LMFDB - Embedded newform 637.2.i.a.538.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(489,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("637.489");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.i (of order $4$, degree $2$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			538.3
Character	$\chi$	$=$	637.538
Dual form			637.2.i.a.489.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12364 + 1.12364i) q^{2} -0.503603i q^{3} -0.525123i q^{4} +(-0.0563066 - 0.0563066i) q^{5} +(0.565867 + 0.565867i) q^{6} +(-1.65723 - 1.65723i) q^{8} +2.74638 q^{9} +O(q^{10})$	\(q+(-1.12364 + 1.12364i) q^{2} -0.503603i q^{3} -0.525123i q^{4} +(-0.0563066 - 0.0563066i) q^{5} +(0.565867 + 0.565867i) q^{6} +(-1.65723 - 1.65723i) q^{8} +2.74638 q^{9} +0.126536 q^{10} +(-2.98841 - 2.98841i) q^{11} -0.264453 q^{12} +(-0.565867 + 3.56087i) q^{13} +(-0.0283562 + 0.0283562i) q^{15} +4.77449 q^{16} +5.80713 q^{17} +(-3.08594 + 3.08594i) q^{18} +(3.74236 + 3.74236i) q^{19} +(-0.0295679 + 0.0295679i) q^{20} +6.71579 q^{22} -0.872266i q^{23} +(-0.834585 + 0.834585i) q^{24} -4.99366i q^{25} +(-3.36530 - 4.63696i) q^{26} -2.89390i q^{27} +0.362759 q^{29} -0.0637241i q^{30} +(0.986425 + 0.986425i) q^{31} +(-2.05034 + 2.05034i) q^{32} +(-1.50497 + 1.50497i) q^{33} +(-6.52511 + 6.52511i) q^{34} -1.44219i q^{36} +(2.75878 + 2.75878i) q^{37} -8.41012 q^{38} +(1.79326 + 0.284972i) q^{39} +0.186626i q^{40} +(7.70995 + 7.70995i) q^{41} +2.65570i q^{43} +(-1.56928 + 1.56928i) q^{44} +(-0.154640 - 0.154640i) q^{45} +(0.980111 + 0.980111i) q^{46} +(2.04584 - 2.04584i) q^{47} -2.40445i q^{48} +(5.61106 + 5.61106i) q^{50} -2.92449i q^{51} +(1.86989 + 0.297150i) q^{52} +10.5366 q^{53} +(3.25169 + 3.25169i) q^{54} +0.336535i q^{55} +(1.88467 - 1.88467i) q^{57} +(-0.407610 + 0.407610i) q^{58} +(-1.56790 + 1.56790i) q^{59} +(0.0148905 + 0.0148905i) q^{60} +4.19882i q^{61} -2.21677 q^{62} +4.94130i q^{64} +(0.232363 - 0.168638i) q^{65} -3.38209i q^{66} +(-7.15178 + 7.15178i) q^{67} -3.04946i q^{68} -0.439276 q^{69} +(3.65698 - 3.65698i) q^{71} +(-4.55138 - 4.55138i) q^{72} +(-8.41477 + 8.41477i) q^{73} -6.19975 q^{74} -2.51482 q^{75} +(1.96520 - 1.96520i) q^{76} +(-2.33519 + 1.69477i) q^{78} +8.55341 q^{79} +(-0.268835 - 0.268835i) q^{80} +6.78178 q^{81} -17.3264 q^{82} +(-4.91372 - 4.91372i) q^{83} +(-0.326980 - 0.326980i) q^{85} +(-2.98404 - 2.98404i) q^{86} -0.182687i q^{87} +9.90496i q^{88} +(5.69688 - 5.69688i) q^{89} +0.347518 q^{90} -0.458047 q^{92} +(0.496767 - 0.496767i) q^{93} +4.59756i q^{94} -0.421440i q^{95} +(1.03256 + 1.03256i) q^{96} +(-6.04128 - 6.04128i) q^{97} +(-8.20733 - 8.20733i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9	$ 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 44 q^{15} - 24 q^{16} + 8 q^{18} - 8 q^{22} + 16 q^{29} - 8 q^{32} + 16 q^{37} + 12 q^{39} + 84 q^{44} - 24 q^{46} + 88 q^{50} + 24 q^{53} + 40 q^{57} - 52 q^{58} - 32 q^{60} + 16 q^{65} - 32 q^{67} - 36 q^{71} - 44 q^{72} - 24 q^{74} - 176 q^{78} + 64 q^{79} - 32 q^{81} - 84 q^{85} - 84 q^{86} + 48 q^{92} - 12 q^{93} - 24 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 44 * q^15 - 24 * q^16 + 8 * q^18 - 8 * q^22 + 16 * q^29 - 8 * q^32 + 16 * q^37 + 12 * q^39 + 84 * q^44 - 24 * q^46 + 88 * q^50 + 24 * q^53 + 40 * q^57 - 52 * q^58 - 32 * q^60 + 16 * q^65 - 32 * q^67 - 36 * q^71 - 44 * q^72 - 24 * q^74 - 176 * q^78 + 64 * q^79 - 32 * q^81 - 84 * q^85 - 84 * q^86 + 48 * q^92 - 12 * q^93 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−1.12364	+	1.12364i	−0.794532	+	0.794532i	−0.982227	−	0.187696i	$-0.939898\pi$
$2$	−1.12364	+	1.12364i	−0.794532	+	0.794532i	0.187696	+	0.982227i	$0.439898\pi$
$3$		−	0.503603i		−	0.290755i	−0.989376	−	0.145378i	$-0.953560\pi$
$3$		−	0.503603i		−	0.290755i	0.989376	−	0.145378i	$-0.0464397\pi$
$4$		−	0.525123i		−	0.262561i
$5$	−0.0563066	−	0.0563066i	−0.0251811	−	0.0251811i	0.694404	−	0.719585i	$-0.255668\pi$
$5$	−0.0563066	−	0.0563066i	−0.0251811	−	0.0251811i	−0.719585	+	0.694404i	$0.755668\pi$
$6$	0.565867	+	0.565867i	0.231014	+	0.231014i
$7$		0			0
$7$		0			0
$8$	−1.65723	−	1.65723i	−0.585918	−	0.585918i
$9$	2.74638			0.915461
$10$	0.126536			0.0400143
$11$	−2.98841	−	2.98841i	−0.901041	−	0.901041i	0.0944854	−	0.995526i	$-0.469879\pi$
$11$	−2.98841	−	2.98841i	−0.901041	−	0.901041i	−0.995526	+	0.0944854i	$0.969879\pi$
$12$	−0.264453			−0.0763411
$13$	−0.565867	+	3.56087i	−0.156943	+	0.987608i
$13$	−0.565867	+	3.56087i	−0.156943	+	0.987608i
$14$		0			0
$15$	−0.0283562	+	0.0283562i	−0.00732153	+	0.00732153i
$16$	4.77449			1.19362
$17$	5.80713			1.40844			0.704218	−	0.709984i	$-0.251298\pi$
$17$	5.80713			1.40844			0.704218	+	0.709984i	$0.251298\pi$
$18$	−3.08594	+	3.08594i	−0.727363	+	0.727363i
$19$	3.74236	+	3.74236i	0.858557	+	0.858557i	0.991168	−	0.132611i	$-0.0423361\pi$
$19$	3.74236	+	3.74236i	0.858557	+	0.858557i	−0.132611	+	0.991168i	$0.542336\pi$
$20$	−0.0295679	+	0.0295679i	−0.00661158	+	0.00661158i
$21$		0			0
$22$	6.71579			1.43181
$23$		−	0.872266i		−	0.181880i	−0.995856	−	0.0909400i	$-0.971013\pi$
$23$		−	0.872266i		−	0.181880i	0.995856	−	0.0909400i	$-0.0289872\pi$
$24$	−0.834585	+	0.834585i	−0.170359	+	0.170359i
$25$		−	4.99366i		−	0.998732i
$26$	−3.36530	−	4.63696i	−0.659989	−	0.909382i
$27$		−	2.89390i		−	0.556931i
$28$		0			0
$29$	0.362759			0.0673627			0.0336814	−	0.999433i	$-0.489277\pi$
$29$	0.362759			0.0673627			0.0336814	+	0.999433i	$0.489277\pi$
$30$		−	0.0637241i		−	0.0116344i
$31$	0.986425	+	0.986425i	0.177167	+	0.177167i	0.790120	−	0.612953i	$-0.210018\pi$
$31$	0.986425	+	0.986425i	0.177167	+	0.177167i	−0.612953	+	0.790120i	$0.710018\pi$
$32$	−2.05034	+	2.05034i	−0.362453	+	0.362453i
$33$	−1.50497	+	1.50497i	−0.261982	+	0.261982i
$34$	−6.52511	+	6.52511i	−1.11905	+	1.11905i
$35$		0			0
$36$		−	1.44219i		−	0.240365i
$37$	2.75878	+	2.75878i	0.453541	+	0.453541i	0.896528	−	0.442987i	$-0.146081\pi$
$37$	2.75878	+	2.75878i	0.453541	+	0.453541i	−0.442987	+	0.896528i	$0.646081\pi$
$38$	−8.41012			−1.36430
$39$	1.79326	+	0.284972i	0.287152	+	0.0456321i
$40$			0.186626i			0.0295081i
$41$	7.70995	+	7.70995i	1.20409	+	1.20409i	0.972911	+	0.231182i	$0.0742592\pi$
$41$	7.70995	+	7.70995i	1.20409	+	1.20409i	0.231182	+	0.972911i	$0.425741\pi$
$42$		0			0
$43$			2.65570i			0.404990i	0.979283	+	0.202495i	$0.0649050\pi$
$43$			2.65570i			0.404990i	−0.979283	+	0.202495i	$0.935095\pi$
$44$	−1.56928	+	1.56928i	−0.236579	+	0.236579i
$45$	−0.154640	−	0.154640i	−0.0230523	−	0.0230523i
$46$	0.980111	+	0.980111i	0.144509	+	0.144509i
$47$	2.04584	−	2.04584i	0.298416	−	0.298416i	−0.541977	−	0.840393i	$-0.682324\pi$
$47$	2.04584	−	2.04584i	0.298416	−	0.298416i	0.840393	+	0.541977i	$0.182324\pi$
$48$		−	2.40445i		−	0.347052i
$49$		0			0
$50$	5.61106	+	5.61106i	0.793524	+	0.793524i
$51$		−	2.92449i		−	0.409510i
$52$	1.86989	+	0.297150i	0.259308	+	0.0412073i
$53$	10.5366			1.44731			0.723657	−	0.690160i	$-0.242460\pi$
$53$	10.5366			1.44731			0.723657	+	0.690160i	$0.242460\pi$
$54$	3.25169	+	3.25169i	0.442499	+	0.442499i
$55$			0.336535i			0.0453784i
$56$		0			0
$57$	1.88467	−	1.88467i	0.249630	−	0.249630i
$58$	−0.407610	+	0.407610i	−0.0535218	+	0.0535218i
$59$	−1.56790	+	1.56790i	−0.204123	+	0.204123i	−0.801764	−	0.597641i	$-0.796105\pi$
$59$	−1.56790	+	1.56790i	−0.204123	+	0.204123i	0.597641	+	0.801764i	$0.296105\pi$
$60$	0.0148905	+	0.0148905i	0.00192235	+	0.00192235i
$61$			4.19882i			0.537604i	0.963196	+	0.268802i	$0.0866277\pi$
$61$			4.19882i			0.537604i	−0.963196	+	0.268802i	$0.913372\pi$
$62$	−2.21677			−0.281530
$63$		0			0
$64$			4.94130i			0.617662i
$65$	0.232363	−	0.168638i	0.0288210	−	0.0209170i
$66$		−	3.38209i		−	0.416307i
$67$	−7.15178	+	7.15178i	−0.873729	+	0.873729i	−0.992877	−	0.119148i	$-0.961984\pi$
$67$	−7.15178	+	7.15178i	−0.873729	+	0.873729i	0.119148	+	0.992877i	$0.461984\pi$
$68$		−	3.04946i		−	0.369801i
$69$	−0.439276			−0.0528826
$70$		0			0
$71$	3.65698	−	3.65698i	0.434004	−	0.434004i	−0.455984	−	0.889988i	$-0.650713\pi$
$71$	3.65698	−	3.65698i	0.434004	−	0.434004i	0.889988	+	0.455984i	$0.150713\pi$
$72$	−4.55138	−	4.55138i	−0.536386	−	0.536386i
$73$	−8.41477	+	8.41477i	−0.984875	+	0.984875i	−0.999887	−	0.0150127i	$-0.995221\pi$
$73$	−8.41477	+	8.41477i	−0.984875	+	0.984875i	0.0150127	+	0.999887i	$0.495221\pi$
$74$	−6.19975			−0.720706
$75$	−2.51482			−0.290387
$76$	1.96520	−	1.96520i	0.225424	−	0.225424i
$77$		0			0
$78$	−2.33519	+	1.69477i	−0.264408	+	0.191895i
$79$	8.55341			0.962334			0.481167	−	0.876629i	$-0.340213\pi$
$79$	8.55341			0.962334			0.481167	+	0.876629i	$0.340213\pi$
$80$	−0.268835	−	0.268835i	−0.0300567	−	0.0300567i
$81$	6.78178			0.753531
$82$	−17.3264			−1.91338
$83$	−4.91372	−	4.91372i	−0.539351	−	0.539351i	0.383987	−	0.923338i	$-0.374551\pi$
$83$	−4.91372	−	4.91372i	−0.539351	−	0.539351i	−0.923338	+	0.383987i	$0.874551\pi$
$84$		0			0
$85$	−0.326980	−	0.326980i	−0.0354659	−	0.0354659i
$86$	−2.98404	−	2.98404i	−0.321778	−	0.321778i
$87$		−	0.182687i		−	0.0195861i
$88$			9.90496i			1.05587i
$89$	5.69688	−	5.69688i	0.603868	−	0.603868i	−0.337469	−	0.941337i	$-0.609571\pi$
$89$	5.69688	−	5.69688i	0.603868	−	0.603868i	0.941337	+	0.337469i	$0.109571\pi$
$90$	0.347518			0.0366316
$91$		0			0
$92$	−0.458047			−0.0477547
$93$	0.496767	−	0.496767i	0.0515123	−	0.0515123i
$94$			4.59756i			0.474202i
$95$		−	0.421440i		−	0.0432388i
$96$	1.03256	+	1.03256i	0.105385	+	0.105385i
$97$	−6.04128	−	6.04128i	−0.613399	−	0.613399i	0.330431	−	0.943830i	$-0.392806\pi$
$97$	−6.04128	−	6.04128i	−0.613399	−	0.613399i	−0.943830	+	0.330431i	$0.892806\pi$
$98$		0			0
$99$	−8.20733	−	8.20733i	−0.824868	−	0.824868i
$100$	−2.62228			−0.262228
$101$	11.2197			1.11641			0.558203	−	0.829704i	$-0.311491\pi$
$101$	11.2197			1.11641			0.558203	+	0.829704i	$0.311491\pi$
$102$	3.28607	+	3.28607i	0.325369	+	0.325369i
$103$	9.65503			0.951339			0.475669	−	0.879624i	$-0.342206\pi$
$103$	9.65503			0.951339			0.475669	+	0.879624i	$0.342206\pi$
$104$	6.83894	−	4.96340i	0.670613	−	0.486701i
$105$		0			0
$106$	−11.8393	+	11.8393i	−1.14994	+	1.14994i
$107$	−17.6282			−1.70418			−0.852089	−	0.523397i	$-0.824665\pi$
$107$	−17.6282			−1.70418			−0.852089	+	0.523397i	$0.824665\pi$
$108$	−1.51965			−0.146228
$109$	9.64725	−	9.64725i	0.924039	−	0.924039i	−0.0732734	−	0.997312i	$-0.523345\pi$
$109$	9.64725	−	9.64725i	0.924039	−	0.924039i	0.997312	+	0.0732734i	$0.0233446\pi$
$110$	−0.378143	−	0.378143i	−0.0360545	−	0.0360545i
$111$	1.38933	−	1.38933i	0.131870	−	0.131870i
$112$		0			0
$113$	−6.02917			−0.567176			−0.283588	−	0.958946i	$-0.591525\pi$
$113$	−6.02917			−0.567176			−0.283588	+	0.958946i	$0.591525\pi$
$114$			4.23536i			0.396678i
$115$	−0.0491143	+	0.0491143i	−0.00457993	+	0.00457993i
$116$		−	0.190493i		−	0.0176869i
$117$	−1.55409	+	9.77952i	−0.143676	+	0.904117i
$118$		−	3.52350i		−	0.324364i
$119$		0			0
$120$	0.0939853			0.00857964
$121$			6.86124i			0.623749i
$122$	−4.71795	−	4.71795i	−0.427143	−	0.427143i
$123$	3.88276	−	3.88276i	0.350096	−	0.350096i
$124$	0.517994	−	0.517994i	0.0465173	−	0.0465173i
$125$	−0.562709	+	0.562709i	−0.0503302	+	0.0503302i
$126$		0			0
$127$		−	0.259825i		−	0.0230558i	−0.999934	−	0.0115279i	$-0.996330\pi$
$127$		−	0.259825i		−	0.0230558i	0.999934	−	0.0115279i	$-0.00366952\pi$
$128$	−9.65291	−	9.65291i	−0.853205	−	0.853205i
$129$	1.33742			0.117753
$130$	−0.0716028	+	0.450580i	−0.00627998	+	0.0395185i
$131$			0.784371i			0.0685308i	0.999413	+	0.0342654i	$0.0109091\pi$
$131$			0.784371i			0.0685308i	−0.999413	+	0.0342654i	$0.989091\pi$
$132$	0.790296	+	0.790296i	0.0687865	+	0.0687865i
$133$		0			0
$134$		−	16.0720i		−	1.38841i
$135$	−0.162945	+	0.162945i	−0.0140241	+	0.0140241i
$136$	−9.62374	−	9.62374i	−0.825229	−	0.825229i
$137$	−9.75464	−	9.75464i	−0.833395	−	0.833395i	0.154585	−	0.987980i	$-0.450596\pi$
$137$	−9.75464	−	9.75464i	−0.833395	−	0.833395i	−0.987980	+	0.154585i	$0.950596\pi$
$138$	0.493587	−	0.493587i	0.0420169	−	0.0420169i
$139$			3.12982i			0.265468i	0.991152	+	0.132734i	$0.0423755\pi$
$139$			3.12982i			0.265468i	−0.991152	+	0.132734i	$0.957624\pi$
$140$		0			0
$141$	−1.03029	−	1.03029i	−0.0867661	−	0.0867661i
$142$			8.21824i			0.689659i
$143$	12.3324	−	8.95031i	1.03129	−	0.748462i
$144$	13.1126			1.09272
$145$	−0.0204257	−	0.0204257i	−0.00169627	−	0.00169627i
$146$		−	18.9103i		−	1.56503i
$147$		0			0
$148$	1.44870	−	1.44870i	0.119082	−	0.119082i
$149$	2.39517	−	2.39517i	0.196220	−	0.196220i	−0.602157	−	0.798377i	$-0.705692\pi$
$149$	2.39517	−	2.39517i	0.196220	−	0.196220i	0.798377	+	0.602157i	$0.205692\pi$
$150$	2.82575	−	2.82575i	0.230721	−	0.230721i
$151$	−11.5036	−	11.5036i	−0.936151	−	0.936151i	0.0619296	−	0.998081i	$-0.480275\pi$
$151$	−11.5036	−	11.5036i	−0.936151	−	0.936151i	−0.998081	+	0.0619296i	$0.980275\pi$
$152$		−	12.4039i		−	1.00609i
$153$	15.9486			1.28937
$154$		0			0
$155$		−	0.111084i		−	0.00892252i
$156$	0.149646	−	0.941684i	0.0119812	−	0.0753951i
$157$		−	19.2201i		−	1.53393i	−0.641688	−	0.766966i	$-0.721765\pi$
$157$		−	19.2201i		−	1.53393i	0.641688	−	0.766966i	$-0.278235\pi$
$158$	−9.61093	+	9.61093i	−0.764605	+	0.764605i
$159$		−	5.30627i		−	0.420814i
$160$	0.230896			0.0182539
$161$		0			0
$162$	−7.62026	+	7.62026i	−0.598704	+	0.598704i
$163$	0.878489	+	0.878489i	0.0688085	+	0.0688085i	0.740674	−	0.671865i	$-0.234507\pi$
$163$	0.878489	+	0.878489i	0.0688085	+	0.0688085i	−0.671865	+	0.740674i	$0.734507\pi$
$164$	4.04867	−	4.04867i	0.316148	−	0.316148i
$165$	0.169480			0.0131940
$166$	11.0425			0.857063
$167$	7.31443	−	7.31443i	0.566007	−	0.566007i	−0.365000	−	0.931007i	$-0.618931\pi$
$167$	7.31443	−	7.31443i	0.566007	−	0.566007i	0.931007	+	0.365000i	$0.118931\pi$
$168$		0			0
$169$	−12.3596	−	4.02996i	−0.950738	−	0.309997i
$170$	0.734814			0.0563576
$171$	10.2780	+	10.2780i	0.785976	+	0.785976i
$172$	1.39457			0.106335
$173$	3.16306			0.240483			0.120241	−	0.992745i	$-0.461633\pi$
$173$	3.16306			0.240483			0.120241	+	0.992745i	$0.461633\pi$
$174$	0.205274	+	0.205274i	0.0155618	+	0.0155618i
$175$		0			0
$176$	−14.2682	−	14.2682i	−1.07550	−	1.07550i
$177$	0.789598	+	0.789598i	0.0593498	+	0.0593498i
$178$			12.8025i			0.959585i
$179$		−	5.80295i		−	0.433733i	−0.976201	−	0.216867i	$-0.930416\pi$
$179$		−	5.80295i		−	0.433733i	0.976201	−	0.216867i	$-0.0695837\pi$
$180$	−0.0812047	+	0.0812047i	−0.00605264	+	0.00605264i
$181$	−13.7005			−1.01835			−0.509176	−	0.860662i	$-0.670050\pi$
$181$	−13.7005			−1.01835			−0.509176	+	0.860662i	$0.670050\pi$
$182$		0			0
$183$	2.11454			0.156311
$184$	−1.44554	+	1.44554i	−0.106567	+	0.106567i
$185$		−	0.310675i		−	0.0228413i
$186$			1.11637i			0.0818563i
$187$	−17.3541	−	17.3541i	−1.26906	−	1.26906i
$188$	−1.07432	−	1.07432i	−0.0783526	−	0.0783526i
$189$		0			0
$190$	0.473545	+	0.473545i	0.0343546	+	0.0343546i
$191$	−8.45722			−0.611943			−0.305972	−	0.952041i	$-0.598981\pi$
$191$	−8.45722			−0.611943			−0.305972	+	0.952041i	$0.598981\pi$
$192$	2.48845			0.179589
$193$	0.349145	+	0.349145i	0.0251320	+	0.0251320i	0.719561	−	0.694429i	$-0.244343\pi$
$193$	0.349145	+	0.349145i	0.0251320	+	0.0251320i	−0.694429	+	0.719561i	$0.744343\pi$
$194$	13.5764			0.974729
$195$	−0.0849268	−	0.117018i	−0.00608173	−	0.00837987i
$196$		0			0
$197$	−2.77899	+	2.77899i	−0.197995	+	0.197995i	−0.799140	−	0.601145i	$-0.794711\pi$
$197$	−2.77899	+	2.77899i	−0.197995	+	0.197995i	0.601145	+	0.799140i	$0.294711\pi$
$198$	18.4441			1.31077
$199$	16.0641			1.13875			0.569377	−	0.822076i	$-0.307184\pi$
$199$	16.0641			1.13875			0.569377	+	0.822076i	$0.307184\pi$
$200$	−8.27563	+	8.27563i	−0.585175	+	0.585175i
$201$	3.60166	+	3.60166i	0.254041	+	0.254041i
$202$	−12.6069	+	12.6069i	−0.887020	+	0.887020i
$203$		0			0
$204$	−1.53572			−0.107522
$205$		−	0.868242i		−	0.0606407i
$206$	−10.8488	+	10.8488i	−0.755869	+	0.755869i
$207$		−	2.39558i		−	0.166504i
$208$	−2.70173	+	17.0013i	−0.187331	+	1.17883i
$209$		−	22.3675i		−	1.54719i
$210$		0			0
$211$	21.0547			1.44947			0.724734	−	0.689029i	$-0.241963\pi$
$211$	21.0547			1.44947			0.724734	+	0.689029i	$0.241963\pi$
$212$		−	5.53301i		−	0.380009i
$213$	−1.84167	−	1.84167i	−0.126189	−	0.126189i
$214$	19.8077	−	19.8077i	1.35402	−	1.35402i
$215$	0.149533	−	0.149533i	0.0101981	−	0.0101981i
$216$	−4.79584	+	4.79584i	−0.326316	+	0.326316i
$217$		0			0
$218$			21.6800i			1.46836i
$219$	4.23771	+	4.23771i	0.286358	+	0.286358i
$220$	0.176722			0.0119146
$221$	−3.28607	+	20.6784i	−0.221045	+	1.39098i
$222$			3.12221i			0.209549i
$223$	19.3108	+	19.3108i	1.29314	+	1.29314i	0.932832	+	0.360311i	$0.117330\pi$
$223$	19.3108	+	19.3108i	1.29314	+	1.29314i	0.360311	+	0.932832i	$0.382670\pi$
$224$		0			0
$225$		−	13.7145i		−	0.914300i
$226$	6.77460	−	6.77460i	0.450640	−	0.450640i
$227$	−2.45108	−	2.45108i	−0.162684	−	0.162684i	0.621071	−	0.783754i	$-0.286698\pi$
$227$	−2.45108	−	2.45108i	−0.162684	−	0.162684i	−0.783754	+	0.621071i	$0.786698\pi$
$228$	−0.989681	−	0.989681i	−0.0655432	−	0.0655432i
$229$	−13.6297	+	13.6297i	−0.900678	+	0.900678i	−0.995495	−	0.0948169i	$-0.969773\pi$
$229$	−13.6297	+	13.6297i	−0.900678	+	0.900678i	0.0948169	+	0.995495i	$0.469773\pi$
$230$		−	0.110373i		−	0.00727781i
$231$		0			0
$232$	−0.601175	−	0.601175i	−0.0394691	−	0.0394691i
$233$		−	5.16965i		−	0.338675i	−0.985558	−	0.169337i	$-0.945837\pi$
$233$		−	5.16965i		−	0.338675i	0.985558	−	0.169337i	$-0.0541628\pi$
$234$	−9.24240	−	12.7349i	−0.604195	−	0.832504i
$235$	−0.230388			−0.0150289
$236$	0.823339	+	0.823339i	0.0535948	+	0.0535948i
$237$		−	4.30752i		−	0.279804i
$238$		0			0
$239$	6.85569	−	6.85569i	0.443458	−	0.443458i	−0.449715	−	0.893172i	$-0.648474\pi$
$239$	6.85569	−	6.85569i	0.443458	−	0.443458i	0.893172	+	0.449715i	$0.148474\pi$
$240$	−0.135386	+	0.135386i	−0.00873915	+	0.00873915i
$241$	−1.58099	+	1.58099i	−0.101841	+	0.101841i	−0.756191	−	0.654351i	$-0.772942\pi$
$241$	−1.58099	+	1.58099i	−0.101841	+	0.101841i	0.654351	+	0.756191i	$0.272942\pi$
$242$	−7.70955	−	7.70955i	−0.495589	−	0.495589i
$243$		−	12.0970i		−	0.776024i
$244$	2.20490			0.141154
$245$		0			0
$246$			8.72562i			0.556325i
$247$	−15.4438	+	11.2084i	−0.982662	+	0.713173i
$248$		−	3.26946i		−	0.207611i
$249$	−2.47457	+	2.47457i	−0.156819	+	0.156819i
$250$		−	1.26456i		−	0.0799779i
$251$	−24.8342			−1.56752			−0.783759	−	0.621064i	$-0.786700\pi$
$251$	−24.8342			−1.56752			−0.783759	+	0.621064i	$0.786700\pi$
$252$		0			0
$253$	−2.60669	+	2.60669i	−0.163881	+	0.163881i
$254$	0.291949	+	0.291949i	0.0183185	+	0.0183185i
$255$	−0.164668	+	0.164668i	−0.0103119	+	0.0103119i
$256$	11.8102			0.738135
$257$	−13.3511			−0.832821			−0.416411	−	0.909177i	$-0.636712\pi$
$257$	−13.3511			−0.832821			−0.416411	+	0.909177i	$0.636712\pi$
$258$	−1.50277	+	1.50277i	−0.0935586	+	0.0935586i
$259$		0			0
$260$	−0.0885559	−	0.122019i	−0.00549200	−	0.00756729i
$261$	0.996277			0.0616680
$262$	−0.881348	−	0.881348i	−0.0544499	−	0.0544499i
$263$	−0.423795			−0.0261323			−0.0130662	−	0.999915i	$-0.504159\pi$
$263$	−0.423795			−0.0261323			−0.0130662	+	0.999915i	$0.504159\pi$
$264$	4.98817			0.307001
$265$	−0.593280	−	0.593280i	−0.0364449	−	0.0364449i
$266$		0			0
$267$	−2.86897	−	2.86897i	−0.175578	−	0.175578i
$268$	3.75556	+	3.75556i	0.229407	+	0.229407i
$269$			14.5143i			0.884951i	0.896781	+	0.442476i	$0.145900\pi$
$269$			14.5143i			0.884951i	−0.896781	+	0.442476i	$0.854100\pi$
$270$		−	0.366183i		−	0.0222852i
$271$	13.9887	−	13.9887i	0.849754	−	0.849754i	−0.140348	−	0.990102i	$-0.544822\pi$
$271$	13.9887	−	13.9887i	0.849754	−	0.849754i	0.990102	+	0.140348i	$0.0448221\pi$
$272$	27.7261			1.68114
$273$		0			0
$274$	21.9213			1.32432
$275$	−14.9231	+	14.9231i	−0.899898	+	0.899898i
$276$			0.230674i			0.0138849i
$277$			23.7541i			1.42725i	0.700530	+	0.713623i	$0.252947\pi$
$277$			23.7541i			1.42725i	−0.700530	+	0.713623i	$0.747053\pi$
$278$	−3.51678	−	3.51678i	−0.210922	−	0.210922i
$279$	2.70910	+	2.70910i	0.162190	+	0.162190i
$280$		0			0
$281$	9.66092	+	9.66092i	0.576322	+	0.576322i	0.933888	−	0.357566i	$-0.116393\pi$
$281$	9.66092	+	9.66092i	0.576322	+	0.576322i	−0.357566	+	0.933888i	$0.616393\pi$
$282$	2.31535			0.137877
$283$	−26.7650			−1.59101			−0.795506	−	0.605945i	$-0.792795\pi$
$283$	−26.7650			−1.59101			−0.795506	+	0.605945i	$0.792795\pi$
$284$	−1.92036	−	1.92036i	−0.113953	−	0.113953i
$285$	−0.212238			−0.0125719
$286$	−3.80025	+	23.9141i	−0.224713	+	1.41407i
$287$		0			0
$288$	−5.63103	+	5.63103i	−0.331812	+	0.331812i
$289$	16.7228			0.983693
$290$	0.0459023			0.00269547
$291$	−3.04240	+	3.04240i	−0.178349	+	0.178349i
$292$	4.41879	+	4.41879i	0.258590	+	0.258590i
$293$	−21.8755	+	21.8755i	−1.27798	+	1.27798i	−0.336181	+	0.941797i	$0.609136\pi$
$293$	−21.8755	+	21.8755i	−1.27798	+	1.27798i	−0.941797	+	0.336181i	$0.890864\pi$
$294$		0			0
$295$	0.176566			0.0102801
$296$		−	9.14386i		−	0.531476i
$297$	−8.64816	+	8.64816i	−0.501817	+	0.501817i
$298$			5.38261i			0.311806i
$299$	3.10603	+	0.493587i	0.179626	+	0.0285449i
$300$			1.32059i			0.0762443i
$301$		0			0
$302$	25.8518			1.48760
$303$		−	5.65030i		−	0.324601i
$304$	17.8679	+	17.8679i	1.02479	+	1.02479i
$305$	0.236421	−	0.236421i	0.0135374	−	0.0135374i
$306$	−17.9205	+	17.9205i	−1.02444	+	1.02444i
$307$	−2.49534	+	2.49534i	−0.142417	+	0.142417i	−0.774720	−	0.632304i	$-0.782109\pi$
$307$	−2.49534	+	2.49534i	−0.142417	+	0.142417i	0.632304	+	0.774720i	$0.282109\pi$
$308$		0			0
$309$		−	4.86230i		−	0.276607i
$310$	0.124819	+	0.124819i	0.00708922	+	0.00708922i
$311$	−30.3106			−1.71876			−0.859378	−	0.511341i	$-0.829149\pi$
$311$	−30.3106			−1.71876			−0.859378	+	0.511341i	$0.829149\pi$
$312$	−2.49958	−	3.44411i	−0.141511	−	0.194984i
$313$			19.4715i			1.10059i	0.834969	+	0.550297i	$0.185486\pi$
$313$			19.4715i			1.10059i	−0.834969	+	0.550297i	$0.814514\pi$
$314$	21.5964	+	21.5964i	1.21876	+	1.21876i
$315$		0			0
$316$		−	4.49159i		−	0.252672i
$317$	−3.54480	+	3.54480i	−0.199096	+	0.199096i	−0.799612	−	0.600517i	$-0.794962\pi$
$317$	−3.54480	+	3.54480i	−0.199096	+	0.199096i	0.600517	+	0.799612i	$0.294962\pi$
$318$	5.96232	+	5.96232i	0.334350	+	0.334350i
$319$	−1.08408	−	1.08408i	−0.0606966	−	0.0606966i
$320$	0.278228	−	0.278228i	0.0155534	−	0.0155534i
$321$			8.87759i			0.495499i
$322$		0			0
$323$	21.7324	+	21.7324i	1.20922	+	1.20922i
$324$		−	3.56127i		−	0.197848i
$325$	17.7818	+	2.82575i	0.986355	+	0.156744i
$326$	−1.97421			−0.109341
$327$	−4.85838	−	4.85838i	−0.268669	−	0.268669i
$328$		−	25.5543i		−	1.41100i
$329$		0			0
$330$	−0.190434	+	0.190434i	−0.0104831	+	0.0104831i
$331$	13.5614	−	13.5614i	0.745400	−	0.745400i	−0.228211	−	0.973612i	$-0.573288\pi$
$331$	13.5614	−	13.5614i	0.745400	−	0.745400i	0.973612	+	0.228211i	$0.0732877\pi$
$332$	−2.58031	+	2.58031i	−0.141613	+	0.141613i
$333$	7.57668	+	7.57668i	0.415199	+	0.415199i
$334$			16.4375i			0.899422i
$335$	0.805384			0.0440029
$336$		0			0
$337$			3.01241i			0.164097i	0.996628	+	0.0820483i	$0.0261462\pi$
$337$			3.01241i			0.164097i	−0.996628	+	0.0820483i	$0.973854\pi$
$338$	18.4159	−	9.35948i	1.00169	−	0.509089i
$339$			3.03631i			0.164910i
$340$	−0.171705	+	0.171705i	−0.00931199	+	0.00931199i
$341$		−	5.89569i		−	0.319270i
$342$	−23.0974			−1.24897
$343$		0			0
$344$	4.40110	−	4.40110i	0.237291	−	0.237291i
$345$	0.0247341	+	0.0247341i	0.00133164	+	0.00133164i
$346$	−3.55413	+	3.55413i	−0.191071	+	0.191071i
$347$	−8.23820			−0.442250			−0.221125	−	0.975246i	$-0.570973\pi$
$347$	−8.23820			−0.442250			−0.221125	+	0.975246i	$0.570973\pi$
$348$	−0.0959330			−0.00514255
$349$	8.06122	−	8.06122i	0.431507	−	0.431507i	−0.457634	−	0.889141i	$-0.651303\pi$
$349$	8.06122	−	8.06122i	0.431507	−	0.431507i	0.889141	+	0.457634i	$0.151303\pi$
$350$		0			0
$351$	10.3048	+	1.63756i	0.550029	+	0.0874066i
$352$	12.2546			0.653170
$353$	−11.9519	−	11.9519i	−0.636133	−	0.636133i	0.313466	−	0.949599i	$-0.398510\pi$
$353$	−11.9519	−	11.9519i	−0.636133	−	0.636133i	−0.949599	+	0.313466i	$0.898510\pi$
$354$	−1.77444			−0.0943106
$355$	−0.411824			−0.0218574
$356$	−2.99156	−	2.99156i	−0.158553	−	0.158553i
$357$		0			0
$358$	6.52042	+	6.52042i	0.344615	+	0.344615i
$359$	−15.9730	−	15.9730i	−0.843023	−	0.843023i	0.146228	−	0.989251i	$-0.453287\pi$
$359$	−15.9730	−	15.9730i	−0.843023	−	0.843023i	−0.989251	+	0.146228i	$0.953287\pi$
$360$			0.512546i			0.0270135i
$361$			9.01058i			0.474241i
$362$	15.3944	−	15.3944i	0.809113	−	0.809113i
$363$	3.45534			0.181358
$364$		0			0
$365$	0.947614			0.0496004
$366$	−2.37597	+	2.37597i	−0.124194	+	0.124194i
$367$			25.6769i			1.34033i	0.742214	+	0.670163i	$0.233776\pi$
$367$			25.6769i			1.34033i	−0.742214	+	0.670163i	$0.766224\pi$
$368$		−	4.16463i		−	0.217096i
$369$	21.1745	+	21.1745i	1.10230	+	1.10230i
$370$	0.349087	+	0.349087i	0.0181481	+	0.0181481i
$371$		0			0
$372$	−0.260863	−	0.260863i	−0.0135251	−	0.0135251i
$373$	16.6240			0.860758			0.430379	−	0.902648i	$-0.358380\pi$
$373$	16.6240			0.860758			0.430379	+	0.902648i	$0.358380\pi$
$374$	38.9995			2.01661
$375$	0.283382	+	0.283382i	0.0146338	+	0.0146338i
$376$	−6.78084			−0.349695
$377$	−0.205274	+	1.29174i	−0.0105721	+	0.0665279i
$378$		0			0
$379$	−27.0566	+	27.0566i	−1.38980	+	1.38980i	−0.564094	+	0.825711i	$0.690774\pi$
$379$	−27.0566	+	27.0566i	−1.38980	+	1.38980i	−0.825711	+	0.564094i	$0.809226\pi$
$380$	−0.221308			−0.0113528
$381$	−0.130849			−0.00670358
$382$	9.50285	−	9.50285i	0.486208	−	0.486208i
$383$	−19.0988	−	19.0988i	−0.975904	−	0.975904i	0.0238125	−	0.999716i	$-0.492420\pi$
$383$	−19.0988	−	19.0988i	−0.975904	−	0.975904i	−0.999716	+	0.0238125i	$0.992420\pi$
$384$	−4.86124	+	4.86124i	−0.248074	+	0.248074i
$385$		0			0
$386$	−0.784626			−0.0399364
$387$			7.29357i			0.370753i
$388$	−3.17241	+	3.17241i	−0.161055	+	0.161055i
$389$		−	19.0504i		−	0.965894i	−0.875650	−	0.482947i	$-0.839566\pi$
$389$		−	19.0504i		−	0.965894i	0.875650	−	0.482947i	$-0.160434\pi$
$390$	0.226913	+	0.0360594i	0.0114902	+	0.00182594i
$391$		−	5.06536i		−	0.256166i
$392$		0			0
$393$	0.395011			0.0199257
$394$		−	6.24515i		−	0.314626i
$395$	−0.481613	−	0.481613i	−0.0242326	−	0.0242326i
$396$	−4.30986	+	4.30986i	−0.216579	+	0.216579i
$397$	2.40773	−	2.40773i	0.120840	−	0.120840i	−0.644100	−	0.764941i	$-0.722768\pi$
$397$	2.40773	−	2.40773i	0.120840	−	0.120840i	0.764941	+	0.644100i	$0.222768\pi$
$398$	−18.0502	+	18.0502i	−0.904777	+	0.904777i
$399$		0			0
$400$		−	23.8422i		−	1.19211i
$401$	26.0897	+	26.0897i	1.30286	+	1.30286i	0.926459	+	0.376397i	$0.122837\pi$
$401$	26.0897	+	26.0897i	1.30286	+	1.30286i	0.376397	+	0.926459i	$0.377163\pi$
$402$	−8.09391			−0.403688
$403$	−4.07072	+	2.95435i	−0.202777	+	0.147166i
$404$		−	5.89174i		−	0.293125i
$405$	−0.381859	−	0.381859i	−0.0189747	−	0.0189747i
$406$		0			0
$407$		−	16.4888i		−	0.817318i
$408$	−4.84654	+	4.84654i	−0.239940	+	0.239940i
$409$	−3.97167	−	3.97167i	−0.196386	−	0.196386i	0.602063	−	0.798449i	$-0.294346\pi$
$409$	−3.97167	−	3.97167i	−0.196386	−	0.196386i	−0.798449	+	0.602063i	$0.794346\pi$
$410$	0.975590	+	0.975590i	0.0481809	+	0.0481809i
$411$	−4.91246	+	4.91246i	−0.242314	+	0.242314i
$412$		−	5.07008i		−	0.249785i
$413$		0			0
$414$	2.69176	+	2.69176i	0.132293	+	0.132293i
$415$			0.553350i			0.0271629i
$416$	−6.14078	−	8.46123i	−0.301077	−	0.414846i
$417$	1.57619			0.0771861
$418$	25.1329	+	25.1329i	1.22929	+	1.22929i
$419$			17.2554i			0.842980i	0.906833	+	0.421490i	$0.138493\pi$
$419$			17.2554i			0.842980i	−0.906833	+	0.421490i	$0.861507\pi$
$420$		0			0
$421$	5.55993	−	5.55993i	0.270974	−	0.270974i	−0.558518	−	0.829492i	$-0.688630\pi$
$421$	5.55993	−	5.55993i	0.270974	−	0.270974i	0.829492	+	0.558518i	$0.188630\pi$
$422$	−23.6579	+	23.6579i	−1.15165	+	1.15165i
$423$	5.61866	−	5.61866i	0.273189	−	0.273189i
$424$	−17.4615	−	17.4615i	−0.848008	−	0.848008i
$425$		−	28.9988i		−	1.40665i
$426$	4.13873			0.200522
$427$		0			0
$428$			9.25695i			0.447451i
$429$	−4.50740	−	6.21063i	−0.217619	−	0.299852i
$430$			0.336043i			0.0162054i
$431$	−5.77933	+	5.77933i	−0.278380	+	0.278380i	−0.832462	−	0.554082i	$-0.813069\pi$
$431$	−5.77933	+	5.77933i	−0.278380	+	0.278380i	0.554082	+	0.832462i	$0.313069\pi$
$432$		−	13.8169i		−	0.664765i
$433$	6.91474			0.332301			0.166151	−	0.986100i	$-0.446866\pi$
$433$	6.91474			0.332301			0.166151	+	0.986100i	$0.446866\pi$
$434$		0			0
$435$	−0.0102865	+	0.0102865i	−0.000493198	+	0.000493198i
$436$	−5.06599	−	5.06599i	−0.242617	−	0.242617i
$437$	3.26434	−	3.26434i	0.156154	−	0.156154i
$438$	−9.52329			−0.455040
$439$	−4.29578			−0.205026			−0.102513	−	0.994732i	$-0.532688\pi$
$439$	−4.29578			−0.205026			−0.102513	+	0.994732i	$0.532688\pi$
$440$	0.557715	−	0.557715i	0.0265880	−	0.0265880i
$441$		0			0
$442$	−19.5427	−	26.9274i	−0.929553	−	1.28081i
$443$	−23.0135			−1.09340			−0.546702	−	0.837327i	$-0.684117\pi$
$443$	−23.0135			−1.09340			−0.546702	+	0.837327i	$0.684117\pi$
$444$	−0.729570	−	0.729570i	−0.0346239	−	0.0346239i
$445$	−0.641544			−0.0304121
$446$	−43.3966			−2.05489
$447$	−1.20622	−	1.20622i	−0.0570521	−	0.0570521i
$448$		0			0
$449$	−7.20816	−	7.20816i	−0.340174	−	0.340174i	0.516259	−	0.856433i	$-0.327324\pi$
$449$	−7.20816	−	7.20816i	−0.340174	−	0.340174i	−0.856433	+	0.516259i	$0.827324\pi$
$450$	15.4101	+	15.4101i	0.726441	+	0.726441i
$451$		−	46.0811i		−	2.16987i
$452$			3.16605i			0.148919i
$453$	−5.79326	+	5.79326i	−0.272191	+	0.272191i
$454$	5.50824			0.258515
$455$		0			0
$456$	−6.24664			−0.292526
$457$	11.0298	−	11.0298i	0.515951	−	0.515951i	−0.400392	−	0.916344i	$-0.631126\pi$
$457$	11.0298	−	11.0298i	0.515951	−	0.515951i	0.916344	+	0.400392i	$0.131126\pi$
$458$		−	30.6297i		−	1.43123i
$459$		−	16.8052i		−	0.784401i
$460$	0.0257911	+	0.0257911i	0.00120251	+	0.00120251i
$461$	10.2849	+	10.2849i	0.479017	+	0.479017i	0.904817	−	0.425800i	$-0.140007\pi$
$461$	10.2849	+	10.2849i	0.479017	+	0.479017i	−0.425800	+	0.904817i	$0.640007\pi$
$462$		0			0
$463$	−15.2514	−	15.2514i	−0.708792	−	0.708792i	0.257489	−	0.966281i	$-0.417105\pi$
$463$	−15.2514	−	15.2514i	−0.708792	−	0.708792i	−0.966281	+	0.257489i	$0.917105\pi$
$464$	1.73199			0.0804057
$465$	−0.0559425			−0.00259427
$466$	5.80881	+	5.80881i	0.269088	+	0.269088i
$467$	17.8133			0.824303			0.412152	−	0.911115i	$-0.364777\pi$
$467$	17.8133			0.824303			0.412152	+	0.911115i	$0.364777\pi$
$468$	5.13545	+	0.816087i	0.237386	+	0.0377237i
$469$		0			0
$470$	0.258873	−	0.258873i	0.0119409	−	0.0119409i
$471$	−9.67931			−0.445999
$472$	5.19673			0.239199
$473$	7.93633	−	7.93633i	0.364913	−	0.364913i
$474$	4.84010	+	4.84010i	0.222313	+	0.222313i
$475$	18.6881	−	18.6881i	0.857468	−	0.857468i
$476$		0			0
$477$	28.9376			1.32496
$478$			15.4066i			0.704683i
$479$	17.9204	−	17.9204i	0.818806	−	0.818806i	−0.167129	−	0.985935i	$-0.553450\pi$
$479$	17.9204	−	17.9204i	0.818806	−	0.818806i	0.985935	+	0.167129i	$0.0534497\pi$
$480$		−	0.116280i		−	0.00530742i
$481$	−11.3848	+	8.26256i	−0.519101	+	0.376741i
$482$		−	3.55293i		−	0.161832i
$483$		0			0
$484$	3.60299			0.163772
$485$			0.680327i			0.0308921i
$486$	13.5927	+	13.5927i	0.616575	+	0.616575i
$487$	−23.6051	+	23.6051i	−1.06965	+	1.06965i	−0.0722632	+	0.997386i	$0.523022\pi$
$487$	−23.6051	+	23.6051i	−1.06965	+	1.06965i	−0.997386	+	0.0722632i	$0.976978\pi$
$488$	6.95840	−	6.95840i	0.314992	−	0.314992i
$489$	0.442410	−	0.442410i	0.0200065	−	0.0200065i
$490$		0			0
$491$			14.4968i			0.654231i	0.944984	+	0.327115i	$0.106077\pi$
$491$			14.4968i			0.654231i	−0.944984	+	0.327115i	$0.893923\pi$
$492$	−2.03892	−	2.03892i	−0.0919218	−	0.0919218i
$493$	2.10659			0.0948761
$494$	4.75901	−	29.9473i	0.214118	−	1.34739i
$495$			0.924254i			0.0415421i
$496$	4.70968	+	4.70968i	0.211471	+	0.211471i
$497$		0			0
$498$		−	5.56103i		−	0.249196i
$499$	6.99500	−	6.99500i	0.313139	−	0.313139i	−0.532985	−	0.846124i	$-0.678930\pi$
$499$	6.99500	−	6.99500i	0.313139	−	0.313139i	0.846124	+	0.532985i	$0.178930\pi$
$500$	0.295491	+	0.295491i	0.0132148	+	0.0132148i
$501$	−3.68357	−	3.68357i	−0.164570	−	0.164570i
$502$	27.9046	−	27.9046i	1.24544	−	1.24544i
$503$		−	32.9620i		−	1.46970i	−0.678229	−	0.734851i	$-0.737252\pi$
$503$		−	32.9620i		−	1.46970i	0.678229	−	0.734851i	$-0.262748\pi$
$504$		0			0
$505$	−0.631745	−	0.631745i	−0.0281123	−	0.0281123i
$506$		−	5.85795i		−	0.260418i
$507$	−2.02950	+	6.22433i	−0.0901333	+	0.276432i
$508$	−0.136440			−0.00605355
$509$	24.3814	+	24.3814i	1.08069	+	1.08069i	0.996445	+	0.0842405i	$0.0268464\pi$
$509$	24.3814	+	24.3814i	1.08069	+	1.08069i	0.0842405	+	0.996445i	$0.473154\pi$
$510$		−	0.370054i		−	0.0163863i
$511$		0			0
$512$	6.03549	−	6.03549i	0.266733	−	0.266733i
$513$	10.8300	−	10.8300i	0.478157	−	0.478157i
$514$	15.0018	−	15.0018i	0.661703	−	0.661703i
$515$	−0.543642	−	0.543642i	−0.0239557	−	0.0239557i
$516$		−	0.702309i		−	0.0309174i
$517$	−12.2276			−0.537770
$518$		0			0
$519$		−	1.59292i		−	0.0699216i
$520$	−0.664550	−	0.105605i	−0.0291424	−	0.00463110i
$521$			32.3387i			1.41679i	0.705818	+	0.708393i	$0.250580\pi$
$521$			32.3387i			1.41679i	−0.705818	+	0.708393i	$0.749420\pi$
$522$	−1.11945	+	1.11945i	−0.0489972	+	0.0489972i
$523$		−	19.4710i		−	0.851405i	−0.904863	−	0.425703i	$-0.860027\pi$
$523$		−	19.4710i		−	0.851405i	0.904863	−	0.425703i	$-0.139973\pi$
$524$	0.411891			0.0179935
$525$		0			0
$526$	0.476192	−	0.476192i	0.0207629	−	0.0207629i
$527$	5.72830	+	5.72830i	0.249529	+	0.249529i
$528$	−7.18549	+	7.18549i	−0.312708	+	0.312708i
$529$	22.2392			0.966920
$530$	1.33326			0.0579133
$531$	−4.30605	+	4.30605i	−0.186867	+	0.186867i
$532$		0			0
$533$	−31.8169	+	23.0913i	−1.37815	+	1.00020i
$534$	6.44736			0.279004
$535$	0.992581	+	0.992581i	0.0429130	+	0.0429130i
$536$	23.7042			1.02387
$537$	−2.92239			−0.126110
$538$	−16.3088	−	16.3088i	−0.703122	−	0.703122i
$539$		0			0
$540$	0.0855664	+	0.0855664i	0.00368219	+	0.00368219i
$541$	−5.41789	−	5.41789i	−0.232933	−	0.232933i	0.580983	−	0.813916i	$-0.302668\pi$
$541$	−5.41789	−	5.41789i	−0.232933	−	0.232933i	−0.813916	+	0.580983i	$0.802668\pi$
$542$			31.4365i			1.35031i
$543$			6.89963i			0.296091i
$544$	−11.9066	+	11.9066i	−0.510492	+	0.510492i
$545$	−1.08641			−0.0465366
$546$		0			0
$547$	−17.3075			−0.740016			−0.370008	−	0.929029i	$-0.620645\pi$
$547$	−17.3075			−0.740016			−0.370008	+	0.929029i	$0.620645\pi$
$548$	−5.12238	+	5.12238i	−0.218817	+	0.218817i
$549$			11.5316i			0.492155i
$550$		−	33.5364i		−	1.43000i
$551$	1.35758	+	1.35758i	0.0578348	+	0.0578348i
$552$	0.727980	+	0.727980i	0.0309849	+	0.0309849i
$553$		0			0
$554$	−26.6910	−	26.6910i	−1.13399	−	1.13399i
$555$	−0.156457			−0.00664123
$556$	1.64354			0.0697016
$557$	11.7670	+	11.7670i	0.498583	+	0.498583i	0.910997	−	0.412413i	$-0.135314\pi$
$557$	11.7670	+	11.7670i	0.498583	+	0.498583i	−0.412413	+	0.910997i	$0.635314\pi$
$558$	−6.08810			−0.257730
$559$	−9.45660	−	1.50277i	−0.399972	−	0.0635605i
$560$		0			0
$561$	−8.73959	+	8.73959i	−0.368986	+	0.368986i
$562$	−21.7107			−0.915812
$563$	−3.90936			−0.164760			−0.0823800	−	0.996601i	$-0.526252\pi$
$563$	−3.90936			−0.164760			−0.0823800	+	0.996601i	$0.526252\pi$
$564$	−0.541029	+	0.541029i	−0.0227814	+	0.0227814i
$565$	0.339482	+	0.339482i	0.0142821	+	0.0142821i
$566$	30.0741	−	30.0741i	1.26411	−	1.26411i
$567$		0			0
$568$	−12.1209			−0.508581
$569$		−	2.63437i		−	0.110438i	−0.998474	−	0.0552192i	$-0.982414\pi$
$569$		−	2.63437i		−	0.110438i	0.998474	−	0.0552192i	$-0.0175858\pi$
$570$	0.238479	−	0.238479i	0.00998878	−	0.00998878i
$571$			18.7981i			0.786675i	0.919394	+	0.393337i	$0.128680\pi$
$571$			18.7981i			0.786675i	−0.919394	+	0.393337i	$0.871320\pi$
$572$	−4.70001	−	6.47602i	−0.196517	−	0.270776i
$573$			4.25908i			0.177926i
$574$		0			0
$575$	−4.35580			−0.181649
$576$			13.5707i			0.565446i
$577$	−31.6931	−	31.6931i	−1.31940	−	1.31940i	−0.914251	−	0.405148i	$-0.867220\pi$
$577$	−31.6931	−	31.6931i	−1.31940	−	1.31940i	−0.405148	−	0.914251i	$-0.632780\pi$
$578$	−18.7903	+	18.7903i	−0.781576	+	0.781576i
$579$	0.175831	−	0.175831i	0.00730727	−	0.00730727i
$580$	−0.0107260	+	0.0107260i	−0.000445374	+	0.000445374i
$581$		0			0
$582$		−	6.83712i		−	0.283408i
$583$	−31.4877	−	31.4877i	−1.30409	−	1.30409i
$584$	27.8904			1.15411
$585$	0.638157	−	0.463146i	0.0263845	−	0.0191487i
$586$		−	49.1602i		−	2.03079i
$587$	−21.2468	−	21.2468i	−0.876947	−	0.876947i	0.116270	−	0.993218i	$-0.462906\pi$
$587$	−21.2468	−	21.2468i	−0.876947	−	0.876947i	−0.993218	+	0.116270i	$0.962906\pi$
$588$		0			0
$589$			7.38312i			0.304216i
$590$	−0.198396	+	0.198396i	−0.00816784	+	0.00816784i
$591$	1.39951	+	1.39951i	0.0575681	+	0.0575681i
$592$	13.1718	+	13.1718i	0.541357	+	0.541357i
$593$	−25.6065	+	25.6065i	−1.05153	+	1.05153i	−0.0529347	+	0.998598i	$0.516858\pi$
$593$	−25.6065	+	25.6065i	−1.05153	+	1.05153i	−0.998598	+	0.0529347i	$0.983142\pi$
$594$		−	19.4348i		−	0.797419i
$595$		0			0
$596$	−1.25776	−	1.25776i	−0.0515198	−	0.0515198i
$597$		−	8.08994i		−	0.331099i
$598$	−4.04466	+	2.93543i	−0.165398	+	0.120039i
$599$	−2.02255			−0.0826393			−0.0413196	−	0.999146i	$-0.513156\pi$
$599$	−2.02255			−0.0826393			−0.0413196	+	0.999146i	$0.513156\pi$
$600$	4.16763	+	4.16763i	0.170143	+	0.170143i
$601$		−	16.8573i		−	0.687623i	−0.939039	−	0.343811i	$-0.888282\pi$
$601$		−	16.8573i		−	0.687623i	0.939039	−	0.343811i	$-0.111718\pi$
$602$		0			0
$603$	−19.6415	+	19.6415i	−0.799865	+	0.799865i
$604$	−6.04081	+	6.04081i	−0.245797	+	0.245797i
$605$	0.386333	−	0.386333i	0.0157067	−	0.0157067i
$606$	6.34888	+	6.34888i	0.257906	+	0.257906i
$607$			23.2547i			0.943880i	0.881631	+	0.471940i	$0.156446\pi$
$607$			23.2547i			0.943880i	−0.881631	+	0.471940i	$0.843554\pi$
$608$	−15.3463			−0.622373
$609$		0			0
$610$			0.531303i			0.0215118i
$611$	6.12729	+	8.44264i	0.247884	+	0.341553i
$612$		−	8.37498i		−	0.338539i
$613$	−1.64831	+	1.64831i	−0.0665746	+	0.0665746i	−0.739610	−	0.673036i	$-0.764990\pi$
$613$	−1.64831	+	1.64831i	−0.0665746	+	0.0665746i	0.673036	+	0.739610i	$0.264990\pi$
$614$		−	5.60772i		−	0.226309i
$615$	−0.437249			−0.0176316
$616$		0			0
$617$	−8.67485	+	8.67485i	−0.349236	+	0.349236i	−0.859825	−	0.510589i	$-0.829428\pi$
$617$	−8.67485	+	8.67485i	−0.349236	+	0.349236i	0.510589	+	0.859825i	$0.329428\pi$
$618$	5.46347	+	5.46347i	0.219773	+	0.219773i
$619$	18.8282	−	18.8282i	0.756767	−	0.756767i	−0.218965	−	0.975733i	$-0.570268\pi$
$619$	18.8282	−	18.8282i	0.756767	−	0.756767i	0.975733	+	0.218965i	$0.0702681\pi$
$620$	−0.0583330			−0.00234271
$621$	−2.52425			−0.101295
$622$	34.0581	−	34.0581i	1.36561	−	1.36561i
$623$		0			0
$624$	8.56193	+	1.36060i	0.342751	+	0.0544675i
$625$	−24.9049			−0.996197
$626$	−21.8789	−	21.8789i	−0.874457	−	0.874457i
$627$	−11.2643			−0.449854
$628$	−10.0929			−0.402751
$629$	16.0206	+	16.0206i	0.638784	+	0.638784i
$630$		0			0
$631$	−2.58488	−	2.58488i	−0.102903	−	0.102903i	0.653781	−	0.756684i	$-0.273182\pi$
$631$	−2.58488	−	2.58488i	−0.102903	−	0.102903i	−0.756684	+	0.653781i	$0.773182\pi$
$632$	−14.1749	−	14.1749i	−0.563849	−	0.563849i
$633$		−	10.6032i		−	0.421441i
$634$		−	7.96614i		−	0.316376i
$635$	−0.0146299	+	0.0146299i	−0.000580569	+	0.000580569i
$636$	−2.78644			−0.110490
$637$		0			0
$638$	2.43622			0.0964507
$639$	10.0435	−	10.0435i	0.397313	−	0.397313i
$640$			1.08705i			0.0429692i
$641$		−	30.9650i		−	1.22305i	−0.791227	−	0.611523i	$-0.790557\pi$
$641$		−	30.9650i		−	1.22305i	0.791227	−	0.611523i	$-0.209443\pi$
$642$	−9.97520	−	9.97520i	−0.393690	−	0.393690i
$643$	9.81258	+	9.81258i	0.386970	+	0.386970i	0.873605	−	0.486635i	$-0.161776\pi$
$643$	9.81258	+	9.81258i	0.386970	+	0.386970i	−0.486635	+	0.873605i	$0.661776\pi$
$644$		0			0
$645$	−0.0753055	−	0.0753055i	−0.00296515	−	0.00296515i
$646$	−48.8387			−1.92153
$647$	−27.4799			−1.08035			−0.540174	−	0.841553i	$-0.681641\pi$
$647$	−27.4799			−1.08035			−0.540174	+	0.841553i	$0.681641\pi$
$648$	−11.2389	−	11.2389i	−0.441508	−	0.441508i
$649$	9.37106			0.367846
$650$	−23.1554	+	16.8051i	−0.908229	+	0.659152i
$651$		0			0
$652$	0.461314	−	0.461314i	0.0180665	−	0.0180665i
$653$	10.1156			0.395853			0.197926	−	0.980217i	$-0.436579\pi$
$653$	10.1156			0.395853			0.197926	+	0.980217i	$0.436579\pi$
$654$	10.9181			0.426932
$655$	0.0441652	−	0.0441652i	0.00172568	−	0.00172568i
$656$	36.8111	+	36.8111i	1.43723	+	1.43723i
$657$	−23.1102	+	23.1102i	−0.901615	+	0.901615i
$658$		0			0
$659$	39.4336			1.53612			0.768058	−	0.640380i	$-0.221223\pi$
$659$	39.4336			1.53612			0.768058	+	0.640380i	$0.221223\pi$
$660$		−	0.0889978i		−	0.00346423i
$661$	−17.9550	+	17.9550i	−0.698370	+	0.698370i	−0.964059	−	0.265689i	$-0.914401\pi$
$661$	−17.9550	+	17.9550i	−0.698370	+	0.698370i	0.265689	+	0.964059i	$0.414401\pi$
$662$			30.4761i			1.18449i
$663$	10.4137	+	1.65487i	0.404436	+	0.0642699i
$664$			16.2863i			0.632032i
$665$		0			0
$666$	−17.0269			−0.659778
$667$		−	0.316423i		−	0.0122519i
$668$	−3.84097	−	3.84097i	−0.148612	−	0.148612i
$669$	9.72495	−	9.72495i	0.375988	−	0.375988i
$670$	−0.904960	+	0.904960i	−0.0349617	+	0.0349617i
$671$	12.5478	−	12.5478i	0.484403	−	0.484403i
$672$		0			0
$673$		−	20.9026i		−	0.805734i	−0.915258	−	0.402867i	$-0.868014\pi$
$673$		−	20.9026i		−	0.805734i	0.915258	−	0.402867i	$-0.131986\pi$
$674$	−3.38486	−	3.38486i	−0.130380	−	0.130380i
$675$	−14.4511			−0.556224
$676$	−2.11622	+	6.49030i	−0.0813932	+	0.249627i
$677$		−	15.8084i		−	0.607567i	−0.952741	−	0.303784i	$-0.901750\pi$
$677$		−	15.8084i		−	0.607567i	0.952741	−	0.303784i	$-0.0982500\pi$
$678$	−3.41171	−	3.41171i	−0.131026	−	0.131026i
$679$		0			0
$680$			1.08376i			0.0415603i
$681$	−1.23437	+	1.23437i	−0.0473011	+	0.0473011i
$682$	6.62462	+	6.62462i	0.253670	+	0.253670i
$683$	8.24323	+	8.24323i	0.315419	+	0.315419i	0.847004	−	0.531586i	$-0.178404\pi$
$683$	8.24323	+	8.24323i	0.315419	+	0.315419i	−0.531586	+	0.847004i	$0.678404\pi$
$684$	5.39720	−	5.39720i	0.206367	−	0.206367i
$685$			1.09850i			0.0419715i
$686$		0			0
$687$	6.86397	+	6.86397i	0.261877	+	0.261877i
$688$			12.6796i			0.483406i
$689$	−5.96232	+	37.5195i	−0.227146	+	1.42938i
$690$	−0.0555844			−0.00211606
$691$	−7.39992	−	7.39992i	−0.281506	−	0.281506i	0.552203	−	0.833710i	$-0.313787\pi$
$691$	−7.39992	−	7.39992i	−0.281506	−	0.281506i	−0.833710	+	0.552203i	$0.813787\pi$
$692$		−	1.66099i		−	0.0631415i
$693$		0			0
$694$	9.25675	−	9.25675i	0.351381	−	0.351381i
$695$	0.176229	−	0.176229i	0.00668476	−	0.00668476i
$696$	−0.302753	+	0.302753i	−0.0114758	+	0.0114758i
$697$	44.7727	+	44.7727i	1.69589	+	1.69589i
$698$			18.1158i			0.685693i
$699$	−2.60345			−0.0984716
$700$		0			0
$701$			36.2902i			1.37066i	0.728232	+	0.685331i	$0.240343\pi$
$701$			36.2902i			1.37066i	−0.728232	+	0.685331i	$0.759657\pi$
$702$	−13.4189	+	9.73882i	−0.506463	+	0.367568i
$703$			20.6487i			0.778782i
$704$	14.7666	−	14.7666i	0.556539	−	0.556539i
$705$			0.116024i			0.00436973i
$706$	26.8591			1.01086
$707$		0			0
$708$	0.414636	−	0.414636i	0.0155830	−	0.0155830i
$709$	4.55738	+	4.55738i	0.171156	+	0.171156i	0.787487	−	0.616331i	$-0.211382\pi$
$709$	4.55738	+	4.55738i	0.171156	+	0.171156i	−0.616331	+	0.787487i	$0.711382\pi$
$710$	0.462741	−	0.462741i	0.0173664	−	0.0173664i
$711$	23.4910			0.880980
$712$	−18.8821			−0.707635
$713$	0.860425	−	0.860425i	0.0322232	−	0.0322232i
$714$		0			0
$715$	−1.19836	−	0.190434i	−0.0448160	−	0.00712183i
$716$	−3.04726			−0.113882
$717$	−3.45255	−	3.45255i	−0.128938	−	0.128938i
$718$	35.8957			1.33962
$719$	−5.18872			−0.193507			−0.0967533	−	0.995308i	$-0.530846\pi$
$719$	−5.18872			−0.193507			−0.0967533	+	0.995308i	$0.530846\pi$
$720$	−0.738325	−	0.738325i	−0.0275158	−	0.0275158i
$721$		0			0
$722$	−10.1246	−	10.1246i	−0.376799	−	0.376799i
$723$	0.796194	+	0.796194i	0.0296108	+	0.0296108i
$724$			7.19446i			0.267380i
$725$		−	1.81150i		−	0.0672773i
$726$	−3.88255	+	3.88255i	−0.144095	+	0.144095i
$727$	23.5345			0.872848			0.436424	−	0.899741i	$-0.356245\pi$
$727$	23.5345			0.872848			0.436424	+	0.899741i	$0.356245\pi$
$728$		0			0
$729$	14.2532			0.527898
$730$	−1.06478	+	1.06478i	−0.0394091	+	0.0394091i
$731$			15.4220i			0.570403i
$732$		−	1.11039i		−	0.0410413i
$733$	−1.34152	−	1.34152i	−0.0495501	−	0.0495501i	0.681898	−	0.731448i	$-0.261155\pi$
$733$	−1.34152	−	1.34152i	−0.0495501	−	0.0495501i	−0.731448	+	0.681898i	$0.761155\pi$
$734$	−28.8516	−	28.8516i	−1.06493	−	1.06493i
$735$		0			0
$736$	1.78844	+	1.78844i	0.0659230	+	0.0659230i
$737$	42.7450			1.57453
$738$	−47.5849			−1.75162
$739$	4.62160	+	4.62160i	0.170008	+	0.170008i	0.786983	−	0.616975i	$-0.211642\pi$
$739$	4.62160	+	4.62160i	0.170008	+	0.170008i	−0.616975	+	0.786983i	$0.711642\pi$
$740$	−0.163143			−0.00599725
$741$	5.64458	+	7.77752i	0.207359	+	0.285714i
$742$		0			0
$743$	12.2516	−	12.2516i	0.449468	−	0.449468i	−0.445709	−	0.895178i	$-0.647049\pi$
$743$	12.2516	−	12.2516i	0.449468	−	0.449468i	0.895178	+	0.445709i	$0.147049\pi$
$744$	−1.64651			−0.0603640
$745$	−0.269728			−0.00988207
$746$	−18.6794	+	18.6794i	−0.683900	+	0.683900i
$747$	−13.4950	−	13.4950i	−0.493755	−	0.493755i
$748$	−9.11304	+	9.11304i	−0.333206	+	0.333206i
$749$		0			0
$750$	−0.636837			−0.0232540
$751$		−	40.9863i		−	1.49561i	−0.663919	−	0.747805i	$-0.731108\pi$
$751$		−	40.9863i		−	1.49561i	0.663919	−	0.747805i	$-0.268892\pi$
$752$	9.76784	−	9.76784i	0.356196	−	0.356196i
$753$			12.5066i			0.455765i
$754$	−1.22079	−	1.68210i	−0.0444587	−	0.0612585i
$755$			1.29546i			0.0471466i
$756$		0			0
$757$	−25.7292			−0.935142			−0.467571	−	0.883955i	$-0.654871\pi$
$757$	−25.7292			−0.935142			−0.467571	+	0.883955i	$0.654871\pi$
$758$		−	60.8036i		−	2.20849i
$759$	1.31274	+	1.31274i	0.0476494	+	0.0476494i
$760$	−0.698421	+	0.698421i	−0.0253344	+	0.0253344i
$761$	−20.0801	+	20.0801i	−0.727901	+	0.727901i	−0.970201	−	0.242300i	$-0.922098\pi$
$761$	−20.0801	+	20.0801i	−0.727901	+	0.727901i	0.242300	+	0.970201i	$0.422098\pi$
$762$	0.147027	−	0.147027i	0.00532621	−	0.00532621i
$763$		0			0
$764$			4.44108i			0.160673i
$765$	−0.898012	−	0.898012i	−0.0324677	−	0.0324677i
$766$	42.9203			1.55077
$767$	−4.69586	−	6.47030i	−0.169558	−	0.233629i
$768$		−	5.94763i		−	0.214617i
$769$	20.7240	+	20.7240i	0.747328	+	0.747328i	0.973977	−	0.226649i	$-0.0727770\pi$
$769$	20.7240	+	20.7240i	0.747328	+	0.747328i	−0.226649	+	0.973977i	$0.572777\pi$
$770$		0			0
$771$			6.72367i			0.242147i
$772$	0.183344	−	0.183344i	0.00659870	−	0.00659870i
$773$	−4.30955	−	4.30955i	−0.155004	−	0.155004i	0.625345	−	0.780349i	$-0.284958\pi$
$773$	−4.30955	−	4.30955i	−0.155004	−	0.155004i	−0.780349	+	0.625345i	$0.784958\pi$
$774$	−8.19533	−	8.19533i	−0.294575	−	0.294575i
$775$	4.92587	−	4.92587i	0.176942	−	0.176942i
$776$			20.0235i			0.718803i
$777$		0			0
$778$	21.4057	+	21.4057i	0.767433	+	0.767433i
$779$			57.7069i			2.06756i
$780$	−0.0614491	+	0.0445970i	−0.00220023	+	0.00159683i
$781$	−21.8571			−0.782110
$782$	5.69163	+	5.69163i	0.203532	+	0.203532i
$783$		−	1.04979i		−	0.0375164i
$784$		0			0
$785$	−1.08222	+	1.08222i	−0.0386261	+	0.0386261i
$786$	−0.443850	+	0.443850i	−0.0158316	+	0.0158316i
$787$	−9.31262	+	9.31262i	−0.331959	+	0.331959i	−0.853330	−	0.521371i	$-0.825421\pi$
$787$	−9.31262	+	9.31262i	−0.331959	+	0.331959i	0.521371	+	0.853330i	$0.325421\pi$
$788$	1.45931	+	1.45931i	0.0519858	+	0.0519858i
$789$			0.213424i			0.00759811i
$790$	1.08232			0.0385071
$791$		0			0
$792$			27.2028i			0.966611i
$793$	−14.9514	−	2.37597i	−0.530941	−	0.0843733i
$794$			5.41083i			0.192023i
$795$	−0.298778	+	0.298778i	−0.0105966	+	0.0105966i
$796$		−	8.43563i		−	0.298993i
$797$	−32.0204			−1.13422			−0.567111	−	0.823642i	$-0.691939\pi$
$797$	−32.0204			−1.13422			−0.567111	+	0.823642i	$0.691939\pi$
$798$		0			0
$799$	11.8805	−	11.8805i	0.420300	−	0.420300i
$800$	10.2387	+	10.2387i	0.361993	+	0.361993i
$801$	15.6458	−	15.6458i	0.552818	−	0.552818i
$802$	−58.6306			−2.07032
$803$	50.2937			1.77482
$804$	1.89131	−	1.89131i	0.0667014	−	0.0667014i
$805$		0			0
$806$	1.25440	−	7.89362i	0.0441842	−	0.278041i
$807$	7.30944			0.257304
$808$	−18.5937	−	18.5937i	−0.654123	−	0.654123i
$809$	−32.4005			−1.13914			−0.569570	−	0.821943i	$-0.692890\pi$
$809$	−32.4005			−1.13914			−0.569570	+	0.821943i	$0.692890\pi$
$810$	0.858142			0.0301520
$811$	−36.2274	−	36.2274i	−1.27212	−	1.27212i	−0.944975	−	0.327142i	$-0.893915\pi$
$811$	−36.2274	−	36.2274i	−1.27212	−	1.27212i	−0.327142	−	0.944975i	$-0.606085\pi$
$812$		0			0
$813$	−7.04476	−	7.04476i	−0.247071	−	0.247071i
$814$	18.5274	+	18.5274i	0.649385	+	0.649385i
$815$		−	0.0989294i		−	0.00346535i
$816$		−	13.9630i		−	0.488801i
$817$	−9.93859	+	9.93859i	−0.347707	+	0.347707i
$818$	8.92543			0.312070
$819$		0			0
$820$	−0.455934			−0.0159219
$821$	−3.78144	+	3.78144i	−0.131973	+	0.131973i	−0.770008	−	0.638035i	$-0.779748\pi$
$821$	−3.78144	+	3.78144i	−0.131973	+	0.131973i	0.638035	+	0.770008i	$0.279748\pi$
$822$		−	11.0397i		−	0.385052i
$823$			15.1249i			0.527221i	0.964629	+	0.263610i	$0.0849133\pi$
$823$			15.1249i			0.527221i	−0.964629	+	0.263610i	$0.915087\pi$
$824$	−16.0006	−	16.0006i	−0.557407	−	0.557407i
$825$	7.51533	+	7.51533i	0.261650	+	0.261650i
$826$		0			0
$827$	18.6451	+	18.6451i	0.648353	+	0.648353i	0.952595	−	0.304242i	$-0.0984030\pi$
$827$	18.6451	+	18.6451i	0.648353	+	0.648353i	−0.304242	+	0.952595i	$0.598403\pi$
$828$	−1.25797			−0.0437176
$829$	16.8683			0.585861			0.292931	−	0.956134i	$-0.405369\pi$
$829$	16.8683			0.585861			0.292931	+	0.956134i	$0.405369\pi$
$830$	−0.621765	−	0.621765i	−0.0215818	−	0.0215818i
$831$	11.9626			0.414980
$832$	−17.5953	−	2.79612i	−0.610008	−	0.0969380i
$833$		0			0
$834$	−1.77106	+	1.77106i	−0.0613268	+	0.0613268i
$835$	−0.823701			−0.0285054
$836$	−11.7457			−0.406232
$837$	2.85461	−	2.85461i	0.0986698	−	0.0986698i
$838$	−19.3888	−	19.3888i	−0.669775	−	0.669775i
$839$	−21.4556	+	21.4556i	−0.740729	+	0.740729i	−0.972718	−	0.231989i	$-0.925477\pi$
$839$	−21.4556	+	21.4556i	−0.740729	+	0.740729i	0.231989	+	0.972718i	$0.425477\pi$
$840$		0			0
$841$	−28.8684			−0.995462
$842$			12.4947i			0.430596i
$843$	4.86527	−	4.86527i	0.167569	−	0.167569i
$844$		−	11.0563i		−	0.380574i
$845$	0.469013	+	0.922840i	0.0161345	+	0.0317466i
$846$			12.6267i			0.434114i
$847$		0			0
$848$	50.3069			1.72755
$849$			13.4789i			0.462595i
$850$	32.5842	+	32.5842i	1.11763	+	1.11763i
$851$	2.40639	−	2.40639i	0.0824901	−	0.0824901i
$852$	−0.967101	+	0.967101i	−0.0331323	+	0.0331323i
$853$	32.1950	−	32.1950i	1.10234	−	1.10234i	0.108209	−	0.994128i	$-0.465488\pi$
$853$	32.1950	−	32.1950i	1.10234	−	1.10234i	0.994128	−	0.108209i	$-0.0345116\pi$
$854$		0			0
$855$		−	1.15743i		−	0.0395834i
$856$	29.2139	+	29.2139i	0.998509	+	0.998509i
$857$	11.7140			0.400143			0.200071	−	0.979781i	$-0.435883\pi$
$857$	11.7140			0.400143			0.200071	+	0.979781i	$0.435883\pi$
$858$	12.0432	+	1.91382i	0.411148	+	0.0653366i
$859$		−	16.0689i		−	0.548263i	−0.961692	−	0.274132i	$-0.911610\pi$
$859$		−	16.0689i		−	0.548263i	0.961692	−	0.274132i	$-0.0883904\pi$
$860$	−0.0785234	−	0.0785234i	−0.00267763	−	0.00267763i
$861$		0			0
$862$		−	12.9877i		−	0.442364i
$863$	31.8712	−	31.8712i	1.08491	−	1.08491i	0.0888650	−	0.996044i	$-0.471676\pi$
$863$	31.8712	−	31.8712i	1.08491	−	1.08491i	0.996044	−	0.0888650i	$-0.0283240\pi$
$864$	5.93348	+	5.93348i	0.201861	+	0.201861i
$865$	−0.178101	−	0.178101i	−0.00605561	−	0.00605561i
$866$	−7.76966	+	7.76966i	−0.264024	+	0.264024i
$867$		−	8.42165i		−	0.286014i
$868$		0			0
$869$	−25.5611	−	25.5611i	−0.867102	−	0.867102i
$870$		−	0.0231165i		−	0.000783724i
$871$	−21.4196	−	29.5135i	−0.725775	−	1.00003i
$872$	−31.9754			−1.08282
$873$	−16.5917	−	16.5917i	−0.561543	−	0.561543i
$874$			7.33586i			0.248139i
$875$		0			0
$876$	2.22532	−	2.22532i	0.0751864	−	0.0751864i
$877$	−3.10240	+	3.10240i	−0.104761	+	0.104761i	−0.757544	−	0.652784i	$-0.773601\pi$
$877$	−3.10240	+	3.10240i	−0.104761	+	0.104761i	0.652784	+	0.757544i	$0.273601\pi$
$878$	4.82690	−	4.82690i	0.162900	−	0.162900i
$879$	11.0166	+	11.0166i	0.371579	+	0.371579i
$880$			1.60678i			0.0541646i
$881$	−38.4369			−1.29497			−0.647487	−	0.762077i	$-0.724180\pi$
$881$	−38.4369			−1.29497			−0.647487	+	0.762077i	$0.724180\pi$
$882$		0			0
$883$		−	20.7346i		−	0.697776i	−0.937164	−	0.348888i	$-0.886559\pi$
$883$		−	20.7346i		−	0.697776i	0.937164	−	0.348888i	$-0.113441\pi$
$884$	10.8587	+	1.72559i	0.365218	+	0.0580378i
$885$		−	0.0889192i		−	0.00298898i
$886$	25.8588	−	25.8588i	0.868745	−	0.868745i
$887$			42.3975i			1.42357i	0.702399	+	0.711784i	$0.252112\pi$
$887$			42.3975i			1.42357i	−0.702399	+	0.711784i	$0.747888\pi$
$888$	−4.60488			−0.154530
$889$		0			0
$890$	0.720863	−	0.720863i	0.0241634	−	0.0241634i
$891$	−20.2668	−	20.2668i	−0.678962	−	0.678962i
$892$	10.1405	−	10.1405i	0.339530	−	0.339530i
$893$	15.3125			0.512415
$894$	2.71070			0.0906594
$895$	−0.326745	+	0.326745i	−0.0109219	+	0.0109219i
$896$		0			0
$897$	0.248572	−	1.56420i	0.00829957	−	0.0522273i
$898$	16.1987			0.540558
$899$	0.357835	+	0.357835i	0.0119345	+	0.0119345i
$900$	−7.20180			−0.240060
$901$	61.1874			2.03845
$902$	51.7784	+	51.7784i	1.72403	+	1.72403i
$903$		0			0
$904$	9.99170	+	9.99170i	0.332319	+	0.332319i
$905$	0.771430	+	0.771430i	0.0256432	+	0.0256432i
$906$		−	13.0190i		−	0.432529i
$907$		−	59.6855i		−	1.98182i	−0.134509	−	0.990912i	$-0.542946\pi$
$907$		−	59.6855i		−	1.98182i	0.134509	−	0.990912i	$-0.457054\pi$
$908$	−1.28712	+	1.28712i	−0.0427144	+	0.0427144i
$909$	30.8137			1.02203
$910$		0			0
$911$	−21.0872			−0.698649			−0.349325	−	0.937002i	$-0.613589\pi$
$911$	−21.0872			−0.698649			−0.349325	+	0.937002i	$0.613589\pi$
$912$	8.99832	−	8.99832i	0.297964	−	0.297964i
$913$			29.3685i			0.971955i
$914$			24.7870i			0.819880i
$915$	−0.119062	−	0.119062i	−0.00393608	−	0.00393608i
$916$	7.15728	+	7.15728i	0.236483	+	0.236483i
$917$		0			0
$918$	18.8830	+	18.8830i	0.623232	+	0.623232i
$919$	15.2571			0.503284			0.251642	−	0.967820i	$-0.419029\pi$
$919$	15.2571			0.503284			0.251642	+	0.967820i	$0.419029\pi$
$920$	0.162787			0.00536694
$921$	1.25666	+	1.25666i	0.0414084	+	0.0414084i
$922$	−23.1131			−0.761189
$923$	10.9527	+	15.0914i	0.360511	+	0.496739i
$924$		0			0
$925$	13.7764	−	13.7764i	0.452966	−	0.452966i
$926$	34.2741			1.12632
$927$	26.5164			0.870914
$928$	−0.743781	+	0.743781i	−0.0244158	+	0.0244158i
$929$	−7.02011	−	7.02011i	−0.230322	−	0.230322i	0.582505	−	0.812827i	$-0.302073\pi$
$929$	−7.02011	−	7.02011i	−0.230322	−	0.230322i	−0.812827	+	0.582505i	$0.802073\pi$
$930$	0.0628591	−	0.0628591i	0.00206123	−	0.00206123i
$931$		0			0
$932$	−2.71470			−0.0889230
$933$			15.2645i			0.499737i
$934$	−20.0157	+	20.0157i	−0.654935	+	0.654935i
$935$			1.95430i			0.0639125i
$936$	18.7824	−	13.6314i	0.613921	−	0.445556i
$937$			55.6823i			1.81906i	0.415636	+	0.909531i	$0.363559\pi$
$937$			55.6823i			1.81906i	−0.415636	+	0.909531i	$0.636441\pi$
$938$		0			0
$939$	9.80591			0.320004
$940$			0.120982i			0.00394600i
$941$	−10.1086	−	10.1086i	−0.329530	−	0.329530i	0.522878	−	0.852408i	$-0.324859\pi$
$941$	−10.1086	−	10.1086i	−0.329530	−	0.329530i	−0.852408	+	0.522878i	$0.824859\pi$
$942$	10.8760	−	10.8760i	0.354360	−	0.354360i
$943$	6.72513	−	6.72513i	0.219000	−	0.219000i
$944$	−7.48592	+	7.48592i	−0.243646	+	0.243646i
$945$		0			0
$946$			17.8351i			0.579870i
$947$	17.5951	+	17.5951i	0.571764	+	0.571764i	0.932621	−	0.360857i	$-0.117516\pi$
$947$	17.5951	+	17.5951i	0.571764	+	0.571764i	−0.360857	+	0.932621i	$0.617516\pi$
$948$	−2.26198			−0.0734657
$949$	−25.2023	−	34.7256i	−0.818100	−	1.12724i
$950$			41.9973i			1.36257i
$951$	1.78517	+	1.78517i	0.0578881	+	0.0578881i
$952$		0			0
$953$		−	0.410134i		−	0.0132855i	−0.999978	−	0.00664276i	$-0.997886\pi$
$953$		−	0.410134i		−	0.0132855i	0.999978	−	0.00664276i	$-0.00211447\pi$
$954$	−32.5153	+	32.5153i	−1.05272	+	1.05272i
$955$	0.476197	+	0.476197i	0.0154094	+	0.0154094i
$956$	−3.60008	−	3.60008i	−0.116435	−	0.116435i
$957$	−0.545944	+	0.545944i	−0.0176479	+	0.0176479i
$958$			40.2722i			1.30113i
$959$		0			0
$960$	−0.140116	−	0.140116i	−0.00452223	−	0.00452223i
$961$		−	29.0539i		−	0.937224i
$962$	3.50823	−	22.0765i	0.113110	−	0.711775i
$963$	−48.4137			−1.56011
$964$	0.830216	+	0.830216i	0.0267395	+	0.0267395i
$965$		−	0.0393184i		−	0.00126570i
$966$		0			0
$967$	24.7994	−	24.7994i	0.797497	−	0.797497i	−0.185204	−	0.982700i	$-0.559294\pi$
$967$	24.7994	−	24.7994i	0.797497	−	0.797497i	0.982700	+	0.185204i	$0.0592945\pi$
$968$	11.3706	−	11.3706i	0.365466	−	0.365466i
$969$	10.9445	−	10.9445i	0.351588	−	0.351588i
$970$	−0.764441	−	0.764441i	−0.0245447	−	0.0245447i
$971$		−	14.5382i		−	0.466554i	−0.972410	−	0.233277i	$-0.925055\pi$
$971$		−	14.5382i		−	0.466554i	0.972410	−	0.233277i	$-0.0749448\pi$
$972$	−6.35242			−0.203754
$973$		0			0
$974$		−	53.0471i		−	1.69974i
$975$	1.42306	−	8.95495i	0.0455742	−	0.286788i
$976$			20.0472i			0.641696i
$977$	24.2818	−	24.2818i	0.776842	−	0.776842i	−0.202450	−	0.979293i	$-0.564890\pi$
$977$	24.2818	−	24.2818i	0.776842	−	0.776842i	0.979293	+	0.202450i	$0.0648904\pi$
$978$			0.994216i			0.0317915i
$979$	−34.0493			−1.08822
$980$		0			0
$981$	26.4950	−	26.4950i	0.845922	−	0.845922i
$982$	−16.2891	−	16.2891i	−0.519807	−	0.519807i
$983$	15.9583	−	15.9583i	0.508991	−	0.508991i	−0.405226	−	0.914217i	$-0.632807\pi$
$983$	15.9583	−	15.9583i	0.508991	−	0.508991i	0.914217	+	0.405226i	$0.132807\pi$
$984$	−12.8692			−0.410256
$985$	0.312951			0.00997144
$986$	−2.36705	+	2.36705i	−0.0753821	+	0.0753821i
$987$		0			0
$988$	5.88578	+	8.10987i	0.187252	+	0.258009i
$989$	2.31648			0.0736597
$990$	−1.03853	−	1.03853i	−0.0330065	−	0.0330065i
$991$	−56.9228			−1.80821			−0.904106	−	0.427309i	$-0.859462\pi$
$991$	−56.9228			−1.80821			−0.904106	+	0.427309i	$0.859462\pi$
$992$	−4.04502			−0.128430
$993$	−6.82955	−	6.82955i	−0.216729	−	0.216729i
$994$		0			0
$995$	−0.904515	−	0.904515i	−0.0286751	−	0.0286751i
$996$	1.29945	+	1.29945i	0.0411747	+	0.0411747i
$997$		−	23.1844i		−	0.734256i	−0.930170	−	0.367128i	$-0.880341\pi$
$997$		−	23.1844i		−	0.734256i	0.930170	−	0.367128i	$-0.119659\pi$
$998$			15.7197i			0.497598i
$999$	7.98363	−	7.98363i	0.252591	−	0.252591i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.i.a.538.3		32
7.2	even	3		91.2.bb.a.31.7	yes	32
7.3	odd	6		91.2.bb.a.5.2	✓	32
7.4	even	3		637.2.bc.b.460.2		32
7.5	odd	6		637.2.bc.b.31.7		32
7.6	odd	2	inner	637.2.i.a.538.4		32
13.8	odd	4	inner	637.2.i.a.489.3		32
21.2	odd	6		819.2.fn.e.577.2		32
21.17	even	6		819.2.fn.e.460.7		32
91.34	even	4	inner	637.2.i.a.489.4		32
91.47	even	12		637.2.bc.b.619.2		32
91.60	odd	12		637.2.bc.b.411.7		32
91.73	even	12		91.2.bb.a.47.7	yes	32
91.86	odd	12		91.2.bb.a.73.2	yes	32
273.86	even	12		819.2.fn.e.73.7		32
273.164	odd	12		819.2.fn.e.775.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bb.a.5.2	✓	32	7.3	odd	6
91.2.bb.a.31.7	yes	32	7.2	even	3
91.2.bb.a.47.7	yes	32	91.73	even	12
91.2.bb.a.73.2	yes	32	91.86	odd	12
637.2.i.a.489.3		32	13.8	odd	4	inner
637.2.i.a.489.4		32	91.34	even	4	inner
637.2.i.a.538.3		32	1.1	even	1	trivial
637.2.i.a.538.4		32	7.6	odd	2	inner
637.2.bc.b.31.7		32	7.5	odd	6
637.2.bc.b.411.7		32	91.60	odd	12
637.2.bc.b.460.2		32	7.4	even	3
637.2.bc.b.619.2		32	91.47	even	12
819.2.fn.e.73.7		32	273.86	even	12
819.2.fn.e.460.7		32	21.17	even	6
819.2.fn.e.577.2		32	21.2	odd	6
819.2.fn.e.775.2		32	273.164	odd	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12364 + 1.12364i) q^{2} -0.503603i q^{3} -0.525123i q^{4} +(-0.0563066 - 0.0563066i) q^{5} +(0.565867 + 0.565867i) q^{6} +(-1.65723 - 1.65723i) q^{8} +2.74638 q^{9} +O(q^{10})\)	\(q+(-1.12364 + 1.12364i) q^{2} -0.503603i q^{3} -0.525123i q^{4} +(-0.0563066 - 0.0563066i) q^{5} +(0.565867 + 0.565867i) q^{6} +(-1.65723 - 1.65723i) q^{8} +2.74638 q^{9} +0.126536 q^{10} +(-2.98841 - 2.98841i) q^{11} -0.264453 q^{12} +(-0.565867 + 3.56087i) q^{13} +(-0.0283562 + 0.0283562i) q^{15} +4.77449 q^{16} +5.80713 q^{17} +(-3.08594 + 3.08594i) q^{18} +(3.74236 + 3.74236i) q^{19} +(-0.0295679 + 0.0295679i) q^{20} +6.71579 q^{22} -0.872266i q^{23} +(-0.834585 + 0.834585i) q^{24} -4.99366i q^{25} +(-3.36530 - 4.63696i) q^{26} -2.89390i q^{27} +0.362759 q^{29} -0.0637241i q^{30} +(0.986425 + 0.986425i) q^{31} +(-2.05034 + 2.05034i) q^{32} +(-1.50497 + 1.50497i) q^{33} +(-6.52511 + 6.52511i) q^{34} -1.44219i q^{36} +(2.75878 + 2.75878i) q^{37} -8.41012 q^{38} +(1.79326 + 0.284972i) q^{39} +0.186626i q^{40} +(7.70995 + 7.70995i) q^{41} +2.65570i q^{43} +(-1.56928 + 1.56928i) q^{44} +(-0.154640 - 0.154640i) q^{45} +(0.980111 + 0.980111i) q^{46} +(2.04584 - 2.04584i) q^{47} -2.40445i q^{48} +(5.61106 + 5.61106i) q^{50} -2.92449i q^{51} +(1.86989 + 0.297150i) q^{52} +10.5366 q^{53} +(3.25169 + 3.25169i) q^{54} +0.336535i q^{55} +(1.88467 - 1.88467i) q^{57} +(-0.407610 + 0.407610i) q^{58} +(-1.56790 + 1.56790i) q^{59} +(0.0148905 + 0.0148905i) q^{60} +4.19882i q^{61} -2.21677 q^{62} +4.94130i q^{64} +(0.232363 - 0.168638i) q^{65} -3.38209i q^{66} +(-7.15178 + 7.15178i) q^{67} -3.04946i q^{68} -0.439276 q^{69} +(3.65698 - 3.65698i) q^{71} +(-4.55138 - 4.55138i) q^{72} +(-8.41477 + 8.41477i) q^{73} -6.19975 q^{74} -2.51482 q^{75} +(1.96520 - 1.96520i) q^{76} +(-2.33519 + 1.69477i) q^{78} +8.55341 q^{79} +(-0.268835 - 0.268835i) q^{80} +6.78178 q^{81} -17.3264 q^{82} +(-4.91372 - 4.91372i) q^{83} +(-0.326980 - 0.326980i) q^{85} +(-2.98404 - 2.98404i) q^{86} -0.182687i q^{87} +9.90496i q^{88} +(5.69688 - 5.69688i) q^{89} +0.347518 q^{90} -0.458047 q^{92} +(0.496767 - 0.496767i) q^{93} +4.59756i q^{94} -0.421440i q^{95} +(1.03256 + 1.03256i) q^{96} +(-6.04128 - 6.04128i) q^{97} +(-8.20733 - 8.20733i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9	\( 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 44 q^{15} - 24 q^{16} + 8 q^{18} - 8 q^{22} + 16 q^{29} - 8 q^{32} + 16 q^{37} + 12 q^{39} + 84 q^{44} - 24 q^{46} + 88 q^{50} + 24 q^{53} + 40 q^{57} - 52 q^{58} - 32 q^{60} + 16 q^{65} - 32 q^{67} - 36 q^{71} - 44 q^{72} - 24 q^{74} - 176 q^{78} + 64 q^{79} - 32 q^{81} - 84 q^{85} - 84 q^{86} + 48 q^{92} - 12 q^{93} - 24 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 44 * q^15 - 24 * q^16 + 8 * q^18 - 8 * q^22 + 16 * q^29 - 8 * q^32 + 16 * q^37 + 12 * q^39 + 84 * q^44 - 24 * q^46 + 88 * q^50 + 24 * q^53 + 40 * q^57 - 52 * q^58 - 32 * q^60 + 16 * q^65 - 32 * q^67 - 36 * q^71 - 44 * q^72 - 24 * q^74 - 176 * q^78 + 64 * q^79 - 32 * q^81 - 84 * q^85 - 84 * q^86 + 48 * q^92 - 12 * q^93 - 24 * q^99

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