LMFDB - Embedded newform 950.2.n.a.39.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(39,950)]

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([3, 0]))

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

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

chi := DirichletCharacter("950.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.n (of order $10$, 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:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.2
Character	$\chi$	$=$	950.39
Dual form			950.2.n.a.609.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(-2.20724 - 0.717177i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.23210 - 0.133199i) q^{5} +(0.717177 + 2.20724i) q^{6} -2.34643i q^{7} +(0.951057 - 0.309017i) q^{8} +(1.93053 + 1.40261i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(-2.20724 - 0.717177i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.23210 - 0.133199i) q^{5} +(0.717177 + 2.20724i) q^{6} -2.34643i q^{7} +(0.951057 - 0.309017i) q^{8} +(1.93053 + 1.40261i) q^{9} +(-1.41975 - 1.72751i) q^{10} +(-2.20593 + 1.60271i) q^{11} +(1.36415 - 1.87759i) q^{12} +(1.49540 - 2.05824i) q^{13} +(-1.89830 + 1.37919i) q^{14} +(-5.02231 - 1.30681i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.25713 - 1.38322i) q^{17} -2.38627i q^{18} +(0.309017 + 0.951057i) q^{19} +(-0.563076 + 2.16401i) q^{20} +(-1.68280 + 5.17914i) q^{21} +(2.59323 + 0.842592i) q^{22} +(0.161561 + 0.222370i) q^{23} -2.32083 q^{24} +(4.96452 - 0.594625i) q^{25} -2.54413 q^{26} +(0.837221 + 1.15234i) q^{27} +(2.23158 + 0.725086i) q^{28} +(1.14515 - 3.52442i) q^{29} +(1.89481 + 4.83126i) q^{30} +(-1.36274 - 4.19407i) q^{31} +1.00000i q^{32} +(6.01846 - 1.95552i) q^{33} +(-3.62133 - 2.63105i) q^{34} +(-0.312541 - 5.23745i) q^{35} +(-1.93053 + 1.40261i) q^{36} +(3.66815 - 5.04878i) q^{37} +(0.587785 - 0.809017i) q^{38} +(-4.77684 + 3.47058i) q^{39} +(2.08169 - 0.816435i) q^{40} +(-3.03641 - 2.20608i) q^{41} +(5.17914 - 1.68280i) q^{42} -1.88527i q^{43} +(-0.842592 - 2.59323i) q^{44} +(4.49596 + 2.87363i) q^{45} +(0.0849378 - 0.261412i) q^{46} +(0.201454 + 0.0654564i) q^{47} +(1.36415 + 1.87759i) q^{48} +1.49428 q^{49} +(-3.39913 - 3.66687i) q^{50} -10.3885 q^{51} +(1.49540 + 2.05824i) q^{52} +(-6.43885 - 2.09211i) q^{53} +(0.440153 - 1.35465i) q^{54} +(-4.71038 + 3.87122i) q^{55} +(-0.725086 - 2.23158i) q^{56} -2.32083i q^{57} +(-3.52442 + 1.14515i) q^{58} +(-7.18163 - 5.21776i) q^{59} +(2.79483 - 4.37268i) q^{60} +(-11.0754 + 8.04676i) q^{61} +(-2.59208 + 3.56769i) q^{62} +(3.29113 - 4.52985i) q^{63} +(0.809017 - 0.587785i) q^{64} +(3.06373 - 4.79339i) q^{65} +(-5.11961 - 3.71961i) q^{66} +(-8.93514 + 2.90320i) q^{67} +4.47621i q^{68} +(-0.197127 - 0.606693i) q^{69} +(-4.05348 + 3.33135i) q^{70} +(-2.80809 + 8.64243i) q^{71} +(2.26948 + 0.737398i) q^{72} +(-4.43376 - 6.10254i) q^{73} -6.24063 q^{74} +(-11.3844 - 2.24795i) q^{75} -1.00000 q^{76} +(3.76063 + 5.17606i) q^{77} +(5.61552 + 1.82459i) q^{78} +(4.09924 - 12.6162i) q^{79} +(-1.88410 - 1.20423i) q^{80} +(-3.23372 - 9.95236i) q^{81} +3.75321i q^{82} +(3.06707 - 0.996553i) q^{83} +(-4.40564 - 3.20088i) q^{84} +(9.31808 - 3.65453i) q^{85} +(-1.52522 + 1.10814i) q^{86} +(-5.05527 + 6.95798i) q^{87} +(-1.60271 + 2.20593i) q^{88} +(2.82756 - 2.05434i) q^{89} +(-0.317848 - 5.32639i) q^{90} +(-4.82952 - 3.50885i) q^{91} +(-0.261412 + 0.0849378i) q^{92} +10.2347i q^{93} +(-0.0654564 - 0.201454i) q^{94} +(0.816435 + 2.08169i) q^{95} +(0.717177 - 2.20724i) q^{96} +(-10.4003 - 3.37925i) q^{97} +(-0.878319 - 1.20890i) q^{98} -6.50661 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9}+O(q^{10}) $ 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9	$ 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9} + 26 q^{11} + 10 q^{12} - 10 q^{14} + 12 q^{15} - 22 q^{16} - 40 q^{17} - 22 q^{19} + 10 q^{23} + 8 q^{24} + 6 q^{25} - 28 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} - 4 q^{30} + 2 q^{31} - 8 q^{34} - 48 q^{35} - 24 q^{36} + 50 q^{37} + 8 q^{39} + 32 q^{41} + 10 q^{42} + 4 q^{44} - 8 q^{45} + 10 q^{46} + 10 q^{48} - 56 q^{49} + 28 q^{50} - 60 q^{51} - 70 q^{53} - 8 q^{54} + 4 q^{55} + 10 q^{56} - 60 q^{58} - 28 q^{59} - 12 q^{60} - 58 q^{61} + 60 q^{63} + 22 q^{64} - 24 q^{65} + 4 q^{66} - 70 q^{67} - 8 q^{69} - 4 q^{70} + 48 q^{71} + 40 q^{73} + 52 q^{74} + 108 q^{75} - 88 q^{76} - 50 q^{78} - 20 q^{79} + 24 q^{81} - 80 q^{83} + 30 q^{85} + 20 q^{86} + 70 q^{87} + 10 q^{88} - 62 q^{89} - 104 q^{90} + 20 q^{91} - 10 q^{92} - 10 q^{94} + 2 q^{96} - 10 q^{97} + 60 q^{98} + 156 q^{99}+O(q^{100}) $ 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9 + 26 * q^11 + 10 * q^12 - 10 * q^14 + 12 * q^15 - 22 * q^16 - 40 * q^17 - 22 * q^19 + 10 * q^23 + 8 * q^24 + 6 * q^25 - 28 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 - 4 * q^30 + 2 * q^31 - 8 * q^34 - 48 * q^35 - 24 * q^36 + 50 * q^37 + 8 * q^39 + 32 * q^41 + 10 * q^42 + 4 * q^44 - 8 * q^45 + 10 * q^46 + 10 * q^48 - 56 * q^49 + 28 * q^50 - 60 * q^51 - 70 * q^53 - 8 * q^54 + 4 * q^55 + 10 * q^56 - 60 * q^58 - 28 * q^59 - 12 * q^60 - 58 * q^61 + 60 * q^63 + 22 * q^64 - 24 * q^65 + 4 * q^66 - 70 * q^67 - 8 * q^69 - 4 * q^70 + 48 * q^71 + 40 * q^73 + 52 * q^74 + 108 * q^75 - 88 * q^76 - 50 * q^78 - 20 * q^79 + 24 * q^81 - 80 * q^83 + 30 * q^85 + 20 * q^86 + 70 * q^87 + 10 * q^88 - 62 * q^89 - 104 * q^90 + 20 * q^91 - 10 * q^92 - 10 * q^94 + 2 * q^96 - 10 * q^97 + 60 * q^98 + 156 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$	−2.20724	−	0.717177i	−1.27435	−	0.414062i	−0.407765	−	0.913087i	$-0.633692\pi$
$3$	−2.20724	−	0.717177i	−1.27435	−	0.414062i	−0.866588	+	0.499024i	$0.833692\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	2.23210	−	0.133199i	0.998224	−	0.0595683i
$5$	2.23210	−	0.133199i	0.998224	−	0.0595683i
$6$	0.717177	+	2.20724i	0.292786	+	0.901104i
$7$		−	2.34643i		−	0.886866i	−0.896308	−	0.443433i	$-0.853760\pi$
$7$		−	2.34643i		−	0.886866i	0.896308	−	0.443433i	$-0.146240\pi$
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	1.93053	+	1.40261i	0.643511	+	0.467538i
$10$	−1.41975	−	1.72751i	−0.448966	−	0.546287i
$11$	−2.20593	+	1.60271i	−0.665114	+	0.483234i	−0.868386	−	0.495888i	$-0.834842\pi$
$11$	−2.20593	+	1.60271i	−0.665114	+	0.483234i	0.203272	+	0.979122i	$0.434842\pi$
$12$	1.36415	−	1.87759i	0.393797	−	0.542015i
$13$	1.49540	−	2.05824i	0.414750	−	0.570854i	−0.549619	−	0.835415i	$-0.685227\pi$
$13$	1.49540	−	2.05824i	0.414750	−	0.570854i	0.964369	+	0.264561i	$0.0852271\pi$
$14$	−1.89830	+	1.37919i	−0.507342	+	0.368605i
$15$	−5.02231	−	1.30681i	−1.29676	−	0.337416i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	4.25713	−	1.38322i	1.03250	−	0.335481i	0.256725	−	0.966485i	$-0.417357\pi$
$17$	4.25713	−	1.38322i	1.03250	−	0.335481i	0.775780	+	0.631003i	$0.217357\pi$
$18$		−	2.38627i		−	0.562449i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$20$	−0.563076	+	2.16401i	−0.125908	+	0.483888i
$21$	−1.68280	+	5.17914i	−0.367218	+	1.13018i
$22$	2.59323	+	0.842592i	0.552879	+	0.179641i
$23$	0.161561	+	0.222370i	0.0336879	+	0.0463674i	0.825529	−	0.564360i	$-0.190877\pi$
$23$	0.161561	+	0.222370i	0.0336879	+	0.0463674i	−0.791841	+	0.610728i	$0.790877\pi$
$24$	−2.32083			−0.473738
$25$	4.96452	−	0.594625i	0.992903	−	0.118925i
$26$	−2.54413			−0.498945
$27$	0.837221	+	1.15234i	0.161123	+	0.221767i
$28$	2.23158	+	0.725086i	0.421730	+	0.137028i
$29$	1.14515	−	3.52442i	0.212650	−	0.654469i	−0.786662	−	0.617384i	$-0.788193\pi$
$29$	1.14515	−	3.52442i	0.212650	−	0.654469i	0.999312	−	0.0370853i	$-0.0118073\pi$
$30$	1.89481	+	4.83126i	0.345944	+	0.882063i
$31$	−1.36274	−	4.19407i	−0.244755	−	0.753278i	−0.995677	−	0.0928867i	$-0.970391\pi$
$31$	−1.36274	−	4.19407i	−0.244755	−	0.753278i	0.750922	−	0.660391i	$-0.229609\pi$
$32$			1.00000i			0.176777i
$33$	6.01846	−	1.95552i	1.04768	−	0.340412i
$34$	−3.62133	−	2.63105i	−0.621053	−	0.451221i
$35$	−0.312541	−	5.23745i	−0.0528291	−	0.885291i
$36$	−1.93053	+	1.40261i	−0.321755	+	0.233769i
$37$	3.66815	−	5.04878i	0.603040	−	0.830014i	−0.392942	−	0.919563i	$-0.628543\pi$
$37$	3.66815	−	5.04878i	0.603040	−	0.830014i	0.995982	+	0.0895493i	$0.0285427\pi$
$38$	0.587785	−	0.809017i	0.0953514	−	0.131240i
$39$	−4.77684	+	3.47058i	−0.764907	+	0.555737i
$40$	2.08169	−	0.816435i	0.329144	−	0.129090i
$41$	−3.03641	−	2.20608i	−0.474208	−	0.344532i	0.324871	−	0.945758i	$-0.394679\pi$
$41$	−3.03641	−	2.20608i	−0.474208	−	0.344532i	−0.799079	+	0.601226i	$0.794679\pi$
$42$	5.17914	−	1.68280i	0.799158	−	0.259662i
$43$		−	1.88527i		−	0.287502i	−0.989614	−	0.143751i	$-0.954084\pi$
$43$		−	1.88527i		−	0.287502i	0.989614	−	0.143751i	$-0.0459164\pi$
$44$	−0.842592	−	2.59323i	−0.127026	−	0.390944i
$45$	4.49596	+	2.87363i	0.670219	+	0.428375i
$46$	0.0849378	−	0.261412i	0.0125234	−	0.0385431i
$47$	0.201454	+	0.0654564i	0.0293851	+	0.00954780i	0.323673	−	0.946169i	$-0.395082\pi$
$47$	0.201454	+	0.0654564i	0.0293851	+	0.00954780i	−0.294288	+	0.955717i	$0.595082\pi$
$48$	1.36415	+	1.87759i	0.196898	+	0.271007i
$49$	1.49428			0.213469
$50$	−3.39913	−	3.66687i	−0.480710	−	0.518573i
$51$	−10.3885			−1.45469
$52$	1.49540	+	2.05824i	0.207375	+	0.285427i
$53$	−6.43885	−	2.09211i	−0.884445	−	0.287373i	−0.168643	−	0.985677i	$-0.553939\pi$
$53$	−6.43885	−	2.09211i	−0.884445	−	0.287373i	−0.715802	+	0.698304i	$0.753939\pi$
$54$	0.440153	−	1.35465i	0.0598973	−	0.184345i
$55$	−4.71038	+	3.87122i	−0.635148	+	0.521995i
$56$	−0.725086	−	2.23158i	−0.0968936	−	0.298208i
$57$		−	2.32083i		−	0.307402i
$58$	−3.52442	+	1.14515i	−0.462779	+	0.150366i
$59$	−7.18163	−	5.21776i	−0.934969	−	0.679295i	0.0122355	−	0.999925i	$-0.496105\pi$
$59$	−7.18163	−	5.21776i	−0.934969	−	0.679295i	−0.947204	+	0.320631i	$0.896105\pi$
$60$	2.79483	−	4.37268i	0.360811	−	0.564510i
$61$	−11.0754	+	8.04676i	−1.41806	+	1.03028i	−0.425975	+	0.904735i	$0.640069\pi$
$61$	−11.0754	+	8.04676i	−1.41806	+	1.03028i	−0.992088	+	0.125548i	$0.959931\pi$
$62$	−2.59208	+	3.56769i	−0.329194	+	0.453097i
$63$	3.29113	−	4.52985i	0.414643	−	0.570708i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	3.06373	−	4.79339i	0.380009	−	0.594546i
$66$	−5.11961	−	3.71961i	−0.630180	−	0.457853i
$67$	−8.93514	+	2.90320i	−1.09160	+	0.354683i	−0.798865	−	0.601511i	$-0.794566\pi$
$67$	−8.93514	+	2.90320i	−1.09160	+	0.354683i	−0.292736	+	0.956193i	$0.594566\pi$
$68$			4.47621i			0.542820i
$69$	−0.197127	−	0.606693i	−0.0237313	−	0.0730373i
$70$	−4.05348	+	3.33135i	−0.484484	+	0.398172i
$71$	−2.80809	+	8.64243i	−0.333259	+	1.02567i	0.634314	+	0.773076i	$0.281283\pi$
$71$	−2.80809	+	8.64243i	−0.333259	+	1.02567i	−0.967573	+	0.252591i	$0.918717\pi$
$72$	2.26948	+	0.737398i	0.267460	+	0.0869032i
$73$	−4.43376	−	6.10254i	−0.518932	−	0.714248i	0.466462	−	0.884541i	$-0.345529\pi$
$73$	−4.43376	−	6.10254i	−0.518932	−	0.714248i	−0.985393	+	0.170293i	$0.945529\pi$
$74$	−6.24063			−0.725459
$75$	−11.3844	−	2.24795i	−1.31455	−	0.259571i
$76$	−1.00000			−0.114708
$77$	3.76063	+	5.17606i	0.428564	+	0.589867i
$78$	5.61552	+	1.82459i	0.635832	+	0.206594i
$79$	4.09924	−	12.6162i	0.461201	−	1.41943i	−0.402497	−	0.915421i	$-0.631858\pi$
$79$	4.09924	−	12.6162i	0.461201	−	1.41943i	0.863698	−	0.504009i	$-0.168142\pi$
$80$	−1.88410	−	1.20423i	−0.210648	−	0.134637i
$81$	−3.23372	−	9.95236i	−0.359302	−	1.10582i
$82$			3.75321i			0.414473i
$83$	3.06707	−	0.996553i	0.336655	−	0.109386i	−0.135811	−	0.990735i	$-0.543364\pi$
$83$	3.06707	−	0.996553i	0.336655	−	0.109386i	0.472466	+	0.881349i	$0.343364\pi$
$84$	−4.40564	−	3.20088i	−0.480694	−	0.349245i
$85$	9.31808	−	3.65453i	1.01069	−	0.396390i
$86$	−1.52522	+	1.10814i	−0.164469	+	0.119493i
$87$	−5.05527	+	6.95798i	−0.541982	+	0.745974i
$88$	−1.60271	+	2.20593i	−0.170849	+	0.235153i
$89$	2.82756	−	2.05434i	0.299721	−	0.217760i	−0.427753	−	0.903896i	$-0.640695\pi$
$89$	2.82756	−	2.05434i	0.299721	−	0.217760i	0.727473	+	0.686136i	$0.240695\pi$
$90$	−0.317848	−	5.32639i	−0.0335041	−	0.561450i
$91$	−4.82952	−	3.50885i	−0.506271	−	0.367827i
$92$	−0.261412	+	0.0849378i	−0.0272541	+	0.00885538i
$93$			10.2347i			1.06129i
$94$	−0.0654564	−	0.201454i	−0.00675132	−	0.0207784i
$95$	0.816435	+	2.08169i	0.0837645	+	0.213577i
$96$	0.717177	−	2.20724i	0.0731966	−	0.225276i
$97$	−10.4003	−	3.37925i	−1.05599	−	0.343111i	−0.270971	−	0.962587i	$-0.587345\pi$
$97$	−10.4003	−	3.37925i	−1.05599	−	0.343111i	−0.785015	+	0.619477i	$0.787345\pi$
$98$	−0.878319	−	1.20890i	−0.0887236	−	0.122118i
$99$	−6.50661			−0.653939
$100$	−0.968598	+	4.90528i	−0.0968598	+	0.490528i
$101$	4.81901			0.479509			0.239755	−	0.970834i	$-0.422933\pi$
$101$	4.81901			0.479509			0.239755	+	0.970834i	$0.422933\pi$
$102$	6.10623	+	8.40450i	0.604607	+	0.832170i
$103$	0.196180	+	0.0637426i	0.0193301	+	0.00628074i	0.318666	−	0.947867i	$-0.396765\pi$
$103$	0.196180	+	0.0637426i	0.0193301	+	0.00628074i	−0.299336	+	0.954148i	$0.596765\pi$
$104$	0.786179	−	2.41961i	0.0770912	−	0.237262i
$105$	−3.06633	+	11.7845i	−0.299243	+	1.15005i
$106$	2.09211	+	6.43885i	0.203204	+	0.625397i
$107$		−	12.9005i		−	1.24714i	−0.781768	−	0.623569i	$-0.785682\pi$
$107$		−	12.9005i		−	1.24714i	0.781768	−	0.623569i	$-0.214318\pi$
$108$	−1.35465	+	0.440153i	−0.130351	+	0.0423538i
$109$	−7.44136	−	5.40646i	−0.712753	−	0.517845i	0.171308	−	0.985218i	$-0.445201\pi$
$109$	−7.44136	−	5.40646i	−0.712753	−	0.517845i	−0.884061	+	0.467372i	$0.845201\pi$
$110$	5.90058	+	1.53533i	0.562598	+	0.146388i
$111$	−11.7174	+	8.51317i	−1.11216	+	0.808034i
$112$	−1.37919	+	1.89830i	−0.130322	+	0.179372i
$113$	6.87693	−	9.46528i	0.646927	−	0.890418i	−0.352034	−	0.935987i	$-0.614510\pi$
$113$	6.87693	−	9.46528i	0.646927	−	0.890418i	0.998961	+	0.0455686i	$0.0145100\pi$
$114$	−1.87759	+	1.36415i	−0.175853	+	0.127765i
$115$	0.390240	+	0.474832i	0.0363901	+	0.0442783i
$116$	2.99805	+	2.17821i	0.278362	+	0.202242i
$117$	5.77384	−	1.87604i	0.533792	−	0.173440i
$118$			8.87698i			0.817193i
$119$	−3.24563	−	9.98903i	−0.297527	−	0.915693i
$120$	−5.18033	+	0.309132i	−0.472897	+	0.0282198i
$121$	−1.10170	+	3.39070i	−0.100155	+	0.308245i
$122$	13.0199	+	4.23043i	1.17877	+	0.383006i
$123$	5.11995	+	7.04700i	0.461650	+	0.635407i
$124$	4.40991			0.396021
$125$	11.0021	−	1.98853i	0.984056	−	0.177859i
$126$	−5.59921			−0.498817
$127$	−1.25639	−	1.72927i	−0.111486	−	0.153448i	0.749628	−	0.661860i	$-0.230233\pi$
$127$	−1.25639	−	1.72927i	−0.111486	−	0.153448i	−0.861114	+	0.508412i	$0.830233\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	−1.35208	+	4.16126i	−0.119044	+	0.366378i
$130$	−5.67874	+	0.338875i	−0.498059	+	0.0297213i
$131$	3.88778	+	11.9654i	0.339677	+	1.04542i	0.964372	+	0.264550i	$0.0852233\pi$
$131$	3.88778	+	11.9654i	0.339677	+	1.04542i	−0.624695	+	0.780869i	$0.714777\pi$
$132$			6.32818i			0.550798i
$133$	2.23158	−	0.725086i	0.193503	−	0.0628729i
$134$	7.60068	+	5.52222i	0.656599	+	0.477047i
$135$	2.02225	+	2.46061i	0.174047	+	0.211776i
$136$	3.62133	−	2.63105i	0.310526	−	0.225611i
$137$	−5.42510	+	7.46701i	−0.463498	+	0.637950i	−0.975230	−	0.221195i	$-0.929004\pi$
$137$	−5.42510	+	7.46701i	−0.463498	+	0.637950i	0.511732	+	0.859145i	$0.329004\pi$
$138$	−0.374957	+	0.516084i	−0.0319185	+	0.0439320i
$139$	3.36430	−	2.44430i	0.285356	−	0.207323i	−0.435894	−	0.899998i	$-0.643568\pi$
$139$	3.36430	−	2.44430i	0.285356	−	0.207323i	0.721250	+	0.692675i	$0.243568\pi$
$140$	5.07769	+	1.32122i	0.429143	+	0.111663i
$141$	−0.397715	−	0.288957i	−0.0334936	−	0.0243345i
$142$	8.64243	−	2.80809i	0.725256	−	0.235650i
$143$			6.93704i			0.580104i
$144$	−0.737398	−	2.26948i	−0.0614498	−	0.189123i
$145$	2.08665	−	8.01939i	0.173287	−	0.665974i
$146$	−2.33096	+	7.17397i	−0.192912	+	0.593722i
$147$	−3.29825	−	1.07167i	−0.272035	−	0.0883896i
$148$	3.66815	+	5.04878i	0.301520	+	0.415007i
$149$	4.35251			0.356572			0.178286	−	0.983979i	$-0.442945\pi$
$149$	4.35251			0.356572			0.178286	+	0.983979i	$0.442945\pi$
$150$	4.87292	+	10.5314i	0.397872	+	0.859889i
$151$	−12.0525			−0.980823			−0.490411	−	0.871491i	$-0.663153\pi$
$151$	−12.0525			−0.980823			−0.490411	+	0.871491i	$0.663153\pi$
$152$	0.587785	+	0.809017i	0.0476757	+	0.0656199i
$153$	10.1587	+	3.30075i	0.821278	+	0.266849i
$154$	1.97708	−	6.08483i	0.159318	−	0.490329i
$155$	−3.60041	−	9.18006i	−0.289192	−	0.737360i
$156$	−1.82459	−	5.61552i	−0.146084	−	0.449601i
$157$		−	14.7587i		−	1.17787i	−0.808180	−	0.588936i	$-0.799547\pi$
$157$		−	14.7587i		−	1.17787i	0.808180	−	0.588936i	$-0.200453\pi$
$158$	−12.6162	+	4.09924i	−1.00369	+	0.326118i
$159$	12.7117	+	9.23560i	1.00810	+	0.732431i
$160$	0.133199	+	2.23210i	0.0105303	+	0.176463i
$161$	0.521775	−	0.379092i	0.0411216	−	0.0298766i
$162$	−6.15089	+	8.46598i	−0.483260	+	0.665150i
$163$	10.4356	−	14.3633i	0.817376	−	1.12502i	−0.172767	−	0.984963i	$-0.555271\pi$
$163$	10.4356	−	14.3633i	0.817376	−	1.12502i	0.990143	−	0.140059i	$-0.0447292\pi$
$164$	3.03641	−	2.20608i	0.237104	−	0.172266i
$165$	13.1733	−	5.16655i	1.02554	−	0.402216i
$166$	−2.60901	−	1.89556i	−0.202498	−	0.147124i
$167$	13.8566	−	4.50228i	1.07225	−	0.348397i	0.280889	−	0.959740i	$-0.409371\pi$
$167$	13.8566	−	4.50228i	1.07225	−	0.348397i	0.791365	+	0.611344i	$0.209371\pi$
$168$			5.44567i			0.420142i
$169$	2.01708	+	6.20793i	0.155160	+	0.477533i
$170$	−8.43361	−	5.39040i	−0.646828	−	0.413425i
$171$	−0.737398	+	2.26948i	−0.0563902	+	0.173551i
$172$	1.79300	+	0.582582i	0.136715	+	0.0444214i
$173$	7.80546	+	10.7433i	0.593438	+	0.816798i	0.995088	−	0.0989958i	$-0.0315630\pi$
$173$	7.80546	+	10.7433i	0.593438	+	0.816798i	−0.401650	+	0.915793i	$0.631563\pi$
$174$	8.60054			0.652005
$175$	−1.39524	−	11.6489i	−0.105470	−	0.880572i
$176$	2.72669			0.205532
$177$	12.1096	+	16.6674i	0.910210	+	1.25280i
$178$	−3.32399	−	1.08003i	−0.249144	−	0.0809518i
$179$	2.58909	−	7.96840i	0.193518	−	0.595586i	−0.806473	−	0.591271i	$-0.798626\pi$
$179$	2.58909	−	7.96840i	0.193518	−	0.595586i	0.999991	−	0.00431539i	$-0.00137364\pi$
$180$	−4.12231	+	3.38792i	−0.307259	+	0.252520i
$181$	3.49713	+	10.7631i	0.259939	+	0.800011i	0.992816	+	0.119650i	$0.0381772\pi$
$181$	3.49713	+	10.7631i	0.259939	+	0.800011i	−0.732877	+	0.680361i	$0.761823\pi$
$182$			5.96961i			0.442497i
$183$	30.2171	−	9.81814i	2.23371	−	0.725777i
$184$	0.222370	+	0.161561i	0.0163933	+	0.0119105i
$185$	7.51518	−	11.7580i	0.552527	−	0.864462i
$186$	8.28002	−	6.01579i	0.607120	−	0.441099i
$187$	−7.17404	+	9.87422i	−0.524618	+	0.722075i
$188$	−0.124506	+	0.171367i	−0.00908050	+	0.0124982i
$189$	2.70387	−	1.96448i	0.196678	−	0.142895i
$190$	1.20423	−	1.88410i	0.0873643	−	0.136687i
$191$	14.2409	+	10.3466i	1.03044	+	0.748656i	0.968396	−	0.249417i	$-0.0802390\pi$
$191$	14.2409	+	10.3466i	1.03044	+	0.748656i	0.0620411	+	0.998074i	$0.480239\pi$
$192$	−2.20724	+	0.717177i	−0.159294	+	0.0517578i
$193$		−	5.06648i		−	0.364693i	−0.983234	−	0.182346i	$-0.941631\pi$
$193$		−	5.06648i		−	0.364693i	0.983234	−	0.182346i	$-0.0583692\pi$
$194$	3.37925	+	10.4003i	0.242616	+	0.746695i
$195$	−10.2001	+	8.38294i	−0.730444	+	0.600315i
$196$	−0.461759	+	1.42115i	−0.0329828	+	0.101511i
$197$	−3.00925	−	0.977765i	−0.214400	−	0.0696629i	0.199848	−	0.979827i	$-0.435955\pi$
$197$	−3.00925	−	0.977765i	−0.214400	−	0.0696629i	−0.414248	+	0.910164i	$0.635955\pi$
$198$	3.82449	+	5.26396i	0.271794	+	0.374093i
$199$	17.5583			1.24468			0.622339	−	0.782748i	$-0.286183\pi$
$199$	17.5583			1.24468			0.622339	+	0.782748i	$0.286183\pi$
$200$	4.53779	−	2.09964i	0.320870	−	0.148467i
$201$	21.8041			1.53795
$202$	−2.83254	−	3.89866i	−0.199297	−	0.274309i
$203$	−8.26980	−	2.68702i	−0.580426	−	0.188592i
$204$	3.21023	−	9.88008i	0.224761	−	0.691744i
$205$	−7.07141	−	4.51974i	−0.493889	−	0.315672i
$206$	−0.0637426	−	0.196180i	−0.00444116	−	0.0136685i
$207$			0.655901i			0.0455883i
$208$	−2.41961	+	0.786179i	−0.167770	+	0.0545117i
$209$	−2.20593	−	1.60271i	−0.152588	−	0.110861i
$210$	11.3362	−	4.44603i	0.782271	−	0.306806i
$211$	−15.4888	+	11.2533i	−1.06629	+	0.774707i	−0.975242	−	0.221140i	$-0.929022\pi$
$211$	−15.4888	+	11.2533i	−1.06629	+	0.774707i	−0.0910499	+	0.995846i	$0.529022\pi$
$212$	3.97943	−	5.47722i	0.273308	−	0.376177i
$213$	12.3963	−	17.0620i	0.849380	−	1.16907i
$214$	−10.4367	+	7.58272i	−0.713440	+	0.518344i
$215$	−0.251116	−	4.20811i	−0.0171260	−	0.286991i
$216$	1.15234	+	0.837221i	0.0784066	+	0.0569657i
$217$	−9.84108	+	3.19756i	−0.668056	+	0.217065i
$218$			9.19803i			0.622969i
$219$	5.40978	+	16.6496i	0.365559	+	1.12507i
$220$	−2.22616	−	5.67611i	−0.150088	−	0.382683i
$221$	3.51910	−	10.8307i	0.236720	−	0.728550i
$222$	13.7746	+	4.47564i	0.924491	+	0.300385i
$223$	−15.1271	−	20.8206i	−1.01298	−	1.39425i	−0.917008	−	0.398869i	$-0.869403\pi$
$223$	−15.1271	−	20.8206i	−1.01298	−	1.39425i	−0.0959763	−	0.995384i	$-0.530597\pi$
$224$	2.34643			0.156777
$225$	10.4182	+	5.81536i	0.694546	+	0.387691i
$226$	−11.6997			−0.778254
$227$	10.3692	+	14.2720i	0.688230	+	0.947267i	0.999996	−	0.00289217i	$-0.000920607\pi$
$227$	10.3692	+	14.2720i	0.688230	+	0.947267i	−0.311766	+	0.950159i	$0.600921\pi$
$228$	2.20724	+	0.717177i	0.146178	+	0.0474962i
$229$	−5.15382	+	15.8618i	−0.340574	+	1.04818i	0.623336	+	0.781954i	$0.285777\pi$
$229$	−5.15382	+	15.8618i	−0.340574	+	1.04818i	−0.963911	+	0.266226i	$0.914223\pi$
$230$	0.154770	−	0.594810i	0.0102052	−	0.0392206i
$231$	−4.58847	−	14.1219i	−0.301899	−	0.929151i
$232$		−	3.70580i		−	0.243298i
$233$	15.0015	−	4.87428i	0.982780	−	0.319325i	0.226816	−	0.973938i	$-0.427168\pi$
$233$	15.0015	−	4.87428i	0.982780	−	0.319325i	0.755964	+	0.654613i	$0.227168\pi$
$234$	−4.91153	−	3.56843i	−0.321076	−	0.233276i
$235$	0.458384	+	0.119272i	0.0299017	+	0.00778043i
$236$	7.18163	−	5.21776i	0.467484	−	0.339647i
$237$	−18.0961	+	24.9071i	−1.17547	+	1.61789i
$238$	−6.17356	+	8.49718i	−0.400173	+	0.550790i
$239$	4.86567	−	3.53511i	0.314734	−	0.228668i	−0.419191	−	0.907898i	$-0.637686\pi$
$239$	4.86567	−	3.53511i	0.314734	−	0.228668i	0.733925	+	0.679230i	$0.237686\pi$
$240$	3.29501	+	4.00927i	0.212692	+	0.258797i
$241$	3.87275	+	2.81371i	0.249466	+	0.181247i	0.705490	−	0.708720i	$-0.250727\pi$
$241$	3.87275	+	2.81371i	0.249466	+	0.181247i	−0.456024	+	0.889967i	$0.650727\pi$
$242$	3.39070	−	1.10170i	0.217962	−	0.0708202i
$243$			20.0133i			1.28386i
$244$	−4.23043	−	13.0199i	−0.270826	−	0.833516i
$245$	3.33539	−	0.199037i	0.213090	−	0.0127160i
$246$	2.69172	−	8.28425i	0.171618	−	0.528184i
$247$	2.41961	+	0.786179i	0.153956	+	0.0500234i
$248$	−2.59208	−	3.56769i	−0.164597	−	0.226549i
$249$	−7.48449			−0.474310
$250$	−8.07561	−	7.73204i	−0.510747	−	0.489017i
$251$	−6.18250			−0.390236			−0.195118	−	0.980780i	$-0.562509\pi$
$251$	−6.18250			−0.390236			−0.195118	+	0.980780i	$0.562509\pi$
$252$	3.29113	+	4.52985i	0.207322	+	0.285354i
$253$	−0.712788	−	0.231599i	−0.0448126	−	0.0145605i
$254$	−0.660522	+	2.03288i	−0.0414448	+	0.127554i
$255$	−23.1882	+	1.38374i	−1.45210	+	0.0866531i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$			17.6101i			1.09849i	0.835663	+	0.549243i	$0.185084\pi$
$257$			17.6101i			1.09849i	−0.835663	+	0.549243i	$0.814916\pi$
$258$	4.16126	−	1.35208i	0.259069	−	0.0841765i
$259$	−11.8466	−	8.60705i	−0.736111	−	0.534816i
$260$	3.61204	+	4.39502i	0.224009	+	0.272567i
$261$	7.15416	−	5.19780i	0.442832	−	0.321736i
$262$	7.39500	−	10.1783i	0.456865	−	0.628820i
$263$	13.9134	−	19.1501i	0.857935	−	1.18085i	−0.124123	−	0.992267i	$-0.539612\pi$
$263$	13.9134	−	19.1501i	0.857935	−	1.18085i	0.982058	−	0.188579i	$-0.0603883\pi$
$264$	5.11961	−	3.71961i	0.315090	−	0.228926i
$265$	−14.6508	−	3.81215i	−0.899992	−	0.234178i
$266$	−1.89830	−	1.37919i	−0.116392	−	0.0845638i
$267$	−7.71444	+	2.50657i	−0.472116	+	0.153400i
$268$		−	9.39496i		−	0.573889i
$269$	2.65366	+	8.16713i	0.161797	+	0.497959i	0.998786	−	0.0492605i	$-0.0156864\pi$
$269$	2.65366	+	8.16713i	0.161797	+	0.497959i	−0.836989	+	0.547219i	$0.815686\pi$
$270$	0.802027	−	3.08234i	0.0488098	−	0.187585i
$271$	6.76256	−	20.8130i	0.410796	−	1.26430i	−0.505161	−	0.863025i	$-0.668567\pi$
$271$	6.76256	−	20.8130i	0.410796	−	1.26430i	0.915957	−	0.401276i	$-0.131433\pi$
$272$	−4.25713	−	1.38322i	−0.258126	−	0.0838703i
$273$	8.14346	+	11.2085i	0.492864	+	0.678370i
$274$	9.22974			0.557589
$275$	−9.99839	+	9.26836i	−0.602926	+	0.558903i
$276$	0.637915			0.0383980
$277$	6.29231	+	8.66062i	0.378068	+	0.520366i	0.955071	−	0.296376i	$-0.0957780\pi$
$277$	6.29231	+	8.66062i	0.378068	+	0.520366i	−0.577003	+	0.816742i	$0.695778\pi$
$278$	−3.95497	−	1.28505i	−0.237203	−	0.0770720i
$279$	3.25186	−	10.0082i	0.194684	−	0.599175i
$280$	−1.91571	−	4.88453i	−0.114485	−	0.291907i
$281$	−1.70709	−	5.25389i	−0.101837	−	0.313421i	0.887138	−	0.461504i	$-0.152690\pi$
$281$	−1.70709	−	5.25389i	−0.101837	−	0.313421i	−0.988975	+	0.148083i	$0.952690\pi$
$282$			0.491602i			0.0292745i
$283$	−17.6310	+	5.72866i	−1.04805	+	0.340534i	−0.781905	−	0.623398i	$-0.785752\pi$
$283$	−17.6310	+	5.72866i	−1.04805	+	0.340534i	−0.266150	+	0.963932i	$0.585752\pi$
$284$	−7.35169	−	5.34131i	−0.436242	−	0.316949i
$285$	−0.309132	−	5.18033i	−0.0183114	−	0.306856i
$286$	5.61218	−	4.07749i	0.331855	−	0.241107i
$287$	−5.17641	+	7.12471i	−0.305554	+	0.420558i
$288$	−1.40261	+	1.93053i	−0.0826498	+	0.113758i
$289$	2.45653	−	1.78477i	0.144502	−	0.104987i
$290$	−7.71432	+	3.02554i	−0.453001	+	0.177666i
$291$	20.5324	+	14.9177i	1.20363	+	0.874488i
$292$	7.17397	−	2.33096i	0.419825	−	0.136409i
$293$			24.4063i			1.42583i	0.701249	+	0.712916i	$0.252626\pi$
$293$			24.4063i			1.42583i	−0.701249	+	0.712916i	$0.747374\pi$
$294$	1.07167	+	3.29825i	0.0625009	+	0.192358i
$295$	−16.7251	−	10.6900i	−0.973773	−	0.622394i
$296$	1.92846	−	5.93519i	0.112090	−	0.344976i
$297$	−3.69371	−	1.20016i	−0.214331	−	0.0696403i
$298$	−2.55834	−	3.52126i	−0.148201	−	0.203981i
$299$	0.699291			0.0404410
$300$	5.65589	−	10.1325i	0.326543	−	0.585000i
$301$	−4.42366			−0.254975
$302$	7.08431	+	9.75072i	0.407656	+	0.561091i
$303$	−10.6367	−	3.45608i	−0.611064	−	0.198547i
$304$	0.309017	−	0.951057i	0.0177233	−	0.0545468i
$305$	−23.6496	+	19.4364i	−1.35417	+	1.11292i
$306$	−3.30075	−	10.1587i	−0.188691	−	0.580731i
$307$		−	31.5181i		−	1.79883i	−0.437091	−	0.899417i	$-0.643991\pi$
$307$		−	31.5181i		−	1.79883i	0.437091	−	0.899417i	$-0.356009\pi$
$308$	−6.08483	+	1.97708i	−0.346715	+	0.112655i
$309$	−0.387301	−	0.281391i	−0.0220328	−	0.0160078i
$310$	−5.31056	+	8.30869i	−0.301620	+	0.471902i
$311$	−12.6783	+	9.21132i	−0.718920	+	0.522326i	−0.886039	−	0.463611i	$-0.846554\pi$
$311$	−12.6783	+	9.21132i	−0.718920	+	0.522326i	0.167119	+	0.985937i	$0.446554\pi$
$312$	−3.47058	+	4.77684i	−0.196483	+	0.270435i
$313$	10.9710	−	15.1003i	0.620119	−	0.853520i	−0.377243	−	0.926114i	$-0.623128\pi$
$313$	10.9710	−	15.1003i	0.620119	−	0.853520i	0.997362	+	0.0725943i	$0.0231278\pi$
$314$	−11.9400	+	8.67494i	−0.673815	+	0.489555i
$315$	6.74275	−	10.5494i	0.379911	−	0.594394i
$316$	10.7320	+	7.79722i	0.603720	+	0.438628i
$317$	10.7821	−	3.50332i	0.605584	−	0.196766i	0.00985491	−	0.999951i	$-0.496863\pi$
$317$	10.7821	−	3.50332i	0.605584	−	0.196766i	0.595729	+	0.803185i	$0.296863\pi$
$318$		−	15.7125i		−	0.881115i
$319$	3.12248	+	9.60999i	0.174825	+	0.538056i
$320$	1.72751	−	1.41975i	0.0965709	−	0.0793667i
$321$	−9.25194	+	28.4745i	−0.516393	+	1.58929i
$322$	−0.613383	−	0.199300i	−0.0341825	−	0.0111066i
$323$	2.63105	+	3.62133i	0.146395	+	0.201496i
$324$	10.4645			0.581363
$325$	6.20006	−	11.1074i	0.343918	−	0.616127i
$326$	−17.7540			−0.983305
$327$	12.5475	+	17.2702i	0.693879	+	0.955042i
$328$	−3.56951	−	1.15981i	−0.197093	−	0.0640395i
$329$	0.153589	−	0.472697i	0.00846762	−	0.0260607i
$330$	−11.9229	−	7.62061i	−0.656335	−	0.419501i
$331$	5.23847	+	16.1223i	0.287932	+	0.886164i	0.985504	+	0.169650i	$0.0542637\pi$
$331$	5.23847	+	16.1223i	0.287932	+	0.886164i	−0.697572	+	0.716515i	$0.745736\pi$
$332$			3.22491i			0.176990i
$333$	14.1630	−	4.60183i	0.776126	−	0.252179i
$334$	−11.7871	−	8.56384i	−0.644962	−	0.468592i
$335$	−19.5574	+	7.67038i	−1.06853	+	0.419078i
$336$	4.40564	−	3.20088i	0.240347	−	0.174622i
$337$	−4.94448	+	6.80549i	−0.269343	+	0.370719i	−0.922168	−	0.386790i	$-0.873584\pi$
$337$	−4.94448	+	6.80549i	−0.269343	+	0.370719i	0.652825	+	0.757509i	$0.273584\pi$
$338$	3.83671	−	5.28078i	0.208690	−	0.287237i
$339$	−21.9673	+	15.9602i	−1.19310	+	0.866839i
$340$	0.596225	+	9.99133i	0.0323348	+	0.541856i
$341$	9.72797	+	7.06778i	0.526799	+	0.382742i
$342$	2.26948	−	0.737398i	0.122719	−	0.0398739i
$343$		−	19.9312i		−	1.07618i
$344$	−0.582582	−	1.79300i	−0.0314107	−	0.0966722i
$345$	−0.520816	−	1.32794i	−0.0280398	−	0.0714940i
$346$	4.10357	−	12.6295i	0.220609	−	0.678966i
$347$	5.68917	+	1.84852i	0.305411	+	0.0992340i	0.457713	−	0.889100i	$-0.348669\pi$
$347$	5.68917	+	1.84852i	0.305411	+	0.0992340i	−0.152302	+	0.988334i	$0.548669\pi$
$348$	−5.05527	−	6.95798i	−0.270991	−	0.372987i
$349$	−2.45997			−0.131679			−0.0658396	−	0.997830i	$-0.520973\pi$
$349$	−2.45997			−0.131679			−0.0658396	+	0.997830i	$0.520973\pi$
$350$	−8.60403	+	7.97581i	−0.459905	+	0.426325i
$351$	3.62377			0.193423
$352$	−1.60271	−	2.20593i	−0.0854245	−	0.117577i
$353$	−16.9540	−	5.50870i	−0.902372	−	0.293199i	−0.179156	−	0.983821i	$-0.557337\pi$
$353$	−16.9540	−	5.50870i	−0.902372	−	0.293199i	−0.723216	+	0.690622i	$0.757337\pi$
$354$	6.36637	−	19.5937i	0.338369	−	1.04139i
$355$	−5.11678	+	19.6648i	−0.271570	+	1.04370i
$356$	1.08003	+	3.32399i	0.0572415	+	0.176171i
$357$			24.3759i			1.29011i
$358$	−7.96840	+	2.58909i	−0.421143	+	0.136838i
$359$	11.0184	+	8.00536i	0.581531	+	0.422507i	0.839276	−	0.543706i	$-0.182979\pi$
$359$	11.0184	+	8.00536i	0.581531	+	0.422507i	−0.257745	+	0.966213i	$0.582979\pi$
$360$	5.16391	+	1.34365i	0.272162	+	0.0708167i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	6.65193	−	9.15560i	0.349618	−	0.481208i
$363$	4.86346	−	6.69398i	0.255265	−	0.351343i
$364$	4.82952	−	3.50885i	0.253136	−	0.183914i
$365$	−10.7094	−	13.0309i	−0.560557	−	0.682068i
$366$	−25.7042	−	18.6752i	−1.34358	−	0.976169i
$367$	−3.16336	+	1.02784i	−0.165126	+	0.0536528i	−0.390413	−	0.920640i	$-0.627668\pi$
$367$	−3.16336	+	1.02784i	−0.165126	+	0.0536528i	0.225287	+	0.974292i	$0.427668\pi$
$368$		−	0.274865i		−	0.0143283i
$369$	−2.76761	−	8.51782i	−0.144076	−	0.443420i
$370$	−13.9297	+	0.831244i	−0.724171	+	0.0432143i
$371$	−4.90898	+	15.1083i	−0.254862	+	0.784384i
$372$	−9.73374	−	3.16269i	−0.504671	−	0.163978i
$373$	19.7276	+	27.1527i	1.02146	+	1.40592i	0.911177	+	0.412015i	$0.135175\pi$
$373$	19.7276	+	27.1527i	1.02146	+	1.40592i	0.110281	+	0.993900i	$0.464825\pi$
$374$	12.2052			0.631116
$375$	−25.7104	−	3.50127i	−1.32768	−	0.180805i
$376$	0.211821			0.0109239
$377$	−5.54166	−	7.62744i	−0.285410	−	0.392833i
$378$	−3.17859	−	1.03279i	−0.163489	−	0.0531208i
$379$	9.08643	−	27.9651i	0.466738	−	1.43647i	−0.390045	−	0.920796i	$-0.627540\pi$
$379$	9.08643	−	27.9651i	0.466738	−	1.43647i	0.856783	−	0.515677i	$-0.172460\pi$
$380$	−2.23210	+	0.133199i	−0.114504	+	0.00683295i
$381$	1.53296	+	4.71797i	0.0785360	+	0.241709i
$382$		−	17.6028i		−	0.900635i
$383$	25.1596	−	8.17486i	1.28560	−	0.417716i	0.415049	−	0.909799i	$-0.363764\pi$
$383$	25.1596	−	8.17486i	1.28560	−	0.417716i	0.870548	+	0.492083i	$0.163764\pi$
$384$	1.87759	+	1.36415i	0.0958156	+	0.0696141i
$385$	9.08354	+	11.0526i	0.462940	+	0.563291i
$386$	−4.09886	+	2.97800i	−0.208627	+	0.151576i
$387$	2.64431	−	3.63958i	0.134418	−	0.185010i
$388$	6.42771	−	8.84699i	0.326318	−	0.449138i
$389$	−11.3463	+	8.24357i	−0.575281	+	0.417966i	−0.837020	−	0.547173i	$-0.815704\pi$
$389$	−11.3463	+	8.24357i	−0.575281	+	0.417966i	0.261739	+	0.965139i	$0.415704\pi$
$390$	12.7774	+	3.32469i	0.647009	+	0.168352i
$391$	0.995375	+	0.723182i	0.0503383	+	0.0365729i
$392$	1.42115	−	0.461759i	0.0717789	−	0.0233224i
$393$		−	29.1987i		−	1.47288i
$394$	0.977765	+	3.00925i	0.0492591	+	0.151604i
$395$	7.46945	−	28.7065i	0.375829	−	1.44438i
$396$	2.01065	−	6.18815i	0.101039	−	0.310966i
$397$	−5.97967	−	1.94291i	−0.300111	−	0.0975120i	0.155091	−	0.987900i	$-0.450433\pi$
$397$	−5.97967	−	1.94291i	−0.300111	−	0.0975120i	−0.455202	+	0.890388i	$0.650433\pi$
$398$	−10.3205	−	14.2050i	−0.517322	−	0.712032i
$399$	−5.44567			−0.272624
$400$	−4.36589	−	2.43701i	−0.218294	−	0.121850i
$401$	18.8998			0.943811			0.471905	−	0.881649i	$-0.343566\pi$
$401$	18.8998			0.943811			0.471905	+	0.881649i	$0.343566\pi$
$402$	−12.8162	−	17.6399i	−0.639212	−	0.879799i
$403$	−10.6703	−	3.46698i	−0.531524	−	0.172703i
$404$	−1.48916	+	4.58315i	−0.0740883	+	0.228020i
$405$	−8.54361	−	21.7839i	−0.424535	−	1.08245i
$406$	2.68702	+	8.26980i	0.133355	+	0.410423i
$407$			17.0162i			0.843464i
$408$	−9.88008	+	3.21023i	−0.489137	+	0.158930i
$409$	16.4215	+	11.9309i	0.811993	+	0.589947i	0.914408	−	0.404794i	$-0.132657\pi$
$409$	16.4215	+	11.9309i	0.811993	+	0.589947i	−0.102415	+	0.994742i	$0.532657\pi$
$410$	0.499923	+	8.37753i	0.0246894	+	0.413737i
$411$	17.3297	−	12.5908i	0.854811	−	0.621057i
$412$	−0.121246	+	0.166880i	−0.00597334	+	0.00822160i
$413$	−12.2431	+	16.8512i	−0.602443	+	0.829192i
$414$	0.530635	−	0.385529i	0.0260793	−	0.0189477i
$415$	6.71327	−	2.63293i	0.329541	−	0.129246i
$416$	2.05824	+	1.49540i	0.100914	+	0.0733181i
$417$	−9.17882	+	2.98238i	−0.449489	+	0.146048i
$418$			2.72669i			0.133367i
$419$	4.75054	+	14.6207i	0.232079	+	0.714266i	0.997495	+	0.0707308i	$0.0225331\pi$
$419$	4.75054	+	14.6207i	0.232079	+	0.714266i	−0.765416	+	0.643536i	$0.777467\pi$
$420$	−10.2602	−	6.55785i	−0.500645	−	0.319991i
$421$	2.04211	−	6.28498i	0.0995266	−	0.306311i	−0.888880	−	0.458139i	$-0.848516\pi$
$421$	2.04211	−	6.28498i	0.0995266	−	0.306311i	0.988407	+	0.151828i	$0.0485160\pi$
$422$	18.2082	+	5.91619i	0.886359	+	0.287996i
$423$	0.297104	+	0.408928i	0.0144457	+	0.0198828i
$424$	−6.77021			−0.328791
$425$	20.3121	−	9.39843i	0.985280	−	0.455891i
$426$	−21.0898			−1.02181
$427$	18.8811	+	25.9877i	0.913722	+	1.25763i
$428$	12.2691	+	3.98647i	0.593049	+	0.192693i
$429$	4.97509	−	15.3117i	0.240199	−	0.739258i
$430$	−3.25683	+	2.67662i	−0.157058	+	0.129078i
$431$	8.37795	+	25.7847i	0.403552	+	1.24200i	0.922099	+	0.386955i	$0.126473\pi$
$431$	8.37795	+	25.7847i	0.403552	+	1.24200i	−0.518547	+	0.855049i	$0.673527\pi$
$432$		−	1.42437i		−	0.0685298i
$433$	−36.8085	+	11.9598i	−1.76890	+	0.574752i	−0.998059	−	0.0622701i	$-0.980166\pi$
$433$	−36.8085	+	11.9598i	−1.76890	+	0.574752i	−0.770846	+	0.637022i	$0.780166\pi$
$434$	8.37132	+	6.08212i	0.401836	+	0.291951i
$435$	−10.3571	+	16.2043i	−0.496583	+	0.776934i
$436$	7.44136	−	5.40646i	0.356376	−	0.258923i
$437$	−0.161561	+	0.222370i	−0.00772853	+	0.0106374i
$438$	10.2900	−	14.1630i	0.491676	−	0.676734i
$439$	22.4953	−	16.3438i	1.07364	−	0.780048i	0.0970802	−	0.995277i	$-0.469050\pi$
$439$	22.4953	−	16.3438i	1.07364	−	0.780048i	0.976564	+	0.215229i	$0.0690497\pi$
$440$	−3.28357	+	5.13734i	−0.156538	+	0.244913i
$441$	2.88477	+	2.09590i	0.137370	+	0.0998050i
$442$	−10.8307	+	3.51910i	−0.515163	+	0.167387i
$443$			27.1599i			1.29040i	0.764012	+	0.645202i	$0.223227\pi$
$443$			27.1599i			1.29040i	−0.764012	+	0.645202i	$0.776773\pi$
$444$	−4.47564	−	13.7746i	−0.212404	−	0.653714i
$445$	6.03775	−	4.96212i	0.286217	−	0.235227i
$446$	−7.95278	+	24.4761i	−0.376575	+	1.15898i
$447$	−9.60706	−	3.12152i	−0.454398	−	0.147643i
$448$	−1.37919	−	1.89830i	−0.0651608	−	0.0896862i
$449$	−34.0061			−1.60485			−0.802423	−	0.596755i	$-0.796456\pi$
$449$	−34.0061			−1.60485			−0.802423	+	0.596755i	$0.796456\pi$
$450$	−1.41894	−	11.8467i	−0.0668893	−	0.558458i
$451$	10.2338			0.481892
$452$	6.87693	+	9.46528i	0.323463	+	0.445209i
$453$	26.6029	+	8.64381i	1.24991	+	0.406122i
$454$	5.45142	−	16.7778i	0.255848	−	0.787419i
$455$	−11.2473	−	7.18881i	−0.527283	−	0.337017i
$456$	−0.717177	−	2.20724i	−0.0335849	−	0.103364i
$457$			3.83411i			0.179352i	0.995971	+	0.0896761i	$0.0285832\pi$
$457$			3.83411i			0.179352i	−0.995971	+	0.0896761i	$0.971417\pi$
$458$	15.8618	−	5.15382i	0.741175	−	0.240822i
$459$	5.15810	+	3.74758i	0.240759	+	0.174922i
$460$	−0.572183	+	0.224409i	−0.0266782	+	0.0104631i
$461$	15.4094	−	11.1956i	0.717689	−	0.521432i	−0.167956	−	0.985795i	$-0.553717\pi$
$461$	15.4094	−	11.1956i	0.717689	−	0.521432i	0.885645	+	0.464363i	$0.153717\pi$
$462$	−8.72780	+	12.0128i	−0.406054	+	0.558885i
$463$	0.785619	−	1.08131i	0.0365108	−	0.0502528i	−0.790371	−	0.612628i	$-0.790112\pi$
$463$	0.785619	−	1.08131i	0.0365108	−	0.0502528i	0.826882	+	0.562375i	$0.190112\pi$
$464$	−2.99805	+	2.17821i	−0.139181	+	0.101121i
$465$	1.36324	+	22.8448i	0.0632189	+	1.05940i
$466$	−12.7610	−	9.27143i	−0.591143	−	0.429491i
$467$	−40.8746	+	13.2810i	−1.89145	+	0.614570i	−0.913052	+	0.407843i	$0.866281\pi$
$467$	−40.8746	+	13.2810i	−1.89145	+	0.614570i	−0.978399	+	0.206726i	$0.933719\pi$
$468$			6.07098i			0.280631i
$469$	6.81215	+	20.9656i	0.314556	+	0.968103i
$470$	−0.172939	−	0.440947i	−0.00797706	−	0.0203394i
$471$	−10.5846	+	32.5760i	−0.487713	+	1.50103i
$472$	−8.44251	−	2.74314i	−0.388598	−	0.126263i
$473$	3.02154	+	4.15879i	0.138930	+	0.191221i
$474$	30.7869			1.41409
$475$	2.09964	+	4.53779i	0.0963382	+	0.208208i
$476$	10.5031			0.481408
$477$	−9.49599	−	13.0701i	−0.434792	−	0.598439i
$478$	−5.71994	−	1.85852i	−0.261624	−	0.0850067i
$479$	3.12007	−	9.60260i	0.142560	−	0.438754i	−0.854129	−	0.520061i	$-0.825909\pi$
$479$	3.12007	−	9.60260i	0.142560	−	0.438754i	0.996689	+	0.0813066i	$0.0259093\pi$
$480$	1.30681	−	5.02231i	0.0596473	−	0.229236i
$481$	−4.90626	−	15.0999i	−0.223706	−	0.688496i
$482$		−	4.78698i		−	0.218041i
$483$	−1.42356	+	0.462543i	−0.0647743	+	0.0210464i
$484$	−2.88430	−	2.09556i	−0.131104	−	0.0952529i
$485$	−23.6645	−	6.15751i	−1.07455	−	0.279598i
$486$	16.1911	−	11.7635i	0.734444	−	0.533605i
$487$	11.7312	−	16.1467i	0.531593	−	0.731675i	−0.455779	−	0.890093i	$-0.650639\pi$
$487$	11.7312	−	16.1467i	0.531593	−	0.731675i	0.987372	+	0.158418i	$0.0506394\pi$
$488$	−8.04676	+	11.0754i	−0.364260	+	0.501361i
$489$	−33.3349	+	24.2192i	−1.50745	+	1.09523i
$490$	−2.12152	−	2.58140i	−0.0958403	−	0.116616i
$491$	34.5843	+	25.1270i	1.56077	+	1.13397i	0.935375	+	0.353657i	$0.115062\pi$
$491$	34.5843	+	25.1270i	1.56077	+	1.13397i	0.625395	+	0.780309i	$0.284938\pi$
$492$	−8.28425	+	2.69172i	−0.373483	+	0.121352i
$493$		−	16.5879i		−	0.747082i
$494$	−0.786179	−	2.41961i	−0.0353719	−	0.108863i
$495$	−14.5234	+	0.866672i	−0.652777	+	0.0389540i
$496$	−1.36274	+	4.19407i	−0.0611887	+	0.188319i
$497$	20.2788	+	6.58899i	0.909629	+	0.295556i
$498$	4.39927	+	6.05508i	0.197136	+	0.271334i
$499$	−6.69590			−0.299750			−0.149875	−	0.988705i	$-0.547887\pi$
$499$	−6.69590			−0.299750			−0.149875	+	0.988705i	$0.547887\pi$
$500$	−1.50863	+	11.0781i	−0.0674679	+	0.495427i
$501$	−33.8138			−1.51069
$502$	3.63398	+	5.00175i	0.162192	+	0.223239i
$503$	1.43365	+	0.465821i	0.0639232	+	0.0207699i	0.340804	−	0.940134i	$-0.389301\pi$
$503$	1.43365	+	0.465821i	0.0639232	+	0.0207699i	−0.276881	+	0.960904i	$0.589301\pi$
$504$	1.73025	−	5.32516i	0.0770714	−	0.237202i
$505$	10.7565	−	0.641886i	0.478658	−	0.0285635i
$506$	0.231599	+	0.712788i	0.0102958	+	0.0316873i
$507$		−	15.1490i		−	0.672792i
$508$	2.03288	−	0.660522i	0.0901943	−	0.0293059i
$509$	21.2215	+	15.4183i	0.940627	+	0.683405i	0.948571	−	0.316563i	$-0.102529\pi$
$509$	21.2215	+	15.4183i	0.940627	+	0.683405i	−0.00794462	+	0.999968i	$0.502529\pi$
$510$	14.7492	+	17.9463i	0.653104	+	0.794676i
$511$	−14.3192	+	10.4035i	−0.633442	+	0.460223i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	−0.837221	+	1.15234i	−0.0369642	+	0.0508769i
$514$	14.2469	−	10.3509i	0.628402	−	0.456561i
$515$	0.446382	+	0.116149i	0.0196700	+	0.00511813i
$516$	−3.53978	−	2.57180i	−0.155830	−	0.113217i
$517$	−0.549302	+	0.178479i	−0.0241583	+	0.00784950i
$518$			14.6432i			0.643385i
$519$	−9.52371	−	29.3110i	−0.418045	−	1.28661i
$520$	1.43254	−	5.50553i	0.0628210	−	0.241433i
$521$	12.2981	−	37.8496i	0.538789	−	1.65822i	−0.196528	−	0.980498i	$-0.562967\pi$
$521$	12.2981	−	37.8496i	0.538789	−	1.65822i	0.735317	−	0.677723i	$-0.237033\pi$
$522$	−8.41022	−	2.73265i	−0.368105	−	0.119605i
$523$	7.41354	+	10.2039i	0.324172	+	0.446184i	0.939735	−	0.341903i	$-0.111072\pi$
$523$	7.41354	+	10.2039i	0.324172	+	0.446184i	−0.615563	+	0.788087i	$0.711072\pi$
$524$	−12.5811			−0.549609
$525$	−5.27466	+	26.7125i	−0.230205	+	1.16583i
$526$	−23.6708			−1.03210
$527$	−11.6027	−	15.9697i	−0.505421	−	0.695652i
$528$	−6.01846	−	1.95552i	−0.261920	−	0.0851029i
$529$	7.08404	−	21.8024i	0.308002	−	0.947932i
$530$	5.52744	+	14.0935i	0.240097	+	0.612182i
$531$	−6.54587	−	20.1461i	−0.284067	−	0.874267i
$532$			2.34643i			0.101730i
$533$	−9.08131	+	2.95070i	−0.393355	+	0.127809i
$534$	6.56229	+	4.76778i	0.283978	+	0.206322i
$535$	−1.71833	−	28.7952i	−0.0742899	−	1.24492i
$536$	−7.60068	+	5.52222i	−0.328300	+	0.238524i
$537$	−11.4295	+	15.7314i	−0.493220	+	0.678859i
$538$	5.04756	−	6.94737i	0.217616	−	0.299523i
$539$	−3.29629	+	2.39490i	−0.141981	+	0.103156i
$540$	−2.96509	+	1.16290i	−0.127597	+	0.0500434i
$541$	−25.2015	−	18.3100i	−1.08350	−	0.787206i	−0.105207	−	0.994450i	$-0.533551\pi$
$541$	−25.2015	−	18.3100i	−1.08350	−	0.787206i	−0.978289	+	0.207244i	$0.933551\pi$
$542$	−20.8130	+	6.76256i	−0.893996	+	0.290477i
$543$		−	26.2647i		−	1.12713i
$544$	1.38322	+	4.25713i	0.0593052	+	0.182523i
$545$	−17.3300	−	11.0766i	−0.742334	−	0.474468i
$546$	4.28127	−	13.1764i	0.183221	−	0.563897i
$547$	10.3902	+	3.37598i	0.444252	+	0.144346i	0.522597	−	0.852580i	$-0.324963\pi$
$547$	10.3902	+	3.37598i	0.444252	+	0.144346i	−0.0783444	+	0.996926i	$0.524963\pi$
$548$	−5.42510	−	7.46701i	−0.231749	−	0.318975i
$549$	−32.6680			−1.39424
$550$	13.3752	+	2.64106i	0.570319	+	0.112615i
$551$	3.70580			0.157872
$552$	−0.374957	−	0.516084i	−0.0159592	−	0.0219660i
$553$	−29.6029	−	9.61857i	−1.25884	−	0.409023i
$554$	3.30806	−	10.1812i	0.140546	−	0.432557i
$555$	−25.0204	+	20.5630i	−1.06206	+	0.872849i
$556$	1.28505	+	3.95497i	0.0544981	+	0.167728i
$557$		−	34.7205i		−	1.47116i	−0.677440	−	0.735578i	$-0.736911\pi$
$557$		−	34.7205i		−	1.47116i	0.677440	−	0.735578i	$-0.263089\pi$
$558$	−10.0082	+	3.25186i	−0.423680	+	0.137662i
$559$	−3.88035	−	2.81924i	−0.164121	−	0.119241i
$560$	−2.82565	+	4.42089i	−0.119405	+	0.186817i
$561$	22.9164	−	16.6498i	0.967532	−	0.702953i
$562$	−3.24708	+	4.46923i	−0.136970	+	0.188523i
$563$	−1.17182	+	1.61287i	−0.0493862	+	0.0679743i	−0.832996	−	0.553279i	$-0.813376\pi$
$563$	−1.17182	+	1.61287i	−0.0493862	+	0.0679743i	0.783610	+	0.621253i	$0.213376\pi$
$564$	0.397715	−	0.288957i	0.0167468	−	0.0121673i
$565$	14.0892	−	22.0434i	0.592737	−	0.927374i
$566$	14.9978	+	10.8966i	0.630406	+	0.458017i
$567$	−23.3525	+	7.58768i	−0.980711	+	0.318652i
$568$			9.08718i			0.381290i
$569$	−5.56507	−	17.1275i	−0.233300	−	0.718024i	−0.997342	−	0.0728575i	$-0.976788\pi$
$569$	−5.56507	−	17.1275i	−0.233300	−	0.718024i	0.764042	−	0.645166i	$-0.223212\pi$
$570$	−4.00927	+	3.29501i	−0.167930	+	0.138013i
$571$	−5.87844	+	18.0920i	−0.246005	+	0.757125i	0.749465	+	0.662044i	$0.230311\pi$
$571$	−5.87844	+	18.0920i	−0.246005	+	0.757125i	−0.995470	+	0.0950808i	$0.969689\pi$
$572$	−6.59752	−	2.14366i	−0.275856	−	0.0896311i
$573$	−24.0128	−	33.0508i	−1.00315	−	1.38072i
$574$	8.80663			0.367582
$575$	0.934301	+	1.00789i	0.0389630	+	0.0420320i
$576$	2.38627			0.0994279
$577$	−22.4648	−	30.9202i	−0.935224	−	1.28723i	−0.957787	−	0.287480i	$-0.907183\pi$
$577$	−22.4648	−	30.9202i	−0.935224	−	1.28723i	0.0225628	−	0.999745i	$-0.492817\pi$
$578$	−2.88782	−	0.938309i	−0.120117	−	0.0390285i
$579$	−3.63356	+	11.1829i	−0.151006	+	0.464747i
$580$	6.98208	+	4.46265i	0.289915	+	0.185301i
$581$	−2.33834	−	7.19666i	−0.0970106	−	0.298568i
$582$		−	25.3794i		−	1.05201i
$583$	17.5567	−	5.70453i	0.727125	−	0.236257i
$584$	−6.10254	−	4.43376i	−0.252525	−	0.183470i
$585$	12.6379	−	4.95656i	0.522513	−	0.204929i
$586$	19.7451	−	14.3457i	0.815664	−	0.592614i
$587$	21.5309	−	29.6348i	0.888676	−	1.22316i	−0.0852652	−	0.996358i	$-0.527174\pi$
$587$	21.5309	−	29.6348i	0.888676	−	1.22316i	0.973941	−	0.226800i	$-0.0728262\pi$
$588$	2.03843	−	2.80566i	0.0840635	−	0.115703i
$589$	3.56769	−	2.59208i	0.147004	−	0.106805i
$590$	1.18240	+	19.8143i	0.0486788	+	0.815742i
$591$	5.94092	+	4.31633i	0.244377	+	0.177550i
$592$	−5.93519	+	1.92846i	−0.243935	+	0.0792593i
$593$			21.1528i			0.868642i	0.900758	+	0.434321i	$0.143012\pi$
$593$			21.1528i			0.868642i	−0.900758	+	0.434321i	$0.856988\pi$
$594$	1.20016	+	3.69371i	0.0492431	+	0.151555i
$595$	−8.57510	−	21.8642i	−0.351545	−	0.896344i
$596$	−1.34500	+	4.13949i	−0.0550934	+	0.169560i
$597$	−38.7555	−	12.5924i	−1.58616	−	0.515374i
$598$	−0.411033	−	0.565738i	−0.0168084	−	0.0231348i
$599$	9.59705			0.392125			0.196062	−	0.980591i	$-0.437184\pi$
$599$	9.59705			0.392125			0.196062	+	0.980591i	$0.437184\pi$
$600$	−11.5218	+	1.38003i	−0.470376	+	0.0563393i
$601$	−20.1582			−0.822272			−0.411136	−	0.911574i	$-0.634868\pi$
$601$	−20.1582			−0.822272			−0.411136	+	0.911574i	$0.634868\pi$
$602$	2.60016	+	3.57881i	0.105975	+	0.145862i
$603$	−21.3217	−	6.92782i	−0.868285	−	0.282123i
$604$	3.72444	−	11.4627i	0.151545	−	0.466409i
$605$	−2.00747	+	7.71511i	−0.0816154	+	0.313664i
$606$	3.45608	+	10.6367i	0.140394	+	0.432088i
$607$		−	23.1872i		−	0.941140i	−0.882363	−	0.470570i	$-0.844048\pi$
$607$		−	23.1872i		−	0.941140i	0.882363	−	0.470570i	$-0.155952\pi$
$608$	−0.951057	+	0.309017i	−0.0385704	+	0.0125323i
$609$	16.3264	+	11.8618i	0.661579	+	0.480665i
$610$	29.6253	+	7.70850i	1.19949	+	0.312108i
$611$	0.435980	−	0.316758i	0.0176379	−	0.0128147i
$612$	−6.27839	+	8.64147i	−0.253789	+	0.349311i
$613$	−17.5083	+	24.0980i	−0.707152	+	0.973311i	0.292702	+	0.956204i	$0.405446\pi$
$613$	−17.5083	+	24.0980i	−0.707152	+	0.973311i	−0.999854	+	0.0171070i	$0.994554\pi$
$614$	−25.4987	+	18.5259i	−1.02904	+	0.747644i
$615$	12.3669	+	15.0476i	0.498680	+	0.606779i
$616$	5.17606	+	3.76063i	0.208550	+	0.151520i
$617$	17.4180	−	5.65945i	0.701222	−	0.227841i	0.0633593	−	0.997991i	$-0.479819\pi$
$617$	17.4180	−	5.65945i	0.701222	−	0.227841i	0.637863	+	0.770150i	$0.279819\pi$
$618$			0.478731i			0.0192574i
$619$	−9.29108	−	28.5950i	−0.373440	−	1.14933i	−0.944525	−	0.328439i	$-0.893477\pi$
$619$	−9.29108	−	28.5950i	−0.373440	−	1.14933i	0.571085	−	0.820891i	$-0.306523\pi$
$620$	9.84334	−	0.587394i	0.395318	−	0.0235903i
$621$	−0.120983	+	0.372346i	−0.00485486	+	0.0149417i
$622$	14.9042	+	4.84268i	0.597605	+	0.194174i
$623$	−4.82036	−	6.63466i	−0.193124	−	0.265812i
$624$	5.90450			0.236369
$625$	24.2928	−	5.90405i	0.971714	−	0.236162i
$626$	−18.6650			−0.746004
$627$	3.71961	+	5.11961i	0.148547	+	0.204457i
$628$	14.0364	+	4.56069i	0.560112	+	0.181991i
$629$	8.63219	−	26.5672i	0.344188	−	1.05930i
$630$	−12.4980	+	0.745807i	−0.497931	+	0.0297137i
$631$	10.7379	+	33.0477i	0.427467	+	1.31561i	0.900612	+	0.434624i	$0.143119\pi$
$631$	10.7379	+	33.0477i	0.427467	+	1.31561i	−0.473145	+	0.880985i	$0.656881\pi$
$632$		−	13.2654i		−	0.527670i
$633$	42.2581	−	13.7305i	1.67961	−	0.545738i
$634$	−9.17182	−	6.66372i	−0.364260	−	0.264650i
$635$	−3.03471	−	3.69255i	−0.120429	−	0.146534i
$636$	−12.7117	+	9.23560i	−0.504052	+	0.366215i
$637$	2.23456	−	3.07560i	0.0885363	−	0.121860i
$638$	5.93930	−	8.17475i	0.235139	−	0.323641i
$639$	−17.5431	+	12.7458i	−0.693995	+	0.504217i
$640$	−2.16401	−	0.563076i	−0.0855401	−	0.0222576i
$641$	14.8409	+	10.7826i	0.586181	+	0.425885i	0.840947	−	0.541117i	$-0.181998\pi$
$641$	14.8409	+	10.7826i	0.586181	+	0.425885i	−0.254766	+	0.967003i	$0.581998\pi$
$642$	28.4745	−	9.25194i	1.12380	−	0.365145i
$643$			34.0072i			1.34111i	0.741859	+	0.670556i	$0.233944\pi$
$643$			34.0072i			1.34111i	−0.741859	+	0.670556i	$0.766056\pi$
$644$	0.199300	+	0.613383i	0.00785353	+	0.0241707i
$645$	−2.46369	+	9.46843i	−0.0970077	+	0.372819i
$646$	1.38322	−	4.25713i	0.0544222	−	0.167494i
$647$	−18.9487	−	6.15682i	−0.744951	−	0.242049i	−0.0881440	−	0.996108i	$-0.528094\pi$
$647$	−18.9487	−	6.15682i	−0.744951	−	0.242049i	−0.656807	+	0.754058i	$0.728094\pi$
$648$	−6.15089	−	8.46598i	−0.241630	−	0.332575i
$649$	24.2047			0.950119
$650$	−12.6304	+	1.51280i	−0.495404	+	0.0593370i
$651$	24.0149			0.941218
$652$	10.4356	+	14.3633i	0.408688	+	0.562511i
$653$	−34.2323	−	11.1228i	−1.33961	−	0.435267i	−0.450428	−	0.892813i	$-0.648729\pi$
$653$	−34.2323	−	11.1228i	−1.33961	−	0.435267i	−0.889186	+	0.457546i	$0.848729\pi$
$654$	6.59661	−	20.3023i	0.257948	−	0.793882i
$655$	10.2717	+	26.1900i	0.401348	+	1.02333i
$656$	1.15981	+	3.56951i	0.0452828	+	0.139366i
$657$		−	18.0000i		−	0.702247i
$658$	−0.472697	+	0.153589i	−0.0184277	+	0.00598751i
$659$	−11.2974	−	8.20806i	−0.440085	−	0.319741i	0.345584	−	0.938388i	$-0.387681\pi$
$659$	−11.2974	−	8.20806i	−0.440085	−	0.319741i	−0.785669	+	0.618647i	$0.787681\pi$
$660$	0.842906	+	14.1251i	0.0328101	+	0.549820i
$661$	−9.13802	+	6.63916i	−0.355428	+	0.258233i	−0.751143	−	0.660140i	$-0.770497\pi$
$661$	−9.13802	+	6.63916i	−0.355428	+	0.258233i	0.395715	+	0.918373i	$0.370497\pi$
$662$	9.96416	−	13.7145i	0.387268	−	0.533029i
$663$	−15.5350	+	21.3821i	−0.603331	+	0.830413i
$664$	2.60901	−	1.89556i	0.101249	−	0.0735618i
$665$	4.88453	−	1.91571i	0.189414	−	0.0742879i
$666$	−12.0477	−	8.75320i	−0.466841	−	0.339180i
$667$	0.968739	−	0.314762i	0.0375097	−	0.0121876i
$668$			14.5697i			0.563718i
$669$	18.4571	+	56.8050i	0.713592	+	2.19621i
$670$	17.7010	+	11.3137i	0.683850	+	0.437088i
$671$	11.5351	−	35.5013i	0.445306	−	1.37051i
$672$	−5.17914	−	1.68280i	−0.199789	−	0.0649155i
$673$	24.8047	+	34.1408i	0.956152	+	1.31603i	0.948740	+	0.316058i	$0.102359\pi$
$673$	24.8047	+	34.1408i	0.956152	+	1.31603i	0.00741183	+	0.999973i	$0.497641\pi$
$674$	8.41204			0.324020
$675$	4.84161	+	5.22296i	0.186354	+	0.201032i
$676$	−6.52740			−0.251054
$677$	16.9741	+	23.3629i	0.652368	+	0.897908i	0.999199	−	0.0400200i	$-0.0127422\pi$
$677$	16.9741	+	23.3629i	0.652368	+	0.897908i	−0.346831	+	0.937928i	$0.612742\pi$
$678$	25.8242	+	8.39078i	0.991771	+	0.322246i
$679$	−7.92916	+	24.4034i	−0.304293	+	0.936518i
$680$	7.73270	−	6.35511i	0.296536	−	0.243707i
$681$	−12.6518	−	38.9384i	−0.484820	−	1.49212i
$682$		−	12.0244i		−	0.460439i
$683$	26.7941	−	8.70592i	1.02525	−	0.333123i	0.252337	−	0.967639i	$-0.418801\pi$
$683$	26.7941	−	8.70592i	1.02525	−	0.333123i	0.772909	+	0.634516i	$0.218801\pi$
$684$	−1.93053	−	1.40261i	−0.0738158	−	0.0536303i
$685$	−11.1148	+	17.3897i	−0.424673	+	0.664427i
$686$	−16.1247	+	11.7153i	−0.615643	+	0.447291i
$687$	22.7515	−	31.3147i	0.868024	−	1.19473i
$688$	−1.10814	+	1.52522i	−0.0422473	+	0.0581484i
$689$	−13.9347	+	10.1242i	−0.530872	+	0.385701i
$690$	−0.768199	+	1.20189i	−0.0292448	+	0.0457553i
$691$	−3.74422	−	2.72034i	−0.142437	−	0.103486i	0.514285	−	0.857619i	$-0.328057\pi$
$691$	−3.74422	−	2.72034i	−0.142437	−	0.103486i	−0.656722	+	0.754133i	$0.728057\pi$
$692$	−12.6295	+	4.10357i	−0.480102	+	0.155994i
$693$			15.2673i			0.579956i
$694$	−1.84852	−	5.68917i	−0.0701690	−	0.215958i
$695$	7.18386	−	5.90405i	0.272499	−	0.223953i
$696$	−2.65771	+	8.17960i	−0.100740	+	0.310047i
$697$	−15.9779	−	5.19153i	−0.605206	−	0.196643i
$698$	1.44593	+	1.99016i	0.0547294	+	0.0753286i
$699$	−36.6077			−1.38463
$700$	11.5099	+	2.27274i	0.435033	+	0.0859016i
$701$	30.3487			1.14626			0.573128	−	0.819466i	$-0.305730\pi$
$701$	30.3487			1.14626			0.573128	+	0.819466i	$0.305730\pi$
$702$	−2.13000	−	2.93169i	−0.0803917	−	0.110650i
$703$	5.93519	+	1.92846i	0.223850	+	0.0727333i
$704$	−0.842592	+	2.59323i	−0.0317564	+	0.0977361i
$705$	−0.926227	−	0.592004i	−0.0348837	−	0.0222962i
$706$	5.50870	+	16.9540i	0.207323	+	0.638074i
$707$		−	11.3074i		−	0.425260i
$708$	−19.5937	+	6.36637i	−0.736375	+	0.239263i
$709$	34.2946	+	24.9165i	1.28796	+	0.935759i	0.999762	−	0.0218117i	$-0.00694342\pi$
$709$	34.2946	+	24.9165i	1.28796	+	0.935759i	0.288199	+	0.957570i	$0.406943\pi$
$710$	18.9167	−	7.41910i	0.709931	−	0.278434i
$711$	25.6093	−	18.6063i	0.960425	−	0.697790i
$712$	2.05434	−	2.82756i	0.0769897	−	0.105967i
$713$	0.712471	−	0.980632i	0.0266822	−	0.0367250i
$714$	19.7205	−	14.3278i	0.738023	−	0.536205i
$715$	0.924005	+	15.4841i	0.0345558	+	0.579074i
$716$	6.77833	+	4.92474i	0.253318	+	0.184046i
$717$	−13.2750	+	4.31332i	−0.495765	+	0.161084i
$718$		−	13.6195i		−	0.508276i
$719$	−3.52307	−	10.8429i	−0.131388	−	0.404372i	0.863622	−	0.504139i	$-0.168190\pi$
$719$	−3.52307	−	10.8429i	−0.131388	−	0.404372i	−0.995011	+	0.0997673i	$0.968190\pi$
$720$	−1.94824	−	4.96747i	−0.0726064	−	0.185127i
$721$	0.149567	−	0.460321i	0.00557018	−	0.0171432i
$722$	0.951057	+	0.309017i	0.0353947	+	0.0115004i
$723$	−6.53016	−	8.98800i	−0.242859	−	0.334267i
$724$	−11.3169			−0.420591
$725$	3.58943	−	18.1780i	0.133308	−	0.675114i
$726$	−8.27421			−0.307085
$727$	−14.1290	−	19.4470i	−0.524017	−	0.721248i	0.462187	−	0.886783i	$-0.347065\pi$
$727$	−14.1290	−	19.4470i	−0.524017	−	0.721248i	−0.986204	+	0.165535i	$0.947065\pi$
$728$	−5.67744	−	1.84471i	−0.210420	−	0.0683696i
$729$	4.65195	−	14.3172i	0.172295	−	0.530268i
$730$	−4.24737	+	16.3235i	−0.157202	+	0.604159i
$731$	−2.60776	−	8.02585i	−0.0964514	−	0.296847i
$732$			31.7722i			1.17433i
$733$	2.24875	−	0.730664i	0.0830596	−	0.0269877i	−0.267192	−	0.963643i	$-0.586096\pi$
$733$	2.24875	−	0.730664i	0.0830596	−	0.0269877i	0.350252	+	0.936655i	$0.386096\pi$
$734$	2.69092	+	1.95507i	0.0993236	+	0.0721628i
$735$	−7.50476	−	1.95274i	−0.276817	−	0.0720280i
$736$	−0.222370	+	0.161561i	−0.00819667	+	0.00595523i
$737$	15.0574	−	20.7247i	0.554645	−	0.763403i
$738$	−5.26431	+	7.24569i	−0.193782	+	0.266718i
$739$	2.41830	−	1.75700i	0.0889587	−	0.0646323i	−0.542417	−	0.840109i	$-0.682491\pi$
$739$	2.41830	−	1.75700i	0.0889587	−	0.0646323i	0.631376	+	0.775477i	$0.282491\pi$
$740$	8.86016	+	10.7808i	0.325706	+	0.396309i
$741$	−4.77684	−	3.47058i	−0.175482	−	0.127495i
$742$	15.1083	−	4.90898i	0.554643	−	0.180214i
$743$			31.4764i			1.15476i	0.816476	+	0.577379i	$0.195924\pi$
$743$			31.4764i			1.15476i	−0.816476	+	0.577379i	$0.804076\pi$
$744$	3.16269	+	9.73374i	0.115950	+	0.356856i
$745$	9.71523	−	0.579749i	0.355939	−	0.0212404i
$746$	10.3714	−	31.9200i	0.379725	−	1.16867i
$747$	7.31887	+	2.37804i	0.267783	+	0.0870081i
$748$	−7.17404	−	9.87422i	−0.262309	−	0.361037i
$749$	−30.2701			−1.10604
$750$	12.2796	+	22.8581i	0.448388	+	0.834662i
$751$	16.6081			0.606040			0.303020	−	0.952984i	$-0.402005\pi$
$751$	16.6081			0.606040			0.303020	+	0.952984i	$0.402005\pi$
$752$	−0.124506	−	0.171367i	−0.00454025	−	0.00624912i
$753$	13.6463	+	4.43395i	0.497298	+	0.161582i
$754$	−2.91342	+	8.96659i	−0.106101	+	0.326544i
$755$	−26.9025	+	1.60538i	−0.979081	+	0.0584259i
$756$	1.03279	+	3.17859i	0.0375621	+	0.115604i
$757$		−	18.8892i		−	0.686539i	−0.939237	−	0.343269i	$-0.888466\pi$
$757$		−	18.8892i		−	0.686539i	0.939237	−	0.343269i	$-0.111534\pi$
$758$	−27.9651	+	9.08643i	−1.01574	+	0.330034i
$759$	1.40720	+	1.02239i	0.0510781	+	0.0371104i
$760$	1.41975	+	1.72751i	0.0514999	+	0.0626635i
$761$	31.7314	−	23.0542i	1.15026	−	0.835715i	0.161747	−	0.986832i	$-0.448287\pi$
$761$	31.7314	−	23.0542i	1.15026	−	0.835715i	0.988516	+	0.151117i	$0.0482872\pi$
$762$	2.91587	−	4.01334i	0.105631	−	0.145388i
$763$	−12.6859	+	17.4606i	−0.459259	+	0.632116i
$764$	−14.2409	+	10.3466i	−0.515219	+	0.374328i
$765$	23.1148	+	6.01447i	0.835716	+	0.217454i
$766$	−21.4021	−	15.5495i	−0.773288	−	0.561826i
$767$	−21.4789	+	6.97890i	−0.775556	+	0.251994i
$768$		−	2.32083i		−	0.0837459i
$769$	−5.72993	−	17.6349i	−0.206626	−	0.635931i	−0.999643	−	0.0267303i	$-0.991490\pi$
$769$	−5.72993	−	17.6349i	−0.206626	−	0.635931i	0.793016	−	0.609200i	$-0.208510\pi$
$770$	3.60254	−	13.8453i	0.129827	−	0.498949i
$771$	12.6295	−	38.8697i	0.454842	−	1.39986i
$772$	4.81850	+	1.56563i	0.173422	+	0.0563481i
$773$	8.40375	+	11.5668i	0.302262	+	0.416028i	0.932948	−	0.360010i	$-0.117227\pi$
$773$	8.40375	+	11.5668i	0.302262	+	0.416028i	−0.630687	+	0.776038i	$0.717227\pi$
$774$	−4.49877			−0.161705
$775$	−9.25923	−	20.0112i	−0.332601	−	0.718824i
$776$	−10.9355			−0.392561
$777$	19.9755	+	27.4940i	0.716618	+	0.986340i
$778$	13.3384	+	4.33390i	0.478204	+	0.155378i
$779$	1.15981	−	3.56951i	0.0415543	−	0.127891i
$780$	−4.82065	−	12.2913i	−0.172607	−	0.440101i
$781$	−7.65679	−	23.5652i	−0.273981	−	0.843228i
$782$		−	1.23035i		−	0.0439973i
$783$	5.02007	−	1.63112i	0.179403	−	0.0582914i
$784$	−1.20890	−	0.878319i	−0.0431751	−	0.0313685i
$785$	−1.96584	−	32.9428i	−0.0701638	−	1.17578i
$786$	−23.6222	+	17.1626i	−0.842578	+	0.612169i
$787$	−10.4130	+	14.3322i	−0.371182	+	0.510888i	−0.953222	−	0.302273i	$-0.902255\pi$
$787$	−10.4130	+	14.3322i	−0.371182	+	0.510888i	0.582040	+	0.813160i	$0.302255\pi$
$788$	1.85982	−	2.55982i	0.0662533	−	0.0911899i
$789$	−44.4442	+	32.2906i	−1.58226	+	1.14958i
$790$	−27.6145	+	10.8304i	−0.982480	+	0.385327i
$791$	−22.2096	−	16.1362i	−0.789682	−	0.573737i
$792$	−6.18815	+	2.01065i	−0.219886	+	0.0714454i
$793$			34.8291i			1.23682i
$794$	1.94291	+	5.97967i	0.0689514	+	0.212211i
$795$	29.6039	+	18.9216i	1.04994	+	0.671079i
$796$	−5.42583	+	16.6990i	−0.192313	+	0.591879i
$797$	−41.2542	−	13.4043i	−1.46130	−	0.474805i	−0.532833	−	0.846221i	$-0.678873\pi$
$797$	−41.2542	−	13.4043i	−1.46130	−	0.474805i	−0.928467	+	0.371416i	$0.878873\pi$
$798$	3.20088	+	4.40564i	0.113310	+	0.155958i
$799$	0.948157			0.0335434
$800$	0.594625	+	4.96452i	0.0210232	+	0.175522i
$801$	8.34014			0.294684
$802$	−11.1090	−	15.2903i	−0.392273	−	0.539918i
$803$	19.5612	+	6.35580i	0.690298	+	0.224291i
$804$	−6.73785	+	20.7370i	−0.237626	+	0.731337i
$805$	1.11416	−	0.915669i	0.0392689	−	0.0322731i
$806$	3.46698	+	10.6703i	0.122119	+	0.375844i
$807$		−	19.9300i		−	0.701569i
$808$	4.58315	−	1.48916i	0.161235	−	0.0523883i
$809$	24.2584	+	17.6247i	0.852879	+	0.619653i	0.925938	−	0.377675i	$-0.123276\pi$
$809$	24.2584	+	17.6247i	0.852879	+	0.619653i	−0.0730594	+	0.997328i	$0.523276\pi$
$810$	−12.6017	+	19.7162i	−0.442780	+	0.692756i
$811$	−40.1265	+	29.1536i	−1.40903	+	1.02372i	−0.415568	+	0.909562i	$0.636417\pi$
$811$	−40.1265	+	29.1536i	−1.40903	+	1.02372i	−0.993463	+	0.114159i	$0.963583\pi$
$812$	5.11102	−	7.03471i	0.179362	−	0.246870i
$813$	−29.8532	+	41.0895i	−1.04700	+	1.44107i
$814$	13.7664	−	10.0019i	0.482513	−	0.350566i
$815$	21.3800	−	33.4503i	0.748909	−	1.17171i
$816$	8.40450	+	6.10623i	0.294216	+	0.213761i
$817$	1.79300	−	0.582582i	0.0627292	−	0.0203820i
$818$		−	20.2981i		−	0.709708i
$819$	−4.40198	−	13.5479i	−0.153818	−	0.473402i
$820$	6.48372	−	5.32863i	0.226421	−	0.186084i
$821$	−13.2623	+	40.8171i	−0.462857	+	1.42453i	0.398802	+	0.917037i	$0.369426\pi$
$821$	−13.2623	+	40.8171i	−0.462857	+	1.42453i	−0.861658	+	0.507489i	$0.830574\pi$
$822$	−20.3723	−	6.61936i	−0.710565	−	0.230877i
$823$	30.7824	+	42.3684i	1.07301	+	1.47687i	0.866993	+	0.498320i	$0.166049\pi$
$823$	30.7824	+	42.3684i	1.07301	+	1.47687i	0.206015	+	0.978549i	$0.433951\pi$
$824$	0.206275			0.00718594
$825$	28.7159	−	13.2869i	0.999761	−	0.462591i
$826$	20.8292			0.724740
$827$	17.6698	+	24.3204i	0.614439	+	0.845703i	0.996933	−	0.0782549i	$-0.0249348\pi$
$827$	17.6698	+	24.3204i	0.614439	+	0.845703i	−0.382494	+	0.923958i	$0.624935\pi$
$828$	−0.623799	−	0.202685i	−0.0216785	−	0.00704378i
$829$	−9.87090	+	30.3795i	−0.342831	+	1.05512i	0.619904	+	0.784677i	$0.287171\pi$
$829$	−9.87090	+	30.3795i	−0.342831	+	1.05512i	−0.962735	+	0.270447i	$0.912829\pi$
$830$	−6.07605	−	3.88355i	−0.210903	−	0.134800i
$831$	−7.67746	−	23.6288i	−0.266328	−	0.819674i
$832$		−	2.54413i		−	0.0882018i
$833$	6.36136	−	2.06693i	0.220408	−	0.0716149i
$834$	7.80797	+	5.67282i	0.270368	+	0.196434i
$835$	30.3295	−	11.8952i	1.04960	−	0.411650i
$836$	2.20593	−	1.60271i	0.0762938	−	0.0554307i
$837$	3.69207	−	5.08170i	0.127617	−	0.175649i
$838$	9.03607	−	12.4371i	0.312146	−	0.429632i
$839$	−15.5280	+	11.2818i	−0.536087	+	0.389490i	−0.822630	−	0.568577i	$-0.807494\pi$
$839$	−15.5280	+	11.2818i	−0.536087	+	0.389490i	0.286543	+	0.958067i	$0.407494\pi$
$840$	0.725356	+	12.1553i	0.0250271	+	0.419396i
$841$	12.3513	+	8.97376i	0.425907	+	0.309440i
$842$	−6.28498	+	2.04211i	−0.216595	+	0.0703759i
$843$			12.8209i			0.441576i
$844$	−5.91619	−	18.2082i	−0.203644	−	0.626751i
$845$	5.32920	+	13.5880i	0.183330	+	0.467443i
$846$	0.156197	−	0.480724i	0.00537015	−	0.0165276i
$847$	7.95602	+	2.58507i	0.273372	+	0.0888239i
$848$	3.97943	+	5.47722i	0.136654	+	0.188088i
$849$	43.0244			1.47659
$850$	−19.5426	−	10.9086i	−0.670307	−	0.374160i
$851$	1.71533			0.0588007
$852$	12.3963	+	17.0620i	0.424690	+	0.584536i
$853$	−13.4180	−	4.35976i	−0.459422	−	0.149275i	0.0701567	−	0.997536i	$-0.477650\pi$
$853$	−13.4180	−	4.35976i	−0.459422	−	0.149275i	−0.529579	+	0.848261i	$0.677650\pi$
$854$	9.92640	−	30.5503i	0.339674	−	1.04541i
$855$	−1.34365	+	5.16391i	−0.0459519	+	0.176602i
$856$	−3.98647	−	12.2691i	−0.136255	−	0.419349i
$857$			8.81440i			0.301094i	0.988603	+	0.150547i	$0.0481035\pi$
$857$			8.81440i			0.301094i	−0.988603	+	0.150547i	$0.951896\pi$
$858$	−15.3117	+	4.97509i	−0.522734	+	0.169847i
$859$	25.5032	+	18.5291i	0.870157	+	0.632206i	0.930629	−	0.365964i	$-0.119261\pi$
$859$	25.5032	+	18.5291i	0.870157	+	0.632206i	−0.0604721	+	0.998170i	$0.519261\pi$
$860$	4.07975	+	1.06155i	0.139118	+	0.0361987i
$861$	16.5353	−	12.0136i	0.563521	−	0.409422i
$862$	15.9358	−	21.9338i	0.542776	−	0.747067i
$863$	−25.3277	+	34.8605i	−0.862164	+	1.18667i	0.118886	+	0.992908i	$0.462068\pi$
$863$	−25.3277	+	34.8605i	−0.862164	+	1.18667i	−0.981049	+	0.193758i	$0.937932\pi$
$864$	−1.15234	+	0.837221i	−0.0392033	+	0.0284828i
$865$	18.8535	+	22.9404i	0.641040	+	0.779997i
$866$	31.3112	+	22.7489i	1.06400	+	0.773040i
$867$	−6.70215	+	2.17766i	−0.227617	+	0.0739572i
$868$		−	10.3475i		−	0.351218i
$869$	11.1773	+	34.4003i	0.379165	+	1.16695i
$870$	19.1972	−	1.14558i	0.650847	−	0.0388388i
$871$	−7.38612	+	22.7322i	−0.250269	+	0.770250i
$872$	−8.74784	−	2.84235i	−0.296239	−	0.0962540i
$873$	−15.3383	−	21.1113i	−0.519121	−	0.714509i
$874$	0.274865			0.00929743
$875$	−4.66593	−	25.8156i	−0.157737	−	0.872725i
$876$	−17.5064			−0.591487
$877$	22.9201	+	31.5468i	0.773957	+	1.06526i	0.995923	+	0.0902066i	$0.0287527\pi$
$877$	22.9201	+	31.5468i	0.773957	+	1.06526i	−0.221966	+	0.975054i	$0.571247\pi$
$878$	−26.4449	−	8.59245i	−0.892471	−	0.289981i
$879$	17.5037	−	53.8707i	0.590383	−	1.81701i
$880$	6.08623	−	0.363191i	0.205167	−	0.0122432i
$881$	−12.6860	−	39.0435i	−0.427403	−	1.31541i	−0.900675	−	0.434494i	$-0.856927\pi$
$881$	−12.6860	−	39.0435i	−0.427403	−	1.31541i	0.473272	−	0.880916i	$-0.343073\pi$
$882$		−	3.56577i		−	0.120066i
$883$	0.934669	−	0.303692i	0.0314541	−	0.0102201i	−0.293248	−	0.956037i	$-0.594736\pi$
$883$	0.934669	−	0.303692i	0.0314541	−	0.0102201i	0.324702	+	0.945816i	$0.394736\pi$
$884$	9.21313	+	6.69373i	0.309871	+	0.225134i
$885$	29.2498	+	35.5902i	0.983221	+	1.19635i
$886$	21.9728	−	15.9642i	0.738190	−	0.536327i
$887$	31.6321	−	43.5378i	1.06210	−	1.46186i	0.184277	−	0.982874i	$-0.441006\pi$
$887$	31.6321	−	43.5378i	1.06210	−	1.46186i	0.877824	−	0.478983i	$-0.158994\pi$
$888$	−8.51317	+	11.7174i	−0.285683	+	0.393209i
$889$	−4.05760	+	2.94802i	−0.136088	+	0.0988734i
$890$	−7.56334	−	1.96798i	−0.253524	−	0.0659669i
$891$	23.0841	+	16.7716i	0.773345	+	0.561868i
$892$	24.4761	−	7.95278i	0.819521	−	0.266279i
$893$			0.211821i			0.00708834i
$894$	3.12152	+	9.60706i	0.104399	+	0.321308i
$895$	4.71772	−	18.1311i	0.157696	−	0.606056i
$896$	−0.725086	+	2.23158i	−0.0242234	+	0.0745520i
$897$	−1.54351	−	0.501516i	−0.0515362	−	0.0167451i
$898$	19.9883	+	27.5115i	0.667017	+	0.918071i
$899$	−16.3422			−0.545044
$900$	−8.75013	+	8.11124i	−0.291671	+	0.270375i
$901$	−30.3049			−1.00960
$902$	−6.01529	−	8.27934i	−0.200287	−	0.275672i
$903$	9.76409	+	3.17254i	0.324929	+	0.105576i
$904$	3.61541	−	11.1271i	0.120247	−	0.370082i
$905$	9.23955	+	23.5584i	0.307133	+	0.783107i
$906$	−8.64381	−	26.6029i	−0.287171	−	0.883823i
$907$			9.79497i			0.325237i	0.986689	+	0.162618i	$0.0519939\pi$
$907$			9.79497i			0.325237i	−0.986689	+	0.162618i	$0.948006\pi$
$908$	−16.7778	+	5.45142i	−0.556789	+	0.180912i
$909$	9.30326	+	6.75921i	0.308570	+	0.224189i
$910$	0.795145	+	13.3248i	0.0263588	+	0.441711i
$911$	−12.7463	+	9.26070i	−0.422302	+	0.306821i	−0.778563	−	0.627566i	$-0.784051\pi$
$911$	−12.7463	+	9.26070i	−0.422302	+	0.306821i	0.356261	+	0.934386i	$0.384051\pi$
$912$	−1.36415	+	1.87759i	−0.0451716	+	0.0621734i
$913$	−5.16858	+	7.11395i	−0.171055	+	0.235437i
$914$	3.10186	−	2.25363i	0.102600	−	0.0745436i
$915$	66.1398	−	25.9399i	2.18651	−	0.857547i
$916$	−13.4929	−	9.80315i	−0.445817	−	0.323905i
$917$	28.0758	−	9.12239i	0.927146	−	0.301248i
$918$		−	6.37576i		−	0.210431i
$919$	2.08416	+	6.41437i	0.0687500	+	0.211591i	0.979529	−	0.201304i	$-0.0645178\pi$
$919$	2.08416	+	6.41437i	0.0687500	+	0.211591i	−0.910779	+	0.412894i	$0.864518\pi$
$920$	0.517871	+	0.331001i	0.0170737	+	0.0109128i
$921$	−22.6041	+	69.5682i	−0.744830	+	2.29235i
$922$	−18.1149	−	5.88588i	−0.596582	−	0.193841i
$923$	13.5890	+	18.7036i	0.447287	+	0.615638i
$924$	14.8486			0.488484
$925$	15.2085	−	27.2459i	0.500051	−	0.895840i
$926$	−1.33657			−0.0439226
$927$	0.289325	+	0.398221i	0.00950267	+	0.0130793i
$928$	3.52442	+	1.14515i	0.115695	+	0.0375915i
$929$	2.09039	−	6.43357i	0.0685836	−	0.211079i	−0.910891	−	0.412648i	$-0.864604\pi$
$929$	2.09039	−	6.43357i	0.0685836	−	0.211079i	0.979474	+	0.201569i	$0.0646040\pi$
$930$	17.6805	−	14.5307i	0.579767	−	0.476481i
$931$	0.461759	+	1.42115i	0.0151336	+	0.0465763i
$932$			15.7735i			0.516678i
$933$	34.5902	−	11.2391i	1.13243	−	0.367950i
$934$	34.7700	+	25.2619i	1.13771	+	0.826594i
$935$	−14.6979	+	22.9958i	−0.480674	+	0.752043i
$936$	4.91153	−	3.56843i	0.160538	−	0.116638i
$937$	4.42170	−	6.08595i	0.144451	−	0.198819i	−0.730661	−	0.682741i	$-0.760788\pi$
$937$	4.42170	−	6.08595i	0.144451	−	0.198819i	0.875112	+	0.483921i	$0.160788\pi$
$938$	12.9575	−	17.8344i	0.423077	−	0.582315i
$939$	−35.0453	+	25.4619i	−1.14366	+	0.830918i
$940$	−0.255083	+	0.399092i	−0.00831988	+	0.0130170i
$941$	−1.65864	−	1.20507i	−0.0540701	−	0.0392842i	0.560422	−	0.828207i	$-0.310639\pi$
$941$	−1.65864	−	1.20507i	−0.0540701	−	0.0392842i	−0.614492	+	0.788923i	$0.710639\pi$
$942$	32.5760	−	10.5846i	1.06139	−	0.344865i
$943$		−	1.03162i		−	0.0335943i
$944$	2.74314	+	8.44251i	0.0892816	+	0.274780i
$945$	5.77364	−	4.74506i	0.187816	−	0.154357i
$946$	1.58852	−	4.88895i	0.0516471	−	0.158954i
$947$	0.813944	+	0.264466i	0.0264496	+	0.00859400i	0.322212	−	0.946668i	$-0.395574\pi$
$947$	0.813944	+	0.264466i	0.0264496	+	0.00859400i	−0.295762	+	0.955262i	$0.595574\pi$
$948$	−18.0961	−	24.9071i	−0.587733	−	0.808945i
$949$	−19.1908			−0.622959
$950$	2.43701	−	4.36589i	0.0790670	−	0.141648i
$951$	−26.3113			−0.853202
$952$	−6.17356	−	8.49718i	−0.200086	−	0.275395i
$953$	−15.8061	−	5.13571i	−0.512010	−	0.166362i	0.0416063	−	0.999134i	$-0.486752\pi$
$953$	−15.8061	−	5.13571i	−0.512010	−	0.166362i	−0.553616	+	0.832772i	$0.686752\pi$
$954$	−4.99234	+	15.3648i	−0.161633	+	0.497455i
$955$	33.1653	+	21.1978i	1.07320	+	0.685946i
$956$	1.85852	+	5.71994i	0.0601088	+	0.184996i
$957$		−	23.4510i		−	0.758062i
$958$	−9.60260	+	3.12007i	−0.310246	+	0.100805i
$959$	17.5208	+	12.7296i	0.565776	+	0.411060i
$960$	−4.83126	+	1.89481i	−0.155928	+	0.0611548i
$961$	9.34634	−	6.79051i	0.301495	−	0.219049i
$962$	−9.33225	+	12.8447i	−0.300884	+	0.414131i
$963$	18.0944	−	24.9048i	0.583085	−	0.802547i
$964$	−3.87275	+	2.81371i	−0.124733	+	0.0906237i
$965$	−0.674848	−	11.3089i	−0.0217241	−	0.364045i
$966$	1.21095	+	0.879809i	0.0389618	+	0.0283074i
$967$	4.69925	−	1.52688i	0.151118	−	0.0491011i	−0.232481	−	0.972601i	$-0.574684\pi$
$967$	4.69925	−	1.52688i	0.151118	−	0.0491011i	0.383599	+	0.923500i	$0.374684\pi$
$968$			3.56519i			0.114589i
$969$	−3.21023	−	9.88008i	−0.103128	−	0.317394i
$970$	8.92811	+	22.7643i	0.286664	+	0.730917i
$971$	16.0704	−	49.4595i	0.515723	−	1.58723i	−0.266240	−	0.963907i	$-0.585781\pi$
$971$	16.0704	−	49.4595i	0.515723	−	1.58723i	0.781963	−	0.623325i	$-0.214219\pi$
$972$	−19.0338	−	6.18446i	−0.610510	−	0.198367i
$973$	−5.73538	−	7.89407i	−0.183868	−	0.253072i
$974$	−19.9584			−0.639507
$975$	−21.6510	+	20.0702i	−0.693388	+	0.642760i
$976$	13.6900			0.438205
$977$	11.5754	+	15.9322i	0.370330	+	0.509716i	0.952991	−	0.303000i	$-0.0979882\pi$
$977$	11.5754	+	15.9322i	0.370330	+	0.509716i	−0.582660	+	0.812716i	$0.697988\pi$
$978$	39.1875	+	12.7328i	1.25308	+	0.407150i
$979$	−2.94490	+	9.06349i	−0.0941196	+	0.289670i
$980$	−0.841397	+	3.23365i	−0.0268774	+	0.103295i
$981$	−6.78260	−	20.8747i	−0.216552	−	0.666478i
$982$		−	42.7486i		−	1.36416i
$983$	3.62821	−	1.17888i	0.115722	−	0.0376003i	−0.250584	−	0.968095i	$-0.580623\pi$
$983$	3.62821	−	1.17888i	0.115722	−	0.0376003i	0.366306	+	0.930495i	$0.380623\pi$
$984$	7.04700	+	5.11995i	0.224650	+	0.163218i
$985$	−6.84718	−	1.78164i	−0.218169	−	0.0567677i
$986$	−13.4199	+	9.75013i	−0.427377	+	0.310508i
$987$	−0.678015	+	0.933208i	−0.0215815	+	0.0297043i
$988$	−1.49540	+	2.05824i	−0.0475751	+	0.0654815i
$989$	0.419229	−	0.304587i	0.0133307	−	0.00968531i
$990$	9.23778	+	11.2402i	0.293596	+	0.357238i
$991$	16.4634	+	11.9614i	0.522977	+	0.379965i	0.817724	−	0.575610i	$-0.195235\pi$
$991$	16.4634	+	11.9614i	0.522977	+	0.379965i	−0.294747	+	0.955575i	$0.595235\pi$
$992$	4.19407	−	1.36274i	0.133162	−	0.0432669i
$993$		−	39.3429i		−	1.24851i
$994$	−6.58899	−	20.2788i	−0.208990	−	0.643205i
$995$	39.1919	−	2.33875i	1.24247	−	0.0741433i
$996$	2.31283	−	7.11817i	0.0732849	−	0.225548i
$997$	−26.8420	−	8.72148i	−0.850093	−	0.276212i	−0.148608	−	0.988896i	$-0.547479\pi$
$997$	−26.8420	−	8.72148i	−0.850093	−	0.276212i	−0.701485	+	0.712684i	$0.747479\pi$
$998$	3.93575	+	5.41710i	0.124584	+	0.171475i
$999$	8.88895			0.281234

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.n.a.39.2	✓	88
25.9	even	10	inner	950.2.n.a.609.2	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.n.a.39.2	✓	88	1.1	even	1	trivial
950.2.n.a.609.2	yes	88	25.9	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-2.20724 - 0.717177i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.23210 - 0.133199i) q^{5} +(0.717177 + 2.20724i) q^{6} -2.34643i q^{7} +(0.951057 - 0.309017i) q^{8} +(1.93053 + 1.40261i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-2.20724 - 0.717177i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.23210 - 0.133199i) q^{5} +(0.717177 + 2.20724i) q^{6} -2.34643i q^{7} +(0.951057 - 0.309017i) q^{8} +(1.93053 + 1.40261i) q^{9} +(-1.41975 - 1.72751i) q^{10} +(-2.20593 + 1.60271i) q^{11} +(1.36415 - 1.87759i) q^{12} +(1.49540 - 2.05824i) q^{13} +(-1.89830 + 1.37919i) q^{14} +(-5.02231 - 1.30681i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.25713 - 1.38322i) q^{17} -2.38627i q^{18} +(0.309017 + 0.951057i) q^{19} +(-0.563076 + 2.16401i) q^{20} +(-1.68280 + 5.17914i) q^{21} +(2.59323 + 0.842592i) q^{22} +(0.161561 + 0.222370i) q^{23} -2.32083 q^{24} +(4.96452 - 0.594625i) q^{25} -2.54413 q^{26} +(0.837221 + 1.15234i) q^{27} +(2.23158 + 0.725086i) q^{28} +(1.14515 - 3.52442i) q^{29} +(1.89481 + 4.83126i) q^{30} +(-1.36274 - 4.19407i) q^{31} +1.00000i q^{32} +(6.01846 - 1.95552i) q^{33} +(-3.62133 - 2.63105i) q^{34} +(-0.312541 - 5.23745i) q^{35} +(-1.93053 + 1.40261i) q^{36} +(3.66815 - 5.04878i) q^{37} +(0.587785 - 0.809017i) q^{38} +(-4.77684 + 3.47058i) q^{39} +(2.08169 - 0.816435i) q^{40} +(-3.03641 - 2.20608i) q^{41} +(5.17914 - 1.68280i) q^{42} -1.88527i q^{43} +(-0.842592 - 2.59323i) q^{44} +(4.49596 + 2.87363i) q^{45} +(0.0849378 - 0.261412i) q^{46} +(0.201454 + 0.0654564i) q^{47} +(1.36415 + 1.87759i) q^{48} +1.49428 q^{49} +(-3.39913 - 3.66687i) q^{50} -10.3885 q^{51} +(1.49540 + 2.05824i) q^{52} +(-6.43885 - 2.09211i) q^{53} +(0.440153 - 1.35465i) q^{54} +(-4.71038 + 3.87122i) q^{55} +(-0.725086 - 2.23158i) q^{56} -2.32083i q^{57} +(-3.52442 + 1.14515i) q^{58} +(-7.18163 - 5.21776i) q^{59} +(2.79483 - 4.37268i) q^{60} +(-11.0754 + 8.04676i) q^{61} +(-2.59208 + 3.56769i) q^{62} +(3.29113 - 4.52985i) q^{63} +(0.809017 - 0.587785i) q^{64} +(3.06373 - 4.79339i) q^{65} +(-5.11961 - 3.71961i) q^{66} +(-8.93514 + 2.90320i) q^{67} +4.47621i q^{68} +(-0.197127 - 0.606693i) q^{69} +(-4.05348 + 3.33135i) q^{70} +(-2.80809 + 8.64243i) q^{71} +(2.26948 + 0.737398i) q^{72} +(-4.43376 - 6.10254i) q^{73} -6.24063 q^{74} +(-11.3844 - 2.24795i) q^{75} -1.00000 q^{76} +(3.76063 + 5.17606i) q^{77} +(5.61552 + 1.82459i) q^{78} +(4.09924 - 12.6162i) q^{79} +(-1.88410 - 1.20423i) q^{80} +(-3.23372 - 9.95236i) q^{81} +3.75321i q^{82} +(3.06707 - 0.996553i) q^{83} +(-4.40564 - 3.20088i) q^{84} +(9.31808 - 3.65453i) q^{85} +(-1.52522 + 1.10814i) q^{86} +(-5.05527 + 6.95798i) q^{87} +(-1.60271 + 2.20593i) q^{88} +(2.82756 - 2.05434i) q^{89} +(-0.317848 - 5.32639i) q^{90} +(-4.82952 - 3.50885i) q^{91} +(-0.261412 + 0.0849378i) q^{92} +10.2347i q^{93} +(-0.0654564 - 0.201454i) q^{94} +(0.816435 + 2.08169i) q^{95} +(0.717177 - 2.20724i) q^{96} +(-10.4003 - 3.37925i) q^{97} +(-0.878319 - 1.20890i) q^{98} -6.50661 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9}+O(q^{10}) \) 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9	\( 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9} + 26 q^{11} + 10 q^{12} - 10 q^{14} + 12 q^{15} - 22 q^{16} - 40 q^{17} - 22 q^{19} + 10 q^{23} + 8 q^{24} + 6 q^{25} - 28 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} - 4 q^{30} + 2 q^{31} - 8 q^{34} - 48 q^{35} - 24 q^{36} + 50 q^{37} + 8 q^{39} + 32 q^{41} + 10 q^{42} + 4 q^{44} - 8 q^{45} + 10 q^{46} + 10 q^{48} - 56 q^{49} + 28 q^{50} - 60 q^{51} - 70 q^{53} - 8 q^{54} + 4 q^{55} + 10 q^{56} - 60 q^{58} - 28 q^{59} - 12 q^{60} - 58 q^{61} + 60 q^{63} + 22 q^{64} - 24 q^{65} + 4 q^{66} - 70 q^{67} - 8 q^{69} - 4 q^{70} + 48 q^{71} + 40 q^{73} + 52 q^{74} + 108 q^{75} - 88 q^{76} - 50 q^{78} - 20 q^{79} + 24 q^{81} - 80 q^{83} + 30 q^{85} + 20 q^{86} + 70 q^{87} + 10 q^{88} - 62 q^{89} - 104 q^{90} + 20 q^{91} - 10 q^{92} - 10 q^{94} + 2 q^{96} - 10 q^{97} + 60 q^{98} + 156 q^{99}+O(q^{100}) \) 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9 + 26 * q^11 + 10 * q^12 - 10 * q^14 + 12 * q^15 - 22 * q^16 - 40 * q^17 - 22 * q^19 + 10 * q^23 + 8 * q^24 + 6 * q^25 - 28 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 - 4 * q^30 + 2 * q^31 - 8 * q^34 - 48 * q^35 - 24 * q^36 + 50 * q^37 + 8 * q^39 + 32 * q^41 + 10 * q^42 + 4 * q^44 - 8 * q^45 + 10 * q^46 + 10 * q^48 - 56 * q^49 + 28 * q^50 - 60 * q^51 - 70 * q^53 - 8 * q^54 + 4 * q^55 + 10 * q^56 - 60 * q^58 - 28 * q^59 - 12 * q^60 - 58 * q^61 + 60 * q^63 + 22 * q^64 - 24 * q^65 + 4 * q^66 - 70 * q^67 - 8 * q^69 - 4 * q^70 + 48 * q^71 + 40 * q^73 + 52 * q^74 + 108 * q^75 - 88 * q^76 - 50 * q^78 - 20 * q^79 + 24 * q^81 - 80 * q^83 + 30 * q^85 + 20 * q^86 + 70 * q^87 + 10 * q^88 - 62 * q^89 - 104 * q^90 + 20 * q^91 - 10 * q^92 - 10 * q^94 + 2 * q^96 - 10 * q^97 + 60 * q^98 + 156 * q^99

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