LMFDB - Embedded newform 185.2.u.a.8.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(8,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.u (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			8.13
Character	$\chi$	$=$	185.8
Dual form			185.2.u.a.162.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.971183 - 0.560713i) q^{2} +(0.168506 + 0.628874i) q^{3} +(-0.371203 + 0.642942i) q^{4} +(0.550691 + 2.16720i) q^{5} +(0.516268 + 0.516268i) q^{6} +(-0.377247 - 1.40791i) q^{7} +3.07540i q^{8} +(2.23099 - 1.28806i) q^{9} +(1.75000 + 1.79596i) q^{10} +0.304712i q^{11} +(-0.466879 - 0.125100i) q^{12} +(-0.187550 - 0.108282i) q^{13} +(-1.15581 - 1.15581i) q^{14} +(-1.27010 + 0.711501i) q^{15} +(0.982011 + 1.70089i) q^{16} +(0.836960 + 1.44966i) q^{17} +(1.44446 - 2.50189i) q^{18} +(-1.91513 - 7.14737i) q^{19} +(-1.59780 - 0.450407i) q^{20} +(0.821827 - 0.474482i) q^{21} +(0.170856 + 0.295931i) q^{22} -5.69268i q^{23} +(-1.93404 + 0.518224i) q^{24} +(-4.39348 + 2.38691i) q^{25} -0.242860 q^{26} +(2.56707 + 2.56707i) q^{27} +(1.04524 + 0.280071i) q^{28} +(-1.05734 - 1.05734i) q^{29} +(-0.834549 + 1.40316i) q^{30} +(2.64214 - 2.64214i) q^{31} +(-3.41933 - 1.97415i) q^{32} +(-0.191625 + 0.0513459i) q^{33} +(1.62568 + 0.938587i) q^{34} +(2.84346 - 1.59289i) q^{35} +1.91253i q^{36} +(-6.04562 + 0.671196i) q^{37} +(-5.86756 - 5.86756i) q^{38} +(0.0364924 - 0.136191i) q^{39} +(-6.66500 + 1.69360i) q^{40} +(2.07096 + 1.19567i) q^{41} +(0.532096 - 0.921617i) q^{42} +7.13995i q^{43} +(-0.195912 - 0.113110i) q^{44} +(4.02007 + 4.12567i) q^{45} +(-3.19196 - 5.52863i) q^{46} +(-3.92274 + 3.92274i) q^{47} +(-0.904172 + 0.904172i) q^{48} +(4.22229 - 2.43774i) q^{49} +(-2.92850 + 4.78160i) q^{50} +(-0.770618 + 0.770618i) q^{51} +(0.139238 - 0.0803891i) q^{52} +(2.13924 - 7.98376i) q^{53} +(3.93248 + 1.05370i) q^{54} +(-0.660371 + 0.167802i) q^{55} +(4.32988 - 1.16019i) q^{56} +(4.17208 - 2.40875i) q^{57} +(-1.61973 - 0.434004i) q^{58} +(6.39295 + 1.71299i) q^{59} +(0.0140099 - 1.08071i) q^{60} +(2.09439 + 7.81639i) q^{61} +(1.08452 - 4.04748i) q^{62} +(-2.65511 - 2.65511i) q^{63} -8.35577 q^{64} +(0.131386 - 0.466087i) q^{65} +(-0.157313 + 0.157313i) q^{66} +(-7.56615 + 2.02734i) q^{67} -1.24273 q^{68} +(3.57998 - 0.959252i) q^{69} +(1.86837 - 3.14135i) q^{70} +(5.55820 - 9.62708i) q^{71} +(3.96131 + 6.86119i) q^{72} +(-8.42960 + 8.42960i) q^{73} +(-5.49505 + 4.04171i) q^{74} +(-2.24139 - 2.36073i) q^{75} +(5.30625 + 1.42180i) q^{76} +(0.429006 - 0.114952i) q^{77} +(-0.0409234 - 0.152728i) q^{78} +(-1.51908 - 5.66927i) q^{79} +(-3.14538 + 3.06488i) q^{80} +(2.68239 - 4.64604i) q^{81} +2.68171 q^{82} +(1.06045 - 3.95767i) q^{83} +0.704516i q^{84} +(-2.68078 + 2.61217i) q^{85} +(4.00346 + 6.93419i) q^{86} +(0.486763 - 0.843098i) q^{87} -0.937113 q^{88} +(0.842850 - 3.14556i) q^{89} +(6.21753 + 1.75267i) q^{90} +(-0.0816982 + 0.304902i) q^{91} +(3.66007 + 2.11314i) q^{92} +(2.10679 + 1.21635i) q^{93} +(-1.61017 + 6.00923i) q^{94} +(14.4351 - 8.08646i) q^{95} +(0.665313 - 2.48298i) q^{96} -4.65513 q^{97} +(2.73374 - 4.73498i) q^{98} +(0.392488 + 0.679809i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{2} - 4 q^{3} + 30 q^{4} - 8 q^{6} - 2 q^{7} - 6 q^{10} - 10 q^{12} - 6 q^{13} - 16 q^{15} - 26 q^{16} - 10 q^{17} - 8 q^{18} - 4 q^{19} - 28 q^{20} - 12 q^{21} - 14 q^{22} + 20 q^{25} - 24 q^{26}+ \cdots - 32 q^{99}+O(q^{100}) $ 68 * q - 6 * q^2 - 4 * q^3 + 30 * q^4 - 8 * q^6 - 2 * q^7 - 6 * q^10 - 10 * q^12 - 6 * q^13 - 16 * q^15 - 26 * q^16 - 10 * q^17 - 8 * q^18 - 4 * q^19 - 28 * q^20 - 12 * q^21 - 14 * q^22 + 20 * q^25 - 24 * q^26 + 68 * q^27 + 14 * q^28 - 14 * q^29 + 26 * q^30 - 24 * q^31 + 18 * q^32 + 10 * q^33 - 22 * q^35 - 18 * q^37 - 36 * q^38 - 52 * q^39 + 84 * q^40 - 18 * q^41 - 40 * q^42 + 36 * q^44 - 66 * q^45 - 52 * q^46 - 24 * q^47 + 60 * q^48 + 36 * q^49 - 12 * q^50 - 8 * q^51 - 78 * q^52 - 38 * q^53 - 40 * q^54 + 6 * q^55 + 16 * q^56 + 90 * q^57 + 16 * q^58 + 8 * q^59 - 52 * q^60 + 4 * q^61 - 22 * q^62 - 48 * q^63 + 20 * q^64 - 20 * q^65 + 80 * q^66 - 56 * q^67 - 20 * q^68 - 8 * q^69 + 62 * q^70 + 4 * q^71 + 32 * q^72 + 60 * q^73 + 44 * q^74 + 64 * q^75 + 72 * q^76 + 6 * q^77 - 24 * q^78 - 56 * q^79 - 76 * q^80 - 6 * q^81 - 8 * q^82 + 12 * q^83 + 20 * q^85 - 4 * q^86 - 32 * q^87 - 36 * q^88 + 22 * q^89 - 74 * q^90 + 44 * q^91 + 156 * q^92 - 30 * q^93 + 20 * q^94 + 28 * q^95 - 8 * q^96 + 16 * q^97 + 48 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.971183	−	0.560713i	0.686730	−	0.396484i	−0.115656	−	0.993289i	$-0.536897\pi$
$2$	0.971183	−	0.560713i	0.686730	−	0.396484i	0.802386	+	0.596806i	$0.203564\pi$
$3$	0.168506	+	0.628874i	0.0972871	+	0.363080i	0.997356	−	0.0726666i	$-0.0231509\pi$
$3$	0.168506	+	0.628874i	0.0972871	+	0.363080i	−0.900069	+	0.435747i	$0.856484\pi$
$4$	−0.371203	+	0.642942i	−0.185601	+	0.321471i
$5$	0.550691	+	2.16720i	0.246276	+	0.969200i
$5$	0.550691	+	2.16720i	0.246276	+	0.969200i
$6$	0.516268	+	0.516268i	0.210765	+	0.210765i
$7$	−0.377247	−	1.40791i	−0.142586	−	0.532139i	−0.999851	−	0.0172630i	$-0.994505\pi$
$7$	−0.377247	−	1.40791i	−0.142586	−	0.532139i	0.857265	−	0.514876i	$-0.172162\pi$
$8$			3.07540i			1.08732i
$9$	2.23099	−	1.28806i	0.743663	−	0.429354i
$10$	1.75000	+	1.79596i	0.553397	+	0.567934i
$11$			0.304712i			0.0918742i	0.998944	+	0.0459371i	$0.0146274\pi$
$11$			0.304712i			0.0918742i	−0.998944	+	0.0459371i	$0.985373\pi$
$12$	−0.466879	−	0.125100i	−0.134776	−	0.0361132i
$13$	−0.187550	−	0.108282i	−0.0520170	−	0.0300320i	0.473766	−	0.880651i	$-0.342894\pi$
$13$	−0.187550	−	0.108282i	−0.0520170	−	0.0300320i	−0.525783	+	0.850619i	$0.676228\pi$
$14$	−1.15581	−	1.15581i	−0.308902	−	0.308902i
$15$	−1.27010	+	0.711501i	−0.327938	+	0.183709i
$16$	0.982011	+	1.70089i	0.245503	+	0.425223i
$17$	0.836960	+	1.44966i	0.202993	+	0.351593i	0.949491	−	0.313793i	$-0.101600\pi$
$17$	0.836960	+	1.44966i	0.202993	+	0.351593i	−0.746499	+	0.665387i	$0.768267\pi$
$18$	1.44446	−	2.50189i	0.340464	−	0.589700i
$19$	−1.91513	−	7.14737i	−0.439361	−	1.63972i	−0.730409	−	0.683010i	$-0.760671\pi$
$19$	−1.91513	−	7.14737i	−0.439361	−	1.63972i	0.291048	−	0.956708i	$-0.405996\pi$
$20$	−1.59780	−	0.450407i	−0.357279	−	0.100714i
$21$	0.821827	−	0.474482i	0.179337	−	0.103540i
$22$	0.170856	+	0.295931i	0.0364266	+	0.0630927i
$23$		−	5.69268i		−	1.18701i	−0.804832	−	0.593503i	$-0.797744\pi$
$23$		−	5.69268i		−	1.18701i	0.804832	−	0.593503i	$-0.202256\pi$
$24$	−1.93404	+	0.518224i	−0.394784	+	0.105782i
$25$	−4.39348	+	2.38691i	−0.878696	+	0.477382i
$26$	−0.242860			−0.0476288
$27$	2.56707	+	2.56707i	0.494032	+	0.494032i
$28$	1.04524	+	0.280071i	0.197531	+	0.0529284i
$29$	−1.05734	−	1.05734i	−0.196342	−	0.196342i	0.602088	−	0.798430i	$-0.294336\pi$
$29$	−1.05734	−	1.05734i	−0.196342	−	0.196342i	−0.798430	+	0.602088i	$0.794336\pi$
$30$	−0.834549	+	1.40316i	−0.152367	+	0.256180i
$31$	2.64214	−	2.64214i	0.474542	−	0.474542i	−0.428839	−	0.903381i	$-0.641077\pi$
$31$	2.64214	−	2.64214i	0.474542	−	0.474542i	0.903381	+	0.428839i	$0.141077\pi$
$32$	−3.41933	−	1.97415i	−0.604458	−	0.348984i
$33$	−0.191625	+	0.0513459i	−0.0333577	+	0.00893817i
$34$	1.62568	+	0.938587i	0.278802	+	0.160966i
$35$	2.84346	−	1.59289i	0.480633	−	0.269248i
$36$			1.91253i			0.318755i
$37$	−6.04562	+	0.671196i	−0.993893	+	0.110344i
$37$	−6.04562	+	0.671196i	−0.993893	+	0.110344i
$38$	−5.86756	−	5.86756i	−0.951844	−	0.951844i
$39$	0.0364924	−	0.136191i	0.00584345	−	0.0218081i
$40$	−6.66500	+	1.69360i	−1.05383	+	0.267781i
$41$	2.07096	+	1.19567i	0.323430	+	0.186732i	0.652920	−	0.757427i	$-0.273544\pi$
$41$	2.07096	+	1.19567i	0.323430	+	0.186732i	−0.329491	+	0.944159i	$0.606877\pi$
$42$	0.532096	−	0.921617i	0.0821042	−	0.142209i
$43$			7.13995i			1.08883i	0.838815	+	0.544416i	$0.183249\pi$
$43$			7.13995i			1.08883i	−0.838815	+	0.544416i	$0.816751\pi$
$44$	−0.195912	−	0.113110i	−0.0295349	−	0.0170520i
$45$	4.02007	+	4.12567i	0.599276	+	0.615018i
$46$	−3.19196	−	5.52863i	−0.470629	−	0.815153i
$47$	−3.92274	+	3.92274i	−0.572191	+	0.572191i	−0.932740	−	0.360549i	$-0.882589\pi$
$47$	−3.92274	+	3.92274i	−0.572191	+	0.572191i	0.360549	+	0.932740i	$0.382589\pi$
$48$	−0.904172	+	0.904172i	−0.130506	+	0.130506i
$49$	4.22229	−	2.43774i	0.603185	−	0.348249i
$50$	−2.92850	+	4.78160i	−0.414152	+	0.676221i
$51$	−0.770618	+	0.770618i	−0.107908	+	0.107908i
$52$	0.139238	−	0.0803891i	0.0193088	−	0.0111480i
$53$	2.13924	−	7.98376i	0.293848	−	1.09665i	−0.648281	−	0.761401i	$-0.724512\pi$
$53$	2.13924	−	7.98376i	0.293848	−	1.09665i	0.942128	−	0.335253i	$-0.108822\pi$
$54$	3.93248	+	1.05370i	0.535142	+	0.143391i
$55$	−0.660371	+	0.167802i	−0.0890444	+	0.0226265i
$56$	4.32988	−	1.16019i	0.578605	−	0.155037i
$57$	4.17208	−	2.40875i	0.552605	−	0.319047i
$58$	−1.61973	−	0.434004i	−0.212681	−	0.0569876i
$59$	6.39295	+	1.71299i	0.832291	+	0.223012i	0.649713	−	0.760180i	$-0.274889\pi$
$59$	6.39295	+	1.71299i	0.832291	+	0.223012i	0.182578	+	0.983191i	$0.441556\pi$
$60$	0.0140099	−	1.08071i	0.00180867	−	0.139519i
$61$	2.09439	+	7.81639i	0.268160	+	1.00079i	0.960288	+	0.279011i	$0.0900066\pi$
$61$	2.09439	+	7.81639i	0.268160	+	1.00079i	−0.692128	+	0.721775i	$0.743327\pi$
$62$	1.08452	−	4.04748i	0.137734	−	0.514030i
$63$	−2.65511	−	2.65511i	−0.334512	−	0.334512i
$64$	−8.35577			−1.04447
$65$	0.131386	−	0.466087i	0.0162965	−	0.0578110i
$66$	−0.157313	+	0.157313i	−0.0193639	+	0.0193639i
$67$	−7.56615	+	2.02734i	−0.924353	+	0.247680i	−0.689445	−	0.724338i	$-0.742145\pi$
$67$	−7.56615	+	2.02734i	−0.924353	+	0.247680i	−0.234908	+	0.972018i	$0.575479\pi$
$68$	−1.24273			−0.150703
$69$	3.57998	−	0.959252i	0.430979	−	0.115480i
$70$	1.86837	−	3.14135i	0.223313	−	0.375464i
$71$	5.55820	−	9.62708i	0.659637	−	1.14252i	−0.321073	−	0.947054i	$-0.604044\pi$
$71$	5.55820	−	9.62708i	0.659637	−	1.14252i	0.980710	−	0.195470i	$-0.0626231\pi$
$72$	3.96131	+	6.86119i	0.466845	+	0.808599i
$73$	−8.42960	+	8.42960i	−0.986611	+	0.986611i	−0.999912	−	0.0133009i	$-0.995766\pi$
$73$	−8.42960	+	8.42960i	−0.986611	+	0.986611i	0.0133009	+	0.999912i	$0.495766\pi$
$74$	−5.49505	+	4.04171i	−0.638787	+	0.469839i
$75$	−2.24139	−	2.36073i	−0.258814	−	0.272594i
$76$	5.30625	+	1.42180i	0.608668	+	0.163092i
$77$	0.429006	−	0.114952i	0.0488898	−	0.0131000i
$78$	−0.0409234	−	0.152728i	−0.00463367	−	0.0172931i
$79$	−1.51908	−	5.66927i	−0.170909	−	0.637843i	−0.997212	−	0.0746166i	$-0.976227\pi$
$79$	−1.51908	−	5.66927i	−0.170909	−	0.637843i	0.826303	−	0.563226i	$-0.190440\pi$
$80$	−3.14538	+	3.06488i	−0.351665	+	0.342664i
$81$	2.68239	−	4.64604i	0.298044	−	0.516227i
$82$	2.68171			0.296145
$83$	1.06045	−	3.95767i	0.116400	−	0.434410i	−0.882988	−	0.469396i	$-0.844472\pi$
$83$	1.06045	−	3.95767i	0.116400	−	0.434410i	0.999388	+	0.0349854i	$0.0111385\pi$
$84$			0.704516i			0.0768690i
$85$	−2.68078	+	2.61217i	−0.290772	+	0.283329i
$86$	4.00346	+	6.93419i	0.431704	+	0.747733i
$87$	0.486763	−	0.843098i	0.0521864	−	0.0903896i
$88$	−0.937113			−0.0998966
$89$	0.842850	−	3.14556i	0.0893419	−	0.333429i	−0.906759	−	0.421649i	$-0.861451\pi$
$89$	0.842850	−	3.14556i	0.0893419	−	0.333429i	0.996101	+	0.0882206i	$0.0281181\pi$
$90$	6.21753	+	1.75267i	0.655385	+	0.184748i
$91$	−0.0816982	+	0.304902i	−0.00856430	+	0.0319624i
$92$	3.66007	+	2.11314i	0.381588	+	0.220310i
$93$	2.10679	+	1.21635i	0.218464	+	0.126130i
$94$	−1.61017	+	6.00923i	−0.166076	+	0.619805i
$95$	14.4351	−	8.08646i	1.48101	−	0.829653i
$96$	0.665313	−	2.48298i	0.0679032	−	0.253418i
$97$	−4.65513			−0.472657			−0.236328	−	0.971673i	$-0.575944\pi$
$97$	−4.65513			−0.472657			−0.236328	+	0.971673i	$0.575944\pi$
$98$	2.73374	−	4.73498i	0.276150	−	0.478306i
$99$	0.392488	+	0.679809i	0.0394465	+	0.0683234i
$100$	0.0962263	−	3.71078i	0.00962263	−	0.371078i
$101$			17.1782i			1.70929i	0.519212	+	0.854646i	$0.326226\pi$
$101$			17.1782i			1.70929i	−0.519212	+	0.854646i	$0.673774\pi$
$102$	−0.316316	+	1.18051i	−0.0313199	+	0.116887i
$103$	2.88061			0.283835			0.141917	−	0.989879i	$-0.454673\pi$
$103$	2.88061			0.283835			0.141917	+	0.989879i	$0.454673\pi$
$104$	0.333011	−	0.576791i	0.0326544	−	0.0565590i
$105$	1.48087	+	1.51977i	0.144518	+	0.148314i
$106$	−2.39900	−	8.95319i	−0.233012	−	0.869611i
$107$	2.31406	+	8.63621i	0.223709	+	0.834894i	0.982918	+	0.184046i	$0.0589196\pi$
$107$	2.31406	+	8.63621i	0.223709	+	0.834894i	−0.759208	+	0.650848i	$0.774414\pi$
$108$	−2.60338	+	0.697573i	−0.250510	+	0.0671240i
$109$	−7.23354	−	1.93822i	−0.692847	−	0.185648i	−0.104823	−	0.994491i	$-0.533427\pi$
$109$	−7.23354	−	1.93822i	−0.692847	−	0.185648i	−0.588024	+	0.808843i	$0.700094\pi$
$110$	−0.547252	+	0.533245i	−0.0521784	+	0.0508429i
$111$	−1.44082	−	3.68883i	−0.136757	−	0.350128i
$112$	2.02424	−	2.02424i	0.191272	−	0.191272i
$113$	4.73356	+	8.19876i	0.445296	+	0.771274i	0.998073	−	0.0620546i	$-0.0197653\pi$
$113$	4.73356	+	8.19876i	0.445296	+	0.771274i	−0.552777	+	0.833329i	$0.686432\pi$
$114$	2.70123	−	4.67867i	0.252994	−	0.438198i
$115$	12.3372	−	3.13491i	1.15045	−	0.292332i
$116$	1.07229	−	0.287320i	0.0995597	−	0.0266770i
$117$	−0.557895			−0.0515774
$118$	7.16921	−	1.92099i	0.659980	−	0.176841i
$119$	1.72524	−	1.72524i	0.158153	−	0.158153i
$120$	−2.18815	−	3.90606i	−0.199750	−	0.356573i
$121$	10.9072			0.991559
$122$	6.41678	+	6.41678i	0.580948	+	0.580948i
$123$	−0.402955	+	1.50385i	−0.0363333	+	0.135598i
$124$	0.717973	+	2.67951i	0.0644759	+	0.240627i
$125$	−7.59235	−	8.20708i	−0.679081	−	0.734064i
$126$	−4.06734	−	1.08984i	−0.362348	−	0.0970908i
$127$	−13.0380	−	3.49352i	−1.15694	−	0.310000i	−0.371195	−	0.928555i	$-0.621052\pi$
$127$	−13.0380	−	3.49352i	−1.15694	−	0.310000i	−0.785742	+	0.618555i	$0.787718\pi$
$128$	−1.27632	+	0.736883i	−0.112812	+	0.0651319i
$129$	−4.49013	+	1.20313i	−0.395334	+	0.105929i
$130$	−0.133741	−	0.526326i	−0.0117299	−	0.0461618i
$131$	−4.26758	−	1.14350i	−0.372861	−	0.0999077i	0.0675223	−	0.997718i	$-0.478491\pi$
$131$	−4.26758	−	1.14350i	−0.372861	−	0.0999077i	−0.440383	+	0.897810i	$0.645157\pi$
$132$	0.0381195	−	0.142264i	0.00331788	−	0.0123825i
$133$	−9.34035	+	5.39265i	−0.809911	+	0.467602i
$134$	−6.21136	+	6.21136i	−0.536580	+	0.536580i
$135$	−4.14968	+	6.97700i	−0.357147	+	0.600484i
$136$	−4.45828	+	2.57399i	−0.382294	+	0.220718i
$137$	−6.35777	+	6.35777i	−0.543181	+	0.543181i	−0.924460	−	0.381279i	$-0.875484\pi$
$137$	−6.35777	+	6.35777i	−0.543181	+	0.543181i	0.381279	+	0.924460i	$0.375484\pi$
$138$	2.93895	−	2.93895i	0.250180	−	0.250180i
$139$	11.4157	+	19.7725i	0.968263	+	1.67708i	0.700580	+	0.713574i	$0.252925\pi$
$139$	11.4157	+	19.7725i	0.968263	+	1.67708i	0.267683	+	0.963507i	$0.413742\pi$
$140$	−0.0313650	+	2.41947i	−0.00265083	+	0.204482i
$141$	−3.12792	−	1.80590i	−0.263418	−	0.152084i
$142$		−	12.4662i		−	1.04614i
$143$	0.0329948	−	0.0571487i	0.00275917	−	0.00477902i
$144$	4.38171	+	2.52978i	0.365143	+	0.210815i
$145$	1.70919	−	2.87372i	0.141940	−	0.238649i
$146$	−3.46010	+	12.9133i	−0.286360	+	1.06871i
$147$	2.24451	+	2.24451i	0.185124	+	0.185124i
$148$	1.81261	−	4.13613i	0.148996	−	0.339988i
$149$			13.4493i			1.10181i	0.834567	+	0.550906i	$0.185718\pi$
$149$			13.4493i			1.10181i	−0.834567	+	0.550906i	$0.814282\pi$
$150$	−3.50050	−	1.03593i	−0.285814	−	0.0845830i
$151$	−14.7480	−	8.51479i	−1.20018	−	0.692924i	−0.239584	−	0.970876i	$-0.577011\pi$
$151$	−14.7480	−	8.51479i	−1.20018	−	0.692924i	−0.960595	+	0.277952i	$0.910344\pi$
$152$	21.9810	−	5.88980i	1.78290	−	0.477726i
$153$	3.73449	+	2.15611i	0.301916	+	0.174311i
$154$	0.352189	−	0.352189i	0.0283802	−	0.0283802i
$155$	7.18103	+	4.27103i	0.576794	+	0.343057i
$156$	0.0740171	+	0.0740171i	0.00592611	+	0.00592611i
$157$	−18.1462	−	4.86225i	−1.44822	−	0.388050i	−0.552816	−	0.833303i	$-0.686447\pi$
$157$	−18.1462	−	4.86225i	−1.44822	−	0.388050i	−0.895404	+	0.445254i	$0.853113\pi$
$158$	−4.65413	−	4.65413i	−0.370263	−	0.370263i
$159$	5.38125			0.426761
$160$	2.39538	−	8.49750i	0.189371	−	0.671787i
$161$	−8.01477	+	2.14755i	−0.631652	+	0.169251i
$162$		−	6.01620i		−	0.472678i
$163$	−1.48872	−	2.57854i	−0.116606	−	0.201967i	0.801815	−	0.597573i	$-0.203868\pi$
$163$	−1.48872	−	2.57854i	−0.116606	−	0.201967i	−0.918421	+	0.395606i	$0.870535\pi$
$164$	−1.53749	+	0.887672i	−0.120058	+	0.0693155i
$165$	−0.216803	−	0.387014i	−0.0168781	−	0.0301290i
$166$	−1.18922	−	4.43823i	−0.0923013	−	0.344473i
$167$	7.96741	−	13.8000i	0.616536	−	1.06787i	−0.373577	−	0.927599i	$-0.621869\pi$
$167$	7.96741	−	13.8000i	0.616536	−	1.06787i	0.990113	−	0.140273i	$-0.0447980\pi$
$168$	1.45922	+	2.52745i	0.112582	+	0.194997i
$169$	−6.47655	−	11.2177i	−0.498196	−	0.862901i
$170$	−1.13886	+	4.04004i	−0.0873462	+	0.309857i
$171$	−13.4789	−	13.4789i	−1.03076	−	1.03076i
$172$	−4.59057	−	2.65037i	−0.350028	−	0.202089i
$173$	4.09940	+	1.09843i	0.311672	+	0.0835122i	0.411264	−	0.911516i	$-0.365087\pi$
$173$	4.09940	+	1.09843i	0.311672	+	0.0835122i	−0.0995926	+	0.995028i	$0.531754\pi$
$174$		−	1.09174i		−	0.0827643i
$175$	5.01798	+	5.28515i	0.379323	+	0.399520i
$176$	−0.518283	+	0.299231i	−0.0390670	+	0.0225554i
$177$			4.30901i			0.323885i
$178$	−0.945193	−	3.52751i	−0.0708452	−	0.264398i
$179$	−7.33159	−	7.33159i	−0.547989	−	0.547989i	0.377870	−	0.925859i	$-0.376657\pi$
$179$	−7.33159	−	7.33159i	−0.547989	−	0.547989i	−0.925859	+	0.377870i	$0.876657\pi$
$180$	−4.14483	+	1.05321i	−0.308937	+	0.0785018i
$181$	−10.6139	+	18.3839i	−0.788929	+	1.36646i	0.137695	+	0.990475i	$0.456031\pi$
$181$	−10.6139	+	18.3839i	−0.788929	+	1.36646i	−0.926624	+	0.375990i	$0.877303\pi$
$182$	0.0916184	+	0.341925i	0.00679121	+	0.0253451i
$183$	−4.56260	+	2.63422i	−0.337277	+	0.194727i
$184$	17.5073			1.29065
$185$	−4.78388	−	12.7324i	−0.351718	−	0.936106i
$186$	2.72810			0.200034
$187$	−0.441728	+	0.255032i	−0.0323024	+	0.0186498i
$188$	−1.06596	−	3.97823i	−0.0777434	−	0.290142i
$189$	2.64577	−	4.58261i	0.192451	−	0.333336i
$190$	9.48494	−	15.9474i	0.688110	−	1.15694i
$191$	−13.0799	−	13.0799i	−0.946426	−	0.946426i	0.0522100	−	0.998636i	$-0.483373\pi$
$191$	−13.0799	−	13.0799i	−0.946426	−	0.946426i	−0.998636	+	0.0522100i	$0.983373\pi$
$192$	−1.40800	−	5.25472i	−0.101614	−	0.379227i
$193$			10.5415i			0.758797i	0.925233	+	0.379398i	$0.123869\pi$
$193$			10.5415i			0.758797i	−0.925233	+	0.379398i	$0.876131\pi$
$194$	−4.52098	+	2.61019i	−0.324587	+	0.187401i
$195$	0.315249	+	0.00408676i	0.0225755	+	0.000292659i
$196$			3.61959i			0.258542i
$197$	12.1424	+	3.25354i	0.865109	+	0.231805i	0.663972	−	0.747758i	$-0.268869\pi$
$197$	12.1424	+	3.25354i	0.865109	+	0.231805i	0.201138	+	0.979563i	$0.435536\pi$
$198$	0.762355	+	0.440146i	0.0541782	+	0.0312798i
$199$	−4.51277	−	4.51277i	−0.319902	−	0.319902i	0.528828	−	0.848729i	$-0.322632\pi$
$199$	−4.51277	−	4.51277i	−0.319902	−	0.319902i	−0.848729	+	0.528828i	$0.822632\pi$
$200$	−7.34071	−	13.5117i	−0.519067	−	0.955423i
$201$	−2.54989	−	4.41653i	−0.179855	−	0.311518i
$202$	9.63201	+	16.6831i	0.677706	+	1.17382i
$203$	−1.08975	+	1.88751i	−0.0764856	+	0.132477i
$204$	−0.209407	−	0.781518i	−0.0146614	−	0.0547172i
$205$	−1.45079	+	5.14662i	−0.101328	+	0.359456i
$206$	2.79759	−	1.61519i	0.194918	−	0.112536i
$207$	−7.33253	−	12.7003i	−0.509646	−	0.882732i
$208$		−	0.425336i		−	0.0294918i
$209$	2.17789	−	0.583564i	0.150648	−	0.0403660i
$210$	2.29035	+	0.645630i	0.158049	+	0.0445527i
$211$	−22.3168			−1.53635			−0.768175	−	0.640240i	$-0.778835\pi$
$211$	−22.3168			−1.53635			−0.768175	+	0.640240i	$0.778835\pi$
$212$	4.33901	+	4.33901i	0.298004	+	0.298004i
$213$	6.99081	+	1.87318i	0.479002	+	0.128348i
$214$	7.08981	+	7.08981i	0.484649	+	0.484649i
$215$	−15.4737	+	3.93191i	−1.05530	+	0.268154i
$216$	−7.89476	+	7.89476i	−0.537170	+	0.537170i
$217$	−4.71662	−	2.72314i	−0.320185	−	0.184859i
$218$	−8.11187	+	2.17357i	−0.549405	+	0.147213i
$219$	−6.72160	−	3.88072i	−0.454203	−	0.262234i
$220$	0.137245	−	0.486869i	0.00925302	−	0.0328247i
$221$		−	0.362510i		−	0.0243851i
$222$	−3.46767	−	2.77464i	−0.232735	−	0.186222i
$223$	12.4242	+	12.4242i	0.831985	+	0.831985i	0.987788	−	0.155803i	$-0.0497965\pi$
$223$	12.4242	+	12.4242i	0.831985	+	0.831985i	−0.155803	+	0.987788i	$0.549796\pi$
$224$	−1.48949	+	5.55884i	−0.0995205	+	0.371416i
$225$	−6.72731	+	10.9842i	−0.448487	+	0.732283i
$226$	9.19430	+	5.30833i	0.611595	+	0.353105i
$227$	2.33447	−	4.04343i	0.154944	−	0.268372i	−0.778094	−	0.628147i	$-0.783813\pi$
$227$	2.33447	−	4.04343i	0.154944	−	0.268372i	0.933039	+	0.359776i	$0.117147\pi$
$228$			3.57654i			0.236862i
$229$	5.96381	+	3.44321i	0.394100	+	0.227534i	0.683935	−	0.729543i	$-0.260267\pi$
$229$	5.96381	+	3.44321i	0.394100	+	0.227534i	−0.289835	+	0.957077i	$0.593601\pi$
$230$	10.2239	−	9.96217i	0.674141	−	0.656886i
$231$	0.144580	+	0.250421i	0.00951270	+	0.0164765i
$232$	3.25173	−	3.25173i	0.213487	−	0.213487i
$233$	9.81662	−	9.81662i	0.643108	−	0.643108i	−0.308210	−	0.951318i	$-0.599730\pi$
$233$	9.81662	−	9.81662i	0.643108	−	0.643108i	0.951318	+	0.308210i	$0.0997301\pi$
$234$	−0.541818	+	0.312819i	−0.0354198	+	0.0204496i
$235$	−10.6616	−	6.34114i	−0.695484	−	0.413650i
$236$	−3.47443	+	3.47443i	−0.226166	+	0.226166i
$237$	3.30928	−	1.91061i	0.214961	−	0.124108i
$238$	0.708160	−	2.64289i	0.0459032	−	0.171313i
$239$	−13.0805	−	3.50490i	−0.846105	−	0.226713i	−0.190378	−	0.981711i	$-0.560971\pi$
$239$	−13.0805	−	3.50490i	−0.846105	−	0.226713i	−0.655727	+	0.754998i	$0.727638\pi$
$240$	−2.45744	−	1.46160i	−0.158627	−	0.0943458i
$241$	16.2982	−	4.36708i	1.04986	−	0.281308i	0.307664	−	0.951495i	$-0.400453\pi$
$241$	16.2982	−	4.36708i	1.04986	−	0.281308i	0.742192	+	0.670187i	$0.233786\pi$
$242$	10.5928	−	6.11578i	0.680933	−	0.393137i
$243$	13.8938	+	3.72283i	0.891288	+	0.238820i
$244$	−5.80293	−	1.55489i	−0.371494	−	0.0995416i
$245$	7.60824	+	7.80809i	0.486073	+	0.498841i
$246$	0.451884	+	1.68645i	0.0288111	+	0.107524i
$247$	−0.414748	+	1.54786i	−0.0263898	+	0.0984881i
$248$	8.12564	+	8.12564i	0.515978	+	0.515978i
$249$	2.66756			0.169050
$250$	−11.9754	−	3.71345i	−0.757389	−	0.234859i
$251$	15.8893	−	15.8893i	1.00292	−	1.00292i	0.00292894	−	0.999996i	$-0.499068\pi$
$251$	15.8893	−	15.8893i	1.00292	−	1.00292i	0.999996	−	0.00292894i	$-0.000932313\pi$
$252$	2.69266	−	0.721497i	0.169622	−	0.0454500i
$253$	1.73463			0.109055
$254$	−14.6212	+	3.91773i	−0.917413	+	0.245820i
$255$	−2.09445	−	1.24571i	−0.131160	−	0.0780093i
$256$	7.52941	−	13.0413i	0.470588	−	0.815083i
$257$	9.47446	+	16.4102i	0.591001	+	1.02364i	0.994098	+	0.108486i	$0.0346003\pi$
$257$	9.47446	+	16.4102i	0.591001	+	1.02364i	−0.403097	+	0.915157i	$0.632066\pi$
$258$	−3.68612	+	3.68612i	−0.229488	+	0.229488i
$259$	3.22568	+	8.25846i	0.200434	+	0.513156i
$260$	0.250896	+	0.257487i	0.0155599	+	0.0159686i
$261$	−3.72082	−	0.996990i	−0.230313	−	0.0617121i
$262$	−4.78578	+	1.28234i	−0.295666	+	0.0792235i
$263$	6.37326	+	23.7853i	0.392992	+	1.46667i	0.825174	+	0.564879i	$0.191077\pi$
$263$	6.37326	+	23.7853i	0.392992	+	1.46667i	−0.432182	+	0.901786i	$0.642256\pi$
$264$	−0.157909	−	0.589325i	−0.00971864	−	0.0362705i
$265$	18.4804	+	0.239573i	1.13524	+	0.0147168i
$266$	−6.04746	+	10.4745i	−0.370793	+	0.642233i
$267$	2.12018			0.129753
$268$	1.50511	−	5.61716i	0.0919394	−	0.343122i
$269$			0.947483i			0.0577691i	0.999583	+	0.0288845i	$0.00919551\pi$
$269$			0.947483i			0.0577691i	−0.999583	+	0.0288845i	$0.990804\pi$
$270$	−0.118004	+	9.10271i	−0.00718148	+	0.553973i
$271$	6.62074	+	11.4675i	0.402181	+	0.696599i	0.993989	−	0.109481i	$-0.0349188\pi$
$271$	6.62074	+	11.4675i	0.402181	+	0.696599i	−0.591807	+	0.806079i	$0.701585\pi$
$272$	−1.64381	+	2.84716i	−0.0996704	+	0.172634i
$273$	−0.205511			−0.0124381
$274$	−2.60967	+	9.73943i	−0.157656	+	0.588380i
$275$	−0.727321	−	1.33875i	−0.0438591	−	0.0807295i
$276$	−0.712154	+	2.65780i	−0.0428667	+	0.159981i
$277$	−1.88762	−	1.08982i	−0.113416	−	0.0654810i	0.442219	−	0.896907i	$-0.354191\pi$
$277$	−1.88762	−	1.08982i	−0.113416	−	0.0654810i	−0.555635	+	0.831426i	$0.687525\pi$
$278$	22.1734	+	12.8018i	1.32987	+	0.767801i
$279$	2.49134	−	9.29782i	0.149153	−	0.556646i
$280$	4.89878	+	8.74480i	0.292758	+	0.522601i
$281$	−4.03027	+	15.0412i	−0.240426	+	0.897280i	0.735202	+	0.677848i	$0.237087\pi$
$281$	−4.03027	+	15.0412i	−0.240426	+	0.897280i	−0.975628	+	0.219432i	$0.929579\pi$
$282$	−4.05037			−0.241196
$283$	3.98498	−	6.90219i	0.236882	−	0.410292i	−0.722936	−	0.690915i	$-0.757208\pi$
$283$	3.98498	−	6.90219i	0.236882	−	0.410292i	0.959818	+	0.280623i	$0.0905410\pi$
$284$	4.12644	+	7.14720i	0.244859	+	0.424108i
$285$	7.51776	+	7.71524i	0.445314	+	0.457011i
$286$		−	0.0740025i		−	0.00437586i
$287$	0.902127	−	3.36678i	0.0532508	−	0.198735i
$288$	−10.1713			−0.599350
$289$	7.09900	−	12.2958i	0.417588	−	0.723284i
$290$	0.0486040	−	3.74927i	0.00285412	−	0.220165i
$291$	−0.784418	−	2.92749i	−0.0459834	−	0.171612i
$292$	−2.29066	−	8.54884i	−0.134050	−	0.500283i
$293$	4.80738	−	1.28813i	0.280850	−	0.0752536i	−0.115644	−	0.993291i	$-0.536893\pi$
$293$	4.80738	−	1.28813i	0.280850	−	0.0752536i	0.396494	+	0.918037i	$0.370227\pi$
$294$	3.43836	+	0.921306i	0.200529	+	0.0537316i
$295$	−0.191837	+	14.7981i	−0.0111692	+	0.861579i
$296$	−2.06420	−	18.5927i	−0.119979	−	1.08068i
$297$	−0.782216	+	0.782216i	−0.0453888	+	0.0453888i
$298$	7.54121	+	13.0618i	0.436851	+	0.756648i
$299$	−0.616415	+	1.06766i	−0.0356482	+	0.0617445i
$300$	2.34983	−	0.564775i	0.135667	−	0.0326073i
$301$	10.0524	−	2.69353i	0.579410	−	0.155252i
$302$	−19.0974			−1.09893
$303$	−10.8029	+	2.89463i	−0.620610	+	0.166292i
$304$	10.2762	−	10.2762i	0.589382	−	0.589382i
$305$	−15.7863	+	8.84338i	−0.903920	+	0.506370i
$306$	4.83583			0.276446
$307$	17.8239	+	17.8239i	1.01726	+	1.01726i	0.999848	+	0.0174137i	$0.00554325\pi$
$307$	17.8239	+	17.8239i	1.01726	+	1.01726i	0.0174137	+	0.999848i	$0.494457\pi$
$308$	−0.0853410	+	0.318497i	−0.00486275	+	0.0181480i
$309$	0.485400	+	1.81154i	0.0276134	+	0.103055i
$310$	9.36891	+	0.121455i	0.532119	+	0.00689817i
$311$	12.9139	+	3.46026i	0.732278	+	0.196213i	0.605643	−	0.795736i	$-0.292916\pi$
$311$	12.9139	+	3.46026i	0.732278	+	0.196213i	0.126634	+	0.991949i	$0.459582\pi$
$312$	0.418843	+	0.112229i	0.0237123	+	0.00635370i
$313$	4.14421	−	2.39266i	0.234244	−	0.135241i	−0.378284	−	0.925690i	$-0.623486\pi$
$313$	4.14421	−	2.39266i	0.234244	−	0.135241i	0.612529	+	0.790448i	$0.290152\pi$
$314$	−20.3495	+	5.45265i	−1.14839	+	0.307711i
$315$	4.29199	−	7.21628i	0.241826	−	0.406591i
$316$	4.20890	+	1.12777i	0.236769	+	0.0634421i
$317$	8.43852	−	31.4930i	0.473955	−	1.76882i	−0.151390	−	0.988474i	$-0.548375\pi$
$317$	8.43852	−	31.4930i	0.473955	−	1.76882i	0.625345	−	0.780349i	$-0.284958\pi$
$318$	5.22618	−	3.01734i	0.293070	−	0.169204i
$319$	0.322183	−	0.322183i	0.0180388	−	0.0180388i
$320$	−4.60145	−	18.1086i	−0.257229	−	1.01230i
$321$	−5.04115	+	2.91051i	−0.281370	+	0.162449i
$322$	−6.57964	+	6.57964i	−0.366669	+	0.366669i
$323$	8.75834	−	8.75834i	0.487327	−	0.487327i
$324$	1.99142	+	3.44925i	0.110635	+	0.191625i
$325$	1.08246	+	0.0280697i	0.0600438	+	0.00155703i
$326$	−2.89164	−	1.66949i	−0.160153	−	0.0924646i
$327$		−	4.87558i		−	0.269620i
$328$	−3.67716	+	6.36904i	−0.203037	+	0.351671i
$329$	7.00270	+	4.04301i	0.386071	+	0.222898i
$330$	−0.427559	−	0.254297i	−0.0235364	−	0.0139986i
$331$	−2.05282	+	7.66123i	−0.112833	+	0.421099i	−0.999116	−	0.0420458i	$-0.986612\pi$
$331$	−2.05282	+	7.66123i	−0.112833	+	0.421099i	0.886282	+	0.463145i	$0.153279\pi$
$332$	2.15091	+	2.15091i	0.118046	+	0.118046i
$333$	−12.6232	+	9.28456i	−0.691745	+	0.508791i
$334$		−	17.8697i		−	0.977786i
$335$	−8.56026	−	15.2809i	−0.467697	−	0.834885i
$336$	1.61409	+	0.931893i	0.0880556	+	0.0508389i
$337$	5.86295	−	1.57097i	0.319375	−	0.0855764i	−0.0955700	−	0.995423i	$-0.530467\pi$
$337$	5.86295	−	1.57097i	0.319375	−	0.0855764i	0.414945	+	0.909846i	$0.363801\pi$
$338$	−12.5798	−	7.26297i	−0.684252	−	0.395053i
$339$	−4.35835	+	4.35835i	−0.236713	+	0.236713i
$340$	−0.684359	−	2.69323i	−0.0371146	−	0.146061i
$341$	0.805092	+	0.805092i	0.0435982	+	0.0435982i
$342$	−20.6482	−	5.53268i	−1.11653	−	0.299173i
$343$	−12.2396	−	12.2396i	−0.660875	−	0.660875i
$344$	−21.9582			−1.18391
$345$	4.05035	+	7.23026i	0.218063	+	0.389264i
$346$	4.59717	−	1.23181i	0.247146	−	0.0662225i
$347$		−	6.64889i		−	0.356931i	−0.983946	−	0.178466i	$-0.942887\pi$
$347$		−	6.64889i		−	0.356931i	0.983946	−	0.178466i	$-0.0571133\pi$
$348$	0.361375	+	0.625921i	0.0193718	+	0.0335529i
$349$	30.0699	−	17.3608i	1.60960	−	0.929305i	0.620144	−	0.784488i	$-0.287074\pi$
$349$	30.0699	−	17.3608i	1.60960	−	0.929305i	0.989458	−	0.144817i	$-0.0462594\pi$
$350$	7.83682	+	2.31921i	0.418896	+	0.123967i
$351$	−0.203486	−	0.759420i	−0.0108613	−	0.0405348i
$352$	0.601548	−	1.04191i	0.0320626	−	0.0555341i
$353$	−16.1620	−	27.9934i	−0.860217	−	1.48994i	−0.871719	−	0.490006i	$-0.836995\pi$
$353$	−16.1620	−	27.9934i	−0.860217	−	1.48994i	0.0115020	−	0.999934i	$-0.496339\pi$
$354$	2.41611	+	4.18483i	0.128415	+	0.222421i
$355$	23.9246	+	6.74416i	1.26979	+	0.357943i
$356$	1.70954	+	1.70954i	0.0906057	+	0.0906057i
$357$	1.37567	+	0.794244i	0.0728083	+	0.0420359i
$358$	−11.2312	−	3.00940i	−0.593589	−	0.159052i
$359$			27.1360i			1.43218i	0.698007	+	0.716091i	$0.254071\pi$
$359$			27.1360i			1.43218i	−0.698007	+	0.716091i	$0.745929\pi$
$360$	−12.6881	+	12.3633i	−0.668721	+	0.651605i
$361$	−30.9626	+	17.8763i	−1.62961	+	0.940857i
$362$			23.8055i			1.25119i
$363$	1.83792	+	6.85922i	0.0964659	+	0.360016i
$364$	−0.165708	−	0.165708i	−0.00868544	−	0.00868544i
$365$	−22.9107	−	13.6265i	−1.19920	−	0.713244i
$366$	−2.95408	+	5.11661i	−0.154412	+	0.267450i
$367$	−0.861087	−	3.21362i	−0.0449484	−	0.167750i	0.939803	−	0.341716i	$-0.111008\pi$
$367$	−0.861087	−	3.21362i	−0.0449484	−	0.167750i	−0.984752	+	0.173967i	$0.944342\pi$
$368$	9.68264	−	5.59028i	0.504743	−	0.291413i
$369$	6.16038			0.320697
$370$	−11.7852	−	9.68312i	−0.612686	−	0.503402i
$371$	−12.0474			−0.625471
$372$	−1.56409	+	0.903028i	−0.0810943	+	0.0468198i
$373$	−1.71380	−	6.39597i	−0.0887370	−	0.331171i	0.907259	−	0.420573i	$-0.138171\pi$
$373$	−1.71380	−	6.39597i	−0.0887370	−	0.331171i	−0.995996	+	0.0894022i	$0.971504\pi$
$374$	−0.285999	+	0.495365i	−0.0147887	+	0.0256147i
$375$	3.88186	−	6.15757i	0.200458	−	0.317976i
$376$	−12.0640	−	12.0640i	−0.622154	−	0.622154i
$377$	0.0838127	+	0.312793i	0.00431658	+	0.0161097i
$378$		−	5.93407i		−	0.305215i
$379$	−4.32757	+	2.49852i	−0.222292	+	0.128340i	−0.607011	−	0.794693i	$-0.707632\pi$
$379$	−4.32757	+	2.49852i	−0.222292	+	0.128340i	0.384719	+	0.923034i	$0.374298\pi$
$380$	−0.159227	+	12.2827i	−0.00816819	+	0.630087i
$381$		−	8.78794i		−	0.450220i
$382$	−20.0370	−	5.36889i	−1.02518	−	0.274697i
$383$	−26.9406	−	15.5541i	−1.37660	−	0.794779i	−0.384850	−	0.922979i	$-0.625747\pi$
$383$	−26.9406	−	15.5541i	−1.37660	−	0.794779i	−0.991748	+	0.128200i	$0.959080\pi$
$384$	−0.678474	−	0.678474i	−0.0346232	−	0.0346232i
$385$	0.485373	+	0.866438i	0.0247369	+	0.0441578i
$386$	5.91077	+	10.2378i	0.300850	+	0.521088i
$387$	9.19670	+	15.9291i	0.467494	+	0.809724i
$388$	1.72800	−	2.99298i	0.0877257	−	0.151945i
$389$	−7.78268	−	29.0453i	−0.394597	−	1.47266i	−0.822465	−	0.568816i	$-0.807402\pi$
$389$	−7.78268	−	29.0453i	−0.394597	−	1.47266i	0.427867	−	0.903842i	$-0.359265\pi$
$390$	0.308456	−	0.172795i	0.0156193	−	0.00874983i
$391$	8.25243	−	4.76454i	0.417344	−	0.240953i
$392$	7.49704	+	12.9852i	0.378658	+	0.655854i
$393$		−	2.87646i		−	0.145098i
$394$	13.6168	−	3.64861i	0.686003	−	0.183814i
$395$	11.4499	−	6.41415i	0.576106	−	0.322731i
$396$	−0.582771			−0.0292853
$397$	14.9255	+	14.9255i	0.749091	+	0.749091i	0.974308	−	0.225218i	$-0.0723094\pi$
$397$	14.9255	+	14.9255i	0.749091	+	0.749091i	−0.225218	+	0.974308i	$0.572309\pi$
$398$	−6.91309	−	1.85236i	−0.346522	−	0.0928502i
$399$	−4.96520	−	4.96520i	−0.248571	−	0.248571i
$400$	−8.37432	−	5.12887i	−0.418716	−	0.256443i
$401$	13.4254	−	13.4254i	0.670431	−	0.670431i	−0.287385	−	0.957815i	$-0.592786\pi$
$401$	13.4254	−	13.4254i	0.670431	−	0.670431i	0.957815	+	0.287385i	$0.0927858\pi$
$402$	−4.95281	−	2.85951i	−0.247024	−	0.142619i
$403$	−0.781628	+	0.209437i	−0.0389357	+	0.0104328i
$404$	−11.0446	−	6.37658i	−0.549488	−	0.317247i
$405$	11.5460	+	3.25474i	0.573728	+	0.161729i
$406$			2.44415i			0.121301i
$407$	−0.204522	−	1.84217i	−0.0101378	−	0.0913132i
$408$	−2.36996	−	2.36996i	−0.117331	−	0.117331i
$409$	4.92570	−	18.3829i	0.243560	−	0.908978i	−0.730542	−	0.682868i	$-0.760732\pi$
$409$	4.92570	−	18.3829i	0.243560	−	0.908978i	0.974102	−	0.226110i	$-0.0726010\pi$
$410$	1.47679	+	5.81179i	0.0729336	+	0.287024i
$411$	−5.06955	−	2.92691i	−0.250063	−	0.144374i
$412$	−1.06929	+	1.85206i	−0.0526801	+	0.0912446i
$413$		−	9.64690i		−	0.474693i
$414$	−14.2424	−	8.22288i	−0.699978	−	0.404132i
$415$	9.16102	+	0.118760i	0.449697	+	0.00582968i
$416$	0.427530	+	0.740503i	0.0209614	+	0.0363062i
$417$	−10.5108	+	10.5108i	−0.514716	+	0.514716i
$418$	1.78792	−	1.78792i	0.0874499	−	0.0874499i
$419$	5.69651	−	3.28888i	0.278293	−	0.160672i	−0.354358	−	0.935110i	$-0.615300\pi$
$419$	5.69651	−	3.28888i	0.278293	−	0.160672i	0.632650	+	0.774438i	$0.281967\pi$
$420$	−1.52683	+	0.387971i	−0.0745014	+	0.0189310i
$421$	20.7180	−	20.7180i	1.00973	−	1.00973i	0.00978057	−	0.999952i	$-0.496887\pi$
$421$	20.7180	−	20.7180i	1.00973	−	1.00973i	0.999952	−	0.00978057i	$-0.00311330\pi$
$422$	−21.6737	+	12.5133i	−1.05506	+	0.609138i
$423$	−3.69886	+	13.8043i	−0.179845	+	0.671190i
$424$	24.5533	+	6.57903i	1.19241	+	0.319506i
$425$	−7.13736	−	4.37129i	−0.346213	−	0.212039i
$426$	7.83967	−	2.10063i	0.379833	−	0.101776i
$427$	10.2146	−	5.89742i	0.494321	−	0.285396i
$428$	−6.41157	−	1.71798i	−0.309915	−	0.0830415i
$429$	0.0414992	+	0.0111197i	0.00200360	+	0.000536863i
$430$	−12.8231	+	12.4949i	−0.618384	+	0.602557i
$431$	0.999182	+	3.72900i	0.0481289	+	0.179620i	0.985806	−	0.167888i	$-0.0536947\pi$
$431$	0.999182	+	3.72900i	0.0481289	+	0.179620i	−0.937677	+	0.347508i	$0.887028\pi$
$432$	−1.84542	+	6.88719i	−0.0887877	+	0.331360i
$433$	−3.44115	−	3.44115i	−0.165371	−	0.165371i	0.619570	−	0.784941i	$-0.287307\pi$
$433$	−3.44115	−	3.44115i	−0.165371	−	0.165371i	−0.784941	+	0.619570i	$0.787307\pi$
$434$	−6.10760			−0.293174
$435$	2.09521	+	0.590624i	0.100458	+	0.0283183i
$436$	3.93127	−	3.93127i	0.188274	−	0.188274i
$437$	−40.6877	+	10.9022i	−1.94636	+	0.521525i
$438$	−8.70386			−0.415887
$439$	−16.0618	+	4.30375i	−0.766589	+	0.205407i	−0.620864	−	0.783918i	$-0.713218\pi$
$439$	−16.0618	+	4.30375i	−0.766589	+	0.205407i	−0.145725	+	0.989325i	$0.546551\pi$
$440$	−0.516060	−	2.03091i	−0.0246022	−	0.0968197i
$441$	6.27992	−	10.8771i	0.299044	−	0.517959i
$442$	−0.203264	−	0.352064i	−0.00966829	−	0.0167460i
$443$	10.2533	−	10.2533i	0.487148	−	0.487148i	−0.420257	−	0.907405i	$-0.638060\pi$
$443$	10.2533	−	10.2533i	0.487148	−	0.487148i	0.907405	+	0.420257i	$0.138060\pi$
$444$	2.90654	+	0.442939i	0.137938	+	0.0210210i
$445$	7.28119	+	0.0943904i	0.345162	+	0.00447453i
$446$	19.0326	+	5.09976i	0.901218	+	0.241481i
$447$	−8.45794	+	2.26630i	−0.400047	+	0.107192i
$448$	3.15219	+	11.7641i	0.148927	+	0.555804i
$449$	9.86280	+	36.8085i	0.465454	+	1.73710i	0.655379	+	0.755301i	$0.272509\pi$
$449$	9.86280	+	36.8085i	0.465454	+	1.73710i	−0.189924	+	0.981799i	$0.560824\pi$
$450$	−0.374446	+	14.4398i	−0.0176516	+	0.680698i
$451$	−0.364335	+	0.631047i	−0.0171559	+	0.0297148i
$452$	−7.02844			−0.330590
$453$	2.86959	−	10.7095i	0.134825	−	0.503174i
$454$		−	5.23587i		−	0.245732i
$455$	−0.705772	−	0.00914935i	−0.0330871	−	0.000428928i
$456$	7.40788	+	12.8308i	0.346906	+	0.600858i
$457$	−1.69499	+	2.93581i	−0.0792884	+	0.137332i	−0.902943	−	0.429760i	$-0.858598\pi$
$457$	−1.69499	+	2.93581i	−0.0792884	+	0.137332i	0.823655	+	0.567092i	$0.191931\pi$
$458$	7.72260			0.360853
$459$	−1.57283	+	5.86989i	−0.0734136	+	0.273983i
$460$	−2.56402	+	9.09577i	−0.119548	+	0.424092i
$461$	−7.45792	+	27.8333i	−0.347350	+	1.29633i	0.542493	+	0.840061i	$0.317481\pi$
$461$	−7.45792	+	27.8333i	−0.347350	+	1.29633i	−0.889843	+	0.456267i	$0.849186\pi$
$462$	0.280828	+	0.162136i	0.0130653	+	0.00754326i
$463$	−16.2095	−	9.35855i	−0.753319	−	0.434929i	0.0735730	−	0.997290i	$-0.476560\pi$
$463$	−16.2095	−	9.35855i	−0.753319	−	0.434929i	−0.826892	+	0.562361i	$0.809893\pi$
$464$	0.760099	−	2.83673i	0.0352867	−	0.131692i
$465$	−1.47589	+	5.23566i	−0.0684427	+	0.242798i
$466$	4.02943	−	15.0380i	0.186660	−	0.696623i
$467$	29.5406			1.36698			0.683488	−	0.729962i	$-0.260462\pi$
$467$	29.5406			1.36698			0.683488	+	0.729962i	$0.260462\pi$
$468$	0.207092	−	0.358695i	0.00957285	−	0.0165807i
$469$	5.70862	+	9.88763i	0.263600	+	0.456568i
$470$	−13.9099	−	0.180322i	−0.641615	−	0.00831764i
$471$		−	12.2310i		−	0.563573i
$472$	−5.26812	+	19.6609i	−0.242485	+	0.904966i
$473$	−2.17563			−0.100036
$474$	2.14261	−	3.71111i	0.0984133	−	0.170457i
$475$	25.4742	+	26.8306i	1.16884	+	1.23107i
$476$	0.468816	+	1.74964i	0.0214881	+	0.0801948i
$477$	−5.51095	−	20.5672i	−0.252329	−	0.941706i
$478$	−14.6688	+	3.93048i	−0.670934	+	0.179776i
$479$	−24.6241	−	6.59800i	−1.12510	−	0.301470i	−0.352156	−	0.935941i	$-0.614551\pi$
$479$	−24.6241	−	6.59800i	−1.12510	−	0.301470i	−0.772947	+	0.634471i	$0.781218\pi$
$480$	5.74749	+	0.0745081i	0.262336	+	0.00340082i
$481$	1.20653	+	0.528749i	0.0550132	+	0.0241089i
$482$	13.3798	−	13.3798i	0.609433	−	0.609433i
$483$	−2.70108	−	4.67840i	−0.122903	−	0.212875i
$484$	−4.04877	+	7.01267i	−0.184035	+	0.318758i
$485$	−2.56354	−	10.0886i	−0.116404	−	0.458099i
$486$	15.5809	−	4.17488i	0.706762	−	0.189376i
$487$	20.4907			0.928523			0.464262	−	0.885698i	$-0.346320\pi$
$487$	20.4907			0.928523			0.464262	+	0.885698i	$0.346320\pi$
$488$	−24.0385	+	6.44111i	−1.08817	+	0.291575i
$489$	1.37072	−	1.37072i	0.0619861	−	0.0619861i
$490$	11.7671	+	3.31705i	0.531583	+	0.149849i
$491$	10.9509			0.494205			0.247103	−	0.968989i	$-0.420522\pi$
$491$	10.9509			0.494205			0.247103	+	0.968989i	$0.420522\pi$
$492$	−0.817310	−	0.817310i	−0.0368472	−	0.0368472i
$493$	0.647826	−	2.41772i	0.0291766	−	0.108889i
$494$	0.465109	+	1.73581i	0.0209262	+	0.0780978i
$495$	−1.25714	+	1.22496i	−0.0565043	+	0.0550580i
$496$	7.08860	+	1.89939i	0.318288	+	0.0852849i
$497$	−15.6508	−	4.19363i	−0.702036	−	0.188110i
$498$	2.59069	−	1.49574i	0.116092	−	0.0670256i
$499$	10.0040	−	2.68057i	0.447842	−	0.119999i	−0.0278474	−	0.999612i	$-0.508865\pi$
$499$	10.0040	−	2.68057i	0.447842	−	0.119999i	0.475690	+	0.879613i	$0.342199\pi$
$500$	8.09498	−	1.83495i	0.362019	−	0.0820616i
$501$	10.0210	+	2.68511i	0.447704	+	0.119962i
$502$	6.52209	−	24.3408i	0.291095	−	1.08638i
$503$	−9.95261	+	5.74614i	−0.443765	+	0.256208i	−0.705193	−	0.709015i	$-0.749140\pi$
$503$	−9.95261	+	5.74614i	−0.443765	+	0.256208i	0.261428	+	0.965223i	$0.415806\pi$
$504$	8.16552	−	8.16552i	0.363721	−	0.363721i
$505$	−37.2285	+	9.45986i	−1.65664	+	0.420958i
$506$	1.68464	−	0.972629i	0.0748915	−	0.0432386i
$507$	5.96319	−	5.96319i	0.264834	−	0.264834i
$508$	7.08588	−	7.08588i	0.314385	−	0.314385i
$509$	−1.18398	−	2.05071i	−0.0524789	−	0.0908962i	0.838593	−	0.544759i	$-0.183379\pi$
$509$	−1.18398	−	2.05071i	−0.0524789	−	0.0908962i	−0.891072	+	0.453863i	$0.850046\pi$
$510$	−2.73258	−	0.0354240i	−0.121001	−	0.00156860i
$511$	15.0481	+	8.68805i	0.665691	+	0.384337i
$512$		−	19.8349i		−	0.876586i
$513$	13.4315	−	23.2640i	0.593015	−	1.02713i
$514$	18.4029	+	10.6249i	0.811716	+	0.468644i
$515$	1.58632	+	6.24284i	0.0699018	+	0.275092i
$516$	0.893207	−	3.33350i	0.0393213	−	0.146749i
$517$	−1.19531	−	1.19531i	−0.0525696	−	0.0525696i
$518$	7.76334	+	6.21180i	0.341102	+	0.272931i
$519$			2.76310i			0.121287i
$520$	1.43341	+	0.404066i	0.0628590	+	0.0177194i
$521$	20.3329	+	11.7392i	0.890800	+	0.514303i	0.874204	−	0.485559i	$-0.161384\pi$
$521$	20.3329	+	11.7392i	0.890800	+	0.514303i	0.0165956	+	0.999862i	$0.494717\pi$
$522$	−4.17262	+	1.11805i	−0.182630	+	0.0489357i
$523$	−5.78356	−	3.33914i	−0.252898	−	0.146010i	0.368193	−	0.929749i	$-0.379977\pi$
$523$	−5.78356	−	3.33914i	−0.252898	−	0.146010i	−0.621090	+	0.783739i	$0.713310\pi$
$524$	2.31934	−	2.31934i	0.101321	−	0.101321i
$525$	−2.47813	+	4.04625i	−0.108155	+	0.176593i
$526$	19.5263	+	19.5263i	0.851388	+	0.851388i
$527$	6.04155	+	1.61883i	0.263174	+	0.0705173i
$528$	−0.275512	−	0.275512i	−0.0119901	−	0.0119901i
$529$	−9.40663			−0.408984
$530$	18.0822	−	10.1295i	0.785441	−	0.439999i
$531$	16.4690	−	4.41286i	0.714695	−	0.191502i
$532$		−	8.00707i		−	0.347151i
$533$	−0.258939	−	0.448495i	−0.0112159	−	0.0194265i
$534$	2.05909	−	1.18881i	0.0891054	−	0.0514450i
$535$	−17.4420	+	9.77091i	−0.754084	+	0.422433i
$536$	−6.23490	−	23.2690i	−0.269307	−	1.00507i
$537$	3.37523	−	5.84606i	0.145652	−	0.252276i
$538$	0.531266	+	0.920179i	0.0229045	+	0.0396718i
$539$	0.742810	+	1.28658i	0.0319951	+	0.0554171i
$540$	−2.94543	−	5.25788i	−0.126751	−	0.226263i
$541$	−0.605374	−	0.605374i	−0.0260271	−	0.0260271i	0.693973	−	0.720001i	$-0.255858\pi$
$541$	−0.605374	−	0.605374i	−0.0260271	−	0.0260271i	−0.720001	+	0.693973i	$0.755858\pi$
$542$	12.8599	+	7.42467i	0.552380	+	0.318917i
$543$	−13.3497	−	3.57703i	−0.572889	−	0.153505i
$544$		−	6.60914i		−	0.283364i
$545$	0.217060	−	16.7439i	0.00929785	−	0.717228i
$546$	−0.199589	+	0.115233i	−0.00854162	+	0.00493151i
$547$			41.1854i			1.76096i	0.474084	+	0.880479i	$0.342779\pi$
$547$			41.1854i			1.76096i	−0.474084	+	0.880479i	$0.657221\pi$
$548$	−1.72766	−	6.44770i	−0.0738018	−	0.275432i
$549$	14.7406	+	14.7406i	0.629112	+	0.629112i
$550$	−1.45701	−	0.892350i	−0.0621273	−	0.0380499i
$551$	−5.53223	+	9.58210i	−0.235681	+	0.408211i
$552$	2.95009	+	11.0099i	0.125564	+	0.468611i
$553$	−7.40873	+	4.27743i	−0.315051	+	0.181895i
$554$	−2.44430			−0.103849
$555$	7.20097	−	5.15395i	0.305664	−	0.218773i
$556$	−16.9501			−0.718844
$557$	−21.6691	+	12.5106i	−0.918148	+	0.530093i	−0.883044	−	0.469291i	$-0.844510\pi$
$557$	−21.6691	+	12.5106i	−0.918148	+	0.530093i	−0.0351044	+	0.999384i	$0.511176\pi$
$558$	−2.79385	−	10.4268i	−0.118273	−	0.441402i
$559$	0.773128	−	1.33910i	0.0326998	−	0.0566377i
$560$	5.50165	+	3.27219i	0.232487	+	0.138275i
$561$	−0.234817	−	0.234817i	−0.00991397	−	0.00991397i
$562$	4.51964	+	16.8675i	0.190650	+	0.711514i
$563$			27.0919i			1.14179i	0.821024	+	0.570894i	$0.193403\pi$
$563$			27.0919i			1.14179i	−0.821024	+	0.570894i	$0.806597\pi$
$564$	2.32218	−	1.34071i	0.0977815	−	0.0564542i
$565$	−15.1616	+	14.7735i	−0.637853	+	0.621527i
$566$		−	8.93771i		−	0.375680i
$567$	−7.55312	−	2.02385i	−0.317201	−	0.0849938i
$568$	29.6071	+	17.0937i	1.24229	+	0.717235i
$569$	0.342231	+	0.342231i	0.0143471	+	0.0143471i	0.714244	−	0.699897i	$-0.246771\pi$
$569$	0.342231	+	0.342231i	0.0143471	+	0.0143471i	−0.699897	+	0.714244i	$0.746771\pi$
$570$	11.6271	+	3.27760i	0.487008	+	0.137284i
$571$	10.4604	+	18.1179i	0.437754	+	0.758212i	0.997516	−	0.0704415i	$-0.0224408\pi$
$571$	10.4604	+	18.1179i	0.437754	+	0.758212i	−0.559762	+	0.828653i	$0.689107\pi$
$572$	0.0244956	+	0.0424275i	0.00102421	+	0.00177398i
$573$	6.02155	−	10.4296i	0.251554	−	0.435704i
$574$	−1.01167	−	3.77559i	−0.0422262	−	0.157590i
$575$	13.5879	+	25.0107i	0.566656	+	1.04302i
$576$	−18.6416	+	10.7627i	−0.776734	+	0.448448i
$577$	−21.7763	−	37.7177i	−0.906561	−	1.57021i	−0.818808	−	0.574067i	$-0.805365\pi$
$577$	−21.7763	−	37.7177i	−0.906561	−	1.57021i	−0.0877527	−	0.996142i	$-0.527969\pi$
$578$		−	15.9220i		−	0.662267i
$579$	−6.62930	+	1.77631i	−0.275504	+	0.0738211i
$580$	1.21318	+	2.16564i	0.0503745	+	0.0899234i
$581$	−5.97208			−0.247764
$582$	−2.40329	−	2.40329i	−0.0996196	−	0.0996196i
$583$	2.43275	+	0.651853i	0.100754	+	0.0269970i
$584$	−25.9244	−	25.9244i	−1.07276	−	1.07276i
$585$	−0.307228	−	1.20907i	−0.0127023	−	0.0499888i
$586$	3.94657	−	3.94657i	0.163031	−	0.163031i
$587$	5.95996	+	3.44098i	0.245994	+	0.142025i	0.617929	−	0.786234i	$-0.287972\pi$
$587$	5.95996	+	3.44098i	0.245994	+	0.142025i	−0.371935	+	0.928259i	$0.621305\pi$
$588$	−2.27626	+	0.609923i	−0.0938715	+	0.0251528i
$589$	−23.9444	−	13.8243i	−0.986610	−	0.569620i
$590$	8.11117	+	14.4792i	0.333932	+	0.596100i
$591$			8.18427i			0.336656i
$592$	−7.07850	−	9.62383i	−0.290924	−	0.395537i
$593$	20.5768	+	20.5768i	0.844989	+	0.844989i	0.989503	−	0.144514i	$-0.0461618\pi$
$593$	20.5768	+	20.5768i	0.844989	+	0.844989i	−0.144514	+	0.989503i	$0.546162\pi$
$594$	−0.321076	+	1.19827i	−0.0131739	+	0.0491658i
$595$	4.68901	+	2.78886i	0.192231	+	0.114332i
$596$	−8.64715	−	4.99243i	−0.354201	−	0.204498i
$597$	2.07753	−	3.59839i	0.0850277	−	0.147272i
$598$			1.38253i			0.0565357i
$599$	8.65201	+	4.99524i	0.353511	+	0.204100i	0.666231	−	0.745746i	$-0.267907\pi$
$599$	8.65201	+	4.99524i	0.353511	+	0.204100i	−0.312719	+	0.949846i	$0.601240\pi$
$600$	7.26021	−	6.89319i	0.296397	−	0.281413i
$601$	−4.37991	−	7.58622i	−0.178660	−	0.309448i	0.762762	−	0.646680i	$-0.223843\pi$
$601$	−4.37991	−	7.58622i	−0.178660	−	0.309448i	−0.941422	+	0.337231i	$0.890510\pi$
$602$	8.25240	−	8.25240i	0.336343	−	0.336343i
$603$	−14.2687	+	14.2687i	−0.581064	+	0.581064i
$604$	10.9490	−	6.32143i	0.445510	−	0.257215i
$605$	6.00647	+	23.6379i	0.244198	+	0.961019i
$606$	−8.86853	+	8.86853i	−0.360259	+	0.360259i
$607$	7.78561	−	4.49502i	0.316008	−	0.182447i	−0.333604	−	0.942713i	$-0.608265\pi$
$607$	7.78561	−	4.49502i	0.316008	−	0.182447i	0.649612	+	0.760266i	$0.274931\pi$
$608$	−7.56152	+	28.2200i	−0.306660	+	1.14447i
$609$	−1.37063	−	0.367260i	−0.0555409	−	0.0148821i
$610$	−10.3728	+	17.4401i	−0.419981	+	0.706129i
$611$	1.16047	−	0.310948i	0.0469477	−	0.0125796i
$612$	−2.77251	+	1.60071i	−0.112072	+	0.0647048i
$613$	−31.2871	−	8.38336i	−1.26368	−	0.338601i	−0.436071	−	0.899912i	$-0.643630\pi$
$613$	−31.2871	−	8.38336i	−1.26368	−	0.338601i	−0.827605	+	0.561311i	$0.810297\pi$
$614$	27.3043	+	7.31617i	1.10191	+	0.295256i
$615$	−3.48104	−	0.0451268i	−0.140369	−	0.00181969i
$616$	0.353523	+	1.31937i	0.0142439	+	0.0531588i
$617$	6.50389	−	24.2728i	0.261837	−	0.977188i	−0.702321	−	0.711860i	$-0.747853\pi$
$617$	6.50389	−	24.2728i	0.261837	−	0.977188i	0.964158	−	0.265328i	$-0.0854803\pi$
$618$	1.48716	+	1.48716i	0.0598225	+	0.0598225i
$619$	2.68730			0.108012			0.0540058	−	0.998541i	$-0.482801\pi$
$619$	2.68730			0.108012			0.0540058	+	0.998541i	$0.482801\pi$
$620$	−5.41165	+	3.03157i	−0.217337	+	0.121751i
$621$	14.6135	−	14.6135i	0.586419	−	0.586419i
$622$	14.4819	−	3.88042i	0.580672	−	0.155591i
$623$	−4.74662			−0.190169
$624$	0.267483	−	0.0716718i	0.0107079	−	0.00286917i
$625$	13.6053	−	20.9737i	0.544213	−	0.838947i
$626$	2.68319	−	4.64742i	0.107242	−	0.185748i
$627$	0.733976	+	1.27128i	0.0293122	+	0.0507702i
$628$	9.86205	−	9.86205i	0.393539	−	0.393539i
$629$	−6.03294	−	8.20231i	−0.240549	−	0.327047i
$630$	0.122051	−	9.41490i	0.00486262	−	0.375099i
$631$	−28.7677	−	7.70828i	−1.14522	−	0.306862i	−0.364174	−	0.931331i	$-0.618649\pi$
$631$	−28.7677	−	7.70828i	−1.14522	−	0.306862i	−0.781049	+	0.624469i	$0.785315\pi$
$632$	17.4353	−	4.67177i	0.693538	−	0.185833i
$633$	−3.76052	−	14.0344i	−0.149467	−	0.557819i
$634$	−9.46317	−	35.3170i	−0.375831	−	1.40262i
$635$	0.391238	−	30.1798i	0.0155258	−	1.19765i
$636$	−1.99754	+	3.45984i	−0.0792075	+	0.137191i
$637$	−1.05585			−0.0418344
$638$	0.132246	−	0.493550i	0.00523569	−	0.0195399i
$639$		−	28.6372i		−	1.13287i
$640$	−2.29983	−	2.36024i	−0.0909086	−	0.0932966i
$641$	17.3530	+	30.0563i	0.685403	+	1.18715i	0.973310	+	0.229494i	$0.0737071\pi$
$641$	17.3530	+	30.0563i	0.685403	+	1.18715i	−0.287908	+	0.957658i	$0.592960\pi$
$642$	−3.26392	+	5.65327i	−0.128817	+	0.223117i
$643$	36.7811			1.45050			0.725252	−	0.688484i	$-0.241723\pi$
$643$	36.7811			1.45050			0.725252	+	0.688484i	$0.241723\pi$
$644$	1.59435	−	5.95021i	0.0628263	−	0.234471i
$645$	−5.08008	−	9.06843i	−0.200028	−	0.357069i
$646$	3.59504	−	13.4169i	0.141445	−	0.527879i
$647$	−11.1099	−	6.41429i	−0.436775	−	0.252172i	0.265454	−	0.964124i	$-0.414478\pi$
$647$	−11.1099	−	6.41429i	−0.436775	−	0.252172i	−0.702229	+	0.711952i	$0.747812\pi$
$648$	14.2884	+	8.24944i	0.561303	+	0.324068i
$649$	−0.521968	+	1.94801i	−0.0204890	+	0.0764661i
$650$	1.06700	−	0.579686i	0.0418512	−	0.0227371i
$651$	0.917733	−	3.42503i	0.0359688	−	0.134237i
$652$	2.21047			0.0865688
$653$	2.16024	−	3.74165i	0.0845368	−	0.146422i	−0.820657	−	0.571421i	$-0.806392\pi$
$653$	2.16024	−	3.74165i	0.0845368	−	0.146422i	0.905194	+	0.424999i	$0.139726\pi$
$654$	−2.73380	−	4.73508i	−0.106900	−	0.185156i
$655$	0.128060	−	9.87841i	0.00500370	−	0.385981i
$656$			4.69664i			0.183373i
$657$	−7.94850	+	29.6642i	−0.310100	+	1.15731i
$658$	9.06787			0.353502
$659$	−21.0003	+	36.3737i	−0.818057	+	1.41692i	0.0890543	+	0.996027i	$0.471616\pi$
$659$	−21.0003	+	36.3737i	−0.818057	+	1.41692i	−0.907112	+	0.420890i	$0.861718\pi$
$660$	0.329306	+	0.00426898i	0.0128182	+	0.000166170i
$661$	−0.968343	−	3.61391i	−0.0376642	−	0.140565i	0.944533	−	0.328415i	$-0.106515\pi$
$661$	−0.968343	−	3.61391i	−0.0376642	−	0.140565i	−0.982198	+	0.187851i	$0.939848\pi$
$662$	2.30208	+	8.59150i	0.0894731	+	0.333918i
$663$	0.227973	−	0.0610853i	0.00885375	−	0.00237235i
$664$	12.1714	+	3.26132i	0.472342	+	0.126564i
$665$	−16.8306	−	17.2727i	−0.652662	−	0.669806i
$666$	−7.05343	+	16.0950i	−0.273315	+	0.623667i
$667$	−6.01907	+	6.01907i	−0.233059	+	0.233059i
$668$	5.91505	+	10.2452i	0.228860	+	0.396397i
$669$	−5.71969	+	9.90680i	−0.221136	+	0.383019i
$670$	−16.8818	−	10.0407i	−0.652200	−	0.387906i
$671$	−2.38175	+	0.638187i	−0.0919464	+	0.0246370i
$672$	−3.74680			−0.144536
$673$	31.2551	−	8.37477i	1.20479	−	0.322824i	0.400077	−	0.916482i	$-0.368983\pi$
$673$	31.2551	−	8.37477i	1.20479	−	0.322824i	0.804717	+	0.593658i	$0.202317\pi$
$674$	4.81313	−	4.81313i	0.185395	−	0.185395i
$675$	−17.4057	−	5.15099i	−0.669946	−	0.198262i
$676$	9.61646			0.369864
$677$	29.3319	+	29.3319i	1.12732	+	1.12732i	0.990612	+	0.136704i	$0.0436510\pi$
$677$	29.3319	+	29.3319i	1.12732	+	1.12732i	0.136704	+	0.990612i	$0.456349\pi$
$678$	−1.78897	+	6.67654i	−0.0687051	+	0.256411i
$679$	1.75614	+	6.55399i	0.0673943	+	0.251519i
$680$	−8.03347	−	8.24449i	−0.308069	−	0.316162i
$681$	2.93618	+	0.786746i	0.112515	+	0.0301482i
$682$	1.23332	+	0.330466i	0.0472261	+	0.0126542i
$683$	−8.59531	+	4.96250i	−0.328890	+	0.189885i	−0.655348	−	0.755327i	$-0.727478\pi$
$683$	−8.59531	+	4.96250i	−0.328890	+	0.189885i	0.326458	+	0.945212i	$0.394145\pi$
$684$	13.6695	−	3.66274i	0.522668	−	0.140049i
$685$	−17.2797	−	10.2774i	−0.660223	−	0.392678i
$686$	−18.7497	−	5.02398i	−0.715869	−	0.191816i
$687$	−1.16040	+	4.33069i	−0.0442722	+	0.165226i
$688$	−12.1443	+	7.01151i	−0.462997	+	0.267311i
$689$	−1.26571	+	1.26571i	−0.0482198	+	0.0482198i
$690$	7.98773	+	4.75082i	0.304088	+	0.180861i
$691$	−18.1286	+	10.4665i	−0.689643	+	0.398165i	−0.803478	−	0.595334i	$-0.797020\pi$
$691$	−18.1286	+	10.4665i	−0.689643	+	0.398165i	0.113836	+	0.993500i	$0.463686\pi$
$692$	−2.22794	+	2.22794i	−0.0846935	+	0.0846935i
$693$	0.809043	−	0.809043i	0.0307330	−	0.0307330i
$694$	−3.72811	−	6.45728i	−0.141517	−	0.245115i
$695$	−36.5644	+	35.6285i	−1.38697	+	1.35147i
$696$	2.59286	+	1.49699i	0.0982823	+	0.0567433i
$697$			4.00291i			0.151621i
$698$	19.4689	−	33.7211i	0.736908	−	1.27636i
$699$	7.82757	+	4.51925i	0.296066	+	0.170934i
$700$	−5.26074	+	1.26441i	−0.198837	+	0.0477900i
$701$	10.8748	−	40.5851i	0.410734	−	1.53288i	−0.382496	−	0.923957i	$-0.624935\pi$
$701$	10.8748	−	40.5851i	0.410734	−	1.53288i	0.793230	−	0.608922i	$-0.208398\pi$
$702$	−0.623438	−	0.623438i	−0.0235302	−	0.0235302i
$703$	16.3754	+	41.9248i	0.617611	+	1.58122i
$704$		−	2.54610i		−	0.0959599i
$705$	2.19123	−	7.77330i	0.0825266	−	0.292760i
$706$	−31.3925	−	18.1245i	−1.18147	−	0.682124i
$707$	24.1853	−	6.48042i	0.909580	−	0.243721i
$708$	−2.77044	−	1.59952i	−0.104120	−	0.0601135i
$709$	−26.6934	+	26.6934i	−1.00249	+	1.00249i	−0.00249582	+	0.999997i	$0.500794\pi$
$709$	−26.6934	+	26.6934i	−1.00249	+	1.00249i	−0.999997	+	0.00249582i	$0.999206\pi$
$710$	27.0167	−	6.86502i	1.01392	−	0.257640i
$711$	−10.6914	−	10.6914i	−0.400959	−	0.400959i
$712$	9.67386	+	2.59210i	0.362543	+	0.0971431i
$713$	−15.0409	−	15.0409i	−0.563284	−	0.563284i
$714$	1.78137			0.0666661
$715$	0.142022	+	0.0400350i	0.00531134	+	0.00149722i
$716$	7.43530	−	1.99228i	0.277870	−	0.0744551i
$717$		−	8.81656i		−	0.329260i
$718$	15.2155	+	26.3540i	0.567837	+	0.983522i
$719$	−9.07260	+	5.23807i	−0.338351	+	0.195347i	−0.659542	−	0.751667i	$-0.729250\pi$
$719$	−9.07260	+	5.23807i	−0.338351	+	0.195347i	0.321192	+	0.947014i	$0.395917\pi$
$720$	−3.06957	+	10.8892i	−0.114396	+	0.405815i
$721$	−1.08670	−	4.05562i	−0.0404709	−	0.151039i
$722$	−20.0469	+	34.7223i	−0.746069	+	1.29223i
$723$	5.49268	+	9.51360i	0.204275	+	0.353815i
$724$	−7.87986	−	13.6483i	−0.292853	−	0.507236i
$725$	7.16914	+	2.12162i	0.266255	+	0.0787948i
$726$	5.63101	+	5.63101i	0.208986	+	0.208986i
$727$	−29.1355	−	16.8214i	−1.08058	−	0.623871i	−0.149524	−	0.988758i	$-0.547774\pi$
$727$	−29.1355	−	16.8214i	−1.08058	−	0.623871i	−0.931052	+	0.364887i	$0.881108\pi$
$728$	−0.937696	−	0.251255i	−0.0347533	−	0.00931212i
$729$		−	6.72958i		−	0.249244i
$730$	−29.8910	−	0.387495i	−1.10632	−	0.0143418i
$731$	−10.3505	+	5.97585i	−0.382826	+	0.221025i
$732$		−	3.91132i		−	0.144566i
$733$	−6.28732	−	23.4646i	−0.232227	−	0.866685i	−0.979379	−	0.202031i	$-0.935246\pi$
$733$	−6.28732	−	23.4646i	−0.232227	−	0.866685i	0.747152	−	0.664654i	$-0.231421\pi$
$734$	−2.63819	−	2.63819i	−0.0973774	−	0.0973774i
$735$	−3.62827	+	6.10033i	−0.133831	+	0.225014i
$736$	−11.2382	+	19.4652i	−0.414246	+	0.717495i
$737$	−0.617757	−	2.30550i	−0.0227554	−	0.0849241i
$738$	5.98286	−	3.45420i	0.220232	−	0.127151i
$739$	−19.6504			−0.722850			−0.361425	−	0.932401i	$-0.617710\pi$
$739$	−19.6504			−0.722850			−0.361425	+	0.932401i	$0.617710\pi$
$740$	9.96200	+	1.65055i	0.366210	+	0.0606755i
$741$	−1.04330			−0.0383265
$742$	−11.7002	+	6.75514i	−0.429529	+	0.247989i
$743$	−0.143337	−	0.534940i	−0.00525852	−	0.0196250i	0.963247	−	0.268618i	$-0.0865670\pi$
$743$	−0.143337	−	0.534940i	−0.00525852	−	0.0196250i	−0.968505	+	0.248993i	$0.919900\pi$
$744$	−3.74078	+	6.47922i	−0.137144	+	0.237540i
$745$	−29.1474	+	7.40643i	−1.06788	+	0.271351i
$746$	−5.25071	−	5.25071i	−0.192242	−	0.192242i
$747$	−2.73186	−	10.1954i	−0.0999535	−	0.373031i
$748$		−	0.378674i		−	0.0138457i
$749$	11.2860	−	6.51598i	0.412381	−	0.238089i
$750$	0.317364	−	8.15674i	0.0115885	−	0.297842i
$751$		−	35.5149i		−	1.29596i	−0.761658	−	0.647979i	$-0.775614\pi$
$751$		−	35.5149i		−	1.29596i	0.761658	−	0.647979i	$-0.224386\pi$
$752$	−10.5243	−	2.81999i	−0.383783	−	0.102834i
$753$	12.6698	+	7.31492i	0.461714	+	0.266571i
$754$	0.256785	+	0.256785i	0.00935154	+	0.00935154i
$755$	10.3316	−	36.6509i	0.376005	−	1.33386i
$756$	1.96424	+	3.40216i	0.0714385	+	0.123735i
$757$	0.838715	+	1.45270i	0.0304836	+	0.0527992i	0.880865	−	0.473368i	$-0.156962\pi$
$757$	0.838715	+	1.45270i	0.0304836	+	0.0527992i	−0.850381	+	0.526167i	$0.823629\pi$
$758$	−2.80191	+	4.85304i	−0.101770	+	0.176270i
$759$	0.292296	+	1.09086i	0.0106097	+	0.0395958i
$760$	24.8691	+	44.3937i	0.902097	+	1.61033i
$761$	−36.9267	+	21.3196i	−1.33859	+	0.772836i	−0.986598	−	0.163167i	$-0.947829\pi$
$761$	−36.9267	+	21.3196i	−1.33859	+	0.772836i	−0.351992	+	0.936003i	$0.614496\pi$
$762$	−4.92751	−	8.53470i	−0.178505	−	0.309179i
$763$			10.9153i			0.395162i
$764$	13.2649	−	3.55432i	0.479907	−	0.128591i
$765$	−2.61616	+	9.28073i	−0.0945876	+	0.335546i
$766$	−34.8856			−1.26047
$767$	−1.01351	−	1.01351i	−0.0365958	−	0.0365958i
$768$	9.47009	+	2.53750i	0.341723	+	0.0915643i
$769$	−10.2716	−	10.2716i	−0.370402	−	0.370402i	0.497222	−	0.867623i	$-0.334354\pi$
$769$	−10.2716	−	10.2716i	−0.370402	−	0.370402i	−0.867623	+	0.497222i	$0.834354\pi$
$770$	0.957209	+	0.569315i	0.0344954	+	0.0205167i
$771$	−8.72347	+	8.72347i	−0.314168	+	0.314168i
$772$	−6.77760	−	3.91305i	−0.243931	−	0.140834i
$773$	43.3603	−	11.6184i	1.55956	−	0.417883i	0.627037	−	0.778990i	$-0.284268\pi$
$773$	43.3603	−	11.6184i	1.55956	−	0.417883i	0.932525	+	0.361107i	$0.117601\pi$
$774$	17.8633	+	10.3134i	0.642085	+	0.370708i
$775$	−5.30163	+	17.9147i	−0.190440	+	0.643516i
$776$		−	14.3164i		−	0.513928i
$777$	−4.64998	+	3.42014i	−0.166817	+	0.122697i
$778$	−23.8445	−	23.8445i	−0.854866	−	0.854866i
$779$	4.57973	−	17.0918i	0.164086	−	0.612376i
$780$	−0.119649	+	0.201170i	−0.00428412	+	0.00720305i
$781$	2.93349	+	1.69365i	0.104968	+	0.0606036i
$782$	5.34308	−	9.25449i	0.191068	−	0.330940i
$783$		−	5.42850i		−	0.193999i
$784$	8.29267	+	4.78778i	0.296167	+	0.170992i
$785$	0.544521	−	42.0039i	0.0194348	−	1.49918i
$786$	−1.61287	−	2.79357i	−0.0575290	−	0.0996432i
$787$	−8.11887	+	8.11887i	−0.289407	+	0.289407i	−0.836846	−	0.547439i	$-0.815603\pi$
$787$	−8.11887	+	8.11887i	−0.289407	+	0.289407i	0.547439	+	0.836846i	$0.315603\pi$
$788$	−6.59913	+	6.59913i	−0.235084	+	0.235084i
$789$	−13.8840	+	8.01594i	−0.494284	+	0.285375i
$790$	7.52343	−	12.6494i	0.267671	−	0.450045i
$791$	9.75737	−	9.75737i	0.346932	−	0.346932i
$792$	−2.09069	+	1.20706i	−0.0742894	+	0.0428910i
$793$	0.453570	−	1.69275i	0.0161067	−	0.0601112i
$794$	22.8643	+	6.12648i	0.811425	+	0.217421i
$795$	2.96341	+	11.6622i	0.105101	+	0.413617i
$796$	4.57660	−	1.22630i	0.162213	−	0.0434649i
$797$	−11.1254	+	6.42328i	−0.394083	+	0.227524i	−0.683928	−	0.729550i	$-0.739730\pi$
$797$	−11.1254	+	6.42328i	−0.394083	+	0.227524i	0.289845	+	0.957074i	$0.406396\pi$
$798$	−7.60617	−	2.03807i	−0.269256	−	0.0721468i
$799$	−8.96981	−	2.40345i	−0.317329	−	0.0850280i
$800$	19.7349	+	0.511756i	0.697733	+	0.0180933i
$801$	−2.17129	−	8.10335i	−0.0767186	−	0.286318i
$802$	5.51071	−	20.5662i	0.194590	−	0.726219i
$803$	−2.56860	−	2.56860i	−0.0906440	−	0.0906440i
$804$	3.78610			0.133526
$805$	−9.06782	−	16.1869i	−0.319599	−	0.570514i
$806$	−0.641670	+	0.641670i	−0.0226019	+	0.0226019i
$807$	−0.595847	+	0.159657i	−0.0209748	+	0.00562019i
$808$	−52.8298			−1.85855
$809$	38.4820	−	10.3112i	1.35296	−	0.362523i	0.491730	−	0.870747i	$-0.336365\pi$
$809$	38.4820	−	10.3112i	1.35296	−	0.362523i	0.861225	+	0.508224i	$0.169698\pi$
$810$	13.0383	−	3.31307i	0.458119	−	0.116409i
$811$	3.73404	−	6.46755i	0.131120	−	0.227106i	−0.792989	−	0.609236i	$-0.791476\pi$
$811$	3.73404	−	6.46755i	0.131120	−	0.227106i	0.924109	+	0.382130i	$0.124809\pi$
$812$	−0.809038	−	1.40130i	−0.0283917	−	0.0491758i
$813$	−6.09595	+	6.09595i	−0.213794	+	0.213794i
$814$	−1.23156	−	1.67441i	−0.0431661	−	0.0586880i
$815$	4.76839	−	4.64634i	0.167029	−	0.162754i
$816$	−2.06749	−	0.553983i	−0.0723768	−	0.0193933i
$817$	51.0318	−	13.6739i	1.78538	−	0.478391i
$818$	−5.52380	−	20.6151i	−0.193135	−	0.720790i
$819$	0.210465	+	0.785465i	0.00735423	+	0.0274464i
$820$	−2.77044	−	2.84322i	−0.0967480	−	0.0992894i
$821$	−27.5640	+	47.7422i	−0.961990	+	1.66622i	−0.244496	+	0.969650i	$0.578622\pi$
$821$	−27.5640	+	47.7422i	−0.961990	+	1.66622i	−0.717494	+	0.696565i	$0.754711\pi$
$822$	−6.56462			−0.228967
$823$	−13.5807	+	50.6839i	−0.473393	+	1.76673i	0.154046	+	0.988064i	$0.450769\pi$
$823$	−13.5807	+	50.6839i	−0.473393	+	1.76673i	−0.627440	+	0.778665i	$0.715897\pi$
$824$			8.85902i			0.308619i
$825$	0.719344	−	0.682980i	0.0250444	−	0.0237783i
$826$	−5.40914	−	9.36890i	−0.188208	−	0.325986i
$827$	14.6165	−	25.3166i	0.508267	−	0.880344i	−0.491687	−	0.870772i	$-0.663620\pi$
$827$	14.6165	−	25.3166i	0.508267	−	0.880344i	0.999954	−	0.00957215i	$-0.00304696\pi$
$828$	10.8874			0.378364
$829$	−4.99822	+	18.6536i	−0.173595	+	0.647867i	0.823191	+	0.567764i	$0.192192\pi$
$829$	−4.99822	+	18.6536i	−0.173595	+	0.647867i	−0.996787	+	0.0801028i	$0.974475\pi$
$830$	8.96361	−	5.02136i	0.311132	−	0.174294i
$831$	0.367283	−	1.37072i	0.0127409	−	0.0475497i
$832$	1.56712	+	0.904779i	0.0543302	+	0.0313676i
$833$	7.06778	+	4.08058i	0.244884	+	0.141384i
$834$	−4.31436	+	16.1014i	−0.149394	+	0.557547i
$835$	34.2948	+	9.66742i	1.18682	+	0.334555i
$836$	−0.433241	+	1.61688i	−0.0149840	+	0.0559209i
$837$	13.5651			0.468878
$838$	3.68823	−	6.38821i	0.127408	−	0.220677i
$839$	−2.06406	−	3.57506i	−0.0712593	−	0.123425i	0.828194	−	0.560441i	$-0.189368\pi$
$839$	−2.06406	−	3.57506i	−0.0712593	−	0.123425i	−0.899453	+	0.437017i	$0.856035\pi$
$840$	−4.67390	+	4.55427i	−0.161265	+	0.157137i
$841$		−	26.7641i		−	0.922899i
$842$	8.50411	−	31.7378i	0.293071	−	1.09376i
$843$	−10.1381			−0.349175
$844$	8.28405	−	14.3484i	0.285149	−	0.493892i
$845$	20.7444	−	20.2134i	0.713629	−	0.695364i
$846$	4.14799	+	15.4805i	0.142611	+	0.532231i
$847$	−4.11470	−	15.3563i	−0.141383	−	0.527647i
$848$	15.6803	−	4.20152i	0.538463	−	0.144281i
$849$	5.01210	+	1.34299i	0.172015	+	0.0460912i
$850$	−9.38272	−	0.243308i	−0.321825	−	0.00834541i
$851$	3.82090	+	34.4158i	0.130979	+	1.17976i
$852$	−3.79935	+	3.79935i	−0.130164	+	0.130164i
$853$	−14.1534	−	24.5144i	−0.484604	−	0.839359i	0.515240	−	0.857046i	$-0.327703\pi$
$853$	−14.1534	−	24.5144i	−0.484604	−	0.839359i	−0.999844	+	0.0176876i	$0.994370\pi$
$854$	6.61352	−	11.4550i	0.226310	−	0.391980i
$855$	21.7887	−	36.6341i	0.745157	−	1.25286i
$856$	−26.5598	+	7.11668i	−0.907796	+	0.243243i
$857$	12.8826			0.440060			0.220030	−	0.975493i	$-0.429385\pi$
$857$	12.8826			0.440060			0.220030	+	0.975493i	$0.429385\pi$
$858$	0.0465382	−	0.0124699i	0.00158879	−	0.000425714i
$859$	−33.1013	+	33.1013i	−1.12940	+	1.12940i	−0.139127	+	0.990275i	$0.544429\pi$
$859$	−33.1013	+	33.1013i	−1.12940	+	1.12940i	−0.990275	+	0.139127i	$0.955571\pi$
$860$	3.21588	−	11.4082i	0.109661	−	0.389017i
$861$	2.26929			0.0773373
$862$	3.06128	+	3.06128i	0.104268	+	0.104268i
$863$	−4.47233	+	16.6909i	−0.152240	+	0.568166i	0.847086	+	0.531456i	$0.178355\pi$
$863$	−4.47233	+	16.6909i	−0.152240	+	0.568166i	−0.999326	+	0.0367109i	$0.988312\pi$
$864$	−3.70987	−	13.8454i	−0.126212	−	0.471031i
$865$	−0.123013	+	9.48911i	−0.00418256	+	0.322639i
$866$	−5.27147	−	1.41249i	−0.179132	−	0.0479983i
$867$	8.92874	+	2.39245i	0.303236	+	0.0812519i
$868$	3.50165	−	2.02168i	0.118854	−	0.0686202i
$869$	1.72750	−	0.462881i	0.0586013	−	0.0157022i
$870$	2.36601	−	0.601209i	0.0802151	−	0.0203829i
$871$	1.63856	+	0.439050i	0.0555203	+	0.0148766i
$872$	5.96081	−	22.2460i	0.201858	−	0.753346i
$873$	−10.3855	+	5.99609i	−0.351497	+	0.202937i
$874$	−33.4022	+	33.4022i	−1.12984	+	1.12984i
$875$	−8.69061	+	13.7854i	−0.293796	+	0.466032i
$876$	4.99015	−	2.88107i	0.168602	−	0.0973422i
$877$	41.3950	−	41.3950i	1.39781	−	1.39781i	0.591523	−	0.806288i	$-0.298527\pi$
$877$	41.3950	−	41.3950i	1.39781	−	1.39781i	0.806288	−	0.591523i	$-0.201473\pi$
$878$	−13.1858	+	13.1858i	−0.444999	+	0.444999i
$879$	1.62015	+	2.80618i	0.0546462	+	0.0946500i
$880$	−0.933905	−	0.958437i	−0.0314819	−	0.0323089i
$881$	47.1023	+	27.1945i	1.58692	+	0.916206i	0.993811	+	0.111080i	$0.0354311\pi$
$881$	47.1023	+	27.1945i	1.58692	+	0.916206i	0.593104	+	0.805126i	$0.297902\pi$
$882$		−	14.0849i		−	0.474264i
$883$	10.2127	−	17.6889i	0.343684	−	0.595278i	−0.641430	−	0.767182i	$-0.721658\pi$
$883$	10.2127	−	17.6889i	0.343684	−	0.595278i	0.985114	+	0.171904i	$0.0549918\pi$
$884$	0.233073	+	0.134565i	0.00783910	+	0.00452591i
$885$	−9.33846	+	2.37293i	−0.313909	+	0.0797652i
$886$	4.20866	−	15.7069i	0.141393	−	0.527685i
$887$	10.3419	+	10.3419i	0.347246	+	0.347246i	0.859083	−	0.511837i	$-0.171035\pi$
$887$	10.3419	+	10.3419i	0.347246	+	0.347246i	−0.511837	+	0.859083i	$0.671035\pi$
$888$	11.3446	−	4.43111i	0.380701	−	0.148698i
$889$			19.6742i			0.659852i
$890$	7.12429	−	3.99099i	0.238807	−	0.133778i
$891$	1.41570	+	0.817358i	0.0474279	+	0.0273825i
$892$	−12.5999	+	3.37614i	−0.421877	+	0.113042i
$893$	35.5499	+	20.5247i	1.18963	+	0.686833i
$894$	−6.94346	+	6.94346i	−0.232224	+	0.232224i
$895$	11.8516	−	19.9264i	0.396154	−	0.666067i
$896$	1.51895	+	1.51895i	0.0507446	+	0.0507446i
$897$	−0.775294	−	0.207739i	−0.0258863	−	0.00693622i
$898$	30.2176	+	30.2176i	1.00837	+	1.00837i
$899$	−5.58725			−0.186345
$900$	−4.56504	−	8.40266i	−0.152168	−	0.280089i
$901$	13.3642	−	3.58092i	0.445225	−	0.119298i
$902$			0.817149i			0.0272081i
$903$	3.38778	+	5.86780i	0.112738	+	0.195268i
$904$	−25.2145	+	14.5576i	−0.838621	+	0.484178i
$905$	−45.6865	−	12.8787i	−1.51867	−	0.428101i
$906$	−3.21803	−	12.0098i	−0.106912	−	0.399000i
$907$	−22.9241	+	39.7058i	−0.761184	+	1.31841i	0.181057	+	0.983473i	$0.442048\pi$
$907$	−22.9241	+	39.7058i	−0.761184	+	1.31841i	−0.942241	+	0.334936i	$0.891285\pi$
$908$	1.73313	+	3.00186i	0.0575158	+	0.0996203i
$909$	22.1265	+	38.3243i	0.733891	+	1.27114i
$910$	−0.690564	+	0.386850i	−0.0228920	+	0.0128239i
$911$	−9.77449	−	9.77449i	−0.323843	−	0.323843i	0.526396	−	0.850239i	$-0.323543\pi$
$911$	−9.77449	−	9.77449i	−0.323843	−	0.323843i	−0.850239	+	0.526396i	$0.823543\pi$
$912$	8.19406	+	4.73084i	0.271332	+	0.156654i
$913$	1.20595	+	0.323133i	0.0399111	+	0.0106941i
$914$			3.80161i			0.125746i
$915$	−8.22145	−	8.43741i	−0.271793	−	0.278932i
$916$	−4.42757	+	2.55626i	−0.146291	+	0.0844611i
$917$			6.43974i			0.212659i
$918$	1.76381	+	6.58265i	0.0582146	+	0.217260i
$919$	15.6733	+	15.6733i	0.517015	+	0.517015i	0.916667	−	0.399652i	$-0.130869\pi$
$919$	15.6733	+	15.6733i	0.517015	+	0.517015i	−0.399652	+	0.916667i	$0.630869\pi$
$920$	9.64111	+	37.9417i	0.317858	+	1.25090i
$921$	−8.20553	+	14.2124i	−0.270381	+	0.468314i
$922$	8.36350	+	31.2130i	0.275437	+	1.02795i
$923$	−2.08488	+	1.20370i	−0.0686246	+	0.0396204i
$924$	−0.214675			−0.00706228
$925$	24.9592	−	17.3792i	0.820654	−	0.571426i
$926$	−20.9898			−0.689769
$927$	6.42660	−	3.71040i	0.211077	−	0.121865i
$928$	1.52804	+	5.70272i	0.0501603	+	0.187201i
$929$	−17.3589	+	30.0664i	−0.569526	+	0.986447i	0.427087	+	0.904210i	$0.359540\pi$
$929$	−17.3589	+	30.0664i	−0.569526	+	0.986447i	−0.996613	+	0.0822368i	$0.973794\pi$
$930$	1.50234	+	5.91233i	0.0492637	+	0.193873i
$931$	−25.5097	−	25.5097i	−0.836046	−	0.836046i
$932$	2.66756	+	9.95547i	0.0873789	+	0.326102i
$933$			8.70426i			0.284965i
$934$	28.6893	−	16.5638i	0.938743	−	0.541983i
$935$	−0.795960	−	0.816868i	−0.0260307	−	0.0267144i
$936$		−	1.71575i		−	0.0560811i
$937$	−55.8758	−	14.9719i	−1.82538	−	0.489110i	−0.827955	−	0.560794i	$-0.810496\pi$
$937$	−55.8758	−	14.9719i	−1.82538	−	0.489110i	−0.997427	+	0.0716843i	$0.977163\pi$
$938$	11.0882	+	6.40179i	0.362044	+	0.209026i
$939$	2.20300	+	2.20300i	0.0718923	+	0.0718923i
$940$	8.03459	−	4.50093i	0.262059	−	0.146804i
$941$	8.50292	+	14.7275i	0.277187	+	0.480102i	0.970685	−	0.240357i	$-0.0772644\pi$
$941$	8.50292	+	14.7275i	0.277187	+	0.480102i	−0.693497	+	0.720459i	$0.743931\pi$
$942$	−6.85805	−	11.8785i	−0.223447	−	0.387022i
$943$	6.80657	−	11.7893i	0.221652	−	0.383913i
$944$	3.36434	+	12.5559i	0.109500	+	0.408660i
$945$	11.3884	+	3.21030i	0.370465	+	0.104431i
$946$	−2.11293	+	1.21990i	−0.0686974	+	0.0396625i
$947$	19.8712	+	34.4179i	0.645727	+	1.11843i	0.984133	+	0.177432i	$0.0567791\pi$
$947$	19.8712	+	34.4179i	0.645727	+	1.11843i	−0.338406	+	0.941000i	$0.609888\pi$
$948$			2.83690i			0.0921383i
$949$	2.49375	−	0.668197i	0.0809504	−	0.0216906i
$950$	39.7843	+	11.7737i	1.29077	+	0.381988i
$951$	21.2271			0.688334
$952$	5.30581	+	5.30581i	0.171962	+	0.171962i
$953$	7.54213	+	2.02091i	0.244314	+	0.0654636i	0.378898	−	0.925439i	$-0.376303\pi$
$953$	7.54213	+	2.02091i	0.244314	+	0.0654636i	−0.134584	+	0.990902i	$0.542970\pi$
$954$	−16.8844	−	16.8844i	−0.546653	−	0.546653i
$955$	21.1437	−	35.5496i	0.684193	−	1.15036i
$956$	7.10896	−	7.10896i	0.229920	−	0.229920i
$957$	0.256902	+	0.148323i	0.00830447	+	0.00479459i
$958$	−27.6141	+	7.39917i	−0.892170	+	0.239056i
$959$	11.3496	+	6.55269i	0.366497	+	0.211597i
$960$	10.6126	−	5.94514i	0.342522	−	0.191878i
$961$			17.0382i			0.549620i
$962$	1.46824	−	0.163007i	0.0473380	−	0.00525555i
$963$	16.2866	+	16.2866i	0.524829	+	0.524829i
$964$	−3.24214	+	12.0998i	−0.104422	+	0.389710i
$965$	−22.8456	+	5.80513i	−0.735426	+	0.186874i
$966$	−5.24647	−	3.02905i	−0.168803	−	0.0974582i
$967$	16.7585	−	29.0265i	0.538916	−	0.933429i	−0.460047	−	0.887895i	$-0.652167\pi$
$967$	16.7585	−	29.0265i	0.538916	−	0.933429i	0.998963	−	0.0455348i	$-0.0144992\pi$
$968$			33.5439i			1.07814i
$969$	6.98372	+	4.03205i	0.224350	+	0.129528i
$970$	−8.14645	−	8.36044i	−0.261567	−	0.268438i
$971$	25.5539	+	44.2607i	0.820064	+	1.42039i	0.905634	+	0.424061i	$0.139396\pi$
$971$	25.5539	+	44.2607i	0.820064	+	1.42039i	−0.0855692	+	0.996332i	$0.527271\pi$
$972$	−7.55099	+	7.55099i	−0.242198	+	0.242198i
$973$	23.5313	−	23.5313i	0.754379	−	0.754379i
$974$	19.9002	−	11.4894i	0.637645	−	0.368144i
$975$	0.164748	+	0.685458i	0.00527616	+	0.0219522i
$976$	−11.2381	+	11.2381i	−0.359723	+	0.359723i
$977$	11.6861	−	6.74695i	0.373870	−	0.215854i	−0.301278	−	0.953536i	$-0.597413\pi$
$977$	11.6861	−	6.74695i	0.373870	−	0.215854i	0.675148	+	0.737682i	$0.264080\pi$
$978$	0.562639	−	2.09980i	0.0179912	−	0.0671442i
$979$	0.958490	+	0.256827i	0.0306335	+	0.00820821i
$980$	−7.84435	+	1.99327i	−0.250579	+	0.0636728i
$981$	−18.6345	+	4.99309i	−0.594953	+	0.159417i
$982$	10.6353	−	6.14028i	0.339385	−	0.195944i
$983$	−33.9029	−	9.08426i	−1.08134	−	0.289743i	−0.326193	−	0.945303i	$-0.605766\pi$
$983$	−33.9029	−	9.08426i	−1.08134	−	0.289743i	−0.755143	+	0.655560i	$0.772433\pi$
$984$	−4.62494	−	1.23925i	−0.147438	−	0.0395058i
$985$	−0.364363	+	28.1066i	−0.0116096	+	0.895552i
$986$	−0.726488	−	2.71129i	−0.0231361	−	0.0863451i
$987$	−1.36254	+	5.08509i	−0.0433703	+	0.161860i
$988$	−0.841230	−	0.841230i	−0.0267631	−	0.0267631i
$989$	40.6455			1.29245
$990$	−0.534061	+	1.89456i	−0.0169736	+	0.0602130i
$991$	17.5135	−	17.5135i	0.556333	−	0.556333i	−0.371928	−	0.928262i	$-0.621303\pi$
$991$	17.5135	−	17.5135i	0.556333	−	0.556333i	0.928262	+	0.371928i	$0.121303\pi$
$992$	−14.2503	+	3.81836i	−0.452448	+	0.121233i
$993$	−5.16386			−0.163870
$994$	−17.5513	+	4.70284i	−0.556692	+	0.149165i
$995$	7.29491	−	12.2652i	0.231264	−	0.388833i
$996$	−0.990208	+	1.71509i	−0.0313759	+	0.0543447i
$997$	−5.20395	−	9.01350i	−0.164811	−	0.285461i	0.771777	−	0.635893i	$-0.219368\pi$
$997$	−5.20395	−	9.01350i	−0.164811	−	0.285461i	−0.936588	+	0.350432i	$0.886035\pi$
$998$	8.21271	−	8.21271i	0.259969	−	0.259969i
$999$	−17.2425	−	13.7965i	−0.545529	−	0.436502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.u.a.8.13	yes	68
5.2	odd	4		185.2.p.a.82.13	✓	68
5.3	odd	4		925.2.t.b.82.5		68
5.4	even	2		925.2.y.b.193.5		68
37.14	odd	12		185.2.p.a.88.13	yes	68
185.14	odd	12		925.2.t.b.643.5		68
185.88	even	12		925.2.y.b.532.5		68
185.162	even	12	inner	185.2.u.a.162.13	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.82.13	✓	68	5.2	odd	4
185.2.p.a.88.13	yes	68	37.14	odd	12
185.2.u.a.8.13	yes	68	1.1	even	1	trivial
185.2.u.a.162.13	yes	68	185.162	even	12	inner
925.2.t.b.82.5		68	5.3	odd	4
925.2.t.b.643.5		68	185.14	odd	12
925.2.y.b.193.5		68	5.4	even	2
925.2.y.b.532.5		68	185.88	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.971183 - 0.560713i) q^{2} +(0.168506 + 0.628874i) q^{3} +(-0.371203 + 0.642942i) q^{4} +(0.550691 + 2.16720i) q^{5} +(0.516268 + 0.516268i) q^{6} +(-0.377247 - 1.40791i) q^{7} +3.07540i q^{8} +(2.23099 - 1.28806i) q^{9} +(1.75000 + 1.79596i) q^{10} +0.304712i q^{11} +(-0.466879 - 0.125100i) q^{12} +(-0.187550 - 0.108282i) q^{13} +(-1.15581 - 1.15581i) q^{14} +(-1.27010 + 0.711501i) q^{15} +(0.982011 + 1.70089i) q^{16} +(0.836960 + 1.44966i) q^{17} +(1.44446 - 2.50189i) q^{18} +(-1.91513 - 7.14737i) q^{19} +(-1.59780 - 0.450407i) q^{20} +(0.821827 - 0.474482i) q^{21} +(0.170856 + 0.295931i) q^{22} -5.69268i q^{23} +(-1.93404 + 0.518224i) q^{24} +(-4.39348 + 2.38691i) q^{25} -0.242860 q^{26} +(2.56707 + 2.56707i) q^{27} +(1.04524 + 0.280071i) q^{28} +(-1.05734 - 1.05734i) q^{29} +(-0.834549 + 1.40316i) q^{30} +(2.64214 - 2.64214i) q^{31} +(-3.41933 - 1.97415i) q^{32} +(-0.191625 + 0.0513459i) q^{33} +(1.62568 + 0.938587i) q^{34} +(2.84346 - 1.59289i) q^{35} +1.91253i q^{36} +(-6.04562 + 0.671196i) q^{37} +(-5.86756 - 5.86756i) q^{38} +(0.0364924 - 0.136191i) q^{39} +(-6.66500 + 1.69360i) q^{40} +(2.07096 + 1.19567i) q^{41} +(0.532096 - 0.921617i) q^{42} +7.13995i q^{43} +(-0.195912 - 0.113110i) q^{44} +(4.02007 + 4.12567i) q^{45} +(-3.19196 - 5.52863i) q^{46} +(-3.92274 + 3.92274i) q^{47} +(-0.904172 + 0.904172i) q^{48} +(4.22229 - 2.43774i) q^{49} +(-2.92850 + 4.78160i) q^{50} +(-0.770618 + 0.770618i) q^{51} +(0.139238 - 0.0803891i) q^{52} +(2.13924 - 7.98376i) q^{53} +(3.93248 + 1.05370i) q^{54} +(-0.660371 + 0.167802i) q^{55} +(4.32988 - 1.16019i) q^{56} +(4.17208 - 2.40875i) q^{57} +(-1.61973 - 0.434004i) q^{58} +(6.39295 + 1.71299i) q^{59} +(0.0140099 - 1.08071i) q^{60} +(2.09439 + 7.81639i) q^{61} +(1.08452 - 4.04748i) q^{62} +(-2.65511 - 2.65511i) q^{63} -8.35577 q^{64} +(0.131386 - 0.466087i) q^{65} +(-0.157313 + 0.157313i) q^{66} +(-7.56615 + 2.02734i) q^{67} -1.24273 q^{68} +(3.57998 - 0.959252i) q^{69} +(1.86837 - 3.14135i) q^{70} +(5.55820 - 9.62708i) q^{71} +(3.96131 + 6.86119i) q^{72} +(-8.42960 + 8.42960i) q^{73} +(-5.49505 + 4.04171i) q^{74} +(-2.24139 - 2.36073i) q^{75} +(5.30625 + 1.42180i) q^{76} +(0.429006 - 0.114952i) q^{77} +(-0.0409234 - 0.152728i) q^{78} +(-1.51908 - 5.66927i) q^{79} +(-3.14538 + 3.06488i) q^{80} +(2.68239 - 4.64604i) q^{81} +2.68171 q^{82} +(1.06045 - 3.95767i) q^{83} +0.704516i q^{84} +(-2.68078 + 2.61217i) q^{85} +(4.00346 + 6.93419i) q^{86} +(0.486763 - 0.843098i) q^{87} -0.937113 q^{88} +(0.842850 - 3.14556i) q^{89} +(6.21753 + 1.75267i) q^{90} +(-0.0816982 + 0.304902i) q^{91} +(3.66007 + 2.11314i) q^{92} +(2.10679 + 1.21635i) q^{93} +(-1.61017 + 6.00923i) q^{94} +(14.4351 - 8.08646i) q^{95} +(0.665313 - 2.48298i) q^{96} -4.65513 q^{97} +(2.73374 - 4.73498i) q^{98} +(0.392488 + 0.679809i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{2} - 4 q^{3} + 30 q^{4} - 8 q^{6} - 2 q^{7} - 6 q^{10} - 10 q^{12} - 6 q^{13} - 16 q^{15} - 26 q^{16} - 10 q^{17} - 8 q^{18} - 4 q^{19} - 28 q^{20} - 12 q^{21} - 14 q^{22} + 20 q^{25} - 24 q^{26}+ \cdots - 32 q^{99}+O(q^{100}) \) 68 * q - 6 * q^2 - 4 * q^3 + 30 * q^4 - 8 * q^6 - 2 * q^7 - 6 * q^10 - 10 * q^12 - 6 * q^13 - 16 * q^15 - 26 * q^16 - 10 * q^17 - 8 * q^18 - 4 * q^19 - 28 * q^20 - 12 * q^21 - 14 * q^22 + 20 * q^25 - 24 * q^26 + 68 * q^27 + 14 * q^28 - 14 * q^29 + 26 * q^30 - 24 * q^31 + 18 * q^32 + 10 * q^33 - 22 * q^35 - 18 * q^37 - 36 * q^38 - 52 * q^39 + 84 * q^40 - 18 * q^41 - 40 * q^42 + 36 * q^44 - 66 * q^45 - 52 * q^46 - 24 * q^47 + 60 * q^48 + 36 * q^49 - 12 * q^50 - 8 * q^51 - 78 * q^52 - 38 * q^53 - 40 * q^54 + 6 * q^55 + 16 * q^56 + 90 * q^57 + 16 * q^58 + 8 * q^59 - 52 * q^60 + 4 * q^61 - 22 * q^62 - 48 * q^63 + 20 * q^64 - 20 * q^65 + 80 * q^66 - 56 * q^67 - 20 * q^68 - 8 * q^69 + 62 * q^70 + 4 * q^71 + 32 * q^72 + 60 * q^73 + 44 * q^74 + 64 * q^75 + 72 * q^76 + 6 * q^77 - 24 * q^78 - 56 * q^79 - 76 * q^80 - 6 * q^81 - 8 * q^82 + 12 * q^83 + 20 * q^85 - 4 * q^86 - 32 * q^87 - 36 * q^88 + 22 * q^89 - 74 * q^90 + 44 * q^91 + 156 * q^92 - 30 * q^93 + 20 * q^94 + 28 * q^95 - 8 * q^96 + 16 * q^97 + 48 * q^98 - 32 * q^99

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