LMFDB - Embedded newform 220.2.r.c.51.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(51,220)] 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("220.51"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.r (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-10,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			51.8
Character	$\chi$	$=$	220.51
Dual form			220.2.r.c.151.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.988310 + 1.01156i) q^{2} +(1.88633 + 0.612906i) q^{3} +(-0.0464877 + 1.99946i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.24429 + 2.51387i) q^{6} +(-0.668539 - 2.05755i) q^{7} +(-2.06851 + 1.92906i) q^{8} +(0.755537 + 0.548930i) q^{9} +(1.39414 + 0.237451i) q^{10} +(-3.31496 - 0.105060i) q^{11} +(-1.31317 + 3.74315i) q^{12} +(1.85832 - 2.55775i) q^{13} +(1.42060 - 2.70976i) q^{14} +(1.88633 - 0.612906i) q^{15} +(-3.99568 - 0.185901i) q^{16} +(-2.62058 - 3.60691i) q^{17} +(0.191432 + 1.30678i) q^{18} +(-1.21650 + 3.74402i) q^{19} +(1.13764 + 1.64492i) q^{20} -4.29097i q^{21} +(-3.16993 - 3.45710i) q^{22} +8.67477i q^{23} +(-5.08422 + 2.37104i) q^{24} +(0.309017 - 0.951057i) q^{25} +(4.42390 - 0.648063i) q^{26} +(-2.40870 - 3.31529i) q^{27} +(4.14507 - 1.24107i) q^{28} +(6.12821 - 1.99118i) q^{29} +(2.48427 + 1.30239i) q^{30} +(0.673670 - 0.927228i) q^{31} +(-3.76092 - 4.22558i) q^{32} +(-6.18872 - 2.22994i) q^{33} +(1.05865 - 6.21560i) q^{34} +(-1.75026 - 1.27164i) q^{35} +(-1.13269 + 1.48515i) q^{36} +(3.17897 + 9.78387i) q^{37} +(-4.98956 + 2.46969i) q^{38} +(5.07306 - 3.68579i) q^{39} +(-0.539585 + 2.77648i) q^{40} +(-1.29856 - 0.421929i) q^{41} +(4.34055 - 4.24081i) q^{42} +4.00994 q^{43} +(0.364168 - 6.62325i) q^{44} +0.933895 q^{45} +(-8.77500 + 8.57336i) q^{46} +(-3.61139 - 1.17341i) q^{47} +(-7.42323 - 2.79964i) q^{48} +(1.87655 - 1.36339i) q^{49} +(1.26745 - 0.627351i) q^{50} +(-2.73257 - 8.40999i) q^{51} +(5.02774 + 3.83453i) q^{52} +(6.21075 + 4.51237i) q^{53} +(0.973058 - 5.71306i) q^{54} +(-2.74361 + 1.86349i) q^{55} +(5.35202 + 2.96641i) q^{56} +(-4.58946 + 6.31685i) q^{57} +(8.07075 + 4.23112i) q^{58} +(-0.112673 + 0.0366097i) q^{59} +(1.13779 + 3.80013i) q^{60} +(-7.07767 - 9.74158i) q^{61} +(1.60374 - 0.234933i) q^{62} +(0.624345 - 1.92153i) q^{63} +(0.557451 - 7.98055i) q^{64} -3.16156i q^{65} +(-3.86067 - 8.46410i) q^{66} -6.69412i q^{67} +(7.33370 - 5.07206i) q^{68} +(-5.31681 + 16.3635i) q^{69} +(-0.443466 - 3.02725i) q^{70} +(0.556753 + 0.766305i) q^{71} +(-2.62175 + 0.322011i) q^{72} +(1.45249 - 0.471942i) q^{73} +(-6.75512 + 12.8852i) q^{74} +(1.16582 - 1.60461i) q^{75} +(-7.42946 - 2.60640i) q^{76} +(2.00001 + 6.89093i) q^{77} +(8.74214 + 1.48897i) q^{78} +(3.49460 + 2.53897i) q^{79} +(-3.34184 + 2.19820i) q^{80} +(-3.37741 - 10.3946i) q^{81} +(-0.856579 - 1.73057i) q^{82} +(-0.790772 + 0.574530i) q^{83} +(8.57962 + 0.199477i) q^{84} +(-4.24018 - 1.37772i) q^{85} +(3.96306 + 4.05627i) q^{86} +12.7802 q^{87} +(7.05969 - 6.17744i) q^{88} -13.2930 q^{89} +(0.922977 + 0.944686i) q^{90} +(-6.50506 - 2.11362i) q^{91} +(-17.3448 - 0.403270i) q^{92} +(1.83907 - 1.33616i) q^{93} +(-2.38220 - 4.81282i) q^{94} +(1.21650 + 3.74402i) q^{95} +(-4.50445 - 10.2759i) q^{96} +(11.7313 + 8.52327i) q^{97} +(3.23376 + 0.550779i) q^{98} +(-2.44690 - 1.89906i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{2} - 2 q^{4} + 8 q^{5} - 15 q^{6} - 10 q^{8} + 10 q^{9} + 6 q^{12} - 10 q^{13} + 21 q^{14} - 34 q^{16} + 10 q^{17} - 25 q^{18} + 2 q^{20} - 36 q^{22} - 15 q^{24} - 8 q^{25} + 12 q^{26} + 30 q^{28}+ \cdots + 94 q^{97}+O(q^{100}) $ 32 * q - 10 * q^2 - 2 * q^4 + 8 * q^5 - 15 * q^6 - 10 * q^8 + 10 * q^9 + 6 * q^12 - 10 * q^13 + 21 * q^14 - 34 * q^16 + 10 * q^17 - 25 * q^18 + 2 * q^20 - 36 * q^22 - 15 * q^24 - 8 * q^25 + 12 * q^26 + 30 * q^28 - 10 * q^29 + 10 * q^30 + 36 * q^33 + 18 * q^34 + 15 * q^36 - 44 * q^37 + 29 * q^38 - 10 * q^40 - 30 * q^41 + 18 * q^42 + 9 * q^44 + 60 * q^45 - 10 * q^46 + 38 * q^48 + 12 * q^49 + 10 * q^50 + 10 * q^52 - 14 * q^53 - 34 * q^56 - 60 * q^57 + 10 * q^58 - 11 * q^60 + 20 * q^61 + 40 * q^62 - 74 * q^64 - 118 * q^66 - 20 * q^68 - 22 * q^69 - 21 * q^70 + 70 * q^72 + 10 * q^73 + 20 * q^74 + 44 * q^77 - 92 * q^78 - 46 * q^80 - 58 * q^81 + 37 * q^82 + 100 * q^84 - 10 * q^85 + 57 * q^86 + 19 * q^88 - 72 * q^89 + 10 * q^90 - 63 * q^92 - 26 * q^93 - 25 * q^94 + 94 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.988310	+	1.01156i	0.698841	+	0.715278i
$2$	0.988310	+	1.01156i	0.698841	+	0.715278i
$3$	1.88633	+	0.612906i	1.08907	+	0.353861i	0.797888	−	0.602805i	$-0.205950\pi$
$3$	1.88633	+	0.612906i	1.08907	+	0.353861i	0.291185	+	0.956667i	$0.405950\pi$
$4$	−0.0464877	+	1.99946i	−0.0232439	+	0.999730i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$	1.24429	+	2.51387i	0.507979	+	1.02628i
$7$	−0.668539	−	2.05755i	−0.252684	−	0.777681i	−0.994277	−	0.106831i	$-0.965930\pi$
$7$	−0.668539	−	2.05755i	−0.252684	−	0.777681i	0.741593	−	0.670850i	$-0.234070\pi$
$8$	−2.06851	+	1.92906i	−0.731328	+	0.682026i
$9$	0.755537	+	0.548930i	0.251846	+	0.182977i
$10$	1.39414	+	0.237451i	0.440865	+	0.0750887i
$11$	−3.31496	−	0.105060i	−0.999498	−	0.0316768i
$11$	−3.31496	−	0.105060i	−0.999498	−	0.0316768i
$12$	−1.31317	+	3.74315i	−0.379080	+	1.08055i
$13$	1.85832	−	2.55775i	0.515404	−	0.709393i	−0.469415	−	0.882978i	$-0.655535\pi$
$13$	1.85832	−	2.55775i	0.515404	−	0.709393i	0.984819	+	0.173585i	$0.0555350\pi$
$14$	1.42060	−	2.70976i	0.379672	−	0.724214i
$15$	1.88633	−	0.612906i	0.487048	−	0.158252i
$16$	−3.99568	−	0.185901i	−0.998919	−	0.0464751i
$17$	−2.62058	−	3.60691i	−0.635583	−	0.874805i	0.362787	−	0.931872i	$-0.381825\pi$
$17$	−2.62058	−	3.60691i	−0.635583	−	0.874805i	−0.998370	+	0.0570671i	$0.981825\pi$
$18$	0.191432	+	1.30678i	0.0451209	+	0.308011i
$19$	−1.21650	+	3.74402i	−0.279085	+	0.858936i	0.709024	+	0.705184i	$0.249136\pi$
$19$	−1.21650	+	3.74402i	−0.279085	+	0.858936i	−0.988109	+	0.153752i	$0.950864\pi$
$20$	1.13764	+	1.64492i	0.254385	+	0.367816i
$21$		−	4.29097i		−	0.936366i
$22$	−3.16993	−	3.45710i	−0.675832	−	0.737056i
$23$			8.67477i			1.80881i	0.426671	+	0.904407i	$0.359686\pi$
$23$			8.67477i			1.80881i	−0.426671	+	0.904407i	$0.640314\pi$
$24$	−5.08422	+	2.37104i	−1.03781	+	0.483987i
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	4.42390	−	0.648063i	0.867598	−	0.127096i
$27$	−2.40870	−	3.31529i	−0.463554	−	0.638028i
$28$	4.14507	−	1.24107i	0.783344	−	0.234539i
$29$	6.12821	−	1.99118i	1.13798	−	0.369752i	0.321377	−	0.946951i	$-0.395854\pi$
$29$	6.12821	−	1.99118i	1.13798	−	0.369752i	0.816603	+	0.577199i	$0.195854\pi$
$30$	2.48427	+	1.30239i	0.453563	+	0.237782i
$31$	0.673670	−	0.927228i	0.120995	−	0.166535i	−0.744223	−	0.667931i	$-0.767180\pi$
$31$	0.673670	−	0.927228i	0.120995	−	0.166535i	0.865218	+	0.501396i	$0.167180\pi$
$32$	−3.76092	−	4.22558i	−0.664843	−	0.746983i
$33$	−6.18872	−	2.22994i	−1.07732	−	0.388182i
$34$	1.05865	−	6.21560i	0.181557	−	1.06597i
$35$	−1.75026	−	1.27164i	−0.295847	−	0.214946i
$36$	−1.13269	+	1.48515i	−0.188781	+	0.247524i
$37$	3.17897	+	9.78387i	0.522620	+	1.60846i	0.768975	+	0.639279i	$0.220767\pi$
$37$	3.17897	+	9.78387i	0.522620	+	1.60846i	−0.246355	+	0.969180i	$0.579233\pi$
$38$	−4.98956	+	2.46969i	−0.809414	+	0.400636i
$39$	5.07306	−	3.68579i	0.812340	−	0.590199i
$40$	−0.539585	+	2.77648i	−0.0853158	+	0.439000i
$41$	−1.29856	−	0.421929i	−0.202802	−	0.0658943i	0.205855	−	0.978583i	$-0.434003\pi$
$41$	−1.29856	−	0.421929i	−0.202802	−	0.0658943i	−0.408656	+	0.912688i	$0.634003\pi$
$42$	4.34055	−	4.24081i	0.669762	−	0.654371i
$43$	4.00994			0.611510			0.305755	−	0.952110i	$-0.401091\pi$
$43$	4.00994			0.611510			0.305755	+	0.952110i	$0.401091\pi$
$44$	0.364168	−	6.62325i	0.0549004	−	0.998492i
$45$	0.933895			0.139217
$46$	−8.77500	+	8.57336i	−1.29380	+	1.26407i
$47$	−3.61139	−	1.17341i	−0.526776	−	0.171160i	0.0335423	−	0.999437i	$-0.489321\pi$
$47$	−3.61139	−	1.17341i	−0.526776	−	0.171160i	−0.560318	+	0.828277i	$0.689321\pi$
$48$	−7.42323	−	2.79964i	−1.07145	−	0.404094i
$49$	1.87655	−	1.36339i	0.268079	−	0.194771i
$50$	1.26745	−	0.627351i	0.179245	−	0.0887208i
$51$	−2.73257	−	8.40999i	−0.382637	−	1.17763i
$52$	5.02774	+	3.83453i	0.697221	+	0.531754i
$53$	6.21075	+	4.51237i	0.853112	+	0.619822i	0.926002	−	0.377518i	$-0.123222\pi$
$53$	6.21075	+	4.51237i	0.853112	+	0.619822i	−0.0728901	+	0.997340i	$0.523222\pi$
$54$	0.973058	−	5.71306i	0.132416	−	0.777450i
$55$	−2.74361	+	1.86349i	−0.369949	+	0.251273i
$56$	5.35202	+	2.96641i	0.715193	+	0.396403i
$57$	−4.58946	+	6.31685i	−0.607889	+	0.836687i
$58$	8.07075	+	4.23112i	1.05974	+	0.555574i
$59$	−0.112673	+	0.0366097i	−0.0146688	+	0.00476618i	−0.316342	−	0.948645i	$-0.602455\pi$
$59$	−0.112673	+	0.0366097i	−0.0146688	+	0.00476618i	0.301673	+	0.953411i	$0.402455\pi$
$60$	1.13779	+	3.80013i	0.146888	+	0.490595i
$61$	−7.07767	−	9.74158i	−0.906203	−	1.24728i	−0.968447	−	0.249221i	$-0.919826\pi$
$61$	−7.07767	−	9.74158i	−0.906203	−	1.24728i	0.0622434	−	0.998061i	$-0.480174\pi$
$62$	1.60374	−	0.234933i	0.203675	−	0.0298366i
$63$	0.624345	−	1.92153i	0.0786600	−	0.242091i
$64$	0.557451	−	7.98055i	0.0696813	−	0.997569i
$65$		−	3.16156i		−	0.392143i
$66$	−3.86067	−	8.46410i	−0.475215	−	1.04186i
$67$		−	6.69412i		−	0.817817i	−0.912575	−	0.408909i	$-0.865909\pi$
$67$		−	6.69412i		−	0.817817i	0.912575	−	0.408909i	$-0.134091\pi$
$68$	7.33370	−	5.07206i	0.889342	−	0.615077i
$69$	−5.31681	+	16.3635i	−0.640069	+	1.96993i
$70$	−0.443466	−	3.02725i	−0.0530043	−	0.361826i
$71$	0.556753	+	0.766305i	0.0660744	+	0.0909436i	0.840775	−	0.541384i	$-0.182100\pi$
$71$	0.556753	+	0.766305i	0.0660744	+	0.0909436i	−0.774701	+	0.632328i	$0.782100\pi$
$72$	−2.62175	+	0.322011i	−0.308976	+	0.0379493i
$73$	1.45249	−	0.471942i	0.170001	−	0.0552366i	−0.222780	−	0.974869i	$-0.571513\pi$
$73$	1.45249	−	0.471942i	0.170001	−	0.0552366i	0.392781	+	0.919632i	$0.371513\pi$
$74$	−6.75512	+	12.8852i	−0.785266	+	1.49787i
$75$	1.16582	−	1.60461i	0.134617	−	0.185284i
$76$	−7.42946	−	2.60640i	−0.852217	−	0.298975i
$77$	2.00001	+	6.89093i	0.227923	+	0.785295i
$78$	8.74214	+	1.48897i	0.989852	+	0.168593i
$79$	3.49460	+	2.53897i	0.393173	+	0.285657i	0.766754	−	0.641941i	$-0.221870\pi$
$79$	3.49460	+	2.53897i	0.393173	+	0.285657i	−0.373582	+	0.927597i	$0.621870\pi$
$80$	−3.34184	+	2.19820i	−0.373629	+	0.245767i
$81$	−3.37741	−	10.3946i	−0.375268	−	1.15496i
$82$	−0.856579	−	1.73057i	−0.0945933	−	0.191109i
$83$	−0.790772	+	0.574530i	−0.0867985	+	0.0630628i	−0.630338	−	0.776321i	$-0.717084\pi$
$83$	−0.790772	+	0.574530i	−0.0867985	+	0.0630628i	0.543540	+	0.839384i	$0.317084\pi$
$84$	8.57962	+	0.199477i	0.936113	+	0.0217648i
$85$	−4.24018	−	1.37772i	−0.459912	−	0.149435i
$86$	3.96306	+	4.05627i	0.427348	+	0.437399i
$87$	12.7802			1.37018
$88$	7.05969	−	6.17744i	0.752565	−	0.658518i
$89$	−13.2930			−1.40905			−0.704527	−	0.709677i	$-0.748841\pi$
$89$	−13.2930			−1.40905			−0.704527	+	0.709677i	$0.748841\pi$
$90$	0.922977	+	0.944686i	0.0972903	+	0.0995786i
$91$	−6.50506	−	2.11362i	−0.681916	−	0.221568i
$92$	−17.3448	−	0.403270i	−1.80833	−	0.0420438i
$93$	1.83907	−	1.33616i	0.190702	−	0.138553i
$94$	−2.38220	−	4.81282i	−0.245706	−	0.496404i
$95$	1.21650	+	3.74402i	0.124811	+	0.384128i
$96$	−4.50445	−	10.2759i	−0.459734	−	1.04878i
$97$	11.7313	+	8.52327i	1.19113	+	0.865407i	0.993383	−	0.114846i	$-0.0366375\pi$
$97$	11.7313	+	8.52327i	1.19113	+	0.865407i	0.197747	+	0.980253i	$0.436638\pi$
$98$	3.23376	+	0.550779i	0.326659	+	0.0556371i
$99$	−2.44690	−	1.89906i	−0.245923	−	0.190862i
$100$	1.88723	+	0.662079i	0.188723	+	0.0662079i
$101$	−4.97379	+	6.84583i	−0.494911	+	0.681186i	−0.981284	−	0.192565i	$-0.938319\pi$
$101$	−4.97379	+	6.84583i	−0.494911	+	0.681186i	0.486374	+	0.873751i	$0.338319\pi$
$102$	5.80654	−	11.0758i	0.574934	−	1.09667i
$103$	7.12868	−	2.31625i	0.702410	−	0.228227i	0.0640295	−	0.997948i	$-0.479605\pi$
$103$	7.12868	−	2.31625i	0.702410	−	0.228227i	0.638380	+	0.769721i	$0.279605\pi$
$104$	1.09012	+	8.87554i	0.106895	+	0.870318i
$105$	−2.52217	−	3.47147i	−0.246138	−	0.338781i
$106$	1.57363	+	10.7421i	0.152844	+	1.04337i
$107$	−3.11661	+	9.59195i	−0.301294	+	0.927288i	0.679740	+	0.733453i	$0.262093\pi$
$107$	−3.11661	+	9.59195i	−0.301294	+	0.927288i	−0.981034	+	0.193835i	$0.937907\pi$
$108$	6.74076	−	4.66198i	0.648630	−	0.448599i
$109$			0.409727i			0.0392447i	0.999807	+	0.0196224i	$0.00624639\pi$
$109$			0.409727i			0.0392447i	−0.999807	+	0.0196224i	$0.993754\pi$
$110$	−4.59656	−	0.933610i	−0.438265	−	0.0890162i
$111$			20.4040i			1.93666i
$112$	2.28876	+	8.34559i	0.216268	+	0.788584i
$113$	−4.42188	+	13.6091i	−0.415975	+	1.28024i	0.495400	+	0.868665i	$0.335021\pi$
$113$	−4.42188	+	13.6091i	−0.415975	+	1.28024i	−0.911376	+	0.411575i	$0.864979\pi$
$114$	−10.9256	+	1.60051i	−1.02328	+	0.149902i
$115$	5.09890	+	7.01803i	0.475475	+	0.654435i
$116$	3.69639	+	12.3457i	0.343201	+	1.14627i
$117$	2.80805	−	0.912392i	0.259605	−	0.0843506i
$118$	−0.148389	−	0.0777933i	−0.0136603	−	0.00716145i
$119$	−5.66945	+	7.80332i	−0.519717	+	0.715330i
$120$	−2.71956	+	4.90665i	−0.248260	+	0.447913i
$121$	10.9779	+	0.696539i	0.997993	+	0.0633217i
$122$	2.85921	−	16.7872i	0.258861	−	1.51984i
$123$	−2.19092	−	1.59180i	−0.197548	−	0.143527i
$124$	1.82264	+	1.39008i	0.163678	+	0.124833i
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$	2.56078	−	1.26751i	0.228133	−	0.112919i
$127$	−7.10692	+	5.16348i	−0.630638	+	0.458185i	−0.856621	−	0.515946i	$-0.827440\pi$
$127$	−7.10692	+	5.16348i	−0.630638	+	0.458185i	0.225983	+	0.974131i	$0.427440\pi$
$128$	8.62370	−	7.32337i	0.762235	−	0.647300i
$129$	7.56407	+	2.45772i	0.665979	+	0.216390i
$130$	3.19809	−	3.12460i	0.280491	−	0.274045i
$131$	−0.809002			−0.0706829			−0.0353414	−	0.999375i	$-0.511252\pi$
$131$	−0.809002			−0.0706829			−0.0353414	+	0.999375i	$0.511252\pi$
$132$	4.74637	−	12.2704i	0.413118	−	1.06800i
$133$	8.51678			0.738499
$134$	6.77147	−	6.61587i	0.584966	−	0.571524i
$135$	−3.89736	−	1.26633i	−0.335431	−	0.108988i
$136$	12.3786	+	2.40568i	1.06146	+	0.206285i
$137$	−17.1284	+	12.4445i	−1.46337	+	1.06320i	−0.480906	+	0.876772i	$0.659692\pi$
$137$	−17.1284	+	12.4445i	−1.46337	+	1.06320i	−0.982468	+	0.186431i	$0.940308\pi$
$138$	−21.8072	+	10.7939i	−1.85635	+	0.918840i
$139$	−5.01958	−	15.4487i	−0.425755	−	1.31034i	−0.902270	−	0.431172i	$-0.858100\pi$
$139$	−5.01958	−	15.4487i	−0.425755	−	1.31034i	0.476515	−	0.879167i	$-0.341900\pi$
$140$	2.62395	−	3.44045i	0.221764	−	0.290771i
$141$	−6.09309	−	4.42689i	−0.513131	−	0.372811i
$142$	−0.224915	+	1.32053i	−0.0188745	+	0.110817i
$143$	−6.42896	+	8.28362i	−0.537617	+	0.692711i
$144$	−2.91683	−	2.33380i	−0.243070	−	0.194483i
$145$	3.78744	−	5.21297i	0.314530	−	0.432913i
$146$	1.91290	+	1.00285i	0.158313	+	0.0829961i
$147$	4.37543	−	1.42166i	0.360879	−	0.117257i
$148$	−19.7102	+	5.90140i	−1.62017	+	0.485092i
$149$	−3.71483	−	5.11302i	−0.304331	−	0.418875i	0.629272	−	0.777185i	$-0.283353\pi$
$149$	−3.71483	−	5.11302i	−0.304331	−	0.418875i	−0.933603	+	0.358310i	$0.883353\pi$
$150$	2.77534	−	0.406563i	0.226605	−	0.0331957i
$151$	4.36717	−	13.4408i	0.355395	−	1.09379i	−0.600385	−	0.799711i	$-0.704986\pi$
$151$	4.36717	−	13.4408i	0.355395	−	1.09379i	0.955780	−	0.294082i	$-0.0950140\pi$
$152$	−4.70608	−	10.0912i	−0.381714	−	0.818508i
$153$		−	4.16367i		−	0.336612i
$154$	−4.99393	+	8.83350i	−0.402422	+	0.711824i
$155$		−	1.14612i		−	0.0920583i
$156$	7.13376	+	10.3147i	0.571158	+	0.825839i
$157$	4.63070	−	14.2518i	0.369570	−	1.13742i	−0.577499	−	0.816391i	$-0.695971\pi$
$157$	4.63070	−	14.2518i	0.369570	−	1.13742i	0.947070	−	0.321029i	$-0.104029\pi$
$158$	0.885433	+	6.04427i	0.0704412	+	0.480856i
$159$	8.94987	+	12.3184i	0.709771	+	0.976915i
$160$	−5.52638	−	1.20795i	−0.436899	−	0.0954968i
$161$	17.8488	−	5.79942i	1.40668	−	0.457058i
$162$	7.17678	−	13.6895i	0.563861	−	1.07555i
$163$	2.27783	−	3.13516i	0.178413	−	0.245565i	−0.710439	−	0.703759i	$-0.751504\pi$
$163$	2.27783	−	3.13516i	0.178413	−	0.245565i	0.888852	+	0.458194i	$0.151504\pi$
$164$	0.903998	−	2.57681i	0.0705903	−	0.201215i
$165$	−6.31750	+	1.83358i	−0.491817	+	0.142744i
$166$	−1.36270	−	0.232097i	−0.105766	−	0.0180142i
$167$	17.8746	+	12.9866i	1.38317	+	1.00494i	0.996576	+	0.0826873i	$0.0263503\pi$
$167$	17.8746	+	12.9866i	1.38317	+	1.00494i	0.386599	+	0.922248i	$0.373650\pi$
$168$	8.27754	+	8.87590i	0.638626	+	0.684791i
$169$	0.928459	+	2.85750i	0.0714200	+	0.219808i
$170$	−2.79697	−	5.65079i	−0.214518	−	0.433396i
$171$	−2.97432	+	2.16097i	−0.227452	+	0.165253i
$172$	−0.186413	+	8.01771i	−0.0142138	+	0.611345i
$173$	−7.70232	−	2.50263i	−0.585596	−	0.190272i	0.00120986	−	0.999999i	$-0.499615\pi$
$173$	−7.70232	−	2.50263i	−0.585596	−	0.190272i	−0.586806	+	0.809728i	$0.699615\pi$
$174$	12.6308	+	12.9279i	0.957541	+	0.980062i
$175$	−2.16344			−0.163540
$176$	13.2260	+	1.03604i	0.996946	+	0.0780944i
$177$	−0.234977			−0.0176619
$178$	−13.1376	−	13.4466i	−0.984705	−	1.00787i
$179$	−17.3150	−	5.62597i	−1.29418	−	0.420505i	−0.420627	−	0.907234i	$-0.638190\pi$
$179$	−17.3150	−	5.62597i	−1.29418	−	0.420505i	−0.873553	+	0.486729i	$0.838190\pi$
$180$	−0.0434146	+	1.86728i	−0.00323593	+	0.139179i
$181$	1.65843	−	1.20492i	0.123270	−	0.0895611i	−0.524442	−	0.851446i	$-0.675726\pi$
$181$	1.65843	−	1.20492i	0.123270	−	0.0895611i	0.647712	+	0.761885i	$0.275726\pi$
$182$	−4.29097	−	8.66914i	−0.318068	−	0.642600i
$183$	−7.38016	−	22.7138i	−0.545557	−	1.67905i
$184$	−16.7341	−	17.9438i	−1.23366	−	1.32284i
$185$	8.32266	+	6.04677i	0.611894	+	0.444567i
$186$	3.16917	+	0.539778i	0.232375	+	0.0395784i
$187$	8.30816	+	12.2321i	0.607553	+	0.894499i
$188$	2.51408	−	7.16629i	0.183358	−	0.522655i
$189$	−5.21107	+	7.17242i	−0.379049	+	0.521717i
$190$	−2.58500	+	4.93081i	−0.187535	+	0.357719i
$191$	21.9303	−	7.12559i	1.58682	−	0.515589i	0.623019	−	0.782207i	$-0.285906\pi$
$191$	21.9303	−	7.12559i	1.58682	−	0.515589i	0.963802	+	0.266617i	$0.0859060\pi$
$192$	5.94286	−	14.7123i	0.428889	−	1.06177i
$193$	3.91182	+	5.38415i	0.281579	+	0.387560i	0.926256	−	0.376895i	$-0.123008\pi$
$193$	3.91182	+	5.38415i	0.281579	+	0.387560i	−0.644677	+	0.764455i	$0.723008\pi$
$194$	2.97237	+	20.2905i	0.213404	+	1.45677i
$195$	1.93774	−	5.96374i	0.138764	−	0.427072i
$196$	2.63881	+	3.81547i	0.188487	+	0.272533i
$197$		−	5.72912i		−	0.408183i	−0.978952	−	0.204092i	$-0.934576\pi$
$197$		−	5.72912i		−	0.408183i	0.978952	−	0.204092i	$-0.0654240\pi$
$198$	−0.497298	−	4.35203i	−0.0353415	−	0.309286i
$199$		−	9.49871i		−	0.673346i	−0.941622	−	0.336673i	$-0.890698\pi$
$199$		−	9.49871i		−	0.673346i	0.941622	−	0.336673i	$-0.109302\pi$
$200$	1.19544	+	2.56338i	0.0845305	+	0.181258i
$201$	4.10287	−	12.6273i	0.289394	−	0.890663i
$202$	−11.8406	+	1.73454i	−0.833100	+	0.122042i
$203$	−8.19389	−	11.2779i	−0.575098	−	0.791555i
$204$	16.9425	−	5.07271i	1.18621	−	0.355161i
$205$	−1.29856	+	0.421929i	−0.0906957	+	0.0294688i
$206$	9.38836	+	4.92188i	0.654118	+	0.342924i
$207$	−4.76184	+	6.55410i	−0.330970	+	0.455542i
$208$	−7.90072	+	9.87450i	−0.547816	+	0.684673i
$209$	4.42601	−	12.2835i	0.306154	−	0.849665i
$210$	1.01890	−	5.98220i	0.0703106	−	0.412811i
$211$	−19.8848	−	14.4472i	−1.36893	−	0.994585i	−0.997820	−	0.0659952i	$-0.978978\pi$
$211$	−19.8848	−	14.4472i	−1.36893	−	0.994585i	−0.371109	−	0.928590i	$-0.621022\pi$
$212$	−9.31104	+	12.2084i	−0.639485	+	0.838475i
$213$	0.580547	+	1.78674i	0.0397784	+	0.122425i
$214$	−12.7830	+	6.32719i	−0.873825	+	0.432518i
$215$	3.24411	−	2.35698i	0.221246	−	0.160745i
$216$	11.3778	+	2.21118i	0.774162	+	0.150452i
$217$	−2.35819	−	0.766223i	−0.160085	−	0.0520146i
$218$	−0.414461	+	0.404937i	−0.0280709	+	0.0274258i
$219$	3.02913			0.204689
$220$	−3.59843	−	5.57237i	−0.242606	−	0.375689i
$221$	−14.0955			−0.948163
$222$	−20.6398	+	20.1655i	−1.38525	+	1.35342i
$223$	−5.05248	−	1.64165i	−0.338339	−	0.109933i	0.134920	−	0.990857i	$-0.456922\pi$
$223$	−5.05248	−	1.64165i	−0.338339	−	0.109933i	−0.473259	+	0.880924i	$0.656922\pi$
$224$	−6.18001	+	10.5632i	−0.412920	+	0.705786i
$225$	0.755537	−	0.548930i	0.0503691	−	0.0365953i
$226$	−18.1366	+	8.97707i	−1.20643	+	0.597146i
$227$	−7.14832	−	22.0003i	−0.474451	−	1.46021i	−0.846697	−	0.532075i	$-0.821412\pi$
$227$	−7.14832	−	22.0003i	−0.474451	−	1.46021i	0.372247	−	0.928134i	$-0.378588\pi$
$228$	−12.4169	−	9.47009i	−0.822331	−	0.627172i
$229$	−3.45085	−	2.50719i	−0.228038	−	0.165680i	0.467899	−	0.883782i	$-0.345011\pi$
$229$	−3.45085	−	2.50719i	−0.228038	−	0.165680i	−0.695938	+	0.718102i	$0.745011\pi$
$230$	−2.05984	+	12.0938i	−0.135822	+	0.797442i
$231$	−0.450809	+	14.2244i	−0.0296611	+	0.935896i
$232$	−8.83515	+	15.9405i	−0.580056	+	1.04654i
$233$	−3.63198	+	4.99899i	−0.237939	+	0.327495i	−0.911242	−	0.411872i	$-0.864875\pi$
$233$	−3.63198	+	4.99899i	−0.237939	+	0.327495i	0.673303	+	0.739367i	$0.264875\pi$
$234$	3.69816	+	1.93877i	0.241756	+	0.126742i
$235$	−3.61139	+	1.17341i	−0.235581	+	0.0765450i
$236$	−0.0679617	−	0.226987i	−0.00442393	−	0.0147756i
$237$	5.03581	+	6.93120i	0.327111	+	0.450230i
$238$	−13.4967	+	1.97714i	−0.874859	+	0.128159i
$239$	2.43080	−	7.48124i	0.157236	−	0.483921i	−0.841145	−	0.540810i	$-0.818118\pi$
$239$	2.43080	−	7.48124i	0.157236	−	0.483921i	0.998381	+	0.0568884i	$0.0181179\pi$
$240$	−7.65111	+	2.09830i	−0.493877	+	0.135445i
$241$		−	7.93127i		−	0.510898i	−0.966822	−	0.255449i	$-0.917777\pi$
$241$		−	7.93127i		−	0.510898i	0.966822	−	0.255449i	$-0.0822233\pi$
$242$	10.1450	+	11.7932i	0.652145	+	0.758094i
$243$		−	9.38390i		−	0.601978i
$244$	19.8069	−	13.6987i	1.26801	−	0.876967i
$245$	0.716779	−	2.20602i	0.0457933	−	0.140937i
$246$	−0.555117	−	3.78942i	−0.0353930	−	0.241605i
$247$	7.31562	+	10.0691i	0.465482	+	0.640681i
$248$	0.395186	+	3.21753i	0.0250943	+	0.204313i
$249$	−1.84379	+	0.599084i	−0.116845	+	0.0379654i
$250$	0.656642	−	1.25253i	0.0415297	−	0.0792167i
$251$	2.01865	−	2.77843i	0.127416	−	0.175373i	−0.740543	−	0.672009i	$-0.765432\pi$
$251$	2.01865	−	2.77843i	0.127416	−	0.175373i	0.867959	+	0.496636i	$0.165432\pi$
$252$	3.81301	+	1.33768i	0.240197	+	0.0842659i
$253$	0.911371	−	28.7565i	0.0572974	−	1.80791i
$254$	−12.2470	−	2.08593i	−0.768444	−	0.130883i
$255$	−7.15397	−	5.19766i	−0.447999	−	0.325490i
$256$	15.9309	+	1.48560i	0.995680	+	0.0928499i
$257$	−4.96642	−	15.2851i	−0.309797	−	0.953457i	−0.977843	−	0.209337i	$-0.932869\pi$
$257$	−4.96642	−	15.2851i	−0.309797	−	0.953457i	0.668047	−	0.744119i	$-0.267131\pi$
$258$	4.98953	+	10.0805i	0.310634	+	0.627582i
$259$	18.0055	−	13.0818i	1.11881	−	0.812863i
$260$	6.32141	+	0.146974i	0.392037	+	0.00911491i
$261$	5.72310	+	1.85955i	0.354251	+	0.115103i
$262$	−0.799545	−	0.818350i	−0.0493960	−	0.0505579i
$263$	2.73012			0.168347			0.0841733	−	0.996451i	$-0.473175\pi$
$263$	2.73012			0.168347			0.0841733	+	0.996451i	$0.473175\pi$
$264$	17.1031	−	7.32577i	1.05262	−	0.450870i
$265$	7.67691			0.471589
$266$	8.41722	+	8.61519i	0.516093	+	0.528231i
$267$	−25.0750	−	8.14736i	−1.53456	−	0.498610i
$268$	13.3846	+	0.311194i	0.817596	+	0.0190092i
$269$	19.8056	−	14.3896i	1.20757	−	0.877350i	0.212561	−	0.977148i	$-0.431820\pi$
$269$	19.8056	−	14.3896i	1.20757	−	0.877350i	0.995008	+	0.0997979i	$0.0318196\pi$
$270$	−2.57083	−	5.19392i	−0.156456	−	0.316092i
$271$	6.26330	+	19.2765i	0.380469	+	1.17096i	0.939714	+	0.341960i	$0.111091\pi$
$271$	6.26330	+	19.2765i	0.380469	+	1.17096i	−0.559246	+	0.829002i	$0.688909\pi$
$272$	9.80045	+	14.8992i	0.594239	+	0.903398i
$273$	−10.9752	−	7.97398i	−0.664252	−	0.482607i
$274$	−29.5164	−	5.02728i	−1.78315	−	0.303709i
$275$	−1.12430	+	3.12025i	−0.0677977	+	0.188158i
$276$	−32.4709	−	11.3915i	−1.95452	−	0.685685i
$277$	17.0989	−	23.5346i	1.02737	−	1.41406i	0.120468	−	0.992717i	$-0.461560\pi$
$277$	17.0989	−	23.5346i	1.02737	−	1.41406i	0.906903	−	0.421339i	$-0.138440\pi$
$278$	10.6663	−	20.3456i	0.639721	−	1.22025i
$279$	1.01797	−	0.330757i	0.0609440	−	0.0198019i
$280$	6.07348	−	0.745962i	0.362960	−	0.0445798i
$281$	15.4637	+	21.2840i	0.922488	+	1.26970i	0.962718	+	0.270506i	$0.0871909\pi$
$281$	15.4637	+	21.2840i	0.922488	+	1.26970i	−0.0402301	+	0.999190i	$0.512809\pi$
$282$	−1.54382	−	10.5386i	−0.0919330	−	0.627566i
$283$	−7.24916	+	22.3106i	−0.430918	+	1.32623i	0.466295	+	0.884629i	$0.345589\pi$
$283$	−7.24916	+	22.3106i	−0.430918	+	1.32623i	−0.897213	+	0.441599i	$0.854411\pi$
$284$	−1.55808	+	1.07758i	−0.0924549	+	0.0639427i
$285$			7.80805i			0.462509i
$286$	−14.7331	+	1.68353i	−0.871189	+	0.0995491i
$287$			2.95394i			0.174365i
$288$	−0.521969	−	5.25706i	−0.0307573	−	0.309775i
$289$	−0.889114	+	2.73641i	−0.0523008	+	0.160965i
$290$	9.01637	−	1.32082i	0.529459	−	0.0775612i
$291$	16.9051	+	23.2679i	0.990994	+	1.36399i
$292$	0.876105	+	2.92613i	0.0512702	+	0.171239i
$293$	−31.9767	+	10.3899i	−1.86810	+	0.606983i	−0.875874	+	0.482540i	$0.839714\pi$
$293$	−31.9767	+	10.3899i	−1.86810	+	0.606983i	−0.992227	+	0.124443i	$0.960286\pi$
$294$	5.76237	+	3.02094i	0.336068	+	0.176185i
$295$	−0.0696358	+	0.0958454i	−0.00405435	+	0.00558033i
$296$	−25.4494	−	14.1056i	−1.47922	−	0.819871i
$297$	7.63644	+	11.2431i	0.443111	+	0.652391i
$298$	1.50070	−	8.81100i	0.0869334	−	0.510408i
$299$	22.1879	+	16.1205i	1.28316	+	0.932270i
$300$	3.15415	+	2.40560i	0.182105	+	0.138887i
$301$	−2.68080	−	8.25065i	−0.154519	−	0.475560i
$302$	17.9122	−	8.86600i	1.03073	−	0.510181i
$303$	−13.5781	+	9.86504i	−0.780039	+	0.566732i
$304$	5.55678	−	14.7337i	0.318703	−	0.845038i
$305$	−11.4519	−	3.72095i	−0.655735	−	0.213061i
$306$	4.21178	−	4.11499i	0.240771	−	0.235238i
$307$	−9.76104			−0.557092			−0.278546	−	0.960423i	$-0.589852\pi$
$307$	−9.76104			−0.557092			−0.278546	+	0.960423i	$0.589852\pi$
$308$	−13.8711	+	3.67860i	−0.790380	+	0.209608i
$309$	14.8667			0.845736
$310$	1.15936	−	1.13272i	0.0658472	−	0.0643341i
$311$	12.1346	+	3.94278i	0.688092	+	0.223574i	0.632134	−	0.774859i	$-0.282179\pi$
$311$	12.1346	+	3.94278i	0.688092	+	0.223574i	0.0559570	+	0.998433i	$0.482179\pi$
$312$	−3.38355	+	17.4103i	−0.191556	+	0.985666i
$313$	10.5101	−	7.63602i	0.594065	−	0.431613i	−0.249702	−	0.968323i	$-0.580333\pi$
$313$	10.5101	−	7.63602i	0.594065	−	0.431613i	0.843767	+	0.536709i	$0.180333\pi$
$314$	18.9931	−	9.40101i	1.07184	−	0.530530i
$315$	−0.624345	−	1.92153i	−0.0351778	−	0.108266i
$316$	−5.23903	+	6.86927i	−0.294719	+	0.386427i
$317$	12.6756	+	9.20938i	0.711934	+	0.517250i	0.883797	−	0.467871i	$-0.154979\pi$
$317$	12.6756	+	9.20938i	0.711934	+	0.517250i	−0.171863	+	0.985121i	$0.554979\pi$
$318$	−3.61554	+	21.2277i	−0.202749	+	1.19039i
$319$	−20.5240	+	5.95684i	−1.14912	+	0.333519i
$320$	−4.23987	−	6.78407i	−0.237016	−	0.379241i
$321$	−11.7579	+	16.1834i	−0.656263	+	0.903269i
$322$	23.5065	+	12.3234i	1.30997	+	0.686756i
$323$	16.6923	−	5.42365i	0.928783	−	0.301780i
$324$	20.9406	−	6.26977i	1.16337	−	0.348321i
$325$	−1.85832	−	2.55775i	−0.103081	−	0.141879i
$326$	5.42258	−	0.794361i	0.300329	−	0.0439956i
$327$	−0.251124	+	0.772880i	−0.0138872	+	0.0427404i
$328$	3.50002	−	1.63225i	0.193256	−	0.0901257i
$329$			8.21509i			0.452913i
$330$	−8.09842	−	4.57836i	−0.445803	−	0.252030i
$331$			20.7468i			1.14035i	0.821523	+	0.570175i	$0.193125\pi$
$331$			20.7468i			1.14035i	−0.821523	+	0.570175i	$0.806875\pi$
$332$	−1.11199	−	1.60783i	−0.0610283	−	0.0882409i
$333$	−2.96883	+	9.13711i	−0.162691	+	0.500710i
$334$	4.52891	+	30.9159i	0.247811	+	1.69164i
$335$	−3.93471	−	5.41566i	−0.214976	−	0.295889i
$336$	−0.797694	+	17.1453i	−0.0435178	+	0.935355i
$337$	−24.5682	+	7.98269i	−1.33831	+	0.434845i	−0.888746	−	0.458401i	$-0.848423\pi$
$337$	−24.5682	+	7.98269i	−1.33831	+	0.434845i	−0.449569	+	0.893245i	$0.648423\pi$
$338$	−1.97292	+	3.76329i	−0.107313	+	0.204696i
$339$	−16.6822	+	22.9611i	−0.906055	+	1.24708i
$340$	2.95181	−	8.41402i	0.160084	−	0.456314i
$341$	−2.33061	+	3.00295i	−0.126209	+	0.162619i
$342$	−5.12548	−	0.872980i	−0.277154	−	0.0472053i
$343$	−16.3116	−	11.8511i	−0.880743	−	0.639897i
$344$	−8.29459	+	7.73542i	−0.447214	+	0.417066i
$345$	5.31681	+	16.3635i	0.286248	+	0.880980i
$346$	−5.08072	−	10.2647i	−0.273141	−	0.551833i
$347$	12.2474	−	8.89825i	0.657474	−	0.477683i	−0.208335	−	0.978058i	$-0.566804\pi$
$347$	12.2474	−	8.89825i	0.657474	−	0.477683i	0.865809	+	0.500375i	$0.166804\pi$
$348$	−0.594124	+	25.5536i	−0.0318484	+	1.36981i
$349$	16.7168	+	5.43162i	0.894831	+	0.290748i	0.720102	−	0.693868i	$-0.244095\pi$
$349$	16.7168	+	5.43162i	0.894831	+	0.290748i	0.174729	+	0.984617i	$0.444095\pi$
$350$	−2.13814	−	2.18843i	−0.114289	−	0.116977i
$351$	−12.9558			−0.691530
$352$	12.0234	+	14.4027i	0.640847	+	0.767669i
$353$	27.7541			1.47720			0.738602	−	0.674142i	$-0.235486\pi$
$353$	27.7541			1.47720			0.738602	+	0.674142i	$0.235486\pi$
$354$	−0.232230	−	0.237692i	−0.0123429	−	0.0126332i
$355$	0.900845	+	0.292702i	0.0478119	+	0.0155350i
$356$	0.617961	−	26.5788i	0.0327519	−	1.40867i
$357$	−15.4772	+	11.2448i	−0.819138	+	0.595138i
$358$	−11.4216	−	23.0752i	−0.603648	−	1.21956i
$359$	4.23768	+	13.0422i	0.223656	+	0.688344i	0.998425	+	0.0560990i	$0.0178662\pi$
$359$	4.23768	+	13.0422i	0.223656	+	0.688344i	−0.774769	+	0.632245i	$0.782134\pi$
$360$	−1.93177	+	1.80154i	−0.101813	+	0.0949495i
$361$	2.83355	+	2.05869i	0.149134	+	0.108352i
$362$	2.85789	+	0.486760i	0.150207	+	0.0255835i
$363$	20.2811	+	8.04234i	1.06448	+	0.422113i
$364$	4.52851	−	12.9084i	0.237358	−	0.676581i
$365$	0.897686	−	1.23556i	0.0469870	−	0.0646721i
$366$	15.6824	−	29.9137i	0.819730	−	1.56361i
$367$	26.9913	−	8.77001i	1.40893	−	0.457791i	0.496866	−	0.867827i	$-0.334484\pi$
$367$	26.9913	−	8.77001i	1.40893	−	0.457791i	0.912069	+	0.410037i	$0.134484\pi$
$368$	1.61264	−	34.6616i	0.0840649	−	1.80686i
$369$	−0.749504	−	1.03160i	−0.0390176	−	0.0537031i
$370$	2.10873	+	14.3949i	0.109628	+	0.748356i
$371$	5.13231	−	15.7956i	0.266456	−	0.820068i
$372$	2.58611	+	3.73926i	0.134083	+	0.193871i
$373$			36.8629i			1.90869i	0.298708	+	0.954345i	$0.403444\pi$
$373$			36.8629i			1.90869i	−0.298708	+	0.954345i	$0.596556\pi$
$374$	−4.16240	+	20.4933i	−0.215232	+	1.05968i
$375$		−	1.98340i		−	0.102423i
$376$	9.73378	−	4.53938i	0.501981	−	0.234101i
$377$	6.29522	−	19.3747i	0.324220	−	0.997847i
$378$	−12.4054	+	1.81729i	−0.638067	+	0.0934713i
$379$	−7.95643	−	10.9511i	−0.408695	−	0.562520i	0.554205	−	0.832380i	$-0.313022\pi$
$379$	−7.95643	−	10.9511i	−0.408695	−	0.562520i	−0.962899	+	0.269861i	$0.913022\pi$
$380$	−7.54256	+	2.25830i	−0.386925	+	0.115848i
$381$	−16.5707	+	5.38416i	−0.848944	+	0.275839i
$382$	28.8819	+	15.1414i	1.47772	+	0.774703i
$383$	−15.0329	+	20.6910i	−0.768143	+	1.05726i	0.228350	+	0.973579i	$0.426667\pi$
$383$	−15.0329	+	20.6910i	−0.768143	+	1.05726i	−0.996493	+	0.0836790i	$0.973333\pi$
$384$	20.7557	−	8.52877i	1.05918	−	0.435232i
$385$	5.66843	+	4.39930i	0.288890	+	0.224209i
$386$	−1.58028	+	9.27823i	−0.0804342	+	0.472249i
$387$	3.02966	+	2.20117i	0.154006	+	0.111892i
$388$	−17.5873	+	23.0600i	−0.892859	+	1.17069i
$389$	−7.70500	−	23.7135i	−0.390659	−	1.20232i	−0.932291	−	0.361709i	$-0.882193\pi$
$389$	−7.70500	−	23.7135i	−0.390659	−	1.20232i	0.541632	−	0.840616i	$-0.317807\pi$
$390$	7.94774	−	3.93389i	0.402449	−	0.199201i
$391$	31.2891	−	22.7329i	1.58236	−	1.14965i
$392$	−1.25159	+	6.44017i	−0.0632149	+	0.325278i
$393$	−1.52605	−	0.495842i	−0.0769788	−	0.0250119i
$394$	5.79532	−	5.66215i	0.291964	−	0.285255i
$395$	4.31956			0.217341
$396$	3.91084	−	4.80420i	0.196527	−	0.241420i
$397$	5.97091			0.299671			0.149836	−	0.988711i	$-0.452126\pi$
$397$	5.97091			0.299671			0.149836	+	0.988711i	$0.452126\pi$
$398$	9.60847	−	9.38766i	0.481629	−	0.470561i
$399$	16.0655	+	5.21998i	0.804279	+	0.261326i
$400$	−1.41153	+	3.74267i	−0.0705767	+	0.187133i
$401$	−20.7320	+	15.0627i	−1.03531	+	0.752195i	−0.969364	−	0.245628i	$-0.921006\pi$
$401$	−20.7320	+	15.0627i	−1.03531	+	0.752195i	−0.0659435	+	0.997823i	$0.521006\pi$
$402$	16.8281	−	8.32943i	0.839311	−	0.415434i
$403$	−1.11973	−	3.44617i	−0.0557776	−	0.171666i
$404$	−13.4567	−	10.2631i	−0.669498	−	0.510610i
$405$	−8.84217	−	6.42421i	−0.439371	−	0.319222i
$406$	3.31014	−	19.4347i	0.164279	−	0.964526i
$407$	−9.51028	−	32.7671i	−0.471407	−	1.62421i
$408$	21.8757	+	12.1248i	1.08301	+	0.600269i
$409$	−7.03003	+	9.67600i	−0.347612	+	0.478447i	−0.946645	−	0.322277i	$-0.895552\pi$
$409$	−7.03003	+	9.67600i	−0.347612	+	0.478447i	0.599033	+	0.800724i	$0.295552\pi$
$410$	−1.71019	−	0.896573i	−0.0844602	−	0.0442786i
$411$	−39.9370	+	12.9763i	−1.96995	+	0.640075i
$412$	4.29985	+	14.3612i	0.211838	+	0.707525i
$413$	0.150653	+	0.207355i	0.00741313	+	0.0102033i
$414$	−11.3360	+	1.66063i	−0.557134	+	0.0816153i
$415$	−0.302048	+	0.929609i	−0.0148270	+	0.0456327i
$416$	−17.7970	+	1.76704i	−0.872568	+	0.0866365i
$417$		−	32.2178i		−	1.57771i
$418$	16.7997	−	7.66271i	0.821699	−	0.374795i
$419$		−	13.1418i		−	0.642018i	−0.947076	−	0.321009i	$-0.895978\pi$
$419$		−	13.1418i		−	0.642018i	0.947076	−	0.321009i	$-0.104022\pi$
$420$	7.05831	−	4.88159i	0.344410	−	0.238197i
$421$	−2.76091	+	8.49720i	−0.134558	+	0.414128i	−0.995521	−	0.0945400i	$-0.969862\pi$
$421$	−2.76091	+	8.49720i	−0.134558	+	0.414128i	0.860963	+	0.508668i	$0.169862\pi$
$422$	−5.03826	−	34.3929i	−0.245259	−	1.67422i
$423$	−2.08442	−	2.86896i	−0.101348	−	0.139493i
$424$	−21.5516	+	2.64703i	−1.04664	+	0.128551i
$425$	−4.24018	+	1.37772i	−0.205679	+	0.0668291i
$426$	−1.23363	+	2.35311i	−0.0597694	+	0.114008i
$427$	−15.3121	+	21.0753i	−0.741004	+	1.01990i
$428$	−19.0338	−	6.67745i	−0.920035	−	0.322767i
$429$	−17.2042	+	11.6853i	−0.830628	+	0.564171i
$430$	5.59040	+	0.952166i	0.269593	+	0.0459175i
$431$	−19.1954	−	13.9462i	−0.924608	−	0.671767i	0.0200586	−	0.999799i	$-0.493615\pi$
$431$	−19.1954	−	13.9462i	−0.924608	−	0.671767i	−0.944667	+	0.328032i	$0.893615\pi$
$432$	9.00807	+	13.6946i	0.433401	+	0.658882i
$433$	1.25353	+	3.85797i	0.0602408	+	0.185402i	0.976648	−	0.214844i	$-0.0689245\pi$
$433$	1.25353	+	3.85797i	0.0602408	+	0.185402i	−0.916407	+	0.400247i	$0.868924\pi$
$434$	−1.55555	−	3.14271i	−0.0746687	−	0.150855i
$435$	10.3394	−	7.51203i	0.495737	−	0.360174i
$436$	−0.819232	−	0.0190473i	−0.0392341	−	0.000912199i
$437$	−32.4785	−	10.5529i	−1.55366	−	0.504813i
$438$	2.99371	+	3.06413i	0.143045	+	0.146410i
$439$	15.9976			0.763526			0.381763	−	0.924260i	$-0.375317\pi$
$439$	15.9976			0.763526			0.381763	+	0.924260i	$0.375317\pi$
$440$	2.08040	−	9.14724i	0.0991791	−	0.436077i
$441$	2.16621			0.103153
$442$	−13.9307	−	14.2583i	−0.662614	−	0.678199i
$443$	18.5635	+	6.03163i	0.881976	+	0.286572i	0.714778	−	0.699352i	$-0.246528\pi$
$443$	18.5635	+	6.03163i	0.881976	+	0.286572i	0.167199	+	0.985923i	$0.446528\pi$
$444$	−40.7970	−	0.948536i	−1.93614	−	0.0450155i
$445$	−10.7543	+	7.81343i	−0.509801	+	0.370392i
$446$	−3.33279	−	6.73332i	−0.157812	−	0.318832i
$447$	−3.87359	−	11.9217i	−0.183215	−	0.563876i
$448$	−16.7931	+	4.18833i	−0.793398	+	0.197880i
$449$	−9.22004	−	6.69875i	−0.435121	−	0.316134i	0.348572	−	0.937282i	$-0.386667\pi$
$449$	−9.22004	−	6.69875i	−0.435121	−	0.316134i	−0.783693	+	0.621148i	$0.786667\pi$
$450$	1.30198	+	0.221755i	0.0613758	+	0.0104536i
$451$	4.26036	+	1.53511i	0.200613	+	0.0722853i
$452$	−27.0054	−	9.47402i	−1.27023	−	0.445621i
$453$	16.4758	−	22.6770i	0.774102	−	1.06546i
$454$	15.1897	−	28.9740i	0.712889	−	1.35982i
$455$	−6.50506	+	2.11362i	−0.304962	+	0.0990882i
$456$	−2.69225	−	21.9198i	−0.126076	−	1.02649i
$457$	2.44913	+	3.37094i	0.114566	+	0.157686i	0.862449	−	0.506144i	$-0.168930\pi$
$457$	2.44913	+	3.37094i	0.114566	+	0.157686i	−0.747883	+	0.663830i	$0.768930\pi$
$458$	−0.874348	−	5.96860i	−0.0408556	−	0.278894i
$459$	−5.64578	+	17.3759i	−0.263523	+	0.811039i
$460$	−14.2693	+	9.86879i	−0.665310	+	0.460135i
$461$			23.9567i			1.11577i	0.829917	+	0.557887i	$0.188388\pi$
$461$			23.9567i			1.11577i	−0.829917	+	0.557887i	$0.811612\pi$
$462$	−14.8343	+	13.6021i	−0.690154	+	0.632826i
$463$			2.35157i			0.109287i	0.998506	+	0.0546433i	$0.0174022\pi$
$463$			2.35157i			0.109287i	−0.998506	+	0.0546433i	$0.982598\pi$
$464$	−24.8565	+	6.81686i	−1.15393	+	0.316465i
$465$	0.702461	−	2.16195i	0.0325759	−	0.100258i
$466$	−8.64628	+	1.26660i	−0.400531	+	0.0586743i
$467$	−18.2786	−	25.1583i	−0.845833	−	1.16419i	−0.984766	−	0.173887i	$-0.944367\pi$
$467$	−18.2786	−	25.1583i	−0.845833	−	1.16419i	0.138933	−	0.990302i	$-0.455633\pi$
$468$	1.69375	+	5.65700i	0.0782936	+	0.261495i
$469$	−13.7735	+	4.47528i	−0.636001	+	0.206649i
$470$	−4.75615	−	2.49343i	−0.219385	−	0.115013i
$471$	17.4701	−	24.0455i	0.804978	−	1.10796i
$472$	0.162443	−	0.293081i	0.00747703	−	0.0134901i
$473$	−13.2928	−	0.421284i	−0.611203	−	0.0193707i
$474$	−2.03435	+	11.9442i	−0.0934408	+	0.548614i
$475$	3.18485	+	2.31393i	0.146131	+	0.106170i
$476$	−15.3389	−	11.6986i	−0.703056	−	0.536204i
$477$	2.21547	+	6.81853i	0.101440	+	0.312199i
$478$	9.97007	−	4.93489i	0.456021	−	0.225717i
$479$	−13.7911	+	10.0198i	−0.630133	+	0.457819i	−0.856446	−	0.516236i	$-0.827333\pi$
$479$	−13.7911	+	10.0198i	−0.630133	+	0.457819i	0.226313	+	0.974055i	$0.427333\pi$
$480$	−9.68421	−	5.66574i	−0.442022	−	0.258605i
$481$	30.9323	+	10.0505i	1.41039	+	0.458264i
$482$	8.02292	−	7.83856i	0.365434	−	0.357036i
$483$	37.2232			1.69371
$484$	−1.90304	+	21.9175i	−0.0865018	+	0.996252i
$485$	14.5007			0.658441
$486$	9.49233	−	9.27420i	0.430581	−	0.420686i
$487$	−3.58219	−	1.16392i	−0.162324	−	0.0527424i	0.226728	−	0.973958i	$-0.427197\pi$
$487$	−3.58219	−	1.16392i	−0.162324	−	0.0527424i	−0.389052	+	0.921216i	$0.627197\pi$
$488$	33.4323	+	6.49728i	1.51341	+	0.294118i
$489$	6.21829	−	4.51785i	0.281201	−	0.204304i
$490$	2.93991	−	1.45517i	0.132811	−	0.0657378i
$491$	−11.9119	−	36.6612i	−0.537579	−	1.65450i	−0.738010	−	0.674789i	$-0.764234\pi$
$491$	−11.9119	−	36.6612i	−0.537579	−	1.65450i	0.200432	−	0.979708i	$-0.435766\pi$
$492$	3.28458	−	4.30665i	0.148080	−	0.194159i
$493$	−23.2414	−	16.8859i	−1.04674	−	0.760502i
$494$	−2.95534	+	17.3515i	−0.132967	+	0.780682i
$495$	−3.09582	−	0.0981149i	−0.139147	−	0.00440994i
$496$	−2.86414	+	3.57967i	−0.128604	+	0.160732i
$497$	1.20450	−	1.65785i	0.0540292	−	0.0743648i
$498$	−2.42824	−	1.27302i	−0.108812	−	0.0570452i
$499$	8.45653	−	2.74769i	0.378566	−	0.123004i	−0.113552	−	0.993532i	$-0.536223\pi$
$499$	8.45653	−	2.74769i	0.378566	−	0.123004i	0.492118	+	0.870528i	$0.336223\pi$
$500$	1.91596	−	0.573655i	0.0856845	−	0.0256546i
$501$	25.7577	+	35.4525i	1.15077	+	1.58390i
$502$	4.80558	−	0.703975i	0.214484	−	0.0314200i
$503$	2.67219	−	8.22415i	0.119147	−	0.366697i	−0.873642	−	0.486569i	$-0.838248\pi$
$503$	2.67219	−	8.22415i	0.119147	−	0.366697i	0.992789	+	0.119872i	$0.0382484\pi$
$504$	2.41530	+	5.17911i	0.107586	+	0.230696i
$505$			8.46192i			0.376550i
$506$	29.9895	−	27.4984i	1.33320	−	1.22245i
$507$			5.95925i			0.264660i
$508$	−9.99379	−	14.4500i	−0.443403	−	0.641117i
$509$	2.61645	−	8.05261i	0.115972	−	0.356926i	−0.876176	−	0.481991i	$-0.839914\pi$
$509$	2.61645	−	8.05261i	0.115972	−	0.356926i	0.992149	+	0.125065i	$0.0399139\pi$
$510$	−1.81261	−	12.3735i	−0.0802639	−	0.547909i
$511$	−1.94209	−	2.67305i	−0.0859129	−	0.118249i
$512$	14.2419	+	17.5832i	0.629408	+	0.777075i
$513$	15.3427	−	4.98514i	0.677396	−	0.220099i
$514$	10.5533	−	20.1302i	0.465488	−	0.887905i
$515$	4.40577	−	6.06402i	0.194141	−	0.267213i
$516$	−5.26574	+	15.0098i	−0.231811	+	0.660769i
$517$	11.8483	+	4.26923i	0.521090	+	0.187761i
$518$	31.0280	+	5.28474i	1.36329	+	0.232198i
$519$	−12.9952	−	9.44159i	−0.570427	−	0.414440i
$520$	6.09883	+	6.53971i	0.267452	+	0.286785i
$521$	1.75482	+	5.40078i	0.0768801	+	0.236613i	0.982110	−	0.188311i	$-0.0603011\pi$
$521$	1.75482	+	5.40078i	0.0768801	+	0.236613i	−0.905229	+	0.424923i	$0.860301\pi$
$522$	3.77516	+	7.62704i	0.165234	+	0.333827i
$523$	−4.73587	+	3.44081i	−0.207085	+	0.150456i	−0.686494	−	0.727136i	$-0.740851\pi$
$523$	−4.73587	+	3.44081i	−0.207085	+	0.150456i	0.479409	+	0.877592i	$0.340851\pi$
$524$	0.0376087	−	1.61757i	0.00164294	−	0.0706638i
$525$	−4.08095	−	1.32598i	−0.178107	−	0.0578706i
$526$	2.69821	+	2.76167i	0.117647	+	0.120415i
$527$	−5.10983			−0.222588
$528$	24.3136	+	10.0606i	1.05811	+	0.437831i
$529$	−52.2516			−2.27181
$530$	7.58717	+	7.76562i	0.329565	+	0.337317i
$531$	−0.105225	−	0.0341896i	−0.00456636	−	0.00148370i
$532$	−0.395926	+	17.0290i	−0.0171656	+	0.738299i
$533$	−3.49233	+	2.53733i	−0.151270	+	0.109904i
$534$	−16.5403	−	33.4168i	−0.715771	−	1.44609i
$535$	3.11661	+	9.59195i	0.134743	+	0.414696i
$536$	12.9134	+	13.8468i	0.557773	+	0.598093i
$537$	−29.2135	−	21.2249i	−1.26066	−	0.915921i
$538$	34.1299	+	5.81306i	1.47145	+	0.250619i
$539$	−6.36393	+	4.32245i	−0.274114	+	0.186181i
$540$	2.71315	−	7.73374i	0.116755	−	0.332807i
$541$	−8.71813	+	11.9995i	−0.374822	+	0.515898i	−0.954203	−	0.299159i	$-0.903294\pi$
$541$	−8.71813	+	11.9995i	−0.374822	+	0.515898i	0.579382	+	0.815056i	$0.303294\pi$
$542$	−13.3091	+	25.3868i	−0.571676	+	1.09046i
$543$	3.86685	−	1.25642i	0.165943	−	0.0539180i
$544$	−5.38551	+	24.6387i	−0.230902	+	1.05638i
$545$	0.240831	+	0.331476i	0.0103161	+	0.0141989i
$546$	−2.78082	−	18.9828i	−0.119008	−	0.812390i
$547$	−4.35574	+	13.4056i	−0.186238	+	0.573182i	−0.999968	−	0.00806215i	$-0.997434\pi$
$547$	−4.35574	+	13.4056i	−0.186238	+	0.573182i	0.813730	+	0.581244i	$0.197434\pi$
$548$	−24.0860	−	34.8260i	−1.02890	−	1.48769i
$549$		−	11.2453i		−	0.479936i
$550$	−4.26746	+	1.94648i	−0.181965	+	0.0829984i
$551$			25.3664i			1.08064i
$552$	−20.5683	−	44.1044i	−0.875443	−	1.87721i
$553$	2.88779	−	8.88771i	0.122801	−	0.377944i
$554$	40.7055	−	5.96300i	1.72941	−	0.253344i
$555$	11.9932	+	16.5072i	0.509082	+	0.700692i
$556$	31.1223	−	9.31827i	1.31988	−	0.395183i
$557$	16.3059	−	5.29811i	0.690904	−	0.224488i	0.0575410	−	0.998343i	$-0.481674\pi$
$557$	16.3059	−	5.29811i	0.690904	−	0.224488i	0.633363	+	0.773855i	$0.281674\pi$
$558$	1.34064	+	0.702838i	0.0567540	+	0.0297535i
$559$	7.45174	−	10.2564i	0.315175	−	0.433801i
$560$	6.75706	+	5.40642i	0.285538	+	0.228463i
$561$	8.17482	+	28.1659i	0.345141	+	1.18916i
$562$	−6.24698	+	36.6776i	−0.263513	+	1.54715i
$563$	28.3227	+	20.5777i	1.19366	+	0.867245i	0.993646	−	0.112548i	$-0.0359011\pi$
$563$	28.3227	+	20.5777i	1.19366	+	0.867245i	0.200014	+	0.979793i	$0.435901\pi$
$564$	9.13464	−	11.9771i	0.384638	−	0.504326i
$565$	4.42188	+	13.6091i	0.186030	+	0.572541i
$566$	−29.7328	+	14.7169i	−1.24976	+	0.618596i
$567$	−19.1295	+	13.8984i	−0.803362	+	0.583677i
$568$	−2.62990	−	0.511097i	−0.110348	−	0.0214452i
$569$	24.8973	+	8.08962i	1.04375	+	0.339135i	0.780212	−	0.625515i	$-0.215111\pi$
$569$	24.8973	+	8.08962i	1.04375	+	0.339135i	0.263537	+	0.964649i	$0.415111\pi$
$570$	−7.89828	+	7.71678i	−0.330822	+	0.323220i
$571$	−0.540313			−0.0226114			−0.0113057	−	0.999936i	$-0.503599\pi$
$571$	−0.540313			−0.0226114			−0.0113057	+	0.999936i	$0.503599\pi$
$572$	−16.2639	−	13.2395i	−0.680027	−	0.553573i
$573$	45.7351			1.91061
$574$	−2.98807	+	2.91940i	−0.124720	+	0.121854i
$575$	8.25019	+	2.68065i	0.344057	+	0.111791i
$576$	4.80194	−	5.72360i	0.200081	−	0.238483i
$577$	17.1276	−	12.4439i	0.713031	−	0.518047i	−0.171119	−	0.985250i	$-0.554738\pi$
$577$	17.1276	−	12.4439i	0.713031	−	0.518047i	0.884150	+	0.467203i	$0.154738\pi$
$578$	−3.64675	+	1.80503i	−0.151685	+	0.0750796i
$579$	4.07900	+	12.5539i	0.169517	+	0.521721i
$580$	10.2470	+	7.81518i	0.425486	+	0.324508i
$581$	1.71079	+	1.24296i	0.0709753	+	0.0515666i
$582$	−6.82926	+	40.0963i	−0.283082	+	1.66204i
$583$	−20.1143	−	15.6108i	−0.833050	−	0.646535i
$584$	−2.09408	+	3.77815i	−0.0866535	+	0.156341i
$585$	1.73547	−	2.38867i	0.0717529	−	0.0987594i
$586$	−42.1128	−	22.0778i	−1.73967	−	0.912026i
$587$	−6.33408	+	2.05807i	−0.261435	+	0.0849455i	−0.436802	−	0.899558i	$-0.643889\pi$
$587$	−6.33408	+	2.05807i	−0.261435	+	0.0849455i	0.175367	+	0.984503i	$0.443889\pi$
$588$	2.63915	+	8.81458i	0.108837	+	0.363507i
$589$	2.65203	+	3.65021i	0.109275	+	0.150404i
$590$	−0.165775	+	0.0242845i	−0.00682483	+	0.000999778i
$591$	3.51141	−	10.8070i	0.144440	−	0.444541i
$592$	−10.8833	−	39.6842i	−0.447302	−	1.63101i
$593$			17.3655i			0.713114i	0.934274	+	0.356557i	$0.116049\pi$
$593$			17.3655i			0.713114i	−0.934274	+	0.356557i	$0.883951\pi$
$594$	−3.82586	+	18.8364i	−0.156977	+	0.772865i
$595$			9.64544i			0.395424i
$596$	10.3960	−	7.18996i	0.425836	−	0.294512i
$597$	5.82181	−	17.9177i	0.238271	−	0.733323i
$598$	5.62179	+	38.3763i	0.229892	+	1.56932i
$599$	−10.2918	−	14.1655i	−0.420512	−	0.578785i	0.545231	−	0.838286i	$-0.316442\pi$
$599$	−10.2918	−	14.1655i	−0.420512	−	0.578785i	−0.965743	+	0.259501i	$0.916442\pi$
$600$	0.683887	+	5.56807i	0.0279195	+	0.227316i
$601$	−16.4987	+	5.36075i	−0.672995	+	0.218669i	−0.625526	−	0.780203i	$-0.715116\pi$
$601$	−16.4987	+	5.36075i	−0.672995	+	0.218669i	−0.0474692	+	0.998873i	$0.515116\pi$
$602$	5.69653	−	10.8660i	0.232173	−	0.442864i
$603$	3.67460	−	5.05765i	0.149641	−	0.205964i
$604$	26.6712	+	9.35680i	1.08524	+	0.380723i
$605$	9.29074	−	5.88915i	0.377722	−	0.239428i
$606$	−23.3984	−	3.98524i	−0.950493	−	0.161889i
$607$	13.4664	+	9.78390i	0.546583	+	0.397116i	0.826524	−	0.562901i	$-0.190315\pi$
$607$	13.4664	+	9.78390i	0.546583	+	0.397116i	−0.279941	+	0.960017i	$0.590315\pi$
$608$	20.3958	−	8.94051i	0.827159	−	0.362585i
$609$	−8.54408	−	26.2960i	−0.346223	−	1.06557i
$610$	−7.55409	−	15.2617i	−0.305856	−	0.617928i
$611$	−9.71241	+	7.05648i	−0.392922	+	0.285475i
$612$	8.32508	+	0.193559i	0.336521	+	0.00782417i
$613$	20.1537	+	6.54833i	0.814000	+	0.264485i	0.686291	−	0.727327i	$-0.259238\pi$
$613$	20.1537	+	6.54833i	0.814000	+	0.264485i	0.127709	+	0.991812i	$0.459238\pi$
$614$	−9.64693	−	9.87383i	−0.389318	−	0.398475i
$615$	−2.70812			−0.109202
$616$	−17.4301	−	10.3958i	−0.702278	−	0.418859i
$617$	−25.8431			−1.04040			−0.520202	−	0.854043i	$-0.674143\pi$
$617$	−25.8431			−1.04040			−0.520202	+	0.854043i	$0.674143\pi$
$618$	14.6929	+	15.0385i	0.591035	+	0.604936i
$619$	−34.2763	−	11.1371i	−1.37768	−	0.447636i	−0.475775	−	0.879567i	$-0.657832\pi$
$619$	−34.2763	−	11.1371i	−1.37768	−	0.447636i	−0.901907	+	0.431931i	$0.857832\pi$
$620$	2.29161	+	0.0532803i	0.0920334	+	0.00213979i
$621$	28.7594	−	20.8949i	1.15407	−	0.838483i
$622$	8.00443	+	16.1715i	0.320948	+	0.648419i
$623$	8.88688	+	27.3510i	0.356045	+	1.09579i
$624$	−20.9555	+	13.7842i	−0.838892	+	0.551808i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	18.1115	+	3.08477i	0.723880	+	0.123292i
$627$	15.8775	−	20.4579i	0.634087	−	0.817011i
$628$	28.2807	+	9.92143i	1.12852	+	0.395908i
$629$	26.9588	−	37.1057i	1.07492	−	1.47950i
$630$	1.32669	−	2.53063i	0.0528567	−	0.100823i
$631$	−27.4535	+	8.92019i	−1.09291	+	0.355107i	−0.799369	−	0.600840i	$-0.794833\pi$
$631$	−27.4535	+	8.92019i	−1.09291	+	0.355107i	−0.293539	+	0.955947i	$0.594833\pi$
$632$	−12.1264	+	1.48940i	−0.482364	+	0.0592453i
$633$	−28.6546	−	39.4397i	−1.13892	−	1.56759i
$634$	3.21165	+	21.9238i	0.127551	+	0.870706i
$635$	−2.71460	+	8.35469i	−0.107726	+	0.331546i
$636$	−25.0463	+	17.3222i	−0.993149	+	0.686872i
$637$		−	7.33337i		−	0.290559i
$638$	−26.3097	−	14.8739i	−1.04161	−	0.588864i
$639$			0.884589i			0.0349938i
$640$	2.67216	−	10.9936i	0.105626	−	0.434561i
$641$	6.10563	−	18.7912i	0.241158	−	0.742207i	−0.755087	−	0.655625i	$-0.772405\pi$
$641$	6.10563	−	18.7912i	0.241158	−	0.742207i	0.996245	−	0.0865825i	$-0.0275946\pi$
$642$	−27.9909	+	4.10042i	−1.10471	+	0.161830i
$643$	14.1640	+	19.4951i	0.558576	+	0.768813i	0.991145	−	0.132788i	$-0.0423928\pi$
$643$	14.1640	+	19.4951i	0.558576	+	0.768813i	−0.432569	+	0.901601i	$0.642393\pi$
$644$	10.7659	+	35.9575i	0.424238	+	1.41692i
$645$	7.56407	−	2.45772i	0.297835	−	0.0967724i
$646$	21.9835	+	11.5249i	0.864928	+	0.453442i
$647$	−10.4606	+	14.3978i	−0.411250	+	0.566038i	−0.963523	−	0.267626i	$-0.913761\pi$
$647$	−10.4606	+	14.3978i	−0.411250	+	0.566038i	0.552272	+	0.833664i	$0.313761\pi$
$648$	27.0380	+	14.9861i	1.06215	+	0.588709i
$649$	0.377353	−	0.109522i	0.0148124	−	0.00429912i
$650$	0.750716	−	4.40764i	0.0294455	−	0.172882i
$651$	−3.97871	−	2.89070i	−0.155938	−	0.113295i
$652$	6.16273	+	4.70017i	0.241351	+	0.184073i
$653$	−2.84702	−	8.76222i	−0.111412	−	0.342892i	0.879769	−	0.475401i	$-0.157697\pi$
$653$	−2.84702	−	8.76222i	−0.111412	−	0.342892i	−0.991182	+	0.132508i	$0.957697\pi$
$654$	−1.03000	+	0.509819i	−0.0402762	+	0.0199355i
$655$	−0.654497	+	0.475520i	−0.0255733	+	0.0185801i
$656$	5.11021	+	1.92730i	0.199520	+	0.0752483i
$657$	1.35647	+	0.440744i	0.0529209	+	0.0171951i
$658$	−8.31002	+	8.11906i	−0.323958	+	0.316514i
$659$	23.7876			0.926633			0.463317	−	0.886193i	$-0.346659\pi$
$659$	23.7876			0.926633			0.463317	+	0.886193i	$0.346659\pi$
$660$	−3.37248	−	12.7168i	−0.131274	−	0.495002i
$661$	−30.7116			−1.19454			−0.597272	−	0.802038i	$-0.703749\pi$
$661$	−30.7116			−1.19454			−0.597272	+	0.802038i	$0.703749\pi$
$662$	−20.9866	+	20.5043i	−0.815666	+	0.796923i
$663$	−26.5887	−	8.63918i	−1.03262	−	0.335518i
$664$	0.527416	−	2.71387i	0.0204677	−	0.105318i
$665$	6.89022	−	5.00604i	0.267191	−	0.194126i
$666$	−12.1768	+	6.02716i	−0.471842	+	0.233548i
$667$	17.2730	+	53.1608i	0.668813	+	2.05839i
$668$	−26.7972	+	35.1357i	−1.03681	+	1.35944i
$669$	−8.52447	−	6.19339i	−0.329575	−	0.239450i
$670$	1.58953	−	9.33252i	0.0614089	−	0.360547i
$671$	22.4388	+	33.0365i	0.866239	+	1.27536i
$672$	−18.1318	+	16.1380i	−0.699450	+	0.622536i
$673$	6.35951	−	8.75312i	0.245141	−	0.337408i	−0.668661	−	0.743567i	$-0.733132\pi$
$673$	6.35951	−	8.75312i	0.245141	−	0.337408i	0.913802	+	0.406159i	$0.133132\pi$
$674$	−32.3559	−	16.9627i	−1.24630	−	0.653379i
$675$	−3.89736	+	1.26633i	−0.150009	+	0.0487410i
$676$	−5.75663	+	1.72358i	−0.221409	+	0.0662915i
$677$	4.03856	+	5.55860i	0.155214	+	0.213634i	0.879542	−	0.475822i	$-0.157849\pi$
$677$	4.03856	+	5.55860i	0.155214	+	0.213634i	−0.724327	+	0.689457i	$0.757849\pi$
$678$	−39.7137	+	5.81771i	−1.52519	+	0.223428i
$679$	9.69424	−	29.8358i	0.372031	−	1.14499i
$680$	11.4285	−	5.32974i	0.438265	−	0.204386i
$681$		−	45.8810i		−	1.75816i
$682$	−5.34101	+	0.610307i	−0.204518	+	0.0233698i
$683$		−	10.6775i		−	0.408562i	−0.978912	−	0.204281i	$-0.934514\pi$
$683$		−	10.6775i		−	0.408562i	0.978912	−	0.204281i	$-0.0654857\pi$
$684$	−4.18250	−	6.04748i	−0.159922	−	0.231231i
$685$	−6.54245	+	20.1356i	−0.249974	+	0.769341i
$686$	−4.13290	−	28.2126i	−0.157795	−	1.07716i
$687$	−4.97277	−	6.84443i	−0.189723	−	0.261131i
$688$	−16.0224	−	0.745450i	−0.610849	−	0.0284200i
$689$	23.0831	−	7.50015i	0.879395	−	0.285733i
$690$	−11.2979	+	21.5504i	−0.430104	+	0.820411i
$691$	27.8181	−	38.2883i	1.05825	−	1.45656i	0.176819	−	0.984243i	$-0.443419\pi$
$691$	27.8181	−	38.2883i	1.05825	−	1.45656i	0.881431	−	0.472313i	$-0.156581\pi$
$692$	5.36198	−	15.2841i	0.203832	−	0.581015i
$693$	−2.27155	+	6.30422i	−0.0862892	+	0.239477i
$694$	21.1053	+	3.59468i	0.801146	+	0.136452i
$695$	−13.1414	−	9.54780i	−0.498483	−	0.362169i
$696$	−26.4360	+	24.6538i	−1.00205	+	0.934501i
$697$	1.88112	+	5.78951i	0.0712527	+	0.219293i
$698$	11.0270	+	22.2781i	0.417378	+	0.843239i
$699$	−9.91503	+	7.20369i	−0.375021	+	0.272469i
$700$	0.100573	−	4.32570i	0.00380131	−	0.163496i
$701$	0.689187	+	0.223930i	0.0260302	+	0.00845774i	0.322003	−	0.946739i	$-0.395644\pi$
$701$	0.689187	+	0.223930i	0.0260302	+	0.00845774i	−0.295973	+	0.955196i	$0.595644\pi$
$702$	−12.8044	−	13.1055i	−0.483269	−	0.494636i
$703$	−40.4982			−1.52742
$704$	−2.68636	+	26.3967i	−0.101246	+	0.994861i
$705$	−7.53147			−0.283652
$706$	27.4297	+	28.0748i	1.03233	+	1.05661i
$707$	17.4108	+	5.65712i	0.654801	+	0.212758i
$708$	0.0109235	−	0.469827i	0.000410531	−	0.0176572i
$709$	−12.6604	+	9.19829i	−0.475470	+	0.345449i	−0.799569	−	0.600574i	$-0.794939\pi$
$709$	−12.6604	+	9.19829i	−0.475470	+	0.345449i	0.324099	+	0.946023i	$0.394939\pi$
$710$	0.594230	+	1.20054i	0.0223010	+	0.0450553i
$711$	1.24658	+	3.83658i	0.0467504	+	0.143883i
$712$	27.4967	−	25.6430i	1.03048	−	0.961012i
$713$	8.04348	+	5.84393i	0.301231	+	0.218857i
$714$	−26.6710	−	4.54264i	−0.998136	−	0.170004i
$715$	−0.332153	+	10.4804i	−0.0124218	+	0.391946i
$716$	12.0538	−	34.3590i	0.450473	−	1.28406i
$717$	9.17059	−	12.6222i	0.342482	−	0.471386i
$718$	−9.00481	+	17.1764i	−0.336057	+	0.641019i
$719$	−10.4581	+	3.39806i	−0.390023	+	0.126726i	−0.497463	−	0.867485i	$-0.665735\pi$
$719$	−10.4581	+	3.39806i	−0.390023	+	0.126726i	0.107440	+	0.994212i	$0.465735\pi$
$720$	−3.73154	−	0.173612i	−0.139066	−	0.00647012i
$721$	−9.53159	−	13.1191i	−0.354975	−	0.488581i
$722$	0.717941	+	4.90092i	0.0267190	+	0.182393i
$723$	4.86112	−	14.9610i	0.180787	−	0.556406i
$724$	2.33209	+	3.37198i	0.0866716	+	0.125319i
$725$		−	6.44358i		−	0.239309i
$726$	11.9087	+	28.4637i	0.441974	+	1.05639i
$727$		−	7.80710i		−	0.289549i	−0.989465	−	0.144775i	$-0.953754\pi$
$727$		−	7.80710i		−	0.289549i	0.989465	−	0.144775i	$-0.0462457\pi$
$728$	17.5331	−	8.17661i	0.649819	−	0.303045i
$729$	−4.38078	+	13.4827i	−0.162251	+	0.499357i
$730$	2.13703	−	0.313056i	0.0790950	−	0.0115867i
$731$	−10.5083	−	14.4635i	−0.388665	−	0.534952i
$732$	45.7584	−	13.7004i	1.69128	−	0.506382i
$733$	0.776549	−	0.252316i	0.0286825	−	0.00931951i	−0.294641	−	0.955608i	$-0.595200\pi$
$733$	0.776549	−	0.252316i	0.0286825	−	0.00931951i	0.323323	+	0.946289i	$0.395200\pi$
$734$	35.5471	+	18.6357i	1.31207	+	0.687857i
$735$	2.70416	−	3.72196i	0.0997445	−	0.137287i
$736$	36.6559	−	32.6251i	1.35115	−	1.20258i
$737$	−0.703284	+	22.1908i	−0.0259058	+	0.817407i
$738$	0.302782	−	1.77771i	0.0111456	−	0.0654383i
$739$	6.06980	+	4.40997i	0.223281	+	0.162223i	0.693802	−	0.720165i	$-0.255934\pi$
$739$	6.06980	+	4.40997i	0.223281	+	0.162223i	−0.470521	+	0.882389i	$0.655934\pi$
$740$	−12.4772	+	16.3597i	−0.458670	+	0.601395i
$741$	7.62827	+	23.4774i	0.280232	+	0.862464i
$742$	21.0505	−	10.4194i	0.772787	−	0.382507i
$743$	−8.89011	+	6.45904i	−0.326147	+	0.236959i	−0.738794	−	0.673932i	$-0.764604\pi$
$743$	−8.89011	+	6.45904i	−0.326147	+	0.236959i	0.412647	+	0.910891i	$0.364604\pi$
$744$	−1.22659	+	6.31153i	−0.0449690	+	0.231392i
$745$	−6.01072	−	1.95300i	−0.220216	−	0.0715524i
$746$	−37.2889	+	36.4320i	−1.36524	+	1.33387i
$747$	−0.912834			−0.0333988
$748$	−24.8438	+	16.0432i	−0.908379	+	0.586597i
$749$	21.8195			0.797267
$750$	2.00632	−	1.96022i	0.0732606	−	0.0715771i
$751$	−11.1966	−	3.63801i	−0.408571	−	0.132753i	0.0975185	−	0.995234i	$-0.468909\pi$
$751$	−11.1966	−	3.63801i	−0.408571	−	0.132753i	−0.506090	+	0.862481i	$0.668909\pi$
$752$	14.2118	+	5.35994i	0.518252	+	0.195457i
$753$	5.51075	−	4.00379i	0.200823	−	0.145906i
$754$	25.8202	−	12.7802i	0.940316	−	0.465429i
$755$	−4.36717	−	13.4408i	−0.158937	−	0.489159i
$756$	−14.0987	−	10.7527i	−0.512765	−	0.391074i
$757$	0.669234	+	0.486227i	0.0243237	+	0.0176722i	0.599881	−	0.800089i	$-0.295215\pi$
$757$	0.669234	+	0.486227i	0.0243237	+	0.0176722i	−0.575557	+	0.817762i	$0.695215\pi$
$758$	3.21421	−	18.8714i	0.116745	−	0.685442i
$759$	19.3442	−	53.6857i	0.702149	−	1.94867i
$760$	−9.73878	−	5.39782i	−0.353263	−	0.195799i
$761$	−8.42620	+	11.5977i	−0.305449	+	0.420415i	−0.933955	−	0.357390i	$-0.883667\pi$
$761$	−8.42620	+	11.5977i	−0.305449	+	0.420415i	0.628506	+	0.777805i	$0.283667\pi$
$762$	−21.8234	−	11.4410i	−0.790578	−	0.414464i
$763$	0.843034	−	0.273918i	0.0305199	−	0.00991651i
$764$	13.2278	+	44.1800i	0.478566	+	1.59838i
$765$	−2.44734	−	3.36848i	−0.0884838	−	0.121788i
$766$	−35.7872	+	5.24251i	−1.29304	+	0.189419i
$767$	−0.115744	+	0.356222i	−0.00417926	+	0.0128624i
$768$	29.1404	+	12.5665i	1.05151	+	0.453453i
$769$			2.50888i			0.0904725i	0.998976	+	0.0452362i	$0.0144041\pi$
$769$			2.50888i			0.0904725i	−0.998976	+	0.0452362i	$0.985596\pi$
$770$	1.15203	+	10.0818i	0.0415162	+	0.363323i
$771$		−	31.8766i		−	1.14801i
$772$	−10.9472	+	7.57122i	−0.394000	+	0.272494i
$773$	−4.73441	+	14.5710i	−0.170285	+	0.524083i	−0.999387	−	0.0350147i	$-0.988852\pi$
$773$	−4.73441	+	14.5710i	−0.170285	+	0.524083i	0.829102	+	0.559097i	$0.188852\pi$
$774$	0.767630	+	5.24011i	0.0275919	+	0.188352i
$775$	−0.673670	−	0.927228i	−0.0241990	−	0.0333070i
$776$	−40.7081	+	4.99989i	−1.46134	+	0.179485i
$777$	41.9823	−	13.6409i	1.50611	−	0.489364i
$778$	16.3726	−	31.2304i	0.586987	−	1.11966i
$779$	3.15942	−	4.34857i	0.113198	−	0.155804i
$780$	11.8342	+	4.15167i	0.423731	+	0.148654i
$781$	−1.76511	−	2.59876i	−0.0631605	−	0.0929910i
$782$	53.9189	+	9.18355i	1.92814	+	0.328403i
$783$	−21.3623	−	15.5206i	−0.763428	−	0.554663i
$784$	−7.75155	+	5.09883i	−0.276841	+	0.182101i
$785$	−4.63070	−	14.2518i	−0.165277	−	0.508670i
$786$	−1.00663	−	2.03372i	−0.0359054	−	0.0725406i
$787$	−10.8975	+	7.91747i	−0.388453	+	0.282227i	−0.764821	−	0.644243i	$-0.777173\pi$
$787$	−10.8975	+	7.91747i	−0.388453	+	0.282227i	0.376368	+	0.926470i	$0.377173\pi$
$788$	11.4551	+	0.266334i	0.408073	+	0.00948775i
$789$	5.14992	+	1.67331i	0.183342	+	0.0595714i
$790$	4.26906	+	4.36947i	0.151886	+	0.155459i
$791$	30.9577			1.10073
$792$	8.72483	−	0.792012i	0.310023	−	0.0281429i
$793$	−38.0691			−1.35187
$794$	5.90111	+	6.03991i	0.209423	+	0.214348i
$795$	14.4812	+	4.70522i	0.513595	+	0.166877i
$796$	18.9923	+	0.441573i	0.673164	+	0.0156511i
$797$	2.14733	−	1.56012i	0.0760622	−	0.0552624i	−0.549104	−	0.835754i	$-0.685031\pi$
$797$	2.14733	−	1.56012i	0.0760622	−	0.0552624i	0.625167	+	0.780491i	$0.285031\pi$
$798$	10.5973	+	21.4101i	0.375142	+	0.757908i
$799$	5.23153	+	16.1010i	0.185078	+	0.569612i
$800$	−5.18095	+	2.27107i	−0.183174	+	0.0802945i
$801$	−10.0433	−	7.29692i	−0.354864	−	0.257824i
$802$	−35.7264	−	6.08497i	−1.26154	−	0.214868i
$803$	−4.86452	+	1.41187i	−0.171665	+	0.0498238i
$804$	25.0571	+	8.79053i	0.883696	+	0.310018i
$805$	11.0311	−	15.1831i	0.388797	−	0.535133i
$806$	2.37935	−	4.53854i	0.0838090	−	0.159863i
$807$	46.1794	−	15.0046i	1.62559	−	0.528186i
$808$	−2.91770	−	23.7554i	−0.102645	−	0.835712i
$809$	8.10115	+	11.1503i	0.284821	+	0.392023i	0.927323	−	0.374261i	$-0.122104\pi$
$809$	8.10115	+	11.1503i	0.284821	+	0.392023i	−0.642502	+	0.766284i	$0.722104\pi$
$810$	−2.24036	−	15.2935i	−0.0787181	−	0.537357i
$811$	−12.3429	+	37.9876i	−0.433418	+	1.33392i	0.461280	+	0.887255i	$0.347390\pi$
$811$	−12.3429	+	37.9876i	−0.433418	+	1.33392i	−0.894699	+	0.446670i	$0.852610\pi$
$812$	22.9307	−	15.8591i	0.804709	−	0.556544i
$813$			40.2006i			1.40990i
$814$	23.7467	−	42.0043i	0.832320	−	1.47225i
$815$		−	3.87527i		−	0.135745i
$816$	9.35506	+	34.1116i	0.327492	+	1.19415i
$817$	−4.87811	+	15.0133i	−0.170663	+	0.525248i
$818$	−16.7357	+	2.45163i	−0.585148	+	0.0857191i
$819$	−3.75458	−	5.16774i	−0.131196	−	0.180575i
$820$	−0.783263	−	2.61604i	−0.0273527	−	0.0913561i
$821$	2.79822	−	0.909197i	0.0976586	−	0.0317312i	−0.259780	−	0.965668i	$-0.583650\pi$
$821$	2.79822	−	0.909197i	0.0976586	−	0.0317312i	0.357439	+	0.933937i	$0.383650\pi$
$822$	−52.5964	−	27.5739i	−1.83451	−	0.961749i
$823$	17.5777	−	24.1937i	0.612721	−	0.843338i	−0.384077	−	0.923301i	$-0.625480\pi$
$823$	17.5777	−	24.1937i	0.612721	−	0.843338i	0.996798	+	0.0799631i	$0.0254802\pi$
$824$	−10.2775	+	18.5428i	−0.358035	+	0.645970i
$825$	−4.03321	+	5.19673i	−0.140418	+	0.180927i
$826$	−0.0608601	+	0.357325i	−0.00211759	+	0.0124329i
$827$	14.4618	+	10.5071i	0.502886	+	0.365368i	0.810118	−	0.586267i	$-0.199403\pi$
$827$	14.4618	+	10.5071i	0.502886	+	0.365368i	−0.307232	+	0.951635i	$0.599403\pi$
$828$	−12.8833	−	9.82578i	−0.447726	−	0.341470i
$829$	16.1777	+	49.7899i	0.561876	+	1.72928i	0.677056	+	0.735931i	$0.263255\pi$
$829$	16.1777	+	49.7899i	0.561876	+	1.72928i	−0.115180	+	0.993345i	$0.536745\pi$
$830$	−1.23887	+	0.613203i	−0.0430017	+	0.0212846i
$831$	46.6786	−	33.9140i	1.61926	−	1.17646i
$832$	−19.3764	−	16.2562i	−0.671755	−	0.563583i
$833$	−9.83529	−	3.19568i	−0.340772	−	0.110724i
$834$	32.5901	−	31.8412i	1.12850	−	1.10257i
$835$	22.0942			0.764600
$836$	24.3545	+	9.42066i	0.842319	+	0.325820i
$837$	−4.69670			−0.162342
$838$	13.2936	−	12.9882i	0.459221	−	0.448668i
$839$	−5.94199	−	1.93067i	−0.205140	−	0.0666541i	0.204644	−	0.978836i	$-0.434396\pi$
$839$	−5.94199	−	1.93067i	−0.205140	−	0.0666541i	−0.409785	+	0.912182i	$0.634396\pi$
$840$	11.9138	+	2.31534i	0.411065	+	0.0798869i
$841$	10.1287	−	7.35892i	0.349265	−	0.253756i
$842$	−11.3240	+	5.60505i	−0.390251	+	0.193163i
$843$	16.1246	+	49.6264i	0.555361	+	1.70922i
$844$	29.8109	−	39.0873i	1.02614	−	1.34544i
$845$	2.43074	+	1.76603i	0.0836199	+	0.0607534i
$846$	0.842056	−	4.94392i	0.0289505	−	0.169976i
$847$	−5.90600	−	23.0533i	−0.202933	−	0.792121i
$848$	−23.9773	−	19.1846i	−0.823384	−	0.658801i
$849$	−27.3486	+	37.6421i	−0.938602	+	1.29187i
$850$	−5.58425	−	2.92756i	−0.191538	−	0.100415i
$851$	−84.8728	+	27.5768i	−2.90940	+	0.945322i
$852$	−3.59950	+	1.07772i	−0.123317	+	0.0369221i
$853$	−25.2147	−	34.7051i	−0.863335	−	1.18828i	−0.980764	−	0.195198i	$-0.937465\pi$
$853$	−25.2147	−	34.7051i	−0.863335	−	1.18828i	0.117429	−	0.993081i	$-0.462535\pi$
$854$	−36.4519	+	5.33989i	−1.24736	+	0.182727i
$855$	−1.13609	+	3.49652i	−0.0388534	+	0.119578i
$856$	−12.0567	−	25.8532i	−0.412090	−	0.883643i
$857$			1.34505i			0.0459459i	0.999736	+	0.0229729i	$0.00731316\pi$
$857$			1.34505i			0.0459459i	−0.999736	+	0.0229729i	$0.992687\pi$
$858$	−28.8234	−	5.85434i	−0.984015	−	0.199864i
$859$			8.64868i			0.295089i	0.989055	+	0.147545i	$0.0471370\pi$
$859$			8.64868i			0.295089i	−0.989055	+	0.147545i	$0.952863\pi$
$860$	4.56188	+	6.59604i	0.155559	+	0.224923i
$861$	−1.81049	+	5.57210i	−0.0617012	+	0.189897i
$862$	−4.86357	−	33.2004i	−0.165654	−	1.13081i
$863$	−23.9258	−	32.9311i	−0.814445	−	1.12099i	−0.990622	−	0.136629i	$-0.956373\pi$
$863$	−23.9258	−	32.9311i	−0.814445	−	1.12099i	0.176178	−	0.984358i	$-0.443627\pi$
$864$	−4.95009	+	22.6467i	−0.168405	+	0.770455i
$865$	−7.70232	+	2.50263i	−0.261887	+	0.0850921i
$866$	−2.66367	+	5.08088i	−0.0905153	+	0.172655i
$867$	−3.35433	+	4.61683i	−0.113919	+	0.156796i
$868$	1.64166	−	4.67949i	0.0557215	−	0.158832i
$869$	−11.3177	−	8.78374i	−0.383927	−	0.297968i
$870$	17.8174	+	3.03468i	0.604066	+	0.102885i
$871$	−17.1219	−	12.4398i	−0.580154	−	0.421506i
$872$	−0.790388	−	0.847523i	−0.0267659	−	0.0287008i
$873$	4.18473	+	12.8793i	0.141632	+	0.435898i
$874$	−21.4240	−	43.2833i	−0.724676	−	1.46408i
$875$	−1.75026	+	1.27164i	−0.0591695	+	0.0429891i
$876$	−0.140817	+	6.05661i	−0.00475777	+	0.204634i
$877$	−26.7095	−	8.67845i	−0.901916	−	0.293050i	−0.178889	−	0.983869i	$-0.557250\pi$
$877$	−26.7095	−	8.67845i	−0.901916	−	0.293050i	−0.723028	+	0.690819i	$0.757250\pi$
$878$	15.8106	+	16.1825i	0.533583	+	0.546133i
$879$	−66.6867			−2.24929
$880$	11.3090	−	6.93586i	0.381227	−	0.233808i
$881$	−42.5103			−1.43221			−0.716105	−	0.697993i	$-0.754077\pi$
$881$	−42.5103			−1.43221			−0.716105	+	0.697993i	$0.754077\pi$
$882$	2.14089	+	2.19124i	0.0720874	+	0.0737829i
$883$	48.5687	+	15.7809i	1.63447	+	0.531070i	0.975292	−	0.220920i	$-0.0709061\pi$
$883$	48.5687	+	15.7809i	1.63447	+	0.531070i	0.659174	+	0.751990i	$0.270906\pi$
$884$	0.655265	−	28.1833i	0.0220390	−	0.947906i
$885$	−0.190100	+	0.138116i	−0.00639015	+	0.00464272i
$886$	12.2451	+	24.7391i	0.411383	+	0.831126i
$887$	4.42344	+	13.6139i	0.148525	+	0.457111i	0.997447	−	0.0714053i	$-0.0227484\pi$
$887$	4.42344	+	13.6139i	0.148525	+	0.457111i	−0.848923	+	0.528517i	$0.822748\pi$
$888$	−39.3606	−	42.2059i	−1.32086	−	1.41634i
$889$	15.3754	+	11.1709i	0.515674	+	0.374659i
$890$	−18.5323	−	3.15644i	−0.621203	−	0.105804i
$891$	10.1039	+	34.8125i	0.338494	+	1.16626i
$892$	3.51729	−	10.0259i	0.117768	−	0.335692i
$893$	8.78655	−	12.0937i	0.294031	−	0.404699i
$894$	8.23114	−	15.7007i	0.275290	−	0.525109i
$895$	−17.3150	+	5.62597i	−0.578775	+	0.188055i
$896$	−20.8335	−	12.8478i	−0.695998	−	0.429213i
$897$	31.9734	+	44.0076i	1.06756	+	1.46937i
$898$	−2.33610	−	15.9470i	−0.0779566	−	0.532159i
$899$	2.28212	−	7.02364i	0.0761130	−	0.234252i
$900$	1.06244	+	1.53618i	0.0354146	+	0.0512061i
$901$		−	34.2267i		−	1.14026i
$902$	2.65771	+	5.82675i	0.0884922	+	0.194010i
$903$		−	17.2065i		−	0.572597i
$904$	−17.1062	−	36.6807i	−0.568943	−	1.21998i
$905$	0.633465	−	1.94960i	0.0210571	−	0.0648070i
$906$	39.2223	−	5.74573i	1.30307	−	0.190889i
$907$	−9.79869	−	13.4867i	−0.325360	−	0.447820i	0.614734	−	0.788734i	$-0.289263\pi$
$907$	−9.79869	−	13.4867i	−0.325360	−	0.447820i	−0.940094	+	0.340915i	$0.889263\pi$
$908$	44.3210	−	13.2700i	1.47084	−	0.440382i
$909$	−7.51576	+	2.44202i	−0.249282	+	0.0809966i
$910$	−8.56706	−	4.49131i	−0.283995	−	0.148886i
$911$	−14.6953	+	20.2263i	−0.486876	+	0.670128i	−0.979808	−	0.199940i	$-0.935925\pi$
$911$	−14.6953	+	20.2263i	−0.486876	+	0.670128i	0.492932	+	0.870068i	$0.335925\pi$
$912$	19.5123	−	24.3869i	0.646117	−	0.807531i
$913$	2.68174	−	1.82146i	0.0887526	−	0.0602817i
$914$	−0.989393	+	5.80897i	−0.0327262	+	0.192144i
$915$	−19.3215	−	14.0379i	−0.638749	−	0.464078i
$916$	5.17344	−	6.78328i	0.170935	−	0.224126i
$917$	0.540849	+	1.66456i	0.0178604	+	0.0549687i
$918$	−23.1565	+	11.4618i	−0.764278	+	0.378295i
$919$	−37.0121	+	26.8909i	−1.22092	+	0.887048i	−0.996176	−	0.0873709i	$-0.972153\pi$
$919$	−37.0121	+	26.8909i	−1.22092	+	0.887048i	−0.224741	+	0.974419i	$0.572153\pi$
$920$	−24.0853	−	4.68077i	−0.794070	−	0.154320i
$921$	−18.4125	−	5.98260i	−0.606714	−	0.197133i
$922$	−24.2335	+	23.6766i	−0.798088	+	0.779748i
$923$	2.99464			0.0985698
$924$	−28.4201	−	1.56263i	−0.934954	−	0.0514069i
$925$	10.2874			0.338247
$926$	−2.37874	+	2.32408i	−0.0781702	+	0.0763739i
$927$	6.65744	+	2.16313i	0.218659	+	0.0710466i
$928$	−31.4616	−	18.4066i	−1.03278	−	0.604225i
$929$	34.1164	−	24.7870i	1.11932	−	0.813236i	0.135217	−	0.990816i	$-0.456827\pi$
$929$	34.1164	−	24.7870i	1.11932	−	0.813236i	0.984106	+	0.177580i	$0.0568269\pi$
$930$	2.88119	−	1.42610i	0.0944778	−	0.0467637i
$931$	2.82174	+	8.68441i	0.0924787	+	0.284620i
$932$	−9.82644	−	7.49439i	−0.321876	−	0.245487i
$933$	20.4734	+	14.8748i	0.670268	+	0.486978i
$934$	7.38413	−	43.3541i	0.241616	−	1.41859i
$935$	13.9113	+	5.01255i	0.454948	+	0.163928i
$936$	−4.04842	+	7.30419i	−0.132327	+	0.238745i
$937$	−6.67224	+	9.18355i	−0.217973	+	0.300014i	−0.903975	−	0.427586i	$-0.859364\pi$
$937$	−6.67224	+	9.18355i	−0.217973	+	0.300014i	0.686002	+	0.727600i	$0.259364\pi$
$938$	−18.1395	−	9.50969i	−0.592275	−	0.310502i
$939$	24.5056	−	7.96236i	0.799711	−	0.259842i
$940$	−2.17831	−	7.27538i	−0.0710485	−	0.237297i
$941$	−33.8939	−	46.6510i	−1.10491	−	1.52078i	−0.828710	−	0.559678i	$-0.810925\pi$
$941$	−33.8939	−	46.6510i	−1.10491	−	1.52078i	−0.276199	−	0.961100i	$-0.589075\pi$
$942$	41.5891	−	6.09245i	1.35505	−	0.198503i
$943$	3.66014	−	11.2647i	0.119190	−	0.366830i
$944$	0.457011	−	0.125335i	0.0148744	−	0.00407929i
$945$			8.86560i			0.288398i
$946$	−12.7112	−	13.8627i	−0.413278	−	0.450717i
$947$		−	40.2825i		−	1.30900i	−0.756060	−	0.654502i	$-0.772878\pi$
$947$		−	40.2825i		−	1.30900i	0.756060	−	0.654502i	$-0.227122\pi$
$948$	−14.0928	+	9.74669i	−0.457712	+	0.316558i
$949$	1.49207	−	4.59212i	0.0484347	−	0.149067i
$950$	0.806952	+	5.50853i	0.0261810	+	0.178720i
$951$	18.2659	+	25.1409i	0.592313	+	0.815249i
$952$	−3.32579	−	27.0779i	−0.107789	−	0.877601i
$953$	−19.1705	+	6.22886i	−0.620992	+	0.201773i	−0.602581	−	0.798058i	$-0.705861\pi$
$953$	−19.1705	+	6.22886i	−0.620992	+	0.201773i	−0.0184114	+	0.999830i	$0.505861\pi$
$954$	−4.70774	+	8.97989i	−0.152419	+	0.290735i
$955$	13.5537	−	18.6550i	0.438587	−	0.603663i
$956$	14.8454	+	5.20808i	0.480136	+	0.168441i
$957$	−42.3660	−	1.34269i	−1.36950	−	0.0434030i
$958$	−23.7655	−	4.04778i	−0.767830	−	0.130778i
$959$	37.0561	+	26.9228i	1.19660	+	0.869384i
$960$	−3.83979	−	15.3956i	−0.123929	−	0.496892i
$961$	9.17361	+	28.2335i	0.295923	+	0.910757i
$962$	20.4040	+	41.2227i	0.657852	+	1.32907i
$963$	−7.62002	+	5.53627i	−0.245552	+	0.178404i
$964$	15.8583	+	0.368707i	0.510760	+	0.0118752i
$965$	6.32945	+	2.05656i	0.203752	+	0.0662031i
$966$	36.7880	+	37.6533i	1.18363	+	1.21147i
$967$	−36.5643			−1.17583			−0.587915	−	0.808923i	$-0.700051\pi$
$967$	−36.5643			−1.17583			−0.587915	+	0.808923i	$0.700051\pi$
$968$	−24.0516	+	19.7363i	−0.773047	+	0.634348i
$969$	34.8113			1.11830
$970$	14.3311	+	14.6682i	0.460145	+	0.470968i
$971$	53.3853	+	17.3459i	1.71322	+	0.556658i	0.990864	−	0.134867i	$-0.0430606\pi$
$971$	53.3853	+	17.3459i	1.71322	+	0.556658i	0.722353	+	0.691524i	$0.243061\pi$
$972$	18.7627	+	0.436236i	0.601815	+	0.0139923i
$973$	−28.4306	+	20.6561i	−0.911444	+	0.662203i
$974$	−2.36294	−	4.77390i	−0.0757134	−	0.152965i
$975$	−1.93774	−	5.96374i	−0.0620572	−	0.190993i
$976$	26.4691	+	40.2400i	0.847256	+	1.28805i
$977$	37.3247	+	27.1180i	1.19412	+	0.867581i	0.993694	−	0.112128i	$-0.0357666\pi$
$977$	37.3247	+	27.1180i	1.19412	+	0.867581i	0.200428	+	0.979708i	$0.435767\pi$
$978$	10.7157	+	1.82511i	0.342649	+	0.0583604i
$979$	44.0658	+	1.39656i	1.40835	+	0.0446343i
$980$	4.37752	+	1.53572i	0.139835	+	0.0490569i
$981$	−0.224911	+	0.309564i	−0.00718086	+	0.00988361i
$982$	25.3121	−	48.2822i	0.807743	−	1.54075i
$983$	−17.4194	+	5.65990i	−0.555592	+	0.180523i	−0.573337	−	0.819320i	$-0.694351\pi$
$983$	−17.4194	+	5.65990i	−0.555592	+	0.180523i	0.0177449	+	0.999843i	$0.494351\pi$
$984$	7.60260	−	0.933773i	0.242362	−	0.0297676i
$985$	−3.36749	−	4.63496i	−0.107297	−	0.147682i
$986$	−5.88873	−	40.1985i	−0.187535	−	1.28018i
$987$	−5.03508	+	15.4964i	−0.160268	+	0.493255i
$988$	−20.4728	+	14.1592i	−0.651327	+	0.450464i
$989$			34.7853i			1.10611i
$990$	−2.96038	−	3.22856i	−0.0940872	−	0.102611i
$991$			15.4087i			0.489473i	0.969590	+	0.244737i	$0.0787015\pi$
$991$			15.4087i			0.489473i	−0.969590	+	0.244737i	$0.921298\pi$
$992$	−6.45169	+	0.640583i	−0.204841	+	0.0203385i
$993$	−12.7159	+	39.1354i	−0.403526	+	1.24192i
$994$	2.86743	−	0.420053i	0.0909492	−	0.0133233i
$995$	−5.58320	−	7.68462i	−0.176999	−	0.243619i
$996$	−1.11213	−	3.71443i	−0.0352392	−	0.117696i
$997$	−33.2801	+	10.8134i	−1.05399	+	0.342463i	−0.784234	−	0.620465i	$-0.786944\pi$
$997$	−33.2801	+	10.8134i	−1.05399	+	0.342463i	−0.269759	+	0.962928i	$0.586944\pi$
$998$	11.1371	+	5.83868i	0.352539	+	0.184820i
$999$	24.7792	−	34.1056i	0.783979	−	1.07905i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.r.c.51.8	yes	32
4.3	odd	2	inner	220.2.r.c.51.1	✓	32
11.8	odd	10	inner	220.2.r.c.151.1	yes	32
44.19	even	10	inner	220.2.r.c.151.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.r.c.51.1	✓	32	4.3	odd	2	inner
220.2.r.c.51.8	yes	32	1.1	even	1	trivial
220.2.r.c.151.1	yes	32	11.8	odd	10	inner
220.2.r.c.151.8	yes	32	44.19	even	10	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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.988310 + 1.01156i) q^{2} +(1.88633 + 0.612906i) q^{3} +(-0.0464877 + 1.99946i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.24429 + 2.51387i) q^{6} +(-0.668539 - 2.05755i) q^{7} +(-2.06851 + 1.92906i) q^{8} +(0.755537 + 0.548930i) q^{9} +(1.39414 + 0.237451i) q^{10} +(-3.31496 - 0.105060i) q^{11} +(-1.31317 + 3.74315i) q^{12} +(1.85832 - 2.55775i) q^{13} +(1.42060 - 2.70976i) q^{14} +(1.88633 - 0.612906i) q^{15} +(-3.99568 - 0.185901i) q^{16} +(-2.62058 - 3.60691i) q^{17} +(0.191432 + 1.30678i) q^{18} +(-1.21650 + 3.74402i) q^{19} +(1.13764 + 1.64492i) q^{20} -4.29097i q^{21} +(-3.16993 - 3.45710i) q^{22} +8.67477i q^{23} +(-5.08422 + 2.37104i) q^{24} +(0.309017 - 0.951057i) q^{25} +(4.42390 - 0.648063i) q^{26} +(-2.40870 - 3.31529i) q^{27} +(4.14507 - 1.24107i) q^{28} +(6.12821 - 1.99118i) q^{29} +(2.48427 + 1.30239i) q^{30} +(0.673670 - 0.927228i) q^{31} +(-3.76092 - 4.22558i) q^{32} +(-6.18872 - 2.22994i) q^{33} +(1.05865 - 6.21560i) q^{34} +(-1.75026 - 1.27164i) q^{35} +(-1.13269 + 1.48515i) q^{36} +(3.17897 + 9.78387i) q^{37} +(-4.98956 + 2.46969i) q^{38} +(5.07306 - 3.68579i) q^{39} +(-0.539585 + 2.77648i) q^{40} +(-1.29856 - 0.421929i) q^{41} +(4.34055 - 4.24081i) q^{42} +4.00994 q^{43} +(0.364168 - 6.62325i) q^{44} +0.933895 q^{45} +(-8.77500 + 8.57336i) q^{46} +(-3.61139 - 1.17341i) q^{47} +(-7.42323 - 2.79964i) q^{48} +(1.87655 - 1.36339i) q^{49} +(1.26745 - 0.627351i) q^{50} +(-2.73257 - 8.40999i) q^{51} +(5.02774 + 3.83453i) q^{52} +(6.21075 + 4.51237i) q^{53} +(0.973058 - 5.71306i) q^{54} +(-2.74361 + 1.86349i) q^{55} +(5.35202 + 2.96641i) q^{56} +(-4.58946 + 6.31685i) q^{57} +(8.07075 + 4.23112i) q^{58} +(-0.112673 + 0.0366097i) q^{59} +(1.13779 + 3.80013i) q^{60} +(-7.07767 - 9.74158i) q^{61} +(1.60374 - 0.234933i) q^{62} +(0.624345 - 1.92153i) q^{63} +(0.557451 - 7.98055i) q^{64} -3.16156i q^{65} +(-3.86067 - 8.46410i) q^{66} -6.69412i q^{67} +(7.33370 - 5.07206i) q^{68} +(-5.31681 + 16.3635i) q^{69} +(-0.443466 - 3.02725i) q^{70} +(0.556753 + 0.766305i) q^{71} +(-2.62175 + 0.322011i) q^{72} +(1.45249 - 0.471942i) q^{73} +(-6.75512 + 12.8852i) q^{74} +(1.16582 - 1.60461i) q^{75} +(-7.42946 - 2.60640i) q^{76} +(2.00001 + 6.89093i) q^{77} +(8.74214 + 1.48897i) q^{78} +(3.49460 + 2.53897i) q^{79} +(-3.34184 + 2.19820i) q^{80} +(-3.37741 - 10.3946i) q^{81} +(-0.856579 - 1.73057i) q^{82} +(-0.790772 + 0.574530i) q^{83} +(8.57962 + 0.199477i) q^{84} +(-4.24018 - 1.37772i) q^{85} +(3.96306 + 4.05627i) q^{86} +12.7802 q^{87} +(7.05969 - 6.17744i) q^{88} -13.2930 q^{89} +(0.922977 + 0.944686i) q^{90} +(-6.50506 - 2.11362i) q^{91} +(-17.3448 - 0.403270i) q^{92} +(1.83907 - 1.33616i) q^{93} +(-2.38220 - 4.81282i) q^{94} +(1.21650 + 3.74402i) q^{95} +(-4.50445 - 10.2759i) q^{96} +(11.7313 + 8.52327i) q^{97} +(3.23376 + 0.550779i) q^{98} +(-2.44690 - 1.89906i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{2} - 2 q^{4} + 8 q^{5} - 15 q^{6} - 10 q^{8} + 10 q^{9} + 6 q^{12} - 10 q^{13} + 21 q^{14} - 34 q^{16} + 10 q^{17} - 25 q^{18} + 2 q^{20} - 36 q^{22} - 15 q^{24} - 8 q^{25} + 12 q^{26} + 30 q^{28}+ \cdots + 94 q^{97}+O(q^{100}) \) 32 * q - 10 * q^2 - 2 * q^4 + 8 * q^5 - 15 * q^6 - 10 * q^8 + 10 * q^9 + 6 * q^12 - 10 * q^13 + 21 * q^14 - 34 * q^16 + 10 * q^17 - 25 * q^18 + 2 * q^20 - 36 * q^22 - 15 * q^24 - 8 * q^25 + 12 * q^26 + 30 * q^28 - 10 * q^29 + 10 * q^30 + 36 * q^33 + 18 * q^34 + 15 * q^36 - 44 * q^37 + 29 * q^38 - 10 * q^40 - 30 * q^41 + 18 * q^42 + 9 * q^44 + 60 * q^45 - 10 * q^46 + 38 * q^48 + 12 * q^49 + 10 * q^50 + 10 * q^52 - 14 * q^53 - 34 * q^56 - 60 * q^57 + 10 * q^58 - 11 * q^60 + 20 * q^61 + 40 * q^62 - 74 * q^64 - 118 * q^66 - 20 * q^68 - 22 * q^69 - 21 * q^70 + 70 * q^72 + 10 * q^73 + 20 * q^74 + 44 * q^77 - 92 * q^78 - 46 * q^80 - 58 * q^81 + 37 * q^82 + 100 * q^84 - 10 * q^85 + 57 * q^86 + 19 * q^88 - 72 * q^89 + 10 * q^90 - 63 * q^92 - 26 * q^93 - 25 * q^94 + 94 * q^97

Introduction

L-functions

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