LMFDB - Embedded newform 630.2.bw.a.493.34

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(103,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([4, 9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.103"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bw (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			493.34
Character	$\chi$	$=$	630.493
Dual form			630.2.bw.a.607.34

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.345692 - 1.69720i) q^{3} -1.00000i q^{4} +(1.87055 - 1.22517i) q^{5} +(-1.44454 - 0.955663i) q^{6} +(1.36243 - 2.26799i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.76099 + 1.17342i) q^{9} +(0.456350 - 2.18901i) q^{10} +(0.0834918 + 0.144612i) q^{11} +(-1.69720 + 0.345692i) q^{12} +(-2.26834 - 0.607801i) q^{13} +(-0.640332 - 2.56709i) q^{14} +(-2.72600 - 2.75117i) q^{15} -1.00000 q^{16} +(3.82109 - 1.02386i) q^{17} +(-1.12259 + 2.78205i) q^{18} +(2.72986 + 4.72826i) q^{19} +(-1.22517 - 1.87055i) q^{20} +(-4.32022 - 1.52829i) q^{21} +(0.161294 + 0.0432185i) q^{22} +(-1.65857 + 0.444413i) q^{23} +(-0.955663 + 1.44454i) q^{24} +(1.99790 - 4.58349i) q^{25} +(-2.03374 + 1.17418i) q^{26} +(2.94598 + 4.28033i) q^{27} +(-2.26799 - 1.36243i) q^{28} +(0.515067 + 0.297374i) q^{29} +(-3.87294 - 0.0177970i) q^{30} +4.29454i q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.216573 - 0.191694i) q^{33} +(1.97794 - 3.42590i) q^{34} +(-0.230197 - 5.91160i) q^{35} +(1.17342 + 2.76099i) q^{36} +(-3.70687 - 0.993252i) q^{37} +(5.27369 + 1.41308i) q^{38} +(-0.247414 + 4.05995i) q^{39} +(-2.18901 - 0.456350i) q^{40} +(-9.70992 + 5.60603i) q^{41} +(-4.13552 + 1.97420i) q^{42} +(9.11376 - 2.44202i) q^{43} +(0.144612 - 0.0834918i) q^{44} +(-3.72694 + 5.57763i) q^{45} +(-0.858541 + 1.48704i) q^{46} +(-0.553347 - 0.553347i) q^{47} +(0.345692 + 1.69720i) q^{48} +(-3.28758 - 6.17995i) q^{49} +(-1.82829 - 4.65375i) q^{50} +(-3.05862 - 6.13123i) q^{51} +(-0.607801 + 2.26834i) q^{52} +(-6.98049 + 1.87042i) q^{53} +(5.10977 + 0.943526i) q^{54} +(0.333350 + 0.168212i) q^{55} +(-2.56709 + 0.640332i) q^{56} +(7.08112 - 6.26765i) q^{57} +(0.574483 - 0.153932i) q^{58} +1.05296 q^{59} +(-2.75117 + 2.72600i) q^{60} -5.61224i q^{61} +(3.03670 + 3.03670i) q^{62} +(-1.10035 + 7.86061i) q^{63} +1.00000i q^{64} +(-4.98771 + 1.64219i) q^{65} +(0.0175927 - 0.288688i) q^{66} +(8.91236 - 8.91236i) q^{67} +(-1.02386 - 3.82109i) q^{68} +(1.32761 + 2.66130i) q^{69} +(-4.34291 - 4.01736i) q^{70} +9.49875 q^{71} +(2.78205 + 1.12259i) q^{72} +(1.56169 + 5.82830i) q^{73} +(-3.32349 + 1.91882i) q^{74} +(-8.46977 - 1.80637i) q^{75} +(4.72826 - 2.72986i) q^{76} +(0.441730 + 0.00766457i) q^{77} +(2.69587 + 3.04577i) q^{78} +8.67068i q^{79} +(-1.87055 + 1.22517i) q^{80} +(6.24618 - 6.47960i) q^{81} +(-2.90189 + 10.8300i) q^{82} +(1.70285 + 6.35513i) q^{83} +(-1.52829 + 4.32022i) q^{84} +(5.89314 - 6.59668i) q^{85} +(4.71763 - 8.17117i) q^{86} +(0.326650 - 0.976974i) q^{87} +(0.0432185 - 0.161294i) q^{88} +(-7.25597 - 12.5677i) q^{89} +(1.30864 + 6.57932i) q^{90} +(-4.46894 + 4.31650i) q^{91} +(0.444413 + 1.65857i) q^{92} +(7.28870 - 1.48459i) q^{93} -0.782550 q^{94} +(10.8993 + 5.49989i) q^{95} +(1.44454 + 0.955663i) q^{96} +(13.8533 - 3.71198i) q^{97} +(-6.69456 - 2.04521i) q^{98} +(-0.400211 - 0.301302i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{11} - 12 q^{15} - 192 q^{16} + 36 q^{17} - 8 q^{18} + 8 q^{23} + 36 q^{27} + 12 q^{30} + 48 q^{35} - 16 q^{36} - 12 q^{41} + 4 q^{42} + 48 q^{45} + 12 q^{46} - 16 q^{50} - 24 q^{51} - 40 q^{53}+ \cdots - 48 q^{98}+O(q^{100}) $ 192 * q + 8 * q^11 - 12 * q^15 - 192 * q^16 + 36 * q^17 - 8 * q^18 + 8 * q^23 + 36 * q^27 + 12 * q^30 + 48 * q^35 - 16 * q^36 - 12 * q^41 + 4 * q^42 + 48 * q^45 + 12 * q^46 - 16 * q^50 - 24 * q^51 - 40 * q^53 - 4 * q^56 - 32 * q^57 - 12 * q^58 - 16 * q^60 - 12 * q^63 + 16 * q^65 - 36 * q^68 + 16 * q^71 - 8 * q^72 + 96 * q^75 - 64 * q^77 - 16 * q^78 + 16 * q^81 + 168 * q^83 + 8 * q^86 - 36 * q^87 - 36 * q^90 + 8 * q^92 - 48 * q^93 - 128 * q^95 - 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.345692	−	1.69720i	−0.199585	−	0.979880i
$3$	−0.345692	−	1.69720i	−0.199585	−	0.979880i
$4$		−	1.00000i		−	0.500000i
$5$	1.87055	−	1.22517i	0.836535	−	0.547914i
$5$	1.87055	−	1.22517i	0.836535	−	0.547914i
$6$	−1.44454	−	0.955663i	−0.589733	−	0.390148i
$7$	1.36243	−	2.26799i	0.514949	−	0.857221i
$7$	1.36243	−	2.26799i	0.514949	−	0.857221i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.76099	+	1.17342i	−0.920332	+	0.391139i
$10$	0.456350	−	2.18901i	0.144310	−	0.692224i
$11$	0.0834918	+	0.144612i	0.0251737	+	0.0436022i	0.878338	−	0.478040i	$-0.158653\pi$
$11$	0.0834918	+	0.144612i	0.0251737	+	0.0436022i	−0.853164	+	0.521643i	$0.825319\pi$
$12$	−1.69720	+	0.345692i	−0.489940	+	0.0997926i
$13$	−2.26834	−	0.607801i	−0.629125	−	0.168574i	−0.0698525	−	0.997557i	$-0.522253\pi$
$13$	−2.26834	−	0.607801i	−0.629125	−	0.168574i	−0.559273	+	0.828984i	$0.688920\pi$
$14$	−0.640332	−	2.56709i	−0.171136	−	0.686085i
$15$	−2.72600	−	2.75117i	−0.703850	−	0.710349i
$16$	−1.00000			−0.250000
$17$	3.82109	−	1.02386i	0.926752	−	0.248322i	0.236283	−	0.971684i	$-0.424071\pi$
$17$	3.82109	−	1.02386i	0.926752	−	0.248322i	0.690469	+	0.723362i	$0.257404\pi$
$18$	−1.12259	+	2.78205i	−0.264596	+	0.655735i
$19$	2.72986	+	4.72826i	0.626273	+	1.08474i	0.988293	+	0.152567i	$0.0487538\pi$
$19$	2.72986	+	4.72826i	0.626273	+	1.08474i	−0.362020	+	0.932170i	$0.617913\pi$
$20$	−1.22517	−	1.87055i	−0.273957	−	0.418267i
$21$	−4.32022	−	1.52829i	−0.942750	−	0.333500i
$22$	0.161294	+	0.0432185i	0.0343879	+	0.00921422i
$23$	−1.65857	+	0.444413i	−0.345836	+	0.0926666i	−0.427556	−	0.903989i	$-0.640625\pi$
$23$	−1.65857	+	0.444413i	−0.345836	+	0.0926666i	0.0817198	+	0.996655i	$0.473959\pi$
$24$	−0.955663	+	1.44454i	−0.195074	+	0.294866i
$25$	1.99790	−	4.58349i	0.399581	−	0.916698i
$26$	−2.03374	+	1.17418i	−0.398849	+	0.230276i
$27$	2.94598	+	4.28033i	0.566954	+	0.823749i
$28$	−2.26799	−	1.36243i	−0.428610	−	0.257475i
$29$	0.515067	+	0.297374i	0.0956456	+	0.0552210i	0.547060	−	0.837093i	$-0.315747\pi$
$29$	0.515067	+	0.297374i	0.0956456	+	0.0552210i	−0.451414	+	0.892314i	$0.649080\pi$
$30$	−3.87294	−	0.0177970i	−0.707099	−	0.00324927i
$31$			4.29454i			0.771322i	0.922641	+	0.385661i	$0.126027\pi$
$31$			4.29454i			0.771322i	−0.922641	+	0.385661i	$0.873973\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	0.216573	−	0.191694i	0.0377006	−	0.0333696i
$34$	1.97794	−	3.42590i	0.339215	−	0.587537i
$35$	−0.230197	−	5.91160i	−0.0389103	−	0.999243i
$36$	1.17342	+	2.76099i	0.195570	+	0.460166i
$37$	−3.70687	−	0.993252i	−0.609405	−	0.163290i	−0.0590983	−	0.998252i	$-0.518823\pi$
$37$	−3.70687	−	0.993252i	−0.609405	−	0.163290i	−0.550307	+	0.834963i	$0.685489\pi$
$38$	5.27369	+	1.41308i	0.855505	+	0.229232i
$39$	−0.247414	+	4.05995i	−0.0396179	+	0.650112i
$40$	−2.18901	−	0.456350i	−0.346112	−	0.0721552i
$41$	−9.70992	+	5.60603i	−1.51643	+	0.875514i	−0.516621	+	0.856214i	$0.672810\pi$
$41$	−9.70992	+	5.60603i	−1.51643	+	0.875514i	−0.999814	+	0.0193001i	$0.993856\pi$
$42$	−4.13552	+	1.97420i	−0.638125	+	0.304625i
$43$	9.11376	−	2.44202i	1.38984	−	0.372405i	0.515152	−	0.857099i	$-0.327736\pi$
$43$	9.11376	−	2.44202i	1.38984	−	0.372405i	0.874684	+	0.484694i	$0.161069\pi$
$44$	0.144612	−	0.0834918i	0.0218011	−	0.0125869i
$45$	−3.72694	+	5.57763i	−0.555579	+	0.831464i
$46$	−0.858541	+	1.48704i	−0.126585	+	0.219251i
$47$	−0.553347	−	0.553347i	−0.0807139	−	0.0807139i	0.665597	−	0.746311i	$-0.268177\pi$
$47$	−0.553347	−	0.553347i	−0.0807139	−	0.0807139i	−0.746311	+	0.665597i	$0.768177\pi$
$48$	0.345692	+	1.69720i	0.0498963	+	0.244970i
$49$	−3.28758	−	6.17995i	−0.469655	−	0.882850i
$50$	−1.82829	−	4.65375i	−0.258559	−	0.658139i
$51$	−3.05862	−	6.13123i	−0.428292	−	0.858544i
$52$	−0.607801	+	2.26834i	−0.0842868	+	0.314563i
$53$	−6.98049	+	1.87042i	−0.958845	+	0.256922i	−0.704111	−	0.710090i	$-0.748654\pi$
$53$	−6.98049	+	1.87042i	−0.958845	+	0.256922i	−0.254733	+	0.967011i	$0.581988\pi$
$54$	5.10977	+	0.943526i	0.695352	+	0.128398i
$55$	0.333350	+	0.168212i	0.0449489	+	0.0226817i
$56$	−2.56709	+	0.640332i	−0.343042	+	0.0855679i
$57$	7.08112	−	6.26765i	0.937918	−	0.830170i
$58$	0.574483	−	0.153932i	0.0754333	−	0.0202123i
$59$	1.05296			0.137084			0.0685418	−	0.997648i	$-0.478165\pi$
$59$	1.05296			0.137084			0.0685418	+	0.997648i	$0.478165\pi$
$60$	−2.75117	+	2.72600i	−0.355174	+	0.351925i
$61$		−	5.61224i		−	0.718574i	−0.933227	−	0.359287i	$-0.883020\pi$
$61$		−	5.61224i		−	0.718574i	0.933227	−	0.359287i	$-0.116980\pi$
$62$	3.03670	+	3.03670i	0.385661	+	0.385661i
$63$	−1.10035	+	7.86061i	−0.138631	+	0.990344i
$64$			1.00000i			0.125000i
$65$	−4.98771	+	1.64219i	−0.618649	+	0.203689i
$66$	0.0175927	−	0.288688i	0.00216551	−	0.0355351i
$67$	8.91236	−	8.91236i	1.08882	−	1.08882i	0.0931683	−	0.995650i	$-0.470301\pi$
$67$	8.91236	−	8.91236i	1.08882	−	1.08882i	0.995650	−	0.0931683i	$-0.0296995\pi$
$68$	−1.02386	−	3.82109i	−0.124161	−	0.463376i
$69$	1.32761	+	2.66130i	0.159826	+	0.320383i
$70$	−4.34291	−	4.01736i	−0.519077	−	0.480166i
$71$	9.49875			1.12729			0.563647	−	0.826016i	$-0.309398\pi$
$71$	9.49875			1.12729			0.563647	+	0.826016i	$0.309398\pi$
$72$	2.78205	+	1.12259i	0.327868	+	0.132298i
$73$	1.56169	+	5.82830i	0.182782	+	0.682151i	0.995095	+	0.0989286i	$0.0315415\pi$
$73$	1.56169	+	5.82830i	0.182782	+	0.682151i	−0.812313	+	0.583222i	$0.801792\pi$
$74$	−3.32349	+	1.91882i	−0.386347	+	0.223058i
$75$	−8.46977	−	1.80637i	−0.978005	−	0.208582i
$76$	4.72826	−	2.72986i	0.542368	−	0.313137i
$77$	0.441730	+	0.00766457i	0.0503399	+	0.000873459i
$78$	2.69587	+	3.04577i	0.305247	+	0.344865i
$79$			8.67068i			0.975527i	0.872976	+	0.487764i	$0.162187\pi$
$79$			8.67068i			0.975527i	−0.872976	+	0.487764i	$0.837813\pi$
$80$	−1.87055	+	1.22517i	−0.209134	+	0.136978i
$81$	6.24618	−	6.47960i	0.694020	−	0.719955i
$82$	−2.90189	+	10.8300i	−0.320460	+	1.19597i
$83$	1.70285	+	6.35513i	0.186912	+	0.697566i	0.994213	+	0.107426i	$0.0342609\pi$
$83$	1.70285	+	6.35513i	0.186912	+	0.697566i	−0.807301	+	0.590140i	$0.799072\pi$
$84$	−1.52829	+	4.32022i	−0.166750	+	0.471375i
$85$	5.89314	−	6.59668i	0.639201	−	0.715510i
$86$	4.71763	−	8.17117i	0.508715	−	0.881120i
$87$	0.326650	−	0.976974i	0.0350206	−	0.104743i
$88$	0.0432185	−	0.161294i	0.00460711	−	0.0171940i
$89$	−7.25597	−	12.5677i	−0.769131	−	1.33217i	−0.938035	−	0.346542i	$-0.887356\pi$
$89$	−7.25597	−	12.5677i	−0.769131	−	1.33217i	0.168903	−	0.985633i	$-0.445977\pi$
$90$	1.30864	+	6.57932i	0.137943	+	0.693521i
$91$	−4.46894	+	4.31650i	−0.468472	+	0.452492i
$92$	0.444413	+	1.65857i	0.0463333	+	0.172918i
$93$	7.28870	−	1.48459i	0.755803	−	0.153944i
$94$	−0.782550			−0.0807139
$95$	10.8993	+	5.49989i	1.11824	+	0.564276i
$96$	1.44454	+	0.955663i	0.147433	+	0.0975369i
$97$	13.8533	−	3.71198i	1.40659	−	0.376894i	0.525882	−	0.850557i	$-0.323735\pi$
$97$	13.8533	−	3.71198i	1.40659	−	0.376894i	0.880706	+	0.473663i	$0.157069\pi$
$98$	−6.69456	−	2.04521i	−0.676252	−	0.206598i
$99$	−0.400211	−	0.301302i	−0.0402227	−	0.0302820i
$100$	−4.58349	−	1.99790i	−0.458349	−	0.199790i
$101$	−0.819090	+	0.472902i	−0.0815025	+	0.0470555i	−0.540197	−	0.841538i	$-0.681650\pi$
$101$	−0.819090	+	0.472902i	−0.0815025	+	0.0470555i	0.458695	+	0.888594i	$0.348317\pi$
$102$	−6.49821	−	2.17267i	−0.643418	−	0.215126i
$103$	3.83499	+	14.3124i	0.377873	+	1.41024i	0.849101	+	0.528230i	$0.177144\pi$
$103$	3.83499	+	14.3124i	0.377873	+	1.41024i	−0.471228	+	0.882011i	$0.656189\pi$
$104$	1.17418	+	2.03374i	0.115138	+	0.199425i
$105$	−9.95361	+	2.43428i	−0.971373	+	0.237561i
$106$	−3.61337	+	6.25854i	−0.350961	+	0.607883i
$107$	−10.1920	−	2.73094i	−0.985298	−	0.264010i	−0.270023	−	0.962854i	$-0.587031\pi$
$107$	−10.1920	−	2.73094i	−0.985298	−	0.264010i	−0.715274	+	0.698844i	$0.753698\pi$
$108$	4.28033	−	2.94598i	0.411875	−	0.283477i
$109$	16.9426	+	9.78181i	1.62281	+	0.936927i	0.986165	+	0.165766i	$0.0530097\pi$
$109$	16.9426	+	9.78181i	1.62281	+	0.936927i	0.636640	+	0.771161i	$0.280324\pi$
$110$	0.354658	−	0.116770i	0.0338153	−	0.0111336i
$111$	−0.404317	+	6.63466i	−0.0383761	+	0.629734i
$112$	−1.36243	+	2.26799i	−0.128737	+	0.214305i
$113$	−1.07718	+	4.02009i	−0.101333	+	0.378178i	−0.997903	−	0.0647222i	$-0.979384\pi$
$113$	−1.07718	+	4.02009i	−0.101333	+	0.378178i	0.896571	+	0.442901i	$0.146051\pi$
$114$	0.575214	−	9.43901i	0.0538738	−	0.884044i
$115$	−2.55796	+	2.86333i	−0.238531	+	0.267007i
$116$	0.297374	−	0.515067i	0.0276105	−	0.0478228i
$117$	6.97609	−	0.983579i	0.644939	−	0.0909319i
$118$	0.744555	−	0.744555i	0.0685418	−	0.0685418i
$119$	2.88386	−	10.0612i	0.264363	−	0.922304i
$120$	−0.0177970	+	3.87294i	−0.00162464	+	0.353550i
$121$	5.48606	−	9.50213i	0.498733	−	0.863830i
$122$	−3.96845	−	3.96845i	−0.359287	−	0.359287i
$123$	12.8712	+	14.5417i	1.16056	+	1.31119i
$124$	4.29454			0.385661
$125$	−1.87839	−	11.0214i	−0.168008	−	0.985786i
$126$	4.78023	+	6.33636i	0.425856	+	0.564488i
$127$	8.47664	−	8.47664i	0.752181	−	0.752181i	−0.222705	−	0.974886i	$-0.571489\pi$
$127$	8.47664	−	8.47664i	0.752181	−	0.752181i	0.974886	+	0.222705i	$0.0714888\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−7.29516	−	14.6237i	−0.642303	−	1.28755i
$130$	−2.36564	+	4.68805i	−0.207480	+	0.411169i
$131$	−3.17847	−	1.83509i	−0.277704	−	0.160332i	0.354680	−	0.934988i	$-0.384590\pi$
$131$	−3.17847	−	1.83509i	−0.277704	−	0.160332i	−0.632383	+	0.774655i	$0.717923\pi$
$132$	−0.191694	−	0.216573i	−0.0166848	−	0.0188503i
$133$	14.4429	+	0.250602i	1.25236	+	0.0217300i
$134$		−	12.6040i		−	1.08882i
$135$	10.7547	+	4.39723i	0.925621	+	0.378453i
$136$	−3.42590	−	1.97794i	−0.293769	−	0.169607i
$137$	19.8675	+	5.32347i	1.69739	+	0.454815i	0.972281	−	0.233815i	$-0.0751212\pi$
$137$	19.8675	+	5.32347i	1.69739	+	0.454815i	0.725112	+	0.688631i	$0.241788\pi$
$138$	2.82059	+	0.943062i	0.240105	+	0.0802787i
$139$	8.69051	+	15.0524i	0.737120	+	1.27673i	0.953787	+	0.300483i	$0.0971480\pi$
$139$	8.69051	+	15.0524i	0.737120	+	1.27673i	−0.216667	+	0.976246i	$0.569519\pi$
$140$	−5.91160	+	0.230197i	−0.499621	+	0.0194552i
$141$	−0.747854	+	1.13043i	−0.0629807	+	0.0951993i
$142$	6.71663	−	6.71663i	0.563647	−	0.563647i
$143$	−0.101493	−	0.378776i	−0.00848725	−	0.0316748i
$144$	2.76099	−	1.17342i	0.230083	−	0.0977848i
$145$	1.32779	−	0.0747935i	0.110267	−	0.00621126i
$146$	5.22551	+	3.01695i	0.432466	+	0.249684i
$147$	−9.35214	+	7.71605i	−0.771351	+	0.636409i
$148$	−0.993252	+	3.70687i	−0.0816448	+	0.304703i
$149$	−17.1519	−	9.90268i	−1.40514	−	0.811259i	−0.410228	−	0.911983i	$-0.634551\pi$
$149$	−17.1519	−	9.90268i	−1.40514	−	0.811259i	−0.994914	+	0.100724i	$0.967884\pi$
$150$	−7.26633	+	4.71173i	−0.593293	+	0.384711i
$151$	−8.41293	−	14.5716i	−0.684635	−	1.18582i	−0.973552	−	0.228468i	$-0.926628\pi$
$151$	−8.41293	−	14.5716i	−0.684635	−	1.18582i	0.288917	−	0.957354i	$-0.406705\pi$
$152$	1.41308	−	5.27369i	0.114616	−	0.427752i
$153$	−9.34861	+	7.31061i	−0.755790	+	0.591028i
$154$	0.317770	−	0.306931i	0.0256067	−	0.0247332i
$155$	5.26155	+	8.03314i	0.422618	+	0.645238i
$156$	4.05995	+	0.247414i	0.325056	+	0.0198090i
$157$	−1.26056	−	1.26056i	−0.100604	−	0.100604i	0.655013	−	0.755617i	$-0.272663\pi$
$157$	−1.26056	−	1.26056i	−0.100604	−	0.100604i	−0.755617	+	0.655013i	$0.772663\pi$
$158$	6.13110	+	6.13110i	0.487764	+	0.487764i
$159$	5.58758	+	11.2007i	0.443124	+	0.888275i
$160$	−0.456350	+	2.18901i	−0.0360776	+	0.173056i
$161$	−1.25176	+	4.36711i	−0.0986524	+	0.344177i
$162$	−0.165050	−	8.99849i	−0.0129676	−	0.706988i
$163$	−0.381715	+	1.42458i	−0.0298982	+	0.111582i	−0.979262	−	0.202596i	$-0.935062\pi$
$163$	−0.381715	+	1.42458i	−0.0298982	+	0.111582i	0.949364	+	0.314178i	$0.101729\pi$
$164$	5.60603	+	9.70992i	0.437757	+	0.758217i
$165$	0.170253	−	0.623912i	0.0132542	−	0.0485715i
$166$	5.69786	+	3.28966i	0.442239	+	0.255327i
$167$	−1.87017	+	6.97959i	−0.144718	+	0.540097i	0.855049	+	0.518547i	$0.173527\pi$
$167$	−1.87017	+	6.97959i	−0.144718	+	0.540097i	−0.999768	+	0.0215500i	$0.993140\pi$
$168$	1.97420	+	4.13552i	0.152313	+	0.319063i
$169$	−6.48237	−	3.74260i	−0.498644	−	0.287892i
$170$	−0.497478	−	8.83164i	−0.0381549	−	0.677356i
$171$	−13.0854	−	9.85143i	−1.00066	−	0.753358i
$172$	−2.44202	−	9.11376i	−0.186203	−	0.694918i
$173$	−10.4006	+	10.4006i	−0.790740	+	0.790740i	−0.981614	−	0.190875i	$-0.938868\pi$
$173$	−10.4006	+	10.4006i	−0.790740	+	0.790740i	0.190875	+	0.981614i	$0.438868\pi$
$174$	−0.459848	−	0.921801i	−0.0348610	−	0.0698816i
$175$	−7.67332	−	10.7759i	−0.580049	−	0.814582i
$176$	−0.0834918	−	0.144612i	−0.00629343	−	0.0109005i
$177$	−0.363999	−	1.78709i	−0.0273599	−	0.134326i
$178$	−14.0175	−	3.75597i	−1.05065	−	0.281522i
$179$	−7.13676	−	4.12041i	−0.533426	−	0.307974i	0.208984	−	0.977919i	$-0.432984\pi$
$179$	−7.13676	−	4.12041i	−0.533426	−	0.307974i	−0.742410	+	0.669945i	$0.766318\pi$
$180$	5.57763	+	3.72694i	0.415732	+	0.277789i
$181$			8.70366i			0.646938i	0.946239	+	0.323469i	$0.104849\pi$
$181$			8.70366i			0.646938i	−0.946239	+	0.323469i	$0.895151\pi$
$182$	−0.107790	+	6.21225i	−0.00798994	+	0.460482i
$183$	−9.52511	+	1.94010i	−0.704116	+	0.143417i
$184$	1.48704	+	0.858541i	0.109626	+	0.0632924i
$185$	−8.15078	+	2.68363i	−0.599257	+	0.197304i
$186$	4.10413	−	6.20365i	0.300929	−	0.454874i
$187$	0.467092	+	0.467092i	0.0341572	+	0.0341572i
$188$	−0.553347	+	0.553347i	−0.0403570	+	0.0403570i
$189$	13.7214	−	0.849828i	0.998088	−	0.0618159i
$190$	11.5960	−	3.81794i	0.841259	−	0.276983i
$191$	−1.49000			−0.107812			−0.0539062	−	0.998546i	$-0.517167\pi$
$191$	−1.49000			−0.107812			−0.0539062	+	0.998546i	$0.517167\pi$
$192$	1.69720	−	0.345692i	0.122485	−	0.0249481i
$193$	−13.7338	−	13.7338i	−0.988584	−	0.988584i	0.0113514	−	0.999936i	$-0.496387\pi$
$193$	−13.7338	−	13.7338i	−0.988584	−	0.988584i	−0.999936	+	0.0113514i	$0.996387\pi$
$194$	7.17099	−	12.4205i	0.514847	−	0.891741i
$195$	4.51134	+	7.89746i	0.323064	+	0.565549i
$196$	−6.17995	+	3.28758i	−0.441425	+	0.234827i
$197$	7.63439	−	7.63439i	0.543928	−	0.543928i	−0.380750	−	0.924678i	$-0.624334\pi$
$197$	7.63439	−	7.63439i	0.543928	−	0.543928i	0.924678	+	0.380750i	$0.124334\pi$
$198$	−0.496045	+	0.0699388i	−0.0352523	+	0.00497033i
$199$	5.86400	−	10.1567i	0.415688	−	0.719993i	−0.579812	−	0.814750i	$-0.696874\pi$
$199$	5.86400	−	10.1567i	0.415688	−	0.719993i	0.995500	+	0.0947573i	$0.0302075\pi$
$200$	−4.65375	+	1.82829i	−0.329070	+	0.129279i
$201$	−18.2070	−	12.0452i	−1.28422	−	0.849600i
$202$	−0.244792	+	0.913576i	−0.0172235	+	0.0642790i
$203$	1.37618	−	0.763018i	0.0965892	−	0.0535534i
$204$	−6.13123	+	3.05862i	−0.429272	+	0.214146i
$205$	−11.2945	+	22.3827i	−0.788844	+	1.56327i
$206$	12.8321	+	7.40864i	0.894057	+	0.516184i
$207$	4.05783	−	3.17322i	0.282039	−	0.220554i
$208$	2.26834	+	0.607801i	0.157281	+	0.0421434i
$209$	−0.455842	+	0.789541i	−0.0315312	+	0.0546137i
$210$	−5.31697	+	8.75956i	−0.366906	+	0.604467i
$211$	9.53792	+	16.5202i	0.656618	+	1.13730i	0.981486	+	0.191536i	$0.0613468\pi$
$211$	9.53792	+	16.5202i	0.656618	+	1.13730i	−0.324868	+	0.945759i	$0.605320\pi$
$212$	1.87042	+	6.98049i	0.128461	+	0.479422i
$213$	−3.28364	−	16.1213i	−0.224991	−	1.10461i
$214$	−9.13789	+	5.27577i	−0.624654	+	0.360644i
$215$	14.0558	−	15.7339i	0.958600	−	1.07304i
$216$	0.943526	−	5.10977i	0.0641988	−	0.347676i
$217$	9.73998	+	5.85100i	0.661193	+	0.397192i
$218$	18.8970	−	5.06344i	1.27987	−	0.342939i
$219$	9.35194	−	4.66529i	0.631945	−	0.315251i
$220$	0.168212	−	0.333350i	0.0113408	−	0.0224745i
$221$	−9.28986			−0.624903
$222$	4.40552	+	4.97731i	0.295679	+	0.334055i
$223$	1.70472	+	6.36209i	0.114156	+	0.426037i	0.999222	−	0.0394283i	$-0.0125537\pi$
$223$	1.70472	+	6.36209i	0.114156	+	0.426037i	−0.885066	+	0.465465i	$0.845887\pi$
$224$	0.640332	+	2.56709i	0.0427840	+	0.171521i
$225$	−0.137854	+	14.9994i	−0.00919024	+	0.999958i
$226$	2.08095	+	3.60431i	0.138423	+	0.239755i
$227$	−5.05588	+	18.8688i	−0.335570	+	1.25237i	0.567679	+	0.823250i	$0.307841\pi$
$227$	−5.05588	+	18.8688i	−0.335570	+	1.25237i	−0.903250	+	0.429116i	$0.858825\pi$
$228$	−6.26765	−	7.08112i	−0.415085	−	0.468959i
$229$	−9.06530	+	15.7016i	−0.599052	+	1.03759i	0.393910	+	0.919149i	$0.371122\pi$
$229$	−9.06530	+	15.7016i	−0.599052	+	1.03759i	−0.992961	+	0.118439i	$0.962211\pi$
$230$	0.215934	+	3.83343i	0.0142383	+	0.252769i
$231$	−0.139694	−	0.752356i	−0.00919120	−	0.0495014i
$232$	−0.153932	−	0.574483i	−0.0101061	−	0.0377167i
$233$	3.19471	−	11.9228i	0.209292	−	0.781089i	−0.778806	−	0.627265i	$-0.784174\pi$
$233$	3.19471	−	11.9228i	0.209292	−	0.781089i	0.988098	−	0.153824i	$-0.0491589\pi$
$234$	4.23734	−	5.62833i	0.277004	−	0.367936i
$235$	−1.71301	−	0.357117i	−0.111744	−	0.0232957i
$236$		−	1.05296i		−	0.0685418i
$237$	14.7159	−	2.99738i	0.955900	−	0.194701i
$238$	−5.07511	−	9.15350i	−0.328971	−	0.593333i
$239$	−14.3393	+	8.27882i	−0.927535	+	0.535513i	−0.886031	−	0.463626i	$-0.846548\pi$
$239$	−14.3393	+	8.27882i	−0.927535	+	0.535513i	−0.0415039	+	0.999138i	$0.513215\pi$
$240$	2.72600	+	2.75117i	0.175963	+	0.177587i
$241$	−5.30774	+	3.06443i	−0.341902	+	0.197397i	−0.661113	−	0.750287i	$-0.729916\pi$
$241$	−5.30774	+	3.06443i	−0.341902	+	0.197397i	0.319211	+	0.947684i	$0.396582\pi$
$242$	−2.83979	−	10.5983i	−0.182549	−	0.681281i
$243$	−13.1564	−	8.36110i	−0.843986	−	0.536365i
$244$	−5.61224			−0.359287
$245$	−13.7211	−	7.53204i	−0.876608	−	0.481204i
$246$	19.3839	+	1.18126i	1.23587	+	0.0753142i
$247$	−3.31842	−	12.3845i	−0.211146	−	0.788008i
$248$	3.03670	−	3.03670i	0.192830	−	0.192830i
$249$	10.1973	−	5.08700i	0.646227	−	0.322376i
$250$	−9.12154	−	6.46510i	−0.576897	−	0.408889i
$251$			13.8250i			0.872626i	0.899795	+	0.436313i	$0.143716\pi$
$251$			13.8250i			0.872626i	−0.899795	+	0.436313i	$0.856284\pi$
$252$	7.86061	+	1.10035i	0.495172	+	0.0693156i
$253$	−0.202745	−	0.202745i	−0.0127465	−	0.0127465i
$254$		−	11.9878i		−	0.752181i
$255$	−13.2331	−	7.72144i	−0.828690	−	0.483535i
$256$	1.00000			0.0625000
$257$	−14.4658	+	3.87611i	−0.902354	+	0.241785i	−0.680027	−	0.733187i	$-0.738032\pi$
$257$	−14.4658	+	3.87611i	−0.902354	+	0.241785i	−0.222327	+	0.974972i	$0.571365\pi$
$258$	−15.4990	−	5.18207i	−0.964925	−	0.322621i
$259$	−7.30302	+	7.05391i	−0.453788	+	0.438309i
$260$	1.64219	+	4.98771i	0.101844	+	0.309324i
$261$	−1.77104	−	0.216660i	−0.109625	−	0.0134109i
$262$	−3.54512	+	0.949912i	−0.219018	+	0.0586857i
$263$	−2.46690	+	9.20661i	−0.152116	+	0.567704i	0.847219	+	0.531243i	$0.178275\pi$
$263$	−2.46690	+	9.20661i	−0.152116	+	0.567704i	−0.999335	+	0.0364605i	$0.988392\pi$
$264$	−0.288688	−	0.0175927i	−0.0177675	−	0.00108276i
$265$	−10.7658	+	12.0510i	−0.661336	+	0.740288i
$266$	10.3899	−	10.0355i	0.637044	−	0.615314i
$267$	−18.8216	+	16.6594i	−1.15186	+	1.01954i
$268$	−8.91236	−	8.91236i	−0.544409	−	0.544409i
$269$	−5.21711	+	9.03630i	−0.318093	+	0.550953i	−0.980090	−	0.198553i	$-0.936376\pi$
$269$	−5.21711	+	9.03630i	−0.318093	+	0.550953i	0.661997	+	0.749506i	$0.269709\pi$
$270$	10.7141	−	4.49544i	0.652037	−	0.273584i
$271$	0.986098	−	0.569324i	0.0599012	−	0.0345840i	−0.469750	−	0.882799i	$-0.655656\pi$
$271$	0.986098	−	0.569324i	0.0599012	−	0.0345840i	0.529651	+	0.848215i	$0.322323\pi$
$272$	−3.82109	+	1.02386i	−0.231688	+	0.0620806i
$273$	8.87085	+	6.09252i	0.536888	+	0.368736i
$274$	17.8127	−	10.2842i	1.07610	−	0.621289i
$275$	0.829636	−	0.0937629i	0.0500289	−	0.00565412i
$276$	2.66130	−	1.32761i	0.160192	−	0.0799130i
$277$	16.6921	+	4.47263i	1.00293	+	0.268734i	0.722673	−	0.691191i	$-0.242913\pi$
$277$	16.6921	+	4.47263i	1.00293	+	0.268734i	0.280257	+	0.959925i	$0.409580\pi$
$278$	16.7888	+	4.49854i	1.00692	+	0.269805i
$279$	−5.03929	−	11.8572i	−0.301694	−	0.709872i
$280$	−4.01736	+	4.34291i	−0.240083	+	0.259538i
$281$	3.98217	−	6.89732i	0.237556	−	0.411460i	−0.722456	−	0.691417i	$-0.756987\pi$
$281$	3.98217	−	6.89732i	0.237556	−	0.411460i	0.960013	+	0.279957i	$0.0903202\pi$
$282$	0.270521	+	1.32815i	0.0161093	+	0.0790900i
$283$	−3.25459	+	3.25459i	−0.193465	+	0.193465i	−0.797192	−	0.603726i	$-0.793682\pi$
$283$	−3.25459	+	3.25459i	−0.193465	+	0.193465i	0.603726	+	0.797192i	$0.293682\pi$
$284$		−	9.49875i		−	0.563647i
$285$	5.56663	−	20.3995i	0.329739	−	1.20836i
$286$	−0.339601	−	0.196069i	−0.0200810	−	0.0115938i
$287$	−0.514635	+	29.6598i	−0.0303779	+	1.75076i
$288$	1.12259	−	2.78205i	0.0661490	−	0.163934i
$289$	−1.16995	+	0.675473i	−0.0688208	+	0.0397337i
$290$	0.886005	−	0.991779i	0.0520280	−	0.0582393i
$291$	−11.0889	−	22.2286i	−0.650045	−	1.30307i
$292$	5.82830	−	1.56169i	0.341075	−	0.0913908i
$293$	6.58517	+	1.76449i	0.384710	+	0.103083i	0.445990	−	0.895038i	$-0.352852\pi$
$293$	6.58517	+	1.76449i	0.384710	+	0.103083i	−0.0612803	+	0.998121i	$0.519518\pi$
$294$	−1.15689	+	12.0690i	−0.0674711	+	0.703880i
$295$	1.96961	−	1.29006i	0.114675	−	0.0751100i
$296$	1.91882	+	3.32349i	0.111529	+	0.193174i
$297$	−0.373022	+	0.783396i	−0.0216449	+	0.0454573i
$298$	−19.1305	+	5.12600i	−1.10820	+	0.296941i
$299$	4.03233			0.233195
$300$	−1.80637	+	8.46977i	−0.104291	+	0.489002i
$301$	6.87834	−	23.9970i	0.396461	−	1.38317i
$302$	−16.2525	−	4.35485i	−0.935228	−	0.250594i
$303$	1.08576	+	1.22668i	0.0623755	+	0.0704711i
$304$	−2.72986	−	4.72826i	−0.156568	−	0.271184i
$305$	−6.87596	−	10.4980i	−0.393716	−	0.601112i
$306$	−1.44108	+	11.7798i	−0.0823812	+	0.673409i
$307$	−13.2330	−	13.2330i	−0.755247	−	0.755247i	0.220206	−	0.975453i	$-0.429327\pi$
$307$	−13.2330	−	13.2330i	−0.755247	−	0.755247i	−0.975453	+	0.220206i	$0.929327\pi$
$308$	0.00766457	−	0.441730i	0.000436730	−	0.0251699i
$309$	22.9653	−	11.4564i	1.30645	−	0.651734i
$310$	9.40077	+	1.95981i	0.533928	+	0.111310i
$311$		−	28.5062i		−	1.61644i	−0.588882	−	0.808219i	$-0.700432\pi$
$311$		−	28.5062i		−	1.61644i	0.588882	−	0.808219i	$-0.299568\pi$
$312$	3.04577	−	2.69587i	0.172433	−	0.152624i
$313$	−1.73310	+	1.73310i	−0.0979608	+	0.0979608i	−0.754389	−	0.656428i	$-0.772067\pi$
$313$	−1.73310	+	1.73310i	−0.0979608	+	0.0979608i	0.656428	+	0.754389i	$0.272067\pi$
$314$	−1.78270			−0.100604
$315$	7.57235	+	16.0518i	0.426653	+	0.904415i
$316$	8.67068			0.487764
$317$	−11.6319	+	11.6319i	−0.653310	+	0.653310i	−0.953789	−	0.300479i	$-0.902854\pi$
$317$	−11.6319	+	11.6319i	−0.653310	+	0.653310i	0.300479	+	0.953789i	$0.402854\pi$
$318$	11.8711	+	3.96910i	0.665700	+	0.222576i
$319$			0.0993132i			0.00556047i
$320$	1.22517	+	1.87055i	0.0684892	+	0.104567i
$321$	−1.11167	+	18.2419i	−0.0620472	+	1.01817i
$322$	2.20289	+	3.97314i	0.122762	+	0.221415i
$323$	15.2721	+	15.2721i	0.849764	+	0.849764i
$324$	−6.47960	−	6.24618i	−0.359978	−	0.347010i
$325$	−7.31778	+	9.18260i	−0.405917	+	0.509359i
$326$	0.737417	+	1.27724i	0.0408417	+	0.0707400i
$327$	10.7448	−	32.1365i	0.594189	−	1.77715i
$328$	10.8300	+	2.90189i	0.597987	+	0.160230i
$329$	−2.00888	+	0.501092i	−0.110753	+	0.0276261i
$330$	−0.320785	−	0.561560i	−0.0176586	−	0.0309129i
$331$	6.98544			0.383955			0.191977	−	0.981399i	$-0.438510\pi$
$331$	6.98544			0.383955			0.191977	+	0.981399i	$0.438510\pi$
$332$	6.35513	−	1.70285i	0.348783	−	0.0934562i
$333$	11.4001	−	1.60734i	0.624724	−	0.0880816i
$334$	3.61290	+	6.25773i	0.197689	+	0.342408i
$335$	5.75182	−	27.5902i	0.314256	−	1.50741i
$336$	4.32022	+	1.52829i	0.235688	+	0.0833750i
$337$	−23.8402	−	6.38796i	−1.29866	−	0.347974i	−0.457716	−	0.889099i	$-0.651332\pi$
$337$	−23.8402	−	6.38796i	−1.29866	−	0.347974i	−0.840943	+	0.541124i	$0.817999\pi$
$338$	−7.23015	+	1.93731i	−0.393268	+	0.105376i
$339$	7.19528	+	0.438481i	0.390794	+	0.0238150i
$340$	−6.59668	−	5.89314i	−0.357755	−	0.319600i
$341$	−0.621042	+	0.358559i	−0.0336313	+	0.0194170i
$342$	−16.2188	+	2.28673i	−0.877010	+	0.123652i
$343$	−18.4952	−	0.963517i	−0.998646	−	0.0520250i
$344$	−8.17117	−	4.71763i	−0.440560	−	0.254358i
$345$	5.74392	+	3.35154i	0.309243	+	0.180441i
$346$			14.7086i			0.790740i
$347$	−15.0775	+	15.0775i	−0.809401	+	0.809401i	−0.984543	−	0.175142i	$-0.943961\pi$
$347$	−15.0775	+	15.0775i	−0.809401	+	0.809401i	0.175142	+	0.984543i	$0.443961\pi$
$348$	−0.976974	−	0.326650i	−0.0523713	−	0.0175103i
$349$	−11.3424	+	19.6456i	−0.607143	+	1.05160i	0.384566	+	0.923098i	$0.374351\pi$
$349$	−11.3424	+	19.6456i	−0.607143	+	1.05160i	−0.991709	+	0.128505i	$0.958982\pi$
$350$	−13.0456	−	2.19385i	−0.697315	−	0.117266i
$351$	−4.08091	−	11.4998i	−0.217823	−	0.613815i
$352$	−0.161294	−	0.0432185i	−0.00859698	−	0.00230356i
$353$	24.4310	+	6.54626i	1.30033	+	0.348422i	0.841575	−	0.540141i	$-0.181629\pi$
$353$	24.4310	+	6.54626i	1.30033	+	0.348422i	0.458755	+	0.888563i	$0.348296\pi$
$354$	−1.52105	−	1.00627i	−0.0808427	−	0.0534829i
$355$	17.7679	−	11.6376i	0.943021	−	0.617660i
$356$	−12.5677	+	7.25597i	−0.666087	+	0.384566i
$357$	−18.0727	−	1.41644i	−0.956511	−	0.0749658i
$358$	−7.96002	+	2.13288i	−0.420700	+	0.112726i
$359$	19.6461	−	11.3427i	1.03688	−	0.598643i	0.117932	−	0.993022i	$-0.462374\pi$
$359$	19.6461	−	11.3427i	1.03688	−	0.598643i	0.918948	+	0.394379i	$0.129040\pi$
$360$	6.57932	−	1.30864i	0.346761	−	0.0689713i
$361$	−5.40428	+	9.36050i	−0.284436	+	0.492658i
$362$	6.15442	+	6.15442i	0.323469	+	0.323469i
$363$	−18.0235	−	6.02615i	−0.945990	−	0.316291i
$364$	4.31650	+	4.46894i	0.226246	+	0.234236i
$365$	10.0619	+	8.98877i	0.526663	+	0.470494i
$366$	−5.36341	+	8.10713i	−0.280350	+	0.423766i
$367$	−1.75982	+	6.56775i	−0.0918620	+	0.342834i	−0.996525	−	0.0832940i	$-0.973456\pi$
$367$	−1.75982	+	6.56775i	−0.0918620	+	0.342834i	0.904663	+	0.426128i	$0.140123\pi$
$368$	1.65857	−	0.444413i	0.0864591	−	0.0231666i
$369$	20.2308	−	26.8720i	1.05318	−	1.39890i
$370$	−3.86586	+	7.66108i	−0.200977	+	0.398281i
$371$	−5.26832	+	18.3800i	−0.273518	+	0.954243i
$372$	−1.48459	−	7.28870i	−0.0769722	−	0.377902i
$373$	−28.9903	+	7.76793i	−1.50106	+	0.402208i	−0.913456	−	0.406938i	$-0.866596\pi$
$373$	−28.9903	+	7.76793i	−1.50106	+	0.402208i	−0.587606	+	0.809147i	$0.699930\pi$
$374$	0.660568			0.0341572
$375$	−18.0562	+	6.99802i	−0.932420	+	0.361376i
$376$			0.782550i			0.0403570i
$377$	−0.987605	−	0.987605i	−0.0508643	−	0.0508643i
$378$	9.10160	−	10.3034i	0.468136	−	0.529952i
$379$		−	4.98082i		−	0.255847i	−0.991784	−	0.127924i	$-0.959169\pi$
$379$		−	4.98082i		−	0.255847i	0.991784	−	0.127924i	$-0.0408313\pi$
$380$	5.49989	−	10.8993i	0.282138	−	0.559121i
$381$	−17.3169	−	11.4563i	−0.887171	−	0.586923i
$382$	−1.05359	+	1.05359i	−0.0539062	+	0.0539062i
$383$	2.67113	+	9.96881i	0.136489	+	0.509382i	0.999987	+	0.00503141i	$0.00160155\pi$
$383$	2.67113	+	9.96881i	0.136489	+	0.509382i	−0.863499	+	0.504351i	$0.831732\pi$
$384$	0.955663	−	1.44454i	0.0487685	−	0.0737166i
$385$	0.835669	−	0.526859i	0.0425896	−	0.0268512i
$386$	−19.4226			−0.988584
$387$	−22.2975	+	17.4367i	−1.13345	+	0.886355i
$388$	−3.71198	−	13.8533i	−0.188447	−	0.703294i
$389$	−7.59809	+	4.38676i	−0.385239	+	0.222418i	−0.680095	−	0.733124i	$-0.738062\pi$
$389$	−7.59809	+	4.38676i	−0.385239	+	0.222418i	0.294856	+	0.955542i	$0.404728\pi$
$390$	8.77434	+	2.39435i	0.444306	+	0.121242i
$391$	−5.88255	+	3.39629i	−0.297493	+	0.171758i
$392$	−2.04521	+	6.69456i	−0.103299	+	0.338126i
$393$	−2.01575	+	6.02888i	−0.101681	+	0.304117i
$394$		−	10.7967i		−	0.543928i
$395$	10.6231	+	16.2189i	0.534505	+	0.816063i
$396$	−0.301302	+	0.400211i	−0.0151410	+	0.0201113i
$397$	1.62839	−	6.07724i	0.0817266	−	0.305008i	−0.912948	−	0.408077i	$-0.866200\pi$
$397$	1.62839	−	6.07724i	0.0817266	−	0.305008i	0.994674	+	0.103069i	$0.0328662\pi$
$398$	−3.03543	−	11.3284i	−0.152152	−	0.567840i
$399$	−4.56746	−	24.5992i	−0.228659	−	1.23150i
$400$	−1.99790	+	4.58349i	−0.0998952	+	0.229175i
$401$	4.47946	−	7.75866i	0.223694	−	0.387449i	−0.732233	−	0.681054i	$-0.761522\pi$
$401$	4.47946	−	7.75866i	0.223694	−	0.387449i	0.955927	+	0.293605i	$0.0948552\pi$
$402$	−21.3915	+	4.35709i	−1.06691	+	0.217312i
$403$	2.61022	−	9.74149i	0.130024	−	0.485258i
$404$	0.472902	+	0.819090i	0.0235277	+	0.0407513i
$405$	3.74516	−	19.7731i	0.186098	−	0.982531i
$406$	0.433574	−	1.51265i	0.0215179	−	0.0750713i
$407$	−0.165857	−	0.618986i	−0.00822121	−	0.0306820i
$408$	−2.17267	+	6.49821i	−0.107563	+	0.321709i
$409$	0.772191			0.0381824			0.0190912	−	0.999818i	$-0.493923\pi$
$409$	0.772191			0.0381824			0.0190912	+	0.999818i	$0.493923\pi$
$410$	7.84050	+	23.8134i	0.387215	+	1.17606i
$411$	2.16700	−	35.5594i	0.106890	−	1.75402i
$412$	14.3124	−	3.83499i	0.705121	−	0.188936i
$413$	1.43458	−	2.38810i	0.0705911	−	0.117511i
$414$	0.625512	−	5.11312i	0.0307422	−	0.251296i
$415$	10.9714	+	9.80130i	0.538565	+	0.481127i
$416$	2.03374	−	1.17418i	0.0997123	−	0.0575689i
$417$	22.5428	−	19.9531i	1.10392	−	0.977105i
$418$	0.235961	+	0.880619i	0.0115412	+	0.0430725i
$419$	−9.61903	−	16.6607i	−0.469920	−	0.813926i	0.529488	−	0.848317i	$-0.322384\pi$
$419$	−9.61903	−	16.6607i	−0.469920	−	0.813926i	−0.999408	+	0.0343913i	$0.989051\pi$
$420$	2.43428	+	9.95361i	0.118781	+	0.485686i
$421$	−11.3336	+	19.6303i	−0.552364	+	0.956723i	0.445739	+	0.895163i	$0.352941\pi$
$421$	−11.3336	+	19.6303i	−0.552364	+	0.956723i	−0.998103	+	0.0615599i	$0.980392\pi$
$422$	18.4259	+	4.93719i	0.896956	+	0.240339i
$423$	2.17709	+	0.878481i	0.105854	+	0.0427132i
$424$	6.25854	+	3.61337i	0.303942	+	0.175481i
$425$	2.94133	−	19.5595i	0.142675	−	0.948776i
$426$	−13.7214	−	9.07761i	−0.664803	−	0.439811i
$427$	−12.7285	−	7.64627i	−0.615976	−	0.370029i
$428$	−2.73094	+	10.1920i	−0.132005	+	0.492649i
$429$	−0.607774	+	0.303193i	−0.0293436	+	0.0146383i
$430$	−1.18654	−	21.0645i	−0.0572203	−	1.01582i
$431$	−12.5020	+	21.6541i	−0.602200	+	1.04304i	0.390287	+	0.920693i	$0.372376\pi$
$431$	−12.5020	+	21.6541i	−0.602200	+	1.04304i	−0.992487	+	0.122348i	$0.960958\pi$
$432$	−2.94598	−	4.28033i	−0.141739	−	0.205937i
$433$	23.5662	−	23.5662i	1.13252	−	1.13252i	0.142760	−	0.989757i	$-0.454402\pi$
$433$	23.5662	−	23.5662i	1.13252	−	1.13252i	0.989757	−	0.142760i	$-0.0455976\pi$
$434$	11.0245	−	2.74993i	0.529192	−	0.132001i
$435$	−0.585947	−	2.22768i	−0.0280940	−	0.106809i
$436$	9.78181	−	16.9426i	0.468464	−	0.811403i
$437$	−6.62897	−	6.62897i	−0.317107	−	0.317107i
$438$	3.31396	−	9.91168i	0.158347	−	0.473598i
$439$	−39.0058			−1.86164			−0.930822	−	0.365474i	$-0.880907\pi$
$439$	−39.0058			−1.86164			−0.930822	+	0.365474i	$0.880907\pi$
$440$	−0.116770	−	0.354658i	−0.00556681	−	0.0169077i
$441$	16.3287	+	13.2051i	0.777555	+	0.628814i
$442$	−6.56892	+	6.56892i	−0.312452	+	0.312452i
$443$	−17.3617	−	17.3617i	−0.824879	−	0.824879i	0.161924	−	0.986803i	$-0.448230\pi$
$443$	−17.3617	−	17.3617i	−0.824879	−	0.824879i	−0.986803	+	0.161924i	$0.948230\pi$
$444$	6.63466	+	0.404317i	0.314867	+	0.0191880i
$445$	−28.9703	−	14.6187i	−1.37332	−	0.692992i
$446$	5.70409	+	3.29326i	0.270097	+	0.155940i
$447$	−10.8776	+	32.5336i	−0.514492	+	1.53879i
$448$	2.26799	+	1.36243i	0.107153	+	0.0643686i
$449$		−	10.0900i		−	0.476178i	−0.971243	−	0.238089i	$-0.923479\pi$
$449$		−	10.0900i		−	0.476178i	0.971243	−	0.238089i	$-0.0765210\pi$
$450$	10.5087	+	10.7036i	0.495384	+	0.504574i
$451$	−1.62140	−	0.936114i	−0.0763486	−	0.0440799i
$452$	4.02009	+	1.07718i	0.189089	+	0.0506663i
$453$	−21.8227	+	19.3157i	−1.02532	+	0.907532i
$454$	9.76720	+	16.9173i	0.458398	+	0.793968i
$455$	−3.07091	+	13.5494i	−0.143966	+	0.635208i
$456$	−9.43901	−	0.575214i	−0.442022	−	0.0269369i
$457$	4.16737	−	4.16737i	0.194941	−	0.194941i	−0.602886	−	0.797827i	$-0.705983\pi$
$457$	4.16737	−	4.16737i	0.194941	−	0.194941i	0.797827	+	0.602886i	$0.205983\pi$
$458$	4.69254	+	17.5128i	0.219268	+	0.818320i
$459$	15.6393	+	13.3393i	0.729981	+	0.622624i
$460$	2.86333	+	2.55796i	0.133504	+	0.119265i
$461$	−27.8161	−	16.0597i	−1.29553	−	0.747973i	−0.315898	−	0.948793i	$-0.602306\pi$
$461$	−27.8161	−	16.0597i	−1.29553	−	0.747973i	−0.979628	+	0.200820i	$0.935639\pi$
$462$	−0.630775	−	0.433217i	−0.0293463	−	0.0201551i
$463$	−0.618271	+	2.30742i	−0.0287335	+	0.107235i	−0.978803	−	0.204803i	$-0.934345\pi$
$463$	−0.618271	+	2.30742i	−0.0287335	+	0.107235i	0.950070	+	0.312037i	$0.101011\pi$
$464$	−0.515067	−	0.297374i	−0.0239114	−	0.0138053i
$465$	11.8150	−	11.7069i	0.547907	−	0.542895i
$466$	−6.17170	−	10.6897i	−0.285898	−	0.495190i
$467$	−5.64396	+	21.0635i	−0.261171	+	0.974704i	0.703381	+	0.710813i	$0.251673\pi$
$467$	−5.64396	+	21.0635i	−0.261171	+	0.974704i	−0.964552	+	0.263891i	$0.914994\pi$
$468$	−0.983579	−	6.97609i	−0.0454660	−	0.322470i
$469$	−8.07073	−	32.3556i	−0.372672	−	1.49404i
$470$	−1.46380	+	0.958759i	−0.0675200	+	0.0442243i
$471$	−1.70366	+	2.57520i	−0.0785007	+	0.118659i
$472$	−0.744555	−	0.744555i	−0.0342709	−	0.0342709i
$473$	1.11407	+	1.11407i	0.0512250	+	0.0512250i
$474$	8.28624	−	12.5252i	0.380600	−	0.575301i
$475$	27.1259	−	3.06569i	1.24462	−	0.140663i
$476$	−10.0612	−	2.88386i	−0.461152	−	0.132181i
$477$	17.0783	−	13.3552i	0.781963	−	0.611495i
$478$	−4.28543	+	15.9935i	−0.196011	+	0.731524i
$479$	19.6299	+	34.0000i	0.896914	+	1.55350i	0.831418	+	0.555648i	$0.187530\pi$
$479$	19.6299	+	34.0000i	0.896914	+	1.55350i	0.0654963	+	0.997853i	$0.479137\pi$
$480$	3.87294	+	0.0177970i	0.176775	+	0.000812318i
$481$	7.80474	+	4.50607i	0.355866	+	0.205459i
$482$	−1.58626	+	5.92002i	−0.0722524	+	0.269650i
$483$	7.84460	+	0.614814i	0.356942	+	0.0279750i
$484$	−9.50213	−	5.48606i	−0.431915	−	0.249366i
$485$	21.3654	−	23.9161i	0.970154	−	1.08597i
$486$	−15.2152	+	3.39082i	−0.690175	+	0.153811i
$487$	−6.66426	−	24.8714i	−0.301987	−	1.12703i	−0.935508	−	0.353304i	$-0.885058\pi$
$487$	−6.66426	−	24.8714i	−0.301987	−	1.12703i	0.633522	−	0.773725i	$-0.281609\pi$
$488$	−3.96845	+	3.96845i	−0.179643	+	0.179643i
$489$	2.54976	+	0.155382i	0.115304	+	0.00702664i
$490$	−15.0282	+	4.37632i	−0.678906	+	0.197702i
$491$	17.7582	+	30.7581i	0.801417	+	1.38810i	0.918683	+	0.394995i	$0.129254\pi$
$491$	17.7582	+	30.7581i	0.801417	+	1.38810i	−0.117266	+	0.993100i	$0.537413\pi$
$492$	14.5417	−	12.8712i	0.655593	−	0.580279i
$493$	2.27259	+	0.608939i	0.102352	+	0.0274252i
$494$	−11.1037	−	6.41070i	−0.499577	−	0.288431i
$495$	−1.11776	−	0.0732734i	−0.0502396	−	0.00329339i
$496$		−	4.29454i		−	0.192830i
$497$	12.9414	−	21.5431i	0.580499	−	0.966340i
$498$	3.61352	−	10.8076i	0.161926	−	0.484301i
$499$	8.89076	+	5.13308i	0.398005	+	0.229788i	0.685623	−	0.727957i	$-0.259530\pi$
$499$	8.89076	+	5.13308i	0.398005	+	0.229788i	−0.287618	+	0.957745i	$0.592863\pi$
$500$	−11.0214	+	1.87839i	−0.492893	+	0.0840042i
$501$	12.4923	+	0.761281i	0.558114	+	0.0340115i
$502$	9.77575	+	9.77575i	0.436313	+	0.436313i
$503$	28.0275	−	28.0275i	1.24968	−	1.24968i	0.293824	−	0.955860i	$-0.405072\pi$
$503$	28.0275	−	28.0275i	1.24968	−	1.24968i	0.955860	−	0.293824i	$-0.0949279\pi$
$504$	6.33636	−	4.78023i	0.282244	−	0.212928i
$505$	−0.952761	+	1.88811i	−0.0423973	+	0.0840199i
$506$	−0.286724			−0.0127465
$507$	−4.11105	+	12.2957i	−0.182578	+	0.546071i
$508$	−8.47664	−	8.47664i	−0.376090	−	0.376090i
$509$	−15.1819	+	26.2959i	−0.672927	+	1.16554i	0.304144	+	0.952626i	$0.401630\pi$
$509$	−15.1819	+	26.2959i	−0.672927	+	1.16554i	−0.977070	+	0.212917i	$0.931704\pi$
$510$	−14.8171	+	3.89734i	−0.656112	+	0.172577i
$511$	15.3462	+	4.39873i	0.678877	+	0.194589i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−12.1964	+	25.6141i	−0.538483	+	1.13089i
$514$	−7.48807	+	12.9697i	−0.330285	+	0.572070i
$515$	24.7087	+	22.0735i	1.08879	+	0.972674i
$516$	−14.6237	+	7.29516i	−0.643773	+	0.321152i
$517$	0.0338207	−	0.126220i	0.00148743	−	0.00555117i
$518$	−0.176148	+	10.1519i	−0.00773949	+	0.446048i
$519$	21.2472	+	14.0565i	0.932651	+	0.617011i
$520$	4.68805	+	2.36564i	0.205584	+	0.103740i
$521$	23.8765	+	13.7851i	1.04605	+	0.603936i	0.921540	−	0.388282i	$-0.126931\pi$
$521$	23.8765	+	13.7851i	1.04605	+	0.603936i	0.124508	+	0.992219i	$0.460265\pi$
$522$	−1.40552	+	1.09911i	−0.0615178	+	0.0481069i
$523$	−3.55053	−	0.951362i	−0.155254	−	0.0416002i	0.180355	−	0.983602i	$-0.442275\pi$
$523$	−3.55053	−	0.951362i	−0.155254	−	0.0416002i	−0.335609	+	0.942001i	$0.608942\pi$
$524$	−1.83509	+	3.17847i	−0.0801662	+	0.138852i
$525$	−15.6363	+	16.7483i	−0.682424	+	0.730957i
$526$	4.76569	+	8.25442i	0.207794	+	0.359910i
$527$	4.39700	+	16.4098i	0.191536	+	0.714824i
$528$	−0.216573	+	0.191694i	−0.00942515	+	0.00834239i
$529$	−17.3652	+	10.0258i	−0.755010	+	0.435905i
$530$	0.908809	+	16.1339i	0.0394761	+	0.700812i
$531$	−2.90722	+	1.23556i	−0.126162	+	0.0536188i
$532$	0.250602	−	14.4429i	0.0108650	−	0.626179i
$533$	25.4328	−	6.81469i	1.10162	−	0.295177i
$534$	−1.52892	+	25.0889i	−0.0661628	+	1.08570i
$535$	−22.4105	+	7.37861i	−0.968890	+	0.319005i
$536$	−12.6040			−0.544409
$537$	−4.52605	+	13.5369i	−0.195314	+	0.584161i
$538$	2.70057	+	10.0787i	0.116430	+	0.434523i
$539$	0.619209	−	0.991399i	0.0266712	−	0.0427026i
$540$	4.39723	−	10.7547i	0.189226	−	0.462810i
$541$	−17.9512	−	31.0923i	−0.771781	−	1.33676i	−0.936586	−	0.350438i	$-0.886033\pi$
$541$	−17.9512	−	31.0923i	−0.771781	−	1.33676i	0.164805	−	0.986326i	$-0.447301\pi$
$542$	0.294704	−	1.09985i	0.0126586	−	0.0472426i
$543$	14.7719	−	3.00878i	0.633922	−	0.129119i
$544$	−1.97794	+	3.42590i	−0.0848037	+	0.146884i
$545$	43.6763	−	2.46025i	1.87089	−	0.105386i
$546$	10.5807	−	1.96458i	0.452812	−	0.0840762i
$547$	−5.32856	−	19.8865i	−0.227833	−	0.850284i	−0.981250	−	0.192741i	$-0.938262\pi$
$547$	−5.32856	−	19.8865i	−0.227833	−	0.850284i	0.753417	−	0.657543i	$-0.228404\pi$
$548$	5.32347	−	19.8675i	0.227408	−	0.848697i
$549$	6.58550	+	15.4954i	0.281062	+	0.661326i
$550$	0.520341	−	0.652942i	0.0221874	−	0.0278415i
$551$			3.24716i			0.138334i
$552$	0.943062	−	2.82059i	0.0401394	−	0.120052i
$553$	19.6650	+	11.8132i	0.836242	+	0.502347i
$554$	14.9657	−	8.64046i	0.635832	−	0.367098i
$555$	7.37231	+	12.9058i	0.312937	+	0.547821i
$556$	15.0524	−	8.69051i	0.638364	−	0.368560i
$557$	1.16206	+	4.33688i	0.0492382	+	0.183759i	0.986165	−	0.165766i	$-0.0530096\pi$
$557$	1.16206	+	4.33688i	0.0492382	+	0.183759i	−0.936927	+	0.349525i	$0.886343\pi$
$558$	−11.9476	−	4.82099i	−0.505783	−	0.204089i
$559$	−22.1574			−0.937158
$560$	0.230197	+	5.91160i	0.00972759	+	0.249811i
$561$	0.631281	−	0.954220i	0.0266527	−	0.0402872i
$562$	−2.06132	−	7.69296i	−0.0869517	−	0.324508i
$563$	19.9551	−	19.9551i	0.841009	−	0.841009i	−0.147981	−	0.988990i	$-0.547277\pi$
$563$	19.9551	−	19.9551i	0.841009	−	0.841009i	0.988990	+	0.147981i	$0.0472774\pi$
$564$	1.13043	+	0.747854i	0.0475996	+	0.0314903i
$565$	2.91039	+	8.83951i	0.122441	+	0.371881i
$566$			4.60269i			0.193465i
$567$	−6.18571	−	22.9943i	−0.259776	−	0.965669i
$568$	−6.71663	−	6.71663i	−0.281824	−	0.281824i
$569$			38.1551i			1.59954i	0.600303	+	0.799772i	$0.295047\pi$
$569$			38.1551i			1.59954i	−0.600303	+	0.799772i	$0.704953\pi$
$570$	−10.4884	−	18.3609i	−0.439313	−	0.769052i
$571$	20.3768			0.852742			0.426371	−	0.904548i	$-0.359792\pi$
$571$	20.3768			0.852742			0.426371	+	0.904548i	$0.359792\pi$
$572$	−0.378776	+	0.101493i	−0.0158374	+	0.00424362i
$573$	0.515079	+	2.52883i	0.0215177	+	0.105643i
$574$	20.6088	+	21.3366i	0.860193	+	0.890571i
$575$	−1.27670	+	8.48995i	−0.0532423	+	0.354055i
$576$	−1.17342	−	2.76099i	−0.0488924	−	0.115041i
$577$	35.5963	−	9.53801i	1.48190	−	0.397073i	0.574904	−	0.818221i	$-0.305040\pi$
$577$	35.5963	−	9.53801i	1.48190	−	0.397073i	0.906992	+	0.421149i	$0.138373\pi$
$578$	−0.349650	+	1.30491i	−0.0145435	+	0.0542772i
$579$	−18.5615	+	28.0568i	−0.771388	+	1.16600i
$580$	−0.0747935	−	1.32779i	−0.00310563	−	0.0551336i
$581$	16.7334	+	4.79635i	0.694219	+	0.198986i
$582$	−23.5591	−	7.87695i	−0.976556	−	0.326510i
$583$	−0.853299	−	0.853299i	−0.0353400	−	0.0353400i
$584$	3.01695	−	5.22551i	0.124842	−	0.216233i
$585$	11.8441	−	10.3867i	0.489691	−	0.429439i
$586$	5.90410	−	3.40873i	0.243896	−	0.140814i
$587$	9.32497	−	2.49862i	0.384883	−	0.103129i	−0.0611892	−	0.998126i	$-0.519489\pi$
$587$	9.32497	−	2.49862i	0.384883	−	0.103129i	0.446072	+	0.894997i	$0.352823\pi$
$588$	7.71605	+	9.35214i	0.318205	+	0.385676i
$589$	−20.3057	+	11.7235i	−0.836681	+	0.483058i
$590$	0.480518	−	2.30493i	0.0197826	−	0.0948926i
$591$	−15.5962	−	10.3180i	−0.641544	−	0.424424i
$592$	3.70687	+	0.993252i	0.152351	+	0.0408224i
$593$	13.9646	+	3.74179i	0.573456	+	0.153657i	0.533881	−	0.845560i	$-0.320733\pi$
$593$	13.9646	+	3.74179i	0.573456	+	0.153657i	0.0395748	+	0.999217i	$0.487400\pi$
$594$	0.290179	+	0.817711i	0.0119062	+	0.0335511i
$595$	−6.93225	−	22.3531i	−0.284195	−	0.916388i
$596$	−9.90268	+	17.1519i	−0.405630	+	0.702571i
$597$	−19.2652	−	6.44130i	−0.788472	−	0.263625i
$598$	2.85129	−	2.85129i	0.116598	−	0.116598i
$599$			6.88142i			0.281167i	0.990069	+	0.140584i	$0.0448979\pi$
$599$			6.88142i			0.281167i	−0.990069	+	0.140584i	$0.955102\pi$
$600$	4.71173	+	7.26633i	0.192356	+	0.296647i
$601$	33.1921	+	19.1635i	1.35393	+	0.781693i	0.988798	−	0.149261i	$-0.0476895\pi$
$601$	33.1921	+	19.1635i	1.35393	+	0.781693i	0.365135	+	0.930955i	$0.381023\pi$
$602$	−12.1047	−	21.8322i	−0.493352	−	0.889813i
$603$	−14.1491	+	35.0649i	−0.576195	+	1.42795i
$604$	−14.5716	+	8.41293i	−0.592911	+	0.342317i
$605$	−1.37981	−	24.4956i	−0.0560974	−	0.995886i
$606$	1.63515	+	0.0996461i	0.0664233	+	0.00404784i
$607$	32.1372	−	8.61115i	1.30441	−	0.349516i	0.461294	−	0.887247i	$-0.347385\pi$
$607$	32.1372	−	8.61115i	1.30441	−	0.349516i	0.843116	+	0.537731i	$0.180719\pi$
$608$	−5.27369	−	1.41308i	−0.213876	−	0.0573080i
$609$	−1.77073	−	2.07190i	−0.0717537	−	0.0839574i
$610$	−12.2852	−	2.56114i	−0.497414	−	0.103698i
$611$	0.918856	+	1.59150i	0.0371729	+	0.0643854i
$612$	7.31061	+	9.34861i	0.295514	+	0.377895i
$613$	−1.69904	+	0.455255i	−0.0686234	+	0.0183876i	−0.292967	−	0.956122i	$-0.594643\pi$
$613$	−1.69904	+	0.455255i	−0.0686234	+	0.0183876i	0.224344	+	0.974510i	$0.427976\pi$
$614$	−18.7143			−0.755247
$615$	41.8924	+	11.4316i	1.68926	+	0.460967i
$616$	−0.306931	−	0.317770i	−0.0123666	−	0.0128033i
$617$	5.90574	+	1.58244i	0.237756	+	0.0637066i	0.375730	−	0.926729i	$-0.377392\pi$
$617$	5.90574	+	1.58244i	0.237756	+	0.0637066i	−0.137973	+	0.990436i	$0.544059\pi$
$618$	8.13800	−	24.3398i	0.327358	−	0.979092i
$619$	−1.64801	−	2.85444i	−0.0662392	−	0.114730i	0.831004	−	0.556267i	$-0.187767\pi$
$619$	−1.64801	−	2.85444i	−0.0662392	−	0.114730i	−0.897243	+	0.441537i	$0.854433\pi$
$620$	8.03314	−	5.26155i	0.322619	−	0.211309i
$621$	−6.78836	−	5.79000i	−0.272407	−	0.232345i
$622$	−20.1569	−	20.1569i	−0.808219	−	0.808219i
$623$	−38.3892	−	0.666100i	−1.53803	−	0.0266868i
$624$	0.247414	−	4.05995i	0.00990448	−	0.162528i
$625$	−17.0168	−	18.3147i	−0.680670	−	0.732590i
$626$			2.45098i			0.0979608i
$627$	1.49759	+	0.500718i	0.0598081	+	0.0199968i
$628$	−1.26056	+	1.26056i	−0.0503019	+	0.0503019i
$629$	−15.1812			−0.605316
$630$	16.7048	+	5.99586i	0.665534	+	0.238881i
$631$	−21.7142			−0.864428			−0.432214	−	0.901771i	$-0.642268\pi$
$631$	−21.7142			−0.864428			−0.432214	+	0.901771i	$0.642268\pi$
$632$	6.13110	−	6.13110i	0.243882	−	0.243882i
$633$	24.7409	−	21.8987i	0.983362	−	0.870394i
$634$			16.4499i			0.653310i
$635$	5.47062	−	26.2413i	0.217095	−	1.04136i
$636$	11.2007	−	5.58758i	0.444138	−	0.221562i
$637$	3.70119	+	16.0164i	0.146646	+	0.634595i
$638$	0.0702251	+	0.0702251i	0.00278024	+	0.00278024i
$639$	−26.2260	+	11.1460i	−1.03748	+	0.440929i
$640$	2.18901	+	0.456350i	0.0865280	+	0.0180388i
$641$	6.57338	+	11.3854i	0.259633	+	0.449698i	0.966144	−	0.258005i	$-0.0830651\pi$
$641$	6.57338	+	11.3854i	0.259633	+	0.449698i	−0.706511	+	0.707702i	$0.749732\pi$
$642$	12.1129	+	13.6851i	0.478060	+	0.540107i
$643$	13.9541	+	3.73898i	0.550295	+	0.147451i	0.523244	−	0.852183i	$-0.324722\pi$
$643$	13.9541	+	3.73898i	0.550295	+	0.147451i	0.0270510	+	0.999634i	$0.491388\pi$
$644$	4.36711	+	1.25176i	0.172088	+	0.0493262i
$645$	−31.5625	−	18.4165i	−1.24277	−	0.725150i
$646$	21.5981			0.849764
$647$	−13.4845	+	3.61315i	−0.530128	+	0.142047i	−0.513948	−	0.857822i	$-0.671817\pi$
$647$	−13.4845	+	3.61315i	−0.530128	+	0.142047i	−0.0161809	+	0.999869i	$0.505151\pi$
$648$	−8.99849	+	0.165050i	−0.353494	+	0.00648379i
$649$	0.0879135	+	0.152271i	0.00345091	+	0.00597714i
$650$	1.31863	+	11.6675i	0.0517208	+	0.457638i
$651$	6.56330	−	18.5534i	0.257236	−	0.727164i
$652$	1.42458	+	0.381715i	0.0557908	+	0.0149491i
$653$	−28.4826	+	7.63190i	−1.11461	+	0.298659i	−0.768701	−	0.639608i	$-0.779097\pi$
$653$	−28.4826	+	7.63190i	−1.11461	+	0.298659i	−0.345910	+	0.938268i	$0.612430\pi$
$654$	−15.1262	−	30.3216i	−0.591482	−	1.18567i
$655$	−8.19378	+	0.461548i	−0.320157	+	0.0180342i
$656$	9.70992	−	5.60603i	0.379109	−	0.218879i
$657$	−11.1508	−	14.2594i	−0.435036	−	0.556312i
$658$	−1.06617	+	1.77482i	−0.0415636	+	0.0691896i
$659$	9.00663	+	5.19998i	0.350849	+	0.202563i	0.665059	−	0.746791i	$-0.268406\pi$
$659$	9.00663	+	5.19998i	0.350849	+	0.202563i	−0.314210	+	0.949353i	$0.601740\pi$
$660$	−0.623912	−	0.170253i	−0.0242857	−	0.00662710i
$661$			42.2941i			1.64505i	0.568729	+	0.822525i	$0.307435\pi$
$661$			42.2941i			1.64505i	−0.568729	+	0.822525i	$0.692565\pi$
$662$	4.93945	−	4.93945i	0.191977	−	0.191977i
$663$	3.21143	+	15.7668i	0.124721	+	0.612331i
$664$	3.28966	−	5.69786i	0.127664	−	0.221120i
$665$	27.3232	−	17.2263i	1.05955	−	0.668006i
$666$	6.92455	−	9.19767i	0.268321	−	0.356403i
$667$	−0.986434	−	0.264314i	−0.0381949	−	0.0102343i
$668$	6.97959	+	1.87017i	0.270048	+	0.0723592i
$669$	10.2084	−	5.09257i	0.394681	−	0.196890i
$670$	−15.4421	−	23.5764i	−0.596579	−	0.910835i
$671$	0.811597	−	0.468576i	0.0313314	−	0.0180892i
$672$	4.13552	−	1.97420i	0.159531	−	0.0761563i
$673$	20.5230	−	5.49912i	0.791104	−	0.211976i	0.159429	−	0.987209i	$-0.449035\pi$
$673$	20.5230	−	5.49912i	0.791104	−	0.211976i	0.631674	+	0.775234i	$0.282368\pi$
$674$	−21.3745	+	12.3406i	−0.823316	+	0.475342i
$675$	25.5046	−	4.95119i	0.981673	−	0.190571i
$676$	−3.74260	+	6.48237i	−0.143946	+	0.249322i
$677$	−18.3432	−	18.3432i	−0.704985	−	0.704985i	0.260491	−	0.965476i	$-0.416115\pi$
$677$	−18.3432	−	18.3432i	−0.704985	−	0.704985i	−0.965476	+	0.260491i	$0.916115\pi$
$678$	5.39789	−	4.77778i	0.207305	−	0.183489i
$679$	10.4554	−	36.4765i	0.401240	−	1.39984i
$680$	−8.83164	+	0.497478i	−0.338678	+	0.0190774i
$681$	33.7719	+	2.05807i	1.29414	+	0.0788653i
$682$	−0.185604	+	0.692682i	−0.00710713	+	0.0265242i
$683$	−24.5633	+	6.58171i	−0.939887	+	0.251842i	−0.696066	−	0.717978i	$-0.745068\pi$
$683$	−24.5633	+	6.58171i	−0.939887	+	0.251842i	−0.243822	+	0.969820i	$0.578401\pi$
$684$	−9.85143	+	13.0854i	−0.376679	+	0.500331i
$685$	43.6853	−	14.3833i	1.66913	−	0.549557i
$686$	−13.7594	+	12.3968i	−0.525335	+	0.473310i
$687$	29.7825	+	9.95775i	1.13627	+	0.379912i
$688$	−9.11376	+	2.44202i	−0.347459	+	0.0931013i
$689$	16.9710			0.646543
$690$	6.43147	−	1.69167i	0.244842	−	0.0644008i
$691$		−	5.69649i		−	0.216705i	−0.994113	−	0.108352i	$-0.965443\pi$
$691$		−	5.69649i		−	0.216705i	0.994113	−	0.108352i	$-0.0345575\pi$
$692$	10.4006	+	10.4006i	0.395370	+	0.395370i
$693$	−1.22861	+	0.497172i	−0.0466710	+	0.0188860i
$694$			21.3228i			0.809401i
$695$	34.6978	+	17.5089i	1.31616	+	0.664150i
$696$	−0.921801	+	0.459848i	−0.0349408	+	0.0174305i
$697$	−31.3628	+	31.3628i	−1.18795	+	1.18795i
$698$	5.87124	+	21.9118i	0.222230	+	0.829373i
$699$	−21.3398	−	1.30045i	−0.807145	−	0.0491875i
$700$	−10.7759	+	7.67332i	−0.407291	+	0.290024i
$701$	−5.56170			−0.210063			−0.105031	−	0.994469i	$-0.533494\pi$
$701$	−5.56170			−0.210063			−0.105031	+	0.994469i	$0.533494\pi$
$702$	−11.0172	−	5.24596i	−0.415819	−	0.197996i
$703$	−5.42288	−	20.2385i	−0.204528	−	0.763308i
$704$	−0.144612	+	0.0834918i	−0.00545027	+	0.00314671i
$705$	−0.0139271	+	3.03077i	−0.000524523	+	0.114146i
$706$	21.9042	−	12.6464i	0.824376	−	0.475954i
$707$	−0.0434126	+	2.50198i	−0.00163270	+	0.0940968i
$708$	−1.78709	+	0.363999i	−0.0671628	+	0.0136799i
$709$			11.5991i			0.435615i	0.975992	+	0.217807i	$0.0698905\pi$
$709$			11.5991i			0.435615i	−0.975992	+	0.217807i	$0.930110\pi$
$710$	4.33475	−	20.7928i	0.162680	−	0.780341i
$711$	−10.1743	−	23.9397i	−0.381567	−	0.897809i
$712$	−3.75597	+	14.0175i	−0.140761	+	0.525326i
$713$	−1.90855	−	7.12281i	−0.0714758	−	0.266751i
$714$	−13.7809	+	11.7778i	−0.515738	+	0.440772i
$715$	−0.653913	−	0.584173i	−0.0244550	−	0.0218468i
$716$	−4.12041	+	7.13676i	−0.153987	+	0.266713i
$717$	19.0078	+	21.4749i	0.709861	+	0.801993i
$718$	5.87139	−	21.9123i	0.219118	−	0.817761i
$719$	19.2115	+	33.2753i	0.716469	+	1.24096i	0.962390	+	0.271671i	$0.0875762\pi$
$719$	19.2115	+	33.2753i	0.716469	+	1.24096i	−0.245921	+	0.969290i	$0.579091\pi$
$720$	3.72694	−	5.57763i	0.138895	−	0.207866i
$721$	37.6853	+	10.8018i	1.40347	+	0.402282i
$722$	2.79746	+	10.4403i	0.104111	+	0.388547i
$723$	7.03580	+	7.94897i	0.261664	+	0.295625i
$724$	8.70366			0.323469
$725$	2.39207	−	1.76668i	0.0888392	−	0.0656129i
$726$	−17.0057	+	8.48343i	−0.631140	+	0.314850i
$727$	−25.4538	+	6.82031i	−0.944027	+	0.252951i	−0.697826	−	0.716267i	$-0.745849\pi$
$727$	−25.4538	+	6.82031i	−0.944027	+	0.252951i	−0.246201	+	0.969219i	$0.579182\pi$
$728$	6.21225	+	0.107790i	0.230241	+	0.00399497i
$729$	−9.64240	+	25.2195i	−0.357126	+	0.934056i
$730$	13.4708	−	0.758801i	0.498578	−	0.0280845i
$731$	32.3243	−	18.6624i	1.19556	−	0.690254i
$732$	1.94010	+	9.52511i	0.0717083	+	0.352058i
$733$	8.39579	+	31.3335i	0.310106	+	1.15733i	0.928461	+	0.371431i	$0.121133\pi$
$733$	8.39579	+	31.3335i	0.310106	+	1.15733i	−0.618355	+	0.785899i	$0.712201\pi$
$734$	3.39972	+	5.88848i	0.125486	+	0.217348i
$735$	−8.04013	+	25.8912i	−0.296565	+	0.955013i
$736$	0.858541	−	1.48704i	0.0316462	−	0.0548129i
$737$	2.03294	+	0.544726i	0.0748845	+	0.0200652i
$738$	−4.69601	−	33.3067i	−0.172863	−	1.22604i
$739$	22.9824	+	13.2689i	0.845422	+	0.488104i	0.859103	−	0.511802i	$-0.171022\pi$
$739$	22.9824	+	13.2689i	0.845422	+	0.488104i	−0.0136817	+	0.999906i	$0.504355\pi$
$740$	2.68363	+	8.15078i	0.0986520	+	0.299629i
$741$	−19.8719	+	9.91326i	−0.730012	+	0.364173i
$742$	9.27137	+	16.7219i	0.340363	+	0.613880i
$743$	11.5457	−	43.0891i	0.423570	−	1.58078i	−0.343457	−	0.939169i	$-0.611598\pi$
$743$	11.5457	−	43.0891i	0.423570	−	1.58078i	0.767026	−	0.641615i	$-0.221735\pi$
$744$	−6.20365	−	4.10413i	−0.227437	−	0.150465i
$745$	−44.2160	+	2.49065i	−1.61995	+	0.0912504i
$746$	−15.0065	+	25.9920i	−0.549427	+	0.951635i
$747$	−12.1588	−	15.5483i	−0.444867	−	0.568884i
$748$	0.467092	−	0.467092i	0.0170786	−	0.0170786i
$749$	−20.0796	+	19.3947i	−0.733693	+	0.708666i
$750$	−7.81934	+	17.7160i	−0.285522	+	0.646898i
$751$	−9.09092	+	15.7459i	−0.331732	+	0.574577i	−0.982852	−	0.184398i	$-0.940966\pi$
$751$	−9.09092	+	15.7459i	−0.331732	+	0.574577i	0.651119	+	0.758975i	$0.274300\pi$
$752$	0.553347	+	0.553347i	0.0201785	+	0.0201785i
$753$	23.4638	−	4.77918i	0.855069	−	0.174163i
$754$	−1.39668			−0.0508643
$755$	−33.5895	−	16.9496i	−1.22245	−	0.616860i
$756$	−0.849828	−	13.7214i	−0.0309079	−	0.499044i
$757$	−19.1776	+	19.1776i	−0.697020	+	0.697020i	−0.963767	−	0.266747i	$-0.914051\pi$
$757$	−19.1776	+	19.1776i	−0.697020	+	0.697020i	0.266747	+	0.963767i	$0.414051\pi$
$758$	−3.52197	−	3.52197i	−0.127924	−	0.127924i
$759$	−0.274012	+	0.414186i	−0.00994600	+	0.0150340i
$760$	−3.81794	−	11.5960i	−0.138491	−	0.420629i
$761$	−40.4967	−	23.3808i	−1.46801	−	0.847553i	−0.468648	−	0.883385i	$-0.655259\pi$
$761$	−40.4967	−	23.3808i	−1.46801	−	0.847553i	−0.999358	+	0.0358318i	$0.988592\pi$
$762$	−20.3457	+	4.14408i	−0.737047	+	0.150124i
$763$	45.2681	−	25.0987i	1.63882	−	0.908633i
$764$			1.49000i			0.0539062i
$765$	−8.53027	+	25.1285i	−0.308412	+	0.908523i
$766$	8.93779	+	5.16024i	0.322936	+	0.186447i
$767$	−2.38847	−	0.639990i	−0.0862428	−	0.0231087i
$768$	−0.345692	−	1.69720i	−0.0124741	−	0.0612425i
$769$	17.6862	+	30.6333i	0.637780	+	1.10467i	0.985919	+	0.167224i	$0.0534803\pi$
$769$	17.6862	+	30.6333i	0.637780	+	1.10467i	−0.348139	+	0.937443i	$0.613186\pi$
$770$	0.218361	−	0.963453i	0.00786920	−	0.0347204i
$771$	11.5793	+	23.2115i	0.417017	+	0.835943i
$772$	−13.7338	+	13.7338i	−0.494292	+	0.494292i
$773$	−6.20664	−	23.1635i	−0.223237	−	0.833133i	−0.983103	−	0.183053i	$-0.941402\pi$
$773$	−6.20664	−	23.1635i	−0.223237	−	0.833133i	0.759866	−	0.650080i	$-0.225265\pi$
$774$	−3.43715	+	28.0963i	−0.123546	+	1.00990i
$775$	19.6840	+	8.58007i	0.707069	+	0.308205i
$776$	−12.4205	−	7.17099i	−0.445871	−	0.257424i
$777$	14.4965	+	9.95623i	0.520060	+	0.357178i
$778$	−2.27075	+	8.47457i	−0.0814105	+	0.303828i
$779$	−53.0135	−	30.6073i	−1.89940	−	1.09662i
$780$	7.89746	−	4.51134i	0.282774	−	0.161532i
$781$	0.793068	+	1.37363i	0.0283782	+	0.0491525i
$782$	−1.75805	+	6.56113i	−0.0628677	+	0.234626i
$783$	0.244519	+	3.08072i	0.00873840	+	0.110096i
$784$	3.28758	+	6.17995i	0.117414	+	0.220713i
$785$	−3.90235	−	0.813537i	−0.139281	−	0.0290364i
$786$	2.83771	+	5.68841i	0.101218	+	0.202899i
$787$	25.2411	+	25.2411i	0.899750	+	0.899750i	0.995414	−	0.0956641i	$-0.0304975\pi$
$787$	25.2411	+	25.2411i	0.899750	+	0.899750i	−0.0956641	+	0.995414i	$0.530497\pi$
$788$	−7.63439	−	7.63439i	−0.271964	−	0.271964i
$789$	16.4783	+	1.00419i	0.586642	+	0.0357500i
$790$	18.9802	+	3.95686i	0.675284	+	0.140779i
$791$	7.64996	+	7.92012i	0.272001	+	0.281607i
$792$	0.0699388	+	0.496045i	0.00248517	+	0.0176262i
$793$	−3.41112	+	12.7305i	−0.121133	+	0.452073i
$794$	−3.14581	−	5.44870i	−0.111641	−	0.193367i
$795$	24.1747	+	14.1058i	0.857387	+	0.500280i
$796$	−10.1567	−	5.86400i	−0.359996	−	0.207844i
$797$	6.46506	−	24.1279i	0.229004	−	0.854655i	−0.751757	−	0.659441i	$-0.770793\pi$
$797$	6.46506	−	24.1279i	0.229004	−	0.854655i	0.980761	−	0.195214i	$-0.0625402\pi$
$798$	−20.6239	−	14.1645i	−0.730079	−	0.501419i
$799$	−2.68094	−	1.54784i	−0.0948448	−	0.0547587i
$800$	1.82829	+	4.65375i	0.0646397	+	0.164535i
$801$	34.7809	+	26.1851i	1.22892	+	0.925205i
$802$	−2.31874	−	8.65366i	−0.0818776	−	0.305571i
$803$	−0.712454	+	0.712454i	−0.0251419	+	0.0251419i
$804$	−12.0452	+	18.2070i	−0.424800	+	0.642112i
$805$	3.00899	+	9.70252i	0.106053	+	0.341969i
$806$	−5.04256	−	8.73398i	−0.177617	−	0.307641i
$807$	17.1399	+	5.73072i	0.603354	+	0.201731i
$808$	0.913576	+	0.244792i	0.0321395	+	0.00861175i
$809$	−45.2547	−	26.1278i	−1.59107	−	0.918604i	−0.993124	−	0.117067i	$-0.962651\pi$
$809$	−45.2547	−	26.1278i	−1.59107	−	0.918604i	−0.597945	−	0.801537i	$-0.704016\pi$
$810$	−11.3334	−	16.6299i	−0.398216	−	0.584315i
$811$			3.77916i			0.132704i	0.997796	+	0.0663521i	$0.0211361\pi$
$811$			3.77916i			0.132704i	−0.997796	+	0.0663521i	$0.978864\pi$
$812$	−0.763018	−	1.37618i	−0.0267767	−	0.0482946i
$813$	−1.30714	−	1.47680i	−0.0458435	−	0.0517936i
$814$	−0.554967	−	0.320411i	−0.0194516	−	0.0112304i
$815$	1.03134	+	3.13241i	0.0361263	+	0.109724i
$816$	3.05862	+	6.13123i	0.107073	+	0.214636i
$817$	36.4258	+	36.4258i	1.27438	+	1.27438i
$818$	0.546022	−	0.546022i	0.0190912	−	0.0190912i
$819$	7.27366	−	17.1618i	0.254162	−	0.599681i
$820$	22.3827	+	11.2945i	0.781637	+	0.394422i
$821$	12.5243			0.437101			0.218551	−	0.975826i	$-0.429867\pi$
$821$	12.5243			0.437101			0.218551	+	0.975826i	$0.429867\pi$
$822$	−23.6120	−	26.6766i	−0.823563	−	0.930453i
$823$	−31.2172	−	31.2172i	−1.08816	−	1.08816i	−0.995718	−	0.0924468i	$-0.970531\pi$
$823$	−31.2172	−	31.2172i	−1.08816	−	1.08816i	−0.0924468	−	0.995718i	$-0.529469\pi$
$824$	7.40864	−	12.8321i	0.258092	−	0.447029i
$825$	−0.445933	−	1.37565i	−0.0155254	−	0.0478939i
$826$	−0.674243	−	2.70305i	−0.0234599	−	0.0940510i
$827$	5.40704	−	5.40704i	0.188021	−	0.188021i	−0.606819	−	0.794840i	$-0.707555\pi$
$827$	5.40704	−	5.40704i	0.188021	−	0.188021i	0.794840	+	0.606819i	$0.207555\pi$
$828$	−3.17322	−	4.05783i	−0.110277	−	0.141019i
$829$	−15.3365	+	26.5637i	−0.532660	+	0.922594i	0.466613	+	0.884462i	$0.345474\pi$
$829$	−15.3365	+	26.5637i	−0.532660	+	0.922594i	−0.999273	+	0.0381321i	$0.987859\pi$
$830$	14.6885	−	0.827392i	0.509846	−	0.0287192i
$831$	1.82065	−	29.8760i	0.0631576	−	1.03639i
$832$	0.607801	−	2.26834i	0.0210717	−	0.0786406i
$833$	−18.8896	−	20.2482i	−0.654485	−	0.701557i
$834$	1.83119	−	30.0491i	0.0634091	−	1.04051i
$835$	5.05295	+	15.3469i	0.174864	+	0.531103i
$836$	0.789541	+	0.455842i	0.0273069	+	0.0157656i
$837$	−18.3820	+	12.6516i	−0.635376	+	0.437304i
$838$	−18.5825	−	4.97918i	−0.641923	−	0.172003i
$839$	14.9676	−	25.9246i	0.516739	−	0.895017i	−0.483073	−	0.875580i	$-0.660479\pi$
$839$	14.9676	−	25.9246i	0.516739	−	0.895017i	0.999811	−	0.0194370i	$-0.00618739\pi$
$840$	8.75956	+	5.31697i	0.302233	+	0.183453i
$841$	−14.3231	−	24.8084i	−0.493901	−	0.855462i
$842$	5.86669	+	21.8948i	0.202179	+	0.754543i
$843$	−13.0828	−	4.37421i	−0.450594	−	0.150656i
$844$	16.5202	−	9.53792i	0.568648	−	0.328309i
$845$	−16.7109	+	0.941312i	−0.574873	+	0.0323821i
$846$	2.16062	−	0.918258i	0.0742836	−	0.0315704i
$847$	−14.0764	−	25.3883i	−0.483671	−	0.872352i
$848$	6.98049	−	1.87042i	0.239711	−	0.0642304i
$849$	6.64879	+	4.39862i	0.228186	+	0.150960i
$850$	−11.7508	−	15.9105i	−0.403050	−	0.545726i
$851$	6.58952			0.225886
$852$	−16.1213	+	3.28364i	−0.552307	+	0.112496i
$853$	−14.9862	−	55.9292i	−0.513117	−	1.91498i	−0.383942	−	0.923357i	$-0.625434\pi$
$853$	−14.9862	−	55.9292i	−0.513117	−	1.91498i	−0.129175	−	0.991622i	$-0.541233\pi$
$854$	−14.4071	+	3.59369i	−0.493002	+	0.122974i
$855$	−36.5465	−	2.39576i	−1.24986	−	0.0819332i
$856$	5.27577	+	9.13789i	0.180322	+	0.312327i
$857$	8.86459	−	33.0831i	0.302808	−	1.13010i	−0.632007	−	0.774963i	$-0.717769\pi$
$857$	8.86459	−	33.0831i	0.302808	−	1.13010i	0.934815	−	0.355134i	$-0.115565\pi$
$858$	−0.215371	+	0.644152i	−0.00735266	+	0.0219910i
$859$	−0.398786	+	0.690717i	−0.0136064	+	0.0235670i	−0.872748	−	0.488170i	$-0.837665\pi$
$859$	−0.398786	+	0.690717i	−0.0136064	+	0.0235670i	0.859142	+	0.511737i	$0.170998\pi$
$860$	−15.7339	−	14.0558i	−0.536520	−	0.479300i
$861$	50.5167	−	9.37972i	1.72160	−	0.319660i
$862$	6.47151	+	24.1520i	0.220421	+	0.822621i
$863$	9.61208	−	35.8728i	0.327199	−	1.22112i	−0.584883	−	0.811117i	$-0.698860\pi$
$863$	9.61208	−	35.8728i	0.327199	−	1.22112i	0.912083	−	0.410006i	$-0.134474\pi$
$864$	−5.10977	−	0.943526i	−0.173838	−	0.0320994i
$865$	−6.71227	+	32.1972i	−0.228224	+	1.09474i
$866$		−	33.3276i		−	1.13252i
$867$	1.55086	+	1.75214i	0.0526699	+	0.0595059i
$868$	5.85100	−	9.73998i	0.198596	−	0.330597i
$869$	−1.25388	+	0.723930i	−0.0425351	+	0.0245577i
$870$	−1.98953	−	1.16088i	−0.0674515	−	0.0393575i
$871$	−25.6332	+	14.7994i	−0.868549	+	0.501457i
$872$	−5.06344	−	18.8970i	−0.171470	−	0.639933i
$873$	−33.8932	+	26.5044i	−1.14711	+	0.897039i
$874$	−9.37479			−0.317107
$875$	−27.5557	−	10.7557i	−0.931552	−	0.363609i
$876$	−4.66529	−	9.35194i	−0.157626	−	0.315973i
$877$	5.81421	+	21.6989i	0.196332	+	0.732721i	0.991918	+	0.126880i	$0.0404964\pi$
$877$	5.81421	+	21.6989i	0.196332	+	0.732721i	−0.795586	+	0.605840i	$0.792837\pi$
$878$	−27.5812	+	27.5812i	−0.930822	+	0.930822i
$879$	0.718261	−	11.7863i	0.0242263	−	0.397543i
$880$	−0.333350	−	0.168212i	−0.0112372	−	0.00567042i
$881$		−	39.0129i		−	1.31438i	−0.753726	−	0.657189i	$-0.771745\pi$
$881$		−	39.0129i		−	1.31438i	0.753726	−	0.657189i	$-0.228255\pi$
$882$	20.8835	−	2.20869i	0.703185	−	0.0743705i
$883$	−23.4714	−	23.4714i	−0.789874	−	0.789874i	0.191599	−	0.981473i	$-0.438633\pi$
$883$	−23.4714	−	23.4714i	−0.789874	−	0.789874i	−0.981473	+	0.191599i	$0.938633\pi$
$884$			9.28986i			0.312452i
$885$	−2.87037	−	2.89687i	−0.0964863	−	0.0973772i
$886$	−24.5531			−0.824879
$887$	34.2083	−	9.16607i	1.14860	−	0.307767i	0.366196	−	0.930538i	$-0.380660\pi$
$887$	34.2083	−	9.16607i	1.14860	−	0.307767i	0.782404	+	0.622771i	$0.213993\pi$
$888$	4.97731	−	4.40552i	0.167028	−	0.147840i
$889$	−7.67616	−	30.7738i	−0.257450	−	1.03212i
$890$	−30.8220	+	10.1481i	−1.03316	+	0.340165i
$891$	1.45853	+	0.362280i	0.0488627	+	0.0121368i
$892$	6.36209	−	1.70472i	0.213018	−	0.0570781i
$893$	1.10581	−	4.12693i	0.0370044	−	0.138102i
$894$	15.3131	+	30.6963i	0.512147	+	1.02664i
$895$	−18.3979	+	1.03634i	−0.614973	+	0.0346409i
$896$	2.56709	−	0.640332i	0.0857606	−	0.0213920i
$897$	−1.39394	−	6.84368i	−0.0465424	−	0.228504i
$898$	−7.13473	−	7.13473i	−0.238089	−	0.238089i
$899$	−1.27709	+	2.21198i	−0.0425932	+	0.0737736i
$900$	14.9994	+	0.137854i	0.499979	+	0.00459512i
$901$	−24.7581	+	14.2941i	−0.824811	+	0.476205i
$902$	−1.80843	+	0.484568i	−0.0602143	+	0.0161344i
$903$	−43.1056	−	3.37837i	−1.43446	−	0.112425i
$904$	3.60431	−	2.08095i	0.119878	−	0.0692114i
$905$	10.6635	+	16.2806i	0.354466	+	0.541186i
$906$	−1.77270	+	29.0893i	−0.0588942	+	0.966427i
$907$	3.36945	+	0.902841i	0.111881	+	0.0299783i	0.314325	−	0.949315i	$-0.398222\pi$
$907$	3.36945	+	0.902841i	0.111881	+	0.0299783i	−0.202444	+	0.979294i	$0.564889\pi$
$908$	18.8688	+	5.05588i	0.626183	+	0.167785i
$909$	1.70659	−	2.26681i	0.0566041	−	0.0751855i
$910$	7.40945	+	11.7524i	0.245621	+	0.389587i
$911$	−5.27969	+	9.14468i	−0.174924	+	0.302977i	−0.940135	−	0.340803i	$-0.889301\pi$
$911$	−5.27969	+	9.14468i	−0.174924	+	0.302977i	0.765211	+	0.643779i	$0.222635\pi$
$912$	−7.08112	+	6.26765i	−0.234479	+	0.207543i
$913$	−0.776854	+	0.776854i	−0.0257101	+	0.0257101i
$914$		−	5.89356i		−	0.194941i
$915$	−15.4402	+	15.2990i	−0.510438	+	0.505768i
$916$	15.7016	+	9.06530i	0.518794	+	0.299526i
$917$	−8.49240	+	4.70857i	−0.280444	+	0.155491i
$918$	20.4910	−	1.62638i	0.676302	−	0.0536787i
$919$	52.4185	−	30.2638i	1.72913	−	0.998312i	0.835524	−	0.549454i	$-0.185164\pi$
$919$	52.4185	−	30.2638i	1.72913	−	0.998312i	0.893603	−	0.448858i	$-0.148169\pi$
$920$	3.83343	−	0.215934i	0.126385	−	0.00711913i
$921$	−17.8845	+	27.0336i	−0.589316	+	0.890788i
$922$	−31.0249	+	8.31309i	−1.02175	+	0.273777i
$923$	−21.5464	−	5.77335i	−0.709209	−	0.190032i
$924$	−0.752356	+	0.139694i	−0.0247507	+	0.00459560i
$925$	−11.9585	+	15.0060i	−0.393194	+	0.493393i
$926$	1.19441	+	2.06877i	0.0392507	+	0.0679841i
$927$	−27.3828	−	35.0164i	−0.899369	−	1.15009i
$928$	−0.574483	+	0.153932i	−0.0188583	+	0.00505307i
$929$	−32.6063			−1.06978			−0.534890	−	0.844922i	$-0.679647\pi$
$929$	−32.6063			−1.06978			−0.534890	+	0.844922i	$0.679647\pi$
$930$	0.0764299	−	16.6325i	0.00250624	−	0.545401i
$931$	20.2458	−	32.4150i	0.663528	−	1.06236i
$932$	−11.9228	−	3.19471i	−0.390544	−	0.104646i
$933$	−48.3808	+	9.85435i	−1.58392	+	0.322617i
$934$	10.9033	+	18.8851i	0.356767	+	0.617938i
$935$	1.44599	+	0.301450i	0.0472889	+	0.00985847i
$936$	−5.62833	−	4.23734i	−0.183968	−	0.138502i
$937$	−17.5113	−	17.5113i	−0.572068	−	0.572068i	0.360638	−	0.932706i	$-0.382559\pi$
$937$	−17.5113	−	17.5113i	−0.572068	−	0.572068i	−0.932706	+	0.360638i	$0.882559\pi$
$938$	−28.5858	−	17.1720i	−0.933358	−	0.560686i
$939$	3.54055	+	2.34231i	0.115541	+	0.0764384i
$940$	−0.357117	+	1.71301i	−0.0116479	+	0.0558721i
$941$			36.1704i			1.17912i	0.807725	+	0.589560i	$0.200699\pi$
$941$			36.1704i			1.17912i	−0.807725	+	0.589560i	$0.799301\pi$
$942$	0.616266	+	3.02561i	0.0200790	+	0.0985797i
$943$	13.6132	−	13.6132i	0.443307	−	0.443307i
$944$	−1.05296			−0.0342709
$945$	24.6254	−	18.4008i	0.801065	−	0.598577i
$946$	1.57553			0.0512250
$947$	−4.18856	+	4.18856i	−0.136110	+	0.136110i	−0.771879	−	0.635769i	$-0.780683\pi$
$947$	−4.18856	+	4.18856i	−0.136110	+	0.136110i	0.635769	+	0.771879i	$0.280683\pi$
$948$	−2.99738	−	14.7159i	−0.0973504	−	0.477950i
$949$		−	14.1698i		−	0.459970i
$950$	17.0132	−	21.3487i	0.551980	−	0.692643i
$951$	23.7626	+	15.7206i	0.770557	+	0.509775i
$952$	−9.15350	+	5.07511i	−0.296667	+	0.164485i
$953$	−35.5250	−	35.5250i	−1.15077	−	1.15077i	−0.986399	−	0.164370i	$-0.947441\pi$
$953$	−35.5250	−	35.5250i	−1.15077	−	1.15077i	−0.164370	−	0.986399i	$-0.552559\pi$
$954$	2.63261	−	21.5198i	0.0852340	−	0.696729i
$955$	−2.78711	+	1.82550i	−0.0901888	+	0.0590719i
$956$	8.27882	+	14.3393i	0.267756	+	0.463768i
$957$	0.168555	−	0.0343318i	0.00544860	−	0.00110979i
$958$	37.9221	+	10.1612i	1.22521	+	0.328293i
$959$	39.1416	−	37.8065i	1.26395	−	1.22083i
$960$	2.75117	−	2.72600i	0.0887936	−	0.0879813i
$961$	12.5569			0.405062
$962$	8.70506	−	2.33251i	0.280662	−	0.0752033i
$963$	31.3446	−	4.41936i	1.01006	−	0.142412i
$964$	3.06443	+	5.30774i	0.0986986	+	0.170951i
$965$	−42.5162	−	8.86349i	−1.36864	−	0.285326i
$966$	5.98171	−	5.11223i	0.192458	−	0.164483i
$967$	−3.58824	−	0.961467i	−0.115390	−	0.0309187i	0.200662	−	0.979661i	$-0.435691\pi$
$967$	−3.58824	−	0.961467i	−0.115390	−	0.0309187i	−0.316052	+	0.948742i	$0.602357\pi$
$968$	−10.5983	+	2.83979i	−0.340641	+	0.0912744i
$969$	20.6405	−	31.1993i	0.663067	−	1.00227i
$970$	−1.80360	−	32.0189i	−0.0579100	−	1.02806i
$971$	−16.6527	+	9.61441i	−0.534409	+	0.308541i	−0.742810	−	0.669502i	$-0.766507\pi$
$971$	−16.6527	+	9.61441i	−0.534409	+	0.308541i	0.208401	+	0.978043i	$0.433174\pi$
$972$	−8.36110	+	13.1564i	−0.268182	+	0.421993i
$973$	45.9790	+	0.797792i	1.47402	+	0.0255760i
$974$	−22.2991	−	12.8744i	−0.714508	−	0.412521i
$975$	18.1144	+	9.24541i	0.580126	+	0.296090i
$976$			5.61224i			0.179643i
$977$	−3.32800	+	3.32800i	−0.106472	+	0.106472i	−0.758336	−	0.651864i	$-0.773987\pi$
$977$	−3.32800	+	3.32800i	−0.106472	+	0.106472i	0.651864	+	0.758336i	$0.273987\pi$
$978$	1.91282	−	1.69308i	0.0611653	−	0.0541387i
$979$	1.21163	−	2.09860i	0.0387238	−	0.0670716i
$980$	−7.53204	+	13.7211i	−0.240602	+	0.438304i
$981$	−58.2565	−	7.12679i	−1.85999	−	0.227541i
$982$	34.3062	+	9.19233i	1.09476	+	0.293339i
$983$	−14.1871	−	3.80141i	−0.452497	−	0.121246i	0.0253705	−	0.999678i	$-0.491923\pi$
$983$	−14.1871	−	3.80141i	−0.452497	−	0.121246i	−0.477868	+	0.878432i	$0.658590\pi$
$984$	1.18126	−	19.3839i	0.0376571	−	0.617936i
$985$	4.92705	−	23.6339i	0.156989	−	0.753040i
$986$	2.03755	−	1.17638i	0.0648888	−	0.0374636i
$987$	1.54491	+	3.23626i	0.0491750	+	0.103011i
$988$	−12.3845	+	3.31842i	−0.394004	+	0.105573i
$989$	−14.0306	+	8.10055i	−0.446146	+	0.257583i
$990$	−0.842188	+	0.738564i	−0.0267665	+	0.0234731i
$991$	4.01128	−	6.94775i	0.127423	−	0.220703i	−0.795255	−	0.606276i	$-0.792663\pi$
$991$	4.01128	−	6.94775i	0.127423	−	0.220703i	0.922677	+	0.385573i	$0.125996\pi$
$992$	−3.03670	−	3.03670i	−0.0964152	−	0.0964152i
$993$	−2.41481	−	11.8557i	−0.0766316	−	0.376230i
$994$	−6.08235	−	24.3842i	−0.192921	−	0.773420i
$995$	−1.47487	−	26.1831i	−0.0467566	−	0.830060i
$996$	−5.08700	−	10.1973i	−0.161188	−	0.323113i
$997$	1.23582	−	4.61215i	0.0391389	−	0.146068i	−0.943591	−	0.331112i	$-0.892576\pi$
$997$	1.23582	−	4.61215i	0.0391389	−	0.146068i	0.982730	+	0.185044i	$0.0592428\pi$
$998$	9.91635	−	2.65708i	0.313897	−	0.0841084i
$999$	−6.66891	−	18.7927i	−0.210995	−	0.594575i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bw.a.493.34	yes	192
5.2	odd	4	inner	630.2.bw.a.367.25	yes	192
7.5	odd	6		630.2.cg.a.313.3	yes	192
9.4	even	3		630.2.cg.a.283.35	yes	192
35.12	even	12		630.2.cg.a.187.35	yes	192
45.22	odd	12		630.2.cg.a.157.3	yes	192
63.40	odd	6	inner	630.2.bw.a.103.25	✓	192
315.292	even	12	inner	630.2.bw.a.607.34	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bw.a.103.25	✓	192	63.40	odd	6	inner
630.2.bw.a.367.25	yes	192	5.2	odd	4	inner
630.2.bw.a.493.34	yes	192	1.1	even	1	trivial
630.2.bw.a.607.34	yes	192	315.292	even	12	inner
630.2.cg.a.157.3	yes	192	45.22	odd	12
630.2.cg.a.187.35	yes	192	35.12	even	12
630.2.cg.a.283.35	yes	192	9.4	even	3
630.2.cg.a.313.3	yes	192	7.5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bw (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.345692 - 1.69720i) q^{3} -1.00000i q^{4} +(1.87055 - 1.22517i) q^{5} +(-1.44454 - 0.955663i) q^{6} +(1.36243 - 2.26799i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.76099 + 1.17342i) q^{9} +(0.456350 - 2.18901i) q^{10} +(0.0834918 + 0.144612i) q^{11} +(-1.69720 + 0.345692i) q^{12} +(-2.26834 - 0.607801i) q^{13} +(-0.640332 - 2.56709i) q^{14} +(-2.72600 - 2.75117i) q^{15} -1.00000 q^{16} +(3.82109 - 1.02386i) q^{17} +(-1.12259 + 2.78205i) q^{18} +(2.72986 + 4.72826i) q^{19} +(-1.22517 - 1.87055i) q^{20} +(-4.32022 - 1.52829i) q^{21} +(0.161294 + 0.0432185i) q^{22} +(-1.65857 + 0.444413i) q^{23} +(-0.955663 + 1.44454i) q^{24} +(1.99790 - 4.58349i) q^{25} +(-2.03374 + 1.17418i) q^{26} +(2.94598 + 4.28033i) q^{27} +(-2.26799 - 1.36243i) q^{28} +(0.515067 + 0.297374i) q^{29} +(-3.87294 - 0.0177970i) q^{30} +4.29454i q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.216573 - 0.191694i) q^{33} +(1.97794 - 3.42590i) q^{34} +(-0.230197 - 5.91160i) q^{35} +(1.17342 + 2.76099i) q^{36} +(-3.70687 - 0.993252i) q^{37} +(5.27369 + 1.41308i) q^{38} +(-0.247414 + 4.05995i) q^{39} +(-2.18901 - 0.456350i) q^{40} +(-9.70992 + 5.60603i) q^{41} +(-4.13552 + 1.97420i) q^{42} +(9.11376 - 2.44202i) q^{43} +(0.144612 - 0.0834918i) q^{44} +(-3.72694 + 5.57763i) q^{45} +(-0.858541 + 1.48704i) q^{46} +(-0.553347 - 0.553347i) q^{47} +(0.345692 + 1.69720i) q^{48} +(-3.28758 - 6.17995i) q^{49} +(-1.82829 - 4.65375i) q^{50} +(-3.05862 - 6.13123i) q^{51} +(-0.607801 + 2.26834i) q^{52} +(-6.98049 + 1.87042i) q^{53} +(5.10977 + 0.943526i) q^{54} +(0.333350 + 0.168212i) q^{55} +(-2.56709 + 0.640332i) q^{56} +(7.08112 - 6.26765i) q^{57} +(0.574483 - 0.153932i) q^{58} +1.05296 q^{59} +(-2.75117 + 2.72600i) q^{60} -5.61224i q^{61} +(3.03670 + 3.03670i) q^{62} +(-1.10035 + 7.86061i) q^{63} +1.00000i q^{64} +(-4.98771 + 1.64219i) q^{65} +(0.0175927 - 0.288688i) q^{66} +(8.91236 - 8.91236i) q^{67} +(-1.02386 - 3.82109i) q^{68} +(1.32761 + 2.66130i) q^{69} +(-4.34291 - 4.01736i) q^{70} +9.49875 q^{71} +(2.78205 + 1.12259i) q^{72} +(1.56169 + 5.82830i) q^{73} +(-3.32349 + 1.91882i) q^{74} +(-8.46977 - 1.80637i) q^{75} +(4.72826 - 2.72986i) q^{76} +(0.441730 + 0.00766457i) q^{77} +(2.69587 + 3.04577i) q^{78} +8.67068i q^{79} +(-1.87055 + 1.22517i) q^{80} +(6.24618 - 6.47960i) q^{81} +(-2.90189 + 10.8300i) q^{82} +(1.70285 + 6.35513i) q^{83} +(-1.52829 + 4.32022i) q^{84} +(5.89314 - 6.59668i) q^{85} +(4.71763 - 8.17117i) q^{86} +(0.326650 - 0.976974i) q^{87} +(0.0432185 - 0.161294i) q^{88} +(-7.25597 - 12.5677i) q^{89} +(1.30864 + 6.57932i) q^{90} +(-4.46894 + 4.31650i) q^{91} +(0.444413 + 1.65857i) q^{92} +(7.28870 - 1.48459i) q^{93} -0.782550 q^{94} +(10.8993 + 5.49989i) q^{95} +(1.44454 + 0.955663i) q^{96} +(13.8533 - 3.71198i) q^{97} +(-6.69456 - 2.04521i) q^{98} +(-0.400211 - 0.301302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{11} - 12 q^{15} - 192 q^{16} + 36 q^{17} - 8 q^{18} + 8 q^{23} + 36 q^{27} + 12 q^{30} + 48 q^{35} - 16 q^{36} - 12 q^{41} + 4 q^{42} + 48 q^{45} + 12 q^{46} - 16 q^{50} - 24 q^{51} - 40 q^{53}+ \cdots - 48 q^{98}+O(q^{100}) \) 192 * q + 8 * q^11 - 12 * q^15 - 192 * q^16 + 36 * q^17 - 8 * q^18 + 8 * q^23 + 36 * q^27 + 12 * q^30 + 48 * q^35 - 16 * q^36 - 12 * q^41 + 4 * q^42 + 48 * q^45 + 12 * q^46 - 16 * q^50 - 24 * q^51 - 40 * q^53 - 4 * q^56 - 32 * q^57 - 12 * q^58 - 16 * q^60 - 12 * q^63 + 16 * q^65 - 36 * q^68 + 16 * q^71 - 8 * q^72 + 96 * q^75 - 64 * q^77 - 16 * q^78 + 16 * q^81 + 168 * q^83 + 8 * q^86 - 36 * q^87 - 36 * q^90 + 8 * q^92 - 48 * q^93 - 128 * q^95 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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