LMFDB - Embedded newform 1617.2.c.a.538.14

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			538.14
Character	$\chi$	$=$	1617.538
Dual form			1617.2.c.a.538.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.615506i q^{2} +1.00000i q^{3} +1.62115 q^{4} -3.28584i q^{5} +0.615506 q^{6} -2.22884i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-0.615506i q^{2} +1.00000i q^{3} +1.62115 q^{4} -3.28584i q^{5} +0.615506 q^{6} -2.22884i q^{8} -1.00000 q^{9} -2.02245 q^{10} +(-0.0656613 - 3.31597i) q^{11} +1.62115i q^{12} +0.142630 q^{13} +3.28584 q^{15} +1.87044 q^{16} -7.26368 q^{17} +0.615506i q^{18} -0.869142 q^{19} -5.32684i q^{20} +(-2.04100 + 0.0404149i) q^{22} -3.56308 q^{23} +2.22884 q^{24} -5.79672 q^{25} -0.0877894i q^{26} -1.00000i q^{27} -3.70637i q^{29} -2.02245i q^{30} -4.82080i q^{31} -5.60895i q^{32} +(3.31597 - 0.0656613i) q^{33} +4.47084i q^{34} -1.62115 q^{36} +9.39271 q^{37} +0.534962i q^{38} +0.142630i q^{39} -7.32361 q^{40} -3.19487 q^{41} +9.66641i q^{43} +(-0.106447 - 5.37570i) q^{44} +3.28584i q^{45} +2.19310i q^{46} +8.76297i q^{47} +1.87044i q^{48} +3.56792i q^{50} -7.26368i q^{51} +0.231224 q^{52} -6.62537 q^{53} -0.615506 q^{54} +(-10.8958 + 0.215752i) q^{55} -0.869142i q^{57} -2.28130 q^{58} -1.54704i q^{59} +5.32684 q^{60} -15.2529 q^{61} -2.96723 q^{62} +0.288529 q^{64} -0.468657i q^{65} +(-0.0404149 - 2.04100i) q^{66} +13.0157 q^{67} -11.7755 q^{68} -3.56308i q^{69} +2.66532 q^{71} +2.22884i q^{72} +5.48838 q^{73} -5.78127i q^{74} -5.79672i q^{75} -1.40901 q^{76} +0.0877894 q^{78} -7.05347i q^{79} -6.14595i q^{80} +1.00000 q^{81} +1.96646i q^{82} +6.31032 q^{83} +23.8673i q^{85} +5.94974 q^{86} +3.70637 q^{87} +(-7.39078 + 0.146349i) q^{88} -7.87864i q^{89} +2.02245 q^{90} -5.77630 q^{92} +4.82080 q^{93} +5.39367 q^{94} +2.85586i q^{95} +5.60895 q^{96} -8.07193i q^{97} +(0.0656613 + 3.31597i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	0.615506i		−	0.435229i	−0.976035	−	0.217614i	$-0.930172\pi$
$2$		−	0.615506i		−	0.435229i	0.976035	−	0.217614i	$-0.0698275\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.62115			0.810576
$5$		−	3.28584i		−	1.46947i	−0.678354	−	0.734735i	$-0.737306\pi$
$5$		−	3.28584i		−	1.46947i	0.678354	−	0.734735i	$-0.262694\pi$
$6$	0.615506			0.251279
$7$		0			0
$7$		0			0
$8$		−	2.22884i		−	0.788015i
$9$	−1.00000			−0.333333
$10$	−2.02245			−0.639556
$11$	−0.0656613	−	3.31597i	−0.0197976	−	0.999804i
$11$	−0.0656613	−	3.31597i	−0.0197976	−	0.999804i
$12$			1.62115i			0.467986i
$13$	0.142630			0.0395583			0.0197792	−	0.999804i	$-0.493704\pi$
$13$	0.142630			0.0395583			0.0197792	+	0.999804i	$0.493704\pi$
$14$		0			0
$15$	3.28584			0.848399
$16$	1.87044			0.467609
$17$	−7.26368			−1.76170			−0.880851	−	0.473394i	$-0.843029\pi$
$17$	−7.26368			−1.76170			−0.880851	+	0.473394i	$0.843029\pi$
$18$			0.615506i			0.145076i
$19$	−0.869142			−0.199395			−0.0996974	−	0.995018i	$-0.531787\pi$
$19$	−0.869142			−0.199395			−0.0996974	+	0.995018i	$0.531787\pi$
$20$		−	5.32684i		−	1.19112i
$21$		0			0
$22$	−2.04100	+	0.0404149i	−0.435143	+	0.00861650i
$23$	−3.56308			−0.742954			−0.371477	−	0.928442i	$-0.621149\pi$
$23$	−3.56308			−0.742954			−0.371477	+	0.928442i	$0.621149\pi$
$24$	2.22884			0.454961
$25$	−5.79672			−1.15934
$26$		−	0.0877894i		−	0.0172169i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$		−	3.70637i		−	0.688256i	−0.938923	−	0.344128i	$-0.888175\pi$
$29$		−	3.70637i		−	0.688256i	0.938923	−	0.344128i	$-0.111825\pi$
$30$		−	2.02245i		−	0.369248i
$31$		−	4.82080i		−	0.865841i	−0.901432	−	0.432921i	$-0.857483\pi$
$31$		−	4.82080i		−	0.865841i	0.901432	−	0.432921i	$-0.142517\pi$
$32$		−	5.60895i		−	0.991532i
$33$	3.31597	−	0.0656613i	0.577237	−	0.0114302i
$34$			4.47084i			0.766743i
$35$		0			0
$36$	−1.62115			−0.270192
$37$	9.39271			1.54415			0.772076	−	0.635531i	$-0.219219\pi$
$37$	9.39271			1.54415			0.772076	+	0.635531i	$0.219219\pi$
$38$			0.534962i			0.0867824i
$39$			0.142630i			0.0228390i
$40$	−7.32361			−1.15796
$41$	−3.19487			−0.498954			−0.249477	−	0.968381i	$-0.580259\pi$
$41$	−3.19487			−0.498954			−0.249477	+	0.968381i	$0.580259\pi$
$42$		0			0
$43$			9.66641i			1.47411i	0.675831	+	0.737057i	$0.263785\pi$
$43$			9.66641i			1.47411i	−0.675831	+	0.737057i	$0.736215\pi$
$44$	−0.106447	−	5.37570i	−0.0160475	−	0.810417i
$45$			3.28584i			0.489824i
$46$			2.19310i			0.323355i
$47$			8.76297i			1.27821i	0.769119	+	0.639106i	$0.220695\pi$
$47$			8.76297i			1.27821i	−0.769119	+	0.639106i	$0.779305\pi$
$48$			1.87044i			0.269974i
$49$		0			0
$50$			3.56792i			0.504580i
$51$		−	7.26368i		−	1.01712i
$52$	0.231224			0.0320650
$53$	−6.62537			−0.910065			−0.455032	−	0.890475i	$-0.650372\pi$
$53$	−6.62537			−0.910065			−0.455032	+	0.890475i	$0.650372\pi$
$54$	−0.615506			−0.0837598
$55$	−10.8958	+	0.215752i	−1.46918	+	0.0290920i
$56$		0			0
$57$		−	0.869142i		−	0.115121i
$58$	−2.28130			−0.299549
$59$		−	1.54704i		−	0.201408i	−0.994916	−	0.100704i	$-0.967890\pi$
$59$		−	1.54704i		−	0.201408i	0.994916	−	0.100704i	$-0.0321095\pi$
$60$	5.32684			0.687692
$61$	−15.2529			−1.95293			−0.976467	−	0.215669i	$-0.930807\pi$
$61$	−15.2529			−1.95293			−0.976467	+	0.215669i	$0.930807\pi$
$62$	−2.96723			−0.376839
$63$		0			0
$64$	0.288529			0.0360662
$65$		−	0.468657i		−	0.0581298i
$66$	−0.0404149	−	2.04100i	−0.00497474	−	0.251230i
$67$	13.0157			1.59012			0.795061	−	0.606530i	$-0.207439\pi$
$67$	13.0157			1.59012			0.795061	+	0.606530i	$0.207439\pi$
$68$	−11.7755			−1.42799
$69$		−	3.56308i		−	0.428945i
$70$		0			0
$71$	2.66532			0.316315			0.158158	−	0.987414i	$-0.449445\pi$
$71$	2.66532			0.316315			0.158158	+	0.987414i	$0.449445\pi$
$72$			2.22884i			0.262672i
$73$	5.48838			0.642366			0.321183	−	0.947017i	$-0.395920\pi$
$73$	5.48838			0.642366			0.321183	+	0.947017i	$0.395920\pi$
$74$		−	5.78127i		−	0.672059i
$75$		−	5.79672i		−	0.669348i
$76$	−1.40901			−0.161625
$77$		0			0
$78$	0.0877894			0.00994019
$79$		−	7.05347i		−	0.793577i	−0.917910	−	0.396789i	$-0.870125\pi$
$79$		−	7.05347i		−	0.793577i	0.917910	−	0.396789i	$-0.129875\pi$
$80$		−	6.14595i		−	0.687138i
$81$	1.00000			0.111111
$82$			1.96646i			0.217159i
$83$	6.31032			0.692648			0.346324	−	0.938115i	$-0.387430\pi$
$83$	6.31032			0.692648			0.346324	+	0.938115i	$0.387430\pi$
$84$		0			0
$85$			23.8673i			2.58877i
$86$	5.94974			0.641577
$87$	3.70637			0.397365
$88$	−7.39078	+	0.146349i	−0.787860	+	0.0156008i
$89$		−	7.87864i		−	0.835134i	−0.908646	−	0.417567i	$-0.862883\pi$
$89$		−	7.87864i		−	0.835134i	0.908646	−	0.417567i	$-0.137117\pi$
$90$	2.02245			0.213185
$91$		0			0
$92$	−5.77630			−0.602221
$93$	4.82080			0.499894
$94$	5.39367			0.556314
$95$			2.85586i			0.293005i
$96$	5.60895			0.572461
$97$		−	8.07193i		−	0.819580i	−0.912180	−	0.409790i	$-0.865602\pi$
$97$		−	8.07193i		−	0.819580i	0.912180	−	0.409790i	$-0.134398\pi$
$98$		0			0
$99$	0.0656613	+	3.31597i	0.00659921	+	0.333268i
$100$	−9.39737			−0.939737
$101$	6.89607			0.686185			0.343092	−	0.939302i	$-0.388526\pi$
$101$	6.89607			0.686185			0.343092	+	0.939302i	$0.388526\pi$
$102$	−4.47084			−0.442679
$103$		−	3.46014i		−	0.340938i	−0.985363	−	0.170469i	$-0.945472\pi$
$103$		−	3.46014i		−	0.340938i	0.985363	−	0.170469i	$-0.0545282\pi$
$104$		−	0.317899i		−	0.0311725i
$105$		0			0
$106$			4.07796i			0.396086i
$107$		−	2.12139i		−	0.205082i	−0.994729	−	0.102541i	$-0.967303\pi$
$107$		−	2.12139i		−	0.205082i	0.994729	−	0.102541i	$-0.0326973\pi$
$108$		−	1.62115i		−	0.155995i
$109$		−	3.22456i		−	0.308857i	−0.988004	−	0.154428i	$-0.950646\pi$
$109$		−	3.22456i		−	0.308857i	0.988004	−	0.154428i	$-0.0493536\pi$
$110$	0.132797	+	6.70641i	0.0126617	+	0.639431i
$111$			9.39271i			0.891516i
$112$		0			0
$113$	11.8894			1.11846			0.559228	−	0.829014i	$-0.311098\pi$
$113$	11.8894			1.11846			0.559228	+	0.829014i	$0.311098\pi$
$114$	−0.534962			−0.0501038
$115$			11.7077i			1.09175i
$116$		−	6.00859i		−	0.557884i
$117$	−0.142630			−0.0131861
$118$	−0.952216			−0.0876586
$119$		0			0
$120$		−	7.32361i		−	0.668551i
$121$	−10.9914	+	0.435462i	−0.999216	+	0.0395875i
$122$			9.38825i			0.849973i
$123$		−	3.19487i		−	0.288071i
$124$		−	7.81525i		−	0.701830i
$125$			2.61791i			0.234153i
$126$		0			0
$127$		−	15.6821i		−	1.39156i	−0.718254	−	0.695781i	$-0.755058\pi$
$127$		−	15.6821i		−	1.39156i	0.718254	−	0.695781i	$-0.244942\pi$
$128$		−	11.3955i		−	1.00723i
$129$	−9.66641			−0.851080
$130$	−0.288462			−0.0252998
$131$	10.0286			0.876200			0.438100	−	0.898926i	$-0.355652\pi$
$131$	10.0286			0.876200			0.438100	+	0.898926i	$0.355652\pi$
$132$	5.37570	−	0.106447i	0.467895	−	0.00926502i
$133$		0			0
$134$		−	8.01125i		−	0.692067i
$135$	−3.28584			−0.282800
$136$			16.1896i			1.38825i
$137$	14.6785			1.25407			0.627033	−	0.778993i	$-0.284269\pi$
$137$	14.6785			1.25407			0.627033	+	0.778993i	$0.284269\pi$
$138$	−2.19310			−0.186689
$139$	4.45534			0.377897			0.188948	−	0.981987i	$-0.439492\pi$
$139$	4.45534			0.377897			0.188948	+	0.981987i	$0.439492\pi$
$140$		0			0
$141$	−8.76297			−0.737976
$142$		−	1.64052i		−	0.137669i
$143$	−0.00936524	−	0.472956i	−0.000783161	−	0.0395506i
$144$	−1.87044			−0.155870
$145$	−12.1785			−1.01137
$146$		−	3.37813i		−	0.279576i
$147$		0			0
$148$	15.2270			1.25165
$149$		−	5.01591i		−	0.410920i	−0.978666	−	0.205460i	$-0.934131\pi$
$149$		−	5.01591i		−	0.410920i	0.978666	−	0.205460i	$-0.0658690\pi$
$150$	−3.56792			−0.291320
$151$		−	14.7324i		−	1.19890i	−0.800411	−	0.599452i	$-0.795385\pi$
$151$		−	14.7324i		−	1.19890i	0.800411	−	0.599452i	$-0.204615\pi$
$152$			1.93718i			0.157126i
$153$	7.26368			0.587234
$154$		0			0
$155$	−15.8404			−1.27233
$156$			0.231224i			0.0185127i
$157$		−	10.3667i		−	0.827354i	−0.910424	−	0.413677i	$-0.864244\pi$
$157$		−	10.3667i		−	0.827354i	0.910424	−	0.413677i	$-0.135756\pi$
$158$	−4.34146			−0.345388
$159$		−	6.62537i		−	0.525426i
$160$	−18.4301			−1.45703
$161$		0			0
$162$		−	0.615506i		−	0.0483588i
$163$	−6.22238			−0.487374			−0.243687	−	0.969854i	$-0.578357\pi$
$163$	−6.22238			−0.487374			−0.243687	+	0.969854i	$0.578357\pi$
$164$	−5.17936			−0.404440
$165$	−0.215752	−	10.8958i	−0.0167963	−	0.848233i
$166$		−	3.88404i		−	0.301460i
$167$	21.3050			1.64863			0.824316	−	0.566129i	$-0.191560\pi$
$167$	21.3050			1.64863			0.824316	+	0.566129i	$0.191560\pi$
$168$		0			0
$169$	−12.9797			−0.998435
$170$	14.6905			1.12671
$171$	0.869142			0.0664650
$172$			15.6707i			1.19488i
$173$	1.49705			0.113818			0.0569091	−	0.998379i	$-0.481875\pi$
$173$	1.49705			0.113818			0.0569091	+	0.998379i	$0.481875\pi$
$174$		−	2.28130i		−	0.172945i
$175$		0			0
$176$	−0.122815	−	6.20232i	−0.00925755	−	0.467518i
$177$	1.54704			0.116283
$178$	−4.84935			−0.363474
$179$	−15.3266			−1.14556			−0.572780	−	0.819709i	$-0.694135\pi$
$179$	−15.3266			−1.14556			−0.572780	+	0.819709i	$0.694135\pi$
$180$			5.32684i			0.397039i
$181$			14.5930i			1.08469i	0.840156	+	0.542345i	$0.182463\pi$
$181$			14.5930i			1.08469i	−0.840156	+	0.542345i	$0.817537\pi$
$182$		0			0
$183$		−	15.2529i		−	1.12753i
$184$			7.94155i			0.585459i
$185$		−	30.8629i		−	2.26909i
$186$		−	2.96723i		−	0.217568i
$187$	0.476943	+	24.0862i	0.0348775	+	1.76136i
$188$			14.2061i			1.03609i
$189$		0			0
$190$	1.75780			0.127524
$191$	−8.97161			−0.649163			−0.324582	−	0.945858i	$-0.605223\pi$
$191$	−8.97161			−0.649163			−0.324582	+	0.945858i	$0.605223\pi$
$192$			0.288529i			0.0208228i
$193$		−	2.11199i		−	0.152025i	−0.997107	−	0.0760123i	$-0.975781\pi$
$193$		−	2.11199i		−	0.152025i	0.997107	−	0.0760123i	$-0.0242188\pi$
$194$	−4.96832			−0.356705
$195$	0.468657			0.0335613
$196$		0			0
$197$			9.47897i			0.675348i	0.941263	+	0.337674i	$0.109640\pi$
$197$			9.47897i			0.675348i	−0.941263	+	0.337674i	$0.890360\pi$
$198$	2.04100	−	0.0404149i	0.145048	−	0.00287217i
$199$			1.33263i			0.0944675i	0.998884	+	0.0472337i	$0.0150406\pi$
$199$			1.33263i			0.0944675i	−0.998884	+	0.0472337i	$0.984959\pi$
$200$			12.9200i			0.913581i
$201$			13.0157i			0.918057i
$202$		−	4.24458i		−	0.298647i
$203$		0			0
$204$		−	11.7755i		−	0.824452i
$205$			10.4978i			0.733199i
$206$	−2.12974			−0.148386
$207$	3.56308			0.247651
$208$	0.266780			0.0184978
$209$	0.0570690	+	2.88205i	0.00394754	+	0.199356i
$210$		0			0
$211$			5.34281i			0.367814i	0.982944	+	0.183907i	$0.0588745\pi$
$211$			5.34281i			0.367814i	−0.982944	+	0.183907i	$0.941125\pi$
$212$	−10.7407			−0.737676
$213$			2.66532i			0.182625i
$214$	−1.30573			−0.0892577
$215$	31.7623			2.16617
$216$	−2.22884			−0.151654
$217$		0			0
$218$	−1.98474			−0.134423
$219$			5.48838i			0.370870i
$220$	−17.6637	+	0.349767i	−1.19088	+	0.0235813i
$221$	−1.03602			−0.0696900
$222$	5.78127			0.388014
$223$		−	24.5309i		−	1.64271i	−0.570415	−	0.821356i	$-0.693218\pi$
$223$		−	24.5309i		−	1.64271i	0.570415	−	0.821356i	$-0.306782\pi$
$224$		0			0
$225$	5.79672			0.386448
$226$		−	7.31797i		−	0.486784i
$227$	13.1568			0.873249			0.436625	−	0.899644i	$-0.356174\pi$
$227$	13.1568			0.873249			0.436625	+	0.899644i	$0.356174\pi$
$228$		−	1.40901i		−	0.0933140i
$229$		−	14.0607i		−	0.929160i	−0.885531	−	0.464580i	$-0.846205\pi$
$229$		−	14.0607i		−	0.929160i	0.885531	−	0.464580i	$-0.153795\pi$
$230$	7.20617			0.475161
$231$		0			0
$232$	−8.26092			−0.542356
$233$			25.8509i			1.69355i	0.531953	+	0.846774i	$0.321458\pi$
$233$			25.8509i			1.69355i	−0.531953	+	0.846774i	$0.678542\pi$
$234$			0.0877894i			0.00573897i
$235$	28.7937			1.87829
$236$		−	2.50799i		−	0.163257i
$237$	7.05347			0.458172
$238$		0			0
$239$		−	7.49156i		−	0.484589i	−0.970203	−	0.242294i	$-0.922100\pi$
$239$		−	7.49156i		−	0.484589i	0.970203	−	0.242294i	$-0.0779000\pi$
$240$	6.14595			0.396719
$241$	18.1572			1.16961			0.584803	−	0.811176i	$-0.301172\pi$
$241$	18.1572			1.16961			0.584803	+	0.811176i	$0.301172\pi$
$242$	0.268030	+	6.76526i	0.0172296	+	0.434888i
$243$			1.00000i			0.0641500i
$244$	−24.7273			−1.58300
$245$		0			0
$246$	−1.96646			−0.125377
$247$	−0.123965			−0.00788772
$248$	−10.7448			−0.682296
$249$			6.31032i			0.399900i
$250$	1.61134			0.101910
$251$			3.07493i			0.194088i	0.995280	+	0.0970441i	$0.0309388\pi$
$251$			3.07493i			0.194088i	−0.995280	+	0.0970441i	$0.969061\pi$
$252$		0			0
$253$	0.233957	+	11.8151i	0.0147087	+	0.742809i
$254$	−9.65244			−0.605648
$255$	−23.8673			−1.49463
$256$	−6.43694			−0.402309
$257$			3.48778i			0.217562i	0.994066	+	0.108781i	$0.0346947\pi$
$257$			3.48778i			0.217562i	−0.994066	+	0.108781i	$0.965305\pi$
$258$			5.94974i			0.370415i
$259$		0			0
$260$		−	0.759765i		−	0.0471186i
$261$			3.70637i			0.229419i
$262$		−	6.17265i		−	0.381348i
$263$		−	6.46276i		−	0.398511i	−0.979948	−	0.199255i	$-0.936148\pi$
$263$		−	6.46276i		−	0.398511i	0.979948	−	0.199255i	$-0.0638523\pi$
$264$	−0.146349	−	7.39078i	−0.00900714	−	0.454871i
$265$			21.7699i			1.33731i
$266$		0			0
$267$	7.87864			0.482165
$268$	21.1004			1.28891
$269$			16.5450i			1.00877i	0.863479	+	0.504384i	$0.168280\pi$
$269$			16.5450i			1.00877i	−0.863479	+	0.504384i	$0.831720\pi$
$270$			2.02245i			0.123083i
$271$	4.03699			0.245230			0.122615	−	0.992454i	$-0.460872\pi$
$271$	4.03699			0.245230			0.122615	+	0.992454i	$0.460872\pi$
$272$	−13.5863			−0.823788
$273$		0			0
$274$		−	9.03469i		−	0.545806i
$275$	0.380620	+	19.2218i	0.0229523	+	1.15912i
$276$		−	5.77630i		−	0.347692i
$277$			2.44867i			0.147126i	0.997291	+	0.0735632i	$0.0234371\pi$
$277$			2.44867i			0.147126i	−0.997291	+	0.0735632i	$0.976563\pi$
$278$		−	2.74229i		−	0.164472i
$279$			4.82080i			0.288614i
$280$		0			0
$281$			14.1901i			0.846509i	0.906011	+	0.423254i	$0.139112\pi$
$281$			14.1901i			0.846509i	−0.906011	+	0.423254i	$0.860888\pi$
$282$			5.39367i			0.321188i
$283$	26.6806			1.58599			0.792997	−	0.609225i	$-0.208519\pi$
$283$	26.6806			1.58599			0.792997	+	0.609225i	$0.208519\pi$
$284$	4.32089			0.256398
$285$	−2.85586			−0.169166
$286$	−0.291107	+	0.00576437i	−0.0172135	+	0.000340854i
$287$		0			0
$288$			5.60895i			0.330511i
$289$	35.7611			2.10359
$290$			7.49597i			0.440178i
$291$	8.07193			0.473185
$292$	8.89749			0.520686
$293$	18.4082			1.07542			0.537708	−	0.843131i	$-0.319290\pi$
$293$	18.4082			1.07542			0.537708	+	0.843131i	$0.319290\pi$
$294$		0			0
$295$	−5.08334			−0.295963
$296$		−	20.9349i		−	1.21681i
$297$	−3.31597	+	0.0656613i	−0.192412	+	0.00381005i
$298$	−3.08733			−0.178844
$299$	−0.508201			−0.0293900
$300$		−	9.39737i		−	0.542557i
$301$		0			0
$302$	−9.06787			−0.521798
$303$			6.89607i			0.396169i
$304$	−1.62568			−0.0932389
$305$			50.1185i			2.86978i
$306$		−	4.47084i		−	0.255581i
$307$	−24.2462			−1.38380			−0.691902	−	0.721991i	$-0.743227\pi$
$307$	−24.2462			−1.38380			−0.691902	+	0.721991i	$0.743227\pi$
$308$		0			0
$309$	3.46014			0.196841
$310$			9.74984i			0.553754i
$311$			12.5362i			0.710861i	0.934703	+	0.355431i	$0.115666\pi$
$311$			12.5362i			0.710861i	−0.934703	+	0.355431i	$0.884334\pi$
$312$	0.317899			0.0179975
$313$			9.56160i			0.540453i	0.962797	+	0.270227i	$0.0870986\pi$
$313$			9.56160i			0.540453i	−0.962797	+	0.270227i	$0.912901\pi$
$314$	−6.38078			−0.360088
$315$		0			0
$316$		−	11.4347i		−	0.643255i
$317$	−13.8291			−0.776718			−0.388359	−	0.921508i	$-0.626958\pi$
$317$	−13.8291			−0.776718			−0.388359	+	0.921508i	$0.626958\pi$
$318$	−4.07796			−0.228681
$319$	−12.2902	+	0.243365i	−0.688121	+	0.0136258i
$320$		−	0.948060i		−	0.0529982i
$321$	2.12139			0.118404
$322$		0			0
$323$	6.31317			0.351274
$324$	1.62115			0.0900640
$325$	−0.826784			−0.0458617
$326$			3.82991i			0.212119i
$327$	3.22456			0.178318
$328$			7.12085i			0.393183i
$329$		0			0
$330$	−6.70641	+	0.132797i	−0.369175	+	0.00731023i
$331$	−18.2492			−1.00307			−0.501533	−	0.865139i	$-0.667230\pi$
$331$	−18.2492			−1.00307			−0.501533	+	0.865139i	$0.667230\pi$
$332$	10.2300			0.561443
$333$	−9.39271			−0.514717
$334$		−	13.1134i		−	0.717532i
$335$		−	42.7675i		−	2.33664i
$336$		0			0
$337$			31.5515i			1.71872i	0.511370	+	0.859360i	$0.329138\pi$
$337$			31.5515i			1.71872i	−0.511370	+	0.859360i	$0.670862\pi$
$338$			7.98906i			0.434548i
$339$			11.8894i			0.645741i
$340$			38.6925i			2.09839i
$341$	−15.9856	+	0.316540i	−0.865671	+	0.0171416i
$342$		−	0.534962i		−	0.0289275i
$343$		0			0
$344$	21.5449			1.16162
$345$	−11.7077			−0.630322
$346$		−	0.921441i		−	0.0495370i
$347$		−	16.2883i		−	0.874401i	−0.899364	−	0.437200i	$-0.855970\pi$
$347$		−	16.2883i		−	0.874401i	0.899364	−	0.437200i	$-0.144030\pi$
$348$	6.00859			0.322094
$349$	16.8476			0.901829			0.450915	−	0.892567i	$-0.351098\pi$
$349$	16.8476			0.901829			0.450915	+	0.892567i	$0.351098\pi$
$350$		0			0
$351$		−	0.142630i		−	0.00761300i
$352$	−18.5991	+	0.368291i	−0.991337	+	0.0196300i
$353$			10.0756i			0.536272i	0.963381	+	0.268136i	$0.0864076\pi$
$353$			10.0756i			0.536272i	−0.963381	+	0.268136i	$0.913592\pi$
$354$		−	0.952216i		−	0.0506097i
$355$		−	8.75780i		−	0.464816i
$356$		−	12.7725i		−	0.676939i
$357$		0			0
$358$			9.43359i			0.498581i
$359$			13.4533i			0.710036i	0.934859	+	0.355018i	$0.115525\pi$
$359$			13.4533i			0.710036i	−0.934859	+	0.355018i	$0.884475\pi$
$360$	7.32361			0.385988
$361$	−18.2446			−0.960242
$362$	8.98209			0.472088
$363$	−0.435462	−	10.9914i	−0.0228558	−	0.576898i
$364$		0			0
$365$		−	18.0339i		−	0.943938i
$366$	−9.38825			−0.490732
$367$		−	18.3475i		−	0.957729i	−0.877889	−	0.478865i	$-0.841048\pi$
$367$		−	18.3475i		−	0.957729i	0.877889	−	0.478865i	$-0.158952\pi$
$368$	−6.66452			−0.347412
$369$	3.19487			0.166318
$370$	−18.9963			−0.987571
$371$		0			0
$372$	7.81525			0.405202
$373$			24.1790i			1.25194i	0.779847	+	0.625970i	$0.215297\pi$
$373$			24.1790i			1.25194i	−0.779847	+	0.625970i	$0.784703\pi$
$374$	14.8252	−	0.293561i	0.766593	−	0.0151797i
$375$	−2.61791			−0.135188
$376$	19.5313			1.00725
$377$		−	0.528638i		−	0.0272263i
$378$		0			0
$379$	17.5684			0.902427			0.451214	−	0.892416i	$-0.350991\pi$
$379$	17.5684			0.902427			0.451214	+	0.892416i	$0.350991\pi$
$380$			4.62978i			0.237503i
$381$	15.6821			0.803419
$382$			5.52209i			0.282534i
$383$		−	11.3567i		−	0.580298i	−0.956981	−	0.290149i	$-0.906295\pi$
$383$		−	11.3567i		−	0.580298i	0.956981	−	0.290149i	$-0.0937049\pi$
$384$	11.3955			0.581524
$385$		0			0
$386$	−1.29995			−0.0661655
$387$		−	9.66641i		−	0.491371i
$388$		−	13.0858i		−	0.664332i
$389$	0.196302			0.00995292			0.00497646	−	0.999988i	$-0.498416\pi$
$389$	0.196302			0.00995292			0.00497646	+	0.999988i	$0.498416\pi$
$390$		−	0.288462i		−	0.0146068i
$391$	25.8811			1.30886
$392$		0			0
$393$			10.0286i			0.505874i
$394$	5.83437			0.293931
$395$	−23.1766			−1.16614
$396$	0.106447	+	5.37570i	0.00534916	+	0.270139i
$397$			11.6923i			0.586818i	0.955987	+	0.293409i	$0.0947898\pi$
$397$			11.6923i			0.586818i	−0.955987	+	0.293409i	$0.905210\pi$
$398$	0.820241			0.0411150
$399$		0			0
$400$	−10.8424			−0.542120
$401$	28.2224			1.40936			0.704680	−	0.709525i	$-0.251091\pi$
$401$	28.2224			1.40936			0.704680	+	0.709525i	$0.251091\pi$
$402$	8.01125			0.399565
$403$		−	0.687588i		−	0.0342512i
$404$	11.1796			0.556205
$405$		−	3.28584i		−	0.163275i
$406$		0			0
$407$	−0.616737	−	31.1460i	−0.0305705	−	1.54385i
$408$	−16.1896			−0.801505
$409$	20.5708			1.01716			0.508581	−	0.861014i	$-0.330170\pi$
$409$	20.5708			1.01716			0.508581	+	0.861014i	$0.330170\pi$
$410$	6.46147			0.319109
$411$			14.6785i			0.724036i
$412$		−	5.60941i		−	0.276356i
$413$		0			0
$414$		−	2.19310i		−	0.107785i
$415$		−	20.7347i		−	1.01783i
$416$		−	0.800002i		−	0.0392233i
$417$			4.45534i			0.218179i
$418$	1.77392	−	0.0351263i	0.0867654	−	0.00171808i
$419$			24.6522i			1.20434i	0.798368	+	0.602170i	$0.205697\pi$
$419$			24.6522i			1.20434i	−0.798368	+	0.602170i	$0.794303\pi$
$420$		0			0
$421$	28.5775			1.39278			0.696391	−	0.717663i	$-0.254788\pi$
$421$	28.5775			1.39278			0.696391	+	0.717663i	$0.254788\pi$
$422$	3.28853			0.160083
$423$		−	8.76297i		−	0.426070i
$424$			14.7669i			0.717144i
$425$	42.1056			2.04242
$426$	1.64052			0.0794835
$427$		0			0
$428$		−	3.43909i		−	0.166235i
$429$	0.472956	−	0.00936524i	0.0228345	−	0.000452158i
$430$		−	19.5499i		−	0.942779i
$431$		−	18.9985i		−	0.915128i	−0.889177	−	0.457564i	$-0.848722\pi$
$431$		−	18.9985i		−	0.915128i	0.889177	−	0.457564i	$-0.151278\pi$
$432$		−	1.87044i		−	0.0899914i
$433$			13.5205i			0.649755i	0.945756	+	0.324878i	$0.105323\pi$
$433$			13.5205i			0.649755i	−0.945756	+	0.324878i	$0.894677\pi$
$434$		0			0
$435$		−	12.1785i		−	0.583916i
$436$		−	5.22750i		−	0.250352i
$437$	3.09683			0.148141
$438$	3.37813			0.161413
$439$	2.40989			0.115018			0.0575089	−	0.998345i	$-0.481684\pi$
$439$	2.40989			0.115018			0.0575089	+	0.998345i	$0.481684\pi$
$440$	0.480878	+	24.2849i	0.0229250	+	1.15774i
$441$		0			0
$442$			0.637674i			0.0303311i
$443$	23.7193			1.12694			0.563470	−	0.826136i	$-0.309466\pi$
$443$	23.7193			1.12694			0.563470	+	0.826136i	$0.309466\pi$
$444$			15.2270i			0.722642i
$445$	−25.8879			−1.22720
$446$	−15.0989			−0.714956
$447$	5.01591			0.237245
$448$		0			0
$449$	−0.0666558			−0.00314568			−0.00157284	−	0.999999i	$-0.500501\pi$
$449$	−0.0666558			−0.00314568			−0.00157284	+	0.999999i	$0.500501\pi$
$450$		−	3.56792i		−	0.168193i
$451$	0.209779	+	10.5941i	0.00987811	+	0.498856i
$452$	19.2744			0.906594
$453$	14.7324			0.692188
$454$		−	8.09811i		−	0.380063i
$455$		0			0
$456$	−1.93718			−0.0907168
$457$			31.1211i			1.45578i	0.685692	+	0.727892i	$0.259500\pi$
$457$			31.1211i			1.45578i	−0.685692	+	0.727892i	$0.740500\pi$
$458$	−8.65448			−0.404397
$459$			7.26368i			0.339040i
$460$			18.9800i			0.884946i
$461$	−3.58542			−0.166990			−0.0834948	−	0.996508i	$-0.526608\pi$
$461$	−3.58542			−0.166990			−0.0834948	+	0.996508i	$0.526608\pi$
$462$		0			0
$463$	−20.7914			−0.966260			−0.483130	−	0.875549i	$-0.660500\pi$
$463$	−20.7914			−0.966260			−0.483130	+	0.875549i	$0.660500\pi$
$464$		−	6.93254i		−	0.321835i
$465$		−	15.8404i		−	0.734579i
$466$	15.9114			0.737081
$467$		−	38.8763i		−	1.79898i	−0.436939	−	0.899491i	$-0.643937\pi$
$467$		−	38.8763i		−	1.79898i	0.436939	−	0.899491i	$-0.356063\pi$
$468$	−0.231224			−0.0106883
$469$		0			0
$470$		−	17.7227i		−	0.817488i
$471$	10.3667			0.477673
$472$	−3.44812			−0.158713
$473$	32.0536	−	0.634709i	1.47383	−	0.0291840i
$474$		−	4.34146i		−	0.199410i
$475$	5.03818			0.231167
$476$		0			0
$477$	6.62537			0.303355
$478$	−4.61110			−0.210907
$479$	−16.1591			−0.738329			−0.369164	−	0.929364i	$-0.620356\pi$
$479$	−16.1591			−0.738329			−0.369164	+	0.929364i	$0.620356\pi$
$480$		−	18.4301i		−	0.841215i
$481$	1.33968			0.0610840
$482$		−	11.1758i		−	0.509046i
$483$		0			0
$484$	−17.8187	+	0.705951i	−0.809941	+	0.0320887i
$485$	−26.5230			−1.20435
$486$	0.615506			0.0279199
$487$	−0.0472275			−0.00214008			−0.00107004	−	0.999999i	$-0.500341\pi$
$487$	−0.0472275			−0.00214008			−0.00107004	+	0.999999i	$0.500341\pi$
$488$			33.9963i			1.53894i
$489$		−	6.22238i		−	0.281386i
$490$		0			0
$491$			30.2054i			1.36315i	0.731748	+	0.681576i	$0.238705\pi$
$491$			30.2054i			1.36315i	−0.731748	+	0.681576i	$0.761295\pi$
$492$		−	5.17936i		−	0.233504i
$493$			26.9219i			1.21250i
$494$			0.0763015i			0.00343296i
$495$	10.8958	−	0.215752i	0.489728	−	0.00969734i
$496$		−	9.01700i		−	0.404875i
$497$		0			0
$498$	3.88404			0.174048
$499$	1.50934			0.0675673			0.0337836	−	0.999429i	$-0.489244\pi$
$499$	1.50934			0.0675673			0.0337836	+	0.999429i	$0.489244\pi$
$500$			4.24402i			0.189798i
$501$			21.3050i			0.951839i
$502$	1.89264			0.0844727
$503$	37.3354			1.66471			0.832353	−	0.554247i	$-0.186994\pi$
$503$	37.3354			1.66471			0.832353	+	0.554247i	$0.186994\pi$
$504$		0			0
$505$		−	22.6594i		−	1.00833i
$506$	7.27227	−	0.144002i	0.323292	−	0.00640166i
$507$		−	12.9797i		−	0.576447i
$508$		−	25.4231i		−	1.12797i
$509$			10.8665i			0.481650i	0.970569	+	0.240825i	$0.0774180\pi$
$509$			10.8665i			0.481650i	−0.970569	+	0.240825i	$0.922582\pi$
$510$			14.6905i			0.650505i
$511$		0			0
$512$		−	18.8290i		−	0.832132i
$513$			0.869142i			0.0383736i
$514$	2.14675			0.0946891
$515$	−11.3695			−0.500998
$516$	−15.6707			−0.689865
$517$	29.0578	−	0.575388i	1.27796	−	0.0253055i
$518$		0			0
$519$			1.49705i			0.0657130i
$520$	−1.04456			−0.0458071
$521$		−	17.8174i		−	0.780593i	−0.920689	−	0.390297i	$-0.872372\pi$
$521$		−	17.8174i		−	0.780593i	0.920689	−	0.390297i	$-0.127628\pi$
$522$	2.28130			0.0998496
$523$	−32.3763			−1.41572			−0.707858	−	0.706355i	$-0.750338\pi$
$523$	−32.3763			−1.41572			−0.707858	+	0.706355i	$0.750338\pi$
$524$	16.2578			0.710227
$525$		0			0
$526$	−3.97787			−0.173443
$527$			35.0168i			1.52535i
$528$	6.20232	−	0.122815i	0.269921	−	0.00534485i
$529$	−10.3044			−0.448019
$530$	13.3995			0.582037
$531$			1.54704i			0.0671360i
$532$		0			0
$533$	−0.455682			−0.0197378
$534$		−	4.84935i		−	0.209852i
$535$	−6.97053			−0.301362
$536$		−	29.0100i		−	1.25304i
$537$		−	15.3266i		−	0.661390i
$538$	10.1836			0.439045
$539$		0			0
$540$	−5.32684			−0.229231
$541$		−	24.7892i		−	1.06577i	−0.846187	−	0.532886i	$-0.821107\pi$
$541$		−	24.7892i		−	1.06577i	0.846187	−	0.532886i	$-0.178893\pi$
$542$		−	2.48479i		−	0.106731i
$543$	−14.5930			−0.626246
$544$			40.7416i			1.74678i
$545$	−10.5954			−0.453856
$546$		0			0
$547$		−	15.2233i		−	0.650903i	−0.945559	−	0.325452i	$-0.894484\pi$
$547$		−	15.2233i		−	0.650903i	0.945559	−	0.325452i	$-0.105516\pi$
$548$	23.7960			1.01652
$549$	15.2529			0.650978
$550$	11.8311	−	0.234274i	0.504481	−	0.00998949i
$551$			3.22136i			0.137235i
$552$	−7.94155			−0.338015
$553$		0			0
$554$	1.50717			0.0640337
$555$	30.8629			1.31006
$556$	7.22278			0.306314
$557$		−	22.0992i		−	0.936375i	−0.883629	−	0.468187i	$-0.844907\pi$
$557$		−	22.0992i		−	0.936375i	0.883629	−	0.468187i	$-0.155093\pi$
$558$	2.96723			0.125613
$559$			1.37872i			0.0583135i
$560$		0			0
$561$	−24.0862	+	0.476943i	−1.01692	+	0.0201365i
$562$	8.73408			0.368425
$563$	−25.9110			−1.09202			−0.546009	−	0.837779i	$-0.683854\pi$
$563$	−25.9110			−1.09202			−0.546009	+	0.837779i	$0.683854\pi$
$564$	−14.2061			−0.598185
$565$		−	39.0665i		−	1.64354i
$566$		−	16.4221i		−	0.690270i
$567$		0			0
$568$		−	5.94058i		−	0.249261i
$569$		−	29.6107i		−	1.24134i	−0.784070	−	0.620672i	$-0.786860\pi$
$569$		−	29.6107i		−	1.24134i	0.784070	−	0.620672i	$-0.213140\pi$
$570$			1.75780i			0.0736261i
$571$		−	8.32745i		−	0.348493i	−0.984702	−	0.174246i	$-0.944251\pi$
$571$		−	8.32745i		−	0.348493i	0.984702	−	0.174246i	$-0.0557489\pi$
$572$	−0.0151825	−	0.766733i	−0.000634811	−	0.0320587i
$573$		−	8.97161i		−	0.374795i
$574$		0			0
$575$	20.6542			0.861340
$576$	−0.288529			−0.0120221
$577$		−	28.5782i		−	1.18973i	−0.803827	−	0.594864i	$-0.797206\pi$
$577$		−	28.5782i		−	1.18973i	0.803827	−	0.594864i	$-0.202794\pi$
$578$		−	22.0112i		−	0.915544i
$579$	2.11199			0.0877714
$580$	−19.7433			−0.819794
$581$		0			0
$582$		−	4.96832i		−	0.205944i
$583$	0.435030	+	21.9696i	0.0180171	+	0.909886i
$584$		−	12.2327i		−	0.506194i
$585$			0.468657i			0.0193766i
$586$		−	11.3303i		−	0.468052i
$587$			26.8088i			1.10652i	0.833009	+	0.553260i	$0.186616\pi$
$587$			26.8088i			1.10652i	−0.833009	+	0.553260i	$0.813384\pi$
$588$		0			0
$589$			4.18996i			0.172644i
$590$			3.12883i			0.128812i
$591$	−9.47897			−0.389913
$592$	17.5685			0.722060
$593$	−24.3666			−1.00062			−0.500308	−	0.865848i	$-0.666780\pi$
$593$	−24.3666			−1.00062			−0.500308	+	0.865848i	$0.666780\pi$
$594$	0.0404149	+	2.04100i	0.00165825	+	0.0837434i
$595$		0			0
$596$		−	8.13156i		−	0.333082i
$597$	−1.33263			−0.0545408
$598$			0.312801i			0.0127914i
$599$	−37.3795			−1.52728			−0.763642	−	0.645640i	$-0.776591\pi$
$599$	−37.3795			−1.52728			−0.763642	+	0.645640i	$0.776591\pi$
$600$	−12.9200			−0.527456
$601$	0.423296			0.0172666			0.00863329	−	0.999963i	$-0.497252\pi$
$601$	0.423296			0.0172666			0.00863329	+	0.999963i	$0.497252\pi$
$602$		0			0
$603$	−13.0157			−0.530041
$604$		−	23.8834i		−	0.971803i
$605$	1.43086	+	36.1159i	0.0581727	+	1.46832i
$606$	4.24458			0.172424
$607$	31.5129			1.27907			0.639534	−	0.768763i	$-0.279127\pi$
$607$	31.5129			1.27907			0.639534	+	0.768763i	$0.279127\pi$
$608$			4.87497i			0.197706i
$609$		0			0
$610$	30.8483			1.24901
$611$			1.24986i			0.0505639i
$612$	11.7755			0.475998
$613$			28.0471i			1.13281i	0.824127	+	0.566405i	$0.191666\pi$
$613$			28.0471i			1.13281i	−0.824127	+	0.566405i	$0.808334\pi$
$614$			14.9237i			0.602271i
$615$	−10.4978			−0.423313
$616$		0			0
$617$	−41.4810			−1.66996			−0.834981	−	0.550279i	$-0.814521\pi$
$617$	−41.4810			−1.66996			−0.834981	+	0.550279i	$0.814521\pi$
$618$		−	2.12974i		−	0.0856707i
$619$			10.7333i			0.431409i	0.976459	+	0.215704i	$0.0692047\pi$
$619$			10.7333i			0.431409i	−0.976459	+	0.215704i	$0.930795\pi$
$620$	−25.6796			−1.03132
$621$			3.56308i			0.142982i
$622$	7.71610			0.309387
$623$		0			0
$624$			0.266780i			0.0106797i
$625$	−20.3816			−0.815264
$626$	5.88522			0.235221
$627$	−2.88205	+	0.0570690i	−0.115098	+	0.00227912i
$628$		−	16.8060i		−	0.670633i
$629$	−68.2256			−2.72033
$630$		0			0
$631$	3.36006			0.133762			0.0668809	−	0.997761i	$-0.478695\pi$
$631$	3.36006			0.133762			0.0668809	+	0.997761i	$0.478695\pi$
$632$	−15.7211			−0.625351
$633$	−5.34281			−0.212358
$634$			8.51189i			0.338050i
$635$	−51.5289			−2.04486
$636$		−	10.7407i		−	0.425898i
$637$		0			0
$638$	0.149793	+	7.56472i	0.00593036	+	0.299490i
$639$	−2.66532			−0.105438
$640$	−37.4437			−1.48009
$641$	33.6673			1.32978			0.664890	−	0.746941i	$-0.268478\pi$
$641$	33.6673			1.32978			0.664890	+	0.746941i	$0.268478\pi$
$642$		−	1.30573i		−	0.0515330i
$643$		−	37.8334i		−	1.49200i	−0.665944	−	0.746002i	$-0.731971\pi$
$643$		−	37.8334i		−	1.49200i	0.665944	−	0.746002i	$-0.268029\pi$
$644$		0			0
$645$			31.7623i			1.25064i
$646$		−	3.88580i		−	0.152885i
$647$		−	5.02324i		−	0.197484i	−0.995113	−	0.0987421i	$-0.968518\pi$
$647$		−	5.02324i		−	0.197484i	0.995113	−	0.0987421i	$-0.0314819\pi$
$648$		−	2.22884i		−	0.0875572i
$649$	−5.12996	+	0.101581i	−0.201369	+	0.00398740i
$650$			0.508891i			0.0199603i
$651$		0			0
$652$	−10.0874			−0.395054
$653$	−31.7175			−1.24120			−0.620601	−	0.784126i	$-0.713111\pi$
$653$	−31.7175			−1.24120			−0.620601	+	0.784126i	$0.713111\pi$
$654$		−	1.98474i		−	0.0776093i
$655$		−	32.9522i		−	1.28755i
$656$	−5.97580			−0.233316
$657$	−5.48838			−0.214122
$658$		0			0
$659$			3.15699i			0.122979i	0.998108	+	0.0614894i	$0.0195851\pi$
$659$			3.15699i			0.122979i	−0.998108	+	0.0614894i	$0.980415\pi$
$660$	−0.349767	−	17.6637i	−0.0136147	−	0.687557i
$661$			44.4762i			1.72992i	0.501837	+	0.864962i	$0.332658\pi$
$661$			44.4762i			1.72992i	−0.501837	+	0.864962i	$0.667342\pi$
$662$			11.2325i			0.436563i
$663$		−	1.03602i		−	0.0402355i
$664$		−	14.0647i		−	0.545816i
$665$		0			0
$666$			5.78127i			0.224020i
$667$			13.2061i			0.511343i
$668$	34.5387			1.33634
$669$	24.5309			0.948421
$670$	−26.3237			−1.01697
$671$	1.00152	+	50.5782i	0.0386634	+	1.95255i
$672$		0			0
$673$			29.7473i			1.14667i	0.819319	+	0.573337i	$0.194352\pi$
$673$			29.7473i			1.14667i	−0.819319	+	0.573337i	$0.805648\pi$
$674$	19.4202			0.748037
$675$			5.79672i			0.223116i
$676$	−21.0420			−0.809307
$677$	14.3360			0.550978			0.275489	−	0.961304i	$-0.411160\pi$
$677$	14.3360			0.550978			0.275489	+	0.961304i	$0.411160\pi$
$678$	7.31797			0.281045
$679$		0			0
$680$	53.1964			2.03999
$681$			13.1568i			0.504171i
$682$	0.194832	+	9.83927i	0.00746052	+	0.376765i
$683$	14.2841			0.546567			0.273284	−	0.961933i	$-0.411890\pi$
$683$	14.2841			0.546567			0.273284	+	0.961933i	$0.411890\pi$
$684$	1.40901			0.0538749
$685$		−	48.2311i		−	1.84281i
$686$		0			0
$687$	14.0607			0.536451
$688$			18.0804i			0.689309i
$689$	−0.944973			−0.0360006
$690$			7.20617i			0.274334i
$691$		−	20.5745i		−	0.782691i	−0.920244	−	0.391345i	$-0.872010\pi$
$691$		−	20.5745i		−	0.782691i	0.920244	−	0.391345i	$-0.127990\pi$
$692$	2.42694			0.0922583
$693$		0			0
$694$	−10.0255			−0.380564
$695$		−	14.6395i		−	0.555308i
$696$		−	8.26092i		−	0.313129i
$697$	23.2065			0.879009
$698$		−	10.3698i		−	0.392502i
$699$	−25.8509			−0.977770
$700$		0			0
$701$			7.46334i			0.281886i	0.990018	+	0.140943i	$0.0450135\pi$
$701$			7.46334i			0.281886i	−0.990018	+	0.140943i	$0.954987\pi$
$702$	−0.0877894			−0.00331340
$703$	−8.16360			−0.307896
$704$	−0.0189452	−	0.956756i	−0.000714024	−	0.0360591i
$705$			28.7937i			1.08443i
$706$	6.20162			0.233401
$707$		0			0
$708$	2.50799			0.0942562
$709$	−35.0131			−1.31495			−0.657473	−	0.753478i	$-0.728374\pi$
$709$	−35.0131			−1.31495			−0.657473	+	0.753478i	$0.728374\pi$
$710$	−5.39049			−0.202301
$711$			7.05347i			0.264526i
$712$	−17.5602			−0.658098
$713$			17.1769i			0.643280i
$714$		0			0
$715$	−1.55406	+	0.0307727i	−0.0581184	+	0.00115083i
$716$	−24.8467			−0.928564
$717$	7.49156			0.279777
$718$	8.28057			0.309028
$719$			27.2316i			1.01557i	0.861484	+	0.507784i	$0.169535\pi$
$719$			27.2316i			1.01557i	−0.861484	+	0.507784i	$0.830465\pi$
$720$			6.14595i			0.229046i
$721$		0			0
$722$			11.2297i			0.417925i
$723$			18.1572i			0.675272i
$724$			23.6575i			0.879224i
$725$			21.4848i			0.797926i
$726$	−6.76526	+	0.268030i	−0.251082	+	0.00994752i
$727$			31.0062i			1.14996i	0.818168	+	0.574979i	$0.194990\pi$
$727$			31.0062i			1.14996i	−0.818168	+	0.574979i	$0.805010\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−11.1000			−0.410829
$731$		−	70.2137i		−	2.59695i
$732$		−	24.7273i		−	0.913946i
$733$	−29.6380			−1.09471			−0.547353	−	0.836902i	$-0.684364\pi$
$733$	−29.6380			−1.09471			−0.547353	+	0.836902i	$0.684364\pi$
$734$	−11.2930			−0.416831
$735$		0			0
$736$			19.9852i			0.736663i
$737$	−0.854628	−	43.1598i	−0.0314806	−	1.58981i
$738$		−	1.96646i		−	0.0723864i
$739$		−	30.9252i		−	1.13760i	−0.822476	−	0.568800i	$-0.807408\pi$
$739$		−	30.9252i		−	1.13760i	0.822476	−	0.568800i	$-0.192592\pi$
$740$		−	50.0335i		−	1.83927i
$741$		−	0.123965i		−	0.00455398i
$742$		0			0
$743$			34.4931i			1.26543i	0.774385	+	0.632715i	$0.218059\pi$
$743$			34.4931i			1.26543i	−0.774385	+	0.632715i	$0.781941\pi$
$744$		−	10.7448i		−	0.393924i
$745$	−16.4815			−0.603834
$746$	14.8823			0.544881
$747$	−6.31032			−0.230883
$748$	0.773197	+	39.0474i	0.0282709	+	1.42771i
$749$		0			0
$750$			1.61134i			0.0588377i
$751$	33.8376			1.23475			0.617376	−	0.786669i	$-0.288196\pi$
$751$	33.8376			1.23475			0.617376	+	0.786669i	$0.288196\pi$
$752$			16.3906i			0.597703i
$753$	−3.07493			−0.112057
$754$	−0.325380			−0.0118496
$755$	−48.4082			−1.76175
$756$		0			0
$757$	20.9449			0.761257			0.380628	−	0.924728i	$-0.375708\pi$
$757$	20.9449			0.761257			0.380628	+	0.924728i	$0.375708\pi$
$758$		−	10.8135i		−	0.392762i
$759$	−11.8151	+	0.233957i	−0.428861	+	0.00849209i
$760$	6.36526			0.230892
$761$	−25.8678			−0.937708			−0.468854	−	0.883276i	$-0.655333\pi$
$761$	−25.8678			−0.937708			−0.468854	+	0.883276i	$0.655333\pi$
$762$		−	9.65244i		−	0.349671i
$763$		0			0
$764$	−14.5443			−0.526196
$765$		−	23.8673i		−	0.862923i
$766$	−6.99010			−0.252562
$767$		−	0.220654i		−	0.00796737i
$768$		−	6.43694i		−	0.232273i
$769$	−2.66035			−0.0959346			−0.0479673	−	0.998849i	$-0.515274\pi$
$769$	−2.66035			−0.0959346			−0.0479673	+	0.998849i	$0.515274\pi$
$770$		0			0
$771$	−3.48778			−0.125609
$772$		−	3.42386i		−	0.123227i
$773$			33.2866i			1.19724i	0.801035	+	0.598618i	$0.204283\pi$
$773$			33.2866i			1.19724i	−0.801035	+	0.598618i	$0.795717\pi$
$774$	−5.94974			−0.213859
$775$			27.9448i			1.00381i
$776$	−17.9911			−0.645841
$777$		0			0
$778$		−	0.120825i		−	0.00433180i
$779$	2.77679			0.0994889
$780$	0.759765			0.0272039
$781$	−0.175008	−	8.83813i	−0.00626229	−	0.316253i
$782$		−	15.9300i		−	0.569655i
$783$	−3.70637			−0.132455
$784$		0			0
$785$	−34.0633			−1.21577
$786$	6.17265			0.220171
$787$	−14.9131			−0.531595			−0.265797	−	0.964029i	$-0.585635\pi$
$787$	−14.9131			−0.531595			−0.265797	+	0.964029i	$0.585635\pi$
$788$			15.3668i			0.547421i
$789$	6.46276			0.230080
$790$			14.2653i			0.507537i
$791$		0			0
$792$	7.39078	−	0.146349i	0.262620	−	0.00520027i
$793$	−2.17551			−0.0772547
$794$	7.19667			0.255400
$795$	−21.7699			−0.772098
$796$			2.16039i			0.0765730i
$797$		−	37.8391i		−	1.34033i	−0.742212	−	0.670165i	$-0.766223\pi$
$797$		−	37.8391i		−	1.34033i	0.742212	−	0.670165i	$-0.233777\pi$
$798$		0			0
$799$		−	63.6515i		−	2.25183i
$800$			32.5135i			1.14953i
$801$			7.87864i			0.278378i
$802$		−	17.3711i		−	0.613394i
$803$	−0.360374	−	18.1993i	−0.0127173	−	0.642240i
$804$			21.1004i			0.744155i
$805$		0			0
$806$	−0.423215			−0.0149071
$807$	−16.5450			−0.582413
$808$		−	15.3703i		−	0.540724i
$809$			41.5952i			1.46241i	0.682158	+	0.731204i	$0.261041\pi$
$809$			41.5952i			1.46241i	−0.682158	+	0.731204i	$0.738959\pi$
$810$	−2.02245			−0.0710618
$811$	10.1870			0.357713			0.178857	−	0.983875i	$-0.442760\pi$
$811$	10.1870			0.357713			0.178857	+	0.983875i	$0.442760\pi$
$812$		0			0
$813$			4.03699i			0.141583i
$814$	−19.1705	+	0.379606i	−0.671927	+	0.0133052i
$815$			20.4457i			0.716182i
$816$		−	13.5863i		−	0.475614i
$817$		−	8.40149i		−	0.293931i
$818$		−	12.6615i		−	0.442698i
$819$		0			0
$820$			17.0185i			0.594313i
$821$		−	35.9322i		−	1.25404i	−0.779003	−	0.627021i	$-0.784274\pi$
$821$		−	35.9322i		−	1.25404i	0.779003	−	0.627021i	$-0.215726\pi$
$822$	9.03469			0.315121
$823$	4.64415			0.161885			0.0809425	−	0.996719i	$-0.474207\pi$
$823$	4.64415			0.161885			0.0809425	+	0.996719i	$0.474207\pi$
$824$	−7.71211			−0.268664
$825$	−19.2218	+	0.380620i	−0.669217	+	0.0132515i
$826$		0			0
$827$			28.9418i			1.00641i	0.864168	+	0.503203i	$0.167845\pi$
$827$			28.9418i			1.00641i	−0.864168	+	0.503203i	$0.832155\pi$
$828$	5.77630			0.200740
$829$		−	6.60597i		−	0.229435i	−0.993398	−	0.114717i	$-0.963404\pi$
$829$		−	6.60597i		−	0.229435i	0.993398	−	0.114717i	$-0.0365963\pi$
$830$	−12.7623			−0.442987
$831$	−2.44867			−0.0849435
$832$	0.0411528			0.00142672
$833$		0			0
$834$	2.74229			0.0949577
$835$		−	70.0049i		−	2.42262i
$836$	0.0925175	+	4.67225i	0.00319978	+	0.161593i
$837$	−4.82080			−0.166631
$838$	15.1736			0.524164
$839$		−	10.2775i		−	0.354817i	−0.984137	−	0.177409i	$-0.943229\pi$
$839$		−	10.2775i		−	0.354817i	0.984137	−	0.177409i	$-0.0567714\pi$
$840$		0			0
$841$	15.2628			0.526304
$842$		−	17.5896i		−	0.606179i
$843$	−14.1901			−0.488732
$844$			8.66150i			0.298141i
$845$			42.6490i			1.46717i
$846$	−5.39367			−0.185438
$847$		0			0
$848$	−12.3923			−0.425555
$849$			26.6806i			0.915674i
$850$		−	25.9162i		−	0.888920i
$851$	−33.4670			−1.14723
$852$			4.32089i			0.148031i
$853$	11.9462			0.409031			0.204516	−	0.978863i	$-0.434438\pi$
$853$	11.9462			0.409031			0.204516	+	0.978863i	$0.434438\pi$
$854$		0			0
$855$		−	2.85586i		−	0.0976683i
$856$	−4.72824			−0.161608
$857$	42.2024			1.44160			0.720802	−	0.693141i	$-0.243773\pi$
$857$	42.2024			1.44160			0.720802	+	0.693141i	$0.243773\pi$
$858$	−0.00576437	−	0.291107i	−0.000196792	−	0.00993824i
$859$			40.8408i			1.39347i	0.717329	+	0.696735i	$0.245365\pi$
$859$			40.8408i			1.39347i	−0.717329	+	0.696735i	$0.754635\pi$
$860$	51.4914			1.75584
$861$		0			0
$862$	−11.6937			−0.398290
$863$	−5.24851			−0.178661			−0.0893307	−	0.996002i	$-0.528473\pi$
$863$	−5.24851			−0.178661			−0.0893307	+	0.996002i	$0.528473\pi$
$864$	−5.60895			−0.190820
$865$		−	4.91905i		−	0.167253i
$866$	8.32198			0.282792
$867$			35.7611i			1.21451i
$868$		0			0
$869$	−23.3891	+	0.463140i	−0.793422	+	0.0157109i
$870$	−7.49597			−0.254137
$871$	1.85642			0.0629025
$872$	−7.18703			−0.243384
$873$			8.07193i			0.273193i
$874$		−	1.90612i		−	0.0644753i
$875$		0			0
$876$			8.89749i			0.300618i
$877$		−	9.72659i		−	0.328444i	−0.986423	−	0.164222i	$-0.947489\pi$
$877$		−	9.72659i		−	0.328444i	0.986423	−	0.164222i	$-0.0525113\pi$
$878$		−	1.48330i		−	0.0500590i
$879$			18.4082i			0.620892i
$880$	−20.3798	+	0.403551i	−0.687004	+	0.0136037i
$881$		−	16.1119i		−	0.542824i	−0.962463	−	0.271412i	$-0.912509\pi$
$881$		−	16.1119i		−	0.542824i	0.962463	−	0.271412i	$-0.0874906\pi$
$882$		0			0
$883$	−4.01412			−0.135086			−0.0675430	−	0.997716i	$-0.521516\pi$
$883$	−4.01412			−0.135086			−0.0675430	+	0.997716i	$0.521516\pi$
$884$	−1.67954			−0.0564890
$885$		−	5.08334i		−	0.170875i
$886$		−	14.5994i		−	0.490477i
$887$	−28.2123			−0.947276			−0.473638	−	0.880720i	$-0.657059\pi$
$887$	−28.2123			−0.947276			−0.473638	+	0.880720i	$0.657059\pi$
$888$	20.9349			0.702528
$889$		0			0
$890$			15.9342i			0.534115i
$891$	−0.0656613	−	3.31597i	−0.00219974	−	0.111089i
$892$		−	39.7684i		−	1.33154i
$893$		−	7.61627i		−	0.254869i
$894$		−	3.08733i		−	0.103256i
$895$			50.3606i			1.68337i
$896$		0			0
$897$		−	0.508201i		−	0.0169683i
$898$			0.0410271i			0.00136909i
$899$	−17.8677			−0.595920
$900$	9.39737			0.313246
$901$	48.1246			1.60326
$902$	6.52073	−	0.129120i	0.217117	−	0.00429924i
$903$		0			0
$904$		−	26.4995i		−	0.881360i
$905$	47.9503			1.59392
$906$		−	9.06787i		−	0.301260i
$907$	−7.21757			−0.239655			−0.119828	−	0.992795i	$-0.538234\pi$
$907$	−7.21757			−0.239655			−0.119828	+	0.992795i	$0.538234\pi$
$908$	21.3292			0.707835
$909$	−6.89607			−0.228728
$910$		0			0
$911$	−15.0138			−0.497431			−0.248715	−	0.968577i	$-0.580008\pi$
$911$	−15.0138			−0.497431			−0.248715	+	0.968577i	$0.580008\pi$
$912$		−	1.62568i		−	0.0538315i
$913$	−0.414344	−	20.9249i	−0.0137128	−	0.692512i
$914$	19.1552			0.633599
$915$	−50.1185			−1.65687
$916$		−	22.7946i		−	0.753155i
$917$		0			0
$918$	4.47084			0.147560
$919$		−	18.7654i		−	0.619013i	−0.950897	−	0.309507i	$-0.899836\pi$
$919$		−	18.7654i		−	0.619013i	0.950897	−	0.309507i	$-0.100164\pi$
$920$	26.0946			0.860315
$921$		−	24.2462i		−	0.798940i
$922$			2.20685i			0.0726787i
$923$	0.380153			0.0125129
$924$		0			0
$925$	−54.4469			−1.79020
$926$			12.7973i			0.420544i
$927$			3.46014i			0.113646i
$928$	−20.7889			−0.682428
$929$		−	1.14582i		−	0.0375933i	−0.999823	−	0.0187966i	$-0.994016\pi$
$929$		−	1.14582i		−	0.0375933i	0.999823	−	0.0187966i	$-0.00598351\pi$
$930$	−9.74984			−0.319710
$931$		0			0
$932$			41.9082i			1.37275i
$933$	−12.5362			−0.410416
$934$	−23.9286			−0.782969
$935$	79.1433	−	1.56716i	2.58826	−	0.0512515i
$936$			0.317899i			0.0103908i
$937$	46.7125			1.52603			0.763015	−	0.646380i	$-0.223718\pi$
$937$	46.7125			1.52603			0.763015	+	0.646380i	$0.223718\pi$
$938$		0			0
$939$	−9.56160			−0.312031
$940$	46.6790			1.52250
$941$	5.32897			0.173719			0.0868597	−	0.996221i	$-0.472317\pi$
$941$	5.32897			0.173719			0.0868597	+	0.996221i	$0.472317\pi$
$942$		−	6.38078i		−	0.207897i
$943$	11.3836			0.370700
$944$		−	2.89365i		−	0.0941803i
$945$		0			0
$946$	−0.390668	−	19.7292i	−0.0127017	−	0.641451i
$947$	30.7126			0.998025			0.499012	−	0.866595i	$-0.333696\pi$
$947$	30.7126			0.998025			0.499012	+	0.866595i	$0.333696\pi$
$948$	11.4347			0.371383
$949$	0.782805			0.0254109
$950$		−	3.10103i		−	0.100611i
$951$		−	13.8291i		−	0.448439i
$952$		0			0
$953$			13.1207i			0.425021i	0.977159	+	0.212510i	$0.0681640\pi$
$953$			13.1207i			0.425021i	−0.977159	+	0.212510i	$0.931836\pi$
$954$		−	4.07796i		−	0.132029i
$955$			29.4793i			0.953926i
$956$		−	12.1450i		−	0.392796i
$957$	−0.243365	−	12.2902i	−0.00786688	−	0.397287i
$958$			9.94604i			0.321342i
$959$		0			0
$960$	0.948060			0.0305985
$961$	7.75989			0.250319
$962$		−	0.824580i		−	0.0265855i
$963$			2.12139i			0.0683608i
$964$	29.4355			0.948054
$965$	−6.93966			−0.223396
$966$		0			0
$967$		−	25.7216i		−	0.827150i	−0.910470	−	0.413575i	$-0.864280\pi$
$967$		−	25.7216i		−	0.827150i	0.910470	−	0.413575i	$-0.135720\pi$
$968$	0.970577	+	24.4980i	0.0311955	+	0.787397i
$969$			6.31317i			0.202808i
$970$			16.3251i			0.524167i
$971$			14.4915i			0.465055i	0.972590	+	0.232528i	$0.0746996\pi$
$971$			14.4915i			0.465055i	−0.972590	+	0.232528i	$0.925300\pi$
$972$			1.62115i			0.0519985i
$973$		0			0
$974$			0.0290688i			0.000931425i
$975$		−	0.826784i		−	0.0264783i
$976$	−28.5296			−0.913210
$977$	−46.0408			−1.47298			−0.736488	−	0.676451i	$-0.763517\pi$
$977$	−46.0408			−1.47298			−0.736488	+	0.676451i	$0.763517\pi$
$978$	−3.82991			−0.122467
$979$	−26.1254	+	0.517321i	−0.834970	+	0.0165337i
$980$		0			0
$981$			3.22456i			0.102952i
$982$	18.5916			0.593283
$983$		−	7.22848i		−	0.230553i	−0.993333	−	0.115276i	$-0.963225\pi$
$983$		−	7.22848i		−	0.230553i	0.993333	−	0.115276i	$-0.0367753\pi$
$984$	−7.12085			−0.227004
$985$	31.1463			0.992405
$986$	16.5706			0.527716
$987$		0			0
$988$	−0.200967			−0.00639360
$989$		−	34.4422i		−	1.09520i
$990$	−0.132797	−	6.70641i	−0.00422056	−	0.213144i
$991$	−18.2014			−0.578187			−0.289093	−	0.957301i	$-0.593354\pi$
$991$	−18.2014			−0.578187			−0.289093	+	0.957301i	$0.593354\pi$
$992$	−27.0396			−0.858509
$993$		−	18.2492i		−	0.579120i
$994$		0			0
$995$	4.37880			0.138817
$996$			10.2300i			0.324150i
$997$	1.43859			0.0455605			0.0227802	−	0.999740i	$-0.492748\pi$
$997$	1.43859			0.0455605			0.0227802	+	0.999740i	$0.492748\pi$
$998$		−	0.929007i		−	0.0294072i
$999$		−	9.39271i		−	0.297172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.c.a.538.14		32
7.4	even	3		231.2.p.a.208.10	yes	32
7.5	odd	6		231.2.p.a.10.7	✓	32
7.6	odd	2	inner	1617.2.c.a.538.13		32
11.10	odd	2	inner	1617.2.c.a.538.20		32
21.5	even	6		693.2.bg.b.10.10		32
21.11	odd	6		693.2.bg.b.208.7		32
77.32	odd	6		231.2.p.a.208.7	yes	32
77.54	even	6		231.2.p.a.10.10	yes	32
77.76	even	2	inner	1617.2.c.a.538.19		32
231.32	even	6		693.2.bg.b.208.10		32
231.131	odd	6		693.2.bg.b.10.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.p.a.10.7	✓	32	7.5	odd	6
231.2.p.a.10.10	yes	32	77.54	even	6
231.2.p.a.208.7	yes	32	77.32	odd	6
231.2.p.a.208.10	yes	32	7.4	even	3
693.2.bg.b.10.7		32	231.131	odd	6
693.2.bg.b.10.10		32	21.5	even	6
693.2.bg.b.208.7		32	21.11	odd	6
693.2.bg.b.208.10		32	231.32	even	6
1617.2.c.a.538.13		32	7.6	odd	2	inner
1617.2.c.a.538.14		32	1.1	even	1	trivial
1617.2.c.a.538.19		32	77.76	even	2	inner
1617.2.c.a.538.20		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)

\(f(q)\)	\(=\)	\(q-0.615506i q^{2} +1.00000i q^{3} +1.62115 q^{4} -3.28584i q^{5} +0.615506 q^{6} -2.22884i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-0.615506i q^{2} +1.00000i q^{3} +1.62115 q^{4} -3.28584i q^{5} +0.615506 q^{6} -2.22884i q^{8} -1.00000 q^{9} -2.02245 q^{10} +(-0.0656613 - 3.31597i) q^{11} +1.62115i q^{12} +0.142630 q^{13} +3.28584 q^{15} +1.87044 q^{16} -7.26368 q^{17} +0.615506i q^{18} -0.869142 q^{19} -5.32684i q^{20} +(-2.04100 + 0.0404149i) q^{22} -3.56308 q^{23} +2.22884 q^{24} -5.79672 q^{25} -0.0877894i q^{26} -1.00000i q^{27} -3.70637i q^{29} -2.02245i q^{30} -4.82080i q^{31} -5.60895i q^{32} +(3.31597 - 0.0656613i) q^{33} +4.47084i q^{34} -1.62115 q^{36} +9.39271 q^{37} +0.534962i q^{38} +0.142630i q^{39} -7.32361 q^{40} -3.19487 q^{41} +9.66641i q^{43} +(-0.106447 - 5.37570i) q^{44} +3.28584i q^{45} +2.19310i q^{46} +8.76297i q^{47} +1.87044i q^{48} +3.56792i q^{50} -7.26368i q^{51} +0.231224 q^{52} -6.62537 q^{53} -0.615506 q^{54} +(-10.8958 + 0.215752i) q^{55} -0.869142i q^{57} -2.28130 q^{58} -1.54704i q^{59} +5.32684 q^{60} -15.2529 q^{61} -2.96723 q^{62} +0.288529 q^{64} -0.468657i q^{65} +(-0.0404149 - 2.04100i) q^{66} +13.0157 q^{67} -11.7755 q^{68} -3.56308i q^{69} +2.66532 q^{71} +2.22884i q^{72} +5.48838 q^{73} -5.78127i q^{74} -5.79672i q^{75} -1.40901 q^{76} +0.0877894 q^{78} -7.05347i q^{79} -6.14595i q^{80} +1.00000 q^{81} +1.96646i q^{82} +6.31032 q^{83} +23.8673i q^{85} +5.94974 q^{86} +3.70637 q^{87} +(-7.39078 + 0.146349i) q^{88} -7.87864i q^{89} +2.02245 q^{90} -5.77630 q^{92} +4.82080 q^{93} +5.39367 q^{94} +2.85586i q^{95} +5.60895 q^{96} -8.07193i q^{97} +(0.0656613 + 3.31597i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 24 q^{4} - 32 q^{9}+O(q^{10}) \) 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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