LMFDB - Embedded newform 637.2.i.a.489.8

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			489.8
Character	$\chi$	$=$	637.489
Dual form			637.2.i.a.538.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.508388 - 0.508388i) q^{2} +1.66432i q^{3} -1.48308i q^{4} +(-1.36989 + 1.36989i) q^{5} +(0.846120 - 0.846120i) q^{6} +(-1.77076 + 1.77076i) q^{8} +0.230041 q^{9} +O(q^{10})$	\(q+(-0.508388 - 0.508388i) q^{2} +1.66432i q^{3} -1.48308i q^{4} +(-1.36989 + 1.36989i) q^{5} +(0.846120 - 0.846120i) q^{6} +(-1.77076 + 1.77076i) q^{8} +0.230041 q^{9} +1.39287 q^{10} +(2.25576 - 2.25576i) q^{11} +2.46832 q^{12} +(-0.846120 + 3.50487i) q^{13} +(-2.27993 - 2.27993i) q^{15} -1.16570 q^{16} -0.508296 q^{17} +(-0.116950 - 0.116950i) q^{18} +(-1.94054 + 1.94054i) q^{19} +(2.03166 + 2.03166i) q^{20} -2.29361 q^{22} +2.88269i q^{23} +(-2.94711 - 2.94711i) q^{24} +1.24682i q^{25} +(2.21199 - 1.35167i) q^{26} +5.37582i q^{27} -2.40426 q^{29} +2.31818i q^{30} +(-2.26099 + 2.26099i) q^{31} +(4.13414 + 4.13414i) q^{32} +(3.75431 + 3.75431i) q^{33} +(0.258412 + 0.258412i) q^{34} -0.341170i q^{36} +(-6.88232 + 6.88232i) q^{37} +1.97309 q^{38} +(-5.83322 - 1.40821i) q^{39} -4.85148i q^{40} +(5.34023 - 5.34023i) q^{41} +12.5736i q^{43} +(-3.34549 - 3.34549i) q^{44} +(-0.315130 + 0.315130i) q^{45} +(1.46552 - 1.46552i) q^{46} +(-7.89233 - 7.89233i) q^{47} -1.94010i q^{48} +(0.633867 - 0.633867i) q^{50} -0.845967i q^{51} +(5.19801 + 1.25487i) q^{52} +6.84953 q^{53} +(2.73300 - 2.73300i) q^{54} +6.18029i q^{55} +(-3.22968 - 3.22968i) q^{57} +(1.22230 + 1.22230i) q^{58} +(2.74167 + 2.74167i) q^{59} +(-3.38133 + 3.38133i) q^{60} +6.37071i q^{61} +2.29892 q^{62} -1.87209i q^{64} +(-3.64218 - 5.96036i) q^{65} -3.81730i q^{66} +(-4.80431 - 4.80431i) q^{67} +0.753846i q^{68} -4.79771 q^{69} +(-1.90492 - 1.90492i) q^{71} +(-0.407347 + 0.407347i) q^{72} +(0.184807 + 0.184807i) q^{73} +6.99778 q^{74} -2.07510 q^{75} +(2.87798 + 2.87798i) q^{76} +(2.24962 + 3.68146i) q^{78} +5.56760 q^{79} +(1.59688 - 1.59688i) q^{80} -8.25696 q^{81} -5.42982 q^{82} +(-5.86182 + 5.86182i) q^{83} +(0.696309 - 0.696309i) q^{85} +(6.39229 - 6.39229i) q^{86} -4.00145i q^{87} +7.98883i q^{88} +(8.66439 + 8.66439i) q^{89} +0.320417 q^{90} +4.27526 q^{92} +(-3.76301 - 3.76301i) q^{93} +8.02474i q^{94} -5.31664i q^{95} +(-6.88054 + 6.88054i) q^{96} +(7.04713 - 7.04713i) q^{97} +(0.518918 - 0.518918i) 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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.508388	−	0.508388i	−0.359485	−	0.359485i	0.504138	−	0.863623i	$-0.331810\pi$
$2$	−0.508388	−	0.508388i	−0.359485	−	0.359485i	−0.863623	+	0.504138i	$0.831810\pi$
$3$			1.66432i			0.960895i	0.877023	+	0.480448i	$0.159526\pi$
$3$			1.66432i			0.960895i	−0.877023	+	0.480448i	$0.840474\pi$
$4$		−	1.48308i		−	0.741542i
$5$	−1.36989	+	1.36989i	−0.612632	+	0.612632i	−0.943631	−	0.330999i	$-0.892614\pi$
$5$	−1.36989	+	1.36989i	−0.612632	+	0.612632i	0.330999	+	0.943631i	$0.392614\pi$
$6$	0.846120	−	0.846120i	0.345427	−	0.345427i
$7$		0			0
$7$		0			0
$8$	−1.77076	+	1.77076i	−0.626057	+	0.626057i
$9$	0.230041			0.0766804
$10$	1.39287			0.440464
$11$	2.25576	−	2.25576i	0.680139	−	0.680139i	−0.279893	−	0.960031i	$-0.590299\pi$
$11$	2.25576	−	2.25576i	0.680139	−	0.680139i	0.960031	+	0.279893i	$0.0902989\pi$
$12$	2.46832			0.712544
$13$	−0.846120	+	3.50487i	−0.234671	+	0.972075i
$13$	−0.846120	+	3.50487i	−0.234671	+	0.972075i
$14$		0			0
$15$	−2.27993	−	2.27993i	−0.588675	−	0.588675i
$16$	−1.16570			−0.291426
$17$	−0.508296			−0.123280			−0.0616400	−	0.998098i	$-0.519633\pi$
$17$	−0.508296			−0.123280			−0.0616400	+	0.998098i	$0.519633\pi$
$18$	−0.116950	−	0.116950i	−0.0275654	−	0.0275654i
$19$	−1.94054	+	1.94054i	−0.445190	+	0.445190i	−0.893752	−	0.448562i	$-0.851936\pi$
$19$	−1.94054	+	1.94054i	−0.445190	+	0.445190i	0.448562	+	0.893752i	$0.351936\pi$
$20$	2.03166	+	2.03166i	0.454292	+	0.454292i
$21$		0			0
$22$	−2.29361			−0.488999
$23$			2.88269i			0.601082i	0.953769	+	0.300541i	$0.0971671\pi$
$23$			2.88269i			0.601082i	−0.953769	+	0.300541i	$0.902833\pi$
$24$	−2.94711	−	2.94711i	−0.601576	−	0.601576i
$25$			1.24682i			0.249363i
$26$	2.21199	−	1.35167i	0.433807	−	0.265085i
$27$			5.37582i			1.03458i
$28$		0			0
$29$	−2.40426			−0.446460			−0.223230	−	0.974766i	$-0.571660\pi$
$29$	−2.40426			−0.446460			−0.223230	+	0.974766i	$0.571660\pi$
$30$			2.31818i			0.423240i
$31$	−2.26099	+	2.26099i	−0.406086	+	0.406086i	−0.880371	−	0.474285i	$-0.842707\pi$
$31$	−2.26099	+	2.26099i	−0.406086	+	0.406086i	0.474285	+	0.880371i	$0.342707\pi$
$32$	4.13414	+	4.13414i	0.730820	+	0.730820i
$33$	3.75431	+	3.75431i	0.653542	+	0.653542i
$34$	0.258412	+	0.258412i	0.0443172	+	0.0443172i
$35$		0			0
$36$		−	0.341170i		−	0.0568617i
$37$	−6.88232	+	6.88232i	−1.13145	+	1.13145i	−0.141510	+	0.989937i	$0.545196\pi$
$37$	−6.88232	+	6.88232i	−1.13145	+	1.13145i	−0.989937	+	0.141510i	$0.954804\pi$
$38$	1.97309			0.320078
$39$	−5.83322	−	1.40821i	−0.934062	−	0.225495i
$40$		−	4.85148i		−	0.767086i
$41$	5.34023	−	5.34023i	0.834004	−	0.834004i	−0.154058	−	0.988062i	$-0.549234\pi$
$41$	5.34023	−	5.34023i	0.834004	−	0.834004i	0.988062	+	0.154058i	$0.0492342\pi$
$42$		0			0
$43$			12.5736i			1.91746i	0.284313	+	0.958732i	$0.408235\pi$
$43$			12.5736i			1.91746i	−0.284313	+	0.958732i	$0.591765\pi$
$44$	−3.34549	−	3.34549i	−0.504351	−	0.504351i
$45$	−0.315130	+	0.315130i	−0.0469769	+	0.0469769i
$46$	1.46552	−	1.46552i	0.216080	−	0.216080i
$47$	−7.89233	−	7.89233i	−1.15122	−	1.15122i	−0.986309	−	0.164906i	$-0.947268\pi$
$47$	−7.89233	−	7.89233i	−1.15122	−	1.15122i	−0.164906	−	0.986309i	$-0.552732\pi$
$48$		−	1.94010i		−	0.280029i
$49$		0			0
$50$	0.633867	−	0.633867i	0.0896423	−	0.0896423i
$51$		−	0.845967i		−	0.118459i
$52$	5.19801	+	1.25487i	0.720834	+	0.174019i
$53$	6.84953			0.940856			0.470428	−	0.882438i	$-0.344100\pi$
$53$	6.84953			0.940856			0.470428	+	0.882438i	$0.344100\pi$
$54$	2.73300	−	2.73300i	0.371915	−	0.371915i
$55$			6.18029i			0.833350i
$56$		0			0
$57$	−3.22968	−	3.22968i	−0.427781	−	0.427781i
$58$	1.22230	+	1.22230i	0.160495	+	0.160495i
$59$	2.74167	+	2.74167i	0.356935	+	0.356935i	0.862682	−	0.505747i	$-0.168783\pi$
$59$	2.74167	+	2.74167i	0.356935	+	0.356935i	−0.505747	+	0.862682i	$0.668783\pi$
$60$	−3.38133	+	3.38133i	−0.436527	+	0.436527i
$61$			6.37071i			0.815686i	0.913052	+	0.407843i	$0.133719\pi$
$61$			6.37071i			0.815686i	−0.913052	+	0.407843i	$0.866281\pi$
$62$	2.29892			0.291963
$63$		0			0
$64$		−	1.87209i		−	0.234012i
$65$	−3.64218	−	5.96036i	−0.451757	−	0.739292i
$66$		−	3.81730i		−	0.469877i
$67$	−4.80431	−	4.80431i	−0.586940	−	0.586940i	0.349862	−	0.936801i	$-0.386229\pi$
$67$	−4.80431	−	4.80431i	−0.586940	−	0.586940i	−0.936801	+	0.349862i	$0.886229\pi$
$68$			0.753846i			0.0914172i
$69$	−4.79771			−0.577576
$70$		0			0
$71$	−1.90492	−	1.90492i	−0.226072	−	0.226072i	0.584978	−	0.811049i	$-0.301103\pi$
$71$	−1.90492	−	1.90492i	−0.226072	−	0.226072i	−0.811049	+	0.584978i	$0.801103\pi$
$72$	−0.407347	+	0.407347i	−0.0480063	+	0.0480063i
$73$	0.184807	+	0.184807i	0.0216301	+	0.0216301i	0.717839	−	0.696209i	$-0.245131\pi$
$73$	0.184807	+	0.184807i	0.0216301	+	0.0216301i	−0.696209	+	0.717839i	$0.745131\pi$
$74$	6.99778			0.813475
$75$	−2.07510			−0.239612
$76$	2.87798	+	2.87798i	0.330127	+	0.330127i
$77$		0			0
$78$	2.24962	+	3.68146i	0.254719	+	0.416843i
$79$	5.56760			0.626403			0.313202	−	0.949687i	$-0.398598\pi$
$79$	5.56760			0.626403			0.313202	+	0.949687i	$0.398598\pi$
$80$	1.59688	−	1.59688i	0.178537	−	0.178537i
$81$	−8.25696			−0.917440
$82$	−5.42982			−0.599623
$83$	−5.86182	+	5.86182i	−0.643419	+	0.643419i	−0.951394	−	0.307975i	$-0.900349\pi$
$83$	−5.86182	+	5.86182i	−0.643419	+	0.643419i	0.307975	+	0.951394i	$0.400349\pi$
$84$		0			0
$85$	0.696309	−	0.696309i	0.0755253	−	0.0755253i
$86$	6.39229	−	6.39229i	0.689298	−	0.689298i
$87$		−	4.00145i		−	0.429001i
$88$			7.98883i			0.851612i
$89$	8.66439	+	8.66439i	0.918424	+	0.918424i	0.996915	−	0.0784912i	$-0.0250102\pi$
$89$	8.66439	+	8.66439i	0.918424	+	0.918424i	−0.0784912	+	0.996915i	$0.525010\pi$
$90$	0.320417			0.0337749
$91$		0			0
$92$	4.27526			0.445727
$93$	−3.76301	−	3.76301i	−0.390206	−	0.390206i
$94$			8.02474i			0.827688i
$95$		−	5.31664i		−	0.545476i
$96$	−6.88054	+	6.88054i	−0.702242	+	0.702242i
$97$	7.04713	−	7.04713i	0.715528	−	0.715528i	−0.252158	−	0.967686i	$-0.581140\pi$
$97$	7.04713	−	7.04713i	0.715528	−	0.715528i	0.967686	+	0.252158i	$0.0811403\pi$
$98$		0			0
$99$	0.518918	−	0.518918i	0.0521533	−	0.0521533i
$100$	1.84913			0.184913
$101$	−4.71948			−0.469606			−0.234803	−	0.972043i	$-0.575444\pi$
$101$	−4.71948			−0.469606			−0.234803	+	0.972043i	$0.575444\pi$
$102$	−0.430080	+	0.430080i	−0.0425842	+	0.0425842i
$103$	4.45942			0.439399			0.219700	−	0.975568i	$-0.429492\pi$
$103$	4.45942			0.439399			0.219700	+	0.975568i	$0.429492\pi$
$104$	−4.70799	−	7.70454i	−0.461657	−	0.755492i
$105$		0			0
$106$	−3.48222	−	3.48222i	−0.338223	−	0.338223i
$107$	19.3106			1.86683			0.933413	−	0.358804i	$-0.116815\pi$
$107$	19.3106			1.86683			0.933413	+	0.358804i	$0.116815\pi$
$108$	7.97279			0.767182
$109$	−7.69601	−	7.69601i	−0.737144	−	0.737144i	0.234880	−	0.972024i	$-0.424530\pi$
$109$	−7.69601	−	7.69601i	−0.737144	−	0.737144i	−0.972024	+	0.234880i	$0.924530\pi$
$110$	3.14198	−	3.14198i	0.299576	−	0.299576i
$111$	−11.4544	−	11.4544i	−1.08720	−	1.08720i
$112$		0			0
$113$	11.1771			1.05145			0.525726	−	0.850654i	$-0.323794\pi$
$113$	11.1771			1.05145			0.525726	+	0.850654i	$0.323794\pi$
$114$			3.28386i			0.307561i
$115$	−3.94895	−	3.94895i	−0.368242	−	0.368242i
$116$			3.56572i			0.331068i
$117$	−0.194642	+	0.806263i	−0.0179947	+	0.0745390i
$118$		−	2.78767i		−	0.256626i
$119$		0			0
$120$	8.07441			0.737089
$121$			0.823054i			0.0748231i
$122$	3.23879	−	3.23879i	0.293226	−	0.293226i
$123$	8.88785	+	8.88785i	0.801390	+	0.801390i
$124$	3.35324	+	3.35324i	0.301130	+	0.301130i
$125$	−8.55744	−	8.55744i	−0.765400	−	0.765400i
$126$		0			0
$127$		−	14.7463i		−	1.30852i	−0.756269	−	0.654261i	$-0.772980\pi$
$127$		−	14.7463i		−	1.30852i	0.756269	−	0.654261i	$-0.227020\pi$
$128$	7.31654	−	7.31654i	0.646697	−	0.646697i
$129$	−20.9266			−1.84248
$130$	−1.17853	+	4.88182i	−0.103364	+	0.428164i
$131$		−	20.2151i		−	1.76620i	−0.469186	−	0.883100i	$-0.655453\pi$
$131$		−	20.2151i		−	1.76620i	0.469186	−	0.883100i	$-0.344547\pi$
$132$	5.56796	−	5.56796i	0.484629	−	0.484629i
$133$		0			0
$134$			4.88491i			0.421992i
$135$	−7.36427	−	7.36427i	−0.633815	−	0.633815i
$136$	0.900070	−	0.900070i	0.0771803	−	0.0771803i
$137$	−5.99149	+	5.99149i	−0.511887	+	0.511887i	−0.915104	−	0.403217i	$-0.867892\pi$
$137$	−5.99149	+	5.99149i	−0.511887	+	0.511887i	0.403217	+	0.915104i	$0.367892\pi$
$138$	2.43910	+	2.43910i	0.207630	+	0.207630i
$139$		−	2.42919i		−	0.206041i	−0.994679	−	0.103021i	$-0.967149\pi$
$139$		−	2.42919i		−	0.206041i	0.994679	−	0.103021i	$-0.0328507\pi$
$140$		0			0
$141$	13.1354	−	13.1354i	1.10620	−	1.10620i
$142$			1.93687i			0.162539i
$143$	5.99750	+	9.81480i	0.501536	+	0.820755i
$144$	−0.268159			−0.0223466
$145$	3.29356	−	3.29356i	0.273516	−	0.273516i
$146$		−	0.187908i		−	0.0155513i
$147$		0			0
$148$	10.2071	+	10.2071i	0.839015	+	0.839015i
$149$	4.19617	+	4.19617i	0.343763	+	0.343763i	0.857780	−	0.514017i	$-0.171843\pi$
$149$	4.19617	+	4.19617i	0.343763	+	0.343763i	−0.514017	+	0.857780i	$0.671843\pi$
$150$	1.05496	+	1.05496i	0.0861369	+	0.0861369i
$151$	4.57313	−	4.57313i	0.372156	−	0.372156i	−0.496106	−	0.868262i	$-0.665237\pi$
$151$	4.57313	−	4.57313i	0.372156	−	0.372156i	0.868262	+	0.496106i	$0.165237\pi$
$152$		−	6.87245i		−	0.557429i
$153$	−0.116929			−0.00945315
$154$		0			0
$155$		−	6.19461i		−	0.497563i
$156$	−2.08850	+	8.65114i	−0.167214	+	0.692646i
$157$			6.40823i			0.511432i	0.966752	+	0.255716i	$0.0823113\pi$
$157$			6.40823i			0.511432i	−0.966752	+	0.255716i	$0.917689\pi$
$158$	−2.83050	−	2.83050i	−0.225182	−	0.225182i
$159$			11.3998i			0.904064i
$160$	−11.3266			−0.895448
$161$		0			0
$162$	4.19774	+	4.19774i	0.329805	+	0.329805i
$163$	0.483882	−	0.483882i	0.0379006	−	0.0379006i	−0.687903	−	0.725803i	$-0.741468\pi$
$163$	0.483882	−	0.483882i	0.0379006	−	0.0379006i	0.725803	+	0.687903i	$0.241468\pi$
$164$	−7.92001	−	7.92001i	−0.618449	−	0.618449i
$165$	−10.2860			−0.800762
$166$	5.96016			0.462598
$167$	2.47505	+	2.47505i	0.191525	+	0.191525i	0.796355	−	0.604830i	$-0.206759\pi$
$167$	2.47505	+	2.47505i	0.191525	+	0.191525i	−0.604830	+	0.796355i	$0.706759\pi$
$168$		0			0
$169$	−11.5682	−	5.93107i	−0.889859	−	0.456236i
$170$	−0.707990			−0.0543004
$171$	−0.446403	+	0.446403i	−0.0341373	+	0.0341373i
$172$	18.6478			1.42188
$173$	−24.7719			−1.88337			−0.941687	−	0.336489i	$-0.890760\pi$
$173$	−24.7719			−1.88337			−0.941687	+	0.336489i	$0.890760\pi$
$174$	−2.03429	+	2.03429i	−0.154219	+	0.154219i
$175$		0			0
$176$	−2.62955	+	2.62955i	−0.198210	+	0.198210i
$177$	−4.56302	+	4.56302i	−0.342978	+	0.342978i
$178$		−	8.80975i		−	0.660318i
$179$		−	19.1893i		−	1.43427i	−0.696932	−	0.717137i	$-0.745452\pi$
$179$		−	19.1893i		−	1.43427i	0.696932	−	0.717137i	$-0.254548\pi$
$180$	0.467365	+	0.467365i	0.0348353	+	0.0348353i
$181$	11.0428			0.820803			0.410401	−	0.911905i	$-0.365389\pi$
$181$	11.0428			0.820803			0.410401	+	0.911905i	$0.365389\pi$
$182$		0			0
$183$	−10.6029			−0.783788
$184$	−5.10454	−	5.10454i	−0.376312	−	0.376312i
$185$		−	18.8560i		−	1.38632i
$186$			3.82614i			0.280546i
$187$	−1.14660	+	1.14660i	−0.0838475	+	0.0838475i
$188$	−11.7050	+	11.7050i	−0.853674	+	0.853674i
$189$		0			0
$190$	−2.70291	+	2.70291i	−0.196090	+	0.196090i
$191$	11.3626			0.822172			0.411086	−	0.911597i	$-0.365150\pi$
$191$	11.3626			0.822172			0.411086	+	0.911597i	$0.365150\pi$
$192$	3.11576			0.224861
$193$	−8.82027	+	8.82027i	−0.634897	+	0.634897i	−0.949292	−	0.314395i	$-0.898198\pi$
$193$	−8.82027	+	8.82027i	−0.634897	+	0.634897i	0.314395	+	0.949292i	$0.398198\pi$
$194$	−7.16536			−0.514443
$195$	9.91994	−	6.06175i	0.710382	−	0.434091i
$196$		0			0
$197$	−13.9343	−	13.9343i	−0.992775	−	0.992775i	0.00719943	−	0.999974i	$-0.497708\pi$
$197$	−13.9343	−	13.9343i	−0.992775	−	0.992775i	−0.999974	+	0.00719943i	$0.997708\pi$
$198$	−0.527624			−0.0374966
$199$	0.827484			0.0586588			0.0293294	−	0.999570i	$-0.490663\pi$
$199$	0.827484			0.0586588			0.0293294	+	0.999570i	$0.490663\pi$
$200$	−2.20781	−	2.20781i	−0.156116	−	0.156116i
$201$	7.99591	−	7.99591i	0.563988	−	0.563988i
$202$	2.39933	+	2.39933i	0.168816	+	0.168816i
$203$		0			0
$204$	−1.25464			−0.0878424
$205$			14.6310i			1.02188i
$206$	−2.26711	−	2.26711i	−0.157957	−	0.157957i
$207$			0.663136i			0.0460911i
$208$	0.986324	−	4.08563i	0.0683893	−	0.283287i
$209$			8.75479i			0.605582i
$210$		0			0
$211$	18.8543			1.29798			0.648992	−	0.760795i	$-0.275191\pi$
$211$	18.8543			1.29798			0.648992	+	0.760795i	$0.275191\pi$
$212$		−	10.1584i		−	0.697684i
$213$	3.17039	−	3.17039i	0.217231	−	0.217231i
$214$	−9.81728	−	9.81728i	−0.671095	−	0.671095i
$215$	−17.2245	−	17.2245i	−1.17470	−	1.17470i
$216$	−9.51928	−	9.51928i	−0.647705	−	0.647705i
$217$		0			0
$218$			7.82512i			0.529984i
$219$	−0.307578	+	0.307578i	−0.0207842	+	0.0207842i
$220$	9.16588			0.617963
$221$	0.430080	−	1.78151i	0.0289303	−	0.119837i
$222$			11.6465i			0.781664i
$223$	9.83194	−	9.83194i	0.658396	−	0.658396i	−0.296605	−	0.955000i	$-0.595854\pi$
$223$	9.83194	−	9.83194i	0.658396	−	0.658396i	0.955000	+	0.296605i	$0.0958543\pi$
$224$		0			0
$225$			0.286819i			0.0191213i
$226$	−5.68230	−	5.68230i	−0.377981	−	0.377981i
$227$	−11.0705	+	11.0705i	−0.734772	+	0.734772i	−0.971561	−	0.236789i	$-0.923905\pi$
$227$	−11.0705	+	11.0705i	−0.734772	+	0.734772i	0.236789	+	0.971561i	$0.423905\pi$
$228$	−4.78988	+	4.78988i	−0.317217	+	0.317217i
$229$	3.38472	+	3.38472i	0.223669	+	0.223669i	0.810041	−	0.586373i	$-0.199445\pi$
$229$	3.38472	+	3.38472i	0.223669	+	0.223669i	−0.586373	+	0.810041i	$0.699445\pi$
$230$			4.01520i			0.264755i
$231$		0			0
$232$	4.25736	−	4.25736i	0.279509	−	0.279509i
$233$		−	3.17008i		−	0.207679i	−0.994594	−	0.103839i	$-0.966887\pi$
$233$		−	3.17008i		−	0.207679i	0.994594	−	0.103839i	$-0.0331128\pi$
$234$	0.508848	−	0.310941i	0.0332645	−	0.0203268i
$235$	21.6232			1.41054
$236$	4.06613	−	4.06613i	0.264683	−	0.264683i
$237$			9.26626i			0.601908i
$238$		0			0
$239$	7.52256	+	7.52256i	0.486594	+	0.486594i	0.907230	−	0.420636i	$-0.138193\pi$
$239$	7.52256	+	7.52256i	0.486594	+	0.486594i	−0.420636	+	0.907230i	$0.638193\pi$
$240$	2.65772	+	2.65772i	0.171555	+	0.171555i
$241$	−1.38666	−	1.38666i	−0.0893225	−	0.0893225i	0.661034	−	0.750356i	$-0.270118\pi$
$241$	−1.38666	−	1.38666i	−0.0893225	−	0.0893225i	−0.750356	+	0.661034i	$0.770118\pi$
$242$	0.418431	−	0.418431i	0.0268977	−	0.0268977i
$243$			2.38524i			0.153014i
$244$	9.44829			0.604865
$245$		0			0
$246$		−	9.03695i		−	0.576175i
$247$	−5.15940	−	8.44325i	−0.328285	−	0.537231i
$248$		−	8.00734i		−	0.508467i
$249$	−9.75595	−	9.75595i	−0.618258	−	0.618258i
$250$			8.70100i			0.550299i
$251$	1.64155			0.103614			0.0518070	−	0.998657i	$-0.483502\pi$
$251$	1.64155			0.103614			0.0518070	+	0.998657i	$0.483502\pi$
$252$		0			0
$253$	6.50266	+	6.50266i	0.408819	+	0.408819i
$254$	−7.49684	+	7.49684i	−0.470394	+	0.470394i
$255$	1.15888	+	1.15888i	0.0725719	+	0.0725719i
$256$	−11.1835			−0.698967
$257$	21.8235			1.36131			0.680657	−	0.732602i	$-0.261694\pi$
$257$	21.8235			1.36131			0.680657	+	0.732602i	$0.261694\pi$
$258$	10.6388	+	10.6388i	0.662344	+	0.662344i
$259$		0			0
$260$	−8.83971	+	5.40166i	−0.548216	+	0.334997i
$261$	−0.553078			−0.0342347
$262$	−10.2771	+	10.2771i	−0.634921	+	0.634921i
$263$	16.6667			1.02771			0.513856	−	0.857877i	$-0.328217\pi$
$263$	16.6667			1.02771			0.513856	+	0.857877i	$0.328217\pi$
$264$	−13.2960			−0.818310
$265$	−9.38309	+	9.38309i	−0.576399	+	0.576399i
$266$		0			0
$267$	−14.4203	+	14.4203i	−0.882509	+	0.882509i
$268$	−7.12519	+	7.12519i	−0.435240	+	0.435240i
$269$			16.9241i			1.03188i	0.856624	+	0.515942i	$0.172558\pi$
$269$			16.9241i			1.03188i	−0.856624	+	0.515942i	$0.827442\pi$
$270$			7.48781i			0.455694i
$271$	9.82519	+	9.82519i	0.596838	+	0.596838i	0.939470	−	0.342632i	$-0.111318\pi$
$271$	9.82519	+	9.82519i	0.596838	+	0.596838i	−0.342632	+	0.939470i	$0.611318\pi$
$272$	0.592522			0.0359269
$273$		0			0
$274$	6.09200			0.368031
$275$	2.81253	+	2.81253i	0.169602	+	0.169602i
$276$			7.11540i			0.428297i
$277$			19.6396i			1.18003i	0.807392	+	0.590015i	$0.200878\pi$
$277$			19.6396i			1.18003i	−0.807392	+	0.590015i	$0.799122\pi$
$278$	−1.23497	+	1.23497i	−0.0740686	+	0.0740686i
$279$	−0.520121	+	0.520121i	−0.0311388	+	0.0311388i
$280$		0			0
$281$	−17.2002	+	17.2002i	−1.02608	+	1.02608i	−0.0264298	+	0.999651i	$0.508414\pi$
$281$	−17.2002	+	17.2002i	−1.02608	+	1.02608i	−0.999651	+	0.0264298i	$0.991586\pi$
$282$	−13.3557			−0.795322
$283$	11.7949			0.701134			0.350567	−	0.936538i	$-0.385989\pi$
$283$	11.7949			0.701134			0.350567	+	0.936538i	$0.385989\pi$
$284$	−2.82515	+	2.82515i	−0.167642	+	0.167642i
$285$	8.84858			0.524145
$286$	1.94067	−	8.03878i	0.114754	−	0.475343i
$287$		0			0
$288$	0.951023	+	0.951023i	0.0560396	+	0.0560396i
$289$	−16.7416			−0.984802
$290$	−3.34882			−0.196649
$291$	11.7287	+	11.7287i	0.687547	+	0.687547i
$292$	0.274085	−	0.274085i	0.0160396	−	0.0160396i
$293$	−18.5497	−	18.5497i	−1.08368	−	1.08368i	−0.996163	−	0.0875204i	$-0.972106\pi$
$293$	−18.5497	−	18.5497i	−1.08368	−	1.08368i	−0.0875204	−	0.996163i	$-0.527894\pi$
$294$		0			0
$295$	−7.51157			−0.437340
$296$		−	24.3738i		−	1.41670i
$297$	12.1266	+	12.1266i	0.703656	+	0.703656i
$298$		−	4.26656i		−	0.247155i
$299$	−10.1034	−	2.43910i	−0.584296	−	0.141057i
$300$			3.07755i			0.177682i
$301$		0			0
$302$	−4.64985			−0.267569
$303$		−	7.85472i		−	0.451242i
$304$	2.26209	−	2.26209i	0.129740	−	0.129740i
$305$	−8.72715	−	8.72715i	−0.499715	−	0.499715i
$306$	0.0594453	+	0.0594453i	0.00339826	+	0.00339826i
$307$	−1.29211	−	1.29211i	−0.0737445	−	0.0737445i	0.669273	−	0.743017i	$-0.266606\pi$
$307$	−1.29211	−	1.29211i	−0.0737445	−	0.0737445i	−0.743017	+	0.669273i	$0.766606\pi$
$308$		0			0
$309$			7.42189i			0.422217i
$310$	−3.14927	+	3.14927i	−0.178866	+	0.178866i
$311$	−2.71619			−0.154021			−0.0770104	−	0.997030i	$-0.524537\pi$
$311$	−2.71619			−0.154021			−0.0770104	+	0.997030i	$0.524537\pi$
$312$	12.8228	−	7.83561i	0.725949	−	0.443604i
$313$			25.4201i			1.43683i	0.695614	+	0.718415i	$0.255132\pi$
$313$			25.4201i			1.43683i	−0.695614	+	0.718415i	$0.744868\pi$
$314$	3.25787	−	3.25787i	0.183852	−	0.183852i
$315$		0			0
$316$		−	8.25721i		−	0.464504i
$317$	21.4981	+	21.4981i	1.20746	+	1.20746i	0.971848	+	0.235608i	$0.0757081\pi$
$317$	21.4981	+	21.4981i	1.20746	+	1.20746i	0.235608	+	0.971848i	$0.424292\pi$
$318$	5.79553	−	5.79553i	0.324997	−	0.324997i
$319$	−5.42344	+	5.42344i	−0.303654	+	0.303654i
$320$	2.56456	+	2.56456i	0.143363	+	0.143363i
$321$			32.1390i			1.79382i
$322$		0			0
$323$	0.986368	−	0.986368i	0.0548830	−	0.0548830i
$324$			12.2458i			0.680320i
$325$	−4.36993	−	1.05496i	−0.242400	−	0.0585185i
$326$	−0.492000			−0.0272493
$327$	12.8086	−	12.8086i	0.708318	−	0.708318i
$328$			18.9125i			1.04427i
$329$		0			0
$330$	5.22926	+	5.22926i	0.287862	+	0.287862i
$331$	1.33861	+	1.33861i	0.0735768	+	0.0735768i	0.742938	−	0.669361i	$-0.233432\pi$
$331$	1.33861	+	1.33861i	0.0735768	+	0.0735768i	−0.669361	+	0.742938i	$0.733432\pi$
$332$	8.69357	+	8.69357i	0.477122	+	0.477122i
$333$	−1.58322	+	1.58322i	−0.0867597	+	0.0867597i
$334$		−	2.51657i		−	0.137701i
$335$	13.1627			0.719157
$336$		0			0
$337$			15.8664i			0.864300i	0.901802	+	0.432150i	$0.142245\pi$
$337$			15.8664i			0.864300i	−0.901802	+	0.432150i	$0.857755\pi$
$338$	2.86583	+	8.89640i	0.155881	+	0.483900i
$339$			18.6022i			1.01034i
$340$	−1.03268	−	1.03268i	−0.0560051	−	0.0560051i
$341$			10.2005i			0.552390i
$342$	0.453892			0.0245437
$343$		0			0
$344$	−22.2649	−	22.2649i	−1.20044	−	1.20044i
$345$	6.57232	−	6.57232i	0.353842	−	0.353842i
$346$	12.5938	+	12.5938i	0.677044	+	0.677044i
$347$	16.2015			0.869741			0.434871	−	0.900493i	$-0.356794\pi$
$347$	16.2015			0.869741			0.434871	+	0.900493i	$0.356794\pi$
$348$	−5.93449			−0.318122
$349$	18.7058	+	18.7058i	1.00130	+	1.00130i	0.999999	+	0.00129933i	$0.000413590\pi$
$349$	18.7058	+	18.7058i	1.00130	+	1.00130i	0.00129933	+	0.999999i	$0.499586\pi$
$350$		0			0
$351$	−18.8415	−	4.54859i	−1.00569	−	0.242786i
$352$	18.6513			0.994118
$353$	16.2223	−	16.2223i	0.863425	−	0.863425i	−0.128309	−	0.991734i	$-0.540955\pi$
$353$	16.2223	−	16.2223i	0.863425	−	0.863425i	0.991734	+	0.128309i	$0.0409550\pi$
$354$	4.63957			0.246590
$355$	5.21904			0.276998
$356$	12.8500	−	12.8500i	0.681049	−	0.681049i
$357$		0			0
$358$	−9.75560	+	9.75560i	−0.515600	+	0.515600i
$359$	5.26830	−	5.26830i	0.278050	−	0.278050i	−0.554280	−	0.832330i	$-0.687006\pi$
$359$	5.26830	−	5.26830i	0.278050	−	0.278050i	0.832330	+	0.554280i	$0.187006\pi$
$360$		−	1.11604i		−	0.0588204i
$361$			11.4686i			0.603612i
$362$	−5.61401	−	5.61401i	−0.295066	−	0.295066i
$363$	−1.36982			−0.0718971
$364$		0			0
$365$	−0.506330			−0.0265025
$366$	5.39038	+	5.39038i	0.281760	+	0.281760i
$367$		−	35.1007i		−	1.83224i	−0.400901	−	0.916122i	$-0.631303\pi$
$367$		−	35.1007i		−	1.83224i	0.400901	−	0.916122i	$-0.368697\pi$
$368$		−	3.36035i		−	0.175171i
$369$	1.22847	−	1.22847i	0.0639517	−	0.0639517i
$370$	−9.58617	+	9.58617i	−0.498361	+	0.498361i
$371$		0			0
$372$	−5.58086	+	5.58086i	−0.289354	+	0.289354i
$373$	−15.6539			−0.810528			−0.405264	−	0.914200i	$-0.632820\pi$
$373$	−15.6539			−0.810528			−0.405264	+	0.914200i	$0.632820\pi$
$374$	1.16583			0.0602837
$375$	14.2423	−	14.2423i	0.735470	−	0.735470i
$376$	27.9508			1.44145
$377$	2.03429	−	8.42660i	0.104771	−	0.433992i
$378$		0			0
$379$	−17.5478	−	17.5478i	−0.901371	−	0.901371i	0.0941840	−	0.995555i	$-0.469976\pi$
$379$	−17.5478	−	17.5478i	−0.901371	−	0.901371i	−0.995555	+	0.0941840i	$0.969976\pi$
$380$	−7.88502			−0.404493
$381$	24.5425			1.25735
$382$	−5.77663	−	5.77663i	−0.295558	−	0.295558i
$383$	0.696891	−	0.696891i	0.0356095	−	0.0356095i	−0.689078	−	0.724687i	$-0.741984\pi$
$383$	0.696891	−	0.696891i	0.0356095	−	0.0356095i	0.724687	+	0.689078i	$0.241984\pi$
$384$	12.1771	+	12.1771i	0.621408	+	0.621408i
$385$		0			0
$386$	8.96824			0.456471
$387$			2.89245i			0.147032i
$388$	−10.4515	−	10.4515i	−0.530594	−	0.530594i
$389$		−	5.05662i		−	0.256381i	−0.991750	−	0.128190i	$-0.959083\pi$
$389$		−	5.05662i		−	0.256381i	0.991750	−	0.128190i	$-0.0409169\pi$
$390$	−8.12490	−	1.96146i	−0.411420	−	0.0993222i
$391$		−	1.46526i		−	0.0741013i
$392$		0			0
$393$	33.6443			1.69713
$394$			14.1680i			0.713774i
$395$	−7.62698	+	7.62698i	−0.383755	+	0.383755i
$396$	−0.769599	−	0.769599i	−0.0386738	−	0.0386738i
$397$	0.823177	+	0.823177i	0.0413141	+	0.0413141i	0.727462	−	0.686148i	$-0.240700\pi$
$397$	0.823177	+	0.823177i	0.0413141	+	0.0413141i	−0.686148	+	0.727462i	$0.740700\pi$
$398$	−0.420683	−	0.420683i	−0.0210869	−	0.0210869i
$399$		0			0
$400$		−	1.45342i		−	0.0726709i
$401$	1.08454	−	1.08454i	0.0541593	−	0.0541593i	−0.679508	−	0.733668i	$-0.737807\pi$
$401$	1.08454	−	1.08454i	0.0541593	−	0.0541593i	0.733668	+	0.679508i	$0.237807\pi$
$402$	−8.13005			−0.405490
$403$	−6.01140	−	9.83754i	−0.299449	−	0.490043i
$404$			6.99938i			0.348232i
$405$	11.3111	−	11.3111i	0.562053	−	0.562053i
$406$		0			0
$407$			31.0498i			1.53908i
$408$	1.49800	+	1.49800i	0.0741622	+	0.0741622i
$409$	−7.54912	+	7.54912i	−0.373280	+	0.373280i	−0.868670	−	0.495391i	$-0.835025\pi$
$409$	−7.54912	+	7.54912i	−0.373280	+	0.373280i	0.495391	+	0.868670i	$0.335025\pi$
$410$	7.43824	−	7.43824i	0.367348	−	0.367348i
$411$	−9.97175	−	9.97175i	−0.491870	−	0.491870i
$412$		−	6.61369i		−	0.325833i
$413$		0			0
$414$	0.337130	−	0.337130i	0.0165691	−	0.0165691i
$415$		−	16.0601i		−	0.788358i
$416$	−17.9876	+	10.9916i	−0.881915	+	0.538909i
$417$	4.04294			0.197984
$418$	4.45083	−	4.45083i	0.217697	−	0.217697i
$419$			11.8652i			0.579653i	0.957079	+	0.289826i	$0.0935976\pi$
$419$			11.8652i			0.579653i	−0.957079	+	0.289826i	$0.906402\pi$
$420$		0			0
$421$	3.15236	+	3.15236i	0.153636	+	0.153636i	0.779740	−	0.626103i	$-0.215351\pi$
$421$	3.15236	+	3.15236i	0.153636	+	0.153636i	−0.626103	+	0.779740i	$0.715351\pi$
$422$	−9.58531	−	9.58531i	−0.466605	−	0.466605i
$423$	−1.81556	−	1.81556i	−0.0882756	−	0.0882756i
$424$	−12.1289	+	12.1289i	−0.589030	+	0.589030i
$425$		−	0.633752i		−	0.0307415i
$426$	−3.22357			−0.156183
$427$		0			0
$428$		−	28.6392i		−	1.38433i
$429$	−16.3350	+	9.98176i	−0.788659	+	0.481924i
$430$			17.5134i			0.844573i
$431$	0.863856	+	0.863856i	0.0416105	+	0.0416105i	0.727606	−	0.685995i	$-0.240633\pi$
$431$	0.863856	+	0.863856i	0.0416105	+	0.0416105i	−0.685995	+	0.727606i	$0.740633\pi$
$432$		−	6.26661i		−	0.301502i
$433$	−18.1346			−0.871493			−0.435747	−	0.900069i	$-0.643516\pi$
$433$	−18.1346			−0.871493			−0.435747	+	0.900069i	$0.643516\pi$
$434$		0			0
$435$	5.48154	+	5.48154i	0.262820	+	0.262820i
$436$	−11.4138	+	11.4138i	−0.546623	+	0.546623i
$437$	−5.59396	−	5.59396i	−0.267595	−	0.267595i
$438$	0.312738			0.0149432
$439$	−31.2506			−1.49151			−0.745755	−	0.666221i	$-0.767911\pi$
$439$	−31.2506			−1.49151			−0.745755	+	0.666221i	$0.767911\pi$
$440$	−10.9438	−	10.9438i	−0.521725	−	0.521725i
$441$		0			0
$442$	−1.12435	+	0.687051i	−0.0534797	+	0.0326797i
$443$	−24.7734			−1.17702			−0.588510	−	0.808490i	$-0.700285\pi$
$443$	−24.7734			−1.17702			−0.588510	+	0.808490i	$0.700285\pi$
$444$	−16.9878	+	16.9878i	−0.806205	+	0.806205i
$445$	−23.7385			−1.12531
$446$	−9.99689			−0.473366
$447$	−6.98376	+	6.98376i	−0.330321	+	0.330321i
$448$		0			0
$449$	7.07560	−	7.07560i	0.333918	−	0.333918i	−0.520154	−	0.854072i	$-0.674126\pi$
$449$	7.07560	−	7.07560i	0.333918	−	0.333918i	0.854072	+	0.520154i	$0.174126\pi$
$450$	0.145815	−	0.145815i	0.00687380	−	0.00687380i
$451$		−	24.0926i		−	1.13448i
$452$		−	16.5766i		−	0.779696i
$453$	7.61115	+	7.61115i	0.357603	+	0.357603i
$454$	11.2562			0.528278
$455$		0			0
$456$	11.4379			0.535631
$457$	−14.8172	−	14.8172i	−0.693121	−	0.693121i	0.269796	−	0.962917i	$-0.413044\pi$
$457$	−14.8172	−	14.8172i	−0.693121	−	0.693121i	−0.962917	+	0.269796i	$0.913044\pi$
$458$		−	3.44150i		−	0.160811i
$459$		−	2.73251i		−	0.127543i
$460$	−5.85663	+	5.85663i	−0.273067	+	0.273067i
$461$	8.07954	−	8.07954i	0.376302	−	0.376302i	−0.493464	−	0.869766i	$-0.664270\pi$
$461$	8.07954	−	8.07954i	0.376302	−	0.376302i	0.869766	+	0.493464i	$0.164270\pi$
$462$		0			0
$463$	−0.417027	+	0.417027i	−0.0193809	+	0.0193809i	−0.716731	−	0.697350i	$-0.754362\pi$
$463$	−0.417027	+	0.417027i	−0.0193809	+	0.0193809i	0.697350	+	0.716731i	$0.254362\pi$
$464$	2.80265			0.130110
$465$	10.3098			0.478106
$466$	−1.61163	+	1.61163i	−0.0746573	+	0.0746573i
$467$	5.60998			0.259599			0.129800	−	0.991540i	$-0.458567\pi$
$467$	5.60998			0.259599			0.129800	+	0.991540i	$0.458567\pi$
$468$	1.19576	+	0.288671i	0.0552738	+	0.0133438i
$469$		0			0
$470$	−10.9930	−	10.9930i	−0.507069	−	0.507069i
$471$	−10.6653			−0.491433
$472$	−9.70968			−0.446924
$473$	28.3632	+	28.3632i	1.30414	+	1.30414i
$474$	4.71085	−	4.71085i	0.216377	−	0.216377i
$475$	−2.41950	−	2.41950i	−0.111014	−	0.111014i
$476$		0			0
$477$	1.57567			0.0721452
$478$		−	7.64876i		−	0.349846i
$479$	−10.1210	−	10.1210i	−0.462439	−	0.462439i	0.437015	−	0.899454i	$-0.356036\pi$
$479$	−10.1210	−	10.1210i	−0.462439	−	0.462439i	−0.899454	+	0.437015i	$0.856036\pi$
$480$		−	18.8511i		−	0.860432i
$481$	−18.2983	−	29.9449i	−0.834332	−	1.36537i
$482$			1.40992i			0.0642201i
$483$		0			0
$484$	1.22066			0.0554844
$485$			19.3076i			0.876711i
$486$	1.21263	−	1.21263i	0.0550060	−	0.0550060i
$487$	−11.1514	−	11.1514i	−0.505319	−	0.505319i	0.407767	−	0.913086i	$-0.366307\pi$
$487$	−11.1514	−	11.1514i	−0.505319	−	0.505319i	−0.913086	+	0.407767i	$0.866307\pi$
$488$	−11.2810	−	11.2810i	−0.510666	−	0.510666i
$489$	0.805334	+	0.805334i	0.0364185	+	0.0364185i
$490$		0			0
$491$			25.0495i			1.13047i	0.824930	+	0.565234i	$0.191214\pi$
$491$			25.0495i			1.13047i	−0.824930	+	0.565234i	$0.808786\pi$
$492$	13.1814	−	13.1814i	0.594264	−	0.594264i
$493$	1.22208			0.0550395
$494$	−1.66947	+	6.91542i	−0.0751132	+	0.311140i
$495$			1.42172i			0.0639015i
$496$	2.63564	−	2.63564i	0.118344	−	0.118344i
$497$		0			0
$498$			9.91961i			0.444509i
$499$	16.5763	+	16.5763i	0.742058	+	0.742058i	0.972974	−	0.230915i	$-0.0741721\pi$
$499$	16.5763	+	16.5763i	0.742058	+	0.742058i	−0.230915	+	0.972974i	$0.574172\pi$
$500$	−12.6914	+	12.6914i	−0.567576	+	0.567576i
$501$	−4.11928	+	4.11928i	−0.184036	+	0.184036i
$502$	−0.834547	−	0.834547i	−0.0372476	−	0.0372476i
$503$		−	0.879009i		−	0.0391931i	−0.999808	−	0.0195965i	$-0.993762\pi$
$503$		−	0.879009i		−	0.0391931i	0.999808	−	0.0195965i	$-0.00623817\pi$
$504$		0			0
$505$	6.46516	−	6.46516i	0.287696	−	0.287696i
$506$		−	6.61175i		−	0.293928i
$507$	9.87120	−	19.2531i	0.438395	−	0.855061i
$508$	−21.8700			−0.970324
$509$	−7.05957	+	7.05957i	−0.312910	+	0.312910i	−0.846036	−	0.533126i	$-0.821017\pi$
$509$	−7.05957	+	7.05957i	−0.312910	+	0.312910i	0.533126	+	0.846036i	$0.321017\pi$
$510$		−	1.17832i		−	0.0521769i
$511$		0			0
$512$	−8.94753	−	8.94753i	−0.395429	−	0.395429i
$513$	−10.4320	−	10.4320i	−0.460583	−	0.460583i
$514$	−11.0948	−	11.0948i	−0.489371	−	0.489371i
$515$	−6.10890	+	6.10890i	−0.269190	+	0.269190i
$516$			31.0358i			1.36628i
$517$	−35.6065			−1.56597
$518$		0			0
$519$		−	41.2284i		−	1.80973i
$520$	17.0038	+	4.10493i	0.745665	+	0.180013i
$521$		−	15.5701i		−	0.682138i	−0.940038	−	0.341069i	$-0.889211\pi$
$521$		−	15.5701i		−	0.682138i	0.940038	−	0.341069i	$-0.110789\pi$
$522$	0.281178	+	0.281178i	0.0123068	+	0.0123068i
$523$		−	12.8747i		−	0.562973i	−0.959565	−	0.281486i	$-0.909173\pi$
$523$		−	12.8747i		−	0.562973i	0.959565	−	0.281486i	$-0.0908274\pi$
$524$	−29.9806			−1.30971
$525$		0			0
$526$	−8.47314	−	8.47314i	−0.369447	−	0.369447i
$527$	1.14925	−	1.14925i	0.0500623	−	0.0500623i
$528$	−4.37641	−	4.37641i	−0.190459	−	0.190459i
$529$	14.6901			0.638701
$530$	9.54050			0.414413
$531$	0.630697	+	0.630697i	0.0273699	+	0.0273699i
$532$		0			0
$533$	14.1983	+	23.2353i	0.614997	+	1.00643i
$534$	14.6622			0.634497
$535$	−26.4533	+	26.4533i	−1.14368	+	1.14368i
$536$	17.0145			0.734916
$537$	31.9371			1.37819
$538$	8.60403	−	8.60403i	0.370946	−	0.370946i
$539$		0			0
$540$	−10.9218	+	10.9218i	−0.470000	+	0.470000i
$541$	−11.2291	+	11.2291i	−0.482777	+	0.482777i	−0.906017	−	0.423241i	$-0.860892\pi$
$541$	−11.2291	+	11.2291i	−0.482777	+	0.482777i	0.423241	+	0.906017i	$0.360892\pi$
$542$		−	9.99002i		−	0.429108i
$543$			18.3787i			0.788706i
$544$	−2.10137	−	2.10137i	−0.0900955	−	0.0900955i
$545$	21.0853			0.903197
$546$		0			0
$547$	29.5180			1.26210			0.631048	−	0.775743i	$-0.282625\pi$
$547$	29.5180			1.26210			0.631048	+	0.775743i	$0.282625\pi$
$548$	8.88587	+	8.88587i	0.379586	+	0.379586i
$549$			1.46552i			0.0625471i
$550$		−	2.85971i		−	0.121938i
$551$	4.66556	−	4.66556i	0.198759	−	0.198759i
$552$	8.49558	−	8.49558i	0.361596	−	0.361596i
$553$		0			0
$554$	9.98454	−	9.98454i	0.424203	−	0.424203i
$555$	31.3824			1.33211
$556$	−3.60269			−0.152788
$557$	−1.43563	+	1.43563i	−0.0608296	+	0.0608296i	−0.736867	−	0.676038i	$-0.763696\pi$
$557$	−1.43563	+	1.43563i	−0.0608296	+	0.0608296i	0.676038	+	0.736867i	$0.263696\pi$
$558$	0.528847			0.0223879
$559$	−44.0689	−	10.6388i	−1.86392	−	0.449974i
$560$		0			0
$561$	−1.90830	−	1.90830i	−0.0805686	−	0.0805686i
$562$	17.4888			0.737720
$563$	23.8088			1.00342			0.501711	−	0.865036i	$-0.332704\pi$
$563$	23.8088			1.00342			0.501711	+	0.865036i	$0.332704\pi$
$564$	−19.4808	−	19.4808i	−0.820291	−	0.820291i
$565$	−15.3114	+	15.3114i	−0.644154	+	0.644154i
$566$	−5.99639	−	5.99639i	−0.252047	−	0.252047i
$567$		0			0
$568$	6.74629			0.283068
$569$		−	22.8381i		−	0.957424i	−0.877972	−	0.478712i	$-0.841104\pi$
$569$		−	22.8381i		−	0.957424i	0.877972	−	0.478712i	$-0.158896\pi$
$570$	−4.49851	−	4.49851i	−0.188422	−	0.188422i
$571$			16.6045i			0.694875i	0.937703	+	0.347437i	$0.112948\pi$
$571$			16.6045i			0.694875i	−0.937703	+	0.347437i	$0.887052\pi$
$572$	14.5562	−	8.89480i	0.608624	−	0.371910i
$573$			18.9111i			0.790021i
$574$		0			0
$575$	−3.59418			−0.149888
$576$		−	0.430659i		−	0.0179441i
$577$	17.4110	−	17.4110i	0.724829	−	0.724829i	−0.244756	−	0.969585i	$-0.578708\pi$
$577$	17.4110	−	17.4110i	0.724829	−	0.724829i	0.969585	+	0.244756i	$0.0787079\pi$
$578$	8.51125	+	8.51125i	0.354021	+	0.354021i
$579$	−14.6797	−	14.6797i	−0.610070	−	0.610070i
$580$	−4.88463	−	4.88463i	−0.202823	−	0.202823i
$581$		0			0
$582$		−	11.9254i		−	0.494325i
$583$	15.4509	−	15.4509i	0.639912	−	0.639912i
$584$	−0.654498			−0.0270833
$585$	−0.837851	−	1.37113i	−0.0346409	−	0.0566891i
$586$			18.8609i			0.779135i
$587$	30.7522	−	30.7522i	1.26928	−	1.26928i	0.322819	−	0.946461i	$-0.395369\pi$
$587$	30.7522	−	30.7522i	1.26928	−	1.26928i	0.946461	−	0.322819i	$-0.104631\pi$
$588$		0			0
$589$		−	8.77508i		−	0.361571i
$590$	3.81879	+	3.81879i	0.157217	+	0.157217i
$591$	23.1911	−	23.1911i	0.953952	−	0.953952i
$592$	8.02274	−	8.02274i	0.329732	−	0.329732i
$593$	−6.96530	−	6.96530i	−0.286031	−	0.286031i	0.549478	−	0.835508i	$-0.314827\pi$
$593$	−6.96530	−	6.96530i	−0.286031	−	0.286031i	−0.835508	+	0.549478i	$0.814827\pi$
$594$		−	12.3300i		−	0.505907i
$595$		0			0
$596$	6.22327	−	6.22327i	0.254915	−	0.254915i
$597$			1.37720i			0.0563650i
$598$	3.89645	+	6.37647i	0.159338	+	0.260753i
$599$	−40.6987			−1.66290			−0.831452	−	0.555597i	$-0.812490\pi$
$599$	−40.6987			−1.66290			−0.831452	+	0.555597i	$0.812490\pi$
$600$	3.67450	−	3.67450i	0.150011	−	0.150011i
$601$		−	10.7311i		−	0.437731i	−0.975755	−	0.218865i	$-0.929764\pi$
$601$		−	10.7311i		−	0.437731i	0.975755	−	0.218865i	$-0.0702356\pi$
$602$		0			0
$603$	−1.10519	−	1.10519i	−0.0450068	−	0.0450068i
$604$	−6.78233	−	6.78233i	−0.275969	−	0.275969i
$605$	−1.12749	−	1.12749i	−0.0458390	−	0.0458390i
$606$	−3.99325	+	3.99325i	−0.162215	+	0.162215i
$607$			11.6165i			0.471500i	0.971814	+	0.235750i	$0.0757546\pi$
$607$			11.6165i			0.471500i	−0.971814	+	0.235750i	$0.924245\pi$
$608$	−16.0449			−0.650708
$609$		0			0
$610$			8.87356i			0.359280i
$611$	34.3394	−	20.9837i	1.38922	−	0.848910i
$612$			0.173415i			0.00700990i
$613$	14.1979	+	14.1979i	0.573447	+	0.573447i	0.933090	−	0.359643i	$-0.117102\pi$
$613$	14.1979	+	14.1979i	0.573447	+	0.573447i	−0.359643	+	0.933090i	$0.617102\pi$
$614$			1.31378i			0.0530200i
$615$	−24.3507			−0.981915
$616$		0			0
$617$	−2.09240	−	2.09240i	−0.0842369	−	0.0842369i	0.663733	−	0.747970i	$-0.268971\pi$
$617$	−2.09240	−	2.09240i	−0.0842369	−	0.0842369i	−0.747970	+	0.663733i	$0.768971\pi$
$618$	3.77320	−	3.77320i	0.151780	−	0.151780i
$619$	25.1832	+	25.1832i	1.01220	+	1.01220i	0.999925	+	0.0122750i	$0.00390735\pi$
$619$	25.1832	+	25.1832i	1.01220	+	1.01220i	0.0122750	+	0.999925i	$0.496093\pi$
$620$	−9.18712			−0.368964
$621$	−15.4968			−0.621865
$622$	1.38088	+	1.38088i	0.0553681	+	0.0553681i
$623$		0			0
$624$	6.79979	+	1.64156i	0.272210	+	0.0657149i
$625$	17.2114			0.688454
$626$	12.9233	−	12.9233i	0.516519	−	0.516519i
$627$	−14.5708			−0.581901
$628$	9.50394			0.379248
$629$	3.49826	−	3.49826i	0.139485	−	0.139485i
$630$		0			0
$631$	9.03483	−	9.03483i	0.359671	−	0.359671i	−0.504021	−	0.863692i	$-0.668146\pi$
$631$	9.03483	−	9.03483i	0.359671	−	0.359671i	0.863692	+	0.504021i	$0.168146\pi$
$632$	−9.85886	+	9.85886i	−0.392165	+	0.392165i
$633$			31.3796i			1.24723i
$634$		−	21.8588i		−	0.868124i
$635$	20.2008	+	20.2008i	0.801643	+	0.801643i
$636$	16.9069			0.670401
$637$		0			0
$638$	5.51443			0.218318
$639$	−0.438209	−	0.438209i	−0.0173353	−	0.0173353i
$640$			20.0457i			0.792375i
$641$		−	18.3580i		−	0.725096i	−0.931965	−	0.362548i	$-0.881907\pi$
$641$		−	18.3580i		−	0.725096i	0.931965	−	0.362548i	$-0.118093\pi$
$642$	16.3391	−	16.3391i	0.644852	−	0.644852i
$643$	29.9544	−	29.9544i	1.18129	−	1.18129i	0.201874	−	0.979412i	$-0.435297\pi$
$643$	29.9544	−	29.9544i	1.18129	−	1.18129i	0.979412	−	0.201874i	$-0.0647030\pi$
$644$		0			0
$645$	28.6670	−	28.6670i	1.12876	−	1.12876i
$646$	−1.00292			−0.0394592
$647$	−19.7382			−0.775987			−0.387993	−	0.921662i	$-0.626832\pi$
$647$	−19.7382			−0.775987			−0.387993	+	0.921662i	$0.626832\pi$
$648$	14.6211	−	14.6211i	0.574370	−	0.574370i
$649$	12.3691			0.485531
$650$	1.68529	+	2.75795i	0.0661025	+	0.108176i
$651$		0			0
$652$	−0.717637	−	0.717637i	−0.0281049	−	0.0281049i
$653$	−0.0838864			−0.00328273			−0.00164136	−	0.999999i	$-0.500522\pi$
$653$	−0.0838864			−0.00328273			−0.00164136	+	0.999999i	$0.500522\pi$
$654$	−13.0235			−0.509259
$655$	27.6924	+	27.6924i	1.08203	+	1.08203i
$656$	−6.22512	+	6.22512i	−0.243050	+	0.243050i
$657$	0.0425133	+	0.0425133i	0.00165860	+	0.00165860i
$658$		0			0
$659$	40.2054			1.56618			0.783089	−	0.621909i	$-0.213643\pi$
$659$	40.2054			1.56618			0.783089	+	0.621909i	$0.213643\pi$
$660$			15.2549i			0.593798i
$661$	18.8246	+	18.8246i	0.732194	+	0.732194i	0.971054	−	0.238860i	$-0.0767738\pi$
$661$	18.8246	+	18.8246i	0.732194	+	0.732194i	−0.238860	+	0.971054i	$0.576774\pi$
$662$		−	1.36107i		−	0.0528995i
$663$	2.96500	+	0.715790i	0.115151	+	0.0277990i
$664$		−	20.7597i		−	0.805634i
$665$		0			0
$666$	1.60978			0.0623776
$667$		−	6.93072i		−	0.268359i
$668$	3.67071	−	3.67071i	0.142024	−	0.142024i
$669$	16.3635	+	16.3635i	0.632649	+	0.632649i
$670$	−6.69177	−	6.69177i	−0.258526	−	0.258526i
$671$	14.3708	+	14.3708i	0.554779	+	0.554779i
$672$		0			0
$673$			2.18487i			0.0842204i	0.999113	+	0.0421102i	$0.0134081\pi$
$673$			2.18487i			0.0842204i	−0.999113	+	0.0421102i	$0.986592\pi$
$674$	8.06631	−	8.06631i	0.310703	−	0.310703i
$675$	−6.70266			−0.257986
$676$	−8.79628	+	17.1565i	−0.338318	+	0.659867i
$677$			4.18691i			0.160916i	0.996758	+	0.0804580i	$0.0256383\pi$
$677$			4.18691i			0.160916i	−0.996758	+	0.0804580i	$0.974362\pi$
$678$	9.45716	−	9.45716i	0.363200	−	0.363200i
$679$		0			0
$680$			2.46599i			0.0945663i
$681$	−18.4248	−	18.4248i	−0.706039	−	0.706039i
$682$	5.18583	−	5.18583i	0.198576	−	0.198576i
$683$	−8.41293	+	8.41293i	−0.321912	+	0.321912i	−0.849500	−	0.527588i	$-0.823096\pi$
$683$	−8.41293	+	8.41293i	−0.321912	+	0.321912i	0.527588	+	0.849500i	$0.323096\pi$
$684$	0.662054	+	0.662054i	0.0253142	+	0.0253142i
$685$		−	16.4153i		−	0.627197i
$686$		0			0
$687$	−5.63326	+	5.63326i	−0.214922	+	0.214922i
$688$		−	14.6571i		−	0.558798i
$689$	−5.79553	+	24.0067i	−0.220792	+	0.914582i
$690$	−6.68258			−0.254401
$691$	26.5057	−	26.5057i	1.00833	−	1.00833i	0.00836045	−	0.999965i	$-0.497339\pi$
$691$	26.5057	−	26.5057i	1.00833	−	1.00833i	0.999965	−	0.00836045i	$-0.00266125\pi$
$692$			36.7388i			1.39660i
$693$		0			0
$694$	−8.23664	−	8.23664i	−0.312659	−	0.312659i
$695$	3.32771	+	3.32771i	0.126227	+	0.126227i
$696$	7.08561	+	7.08561i	0.268579	+	0.268579i
$697$	−2.71442	+	2.71442i	−0.102816	+	0.102816i
$698$		−	19.0196i		−	0.719903i
$699$	5.27603			0.199558
$700$		0			0
$701$			31.0974i			1.17453i	0.809394	+	0.587266i	$0.199796\pi$
$701$			31.0974i			1.17453i	−0.809394	+	0.587266i	$0.800204\pi$
$702$	7.26636	+	11.8913i	0.274251	+	0.448806i
$703$		−	26.7108i		−	1.00742i
$704$	−4.22301	−	4.22301i	−0.159160	−	0.159160i
$705$			35.9879i			1.35538i
$706$	−16.4944			−0.620776
$707$		0			0
$708$	6.76734	+	6.76734i	0.254332	+	0.254332i
$709$	10.7112	−	10.7112i	0.402268	−	0.402268i	−0.476764	−	0.879031i	$-0.658190\pi$
$709$	10.7112	−	10.7112i	0.402268	−	0.402268i	0.879031	+	0.476764i	$0.158190\pi$
$710$	−2.65330	−	2.65330i	−0.0995765	−	0.0995765i
$711$	1.28078			0.0480328
$712$	−30.6851			−1.14997
$713$	−6.51773	−	6.51773i	−0.244091	−	0.244091i
$714$		0			0
$715$	−21.6611	−	5.22926i	−0.810078	−	0.195563i
$716$	−28.4593			−1.06357
$717$	−12.5199	+	12.5199i	−0.467566	+	0.467566i
$718$	−5.35668			−0.199910
$719$	21.4176			0.798743			0.399371	−	0.916789i	$-0.369228\pi$
$719$	21.4176			0.798743			0.399371	+	0.916789i	$0.369228\pi$
$720$	0.367348	−	0.367348i	0.0136903	−	0.0136903i
$721$		0			0
$722$	5.83051	−	5.83051i	0.216989	−	0.216989i
$723$	2.30784	−	2.30784i	0.0858295	−	0.0858295i
$724$		−	16.3774i		−	0.608660i
$725$		−	2.99767i		−	0.111331i
$726$	0.696402	+	0.696402i	0.0258459	+	0.0258459i
$727$	−39.0080			−1.44673			−0.723363	−	0.690468i	$-0.757405\pi$
$727$	−39.0080			−1.44673			−0.723363	+	0.690468i	$0.757405\pi$
$728$		0			0
$729$	−28.7407			−1.06447
$730$	0.257412	+	0.257412i	0.00952726	+	0.00952726i
$731$		−	6.39114i		−	0.236385i
$732$			15.7250i			0.581212i
$733$	1.17566	−	1.17566i	0.0434240	−	0.0434240i	−0.685061	−	0.728485i	$-0.740225\pi$
$733$	1.17566	−	1.17566i	0.0434240	−	0.0434240i	0.728485	+	0.685061i	$0.240225\pi$
$734$	−17.8448	+	17.8448i	−0.658663	+	0.658663i
$735$		0			0
$736$	−11.9174	+	11.9174i	−0.439283	+	0.439283i
$737$	−21.6748			−0.798401
$738$	−1.24908			−0.0459793
$739$	25.5978	−	25.5978i	0.941632	−	0.941632i	−0.0567563	−	0.998388i	$-0.518076\pi$
$739$	25.5978	−	25.5978i	0.941632	−	0.941632i	0.998388	+	0.0567563i	$0.0180758\pi$
$740$	−27.9650			−1.02801
$741$	14.0523	−	8.58688i	0.516223	−	0.315447i
$742$		0			0
$743$	−2.82866	−	2.82866i	−0.103773	−	0.103773i	0.653314	−	0.757087i	$-0.273378\pi$
$743$	−2.82866	−	2.82866i	−0.103773	−	0.103773i	−0.757087	+	0.653314i	$0.773378\pi$
$744$	13.3268			0.488583
$745$	−11.4966			−0.421201
$746$	7.95826	+	7.95826i	0.291372	+	0.291372i
$747$	−1.34846	+	1.34846i	−0.0493376	+	0.0493376i
$748$	1.70050	+	1.70050i	0.0621764	+	0.0621764i
$749$		0			0
$750$	−14.4812			−0.528780
$751$		−	13.3226i		−	0.486150i	−0.970007	−	0.243075i	$-0.921844\pi$
$751$		−	13.3226i		−	0.486150i	0.970007	−	0.243075i	$-0.0781562\pi$
$752$	9.20011	+	9.20011i	0.335493	+	0.335493i
$753$			2.73207i			0.0995622i
$754$	−5.31819	+	3.24978i	−0.193677	+	0.118350i
$755$			12.5293i			0.455989i
$756$		0			0
$757$	16.0291			0.582587			0.291294	−	0.956634i	$-0.405914\pi$
$757$	16.0291			0.582587			0.291294	+	0.956634i	$0.405914\pi$
$758$			17.8422i			0.648058i
$759$	−10.8225	+	10.8225i	−0.392832	+	0.392832i
$760$	9.41448	+	9.41448i	0.341499	+	0.341499i
$761$	4.90439	+	4.90439i	0.177784	+	0.177784i	0.790389	−	0.612605i	$-0.209878\pi$
$761$	4.90439	+	4.90439i	0.177784	+	0.177784i	−0.612605	+	0.790389i	$0.709878\pi$
$762$	−12.4771	−	12.4771i	−0.451999	−	0.451999i
$763$		0			0
$764$		−	16.8517i		−	0.609675i
$765$	0.160180	−	0.160180i	0.00579130	−	0.00579130i
$766$	−0.708582			−0.0256021
$767$	−11.9290	+	7.28941i	−0.430731	+	0.263205i
$768$		−	18.6129i		−	0.671634i
$769$	−12.5271	+	12.5271i	−0.451740	+	0.451740i	−0.895932	−	0.444192i	$-0.853491\pi$
$769$	−12.5271	+	12.5271i	−0.451740	+	0.451740i	0.444192	+	0.895932i	$0.353491\pi$
$770$		0			0
$771$			36.3213i			1.30808i
$772$	13.0812	+	13.0812i	0.470803	+	0.470803i
$773$	34.6168	−	34.6168i	1.24508	−	1.24508i	0.287211	−	0.957867i	$-0.407272\pi$
$773$	34.6168	−	34.6168i	1.24508	−	1.24508i	0.957867	−	0.287211i	$-0.0927279\pi$
$774$	1.47049	−	1.47049i	0.0528557	−	0.0528557i
$775$	−2.81904	−	2.81904i	−0.101263	−	0.101263i
$776$			24.9575i			0.895923i
$777$		0			0
$778$	−2.57073	+	2.57073i	−0.0921650	+	0.0921650i
$779$			20.7258i			0.742580i
$780$	−8.99008	−	14.7121i	−0.321897	−	0.526778i
$781$	−8.59408			−0.307520
$782$	−0.744920	+	0.744920i	−0.0266383	+	0.0266383i
$783$		−	12.9249i		−	0.461897i
$784$		0			0
$785$	−8.77855	−	8.77855i	−0.313320	−	0.313320i
$786$	−17.1044	−	17.1044i	−0.610093	−	0.610093i
$787$	−10.2521	−	10.2521i	−0.365447	−	0.365447i	0.500367	−	0.865814i	$-0.333198\pi$
$787$	−10.2521	−	10.2521i	−0.365447	−	0.365447i	−0.865814	+	0.500367i	$0.833198\pi$
$788$	−20.6657	+	20.6657i	−0.736184	+	0.736184i
$789$			27.7387i			0.987523i
$790$	7.75493			0.275908
$791$		0			0
$792$			1.83776i			0.0653019i
$793$	−22.3285	−	5.39038i	−0.792907	−	0.191418i
$794$		−	0.836986i		−	0.0297035i
$795$	−15.6165	−	15.6165i	−0.553859	−	0.553859i
$796$		−	1.22723i		−	0.0434979i
$797$	25.6379			0.908139			0.454070	−	0.890966i	$-0.349972\pi$
$797$	25.6379			0.908139			0.454070	+	0.890966i	$0.349972\pi$
$798$		0			0
$799$	4.01164	+	4.01164i	0.141922	+	0.141922i
$800$	−5.15452	+	5.15452i	−0.182240	+	0.182240i
$801$	1.99317	+	1.99317i	0.0704251	+	0.0704251i
$802$	−1.10273			−0.0389389
$803$	0.833763			0.0294229
$804$	−11.8586	−	11.8586i	−0.418220	−	0.418220i
$805$		0			0
$806$	−1.94516	+	8.05742i	−0.0685155	+	0.283810i
$807$	−28.1672			−0.991532
$808$	8.35706	−	8.35706i	0.294000	−	0.294000i
$809$	−39.5081			−1.38903			−0.694515	−	0.719478i	$-0.744381\pi$
$809$	−39.5081			−1.38903			−0.694515	+	0.719478i	$0.744381\pi$
$810$	−11.5009			−0.404099
$811$	−17.7080	+	17.7080i	−0.621813	+	0.621813i	−0.945995	−	0.324182i	$-0.894911\pi$
$811$	−17.7080	+	17.7080i	−0.621813	+	0.621813i	0.324182	+	0.945995i	$0.394911\pi$
$812$		0			0
$813$	−16.3523	+	16.3523i	−0.573498	+	0.573498i
$814$	15.7853	−	15.7853i	0.553276	−	0.553276i
$815$			1.32573i			0.0464382i
$816$			0.986146i			0.0345220i
$817$	−24.3996	−	24.3996i	−0.853635	−	0.853635i
$818$	7.67576			0.268377
$819$		0			0
$820$	21.6990			0.757763
$821$	13.8641	+	13.8641i	0.483861	+	0.483861i	0.906362	−	0.422501i	$-0.138848\pi$
$821$	13.8641	+	13.8641i	0.483861	+	0.483861i	−0.422501	+	0.906362i	$0.638848\pi$
$822$			10.1390i			0.353639i
$823$			20.6613i			0.720207i	0.932912	+	0.360103i	$0.117259\pi$
$823$			20.6613i			0.720207i	−0.932912	+	0.360103i	$0.882741\pi$
$824$	−7.89655	+	7.89655i	−0.275089	+	0.275089i
$825$	−4.68094	+	4.68094i	−0.162969	+	0.162969i
$826$		0			0
$827$	−18.0688	+	18.0688i	−0.628315	+	0.628315i	−0.947644	−	0.319329i	$-0.896543\pi$
$827$	−18.0688	+	18.0688i	−0.628315	+	0.628315i	0.319329	+	0.947644i	$0.396543\pi$
$828$	0.983486			0.0341785
$829$	−40.5223			−1.40740			−0.703700	−	0.710498i	$-0.748470\pi$
$829$	−40.5223			−1.40740			−0.703700	+	0.710498i	$0.748470\pi$
$830$	−8.16475	+	8.16475i	−0.283403	+	0.283403i
$831$	−32.6866			−1.13388
$832$	6.56144	+	1.58402i	0.227477	+	0.0549159i
$833$		0			0
$834$	−2.05538	−	2.05538i	−0.0711721	−	0.0711721i
$835$	−6.78109			−0.234669
$836$	12.9841			0.449064
$837$	−12.1547	−	12.1547i	−0.420127	−	0.420127i
$838$	6.03213	−	6.03213i	0.208376	−	0.208376i
$839$	2.12585	+	2.12585i	0.0733926	+	0.0733926i	0.742850	−	0.669458i	$-0.233473\pi$
$839$	2.12585	+	2.12585i	0.0733926	+	0.0733926i	−0.669458	+	0.742850i	$0.733473\pi$
$840$		0			0
$841$	−23.2195			−0.800674
$842$		−	3.20524i		−	0.110460i
$843$	−28.6267	−	28.6267i	−0.985956	−	0.985956i
$844$		−	27.9625i		−	0.962509i
$845$	23.9720	−	7.72218i	0.824661	−	0.265651i
$846$			1.84602i			0.0634674i
$847$		0			0
$848$	−7.98452			−0.274189
$849$			19.6305i			0.673717i
$850$	−0.322192	+	0.322192i	−0.0110511	+	0.0110511i
$851$	−19.8396	−	19.8396i	−0.680092	−	0.680092i
$852$	−4.70195	−	4.70195i	−0.161086	−	0.161086i
$853$	38.1991	+	38.1991i	1.30791	+	1.30791i	0.922920	+	0.384992i	$0.125796\pi$
$853$	38.1991	+	38.1991i	1.30791	+	1.30791i	0.384992	+	0.922920i	$0.374204\pi$
$854$		0			0
$855$		−	1.22304i		−	0.0418273i
$856$	−34.1944	+	34.1944i	−1.16874	+	1.16874i
$857$	21.5401			0.735796			0.367898	−	0.929866i	$-0.380078\pi$
$857$	21.5401			0.735796			0.367898	+	0.929866i	$0.380078\pi$
$858$	13.3791	+	3.22989i	0.456755	+	0.110267i
$859$		−	1.08210i		−	0.0369207i	−0.999830	−	0.0184603i	$-0.994124\pi$
$859$		−	1.08210i		−	0.0369207i	0.999830	−	0.0184603i	$-0.00587644\pi$
$860$	−25.5453	+	25.5453i	−0.871089	+	0.871089i
$861$		0			0
$862$		−	0.878348i		−	0.0299167i
$863$	−2.29414	−	2.29414i	−0.0780934	−	0.0780934i	0.666981	−	0.745075i	$-0.267586\pi$
$863$	−2.29414	−	2.29414i	−0.0780934	−	0.0780934i	−0.745075	+	0.666981i	$0.767586\pi$
$864$	−22.2244	+	22.2244i	−0.756090	+	0.756090i
$865$	33.9347	−	33.9347i	1.15382	−	1.15382i
$866$	9.21941	+	9.21941i	0.313288	+	0.313288i
$867$		−	27.8634i		−	0.946292i
$868$		0			0
$869$	12.5592	−	12.5592i	0.426041	−	0.426041i
$870$		−	5.57350i		−	0.188959i
$871$	20.9035	−	12.7734i	0.708287	−	0.432811i
$872$	27.2555			0.922989
$873$	1.62113	−	1.62113i	0.0548669	−	0.0548669i
$874$			5.68781i			0.192393i
$875$		0			0
$876$	0.456164	+	0.456164i	0.0154124	+	0.0154124i
$877$	15.0499	+	15.0499i	0.508198	+	0.508198i	0.913973	−	0.405775i	$-0.132998\pi$
$877$	15.0499	+	15.0499i	0.508198	+	0.508198i	−0.405775	+	0.913973i	$0.632998\pi$
$878$	15.8874	+	15.8874i	0.536175	+	0.536175i
$879$	30.8726	−	30.8726i	1.04131	−	1.04131i
$880$		−	7.20437i		−	0.242859i
$881$	34.2796			1.15491			0.577455	−	0.816423i	$-0.304046\pi$
$881$	34.2796			1.15491			0.577455	+	0.816423i	$0.304046\pi$
$882$		0			0
$883$		−	8.76503i		−	0.294967i	−0.989065	−	0.147483i	$-0.952883\pi$
$883$		−	8.76503i		−	0.294967i	0.989065	−	0.147483i	$-0.0471173\pi$
$884$	−2.64213	−	0.637844i	−0.0888644	−	0.0214530i
$885$		−	12.5016i		−	0.420238i
$886$	12.5945	+	12.5945i	0.423121	+	0.423121i
$887$			8.34014i			0.280035i	0.990149	+	0.140017i	$0.0447158\pi$
$887$			8.34014i			0.280035i	−0.990149	+	0.140017i	$0.955284\pi$
$888$	40.5659			1.36130
$889$		0			0
$890$	12.0684	+	12.0684i	0.404532	+	0.404532i
$891$	−18.6258	+	18.6258i	−0.623986	+	0.623986i
$892$	−14.5816	−	14.5816i	−0.488228	−	0.488228i
$893$	30.6307			1.02502
$894$	7.10092			0.237490
$895$	26.2872	+	26.2872i	0.878683	+	0.878683i
$896$		0			0
$897$	4.05944	−	16.8153i	0.135541	−	0.561447i
$898$	−7.19430			−0.240077
$899$	5.43601	−	5.43601i	0.181301	−	0.181301i
$900$	0.425377			0.0141792
$901$	−3.48159			−0.115989
$902$	−12.2484	+	12.2484i	−0.407827	+	0.407827i
$903$		0			0
$904$	−19.7919	+	19.7919i	−0.658269	+	0.658269i
$905$	−15.1274	+	15.1274i	−0.502850	+	0.502850i
$906$		−	7.73883i		−	0.257105i
$907$			4.23968i			0.140776i	0.997520	+	0.0703882i	$0.0224238\pi$
$907$			4.23968i			0.140776i	−0.997520	+	0.0703882i	$0.977576\pi$
$908$	16.4184	+	16.4184i	0.544864	+	0.544864i
$909$	−1.08567			−0.0360096
$910$		0			0
$911$	−1.59871			−0.0529676			−0.0264838	−	0.999649i	$-0.508431\pi$
$911$	−1.59871			−0.0529676			−0.0264838	+	0.999649i	$0.508431\pi$
$912$	3.76484	+	3.76484i	0.124666	+	0.124666i
$913$			26.4458i			0.875228i
$914$			15.0658i			0.498333i
$915$	14.5248	−	14.5248i	0.480174	−	0.480174i
$916$	5.01982	−	5.01982i	0.165860	−	0.165860i
$917$		0			0
$918$	−1.38917	+	1.38917i	−0.0458496	+	0.0458496i
$919$	−12.1998			−0.402434			−0.201217	−	0.979547i	$-0.564490\pi$
$919$	−12.1998			−0.402434			−0.201217	+	0.979547i	$0.564490\pi$
$920$	13.9853			0.461081
$921$	2.15048	−	2.15048i	0.0708607	−	0.0708607i
$922$	−8.21509			−0.270549
$923$	8.28826	−	5.06469i	0.272811	−	0.166706i
$924$		0			0
$925$	−8.58099	−	8.58099i	−0.282141	−	0.282141i
$926$	0.424023			0.0139343
$927$	1.02585			0.0336933
$928$	−9.93955	−	9.93955i	−0.326282	−	0.326282i
$929$	−0.432165	+	0.432165i	−0.0141789	+	0.0141789i	−0.714161	−	0.699982i	$-0.753191\pi$
$929$	−0.432165	+	0.432165i	−0.0141789	+	0.0141789i	0.699982	+	0.714161i	$0.253191\pi$
$930$	−5.24138	−	5.24138i	−0.171872	−	0.171872i
$931$		0			0
$932$	−4.70149			−0.154002
$933$		−	4.52060i		−	0.147998i
$934$	−2.85205	−	2.85205i	−0.0933219	−	0.0933219i
$935$		−	3.14142i		−	0.102735i
$936$	−1.08303	−	1.77236i	−0.0354000	−	0.0579314i
$937$		−	5.03265i		−	0.164410i	−0.996615	−	0.0822048i	$-0.973804\pi$
$937$		−	5.03265i		−	0.164410i	0.996615	−	0.0822048i	$-0.0261961\pi$
$938$		0			0
$939$	−42.3072			−1.38064
$940$		−	32.0690i		−	1.04598i
$941$	−34.0696	+	34.0696i	−1.11064	+	1.11064i	−0.117573	+	0.993064i	$0.537512\pi$
$941$	−34.0696	+	34.0696i	−1.11064	+	1.11064i	−0.993064	+	0.117573i	$0.962488\pi$
$942$	5.42213	+	5.42213i	0.176663	+	0.176663i
$943$	15.3942	+	15.3942i	0.501304	+	0.501304i
$944$	−3.19597	−	3.19597i	−0.104020	−	0.104020i
$945$		0			0
$946$		−	28.8390i		−	0.937637i
$947$	8.21328	−	8.21328i	0.266896	−	0.266896i	−0.560952	−	0.827848i	$-0.689565\pi$
$947$	8.21328	−	8.21328i	0.266896	−	0.266896i	0.827848	+	0.560952i	$0.189565\pi$
$948$	13.7426			0.446340
$949$	−0.804094	+	0.491355i	−0.0261020	+	0.0159501i
$950$			2.46009i			0.0798157i
$951$	−35.7798	+	35.7798i	−1.16024	+	1.16024i
$952$		0			0
$953$		−	12.7370i		−	0.412592i	−0.978490	−	0.206296i	$-0.933859\pi$
$953$		−	12.7370i		−	0.412592i	0.978490	−	0.206296i	$-0.0661409\pi$
$954$	−0.801054	−	0.801054i	−0.0259351	−	0.0259351i
$955$	−15.5655	+	15.5655i	−0.503689	+	0.503689i
$956$	11.1566	−	11.1566i	0.360830	−	0.360830i
$957$	−9.02634	−	9.02634i	−0.291780	−	0.291780i
$958$			10.2908i			0.332479i
$959$		0			0
$960$	−4.26825	+	4.26825i	−0.137757	+	0.137757i
$961$			20.7758i			0.670188i
$962$	−5.92096	+	24.5263i	−0.190899	+	0.790759i
$963$	4.44223			0.143149
$964$	−2.05653	+	2.05653i	−0.0662363	+	0.0662363i
$965$		−	24.1656i		−	0.777917i
$966$		0			0
$967$	1.70551	+	1.70551i	0.0548455	+	0.0548455i	0.733998	−	0.679152i	$-0.237652\pi$
$967$	1.70551	+	1.70551i	0.0548455	+	0.0548455i	−0.679152	+	0.733998i	$0.737652\pi$
$968$	−1.45743	−	1.45743i	−0.0468435	−	0.0468435i
$969$	1.64163	+	1.64163i	0.0527368	+	0.0527368i
$970$	9.81573	−	9.81573i	0.315164	−	0.315164i
$971$		−	25.3989i		−	0.815088i	−0.913186	−	0.407544i	$-0.866385\pi$
$971$		−	25.3989i		−	0.815088i	0.913186	−	0.407544i	$-0.133615\pi$
$972$	3.53752			0.113466
$973$		0			0
$974$			11.3385i			0.363309i
$975$	1.75579	−	7.27295i	0.0562301	−	0.232921i
$976$		−	7.42635i		−	0.237712i
$977$	15.2036	+	15.2036i	0.486406	+	0.486406i	0.907170	−	0.420764i	$-0.138238\pi$
$977$	15.2036	+	15.2036i	0.486406	+	0.486406i	−0.420764	+	0.907170i	$0.638238\pi$
$978$		−	0.818845i		−	0.0261838i
$979$	39.0897			1.24931
$980$		0			0
$981$	−1.77040	−	1.77040i	−0.0565245	−	0.0565245i
$982$	12.7349	−	12.7349i	0.406386	−	0.406386i
$983$	25.3916	+	25.3916i	0.809866	+	0.809866i	0.984613	−	0.174747i	$-0.0559109\pi$
$983$	25.3916	+	25.3916i	0.809866	+	0.809866i	−0.174747	+	0.984613i	$0.555911\pi$
$984$	−31.4765			−1.00343
$985$	38.1767			1.21641
$986$	−0.621289	−	0.621289i	−0.0197859	−	0.0197859i
$987$		0			0
$988$	−12.5220	+	7.65181i	−0.398379	+	0.243437i
$989$	−36.2459			−1.15255
$990$	0.722785	−	0.722785i	0.0229716	−	0.0229716i
$991$	42.6344			1.35433			0.677164	−	0.735832i	$-0.263209\pi$
$991$	42.6344			1.35433			0.677164	+	0.735832i	$0.263209\pi$
$992$	−18.6945			−0.593552
$993$	−2.22788	+	2.22788i	−0.0706996	+	0.0706996i
$994$		0			0
$995$	−1.13356	+	1.13356i	−0.0359363	+	0.0359363i
$996$	−14.4689	+	14.4689i	−0.458464	+	0.458464i
$997$			57.7022i			1.82745i	0.406335	+	0.913724i	$0.366807\pi$
$997$			57.7022i			1.82745i	−0.406335	+	0.913724i	$0.633193\pi$
$998$		−	16.8544i		−	0.533517i
$999$	−36.9981	−	36.9981i	−1.17057	−	1.17057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.i.a.489.8		32
7.2	even	3		637.2.bc.b.619.4		32
7.3	odd	6		637.2.bc.b.411.5		32
7.4	even	3		91.2.bb.a.47.5	yes	32
7.5	odd	6		91.2.bb.a.73.4	yes	32
7.6	odd	2	inner	637.2.i.a.489.7		32
13.5	odd	4	inner	637.2.i.a.538.8		32
21.5	even	6		819.2.fn.e.73.5		32
21.11	odd	6		819.2.fn.e.775.4		32
91.5	even	12		91.2.bb.a.31.5	yes	32
91.18	odd	12		91.2.bb.a.5.4	✓	32
91.31	even	12		637.2.bc.b.460.4		32
91.44	odd	12		637.2.bc.b.31.5		32
91.83	even	4	inner	637.2.i.a.538.7		32
273.5	odd	12		819.2.fn.e.577.4		32
273.200	even	12		819.2.fn.e.460.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bb.a.5.4	✓	32	91.18	odd	12
91.2.bb.a.31.5	yes	32	91.5	even	12
91.2.bb.a.47.5	yes	32	7.4	even	3
91.2.bb.a.73.4	yes	32	7.5	odd	6
637.2.i.a.489.7		32	7.6	odd	2	inner
637.2.i.a.489.8		32	1.1	even	1	trivial
637.2.i.a.538.7		32	91.83	even	4	inner
637.2.i.a.538.8		32	13.5	odd	4	inner
637.2.bc.b.31.5		32	91.44	odd	12
637.2.bc.b.411.5		32	7.3	odd	6
637.2.bc.b.460.4		32	91.31	even	12
637.2.bc.b.619.4		32	7.2	even	3
819.2.fn.e.73.5		32	21.5	even	6
819.2.fn.e.460.5		32	273.200	even	12
819.2.fn.e.577.4		32	273.5	odd	12
819.2.fn.e.775.4		32	21.11	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-0.508388 - 0.508388i) q^{2} +1.66432i q^{3} -1.48308i q^{4} +(-1.36989 + 1.36989i) q^{5} +(0.846120 - 0.846120i) q^{6} +(-1.77076 + 1.77076i) q^{8} +0.230041 q^{9} +O(q^{10})\)	\(q+(-0.508388 - 0.508388i) q^{2} +1.66432i q^{3} -1.48308i q^{4} +(-1.36989 + 1.36989i) q^{5} +(0.846120 - 0.846120i) q^{6} +(-1.77076 + 1.77076i) q^{8} +0.230041 q^{9} +1.39287 q^{10} +(2.25576 - 2.25576i) q^{11} +2.46832 q^{12} +(-0.846120 + 3.50487i) q^{13} +(-2.27993 - 2.27993i) q^{15} -1.16570 q^{16} -0.508296 q^{17} +(-0.116950 - 0.116950i) q^{18} +(-1.94054 + 1.94054i) q^{19} +(2.03166 + 2.03166i) q^{20} -2.29361 q^{22} +2.88269i q^{23} +(-2.94711 - 2.94711i) q^{24} +1.24682i q^{25} +(2.21199 - 1.35167i) q^{26} +5.37582i q^{27} -2.40426 q^{29} +2.31818i q^{30} +(-2.26099 + 2.26099i) q^{31} +(4.13414 + 4.13414i) q^{32} +(3.75431 + 3.75431i) q^{33} +(0.258412 + 0.258412i) q^{34} -0.341170i q^{36} +(-6.88232 + 6.88232i) q^{37} +1.97309 q^{38} +(-5.83322 - 1.40821i) q^{39} -4.85148i q^{40} +(5.34023 - 5.34023i) q^{41} +12.5736i q^{43} +(-3.34549 - 3.34549i) q^{44} +(-0.315130 + 0.315130i) q^{45} +(1.46552 - 1.46552i) q^{46} +(-7.89233 - 7.89233i) q^{47} -1.94010i q^{48} +(0.633867 - 0.633867i) q^{50} -0.845967i q^{51} +(5.19801 + 1.25487i) q^{52} +6.84953 q^{53} +(2.73300 - 2.73300i) q^{54} +6.18029i q^{55} +(-3.22968 - 3.22968i) q^{57} +(1.22230 + 1.22230i) q^{58} +(2.74167 + 2.74167i) q^{59} +(-3.38133 + 3.38133i) q^{60} +6.37071i q^{61} +2.29892 q^{62} -1.87209i q^{64} +(-3.64218 - 5.96036i) q^{65} -3.81730i q^{66} +(-4.80431 - 4.80431i) q^{67} +0.753846i q^{68} -4.79771 q^{69} +(-1.90492 - 1.90492i) q^{71} +(-0.407347 + 0.407347i) q^{72} +(0.184807 + 0.184807i) q^{73} +6.99778 q^{74} -2.07510 q^{75} +(2.87798 + 2.87798i) q^{76} +(2.24962 + 3.68146i) q^{78} +5.56760 q^{79} +(1.59688 - 1.59688i) q^{80} -8.25696 q^{81} -5.42982 q^{82} +(-5.86182 + 5.86182i) q^{83} +(0.696309 - 0.696309i) q^{85} +(6.39229 - 6.39229i) q^{86} -4.00145i q^{87} +7.98883i q^{88} +(8.66439 + 8.66439i) q^{89} +0.320417 q^{90} +4.27526 q^{92} +(-3.76301 - 3.76301i) q^{93} +8.02474i q^{94} -5.31664i q^{95} +(-6.88054 + 6.88054i) q^{96} +(7.04713 - 7.04713i) q^{97} +(0.518918 - 0.518918i) 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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