LMFDB - Embedded newform 630.2.bk.c.101.15

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			101.15
Character	$\chi$	$=$	630.101
Dual form			630.2.bk.c.131.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(1.51441 - 0.840572i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.840572 + 1.51441i) q^{6} +(-1.15079 - 2.38237i) q^{7} -1.00000i q^{8} +(1.58688 - 2.54594i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$			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	−0.747522	−	0.664237i	$-0.768757\pi$
$11$	−1.81100	+	1.04558i	−0.546037	+	0.315255i	0.201485	+	0.979492i	$0.435423\pi$
$12$	−1.51441	+	0.840572i	−0.437173	+	0.242652i
$13$	0.413776	−	0.238893i	0.114761	−	0.0662571i	−0.441521	−	0.897251i	$-0.645561\pi$
$13$	0.413776	−	0.238893i	0.114761	−	0.0662571i	0.556282	+	0.830994i	$0.312228\pi$
$14$	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	−0.636665	−	0.771141i	$-0.719687\pi$
$17$	1.44100	−	2.49589i	0.349495	−	0.605343i	0.986160	+	0.165798i	$0.0530198\pi$
$18$	2.54594	+	1.58688i	0.600084	+	0.374031i
$19$	4.03431	−	2.32921i	0.925535	−	0.534358i	0.0401380	−	0.999194i	$-0.487220\pi$
$19$	4.03431	−	2.32921i	0.925535	−	0.534358i	0.885397	+	0.464837i	$0.153887\pi$
$20$	−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	0.305626	−	0.952152i	$-0.401134\pi$
$23$	−1.75599	−	1.01382i	−0.366148	−	0.211396i	−0.671774	+	0.740756i	$0.734468\pi$
$24$	−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	0.733058	−	0.680166i	$-0.238092\pi$
$29$	2.74938	+	1.58735i	0.510547	+	0.294764i	−0.222512	+	0.974930i	$0.571426\pi$
$30$	1.73180	+	0.0292487i	0.316183	+	0.00534006i
$31$		−	5.30392i		−	0.952613i	−0.879279	−	0.476306i	$-0.841975\pi$
$31$		−	5.30392i		−	0.952613i	0.879279	−	0.476306i	$-0.158025\pi$
$32$			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	0.662412	−	0.749140i	$-0.269533\pi$
$37$	−1.93169	−	3.34578i	−0.317568	−	0.550043i	−0.979980	+	0.199096i	$0.936199\pi$
$38$	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	0.987392	+	0.158294i	$0.0505995\pi$
$41$	4.03898	+	6.99572i	0.630783	+	1.09255i	−0.356609	+	0.934254i	$0.616067\pi$
$42$	2.64057	−	3.74532i	0.407448	−	0.577915i
$43$	−2.96902	+	5.14250i	−0.452772	+	0.784224i	−0.998557	−	0.0537015i	$-0.982898\pi$
$43$	−2.96902	+	5.14250i	−0.452772	+	0.784224i	0.545785	+	0.837925i	$0.316231\pi$
$44$	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	0.763813	−	0.645437i	$-0.223325\pi$
$53$	4.27164	+	2.46623i	0.586755	+	0.338763i	−0.177058	+	0.984200i	$0.556658\pi$
$54$	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	$-0.911376\pi$
$61$		−	4.29310i		−	0.549675i	0.961491	−	0.274838i	$-0.0886241\pi$
$62$	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	$0.222621\pi$
$71$			10.8486i			1.28750i	−0.765238	+	0.643748i	$0.777379\pi$
$72$	−2.54594	−	1.58688i	−0.300042	−	0.187015i
$73$	5.64929	+	3.26162i	0.661199	+	0.381744i	0.792734	−	0.609568i	$-0.208657\pi$
$73$	5.64929	+	3.26162i	0.661199	+	0.381744i	−0.131535	+	0.991312i	$0.541990\pi$
$74$	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	0.377112	+	0.926168i	$0.376917\pi$
$83$	−5.58951	+	9.68132i	−0.613529	+	1.06266i	−0.990641	+	0.136495i	$0.956416\pi$
$84$	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	0.968951	+	0.247252i	$0.0795276\pi$
$89$	6.59060	+	11.4153i	0.698602	+	1.21001i	−0.270349	+	0.962762i	$0.587139\pi$
$90$	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	0.0366553	−	0.999328i	$-0.488330\pi$
$97$	−7.98211	−	4.60847i	−0.810460	−	0.467920i	−0.847116	+	0.531408i	$0.821663\pi$
$98$	−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	0.768317	+	0.640070i	$0.221095\pi$
$101$	9.43156	+	16.3359i	0.938475	+	1.62549i	0.170158	+	0.985417i	$0.445572\pi$
$102$	4.99107	+	0.0842951i	0.494190	+	0.00834646i
$103$	8.79688	+	5.07888i	0.866783	+	0.500437i	0.866278	−	0.499563i	$-0.166506\pi$
$103$	8.79688	+	5.07888i	0.866783	+	0.500437i	0.000504907		1.00000i	$0.499839\pi$
$104$	−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	0.536086	−	0.844163i	$-0.319902\pi$
$107$	15.8802	−	9.16843i	1.53520	−	0.886346i	0.999110	−	0.0421823i	$-0.0134310\pi$
$108$	−0.263138	+	5.18949i	−0.0253205	+	0.499358i
$109$	7.08626	−	12.2738i	0.678741	−	1.17561i	−0.296619	−	0.954996i	$-0.595859\pi$
$109$	7.08626	−	12.2738i	0.678741	−	1.17561i	0.975360	−	0.220618i	$-0.0708074\pi$
$110$	−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	−0.138268	−	0.990395i	$-0.544153\pi$
$113$	6.91284	−	3.99113i	0.650305	−	0.375454i	0.788573	+	0.614941i	$0.210820\pi$
$114$	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	−0.998756	−	0.0498622i	$-0.984122\pi$
$131$	−5.22140	+	9.04374i	−0.456196	+	0.790155i	0.542560	+	0.840017i	$0.317455\pi$
$132$	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	−0.978653	−	0.205517i	$-0.934112\pi$
$137$	−15.0990	+	8.71743i	−1.29000	+	0.744780i	−0.311343	+	0.950297i	$0.600779\pi$
$138$	0.0593058	−	3.51147i	0.00504844	−	0.298916i
$139$	−11.1168	+	6.41827i	−0.942912	+	0.544390i	−0.890872	−	0.454255i	$-0.849906\pi$
$139$	−11.1168	+	6.41827i	−0.942912	+	0.544390i	−0.0520399	+	0.998645i	$0.516572\pi$
$140$	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	0.457158	−	0.889385i	$-0.348867\pi$
$149$	−1.03136	−	0.595458i	−0.0844926	−	0.0487818i	−0.541651	+	0.840603i	$0.682201\pi$
$150$	0.891232	−	1.48516i	0.0727688	−	0.121263i
$151$	−0.791747	−	1.37135i	−0.0644314	−	0.111599i	0.832010	−	0.554760i	$-0.187190\pi$
$151$	−0.791747	−	1.37135i	−0.0644314	−	0.111599i	−0.896442	+	0.443162i	$0.853857\pi$
$152$	−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	$-0.765754\pi$
$157$		−	16.8217i		−	1.34252i	0.741223	−	0.671259i	$-0.234246\pi$
$158$		−	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	0.599920	−	0.800060i	$-0.295199\pi$
$163$	−5.01637	−	8.68860i	−0.392912	−	0.680544i	−0.992832	+	0.119516i	$0.961866\pi$
$164$	−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	−0.997914	−	0.0645506i	$-0.979439\pi$
$167$	−7.17037	−	12.4194i	−0.554860	−	0.961045i	0.443055	−	0.896495i	$-0.353895\pi$
$168$	−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	0.496867	−	0.867827i	$-0.334484\pi$
$179$	−0.0837491	−	0.0483526i	−0.00625970	−	0.00361404i	−0.503127	+	0.864213i	$0.667817\pi$
$180$	1.41141	+	2.64725i	0.105200	+	0.197314i
$181$			20.0938i			1.49356i	0.665072	+	0.746779i	$0.268401\pi$
$181$			20.0938i			1.49356i	−0.665072	+	0.746779i	$0.731599\pi$
$182$	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	$-0.959201\pi$
$191$		−	3.53308i		−	0.255645i	0.991797	−	0.127822i	$-0.0407987\pi$
$192$	−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	$-0.895981\pi$
$197$		−	9.01088i		−	0.641999i	0.947079	−	0.320999i	$-0.104019\pi$
$198$	−6.26991	−	0.211848i	−0.445583	−	0.0150553i
$199$	−12.3893	−	7.15296i	−0.878254	−	0.507060i	−0.00817145	−	0.999967i	$-0.502601\pi$
$199$	−12.3893	−	7.15296i	−0.878254	−	0.507060i	−0.870082	+	0.492907i	$0.835934\pi$
$200$	−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	0.850381	−	0.526167i	$-0.176371\pi$
$211$	−0.442791	−	0.766937i	−0.0304830	−	0.0527981i	−0.880864	+	0.473369i	$0.843038\pi$
$212$	−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	0.497981	−	0.867188i	$-0.334075\pi$
$223$	−0.0602532	−	0.0347872i	−0.00403485	−	0.00232952i	−0.502016	+	0.864858i	$0.667408\pi$
$224$	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	−0.991246	−	0.132030i	$-0.957851\pi$
$227$	−9.19003	−	15.9176i	−0.609964	−	1.05649i	0.381282	−	0.924459i	$-0.375483\pi$
$228$	−4.15173	+	6.91851i	−0.274955	+	0.458189i
$229$	13.9168	+	8.03486i	0.919647	+	0.530958i	0.883522	−	0.468389i	$-0.155165\pi$
$229$	13.9168	+	8.03486i	0.919647	+	0.530958i	0.0361243	+	0.999347i	$0.488499\pi$
$230$	−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	0.472408	−	0.881380i	$-0.343385\pi$
$233$	22.4677	−	12.9717i	1.47191	−	0.849808i	0.999501	+	0.0315722i	$0.0100514\pi$
$234$	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	−0.748121	−	0.663563i	$-0.769044\pi$
$239$	−8.46444	+	4.88695i	−0.547519	+	0.316110i	0.200602	+	0.979673i	$0.435710\pi$
$240$	0.0292487	−	1.73180i	0.00188800	−	0.111787i
$241$	22.1792	−	12.8052i	1.42869	−	0.824854i	0.431672	−	0.902031i	$-0.357924\pi$
$241$	22.1792	−	12.8052i	1.42869	−	0.824854i	0.997017	+	0.0771761i	$0.0245904\pi$
$242$	−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	−0.884895	−	0.465791i	$-0.845770\pi$
$257$	−0.626193	+	1.08460i	−0.0390608	+	0.0676553i	0.845834	+	0.533446i	$0.179103\pi$
$258$	−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	−0.294307	−	0.955711i	$-0.595089\pi$
$263$	6.26326	−	3.61609i	0.386209	−	0.222978i	0.680516	+	0.732733i	$0.261756\pi$
$264$	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	−0.985362	−	0.170478i	$-0.945469\pi$
$269$	−5.65912	+	9.80188i	−0.345043	+	0.597631i	0.640319	+	0.768109i	$0.278802\pi$
$270$	2.82263	−	4.36266i	0.171780	−	0.265503i
$271$	3.52208	−	2.03347i	0.213951	−	0.123525i	−0.389195	−	0.921155i	$-0.627247\pi$
$271$	3.52208	−	2.03347i	0.213951	−	0.123525i	0.603146	+	0.797631i	$0.293914\pi$
$272$	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	0.916122	−	0.400901i	$-0.131303\pi$
$277$	1.84526	+	3.19608i	0.110871	+	0.192034i	−0.805251	+	0.592934i	$0.797969\pi$
$278$	−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	0.975260	−	0.221063i	$-0.0709527\pi$
$281$	21.3133	+	12.3052i	1.27144	+	0.734068i	0.296184	+	0.955131i	$0.404286\pi$
$282$	0.0883217	+	0.159124i	0.00525948	+	0.00947570i
$283$		−	1.80228i		−	0.107134i	−0.998564	−	0.0535671i	$-0.982941\pi$
$283$		−	1.80228i		−	0.107134i	0.998564	−	0.0535671i	$-0.0170591\pi$
$284$		−	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	0.970288	+	0.241953i	$0.0777881\pi$
$293$	11.8910	+	20.5959i	0.694682	+	1.20322i	−0.275606	+	0.961271i	$0.588879\pi$
$294$	−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	$-0.945241\pi$
$307$		−	5.99873i		−	0.342366i	0.985239	−	0.171183i	$-0.0547589\pi$
$308$	−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	$-0.973291\pi$
$313$		−	2.96556i		−	0.167623i	0.996482	−	0.0838116i	$-0.0267094\pi$
$314$	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	$-0.881521\pi$
$317$		−	12.9502i		−	0.727353i	0.931525	−	0.363677i	$-0.118479\pi$
$318$	−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	0.990137	+	0.140105i	$0.0447440\pi$
$337$	11.3157	+	19.5993i	0.616403	+	1.06764i	−0.373734	+	0.927536i	$0.621923\pi$
$338$	−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	$-0.888565\pi$
$347$		−	12.7779i		−	0.685955i	0.939344	−	0.342977i	$-0.111435\pi$
$348$	−5.49797	−	0.0928562i	−0.294722	−	0.00497761i
$349$	3.95316	+	2.28236i	0.211608	+	0.122172i	0.602058	−	0.798452i	$-0.294347\pi$
$349$	3.95316	+	2.28236i	0.211608	+	0.122172i	−0.390451	+	0.920624i	$0.627681\pi$
$350$	−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	0.996250	−	0.0865250i	$-0.0275762\pi$
$353$	7.95106	+	13.7716i	0.423192	+	0.732990i	−0.573058	+	0.819515i	$0.694243\pi$
$354$	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	0.0217726	−	0.999763i	$-0.493069\pi$
$359$	17.0237	−	9.82867i	0.898479	−	0.518737i	0.876706	+	0.481026i	$0.159736\pi$
$360$	−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	0.0879033	−	0.996129i	$-0.471983\pi$
$367$	19.0524	−	10.9999i	0.994528	−	0.574191i	0.906625	+	0.421938i	$0.138650\pi$
$368$	−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	−0.388162	−	0.921591i	$-0.626890\pi$
$373$	11.6660	−	20.2060i	0.604041	−	1.04623i	0.992202	−	0.124638i	$-0.0397769\pi$
$374$	−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	−0.910722	−	0.413019i	$-0.864474\pi$
$383$	−1.91156	+	3.31092i	−0.0976762	+	0.169180i	0.813046	+	0.582199i	$0.197808\pi$
$384$	−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	−0.860422	−	0.509583i	$-0.829800\pi$
$389$	−16.7512	+	9.67132i	−0.849321	+	0.490356i	0.0111008	+	0.999938i	$0.496466\pi$
$390$	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	−0.983212	−	0.182467i	$-0.941592\pi$
$397$	−26.2370	+	15.1479i	−1.31680	+	0.760253i	−0.333585	+	0.942720i	$0.608258\pi$
$398$	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	−0.432968	−	0.901409i	$-0.642534\pi$
$401$	−28.6376	−	16.5340i	−1.43010	−	0.825666i	−0.997127	+	0.0757431i	$0.975867\pi$
$402$	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	$-0.861729\pi$
$409$		−	17.0227i		−	0.841716i	0.907126	−	0.420858i	$-0.138271\pi$
$410$			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	0.945300	−	0.326203i	$-0.105769\pi$
$419$	3.89228	+	6.74162i	0.190150	+	0.329350i	−0.755150	+	0.655552i	$0.772436\pi$
$420$	4.15946	−	1.92326i	0.202961	−	0.0938454i
$421$	15.4668	−	26.7894i	0.753808	−	1.30563i	−0.192157	−	0.981364i	$-0.561548\pi$
$421$	15.4668	−	26.7894i	0.753808	−	1.30563i	0.945965	−	0.324269i	$-0.105118\pi$
$422$	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	0.0310795	−	0.999517i	$-0.490105\pi$
$431$	−17.0026	−	9.81647i	−0.818988	−	0.472843i	−0.850067	+	0.526674i	$0.823439\pi$
$432$	0.263138	−	5.18949i	0.0126603	−	0.249679i
$433$			35.9562i			1.72794i	0.503540	+	0.863972i	$0.332031\pi$
$433$			35.9562i			1.72794i	−0.503540	+	0.863972i	$0.667969\pi$
$434$	−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	$-0.802698\pi$
$439$		−	24.3427i		−	1.16181i	0.813971	−	0.580906i	$-0.197302\pi$
$440$	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	$-0.954916\pi$
$443$		−	5.94231i		−	0.282328i	0.989986	−	0.141164i	$-0.0450845\pi$
$444$	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	$-0.973000\pi$
$449$		−	3.59042i		−	0.169442i	0.996405	−	0.0847211i	$-0.0269999\pi$
$450$	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	0.355495	+	0.934678i	$0.384312\pi$
$461$	−13.5633	+	23.4924i	−0.631708	+	1.09415i	−0.987202	+	0.159472i	$0.949021\pi$
$462$	−0.866031	+	9.54370i	−0.0402914	+	0.444013i
$463$	−15.9746	−	27.6688i	−0.742403	−	1.28588i	−0.951398	−	0.307963i	$-0.900353\pi$
$463$	−15.9746	−	27.6688i	−0.742403	−	1.28588i	0.208995	−	0.977917i	$-0.432981\pi$
$464$	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	0.879789	+	0.475364i	$0.157684\pi$
$467$	18.4026	+	31.8743i	0.851572	+	1.47497i	−0.0282177	+	0.999602i	$0.508983\pi$
$468$	−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	0.590907	−	0.806739i	$-0.298770\pi$
$479$	−8.82453	−	15.2845i	−0.403203	−	0.698368i	−0.994111	+	0.108371i	$0.965437\pi$
$480$	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	−0.715875	−	0.698228i	$-0.753972\pi$
$487$	5.44521	−	9.43137i	0.246746	−	0.427376i	0.962621	+	0.270852i	$0.0873054\pi$
$488$	−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	−0.899578	−	0.436760i	$-0.856126\pi$
$491$	−21.5186	+	12.4238i	−0.971123	+	0.560678i	−0.0715443	+	0.997437i	$0.522793\pi$
$492$	−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	0.0758658	+	0.997118i	$0.475828\pi$
$499$	−18.4424	+	31.9432i	−0.825597	+	1.42998i	−0.901462	+	0.432857i	$0.857505\pi$
$500$	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	−0.461649	−	0.887063i	$-0.652742\pi$
$509$	12.1242	−	20.9997i	0.537394	−	0.930794i	0.999043	−	0.0437312i	$-0.0139245\pi$
$510$	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	−0.119173	+	0.992874i	$0.538024\pi$
$521$	−20.9866	+	36.3499i	−0.919440	+	1.59252i	−0.800267	+	0.599643i	$0.795309\pi$
$522$	4.48082	+	8.40424i	0.196120	+	0.367844i
$523$	−2.05664	+	1.18740i	−0.0899304	+	0.0519213i	−0.544291	−	0.838897i	$-0.683201\pi$
$523$	−2.05664	+	1.18740i	−0.0899304	+	0.0519213i	0.454360	+	0.890818i	$0.349868\pi$
$524$	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	0.750671	−	0.660676i	$-0.229730\pi$
$541$	−4.57807	−	7.92946i	−0.196827	−	0.340914i	−0.947498	+	0.319762i	$0.896397\pi$
$542$	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	−0.336212	+	0.941786i	$0.609146\pi$
$547$	−23.0072	+	39.8496i	−0.983717	+	1.70385i	−0.647505	+	0.762061i	$0.724187\pi$
$548$	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	0.100752	−	0.994912i	$-0.467875\pi$
$557$	−16.7682	−	9.68111i	−0.710490	−	0.410202i	−0.811242	+	0.584710i	$0.801208\pi$
$558$	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	$0.146564\pi$
$569$			21.1986i			0.888691i	−0.895855	+	0.444346i	$0.853436\pi$
$570$	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	−0.199423	−	0.979914i	$-0.563907\pi$
$577$	−27.5702	−	15.9177i	−1.14776	−	0.662662i	−0.948341	+	0.317251i	$0.897240\pi$
$578$	−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	−0.382006	−	0.924160i	$-0.624767\pi$
$587$	14.7632	−	25.5706i	0.609343	−	1.05541i	0.991349	−	0.131253i	$-0.0419000\pi$
$588$	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	0.998435	−	0.0559309i	$-0.0178126\pi$
$593$	10.9772	+	19.0131i	0.450780	+	0.780773i	−0.547655	+	0.836704i	$0.684479\pi$
$594$	−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	$-0.817088\pi$
$599$		−	26.6051i		−	1.08706i	0.839391	−	0.543528i	$-0.182912\pi$
$600$	−0.891232	+	1.48516i	−0.0363844	+	0.0606315i
$601$	33.3026	+	19.2273i	1.35844	+	0.784296i	0.989414	−	0.145122i	$-0.0463575\pi$
$601$	33.3026	+	19.2273i	1.35844	+	0.784296i	0.369027	+	0.929419i	$0.379691\pi$
$602$	−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	0.853405	−	0.521248i	$-0.174533\pi$
$607$	20.4168	+	11.7877i	0.828693	+	0.478446i	−0.0247118	+	0.999695i	$0.507867\pi$
$608$	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	−0.979199	−	0.202900i	$-0.934963\pi$
$613$	−7.77138	+	13.4604i	−0.313883	+	0.543661i	0.665316	+	0.746561i	$0.268297\pi$
$614$	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	−0.716997	−	0.697076i	$-0.754484\pi$
$617$	−11.7195	+	6.76627i	−0.471810	+	0.272400i	0.245187	+	0.969476i	$0.421151\pi$
$618$	−0.297102	+	17.5913i	−0.0119512	+	0.707624i
$619$	20.4550	−	11.8097i	0.822157	−	0.474672i	−0.0290029	−	0.999579i	$-0.509233\pi$
$619$	20.4550	−	11.8097i	0.822157	−	0.474672i	0.851160	+	0.524907i	$0.175900\pi$
$620$	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	−0.403412	−	0.915018i	$-0.632176\pi$
$641$	4.74232	−	2.73798i	0.187311	−	0.108144i	0.590723	+	0.806874i	$0.298843\pi$
$642$	27.2332	+	16.3424i	1.07481	+	0.644983i
$643$	−22.6584	+	13.0818i	−0.893560	+	0.515897i	−0.875105	−	0.483933i	$-0.839208\pi$
$643$	−22.6584	+	13.0818i	−0.893560	+	0.515897i	−0.0184548	+	0.999830i	$0.505875\pi$
$644$	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	−0.971473	−	0.237151i	$-0.923786\pi$
$647$	−7.13123	+	12.3517i	−0.280358	+	0.485594i	0.691115	+	0.722745i	$0.257120\pi$
$648$	−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	0.235426	−	0.971892i	$-0.424352\pi$
$653$	−12.4842	−	7.20776i	−0.488545	−	0.282062i	−0.723971	+	0.689831i	$0.757685\pi$
$654$	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	−0.0218413	−	0.999761i	$-0.506953\pi$
$659$	−23.0675	−	13.3180i	−0.898581	−	0.518796i	−0.876739	+	0.480966i	$0.840286\pi$
$660$	−1.75777	−	3.16688i	−0.0684212	−	0.123271i
$661$			12.6233i			0.490991i	0.969398	+	0.245496i	$0.0789507\pi$
$661$			12.6233i			0.490991i	−0.969398	+	0.245496i	$0.921049\pi$
$662$			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	−0.893784	−	0.448499i	$-0.851959\pi$
$673$	−1.51712	+	2.62772i	−0.0584805	+	0.101291i	0.835303	+	0.549790i	$0.185292\pi$
$674$	−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	−0.0342719	−	0.999413i	$-0.510911\pi$
$683$	−23.9631	−	13.8351i	−0.916924	−	0.529387i	−0.882653	+	0.470026i	$0.844245\pi$
$684$	−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	$0.0830026\pi$
$691$			13.5543i			0.515630i	−0.966194	+	0.257815i	$0.916997\pi$
$692$	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	$-0.672028\pi$
$701$		−	45.4060i		−	1.71496i	0.514516	−	0.857481i	$-0.327972\pi$
$702$	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	0.961422	+	0.275077i	$0.0887033\pi$
$719$	19.2776	+	33.3899i	0.718935	+	1.24523i	−0.242488	+	0.970155i	$0.577963\pi$
$720$	−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	0.0414296	−	0.999141i	$-0.486809\pi$
$727$	−21.6549	−	12.5025i	−0.803137	−	0.463692i	−0.844567	+	0.535450i	$0.820142\pi$
$728$	−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	−0.995048	−	0.0993963i	$-0.968309\pi$
$733$	−42.7404	−	24.6762i	−1.57865	−	0.911435i	−0.583604	−	0.812039i	$-0.698358\pi$
$734$	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	−0.611170	−	0.791500i	$-0.709301\pi$
$739$	10.3267	−	17.8864i	0.379874	−	0.657961i	0.991044	+	0.133539i	$0.0426340\pi$
$740$	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	−0.353556	−	0.935413i	$-0.615028\pi$
$743$	7.62562	−	4.40265i	0.279757	−	0.161518i	0.633313	+	0.773895i	$0.281694\pi$
$744$	−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	0.153255	+	0.988187i	$0.451024\pi$
$751$	−21.3526	+	36.9838i	−0.779167	+	1.34956i	−0.932422	+	0.361371i	$0.882309\pi$
$752$	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	−0.925183	−	0.379522i	$-0.876088\pi$
$761$	−3.69423	+	6.39860i	−0.133916	+	0.231949i	0.791267	+	0.611471i	$0.209422\pi$
$762$	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	0.506982	−	0.861957i	$-0.330761\pi$
$769$	41.7890	−	24.1269i	1.50695	−	0.870038i	0.999967	−	0.00808106i	$-0.00257231\pi$
$770$	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	−0.544253	−	0.838921i	$-0.683187\pi$
$773$	12.6336	−	21.8821i	0.454401	−	0.787045i	0.998654	+	0.0518761i	$0.0165201\pi$
$774$	−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	$0.417561\pi$
$787$			54.2358i			1.93330i	−0.256104	+	0.966649i	$0.582439\pi$
$788$			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	0.698645	−	0.715469i	$-0.253787\pi$
$797$	−7.63066	−	13.2167i	−0.270292	−	0.468159i	−0.968936	+	0.247310i	$0.920454\pi$
$798$	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	0.253953	−	0.967216i	$-0.418269\pi$
$809$	−12.9900	−	7.49978i	−0.456704	−	0.263678i	−0.710657	+	0.703538i	$0.751602\pi$
$810$	0.607490	−	8.97947i	0.0213450	−	0.315507i
$811$		−	15.3625i		−	0.539451i	−0.962937	−	0.269726i	$-0.913067\pi$
$811$		−	15.3625i		−	0.539451i	0.962937	−	0.269726i	$-0.0869330\pi$
$812$	−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	$0.162512\pi$
$821$			28.0028i			0.977306i	−0.872478	+	0.488653i	$0.837488\pi$
$822$	−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	$-0.855376\pi$
$827$		−	25.2422i		−	0.877758i	0.898546	−	0.438879i	$-0.144624\pi$
$828$	5.36766	−	2.86183i	0.186539	−	0.0994555i
$829$	−35.8687	−	20.7088i	−1.24577	−	0.719246i	−0.275508	−	0.961299i	$-0.588846\pi$
$829$	−35.8687	−	20.7088i	−1.24577	−	0.719246i	−0.970263	+	0.242053i	$0.922179\pi$
$830$	−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	−0.969034	−	0.246928i	$-0.920579\pi$
$839$	−7.84013	+	13.5795i	−0.270671	+	0.468817i	0.698363	+	0.715744i	$0.253912\pi$
$840$	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	0.259095	−	0.965852i	$-0.416576\pi$
$853$	−13.0788	−	7.55104i	−0.447809	−	0.258543i	−0.706904	+	0.707309i	$0.749909\pi$
$854$	−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	0.888342	−	0.459182i	$-0.151857\pi$
$857$	1.36149	+	2.35818i	0.0465077	+	0.0805537i	−0.841834	+	0.539736i	$0.818524\pi$
$858$	−1.73030	−	0.0292233i	−0.0590714	−	0.000997666i
$859$	−24.4210	−	14.0995i	−0.833235	−	0.481068i	0.0217243	−	0.999764i	$-0.493084\pi$
$859$	−24.4210	−	14.0995i	−0.833235	−	0.481068i	−0.854959	+	0.518696i	$0.826418\pi$
$860$	−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	−0.661404	−	0.750030i	$-0.730039\pi$
$863$	−10.0634	+	5.81009i	−0.342561	+	0.197778i	0.318843	+	0.947808i	$0.396706\pi$
$864$	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	−0.543072	−	0.839686i	$-0.682739\pi$
$877$	13.4938	−	23.3720i	0.455654	−	0.789215i	0.998726	+	0.0504709i	$0.0160722\pi$
$878$	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	−0.646124	−	0.763232i	$-0.723611\pi$
$887$	10.0640	−	17.4314i	0.337917	−	0.585289i	0.984041	+	0.177944i	$0.0569445\pi$
$888$	−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	0.997560	+	0.0698166i	$0.0222414\pi$
$907$	16.8424	+	29.1719i	0.559243	+	0.968637i	−0.438317	+	0.898820i	$0.644425\pi$
$908$	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	−0.187549	−	0.982255i	$-0.560054\pi$
$911$	−34.1663	−	19.7259i	−1.13198	−	0.653550i	−0.944432	+	0.328706i	$0.893388\pi$
$912$	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	0.912622	+	0.408804i	$0.134054\pi$
$919$	24.5657	+	42.5490i	0.810346	+	1.40356i	−0.102276	+	0.994756i	$0.532612\pi$
$920$	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	$0.197700\pi$
$937$			35.6260i			1.16385i	−0.813243	+	0.581925i	$0.802300\pi$
$938$	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	$0.242263\pi$
$947$			42.4495i			1.37942i	−0.724084	+	0.689712i	$0.757737\pi$
$948$	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	$-0.976309\pi$
$953$		−	4.59106i		−	0.148719i	0.997232	−	0.0743595i	$-0.0236912\pi$
$954$	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	0.915437	−	0.402462i	$-0.131845\pi$
$967$	3.39500	+	5.88032i	0.109176	+	0.189098i	−0.806261	+	0.591560i	$0.798512\pi$
$968$	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	−0.853105	−	0.521739i	$-0.825284\pi$
$971$	−27.3715	−	47.4087i	−0.878392	−	1.52142i	−0.0252864	−	0.999680i	$-0.508050\pi$
$972$	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	$0.0171282\pi$
$977$			3.36225i			0.107568i	−0.998553	+	0.0537840i	$0.982872\pi$
$978$	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	0.925506	+	0.378732i	$0.123640\pi$
$983$	24.7921	+	42.9411i	0.790745	+	1.36961i	−0.134762	+	0.990878i	$0.543027\pi$
$984$	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	0.127001	+	0.991903i	$0.459465\pi$
$991$	−25.0428	+	43.3755i	−0.795512	+	1.37787i	−0.922513	+	0.385965i	$0.873869\pi$
$992$	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	−0.00516072	−	0.999987i	$-0.501643\pi$
$997$	27.1002	−	15.6463i	0.858273	−	0.495524i	0.863434	+	0.504463i	$0.168309\pi$
$998$	−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.101.15	yes	32
3.2	odd	2		1890.2.bk.c.521.14		32
7.5	odd	6		630.2.t.c.551.13	yes	32
9.4	even	3		1890.2.t.c.1151.2		32
9.5	odd	6		630.2.t.c.311.13	✓	32
21.5	even	6		1890.2.t.c.1601.2		32
63.5	even	6	inner	630.2.bk.c.131.7	yes	32
63.40	odd	6		1890.2.bk.c.341.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.13	✓	32	9.5	odd	6
630.2.t.c.551.13	yes	32	7.5	odd	6
630.2.bk.c.101.15	yes	32	1.1	even	1	trivial
630.2.bk.c.131.7	yes	32	63.5	even	6	inner
1890.2.t.c.1151.2		32	9.4	even	3
1890.2.t.c.1601.2		32	21.5	even	6
1890.2.bk.c.341.14		32	63.40	odd	6
1890.2.bk.c.521.14		32	3.2	odd	2

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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