LMFDB - Embedded newform 228.2.c.a.191.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,2,Mod(191,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("228.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.c (of order $2$, degree $1$, 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:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			191.34
Character	$\chi$	$=$	228.191
Dual form			228.2.c.a.191.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39068 + 0.256903i) q^{2} +(-1.58499 - 0.698441i) q^{3} +(1.86800 + 0.714541i) q^{4} +3.19367i q^{5} +(-2.02478 - 1.37850i) q^{6} -0.170940i q^{7} +(2.41423 + 1.47359i) q^{8} +(2.02436 + 2.21404i) q^{9} +O(q^{10})$	\(q+(1.39068 + 0.256903i) q^{2} +(-1.58499 - 0.698441i) q^{3} +(1.86800 + 0.714541i) q^{4} +3.19367i q^{5} +(-2.02478 - 1.37850i) q^{6} -0.170940i q^{7} +(2.41423 + 1.47359i) q^{8} +(2.02436 + 2.21404i) q^{9} +(-0.820463 + 4.44139i) q^{10} +2.51166 q^{11} +(-2.46169 - 2.43723i) q^{12} -0.910042 q^{13} +(0.0439149 - 0.237723i) q^{14} +(2.23059 - 5.06192i) q^{15} +(2.97886 + 2.66953i) q^{16} -4.74351i q^{17} +(2.24645 + 3.59909i) q^{18} -1.00000i q^{19} +(-2.28201 + 5.96579i) q^{20} +(-0.119391 + 0.270937i) q^{21} +(3.49292 + 0.645252i) q^{22} -5.70287 q^{23} +(-2.79731 - 4.02183i) q^{24} -5.19954 q^{25} +(-1.26558 - 0.233792i) q^{26} +(-1.66221 - 4.92311i) q^{27} +(0.122144 - 0.319316i) q^{28} +4.36923i q^{29} +(4.40247 - 6.46649i) q^{30} -5.77040i q^{31} +(3.45685 + 4.47774i) q^{32} +(-3.98094 - 1.75424i) q^{33} +(1.21862 - 6.59672i) q^{34} +0.545926 q^{35} +(2.19949 + 5.58231i) q^{36} +2.04943 q^{37} +(0.256903 - 1.39068i) q^{38} +(1.44240 + 0.635610i) q^{39} +(-4.70618 + 7.71027i) q^{40} -10.9620i q^{41} +(-0.235640 + 0.346116i) q^{42} +5.51345i q^{43} +(4.69178 + 1.79468i) q^{44} +(-7.07091 + 6.46514i) q^{45} +(-7.93089 - 1.46508i) q^{46} -12.4258 q^{47} +(-2.85695 - 6.31172i) q^{48} +6.97078 q^{49} +(-7.23091 - 1.33577i) q^{50} +(-3.31306 + 7.51839i) q^{51} +(-1.69996 - 0.650262i) q^{52} -12.5541i q^{53} +(-1.04685 - 7.27352i) q^{54} +8.02141i q^{55} +(0.251896 - 0.412689i) q^{56} +(-0.698441 + 1.58499i) q^{57} +(-1.12247 + 6.07622i) q^{58} +7.82741 q^{59} +(7.78370 - 7.86184i) q^{60} -8.29853 q^{61} +(1.48243 - 8.02480i) q^{62} +(0.378468 - 0.346044i) q^{63} +(3.65704 + 7.11520i) q^{64} -2.90637i q^{65} +(-5.08556 - 3.46231i) q^{66} +1.21875i q^{67} +(3.38943 - 8.86088i) q^{68} +(9.03897 + 3.98312i) q^{69} +(0.759211 + 0.140250i) q^{70} +3.94565 q^{71} +(1.62469 + 8.32829i) q^{72} +12.9265 q^{73} +(2.85011 + 0.526503i) q^{74} +(8.24119 + 3.63157i) q^{75} +(0.714541 - 1.86800i) q^{76} -0.429343i q^{77} +(1.84264 + 1.25449i) q^{78} +0.0130423i q^{79} +(-8.52559 + 9.51351i) q^{80} +(-0.803924 + 8.96402i) q^{81} +(2.81618 - 15.2447i) q^{82} +7.86488 q^{83} +(-0.416619 + 0.420802i) q^{84} +15.1492 q^{85} +(-1.41642 + 7.66746i) q^{86} +(3.05165 - 6.92518i) q^{87} +(6.06373 + 3.70117i) q^{88} -3.43793i q^{89} +(-11.4943 + 7.17444i) q^{90} +0.155562i q^{91} +(-10.6530 - 4.07493i) q^{92} +(-4.03028 + 9.14600i) q^{93} +(-17.2804 - 3.19222i) q^{94} +3.19367 q^{95} +(-2.35162 - 9.51157i) q^{96} -13.5712 q^{97} +(9.69415 + 1.79081i) q^{98} +(5.08450 + 5.56091i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{6}+O(q^{10}) $ 36 * q - 6 * q^6	$ 36 q - 6 q^{6} + 8 q^{10} + 4 q^{12} - 8 q^{16} + 16 q^{18} + 8 q^{21} - 12 q^{22} - 2 q^{24} - 28 q^{25} + 12 q^{28} - 12 q^{30} - 28 q^{34} - 22 q^{36} - 16 q^{37} - 12 q^{40} + 10 q^{42} + 16 q^{45} - 4 q^{46} + 32 q^{48} - 44 q^{49} - 36 q^{52} - 20 q^{54} - 4 q^{58} - 4 q^{60} + 16 q^{61} + 24 q^{64} + 24 q^{66} - 16 q^{69} + 36 q^{70} - 36 q^{72} - 8 q^{73} - 32 q^{78} - 40 q^{81} + 72 q^{82} - 20 q^{84} + 16 q^{85} - 16 q^{88} - 56 q^{90} + 8 q^{93} - 56 q^{94} + 2 q^{96} + 40 q^{97}+O(q^{100}) $ 36 * q - 6 * q^6 + 8 * q^10 + 4 * q^12 - 8 * q^16 + 16 * q^18 + 8 * q^21 - 12 * q^22 - 2 * q^24 - 28 * q^25 + 12 * q^28 - 12 * q^30 - 28 * q^34 - 22 * q^36 - 16 * q^37 - 12 * q^40 + 10 * q^42 + 16 * q^45 - 4 * q^46 + 32 * q^48 - 44 * q^49 - 36 * q^52 - 20 * q^54 - 4 * q^58 - 4 * q^60 + 16 * q^61 + 24 * q^64 + 24 * q^66 - 16 * q^69 + 36 * q^70 - 36 * q^72 - 8 * q^73 - 32 * q^78 - 40 * q^81 + 72 * q^82 - 20 * q^84 + 16 * q^85 - 16 * q^88 - 56 * q^90 + 8 * q^93 - 56 * q^94 + 2 * q^96 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.39068	+	0.256903i	0.983362	+	0.181658i
$2$	1.39068	+	0.256903i	0.983362	+	0.181658i
$3$	−1.58499	−	0.698441i	−0.915092	−	0.403245i
$3$	−1.58499	−	0.698441i	−0.915092	−	0.403245i
$4$	1.86800	+	0.714541i	0.934001	+	0.357270i
$5$			3.19367i			1.42825i	0.700017	+	0.714127i	$0.253176\pi$
$5$			3.19367i			1.42825i	−0.700017	+	0.714127i	$0.746824\pi$
$6$	−2.02478	−	1.37850i	−0.826614	−	0.562769i
$7$		−	0.170940i		−	0.0646092i	−0.999478	−	0.0323046i	$-0.989715\pi$
$7$		−	0.170940i		−	0.0646092i	0.999478	−	0.0323046i	$-0.0102847\pi$
$8$	2.41423	+	1.47359i	0.853560	+	0.520994i
$9$	2.02436	+	2.21404i	0.674787	+	0.738012i
$10$	−0.820463	+	4.44139i	−0.259453	+	1.40449i
$11$	2.51166			0.757293			0.378647	−	0.925541i	$-0.376390\pi$
$11$	2.51166			0.757293			0.378647	+	0.925541i	$0.376390\pi$
$12$	−2.46169	−	2.43723i	−0.710630	−	0.703566i
$13$	−0.910042			−0.252400			−0.126200	−	0.992005i	$-0.540278\pi$
$13$	−0.910042			−0.252400			−0.126200	+	0.992005i	$0.540278\pi$
$14$	0.0439149	−	0.237723i	0.0117368	−	0.0635343i
$15$	2.23059	−	5.06192i	0.575936	−	1.30698i
$16$	2.97886	+	2.66953i	0.744716	+	0.667382i
$17$		−	4.74351i		−	1.15047i	−0.817988	−	0.575235i	$-0.804911\pi$
$17$		−	4.74351i		−	1.15047i	0.817988	−	0.575235i	$-0.195089\pi$
$18$	2.24645	+	3.59909i	0.529494	+	0.848314i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−2.28201	+	5.96579i	−0.510272	+	1.33399i
$21$	−0.119391	+	0.270937i	−0.0260533	+	0.0591234i
$22$	3.49292	+	0.645252i	0.744693	+	0.137568i
$23$	−5.70287			−1.18913			−0.594566	−	0.804047i	$-0.702676\pi$
$23$	−5.70287			−1.18913			−0.594566	+	0.804047i	$0.702676\pi$
$24$	−2.79731	−	4.02183i	−0.570998	−	0.820952i
$25$	−5.19954			−1.03991
$26$	−1.26558	−	0.233792i	−0.248201	−	0.0458504i
$27$	−1.66221	−	4.92311i	−0.319892	−	0.947454i
$28$	0.122144	−	0.319316i	0.0230830	−	0.0603451i
$29$			4.36923i			0.811347i	0.914018	+	0.405673i	$0.132963\pi$
$29$			4.36923i			0.811347i	−0.914018	+	0.405673i	$0.867037\pi$
$30$	4.40247	−	6.46649i	0.803777	−	1.18061i
$31$		−	5.77040i		−	1.03639i	−0.855261	−	0.518197i	$-0.826603\pi$
$31$		−	5.77040i		−	1.03639i	0.855261	−	0.518197i	$-0.173397\pi$
$32$	3.45685	+	4.47774i	0.611090	+	0.791561i
$33$	−3.98094	−	1.75424i	−0.692993	−	0.305375i
$34$	1.21862	−	6.59672i	0.208992	−	1.13133i
$35$	0.545926			0.0922784
$36$	2.19949	+	5.58231i	0.366582	+	0.930386i
$37$	2.04943			0.336924			0.168462	−	0.985708i	$-0.446120\pi$
$37$	2.04943			0.336924			0.168462	+	0.985708i	$0.446120\pi$
$38$	0.256903	−	1.39068i	0.0416751	−	0.225599i
$39$	1.44240	+	0.635610i	0.230969	+	0.101779i
$40$	−4.70618	+	7.71027i	−0.744112	+	1.21910i
$41$		−	10.9620i		−	1.71198i	−0.516990	−	0.855991i	$-0.672948\pi$
$41$		−	10.9620i		−	1.71198i	0.516990	−	0.855991i	$-0.327052\pi$
$42$	−0.235640	+	0.346116i	−0.0363601	+	0.0534069i
$43$			5.51345i			0.840793i	0.907341	+	0.420396i	$0.138109\pi$
$43$			5.51345i			0.840793i	−0.907341	+	0.420396i	$0.861891\pi$
$44$	4.69178	+	1.79468i	0.707313	+	0.270558i
$45$	−7.07091	+	6.46514i	−1.05407	+	0.963767i
$46$	−7.93089	−	1.46508i	−1.16935	−	0.216015i
$47$	−12.4258			−1.81249			−0.906245	−	0.422753i	$-0.861064\pi$
$47$	−12.4258			−1.81249			−0.906245	+	0.422753i	$0.861064\pi$
$48$	−2.85695	−	6.31172i	−0.412365	−	0.911019i
$49$	6.97078			0.995826
$50$	−7.23091	−	1.33577i	−1.02261	−	0.188907i
$51$	−3.31306	+	7.51839i	−0.463921	+	1.05279i
$52$	−1.69996	−	0.650262i	−0.235742	−	0.0901751i
$53$		−	12.5541i		−	1.72444i	−0.506536	−	0.862219i	$-0.669074\pi$
$53$		−	12.5541i		−	1.72444i	0.506536	−	0.862219i	$-0.330926\pi$
$54$	−1.04685	−	7.27352i	−0.142458	−	0.989801i
$55$			8.02141i			1.08161i
$56$	0.251896	−	0.412689i	0.0336610	−	0.0551479i
$57$	−0.698441	+	1.58499i	−0.0925107	+	0.209937i
$58$	−1.12247	+	6.07622i	−0.147387	+	0.797847i
$59$	7.82741			1.01904			0.509521	−	0.860458i	$-0.329823\pi$
$59$	7.82741			1.01904			0.509521	+	0.860458i	$0.329823\pi$
$60$	7.78370	−	7.86184i	1.00487	−	1.01496i
$61$	−8.29853			−1.06252			−0.531259	−	0.847209i	$-0.678281\pi$
$61$	−8.29853			−1.06252			−0.531259	+	0.847209i	$0.678281\pi$
$62$	1.48243	−	8.02480i	0.188269	−	1.01915i
$63$	0.378468	−	0.346044i	0.0476824	−	0.0435975i
$64$	3.65704	+	7.11520i	0.457130	+	0.889400i
$65$		−	2.90637i		−	0.360491i
$66$	−5.08556	−	3.46231i	−0.625989	−	0.426181i
$67$			1.21875i			0.148895i	0.997225	+	0.0744473i	$0.0237193\pi$
$67$			1.21875i			0.148895i	−0.997225	+	0.0744473i	$0.976281\pi$
$68$	3.38943	−	8.86088i	0.411029	−	1.07454i
$69$	9.03897	+	3.98312i	1.08816	+	0.479511i
$70$	0.759211	+	0.140250i	0.0907430	+	0.0167631i
$71$	3.94565			0.468262			0.234131	−	0.972205i	$-0.424776\pi$
$71$	3.94565			0.468262			0.234131	+	0.972205i	$0.424776\pi$
$72$	1.62469	+	8.32829i	0.191471	+	0.981498i
$73$	12.9265			1.51293			0.756467	−	0.654032i	$-0.226924\pi$
$73$	12.9265			1.51293			0.756467	+	0.654032i	$0.226924\pi$
$74$	2.85011	+	0.526503i	0.331318	+	0.0612048i
$75$	8.24119	+	3.63157i	0.951611	+	0.419337i
$76$	0.714541	−	1.86800i	0.0819634	−	0.214275i
$77$		−	0.429343i		−	0.0489282i
$78$	1.84264	+	1.25449i	0.208638	+	0.142043i
$79$			0.0130423i			0.00146737i	1.00000		0.000733685i	$0.000233539\pi$
$79$			0.0130423i			0.00146737i	−1.00000		0.000733685i	$0.999766\pi$
$80$	−8.52559	+	9.51351i	−0.953190	+	1.06364i
$81$	−0.803924	+	8.96402i	−0.0893249	+	0.996003i
$82$	2.81618	−	15.2447i	0.310995	−	1.68350i
$83$	7.86488			0.863283			0.431642	−	0.902045i	$-0.357935\pi$
$83$	7.86488			0.863283			0.431642	+	0.902045i	$0.357935\pi$
$84$	−0.416619	+	0.420802i	−0.0454569	+	0.0459132i
$85$	15.1492			1.64316
$86$	−1.41642	+	7.66746i	−0.152736	+	0.826803i
$87$	3.05165	−	6.92518i	0.327171	−	0.742457i
$88$	6.06373	+	3.70117i	0.646395	+	0.394546i
$89$		−	3.43793i		−	0.364420i	−0.983260	−	0.182210i	$-0.941675\pi$
$89$		−	3.43793i		−	0.364420i	0.983260	−	0.182210i	$-0.0583251\pi$
$90$	−11.4943	+	7.17444i	−1.21161	+	0.756252i
$91$			0.155562i			0.0163074i
$92$	−10.6530	−	4.07493i	−1.11065	−	0.424841i
$93$	−4.03028	+	9.14600i	−0.417921	+	0.948396i
$94$	−17.2804	−	3.19222i	−1.78233	−	0.329253i
$95$	3.19367			0.327664
$96$	−2.35162	−	9.51157i	−0.240011	−	0.970770i
$97$	−13.5712			−1.37795			−0.688975	−	0.724785i	$-0.741939\pi$
$97$	−13.5712			−1.37795			−0.688975	+	0.724785i	$0.741939\pi$
$98$	9.69415	+	1.79081i	0.979257	+	0.180899i
$99$	5.08450	+	5.56091i	0.511012	+	0.558892i
$100$	−9.71275	−	3.71528i	−0.971275	−	0.371528i
$101$			15.6006i			1.55232i	0.630537	+	0.776159i	$0.282835\pi$
$101$			15.6006i			1.55232i	−0.630537	+	0.776159i	$0.717165\pi$
$102$	−6.53891	+	9.60457i	−0.647449	+	0.950995i
$103$			14.3532i			1.41426i	0.707082	+	0.707131i	$0.250011\pi$
$103$			14.3532i			1.41426i	−0.707082	+	0.707131i	$0.749989\pi$
$104$	−2.19705	−	1.34103i	−0.215439	−	0.131499i
$105$	−0.865285	−	0.381297i	−0.0844432	−	0.0372108i
$106$	3.22518	−	17.4588i	0.313257	−	1.69575i
$107$	−2.16227			−0.209035			−0.104517	−	0.994523i	$-0.533330\pi$
$107$	−2.16227			−0.209035			−0.104517	+	0.994523i	$0.533330\pi$
$108$	0.412753	−	10.3841i	0.0397172	−	0.999211i
$109$	−1.80620			−0.173002			−0.0865012	−	0.996252i	$-0.527569\pi$
$109$	−1.80620			−0.173002			−0.0865012	+	0.996252i	$0.527569\pi$
$110$	−2.06072	+	11.1552i	−0.196482	+	1.06361i
$111$	−3.24831	−	1.43140i	−0.308316	−	0.135863i
$112$	0.456329	−	0.509207i	0.0431190	−	0.0481155i
$113$		−	7.79014i		−	0.732835i	−0.930451	−	0.366417i	$-0.880584\pi$
$113$		−	7.79014i		−	0.732835i	0.930451	−	0.366417i	$-0.119416\pi$
$114$	−1.37850	+	2.02478i	−0.129108	+	0.189638i
$115$		−	18.2131i		−	1.69838i
$116$	−3.12200	+	8.16174i	−0.289870	+	0.757799i
$117$	−1.84225	−	2.01487i	−0.170316	−	0.186274i
$118$	10.8855	+	2.01088i	1.00209	+	0.185117i
$119$	−0.810855			−0.0743310
$120$	12.8444	−	8.93368i	1.17253	−	0.815529i
$121$	−4.69157			−0.426507
$122$	−11.5406	−	2.13191i	−1.04484	−	0.193014i
$123$	−7.65633	+	17.3747i	−0.690348	+	1.56662i
$124$	4.12318	−	10.7791i	0.370273	−	0.967993i
$125$		−	0.637258i		−	0.0569981i
$126$	0.615228	−	0.384009i	0.0548089	−	0.0342102i
$127$		−	6.48515i		−	0.575464i	−0.957711	−	0.287732i	$-0.907099\pi$
$127$		−	6.48515i		−	0.575464i	0.957711	−	0.287732i	$-0.0929012\pi$
$128$	3.25787	+	10.8345i	0.287958	+	0.957643i
$129$	3.85082	−	8.73874i	0.339045	−	0.769403i
$130$	0.746655	−	4.04185i	0.0654860	−	0.354493i
$131$	−17.6837			−1.54503			−0.772517	−	0.634994i	$-0.781003\pi$
$131$	−17.6837			−1.54503			−0.772517	+	0.634994i	$0.781003\pi$
$132$	−6.18293	−	6.12148i	−0.538155	−	0.532806i
$133$	−0.170940			−0.0148224
$134$	−0.313101	+	1.69490i	−0.0270478	+	0.146417i
$135$	15.7228	−	5.30855i	1.35320	−	0.456888i
$136$	6.99001	−	11.4519i	0.599388	−	0.981995i
$137$			2.61564i			0.223469i	0.993738	+	0.111734i	$0.0356406\pi$
$137$			2.61564i			0.223469i	−0.993738	+	0.111734i	$0.964359\pi$
$138$	11.5471	+	7.86139i	0.982953	+	0.669206i
$139$			20.4109i			1.73123i	0.500714	+	0.865613i	$0.333071\pi$
$139$			20.4109i			1.73123i	−0.500714	+	0.865613i	$0.666929\pi$
$140$	1.01979	+	0.390086i	0.0861881	+	0.0329683i
$141$	19.6947	+	8.67869i	1.65860	+	0.730878i
$142$	5.48715	+	1.01365i	0.460471	+	0.0850633i
$143$	−2.28571			−0.191141
$144$	0.119864	+	11.9994i	0.00998866	+	0.999950i
$145$	−13.9539			−1.15881
$146$	17.9767	+	3.32085i	1.48776	+	0.274836i
$147$	−11.0486	−	4.86868i	−0.911272	−	0.401562i
$148$	3.82833	+	1.46440i	0.314687	+	0.120373i
$149$			6.36477i			0.521422i	0.965417	+	0.260711i	$0.0839570\pi$
$149$			6.36477i			0.521422i	−0.965417	+	0.260711i	$0.916043\pi$
$150$	10.5279	+	7.16755i	0.859602	+	0.585228i
$151$		−	4.47696i		−	0.364330i	−0.983268	−	0.182165i	$-0.941690\pi$
$151$		−	4.47696i		−	0.364330i	0.983268	−	0.182165i	$-0.0583104\pi$
$152$	1.47359	−	2.41423i	0.119524	−	0.195820i
$153$	10.5023	−	9.60257i	0.849061	−	0.776322i
$154$	0.110299	−	0.597080i	0.00888817	−	0.0481141i
$155$	18.4288			1.48023
$156$	2.24024	+	2.21798i	0.179363	+	0.177580i
$157$	0.214512			0.0171199			0.00855996	−	0.999963i	$-0.497275\pi$
$157$	0.214512			0.0171199			0.00855996	+	0.999963i	$0.497275\pi$
$158$	−0.00335059	+	0.0181377i	−0.000266559	+	0.00144296i
$159$	−8.76829	+	19.8981i	−0.695371	+	1.57802i
$160$	−14.3004	+	11.0400i	−1.13055	+	0.872792i
$161$			0.974849i			0.0768289i
$162$	−3.42088	+	12.2596i	−0.268770	+	0.963204i
$163$		−	7.93560i		−	0.621564i	−0.950481	−	0.310782i	$-0.899409\pi$
$163$		−	7.93560i		−	0.621564i	0.950481	−	0.310782i	$-0.100591\pi$
$164$	7.83282	−	20.4771i	0.611640	−	1.59899i
$165$	5.60248	−	12.7138i	0.436152	−	0.989770i
$166$	10.9376	+	2.02051i	0.848920	+	0.156822i
$167$	−3.67743			−0.284568			−0.142284	−	0.989826i	$-0.545445\pi$
$167$	−3.67743			−0.284568			−0.142284	+	0.989826i	$0.545445\pi$
$168$	−0.687491	+	0.478171i	−0.0530411	+	0.0368917i
$169$	−12.1718			−0.936294
$170$	21.0678	+	3.89187i	1.61582	+	0.298493i
$171$	2.21404	−	2.02436i	0.169312	−	0.154807i
$172$	−3.93958	+	10.2991i	−0.300390	+	0.785301i
$173$			8.00279i			0.608440i	0.952602	+	0.304220i	$0.0983959\pi$
$173$			8.00279i			0.608440i	−0.952602	+	0.304220i	$0.901604\pi$
$174$	6.02298	−	8.84675i	0.456601	−	0.670671i
$175$			0.888809i			0.0671876i
$176$	7.48189	+	6.70494i	0.563968	+	0.505404i
$177$	−12.4063	−	5.46698i	−0.932518	−	0.410924i
$178$	0.883214	−	4.78108i	0.0661997	−	0.358357i
$179$	6.19360			0.462932			0.231466	−	0.972843i	$-0.425648\pi$
$179$	6.19360			0.462932			0.231466	+	0.972843i	$0.425648\pi$
$180$	−17.8281	+	7.02445i	−1.32883	+	0.523572i
$181$	0.538014			0.0399903			0.0199951	−	0.999800i	$-0.493635\pi$
$181$	0.538014			0.0399903			0.0199951	+	0.999800i	$0.493635\pi$
$182$	−0.0399644	+	0.216338i	−0.00296236	+	0.0160361i
$183$	13.1531	+	5.79603i	0.972302	+	0.428455i
$184$	−13.7681	−	8.40372i	−1.01500	−	0.619531i
$185$			6.54520i			0.481213i
$186$	−7.95448	+	11.6838i	−0.583250	+	0.856698i
$187$		−	11.9141i		−	0.871243i
$188$	−23.2114	−	8.87874i	−1.69287	−	0.647549i
$189$	−0.841557	+	0.284138i	−0.0612143	+	0.0206680i
$190$	4.44139	+	0.820463i	0.322212	+	0.0595226i
$191$	19.4448			1.40698			0.703488	−	0.710707i	$-0.251625\pi$
$191$	19.4448			1.40698			0.703488	+	0.710707i	$0.251625\pi$
$192$	−0.826809	−	13.8317i	−0.0596698	−	0.998218i
$193$	−22.6223			−1.62839			−0.814194	−	0.580593i	$-0.802821\pi$
$193$	−22.6223			−1.62839			−0.814194	+	0.580593i	$0.802821\pi$
$194$	−18.8733	−	3.48649i	−1.35502	−	0.250315i
$195$	−2.02993	+	4.60656i	−0.145366	+	0.329883i
$196$	13.0214	+	4.98090i	0.930102	+	0.355779i
$197$		−	14.8613i		−	1.05882i	−0.848366	−	0.529411i	$-0.822413\pi$
$197$		−	14.8613i		−	1.05882i	0.848366	−	0.529411i	$-0.177587\pi$
$198$	5.64232	+	9.03968i	0.400983	+	0.642422i
$199$		−	9.86354i		−	0.699208i	−0.936898	−	0.349604i	$-0.886316\pi$
$199$		−	9.86354i		−	0.699208i	0.936898	−	0.349604i	$-0.113684\pi$
$200$	−12.5529	−	7.66201i	−0.887624	−	0.541786i
$201$	0.851228	−	1.93171i	0.0600410	−	0.136252i
$202$	−4.00784	+	21.6955i	−0.281991	+	1.52649i
$203$	0.746877			0.0524205
$204$	−11.5610	+	11.6771i	−0.809432	+	0.817558i
$205$	35.0091			2.44514
$206$	−3.68737	+	19.9608i	−0.256911	+	1.39073i
$207$	−11.5447	−	12.6264i	−0.802410	−	0.877594i
$208$	−2.71089	−	2.42938i	−0.187966	−	0.168447i
$209$		−	2.51166i		−	0.173735i
$210$	−1.10538	−	0.752558i	−0.0762786	−	0.0519314i
$211$		−	18.8262i		−	1.29605i	−0.761619	−	0.648025i	$-0.775595\pi$
$211$		−	18.8262i		−	1.29605i	0.761619	−	0.648025i	$-0.224405\pi$
$212$	8.97041	−	23.4511i	0.616090	−	1.61063i
$213$	−6.25379	−	2.75580i	−0.428503	−	0.188824i
$214$	−3.00703	−	0.555493i	−0.205557	−	0.0379727i
$215$	−17.6081			−1.20087
$216$	3.24171	−	14.3350i	0.220571	−	0.975371i
$217$	−0.986392			−0.0669606
$218$	−2.51185	−	0.464017i	−0.170124	−	0.0314272i
$219$	−20.4883	−	9.02840i	−1.38447	−	0.610083i
$220$	−5.73162	+	14.9840i	−0.386426	+	1.01022i
$221$			4.31679i			0.290379i
$222$	−4.14965	−	2.82513i	−0.278506	−	0.189610i
$223$			18.0626i			1.20956i	0.796393	+	0.604780i	$0.206739\pi$
$223$			18.0626i			1.20956i	−0.796393	+	0.604780i	$0.793261\pi$
$224$	0.765426	−	0.590914i	0.0511421	−	0.0394821i
$225$	−10.5257	−	11.5120i	−0.701716	−	0.767465i
$226$	2.00131	−	10.8336i	0.133125	−	0.720642i
$227$	−9.57770			−0.635694			−0.317847	−	0.948142i	$-0.602960\pi$
$227$	−9.57770			−0.635694			−0.317847	+	0.948142i	$0.602960\pi$
$228$	−2.43723	+	2.46169i	−0.161409	+	0.163030i
$229$	15.9622			1.05481			0.527405	−	0.849614i	$-0.323165\pi$
$229$	15.9622			1.05481			0.527405	+	0.849614i	$0.323165\pi$
$230$	4.67899	−	25.3287i	0.308524	−	1.67012i
$231$	−0.299870	+	0.680502i	−0.0197300	+	0.0447738i
$232$	−6.43848	+	10.5483i	−0.422707	+	0.692533i
$233$		−	9.30430i		−	0.609545i	−0.952425	−	0.304773i	$-0.901420\pi$
$233$		−	9.30430i		−	0.609545i	0.952425	−	0.304773i	$-0.0985805\pi$
$234$	−2.04437	−	3.27532i	−0.133644	−	0.214114i
$235$		−	39.6839i		−	2.58870i
$236$	14.6216	+	5.59300i	0.951787	+	0.364074i
$237$	0.00910925	−	0.0206718i	0.000591710	−	0.00134278i
$238$	−1.12764	−	0.208311i	−0.0730942	−	0.0135028i
$239$	6.56837			0.424873			0.212436	−	0.977175i	$-0.431860\pi$
$239$	6.56837			0.424873			0.212436	+	0.977175i	$0.431860\pi$
$240$	20.1576	−	9.12416i	1.30117	−	0.588962i
$241$	−1.87133			−0.120543			−0.0602714	−	0.998182i	$-0.519197\pi$
$241$	−1.87133			−0.120543			−0.0602714	+	0.998182i	$0.519197\pi$
$242$	−6.52449	−	1.20528i	−0.419410	−	0.0774782i
$243$	7.53505	−	13.6464i	0.483373	−	0.875414i
$244$	−15.5017	−	5.92964i	−0.992393	−	0.379606i
$245$			22.2624i			1.42229i
$246$	−15.1111	+	22.1957i	−0.963451	+	1.41515i
$247$			0.910042i			0.0579046i
$248$	8.50323	−	13.9311i	0.539955	−	0.884625i
$249$	−12.4657	−	5.49315i	−0.789983	−	0.348115i
$250$	0.163713	−	0.886224i	0.0103541	−	0.0560498i
$251$	−19.8957			−1.25581			−0.627903	−	0.778292i	$-0.716086\pi$
$251$	−19.8957			−1.25581			−0.627903	+	0.778292i	$0.716086\pi$
$252$	0.954241	−	0.375981i	0.0601115	−	0.0236846i
$253$	−14.3237			−0.900521
$254$	1.66605	−	9.01879i	0.104537	−	0.565889i
$255$	−24.0113	−	10.5808i	−1.50364	−	0.662597i
$256$	1.74726	+	15.9043i	0.109204	+	0.994019i
$257$			8.35519i			0.521182i	0.965449	+	0.260591i	$0.0839174\pi$
$257$			8.35519i			0.521182i	−0.965449	+	0.260591i	$0.916083\pi$
$258$	7.60027	−	11.1635i	0.473172	−	0.695011i
$259$		−	0.350329i		−	0.0217684i
$260$	2.07672	−	5.42911i	0.128793	−	0.336699i
$261$	−9.67365	+	8.84491i	−0.598784	+	0.547486i
$262$	−24.5925	−	4.54300i	−1.51933	−	0.280667i
$263$	−2.61091			−0.160996			−0.0804979	−	0.996755i	$-0.525651\pi$
$263$	−2.61091			−0.160996			−0.0804979	+	0.996755i	$0.525651\pi$
$264$	−7.02588	−	10.1014i	−0.432413	−	0.621701i
$265$	40.0937			2.46293
$266$	−0.237723	−	0.0439149i	−0.0145758	−	0.00269260i
$267$	−2.40119	+	5.44908i	−0.146951	+	0.333478i
$268$	−0.870850	+	2.27664i	−0.0531956	+	0.139068i
$269$			23.4388i			1.42909i	0.699591	+	0.714544i	$0.253366\pi$
$269$			23.4388i			1.42909i	−0.699591	+	0.714544i	$0.746634\pi$
$270$	23.2292	−	3.34329i	1.41369	−	0.203466i
$271$			4.19984i			0.255122i	0.991831	+	0.127561i	$0.0407149\pi$
$271$			4.19984i			0.255122i	−0.991831	+	0.127561i	$0.959285\pi$
$272$	12.6629	−	14.1303i	0.767802	−	0.856773i
$273$	0.108651	−	0.246564i	0.00657587	−	0.0149228i
$274$	−0.671964	+	3.63752i	−0.0405948	+	0.219751i
$275$	−13.0595			−0.787515
$276$	14.0387	+	13.8992i	0.845032	+	0.836633i
$277$	−28.7428			−1.72699			−0.863494	−	0.504359i	$-0.831729\pi$
$277$	−28.7428			−1.72699			−0.863494	+	0.504359i	$0.831729\pi$
$278$	−5.24360	+	28.3850i	−0.314490	+	1.70242i
$279$	12.7759	−	11.6814i	0.764872	−	0.699345i
$280$	1.31799	+	0.804474i	0.0787651	+	0.0480765i
$281$			20.0095i			1.19367i	0.802365	+	0.596834i	$0.203575\pi$
$281$			20.0095i			1.19367i	−0.802365	+	0.596834i	$0.796425\pi$
$282$	25.1596	+	17.1289i	1.49823	+	1.02001i
$283$			23.6437i			1.40547i	0.711451	+	0.702735i	$0.248038\pi$
$283$			23.6437i			1.40547i	−0.711451	+	0.702735i	$0.751962\pi$
$284$	7.37047	+	2.81932i	0.437357	+	0.167296i
$285$	−5.06192	−	2.23059i	−0.299843	−	0.132129i
$286$	−3.17870	−	0.587206i	−0.187961	−	0.0347222i
$287$	−1.87385			−0.110610
$288$	−2.91598	+	16.7182i	−0.171826	+	0.985127i
$289$	−5.50087			−0.323581
$290$	−19.4055	−	3.58479i	−1.13953	−	0.210506i
$291$	21.5102	+	9.47871i	1.26095	+	0.555652i
$292$	24.1467	+	9.23651i	1.41308	+	0.540526i
$293$		−	10.8722i		−	0.635161i	−0.948231	−	0.317580i	$-0.897130\pi$
$293$		−	10.8722i		−	0.635161i	0.948231	−	0.317580i	$-0.102870\pi$
$294$	−14.1143	−	9.60920i	−0.823164	−	0.560420i
$295$			24.9982i			1.45545i
$296$	4.94779	+	3.02003i	0.287585	+	0.175535i
$297$	−4.17490	−	12.3652i	−0.242252	−	0.717501i
$298$	−1.63513	+	8.85138i	−0.0947203	+	0.512747i
$299$	5.18985			0.300137
$300$	12.7997	+	12.6724i	0.738989	+	0.731644i
$301$	0.942468			0.0543230
$302$	1.15014	−	6.22603i	0.0661832	−	0.358268i
$303$	10.8961	−	24.7268i	0.625965	−	1.42051i
$304$	2.66953	−	2.97886i	0.153108	−	0.170850i
$305$		−	26.5028i		−	1.51755i
$306$	17.0723	−	10.6561i	0.975959	−	0.609167i
$307$		−	1.18303i		−	0.0675193i	−0.999430	−	0.0337596i	$-0.989252\pi$
$307$		−	1.18303i		−	0.0675193i	0.999430	−	0.0337596i	$-0.0107481\pi$
$308$	0.306783	−	0.802013i	0.0174806	−	0.0456989i
$309$	10.0249	−	22.7496i	0.570294	−	1.29418i
$310$	25.6286	+	4.73439i	1.45560	+	0.268896i
$311$	21.8994			1.24180			0.620902	−	0.783889i	$-0.286767\pi$
$311$	21.8994			1.24180			0.620902	+	0.783889i	$0.286767\pi$
$312$	2.54567	+	3.66003i	0.144120	+	0.207208i
$313$	14.8808			0.841112			0.420556	−	0.907267i	$-0.361835\pi$
$313$	14.8808			0.841112			0.420556	+	0.907267i	$0.361835\pi$
$314$	0.298318	+	0.0551087i	0.0168351	+	0.00310996i
$315$	1.10515	+	1.20870i	0.0622682	+	0.0681026i
$316$	−0.00931923	+	0.0243630i	−0.000524248	+	0.00137053i
$317$			11.2174i			0.630033i	0.949086	+	0.315016i	$0.102010\pi$
$317$			11.2174i			0.630033i	−0.949086	+	0.315016i	$0.897990\pi$
$318$	−17.3058	+	25.4193i	−0.970461	+	1.42544i
$319$			10.9740i			0.614427i
$320$	−22.7236	+	11.6794i	−1.27029	+	0.652897i
$321$	3.42717	+	1.51022i	0.191286	+	0.0842921i
$322$	−0.250441	+	1.35571i	−0.0139565	+	0.0755506i
$323$	−4.74351			−0.263936
$324$	−7.90689	+	16.1704i	−0.439272	+	0.898354i
$325$	4.73180			0.262473
$326$	2.03868	−	11.0359i	0.112912	−	0.611223i
$327$	2.86280	+	1.26152i	0.158313	+	0.0697624i
$328$	16.1536	−	26.4649i	0.891933	−	1.46128i
$329$			2.12407i			0.117104i
$330$	11.0575	−	16.2416i	0.608695	−	0.894072i
$331$		−	8.93007i		−	0.490841i	−0.969417	−	0.245420i	$-0.921074\pi$
$331$		−	8.93007i		−	0.490841i	0.969417	−	0.245420i	$-0.0789260\pi$
$332$	14.6916	+	5.61978i	0.806307	+	0.308425i
$333$	4.14878	+	4.53751i	0.227352	+	0.248654i
$334$	−5.11414	−	0.944741i	−0.279833	−	0.0516939i
$335$	−3.89230			−0.212659
$336$	−1.07893	+	0.488367i	−0.0588602	+	0.0266426i
$337$	17.3650			0.945934			0.472967	−	0.881080i	$-0.343183\pi$
$337$	17.3650			0.945934			0.472967	+	0.881080i	$0.343183\pi$
$338$	−16.9272	−	3.12697i	−0.920716	−	0.170085i
$339$	−5.44095	+	12.3473i	−0.295512	+	0.670611i
$340$	28.2988	+	10.8247i	1.53472	+	0.587053i
$341$		−	14.4933i		−	0.784854i
$342$	3.59909	−	2.24645i	0.194616	−	0.121474i
$343$		−	2.38816i		−	0.128949i
$344$	−8.12458	+	13.3107i	−0.438048	+	0.717667i
$345$	−12.7208	+	28.8675i	−0.684863	+	1.55417i
$346$	−2.05594	+	11.1293i	−0.110528	+	0.598317i
$347$	9.32490			0.500587			0.250293	−	0.968170i	$-0.419473\pi$
$347$	9.32490			0.500587			0.250293	+	0.968170i	$0.419473\pi$
$348$	10.6488	−	10.7557i	0.570836	−	0.576567i
$349$	−5.48460			−0.293584			−0.146792	−	0.989167i	$-0.546895\pi$
$349$	−5.48460			−0.293584			−0.146792	+	0.989167i	$0.546895\pi$
$350$	−0.228337	+	1.23605i	−0.0122051	+	0.0660698i
$351$	1.51268	+	4.48024i	0.0807409	+	0.239137i
$352$	8.68242	+	11.2466i	0.462775	+	0.599444i
$353$		−	4.93775i		−	0.262810i	−0.991329	−	0.131405i	$-0.958051\pi$
$353$		−	4.93775i		−	0.262810i	0.991329	−	0.131405i	$-0.0419488\pi$
$354$	−15.8488	−	10.7901i	−0.842355	−	0.573486i
$355$			12.6011i			0.668797i
$356$	2.45654	−	6.42207i	0.130197	−	0.340369i
$357$	1.28519	+	0.566334i	0.0680197	+	0.0299736i
$358$	8.61334	+	1.59115i	0.455229	+	0.0840950i
$359$	2.96523			0.156499			0.0782495	−	0.996934i	$-0.475067\pi$
$359$	2.96523			0.156499			0.0782495	+	0.996934i	$0.475067\pi$
$360$	−26.5978	+	5.18871i	−1.40183	+	0.273469i
$361$	−1.00000			−0.0526316
$362$	0.748207	+	0.138217i	0.0393249	+	0.00726453i
$363$	7.43608	+	3.27679i	0.390293	+	0.171987i
$364$	−0.111156	+	0.290591i	−0.00582614	+	0.0152311i
$365$			41.2830i			2.16085i
$366$	16.8027	+	11.4395i	0.878293	+	0.597952i
$367$		−	33.4882i		−	1.74807i	−0.485865	−	0.874034i	$-0.661495\pi$
$367$		−	33.4882i		−	1.74807i	0.485865	−	0.874034i	$-0.338505\pi$
$368$	−16.9881	−	15.2240i	−0.885565	−	0.793604i
$369$	24.2704	−	22.1911i	1.26346	−	1.15522i
$370$	−1.68148	+	9.10230i	−0.0874159	+	0.473206i
$371$	−2.14600			−0.111415
$372$	−14.0638	+	14.2049i	−0.729172	+	0.736492i
$373$	−30.1155			−1.55932			−0.779662	−	0.626201i	$-0.784609\pi$
$373$	−30.1155			−1.55932			−0.779662	+	0.626201i	$0.784609\pi$
$374$	3.06076	−	16.5687i	0.158268	−	0.856747i
$375$	−0.445087	+	1.01005i	−0.0229842	+	0.0521585i
$376$	−29.9988	−	18.3106i	−1.54707	−	0.944297i
$377$		−	3.97619i		−	0.204784i
$378$	−1.24334	+	0.178948i	−0.0639503	+	0.00920410i
$379$			7.22631i			0.371190i	0.982626	+	0.185595i	$0.0594213\pi$
$379$			7.22631i			0.371190i	−0.982626	+	0.185595i	$0.940579\pi$
$380$	5.96579	+	2.28201i	0.306038	+	0.117065i
$381$	−4.52949	+	10.2789i	−0.232053	+	0.526602i
$382$	27.0415	+	4.99542i	1.38357	+	0.255588i
$383$	32.8471			1.67841			0.839204	−	0.543816i	$-0.183021\pi$
$383$	32.8471			1.67841			0.839204	+	0.543816i	$0.183021\pi$
$384$	2.40357	−	19.4480i	0.122657	−	0.992449i
$385$	1.37118			0.0698818
$386$	−31.4604	−	5.81172i	−1.60129	−	0.295809i
$387$	−12.2070	+	11.1612i	−0.620516	+	0.567356i
$388$	−25.3511	−	9.69720i	−1.28701	−	0.492301i
$389$		−	11.8958i		−	0.603141i	−0.953444	−	0.301571i	$-0.902489\pi$
$389$		−	11.8958i		−	0.603141i	0.953444	−	0.301571i	$-0.0975109\pi$
$390$	−4.00643	+	5.88478i	−0.202873	+	0.297987i
$391$			27.0516i			1.36806i
$392$	16.8291	+	10.2721i	0.849997	+	0.518820i
$393$	28.0285	+	12.3510i	1.41385	+	0.623027i
$394$	3.81790	−	20.6673i	0.192343	−	1.04120i
$395$	−0.0416527			−0.00209578
$396$	5.52437	+	14.0209i	0.277610	+	0.704575i
$397$	−6.43973			−0.323201			−0.161600	−	0.986856i	$-0.551666\pi$
$397$	−6.43973			−0.323201			−0.161600	+	0.986856i	$0.551666\pi$
$398$	2.53397	−	13.7171i	0.127016	−	0.687574i
$399$	0.270937	+	0.119391i	0.0135638	+	0.00597705i
$400$	−15.4887	−	13.8803i	−0.774436	−	0.694015i
$401$		−	3.66954i		−	0.183248i	−0.995794	−	0.0916240i	$-0.970794\pi$
$401$		−	3.66954i		−	0.183248i	0.995794	−	0.0916240i	$-0.0292058\pi$
$402$	1.68005	−	2.46771i	0.0837933	−	0.123078i
$403$			5.25130i			0.261586i
$404$	−11.1473	+	29.1420i	−0.554597	+	1.44987i
$405$	−28.6281	−	2.56747i	−1.42254	−	0.127579i
$406$	1.03867	+	0.191875i	0.0515483	+	0.00952258i
$407$	5.14746			0.255150
$408$	−19.0776	+	13.2690i	−0.944480	+	0.656916i
$409$	−17.2918			−0.855027			−0.427513	−	0.904009i	$-0.640610\pi$
$409$	−17.2918			−0.855027			−0.427513	+	0.904009i	$0.640610\pi$
$410$	48.6866	+	8.99394i	2.40446	+	0.444179i
$411$	1.82687	−	4.14575i	0.0901127	−	0.204495i
$412$	−10.2559	+	26.8118i	−0.505274	+	1.32092i
$413$		−	1.33802i		−	0.0658396i
$414$	−12.8112	−	20.5252i	−0.629638	−	1.00876i
$415$			25.1179i			1.23299i
$416$	−3.14588	−	4.07493i	−0.154239	−	0.199790i
$417$	14.2558	−	32.3509i	0.698108	−	1.58423i
$418$	0.645252	−	3.49292i	0.0315603	−	0.170844i
$419$	−15.2251			−0.743796			−0.371898	−	0.928274i	$-0.621293\pi$
$419$	−15.2251			−0.743796			−0.371898	+	0.928274i	$0.621293\pi$
$420$	−1.34390	−	1.33055i	−0.0655757	−	0.0649240i
$421$	−1.23549			−0.0602139			−0.0301069	−	0.999547i	$-0.509585\pi$
$421$	−1.23549			−0.0602139			−0.0301069	+	0.999547i	$0.509585\pi$
$422$	4.83650	−	26.1813i	0.235437	−	1.27449i
$423$	−25.1543	−	27.5112i	−1.22304	−	1.33764i
$424$	18.4997	−	30.3085i	0.898423	−	1.47191i
$425$			24.6641i			1.19638i
$426$	−7.98908	−	5.43906i	−0.387072	−	0.263523i
$427$			1.41855i			0.0686485i
$428$	−4.03913	−	1.54503i	−0.195238	−	0.0746818i
$429$	3.62282	+	1.59644i	0.174912	+	0.0770766i
$430$	−24.4873	−	4.52358i	−1.18088	−	0.218146i
$431$	−13.9335			−0.671151			−0.335576	−	0.942013i	$-0.608931\pi$
$431$	−13.9335			−0.671151			−0.335576	+	0.942013i	$0.608931\pi$
$432$	8.19089	−	19.1026i	0.394084	−	0.919074i
$433$	9.62116			0.462363			0.231182	−	0.972911i	$-0.425741\pi$
$433$	9.62116			0.462363			0.231182	+	0.972911i	$0.425741\pi$
$434$	−1.37176	−	0.253407i	−0.0658465	−	0.0121639i
$435$	22.1167	+	9.74597i	1.06042	+	0.467284i
$436$	−3.37398	−	1.29060i	−0.161584	−	0.0618086i
$437$			5.70287i			0.272805i
$438$	−26.1734	−	17.8192i	−1.25061	−	0.851432i
$439$			32.3438i			1.54369i	0.635813	+	0.771843i	$0.280665\pi$
$439$			32.3438i			1.54369i	−0.635813	+	0.771843i	$0.719335\pi$
$440$	−11.8203	+	19.3656i	−0.563511	+	0.923216i
$441$	14.1114	+	15.4336i	0.671970	+	0.734932i
$442$	−1.10899	+	6.00329i	−0.0527495	+	0.285547i
$443$	15.0856			0.716740			0.358370	−	0.933580i	$-0.383333\pi$
$443$	15.0856			0.716740			0.358370	+	0.933580i	$0.383333\pi$
$444$	−5.04506	−	4.99492i	−0.239428	−	0.237048i
$445$	10.9796			0.520484
$446$	−4.64033	+	25.1193i	−0.219726	+	1.18944i
$447$	4.44541	−	10.0881i	0.210261	−	0.477149i
$448$	1.21627	−	0.625134i	0.0574635	−	0.0295348i
$449$			17.4000i			0.821157i	0.911825	+	0.410578i	$0.134673\pi$
$449$			17.4000i			0.821157i	−0.911825	+	0.410578i	$0.865327\pi$
$450$	−11.6805	−	18.7136i	−0.550625	−	0.882168i
$451$		−	27.5329i		−	1.29647i
$452$	5.56637	−	14.5520i	0.261820	−	0.684469i
$453$	−3.12689	+	7.09591i	−0.146914	+	0.333395i
$454$	−13.3196	−	2.46054i	−0.625118	−	0.115479i
$455$	−0.496815			−0.0232911
$456$	−4.02183	+	2.79731i	−0.188339	+	0.130996i
$457$	34.2267			1.60106			0.800529	−	0.599294i	$-0.204552\pi$
$457$	34.2267			1.60106			0.800529	+	0.599294i	$0.204552\pi$
$458$	22.1983	+	4.10072i	1.03726	+	0.191614i
$459$	−23.3528	+	7.88471i	−1.09002	+	0.368027i
$460$	13.0140	−	34.0221i	0.606781	−	1.58629i
$461$		−	12.6198i		−	0.587763i	−0.955842	−	0.293881i	$-0.905053\pi$
$461$		−	12.6198i		−	0.587763i	0.955842	−	0.293881i	$-0.0949470\pi$
$462$	−0.591848	+	0.869326i	−0.0275353	+	0.0404447i
$463$			25.3160i			1.17654i	0.808666	+	0.588268i	$0.200190\pi$
$463$			25.3160i			1.17654i	−0.808666	+	0.588268i	$0.799810\pi$
$464$	−11.6638	+	13.0154i	−0.541478	+	0.604223i
$465$	−29.2093	−	12.8714i	−1.35455	−	0.596896i
$466$	2.39030	−	12.9393i	0.110729	−	0.599404i
$467$	22.8110			1.05557			0.527783	−	0.849380i	$-0.323024\pi$
$467$	22.8110			1.05557			0.527783	+	0.849380i	$0.323024\pi$
$468$	−2.00163	−	5.08014i	−0.0925253	−	0.234829i
$469$	0.208334			0.00961997
$470$	10.1949	−	55.1878i	0.470256	−	2.54562i
$471$	−0.339998	−	0.149824i	−0.0156663	−	0.00690352i
$472$	18.8972	+	11.5344i	0.869814	+	0.530915i
$473$			13.8479i			0.636727i
$474$	0.0179787	−	0.0264078i	0.000825791	−	0.00121295i
$475$			5.19954i			0.238571i
$476$	−1.51468	−	0.579389i	−0.0694252	−	0.0265562i
$477$	27.7952	−	25.4140i	1.27266	−	1.16363i
$478$	9.13453	+	1.68743i	0.417804	+	0.0771814i
$479$	2.27176			0.103799			0.0518997	−	0.998652i	$-0.483472\pi$
$479$	2.27176			0.103799			0.0518997	+	0.998652i	$0.483472\pi$
$480$	30.3768	−	7.51029i	1.38651	−	0.342796i
$481$	−1.86506			−0.0850396
$482$	−2.60243	−	0.480749i	−0.118537	−	0.0218975i
$483$	0.680874	−	1.54512i	0.0309808	−	0.0703055i
$484$	−8.76387	−	3.35232i	−0.398358	−	0.152378i
$485$		−	43.3421i		−	1.96806i
$486$	13.9847	−	17.0420i	0.634357	−	0.773041i
$487$			15.4181i			0.698662i	0.936999	+	0.349331i	$0.113591\pi$
$487$			15.4181i			0.698662i	−0.936999	+	0.349331i	$0.886409\pi$
$488$	−20.0346	−	12.2287i	−0.906923	−	0.553566i
$489$	−5.54255	+	12.5778i	−0.250643	+	0.568788i
$490$	−5.71926	+	30.9599i	−0.258370	+	1.39863i
$491$	11.7119			0.528550			0.264275	−	0.964447i	$-0.414867\pi$
$491$	11.7119			0.528550			0.264275	+	0.964447i	$0.414867\pi$
$492$	−26.7170	+	26.9852i	−1.20449	+	1.21659i
$493$	20.7255			0.933430
$494$	−0.233792	+	1.26558i	−0.0105188	+	0.0569411i
$495$	−17.7597	+	16.2382i	−0.798239	+	0.729854i
$496$	15.4042	−	17.1892i	0.691670	−	0.771819i
$497$		−	0.674469i		−	0.0302541i
$498$	−15.9247	−	10.8417i	−0.713602	−	0.485829i
$499$		−	3.55762i		−	0.159261i	−0.996824	−	0.0796306i	$-0.974626\pi$
$499$		−	3.55762i		−	0.159261i	0.996824	−	0.0796306i	$-0.0253741\pi$
$500$	0.455347	−	1.19040i	0.0203637	−	0.0532363i
$501$	5.82867	+	2.56846i	0.260406	+	0.114751i
$502$	−27.6686	−	5.11126i	−1.23491	−	0.228127i
$503$	−4.36020			−0.194412			−0.0972059	−	0.995264i	$-0.530991\pi$
$503$	−4.36020			−0.194412			−0.0972059	+	0.995264i	$0.530991\pi$
$504$	1.42364	−	0.277724i	0.0634139	−	0.0123708i
$505$	−49.8232			−2.21710
$506$	−19.9197	−	3.67979i	−0.885538	−	0.163587i
$507$	19.2922	+	8.50130i	0.856795	+	0.377556i
$508$	4.63390	−	12.1143i	0.205596	−	0.537484i
$509$		−	8.63300i		−	0.382651i	−0.981527	−	0.191325i	$-0.938721\pi$
$509$		−	8.63300i		−	0.382651i	0.981527	−	0.191325i	$-0.0612786\pi$
$510$	−30.6739	−	20.8831i	−1.35826	−	0.924721i
$511$		−	2.20966i		−	0.0977494i
$512$	−1.65598	+	22.5667i	−0.0731846	+	0.997318i
$513$	−4.92311	+	1.66221i	−0.217361	+	0.0733884i
$514$	−2.14647	+	11.6194i	−0.0946767	+	0.512511i
$515$	−45.8394			−2.01992
$516$	13.4375	−	13.5724i	0.591554	−	0.597492i
$517$	−31.2094			−1.37259
$518$	0.0900005	−	0.487197i	0.00395439	−	0.0214062i
$519$	5.58947	−	12.6843i	0.245351	−	0.556779i
$520$	4.28282	−	7.01666i	0.187814	−	0.307701i
$521$		−	26.1836i		−	1.14713i	−0.819162	−	0.573563i	$-0.805561\pi$
$521$		−	26.1836i		−	1.14713i	0.819162	−	0.573563i	$-0.194439\pi$
$522$	−15.7253	+	9.81528i	−0.688276	+	0.429603i
$523$			0.816068i			0.0356842i	0.999841	+	0.0178421i	$0.00567961\pi$
$523$			0.816068i			0.0356842i	−0.999841	+	0.0178421i	$0.994320\pi$
$524$	−33.0332	−	12.6357i	−1.44306	−	0.551995i
$525$	0.620780	−	1.40875i	0.0270931	−	0.0614829i
$526$	−3.63095	−	0.670750i	−0.158317	−	0.0292461i
$527$	−27.3719			−1.19234
$528$	−7.17568	−	15.8529i	−0.312282	−	0.689908i
$529$	9.52276			0.414033
$530$	55.7576	+	10.3002i	2.42196	+	0.447411i
$531$	15.8455	+	17.3302i	0.687637	+	0.752066i
$532$	−0.319316	−	0.122144i	−0.0138441	−	0.00529559i
$533$			9.97591i			0.432105i
$534$	−4.73918	+	6.96107i	−0.205084	+	0.301235i
$535$		−	6.90558i		−	0.298554i
$536$	−1.79595	+	2.94236i	−0.0775732	+	0.127090i
$537$	−9.81677	−	4.32586i	−0.423625	−	0.186675i
$538$	−6.02148	+	32.5959i	−0.259605	+	1.40531i
$539$	17.5082			0.754132
$540$	33.1634	+	1.31820i	1.42713	+	0.0567262i
$541$	22.2244			0.955500			0.477750	−	0.878496i	$-0.341453\pi$
$541$	22.2244			0.955500			0.477750	+	0.878496i	$0.341453\pi$
$542$	−1.07895	+	5.84065i	−0.0463448	+	0.250877i
$543$	−0.852745	−	0.375771i	−0.0365948	−	0.0161259i
$544$	21.2402	−	16.3976i	0.910667	−	0.703041i
$545$		−	5.76841i		−	0.247091i
$546$	0.214442	−	0.314980i	0.00917729	−	0.0134799i
$547$		−	16.2455i		−	0.694608i	−0.937753	−	0.347304i	$-0.887097\pi$
$547$		−	16.2455i		−	0.694608i	0.937753	−	0.347304i	$-0.112903\pi$
$548$	−1.86898	+	4.88602i	−0.0798388	+	0.208720i
$549$	−16.7992	−	18.3733i	−0.716974	−	0.784152i
$550$	−18.1616	−	3.35501i	−0.774412	−	0.143058i
$551$	4.36923			0.186136
$552$	15.9527	+	22.9360i	0.678991	+	0.976219i
$553$	0.00222945			9.48057e−5
$554$	−39.9722	−	7.38410i	−1.69825	−	0.313721i
$555$	4.57143	−	10.3740i	0.194047	−	0.440354i
$556$	−14.5844	+	38.1275i	−0.618516	+	1.61697i
$557$		−	4.68280i		−	0.198417i	−0.995067	−	0.0992083i	$-0.968369\pi$
$557$		−	4.68280i		−	0.198417i	0.995067	−	0.0992083i	$-0.0316310\pi$
$558$	20.7682	−	12.9629i	0.879187	−	0.548765i
$559$		−	5.01747i		−	0.212216i
$560$	1.62624	+	1.45736i	0.0687212	+	0.0615849i
$561$	−8.32127	+	18.8836i	−0.351324	+	0.797268i
$562$	−5.14050	+	27.8269i	−0.216839	+	1.17381i
$563$	−42.9275			−1.80918			−0.904590	−	0.426283i	$-0.859823\pi$
$563$	−42.9275			−1.80918			−0.904590	+	0.426283i	$0.859823\pi$
$564$	30.5885	+	30.2845i	1.28801	+	1.27521i
$565$	24.8792			1.04667
$566$	−6.07412	+	32.8809i	−0.255314	+	1.38209i
$567$	1.53231	+	0.137423i	0.0643510	+	0.00577121i
$568$	9.52571	+	5.81428i	0.399690	+	0.243962i
$569$			17.5383i			0.735244i	0.929975	+	0.367622i	$0.119828\pi$
$569$			17.5383i			0.735244i	−0.929975	+	0.367622i	$0.880172\pi$
$570$	−6.46649	−	4.40247i	−0.270852	−	0.184399i
$571$		−	10.6555i		−	0.445919i	−0.974828	−	0.222960i	$-0.928428\pi$
$571$		−	10.6555i		−	0.445919i	0.974828	−	0.222960i	$-0.0715718\pi$
$572$	−4.26972	−	1.63323i	−0.178526	−	0.0682890i
$573$	−30.8197	−	13.5810i	−1.28751	−	0.567356i
$574$	−2.60593	−	0.481397i	−0.108770	−	0.0200931i
$575$	29.6523			1.23659
$576$	−8.35015	+	22.5006i	−0.347923	+	0.937523i
$577$	4.48098			0.186546			0.0932729	−	0.995641i	$-0.470267\pi$
$577$	4.48098			0.186546			0.0932729	+	0.995641i	$0.470267\pi$
$578$	−7.64998	−	1.41319i	−0.318197	−	0.0587809i
$579$	35.8560	+	15.8003i	1.49012	+	0.656639i
$580$	−26.0659	−	9.97063i	−1.08233	−	0.414008i
$581$		−	1.34442i		−	0.0557761i
$582$	27.4788	+	18.7079i	1.13903	+	0.775468i
$583$		−	31.5316i		−	1.30591i
$584$	31.2076	+	19.0484i	1.29138	+	0.788230i
$585$	6.43482	−	5.88355i	0.266047	−	0.243255i
$586$	2.79310	−	15.1198i	0.115382	−	0.624593i
$587$	11.5375			0.476205			0.238103	−	0.971240i	$-0.423475\pi$
$587$	11.5375			0.476205			0.238103	+	0.971240i	$0.423475\pi$
$588$	−17.1599	−	16.9894i	−0.707663	−	0.700629i
$589$	−5.77040			−0.237765
$590$	−6.42210	+	34.7646i	−0.264394	+	1.43123i
$591$	−10.3797	+	23.5549i	−0.426964	+	0.968919i
$592$	6.10497	+	5.47100i	0.250913	+	0.224857i
$593$		−	12.4726i		−	0.512190i	−0.966652	−	0.256095i	$-0.917564\pi$
$593$		−	12.4726i		−	0.512190i	0.966652	−	0.256095i	$-0.0824360\pi$
$594$	−2.62932	−	18.2686i	−0.107882	−	0.749570i
$595$		−	2.58961i		−	0.106163i
$596$	−4.54789	+	11.8894i	−0.186289	+	0.487009i
$597$	−6.88910	+	15.6336i	−0.281952	+	0.639839i
$598$	7.21744	+	1.33329i	0.295143	+	0.0545221i
$599$	34.4412			1.40723			0.703615	−	0.710581i	$-0.251568\pi$
$599$	34.4412			1.40723			0.703615	+	0.710581i	$0.251568\pi$
$600$	14.5447	+	20.9116i	0.593785	+	0.853714i
$601$	2.69880			0.110086			0.0550431	−	0.998484i	$-0.482470\pi$
$601$	2.69880			0.110086			0.0550431	+	0.998484i	$0.482470\pi$
$602$	1.31068	+	0.242123i	0.0534191	+	0.00986818i
$603$	−2.69837	+	2.46720i	−0.109886	+	0.100472i
$604$	3.19897	−	8.36296i	0.130164	−	0.340284i
$605$		−	14.9833i		−	0.609160i
$606$	21.5054	−	31.5879i	0.873597	−	1.28317i
$607$		−	35.8302i		−	1.45430i	−0.686477	−	0.727151i	$-0.740844\pi$
$607$		−	35.8302i		−	1.45430i	0.686477	−	0.727151i	$-0.259156\pi$
$608$	4.47774	−	3.45685i	0.181597	−	0.140194i
$609$	−1.18379	−	0.521649i	−0.0479696	−	0.0211383i
$610$	6.80864	−	36.8570i	0.275674	−	1.49230i
$611$	11.3080			0.457473
$612$	26.4798	−	10.4333i	1.07038	−	0.421741i
$613$	−5.96259			−0.240827			−0.120413	−	0.992724i	$-0.538422\pi$
$613$	−5.96259			−0.240827			−0.120413	+	0.992724i	$0.538422\pi$
$614$	0.303924	−	1.64522i	0.0122654	−	0.0663959i
$615$	−55.4890	−	24.4518i	−2.23753	−	0.985992i
$616$	0.632677	−	1.03653i	0.0254913	−	0.0417631i
$617$			22.6156i			0.910470i	0.890371	+	0.455235i	$0.150445\pi$
$617$			22.6156i			0.910470i	−0.890371	+	0.455235i	$0.849555\pi$
$618$	19.7858	−	29.0621i	0.795903	−	1.16905i
$619$			12.3837i			0.497742i	0.968537	+	0.248871i	$0.0800595\pi$
$619$			12.3837i			0.497742i	−0.968537	+	0.248871i	$0.919940\pi$
$620$	34.4249	+	13.1681i	1.38254	+	0.528843i
$621$	9.47937	+	28.0759i	0.380394	+	1.12665i
$622$	30.4552	+	5.62602i	1.22114	+	0.225583i
$623$	−0.587680			−0.0235449
$624$	2.59994	+	5.74393i	0.104081	+	0.229941i
$625$	−23.9625			−0.958500
$626$	20.6945	+	3.82291i	0.827117	+	0.152794i
$627$	−1.75424	+	3.98094i	−0.0700578	+	0.158984i
$628$	0.400709	+	0.153277i	0.0159900	+	0.00611644i
$629$		−	9.72148i		−	0.387621i
$630$	1.22640	+	1.96484i	0.0488609	+	0.0782810i
$631$			20.6331i			0.821391i	0.911773	+	0.410696i	$0.134714\pi$
$631$			20.6331i			0.821391i	−0.911773	+	0.410696i	$0.865286\pi$
$632$	−0.0192190	+	0.0314871i	−0.000764492	+	0.00125249i
$633$	−13.1490	+	29.8393i	−0.522625	+	1.18600i
$634$	−2.88178	+	15.5999i	−0.114450	+	0.619550i
$635$	20.7114			0.821908
$636$	−30.5972	+	30.9043i	−1.21326	+	1.22544i
$637$	−6.34370			−0.251347
$638$	−2.81926	+	15.2614i	−0.111615	+	0.604204i
$639$	7.98741	+	8.73581i	0.315977	+	0.345583i
$640$	−34.6018	+	10.4046i	−1.36776	+	0.411277i
$641$		−	44.2257i		−	1.74681i	−0.486996	−	0.873404i	$-0.661907\pi$
$641$		−	44.2257i		−	1.74681i	0.486996	−	0.873404i	$-0.338093\pi$
$642$	4.37813	+	2.98068i	0.172791	+	0.117638i
$643$		−	23.7238i		−	0.935575i	−0.883841	−	0.467787i	$-0.845051\pi$
$643$		−	23.7238i		−	0.935575i	0.883841	−	0.467787i	$-0.154949\pi$
$644$	−0.696569	+	1.82102i	−0.0274487	+	0.0717582i
$645$	27.9087	+	12.2982i	1.09890	+	0.484243i
$646$	−6.59672	−	1.21862i	−0.259544	−	0.0479460i
$647$	−11.4189			−0.448923			−0.224461	−	0.974483i	$-0.572062\pi$
$647$	−11.4189			−0.448923			−0.224461	+	0.974483i	$0.572062\pi$
$648$	−15.1502	+	20.4566i	−0.595156	+	0.803610i
$649$	19.6598			0.771714
$650$	6.58043	+	1.21561i	0.258106	+	0.0476802i
$651$	1.56342	+	0.688936i	0.0612751	+	0.0270015i
$652$	5.67031	−	14.8237i	0.222066	−	0.580542i
$653$			15.1707i			0.593677i	0.954928	+	0.296839i	$0.0959323\pi$
$653$			15.1707i			0.593677i	−0.954928	+	0.296839i	$0.904068\pi$
$654$	3.65716	+	2.48984i	0.143006	+	0.0973604i
$655$		−	56.4760i		−	2.20670i
$656$	29.2634	−	32.6544i	1.14255	−	1.27494i
$657$	26.1679	+	28.6198i	1.02091	+	1.11656i
$658$	−0.545678	+	2.95391i	−0.0212728	+	0.115155i
$659$	−10.6031			−0.413037			−0.206518	−	0.978443i	$-0.566213\pi$
$659$	−10.6031			−0.413037			−0.206518	+	0.978443i	$0.566213\pi$
$660$	19.5500	−	19.7463i	0.760982	−	0.768622i
$661$	6.08534			0.236692			0.118346	−	0.992972i	$-0.462241\pi$
$661$	6.08534			0.236692			0.118346	+	0.992972i	$0.462241\pi$
$662$	2.29416	−	12.4189i	0.0891650	−	0.482674i
$663$	3.01502	−	6.84205i	0.117094	−	0.265723i
$664$	18.9877	+	11.5896i	0.736864	+	0.449766i
$665$		−	0.545926i		−	0.0211701i
$666$	4.60394	+	7.37607i	0.178399	+	0.285817i
$667$		−	24.9172i		−	0.964798i
$668$	−6.86944	−	2.62767i	−0.265787	−	0.101668i
$669$	12.6156	−	28.6289i	0.487749	−	1.10686i
$670$	−5.41296	−	0.999943i	−0.209121	−	0.0386312i
$671$	−20.8431			−0.804638
$672$	−1.62591	+	0.401985i	−0.0627207	+	0.0155069i
$673$	28.5485			1.10046			0.550232	−	0.835012i	$-0.314539\pi$
$673$	28.5485			1.10046			0.550232	+	0.835012i	$0.314539\pi$
$674$	24.1493	+	4.46113i	0.930196	+	0.171836i
$675$	8.64272	+	25.5979i	0.332659	+	0.985264i
$676$	−22.7370	−	8.69726i	−0.874500	−	0.334510i
$677$		−	14.3823i		−	0.552755i	−0.961049	−	0.276377i	$-0.910866\pi$
$677$		−	14.3823i		−	0.552755i	0.961049	−	0.276377i	$-0.0891340\pi$
$678$	−10.7387	+	15.7733i	−0.412417	+	0.605772i
$679$			2.31987i			0.0890284i
$680$	36.5737	+	22.3238i	1.40254	+	0.856078i
$681$	15.1805	+	6.68946i	0.581719	+	0.256341i
$682$	3.72336	−	20.1555i	0.142575	−	0.771796i
$683$	−51.9304			−1.98706			−0.993531	−	0.113562i	$-0.963774\pi$
$683$	−51.9304			−1.98706			−0.993531	+	0.113562i	$0.963774\pi$
$684$	5.58231	−	2.19949i	0.213445	−	0.0840997i
$685$	−8.35349			−0.319170
$686$	0.613526	−	3.32118i	0.0234245	−	0.126803i
$687$	−25.2998	−	11.1486i	−0.965248	−	0.425347i
$688$	−14.7183	+	16.4238i	−0.561130	+	0.626152i
$689$			11.4248i			0.435248i
$690$	−25.1067	+	36.8776i	−0.955796	+	1.40391i
$691$			33.8692i			1.28845i	0.764838	+	0.644223i	$0.222819\pi$
$691$			33.8692i			1.28845i	−0.764838	+	0.644223i	$0.777181\pi$
$692$	−5.71831	+	14.9492i	−0.217378	+	0.568284i
$693$	0.950581	−	0.869145i	0.0361096	−	0.0330161i
$694$	12.9680	+	2.39559i	0.492258	+	0.0909354i
$695$	−65.1856			−2.47263
$696$	17.5723	−	12.2221i	0.666076	−	0.463277i
$697$	−51.9985			−1.96958
$698$	−7.62735	−	1.40901i	−0.288699	−	0.0533318i
$699$	−6.49851	+	14.7472i	−0.245796	+	0.557790i
$700$	−0.635090	+	1.66030i	−0.0240041	+	0.0627533i
$701$		−	11.7535i		−	0.443925i	−0.975055	−	0.221962i	$-0.928754\pi$
$701$		−	11.7535i		−	0.443925i	0.975055	−	0.221962i	$-0.0712462\pi$
$702$	0.952675	+	6.61921i	0.0359564	+	0.249826i
$703$		−	2.04943i		−	0.0772956i
$704$	9.18523	+	17.8710i	0.346181	+	0.673537i
$705$	−27.7169	+	62.8985i	−1.04388	+	2.36889i
$706$	1.26852	−	6.86684i	0.0477414	−	0.258437i
$707$	2.66677			0.100294
$708$	−19.2687	−	19.0772i	−0.724162	−	0.716964i
$709$	−27.0542			−1.01604			−0.508020	−	0.861345i	$-0.669622\pi$
$709$	−27.0542			−1.01604			−0.508020	+	0.861345i	$0.669622\pi$
$710$	−3.23725	+	17.5241i	−0.121492	+	0.657669i
$711$	−0.0288761	+	0.0264023i	−0.00108294	+	0.000990162i
$712$	5.06612	−	8.29997i	0.189861	−	0.311055i
$713$			32.9078i			1.23241i
$714$	1.64181	+	1.11776i	0.0614430	+	0.0418312i
$715$		−	7.29982i		−	0.272998i
$716$	11.5697	+	4.42558i	0.432379	+	0.165392i
$717$	−10.4108	−	4.58762i	−0.388798	−	0.171328i
$718$	4.12370	+	0.761776i	0.153895	+	0.0284292i
$719$	23.5644			0.878804			0.439402	−	0.898290i	$-0.355190\pi$
$719$	23.5644			0.878804			0.439402	+	0.898290i	$0.355190\pi$
$720$	−38.3221	+	0.382806i	−1.42818	+	0.0142663i
$721$	2.45353			0.0913744
$722$	−1.39068	−	0.256903i	−0.0517559	−	0.00956093i
$723$	2.96603	+	1.30701i	0.110308	+	0.0486083i
$724$	1.00501	+	0.384433i	0.0373509	+	0.0142873i
$725$		−	22.7180i		−	0.843725i
$726$	9.49942	+	6.46732i	0.352556	+	0.240025i
$727$		−	50.2334i		−	1.86305i	−0.363672	−	0.931527i	$-0.618477\pi$
$727$		−	50.2334i		−	1.86305i	0.363672	−	0.931527i	$-0.381523\pi$
$728$	−0.229236	+	0.375564i	−0.00849605	+	0.0139193i
$729$	−21.4741	+	16.3665i	−0.795338	+	0.606167i
$730$	−10.6057	+	57.4116i	−0.392535	+	2.12490i
$731$	26.1531			0.967307
$732$	20.4284	+	20.2254i	0.755057	+	0.747552i
$733$	27.9805			1.03348			0.516742	−	0.856141i	$-0.327145\pi$
$733$	27.9805			1.03348			0.516742	+	0.856141i	$0.327145\pi$
$734$	8.60319	−	46.5714i	0.317550	−	1.71898i
$735$	15.5490	−	35.2856i	0.573532	−	1.30153i
$736$	−19.7140	−	25.5360i	−0.726667	−	0.941270i
$737$			3.06110i			0.112757i
$738$	39.4534	−	24.6257i	1.45230	−	0.906485i
$739$		−	49.8109i		−	1.83232i	−0.400809	−	0.916162i	$-0.631271\pi$
$739$		−	49.8109i		−	1.83232i	0.400809	−	0.916162i	$-0.368729\pi$
$740$	−4.67681	+	12.2264i	−0.171923	+	0.449453i
$741$	0.635610	−	1.44240i	0.0233497	−	0.0529880i
$742$	−2.98440	−	0.551312i	−0.109561	−	0.0202393i
$743$	0.736246			0.0270102			0.0135051	−	0.999909i	$-0.495701\pi$
$743$	0.736246			0.0270102			0.0135051	+	0.999909i	$0.495701\pi$
$744$	−23.2075	+	16.1416i	−0.850829	+	0.591779i
$745$	−20.3270			−0.744723
$746$	−41.8812	−	7.73676i	−1.53338	−	0.283263i
$747$	15.9214	+	17.4131i	0.582532	+	0.637114i
$748$	8.51309	−	22.2555i	0.311269	−	0.813742i
$749$			0.369618i			0.0135056i
$750$	−0.878459	+	1.29031i	−0.0320768	+	0.0471154i
$751$		−	31.9553i		−	1.16606i	−0.812449	−	0.583032i	$-0.801866\pi$
$751$		−	31.9553i		−	1.16606i	0.812449	−	0.583032i	$-0.198134\pi$
$752$	−37.0148	−	33.1710i	−1.34979	−	1.20962i
$753$	31.5344	+	13.8960i	1.14918	+	0.506397i
$754$	1.02149	−	5.52962i	0.0372006	−	0.201377i
$755$	14.2979			0.520355
$756$	−1.77506	−	0.0705560i	−0.0645583	−	0.00256610i
$757$	2.72922			0.0991952			0.0495976	−	0.998769i	$-0.484206\pi$
$757$	2.72922			0.0991952			0.0495976	+	0.998769i	$0.484206\pi$
$758$	−1.85646	+	10.0495i	−0.0674296	+	0.365015i
$759$	22.7028	+	10.0042i	0.824060	+	0.363131i
$760$	7.71027	+	4.70618i	0.279681	+	0.170711i
$761$			21.0816i			0.764207i	0.924120	+	0.382103i	$0.124800\pi$
$761$			21.0816i			0.764207i	−0.924120	+	0.382103i	$0.875200\pi$
$762$	−8.93976	+	13.1310i	−0.323853	+	0.475686i
$763$			0.308752i			0.0111776i
$764$	36.3229	+	13.8941i	1.31412	+	0.502670i
$765$	30.6675	+	33.5409i	1.10878	+	1.21267i
$766$	45.6799	+	8.43851i	1.65048	+	0.304896i
$767$	−7.12327			−0.257206
$768$	8.33884	−	26.4285i	0.300902	−	0.953655i
$769$	9.76925			0.352288			0.176144	−	0.984364i	$-0.443638\pi$
$769$	9.76925			0.352288			0.176144	+	0.984364i	$0.443638\pi$
$770$	1.90688	+	0.352260i	0.0687191	+	0.0126946i
$771$	5.83560	−	13.2429i	0.210164	−	0.476930i
$772$	−42.2585	−	16.1645i	−1.52092	−	0.581774i
$773$		−	37.9913i		−	1.36645i	−0.730207	−	0.683226i	$-0.760576\pi$
$773$		−	37.9913i		−	1.36645i	0.730207	−	0.683226i	$-0.239424\pi$
$774$	−19.8434	+	12.3857i	−0.713256	+	0.445195i
$775$			30.0034i			1.07775i
$776$	−32.7641	−	19.9985i	−1.17616	−	0.717905i
$777$	−0.244684	+	0.555267i	−0.00877799	+	0.0199201i
$778$	3.05606	−	16.5433i	0.109565	−	0.593106i
$779$	−10.9620			−0.392756
$780$	−7.08349	+	7.15460i	−0.253630	+	0.256176i
$781$	9.91011			0.354612
$782$	−6.94963	+	37.6203i	−0.248518	+	1.34530i
$783$	21.5102	−	7.26259i	0.768713	−	0.259544i
$784$	20.7650	+	18.6087i	0.741607	+	0.664596i
$785$			0.685080i			0.0244516i
$786$	35.8057	+	24.3770i	1.27715	+	0.869498i
$787$			8.21956i			0.292996i	0.989211	+	0.146498i	$0.0468002\pi$
$787$			8.21956i			0.292996i	−0.989211	+	0.146498i	$0.953200\pi$
$788$	10.6190	−	27.7609i	0.378285	−	0.988940i
$789$	4.13826	+	1.82357i	0.147326	+	0.0649207i
$790$	−0.0579258	−	0.0107007i	−0.00206091	−	0.000380714i
$791$	−1.33165			−0.0473479
$792$	4.08065	+	20.9178i	0.145000	+	0.743282i
$793$	7.55201			0.268180
$794$	−8.95563	−	1.65438i	−0.317823	−	0.0587119i
$795$	−63.5479	−	28.0031i	−2.25381	−	0.993166i
$796$	7.04790	−	18.4251i	0.249806	−	0.653061i
$797$		−	17.8860i		−	0.633556i	−0.948500	−	0.316778i	$-0.897399\pi$
$797$		−	17.8860i		−	0.633556i	0.948500	−	0.316778i	$-0.102601\pi$
$798$	0.346116	+	0.235640i	0.0122524	+	0.00834157i
$799$			58.9419i			2.08522i
$800$	−17.9740	−	23.2822i	−0.635477	−	0.823150i
$801$	7.61171	−	6.95962i	0.268947	−	0.245906i
$802$	0.942714	−	5.10317i	0.0332884	−	0.180199i
$803$	32.4670			1.14573
$804$	2.97038	−	3.00020i	0.104757	−	0.105809i
$805$	−3.11335			−0.109731
$806$	−1.34907	+	7.30290i	−0.0475191	+	0.257234i
$807$	16.3706	−	37.1501i	0.576272	−	1.30775i
$808$	−22.9890	+	37.6635i	−0.808749	+	1.32500i
$809$			21.7287i			0.763942i	0.924174	+	0.381971i	$0.124755\pi$
$809$			21.7287i			0.763942i	−0.924174	+	0.381971i	$0.875245\pi$
$810$	−39.1531	−	10.9252i	−1.37570	−	0.383872i
$811$			41.4765i			1.45644i	0.685344	+	0.728219i	$0.259652\pi$
$811$			41.4765i			1.45644i	−0.685344	+	0.728219i	$0.740348\pi$
$812$	1.39517	+	0.533674i	0.0489608	+	0.0187283i
$813$	2.93334	−	6.65668i	0.102877	−	0.233460i
$814$	7.15849	+	1.32240i	0.250905	+	0.0463500i
$815$	25.3437			0.887751
$816$	−29.9397	+	13.5520i	−1.04810	+	0.474414i
$817$	5.51345			0.192891
$818$	−24.0475	−	4.44232i	−0.840801	−	0.155322i
$819$	−0.344421	+	0.314915i	−0.0120351	+	0.0110040i
$820$	65.3972	+	25.0155i	2.28377	+	0.873578i
$821$		−	20.0539i		−	0.699886i	−0.936771	−	0.349943i	$-0.886201\pi$
$821$		−	20.0539i		−	0.699886i	0.936771	−	0.349943i	$-0.113799\pi$
$822$	3.60565	−	5.29610i	0.125761	−	0.184723i
$823$			26.7511i			0.932485i	0.884657	+	0.466242i	$0.154393\pi$
$823$			26.7511i			0.932485i	−0.884657	+	0.466242i	$0.845607\pi$
$824$	−21.1508	+	34.6519i	−0.736823	+	1.20716i
$825$	20.6991	+	9.12126i	0.720649	+	0.317561i
$826$	0.343740	−	1.86076i	0.0119603	−	0.0647441i
$827$	−25.6966			−0.893559			−0.446779	−	0.894644i	$-0.647429\pi$
$827$	−25.6966			−0.893559			−0.446779	+	0.894644i	$0.647429\pi$
$828$	−12.5434	−	31.8352i	−0.435914	−	1.10635i
$829$	14.7839			0.513467			0.256733	−	0.966482i	$-0.417354\pi$
$829$	14.7839			0.513467			0.256733	+	0.966482i	$0.417354\pi$
$830$	−6.45284	+	34.9310i	−0.223981	+	1.21247i
$831$	45.5570	+	20.0751i	1.58035	+	0.696399i
$832$	−3.32806	−	6.47513i	−0.115380	−	0.224485i
$833$		−	33.0660i		−	1.14567i
$834$	28.1363	−	41.3275i	0.974280	−	1.43106i
$835$		−	11.7445i		−	0.406435i
$836$	1.79468	−	4.69178i	0.0620704	−	0.162269i
$837$	−28.4083	+	9.59161i	−0.981935	+	0.331535i
$838$	−21.1733	−	3.91138i	−0.731421	−	0.135116i
$839$	−26.4933			−0.914650			−0.457325	−	0.889300i	$-0.651192\pi$
$839$	−26.4933			−0.914650			−0.457325	+	0.889300i	$0.651192\pi$
$840$	−1.52712	−	2.19562i	−0.0526907	−	0.0757561i
$841$	9.90979			0.341717
$842$	−1.71817	−	0.317399i	−0.0592120	−	0.0109383i
$843$	13.9755	−	31.7148i	0.481340	−	1.09232i
$844$	13.4521	−	35.1674i	0.463040	−	1.21051i
$845$		−	38.8728i		−	1.33727i
$846$	−27.9140	−	44.7216i	−0.959703	−	1.53756i
$847$			0.801977i			0.0275563i
$848$	33.5135	−	37.3969i	1.15086	−	1.28422i
$849$	16.5137	−	37.4749i	0.566749	−	1.28613i
$850$	−6.33626	+	34.2999i	−0.217332	+	1.17648i
$851$	−11.6876			−0.400647
$852$	−9.71297	−	9.61643i	−0.332761	−	0.329453i
$853$	−33.1007			−1.13335			−0.566673	−	0.823943i	$-0.691770\pi$
$853$	−33.1007			−1.13335			−0.566673	+	0.823943i	$0.691770\pi$
$854$	−0.364429	+	1.97276i	−0.0124705	+	0.0675063i
$855$	6.46514	+	7.07091i	0.221103	+	0.241820i
$856$	−5.22022	−	3.18631i	−0.178424	−	0.108906i
$857$			42.5586i			1.45377i	0.686757	+	0.726887i	$0.259034\pi$
$857$			42.5586i			1.45377i	−0.686757	+	0.726887i	$0.740966\pi$
$858$	4.62807	+	3.15085i	0.158000	+	0.107568i
$859$		−	18.9766i		−	0.647472i	−0.946148	−	0.323736i	$-0.895061\pi$
$859$		−	18.9766i		−	0.647472i	0.946148	−	0.323736i	$-0.104939\pi$
$860$	−32.8920	−	12.5817i	−1.12161	−	0.429033i
$861$	2.97003	+	1.30877i	0.101218	+	0.0446029i
$862$	−19.3770	−	3.57954i	−0.659985	−	0.121920i
$863$	4.20683			0.143202			0.0716011	−	0.997433i	$-0.477189\pi$
$863$	4.20683			0.143202			0.0716011	+	0.997433i	$0.477189\pi$
$864$	16.2984	−	24.4614i	0.554484	−	0.832194i
$865$	−25.5583			−0.869007
$866$	13.3800	+	2.47170i	0.454671	+	0.0839918i
$867$	8.71881	+	3.84203i	0.296106	+	0.130482i
$868$	−1.84258	−	0.704817i	−0.0625413	−	0.0239230i
$869$			0.0327577i			0.00111123i
$870$	28.2536	+	19.2354i	0.957887	+	0.652142i
$871$		−	1.10912i		−	0.0375810i
$872$	−4.36058	−	2.66160i	−0.147668	−	0.0901333i
$873$	−27.4731	−	30.0472i	−0.929823	−	1.01695i
$874$	−1.46508	+	7.93089i	−0.0495572	+	0.268266i
$875$	−0.108933			−0.00368260
$876$	−31.8211	−	31.5048i	−1.07513	−	1.06445i
$877$	6.88439			0.232469			0.116235	−	0.993222i	$-0.462918\pi$
$877$	6.88439			0.232469			0.116235	+	0.993222i	$0.462918\pi$
$878$	−8.30921	+	44.9800i	−0.280422	+	1.51800i
$879$	−7.59359	+	17.2323i	−0.256125	+	0.581231i
$880$	−21.4134	+	23.8947i	−0.721845	+	0.805490i
$881$		−	54.1854i		−	1.82555i	−0.408461	−	0.912776i	$-0.633934\pi$
$881$		−	54.1854i		−	1.82555i	0.408461	−	0.912776i	$-0.366066\pi$
$882$	15.6595	+	25.0885i	0.527284	+	0.844772i
$883$			22.8335i			0.768409i	0.923248	+	0.384204i	$0.125524\pi$
$883$			22.8335i			0.768409i	−0.923248	+	0.384204i	$0.874476\pi$
$884$	−3.08452	+	8.06377i	−0.103744	+	0.271214i
$885$	17.4598	−	39.6218i	0.586903	−	1.33187i
$886$	20.9793	+	3.87554i	0.704814	+	0.130201i
$887$	−8.39821			−0.281984			−0.140992	−	0.990011i	$-0.545029\pi$
$887$	−8.39821			−0.281984			−0.140992	+	0.990011i	$0.545029\pi$
$888$	−5.73288	−	8.24244i	−0.192383	−	0.276598i
$889$	−1.10857			−0.0371803
$890$	15.2692	+	2.82070i	0.511824	+	0.0945499i
$891$	−2.01918	+	22.5146i	−0.0676451	+	0.754266i
$892$	−12.9064	+	33.7409i	−0.432140	+	1.12973i
$893$			12.4258i			0.415814i
$894$	8.77382	−	12.8873i	0.293440	−	0.431015i
$895$			19.7803i			0.661184i
$896$	1.85205	−	0.556900i	0.0618726	−	0.0186047i
$897$	−8.22584	−	3.62480i	−0.274653	−	0.121029i
$898$	−4.47010	+	24.1979i	−0.149169	+	0.807494i
$899$	25.2122			0.840875
$900$	−11.4363	−	29.0255i	−0.381211	−	0.967515i
$901$	−59.5505			−1.98391
$902$	7.07327	−	38.2895i	0.235514	−	1.27490i
$903$	−1.49380	−	0.658258i	−0.0497105	−	0.0219055i
$904$	11.4795	−	18.8072i	0.381803	−	0.625519i
$905$			1.71824i			0.0571162i
$906$	−6.17147	+	9.06486i	−0.205033	+	0.301160i
$907$			19.0263i			0.631759i	0.948799	+	0.315879i	$0.102299\pi$
$907$			19.0263i			0.631759i	−0.948799	+	0.315879i	$0.897701\pi$
$908$	−17.8912	−	6.84366i	−0.593739	−	0.227115i
$909$	−34.5403	+	31.5813i	−1.14563	+	1.04748i
$910$	−0.690913	−	0.127633i	−0.0229035	−	0.00423100i
$911$	−55.1764			−1.82807			−0.914037	−	0.405631i	$-0.867052\pi$
$911$	−55.1764			−1.82807			−0.914037	+	0.405631i	$0.867052\pi$
$912$	−6.31172	+	2.85695i	−0.209002	+	0.0946031i
$913$	19.7539			0.653759
$914$	47.5985	+	8.79293i	1.57442	+	0.290844i
$915$	−18.5106	+	42.0065i	−0.611942	+	1.38869i
$916$	29.8174	+	11.4056i	0.985193	+	0.376852i
$917$			3.02286i			0.0998235i
$918$	−34.5020	+	4.96573i	−1.13874	+	0.163894i
$919$			26.0948i			0.860788i	0.902641	+	0.430394i	$0.141625\pi$
$919$			26.0948i			0.860788i	−0.902641	+	0.430394i	$0.858375\pi$
$920$	26.8387	−	43.9707i	0.884847	−	1.44967i
$921$	−0.826279	+	1.87509i	−0.0272268	+	0.0617864i
$922$	3.24206	−	17.5501i	0.106772	−	0.577983i
$923$	−3.59070			−0.118189
$924$	−1.04641	+	1.05691i	−0.0344242	+	0.0347698i
$925$	−10.6561			−0.350370
$926$	−6.50375	+	35.2066i	−0.213727	+	1.15696i
$927$	−31.7785	+	29.0560i	−1.04374	+	0.954326i
$928$	−19.5643	+	15.1038i	−0.642230	+	0.495806i
$929$		−	13.0346i		−	0.427650i	−0.976872	−	0.213825i	$-0.931408\pi$
$929$		−	13.0346i		−	0.427650i	0.976872	−	0.213825i	$-0.0685922\pi$
$930$	−37.3142	−	25.4040i	−1.22358	−	0.833029i
$931$		−	6.97078i		−	0.228458i
$932$	6.64830	−	17.3805i	0.217772	−	0.569316i
$933$	−34.7103	−	15.2955i	−1.13636	−	0.500751i
$934$	31.7228	+	5.86019i	1.03800	+	0.191751i
$935$	38.0496			1.24436
$936$	−1.47853	−	7.57909i	−0.0483273	−	0.247730i
$937$	41.9278			1.36972			0.684861	−	0.728674i	$-0.259863\pi$
$937$	41.9278			1.36972			0.684861	+	0.728674i	$0.259863\pi$
$938$	0.289727	+	0.0535215i	0.00945991	+	0.00174754i
$939$	−23.5858	−	10.3933i	−0.769694	−	0.339174i
$940$	28.3558	−	74.1297i	0.924864	−	2.41784i
$941$			2.74678i			0.0895426i	0.998997	+	0.0447713i	$0.0142559\pi$
$941$			2.74678i			0.0895426i	−0.998997	+	0.0447713i	$0.985744\pi$
$942$	−0.434340	−	0.295704i	−0.0141516	−	0.00963456i
$943$			62.5151i			2.03577i
$944$	23.3168	+	20.8955i	0.758897	+	0.680090i
$945$	−0.907444	−	2.68766i	−0.0295192	−	0.0874295i
$946$	−3.55756	+	19.2580i	−0.115666	+	0.626133i
$947$	39.4193			1.28095			0.640477	−	0.767977i	$-0.278737\pi$
$947$	39.4193			1.28095			0.640477	+	0.767977i	$0.278737\pi$
$948$	0.0317870	−	0.0321061i	0.00103239	−	0.00104276i
$949$	−11.7637			−0.381865
$950$	−1.33577	+	7.23091i	−0.0433383	+	0.234602i
$951$	7.83470	−	17.7794i	0.254058	−	0.576538i
$952$	−1.95759	−	1.19487i	−0.0634460	−	0.0387260i
$953$			14.1225i			0.457474i	0.973488	+	0.228737i	$0.0734595\pi$
$953$			14.1225i			0.457474i	−0.973488	+	0.228737i	$0.926540\pi$
$954$	45.1833	−	28.2022i	1.46286	−	0.913080i
$955$			62.1003i			2.00952i
$956$	12.2697	+	4.69337i	0.396832	+	0.151794i
$957$	7.66471	−	17.3937i	0.247765	−	0.562258i
$958$	3.15930	+	0.583621i	0.102072	+	0.0188559i
$959$	0.447117			0.0144382
$960$	44.1740	−	2.64056i	1.42571	−	0.0852236i
$961$	−2.29748			−0.0741123
$962$	−2.59371	−	0.479140i	−0.0836247	−	0.0154481i
$963$	−4.37722	−	4.78735i	−0.141054	−	0.154270i
$964$	−3.49565	−	1.33714i	−0.112587	−	0.0430664i
$965$		−	72.2481i		−	2.32575i
$966$	1.34383	−	1.97386i	0.0432369	−	0.0635078i
$967$		−	25.6193i		−	0.823861i	−0.911215	−	0.411931i	$-0.864855\pi$
$967$		−	25.6193i		−	0.823861i	0.911215	−	0.411931i	$-0.135145\pi$
$968$	−11.3265	−	6.91348i	−0.364049	−	0.222208i
$969$	7.51839	+	3.31306i	0.241526	+	0.106431i
$970$	11.1347	−	60.2751i	0.357514	−	1.93532i
$971$	−24.7819			−0.795290			−0.397645	−	0.917539i	$-0.630172\pi$
$971$	−24.7819			−0.795290			−0.397645	+	0.917539i	$0.630172\pi$
$972$	23.8264	−	20.1073i	0.764231	−	0.644943i
$973$	3.48903			0.111853
$974$	−3.96096	+	21.4417i	−0.126917	+	0.687038i
$975$	−7.49983	−	3.30488i	−0.240187	−	0.105841i
$976$	−24.7202	−	22.1532i	−0.791274	−	0.709105i
$977$			49.9437i			1.59784i	0.601438	+	0.798920i	$0.294595\pi$
$977$			49.9437i			1.59784i	−0.601438	+	0.798920i	$0.705405\pi$
$978$	−10.9392	+	16.0679i	−0.349797	+	0.513794i
$979$		−	8.63491i		−	0.275973i
$980$	−15.9074	+	41.5862i	−0.508142	+	1.32842i
$981$	−3.65640	−	3.99899i	−0.116740	−	0.127678i
$982$	16.2875	+	3.00881i	0.519756	+	0.0960151i
$983$	−12.6486			−0.403427			−0.201714	−	0.979445i	$-0.564651\pi$
$983$	−12.6486			−0.403427			−0.201714	+	0.979445i	$0.564651\pi$
$984$	−44.0874	+	30.6642i	−1.40545	+	0.977538i
$985$	47.4620			1.51227
$986$	28.8226	+	5.32444i	0.917899	+	0.169565i
$987$	1.48353	−	3.36662i	0.0472214	−	0.107161i
$988$	−0.650262	+	1.69996i	−0.0206876	+	0.0540829i
$989$		−	31.4425i		−	0.999813i
$990$	−28.8698	+	18.0197i	−0.917542	+	0.572705i
$991$		−	21.7553i		−	0.691079i	−0.938404	−	0.345540i	$-0.887696\pi$
$991$		−	21.7553i		−	0.691079i	0.938404	−	0.345540i	$-0.112304\pi$
$992$	25.8384	−	19.9474i	0.820369	−	0.633330i
$993$	−6.23712	+	14.1540i	−0.197929	+	0.449165i
$994$	0.173273	−	0.937972i	0.00549588	−	0.0297507i
$995$	31.5009			0.998646
$996$	−19.3609	−	19.1685i	−0.613474	−	0.607377i
$997$	31.1612			0.986886			0.493443	−	0.869778i	$-0.335738\pi$
$997$	31.1612			0.986886			0.493443	+	0.869778i	$0.335738\pi$
$998$	0.913963	−	4.94753i	0.0289310	−	0.156611i
$999$	−3.40658	−	10.0896i	−0.107779	−	0.319220i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.c.a.191.34	yes	36
3.2	odd	2	inner	228.2.c.a.191.3	✓	36
4.3	odd	2	inner	228.2.c.a.191.4	yes	36
12.11	even	2	inner	228.2.c.a.191.33	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.c.a.191.3	✓	36	3.2	odd	2	inner
228.2.c.a.191.4	yes	36	4.3	odd	2	inner
228.2.c.a.191.33	yes	36	12.11	even	2	inner
228.2.c.a.191.34	yes	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39068 + 0.256903i) q^{2} +(-1.58499 - 0.698441i) q^{3} +(1.86800 + 0.714541i) q^{4} +3.19367i q^{5} +(-2.02478 - 1.37850i) q^{6} -0.170940i q^{7} +(2.41423 + 1.47359i) q^{8} +(2.02436 + 2.21404i) q^{9} +O(q^{10})\)	\(q+(1.39068 + 0.256903i) q^{2} +(-1.58499 - 0.698441i) q^{3} +(1.86800 + 0.714541i) q^{4} +3.19367i q^{5} +(-2.02478 - 1.37850i) q^{6} -0.170940i q^{7} +(2.41423 + 1.47359i) q^{8} +(2.02436 + 2.21404i) q^{9} +(-0.820463 + 4.44139i) q^{10} +2.51166 q^{11} +(-2.46169 - 2.43723i) q^{12} -0.910042 q^{13} +(0.0439149 - 0.237723i) q^{14} +(2.23059 - 5.06192i) q^{15} +(2.97886 + 2.66953i) q^{16} -4.74351i q^{17} +(2.24645 + 3.59909i) q^{18} -1.00000i q^{19} +(-2.28201 + 5.96579i) q^{20} +(-0.119391 + 0.270937i) q^{21} +(3.49292 + 0.645252i) q^{22} -5.70287 q^{23} +(-2.79731 - 4.02183i) q^{24} -5.19954 q^{25} +(-1.26558 - 0.233792i) q^{26} +(-1.66221 - 4.92311i) q^{27} +(0.122144 - 0.319316i) q^{28} +4.36923i q^{29} +(4.40247 - 6.46649i) q^{30} -5.77040i q^{31} +(3.45685 + 4.47774i) q^{32} +(-3.98094 - 1.75424i) q^{33} +(1.21862 - 6.59672i) q^{34} +0.545926 q^{35} +(2.19949 + 5.58231i) q^{36} +2.04943 q^{37} +(0.256903 - 1.39068i) q^{38} +(1.44240 + 0.635610i) q^{39} +(-4.70618 + 7.71027i) q^{40} -10.9620i q^{41} +(-0.235640 + 0.346116i) q^{42} +5.51345i q^{43} +(4.69178 + 1.79468i) q^{44} +(-7.07091 + 6.46514i) q^{45} +(-7.93089 - 1.46508i) q^{46} -12.4258 q^{47} +(-2.85695 - 6.31172i) q^{48} +6.97078 q^{49} +(-7.23091 - 1.33577i) q^{50} +(-3.31306 + 7.51839i) q^{51} +(-1.69996 - 0.650262i) q^{52} -12.5541i q^{53} +(-1.04685 - 7.27352i) q^{54} +8.02141i q^{55} +(0.251896 - 0.412689i) q^{56} +(-0.698441 + 1.58499i) q^{57} +(-1.12247 + 6.07622i) q^{58} +7.82741 q^{59} +(7.78370 - 7.86184i) q^{60} -8.29853 q^{61} +(1.48243 - 8.02480i) q^{62} +(0.378468 - 0.346044i) q^{63} +(3.65704 + 7.11520i) q^{64} -2.90637i q^{65} +(-5.08556 - 3.46231i) q^{66} +1.21875i q^{67} +(3.38943 - 8.86088i) q^{68} +(9.03897 + 3.98312i) q^{69} +(0.759211 + 0.140250i) q^{70} +3.94565 q^{71} +(1.62469 + 8.32829i) q^{72} +12.9265 q^{73} +(2.85011 + 0.526503i) q^{74} +(8.24119 + 3.63157i) q^{75} +(0.714541 - 1.86800i) q^{76} -0.429343i q^{77} +(1.84264 + 1.25449i) q^{78} +0.0130423i q^{79} +(-8.52559 + 9.51351i) q^{80} +(-0.803924 + 8.96402i) q^{81} +(2.81618 - 15.2447i) q^{82} +7.86488 q^{83} +(-0.416619 + 0.420802i) q^{84} +15.1492 q^{85} +(-1.41642 + 7.66746i) q^{86} +(3.05165 - 6.92518i) q^{87} +(6.06373 + 3.70117i) q^{88} -3.43793i q^{89} +(-11.4943 + 7.17444i) q^{90} +0.155562i q^{91} +(-10.6530 - 4.07493i) q^{92} +(-4.03028 + 9.14600i) q^{93} +(-17.2804 - 3.19222i) q^{94} +3.19367 q^{95} +(-2.35162 - 9.51157i) q^{96} -13.5712 q^{97} +(9.69415 + 1.79081i) q^{98} +(5.08450 + 5.56091i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{6}+O(q^{10}) \) 36 * q - 6 * q^6	\( 36 q - 6 q^{6} + 8 q^{10} + 4 q^{12} - 8 q^{16} + 16 q^{18} + 8 q^{21} - 12 q^{22} - 2 q^{24} - 28 q^{25} + 12 q^{28} - 12 q^{30} - 28 q^{34} - 22 q^{36} - 16 q^{37} - 12 q^{40} + 10 q^{42} + 16 q^{45} - 4 q^{46} + 32 q^{48} - 44 q^{49} - 36 q^{52} - 20 q^{54} - 4 q^{58} - 4 q^{60} + 16 q^{61} + 24 q^{64} + 24 q^{66} - 16 q^{69} + 36 q^{70} - 36 q^{72} - 8 q^{73} - 32 q^{78} - 40 q^{81} + 72 q^{82} - 20 q^{84} + 16 q^{85} - 16 q^{88} - 56 q^{90} + 8 q^{93} - 56 q^{94} + 2 q^{96} + 40 q^{97}+O(q^{100}) \) 36 * q - 6 * q^6 + 8 * q^10 + 4 * q^12 - 8 * q^16 + 16 * q^18 + 8 * q^21 - 12 * q^22 - 2 * q^24 - 28 * q^25 + 12 * q^28 - 12 * q^30 - 28 * q^34 - 22 * q^36 - 16 * q^37 - 12 * q^40 + 10 * q^42 + 16 * q^45 - 4 * q^46 + 32 * q^48 - 44 * q^49 - 36 * q^52 - 20 * q^54 - 4 * q^58 - 4 * q^60 + 16 * q^61 + 24 * q^64 + 24 * q^66 - 16 * q^69 + 36 * q^70 - 36 * q^72 - 8 * q^73 - 32 * q^78 - 40 * q^81 + 72 * q^82 - 20 * q^84 + 16 * q^85 - 16 * q^88 - 56 * q^90 + 8 * q^93 - 56 * q^94 + 2 * q^96 + 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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