LMFDB - Embedded newform 165.2.p.b.41.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(41,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("165.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.p (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:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			41.9
Character	$\chi$	$=$	165.41
Dual form			165.2.p.b.161.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37228 - 0.997022i) q^{2} +(-0.579977 + 1.63206i) q^{3} +(0.271073 - 0.834277i) q^{4} +(-0.587785 + 0.809017i) q^{5} +(0.831309 + 2.81790i) q^{6} +(3.82974 + 1.24436i) q^{7} +(0.588527 + 1.81130i) q^{8} +(-2.32725 - 1.89312i) q^{9} +O(q^{10})$	\(q+(1.37228 - 0.997022i) q^{2} +(-0.579977 + 1.63206i) q^{3} +(0.271073 - 0.834277i) q^{4} +(-0.587785 + 0.809017i) q^{5} +(0.831309 + 2.81790i) q^{6} +(3.82974 + 1.24436i) q^{7} +(0.588527 + 1.81130i) q^{8} +(-2.32725 - 1.89312i) q^{9} +1.69623i q^{10} +(0.328772 - 3.30029i) q^{11} +(1.20438 + 0.926269i) q^{12} +(-3.28394 - 4.51996i) q^{13} +(6.49614 - 2.11072i) q^{14} +(-0.979464 - 1.42851i) q^{15} +(4.03289 + 2.93006i) q^{16} +(0.766360 + 0.556793i) q^{17} +(-5.08113 - 0.277567i) q^{18} +(-4.31938 + 1.40345i) q^{19} +(0.515612 + 0.709679i) q^{20} +(-4.25203 + 5.52868i) q^{21} +(-2.83929 - 4.85672i) q^{22} -2.88723i q^{23} +(-3.29749 - 0.0899989i) q^{24} +(-0.309017 - 0.951057i) q^{25} +(-9.01300 - 2.92850i) q^{26} +(4.43944 - 2.70026i) q^{27} +(2.07628 - 2.85775i) q^{28} +(-1.65920 + 5.10648i) q^{29} +(-2.76836 - 0.983776i) q^{30} +(1.46504 - 1.06441i) q^{31} +4.64657 q^{32} +(5.19560 + 2.45067i) q^{33} +1.60680 q^{34} +(-3.25777 + 2.36691i) q^{35} +(-2.21024 + 1.42840i) q^{36} +(2.46634 - 7.59061i) q^{37} +(-4.52813 + 6.23244i) q^{38} +(9.28147 - 2.73813i) q^{39} +(-1.81130 - 0.588527i) q^{40} +(-0.413653 - 1.27309i) q^{41} +(-0.322777 + 11.8263i) q^{42} -8.82336i q^{43} +(-2.66423 - 1.16891i) q^{44} +(2.89949 - 0.770043i) q^{45} +(-2.87863 - 3.96209i) q^{46} +(-7.05759 + 2.29315i) q^{47} +(-7.12103 + 4.88255i) q^{48} +(7.45538 + 5.41665i) q^{49} +(-1.37228 - 0.997022i) q^{50} +(-1.35319 + 0.927821i) q^{51} +(-4.66109 + 1.51448i) q^{52} +(5.57751 + 7.67679i) q^{53} +(3.39994 - 8.13173i) q^{54} +(2.47674 + 2.20584i) q^{55} +7.66915i q^{56} +(0.214619 - 7.86346i) q^{57} +(2.81439 + 8.66179i) q^{58} +(-1.84920 - 0.600843i) q^{59} +(-1.45728 + 0.429913i) q^{60} +(-7.71633 + 10.6206i) q^{61} +(0.949206 - 2.92135i) q^{62} +(-6.55707 - 10.1461i) q^{63} +(-1.68937 + 1.22740i) q^{64} +5.58698 q^{65} +(9.57319 - 1.81711i) q^{66} -1.99934 q^{67} +(0.672260 - 0.488425i) q^{68} +(4.71214 + 1.67452i) q^{69} +(-2.11072 + 6.49614i) q^{70} +(1.44240 - 1.98529i) q^{71} +(2.05935 - 5.32951i) q^{72} +(9.21799 + 2.99511i) q^{73} +(-4.18349 - 12.8755i) q^{74} +(1.73141 + 0.0472556i) q^{75} +3.98399i q^{76} +(5.36586 - 12.2301i) q^{77} +(10.0068 - 13.0113i) q^{78} +(-1.25135 - 1.72234i) q^{79} +(-4.74094 + 1.54043i) q^{80} +(1.83222 + 8.81152i) q^{81} +(-1.83695 - 1.33462i) q^{82} +(2.50390 + 1.81919i) q^{83} +(3.45984 + 5.04605i) q^{84} +(-0.900911 + 0.292724i) q^{85} +(-8.79708 - 12.1081i) q^{86} +(-7.37180 - 5.66955i) q^{87} +(6.17130 - 1.34680i) q^{88} +11.0376i q^{89} +(3.21117 - 3.94757i) q^{90} +(-6.95221 - 21.3967i) q^{91} +(-2.40875 - 0.782650i) q^{92} +(0.887501 + 3.00837i) q^{93} +(-7.39869 + 10.1834i) q^{94} +(1.40345 - 4.31938i) q^{95} +(-2.69490 + 7.58349i) q^{96} +(-6.43282 + 4.67372i) q^{97} +15.6314 q^{98} +(-7.01297 + 7.05821i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9}+O(q^{10}) $ 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9	$ 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9} + 8 q^{12} + 6 q^{15} + 32 q^{16} - 30 q^{18} - 100 q^{19} - 82 q^{22} + 100 q^{24} + 12 q^{25} + 14 q^{27} + 30 q^{28} + 10 q^{30} + 10 q^{31} - 46 q^{33} - 28 q^{34} + 14 q^{36} + 6 q^{37} - 50 q^{40} - 52 q^{42} + 32 q^{45} + 20 q^{46} - 80 q^{48} - 26 q^{49} - 30 q^{51} + 40 q^{52} + 6 q^{55} - 70 q^{57} + 92 q^{58} + 44 q^{60} + 70 q^{61} - 20 q^{63} + 18 q^{64} + 76 q^{66} + 20 q^{67} + 42 q^{69} - 4 q^{70} - 80 q^{72} + 90 q^{73} - 6 q^{75} - 108 q^{78} - 100 q^{79} + 38 q^{81} - 34 q^{82} + 70 q^{84} + 20 q^{85} + 74 q^{88} + 20 q^{90} - 86 q^{91} + 76 q^{93} + 10 q^{94} - 30 q^{96} + 6 q^{97} - 28 q^{99}+O(q^{100}) $ 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9 + 8 * q^12 + 6 * q^15 + 32 * q^16 - 30 * q^18 - 100 * q^19 - 82 * q^22 + 100 * q^24 + 12 * q^25 + 14 * q^27 + 30 * q^28 + 10 * q^30 + 10 * q^31 - 46 * q^33 - 28 * q^34 + 14 * q^36 + 6 * q^37 - 50 * q^40 - 52 * q^42 + 32 * q^45 + 20 * q^46 - 80 * q^48 - 26 * q^49 - 30 * q^51 + 40 * q^52 + 6 * q^55 - 70 * q^57 + 92 * q^58 + 44 * q^60 + 70 * q^61 - 20 * q^63 + 18 * q^64 + 76 * q^66 + 20 * q^67 + 42 * q^69 - 4 * q^70 - 80 * q^72 + 90 * q^73 - 6 * q^75 - 108 * q^78 - 100 * q^79 + 38 * q^81 - 34 * q^82 + 70 * q^84 + 20 * q^85 + 74 * q^88 + 20 * q^90 - 86 * q^91 + 76 * q^93 + 10 * q^94 - 30 * q^96 + 6 * q^97 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.37228	−	0.997022i	0.970350	−	0.705001i	0.0148188	−	0.999890i	$-0.495283\pi$
$2$	1.37228	−	0.997022i	0.970350	−	0.705001i	0.955531	+	0.294890i	$0.0952828\pi$
$3$	−0.579977	+	1.63206i	−0.334850	+	0.942272i
$3$	−0.579977	+	1.63206i	−0.334850	+	0.942272i
$4$	0.271073	−	0.834277i	0.135537	−	0.417139i
$5$	−0.587785	+	0.809017i	−0.262866	+	0.361803i
$5$	−0.587785	+	0.809017i	−0.262866	+	0.361803i
$6$	0.831309	+	2.81790i	0.339381	+	1.15040i
$7$	3.82974	+	1.24436i	1.44751	+	0.470323i	0.924229	−	0.381839i	$-0.124709\pi$
$7$	3.82974	+	1.24436i	1.44751	+	0.470323i	0.523278	+	0.852162i	$0.324709\pi$
$8$	0.588527	+	1.81130i	0.208076	+	0.640391i
$9$	−2.32725	−	1.89312i	−0.775751	−	0.631039i
$10$			1.69623i			0.536396i
$11$	0.328772	−	3.30029i	0.0991285	−	0.995075i
$11$	0.328772	−	3.30029i	0.0991285	−	0.995075i
$12$	1.20438	+	0.926269i	0.347673	+	0.267391i
$13$	−3.28394	−	4.51996i	−0.910802	−	1.25361i	−0.966892	−	0.255186i	$-0.917863\pi$
$13$	−3.28394	−	4.51996i	−0.910802	−	1.25361i	0.0560899	−	0.998426i	$-0.482137\pi$
$14$	6.49614	−	2.11072i	1.73617	−	0.564115i
$15$	−0.979464	−	1.42851i	−0.252897	−	0.368840i
$16$	4.03289	+	2.93006i	1.00822	+	0.732516i
$17$	0.766360	+	0.556793i	0.185870	+	0.135042i	0.676829	−	0.736140i	$-0.263354\pi$
$17$	0.766360	+	0.556793i	0.185870	+	0.135042i	−0.490959	+	0.871183i	$0.663354\pi$
$18$	−5.08113	−	0.277567i	−1.19763	−	0.0654232i
$19$	−4.31938	+	1.40345i	−0.990933	+	0.321974i	−0.759237	−	0.650815i	$-0.774427\pi$
$19$	−4.31938	+	1.40345i	−0.990933	+	0.321974i	−0.231696	+	0.972788i	$0.574427\pi$
$20$	0.515612	+	0.709679i	0.115294	+	0.158689i
$21$	−4.25203	+	5.52868i	−0.927870	+	1.20646i
$22$	−2.83929	−	4.85672i	−0.605339	−	1.03546i
$23$		−	2.88723i		−	0.602029i	−0.953620	−	0.301014i	$-0.902675\pi$
$23$		−	2.88723i		−	0.602029i	0.953620	−	0.301014i	$-0.0973252\pi$
$24$	−3.29749	−	0.0899989i	−0.673097	−	0.0183709i
$25$	−0.309017	−	0.951057i	−0.0618034	−	0.190211i
$26$	−9.01300	−	2.92850i	−1.76759	−	0.574326i
$27$	4.43944	−	2.70026i	0.854370	−	0.519665i
$28$	2.07628	−	2.85775i	0.392380	−	0.540065i
$29$	−1.65920	+	5.10648i	−0.308105	+	0.948250i	0.670395	+	0.742004i	$0.266125\pi$
$29$	−1.65920	+	5.10648i	−0.308105	+	0.948250i	−0.978500	+	0.206246i	$0.933875\pi$
$30$	−2.76836	−	0.983776i	−0.505431	−	0.179612i
$31$	1.46504	−	1.06441i	0.263129	−	0.191175i	−0.448396	−	0.893835i	$-0.648005\pi$
$31$	1.46504	−	1.06441i	0.263129	−	0.191175i	0.711525	+	0.702660i	$0.248005\pi$
$32$	4.64657			0.821405
$33$	5.19560	+	2.45067i	0.904437	+	0.426606i
$34$	1.60680			0.275564
$35$	−3.25777	+	2.36691i	−0.550664	+	0.400081i
$36$	−2.21024	+	1.42840i	−0.368373	+	0.238067i
$37$	2.46634	−	7.59061i	0.405463	−	1.24789i	−0.515044	−	0.857164i	$-0.672224\pi$
$37$	2.46634	−	7.59061i	0.405463	−	1.24789i	0.920508	−	0.390725i	$-0.127776\pi$
$38$	−4.52813	+	6.23244i	−0.734560	+	1.01104i
$39$	9.28147	−	2.73813i	1.48622	−	0.438452i
$40$	−1.81130	−	0.588527i	−0.286392	−	0.0930543i
$41$	−0.413653	−	1.27309i	−0.0646017	−	0.198824i	0.913546	−	0.406736i	$-0.133333\pi$
$41$	−0.413653	−	1.27309i	−0.0646017	−	0.198824i	−0.978147	+	0.207912i	$0.933333\pi$
$42$	−0.322777	+	11.8263i	−0.0498055	+	1.82483i
$43$		−	8.82336i		−	1.34555i	−0.739847	−	0.672775i	$-0.765102\pi$
$43$		−	8.82336i		−	1.34555i	0.739847	−	0.672775i	$-0.234898\pi$
$44$	−2.66423	−	1.16891i	−0.401648	−	0.176219i
$45$	2.89949	−	0.770043i	0.432230	−	0.114791i
$46$	−2.87863	−	3.96209i	−0.424431	−	0.584179i
$47$	−7.05759	+	2.29315i	−1.02946	+	0.334490i	−0.774575	−	0.632482i	$-0.782036\pi$
$47$	−7.05759	+	2.29315i	−1.02946	+	0.334490i	−0.254881	+	0.966973i	$0.582036\pi$
$48$	−7.12103	+	4.88255i	−1.02783	+	0.704736i
$49$	7.45538	+	5.41665i	1.06505	+	0.773807i
$50$	−1.37228	−	0.997022i	−0.194070	−	0.141000i
$51$	−1.35319	+	0.927821i	−0.189485	+	0.129921i
$52$	−4.66109	+	1.51448i	−0.646377	+	0.210021i
$53$	5.57751	+	7.67679i	0.766130	+	1.05449i	0.996679	+	0.0814270i	$0.0259477\pi$
$53$	5.57751	+	7.67679i	0.766130	+	1.05449i	−0.230549	+	0.973061i	$0.574052\pi$
$54$	3.39994	−	8.13173i	0.462673	−	1.10659i
$55$	2.47674	+	2.20584i	0.333964	+	0.297436i
$56$			7.66915i			1.02483i
$57$	0.214619	−	7.86346i	0.0284270	−	1.04154i
$58$	2.81439	+	8.66179i	0.369547	+	1.13735i
$59$	−1.84920	−	0.600843i	−0.240746	−	0.0782230i	0.186159	−	0.982520i	$-0.440396\pi$
$59$	−1.84920	−	0.600843i	−0.240746	−	0.0782230i	−0.426905	+	0.904297i	$0.640396\pi$
$60$	−1.45728	+	0.429913i	−0.188134	+	0.0555016i
$61$	−7.71633	+	10.6206i	−0.987975	+	1.35983i	−0.0555540	+	0.998456i	$0.517693\pi$
$61$	−7.71633	+	10.6206i	−0.987975	+	1.35983i	−0.932421	+	0.361375i	$0.882307\pi$
$62$	0.949206	−	2.92135i	0.120549	−	0.371012i
$63$	−6.55707	−	10.1461i	−0.826113	−	1.27829i
$64$	−1.68937	+	1.22740i	−0.211171	+	0.153425i
$65$	5.58698			0.692979
$66$	9.57319	−	1.81711i	1.17838	−	0.223671i
$67$	−1.99934			−0.244258			−0.122129	−	0.992514i	$-0.538972\pi$
$67$	−1.99934			−0.244258			−0.122129	+	0.992514i	$0.538972\pi$
$68$	0.672260	−	0.488425i	0.0815235	−	0.0592303i
$69$	4.71214	+	1.67452i	0.567275	+	0.201589i
$70$	−2.11072	+	6.49614i	−0.252280	+	0.776437i
$71$	1.44240	−	1.98529i	0.171181	−	0.235610i	−0.714803	−	0.699325i	$-0.753484\pi$
$71$	1.44240	−	1.98529i	0.171181	−	0.235610i	0.885984	+	0.463715i	$0.153484\pi$
$72$	2.05935	−	5.32951i	0.242697	−	0.628088i
$73$	9.21799	+	2.99511i	1.07888	+	0.350551i	0.793942	−	0.607994i	$-0.208026\pi$
$73$	9.21799	+	2.99511i	1.07888	+	0.350551i	0.284942	+	0.958545i	$0.408026\pi$
$74$	−4.18349	−	12.8755i	−0.486321	−	1.49674i
$75$	1.73141	+	0.0472556i	0.199926	+	0.00545660i
$76$			3.98399i			0.456995i
$77$	5.36586	−	12.2301i	0.611496	−	1.39375i
$78$	10.0068	−	13.0113i	1.13305	−	1.47324i
$79$	−1.25135	−	1.72234i	−0.140788	−	0.193779i	0.732800	−	0.680444i	$-0.238213\pi$
$79$	−1.25135	−	1.72234i	−0.140788	−	0.193779i	−0.873588	+	0.486665i	$0.838213\pi$
$80$	−4.74094	+	1.54043i	−0.530054	+	0.172225i
$81$	1.83222	+	8.81152i	0.203580	+	0.979058i
$82$	−1.83695	−	1.33462i	−0.202857	−	0.147384i
$83$	2.50390	+	1.81919i	0.274839	+	0.199682i	0.716663	−	0.697419i	$-0.245668\pi$
$83$	2.50390	+	1.81919i	0.274839	+	0.199682i	−0.441824	+	0.897102i	$0.645668\pi$
$84$	3.45984	+	5.04605i	0.377499	+	0.550569i
$85$	−0.900911	+	0.292724i	−0.0977175	+	0.0317503i
$86$	−8.79708	−	12.1081i	−0.948614	−	1.30566i
$87$	−7.37180	−	5.66955i	−0.790340	−	0.607840i
$88$	6.17130	−	1.34680i	0.657863	−	0.143570i
$89$			11.0376i			1.16998i	0.811041	+	0.584989i	$0.198901\pi$
$89$			11.0376i			1.16998i	−0.811041	+	0.584989i	$0.801099\pi$
$90$	3.21117	−	3.94757i	0.338487	−	0.416110i
$91$	−6.95221	−	21.3967i	−0.728789	−	2.24298i
$92$	−2.40875	−	0.782650i	−0.251129	−	0.0815969i
$93$	0.887501	+	3.00837i	0.0920296	+	0.311954i
$94$	−7.39869	+	10.1834i	−0.763116	+	1.05034i
$95$	1.40345	−	4.31938i	0.143991	−	0.443159i
$96$	−2.69490	+	7.58349i	−0.275047	+	0.773987i
$97$	−6.43282	+	4.67372i	−0.653154	+	0.474544i	−0.864344	−	0.502901i	$-0.832266\pi$
$97$	−6.43282	+	4.67372i	−0.653154	+	0.474544i	0.211190	+	0.977445i	$0.432266\pi$
$98$	15.6314			1.57901
$99$	−7.01297	+	7.05821i	−0.704830	+	0.709377i
$100$	−0.877211			−0.0877211
$101$	−3.33294	+	2.42153i	−0.331640	+	0.240951i	−0.741126	−	0.671366i	$-0.765708\pi$
$101$	−3.33294	+	2.42153i	−0.331640	+	0.240951i	0.409486	+	0.912316i	$0.365708\pi$
$102$	−0.931905	+	2.62239i	−0.0922724	+	0.259656i
$103$	−0.999014	+	3.07465i	−0.0984358	+	0.302954i	−0.988134	−	0.153595i	$-0.950915\pi$
$103$	−0.999014	+	3.07465i	−0.0984358	+	0.302954i	0.889698	+	0.456549i	$0.150915\pi$
$104$	6.25432	−	8.60833i	0.613286	−	0.844116i
$105$	−1.97351	−	6.68964i	−0.192595	−	0.652842i
$106$	15.3078	+	4.97382i	1.48683	+	0.483100i
$107$	0.111546	+	0.343303i	0.0107835	+	0.0331883i	0.956304	−	0.292376i	$-0.0944458\pi$
$107$	0.111546	+	0.343303i	0.0107835	+	0.0331883i	−0.945520	+	0.325564i	$0.894446\pi$
$108$	−1.04935	−	4.43569i	−0.100974	−	0.426824i
$109$			5.63138i			0.539388i	0.962946	+	0.269694i	$0.0869226\pi$
$109$			5.63138i			0.539388i	−0.962946	+	0.269694i	$0.913077\pi$
$110$	5.59806	+	0.557675i	0.533754	+	0.0531722i
$111$	10.9579	+	8.42759i	1.04008	+	0.799912i
$112$	11.7989	+	16.2398i	1.11489	+	1.53451i
$113$	9.96341	−	3.23731i	0.937279	−	0.304540i	0.199743	−	0.979848i	$-0.435989\pi$
$113$	9.96341	−	3.23731i	0.937279	−	0.304540i	0.737536	+	0.675308i	$0.235989\pi$
$114$	−7.54552	−	11.0049i	−0.706703	−	1.03070i
$115$	2.33582	+	1.69707i	0.217816	+	0.158253i
$116$	3.81046	+	2.76846i	0.353792	+	0.257045i
$117$	−0.914238	+	16.7360i	−0.0845213	+	1.54724i
$118$	−3.13668	+	1.01917i	−0.288755	+	0.0938222i
$119$	2.24211	+	3.08600i	0.205534	+	0.282893i
$120$	2.01102	−	2.61482i	0.183581	−	0.238700i
$121$	−10.7838	−	2.17009i	−0.980347	−	0.197281i
$122$			22.2678i			2.01603i
$123$	2.31768	+	0.0632568i	0.208978	+	0.00570367i
$124$	−0.490884	−	1.51078i	−0.0440826	−	0.135672i
$125$	0.951057	+	0.309017i	0.0850651	+	0.0276393i
$126$	−19.1140	−	7.38576i	−1.70281	−	0.657975i
$127$	2.21288	−	3.04576i	0.196361	−	0.270268i	−0.699471	−	0.714661i	$-0.746581\pi$
$127$	2.21288	−	3.04576i	0.196361	−	0.270268i	0.895832	+	0.444394i	$0.146581\pi$
$128$	−3.96629	+	12.2070i	−0.350573	+	1.07895i
$129$	14.4003	+	5.11735i	1.26787	+	0.450557i
$130$	7.66691	−	5.57034i	0.672433	−	0.488551i
$131$	−4.63385			−0.404862			−0.202431	−	0.979297i	$-0.564884\pi$
$131$	−4.63385			−0.404862			−0.202431	+	0.979297i	$0.564884\pi$
$132$	3.45292	−	3.67026i	0.300538	−	0.319455i
$133$	−18.2885			−1.58581
$134$	−2.74365	+	1.99338i	−0.237016	+	0.172202i
$135$	−0.424878	+	5.17875i	−0.0365677	+	0.445716i
$136$	−0.557496	+	1.71580i	−0.0478049	+	0.147128i
$137$	0.483276	−	0.665172i	0.0412891	−	0.0568295i	−0.787873	−	0.615837i	$-0.788818\pi$
$137$	0.483276	−	0.665172i	0.0412891	−	0.0568295i	0.829162	+	0.559008i	$0.188818\pi$
$138$	8.13592	−	2.40018i	0.692575	−	0.204317i
$139$	−6.73933	−	2.18974i	−0.571623	−	0.185732i	0.00892145	−	0.999960i	$-0.497160\pi$
$139$	−6.73933	−	2.18974i	−0.571623	−	0.185732i	−0.580544	+	0.814229i	$0.697160\pi$
$140$	1.09157	+	3.35949i	0.0922541	+	0.283929i
$141$	0.350674	−	12.8484i	0.0295321	−	1.08203i
$142$		−	4.16248i		−	0.349307i
$143$	−15.9968	+	9.35193i	−1.33772	+	0.782047i
$144$	−3.83860	−	14.4537i	−0.319884	−	1.20448i
$145$	−3.15598	−	4.34383i	−0.262090	−	0.360736i
$146$	15.6359	−	5.08040i	1.29403	−	0.420457i
$147$	−13.1643	+	9.02611i	−1.08577	+	0.744461i
$148$	−5.66411	−	4.11522i	−0.465587	−	0.338269i
$149$	−4.88157	−	3.54667i	−0.399914	−	0.290555i	0.369592	−	0.929194i	$-0.379498\pi$
$149$	−4.88157	−	3.54667i	−0.399914	−	0.290555i	−0.769506	+	0.638640i	$0.779498\pi$
$150$	2.42309	−	1.66140i	0.197845	−	0.135653i
$151$	2.54788	−	0.827856i	0.207343	−	0.0673700i	−0.203504	−	0.979074i	$-0.565233\pi$
$151$	2.54788	−	0.827856i	0.207343	−	0.0673700i	0.410847	+	0.911704i	$0.365233\pi$
$152$	−5.08414	−	6.99772i	−0.412378	−	0.567590i
$153$	−0.729441	−	2.74661i	−0.0589718	−	0.222050i
$154$	−4.83025	−	22.1331i	−0.389233	−	1.78354i
$155$			1.81089i			0.145454i
$156$	0.231598	−	8.48555i	0.0185427	−	0.679388i
$157$	1.96766	+	6.05583i	0.157036	+	0.483308i	0.998362	−	0.0572212i	$-0.0182240\pi$
$157$	1.96766	+	6.05583i	0.157036	+	0.483308i	−0.841325	+	0.540529i	$0.818224\pi$
$158$	−3.43442	−	1.11591i	−0.273228	−	0.0887772i
$159$	−15.7638	+	4.65049i	−1.25015	+	0.368808i
$160$	−2.73119	+	3.75915i	−0.215919	+	0.297187i
$161$	3.59275	−	11.0573i	0.283148	−	0.871441i
$162$	11.2996	+	10.2651i	0.887781	+	0.806505i
$163$	1.20178	−	0.873143i	0.0941305	−	0.0683898i	−0.539724	−	0.841842i	$-0.681472\pi$
$163$	1.20178	−	0.873143i	0.0941305	−	0.0683898i	0.633855	+	0.773452i	$0.281472\pi$
$164$	−1.17424			−0.0916929
$165$	−5.03653	+	2.76286i	−0.392093	+	0.215088i
$166$	5.24984			0.407467
$167$	7.58804	−	5.51303i	0.587180	−	0.426611i	−0.254125	−	0.967171i	$-0.581788\pi$
$167$	7.58804	−	5.51303i	0.587180	−	0.426611i	0.841306	+	0.540560i	$0.181788\pi$
$168$	−12.5165	−	4.44793i	−0.965671	−	0.343165i
$169$	−5.62854	+	17.3229i	−0.432964	+	1.33253i
$170$	−0.944452	+	1.29993i	−0.0724362	+	0.0996998i
$171$	12.7092	+	4.91089i	0.971895	+	0.375545i
$172$	−7.36113	−	2.39178i	−0.561281	−	0.182371i
$173$	−7.70635	−	23.7177i	−0.585903	−	1.80322i	−0.595614	−	0.803271i	$-0.703091\pi$
$173$	−7.70635	−	23.7177i	−0.585903	−	1.80322i	0.00971101	−	0.999953i	$-0.496909\pi$
$174$	−15.7689	−	0.430382i	−1.19543	−	0.0326272i
$175$		−	4.02683i		−	0.304400i
$176$	10.9960	−	12.3464i	0.828852	−	0.930643i
$177$	2.05311	−	2.66954i	0.154321	−	0.200655i
$178$	11.0047	+	15.1466i	0.824835	+	1.13529i
$179$	−9.76533	+	3.17295i	−0.729895	+	0.237157i	−0.650308	−	0.759671i	$-0.725360\pi$
$179$	−9.76533	+	3.17295i	−0.729895	+	0.237157i	−0.0795870	+	0.996828i	$0.525360\pi$
$180$	0.143544	−	2.62771i	0.0106992	−	0.195858i
$181$	−4.59606	−	3.33923i	−0.341622	−	0.248203i	0.403724	−	0.914881i	$-0.367716\pi$
$181$	−4.59606	−	3.33923i	−0.341622	−	0.248203i	−0.745346	+	0.666678i	$0.767716\pi$
$182$	−30.8734	−	22.4308i	−2.28849	−	1.66268i
$183$	−12.8582	−	18.7532i	−0.950507	−	1.38628i
$184$	5.22964	−	1.69921i	0.385534	−	0.125268i
$185$	4.69125	+	6.45696i	0.344908	+	0.474725i
$186$	4.21732	+	3.24348i	0.309229	+	0.237824i
$187$	2.08954	−	2.34615i	0.152802	−	0.171568i
$188$			6.50960i			0.474761i
$189$	20.3620	−	4.81705i	1.48112	−	0.350389i
$190$	−2.38058	−	7.32667i	−0.172705	−	0.531533i
$191$	18.3151	+	5.95095i	1.32524	+	0.430596i	0.884290	−	0.466938i	$-0.154643\pi$
$191$	18.3151	+	5.95095i	1.32524	+	0.430596i	0.440947	+	0.897533i	$0.354643\pi$
$192$	−1.02340	−	3.46902i	−0.0738572	−	0.250355i
$193$	−9.15177	+	12.5963i	−0.658759	+	0.906704i	−0.999440	−	0.0334754i	$-0.989342\pi$
$193$	−9.15177	+	12.5963i	−0.658759	+	0.906704i	0.340681	+	0.940179i	$0.389342\pi$
$194$	−4.16785	+	12.8273i	−0.299234	+	0.920948i
$195$	−3.24032	+	9.11830i	−0.232044	+	0.652975i
$196$	6.53994	−	4.75155i	0.467139	−	0.339396i
$197$	−8.67691			−0.618204			−0.309102	−	0.951029i	$-0.600028\pi$
$197$	−8.67691			−0.618204			−0.309102	+	0.951029i	$0.600028\pi$
$198$	−2.58658	+	16.6779i	−0.183821	+	1.18525i
$199$	12.7007			0.900332			0.450166	−	0.892945i	$-0.351365\pi$
$199$	12.7007			0.900332			0.450166	+	0.892945i	$0.351365\pi$
$200$	1.54078	−	1.11944i	0.108950	−	0.0791567i
$201$	1.15957	−	3.26304i	0.0817897	−	0.230157i
$202$	−2.15943	+	6.64603i	−0.151937	+	0.467613i
$203$	−12.7086	+	17.4919i	−0.891968	+	1.22769i
$204$	0.407246	+	1.38044i	0.0285129	+	0.0966505i
$205$	1.27309	+	0.413653i	0.0889167	+	0.0288908i
$206$	1.69456	+	5.21533i	0.118066	+	0.363369i
$207$	−5.46586	+	6.71931i	−0.379903	+	0.467025i
$208$		−	27.8507i		−	1.93110i
$209$	3.21170	+	14.7166i	0.222158	+	1.01797i
$210$	−9.37794	−	7.21244i	−0.647139	−	0.497706i
$211$	−6.22228	−	8.56423i	−0.428359	−	0.589586i	0.539216	−	0.842167i	$-0.318721\pi$
$211$	−6.22228	−	8.56423i	−0.428359	−	0.589586i	−0.967576	+	0.252581i	$0.918721\pi$
$212$	7.91648	−	2.57222i	0.543706	−	0.176661i
$213$	2.40356	+	3.50550i	0.164689	+	0.240193i
$214$	0.495353	+	0.359895i	0.0338616	+	0.0246019i
$215$	7.13825	+	5.18624i	0.486825	+	0.353699i
$216$	7.50371	+	6.45197i	0.510563	+	0.439001i
$217$	6.93524	−	2.25340i	0.470795	−	0.152971i
$218$	5.61461	+	7.72784i	0.380269	+	0.523395i
$219$	−10.2344	+	13.3072i	−0.691578	+	0.899220i
$220$	2.51166	−	1.46834i	0.169336	−	0.0989958i
$221$		−	5.29240i		−	0.356005i
$222$	23.4399	+	0.639748i	1.57318	+	0.0429371i
$223$	0.833477	+	2.56518i	0.0558137	+	0.171777i	0.975077	−	0.221866i	$-0.0712147\pi$
$223$	0.833477	+	2.56518i	0.0558137	+	0.171777i	−0.919263	+	0.393643i	$0.871215\pi$
$224$	17.7952	+	5.78200i	1.18899	+	0.386326i
$225$	−1.08130	+	2.79836i	−0.0720866	+	0.186557i
$226$	10.4449	−	14.3762i	0.694787	−	0.956293i
$227$	−0.485774	+	1.49506i	−0.0322420	+	0.0992306i	−0.965882	−	0.258981i	$-0.916613\pi$
$227$	−0.485774	+	1.49506i	−0.0322420	+	0.0992306i	0.933640	+	0.358211i	$0.116613\pi$
$228$	−6.50213	−	2.31062i	−0.430614	−	0.153025i
$229$	13.8891	−	10.0910i	0.917819	−	0.666834i	−0.0251613	−	0.999683i	$-0.508010\pi$
$229$	13.8891	−	10.0910i	0.917819	−	0.666834i	0.942980	+	0.332849i	$0.108010\pi$
$230$	4.89742			0.322926
$231$	16.8483	+	15.8506i	1.10854	+	1.04289i
$232$	−10.2259			−0.671360
$233$	−5.39838	+	3.92215i	−0.353659	+	0.256949i	−0.750403	−	0.660981i	$-0.770140\pi$
$233$	−5.39838	+	3.92215i	−0.353659	+	0.256949i	0.396743	+	0.917930i	$0.370140\pi$
$234$	15.4315	+	23.8780i	1.00879	+	1.56095i
$235$	2.29315	−	7.05759i	0.149589	−	0.460387i
$236$	−1.00254	+	1.37988i	−0.0652597	+	0.0898223i
$237$	3.53673	−	1.04337i	0.229735	−	0.0677742i
$238$	6.15362	+	1.99943i	0.398880	+	0.129604i
$239$	−7.85694	−	24.1812i	−0.508223	−	1.56415i	−0.795284	−	0.606237i	$-0.792678\pi$
$239$	−7.85694	−	24.1812i	−0.508223	−	1.56415i	0.287061	−	0.957912i	$-0.407322\pi$
$240$	0.235565	−	8.63093i	0.0152057	−	0.557124i
$241$			22.6905i			1.46162i	0.682580	+	0.730811i	$0.260858\pi$
$241$			22.6905i			1.46162i	−0.682580	+	0.730811i	$0.739142\pi$
$242$	−16.9621	+	7.77373i	−1.09036	+	0.499714i
$243$	−15.4436	−	2.12017i	−0.990708	−	0.136009i
$244$	6.76885	+	9.31652i	0.433331	+	0.596429i
$245$	−8.76433	+	2.84770i	−0.559932	+	0.181933i
$246$	3.24357	−	2.22397i	0.206803	−	0.141795i
$247$	20.5281	+	14.9146i	1.30617	+	0.948991i
$248$	2.79019	+	2.02719i	0.177177	+	0.128727i
$249$	−4.42124	+	3.03144i	−0.280185	+	0.192110i
$250$	1.61321	−	0.524165i	0.102029	−	0.0331511i
$251$	−10.6101	−	14.6036i	−0.669705	−	0.921770i	0.330048	−	0.943964i	$-0.392935\pi$
$251$	−10.6101	−	14.6036i	−0.669705	−	0.921770i	−0.999754	+	0.0221937i	$0.992935\pi$
$252$	−10.2421	+	2.72008i	−0.645191	+	0.171349i
$253$	−9.52869	−	0.949240i	−0.599063	−	0.0596782i
$254$		−	6.38593i		−	0.400689i
$255$	0.0447640	−	1.64012i	0.00280323	−	0.102708i
$256$	5.43719	+	16.7339i	0.339824	+	1.04587i
$257$	17.8634	+	5.80418i	1.11429	+	0.362055i	0.807586	−	0.589750i	$-0.200774\pi$
$257$	17.8634	+	5.80418i	1.11429	+	0.362055i	0.306705	+	0.951805i	$0.400774\pi$
$258$	24.8634	−	7.33495i	1.54792	−	0.456654i
$259$	18.8909	−	26.0011i	1.17382	−	1.61563i
$260$	1.51448	−	4.66109i	0.0939240	−	0.289068i
$261$	13.5285	−	8.74303i	0.837395	−	0.541180i
$262$	−6.35895	+	4.62005i	−0.392858	+	0.285428i
$263$	26.3434			1.62440			0.812200	−	0.583379i	$-0.198270\pi$
$263$	26.3434			1.62440			0.812200	+	0.583379i	$0.198270\pi$
$264$	−1.38114	+	10.8531i	−0.0850035	+	0.667960i
$265$	−9.48903			−0.582906
$266$	−25.0970	+	18.2340i	−1.53879	+	1.11800i
$267$	−18.0140	−	6.40152i	−1.10244	−	0.391767i
$268$	−0.541966	+	1.66800i	−0.0331059	+	0.101889i
$269$	6.70808	−	9.23287i	0.408999	−	0.562938i	−0.553975	−	0.832533i	$-0.686890\pi$
$269$	6.70808	−	9.23287i	0.408999	−	0.562938i	0.962974	+	0.269595i	$0.0868898\pi$
$270$	4.58027	+	7.53032i	0.278747	+	0.458281i
$271$	12.5278	+	4.07055i	0.761013	+	0.247268i	0.663713	−	0.747987i	$-0.268980\pi$
$271$	12.5278	+	4.07055i	0.761013	+	0.247268i	0.0972995	+	0.995255i	$0.468980\pi$
$272$	1.45920	+	4.49097i	0.0884773	+	0.272305i
$273$	38.9528	+	1.06315i	2.35753	+	0.0643446i
$274$		−	1.39464i		−	0.0842533i
$275$	−3.24036	+	0.707165i	−0.195401	+	0.0426436i
$276$	2.67435	−	3.47731i	0.160977	−	0.209309i
$277$	−2.62761	−	3.61660i	−0.157878	−	0.217300i	0.722749	−	0.691111i	$-0.242878\pi$
$277$	−2.62761	−	3.61660i	−0.157878	−	0.217300i	−0.880627	+	0.473810i	$0.842878\pi$
$278$	−11.4315	+	3.71432i	−0.685615	+	0.222770i
$279$	−5.42458	−	0.296329i	−0.324761	−	0.0177408i
$280$	−6.20447	−	4.50781i	−0.370788	−	0.269393i
$281$	−6.58911	−	4.78727i	−0.393073	−	0.285585i	0.373640	−	0.927574i	$-0.378109\pi$
$281$	−6.58911	−	4.78727i	−0.393073	−	0.285585i	−0.766714	+	0.641989i	$0.778109\pi$
$282$	−12.3289	−	17.9813i	−0.734176	−	1.07077i
$283$	1.49169	−	0.484680i	0.0886719	−	0.0288112i	−0.264345	−	0.964428i	$-0.585156\pi$
$283$	1.49169	−	0.484680i	0.0886719	−	0.0288112i	0.353017	+	0.935617i	$0.385156\pi$
$284$	−1.26529	−	1.74152i	−0.0750809	−	0.103340i
$285$	6.23552	+	4.79565i	0.369360	+	0.284070i
$286$	−12.6281	+	28.7827i	−0.746716	+	1.70196i
$287$		−	5.39035i		−	0.318182i
$288$	−10.8138	−	8.79650i	−0.637206	−	0.518339i
$289$	−4.97600	−	15.3146i	−0.292706	−	0.900856i
$290$	−8.66179	−	2.81439i	−0.508638	−	0.165266i
$291$	−3.89691	−	13.2094i	−0.228441	−	0.774349i
$292$	4.99750	−	6.87846i	0.292456	−	0.402532i
$293$	8.38029	−	25.7919i	0.489582	−	1.50678i	−0.335652	−	0.941986i	$-0.608957\pi$
$293$	8.38029	−	25.7919i	0.489582	−	1.50678i	0.825234	−	0.564791i	$-0.191043\pi$
$294$	−9.06585	+	25.5114i	−0.528731	+	1.48786i
$295$	1.57303	−	1.14287i	0.0915851	−	0.0665405i
$296$	15.2004			0.883504
$297$	−7.45208	−	15.5392i	−0.432413	−	0.901675i
$298$	−10.2350			−0.592898
$299$	−13.0502	+	9.48149i	−0.754710	+	0.548329i
$300$	0.508762	−	1.43166i	0.0293734	−	0.0826571i
$301$	10.9794	−	33.7912i	0.632844	−	1.94769i
$302$	2.67102	−	3.67634i	0.153700	−	0.211550i
$303$	−2.01905	−	6.84400i	−0.115991	−	0.393177i
$304$	−21.5318	−	6.99609i	−1.23493	−	0.401253i
$305$	−4.05671	−	12.4853i	−0.232287	−	0.714905i
$306$	−3.73943	−	3.04185i	−0.213769	−	0.173891i
$307$			22.1843i			1.26612i	0.774101	+	0.633062i	$0.218202\pi$
$307$			22.1843i			1.26612i	−0.774101	+	0.633062i	$0.781798\pi$
$308$	−8.74879	−	7.79188i	−0.498509	−	0.443983i
$309$	−4.43861	−	3.41368i	−0.252504	−	0.194197i
$310$	1.80550	+	2.48505i	0.102545	+	0.141142i
$311$	−1.19760	+	0.389125i	−0.0679098	+	0.0220652i	−0.342775	−	0.939418i	$-0.611367\pi$
$311$	−1.19760	+	0.389125i	−0.0679098	+	0.0220652i	0.274865	+	0.961483i	$0.411367\pi$
$312$	10.4220	+	15.2001i	0.590028	+	0.860534i
$313$	20.9641	+	15.2313i	1.18496	+	0.860923i	0.992722	−	0.120426i	$-0.0384259\pi$
$313$	20.9641	+	15.2313i	1.18496	+	0.860923i	0.192237	+	0.981349i	$0.438426\pi$
$314$	8.73798	+	6.34851i	0.493113	+	0.358267i
$315$	12.0625	+	0.658939i	0.679645	+	0.0371270i
$316$	−1.77612	+	0.577096i	−0.0999145	+	0.0324642i
$317$	17.2269	+	23.7108i	0.967558	+	1.33173i	0.943271	+	0.332024i	$0.107732\pi$
$317$	17.2269	+	23.7108i	0.967558	+	1.33173i	0.0242873	+	0.999705i	$0.492268\pi$
$318$	−16.9958	+	22.0987i	−0.953076	+	1.23923i
$319$	16.3074	+	7.15470i	0.913037	+	0.400586i
$320$		−	2.08817i		−	0.116732i
$321$	−0.624985	−	0.0170578i	−0.0348833	−	0.000952076i
$322$	−6.09414	−	18.7558i	−0.339613	−	1.04522i
$323$	−4.09163	−	1.32945i	−0.227664	−	0.0739727i
$324$	7.84792	+	0.859984i	0.435996	+	0.0477769i
$325$	−3.28394	+	4.51996i	−0.182160	+	0.250722i
$326$	0.778637	−	2.39640i	0.0431247	−	0.132724i
$327$	−9.19076	−	3.26607i	−0.508250	−	0.180614i
$328$	2.06251	−	1.49850i	0.113883	−	0.0827408i
$329$	−29.8823			−1.64746
$330$	−4.15691	+	8.81295i	−0.228830	+	0.485137i
$331$	−5.07917			−0.279176			−0.139588	−	0.990210i	$-0.544578\pi$
$331$	−5.07917			−0.279176			−0.139588	+	0.990210i	$0.544578\pi$
$332$	2.19645	−	1.59582i	0.120546	−	0.0875818i
$333$	−20.1097	+	12.9962i	−1.10200	+	0.712188i
$334$	4.91632	−	15.1309i	0.269009	−	0.827925i
$335$	1.17518	−	1.61750i	0.0642070	−	0.0883733i
$336$	−33.3474	+	9.83781i	−1.81925	+	0.536697i
$337$	−33.4694	−	10.8749i	−1.82320	−	0.592393i	−0.999685	−	0.0250933i	$-0.992012\pi$
$337$	−33.4694	−	10.8749i	−1.82320	−	0.592393i	−0.823512	−	0.567299i	$-0.807988\pi$
$338$	9.54732	+	29.3836i	0.519306	+	1.59826i
$339$	−0.495056	+	18.1385i	−0.0268878	+	0.985146i
$340$			0.830959i			0.0450651i
$341$	−3.03121	−	5.18501i	−0.164149	−	0.280784i
$342$	22.3368	−	5.93219i	1.20784	−	0.320776i
$343$	5.24355	+	7.21713i	0.283125	+	0.389689i
$344$	15.9818	−	5.19279i	0.861679	−	0.279976i
$345$	−4.12444	+	2.82794i	−0.222053	+	0.152251i
$346$	−34.2223	−	24.8640i	−1.83980	−	1.33670i
$347$	10.8628	+	7.89226i	0.583144	+	0.423679i	0.839856	−	0.542809i	$-0.182639\pi$
$347$	10.8628	+	7.89226i	0.583144	+	0.423679i	−0.256712	+	0.966488i	$0.582639\pi$
$348$	−6.72827	+	4.61326i	−0.360673	+	0.247297i
$349$	−2.91467	+	0.947035i	−0.156019	+	0.0506936i	−0.385985	−	0.922505i	$-0.626138\pi$
$349$	−2.91467	+	0.947035i	−0.156019	+	0.0506936i	0.229966	+	0.973199i	$0.426138\pi$
$350$	−4.01484	−	5.52595i	−0.214602	−	0.295374i
$351$	−26.7839	−	11.1986i	−1.42962	−	0.597736i
$352$	1.52766	−	15.3350i	0.0814247	−	0.817360i
$353$			0.176884i			0.00941460i	0.999989	+	0.00470730i	$0.00149839\pi$
$353$			0.176884i			0.00941460i	−0.999989	+	0.00470730i	$0.998502\pi$
$354$	0.155854	−	5.71035i	0.00828353	−	0.303502i
$355$	0.758313	+	2.33385i	0.0402471	+	0.123868i
$356$	9.20838	+	2.99198i	0.488043	+	0.158575i
$357$	−6.33692	+	1.86946i	−0.335385	+	0.0989422i
$358$	−10.2373	+	14.0904i	−0.541058	+	0.744702i
$359$	9.41063	−	28.9629i	0.496674	−	1.52861i	−0.317658	−	0.948205i	$-0.602896\pi$
$359$	9.41063	−	28.9629i	0.496674	−	1.52861i	0.814332	−	0.580400i	$-0.197104\pi$
$360$	3.10121	+	4.79865i	0.163448	+	0.252911i
$361$	1.31601	−	0.956137i	0.0692637	−	0.0503230i
$362$	−9.63637			−0.506476
$363$	9.79608	−	16.3413i	0.514161	−	0.857694i
$364$	−19.7353			−1.03441
$365$	−7.84129	+	5.69703i	−0.410432	+	0.298196i
$366$	−36.3425	−	12.9148i	−1.89965	−	0.675068i
$367$	8.87370	−	27.3104i	0.463204	−	1.42559i	−0.398024	−	0.917375i	$-0.630304\pi$
$367$	8.87370	−	27.3104i	0.463204	−	1.42559i	0.861228	−	0.508219i	$-0.169696\pi$
$368$	8.45976	−	11.6439i	0.440996	−	0.606978i
$369$	−1.44744	+	3.74590i	−0.0753506	+	0.195004i
$370$	12.8755	+	4.18349i	0.669363	+	0.217489i
$371$	11.8078	+	36.3405i	0.613028	+	1.88671i
$372$	2.75040	+	0.0750670i	0.142601	+	0.00389204i
$373$		−	3.15562i		−	0.163392i	−0.996657	−	0.0816960i	$-0.973966\pi$
$373$		−	3.15562i		−	0.163392i	0.996657	−	0.0816960i	$-0.0260337\pi$
$374$	0.528270	−	5.30290i	0.0273162	−	0.274206i
$375$	−1.05593	+	1.37296i	−0.0545278	+	0.0708994i
$376$	−8.30717	−	11.4338i	−0.428409	−	0.589655i
$377$	28.5298	−	9.26990i	1.46936	−	0.477424i
$378$	23.1397	−	26.9117i	1.19018	−	1.38419i
$379$	3.95173	+	2.87110i	0.202987	+	0.147479i	0.684635	−	0.728886i	$-0.259962\pi$
$379$	3.95173	+	2.87110i	0.202987	+	0.147479i	−0.481648	+	0.876365i	$0.659962\pi$
$380$	−3.22312	−	2.34173i	−0.165343	−	0.120128i
$381$	3.68746	+	5.37802i	0.188914	+	0.275525i
$382$	31.0668	−	10.0942i	1.58951	−	0.516465i
$383$	−18.8663	−	25.9672i	−0.964021	−	1.32686i	−0.945010	−	0.327041i	$-0.893948\pi$
$383$	−18.8663	−	25.9672i	−0.964021	−	1.32686i	−0.0190107	−	0.999819i	$-0.506052\pi$
$384$	−17.6222	−	13.5530i	−0.899279	−	0.691623i
$385$	6.74043	+	11.5298i	0.343524	+	0.587611i
$386$			26.4102i			1.34425i
$387$	−16.7037	+	20.5342i	−0.849094	+	1.04381i
$388$	2.15541	+	6.63367i	0.109424	+	0.336774i
$389$	19.1264	+	6.21456i	0.969749	+	0.315091i	0.750715	−	0.660627i	$-0.229709\pi$
$389$	19.1264	+	6.21456i	0.969749	+	0.315091i	0.219034	+	0.975717i	$0.429709\pi$
$390$	4.64451	+	15.7435i	0.235184	+	0.797205i
$391$	1.60759	−	2.21266i	0.0812993	−	0.111899i
$392$	−5.42349	+	16.6918i	−0.273927	+	0.843062i
$393$	2.68753	−	7.56274i	0.135568	−	0.381490i
$394$	−11.9072	+	8.65107i	−0.599875	+	0.435834i
$395$	2.12893			0.107118
$396$	3.98748	+	7.76405i	0.200378	+	0.390158i
$397$	25.9749			1.30364			0.651822	−	0.758372i	$-0.274005\pi$
$397$	25.9749			1.30364			0.651822	+	0.758372i	$0.274005\pi$
$398$	17.4290	−	12.6629i	0.873637	−	0.634735i
$399$	10.6069	−	29.8480i	0.531009	−	1.49427i
$400$	1.54043	−	4.74094i	0.0770213	−	0.237047i
$401$	−19.9446	+	27.4513i	−0.995984	+	1.37085i	−0.0682270	+	0.997670i	$0.521734\pi$
$401$	−19.9446	+	27.4513i	−0.995984	+	1.37085i	−0.927757	+	0.373185i	$0.878266\pi$
$402$	−1.66207	−	5.63393i	−0.0828964	−	0.280995i
$403$	−9.62222	−	3.12645i	−0.479317	−	0.155740i
$404$	1.11675	+	3.43701i	0.0555605	+	0.170998i
$405$	−8.20563	−	3.69698i	−0.407741	−	0.183705i
$406$			36.6745i			1.82013i
$407$	−24.2403	−	10.6352i	−1.20155	−	0.527168i
$408$	−2.47695	−	1.90499i	−0.122627	−	0.0943111i
$409$	−1.06515	−	1.46605i	−0.0526681	−	0.0724915i	0.781871	−	0.623441i	$-0.214266\pi$
$409$	−1.06515	−	1.46605i	−0.0526681	−	0.0724915i	−0.834539	+	0.550949i	$0.814266\pi$
$410$	2.15946	−	0.701652i	0.106648	−	0.0346521i
$411$	0.805314	+	1.17452i	0.0397232	+	0.0579348i
$412$	2.29430	+	1.66691i	0.113032	+	0.0821227i
$413$	−6.33431	−	4.60214i	−0.311691	−	0.226457i
$414$	−0.801399	+	14.6704i	−0.0393866	+	0.721010i
$415$	−2.94352	+	0.956406i	−0.144492	+	0.0469481i
$416$	−15.2591	−	21.0023i	−0.748138	−	1.02972i
$417$	7.48245	−	9.72901i	0.366417	−	0.476432i
$418$	19.0801	+	16.9932i	0.933240	+	0.831165i
$419$			18.0158i			0.880127i	0.897967	+	0.440064i	$0.145044\pi$
$419$			18.0158i			0.880127i	−0.897967	+	0.440064i	$0.854956\pi$
$420$	−6.11598	−	0.166925i	−0.298429	−	0.00814509i
$421$	11.5137	+	35.4355i	0.561142	+	1.72702i	0.679144	+	0.734005i	$0.262351\pi$
$421$	11.5137	+	35.4355i	0.561142	+	1.72702i	−0.118001	+	0.993013i	$0.537649\pi$
$422$	−17.0774	−	5.54880i	−0.831317	−	0.270111i
$423$	20.7660	+	8.02409i	1.00968	+	0.390145i
$424$	−10.6224	+	14.6205i	−0.515872	+	0.710036i
$425$	0.292724	−	0.900911i	0.0141992	−	0.0437006i
$426$	6.79342	+	2.41414i	0.329142	+	0.116965i
$427$	−42.7674	+	31.0723i	−2.06966	+	1.50370i
$428$	0.316647			0.0153057
$429$	−5.98513	−	31.5317i	−0.288965	−	1.52237i
$430$	14.9665			0.721748
$431$	−1.82416	+	1.32533i	−0.0878669	+	0.0638390i	−0.630851	−	0.775904i	$-0.717294\pi$
$431$	−1.82416	+	1.32533i	−0.0878669	+	0.0638390i	0.542984	+	0.839743i	$0.317294\pi$
$432$	25.8157	+	2.11798i	1.24206	+	0.101902i
$433$	0.952553	−	2.93166i	0.0457768	−	0.140886i	−0.925556	−	0.378611i	$-0.876402\pi$
$433$	0.952553	−	2.93166i	0.0457768	−	0.140886i	0.971333	+	0.237725i	$0.0764017\pi$
$434$	7.27043	−	10.0069i	0.348992	−	0.480346i
$435$	8.91980	−	2.63143i	0.427672	−	0.126168i
$436$	4.69813	+	1.52652i	0.225000	+	0.0731068i
$437$	4.05208	+	12.4710i	0.193837	+	0.596570i
$438$	−0.776907	+	28.4652i	−0.0371220	+	1.36012i
$439$		−	12.4790i		−	0.595591i	−0.954630	−	0.297796i	$-0.903749\pi$
$439$		−	12.4790i		−	0.595591i	0.954630	−	0.297796i	$-0.0962514\pi$
$440$	−2.53781	+	5.78432i	−0.120986	+	0.275757i
$441$	−7.09622	−	26.7198i	−0.337915	−	1.27237i
$442$	−5.27663	−	7.26266i	−0.250984	−	0.345450i
$443$	34.6864	−	11.2703i	1.64800	−	0.535468i	0.669696	−	0.742636i	$-0.266425\pi$
$443$	34.6864	−	11.2703i	1.64800	−	0.535468i	0.978305	+	0.207168i	$0.0664245\pi$
$444$	10.0013	−	6.85745i	0.474643	−	0.325440i
$445$	−8.92957	−	6.48771i	−0.423302	−	0.307547i
$446$	3.70130	+	2.68915i	0.175262	+	0.127335i
$447$	8.61959	−	5.91005i	0.407693	−	0.279536i
$448$	−7.99717	+	2.59844i	−0.377831	+	0.122765i
$449$	12.9893	+	17.8783i	0.613004	+	0.843727i	0.996820	−	0.0796821i	$-0.0253905\pi$
$449$	12.9893	+	17.8783i	0.613004	+	0.843727i	−0.383817	+	0.923409i	$0.625391\pi$
$450$	1.30617	+	4.91821i	0.0615736	+	0.231847i
$451$	−4.33757	+	0.946617i	−0.204248	+	0.0445745i
$452$		−	9.18979i		−	0.432251i
$453$	−0.126598	+	4.63843i	−0.00594808	+	0.217933i
$454$	0.823987	+	2.53597i	0.0386716	+	0.119019i
$455$	21.3967	+	6.95221i	1.00309	+	0.325924i
$456$	14.3694	−	4.23912i	0.672908	−	0.198515i
$457$	7.80414	−	10.7415i	0.365062	−	0.502465i	−0.586488	−	0.809958i	$-0.699490\pi$
$457$	7.80414	−	10.7415i	0.365062	−	0.502465i	0.951550	+	0.307493i	$0.0994900\pi$
$458$	8.99881	−	27.6955i	0.420487	−	1.29413i
$459$	4.90570	+	0.402476i	0.228978	+	0.0187860i
$460$	2.04900	−	1.48869i	0.0955353	−	0.0694105i
$461$	−13.9893			−0.651545			−0.325773	−	0.945448i	$-0.605624\pi$
$461$	−13.9893			−0.651545			−0.325773	+	0.945448i	$0.605624\pi$
$462$	38.9240	+	4.95341i	1.81091	+	0.230453i
$463$	23.8705			1.10935			0.554677	−	0.832066i	$-0.312842\pi$
$463$	23.8705			1.10935			0.554677	+	0.832066i	$0.312842\pi$
$464$	−21.6537	+	15.7323i	−1.00525	+	0.730354i
$465$	−2.95549	−	1.05027i	−0.137057	−	0.0487053i
$466$	−3.49763	+	10.7646i	−0.162025	+	0.498660i
$467$	15.0009	−	20.6470i	0.694159	−	0.955428i	−0.305836	−	0.952084i	$-0.598936\pi$
$467$	15.0009	−	20.6470i	0.694159	−	0.955428i	0.999994	−	0.00334320i	$-0.00106418\pi$
$468$	13.7146	+	5.29940i	0.633959	+	0.244965i
$469$	−7.65694	−	2.48789i	−0.353565	−	0.114880i
$470$	−3.88972	−	11.9713i	−0.179419	−	0.552196i
$471$	−11.0247	−	0.300899i	−0.507991	−	0.0138647i
$472$		−	3.70307i		−	0.170448i
$473$	−29.1197	−	2.90088i	−1.33892	−	0.133382i
$474$	3.81312	−	4.95799i	0.175143	−	0.227728i
$475$	2.66952	+	3.67428i	0.122486	+	0.168588i
$476$	3.18236	−	1.03401i	0.145863	−	0.0473938i
$477$	1.55276	−	28.4247i	0.0710959	−	1.30148i
$478$	−34.8911	−	25.3499i	−1.59588	−	1.15948i
$479$	−15.4580	−	11.2309i	−0.706295	−	0.513154i	0.175681	−	0.984447i	$-0.443787\pi$
$479$	−15.4580	−	11.2309i	−0.706295	−	0.513154i	−0.881976	+	0.471294i	$0.843787\pi$
$480$	−4.55115	−	6.63769i	−0.207731	−	0.302968i
$481$	−42.4086	+	13.7794i	−1.93366	+	0.628286i
$482$	22.6229	+	31.1378i	1.03044	+	1.41829i
$483$	15.9626	+	12.2766i	0.726322	+	0.558604i
$484$	−4.73366	+	8.40844i	−0.215166	+	0.382202i
$485$		−	7.95140i		−	0.361055i
$486$	−23.3068	+	12.4881i	−1.05722	+	0.566473i
$487$	9.12667	+	28.0890i	0.413569	+	1.27283i	0.913525	+	0.406783i	$0.133350\pi$
$487$	9.12667	+	28.0890i	0.413569	+	1.27283i	−0.499956	+	0.866051i	$0.666650\pi$
$488$	−23.7784	−	7.72607i	−1.07640	−	0.349743i
$489$	0.728020	+	2.46778i	0.0329222	+	0.111597i
$490$	−9.18791	+	12.6461i	−0.415067	+	0.571291i
$491$	1.76623	−	5.43590i	0.0797088	−	0.245319i	−0.903259	−	0.429095i	$-0.858832\pi$
$491$	1.76623	−	5.43590i	0.0797088	−	0.245319i	0.982968	+	0.183777i	$0.0588324\pi$
$492$	0.681033	−	1.91644i	0.0307034	−	0.0863997i
$493$	−4.11480	+	2.98958i	−0.185321	+	0.134644i
$494$	43.0405			1.93648
$495$	−1.58809	−	9.82232i	−0.0713794	−	0.441480i
$496$	9.02715			0.405331
$497$	7.99442	−	5.80829i	0.358599	−	0.260537i
$498$	−3.04478	+	8.56806i	−0.136440	+	0.383944i
$499$	−3.65066	+	11.2356i	−0.163426	+	0.502974i	−0.998917	−	0.0465305i	$-0.985184\pi$
$499$	−3.65066	+	11.2356i	−0.163426	+	0.502974i	0.835491	+	0.549505i	$0.185184\pi$
$500$	0.515612	−	0.709679i	0.0230589	−	0.0317378i
$501$	4.59673	+	15.5816i	0.205367	+	0.696134i
$502$	−29.1202	−	9.46172i	−1.29970	−	0.422297i
$503$	11.1589	+	34.3436i	0.497551	+	1.53130i	0.812944	+	0.582342i	$0.197864\pi$
$503$	11.1589	+	34.3436i	0.497551	+	1.53130i	−0.315393	+	0.948961i	$0.602136\pi$
$504$	14.5186	−	17.8481i	0.646709	−	0.795016i
$505$		−	4.11974i		−	0.183326i
$506$	−14.0225	+	8.19768i	−0.623375	+	0.364431i
$507$	−25.0076	−	19.2330i	−1.11062	−	0.854167i
$508$	−1.94116	−	2.67178i	−0.0861250	−	0.118541i
$509$	−28.7498	+	9.34137i	−1.27431	+	0.414049i	−0.866573	−	0.499050i	$-0.833682\pi$
$509$	−28.7498	+	9.34137i	−1.27431	+	0.414049i	−0.407738	+	0.913099i	$0.633682\pi$
$510$	−1.57380	−	2.29533i	−0.0696891	−	0.101639i
$511$	31.5755	+	22.9410i	1.39682	+	1.01485i
$512$	3.37772	+	2.45406i	0.149275	+	0.108455i
$513$	−15.3859	+	17.8940i	−0.679305	+	0.790038i
$514$	30.3006	−	9.84526i	1.33650	−	0.434256i
$515$	−1.90024	−	2.61545i	−0.0837345	−	0.115251i
$516$	8.17281	−	10.6267i	0.359788	−	0.467812i
$517$	5.24772	+	24.0460i	0.230794	+	1.05754i
$518$		−	54.5154i		−	2.39527i
$519$	43.1783	+	1.17847i	1.89532	+	0.0517292i
$520$	3.28809	+	10.1197i	0.144192	+	0.443778i
$521$	−29.2567	−	9.50607i	−1.28176	−	0.416468i	−0.412559	−	0.910931i	$-0.635365\pi$
$521$	−29.2567	−	9.50607i	−1.28176	−	0.416468i	−0.869199	+	0.494463i	$0.835365\pi$
$522$	9.84798	−	25.4861i	0.431034	−	1.11550i
$523$	5.06830	−	6.97592i	0.221621	−	0.305036i	−0.683700	−	0.729763i	$-0.739630\pi$
$523$	5.06830	−	6.97592i	0.221621	−	0.305036i	0.905321	+	0.424728i	$0.139630\pi$
$524$	−1.25611	+	3.86592i	−0.0548735	+	0.168883i
$525$	6.57204	+	2.33547i	0.286827	+	0.101928i
$526$	36.1505	−	26.2649i	1.57624	−	1.14520i
$527$	1.71541			0.0747244
$528$	13.7726	+	25.1067i	0.599377	+	1.09263i
$529$	14.6639			0.637561
$530$	−13.0216	+	9.46077i	−0.565623	+	0.410949i
$531$	3.16610	+	4.89907i	0.137397	+	0.212601i
$532$	−4.95752	+	15.2577i	−0.214936	+	0.661504i
$533$	−4.39592	+	6.05046i	−0.190408	+	0.262075i
$534$	−31.1027	+	9.17562i	−1.34595	+	0.397068i
$535$	−0.343303	−	0.111546i	−0.0148423	−	0.00482255i
$536$	−1.17666	−	3.62140i	−0.0508241	−	0.156421i
$537$	0.485214	−	17.7779i	0.0209386	−	0.767171i
$538$		−	19.3582i		−	0.834591i
$539$	20.3276	−	22.8241i	0.875573	−	0.983102i
$540$	4.20534	+	1.75829i	0.180969	+	0.0756646i
$541$	−15.8832	−	21.8613i	−0.682871	−	0.939891i	0.317093	−	0.948395i	$-0.397293\pi$
$541$	−15.8832	−	21.8613i	−0.682871	−	0.939891i	−0.999964	+	0.00850319i	$0.997293\pi$
$542$	21.2502	−	6.90460i	0.912773	−	0.296578i
$543$	8.11544	−	5.56437i	0.348267	−	0.238790i
$544$	3.56095	+	2.58718i	0.152674	+	0.110924i
$545$	−4.55588	−	3.31004i	−0.195152	−	0.141787i
$546$	54.5143	−	37.3779i	2.33300	−	1.59963i
$547$	0.584542	−	0.189929i	0.0249932	−	0.00812078i	−0.296494	−	0.955035i	$-0.595817\pi$
$547$	0.584542	−	0.189929i	0.0249932	−	0.00812078i	0.321487	+	0.946914i	$0.395817\pi$
$548$	−0.423935	−	0.583496i	−0.0181096	−	0.0249257i
$549$	38.0639	−	10.1090i	1.62453	−	0.431440i
$550$	−3.74163	+	4.20114i	−0.159544	+	0.179137i
$551$		−	24.3854i		−	1.03885i
$552$	−0.259847	+	9.52059i	−0.0110598	+	0.405223i
$553$	−2.64916	−	8.15326i	−0.112654	−	0.346712i
$554$	−7.21165	−	2.34321i	−0.306394	−	0.0995533i
$555$	−13.2590	+	3.91153i	−0.562812	+	0.166035i
$556$	−3.65370	+	5.02889i	−0.154952	+	0.213273i
$557$	−12.5626	+	38.6637i	−0.532294	+	1.63823i	0.217129	+	0.976143i	$0.430331\pi$
$557$	−12.5626	+	38.6637i	−0.532294	+	1.63823i	−0.749423	+	0.662091i	$0.769669\pi$
$558$	−7.73951	+	5.00178i	−0.327639	+	0.211742i
$559$	−39.8813	+	28.9754i	−1.68680	+	1.22553i
$560$	−20.0734			−0.848257
$561$	2.61718	+	4.77097i	0.110498	+	0.201430i
$562$	−13.8151			−0.582756
$563$	−22.5172	+	16.3597i	−0.948986	+	0.689479i	−0.950567	−	0.310520i	$-0.899497\pi$
$563$	−22.5172	+	16.3597i	−0.948986	+	0.689479i	0.00158077	+	0.999999i	$0.499497\pi$
$564$	−10.6241	−	3.77542i	−0.447354	−	0.158974i
$565$	−3.23731	+	9.96341i	−0.136195	+	0.419164i
$566$	1.56379	−	2.15237i	0.0657308	−	0.0904707i
$567$	−3.94775	+	36.0258i	−0.165790	+	1.51294i
$568$	4.44484	+	1.44422i	0.186502	+	0.0605980i
$569$	4.69957	+	14.4638i	0.197016	+	0.606353i	0.999947	+	0.0102814i	$0.00327274\pi$
$569$	4.69957	+	14.4638i	0.197016	+	0.606353i	−0.802931	+	0.596072i	$0.796727\pi$
$570$	13.3383	+	0.364044i	0.558679	+	0.0152481i
$571$			10.1263i			0.423772i	0.977294	+	0.211886i	$0.0679606\pi$
$571$			10.1263i			0.423772i	−0.977294	+	0.211886i	$0.932039\pi$
$572$	3.46578	+	15.8809i	0.144912	+	0.664012i
$573$	−20.3347	+	26.4400i	−0.849493	+	1.10455i
$574$	−5.37430	−	7.39708i	−0.224319	−	0.308748i
$575$	−2.74592	+	0.892203i	−0.114513	+	0.0372074i
$576$	6.25519	+	0.341703i	0.260633	+	0.0142376i
$577$	−14.5755	−	10.5898i	−0.606788	−	0.440857i	0.241494	−	0.970402i	$-0.422363\pi$
$577$	−14.5755	−	10.5898i	−0.606788	−	0.440857i	−0.848282	+	0.529545i	$0.822363\pi$
$578$	−22.0974	−	16.0547i	−0.919131	−	0.667788i
$579$	−15.2502	−	22.2418i	−0.633776	−	0.924339i
$580$	−4.47946	+	1.45547i	−0.186000	+	0.0604349i
$581$	7.32558	+	10.0828i	0.303916	+	0.418305i
$582$	−18.5177	−	14.2417i	−0.767585	−	0.590339i
$583$	27.1693	−	15.8835i	1.12524	−	0.657827i
$584$			18.4592i			0.763849i
$585$	−13.0023	−	10.5768i	−0.537580	−	0.437297i
$586$	−14.2149	−	43.7491i	−0.587213	−	1.80726i
$587$	31.2817	+	10.1640i	1.29113	+	0.419515i	0.872488	−	0.488635i	$-0.162505\pi$
$587$	31.2817	+	10.1640i	1.29113	+	0.419515i	0.418645	+	0.908150i	$0.362505\pi$
$588$	3.96180	+	13.4294i	0.163382	+	0.553818i
$589$	−4.83421	+	6.65372i	−0.199190	+	0.274162i
$590$	1.01917	−	3.13668i	0.0419586	−	0.129135i
$591$	5.03240	−	14.1613i	0.207005	−	0.582516i
$592$	32.1874	−	23.3855i	1.32290	−	0.961140i
$593$	−36.3760			−1.49378			−0.746891	−	0.664946i	$-0.768454\pi$
$593$	−36.3760			−1.49378			−0.746891	+	0.664946i	$0.768454\pi$
$594$	−25.7193	−	13.8943i	−1.05527	−	0.570089i
$595$	−3.81451			−0.156380
$596$	−4.28217	+	3.11118i	−0.175405	+	0.127439i
$597$	−7.36614	+	20.7284i	−0.301476	+	0.848357i
$598$	−8.45525	+	26.0226i	−0.345761	+	1.06414i
$599$	−5.49113	+	7.55789i	−0.224361	+	0.308807i	−0.906327	−	0.422577i	$-0.861125\pi$
$599$	−5.49113	+	7.55789i	−0.224361	+	0.308807i	0.681965	+	0.731384i	$0.261125\pi$
$600$	0.933385	+	3.16391i	0.0381053	+	0.129166i
$601$	5.22104	+	1.69642i	0.212971	+	0.0691984i	0.413559	−	0.910477i	$-0.364285\pi$
$601$	5.22104	+	1.69642i	0.212971	+	0.0691984i	−0.200589	+	0.979676i	$0.564285\pi$
$602$	−18.6237	−	57.3178i	−0.759045	−	2.33610i
$603$	4.65296	+	3.78498i	0.189483	+	0.154136i
$604$		−	2.35005i		−	0.0956221i
$605$	8.09421	−	7.44875i	0.329076	−	0.302835i
$606$	−9.59432	−	7.37886i	−0.389743	−	0.299746i
$607$	9.61165	+	13.2293i	0.390125	+	0.536961i	0.958231	−	0.285994i	$-0.0923239\pi$
$607$	9.61165	+	13.2293i	0.390125	+	0.536961i	−0.568107	+	0.822955i	$0.692324\pi$
$608$	−20.0703	+	6.52123i	−0.813957	+	0.264471i
$609$	−21.1771	−	30.8861i	−0.858141	−	1.25157i
$610$	−18.0151	−	13.0887i	−0.729408	−	0.529946i
$611$	33.5417	+	24.3695i	1.35695	+	0.985883i
$612$	−2.48917	−	0.135976i	−0.100619	−	0.00549649i
$613$	36.1717	−	11.7529i	1.46096	−	0.474695i	0.532598	−	0.846368i	$-0.321216\pi$
$613$	36.1717	−	11.7529i	1.46096	−	0.474695i	0.928364	+	0.371673i	$0.121216\pi$
$614$	22.1182	+	30.4431i	0.892618	+	1.22858i
$615$	−1.41347	+	1.83786i	−0.0569967	+	0.0741096i
$616$	25.3104	+	2.52140i	1.01979	+	0.101590i
$617$			9.52278i			0.383373i	0.981456	+	0.191686i	$0.0613956\pi$
$617$			9.52278i			0.383373i	−0.981456	+	0.191686i	$0.938604\pi$
$618$	−9.49454	−	0.259136i	−0.381927	−	0.0104240i
$619$	8.98469	+	27.6520i	0.361125	+	1.11143i	0.952372	+	0.304938i	$0.0986358\pi$
$619$	8.98469	+	27.6520i	0.361125	+	1.11143i	−0.591247	+	0.806491i	$0.701364\pi$
$620$	1.51078	+	0.490884i	0.0606746	+	0.0197144i
$621$	−7.79627	−	12.8177i	−0.312853	−	0.514355i
$622$	−1.25548	+	1.72802i	−0.0503403	+	0.0692875i
$623$	−13.7347	+	42.2710i	−0.550268	+	1.69355i
$624$	45.4540	+	16.1527i	1.81962	+	0.646627i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	43.9545			1.75678
$627$	−25.8811	−	3.29359i	−1.03359	−	0.131533i
$628$	5.58562			0.222891
$629$	6.11651	−	4.44390i	0.243881	−	0.177190i
$630$	17.2101	−	11.1223i	0.685668	−	0.443124i
$631$	0.748409	−	2.30337i	0.0297937	−	0.0916956i	−0.935054	−	0.354505i	$-0.884649\pi$
$631$	0.748409	−	2.30337i	0.0297937	−	0.0916956i	0.964848	+	0.262810i	$0.0846492\pi$
$632$	2.38322	−	3.28022i	0.0947995	−	0.130480i
$633$	17.5861	−	5.18809i	0.698986	−	0.206208i
$634$	47.2803	+	15.3623i	1.87774	+	0.610115i
$635$	1.16338	+	3.58051i	0.0461673	+	0.142088i
$636$	−0.393350	+	14.4120i	−0.0155973	+	0.571474i
$637$		−	51.4860i		−	2.03995i
$638$	29.5117	−	6.44053i	1.16838	−	0.254983i
$639$	−7.11521	+	1.88965i	−0.281473	+	0.0747533i
$640$	−7.54432	−	10.3839i	−0.298216	−	0.410459i
$641$	−19.9789	+	6.49154i	−0.789120	+	0.256401i	−0.675729	−	0.737150i	$-0.736171\pi$
$641$	−19.9789	+	6.49154i	−0.789120	+	0.256401i	−0.113390	+	0.993551i	$0.536171\pi$
$642$	−0.874663	+	0.599716i	−0.0345202	+	0.0236689i
$643$	−37.4319	−	27.1959i	−1.47617	−	1.07250i	−0.978765	−	0.204984i	$-0.934286\pi$
$643$	−37.4319	−	27.1959i	−1.47617	−	1.07250i	−0.497407	−	0.867518i	$-0.665714\pi$
$644$	−8.25099	−	5.99469i	−0.325135	−	0.236224i
$645$	−12.6043	+	8.64217i	−0.496293	+	0.340285i
$646$	−6.94036	+	2.25506i	−0.273065	+	0.0887242i
$647$	−26.3722	−	36.2982i	−1.03680	−	1.42703i	−0.899719	−	0.436469i	$-0.856229\pi$
$647$	−26.3722	−	36.2982i	−1.03680	−	1.42703i	−0.137079	−	0.990560i	$-0.543771\pi$
$648$	−14.8820	+	8.50453i	−0.584620	+	0.334089i
$649$	−2.59092	+	5.90536i	−0.101703	+	0.231806i
$650$			9.47683i			0.371712i
$651$	−0.344595	+	12.6257i	−0.0135057	+	0.494839i
$652$	−0.402673	−	1.23930i	−0.0157699	−	0.0485348i
$653$	22.1468	+	7.19592i	0.866670	+	0.281598i	0.708411	−	0.705800i	$-0.249412\pi$
$653$	22.1468	+	7.19592i	0.866670	+	0.281598i	0.158258	+	0.987398i	$0.449412\pi$
$654$	−15.8687	+	4.68142i	−0.620514	+	0.183058i
$655$	2.72371	−	3.74887i	0.106424	−	0.146480i
$656$	2.06203	−	6.34627i	0.0805087	−	0.247780i
$657$	−15.7825	−	24.4211i	−0.615735	−	0.952758i
$658$	−41.0069	+	29.7933i	−1.59862	+	1.16146i
$659$	−28.1656			−1.09718			−0.548589	−	0.836092i	$-0.684835\pi$
$659$	−28.1656			−1.09718			−0.548589	+	0.836092i	$0.684835\pi$
$660$	0.939725	+	4.95080i	0.0365787	+	0.192709i
$661$	2.19156			0.0852420			0.0426210	−	0.999091i	$-0.486429\pi$
$661$	2.19156			0.0852420			0.0426210	+	0.999091i	$0.486429\pi$
$662$	−6.97005	+	5.06404i	−0.270899	+	0.196819i
$663$	8.63752	+	3.06947i	0.335454	+	0.119208i
$664$	−1.82149	+	5.60597i	−0.0706875	+	0.217554i
$665$	10.7497	−	14.7957i	0.416856	−	0.573753i
$666$	−14.6387	+	37.8843i	−0.567237	+	1.46799i
$667$	14.7436	+	4.79048i	0.570874	+	0.185488i
$668$	−2.54248	−	7.82496i	−0.0983717	−	0.302757i
$669$	−4.66993	−	0.127457i	−0.180550	−	0.00492778i
$670$		−	3.39134i		−	0.131019i
$671$	32.5142	+	28.9579i	1.25520	+	1.11791i
$672$	−19.7574	+	25.6894i	−0.762157	+	0.990990i
$673$	−21.8862	−	30.1238i	−0.843650	−	1.16119i	−0.985226	−	0.171258i	$-0.945217\pi$
$673$	−21.8862	−	30.1238i	−0.843650	−	1.16119i	0.141576	−	0.989927i	$-0.454783\pi$
$674$	−56.7720	+	18.4463i	−2.18678	+	0.710527i
$675$	−3.93996	−	3.38773i	−0.151649	−	0.130394i
$676$	12.9263	+	9.39152i	0.497166	+	0.361212i
$677$	9.32509	+	6.77508i	0.358392	+	0.260387i	0.752381	−	0.658728i	$-0.228905\pi$
$677$	9.32509	+	6.77508i	0.358392	+	0.260387i	−0.393989	+	0.919115i	$0.628905\pi$
$678$	17.4051	+	25.3847i	0.668438	+	0.974893i
$679$	−30.4518	+	9.89440i	−1.16863	+	0.379712i
$680$	−1.06042	−	1.45954i	−0.0406653	−	0.0559709i
$681$	−2.15829	−	1.65991i	−0.0827059	−	0.0636080i
$682$	−9.32924	−	4.09311i	−0.357235	−	0.156733i
$683$			4.01798i			0.153744i	0.997041	+	0.0768719i	$0.0244933\pi$
$683$			4.01798i			0.153744i	−0.997041	+	0.0768719i	$0.975507\pi$
$684$	7.54216	−	9.27177i	0.288382	−	0.354515i
$685$	0.254073	+	0.781957i	0.00970764	+	0.0298770i
$686$	14.3913	+	4.67601i	0.549461	+	0.178531i
$687$	8.41383	+	28.5205i	0.321008	+	1.08812i
$688$	25.8530	−	35.5836i	0.985637	−	1.35661i
$689$	16.3825	−	50.4203i	0.624125	−	1.92086i
$690$	−2.84039	+	7.99289i	−0.108132	+	0.304284i
$691$	36.9716	−	26.8614i	1.40647	−	1.02186i	0.412640	−	0.910894i	$-0.364607\pi$
$691$	36.9716	−	26.8614i	1.40647	−	1.02186i	0.993825	−	0.110963i	$-0.0353934\pi$
$692$	−21.8761			−0.831605
$693$	−35.6408	+	18.3045i	−1.35388	+	0.695330i
$694$	22.7755			0.864548
$695$	5.73282	−	4.16514i	0.217458	−	0.157993i
$696$	5.93076	−	16.6892i	0.224805	−	0.632604i
$697$	0.391843	−	1.20597i	0.0148421	−	0.0456793i
$698$	−3.05554	+	4.20559i	−0.115654	+	0.159184i
$699$	−3.27026	−	11.0852i	−0.123693	−	0.419282i
$700$	−3.35949	−	1.09157i	−0.126977	−	0.0412573i
$701$	4.14880	+	12.7687i	0.156698	+	0.482267i	0.998329	−	0.0577861i	$-0.0184041\pi$
$701$	4.14880	+	12.7687i	0.156698	+	0.482267i	−0.841631	+	0.540053i	$0.818404\pi$
$702$	−47.9203	+	11.3366i	−1.80864	+	0.427871i
$703$			36.2481i			1.36712i
$704$	3.49535	+	5.97894i	0.131736	+	0.225340i
$705$	10.1885	+	7.83580i	0.383719	+	0.295113i
$706$	0.176357	+	0.242735i	0.00663730	+	0.00913546i
$707$	−15.7776	+	5.12644i	−0.593376	+	0.192800i
$708$	−1.67059	−	2.43650i	−0.0627848	−	0.0915693i
$709$	−26.0022	−	18.8917i	−0.976534	−	0.709493i	−0.0196024	−	0.999808i	$-0.506240\pi$
$709$	−26.0022	−	18.8917i	−0.976534	−	0.709493i	−0.956931	+	0.290315i	$0.906240\pi$
$710$	3.36752	+	2.44664i	0.126381	+	0.0918209i
$711$	−0.348373	+	6.37729i	−0.0130650	+	0.239167i
$712$	−19.9923	+	6.49590i	−0.749244	+	0.243444i
$713$	−3.07321	−	4.22991i	−0.115093	−	0.158411i
$714$	−6.83216	+	8.88347i	−0.255687	+	0.332456i
$715$	1.83684	−	18.4386i	0.0686940	−	0.689566i
$716$			9.00709i			0.336611i
$717$	44.0220	+	1.20150i	1.64403	+	0.0448709i
$718$	−15.9626	−	49.1279i	−0.595720	−	1.83344i
$719$	5.86776	+	1.90655i	0.218830	+	0.0711023i	0.416380	−	0.909190i	$-0.363298\pi$
$719$	5.86776	+	1.90655i	0.218830	+	0.0711023i	−0.197550	+	0.980293i	$0.563298\pi$
$720$	13.9496	+	5.39019i	0.519870	+	0.200881i
$721$	−7.65193	+	10.5320i	−0.284973	+	0.392232i
$722$	0.852648	−	2.62418i	0.0317323	−	0.0976619i
$723$	−37.0323	−	13.1600i	−1.37725	−	0.489424i
$724$	−4.03171	+	2.92921i	−0.149837	+	0.108863i
$725$	5.36927			0.199410
$726$	−2.84961	−	32.1917i	−0.105759	−	1.19475i
$727$	−22.8281			−0.846646			−0.423323	−	0.905979i	$-0.639137\pi$
$727$	−22.8281			−0.846646			−0.423323	+	0.905979i	$0.639137\pi$
$728$	34.6643	−	25.1851i	1.28474	−	0.933420i
$729$	12.4172	−	23.9753i	0.459896	−	0.887973i
$730$	−5.08040	+	15.6359i	−0.188034	+	0.578709i
$731$	4.91279	−	6.76188i	0.181706	−	0.250097i
$732$	−19.1309	+	5.64382i	−0.707099	+	0.208601i
$733$	−25.7765	−	8.37529i	−0.952076	−	0.309348i	−0.208517	−	0.978019i	$-0.566864\pi$
$733$	−25.7765	−	8.37529i	−0.952076	−	0.309348i	−0.743559	+	0.668670i	$0.766864\pi$
$734$	−15.0519	−	46.3249i	−0.555575	−	1.70988i
$735$	0.435477	−	15.9555i	0.0160628	−	0.588528i
$736$		−	13.4157i		−	0.494510i
$737$	−0.657326	+	6.59839i	−0.0242129	+	0.243055i
$738$	1.74845	+	6.58356i	0.0643615	+	0.242344i
$739$	5.47375	+	7.53398i	0.201355	+	0.277142i	0.897739	−	0.440528i	$-0.145209\pi$
$739$	5.47375	+	7.53398i	0.201355	+	0.277142i	−0.696384	+	0.717670i	$0.745209\pi$
$740$	6.65856	−	2.16350i	0.244774	−	0.0795318i
$741$	−36.2473	+	24.8531i	−1.33158	+	0.913001i
$742$	52.4359	+	38.0969i	1.92498	+	1.39858i
$743$	−16.1043	−	11.7005i	−0.590811	−	0.429250i	0.251794	−	0.967781i	$-0.418979\pi$
$743$	−16.1043	−	11.7005i	−0.590811	−	0.429250i	−0.842606	+	0.538531i	$0.818979\pi$
$744$	−4.92675	+	3.37804i	−0.180623	+	0.123845i
$745$	5.73864	−	1.86460i	0.210247	−	0.0683135i
$746$	−3.14622	−	4.33041i	−0.115191	−	0.158547i
$747$	−2.38328	−	8.97391i	−0.0871996	−	0.328338i
$748$	−1.39092	−	2.37923i	−0.0508572	−	0.0869933i
$749$			1.45356i			0.0531121i
$750$	−0.0801565	+	2.93687i	−0.00292690	+	0.107239i
$751$	−9.77409	−	30.0816i	−0.356662	−	1.09769i	−0.955040	−	0.296478i	$-0.904188\pi$
$751$	−9.77409	−	30.0816i	−0.356662	−	1.09769i	0.598378	−	0.801214i	$-0.295812\pi$
$752$	−35.1815	−	11.4312i	−1.28294	−	0.416852i
$753$	29.9876	−	8.84665i	1.09281	−	0.322390i
$754$	29.9087	−	41.1657i	1.08921	−	1.49917i
$755$	−0.827856	+	2.54788i	−0.0301288	+	0.0927268i
$756$	1.50083	−	18.2933i	0.0545847	−	0.665321i
$757$	18.5034	−	13.4435i	0.672519	−	0.488613i	−0.198349	−	0.980132i	$-0.563558\pi$
$757$	18.5034	−	13.4435i	0.672519	−	0.488613i	0.870867	+	0.491518i	$0.163558\pi$
$758$	8.28544			0.300941
$759$	7.07564	−	15.0009i	0.256829	−	0.544497i
$760$	8.64965			0.313756
$761$	35.2851	−	25.6362i	1.27909	−	0.929310i	0.279560	−	0.960128i	$-0.409811\pi$
$761$	35.2851	−	25.6362i	1.27909	−	0.929310i	0.999525	+	0.0308183i	$0.00981134\pi$
$762$	10.4222	+	3.70369i	0.377558	+	0.134171i
$763$	−7.00746	+	21.5667i	−0.253687	+	0.780768i
$764$	9.92948	−	13.6668i	0.359236	−	0.494446i
$765$	2.65081	+	1.02429i	0.0958402	+	0.0370331i
$766$	−51.7797	−	16.8242i	−1.87088	−	0.607884i
$767$	3.35689	+	10.3315i	0.121210	+	0.373047i
$768$	−30.4643	−	0.831467i	−1.09929	−	0.0300030i
$769$			5.82302i			0.209984i	0.994473	+	0.104992i	$0.0334816\pi$
$769$			5.82302i			0.209984i	−0.994473	+	0.104992i	$0.966518\pi$
$770$	20.7452	+	9.10175i	0.747605	+	0.328004i
$771$	−19.8332	+	25.7880i	−0.714274	+	0.928731i
$772$	8.02803	+	11.0496i	0.288935	+	0.397685i
$773$	40.0822	−	13.0235i	1.44166	−	0.468423i	0.519243	−	0.854627i	$-0.326214\pi$
$773$	40.0822	−	13.0235i	1.44166	−	0.468423i	0.922413	+	0.386204i	$0.126214\pi$
$774$	−2.44908	+	44.8326i	−0.0880302	+	1.61148i
$775$	−1.46504	−	1.06441i	−0.0526258	−	0.0382349i
$776$	−12.2514	−	8.90116i	−0.439799	−	0.319533i
$777$	31.4791	+	45.9111i	1.12931	+	1.64705i
$778$	32.4429	−	10.5413i	1.16314	−	0.377926i
$779$	3.57345	+	4.91843i	0.128032	+	0.176221i
$780$	6.72882	+	5.17505i	0.240931	+	0.185296i
$781$	−6.07781	−	5.41304i	−0.217481	−	0.193694i
$782$		−	4.63919i		−	0.165897i
$783$	6.42294	+	27.1502i	0.229537	+	0.970268i
$784$	14.1956	+	43.6895i	0.506985	+	1.56034i
$785$	−6.05583	−	1.96766i	−0.216142	−	0.0702288i
$786$	−3.85217	−	13.0577i	−0.137402	−	0.465754i
$787$	24.5743	−	33.8236i	0.875978	−	1.20568i	−0.101540	−	0.994831i	$-0.532377\pi$
$787$	24.5743	−	33.8236i	0.875978	−	1.20568i	0.977519	−	0.210849i	$-0.0676229\pi$
$788$	−2.35208	+	7.23895i	−0.0837893	+	0.257877i
$789$	−15.2785	+	42.9940i	−0.543930	+	1.53063i
$790$	2.92150	−	2.12259i	0.103942	−	0.0755184i
$791$	42.1857			1.49995
$792$	−16.9119	−	8.54864i	−0.600936	−	0.303763i
$793$	73.3448			2.60455
$794$	35.6449	−	25.8976i	1.26499	−	0.919070i
$795$	5.50342	−	15.4867i	0.195186	−	0.549256i
$796$	3.44283	−	10.5959i	0.122028	−	0.375563i
$797$	−2.61692	+	3.60187i	−0.0926959	+	0.127585i	−0.852846	−	0.522163i	$-0.825125\pi$
$797$	−2.61692	+	3.60187i	−0.0926959	+	0.127585i	0.760150	+	0.649748i	$0.225125\pi$
$798$	−15.2034	−	51.5351i	−0.538194	−	1.82432i
$799$	−6.68547	−	2.17224i	−0.236515	−	0.0768484i
$800$	−1.43587	−	4.41915i	−0.0507656	−	0.156241i
$801$	20.8954	−	25.6872i	0.738301	−	0.907612i
$802$			57.5562i			2.03238i
$803$	12.9153	−	29.4373i	0.455772	−	1.03882i
$804$	−2.40795	−	1.85192i	−0.0849220	−	0.0653123i
$805$	6.83381	+	9.40594i	0.240860	+	0.331516i
$806$	−16.3215	+	5.30319i	−0.574902	+	0.186797i
$807$	11.1781	+	16.3028i	0.393488	+	0.573887i
$808$	−6.34764	−	4.61183i	−0.223309	−	0.162244i
$809$	−13.3643	−	9.70972i	−0.469863	−	0.341375i	0.327525	−	0.944843i	$-0.393785\pi$
$809$	−13.3643	−	9.70972i	−0.469863	−	0.341375i	−0.797388	+	0.603467i	$0.793785\pi$
$810$	−14.9464	+	3.10788i	−0.525163	+	0.109200i
$811$	24.3731	−	7.91931i	0.855856	−	0.278085i	0.151959	−	0.988387i	$-0.451442\pi$
$811$	24.3731	−	7.91931i	0.855856	−	0.278085i	0.703897	+	0.710302i	$0.251442\pi$
$812$	11.1481	+	15.3441i	0.391222	+	0.538471i
$813$	−13.9092	+	18.0854i	−0.487818	+	0.634283i
$814$	−43.8681	+	9.57363i	−1.53758	+	0.335556i
$815$			1.48548i			0.0520341i
$816$	−8.17585	−	0.223145i	−0.286212	−	0.00781163i
$817$	12.3832	+	38.1114i	0.433232	+	1.33335i
$818$	−2.92337	−	0.949859i	−0.102213	−	0.0332110i
$819$	−24.3269	+	62.9569i	−0.850049	+	2.19989i
$820$	0.690202	−	0.949982i	0.0241029	−	0.0331748i
$821$	6.52224	−	20.0734i	0.227628	−	0.700566i	−0.770387	−	0.637577i	$-0.779937\pi$
$821$	6.52224	−	20.0734i	0.227628	−	0.700566i	0.998014	−	0.0629888i	$-0.0200632\pi$
$822$	2.27614	+	0.808859i	0.0793895	+	0.0282122i
$823$	9.58473	−	6.96371i	0.334103	−	0.242740i	−0.408067	−	0.912952i	$-0.633797\pi$
$823$	9.58473	−	6.96371i	0.334103	−	0.242740i	0.742169	+	0.670212i	$0.233797\pi$
$824$	−6.15706			−0.214491
$825$	0.725195	−	5.69860i	0.0252481	−	0.198400i
$826$	−13.2809			−0.462101
$827$	−27.7685	+	20.1750i	−0.965604	+	0.701552i	−0.954445	−	0.298385i	$-0.903552\pi$
$827$	−27.7685	+	20.1750i	−0.965604	+	0.701552i	−0.0111586	+	0.999938i	$0.503552\pi$
$828$	4.12412	+	6.38147i	0.143323	+	0.221771i
$829$	5.14620	−	15.8384i	0.178735	−	0.550089i	−0.821049	−	0.570857i	$-0.806611\pi$
$829$	5.14620	−	15.8384i	0.178735	−	0.550089i	0.999784	+	0.0207676i	$0.00661102\pi$
$830$	−3.08578	+	4.24721i	−0.107109	+	0.147423i
$831$	7.42647	−	2.19088i	0.257621	−	0.0760009i
$832$	11.0956	+	3.60517i	0.384670	+	0.124987i
$833$	2.69755	+	8.30221i	0.0934647	+	0.287655i
$834$	0.568002	−	20.8111i	0.0196683	−	0.720630i
$835$			9.37933i			0.324585i
$836$	13.1483	+	1.30983i	0.454745	+	0.0453013i
$837$	3.62976	−	8.68139i	0.125463	−	0.300073i
$838$	17.9621	+	24.7227i	0.620490	+	0.854032i
$839$	−4.80401	+	1.56092i	−0.165853	+	0.0538889i	−0.390767	−	0.920490i	$-0.627790\pi$
$839$	−4.80401	+	1.56092i	−0.165853	+	0.0538889i	0.224914	+	0.974379i	$0.427790\pi$
$840$	10.9555	−	7.51166i	0.378000	−	0.259177i
$841$	0.138267	+	0.100457i	0.00476782	+	0.00346403i
$842$	51.1299	+	37.1481i	1.76205	+	1.28021i
$843$	11.6347	−	7.97734i	0.400719	−	0.274754i
$844$	−8.83164	+	2.86957i	−0.303997	+	0.0987748i
$845$	−10.7061	−	14.7357i	−0.368302	−	0.506924i
$846$	36.4970	−	9.69283i	1.25479	−	0.333247i
$847$	−38.5989	−	21.7298i	−1.32627	−	0.746645i
$848$			47.3021i			1.62436i
$849$	−0.0741184	+	2.71564i	−0.00254374	+	0.0932004i
$850$	−0.496528	−	1.52816i	−0.0170308	−	0.0524153i
$851$	−21.9158	−	7.12088i	−0.751265	−	0.244101i
$852$	3.57610	−	1.05499i	0.122515	−	0.0361433i
$853$	−20.6012	+	28.3551i	−0.705372	+	0.970862i	0.294512	+	0.955648i	$0.404843\pi$
$853$	−20.6012	+	28.3551i	−0.705372	+	0.970862i	−0.999884	+	0.0152139i	$0.995157\pi$
$854$	−27.7092	+	85.2801i	−0.948188	+	2.91822i
$855$	−11.4433	+	7.39539i	−0.391351	+	0.252917i
$856$	−0.556176	+	0.404086i	−0.0190097	+	0.0138114i
$857$	−7.13519			−0.243734			−0.121867	−	0.992546i	$-0.538888\pi$
$857$	−7.13519			−0.243734			−0.121867	+	0.992546i	$0.538888\pi$
$858$	−39.6511	−	37.3032i	−1.35367	−	1.27351i
$859$	−47.4939			−1.62047			−0.810235	−	0.586105i	$-0.800661\pi$
$859$	−47.4939			−1.62047			−0.810235	+	0.586105i	$0.800661\pi$
$860$	6.26175	−	4.54943i	0.213524	−	0.155134i
$861$	8.79739	+	3.12628i	0.299814	+	0.106543i
$862$	−1.18188	+	3.63746i	−0.0402551	+	0.123892i
$863$	−12.6153	+	17.3635i	−0.429431	+	0.591061i	−0.967823	−	0.251633i	$-0.919032\pi$
$863$	−12.6153	+	17.3635i	−0.429431	+	0.591061i	0.538391	+	0.842695i	$0.319032\pi$
$864$	20.6282	−	12.5470i	0.701784	−	0.426856i
$865$	23.7177	+	7.70635i	0.806426	+	0.262024i
$866$	−1.61575	−	4.97278i	−0.0549055	−	0.168982i
$867$	27.8803	+	0.760941i	0.946863	+	0.0258429i
$868$		−	6.39675i		−	0.217120i
$869$	−6.09564	+	3.56358i	−0.206780	+	0.120886i
$870$	9.61689	−	12.5043i	0.326043	−	0.423936i
$871$	6.56571	+	9.03692i	0.222471	+	0.306204i
$872$	−10.2001	+	3.31422i	−0.345419	+	0.112234i
$873$	23.8187	+	1.30115i	0.806141	+	0.0440371i
$874$	17.9945	+	13.0738i	0.608672	+	0.442226i
$875$	3.25777	+	2.36691i	0.110133	+	0.0800162i
$876$	8.32765	+	12.1456i	0.281365	+	0.410361i
$877$	−8.25120	+	2.68098i	−0.278623	+	0.0905301i	−0.444995	−	0.895533i	$-0.646795\pi$
$877$	−8.25120	+	2.68098i	−0.278623	+	0.0905301i	0.166372	+	0.986063i	$0.446795\pi$
$878$	−12.4419	−	17.1247i	−0.419892	−	0.577932i
$879$	37.2336	+	28.6358i	1.25586	+	0.965863i
$880$	3.52516	+	16.1529i	0.118833	+	0.544515i
$881$			1.51335i			0.0509859i	0.999675	+	0.0254929i	$0.00811554\pi$
$881$			1.51335i			0.0509859i	−0.999675	+	0.0254929i	$0.991884\pi$
$882$	−36.3783	−	29.5921i	−1.22492	−	0.996417i
$883$	13.2378	+	40.7416i	0.445486	+	1.37107i	0.881950	+	0.471344i	$0.156231\pi$
$883$	13.2378	+	40.7416i	0.445486	+	1.37107i	−0.436464	+	0.899722i	$0.643769\pi$
$884$	−4.41533	−	1.43463i	−0.148503	−	0.0482517i
$885$	0.952917	+	3.23011i	0.0320320	+	0.108579i
$886$	36.3628	−	50.0491i	1.22163	−	1.68143i
$887$	7.75253	−	23.8598i	0.260304	−	0.801135i	−0.732434	−	0.680838i	$-0.761616\pi$
$887$	7.75253	−	23.8598i	0.260304	−	0.801135i	0.992738	−	0.120296i	$-0.0383844\pi$
$888$	−8.81586	+	24.8080i	−0.295841	+	0.832501i
$889$	12.2648	−	8.91088i	0.411347	−	0.298861i
$890$	−18.7223			−0.627572
$891$	29.6830	−	3.14989i	0.994417	−	0.105525i
$892$	2.36600			0.0792196
$893$	27.2661	−	19.8100i	0.912424	−	0.662915i
$894$	5.93606	−	16.7042i	0.198532	−	0.558671i
$895$	3.17295	−	9.76533i	0.106060	−	0.326419i
$896$	−30.3797	+	41.8141i	−1.01491	+	1.39691i
$897$	−7.90560	−	26.7977i	−0.263960	−	0.894750i
$898$	35.6500	+	11.5834i	1.18966	+	0.386543i
$899$	3.00462	+	9.24728i	0.100210	+	0.308414i
$900$	2.04149	+	1.66066i	0.0680498	+	0.0553554i
$901$			8.98871i			0.299457i
$902$	−5.00858	+	5.62368i	−0.166767	+	0.187248i
$903$	48.7816	+	37.5172i	1.62335	+	1.24850i
$904$	11.7275	+	16.1415i	0.390050	+	0.536858i
$905$	5.40299	−	1.75554i	0.179601	−	0.0583560i
$906$	4.45089	+	6.49146i	0.147871	+	0.215664i
$907$	−20.5789	−	14.9515i	−0.683312	−	0.496455i	0.191143	−	0.981562i	$-0.438781\pi$
$907$	−20.5789	−	14.9515i	−0.683312	−	0.496455i	−0.874455	+	0.485107i	$0.838781\pi$
$908$	1.11561	+	0.810541i	0.0370229	+	0.0268987i
$909$	12.3408	+	0.674143i	0.409320	+	0.0223599i
$910$	36.2938	−	11.7926i	1.20313	−	0.390920i
$911$	17.2315	+	23.7171i	0.570904	+	0.785781i	0.992661	−	0.120927i	$-0.0385868\pi$
$911$	17.2315	+	23.7171i	0.570904	+	0.785781i	−0.421758	+	0.906709i	$0.638587\pi$
$912$	23.9060	−	31.0836i	0.791606	−	1.02928i
$913$	6.82708	−	7.66551i	0.225943	−	0.253691i
$914$		−	22.5212i		−	0.744936i
$915$	22.7296	+	0.620362i	0.751416	+	0.0205085i
$916$	−4.65375	−	14.3228i	−0.153764	−	0.473238i
$917$	−17.7465	−	5.76618i	−0.586040	−	0.190416i
$918$	7.13328	−	4.33877i	0.235433	−	0.143201i
$919$	4.78048	−	6.57977i	0.157694	−	0.217047i	−0.722858	−	0.690996i	$-0.757172\pi$
$919$	4.78048	−	6.57977i	0.157694	−	0.217047i	0.880552	+	0.473950i	$0.157172\pi$
$920$	−1.69921	+	5.22964i	−0.0560214	+	0.172416i
$921$	−36.2061	−	12.8664i	−1.19303	−	0.423961i
$922$	−19.1972	+	13.9476i	−0.632227	+	0.459340i
$923$	−13.7102			−0.451276
$924$	17.7909	−	9.75947i	0.585278	−	0.321063i
$925$	−7.98124			−0.262421
$926$	32.7570	−	23.7994i	1.07646	−	0.782096i
$927$	8.14563	−	5.26424i	0.267538	−	0.172900i
$928$	−7.70957	+	23.7276i	−0.253079	+	0.778898i
$929$	31.9947	−	44.0370i	1.04971	−	1.44481i	0.160656	−	0.987011i	$-0.448639\pi$
$929$	31.9947	−	44.0370i	1.04971	−	1.44481i	0.889058	−	0.457796i	$-0.151361\pi$
$930$	−5.10291	+	1.50541i	−0.167331	+	0.0493643i
$931$	−39.8046	−	12.9333i	−1.30454	−	0.423872i
$932$	1.80881	+	5.56693i	0.0592494	+	0.182351i
$933$	0.0595058	−	2.18024i	0.00194813	−	0.0713780i
$934$		−	43.2897i		−	1.41648i
$935$	0.669878	+	3.06951i	0.0219074	+	0.100384i
$936$	−30.8519	+	8.19362i	−1.00843	+	0.267817i
$937$	10.1377	+	13.9533i	0.331183	+	0.455835i	0.941840	−	0.336060i	$-0.109095\pi$
$937$	10.1377	+	13.9533i	0.331183	+	0.455835i	−0.610657	+	0.791895i	$0.709095\pi$
$938$	−12.9880	+	4.22005i	−0.424072	+	0.137789i
$939$	−37.0171	+	25.3809i	−1.20801	+	0.828273i
$940$	−5.26638	−	3.82625i	−0.171770	−	0.124798i
$941$	−6.82285	−	4.95709i	−0.222418	−	0.161596i	0.470996	−	0.882135i	$-0.343895\pi$
$941$	−6.82285	−	4.95709i	−0.222418	−	0.161596i	−0.693415	+	0.720539i	$0.743895\pi$
$942$	−15.4290	+	10.5789i	−0.502704	+	0.344680i
$943$	−3.67571	+	1.19431i	−0.119698	+	0.0388921i
$944$	−5.69712	−	7.84141i	−0.185425	−	0.255216i
$945$	−8.07140	+	19.3046i	−0.262563	+	0.627978i
$946$	−42.8526	+	25.0521i	−1.39326	+	0.814514i
$947$		−	45.4509i		−	1.47696i	−0.674278	−	0.738478i	$-0.735545\pi$
$947$		−	45.4509i		−	1.47696i	0.674278	−	0.738478i	$-0.264455\pi$
$948$	0.0882509	−	3.23344i	0.00286625	−	0.105017i
$949$	−16.7336	−	51.5007i	−0.543195	−	1.67178i
$950$	7.32667	+	2.38058i	0.237709	+	0.0772362i
$951$	−48.6886	+	14.3637i	−1.57884	+	0.465773i
$952$	−4.27013	+	5.87733i	−0.138396	+	0.190485i
$953$	2.10885	−	6.49039i	0.0683125	−	0.210244i	−0.911073	−	0.412246i	$-0.864745\pi$
$953$	2.10885	−	6.49039i	0.0683125	−	0.210244i	0.979385	+	0.202001i	$0.0647446\pi$
$954$	−26.2092	−	40.5549i	−0.848555	−	1.31301i
$955$	−15.5798	+	11.3194i	−0.504150	+	0.366287i
$956$	−22.3036			−0.721350
$957$	−21.1348	+	22.4651i	−0.683191	+	0.726193i
$958$	−32.4102			−1.04713
$959$	2.67854	−	1.94607i	0.0864944	−	0.0628419i
$960$	3.40803	+	1.21109i	0.109994	+	0.0390878i
$961$	−8.56616	+	26.3639i	−0.276328	+	0.850449i
$962$	−44.4582	+	61.1915i	−1.43339	+	1.97289i
$963$	0.390316	−	1.01012i	0.0125778	−	0.0325507i
$964$	18.9302	+	6.15078i	0.609699	+	0.198103i
$965$	−4.81137	−	14.8079i	−0.154883	−	0.476682i
$966$	34.1452	+	0.931930i	1.09860	+	0.0299844i
$967$		−	50.1703i		−	1.61337i	−0.590982	−	0.806684i	$-0.701260\pi$
$967$		−	50.1703i		−	1.61337i	0.590982	−	0.806684i	$-0.298740\pi$
$968$	−2.41589	−	20.8099i	−0.0776497	−	0.668855i
$969$	4.54280	−	5.90674i	0.145936	−	0.189752i
$970$	−7.92772	−	10.9116i	−0.254544	−	0.350349i
$971$	−7.97836	+	2.59233i	−0.256038	+	0.0831917i	−0.434224	−	0.900805i	$-0.642977\pi$
$971$	−7.97836	+	2.59233i	−0.256038	+	0.0831917i	0.178186	+	0.983997i	$0.442977\pi$
$972$	−5.95516	+	12.3095i	−0.191012	+	0.394828i
$973$	−23.0851	−	16.7723i	−0.740074	−	0.537695i
$974$	40.5297	+	29.4466i	1.29866	+	0.943528i
$975$	−5.47225	−	7.98107i	−0.175252	−	0.255599i
$976$	−62.2382	+	20.2224i	−1.99220	+	0.647303i
$977$	−17.4157	−	23.9707i	−0.557178	−	0.766889i	0.433787	−	0.901016i	$-0.357177\pi$
$977$	−17.4157	−	23.9707i	−0.557178	−	0.766889i	−0.990964	+	0.134126i	$0.957177\pi$
$978$	3.45948	+	2.66064i	0.110622	+	0.0850778i
$979$	36.4271	+	3.62884i	1.16422	+	0.115978i
$980$			8.08381i			0.258228i
$981$	10.6609	−	13.1056i	0.340375	−	0.418431i
$982$	−2.99594	−	9.22055i	−0.0956043	−	0.294240i
$983$	−39.7619	−	12.9194i	−1.26821	−	0.412066i	−0.403796	−	0.914849i	$-0.632309\pi$
$983$	−39.7619	−	12.9194i	−1.26821	−	0.412066i	−0.864413	+	0.502783i	$0.832309\pi$
$984$	1.24944	+	4.23523i	0.0398306	+	0.135014i
$985$	5.10016	−	7.01977i	0.162505	−	0.223668i
$986$	−2.66599	+	8.20509i	−0.0849025	+	0.261303i
$987$	17.3310	−	48.7697i	0.551652	−	1.55236i
$988$	18.0075	−	13.0832i	0.572895	−	0.416232i
$989$	−25.4751			−0.810060
$990$	−11.9724	−	11.8956i	−0.380507	−	0.378068i
$991$	42.7671			1.35854			0.679271	−	0.733887i	$-0.262296\pi$
$991$	42.7671			1.35854			0.679271	+	0.733887i	$0.262296\pi$
$992$	6.80742	−	4.94588i	0.216136	−	0.157032i
$993$	2.94580	−	8.28952i	0.0934821	−	0.263060i
$994$	5.17962	−	15.9412i	0.164287	−	0.505625i
$995$	−7.46531	+	10.2751i	−0.236666	+	0.325743i
$996$	1.33058	+	4.51028i	0.0421610	+	0.142914i
$997$	−9.25930	−	3.00853i	−0.293245	−	0.0952811i	0.158700	−	0.987327i	$-0.449270\pi$
$997$	−9.25930	−	3.00853i	−0.293245	−	0.0952811i	−0.451945	+	0.892046i	$0.649270\pi$
$998$	6.19238	+	19.0582i	0.196016	+	0.603277i
$999$	−9.54747	−	40.3578i	−0.302069	−	1.27686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.p.b.41.9	yes	48
3.2	odd	2	inner	165.2.p.b.41.4	✓	48
5.2	odd	4		825.2.bs.h.74.10		48
5.3	odd	4		825.2.bs.g.74.3		48
5.4	even	2		825.2.bi.e.701.4		48
11.7	odd	10	inner	165.2.p.b.161.4	yes	48
15.2	even	4		825.2.bs.g.74.4		48
15.8	even	4		825.2.bs.h.74.9		48
15.14	odd	2		825.2.bi.e.701.9		48
33.29	even	10	inner	165.2.p.b.161.9	yes	48
55.7	even	20		825.2.bs.h.524.9		48
55.18	even	20		825.2.bs.g.524.4		48
55.29	odd	10		825.2.bi.e.326.9		48
165.29	even	10		825.2.bi.e.326.4		48
165.62	odd	20		825.2.bs.g.524.3		48
165.128	odd	20		825.2.bs.h.524.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.p.b.41.4	✓	48	3.2	odd	2	inner
165.2.p.b.41.9	yes	48	1.1	even	1	trivial
165.2.p.b.161.4	yes	48	11.7	odd	10	inner
165.2.p.b.161.9	yes	48	33.29	even	10	inner
825.2.bi.e.326.4		48	165.29	even	10
825.2.bi.e.326.9		48	55.29	odd	10
825.2.bi.e.701.4		48	5.4	even	2
825.2.bi.e.701.9		48	15.14	odd	2
825.2.bs.g.74.3		48	5.3	odd	4
825.2.bs.g.74.4		48	15.2	even	4
825.2.bs.g.524.3		48	165.62	odd	20
825.2.bs.g.524.4		48	55.18	even	20
825.2.bs.h.74.9		48	15.8	even	4
825.2.bs.h.74.10		48	5.2	odd	4
825.2.bs.h.524.9		48	55.7	even	20
825.2.bs.h.524.10		48	165.128	odd	20

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37228 - 0.997022i) q^{2} +(-0.579977 + 1.63206i) q^{3} +(0.271073 - 0.834277i) q^{4} +(-0.587785 + 0.809017i) q^{5} +(0.831309 + 2.81790i) q^{6} +(3.82974 + 1.24436i) q^{7} +(0.588527 + 1.81130i) q^{8} +(-2.32725 - 1.89312i) q^{9} +O(q^{10})\)	\(q+(1.37228 - 0.997022i) q^{2} +(-0.579977 + 1.63206i) q^{3} +(0.271073 - 0.834277i) q^{4} +(-0.587785 + 0.809017i) q^{5} +(0.831309 + 2.81790i) q^{6} +(3.82974 + 1.24436i) q^{7} +(0.588527 + 1.81130i) q^{8} +(-2.32725 - 1.89312i) q^{9} +1.69623i q^{10} +(0.328772 - 3.30029i) q^{11} +(1.20438 + 0.926269i) q^{12} +(-3.28394 - 4.51996i) q^{13} +(6.49614 - 2.11072i) q^{14} +(-0.979464 - 1.42851i) q^{15} +(4.03289 + 2.93006i) q^{16} +(0.766360 + 0.556793i) q^{17} +(-5.08113 - 0.277567i) q^{18} +(-4.31938 + 1.40345i) q^{19} +(0.515612 + 0.709679i) q^{20} +(-4.25203 + 5.52868i) q^{21} +(-2.83929 - 4.85672i) q^{22} -2.88723i q^{23} +(-3.29749 - 0.0899989i) q^{24} +(-0.309017 - 0.951057i) q^{25} +(-9.01300 - 2.92850i) q^{26} +(4.43944 - 2.70026i) q^{27} +(2.07628 - 2.85775i) q^{28} +(-1.65920 + 5.10648i) q^{29} +(-2.76836 - 0.983776i) q^{30} +(1.46504 - 1.06441i) q^{31} +4.64657 q^{32} +(5.19560 + 2.45067i) q^{33} +1.60680 q^{34} +(-3.25777 + 2.36691i) q^{35} +(-2.21024 + 1.42840i) q^{36} +(2.46634 - 7.59061i) q^{37} +(-4.52813 + 6.23244i) q^{38} +(9.28147 - 2.73813i) q^{39} +(-1.81130 - 0.588527i) q^{40} +(-0.413653 - 1.27309i) q^{41} +(-0.322777 + 11.8263i) q^{42} -8.82336i q^{43} +(-2.66423 - 1.16891i) q^{44} +(2.89949 - 0.770043i) q^{45} +(-2.87863 - 3.96209i) q^{46} +(-7.05759 + 2.29315i) q^{47} +(-7.12103 + 4.88255i) q^{48} +(7.45538 + 5.41665i) q^{49} +(-1.37228 - 0.997022i) q^{50} +(-1.35319 + 0.927821i) q^{51} +(-4.66109 + 1.51448i) q^{52} +(5.57751 + 7.67679i) q^{53} +(3.39994 - 8.13173i) q^{54} +(2.47674 + 2.20584i) q^{55} +7.66915i q^{56} +(0.214619 - 7.86346i) q^{57} +(2.81439 + 8.66179i) q^{58} +(-1.84920 - 0.600843i) q^{59} +(-1.45728 + 0.429913i) q^{60} +(-7.71633 + 10.6206i) q^{61} +(0.949206 - 2.92135i) q^{62} +(-6.55707 - 10.1461i) q^{63} +(-1.68937 + 1.22740i) q^{64} +5.58698 q^{65} +(9.57319 - 1.81711i) q^{66} -1.99934 q^{67} +(0.672260 - 0.488425i) q^{68} +(4.71214 + 1.67452i) q^{69} +(-2.11072 + 6.49614i) q^{70} +(1.44240 - 1.98529i) q^{71} +(2.05935 - 5.32951i) q^{72} +(9.21799 + 2.99511i) q^{73} +(-4.18349 - 12.8755i) q^{74} +(1.73141 + 0.0472556i) q^{75} +3.98399i q^{76} +(5.36586 - 12.2301i) q^{77} +(10.0068 - 13.0113i) q^{78} +(-1.25135 - 1.72234i) q^{79} +(-4.74094 + 1.54043i) q^{80} +(1.83222 + 8.81152i) q^{81} +(-1.83695 - 1.33462i) q^{82} +(2.50390 + 1.81919i) q^{83} +(3.45984 + 5.04605i) q^{84} +(-0.900911 + 0.292724i) q^{85} +(-8.79708 - 12.1081i) q^{86} +(-7.37180 - 5.66955i) q^{87} +(6.17130 - 1.34680i) q^{88} +11.0376i q^{89} +(3.21117 - 3.94757i) q^{90} +(-6.95221 - 21.3967i) q^{91} +(-2.40875 - 0.782650i) q^{92} +(0.887501 + 3.00837i) q^{93} +(-7.39869 + 10.1834i) q^{94} +(1.40345 - 4.31938i) q^{95} +(-2.69490 + 7.58349i) q^{96} +(-6.43282 + 4.67372i) q^{97} +15.6314 q^{98} +(-7.01297 + 7.05821i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9}+O(q^{10}) \) 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9	\( 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9} + 8 q^{12} + 6 q^{15} + 32 q^{16} - 30 q^{18} - 100 q^{19} - 82 q^{22} + 100 q^{24} + 12 q^{25} + 14 q^{27} + 30 q^{28} + 10 q^{30} + 10 q^{31} - 46 q^{33} - 28 q^{34} + 14 q^{36} + 6 q^{37} - 50 q^{40} - 52 q^{42} + 32 q^{45} + 20 q^{46} - 80 q^{48} - 26 q^{49} - 30 q^{51} + 40 q^{52} + 6 q^{55} - 70 q^{57} + 92 q^{58} + 44 q^{60} + 70 q^{61} - 20 q^{63} + 18 q^{64} + 76 q^{66} + 20 q^{67} + 42 q^{69} - 4 q^{70} - 80 q^{72} + 90 q^{73} - 6 q^{75} - 108 q^{78} - 100 q^{79} + 38 q^{81} - 34 q^{82} + 70 q^{84} + 20 q^{85} + 74 q^{88} + 20 q^{90} - 86 q^{91} + 76 q^{93} + 10 q^{94} - 30 q^{96} + 6 q^{97} - 28 q^{99}+O(q^{100}) \) 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9 + 8 * q^12 + 6 * q^15 + 32 * q^16 - 30 * q^18 - 100 * q^19 - 82 * q^22 + 100 * q^24 + 12 * q^25 + 14 * q^27 + 30 * q^28 + 10 * q^30 + 10 * q^31 - 46 * q^33 - 28 * q^34 + 14 * q^36 + 6 * q^37 - 50 * q^40 - 52 * q^42 + 32 * q^45 + 20 * q^46 - 80 * q^48 - 26 * q^49 - 30 * q^51 + 40 * q^52 + 6 * q^55 - 70 * q^57 + 92 * q^58 + 44 * q^60 + 70 * q^61 - 20 * q^63 + 18 * q^64 + 76 * q^66 + 20 * q^67 + 42 * q^69 - 4 * q^70 - 80 * q^72 + 90 * q^73 - 6 * q^75 - 108 * q^78 - 100 * q^79 + 38 * q^81 - 34 * q^82 + 70 * q^84 + 20 * q^85 + 74 * q^88 + 20 * q^90 - 86 * q^91 + 76 * q^93 + 10 * q^94 - 30 * q^96 + 6 * q^97 - 28 * q^99

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