LMFDB - Embedded newform 950.2.h.e.191.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(191,950)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("950.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.11
Character	$\chi$	$=$	950.191
Dual form			950.2.h.e.761.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.971450 + 2.98981i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.62433 + 1.53673i) q^{5} +(-0.971450 + 2.98981i) q^{6} -0.243654 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-5.56823 + 4.04555i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.971450 + 2.98981i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.62433 + 1.53673i) q^{5} +(-0.971450 + 2.98981i) q^{6} -0.243654 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-5.56823 + 4.04555i) q^{9} +(0.410843 + 2.19800i) q^{10} +(0.852506 + 0.619382i) q^{11} +(-2.54329 + 1.84781i) q^{12} +(2.44365 - 1.77542i) q^{13} +(-0.197121 - 0.143216i) q^{14} +(-3.01659 + 6.34931i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.69866 - 5.22794i) q^{17} -6.88271 q^{18} +(0.309017 - 0.951057i) q^{19} +(-0.959574 + 2.01971i) q^{20} +(-0.236698 - 0.728481i) q^{21} +(0.325628 + 1.00218i) q^{22} +(-1.77546 - 1.28995i) q^{23} -3.14368 q^{24} +(0.276905 + 4.99233i) q^{25} +3.02052 q^{26} +(-9.87484 - 7.17449i) q^{27} +(-0.0752933 - 0.231729i) q^{28} +(1.31277 + 4.04029i) q^{29} +(-6.17250 + 3.36359i) q^{30} +(2.98101 - 9.17462i) q^{31} -1.00000 q^{32} +(-1.02367 + 3.15053i) q^{33} +(4.44715 - 3.23104i) q^{34} +(-0.395775 - 0.374432i) q^{35} +(-5.56823 - 4.04555i) q^{36} +(-2.19186 + 1.59248i) q^{37} +(0.809017 - 0.587785i) q^{38} +(7.68205 + 5.58133i) q^{39} +(-1.96347 + 1.06995i) q^{40} +(-1.72948 + 1.25654i) q^{41} +(0.236698 - 0.728481i) q^{42} +9.43799 q^{43} +(-0.325628 + 1.00218i) q^{44} +(-15.2616 - 1.98556i) q^{45} +(-0.678166 - 2.08718i) q^{46} +(-2.09794 - 6.45680i) q^{47} +(-2.54329 - 1.84781i) q^{48} -6.94063 q^{49} +(-2.71039 + 4.20164i) q^{50} +17.2807 q^{51} +(2.44365 + 1.77542i) q^{52} +(-0.392803 - 1.20892i) q^{53} +(-3.77185 - 11.6086i) q^{54} +(0.432928 + 2.31615i) q^{55} +(0.0752933 - 0.231729i) q^{56} +3.14368 q^{57} +(-1.31277 + 4.04029i) q^{58} +(10.3288 - 7.50428i) q^{59} +(-6.97073 - 0.906903i) q^{60} +(4.02012 + 2.92079i) q^{61} +(7.80440 - 5.67023i) q^{62} +(1.35672 - 0.985717i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(6.69764 + 0.871374i) q^{65} +(-2.68000 + 1.94714i) q^{66} +(-2.88176 + 8.86914i) q^{67} +5.49698 q^{68} +(2.13193 - 6.56142i) q^{69} +(-0.100104 - 0.535553i) q^{70} +(-0.524310 - 1.61366i) q^{71} +(-2.12687 - 6.54584i) q^{72} +(-9.34657 - 6.79068i) q^{73} -2.70929 q^{74} +(-14.6571 + 5.67769i) q^{75} +1.00000 q^{76} +(-0.207717 - 0.150915i) q^{77} +(2.93428 + 9.03079i) q^{78} +(-0.197630 - 0.608241i) q^{79} +(-2.21738 - 0.288485i) q^{80} +(5.47687 - 16.8561i) q^{81} -2.13775 q^{82} +(-3.40058 + 10.4659i) q^{83} +(0.619683 - 0.450226i) q^{84} +(10.7931 - 5.88152i) q^{85} +(7.63550 + 5.54751i) q^{86} +(-10.8044 + 7.84988i) q^{87} +(-0.852506 + 0.619382i) q^{88} +(-13.9560 - 10.1396i) q^{89} +(-11.1798 - 10.5769i) q^{90} +(-0.595406 + 0.432588i) q^{91} +(0.678166 - 2.08718i) q^{92} +30.3263 q^{93} +(2.09794 - 6.45680i) q^{94} +(1.96347 - 1.06995i) q^{95} +(-0.971450 - 2.98981i) q^{96} +(-0.862454 - 2.65436i) q^{97} +(-5.61509 - 4.07960i) q^{98} -7.25268 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9}+O(q^{10}) $ 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 5 * q^5 + q^6 + 28 * q^7 + 11 * q^8 - 8 * q^9	$ 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9} + 5 q^{10} - 6 q^{12} - 10 q^{13} + 12 q^{14} - 11 q^{16} - 20 q^{17} - 42 q^{18} - 11 q^{19} + 5 q^{20} - 3 q^{21} - 10 q^{22} - 6 q^{23} - 14 q^{24} - 15 q^{25} - 40 q^{26} + 5 q^{27} - 2 q^{28} + 6 q^{29} - 5 q^{31} - 44 q^{32} - 36 q^{33} - 10 q^{34} - 8 q^{36} - 10 q^{37} + 11 q^{38} + 39 q^{39} - 22 q^{41} + 3 q^{42} + 68 q^{43} + 10 q^{44} + 20 q^{45} + 6 q^{46} + 19 q^{47} - 6 q^{48} + 40 q^{49} - 30 q^{50} + 86 q^{51} - 10 q^{52} + 30 q^{54} + 2 q^{56} + 14 q^{57} - 6 q^{58} - 4 q^{59} + 15 q^{60} + 26 q^{61} - 15 q^{62} - 41 q^{63} - 11 q^{64} + 30 q^{65} - 4 q^{66} - 59 q^{67} + 20 q^{68} - 59 q^{69} - 25 q^{70} + 30 q^{71} + 13 q^{72} - 38 q^{73} - 50 q^{74} - 15 q^{75} + 44 q^{76} + 29 q^{77} + 16 q^{78} + 3 q^{79} + 5 q^{80} - 54 q^{81} - 8 q^{82} + 9 q^{83} + 7 q^{84} + 12 q^{86} - 43 q^{87} + 33 q^{89} - 6 q^{91} - 6 q^{92} + 84 q^{93} - 19 q^{94} + q^{96} + 30 q^{97} - 15 q^{98} - 54 q^{99}+O(q^{100}) $ 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 5 * q^5 + q^6 + 28 * q^7 + 11 * q^8 - 8 * q^9 + 5 * q^10 - 6 * q^12 - 10 * q^13 + 12 * q^14 - 11 * q^16 - 20 * q^17 - 42 * q^18 - 11 * q^19 + 5 * q^20 - 3 * q^21 - 10 * q^22 - 6 * q^23 - 14 * q^24 - 15 * q^25 - 40 * q^26 + 5 * q^27 - 2 * q^28 + 6 * q^29 - 5 * q^31 - 44 * q^32 - 36 * q^33 - 10 * q^34 - 8 * q^36 - 10 * q^37 + 11 * q^38 + 39 * q^39 - 22 * q^41 + 3 * q^42 + 68 * q^43 + 10 * q^44 + 20 * q^45 + 6 * q^46 + 19 * q^47 - 6 * q^48 + 40 * q^49 - 30 * q^50 + 86 * q^51 - 10 * q^52 + 30 * q^54 + 2 * q^56 + 14 * q^57 - 6 * q^58 - 4 * q^59 + 15 * q^60 + 26 * q^61 - 15 * q^62 - 41 * q^63 - 11 * q^64 + 30 * q^65 - 4 * q^66 - 59 * q^67 + 20 * q^68 - 59 * q^69 - 25 * q^70 + 30 * q^71 + 13 * q^72 - 38 * q^73 - 50 * q^74 - 15 * q^75 + 44 * q^76 + 29 * q^77 + 16 * q^78 + 3 * q^79 + 5 * q^80 - 54 * q^81 - 8 * q^82 + 9 * q^83 + 7 * q^84 + 12 * q^86 - 43 * q^87 + 33 * q^89 - 6 * q^91 - 6 * q^92 + 84 * q^93 - 19 * q^94 + q^96 + 30 * q^97 - 15 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	0.971450	+	2.98981i	0.560867	+	1.72617i	0.679924	+	0.733283i	$0.262013\pi$
$3$	0.971450	+	2.98981i	0.560867	+	1.72617i	−0.119057	+	0.992887i	$0.537987\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	1.62433	+	1.53673i	0.726423	+	0.687248i
$5$	1.62433	+	1.53673i	0.726423	+	0.687248i
$6$	−0.971450	+	2.98981i	−0.396593	+	1.22059i
$7$	−0.243654			−0.0920927			−0.0460463	−	0.998939i	$-0.514662\pi$
$7$	−0.243654			−0.0920927			−0.0460463	+	0.998939i	$0.514662\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−5.56823	+	4.04555i	−1.85608	+	1.34852i
$10$	0.410843	+	2.19800i	0.129920	+	0.695069i
$11$	0.852506	+	0.619382i	0.257040	+	0.186751i	0.708841	−	0.705368i	$-0.249218\pi$
$11$	0.852506	+	0.619382i	0.257040	+	0.186751i	−0.451801	+	0.892119i	$0.649218\pi$
$12$	−2.54329	+	1.84781i	−0.734184	+	0.533416i
$13$	2.44365	−	1.77542i	0.677747	−	0.492412i	−0.194863	−	0.980831i	$-0.562426\pi$
$13$	2.44365	−	1.77542i	0.677747	−	0.492412i	0.872609	+	0.488419i	$0.162426\pi$
$14$	−0.197121	−	0.143216i	−0.0526827	−	0.0382762i
$15$	−3.01659	+	6.34931i	−0.778880	+	1.63938i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	1.69866	−	5.22794i	0.411985	−	1.26796i	−0.502934	−	0.864325i	$-0.667746\pi$
$17$	1.69866	−	5.22794i	0.411985	−	1.26796i	0.914920	−	0.403636i	$-0.132254\pi$
$18$	−6.88271			−1.62227
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$20$	−0.959574	+	2.01971i	−0.214567	+	0.451620i
$21$	−0.236698	−	0.728481i	−0.0516517	−	0.158968i
$22$	0.325628	+	1.00218i	0.0694242	+	0.213666i
$23$	−1.77546	−	1.28995i	−0.370209	−	0.268973i	0.387088	−	0.922043i	$-0.373481\pi$
$23$	−1.77546	−	1.28995i	−0.370209	−	0.268973i	−0.757298	+	0.653070i	$0.773481\pi$
$24$	−3.14368			−0.641700
$25$	0.276905	+	4.99233i	0.0553810	+	0.998465i
$26$	3.02052			0.592372
$27$	−9.87484	−	7.17449i	−1.90041	−	1.38073i
$28$	−0.0752933	−	0.231729i	−0.0142291	−	0.0437927i
$29$	1.31277	+	4.04029i	0.243775	+	0.750263i	0.995835	+	0.0911688i	$0.0290603\pi$
$29$	1.31277	+	4.04029i	0.243775	+	0.750263i	−0.752060	+	0.659095i	$0.770940\pi$
$30$	−6.17250	+	3.36359i	−1.12694	+	0.614105i
$31$	2.98101	−	9.17462i	0.535406	−	1.64781i	−0.207364	−	0.978264i	$-0.566488\pi$
$31$	2.98101	−	9.17462i	0.535406	−	1.64781i	0.742770	−	0.669547i	$-0.233512\pi$
$32$	−1.00000			−0.176777
$33$	−1.02367	+	3.15053i	−0.178198	+	0.548437i
$34$	4.44715	−	3.23104i	0.762680	−	0.554119i
$35$	−0.395775	−	0.374432i	−0.0668983	−	0.0632905i
$36$	−5.56823	−	4.04555i	−0.928038	−	0.674259i
$37$	−2.19186	+	1.59248i	−0.360340	+	0.261802i	−0.753194	−	0.657798i	$-0.771488\pi$
$37$	−2.19186	+	1.59248i	−0.360340	+	0.261802i	0.392854	+	0.919601i	$0.371488\pi$
$38$	0.809017	−	0.587785i	0.131240	−	0.0953514i
$39$	7.68205	+	5.58133i	1.23011	+	0.893729i
$40$	−1.96347	+	1.06995i	−0.310451	+	0.169175i
$41$	−1.72948	+	1.25654i	−0.270099	+	0.196239i	−0.714587	−	0.699546i	$-0.753386\pi$
$41$	−1.72948	+	1.25654i	−0.270099	+	0.196239i	0.444488	+	0.895785i	$0.353386\pi$
$42$	0.236698	−	0.728481i	0.0365233	−	0.112407i
$43$	9.43799			1.43928			0.719640	−	0.694347i	$-0.244307\pi$
$43$	9.43799			1.43928			0.719640	+	0.694347i	$0.244307\pi$
$44$	−0.325628	+	1.00218i	−0.0490903	+	0.151084i
$45$	−15.2616	−	1.98556i	−2.27506	−	0.295989i
$46$	−0.678166	−	2.08718i	−0.0999901	−	0.307738i
$47$	−2.09794	−	6.45680i	−0.306016	−	0.941821i	−0.979296	−	0.202433i	$-0.935115\pi$
$47$	−2.09794	−	6.45680i	−0.306016	−	0.941821i	0.673280	−	0.739388i	$-0.264885\pi$
$48$	−2.54329	−	1.84781i	−0.367092	−	0.266708i
$49$	−6.94063			−0.991519
$50$	−2.71039	+	4.20164i	−0.383308	+	0.594201i
$51$	17.2807			2.41978
$52$	2.44365	+	1.77542i	0.338873	+	0.246206i
$53$	−0.392803	−	1.20892i	−0.0539556	−	0.166058i	0.920447	−	0.390866i	$-0.127824\pi$
$53$	−0.392803	−	1.20892i	−0.0539556	−	0.166058i	−0.974403	+	0.224808i	$0.927824\pi$
$54$	−3.77185	−	11.6086i	−0.513284	−	1.57973i
$55$	0.432928	+	2.31615i	0.0583760	+	0.312310i
$56$	0.0752933	−	0.231729i	0.0100615	−	0.0309661i
$57$	3.14368			0.416390
$58$	−1.31277	+	4.04029i	−0.172375	+	0.530516i
$59$	10.3288	−	7.50428i	1.34469	−	0.976974i	0.345431	−	0.938444i	$-0.387733\pi$
$59$	10.3288	−	7.50428i	1.34469	−	0.976974i	0.999257	−	0.0385297i	$-0.0122674\pi$
$60$	−6.97073	−	0.906903i	−0.899917	−	0.117081i
$61$	4.02012	+	2.92079i	0.514724	+	0.373969i	0.814613	−	0.580005i	$-0.196950\pi$
$61$	4.02012	+	2.92079i	0.514724	+	0.373969i	−0.299889	+	0.953974i	$0.596950\pi$
$62$	7.80440	−	5.67023i	0.991160	−	0.720120i
$63$	1.35672	−	0.985717i	0.170931	−	0.124189i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	6.69764	+	0.871374i	0.830740	+	0.108081i
$66$	−2.68000	+	1.94714i	−0.329885	+	0.239676i
$67$	−2.88176	+	8.86914i	−0.352063	+	1.08354i	0.605630	+	0.795746i	$0.292921\pi$
$67$	−2.88176	+	8.86914i	−0.352063	+	1.08354i	−0.957693	+	0.287792i	$0.907079\pi$
$68$	5.49698			0.666606
$69$	2.13193	−	6.56142i	0.256655	−	0.789902i
$70$	−0.100104	−	0.535553i	−0.0119647	−	0.0640108i
$71$	−0.524310	−	1.61366i	−0.0622242	−	0.191506i	0.915112	−	0.403200i	$-0.132102\pi$
$71$	−0.524310	−	1.61366i	−0.0622242	−	0.191506i	−0.977336	+	0.211694i	$0.932102\pi$
$72$	−2.12687	−	6.54584i	−0.250654	−	0.771435i
$73$	−9.34657	−	6.79068i	−1.09393	−	0.794789i	−0.113875	−	0.993495i	$-0.536326\pi$
$73$	−9.34657	−	6.79068i	−1.09393	−	0.794789i	−0.980059	+	0.198706i	$0.936326\pi$
$74$	−2.70929			−0.314949
$75$	−14.6571	+	5.67769i	−1.69246	+	0.655603i
$76$	1.00000			0.114708
$77$	−0.207717	−	0.150915i	−0.0236715	−	0.0171984i
$78$	2.93428	+	9.03079i	0.332242	+	1.02254i
$79$	−0.197630	−	0.608241i	−0.0222351	−	0.0684325i	0.939323	−	0.343033i	$-0.111454\pi$
$79$	−0.197630	−	0.608241i	−0.0222351	−	0.0684325i	−0.961558	+	0.274601i	$0.911454\pi$
$80$	−2.21738	−	0.288485i	−0.247911	−	0.0322536i
$81$	5.47687	−	16.8561i	0.608541	−	1.87290i
$82$	−2.13775			−0.236075
$83$	−3.40058	+	10.4659i	−0.373262	+	1.14878i	0.571382	+	0.820684i	$0.306408\pi$
$83$	−3.40058	+	10.4659i	−0.373262	+	1.14878i	−0.944644	+	0.328098i	$0.893592\pi$
$84$	0.619683	−	0.450226i	0.0676130	−	0.0491237i
$85$	10.7931	−	5.88152i	1.17068	−	0.637940i
$86$	7.63550	+	5.54751i	0.823357	+	0.598204i
$87$	−10.8044	+	7.84988i	−1.15836	+	0.841595i
$88$	−0.852506	+	0.619382i	−0.0908774	+	0.0660263i
$89$	−13.9560	−	10.1396i	−1.47933	−	1.07480i	−0.977771	−	0.209676i	$-0.932759\pi$
$89$	−13.9560	−	10.1396i	−1.47933	−	1.07480i	−0.501562	−	0.865122i	$-0.667241\pi$
$90$	−11.1798	−	10.5769i	−1.17845	−	1.11490i
$91$	−0.595406	+	0.432588i	−0.0624155	+	0.0453475i
$92$	0.678166	−	2.08718i	0.0707037	−	0.217604i
$93$	30.3263			3.14469
$94$	2.09794	−	6.45680i	0.216386	−	0.665968i
$95$	1.96347	−	1.06995i	0.201447	−	0.109775i
$96$	−0.971450	−	2.98981i	−0.0991482	−	0.305147i
$97$	−0.862454	−	2.65436i	−0.0875689	−	0.269509i	0.897677	−	0.440654i	$-0.145253\pi$
$97$	−0.862454	−	2.65436i	−0.0875689	−	0.269509i	−0.985246	+	0.171145i	$0.945253\pi$
$98$	−5.61509	−	4.07960i	−0.567210	−	0.412102i
$99$	−7.25268			−0.728922
$100$	−4.66242	+	1.80607i	−0.466242	+	0.180607i
$101$	−6.90383			−0.686957			−0.343478	−	0.939161i	$-0.611605\pi$
$101$	−6.90383			−0.686957			−0.343478	+	0.939161i	$0.611605\pi$
$102$	13.9804	+	10.1574i	1.38427	+	1.00573i
$103$	5.09396	+	15.6776i	0.501923	+	1.54476i	0.805883	+	0.592075i	$0.201691\pi$
$103$	5.09396	+	15.6776i	0.501923	+	1.54476i	−0.303960	+	0.952685i	$0.598309\pi$
$104$	0.933391	+	2.87268i	0.0915266	+	0.281690i
$105$	0.735005	−	1.54704i	0.0717292	−	0.150975i
$106$	0.392803	−	1.20892i	0.0381524	−	0.117421i
$107$	2.16069			0.208882			0.104441	−	0.994531i	$-0.466695\pi$
$107$	2.16069			0.208882			0.104441	+	0.994531i	$0.466695\pi$
$108$	3.77185	−	11.6086i	0.362947	−	1.11703i
$109$	−8.66717	+	6.29707i	−0.830164	+	0.603150i	−0.919606	−	0.392842i	$-0.871492\pi$
$109$	−8.66717	+	6.29707i	−0.830164	+	0.603150i	0.0894416	+	0.995992i	$0.471492\pi$
$110$	−1.01116	+	2.12828i	−0.0964099	+	0.202923i
$111$	−6.89051	−	5.00625i	−0.654018	−	0.475172i
$112$	0.197121	−	0.143216i	0.0186261	−	0.0135327i
$113$	−8.18513	+	5.94684i	−0.769992	+	0.559432i	−0.901959	−	0.431822i	$-0.857871\pi$
$113$	−8.18513	+	5.94684i	−0.769992	+	0.559432i	0.131967	+	0.991254i	$0.457871\pi$
$114$	2.54329	+	1.84781i	0.238201	+	0.173063i
$115$	−0.901632	−	4.82371i	−0.0840776	−	0.449814i
$116$	−3.43688	+	2.49704i	−0.319106	+	0.231844i
$117$	−6.42426	+	19.7718i	−0.593923	+	1.82791i
$118$	12.7670			1.17530
$119$	−0.413886	+	1.27381i	−0.0379408	+	0.116770i
$120$	−5.10637	−	4.83099i	−0.466146	−	0.441007i
$121$	−3.05605	−	9.40557i	−0.277823	−	0.855052i
$122$	1.53555	+	4.72594i	0.139022	+	0.427866i
$123$	−5.43692	−	3.95016i	−0.490231	−	0.356173i
$124$	9.64677			0.866305
$125$	−7.22209	+	8.53472i	−0.645963	+	0.763369i
$126$	1.67700			0.149399
$127$	5.05905	+	3.67562i	0.448918	+	0.326158i	0.789169	−	0.614177i	$-0.210512\pi$
$127$	5.05905	+	3.67562i	0.448918	+	0.326158i	−0.340250	+	0.940335i	$0.610512\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	9.16854	+	28.2178i	0.807245	+	2.48444i
$130$	4.90632	+	4.64173i	0.430313	+	0.407107i
$131$	2.51033	−	7.72599i	0.219328	−	0.675023i	−0.779490	−	0.626415i	$-0.784522\pi$
$131$	2.51033	−	7.72599i	0.219328	−	0.675023i	0.998818	−	0.0486079i	$-0.0154785\pi$
$132$	−3.31266			−0.288330
$133$	−0.0752933	+	0.231729i	−0.00652876	+	0.0200935i
$134$	−7.54454	+	5.48143i	−0.651749	+	0.473523i
$135$	−5.01474	−	26.8287i	−0.431600	−	2.30905i
$136$	4.44715	+	3.23104i	0.381340	+	0.277060i
$137$	−12.8439	+	9.33163i	−1.09733	+	0.797255i	−0.980621	−	0.195912i	$-0.937233\pi$
$137$	−12.8439	+	9.33163i	−1.09733	+	0.797255i	−0.116705	+	0.993167i	$0.537233\pi$
$138$	5.58148	−	4.05518i	0.475127	−	0.345200i
$139$	10.2040	+	7.41365i	0.865493	+	0.628818i	0.929374	−	0.369140i	$-0.120348\pi$
$139$	10.2040	+	7.41365i	0.865493	+	0.628818i	−0.0638805	+	0.997958i	$0.520348\pi$
$140$	0.233804	−	0.492111i	0.0197601	−	0.0415909i
$141$	17.2666	−	12.5449i	1.45411	−	1.05647i
$142$	0.524310	−	1.61366i	0.0439992	−	0.135415i
$143$	3.18289			0.266166
$144$	2.12687	−	6.54584i	0.177239	−	0.545487i
$145$	−4.07647	+	8.58015i	−0.338533	+	0.712543i
$146$	−3.57007	−	10.9876i	−0.295461	−	0.909337i
$147$	−6.74247	−	20.7512i	−0.556110	−	1.71153i
$148$	−2.19186	−	1.59248i	−0.180170	−	0.130901i
$149$	11.4463			0.937715			0.468857	−	0.883274i	$-0.344666\pi$
$149$	11.4463			0.937715			0.468857	+	0.883274i	$0.344666\pi$
$150$	−15.1951	−	4.02190i	−1.24068	−	0.328387i
$151$	10.1422			0.825363			0.412681	−	0.910875i	$-0.364592\pi$
$151$	10.1422			0.825363			0.412681	+	0.910875i	$0.364592\pi$
$152$	0.809017	+	0.587785i	0.0656199	+	0.0476757i
$153$	11.6914	+	35.9823i	0.945191	+	2.90900i
$154$	−0.0793407	−	0.244186i	−0.00639346	−	0.0196770i
$155$	18.9411	−	10.3216i	1.52139	−	0.829051i
$156$	−2.93428	+	9.03079i	−0.234931	+	0.723042i
$157$	13.4461			1.07312			0.536558	−	0.843863i	$-0.319724\pi$
$157$	13.4461			1.07312			0.536558	+	0.843863i	$0.319724\pi$
$158$	0.197630	−	0.608241i	0.0157226	−	0.0483891i
$159$	3.23286	−	2.34881i	0.256383	−	0.186273i
$160$	−1.62433	−	1.53673i	−0.128415	−	0.121489i
$161$	0.432599	+	0.314301i	0.0340936	+	0.0247704i
$162$	14.3386	−	10.4176i	1.12655	−	0.818486i
$163$	2.41677	−	1.75589i	0.189296	−	0.137532i	−0.489101	−	0.872227i	$-0.662675\pi$
$163$	2.41677	−	1.75589i	0.189296	−	0.137532i	0.678397	+	0.734696i	$0.262675\pi$
$164$	−1.72948	−	1.25654i	−0.135050	−	0.0981193i
$165$	−6.50430	+	3.54440i	−0.506359	+	0.275931i
$166$	−8.90283	+	6.46828i	−0.690994	+	0.502036i
$167$	−0.563386	+	1.73392i	−0.0435961	+	0.134175i	−0.970485	−	0.241160i	$-0.922472\pi$
$167$	−0.563386	+	1.73392i	−0.0435961	+	0.134175i	0.926889	+	0.375335i	$0.122472\pi$
$168$	0.765971			0.0590959
$169$	−1.19790	+	3.68674i	−0.0921458	+	0.283596i
$170$	12.1889	+	1.58579i	0.934845	+	0.121625i
$171$	2.12687	+	6.54584i	0.162646	+	0.500573i
$172$	2.91650	+	8.97607i	0.222381	+	0.684419i
$173$	0.643934	+	0.467846i	0.0489574	+	0.0355697i	0.611995	−	0.790862i	$-0.290367\pi$
$173$	0.643934	+	0.467846i	0.0489574	+	0.0355697i	−0.563037	+	0.826431i	$0.690367\pi$
$174$	−13.3550			−1.01244
$175$	−0.0674691	−	1.21640i	−0.00510019	−	0.0919514i
$176$	−1.05375			−0.0794298
$177$	32.4703	+	23.5910i	2.44061	+	1.77321i
$178$	−5.33072	−	16.4063i	−0.399554	−	1.22970i
$179$	−4.72455	−	14.5407i	−0.353129	−	1.08682i	−0.957086	−	0.289803i	$-0.906410\pi$
$179$	−4.72455	−	14.5407i	−0.353129	−	1.08682i	0.603957	−	0.797017i	$-0.293590\pi$
$180$	−2.82771	−	15.1282i	−0.210765	−	1.12759i
$181$	5.30995	−	16.3424i	0.394686	−	1.21472i	−0.534520	−	0.845156i	$-0.679508\pi$
$181$	5.30995	−	16.3424i	0.394686	−	1.21472i	0.929206	−	0.369562i	$-0.120492\pi$
$182$	−0.735962			−0.0545532
$183$	−4.82727	+	14.8568i	−0.356842	+	1.09825i
$184$	1.77546	−	1.28995i	0.130889	−	0.0950962i
$185$	−6.00753	−	0.781590i	−0.441683	−	0.0574636i
$186$	24.5345	+	17.8254i	1.79896	+	1.30702i
$187$	4.68620	−	3.40473i	0.342689	−	0.248978i
$188$	5.49248	−	3.99052i	0.400581	−	0.291039i
$189$	2.40605	+	1.74810i	0.175014	+	0.127155i
$190$	2.21738	+	0.288485i	0.160866	+	0.0209289i
$191$	10.2940	−	7.47903i	0.744848	−	0.541164i	−0.149378	−	0.988780i	$-0.547727\pi$
$191$	10.2940	−	7.47903i	0.744848	−	0.541164i	0.894226	+	0.447616i	$0.147727\pi$
$192$	0.971450	−	2.98981i	0.0701083	−	0.215771i
$193$	−15.7116			−1.13095			−0.565474	−	0.824766i	$-0.691307\pi$
$193$	−15.7116			−1.13095			−0.565474	+	0.824766i	$0.691307\pi$
$194$	0.862454	−	2.65436i	0.0619206	−	0.190572i
$195$	3.90117	+	20.8712i	0.279369	+	1.49462i
$196$	−2.14477	−	6.60093i	−0.153198	−	0.471495i
$197$	3.15087	+	9.69739i	0.224490	+	0.690911i	0.998343	+	0.0575447i	$0.0183272\pi$
$197$	3.15087	+	9.69739i	0.224490	+	0.690911i	−0.773852	+	0.633366i	$0.781673\pi$
$198$	−5.86754	−	4.26302i	−0.416988	−	0.302960i
$199$	−3.25676			−0.230865			−0.115433	−	0.993315i	$-0.536825\pi$
$199$	−3.25676			−0.230865			−0.115433	+	0.993315i	$0.536825\pi$
$200$	−4.83355	−	1.27936i	−0.341784	−	0.0904645i
$201$	−29.3166			−2.06783
$202$	−5.58532	−	4.05797i	−0.392981	−	0.285518i
$203$	−0.319862	−	0.984435i	−0.0224499	−	0.0690938i
$204$	5.34004	+	16.4349i	0.373877	+	1.15068i
$205$	−4.74021	−	0.616709i	−0.331071	−	0.0430728i
$206$	−5.09396	+	15.6776i	−0.354913	+	1.09231i
$207$	15.1047			1.04985
$208$	−0.933391	+	2.87268i	−0.0647190	+	0.199185i
$209$	0.852506	−	0.619382i	0.0589690	−	0.0428435i
$210$	1.50396	−	0.819554i	0.103783	−	0.0565546i
$211$	5.72515	+	4.15956i	0.394135	+	0.286356i	0.767148	−	0.641470i	$-0.221675\pi$
$211$	5.72515	+	4.15956i	0.394135	+	0.286356i	−0.373013	+	0.927826i	$0.621675\pi$
$212$	1.02837	−	0.747155i	0.0706288	−	0.0513148i
$213$	4.31521	−	3.13518i	0.295673	−	0.214819i
$214$	1.74803	+	1.27002i	0.119493	+	0.0868168i
$215$	15.3304	+	14.5037i	1.04553	+	0.989142i
$216$	9.87484	−	7.17449i	0.671898	−	0.488162i
$217$	−0.726337	+	2.23544i	−0.0493070	+	0.151751i
$218$	−10.7132			−0.725590
$219$	11.2232	−	34.5413i	0.758391	−	2.33409i
$220$	−2.06901	+	1.12747i	−0.139493	+	0.0760140i
$221$	−5.13083	−	15.7911i	−0.345137	−	1.06222i
$222$	−2.63194	−	8.10028i	−0.176644	−	0.543655i
$223$	−9.37387	−	6.81052i	−0.627721	−	0.456066i	0.227889	−	0.973687i	$-0.426818\pi$
$223$	−9.37387	−	6.81052i	−0.627721	−	0.456066i	−0.855610	+	0.517621i	$0.826818\pi$
$224$	0.243654			0.0162798
$225$	−21.7386	−	26.6782i	−1.44924	−	1.77854i
$226$	−10.1174			−0.672998
$227$	0.726007	+	0.527475i	0.0481868	+	0.0350097i	0.611618	−	0.791153i	$-0.290519\pi$
$227$	0.726007	+	0.527475i	0.0481868	+	0.0350097i	−0.563431	+	0.826163i	$0.690519\pi$
$228$	0.971450	+	2.98981i	0.0643358	+	0.198005i
$229$	8.63259	+	26.5684i	0.570458	+	1.75569i	0.651150	+	0.758949i	$0.274287\pi$
$229$	8.63259	+	26.5684i	0.570458	+	1.75569i	−0.0806920	+	0.996739i	$0.525713\pi$
$230$	2.10587	−	4.43243i	0.138857	−	0.292266i
$231$	0.249422	−	0.767641i	0.0164107	−	0.0505071i
$232$	−4.24821			−0.278909
$233$	−5.77515	+	17.7741i	−0.378342	+	1.16442i	0.562853	+	0.826557i	$0.309704\pi$
$233$	−5.77515	+	17.7741i	−0.378342	+	1.16442i	−0.941196	+	0.337861i	$0.890296\pi$
$234$	−16.8189	+	12.2197i	−1.09949	+	0.798824i
$235$	6.51463	−	13.7120i	0.424967	−	0.894470i
$236$	10.3288	+	7.50428i	0.672344	+	0.488487i
$237$	1.62654	−	1.18175i	0.105655	−	0.0767630i
$238$	−1.08357	+	0.787258i	−0.0702372	+	0.0510303i
$239$	1.96640	+	1.42867i	0.127196	+	0.0924131i	0.649564	−	0.760307i	$-0.274951\pi$
$239$	1.96640	+	1.42867i	0.127196	+	0.0924131i	−0.522368	+	0.852720i	$0.674951\pi$
$240$	−1.29156	−	6.90980i	−0.0833697	−	0.446026i
$241$	3.60827	−	2.62156i	0.232429	−	0.168869i	−0.465475	−	0.885061i	$-0.654116\pi$
$241$	3.60827	−	2.62156i	0.232429	−	0.168869i	0.697904	+	0.716192i	$0.254116\pi$
$242$	3.05605	−	9.40557i	0.196451	−	0.604613i
$243$	19.0991			1.22521
$244$	−1.53555	+	4.72594i	−0.0983035	+	0.302547i
$245$	−11.2739	−	10.6659i	−0.720262	−	0.681419i
$246$	−2.07672	−	6.39149i	−0.132407	−	0.407506i
$247$	−0.933391	−	2.87268i	−0.0593903	−	0.182784i
$248$	7.80440	+	5.67023i	0.495580	+	0.360060i
$249$	−34.5946			−2.19234
$250$	−10.8594	+	2.65970i	−0.686807	+	0.168214i
$251$	9.00332			0.568284			0.284142	−	0.958782i	$-0.408291\pi$
$251$	9.00332			0.568284			0.284142	+	0.958782i	$0.408291\pi$
$252$	1.35672	+	0.985717i	0.0854655	+	0.0620943i
$253$	−0.714621	−	2.19938i	−0.0449278	−	0.138274i
$254$	1.93239	+	5.94727i	0.121249	+	0.373165i
$255$	28.0696	+	26.5558i	1.75779	+	1.66299i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	17.5066			1.09203			0.546015	−	0.837775i	$-0.316144\pi$
$257$	17.5066			1.09203			0.546015	+	0.837775i	$0.316144\pi$
$258$	−9.16854	+	28.2178i	−0.570808	+	1.75677i
$259$	0.534057	−	0.388015i	0.0331847	−	0.0241101i
$260$	1.24096	+	6.63910i	0.0769610	+	0.411740i
$261$	−23.6550	−	17.1864i	−1.46421	−	1.06381i
$262$	6.57212	−	4.77492i	0.406027	−	0.294996i
$263$	−22.8822	+	16.6249i	−1.41098	+	1.02514i	−0.417799	+	0.908540i	$0.637198\pi$
$263$	−22.8822	+	16.6249i	−1.41098	+	1.02514i	−0.993179	+	0.116596i	$0.962802\pi$
$264$	−2.68000	−	1.94714i	−0.164943	−	0.119838i
$265$	1.21975	−	2.56732i	0.0749285	−	0.157709i
$266$	−0.197121	+	0.143216i	−0.0120862	+	0.00878116i
$267$	16.7580	−	51.5760i	1.02558	−	3.15640i
$268$	−9.32556			−0.569649
$269$	−3.82394	+	11.7689i	−0.233150	+	0.717561i	0.764212	+	0.644966i	$0.223128\pi$
$269$	−3.82394	+	11.7689i	−0.233150	+	0.717561i	−0.997361	+	0.0725958i	$0.976872\pi$
$270$	11.7125	−	24.6525i	0.712802	−	1.50030i
$271$	−9.72905	−	29.9429i	−0.590998	−	1.81890i	−0.573717	−	0.819054i	$-0.694499\pi$
$271$	−9.72905	−	29.9429i	−0.590998	−	1.81890i	−0.0172814	−	0.999851i	$-0.505501\pi$
$272$	1.69866	+	5.22794i	0.102996	+	0.316990i
$273$	−1.87176	−	1.35992i	−0.113284	−	0.0823059i
$274$	−15.8759			−0.959099
$275$	−2.85609	+	4.42750i	−0.172229	+	0.266988i
$276$	6.89908			0.415276
$277$	5.58346	+	4.05662i	0.335478	+	0.243739i	0.742751	−	0.669567i	$-0.233520\pi$
$277$	5.58346	+	4.05662i	0.335478	+	0.243739i	−0.407274	+	0.913306i	$0.633520\pi$
$278$	3.89759	+	11.9955i	0.233762	+	0.719445i
$279$	20.5174	+	63.1462i	1.22835	+	3.78046i
$280$	0.478407	−	0.260699i	0.0285903	−	0.0155797i
$281$	9.92556	−	30.5477i	0.592109	−	1.82233i	0.0234910	−	0.999724i	$-0.492522\pi$
$281$	9.92556	−	30.5477i	0.592109	−	1.82233i	0.568618	−	0.822601i	$-0.307478\pi$
$282$	21.3427			1.27094
$283$	8.26857	−	25.4480i	0.491515	−	1.51273i	−0.330803	−	0.943700i	$-0.607319\pi$
$283$	8.26857	−	25.4480i	0.491515	−	1.51273i	0.822318	−	0.569028i	$-0.192681\pi$
$284$	1.37266	−	0.997298i	0.0814525	−	0.0591787i
$285$	5.10637	+	4.83099i	0.302475	+	0.286163i
$286$	2.57501	+	1.87085i	0.152263	+	0.110626i
$287$	0.421395	−	0.306161i	0.0248742	−	0.0180721i
$288$	5.56823	−	4.04555i	0.328111	−	0.238386i
$289$	−10.6926	−	7.76862i	−0.628975	−	0.456977i
$290$	−8.34122	+	4.54540i	−0.489813	+	0.266915i
$291$	7.09822	−	5.15716i	0.416105	−	0.302318i
$292$	3.57007	−	10.9876i	0.208923	−	0.642998i
$293$	−23.1970			−1.35518			−0.677590	−	0.735440i	$-0.736976\pi$
$293$	−23.1970			−1.35518			−0.677590	+	0.735440i	$0.736976\pi$
$294$	6.74247	−	20.7512i	0.393229	−	1.21023i
$295$	28.3094	+	3.68310i	1.64824	+	0.214438i
$296$	−0.837217	−	2.57669i	−0.0486623	−	0.149767i
$297$	−3.97461	−	12.2326i	−0.230630	−	0.709807i
$298$	9.26022	+	6.72795i	0.536430	+	0.389739i
$299$	−6.62880			−0.383353
$300$	−9.92911	−	12.1853i	−0.573257	−	0.703516i
$301$	−2.29961			−0.132547
$302$	8.20523	+	5.96145i	0.472158	+	0.343043i
$303$	−6.70672	−	20.6412i	−0.385291	−	1.18580i
$304$	0.309017	+	0.951057i	0.0177233	+	0.0545468i
$305$	2.04154	+	10.9222i	0.116898	+	0.625402i
$306$	−11.6914	+	35.9823i	−0.668351	+	2.05697i
$307$	0.177359			0.0101224			0.00506122	−	0.999987i	$-0.498389\pi$
$307$	0.177359			0.0101224			0.00506122	+	0.999987i	$0.498389\pi$
$308$	0.0793407	−	0.244186i	0.00452086	−	0.0139138i
$309$	−41.9246	+	30.4600i	−2.38501	+	1.73281i
$310$	21.3906	+	2.78295i	1.21490	+	0.158061i
$311$	−10.6441	−	7.73341i	−0.603573	−	0.438521i	0.243572	−	0.969883i	$-0.421681\pi$
$311$	−10.6441	−	7.73341i	−0.603573	−	0.438521i	−0.847145	+	0.531361i	$0.821681\pi$
$312$	−7.68205	+	5.58133i	−0.434910	+	0.315981i
$313$	13.0385	−	9.47304i	0.736981	−	0.535448i	−0.154783	−	0.987948i	$-0.549468\pi$
$313$	13.0385	−	9.47304i	0.736981	−	0.535448i	0.891764	+	0.452500i	$0.149468\pi$
$314$	10.8781	+	7.90342i	0.613888	+	0.446016i
$315$	3.71855	+	0.483789i	0.209517	+	0.0272584i
$316$	0.517401	−	0.375914i	0.0291061	−	0.0211468i
$317$	−7.30473	+	22.4817i	−0.410275	+	1.26270i	0.506135	+	0.862454i	$0.331074\pi$
$317$	−7.30473	+	22.4817i	−0.410275	+	1.26270i	−0.916410	+	0.400241i	$0.868926\pi$
$318$	3.99604			0.224087
$319$	−1.38334	+	4.25748i	−0.0774521	+	0.238373i
$320$	−0.410843	−	2.19800i	−0.0229668	−	0.122872i
$321$	2.09900	+	6.46005i	0.117155	+	0.360565i
$322$	0.165238	+	0.508550i	0.00920836	+	0.0283404i
$323$	−4.44715	−	3.23104i	−0.247446	−	0.179780i
$324$	17.7235			0.984640
$325$	9.54012	+	11.7079i	0.529190	+	0.649436i
$326$	2.98729			0.165451
$327$	−27.2468	−	19.7959i	−1.50675	−	1.09472i
$328$	−0.660602	−	2.03312i	−0.0364756	−	0.112260i
$329$	0.511173	+	1.57323i	0.0281819	+	0.0867349i
$330$	−7.34544	−	0.955654i	−0.404353	−	0.0526070i
$331$	−7.32061	+	22.5305i	−0.402377	+	1.23839i	0.520688	+	0.853747i	$0.325675\pi$
$331$	−7.32061	+	22.5305i	−0.402377	+	1.23839i	−0.923065	+	0.384643i	$0.874325\pi$
$332$	−11.0045			−0.603951
$333$	5.76232	−	17.7346i	0.315773	−	0.971850i
$334$	−1.47496	+	1.07162i	−0.0807064	+	0.0586366i
$335$	−18.3104	+	9.97793i	−1.00041	+	0.545152i
$336$	0.619683	+	0.450226i	0.0338065	+	0.0245619i
$337$	20.7352	−	15.0650i	1.12952	−	0.820641i	0.143892	−	0.989593i	$-0.454038\pi$
$337$	20.7352	−	15.0650i	1.12952	−	0.820641i	0.985624	+	0.168952i	$0.0540383\pi$
$338$	−3.13613	+	2.27853i	−0.170583	+	0.123936i
$339$	−25.7314	−	18.6950i	−1.39754	−	1.01537i
$340$	8.92891	+	8.44738i	0.484238	+	0.458124i
$341$	8.22392	−	5.97503i	0.445350	−	0.323566i
$342$	−2.12687	+	6.54584i	−0.115008	+	0.353959i
$343$	3.39670			0.183404
$344$	−2.91650	+	8.97607i	−0.157247	+	0.483957i
$345$	13.5461	−	7.38171i	0.729298	−	0.397418i
$346$	0.245961	+	0.756990i	0.0132229	+	0.0406961i
$347$	−1.03542	−	3.18668i	−0.0555840	−	0.171070i	0.919410	−	0.393300i	$-0.128667\pi$
$347$	−1.03542	−	3.18668i	−0.0555840	−	0.171070i	−0.974994	+	0.222230i	$0.928667\pi$
$348$	−10.8044	−	7.84988i	−0.579178	−	0.420798i
$349$	33.1506			1.77451			0.887256	−	0.461278i	$-0.152609\pi$
$349$	33.1506			1.77451			0.887256	+	0.461278i	$0.152609\pi$
$350$	0.660400	−	1.02375i	0.0352998	−	0.0547216i
$351$	−36.8684			−1.96789
$352$	−0.852506	−	0.619382i	−0.0454387	−	0.0330131i
$353$	−3.29666	−	10.1461i	−0.175463	−	0.540021i	0.824191	−	0.566312i	$-0.191630\pi$
$353$	−3.29666	−	10.1461i	−0.175463	−	0.540021i	−0.999654	+	0.0262912i	$0.991630\pi$
$354$	12.4025	+	38.1711i	0.659187	+	2.02877i
$355$	1.62811	−	3.42685i	0.0864112	−	0.181878i
$356$	5.33072	−	16.4063i	0.282527	−	0.869530i
$357$	−4.21052			−0.222845
$358$	4.72455	−	14.5407i	0.249700	−	0.768498i
$359$	6.11458	−	4.44250i	0.322715	−	0.234466i	−0.414618	−	0.909996i	$-0.636085\pi$
$359$	6.11458	−	4.44250i	0.322715	−	0.234466i	0.737333	+	0.675529i	$0.236085\pi$
$360$	6.60446	−	13.9011i	0.348086	−	0.732650i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	13.9016	−	10.1001i	0.730654	−	0.530851i
$363$	25.1521	−	18.2741i	1.32014	−	0.959140i
$364$	−0.595406	−	0.432588i	−0.0312078	−	0.0226738i
$365$	−4.74647	−	25.3935i	−0.248442	−	1.32916i
$366$	−12.6380	+	9.18202i	−0.660597	+	0.479952i
$367$	3.93172	−	12.1006i	0.205234	−	0.631646i	−0.794470	−	0.607304i	$-0.792251\pi$
$367$	3.93172	−	12.1006i	0.205234	−	0.631646i	0.999704	−	0.0243417i	$-0.00774898\pi$
$368$	2.19459			0.114401
$369$	4.54673	−	13.9934i	0.236693	−	0.728467i
$370$	−4.40079	−	4.16346i	−0.228786	−	0.216448i
$371$	0.0957081	+	0.294559i	0.00496891	+	0.0152927i
$372$	9.37135	+	28.8420i	0.485882	+	1.49539i
$373$	−24.6289	−	17.8939i	−1.27524	−	0.926513i	−0.275838	−	0.961204i	$-0.588955\pi$
$373$	−24.6289	−	17.8939i	−1.27524	−	0.926513i	−0.999398	+	0.0346911i	$0.988955\pi$
$374$	5.79247			0.299521
$375$	−32.5331	−	13.3016i	−1.68000	−	0.686894i
$376$	6.78908			0.350120
$377$	10.3811	+	7.54235i	0.534656	+	0.388451i
$378$	0.919028	+	2.82848i	0.0472697	+	0.145481i
$379$	−10.4102	−	32.0392i	−0.534734	−	1.64574i	−0.744222	−	0.667932i	$-0.767180\pi$
$379$	−10.4102	−	32.0392i	−0.534734	−	1.64574i	0.209488	−	0.977811i	$-0.432820\pi$
$380$	1.62433	+	1.53673i	0.0833264	+	0.0788327i
$381$	−6.07480	+	18.6963i	−0.311221	+	0.957841i
$382$	12.7241			0.651021
$383$	4.94043	−	15.2051i	0.252444	−	0.776944i	−0.741878	−	0.670535i	$-0.766065\pi$
$383$	4.94043	−	15.2051i	0.252444	−	0.776944i	0.994322	−	0.106409i	$-0.0339353\pi$
$384$	2.54329	−	1.84781i	0.129787	−	0.0942955i
$385$	−0.105485	−	0.564341i	−0.00537600	−	0.0287615i
$386$	−12.7110	−	9.23506i	−0.646971	−	0.470052i
$387$	−52.5529	+	38.1819i	−2.67141	+	1.94089i
$388$	2.25793	−	1.64049i	0.114629	−	0.0832830i
$389$	−0.603956	−	0.438800i	−0.0306218	−	0.0222480i	0.572369	−	0.819996i	$-0.306024\pi$
$389$	−0.603956	−	0.438800i	−0.0306218	−	0.0222480i	−0.602991	+	0.797748i	$0.706024\pi$
$390$	−9.11166	+	19.1782i	−0.461387	+	0.971126i
$391$	−9.75967	+	7.09082i	−0.493568	+	0.358598i
$392$	2.14477	−	6.60093i	0.108327	−	0.333398i
$393$	25.5379			1.28822
$394$	−3.15087	+	9.69739i	−0.158739	+	0.488548i
$395$	0.613689	−	1.29169i	0.0308780	−	0.0649920i
$396$	−2.24120	−	6.89771i	−0.112625	−	0.346623i
$397$	−1.32540	−	4.07915i	−0.0665197	−	0.204727i	0.912272	−	0.409585i	$-0.134327\pi$
$397$	−1.32540	−	4.07915i	−0.0665197	−	0.204727i	−0.978792	+	0.204859i	$0.934327\pi$
$398$	−2.63477	−	1.91427i	−0.132069	−	0.0959539i
$399$	−0.765971			−0.0383465
$400$	−3.15844	−	3.87612i	−0.157922	−	0.193806i
$401$	−15.5094			−0.774505			−0.387252	−	0.921974i	$-0.626576\pi$
$401$	−15.5094			−0.774505			−0.387252	+	0.921974i	$0.626576\pi$
$402$	−23.7176	−	17.2318i	−1.18293	−	0.859446i
$403$	−9.00421	−	27.7121i	−0.448532	−	1.38044i
$404$	−2.13340	−	6.56593i	−0.106141	−	0.326667i
$405$	34.7995	−	18.9634i	1.72920	−	0.942297i
$406$	0.319862	−	0.984435i	0.0158745	−	0.0488567i
$407$	−2.85493			−0.141514
$408$	−5.34004	+	16.4349i	−0.264371	+	0.813651i
$409$	−0.879133	+	0.638728i	−0.0434703	+	0.0315831i	−0.609308	−	0.792933i	$-0.708553\pi$
$409$	−0.879133	+	0.638728i	−0.0434703	+	0.0315831i	0.565838	+	0.824516i	$0.308553\pi$
$410$	−3.47242	−	3.28516i	−0.171491	−	0.162242i
$411$	−40.3770	−	29.3356i	−1.99165	−	1.44702i
$412$	−13.3362	+	9.68929i	−0.657026	+	0.477357i
$413$	−2.51665	+	1.82845i	−0.123836	+	0.0899721i
$414$	12.2200	+	8.87833i	0.600579	+	0.436346i
$415$	−21.6070	+	11.7743i	−1.06064	+	0.577979i
$416$	−2.44365	+	1.77542i	−0.119810	+	0.0870469i
$417$	−12.2528	+	37.7101i	−0.600020	+	1.84667i
$418$	1.05375			0.0515408
$419$	−0.0702198	+	0.216114i	−0.00343046	+	0.0105579i	−0.952757	−	0.303733i	$-0.901767\pi$
$419$	−0.0702198	+	0.216114i	−0.00343046	+	0.0105579i	0.949327	+	0.314291i	$0.101767\pi$
$420$	1.69845	+	0.220971i	0.0828758	+	0.0107823i
$421$	9.21680	+	28.3664i	0.449199	+	1.38249i	0.877812	+	0.479005i	$0.159002\pi$
$421$	9.21680	+	28.3664i	0.449199	+	1.38249i	−0.428613	+	0.903488i	$0.640998\pi$
$422$	2.18681	+	6.73031i	0.106452	+	0.327626i
$423$	37.8031	+	27.4656i	1.83805	+	1.33542i
$424$	1.27114			0.0617318
$425$	26.5699	+	7.03262i	1.28883	+	0.341132i
$426$	5.33389			0.258428
$427$	−0.979520	−	0.711663i	−0.0474023	−	0.0344398i
$428$	0.667689	+	2.05494i	0.0322740	+	0.0993291i
$429$	3.09201	+	9.51624i	0.149284	+	0.459448i
$430$	3.87753	+	20.7447i	0.186991	+	1.00040i
$431$	−11.7676	+	36.2168i	−0.566824	+	1.74450i	0.0956460	+	0.995415i	$0.469508\pi$
$431$	−11.7676	+	36.2168i	−0.566824	+	1.74450i	−0.662470	+	0.749089i	$0.730492\pi$
$432$	12.2060			0.587260
$433$	−6.92726	+	21.3199i	−0.332903	+	1.02457i	0.634843	+	0.772641i	$0.281065\pi$
$433$	−6.92726	+	21.3199i	−0.332903	+	1.02457i	−0.967746	+	0.251929i	$0.918935\pi$
$434$	−1.90158	+	1.38158i	−0.0912786	+	0.0663178i
$435$	−29.6131	−	3.85272i	−1.41984	−	0.184724i
$436$	−8.66717	−	6.29707i	−0.415082	−	0.301575i
$437$	−1.77546	+	1.28995i	−0.0849318	+	0.0617066i
$438$	29.3826	−	21.3477i	1.40396	−	1.02003i
$439$	−20.8133	−	15.1217i	−0.993362	−	0.721720i	−0.0327075	−	0.999465i	$-0.510413\pi$
$439$	−20.8133	−	15.1217i	−0.993362	−	0.721720i	−0.960655	+	0.277745i	$0.910413\pi$
$440$	−2.33658	−	0.303992i	−0.111392	−	0.0144923i
$441$	38.6470	−	28.0787i	1.84033	−	1.33708i
$442$	5.13083	−	15.7911i	0.244049	−	0.751105i
$443$	10.4338			0.495726			0.247863	−	0.968795i	$-0.420272\pi$
$443$	10.4338			0.495726			0.247863	+	0.968795i	$0.420272\pi$
$444$	2.63194	−	8.10028i	0.124906	−	0.384422i
$445$	−7.08727	−	37.9167i	−0.335969	−	1.79743i
$446$	−3.58050	−	11.0196i	−0.169542	−	0.521795i
$447$	11.1195	+	34.2222i	0.525933	+	1.61866i
$448$	0.197121	+	0.143216i	0.00931307	+	0.00676634i
$449$	−20.1190			−0.949475			−0.474737	−	0.880127i	$-0.657457\pi$
$449$	−20.1190			−0.949475			−0.474737	+	0.880127i	$0.657457\pi$
$450$	−1.90586	−	34.3607i	−0.0898429	−	1.61978i
$451$	−2.25267			−0.106074
$452$	−8.18513	−	5.94684i	−0.384996	−	0.279716i
$453$	9.85266	+	30.3234i	0.462918	+	1.42472i
$454$	0.277310	+	0.853472i	0.0130148	+	0.0400554i
$455$	−1.63191	−	0.212314i	−0.0765051	−	0.00995343i
$456$	−0.971450	+	2.98981i	−0.0454923	+	0.140011i
$457$	19.3152			0.903527			0.451763	−	0.892138i	$-0.350795\pi$
$457$	19.3152			0.903527			0.451763	+	0.892138i	$0.350795\pi$
$458$	−8.63259	+	26.5684i	−0.403375	+	1.24146i
$459$	−54.2818	+	39.4380i	−2.53366	+	1.84081i
$460$	4.30900	−	2.34811i	0.200908	−	0.109481i
$461$	−25.3044	−	18.3847i	−1.17854	−	0.856263i	−0.186538	−	0.982448i	$-0.559727\pi$
$461$	−25.3044	−	18.3847i	−1.17854	−	0.856263i	−0.992007	+	0.126185i	$0.959727\pi$
$462$	0.652994	−	0.474428i	0.0303800	−	0.0220724i
$463$	12.3504	−	8.97310i	0.573972	−	0.417015i	−0.262574	−	0.964912i	$-0.584571\pi$
$463$	12.3504	−	8.97310i	0.573972	−	0.417015i	0.836546	+	0.547897i	$0.184571\pi$
$464$	−3.43688	−	2.49704i	−0.159553	−	0.115922i
$465$	49.2600	+	46.6034i	2.28438	+	2.16118i
$466$	−15.1195	+	10.9850i	−0.700399	+	0.508869i
$467$	2.00095	−	6.15828i	0.0925928	−	0.284971i	−0.894026	−	0.448015i	$-0.852131\pi$
$467$	2.00095	−	6.15828i	0.0925928	−	0.284971i	0.986619	+	0.163044i	$0.0521311\pi$
$468$	−20.7893			−0.960987
$469$	0.702153	−	2.16100i	0.0324224	−	0.0997859i
$470$	13.3301	−	7.26401i	0.614873	−	0.335064i
$471$	13.0622	+	40.2014i	0.601875	+	1.85238i
$472$	3.94523	+	12.1422i	0.181594	+	0.558889i
$473$	8.04594	+	5.84572i	0.369953	+	0.268786i
$474$	2.01052			0.0923461
$475$	4.83355	+	1.27936i	0.221779	+	0.0587011i
$476$	−1.33936			−0.0613896
$477$	7.07797	+	5.14245i	0.324078	+	0.235456i
$478$	0.751097	+	2.31164i	0.0343544	+	0.105732i
$479$	8.98382	+	27.6494i	0.410481	+	1.26333i	0.916231	+	0.400651i	$0.131216\pi$
$479$	8.98382	+	27.6494i	0.410481	+	1.26333i	−0.505749	+	0.862681i	$0.668784\pi$
$480$	3.01659	−	6.34931i	0.137688	−	0.289805i
$481$	−2.52883	+	7.78294i	−0.115305	+	0.354871i
$482$	4.46006			0.203150
$483$	−0.519455	+	1.59872i	−0.0236360	+	0.0727442i
$484$	8.00086	−	5.81296i	0.363675	−	0.264226i
$485$	2.67813	−	5.63692i	0.121608	−	0.255959i
$486$	15.4515	+	11.2262i	0.700894	+	0.509229i
$487$	20.0371	−	14.5578i	0.907969	−	0.659678i	−0.0325317	−	0.999471i	$-0.510357\pi$
$487$	20.0371	−	14.5578i	0.907969	−	0.659678i	0.940500	+	0.339793i	$0.110357\pi$
$488$	−4.02012	+	2.92079i	−0.181982	+	0.132218i
$489$	7.59755	+	5.51994i	0.343573	+	0.249620i
$490$	−2.85151	−	15.2555i	−0.128818	−	0.689174i
$491$	−8.33929	+	6.05885i	−0.376347	+	0.273432i	−0.759838	−	0.650113i	$-0.774722\pi$
$491$	−8.33929	+	6.05885i	−0.376347	+	0.273432i	0.383491	+	0.923545i	$0.374722\pi$
$492$	2.07672	−	6.39149i	0.0936257	−	0.288150i
$493$	23.3523			1.05174
$494$	0.933391	−	2.87268i	0.0419953	−	0.129248i
$495$	−11.7808	−	11.1454i	−0.529506	−	0.500950i
$496$	2.98101	+	9.17462i	0.133852	+	0.411953i
$497$	0.127751	+	0.393176i	0.00573039	+	0.0176363i
$498$	−27.9876	−	20.3342i	−1.25416	−	0.911197i
$499$	24.9685			1.11774			0.558872	−	0.829254i	$-0.311234\pi$
$499$	24.9685			1.11774			0.558872	+	0.829254i	$0.311234\pi$
$500$	−10.3488	−	4.23124i	−0.462810	−	0.189227i
$501$	−5.73141			−0.256060
$502$	7.28384	+	5.29202i	0.325093	+	0.236194i
$503$	8.83522	+	27.1920i	0.393943	+	1.21243i	0.929782	+	0.368111i	$0.119995\pi$
$503$	8.83522	+	27.1920i	0.393943	+	1.21243i	−0.535839	+	0.844320i	$0.680005\pi$
$504$	0.518222	+	1.59492i	0.0230834	+	0.0710435i
$505$	−11.2141	−	10.6093i	−0.499021	−	0.472110i
$506$	0.714621	−	2.19938i	0.0317688	−	0.0977742i
$507$	−12.1864			−0.541216
$508$	−1.93239	+	5.94727i	−0.0857358	+	0.263868i
$509$	−23.2522	+	16.8937i	−1.03064	+	0.748802i	−0.968436	−	0.249262i	$-0.919812\pi$
$509$	−23.2522	+	16.8937i	−1.03064	+	0.748802i	−0.0622012	+	0.998064i	$0.519812\pi$
$510$	7.09966	+	37.9830i	0.314378	+	1.68192i
$511$	2.27733	+	1.65458i	0.100743	+	0.0731943i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−9.87484	+	7.17449i	−0.435985	+	0.316761i
$514$	14.1631	+	10.2901i	0.624709	+	0.453877i
$515$	−15.8180	+	33.2937i	−0.697025	+	1.46709i
$516$	−24.0035	+	17.4396i	−1.05670	+	0.767735i
$517$	2.21072	−	6.80389i	0.0972272	−	0.299235i
$518$	0.660131			0.0290045
$519$	−0.773222	+	2.37973i	−0.0339407	+	0.104459i
$520$	−2.89841	+	6.10056i	−0.127104	+	0.267527i
$521$	8.58799	+	26.4311i	0.376246	+	1.15797i	0.942634	+	0.333828i	$0.108341\pi$
$521$	8.58799	+	26.4311i	0.376246	+	1.15797i	−0.566387	+	0.824139i	$0.691659\pi$
$522$	−9.03541	−	27.8081i	−0.395469	−	1.21713i
$523$	−33.4079	−	24.2723i	−1.46083	−	1.06135i	−0.983146	−	0.182820i	$-0.941478\pi$
$523$	−33.4079	−	24.2723i	−1.46083	−	1.06135i	−0.477681	−	0.878533i	$-0.658522\pi$
$524$	8.12359			0.354881
$525$	3.57127	−	1.38339i	0.155863	−	0.0603762i
$526$	−28.2840			−1.23324
$527$	−42.9006	−	31.1691i	−1.86878	−	1.35775i
$528$	−1.02367	−	3.15053i	−0.0445495	−	0.137109i
$529$	−5.61909	−	17.2938i	−0.244308	−	0.751904i
$530$	2.49583	−	1.36006i	0.108412	−	0.0590771i
$531$	−27.1539	+	83.5710i	−1.17838	+	3.62667i
$532$	−0.243654			−0.0105638
$533$	−1.99536	+	6.14109i	−0.0864287	+	0.266000i
$534$	43.8731	−	31.8757i	1.89858	−	1.37940i
$535$	3.50967	+	3.32040i	0.151736	+	0.143553i
$536$	−7.54454	−	5.48143i	−0.325874	−	0.236762i
$537$	38.8842	−	28.2510i	1.67798	−	1.21912i
$538$	−10.0112	+	7.27357i	−0.431614	+	0.313586i
$539$	−5.91693	−	4.29890i	−0.254860	−	0.185167i
$540$	23.9660	−	13.0598i	1.03133	−	0.562006i
$541$	9.46597	−	6.87743i	0.406974	−	0.295684i	−0.365402	−	0.930850i	$-0.619068\pi$
$541$	9.46597	−	6.87743i	0.406974	−	0.295684i	0.772375	+	0.635166i	$0.219068\pi$
$542$	9.72905	−	29.9429i	0.417899	−	1.28616i
$543$	54.0190			2.31818
$544$	−1.69866	+	5.22794i	−0.0728294	+	0.224146i
$545$	−23.7553	−	3.09060i	−1.01756	−	0.132387i
$546$	−0.714950	−	2.20039i	−0.0305971	−	0.0941680i
$547$	8.20708	+	25.2588i	0.350909	+	1.07999i	0.958344	+	0.285618i	$0.0921988\pi$
$547$	8.20708	+	25.2588i	0.350909	+	1.07999i	−0.607434	+	0.794370i	$0.707801\pi$
$548$	−12.8439	−	9.33163i	−0.548663	−	0.398627i
$549$	−34.2011			−1.45967
$550$	−4.91304	+	1.90315i	−0.209493	+	0.0811506i
$551$	4.24821			0.180980
$552$	5.58148	+	4.05518i	0.237563	+	0.172600i
$553$	0.0481533	+	0.148201i	0.00204769	+	0.00630213i
$554$	2.13269	+	6.56375i	0.0906094	+	0.278867i
$555$	−3.49921	−	18.7207i	−0.148533	−	0.794649i
$556$	−3.89759	+	11.9955i	−0.165295	+	0.508724i
$557$	−13.6886			−0.580003			−0.290001	−	0.957026i	$-0.593656\pi$
$557$	−13.6886			−0.580003			−0.290001	+	0.957026i	$0.593656\pi$
$558$	−20.5174	+	63.1462i	−0.868573	+	2.67319i
$559$	23.0632	−	16.7564i	0.975468	−	0.708719i
$560$	0.540274	+	0.0702906i	0.0228308	+	0.00297032i
$561$	14.7319	+	10.7034i	0.621982	+	0.451896i
$562$	25.9855	−	18.8795i	1.09613	−	0.796385i
$563$	−11.8168	+	8.58543i	−0.498020	+	0.361833i	−0.808260	−	0.588825i	$-0.799591\pi$
$563$	−11.8168	+	8.58543i	−0.498020	+	0.361833i	0.310240	+	0.950658i	$0.399591\pi$
$564$	17.2666	+	12.5449i	0.727055	+	0.528236i
$565$	−22.4341	−	2.91871i	−0.943809	−	0.122791i
$566$	21.6474	−	15.7277i	0.909908	−	0.661086i
$567$	−1.33446	+	4.10705i	−0.0560422	+	0.172480i
$568$	1.69670			0.0711921
$569$	13.6654	−	42.0579i	0.572885	−	1.76316i	−0.0703866	−	0.997520i	$-0.522423\pi$
$569$	13.6654	−	42.0579i	0.572885	−	1.76316i	0.643271	−	0.765638i	$-0.277577\pi$
$570$	1.29156	+	6.90980i	0.0540974	+	0.289420i
$571$	−11.6407	−	35.8265i	−0.487149	−	1.49929i	−0.828843	−	0.559481i	$-0.811001\pi$
$571$	−11.6407	−	35.8265i	−0.487149	−	1.49929i	0.341694	−	0.939811i	$-0.388999\pi$
$572$	0.983566	+	3.02710i	0.0411249	+	0.126570i
$573$	32.3610	+	23.5117i	1.35190	+	0.982214i
$574$	0.520873			0.0217408
$575$	5.94821	−	9.22088i	0.248057	−	0.384537i
$576$	6.88271			0.286779
$577$	−5.67571	−	4.12365i	−0.236283	−	0.171670i	0.463343	−	0.886179i	$-0.346650\pi$
$577$	−5.67571	−	4.12365i	−0.236283	−	0.171670i	−0.699626	+	0.714510i	$0.746650\pi$
$578$	−4.08420	−	12.5699i	−0.169880	−	0.522838i
$579$	−15.2630	−	46.9748i	−0.634311	−	1.95221i
$580$	−9.41991	−	1.22555i	−0.391140	−	0.0508880i
$581$	0.828566	−	2.55006i	0.0343747	−	0.105794i
$582$	8.77388			0.363689
$583$	0.413918	−	1.27391i	0.0171427	−	0.0527598i
$584$	9.34657	−	6.79068i	0.386764	−	0.281000i
$585$	−40.8191	+	22.2436i	−1.68766	+	0.919661i
$586$	−18.7667	−	13.6348i	−0.775246	−	0.563250i
$587$	−8.21410	+	5.96789i	−0.339032	+	0.246321i	−0.744253	−	0.667897i	$-0.767194\pi$
$587$	−8.21410	+	5.96789i	−0.339032	+	0.246321i	0.405221	+	0.914219i	$0.367194\pi$
$588$	17.6520	−	12.8249i	0.727957	−	0.528892i
$589$	−7.80440	−	5.67023i	−0.321575	−	0.233638i
$590$	20.7379	+	19.6195i	0.853766	+	0.807723i
$591$	−25.9325	+	18.8411i	−1.06672	+	0.775017i
$592$	0.837217	−	2.57669i	0.0344094	−	0.105901i
$593$	−14.0658			−0.577613			−0.288807	−	0.957387i	$-0.593258\pi$
$593$	−14.0658			−0.577613			−0.288807	+	0.957387i	$0.593258\pi$
$594$	3.97461	−	12.2326i	0.163080	−	0.501909i
$595$	−2.62979	+	1.43306i	−0.107811	+	0.0587496i
$596$	3.53709	+	10.8860i	0.144885	+	0.445910i
$597$	−3.16378	−	9.73710i	−0.129485	−	0.398513i
$598$	−5.36281	−	3.89631i	−0.219302	−	0.159332i
$599$	−32.3145			−1.32033			−0.660167	−	0.751119i	$-0.729515\pi$
$599$	−32.3145			−1.32033			−0.660167	+	0.751119i	$0.729515\pi$
$600$	−0.870500	−	15.6943i	−0.0355380	−	0.640716i
$601$	−23.1551			−0.944518			−0.472259	−	0.881460i	$-0.656561\pi$
$601$	−23.1551			−0.944518			−0.472259	+	0.881460i	$0.656561\pi$
$602$	−1.86042	−	1.35168i	−0.0758252	−	0.0550902i
$603$	−19.8343	−	61.0437i	−0.807715	−	2.48589i
$604$	3.13412	+	9.64583i	0.127526	+	0.392483i
$605$	9.48980	−	19.9741i	0.385815	−	0.812063i
$606$	6.70672	−	20.6412i	0.272442	−	0.838490i
$607$	−9.84930			−0.399771			−0.199885	−	0.979819i	$-0.564057\pi$
$607$	−9.84930			−0.399771			−0.199885	+	0.979819i	$0.564057\pi$
$608$	−0.309017	+	0.951057i	−0.0125323	+	0.0385704i
$609$	2.63255	−	1.91266i	0.106676	−	0.0775048i
$610$	−4.76826	+	10.0362i	−0.193061	+	0.406354i
$611$	−16.5901	−	12.0534i	−0.671165	−	0.487630i
$612$	−30.6084	+	22.2383i	−1.23727	+	0.898930i
$613$	−23.4587	+	17.0438i	−0.947490	+	0.688392i	−0.950212	−	0.311605i	$-0.899134\pi$
$613$	−23.4587	+	17.0438i	−0.947490	+	0.688392i	0.00272212	+	0.999996i	$0.499134\pi$
$614$	0.143487	+	0.104249i	0.00579066	+	0.00420716i
$615$	−2.76103	−	14.7715i	−0.111336	−	0.595643i
$616$	0.207717	−	0.150915i	0.00836914	−	0.00608054i
$617$	−7.80573	+	24.0236i	−0.314247	+	0.967153i	0.661816	+	0.749666i	$0.269786\pi$
$617$	−7.80573	+	24.0236i	−0.314247	+	0.967153i	−0.976063	+	0.217487i	$0.930214\pi$
$618$	−51.8217			−2.08457
$619$	9.41720	−	28.9832i	0.378509	−	1.16493i	−0.562571	−	0.826749i	$-0.690188\pi$
$619$	9.41720	−	28.9832i	0.378509	−	1.16493i	0.941081	−	0.338183i	$-0.109812\pi$
$620$	15.6695	+	14.8245i	0.629304	+	0.595366i
$621$	8.27767	+	25.4761i	0.332172	+	1.02232i
$622$	−4.06569	−	12.5129i	−0.163019	−	0.501722i
$623$	3.40044	+	2.47056i	0.136236	+	0.0989811i
$624$	−9.49553			−0.380126
$625$	−24.8466	+	2.76480i	−0.993866	+	0.110592i
$626$	16.1165			0.644145
$627$	2.68000	+	1.94714i	0.107029	+	0.0777611i
$628$	4.15508	+	12.7880i	0.165806	+	0.510297i
$629$	4.60216	+	14.1640i	0.183500	+	0.564756i
$630$	2.72401	+	2.57710i	0.108527	+	0.102674i
$631$	2.09598	−	6.45077i	0.0834398	−	0.256801i	−0.900629	−	0.434588i	$-0.856894\pi$
$631$	2.09598	−	6.45077i	0.0834398	−	0.256801i	0.984069	+	0.177787i	$0.0568939\pi$
$632$	0.639543			0.0254397
$633$	−6.87463	+	21.1579i	−0.273242	+	0.840952i
$634$	−19.1240	+	13.8944i	−0.759513	+	0.551818i
$635$	2.56914	+	13.7448i	0.101953	+	0.545447i
$636$	3.23286	+	2.34881i	0.128191	+	0.0931365i
$637$	−16.9605	+	12.3225i	−0.671999	+	0.488236i
$638$	−3.62163	+	2.63127i	−0.143382	+	0.104173i
$639$	9.44763	+	6.86411i	0.373743	+	0.271540i
$640$	0.959574	−	2.01971i	0.0379305	−	0.0798359i
$641$	36.6003	−	26.5917i	1.44563	−	1.05031i	0.458797	−	0.888541i	$-0.348280\pi$
$641$	36.6003	−	26.5917i	1.44563	−	1.05031i	0.986829	−	0.161768i	$-0.0517196\pi$
$642$	−2.09900	+	6.46005i	−0.0828409	+	0.254958i
$643$	8.29254			0.327026			0.163513	−	0.986541i	$-0.447717\pi$
$643$	8.29254			0.327026			0.163513	+	0.986541i	$0.447717\pi$
$644$	−0.165238	+	0.508550i	−0.00651129	+	0.0200397i
$645$	−28.4706	+	59.9247i	−1.12103	+	2.35953i
$646$	−1.69866	−	5.22794i	−0.0668329	−	0.205690i
$647$	−2.58438	−	7.95389i	−0.101602	−	0.312700i	0.887316	−	0.461163i	$-0.152567\pi$
$647$	−2.58438	−	7.95389i	−0.101602	−	0.312700i	−0.988918	+	0.148463i	$0.952567\pi$
$648$	14.3386	+	10.4176i	0.563274	+	0.409243i
$649$	13.4533			0.528089
$650$	0.836397	+	15.0794i	0.0328062	+	0.591463i
$651$	−7.38914			−0.289603
$652$	2.41677	+	1.75589i	0.0946481	+	0.0687659i
$653$	−8.48521	−	26.1148i	−0.332052	−	1.02195i	−0.968156	−	0.250348i	$-0.919455\pi$
$653$	−8.48521	−	26.1148i	−0.332052	−	1.02195i	0.636104	−	0.771603i	$-0.280545\pi$
$654$	−10.4073	−	32.0305i	−0.406959	−	1.25249i
$655$	15.9504	−	8.69187i	0.623233	−	0.339619i
$656$	0.660602	−	2.03312i	0.0257922	−	0.0793802i
$657$	79.5159			3.10221
$658$	−0.511173	+	1.57323i	−0.0199276	+	0.0613308i
$659$	−24.5163	+	17.8121i	−0.955019	+	0.693862i	−0.951989	−	0.306134i	$-0.900965\pi$
$659$	−24.5163	+	17.8121i	−0.955019	+	0.693862i	−0.00303037	+	0.999995i	$0.500965\pi$
$660$	−5.38087	−	5.09068i	−0.209450	−	0.198154i
$661$	15.4749	+	11.2432i	0.601906	+	0.437310i	0.846555	−	0.532302i	$-0.178673\pi$
$661$	15.4749	+	11.2432i	0.601906	+	0.437310i	−0.244649	+	0.969612i	$0.578673\pi$
$662$	−19.1656	+	13.9246i	−0.744893	+	0.541196i
$663$	42.2280	−	30.6805i	1.64000	−	1.19153i
$664$	−8.90283	−	6.46828i	−0.345497	−	0.251018i
$665$	−0.478407	+	0.260699i	−0.0185518	+	0.0101095i
$666$	15.0860	−	10.9606i	0.584569	−	0.424714i
$667$	2.88099	−	8.86679i	0.111553	−	0.343323i
$668$	−1.82315			−0.0705399
$669$	11.2559	−	34.6422i	0.435180	−	1.33935i
$670$	−20.6783	−	2.69028i	−0.798873	−	0.103935i
$671$	1.61809	+	4.97998i	0.0624658	+	0.192250i
$672$	0.236698	+	0.728481i	0.00913082	+	0.0281018i
$673$	−35.7860	−	26.0001i	−1.37945	−	1.00223i	−0.996931	−	0.0782802i	$-0.975057\pi$
$673$	−35.7860	−	26.0001i	−1.37945	−	1.00223i	−0.382518	−	0.923948i	$-0.624943\pi$
$674$	25.6301			0.987233
$675$	33.0830	−	51.2851i	1.27337	−	1.97396i
$676$	−3.87647			−0.149095
$677$	−26.5438	−	19.2852i	−1.02016	−	0.741192i	−0.0538467	−	0.998549i	$-0.517148\pi$
$677$	−26.5438	−	19.2852i	−1.02016	−	0.741192i	−0.966316	+	0.257357i	$0.917148\pi$
$678$	−9.82852	−	30.2491i	−0.377462	−	1.16171i
$679$	0.210141	+	0.646747i	0.00806446	+	0.0248199i
$680$	2.25839	+	12.0824i	0.0866055	+	0.463337i
$681$	−0.871773	+	2.68304i	−0.0334064	+	0.102814i
$682$	10.1653			0.389250
$683$	−7.98687	+	24.5811i	−0.305609	+	0.940568i	0.673840	+	0.738877i	$0.264644\pi$
$683$	−7.98687	+	24.5811i	−0.305609	+	0.940568i	−0.979449	+	0.201691i	$0.935356\pi$
$684$	−5.56823	+	4.04555i	−0.212906	+	0.154686i
$685$	−35.2029	−	4.57996i	−1.34504	−	0.174991i
$686$	2.74798	+	1.99653i	0.104919	+	0.0762278i
$687$	−71.0484	+	51.6197i	−2.71067	+	1.96941i
$688$	−7.63550	+	5.54751i	−0.291101	+	0.211497i
$689$	−3.10621	−	2.25679i	−0.118337	−	0.0859770i
$690$	15.2979	+	1.99028i	0.582381	+	0.0757687i
$691$	25.0101	−	18.1709i	0.951430	−	0.691254i	0.000285107	−	1.00000i	$-0.499909\pi$
$691$	25.0101	−	18.1709i	0.951430	−	0.691254i	0.951145	+	0.308746i	$0.0999092\pi$
$692$	−0.245961	+	0.756990i	−0.00935004	+	0.0287765i
$693$	1.76715			0.0671284
$694$	1.03542	−	3.18668i	0.0393038	−	0.120965i
$695$	5.18190	+	27.7231i	0.196561	+	1.05160i
$696$	−4.12693	−	12.7014i	−0.156431	−	0.481444i
$697$	3.63131	+	11.1760i	0.137546	+	0.423323i
$698$	26.8194	+	19.4854i	1.01513	+	0.737535i
$699$	−58.7514			−2.22218
$700$	1.13602	−	0.440056i	0.0429374	−	0.0166325i
$701$	4.31902			0.163127			0.0815636	−	0.996668i	$-0.474009\pi$
$701$	4.31902			0.163127			0.0815636	+	0.996668i	$0.474009\pi$
$702$	−29.8271	−	21.6707i	−1.12575	−	0.817907i
$703$	0.837217	+	2.57669i	0.0315763	+	0.0971817i
$704$	−0.325628	−	1.00218i	−0.0122726	−	0.0377711i
$705$	47.3249	+	6.15704i	1.78236	+	0.231888i
$706$	3.29666	−	10.1461i	0.124071	−	0.381852i
$707$	1.68215			0.0632637
$708$	−12.4025	+	38.1711i	−0.466116	+	1.43456i
$709$	−3.12636	+	2.27143i	−0.117413	+	0.0853054i	−0.644942	−	0.764231i	$-0.723118\pi$
$709$	−3.12636	+	2.27143i	−0.117413	+	0.0853054i	0.527529	+	0.849537i	$0.323118\pi$
$710$	3.33142	−	1.81540i	0.125026	−	0.0681306i
$711$	3.56112	+	2.58730i	0.133552	+	0.0970315i
$712$	13.9560	−	10.1396i	0.523023	−	0.379999i
$713$	−17.1275	+	12.4438i	−0.641428	+	0.466025i
$714$	−3.40638	−	2.47488i	−0.127481	−	0.0926202i
$715$	5.17006	+	4.89124i	0.193349	+	0.182922i
$716$	12.3690	−	8.98662i	0.462252	−	0.335846i
$717$	−2.36121	+	7.26705i	−0.0881809	+	0.271393i
$718$	7.55803			0.282063
$719$	13.6556	−	42.0276i	0.509268	−	1.56737i	−0.284207	−	0.958763i	$-0.591730\pi$
$719$	13.6556	−	42.0276i	0.509268	−	1.56737i	0.793475	−	0.608603i	$-0.208270\pi$
$720$	13.5140	−	7.36418i	0.503635	−	0.274447i
$721$	−1.24117	−	3.81992i	−0.0462234	−	0.142261i
$722$	−0.309017	−	0.951057i	−0.0115004	−	0.0353947i
$723$	11.3432	+	8.24133i	0.421859	+	0.306499i
$724$	17.1834			0.638615
$725$	−19.8069	+	7.67256i	−0.735611	+	0.284952i
$726$	31.0897			1.15385
$727$	32.7088	+	23.7644i	1.21310	+	0.881371i	0.995509	−	0.0946680i	$-0.0301790\pi$
$727$	32.7088	+	23.7644i	1.21310	+	0.881371i	0.217595	+	0.976039i	$0.430179\pi$
$728$	−0.227425	−	0.699942i	−0.00842893	−	0.0259416i
$729$	2.12320	+	6.53455i	0.0786372	+	0.242020i
$730$	11.0860	−	23.3337i	0.410310	−	0.863618i
$731$	16.0319	−	49.3412i	0.592963	−	1.82495i
$732$	−15.6214			−0.577383
$733$	−5.26554	+	16.2057i	−0.194487	+	0.598570i	0.805495	+	0.592603i	$0.201900\pi$
$733$	−5.26554	+	16.2057i	−0.194487	+	0.598570i	−0.999982	+	0.00596753i	$0.998100\pi$
$734$	10.2934	−	7.47858i	0.379935	−	0.276039i
$735$	20.9370	−	44.0682i	0.772274	−	1.62548i
$736$	1.77546	+	1.28995i	0.0654444	+	0.0475481i
$737$	−7.95009	+	5.77608i	−0.292846	+	0.212765i
$738$	11.9035	−	8.64839i	0.438174	−	0.318352i
$739$	19.3503	+	14.0588i	0.711811	+	0.517161i	0.883757	−	0.467945i	$-0.155006\pi$
$739$	19.3503	+	14.0588i	0.711811	+	0.517161i	−0.171947	+	0.985106i	$0.555006\pi$
$740$	−1.11309	−	5.95503i	−0.0409181	−	0.218911i
$741$	7.68205	−	5.58133i	0.282207	−	0.205035i
$742$	−0.0957081	+	0.294559i	−0.00351355	+	0.0108136i
$743$	−41.4629			−1.52113			−0.760564	−	0.649263i	$-0.775077\pi$
$743$	−41.4629			−1.52113			−0.760564	+	0.649263i	$0.775077\pi$
$744$	−9.37135	+	28.8420i	−0.343570	+	1.05740i
$745$	18.5925	+	17.5899i	0.681178	+	0.644442i
$746$	−9.40740	−	28.9530i	−0.344429	−	1.06004i
$747$	−23.4052	−	72.0337i	−0.856351	−	2.63558i
$748$	4.68620	+	3.40473i	0.171345	+	0.124489i
$749$	−0.526461			−0.0192365
$750$	−18.5013	−	29.8837i	−0.675574	−	1.09120i
$751$	−19.4648			−0.710282			−0.355141	−	0.934813i	$-0.615567\pi$
$751$	−19.4648			−0.710282			−0.355141	+	0.934813i	$0.615567\pi$
$752$	5.49248	+	3.99052i	0.200290	+	0.145519i
$753$	8.74627	+	26.9182i	0.318732	+	0.980955i
$754$	3.96525	+	12.2038i	0.144406	+	0.444435i
$755$	16.4743	+	15.5859i	0.599563	+	0.567229i
$756$	−0.919028	+	2.82848i	−0.0334247	+	0.102871i
$757$	33.4766			1.21673			0.608364	−	0.793658i	$-0.291826\pi$
$757$	33.4766			1.21673			0.608364	+	0.793658i	$0.291826\pi$
$758$	10.4102	−	32.0392i	0.378114	−	1.16372i
$759$	5.88151	−	4.27317i	0.213485	−	0.155106i
$760$	0.410843	+	2.19800i	0.0149028	+	0.0797299i
$761$	44.2040	+	32.1161i	1.60240	+	1.16421i	0.882722	+	0.469895i	$0.155708\pi$
$761$	44.2040	+	32.1161i	1.60240	+	1.16421i	0.719673	+	0.694313i	$0.244292\pi$
$762$	−15.9040	+	11.5550i	−0.576142	+	0.418592i
$763$	2.11179	−	1.53431i	0.0764521	−	0.0555457i
$764$	10.2940	+	7.47903i	0.372424	+	0.270582i
$765$	−36.3046	+	76.4138i	−1.31259	+	2.76275i
$766$	12.9342	−	9.39726i	0.467333	−	0.339537i
$767$	11.9166	−	36.6757i	0.430285	−	1.32428i
$768$	3.14368			0.113438
$769$	12.0113	−	36.9670i	0.433139	−	1.33306i	−0.461843	−	0.886962i	$-0.652812\pi$
$769$	12.0113	−	36.9670i	0.433139	−	1.33306i	0.894982	−	0.446103i	$-0.147188\pi$
$770$	0.246372	−	0.518564i	0.00887865	−	0.0186877i
$771$	17.0068	+	52.3414i	0.612484	+	1.88503i
$772$	−4.85516	−	14.9426i	−0.174741	−	0.537797i
$773$	−26.4142	−	19.1910i	−0.950051	−	0.690252i	0.000767914	−	1.00000i	$-0.499756\pi$
$773$	−26.4142	−	19.1910i	−0.950051	−	0.690252i	−0.950819	+	0.309747i	$0.899756\pi$
$774$	−64.9589			−2.33490
$775$	46.6282	+	12.3417i	1.67493	+	0.443327i
$776$	2.79096			0.100190
$777$	1.67890	+	1.21979i	0.0602303	+	0.0437599i
$778$	−0.230691	−	0.709993i	−0.00827066	−	0.0254545i
$779$	0.660602	+	2.03312i	0.0236685	+	0.0728442i
$780$	−18.6442	+	10.1598i	−0.667568	+	0.363779i
$781$	0.552495	−	1.70040i	0.0197698	−	0.0608452i
$782$	−12.0636			−0.431394
$783$	16.0236	−	49.3157i	0.572638	−	1.76240i
$784$	5.61509	−	4.07960i	0.200539	−	0.145700i
$785$	21.8409	+	20.6631i	0.779536	+	0.737497i
$786$	20.6606	+	15.0108i	0.736940	+	0.535418i
$787$	−2.45448	+	1.78328i	−0.0874926	+	0.0635671i	−0.630672	−	0.776050i	$-0.717220\pi$
$787$	−2.45448	+	1.78328i	−0.0874926	+	0.0635671i	0.543179	+	0.839617i	$0.317220\pi$
$788$	−8.24909	+	5.99332i	−0.293862	+	0.213503i
$789$	−71.9343	−	52.2633i	−2.56093	−	1.86062i
$790$	1.25572	−	0.684282i	0.0446765	−	0.0243457i
$791$	1.99434	−	1.44897i	0.0709107	−	0.0515196i
$792$	2.24120	−	6.89771i	0.0796377	−	0.245100i
$793$	15.0094			0.532999
$794$	1.32540	−	4.07915i	0.0470366	−	0.144764i
$795$	8.86074	+	1.15280i	0.314258	+	0.0408855i
$796$	−1.00639	−	3.09736i	−0.0356707	−	0.109783i
$797$	7.17729	+	22.0894i	0.254233	+	0.782448i	0.993980	+	0.109563i	$0.0349451\pi$
$797$	7.17729	+	22.0894i	0.254233	+	0.782448i	−0.739747	+	0.672885i	$0.765055\pi$
$798$	−0.619683	−	0.450226i	−0.0219365	−	0.0159378i
$799$	−37.3194			−1.32027
$800$	−0.276905	−	4.99233i	−0.00979007	−	0.176505i
$801$	118.731			4.19514
$802$	−12.5474	−	9.11623i	−0.443064	−	0.321905i
$803$	−3.76198	−	11.5782i	−0.132757	−	0.408585i
$804$	−9.05932	−	27.8817i	−0.319497	−	0.983312i
$805$	0.219687	+	1.17532i	0.00774293	+	0.0414245i
$806$	9.00421	−	27.7121i	0.317160	−	0.976117i
$807$	−38.9015			−1.36940
$808$	2.13340	−	6.56593i	0.0750528	−	0.230989i
$809$	10.8474	−	7.88110i	0.381375	−	0.277085i	−0.380537	−	0.924766i	$-0.624261\pi$
$809$	10.8474	−	7.88110i	0.381375	−	0.277085i	0.761912	+	0.647681i	$0.224261\pi$
$810$	39.2998	+	5.11296i	1.38085	+	0.179651i
$811$	34.1868	+	24.8381i	1.20046	+	0.872185i	0.994330	−	0.106340i	$-0.0339132\pi$
$811$	34.1868	+	24.8381i	1.20046	+	0.872185i	0.206129	+	0.978525i	$0.433913\pi$
$812$	0.837410	−	0.608414i	0.0293873	−	0.0213511i
$813$	80.0726	−	58.1761i	2.80827	−	2.04033i
$814$	−2.30969	−	1.67809i	−0.0809545	−	0.0588169i
$815$	6.62397	+	0.861789i	0.232027	+	0.0301872i
$816$	−13.9804	+	10.1574i	−0.489412	+	0.355578i
$817$	2.91650	−	8.97607i	0.102035	−	0.314033i
$818$	−1.08667			−0.0379945
$819$	1.56530	−	4.81749i	0.0546960	−	0.168337i
$820$	−0.878281	−	4.69878i	−0.0306709	−	0.164089i
$821$	−3.37762	−	10.3952i	−0.117880	−	0.362796i	0.874657	−	0.484742i	$-0.161087\pi$
$821$	−3.37762	−	10.3952i	−0.117880	−	0.362796i	−0.992537	+	0.121946i	$0.961087\pi$
$822$	−15.4226	−	47.4660i	−0.537927	−	1.65557i
$823$	1.87280	+	1.36067i	0.0652817	+	0.0474299i	0.619947	−	0.784643i	$-0.287154\pi$
$823$	1.87280	+	1.36067i	0.0652817	+	0.0474299i	−0.554666	+	0.832073i	$0.687154\pi$
$824$	−16.4844			−0.574262
$825$	−16.0119	−	4.23810i	−0.557464	−	0.147552i
$826$	−3.11074			−0.108237
$827$	36.7231	+	26.6809i	1.27699	+	0.927787i	0.999458	−	0.0329302i	$-0.0104839\pi$
$827$	36.7231	+	26.6809i	1.27699	+	0.927787i	0.277531	+	0.960717i	$0.410484\pi$
$828$	4.66762	+	14.3654i	0.162211	+	0.499234i
$829$	4.85102	+	14.9299i	0.168483	+	0.518537i	0.999276	−	0.0380442i	$-0.0121128\pi$
$829$	4.85102	+	14.9299i	0.168483	+	0.518537i	−0.830793	+	0.556581i	$0.812113\pi$
$830$	−24.4012	−	3.17463i	−0.846977	−	0.110193i
$831$	−6.70450	+	20.6343i	−0.232576	+	0.715797i
$832$	−3.02052			−0.104718
$833$	−11.7898	+	36.2852i	−0.408491	+	1.25721i
$834$	−32.0781	+	23.3061i	−1.11077	+	0.807025i
$835$	−3.57970	+	1.95069i	−0.123881	+	0.0675065i
$836$	0.852506	+	0.619382i	0.0294845	+	0.0214218i
$837$	−95.2603	+	69.2106i	−3.29268	+	2.39227i
$838$	−0.183838	+	0.133566i	−0.00635057	+	0.00461396i
$839$	33.6517	+	24.4494i	1.16179	+	0.844087i	0.990003	−	0.141048i	$-0.0450470\pi$
$839$	33.6517	+	24.4494i	1.16179	+	0.844087i	0.171784	+	0.985135i	$0.445047\pi$
$840$	1.24419	+	1.17709i	0.0429286	+	0.0406135i
$841$	8.86090	−	6.43782i	0.305548	−	0.221994i
$842$	−9.21680	+	28.3664i	−0.317632	+	0.977570i
$843$	100.974			3.47774
$844$	−2.18681	+	6.73031i	−0.0752731	+	0.231667i
$845$	−7.61132	+	4.14765i	−0.261837	+	0.142683i
$846$	14.4395	+	44.4403i	0.496441	+	1.52789i
$847$	0.744621	+	2.29171i	0.0255855	+	0.0787440i
$848$	1.02837	+	0.747155i	0.0353144	+	0.0256574i
$849$	84.1174			2.88690
$850$	17.3619	+	21.3069i	0.595507	+	0.730821i
$851$	5.94579			0.203819
$852$	4.31521	+	3.13518i	0.147837	+	0.107410i
$853$	16.7672	+	51.6042i	0.574099	+	1.76689i	0.639229	+	0.769017i	$0.279254\pi$
$853$	16.7672	+	51.6042i	0.574099	+	1.76689i	−0.0651300	+	0.997877i	$0.520746\pi$
$854$	−0.374143	−	1.15149i	−0.0128029	−	0.0394033i
$855$	−6.60446	+	13.9011i	−0.225868	+	0.475406i
$856$	−0.667689	+	2.05494i	−0.0228211	+	0.0702363i
$857$	−21.6636			−0.740013			−0.370007	−	0.929029i	$-0.620645\pi$
$857$	−21.6636			−0.740013			−0.370007	+	0.929029i	$0.620645\pi$
$858$	−3.09201	+	9.51624i	−0.105560	+	0.324879i
$859$	−21.7551	+	15.8060i	−0.742276	+	0.539295i	−0.893423	−	0.449216i	$-0.851703\pi$
$859$	−21.7551	+	15.8060i	−0.742276	+	0.539295i	0.151147	+	0.988511i	$0.451703\pi$
$860$	−9.05645	+	19.0620i	−0.308822	+	0.650008i
$861$	1.32473	+	0.962473i	0.0451467	+	0.0328010i
$862$	−30.8079	+	22.3832i	−1.04932	+	0.762376i
$863$	−41.2196	+	29.9478i	−1.40313	+	1.01944i	−0.408856	+	0.912599i	$0.634072\pi$
$863$	−41.2196	+	29.9478i	−1.40313	+	1.01944i	−0.994277	+	0.106837i	$0.965928\pi$
$864$	9.87484	+	7.17449i	0.335949	+	0.244081i
$865$	0.327009	+	1.74949i	0.0111186	+	0.0594845i
$866$	−18.1358	+	13.1764i	−0.616280	+	0.447753i
$867$	12.8394	−	39.5157i	0.436049	−	1.34202i
$868$	−2.35048			−0.0797804
$869$	0.208253	−	0.640937i	0.00706450	−	0.0217423i
$870$	−21.6930	−	20.5231i	−0.735460	−	0.695798i
$871$	8.70440	+	26.7894i	0.294937	+	0.907724i
$872$	−3.31056	−	10.1889i	−0.112110	−	0.345039i
$873$	15.5407	+	11.2910i	0.525973	+	0.382142i
$874$	−2.19459			−0.0742331
$875$	1.75969	−	2.07952i	0.0594885	−	0.0703007i
$876$	36.3189			1.22710
$877$	12.5483	+	9.11691i	0.423728	+	0.307856i	0.779136	−	0.626855i	$-0.215658\pi$
$877$	12.5483	+	9.11691i	0.423728	+	0.307856i	−0.355408	+	0.934711i	$0.615658\pi$
$878$	−7.94996	−	24.4674i	−0.268298	−	0.825736i
$879$	−22.5347	−	69.3546i	−0.760076	−	2.33927i
$880$	−1.71165	−	1.61934i	−0.0576996	−	0.0545879i
$881$	1.74150	−	5.35978i	0.0586725	−	0.180575i	−0.917425	−	0.397909i	$-0.869736\pi$
$881$	1.74150	−	5.35978i	0.0586725	−	0.180575i	0.976097	+	0.217334i	$0.0697360\pi$
$882$	47.7703			1.60851
$883$	7.83488	−	24.1133i	0.263665	−	0.811476i	−0.728334	−	0.685223i	$-0.759705\pi$
$883$	7.83488	−	24.1133i	0.263665	−	0.811476i	0.991998	−	0.126253i	$-0.0402952\pi$
$884$	13.4327	−	9.75942i	0.451790	−	0.328245i
$885$	16.4894	+	88.2177i	0.554284	+	2.96541i
$886$	8.44113	+	6.13284i	0.283585	+	0.206037i
$887$	−13.4522	+	9.77363i	−0.451682	+	0.328166i	−0.790260	−	0.612772i	$-0.790054\pi$
$887$	−13.4522	+	9.77363i	−0.451682	+	0.328166i	0.338577	+	0.940939i	$0.390054\pi$
$888$	6.89051	−	5.00625i	0.231230	−	0.167999i
$889$	−1.23266	−	0.895580i	−0.0413421	−	0.0300368i
$890$	16.5532	−	34.8411i	0.554864	−	1.16788i
$891$	15.1094	−	10.9776i	0.506184	−	0.367764i
$892$	3.58050	−	11.0196i	0.119884	−	0.368965i
$893$	−6.78908			−0.227188
$894$	−11.1195	+	34.2222i	−0.371891	+	1.14456i
$895$	14.6709	−	30.8792i	0.490394	−	1.03218i
$896$	0.0752933	+	0.231729i	0.00251537	+	0.00774153i
$897$	−6.43955	−	19.8189i	−0.215010	−	0.661733i
$898$	−16.2766	−	11.8257i	−0.543158	−	0.394627i
$899$	40.9815			1.36681
$900$	18.6548	−	28.9186i	0.621828	−	0.963954i
$901$	−6.98740			−0.232784
$902$	−1.82245	−	1.32408i	−0.0606808	−	0.0440872i
$903$	−2.23395	−	6.87540i	−0.0743413	−	0.228799i
$904$	−3.12644	−	9.62220i	−0.103984	−	0.320029i
$905$	33.7390	−	18.3854i	1.12152	−	0.611152i
$906$	−9.85266	+	30.3234i	−0.327333	+	1.00743i
$907$	52.2533			1.73504			0.867521	−	0.497400i	$-0.165712\pi$
$907$	52.2533			1.73504			0.867521	+	0.497400i	$0.165712\pi$
$908$	−0.277310	+	0.853472i	−0.00920285	+	0.0283235i
$909$	38.4421	−	27.9298i	1.27504	−	0.926373i
$910$	−1.19545	−	1.13098i	−0.0396287	−	0.0374915i
$911$	5.24306	+	3.80931i	0.173710	+	0.126208i	0.671243	−	0.741237i	$-0.265761\pi$
$911$	5.24306	+	3.80931i	0.173710	+	0.126208i	−0.497533	+	0.867445i	$0.665761\pi$
$912$	−2.54329	+	1.84781i	−0.0842167	+	0.0611870i
$913$	−9.38140	+	6.81599i	−0.310479	+	0.225576i
$914$	15.6263	+	11.3532i	0.516873	+	0.375530i
$915$	−30.6720	+	16.7142i	−1.01399	+	0.552553i
$916$	−22.6004	+	16.4202i	−0.746739	+	0.542538i
$917$	−0.611652	+	1.88247i	−0.0201985	+	0.0621647i
$918$	−67.0959			−2.21450
$919$	−2.13422	+	6.56847i	−0.0704016	+	0.216674i	−0.980067	−	0.198669i	$-0.936338\pi$
$919$	−2.13422	+	6.56847i	−0.0704016	+	0.216674i	0.909665	+	0.415342i	$0.136338\pi$
$920$	4.86624	+	0.633106i	0.160435	+	0.0208729i
$921$	0.172296	+	0.530272i	0.00567734	+	0.0174731i
$922$	−9.66543	−	29.7471i	−0.318314	−	0.979670i
$923$	−4.14615	−	3.01236i	−0.136472	−	0.0991529i
$924$	0.807145			0.0265531
$925$	−8.55713	−	10.5015i	−0.281357	−	0.345288i
$926$	15.2659			0.501670
$927$	−91.7889	−	66.6885i	−3.01474	−	2.19034i
$928$	−1.31277	−	4.04029i	−0.0430938	−	0.132629i
$929$	−7.90168	−	24.3189i	−0.259246	−	0.797877i	−0.992963	−	0.118422i	$-0.962216\pi$
$929$	−7.90168	−	24.3189i	−0.259246	−	0.797877i	0.733717	−	0.679455i	$-0.237784\pi$
$930$	12.4594	+	66.6573i	0.408558	+	2.18578i
$931$	−2.14477	+	6.60093i	−0.0702921	+	0.216337i
$932$	−18.6888			−0.612171
$933$	12.7812	−	39.3366i	0.418439	−	1.28782i
$934$	5.23855	−	3.80603i	0.171411	−	0.124537i
$935$	12.8441	+	1.67104i	0.420047	+	0.0546488i
$936$	−16.8189	−	12.2197i	−0.549744	−	0.399412i
$937$	12.0113	−	8.72674i	0.392393	−	0.285090i	−0.374042	−	0.927412i	$-0.622029\pi$
$937$	12.0113	−	8.72674i	0.392393	−	0.285090i	0.766435	+	0.642321i	$0.222029\pi$
$938$	1.83826	−	1.33557i	0.0600213	−	0.0436080i
$939$	40.9889	+	29.7802i	1.33762	+	0.971840i
$940$	15.0540	+	1.95855i	0.491007	+	0.0638808i
$941$	−12.1617	+	8.83600i	−0.396460	+	0.288045i	−0.768098	−	0.640333i	$-0.778796\pi$
$941$	−12.1617	+	8.83600i	−0.396460	+	0.288045i	0.371637	+	0.928378i	$0.378796\pi$
$942$	−13.0622	+	40.2014i	−0.425590	+	1.30983i
$943$	4.69149			0.152776
$944$	−3.94523	+	12.1422i	−0.128406	+	0.395194i
$945$	1.22186	+	6.53694i	0.0397472	+	0.212647i
$946$	3.07328	+	9.45857i	0.0999208	+	0.307525i
$947$	3.05406	+	9.39942i	0.0992435	+	0.305440i	0.988336	−	0.152287i	$-0.0486637\pi$
$947$	3.05406	+	9.39942i	0.0992435	+	0.305440i	−0.889093	+	0.457727i	$0.848664\pi$
$948$	1.62654	+	1.18175i	0.0528276	+	0.0383815i
$949$	−34.8960			−1.13277
$950$	3.15844	+	3.87612i	0.102473	+	0.125758i
$951$	−74.3122			−2.40974
$952$	−1.08357	−	0.787258i	−0.0351186	−	0.0255152i
$953$	14.4720	+	44.5401i	0.468793	+	1.44280i	0.854149	+	0.520028i	$0.174079\pi$
$953$	14.4720	+	44.5401i	0.468793	+	1.44280i	−0.385356	+	0.922768i	$0.625921\pi$
$954$	2.70354	+	8.32065i	0.0875305	+	0.269391i
$955$	28.2142	+	3.67071i	0.912988	+	0.118781i
$956$	−0.751097	+	2.31164i	−0.0242922	+	0.0747638i
$957$	−14.0729			−0.454913
$958$	−8.98382	+	27.6494i	−0.290254	+	0.893310i
$959$	3.12947	−	2.27369i	0.101056	−	0.0734213i
$960$	6.17250	−	3.36359i	0.199217	−	0.108559i
$961$	−50.2077	−	36.4780i	−1.61960	−	1.17671i
$962$	−6.62056	+	4.81012i	−0.213456	+	0.155085i
$963$	−12.0312	+	8.74117i	−0.387700	+	0.281680i
$964$	3.60827	+	2.62156i	0.116214	+	0.0844347i
$965$	−25.5209	−	24.1446i	−0.821546	−	0.777241i
$966$	−1.35995	+	0.988062i	−0.0437557	+	0.0317904i
$967$	5.61188	−	17.2716i	0.180466	−	0.555417i	−0.819375	−	0.573258i	$-0.805679\pi$
$967$	5.61188	−	17.2716i	0.180466	−	0.555417i	0.999841	+	0.0178412i	$0.00567934\pi$
$968$	9.88960			0.317864
$969$	5.34004	−	16.4349i	0.171547	−	0.527966i
$970$	5.47995	−	2.98620i	0.175951	−	0.0958811i
$971$	−12.0052	−	36.9482i	−0.385265	−	1.18572i	−0.936288	−	0.351234i	$-0.885762\pi$
$971$	−12.0052	−	36.9482i	−0.385265	−	1.18572i	0.551022	−	0.834491i	$-0.314238\pi$
$972$	5.90194	+	18.1643i	0.189305	+	0.582621i
$973$	−2.48625	−	1.80637i	−0.0797056	−	0.0579095i
$974$	24.7672			0.793594
$975$	−25.7366	+	39.8968i	−0.824232	+	1.27772i
$976$	−4.96914			−0.159058
$977$	−14.4494	−	10.4981i	−0.462277	−	0.335864i	0.332147	−	0.943228i	$-0.392227\pi$
$977$	−14.4494	−	10.4981i	−0.462277	−	0.335864i	−0.794424	+	0.607364i	$0.792227\pi$
$978$	2.90201	+	8.93146i	0.0927959	+	0.285596i
$979$	−5.61727	−	17.2882i	−0.179529	−	0.552532i
$980$	6.66005	−	14.0180i	0.212747	−	0.447790i
$981$	22.7856	−	70.1270i	0.727489	−	2.23898i
$982$	−10.3079			−0.328939
$983$	8.30659	−	25.5650i	0.264939	−	0.815398i	−0.726768	−	0.686883i	$-0.758979\pi$
$983$	8.30659	−	25.5650i	0.264939	−	0.815398i	0.991707	−	0.128516i	$-0.0410213\pi$
$984$	5.43692	−	3.95016i	0.173323	−	0.125926i
$985$	−9.78424	+	20.5938i	−0.311752	+	0.656174i
$986$	18.8924	+	13.7262i	0.601658	+	0.437130i
$987$	−4.20708	+	3.05662i	−0.133913	+	0.0972934i
$988$	2.44365	−	1.77542i	0.0777429	−	0.0564835i
$989$	−16.7568	−	12.1745i	−0.532835	−	0.387127i
$990$	−2.97971	−	15.9414i	−0.0947015	−	0.506651i
$991$	29.9853	−	21.7856i	0.952515	−	0.692042i	0.00111440	−	0.999999i	$-0.499645\pi$
$991$	29.9853	−	21.7856i	0.952515	−	0.692042i	0.951400	+	0.307957i	$0.0996453\pi$
$992$	−2.98101	+	9.17462i	−0.0946473	+	0.291294i
$993$	−74.4737			−2.36335
$994$	−0.127751	+	0.393176i	−0.00405200	+	0.0124708i
$995$	−5.29005	−	5.00477i	−0.167706	−	0.158662i
$996$	−10.6903	−	32.9014i	−0.338736	−	1.04252i
$997$	10.7978	+	33.2321i	0.341969	+	1.05247i	0.963187	+	0.268833i	$0.0866381\pi$
$997$	10.7978	+	33.2321i	0.341969	+	1.05247i	−0.621218	+	0.783638i	$0.713362\pi$
$998$	20.1999	+	14.6761i	0.639418	+	0.464564i
$999$	33.0695			1.04627

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.h.e.191.11	✓	44
25.11	even	5	inner	950.2.h.e.761.11	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.h.e.191.11	✓	44	1.1	even	1	trivial
950.2.h.e.761.11	yes	44	25.11	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.971450 + 2.98981i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.62433 + 1.53673i) q^{5} +(-0.971450 + 2.98981i) q^{6} -0.243654 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-5.56823 + 4.04555i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.971450 + 2.98981i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.62433 + 1.53673i) q^{5} +(-0.971450 + 2.98981i) q^{6} -0.243654 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-5.56823 + 4.04555i) q^{9} +(0.410843 + 2.19800i) q^{10} +(0.852506 + 0.619382i) q^{11} +(-2.54329 + 1.84781i) q^{12} +(2.44365 - 1.77542i) q^{13} +(-0.197121 - 0.143216i) q^{14} +(-3.01659 + 6.34931i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.69866 - 5.22794i) q^{17} -6.88271 q^{18} +(0.309017 - 0.951057i) q^{19} +(-0.959574 + 2.01971i) q^{20} +(-0.236698 - 0.728481i) q^{21} +(0.325628 + 1.00218i) q^{22} +(-1.77546 - 1.28995i) q^{23} -3.14368 q^{24} +(0.276905 + 4.99233i) q^{25} +3.02052 q^{26} +(-9.87484 - 7.17449i) q^{27} +(-0.0752933 - 0.231729i) q^{28} +(1.31277 + 4.04029i) q^{29} +(-6.17250 + 3.36359i) q^{30} +(2.98101 - 9.17462i) q^{31} -1.00000 q^{32} +(-1.02367 + 3.15053i) q^{33} +(4.44715 - 3.23104i) q^{34} +(-0.395775 - 0.374432i) q^{35} +(-5.56823 - 4.04555i) q^{36} +(-2.19186 + 1.59248i) q^{37} +(0.809017 - 0.587785i) q^{38} +(7.68205 + 5.58133i) q^{39} +(-1.96347 + 1.06995i) q^{40} +(-1.72948 + 1.25654i) q^{41} +(0.236698 - 0.728481i) q^{42} +9.43799 q^{43} +(-0.325628 + 1.00218i) q^{44} +(-15.2616 - 1.98556i) q^{45} +(-0.678166 - 2.08718i) q^{46} +(-2.09794 - 6.45680i) q^{47} +(-2.54329 - 1.84781i) q^{48} -6.94063 q^{49} +(-2.71039 + 4.20164i) q^{50} +17.2807 q^{51} +(2.44365 + 1.77542i) q^{52} +(-0.392803 - 1.20892i) q^{53} +(-3.77185 - 11.6086i) q^{54} +(0.432928 + 2.31615i) q^{55} +(0.0752933 - 0.231729i) q^{56} +3.14368 q^{57} +(-1.31277 + 4.04029i) q^{58} +(10.3288 - 7.50428i) q^{59} +(-6.97073 - 0.906903i) q^{60} +(4.02012 + 2.92079i) q^{61} +(7.80440 - 5.67023i) q^{62} +(1.35672 - 0.985717i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(6.69764 + 0.871374i) q^{65} +(-2.68000 + 1.94714i) q^{66} +(-2.88176 + 8.86914i) q^{67} +5.49698 q^{68} +(2.13193 - 6.56142i) q^{69} +(-0.100104 - 0.535553i) q^{70} +(-0.524310 - 1.61366i) q^{71} +(-2.12687 - 6.54584i) q^{72} +(-9.34657 - 6.79068i) q^{73} -2.70929 q^{74} +(-14.6571 + 5.67769i) q^{75} +1.00000 q^{76} +(-0.207717 - 0.150915i) q^{77} +(2.93428 + 9.03079i) q^{78} +(-0.197630 - 0.608241i) q^{79} +(-2.21738 - 0.288485i) q^{80} +(5.47687 - 16.8561i) q^{81} -2.13775 q^{82} +(-3.40058 + 10.4659i) q^{83} +(0.619683 - 0.450226i) q^{84} +(10.7931 - 5.88152i) q^{85} +(7.63550 + 5.54751i) q^{86} +(-10.8044 + 7.84988i) q^{87} +(-0.852506 + 0.619382i) q^{88} +(-13.9560 - 10.1396i) q^{89} +(-11.1798 - 10.5769i) q^{90} +(-0.595406 + 0.432588i) q^{91} +(0.678166 - 2.08718i) q^{92} +30.3263 q^{93} +(2.09794 - 6.45680i) q^{94} +(1.96347 - 1.06995i) q^{95} +(-0.971450 - 2.98981i) q^{96} +(-0.862454 - 2.65436i) q^{97} +(-5.61509 - 4.07960i) q^{98} -7.25268 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9}+O(q^{10}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 5 * q^5 + q^6 + 28 * q^7 + 11 * q^8 - 8 * q^9	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9} + 5 q^{10} - 6 q^{12} - 10 q^{13} + 12 q^{14} - 11 q^{16} - 20 q^{17} - 42 q^{18} - 11 q^{19} + 5 q^{20} - 3 q^{21} - 10 q^{22} - 6 q^{23} - 14 q^{24} - 15 q^{25} - 40 q^{26} + 5 q^{27} - 2 q^{28} + 6 q^{29} - 5 q^{31} - 44 q^{32} - 36 q^{33} - 10 q^{34} - 8 q^{36} - 10 q^{37} + 11 q^{38} + 39 q^{39} - 22 q^{41} + 3 q^{42} + 68 q^{43} + 10 q^{44} + 20 q^{45} + 6 q^{46} + 19 q^{47} - 6 q^{48} + 40 q^{49} - 30 q^{50} + 86 q^{51} - 10 q^{52} + 30 q^{54} + 2 q^{56} + 14 q^{57} - 6 q^{58} - 4 q^{59} + 15 q^{60} + 26 q^{61} - 15 q^{62} - 41 q^{63} - 11 q^{64} + 30 q^{65} - 4 q^{66} - 59 q^{67} + 20 q^{68} - 59 q^{69} - 25 q^{70} + 30 q^{71} + 13 q^{72} - 38 q^{73} - 50 q^{74} - 15 q^{75} + 44 q^{76} + 29 q^{77} + 16 q^{78} + 3 q^{79} + 5 q^{80} - 54 q^{81} - 8 q^{82} + 9 q^{83} + 7 q^{84} + 12 q^{86} - 43 q^{87} + 33 q^{89} - 6 q^{91} - 6 q^{92} + 84 q^{93} - 19 q^{94} + q^{96} + 30 q^{97} - 15 q^{98} - 54 q^{99}+O(q^{100}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 5 * q^5 + q^6 + 28 * q^7 + 11 * q^8 - 8 * q^9 + 5 * q^10 - 6 * q^12 - 10 * q^13 + 12 * q^14 - 11 * q^16 - 20 * q^17 - 42 * q^18 - 11 * q^19 + 5 * q^20 - 3 * q^21 - 10 * q^22 - 6 * q^23 - 14 * q^24 - 15 * q^25 - 40 * q^26 + 5 * q^27 - 2 * q^28 + 6 * q^29 - 5 * q^31 - 44 * q^32 - 36 * q^33 - 10 * q^34 - 8 * q^36 - 10 * q^37 + 11 * q^38 + 39 * q^39 - 22 * q^41 + 3 * q^42 + 68 * q^43 + 10 * q^44 + 20 * q^45 + 6 * q^46 + 19 * q^47 - 6 * q^48 + 40 * q^49 - 30 * q^50 + 86 * q^51 - 10 * q^52 + 30 * q^54 + 2 * q^56 + 14 * q^57 - 6 * q^58 - 4 * q^59 + 15 * q^60 + 26 * q^61 - 15 * q^62 - 41 * q^63 - 11 * q^64 + 30 * q^65 - 4 * q^66 - 59 * q^67 + 20 * q^68 - 59 * q^69 - 25 * q^70 + 30 * q^71 + 13 * q^72 - 38 * q^73 - 50 * q^74 - 15 * q^75 + 44 * q^76 + 29 * q^77 + 16 * q^78 + 3 * q^79 + 5 * q^80 - 54 * q^81 - 8 * q^82 + 9 * q^83 + 7 * q^84 + 12 * q^86 - 43 * q^87 + 33 * q^89 - 6 * q^91 - 6 * q^92 + 84 * q^93 - 19 * q^94 + q^96 + 30 * q^97 - 15 * q^98 - 54 * q^99

Introduction

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