LMFDB - Embedded newform 507.2.m.b.79.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [507,2,Mod(40,507)] 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("507.40"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(507, base_ring=CyclotomicField(26)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [204] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$17$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			79.2
Character	$\chi$	$=$	507.79
Dual form			507.2.m.b.430.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.97300 - 1.03551i) q^{2} +(-0.970942 - 0.239316i) q^{3} +(1.68431 + 2.44014i) q^{4} +(1.49468 + 3.94114i) q^{5} +(1.66785 + 1.47759i) q^{6} +(-0.165780 - 1.36532i) q^{7} +(-0.259180 - 2.13454i) q^{8} +(0.885456 + 0.464723i) q^{9} +(1.13209 - 9.32359i) q^{10} +(3.85985 - 2.02580i) q^{11} +(-1.05140 - 2.77231i) q^{12} +(-2.70486 + 2.38406i) q^{13} +(-1.08671 + 2.86543i) q^{14} +(-0.508068 - 4.18431i) q^{15} +(0.403829 - 1.06481i) q^{16} +(0.480644 + 3.95846i) q^{17} +(-1.26578 - 1.83379i) q^{18} -2.11542 q^{19} +(-7.09943 + 10.2853i) q^{20} +(-0.165780 + 1.36532i) q^{21} -9.71320 q^{22} -2.48138 q^{23} +(-0.259180 + 2.13454i) q^{24} +(-9.55594 + 8.46583i) q^{25} +(7.80539 - 1.90284i) q^{26} +(-0.748511 - 0.663123i) q^{27} +(3.05234 - 2.70414i) q^{28} +(6.73571 + 3.53517i) q^{29} +(-3.33047 + 8.78174i) q^{30} +(-4.66935 - 4.13668i) q^{31} +(-5.11829 + 4.53441i) q^{32} +(-4.23249 + 1.04322i) q^{33} +(3.15071 - 8.30773i) q^{34} +(5.13311 - 2.69407i) q^{35} +(0.357390 + 2.94337i) q^{36} +(5.29893 + 4.69444i) q^{37} +(4.17372 + 2.19054i) q^{38} +(3.19680 - 1.66747i) q^{39} +(8.02512 - 4.21191i) q^{40} +(-6.61641 - 1.63080i) q^{41} +(1.74088 - 2.52210i) q^{42} +(0.411878 - 0.364893i) q^{43} +(11.4444 + 6.00649i) q^{44} +(-0.508068 + 4.18431i) q^{45} +(4.89575 + 2.56949i) q^{46} +(-0.684738 + 0.992014i) q^{47} +(-0.646920 + 0.937226i) q^{48} +(4.95998 - 1.22253i) q^{49} +(27.6203 - 6.80778i) q^{50} +(0.480644 - 3.95846i) q^{51} +(-10.3732 - 2.58475i) q^{52} +(1.32227 + 10.8899i) q^{53} +(0.790140 + 2.08343i) q^{54} +(13.7532 + 12.1843i) q^{55} +(-2.87136 + 0.707725i) q^{56} +(2.05395 + 0.506254i) q^{57} +(-9.62883 - 13.9498i) q^{58} +(4.52394 + 11.9286i) q^{59} +(9.35456 - 8.28742i) q^{60} +(1.27675 - 10.5149i) q^{61} +(4.92904 + 12.9968i) q^{62} +(0.487704 - 1.28597i) q^{63} +(12.5823 - 3.10127i) q^{64} +(-13.4388 - 7.09682i) q^{65} +(9.43095 + 2.32452i) q^{66} +(-4.92639 + 7.13711i) q^{67} +(-8.84964 + 7.84009i) q^{68} +(2.40927 + 0.593832i) q^{69} -12.9173 q^{70} +(-4.62513 - 1.13999i) q^{71} +(0.762477 - 2.01049i) q^{72} +(3.18342 - 1.67079i) q^{73} +(-5.59364 - 14.7492i) q^{74} +(11.3043 - 5.93294i) q^{75} +(-3.56302 - 5.16193i) q^{76} +(-3.40575 - 4.93408i) q^{77} +(-8.03396 - 0.0204086i) q^{78} +(-7.17593 + 10.3961i) q^{79} +4.80015 q^{80} +(0.568065 + 0.822984i) q^{81} +(11.3654 + 10.0689i) q^{82} +(-8.27391 + 2.03933i) q^{83} +(-3.61079 + 1.89509i) q^{84} +(-14.8824 + 7.81089i) q^{85} +(-1.19048 + 0.293428i) q^{86} +(-5.69396 - 5.04441i) q^{87} +(-5.32455 - 7.71395i) q^{88} -5.33339 q^{89} +(5.33531 - 7.72952i) q^{90} +(3.70341 + 3.29776i) q^{91} +(-4.17940 - 6.05490i) q^{92} +(3.54369 + 5.13393i) q^{93} +(2.37822 - 1.24819i) q^{94} +(-3.16187 - 8.33717i) q^{95} +(6.05472 - 3.17776i) q^{96} +(-5.10303 + 13.4556i) q^{97} +(-11.0520 - 2.72406i) q^{98} +4.35916 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19}+ \cdots + 18 q^{99}+O(q^{100}) $ 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{2}{13}\right)$

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 $

$2$	−1.97300	−	1.03551i	−1.39512	−	0.732215i	−0.411320	−	0.911491i	$-0.634932\pi$
$2$	−1.97300	−	1.03551i	−1.39512	−	0.732215i	−0.983799	+	0.179276i	$0.942624\pi$
$3$	−0.970942	−	0.239316i	−0.560574	−	0.138169i
$3$	−0.970942	−	0.239316i	−0.560574	−	0.138169i
$4$	1.68431	+	2.44014i	0.842153	+	1.22007i
$5$	1.49468	+	3.94114i	0.668439	+	1.76253i	0.646674	+	0.762766i	$0.276159\pi$
$5$	1.49468	+	3.94114i	0.668439	+	1.76253i	0.0217651	+	0.999763i	$0.493071\pi$
$6$	1.66785	+	1.47759i	0.680897	+	0.603222i
$7$	−0.165780	−	1.36532i	−0.0626588	−	0.516041i	−0.989920	−	0.141627i	$-0.954767\pi$
$7$	−0.165780	−	1.36532i	−0.0626588	−	0.516041i	0.927261	−	0.374415i	$-0.122156\pi$
$8$	−0.259180	−	2.13454i	−0.0916339	−	0.754673i
$9$	0.885456	+	0.464723i	0.295152	+	0.154908i
$10$	1.13209	−	9.32359i	0.357998	−	2.94838i
$11$	3.85985	−	2.02580i	1.16379	−	0.610803i	0.231612	−	0.972808i	$-0.425600\pi$
$11$	3.85985	−	2.02580i	1.16379	−	0.610803i	0.932176	+	0.362005i	$0.117908\pi$
$12$	−1.05140	−	2.77231i	−0.303513	−	0.800298i
$13$	−2.70486	+	2.38406i	−0.750193	+	0.661219i
$13$	−2.70486	+	2.38406i	−0.750193	+	0.661219i
$14$	−1.08671	+	2.86543i	−0.290437	+	0.765819i
$15$	−0.508068	−	4.18431i	−0.131182	−	1.08038i
$16$	0.403829	−	1.06481i	0.100957	−	0.266202i
$17$	0.480644	+	3.95846i	0.116573	+	0.960067i	0.927216	+	0.374526i	$0.122195\pi$
$17$	0.480644	+	3.95846i	0.116573	+	0.960067i	−0.810643	+	0.585541i	$0.800882\pi$
$18$	−1.26578	−	1.83379i	−0.298346	−	0.432229i
$19$	−2.11542			−0.485311			−0.242656	−	0.970112i	$-0.578019\pi$
$19$	−2.11542			−0.485311			−0.242656	+	0.970112i	$0.578019\pi$
$20$	−7.09943	+	10.2853i	−1.58748	+	2.29986i
$21$	−0.165780	+	1.36532i	−0.0361761	+	0.297937i
$22$	−9.71320			−2.07086
$23$	−2.48138			−0.517403			−0.258701	−	0.965957i	$-0.583295\pi$
$23$	−2.48138			−0.517403			−0.258701	+	0.965957i	$0.583295\pi$
$24$	−0.259180	+	2.13454i	−0.0529049	+	0.435711i
$25$	−9.55594	+	8.46583i	−1.91119	+	1.69317i
$26$	7.80539	−	1.90284i	1.53076	−	0.373177i
$27$	−0.748511	−	0.663123i	−0.144051	−	0.127618i
$28$	3.05234	−	2.70414i	0.576838	−	0.511034i
$29$	6.73571	+	3.53517i	1.25079	+	0.656465i	0.954380	−	0.298595i	$-0.0965181\pi$
$29$	6.73571	+	3.53517i	1.25079	+	0.656465i	0.296410	+	0.955061i	$0.404210\pi$
$30$	−3.33047	+	8.78174i	−0.608059	+	1.60332i
$31$	−4.66935	−	4.13668i	−0.838640	−	0.742970i	0.129980	−	0.991517i	$-0.458509\pi$
$31$	−4.66935	−	4.13668i	−0.838640	−	0.742970i	−0.968620	+	0.248547i	$0.920047\pi$
$32$	−5.11829	+	4.53441i	−0.904795	+	0.801578i
$33$	−4.23249	+	1.04322i	−0.736783	+	0.181601i
$34$	3.15071	−	8.30773i	0.540342	−	1.42476i
$35$	5.13311	−	2.69407i	0.867655	−	0.455380i
$36$	0.357390	+	2.94337i	0.0595650	+	0.490562i
$37$	5.29893	+	4.69444i	0.871139	+	0.771762i	0.974854	−	0.222845i	$-0.0715345\pi$
$37$	5.29893	+	4.69444i	0.871139	+	0.771762i	−0.103715	+	0.994607i	$0.533073\pi$
$38$	4.17372	+	2.19054i	0.677067	+	0.355352i
$39$	3.19680	−	1.66747i	0.511898	−	0.267009i
$40$	8.02512	−	4.21191i	1.26888	−	0.665961i
$41$	−6.61641	−	1.63080i	−1.03331	−	0.254688i	−0.314033	−	0.949412i	$-0.601680\pi$
$41$	−6.61641	−	1.63080i	−1.03331	−	0.254688i	−0.719276	+	0.694724i	$0.755526\pi$
$42$	1.74088	−	2.52210i	0.268624	−	0.389168i
$43$	0.411878	−	0.364893i	0.0628109	−	0.0556456i	−0.631133	−	0.775674i	$-0.717410\pi$
$43$	0.411878	−	0.364893i	0.0628109	−	0.0556456i	0.693944	+	0.720029i	$0.255871\pi$
$44$	11.4444	+	6.00649i	1.72531	+	0.905513i
$45$	−0.508068	+	4.18431i	−0.0757382	+	0.623761i
$46$	4.89575	+	2.56949i	0.721838	+	0.378850i
$47$	−0.684738	+	0.992014i	−0.0998793	+	0.144700i	−0.869737	−	0.493515i	$-0.835712\pi$
$47$	−0.684738	+	0.992014i	−0.0998793	+	0.144700i	0.769858	+	0.638215i	$0.220327\pi$
$48$	−0.646920	+	0.937226i	−0.0933749	+	0.135277i
$49$	4.95998	−	1.22253i	0.708569	−	0.174647i
$50$	27.6203	−	6.80778i	3.90610	−	0.962766i
$51$	0.480644	−	3.95846i	0.0673036	−	0.554295i
$52$	−10.3732	−	2.58475i	−1.43851	−	0.358440i
$53$	1.32227	+	10.8899i	0.181628	+	1.49584i	0.743565	+	0.668663i	$0.233133\pi$
$53$	1.32227	+	10.8899i	0.181628	+	1.49584i	−0.561937	+	0.827180i	$0.689944\pi$
$54$	0.790140	+	2.08343i	0.107524	+	0.283519i
$55$	13.7532	+	12.1843i	1.85448	+	1.64293i
$56$	−2.87136	+	0.707725i	−0.383701	+	0.0945738i
$57$	2.05395	+	0.506254i	0.272053	+	0.0670550i
$58$	−9.62883	−	13.9498i	−1.26433	−	1.83169i
$59$	4.52394	+	11.9286i	0.588966	+	1.55298i	0.815368	+	0.578943i	$0.196535\pi$
$59$	4.52394	+	11.9286i	0.588966	+	1.55298i	−0.226402	+	0.974034i	$0.572696\pi$
$60$	9.35456	−	8.28742i	1.20767	−	1.06990i
$61$	1.27675	−	10.5149i	0.163470	−	1.34630i	−0.647881	−	0.761742i	$-0.724345\pi$
$61$	1.27675	−	10.5149i	0.163470	−	1.34630i	0.811351	−	0.584559i	$-0.198732\pi$
$62$	4.92904	+	12.9968i	0.625988	+	1.65060i
$63$	0.487704	−	1.28597i	0.0614449	−	0.162017i
$64$	12.5823	−	3.10127i	1.57279	−	0.387659i
$65$	−13.4388	−	7.09682i	−1.66688	−	0.880252i
$66$	9.43095	+	2.32452i	1.16087	+	0.286129i
$67$	−4.92639	+	7.13711i	−0.601854	+	0.871936i	−0.998949	−	0.0458413i	$-0.985403\pi$
$67$	−4.92639	+	7.13711i	−0.601854	+	0.871936i	0.397094	+	0.917778i	$0.370019\pi$
$68$	−8.84964	+	7.84009i	−1.07318	+	0.950751i
$69$	2.40927	+	0.593832i	0.290042	+	0.0714890i
$70$	−12.9173			−1.54392
$71$	−4.62513	−	1.13999i	−0.548902	−	0.135292i	−0.0448949	−	0.998992i	$-0.514295\pi$
$71$	−4.62513	−	1.13999i	−0.548902	−	0.135292i	−0.504007	+	0.863700i	$0.668141\pi$
$72$	0.762477	−	2.01049i	0.0898588	−	0.236938i
$73$	3.18342	−	1.67079i	0.372591	−	0.195551i	−0.268025	−	0.963412i	$-0.586371\pi$
$73$	3.18342	−	1.67079i	0.372591	−	0.195551i	0.640617	+	0.767861i	$0.278679\pi$
$74$	−5.59364	−	14.7492i	−0.650247	−	1.71456i
$75$	11.3043	−	5.93294i	1.30530	−	0.685077i
$76$	−3.56302	−	5.16193i	−0.408707	−	0.592114i
$77$	−3.40575	−	4.93408i	−0.388121	−	0.562291i
$78$	−8.03396	−	0.0204086i	−0.909666	−	0.00231082i
$79$	−7.17593	+	10.3961i	−0.807355	+	1.16966i	0.175355	+	0.984505i	$0.443893\pi$
$79$	−7.17593	+	10.3961i	−0.807355	+	1.16966i	−0.982710	+	0.185150i	$0.940723\pi$
$80$	4.80015			0.536673
$81$	0.568065	+	0.822984i	0.0631183	+	0.0914427i
$82$	11.3654	+	10.0689i	1.25510	+	1.11192i
$83$	−8.27391	+	2.03933i	−0.908179	+	0.223846i	−0.665620	−	0.746291i	$-0.731833\pi$
$83$	−8.27391	+	2.03933i	−0.908179	+	0.223846i	−0.242559	+	0.970137i	$0.577987\pi$
$84$	−3.61079	+	1.89509i	−0.393969	+	0.206771i
$85$	−14.8824	+	7.81089i	−1.61422	+	0.847210i
$86$	−1.19048	+	0.293428i	−0.128373	+	0.0316411i
$87$	−5.69396	−	5.04441i	−0.610457	−	0.540817i
$88$	−5.32455	−	7.71395i	−0.567599	−	0.822309i
$89$	−5.33339			−0.565338			−0.282669	−	0.959218i	$-0.591220\pi$
$89$	−5.33339			−0.565338			−0.282669	+	0.959218i	$0.591220\pi$
$90$	5.33531	−	7.72952i	0.562391	−	0.814763i
$91$	3.70341	+	3.29776i	0.388223	+	0.345699i
$92$	−4.17940	−	6.05490i	−0.435732	−	0.631267i
$93$	3.54369	+	5.13393i	0.367464	+	0.532363i
$94$	2.37822	−	1.24819i	0.245295	−	0.128741i
$95$	−3.16187	−	8.33717i	−0.324401	−	0.855376i
$96$	6.05472	−	3.17776i	0.617957	−	0.324329i
$97$	−5.10303	+	13.4556i	−0.518134	+	1.36621i	0.379388	+	0.925238i	$0.376134\pi$
$97$	−5.10303	+	13.4556i	−0.518134	+	1.36621i	−0.897522	+	0.440969i	$0.854635\pi$
$98$	−11.0520	−	2.72406i	−1.11642	−	0.275172i
$99$	4.35916			0.438112
$100$	−36.7529	−	9.05878i	−3.67529	−	0.905878i
$101$	−2.66544	+	2.36137i	−0.265221	+	0.234965i	−0.785243	−	0.619187i	$-0.787462\pi$
$101$	−2.66544	+	2.36137i	−0.265221	+	0.234965i	0.520022	+	0.854153i	$0.325924\pi$
$102$	−5.04732	+	7.31231i	−0.499760	+	0.724027i
$103$	9.23581	+	2.27642i	0.910031	+	0.224303i	0.666425	−	0.745572i	$-0.267824\pi$
$103$	9.23581	+	2.27642i	0.910031	+	0.224303i	0.243606	+	0.969874i	$0.421670\pi$
$104$	5.78991	+	5.15572i	0.567747	+	0.505560i
$105$	−5.62869	+	1.38735i	−0.549304	+	0.135391i
$106$	8.66774	−	22.8550i	0.841886	−	2.21987i
$107$	−1.76486	−	4.65355i	−0.170615	−	0.449876i	0.822249	−	0.569129i	$-0.192719\pi$
$107$	−1.76486	−	4.65355i	−0.170615	−	0.449876i	−0.992864	+	0.119253i	$0.961950\pi$
$108$	0.357390	−	2.94337i	0.0343899	−	0.283226i
$109$	3.46744	−	3.07188i	0.332120	−	0.294233i	−0.480537	−	0.876974i	$-0.659558\pi$
$109$	3.46744	−	3.07188i	0.332120	−	0.294233i	0.812658	+	0.582741i	$0.198020\pi$
$110$	−14.5181	−	38.2810i	−1.38425	−	3.64995i
$111$	−4.02150	−	5.82615i	−0.381704	−	0.552994i
$112$	−1.52075	−	0.374831i	−0.143697	−	0.0354182i
$113$	7.73806	−	1.90726i	0.727936	−	0.179420i	0.142103	−	0.989852i	$-0.454614\pi$
$113$	7.73806	−	1.90726i	0.727936	−	0.179420i	0.585833	+	0.810432i	$0.300767\pi$
$114$	−3.52821	−	3.12572i	−0.330447	−	0.292751i
$115$	−3.70885	−	9.77944i	−0.345852	−	0.911938i
$116$	2.71868	+	22.3904i	0.252424	+	2.07890i
$117$	−3.50296	+	0.853969i	−0.323849	+	0.0789495i
$118$	3.42650	−	28.2197i	0.315435	−	2.59784i
$119$	5.32487	−	1.31246i	0.488130	−	0.120313i
$120$	−8.79989	+	2.16898i	−0.803317	+	0.198000i
$121$	4.54583	−	6.58577i	0.413257	−	0.598707i
$122$	−13.4073	+	19.4239i	−1.21384	+	1.75855i
$123$	6.03387	+	3.16682i	0.544056	+	0.285543i
$124$	2.22947	−	18.3613i	0.200212	−	1.64889i
$125$	−28.9868	−	15.2135i	−2.59266	−	1.36073i
$126$	−2.29387	+	2.03219i	−0.204354	+	0.181042i
$127$	8.18596	−	11.8594i	0.726386	−	1.05235i	−0.269611	−	0.962969i	$-0.586895\pi$
$127$	8.18596	−	11.8594i	0.726386	−	1.05235i	0.995997	−	0.0893831i	$-0.0284895\pi$
$128$	−14.7578	−	3.63746i	−1.30441	−	0.321509i
$129$	−0.487235	+	0.255720i	−0.0428986	+	0.0225149i
$130$	19.1659	+	27.9180i	1.68096	+	2.44857i
$131$	11.2793	+	5.91985i	0.985479	+	0.517219i	0.878860	−	0.477081i	$-0.158305\pi$
$131$	11.2793	+	5.91985i	0.985479	+	0.517219i	0.106619	+	0.994300i	$0.465997\pi$
$132$	−9.67441	−	8.57078i	−0.842049	−	0.745991i
$133$	0.350694	+	2.88822i	0.0304090	+	0.250441i
$134$	17.1103	−	8.98017i	1.47810	−	0.775768i
$135$	1.49468	−	3.94114i	0.128641	−	0.339199i
$136$	8.32491	−	2.05191i	0.713855	−	0.175949i
$137$	−3.36838	+	2.98413i	−0.287780	+	0.254951i	−0.794645	−	0.607075i	$-0.792343\pi$
$137$	−3.36838	+	2.98413i	−0.287780	+	0.254951i	0.506865	+	0.862026i	$0.330804\pi$
$138$	−4.13857	−	3.66645i	−0.352298	−	0.312109i
$139$	−1.15708	+	3.05097i	−0.0981423	+	0.258780i	−0.975091	−	0.221803i	$-0.928806\pi$
$139$	−1.15708	+	3.05097i	−0.0981423	+	0.258780i	0.876949	+	0.480583i	$0.159575\pi$
$140$	15.2196	+	7.98788i	1.28629	+	0.675099i
$141$	0.902245	−	0.799320i	0.0759828	−	0.0673149i
$142$	7.94489	+	7.03856i	0.666721	+	0.590663i
$143$	−5.61071	+	14.6816i	−0.469191	+	1.22774i
$144$	0.852414	−	0.755173i	0.0710345	−	0.0629311i
$145$	−3.86490	+	31.8303i	−0.320962	+	2.64336i
$146$	−8.01099			−0.662994
$147$	−5.10843			−0.421336
$148$	−2.53007	+	20.8370i	−0.207971	+	1.71279i
$149$	−5.65543	+	8.19331i	−0.463311	+	0.671222i	−0.983099	−	0.183073i	$-0.941396\pi$
$149$	−5.65543	+	8.19331i	−0.463311	+	0.671222i	0.519788	+	0.854295i	$0.326011\pi$
$150$	−28.4469			−2.32268
$151$	5.79367	+	8.39358i	0.471482	+	0.683060i	0.984513	−	0.175310i	$-0.0560929\pi$
$151$	5.79367	+	8.39358i	0.471482	+	0.683060i	−0.513031	+	0.858370i	$0.671477\pi$
$152$	0.548275	+	4.51545i	0.0444710	+	0.366251i
$153$	−1.41400	+	3.72841i	−0.114315	+	0.301424i
$154$	1.61025	+	13.2616i	0.129758	+	1.06865i
$155$	9.32406	−	24.5855i	0.748927	−	1.97476i
$156$	9.45325	+	4.99212i	0.756866	+	0.399689i
$157$	−6.04146	−	15.9300i	−0.482161	−	1.27135i	−0.926770	−	0.375629i	$-0.877427\pi$
$157$	−6.04146	−	15.9300i	−0.482161	−	1.27135i	0.444609	−	0.895725i	$-0.353343\pi$
$158$	24.9233	−	13.0808i	1.98280	−	1.04065i
$159$	1.32227	−	10.8899i	0.104863	−	0.863625i
$160$	−25.5209	−	13.3944i	−2.01761	−	1.05892i
$161$	0.411361	+	3.38787i	0.0324198	+	0.267001i
$162$	−0.268583	−	2.21198i	−0.0211019	−	0.173790i
$163$	5.33188	+	4.72363i	0.417625	+	0.369983i	0.845609	−	0.533803i	$-0.179238\pi$
$163$	5.33188	+	4.72363i	0.417625	+	0.369983i	−0.427984	+	0.903786i	$0.640776\pi$
$164$	−7.16468	−	18.8917i	−0.559468	−	1.47520i
$165$	−10.4377	−	15.1216i	−0.812571	−	1.17721i
$166$	18.4361	+	4.54410i	1.43092	+	0.352690i
$167$	−20.1327	−	10.5665i	−1.55792	−	0.817658i	−0.557991	−	0.829847i	$-0.688428\pi$
$167$	−20.1327	−	10.5665i	−1.55792	−	0.817658i	−0.999926	+	0.0121894i	$0.996120\pi$
$168$	2.95729			0.228160
$169$	1.63252	−	12.8971i	0.125579	−	0.992084i
$170$	37.4512			2.87237
$171$	−1.87311	−	0.983086i	−0.143241	−	0.0751785i
$172$	1.58412	+	0.390450i	0.120788	+	0.0297715i
$173$	4.61733	+	6.68936i	0.351049	+	0.508582i	0.958237	−	0.285976i	$-0.0923178\pi$
$173$	4.61733	+	6.68936i	0.351049	+	0.508582i	−0.607188	+	0.794558i	$0.707702\pi$
$174$	6.01063	+	15.8487i	0.455665	+	1.20149i
$175$	13.1427	+	11.6434i	0.993496	+	0.880161i
$176$	−0.598377	−	4.92808i	−0.0451044	−	0.371468i
$177$	−1.53777	−	12.6647i	−0.115586	−	0.951934i
$178$	10.5228	+	5.52277i	0.788714	+	0.413949i
$179$	0.113442	−	0.934278i	0.00847904	−	0.0698312i	−0.987855	−	0.155378i	$-0.950341\pi$
$179$	0.113442	−	0.934278i	0.00847904	−	0.0698312i	0.996334	+	0.0855465i	$0.0272636\pi$
$180$	−11.0660	+	5.80791i	−0.824814	+	0.432896i
$181$	−3.04219	−	8.02159i	−0.226124	−	0.596240i	0.773155	−	0.634218i	$-0.218678\pi$
$181$	−3.04219	−	8.02159i	−0.226124	−	0.596240i	−0.999279	+	0.0379777i	$0.987908\pi$
$182$	−3.89195	−	10.3414i	−0.288490	−	0.766554i
$183$	−3.75604	+	9.90385i	−0.277654	+	0.732114i
$184$	0.643123	+	5.29659i	0.0474116	+	0.390470i
$185$	−10.5813	+	27.9005i	−0.777949	+	2.05128i
$186$	−1.67547	−	13.7987i	−0.122851	−	1.01177i
$187$	9.87427	+	14.3054i	0.722078	+	1.04611i
$188$	−3.57396			−0.260658
$189$	−0.781285	+	1.13189i	−0.0568301	+	0.0823326i
$190$	−2.39485	+	19.7233i	−0.173741	+	1.43088i
$191$	16.6738			1.20647			0.603235	−	0.797563i	$-0.293878\pi$
$191$	16.6738			1.20647			0.603235	+	0.797563i	$0.293878\pi$
$192$	−12.9589			−0.935228
$193$	2.66021	−	21.9088i	0.191486	−	1.57703i	−0.507344	−	0.861743i	$-0.669373\pi$
$193$	2.66021	−	21.9088i	0.191486	−	1.57703i	0.698831	−	0.715287i	$-0.253704\pi$
$194$	24.0016	−	21.2636i	1.72322	−	1.52664i
$195$	11.3499	+	10.1067i	0.812783	+	0.723757i
$196$	11.3373	+	10.0439i	0.809805	+	0.717424i
$197$	11.5747	−	10.2543i	0.824665	−	0.730589i	−0.141104	−	0.989995i	$-0.545065\pi$
$197$	11.5747	−	10.2543i	0.824665	−	0.730589i	0.965768	+	0.259406i	$0.0835267\pi$
$198$	−8.60061	−	4.51395i	−0.611219	−	0.320792i
$199$	−6.01668	+	15.8647i	−0.426511	+	1.12462i	0.533782	+	0.845622i	$0.320770\pi$
$199$	−6.01668	+	15.8647i	−0.426511	+	1.12462i	−0.960293	+	0.278995i	$0.909999\pi$
$200$	20.5473	+	18.2034i	1.45292	+	1.28717i
$201$	6.49126	−	5.75075i	0.457858	−	0.405627i
$202$	7.70412	−	1.89889i	0.542060	−	0.133606i
$203$	3.70999	−	9.78244i	0.260390	−	0.686593i
$204$	10.4687	−	5.49442i	0.732958	−	0.384686i
$205$	−3.46219	−	28.5137i	−0.241810	−	1.99148i
$206$	−15.8650	−	14.0551i	−1.10536	−	0.979267i
$207$	−2.19715	−	1.15315i	−0.152712	−	0.0801497i
$208$	1.44627	+	3.84291i	0.100281	+	0.266458i
$209$	−8.16521	+	4.28543i	−0.564800	+	0.296430i
$210$	12.5420	+	3.09132i	0.865479	+	0.213321i
$211$	0.716472	−	1.03799i	0.0493240	−	0.0714581i	−0.797546	−	0.603258i	$-0.793869\pi$
$211$	0.716472	−	1.03799i	0.0493240	−	0.0714581i	0.846870	+	0.531800i	$0.178484\pi$
$212$	−24.3458	+	21.5685i	−1.67207	+	1.48133i
$213$	4.21791	+	2.21373i	0.289007	+	0.151682i
$214$	−1.33673	+	11.0090i	−0.0913770	+	0.752557i
$215$	2.05372	+	1.07787i	0.140062	+	0.0735103i
$216$	−1.22146	+	1.76959i	−0.0831099	+	0.120406i
$217$	−4.87380	+	7.06092i	−0.330855	+	0.479326i
$218$	−10.0222	+	2.47025i	−0.678789	+	0.167306i
$219$	−3.49076	+	0.860395i	−0.235884	+	0.0581401i
$220$	−6.56671	+	54.0817i	−0.442728	+	3.64619i
$221$	−10.7373	−	9.56119i	−0.722267	−	0.643155i
$222$	1.90138	+	15.6593i	0.127612	+	1.05098i
$223$	−2.21964	−	5.85270i	−0.148638	−	0.391926i	0.839932	−	0.542692i	$-0.182595\pi$
$223$	−2.21964	−	5.85270i	−0.148638	−	0.391926i	−0.988569	+	0.150767i	$0.951826\pi$
$224$	7.03942	+	6.23638i	0.470341	+	0.416686i
$225$	−12.3956	+	3.05525i	−0.826375	+	0.203683i
$226$	−17.2422	−	4.24981i	−1.14693	−	0.282693i
$227$	−9.85887	−	14.2830i	−0.654356	−	0.947999i	−0.999954	−	0.00961604i	$-0.996939\pi$
$227$	−9.85887	−	14.2830i	−0.654356	−	0.947999i	0.345597	−	0.938383i	$-0.387676\pi$
$228$	2.22416	+	5.86462i	0.147298	+	0.388394i
$229$	11.5758	−	10.2553i	0.764951	−	0.677688i	−0.187539	−	0.982257i	$-0.560051\pi$
$229$	11.5758	−	10.2553i	0.764951	−	0.677688i	0.952490	+	0.304569i	$0.0985126\pi$
$230$	−2.80914	+	23.1353i	−0.185229	+	1.52550i
$231$	2.12598	+	5.60575i	0.139879	+	0.368832i
$232$	5.80020	−	15.2939i	0.380802	−	1.00409i
$233$	17.1586	−	4.22922i	1.12410	−	0.277066i	0.366907	−	0.930258i	$-0.380417\pi$
$233$	17.1586	−	4.22922i	1.12410	−	0.277066i	0.757192	+	0.653192i	$0.226571\pi$
$234$	7.79562	+	1.94247i	0.509616	+	0.126983i
$235$	−4.93312	−	1.21591i	−0.321802	−	0.0793170i
$236$	−21.4878	+	31.1305i	−1.39874	+	2.02642i
$237$	9.45536	−	8.37672i	0.614192	−	0.544127i
$238$	−11.8650	−	2.92446i	−0.769094	−	0.189565i
$239$	2.44512			0.158162			0.0790809	−	0.996868i	$-0.474801\pi$
$239$	2.44512			0.158162			0.0790809	+	0.996868i	$0.474801\pi$
$240$	−4.66067	−	1.14875i	−0.300845	−	0.0741516i
$241$	−4.29548	+	11.3263i	−0.276696	+	0.729588i	0.722570	+	0.691298i	$0.242961\pi$
$241$	−4.29548	+	11.3263i	−0.276696	+	0.729588i	−0.999267	+	0.0382909i	$0.987809\pi$
$242$	−15.7885	+	8.28646i	−1.01493	+	0.532674i
$243$	−0.354605	−	0.935016i	−0.0227479	−	0.0599813i
$244$	27.8084	−	14.5949i	1.78025	−	0.934346i
$245$	12.2317	+	17.7207i	0.781455	+	1.13213i
$246$	−8.62553	−	12.4962i	−0.549944	−	0.796731i
$247$	5.72192	−	5.04329i	0.364077	−	0.320897i
$248$	−7.61970	+	11.0390i	−0.483852	+	0.700980i
$249$	8.52153			0.540030
$250$	41.4372	+	60.0322i	2.62072	+	3.79677i
$251$	5.39845	+	4.78261i	0.340747	+	0.301875i	0.816090	−	0.577925i	$-0.196137\pi$
$251$	5.39845	+	4.78261i	0.340747	+	0.301875i	−0.475343	+	0.879801i	$0.657676\pi$
$252$	3.95939	−	0.975902i	0.249418	−	0.0614760i
$253$	−9.57774	+	5.02678i	−0.602147	+	0.316031i
$254$	−28.4314	+	14.9219i	−1.78394	+	0.936286i
$255$	16.3192	−	4.02233i	1.02195	−	0.251888i
$256$	5.95063	+	5.27180i	0.371914	+	0.329487i
$257$	9.74589	+	14.1194i	0.607932	+	0.880741i	0.999218	−	0.0395278i	$-0.0125854\pi$
$257$	9.74589	+	14.1194i	0.607932	+	0.880741i	−0.391287	+	0.920269i	$0.627970\pi$
$258$	1.22611			0.0763344
$259$	5.53095	−	8.01297i	0.343677	−	0.497901i
$260$	−5.31781	−	44.7457i	−0.329796	−	2.77501i
$261$	4.32130	+	6.26048i	0.267482	+	0.387514i
$262$	−16.1240	−	23.3597i	−0.996145	−	1.44316i
$263$	23.0987	−	12.1231i	1.42432	−	0.747543i	0.436005	−	0.899944i	$-0.356393\pi$
$263$	23.0987	−	12.1231i	1.42432	−	0.747543i	0.988319	+	0.152401i	$0.0487006\pi$
$264$	3.32376	+	8.76404i	0.204563	+	0.539389i
$265$	−40.9422	+	21.4881i	−2.51506	+	1.32001i
$266$	2.29886	−	6.06160i	0.140952	−	0.371661i
$267$	5.17841	+	1.27636i	0.316913	+	0.0781122i
$268$	−25.7131			−1.57068
$269$	9.87544	+	2.43408i	0.602116	+	0.148408i	0.528579	−	0.848884i	$-0.322725\pi$
$269$	9.87544	+	2.43408i	0.602116	+	0.148408i	0.0735373	+	0.997292i	$0.476571\pi$
$270$	−7.03007	+	6.22810i	−0.427836	+	0.379030i
$271$	14.4590	−	20.9475i	0.878325	−	1.27247i	−0.0828583	−	0.996561i	$-0.526405\pi$
$271$	14.4590	−	20.9475i	0.878325	−	1.27247i	0.961183	−	0.275912i	$-0.0889797\pi$
$272$	4.40910	+	1.08675i	0.267341	+	0.0658937i
$273$	−2.80659	−	4.08822i	−0.169862	−	0.247430i
$274$	9.73589	−	2.39968i	0.588167	−	0.144970i
$275$	−19.7344	+	52.0353i	−1.19003	+	3.13784i
$276$	2.60892	+	6.87915i	0.157038	+	0.414076i
$277$	1.25385	−	10.3264i	0.0753365	−	0.620452i	−0.905322	−	0.424726i	$-0.860370\pi$
$277$	1.25385	−	10.3264i	0.0753365	−	0.620452i	0.980659	−	0.195726i	$-0.0627064\pi$
$278$	5.44222	−	4.82139i	0.326403	−	0.289168i
$279$	−2.21209	−	5.83280i	−0.132434	−	0.349201i
$280$	−7.08099	−	10.2586i	−0.423170	−	0.613067i
$281$	8.82143	+	2.17429i	0.526243	+	0.129707i	0.493482	−	0.869756i	$-0.335724\pi$
$281$	8.82143	+	2.17429i	0.526243	+	0.129707i	0.0327607	+	0.999463i	$0.489570\pi$
$282$	−2.60783	+	0.642772i	−0.155294	+	0.0382765i
$283$	−1.09366	−	0.968901i	−0.0650115	−	0.0575952i	0.629991	−	0.776602i	$-0.283058\pi$
$283$	−1.09366	−	0.968901i	−0.0650115	−	0.0575952i	−0.695003	+	0.719007i	$0.744597\pi$
$284$	−5.00840	−	13.2061i	−0.297194	−	0.783635i
$285$	1.07478	+	8.85159i	0.0636643	+	0.524323i
$286$	26.2728	−	23.1569i	1.55355	−	1.36929i
$287$	−1.12969	+	9.30385i	−0.0666836	+	0.549189i
$288$	−6.63927	+	1.63643i	−0.391223	+	0.0964277i
$289$	1.06764	−	0.263150i	0.0628024	−	0.0154794i
$290$	40.5859	−	58.7989i	2.38329	−	3.45279i
$291$	8.17487	−	11.8433i	0.479220	−	0.694269i
$292$	9.43881	+	4.95387i	0.552364	+	0.289903i
$293$	1.44393	−	11.8918i	0.0843551	−	0.694727i	−0.887774	−	0.460280i	$-0.847749\pi$
$293$	1.44393	−	11.8918i	0.0843551	−	0.694727i	0.972129	−	0.234447i	$-0.0753279\pi$
$294$	10.0789	+	5.28982i	0.587814	+	0.308508i
$295$	−40.2506	+	35.6589i	−2.34348	+	2.07614i
$296$	8.64709	−	12.5275i	0.502602	−	0.728145i
$297$	−4.23249	−	1.04322i	−0.245594	−	0.0605335i
$298$	19.6424	−	10.3091i	1.13785	−	0.597191i
$299$	6.71177	−	5.91575i	0.388152	−	0.342117i
$300$	33.5170	+	17.5911i	1.93511	+	1.01562i
$301$	−0.566475	−	0.501853i	−0.0326511	−	0.0289263i
$302$	−2.73927	−	22.5599i	−0.157627	−	1.29818i
$303$	3.15310	−	1.65487i	0.181141	−	0.0950700i
$304$	−0.854269	+	2.25252i	−0.0489957	+	0.129191i
$305$	43.3491	−	10.6846i	2.48216	−	0.611799i
$306$	6.65061	−	5.89192i	0.380190	−	0.336819i
$307$	−20.6727	−	18.3144i	−1.17985	−	1.04526i	−0.998081	−	0.0619163i	$-0.980279\pi$
$307$	−20.6727	−	18.3144i	−1.17985	−	1.04526i	−0.181770	−	0.983341i	$-0.558183\pi$
$308$	6.30352	−	16.6210i	0.359176	−	0.947070i
$309$	−8.42265	−	4.42055i	−0.479148	−	0.251476i
$310$	−43.8549	+	38.8520i	−2.49079	+	2.20665i
$311$	8.76110	+	7.76165i	0.496796	+	0.440123i	0.873942	−	0.486031i	$-0.161556\pi$
$311$	8.76110	+	7.76165i	0.496796	+	0.440123i	−0.377145	+	0.926154i	$0.623094\pi$
$312$	−4.38782	−	6.39152i	−0.248411	−	0.361849i
$313$	−12.3192	+	10.9138i	−0.696321	+	0.616886i	−0.935182	−	0.354167i	$-0.884764\pi$
$313$	−12.3192	+	10.9138i	−0.696321	+	0.616886i	0.238861	+	0.971054i	$0.423226\pi$
$314$	−4.57589	+	37.6858i	−0.258232	+	2.12674i
$315$	5.79714			0.326632
$316$	−37.4545			−2.10698
$317$	2.01959	−	16.6329i	0.113432	−	0.934195i	−0.819236	−	0.573457i	$-0.805602\pi$
$317$	2.01959	−	16.6329i	0.113432	−	0.934195i	0.932667	−	0.360737i	$-0.117475\pi$
$318$	−13.8854	+	20.1165i	−0.778656	+	1.12808i
$319$	33.1604			1.85663
$320$	31.0290	+	44.9533i	1.73458	+	2.51297i
$321$	0.599908	+	4.94068i	0.0334836	+	0.275762i
$322$	2.69655	−	7.11021i	0.150273	−	0.396237i
$323$	−1.01677	−	8.37381i	−0.0565743	−	0.465931i
$324$	−1.05140	+	2.77231i	−0.0584111	+	0.154017i
$325$	5.66444	−	45.6808i	0.314207	−	2.53391i
$326$	−5.62841	−	14.8409i	−0.311729	−	0.821962i
$327$	−4.10183	+	2.15281i	−0.226832	+	0.119050i
$328$	−1.76616	+	14.5456i	−0.0975199	+	0.803149i
$329$	1.46793	+	0.770429i	0.0809296	+	0.0424751i
$330$	4.93496	+	40.6431i	0.271661	+	2.23733i
$331$	2.09655	+	17.2666i	0.115237	+	0.949061i	0.929566	+	0.368657i	$0.120182\pi$
$331$	2.09655	+	17.2666i	0.115237	+	0.949061i	−0.814329	+	0.580404i	$0.802895\pi$
$332$	−18.9121	−	16.7546i	−1.03793	−	0.919529i
$333$	2.51035	+	6.61926i	0.137567	+	0.362733i
$334$	28.7801	+	41.6952i	1.57478	+	2.28146i
$335$	−35.4917	−	8.74791i	−1.93912	−	0.477949i
$336$	1.38686	+	0.727878i	0.0756592	+	0.0397090i
$337$	−13.2280			−0.720577			−0.360289	−	0.932841i	$-0.617322\pi$
$337$	−13.2280			−0.720577			−0.360289	+	0.932841i	$0.617322\pi$
$338$	−16.5760	+	23.7554i	−0.901616	+	1.29212i
$339$	−7.96965			−0.432852
$340$	−44.1262	−	23.1592i	−2.39308	−	1.25599i
$341$	−26.4031	−	6.50778i	−1.42981	−	0.352416i
$342$	2.67765	+	3.87925i	0.144791	+	0.209766i
$343$	−5.90533	−	15.5711i	−0.318858	−	0.840759i
$344$	−0.885628	−	0.784598i	−0.0477498	−	0.0423027i
$345$	1.26071	+	10.3829i	0.0678742	+	0.558994i
$346$	−2.18309	−	17.9794i	−0.117364	−	0.966576i
$347$	3.85282	+	2.02212i	0.206830	+	0.108553i	0.564958	−	0.825120i	$-0.308892\pi$
$347$	3.85282	+	2.02212i	0.206830	+	0.108553i	−0.358128	+	0.933673i	$0.616585\pi$
$348$	2.71868	−	22.3904i	0.145737	−	1.20025i
$349$	27.4354	−	14.3992i	1.46858	−	0.770772i	0.474589	−	0.880207i	$-0.342597\pi$
$349$	27.4354	−	14.3992i	1.46858	−	0.770772i	0.993994	+	0.109435i	$0.0349043\pi$
$350$	−13.8737	−	36.5818i	−0.741578	−	1.95538i
$351$	3.60554	+	0.00915914i	0.192449	+	0.000488879i
$352$	−10.5700	+	27.8708i	−0.563383	+	1.48552i
$353$	−1.26585	−	10.4252i	−0.0673744	−	0.554878i	−0.986839	−	0.161706i	$-0.948300\pi$
$353$	−1.26585	−	10.4252i	−0.0673744	−	0.554878i	0.919465	−	0.393173i	$-0.128623\pi$
$354$	−10.0804	+	26.5797i	−0.535765	+	1.41270i
$355$	−2.42021	−	19.9322i	−0.128451	−	1.05789i
$356$	−8.98306	−	13.0142i	−0.476101	−	0.689752i
$357$	−5.48423			−0.290256
$358$	−1.19127	+	1.72586i	−0.0629607	+	0.0912143i
$359$	−0.601651	+	4.95504i	−0.0317539	+	0.261517i	0.968183	+	0.250245i	$0.0805111\pi$
$359$	−0.601651	+	4.95504i	−0.0317539	+	0.261517i	−0.999936	+	0.0112720i	$0.996412\pi$
$360$	9.06326			0.477676
$361$	−14.5250			−0.764473
$362$	−2.30420	+	18.9768i	−0.121106	+	0.997397i
$363$	−5.98982	+	5.30652i	−0.314384	+	0.278520i
$364$	−1.80933	+	14.5913i	−0.0948344	+	0.764790i
$365$	11.3430	+	10.0490i	0.593719	+	0.525989i
$366$	17.6662	−	15.6509i	0.923425	−	0.818083i
$367$	25.2342	+	13.2440i	1.31722	+	0.691329i	0.969227	−	0.246170i	$-0.0791721\pi$
$367$	25.2342	+	13.2440i	1.31722	+	0.691329i	0.347990	+	0.937498i	$0.386864\pi$
$368$	−1.00205	+	2.64219i	−0.0522356	+	0.137734i
$369$	−5.10067	−	4.51880i	−0.265530	−	0.235239i
$370$	49.7680	−	44.0906i	2.58731	−	2.29216i
$371$	14.6490	−	3.61065i	0.760536	−	0.187455i
$372$	−6.55883	+	17.2942i	−0.340059	+	0.896663i
$373$	25.8382	−	13.5609i	1.33785	−	0.702158i	0.364439	−	0.931227i	$-0.381261\pi$
$373$	25.8382	−	13.5609i	1.33785	−	0.702158i	0.973410	+	0.229070i	$0.0735683\pi$
$374$	−4.66859	−	38.4493i	−0.241407	−	1.98817i
$375$	24.5037	+	21.7084i	1.26537	+	1.12102i
$376$	2.29496	+	1.20449i	0.118354	+	0.0621168i
$377$	−26.6472	+	6.49619i	−1.37240	+	0.334571i
$378$	2.71355	−	1.42418i	0.139570	−	0.0732520i
$379$	−10.7361	−	2.64622i	−0.551479	−	0.135927i	−0.0462770	−	0.998929i	$-0.514736\pi$
$379$	−10.7361	−	2.64622i	−0.551479	−	0.135927i	−0.505202	+	0.863001i	$0.668582\pi$
$380$	15.0183	−	21.7578i	0.770422	−	1.11615i
$381$	−10.7862	+	9.55577i	−0.552595	+	0.489557i
$382$	−32.8973	−	17.2658i	−1.68317	−	0.883396i
$383$	−2.07456	+	17.0855i	−0.106005	+	0.873030i	0.838583	+	0.544773i	$0.183384\pi$
$383$	−2.07456	+	17.0855i	−0.106005	+	0.873030i	−0.944589	+	0.328257i	$0.893539\pi$
$384$	13.4584	+	7.06353i	0.686798	+	0.360459i
$385$	14.3554	−	20.7974i	0.731618	−	1.05993i
$386$	−27.9353	+	40.4713i	−1.42187	+	2.05994i
$387$	0.534274	−	0.131687i	0.0271587	−	0.00669402i
$388$	−41.4285	+	10.2112i	−2.10322	+	0.518396i
$389$	−0.0162010	+	0.133428i	−0.000821426	+	0.00676505i	−0.993114	−	0.117153i	$-0.962623\pi$
$389$	−0.0162010	+	0.133428i	−0.000821426	+	0.00676505i	0.992292	+	0.123919i	$0.0395461\pi$
$390$	−11.9277	−	31.6934i	−0.603984	−	1.60486i
$391$	−1.19266	−	9.82242i	−0.0603153	−	0.496741i
$392$	−3.89506	−	10.2704i	−0.196730	−	0.518735i
$393$	−9.53485	−	8.44714i	−0.480970	−	0.426102i
$394$	−33.4553	+	8.24599i	−1.68545	+	0.415427i
$395$	−51.6982	−	12.7425i	−2.60122	−	0.641143i
$396$	7.34217	+	10.6370i	0.368958	+	0.534528i
$397$	−2.76068	−	7.27931i	−0.138555	−	0.365338i	0.847722	−	0.530441i	$-0.177974\pi$
$397$	−2.76068	−	7.27931i	−0.138555	−	0.365338i	−0.986276	+	0.165103i	$0.947204\pi$
$398$	28.2989	−	25.0706i	1.41849	−	1.25668i
$399$	0.350694	−	2.88822i	0.0175567	−	0.144592i
$400$	5.15553	+	13.5940i	0.257776	+	0.679700i
$401$	−6.77199	+	17.8563i	−0.338177	+	0.891700i	0.652783	+	0.757545i	$0.273601\pi$
$401$	−6.77199	+	17.8563i	−0.338177	+	0.891700i	−0.990960	+	0.134155i	$0.957168\pi$
$402$	−18.7622	+	4.62446i	−0.935772	+	0.230647i
$403$	22.4920	+	0.0571364i	1.12041	+	0.00284617i
$404$	−10.2515	−	2.52677i	−0.510031	−	0.125711i
$405$	−2.39442	+	3.46891i	−0.118980	+	0.172372i
$406$	−17.4496	+	15.4590i	−0.866009	+	0.767217i
$407$	29.9631	+	7.38524i	1.48522	+	0.366073i
$408$	−8.57405			−0.424479
$409$	32.7725	+	8.07770i	1.62050	+	0.399417i	0.942114	−	0.335292i	$-0.108835\pi$
$409$	32.7725	+	8.07770i	1.62050	+	0.399417i	0.678383	+	0.734709i	$0.262681\pi$
$410$	−22.6953	+	59.8425i	−1.12084	+	2.95541i
$411$	3.98465	−	2.09131i	0.196548	−	0.103157i
$412$	10.0011	+	26.3708i	0.492721	+	1.29920i
$413$	15.5364	−	8.15413i	0.764496	−	0.401239i
$414$	3.14087	+	4.55033i	0.154365	+	0.223637i
$415$	−20.4041	−	29.5604i	−1.00160	−	1.45106i
$416$	3.03395	−	24.4672i	0.148752	−	1.19961i
$417$	1.85360	−	2.68541i	0.0907713	−	0.131505i
$418$	20.5475			1.00501
$419$	−8.82021	−	12.7783i	−0.430896	−	0.624260i	0.546049	−	0.837753i	$-0.316131\pi$
$419$	−8.82021	−	12.7783i	−0.430896	−	0.624260i	−0.976945	+	0.213493i	$0.931516\pi$
$420$	−12.8658	−	11.3981i	−0.627784	−	0.556168i
$421$	15.2172	−	3.75071i	0.741641	−	0.182798i	0.149646	−	0.988740i	$-0.452187\pi$
$421$	15.2172	−	3.75071i	0.741641	−	0.182798i	0.591995	+	0.805941i	$0.298340\pi$
$422$	−2.48844	+	1.30604i	−0.121136	+	0.0635768i
$423$	−1.06732	+	0.560171i	−0.0518947	+	0.0272365i
$424$	22.9022	−	5.64489i	1.11223	−	0.274140i
$425$	−38.1046	−	33.7577i	−1.84835	−	1.63749i
$426$	−6.02959	−	8.73537i	−0.292135	−	0.423230i
$427$	−14.5679			−0.704990
$428$	8.38275	−	12.1445i	0.405195	−	0.587027i
$429$	8.96121	−	12.9123i	0.432651	−	0.623410i
$430$	−2.93583	−	4.25328i	−0.141578	−	0.205111i
$431$	−13.4931	−	19.5482i	−0.649942	−	0.941604i	−0.999988	−	0.00487115i	$-0.998449\pi$
$431$	−13.4931	−	19.5482i	−0.649942	−	0.941604i	0.350046	−	0.936732i	$-0.386166\pi$
$432$	−1.00837	+	0.529233i	−0.0485152	+	0.0254627i
$433$	−1.92791	−	5.08349i	−0.0926496	−	0.244297i	0.880678	−	0.473714i	$-0.157087\pi$
$433$	−1.92791	−	5.08349i	−0.0926496	−	0.244297i	−0.973328	+	0.229417i	$0.926318\pi$
$434$	16.9276	−	8.88430i	0.812552	−	0.426460i
$435$	11.3701	−	29.9804i	0.545153	−	1.43745i
$436$	13.3360	+	3.28704i	0.638681	+	0.157421i
$437$	5.24916			0.251101
$438$	7.77820	+	1.91715i	0.371657	+	0.0916052i
$439$	−7.51684	+	6.65934i	−0.358759	+	0.317833i	−0.823179	−	0.567783i	$-0.807801\pi$
$439$	−7.51684	+	6.65934i	−0.358759	+	0.317833i	0.464420	+	0.885615i	$0.346263\pi$
$440$	22.4432	−	32.5146i	1.06994	−	1.55007i
$441$	4.95998	+	1.22253i	0.236190	+	0.0582155i
$442$	11.2839	+	29.9827i	0.536721	+	1.42613i
$443$	2.26755	−	0.558902i	0.107735	−	0.0265542i	−0.185080	−	0.982724i	$-0.559254\pi$
$443$	2.26755	−	0.558902i	0.107735	−	0.0265542i	0.292814	+	0.956169i	$0.405408\pi$
$444$	7.44318	−	19.6260i	0.353237	−	0.931411i
$445$	−7.97168	−	21.0196i	−0.377894	−	0.996425i
$446$	−1.68118	+	13.8458i	−0.0796064	+	0.655618i
$447$	7.45189	−	6.60179i	0.352462	−	0.312254i
$448$	−6.32011	−	16.6648i	−0.298597	−	0.787336i
$449$	−12.0847	−	17.5078i	−0.570314	−	0.826242i	0.426625	−	0.904429i	$-0.359702\pi$
$449$	−12.0847	−	17.5078i	−0.570314	−	0.826242i	−0.996939	+	0.0781866i	$0.975087\pi$
$450$	27.6203	+	6.80778i	1.30203	+	0.320922i
$451$	−28.8420	+	7.10892i	−1.35812	+	0.334746i
$452$	17.6873	+	15.6695i	0.831939	+	0.737033i
$453$	−3.61660	−	9.53619i	−0.169923	−	0.448049i
$454$	4.66131	+	38.3893i	0.218766	+	1.80170i
$455$	−7.46153	+	19.5247i	−0.349802	+	0.915333i
$456$	0.548275	−	4.51545i	0.0256753	−	0.211455i
$457$	14.9066	−	3.67414i	0.697299	−	0.171869i	0.125295	−	0.992120i	$-0.460012\pi$
$457$	14.9066	−	3.67414i	0.697299	−	0.171869i	0.572004	+	0.820251i	$0.306166\pi$
$458$	−33.4585	+	8.24677i	−1.56341	+	0.385346i
$459$	2.26518	−	3.28167i	0.105729	−	0.153175i
$460$	17.6164	−	25.5217i	0.821367	−	1.18996i
$461$	16.3775	+	8.59556i	0.762775	+	0.400335i	0.800792	−	0.598942i	$-0.204412\pi$
$461$	16.3775	+	8.59556i	0.762775	+	0.400335i	−0.0380175	+	0.999277i	$0.512104\pi$
$462$	1.61025	−	13.2616i	0.0749156	−	0.616986i
$463$	−9.95335	−	5.22392i	−0.462571	−	0.242776i	0.217304	−	0.976104i	$-0.430274\pi$
$463$	−9.95335	−	5.22392i	−0.462571	−	0.242776i	−0.679875	+	0.733328i	$0.737966\pi$
$464$	6.48436	−	5.74464i	0.301029	−	0.266688i
$465$	−14.9368	+	21.6397i	−0.692679	+	1.00352i
$466$	−38.2333	−	9.42366i	−1.77112	−	0.436543i
$467$	−2.24298	+	1.17721i	−0.103793	+	0.0544746i	−0.515821	−	0.856697i	$-0.672513\pi$
$467$	−2.24298	+	1.17721i	−0.103793	+	0.0544746i	0.412028	+	0.911171i	$0.364821\pi$
$468$	−7.98386	−	7.10937i	−0.369054	−	0.328631i
$469$	10.5611	+	5.54290i	0.487667	+	0.255947i
$470$	8.47395	+	7.50727i	0.390874	+	0.346284i
$471$	2.05360	+	16.9129i	0.0946250	+	0.779307i
$472$	24.2896	−	12.7482i	1.11802	−	0.586783i
$473$	0.850588	−	2.24282i	0.0391101	−	0.103125i
$474$	−27.3296	+	6.73613i	−1.25529	+	0.309401i
$475$	20.2149	−	17.9088i	0.927521	−	0.821712i
$476$	12.1713	+	10.7828i	0.557871	+	0.494230i
$477$	−3.88997	+	10.2570i	−0.178110	+	0.469637i
$478$	−4.82422	−	2.53194i	−0.220654	−	0.115808i
$479$	−20.8617	+	18.4819i	−0.953197	+	0.844459i	−0.987924	−	0.154938i	$-0.950482\pi$
$479$	−20.8617	+	18.4819i	−0.953197	+	0.844459i	0.0347271	+	0.999397i	$0.488944\pi$
$480$	21.5738	+	19.1127i	0.984706	+	0.872373i
$481$	−25.5247	−	0.0648403i	−1.16383	−	0.00295646i
$482$	20.2034	−	17.8987i	0.920240	−	0.815261i
$483$	0.411361	−	3.38787i	0.0187176	−	0.154153i
$484$	23.7268			1.07849
$485$	−60.6576			−2.75432
$486$	−0.268583	+	2.21198i	−0.0121832	+	0.100337i
$487$	12.9399	−	18.7467i	0.586363	−	0.849493i	−0.411725	−	0.911308i	$-0.635074\pi$
$487$	12.9399	−	18.7467i	0.586363	−	0.849493i	0.998088	+	0.0618153i	$0.0196890\pi$
$488$	−22.7755			−1.03100
$489$	−4.04650	−	5.86237i	−0.182989	−	0.265106i
$490$	−5.78319	−	47.6289i	−0.261258	−	2.15165i
$491$	−11.5085	+	30.3455i	−0.519372	+	1.36947i	0.377018	+	0.926206i	$0.376949\pi$
$491$	−11.5085	+	30.3455i	−0.519372	+	1.36947i	−0.896390	+	0.443266i	$0.853820\pi$
$492$	2.43541	+	20.0574i	0.109797	+	0.904256i
$493$	−10.7564	+	28.3622i	−0.484442	+	1.27737i
$494$	−16.5117	+	4.02530i	−0.742896	+	0.181107i
$495$	6.51554	+	17.1801i	0.292852	+	0.772186i
$496$	−6.29040	+	3.30145i	−0.282447	+	0.148240i
$497$	−0.789699	+	6.50376i	−0.0354228	+	0.291733i
$498$	−16.8129	−	8.82411i	−0.753406	−	0.395418i
$499$	4.33782	+	35.7252i	0.194188	+	1.59928i	0.685352	+	0.728212i	$0.259649\pi$
$499$	4.33782	+	35.7252i	0.194188	+	1.59928i	−0.491164	+	0.871067i	$0.663428\pi$
$500$	−11.6997	−	96.3560i	−0.523228	−	4.30917i
$501$	17.0190	+	15.0775i	0.760352	+	0.673613i
$502$	−5.69869	−	15.0262i	−0.254345	−	0.670652i
$503$	−4.16174	−	6.02932i	−0.185563	−	0.268834i	0.719151	−	0.694854i	$-0.244531\pi$
$503$	−4.16174	−	6.02932i	−0.185563	−	0.268834i	−0.904714	+	0.426020i	$0.859915\pi$
$504$	−2.87136	−	0.707725i	−0.127900	−	0.0315246i
$505$	−13.2905	−	6.97537i	−0.591417	−	0.310400i
$506$	24.1021			1.07147
$507$	−4.67156	+	12.1316i	−0.207471	+	0.538785i
$508$	42.7263			1.89567
$509$	5.06818	+	2.65999i	0.224643	+	0.117902i	0.573291	−	0.819352i	$-0.305667\pi$
$509$	5.06818	+	2.65999i	0.224643	+	0.117902i	−0.348647	+	0.937254i	$0.613359\pi$
$510$	−36.3629	−	8.96265i	−1.61018	−	0.396873i
$511$	−2.80890	−	4.06940i	−0.124258	−	0.180019i
$512$	4.49801	+	11.8603i	0.198786	+	0.524155i
$513$	1.58342	+	1.40279i	0.0699096	+	0.0619345i
$514$	−4.60789	−	37.9494i	−0.203245	−	1.67387i
$515$	4.83285	+	39.8021i	0.212961	+	1.75389i
$516$	−1.44465	−	0.758208i	−0.0635970	−	0.0333783i
$517$	−0.633358	+	5.21617i	−0.0278550	+	0.229407i
$518$	−19.2100	+	10.0822i	−0.844040	+	0.442987i
$519$	−2.88229	−	7.59998i	−0.126519	−	0.333602i
$520$	−11.6654	+	30.5250i	−0.511560	+	1.33861i
$521$	−1.68595	+	4.44548i	−0.0738627	+	0.194760i	−0.966863	−	0.255297i	$-0.917827\pi$
$521$	−1.68595	+	4.44548i	−0.0738627	+	0.194760i	0.893000	+	0.450056i	$0.148596\pi$
$522$	−2.04312	−	16.8266i	−0.0894251	−	0.736482i
$523$	0.906802	−	2.39104i	0.0396517	−	0.104553i	−0.913728	−	0.406327i	$-0.866809\pi$
$523$	0.906802	−	2.39104i	0.0396517	−	0.104553i	0.953380	+	0.301774i	$0.0975787\pi$
$524$	4.55259	+	37.4939i	0.198881	+	1.63793i
$525$	−9.97436	−	14.4504i	−0.435317	−	0.630665i
$526$	−58.1271			−2.53446
$527$	14.1306	−	20.4717i	0.615538	−	0.891761i
$528$	−0.598377	+	4.92808i	−0.0260410	+	0.214467i
$529$	−16.8428			−0.732294
$530$	103.030			4.47534
$531$	−1.53777	+	12.6647i	−0.0667335	+	0.549600i
$532$	−6.45699	+	5.72039i	−0.279946	+	0.248011i
$533$	21.7844	−	11.3628i	0.943586	−	0.492179i
$534$	−8.89529	−	7.88054i	−0.384937	−	0.341024i
$535$	15.7024	−	13.9111i	0.678873	−	0.601429i
$536$	16.5112	+	8.66577i	0.713177	+	0.374304i
$537$	−0.333733	+	0.879981i	−0.0144016	+	0.0379740i
$538$	−16.9637	−	15.0285i	−0.731357	−	0.647926i
$539$	16.6682	−	14.7667i	0.717950	−	0.636048i
$540$	12.1344	−	2.99086i	0.522182	−	0.128706i
$541$	−7.01674	+	18.5016i	−0.301673	+	0.795447i	0.695374	+	0.718648i	$0.255239\pi$
$541$	−7.01674	+	18.5016i	−0.301673	+	0.795447i	−0.997047	+	0.0767982i	$0.975530\pi$
$542$	−50.2190	+	26.3570i	−2.15709	+	1.13213i
$543$	1.03409	+	8.51654i	0.0443773	+	0.365480i
$544$	−20.4093	−	18.0811i	−0.875044	−	0.775221i
$545$	17.2894	+	9.07417i	0.740596	+	0.388695i
$546$	1.30400	+	10.9723i	0.0558061	+	0.469570i
$547$	8.59976	−	4.51350i	0.367699	−	0.192983i	−0.270746	−	0.962651i	$-0.587270\pi$
$547$	8.59976	−	4.51350i	0.367699	−	0.192983i	0.638445	+	0.769667i	$0.279578\pi$
$548$	−12.9551	−	3.19314i	−0.553413	−	0.136404i
$549$	6.01704	−	8.71719i	0.256801	−	0.372040i
$550$	92.8188	−	82.2303i	3.95781	−	3.50631i
$551$	−14.2489	−	7.47839i	−0.607023	−	0.318590i
$552$	0.643123	−	5.29659i	0.0273731	−	0.225438i
$553$	15.3836	+	8.07395i	0.654179	+	0.343339i
$554$	−13.1669	+	19.0755i	−0.559408	+	0.810442i
$555$	16.9508	−	24.5575i	0.719522	−	1.04241i
$556$	−9.39367	+	2.31533i	−0.398380	+	0.0981920i
$557$	24.7036	−	6.08888i	1.04672	−	0.257994i	0.321789	−	0.946812i	$-0.395716\pi$
$557$	24.7036	−	6.08888i	1.04672	−	0.257994i	0.724935	+	0.688817i	$0.241870\pi$
$558$	−1.67547	+	13.7987i	−0.0709283	+	0.584147i
$559$	−0.244148	+	1.96893i	−0.0103264	+	0.0832767i
$560$	−0.795767	−	6.55373i	−0.0336273	−	0.276946i
$561$	−6.16385	−	16.2527i	−0.260238	−	0.686191i
$562$	−15.1532	−	13.4245i	−0.639197	−	0.566280i
$563$	32.2293	−	7.94381i	1.35830	−	0.334792i	0.508124	−	0.861284i	$-0.330339\pi$
$563$	32.2293	−	7.94381i	1.35830	−	0.334792i	0.850180	+	0.526492i	$0.176493\pi$
$564$	3.47011	+	0.855305i	0.146118	+	0.0360148i
$565$	19.0827	+	27.6460i	0.802814	+	1.16308i
$566$	1.15449	+	3.04414i	0.0485268	+	0.127955i
$567$	1.02946	−	0.912022i	0.0432333	−	0.0383013i
$568$	−1.23462	+	10.1680i	−0.0518034	+	0.426639i
$569$	2.92831	+	7.72133i	0.122761	+	0.323695i	0.982283	−	0.187405i	$-0.0600076\pi$
$569$	2.92831	+	7.72133i	0.122761	+	0.323695i	−0.859521	+	0.511100i	$0.829238\pi$
$570$	7.04536	−	18.5771i	0.295098	−	0.778109i
$571$	23.3818	−	5.76309i	0.978497	−	0.241178i	0.282536	−	0.959257i	$-0.408824\pi$
$571$	23.3818	−	5.76309i	0.978497	−	0.241178i	0.695962	+	0.718079i	$0.254978\pi$
$572$	−45.2753	+	11.0374i	−1.89306	+	0.461499i
$573$	−16.1893	−	3.99029i	−0.676316	−	0.166697i
$574$	11.8631	−	17.1866i	0.495156	−	0.717357i
$575$	23.7119	−	21.0069i	0.988854	−	0.876048i
$576$	12.5823	+	3.10127i	0.524264	+	0.129220i
$577$	43.1092			1.79466			0.897329	−	0.441362i	$-0.145504\pi$
$577$	43.1092			1.79466			0.897329	+	0.441362i	$0.145504\pi$
$578$	−2.37894	−	0.586357i	−0.0989510	−	0.0243892i
$579$	−7.82603	+	20.6355i	−0.325239	+	0.857584i
$580$	−84.1800	+	44.1811i	−3.49538	+	1.83452i
$581$	4.15598	+	10.9584i	0.172419	+	0.454632i
$582$	−28.3929	+	14.9017i	−1.17692	+	0.617697i
$583$	27.1646	+	39.3547i	1.12504	+	1.62991i
$584$	−4.39144	−	6.36210i	−0.181719	−	0.263265i
$585$	−8.60140	−	12.5292i	−0.355624	−	0.518020i
$586$	−15.1629	+	21.9673i	−0.626375	+	0.907460i
$587$	−34.7013			−1.43227			−0.716137	−	0.697960i	$-0.754092\pi$
$587$	−34.7013			−1.43227			−0.716137	+	0.697960i	$0.754092\pi$
$588$	−8.60415	−	12.4653i	−0.354829	−	0.514059i
$589$	9.87765	+	8.75083i	0.407001	+	0.360572i
$590$	116.339	−	28.6751i	4.78961	−	1.18053i
$591$	−13.6924	+	7.18632i	−0.563230	+	0.295606i
$592$	7.13855	−	3.74660i	0.293393	−	0.153984i
$593$	5.08328	−	1.25292i	0.208745	−	0.0514511i	−0.133556	−	0.991041i	$-0.542640\pi$
$593$	5.08328	−	1.25292i	0.208745	−	0.0514511i	0.342302	+	0.939590i	$0.388794\pi$
$594$	7.27044	+	6.44104i	0.298310	+	0.264279i
$595$	13.1315	+	19.0243i	0.538341	+	0.779921i
$596$	−29.5183			−1.20912
$597$	9.63851	−	13.9638i	0.394478	−	0.571500i
$598$	−19.3681	+	4.72165i	−0.792021	+	0.193083i
$599$	14.0523	+	20.3582i	0.574160	+	0.831814i	0.997237	−	0.0742791i	$-0.0236656\pi$
$599$	14.0523	+	20.3582i	0.574160	+	0.831814i	−0.423077	+	0.906094i	$0.639050\pi$
$600$	−15.5939	−	22.5917i	−0.636619	−	0.922302i
$601$	−39.5397	+	20.7520i	−1.61286	+	0.846493i	−0.614518	+	0.788903i	$0.710649\pi$
$601$	−39.5397	+	20.7520i	−1.61286	+	0.846493i	−0.998340	+	0.0575905i	$0.981658\pi$
$602$	0.597980	+	1.57674i	0.0243718	+	0.0642633i
$603$	−7.67888	+	4.03019i	−0.312708	+	0.164122i
$604$	−10.7232	+	28.2747i	−0.436320	+	1.15048i
$605$	32.7500	+	8.07214i	1.33148	+	0.328179i
$606$	−7.93469			−0.322325
$607$	39.8867	+	9.83120i	1.61895	+	0.399036i	0.941630	−	0.336650i	$-0.109294\pi$
$607$	39.8867	+	9.83120i	1.61895	+	0.399036i	0.677323	+	0.735686i	$0.263140\pi$
$608$	10.8274	−	9.59220i	0.439107	−	0.389015i
$609$	−5.94328	+	8.61032i	−0.240834	+	0.348908i
$610$	−96.5917	−	23.8077i	−3.91088	−	0.963946i
$611$	−0.512901	−	4.31571i	−0.0207498	−	0.174595i
$612$	−11.4794	+	2.82943i	−0.464029	+	0.114373i
$613$	−13.4324	+	35.4183i	−0.542529	+	1.43053i	0.330940	+	0.943652i	$0.392634\pi$
$613$	−13.4324	+	35.4183i	−0.542529	+	1.43053i	−0.873469	+	0.486879i	$0.838135\pi$
$614$	21.8224	+	57.5409i	0.880680	+	2.32216i
$615$	−3.46219	+	28.5137i	−0.139609	+	1.14978i
$616$	−9.64928	+	8.54852i	−0.388781	+	0.344430i
$617$	7.26916	+	19.1672i	0.292645	+	0.771642i	0.998025	+	0.0628129i	$0.0200071\pi$
$617$	7.26916	+	19.1672i	0.292645	+	0.771642i	−0.705380	+	0.708829i	$0.749224\pi$
$618$	12.0403	+	17.4434i	0.484333	+	0.701678i
$619$	23.9423	+	5.90124i	0.962322	+	0.237191i	0.689024	−	0.724738i	$-0.258039\pi$
$619$	23.9423	+	5.90124i	0.962322	+	0.237191i	0.273298	+	0.961929i	$0.411886\pi$
$620$	75.6967	−	18.6576i	3.04005	−	0.749306i
$621$	1.85734	+	1.64546i	0.0745324	+	0.0660299i
$622$	−9.24835	−	24.3859i	−0.370825	−	0.977785i
$623$	0.884166	+	7.28176i	0.0354234	+	0.291738i
$624$	−0.484574	−	4.07736i	−0.0193985	−	0.163225i
$625$	8.93818	−	73.6125i	0.357527	−	2.94450i
$626$	35.6070	−	8.77635i	1.42314	−	0.350773i
$627$	8.95352	−	2.20684i	0.357569	−	0.0881329i
$628$	28.6958	−	41.5730i	1.14509	−	1.65894i
$629$	−16.0359	+	23.2320i	−0.639392	+	0.926319i
$630$	−11.4377	−	6.00299i	−0.455690	−	0.239165i
$631$	0.773974	−	6.37425i	0.0308114	−	0.253755i	−0.969162	−	0.246426i	$-0.920744\pi$
$631$	0.773974	−	6.37425i	0.0308114	−	0.253755i	0.999973	−	0.00732929i	$-0.00233301\pi$
$632$	24.0508	+	12.6228i	0.956689	+	0.502109i
$633$	−0.944060	+	0.836364i	−0.0375230	+	0.0332425i
$634$	−21.2081	+	30.7253i	−0.842282	+	1.22026i
$635$	58.9749	+	14.5360i	2.34035	+	0.576844i
$636$	28.8000	−	15.1154i	1.14199	−	0.599365i
$637$	−10.5015	+	15.1317i	−0.416084	+	0.599538i
$638$	−65.4253	−	34.3379i	−2.59021	−	1.35945i
$639$	−3.56557	−	3.15882i	−0.141052	−	0.124961i
$640$	−7.72234	−	63.5992i	−0.305252	−	2.51398i
$641$	19.6953	−	10.3369i	0.777917	−	0.408282i	−0.0285269	−	0.999593i	$-0.509082\pi$
$641$	19.6953	−	10.3369i	0.777917	−	0.408282i	0.806444	+	0.591311i	$0.201389\pi$
$642$	3.93250	−	10.3692i	0.155204	−	0.409238i
$643$	−36.9982	+	9.11924i	−1.45907	+	0.359628i	−0.887454	−	0.460896i	$-0.847528\pi$
$643$	−36.9982	+	9.11924i	−1.45907	+	0.359628i	−0.571613	+	0.820523i	$0.693682\pi$
$644$	−7.57401	+	6.70998i	−0.298458	+	0.264410i
$645$	−1.73609	−	1.53804i	−0.0683583	−	0.0605602i
$646$	−6.66508	+	17.5744i	−0.262234	+	0.691454i
$647$	−23.7805	−	12.4810i	−0.934908	−	0.490678i	−0.0727690	−	0.997349i	$-0.523184\pi$
$647$	−23.7805	−	12.4810i	−0.934908	−	0.490678i	−0.862139	+	0.506671i	$0.830876\pi$
$648$	1.60946	−	1.42586i	0.0632255	−	0.0560129i
$649$	41.6268	+	36.8781i	1.63399	+	1.44759i
$650$	−58.4788	+	84.2624i	−2.29373	+	3.30504i
$651$	6.42196	−	5.68936i	0.251697	−	0.222984i
$652$	−2.54580	+	20.9666i	−0.0997013	+	0.821114i
$653$	11.3262			0.443228			0.221614	−	0.975134i	$-0.428867\pi$
$653$	11.3262			0.443228			0.221614	+	0.975134i	$0.428867\pi$
$654$	10.3221			0.403628
$655$	−6.47198	+	53.3016i	−0.252881	+	2.08267i
$656$	−4.40839	+	6.38665i	−0.172119	+	0.249357i
$657$	3.59523			0.140263
$658$	−2.09843	−	3.04011i	−0.0818055	−	0.118516i
$659$	−1.74238	−	14.3498i	−0.0678734	−	0.558988i	−0.986488	−	0.163833i	$-0.947614\pi$
$659$	−1.74238	−	14.3498i	−0.0678734	−	0.558988i	0.918615	−	0.395154i	$-0.129309\pi$
$660$	19.3185	−	50.9387i	0.751972	−	1.98279i
$661$	1.75687	+	14.4691i	0.0683344	+	0.562784i	0.986160	+	0.165799i	$0.0530204\pi$
$661$	1.75687	+	14.4691i	0.0683344	+	0.562784i	−0.917825	+	0.396985i	$0.870057\pi$
$662$	13.7433	−	36.2380i	0.534147	−	1.40843i
$663$	8.13712	+	11.8530i	0.316020	+	0.460331i
$664$	6.49747	+	17.1324i	0.252151	+	0.664867i
$665$	−10.8587	+	5.69909i	−0.421083	+	0.221001i
$666$	1.90138	−	15.6593i	0.0736769	−	0.606784i
$667$	−16.7138	−	8.77210i	−0.647162	−	0.339657i
$668$	−8.12602	−	66.9238i	−0.314405	−	2.58936i
$669$	0.754495	+	6.21382i	0.0291705	+	0.240240i
$670$	60.9664	+	54.0115i	2.35534	+	2.08665i
$671$	−16.3732	−	43.1725i	−0.632080	−	1.66666i
$672$	−5.34240	−	7.73980i	−0.206088	−	0.298569i
$673$	−1.31554	−	0.324251i	−0.0507103	−	0.0124990i	0.213879	−	0.976860i	$-0.431390\pi$
$673$	−1.31554	−	0.324251i	−0.0507103	−	0.0124990i	−0.264589	+	0.964361i	$0.585236\pi$
$674$	26.0989	+	13.6977i	1.00529	+	0.527617i
$675$	12.7666			0.491387
$676$	34.2204	−	17.7391i	1.31617	−	0.682272i
$677$	−37.6370			−1.44651			−0.723254	−	0.690583i	$-0.757354\pi$
$677$	−37.6370			−1.44651			−0.723254	+	0.690583i	$0.757354\pi$
$678$	15.7241	+	8.25264i	0.603880	+	0.316941i
$679$	19.2171	+	4.73659i	0.737485	+	0.181774i
$680$	20.5299	+	29.7427i	0.787285	+	1.14058i
$681$	6.15424	+	16.2274i	0.235831	+	0.621835i
$682$	45.3543	+	40.1804i	1.73671	+	1.53859i
$683$	4.01665	+	33.0801i	0.153693	+	1.26577i	0.841650	+	0.540023i	$0.181584\pi$
$683$	4.01665	+	33.0801i	0.153693	+	1.26577i	−0.687958	+	0.725751i	$0.741492\pi$
$684$	−0.756031	−	6.22648i	−0.0289076	−	0.238075i
$685$	−16.7955	−	8.81495i	−0.641722	−	0.336802i
$686$	−4.47278	+	36.8367i	−0.170772	+	1.40643i
$687$	−13.6937	+	7.18700i	−0.522447	+	0.274201i
$688$	−0.222213	−	0.585926i	−0.00847177	−	0.0223382i
$689$	−29.5387	−	26.3033i	−1.12534	−	1.00207i
$690$	8.26416	−	21.7908i	0.314611	−	0.829562i
$691$	−4.78002	−	39.3670i	−0.181840	−	1.49759i	−0.742669	−	0.669659i	$-0.766440\pi$
$691$	−4.78002	−	39.3670i	−0.181840	−	1.49759i	0.560829	−	0.827932i	$-0.310483\pi$
$692$	−8.54596	+	22.5339i	−0.324869	+	0.856609i
$693$	−0.722660	−	5.95164i	−0.0274516	−	0.226084i
$694$	−5.50768	−	7.97925i	−0.209069	−	0.302888i
$695$	−13.7538			−0.521710
$696$	−9.29172	+	13.4614i	−0.352202	+	0.510253i
$697$	3.27531	−	26.9746i	0.124061	−	1.02174i
$698$	−69.0404			−2.61322
$699$	−17.6721			−0.668422
$700$	−6.27523	+	51.6812i	−0.237181	+	1.95336i
$701$	16.7383	−	14.8289i	0.632198	−	0.560078i	−0.284992	−	0.958530i	$-0.591991\pi$
$701$	16.7383	−	14.8289i	0.632198	−	0.560078i	0.917189	+	0.398452i	$0.130452\pi$
$702$	−7.10423	−	3.75164i	−0.268132	−	0.141596i
$703$	−11.2095	−	9.93074i	−0.422774	−	0.374545i
$704$	42.2834	−	37.4598i	1.59361	−	1.41182i
$705$	4.49879	+	2.36115i	0.169434	+	0.0889260i
$706$	−8.29788	+	21.8797i	−0.312295	+	0.823454i
$707$	3.66590	+	3.24770i	0.137870	+	0.122142i
$708$	28.3135	−	25.0835i	1.06409	−	0.942697i
$709$	16.9825	−	4.18581i	0.637791	−	0.157201i	0.0928558	−	0.995680i	$-0.470400\pi$
$709$	16.9825	−	4.18581i	0.637791	−	0.157201i	0.544935	+	0.838478i	$0.316554\pi$
$710$	−15.8649	+	41.8323i	−0.595399	+	1.56994i
$711$	−11.1853	+	5.87049i	−0.419481	+	0.220161i
$712$	1.38231	+	11.3843i	0.0518041	+	0.426645i
$713$	11.5864	+	10.2647i	0.433915	+	0.384415i
$714$	10.8204	+	5.67897i	0.404942	+	0.212530i
$715$	−66.2485	−	0.168291i	−2.47755	−	0.00629372i
$716$	2.47084	−	1.29680i	0.0923395	−	0.0484635i
$717$	−2.37407	−	0.585156i	−0.0886613	−	0.0218531i
$718$	6.31804	−	9.15326i	0.235787	−	0.341596i
$719$	26.2601	−	23.2645i	0.979338	−	0.867618i	−0.0118700	−	0.999930i	$-0.503778\pi$
$719$	26.2601	−	23.2645i	0.979338	−	0.867618i	0.991208	+	0.132312i	$0.0422400\pi$
$720$	4.25032	+	2.23074i	0.158400	+	0.0831348i
$721$	1.57693	−	12.9872i	0.0587280	−	0.483668i
$722$	28.6577	+	15.0407i	1.06653	+	0.559758i
$723$	6.88122	−	9.96916i	0.255915	−	0.370757i
$724$	14.4498	−	20.9342i	0.537023	−	0.778012i
$725$	−94.2942	+	23.2414i	−3.50200	+	0.863165i
$726$	17.3128	−	4.26723i	0.642539	−	0.158372i
$727$	−3.80683	+	31.3521i	−0.141188	+	1.16278i	0.734051	+	0.679094i	$0.237627\pi$
$727$	−3.80683	+	31.3521i	−0.141188	+	1.16278i	−0.875239	+	0.483691i	$0.839296\pi$
$728$	6.07935	−	8.75978i	0.225316	−	0.324659i
$729$	0.120537	+	0.992709i	0.00446432	+	0.0367670i
$730$	−11.9738	−	31.5724i	−0.443171	−	1.16855i
$731$	1.64238	+	1.45502i	0.0607456	+	0.0538159i
$732$	−30.4931	+	7.51587i	−1.12706	+	0.277795i
$733$	−32.4844	−	8.00669i	−1.19984	−	0.295734i	−0.411751	−	0.911296i	$-0.635083\pi$
$733$	−32.4844	−	8.00669i	−1.19984	−	0.295734i	−0.788088	+	0.615563i	$0.788929\pi$
$734$	−36.0728	−	52.2605i	−1.33147	−	1.92897i
$735$	−7.63544	−	20.1330i	−0.281637	−	0.742617i
$736$	12.7004	−	11.2516i	0.468143	−	0.414739i
$737$	−4.55673	+	37.5281i	−0.167849	+	1.38236i
$738$	5.38435	+	14.1974i	0.198200	+	0.522612i
$739$	15.5621	−	41.0338i	0.572460	−	1.50945i	−0.265714	−	0.964052i	$-0.585608\pi$
$739$	15.5621	−	41.0338i	0.572460	−	1.50945i	0.838175	−	0.545402i	$-0.183623\pi$
$740$	−85.9031	+	21.1732i	−3.15786	+	0.778343i
$741$	−6.76259	+	3.52740i	−0.248430	+	0.129582i
$742$	−32.6412	−	8.04533i	−1.19830	−	0.295353i
$743$	22.3779	−	32.4199i	0.820964	−	1.18937i	−0.158421	−	0.987372i	$-0.550640\pi$
$743$	22.3779	−	32.4199i	0.820964	−	1.18937i	0.979385	−	0.202001i	$-0.0647443\pi$
$744$	10.0401	−	8.89476i	0.368088	−	0.326098i
$745$	−40.7440	−	10.0425i	−1.49274	−	0.367928i
$746$	−65.0210			−2.38059
$747$	−8.27391	−	2.03933i	−0.302726	−	0.0746153i
$748$	−18.2758	+	48.1892i	−0.668228	+	1.76197i
$749$	−6.06099	+	3.18106i	−0.221464	+	0.116233i
$750$	−25.8665	−	68.2043i	−0.944510	−	2.49047i
$751$	3.45055	−	1.81099i	0.125912	−	0.0660840i	−0.400591	−	0.916257i	$-0.631195\pi$
$751$	3.45055	−	1.81099i	0.125912	−	0.0660840i	0.526503	+	0.850173i	$0.323503\pi$
$752$	0.779789	+	1.12972i	0.0284360	+	0.0411966i
$753$	−4.09702	−	5.93556i	−0.149304	−	0.216304i
$754$	59.3017	+	14.7764i	2.15964	+	0.538127i
$755$	−24.4206	+	35.3793i	−0.888756	+	1.28758i
$756$	−4.07788			−0.148311
$757$	−8.33464	−	12.0748i	−0.302928	−	0.438866i	0.641727	−	0.766933i	$-0.278218\pi$
$757$	−8.33464	−	12.0748i	−0.302928	−	0.438866i	−0.944654	+	0.328067i	$0.893603\pi$
$758$	18.4422	+	16.3383i	0.669850	+	0.593435i
$759$	10.5024	−	2.58861i	0.381213	−	0.0939607i
$760$	−16.9765	+	8.90996i	−0.615803	+	0.323198i
$761$	−35.8011	+	18.7899i	−1.29779	+	0.681132i	−0.965094	−	0.261903i	$-0.915650\pi$
$761$	−35.8011	+	18.7899i	−1.29779	+	0.681132i	−0.332694	+	0.943035i	$0.607958\pi$
$762$	31.1763	−	7.68426i	1.12940	−	0.278371i
$763$	−4.76892	−	4.22490i	−0.172647	−	0.152952i
$764$	28.0837	+	40.6863i	1.01603	+	1.47198i
$765$	−16.8076			−0.607681
$766$	21.7853	−	31.5615i	0.787135	−	1.14036i
$767$	−40.6752	−	21.4800i	−1.46870	−	0.775596i
$768$	−4.51609	−	6.54269i	−0.162960	−	0.236089i
$769$	15.2053	+	22.0286i	0.548316	+	0.794373i	0.994953	−	0.100342i	$-0.0319938\pi$
$769$	15.2053	+	22.0286i	0.548316	+	0.794373i	−0.446637	+	0.894715i	$0.647378\pi$
$770$	−49.8590	+	26.1680i	−1.79679	+	0.943029i
$771$	−6.08371	−	16.0414i	−0.219099	−	0.577717i
$772$	57.9412	−	30.4099i	2.08535	−	1.09447i
$773$	−19.3158	+	50.9316i	−0.694742	+	1.83188i	−0.159472	+	0.987202i	$0.550979\pi$
$773$	−19.3158	+	50.9316i	−0.694742	+	1.83188i	−0.535270	+	0.844681i	$0.679790\pi$
$774$	−1.19048	−	0.293428i	−0.0427911	−	0.0105470i
$775$	79.6404			2.86077
$776$	30.0440	+	7.40519i	1.07852	+	0.265831i
$777$	−7.28786	+	6.45648i	−0.261450	+	0.231625i
$778$	0.170130	−	0.246476i	0.00609945	−	0.00883659i
$779$	13.9965	+	3.44983i	0.501477	+	0.123603i
$780$	−5.54507	+	44.7181i	−0.198545	+	1.60117i
$781$	−20.1617	+	4.96941i	−0.721442	+	0.177820i
$782$	−7.81809	+	20.6146i	−0.279574	+	0.737177i
$783$	−2.69750	−	7.11272i	−0.0964007	−	0.254188i
$784$	0.701228	−	5.77513i	0.0250439	−	0.206255i
$785$	53.7523	−	47.6204i	1.91850	−	1.69965i
$786$	10.0651	+	26.5396i	0.359012	+	0.946636i
$787$	−4.69829	−	6.80664i	−0.167476	−	0.242631i	0.730255	−	0.683174i	$-0.239401\pi$
$787$	−4.69829	−	6.80664i	−0.167476	−	0.242631i	−0.897731	+	0.440544i	$0.854786\pi$
$788$	44.5173	+	10.9725i	1.58586	+	0.390880i
$789$	−25.3287	+	6.24296i	−0.901726	+	0.222255i
$790$	88.8055	+	78.6748i	3.15956	+	2.79912i
$791$	−3.88683	−	10.2487i	−0.138200	−	0.364403i
$792$	−1.12981	−	9.30480i	−0.0401460	−	0.330632i
$793$	21.6148	+	31.4853i	0.767565	+	1.11807i
$794$	−2.09098	+	17.2208i	−0.0742061	+	0.611142i
$795$	44.8950	−	11.0656i	1.59226	−	0.392457i
$796$	−48.8459	+	12.0394i	−1.73130	+	0.426727i
$797$	13.8067	−	20.0025i	0.489060	−	0.708526i	−0.498303	−	0.867003i	$-0.666043\pi$
$797$	13.8067	−	20.0025i	0.489060	−	0.708526i	0.987363	+	0.158477i	$0.0506585\pi$
$798$	−3.68270	+	5.33531i	−0.130366	+	0.188868i
$799$	−4.25596	−	2.23370i	−0.150565	−	0.0790227i
$800$	10.5226	−	86.6611i	0.372029	−	3.06393i
$801$	−4.72248	−	2.47855i	−0.166861	−	0.0875752i
$802$	31.8514	−	28.2179i	1.12471	−	0.996409i
$803$	8.90283	−	12.8980i	0.314174	−	0.455160i
$804$	24.9659	+	6.15354i	0.880480	+	0.217019i
$805$	−12.7372	+	6.68499i	−0.448927	+	0.235615i
$806$	−44.3175	−	23.4034i	−1.56102	−	0.824350i
$807$	−9.00596	−	4.72669i	−0.317025	−	0.166388i
$808$	5.73127	+	5.07746i	0.201625	+	0.178624i
$809$	2.26126	+	18.6232i	0.0795018	+	0.654756i	0.976925	+	0.213584i	$0.0685139\pi$
$809$	2.26126	+	18.6232i	0.0795018	+	0.654756i	−0.897423	+	0.441171i	$0.854563\pi$
$810$	8.31627	−	4.36471i	0.292204	−	0.153360i
$811$	7.76812	−	20.4829i	0.272776	−	0.719250i	−0.726703	−	0.686952i	$-0.758948\pi$
$811$	7.76812	−	20.4829i	0.272776	−	0.719250i	0.999478	−	0.0322980i	$-0.0102826\pi$
$812$	30.1193	−	7.42373i	1.05698	−	0.260522i
$813$	−19.0520	+	16.8786i	−0.668182	+	0.591957i
$814$	−51.4696	−	45.5981i	−1.80401	−	1.59821i
$815$	−10.6470	+	28.0739i	−0.372950	+	0.983387i
$816$	−4.02091	−	2.11033i	−0.140760	−	0.0738765i
$817$	−0.871297	+	0.771902i	−0.0304828	+	0.0270054i
$818$	−56.2955	−	49.8735i	−1.96833	−	1.74379i
$819$	1.74666	+	4.64108i	0.0610332	+	0.162173i
$820$	63.7459	−	56.4740i	2.22610	−	1.97216i
$821$	2.39559	−	19.7294i	0.0836066	−	0.688562i	−0.889294	−	0.457337i	$-0.848803\pi$
$821$	2.39559	−	19.7294i	0.0836066	−	0.688562i	0.972900	−	0.231226i	$-0.0742735\pi$
$822$	−10.0273			−0.349741
$823$	46.2605			1.61254			0.806270	−	0.591547i	$-0.201483\pi$
$823$	46.2605			1.61254			0.806270	+	0.591547i	$0.201483\pi$
$824$	2.46537	−	20.3042i	0.0858854	−	0.707330i
$825$	31.6138	−	45.8005i	1.10065	−	1.59457i
$826$	−39.0969			−1.36036
$827$	−22.0032	−	31.8771i	−0.765125	−	1.10848i	−0.990940	−	0.134305i	$-0.957120\pi$
$827$	−22.0032	−	31.8771i	−0.765125	−	1.10848i	0.225815	−	0.974170i	$-0.427496\pi$
$828$	−0.886819	−	7.30361i	−0.0308191	−	0.253818i
$829$	14.8073	−	39.0437i	0.514279	−	1.35604i	−0.386710	−	0.922202i	$-0.626388\pi$
$829$	14.8073	−	39.0437i	0.514279	−	1.35604i	0.900989	−	0.433842i	$-0.142842\pi$
$830$	9.64713	+	79.4512i	0.334857	+	2.75779i
$831$	−3.68868	+	9.72625i	−0.127959	+	0.337400i
$832$	−26.6399	+	38.3855i	−0.923571	+	1.33078i
$833$	7.22331	+	19.0463i	0.250273	+	0.659915i
$834$	−6.43791	+	3.37888i	−0.222927	+	0.117001i
$835$	11.5520	−	95.1392i	0.399773	−	3.29243i
$836$	−24.2098	−	12.7063i	−0.837313	−	0.439456i
$837$	0.751930	+	6.19270i	0.0259905	+	0.214051i
$838$	4.17023	+	34.3449i	0.144058	+	1.18642i
$839$	−9.74261	−	8.63120i	−0.336352	−	0.297982i	0.477992	−	0.878364i	$-0.341365\pi$
$839$	−9.74261	−	8.63120i	−0.336352	−	0.297982i	−0.814344	+	0.580382i	$0.802903\pi$
$840$	4.42019	+	11.6551i	0.152511	+	0.402138i
$841$	16.3985	+	23.7573i	0.565464	+	0.819216i
$842$	−33.9074	−	8.35742i	−1.16853	−	0.288016i
$843$	−8.04476	−	4.22221i	−0.277076	−	0.145421i
$844$	3.73960			0.128722
$845$	53.2693	−	12.8430i	1.83252	−	0.441812i
$846$	2.68587			0.0923423
$847$	−9.74528	−	5.11472i	−0.334852	−	0.175744i
$848$	12.1296	+	2.98969i	0.416534	+	0.102666i
$849$	0.830010	+	1.20248i	0.0284859	+	0.0412689i
$850$	40.2238	+	106.062i	1.37967	+	3.63788i
$851$	−13.1486	−	11.6487i	−0.450730	−	0.399312i
$852$	1.70245	+	14.0209i	0.0583248	+	0.480348i
$853$	−4.30350	−	35.4425i	−0.147349	−	1.21353i	−0.859364	−	0.511365i	$-0.829140\pi$
$853$	−4.30350	−	35.4425i	−0.147349	−	1.21353i	0.712015	−	0.702165i	$-0.247783\pi$
$854$	28.7424	+	15.0852i	0.983544	+	0.516204i
$855$	1.07478	−	8.85159i	0.0367566	−	0.302718i
$856$	−9.47576	+	4.97326i	−0.323875	+	0.169983i
$857$	3.14956	+	8.30470i	0.107587	+	0.283683i	0.977988	−	0.208659i	$-0.0669100\pi$
$857$	3.14956	+	8.30470i	0.107587	+	0.283683i	−0.870402	+	0.492342i	$0.836141\pi$
$858$	−31.0512	+	16.1965i	−1.06007	+	0.552938i
$859$	−0.684103	+	1.80383i	−0.0233413	+	0.0615459i	−0.946180	−	0.323640i	$-0.895093\pi$
$859$	−0.684103	+	1.80383i	−0.0233413	+	0.0615459i	0.922839	+	0.385186i	$0.125863\pi$
$860$	0.828926	+	6.82682i	0.0282661	+	0.232793i
$861$	3.32342	−	8.76314i	0.113262	−	0.298647i
$862$	6.37961	+	52.5408i	0.217290	+	1.78955i
$863$	8.59768	+	12.4559i	0.292668	+	0.424003i	0.941543	−	0.336892i	$-0.109376\pi$
$863$	8.59768	+	12.4559i	0.292668	+	0.424003i	−0.648875	+	0.760895i	$0.724760\pi$
$864$	6.83797			0.232632
$865$	−19.4623	+	28.1959i	−0.661736	+	0.958691i
$866$	−1.46023	+	12.0261i	−0.0496206	+	0.408663i
$867$	−1.09959			−0.0373441
$868$	−25.4386			−0.863442
$869$	−6.63747	+	54.6645i	−0.225161	+	1.85437i
$870$	−53.4781	+	47.3775i	−1.81308	+	1.60625i
$871$	−3.69010	−	31.0497i	−0.125034	−	1.05208i
$872$	−7.45574	−	6.60521i	−0.252483	−	0.223681i
$873$	−10.7716	+	9.54283i	−0.364564	+	0.322976i
$874$	−10.3566	−	5.43555i	−0.350316	−	0.183860i
$875$	−15.9658	+	42.0983i	−0.539741	+	1.42318i
$876$	−7.97899	−	7.06877i	−0.269585	−	0.238832i
$877$	−12.4712	+	11.0485i	−0.421123	+	0.373082i	−0.846906	−	0.531743i	$-0.821537\pi$
$877$	−12.4712	+	11.0485i	−0.421123	+	0.373082i	0.425783	+	0.904825i	$0.359999\pi$
$878$	21.7265	−	5.35510i	0.733233	−	0.180726i
$879$	−4.24786	+	11.2007i	−0.143277	+	0.377790i
$880$	18.5279	−	9.72417i	0.624574	−	0.327802i
$881$	0.850412	+	7.00377i	0.0286511	+	0.235963i	0.999999	−	0.00170078i	$-0.000541377\pi$
$881$	0.850412	+	7.00377i	0.0286511	+	0.235963i	−0.971347	+	0.237664i	$0.923618\pi$
$882$	−8.52009	−	7.54814i	−0.286886	−	0.254159i
$883$	−28.2633	−	14.8337i	−0.951137	−	0.499195i	−0.0835626	−	0.996503i	$-0.526630\pi$
$883$	−28.2633	−	14.8337i	−0.951137	−	0.499195i	−0.867574	+	0.497307i	$0.834322\pi$
$884$	5.24577	−	42.3044i	0.176434	−	1.42285i
$885$	47.6147	−	24.9901i	1.60055	−	0.840034i
$886$	−5.05262	−	1.24536i	−0.169746	−	0.0418386i
$887$	3.26767	−	4.73403i	0.109718	−	0.158953i	−0.764279	−	0.644886i	$-0.776905\pi$
$887$	3.26767	−	4.73403i	0.109718	−	0.158953i	0.873996	+	0.485933i	$0.161520\pi$
$888$	−11.3938	+	10.0941i	−0.382352	+	0.338735i
$889$	−17.5489	−	9.21038i	−0.588572	−	0.308906i
$890$	−6.03787	+	49.7263i	−0.202390	+	1.66683i
$891$	3.85985	+	2.02580i	0.129310	+	0.0678670i
$892$	10.5429	−	15.2740i	0.353001	−	0.511410i
$893$	1.44851	−	2.09853i	0.0484726	−	0.0702246i
$894$	−21.5388	+	5.30883i	−0.720364	+	0.177554i
$895$	3.85167	−	0.949352i	0.128747	−	0.0317333i
$896$	−2.51975	+	20.7520i	−0.0841791	+	0.693277i
$897$	−7.93247	+	4.13762i	−0.264858	+	0.138151i
$898$	5.71370	+	47.0566i	0.190669	+	1.57030i
$899$	−16.8275	−	44.3704i	−0.561228	−	1.47984i
$900$	−28.3333	−	25.1011i	−0.944442	−	0.836703i
$901$	−42.4717	+	10.4683i	−1.41494	+	0.348751i
$902$	64.2665	+	15.8403i	2.13984	+	0.527423i
$903$	0.429913	+	0.622836i	0.0143066	+	0.0207267i
$904$	−6.07667	−	16.0229i	−0.202107	−	0.532913i
$905$	27.0671	−	23.9793i	0.899740	−	0.797100i
$906$	−2.73927	+	22.5599i	−0.0910060	+	0.749502i
$907$	−6.24032	−	16.4544i	−0.207207	−	0.546359i	0.790616	−	0.612312i	$-0.209760\pi$
$907$	−6.24032	−	16.4544i	−0.207207	−	0.546359i	−0.997823	+	0.0659533i	$0.978991\pi$
$908$	18.2473	−	48.1140i	0.605556	−	1.59672i
$909$	−3.45751	+	0.852200i	−0.114678	+	0.0282657i
$910$	34.9396	−	30.7957i	1.15824	−	1.02087i
$911$	−45.2577	−	11.1550i	−1.49946	−	0.369582i	−0.597661	−	0.801749i	$-0.703903\pi$
$911$	−45.2577	−	11.1550i	−1.49946	−	0.369582i	−0.901794	+	0.432166i	$0.857749\pi$
$912$	1.36851	−	1.98263i	0.0453159	−	0.0656514i
$913$	−27.8047	+	24.6328i	−0.920202	+	0.815228i
$914$	−33.2152	−	8.18681i	−1.09866	−	0.270795i
$915$	−44.6465			−1.47597
$916$	44.5215	+	10.9736i	1.47103	+	0.362577i
$917$	6.21259	−	16.3812i	0.205158	−	0.540956i
$918$	−7.86738	+	4.12912i	−0.259662	+	0.136281i
$919$	8.61586	+	22.7182i	0.284211	+	0.749403i	0.998758	+	0.0498159i	$0.0158635\pi$
$919$	8.61586	+	22.7182i	0.284211	+	0.749403i	−0.714547	+	0.699587i	$0.753367\pi$
$920$	−19.9133	+	10.4513i	−0.656523	+	0.344570i
$921$	15.6890	+	22.7295i	0.516971	+	0.748962i
$922$	−23.4119	−	33.9180i	−0.771030	−	1.11703i
$923$	15.2281	−	7.94307i	0.501240	−	0.261449i
$924$	−10.0980	+	14.6295i	−0.332200	+	0.481275i
$925$	−90.3786			−2.97163
$926$	14.2285	+	20.6136i	0.467578	+	0.677403i
$927$	7.12000	+	6.30777i	0.233851	+	0.207174i
$928$	−50.5053	+	12.4484i	−1.65792	+	0.408640i
$929$	29.6927	−	15.5839i	0.974185	−	0.511292i	0.0990037	−	0.995087i	$-0.468434\pi$
$929$	29.6927	−	15.5839i	0.974185	−	0.511292i	0.875181	+	0.483795i	$0.160742\pi$
$930$	51.8784	−	27.2279i	1.70116	−	0.892838i
$931$	−10.4925	+	2.58616i	−0.343877	+	0.0847580i
$932$	39.2203	+	34.7461i	1.28470	+	1.13815i
$933$	−6.64903	−	9.63278i	−0.217679	−	0.315363i
$934$	5.64440			0.184690
$935$	−41.6205	+	60.2977i	−1.36114	+	1.97195i
$936$	2.73073	+	7.25587i	0.0892566	+	0.237166i
$937$	1.19259	+	1.72777i	0.0389603	+	0.0564437i	0.841980	−	0.539509i	$-0.181390\pi$
$937$	1.19259	+	1.72777i	0.0389603	+	0.0564437i	−0.803020	+	0.595952i	$0.796775\pi$
$938$	−15.0973	−	21.8722i	−0.492945	−	0.714154i
$939$	14.5731	−	7.64853i	0.475574	−	0.249600i
$940$	−5.34191	−	14.0855i	−0.174234	−	0.459417i
$941$	45.6755	−	23.9724i	1.48898	−	0.781477i	0.492912	−	0.870079i	$-0.335932\pi$
$941$	45.6755	−	23.9724i	1.48898	−	0.781477i	0.996067	+	0.0886022i	$0.0282400\pi$
$942$	13.4617	−	35.4957i	0.438607	−	1.15651i
$943$	16.4178	+	4.04662i	0.534637	+	0.131776i
$944$	14.5286			0.472867
$945$	−5.62869	−	1.38735i	−0.183101	−	0.0451304i
$946$	−4.00066	+	3.54427i	−0.130073	+	0.115234i
$947$	13.7632	−	19.9394i	0.447244	−	0.647944i	−0.532913	−	0.846170i	$-0.678903\pi$
$947$	13.7632	−	19.9394i	0.447244	−	0.647944i	0.980156	+	0.198226i	$0.0635180\pi$
$948$	36.3661	+	8.96344i	1.18112	+	0.291119i
$949$	−4.62744	+	12.1087i	−0.150213	+	0.393065i
$950$	−58.4285	+	14.4013i	−1.89567	+	0.467241i
$951$	−5.94141	+	15.6662i	−0.192664	+	0.508012i
$952$	−4.18160	−	11.0260i	−0.135526	−	0.357354i
$953$	−3.37606	+	27.8044i	−0.109361	+	0.900672i	0.830005	+	0.557756i	$0.188338\pi$
$953$	−3.37606	+	27.8044i	−0.109361	+	0.900672i	−0.939366	+	0.342916i	$0.888585\pi$
$954$	18.2961	−	16.2090i	0.592359	−	0.524784i
$955$	24.9219	+	65.7136i	0.806453	+	2.12644i
$956$	4.11833	+	5.96644i	0.133196	+	0.192968i
$957$	−32.1968	−	7.93580i	−1.04078	−	0.256528i
$958$	60.2983	−	14.8622i	1.94815	−	0.480176i
$959$	4.63269	+	4.10420i	0.149597	+	0.132532i
$960$	−19.3694	−	51.0728i	−0.625143	−	1.64837i
$961$	0.954042	+	7.85724i	0.0307755	+	0.253459i
$962$	50.2930	+	26.5590i	1.62151	+	0.856295i
$963$	0.599908	−	4.94068i	0.0193318	−	0.159211i
$964$	−34.8726	+	8.59531i	−1.12317	+	0.276836i
$965$	90.3217	−	22.2623i	2.90756	−	0.716649i
$966$	−4.31978	+	6.25828i	−0.138987	+	0.201357i
$967$	26.4743	−	38.3546i	0.851355	−	1.23340i	−0.119284	−	0.992860i	$-0.538060\pi$
$967$	26.4743	−	38.3546i	0.851355	−	1.23340i	0.970639	−	0.240541i	$-0.0773247\pi$
$968$	−15.2358	−	7.99635i	−0.489696	−	0.257012i
$969$	−1.01677	+	8.37381i	−0.0326632	+	0.269006i
$970$	119.677	+	62.8115i	3.84261	+	2.01675i
$971$	7.59478	−	6.72839i	0.243728	−	0.215924i	−0.532411	−	0.846486i	$-0.678714\pi$
$971$	7.59478	−	6.72839i	0.243728	−	0.215924i	0.776139	+	0.630562i	$0.217175\pi$
$972$	1.68431	−	2.44014i	0.0540242	−	0.0782675i
$973$	4.35736	+	1.07399i	0.139691	+	0.0344307i
$974$	−44.9427	+	23.5877i	−1.44006	+	0.755800i
$975$	−16.4320	+	42.9978i	−0.526244	+	1.37703i
$976$	−10.6808	−	5.60573i	−0.341885	−	0.179435i
$977$	6.32893	+	5.60694i	0.202480	+	0.179382i	0.758269	−	0.651942i	$-0.226045\pi$
$977$	6.32893	+	5.60694i	0.202480	+	0.179382i	−0.555789	+	0.831323i	$0.687584\pi$
$978$	1.91320	+	15.7566i	0.0611774	+	0.503841i
$979$	−20.5861	+	10.8044i	−0.657933	+	0.345310i
$980$	−22.6390	+	59.6941i	−0.723176	+	1.90686i
$981$	4.49784	−	1.10862i	0.143605	−	0.0353954i
$982$	54.1292	−	47.9543i	1.72733	−	1.53028i
$983$	2.06708	+	1.83128i	0.0659297	+	0.0584086i	0.695444	−	0.718580i	$-0.255208\pi$
$983$	2.06708	+	1.83128i	0.0659297	+	0.0584086i	−0.629514	+	0.776989i	$0.716746\pi$
$984$	5.19584	−	13.7003i	0.165637	−	0.436750i
$985$	57.7141	+	30.2907i	1.83892	+	0.965141i
$986$	50.5915	−	44.8202i	1.61116	−	1.42737i
$987$	−1.24090	−	1.09934i	−0.0394982	−	0.0349924i
$988$	21.9438	+	5.46783i	0.698126	+	0.173955i
$989$	−1.02203	+	0.905436i	−0.0324985	+	0.0287912i
$990$	4.93496	−	40.6431i	0.156843	−	1.29172i
$991$	−20.9826			−0.666534			−0.333267	−	0.942833i	$-0.608151\pi$
$991$	−20.9826			−0.666534			−0.333267	+	0.942833i	$0.608151\pi$
$992$	42.6565			1.35435
$993$	2.09655	−	17.2666i	0.0665320	−	0.547940i
$994$	8.29277	−	12.0141i	0.263031	−	0.381066i
$995$	−71.5178			−2.26727
$996$	14.3529	+	20.7937i	0.454788	+	0.658874i
$997$	0.0958126	+	0.789088i	0.00303442	+	0.0249907i	0.994147	−	0.108032i	$-0.0344548\pi$
$997$	0.0958126	+	0.789088i	0.00303442	+	0.0249907i	−0.991113	+	0.133022i	$0.957532\pi$
$998$	28.4352	−	74.9775i	0.900101	−	2.37337i
$999$	−0.853315	−	7.02768i	−0.0269977	−	0.222346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.b.79.2	✓	204
169.92	even	13	inner	507.2.m.b.430.2	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.b.79.2	✓	204	1.1	even	1	trivial
507.2.m.b.430.2	yes	204	169.92	even	13	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.m (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.97300 - 1.03551i) q^{2} +(-0.970942 - 0.239316i) q^{3} +(1.68431 + 2.44014i) q^{4} +(1.49468 + 3.94114i) q^{5} +(1.66785 + 1.47759i) q^{6} +(-0.165780 - 1.36532i) q^{7} +(-0.259180 - 2.13454i) q^{8} +(0.885456 + 0.464723i) q^{9} +(1.13209 - 9.32359i) q^{10} +(3.85985 - 2.02580i) q^{11} +(-1.05140 - 2.77231i) q^{12} +(-2.70486 + 2.38406i) q^{13} +(-1.08671 + 2.86543i) q^{14} +(-0.508068 - 4.18431i) q^{15} +(0.403829 - 1.06481i) q^{16} +(0.480644 + 3.95846i) q^{17} +(-1.26578 - 1.83379i) q^{18} -2.11542 q^{19} +(-7.09943 + 10.2853i) q^{20} +(-0.165780 + 1.36532i) q^{21} -9.71320 q^{22} -2.48138 q^{23} +(-0.259180 + 2.13454i) q^{24} +(-9.55594 + 8.46583i) q^{25} +(7.80539 - 1.90284i) q^{26} +(-0.748511 - 0.663123i) q^{27} +(3.05234 - 2.70414i) q^{28} +(6.73571 + 3.53517i) q^{29} +(-3.33047 + 8.78174i) q^{30} +(-4.66935 - 4.13668i) q^{31} +(-5.11829 + 4.53441i) q^{32} +(-4.23249 + 1.04322i) q^{33} +(3.15071 - 8.30773i) q^{34} +(5.13311 - 2.69407i) q^{35} +(0.357390 + 2.94337i) q^{36} +(5.29893 + 4.69444i) q^{37} +(4.17372 + 2.19054i) q^{38} +(3.19680 - 1.66747i) q^{39} +(8.02512 - 4.21191i) q^{40} +(-6.61641 - 1.63080i) q^{41} +(1.74088 - 2.52210i) q^{42} +(0.411878 - 0.364893i) q^{43} +(11.4444 + 6.00649i) q^{44} +(-0.508068 + 4.18431i) q^{45} +(4.89575 + 2.56949i) q^{46} +(-0.684738 + 0.992014i) q^{47} +(-0.646920 + 0.937226i) q^{48} +(4.95998 - 1.22253i) q^{49} +(27.6203 - 6.80778i) q^{50} +(0.480644 - 3.95846i) q^{51} +(-10.3732 - 2.58475i) q^{52} +(1.32227 + 10.8899i) q^{53} +(0.790140 + 2.08343i) q^{54} +(13.7532 + 12.1843i) q^{55} +(-2.87136 + 0.707725i) q^{56} +(2.05395 + 0.506254i) q^{57} +(-9.62883 - 13.9498i) q^{58} +(4.52394 + 11.9286i) q^{59} +(9.35456 - 8.28742i) q^{60} +(1.27675 - 10.5149i) q^{61} +(4.92904 + 12.9968i) q^{62} +(0.487704 - 1.28597i) q^{63} +(12.5823 - 3.10127i) q^{64} +(-13.4388 - 7.09682i) q^{65} +(9.43095 + 2.32452i) q^{66} +(-4.92639 + 7.13711i) q^{67} +(-8.84964 + 7.84009i) q^{68} +(2.40927 + 0.593832i) q^{69} -12.9173 q^{70} +(-4.62513 - 1.13999i) q^{71} +(0.762477 - 2.01049i) q^{72} +(3.18342 - 1.67079i) q^{73} +(-5.59364 - 14.7492i) q^{74} +(11.3043 - 5.93294i) q^{75} +(-3.56302 - 5.16193i) q^{76} +(-3.40575 - 4.93408i) q^{77} +(-8.03396 - 0.0204086i) q^{78} +(-7.17593 + 10.3961i) q^{79} +4.80015 q^{80} +(0.568065 + 0.822984i) q^{81} +(11.3654 + 10.0689i) q^{82} +(-8.27391 + 2.03933i) q^{83} +(-3.61079 + 1.89509i) q^{84} +(-14.8824 + 7.81089i) q^{85} +(-1.19048 + 0.293428i) q^{86} +(-5.69396 - 5.04441i) q^{87} +(-5.32455 - 7.71395i) q^{88} -5.33339 q^{89} +(5.33531 - 7.72952i) q^{90} +(3.70341 + 3.29776i) q^{91} +(-4.17940 - 6.05490i) q^{92} +(3.54369 + 5.13393i) q^{93} +(2.37822 - 1.24819i) q^{94} +(-3.16187 - 8.33717i) q^{95} +(6.05472 - 3.17776i) q^{96} +(-5.10303 + 13.4556i) q^{97} +(-11.0520 - 2.72406i) q^{98} +4.35916 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19}+ \cdots + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

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Database

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