LMFDB - Embedded newform 504.2.cs.b.85.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(85,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("504.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cs (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			85.10
Character	$\chi$	$=$	504.85
Dual form			504.2.cs.b.421.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.908808 + 1.08354i) q^{2} +(1.55167 - 0.769621i) q^{3} +(-0.348135 - 1.96947i) q^{4} +(-1.05668 - 0.610074i) q^{5} +(-0.576254 + 2.38074i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(2.45039 + 1.41265i) q^{8} +(1.81537 - 2.38840i) q^{9} +O(q^{10})$	\(q+(-0.908808 + 1.08354i) q^{2} +(1.55167 - 0.769621i) q^{3} +(-0.348135 - 1.96947i) q^{4} +(-1.05668 - 0.610074i) q^{5} +(-0.576254 + 2.38074i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(2.45039 + 1.41265i) q^{8} +(1.81537 - 2.38840i) q^{9} +(1.62136 - 0.590518i) q^{10} +(-0.109000 + 0.0629313i) q^{11} +(-2.05593 - 2.78803i) q^{12} +(-2.91751 - 1.68442i) q^{13} +(1.39278 + 0.245279i) q^{14} +(-2.10914 - 0.133392i) q^{15} +(-3.75760 + 1.37128i) q^{16} +3.74320 q^{17} +(0.938113 + 4.13763i) q^{18} -4.78182i q^{19} +(-0.833654 + 2.29348i) q^{20} +(-1.44235 - 0.958976i) q^{21} +(0.0308715 - 0.175299i) q^{22} +(0.325176 - 0.563221i) q^{23} +(4.88941 + 0.306094i) q^{24} +(-1.75562 - 3.04082i) q^{25} +(4.47660 - 1.63043i) q^{26} +(0.978691 - 5.10315i) q^{27} +(-1.53154 + 1.28623i) q^{28} +(0.306412 - 0.176907i) q^{29} +(2.06134 - 2.16412i) q^{30} +(0.967654 - 1.67603i) q^{31} +(1.92910 - 5.31776i) q^{32} +(-0.120699 + 0.181537i) q^{33} +(-3.40185 + 4.05592i) q^{34} +1.22015i q^{35} +(-5.33586 - 2.74382i) q^{36} -6.46775i q^{37} +(5.18131 + 4.34575i) q^{38} +(-5.82338 - 0.368296i) q^{39} +(-1.72746 - 2.98764i) q^{40} +(-1.92471 + 3.33369i) q^{41} +(2.34991 - 0.691321i) q^{42} +(0.0462098 - 0.0266792i) q^{43} +(0.161888 + 0.192764i) q^{44} +(-3.37536 + 1.41626i) q^{45} +(0.314752 + 0.864202i) q^{46} +(-3.25228 - 5.63312i) q^{47} +(-4.77520 + 5.01971i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(4.89039 + 0.861234i) q^{50} +(5.80821 - 2.88084i) q^{51} +(-2.30173 + 6.33234i) q^{52} +9.88039i q^{53} +(4.64005 + 5.69824i) q^{54} +0.153571 q^{55} +(-0.00180565 - 2.82843i) q^{56} +(-3.68019 - 7.41981i) q^{57} +(-0.0867832 + 0.492785i) q^{58} +(11.2403 + 6.48957i) q^{59} +(0.471556 + 4.20033i) q^{60} +(0.775046 - 0.447473i) q^{61} +(0.936636 + 2.57168i) q^{62} +(-2.97610 - 0.377955i) q^{63} +(4.00884 + 6.92309i) q^{64} +(2.05524 + 3.55979i) q^{65} +(-0.0870114 - 0.295766i) q^{66} +(9.06930 + 5.23616i) q^{67} +(-1.30314 - 7.37211i) q^{68} +(0.0710991 - 1.12420i) q^{69} +(-1.32208 - 1.10888i) q^{70} -1.31296 q^{71} +(7.82233 - 3.28803i) q^{72} +0.515433 q^{73} +(7.00809 + 5.87794i) q^{74} +(-5.06443 - 3.36719i) q^{75} +(-9.41763 + 1.66472i) q^{76} +(0.109000 + 0.0629313i) q^{77} +(5.69140 - 5.97517i) q^{78} +(7.16498 + 12.4101i) q^{79} +(4.80716 + 0.843414i) q^{80} +(-2.40889 - 8.67164i) q^{81} +(-1.86301 - 5.11520i) q^{82} +(12.7247 - 7.34662i) q^{83} +(-1.38654 + 3.17451i) q^{84} +(-3.95536 - 2.28363i) q^{85} +(-0.0130877 + 0.0743167i) q^{86} +(0.339299 - 0.510322i) q^{87} +(-0.355993 + 0.000227263i) q^{88} -6.87704 q^{89} +(1.53297 - 4.94446i) q^{90} +3.36885i q^{91} +(-1.22245 - 0.444346i) q^{92} +(0.211576 - 3.34537i) q^{93} +(9.05943 + 1.59543i) q^{94} +(-2.91726 + 5.05284i) q^{95} +(-1.09933 - 9.73609i) q^{96} +(-3.75514 - 6.50410i) q^{97} +(-0.483972 - 1.32882i) q^{98} +(-0.0475703 + 0.374579i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.908808	+	1.08354i	−0.642625	+	0.766181i
$2$	−0.908808	+	1.08354i	−0.642625	+	0.766181i
$3$	1.55167	−	0.769621i	0.895858	−	0.444341i
$3$	1.55167	−	0.769621i	0.895858	−	0.444341i
$4$	−0.348135	−	1.96947i	−0.174067	−	0.984734i
$5$	−1.05668	−	0.610074i	−0.472561	−	0.272833i	0.244750	−	0.969586i	$-0.421294\pi$
$5$	−1.05668	−	0.610074i	−0.472561	−	0.272833i	−0.717311	+	0.696753i	$0.754627\pi$
$6$	−0.576254	+	2.38074i	−0.235255	+	0.971934i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	2.45039	+	1.41265i	0.866344	+	0.499447i
$9$	1.81537	−	2.38840i	0.605122	−	0.796133i
$10$	1.62136	−	0.590518i	0.512719	−	0.186738i
$11$	−0.109000	+	0.0629313i	−0.0328648	+	0.0189745i	−0.516342	−	0.856382i	$-0.672707\pi$
$11$	−0.109000	+	0.0629313i	−0.0328648	+	0.0189745i	0.483478	+	0.875357i	$0.339373\pi$
$12$	−2.05593	−	2.78803i	−0.593497	−	0.804836i
$13$	−2.91751	−	1.68442i	−0.809171	−	0.467175i	0.0374972	−	0.999297i	$-0.488061\pi$
$13$	−2.91751	−	1.68442i	−0.809171	−	0.467175i	−0.846668	+	0.532122i	$0.821395\pi$
$14$	1.39278	+	0.245279i	0.372236	+	0.0655536i
$15$	−2.10914	−	0.133392i	−0.544579	−	0.0344416i
$16$	−3.75760	+	1.37128i	−0.939401	+	0.342820i
$17$	3.74320			0.907859			0.453930	−	0.891038i	$-0.350022\pi$
$17$	3.74320			0.907859			0.453930	+	0.891038i	$0.350022\pi$
$18$	0.938113	+	4.13763i	0.221115	+	0.975248i
$19$		−	4.78182i		−	1.09702i	−0.836143	−	0.548512i	$-0.815195\pi$
$19$		−	4.78182i		−	1.09702i	0.836143	−	0.548512i	$-0.184805\pi$
$20$	−0.833654	+	2.29348i	−0.186411	+	0.512838i
$21$	−1.44235	−	0.958976i	−0.314746	−	0.209266i
$22$	0.0308715	−	0.175299i	0.00658182	−	0.0373739i
$23$	0.325176	−	0.563221i	0.0678038	−	0.117440i	−0.830130	−	0.557569i	$-0.811734\pi$
$23$	0.325176	−	0.563221i	0.0678038	−	0.117440i	0.897934	+	0.440130i	$0.145067\pi$
$24$	4.88941	+	0.306094i	0.998046	+	0.0624812i
$25$	−1.75562	−	3.04082i	−0.351124	−	0.608165i
$26$	4.47660	−	1.63043i	0.877934	−	0.319753i
$27$	0.978691	−	5.10315i	0.188349	−	0.982102i
$28$	−1.53154	+	1.28623i	−0.289434	+	0.243074i
$29$	0.306412	−	0.176907i	0.0568993	−	0.0328508i	−0.471281	−	0.881983i	$-0.656208\pi$
$29$	0.306412	−	0.176907i	0.0568993	−	0.0328508i	0.528180	+	0.849133i	$0.322875\pi$
$30$	2.06134	−	2.16412i	0.376348	−	0.395113i
$31$	0.967654	−	1.67603i	0.173796	−	0.301023i	−0.765948	−	0.642902i	$-0.777730\pi$
$31$	0.967654	−	1.67603i	0.173796	−	0.301023i	0.939744	+	0.341879i	$0.111063\pi$
$32$	1.92910	−	5.31776i	0.341020	−	0.940056i
$33$	−0.120699	+	0.181537i	−0.0210110	+	0.0316016i
$34$	−3.40185	+	4.05592i	−0.583413	+	0.695585i
$35$			1.22015i			0.206243i
$36$	−5.33586	−	2.74382i	−0.889311	−	0.457304i
$37$		−	6.46775i		−	1.06329i	−0.846967	−	0.531646i	$-0.821574\pi$
$37$		−	6.46775i		−	1.06329i	0.846967	−	0.531646i	$-0.178426\pi$
$38$	5.18131	+	4.34575i	0.840519	+	0.704974i
$39$	−5.82338	−	0.368296i	−0.932487	−	0.0589746i
$40$	−1.72746	−	2.98764i	−0.273135	−	0.472387i
$41$	−1.92471	+	3.33369i	−0.300589	+	0.520636i	−0.976270	−	0.216559i	$-0.930517\pi$
$41$	−1.92471	+	3.33369i	−0.300589	+	0.520636i	0.675680	+	0.737195i	$0.263850\pi$
$42$	2.34991	−	0.691321i	0.362599	−	0.106673i
$43$	0.0462098	−	0.0266792i	0.00704693	−	0.00406855i	−0.496472	−	0.868053i	$-0.665372\pi$
$43$	0.0462098	−	0.0266792i	0.00704693	−	0.00406855i	0.503519	+	0.863984i	$0.332038\pi$
$44$	0.161888	+	0.192764i	0.0244055	+	0.0290602i
$45$	−3.37536	+	1.41626i	−0.503169	+	0.211124i
$46$	0.314752	+	0.864202i	0.0464076	+	0.127420i
$47$	−3.25228	−	5.63312i	−0.474394	−	0.821675i	0.525176	−	0.850994i	$-0.323999\pi$
$47$	−3.25228	−	5.63312i	−0.474394	−	0.821675i	−0.999570	+	0.0293190i	$0.990666\pi$
$48$	−4.77520	+	5.01971i	−0.689241	+	0.724532i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	4.89039	+	0.861234i	0.691605	+	0.121797i
$51$	5.80821	−	2.88084i	0.813313	−	0.403399i
$52$	−2.30173	+	6.33234i	−0.319193	+	0.878137i
$53$			9.88039i			1.35718i	0.734519	+	0.678588i	$0.237408\pi$
$53$			9.88039i			1.35718i	−0.734519	+	0.678588i	$0.762592\pi$
$54$	4.64005	+	5.69824i	0.631430	+	0.775433i
$55$	0.153571			0.0207075
$56$	−0.00180565	−	2.82843i	−0.000241290	−	0.377964i
$57$	−3.68019	−	7.41981i	−0.487453	−	0.982777i
$58$	−0.0867832	+	0.492785i	−0.0113952	+	0.0647059i
$59$	11.2403	+	6.48957i	1.46336	+	0.844870i	0.999165	−	0.0408642i	$-0.0130111\pi$
$59$	11.2403	+	6.48957i	1.46336	+	0.844870i	0.464193	+	0.885734i	$0.346344\pi$
$60$	0.471556	+	4.20033i	0.0608776	+	0.542260i
$61$	0.775046	−	0.447473i	0.0992345	−	0.0572931i	−0.449561	−	0.893249i	$-0.648420\pi$
$61$	0.775046	−	0.447473i	0.0992345	−	0.0572931i	0.548796	+	0.835956i	$0.315086\pi$
$62$	0.936636	+	2.57168i	0.118953	+	0.326604i
$63$	−2.97610	−	0.377955i	−0.374953	−	0.0476178i
$64$	4.00884	+	6.92309i	0.501105	+	0.865386i
$65$	2.05524	+	3.55979i	0.254922	+	0.441537i
$66$	−0.0870114	−	0.295766i	−0.0107104	−	0.0364062i
$67$	9.06930	+	5.23616i	1.10799	+	0.639699i	0.938308	−	0.345800i	$-0.112392\pi$
$67$	9.06930	+	5.23616i	1.10799	+	0.639699i	0.169683	+	0.985499i	$0.445726\pi$
$68$	−1.30314	−	7.37211i	−0.158029	−	0.893999i
$69$	0.0710991	−	1.12420i	0.00855932	−	0.135337i
$70$	−1.32208	−	1.10888i	−0.158019	−	0.132537i
$71$	−1.31296			−0.155820			−0.0779099	−	0.996960i	$-0.524825\pi$
$71$	−1.31296			−0.155820			−0.0779099	+	0.996960i	$0.524825\pi$
$72$	7.82233	−	3.28803i	0.921870	−	0.387499i
$73$	0.515433			0.0603268			0.0301634	−	0.999545i	$-0.490397\pi$
$73$	0.515433			0.0603268			0.0301634	+	0.999545i	$0.490397\pi$
$74$	7.00809	+	5.87794i	0.814674	+	0.683297i
$75$	−5.06443	−	3.36719i	−0.584790	−	0.388810i
$76$	−9.41763	+	1.66472i	−1.08028	+	0.190956i
$77$	0.109000	+	0.0629313i	0.0124217	+	0.00717168i
$78$	5.69140	−	5.97517i	0.644424	−	0.676555i
$79$	7.16498	+	12.4101i	0.806123	+	1.39625i	0.915530	+	0.402249i	$0.131771\pi$
$79$	7.16498	+	12.4101i	0.806123	+	1.39625i	−0.109407	+	0.993997i	$0.534895\pi$
$80$	4.80716	+	0.843414i	0.537457	+	0.0942966i
$81$	−2.40889	−	8.67164i	−0.267654	−	0.963515i
$82$	−1.86301	−	5.11520i	−0.205735	−	0.564879i
$83$	12.7247	−	7.34662i	1.39672	−	0.806396i	0.402671	−	0.915345i	$-0.368082\pi$
$83$	12.7247	−	7.34662i	1.39672	−	0.806396i	0.994047	+	0.108949i	$0.0347484\pi$
$84$	−1.38654	+	3.17451i	−0.151284	+	0.346367i
$85$	−3.95536	−	2.28363i	−0.429019	−	0.247694i
$86$	−0.0130877	+	0.0743167i	−0.00141129	+	0.00801377i
$87$	0.339299	−	0.510322i	0.0363767	−	0.0547123i
$88$	−0.355993		0.000227263i	−0.0379490		2.42263e-5i
$89$	−6.87704			−0.728964			−0.364482	−	0.931210i	$-0.618754\pi$
$89$	−6.87704			−0.728964			−0.364482	+	0.931210i	$0.618754\pi$
$90$	1.53297	−	4.94446i	0.161589	−	0.521192i
$91$			3.36885i			0.353151i
$92$	−1.22245	−	0.444346i	−0.127449	−	0.0463263i
$93$	0.211576	−	3.34537i	0.0219394	−	0.346899i
$94$	9.05943	+	1.59543i	0.934409	+	0.164556i
$95$	−2.91726	+	5.05284i	−0.299305	+	0.518411i
$96$	−1.09933	−	9.73609i	−0.112200	−	0.993686i
$97$	−3.75514	−	6.50410i	−0.381277	−	0.660391i	0.609968	−	0.792426i	$-0.291182\pi$
$97$	−3.75514	−	6.50410i	−0.381277	−	0.660391i	−0.991245	+	0.132035i	$0.957849\pi$
$98$	−0.483972	−	1.32882i	−0.0488886	−	0.134231i
$99$	−0.0475703	+	0.374579i	−0.00478100	+	0.0376466i
$100$	−5.37761	+	4.51625i	−0.537761	+	0.451625i
$101$	3.34249	−	1.92979i	0.332590	−	0.192021i	−0.324400	−	0.945920i	$-0.605163\pi$
$101$	3.34249	−	1.92979i	0.332590	−	0.192021i	0.656990	+	0.753899i	$0.271829\pi$
$102$	−2.15703	+	8.91159i	−0.213578	+	0.882379i
$103$	−6.94555	+	12.0301i	−0.684366	+	1.18536i	0.289270	+	0.957248i	$0.406587\pi$
$103$	−6.94555	+	12.0301i	−0.684366	+	1.18536i	−0.973636	+	0.228109i	$0.926746\pi$
$104$	−4.76953	−	8.24891i	−0.467691	−	0.808872i
$105$	0.939051	+	1.89327i	0.0916420	+	0.184764i
$106$	−10.7058	−	8.97938i	−1.03984	−	0.872155i
$107$			16.0491i			1.55153i	0.631025	+	0.775763i	$0.282635\pi$
$107$			16.0491i			1.55153i	−0.631025	+	0.775763i	$0.717365\pi$
$108$	−10.3912	−	0.150915i	−0.999895	−	0.0145218i
$109$		−	5.29078i		−	0.506765i	−0.967366	−	0.253383i	$-0.918457\pi$
$109$		−	5.29078i		−	0.506765i	0.967366	−	0.253383i	$-0.0815432\pi$
$110$	−0.139566	+	0.166401i	−0.0133071	+	0.0158657i
$111$	−4.97772	−	10.0358i	−0.472464	−	0.952558i
$112$	3.06637	+	2.56854i	0.289744	+	0.242704i
$113$	−8.21459	+	14.2281i	−0.772763	+	1.33847i	0.163280	+	0.986580i	$0.447793\pi$
$113$	−8.21459	+	14.2281i	−0.772763	+	1.33847i	−0.936043	+	0.351885i	$0.885541\pi$
$114$	11.3843	+	2.75554i	1.06623	+	0.258080i
$115$	−0.687212	+	0.396762i	−0.0640829	+	0.0369983i
$116$	−0.455085	−	0.541881i	−0.0422536	−	0.0503124i
$117$	−9.31942	+	3.91032i	−0.861580	+	0.361509i
$118$	−17.2470	+	6.28154i	−1.58771	+	0.578263i
$119$	−1.87160	−	3.24171i	−0.171569	−	0.297167i
$120$	−4.97979	−	3.30634i	−0.454591	−	0.301826i
$121$	−5.49208	+	9.51256i	−0.499280	+	0.864778i
$122$	−0.219512	+	1.24646i	−0.0198737	+	0.112850i
$123$	−0.420834	+	6.65409i	−0.0379453	+	0.599979i
$124$	−3.63775	−	1.32228i	−0.326680	−	0.118744i
$125$			10.3850i			0.928860i
$126$	3.11423	−	2.88124i	0.277438	−	0.256681i
$127$	14.8378			1.31664			0.658322	−	0.752736i	$-0.271266\pi$
$127$	14.8378			1.31664			0.658322	+	0.752736i	$0.271266\pi$
$128$	−11.1447	−	1.94801i	−0.985065	−	0.172181i
$129$	0.0511695	−	0.0769615i	0.00450522	−	0.00677608i
$130$	−5.72501	−	1.00822i	−0.502117	−	0.0884265i
$131$	−4.68175	−	2.70301i	−0.409046	−	0.236163i	0.281334	−	0.959610i	$-0.409223\pi$
$131$	−4.68175	−	2.70301i	−0.409046	−	0.236163i	−0.690380	+	0.723447i	$0.742557\pi$
$132$	0.399552	+	0.174514i	0.0347765	+	0.0151895i
$133$	−4.14117	+	2.39091i	−0.359085	+	0.207318i
$134$	−13.9159	+	5.06832i	−1.20215	+	0.437836i
$135$	−4.14746	+	4.79532i	−0.356957	+	0.412715i
$136$	9.17230	+	5.28783i	0.786519	+	0.453428i
$137$	−8.40556	−	14.5589i	−0.718135	−	1.24385i	−0.961738	−	0.273972i	$-0.911663\pi$
$137$	−8.40556	−	14.5589i	−0.718135	−	1.24385i	0.243603	−	0.969875i	$-0.421671\pi$
$138$	1.15350	+	1.09872i	0.0981924	+	0.0935290i
$139$	3.72679	+	2.15166i	0.316102	+	0.182501i	0.649654	−	0.760230i	$-0.274914\pi$
$139$	3.72679	+	2.15166i	0.316102	+	0.182501i	−0.333552	+	0.942732i	$0.608247\pi$
$140$	2.40304	−	0.424776i	0.203094	−	0.0359001i
$141$	−9.38184	−	6.23772i	−0.790093	−	0.525311i
$142$	1.19323	−	1.42265i	0.100134	−	0.119386i
$143$	0.424011			0.0354576
$144$	−3.54627	+	11.4640i	−0.295522	+	0.955336i
$145$	−0.431705			−0.0358512
$146$	−0.468429	+	0.558494i	−0.0387675	+	0.0462213i
$147$	−0.109324	+	1.72860i	−0.00901690	+	0.142572i
$148$	−12.7380	+	2.25165i	−1.04706	+	0.185084i
$149$	−8.60681	−	4.96914i	−0.705097	−	0.407088i	0.104146	−	0.994562i	$-0.466789\pi$
$149$	−8.60681	−	4.96914i	−0.705097	−	0.407088i	−0.809243	+	0.587474i	$0.800122\pi$
$150$	8.25110	−	2.42739i	0.673699	−	0.198196i
$151$	8.33653	+	14.4393i	0.678417	+	1.17505i	0.975457	+	0.220188i	$0.0706670\pi$
$151$	8.33653	+	14.4393i	0.678417	+	1.17505i	−0.297040	+	0.954865i	$0.596000\pi$
$152$	6.75503	−	11.7173i	0.547905	−	0.950400i
$153$	6.79528	−	8.94025i	0.549366	−	0.722776i
$154$	−0.167249	+	0.0609140i	−0.0134773	+	0.00490859i
$155$	−2.04500	+	1.18068i	−0.164258	+	0.0948346i
$156$	1.30197	+	11.5972i	0.104241	+	0.928517i
$157$	−6.27857	−	3.62493i	−0.501084	−	0.289301i	0.228077	−	0.973643i	$-0.426756\pi$
$157$	−6.27857	−	3.62493i	−0.501084	−	0.289301i	−0.729161	+	0.684342i	$0.760090\pi$
$158$	−19.9585	−	3.51484i	−1.58781	−	0.279626i
$159$	7.60416	+	15.3311i	0.603049	+	1.21584i
$160$	−5.28267	+	4.44227i	−0.417631	+	0.351192i
$161$	−0.650351			−0.0512549
$162$	11.5853	+	5.27072i	0.910228	+	0.414107i
$163$		−	16.6659i		−	1.30538i	−0.757627	−	0.652688i	$-0.773641\pi$
$163$		−	16.6659i		−	1.30538i	0.757627	−	0.652688i	$-0.226359\pi$
$164$	7.23566	+	2.63008i	0.565010	+	0.205375i
$165$	0.238291	−	0.118191i	0.0185510	−	0.00920119i
$166$	−3.60395	+	20.4645i	−0.279720	+	1.58835i
$167$	11.9190	−	20.6444i	0.922323	−	1.59751i	0.126513	−	0.991965i	$-0.459621\pi$
$167$	11.9190	−	20.6444i	0.922323	−	1.59751i	0.795810	−	0.605546i	$-0.207045\pi$
$168$	−2.17962	−	4.38740i	−0.168161	−	0.338495i
$169$	−0.825439	−	1.42970i	−0.0634953	−	0.109977i
$170$	6.06907	−	2.21043i	0.465477	−	0.169532i
$171$	−11.4209	−	8.68075i	−0.873376	−	0.663833i
$172$	−0.0686311	−	0.0817207i	−0.00523308	−	0.00623115i
$173$	−4.40039	+	2.54057i	−0.334556	+	0.193156i	−0.657862	−	0.753139i	$-0.728539\pi$
$173$	−4.40039	+	2.54057i	−0.334556	+	0.193156i	0.323306	+	0.946294i	$0.395206\pi$
$174$	0.244599	+	0.831431i	0.0185430	+	0.0630306i
$175$	−1.75562	+	3.04082i	−0.132712	+	0.229865i
$176$	0.323283	−	0.385940i	0.0243684	−	0.0290914i
$177$	22.4357	+	1.41893i	1.68637	+	0.106654i
$178$	6.24991	−	7.45157i	0.468450	−	0.558519i
$179$			12.4612i			0.931398i	0.884943	+	0.465699i	$0.154197\pi$
$179$			12.4612i			0.931398i	−0.884943	+	0.465699i	$0.845803\pi$
$180$	3.96436	+	6.15461i	0.295486	+	0.458737i
$181$		−	2.98200i		−	0.221650i	−0.993840	−	0.110825i	$-0.964651\pi$
$181$		−	2.98200i		−	0.221650i	0.993840	−	0.110825i	$-0.0353494\pi$
$182$	−3.65029	−	3.06164i	−0.270578	−	0.226944i
$183$	0.858232	−	1.29082i	0.0634423	−	0.0954204i
$184$	1.59244	−	0.920752i	0.117396	−	0.0678788i
$185$	−3.94580	+	6.83433i	−0.290101	+	0.502470i
$186$	3.43257	+	3.26955i	0.251688	+	0.239735i
$187$	−0.408009	+	0.235564i	−0.0298366	+	0.0172262i
$188$	−9.96201	+	8.36635i	−0.726554	+	0.610179i
$189$	−4.90880	+	1.70401i	−0.357063	+	0.123948i
$190$	−2.82375	−	7.75305i	−0.204856	−	0.562465i
$191$	2.76187	+	4.78369i	0.199842	+	0.346136i	0.948477	−	0.316846i	$-0.102624\pi$
$191$	2.76187	+	4.78369i	0.199842	+	0.346136i	−0.748635	+	0.662982i	$0.769291\pi$
$192$	11.5486	+	7.65707i	0.833446	+	0.552601i
$193$	3.43038	−	5.94159i	0.246924	−	0.427685i	−0.715747	−	0.698360i	$-0.753914\pi$
$193$	3.43038	−	5.94159i	0.246924	−	0.427685i	0.962671	+	0.270675i	$0.0872469\pi$
$194$	10.4602	+	1.84212i	0.750998	+	0.132256i
$195$	5.92875	+	3.94186i	0.424567	+	0.282283i
$196$	1.87968	+	0.683240i	0.134263	+	0.0488029i
$197$			14.8883i			1.06075i	0.847764	+	0.530373i	$0.177948\pi$
$197$			14.8883i			1.06075i	−0.847764	+	0.530373i	$0.822052\pi$
$198$	−0.362640	−	0.391965i	−0.0257717	−	0.0278557i
$199$	25.9295			1.83809			0.919047	−	0.394147i	$-0.128960\pi$
$199$	25.9295			1.83809			0.919047	+	0.394147i	$0.128960\pi$
$200$	−0.00634005	−	9.93128i	−0.000448310	−	0.702248i
$201$	18.1024	+	1.14488i	1.27685	+	0.0807534i
$202$	−0.946673	+	5.37554i	−0.0666077	+	0.378222i
$203$	−0.306412	−	0.176907i	−0.0215059	−	0.0124164i
$204$	−7.69577	−	10.4362i	−0.538812	−	0.730678i
$205$	4.06760	−	2.34843i	0.284093	−	0.164021i
$206$	−6.72291	−	18.4588i	−0.468407	−	1.28609i
$207$	−0.754882	−	1.79910i	−0.0524679	−	0.125046i
$208$	13.2726	+	2.32868i	0.920293	+	0.161465i
$209$	0.300926	+	0.521219i	0.0208155	+	0.0360534i
$210$	−2.90486	−	0.703114i	−0.200454	−	0.0485195i
$211$	−9.92024	−	5.72746i	−0.682938	−	0.394294i	0.118023	−	0.993011i	$-0.462344\pi$
$211$	−9.92024	−	5.72746i	−0.682938	−	0.394294i	−0.800961	+	0.598717i	$0.795678\pi$
$212$	19.4591	−	3.43971i	1.33646	−	0.236240i
$213$	−2.03728	+	1.01048i	−0.139592	+	0.0692371i
$214$	−17.3899	−	14.5856i	−1.18875	−	0.997048i
$215$	−0.0651052			−0.00444014
$216$	9.60714	−	11.1222i	0.653683	−	0.756768i
$217$	−1.93531			−0.131377
$218$	5.73280	+	4.80831i	0.388274	+	0.325660i
$219$	0.799782	−	0.396688i	0.0540442	−	0.0268057i
$220$	−0.0534633	−	0.302453i	−0.00360450	−	0.0203914i
$221$	−10.9208	−	6.30513i	−0.734613	−	0.424129i
$222$	15.3980	+	3.72706i	1.03345	+	0.250144i
$223$	−6.46864	−	11.2040i	−0.433172	−	0.750276i	0.563972	−	0.825794i	$-0.309272\pi$
$223$	−6.46864	−	11.2040i	−0.433172	−	0.750276i	−0.997144	+	0.0755174i	$0.975939\pi$
$224$	−5.56987	+	0.988229i	−0.372152	+	0.0660288i
$225$	−10.4498	−	1.32709i	−0.696653	−	0.0884726i
$226$	−7.95126	−	21.8315i	−0.528910	−	1.45221i
$227$	8.82691	−	5.09622i	0.585863	−	0.338248i	−0.177597	−	0.984103i	$-0.556832\pi$
$227$	8.82691	−	5.09622i	0.585863	−	0.338248i	0.763460	+	0.645855i	$0.223499\pi$
$228$	−13.3319	+	9.83110i	−0.882924	+	0.651080i
$229$	25.2758	+	14.5930i	1.67027	+	0.964333i	0.967483	+	0.252936i	$0.0813962\pi$
$229$	25.2758	+	14.5930i	1.67027	+	0.964333i	0.702791	+	0.711397i	$0.251937\pi$
$230$	0.194635	−	1.10521i	0.0128339	−	0.0728751i
$231$	0.217566	+	0.0137598i	0.0143148	+	0.000905329i
$232$	1.00074		0.000638863i	0.0657016		4.19434e-5i
$233$	13.7754			0.902458			0.451229	−	0.892408i	$-0.350986\pi$
$233$	13.7754			0.902458			0.451229	+	0.892408i	$0.350986\pi$
$234$	4.23256	−	13.6517i	0.276691	−	0.892441i
$235$			7.93653i			0.517722i
$236$	8.86787	−	24.3966i	0.577249	−	1.58808i
$237$	20.6688	+	13.7421i	1.34258	+	0.892644i
$238$	5.21345	+	0.918129i	0.337938	+	0.0595135i
$239$	−7.95536	+	13.7791i	−0.514589	+	0.891295i	0.485267	+	0.874366i	$0.338722\pi$
$239$	−7.95536	+	13.7791i	−0.514589	+	0.891295i	−0.999857	+	0.0169292i	$0.994611\pi$
$240$	8.10825	−	2.39099i	0.523385	−	0.154338i
$241$	4.28468	+	7.42129i	0.276001	+	0.478047i	0.970387	−	0.241555i	$-0.0776574\pi$
$241$	4.28468	+	7.42129i	0.276001	+	0.478047i	−0.694386	+	0.719602i	$0.744324\pi$
$242$	−5.31603	−	14.5960i	−0.341727	−	0.938267i
$243$	−10.4117	−	11.6016i	−0.667909	−	0.744243i
$244$	−1.15110	−	1.37065i	−0.0736919	−	0.0877467i
$245$	1.05668	−	0.610074i	0.0675087	−	0.0389762i
$246$	−6.82754	−	6.50329i	−0.435308	−	0.414635i
$247$	−8.05460	+	13.9510i	−0.512502	+	0.887679i
$248$	4.73877	−	2.73997i	0.300912	−	0.173988i
$249$	14.0905	−	21.1927i	0.892947	−	1.34304i
$250$	−11.2526	−	9.43795i	−0.711675	−	0.596908i
$251$			7.11281i			0.448957i	0.974479	+	0.224478i	$0.0720678\pi$
$251$			7.11281i			0.448957i	−0.974479	+	0.224478i	$0.927932\pi$
$252$	0.291713	+	5.99290i	0.0183762	+	0.377517i
$253$			0.0818548i			0.00514617i
$254$	−13.4847	+	16.0774i	−0.846108	+	1.00879i
$255$	−7.89494	−	0.499311i	−0.494401	−	0.0312681i
$256$	12.2392	−	10.3055i	0.764949	−	0.644091i
$257$	−7.91783	+	13.7141i	−0.493900	+	0.855461i	−0.999975	−	0.00702891i	$-0.997763\pi$
$257$	−7.91783	+	13.7141i	−0.493900	+	0.855461i	0.506075	+	0.862490i	$0.331096\pi$
$258$	0.0368878	+	0.125388i	0.00229654	+	0.00780629i
$259$	−5.60123	+	3.23387i	−0.348044	+	0.200943i
$260$	6.29539	−	5.28702i	0.390423	−	0.327887i
$261$	0.133726	−	1.05298i	0.00827741	−	0.0651781i
$262$	7.18364	−	2.61636i	0.443807	−	0.161639i
$263$	−10.7322	−	18.5888i	−0.661778	−	1.14623i	−0.980148	−	0.198266i	$-0.936469\pi$
$263$	−10.7322	−	18.5888i	−0.661778	−	1.14623i	0.318370	−	0.947966i	$-0.396864\pi$
$264$	−0.552209	+	0.274332i	−0.0339861	+	0.0168840i
$265$	6.02777	−	10.4404i	0.370283	−	0.641349i
$266$	1.17288	−	6.66002i	0.0719139	−	0.408352i
$267$	−10.6709	+	5.29271i	−0.653048	+	0.323909i
$268$	7.15512	−	19.6846i	0.437068	−	1.20243i
$269$		−	25.7604i		−	1.57064i	−0.619092	−	0.785318i	$-0.712499\pi$
$269$		−	25.7604i		−	1.57064i	0.619092	−	0.785318i	$-0.287501\pi$
$270$	−1.42669	−	8.85198i	−0.0868257	−	0.538715i
$271$	27.4790			1.66923			0.834614	−	0.550836i	$-0.185691\pi$
$271$	27.4790			1.66923			0.834614	+	0.550836i	$0.185691\pi$
$272$	−14.0655	+	5.13297i	−0.852844	+	0.311232i
$273$	2.59274	+	5.22734i	0.156919	+	0.316373i
$274$	23.4142	+	4.12342i	1.41450	+	0.249105i
$275$	0.382726	+	0.220967i	0.0230792	+	0.0133248i
$276$	−2.23882	+	0.251344i	−0.134761	+	0.0151291i
$277$	24.7384	−	14.2827i	1.48639	−	0.858167i	0.486508	−	0.873676i	$-0.338270\pi$
$277$	24.7384	−	14.2827i	1.48639	−	0.858167i	0.999880	+	0.0155093i	$0.00493698\pi$
$278$	−5.71835	+	2.08269i	−0.342964	+	0.124911i
$279$	−2.24637	−	5.35375i	−0.134487	−	0.320520i
$280$	−1.72364	+	2.98984i	−0.103007	+	0.178677i
$281$	10.7682	+	18.6511i	0.642379	+	1.11263i	0.984900	+	0.173124i	$0.0553860\pi$
$281$	10.7682	+	18.6511i	0.642379	+	1.11263i	−0.342521	+	0.939510i	$0.611281\pi$
$282$	15.2851	−	4.49674i	0.910217	−	0.267777i
$283$	15.2611	+	8.81102i	0.907180	+	0.523761i	0.879523	−	0.475857i	$-0.157862\pi$
$283$	15.2611	+	8.81102i	0.907180	+	0.523761i	0.0276576	+	0.999617i	$0.491195\pi$
$284$	0.457087	+	2.58583i	0.0271231	+	0.153441i
$285$	−0.637854	+	10.0855i	−0.0377832	+	0.597416i
$286$	−0.385345	+	0.459435i	−0.0227859	+	0.0271670i
$287$	3.84942			0.227224
$288$	−9.19890	−	14.2611i	−0.542050	−	0.840346i
$289$	−2.98846			−0.175792
$290$	0.392337	−	0.467772i	0.0230388	−	0.0274685i
$291$	−10.8324	−	7.20219i	−0.635009	−	0.422200i
$292$	−0.179440	−	1.01513i	−0.0105009	−	0.0594059i
$293$	0.484198	+	0.279552i	0.0282871	+	0.0163316i	0.514077	−	0.857744i	$-0.328135\pi$
$293$	0.484198	+	0.279552i	0.0282871	+	0.0163316i	−0.485790	+	0.874076i	$0.661468\pi$
$294$	−1.77366	−	1.68942i	−0.103442	−	0.0985290i
$295$	−7.91823	−	13.7148i	−0.461017	−	0.798505i
$296$	9.13666	−	15.8485i	0.531058	−	0.921176i
$297$	0.214470	+	0.617835i	0.0124448	+	0.0358504i
$298$	13.2062	−	4.80986i	0.765016	−	0.278627i
$299$	−1.89740	+	1.09547i	−0.109730	+	0.0633525i
$300$	−4.86848	+	11.1465i	−0.281082	+	0.643541i
$301$	−0.0462098	−	0.0266792i	−0.00266349	−	0.00153777i
$302$	−23.2219	−	4.08955i	−1.33627	−	0.235327i
$303$	3.70124	−	5.56684i	0.212631	−	0.319807i
$304$	6.55721	+	17.9682i	0.376082	+	1.03055i
$305$	−1.09197			−0.0625258
$306$	3.51154	+	15.4880i	0.200742	+	0.885387i
$307$		−	4.54636i		−	0.259474i	−0.991548	−	0.129737i	$-0.958587\pi$
$307$		−	4.54636i		−	0.259474i	0.991548	−	0.129737i	$-0.0414133\pi$
$308$	0.0859944	−	0.236581i	0.00489998	−	0.0134804i
$309$	−1.51863	+	24.0121i	−0.0863920	+	1.36600i
$310$	0.579193	−	3.28886i	0.0328960	−	0.186795i
$311$	−4.40555	+	7.63064i	−0.249816	+	0.432694i	−0.963475	−	0.267800i	$-0.913703\pi$
$311$	−4.40555	+	7.63064i	−0.249816	+	0.432694i	0.713659	+	0.700494i	$0.247037\pi$
$312$	−13.7493	−	9.12886i	−0.778400	−	0.516820i
$313$	−11.3743	−	19.7008i	−0.642911	−	1.11355i	−0.984780	−	0.173806i	$-0.944393\pi$
$313$	−11.3743	−	19.7008i	−0.642911	−	1.11355i	0.341869	−	0.939748i	$-0.388940\pi$
$314$	9.63379	−	3.50874i	0.543666	−	0.198009i
$315$	2.91420	+	2.21502i	0.164196	+	0.124802i
$316$	21.9469	−	18.4316i	1.23461	−	1.03686i
$317$	−15.5436	+	8.97409i	−0.873015	+	0.504035i	−0.868349	−	0.495954i	$-0.834819\pi$
$317$	−15.5436	+	8.97409i	−0.873015	+	0.504035i	−0.00466582	+	0.999989i	$0.501485\pi$
$318$	−23.5227	−	5.69361i	−1.31909	−	0.319282i
$319$	−0.0222660	+	0.0385658i	−0.00124665	+	0.00215927i
$320$	−0.0124629	−	9.76117i	−0.000696698	−	0.545666i
$321$	12.3517	+	24.9029i	0.689406	+	1.38995i
$322$	0.591045	−	0.704684i	0.0329376	−	0.0392705i
$323$		−	17.8993i		−	0.995943i
$324$	−16.2399	+	7.76312i	−0.902216	+	0.431285i
$325$			11.8288i			0.656145i
$326$	18.0583	+	15.1461i	1.00015	+	0.838867i
$327$	−4.07190	−	8.20956i	−0.225177	−	0.453990i
$328$	−9.42563	+	5.44992i	−0.520444	+	0.300921i
$329$	−3.25228	+	5.63312i	−0.179304	+	0.310564i
$330$	−0.0884958	+	0.365613i	−0.00487153	+	0.0201263i
$331$	−13.5687	+	7.83387i	−0.745801	+	0.430588i	−0.824175	−	0.566336i	$-0.808361\pi$
$331$	−13.5687	+	7.83387i	−0.745801	+	0.430588i	0.0783736	+	0.996924i	$0.475027\pi$
$332$	−18.8988	−	22.5033i	−1.03721	−	1.23503i
$333$	−15.4476	−	11.7413i	−0.846521	−	0.643421i
$334$	11.5370	+	31.6766i	0.631275	+	1.73327i
$335$	−6.38889	−	11.0659i	−0.349062	−	0.604594i
$336$	6.73479	+	1.62559i	0.367413	+	0.0886833i
$337$	−8.35049	+	14.4635i	−0.454880	+	0.787875i	−0.998681	−	0.0513387i	$-0.983651\pi$
$337$	−8.35049	+	14.4635i	−0.454880	+	0.787875i	0.543801	+	0.839214i	$0.316985\pi$
$338$	2.29931	+	0.404926i	0.125066	+	0.0220251i
$339$	−1.79610	+	28.3994i	−0.0975510	+	1.54244i
$340$	−3.12053	+	8.58496i	−0.169235	+	0.465585i
$341$			0.243583i			0.0131908i
$342$	19.7854	−	4.48589i	1.06987	−	0.242569i
$343$	1.00000			0.0539949
$344$	0.150921		9.63465e-5i	0.00813709		5.19466e-6i
$345$	−0.760971	+	1.14454i	−0.0409693	+	0.0616198i
$346$	1.24630	−	7.07691i	0.0670013	−	0.380457i
$347$	−4.06391	−	2.34630i	−0.218162	−	0.125956i	0.386937	−	0.922106i	$-0.373533\pi$
$347$	−4.06391	−	2.34630i	−0.218162	−	0.125956i	−0.605099	+	0.796150i	$0.706866\pi$
$348$	−1.12319	−	0.490578i	−0.0602091	−	0.0262977i
$349$	19.7945	−	11.4284i	1.05958	−	0.611747i	0.134262	−	0.990946i	$-0.457134\pi$
$349$	19.7945	−	11.4284i	1.05958	−	0.611747i	0.925315	+	0.379199i	$0.123800\pi$
$350$	−1.69934	−	4.66582i	−0.0908337	−	0.249398i
$351$	−11.4512	+	13.2399i	−0.611220	+	0.706696i
$352$	0.124381	+	0.701037i	0.00662953	+	0.0373654i
$353$	10.3132	+	17.8629i	0.548914	+	0.950747i	0.998349	+	0.0574343i	$0.0182920\pi$
$353$	10.3132	+	17.8629i	0.548914	+	0.950747i	−0.449435	+	0.893313i	$0.648375\pi$
$354$	−21.9272	+	23.0205i	−1.16542	+	1.22353i
$355$	1.38738	+	0.801003i	0.0736344	+	0.0425128i
$356$	2.39413	+	13.5441i	0.126889	+	0.717836i
$357$	−5.39899	−	3.58964i	−0.285745	−	0.189984i
$358$	−13.5023	−	11.3249i	−0.713619	−	0.598539i
$359$	7.54392			0.398153			0.199076	−	0.979984i	$-0.436206\pi$
$359$	7.54392			0.398153			0.199076	+	0.979984i	$0.436206\pi$
$360$	−10.2716	−	1.29780i	−0.541363	−	0.0684002i
$361$	−3.86576			−0.203461
$362$	3.23113	+	2.71007i	0.169824	+	0.142438i
$363$	−1.20083	+	18.9872i	−0.0630274	+	0.996569i
$364$	6.63483	−	1.17281i	0.347760	−	0.0614720i
$365$	−0.544647	−	0.314452i	−0.0285081	−	0.0164592i
$366$	0.618695	+	2.10304i	0.0323397	+	0.109928i
$367$	−5.41216	−	9.37414i	−0.282513	−	0.489326i	0.689490	−	0.724295i	$-0.257835\pi$
$367$	−5.41216	−	9.37414i	−0.282513	−	0.489326i	−0.972003	+	0.234969i	$0.924501\pi$
$368$	−0.449548	+	2.56227i	−0.0234343	+	0.133567i
$369$	4.46814	+	10.6488i	0.232602	+	0.554357i
$370$	−3.81932	−	10.4866i	−0.198557	−	0.545170i
$371$	8.55667	−	4.94020i	0.444240	−	0.256482i
$372$	−6.66225	+	0.747947i	−0.345422	+	0.0387792i
$373$	−23.8455	−	13.7672i	−1.23467	−	0.712840i	−0.266674	−	0.963787i	$-0.585925\pi$
$373$	−23.8455	−	13.7672i	−1.23467	−	0.712840i	−0.968001	+	0.250947i	$0.919258\pi$
$374$	0.115558	−	0.656179i	0.00597536	−	0.0339302i
$375$	7.99249	+	16.1141i	0.412731	+	0.832126i
$376$	−0.0117449	−	18.3977i	−0.000605699	−	0.948788i
$377$	−1.19194			−0.0613883
$378$	2.61480	−	6.86752i	0.134491	−	0.353227i
$379$		−	9.33714i		−	0.479617i	−0.970820	−	0.239808i	$-0.922915\pi$
$379$		−	9.33714i		−	0.479617i	0.970820	−	0.239808i	$-0.0770846\pi$
$380$	10.9670	+	3.98638i	0.562596	+	0.204497i
$381$	23.0234	−	11.4195i	1.17953	−	0.585039i
$382$	−7.69335	−	1.35486i	−0.393626	−	0.0693205i
$383$	10.5907	−	18.3437i	0.541162	−	0.937320i	−0.457676	−	0.889119i	$-0.651318\pi$
$383$	10.5907	−	18.3437i	0.541162	−	0.937320i	0.998838	−	0.0482005i	$-0.0153486\pi$
$384$	−18.7922	+	5.55456i	−0.958985	+	0.283455i
$385$	−0.0767854	−	0.132996i	−0.00391335	−	0.00677812i
$386$	3.32041	+	9.11673i	0.169005	+	0.464029i
$387$	0.0201671	−	0.158800i	0.00102515	−	0.00807226i
$388$	−11.5023	+	9.65994i	−0.583942	+	0.490409i
$389$	13.1070	−	7.56731i	0.664549	−	0.383678i	−0.129459	−	0.991585i	$-0.541324\pi$
$389$	13.1070	−	7.56731i	0.664549	−	0.383678i	0.794008	+	0.607907i	$0.207991\pi$
$390$	−9.65928	+	2.84167i	−0.489117	+	0.143893i
$391$	1.21720	−	2.10825i	0.0615563	−	0.106619i
$392$	−2.44859	+	1.41578i	−0.123672	+	0.0715075i
$393$	−9.34483	−	0.591008i	−0.471384	−	0.0298124i
$394$	−16.1321	−	13.5306i	−0.812724	−	0.681662i
$395$		−	17.4847i		−	0.879749i
$396$	0.754282	−	0.0367157i	0.0379041	−	0.00184503i
$397$			33.3037i			1.67146i	0.549137	+	0.835732i	$0.314956\pi$
$397$			33.3037i			1.67146i	−0.549137	+	0.835732i	$0.685044\pi$
$398$	−23.5650	+	28.0958i	−1.18121	+	1.40831i
$399$	−4.58565	+	6.89704i	−0.229569	+	0.345284i
$400$	10.7667	+	9.01876i	0.538337	+	0.450938i
$401$	−14.3899	+	24.9241i	−0.718599	+	1.24465i	0.242956	+	0.970037i	$0.421883\pi$
$401$	−14.3899	+	24.9241i	−0.718599	+	1.24465i	−0.961555	+	0.274612i	$0.911451\pi$
$402$	−17.6922	+	18.5743i	−0.882405	+	0.926402i
$403$	−5.64628	+	3.25988i	−0.281261	+	0.162386i
$404$	−4.96429	−	5.91110i	−0.246983	−	0.294088i
$405$	−2.74492	+	10.6327i	−0.136396	+	0.528345i
$406$	0.470156	−	0.171236i	0.0233335	−	0.00849831i
$407$	0.407024	+	0.704985i	0.0201754	+	0.0349448i
$408$	18.3020	+	1.14577i	0.906085	+	0.0567241i
$409$	17.6401	−	30.5536i	0.872249	−	1.51078i	0.0125846	−	0.999921i	$-0.495994\pi$
$409$	17.6401	−	30.5536i	0.872249	−	1.51078i	0.859665	−	0.510859i	$-0.170673\pi$
$410$	−1.15204	+	6.54169i	−0.0568953	+	0.323071i
$411$	−24.2475	−	16.1215i	−1.19604	−	0.795213i
$412$	26.1108	+	9.49096i	1.28639	+	0.467586i
$413$		−	12.9791i		−	0.638662i
$414$	2.63545	+	0.817090i	0.129525	+	0.0401578i
$415$	−17.9279			−0.880047
$416$	−14.5855	+	12.2652i	−0.715114	+	0.601350i
$417$	7.43871	+	0.470457i	0.364275	+	0.0230384i
$418$	−0.838247	−	0.147622i	−0.0410000	−	0.00722041i
$419$	−3.67582	−	2.12224i	−0.179576	−	0.103678i	0.407518	−	0.913197i	$-0.366395\pi$
$419$	−3.67582	−	2.12224i	−0.179576	−	0.103678i	−0.587093	+	0.809519i	$0.699728\pi$
$420$	3.40181	−	2.50854i	0.165991	−	0.122404i
$421$	−1.81919	+	1.05031i	−0.0886619	+	0.0511889i	−0.543675	−	0.839296i	$-0.682968\pi$
$421$	−1.81919	+	1.05031i	−0.0886619	+	0.0511889i	0.455014	+	0.890485i	$0.349634\pi$
$422$	15.2215	−	5.54386i	0.740973	−	0.269871i
$423$	−19.3582	−	2.45843i	−0.941228	−	0.119533i
$424$	−13.9575	+	24.2108i	−0.677838	+	1.17578i
$425$	−6.57163	−	11.3824i	−0.318771	−	0.552128i
$426$	0.756599	−	3.12582i	0.0366573	−	0.151447i
$427$	−0.775046	−	0.447473i	−0.0375071	−	0.0216547i
$428$	31.6082	−	5.58725i	1.52784	−	0.270070i
$429$	0.657926	−	0.326328i	0.0317650	−	0.0157553i
$430$	0.0591682	−	0.0705444i	0.00285334	−	0.00340195i
$431$	−9.47578			−0.456432			−0.228216	−	0.973611i	$-0.573289\pi$
$431$	−9.47578			−0.456432			−0.228216	+	0.973611i	$0.573289\pi$
$432$	3.32032	+	20.5177i	0.159749	+	0.987158i
$433$	−30.9026			−1.48508			−0.742542	−	0.669800i	$-0.766380\pi$
$433$	−30.9026			−1.48508			−0.742542	+	0.669800i	$0.766380\pi$
$434$	1.75882	−	2.09699i	0.0844263	−	0.100659i
$435$	−0.669865	+	0.332249i	−0.0321175	+	0.0159301i
$436$	−10.4200	+	1.84191i	−0.499029	+	0.0882113i
$437$	−2.69322	−	1.55493i	−0.128834	−	0.0743824i
$438$	−0.297020	+	1.22711i	−0.0141922	+	0.0586337i
$439$	6.10595	+	10.5758i	0.291421	+	0.504756i	0.974146	−	0.225919i	$-0.0725386\pi$
$439$	6.10595	+	10.5758i	0.291421	+	0.504756i	−0.682725	+	0.730675i	$0.739205\pi$
$440$	0.376309	+	0.216942i	0.0179398	+	0.0103423i
$441$	1.16073	+	2.76635i	0.0552729	+	0.131731i
$442$	16.7568	−	6.10302i	0.797040	−	0.290291i
$443$	−27.5846	+	15.9260i	−1.31059	+	0.756667i	−0.982193	−	0.187874i	$-0.939840\pi$
$443$	−27.5846	+	15.9260i	−1.31059	+	0.756667i	−0.328393	+	0.944541i	$0.606507\pi$
$444$	−18.0323	+	13.2973i	−0.855775	+	0.631060i
$445$	7.26682	+	4.19550i	0.344480	+	0.198886i
$446$	18.0188	+	3.17325i	0.853215	+	0.150258i
$447$	−17.1793	−	1.08649i	−0.812553	−	0.0513894i
$448$	3.99115	−	6.93330i	0.188564	−	0.327568i
$449$	17.0206			0.803254			0.401627	−	0.915803i	$-0.368445\pi$
$449$	17.0206			0.803254			0.401627	+	0.915803i	$0.368445\pi$
$450$	10.9348	−	10.1167i	0.515472	−	0.476907i
$451$		−	0.484498i		−	0.0228141i
$452$	30.8815	+	11.2251i	1.45254	+	0.527983i
$453$	24.0483	+	15.9891i	1.12989	+	0.751232i
$454$	−2.49999	+	14.1958i	−0.117331	+	0.666244i
$455$	2.05524	−	3.55979i	0.0963514	−	0.166885i
$456$	1.46368	−	23.3802i	0.0685433	−	1.09488i
$457$	−14.2048	−	24.6034i	−0.664473	−	1.15090i	−0.979428	−	0.201794i	$-0.935323\pi$
$457$	−14.2048	−	24.6034i	−0.664473	−	1.15090i	0.314955	−	0.949107i	$-0.398011\pi$
$458$	−38.7830	+	14.1252i	−1.81221	+	0.660028i
$459$	3.66343	−	19.1021i	0.170994	−	0.891610i
$460$	1.02065	+	1.21532i	0.0475882	+	0.0566644i
$461$	14.5534	−	8.40240i	0.677819	−	0.391339i	−0.121214	−	0.992626i	$-0.538679\pi$
$461$	14.5534	−	8.40240i	0.677819	−	0.391339i	0.799033	+	0.601288i	$0.205345\pi$
$462$	−0.212635	+	0.223237i	−0.00989267	+	0.0103859i
$463$	15.4882	−	26.8263i	0.719796	−	1.24672i	−0.241285	−	0.970454i	$-0.577569\pi$
$463$	15.4882	−	26.8263i	0.719796	−	1.24672i	0.961081	−	0.276268i	$-0.0890978\pi$
$464$	−0.908786	+	1.08492i	−0.0421893	+	0.0503663i
$465$	−2.26449	+	3.40590i	−0.105013	+	0.157945i
$466$	−12.5192	+	14.9263i	−0.579941	+	0.691446i
$467$		−	28.2877i		−	1.30900i	−0.756063	−	0.654498i	$-0.772880\pi$
$467$		−	28.2877i		−	1.30900i	0.756063	−	0.654498i	$-0.227120\pi$
$468$	10.9457	+	16.9930i	0.505963	+	0.785500i
$469$		−	10.4723i		−	0.483567i
$470$	−8.59958	−	7.21278i	−0.396669	−	0.332701i
$471$	−12.5321	−	0.792585i	−0.577449	−	0.0365204i
$472$	18.3756	+	31.7805i	0.845804	+	1.46282i
$473$	−0.00335792	+	0.00581608i	−0.000154397	+	0.000267424i
$474$	−33.6741	+	9.90660i	−1.54670	+	0.455025i
$475$	−14.5407	+	8.39505i	−0.667171	+	0.385191i
$476$	−5.73286	+	4.81460i	−0.262765	+	0.220677i
$477$	23.5983	+	17.9365i	1.08049	+	0.821257i
$478$	−7.70035	−	21.1425i	−0.352206	−	0.967037i
$479$	−13.6160	−	23.5836i	−0.622130	−	1.07756i	−0.989088	−	0.147324i	$-0.952934\pi$
$479$	−13.6160	−	23.5836i	−0.622130	−	1.07756i	0.366958	−	0.930238i	$-0.380399\pi$
$480$	−4.77810	+	10.9586i	−0.218089	+	0.500189i
$481$	−10.8944	+	18.8697i	−0.496743	+	0.860384i
$482$	−11.9353	−	2.10189i	−0.543636	−	0.0957384i
$483$	−1.00913	+	0.500524i	−0.0459171	+	0.0227746i
$484$	20.6467	+	7.50482i	0.938485	+	0.341128i
$485$			9.16366i			0.416100i
$486$	22.0331	−	0.737881i	0.999440	−	0.0334709i
$487$	−14.5002			−0.657068			−0.328534	−	0.944492i	$-0.606554\pi$
$487$	−14.5002			−0.657068			−0.328534	+	0.944492i	$0.606554\pi$
$488$	2.53129	−	0.00161596i	0.114586	−	7.31509e-5i
$489$	−12.8265	−	25.8600i	−0.580032	−	1.16943i
$490$	−0.299277	+	1.69940i	−0.0135200	+	0.0767710i
$491$	−20.1776	−	11.6495i	−0.910603	−	0.525737i	−0.0299778	−	0.999551i	$-0.509544\pi$
$491$	−20.1776	−	11.6495i	−0.910603	−	0.525737i	−0.880625	+	0.473814i	$0.842877\pi$
$492$	13.2515	−	1.48770i	0.597425	−	0.0670707i
$493$	1.14696	−	0.662198i	0.0516565	−	0.0298239i
$494$	−7.79641	−	21.4063i	−0.350777	−	0.963114i
$495$	0.278787	−	0.366788i	0.0125306	−	0.0164859i
$496$	−1.33776	+	7.62477i	−0.0600673	+	0.342362i
$497$	0.656481	+	1.13706i	0.0294472	+	0.0510040i
$498$	10.1577	+	34.5278i	0.455179	+	1.54723i
$499$	8.60972	+	4.97082i	0.385424	+	0.222525i	0.680175	−	0.733049i	$-0.261904\pi$
$499$	8.60972	+	4.97082i	0.385424	+	0.222525i	−0.294752	+	0.955574i	$0.595237\pi$
$500$	20.4529	−	3.61537i	0.914680	−	0.161684i
$501$	2.60608	−	41.2065i	0.116431	−	1.84097i
$502$	−7.70704	−	6.46418i	−0.343982	−	0.288511i
$503$	26.9150			1.20008			0.600039	−	0.799971i	$-0.295152\pi$
$503$	26.9150			1.20008			0.600039	+	0.799971i	$0.295152\pi$
$504$	−6.75869	−	5.13032i	−0.301056	−	0.228523i
$505$	−4.70925			−0.209559
$506$	−0.0886933	−	0.0743904i	−0.00394290	−	0.00330706i
$507$	−2.38114	−	1.58315i	−0.105750	−	0.0703102i
$508$	−5.16556	−	29.2226i	−0.229185	−	1.29654i
$509$	29.0784	+	16.7884i	1.28888	+	0.744133i	0.978454	−	0.206465i	$-0.0661960\pi$
$509$	29.0784	+	16.7884i	1.28888	+	0.744133i	0.310423	+	0.950599i	$0.399529\pi$
$510$	7.71602	−	8.10074i	0.341671	−	0.358707i
$511$	−0.257716	−	0.446378i	−0.0114007	−	0.0197466i
$512$	0.0433355	+	22.6274i	0.00191518	+	0.999998i
$513$	−24.4023	−	4.67992i	−1.07739	−	0.206623i
$514$	−7.66402	−	21.0428i	−0.338045	−	0.928157i
$515$	14.6784	−	8.47460i	0.646809	−	0.373436i
$516$	−0.169387	−	0.0739837i	−0.00745685	−	0.00325695i
$517$	0.708998	+	0.409340i	0.0311817	+	0.0180028i
$518$	1.58640	−	9.00815i	0.0697026	−	0.395796i
$519$	−4.87269	+	7.32876i	−0.213887	+	0.321697i
$520$	0.00742209	+	11.6262i	0.000325480	+	0.509843i
$521$	15.2205			0.666820			0.333410	−	0.942782i	$-0.391801\pi$
$521$	15.2205			0.666820			0.333410	+	0.942782i	$0.391801\pi$
$522$	1.01942	+	1.10186i	0.0446190	+	0.0482270i
$523$		−	13.8481i		−	0.605533i	−0.953065	−	0.302767i	$-0.902090\pi$
$523$		−	13.8481i		−	0.605533i	0.953065	−	0.302767i	$-0.0979103\pi$
$524$	−3.69361	+	10.1616i	−0.161356	+	0.443910i
$525$	−0.383863	+	6.06952i	−0.0167532	+	0.264896i
$526$	29.8953	+	5.26479i	1.30350	+	0.229556i
$527$	3.62212	−	6.27370i	0.157782	−	0.273287i
$528$	0.204601	−	0.847658i	0.00890412	−	0.0368896i
$529$	11.2885	+	19.5523i	0.490805	+	0.850100i
$530$	5.83455	+	16.0197i	0.253437	+	0.695850i
$531$	35.9049	−	15.0653i	1.55814	−	0.653777i
$532$	6.15050	+	7.32355i	0.266658	+	0.317516i
$533$	11.2307	−	6.48405i	0.486456	−	0.280855i
$534$	3.96292	−	16.3724i	0.171492	−	0.708505i
$535$	9.79114	−	16.9587i	0.423308	−	0.733191i
$536$	14.8265	+	25.6424i	0.640406	+	1.10758i
$537$	9.59044	+	19.3358i	0.413858	+	0.834400i
$538$	27.9125	+	23.4112i	1.20339	+	1.00933i
$539$		−	0.125863i		−	0.00542128i
$540$	10.8881	+	6.49887i	0.468549	+	0.279667i
$541$		−	7.94545i		−	0.341602i	−0.985306	−	0.170801i	$-0.945365\pi$
$541$		−	7.94545i		−	0.341602i	0.985306	−	0.170801i	$-0.0546355\pi$
$542$	−24.9731	+	29.7746i	−1.07269	+	1.27893i
$543$	−2.29501	−	4.62708i	−0.0984883	−	0.198567i
$544$	7.22101	−	19.9054i	0.309598	−	0.853438i
$545$	−3.22777	+	5.59066i	−0.138262	+	0.239478i
$546$	−8.02035	−	1.94131i	−0.343239	−	0.0830804i
$547$	−21.7161	+	12.5378i	−0.928514	+	0.536078i	−0.886341	−	0.463032i	$-0.846761\pi$
$547$	−21.7161	+	12.5378i	−0.928514	+	0.536078i	−0.0421728	+	0.999110i	$0.513428\pi$
$548$	−25.7469	+	21.6229i	−1.09985	+	0.923685i
$549$	0.338249	−	2.66345i	0.0144361	−	0.113673i
$550$	−0.587251	+	0.213884i	−0.0250405	+	0.00912003i
$551$	−0.845936	−	1.46520i	−0.0360381	−	0.0624198i
$552$	1.76231	−	2.65428i	0.0750091	−	0.112974i
$553$	7.16498	−	12.4101i	0.304686	−	0.527731i
$554$	−7.00652	+	39.7854i	−0.297678	+	1.69032i
$555$	−0.862743	+	13.6414i	−0.0366214	+	0.579046i
$556$	2.94020	−	8.08885i	0.124692	−	0.343044i
$557$			1.02127i			0.0432726i	0.999766	+	0.0216363i	$0.00688759\pi$
$557$			1.02127i			0.0432726i	−0.999766	+	0.0216363i	$0.993112\pi$
$558$	7.84254	+	2.43149i	0.332001	+	0.102933i
$559$	−0.179757			−0.00760289
$560$	−1.67316	−	4.58483i	−0.0707041	−	0.193745i
$561$	−0.451801	+	0.679531i	−0.0190750	+	0.0286898i
$562$	−29.9956	−	5.28245i	−1.26529	−	0.222827i
$563$	3.73834	+	2.15833i	0.157552	+	0.0909629i	0.576703	−	0.816954i	$-0.304339\pi$
$563$	3.73834	+	2.15833i	0.157552	+	0.0909629i	−0.419151	+	0.907917i	$0.637672\pi$
$564$	−9.01885	+	20.6488i	−0.379762	+	0.869471i
$565$	17.3604	−	10.0230i	0.730356	−	0.421671i
$566$	−23.4166	+	8.52858i	−0.984272	+	0.358483i
$567$	−6.30541	+	6.42198i	−0.264802	+	0.269698i
$568$	−3.21727	−	1.85475i	−0.134994	−	0.0778238i
$569$	−8.92555	−	15.4595i	−0.374178	−	0.648096i	0.616025	−	0.787726i	$-0.288742\pi$
$569$	−8.92555	−	15.4595i	−0.374178	−	0.648096i	−0.990204	+	0.139630i	$0.955409\pi$
$570$	−10.3484	−	9.85696i	−0.433448	−	0.412863i
$571$	35.7863	+	20.6613i	1.49761	+	0.864647i	0.999996	−	0.00275072i	$-0.000875583\pi$
$571$	35.7863	+	20.6613i	1.49761	+	0.864647i	0.497616	+	0.867397i	$0.334209\pi$
$572$	−0.147613	−	0.835077i	−0.00617201	−	0.0349163i
$573$	7.96714	+	5.29713i	0.332832	+	0.221291i
$574$	−3.49838	+	4.17101i	−0.146020	+	0.174095i
$575$	−2.28354			−0.0952302
$576$	23.8126	+	2.99324i	0.992192	+	0.124718i
$577$	−29.4908			−1.22772			−0.613859	−	0.789415i	$-0.710384\pi$
$577$	−29.4908			−1.22772			−0.613859	+	0.789415i	$0.710384\pi$
$578$	2.71594	−	3.23813i	0.112968	−	0.134689i
$579$	0.750046	−	11.8595i	0.0311708	−	0.492863i
$580$	0.150292	+	0.850229i	0.00624052	+	0.0353039i
$581$	−12.7247	−	7.34662i	−0.527910	−	0.304789i
$582$	17.6485	−	5.19202i	0.731554	−	0.215216i
$583$	−0.621786	−	1.07696i	−0.0257517	−	0.0446033i
$584$	1.26301	+	0.728126i	0.0522638	+	0.0301300i
$585$	12.2332	+	1.55358i	0.505781	+	0.0642326i
$586$	−0.742949	+	0.270591i	−0.0306910	+	0.0111780i
$587$	−10.7321	+	6.19619i	−0.442962	+	0.255744i	−0.704853	−	0.709353i	$-0.748987\pi$
$587$	−10.7321	+	6.19619i	−0.442962	+	0.255744i	0.261891	+	0.965097i	$0.415654\pi$
$588$	3.44248	−	0.386474i	0.141965	−	0.0159379i
$589$	−8.01445	−	4.62715i	−0.330230	−	0.190658i
$590$	22.0567	+	3.88436i	0.908061	+	0.159916i
$591$	11.4583	+	23.1017i	0.471333	+	0.950278i
$592$	8.86909	+	24.3032i	0.364517	+	0.998857i
$593$	−37.2074			−1.52793			−0.763963	−	0.645260i	$-0.776749\pi$
$593$	−37.2074			−1.52793			−0.763963	+	0.645260i	$0.776749\pi$
$594$	−0.864363	−	0.329105i	−0.0354653	−	0.0135033i
$595$			4.56726i			0.187239i
$596$	−6.79024	+	18.6808i	−0.278139	+	0.765194i
$597$	40.2341	−	19.9559i	1.64667	−	0.816741i
$598$	0.537390	−	3.05149i	0.0219755	−	0.124785i
$599$	−0.896543	+	1.55286i	−0.0366318	+	0.0634481i	−0.883760	−	0.467940i	$-0.844996\pi$
$599$	−0.896543	+	1.55286i	−0.0366318	+	0.0634481i	0.847128	+	0.531388i	$0.178330\pi$
$600$	−7.65316	−	15.4052i	−0.312439	−	0.628915i
$601$	−7.63109	−	13.2174i	−0.311279	−	0.539151i	0.667361	−	0.744735i	$-0.267424\pi$
$601$	−7.63109	−	13.2174i	−0.311279	−	0.539151i	−0.978639	+	0.205584i	$0.934091\pi$
$602$	0.0709040	−	0.0258240i	0.00288983	−	0.00105251i
$603$	28.9701	−	12.1555i	1.17976	−	0.495012i
$604$	25.5355	−	21.4453i	1.03902	−	0.872598i
$605$	11.6067	−	6.70115i	0.471881	−	0.272440i
$606$	2.66820	+	9.06965i	0.108388	+	0.368429i
$607$	−10.2607	+	17.7720i	−0.416468	+	0.721343i	−0.995581	−	0.0939035i	$-0.970065\pi$
$607$	−10.2607	+	17.7720i	−0.416468	+	0.721343i	0.579113	+	0.815247i	$0.303399\pi$
$608$	−25.4285	−	9.22461i	−1.03126	−	0.374107i
$609$	−0.611602	−	0.0386804i	−0.0247834	−	0.00156741i
$610$	0.992388	−	1.18319i	0.0401806	−	0.0479061i
$611$			21.9129i			0.886500i
$612$	−19.9732	−	10.2707i	−0.807369	−	0.415167i
$613$			19.2962i			0.779365i	0.920949	+	0.389682i	$0.127415\pi$
$613$			19.2962i			0.779365i	−0.920949	+	0.389682i	$0.872585\pi$
$614$	4.92618	+	4.13177i	0.198804	+	0.166745i
$615$	4.50418	−	6.77450i	0.181626	−	0.273174i
$616$	0.178193	+	0.308185i	0.00717961	+	0.0124171i
$617$	17.7201	−	30.6922i	0.713386	−	1.23562i	−0.250193	−	0.968196i	$-0.580494\pi$
$617$	17.7201	−	30.6922i	0.713386	−	1.23562i	0.963579	−	0.267425i	$-0.0861727\pi$
$618$	−24.6380	−	23.4679i	−0.991088	−	0.944018i
$619$	−5.63004	+	3.25051i	−0.226291	+	0.130649i	−0.608860	−	0.793278i	$-0.708373\pi$
$619$	−5.63004	+	3.25051i	−0.226291	+	0.130649i	0.382569	+	0.923927i	$0.375039\pi$
$620$	3.03725	+	3.61653i	0.121979	+	0.145243i
$621$	−2.55595	−	2.21064i	−0.102567	−	0.0887099i
$622$	−4.26433	−	11.7084i	−0.170984	−	0.469464i
$623$	3.43852	+	5.95569i	0.137761	+	0.238610i
$624$	22.3870	−	6.60157i	0.896197	−	0.264274i
$625$	−2.44250	+	4.23054i	−0.0977000	+	0.169221i
$626$	31.6837	+	5.57973i	1.26633	+	0.223011i
$627$	0.868079	+	0.577161i	0.0346677	+	0.0230496i
$628$	−4.95340	+	13.6274i	−0.197662	+	0.543793i
$629$		−	24.2101i		−	0.965319i
$630$	−5.04851	+	1.14464i	−0.201138	+	0.0456034i
$631$	−1.71858			−0.0684157			−0.0342078	−	0.999415i	$-0.510891\pi$
$631$	−1.71858			−0.0684157			−0.0342078	+	0.999415i	$0.510891\pi$
$632$	0.0258748	+	40.5312i	0.00102925	+	1.61225i
$633$	−19.8009	−	1.25230i	−0.787016	−	0.0497744i
$634$	4.40232	−	24.9979i	0.174838	−	0.992793i
$635$	−15.6788	−	9.05217i	−0.622195	−	0.359224i
$636$	27.5469	−	20.3134i	1.09230	−	0.805480i
$637$	2.91751	−	1.68442i	0.115596	−	0.0667393i
$638$	−0.0215522	−	0.0591750i	−0.000853260	−	0.00234276i
$639$	−2.38351	+	3.13587i	−0.0942901	+	0.124053i
$640$	10.5880	+	8.85753i	0.418527	+	0.350125i
$641$	0.534074	+	0.925044i	0.0210947	+	0.0365370i	0.876380	−	0.481620i	$-0.159952\pi$
$641$	0.534074	+	0.925044i	0.0210947	+	0.0365370i	−0.855285	+	0.518157i	$0.826618\pi$
$642$	−38.2088	−	9.24835i	−1.50798	−	0.365003i
$643$	−42.2196	−	24.3755i	−1.66498	−	0.961277i	−0.970283	−	0.241974i	$-0.922205\pi$
$643$	−42.2196	−	24.3755i	−1.66498	−	0.961277i	−0.694697	−	0.719302i	$-0.744462\pi$
$644$	0.226410	+	1.28085i	0.00892179	+	0.0504724i
$645$	−0.101022	+	0.0501064i	−0.00397773	+	0.00197294i
$646$	19.3947	+	16.2670i	0.763073	+	0.640017i
$647$	2.36343			0.0929160			0.0464580	−	0.998920i	$-0.485207\pi$
$647$	2.36343			0.0929160			0.0464580	+	0.998920i	$0.485207\pi$
$648$	6.34726	−	24.6518i	0.249344	−	0.968415i
$649$	−1.63359			−0.0641239
$650$	−12.8171	−	10.7501i	−0.502726	−	0.421655i
$651$	−3.00296	+	1.48945i	−0.117695	+	0.0583763i
$652$	−32.8230	+	5.80199i	−1.28545	+	0.227223i
$653$	−28.5596	−	16.4889i	−1.11763	−	0.645261i	−0.176832	−	0.984241i	$-0.556585\pi$
$653$	−28.5596	−	16.4889i	−1.11763	−	0.645261i	−0.940794	+	0.338980i	$0.889918\pi$
$654$	12.5960	+	3.04883i	0.492542	+	0.119219i
$655$	3.29807	+	5.71242i	0.128866	+	0.223203i
$656$	2.66087	−	15.1660i	0.103890	−	0.592134i
$657$	0.935699	−	1.23106i	0.0365051	−	0.0480281i
$658$	−3.14803	−	8.64341i	−0.122723	−	0.336955i
$659$	9.94137	−	5.73965i	0.387261	−	0.223585i	−0.293712	−	0.955894i	$-0.594891\pi$
$659$	9.94137	−	5.73965i	0.387261	−	0.223585i	0.680973	+	0.732309i	$0.261557\pi$
$660$	−0.315732	−	0.428161i	−0.0122898	−	0.0166661i
$661$	−34.5315	−	19.9368i	−1.34312	−	0.775451i	−0.355856	−	0.934541i	$-0.615811\pi$
$661$	−34.5315	−	19.9368i	−1.34312	−	0.775451i	−0.987264	+	0.159090i	$0.949144\pi$
$662$	3.84297	−	21.8217i	0.149361	−	0.848126i
$663$	−21.7981	−	1.37861i	−0.846566	−	0.0535406i
$664$	41.5587	−	0.0265308i	1.61279	−	0.00102959i
$665$	5.83452			0.226253
$666$	26.7611	−	6.06748i	1.03697	−	0.235110i
$667$		−	0.230103i		−	0.00890964i
$668$	−44.8079	−	16.2871i	−1.73367	−	0.630169i
$669$	−18.6601	−	12.4065i	−0.721439	−	0.479665i
$670$	17.7967	+	3.13413i	0.687545	+	0.121082i
$671$	−0.0563201	+	0.0975493i	−0.00217421	+	0.00376585i
$672$	−7.88204	+	5.82009i	−0.304056	+	0.224515i
$673$	17.2863	+	29.9408i	0.666339	+	1.15413i	0.978920	+	0.204243i	$0.0654731\pi$
$673$	17.2863	+	29.9408i	0.666339	+	1.15413i	−0.312581	+	0.949891i	$0.601194\pi$
$674$	−8.08281	−	22.1926i	−0.311338	−	0.854829i
$675$	−17.2360	+	5.98317i	−0.663414	+	0.230292i
$676$	−2.52839	+	2.12340i	−0.0972457	+	0.0816693i
$677$	−7.85158	+	4.53311i	−0.301761	+	0.174222i	−0.643234	−	0.765670i	$-0.722408\pi$
$677$	−7.85158	+	4.53311i	−0.301761	+	0.174222i	0.341473	+	0.939892i	$0.389074\pi$
$678$	−29.1397	−	27.7558i	−1.11910	−	1.06595i
$679$	−3.75514	+	6.50410i	−0.144109	+	0.249605i
$680$	−6.46621	−	11.1833i	−0.247968	−	0.428861i
$681$	9.77431	−	14.7010i	0.374552	−	0.563345i
$682$	−0.263933	−	0.221370i	−0.0101065	−	0.00847670i
$683$			42.8277i			1.63876i	0.573252	+	0.819379i	$0.305682\pi$
$683$			42.8277i			1.63876i	−0.573252	+	0.819379i	$0.694318\pi$
$684$	−13.1204	+	25.5151i	−0.501673	+	0.975595i
$685$			20.5120i			0.783725i
$686$	−0.908808	+	1.08354i	−0.0346985	+	0.0413699i
$687$	50.4509	+	3.19073i	1.92482	+	0.121734i
$688$	−0.137053	+	0.163617i	−0.00522512	+	0.00623782i
$689$	16.6428	−	28.8261i	0.634039	−	1.09819i
$690$	−0.548580	−	1.86471i	−0.0208841	−	0.0709883i
$691$	−31.0851	+	17.9470i	−1.18253	+	0.682736i	−0.956599	−	0.291407i	$-0.905877\pi$
$691$	−31.0851	+	17.9470i	−1.18253	+	0.682736i	−0.225933	+	0.974143i	$0.572543\pi$
$692$	6.53549	+	7.78197i	0.248442	+	0.295826i
$693$	0.348180	−	0.146092i	0.0132263	−	0.00554959i
$694$	6.23564	−	2.27109i	0.236701	−	0.0862093i
$695$	−2.62534	−	4.54723i	−0.0995850	−	0.172486i
$696$	1.55232	−	0.771179i	0.0588406	−	0.0292315i
$697$	−7.20457	+	12.4787i	−0.272893	+	0.472664i
$698$	−5.60629	+	31.8345i	−0.212201	+	1.20495i
$699$	21.3749	−	10.6019i	0.808474	−	0.400999i
$700$	6.59999	+	2.39902i	0.249456	+	0.0906745i
$701$			31.7905i			1.20071i	0.799733	+	0.600355i	$0.204974\pi$
$701$			31.7905i			1.20071i	−0.799733	+	0.600355i	$0.795026\pi$
$702$	−3.93912	−	24.4405i	−0.148672	−	0.922446i
$703$	−30.9276			−1.16646
$704$	−0.872643	−	0.502336i	−0.0328890	−	0.0189325i
$705$	6.10812	+	12.3149i	0.230045	+	0.463805i
$706$	−28.7279	−	5.05921i	−1.08119	−	0.190406i
$707$	−3.34249	−	1.92979i	−0.125707	−	0.0725771i
$708$	−5.01610	−	44.6804i	−0.188517	−	1.67919i
$709$	0.179531	−	0.103652i	0.00674242	−	0.00389274i	−0.496625	−	0.867965i	$-0.665428\pi$
$709$	0.179531	−	0.103652i	0.00674242	−	0.00389274i	0.503367	+	0.864072i	$0.332094\pi$
$710$	−2.12878	+	0.775327i	−0.0798918	+	0.0290975i
$711$	42.6473	+	5.41608i	1.59940	+	0.203119i
$712$	−16.8514	−	9.71484i	−0.631534	−	0.364079i
$713$	−0.629315	−	1.09001i	−0.0235680	−	0.0408210i
$714$	8.79618	−	2.58775i	0.329189	−	0.0968441i
$715$	−0.448044	−	0.258678i	−0.0167559	−	0.00967402i
$716$	24.5420	−	4.33819i	0.917179	−	0.162126i
$717$	−1.73943	+	27.5032i	−0.0649600	+	1.02713i
$718$	−6.85598	+	8.17417i	−0.255863	+	0.305057i
$719$	28.3671			1.05791			0.528957	−	0.848649i	$-0.322583\pi$
$719$	28.3671			1.05791			0.528957	+	0.848649i	$0.322583\pi$
$720$	10.7412	−	9.95031i	0.400300	−	0.370826i
$721$	13.8911			0.517332
$722$	3.51324	−	4.18872i	0.130749	−	0.155888i
$723$	12.3600	+	8.21782i	0.459673	+	0.305624i
$724$	−5.87295	+	1.03814i	−0.218267	+	0.0385821i
$725$	−1.07589	−	0.621163i	−0.0399574	−	0.0230694i
$726$	−19.4821	−	18.5569i	−0.723049	−	0.688710i
$727$	14.3762	+	24.9004i	0.533185	+	0.923504i	0.999249	+	0.0387527i	$0.0123385\pi$
$727$	14.3762	+	24.9004i	0.533185	+	0.923504i	−0.466064	+	0.884751i	$0.654328\pi$
$728$	−4.75900	+	8.25499i	−0.176380	+	0.305950i
$729$	−25.0843	−	9.98881i	−0.929049	−	0.369956i
$730$	0.835702	−	0.304372i	0.0309307	−	0.0112653i
$731$	0.172972	−	0.0998657i	0.00639762	−	0.00369367i
$732$	−2.84101	−	1.24088i	−0.105007	−	0.0458642i
$733$	−17.3805	−	10.0346i	−0.641963	−	0.370638i	0.143407	−	0.989664i	$-0.454194\pi$
$733$	−17.3805	−	10.0346i	−0.641963	−	0.370638i	−0.785370	+	0.619026i	$0.787527\pi$
$734$	15.0759	+	2.65498i	0.556462	+	0.0979972i
$735$	1.17009	−	1.75988i	0.0431595	−	0.0649140i
$736$	−2.36778	−	2.81572i	−0.0872774	−	0.103789i
$737$	−1.31807			−0.0485519
$738$	−15.5992	−	4.83634i	−0.574213	−	0.178028i
$739$			32.6232i			1.20006i	0.799976	+	0.600032i	$0.204846\pi$
$739$			32.6232i			1.20006i	−0.799976	+	0.600032i	$0.795154\pi$
$740$	14.8337	+	5.39186i	0.545296	+	0.198209i
$741$	−1.76112	+	27.8463i	−0.0646965	+	1.02296i
$742$	−2.42346	+	13.7612i	−0.0889678	+	0.505190i
$743$	−2.42291	+	4.19661i	−0.0888881	+	0.153959i	−0.907041	−	0.421041i	$-0.861665\pi$
$743$	−2.42291	+	4.19661i	−0.0888881	+	0.153959i	0.818153	+	0.575000i	$0.194998\pi$
$744$	5.24428	−	7.89858i	0.192265	−	0.289576i
$745$	6.06309	+	10.5016i	0.222134	+	0.384748i
$746$	36.5884	−	13.3259i	1.33960	−	0.487896i
$747$	5.55338	−	43.7285i	0.203187	−	1.59994i
$748$	0.605978	+	0.721553i	0.0221568	+	0.0263826i
$749$	13.8989	−	8.02455i	0.507856	−	0.293211i
$750$	−24.7239	−	5.98437i	−0.902790	−	0.218518i
$751$	−22.3638	+	38.7353i	−0.816067	+	1.41347i	0.0924918	+	0.995713i	$0.470517\pi$
$751$	−22.3638	+	38.7353i	−0.816067	+	1.41347i	−0.908559	+	0.417757i	$0.862817\pi$
$752$	19.9454	+	16.7072i	0.727333	+	0.609250i
$753$	5.47417	+	11.0367i	0.199490	+	0.402201i
$754$	1.08325	−	1.29152i	0.0394496	−	0.0470345i
$755$		−	20.3436i		−	0.740379i
$756$	5.06491	+	9.07451i	0.184209	+	0.330037i
$757$		−	3.60061i		−	0.130867i	−0.997857	−	0.0654333i	$-0.979157\pi$
$757$		−	3.60061i		−	0.130867i	0.997857	−	0.0654333i	$-0.0208429\pi$
$758$	10.1172	+	8.48567i	0.367473	+	0.308214i
$759$	0.0629972	+	0.127012i	0.00228665	+	0.00461024i
$760$	−14.2863	+	8.26038i	−0.518220	+	0.299636i
$761$	6.96304	−	12.0603i	0.252410	−	0.437187i	−0.711779	−	0.702404i	$-0.752110\pi$
$761$	6.96304	−	12.0603i	0.252410	−	0.437187i	0.964189	+	0.265217i	$0.0854435\pi$
$762$	−8.55035	+	35.3250i	−0.309747	+	1.27969i
$763$	−4.58195	+	2.64539i	−0.165878	+	0.0957696i
$764$	8.45983	−	7.10478i	0.306066	−	0.257042i
$765$	−12.6346	+	5.30135i	−0.456806	+	0.191671i
$766$	10.2513	+	28.1464i	0.370393	+	1.01697i
$767$	−21.8624	−	37.8667i	−0.789404	−	1.36729i
$768$	11.0599	−	25.4102i	0.399090	−	0.916912i
$769$	22.6379	−	39.2099i	0.816342	−	1.41395i	−0.0920183	−	0.995757i	$-0.529332\pi$
$769$	22.6379	−	39.2099i	0.816342	−	1.41395i	0.908360	−	0.418188i	$-0.137335\pi$
$770$	0.213891	+	0.0376677i	0.00770808	+	0.00135745i
$771$	−1.73122	+	27.3735i	−0.0623483	+	0.985831i
$772$	−12.8960	−	4.68754i	−0.464137	−	0.168708i
$773$		−	16.5408i		−	0.594932i	−0.954732	−	0.297466i	$-0.903859\pi$
$773$		−	16.5408i		−	0.594932i	0.954732	−	0.297466i	$-0.0961414\pi$
$774$	0.153739	+	0.166171i	0.00552603	+	0.00597288i
$775$	−6.79533			−0.244096
$776$	−0.0135609	−	21.2423i	−0.000486809	−	0.762554i
$777$	−6.20242	+	9.32874i	−0.222510	+	0.334667i
$778$	−3.71221	+	21.0792i	−0.133089	+	0.755726i
$779$	15.9411	+	9.20360i	0.571150	+	0.329753i
$780$	5.69936	−	13.0488i	0.204070	−	0.467221i
$781$	0.143113	−	0.0826263i	0.00512099	−	0.00295660i
$782$	1.17818	+	3.23488i	0.0421316	+	0.115679i
$783$	−0.602901	−	1.73680i	−0.0215459	−	0.0620683i
$784$	0.691239	−	3.93982i	0.0246871	−	0.140708i
$785$	4.42295	+	7.66078i	0.157862	+	0.273425i
$786$	9.13304	−	9.58842i	0.325765	−	0.342008i
$787$	7.59301	+	4.38383i	0.270662	+	0.156267i	0.629188	−	0.777253i	$-0.283387\pi$
$787$	7.59301	+	4.38383i	0.270662	+	0.156267i	−0.358527	+	0.933520i	$0.616721\pi$
$788$	29.3220	−	5.18313i	1.04455	−	0.184641i
$789$	−30.9592	−	20.5839i	−1.10218	−	0.732807i
$790$	18.9454	+	15.8902i	0.674047	+	0.565348i
$791$	16.4292			0.584154
$792$	−0.645715	+	0.850665i	−0.0229445	+	0.0302271i
$793$	−3.01494			−0.107064
$794$	−36.0860	−	30.2667i	−1.28064	−	1.07412i
$795$	1.31796	−	20.8392i	0.0467433	−	0.739089i
$796$	−9.02696	−	51.0673i	−0.319952	−	1.81003i
$797$	7.70687	+	4.44956i	0.272991	+	0.157612i	0.630246	−	0.776395i	$-0.282954\pi$
$797$	7.70687	+	4.44956i	0.272991	+	0.157612i	−0.357255	+	0.934007i	$0.616287\pi$
$798$	−3.30577	−	11.2368i	−0.117023	−	0.397780i
$799$	−12.1739	−	21.0859i	−0.430683	−	0.745965i
$800$	−19.5571	+	3.46991i	−0.691449	+	0.122680i
$801$	−12.4843	+	16.4251i	−0.441113	+	0.580352i
$802$	−13.9287	−	38.2433i	−0.491838	−	1.35042i
$803$	−0.0561822	+	0.0324368i	−0.00198263	+	0.00114467i
$804$	−4.04728	−	36.0507i	−0.142737	−	1.27141i
$805$	0.687212	+	0.396762i	0.0242211	+	0.0139840i
$806$	1.59916	−	9.08059i	0.0563280	−	0.319850i
$807$	−19.8257	−	39.9716i	−0.697898	−	1.40707i
$808$	10.9165	−	0.00696902i	0.384042	−	0.000245169i
$809$	10.2384			0.359963			0.179982	−	0.983670i	$-0.442396\pi$
$809$	10.2384			0.359963			0.179982	+	0.983670i	$0.442396\pi$
$810$	−9.02643	−	12.6374i	−0.317156	−	0.444031i
$811$		−	25.9834i		−	0.912401i	−0.889877	−	0.456201i	$-0.849210\pi$
$811$		−	25.9834i		−	0.912401i	0.889877	−	0.456201i	$-0.150790\pi$
$812$	−0.241740	+	0.665056i	−0.00848341	+	0.0233389i
$813$	42.6383	−	21.1484i	1.49539	−	0.741706i
$814$	−1.13379	−	0.199669i	−0.0397393	−	0.00699839i
$815$	−10.1674	+	17.6105i	−0.356150	+	0.616870i
$816$	−17.8745	+	18.7898i	−0.625734	+	0.657773i
$817$	−0.127575	−	0.220967i	−0.00446329	−	0.00773065i
$818$	17.0747	+	46.8813i	0.597002	+	1.63917i
$819$	8.04614	+	6.11569i	0.281155	+	0.213700i
$820$	−6.04123	−	7.19344i	−0.210969	−	0.251206i
$821$	−10.7317	+	6.19594i	−0.374538	+	0.216240i	−0.675439	−	0.737416i	$-0.736046\pi$
$821$	−10.7317	+	6.19594i	−0.374538	+	0.216240i	0.300901	+	0.953655i	$0.402713\pi$
$822$	39.5046	−	11.6219i	1.37788	−	0.405359i
$823$	6.68671	−	11.5817i	0.233084	−	0.403713i	−0.725630	−	0.688085i	$-0.758452\pi$
$823$	6.68671	−	11.5817i	0.233084	−	0.403713i	0.958714	+	0.284372i	$0.0917850\pi$
$824$	−34.0136	+	19.6667i	−1.18492	+	0.685122i
$825$	0.763925	+	0.0483140i	0.0265965	+	0.00168208i
$826$	14.0635	+	11.7955i	0.489331	+	0.410420i
$827$		−	20.6200i		−	0.717026i	−0.933525	−	0.358513i	$-0.883284\pi$
$827$		−	20.6200i		−	0.717026i	0.933525	−	0.358513i	$-0.116716\pi$
$828$	−3.28047	+	2.11304i	−0.114004	+	0.0734334i
$829$			37.9381i			1.31764i	0.752299	+	0.658822i	$0.228945\pi$
$829$			37.9381i			1.31764i	−0.752299	+	0.658822i	$0.771055\pi$
$830$	16.2930	−	19.4257i	0.565540	−	0.674275i
$831$	27.3936	−	41.2013i	0.950274	−	1.42926i
$832$	−0.0344103	−	26.9507i	−0.00119296	−	0.934349i
$833$	−1.87160	+	3.24171i	−0.0648471	+	0.112318i
$834$	−7.27012	+	7.63261i	−0.251744	+	0.264296i
$835$	−25.1892	+	14.5430i	−0.871708	+	0.503281i
$836$	0.921760	−	0.774118i	0.0318798	−	0.0267734i
$837$	−7.60599	−	6.57840i	−0.262901	−	0.227383i
$838$	5.64016	−	2.05421i	0.194836	−	0.0709615i
$839$	23.7223	+	41.0883i	0.818986	+	1.41852i	0.906430	+	0.422355i	$0.138797\pi$
$839$	23.7223	+	41.0883i	0.818986	+	1.41852i	−0.0874449	+	0.996169i	$0.527870\pi$
$840$	−0.373480	+	5.96580i	−0.0128863	+	0.205840i
$841$	−14.4374	+	25.0063i	−0.497842	+	0.862287i
$842$	0.515238	−	2.92570i	0.0177563	−	0.100826i
$843$	31.0631	+	20.6530i	1.06987	+	0.711326i
$844$	−7.82646	+	21.5315i	−0.269398	+	0.741146i
$845$			2.01431i			0.0692945i
$846$	20.2567	−	18.7412i	0.696440	−	0.644337i
$847$	10.9842			0.377420
$848$	−13.5488	−	37.1266i	−0.465267	−	1.27493i
$849$	30.4614	+	1.92651i	1.04543	+	0.0661178i
$850$	18.3057	+	3.22377i	0.627880	+	0.110574i
$851$	−3.64277	−	2.10315i	−0.124873	−	0.0720952i
$852$	2.69936	+	3.66058i	0.0924786	+	0.125409i
$853$	−24.9623	+	14.4120i	−0.854694	+	0.493458i	−0.862232	−	0.506514i	$-0.830934\pi$
$853$	−24.9623	+	14.4120i	−0.854694	+	0.493458i	0.00753799	+	0.999972i	$0.497601\pi$
$854$	1.18923	−	0.433129i	0.0406945	−	0.0148214i
$855$	6.77230	+	16.1403i	0.231608	+	0.551988i
$856$	−22.6718	+	39.3266i	−0.774905	+	1.34416i
$857$	−19.7218	−	34.1592i	−0.673685	−	1.16686i	−0.976851	−	0.213919i	$-0.931377\pi$
$857$	−19.7218	−	34.1592i	−0.673685	−	1.16686i	0.303166	−	0.952938i	$-0.401956\pi$
$858$	−0.244338	+	1.00946i	−0.00834156	+	0.0344625i
$859$	12.1671	+	7.02466i	0.415135	+	0.239678i	0.692994	−	0.720944i	$-0.256291\pi$
$859$	12.1671	+	7.02466i	0.415135	+	0.239678i	−0.277859	+	0.960622i	$0.589625\pi$
$860$	0.0226654	+	0.128223i	0.000772883	+	0.00437236i
$861$	5.97303	−	2.96259i	0.203560	−	0.100965i
$862$	8.61167	−	10.2674i	0.293315	−	0.349710i
$863$	2.18228			0.0742858			0.0371429	−	0.999310i	$-0.488174\pi$
$863$	2.18228			0.0742858			0.0371429	+	0.999310i	$0.488174\pi$
$864$	−25.2493	−	15.0489i	−0.859000	−	0.511975i
$865$	6.19973			0.210797
$866$	28.0845	−	33.4843i	0.954351	−	1.13784i
$867$	−4.63711	+	2.29998i	−0.157485	+	0.0781116i
$868$	0.673748	+	3.81153i	0.0228685	+	0.129372i
$869$	−1.56197	−	0.901802i	−0.0529861	−	0.0305916i
$870$	0.248772	−	1.02778i	0.00843415	−	0.0348450i
$871$	−17.6398	−	30.5531i	−0.597703	−	1.03525i
$872$	7.47402	−	12.9645i	0.253102	−	0.439033i
$873$	−22.3513	−	2.83855i	−0.756478	−	0.0960703i
$874$	4.13245	−	1.50509i	0.139782	−	0.0509103i
$875$	8.99365	−	5.19248i	0.304041	−	0.175538i
$876$	−1.05970	−	1.43704i	−0.0358038	−	0.0485532i
$877$	−15.1868	−	8.76809i	−0.512821	−	0.296077i	0.221172	−	0.975235i	$-0.429012\pi$
$877$	−15.1868	−	8.76809i	−0.512821	−	0.296077i	−0.733992	+	0.679158i	$0.762345\pi$
$878$	−17.0085	−	2.99533i	−0.574009	−	0.101087i
$879$	0.966464	+	0.0611235i	0.0325980	+	0.00206164i
$880$	−0.577059	+	0.210589i	−0.0194526	+	0.00709894i
$881$	22.8524			0.769918			0.384959	−	0.922934i	$-0.374216\pi$
$881$	22.8524			0.769918			0.384959	+	0.922934i	$0.374216\pi$
$882$	−4.05235	−	1.25638i	−0.136450	−	0.0423046i
$883$		−	3.50280i		−	0.117879i	−0.998262	−	0.0589393i	$-0.981228\pi$
$883$		−	3.50280i		−	0.117879i	0.998262	−	0.0589393i	$-0.0187718\pi$
$884$	−8.61584	+	23.7032i	−0.289782	+	0.797225i
$885$	−22.8417	−	15.1868i	−0.767815	−	0.510498i
$886$	7.81264	−	44.3629i	0.262471	−	1.49040i
$887$	6.75665	−	11.7029i	0.226866	−	0.392943i	−0.730012	−	0.683435i	$-0.760485\pi$
$887$	6.75665	−	11.7029i	0.226866	−	0.392943i	0.956878	+	0.290491i	$0.0938187\pi$
$888$	1.97974	−	31.6235i	0.0664357	−	1.06121i
$889$	−7.41892	−	12.8499i	−0.248822	−	0.430973i
$890$	−11.1502	+	4.06101i	−0.373754	+	0.136125i
$891$	0.808286	+	0.793615i	0.0270786	+	0.0265871i
$892$	−19.8140	+	16.6403i	−0.663421	+	0.557158i
$893$	−26.9365	+	15.5518i	−0.901397	+	0.520422i
$894$	16.7900	−	17.6271i	0.561540	−	0.589539i
$895$	7.60228	−	13.1675i	0.254116	−	0.440142i
$896$	3.88535	+	10.6256i	0.129800	+	0.354977i
$897$	−2.10105	+	3.16009i	−0.0701521	+	0.105512i
$898$	−15.4685	+	18.4426i	−0.516191	+	0.615438i
$899$		−	0.684739i		−	0.0228373i
$900$	1.02427	+	21.0425i	0.0341424	+	0.701417i
$901$			36.9843i			1.23212i
$902$	0.524974	+	0.440315i	0.0174797	+	0.0146609i
$903$	−0.0922353	−	0.00583337i	−0.00306940	−	0.000194122i
$904$	−40.2282	+	23.2600i	−1.33797	+	0.773618i
$905$	−1.81924	+	3.15102i	−0.0604736	+	0.104743i
$906$	−39.1802	+	11.5264i	−1.30167	+	0.382940i
$907$	46.2692	−	26.7135i	1.53634	−	0.887009i	0.537296	−	0.843394i	$-0.319446\pi$
$907$	46.2692	−	26.7135i	1.53634	−	0.887009i	0.999048	−	0.0436147i	$-0.0138874\pi$
$908$	−13.1098	−	15.6101i	−0.435064	−	0.518041i
$909$	1.45874	−	11.4865i	0.0483835	−	0.380982i
$910$	1.98936	+	5.46211i	0.0659467	+	0.181067i
$911$	16.2674	+	28.1760i	0.538964	+	0.933512i	0.998960	+	0.0455917i	$0.0145173\pi$
$911$	16.2674	+	28.1760i	0.538964	+	0.933512i	−0.459997	+	0.887921i	$0.652149\pi$
$912$	24.0033	+	22.8341i	0.794829	+	0.756114i
$913$	−0.924664	+	1.60156i	−0.0306019	+	0.0530041i
$914$	39.5684	+	6.96829i	1.30881	+	0.230491i
$915$	−1.69437	+	0.840401i	−0.0560142	+	0.0277828i
$916$	19.9411	−	54.8602i	0.658871	−	1.81263i
$917$			5.40602i			0.178522i
$918$	17.3686	+	21.3297i	0.573250	+	0.703983i
$919$	21.0290			0.693683			0.346842	−	0.937924i	$-0.387254\pi$
$919$	21.0290			0.693683			0.346842	+	0.937924i	$0.387254\pi$
$920$	−2.24443	+	0.00143282i	−0.0739965	+	4.72388e-5i
$921$	−3.49897	−	7.05445i	−0.115295	−	0.232452i
$922$	−4.12187	+	23.4054i	−0.135746	+	0.770816i
$923$	3.83057	+	2.21158i	0.126085	+	0.0727951i
$924$	−0.0486426	−	0.433279i	−0.00160022	−	0.0142538i
$925$	−19.6673	+	11.3549i	−0.646656	+	0.373347i
$926$	14.9917	+	41.1620i	0.492657	+	1.35267i
$927$	16.1238	+	38.4277i	0.529576	+	1.26213i
$928$	−0.349649	−	1.97070i	−0.0114778	−	0.0646913i
$929$	11.1402	+	19.2954i	0.365497	+	0.633060i	0.988856	−	0.148876i	$-0.0475656\pi$
$929$	11.1402	+	19.2954i	0.365497	+	0.633060i	−0.623358	+	0.781936i	$0.714232\pi$
$930$	−1.63246	−	5.54899i	−0.0535304	−	0.181959i
$931$	4.14117	+	2.39091i	0.135721	+	0.0783588i
$932$	−4.79570	−	27.1302i	−0.157088	−	0.888680i
$933$	−0.963266	+	15.2308i	−0.0315359	+	0.498635i
$934$	30.6509	+	25.7081i	1.00293	+	0.841194i
$935$	0.574846			0.0187995
$936$	−28.3601	−	3.58325i	−0.926980	−	0.117122i
$937$	15.4987			0.506322			0.253161	−	0.967424i	$-0.418530\pi$
$937$	15.4987			0.506322			0.253161	+	0.967424i	$0.418530\pi$
$938$	11.3472	+	9.51734i	0.370500	+	0.310752i
$939$	−32.8112	−	21.8153i	−1.07075	−	0.711914i
$940$	15.6307	−	2.76298i	0.509818	−	0.0901185i
$941$	8.68549	+	5.01457i	0.283139	+	0.163470i	0.634844	−	0.772641i	$-0.281065\pi$
$941$	8.68549	+	5.01457i	0.283139	+	0.163470i	−0.351705	+	0.936111i	$0.614398\pi$
$942$	12.2481	−	12.8588i	0.399064	−	0.418961i
$943$	1.25174	+	2.16807i	0.0407622	+	0.0706021i
$944$	−51.1355	−	8.97169i	−1.66432	−	0.292004i
$945$	6.22660	+	1.19415i	0.202551	+	0.0388456i
$946$	−0.00325028	−	0.00892416i	−0.000105676	−	0.000290149i
$947$	14.0710	−	8.12392i	0.457247	−	0.263992i	−0.253639	−	0.967299i	$-0.581627\pi$
$947$	14.0710	−	8.12392i	0.457247	−	0.263992i	0.710886	+	0.703307i	$0.248294\pi$
$948$	19.8691	−	45.4906i	0.645318	−	1.47747i
$949$	−1.50378	−	0.868206i	−0.0488147	−	0.0281832i
$950$	4.11826	−	23.3849i	0.133614	−	0.758707i
$951$	−17.2119	+	25.8875i	−0.558133	+	0.839460i
$952$	−0.00675889	−	10.5874i	−0.000219057	−	0.343138i
$953$	56.7445			1.83814			0.919068	−	0.394100i	$-0.128943\pi$
$953$	56.7445			1.83814			0.919068	+	0.394100i	$0.128943\pi$
$954$	−40.8814	+	9.26893i	−1.32358	+	0.300093i
$955$		−	6.73977i		−	0.218094i
$956$	29.9070	+	10.8708i	0.967262	+	0.351588i
$957$	−0.00486841	+	0.0769777i	−0.000157373	+	0.00248834i
$958$	37.9282	+	6.67944i	1.22540	+	0.215803i
$959$	−8.40556	+	14.5589i	−0.271430	+	0.470130i
$960$	−7.53174	−	15.1365i	−0.243086	−	0.488530i
$961$	13.6273	+	23.6032i	0.439590	+	0.761392i
$962$	−10.5452	−	28.9535i	−0.339991	−	0.933499i
$963$	38.3316	+	29.1350i	1.23522	+	0.938862i
$964$	13.1243	−	11.0222i	0.422707	−	0.355000i
$965$	−7.24961	+	4.18557i	−0.233373	+	0.134738i
$966$	0.374767	−	1.54832i	0.0120579	−	0.0498163i
$967$	−5.34092	+	9.25074i	−0.171752	+	0.297484i	−0.939033	−	0.343828i	$-0.888276\pi$
$967$	−5.34092	+	9.25074i	−0.171752	+	0.297484i	0.767280	+	0.641312i	$0.221610\pi$
$968$	−26.8957	+	15.5511i	−0.864459	+	0.499832i
$969$	−13.7757	−	27.7738i	−0.442538	−	0.892223i
$970$	−9.92923	−	8.32801i	−0.318808	−	0.267396i
$971$			27.3463i			0.877583i	0.898589	+	0.438792i	$0.144593\pi$
$971$			27.3463i			0.877583i	−0.898589	+	0.438792i	$0.855407\pi$
$972$	−19.2243	+	24.5444i	−0.616620	+	0.787261i
$973$		−	4.30332i		−	0.137958i
$974$	13.1779	−	15.7116i	0.422248	−	0.503433i
$975$	9.10371	+	18.3544i	0.291552	+	0.587813i
$976$	−2.29871	+	2.74423i	−0.0735798	+	0.0878407i
$977$	4.30566	−	7.45763i	0.137750	−	0.238591i	−0.788894	−	0.614529i	$-0.789346\pi$
$977$	4.30566	−	7.45763i	0.137750	−	0.238591i	0.926645	+	0.375938i	$0.122680\pi$
$978$	39.6773	+	9.60380i	1.26874	+	0.307096i
$979$	0.749598	−	0.432781i	0.0239573	−	0.0138317i
$980$	−1.56939	−	1.86871i	−0.0501322	−	0.0596937i
$981$	−12.6365	−	9.60471i	−0.403452	−	0.306655i
$982$	30.9604	−	11.2761i	0.987985	−	0.359835i
$983$	11.3437	+	19.6479i	0.361809	+	0.626671i	0.988259	−	0.152790i	$-0.0488259\pi$
$983$	11.3437	+	19.6479i	0.361809	+	0.626671i	−0.626450	+	0.779462i	$0.715493\pi$
$984$	−10.4311	+	15.7106i	−0.332532	+	0.500837i
$985$	9.08296	−	15.7321i	0.289407	−	0.501268i
$986$	−0.324847	+	1.84459i	−0.0103452	+	0.0587438i
$987$	−0.711106	+	11.2438i	−0.0226347	+	0.357893i
$988$	30.2801	+	11.0065i	0.963338	+	0.350162i
$989$		−	0.0347018i		−	0.00110345i
$990$	0.144067	+	0.635419i	0.00457875	+	0.0201949i
$991$	−17.6246			−0.559862			−0.279931	−	0.960020i	$-0.590312\pi$
$991$	−17.6246			−0.559862			−0.279931	+	0.960020i	$0.590312\pi$
$992$	−7.04600	−	8.37898i	−0.223711	−	0.266033i
$993$	−15.0250	+	22.5983i	−0.476804	+	0.717136i
$994$	−1.82867	−	0.322042i	−0.0580018	−	0.0102146i
$995$	−27.3992	−	15.8189i	−0.868612	−	0.501494i
$996$	−46.6438	−	20.3728i	−1.47797	−	0.645536i
$997$	−10.7922	+	6.23085i	−0.341791	+	0.197333i	−0.661064	−	0.750330i	$-0.729895\pi$
$997$	−10.7922	+	6.23085i	−0.341791	+	0.197333i	0.319273	+	0.947663i	$0.396561\pi$
$998$	−13.2107	+	4.81148i	−0.418177	+	0.152305i
$999$	−33.0059	−	6.32992i	−1.04426	−	0.200270i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cs.b.85.10	✓	72
8.5	even	2	inner	504.2.cs.b.85.36	yes	72
9.7	even	3	inner	504.2.cs.b.421.36	yes	72
72.61	even	6	inner	504.2.cs.b.421.10	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cs.b.85.10	✓	72	1.1	even	1	trivial
504.2.cs.b.85.36	yes	72	8.5	even	2	inner
504.2.cs.b.421.10	yes	72	72.61	even	6	inner
504.2.cs.b.421.36	yes	72	9.7	even	3	inner

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.908808 + 1.08354i) q^{2} +(1.55167 - 0.769621i) q^{3} +(-0.348135 - 1.96947i) q^{4} +(-1.05668 - 0.610074i) q^{5} +(-0.576254 + 2.38074i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(2.45039 + 1.41265i) q^{8} +(1.81537 - 2.38840i) q^{9} +O(q^{10})\)	\(q+(-0.908808 + 1.08354i) q^{2} +(1.55167 - 0.769621i) q^{3} +(-0.348135 - 1.96947i) q^{4} +(-1.05668 - 0.610074i) q^{5} +(-0.576254 + 2.38074i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(2.45039 + 1.41265i) q^{8} +(1.81537 - 2.38840i) q^{9} +(1.62136 - 0.590518i) q^{10} +(-0.109000 + 0.0629313i) q^{11} +(-2.05593 - 2.78803i) q^{12} +(-2.91751 - 1.68442i) q^{13} +(1.39278 + 0.245279i) q^{14} +(-2.10914 - 0.133392i) q^{15} +(-3.75760 + 1.37128i) q^{16} +3.74320 q^{17} +(0.938113 + 4.13763i) q^{18} -4.78182i q^{19} +(-0.833654 + 2.29348i) q^{20} +(-1.44235 - 0.958976i) q^{21} +(0.0308715 - 0.175299i) q^{22} +(0.325176 - 0.563221i) q^{23} +(4.88941 + 0.306094i) q^{24} +(-1.75562 - 3.04082i) q^{25} +(4.47660 - 1.63043i) q^{26} +(0.978691 - 5.10315i) q^{27} +(-1.53154 + 1.28623i) q^{28} +(0.306412 - 0.176907i) q^{29} +(2.06134 - 2.16412i) q^{30} +(0.967654 - 1.67603i) q^{31} +(1.92910 - 5.31776i) q^{32} +(-0.120699 + 0.181537i) q^{33} +(-3.40185 + 4.05592i) q^{34} +1.22015i q^{35} +(-5.33586 - 2.74382i) q^{36} -6.46775i q^{37} +(5.18131 + 4.34575i) q^{38} +(-5.82338 - 0.368296i) q^{39} +(-1.72746 - 2.98764i) q^{40} +(-1.92471 + 3.33369i) q^{41} +(2.34991 - 0.691321i) q^{42} +(0.0462098 - 0.0266792i) q^{43} +(0.161888 + 0.192764i) q^{44} +(-3.37536 + 1.41626i) q^{45} +(0.314752 + 0.864202i) q^{46} +(-3.25228 - 5.63312i) q^{47} +(-4.77520 + 5.01971i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(4.89039 + 0.861234i) q^{50} +(5.80821 - 2.88084i) q^{51} +(-2.30173 + 6.33234i) q^{52} +9.88039i q^{53} +(4.64005 + 5.69824i) q^{54} +0.153571 q^{55} +(-0.00180565 - 2.82843i) q^{56} +(-3.68019 - 7.41981i) q^{57} +(-0.0867832 + 0.492785i) q^{58} +(11.2403 + 6.48957i) q^{59} +(0.471556 + 4.20033i) q^{60} +(0.775046 - 0.447473i) q^{61} +(0.936636 + 2.57168i) q^{62} +(-2.97610 - 0.377955i) q^{63} +(4.00884 + 6.92309i) q^{64} +(2.05524 + 3.55979i) q^{65} +(-0.0870114 - 0.295766i) q^{66} +(9.06930 + 5.23616i) q^{67} +(-1.30314 - 7.37211i) q^{68} +(0.0710991 - 1.12420i) q^{69} +(-1.32208 - 1.10888i) q^{70} -1.31296 q^{71} +(7.82233 - 3.28803i) q^{72} +0.515433 q^{73} +(7.00809 + 5.87794i) q^{74} +(-5.06443 - 3.36719i) q^{75} +(-9.41763 + 1.66472i) q^{76} +(0.109000 + 0.0629313i) q^{77} +(5.69140 - 5.97517i) q^{78} +(7.16498 + 12.4101i) q^{79} +(4.80716 + 0.843414i) q^{80} +(-2.40889 - 8.67164i) q^{81} +(-1.86301 - 5.11520i) q^{82} +(12.7247 - 7.34662i) q^{83} +(-1.38654 + 3.17451i) q^{84} +(-3.95536 - 2.28363i) q^{85} +(-0.0130877 + 0.0743167i) q^{86} +(0.339299 - 0.510322i) q^{87} +(-0.355993 + 0.000227263i) q^{88} -6.87704 q^{89} +(1.53297 - 4.94446i) q^{90} +3.36885i q^{91} +(-1.22245 - 0.444346i) q^{92} +(0.211576 - 3.34537i) q^{93} +(9.05943 + 1.59543i) q^{94} +(-2.91726 + 5.05284i) q^{95} +(-1.09933 - 9.73609i) q^{96} +(-3.75514 - 6.50410i) q^{97} +(-0.483972 - 1.32882i) q^{98} +(-0.0475703 + 0.374579i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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