LMFDB - Embedded newform 630.2.bw.a.493.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(103,630)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.03057532734$
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			493.8
Character	$\chi$	$=$	630.493
Dual form			630.2.bw.a.607.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.09051 - 1.34565i) q^{3} -1.00000i q^{4} +(2.03537 + 0.925883i) q^{5} +(1.72263 + 0.180414i) q^{6} +(1.84497 - 1.89634i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.621572 + 2.93490i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.09051 - 1.34565i) q^{3} -1.00000i q^{4} +(2.03537 + 0.925883i) q^{5} +(1.72263 + 0.180414i) q^{6} +(1.84497 - 1.89634i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.621572 + 2.93490i) q^{9} +(-2.09392 + 0.784528i) q^{10} +(2.76648 + 4.79168i) q^{11} +(-1.34565 + 1.09051i) q^{12} +(-0.576893 - 0.154578i) q^{13} +(0.0363208 + 2.64550i) q^{14} +(-0.973677 - 3.74859i) q^{15} -1.00000 q^{16} +(-4.09100 + 1.09618i) q^{17} +(-1.63577 - 2.51481i) q^{18} +(-0.379130 - 0.656672i) q^{19} +(0.925883 - 2.03537i) q^{20} +(-4.56377 - 0.414718i) q^{21} +(-5.34443 - 1.43204i) q^{22} +(7.83955 - 2.10060i) q^{23} +(0.180414 - 1.72263i) q^{24} +(3.28548 + 3.76903i) q^{25} +(0.517228 - 0.298622i) q^{26} +(4.62719 - 2.36412i) q^{27} +(-1.89634 - 1.84497i) q^{28} +(-2.66805 - 1.54040i) q^{29} +(3.33915 + 1.96216i) q^{30} +4.56695i q^{31} +(0.707107 - 0.707107i) q^{32} +(3.43107 - 8.94811i) q^{33} +(2.11766 - 3.66789i) q^{34} +(5.51098 - 2.15152i) q^{35} +(2.93490 + 0.621572i) q^{36} +(4.38152 + 1.17402i) q^{37} +(0.732423 + 0.196252i) q^{38} +(0.421100 + 0.944868i) q^{39} +(0.784528 + 2.09392i) q^{40} +(1.09609 - 0.632830i) q^{41} +(3.52032 - 2.93382i) q^{42} +(-5.79107 + 1.55171i) q^{43} +(4.79168 - 2.76648i) q^{44} +(-3.98251 + 5.39812i) q^{45} +(-4.05805 + 7.02875i) q^{46} +(6.11165 + 6.11165i) q^{47} +(1.09051 + 1.34565i) q^{48} +(-0.192174 - 6.99736i) q^{49} +(-4.98830 - 0.341922i) q^{50} +(5.93636 + 4.30968i) q^{51} +(-0.154578 + 0.576893i) q^{52} +(9.41113 - 2.52171i) q^{53} +(-1.60023 + 4.94361i) q^{54} +(1.19428 + 12.3143i) q^{55} +(2.64550 - 0.0363208i) q^{56} +(-0.470209 + 1.22629i) q^{57} +(2.97582 - 0.797370i) q^{58} -2.61806 q^{59} +(-3.74859 + 0.973677i) q^{60} -2.26791i q^{61} +(-3.22932 - 3.22932i) q^{62} +(4.41878 + 6.59351i) q^{63} +1.00000i q^{64} +(-1.03107 - 0.848760i) q^{65} +(3.90113 + 8.75341i) q^{66} +(6.41710 - 6.41710i) q^{67} +(1.09618 + 4.09100i) q^{68} +(-11.3758 - 8.25860i) q^{69} +(-2.37550 + 5.41821i) q^{70} +14.8926 q^{71} +(-2.51481 + 1.63577i) q^{72} +(-3.56908 - 13.3200i) q^{73} +(-3.92836 + 2.26804i) q^{74} +(1.48896 - 8.53129i) q^{75} +(-0.656672 + 0.379130i) q^{76} +(14.1907 + 3.59434i) q^{77} +(-0.965885 - 0.370360i) q^{78} +9.40606i q^{79} +(-2.03537 - 0.925883i) q^{80} +(-8.22730 - 3.64850i) q^{81} +(-0.327577 + 1.22253i) q^{82} +(-0.834627 - 3.11487i) q^{83} +(-0.414718 + 4.56377i) q^{84} +(-9.34165 - 1.55665i) q^{85} +(2.99768 - 5.19213i) q^{86} +(0.836693 + 5.27010i) q^{87} +(-1.43204 + 5.34443i) q^{88} +(1.82145 + 3.15484i) q^{89} +(-1.00099 - 6.63310i) q^{90} +(-1.35748 + 0.808791i) q^{91} +(-2.10060 - 7.83955i) q^{92} +(6.14553 - 4.98031i) q^{93} -8.64318 q^{94} +(-0.163669 - 1.68760i) q^{95} +(-1.72263 - 0.180414i) q^{96} +(-5.85017 + 1.56755i) q^{97} +(5.08377 + 4.81199i) q^{98} +(-15.7827 + 5.14097i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * 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} - 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}+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

Display 100 coefficients 10 coefficients

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
$3$	−1.09051	−	1.34565i	−0.629607	−	0.776914i
$3$	−1.09051	−	1.34565i	−0.629607	−	0.776914i
$4$		−	1.00000i		−	0.500000i
$5$	2.03537	+	0.925883i	0.910246	+	0.414067i
$5$	2.03537	+	0.925883i	0.910246	+	0.414067i
$6$	1.72263	+	0.180414i	0.703260	+	0.0736536i
$7$	1.84497	−	1.89634i	0.697333	−	0.716747i
$7$	1.84497	−	1.89634i	0.697333	−	0.716747i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−0.621572	+	2.93490i	−0.207191	+	0.978301i
$10$	−2.09392	+	0.784528i	−0.662157	+	0.248089i
$11$	2.76648	+	4.79168i	0.834125	+	1.44475i	0.894741	+	0.446586i	$0.147360\pi$
$11$	2.76648	+	4.79168i	0.834125	+	1.44475i	−0.0606156	+	0.998161i	$0.519306\pi$
$12$	−1.34565	+	1.09051i	−0.388457	+	0.314803i
$13$	−0.576893	−	0.154578i	−0.160001	−	0.0428723i	0.177929	−	0.984043i	$-0.443060\pi$
$13$	−0.576893	−	0.154578i	−0.160001	−	0.0428723i	−0.337931	+	0.941171i	$0.609727\pi$
$14$	0.0363208	+	2.64550i	0.00970715	+	0.707040i
$15$	−0.973677	−	3.74859i	−0.251402	−	0.967883i
$16$	−1.00000			−0.250000
$17$	−4.09100	+	1.09618i	−0.992214	+	0.265863i	−0.718180	−	0.695857i	$-0.755025\pi$
$17$	−4.09100	+	1.09618i	−0.992214	+	0.265863i	−0.274034	+	0.961720i	$0.588358\pi$
$18$	−1.63577	−	2.51481i	−0.385555	−	0.592746i
$19$	−0.379130	−	0.656672i	−0.0869784	−	0.150651i	0.819254	−	0.573431i	$-0.194388\pi$
$19$	−0.379130	−	0.656672i	−0.0869784	−	0.150651i	−0.906233	+	0.422780i	$0.861054\pi$
$20$	0.925883	−	2.03537i	0.207034	−	0.455123i
$21$	−4.56377	−	0.414718i	−0.995897	−	0.0904988i
$22$	−5.34443	−	1.43204i	−1.13944	−	0.305311i
$23$	7.83955	−	2.10060i	1.63466	−	0.438006i	0.679398	−	0.733770i	$-0.262241\pi$
$23$	7.83955	−	2.10060i	1.63466	−	0.438006i	0.955261	+	0.295764i	$0.0955743\pi$
$24$	0.180414	−	1.72263i	0.0368268	−	0.351630i
$25$	3.28548	+	3.76903i	0.657096	+	0.753807i
$26$	0.517228	−	0.298622i	0.101437	−	0.0585646i
$27$	4.62719	−	2.36412i	0.890504	−	0.454975i
$28$	−1.89634	−	1.84497i	−0.358374	−	0.348666i
$29$	−2.66805	−	1.54040i	−0.495445	−	0.286045i	0.231386	−	0.972862i	$-0.425674\pi$
$29$	−2.66805	−	1.54040i	−0.495445	−	0.286045i	−0.726830	+	0.686817i	$0.759007\pi$
$30$	3.33915	+	1.96216i	0.609643	+	0.358240i
$31$			4.56695i			0.820248i	0.912030	+	0.410124i	$0.134515\pi$
$31$			4.56695i			0.820248i	−0.912030	+	0.410124i	$0.865485\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	3.43107	−	8.94811i	0.597273	−	1.55767i
$34$	2.11766	−	3.66789i	0.363175	−	0.629038i
$35$	5.51098	−	2.15152i	0.931526	−	0.363674i
$36$	2.93490	+	0.621572i	0.489150	+	0.103595i
$37$	4.38152	+	1.17402i	0.720317	+	0.193008i	0.600313	−	0.799765i	$-0.295043\pi$
$37$	4.38152	+	1.17402i	0.720317	+	0.193008i	0.120004	+	0.992773i	$0.461709\pi$
$38$	0.732423	+	0.196252i	0.118815	+	0.0318363i
$39$	0.421100	+	0.944868i	0.0674299	+	0.151300i
$40$	0.784528	+	2.09392i	0.124045	+	0.331078i
$41$	1.09609	−	0.632830i	0.171181	−	0.0988314i	−0.411962	−	0.911201i	$-0.635156\pi$
$41$	1.09609	−	0.632830i	0.171181	−	0.0988314i	0.583143	+	0.812370i	$0.301823\pi$
$42$	3.52032	−	2.93382i	0.543198	−	0.452699i
$43$	−5.79107	+	1.55171i	−0.883130	+	0.236634i	−0.671757	−	0.740771i	$-0.734460\pi$
$43$	−5.79107	+	1.55171i	−0.883130	+	0.236634i	−0.211373	+	0.977405i	$0.567793\pi$
$44$	4.79168	−	2.76648i	0.722374	−	0.417063i
$45$	−3.98251	+	5.39812i	−0.593677	+	0.804704i
$46$	−4.05805	+	7.02875i	−0.598327	+	1.03633i
$47$	6.11165	+	6.11165i	0.891476	+	0.891476i	0.994662	−	0.103186i	$-0.0329038\pi$
$47$	6.11165	+	6.11165i	0.891476	+	0.891476i	−0.103186	+	0.994662i	$0.532904\pi$
$48$	1.09051	+	1.34565i	0.157402	+	0.194228i
$49$	−0.192174	−	6.99736i	−0.0274534	−	0.999623i
$50$	−4.98830	−	0.341922i	−0.705451	−	0.0483551i
$51$	5.93636	+	4.30968i	0.831257	+	0.603476i
$52$	−0.154578	+	0.576893i	−0.0214361	+	0.0800007i
$53$	9.41113	−	2.52171i	1.29272	−	0.346383i	0.454026	−	0.890988i	$-0.349987\pi$
$53$	9.41113	−	2.52171i	1.29272	−	0.346383i	0.838692	+	0.544606i	$0.183321\pi$
$54$	−1.60023	+	4.94361i	−0.217764	+	0.672740i
$55$	1.19428	+	12.3143i	0.161037	+	1.66046i
$56$	2.64550	−	0.0363208i	0.353520	−	0.00485358i
$57$	−0.470209	+	1.22629i	−0.0622807	+	0.162426i
$58$	2.97582	−	0.797370i	0.390745	−	0.104700i
$59$	−2.61806			−0.340842			−0.170421	−	0.985371i	$-0.554513\pi$
$59$	−2.61806			−0.340842			−0.170421	+	0.985371i	$0.554513\pi$
$60$	−3.74859	+	0.973677i	−0.483941	+	0.125701i
$61$		−	2.26791i		−	0.290376i	−0.989404	−	0.145188i	$-0.953621\pi$
$61$		−	2.26791i		−	0.290376i	0.989404	−	0.145188i	$-0.0463787\pi$
$62$	−3.22932	−	3.22932i	−0.410124	−	0.410124i
$63$	4.41878	+	6.59351i	0.556713	+	0.830705i
$64$			1.00000i			0.125000i
$65$	−1.03107	−	0.848760i	−0.127889	−	0.105276i
$66$	3.90113	+	8.75341i	0.480196	+	1.07747i
$67$	6.41710	−	6.41710i	0.783974	−	0.783974i	−0.196525	−	0.980499i	$-0.562966\pi$
$67$	6.41710	−	6.41710i	0.783974	−	0.783974i	0.980499	+	0.196525i	$0.0629658\pi$
$68$	1.09618	+	4.09100i	0.132931	+	0.496107i
$69$	−11.3758	−	8.25860i	−1.36948	−	0.994218i
$70$	−2.37550	+	5.41821i	−0.283926	+	0.647600i
$71$	14.8926			1.76743			0.883713	−	0.468030i	$-0.155036\pi$
$71$	14.8926			1.76743			0.883713	+	0.468030i	$0.155036\pi$
$72$	−2.51481	+	1.63577i	−0.296373	+	0.192777i
$73$	−3.56908	−	13.3200i	−0.417729	−	1.55899i	−0.779306	−	0.626644i	$-0.784428\pi$
$73$	−3.56908	−	13.3200i	−0.417729	−	1.55899i	0.361577	−	0.932342i	$-0.382239\pi$
$74$	−3.92836	+	2.26804i	−0.456663	+	0.263654i
$75$	1.48896	−	8.53129i	0.171931	−	0.985109i
$76$	−0.656672	+	0.379130i	−0.0753255	+	0.0434892i
$77$	14.1907	+	3.59434i	1.61718	+	0.409613i
$78$	−0.965885	−	0.370360i	−0.109365	−	0.0419350i
$79$			9.40606i			1.05826i	0.848539	+	0.529132i	$0.177482\pi$
$79$			9.40606i			1.05826i	−0.848539	+	0.529132i	$0.822518\pi$
$80$	−2.03537	−	0.925883i	−0.227562	−	0.103517i
$81$	−8.22730	−	3.64850i	−0.914144	−	0.405389i
$82$	−0.327577	+	1.22253i	−0.0361748	+	0.135006i
$83$	−0.834627	−	3.11487i	−0.0916122	−	0.341901i	0.904872	−	0.425684i	$-0.139967\pi$
$83$	−0.834627	−	3.11487i	−0.0916122	−	0.341901i	−0.996484	+	0.0837827i	$0.973300\pi$
$84$	−0.414718	+	4.56377i	−0.0452494	+	0.497948i
$85$	−9.34165	−	1.55665i	−1.01324	−	0.168843i
$86$	2.99768	−	5.19213i	0.323248	−	0.559882i
$87$	0.836693	+	5.27010i	0.0897029	+	0.565014i
$88$	−1.43204	+	5.34443i	−0.152655	+	0.569718i
$89$	1.82145	+	3.15484i	0.193073	+	0.334413i	0.946267	−	0.323386i	$-0.104821\pi$
$89$	1.82145	+	3.15484i	0.193073	+	0.334413i	−0.753194	+	0.657798i	$0.771488\pi$
$90$	−1.00099	−	6.63310i	−0.105513	−	0.699190i
$91$	−1.35748	+	0.808791i	−0.142303	+	0.0847844i
$92$	−2.10060	−	7.83955i	−0.219003	−	0.817329i
$93$	6.14553	−	4.98031i	0.637262	−	0.516434i
$94$	−8.64318			−0.891476
$95$	−0.163669	−	1.68760i	−0.0167921	−	0.173144i
$96$	−1.72263	−	0.180414i	−0.175815	−	0.0184134i
$97$	−5.85017	+	1.56755i	−0.593995	+	0.159160i	−0.543278	−	0.839553i	$-0.682817\pi$
$97$	−5.85017	+	1.56755i	−0.593995	+	0.159160i	−0.0507164	+	0.998713i	$0.516150\pi$
$98$	5.08377	+	4.81199i	0.513538	+	0.486085i
$99$	−15.7827	+	5.14097i	−1.58622	+	0.516687i
$100$	3.76903	−	3.28548i	0.376903	−	0.328548i
$101$	−9.80712	+	5.66214i	−0.975845	+	0.563404i	−0.901013	−	0.433792i	$-0.857175\pi$
$101$	−9.80712	+	5.66214i	−0.975845	+	0.563404i	−0.0748319	+	0.997196i	$0.523842\pi$
$102$	−7.24505	+	1.15024i	−0.717366	+	0.113891i
$103$	−2.22088	−	8.28844i	−0.218830	−	0.816684i	−0.984783	−	0.173788i	$-0.944399\pi$
$103$	−2.22088	−	8.28844i	−0.218830	−	0.816684i	0.765953	−	0.642896i	$-0.222267\pi$
$104$	−0.298622	−	0.517228i	−0.0292823	−	0.0507184i
$105$	−8.90499	−	5.06962i	−0.869038	−	0.494745i
$106$	−4.87156	+	8.43779i	−0.473168	+	0.819551i
$107$	−13.5347	−	3.62662i	−1.30845	−	0.350599i	−0.463813	−	0.885933i	$-0.653519\pi$
$107$	−13.5347	−	3.62662i	−1.30845	−	0.350599i	−0.844640	+	0.535334i	$0.820186\pi$
$108$	−2.36412	−	4.62719i	−0.227488	−	0.445252i
$109$	−2.68836	−	1.55212i	−0.257498	−	0.148667i	0.365695	−	0.930735i	$-0.380831\pi$
$109$	−2.68836	−	1.55212i	−0.257498	−	0.148667i	−0.623193	+	0.782068i	$0.714165\pi$
$110$	−9.55201	−	7.86304i	−0.910748	−	0.749712i
$111$	−3.19826	−	7.17629i	−0.303566	−	0.681144i
$112$	−1.84497	+	1.89634i	−0.174333	+	0.179187i
$113$	1.82983	−	6.82903i	0.172136	−	0.642421i	−0.824886	−	0.565300i	$-0.808760\pi$
$113$	1.82983	−	6.82903i	0.172136	−	0.642421i	0.997022	−	0.0771212i	$-0.0245728\pi$
$114$	−0.534628	−	1.19960i	−0.0500725	−	0.112353i
$115$	17.9013	+	2.98300i	1.66931	+	0.278166i
$116$	−1.54040	+	2.66805i	−0.143023	+	0.247722i
$117$	0.812252	−	1.59704i	0.0750928	−	0.147647i
$118$	1.85125	−	1.85125i	0.170421	−	0.170421i
$119$	−5.46905	+	9.78033i	−0.501347	+	0.896562i
$120$	1.96216	−	3.33915i	0.179120	−	0.304821i
$121$	−9.80682	+	16.9859i	−0.891529	+	1.54417i
$122$	1.60366	+	1.60366i	0.145188	+	0.145188i
$123$	−2.04687	−	0.784855i	−0.184560	−	0.0707680i
$124$	4.56695			0.410124
$125$	3.19750	+	10.7134i	0.285993	+	0.958232i
$126$	−7.78686	−	1.53777i	−0.693709	−	0.136996i
$127$	−1.67255	+	1.67255i	−0.148415	+	0.148415i	−0.777410	−	0.628995i	$-0.783467\pi$
$127$	−1.67255	+	1.67255i	−0.148415	+	0.148415i	0.628995	+	0.777410i	$0.283467\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	8.40330	+	6.10062i	0.739869	+	0.537130i
$130$	1.32924	−	0.128914i	0.116582	−	0.0113065i
$131$	3.36134	+	1.94067i	0.293682	+	0.169557i	0.639601	−	0.768707i	$-0.279100\pi$
$131$	3.36134	+	1.94067i	0.293682	+	0.169557i	−0.345919	+	0.938264i	$0.612433\pi$
$132$	−8.94811	−	3.43107i	−0.778833	−	0.298637i
$133$	−1.94475	−	0.492583i	−0.168632	−	0.0427124i
$134$			9.07515i			0.783974i
$135$	11.6070	−	0.527627i	0.998968	−	0.0454109i
$136$	−3.66789	−	2.11766i	−0.314519	−	0.181588i
$137$	−19.2343	−	5.15381i	−1.64329	−	0.440319i	−0.685570	−	0.728007i	$-0.740447\pi$
$137$	−19.2343	−	5.15381i	−1.64329	−	0.440319i	−0.957724	+	0.287687i	$0.907114\pi$
$138$	13.8836	−	2.20419i	1.18185	−	0.187633i
$139$	−2.91240	−	5.04443i	−0.247027	−	0.427863i	0.715673	−	0.698436i	$-0.246120\pi$
$139$	−2.91240	−	5.04443i	−0.247027	−	0.427863i	−0.962700	+	0.270573i	$0.912787\pi$
$140$	−2.15152	−	5.51098i	−0.181837	−	0.465763i
$141$	1.55935	−	14.8890i	0.131321	−	1.25388i
$142$	−10.5307	+	10.5307i	−0.883713	+	0.883713i
$143$	−0.855275	−	3.19193i	−0.0715217	−	0.266922i
$144$	0.621572	−	2.93490i	0.0517977	−	0.244575i
$145$	−4.00425	−	5.60559i	−0.332535	−	0.465519i
$146$	11.9424	+	6.89493i	0.988358	+	0.570628i
$147$	−9.20646	+	7.88930i	−0.759336	+	0.650698i
$148$	1.17402	−	4.38152i	0.0965042	−	0.360158i
$149$	3.99085	+	2.30412i	0.326943	+	0.188761i	0.654483	−	0.756076i	$-0.272886\pi$
$149$	3.99085	+	2.30412i	0.326943	+	0.188761i	−0.327540	+	0.944837i	$0.606220\pi$
$150$	4.97968	+	7.08539i	0.406589	+	0.578520i
$151$	3.97179	+	6.87935i	0.323220	+	0.559834i	0.981151	−	0.193245i	$-0.0619013\pi$
$151$	3.97179	+	6.87935i	0.323220	+	0.559834i	−0.657930	+	0.753079i	$0.728568\pi$
$152$	0.196252	−	0.732423i	0.0159181	−	0.0594073i
$153$	−0.674331	−	12.6880i	−0.0545164	−	1.02577i
$154$	−12.5759	+	7.49277i	−1.01340	+	0.603784i
$155$	−4.22846	+	9.29544i	−0.339638	+	0.746628i
$156$	0.944868	−	0.421100i	0.0756500	−	0.0337150i
$157$	−2.32201	−	2.32201i	−0.185317	−	0.185317i	0.608351	−	0.793668i	$-0.291831\pi$
$157$	−2.32201	−	2.32201i	−0.185317	−	0.185317i	−0.793668	+	0.608351i	$0.791831\pi$
$158$	−6.65109	−	6.65109i	−0.529132	−	0.529132i
$159$	−13.6563	−	9.91419i	−1.08301	−	0.786246i
$160$	2.09392	−	0.784528i	0.165539	−	0.0620223i
$161$	10.4803	−	18.7420i	0.825962	−	1.47707i
$162$	8.39746	−	3.23769i	0.659767	−	0.254377i
$163$	−2.58926	+	9.66325i	−0.202807	+	0.756885i	0.787300	+	0.616570i	$0.211478\pi$
$163$	−2.58926	+	9.66325i	−0.202807	+	0.756885i	−0.990107	+	0.140315i	$0.955189\pi$
$164$	−0.632830	−	1.09609i	−0.0494157	−	0.0855905i
$165$	15.2684	−	15.0360i	1.18864	−	1.17055i
$166$	2.79272	+	1.61238i	0.216757	+	0.125145i
$167$	5.94871	−	22.2009i	0.460325	−	1.71796i	−0.211617	−	0.977353i	$-0.567873\pi$
$167$	5.94871	−	22.2009i	0.460325	−	1.71796i	0.671942	−	0.740604i	$-0.265461\pi$
$168$	−2.93382	−	3.52032i	−0.226349	−	0.271599i
$169$	−10.9494	−	6.32165i	−0.842263	−	0.486281i
$170$	7.70626	−	5.50482i	0.591043	−	0.422201i
$171$	2.16293	−	0.704540i	0.165403	−	0.0538775i
$172$	1.55171	+	5.79107i	0.118317	+	0.441565i
$173$	−12.3387	+	12.3387i	−0.938097	+	0.938097i	−0.998193	−	0.0600952i	$-0.980860\pi$
$173$	−12.3387	+	12.3387i	−0.938097	+	0.938097i	0.0600952	+	0.998193i	$0.480860\pi$
$174$	−4.31815	−	3.13489i	−0.327358	−	0.237655i
$175$	13.2090	+	0.723378i	0.998504	+	0.0546822i
$176$	−2.76648	−	4.79168i	−0.208531	−	0.361187i
$177$	2.85502	+	3.52300i	0.214597	+	0.264805i
$178$	−3.51877	−	0.942851i	−0.263743	−	0.0706697i
$179$	17.8574	+	10.3100i	1.33472	+	0.770603i	0.986020	−	0.166629i	$-0.0532884\pi$
$179$	17.8574	+	10.3100i	1.33472	+	0.770603i	0.348704	+	0.937233i	$0.386622\pi$
$180$	5.39812	+	3.98251i	0.402352	+	0.296838i
$181$		−	22.6041i		−	1.68015i	−0.542472	−	0.840074i	$-0.682512\pi$
$181$		−	22.6041i		−	1.68015i	0.542472	−	0.840074i	$-0.317488\pi$
$182$	0.387983	−	1.53179i	0.0287592	−	0.113544i
$183$	−3.05182	+	2.47318i	−0.225597	+	0.182823i
$184$	7.02875	+	4.05805i	0.518166	+	0.299163i
$185$	7.83101	+	6.44635i	0.575747	+	0.473945i
$186$	−0.823940	+	7.86716i	−0.0604142	+	0.576848i
$187$	−16.5702	−	16.5702i	−1.21174	−	1.21174i
$188$	6.11165	−	6.11165i	0.445738	−	0.445738i
$189$	4.05387	−	13.1364i	0.294875	−	0.955536i
$190$	1.30905	+	1.07758i	0.0949682	+	0.0781762i
$191$	−12.9673			−0.938279			−0.469139	−	0.883124i	$-0.655436\pi$
$191$	−12.9673			−0.938279			−0.469139	+	0.883124i	$0.655436\pi$
$192$	1.34565	−	1.09051i	0.0971142	−	0.0787008i
$193$	15.1833	+	15.1833i	1.09292	+	1.09292i	0.995216	+	0.0976990i	$0.0311482\pi$
$193$	15.1833	+	15.1833i	1.09292	+	1.09292i	0.0976990	+	0.995216i	$0.468852\pi$
$194$	3.02827	−	5.24512i	0.217417	−	0.376577i
$195$	−0.0177425	+	2.31305i	−0.00127057	+	0.165641i
$196$	−6.99736	+	0.192174i	−0.499812	+	0.0137267i
$197$	−13.1565	+	13.1565i	−0.937364	+	0.937364i	−0.998151	−	0.0607872i	$-0.980639\pi$
$197$	−13.1565	+	13.1565i	−0.937364	+	0.937364i	0.0607872	+	0.998151i	$0.480639\pi$
$198$	7.52483	−	14.7953i	0.534766	−	1.05145i
$199$	5.05551	−	8.75641i	0.358376	−	0.620725i	−0.629314	−	0.777151i	$-0.716664\pi$
$199$	5.05551	−	8.75641i	0.358376	−	0.620725i	0.987690	+	0.156426i	$0.0499973\pi$
$200$	−0.341922	+	4.98830i	−0.0241776	+	0.352726i
$201$	−15.6331	−	1.63728i	−1.10268	−	0.115485i
$202$	2.93094	−	10.9384i	0.206220	−	0.769625i
$203$	−7.84359	+	2.21753i	−0.550512	+	0.155640i
$204$	4.30968	−	5.93636i	0.301738	−	0.415629i
$205$	2.81688	−	0.273190i	0.196740	−	0.0190804i
$206$	7.43121	+	4.29041i	0.517757	+	0.298927i
$207$	1.29221	+	24.3140i	0.0898151	+	1.68994i
$208$	0.576893	+	0.154578i	0.0400004	+	0.0107181i
$209$	2.09771	−	3.63334i	0.145102	−	0.251324i
$210$	9.88155	−	2.71202i	0.681891	−	0.187147i
$211$	−7.26796	−	12.5885i	−0.500347	−	0.866627i	−1.00000		0.000400825i	$-0.999872\pi$
$211$	−7.26796	−	12.5885i	−0.500347	−	0.866627i	0.499653	−	0.866226i	$-0.333461\pi$
$212$	−2.52171	−	9.41113i	−0.173191	−	0.646359i
$213$	−16.2405	−	20.0403i	−1.11278	−	1.37314i
$214$	12.1349	−	7.00610i	0.829526	−	0.478927i
$215$	−13.2237	−	2.20354i	−0.901848	−	0.150280i
$216$	4.94361	+	1.60023i	0.336370	+	0.108882i
$217$	8.66046	+	8.42588i	0.587911	+	0.571986i
$218$	2.99847	−	0.803439i	0.203082	−	0.0544157i
$219$	−14.0320	+	19.3283i	−0.948193	+	1.30609i
$220$	12.3143	−	1.19428i	0.830230	−	0.0805183i
$221$	2.52952			0.170154
$222$	7.33592	+	2.81289i	0.492355	+	0.188789i
$223$	1.67795	+	6.26219i	0.112364	+	0.419348i	0.999076	−	0.0429740i	$-0.0136833\pi$
$223$	1.67795	+	6.26219i	0.112364	+	0.419348i	−0.886712	+	0.462322i	$0.847017\pi$
$224$	−0.0363208	−	2.64550i	−0.00242679	−	0.176760i
$225$	−13.1039	+	7.29984i	−0.873594	+	0.486656i
$226$	3.53497	+	6.12274i	0.235142	+	0.407279i
$227$	0.258140	−	0.963392i	0.0171334	−	0.0639426i	−0.956830	−	0.290649i	$-0.906129\pi$
$227$	0.258140	−	0.963392i	0.0171334	−	0.0639426i	0.973963	+	0.226706i	$0.0727956\pi$
$228$	1.22629	+	0.470209i	0.0812128	+	0.0311403i
$229$	−6.91432	+	11.9760i	−0.456911	+	0.791393i	−0.998796	−	0.0490595i	$-0.984378\pi$
$229$	−6.91432	+	11.9760i	−0.456911	+	0.791393i	0.541885	+	0.840453i	$0.317711\pi$
$230$	−14.7674	+	10.5488i	−0.973736	+	0.695570i
$231$	−10.6384	−	23.0155i	−0.699954	−	1.51431i
$232$	−0.797370	−	2.97582i	−0.0523499	−	0.195372i
$233$	−4.83902	+	18.0595i	−0.317015	+	1.18312i	0.605084	+	0.796161i	$0.293139\pi$
$233$	−4.83902	+	18.0595i	−0.317015	+	1.18312i	−0.922099	+	0.386954i	$0.873527\pi$
$234$	0.554932	+	1.70363i	0.0362770	+	0.111370i
$235$	6.78081	+	18.0982i	0.442331	+	1.18059i
$236$			2.61806i			0.170421i
$237$	12.6573	−	10.2574i	0.822181	−	0.666291i
$238$	−3.04854	−	10.7829i	−0.197607	−	0.698954i
$239$	−9.71706	+	5.61014i	−0.628544	+	0.362890i	−0.780188	−	0.625545i	$-0.784877\pi$
$239$	−9.71706	+	5.61014i	−0.628544	+	0.362890i	0.151644	+	0.988435i	$0.451543\pi$
$240$	0.973677	+	3.74859i	0.0628506	+	0.241971i
$241$	14.6872	−	8.47968i	0.946088	−	0.546224i	0.0542248	−	0.998529i	$-0.482731\pi$
$241$	14.6872	−	8.47968i	0.946088	−	0.546224i	0.891864	+	0.452304i	$0.149398\pi$
$242$	−5.07639	−	18.9453i	−0.326322	−	1.21785i
$243$	4.06233	+	15.0498i	0.260599	+	0.965447i
$244$	−2.26791			−0.145188
$245$	6.08759	−	14.4202i	0.388922	−	0.921271i
$246$	2.00233	−	0.892381i	0.127664	−	0.0568961i
$247$	0.117210	+	0.437435i	0.00745792	+	0.0278333i
$248$	−3.22932	+	3.22932i	−0.205062	+	0.205062i
$249$	−3.28137	+	4.51992i	−0.207948	+	0.286438i
$250$	−9.83646	−	5.31452i	−0.622112	−	0.336120i
$251$			23.4487i			1.48007i	0.672571	+	0.740033i	$0.265190\pi$
$251$			23.4487i			1.48007i	−0.672571	+	0.740033i	$0.734810\pi$
$252$	6.59351	−	4.41878i	0.415352	−	0.278357i
$253$	31.7534	+	31.7534i	1.99632	+	1.99632i
$254$		−	2.36535i		−	0.148415i
$255$	8.09245	+	14.2682i	0.506769	+	0.893508i
$256$	1.00000			0.0625000
$257$	−0.656723	+	0.175968i	−0.0409652	+	0.0109766i	−0.279243	−	0.960220i	$-0.590084\pi$
$257$	−0.656723	+	0.175968i	−0.0409652	+	0.0109766i	0.238278	+	0.971197i	$0.423417\pi$
$258$	−10.2558	+	1.62824i	−0.638499	+	0.101370i
$259$	10.3101	−	6.14279i	0.640639	−	0.381694i
$260$	−0.848760	+	1.03107i	−0.0526378	+	0.0639444i
$261$	6.17931	−	6.87300i	0.382490	−	0.425428i
$262$	−3.74909	+	1.00457i	−0.231620	+	0.0620623i
$263$	−4.81349	+	17.9642i	−0.296813	+	1.10772i	0.642954	+	0.765905i	$0.277708\pi$
$263$	−4.81349	+	17.9642i	−0.296813	+	1.10772i	−0.939767	+	0.341816i	$0.888958\pi$
$264$	8.75341	−	3.90113i	0.538735	−	0.240098i
$265$	21.4900	+	3.58100i	1.32012	+	0.219979i
$266$	1.72346	−	1.02684i	0.105672	−	0.0629596i
$267$	2.25902	−	5.89143i	0.138250	−	0.360550i
$268$	−6.41710	−	6.41710i	−0.391987	−	0.391987i
$269$	−12.6351	+	21.8846i	−0.770375	+	1.33433i	0.166983	+	0.985960i	$0.446598\pi$
$269$	−12.6351	+	21.8846i	−0.770375	+	1.33433i	−0.937358	+	0.348368i	$0.886736\pi$
$270$	−7.83427	+	8.58045i	−0.476779	+	0.522190i
$271$	1.06079	−	0.612445i	0.0644382	−	0.0372034i	−0.467435	−	0.884028i	$-0.654822\pi$
$271$	1.06079	−	0.612445i	0.0644382	−	0.0372034i	0.531873	+	0.846824i	$0.321488\pi$
$272$	4.09100	−	1.09618i	0.248053	−	0.0664657i
$273$	2.56870	+	0.944707i	0.155465	+	0.0571763i
$274$	17.2450	−	9.95639i	1.04181	−	0.601487i
$275$	−8.97080	+	26.1699i	−0.540959	+	1.57811i
$276$	−8.25860	+	11.3758i	−0.497109	+	0.684742i
$277$	−8.22314	−	2.20338i	−0.494080	−	0.132388i	0.00317095	−	0.999995i	$-0.498991\pi$
$277$	−8.22314	−	2.20338i	−0.494080	−	0.132388i	−0.497251	+	0.867607i	$0.665657\pi$
$278$	5.62633	+	1.50757i	0.337445	+	0.0904181i
$279$	−13.4035	−	2.83869i	−0.802449	−	0.169948i
$280$	5.41821	+	2.37550i	0.323800	+	0.141963i
$281$	0.0265841	−	0.0460450i	0.00158588	−	0.00274682i	−0.865231	−	0.501373i	$-0.832829\pi$
$281$	0.0265841	−	0.0460450i	0.00158588	−	0.00274682i	0.866817	+	0.498626i	$0.166162\pi$
$282$	9.42548	+	11.6307i	0.561279	+	0.692600i
$283$	8.56057	−	8.56057i	0.508873	−	0.508873i	−0.405308	−	0.914180i	$-0.632836\pi$
$283$	8.56057	−	8.56057i	0.508873	−	0.508873i	0.914180	+	0.405308i	$0.132836\pi$
$284$		−	14.8926i		−	0.883713i
$285$	−2.09245	+	2.06059i	−0.123946	+	0.122059i
$286$	2.86180	+	1.65226i	0.169222	+	0.0977004i
$287$	0.822202	−	3.24611i	0.0485330	−	0.191612i
$288$	1.63577	+	2.51481i	0.0963887	+	0.148186i
$289$	0.812258	−	0.468957i	0.0477799	−	0.0275857i
$290$	6.79518	+	1.13232i	0.399027	+	0.0664922i
$291$	8.48905	+	6.16288i	0.497637	+	0.361274i
$292$	−13.3200	+	3.56908i	−0.779493	+	0.208865i
$293$	−28.3403	−	7.59376i	−1.65566	−	0.443632i	−0.694469	−	0.719523i	$-0.744361\pi$
$293$	−28.3403	−	7.59376i	−1.65566	−	0.443632i	−0.961189	+	0.275891i	$0.911027\pi$
$294$	0.931376	−	12.0885i	0.0543190	−	0.705017i
$295$	−5.32873	−	2.42402i	−0.310250	−	0.141132i
$296$	2.26804	+	3.92836i	0.131827	+	0.228331i
$297$	24.1292	+	15.6318i	1.40012	+	0.907047i
$298$	−4.45122	+	1.19270i	−0.257852	+	0.0690913i
$299$	−4.84729			−0.280326
$300$	−8.53129	−	1.48896i	−0.492555	−	0.0859653i
$301$	−7.74178	+	13.8447i	−0.446229	+	0.797994i
$302$	−7.67292	−	2.05595i	−0.441527	−	0.118307i
$303$	18.3141	+	7.02237i	1.05212	+	0.403424i
$304$	0.379130	+	0.656672i	0.0217446	+	0.0376627i
$305$	2.09982	−	4.61604i	0.120235	−	0.264314i
$306$	9.44863	+	8.49498i	0.540142	+	0.485626i
$307$	−16.7587	−	16.7587i	−0.956471	−	0.956471i	0.0426203	−	0.999091i	$-0.486429\pi$
$307$	−16.7587	−	16.7587i	−0.956471	−	0.956471i	−0.999091	+	0.0426203i	$0.986429\pi$
$308$	3.59434	−	14.1907i	0.204806	−	0.808591i
$309$	−8.73148	+	12.0272i	−0.496717	+	0.684202i
$310$	−3.58290	−	9.56284i	−0.203495	−	0.543133i
$311$		−	25.2432i		−	1.43141i	−0.698401	−	0.715707i	$-0.746105\pi$
$311$		−	25.2432i		−	1.43141i	0.698401	−	0.715707i	$-0.253895\pi$
$312$	−0.370360	+	0.965885i	−0.0209675	+	0.0546825i
$313$	−2.40592	+	2.40592i	−0.135991	+	0.135991i	−0.771825	−	0.635835i	$-0.780656\pi$
$313$	−2.40592	+	2.40592i	−0.135991	+	0.135991i	0.635835	+	0.771825i	$0.280656\pi$
$314$	3.28382			0.185317
$315$	2.88903	+	17.5115i	0.162779	+	0.986663i
$316$	9.40606			0.529132
$317$	11.9695	−	11.9695i	0.672275	−	0.672275i	−0.285965	−	0.958240i	$-0.592314\pi$
$317$	11.9695	−	11.9695i	0.672275	−	0.672275i	0.958240	+	0.285965i	$0.0923141\pi$
$318$	16.6668	−	2.64607i	0.934630	−	0.148384i
$319$		−	17.0459i		−	0.954390i
$320$	−0.925883	+	2.03537i	−0.0517584	+	0.113781i
$321$	9.87960	+	22.1680i	0.551426	+	1.23729i
$322$	5.84188	+	20.6632i	0.325555	+	1.15152i
$323$	2.27085	+	2.27085i	0.126354	+	0.126354i
$324$	−3.64850	+	8.22730i	−0.202695	+	0.457072i
$325$	−1.31276	−	2.68219i	−0.0728190	−	0.148781i
$326$	−5.00207	−	8.66384i	−0.277039	−	0.479846i
$327$	0.843061	+	5.31021i	0.0466214	+	0.293655i
$328$	1.22253	+	0.327577i	0.0675031	+	0.0180874i
$329$	22.8655	−	0.313927i	1.26062	−	0.0173074i
$330$	−0.164369	+	21.4284i	−0.00904822	+	1.17960i
$331$	−14.9513			−0.821795			−0.410898	−	0.911681i	$-0.634785\pi$
$331$	−14.9513			−0.821795			−0.410898	+	0.911681i	$0.634785\pi$
$332$	−3.11487	+	0.834627i	−0.170951	+	0.0458061i
$333$	−6.16907	+	12.1296i	−0.338063	+	0.664697i
$334$	11.4920	+	19.9048i	0.628816	+	1.08914i
$335$	19.0027	−	7.11971i	1.03823	−	0.388991i
$336$	4.56377	+	0.414718i	0.248974	+	0.0226247i
$337$	0.630051	+	0.168822i	0.0343211	+	0.00919631i	0.275939	−	0.961175i	$-0.411011\pi$
$337$	0.630051	+	0.168822i	0.0343211	+	0.00919631i	−0.241618	+	0.970372i	$0.577678\pi$
$338$	12.2125	−	3.27233i	0.664272	−	0.177991i
$339$	−11.1850	+	4.98481i	−0.607484	+	0.270738i
$340$	−1.55665	+	9.34165i	−0.0844214	+	0.506622i
$341$	−21.8834	+	12.6344i	−1.18505	+	0.684189i
$342$	−1.03123	+	2.02760i	−0.0557628	+	0.109640i
$343$	−13.6239	−	12.5455i	−0.735621	−	0.677393i
$344$	−5.19213	−	2.99768i	−0.279941	−	0.161624i
$345$	−15.5075	−	27.3420i	−0.834895	−	1.47204i
$346$		−	17.4496i		−	0.938097i
$347$	−11.5391	+	11.5391i	−0.619450	+	0.619450i	−0.945390	−	0.325941i	$-0.894319\pi$
$347$	−11.5391	+	11.5391i	−0.619450	+	0.619450i	0.325941	+	0.945390i	$0.394319\pi$
$348$	5.27010	−	0.836693i	0.282507	−	0.0448514i
$349$	1.07272	−	1.85801i	0.0574216	−	0.0994571i	−0.835886	−	0.548904i	$-0.815045\pi$
$349$	1.07272	−	1.85801i	0.0574216	−	0.0994571i	0.893307	+	0.449446i	$0.148379\pi$
$350$	−9.85165	+	8.82864i	−0.526593	+	0.471911i
$351$	−3.03484	+	0.648583i	−0.161988	+	0.0346188i
$352$	5.34443	+	1.43204i	0.284859	+	0.0763277i
$353$	0.121176	+	0.0324689i	0.00644952	+	0.00172814i	0.262042	−	0.965056i	$-0.415604\pi$
$353$	0.121176	+	0.0324689i	0.00644952	+	0.00172814i	−0.255593	+	0.966785i	$0.582271\pi$
$354$	−4.50994	−	0.472334i	−0.239701	−	0.0251043i
$355$	30.3120	+	13.7888i	1.60879	+	0.731833i
$356$	3.15484	−	1.82145i	0.167206	−	0.0965366i
$357$	19.1250	−	3.30611i	1.01220	−	0.174978i
$358$	−19.9173	+	5.33683i	−1.05266	+	0.282060i
$359$	25.6482	−	14.8080i	1.35366	−	0.781535i	0.364899	−	0.931047i	$-0.381103\pi$
$359$	25.6482	−	14.8080i	1.35366	−	0.781535i	0.988760	+	0.149512i	$0.0477701\pi$
$360$	−6.63310	+	1.00099i	−0.349595	+	0.0527567i
$361$	9.21252	−	15.9566i	0.484870	−	0.839819i
$362$	15.9835	+	15.9835i	0.840074	+	0.840074i
$363$	33.5516	−	5.32673i	1.76100	−	0.279581i
$364$	0.808791	+	1.35748i	0.0423922	+	0.0711514i
$365$	5.06834	−	30.4157i	0.265289	−	1.59203i
$366$	0.409162	−	3.90677i	0.0213873	−	0.204210i
$367$	6.31257	−	23.5588i	0.329513	−	1.22976i	−0.580183	−	0.814486i	$-0.697019\pi$
$367$	6.31257	−	23.5588i	0.329513	−	1.22976i	0.909696	−	0.415274i	$-0.136314\pi$
$368$	−7.83955	+	2.10060i	−0.408665	+	0.109501i
$369$	1.17599	+	3.61028i	0.0612197	+	0.187943i
$370$	−10.0956	+	0.979104i	−0.524846	+	0.0509012i
$371$	12.5813	−	22.4991i	0.653186	−	1.16810i
$372$	−4.98031	−	6.14553i	−0.258217	−	0.318631i
$373$	−20.4881	+	5.48977i	−1.06083	+	0.284249i	−0.746722	−	0.665137i	$-0.768373\pi$
$373$	−20.4881	+	5.48977i	−1.06083	+	0.284249i	−0.314111	+	0.949386i	$0.601707\pi$
$374$	23.4338			1.21174
$375$	10.9296	−	15.9858i	0.564401	−	0.825501i
$376$			8.64318i			0.445738i
$377$	1.30107	+	1.30107i	0.0670085	+	0.0670085i
$378$	6.42235	+	12.1554i	0.330330	+	0.625206i
$379$		−	13.9296i		−	0.715513i	−0.933815	−	0.357757i	$-0.883542\pi$
$379$		−	13.9296i		−	0.715513i	0.933815	−	0.357757i	$-0.116458\pi$
$380$	−1.68760	+	0.163669i	−0.0865722	+	0.00839604i
$381$	4.07461	+	0.426741i	0.208749	+	0.0218626i
$382$	9.16924	−	9.16924i	0.469139	−	0.469139i
$383$	−8.06741	−	30.1080i	−0.412225	−	1.53845i	−0.790329	−	0.612683i	$-0.790090\pi$
$383$	−8.06741	−	30.1080i	−0.412225	−	1.53845i	0.378103	−	0.925763i	$-0.376576\pi$
$384$	−0.180414	+	1.72263i	−0.00920670	+	0.0879075i
$385$	25.5554	+	20.4548i	1.30243	+	1.04247i
$386$	−21.4724			−1.09292
$387$	−0.954558	−	17.9607i	−0.0485229	−	0.912995i
$388$	1.56755	+	5.85017i	0.0795802	+	0.296997i
$389$	−17.5258	+	10.1185i	−0.888593	+	0.513029i	−0.873482	−	0.486856i	$-0.838143\pi$
$389$	−17.5258	+	10.1185i	−0.888593	+	0.513029i	−0.0151109	+	0.999886i	$0.504810\pi$
$390$	−1.62303	−	1.64812i	−0.0821851	−	0.0834557i
$391$	−29.7690	+	17.1871i	−1.50548	+	0.869190i
$392$	4.81199	−	5.08377i	0.243042	−	0.256769i
$393$	−1.05411	−	6.63953i	−0.0531726	−	0.334920i
$394$		−	18.6061i		−	0.937364i
$395$	−8.70891	+	19.1448i	−0.438193	+	0.963281i
$396$	5.14097	+	15.7827i	0.258344	+	0.793110i
$397$	−1.82014	+	6.79284i	−0.0913500	+	0.340923i	−0.996441	−	0.0842955i	$-0.973136\pi$
$397$	−1.82014	+	6.79284i	−0.0913500	+	0.340923i	0.905091	+	0.425218i	$0.139803\pi$
$398$	2.61693	+	9.76650i	0.131175	+	0.489550i
$399$	1.45793	+	3.15413i	0.0729877	+	0.157904i
$400$	−3.28548	−	3.76903i	−0.164274	−	0.188452i
$401$	−1.22355	+	2.11925i	−0.0611011	+	0.105830i	−0.894958	−	0.446151i	$-0.852795\pi$
$401$	−1.22355	+	2.11925i	−0.0611011	+	0.105830i	0.833857	+	0.551981i	$0.186128\pi$
$402$	12.2120	−	9.89655i	0.609080	−	0.493595i
$403$	0.705950	−	2.63464i	0.0351659	−	0.131241i
$404$	5.66214	+	9.80712i	0.281702	+	0.487923i
$405$	−13.3675	−	15.0436i	−0.664238	−	0.747521i
$406$	3.97823	−	7.11428i	0.197436	−	0.353076i
$407$	6.49583	+	24.2428i	0.321986	+	1.20167i
$408$	1.15024	+	7.24505i	0.0569454	+	0.358683i
$409$	−15.6504			−0.773860			−0.386930	−	0.922109i	$-0.626465\pi$
$409$	−15.6504			−0.773860			−0.386930	+	0.922109i	$0.626465\pi$
$410$	−1.79866	+	2.18501i	−0.0888297	+	0.107910i
$411$	14.0399	+	31.5030i	0.692539	+	1.55393i
$412$	−8.28844	+	2.22088i	−0.408342	+	0.109415i
$413$	−4.83024	+	4.96472i	−0.237681	+	0.244298i
$414$	−18.1063	−	16.2788i	−0.889877	−	0.800062i
$415$	1.18523	−	7.11269i	0.0581806	−	0.349148i
$416$	−0.517228	+	0.298622i	−0.0253592	+	0.0146411i
$417$	−3.61205	+	9.42010i	−0.176883	+	0.461304i
$418$	1.08586	+	4.05247i	0.0531109	+	0.198213i
$419$	10.1419	+	17.5663i	0.495464	+	0.858169i	0.999986	−	0.00523003i	$-0.00166478\pi$
$419$	10.1419	+	17.5663i	0.495464	+	0.858169i	−0.504522	+	0.863399i	$0.668331\pi$
$420$	−5.06962	+	8.90499i	−0.247372	+	0.434519i
$421$	13.5287	−	23.4324i	0.659350	−	1.14203i	−0.321434	−	0.946932i	$-0.604165\pi$
$421$	13.5287	−	23.4324i	0.659350	−	1.14203i	0.980784	−	0.195096i	$-0.0625017\pi$
$422$	14.0406	+	3.76217i	0.683487	+	0.183140i
$423$	−21.7359	+	14.1383i	−1.05684	+	0.687426i
$424$	8.43779	+	4.87156i	0.409775	+	0.236584i
$425$	−17.5725	−	11.8176i	−0.852389	−	0.573240i
$426$	25.6544	+	2.68683i	1.24296	+	0.130177i
$427$	−4.30072	−	4.18423i	−0.208126	−	0.202489i
$428$	−3.62662	+	13.5347i	−0.175299	+	0.654226i
$429$	−3.36255	+	4.63174i	−0.162345	+	0.223622i
$430$	10.9087	−	7.79242i	0.526064	−	0.375784i
$431$	18.5641	−	32.1540i	0.894201	−	1.54880i	0.0594104	−	0.998234i	$-0.481078\pi$
$431$	18.5641	−	32.1540i	0.894201	−	1.54880i	0.834791	−	0.550568i	$-0.185589\pi$
$432$	−4.62719	+	2.36412i	−0.222626	+	0.113744i
$433$	14.8459	−	14.8459i	0.713446	−	0.713446i	−0.253808	−	0.967255i	$-0.581683\pi$
$433$	14.8459	−	14.8459i	0.713446	−	0.713446i	0.967255	+	0.253808i	$0.0816833\pi$
$434$	−12.0819	+	0.165875i	−0.579948	+	0.00796227i
$435$	−3.17651	+	11.5013i	−0.152302	+	0.551445i
$436$	−1.55212	+	2.68836i	−0.0743333	+	0.128749i
$437$	−4.35161	−	4.35161i	−0.208166	−	0.208166i
$438$	−3.74509	−	23.5893i	−0.178947	−	1.12714i
$439$	32.5686			1.55441			0.777207	−	0.629245i	$-0.216636\pi$
$439$	32.5686			1.55441			0.777207	+	0.629245i	$0.216636\pi$
$440$	−7.86304	+	9.55201i	−0.374856	+	0.455374i
$441$	20.6560	+	3.78535i	0.983620	+	0.180255i
$442$	−1.78864	+	1.78864i	−0.0850769	+	0.0850769i
$443$	1.04800	+	1.04800i	0.0497918	+	0.0497918i	0.731564	−	0.681772i	$-0.238791\pi$
$443$	1.04800	+	1.04800i	0.0497918	+	0.0497918i	−0.681772	+	0.731564i	$0.738791\pi$
$444$	−7.17629	+	3.19826i	−0.340572	+	0.151783i
$445$	0.786313	+	8.10773i	0.0372748	+	0.384343i
$446$	−5.61453	−	3.24155i	−0.265856	−	0.153492i
$447$	−1.25152	−	7.88298i	−0.0591948	−	0.372852i
$448$	1.89634	+	1.84497i	0.0895934	+	0.0871666i
$449$		−	36.2043i		−	1.70859i	−0.519792	−	0.854293i	$-0.673991\pi$
$449$		−	36.2043i		−	1.70859i	0.519792	−	0.854293i	$-0.326009\pi$
$450$	4.10409	−	14.4276i	0.193469	−	0.680125i
$451$	6.06464	+	3.50142i	0.285573	+	0.164876i
$452$	−6.82903	−	1.82983i	−0.321210	−	0.0860681i
$453$	4.92594	−	12.8467i	0.231441	−	0.603589i
$454$	0.498689	+	0.863754i	0.0234046	+	0.0405380i
$455$	−3.51183	+	0.389321i	−0.164637	+	0.0182517i
$456$	−1.19960	+	0.534628i	−0.0561766	+	0.0250362i
$457$	−10.7785	+	10.7785i	−0.504196	+	0.504196i	−0.912739	−	0.408543i	$-0.866037\pi$
$457$	−10.7785	+	10.7785i	−0.504196	+	0.504196i	0.408543	+	0.912739i	$0.366037\pi$
$458$	−3.57912	−	13.3574i	−0.167241	−	0.624152i
$459$	−16.3384	+	14.7439i	−0.762609	+	0.688185i
$460$	2.98300	−	17.9013i	0.139083	−	0.834653i
$461$	16.1492	+	9.32377i	0.752146	+	0.434251i	0.826469	−	0.562983i	$-0.190346\pi$
$461$	16.1492	+	9.32377i	0.752146	+	0.434251i	−0.0743231	+	0.997234i	$0.523680\pi$
$462$	23.7969	+	8.75191i	1.10713	+	0.407176i
$463$	−2.77939	+	10.3728i	−0.129169	+	0.482066i	−0.999954	−	0.00959865i	$-0.996945\pi$
$463$	−2.77939	+	10.3728i	−0.129169	+	0.482066i	0.870785	+	0.491664i	$0.163611\pi$
$464$	2.66805	+	1.54040i	0.123861	+	0.0715113i
$465$	17.1196	−	4.44673i	0.793904	−	0.206212i
$466$	−9.34827	−	16.1917i	−0.433050	−	0.750065i
$467$	−6.98686	+	26.0753i	−0.323313	+	1.20662i	0.592684	+	0.805435i	$0.298068\pi$
$467$	−6.98686	+	26.0753i	−0.323313	+	1.20662i	−0.915997	+	0.401186i	$0.868598\pi$
$468$	−1.59704	−	0.812252i	−0.0738234	−	0.0375464i
$469$	−0.329617	−	24.0083i	−0.0152203	−	1.10860i
$470$	−17.5921	−	8.00257i	−0.811462	−	0.369131i
$471$	−0.592446	+	5.65680i	−0.0272985	+	0.260652i
$472$	−1.85125	−	1.85125i	−0.0852106	−	0.0852106i
$473$	−23.4562	−	23.4562i	−1.07852	−	1.07852i
$474$	−1.69698	+	16.2032i	−0.0779450	+	0.744236i
$475$	1.22940	−	3.58644i	0.0564085	−	0.164557i
$476$	9.78033	+	5.46905i	0.448281	+	0.250673i
$477$	1.55126	+	29.1882i	0.0710274	+	1.33643i
$478$	2.90402	−	10.8380i	0.132827	−	0.495717i
$479$	2.52570	+	4.37464i	0.115402	+	0.199883i	0.917940	−	0.396718i	$-0.129851\pi$
$479$	2.52570	+	4.37464i	0.115402	+	0.199883i	−0.802538	+	0.596601i	$0.796518\pi$
$480$	−3.33915	−	1.96216i	−0.152411	−	0.0895600i
$481$	−2.34619	−	1.35457i	−0.106977	−	0.0617632i
$482$	−4.38941	+	16.3815i	−0.199932	+	0.746156i
$483$	−36.6491	+	6.33546i	−1.66759	+	0.288274i
$484$	16.9859	+	9.80682i	0.772087	+	0.445765i
$485$	−13.3586	−	2.22603i	−0.606584	−	0.101079i
$486$	−13.5143	−	7.76934i	−0.613023	−	0.352424i
$487$	−3.60285	−	13.4460i	−0.163261	−	0.609298i	−0.998256	−	0.0590398i	$-0.981196\pi$
$487$	−3.60285	−	13.4460i	−0.163261	−	0.609298i	0.834995	−	0.550258i	$-0.185471\pi$
$488$	1.60366	−	1.60366i	0.0725941	−	0.0725941i
$489$	15.8270	−	7.05363i	0.715723	−	0.318976i
$490$	5.89202	+	14.5012i	0.266174	+	0.655096i
$491$	12.3161	+	21.3321i	0.555818	+	0.962706i	0.997839	+	0.0657011i	$0.0209284\pi$
$491$	12.3161	+	21.3321i	0.555818	+	0.962706i	−0.442021	+	0.897005i	$0.645738\pi$
$492$	−0.784855	+	2.04687i	−0.0353840	+	0.0922801i
$493$	12.6036	+	3.37711i	0.567636	+	0.152098i
$494$	−0.392194	−	0.226433i	−0.0176456	−	0.0101877i
$495$	−36.8836	−	4.14913i	−1.65779	−	0.186490i
$496$		−	4.56695i		−	0.205062i
$497$	27.4764	−	28.2413i	1.23248	−	1.26680i
$498$	−0.875787	−	5.51634i	−0.0392450	−	0.247193i
$499$	−5.80414	−	3.35102i	−0.259829	−	0.150012i	0.364428	−	0.931232i	$-0.381265\pi$
$499$	−5.80414	−	3.35102i	−0.259829	−	0.150012i	−0.624256	+	0.781219i	$0.714598\pi$
$500$	10.7134	−	3.19750i	0.479116	−	0.142996i
$501$	−36.3619	+	16.2054i	−1.62453	+	0.724004i
$502$	−16.5807	−	16.5807i	−0.740033	−	0.740033i
$503$	21.5315	−	21.5315i	0.960041	−	0.960041i	−0.0391907	−	0.999232i	$-0.512478\pi$
$503$	21.5315	−	21.5315i	0.960041	−	0.960041i	0.999232	+	0.0391907i	$0.0124780\pi$
$504$	−1.53777	+	7.78686i	−0.0684978	+	0.346855i
$505$	−25.2036	+	2.44433i	−1.12155	+	0.108771i
$506$	−44.9060			−1.99632
$507$	3.43370	+	21.6280i	0.152496	+	0.960532i
$508$	1.67255	+	1.67255i	0.0742075	+	0.0742075i
$509$	−14.1740	+	24.5500i	−0.628250	+	1.08816i	0.359653	+	0.933086i	$0.382895\pi$
$509$	−14.1740	+	24.5500i	−0.628250	+	1.08816i	−0.987903	+	0.155074i	$0.950438\pi$
$510$	−15.8114	−	4.36690i	−0.700139	−	0.193369i
$511$	−31.8440	−	17.8068i	−1.40870	−	0.787726i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−3.30676	−	2.14224i	−0.145997	−	0.0945823i
$514$	0.339945	−	0.588802i	0.0149943	−	0.0259709i
$515$	3.15381	−	18.9263i	0.138973	−	0.833994i
$516$	6.10062	−	8.40330i	0.268565	−	0.369934i
$517$	−12.3773	+	46.1928i	−0.544355	+	2.03156i
$518$	−2.94674	+	11.6340i	−0.129472	+	0.511167i
$519$	30.0592	+	3.14815i	1.31945	+	0.138189i
$520$	−0.128914	−	1.32924i	−0.00565325	−	0.0582911i
$521$	−4.20237	−	2.42624i	−0.184109	−	0.106295i	0.405113	−	0.914267i	$-0.367232\pi$
$521$	−4.20237	−	2.42624i	−0.184109	−	0.106295i	−0.589222	+	0.807971i	$0.700566\pi$
$522$	0.490513	+	9.22937i	0.0214692	+	0.403959i
$523$	8.26457	+	2.21448i	0.361384	+	0.0968326i	0.434942	−	0.900458i	$-0.356769\pi$
$523$	8.26457	+	2.21448i	0.361384	+	0.0968326i	−0.0735581	+	0.997291i	$0.523435\pi$
$524$	1.94067	−	3.36134i	0.0847786	−	0.146841i
$525$	−13.4311	−	18.5636i	−0.586181	−	0.810180i
$526$	−9.29895	−	16.1063i	−0.405454	−	0.702266i
$527$	−5.00620	−	18.6834i	−0.218074	−	0.813861i
$528$	−3.43107	+	8.94811i	−0.149318	+	0.389417i
$529$	37.1274	−	21.4355i	1.61424	−	0.931979i
$530$	−17.7278	+	12.6636i	−0.770048	+	0.550070i
$531$	1.62731	−	7.68375i	0.0706193	−	0.333446i
$532$	−0.492583	+	1.94475i	−0.0213562	+	0.0843158i
$533$	−0.730151	+	0.195643i	−0.0316263	+	0.00847425i
$534$	2.56850	+	5.76324i	0.111150	+	0.249400i
$535$	−24.1904	−	19.9131i	−1.04584	−	0.860919i
$536$	9.07515			0.391987
$537$	−5.60002	−	35.2730i	−0.241659	−	1.52214i
$538$	−6.54040	−	24.4091i	−0.281977	−	1.05235i
$539$	32.9975	−	20.2789i	1.42130	−	0.873474i
$540$	−0.527627	−	11.6070i	−0.0227055	−	0.499484i
$541$	−9.76486	−	16.9132i	−0.419824	−	0.727157i	0.576097	−	0.817381i	$-0.304575\pi$
$541$	−9.76486	−	16.9132i	−0.419824	−	0.727157i	−0.995921	+	0.0902245i	$0.971242\pi$
$542$	−0.317025	+	1.18315i	−0.0136174	+	0.0508208i
$543$	−30.4173	+	24.6500i	−1.30533	+	1.05783i
$544$	−2.11766	+	3.66789i	−0.0907939	+	0.157260i
$545$	−4.03472	−	5.64826i	−0.172829	−	0.241945i
$546$	−2.48436	+	1.14834i	−0.106321	+	0.0491444i
$547$	−2.07152	−	7.73103i	−0.0885720	−	0.330555i	0.907395	−	0.420280i	$-0.138068\pi$
$547$	−2.07152	−	7.73103i	−0.0885720	−	0.330555i	−0.995967	+	0.0897245i	$0.971401\pi$
$548$	−5.15381	+	19.2343i	−0.220160	+	0.821647i
$549$	6.65610	+	1.40967i	0.284075	+	0.0601632i
$550$	−12.1616	−	24.8483i	−0.518574	−	1.05953i
$551$			2.33605i			0.0995190i
$552$	−2.20419	−	13.8836i	−0.0938167	−	0.590926i
$553$	17.8370	+	17.3539i	0.758508	+	0.737963i
$554$	7.37266	−	4.25661i	0.313234	−	0.180846i
$555$	0.134755	−	17.5676i	0.00572001	−	0.745705i
$556$	−5.04443	+	2.91240i	−0.213932	+	0.123513i
$557$	−9.38078	−	35.0095i	−0.397476	−	1.48340i	−0.817521	−	0.575899i	$-0.804652\pi$
$557$	−9.38078	−	35.0095i	−0.397476	−	1.48340i	0.420045	−	0.907503i	$-0.362014\pi$
$558$	11.4850	−	7.47048i	0.486198	−	0.316251i
$559$	3.58069			0.151447
$560$	−5.51098	+	2.15152i	−0.232882	+	0.0909184i
$561$	−4.22779	+	40.3678i	−0.178497	+	1.70433i
$562$	0.0137610	+	0.0513566i	0.000580471	+	0.00216635i
$563$	−3.78471	+	3.78471i	−0.159507	+	0.159507i	−0.782348	−	0.622842i	$-0.785978\pi$
$563$	−3.78471	+	3.78471i	−0.159507	+	0.159507i	0.622842	+	0.782348i	$0.285978\pi$
$564$	−14.8890	−	1.55935i	−0.626939	−	0.0656604i
$565$	10.0473	−	12.2054i	0.422692	−	0.513485i
$566$			12.1065i			0.508873i
$567$	−22.0979	+	8.87033i	−0.928025	+	0.372519i
$568$	10.5307	+	10.5307i	0.441856	+	0.441856i
$569$			16.6823i			0.699359i	0.936869	+	0.349680i	$0.113710\pi$
$569$			16.6823i			0.699359i	−0.936869	+	0.349680i	$0.886290\pi$
$570$	0.0225258	−	2.93664i	0.000943503	−	0.123002i
$571$	11.7301			0.490888			0.245444	−	0.969411i	$-0.421066\pi$
$571$	11.7301			0.490888			0.245444	+	0.969411i	$0.421066\pi$
$572$	−3.19193	+	0.855275i	−0.133461	+	0.0357608i
$573$	14.1409	+	17.4495i	0.590747	+	0.728962i
$574$	1.71396	+	2.87673i	0.0715395	+	0.120072i
$575$	33.6739	+	22.6460i	1.40430	+	0.944405i
$576$	−2.93490	−	0.621572i	−0.122288	−	0.0258988i
$577$	21.4772	−	5.75480i	0.894108	−	0.239575i	0.217624	−	0.976033i	$-0.430169\pi$
$577$	21.4772	−	5.75480i	0.894108	−	0.239575i	0.676484	+	0.736457i	$0.263503\pi$
$578$	−0.242750	+	0.905956i	−0.0100971	+	0.0376828i
$579$	3.87391	−	36.9889i	0.160994	−	1.53721i
$580$	−5.60559	+	4.00425i	−0.232759	+	0.166267i
$581$	−7.44670	−	4.16411i	−0.308941	−	0.172756i
$582$	−10.3605	+	1.64485i	−0.429456	+	0.0681813i
$583$	38.1189	+	38.1189i	1.57872	+	1.57872i
$584$	6.89493	−	11.9424i	0.285314	−	0.494179i
$585$	3.13191	−	2.49853i	0.129489	−	0.103301i
$586$	25.4092	−	14.6700i	1.04964	−	0.606013i
$587$	−36.5344	+	9.78935i	−1.50793	+	0.404050i	−0.915749	−	0.401752i	$-0.868401\pi$
$587$	−36.5344	+	9.78935i	−1.50793	+	0.404050i	−0.592186	+	0.805801i	$0.701735\pi$
$588$	7.88930	+	9.20646i	0.325349	+	0.379668i
$589$	2.99899	−	1.73147i	0.123571	−	0.0713438i
$590$	5.48202	−	2.05394i	0.225691	−	0.0845594i
$591$	32.0515	+	3.35680i	1.31842	+	0.138080i
$592$	−4.38152	−	1.17402i	−0.180079	−	0.0482521i
$593$	−44.3958	−	11.8958i	−1.82312	−	0.488502i	−0.825950	−	0.563743i	$-0.809361\pi$
$593$	−44.3958	−	11.8958i	−1.82312	−	0.488502i	−0.997165	+	0.0752404i	$0.976028\pi$
$594$	−28.1152	+	6.00857i	−1.15358	+	0.246535i
$595$	−20.1870	+	14.8429i	−0.827586	+	0.608500i
$596$	2.30412	−	3.99085i	0.0943805	−	0.163472i
$597$	−17.2962	+	2.74598i	−0.707886	+	0.112386i
$598$	3.42755	−	3.42755i	0.140163	−	0.140163i
$599$			0.892796i			0.0364787i	0.999834	+	0.0182393i	$0.00580608\pi$
$599$			0.892796i			0.0364787i	−0.999834	+	0.0182393i	$0.994194\pi$
$600$	7.08539	−	4.97968i	0.289260	−	0.203295i
$601$	−15.5394	−	8.97170i	−0.633867	−	0.365963i	0.148381	−	0.988930i	$-0.452594\pi$
$601$	−15.5394	−	8.97170i	−0.633867	−	0.365963i	−0.782248	+	0.622967i	$0.785927\pi$
$602$	−4.31540	−	15.2639i	−0.175882	−	0.622111i
$603$	14.8449	+	22.8222i	0.604530	+	0.929394i
$604$	6.87935	−	3.97179i	0.279917	−	0.161610i
$605$	−35.6875	+	25.4927i	−1.45090	+	1.03643i
$606$	−17.9156	+	7.98443i	−0.727770	+	0.324345i
$607$	36.9459	−	9.89962i	1.49959	−	0.401813i	0.586626	−	0.809858i	$-0.300456\pi$
$607$	36.9459	−	9.89962i	1.49959	−	0.401813i	0.912962	+	0.408045i	$0.133789\pi$
$608$	−0.732423	−	0.196252i	−0.0297037	−	0.00795907i
$609$	11.5375	+	8.13652i	0.467525	+	0.329708i
$610$	1.77924	+	4.74883i	0.0720393	+	0.192275i
$611$	−2.58104	−	4.47050i	−0.104418	−	0.180857i
$612$	−12.6880	+	0.674331i	−0.512884	+	0.0272582i
$613$	21.9480	−	5.88096i	0.886473	−	0.237530i	0.213275	−	0.976992i	$-0.431587\pi$
$613$	21.9480	−	5.88096i	0.886473	−	0.237530i	0.673198	+	0.739463i	$0.264920\pi$
$614$	23.7004			0.956471
$615$	−3.43946	−	3.49264i	−0.138693	−	0.140837i
$616$	7.49277	+	12.5759i	0.301892	+	0.506699i
$617$	10.4617	+	2.80321i	0.421173	+	0.112853i	0.463180	−	0.886264i	$-0.346708\pi$
$617$	10.4617	+	2.80321i	0.421173	+	0.112853i	−0.0420065	+	0.999117i	$0.513375\pi$
$618$	−2.33041	−	14.6786i	−0.0937426	−	0.590459i
$619$	−14.4369	−	25.0055i	−0.580269	−	1.00505i	−0.995447	−	0.0953149i	$-0.969614\pi$
$619$	−14.4369	−	25.0055i	−0.580269	−	1.00505i	0.415178	−	0.909740i	$-0.363719\pi$
$620$	9.29544	+	4.22846i	0.373314	+	0.169819i
$621$	31.3090	−	28.2535i	1.25639	−	1.13378i
$622$	17.8497	+	17.8497i	0.715707	+	0.715707i
$623$	9.34316	+	2.36651i	0.374326	+	0.0948123i
$624$	−0.421100	−	0.944868i	−0.0168575	−	0.0378250i
$625$	−3.41122	+	24.7662i	−0.136449	+	0.990647i
$626$		−	3.40249i		−	0.135991i
$627$	−7.17680	+	1.13940i	−0.286614	+	0.0455034i
$628$	−2.32201	+	2.32201i	−0.0926583	+	0.0926583i
$629$	−19.2117			−0.766022
$630$	−14.4254	−	10.3397i	−0.574721	−	0.411942i
$631$	−34.0014			−1.35357			−0.676787	−	0.736179i	$-0.736628\pi$
$631$	−34.0014			−1.35357			−0.676787	+	0.736179i	$0.736628\pi$
$632$	−6.65109	+	6.65109i	−0.264566	+	0.264566i
$633$	−9.01395	+	23.5080i	−0.358272	+	0.934361i
$634$			16.9275i			0.672275i
$635$	−4.95285	+	1.85568i	−0.196548	+	0.0736404i
$636$	−9.91419	+	13.6563i	−0.393123	+	0.541507i
$637$	−0.970775	+	4.06644i	−0.0384635	+	0.161118i
$638$	12.0533	+	12.0533i	0.477195	+	0.477195i
$639$	−9.25682	+	43.7083i	−0.366194	+	1.72907i
$640$	−0.784528	−	2.09392i	−0.0310112	−	0.0827696i
$641$	−5.54514	−	9.60447i	−0.219020	−	0.379354i	0.735489	−	0.677537i	$-0.236953\pi$
$641$	−5.54514	−	9.60447i	−0.219020	−	0.379354i	−0.954509	+	0.298183i	$0.903619\pi$
$642$	−22.6610	−	8.68918i	−0.894360	−	0.342935i
$643$	−29.0011	−	7.77082i	−1.14369	−	0.306451i	−0.363257	−	0.931689i	$-0.618335\pi$
$643$	−29.0011	−	7.77082i	−1.14369	−	0.306451i	−0.780434	+	0.625238i	$0.785002\pi$
$644$	−18.7420	−	10.4803i	−0.738537	−	0.412981i
$645$	11.4554	+	20.1975i	0.451055	+	0.795276i
$646$	−3.21147			−0.126354
$647$	−25.1162	+	6.72987i	−0.987420	+	0.264578i	−0.716166	−	0.697930i	$-0.754105\pi$
$647$	−25.1162	+	6.72987i	−0.987420	+	0.264578i	−0.271254	+	0.962508i	$0.587438\pi$
$648$	−3.23769	−	8.39746i	−0.127189	−	0.329883i
$649$	−7.24281	−	12.5449i	−0.284305	−	0.492431i
$650$	2.82486	+	0.968334i	0.110800	+	0.0379812i
$651$	1.89399	−	20.8425i	0.0742314	−	0.816882i
$652$	9.66325	+	2.58926i	0.378442	+	0.101403i
$653$	−4.06758	+	1.08990i	−0.159177	+	0.0426512i	−0.337527	−	0.941316i	$-0.609591\pi$
$653$	−4.06758	+	1.08990i	−0.159177	+	0.0426512i	0.178351	+	0.983967i	$0.442924\pi$
$654$	−4.35102	−	3.15875i	−0.170138	−	0.123517i
$655$	5.04475	+	7.06220i	0.197115	+	0.275943i
$656$	−1.09609	+	0.632830i	−0.0427953	+	0.0247079i
$657$	41.3113	−	2.19557i	1.61171	−	0.0856573i
$658$	−15.9464	+	16.3904i	−0.621655	+	0.638963i
$659$	5.20506	+	3.00514i	0.202760	+	0.117064i	0.597942	−	0.801539i	$-0.295985\pi$
$659$	5.20506	+	3.00514i	0.202760	+	0.117064i	−0.395182	+	0.918603i	$0.629318\pi$
$660$	−15.0360	−	15.2684i	−0.585274	−	0.594322i
$661$		−	12.0458i		−	0.468528i	−0.972173	−	0.234264i	$-0.924732\pi$
$661$		−	12.0458i		−	0.468528i	0.972173	−	0.234264i	$-0.0752681\pi$
$662$	10.5721	−	10.5721i	0.410898	−	0.410898i
$663$	−2.75847	−	3.40386i	−0.107130	−	0.132195i
$664$	1.61238	−	2.79272i	0.0625723	−	0.108378i
$665$	−3.50222	−	2.80320i	−0.135810	−	0.108704i
$666$	−4.21472	−	12.9391i	−0.163317	−	0.501380i
$667$	−24.1521	−	6.47153i	−0.935172	−	0.250579i
$668$	−22.2009	−	5.94871i	−0.858978	−	0.230163i
$669$	6.59693	−	9.08693i	0.255052	−	0.351321i
$670$	−8.40253	+	18.4713i	−0.324618	+	0.713609i
$671$	10.8671	−	6.27413i	0.419520	−	0.242210i
$672$	−3.52032	+	2.93382i	−0.135799	+	0.113175i
$673$	−9.19462	+	2.46369i	−0.354427	+	0.0949683i	−0.431639	−	0.902046i	$-0.642065\pi$
$673$	−9.19462	+	2.46369i	−0.354427	+	0.0949683i	0.0772126	+	0.997015i	$0.475398\pi$
$674$	−0.564889	+	0.326139i	−0.0217587	+	0.0125624i
$675$	24.1130	+	9.67277i	0.928110	+	0.372305i
$676$	−6.32165	+	10.9494i	−0.243140	+	0.421131i
$677$	−1.36815	−	1.36815i	−0.0525822	−	0.0525822i	0.680327	−	0.732909i	$-0.261838\pi$
$677$	−1.36815	−	1.36815i	−0.0525822	−	0.0525822i	−0.732909	+	0.680327i	$0.761838\pi$
$678$	4.38417	−	11.4338i	0.168373	−	0.439111i
$679$	−7.82079	+	13.9860i	−0.300134	+	0.536732i
$680$	−5.50482	−	7.70626i	−0.211100	−	0.295522i
$681$	−1.57790	+	0.703222i	−0.0604652	+	0.0269475i
$682$	6.54003	−	24.4077i	0.250431	−	0.934620i
$683$	−14.1977	+	3.80427i	−0.543261	+	0.145566i	−0.520005	−	0.854163i	$-0.674070\pi$
$683$	−14.1977	+	3.80427i	−0.543261	+	0.145566i	−0.0232561	+	0.999730i	$0.507403\pi$
$684$	−0.704540	−	2.16293i	−0.0269388	−	0.0827015i
$685$	−34.3771	−	28.2986i	−1.31348	−	1.08123i
$686$	18.5046	−	0.762546i	0.706507	−	0.0291141i
$687$	23.6556	−	3.75562i	0.902519	−	0.143286i
$688$	5.79107	−	1.55171i	0.220783	−	0.0591585i
$689$	−5.81902			−0.221687
$690$	30.2991	+	8.36824i	1.15347	+	0.318574i
$691$			21.0481i			0.800708i	0.916361	+	0.400354i	$0.131113\pi$
$691$			21.0481i			0.800708i	−0.916361	+	0.400354i	$0.868887\pi$
$692$	12.3387	+	12.3387i	0.469049	+	0.469049i
$693$	−19.3696	+	39.4142i	−0.735789	+	1.49722i
$694$		−	16.3187i		−	0.619450i
$695$	−1.25727	−	12.9638i	−0.0476911	−	0.491747i
$696$	−3.13489	+	4.31815i	−0.118828	+	0.163679i
$697$	−3.79042	+	3.79042i	−0.143573	+	0.143573i
$698$	0.555283	+	2.07234i	0.0210178	+	0.0784393i
$699$	29.5788	−	13.1824i	1.11877	−	0.498604i
$700$	0.723378	−	13.2090i	0.0273411	−	0.499252i
$701$	11.9699			0.452097			0.226049	−	0.974116i	$-0.427419\pi$
$701$	11.9699			0.452097			0.226049	+	0.974116i	$0.427419\pi$
$702$	1.68734	−	2.60457i	0.0636845	−	0.0983033i
$703$	−0.890215	−	3.32233i	−0.0335751	−	0.125304i
$704$	−4.79168	+	2.76648i	−0.180593	+	0.104266i
$705$	16.9593	−	28.8609i	0.638725	−	1.08696i
$706$	−0.108643	+	0.0627251i	−0.00408883	+	0.00236069i
$707$	−7.35652	+	29.0441i	−0.276670	+	1.09231i
$708$	3.52300	−	2.85502i	0.132403	−	0.107298i
$709$			8.54687i			0.320984i	0.987037	+	0.160492i	$0.0513082\pi$
$709$			8.54687i			0.320984i	−0.987037	+	0.160492i	$0.948692\pi$
$710$	−31.1839	+	11.6836i	−1.17031	+	0.438479i
$711$	−27.6059	−	5.84654i	−1.03530	−	0.219263i
$712$	−0.942851	+	3.51877i	−0.0353349	+	0.131871i
$713$	9.59333	+	35.8028i	0.359273	+	1.34083i
$714$	−11.1856	+	15.8612i	−0.418612	+	0.593590i
$715$	1.21455	−	7.28865i	0.0454216	−	0.272580i
$716$	10.3100	−	17.8574i	0.385302	−	0.667362i
$717$	18.1459	+	6.95788i	0.677670	+	0.259847i
$718$	−7.66518	+	28.6068i	−0.286062	+	1.06760i
$719$	22.2048	+	38.4598i	0.828099	+	1.43431i	0.899528	+	0.436863i	$0.143911\pi$
$719$	22.2048	+	38.4598i	0.828099	+	1.43431i	−0.0714292	+	0.997446i	$0.522756\pi$
$720$	3.98251	−	5.39812i	0.148419	−	0.201176i
$721$	−19.8151	−	11.0804i	−0.737953	−	0.412655i
$722$	4.76875	+	17.7972i	0.177475	+	0.662344i
$723$	−27.4273	−	10.5168i	−1.02003	−	0.391123i
$724$	−22.6041			−0.840074
$725$	−2.96001	−	15.1169i	−0.109932	−	0.561429i
$726$	−19.9580	+	27.4911i	−0.740711	+	1.02029i
$727$	−43.9666	+	11.7808i	−1.63063	+	0.436927i	−0.954100	−	0.299487i	$-0.903185\pi$
$727$	−43.9666	+	11.7808i	−1.63063	+	0.436927i	−0.676532	+	0.736413i	$0.736518\pi$
$728$	−1.53179	−	0.387983i	−0.0567718	−	0.0143796i
$729$	15.8219	−	21.8785i	0.585995	−	0.810315i
$730$	17.9233	+	25.0910i	0.663370	+	0.928659i
$731$	21.9903	−	12.6961i	0.813342	−	0.469583i
$732$	2.47318	+	3.05182i	0.0914114	+	0.112799i
$733$	−0.949589	−	3.54391i	−0.0350739	−	0.130897i	0.946169	−	0.323673i	$-0.104918\pi$
$733$	−0.949589	−	3.54391i	−0.0350739	−	0.130897i	−0.981243	+	0.192776i	$0.938251\pi$
$734$	12.1949	+	21.1223i	0.450124	+	0.779637i
$735$	−26.0431	+	7.53355i	−0.960616	+	0.277879i
$736$	4.05805	−	7.02875i	0.149582	−	0.259083i
$737$	48.5015	+	12.9959i	1.78658	+	0.478711i
$738$	−3.38440	−	1.72130i	−0.124582	−	0.0633619i
$739$	2.46460	+	1.42294i	0.0906616	+	0.0523435i	0.544645	−	0.838666i	$-0.316664\pi$
$739$	2.46460	+	1.42294i	0.0906616	+	0.0523435i	−0.453984	+	0.891010i	$0.649998\pi$
$740$	6.44635	−	7.83101i	0.236972	−	0.287874i
$741$	0.460817	−	0.634752i	0.0169285	−	0.0233182i
$742$	7.01300	+	24.8056i	0.257455	+	0.910641i
$743$	8.57883	−	32.0166i	0.314727	−	1.17458i	−0.609517	−	0.792773i	$-0.708637\pi$
$743$	8.57883	−	32.0166i	0.314727	−	1.17458i	0.924244	−	0.381803i	$-0.124697\pi$
$744$	7.86716	+	0.823940i	0.288424	+	0.0302071i
$745$	5.98953	+	8.38481i	0.219439	+	0.307196i
$746$	10.6054	−	18.3691i	0.388292	−	0.672541i
$747$	9.66062	−	0.513432i	0.353464	−	0.0187855i
$748$	−16.5702	+	16.5702i	−0.605868	+	0.605868i
$749$	−31.8485	+	18.9754i	−1.16372	+	0.693346i
$750$	3.57526	+	19.0320i	0.130550	+	0.694951i
$751$	−4.51596	+	7.82188i	−0.164790	+	0.285424i	−0.936581	−	0.350452i	$-0.886028\pi$
$751$	−4.51596	+	7.82188i	−0.164790	+	0.285424i	0.771791	+	0.635877i	$0.219361\pi$
$752$	−6.11165	−	6.11165i	−0.222869	−	0.222869i
$753$	31.5538	−	25.5710i	1.14988	−	0.931859i
$754$	−1.83999			−0.0670085
$755$	1.71461	+	17.6795i	0.0624010	+	0.643421i
$756$	−13.1364	−	4.05387i	−0.477768	−	0.147438i
$757$	5.95693	−	5.95693i	0.216508	−	0.216508i	−0.590517	−	0.807025i	$-0.701076\pi$
$757$	5.95693	−	5.95693i	0.216508	−	0.216508i	0.807025	+	0.590517i	$0.201076\pi$
$758$	9.84968	+	9.84968i	0.357757	+	0.357757i
$759$	8.10167	−	77.3565i	0.294072	−	2.80786i
$760$	1.07758	−	1.30905i	0.0390881	−	0.0474841i
$761$	25.7345	+	14.8578i	0.932874	+	0.538595i	0.887720	−	0.460385i	$-0.152289\pi$
$761$	25.7345	+	14.8578i	0.932874	+	0.538595i	0.0451549	+	0.998980i	$0.485622\pi$
$762$	−3.18294	+	2.57944i	−0.115306	+	0.0934431i
$763$	−7.90329	+	2.23441i	−0.286118	+	0.0808909i
$764$			12.9673i			0.469139i
$765$	10.3751	−	26.4493i	0.375114	−	0.956275i
$766$	26.9941	+	15.5850i	0.975336	+	0.563110i
$767$	1.51034	+	0.404695i	0.0545353	+	0.0146127i
$768$	−1.09051	−	1.34565i	−0.0393504	−	0.0485571i
$769$	11.2961	+	19.5654i	0.407347	+	0.705546i	0.994592	−	0.103864i	$-0.0331206\pi$
$769$	11.2961	+	19.5654i	0.407347	+	0.705546i	−0.587244	+	0.809410i	$0.699787\pi$
$770$	−32.5341	+	3.60673i	−1.17245	+	0.129978i
$771$	0.952956	+	0.691827i	0.0343199	+	0.0249155i
$772$	15.1833	−	15.1833i	0.546458	−	0.546458i
$773$	−0.253753	−	0.947018i	−0.00912685	−	0.0340619i	0.961212	−	0.275810i	$-0.0889460\pi$
$773$	−0.253753	−	0.947018i	−0.00912685	−	0.0340619i	−0.970339	+	0.241748i	$0.922279\pi$
$774$	13.3751	+	12.0252i	0.480759	+	0.432236i
$775$	−17.2130	+	15.0046i	−0.618308	+	0.538982i
$776$	−5.24512	−	3.02827i	−0.188289	−	0.108709i
$777$	−19.5094	−	7.17507i	−0.699894	−	0.257404i
$778$	5.23773	−	19.5475i	0.187782	−	0.700811i
$779$	−0.831124	−	0.479849i	−0.0297781	−	0.0171924i
$780$	2.31305	+	0.0177425i	0.0828204	+	0.000635283i
$781$	41.2001	+	71.3606i	1.47425	+	2.55348i
$782$	8.89671	−	33.2030i	0.318146	−	1.18734i
$783$	−15.9873	−	0.820134i	−0.571339	−	0.0293092i
$784$	0.192174	+	6.99736i	0.00686335	+	0.249906i
$785$	−2.57625	−	6.87606i	−0.0919502	−	0.245417i
$786$	5.44022	+	3.94949i	0.194046	+	0.140874i
$787$	6.43823	+	6.43823i	0.229498	+	0.229498i	0.812483	−	0.582985i	$-0.198115\pi$
$787$	6.43823	+	6.43823i	0.229498	+	0.229498i	−0.582985	+	0.812483i	$0.698115\pi$
$788$	13.1565	+	13.1565i	0.468682	+	0.468682i
$789$	29.4228	−	13.1129i	1.04748	−	0.466830i
$790$	−7.37931	−	19.6956i	−0.262544	−	0.700737i
$791$	−9.57414	−	16.0693i	−0.340417	−	0.571359i
$792$	−14.7953	−	7.52483i	−0.525727	−	0.267383i
$793$	−0.350569	+	1.30834i	−0.0124491	+	0.0464606i
$794$	−3.51623	−	6.09029i	−0.124786	−	0.216136i
$795$	−18.6163	−	32.8232i	−0.660251	−	1.16412i
$796$	−8.75641	−	5.05551i	−0.310363	−	0.179188i
$797$	5.22379	−	19.4954i	0.185036	−	0.690564i	−0.809587	−	0.587000i	$-0.800309\pi$
$797$	5.22379	−	19.4954i	0.185036	−	0.690564i	0.994623	−	0.103564i	$-0.0330246\pi$
$798$	−3.26122	−	1.19940i	−0.115446	−	0.0424582i
$799$	−31.7022	−	18.3033i	−1.12154	−	0.647524i
$800$	4.98830	+	0.341922i	0.176363	+	0.0120888i
$801$	−10.3913	+	3.38481i	−0.367159	+	0.119596i
$802$	−0.633355	−	2.36371i	−0.0223645	−	0.0834656i
$803$	53.9514	−	53.9514i	1.90390	−	1.90390i
$804$	−1.63728	+	15.6331i	−0.0577425	+	0.551338i
$805$	38.6841	−	28.4433i	1.36344	−	1.00250i
$806$	1.36379	+	2.36216i	0.0480375	+	0.0832034i
$807$	43.2278	−	6.86295i	1.52169	−	0.241587i
$808$	−10.9384	−	2.93094i	−0.384812	−	0.103110i
$809$	29.2238	+	16.8724i	1.02745	+	0.593201i	0.916254	−	0.400597i	$-0.131197\pi$
$809$	29.2238	+	16.8724i	1.02745	+	0.593201i	0.111200	+	0.993798i	$0.464530\pi$
$810$	20.0897	+	1.18515i	0.705880	+	0.0416419i
$811$			23.6762i			0.831383i	0.909506	+	0.415691i	$0.136460\pi$
$811$			23.6762i			0.831383i	−0.909506	+	0.415691i	$0.863540\pi$
$812$	2.21753	+	7.84359i	0.0778200	+	0.275256i
$813$	−1.98094	−	0.759574i	−0.0694746	−	0.0266394i
$814$	−21.7355	−	12.5490i	−0.761828	−	0.439841i
$815$	−14.2172	+	17.2710i	−0.498005	+	0.604976i
$816$	−5.93636	−	4.30968i	−0.207814	−	0.150869i
$817$	3.21454	+	3.21454i	0.112462	+	0.112462i
$818$	11.0665	−	11.0665i	0.386930	−	0.386930i
$819$	−1.52995	−	4.48680i	−0.0534608	−	0.156782i
$820$	−0.273190	−	2.81688i	−0.00954021	−	0.0983699i
$821$	−22.0163			−0.768374			−0.384187	−	0.923255i	$-0.625518\pi$
$821$	−22.0163			−0.768374			−0.384187	+	0.923255i	$0.625518\pi$
$822$	−32.2037	−	12.3482i	−1.12323	−	0.430694i
$823$	−36.5585	−	36.5585i	−1.27435	−	1.27435i	−0.943783	−	0.330566i	$-0.892760\pi$
$823$	−36.5585	−	36.5585i	−1.27435	−	1.27435i	−0.330566	−	0.943783i	$-0.607240\pi$
$824$	4.29041	−	7.43121i	0.149464	−	0.258879i
$825$	44.9985	−	16.4670i	1.56665	−	0.573308i
$826$	−0.0950901	−	6.92608i	−0.00330861	−	0.240989i
$827$	24.5302	−	24.5302i	0.852999	−	0.852999i	−0.137503	−	0.990501i	$-0.543908\pi$
$827$	24.5302	−	24.5302i	0.852999	−	0.852999i	0.990501	+	0.137503i	$0.0439076\pi$
$828$	24.3140	−	1.29221i	0.844969	−	0.0449075i
$829$	−23.5521	+	40.7934i	−0.817997	+	1.41681i	0.0891594	+	0.996017i	$0.471582\pi$
$829$	−23.5521	+	40.7934i	−0.817997	+	1.41681i	−0.907156	+	0.420794i	$0.861751\pi$
$830$	4.19135	+	5.86751i	0.145484	+	0.203664i
$831$	6.00243	+	13.4683i	0.208222	+	0.467211i
$832$	0.154578	−	0.576893i	0.00535903	−	0.0200002i
$833$	8.45656	+	28.4156i	0.293002	+	0.984541i
$834$	−4.10691	−	9.21512i	−0.142211	−	0.319094i
$835$	32.6633	−	39.6793i	1.13036	−	1.37316i
$836$	−3.63334	−	2.09771i	−0.125662	−	0.0725508i
$837$	10.7968	+	21.1322i	0.373193	+	0.730434i
$838$	−19.5926	−	5.24983i	−0.676816	−	0.181352i
$839$	15.7770	−	27.3266i	0.544682	−	0.943417i	−0.453944	−	0.891030i	$-0.649984\pi$
$839$	15.7770	−	27.3266i	0.544682	−	0.943417i	0.998627	−	0.0523875i	$-0.0166831\pi$
$840$	−2.71202	−	9.88155i	−0.0935735	−	0.340946i
$841$	−9.75434	−	16.8950i	−0.336356	−	0.582586i
$842$	7.00299	+	26.1355i	0.241339	+	0.900689i
$843$	−0.0909510	+	0.0144396i	−0.00313252	+	0.000497326i
$844$	−12.5885	+	7.26796i	−0.433313	+	0.250174i
$845$	−16.4330	−	23.0048i	−0.565314	−	0.791389i
$846$	5.37236	−	25.3669i	0.184705	−	0.872131i
$847$	14.1177	+	49.9355i	0.485090	+	1.71580i
$848$	−9.41113	+	2.52171i	−0.323180	+	0.0865957i
$849$	−20.8550	−	2.18417i	−0.715740	−	0.0749606i
$850$	20.7819	−	4.06927i	0.712815	−	0.139575i
$851$	36.8153			1.26201
$852$	−20.0403	+	16.2405i	−0.686569	+	0.556391i
$853$	2.02558	+	7.55958i	0.0693546	+	0.258835i	0.991894	−	0.127068i	$-0.0405566\pi$
$853$	2.02558	+	7.55958i	0.0693546	+	0.258835i	−0.922539	+	0.385903i	$0.873890\pi$
$854$	5.99976	−	0.0823724i	0.205308	−	0.00281873i
$855$	5.05468	+	0.568614i	0.172866	+	0.0194462i
$856$	−7.00610	−	12.1349i	−0.239463	−	0.414763i
$857$	3.70381	−	13.8228i	0.126520	−	0.472179i	−0.873369	−	0.487058i	$-0.838070\pi$
$857$	3.70381	−	13.8228i	0.126520	−	0.472179i	0.999889	+	0.0148798i	$0.00473656\pi$
$858$	−0.897453	−	5.65281i	−0.0306385	−	0.192984i
$859$	11.3206	−	19.6079i	0.386255	−	0.669013i	−0.605688	−	0.795702i	$-0.707102\pi$
$859$	11.3206	−	19.6079i	0.386255	−	0.669013i	0.991942	+	0.126690i	$0.0404353\pi$
$860$	−2.20354	+	13.2237i	−0.0751401	+	0.450924i
$861$	−5.26476	+	2.43352i	−0.179423	+	0.0829342i
$862$	9.60948	+	35.8631i	0.327300	+	1.22150i
$863$	−11.8231	+	44.1243i	−0.402462	+	1.50201i	0.406228	+	0.913772i	$0.366844\pi$
$863$	−11.8231	+	44.1243i	−0.402462	+	1.50201i	−0.808690	+	0.588235i	$0.799823\pi$
$864$	1.60023	−	4.94361i	0.0544411	−	0.168185i
$865$	−36.5382	+	13.6897i	−1.24234	+	0.465464i
$866$			20.9952i			0.713446i
$867$	−1.51683	−	0.581615i	−0.0515143	−	0.0197527i
$868$	8.42588	−	8.66046i	0.285993	−	0.293955i
$869$	−45.0709	+	26.0217i	−1.52892	+	0.882725i
$870$	−5.88651	−	10.3788i	−0.199571	−	0.351873i
$871$	−4.69393	+	2.71004i	−0.159048	+	0.0918262i
$872$	−0.803439	−	2.99847i	−0.0272079	−	0.101541i
$873$	−0.964299	−	18.1440i	−0.0326366	−	0.614082i
$874$	6.15411			0.208166
$875$	26.2154	+	13.7023i	0.886242	+	0.463222i
$876$	19.3283	+	14.0320i	0.653044	+	0.474096i
$877$	−6.93747	−	25.8910i	−0.234262	−	0.874277i	−0.978480	−	0.206341i	$-0.933845\pi$
$877$	−6.93747	−	25.8910i	−0.234262	−	0.874277i	0.744218	−	0.667936i	$-0.232822\pi$
$878$	−23.0295	+	23.0295i	−0.777207	+	0.777207i
$879$	20.6868	+	46.4173i	0.697749	+	1.56562i
$880$	−1.19428	−	12.3143i	−0.0402591	−	0.415115i
$881$			12.4605i			0.419804i	0.977722	+	0.209902i	$0.0673144\pi$
$881$			12.4605i			0.419804i	−0.977722	+	0.209902i	$0.932686\pi$
$882$	−17.2827	+	11.9294i	−0.581937	+	0.401683i
$883$	6.78107	+	6.78107i	0.228201	+	0.228201i	0.811941	−	0.583740i	$-0.198411\pi$
$883$	6.78107	+	6.78107i	0.228201	+	0.228201i	−0.583740	+	0.811941i	$0.698411\pi$
$884$		−	2.52952i		−	0.0850769i
$885$	2.54914	+	9.81404i	0.0856886	+	0.329895i
$886$	−1.48209			−0.0497918
$887$	16.9839	−	4.55083i	0.570264	−	0.152802i	0.0378466	−	0.999284i	$-0.487950\pi$
$887$	16.9839	−	4.55083i	0.570264	−	0.152802i	0.532418	+	0.846482i	$0.321284\pi$
$888$	2.81289	−	7.33592i	0.0943945	−	0.246177i
$889$	0.0859114	+	6.25753i	0.00288137	+	0.209871i
$890$	−6.28904	−	5.17702i	−0.210809	−	0.173534i
$891$	−5.27817	−	49.5161i	−0.176825	−	1.65885i
$892$	6.26219	−	1.67795i	0.209674	−	0.0561819i
$893$	1.69624	−	6.33046i	0.0567626	−	0.211841i
$894$	6.45907	+	4.68915i	0.216023	+	0.156829i
$895$	26.8006	+	37.5185i	0.895846	+	1.25410i
$896$	−2.64550	+	0.0363208i	−0.0883800	+	0.00121339i
$897$	5.28602	+	6.52278i	0.176495	+	0.217789i
$898$	25.6003	+	25.6003i	0.854293	+	0.854293i
$899$	7.03493	−	12.1848i	0.234628	−	0.406387i
$900$	7.29984	+	13.1039i	0.243328	+	0.436797i
$901$	−35.7367	+	20.6326i	−1.19056	+	0.687372i
$902$	−6.76423	+	1.81247i	−0.225224	+	0.0603486i
$903$	27.0726	−	4.68000i	0.900921	−	0.155741i
$904$	6.12274	−	3.53497i	0.203639	−	0.117571i
$905$	20.9287	−	46.0077i	0.695694	−	1.52935i
$906$	5.60080	+	12.5671i	0.186074	+	0.417515i
$907$	32.8887	+	8.81250i	1.09205	+	0.292614i	0.759524	−	0.650480i	$-0.225432\pi$
$907$	32.8887	+	8.81250i	1.09205	+	0.292614i	0.332527	+	0.943094i	$0.392099\pi$
$908$	−0.963392	−	0.258140i	−0.0319713	−	0.00856668i
$909$	−10.5220	−	32.3024i	−0.348993	−	1.07140i
$910$	2.20795	−	2.75853i	0.0731927	−	0.0914444i
$911$	−4.60873	+	7.98256i	−0.152694	+	0.264474i	−0.932217	−	0.361900i	$-0.882128\pi$
$911$	−4.60873	+	7.98256i	−0.152694	+	0.264474i	0.779523	+	0.626374i	$0.215462\pi$
$912$	0.470209	−	1.22629i	0.0155702	−	0.0406064i
$913$	12.6165	−	12.6165i	0.417545	−	0.417545i
$914$		−	15.2431i		−	0.504196i
$915$	−8.50148	+	2.20821i	−0.281050	+	0.0730013i
$916$	11.9760	+	6.91432i	0.395697	+	0.228456i
$917$	9.88174	−	2.79375i	0.326324	−	0.0922578i
$918$	1.12748	−	21.9785i	0.0372122	−	0.725397i
$919$	6.11490	−	3.53044i	0.201712	−	0.116459i	−0.395742	−	0.918362i	$-0.629512\pi$
$919$	6.11490	−	3.53044i	0.201712	−	0.116459i	0.597454	+	0.801903i	$0.296179\pi$
$920$	10.5488	+	14.7674i	0.347785	+	0.486868i
$921$	−4.27588	+	40.8270i	−0.140895	+	1.34530i
$922$	−18.0121	+	4.82634i	−0.593198	+	0.158947i
$923$	−8.59144	−	2.30207i	−0.282791	−	0.0757735i
$924$	−23.0155	+	10.6384i	−0.757153	+	0.349977i
$925$	9.97046	+	20.3713i	0.327827	+	0.669805i
$926$	−5.36936	−	9.30001i	−0.176448	−	0.305617i
$927$	25.7062	−	1.36621i	0.844302	−	0.0448721i
$928$	−2.97582	+	0.797370i	−0.0976862	+	0.0261749i
$929$	13.6284			0.447134			0.223567	−	0.974689i	$-0.428230\pi$
$929$	13.6284			0.447134			0.223567	+	0.974689i	$0.428230\pi$
$930$	−8.96109	+	15.2497i	−0.293846	+	0.500058i
$931$	−4.52211	+	2.77910i	−0.148206	+	0.0910815i
$932$	18.0595	+	4.83902i	0.591558	+	0.158507i
$933$	−33.9687	+	27.5280i	−1.11209	+	0.901228i
$934$	−13.4976	−	23.3785i	−0.441654	−	0.764967i
$935$	−18.3845	−	49.0687i	−0.601237	−	1.60472i
$936$	1.70363	−	0.554932i	0.0556849	−	0.0181385i
$937$	17.2444	+	17.2444i	0.563349	+	0.563349i	0.930257	−	0.366908i	$-0.119584\pi$
$937$	17.2444	+	17.2444i	0.563349	+	0.563349i	−0.366908	+	0.930257i	$0.619584\pi$
$938$	17.2095	+	16.7434i	0.561911	+	0.546691i
$939$	5.86123	+	0.613856i	0.191274	+	0.0200324i
$940$	18.0982	−	6.78081i	0.590297	−	0.221166i
$941$		−	19.4182i		−	0.633016i	−0.948590	−	0.316508i	$-0.897490\pi$
$941$		−	19.4182i		−	0.633016i	0.948590	−	0.316508i	$-0.102510\pi$
$942$	−3.58104	−	4.41888i	−0.116677	−	0.143975i
$943$	7.26355	−	7.26355i	0.236534	−	0.236534i
$944$	2.61806			0.0852106
$945$	20.4139	−	22.9841i	0.664065	−	0.747674i
$946$	33.1721			1.07852
$947$	27.0327	−	27.0327i	0.878445	−	0.878445i	−0.114929	−	0.993374i	$-0.536664\pi$
$947$	27.0327	−	27.0327i	0.878445	−	0.878445i	0.993374	+	0.114929i	$0.0366640\pi$
$948$	−10.2574	−	12.6573i	−0.333145	−	0.411090i
$949$			8.23591i			0.267349i
$950$	1.66668	+	3.40531i	0.0540743	+	0.110483i
$951$	−29.1597	−	3.05394i	−0.945569	−	0.0990309i
$952$	−10.7829	+	3.04854i	−0.349477	+	0.0988037i
$953$	−34.0810	−	34.0810i	−1.10399	−	1.10399i	−0.993924	−	0.110069i	$-0.964893\pi$
$953$	−34.0810	−	34.0810i	−1.10399	−	1.10399i	−0.110069	−	0.993924i	$-0.535107\pi$
$954$	−21.7361	−	19.5422i	−0.703731	−	0.632704i
$955$	−26.3932	−	12.0062i	−0.854065	−	0.388511i
$956$	5.61014	+	9.71706i	0.181445	+	0.314272i
$957$	−22.9380	+	18.5888i	−0.741479	+	0.600890i
$958$	−4.87928	−	1.30740i	−0.157642	−	0.0422402i
$959$	−45.2600	+	26.9660i	−1.46152	+	0.870778i
$960$	3.74859	−	0.973677i	0.120985	−	0.0314253i
$961$	10.1430			0.327193
$962$	2.61683	−	0.701179i	0.0843701	−	0.0226069i
$963$	19.0566	−	37.4689i	0.614090	−	1.20742i
$964$	−8.47968	−	14.6872i	−0.273112	−	0.473044i
$965$	16.8457	+	44.9615i	0.542281	+	1.44736i
$966$	21.4350	−	30.3947i	0.689658	−	0.977932i
$967$	41.9941	+	11.2523i	1.35044	+	0.361849i	0.860297	−	0.509793i	$-0.170278\pi$
$967$	41.9941	+	11.2523i	1.35044	+	0.361849i	0.490142	+	0.871642i	$0.336945\pi$
$968$	−18.9453	+	5.07639i	−0.608926	+	0.163161i
$969$	0.579394	−	5.53217i	0.0186128	−	0.177719i
$970$	11.0200	−	7.87194i	0.353832	−	0.252753i
$971$	0.831647	−	0.480151i	0.0266888	−	0.0154088i	−0.486596	−	0.873627i	$-0.661762\pi$
$971$	0.831647	−	0.480151i	0.0266888	−	0.0154088i	0.513285	+	0.858218i	$0.328428\pi$
$972$	15.0498	−	4.06233i	0.482724	−	0.130299i
$973$	−14.9392	−	3.78393i	−0.478930	−	0.121307i
$974$	12.0554	+	6.96017i	0.386279	+	0.223018i
$975$	−2.17772	+	4.69149i	−0.0697430	+	0.150248i
$976$			2.26791i			0.0725941i
$977$	−8.56570	+	8.56570i	−0.274041	+	0.274041i	−0.830725	−	0.556684i	$-0.812074\pi$
$977$	−8.56570	+	8.56570i	−0.274041	+	0.274041i	0.556684	+	0.830725i	$0.312074\pi$
$978$	−6.20372	+	16.1791i	−0.198373	+	0.517349i
$979$	−10.0780	+	17.4556i	−0.322094	+	0.557884i
$980$	−14.4202	−	6.08759i	−0.460635	−	0.194461i
$981$	6.22634	−	6.92531i	0.198792	−	0.221108i
$982$	−23.7929	−	6.37529i	−0.759262	−	0.203444i
$983$	−22.0400	−	5.90559i	−0.702966	−	0.188359i	−0.110407	−	0.993886i	$-0.535215\pi$
$983$	−22.0400	−	5.90559i	−0.702966	−	0.188359i	−0.592559	+	0.805527i	$0.701882\pi$
$984$	−0.892381	−	2.00233i	−0.0284481	−	0.0638321i
$985$	−38.9598	+	14.5970i	−1.24136	+	0.465100i
$986$	−11.3000	+	6.52408i	−0.359867	+	0.207769i
$987$	−25.3576	−	30.4268i	−0.807140	−	0.968495i
$988$	0.437435	−	0.117210i	0.0139167	−	0.00372896i
$989$	−42.1399	+	24.3295i	−1.33997	+	0.773632i
$990$	29.0145	−	23.1468i	0.922142	−	0.735652i
$991$	10.1807	−	17.6335i	0.323402	−	0.560148i	−0.657786	−	0.753205i	$-0.728507\pi$
$991$	10.1807	−	17.6335i	0.323402	−	0.560148i	0.981188	+	0.193057i	$0.0618402\pi$
$992$	3.22932	+	3.22932i	0.102531	+	0.102531i
$993$	16.3045	+	20.1192i	0.517408	+	0.638464i
$994$	0.540911	+	39.3984i	0.0171567	+	1.24964i
$995$	18.3973	−	13.1417i	0.583232	−	0.416621i
$996$	4.51992	+	3.28137i	0.143219	+	0.103974i
$997$	−15.5185	+	57.9157i	−0.491475	+	1.83421i	0.0574665	+	0.998347i	$0.481698\pi$
$997$	−15.5185	+	57.9157i	−0.491475	+	1.83421i	−0.548941	+	0.835861i	$0.684969\pi$
$998$	6.47367	−	1.73462i	0.204921	−	0.0549083i
$999$	23.0497	−	4.92600i	0.729259	−	0.155852i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bw.a.493.8	yes	192
5.2	odd	4	inner	630.2.bw.a.367.6	yes	192
7.5	odd	6		630.2.cg.a.313.25	yes	192
9.4	even	3		630.2.cg.a.283.13	yes	192
35.12	even	12		630.2.cg.a.187.13	yes	192
45.22	odd	12		630.2.cg.a.157.25	yes	192
63.40	odd	6	inner	630.2.bw.a.103.6	✓	192
315.292	even	12	inner	630.2.bw.a.607.8	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bw.a.103.6	✓	192	63.40	odd	6	inner
630.2.bw.a.367.6	yes	192	5.2	odd	4	inner
630.2.bw.a.493.8	yes	192	1.1	even	1	trivial
630.2.bw.a.607.8	yes	192	315.292	even	12	inner
630.2.cg.a.157.25	yes	192	45.22	odd	12
630.2.cg.a.187.13	yes	192	35.12	even	12
630.2.cg.a.283.13	yes	192	9.4	even	3
630.2.cg.a.313.25	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 $\F_{q}$

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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.09051 - 1.34565i) q^{3} -1.00000i q^{4} +(2.03537 + 0.925883i) q^{5} +(1.72263 + 0.180414i) q^{6} +(1.84497 - 1.89634i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.621572 + 2.93490i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.09051 - 1.34565i) q^{3} -1.00000i q^{4} +(2.03537 + 0.925883i) q^{5} +(1.72263 + 0.180414i) q^{6} +(1.84497 - 1.89634i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.621572 + 2.93490i) q^{9} +(-2.09392 + 0.784528i) q^{10} +(2.76648 + 4.79168i) q^{11} +(-1.34565 + 1.09051i) q^{12} +(-0.576893 - 0.154578i) q^{13} +(0.0363208 + 2.64550i) q^{14} +(-0.973677 - 3.74859i) q^{15} -1.00000 q^{16} +(-4.09100 + 1.09618i) q^{17} +(-1.63577 - 2.51481i) q^{18} +(-0.379130 - 0.656672i) q^{19} +(0.925883 - 2.03537i) q^{20} +(-4.56377 - 0.414718i) q^{21} +(-5.34443 - 1.43204i) q^{22} +(7.83955 - 2.10060i) q^{23} +(0.180414 - 1.72263i) q^{24} +(3.28548 + 3.76903i) q^{25} +(0.517228 - 0.298622i) q^{26} +(4.62719 - 2.36412i) q^{27} +(-1.89634 - 1.84497i) q^{28} +(-2.66805 - 1.54040i) q^{29} +(3.33915 + 1.96216i) q^{30} +4.56695i q^{31} +(0.707107 - 0.707107i) q^{32} +(3.43107 - 8.94811i) q^{33} +(2.11766 - 3.66789i) q^{34} +(5.51098 - 2.15152i) q^{35} +(2.93490 + 0.621572i) q^{36} +(4.38152 + 1.17402i) q^{37} +(0.732423 + 0.196252i) q^{38} +(0.421100 + 0.944868i) q^{39} +(0.784528 + 2.09392i) q^{40} +(1.09609 - 0.632830i) q^{41} +(3.52032 - 2.93382i) q^{42} +(-5.79107 + 1.55171i) q^{43} +(4.79168 - 2.76648i) q^{44} +(-3.98251 + 5.39812i) q^{45} +(-4.05805 + 7.02875i) q^{46} +(6.11165 + 6.11165i) q^{47} +(1.09051 + 1.34565i) q^{48} +(-0.192174 - 6.99736i) q^{49} +(-4.98830 - 0.341922i) q^{50} +(5.93636 + 4.30968i) q^{51} +(-0.154578 + 0.576893i) q^{52} +(9.41113 - 2.52171i) q^{53} +(-1.60023 + 4.94361i) q^{54} +(1.19428 + 12.3143i) q^{55} +(2.64550 - 0.0363208i) q^{56} +(-0.470209 + 1.22629i) q^{57} +(2.97582 - 0.797370i) q^{58} -2.61806 q^{59} +(-3.74859 + 0.973677i) q^{60} -2.26791i q^{61} +(-3.22932 - 3.22932i) q^{62} +(4.41878 + 6.59351i) q^{63} +1.00000i q^{64} +(-1.03107 - 0.848760i) q^{65} +(3.90113 + 8.75341i) q^{66} +(6.41710 - 6.41710i) q^{67} +(1.09618 + 4.09100i) q^{68} +(-11.3758 - 8.25860i) q^{69} +(-2.37550 + 5.41821i) q^{70} +14.8926 q^{71} +(-2.51481 + 1.63577i) q^{72} +(-3.56908 - 13.3200i) q^{73} +(-3.92836 + 2.26804i) q^{74} +(1.48896 - 8.53129i) q^{75} +(-0.656672 + 0.379130i) q^{76} +(14.1907 + 3.59434i) q^{77} +(-0.965885 - 0.370360i) q^{78} +9.40606i q^{79} +(-2.03537 - 0.925883i) q^{80} +(-8.22730 - 3.64850i) q^{81} +(-0.327577 + 1.22253i) q^{82} +(-0.834627 - 3.11487i) q^{83} +(-0.414718 + 4.56377i) q^{84} +(-9.34165 - 1.55665i) q^{85} +(2.99768 - 5.19213i) q^{86} +(0.836693 + 5.27010i) q^{87} +(-1.43204 + 5.34443i) q^{88} +(1.82145 + 3.15484i) q^{89} +(-1.00099 - 6.63310i) q^{90} +(-1.35748 + 0.808791i) q^{91} +(-2.10060 - 7.83955i) q^{92} +(6.14553 - 4.98031i) q^{93} -8.64318 q^{94} +(-0.163669 - 1.68760i) q^{95} +(-1.72263 - 0.180414i) q^{96} +(-5.85017 + 1.56755i) q^{97} +(5.08377 + 4.81199i) q^{98} +(-15.7827 + 5.14097i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 8 q^{11} - 12 q^{15} - 192 q^{16} + 36 q^{17} - 8 q^{18} + 8 q^{23} + 36 q^{27} + 12 q^{30} + 48 q^{35} - 16 q^{36} - 12 q^{41} + 4 q^{42} + 48 q^{45} + 12 q^{46} - 16 q^{50} - 24 q^{51} - 40 q^{53} - 4 q^{56} - 32 q^{57} - 12 q^{58} - 16 q^{60} - 12 q^{63} + 16 q^{65} - 36 q^{68} + 16 q^{71} - 8 q^{72} + 96 q^{75} - 64 q^{77} - 16 q^{78} + 16 q^{81} + 168 q^{83} + 8 q^{86} - 36 q^{87} - 36 q^{90} + 8 q^{92} - 48 q^{93} - 128 q^{95} - 48 q^{98}+O(q^{100}) \) 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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