LMFDB - Embedded newform 195.2.bf.a.62.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [195,2,Mod(17,195)] 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("195.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(195, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.bf (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:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			62.8
Character	$\chi$	$=$	195.62
Dual form			195.2.bf.a.173.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.283997 + 1.05989i) q^{2} +(0.872682 - 1.49614i) q^{3} +(0.689337 + 0.397989i) q^{4} +(1.65169 - 1.50729i) q^{5} +(1.33790 + 1.34985i) q^{6} +(-0.0430045 - 0.160495i) q^{7} +(-2.16938 + 2.16938i) q^{8} +(-1.47685 - 2.61130i) q^{9} +(1.12849 + 2.17868i) q^{10} +(-2.43760 - 4.22205i) q^{11} +(1.19702 - 0.684025i) q^{12} +(2.82173 + 2.24451i) q^{13} +0.182320 q^{14} +(-0.813712 - 3.78654i) q^{15} +(-0.887232 - 1.53673i) q^{16} +(1.24864 + 4.65999i) q^{17} +(3.18712 - 0.823701i) q^{18} +(-1.37389 + 2.37966i) q^{19} +(1.73846 - 0.381676i) q^{20} +(-0.277652 - 0.0757204i) q^{21} +(5.16719 - 1.38454i) q^{22} +(-1.51285 + 5.64603i) q^{23} +(1.35251 + 5.13887i) q^{24} +(0.456158 - 4.97915i) q^{25} +(-3.18030 + 2.35330i) q^{26} +(-5.19569 - 0.0692622i) q^{27} +(0.0342306 - 0.127750i) q^{28} +(2.47205 + 4.28172i) q^{29} +(4.24441 + 0.212919i) q^{30} -2.41720i q^{31} +(-4.04612 + 1.08416i) q^{32} +(-8.44403 - 0.0375196i) q^{33} -5.29369 q^{34} +(-0.312942 - 0.200268i) q^{35} +(0.0212203 - 2.38784i) q^{36} +(-4.48963 - 1.20299i) q^{37} +(-2.13199 - 2.13199i) q^{38} +(5.82057 - 2.26296i) q^{39} +(-0.313259 + 6.85303i) q^{40} +(-2.16059 - 3.74226i) q^{41} +(0.159108 - 0.272776i) q^{42} +(-0.340642 - 1.27129i) q^{43} -3.88056i q^{44} +(-6.37529 - 2.08702i) q^{45} +(-5.55453 - 3.20691i) q^{46} +(3.58251 + 3.58251i) q^{47} +(-3.07343 - 0.0136563i) q^{48} +(6.03827 - 3.48620i) q^{49} +(5.14781 + 1.89754i) q^{50} +(8.06165 + 2.19855i) q^{51} +(1.05184 + 2.67024i) q^{52} +(-3.34661 - 3.34661i) q^{53} +(1.54897 - 5.48719i) q^{54} +(-10.3900 - 3.29935i) q^{55} +(0.441468 + 0.254882i) q^{56} +(2.36132 + 4.13222i) q^{57} +(-5.24021 + 1.40411i) q^{58} +(-8.49452 - 4.90431i) q^{59} +(0.946078 - 2.93405i) q^{60} +(-7.20685 + 12.4826i) q^{61} +(2.56197 + 0.686477i) q^{62} +(-0.355590 + 0.349325i) q^{63} -8.14527i q^{64} +(8.04375 - 0.545941i) q^{65} +(2.43784 - 8.93909i) q^{66} +(-0.702294 - 0.188179i) q^{67} +(-0.993890 + 3.70925i) q^{68} +(7.12700 + 7.19061i) q^{69} +(0.301136 - 0.274809i) q^{70} +(-1.37489 + 2.38137i) q^{71} +(8.86877 + 2.46106i) q^{72} +(-5.45193 - 5.45193i) q^{73} +(2.55008 - 4.41687i) q^{74} +(-7.05141 - 5.02769i) q^{75} +(-1.89415 + 1.09359i) q^{76} +(-0.572790 + 0.572790i) q^{77} +(0.745469 + 6.81184i) q^{78} -7.39276i q^{79} +(-3.78173 - 1.20089i) q^{80} +(-4.63781 + 7.71302i) q^{81} +(4.57999 - 1.22720i) q^{82} +(-1.60997 + 1.60997i) q^{83} +(-0.161260 - 0.162699i) q^{84} +(9.08632 + 5.81479i) q^{85} +1.44417 q^{86} +(8.56336 + 0.0380499i) q^{87} +(14.4473 + 3.87115i) q^{88} +(5.98500 - 3.45544i) q^{89} +(4.02257 - 6.16441i) q^{90} +(0.238885 - 0.549398i) q^{91} +(-3.28992 + 3.28992i) q^{92} +(-3.61646 - 2.10944i) q^{93} +(-4.81449 + 2.77964i) q^{94} +(1.31758 + 6.00131i) q^{95} +(-1.90893 + 6.99968i) q^{96} +(4.36286 + 16.2824i) q^{97} +(1.98014 + 7.38997i) q^{98} +(-7.42508 + 12.6007i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 2 q^{3} - 12 q^{6} - 12 q^{7} + 4 q^{10} - 12 q^{12} - 24 q^{13} - 6 q^{15} + 16 q^{16} + 20 q^{22} - 16 q^{25} - 32 q^{27} - 36 q^{28} + 30 q^{33} - 4 q^{36} - 84 q^{37} - 152 q^{40} - 48 q^{42}+ \cdots - 48 q^{97}+O(q^{100}) $ 96 * q - 2 * q^3 - 12 * q^6 - 12 * q^7 + 4 * q^10 - 12 * q^12 - 24 * q^13 - 6 * q^15 + 16 * q^16 + 20 * q^22 - 16 * q^25 - 32 * q^27 - 36 * q^28 + 30 * q^33 - 4 * q^36 - 84 * q^37 - 152 * q^40 - 48 * q^42 + 8 * q^43 + 54 * q^45 - 28 * q^48 - 16 * q^51 + 28 * q^52 - 40 * q^55 + 84 * q^58 - 32 * q^61 + 90 * q^63 + 36 * q^67 + 90 * q^72 - 20 * q^75 + 72 * q^76 + 60 * q^78 + 32 * q^81 - 68 * q^82 + 84 * q^85 - 26 * q^87 - 108 * q^88 - 20 * q^90 - 80 * q^91 + 48 * q^93 - 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.283997	+	1.05989i	−0.200816	+	0.749456i	0.789868	+	0.613277i	$0.210149\pi$
$2$	−0.283997	+	1.05989i	−0.200816	+	0.749456i	−0.990684	+	0.136179i	$0.956518\pi$
$3$	0.872682	−	1.49614i	0.503843	−	0.863795i
$3$	0.872682	−	1.49614i	0.503843	−	0.863795i
$4$	0.689337	+	0.397989i	0.344668	+	0.198994i
$5$	1.65169	−	1.50729i	0.738658	−	0.674080i
$5$	1.65169	−	1.50729i	0.738658	−	0.674080i
$6$	1.33790	+	1.34985i	0.546197	+	0.551072i
$7$	−0.0430045	−	0.160495i	−0.0162542	−	0.0606614i	0.957322	−	0.289022i	$-0.0933301\pi$
$7$	−0.0430045	−	0.160495i	−0.0162542	−	0.0606614i	−0.973577	+	0.228361i	$0.926663\pi$
$8$	−2.16938	+	2.16938i	−0.766992	+	0.766992i
$9$	−1.47685	−	2.61130i	−0.492284	−	0.870434i
$10$	1.12849	+	2.17868i	0.356859	+	0.688958i
$11$	−2.43760	−	4.22205i	−0.734965	−	1.27300i	−0.954739	−	0.297446i	$-0.903865\pi$
$11$	−2.43760	−	4.22205i	−0.734965	−	1.27300i	0.219773	−	0.975551i	$-0.429468\pi$
$12$	1.19702	−	0.684025i	0.345549	−	0.197461i
$13$	2.82173	+	2.24451i	0.782608	+	0.622514i
$13$	2.82173	+	2.24451i	0.782608	+	0.622514i
$14$	0.182320			0.0487271
$15$	−0.813712	−	3.78654i	−0.210100	−	0.977680i
$16$	−0.887232	−	1.53673i	−0.221808	−	0.384183i
$17$	1.24864	+	4.65999i	0.302840	+	1.13021i	0.934789	+	0.355204i	$0.115588\pi$
$17$	1.24864	+	4.65999i	0.302840	+	1.13021i	−0.631949	+	0.775010i	$0.717745\pi$
$18$	3.18712	−	0.823701i	0.751211	−	0.194148i
$19$	−1.37389	+	2.37966i	−0.315193	+	0.545930i	−0.979479	−	0.201549i	$-0.935403\pi$
$19$	−1.37389	+	2.37966i	−0.315193	+	0.545930i	0.664285	+	0.747479i	$0.268736\pi$
$20$	1.73846	−	0.381676i	0.388730	−	0.0853454i
$21$	−0.277652	−	0.0757204i	−0.0605886	−	0.0165235i
$22$	5.16719	−	1.38454i	1.10165	−	0.295186i
$23$	−1.51285	+	5.64603i	−0.315451	+	1.17728i	0.608118	+	0.793846i	$0.291925\pi$
$23$	−1.51285	+	5.64603i	−0.315451	+	1.17728i	−0.923569	+	0.383432i	$0.874742\pi$
$24$	1.35251	+	5.13887i	0.276081	+	1.04897i
$25$	0.456158	−	4.97915i	0.0912315	−	0.995830i
$26$	−3.18030	+	2.35330i	−0.623707	+	0.461520i
$27$	−5.19569	−	0.0692622i	−0.999911	−	0.0133295i
$28$	0.0342306	−	0.127750i	0.00646898	−	0.0241426i
$29$	2.47205	+	4.28172i	0.459049	+	0.795096i	0.998911	−	0.0466574i	$-0.0148569\pi$
$29$	2.47205	+	4.28172i	0.459049	+	0.795096i	−0.539862	+	0.841754i	$0.681524\pi$
$30$	4.24441	+	0.212919i	0.774919	+	0.0388735i
$31$		−	2.41720i		−	0.434142i	−0.976156	−	0.217071i	$-0.930350\pi$
$31$		−	2.41720i		−	0.434142i	0.976156	−	0.217071i	$-0.0696502\pi$
$32$	−4.04612	+	1.08416i	−0.715260	+	0.191653i
$33$	−8.44403	−	0.0375196i	−1.46992	−	0.00653133i
$34$	−5.29369			−0.907860
$35$	−0.312942	−	0.200268i	−0.0528969	−	0.0338514i
$36$	0.0212203	−	2.38784i	0.00353672	−	0.397973i
$37$	−4.48963	−	1.20299i	−0.738090	−	0.197771i	−0.129861	−	0.991532i	$-0.541453\pi$
$37$	−4.48963	−	1.20299i	−0.738090	−	0.197771i	−0.608229	+	0.793762i	$0.708120\pi$
$38$	−2.13199	−	2.13199i	−0.345855	−	0.345855i
$39$	5.82057	−	2.26296i	0.932037	−	0.362364i
$40$	−0.313259	+	6.85303i	−0.0495307	+	1.08356i
$41$	−2.16059	−	3.74226i	−0.337428	−	0.584443i	0.646520	−	0.762897i	$-0.276224\pi$
$41$	−2.16059	−	3.74226i	−0.337428	−	0.584443i	−0.983948	+	0.178454i	$0.942890\pi$
$42$	0.159108	−	0.272776i	0.0245508	−	0.0420903i
$43$	−0.340642	−	1.27129i	−0.0519475	−	0.193871i	0.935076	−	0.354448i	$-0.115331\pi$
$43$	−0.340642	−	1.27129i	−0.0519475	−	0.193871i	−0.987023	+	0.160577i	$0.948664\pi$
$44$		−	3.88056i		−	0.585016i
$45$	−6.37529	−	2.08702i	−0.950373	−	0.311114i
$46$	−5.55453	−	3.20691i	−0.818970	−	0.472833i
$47$	3.58251	+	3.58251i	0.522562	+	0.522562i	0.918344	−	0.395782i	$-0.129526\pi$
$47$	3.58251	+	3.58251i	0.522562	+	0.522562i	−0.395782	+	0.918344i	$0.629526\pi$
$48$	−3.07343	−	0.0136563i	−0.443612	−	0.00197111i
$49$	6.03827	−	3.48620i	0.862610	−	0.498028i
$50$	5.14781	+	1.89754i	0.728010	+	0.268353i
$51$	8.06165	+	2.19855i	1.12886	+	0.307859i
$52$	1.05184	+	2.67024i	0.145864	+	0.370296i
$53$	−3.34661	−	3.34661i	−0.459692	−	0.459692i	0.438862	−	0.898554i	$-0.355382\pi$
$53$	−3.34661	−	3.34661i	−0.459692	−	0.459692i	−0.898554	+	0.438862i	$0.855382\pi$
$54$	1.54897	−	5.48719i	0.210788	−	0.746712i
$55$	−10.3900	−	3.29935i	−1.40099	−	0.444884i
$56$	0.441468	+	0.254882i	0.0589936	+	0.0340600i
$57$	2.36132	+	4.13222i	0.312764	+	0.547326i
$58$	−5.24021	+	1.40411i	−0.688074	+	0.184369i
$59$	−8.49452	−	4.90431i	−1.10589	−	0.638487i	−0.168130	−	0.985765i	$-0.553773\pi$
$59$	−8.49452	−	4.90431i	−1.10589	−	0.638487i	−0.937762	+	0.347278i	$0.887106\pi$
$60$	0.946078	−	2.93405i	0.122138	−	0.378784i
$61$	−7.20685	+	12.4826i	−0.922742	+	1.59824i	−0.127590	+	0.991827i	$0.540724\pi$
$61$	−7.20685	+	12.4826i	−0.922742	+	1.59824i	−0.795153	+	0.606409i	$0.792609\pi$
$62$	2.56197	+	0.686477i	0.325370	+	0.0871826i
$63$	−0.355590	+	0.349325i	−0.0448001	+	0.0440108i
$64$		−	8.14527i		−	1.01816i
$65$	8.04375	−	0.545941i	0.997705	−	0.0677157i
$66$	2.43784	−	8.93909i	0.300078	−	1.10033i
$67$	−0.702294	−	0.188179i	−0.0857989	−	0.0229897i	0.215664	−	0.976468i	$-0.430808\pi$
$67$	−0.702294	−	0.188179i	−0.0857989	−	0.0229897i	−0.301463	+	0.953478i	$0.597475\pi$
$68$	−0.993890	+	3.70925i	−0.120527	+	0.449812i
$69$	7.12700	+	7.19061i	0.857990	+	0.865648i
$70$	0.301136	−	0.274809i	0.0359927	−	0.0328460i
$71$	−1.37489	+	2.38137i	−0.163169	+	0.282617i	−0.936004	−	0.351990i	$-0.885505\pi$
$71$	−1.37489	+	2.38137i	−0.163169	+	0.282617i	0.772834	+	0.634608i	$0.218838\pi$
$72$	8.86877	+	2.46106i	1.04519	+	0.290038i
$73$	−5.45193	−	5.45193i	−0.638101	−	0.638101i	0.311986	−	0.950087i	$-0.399006\pi$
$73$	−5.45193	−	5.45193i	−0.638101	−	0.638101i	−0.950087	+	0.311986i	$0.899006\pi$
$74$	2.55008	−	4.41687i	0.296441	−	0.513450i
$75$	−7.05141	−	5.02769i	−0.814227	−	0.580547i
$76$	−1.89415	+	1.09359i	−0.217274	+	0.125443i
$77$	−0.572790	+	0.572790i	−0.0652755	+	0.0652755i
$78$	0.745469	+	6.81184i	0.0844077	+	0.771289i
$79$		−	7.39276i		−	0.831750i	−0.909422	−	0.415875i	$-0.863475\pi$
$79$		−	7.39276i		−	0.831750i	0.909422	−	0.415875i	$-0.136525\pi$
$80$	−3.78173	−	1.20089i	−0.422810	−	0.134263i
$81$	−4.63781	+	7.71302i	−0.515312	+	0.857002i
$82$	4.57999	−	1.22720i	0.505775	−	0.135522i
$83$	−1.60997	+	1.60997i	−0.176717	+	0.176717i	−0.789923	−	0.613206i	$-0.789880\pi$
$83$	−1.60997	+	1.60997i	−0.176717	+	0.176717i	0.613206	+	0.789923i	$0.289880\pi$
$84$	−0.161260	−	0.162699i	−0.0175949	−	0.0177519i
$85$	9.08632	+	5.81479i	0.985550	+	0.630703i
$86$	1.44417			0.155729
$87$	8.56336	+	0.0380499i	0.918089	+	0.00407937i
$88$	14.4473	+	3.87115i	1.54009	+	0.412666i
$89$	5.98500	−	3.45544i	0.634408	−	0.366276i	−0.148049	−	0.988980i	$-0.547299\pi$
$89$	5.98500	−	3.45544i	0.634408	−	0.366276i	0.782457	+	0.622704i	$0.213966\pi$
$90$	4.02257	−	6.16441i	0.424016	−	0.649785i
$91$	0.238885	−	0.549398i	0.0250419	−	0.0575926i
$92$	−3.28992	+	3.28992i	−0.342998	+	0.342998i
$93$	−3.61646	−	2.10944i	−0.375009	−	0.218739i
$94$	−4.81449	+	2.77964i	−0.496576	+	0.286698i
$95$	1.31758	+	6.00131i	0.135181	+	0.615721i
$96$	−1.90893	+	6.99968i	−0.194830	+	0.714402i
$97$	4.36286	+	16.2824i	0.442981	+	1.65323i	0.721212	+	0.692714i	$0.243585\pi$
$97$	4.36286	+	16.2824i	0.442981	+	1.65323i	−0.278231	+	0.960514i	$0.589748\pi$
$98$	1.98014	+	7.38997i	0.200024	+	0.746500i
$99$	−7.42508	+	12.6007i	−0.746249	+	1.26642i
$100$	2.29609	−	3.25077i	0.229609	−	0.325077i
$101$	13.1605	−	7.59820i	1.30952	−	0.756049i	0.327500	−	0.944851i	$-0.393794\pi$
$101$	13.1605	−	7.59820i	1.30952	−	0.756049i	0.982015	+	0.188802i	$0.0604604\pi$
$102$	−4.61971	+	7.92008i	−0.457419	+	0.784205i
$103$	12.4089	−	12.4089i	1.22268	−	1.22268i	0.256009	−	0.966674i	$-0.417592\pi$
$103$	12.4089	−	12.4089i	1.22268	−	1.22268i	0.966674	−	0.256009i	$-0.0824078\pi$
$104$	−10.9906	+	1.25223i	−1.07772	+	0.122791i
$105$	−0.572727	+	0.293435i	−0.0558924	+	0.0286363i
$106$	4.49746	−	2.59661i	0.436832	−	0.252205i
$107$	−2.10823	−	0.564899i	−0.203811	−	0.0546109i	0.155469	−	0.987841i	$-0.450311\pi$
$107$	−2.10823	−	0.564899i	−0.203811	−	0.0546109i	−0.359280	+	0.933230i	$0.616978\pi$
$108$	−3.55402	−	2.11557i	−0.341985	−	0.203571i
$109$	10.3074			0.987274			0.493637	−	0.869668i	$-0.335667\pi$
$109$	10.3074			0.987274			0.493637	+	0.869668i	$0.335667\pi$
$110$	6.44768	−	10.0753i	0.614762	−	0.960641i
$111$	−5.71785	+	5.66727i	−0.542715	+	0.537913i
$112$	−0.208483	+	0.208483i	−0.0196997	+	0.0196997i
$113$	14.4214	−	3.86420i	1.35665	−	0.363513i	0.494065	−	0.869425i	$-0.335511\pi$
$113$	14.4214	−	3.86420i	1.35665	−	0.363513i	0.862585	+	0.505912i	$0.168844\pi$
$114$	−5.05031	+	1.32920i	−0.473004	+	0.124491i
$115$	6.01144	+	11.6058i	0.560570	+	1.08225i
$116$			3.93540i			0.365393i
$117$	1.69380	−	10.6832i	0.156592	−	0.987663i
$118$	7.61045	−	7.61045i	0.700599	−	0.700599i
$119$	0.694207	−	0.400801i	0.0636379	−	0.0367414i
$120$	9.97970	+	6.44919i	0.911018	+	0.588728i
$121$	−6.38383	+	11.0571i	−0.580348	+	1.00519i
$122$	−11.1835	−	11.1835i	−1.01251	−	1.01251i
$123$	−7.48444	−	0.0332559i	−0.674850	−	0.00299858i
$124$	0.962018	−	1.66626i	0.0863918	−	0.149635i
$125$	−6.75159	−	8.91157i	−0.603880	−	0.797075i
$126$	−0.269260	−	0.476093i	−0.0239876	−	0.0424138i
$127$	−0.365954	+	1.36576i	−0.0324732	+	0.121192i	−0.980260	−	0.197713i	$-0.936648\pi$
$127$	−0.365954	+	1.36576i	−0.0324732	+	0.121192i	0.947787	+	0.318905i	$0.103315\pi$
$128$	0.540851	+	0.144921i	0.0478049	+	0.0128093i
$129$	−2.19930	−	0.599788i	−0.193638	−	0.0528084i
$130$	−1.70576	+	8.68054i	−0.149605	+	0.761334i
$131$			1.23865i			0.108221i	0.998535	+	0.0541107i	$0.0172324\pi$
$131$			1.23865i			0.108221i	−0.998535	+	0.0541107i	$0.982768\pi$
$132$	−5.80585	−	3.38649i	−0.505334	−	0.294756i
$133$	0.441006	+	0.118167i	0.0382401	+	0.0102464i
$134$	0.398899	−	0.690913i	0.0344596	−	0.0596858i
$135$	−8.68607	+	7.71701i	−0.747578	+	0.664174i
$136$	−12.8181	−	7.40052i	−1.09914	−	0.634589i
$137$	3.92054	−	1.05050i	0.334954	−	0.0897507i	−0.0874219	−	0.996171i	$-0.527863\pi$
$137$	3.92054	−	1.05050i	0.334954	−	0.0897507i	0.422376	+	0.906421i	$0.361196\pi$
$138$	−9.64531	+	5.51172i	−0.821063	+	0.469189i
$139$	−6.39677	−	3.69318i	−0.542567	−	0.313251i	0.203552	−	0.979064i	$-0.434752\pi$
$139$	−6.39677	−	3.69318i	−0.542567	−	0.313251i	−0.746119	+	0.665813i	$0.768085\pi$
$140$	−0.136018	−	0.262599i	−0.0114957	−	0.0221937i
$141$	8.48631	−	2.23353i	0.714676	−	0.188097i
$142$	−2.13353	−	2.13353i	−0.179042	−	0.179042i
$143$	2.59816	−	17.3847i	0.217269	−	1.45378i
$144$	−2.70256	+	4.58636i	−0.225213	+	0.382196i
$145$	10.5369	+	3.34598i	0.875039	+	0.277868i
$146$	7.32679	−	4.23012i	0.606369	−	0.350087i
$147$	0.0536595	−	12.0764i	0.00442576	−	0.996046i
$148$	−2.61609	−	2.61609i	−0.215041	−	0.215041i
$149$	5.05279	+	2.91723i	0.413941	+	0.238989i	0.692482	−	0.721435i	$-0.256517\pi$
$149$	5.05279	+	2.91723i	0.413941	+	0.238989i	−0.278541	+	0.960424i	$0.589851\pi$
$150$	7.33138	−	6.04587i	0.598604	−	0.493644i
$151$		−	16.4599i		−	1.33949i	−0.742591	−	0.669745i	$-0.766403\pi$
$151$		−	16.4599i		−	1.33949i	0.742591	−	0.669745i	$-0.233597\pi$
$152$	−2.18188	−	8.14288i	−0.176974	−	0.660475i
$153$	10.3246	−	10.1427i	0.834693	−	0.819988i
$154$	−0.444425	−	0.769766i	−0.0358127	−	0.0620295i
$155$	−3.64342	−	3.99246i	−0.292646	−	0.320682i
$156$	4.91297	+	0.756578i	0.393352	+	0.0605747i
$157$	−5.15467	−	5.15467i	−0.411387	−	0.411387i	0.470834	−	0.882222i	$-0.343953\pi$
$157$	−5.15467	−	5.15467i	−0.411387	−	0.411387i	−0.882222	+	0.470834i	$0.843953\pi$
$158$	7.83551	+	2.09952i	0.623360	+	0.167029i
$159$	−7.92751	+	2.08646i	−0.628692	+	0.165467i
$160$	−5.04880	+	7.88937i	−0.399143	+	0.623709i
$161$	0.971218			0.0765427
$162$	−6.85784	−	7.10605i	−0.538803	−	0.558304i
$163$	−21.2268	+	5.68770i	−1.66261	+	0.445495i	−0.963103	−	0.269131i	$-0.913263\pi$
$163$	−21.2268	+	5.68770i	−1.66261	+	0.445495i	−0.699506	+	0.714626i	$0.746597\pi$
$164$		−	3.43957i		−	0.268585i
$165$	−14.0035	+	12.6656i	−1.09017	+	0.986017i
$166$	−1.24917	−	2.16362i	−0.0969541	−	0.167929i
$167$	3.66650	−	13.6836i	0.283723	−	1.05887i	−0.666045	−	0.745911i	$-0.732014\pi$
$167$	3.66650	−	13.6836i	0.283723	−	1.05887i	0.949768	−	0.312956i	$-0.101319\pi$
$168$	0.766599	−	0.438066i	0.0591444	−	0.0337975i
$169$	2.92437	+	12.6668i	0.224952	+	0.974370i
$170$	−8.74353	+	7.97912i	−0.670598	+	0.611971i
$171$	8.24304	+	0.0732546i	0.630361	+	0.00560192i
$172$	0.271144	−	1.01192i	0.0206745	−	0.0771583i
$173$	0.918542	−	0.246123i	0.0698354	−	0.0187123i	−0.223732	−	0.974651i	$-0.571824\pi$
$173$	0.918542	−	0.246123i	0.0698354	−	0.0187123i	0.293568	+	0.955938i	$0.405157\pi$
$174$	−2.47230	+	9.06542i	−0.187424	+	0.687248i
$175$	−0.818745	+	0.140915i	−0.0618913	+	0.0106522i
$176$	−4.32544	+	7.49188i	−0.326042	+	0.564722i
$177$	−14.7505	+	8.42906i	−1.10872	+	0.633567i
$178$	1.96267	+	7.32477i	0.147108	+	0.549015i
$179$	8.16594	+	14.1438i	0.610351	+	1.05716i	0.991181	+	0.132514i	$0.0423048\pi$
$179$	8.16594	+	14.1438i	0.610351	+	1.05716i	−0.380830	+	0.924645i	$0.624362\pi$
$180$	−3.56411	−	3.97595i	−0.265653	−	0.296350i
$181$	−12.4459			−0.925096			−0.462548	−	0.886594i	$-0.653065\pi$
$181$	−12.4459			−0.925096			−0.462548	+	0.886594i	$0.653065\pi$
$182$	0.514459	+	0.409219i	0.0381343	+	0.0303333i
$183$	12.3864	+	21.6758i	0.915632	+	1.60232i
$184$	−8.96644	−	15.5303i	−0.661015	−	1.14491i
$185$	−9.22872	+	4.78020i	−0.678509	+	0.351447i
$186$	3.26284	−	3.23398i	0.239243	−	0.237127i
$187$	16.6310	−	16.6310i	1.21618	−	1.21618i
$188$	1.04376	+	3.89535i	0.0761238	+	0.284098i
$189$	0.212322	+	0.836861i	0.0154441	+	0.0608726i
$190$	−6.73492	−	0.307860i	−0.488603	−	0.0223345i
$191$	−2.49022	−	1.43773i	−0.180186	−	0.104030i	0.407194	−	0.913342i	$-0.366507\pi$
$191$	−2.49022	−	1.43773i	−0.180186	−	0.104030i	−0.587380	+	0.809311i	$0.699841\pi$
$192$	−12.1864	−	7.10823i	−0.879481	−	0.512992i
$193$	−2.73177	+	10.1951i	−0.196637	+	0.733861i	0.795199	+	0.606348i	$0.207366\pi$
$193$	−2.73177	+	10.1951i	−0.196637	+	0.733861i	−0.991837	+	0.127513i	$0.959301\pi$
$194$	−18.4966			−1.32798
$195$	6.20283	−	12.5110i	0.444194	−	0.895931i
$196$	5.54987			0.396419
$197$	−5.09403	+	19.0112i	−0.362934	+	1.35449i	0.507265	+	0.861790i	$0.330656\pi$
$197$	−5.09403	+	19.0112i	−0.362934	+	1.35449i	−0.870199	+	0.492700i	$0.836010\pi$
$198$	−11.2466	−	11.4483i	−0.799264	−	0.813597i
$199$	10.9231	+	6.30646i	0.774318	+	0.447053i	0.834413	−	0.551140i	$-0.185807\pi$
$199$	10.9231	+	6.30646i	0.774318	+	0.447053i	−0.0600946	+	0.998193i	$0.519140\pi$
$200$	9.81209	+	11.7913i	0.693820	+	0.833768i
$201$	−0.894421	+	0.886508i	−0.0630876	+	0.0625295i
$202$	4.31573	+	16.1065i	0.303654	+	1.13325i
$203$	0.580885	−	0.580885i	0.0407702	−	0.0407702i
$204$	4.68219	+	4.72399i	0.327819	+	0.330745i
$205$	−9.20930	−	2.92441i	−0.643205	−	0.204250i
$206$	9.62798	+	16.6761i	0.670813	+	1.16188i
$207$	16.9777	−	4.38785i	1.18003	−	0.304976i
$208$	0.945670	−	6.32765i	0.0655704	−	0.438743i
$209$	13.3960			0.926624
$210$	−0.148356	−	0.690362i	−0.0102375	−	0.0476395i
$211$	−2.40360	−	4.16317i	−0.165471	−	0.286604i	0.771351	−	0.636409i	$-0.219581\pi$
$211$	−2.40360	−	4.16317i	−0.165471	−	0.286604i	−0.936822	+	0.349805i	$0.886248\pi$
$212$	−0.975028	−	3.63885i	−0.0669652	−	0.249917i
$213$	2.36302	+	4.13520i	0.161912	+	0.283339i
$214$	1.19746	−	2.07407i	0.0818569	−	0.141780i
$215$	−2.47884	−	1.58634i	−0.169056	−	0.108187i
$216$	11.4217	−	11.1212i	0.777148	−	0.756700i
$217$	−0.387948	+	0.103950i	−0.0263356	+	0.00705661i
$218$	−2.92728	+	10.9248i	−0.198260	+	0.739918i
$219$	−12.9146	+	3.39904i	−0.872691	+	0.229686i
$220$	−5.84912	−	6.40948i	−0.394348	−	0.432127i
$221$	−6.93605	+	15.9518i	−0.466569	+	1.07304i
$222$	−4.38283	−	7.66979i	−0.294156	−	0.514762i
$223$	2.95177	−	11.0162i	0.197665	−	0.737697i	−0.793896	−	0.608054i	$-0.791950\pi$
$223$	2.95177	−	11.0162i	0.197665	−	0.737697i	0.991561	−	0.129643i	$-0.0413830\pi$
$224$	0.348003	+	0.602759i	0.0232519	+	0.0402735i
$225$	−13.6757	+	6.16230i	−0.911716	+	0.410820i
$226$			16.3825i			1.08975i
$227$	25.6485	−	6.87249i	1.70235	−	0.456143i	0.728821	−	0.684705i	$-0.240069\pi$
$227$	25.6485	−	6.87249i	1.70235	−	0.456143i	0.973530	+	0.228561i	$0.0734021\pi$
$228$	−0.0168325	+	3.78827i	−0.00111476	+	0.250884i
$229$	6.38857			0.422169			0.211084	−	0.977468i	$-0.432301\pi$
$229$	6.38857			0.422169			0.211084	+	0.977468i	$0.432301\pi$
$230$	−14.0081	+	3.07546i	−0.923666	+	0.202790i
$231$	0.357109	+	1.35684i	0.0234961	+	0.0892733i
$232$	−14.6515	−	3.92586i	−0.961920	−	0.257746i
$233$	−12.9039	−	12.9039i	−0.845365	−	0.845365i	0.144186	−	0.989551i	$-0.453944\pi$
$233$	−12.9039	−	12.9039i	−0.845365	−	0.845365i	−0.989551	+	0.144186i	$0.953944\pi$
$234$	10.8420	+	4.82924i	0.708764	+	0.315698i
$235$	11.3171	+	0.517315i	0.738244	+	0.0337459i
$236$	−3.90372	−	6.76145i	−0.254111	−	0.440133i
$237$	−11.0606	−	6.45152i	−0.718462	−	0.419072i
$238$	0.227652	+	0.849610i	0.0147565	+	0.0550720i
$239$			3.20751i			0.207477i	0.994605	+	0.103738i	$0.0330805\pi$
$239$			3.20751i			0.207477i	−0.994605	+	0.103738i	$0.966920\pi$
$240$	−5.09694	+	4.60999i	−0.329006	+	0.297574i
$241$	5.19991	+	3.00217i	0.334956	+	0.193387i	0.658039	−	0.752984i	$-0.271386\pi$
$241$	5.19991	+	3.00217i	0.334956	+	0.193387i	−0.323083	+	0.946370i	$0.604719\pi$
$242$	−9.90635	−	9.90635i	−0.636804	−	0.636804i
$243$	7.49241	+	13.6698i	0.480638	+	0.876919i
$244$	−9.93589	+	5.73649i	−0.636080	+	0.367241i
$245$	4.71864	−	14.8595i	0.301463	−	0.949341i
$246$	2.16081	−	7.92325i	0.137768	−	0.505168i
$247$	−9.21792	+	3.63104i	−0.586522	+	0.231038i
$248$	5.24382	+	5.24382i	0.332983	+	0.332983i
$249$	1.00374	+	3.81373i	0.0636097	+	0.241685i
$250$	11.3627	−	4.62509i	0.718641	−	0.292516i
$251$	−21.2638	−	12.2767i	−1.34216	−	0.774897i	−0.355036	−	0.934852i	$-0.615532\pi$
$251$	−21.2638	−	12.2767i	−1.34216	−	0.774897i	−0.987124	+	0.159956i	$0.948865\pi$
$252$	−0.384149	+	0.0992820i	−0.0241991	+	0.00625418i
$253$	27.5256	−	7.37545i	1.73052	−	0.463691i
$254$	−1.34363	−	0.775742i	−0.0843066	−	0.0486744i
$255$	16.6292	−	8.51991i	1.04136	−	0.533538i
$256$	7.83807	−	13.5759i	0.489880	−	0.848496i
$257$	−4.64467	−	1.24454i	−0.289727	−	0.0776320i	0.111028	−	0.993817i	$-0.464586\pi$
$257$	−4.64467	−	1.24454i	−0.289727	−	0.0776320i	−0.400755	+	0.916185i	$0.631252\pi$
$258$	1.26030	−	2.16068i	0.0784631	−	0.134518i
$259$			0.772296i			0.0479881i
$260$	5.76213	+	2.82499i	0.357352	+	0.175198i
$261$	7.53002	−	12.7788i	0.466096	−	0.790985i
$262$	−1.31283	−	0.351773i	−0.0811072	−	0.0217326i
$263$	3.04819	−	11.3760i	0.187959	−	0.701474i	−0.806018	−	0.591891i	$-0.798382\pi$
$263$	3.04819	−	11.3760i	0.187959	−	0.701474i	0.993978	−	0.109583i	$-0.0349517\pi$
$264$	18.3997	−	18.2369i	1.13242	−	1.12240i
$265$	−10.5719	−	0.483251i	−0.649424	−	0.0296859i
$266$	−0.250489	+	0.433859i	−0.0153585	+	0.0266016i
$267$	0.0531861	−	11.9699i	0.00325494	−	0.732544i
$268$	−0.409224	−	0.409224i	−0.0249973	−	0.0249973i
$269$	−0.648587	+	1.12339i	−0.0395451	+	0.0684941i	−0.885121	−	0.465362i	$-0.845924\pi$
$269$	−0.648587	+	1.12339i	−0.0395451	+	0.0684941i	0.845575	+	0.533856i	$0.179258\pi$
$270$	−5.71237	−	11.3979i	−0.347644	−	0.693653i
$271$	5.30394	−	3.06223i	0.322191	−	0.186017i	−0.330178	−	0.943919i	$-0.607109\pi$
$271$	5.30394	−	3.06223i	0.322191	−	0.186017i	0.652369	+	0.757902i	$0.273775\pi$
$272$	6.05331	−	6.05331i	0.367036	−	0.367036i
$273$	−0.613504	−	0.836854i	−0.0371310	−	0.0506487i
$274$			4.45368i			0.269057i
$275$	−22.1342	+	10.2113i	−1.33474	+	0.615763i
$276$	2.05112	+	7.79322i	0.123463	+	0.469097i
$277$	−10.0459	+	2.69179i	−0.603600	+	0.161734i	−0.547661	−	0.836700i	$-0.684482\pi$
$277$	−10.0459	+	2.69179i	−0.603600	+	0.161734i	−0.0559386	+	0.998434i	$0.517815\pi$
$278$	5.73103	−	5.73103i	0.343724	−	0.343724i
$279$	−6.31204	+	3.56985i	−0.377892	+	0.213721i
$280$	1.11335	−	0.244435i	0.0665353	−	0.0146078i
$281$	21.9271			1.30806			0.654031	−	0.756468i	$-0.273077\pi$
$281$	21.9271			1.30806			0.654031	+	0.756468i	$0.273077\pi$
$282$	−0.0427843	+	9.62888i	−0.00254777	+	0.573391i
$283$	−5.35432	−	1.43469i	−0.318281	−	0.0852833i	0.0961414	−	0.995368i	$-0.469350\pi$
$283$	−5.35432	−	1.43469i	−0.318281	−	0.0852833i	−0.414423	+	0.910084i	$0.636017\pi$
$284$	−1.89552	+	1.09438i	−0.112479	+	0.0649395i
$285$	10.1286	+	3.26595i	0.599967	+	0.193458i
$286$	17.6881	+	7.69098i	1.04592	+	0.454777i
$287$	−0.507698	+	0.507698i	−0.0299685	+	0.0299685i
$288$	8.80659	+	8.96452i	0.518933	+	0.528239i
$289$	−5.43396	+	3.13730i	−0.319645	+	0.184547i
$290$	−6.53881	+	10.2177i	−0.383972	+	0.600003i
$291$	28.1681	+	7.68193i	1.65124	+	0.450323i
$292$	−1.58841	−	5.92803i	−0.0929547	−	0.346912i
$293$	1.26763	+	4.73086i	0.0740557	+	0.276380i	0.993018	−	0.117967i	$-0.0376376\pi$
$293$	1.26763	+	4.73086i	0.0740557	+	0.276380i	−0.918962	+	0.394347i	$0.870971\pi$
$294$	12.7844	+	3.48654i	0.745604	+	0.203339i
$295$	−21.4225	+	4.70330i	−1.24727	+	0.273836i
$296$	12.3495	−	7.12996i	0.717798	−	0.414421i
$297$	12.3726	+	22.1053i	0.717932	+	1.28268i
$298$	−4.52692	+	4.52692i	−0.262238	+	0.262238i
$299$	−16.9414	+	12.5360i	−0.979747	+	0.724975i
$300$	−2.85983	−	6.27215i	−0.165113	−	0.362123i
$301$	−0.189387	+	0.109343i	−0.0109161	+	0.00630241i
$302$	17.4457	+	4.67457i	1.00389	+	0.268991i
$303$	0.116952	−	26.3207i	0.00671869	−	1.51208i
$304$	4.87585			0.279649
$305$	6.91145	+	31.4802i	0.395749	+	1.80255i
$306$	7.81800	+	13.8234i	0.446925	+	0.790233i
$307$	−15.7142	+	15.7142i	−0.896858	+	0.896858i	−0.995157	−	0.0982987i	$-0.968660\pi$
$307$	−15.7142	+	15.7142i	−0.896858	+	0.896858i	0.0982987	+	0.995157i	$0.468660\pi$
$308$	−0.622810	+	0.166881i	−0.0354879	+	0.00950895i
$309$	−7.73639	−	29.3944i	−0.440108	−	1.67219i
$310$	5.26629	−	2.72778i	0.299105	−	0.154927i
$311$			27.3000i			1.54804i	0.633161	+	0.774020i	$0.281757\pi$
$311$			27.3000i			1.54804i	−0.633161	+	0.774020i	$0.718243\pi$
$312$	−7.71780	+	17.5363i	−0.436935	+	0.992795i
$313$	−13.0107	+	13.0107i	−0.735406	+	0.735406i	−0.971685	−	0.236280i	$-0.924072\pi$
$313$	−13.0107	+	13.0107i	−0.735406	+	0.735406i	0.236280	+	0.971685i	$0.424072\pi$
$314$	6.92729	−	3.99948i	0.390930	−	0.225703i
$315$	−0.0607896	+	1.11295i	−0.00342511	+	0.0627078i
$316$	2.94224	−	5.09610i	0.165514	−	0.286678i
$317$	−6.64936	−	6.64936i	−0.373465	−	0.373465i	0.495272	−	0.868738i	$-0.335068\pi$
$317$	−6.64936	−	6.64936i	−0.373465	−	0.373465i	−0.868738	+	0.495272i	$0.835068\pi$
$318$	0.0399671	−	8.99484i	0.00224124	−	0.504406i
$319$	12.0518	−	20.8743i	0.674770	−	1.16874i
$320$	−12.2773	−	13.4535i	−0.686321	−	0.752071i
$321$	−2.68498	+	2.66123i	−0.149861	+	0.148535i
$322$	−0.275823	+	1.02938i	−0.0153710	+	0.0573654i
$323$	−12.8047	−	3.43100i	−0.712471	−	0.190906i
$324$	−6.26671	+	3.47107i	−0.348151	+	0.192837i
$325$	12.4629	−	13.0260i	0.691317	−	0.722552i
$326$		−	24.1134i		−	1.33552i
$327$	8.99512	−	15.4213i	0.497431	−	0.852802i
$328$	12.8055	+	3.43123i	0.707068	+	0.189458i
$329$	0.420910	−	0.729038i	0.0232055	−	0.0401932i
$330$	−9.44723	−	18.4391i	−0.520053	−	1.01504i
$331$	5.50158	+	3.17634i	0.302394	+	0.174587i	0.643518	−	0.765431i	$-0.277474\pi$
$331$	5.50158	+	3.17634i	0.302394	+	0.174587i	−0.341124	+	0.940018i	$0.610807\pi$
$332$	−1.75056	+	0.469062i	−0.0960746	+	0.0257431i
$333$	3.48914	+	13.5004i	0.191204	+	0.739818i
$334$	13.4618	+	7.77219i	0.736598	+	0.425275i
$335$	−1.44361	+	0.747747i	−0.0788730	+	0.0408538i
$336$	0.129980	+	0.493857i	0.00709097	+	0.0269421i
$337$	12.5904	+	12.5904i	0.685841	+	0.685841i	0.961310	−	0.275469i	$-0.0888332\pi$
$337$	12.5904	+	12.5904i	0.685841	+	0.685841i	−0.275469	+	0.961310i	$0.588833\pi$
$338$	−14.2559	−	0.497817i	−0.775421	−	0.0270777i
$339$	6.80391	−	24.9486i	0.369538	−	1.35502i
$340$	3.94931	+	7.62461i	0.214181	+	0.413502i
$341$	−10.2055	+	5.89217i	−0.552661	+	0.319079i
$342$	−2.41864	+	8.71592i	−0.130785	+	0.471303i
$343$	−1.64162	−	1.64162i	−0.0886393	−	0.0886393i
$344$	3.49691	+	2.01894i	0.188541	+	0.108854i
$345$	22.6099	+	1.13422i	1.21728	+	0.0610642i
$346$			1.04345i			0.0560963i
$347$	−2.07408	−	7.74058i	−0.111343	−	0.415536i	0.887645	−	0.460529i	$-0.152340\pi$
$347$	−2.07408	−	7.74058i	−0.111343	−	0.415536i	−0.998987	+	0.0449927i	$0.985674\pi$
$348$	5.88790	+	3.43435i	0.315625	+	0.184101i
$349$	−9.47261	−	16.4070i	−0.507057	−	0.878249i	−0.999967	−	0.00816849i	$-0.997400\pi$
$349$	−9.47261	−	16.4070i	−0.507057	−	0.878249i	0.492909	−	0.870081i	$-0.335933\pi$
$350$	0.0831667	−	0.907799i	0.00444545	−	0.0485239i
$351$	−14.5054	−	11.8572i	−0.774241	−	0.632891i
$352$	14.4402	+	14.4402i	0.769666	+	0.769666i
$353$	2.20043	+	0.589602i	0.117117	+	0.0313814i	0.316901	−	0.948458i	$-0.397358\pi$
$353$	2.20043	+	0.589602i	0.117117	+	0.0313814i	−0.199785	+	0.979840i	$0.564024\pi$
$354$	−4.74478	−	18.0278i	−0.252182	−	0.958166i
$355$	1.31853	+	6.00565i	0.0699805	+	0.318747i
$356$	5.50091			0.291547
$357$	0.00616913	−	1.38840i	0.000326505	−	0.0734820i
$358$	−17.3100	+	4.63820i	−0.914862	+	0.245136i
$359$			9.83095i			0.518858i	0.965762	+	0.259429i	$0.0835343\pi$
$359$			9.83095i			0.518858i	−0.965762	+	0.259429i	$0.916466\pi$
$360$	18.3580	−	9.30290i	0.967551	−	0.490306i
$361$	5.72483	+	9.91569i	0.301307	+	0.521878i
$362$	3.53460	−	13.1913i	0.185774	−	0.693319i
$363$	10.9719	+	19.2004i	0.575876	+	1.00776i
$364$	0.383326	−	0.283647i	0.0200918	−	0.0148671i
$365$	−17.2225	−	0.787261i	−0.901469	−	0.0412071i
$366$	−26.4917	+	6.97241i	−1.38474	+	0.364454i
$367$	3.06044	−	11.4217i	0.159754	−	0.596209i	−0.838897	−	0.544289i	$-0.816799\pi$
$367$	3.06044	−	11.4217i	0.159754	−	0.596209i	0.998651	−	0.0519198i	$-0.0165340\pi$
$368$	10.0187	−	2.68449i	0.522259	−	0.139939i
$369$	−6.58129	+	11.1687i	−0.342608	+	0.581421i
$370$	−2.44556	−	11.1390i	−0.127138	−	0.579089i
$371$	−0.393194	+	0.681033i	−0.0204136	+	0.0353575i
$372$	−1.65342	−	2.89343i	−0.0857260	−	0.150017i
$373$	−6.36680	−	23.7612i	−0.329661	−	1.23031i	−0.909543	−	0.415610i	$-0.863568\pi$
$373$	−6.36680	−	23.7612i	−0.329661	−	1.23031i	0.579882	−	0.814700i	$-0.303099\pi$
$374$	12.9039	+	22.3502i	0.667246	+	1.15570i
$375$	−19.2249	+	2.32434i	−0.992770	+	0.120028i
$376$	−15.5436			−0.801602
$377$	−2.63488	+	17.6304i	−0.135703	+	0.908013i
$378$	−0.947279	−	0.0126279i	−0.0487228	−	0.000649509i
$379$	7.85016	+	13.5969i	0.403236	+	0.698425i	0.994114	−	0.108336i	$-0.0345522\pi$
$379$	7.85016	+	13.5969i	0.403236	+	0.698425i	−0.590879	+	0.806760i	$0.701219\pi$
$380$	−1.48020	+	4.66131i	−0.0759325	+	0.239120i
$381$	1.72400	+	1.73939i	0.0883233	+	0.0891117i
$382$	2.23105	−	2.23105i	0.114150	−	0.114150i
$383$	0.618182	+	2.30709i	0.0315876	+	0.117887i	0.979920	−	0.199393i	$-0.0638972\pi$
$383$	0.618182	+	2.30709i	0.0315876	+	0.117887i	−0.948332	+	0.317280i	$0.897231\pi$
$384$	0.688812	−	0.682718i	0.0351508	−	0.0348398i
$385$	−0.0827111	+	1.80943i	−0.00421535	+	0.0922172i
$386$	−10.0299	−	5.79076i	−0.510508	−	0.294742i
$387$	−2.81666	+	2.76704i	−0.143179	+	0.140656i
$388$	−3.47274	+	12.9604i	−0.176302	+	0.657966i
$389$	14.0757			0.713666			0.356833	−	0.934168i	$-0.383857\pi$
$389$	14.0757			0.713666			0.356833	+	0.934168i	$0.383857\pi$
$390$	11.4987	+	10.1274i	0.582259	+	0.512821i
$391$	−28.1994			−1.42611
$392$	−5.53642	+	20.6622i	−0.279631	+	1.04360i
$393$	1.85319	+	1.08095i	0.0934812	+	0.0545266i
$394$	−18.7031	−	10.7982i	−0.942247	−	0.544007i
$395$	−11.1430	−	12.2105i	−0.560666	−	0.614379i
$396$	−10.1333	+	5.73101i	−0.509218	+	0.287994i
$397$	−8.32246	−	31.0598i	−0.417692	−	1.55885i	−0.779382	−	0.626549i	$-0.784467\pi$
$397$	−8.32246	−	31.0598i	−0.417692	−	1.55885i	0.361690	−	0.932299i	$-0.382200\pi$
$398$	−9.78628	+	9.78628i	−0.490542	+	0.490542i
$399$	0.561653	−	0.556683i	0.0281178	−	0.0278690i
$400$	−8.05633	+	3.71667i	−0.402816	+	0.185833i
$401$	0.597410	+	1.03474i	0.0298332	+	0.0516726i	0.880557	−	0.473941i	$-0.157169\pi$
$401$	0.597410	+	1.03474i	0.0298332	+	0.0516726i	−0.850723	+	0.525614i	$0.823836\pi$
$402$	−0.685589	−	1.19975i	−0.0341941	−	0.0598383i
$403$	5.42542	−	6.82069i	0.270259	−	0.339763i
$404$	12.0960			0.601798
$405$	3.96553	+	19.7300i	0.197049	+	0.980394i
$406$	0.450705	+	0.780645i	0.0223681	+	0.0387427i
$407$	5.86484	+	21.8879i	0.290709	+	1.08494i
$408$	−22.2583	+	12.7193i	−1.10195	+	0.629699i
$409$	−8.93012	+	15.4674i	−0.441566	+	0.764815i	−0.997806	−	0.0662068i	$-0.978910\pi$
$409$	−8.93012	+	15.4674i	−0.441566	+	0.764815i	0.556240	+	0.831022i	$0.312244\pi$
$410$	5.71497	−	8.93033i	0.282242	−	0.441037i
$411$	1.84968	−	6.78242i	0.0912381	−	0.334552i
$412$	13.4925	−	3.61530i	0.664728	−	0.178113i
$413$	−0.421815	+	1.57423i	−0.0207562	+	0.0774630i
$414$	−0.170989	+	19.2407i	−0.00840364	+	0.945628i
$415$	−0.232480	+	5.08586i	−0.0114120	+	0.249655i
$416$	−13.8505	−	6.02235i	−0.679076	−	0.295270i
$417$	−11.1078	+	6.34748i	−0.543954	+	0.310837i
$418$	−3.80444	+	14.1983i	−0.186081	+	0.694464i
$419$	−5.31145	−	9.19969i	−0.259481	−	0.449435i	0.706622	−	0.707591i	$-0.250218\pi$
$419$	−5.31145	−	9.19969i	−0.259481	−	0.449435i	−0.966103	+	0.258157i	$0.916885\pi$
$420$	−0.511586	−	0.0256635i	−0.0249628	−	0.00125225i
$421$		−	23.8749i		−	1.16359i	−0.813335	−	0.581796i	$-0.802350\pi$
$421$		−	23.8749i		−	1.16359i	0.813335	−	0.581796i	$-0.197650\pi$
$422$	5.09512	−	1.36523i	0.248026	−	0.0664585i
$423$	4.06418	−	14.6458i	0.197607	−	0.712105i
$424$	14.5201			0.705160
$425$	23.7724	−	4.09148i	1.15313	−	0.198466i
$426$	−5.05395	+	1.33016i	−0.244865	+	0.0644466i
$427$	2.31332	+	0.619853i	0.111950	+	0.0299968i
$428$	−1.22846	−	1.22846i	−0.0593798	−	0.0593798i
$429$	−23.7426	−	19.0585i	−1.14630	−	0.920155i
$430$	2.38533	−	2.17679i	0.115031	−	0.104974i
$431$	−8.35107	−	14.4645i	−0.402257	−	0.696729i	0.591741	−	0.806128i	$-0.298441\pi$
$431$	−8.35107	−	14.4645i	−0.402257	−	0.696729i	−0.993998	+	0.109399i	$0.965107\pi$
$432$	4.50335	+	8.04583i	0.216667	+	0.387105i
$433$	−7.11463	−	26.5522i	−0.341907	−	1.27602i	−0.896184	−	0.443683i	$-0.853672\pi$
$433$	−7.11463	−	26.5522i	−0.341907	−	1.27602i	0.554277	−	0.832333i	$-0.312995\pi$
$434$		−	0.440704i		−	0.0211545i
$435$	14.2014	−	12.8446i	0.680904	−	0.615852i
$436$	7.10530	+	4.10225i	0.340282	+	0.196462i
$437$	−11.3571	−	11.3571i	−0.543284	−	0.543284i
$438$	0.0651100	−	14.6534i	0.00311108	−	0.700168i
$439$	−16.5480	+	9.55397i	−0.789791	+	0.455986i	−0.839889	−	0.542758i	$-0.817380\pi$
$439$	−16.5480	+	9.55397i	−0.789791	+	0.455986i	0.0500980	+	0.998744i	$0.484047\pi$
$440$	29.6975	−	15.3824i	1.41577	−	0.733326i
$441$	−18.0212	−	10.6192i	−0.858150	−	0.505674i
$442$	−14.9374	−	11.8817i	−0.710499	−	0.565156i
$443$	8.74698	+	8.74698i	0.415581	+	0.415581i	0.883678	−	0.468096i	$-0.155060\pi$
$443$	8.74698	+	8.74698i	0.415581	+	0.415581i	−0.468096	+	0.883678i	$0.655060\pi$
$444$	−6.19704	+	1.63101i	−0.294098	+	0.0774045i
$445$	4.67701	−	14.7284i	0.221712	−	0.698195i
$446$	10.8376	+	6.25711i	0.513177	+	0.296283i
$447$	8.77406	−	5.01386i	0.414999	−	0.237147i
$448$	−1.30727	+	0.350283i	−0.0617629	+	0.0165493i
$449$	−25.7950	−	14.8928i	−1.21734	−	0.702834i	−0.252994	−	0.967468i	$-0.581415\pi$
$449$	−25.7950	−	14.8928i	−1.21734	−	0.702834i	−0.964349	+	0.264634i	$0.914749\pi$
$450$	−2.64750	−	16.2449i	−0.124804	−	0.765790i
$451$	−10.5333	+	18.2443i	−0.495996	+	0.859090i
$452$	11.4791	+	3.07582i	0.539932	+	0.144674i
$453$	−24.6263	−	14.3643i	−1.15705	−	0.674893i
$454$			29.1364i			1.36744i
$455$	−0.433538	−	1.26750i	−0.0203246	−	0.0594215i
$456$	−14.0870	−	3.84176i	−0.659682	−	0.179907i
$457$	−3.37500	−	0.904330i	−0.157876	−	0.0423028i	0.179015	−	0.983846i	$-0.442709\pi$
$457$	−3.37500	−	0.904330i	−0.157876	−	0.0423028i	−0.336891	+	0.941544i	$0.609376\pi$
$458$	−1.81433	+	6.77119i	−0.0847783	+	0.316397i
$459$	−6.16479	−	24.2983i	−0.287748	−	1.13415i
$460$	−0.475065	+	10.3928i	−0.0221500	+	0.484566i
$461$	1.56492	−	2.71052i	0.0728856	−	0.126242i	−0.827279	−	0.561791i	$-0.810113\pi$
$461$	1.56492	−	2.71052i	0.0728856	−	0.126242i	0.900165	+	0.435549i	$0.143446\pi$
$462$	−1.53952	−	0.00684058i	−0.0716248	−	0.000318253i
$463$	27.4762	+	27.4762i	1.27693	+	1.27693i	0.942379	+	0.334548i	$0.108584\pi$
$463$	27.4762	+	27.4762i	1.27693	+	1.27693i	0.334548	+	0.942379i	$0.391416\pi$
$464$	4.38657	−	7.59776i	0.203641	−	0.352717i
$465$	−9.15281	+	1.96690i	−0.424452	+	0.0912130i
$466$	17.3414	−	10.0121i	0.803327	−	0.463801i
$467$	−20.4027	+	20.4027i	−0.944124	+	0.944124i	−0.998519	−	0.0543954i	$-0.982677\pi$
$467$	−20.4027	+	20.4027i	−0.944124	+	0.944124i	0.0543954	+	0.998519i	$0.482677\pi$
$468$	5.41940	−	6.69022i	0.250512	−	0.309255i
$469$			0.120807i			0.00557836i
$470$	−3.76231	+	11.8479i	−0.173542	+	0.546504i
$471$	−12.2105	+	3.21371i	−0.562629	+	0.148080i
$472$	29.0672	−	7.78853i	1.33793	−	0.358496i
$473$	−4.53712	+	4.53712i	−0.208617	+	0.208617i
$474$	9.97908	−	9.89079i	0.458354	−	0.454299i
$475$	11.2219	+	7.92632i	0.514898	+	0.363685i
$476$	0.638057			0.0292453
$477$	−3.79656	+	13.6815i	−0.173833	+	0.626431i
$478$	−3.39961	−	0.910923i	−0.155495	−	0.0416647i
$479$	0.117001	−	0.0675507i	0.00534593	−	0.00308647i	−0.497325	−	0.867565i	$-0.665684\pi$
$479$	0.117001	−	0.0675507i	0.00534593	−	0.00308647i	0.502671	+	0.864478i	$0.332351\pi$
$480$	7.39758	+	14.4386i	0.337652	+	0.659029i
$481$	−9.96841	−	13.4715i	−0.454520	−	0.614248i
$482$	−4.65873	+	4.65873i	−0.212199	+	0.212199i
$483$	0.847564	−	1.45308i	0.0385655	−	0.0661172i
$484$	−8.80122	+	5.08139i	−0.400056	+	0.230972i
$485$	31.7484	+	20.3174i	1.44162	+	0.922565i
$486$	−16.6163	+	4.05895i	−0.753732	+	0.184118i
$487$	2.52502	+	9.42349i	0.114419	+	0.427019i	0.999243	−	0.0389075i	$-0.0123878\pi$
$487$	2.52502	+	9.42349i	0.114419	+	0.427019i	−0.884823	+	0.465927i	$0.845721\pi$
$488$	−11.4452	−	42.7140i	−0.518099	−	1.93357i
$489$	−10.0146	+	36.7217i	−0.452878	+	1.66061i
$490$	14.4094	+	9.22130i	0.650950	+	0.416576i
$491$	−18.8733	+	10.8965i	−0.851741	+	0.491753i	−0.861238	−	0.508202i	$-0.830310\pi$
$491$	−18.8733	+	10.8965i	−0.851741	+	0.491753i	0.00949666	+	0.999955i	$0.496977\pi$
$492$	−5.14607	−	3.00165i	−0.232003	−	0.135325i
$493$	−16.8661	+	16.8661i	−0.759610	+	0.759610i
$494$	−1.23064	−	10.8012i	−0.0553693	−	0.485969i
$495$	6.72894	+	32.0042i	0.302443	+	1.43848i
$496$	−3.71458	+	2.14462i	−0.166790	+	0.0962961i
$497$	0.441325	+	0.118253i	0.0197961	+	0.00530436i
$498$	−4.32719	−	0.0192272i	−0.193906	−	0.000861589i
$499$	−18.1795			−0.813827			−0.406913	−	0.913467i	$-0.633395\pi$
$499$	−18.1795			−0.813827			−0.406913	+	0.913467i	$0.633395\pi$
$500$	−1.10741	−	8.83013i	−0.0495250	−	0.394895i
$501$	−17.2728	−	17.4270i	−0.771693	−	0.778581i
$502$	19.0508	−	19.0508i	0.850278	−	0.850278i
$503$	−7.30144	+	1.95641i	−0.325555	+	0.0872322i	−0.417895	−	0.908495i	$-0.637232\pi$
$503$	−7.30144	+	1.95641i	−0.325555	+	0.0872322i	0.0923400	+	0.995728i	$0.470565\pi$
$504$	0.0135900	−	1.52923i	0.000605347	−	0.0681173i
$505$	10.2843	−	32.3865i	0.457646	−	1.44118i
$506$			31.2687i			1.39006i
$507$	21.5033	+	6.67883i	0.954996	+	0.296617i
$508$	−0.795823	+	0.795823i	−0.0353089	+	0.0353089i
$509$	38.2650	−	22.0923i	1.69607	−	0.979224i	0.746643	−	0.665225i	$-0.231664\pi$
$509$	38.2650	−	22.0923i	1.69607	−	0.979224i	0.949423	−	0.313999i	$-0.101669\pi$
$510$	4.30754	+	20.0448i	0.190741	+	0.887597i
$511$	−0.640550	+	1.10947i	−0.0283363	+	0.0490799i
$512$	12.9549	+	12.9549i	0.572530	+	0.572530i
$513$	7.30315	−	12.2688i	0.322442	−	0.541681i
$514$	2.63814	−	4.56940i	0.116364	−	0.201548i
$515$	1.79185	−	39.1994i	0.0789582	−	1.72733i
$516$	−1.27735	−	1.28875i	−0.0562323	−	0.0567342i
$517$	6.39281	−	23.8583i	0.281155	−	1.04929i
$518$	−0.818549	−	0.219330i	−0.0359650	−	0.00963679i
$519$	0.433362	−	1.58905i	0.0190225	−	0.0697516i
$520$	−16.2656	+	18.6343i	−0.713294	+	0.817169i
$521$		−	33.6427i		−	1.47391i	−0.675940	−	0.736956i	$-0.736262\pi$
$521$		−	33.6427i		−	1.47391i	0.675940	−	0.736956i	$-0.263738\pi$
$522$	11.4056	+	11.6101i	0.499209	+	0.508161i
$523$	30.4447	+	8.15764i	1.33125	+	0.356709i	0.853183	−	0.521612i	$-0.174669\pi$
$523$	30.4447	+	8.15764i	1.33125	+	0.356709i	0.478072	+	0.878321i	$0.341336\pi$
$524$	−0.492969	+	0.853848i	−0.0215355	+	0.0373005i
$525$	−0.503676	+	1.34793i	−0.0219822	+	0.0588284i
$526$	11.1916	+	6.46150i	0.487979	+	0.281735i
$527$	11.2641	−	3.01821i	0.490673	−	0.131475i
$528$	7.43415	+	13.0095i	0.323530	+	0.566165i
$529$	−9.67033	−	5.58317i	−0.420449	−	0.242746i
$530$	3.51457	−	11.0678i	0.152663	−	0.480754i
$531$	−0.261493	+	29.4247i	−0.0113478	+	1.27692i
$532$	0.256973	+	0.256973i	0.0111412	+	0.0111412i
$533$	2.30290	−	15.4091i	0.0997498	−	0.667444i
$534$	12.6717	+	3.45578i	0.548356	+	0.149546i
$535$	−4.33361	+	2.24468i	−0.187358	+	0.0970460i
$536$	1.93178	−	1.11531i	0.0834400	−	0.0481741i
$537$	28.2874	+	0.125690i	1.22069	+	0.00542393i
$538$	−1.00647	−	1.00647i	−0.0433920	−	0.0433920i
$539$	−29.4378	−	16.9959i	−1.26798	−	0.732067i
$540$	−9.05891	+	1.86266i	−0.389833	+	0.0801562i
$541$			31.8172i			1.36793i	0.729516	+	0.683964i	$0.239745\pi$
$541$			31.8172i			1.36793i	−0.729516	+	0.683964i	$0.760255\pi$
$542$	1.73933	+	6.49126i	0.0747105	+	0.278823i
$543$	−10.8613	+	18.6208i	−0.466103	+	0.799094i
$544$	−10.1043	−	17.5012i	−0.433218	−	0.750356i
$545$	17.0247	−	15.5363i	0.729258	−	0.665502i
$546$	1.06121	−	0.412584i	0.0454155	−	0.0176569i
$547$	3.86162	+	3.86162i	0.165111	+	0.165111i	0.784826	−	0.619716i	$-0.212752\pi$
$547$	3.86162	+	3.86162i	0.165111	+	0.165111i	−0.619716	+	0.784826i	$0.712752\pi$
$548$	3.12066	+	0.836179i	0.133308	+	0.0357198i
$549$	43.2394	+	0.384261i	1.84541	+	0.0163999i
$550$	−4.53680	−	26.3598i	−0.193450	−	1.12398i
$551$	−13.5854			−0.578756
$552$	−31.0604	−	0.138011i	−1.32202	−	0.00587416i
$553$	−1.18650	+	0.317922i	−0.0504551	+	0.0135194i
$554$		−	11.4120i		−	0.484850i
$555$	−0.901911	+	17.9790i	−0.0382840	+	0.763167i
$556$	−2.93969	−	5.09169i	−0.124671	−	0.215936i
$557$	1.87374	−	6.99288i	0.0793928	−	0.296298i	−0.914801	−	0.403906i	$-0.867652\pi$
$557$	1.87374	−	6.99288i	0.0793928	−	0.296298i	0.994193	+	0.107608i	$0.0343191\pi$
$558$	−1.99105	−	7.70389i	−0.0842878	−	0.326132i
$559$	1.89223	−	4.35183i	0.0800327	−	0.184063i
$560$	−0.0301049	+	0.658592i	−0.00127217	+	0.0278306i
$561$	−10.3687	−	39.3959i	−0.437767	−	1.66330i
$562$	−6.22723	+	23.2403i	−0.262680	+	0.980334i
$563$	−3.52688	+	0.945024i	−0.148640	+	0.0398280i	−0.332372	−	0.943148i	$-0.607849\pi$
$563$	−3.52688	+	0.945024i	−0.148640	+	0.0398280i	0.183732	+	0.982976i	$0.441182\pi$
$564$	6.73885	+	1.83780i	0.283757	+	0.0773853i
$565$	17.9952	−	28.1197i	0.757063	−	1.18300i
$566$	3.04122	−	5.26755i	0.127832	−	0.221412i
$567$	1.43735	+	0.412650i	0.0603629	+	0.0173297i
$568$	−2.18346	−	8.14877i	−0.0916158	−	0.341915i
$569$	19.6847	+	34.0948i	0.825224	+	1.42933i	0.901748	+	0.432262i	$0.142285\pi$
$569$	19.6847	+	34.0948i	0.825224	+	1.42933i	−0.0765237	+	0.997068i	$0.524382\pi$
$570$	−6.33804	+	9.80770i	−0.265471	+	0.410799i
$571$	40.5072			1.69517			0.847586	−	0.530658i	$-0.178055\pi$
$571$	40.5072			1.69517			0.847586	+	0.530658i	$0.178055\pi$
$572$	8.70994	−	10.9499i	0.364181	−	0.457839i
$573$	−4.32420	+	2.47103i	−0.180646	+	0.103229i
$574$	−0.393920	−	0.682289i	−0.0164419	−	0.0284782i
$575$	27.4223	+	10.1082i	1.14359	+	0.421540i
$576$	−21.2698	+	12.0294i	−0.886241	+	0.501224i
$577$	−24.8261	+	24.8261i	−1.03352	+	1.03352i	−0.0341041	+	0.999418i	$0.510858\pi$
$577$	−24.8261	+	24.8261i	−1.03352	+	1.03352i	−0.999418	+	0.0341041i	$0.989142\pi$
$578$	−1.78197	−	6.65039i	−0.0741200	−	0.276620i
$579$	12.8693	+	12.9842i	0.534831	+	0.539605i
$580$	5.93179	+	6.50006i	0.246304	+	0.269900i
$581$	0.327628	+	0.189156i	0.0135923	+	0.00784752i
$582$	−16.1417	+	27.6735i	−0.669093	+	1.14710i
$583$	−5.97186	+	22.2873i	−0.247329	+	0.923044i
$584$	23.6547			0.978836
$585$	−13.3051	−	20.1984i	−0.550096	−	0.835101i
$586$	−5.37420			−0.222006
$587$	−0.00360950	+	0.0134708i	−0.000148980	+	0.000556001i	−0.966000	−	0.258541i	$-0.916758\pi$
$587$	−0.00360950	+	0.0134708i	−0.000148980	+	0.000556001i	0.965851	+	0.259097i	$0.0834249\pi$
$588$	4.84327	−	8.30337i	0.199733	−	0.342425i
$589$	5.75210	+	3.32098i	0.237011	+	0.136838i
$590$	1.09895	−	24.0413i	0.0452431	−	0.989763i
$591$	23.9979	+	24.2121i	0.987140	+	0.995951i
$592$	2.13466	+	7.96668i	0.0877342	+	0.327428i
$593$	−25.7961	+	25.7961i	−1.05932	+	1.05932i	−0.0611927	+	0.998126i	$0.519490\pi$
$593$	−25.7961	+	25.7961i	−1.05932	+	1.05932i	−0.998126	+	0.0611927i	$0.980510\pi$
$594$	−26.9430	+	6.83577i	−1.10549	+	0.280475i
$595$	0.542492	−	1.70837i	0.0222400	−	0.0700363i
$596$	2.32205	+	4.02191i	0.0951150	+	0.164744i
$597$	18.9677	−	10.8389i	0.776297	−	0.443608i
$598$	−8.47547	−	21.5162i	−0.346588	−	0.879864i
$599$	−28.2847			−1.15568			−0.577841	−	0.816149i	$-0.696105\pi$
$599$	−28.2847			−1.15568			−0.577841	+	0.816149i	$0.696105\pi$
$600$	26.2042	−	4.39023i	1.06978	−	0.179230i
$601$	8.59509	+	14.8871i	0.350601	+	0.607259i	0.986355	−	0.164633i	$-0.0526440\pi$
$601$	8.59509	+	14.8871i	0.350601	+	0.607259i	−0.635754	+	0.771892i	$0.719311\pi$
$602$	−0.0621060	−	0.231783i	−0.00253125	−	0.00944675i
$603$	0.545792	+	2.11182i	0.0222264	+	0.0859998i
$604$	6.55087	−	11.3464i	0.266551	−	0.461680i
$605$	6.12217	+	27.8852i	0.248902	+	1.13370i
$606$	27.8638	+	7.59895i	1.13189	+	0.308686i
$607$	−11.8481	+	3.17469i	−0.480900	+	0.128857i	−0.491121	−	0.871091i	$-0.663413\pi$
$607$	−11.8481	+	3.17469i	−0.480900	+	0.128857i	0.0102219	+	0.999948i	$0.496746\pi$
$608$	2.97903	−	11.1179i	0.120816	−	0.450890i
$609$	−0.362156	−	1.37601i	−0.0146753	−	0.0557588i
$610$	−35.3284	−	1.61490i	−1.43041	−	0.0653854i
$611$	2.06792	+	18.1498i	0.0836591	+	0.734264i
$612$	11.1538	−	2.88267i	0.450866	−	0.116525i
$613$	−2.76430	+	10.3165i	−0.111649	+	0.416680i	−0.999014	−	0.0443871i	$-0.985866\pi$
$613$	−2.76430	+	10.3165i	−0.111649	+	0.416680i	0.887365	+	0.461067i	$0.152533\pi$
$614$	−12.1926	−	21.1181i	−0.492052	−	0.852259i
$615$	−12.4121	+	11.2263i	−0.500504	+	0.452688i
$616$		−	2.48520i		−	0.100132i
$617$	−4.38758	+	1.17565i	−0.176637	+	0.0473299i	−0.346054	−	0.938215i	$-0.612478\pi$
$617$	−4.38758	+	1.17565i	−0.176637	+	0.0473299i	0.169416	+	0.985545i	$0.445812\pi$
$618$	33.3520	+	0.148194i	1.34161	+	0.00596123i
$619$	31.2573			1.25634			0.628168	−	0.778078i	$-0.283805\pi$
$619$	31.2573			1.25634			0.628168	+	0.778078i	$0.283805\pi$
$620$	−0.922587	−	4.20219i	−0.0370520	−	0.168764i
$621$	8.25135	−	29.2302i	0.331115	−	1.17297i
$622$	−28.9350	−	7.75311i	−1.16019	−	0.310871i
$623$	−0.811962	−	0.811962i	−0.0325306	−	0.0325306i
$624$	−8.64176	−	6.93687i	−0.345947	−	0.277697i
$625$	−24.5838	−	4.54255i	−0.983354	−	0.181702i
$626$	−10.0949	−	17.4849i	−0.403473	−	0.698835i
$627$	11.6905	−	20.0423i	0.466873	−	0.800413i
$628$	−1.50180	−	5.60480i	−0.0599285	−	0.223656i
$629$		−	22.4237i		−	0.894092i
$630$	−1.16234	−	0.380506i	−0.0463089	−	0.0151597i
$631$	31.2944	+	18.0678i	1.24581	+	0.719270i	0.970271	−	0.242020i	$-0.0778099\pi$
$631$	31.2944	+	18.0678i	1.24581	+	0.719270i	0.275540	+	0.961289i	$0.411143\pi$
$632$	16.0377	+	16.0377i	0.637946	+	0.637946i
$633$	−8.32625	−	0.0369963i	−0.330939	−	0.00147047i
$634$	8.93599	−	5.15920i	0.354893	−	0.204898i
$635$	1.45415	+	2.80741i	0.0577062	+	0.111409i
$636$	−6.29511	−	1.71679i	−0.249617	−	0.0680750i
$637$	24.8632	+	3.71582i	0.985115	+	0.147226i
$638$	18.7018	+	18.7018i	0.740411	+	0.740411i
$639$	8.24900	+	0.0733075i	0.326325	+	0.00290000i
$640$	1.11176	−	0.575855i	0.0439460	−	0.0227627i
$641$	−30.0234	−	17.3340i	−1.18585	−	0.684653i	−0.228492	−	0.973546i	$-0.573380\pi$
$641$	−30.0234	−	17.3340i	−1.18585	−	0.684653i	−0.957361	+	0.288893i	$0.906713\pi$
$642$	−2.05808	−	3.60157i	−0.0812261	−	0.142143i
$643$	−27.4633	+	7.35878i	−1.08305	+	0.290202i	−0.755844	−	0.654752i	$-0.772773\pi$
$643$	−27.4633	+	7.35878i	−1.08305	+	0.290202i	−0.327204	+	0.944954i	$0.606107\pi$
$644$	0.669496	+	0.386534i	0.0263819	+	0.0152316i
$645$	−4.53662	+	2.32432i	−0.178629	+	0.0915201i
$646$	7.27297	−	12.5972i	0.286151	−	0.495628i
$647$	−2.90637	−	0.778760i	−0.114261	−	0.0306162i	0.201235	−	0.979543i	$-0.435504\pi$
$647$	−2.90637	−	0.778760i	−0.114261	−	0.0306162i	−0.315497	+	0.948927i	$0.602171\pi$
$648$	−6.67131	−	26.7937i	−0.262074	−	1.05255i
$649$			47.8191i			1.87706i
$650$	10.2667	+	16.9086i	0.402693	+	0.663211i
$651$	−0.183031	+	0.671139i	−0.00717356	+	0.0263040i
$652$	−16.8960	−	4.52728i	−0.661700	−	0.177302i
$653$	1.89279	−	7.06400i	0.0740707	−	0.276436i	−0.918950	−	0.394373i	$-0.870962\pi$
$653$	1.89279	−	7.06400i	0.0740707	−	0.276436i	0.993021	+	0.117938i	$0.0376283\pi$
$654$	13.7904	+	13.9135i	0.539246	+	0.544059i
$655$	1.86701	+	2.04587i	0.0729500	+	0.0799387i
$656$	−3.83390	+	6.64050i	−0.149689	+	0.259268i
$657$	−6.18495	+	22.2884i	−0.241298	+	0.869552i
$658$	0.653163	+	0.653163i	0.0254630	+	0.0254630i
$659$	17.7103	−	30.6751i	0.689894	−	1.19493i	−0.281978	−	0.959421i	$-0.590990\pi$
$659$	17.7103	−	30.6751i	0.689894	−	1.19493i	0.971872	−	0.235511i	$-0.0756762\pi$
$660$	−14.6939	+	3.15766i	−0.571959	+	0.122912i
$661$	29.1120	−	16.8078i	1.13233	−	0.653748i	0.187807	−	0.982206i	$-0.439862\pi$
$661$	29.1120	−	16.8078i	1.13233	−	0.653748i	0.944519	+	0.328458i	$0.106529\pi$
$662$	−4.92901	+	4.92901i	−0.191571	+	0.191571i
$663$	17.8132	+	24.2982i	0.691806	+	0.943662i
$664$		−	6.98528i		−	0.271081i
$665$	0.906518	−	0.469548i	0.0351533	−	0.0182083i
$666$	−15.2999	−	0.135967i	−0.592858	−	0.00526863i
$667$	−27.9146	+	7.47969i	−1.08086	+	0.289615i
$668$	7.97337	−	7.97337i	0.308499	−	0.308499i
$669$	−13.9057	−	14.0299i	−0.537627	−	0.542426i
$670$	−0.382549	−	1.74243i	−0.0147791	−	0.0673159i
$671$	70.2698			2.71273
$672$	1.20551	+	0.00535646i	0.0465034	+	0.000206630i
$673$	−17.7364	−	4.75245i	−0.683688	−	0.183194i	−0.0997751	−	0.995010i	$-0.531812\pi$
$673$	−17.7364	−	4.75245i	−0.683688	−	0.183194i	−0.583913	+	0.811816i	$0.698479\pi$
$674$	−16.9200	+	9.76878i	−0.651735	+	0.376279i
$675$	−2.71492	+	25.8385i	−0.104497	+	0.994525i
$676$	−3.02537	+	9.89557i	−0.116360	+	0.380599i
$677$	−30.5372	+	30.5372i	−1.17364	+	1.17364i	−0.192303	+	0.981336i	$0.561596\pi$
$677$	−30.5372	+	30.5372i	−1.17364	+	1.17364i	−0.981336	+	0.192303i	$0.938404\pi$
$678$	24.5105	+	14.2967i	0.941319	+	0.549062i
$679$	2.42562	−	1.40043i	0.0930868	−	0.0537437i
$680$	−32.3262	+	7.09719i	−1.23965	+	0.272165i
$681$	12.1008	−	44.3712i	0.463703	−	1.70031i
$682$	−3.34672	−	12.4901i	−0.128152	−	0.478271i
$683$	6.30369	+	23.5257i	0.241204	+	0.900186i	0.975253	+	0.221090i	$0.0709614\pi$
$683$	6.30369	+	23.5257i	0.241204	+	0.900186i	−0.734049	+	0.679096i	$0.762372\pi$
$684$	5.65308	+	3.33114i	0.216151	+	0.127369i
$685$	4.89210	−	7.64449i	0.186917	−	0.292081i
$686$	2.20616	−	1.27372i	0.0842314	−	0.0486310i
$687$	5.57519	−	9.55818i	0.212707	−	0.364667i
$688$	−1.65141	+	1.65141i	−0.0629594	+	0.0629594i
$689$	−1.93175	−	16.9547i	−0.0735940	−	0.645924i
$690$	−7.62329	+	23.6419i	−0.290214	+	0.900033i
$691$	0.523687	−	0.302351i	0.0199220	−	0.0115020i	−0.490006	−	0.871719i	$-0.663005\pi$
$691$	0.523687	−	0.302351i	0.0199220	−	0.0115020i	0.509928	+	0.860217i	$0.329672\pi$
$692$	0.731139	+	0.195908i	0.0277937	+	0.00744731i
$693$	2.34166	+	0.649802i	0.0889522	+	0.0246839i
$694$	8.79320			0.333785
$695$	−16.1322	+	3.54180i	−0.611928	+	0.134348i
$696$	−18.6597	+	18.4947i	−0.707296	+	0.701038i
$697$	14.7411	−	14.7411i	0.558358	−	0.558358i
$698$	20.0799	−	5.38038i	0.760034	−	0.203651i
$699$	−30.5671	+	8.04503i	−1.15615	+	0.304291i
$700$	−0.620474	−	0.228714i	−0.0234517	−	0.00864456i
$701$		−	35.7248i		−	1.34931i	−0.738134	−	0.674654i	$-0.764293\pi$
$701$		−	35.7248i		−	1.34931i	0.738134	−	0.674654i	$-0.235707\pi$
$702$	16.6868	−	12.0067i	0.629804	−	0.453165i
$703$	9.03098	−	9.03098i	0.340610	−	0.340610i
$704$	−34.3898	+	19.8550i	−1.29611	+	0.748312i
$705$	10.6502	−	16.4804i	0.401109	−	0.620689i
$706$	−1.24983	+	2.16477i	−0.0470379	+	0.0814720i
$707$	−1.78543	−	1.78543i	−0.0671481	−	0.0671481i
$708$	−13.5228	−	0.0600861i	−0.508217	−	0.00225817i
$709$	2.01558	−	3.49108i	0.0756966	−	0.131110i	−0.825692	−	0.564121i	$-0.809215\pi$
$709$	2.01558	−	3.49108i	0.0756966	−	0.131110i	0.901389	+	0.433010i	$0.142549\pi$
$710$	−6.73979	−	0.308083i	−0.252940	−	0.0115621i
$711$	−19.3047	+	10.9180i	−0.723984	+	0.409458i
$712$	−5.48757	+	20.4799i	−0.205656	+	0.767517i
$713$	13.6476	+	3.65685i	0.511105	+	0.136950i
$714$	1.46980	+	0.400840i	0.0550059	+	0.0150011i
$715$	−21.9125	−	32.6304i	−0.819480	−	1.22031i
$716$			12.9998i			0.485826i
$717$	4.79888	+	2.79914i	0.179217	+	0.104536i
$718$	−10.4197	−	2.79196i	−0.388861	−	0.104195i
$719$	−18.2661	+	31.6378i	−0.681211	+	1.17989i	0.293400	+	0.955990i	$0.405213\pi$
$719$	−18.2661	+	31.6378i	−0.681211	+	1.17989i	−0.974612	+	0.223903i	$0.928120\pi$
$720$	2.44918	+	11.6488i	0.0912755	+	0.434124i
$721$	−2.52520	−	1.45793i	−0.0940434	−	0.0542960i
$722$	−12.1354	+	3.25166i	−0.451632	+	0.121014i
$723$	9.02953	−	5.15984i	0.335812	−	0.191897i
$724$	−8.57942	−	4.95333i	−0.318852	−	0.184089i
$725$	22.4470	−	10.3556i	0.833660	−	0.384597i
$726$	−23.4663	+	6.17617i	−0.870918	+	0.229219i
$727$	−6.38702	−	6.38702i	−0.236881	−	0.236881i	0.578676	−	0.815557i	$-0.303570\pi$
$727$	−6.38702	−	6.38702i	−0.236881	−	0.236881i	−0.815557	+	0.578676i	$0.803570\pi$
$728$	0.673622	+	1.71009i	0.0249661	+	0.0633800i
$729$	26.9904	+	0.719730i	0.999645	+	0.0266567i
$730$	5.72556	−	18.0304i	0.211912	−	0.667336i
$731$	5.49888	−	3.17478i	0.203383	−	0.117423i
$732$	−0.0882961	+	19.8716i	−0.00326352	+	0.734475i
$733$	−15.5660	−	15.5660i	−0.574943	−	0.574943i	0.358562	−	0.933506i	$-0.383267\pi$
$733$	−15.5660	−	15.5660i	−0.574943	−	0.574943i	−0.933506	+	0.358562i	$0.883267\pi$
$734$	11.2366	+	6.48747i	0.414751	+	0.239457i
$735$	−18.1140	−	20.0274i	−0.668146	−	0.738721i
$736$		−	24.4847i		−	0.902518i
$737$	0.917413	+	3.42383i	0.0337933	+	0.126118i
$738$	−9.96857	−	10.1473i	−0.366948	−	0.373529i
$739$	24.9818	+	43.2698i	0.918972	+	1.59171i	0.800980	+	0.598691i	$0.204312\pi$
$739$	24.9818	+	43.2698i	0.918972	+	1.59171i	0.117992	+	0.993015i	$0.462354\pi$
$740$	−8.26417	−	0.377764i	−0.303797	−	0.0138869i
$741$	−2.61178	+	16.9600i	−0.0959461	+	0.623042i
$742$	−0.610154	−	0.610154i	−0.0223995	−	0.0223995i
$743$	26.5434	+	7.11227i	0.973781	+	0.260924i	0.710424	−	0.703774i	$-0.248503\pi$
$743$	26.5434	+	7.11227i	0.973781	+	0.260924i	0.263358	+	0.964698i	$0.415170\pi$
$744$	12.4217	−	3.26929i	0.455401	−	0.119858i
$745$	12.7428	−	2.79766i	0.466859	−	0.102498i
$746$	26.9925			0.988264
$747$	6.58181	+	1.82643i	0.240816	+	0.0668256i
$748$	18.0834	−	4.84542i	0.661193	−	0.177166i
$749$			0.362654i			0.0132511i
$750$	2.99627	−	21.0364i	0.109408	−	0.768141i
$751$	−8.07976	−	13.9946i	−0.294835	−	0.510669i	0.680112	−	0.733108i	$-0.261931\pi$
$751$	−8.07976	−	13.9946i	−0.294835	−	0.510669i	−0.974946	+	0.222440i	$0.928598\pi$
$752$	2.32683	−	8.68386i	0.0848509	−	0.316668i
$753$	−36.9241	+	21.1000i	−1.34559	+	0.768926i
$754$	−17.9380	−	7.79967i	−0.653265	−	0.284047i
$755$	−24.8099	−	27.1867i	−0.902924	−	0.989425i
$756$	−0.186700	+	0.661381i	−0.00679021	+	0.0240542i
$757$	−3.34586	+	12.4869i	−0.121607	+	0.453845i	−0.999696	−	0.0246532i	$-0.992152\pi$
$757$	−3.34586	+	12.4869i	−0.121607	+	0.453845i	0.878089	+	0.478498i	$0.158819\pi$
$758$	−16.6406	+	4.45884i	−0.604415	+	0.161952i
$759$	12.9864	−	47.6184i	0.471375	−	1.72844i
$760$	−15.8775	−	10.1608i	−0.575936	−	0.368571i
$761$	−13.7581	+	23.8298i	−0.498732	+	0.863828i	−0.999999	−	0.00146412i	$-0.999534\pi$
$761$	−13.7581	+	23.8298i	−0.498732	+	0.863828i	0.501267	+	0.865292i	$0.332867\pi$
$762$	−2.33317	+	1.33327i	−0.0845220	+	0.0482993i
$763$	−0.443266	−	1.65429i	−0.0160473	−	0.0598894i
$764$	−1.14440	−	1.98216i	−0.0414029	−	0.0717119i
$765$	1.76503	−	32.3147i	0.0638149	−	1.16834i
$766$	−2.62082			−0.0946941
$767$	−12.9615	−	32.9047i	−0.468013	−	1.18812i
$768$	−13.4713	−	23.5743i	−0.486105	−	0.850665i
$769$	5.76778	+	9.99009i	0.207992	+	0.360252i	0.951082	−	0.308939i	$-0.0999740\pi$
$769$	5.76778	+	9.99009i	0.207992	+	0.360252i	−0.743090	+	0.669191i	$0.766641\pi$
$770$	−1.89431	−	0.601538i	−0.0682662	−	0.0216779i
$771$	−5.91532	+	5.86298i	−0.213035	+	0.211150i
$772$	−5.94066	+	5.94066i	−0.213809	+	0.213809i
$773$	1.34976	+	5.03736i	0.0485474	+	0.181181i	0.985942	−	0.167088i	$-0.0534363\pi$
$773$	1.34976	+	5.03736i	0.0485474	+	0.181181i	−0.937395	+	0.348269i	$0.886770\pi$
$774$	−2.13283	−	3.77118i	−0.0766631	−	0.135552i
$775$	−12.0356	−	1.10262i	−0.432331	−	0.0396074i
$776$	−44.7875	−	25.8581i	−1.60778	−	0.928250i
$777$	1.15546	+	0.673969i	0.0414519	+	0.0241785i
$778$	−3.99745	+	14.9187i	−0.143316	+	0.534861i
$779$	11.8737			0.425420
$780$	9.25508	−	6.15563i	0.331385	−	0.220407i
$781$	13.4057			0.479695
$782$	8.00855	−	29.8883i	0.286385	−	1.06880i
$783$	−12.5475	−	22.4177i	−0.448410	−	0.801144i
$784$	−10.7147	−	6.18613i	−0.382667	−	0.220933i
$785$	−16.2835	−	0.744336i	−0.581183	−	0.0265665i
$786$	−1.67199	+	1.65720i	−0.0596378	+	0.0591102i
$787$	−10.3710	−	38.7052i	−0.369687	−	1.37969i	−0.860954	−	0.508683i	$-0.830133\pi$
$787$	−10.3710	−	38.7052i	−0.369687	−	1.37969i	0.491267	−	0.871009i	$-0.336534\pi$
$788$	−11.0777	+	11.0777i	−0.394628	+	0.394628i
$789$	−14.3600	−	14.4881i	−0.511228	−	0.515791i
$790$	16.1064	−	8.34263i	0.573041	−	0.296818i
$791$	−1.24037	−	2.14838i	−0.0441024	−	0.0763876i
$792$	−11.2278	−	43.4435i	−0.398964	−	1.54370i
$793$	−48.3532	+	19.0468i	−1.71707	+	0.676373i
$794$	35.2836			1.25217
$795$	−9.94888	+	15.3952i	−0.352851	+	0.546013i
$796$	5.01980	+	8.69455i	0.177922	+	0.308170i
$797$	−8.95658	−	33.4264i	−0.317259	−	1.18402i	−0.921868	−	0.387503i	$-0.873338\pi$
$797$	−8.95658	−	33.4264i	−0.317259	−	1.18402i	0.604610	−	0.796522i	$-0.293329\pi$
$798$	0.430516	+	0.753387i	0.0152401	+	0.0266696i
$799$	−12.2212	+	21.1677i	−0.432354	+	0.748859i
$800$	3.55250	+	20.6408i	0.125600	+	0.729762i
$801$	−17.8622	−	10.5255i	−0.631128	−	0.371899i
$802$	−1.26638	+	0.339325i	−0.0447174	+	0.0119820i
$803$	−9.72871	+	36.3080i	−0.343319	+	1.28128i
$804$	−0.969378	+	0.255133i	−0.0341873	+	0.00899785i
$805$	1.60415	−	1.46391i	0.0565389	−	0.0515959i
$806$	5.68838	+	7.68740i	0.200365	+	0.270777i
$807$	1.11473	+	1.95073i	0.0392403	+	0.0686691i
$808$	−12.0667	+	45.0335i	−0.424504	+	1.58427i
$809$	−0.776492	−	1.34492i	−0.0273000	−	0.0472850i	0.852053	−	0.523456i	$-0.175358\pi$
$809$	−0.776492	−	1.34492i	−0.0273000	−	0.0472850i	−0.879353	+	0.476171i	$0.842024\pi$
$810$	−22.0379	−	1.40024i	−0.774332	−	0.0491994i
$811$			15.7167i			0.551889i	0.961174	+	0.275945i	$0.0889906\pi$
$811$			15.7167i			0.551889i	−0.961174	+	0.275945i	$0.911009\pi$
$812$	0.631612	−	0.169240i	0.0221652	−	0.00593915i
$813$	0.0471338	−	10.6078i	0.00165306	−	0.372031i
$814$	−24.8643			−0.871494
$815$	−26.4870	+	41.3892i	−0.927801	+	1.44980i
$816$	−3.77397	−	14.3392i	−0.132115	−	0.501973i
$817$	3.49325	+	0.936013i	0.122213	+	0.0327470i
$818$	−13.8577	−	13.8577i	−0.484522	−	0.484522i
$819$	−1.78744	+	0.187579i	−0.0624583	+	0.00655456i
$820$	−5.18443	−	5.68110i	−0.181048	−	0.198393i
$821$	23.5322	+	40.7590i	0.821280	+	1.42250i	0.904729	+	0.425987i	$0.140073\pi$
$821$	23.5322	+	40.7590i	0.821280	+	1.42250i	−0.0834487	+	0.996512i	$0.526593\pi$
$822$	6.66332	+	3.88665i	0.232410	+	0.135562i
$823$	11.9360	+	44.5459i	0.416064	+	1.55277i	0.782695	+	0.622405i	$0.213844\pi$
$823$	11.9360	+	44.5459i	0.416064	+	1.55277i	−0.366631	+	0.930366i	$0.619489\pi$
$824$			53.8392i			1.87558i
$825$	−4.03862	+	42.0269i	−0.140607	+	1.46319i
$826$	−1.54872	−	0.894155i	−0.0538870	−	0.0311116i
$827$	−25.7893	−	25.7893i	−0.896781	−	0.896781i	0.0983687	−	0.995150i	$-0.468638\pi$
$827$	−25.7893	−	25.7893i	−0.896781	−	0.896781i	−0.995150	+	0.0983687i	$0.968638\pi$
$828$	13.4497	+	3.73225i	0.467409	+	0.129705i
$829$	35.8684	−	20.7086i	1.24576	−	0.719241i	0.275500	−	0.961301i	$-0.411157\pi$
$829$	35.8684	−	20.7086i	1.24576	−	0.719241i	0.970261	+	0.242060i	$0.0778232\pi$
$830$	−5.32443	−	1.69077i	−0.184814	−	0.0586876i
$831$	−4.73959	+	17.3791i	−0.164414	+	0.602875i
$832$	18.2821	−	22.9838i	0.633819	−	0.796820i
$833$	23.7853	+	23.7853i	0.824110	+	0.824110i
$834$	−3.57304	−	13.5758i	−0.123724	−	0.470090i
$835$	−14.5692	−	28.1275i	−0.504188	−	0.973393i
$836$	9.23439	+	5.33148i	0.319378	+	0.184393i
$837$	−0.167420	+	12.5590i	−0.00578689	+	0.434103i
$838$	11.2591	−	3.01687i	0.388939	−	0.104216i
$839$	−12.9769	−	7.49223i	−0.448013	−	0.258660i	0.258978	−	0.965883i	$-0.416614\pi$
$839$	−12.9769	−	7.49223i	−0.448013	−	0.258660i	−0.706991	+	0.707223i	$0.749948\pi$
$840$	0.605891	−	1.87904i	0.0209052	−	0.0648329i
$841$	2.27790	−	3.94543i	0.0785481	−	0.136049i
$842$	25.3048	+	6.78040i	0.872061	+	0.233668i
$843$	19.1354	−	32.8060i	0.659058	−	1.12990i
$844$		−	3.82643i		−	0.131711i
$845$	23.9227	+	16.5138i	0.822966	+	0.568091i
$846$	14.3688	+	8.46696i	0.494009	+	0.291100i
$847$	2.04915	+	0.549067i	0.0704095	+	0.0188662i
$848$	−2.17362	+	8.11205i	−0.0746424	+	0.278569i
$849$	−6.81911	+	6.75878i	−0.234031	+	0.231961i
$850$	−2.41476	+	26.3581i	−0.0828254	+	0.904074i
$851$	13.5842	−	23.5286i	0.465662	−	0.806550i
$852$	−0.0168447	+	3.79101i	−0.000577090	+	0.129878i
$853$	−9.05692	−	9.05692i	−0.310103	−	0.310103i	0.534846	−	0.844949i	$-0.320369\pi$
$853$	−9.05692	−	9.05692i	−0.310103	−	0.310103i	−0.844949	+	0.534846i	$0.820369\pi$
$854$	−1.31395	+	2.27583i	−0.0449626	+	0.0778775i
$855$	13.7254	−	12.3037i	0.469398	−	0.420776i
$856$	5.79905	−	3.34808i	0.198207	−	0.114435i
$857$	−12.8809	+	12.8809i	−0.440004	+	0.440004i	−0.892013	−	0.452009i	$-0.850707\pi$
$857$	−12.8809	+	12.8809i	−0.440004	+	0.440004i	0.452009	+	0.892013i	$0.350707\pi$
$858$	26.9428	−	19.7520i	0.919812	−	0.674321i
$859$			10.9311i			0.372966i	0.982458	+	0.186483i	$0.0597089\pi$
$859$			10.9311i			0.372966i	−0.982458	+	0.186483i	$0.940291\pi$
$860$	−1.07741	−	2.08007i	−0.0367395	−	0.0709299i
$861$	0.316527	+	1.20265i	0.0107872	+	0.0409860i
$862$	17.7024	−	4.74335i	0.602947	−	0.161559i
$863$	−21.3829	+	21.3829i	−0.727881	+	0.727881i	−0.970197	−	0.242316i	$-0.922093\pi$
$863$	−21.3829	+	21.3829i	−0.727881	+	0.727881i	0.242316	+	0.970197i	$0.422093\pi$
$864$	21.0975	−	5.35269i	0.717751	−	0.182102i
$865$	1.14617	−	1.79103i	0.0389709	−	0.0608967i
$866$	30.1629			1.02498
$867$	−0.0482893	+	10.8678i	−0.00163999	+	0.369090i
$868$	−0.308798	−	0.0827422i	−0.0104813	−	0.00280845i
$869$	−31.2126	+	18.0206i	−1.05882	+	0.611308i
$870$	9.58075	+	18.6997i	0.324818	+	0.633980i
$871$	−1.55932	−	2.10730i	−0.0528355	−	0.0714030i
$872$	−22.3608	+	22.3608i	−0.757231	+	0.757231i
$873$	36.0750	−	35.4395i	1.22095	−	1.19944i
$874$	15.2627	−	8.81191i	0.516268	−	0.298067i
$875$	−1.13991	+	1.46683i	−0.0385361	+	0.0495880i
$876$	−10.2553	−	2.79680i	−0.346495	−	0.0944952i
$877$	3.95038	+	14.7430i	0.133395	+	0.497836i	0.999999	−	0.00115930i	$-0.000369018\pi$
$877$	3.95038	+	14.7430i	0.133395	+	0.497836i	−0.866604	+	0.498996i	$0.833702\pi$
$878$	−5.42659	−	20.2523i	−0.183139	−	0.683483i
$879$	8.18425	+	2.23199i	0.276048	+	0.0752830i
$880$	4.14815	+	18.8940i	0.139834	+	0.636915i
$881$	15.6546	−	9.03820i	0.527417	−	0.304505i	−0.212547	−	0.977151i	$-0.568176\pi$
$881$	15.6546	−	9.03820i	0.527417	−	0.304505i	0.739964	+	0.672646i	$0.234842\pi$
$882$	16.3731	−	16.0846i	0.551311	−	0.541598i
$883$	21.5666	−	21.5666i	0.725775	−	0.725775i	−0.244000	−	0.969775i	$-0.578460\pi$
$883$	21.5666	−	21.5666i	0.725775	−	0.725775i	0.969775	+	0.244000i	$0.0784596\pi$
$884$	−11.1299	+	8.23572i	−0.374340	+	0.276997i
$885$	−11.6583	+	36.1555i	−0.391889	+	1.21535i
$886$	−11.7550	+	6.78673i	−0.394915	+	0.228005i
$887$	31.0745	+	8.32639i	1.04338	+	0.279573i	0.739514	−	0.673142i	$-0.235056\pi$
$887$	31.0745	+	8.32639i	1.04338	+	0.279573i	0.303867	+	0.952715i	$0.401722\pi$
$888$	0.109744	−	24.6987i	0.00368278	−	0.828833i
$889$	0.234935			0.00787947
$890$	14.2823	+	9.13995i	0.478743	+	0.306372i
$891$	43.8700	+	0.779792i	1.46970	+	0.0261240i
$892$	6.41908	−	6.41908i	0.214927	−	0.214927i
$893$	−13.4471	+	3.60314i	−0.449991	+	0.120575i
$894$	2.82234	+	10.7235i	0.0943930	+	0.358646i
$895$	34.8064	+	11.0528i	1.16345	+	0.369453i
$896$		−	0.0930361i		−	0.00310812i
$897$	3.97111	+	36.2866i	0.132591	+	1.21157i
$898$	23.1104	−	23.1104i	0.771205	−	0.771205i
$899$	10.3498	−	5.97544i	0.345184	−	0.199292i
$900$	−11.8797	−	1.19489i	−0.395991	−	0.0398297i
$901$	11.4164	−	19.7739i	0.380337	−	0.658763i
$902$	−16.3455	−	16.3455i	−0.544246	−	0.544246i
$903$	−0.00168300	+	0.378771i	−5.60068e−5	+	0.0126047i
$904$	−22.9026	+	39.6684i	−0.761728	+	1.31935i
$905$	−20.5568	+	18.7596i	−0.683330	+	0.623589i
$906$	22.2184	−	22.0218i	0.738156	−	0.731625i
$907$	−3.44249	+	12.8475i	−0.114306	+	0.426596i	−0.999234	−	0.0391321i	$-0.987541\pi$
$907$	−3.44249	+	12.8475i	−0.114306	+	0.426596i	0.884928	+	0.465728i	$0.154207\pi$
$908$	20.4156	+	5.47035i	0.677517	+	0.181540i
$909$	−39.2773	−	23.1446i	−1.30275	−	0.767656i
$910$	1.46654	−	0.0995361i	0.0486153	−	0.00329959i
$911$		−	6.22499i		−	0.206243i	−0.994669	−	0.103122i	$-0.967117\pi$
$911$		−	6.22499i		−	0.206243i	0.994669	−	0.103122i	$-0.0328831\pi$
$912$	4.25507	−	7.29495i	0.140899	−	0.241560i
$913$	10.7219	+	2.87291i	0.354841	+	0.0950795i
$914$	1.91698	−	3.32031i	0.0634081	−	0.109826i
$915$	53.1302	+	17.1317i	1.75643	+	0.566358i
$916$	4.40388	+	2.54258i	0.145508	+	0.0840092i
$917$	0.198797	−	0.0532676i	0.00656486	−	0.00175905i
$918$	27.5044	+	0.366652i	0.907779	+	0.0121013i
$919$	51.3893	+	29.6696i	1.69518	+	0.978711i	0.950210	+	0.311611i	$0.100868\pi$
$919$	51.3893	+	29.6696i	1.69518	+	0.978711i	0.744968	+	0.667101i	$0.232465\pi$
$920$	−38.2185	−	12.1363i	−1.26003	−	0.400121i
$921$	9.79712	+	37.2242i	0.322826	+	1.22658i
$922$	2.42842	+	2.42842i	0.0799759	+	0.0799759i
$923$	−9.22458	+	3.63366i	−0.303631	+	0.119603i
$924$	−0.293837	+	1.07744i	−0.00966654	+	0.0354453i
$925$	−8.03785	+	21.8058i	−0.264283	+	0.716969i
$926$	−36.9249	+	21.3186i	−1.21343	+	0.700573i
$927$	−50.7295	−	14.0773i	−1.66617	−	0.462358i
$928$	−14.6443	−	14.6443i	−0.480722	−	0.480722i
$929$	−9.30395	−	5.37164i	−0.305253	−	0.176238i	0.339548	−	0.940589i	$-0.389726\pi$
$929$	−9.30395	−	5.37164i	−0.305253	−	0.176238i	−0.644800	+	0.764351i	$0.723059\pi$
$930$	0.514667	−	10.2596i	0.0168766	−	0.336425i
$931$			19.1587i			0.627900i
$932$	−3.75954	−	14.0308i	−0.123148	−	0.459594i
$933$	40.8445	+	23.8242i	1.33719	+	0.779969i
$934$	−15.8303	−	27.4189i	−0.517984	−	0.897175i
$935$	2.40153	−	52.5371i	0.0785383	−	1.71815i
$936$	19.5015	+	26.8505i	0.637425	+	0.877635i
$937$	−7.07205	−	7.07205i	−0.231034	−	0.231034i	0.582090	−	0.813124i	$-0.302235\pi$
$937$	−7.07205	−	7.07205i	−0.231034	−	0.231034i	−0.813124	+	0.582090i	$0.802235\pi$
$938$	−0.128042	−	0.0343089i	−0.00418073	−	0.00112022i
$939$	8.11156	+	30.8199i	0.264711	+	1.00577i
$940$	7.59538	+	4.86067i	0.247734	+	0.158538i
$941$	−28.4220			−0.926529			−0.463265	−	0.886220i	$-0.653322\pi$
$941$	−28.4220			−0.926529			−0.463265	+	0.886220i	$0.653322\pi$
$942$	0.0615599	−	13.8545i	0.00200573	−	0.451402i
$943$	24.3975	−	6.53730i	0.794494	−	0.212884i
$944$			17.4051i			0.566486i
$945$	1.61208	+	1.06220i	0.0524410	+	0.0345535i
$946$	−3.52033	−	6.09738i	−0.114456	−	0.198243i
$947$	4.02771	−	15.0316i	0.130883	−	0.488461i	−0.869098	−	0.494640i	$-0.835300\pi$
$947$	4.02771	−	15.0316i	0.130883	−	0.488461i	0.999981	+	0.00617839i	$0.00196666\pi$
$948$	−5.05683	−	8.84926i	−0.164238	−	0.287411i
$949$	−3.14701	−	27.6208i	−0.102156	−	0.896610i
$950$	−11.5880	+	9.64298i	−0.375965	+	0.312860i
$951$	−15.7511	+	4.14558i	−0.510765	+	0.134430i
$952$	−0.636511	+	2.37549i	−0.0206294	+	0.0769901i
$953$	38.2209	−	10.2413i	1.23810	−	0.331747i	0.420369	−	0.907353i	$-0.361901\pi$
$953$	38.2209	−	10.2413i	1.23810	−	0.331747i	0.817727	+	0.575607i	$0.195234\pi$
$954$	−13.4226	−	7.90943i	−0.434574	−	0.256077i
$955$	−6.28014	+	1.37880i	−0.203220	+	0.0446168i
$956$	−1.27655	+	2.21106i	−0.0412867	+	0.0715107i
$957$	−20.7134	−	36.2477i	−0.669571	−	1.17172i
$958$	0.0383684	+	0.143193i	0.00123963	+	0.00462635i
$959$	−0.337201	−	0.584050i	−0.0108888	−	0.0188600i
$960$	−30.8424	+	6.62791i	−0.995434	+	0.213915i
$961$	25.1572			0.811521
$962$	17.1093	−	6.73955i	0.551627	−	0.217292i
$963$	1.63843	+	6.33951i	0.0527976	+	0.204288i
$964$	2.38966	+	4.13901i	0.0769658	+	0.133309i
$965$	10.8550	+	20.9567i	0.349433	+	0.674622i
$966$	1.29940	+	1.31099i	0.0418074	+	0.0421805i
$967$	−32.4327	+	32.4327i	−1.04296	+	1.04296i	−0.0439297	+	0.999035i	$0.513988\pi$
$967$	−32.4327	+	32.4327i	−1.04296	+	1.04296i	−0.999035	+	0.0439297i	$0.986012\pi$
$968$	−10.1381	−	37.8361i	−0.325852	−	1.21610i
$969$	−16.3076	+	16.1634i	−0.523877	+	0.519242i
$970$	−30.5507	+	27.8797i	−0.980922	+	0.895165i
$971$	29.2025	+	16.8601i	0.937154	+	0.541066i	0.889067	−	0.457777i	$-0.151354\pi$
$971$	29.2025	+	16.8601i	0.937154	+	0.541066i	0.0480872	+	0.998843i	$0.484687\pi$
$972$	−0.275641	+	12.4050i	−0.00884120	+	0.397891i
$973$	−0.317646	+	1.18547i	−0.0101833	+	0.0380045i
$974$	−10.7050			−0.343009
$975$	−8.61253	−	30.0137i	−0.275822	−	0.961209i
$976$	25.5766			0.818686
$977$	0.617472	−	2.30444i	0.0197547	−	0.0737254i	−0.955345	−	0.295493i	$-0.904516\pi$
$977$	0.617472	−	2.30444i	0.0197547	−	0.0737254i	0.975100	+	0.221768i	$0.0711827\pi$
$978$	−36.0769	−	21.0433i	−1.15361	−	0.672890i
$979$	−29.1781	−	16.8460i	−0.932536	−	0.538400i
$980$	9.16666	−	8.36526i	0.292818	−	0.267218i
$981$	−15.2226	−	26.9159i	−0.486019	−	0.859357i
$982$	−6.18915	−	23.0982i	−0.197504	−	0.737094i
$983$	2.74521	−	2.74521i	0.0875586	−	0.0875586i	−0.661971	−	0.749530i	$-0.730280\pi$
$983$	2.74521	−	2.74521i	0.0875586	−	0.0875586i	0.749530	+	0.661971i	$0.230280\pi$
$984$	16.3088	−	16.1645i	0.519904	−	0.515305i
$985$	20.2416	+	39.0787i	0.644950	+	1.24515i
$986$	−13.0863	−	22.6661i	−0.416752	−	0.721836i
$987$	−0.723420	−	1.26596i	−0.0230267	−	0.0402959i
$988$	−7.79937	−	1.16562i	−0.248131	−	0.0370833i
$989$	7.69310			0.244626
$990$	−35.8319	−	1.95714i	−1.13881	−	0.0622021i
$991$	−8.53170	−	14.7773i	−0.271019	−	0.469418i	0.698104	−	0.715996i	$-0.254027\pi$
$991$	−8.53170	−	14.7773i	−0.271019	−	0.469418i	−0.969123	+	0.246578i	$0.920694\pi$
$992$	2.62062	+	9.78028i	0.0832047	+	0.310524i
$993$	9.55337	−	5.45919i	0.303167	−	0.173242i
$994$	−0.250670	+	0.434173i	−0.00795076	+	0.0137711i
$995$	27.5472	−	6.04797i	0.873306	−	0.191733i
$996$	−0.825903	+	3.02842i	−0.0261697	+	0.0959592i
$997$	−5.72683	+	1.53450i	−0.181371	+	0.0485981i	−0.348361	−	0.937360i	$-0.613262\pi$
$997$	−5.72683	+	1.53450i	−0.181371	+	0.0485981i	0.166991	+	0.985958i	$0.446595\pi$
$998$	5.16292	−	19.2683i	0.163429	−	0.609927i
$999$	23.2434	+	6.56133i	0.735388	+	0.207591i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.bf.a.62.8	yes	96
3.2	odd	2	inner	195.2.bf.a.62.17	yes	96
5.2	odd	4		975.2.bn.d.218.8		96
5.3	odd	4	inner	195.2.bf.a.23.17	yes	96
5.4	even	2		975.2.bn.d.257.17		96
13.4	even	6	inner	195.2.bf.a.17.8	✓	96
15.2	even	4		975.2.bn.d.218.17		96
15.8	even	4	inner	195.2.bf.a.23.8	yes	96
15.14	odd	2		975.2.bn.d.257.8		96
39.17	odd	6	inner	195.2.bf.a.17.17	yes	96
65.4	even	6		975.2.bn.d.407.17		96
65.17	odd	12		975.2.bn.d.368.8		96
65.43	odd	12	inner	195.2.bf.a.173.17	yes	96
195.17	even	12		975.2.bn.d.368.17		96
195.134	odd	6		975.2.bn.d.407.8		96
195.173	even	12	inner	195.2.bf.a.173.8	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.8	✓	96	13.4	even	6	inner
195.2.bf.a.17.17	yes	96	39.17	odd	6	inner
195.2.bf.a.23.8	yes	96	15.8	even	4	inner
195.2.bf.a.23.17	yes	96	5.3	odd	4	inner
195.2.bf.a.62.8	yes	96	1.1	even	1	trivial
195.2.bf.a.62.17	yes	96	3.2	odd	2	inner
195.2.bf.a.173.8	yes	96	195.173	even	12	inner
195.2.bf.a.173.17	yes	96	65.43	odd	12	inner
975.2.bn.d.218.8		96	5.2	odd	4
975.2.bn.d.218.17		96	15.2	even	4
975.2.bn.d.257.8		96	15.14	odd	2
975.2.bn.d.257.17		96	5.4	even	2
975.2.bn.d.368.8		96	65.17	odd	12
975.2.bn.d.368.17		96	195.17	even	12
975.2.bn.d.407.8		96	195.134	odd	6
975.2.bn.d.407.17		96	65.4	even	6

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:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.283997 + 1.05989i) q^{2} +(0.872682 - 1.49614i) q^{3} +(0.689337 + 0.397989i) q^{4} +(1.65169 - 1.50729i) q^{5} +(1.33790 + 1.34985i) q^{6} +(-0.0430045 - 0.160495i) q^{7} +(-2.16938 + 2.16938i) q^{8} +(-1.47685 - 2.61130i) q^{9} +(1.12849 + 2.17868i) q^{10} +(-2.43760 - 4.22205i) q^{11} +(1.19702 - 0.684025i) q^{12} +(2.82173 + 2.24451i) q^{13} +0.182320 q^{14} +(-0.813712 - 3.78654i) q^{15} +(-0.887232 - 1.53673i) q^{16} +(1.24864 + 4.65999i) q^{17} +(3.18712 - 0.823701i) q^{18} +(-1.37389 + 2.37966i) q^{19} +(1.73846 - 0.381676i) q^{20} +(-0.277652 - 0.0757204i) q^{21} +(5.16719 - 1.38454i) q^{22} +(-1.51285 + 5.64603i) q^{23} +(1.35251 + 5.13887i) q^{24} +(0.456158 - 4.97915i) q^{25} +(-3.18030 + 2.35330i) q^{26} +(-5.19569 - 0.0692622i) q^{27} +(0.0342306 - 0.127750i) q^{28} +(2.47205 + 4.28172i) q^{29} +(4.24441 + 0.212919i) q^{30} -2.41720i q^{31} +(-4.04612 + 1.08416i) q^{32} +(-8.44403 - 0.0375196i) q^{33} -5.29369 q^{34} +(-0.312942 - 0.200268i) q^{35} +(0.0212203 - 2.38784i) q^{36} +(-4.48963 - 1.20299i) q^{37} +(-2.13199 - 2.13199i) q^{38} +(5.82057 - 2.26296i) q^{39} +(-0.313259 + 6.85303i) q^{40} +(-2.16059 - 3.74226i) q^{41} +(0.159108 - 0.272776i) q^{42} +(-0.340642 - 1.27129i) q^{43} -3.88056i q^{44} +(-6.37529 - 2.08702i) q^{45} +(-5.55453 - 3.20691i) q^{46} +(3.58251 + 3.58251i) q^{47} +(-3.07343 - 0.0136563i) q^{48} +(6.03827 - 3.48620i) q^{49} +(5.14781 + 1.89754i) q^{50} +(8.06165 + 2.19855i) q^{51} +(1.05184 + 2.67024i) q^{52} +(-3.34661 - 3.34661i) q^{53} +(1.54897 - 5.48719i) q^{54} +(-10.3900 - 3.29935i) q^{55} +(0.441468 + 0.254882i) q^{56} +(2.36132 + 4.13222i) q^{57} +(-5.24021 + 1.40411i) q^{58} +(-8.49452 - 4.90431i) q^{59} +(0.946078 - 2.93405i) q^{60} +(-7.20685 + 12.4826i) q^{61} +(2.56197 + 0.686477i) q^{62} +(-0.355590 + 0.349325i) q^{63} -8.14527i q^{64} +(8.04375 - 0.545941i) q^{65} +(2.43784 - 8.93909i) q^{66} +(-0.702294 - 0.188179i) q^{67} +(-0.993890 + 3.70925i) q^{68} +(7.12700 + 7.19061i) q^{69} +(0.301136 - 0.274809i) q^{70} +(-1.37489 + 2.38137i) q^{71} +(8.86877 + 2.46106i) q^{72} +(-5.45193 - 5.45193i) q^{73} +(2.55008 - 4.41687i) q^{74} +(-7.05141 - 5.02769i) q^{75} +(-1.89415 + 1.09359i) q^{76} +(-0.572790 + 0.572790i) q^{77} +(0.745469 + 6.81184i) q^{78} -7.39276i q^{79} +(-3.78173 - 1.20089i) q^{80} +(-4.63781 + 7.71302i) q^{81} +(4.57999 - 1.22720i) q^{82} +(-1.60997 + 1.60997i) q^{83} +(-0.161260 - 0.162699i) q^{84} +(9.08632 + 5.81479i) q^{85} +1.44417 q^{86} +(8.56336 + 0.0380499i) q^{87} +(14.4473 + 3.87115i) q^{88} +(5.98500 - 3.45544i) q^{89} +(4.02257 - 6.16441i) q^{90} +(0.238885 - 0.549398i) q^{91} +(-3.28992 + 3.28992i) q^{92} +(-3.61646 - 2.10944i) q^{93} +(-4.81449 + 2.77964i) q^{94} +(1.31758 + 6.00131i) q^{95} +(-1.90893 + 6.99968i) q^{96} +(4.36286 + 16.2824i) q^{97} +(1.98014 + 7.38997i) q^{98} +(-7.42508 + 12.6007i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 2 q^{3} - 12 q^{6} - 12 q^{7} + 4 q^{10} - 12 q^{12} - 24 q^{13} - 6 q^{15} + 16 q^{16} + 20 q^{22} - 16 q^{25} - 32 q^{27} - 36 q^{28} + 30 q^{33} - 4 q^{36} - 84 q^{37} - 152 q^{40} - 48 q^{42}+ \cdots - 48 q^{97}+O(q^{100}) \) 96 * q - 2 * q^3 - 12 * q^6 - 12 * q^7 + 4 * q^10 - 12 * q^12 - 24 * q^13 - 6 * q^15 + 16 * q^16 + 20 * q^22 - 16 * q^25 - 32 * q^27 - 36 * q^28 + 30 * q^33 - 4 * q^36 - 84 * q^37 - 152 * q^40 - 48 * q^42 + 8 * q^43 + 54 * q^45 - 28 * q^48 - 16 * q^51 + 28 * q^52 - 40 * q^55 + 84 * q^58 - 32 * q^61 + 90 * q^63 + 36 * q^67 + 90 * q^72 - 20 * q^75 + 72 * q^76 + 60 * q^78 + 32 * q^81 - 68 * q^82 + 84 * q^85 - 26 * q^87 - 108 * q^88 - 20 * q^90 - 80 * q^91 + 48 * q^93 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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