−12.6505	+	1.89612i	−0.408931	+	0.0612929i
$958$			0.436265i			0.0140951i
$959$		0			0
$960$	−26.6744			−0.860914
$961$	20.6271			0.665389
$962$			44.1801i			1.42442i
$963$		−	17.4321i		−	0.561742i
$964$	23.1274			0.744882
$965$	−2.36891			−0.0762579
$966$		0			0
$967$		−	52.0914i		−	1.67515i	−0.546325	−	0.837573i	$-0.683974\pi$
$967$		−	52.0914i		−	1.67515i	0.546325	−	0.837573i	$-0.316026\pi$
$968$	−9.86248	−	32.1609i	−0.316992	−	1.03369i
$969$			12.4185i			0.398940i
$970$		−	18.1318i		−	0.582178i
$971$		−	7.98142i		−	0.256136i	−0.991765	−	0.128068i	$-0.959122\pi$
$971$		−	7.98142i		−	0.256136i	0.991765	−	0.128068i	$-0.0408776\pi$
$972$			0.842743i			0.0270310i
$973$		0			0
$974$		−	10.4730i		−	0.335578i
$975$		−	28.6393i		−	0.917191i
$976$	−5.53262			−0.177095
$977$	−0.308439			−0.00986783			−0.00493391	−	0.999988i	$-0.501571\pi$
$977$	−0.308439			−0.00986783			−0.00493391	+	0.999988i	$0.501571\pi$
$978$	−11.0801			−0.354304
$979$	−4.22687	−	28.2007i	−0.135091	−	0.901297i
$980$		0			0
$981$		−	11.9884i		−	0.382762i
$982$	−8.85004			−0.282416
$983$			43.9377i			1.40139i	0.713459	+	0.700697i	$0.247128\pi$
$983$			43.9377i			1.40139i	−0.713459	+	0.700697i	$0.752872\pi$
$984$	−20.4125			−0.650726
$985$	66.8097			2.12873
$986$	−7.30883			−0.232761
$987$		0			0
$988$	26.9639			0.857836
$989$		−	35.8832i		−	1.14102i
$990$	−11.8665	+	1.77862i	−0.377142	+	0.0565281i
$991$	11.5066			0.365519			0.182760	−	0.983158i	$-0.441497\pi$
$991$	11.5066			0.365519			0.182760	+	0.983158i	$0.441497\pi$
$992$	14.1401			0.448948
$993$			8.78604i			0.278817i
$994$		0			0
$995$	−51.8304			−1.64314
$996$		−	1.00488i		−	0.0318407i
$997$	−13.7753			−0.436269			−0.218135	−	0.975919i	$-0.569997\pi$
$997$	−13.7753			−0.436269			−0.218135	+	0.975919i	$0.569997\pi$
$998$		−	8.21004i		−	0.259884i
$999$			9.04886i			0.286293i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.c.a.538.10		32
7.2	even	3		231.2.p.a.10.5	✓	32
7.3	odd	6		231.2.p.a.208.12	yes	32
7.6	odd	2	inner	1617.2.c.a.538.9		32
11.10	odd	2	inner	1617.2.c.a.538.24		32
21.2	odd	6		693.2.bg.b.10.12		32
21.17	even	6		693.2.bg.b.208.5		32
77.10	even	6		231.2.p.a.208.5	yes	32
77.65	odd	6		231.2.p.a.10.12	yes	32
77.76	even	2	inner	1617.2.c.a.538.23		32
231.65	even	6		693.2.bg.b.10.5		32
231.164	odd	6		693.2.bg.b.208.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.p.a.10.5	✓	32	7.2	even	3
231.2.p.a.10.12	yes	32	77.65	odd	6
231.2.p.a.208.5	yes	32	77.10	even	6
231.2.p.a.208.12	yes	32	7.3	odd	6
693.2.bg.b.10.5		32	231.65	even	6
693.2.bg.b.10.12		32	21.2	odd	6
693.2.bg.b.208.5		32	21.17	even	6
693.2.bg.b.208.12		32	231.164	odd	6
1617.2.c.a.538.9		32	7.6	odd	2	inner
1617.2.c.a.538.10		32	1.1	even	1	trivial
1617.2.c.a.538.23		32	77.76	even	2	inner
1617.2.c.a.538.24		32	11.10	odd	2	inner

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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.07576i q^{2} +1.00000i q^{3} +0.842743 q^{4} -3.36307i q^{5} +1.07576 q^{6} -3.05811i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.07576i q^{2} +1.00000i q^{3} +0.842743 q^{4} -3.36307i q^{5} +1.07576 q^{6} -3.05811i q^{8} -1.00000 q^{9} -3.61785 q^{10} +(-3.27999 + 0.491622i) q^{11} +0.842743i q^{12} +4.53855 q^{13} +3.36307 q^{15} -1.60430 q^{16} +1.76157 q^{17} +1.07576i q^{18} +7.04969 q^{19} -2.83420i q^{20} +(0.528867 + 3.52847i) q^{22} +3.35161 q^{23} +3.05811 q^{24} -6.31022 q^{25} -4.88239i q^{26} -1.00000i q^{27} -3.85686i q^{29} -3.61785i q^{30} +3.22070i q^{31} -4.39037i q^{32} +(-0.491622 - 3.27999i) q^{33} -1.89502i q^{34} -0.842743 q^{36} -9.04886 q^{37} -7.58377i q^{38} +4.53855i q^{39} -10.2846 q^{40} -6.67488 q^{41} -10.7063i q^{43} +(-2.76418 + 0.414311i) q^{44} +3.36307i q^{45} -3.60552i q^{46} -5.21495i q^{47} -1.60430i q^{48} +6.78828i q^{50} +1.76157i q^{51} +3.82483 q^{52} -11.0581 q^{53} -1.07576 q^{54} +(1.65336 + 11.0308i) q^{55} +7.04969i q^{57} -4.14906 q^{58} -4.52604i q^{59} +2.83420 q^{60} +3.44862 q^{61} +3.46470 q^{62} -7.93158 q^{64} -15.2635i q^{65} +(-3.52847 + 0.528867i) q^{66} +0.302543 q^{67} +1.48455 q^{68} +3.35161i q^{69} +2.04994 q^{71} +3.05811i q^{72} +10.1578 q^{73} +9.73439i q^{74} -6.31022i q^{75} +5.94108 q^{76} +4.88239 q^{78} +0.790546i q^{79} +5.39537i q^{80} +1.00000 q^{81} +7.18056i q^{82} -1.19239 q^{83} -5.92426i q^{85} -11.5174 q^{86} +3.85686 q^{87} +(1.50343 + 10.0305i) q^{88} +8.59780i q^{89} +3.61785 q^{90} +2.82454 q^{92} -3.22070 q^{93} -5.61003 q^{94} -23.7086i q^{95} +4.39037 q^{96} +5.01177i q^{97} +(3.27999 - 0.491622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 24 q^{4} - 32 q^{9}+O(q^{10}) \) 32 * q - 24 * q^4 - 32 * q^9	\( 32 q - 24 q^{4} - 32 q^{9} - 4 q^{11} + 8 q^{15} + 40 q^{16} + 8 q^{22} - 48 q^{23} + 24 q^{36} + 64 q^{37} + 56 q^{44} - 72 q^{53} - 24 q^{58} + 8 q^{64} - 40 q^{67} + 72 q^{71} - 48 q^{78} + 32 q^{81} - 128 q^{86} - 48 q^{88} - 16 q^{92} - 32 q^{93} + 4 q^{99}+O(q^{100}) \) 32 * q - 24 * q^4 - 32 * q^9 - 4 * q^11 + 8 * q^15 + 40 * q^16 + 8 * q^22 - 48 * q^23 + 24 * q^36 + 64 * q^37 + 56 * q^44 - 72 * q^53 - 24 * q^58 + 8 * q^64 - 40 * q^67 + 72 * q^71 - 48 * q^78 + 32 * q^81 - 128 * q^86 - 48 * q^88 - 16 * q^92 - 32 * q^93 + 4 * q^99

Introduction

L-functions

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