LMFDB - Embedded newform 630.2.bk.c.131.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(101,630)]

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, 0, 1]))

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

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

chi := DirichletCharacter("630.101");

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.bk (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			131.7
Character	$\chi$	$=$	630.131
Dual form			630.2.bk.c.101.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.51441 + 0.840572i) q^{3} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.840572 - 1.51441i) q^{6} +(-1.15079 + 2.38237i) q^{7} +1.00000i q^{8} +(1.58688 + 2.54594i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.51441 + 0.840572i) q^{3} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.840572 - 1.51441i) q^{6} +(-1.15079 + 2.38237i) q^{7} +1.00000i q^{8} +(1.58688 + 2.54594i) q^{9} +(0.866025 - 0.500000i) q^{10} +(-1.81100 - 1.04558i) q^{11} +(-1.51441 - 0.840572i) q^{12} +(0.413776 + 0.238893i) q^{13} +(2.38237 + 1.15079i) q^{14} +(0.0292487 + 1.73180i) q^{15} +1.00000 q^{16} +(1.44100 + 2.49589i) q^{17} +(2.54594 - 1.58688i) q^{18} +(4.03431 + 2.32921i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-3.74532 + 2.64057i) q^{21} +(-1.04558 + 1.81100i) q^{22} +(-1.75599 + 1.01382i) q^{23} +(-0.840572 + 1.51441i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.238893 - 0.413776i) q^{26} +(0.263138 + 5.18949i) q^{27} +(1.15079 - 2.38237i) q^{28} +(2.74938 - 1.58735i) q^{29} +(1.73180 - 0.0292487i) q^{30} +5.30392i q^{31} -1.00000i q^{32} +(-1.86371 - 3.10572i) q^{33} +(2.49589 - 1.44100i) q^{34} +(-2.63859 + 0.194573i) q^{35} +(-1.58688 - 2.54594i) q^{36} +(-1.93169 + 3.34578i) q^{37} +(2.32921 - 4.03431i) q^{38} +(0.425819 + 0.709591i) q^{39} +(-0.866025 + 0.500000i) q^{40} +(4.03898 - 6.99572i) q^{41} +(2.64057 + 3.74532i) q^{42} +(-2.96902 - 5.14250i) q^{43} +(1.81100 + 1.04558i) q^{44} +(-1.41141 + 2.64725i) q^{45} +(1.01382 + 1.75599i) q^{46} +0.105073 q^{47} +(1.51441 + 0.840572i) q^{48} +(-4.35137 - 5.48321i) q^{49} +(0.866025 + 0.500000i) q^{50} +(0.0842951 + 4.99107i) q^{51} +(-0.413776 - 0.238893i) q^{52} +(4.27164 - 2.46623i) q^{53} +(5.18949 - 0.263138i) q^{54} -2.09116i q^{55} +(-2.38237 - 1.15079i) q^{56} +(4.15173 + 6.91851i) q^{57} +(-1.58735 - 2.74938i) q^{58} +2.81942 q^{59} +(-0.0292487 - 1.73180i) q^{60} +4.29310i q^{61} +5.30392 q^{62} +(-7.89153 + 0.850692i) q^{63} -1.00000 q^{64} +0.477787i q^{65} +(-3.10572 + 1.86371i) q^{66} +5.47175 q^{67} +(-1.44100 - 2.49589i) q^{68} +(-3.51147 + 0.0593058i) q^{69} +(0.194573 + 2.63859i) q^{70} -10.8486i q^{71} +(-2.54594 + 1.58688i) q^{72} +(5.64929 - 3.26162i) q^{73} +(3.34578 + 1.93169i) q^{74} +(-1.48516 + 0.891232i) q^{75} +(-4.03431 - 2.32921i) q^{76} +(4.57504 - 3.11123i) q^{77} +(0.709591 - 0.425819i) q^{78} -15.6355 q^{79} +(0.500000 + 0.866025i) q^{80} +(-3.96364 + 8.08020i) q^{81} +(-6.99572 - 4.03898i) q^{82} +(-5.58951 - 9.68132i) q^{83} +(3.74532 - 2.64057i) q^{84} +(-1.44100 + 2.49589i) q^{85} +(-5.14250 + 2.96902i) q^{86} +(5.49797 - 0.0928562i) q^{87} +(1.04558 - 1.81100i) q^{88} +(6.59060 - 11.4153i) q^{89} +(2.64725 + 1.41141i) q^{90} +(-1.04530 + 0.710851i) q^{91} +(1.75599 - 1.01382i) q^{92} +(-4.45833 + 8.03232i) q^{93} -0.105073i q^{94} +4.65842i q^{95} +(0.840572 - 1.51441i) q^{96} +(-7.98211 + 4.60847i) q^{97} +(-5.48321 + 4.35137i) q^{98} +(-0.211848 - 6.26991i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7}+O(q^{10}) $ 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7	$ 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7} - 6 q^{11} + 2 q^{12} + 6 q^{14} + 2 q^{15} + 32 q^{16} - 6 q^{17} + 8 q^{18} - 16 q^{20} + 18 q^{23} + 2 q^{24} - 16 q^{25} - 12 q^{26} - 8 q^{27} + 2 q^{28} + 6 q^{29} - 4 q^{30} + 20 q^{33} + 2 q^{35} + 2 q^{37} + 30 q^{39} + 6 q^{41} + 10 q^{42} - 28 q^{43} + 6 q^{44} + 6 q^{45} + 48 q^{47} - 2 q^{48} + 8 q^{49} + 34 q^{51} + 36 q^{53} - 46 q^{54} - 6 q^{56} + 18 q^{57} - 60 q^{59} - 2 q^{60} + 32 q^{63} - 32 q^{64} - 34 q^{66} - 8 q^{67} + 6 q^{68} - 28 q^{69} + 6 q^{70} - 8 q^{72} - 30 q^{73} - 18 q^{74} + 4 q^{75} - 6 q^{77} - 22 q^{78} - 8 q^{79} + 16 q^{80} + 20 q^{81} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 30 q^{86} - 22 q^{87} + 12 q^{89} + 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 2 q^{96} - 96 q^{97} + 24 q^{98} - 24 q^{99}+O(q^{100}) $ 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7 - 6 * q^11 + 2 * q^12 + 6 * q^14 + 2 * q^15 + 32 * q^16 - 6 * q^17 + 8 * q^18 - 16 * q^20 + 18 * q^23 + 2 * q^24 - 16 * q^25 - 12 * q^26 - 8 * q^27 + 2 * q^28 + 6 * q^29 - 4 * q^30 + 20 * q^33 + 2 * q^35 + 2 * q^37 + 30 * q^39 + 6 * q^41 + 10 * q^42 - 28 * q^43 + 6 * q^44 + 6 * q^45 + 48 * q^47 - 2 * q^48 + 8 * q^49 + 34 * q^51 + 36 * q^53 - 46 * q^54 - 6 * q^56 + 18 * q^57 - 60 * q^59 - 2 * q^60 + 32 * q^63 - 32 * q^64 - 34 * q^66 - 8 * q^67 + 6 * q^68 - 28 * q^69 + 6 * q^70 - 8 * q^72 - 30 * q^73 - 18 * q^74 + 4 * q^75 - 6 * q^77 - 22 * q^78 - 8 * q^79 + 16 * q^80 + 20 * q^81 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 30 * q^86 - 22 * q^87 + 12 * q^89 + 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 2 * q^96 - 96 * q^97 + 24 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.51441	+	0.840572i	0.874345	+	0.485304i
$3$	1.51441	+	0.840572i	0.874345	+	0.485304i
$4$	−1.00000			−0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.840572	−	1.51441i	0.343162	−	0.618255i
$7$	−1.15079	+	2.38237i	−0.434957	+	0.900451i
$7$	−1.15079	+	2.38237i	−0.434957	+	0.900451i
$8$			1.00000i			0.353553i
$9$	1.58688	+	2.54594i	0.528959	+	0.848647i
$10$	0.866025	−	0.500000i	0.273861	−	0.158114i
$11$	−1.81100	−	1.04558i	−0.546037	−	0.315255i	0.201485	−	0.979492i	$-0.435423\pi$
$11$	−1.81100	−	1.04558i	−0.546037	−	0.315255i	−0.747522	+	0.664237i	$0.768757\pi$
$12$	−1.51441	−	0.840572i	−0.437173	−	0.242652i
$13$	0.413776	+	0.238893i	0.114761	+	0.0662571i	0.556282	−	0.830994i	$-0.312228\pi$
$13$	0.413776	+	0.238893i	0.114761	+	0.0662571i	−0.441521	+	0.897251i	$0.645561\pi$
$14$	2.38237	+	1.15079i	0.636715	+	0.307561i
$15$	0.0292487	+	1.73180i	0.00755199	+	0.447150i
$16$	1.00000			0.250000
$17$	1.44100	+	2.49589i	0.349495	+	0.605343i	0.986160	−	0.165798i	$-0.0530198\pi$
$17$	1.44100	+	2.49589i	0.349495	+	0.605343i	−0.636665	+	0.771141i	$0.719687\pi$
$18$	2.54594	−	1.58688i	0.600084	−	0.374031i
$19$	4.03431	+	2.32921i	0.925535	+	0.534358i	0.885397	−	0.464837i	$-0.153887\pi$
$19$	4.03431	+	2.32921i	0.925535	+	0.534358i	0.0401380	+	0.999194i	$0.487220\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	−3.74532	+	2.64057i	−0.817295	+	0.576219i
$22$	−1.04558	+	1.81100i	−0.222919	+	0.386107i
$23$	−1.75599	+	1.01382i	−0.366148	+	0.211396i	−0.671774	−	0.740756i	$-0.734468\pi$
$23$	−1.75599	+	1.01382i	−0.366148	+	0.211396i	0.305626	+	0.952152i	$0.401134\pi$
$24$	−0.840572	+	1.51441i	−0.171581	+	0.309128i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.238893	−	0.413776i	0.0468509	−	0.0811481i
$27$	0.263138	+	5.18949i	0.0506410	+	0.998717i
$28$	1.15079	−	2.38237i	0.217478	−	0.450226i
$29$	2.74938	−	1.58735i	0.510547	−	0.294764i	−0.222512	−	0.974930i	$-0.571426\pi$
$29$	2.74938	−	1.58735i	0.510547	−	0.294764i	0.733058	+	0.680166i	$0.238092\pi$
$30$	1.73180	−	0.0292487i	0.316183	−	0.00534006i
$31$			5.30392i			0.952613i	0.879279	+	0.476306i	$0.158025\pi$
$31$			5.30392i			0.952613i	−0.879279	+	0.476306i	$0.841975\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.86371	−	3.10572i	−0.324431	−	0.540636i
$34$	2.49589	−	1.44100i	0.428042	−	0.247130i
$35$	−2.63859	+	0.194573i	−0.446003	+	0.0328889i
$36$	−1.58688	−	2.54594i	−0.264480	−	0.424324i
$37$	−1.93169	+	3.34578i	−0.317568	+	0.550043i	−0.979980	−	0.199096i	$-0.936199\pi$
$37$	−1.93169	+	3.34578i	−0.317568	+	0.550043i	0.662412	+	0.749140i	$0.269533\pi$
$38$	2.32921	−	4.03431i	0.377848	−	0.654452i
$39$	0.425819	+	0.709591i	0.0681856	+	0.113625i
$40$	−0.866025	+	0.500000i	−0.136931	+	0.0790569i
$41$	4.03898	−	6.99572i	0.630783	−	1.09255i	−0.356609	−	0.934254i	$-0.616067\pi$
$41$	4.03898	−	6.99572i	0.630783	−	1.09255i	0.987392	−	0.158294i	$-0.0505995\pi$
$42$	2.64057	+	3.74532i	0.407448	+	0.577915i
$43$	−2.96902	−	5.14250i	−0.452772	−	0.784224i	0.545785	−	0.837925i	$-0.316231\pi$
$43$	−2.96902	−	5.14250i	−0.452772	−	0.784224i	−0.998557	+	0.0537015i	$0.982898\pi$
$44$	1.81100	+	1.04558i	0.273019	+	0.157627i
$45$	−1.41141	+	2.64725i	−0.210401	+	0.394628i
$46$	1.01382	+	1.75599i	0.149479	+	0.258906i
$47$	0.105073			0.0153265			0.00766326	−	0.999971i	$-0.497561\pi$
$47$	0.105073			0.0153265			0.00766326	+	0.999971i	$0.497561\pi$
$48$	1.51441	+	0.840572i	0.218586	+	0.121326i
$49$	−4.35137	−	5.48321i	−0.621625	−	0.783315i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$	0.0842951	+	4.99107i	0.0118037	+	0.698890i
$52$	−0.413776	−	0.238893i	−0.0573804	−	0.0331286i
$53$	4.27164	−	2.46623i	0.586755	−	0.338763i	−0.177058	−	0.984200i	$-0.556658\pi$
$53$	4.27164	−	2.46623i	0.586755	−	0.338763i	0.763813	+	0.645437i	$0.223325\pi$
$54$	5.18949	−	0.263138i	0.706200	−	0.0358086i
$55$		−	2.09116i		−	0.281972i
$56$	−2.38237	−	1.15079i	−0.318358	−	0.153781i
$57$	4.15173	+	6.91851i	0.549911	+	0.916379i
$58$	−1.58735	−	2.74938i	−0.208430	−	0.361011i
$59$	2.81942			0.367057			0.183529	−	0.983014i	$-0.441248\pi$
$59$	2.81942			0.367057			0.183529	+	0.983014i	$0.441248\pi$
$60$	−0.0292487	−	1.73180i	−0.00377599	−	0.223575i
$61$			4.29310i			0.549675i	0.961491	+	0.274838i	$0.0886241\pi$
$61$			4.29310i			0.549675i	−0.961491	+	0.274838i	$0.911376\pi$
$62$	5.30392			0.673599
$63$	−7.89153	+	0.850692i	−0.994240	+	0.107177i
$64$	−1.00000			−0.125000
$65$			0.477787i			0.0592622i
$66$	−3.10572	+	1.86371i	−0.382287	+	0.229407i
$67$	5.47175			0.668481			0.334240	−	0.942488i	$-0.391520\pi$
$67$	5.47175			0.668481			0.334240	+	0.942488i	$0.391520\pi$
$68$	−1.44100	−	2.49589i	−0.174747	−	0.302672i
$69$	−3.51147	+	0.0593058i	−0.422731	+	0.00713958i
$70$	0.194573	+	2.63859i	0.0232560	+	0.315371i
$71$		−	10.8486i		−	1.28750i	−0.765238	−	0.643748i	$-0.777379\pi$
$71$		−	10.8486i		−	1.28750i	0.765238	−	0.643748i	$-0.222621\pi$
$72$	−2.54594	+	1.58688i	−0.300042	+	0.187015i
$73$	5.64929	−	3.26162i	0.661199	−	0.381744i	−0.131535	−	0.991312i	$-0.541990\pi$
$73$	5.64929	−	3.26162i	0.661199	−	0.381744i	0.792734	+	0.609568i	$0.208657\pi$
$74$	3.34578	+	1.93169i	0.388939	+	0.224554i
$75$	−1.48516	+	0.891232i	−0.171492	+	0.102911i
$76$	−4.03431	−	2.32921i	−0.462767	−	0.267179i
$77$	4.57504	−	3.11123i	0.521374	−	0.354558i
$78$	0.709591	−	0.425819i	0.0803454	−	0.0482145i
$79$	−15.6355			−1.75913			−0.879563	−	0.475782i	$-0.842165\pi$
$79$	−15.6355			−1.75913			−0.879563	+	0.475782i	$0.842165\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−3.96364	+	8.08020i	−0.440404	+	0.897800i
$82$	−6.99572	−	4.03898i	−0.772548	−	0.446031i
$83$	−5.58951	−	9.68132i	−0.613529	−	1.06266i	−0.990641	−	0.136495i	$-0.956416\pi$
$83$	−5.58951	−	9.68132i	−0.613529	−	1.06266i	0.377112	−	0.926168i	$-0.376917\pi$
$84$	3.74532	−	2.64057i	0.408648	−	0.288109i
$85$	−1.44100	+	2.49589i	−0.156299	+	0.270718i
$86$	−5.14250	+	2.96902i	−0.554530	+	0.320158i
$87$	5.49797	−	0.0928562i	0.589445	−	0.00995522i
$88$	1.04558	−	1.81100i	0.111459	−	0.193053i
$89$	6.59060	−	11.4153i	0.698602	−	1.21001i	−0.270349	−	0.962762i	$-0.587139\pi$
$89$	6.59060	−	11.4153i	0.698602	−	1.21001i	0.968951	−	0.247252i	$-0.0795276\pi$
$90$	2.64725	+	1.41141i	0.279044	+	0.148776i
$91$	−1.04530	+	0.710851i	−0.109577	+	0.0745174i
$92$	1.75599	−	1.01382i	0.183074	−	0.105698i
$93$	−4.45833	+	8.03232i	−0.462307	+	0.832913i
$94$		−	0.105073i		−	0.0108375i
$95$			4.65842i			0.477944i
$96$	0.840572	−	1.51441i	0.0857905	−	0.154564i
$97$	−7.98211	+	4.60847i	−0.810460	+	0.467920i	−0.847116	−	0.531408i	$-0.821663\pi$
$97$	−7.98211	+	4.60847i	−0.810460	+	0.467920i	0.0366553	+	0.999328i	$0.488330\pi$
$98$	−5.48321	+	4.35137i	−0.553887	+	0.439555i
$99$	−0.211848	−	6.26991i	−0.0212915	−	0.630150i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	9.43156	−	16.3359i	0.938475	−	1.62549i	0.170158	−	0.985417i	$-0.445572\pi$
$101$	9.43156	−	16.3359i	0.938475	−	1.62549i	0.768317	−	0.640070i	$-0.221095\pi$
$102$	4.99107	−	0.0842951i	0.494190	−	0.00834646i
$103$	8.79688	−	5.07888i	0.866783	−	0.500437i	0.000504907	−	1.00000i	$-0.499839\pi$
$103$	8.79688	−	5.07888i	0.866783	−	0.500437i	0.866278	+	0.499563i	$0.166506\pi$
$104$	−0.238893	+	0.413776i	−0.0234254	+	0.0405740i
$105$	−4.15946	−	1.92326i	−0.405921	−	0.187691i
$106$	−2.46623	−	4.27164i	−0.239542	−	0.414898i
$107$	15.8802	+	9.16843i	1.53520	+	0.886346i	0.999110	+	0.0421823i	$0.0134310\pi$
$107$	15.8802	+	9.16843i	1.53520	+	0.886346i	0.536086	+	0.844163i	$0.319902\pi$
$108$	−0.263138	−	5.18949i	−0.0253205	−	0.499358i
$109$	7.08626	+	12.2738i	0.678741	+	1.17561i	0.975360	+	0.220618i	$0.0708074\pi$
$109$	7.08626	+	12.2738i	0.678741	+	1.17561i	−0.296619	+	0.954996i	$0.595859\pi$
$110$	−2.09116			−0.199385
$111$	−5.73774	+	3.44317i	−0.544602	+	0.326811i
$112$	−1.15079	+	2.38237i	−0.108739	+	0.225113i
$113$	6.91284	+	3.99113i	0.650305	+	0.375454i	0.788573	−	0.614941i	$-0.210820\pi$
$113$	6.91284	+	3.99113i	0.650305	+	0.375454i	−0.138268	+	0.990395i	$0.544153\pi$
$114$	6.91851	−	4.15173i	0.647978	−	0.388846i
$115$	−1.75599	−	1.01382i	−0.163747	−	0.0945391i
$116$	−2.74938	+	1.58735i	−0.255273	+	0.147382i
$117$	0.0484027	+	1.43254i	0.00447483	+	0.132439i
$118$		−	2.81942i		−	0.259549i
$119$	−7.60443	+	0.560762i	−0.697097	+	0.0514050i
$120$	−1.73180	+	0.0292487i	−0.158091	+	0.00267003i
$121$	−3.31352	−	5.73918i	−0.301229	−	0.521744i
$122$	4.29310			0.388679
$123$	11.9971	−	7.19934i	1.08174	−	0.649143i
$124$		−	5.30392i		−	0.476306i
$125$	−1.00000			−0.0894427
$126$	0.850692	+	7.89153i	0.0757857	+	0.703034i
$127$	0.449694			0.0399039			0.0199520	−	0.999801i	$-0.493649\pi$
$127$	0.449694			0.0399039			0.0199520	+	0.999801i	$0.493649\pi$
$128$			1.00000i			0.0883883i
$129$	−0.173680	−	10.2835i	−0.0152917	−	0.905414i
$130$	0.477787			0.0419047
$131$	−5.22140	−	9.04374i	−0.456196	−	0.790155i	0.542560	−	0.840017i	$-0.317455\pi$
$131$	−5.22140	−	9.04374i	−0.456196	−	0.790155i	−0.998756	+	0.0498622i	$0.984122\pi$
$132$	1.86371	+	3.10572i	0.162215	+	0.270318i
$133$	−10.1917	+	6.93079i	−0.883731	+	0.600976i
$134$		−	5.47175i		−	0.472687i
$135$	−4.36266	+	2.82263i	−0.375478	+	0.242933i
$136$	−2.49589	+	1.44100i	−0.214021	+	0.123565i
$137$	−15.0990	−	8.71743i	−1.29000	−	0.744780i	−0.311343	−	0.950297i	$-0.600779\pi$
$137$	−15.0990	−	8.71743i	−1.29000	−	0.744780i	−0.978653	+	0.205517i	$0.934112\pi$
$138$	0.0593058	+	3.51147i	0.00504844	+	0.298916i
$139$	−11.1168	−	6.41827i	−0.942912	−	0.544390i	−0.0520399	−	0.998645i	$-0.516572\pi$
$139$	−11.1168	−	6.41827i	−0.942912	−	0.544390i	−0.890872	+	0.454255i	$0.849906\pi$
$140$	2.63859	−	0.194573i	0.223001	−	0.0164445i
$141$	0.159124	+	0.0883217i	0.0134007	+	0.00743803i
$142$	−10.8486			−0.910397
$143$	−0.499565	−	0.865272i	−0.0417757	−	0.0723577i
$144$	1.58688	+	2.54594i	0.132240	+	0.212162i
$145$	2.74938	+	1.58735i	0.228323	+	0.131823i
$146$	−3.26162	−	5.64929i	−0.269933	−	0.467538i
$147$	−1.98074	−	11.9615i	−0.163369	−	0.986565i
$148$	1.93169	−	3.34578i	0.158784	−	0.275022i
$149$	−1.03136	+	0.595458i	−0.0844926	+	0.0487818i	−0.541651	−	0.840603i	$-0.682201\pi$
$149$	−1.03136	+	0.595458i	−0.0844926	+	0.0487818i	0.457158	+	0.889385i	$0.348867\pi$
$150$	0.891232	+	1.48516i	0.0727688	+	0.121263i
$151$	−0.791747	+	1.37135i	−0.0644314	+	0.111599i	−0.896442	−	0.443162i	$-0.853857\pi$
$151$	−0.791747	+	1.37135i	−0.0644314	+	0.111599i	0.832010	+	0.554760i	$0.187190\pi$
$152$	−2.32921	+	4.03431i	−0.188924	+	0.327226i
$153$	−4.06770	+	7.62939i	−0.328854	+	0.616800i
$154$	−3.11123	−	4.57504i	−0.250710	−	0.368667i
$155$	−4.59333	+	2.65196i	−0.368945	+	0.213011i
$156$	−0.425819	−	0.709591i	−0.0340928	−	0.0568127i
$157$			16.8217i			1.34252i	0.741223	+	0.671259i	$0.234246\pi$
$157$			16.8217i			1.34252i	−0.741223	+	0.671259i	$0.765754\pi$
$158$			15.6355i			1.24389i
$159$	8.54206	−	0.144268i	0.677429	−	0.0114412i
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	−0.394524	−	5.35010i	−0.0310929	−	0.421647i
$162$	8.08020	+	3.96364i	0.634840	+	0.311413i
$163$	−5.01637	+	8.68860i	−0.392912	+	0.680544i	−0.992832	−	0.119516i	$-0.961866\pi$
$163$	−5.01637	+	8.68860i	−0.392912	+	0.680544i	0.599920	+	0.800060i	$0.295199\pi$
$164$	−4.03898	+	6.99572i	−0.315391	+	0.546274i
$165$	1.75777	−	3.16688i	0.136842	−	0.246541i
$166$	−9.68132	+	5.58951i	−0.751416	+	0.433830i
$167$	−7.17037	+	12.4194i	−0.554860	+	0.961045i	0.443055	+	0.896495i	$0.353895\pi$
$167$	−7.17037	+	12.4194i	−0.554860	+	0.961045i	−0.997914	+	0.0645506i	$0.979439\pi$
$168$	−2.64057	−	3.74532i	−0.203724	−	0.288958i
$169$	−6.38586	−	11.0606i	−0.491220	−	0.850818i
$170$	2.49589	+	1.44100i	0.191426	+	0.110520i
$171$	0.471926	+	13.9673i	0.0360891	+	1.06811i
$172$	2.96902	+	5.14250i	0.226386	+	0.392112i
$173$	−16.1263			−1.22606			−0.613031	−	0.790059i	$-0.710050\pi$
$173$	−16.1263			−1.22606			−0.613031	+	0.790059i	$0.710050\pi$
$174$	−0.0928562	−	5.49797i	−0.00703941	−	0.416800i
$175$	−1.48780	−	2.18780i	−0.112467	−	0.165382i
$176$	−1.81100	−	1.04558i	−0.136509	−	0.0788137i
$177$	4.26976	+	2.36993i	0.320935	+	0.178135i
$178$	−11.4153	−	6.59060i	−0.855609	−	0.493986i
$179$	−0.0837491	+	0.0483526i	−0.00625970	+	0.00361404i	−0.503127	−	0.864213i	$-0.667817\pi$
$179$	−0.0837491	+	0.0483526i	−0.00625970	+	0.00361404i	0.496867	+	0.867827i	$0.334484\pi$
$180$	1.41141	−	2.64725i	0.105200	−	0.197314i
$181$		−	20.0938i		−	1.49356i	−0.665072	−	0.746779i	$-0.731599\pi$
$181$		−	20.0938i		−	1.49356i	0.665072	−	0.746779i	$-0.268401\pi$
$182$	0.710851	+	1.04530i	0.0526918	+	0.0774828i
$183$	−3.60866	+	6.50152i	−0.266760	+	0.480606i
$184$	−1.01382	−	1.75599i	−0.0747397	−	0.129453i
$185$	−3.86338			−0.284041
$186$	8.03232	+	4.45833i	0.588958	+	0.326901i
$187$		−	6.02675i		−	0.440720i
$188$	−0.105073			−0.00766326
$189$	−12.6661	−	5.34510i	−0.921323	−	0.388799i
$190$	4.65842			0.337957
$191$			3.53308i			0.255645i	0.991797	+	0.127822i	$0.0407987\pi$
$191$			3.53308i			0.255645i	−0.991797	+	0.127822i	$0.959201\pi$
$192$	−1.51441	−	0.840572i	−0.109293	−	0.0606630i
$193$	25.3144			1.82217			0.911084	−	0.412220i	$-0.135247\pi$
$193$	25.3144			1.82217			0.911084	+	0.412220i	$0.135247\pi$
$194$	4.60847	+	7.98211i	0.330869	+	0.573082i
$195$	−0.401614	+	0.723566i	−0.0287602	+	0.0518156i
$196$	4.35137	+	5.48321i	0.310812	+	0.391658i
$197$			9.01088i			0.641999i	0.947079	+	0.320999i	$0.104019\pi$
$197$			9.01088i			0.641999i	−0.947079	+	0.320999i	$0.895981\pi$
$198$	−6.26991	+	0.211848i	−0.445583	+	0.0150553i
$199$	−12.3893	+	7.15296i	−0.878254	+	0.507060i	−0.870082	−	0.492907i	$-0.835934\pi$
$199$	−12.3893	+	7.15296i	−0.878254	+	0.507060i	−0.00817145	+	0.999967i	$0.502601\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$	8.28648	+	4.59940i	0.584483	+	0.324417i
$202$	−16.3359	−	9.43156i	−1.14939	−	0.663602i
$203$	0.617714	+	8.37674i	0.0433550	+	0.587932i
$204$	−0.0842951	−	4.99107i	−0.00590184	−	0.349445i
$205$	8.07796			0.564189
$206$	−5.07888	−	8.79688i	−0.353863	−	0.612908i
$207$	−5.36766	−	2.86183i	−0.373078	−	0.198911i
$208$	0.413776	+	0.238893i	0.0286902	+	0.0165643i
$209$	−4.87076	−	8.43640i	−0.336917	−	0.583558i
$210$	−1.92326	+	4.15946i	−0.132717	+	0.287030i
$211$	−0.442791	+	0.766937i	−0.0304830	+	0.0527981i	−0.880864	−	0.473369i	$-0.843038\pi$
$211$	−0.442791	+	0.766937i	−0.0304830	+	0.0527981i	0.850381	+	0.526167i	$0.176371\pi$
$212$	−4.27164	+	2.46623i	−0.293377	+	0.169382i
$213$	9.11905	−	16.4293i	0.624827	−	1.12572i
$214$	9.16843	−	15.8802i	0.626741	−	1.08555i
$215$	2.96902	−	5.14250i	0.202486	−	0.350715i
$216$	−5.18949	+	0.263138i	−0.353100	+	0.0179043i
$217$	−12.6359	−	6.10369i	−0.857781	−	0.414346i
$218$	12.2738	−	7.08626i	0.831284	−	0.479942i
$219$	11.2970	−	0.190796i	0.763378	−	0.0128928i
$220$			2.09116i			0.140986i
$221$			1.37699i			0.0926261i
$222$	3.44317	+	5.73774i	0.231090	+	0.385092i
$223$	−0.0602532	+	0.0347872i	−0.00403485	+	0.00232952i	−0.502016	−	0.864858i	$-0.667408\pi$
$223$	−0.0602532	+	0.0347872i	−0.00403485	+	0.00232952i	0.497981	+	0.867188i	$0.334075\pi$
$224$	2.38237	+	1.15079i	0.159179	+	0.0768903i
$225$	−2.99829	+	0.101306i	−0.199886	+	0.00675374i
$226$	3.99113	−	6.91284i	0.265486	−	0.459835i
$227$	−9.19003	+	15.9176i	−0.609964	+	1.05649i	0.381282	+	0.924459i	$0.375483\pi$
$227$	−9.19003	+	15.9176i	−0.609964	+	1.05649i	−0.991246	+	0.132030i	$0.957851\pi$
$228$	−4.15173	−	6.91851i	−0.274955	−	0.458189i
$229$	13.9168	−	8.03486i	0.919647	−	0.530958i	0.0361243	−	0.999347i	$-0.488499\pi$
$229$	13.9168	−	8.03486i	0.919647	−	0.530958i	0.883522	+	0.468389i	$0.155165\pi$
$230$	−1.01382	+	1.75599i	−0.0668492	+	0.115786i
$231$	9.54370	−	0.866031i	0.627929	−	0.0569806i
$232$	1.58735	+	2.74938i	0.104215	+	0.180506i
$233$	22.4677	+	12.9717i	1.47191	+	0.849808i	0.999501	−	0.0315722i	$-0.0100514\pi$
$233$	22.4677	+	12.9717i	1.47191	+	0.849808i	0.472408	+	0.881380i	$0.343385\pi$
$234$	1.43254	−	0.0484027i	0.0936483	−	0.00316419i
$235$	0.0525367	+	0.0909962i	0.00342711	+	0.00593593i
$236$	−2.81942			−0.183529
$237$	−23.6785	−	13.1427i	−1.53808	−	0.853712i
$238$	0.560762	+	7.60443i	0.0363488	+	0.492922i
$239$	−8.46444	−	4.88695i	−0.547519	−	0.316110i	0.200602	−	0.979673i	$-0.435710\pi$
$239$	−8.46444	−	4.88695i	−0.547519	−	0.316110i	−0.748121	+	0.663563i	$0.769044\pi$
$240$	0.0292487	+	1.73180i	0.00188800	+	0.111787i
$241$	22.1792	+	12.8052i	1.42869	+	0.824854i	0.997017	−	0.0771761i	$-0.0245904\pi$
$241$	22.1792	+	12.8052i	1.42869	+	0.824854i	0.431672	+	0.902031i	$0.357924\pi$
$242$	−5.73918	+	3.31352i	−0.368929	+	0.213001i
$243$	−12.7946	+	8.90502i	−0.820771	+	0.571257i
$244$		−	4.29310i		−	0.274838i
$245$	2.57291	−	6.51000i	0.164377	−	0.415909i
$246$	−7.19934	−	11.9971i	−0.459013	−	0.764906i
$247$	1.11287	+	1.92754i	0.0708100	+	0.122647i
$248$	−5.30392			−0.336799
$249$	−0.326972	−	19.3599i	−0.0207210	−	1.22688i
$250$			1.00000i			0.0632456i
$251$	8.02626			0.506613			0.253307	−	0.967386i	$-0.418482\pi$
$251$	8.02626			0.506613			0.253307	+	0.967386i	$0.418482\pi$
$252$	7.89153	−	0.850692i	0.497120	−	0.0535886i
$253$	4.24012			0.266574
$254$		−	0.449694i		−	0.0282163i
$255$	−4.28025	+	2.56854i	−0.268040	+	0.160848i
$256$	1.00000			0.0625000
$257$	−0.626193	−	1.08460i	−0.0390608	−	0.0676553i	0.845834	−	0.533446i	$-0.179103\pi$
$257$	−0.626193	−	1.08460i	−0.0390608	−	0.0676553i	−0.884895	+	0.465791i	$0.845770\pi$
$258$	−10.2835	+	0.173680i	−0.640225	+	0.0108129i
$259$	−5.74793	−	8.45229i	−0.357159	−	0.525199i
$260$		−	0.477787i		−	0.0296311i
$261$	8.40424	+	4.48082i	0.520209	+	0.277356i
$262$	−9.04374	+	5.22140i	−0.558724	+	0.322579i
$263$	6.26326	+	3.61609i	0.386209	+	0.222978i	0.680516	−	0.732733i	$-0.261756\pi$
$263$	6.26326	+	3.61609i	0.386209	+	0.222978i	−0.294307	+	0.955711i	$0.595089\pi$
$264$	3.10572	−	1.86371i	0.191144	−	0.114704i
$265$	4.27164	+	2.46623i	0.262405	+	0.151499i
$266$	6.93079	+	10.1917i	0.424954	+	0.624892i
$267$	19.5762	−	11.7475i	1.19804	−	0.718936i
$268$	−5.47175			−0.334240
$269$	−5.65912	−	9.80188i	−0.345043	−	0.597631i	0.640319	−	0.768109i	$-0.278802\pi$
$269$	−5.65912	−	9.80188i	−0.345043	−	0.597631i	−0.985362	+	0.170478i	$0.945469\pi$
$270$	2.82263	+	4.36266i	0.171780	+	0.265503i
$271$	3.52208	+	2.03347i	0.213951	+	0.123525i	0.603146	−	0.797631i	$-0.293914\pi$
$271$	3.52208	+	2.03347i	0.213951	+	0.123525i	−0.389195	+	0.921155i	$0.627247\pi$
$272$	1.44100	+	2.49589i	0.0873737	+	0.151336i
$273$	−2.18054	+	0.197870i	−0.131972	+	0.0119756i
$274$	−8.71743	+	15.0990i	−0.526639	+	0.912165i
$275$	1.81100	−	1.04558i	0.109207	−	0.0630509i
$276$	3.51147	−	0.0593058i	0.211366	−	0.00356979i
$277$	1.84526	−	3.19608i	0.110871	−	0.192034i	−0.805251	−	0.592934i	$-0.797969\pi$
$277$	1.84526	−	3.19608i	0.110871	−	0.192034i	0.916122	+	0.400901i	$0.131303\pi$
$278$	−6.41827	+	11.1168i	−0.384942	+	0.666739i
$279$	−13.5035	+	8.41668i	−0.808432	+	0.503893i
$280$	−0.194573	−	2.63859i	−0.0116280	−	0.157686i
$281$	21.3133	−	12.3052i	1.27144	−	0.734068i	0.296184	−	0.955131i	$-0.404286\pi$
$281$	21.3133	−	12.3052i	1.27144	−	0.734068i	0.975260	+	0.221063i	$0.0709527\pi$
$282$	0.0883217	−	0.159124i	0.00525948	−	0.00947570i
$283$			1.80228i			0.107134i	0.998564	+	0.0535671i	$0.0170591\pi$
$283$			1.80228i			0.107134i	−0.998564	+	0.0535671i	$0.982941\pi$
$284$			10.8486i			0.643748i
$285$	−3.91574	+	7.05476i	−0.231948	+	0.417888i
$286$	−0.865272	+	0.499565i	−0.0511646	+	0.0295399i
$287$	12.0184	+	17.6729i	0.709423	+	1.04320i
$288$	2.54594	−	1.58688i	0.150021	−	0.0935077i
$289$	4.34701	−	7.52924i	0.255707	−	0.442897i
$290$	1.58735	−	2.74938i	0.0932127	−	0.161449i
$291$	−15.9619	+	0.269584i	−0.935706	+	0.0158033i
$292$	−5.64929	+	3.26162i	−0.330600	+	0.190872i
$293$	11.8910	−	20.5959i	0.694682	−	1.20322i	−0.275606	−	0.961271i	$-0.588879\pi$
$293$	11.8910	−	20.5959i	0.694682	−	1.20322i	0.970288	−	0.241953i	$-0.0777881\pi$
$294$	−11.9615	+	1.98074i	−0.697607	+	0.115519i
$295$	1.40971	+	2.44169i	0.0820765	+	0.142161i
$296$	−3.34578	−	1.93169i	−0.194470	−	0.112277i
$297$	4.94949	−	9.67329i	0.287198	−	0.561301i
$298$	0.595458	+	1.03136i	0.0344940	+	0.0597453i
$299$	−0.968779			−0.0560259
$300$	1.48516	−	0.891232i	0.0857459	−	0.0514553i
$301$	15.6680	−	1.15539i	0.903091	−	0.0665953i
$302$	1.37135	+	0.791747i	0.0789121	+	0.0455599i
$303$	28.0148	−	16.8114i	1.60941	−	0.965790i
$304$	4.03431	+	2.32921i	0.231384	+	0.133589i
$305$	−3.71793	+	2.14655i	−0.212888	+	0.122911i
$306$	7.62939	+	4.06770i	0.436143	+	0.232535i
$307$			5.99873i			0.342366i	0.985239	+	0.171183i	$0.0547589\pi$
$307$			5.99873i			0.342366i	−0.985239	+	0.171183i	$0.945241\pi$
$308$	−4.57504	+	3.11123i	−0.260687	+	0.177279i
$309$	17.5913	−	0.297102i	1.00073	−	0.0169015i
$310$	2.65196	+	4.59333i	0.150621	+	0.260884i
$311$	−23.7283			−1.34551			−0.672753	−	0.739867i	$-0.734888\pi$
$311$	−23.7283			−1.34551			−0.672753	+	0.739867i	$0.734888\pi$
$312$	−0.709591	+	0.425819i	−0.0401727	+	0.0241073i
$313$			2.96556i			0.167623i	0.996482	+	0.0838116i	$0.0267094\pi$
$313$			2.96556i			0.167623i	−0.996482	+	0.0838116i	$0.973291\pi$
$314$	16.8217			0.949304
$315$	−4.68249	−	6.40892i	−0.263828	−	0.361102i
$316$	15.6355			0.879563
$317$			12.9502i			0.727353i	0.931525	+	0.363677i	$0.118479\pi$
$317$			12.9502i			0.727353i	−0.931525	+	0.363677i	$0.881521\pi$
$318$	−0.144268	−	8.54206i	−0.00809016	−	0.479015i
$319$	−6.63883			−0.371703
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	16.3424	+	27.2332i	0.912144	+	1.52001i
$322$	−5.35010	+	0.394524i	−0.298149	+	0.0219860i
$323$			13.4256i			0.747021i
$324$	3.96364	−	8.08020i	0.220202	−	0.448900i
$325$	−0.413776	+	0.238893i	−0.0229521	+	0.0132514i
$326$	8.68860	+	5.01637i	0.481217	+	0.277831i
$327$	0.414528	+	24.5440i	0.0229235	+	1.35729i
$328$	6.99572	+	4.03898i	0.386274	+	0.223015i
$329$	−0.120917	+	0.250324i	−0.00666638	+	0.0138008i
$330$	−3.16688	−	1.75777i	−0.174331	−	0.0967622i
$331$	34.0040			1.86903			0.934514	−	0.355926i	$-0.115835\pi$
$331$	34.0040			1.86903			0.934514	+	0.355926i	$0.115835\pi$
$332$	5.58951	+	9.68132i	0.306764	+	0.531332i
$333$	−11.5835	+	0.391384i	−0.634773	+	0.0214477i
$334$	12.4194	+	7.17037i	0.679562	+	0.392345i
$335$	2.73588	+	4.73867i	0.149477	+	0.258901i
$336$	−3.74532	+	2.64057i	−0.204324	+	0.144055i
$337$	11.3157	−	19.5993i	0.616403	−	1.06764i	−0.373734	−	0.927536i	$-0.621923\pi$
$337$	11.3157	−	19.5993i	0.616403	−	1.06764i	0.990137	−	0.140105i	$-0.0447440\pi$
$338$	−11.0606	+	6.38586i	−0.601619	+	0.347345i
$339$	7.11405	+	11.8549i	0.386382	+	0.643872i
$340$	1.44100	−	2.49589i	0.0781495	−	0.135359i
$341$	5.54568	−	9.60541i	0.300316	−	0.520162i
$342$	13.9673	−	0.471926i	0.755265	−	0.0255189i
$343$	18.0705	−	4.05658i	0.975717	−	0.219035i
$344$	5.14250	−	2.96902i	0.277265	−	0.160079i
$345$	−1.80710	−	3.01137i	−0.0972908	−	0.162127i
$346$			16.1263i			0.866956i
$347$			12.7779i			0.685955i	0.939344	+	0.342977i	$0.111435\pi$
$347$			12.7779i			0.685955i	−0.939344	+	0.342977i	$0.888565\pi$
$348$	−5.49797	+	0.0928562i	−0.294722	+	0.00497761i
$349$	3.95316	−	2.28236i	0.211608	−	0.122172i	−0.390451	−	0.920624i	$-0.627681\pi$
$349$	3.95316	−	2.28236i	0.211608	−	0.122172i	0.602058	+	0.798452i	$0.294347\pi$
$350$	−2.18780	+	1.48780i	−0.116943	+	0.0795262i
$351$	−1.13085	+	2.21014i	−0.0603605	+	0.117969i
$352$	−1.04558	+	1.81100i	−0.0557297	+	0.0965266i
$353$	7.95106	−	13.7716i	0.423192	−	0.732990i	−0.573058	−	0.819515i	$-0.694243\pi$
$353$	7.95106	−	13.7716i	0.423192	−	0.732990i	0.996250	+	0.0865250i	$0.0275762\pi$
$354$	2.36993	−	4.26976i	0.125960	−	0.226935i
$355$	9.39519	−	5.42432i	0.498645	−	0.287893i
$356$	−6.59060	+	11.4153i	−0.349301	+	0.605007i
$357$	−11.9876	−	5.54285i	−0.634451	−	0.293359i
$358$	0.0483526	+	0.0837491i	0.00255551	+	0.00442628i
$359$	17.0237	+	9.82867i	0.898479	+	0.518737i	0.876706	−	0.481026i	$-0.159736\pi$
$359$	17.0237	+	9.82867i	0.898479	+	0.518737i	0.0217726	+	0.999763i	$0.493069\pi$
$360$	−2.64725	−	1.41141i	−0.139522	−	0.0743879i
$361$	1.35045	+	2.33904i	0.0710761	+	0.123107i
$362$	−20.0938			−1.05610
$363$	−0.193832	−	11.4767i	−0.0101736	−	0.602372i
$364$	1.04530	−	0.710851i	0.0547886	−	0.0372587i
$365$	5.64929	+	3.26162i	0.295697	+	0.170721i
$366$	6.50152	+	3.60866i	0.339840	+	0.188628i
$367$	19.0524	+	10.9999i	0.994528	+	0.574191i	0.906625	−	0.421938i	$-0.138650\pi$
$367$	19.0524	+	10.9999i	0.994528	+	0.574191i	0.0879033	+	0.996129i	$0.471983\pi$
$368$	−1.75599	+	1.01382i	−0.0915371	+	0.0528490i
$369$	24.2201	−	0.818347i	1.26085	−	0.0426014i
$370$			3.86338i			0.200847i
$371$	0.959726	+	13.0147i	0.0498265	+	0.675691i
$372$	4.45833	−	8.03232i	0.231154	−	0.416456i
$373$	11.6660	+	20.2060i	0.604041	+	1.04623i	0.992202	+	0.124638i	$0.0397769\pi$
$373$	11.6660	+	20.2060i	0.604041	+	1.04623i	−0.388162	+	0.921591i	$0.626890\pi$
$374$	−6.02675			−0.311636
$375$	−1.51441	−	0.840572i	−0.0782038	−	0.0434069i
$376$			0.105073i			0.00541874i
$377$	1.51683			0.0781210
$378$	−5.34510	+	12.6661i	−0.274923	+	0.651473i
$379$	−20.3159			−1.04356			−0.521780	−	0.853080i	$-0.674732\pi$
$379$	−20.3159			−1.04356			−0.521780	+	0.853080i	$0.674732\pi$
$380$		−	4.65842i		−	0.238972i
$381$	0.681022	+	0.378000i	0.0348898	+	0.0193655i
$382$	3.53308			0.180768
$383$	−1.91156	−	3.31092i	−0.0976762	−	0.169180i	0.813046	−	0.582199i	$-0.197808\pi$
$383$	−1.91156	−	3.31092i	−0.0976762	−	0.169180i	−0.910722	+	0.413019i	$0.864474\pi$
$384$	−0.840572	+	1.51441i	−0.0428952	+	0.0772819i
$385$	4.98192	+	2.40649i	0.253902	+	0.122646i
$386$		−	25.3144i		−	1.28847i
$387$	8.38102	−	15.7195i	0.426031	−	0.799066i
$388$	7.98211	−	4.60847i	0.405230	−	0.233960i
$389$	−16.7512	−	9.67132i	−0.849321	−	0.490356i	0.0111008	−	0.999938i	$-0.496466\pi$
$389$	−16.7512	−	9.67132i	−0.849321	−	0.490356i	−0.860422	+	0.509583i	$0.829800\pi$
$390$	0.723566	+	0.401614i	0.0366392	+	0.0203365i
$391$	−5.06077	−	2.92184i	−0.255934	−	0.147764i
$392$	5.48321	−	4.35137i	0.276944	−	0.219778i
$393$	−0.305439	−	18.0849i	−0.0154073	−	0.912262i
$394$	9.01088			0.453962
$395$	−7.81773	−	13.5407i	−0.393353	−	0.681307i
$396$	0.211848	+	6.26991i	0.0106457	+	0.315075i
$397$	−26.2370	−	15.1479i	−1.31680	−	0.760253i	−0.333585	−	0.942720i	$-0.608258\pi$
$397$	−26.2370	−	15.1479i	−1.31680	−	0.760253i	−0.983212	+	0.182467i	$0.941592\pi$
$398$	7.15296	+	12.3893i	0.358546	+	0.621019i
$399$	−21.2602	+	1.92923i	−1.06434	+	0.0965823i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−28.6376	+	16.5340i	−1.43010	+	0.825666i	−0.997127	−	0.0757431i	$-0.975867\pi$
$401$	−28.6376	+	16.5340i	−1.43010	+	0.825666i	−0.432968	+	0.901409i	$0.642534\pi$
$402$	4.59940	−	8.28648i	0.229397	−	0.413292i
$403$	−1.26707	+	2.19463i	−0.0631174	+	0.109323i
$404$	−9.43156	+	16.3359i	−0.469238	+	0.812743i
$405$	−8.97947	+	0.607490i	−0.446194	+	0.0301864i
$406$	8.37674	−	0.617714i	0.415731	−	0.0306566i
$407$	6.99658	−	4.03948i	0.346808	−	0.200229i
$408$	−4.99107	+	0.0842951i	−0.247095	+	0.00417323i
$409$			17.0227i			0.841716i	0.907126	+	0.420858i	$0.138271\pi$
$409$			17.0227i			0.841716i	−0.907126	+	0.420858i	$0.861729\pi$
$410$		−	8.07796i		−	0.398942i
$411$	−15.5385	−	25.8936i	−0.766458	−	1.27724i
$412$	−8.79688	+	5.07888i	−0.433391	+	0.250219i
$413$	−3.24456	+	6.71690i	−0.159654	+	0.330517i
$414$	−2.86183	+	5.36766i	−0.140651	+	0.263806i
$415$	5.58951	−	9.68132i	0.274378	−	0.475237i
$416$	0.238893	−	0.413776i	0.0117127	−	0.0202870i
$417$	−11.4403	−	19.0643i	−0.560235	−	0.933584i
$418$	−8.43640	+	4.87076i	−0.412638	+	0.238237i
$419$	3.89228	−	6.74162i	0.190150	−	0.329350i	−0.755150	−	0.655552i	$-0.772436\pi$
$419$	3.89228	−	6.74162i	0.190150	−	0.329350i	0.945300	+	0.326203i	$0.105769\pi$
$420$	4.15946	+	1.92326i	0.202961	+	0.0938454i
$421$	15.4668	+	26.7894i	0.753808	+	1.30563i	0.945965	+	0.324269i	$0.105118\pi$
$421$	15.4668	+	26.7894i	0.753808	+	1.30563i	−0.192157	+	0.981364i	$0.561548\pi$
$422$	0.766937	+	0.442791i	0.0373339	+	0.0215547i
$423$	0.166739	+	0.267510i	0.00810711	+	0.0130068i
$424$	2.46623	+	4.27164i	0.119771	+	0.207449i
$425$	−2.88201			−0.139798
$426$	−16.4293	−	9.11905i	−0.796001	−	0.441820i
$427$	−10.2278	−	4.94045i	−0.494956	−	0.239085i
$428$	−15.8802	−	9.16843i	−0.767598	−	0.443173i
$429$	−0.0292233	−	1.73030i	−0.00141091	−	0.0835396i
$430$	−5.14250	−	2.96902i	−0.247993	−	0.143179i
$431$	−17.0026	+	9.81647i	−0.818988	+	0.472843i	−0.850067	−	0.526674i	$-0.823439\pi$
$431$	−17.0026	+	9.81647i	−0.818988	+	0.472843i	0.0310795	+	0.999517i	$0.490105\pi$
$432$	0.263138	+	5.18949i	0.0126603	+	0.249679i
$433$		−	35.9562i		−	1.72794i	−0.503540	−	0.863972i	$-0.667969\pi$
$433$		−	35.9562i		−	1.72794i	0.503540	−	0.863972i	$-0.332031\pi$
$434$	−6.10369	+	12.6359i	−0.292987	+	0.606543i
$435$	2.82940	+	4.71496i	0.135659	+	0.226065i
$436$	−7.08626	−	12.2738i	−0.339370	−	0.587807i
$437$	−9.44559			−0.451844
$438$	−0.190796	−	11.2970i	−0.00911660	−	0.539790i
$439$			24.3427i			1.16181i	0.813971	+	0.580906i	$0.197302\pi$
$439$			24.3427i			1.16181i	−0.813971	+	0.580906i	$0.802698\pi$
$440$	2.09116			0.0996923
$441$	7.05482	−	19.7795i	0.335944	−	0.941882i
$442$	1.37699			0.0654966
$443$			5.94231i			0.282328i	0.989986	+	0.141164i	$0.0450845\pi$
$443$			5.94231i			0.282328i	−0.989986	+	0.141164i	$0.954916\pi$
$444$	5.73774	−	3.44317i	0.272301	−	0.163405i
$445$	13.1812			0.624849
$446$	0.0347872	+	0.0602532i	0.00164722	+	0.00285307i
$447$	−2.06243	+	0.0348328i	−0.0975498	+	0.00164753i
$448$	1.15079	−	2.38237i	0.0543696	−	0.112556i
$449$			3.59042i			0.169442i	0.996405	+	0.0847211i	$0.0269999\pi$
$449$			3.59042i			0.169442i	−0.996405	+	0.0847211i	$0.973000\pi$
$450$	0.101306	+	2.99829i	0.00477561	+	0.141341i
$451$	−14.6292	+	8.44617i	−0.688862	+	0.397715i
$452$	−6.91284	−	3.99113i	−0.325153	−	0.187727i
$453$	−2.35174	+	1.41126i	−0.110495	+	0.0663068i
$454$	15.9176	+	9.19003i	0.747050	+	0.431310i
$455$	−1.13827	−	0.549832i	−0.0533627	−	0.0257765i
$456$	−6.91851	+	4.15173i	−0.323989	+	0.194423i
$457$	13.4589			0.629581			0.314791	−	0.949161i	$-0.398066\pi$
$457$	13.4589			0.629581			0.314791	+	0.949161i	$0.398066\pi$
$458$	−8.03486	−	13.9168i	−0.375444	−	0.650288i
$459$	−12.5732	+	8.13484i	−0.586868	+	0.379702i
$460$	1.75599	+	1.01382i	0.0818733	+	0.0472695i
$461$	−13.5633	−	23.4924i	−0.631708	−	1.09415i	−0.987202	−	0.159472i	$-0.949021\pi$
$461$	−13.5633	−	23.4924i	−0.631708	−	1.09415i	0.355495	−	0.934678i	$-0.384312\pi$
$462$	−0.866031	−	9.54370i	−0.0402914	−	0.444013i
$463$	−15.9746	+	27.6688i	−0.742403	+	1.28588i	0.208995	+	0.977917i	$0.432981\pi$
$463$	−15.9746	+	27.6688i	−0.742403	+	1.28588i	−0.951398	+	0.307963i	$0.900353\pi$
$464$	2.74938	−	1.58735i	0.127637	−	0.0736911i
$465$	−9.18536	+	0.155133i	−0.425961	+	0.00719412i
$466$	12.9717	−	22.4677i	0.600905	−	1.04080i
$467$	18.4026	−	31.8743i	0.851572	−	1.47497i	−0.0282177	−	0.999602i	$-0.508983\pi$
$467$	18.4026	−	31.8743i	0.851572	−	1.47497i	0.879789	−	0.475364i	$-0.157684\pi$
$468$	−0.0484027	−	1.43254i	−0.00223742	−	0.0662193i
$469$	−6.29682	+	13.0357i	−0.290760	+	0.601934i
$470$	0.0909962	−	0.0525367i	0.00419734	−	0.00242334i
$471$	−14.1399	+	25.4750i	−0.651530	+	1.17382i
$472$			2.81942i			0.129774i
$473$			12.4174i			0.570954i
$474$	−13.1427	+	23.6785i	−0.603665	+	1.08759i
$475$	−4.03431	+	2.32921i	−0.185107	+	0.106872i
$476$	7.60443	−	0.560762i	0.348549	−	0.0257025i
$477$	13.0575	+	6.96173i	0.597860	+	0.318756i
$478$	−4.88695	+	8.46444i	−0.223524	+	0.387155i
$479$	−8.82453	+	15.2845i	−0.403203	+	0.698368i	−0.994111	−	0.108371i	$-0.965437\pi$
$479$	−8.82453	+	15.2845i	−0.403203	+	0.698368i	0.590907	+	0.806739i	$0.298770\pi$
$480$	1.73180	−	0.0292487i	0.0790457	−	0.00133502i
$481$	−1.59857	+	0.922936i	−0.0728886	+	0.0420823i
$482$	12.8052	−	22.1792i	0.583260	−	1.01024i
$483$	3.89967	−	8.43387i	0.177441	−	0.383754i
$484$	3.31352	+	5.73918i	0.150614	+	0.260872i
$485$	−7.98211	−	4.60847i	−0.362449	−	0.209260i
$486$	8.90502	+	12.7946i	0.403940	+	0.580373i
$487$	5.44521	+	9.43137i	0.246746	+	0.427376i	0.962621	−	0.270852i	$-0.0873054\pi$
$487$	5.44521	+	9.43137i	0.246746	+	0.427376i	−0.715875	+	0.698228i	$0.753972\pi$
$488$	−4.29310			−0.194340
$489$	−14.9002	+	8.94149i	−0.673812	+	0.404348i
$490$	−6.51000	−	2.57291i	−0.294092	−	0.116232i
$491$	−21.5186	−	12.4238i	−0.971123	−	0.560678i	−0.0715443	−	0.997437i	$-0.522793\pi$
$491$	−21.5186	−	12.4238i	−0.971123	−	0.560678i	−0.899578	+	0.436760i	$0.856126\pi$
$492$	−11.9971	+	7.19934i	−0.540870	+	0.324571i
$493$	7.92373	+	4.57477i	0.356867	+	0.206037i
$494$	1.92754	−	1.11287i	0.0867242	−	0.0500702i
$495$	5.32398	−	3.31842i	0.239295	−	0.149152i
$496$			5.30392i			0.238153i
$497$	25.8455	+	12.4845i	1.15933	+	0.560005i
$498$	−19.3599	+	0.326972i	−0.867537	+	0.0146520i
$499$	−18.4424	−	31.9432i	−0.825597	−	1.42998i	−0.901462	−	0.432857i	$-0.857505\pi$
$499$	−18.4424	−	31.9432i	−0.825597	−	1.42998i	0.0758658	−	0.997118i	$-0.475828\pi$
$500$	1.00000			0.0447214
$501$	−21.2983	+	12.7809i	−0.951538	+	0.571009i
$502$		−	8.02626i		−	0.358230i
$503$	−4.02007			−0.179246			−0.0896231	−	0.995976i	$-0.528566\pi$
$503$	−4.02007			−0.179246			−0.0896231	+	0.995976i	$0.528566\pi$
$504$	−0.850692	−	7.89153i	−0.0378928	−	0.351517i
$505$	18.8631			0.839398
$506$		−	4.24012i		−	0.188496i
$507$	−0.373556	−	22.1181i	−0.0165902	−	0.982300i
$508$	−0.449694			−0.0199520
$509$	12.1242	+	20.9997i	0.537394	+	0.930794i	0.999043	+	0.0437312i	$0.0139245\pi$
$509$	12.1242	+	20.9997i	0.537394	+	0.930794i	−0.461649	+	0.887063i	$0.652742\pi$
$510$	2.56854	+	4.28025i	0.113737	+	0.189533i
$511$	1.26925	+	17.2121i	0.0561482	+	0.761420i
$512$		−	1.00000i		−	0.0441942i
$513$	−11.0258	+	21.5489i	−0.486802	+	0.951407i
$514$	−1.08460	+	0.626193i	−0.0478395	+	0.0276202i
$515$	8.79688	+	5.07888i	0.387637	+	0.223802i
$516$	0.173680	+	10.2835i	0.00764584	+	0.452707i
$517$	−0.190288	−	0.109863i	−0.00836885	−	0.00483176i
$518$	−8.45229	+	5.74793i	−0.371372	+	0.252550i
$519$	−24.4219	−	13.5553i	−1.07200	−	0.595013i
$520$	−0.477787			−0.0209523
$521$	−20.9866	−	36.3499i	−0.919440	−	1.59252i	−0.800267	−	0.599643i	$-0.795309\pi$
$521$	−20.9866	−	36.3499i	−0.919440	−	1.59252i	−0.119173	−	0.992874i	$-0.538024\pi$
$522$	4.48082	−	8.40424i	0.196120	−	0.367844i
$523$	−2.05664	−	1.18740i	−0.0899304	−	0.0519213i	0.454360	−	0.890818i	$-0.349868\pi$
$523$	−2.05664	−	1.18740i	−0.0899304	−	0.0519213i	−0.544291	+	0.838897i	$0.683201\pi$
$524$	5.22140	+	9.04374i	0.228098	+	0.395077i
$525$	−0.414138	−	4.56382i	−0.0180745	−	0.199182i
$526$	3.61609	−	6.26326i	0.157669	−	0.273091i
$527$	−13.2380	+	7.64298i	−0.576658	+	0.332933i
$528$	−1.86371	−	3.10572i	−0.0811076	−	0.135159i
$529$	−9.44434	+	16.3581i	−0.410624	+	0.711221i
$530$	2.46623	−	4.27164i	0.107126	−	0.185548i
$531$	4.47408	+	7.17808i	0.194158	+	0.311502i
$532$	10.1917	−	6.93079i	0.441865	−	0.300488i
$533$	3.34246	−	1.92977i	0.144778	−	0.0835877i
$534$	−11.7475	−	19.5762i	−0.508364	−	0.847146i
$535$			18.3369i			0.792772i
$536$			5.47175i			0.236344i
$537$	−0.167474	+	0.00282850i	−0.00722705	+	0.000122059i
$538$	−9.80188	+	5.65912i	−0.422589	+	0.243982i
$539$	2.14720	+	14.4798i	0.0924865	+	0.623689i
$540$	4.36266	−	2.82263i	0.187739	−	0.121467i
$541$	−4.57807	+	7.92946i	−0.196827	+	0.340914i	−0.947498	−	0.319762i	$-0.896397\pi$
$541$	−4.57807	+	7.92946i	−0.196827	+	0.340914i	0.750671	+	0.660676i	$0.229730\pi$
$542$	2.03347	−	3.52208i	0.0873451	−	0.151286i
$543$	16.8903	−	30.4302i	0.724830	−	1.30589i
$544$	2.49589	−	1.44100i	0.107011	−	0.0617826i
$545$	−7.08626	+	12.2738i	−0.303542	+	0.525750i
$546$	0.197870	+	2.18054i	0.00846805	+	0.0933183i
$547$	−23.0072	−	39.8496i	−0.983717	−	1.70385i	−0.647505	−	0.762061i	$-0.724187\pi$
$547$	−23.0072	−	39.8496i	−0.983717	−	1.70385i	−0.336212	−	0.941786i	$-0.609146\pi$
$548$	15.0990	+	8.71743i	0.644998	+	0.372390i
$549$	−10.9300	+	6.81263i	−0.466480	+	0.290756i
$550$	−1.04558	−	1.81100i	−0.0445837	−	0.0772213i
$551$	14.7891			0.630038
$552$	−0.0593058	−	3.51147i	−0.00252422	−	0.149458i
$553$	17.9931	−	37.2494i	0.765144	−	1.58401i
$554$	−3.19608	−	1.84526i	−0.135788	−	0.0783974i
$555$	−5.85074	−	3.24745i	−0.248350	−	0.137846i
$556$	11.1168	+	6.41827i	0.471456	+	0.272195i
$557$	−16.7682	+	9.68111i	−0.710490	+	0.410202i	−0.811242	−	0.584710i	$-0.801208\pi$
$557$	−16.7682	+	9.68111i	−0.710490	+	0.410202i	0.100752	+	0.994912i	$0.467875\pi$
$558$	8.41668	+	13.5035i	0.356307	+	0.571648i
$559$		−	2.83712i		−	0.119997i
$560$	−2.63859	+	0.194573i	−0.111501	+	0.00822223i
$561$	5.06592	−	9.12698i	0.213883	−	0.385341i
$562$	−12.3052	−	21.3133i	−0.519064	−	0.899046i
$563$	−21.7238			−0.915550			−0.457775	−	0.889068i	$-0.651353\pi$
$563$	−21.7238			−0.915550			−0.457775	+	0.889068i	$0.651353\pi$
$564$	−0.159124	−	0.0883217i	−0.00670033	−	0.00371901i
$565$			7.98226i			0.335816i
$566$	1.80228			0.0757554
$567$	−14.6887	−	18.7414i	−0.616868	−	0.787067i
$568$	10.8486			0.455198
$569$		−	21.1986i		−	0.888691i	−0.895855	−	0.444346i	$-0.853436\pi$
$569$		−	21.1986i		−	0.888691i	0.895855	−	0.444346i	$-0.146564\pi$
$570$	7.05476	+	3.91574i	0.295491	+	0.164012i
$571$	−11.0573			−0.462734			−0.231367	−	0.972866i	$-0.574320\pi$
$571$	−11.0573			−0.462734			−0.231367	+	0.972866i	$0.574320\pi$
$572$	0.499565	+	0.865272i	0.0208879	+	0.0361789i
$573$	−2.96981	+	5.35053i	−0.124066	+	0.223522i
$574$	17.6729	−	12.0184i	0.737654	−	0.501638i
$575$		−	2.02764i		−	0.0845583i
$576$	−1.58688	−	2.54594i	−0.0661199	−	0.106081i
$577$	−27.5702	+	15.9177i	−1.14776	+	0.662662i	−0.948341	−	0.317251i	$-0.897240\pi$
$577$	−27.5702	+	15.9177i	−1.14776	+	0.662662i	−0.199423	+	0.979914i	$0.563907\pi$
$578$	−7.52924	−	4.34701i	−0.313175	−	0.180812i
$579$	38.3364	+	21.2785i	1.59320	+	0.884306i
$580$	−2.74938	−	1.58735i	−0.114162	−	0.0659113i
$581$	29.4968	−	2.17514i	1.22373	−	0.0902401i
$582$	0.269584	+	15.9619i	0.0111746	+	0.661644i
$583$	−10.3146			−0.427187
$584$	3.26162	+	5.64929i	0.134967	+	0.233769i
$585$	−1.21642	+	0.758190i	−0.0502927	+	0.0313473i
$586$	−20.5959	−	11.8910i	−0.850808	−	0.491214i
$587$	14.7632	+	25.5706i	0.609343	+	1.05541i	0.991349	+	0.131253i	$0.0419000\pi$
$587$	14.7632	+	25.5706i	0.609343	+	1.05541i	−0.382006	+	0.924160i	$0.624767\pi$
$588$	1.98074	+	11.9615i	0.0816843	+	0.493283i
$589$	−12.3540	+	21.3977i	−0.509036	+	0.881676i
$590$	2.44169	−	1.40971i	0.100523	−	0.0580369i
$591$	−7.57429	+	13.6462i	−0.311565	+	0.561329i
$592$	−1.93169	+	3.34578i	−0.0793919	+	0.137511i
$593$	10.9772	−	19.0131i	0.450780	−	0.780773i	−0.547655	−	0.836704i	$-0.684479\pi$
$593$	10.9772	−	19.0131i	0.450780	−	0.780773i	0.998435	+	0.0559309i	$0.0178126\pi$
$594$	−9.67329	−	4.94949i	−0.396900	−	0.203080i
$595$	−4.28785	−	6.30525i	−0.175785	−	0.258490i
$596$	1.03136	−	0.595458i	0.0422463	−	0.0243909i
$597$	−24.7751	+	0.418430i	−1.01398	+	0.0171252i
$598$			0.968779i			0.0396163i
$599$			26.6051i			1.08706i	0.839391	+	0.543528i	$0.182912\pi$
$599$			26.6051i			1.08706i	−0.839391	+	0.543528i	$0.817088\pi$
$600$	−0.891232	−	1.48516i	−0.0363844	−	0.0606315i
$601$	33.3026	−	19.2273i	1.35844	−	0.784296i	0.369027	−	0.929419i	$-0.379691\pi$
$601$	33.3026	−	19.2273i	1.35844	−	0.784296i	0.989414	+	0.145122i	$0.0463575\pi$
$602$	−1.15539	−	15.6680i	−0.0470900	−	0.638582i
$603$	8.68300	+	13.9308i	0.353599	+	0.567304i
$604$	0.791747	−	1.37135i	0.0322157	−	0.0557993i
$605$	3.31352	−	5.73918i	0.134714	−	0.233331i
$606$	−16.8114	−	28.0148i	−0.682917	−	1.13802i
$607$	20.4168	−	11.7877i	0.828693	−	0.478446i	−0.0247118	−	0.999695i	$-0.507867\pi$
$607$	20.4168	−	11.7877i	0.828693	−	0.478446i	0.853405	+	0.521248i	$0.174533\pi$
$608$	2.32921	−	4.03431i	0.0944620	−	0.163613i
$609$	−6.10578	+	13.2051i	−0.247419	+	0.535096i
$610$	2.14655	+	3.71793i	0.0869113	+	0.150535i
$611$	0.0434768	+	0.0251013i	0.00175888	+	0.00101549i
$612$	4.06770	−	7.62939i	0.164427	−	0.308400i
$613$	−7.77138	−	13.4604i	−0.313883	−	0.543661i	0.665316	−	0.746561i	$-0.268297\pi$
$613$	−7.77138	−	13.4604i	−0.313883	−	0.543661i	−0.979199	+	0.202900i	$0.934963\pi$
$614$	5.99873			0.242089
$615$	12.2334	+	6.79011i	0.493296	+	0.273804i
$616$	3.11123	+	4.57504i	0.125355	+	0.184334i
$617$	−11.7195	−	6.76627i	−0.471810	−	0.272400i	0.245187	−	0.969476i	$-0.421151\pi$
$617$	−11.7195	−	6.76627i	−0.471810	−	0.272400i	−0.716997	+	0.697076i	$0.754484\pi$
$618$	−0.297102	−	17.5913i	−0.0119512	−	0.707624i
$619$	20.4550	+	11.8097i	0.822157	+	0.474672i	0.851160	−	0.524907i	$-0.175900\pi$
$619$	20.4550	+	11.8097i	0.822157	+	0.474672i	−0.0290029	+	0.999579i	$0.509233\pi$
$620$	4.59333	−	2.65196i	0.184473	−	0.106505i
$621$	−5.72326	−	8.84589i	−0.229667	−	0.354973i
$622$			23.7283i			0.951416i
$623$	19.6110	+	28.8378i	0.785697	+	1.15536i
$624$	0.425819	+	0.709591i	0.0170464	+	0.0284064i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	2.96556			0.118527
$627$	−0.284927	−	16.8704i	−0.0113789	−	0.673739i
$628$		−	16.8217i		−	0.671259i
$629$	−11.1343			−0.443953
$630$	−6.40892	+	4.68249i	−0.255338	+	0.186555i
$631$	29.0626			1.15696			0.578482	−	0.815695i	$-0.303645\pi$
$631$	29.0626			1.15696			0.578482	+	0.815695i	$0.303645\pi$
$632$		−	15.6355i		−	0.621945i
$633$	−1.31523	+	0.789259i	−0.0522758	+	0.0313702i
$634$	12.9502			0.514316
$635$	0.224847	+	0.389447i	0.00892279	+	0.0154547i
$636$	−8.54206	+	0.144268i	−0.338715	+	0.00572061i
$637$	−0.490591	−	3.30833i	−0.0194379	−	0.131081i
$638$			6.63883i			0.262834i
$639$	27.6200	−	17.2155i	1.09263	−	0.681033i
$640$	−0.866025	+	0.500000i	−0.0342327	+	0.0197642i
$641$	4.74232	+	2.73798i	0.187311	+	0.108144i	0.590723	−	0.806874i	$-0.298843\pi$
$641$	4.74232	+	2.73798i	0.187311	+	0.108144i	−0.403412	+	0.915018i	$0.632176\pi$
$642$	27.2332	−	16.3424i	1.07481	−	0.644983i
$643$	−22.6584	−	13.0818i	−0.893560	−	0.515897i	−0.0184548	−	0.999830i	$-0.505875\pi$
$643$	−22.6584	−	13.0818i	−0.893560	−	0.515897i	−0.875105	+	0.483933i	$0.839208\pi$
$644$	0.394524	+	5.35010i	0.0155464	+	0.210823i
$645$	8.81896	−	5.29218i	0.347246	−	0.208379i
$646$	13.4256			0.528224
$647$	−7.13123	−	12.3517i	−0.280358	−	0.485594i	0.691115	−	0.722745i	$-0.257120\pi$
$647$	−7.13123	−	12.3517i	−0.280358	−	0.485594i	−0.971473	+	0.237151i	$0.923786\pi$
$648$	−8.08020	−	3.96364i	−0.317420	−	0.155706i
$649$	−5.10597	−	2.94793i	−0.200427	−	0.115717i
$650$	0.238893	+	0.413776i	0.00937017	+	0.0162296i
$651$	−14.0054	−	19.8649i	−0.548913	−	0.778566i
$652$	5.01637	−	8.68860i	0.196456	−	0.340272i
$653$	−12.4842	+	7.20776i	−0.488545	+	0.282062i	−0.723971	−	0.689831i	$-0.757685\pi$
$653$	−12.4842	+	7.20776i	−0.488545	+	0.282062i	0.235426	+	0.971892i	$0.424352\pi$
$654$	24.5440	−	0.414528i	0.959748	−	0.0162093i
$655$	5.22140	−	9.04374i	0.204017	−	0.353368i
$656$	4.03898	−	6.99572i	0.157696	−	0.273137i
$657$	17.2686	+	9.20697i	0.673713	+	0.359198i
$658$	0.250324	+	0.120917i	0.00975863	+	0.00471384i
$659$	−23.0675	+	13.3180i	−0.898581	+	0.518796i	−0.876739	−	0.480966i	$-0.840286\pi$
$659$	−23.0675	+	13.3180i	−0.898581	+	0.518796i	−0.0218413	+	0.999761i	$0.506953\pi$
$660$	−1.75777	+	3.16688i	−0.0684212	+	0.123271i
$661$		−	12.6233i		−	0.490991i	−0.969398	−	0.245496i	$-0.921049\pi$
$661$		−	12.6233i		−	0.490991i	0.969398	−	0.245496i	$-0.0789507\pi$
$662$		−	34.0040i		−	1.32160i
$663$	−1.15746	+	2.08532i	−0.0449519	+	0.0809872i
$664$	9.68132	−	5.58951i	0.375708	−	0.216915i
$665$	−11.0981	−	5.36086i	−0.430365	−	0.207885i
$666$	0.391384	+	11.5835i	0.0151658	+	0.448852i
$667$	−3.21858	+	5.57474i	−0.124624	+	0.215855i
$668$	7.17037	−	12.4194i	0.277430	−	0.480523i
$669$	−0.120489	+	0.00203496i	−0.00465838	+	7.86761e-5i
$670$	4.73867	−	2.73588i	0.183071	−	0.105696i
$671$	4.48879	−	7.77481i	0.173288	−	0.300143i
$672$	2.64057	+	3.74532i	0.101862	+	0.144479i
$673$	−1.51712	−	2.62772i	−0.0584805	−	0.101291i	0.835303	−	0.549790i	$-0.185292\pi$
$673$	−1.51712	−	2.62772i	−0.0584805	−	0.101291i	−0.893784	+	0.448499i	$0.851959\pi$
$674$	−19.5993	−	11.3157i	−0.754936	−	0.435863i
$675$	−4.62580	−	2.36686i	−0.178047	−	0.0911004i
$676$	6.38586	+	11.0606i	0.245610	+	0.425409i
$677$	−11.1748			−0.429481			−0.214741	−	0.976671i	$-0.568891\pi$
$677$	−11.1748			−0.429481			−0.214741	+	0.976671i	$0.568891\pi$
$678$	11.8549	−	7.11405i	0.455287	−	0.273213i
$679$	−1.79337	−	24.3197i	−0.0688233	−	0.933305i
$680$	−2.49589	−	1.44100i	−0.0957131	−	0.0552600i
$681$	−27.2974	+	16.3809i	−1.04604	+	0.627718i
$682$	−9.60541	−	5.54568i	−0.367810	−	0.212355i
$683$	−23.9631	+	13.8351i	−0.916924	+	0.529387i	−0.882653	−	0.470026i	$-0.844245\pi$
$683$	−23.9631	+	13.8351i	−0.916924	+	0.529387i	−0.0342719	+	0.999413i	$0.510911\pi$
$684$	−0.471926	−	13.9673i	−0.0180446	−	0.534053i
$685$		−	17.4349i		−	0.666151i
$686$	−4.05658	−	18.0705i	−0.154881	−	0.689936i
$687$	27.8296	−	0.470018i	1.06176	−	0.0179323i
$688$	−2.96902	−	5.14250i	−0.113193	−	0.196056i
$689$	2.35667			0.0897819
$690$	−3.01137	+	1.80710i	−0.114641	+	0.0687950i
$691$		−	13.5543i		−	0.515630i	−0.966194	−	0.257815i	$-0.916997\pi$
$691$		−	13.5543i		−	0.515630i	0.966194	−	0.257815i	$-0.0830026\pi$
$692$	16.1263			0.613031
$693$	15.1810	+	6.71064i	0.576680	+	0.254916i
$694$	12.7779			0.485043
$695$		−	12.8365i		−	0.486918i
$696$	0.0928562	+	5.49797i	0.00351970	+	0.208400i
$697$	23.2808			0.881822
$698$	−2.28236	−	3.95316i	−0.0863885	−	0.149629i
$699$	23.1217	+	38.5303i	0.874542	+	1.45735i
$700$	1.48780	+	2.18780i	0.0562335	+	0.0826909i
$701$			45.4060i			1.71496i	0.514516	+	0.857481i	$0.327972\pi$
$701$			45.4060i			1.71496i	−0.514516	+	0.857481i	$0.672028\pi$
$702$	2.21014	+	1.13085i	0.0834165	+	0.0426813i
$703$	−15.5861	+	8.99862i	−0.587840	+	0.339389i
$704$	1.81100	+	1.04558i	0.0682546	+	0.0394068i
$705$	0.00307326	+	0.181966i	0.000115746	+	0.00685325i
$706$	−13.7716	−	7.95106i	−0.518302	−	0.299242i
$707$	28.0645	+	41.2687i	1.05548	+	1.55207i
$708$	−4.26976	−	2.36993i	−0.160467	−	0.0890673i
$709$	−20.5914			−0.773325			−0.386663	−	0.922221i	$-0.626372\pi$
$709$	−20.5914			−0.773325			−0.386663	+	0.922221i	$0.626372\pi$
$710$	−5.42432	−	9.39519i	−0.203571	−	0.352595i
$711$	−24.8116	−	39.8070i	−0.930506	−	1.49288i
$712$	11.4153	+	6.59060i	0.427805	+	0.246993i
$713$	−5.37722	−	9.31361i	−0.201378	−	0.348798i
$714$	−5.54285	+	11.9876i	−0.207436	+	0.448624i
$715$	0.499565	−	0.865272i	0.0186827	−	0.0323594i
$716$	0.0837491	−	0.0483526i	0.00312985	−	0.00180702i
$717$	−8.71081	−	14.5158i	−0.325311	−	0.542103i
$718$	9.82867	−	17.0237i	0.366803	−	0.635321i
$719$	19.2776	−	33.3899i	0.718935	−	1.24523i	−0.242488	−	0.970155i	$-0.577963\pi$
$719$	19.2776	−	33.3899i	0.718935	−	1.24523i	0.961422	−	0.275077i	$-0.0887033\pi$
$720$	−1.41141	+	2.64725i	−0.0526002	+	0.0986571i
$721$	1.97643	+	26.8021i	0.0736061	+	0.998164i
$722$	2.33904	−	1.35045i	0.0870501	−	0.0502584i
$723$	22.8248	+	38.0355i	0.848863	+	1.41456i
$724$			20.0938i			0.746779i
$725$			3.17471i			0.117906i
$726$	−11.4767	+	0.193832i	−0.425941	+	0.00719379i
$727$	−21.6549	+	12.5025i	−0.803137	+	0.463692i	−0.844567	−	0.535450i	$-0.820142\pi$
$727$	−21.6549	+	12.5025i	−0.803137	+	0.463692i	0.0414296	+	0.999141i	$0.486809\pi$
$728$	−0.710851	−	1.04530i	−0.0263459	−	0.0387414i
$729$	−26.8615	+	2.73111i	−0.994871	+	0.101152i
$730$	3.26162	−	5.64929i	0.120718	−	0.209090i
$731$	8.55675	−	14.8207i	0.316483	−	0.548164i
$732$	3.60866	−	6.50152i	0.133380	−	0.240303i
$733$	−42.7404	+	24.6762i	−1.57865	+	0.911435i	−0.583604	+	0.812039i	$0.698358\pi$
$733$	−42.7404	+	24.6762i	−1.57865	+	0.911435i	−0.995048	+	0.0993963i	$0.968309\pi$
$734$	10.9999	−	19.0524i	0.406014	−	0.703237i
$735$	9.36856	−	7.69610i	0.345565	−	0.283875i
$736$	1.01382	+	1.75599i	0.0373699	+	0.0647265i
$737$	−9.90934	−	5.72116i	−0.365015	−	0.210742i
$738$	−0.818347	−	24.2201i	−0.0301238	−	0.891553i
$739$	10.3267	+	17.8864i	0.379874	+	0.657961i	0.991044	−	0.133539i	$-0.0426340\pi$
$739$	10.3267	+	17.8864i	0.379874	+	0.657961i	−0.611170	+	0.791500i	$0.709301\pi$
$740$	3.86338			0.142021
$741$	0.0650998	+	3.85453i	0.00239150	+	0.141600i
$742$	13.0147	−	0.959726i	0.477786	−	0.0352327i
$743$	7.62562	+	4.40265i	0.279757	+	0.161518i	0.633313	−	0.773895i	$-0.281694\pi$
$743$	7.62562	+	4.40265i	0.279757	+	0.161518i	−0.353556	+	0.935413i	$0.615028\pi$
$744$	−8.03232	−	4.45833i	−0.294479	−	0.163450i
$745$	−1.03136	−	0.595458i	−0.0377863	−	0.0218159i
$746$	20.2060	−	11.6660i	0.739796	−	0.427121i
$747$	15.7782	−	29.5937i	0.577294	−	1.08278i
$748$			6.02675i			0.220360i
$749$	−40.1173	+	27.2816i	−1.46586	+	0.996847i
$750$	−0.840572	+	1.51441i	−0.0306933	+	0.0552985i
$751$	−21.3526	−	36.9838i	−0.779167	−	1.34956i	−0.932422	−	0.361371i	$-0.882309\pi$
$751$	−21.3526	−	36.9838i	−0.779167	−	1.34956i	0.153255	−	0.988187i	$-0.451024\pi$
$752$	0.105073			0.00383163
$753$	12.1551	+	6.74665i	0.442955	+	0.245862i
$754$		−	1.51683i		−	0.0552399i
$755$	−1.58349			−0.0576292
$756$	12.6661	+	5.34510i	0.460661	+	0.194400i
$757$	−23.4364			−0.851811			−0.425905	−	0.904768i	$-0.640044\pi$
$757$	−23.4364			−0.851811			−0.425905	+	0.904768i	$0.640044\pi$
$758$			20.3159i			0.737908i
$759$	6.42128	+	3.56413i	0.233078	+	0.129370i
$760$	−4.65842			−0.168979
$761$	−3.69423	−	6.39860i	−0.133916	−	0.231949i	0.791267	−	0.611471i	$-0.209422\pi$
$761$	−3.69423	−	6.39860i	−0.133916	−	0.231949i	−0.925183	+	0.379522i	$0.876088\pi$
$762$	0.378000	−	0.681022i	0.0136935	−	0.0246708i
$763$	−37.3954	+	2.75760i	−1.35381	+	0.0998317i
$764$		−	3.53308i		−	0.127822i
$765$	−8.64110	+	0.291965i	−0.312420	+	0.0105560i
$766$	−3.31092	+	1.91156i	−0.119628	+	0.0690675i
$767$	1.16661	+	0.673541i	0.0421238	+	0.0243202i
$768$	1.51441	+	0.840572i	0.0546466	+	0.0303315i
$769$	41.7890	+	24.1269i	1.50695	+	0.870038i	0.999967	+	0.00808106i	$0.00257231\pi$
$769$	41.7890	+	24.1269i	1.50695	+	0.870038i	0.506982	+	0.861957i	$0.330761\pi$
$770$	2.40649	−	4.98192i	0.0867237	−	0.179536i
$771$	−0.0366307	−	2.16889i	−0.00131922	−	0.0781105i
$772$	−25.3144			−0.911084
$773$	12.6336	+	21.8821i	0.454401	+	0.787045i	0.998654	−	0.0518761i	$-0.0165201\pi$
$773$	12.6336	+	21.8821i	0.454401	+	0.787045i	−0.544253	+	0.838921i	$0.683187\pi$
$774$	−15.7195	−	8.38102i	−0.565025	−	0.301250i
$775$	−4.59333	−	2.65196i	−0.164997	−	0.0952613i
$776$	−4.60847	−	7.98211i	−0.165435	−	0.286541i
$777$	−1.59997	−	17.6318i	−0.0573987	−	0.632536i
$778$	−9.67132	+	16.7512i	−0.346734	+	0.600561i
$779$	32.5890	−	18.8153i	1.16762	−	0.674127i
$780$	0.401614	−	0.723566i	0.0143801	−	0.0259078i
$781$	−11.3431	+	19.6469i	−0.405889	+	0.703020i
$782$	−2.92184	+	5.06077i	−0.104485	+	0.180973i
$783$	8.96102	+	13.8502i	0.320241	+	0.494965i
$784$	−4.35137	−	5.48321i	−0.155406	−	0.195829i
$785$	−14.5680	+	8.41085i	−0.519955	+	0.300196i
$786$	−18.0849	+	0.305439i	−0.645067	+	0.0108946i
$787$		−	54.2358i		−	1.93330i	−0.256104	−	0.966649i	$-0.582439\pi$
$787$		−	54.2358i		−	1.93330i	0.256104	−	0.966649i	$-0.417561\pi$
$788$		−	9.01088i		−	0.320999i
$789$	6.44556	+	10.7410i	0.229468	+	0.382389i
$790$	−13.5407	+	7.81773i	−0.481757	+	0.278142i
$791$	−17.4636	+	11.8760i	−0.620933	+	0.422262i
$792$	6.26991	−	0.211848i	0.222792	−	0.00752767i
$793$	−1.02559	+	1.77638i	−0.0364199	+	0.0630811i
$794$	−15.1479	+	26.2370i	−0.537580	+	0.931116i
$795$	4.39597	+	7.32551i	0.155909	+	0.259809i
$796$	12.3893	−	7.15296i	0.439127	−	0.253530i
$797$	−7.63066	+	13.2167i	−0.270292	+	0.468159i	−0.968936	−	0.247310i	$-0.920454\pi$
$797$	−7.63066	+	13.2167i	−0.270292	+	0.468159i	0.698645	+	0.715469i	$0.253787\pi$
$798$	1.92923	+	21.2602i	0.0682940	+	0.752603i
$799$	0.151411	+	0.262252i	0.00535654	+	0.00927780i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	39.5210	−	1.33534i	1.39641	−	0.0471818i
$802$	16.5340	+	28.6376i	0.583834	+	1.01123i
$803$	−13.6412			−0.481386
$804$	−8.28648	−	4.59940i	−0.292241	−	0.162208i
$805$	4.43606	−	3.01672i	0.156351	−	0.106325i
$806$	2.19463	+	1.26707i	0.0773027	+	0.0446307i
$807$	−0.331044	−	19.6010i	−0.0116533	−	0.689987i
$808$	16.3359	+	9.43156i	0.574696	+	0.331801i
$809$	−12.9900	+	7.49978i	−0.456704	+	0.263678i	−0.710657	−	0.703538i	$-0.751602\pi$
$809$	−12.9900	+	7.49978i	−0.456704	+	0.263678i	0.253953	+	0.967216i	$0.418269\pi$
$810$	0.607490	+	8.97947i	0.0213450	+	0.315507i
$811$			15.3625i			0.539451i	0.962937	+	0.269726i	$0.0869330\pi$
$811$			15.3625i			0.539451i	−0.962937	+	0.269726i	$0.913067\pi$
$812$	−0.617714	−	8.37674i	−0.0216775	−	0.293966i
$813$	3.62459	+	6.04007i	0.127120	+	0.211834i
$814$	−4.03948	−	6.99658i	−0.141584	−	0.245230i
$815$	−10.0327			−0.351431
$816$	0.0842951	+	4.99107i	0.00295092	+	0.174723i
$817$		−	27.6619i		−	0.967768i
$818$	17.0227			0.595183
$819$	−3.46855	−	1.53324i	−0.121201	−	0.0535758i
$820$	−8.07796			−0.282095
$821$		−	28.0028i		−	0.977306i	−0.872478	−	0.488653i	$-0.837488\pi$
$821$		−	28.0028i		−	0.977306i	0.872478	−	0.488653i	$-0.162512\pi$
$822$	−25.8936	+	15.5385i	−0.903142	+	0.541967i
$823$	2.03379			0.0708933			0.0354466	−	0.999372i	$-0.488715\pi$
$823$	2.03379			0.0708933			0.0354466	+	0.999372i	$0.488715\pi$
$824$	5.07888	+	8.79688i	0.176931	+	0.306454i
$825$	3.62148	−	0.0611638i	0.126084	−	0.00212945i
$826$	6.71690	+	3.24456i	0.233711	+	0.112893i
$827$			25.2422i			0.877758i	0.898546	+	0.438879i	$0.144624\pi$
$827$			25.2422i			0.877758i	−0.898546	+	0.438879i	$0.855376\pi$
$828$	5.36766	+	2.86183i	0.186539	+	0.0994555i
$829$	−35.8687	+	20.7088i	−1.24577	+	0.719246i	−0.970263	−	0.242053i	$-0.922179\pi$
$829$	−35.8687	+	20.7088i	−1.24577	+	0.719246i	−0.275508	+	0.961299i	$0.588846\pi$
$830$	−9.68132	−	5.58951i	−0.336044	−	0.194015i
$831$	5.48101	−	3.28910i	0.190134	−	0.114098i
$832$	−0.413776	−	0.238893i	−0.0143451	−	0.00828214i
$833$	7.41515	−	18.7619i	0.256920	−	0.650061i
$834$	−19.0643	+	11.4403i	−0.660144	+	0.396146i
$835$	−14.3407			−0.496282
$836$	4.87076	+	8.43640i	0.168459	+	0.291779i
$837$	−27.5246	+	1.39567i	−0.951391	+	0.0482413i
$838$	−6.74162	−	3.89228i	−0.232885	−	0.134456i
$839$	−7.84013	−	13.5795i	−0.270671	−	0.468817i	0.698363	−	0.715744i	$-0.253912\pi$
$839$	−7.84013	−	13.5795i	−0.270671	−	0.468817i	−0.969034	+	0.246928i	$0.920579\pi$
$840$	1.92326	−	4.15946i	0.0663587	−	0.143515i
$841$	−9.46061	+	16.3863i	−0.326228	+	0.565043i
$842$	26.7894	−	15.4668i	0.923222	−	0.533023i
$843$	42.6205	−	0.719824i	1.46793	−	0.0247921i
$844$	0.442791	−	0.766937i	0.0152415	−	0.0263990i
$845$	6.38586	−	11.0606i	0.219680	−	0.380497i
$846$	0.267510	−	0.166739i	0.00919720	−	0.00573259i
$847$	17.4860	−	1.28945i	0.600827	−	0.0443059i
$848$	4.27164	−	2.46623i	0.146689	−	0.0846908i
$849$	−1.51494	+	2.72939i	−0.0519927	+	0.0936724i
$850$			2.88201i			0.0988521i
$851$		−	7.83353i		−	0.268530i
$852$	−9.11905	+	16.4293i	−0.312414	+	0.562858i
$853$	−13.0788	+	7.55104i	−0.447809	+	0.258543i	−0.706904	−	0.707309i	$-0.749909\pi$
$853$	−13.0788	+	7.55104i	−0.447809	+	0.258543i	0.259095	+	0.965852i	$0.416576\pi$
$854$	−4.94045	+	10.2278i	−0.169059	+	0.349987i
$855$	−11.8601	+	7.39235i	−0.405606	+	0.252813i
$856$	−9.16843	+	15.8802i	−0.313371	+	0.542774i
$857$	1.36149	−	2.35818i	0.0465077	−	0.0805537i	−0.841834	−	0.539736i	$-0.818524\pi$
$857$	1.36149	−	2.35818i	0.0465077	−	0.0805537i	0.888342	+	0.459182i	$0.151857\pi$
$858$	−1.73030	+	0.0292233i	−0.0590714	+	0.000997666i
$859$	−24.4210	+	14.0995i	−0.833235	+	0.481068i	−0.854959	−	0.518696i	$-0.826418\pi$
$859$	−24.4210	+	14.0995i	−0.833235	+	0.481068i	0.0217243	+	0.999764i	$0.493084\pi$
$860$	−2.96902	+	5.14250i	−0.101243	+	0.175358i
$861$	3.34539	+	36.8664i	0.114011	+	1.25640i
$862$	9.81647	+	17.0026i	0.334350	+	0.579112i
$863$	−10.0634	−	5.81009i	−0.342561	−	0.197778i	0.318843	−	0.947808i	$-0.396706\pi$
$863$	−10.0634	−	5.81009i	−0.342561	−	0.197778i	−0.661404	+	0.750030i	$0.730039\pi$
$864$	5.18949	−	0.263138i	0.176550	−	0.00895215i
$865$	−8.06316	−	13.9658i	−0.274156	−	0.474851i
$866$	−35.9562			−1.22184
$867$	12.9120	−	7.74839i	0.438515	−	0.263149i
$868$	12.6359	+	6.10369i	0.428891	+	0.207173i
$869$	28.3158	+	16.3481i	0.960548	+	0.554573i
$870$	4.71496	−	2.82940i	0.159852	−	0.0959257i
$871$	2.26408	+	1.30717i	0.0767153	+	0.0442916i
$872$	−12.2738	+	7.08626i	−0.415642	+	0.239971i
$873$	−24.3995	−	13.0089i	−0.825799	−	0.440284i
$874$			9.44559i			0.319502i
$875$	1.15079	−	2.38237i	0.0389037	−	0.0805388i
$876$	−11.2970	+	0.190796i	−0.381689	+	0.00644641i
$877$	13.4938	+	23.3720i	0.455654	+	0.789215i	0.998726	−	0.0504709i	$-0.0160722\pi$
$877$	13.4938	+	23.3720i	0.455654	+	0.789215i	−0.543072	+	0.839686i	$0.682739\pi$
$878$	24.3427			0.821525
$879$	35.3202	−	21.1953i	1.19132	−	0.714901i
$880$		−	2.09116i		−	0.0704931i
$881$	3.38847			0.114160			0.0570802	−	0.998370i	$-0.481821\pi$
$881$	3.38847			0.114160			0.0570802	+	0.998370i	$0.481821\pi$
$882$	−19.7795	−	7.05482i	−0.666011	−	0.237548i
$883$	−28.0287			−0.943241			−0.471621	−	0.881802i	$-0.656331\pi$
$883$	−28.0287			−0.943241			−0.471621	+	0.881802i	$0.656331\pi$
$884$		−	1.37699i		−	0.0463131i
$885$	0.0824644	+	4.88268i	0.00277201	+	0.164130i
$886$	5.94231			0.199636
$887$	10.0640	+	17.4314i	0.337917	+	0.585289i	0.984041	−	0.177944i	$-0.0569445\pi$
$887$	10.0640	+	17.4314i	0.337917	+	0.585289i	−0.646124	+	0.763232i	$0.723611\pi$
$888$	−3.44317	−	5.73774i	−0.115545	−	0.192546i
$889$	−0.517503	+	1.07134i	−0.0173565	+	0.0359315i
$890$		−	13.1812i		−	0.441835i
$891$	15.6266	−	10.4889i	0.523512	−	0.351393i
$892$	0.0602532	−	0.0347872i	0.00201743	−	0.00116476i
$893$	0.423898	+	0.244738i	0.0141852	+	0.00818984i
$894$	0.0348328	+	2.06243i	0.00116498	+	0.0689781i
$895$	−0.0837491	−	0.0483526i	−0.00279942	−	0.00161625i
$896$	−2.38237	−	1.15079i	−0.0795894	−	0.0384451i
$897$	−1.46713	−	0.814328i	−0.0489860	−	0.0271896i
$898$	3.59042			0.119814
$899$	8.41921	+	14.5825i	0.280796	+	0.486353i
$900$	2.99829	−	0.101306i	0.0999430	−	0.00337687i
$901$	12.3109	+	7.10770i	0.410136	+	0.236792i
$902$	8.44617	+	14.6292i	0.281227	+	0.487099i
$903$	24.6990	+	11.4204i	0.821933	+	0.380047i
$904$	−3.99113	+	6.91284i	−0.132743	+	0.229918i
$905$	17.4017	−	10.0469i	0.578452	−	0.333970i
$906$	1.41126	+	2.35174i	0.0468860	+	0.0781315i
$907$	16.8424	−	29.1719i	0.559243	−	0.968637i	−0.438317	−	0.898820i	$-0.644425\pi$
$907$	16.8424	−	29.1719i	0.559243	−	0.968637i	0.997560	−	0.0698166i	$-0.0222414\pi$
$908$	9.19003	−	15.9176i	0.304982	−	0.528244i
$909$	56.5571	−	1.91095i	1.87588	−	0.0633822i
$910$	−0.549832	+	1.13827i	−0.0182267	+	0.0377331i
$911$	−34.1663	+	19.7259i	−1.13198	+	0.653550i	−0.944432	−	0.328706i	$-0.893388\pi$
$911$	−34.1663	+	19.7259i	−1.13198	+	0.653550i	−0.187549	+	0.982255i	$0.560054\pi$
$912$	4.15173	+	6.91851i	0.137478	+	0.229095i
$913$			23.3772i			0.773671i
$914$		−	13.4589i		−	0.445181i
$915$	−7.43481	+	0.125568i	−0.245787	+	0.00415114i
$916$	−13.9168	+	8.03486i	−0.459823	+	0.265479i
$917$	27.5543	−	2.03189i	0.909922	−	0.0670990i
$918$	8.13484	+	12.5732i	0.268490	+	0.414978i
$919$	24.5657	−	42.5490i	0.810346	−	1.40356i	−0.102276	−	0.994756i	$-0.532612\pi$
$919$	24.5657	−	42.5490i	0.810346	−	1.40356i	0.912622	−	0.408804i	$-0.134054\pi$
$920$	1.01382	−	1.75599i	0.0334246	−	0.0578931i
$921$	−5.04236	+	9.08454i	−0.166151	+	0.299346i
$922$	−23.4924	+	13.5633i	−0.773681	+	0.446685i
$923$	2.59167	−	4.48890i	0.0853058	−	0.147754i
$924$	−9.54370	+	0.866031i	−0.313965	+	0.0284903i
$925$	−1.93169	−	3.34578i	−0.0635135	−	0.110009i
$926$	27.6688	+	15.9746i	0.909254	+	0.524958i
$927$	26.8901	+	14.3368i	0.883187	+	0.470882i
$928$	−1.58735	−	2.74938i	−0.0521075	−	0.0902528i
$929$	7.61652			0.249890			0.124945	−	0.992164i	$-0.460125\pi$
$929$	7.61652			0.249890			0.124945	+	0.992164i	$0.460125\pi$
$930$	0.155133	+	9.18536i	0.00508701	+	0.301200i
$931$	−4.78326	−	32.2562i	−0.156765	−	1.05716i
$932$	−22.4677	−	12.9717i	−0.735955	−	0.424904i
$933$	−35.9343	−	19.9453i	−1.17644	−	0.652980i
$934$	−31.8743	−	18.4026i	−1.04296	−	0.602152i
$935$	5.21932	−	3.01338i	0.170690	−	0.0985479i
$936$	−1.43254	+	0.0484027i	−0.0468241	+	0.00158209i
$937$		−	35.6260i		−	1.16385i	−0.813243	−	0.581925i	$-0.802300\pi$
$937$		−	35.6260i		−	1.16385i	0.813243	−	0.581925i	$-0.197700\pi$
$938$	13.0357	+	6.29682i	0.425632	+	0.205599i
$939$	−2.49276	+	4.49107i	−0.0813482	+	0.146560i
$940$	−0.0525367	−	0.0909962i	−0.00171356	−	0.00296797i
$941$	44.9726			1.46606			0.733032	−	0.680194i	$-0.238105\pi$
$941$	44.9726			1.46606			0.733032	+	0.680194i	$0.238105\pi$
$942$	25.4750	+	14.1399i	0.830019	+	0.460701i
$943$			16.3792i			0.533380i
$944$	2.81942			0.0917643
$945$	−1.70405	−	13.6417i	−0.0554327	−	0.443765i
$946$	12.4174			0.403725
$947$		−	42.4495i		−	1.37942i	−0.724084	−	0.689712i	$-0.757737\pi$
$947$		−	42.4495i		−	1.37942i	0.724084	−	0.689712i	$-0.242263\pi$
$948$	23.6785	+	13.1427i	0.769042	+	0.426856i
$949$	3.11672			0.101173
$950$	2.32921	+	4.03431i	0.0755696	+	0.130890i
$951$	−10.8855	+	19.6119i	−0.352988	+	0.635958i
$952$	−0.560762	−	7.60443i	−0.0181744	−	0.246461i
$953$			4.59106i			0.148719i	0.997232	+	0.0743595i	$0.0236912\pi$
$953$			4.59106i			0.148719i	−0.997232	+	0.0743595i	$0.976309\pi$
$954$	6.96173	−	13.0575i	0.225394	−	0.422751i
$955$	−3.05974	+	1.76654i	−0.0990108	+	0.0571639i
$956$	8.46444	+	4.88695i	0.273760	+	0.158055i
$957$	−10.0539	−	5.58042i	−0.324997	−	0.180389i
$958$	15.2845	+	8.82453i	0.493821	+	0.285108i
$959$	38.1439	−	25.9396i	1.23173	−	0.837632i
$960$	−0.0292487	−	1.73180i	−0.000943998	−	0.0558937i
$961$	2.86839			0.0925288
$962$	0.922936	+	1.59857i	0.0297566	+	0.0515400i
$963$	1.85764	+	54.9792i	0.0598615	+	1.77168i
$964$	−22.1792	−	12.8052i	−0.714345	−	0.412427i
$965$	12.6572	+	21.9229i	0.407449	+	0.705723i
$966$	−8.43387	−	3.89967i	−0.271355	−	0.125470i
$967$	3.39500	−	5.88032i	0.109176	−	0.189098i	−0.806261	−	0.591560i	$-0.798512\pi$
$967$	3.39500	−	5.88032i	0.109176	−	0.189098i	0.915437	+	0.402462i	$0.131845\pi$
$968$	5.73918	−	3.31352i	0.184464	−	0.106501i
$969$	−11.2852	+	20.3319i	−0.362533	+	0.653154i
$970$	−4.60847	+	7.98211i	−0.147969	+	0.256290i
$971$	−27.3715	+	47.4087i	−0.878392	+	1.52142i	−0.0252864	+	0.999680i	$0.508050\pi$
$971$	−27.3715	+	47.4087i	−0.878392	+	1.52142i	−0.853105	+	0.521739i	$0.825284\pi$
$972$	12.7946	−	8.90502i	0.410386	−	0.285629i
$973$	28.0837	−	19.0982i	0.900323	−	0.612260i
$974$	9.43137	−	5.44521i	0.302201	−	0.174476i
$975$	−0.827433	+	0.0139747i	−0.0264991	+	0.000447547i
$976$			4.29310i			0.137419i
$977$		−	3.36225i		−	0.107568i	−0.998553	−	0.0537840i	$-0.982872\pi$
$977$		−	3.36225i		−	0.107568i	0.998553	−	0.0537840i	$-0.0171282\pi$
$978$	8.94149	+	14.9002i	0.285917	+	0.476457i
$979$	−23.8712	+	13.7820i	−0.762925	+	0.440475i
$980$	−2.57291	+	6.51000i	−0.0821885	+	0.207954i
$981$	−20.0033	+	37.5182i	−0.638655	+	1.19786i
$982$	−12.4238	+	21.5186i	−0.396459	+	0.686687i
$983$	24.7921	−	42.9411i	0.790745	−	1.36961i	−0.134762	−	0.990878i	$-0.543027\pi$
$983$	24.7921	−	42.9411i	0.790745	−	1.36961i	0.925506	−	0.378732i	$-0.123640\pi$
$984$	7.19934	+	11.9971i	0.229507	+	0.382453i
$985$	−7.80365	+	4.50544i	−0.248645	+	0.143555i
$986$	4.57477	−	7.92373i	0.145690	−	0.252343i
$987$	−0.393533	+	0.277453i	−0.0125263	+	0.00883143i
$988$	−1.11287	−	1.92754i	−0.0354050	−	0.0613233i
$989$	10.4271	+	6.02010i	0.331563	+	0.191428i
$990$	−3.31842	−	5.32398i	−0.105466	−	0.169207i
$991$	−25.0428	−	43.3755i	−0.795512	−	1.37787i	−0.922513	−	0.385965i	$-0.873869\pi$
$991$	−25.0428	−	43.3755i	−0.795512	−	1.37787i	0.127001	−	0.991903i	$-0.459465\pi$
$992$	5.30392			0.168400
$993$	51.4960	+	28.5828i	1.63418	+	0.907047i
$994$	12.4845	−	25.8455i	0.395984	−	0.819768i
$995$	−12.3893	−	7.15296i	−0.392767	−	0.226764i
$996$	0.326972	+	19.3599i	0.0103605	+	0.613441i
$997$	27.1002	+	15.6463i	0.858273	+	0.495524i	0.863434	−	0.504463i	$-0.168309\pi$
$997$	27.1002	+	15.6463i	0.858273	+	0.495524i	−0.00516072	+	0.999987i	$0.501643\pi$
$998$	−31.9432	+	18.4424i	−1.01115	+	0.583785i
$999$	−17.8712	−	9.14407i	−0.565420	−	0.289305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bk.c.131.7	yes	32
3.2	odd	2		1890.2.bk.c.341.14		32
7.3	odd	6		630.2.t.c.311.13	✓	32
9.2	odd	6		630.2.t.c.551.13	yes	32
9.7	even	3		1890.2.t.c.1601.2		32
21.17	even	6		1890.2.t.c.1151.2		32
63.38	even	6	inner	630.2.bk.c.101.15	yes	32
63.52	odd	6		1890.2.bk.c.521.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.13	✓	32	7.3	odd	6
630.2.t.c.551.13	yes	32	9.2	odd	6
630.2.bk.c.101.15	yes	32	63.38	even	6	inner
630.2.bk.c.131.7	yes	32	1.1	even	1	trivial
1890.2.t.c.1151.2		32	21.17	even	6
1890.2.t.c.1601.2		32	9.7	even	3
1890.2.bk.c.341.14		32	3.2	odd	2
1890.2.bk.c.521.14		32	63.52	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.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.51441 + 0.840572i) q^{3} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.840572 - 1.51441i) q^{6} +(-1.15079 + 2.38237i) q^{7} +1.00000i q^{8} +(1.58688 + 2.54594i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.51441 + 0.840572i) q^{3} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.840572 - 1.51441i) q^{6} +(-1.15079 + 2.38237i) q^{7} +1.00000i q^{8} +(1.58688 + 2.54594i) q^{9} +(0.866025 - 0.500000i) q^{10} +(-1.81100 - 1.04558i) q^{11} +(-1.51441 - 0.840572i) q^{12} +(0.413776 + 0.238893i) q^{13} +(2.38237 + 1.15079i) q^{14} +(0.0292487 + 1.73180i) q^{15} +1.00000 q^{16} +(1.44100 + 2.49589i) q^{17} +(2.54594 - 1.58688i) q^{18} +(4.03431 + 2.32921i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-3.74532 + 2.64057i) q^{21} +(-1.04558 + 1.81100i) q^{22} +(-1.75599 + 1.01382i) q^{23} +(-0.840572 + 1.51441i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.238893 - 0.413776i) q^{26} +(0.263138 + 5.18949i) q^{27} +(1.15079 - 2.38237i) q^{28} +(2.74938 - 1.58735i) q^{29} +(1.73180 - 0.0292487i) q^{30} +5.30392i q^{31} -1.00000i q^{32} +(-1.86371 - 3.10572i) q^{33} +(2.49589 - 1.44100i) q^{34} +(-2.63859 + 0.194573i) q^{35} +(-1.58688 - 2.54594i) q^{36} +(-1.93169 + 3.34578i) q^{37} +(2.32921 - 4.03431i) q^{38} +(0.425819 + 0.709591i) q^{39} +(-0.866025 + 0.500000i) q^{40} +(4.03898 - 6.99572i) q^{41} +(2.64057 + 3.74532i) q^{42} +(-2.96902 - 5.14250i) q^{43} +(1.81100 + 1.04558i) q^{44} +(-1.41141 + 2.64725i) q^{45} +(1.01382 + 1.75599i) q^{46} +0.105073 q^{47} +(1.51441 + 0.840572i) q^{48} +(-4.35137 - 5.48321i) q^{49} +(0.866025 + 0.500000i) q^{50} +(0.0842951 + 4.99107i) q^{51} +(-0.413776 - 0.238893i) q^{52} +(4.27164 - 2.46623i) q^{53} +(5.18949 - 0.263138i) q^{54} -2.09116i q^{55} +(-2.38237 - 1.15079i) q^{56} +(4.15173 + 6.91851i) q^{57} +(-1.58735 - 2.74938i) q^{58} +2.81942 q^{59} +(-0.0292487 - 1.73180i) q^{60} +4.29310i q^{61} +5.30392 q^{62} +(-7.89153 + 0.850692i) q^{63} -1.00000 q^{64} +0.477787i q^{65} +(-3.10572 + 1.86371i) q^{66} +5.47175 q^{67} +(-1.44100 - 2.49589i) q^{68} +(-3.51147 + 0.0593058i) q^{69} +(0.194573 + 2.63859i) q^{70} -10.8486i q^{71} +(-2.54594 + 1.58688i) q^{72} +(5.64929 - 3.26162i) q^{73} +(3.34578 + 1.93169i) q^{74} +(-1.48516 + 0.891232i) q^{75} +(-4.03431 - 2.32921i) q^{76} +(4.57504 - 3.11123i) q^{77} +(0.709591 - 0.425819i) q^{78} -15.6355 q^{79} +(0.500000 + 0.866025i) q^{80} +(-3.96364 + 8.08020i) q^{81} +(-6.99572 - 4.03898i) q^{82} +(-5.58951 - 9.68132i) q^{83} +(3.74532 - 2.64057i) q^{84} +(-1.44100 + 2.49589i) q^{85} +(-5.14250 + 2.96902i) q^{86} +(5.49797 - 0.0928562i) q^{87} +(1.04558 - 1.81100i) q^{88} +(6.59060 - 11.4153i) q^{89} +(2.64725 + 1.41141i) q^{90} +(-1.04530 + 0.710851i) q^{91} +(1.75599 - 1.01382i) q^{92} +(-4.45833 + 8.03232i) q^{93} -0.105073i q^{94} +4.65842i q^{95} +(0.840572 - 1.51441i) q^{96} +(-7.98211 + 4.60847i) q^{97} +(-5.48321 + 4.35137i) q^{98} +(-0.211848 - 6.26991i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7}+O(q^{10}) \) 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7	\( 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7} - 6 q^{11} + 2 q^{12} + 6 q^{14} + 2 q^{15} + 32 q^{16} - 6 q^{17} + 8 q^{18} - 16 q^{20} + 18 q^{23} + 2 q^{24} - 16 q^{25} - 12 q^{26} - 8 q^{27} + 2 q^{28} + 6 q^{29} - 4 q^{30} + 20 q^{33} + 2 q^{35} + 2 q^{37} + 30 q^{39} + 6 q^{41} + 10 q^{42} - 28 q^{43} + 6 q^{44} + 6 q^{45} + 48 q^{47} - 2 q^{48} + 8 q^{49} + 34 q^{51} + 36 q^{53} - 46 q^{54} - 6 q^{56} + 18 q^{57} - 60 q^{59} - 2 q^{60} + 32 q^{63} - 32 q^{64} - 34 q^{66} - 8 q^{67} + 6 q^{68} - 28 q^{69} + 6 q^{70} - 8 q^{72} - 30 q^{73} - 18 q^{74} + 4 q^{75} - 6 q^{77} - 22 q^{78} - 8 q^{79} + 16 q^{80} + 20 q^{81} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 30 q^{86} - 22 q^{87} + 12 q^{89} + 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 2 q^{96} - 96 q^{97} + 24 q^{98} - 24 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7 - 6 * q^11 + 2 * q^12 + 6 * q^14 + 2 * q^15 + 32 * q^16 - 6 * q^17 + 8 * q^18 - 16 * q^20 + 18 * q^23 + 2 * q^24 - 16 * q^25 - 12 * q^26 - 8 * q^27 + 2 * q^28 + 6 * q^29 - 4 * q^30 + 20 * q^33 + 2 * q^35 + 2 * q^37 + 30 * q^39 + 6 * q^41 + 10 * q^42 - 28 * q^43 + 6 * q^44 + 6 * q^45 + 48 * q^47 - 2 * q^48 + 8 * q^49 + 34 * q^51 + 36 * q^53 - 46 * q^54 - 6 * q^56 + 18 * q^57 - 60 * q^59 - 2 * q^60 + 32 * q^63 - 32 * q^64 - 34 * q^66 - 8 * q^67 + 6 * q^68 - 28 * q^69 + 6 * q^70 - 8 * q^72 - 30 * q^73 - 18 * q^74 + 4 * q^75 - 6 * q^77 - 22 * q^78 - 8 * q^79 + 16 * q^80 + 20 * q^81 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 30 * q^86 - 22 * q^87 + 12 * q^89 + 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 2 * q^96 - 96 * q^97 + 24 * q^98 - 24 * q^99

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