LMFDB - Embedded newform 228.2.c.a.191.33

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

$q$-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	$-0.746824\pi$
$5$		−	3.19367i		−	1.42825i	0.700017	−	0.714127i	$-0.253176\pi$
$6$	−2.02478	+	1.37850i	−0.826614	+	0.562769i
$7$			0.170940i			0.0646092i	0.999478	+	0.0323046i	$0.0102847\pi$
$7$			0.170940i			0.0646092i	−0.999478	+	0.0323046i	$0.989715\pi$
$8$	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	$0.195089\pi$
$17$			4.74351i			1.15047i	−0.817988	+	0.575235i	$0.804911\pi$
$18$	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	$-0.867037\pi$
$29$		−	4.36923i		−	0.811347i	0.914018	−	0.405673i	$-0.132963\pi$
$30$	4.40247	+	6.46649i	0.803777	+	1.18061i
$31$			5.77040i			1.03639i	0.855261	+	0.518197i	$0.173397\pi$
$31$			5.77040i			1.03639i	−0.855261	+	0.518197i	$0.826603\pi$
$32$	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	$0.327052\pi$
$41$			10.9620i			1.71198i	−0.516990	+	0.855991i	$0.672948\pi$
$42$	−0.235640	−	0.346116i	−0.0363601	−	0.0534069i
$43$		−	5.51345i		−	0.840793i	−0.907341	−	0.420396i	$-0.861891\pi$
$43$		−	5.51345i		−	0.840793i	0.907341	−	0.420396i	$-0.138109\pi$
$44$	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	$0.330926\pi$
$53$			12.5541i			1.72444i	−0.506536	+	0.862219i	$0.669074\pi$
$54$	−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	$-0.976281\pi$
$67$		−	1.21875i		−	0.148895i	0.997225	−	0.0744473i	$-0.0237193\pi$
$68$	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	$-0.999766\pi$
$79$		−	0.0130423i		−	0.00146737i	1.00000		0.000733685i	$-0.000233539\pi$
$80$	−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	$0.0583251\pi$
$89$			3.43793i			0.364420i	−0.983260	+	0.182210i	$0.941675\pi$
$90$	−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	$-0.717165\pi$
$101$		−	15.6006i		−	1.55232i	0.630537	−	0.776159i	$-0.282835\pi$
$102$	−6.53891	−	9.60457i	−0.647449	−	0.950995i
$103$		−	14.3532i		−	1.41426i	−0.707082	−	0.707131i	$-0.749989\pi$
$103$		−	14.3532i		−	1.41426i	0.707082	−	0.707131i	$-0.250011\pi$
$104$	−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	$0.119416\pi$
$113$			7.79014i			0.732835i	−0.930451	+	0.366417i	$0.880584\pi$
$114$	−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	$0.0929012\pi$
$127$			6.48515i			0.575464i	−0.957711	+	0.287732i	$0.907099\pi$
$128$	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	$-0.964359\pi$
$137$		−	2.61564i		−	0.223469i	0.993738	−	0.111734i	$-0.0356406\pi$
$138$	11.5471	−	7.86139i	0.982953	−	0.669206i
$139$		−	20.4109i		−	1.73123i	−0.500714	−	0.865613i	$-0.666929\pi$
$139$		−	20.4109i		−	1.73123i	0.500714	−	0.865613i	$-0.333071\pi$
$140$	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	$-0.916043\pi$
$149$		−	6.36477i		−	0.521422i	0.965417	−	0.260711i	$-0.0839570\pi$
$150$	10.5279	−	7.16755i	0.859602	−	0.585228i
$151$			4.47696i			0.364330i	0.983268	+	0.182165i	$0.0583104\pi$
$151$			4.47696i			0.364330i	−0.983268	+	0.182165i	$0.941690\pi$
$152$	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	$0.100591\pi$
$163$			7.93560i			0.621564i	−0.950481	+	0.310782i	$0.899409\pi$
$164$	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	$-0.901604\pi$
$173$		−	8.00279i		−	0.608440i	0.952602	−	0.304220i	$-0.0983959\pi$
$174$	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	$0.177587\pi$
$197$			14.8613i			1.05882i	−0.848366	+	0.529411i	$0.822413\pi$
$198$	5.64232	−	9.03968i	0.400983	−	0.642422i
$199$			9.86354i			0.699208i	0.936898	+	0.349604i	$0.113684\pi$
$199$			9.86354i			0.699208i	−0.936898	+	0.349604i	$0.886316\pi$
$200$	−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	$0.224405\pi$
$211$			18.8262i			1.29605i	−0.761619	+	0.648025i	$0.775595\pi$
$212$	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	$-0.793261\pi$
$223$		−	18.0626i		−	1.20956i	0.796393	−	0.604780i	$-0.206739\pi$
$224$	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	$0.0985805\pi$
$233$			9.30430i			0.609545i	−0.952425	+	0.304773i	$0.901420\pi$
$234$	−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	$-0.916083\pi$
$257$		−	8.35519i		−	0.521182i	0.965449	−	0.260591i	$-0.0839174\pi$
$258$	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	$-0.746634\pi$
$269$		−	23.4388i		−	1.42909i	0.699591	−	0.714544i	$-0.253366\pi$
$270$	23.2292	+	3.34329i	1.41369	+	0.203466i
$271$		−	4.19984i		−	0.255122i	−0.991831	−	0.127561i	$-0.959285\pi$
$271$		−	4.19984i		−	0.255122i	0.991831	−	0.127561i	$-0.0407149\pi$
$272$	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	$-0.796425\pi$
$281$		−	20.0095i		−	1.19367i	0.802365	−	0.596834i	$-0.203575\pi$
$282$	25.1596	−	17.1289i	1.49823	−	1.02001i
$283$		−	23.6437i		−	1.40547i	−0.711451	−	0.702735i	$-0.751962\pi$
$283$		−	23.6437i		−	1.40547i	0.711451	−	0.702735i	$-0.248038\pi$
$284$	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	$0.102870\pi$
$293$			10.8722i			0.635161i	−0.948231	+	0.317580i	$0.897130\pi$
$294$	−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	$0.0107481\pi$
$307$			1.18303i			0.0675193i	−0.999430	+	0.0337596i	$0.989252\pi$
$308$	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	$-0.897990\pi$
$317$		−	11.2174i		−	0.630033i	0.949086	−	0.315016i	$-0.102010\pi$
$318$	−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	$0.0789260\pi$
$331$			8.93007i			0.490841i	−0.969417	+	0.245420i	$0.921074\pi$
$332$	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	$0.0419488\pi$
$353$			4.93775i			0.262810i	−0.991329	+	0.131405i	$0.958051\pi$
$354$	−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	$0.338505\pi$
$367$			33.4882i			1.74807i	−0.485865	+	0.874034i	$0.661495\pi$
$368$	−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	$-0.940579\pi$
$379$		−	7.22631i		−	0.371190i	0.982626	−	0.185595i	$-0.0594213\pi$
$380$	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	$0.0975109\pi$
$389$			11.8958i			0.603141i	−0.953444	+	0.301571i	$0.902489\pi$
$390$	−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	$0.0292058\pi$
$401$			3.66954i			0.183248i	−0.995794	+	0.0916240i	$0.970794\pi$
$402$	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	$-0.719335\pi$
$439$		−	32.3438i		−	1.54369i	0.635813	−	0.771843i	$-0.280665\pi$
$440$	−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	$-0.865327\pi$
$449$		−	17.4000i		−	0.821157i	0.911825	−	0.410578i	$-0.134673\pi$
$450$	−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	$0.0949470\pi$
$461$			12.6198i			0.587763i	−0.955842	+	0.293881i	$0.905053\pi$
$462$	−0.591848	−	0.869326i	−0.0275353	−	0.0404447i
$463$		−	25.3160i		−	1.17654i	−0.808666	−	0.588268i	$-0.799810\pi$
$463$		−	25.3160i		−	1.17654i	0.808666	−	0.588268i	$-0.200190\pi$
$464$	−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	$-0.886409\pi$
$487$		−	15.4181i		−	0.698662i	0.936999	−	0.349331i	$-0.113591\pi$
$488$	−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	$0.0253741\pi$
$499$			3.55762i			0.159261i	−0.996824	+	0.0796306i	$0.974626\pi$
$500$	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	$0.0612786\pi$
$509$			8.63300i			0.382651i	−0.981527	+	0.191325i	$0.938721\pi$
$510$	−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	$0.194439\pi$
$521$			26.1836i			1.14713i	−0.819162	+	0.573563i	$0.805561\pi$
$522$	−15.7253	−	9.81528i	−0.688276	−	0.429603i
$523$		−	0.816068i		−	0.0356842i	−0.999841	−	0.0178421i	$-0.994320\pi$
$523$		−	0.816068i		−	0.0356842i	0.999841	−	0.0178421i	$-0.00567961\pi$
$524$	−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	$0.112903\pi$
$547$			16.2455i			0.694608i	−0.937753	+	0.347304i	$0.887097\pi$
$548$	−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	$0.0316310\pi$
$557$			4.68280i			0.198417i	−0.995067	+	0.0992083i	$0.968369\pi$
$558$	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	$-0.880172\pi$
$569$		−	17.5383i		−	0.735244i	0.929975	−	0.367622i	$-0.119828\pi$
$570$	−6.46649	+	4.40247i	−0.270852	+	0.184399i
$571$			10.6555i			0.445919i	0.974828	+	0.222960i	$0.0715718\pi$
$571$			10.6555i			0.445919i	−0.974828	+	0.222960i	$0.928428\pi$
$572$	−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	$0.0824360\pi$
$593$			12.4726i			0.512190i	−0.966652	+	0.256095i	$0.917564\pi$
$594$	−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	$0.259156\pi$
$607$			35.8302i			1.45430i	−0.686477	+	0.727151i	$0.740844\pi$
$608$	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	$-0.849555\pi$
$617$		−	22.6156i		−	0.910470i	0.890371	−	0.455235i	$-0.150445\pi$
$618$	19.7858	+	29.0621i	0.795903	+	1.16905i
$619$		−	12.3837i		−	0.497742i	−0.968537	−	0.248871i	$-0.919940\pi$
$619$		−	12.3837i		−	0.497742i	0.968537	−	0.248871i	$-0.0800595\pi$
$620$	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	$-0.865286\pi$
$631$		−	20.6331i		−	0.821391i	0.911773	−	0.410696i	$-0.134714\pi$
$632$	−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	$0.338093\pi$
$641$			44.2257i			1.74681i	−0.486996	+	0.873404i	$0.661907\pi$
$642$	4.37813	−	2.98068i	0.172791	−	0.117638i
$643$			23.7238i			0.935575i	0.883841	+	0.467787i	$0.154949\pi$
$643$			23.7238i			0.935575i	−0.883841	+	0.467787i	$0.845051\pi$
$644$	−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	$-0.904068\pi$
$653$		−	15.1707i		−	0.593677i	0.954928	−	0.296839i	$-0.0959323\pi$
$654$	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	$0.0891340\pi$
$677$			14.3823i			0.552755i	−0.961049	+	0.276377i	$0.910866\pi$
$678$	−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	$-0.777181\pi$
$691$		−	33.8692i		−	1.28845i	0.764838	−	0.644223i	$-0.222819\pi$
$692$	−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	$0.0712462\pi$
$701$			11.7535i			0.443925i	−0.975055	+	0.221962i	$0.928754\pi$
$702$	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	$0.381523\pi$
$727$			50.2334i			1.86305i	−0.363672	+	0.931527i	$0.618477\pi$
$728$	−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	$0.368729\pi$
$739$			49.8109i			1.83232i	−0.400809	+	0.916162i	$0.631271\pi$
$740$	−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	$0.198134\pi$
$751$			31.9553i			1.16606i	−0.812449	+	0.583032i	$0.801866\pi$
$752$	−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	$-0.875200\pi$
$761$		−	21.0816i		−	0.764207i	0.924120	−	0.382103i	$-0.124800\pi$
$762$	−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	$0.239424\pi$
$773$			37.9913i			1.36645i	−0.730207	+	0.683226i	$0.760576\pi$
$774$	−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	$-0.953200\pi$
$787$		−	8.21956i		−	0.292996i	0.989211	−	0.146498i	$-0.0468002\pi$
$788$	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	$0.102601\pi$
$797$			17.8860i			0.633556i	−0.948500	+	0.316778i	$0.897399\pi$
$798$	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	$-0.875245\pi$
$809$		−	21.7287i		−	0.763942i	0.924174	−	0.381971i	$-0.124755\pi$
$810$	−39.1531	+	10.9252i	−1.37570	+	0.383872i
$811$		−	41.4765i		−	1.45644i	−0.685344	−	0.728219i	$-0.740348\pi$
$811$		−	41.4765i		−	1.45644i	0.685344	−	0.728219i	$-0.259652\pi$
$812$	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	$0.113799\pi$
$821$			20.0539i			0.699886i	−0.936771	+	0.349943i	$0.886201\pi$
$822$	3.60565	+	5.29610i	0.125761	+	0.184723i
$823$		−	26.7511i		−	0.932485i	−0.884657	−	0.466242i	$-0.845607\pi$
$823$		−	26.7511i		−	0.932485i	0.884657	−	0.466242i	$-0.154393\pi$
$824$	−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	$-0.740966\pi$
$857$		−	42.5586i		−	1.45377i	0.686757	−	0.726887i	$-0.259034\pi$
$858$	4.62807	−	3.15085i	0.158000	−	0.107568i
$859$			18.9766i			0.647472i	0.946148	+	0.323736i	$0.104939\pi$
$859$			18.9766i			0.647472i	−0.946148	+	0.323736i	$0.895061\pi$
$860$	−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	$0.366066\pi$
$881$			54.1854i			1.82555i	−0.408461	+	0.912776i	$0.633934\pi$
$882$	15.6595	−	25.0885i	0.527284	−	0.844772i
$883$		−	22.8335i		−	0.768409i	−0.923248	−	0.384204i	$-0.874476\pi$
$883$		−	22.8335i		−	0.768409i	0.923248	−	0.384204i	$-0.125524\pi$
$884$	−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	$-0.897701\pi$
$907$		−	19.0263i		−	0.631759i	0.948799	−	0.315879i	$-0.102299\pi$
$908$	−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	$-0.858375\pi$
$919$		−	26.0948i		−	0.860788i	0.902641	−	0.430394i	$-0.141625\pi$
$920$	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	$0.0685922\pi$
$929$			13.0346i			0.427650i	−0.976872	+	0.213825i	$0.931408\pi$
$930$	−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	$-0.985744\pi$
$941$		−	2.74678i		−	0.0895426i	0.998997	−	0.0447713i	$-0.0142559\pi$
$942$	−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	$-0.926540\pi$
$953$		−	14.1225i		−	0.457474i	0.973488	−	0.228737i	$-0.0734595\pi$
$954$	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	$0.135145\pi$
$967$			25.6193i			0.823861i	−0.911215	+	0.411931i	$0.864855\pi$
$968$	−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	$-0.705405\pi$
$977$		−	49.9437i		−	1.59784i	0.601438	−	0.798920i	$-0.294595\pi$
$978$	−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	$0.112304\pi$
$991$			21.7553i			0.691079i	−0.938404	+	0.345540i	$0.887696\pi$
$992$	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.191.33	yes	36
3.2	odd	2	inner	228.2.c.a.191.4	yes	36
4.3	odd	2	inner	228.2.c.a.191.3	✓	36
12.11	even	2	inner	228.2.c.a.191.34	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.c.a.191.3	✓	36	4.3	odd	2	inner
228.2.c.a.191.4	yes	36	3.2	odd	2	inner
228.2.c.a.191.33	yes	36	1.1	even	1	trivial
228.2.c.a.191.34	yes	36	12.11	even	2	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:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
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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