LMFDB - Embedded newform 630.2.bf.f.209.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(209,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3, 3]))

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

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

chi := DirichletCharacter("630.209");

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.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			209.10
Character	$\chi$	$=$	630.209
Dual form			630.2.bf.f.419.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.341957 + 1.69796i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.25628 + 1.84980i) q^{5} +(1.64145 + 0.552836i) q^{6} +(2.62496 - 0.331028i) q^{7} -1.00000 q^{8} +(-2.76613 + 1.16126i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.341957 + 1.69796i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.25628 + 1.84980i) q^{5} +(1.64145 + 0.552836i) q^{6} +(2.62496 - 0.331028i) q^{7} -1.00000 q^{8} +(-2.76613 + 1.16126i) q^{9} +(0.973830 + 2.01287i) q^{10} +(-2.49778 - 1.44209i) q^{11} +(1.29950 - 1.14512i) q^{12} +(3.34607 + 5.79556i) q^{13} +(1.02580 - 2.43880i) q^{14} +(-3.57048 - 1.50057i) q^{15} +(-0.500000 + 0.866025i) q^{16} -2.78519i q^{17} +(-0.377386 + 2.97617i) q^{18} +6.90274i q^{19} +(2.23011 + 0.163074i) q^{20} +(1.45970 + 4.34388i) q^{21} +(-2.49778 + 1.44209i) q^{22} +(2.70072 + 4.67778i) q^{23} +(-0.341957 - 1.69796i) q^{24} +(-1.84350 - 4.64774i) q^{25} +6.69214 q^{26} +(-2.91767 - 4.29968i) q^{27} +(-1.59916 - 2.10777i) q^{28} +(-3.21724 - 1.85747i) q^{29} +(-3.08477 + 2.34184i) q^{30} +(-5.83815 + 3.37066i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.59448 - 4.73426i) q^{33} +(-2.41205 - 1.39260i) q^{34} +(-2.68536 + 5.27151i) q^{35} +(2.38874 + 1.81491i) q^{36} +5.07222i q^{37} +(5.97795 + 3.45137i) q^{38} +(-8.69642 + 7.66332i) q^{39} +(1.25628 - 1.84980i) q^{40} +(-0.0641231 - 0.111064i) q^{41} +(4.49176 + 0.907806i) q^{42} +(-0.156785 - 0.0905199i) q^{43} +2.88419i q^{44} +(1.32695 - 6.57565i) q^{45} +5.40143 q^{46} +(4.40684 + 2.54429i) q^{47} +(-1.64145 - 0.552836i) q^{48} +(6.78084 - 1.73787i) q^{49} +(-4.94681 - 0.727348i) q^{50} +(4.72914 - 0.952416i) q^{51} +(3.34607 - 5.79556i) q^{52} +10.7642 q^{53} +(-5.18246 + 0.376935i) q^{54} +(5.80550 - 2.80871i) q^{55} +(-2.62496 + 0.331028i) q^{56} +(-11.7206 + 2.36044i) q^{57} +(-3.21724 + 1.85747i) q^{58} +(-5.33801 - 9.24571i) q^{59} +(0.485710 + 3.84241i) q^{60} +(6.13972 + 3.54477i) q^{61} +6.74132i q^{62} +(-6.87658 + 3.96392i) q^{63} +1.00000 q^{64} +(-14.9242 - 1.09132i) q^{65} +(-3.30275 - 3.74799i) q^{66} +(13.2772 - 7.66561i) q^{67} +(-2.41205 + 1.39260i) q^{68} +(-7.01915 + 6.18531i) q^{69} +(3.22258 + 4.96135i) q^{70} -8.02961i q^{71} +(2.76613 - 1.16126i) q^{72} -11.5538 q^{73} +(4.39267 + 2.53611i) q^{74} +(7.26127 - 4.71952i) q^{75} +(5.97795 - 3.45137i) q^{76} +(-7.03395 - 2.95861i) q^{77} +(2.28842 + 11.3630i) q^{78} +(5.64821 - 9.78299i) q^{79} +(-0.973830 - 2.01287i) q^{80} +(6.30296 - 6.42438i) q^{81} -0.128246 q^{82} +(0.452007 + 0.260967i) q^{83} +(3.03206 - 3.43607i) q^{84} +(5.15204 + 3.49899i) q^{85} +(-0.156785 + 0.0905199i) q^{86} +(2.05376 - 6.09791i) q^{87} +(2.49778 + 1.44209i) q^{88} +5.69963 q^{89} +(-5.03121 - 4.43700i) q^{90} +(10.7018 + 14.1055i) q^{91} +(2.70072 - 4.67778i) q^{92} +(-7.71964 - 8.76032i) q^{93} +(4.40684 - 2.54429i) q^{94} +(-12.7687 - 8.67180i) q^{95} +(-1.29950 + 1.14512i) q^{96} +(2.06485 - 3.57642i) q^{97} +(1.88538 - 6.74132i) q^{98} +(8.58383 + 1.08845i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} - 6 q^{9}+O(q^{10}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 - 6 * q^9	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} - 6 q^{9} - 24 q^{11} - 12 q^{15} - 16 q^{16} - 6 q^{18} + 2 q^{21} - 24 q^{22} + 24 q^{23} + 50 q^{25} - 36 q^{29} - 18 q^{30} + 16 q^{32} + 48 q^{35} - 66 q^{39} - 2 q^{42} + 54 q^{43} + 48 q^{46} + 32 q^{49} + 58 q^{50} - 26 q^{51} + 24 q^{53} - 110 q^{57} - 36 q^{58} - 6 q^{60} - 20 q^{63} + 32 q^{64} - 66 q^{65} + 66 q^{67} + 12 q^{70} + 6 q^{72} + 12 q^{74} - 18 q^{77} - 60 q^{78} + 34 q^{79} + 2 q^{81} - 4 q^{84} - 32 q^{85} + 54 q^{86} + 24 q^{88} + 16 q^{91} + 24 q^{92} - 28 q^{93} - 24 q^{95} + 64 q^{98} + 58 q^{99}+O(q^{100}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 - 6 * q^9 - 24 * q^11 - 12 * q^15 - 16 * q^16 - 6 * q^18 + 2 * q^21 - 24 * q^22 + 24 * q^23 + 50 * q^25 - 36 * q^29 - 18 * q^30 + 16 * q^32 + 48 * q^35 - 66 * q^39 - 2 * q^42 + 54 * q^43 + 48 * q^46 + 32 * q^49 + 58 * q^50 - 26 * q^51 + 24 * q^53 - 110 * q^57 - 36 * q^58 - 6 * q^60 - 20 * q^63 + 32 * q^64 - 66 * q^65 + 66 * q^67 + 12 * q^70 + 6 * q^72 + 12 * q^74 - 18 * q^77 - 60 * q^78 + 34 * q^79 + 2 * q^81 - 4 * q^84 - 32 * q^85 + 54 * q^86 + 24 * q^88 + 16 * q^91 + 24 * q^92 - 28 * q^93 - 24 * q^95 + 64 * q^98 + 58 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.341957	+	1.69796i	0.197429	+	0.980317i
$3$	0.341957	+	1.69796i	0.197429	+	0.980317i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.25628	+	1.84980i	−0.561827	+	0.827255i
$5$	−1.25628	+	1.84980i	−0.561827	+	0.827255i
$6$	1.64145	+	0.552836i	0.670121	+	0.225694i
$7$	2.62496	−	0.331028i	0.992142	−	0.125117i
$7$	2.62496	−	0.331028i	0.992142	−	0.125117i
$8$	−1.00000			−0.353553
$9$	−2.76613	+	1.16126i	−0.922044	+	0.387086i
$10$	0.973830	+	2.01287i	0.307952	+	0.636526i
$11$	−2.49778	−	1.44209i	−0.753109	−	0.434808i	0.0737072	−	0.997280i	$-0.476517\pi$
$11$	−2.49778	−	1.44209i	−0.753109	−	0.434808i	−0.826816	+	0.562472i	$0.809850\pi$
$12$	1.29950	−	1.14512i	0.375133	−	0.330569i
$13$	3.34607	+	5.79556i	0.928033	+	1.60740i	0.786610	+	0.617451i	$0.211834\pi$
$13$	3.34607	+	5.79556i	0.928033	+	1.60740i	0.141423	+	0.989949i	$0.454832\pi$
$14$	1.02580	−	2.43880i	0.274157	−	0.651796i
$15$	−3.57048	−	1.50057i	−0.921893	−	0.387445i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		−	2.78519i		−	0.675509i	−0.941234	−	0.337754i	$-0.890333\pi$
$17$		−	2.78519i		−	0.675509i	0.941234	−	0.337754i	$-0.109667\pi$
$18$	−0.377386	+	2.97617i	−0.0889508	+	0.701490i
$19$			6.90274i			1.58360i	0.610782	+	0.791799i	$0.290855\pi$
$19$			6.90274i			1.58360i	−0.610782	+	0.791799i	$0.709145\pi$
$20$	2.23011	+	0.163074i	0.498669	+	0.0364645i
$21$	1.45970	+	4.34388i	0.318532	+	0.947912i
$22$	−2.49778	+	1.44209i	−0.532528	+	0.307455i
$23$	2.70072	+	4.67778i	0.563138	+	0.975384i	0.997220	+	0.0745107i	$0.0237395\pi$
$23$	2.70072	+	4.67778i	0.563138	+	0.975384i	−0.434082	+	0.900873i	$0.642927\pi$
$24$	−0.341957	−	1.69796i	−0.0698017	−	0.346594i
$25$	−1.84350	−	4.64774i	−0.368701	−	0.929548i
$26$	6.69214			1.31244
$27$	−2.91767	−	4.29968i	−0.561505	−	0.827473i
$28$	−1.59916	−	2.10777i	−0.302213	−	0.398331i
$29$	−3.21724	−	1.85747i	−0.597426	−	0.344924i	0.170602	−	0.985340i	$-0.445429\pi$
$29$	−3.21724	−	1.85747i	−0.597426	−	0.344924i	−0.768028	+	0.640416i	$0.778762\pi$
$30$	−3.08477	+	2.34184i	−0.563199	+	0.427560i
$31$	−5.83815	+	3.37066i	−1.04856	+	0.605388i	−0.922247	−	0.386602i	$-0.873649\pi$
$31$	−5.83815	+	3.37066i	−1.04856	+	0.605388i	−0.126316	+	0.991990i	$0.540315\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.59448	−	4.73426i	0.277564	−	0.824129i
$34$	−2.41205	−	1.39260i	−0.413663	−	0.238828i
$35$	−2.68536	+	5.27151i	−0.453909	+	0.891048i
$36$	2.38874	+	1.81491i	0.398124	+	0.302485i
$37$			5.07222i			0.833868i	0.908937	+	0.416934i	$0.136895\pi$
$37$			5.07222i			0.833868i	−0.908937	+	0.416934i	$0.863105\pi$
$38$	5.97795	+	3.45137i	0.969751	+	0.559886i
$39$	−8.69642	+	7.66332i	−1.39254	+	1.22711i
$40$	1.25628	−	1.84980i	0.198636	−	0.292479i
$41$	−0.0641231	−	0.111064i	−0.0100143	−	0.0173453i	0.860975	−	0.508648i	$-0.169854\pi$
$41$	−0.0641231	−	0.111064i	−0.0100143	−	0.0173453i	−0.870989	+	0.491302i	$0.836521\pi$
$42$	4.49176	+	0.907806i	0.693093	+	0.140078i
$43$	−0.156785	−	0.0905199i	−0.0239095	−	0.0138041i	0.487998	−	0.872845i	$-0.337727\pi$
$43$	−0.156785	−	0.0905199i	−0.0239095	−	0.0138041i	−0.511907	+	0.859041i	$0.671061\pi$
$44$			2.88419i			0.434808i
$45$	1.32695	−	6.57565i	0.197810	−	0.980240i
$46$	5.40143			0.796398
$47$	4.40684	+	2.54429i	0.642804	+	0.371123i	0.785694	−	0.618616i	$-0.212306\pi$
$47$	4.40684	+	2.54429i	0.642804	+	0.371123i	−0.142890	+	0.989739i	$0.545640\pi$
$48$	−1.64145	−	0.552836i	−0.236924	−	0.0797950i
$49$	6.78084	−	1.73787i	0.968692	−	0.248267i
$50$	−4.94681	−	0.727348i	−0.699585	−	0.102863i
$51$	4.72914	−	0.952416i	0.662213	−	0.133365i
$52$	3.34607	−	5.79556i	0.464016	−	0.803700i
$53$	10.7642			1.47858			0.739290	−	0.673387i	$-0.235161\pi$
$53$	10.7642			1.47858			0.739290	+	0.673387i	$0.235161\pi$
$54$	−5.18246	+	0.376935i	−0.705244	+	0.0512944i
$55$	5.80550	−	2.80871i	0.782814	−	0.378726i
$56$	−2.62496	+	0.331028i	−0.350775	+	0.0442355i
$57$	−11.7206	+	2.36044i	−1.55243	+	0.312648i
$58$	−3.21724	+	1.85747i	−0.422444	+	0.243898i
$59$	−5.33801	−	9.24571i	−0.694950	−	1.20369i	−0.970198	−	0.242315i	$-0.922093\pi$
$59$	−5.33801	−	9.24571i	−0.694950	−	1.20369i	0.275248	−	0.961373i	$-0.411240\pi$
$60$	0.485710	+	3.84241i	0.0627048	+	0.496053i
$61$	6.13972	+	3.54477i	0.786110	+	0.453861i	0.838591	−	0.544761i	$-0.183380\pi$
$61$	6.13972	+	3.54477i	0.786110	+	0.453861i	−0.0524812	+	0.998622i	$0.516713\pi$
$62$			6.74132i			0.856148i
$63$	−6.87658	+	3.96392i	−0.866367	+	0.499407i
$64$	1.00000			0.125000
$65$	−14.9242	−	1.09132i	−1.85112	−	0.135361i
$66$	−3.30275	−	3.74799i	−0.406540	−	0.461346i
$67$	13.2772	−	7.66561i	1.62207	−	0.936503i	0.635706	−	0.771931i	$-0.280709\pi$
$67$	13.2772	−	7.66561i	1.62207	−	0.936503i	0.986365	−	0.164572i	$-0.0526244\pi$
$68$	−2.41205	+	1.39260i	−0.292504	+	0.168877i
$69$	−7.01915	+	6.18531i	−0.845006	+	0.744623i
$70$	3.22258	+	4.96135i	0.385172	+	0.592994i
$71$		−	8.02961i		−	0.952939i	−0.879191	−	0.476470i	$-0.841916\pi$
$71$		−	8.02961i		−	0.952939i	0.879191	−	0.476470i	$-0.158084\pi$
$72$	2.76613	−	1.16126i	0.325992	−	0.136856i
$73$	−11.5538			−1.35226			−0.676132	−	0.736780i	$-0.736345\pi$
$73$	−11.5538			−1.35226			−0.676132	+	0.736780i	$0.736345\pi$
$74$	4.39267	+	2.53611i	0.510638	+	0.294817i
$75$	7.26127	−	4.71952i	0.838460	−	0.544964i
$76$	5.97795	−	3.45137i	0.685718	−	0.395899i
$77$	−7.03395	−	2.95861i	−0.801593	−	0.337164i
$78$	2.28842	+	11.3630i	0.259113	+	1.28660i
$79$	5.64821	−	9.78299i	0.635473	−	1.10067i	−0.350941	−	0.936398i	$-0.614138\pi$
$79$	5.64821	−	9.78299i	0.635473	−	1.10067i	0.986415	−	0.164275i	$-0.0525284\pi$
$80$	−0.973830	−	2.01287i	−0.108878	−	0.225046i
$81$	6.30296	−	6.42438i	0.700329	−	0.713820i
$82$	−0.128246			−0.0141624
$83$	0.452007	+	0.260967i	0.0496142	+	0.0286448i	0.524602	−	0.851348i	$-0.324214\pi$
$83$	0.452007	+	0.260967i	0.0496142	+	0.0286448i	−0.474988	+	0.879992i	$0.657547\pi$
$84$	3.03206	−	3.43607i	0.330825	−	0.374906i
$85$	5.15204	+	3.49899i	0.558818	+	0.379519i
$86$	−0.156785	+	0.0905199i	−0.0169066	+	0.00976101i
$87$	2.05376	−	6.09791i	0.220186	−	0.653765i
$88$	2.49778	+	1.44209i	0.266264	+	0.153728i
$89$	5.69963			0.604160			0.302080	−	0.953283i	$-0.402319\pi$
$89$	5.69963			0.604160			0.302080	+	0.953283i	$0.402319\pi$
$90$	−5.03121	−	4.43700i	−0.530336	−	0.467701i
$91$	10.7018	+	14.1055i	1.12185	+	1.47866i
$92$	2.70072	−	4.67778i	0.281569	−	0.487692i
$93$	−7.71964	−	8.76032i	−0.800489	−	0.908403i
$94$	4.40684	−	2.54429i	0.454531	−	0.262423i
$95$	−12.7687	−	8.67180i	−1.31004	−	0.889708i
$96$	−1.29950	+	1.14512i	−0.132629	+	0.116874i
$97$	2.06485	−	3.57642i	0.209654	−	0.363131i	−0.741952	−	0.670453i	$-0.766100\pi$
$97$	2.06485	−	3.57642i	0.209654	−	0.363131i	0.951605	+	0.307322i	$0.0994330\pi$
$98$	1.88538	−	6.74132i	0.190452	−	0.680976i
$99$	8.58383	+	1.08845i	0.862707	+	0.109394i
$100$	−3.10331	+	3.92039i	−0.310331	+	0.392039i
$101$	1.39285	−	2.41249i	0.138594	−	0.240052i	−0.788371	−	0.615201i	$-0.789075\pi$
$101$	1.39285	−	2.41249i	0.138594	−	0.240052i	0.926965	+	0.375149i	$0.122408\pi$
$102$	1.53976	−	4.57177i	0.152459	−	0.452672i
$103$	−4.24895	−	7.35940i	−0.418662	−	0.725143i	0.577143	−	0.816643i	$-0.304167\pi$
$103$	−4.24895	−	7.35940i	−0.418662	−	0.725143i	−0.995805	+	0.0914994i	$0.970834\pi$
$104$	−3.34607	−	5.79556i	−0.328109	−	0.568302i
$105$	−9.86909	−	2.75700i	−0.963125	−	0.269056i
$106$	5.38211	−	9.32209i	0.522757	−	0.905441i
$107$	7.87180			0.760995			0.380498	−	0.924782i	$-0.375753\pi$
$107$	7.87180			0.760995			0.380498	+	0.924782i	$0.375753\pi$
$108$	−2.26480	+	4.67661i	−0.217930	+	0.450007i
$109$	2.83000			0.271065			0.135532	−	0.990773i	$-0.456726\pi$
$109$	2.83000			0.271065			0.135532	+	0.990773i	$0.456726\pi$
$110$	0.470337	−	6.43207i	0.0448448	−	0.613273i
$111$	−8.61243	+	1.73448i	−0.817455	+	0.164630i
$112$	−1.02580	+	2.43880i	−0.0969292	+	0.230445i
$113$	1.48562	+	2.57317i	0.139756	+	0.242064i	0.927404	−	0.374061i	$-0.122035\pi$
$113$	1.48562	+	2.57317i	0.139756	+	0.242064i	−0.787648	+	0.616125i	$0.788702\pi$
$114$	−3.81608	+	11.3305i	−0.357409	+	1.06120i
$115$	−12.0458	−	0.880835i	−1.12328	−	0.0821383i
$116$			3.71494i			0.344924i
$117$	−15.9858	−	12.1456i	−1.47789	−	1.12286i
$118$	−10.6760			−0.982808
$119$	−0.921977	−	7.31102i	−0.0845174	−	0.670200i
$120$	3.57048	+	1.50057i	0.325938	+	0.136982i
$121$	−1.34073	−	2.32222i	−0.121885	−	0.211110i
$122$	6.13972	−	3.54477i	0.555864	−	0.320928i
$123$	0.166655	−	0.146858i	0.0150268	−	0.0132417i
$124$	5.83815	+	3.37066i	0.524281	+	0.302694i
$125$	10.9133	+	2.42877i	0.976119	+	0.217236i
$126$	−0.00542995	+	7.93725i	−0.000483739	+	0.707107i
$127$			1.22339i			0.108558i	0.998526	+	0.0542790i	$0.0172860\pi$
$127$			1.22339i			0.108558i	−0.998526	+	0.0542790i	$0.982714\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	0.100085	−	0.297168i	0.00881202	−	0.0261642i
$130$	−8.40722	+	12.3791i	−0.737362	+	1.08572i
$131$	1.93558	+	3.35252i	0.169112	+	0.292911i	0.938108	−	0.346343i	$-0.112577\pi$
$131$	1.93558	+	3.35252i	0.169112	+	0.292911i	−0.768996	+	0.639254i	$0.779243\pi$
$132$	−4.89723	+	0.986268i	−0.426249	+	0.0858436i
$133$	2.28500	+	18.1194i	0.198135	+	1.57115i
$134$		−	15.3312i		−	1.32442i
$135$	11.6189	+	0.00451831i	1.00000	+	0.000388874i
$136$			2.78519i			0.238828i
$137$	−9.18261	+	15.9048i	−0.784524	+	1.35883i	0.144760	+	0.989467i	$0.453759\pi$
$137$	−9.18261	+	15.9048i	−0.784524	+	1.35883i	−0.929283	+	0.369368i	$0.879574\pi$
$138$	1.84706	+	9.17141i	0.157232	+	0.780722i
$139$	1.73438	−	1.00134i	0.147108	−	0.0849329i	−0.424639	−	0.905363i	$-0.639599\pi$
$139$	1.73438	−	1.00134i	0.147108	−	0.0849329i	0.571747	+	0.820430i	$0.306266\pi$
$140$	5.90794	−	0.310166i	0.499312	−	0.0262138i
$141$	−2.81315	+	8.35267i	−0.236910	+	0.703422i
$142$	−6.95385	−	4.01480i	−0.583554	−	0.336915i
$143$		−	19.3014i		−	1.61406i
$144$	0.377386	−	2.97617i	0.0314489	−	0.248014i
$145$	7.47771	−	3.61773i	0.620990	−	0.300436i
$146$	−5.77688	+	10.0058i	−0.478098	+	0.828089i
$147$	5.26959	+	10.9193i	0.434628	+	0.900610i
$148$	4.39267	−	2.53611i	0.361075	−	0.208467i
$149$	−3.66784	+	2.11763i	−0.300481	+	0.173483i	−0.642659	−	0.766152i	$-0.722169\pi$
$149$	−3.66784	+	2.11763i	−0.300481	+	0.173483i	0.342178	+	0.939635i	$0.388835\pi$
$150$	−0.456590	−	8.64821i	−0.0372804	−	0.706123i
$151$	7.80273	−	13.5147i	0.634977	−	1.09981i	−0.351543	−	0.936172i	$-0.614343\pi$
$151$	7.80273	−	13.5147i	0.634977	−	1.09981i	0.986520	−	0.163640i	$-0.0523237\pi$
$152$		−	6.90274i		−	0.559886i
$153$	3.23433	+	7.70421i	0.261480	+	0.622848i
$154$	−6.07920	+	4.61227i	−0.489876	+	0.371668i
$155$	1.09934	−	15.0339i	0.0883007	−	1.20755i
$156$	10.9848	+	3.69966i	0.879491	+	0.296210i
$157$	5.31314	+	9.20264i	0.424035	+	0.734450i	0.996330	−	0.0855977i	$-0.0272800\pi$
$157$	5.31314	+	9.20264i	0.424035	+	0.734450i	−0.572295	+	0.820048i	$0.693947\pi$
$158$	−5.64821	−	9.78299i	−0.449348	−	0.778293i
$159$	3.68090	+	18.2772i	0.291914	+	1.44948i
$160$	−2.23011	−	0.163074i	−0.176306	−	0.0128922i
$161$	8.63775	+	11.3850i	0.680750	+	0.897262i
$162$	−2.41220	−	8.67071i	−0.189520	−	0.681236i
$163$		−	15.5123i		−	1.21501i	−0.794314	−	0.607507i	$-0.792170\pi$
$163$		−	15.5123i		−	1.21501i	0.794314	−	0.607507i	$-0.207830\pi$
$164$	−0.0641231	+	0.111064i	−0.00500717	+	0.00867267i
$165$	6.75431	+	8.89705i	0.525822	+	0.692634i
$166$	0.452007	−	0.260967i	0.0350826	−	0.0202549i
$167$	−18.9472	+	10.9392i	−1.46618	+	0.846500i	−0.999285	−	0.0378126i	$-0.987961\pi$
$167$	−18.9472	+	10.9392i	−1.46618	+	0.846500i	−0.466896	+	0.884312i	$0.654628\pi$
$168$	−1.45970	−	4.34388i	−0.112618	−	0.335138i
$169$	−15.8924	+	27.5264i	−1.22249	+	2.11741i
$170$	5.60624	−	2.71231i	0.429979	−	0.208024i
$171$	−8.01586	−	19.0939i	−0.612988	−	1.46015i
$172$			0.181040i			0.0138041i
$173$	0.210768	+	0.121687i	0.0160244	+	0.00925168i	0.507991	−	0.861362i	$-0.330388\pi$
$173$	0.210768	+	0.121687i	0.0160244	+	0.00925168i	−0.491966	+	0.870614i	$0.663722\pi$
$174$	−4.25407	−	4.82756i	−0.322500	−	0.365976i
$175$	−6.37766	−	11.5899i	−0.482106	−	0.876113i
$176$	2.49778	−	1.44209i	0.188277	−	0.108702i
$177$	13.8735	−	12.2254i	1.04279	−	0.918915i
$178$	2.84982	−	4.93603i	0.213603	−	0.369971i
$179$		−	2.36907i		−	0.177073i	−0.996073	−	0.0885365i	$-0.971781\pi$
$179$		−	2.36907i		−	0.177073i	0.996073	−	0.0885365i	$-0.0282190\pi$
$180$	−6.35816	+	2.13865i	−0.473909	+	0.159406i
$181$			6.97633i			0.518546i	0.965804	+	0.259273i	$0.0834830\pi$
$181$			6.97633i			0.518546i	−0.965804	+	0.259273i	$0.916517\pi$
$182$	17.5666	−	2.21528i	1.30212	−	0.164208i
$183$	−3.91935	+	11.6371i	−0.289727	+	0.860243i
$184$	−2.70072	−	4.67778i	−0.199099	−	0.344850i
$185$	−9.38259	−	6.37215i	−0.689821	−	0.468490i
$186$	−11.4465	+	2.30524i	−0.839297	+	0.169028i
$187$	−4.01651	+	6.95680i	−0.293716	+	0.508732i
$188$		−	5.08858i		−	0.371123i
$189$	−9.08207	−	10.3207i	−0.660624	−	0.750717i
$190$	−13.8943	+	6.72210i	−1.00800	+	0.487672i
$191$	9.85202	+	5.68807i	0.712867	+	0.411574i	0.812122	−	0.583488i	$-0.198312\pi$
$191$	9.85202	+	5.68807i	0.712867	+	0.411574i	−0.0992545	+	0.995062i	$0.531646\pi$
$192$	0.341957	+	1.69796i	0.0246786	+	0.122540i
$193$	1.91539	−	1.10585i	0.137873	−	0.0796010i	−0.429477	−	0.903078i	$-0.641302\pi$
$193$	1.91539	−	1.10585i	0.137873	−	0.0796010i	0.567350	+	0.823477i	$0.307969\pi$
$194$	−2.06485	−	3.57642i	−0.148248	−	0.256772i
$195$	−3.25044	−	25.7139i	−0.232769	−	1.84141i
$196$	−4.89546	−	5.00345i	−0.349676	−	0.357389i
$197$	−24.5072			−1.74607			−0.873034	−	0.487660i	$-0.837851\pi$
$197$	−24.5072			−1.74607			−0.873034	+	0.487660i	$0.837851\pi$
$198$	5.23454	−	6.88959i	0.372003	−	0.489622i
$199$		−	10.4878i		−	0.743458i	−0.928341	−	0.371729i	$-0.878765\pi$
$199$		−	10.4878i		−	0.743458i	0.928341	−	0.371729i	$-0.121235\pi$
$200$	1.84350	+	4.64774i	0.130355	+	0.328645i
$201$	17.5561	+	19.9229i	1.23831	+	1.40525i
$202$	−1.39285	−	2.41249i	−0.0980008	−	0.169742i
$203$	−9.05999	−	3.81080i	−0.635887	−	0.267466i
$204$	−3.18939	−	3.61935i	−0.223302	−	0.253405i
$205$	0.286003	+	0.0209136i	0.0199753	+	0.00146067i
$206$	−8.49790			−0.592077
$207$	−12.9026	−	9.80312i	−0.896796	−	0.681364i
$208$	−6.69214			−0.464016
$209$	9.95440	−	17.2415i	0.688560	−	1.19262i
$210$	−7.32218	+	7.16838i	−0.505278	+	0.494665i
$211$	3.83172	+	6.63673i	0.263786	+	0.456891i	0.967245	−	0.253845i	$-0.0816953\pi$
$211$	3.83172	+	6.63673i	0.263786	+	0.456891i	−0.703459	+	0.710736i	$0.748362\pi$
$212$	−5.38211	−	9.32209i	−0.369645	−	0.640244i
$213$	13.6339	−	2.74578i	0.934183	−	0.188138i
$214$	3.93590	−	6.81718i	0.269052	−	0.466013i
$215$	0.364410	−	0.176302i	0.0248525	−	0.0120237i
$216$	2.91767	+	4.29968i	0.198522	+	0.292556i
$217$	−14.2091	+	10.7804i	−0.964579	+	0.731824i
$218$	1.41500	−	2.45085i	0.0958359	−	0.165993i
$219$	−3.95089	−	19.6178i	−0.266976	−	1.32565i
$220$	−5.33516	−	3.62336i	−0.359697	−	0.244287i
$221$	16.1418	−	9.31945i	1.08581	−	0.626894i
$222$	−2.80411	+	8.32582i	−0.188199	+	0.558792i
$223$	6.09914	−	10.5640i	0.408428	−	0.707419i	−0.586285	−	0.810105i	$-0.699410\pi$
$223$	6.09914	−	10.5640i	0.408428	−	0.707419i	0.994714	+	0.102686i	$0.0327436\pi$
$224$	1.59916	+	2.10777i	0.106848	+	0.140831i
$225$	10.4966	+	10.7155i	0.699773	+	0.714365i
$226$	2.97125			0.197644
$227$	5.40529	+	3.12075i	0.358762	+	0.207131i	0.668538	−	0.743678i	$-0.266921\pi$
$227$	5.40529	+	3.12075i	0.358762	+	0.207131i	−0.309776	+	0.950810i	$0.600254\pi$
$228$	7.90449	+	8.97009i	0.523487	+	0.594059i
$229$	4.10058	−	2.36747i	0.270974	−	0.156447i	−0.358356	−	0.933585i	$-0.616663\pi$
$229$	4.10058	−	2.36747i	0.270974	−	0.156447i	0.629330	+	0.777138i	$0.283329\pi$
$230$	−6.78573	+	9.99156i	−0.447438	+	0.658824i
$231$	2.61828	−	12.9551i	0.172270	−	0.852381i
$232$	3.21724	+	1.85747i	0.211222	+	0.121949i
$233$	19.3901			1.27029			0.635143	−	0.772394i	$-0.280941\pi$
$233$	19.3901			1.27029			0.635143	+	0.772394i	$0.280941\pi$
$234$	−18.5113	+	7.77130i	−1.21012	+	0.508026i
$235$	−10.2427	+	4.95541i	−0.668158	+	0.323256i
$236$	−5.33801	+	9.24571i	−0.347475	+	0.601844i
$237$	18.5426	+	6.24507i	1.20447	+	0.405661i
$238$	−6.79252	−	2.85706i	−0.440294	−	0.185195i
$239$	6.40008	−	3.69509i	0.413987	−	0.239015i	−0.278514	−	0.960432i	$-0.589842\pi$
$239$	6.40008	−	3.69509i	0.413987	−	0.239015i	0.692501	+	0.721417i	$0.256509\pi$
$240$	3.08477	−	2.34184i	0.199121	−	0.151165i
$241$	5.66724	+	3.27198i	0.365059	+	0.210767i	0.671298	−	0.741188i	$-0.265737\pi$
$241$	5.66724	+	3.27198i	0.365059	+	0.210767i	−0.306239	+	0.951955i	$0.599071\pi$
$242$	−2.68146			−0.172371
$243$	13.0637	+	8.50530i	0.838036	+	0.545616i
$244$		−	7.08953i		−	0.453861i
$245$	−5.30395	+	14.7264i	−0.338857	+	0.940838i
$246$	−0.0438547	−	0.217757i	−0.00279607	−	0.0138837i
$247$	−40.0053	+	23.0970i	−2.54547	+	1.46963i
$248$	5.83815	−	3.37066i	0.370723	−	0.214037i
$249$	−0.288543	+	0.856729i	−0.0182857	+	0.0542930i
$250$	7.56005	−	8.23685i	0.478139	−	0.520944i
$251$	−4.77100			−0.301143			−0.150571	−	0.988599i	$-0.548111\pi$
$251$	−4.77100			−0.301143			−0.150571	+	0.988599i	$0.548111\pi$
$252$	6.87115	+	3.97333i	0.432842	+	0.250296i
$253$		−	15.5787i		−	0.979427i
$254$	1.05948	+	0.611693i	0.0664779	+	0.0383810i
$255$	−4.17937	+	9.94447i	−0.261722	+	0.622747i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.44184	+	4.29655i	−0.464209	+	0.268011i	−0.713812	−	0.700337i	$-0.753033\pi$
$257$	−7.44184	+	4.29655i	−0.464209	+	0.268011i	0.249603	+	0.968348i	$0.419700\pi$
$258$	−0.207313	−	0.235261i	−0.0129067	−	0.0146467i
$259$	1.67905	+	13.3144i	0.104331	+	0.827316i
$260$	6.51701	+	13.4704i	0.404168	+	0.835400i
$261$	11.0563	+	1.40197i	0.684368	+	0.0867797i
$262$	3.87116			0.239161
$263$	−8.65466	+	14.9903i	−0.533669	+	0.924343i	0.465557	+	0.885018i	$0.345854\pi$
$263$	−8.65466	+	14.9903i	−0.533669	+	0.924343i	−0.999226	+	0.0393247i	$0.987479\pi$
$264$	−1.59448	+	4.73426i	−0.0981336	+	0.291374i
$265$	−13.5229	+	19.9116i	−0.830706	+	1.22316i
$266$	16.8344	+	7.08084i	1.03218	+	0.434154i
$267$	1.94903	+	9.67774i	0.119279	+	0.592268i
$268$	−13.2772	−	7.66561i	−0.811036	−	0.468252i
$269$	−20.2422			−1.23419			−0.617093	−	0.786890i	$-0.711690\pi$
$269$	−20.2422			−1.23419			−0.617093	+	0.786890i	$0.711690\pi$
$270$	5.81339	−	10.0600i	0.353791	−	0.612235i
$271$		−	18.4494i		−	1.12072i	−0.828249	−	0.560361i	$-0.810663\pi$
$271$		−	18.4494i		−	1.12072i	0.828249	−	0.560361i	$-0.189337\pi$
$272$	2.41205	+	1.39260i	0.146252	+	0.0844386i
$273$	−20.2910	+	22.9947i	−1.22807	+	1.39170i
$274$	9.18261	+	15.9048i	0.554742	+	0.960841i
$275$	−2.09781	+	14.2675i	−0.126503	+	0.860365i
$276$	8.86621	+	2.98611i	0.533683	+	0.179743i
$277$	13.5806	+	7.84078i	0.815981	+	0.471107i	0.849029	−	0.528347i	$-0.177188\pi$
$277$	13.5806	+	7.84078i	0.815981	+	0.471107i	−0.0330473	+	0.999454i	$0.510521\pi$
$278$		−	2.00269i		−	0.120113i
$279$	12.2349	−	16.1033i	0.732483	−	0.964078i
$280$	2.68536	−	5.27151i	0.160481	−	0.315033i
$281$	−4.23315	−	2.44401i	−0.252529	−	0.145797i	0.368393	−	0.929670i	$-0.379908\pi$
$281$	−4.23315	−	2.44401i	−0.252529	−	0.145797i	−0.620921	+	0.783873i	$0.713241\pi$
$282$	5.82705	+	6.61260i	0.346996	+	0.393774i
$283$	−8.47758	−	14.6836i	−0.503940	−	0.872849i	−0.999990	−	0.00455536i	$-0.998550\pi$
$283$	−8.47758	−	14.6836i	−0.503940	−	0.872849i	0.496050	−	0.868294i	$-0.334783\pi$
$284$	−6.95385	+	4.01480i	−0.412635	+	0.238235i
$285$	10.3580	−	24.6461i	0.613556	−	1.45991i
$286$	−16.7155	−	9.65069i	−0.988408	−	0.570657i
$287$	−0.205086	−	0.270313i	−0.0121058	−	0.0159561i
$288$	−2.38874	−	1.81491i	−0.140758	−	0.106945i
$289$	9.24270			0.543688
$290$	0.605812	−	8.28475i	0.0355745	−	0.486497i
$291$	6.77871	+	2.28305i	0.397375	+	0.133835i
$292$	5.77688	+	10.0058i	0.338066	+	0.585548i
$293$	29.0414	−	16.7670i	1.69661	−	0.979541i	0.747685	−	0.664054i	$-0.231165\pi$
$293$	29.0414	−	16.7670i	1.69661	−	0.979541i	0.948930	−	0.315487i	$-0.102168\pi$
$294$	12.0912	+	0.896059i	0.705173	+	0.0522592i
$295$	23.8087	+	1.74098i	1.38620	+	0.101364i
$296$		−	5.07222i		−	0.294817i
$297$	1.08715	+	14.9472i	0.0630829	+	0.867324i
$298$			4.23525i			0.245342i
$299$	−18.0736	+	31.3043i	−1.04522	+	1.81038i
$300$	−7.71786	−	3.92869i	−0.445591	−	0.226823i
$301$	−0.441519	−	0.185711i	−0.0254487	−	0.0107042i
$302$	−7.80273	−	13.5147i	−0.448996	−	0.777685i
$303$	4.57261	+	1.54004i	0.262690	+	0.0884729i
$304$	−5.97795	−	3.45137i	−0.342859	−	0.197950i
$305$	−14.2703	+	6.90400i	−0.817117	+	0.395322i
$306$	8.28920	+	1.05109i	0.473862	+	0.0600870i
$307$	10.5457			0.601877			0.300938	−	0.953644i	$-0.402700\pi$
$307$	10.5457			0.601877			0.300938	+	0.953644i	$0.402700\pi$
$308$	0.954746	+	7.57088i	0.0544017	+	0.431391i
$309$	11.0430	−	9.73115i	0.628215	−	0.553586i
$310$	−12.4701	−	8.46900i	−0.708253	−	0.481007i
$311$	−1.05850	−	1.83337i	−0.0600219	−	0.103961i	0.834453	−	0.551079i	$-0.185784\pi$
$311$	−1.05850	−	1.83337i	−0.0600219	−	0.103961i	−0.894475	+	0.447118i	$0.852450\pi$
$312$	8.69642	−	7.66332i	0.492338	−	0.433850i
$313$	−12.9677	+	22.4606i	−0.732975	+	1.26955i	0.222631	+	0.974903i	$0.428536\pi$
$313$	−12.9677	+	22.4606i	−0.732975	+	1.26955i	−0.955606	+	0.294647i	$0.904798\pi$
$314$	10.6263			0.599676
$315$	1.30647	−	17.7001i	0.0736113	−	0.997287i
$316$	−11.2964			−0.635473
$317$	−6.65836	+	11.5326i	−0.373971	+	0.647736i	−0.990172	−	0.139852i	$-0.955337\pi$
$317$	−6.65836	+	11.5326i	−0.373971	+	0.647736i	0.616202	+	0.787588i	$0.288671\pi$
$318$	17.6690	+	5.95085i	0.990827	+	0.333707i
$319$	5.35730	+	9.27911i	0.299951	+	0.519530i
$320$	−1.25628	+	1.84980i	−0.0702284	+	0.103407i
$321$	2.69182	+	13.3660i	0.150243	+	0.746017i
$322$	14.1786	−	1.78802i	0.790140	−	0.0996427i
$323$	19.2255			1.06973
$324$	−8.71516	−	2.24633i	−0.484176	−	0.124796i
$325$	20.7678	−	26.2358i	1.15199	−	1.45530i
$326$	−13.4340	−	7.75613i	−0.744041	−	0.429572i
$327$	0.967738	+	4.80522i	0.0535160	+	0.265729i
$328$	0.0641231	+	0.111064i	0.00354060	+	0.00613250i
$329$	12.4100	+	5.21988i	0.684186	+	0.287781i
$330$	11.0822	−	1.40088i	0.610056	−	0.0771158i
$331$	−6.16750	+	10.6824i	−0.338996	+	0.587159i	−0.984244	−	0.176814i	$-0.943421\pi$
$331$	−6.16750	+	10.6824i	−0.338996	+	0.587159i	0.645248	+	0.763973i	$0.276754\pi$
$332$		−	0.521933i		−	0.0286448i
$333$	−5.89016	−	14.0304i	−0.322779	−	0.768863i
$334$			21.8784i			1.19713i
$335$	−2.50013	+	34.1904i	−0.136597	+	1.86802i
$336$	−4.49176	−	0.907806i	−0.245045	−	0.0495249i
$337$	16.1121	−	9.30233i	0.877683	−	0.506730i	0.00778915	−	0.999970i	$-0.497521\pi$
$337$	16.1121	−	9.30233i	0.877683	−	0.506730i	0.869894	+	0.493239i	$0.164187\pi$
$338$	15.8924	+	27.5264i	0.864431	+	1.49724i
$339$	−3.86113	+	3.40244i	−0.209708	+	0.184795i
$340$	0.454193	−	6.21130i	0.0246321	−	0.336855i
$341$	19.4432			1.05291
$342$	−20.5437	−	2.60500i	−1.11088	−	0.140862i
$343$	17.2242	−	6.80649i	0.930017	−	0.367516i
$344$	0.156785	+	0.0905199i	0.00845328	+	0.00488050i
$345$	−2.62353	−	20.7545i	−0.141246	−	1.11738i
$346$	0.210768	−	0.121687i	0.0113310	−	0.00654193i
$347$	17.8882	+	30.9832i	0.960288	+	1.66327i	0.721774	+	0.692129i	$0.243327\pi$
$347$	17.8882	+	30.9832i	0.960288	+	1.66327i	0.238514	+	0.971139i	$0.423340\pi$
$348$	−6.30782	+	1.27035i	−0.338135	+	0.0680980i
$349$	−0.571123	−	0.329738i	−0.0305715	−	0.0176505i	0.484636	−	0.874716i	$-0.338952\pi$
$349$	−0.571123	−	0.329738i	−0.0305715	−	0.0176505i	−0.515208	+	0.857065i	$0.672285\pi$
$350$	−13.2260	−	0.271728i	−0.706958	−	0.0145245i
$351$	15.1563	−	31.2965i	0.808985	−	1.67049i
$352$		−	2.88419i		−	0.153728i
$353$	5.34455	+	3.08568i	0.284462	+	0.164234i	0.635442	−	0.772149i	$-0.280818\pi$
$353$	5.34455	+	3.08568i	0.284462	+	0.164234i	−0.350980	+	0.936383i	$0.614151\pi$
$354$	−3.65074	−	18.1275i	−0.194035	−	0.963463i
$355$	14.8532	+	10.0875i	0.788324	+	0.535387i
$356$	−2.84982	−	4.93603i	−0.151040	−	0.261609i
$357$	12.0985	−	4.06553i	0.640323	−	0.215171i
$358$	−2.05168	−	1.18454i	−0.108435	−	0.0626047i
$359$			6.18342i			0.326348i	0.986597	+	0.163174i	$0.0521733\pi$
$359$			6.18342i			0.326348i	−0.986597	+	0.163174i	$0.947827\pi$
$360$	−1.32695	+	6.57565i	−0.0699365	+	0.346567i
$361$	−28.6478			−1.50778
$362$	6.04167	+	3.48816i	0.317543	+	0.183334i
$363$	3.48455	−	3.07061i	0.182892	−	0.161165i
$364$	6.86481	−	16.3208i	0.359814	−	0.855441i
$365$	14.5148	−	21.3721i	0.759739	−	1.11867i
$366$	8.11839	+	9.21283i	0.424355	+	0.481562i
$367$	10.8697	−	18.8268i	0.567392	−	0.982751i	−0.429431	−	0.903100i	$-0.641286\pi$
$367$	10.8697	−	18.8268i	0.567392	−	0.982751i	0.996823	−	0.0796516i	$-0.0253808\pi$
$368$	−5.40143			−0.281569
$369$	0.306347	+	0.232755i	0.0159478	+	0.0121168i
$370$	−10.2097	+	4.93948i	−0.530779	+	0.256792i
$371$	28.2557	−	3.56326i	1.46696	−	0.184995i
$372$	−3.72684	+	11.0656i	−0.193228	+	0.573723i
$373$	6.11429	−	3.53009i	0.316586	−	0.182781i	−0.333284	−	0.942827i	$-0.608157\pi$
$373$	6.11429	−	3.53009i	0.316586	−	0.182781i	0.649870	+	0.760046i	$0.274823\pi$
$374$	4.01651	+	6.95680i	0.207689	+	0.359728i
$375$	−0.392053	+	19.3609i	−0.0202455	+	0.999795i
$376$	−4.40684	−	2.54429i	−0.227265	−	0.131212i
$377$		−	24.8609i		−	1.28040i
$378$	−13.4790	+	2.70498i	−0.693284	+	0.139129i
$379$	−3.04121			−0.156216			−0.0781082	−	0.996945i	$-0.524888\pi$
$379$	−3.04121			−0.156216			−0.0781082	+	0.996945i	$0.524888\pi$
$380$	−1.12566	+	15.3939i	−0.0577451	+	0.789690i
$381$	−2.07726	+	0.418345i	−0.106421	+	0.0214325i
$382$	9.85202	−	5.68807i	0.504073	−	0.291027i
$383$	13.7510	−	7.93915i	0.702644	−	0.405672i	−0.105688	−	0.994399i	$-0.533704\pi$
$383$	13.7510	−	7.93915i	0.702644	−	0.405672i	0.808331	+	0.588728i	$0.200371\pi$
$384$	1.64145	+	0.552836i	0.0837651	+	0.0282118i
$385$	14.3095	−	9.29453i	0.729277	−	0.473693i
$386$		−	2.21171i		−	0.112573i
$387$	0.538805	+	0.0683219i	0.0273890	+	0.00347300i
$388$	−4.12970			−0.209654
$389$	3.24150	+	1.87148i	0.164351	+	0.0948879i	0.579919	−	0.814674i	$-0.303084\pi$
$389$	3.24150	+	1.87148i	0.164351	+	0.0948879i	−0.415569	+	0.909562i	$0.636417\pi$
$390$	−23.8941	−	10.0420i	−1.20993	−	0.508496i
$391$	13.0285	−	7.52202i	0.658880	−	0.380405i
$392$	−6.78084	+	1.73787i	−0.342484	+	0.0877757i
$393$	−5.03056	+	4.43295i	−0.253758	+	0.223613i
$394$	−12.2536	+	21.2239i	−0.617328	+	1.06924i
$395$	11.0008	+	22.7383i	0.553510	+	1.14409i
$396$	−3.34929	−	7.97804i	−0.168308	−	0.400912i
$397$	17.9198			0.899367			0.449684	−	0.893188i	$-0.351537\pi$
$397$	17.9198			0.899367			0.449684	+	0.893188i	$0.351537\pi$
$398$	−9.08267	−	5.24388i	−0.455273	−	0.262852i
$399$	−29.9847	+	10.0759i	−1.50111	+	0.504426i
$400$	4.94681	+	0.727348i	0.247341	+	0.0363674i
$401$	−29.2993	+	16.9160i	−1.46314	+	0.844743i	−0.999155	−	0.0411005i	$-0.986914\pi$
$401$	−29.2993	+	16.9160i	−1.46314	+	0.844743i	−0.463983	+	0.885844i	$0.653580\pi$
$402$	26.0318	−	5.24262i	1.29835	−	0.261478i
$403$	−39.0697	−	22.5569i	−1.94620	−	1.12364i
$404$	−2.78571			−0.138594
$405$	3.96551	+	19.7300i	0.197048	+	0.980394i
$406$	−7.83024	+	5.94079i	−0.388608	+	0.294836i
$407$	7.31462	−	12.6693i	0.362572	−	0.627993i
$408$	−4.72914	+	0.952416i	−0.234128	+	0.0471516i
$409$	−4.57928	+	2.64385i	−0.226431	+	0.130730i	−0.608925	−	0.793228i	$-0.708399\pi$
$409$	−4.57928	+	2.64385i	−0.226431	+	0.130730i	0.382493	+	0.923958i	$0.375065\pi$
$410$	0.161113	−	0.237229i	0.00795683	−	0.0117159i
$411$	−30.1457	−	10.1530i	−1.48698	−	0.500809i
$412$	−4.24895	+	7.35940i	−0.209331	+	0.362572i
$413$	−17.0727	−	22.5026i	−0.840091	−	1.10728i
$414$	−14.9411	+	6.27246i	−0.734314	+	0.308274i
$415$	−1.05058	+	0.508274i	−0.0515712	+	0.0249502i
$416$	−3.34607	+	5.79556i	−0.164055	+	0.284151i
$417$	2.29332	+	2.60249i	0.112305	+	0.127444i
$418$	−9.95440	−	17.2415i	−0.486886	−	0.843310i
$419$	−10.9508	−	18.9673i	−0.534981	−	0.926614i	−0.999164	−	0.0408751i	$-0.986985\pi$
$419$	−10.9508	−	18.9673i	−0.534981	−	0.926614i	0.464183	−	0.885739i	$-0.346348\pi$
$420$	2.54691	+	9.92538i	0.124277	+	0.484309i
$421$	−19.2172	+	33.2851i	−0.936587	+	1.62222i	−0.164809	+	0.986326i	$0.552701\pi$
$421$	−19.2172	+	33.2851i	−0.936587	+	1.62222i	−0.771779	+	0.635891i	$0.780633\pi$
$422$	7.66343			0.373050
$423$	−15.1445	−	1.92036i	−0.736349	−	0.0933711i
$424$	−10.7642			−0.522757
$425$	−12.9449	+	5.13452i	−0.627918	+	0.249061i
$426$	4.43906	−	13.1802i	0.215073	−	0.638585i
$427$	17.2899	+	7.27246i	0.836719	+	0.351939i
$428$	−3.93590	−	6.81718i	−0.190249	−	0.329521i
$429$	32.7730	−	6.60024i	1.58229	−	0.318663i
$430$	0.0295229	−	0.403739i	0.00142372	−	0.0194700i
$431$			2.76514i			0.133192i	0.997780	+	0.0665960i	$0.0212139\pi$
$431$			2.76514i			0.133192i	−0.997780	+	0.0665960i	$0.978786\pi$
$432$	5.18246	−	0.376935i	0.249341	−	0.0181353i
$433$	−2.60424			−0.125152			−0.0625759	−	0.998040i	$-0.519932\pi$
$433$	−2.60424			−0.125152			−0.0625759	+	0.998040i	$0.519932\pi$
$434$	2.23156	+	17.6957i	0.107118	+	0.849420i
$435$	8.69980	+	11.4597i	0.417124	+	0.549452i
$436$	−1.41500	−	2.45085i	−0.0677662	−	0.117374i
$437$	−32.2895	+	18.6423i	−1.54462	+	0.891784i
$438$	−18.9650	−	6.38733i	−0.906181	−	0.305199i
$439$	−13.8162	−	7.97681i	−0.659413	−	0.380712i	0.132640	−	0.991164i	$-0.457654\pi$
$439$	−13.8162	−	7.97681i	−0.659413	−	0.380712i	−0.792053	+	0.610452i	$0.790988\pi$
$440$	−5.80550	+	2.80871i	−0.276766	+	0.133900i
$441$	−16.7386	+	12.6815i	−0.797075	+	0.603880i
$442$		−	18.6389i		−	0.886562i
$443$	−9.31694	+	16.1374i	−0.442661	+	0.766711i	−0.997886	−	0.0649889i	$-0.979299\pi$
$443$	−9.31694	+	16.1374i	−0.442661	+	0.766711i	0.555225	+	0.831700i	$0.312632\pi$
$444$	5.80832	+	6.59134i	0.275651	+	0.312811i
$445$	−7.16035	+	10.5432i	−0.339433	+	0.499794i
$446$	−6.09914	−	10.5640i	−0.288803	−	0.500221i
$447$	−4.84988	−	5.50370i	−0.229392	−	0.260316i
$448$	2.62496	−	0.331028i	0.124018	−	0.0156396i
$449$			11.9978i			0.566209i	0.959089	+	0.283105i	$0.0913643\pi$
$449$			11.9978i			0.566209i	−0.959089	+	0.283105i	$0.908636\pi$
$450$	14.5282	−	3.73259i	0.684865	−	0.175956i
$451$			0.369886i			0.0174172i
$452$	1.48562	−	2.57317i	0.0698778	−	0.121032i
$453$	25.6156	+	8.62726i	1.20353	+	0.405344i
$454$	5.40529	−	3.12075i	0.253683	−	0.146464i
$455$	−39.5368	+	2.07567i	−1.85351	+	0.0973091i
$456$	11.7206	−	2.36044i	0.548866	−	0.110538i
$457$	−21.4094	−	12.3607i	−1.00149	−	0.578211i	−0.0928017	−	0.995685i	$-0.529582\pi$
$457$	−21.4094	−	12.3607i	−1.00149	−	0.578211i	−0.908689	+	0.417474i	$0.862916\pi$
$458$		−	4.73494i		−	0.221249i
$459$	−11.9754	+	8.12627i	−0.558965	+	0.379302i
$460$	5.26008	+	10.8724i	0.245252	+	0.506928i
$461$	−11.7641	+	20.3759i	−0.547907	+	0.949002i	0.450511	+	0.892771i	$0.351242\pi$
$461$	−11.7641	+	20.3759i	−0.547907	+	0.949002i	−0.998418	+	0.0562315i	$0.982092\pi$
$462$	−9.91028	−	8.74504i	−0.461068	−	0.406856i
$463$	19.6345	−	11.3360i	0.912492	−	0.526827i	0.0312596	−	0.999511i	$-0.490048\pi$
$463$	19.6345	−	11.3360i	0.912492	−	0.526827i	0.881232	+	0.472684i	$0.156715\pi$
$464$	3.21724	−	1.85747i	0.149356	−	0.0862310i
$465$	25.9029	−	3.27432i	1.20122	−	0.151843i
$466$	9.69504	−	16.7923i	0.449114	−	0.777888i
$467$			12.4405i			0.575678i	0.957679	+	0.287839i	$0.0929367\pi$
$467$			12.4405i			0.575678i	−0.957679	+	0.287839i	$0.907063\pi$
$468$	−2.52552	+	19.9169i	−0.116742	+	0.920661i
$469$	32.3147	−	24.5171i	1.49215	−	1.13209i
$470$	−0.829816	+	11.3481i	−0.0382766	+	0.523449i
$471$	−13.8088	+	12.1684i	−0.636278	+	0.560691i
$472$	5.33801	+	9.24571i	0.245702	+	0.425568i
$473$	0.261076	+	0.452197i	0.0120043	+	0.0207921i
$474$	14.6797	−	12.9358i	0.674260	−	0.594161i
$475$	32.0821	−	12.7252i	1.47203	−	0.583874i
$476$	−5.87054	+	4.45397i	−0.269076	+	0.204147i
$477$	−29.7752	+	12.5000i	−1.36331	+	0.572338i
$478$		−	7.39018i		−	0.338019i
$479$	1.25925	−	2.18108i	0.0575364	−	0.0996559i	−0.835823	−	0.549000i	$-0.815009\pi$
$479$	1.25925	−	2.18108i	0.0575364	−	0.0996559i	0.893359	+	0.449344i	$0.148342\pi$
$480$	−0.485710	−	3.84241i	−0.0221695	−	0.175381i
$481$	−29.3964	+	16.9720i	−1.34036	+	0.773857i
$482$	5.66724	−	3.27198i	0.258136	−	0.149035i
$483$	−16.3775	+	18.5597i	−0.745201	+	0.844496i
$484$	−1.34073	+	2.32222i	−0.0609423	+	0.105555i
$485$	4.02163	+	8.31256i	0.182613	+	0.377454i
$486$	13.8977	−	7.06083i	0.630410	−	0.320286i
$487$			14.1370i			0.640608i	0.947315	+	0.320304i	$0.103785\pi$
$487$			14.1370i			0.640608i	−0.947315	+	0.320304i	$0.896215\pi$
$488$	−6.13972	−	3.54477i	−0.277932	−	0.160464i
$489$	26.3392	−	5.30453i	1.19110	−	0.239879i
$490$	10.1015	+	11.9566i	0.456339	+	0.540143i
$491$	13.9425	−	8.04970i	0.629215	−	0.363278i	−0.151233	−	0.988498i	$-0.548324\pi$
$491$	13.9425	−	8.04970i	0.629215	−	0.363278i	0.780448	+	0.625221i	$0.214991\pi$
$492$	−0.210510	−	0.0708991i	−0.00949053	−	0.00319638i
$493$	−5.17342	+	8.96062i	−0.232999	+	0.403566i
$494$			46.1941i			2.07837i
$495$	−12.7971	+	14.5109i	−0.575189	+	0.652218i
$496$		−	6.74132i		−	0.302694i
$497$	−2.65802	−	21.0774i	−0.119229	−	0.945451i
$498$	0.597678	+	0.678251i	0.0267826	+	0.0303931i
$499$	−13.0145	−	22.5418i	−0.582610	−	1.00911i	−0.995169	−	0.0981795i	$-0.968698\pi$
$499$	−13.0145	−	22.5418i	−0.582610	−	1.00911i	0.412558	−	0.910931i	$-0.364635\pi$
$500$	−3.35330	−	10.6656i	−0.149964	−	0.476981i
$501$	−25.0534	−	28.4309i	−1.11930	−	1.27020i
$502$	−2.38550	+	4.13181i	−0.106470	+	0.184412i
$503$		−	21.8336i		−	0.973514i	−0.873537	−	0.486757i	$-0.838180\pi$
$503$		−	21.8336i		−	0.973514i	0.873537	−	0.486757i	$-0.161820\pi$
$504$	6.87658	−	3.96392i	0.306307	−	0.176567i
$505$	2.71281	+	5.60727i	0.120718	+	0.249520i
$506$	−13.4916	−	7.78937i	−0.599774	−	0.346280i
$507$	−52.1732	−	17.5717i	−2.31709	−	0.780389i
$508$	1.05948	−	0.611693i	0.0470070	−	0.0271395i
$509$	−4.22838	−	7.32378i	−0.187420	−	0.324621i	0.756969	−	0.653450i	$-0.226679\pi$
$509$	−4.22838	−	7.32378i	−0.187420	−	0.324621i	−0.944389	+	0.328830i	$0.893346\pi$
$510$	6.52248	+	8.59167i	0.288820	+	0.380446i
$511$	−30.3282	+	3.82461i	−1.34164	+	0.169191i
$512$	−1.00000			−0.0441942
$513$	29.6796	−	20.1399i	1.31038	−	0.889198i
$514$			8.59310i			0.379025i
$515$	18.9513	+	1.38579i	0.835094	+	0.0610652i
$516$	−0.307398	+	0.0619078i	−0.0135324	+	0.00272534i
$517$	−7.33821	−	12.7102i	−0.322734	−	0.558992i
$518$	12.3701	+	5.20310i	0.543512	+	0.228611i
$519$	−0.134546	+	0.399487i	−0.00590591	+	0.0175355i
$520$	14.9242	+	1.09132i	0.654471	+	0.0478574i
$521$	−14.1520			−0.620011			−0.310006	−	0.950735i	$-0.600331\pi$
$521$	−14.1520			−0.620011			−0.310006	+	0.950735i	$0.600331\pi$
$522$	6.74229	−	8.87405i	0.295102	−	0.388407i
$523$	−20.7524			−0.907437			−0.453719	−	0.891145i	$-0.649903\pi$
$523$	−20.7524			−0.907437			−0.453719	+	0.891145i	$0.649903\pi$
$524$	1.93558	−	3.35252i	0.0845561	−	0.146456i
$525$	17.4983	−	14.7922i	0.763687	−	0.645587i
$526$	8.65466	+	14.9903i	0.377361	+	0.653609i
$527$	9.38793	+	16.2604i	0.408945	+	0.708313i
$528$	3.30275	+	3.74799i	0.143734	+	0.163110i
$529$	−3.08774	+	5.34812i	−0.134250	+	0.232527i
$530$	10.4825	+	21.6670i	0.455332	+	0.941155i
$531$	25.5023	+	19.3760i	1.10671	+	0.840848i
$532$	14.5494	−	11.0386i	0.630796	−	0.478583i
$533$	0.429120	−	0.743258i	0.0185873	−	0.0321941i
$534$	9.35569	+	3.15096i	0.404860	+	0.136356i
$535$	−9.88921	+	14.5612i	−0.427548	+	0.629537i
$536$	−13.2772	+	7.66561i	−0.573489	+	0.331104i
$537$	4.02259	−	0.810121i	0.173588	−	0.0349593i
$538$	−10.1211	+	17.5302i	−0.436351	+	0.755781i
$539$	−19.4432	−	5.43779i	−0.837479	−	0.234222i
$540$	−5.80556	−	10.0646i	−0.249832	−	0.433110i
$541$	16.9636			0.729320			0.364660	−	0.931141i	$-0.381185\pi$
$541$	16.9636			0.729320			0.364660	+	0.931141i	$0.381185\pi$
$542$	−15.9777	−	9.22470i	−0.686299	−	0.396235i
$543$	−11.8455	+	2.38560i	−0.508340	+	0.102376i
$544$	2.41205	−	1.39260i	0.103416	−	0.0597071i
$545$	−3.55528	+	5.23493i	−0.152291	+	0.224240i
$546$	9.76849	+	29.0698i	0.418053	+	1.24407i
$547$	−31.2121	−	18.0203i	−1.33453	−	0.770492i	−0.348541	−	0.937294i	$-0.613323\pi$
$547$	−31.2121	−	18.0203i	−1.33453	−	0.770492i	−0.985990	+	0.166802i	$0.946656\pi$
$548$	18.3652			0.784524
$549$	−21.0997	−	2.67549i	−0.900511	−	0.114187i
$550$	11.3071	+	8.95052i	0.482138	+	0.381652i
$551$	12.8216	−	22.2077i	0.546220	−	0.946082i
$552$	7.01915	−	6.18531i	0.298755	−	0.263264i
$553$	11.5879	−	27.5497i	0.492767	−	1.17153i
$554$	13.5806	−	7.84078i	0.576986	−	0.333123i
$555$	7.61121	−	18.1102i	0.323078	−	0.768737i
$556$	−1.73438	−	1.00134i	−0.0735540	−	0.0424664i
$557$	18.2393			0.772826			0.386413	−	0.922326i	$-0.373714\pi$
$557$	18.2393			0.772826			0.386413	+	0.922326i	$0.373714\pi$
$558$	−7.82841	−	18.6474i	−0.331403	−	0.789406i
$559$		−	1.21154i		−	0.0512428i
$560$	−3.22258	−	4.96135i	−0.136179	−	0.209655i
$561$	−13.1858	−	4.44094i	−0.556706	−	0.187497i
$562$	−4.23315	+	2.44401i	−0.178565	+	0.103094i
$563$	−8.73887	+	5.04539i	−0.368299	+	0.212638i	−0.672715	−	0.739901i	$-0.734872\pi$
$563$	−8.73887	+	5.04539i	−0.368299	+	0.212638i	0.304416	+	0.952539i	$0.401539\pi$
$564$	8.64020	−	1.74008i	0.363818	−	0.0732704i
$565$	−6.62622	−	0.484534i	−0.278767	−	0.0203845i
$566$	−16.9552			−0.712679
$567$	14.4184	−	18.9502i	0.605515	−	0.795834i
$568$			8.02961i			0.336915i
$569$	−18.5060	−	10.6844i	−0.775811	−	0.447915i	0.0591324	−	0.998250i	$-0.481167\pi$
$569$	−18.5060	−	10.6844i	−0.775811	−	0.447915i	−0.834944	+	0.550335i	$0.814500\pi$
$570$	−16.1651	−	21.2933i	−0.677082	−	0.891880i
$571$	−21.1940	−	36.7091i	−0.886942	−	1.53623i	−0.843471	−	0.537175i	$-0.819492\pi$
$571$	−21.1940	−	36.7091i	−0.886942	−	1.53623i	−0.0434713	−	0.999055i	$-0.513842\pi$
$572$	−16.7155	+	9.65069i	−0.698910	+	0.403516i
$573$	−6.28914	+	18.6734i	−0.262733	+	0.780093i
$574$	−0.336641	+	0.0424530i	−0.0140511	+	0.00177196i
$575$	16.7623	−	21.1757i	0.699037	−	0.883089i
$576$	−2.76613	+	1.16126i	−0.115255	+	0.0483858i
$577$	−10.2174			−0.425355			−0.212678	−	0.977122i	$-0.568218\pi$
$577$	−10.2174			−0.425355			−0.212678	+	0.977122i	$0.568218\pi$
$578$	4.62135	−	8.00441i	0.192223	−	0.332940i
$579$	2.53267	+	2.87411i	0.105254	+	0.119444i
$580$	−6.87190	−	4.66702i	−0.285340	−	0.193788i
$581$	1.27289	+	0.535400i	0.0528083	+	0.0222121i
$582$	5.36653	−	4.72901i	0.222450	−	0.196024i
$583$	−26.8867	−	15.5230i	−1.11353	−	0.642898i
$584$	11.5538			0.478098
$585$	42.5497	−	14.3122i	1.75921	−	0.591735i
$586$		−	33.5341i		−	1.38528i
$587$	15.4210	+	8.90330i	0.636492	+	0.367479i	0.783262	−	0.621692i	$-0.213554\pi$
$587$	15.4210	+	8.90330i	0.636492	+	0.367479i	−0.146770	+	0.989171i	$0.546888\pi$
$588$	6.82161	−	10.0233i	0.281318	−	0.413352i
$589$	−23.2668	−	40.2992i	−0.958691	−	1.66050i
$590$	13.4121	−	19.7485i	0.552168	−	0.813032i
$591$	−8.38042	−	41.6123i	−0.344724	−	1.71170i
$592$	−4.39267	−	2.53611i	−0.180538	−	0.104234i
$593$			22.9333i			0.941758i	0.882198	+	0.470879i	$0.156063\pi$
$593$			22.9333i			0.941758i	−0.882198	+	0.470879i	$0.843937\pi$
$594$	13.4882	+	6.53210i	0.553429	+	0.268015i
$595$	14.6822	+	7.47925i	0.601911	+	0.306619i
$596$	3.66784	+	2.11763i	0.150240	+	0.0867413i
$597$	17.8078	−	3.58636i	0.728824	−	0.146780i
$598$	18.0736	+	31.3043i	0.739083	+	1.28013i
$599$	28.2131	−	16.2889i	1.15276	−	0.665544i	0.203199	−	0.979137i	$-0.434866\pi$
$599$	28.2131	−	16.2889i	1.15276	−	0.665544i	0.949558	+	0.313593i	$0.101533\pi$
$600$	−7.26127	+	4.71952i	−0.296440	+	0.192674i
$601$	27.0233	+	15.6019i	1.10230	+	0.636414i	0.936825	−	0.349800i	$-0.113750\pi$
$601$	27.0233	+	15.6019i	1.10230	+	0.636414i	0.165477	+	0.986214i	$0.447084\pi$
$602$	−0.381590	+	0.289511i	−0.0155524	+	0.0117996i
$603$	−27.8248	+	36.6224i	−1.13311	+	1.49138i
$604$	−15.6055			−0.634977
$605$	5.97997	+	0.437278i	0.243120	+	0.0177779i
$606$	3.62002	−	3.18998i	0.147053	−	0.129584i
$607$	−17.4362	−	30.2003i	−0.707712	−	1.22579i	−0.965704	−	0.259646i	$-0.916394\pi$
$607$	−17.4362	−	30.2003i	−0.707712	−	1.22579i	0.257992	−	0.966147i	$-0.416939\pi$
$608$	−5.97795	+	3.45137i	−0.242438	+	0.139972i
$609$	3.37245	−	16.6866i	0.136659	−	0.676176i
$610$	−1.15612	+	15.8105i	−0.0468100	+	0.640147i
$611$			34.0535i			1.37766i
$612$	5.05488	−	6.65311i	0.204331	−	0.268936i
$613$		−	22.6820i		−	0.916116i	−0.888922	−	0.458058i	$-0.848545\pi$
$613$		−	22.6820i		−	0.916116i	0.888922	−	0.458058i	$-0.151455\pi$
$614$	5.27286	−	9.13287i	0.212795	−	0.368573i
$615$	0.0622904	+	0.492774i	0.00251179	+	0.0198706i
$616$	7.03395	+	2.95861i	0.283406	+	0.119206i
$617$	−17.8062	−	30.8413i	−0.716852	−	1.24162i	−0.962241	−	0.272200i	$-0.912249\pi$
$617$	−17.8062	−	30.8413i	−0.716852	−	1.24162i	0.245389	−	0.969425i	$-0.421084\pi$
$618$	−2.90592	−	14.4291i	−0.116893	−	0.580423i
$619$	−8.66174	−	5.00086i	−0.348145	−	0.201001i	0.315723	−	0.948851i	$-0.397753\pi$
$619$	−8.66174	−	5.00086i	−0.348145	−	0.201001i	−0.663868	+	0.747850i	$0.731086\pi$
$620$	−13.5694	+	6.56490i	−0.544961	+	0.263653i
$621$	12.2331	−	25.2604i	0.490899	−	1.01367i
$622$	−2.11699			−0.0848837
$623$	14.9613	−	1.88674i	0.599412	−	0.0755905i
$624$	−2.28842	−	11.3630i	−0.0916103	−	0.454883i
$625$	−18.2030	+	17.1363i	−0.728119	+	0.685451i
$626$	12.9677	+	22.4606i	0.518292	+	0.897708i
$627$	32.6794	+	11.0063i	1.30509	+	0.439549i
$628$	5.31314	−	9.20264i	0.212018	−	0.367225i
$629$	14.1271			0.563285
$630$	−14.6755	−	9.98148i	−0.584686	−	0.397672i
$631$	−14.3788			−0.572413			−0.286206	−	0.958168i	$-0.592394\pi$
$631$	−14.3788			−0.572413			−0.286206	+	0.958168i	$0.592394\pi$
$632$	−5.64821	+	9.78299i	−0.224674	+	0.389146i
$633$	−9.95861	+	8.77557i	−0.395819	+	0.348798i
$634$	6.65836	+	11.5326i	0.264437	+	0.458019i
$635$	−2.26302	−	1.53692i	−0.0898051	−	0.0609908i
$636$	13.9881	−	12.3264i	0.554663	−	0.488772i
$637$	32.7611	+	33.4838i	1.29804	+	1.32667i
$638$	10.7146			0.424195
$639$	9.32445	+	22.2109i	0.368869	+	0.878652i
$640$	0.973830	+	2.01287i	0.0384940	+	0.0795658i
$641$	10.5779	+	6.10714i	0.417801	+	0.241218i	0.694136	−	0.719844i	$-0.255787\pi$
$641$	10.5779	+	6.10714i	0.417801	+	0.241218i	−0.276335	+	0.961061i	$0.589120\pi$
$642$	12.9212	+	4.35181i	0.509959	+	0.171752i
$643$	−3.60040	−	6.23608i	−0.141986	−	0.245927i	0.786258	−	0.617898i	$-0.212015\pi$
$643$	−3.60040	−	6.23608i	−0.141986	−	0.245927i	−0.928244	+	0.371971i	$0.878682\pi$
$644$	5.54080	−	13.1730i	0.218338	−	0.519089i
$645$	0.423966	+	0.558465i	0.0166936	+	0.0219895i
$646$	9.61273	−	16.6497i	0.378208	−	0.655075i
$647$		−	28.4100i		−	1.11691i	−0.829534	−	0.558456i	$-0.811394\pi$
$647$		−	28.4100i		−	1.11691i	0.829534	−	0.558456i	$-0.188606\pi$
$648$	−6.30296	+	6.42438i	−0.247604	+	0.252374i
$649$			30.7917i			1.20868i
$650$	−12.3370	−	31.1033i	−0.483897	−	1.21997i
$651$	−23.1637	−	20.4401i	−0.907855	−	0.801110i
$652$	−13.4340	+	7.75613i	−0.526116	+	0.303754i
$653$	10.9864	+	19.0290i	0.429932	+	0.744663i	0.996867	−	0.0790990i	$-0.0252043\pi$
$653$	10.9864	+	19.0290i	0.429932	+	0.744663i	−0.566935	+	0.823762i	$0.691871\pi$
$654$	4.64531	+	1.56453i	0.181646	+	0.0611778i
$655$	−8.63312	−	0.631286i	−0.337324	−	0.0246664i
$656$	0.128246			0.00500717
$657$	31.9592	−	13.4169i	1.24685	−	0.523443i
$658$	10.7256	−	8.13745i	0.418126	−	0.317231i
$659$	9.68469	+	5.59146i	0.377262	+	0.217812i	0.676626	−	0.736327i	$-0.263441\pi$
$659$	9.68469	+	5.59146i	0.377262	+	0.217812i	−0.299364	+	0.954139i	$0.596775\pi$
$660$	4.32791	−	10.2979i	0.168464	−	0.400846i
$661$	3.24970	−	1.87622i	0.126399	−	0.0729763i	−0.435467	−	0.900204i	$-0.643417\pi$
$661$	3.24970	−	1.87622i	0.126399	−	0.0729763i	0.561866	+	0.827228i	$0.310084\pi$
$662$	6.16750	+	10.6824i	0.239707	+	0.415184i
$663$	21.3438	+	24.2212i	0.828926	+	0.940674i
$664$	−0.452007	−	0.260967i	−0.0175413	−	0.0101275i
$665$	−36.3879	−	18.5363i	−1.41106	−	0.718809i
$666$	−15.0958	−	1.91419i	−0.584950	−	0.0741733i
$667$		−	20.0660i		−	0.776959i
$668$	18.9472	+	10.9392i	0.733090	+	0.423250i
$669$	20.0229	+	6.74365i	0.774130	+	0.260724i
$670$	28.3597	+	19.2604i	1.09563	+	0.744092i
$671$	−10.2238	−	17.7081i	−0.394684	−	0.683613i
$672$	−3.03206	+	3.43607i	−0.116964	+	0.132549i
$673$	24.0608	+	13.8915i	0.927477	+	0.535479i	0.886013	−	0.463661i	$-0.153464\pi$
$673$	24.0608	+	13.8915i	0.927477	+	0.535479i	0.0414644	+	0.999140i	$0.486798\pi$
$674$		−	18.6047i		−	0.716625i
$675$	−14.6050	+	21.4870i	−0.562149	+	0.827036i
$676$	31.7847			1.22249
$677$	−16.0167	−	9.24724i	−0.615571	−	0.355400i	0.159571	−	0.987186i	$-0.448989\pi$
$677$	−16.0167	−	9.24724i	−0.615571	−	0.355400i	−0.775143	+	0.631786i	$0.782322\pi$
$678$	1.01604	+	5.04506i	0.0390207	+	0.193754i
$679$	4.23625	−	10.0715i	0.162572	−	0.386509i
$680$	−5.15204	−	3.49899i	−0.197572	−	0.134180i
$681$	−3.45052	+	10.2451i	−0.132224	+	0.392594i
$682$	9.72161	−	16.8383i	0.372260	−	0.644773i
$683$	35.5612			1.36071			0.680356	−	0.732882i	$-0.261825\pi$
$683$	35.5612			1.36071			0.680356	+	0.732882i	$0.261825\pi$
$684$	−12.5279	+	16.4889i	−0.479015	+	0.630468i
$685$	−17.8846	−	36.9669i	−0.683336	−	1.41243i
$686$	2.71749	−	18.3198i	0.103754	−	0.699453i
$687$	5.42209	+	6.15304i	0.206866	+	0.234753i
$688$	0.156785	−	0.0905199i	0.00597737	−	0.00345104i
$689$	36.0178	+	62.3847i	1.37217	+	2.37667i
$690$	−19.2857	−	8.10521i	−0.734194	−	0.308560i
$691$	11.6077	+	6.70172i	0.441578	+	0.254945i	0.704267	−	0.709935i	$-0.251276\pi$
$691$	11.6077	+	6.70172i	0.441578	+	0.254945i	−0.262689	+	0.964881i	$0.584609\pi$
$692$		−	0.243374i		−	0.00925168i
$693$	22.8925	+	0.0156610i	0.869615	+	0.000594912i
$694$	35.7764			1.35805
$695$	−0.326587	+	4.46622i	−0.0123881	+	0.169413i
$696$	−2.05376	+	6.09791i	−0.0778474	+	0.231141i
$697$	−0.309336	+	0.178595i	−0.0117169	+	0.00676477i
$698$	−0.571123	+	0.329738i	−0.0216173	+	0.0124808i
$699$	6.63057	+	32.9236i	0.250791	+	1.24528i
$700$	−6.84831	+	11.3182i	−0.258842	+	0.427786i
$701$		−	10.5809i		−	0.399633i	−0.979833	−	0.199817i	$-0.935965\pi$
$701$		−	10.5809i		−	0.399633i	0.979833	−	0.199817i	$-0.0640347\pi$
$702$	−19.5254	−	28.7740i	−0.736940	−	1.08601i
$703$	−35.0122			−1.32051
$704$	−2.49778	−	1.44209i	−0.0941386	−	0.0543510i
$705$	−11.9166	−	15.6971i	−0.448807	−	0.591186i
$706$	5.34455	−	3.08568i	0.201145	−	0.116131i
$707$	2.85758	−	6.79377i	0.107470	−	0.255506i
$708$	−17.5242	−	5.90209i	−0.658600	−	0.221814i
$709$	−2.35115	+	4.07231i	−0.0882993	+	0.152939i	−0.906792	−	0.421578i	$-0.861477\pi$
$709$	−2.35115	+	4.07231i	−0.0882993	+	0.152939i	0.818493	+	0.574516i	$0.194810\pi$
$710$	16.1626	−	7.81948i	0.606571	−	0.293460i
$711$	−4.26312	+	33.6201i	−0.159879	+	1.26085i
$712$	−5.69963			−0.213603
$713$	−31.5344	−	18.2064i	−1.18097	−	0.681834i
$714$	2.52842	−	12.5104i	0.0946236	−	0.468190i
$715$	35.7037	+	24.2480i	1.33524	+	0.906824i
$716$	−2.05168	+	1.18454i	−0.0766748	+	0.0442682i
$717$	8.46266	+	9.60351i	0.316044	+	0.358650i
$718$	5.35500	+	3.09171i	0.199847	+	0.115382i
$719$	−5.53422			−0.206392			−0.103196	−	0.994661i	$-0.532907\pi$
$719$	−5.53422			−0.206392			−0.103196	+	0.994661i	$0.532907\pi$
$720$	5.03121	+	4.43700i	0.187502	+	0.165357i
$721$	−13.5895	−	17.9116i	−0.506099	−	0.667064i
$722$	−14.3239	+	24.8097i	−0.533081	+	0.923323i
$723$	−3.61774	+	10.7416i	−0.134545	+	0.399485i
$724$	6.04167	−	3.48816i	0.224537	−	0.129637i
$725$	−2.70206	+	18.3771i	−0.100352	+	0.682510i
$726$	−0.916945	−	4.55301i	−0.0340310	−	0.168978i
$727$	−10.9227	+	18.9186i	−0.405099	+	0.701652i	−0.994333	−	0.106310i	$-0.966096\pi$
$727$	−10.9227	+	18.9186i	−0.405099	+	0.701652i	0.589234	+	0.807962i	$0.299430\pi$
$728$	−10.7018	−	14.1055i	−0.396635	−	0.522784i
$729$	−9.97444	+	25.0900i	−0.369424	+	0.929261i
$730$	−11.2514	−	23.2562i	−0.416433	−	0.860752i
$731$	−0.252115	+	0.436677i	−0.00932482	+	0.0161511i
$732$	12.0377	−	2.42432i	0.444928	−	0.0896053i
$733$	−14.7668	−	25.5768i	−0.545423	−	0.944700i	−0.998580	−	0.0532693i	$-0.983036\pi$
$733$	−14.7668	−	25.5768i	−0.545423	−	0.944700i	0.453158	−	0.891430i	$-0.350297\pi$
$734$	−10.8697	−	18.8268i	−0.401207	−	0.694910i
$735$	−26.8186	−	3.97008i	−0.989220	−	0.146438i
$736$	−2.70072	+	4.67778i	−0.0995497	+	0.172425i
$737$	−44.2181			−1.62880
$738$	0.354746	−	0.148927i	0.0130584	−	0.00548207i
$739$	22.3122			0.820766			0.410383	−	0.911913i	$-0.365395\pi$
$739$	22.3122			0.820766			0.410383	+	0.911913i	$0.365395\pi$
$740$	−0.827149	+	11.3116i	−0.0304066	+	0.415824i
$741$	−52.8979	−	60.0291i	−1.94325	−	2.20522i
$742$	11.0420	−	26.2518i	0.405363	−	0.963732i
$743$	−16.6425	−	28.8256i	−0.610553	−	1.05751i	−0.991147	−	0.132767i	$-0.957614\pi$
$743$	−16.6425	−	28.8256i	−0.610553	−	1.05751i	0.380594	−	0.924742i	$-0.375720\pi$
$744$	7.71964	+	8.76032i	0.283016	+	0.321169i
$745$	0.690661	−	9.44509i	0.0253038	−	0.346041i
$746$		−	7.06017i		−	0.258491i
$747$	−1.55336	−	0.196970i	−0.0568345	−	0.00720677i
$748$	8.03302			0.293716
$749$	20.6632	−	2.60578i	0.755015	−	0.0952133i
$750$	16.5710	+	10.0200i	0.605089	+	0.365879i
$751$	−1.16323	−	2.01477i	−0.0424467	−	0.0735199i	0.844022	−	0.536309i	$-0.180182\pi$
$751$	−1.16323	−	2.01477i	−0.0424467	−	0.0735199i	−0.886468	+	0.462789i	$0.846849\pi$
$752$	−4.40684	+	2.54429i	−0.160701	+	0.0927807i
$753$	−1.63148	−	8.10096i	−0.0594543	−	0.295215i
$754$	−21.5302	−	12.4305i	−0.784083	−	0.452691i
$755$	15.1971	+	31.4118i	0.553078	+	1.14319i
$756$	−4.39691	+	13.0256i	−0.159914	+	0.473738i
$757$			38.5673i			1.40175i	0.713283	+	0.700876i	$0.247207\pi$
$757$			38.5673i			1.40175i	−0.713283	+	0.700876i	$0.752793\pi$
$758$	−1.52060	+	2.63376i	−0.0552308	+	0.0956626i
$759$	26.4521	−	5.32726i	0.960149	−	0.193367i
$760$	12.7687	+	8.67180i	0.463168	+	0.314559i
$761$	−20.1956	−	34.9798i	−0.732090	−	1.26802i	−0.955988	−	0.293405i	$-0.905212\pi$
$761$	−20.1956	−	34.9798i	−0.732090	−	1.26802i	0.223898	−	0.974613i	$-0.428122\pi$
$762$	−0.676332	+	2.00813i	−0.0245009	+	0.0727469i
$763$	7.42864	−	0.936808i	0.268935	−	0.0339147i
$764$		−	11.3761i		−	0.411574i
$765$	−18.3145	−	3.69582i	−0.662161	−	0.133622i
$766$		−	15.8783i		−	0.573706i
$767$	35.7227	−	61.8736i	1.28987	−	2.23413i
$768$	1.29950	−	1.14512i	0.0468916	−	0.0413211i
$769$	−44.7375	+	25.8292i	−1.61328	+	0.931425i	−0.624672	+	0.780887i	$0.714767\pi$
$769$	−44.7375	+	25.8292i	−1.61328	+	0.931425i	−0.988604	+	0.150538i	$0.951899\pi$
$770$	−0.894577	−	17.0396i	−0.0322383	−	0.614065i
$771$	−9.84015	−	11.1667i	−0.354384	−	0.402159i
$772$	−1.91539	−	1.10585i	−0.0689365	−	0.0398005i
$773$			21.0903i			0.758565i	0.925281	+	0.379283i	$0.123829\pi$
$773$			21.0903i			0.758565i	−0.925281	+	0.379283i	$0.876171\pi$
$774$	0.328571	−	0.432458i	0.0118102	−	0.0155444i
$775$	26.4286	+	20.9204i	0.949343	+	0.751482i
$776$	−2.06485	+	3.57642i	−0.0741238	+	0.128386i
$777$	−22.0331	+	7.40390i	−0.790434	+	0.265613i
$778$	3.24150	−	1.87148i	0.116213	−	0.0670959i
$779$	0.766649	−	0.442625i	0.0274680	−	0.0158587i
$780$	−20.6437	+	15.6719i	−0.739163	+	0.561145i
$781$	−11.5794	+	20.0562i	−0.414345	+	0.717667i
$782$		−	15.0440i		−	0.537974i
$783$	1.40029	+	19.2526i	0.0500424	+	0.688030i
$784$	−1.88538	+	6.74132i	−0.0673350	+	0.240761i
$785$	−23.6978	−	1.73287i	−0.845812	−	0.0618489i
$786$	1.32377	+	6.57307i	0.0472173	+	0.234454i
$787$	13.0221	+	22.5550i	0.464189	+	0.803999i	0.999165	−	0.0408685i	$-0.0130125\pi$
$787$	13.0221	+	22.5550i	0.464189	+	0.803999i	−0.534975	+	0.844868i	$0.679679\pi$
$788$	12.2536	+	21.2239i	0.436517	+	0.756069i
$789$	−28.4125	−	9.56922i	−1.01151	−	0.340673i
$790$	25.1923	+	1.84216i	0.896302	+	0.0655410i
$791$	4.75150	+	6.26270i	0.168944	+	0.222676i
$792$	−8.58383	−	1.08845i	−0.305013	−	0.0386765i
$793$			47.4442i			1.68479i
$794$	8.95988	−	15.5190i	0.317974	−	0.550748i
$795$	−38.4334	−	16.1524i	−1.36309	−	0.572868i
$796$	−9.08267	+	5.24388i	−0.321927	+	0.185864i
$797$	28.2940	−	16.3355i	1.00222	−	0.578635i	0.0933188	−	0.995636i	$-0.470252\pi$
$797$	28.2940	−	16.3355i	1.00222	−	0.578635i	0.908906	+	0.417002i	$0.136919\pi$
$798$	−6.26635	+	31.0054i	−0.221826	+	1.09758i
$799$	7.08634	−	12.2739i	0.250697	−	0.434219i
$800$	3.10331	−	3.92039i	0.109719	−	0.138607i
$801$	−15.7659	+	6.61874i	−0.557062	+	0.233862i
$802$			33.8319i			1.19465i
$803$	28.8587	+	16.6616i	1.01840	+	0.587975i
$804$	8.47565	−	25.1655i	0.298913	−	0.887519i
$805$	−31.9114	+	1.67534i	−1.12473	+	0.0590480i
$806$	−39.0697	+	22.5569i	−1.37617	+	0.794533i
$807$	−6.92195	−	34.3704i	−0.243664	−	1.20989i
$808$	−1.39285	+	2.41249i	−0.0490004	+	0.0848712i
$809$		−	35.5787i		−	1.25088i	−0.780271	−	0.625441i	$-0.784919\pi$
$809$		−	35.5787i		−	1.25088i	0.780271	−	0.625441i	$-0.215081\pi$
$810$	19.0695	+	6.43079i	0.670033	+	0.225955i
$811$			23.5867i			0.828243i	0.910222	+	0.414121i	$0.135911\pi$
$811$			23.5867i			0.828243i	−0.910222	+	0.414121i	$0.864089\pi$
$812$	1.22975	+	9.75158i	0.0431558	+	0.342213i
$813$	31.3263	−	6.30890i	1.09866	−	0.221263i
$814$	−7.31462	−	12.6693i	−0.256377	−	0.444058i
$815$	28.6945	+	19.4878i	1.00513	+	0.682628i
$816$	−1.53976	+	4.57177i	−0.0539022	+	0.160044i
$817$	0.624835	−	1.08225i	0.0218602	−	0.0378630i
$818$			5.28770i			0.184880i
$819$	−45.9827	−	26.5901i	−1.60676	−	0.929132i
$820$	−0.124890	−	0.258143i	−0.00436135	−	0.00901475i
$821$	−7.06623	−	4.07969i	−0.246613	−	0.142382i	0.371599	−	0.928393i	$-0.378810\pi$
$821$	−7.06623	−	4.07969i	−0.246613	−	0.142382i	−0.618212	+	0.786011i	$0.712143\pi$
$822$	−23.8656	+	21.0304i	−0.832407	+	0.733521i
$823$	−12.8761	+	7.43404i	−0.448834	+	0.259134i	−0.707338	−	0.706876i	$-0.750104\pi$
$823$	−12.8761	+	7.43404i	−0.448834	+	0.259134i	0.258504	+	0.966010i	$0.416771\pi$
$824$	4.24895	+	7.35940i	0.148019	+	0.256377i
$825$	−24.9431	+	1.31689i	−0.868406	+	0.0458483i
$826$	−28.0241	+	3.53406i	−0.975085	+	0.122966i
$827$	−49.3689			−1.71673			−0.858363	−	0.513043i	$-0.828518\pi$
$827$	−49.3689			−1.71673			−0.858363	+	0.513043i	$0.828518\pi$
$828$	−2.03843	+	16.0756i	−0.0708402	+	0.558665i
$829$			2.02900i			0.0704702i	0.999379	+	0.0352351i	$0.0112180\pi$
$829$			2.02900i			0.0704702i	−0.999379	+	0.0352351i	$0.988782\pi$
$830$	−0.0851138	+	1.16397i	−0.00295434	+	0.0404020i
$831$	−8.66934	+	25.7406i	−0.300736	+	0.892931i
$832$	3.34607	+	5.79556i	0.116004	+	0.200925i
$833$	−4.84030	−	18.8860i	−0.167707	−	0.654360i
$834$	3.40048	−	0.684833i	0.117749	−	0.0237138i
$835$	3.56780	−	48.7913i	0.123469	−	1.68849i
$836$	−19.9088			−0.688560
$837$	31.5265	+	15.2677i	1.08972	+	0.527729i
$838$	−21.9016			−0.756577
$839$	−18.0263	+	31.2225i	−0.622337	+	1.07792i	0.366713	+	0.930334i	$0.380483\pi$
$839$	−18.0263	+	31.2225i	−0.622337	+	1.07792i	−0.989049	+	0.147585i	$0.952850\pi$
$840$	9.86909	+	2.75700i	0.340516	+	0.0951256i
$841$	−7.59960	−	13.1629i	−0.262055	−	0.453893i
$842$	19.2172	+	33.2851i	0.662267	+	1.14708i
$843$	2.70227	−	8.02346i	0.0930713	−	0.276343i
$844$	3.83172	−	6.63673i	0.131893	−	0.228446i
$845$	−30.9529	−	63.9786i	−1.06481	−	2.20093i
$846$	−9.23532	+	12.1553i	−0.317517	+	0.417908i
$847$	−4.28809	−	5.65190i	−0.147340	−	0.194202i
$848$	−5.38211	+	9.32209i	−0.184822	+	0.320122i
$849$	22.0332	−	19.4157i	0.756177	−	0.666347i
$850$	−2.02581	+	13.7778i	−0.0694846	+	0.472576i
$851$	−23.7267	+	13.6986i	−0.813342	+	0.469583i
$852$	−9.19489	−	10.4345i	−0.315012	−	0.357479i
$853$	−4.51925	+	7.82758i	−0.154736	+	0.268011i	−0.932963	−	0.359972i	$-0.882786\pi$
$853$	−4.51925	+	7.82758i	−0.154736	+	0.268011i	0.778227	+	0.627983i	$0.216119\pi$
$854$	14.9431	−	11.3373i	0.511342	−	0.387954i
$855$	45.3900	+	9.15960i	1.55231	+	0.313252i
$856$	−7.87180			−0.269052
$857$	41.3423	+	23.8690i	1.41223	+	0.815349i	0.995598	−	0.0937281i	$-0.0298784\pi$
$857$	41.3423	+	23.8690i	1.41223	+	0.815349i	0.416628	+	0.909077i	$0.363212\pi$
$858$	10.6705	−	31.6823i	0.364285	−	1.08162i
$859$	18.5221	−	10.6937i	0.631964	−	0.364865i	−0.149548	−	0.988754i	$-0.547782\pi$
$859$	18.5221	−	10.6937i	0.631964	−	0.364865i	0.781512	+	0.623890i	$0.214449\pi$
$860$	−0.334887	−	0.227437i	−0.0114195	−	0.00775554i
$861$	0.388850	−	0.440663i	0.0132520	−	0.0150178i
$862$	2.39468	+	1.38257i	0.0815632	+	0.0470905i
$863$	3.30599			0.112537			0.0562687	−	0.998416i	$-0.482080\pi$
$863$	3.30599			0.112537			0.0562687	+	0.998416i	$0.482080\pi$
$864$	2.26480	−	4.67661i	0.0770499	−	0.159102i
$865$	−0.489880	+	0.237005i	−0.0166564	+	0.00805840i
$866$	−1.30212	+	2.25534i	−0.0442478	+	0.0766395i
$867$	3.16061	+	15.6937i	0.107340	+	0.532987i
$868$	16.4407	+	6.91526i	0.558034	+	0.234719i
$869$	−28.2160	+	16.2905i	−0.957161	+	0.552617i
$870$	14.2743	−	1.80438i	0.483945	−	0.0611743i
$871$	88.8530	+	51.2993i	3.01067	+	1.73821i
$872$	−2.83000			−0.0958359
$873$	−1.55849	+	12.2907i	−0.0527470	+	0.415976i
$874$			37.2847i			1.26117i
$875$	29.4511	+	2.76280i	0.995629	+	0.0933996i
$876$	−15.0141	+	13.2305i	−0.507278	+	0.447016i
$877$	−10.8554	+	6.26734i	−0.366559	+	0.211633i	−0.671954	−	0.740593i	$-0.734545\pi$
$877$	−10.8554	+	6.26734i	−0.366559	+	0.211633i	0.305395	+	0.952226i	$0.401212\pi$
$878$	−13.8162	+	7.97681i	−0.466275	+	0.269204i
$879$	38.4006	+	43.5774i	1.29522	+	1.46983i
$880$	−0.470337	+	6.43207i	−0.0158550	+	0.216825i
$881$	44.6453			1.50414			0.752070	−	0.659084i	$-0.229056\pi$
$881$	44.6453			1.50414			0.752070	+	0.659084i	$0.229056\pi$
$882$	2.61320	+	20.8368i	0.0879910	+	0.701611i
$883$			12.7874i			0.430329i	0.976578	+	0.215164i	$0.0690287\pi$
$883$			12.7874i			0.430329i	−0.976578	+	0.215164i	$0.930971\pi$
$884$	−16.1418	−	9.31945i	−0.542906	−	0.313447i
$885$	5.18545	+	41.0216i	0.174307	+	1.37893i
$886$	9.31694	+	16.1374i	0.313009	+	0.542147i
$887$	35.5019	−	20.4970i	1.19204	−	0.688222i	0.233268	−	0.972412i	$-0.425058\pi$
$887$	35.5019	−	20.4970i	1.19204	−	0.688222i	0.958768	+	0.284190i	$0.0917247\pi$
$888$	8.61243	−	1.73448i	0.289014	−	0.0582054i
$889$	0.404975	+	3.21134i	0.0135824	+	0.107705i
$890$	5.55048	+	11.4726i	0.186052	+	0.384564i
$891$	−25.0080	+	6.95724i	−0.837798	+	0.233076i
$892$	−12.1983			−0.408428
$893$	−17.5626	+	30.4193i	−0.587709	+	1.01794i
$894$	−7.19129	+	1.44827i	−0.240513	+	0.0484375i
$895$	4.38231	+	2.97623i	0.146484	+	0.0994843i
$896$	1.02580	−	2.43880i	0.0342696	−	0.0814745i
$897$	−59.3339	−	19.9834i	−1.98110	−	0.667228i
$898$	10.3904	+	5.99888i	0.346731	+	0.200185i
$899$	25.0436			0.835251
$900$	4.03157	−	14.4481i	0.134386	−	0.481602i
$901$		−	29.9804i		−	0.998793i
$902$	0.320331	+	0.184943i	0.0106658	+	0.00615793i
$903$	0.164349	−	0.813187i	0.00546919	−	0.0270612i
$904$	−1.48562	−	2.57317i	−0.0494111	−	0.0855825i
$905$	−12.9048	−	8.76424i	−0.428970	−	0.291333i
$906$	20.2792	−	17.8702i	0.673733	−	0.593696i
$907$	−15.0465	−	8.68711i	−0.499611	−	0.288451i	0.228942	−	0.973440i	$-0.426473\pi$
$907$	−15.0465	−	8.68711i	−0.499611	−	0.288451i	−0.728553	+	0.684989i	$0.759807\pi$
$908$		−	6.24149i		−	0.207131i
$909$	−1.05129	+	8.29073i	−0.0348690	+	0.274986i
$910$	−17.9708	+	35.2777i	−0.595726	+	1.16944i
$911$	−7.62653	−	4.40318i	−0.252678	−	0.145884i	0.368312	−	0.929702i	$-0.379936\pi$
$911$	−7.62653	−	4.40318i	−0.252678	−	0.145884i	−0.620990	+	0.783819i	$0.713269\pi$
$912$	3.81608	−	11.3305i	0.126363	−	0.375191i
$913$	−0.752676	−	1.30367i	−0.0249100	−	0.0431453i
$914$	−21.4094	+	12.3607i	−0.708161	+	0.408857i
$915$	−16.6026	−	21.8696i	−0.548864	−	0.722985i
$916$	−4.10058	−	2.36747i	−0.135487	−	0.0782234i
$917$	6.19060	+	8.15950i	0.204431	+	0.269451i
$918$	1.04984	+	14.4342i	0.0346498	+	0.476398i
$919$	55.5958			1.83394			0.916968	−	0.398962i	$-0.130629\pi$
$919$	55.5958			1.83394			0.916968	+	0.398962i	$0.130629\pi$
$920$	12.0458	+	0.880835i	0.397139	+	0.0290403i
$921$	3.60619	+	17.9062i	0.118828	+	0.590030i
$922$	11.7641	+	20.3759i	0.387429	+	0.671046i
$923$	46.5361	−	26.8676i	1.53175	−	0.884359i
$924$	−12.5286	+	4.21004i	−0.412159	+	0.138500i
$925$	23.5744	−	9.35067i	0.775121	−	0.307448i
$926$		−	22.6719i		−	0.745046i
$927$	20.2993	+	15.4229i	0.666717	+	0.506556i
$928$		−	3.71494i		−	0.121949i
$929$	−3.68452	+	6.38178i	−0.120885	+	0.209379i	−0.920117	−	0.391644i	$-0.871907\pi$
$929$	−3.68452	+	6.38178i	−0.120885	+	0.209379i	0.799232	+	0.601023i	$0.205240\pi$
$930$	10.1158	−	24.0697i	0.331710	−	0.789277i
$931$	11.9961	+	46.8064i	0.393155	+	1.53402i
$932$	−9.69504	−	16.7923i	−0.317572	−	0.550050i
$933$	2.75103	−	2.42422i	0.0900646	−	0.0793654i
$934$	10.7738	+	6.22025i	0.352529	+	0.203533i
$935$	−7.82280	−	16.1694i	−0.255833	−	0.528797i
$936$	15.9858	+	12.1456i	0.522513	+	0.396992i
$937$	21.1973			0.692486			0.346243	−	0.938145i	$-0.387457\pi$
$937$	21.1973			0.692486			0.346243	+	0.938145i	$0.387457\pi$
$938$	−5.07506	−	40.2439i	−0.165707	−	1.31401i
$939$	−42.5716	−	14.3380i	−1.38927	−	0.467902i
$940$	9.41284	+	6.39270i	0.307013	+	0.208507i
$941$	−12.8702	−	22.2918i	−0.419555	−	0.726691i	0.576340	−	0.817210i	$-0.304481\pi$
$941$	−12.8702	−	22.2918i	−0.419555	−	0.726691i	−0.995895	+	0.0905195i	$0.971147\pi$
$942$	3.63373	+	18.0430i	0.118393	+	0.587873i
$943$	0.346356	−	0.599907i	0.0112789	−	0.0195357i
$944$	10.6760			0.347475
$945$	30.5008	−	3.83434i	0.992191	−	0.124731i
$946$	0.522152			0.0169766
$947$	7.14436	−	12.3744i	0.232161	−	0.402114i	−0.726283	−	0.687396i	$-0.758754\pi$
$947$	7.14436	−	12.3744i	0.232161	−	0.402114i	0.958444	+	0.285282i	$0.0920872\pi$
$948$	−3.86289	−	19.1809i	−0.125461	−	0.622966i
$949$	−38.6597	−	66.9605i	−1.25495	−	2.17363i
$950$	5.02070	−	34.1466i	0.162893	−	1.10786i
$951$	−21.8588	−	7.36196i	−0.708820	−	0.238728i
$952$	0.921977	+	7.31102i	0.0298814	+	0.236952i
$953$	21.8222			0.706892			0.353446	−	0.935455i	$-0.385010\pi$
$953$	21.8222			0.706892			0.353446	+	0.935455i	$0.385010\pi$
$954$	−4.06227	+	32.0361i	−0.131521	+	1.03721i
$955$	−22.8987	+	11.0784i	−0.740985	+	0.358489i
$956$	−6.40008	−	3.69509i	−0.206993	−	0.119508i
$957$	−13.9236	+	12.2695i	−0.450086	+	0.396618i
$958$	−1.25925	−	2.18108i	−0.0406844	−	0.0704674i
$959$	−18.8391	+	44.7891i	−0.608346	+	1.44631i
$960$	−3.57048	−	1.50057i	−0.115237	−	0.0484306i
$961$	7.22267	−	12.5100i	0.232989	−	0.403549i
$962$			33.9440i			1.09440i
$963$	−21.7744	+	9.14119i	−0.701671	+	0.294571i
$964$		−	6.54396i		−	0.210767i
$965$	−0.360672	+	4.93235i	−0.0116104	+	0.158778i
$966$	7.88445	+	23.4632i	0.253678	+	0.754915i
$967$	−40.6832	+	23.4884i	−1.30828	+	0.755337i	−0.981809	−	0.189870i	$-0.939193\pi$
$967$	−40.6832	+	23.4884i	−1.30828	+	0.755337i	−0.326473	+	0.945207i	$0.605860\pi$
$968$	1.34073	+	2.32222i	0.0430927	+	0.0746388i
$969$	6.57428	+	32.6441i	0.211196	+	1.04868i
$970$	9.20970	+	0.673447i	0.295706	+	0.0216231i
$971$	9.32339			0.299202			0.149601	−	0.988746i	$-0.452201\pi$
$971$	9.32339			0.299202			0.149601	+	0.988746i	$0.452201\pi$
$972$	0.833969	−	15.5661i	0.0267496	−	0.499284i
$973$	4.22120	−	3.20262i	0.135326	−	0.102671i
$974$	12.2430	+	7.06849i	0.392291	+	0.226489i
$975$	51.6490	+	26.2913i	1.65409	+	0.841996i
$976$	−6.13972	+	3.54477i	−0.196528	+	0.113465i
$977$	−4.15051	−	7.18889i	−0.132787	−	0.229993i	0.791963	−	0.610569i	$-0.209059\pi$
$977$	−4.15051	−	7.18889i	−0.132787	−	0.229993i	−0.924750	+	0.380576i	$0.875726\pi$
$978$	8.57574	−	25.4627i	0.274222	−	0.814206i
$979$	−14.2364	−	8.21940i	−0.454998	−	0.262693i
$980$	15.4054	−	2.76987i	0.492109	−	0.0884802i
$981$	−7.82815	+	3.28636i	−0.249934	+	0.104925i
$982$		−	16.0994i		−	0.513752i
$983$	−48.1941	−	27.8249i	−1.53715	−	0.887476i	−0.999004	−	0.0446272i	$-0.985790\pi$
$983$	−48.1941	−	27.8249i	−1.53715	−	0.887476i	−0.538150	−	0.842849i	$-0.680877\pi$
$984$	−0.166655	+	0.146858i	−0.00531278	+	0.00468165i
$985$	30.7880	−	45.3334i	0.980988	−	1.44444i
$986$	5.17342	+	8.96062i	0.164755	+	0.285364i
$987$	−4.61944	+	22.8567i	−0.147039	+	0.727536i
$988$	40.0053	+	23.0970i	1.27274	+	0.734815i
$989$		−	0.977874i		−	0.0310946i
$990$	6.16828	+	18.3381i	0.196041	+	0.582824i
$991$	−50.8410			−1.61502			−0.807509	−	0.589855i	$-0.799185\pi$
$991$	−50.8410			−1.61502			−0.807509	+	0.589855i	$0.799185\pi$
$992$	−5.83815	−	3.37066i	−0.185361	−	0.107018i
$993$	−20.2473	−	6.81923i	−0.642530	−	0.216402i
$994$	−19.5826	−	8.23679i	−0.621122	−	0.261255i
$995$	19.4002	+	13.1756i	0.615029	+	0.417694i
$996$	0.886221	−	0.178479i	0.0280810	−	0.00565531i
$997$	−18.4584	+	31.9709i	−0.584584	+	1.01253i	0.410343	+	0.911931i	$0.365409\pi$
$997$	−18.4584	+	31.9709i	−0.584584	+	1.01253i	−0.994927	+	0.100598i	$0.967924\pi$
$998$	−26.0291			−0.823935
$999$	21.8089	−	14.7991i	0.690004	−	0.468221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bf.f.209.10	yes	32
3.2	odd	2		1890.2.bf.e.629.11		32
5.4	even	2		630.2.bf.e.209.7	✓	32
7.6	odd	2	inner	630.2.bf.f.209.7	yes	32
9.4	even	3		1890.2.bf.f.1259.16		32
9.5	odd	6		630.2.bf.e.419.10	yes	32
15.14	odd	2		1890.2.bf.f.629.1		32
21.20	even	2		1890.2.bf.e.629.6		32
35.34	odd	2		630.2.bf.e.209.10	yes	32
45.4	even	6		1890.2.bf.e.1259.6		32
45.14	odd	6	inner	630.2.bf.f.419.7	yes	32
63.13	odd	6		1890.2.bf.f.1259.1		32
63.41	even	6		630.2.bf.e.419.7	yes	32
105.104	even	2		1890.2.bf.f.629.16		32
315.104	even	6	inner	630.2.bf.f.419.10	yes	32
315.139	odd	6		1890.2.bf.e.1259.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bf.e.209.7	✓	32	5.4	even	2
630.2.bf.e.209.10	yes	32	35.34	odd	2
630.2.bf.e.419.7	yes	32	63.41	even	6
630.2.bf.e.419.10	yes	32	9.5	odd	6
630.2.bf.f.209.7	yes	32	7.6	odd	2	inner
630.2.bf.f.209.10	yes	32	1.1	even	1	trivial
630.2.bf.f.419.7	yes	32	45.14	odd	6	inner
630.2.bf.f.419.10	yes	32	315.104	even	6	inner
1890.2.bf.e.629.6		32	21.20	even	2
1890.2.bf.e.629.11		32	3.2	odd	2
1890.2.bf.e.1259.6		32	45.4	even	6
1890.2.bf.e.1259.11		32	315.139	odd	6
1890.2.bf.f.629.1		32	15.14	odd	2
1890.2.bf.f.629.16		32	105.104	even	2
1890.2.bf.f.1259.1		32	63.13	odd	6
1890.2.bf.f.1259.16		32	9.4	even	3

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.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.341957 + 1.69796i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.25628 + 1.84980i) q^{5} +(1.64145 + 0.552836i) q^{6} +(2.62496 - 0.331028i) q^{7} -1.00000 q^{8} +(-2.76613 + 1.16126i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.341957 + 1.69796i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.25628 + 1.84980i) q^{5} +(1.64145 + 0.552836i) q^{6} +(2.62496 - 0.331028i) q^{7} -1.00000 q^{8} +(-2.76613 + 1.16126i) q^{9} +(0.973830 + 2.01287i) q^{10} +(-2.49778 - 1.44209i) q^{11} +(1.29950 - 1.14512i) q^{12} +(3.34607 + 5.79556i) q^{13} +(1.02580 - 2.43880i) q^{14} +(-3.57048 - 1.50057i) q^{15} +(-0.500000 + 0.866025i) q^{16} -2.78519i q^{17} +(-0.377386 + 2.97617i) q^{18} +6.90274i q^{19} +(2.23011 + 0.163074i) q^{20} +(1.45970 + 4.34388i) q^{21} +(-2.49778 + 1.44209i) q^{22} +(2.70072 + 4.67778i) q^{23} +(-0.341957 - 1.69796i) q^{24} +(-1.84350 - 4.64774i) q^{25} +6.69214 q^{26} +(-2.91767 - 4.29968i) q^{27} +(-1.59916 - 2.10777i) q^{28} +(-3.21724 - 1.85747i) q^{29} +(-3.08477 + 2.34184i) q^{30} +(-5.83815 + 3.37066i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.59448 - 4.73426i) q^{33} +(-2.41205 - 1.39260i) q^{34} +(-2.68536 + 5.27151i) q^{35} +(2.38874 + 1.81491i) q^{36} +5.07222i q^{37} +(5.97795 + 3.45137i) q^{38} +(-8.69642 + 7.66332i) q^{39} +(1.25628 - 1.84980i) q^{40} +(-0.0641231 - 0.111064i) q^{41} +(4.49176 + 0.907806i) q^{42} +(-0.156785 - 0.0905199i) q^{43} +2.88419i q^{44} +(1.32695 - 6.57565i) q^{45} +5.40143 q^{46} +(4.40684 + 2.54429i) q^{47} +(-1.64145 - 0.552836i) q^{48} +(6.78084 - 1.73787i) q^{49} +(-4.94681 - 0.727348i) q^{50} +(4.72914 - 0.952416i) q^{51} +(3.34607 - 5.79556i) q^{52} +10.7642 q^{53} +(-5.18246 + 0.376935i) q^{54} +(5.80550 - 2.80871i) q^{55} +(-2.62496 + 0.331028i) q^{56} +(-11.7206 + 2.36044i) q^{57} +(-3.21724 + 1.85747i) q^{58} +(-5.33801 - 9.24571i) q^{59} +(0.485710 + 3.84241i) q^{60} +(6.13972 + 3.54477i) q^{61} +6.74132i q^{62} +(-6.87658 + 3.96392i) q^{63} +1.00000 q^{64} +(-14.9242 - 1.09132i) q^{65} +(-3.30275 - 3.74799i) q^{66} +(13.2772 - 7.66561i) q^{67} +(-2.41205 + 1.39260i) q^{68} +(-7.01915 + 6.18531i) q^{69} +(3.22258 + 4.96135i) q^{70} -8.02961i q^{71} +(2.76613 - 1.16126i) q^{72} -11.5538 q^{73} +(4.39267 + 2.53611i) q^{74} +(7.26127 - 4.71952i) q^{75} +(5.97795 - 3.45137i) q^{76} +(-7.03395 - 2.95861i) q^{77} +(2.28842 + 11.3630i) q^{78} +(5.64821 - 9.78299i) q^{79} +(-0.973830 - 2.01287i) q^{80} +(6.30296 - 6.42438i) q^{81} -0.128246 q^{82} +(0.452007 + 0.260967i) q^{83} +(3.03206 - 3.43607i) q^{84} +(5.15204 + 3.49899i) q^{85} +(-0.156785 + 0.0905199i) q^{86} +(2.05376 - 6.09791i) q^{87} +(2.49778 + 1.44209i) q^{88} +5.69963 q^{89} +(-5.03121 - 4.43700i) q^{90} +(10.7018 + 14.1055i) q^{91} +(2.70072 - 4.67778i) q^{92} +(-7.71964 - 8.76032i) q^{93} +(4.40684 - 2.54429i) q^{94} +(-12.7687 - 8.67180i) q^{95} +(-1.29950 + 1.14512i) q^{96} +(2.06485 - 3.57642i) q^{97} +(1.88538 - 6.74132i) q^{98} +(8.58383 + 1.08845i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} - 6 q^{9}+O(q^{10}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 - 6 * q^9	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} - 6 q^{9} - 24 q^{11} - 12 q^{15} - 16 q^{16} - 6 q^{18} + 2 q^{21} - 24 q^{22} + 24 q^{23} + 50 q^{25} - 36 q^{29} - 18 q^{30} + 16 q^{32} + 48 q^{35} - 66 q^{39} - 2 q^{42} + 54 q^{43} + 48 q^{46} + 32 q^{49} + 58 q^{50} - 26 q^{51} + 24 q^{53} - 110 q^{57} - 36 q^{58} - 6 q^{60} - 20 q^{63} + 32 q^{64} - 66 q^{65} + 66 q^{67} + 12 q^{70} + 6 q^{72} + 12 q^{74} - 18 q^{77} - 60 q^{78} + 34 q^{79} + 2 q^{81} - 4 q^{84} - 32 q^{85} + 54 q^{86} + 24 q^{88} + 16 q^{91} + 24 q^{92} - 28 q^{93} - 24 q^{95} + 64 q^{98} + 58 q^{99}+O(q^{100}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 - 6 * q^9 - 24 * q^11 - 12 * q^15 - 16 * q^16 - 6 * q^18 + 2 * q^21 - 24 * q^22 + 24 * q^23 + 50 * q^25 - 36 * q^29 - 18 * q^30 + 16 * q^32 + 48 * q^35 - 66 * q^39 - 2 * q^42 + 54 * q^43 + 48 * q^46 + 32 * q^49 + 58 * q^50 - 26 * q^51 + 24 * q^53 - 110 * q^57 - 36 * q^58 - 6 * q^60 - 20 * q^63 + 32 * q^64 - 66 * q^65 + 66 * q^67 + 12 * q^70 + 6 * q^72 + 12 * q^74 - 18 * q^77 - 60 * q^78 + 34 * q^79 + 2 * q^81 - 4 * q^84 - 32 * q^85 + 54 * q^86 + 24 * q^88 + 16 * q^91 + 24 * q^92 - 28 * q^93 - 24 * q^95 + 64 * q^98 + 58 * q^99

Introduction

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