LMFDB - Embedded newform 770.2.n.k.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(71,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("770.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 18 x^{14} - 35 x^{13} + 89 x^{12} - 185 x^{11} + 837 x^{10} - 1660 x^{9} + 4196 x^{8} + \cdots + 25 $ x^16 - 5x^15 + 18x^14 - 35x^13 + 89x^12 - 185x^11 + 837x^10 - 1660x^9 + 4196x^8 - 8420x^7 + 13485x^6 - 14630x^5 + 11615x^4 - 5200x^3 + 1425x^2 - 225*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			71.1
Root			$2.57883 - 1.87363i$ of defining polynomial
Character	$\chi$	$=$	770.71
Dual form			770.2.n.k.141.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(-2.57883 - 1.87363i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.985024 - 3.03159i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.21282 + 6.81035i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(-2.57883 - 1.87363i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.985024 - 3.03159i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.21282 + 6.81035i) q^{9} -1.00000 q^{10} +(-0.853282 - 3.20498i) q^{11} +3.18761 q^{12} +(1.75862 + 5.41248i) q^{13} +(0.809017 + 0.587785i) q^{14} +(2.57883 - 1.87363i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.231460 + 0.712362i) q^{17} +(-5.79323 + 4.20903i) q^{18} +(-5.49296 - 3.99087i) q^{19} +(-0.309017 - 0.951057i) q^{20} -3.18761 q^{21} +(2.78444 - 1.80191i) q^{22} +3.94010 q^{23} +(0.985024 + 3.03159i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-4.60413 + 3.34510i) q^{26} +(4.09852 - 12.6139i) q^{27} +(-0.309017 + 0.951057i) q^{28} +(4.64244 - 3.37293i) q^{29} +(2.57883 + 1.87363i) q^{30} +(-2.19696 - 6.76156i) q^{31} +1.00000 q^{32} +(-3.80447 + 9.86383i) q^{33} -0.749022 q^{34} +(0.309017 + 0.951057i) q^{35} +(-5.79323 - 4.20903i) q^{36} +(9.38862 - 6.82123i) q^{37} +(2.09812 - 6.45736i) q^{38} +(5.60579 - 17.2529i) q^{39} +(0.809017 - 0.587785i) q^{40} +(-9.25986 - 6.72768i) q^{41} +(-0.985024 - 3.03159i) q^{42} +2.33345 q^{43} +(2.57416 + 2.09134i) q^{44} -7.16083 q^{45} +(1.21756 + 3.74725i) q^{46} +(4.04528 + 2.93907i) q^{47} +(-2.57883 + 1.87363i) q^{48} +(0.309017 - 0.951057i) q^{49} +(0.309017 - 0.951057i) q^{50} +(1.93160 - 1.40339i) q^{51} +(-4.60413 - 3.34510i) q^{52} +(-3.32721 - 10.2401i) q^{53} +13.2631 q^{54} +(3.31180 + 0.178874i) q^{55} -1.00000 q^{56} +(6.68799 + 20.5835i) q^{57} +(4.64244 + 3.37293i) q^{58} +(-4.23038 + 3.07355i) q^{59} +(-0.985024 + 3.03159i) q^{60} +(2.37448 - 7.30790i) q^{61} +(5.75173 - 4.17887i) q^{62} +(5.79323 + 4.20903i) q^{63} +(0.309017 + 0.951057i) q^{64} -5.69102 q^{65} +(-10.5567 - 0.570180i) q^{66} -7.39587 q^{67} +(-0.231460 - 0.712362i) q^{68} +(-10.1608 - 7.38227i) q^{69} +(-0.809017 + 0.587785i) q^{70} +(-0.177744 + 0.547039i) q^{71} +(2.21282 - 6.81035i) q^{72} +(10.1697 - 7.38869i) q^{73} +(9.38862 + 6.82123i) q^{74} +(0.985024 + 3.03159i) q^{75} +6.78967 q^{76} +(-2.57416 - 2.09134i) q^{77} +18.1407 q^{78} +(2.11207 + 6.50029i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-16.8235 + 12.2230i) q^{81} +(3.53695 - 10.8856i) q^{82} +(3.25248 - 10.0101i) q^{83} +(2.57883 - 1.87363i) q^{84} +(-0.605971 - 0.440264i) q^{85} +(0.721074 + 2.21924i) q^{86} -18.2916 q^{87} +(-1.19352 + 3.09443i) q^{88} +4.80467 q^{89} +(-2.21282 - 6.81035i) q^{90} +(4.60413 + 3.34510i) q^{91} +(-3.18761 + 2.31593i) q^{92} +(-7.00305 + 21.5532i) q^{93} +(-1.54516 + 4.75552i) q^{94} +(5.49296 - 3.99087i) q^{95} +(-2.57883 - 1.87363i) q^{96} +(5.02824 + 15.4753i) q^{97} +1.00000 q^{98} +(19.9389 - 12.9032i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 5 q^{3} - 4 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{7} - 4 q^{8} + q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 5 * q^3 - 4 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^7 - 4 * q^8 + q^9	\( 16 q - 4 q^{2} - 5 q^{3} - 4 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{7} - 4 q^{8} + q^{9} - 16 q^{10} - 2 q^{11} + 8 q^{13} + 4 q^{14} + 5 q^{15} - 4 q^{16} - 13 q^{17} - 9 q^{18} + 15 q^{19} + 4 q^{20} - 2 q^{22} + 20 q^{23} + 5 q^{24} - 4 q^{25} - 7 q^{26} + 10 q^{27} + 4 q^{28} - 14 q^{29} + 5 q^{30} - 6 q^{31} + 16 q^{32} - 25 q^{33} + 12 q^{34} - 4 q^{35} - 9 q^{36} + 28 q^{37} - 20 q^{38} + 15 q^{39} + 4 q^{40} + 2 q^{41} - 5 q^{42} - 10 q^{43} + 3 q^{44} - 16 q^{45} - 10 q^{46} - 10 q^{47} - 5 q^{48} - 4 q^{49} - 4 q^{50} - 42 q^{51} - 7 q^{52} - 2 q^{53} - 3 q^{55} - 16 q^{56} + 21 q^{57} - 14 q^{58} + 7 q^{59} - 5 q^{60} + 4 q^{61} + 14 q^{62} + 9 q^{63} - 4 q^{64} + 2 q^{65} - 10 q^{66} + 66 q^{67} - 13 q^{68} - 64 q^{69} - 4 q^{70} + 2 q^{71} + q^{72} + 12 q^{73} + 28 q^{74} + 5 q^{75} + 10 q^{76} - 3 q^{77} + 70 q^{78} + 2 q^{79} + 4 q^{80} - 30 q^{81} - 13 q^{82} - 5 q^{83} + 5 q^{84} - 7 q^{85} + 5 q^{86} - 24 q^{87} - 2 q^{88} + 2 q^{89} - q^{90} + 7 q^{91} - 38 q^{93} + 25 q^{94} - 15 q^{95} - 5 q^{96} + 22 q^{97} + 16 q^{98} - 18 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 5 * q^3 - 4 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^7 - 4 * q^8 + q^9 - 16 * q^10 - 2 * q^11 + 8 * q^13 + 4 * q^14 + 5 * q^15 - 4 * q^16 - 13 * q^17 - 9 * q^18 + 15 * q^19 + 4 * q^20 - 2 * q^22 + 20 * q^23 + 5 * q^24 - 4 * q^25 - 7 * q^26 + 10 * q^27 + 4 * q^28 - 14 * q^29 + 5 * q^30 - 6 * q^31 + 16 * q^32 - 25 * q^33 + 12 * q^34 - 4 * q^35 - 9 * q^36 + 28 * q^37 - 20 * q^38 + 15 * q^39 + 4 * q^40 + 2 * q^41 - 5 * q^42 - 10 * q^43 + 3 * q^44 - 16 * q^45 - 10 * q^46 - 10 * q^47 - 5 * q^48 - 4 * q^49 - 4 * q^50 - 42 * q^51 - 7 * q^52 - 2 * q^53 - 3 * q^55 - 16 * q^56 + 21 * q^57 - 14 * q^58 + 7 * q^59 - 5 * q^60 + 4 * q^61 + 14 * q^62 + 9 * q^63 - 4 * q^64 + 2 * q^65 - 10 * q^66 + 66 * q^67 - 13 * q^68 - 64 * q^69 - 4 * q^70 + 2 * q^71 + q^72 + 12 * q^73 + 28 * q^74 + 5 * q^75 + 10 * q^76 - 3 * q^77 + 70 * q^78 + 2 * q^79 + 4 * q^80 - 30 * q^81 - 13 * q^82 - 5 * q^83 + 5 * q^84 - 7 * q^85 + 5 * q^86 - 24 * q^87 - 2 * q^88 + 2 * q^89 - q^90 + 7 * q^91 - 38 * q^93 + 25 * q^94 - 15 * q^95 - 5 * q^96 + 22 * q^97 + 16 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	−2.57883	−	1.87363i	−1.48889	−	1.08174i	−0.974555	−	0.224148i	$-0.928040\pi$
$3$	−2.57883	−	1.87363i	−1.48889	−	1.08174i	−0.514331	−	0.857592i	$-0.671960\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$	0.985024	−	3.03159i	0.402134	−	1.23764i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	2.21282	+	6.81035i	0.737606	+	2.27012i
$10$	−1.00000			−0.316228
$11$	−0.853282	−	3.20498i	−0.257274	−	0.966338i
$11$	−0.853282	−	3.20498i	−0.257274	−	0.966338i
$12$	3.18761			0.920182
$13$	1.75862	+	5.41248i	0.487754	+	1.50115i	0.827952	+	0.560799i	$0.189506\pi$
$13$	1.75862	+	5.41248i	0.487754	+	1.50115i	−0.340198	+	0.940354i	$0.610494\pi$
$14$	0.809017	+	0.587785i	0.216219	+	0.157092i
$15$	2.57883	−	1.87363i	0.665850	−	0.483769i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.231460	+	0.712362i	−0.0561374	+	0.172773i	−0.975194	−	0.221353i	$-0.928953\pi$
$17$	−0.231460	+	0.712362i	−0.0561374	+	0.172773i	0.919056	+	0.394126i	$0.128953\pi$
$18$	−5.79323	+	4.20903i	−1.36548	+	0.992078i
$19$	−5.49296	−	3.99087i	−1.26017	−	0.915568i	−0.261405	−	0.965229i	$-0.584186\pi$
$19$	−5.49296	−	3.99087i	−1.26017	−	0.915568i	−0.998766	+	0.0496616i	$0.984186\pi$
$20$	−0.309017	−	0.951057i	−0.0690983	−	0.212663i
$21$	−3.18761			−0.695592
$22$	2.78444	−	1.80191i	0.593645	−	0.384169i
$23$	3.94010			0.821567			0.410783	−	0.911733i	$-0.365255\pi$
$23$	3.94010			0.821567			0.410783	+	0.911733i	$0.365255\pi$
$24$	0.985024	+	3.03159i	0.201067	+	0.618821i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−4.60413	+	3.34510i	−0.902945	+	0.656028i
$27$	4.09852	−	12.6139i	0.788760	−	2.42755i
$28$	−0.309017	+	0.951057i	−0.0583987	+	0.179733i
$29$	4.64244	−	3.37293i	0.862079	−	0.626337i	−0.0663710	−	0.997795i	$-0.521142\pi$
$29$	4.64244	−	3.37293i	0.862079	−	0.626337i	0.928450	+	0.371458i	$0.121142\pi$
$30$	2.57883	+	1.87363i	0.470827	+	0.342076i
$31$	−2.19696	−	6.76156i	−0.394586	−	1.21441i	−0.929283	−	0.369368i	$-0.879574\pi$
$31$	−2.19696	−	6.76156i	−0.394586	−	1.21441i	0.534697	−	0.845044i	$-0.320426\pi$
$32$	1.00000			0.176777
$33$	−3.80447	+	9.86383i	−0.662274	+	1.71707i
$34$	−0.749022			−0.128456
$35$	0.309017	+	0.951057i	0.0522334	+	0.160758i
$36$	−5.79323	−	4.20903i	−0.965539	−	0.701505i
$37$	9.38862	−	6.82123i	1.54348	−	1.12140i	0.595374	−	0.803449i	$-0.297004\pi$
$37$	9.38862	−	6.82123i	1.54348	−	1.12140i	0.948106	−	0.317955i	$-0.102996\pi$
$38$	2.09812	−	6.45736i	0.340360	−	1.04752i
$39$	5.60579	−	17.2529i	0.897645	−	2.76267i
$40$	0.809017	−	0.587785i	0.127917	−	0.0929370i
$41$	−9.25986	−	6.72768i	−1.44615	−	1.05069i	−0.986713	−	0.162475i	$-0.948052\pi$
$41$	−9.25986	−	6.72768i	−1.44615	−	1.05069i	−0.459434	−	0.888212i	$-0.651948\pi$
$42$	−0.985024	−	3.03159i	−0.151993	−	0.467785i
$43$	2.33345			0.355847			0.177924	−	0.984044i	$-0.443062\pi$
$43$	2.33345			0.355847			0.177924	+	0.984044i	$0.443062\pi$
$44$	2.57416	+	2.09134i	0.388069	+	0.315281i
$45$	−7.16083			−1.06747
$46$	1.21756	+	3.74725i	0.179519	+	0.552503i
$47$	4.04528	+	2.93907i	0.590065	+	0.428708i	0.842339	−	0.538948i	$-0.181178\pi$
$47$	4.04528	+	2.93907i	0.590065	+	0.428708i	−0.252273	+	0.967656i	$0.581178\pi$
$48$	−2.57883	+	1.87363i	−0.372222	+	0.270435i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	0.309017	−	0.951057i	0.0437016	−	0.134500i
$51$	1.93160	−	1.40339i	0.270478	−	0.196514i
$52$	−4.60413	−	3.34510i	−0.638478	−	0.463882i
$53$	−3.32721	−	10.2401i	−0.457028	−	1.40659i	−0.868738	−	0.495272i	$-0.835068\pi$
$53$	−3.32721	−	10.2401i	−0.457028	−	1.40659i	0.411710	−	0.911315i	$-0.364932\pi$
$54$	13.2631			1.80488
$55$	3.31180	+	0.178874i	0.446563	+	0.0241194i
$56$	−1.00000			−0.133631
$57$	6.68799	+	20.5835i	0.885846	+	2.72635i
$58$	4.64244	+	3.37293i	0.609582	+	0.442887i
$59$	−4.23038	+	3.07355i	−0.550749	+	0.400142i	−0.828061	−	0.560637i	$-0.810556\pi$
$59$	−4.23038	+	3.07355i	−0.550749	+	0.400142i	0.277313	+	0.960780i	$0.410556\pi$
$60$	−0.985024	+	3.03159i	−0.127166	+	0.391377i
$61$	2.37448	−	7.30790i	0.304021	−	0.935681i	−0.676019	−	0.736884i	$-0.736296\pi$
$61$	2.37448	−	7.30790i	0.304021	−	0.935681i	0.980041	−	0.198797i	$-0.0637035\pi$
$62$	5.75173	−	4.17887i	0.730470	−	0.530717i
$63$	5.79323	+	4.20903i	0.729879	+	0.530288i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−5.69102			−0.705884
$66$	−10.5567	−	0.570180i	−1.29944	−	0.0701843i
$67$	−7.39587			−0.903549			−0.451775	−	0.892132i	$-0.649209\pi$
$67$	−7.39587			−0.903549			−0.451775	+	0.892132i	$0.649209\pi$
$68$	−0.231460	−	0.712362i	−0.0280687	−	0.0863866i
$69$	−10.1608	−	7.38227i	−1.22322	−	0.888721i
$70$	−0.809017	+	0.587785i	−0.0966960	+	0.0702538i
$71$	−0.177744	+	0.547039i	−0.0210943	+	0.0649216i	−0.961050	−	0.276376i	$-0.910866\pi$
$71$	−0.177744	+	0.547039i	−0.0210943	+	0.0649216i	0.939955	+	0.341298i	$0.110866\pi$
$72$	2.21282	−	6.81035i	0.260783	−	0.802608i
$73$	10.1697	−	7.38869i	1.19027	−	0.864781i	0.196977	−	0.980408i	$-0.436888\pi$
$73$	10.1697	−	7.38869i	1.19027	−	0.864781i	0.993293	+	0.115627i	$0.0368877\pi$
$74$	9.38862	+	6.82123i	1.09140	+	0.792952i
$75$	0.985024	+	3.03159i	0.113741	+	0.350058i
$76$	6.78967			0.778828
$77$	−2.57416	−	2.09134i	−0.293353	−	0.238330i
$78$	18.1407			2.05403
$79$	2.11207	+	6.50029i	0.237627	+	0.731339i	0.996762	+	0.0804068i	$0.0256219\pi$
$79$	2.11207	+	6.50029i	0.237627	+	0.731339i	−0.759136	+	0.650933i	$0.774378\pi$
$80$	0.809017	+	0.587785i	0.0904508	+	0.0657164i
$81$	−16.8235	+	12.2230i	−1.86928	+	1.35811i
$82$	3.53695	−	10.8856i	0.390591	−	1.20211i
$83$	3.25248	−	10.0101i	0.357006	−	1.09875i	−0.597831	−	0.801622i	$-0.703971\pi$
$83$	3.25248	−	10.0101i	0.357006	−	1.09875i	0.954837	−	0.297130i	$-0.0960294\pi$
$84$	2.57883	−	1.87363i	0.281373	−	0.204430i
$85$	−0.605971	−	0.440264i	−0.0657268	−	0.0477533i
$86$	0.721074	+	2.21924i	0.0777554	+	0.239307i
$87$	−18.2916			−1.96107
$88$	−1.19352	+	3.09443i	−0.127230	+	0.329868i
$89$	4.80467			0.509294			0.254647	−	0.967034i	$-0.418041\pi$
$89$	4.80467			0.509294			0.254647	+	0.967034i	$0.418041\pi$
$90$	−2.21282	−	6.81035i	−0.233251	−	0.717874i
$91$	4.60413	+	3.34510i	0.482644	+	0.350662i
$92$	−3.18761	+	2.31593i	−0.332331	+	0.241452i
$93$	−7.00305	+	21.5532i	−0.726183	+	2.23496i
$94$	−1.54516	+	4.75552i	−0.159371	+	0.490494i
$95$	5.49296	−	3.99087i	0.563566	−	0.409454i
$96$	−2.57883	−	1.87363i	−0.263200	−	0.191226i
$97$	5.02824	+	15.4753i	0.510540	+	1.57128i	0.791253	+	0.611489i	$0.209429\pi$
$97$	5.02824	+	15.4753i	0.510540	+	1.57128i	−0.280713	+	0.959792i	$0.590571\pi$
$98$	1.00000			0.101015
$99$	19.9389	−	12.9032i	2.00393	−	1.29682i
$100$	1.00000			0.100000
$101$	−1.97303	−	6.07238i	−0.196324	−	0.604224i	−0.999959	−	0.00910063i	$-0.997103\pi$
$101$	−1.97303	−	6.07238i	−0.196324	−	0.604224i	0.803634	−	0.595123i	$-0.202897\pi$
$102$	1.93160	+	1.40339i	0.191257	+	0.138956i
$103$	−1.88396	+	1.36878i	−0.185632	+	0.134870i	−0.676720	−	0.736240i	$-0.736599\pi$
$103$	−1.88396	+	1.36878i	−0.185632	+	0.134870i	0.491088	+	0.871110i	$0.336599\pi$
$104$	1.75862	−	5.41248i	0.172447	−	0.530738i
$105$	0.985024	−	3.03159i	0.0961285	−	0.295853i
$106$	8.71076	−	6.32874i	0.846064	−	0.614701i
$107$	−1.52804	−	1.11019i	−0.147721	−	0.107326i	0.511470	−	0.859301i	$-0.329101\pi$
$107$	−1.52804	−	1.11019i	−0.147721	−	0.107326i	−0.659191	+	0.751976i	$0.729101\pi$
$108$	4.09852	+	12.6139i	0.394380	+	1.21378i
$109$	7.76554			0.743804			0.371902	−	0.928272i	$-0.378706\pi$
$109$	7.76554			0.743804			0.371902	+	0.928272i	$0.378706\pi$
$110$	0.853282	+	3.20498i	0.0813573	+	0.305583i
$111$	−36.9921			−3.51113
$112$	−0.309017	−	0.951057i	−0.0291994	−	0.0898664i
$113$	−6.27217	−	4.55700i	−0.590036	−	0.428687i	0.252292	−	0.967651i	$-0.418816\pi$
$113$	−6.27217	−	4.55700i	−0.590036	−	0.428687i	−0.842328	+	0.538965i	$0.818816\pi$
$114$	−17.5094	+	12.7213i	−1.63990	+	1.19146i
$115$	−1.21756	+	3.74725i	−0.113538	+	0.349433i
$116$	−1.77325	+	5.45751i	−0.164642	+	0.506717i
$117$	−32.9694	+	23.9537i	−3.04802	+	2.21452i
$118$	−4.23038	−	3.07355i	−0.389438	−	0.282943i
$119$	0.231460	+	0.712362i	0.0212179	+	0.0653021i
$120$	−3.18761			−0.290987
$121$	−9.54382	+	5.46951i	−0.867620	+	0.497228i
$122$	7.68398			0.695675
$123$	11.2744	+	34.6990i	1.01658	+	3.12871i
$124$	5.75173	+	4.17887i	0.516520	+	0.375274i
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$	−2.21282	+	6.81035i	−0.197133	+	0.606714i
$127$	−4.79878	+	14.7691i	−0.425823	+	1.31055i	0.476381	+	0.879239i	$0.341948\pi$
$127$	−4.79878	+	14.7691i	−0.425823	+	1.31055i	−0.902204	+	0.431310i	$0.858052\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	−6.01755	−	4.37201i	−0.529816	−	0.384934i
$130$	−1.75862	−	5.41248i	−0.154241	−	0.474706i
$131$	0.957959			0.0836973			0.0418486	−	0.999124i	$-0.486675\pi$
$131$	0.957959			0.0836973			0.0418486	+	0.999124i	$0.486675\pi$
$132$	−2.71993	−	10.2162i	−0.236739	−	0.889208i
$133$	−6.78967			−0.588739
$134$	−2.28545	−	7.03389i	−0.197433	−	0.607636i
$135$	10.7301	+	7.79584i	0.923496	+	0.670959i
$136$	0.605971	−	0.440264i	0.0519616	−	0.0377523i
$137$	−1.44056	+	4.43359i	−0.123076	+	0.378788i	−0.993546	−	0.113434i	$-0.963815\pi$
$137$	−1.44056	+	4.43359i	−0.123076	+	0.378788i	0.870470	+	0.492221i	$0.163815\pi$
$138$	3.88109	−	11.9448i	0.330380	−	1.01681i
$139$	−3.61168	+	2.62404i	−0.306339	+	0.222568i	−0.730324	−	0.683101i	$-0.760631\pi$
$139$	−3.61168	+	2.62404i	−0.306339	+	0.222568i	0.423985	+	0.905669i	$0.360631\pi$
$140$	−0.809017	−	0.587785i	−0.0683744	−	0.0496769i
$141$	−4.92536	−	15.1587i	−0.414790	−	1.27659i
$142$	−0.575191			−0.0482690
$143$	15.8463	−	10.2547i	1.32513	−	0.857543i
$144$	7.16083			0.596736
$145$	1.77325	+	5.45751i	0.147261	+	0.453222i
$146$	10.1697	+	7.38869i	0.841647	+	0.611493i
$147$	−2.57883	+	1.87363i	−0.212698	+	0.154534i
$148$	−3.58613	+	11.0370i	−0.294778	+	0.907235i
$149$	4.82830	−	14.8600i	0.395550	−	1.21738i	−0.532983	−	0.846126i	$-0.678929\pi$
$149$	4.82830	−	14.8600i	0.395550	−	1.21738i	0.928532	−	0.371251i	$-0.121071\pi$
$150$	−2.57883	+	1.87363i	−0.210560	+	0.152981i
$151$	14.3883	+	10.4537i	1.17091	+	0.850713i	0.991117	−	0.132992i	$-0.0424583\pi$
$151$	14.3883	+	10.4537i	1.17091	+	0.850713i	0.179789	+	0.983705i	$0.442458\pi$
$152$	2.09812	+	6.45736i	0.170180	+	0.523761i
$153$	−5.36361			−0.433623
$154$	1.19352	−	3.09443i	0.0961767	−	0.249356i
$155$	7.10952			0.571051
$156$	5.60579	+	17.2529i	0.448823	+	1.38133i
$157$	5.96684	+	4.33516i	0.476206	+	0.345984i	0.799855	−	0.600193i	$-0.204910\pi$
$157$	5.96684	+	4.33516i	0.476206	+	0.345984i	−0.323649	+	0.946177i	$0.604910\pi$
$158$	−5.52947	+	4.01740i	−0.439901	+	0.319607i
$159$	−10.6058	+	32.6414i	−0.841098	+	2.58863i
$160$	−0.309017	+	0.951057i	−0.0244299	+	0.0751876i
$161$	3.18761	−	2.31593i	0.251218	−	0.182521i
$162$	−16.8235	−	12.2230i	−1.32178	−	0.960328i
$163$	−3.23276	−	9.94941i	−0.253209	−	0.779298i	−0.994177	−	0.107758i	$-0.965633\pi$
$163$	−3.23276	−	9.94941i	−0.253209	−	0.779298i	0.740968	−	0.671540i	$-0.234367\pi$
$164$	11.4458			0.893768
$165$	−8.20541	−	6.66636i	−0.638790	−	0.518975i
$166$	10.5252			0.816918
$167$	−4.29311	−	13.2128i	−0.332211	−	1.02244i	−0.968080	−	0.250643i	$-0.919358\pi$
$167$	−4.29311	−	13.2128i	−0.332211	−	1.02244i	0.635869	−	0.771797i	$-0.280642\pi$
$168$	2.57883	+	1.87363i	0.198961	+	0.144553i
$169$	−15.6850	+	11.3958i	−1.20654	+	0.876601i
$170$	0.231460	−	0.712362i	0.0177522	−	0.0546357i
$171$	15.0243	−	46.2400i	1.14894	−	3.53606i
$172$	−1.88780	+	1.37156i	−0.143943	+	0.104581i
$173$	−7.92490	−	5.75777i	−0.602519	−	0.437755i	0.244253	−	0.969711i	$-0.421457\pi$
$173$	−7.92490	−	5.75777i	−0.602519	−	0.437755i	−0.846772	+	0.531956i	$0.821457\pi$
$174$	−5.65243	−	17.3964i	−0.428510	−	1.31882i
$175$	−1.00000			−0.0755929
$176$	−3.31180	−	0.178874i	−0.249636	−	0.0134831i
$177$	16.6681			1.25285
$178$	1.48473	+	4.56952i	0.111285	+	0.342500i
$179$	−0.546930	−	0.397368i	−0.0408795	−	0.0297007i	0.567158	−	0.823609i	$-0.308043\pi$
$179$	−0.546930	−	0.397368i	−0.0408795	−	0.0297007i	−0.608037	+	0.793908i	$0.708043\pi$
$180$	5.79323	−	4.20903i	0.431802	−	0.313722i
$181$	−1.69968	+	5.23108i	−0.126336	+	0.388823i	−0.994142	−	0.108080i	$-0.965530\pi$
$181$	−1.69968	+	5.23108i	−0.126336	+	0.388823i	0.867806	+	0.496903i	$0.165530\pi$
$182$	−1.75862	+	5.41248i	−0.130358	+	0.401200i
$183$	−19.8157	+	14.3969i	−1.46482	+	1.06425i
$184$	−3.18761	−	2.31593i	−0.234993	−	0.170733i
$185$	3.58613	+	11.0370i	0.263658	+	0.811455i
$186$	−22.6624			−1.66168
$187$	2.48061	+	0.133981i	0.181400	+	0.00979763i
$188$	−5.00025			−0.364680
$189$	−4.09852	−	12.6139i	−0.298123	−	0.917529i
$190$	5.49296	+	3.99087i	0.398501	+	0.289528i
$191$	10.1906	−	7.40390i	0.737366	−	0.535728i	−0.154519	−	0.987990i	$-0.549383\pi$
$191$	10.1906	−	7.40390i	0.737366	−	0.535728i	0.891885	+	0.452262i	$0.149383\pi$
$192$	0.985024	−	3.03159i	0.0710880	−	0.218786i
$193$	−0.764031	+	2.35145i	−0.0549962	+	0.169261i	−0.974782	−	0.223161i	$-0.928363\pi$
$193$	−0.764031	+	2.35145i	−0.0549962	+	0.169261i	0.919785	+	0.392422i	$0.128363\pi$
$194$	−13.1641	+	9.56427i	−0.945127	+	0.686675i
$195$	14.6762	+	10.6629i	1.05098	+	0.763583i
$196$	0.309017	+	0.951057i	0.0220726	+	0.0679326i
$197$	8.91129			0.634903			0.317451	−	0.948275i	$-0.397173\pi$
$197$	8.91129			0.634903			0.317451	+	0.948275i	$0.397173\pi$
$198$	18.4331	+	14.9757i	1.30998	+	1.06428i
$199$	26.4542			1.87529			0.937644	−	0.347598i	$-0.113002\pi$
$199$	26.4542			1.87529			0.937644	+	0.347598i	$0.113002\pi$
$200$	0.309017	+	0.951057i	0.0218508	+	0.0672499i
$201$	19.0727	+	13.8571i	1.34528	+	0.977405i
$202$	5.16547	−	3.75294i	0.363441	−	0.264056i
$203$	1.77325	−	5.45751i	0.124458	−	0.383042i
$204$	−0.737804	+	2.27073i	−0.0516566	+	0.158983i
$205$	9.25986	−	6.72768i	0.646736	−	0.469881i
$206$	−1.88396	−	1.36878i	−0.131262	−	0.0953672i
$207$	8.71871	+	26.8334i	0.605993	+	1.86505i
$208$	5.69102			0.394601
$209$	−8.10361	+	21.0102i	−0.560539	+	1.45330i
$210$	3.18761			0.219966
$211$	−2.56239	−	7.88622i	−0.176402	−	0.542909i	0.823293	−	0.567617i	$-0.192135\pi$
$211$	−2.56239	−	7.88622i	−0.176402	−	0.542909i	−0.999695	+	0.0247075i	$0.992135\pi$
$212$	8.71076	+	6.32874i	0.598257	+	0.434659i
$213$	1.48332	−	1.07769i	0.101635	−	0.0738424i
$214$	0.583659	−	1.79632i	0.0398981	−	0.122794i
$215$	−0.721074	+	2.21924i	−0.0491769	+	0.151351i
$216$	−10.7301	+	7.79584i	−0.730088	+	0.530440i
$217$	−5.75173	−	4.17887i	−0.390453	−	0.283680i
$218$	2.39968	+	7.38547i	0.162527	+	0.500207i
$219$	−40.0695			−2.70764
$220$	−2.78444	+	1.80191i	−0.187727	+	0.121485i
$221$	−4.26270			−0.286740
$222$	−11.4312	−	35.1816i	−0.767211	−	2.36123i
$223$	−0.316011	−	0.229596i	−0.0211617	−	0.0153749i	0.577154	−	0.816635i	$-0.304163\pi$
$223$	−0.316011	−	0.229596i	−0.0211617	−	0.0153749i	−0.598316	+	0.801260i	$0.704163\pi$
$224$	0.809017	−	0.587785i	0.0540547	−	0.0392731i
$225$	2.21282	−	6.81035i	0.147521	−	0.454023i
$226$	2.39576	−	7.37338i	0.159363	−	0.490470i
$227$	3.97833	−	2.89042i	0.264051	−	0.191844i	−0.447880	−	0.894094i	$-0.647821\pi$
$227$	3.97833	−	2.89042i	0.264051	−	0.191844i	0.711931	+	0.702249i	$0.247821\pi$
$228$	−17.5094	−	12.7213i	−1.15959	−	0.842489i
$229$	−2.83789	−	8.73412i	−0.187533	−	0.577167i	0.812450	−	0.583031i	$-0.198133\pi$
$229$	−2.83789	−	8.73412i	−0.187533	−	0.577167i	−0.999983	+	0.00586411i	$0.998133\pi$
$230$	−3.94010			−0.259802
$231$	2.71993	+	10.2162i	0.178958	+	0.672178i
$232$	−5.73837			−0.376742
$233$	−6.22975	−	19.1732i	−0.408124	−	1.25608i	−0.918258	−	0.395982i	$-0.870404\pi$
$233$	−6.22975	−	19.1732i	−0.408124	−	1.25608i	0.510134	−	0.860095i	$-0.329596\pi$
$234$	−32.9694	−	23.9537i	−2.15528	−	1.56590i
$235$	−4.04528	+	2.93907i	−0.263885	+	0.191724i
$236$	1.61586	−	4.97311i	0.105184	−	0.323722i
$237$	6.73245	−	20.7203i	0.437320	−	1.34593i
$238$	−0.605971	+	0.440264i	−0.0392793	+	0.0285381i
$239$	−7.91099	−	5.74767i	−0.511719	−	0.371786i	0.301756	−	0.953385i	$-0.402427\pi$
$239$	−7.91099	−	5.74767i	−0.511719	−	0.371786i	−0.813475	+	0.581599i	$0.802427\pi$
$240$	−0.985024	−	3.03159i	−0.0635830	−	0.195688i
$241$	−12.3008			−0.792366			−0.396183	−	0.918172i	$-0.629665\pi$
$241$	−12.3008			−0.792366			−0.396183	+	0.918172i	$0.629665\pi$
$242$	−8.15101	−	7.38654i	−0.523967	−	0.474825i
$243$	26.4969			1.69978
$244$	2.37448	+	7.30790i	0.152011	+	0.467841i
$245$	0.809017	+	0.587785i	0.0516862	+	0.0375522i
$246$	−29.5168	+	21.4452i	−1.88192	+	1.36729i
$247$	11.9405	−	36.7490i	0.759753	−	2.33828i
$248$	−2.19696	+	6.76156i	−0.139507	+	0.429359i
$249$	−27.1428	+	19.7204i	−1.72010	+	1.24973i
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	−6.44117	−	19.8239i	−0.406563	−	1.25127i	−0.919583	−	0.392896i	$-0.871473\pi$
$251$	−6.44117	−	19.8239i	−0.406563	−	1.25127i	0.513020	−	0.858377i	$-0.328527\pi$
$252$	−7.16083			−0.451090
$253$	−3.36202	−	12.6279i	−0.211368	−	0.793912i
$254$	−15.5292			−0.974388
$255$	0.737804	+	2.27073i	0.0462031	+	0.142199i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−6.09118	+	4.42550i	−0.379957	+	0.276055i	−0.761328	−	0.648367i	$-0.775452\pi$
$257$	−6.09118	+	4.42550i	−0.379957	+	0.276055i	0.381370	+	0.924422i	$0.375452\pi$
$258$	2.29850	−	7.07406i	0.143098	−	0.440412i
$259$	3.58613	−	11.0370i	0.222832	−	0.685805i
$260$	4.60413	−	3.34510i	0.285536	−	0.207454i
$261$	33.2437	+	24.1529i	2.05773	+	1.49503i
$262$	0.296026	+	0.911073i	0.0182885	+	0.0562863i
$263$	3.27610			0.202013			0.101007	−	0.994886i	$-0.467794\pi$
$263$	3.27610			0.202013			0.101007	+	0.994886i	$0.467794\pi$
$264$	8.87570	−	5.74379i	0.546261	−	0.353506i
$265$	10.7671			0.661417
$266$	−2.09812	−	6.45736i	−0.128644	−	0.395926i
$267$	−12.3904	−	9.00217i	−0.758281	−	0.550924i
$268$	5.98339	−	4.34718i	0.365493	−	0.265547i
$269$	0.346940	−	1.06777i	0.0211533	−	0.0651031i	−0.939923	−	0.341387i	$-0.889103\pi$
$269$	0.346940	−	1.06777i	0.0211533	−	0.0651031i	0.961076	+	0.276284i	$0.0891032\pi$
$270$	−4.09852	+	12.6139i	−0.249428	+	0.767660i
$271$	−7.94628	+	5.77331i	−0.482702	+	0.350703i	−0.802371	−	0.596826i	$-0.796428\pi$
$271$	−7.94628	+	5.77331i	−0.482702	+	0.350703i	0.319669	+	0.947529i	$0.396428\pi$
$272$	0.605971	+	0.440264i	0.0367424	+	0.0266949i
$273$	−5.60579	−	17.2529i	−0.339278	−	1.04419i
$274$	−4.66176			−0.281627
$275$	−1.19352	+	3.09443i	−0.0719720	+	0.186601i
$276$	12.5595			0.755991
$277$	−0.275402	−	0.847599i	−0.0165473	−	0.0509273i	0.942442	−	0.334370i	$-0.108523\pi$
$277$	−0.275402	−	0.847599i	−0.0165473	−	0.0509273i	−0.958989	+	0.283443i	$0.908523\pi$
$278$	−3.61168	−	2.62404i	−0.216614	−	0.157379i
$279$	41.1871	−	29.9242i	2.46581	−	1.79151i
$280$	0.309017	−	0.951057i	0.0184673	−	0.0568365i
$281$	5.36365	−	16.5076i	0.319969	−	0.984763i	−0.653692	−	0.756761i	$-0.726781\pi$
$281$	5.36365	−	16.5076i	0.319969	−	0.984763i	0.973661	−	0.228002i	$-0.0732192\pi$
$282$	12.8948	−	9.36860i	0.767872	−	0.557892i
$283$	2.41840	+	1.75707i	0.143759	+	0.104447i	0.657340	−	0.753594i	$-0.271681\pi$
$283$	2.41840	+	1.75707i	0.143759	+	0.104447i	−0.513581	+	0.858041i	$0.671681\pi$
$284$	−0.177744	−	0.547039i	−0.0105472	−	0.0324608i
$285$	−21.6428			−1.28201
$286$	14.6496	+	11.9018i	0.866249	+	0.703771i
$287$	−11.4458			−0.675625
$288$	2.21282	+	6.81035i	0.130392	+	0.401304i
$289$	13.2994	+	9.66258i	0.782318	+	0.568387i
$290$	−4.64244	+	3.37293i	−0.272613	+	0.198065i
$291$	16.0280	−	49.3292i	0.939580	−	2.89173i
$292$	−3.88447	+	11.9552i	−0.227321	+	0.699623i
$293$	−14.2295	+	10.3384i	−0.831299	+	0.603974i	−0.919926	−	0.392091i	$-0.871752\pi$
$293$	−14.2295	+	10.3384i	−0.831299	+	0.603974i	0.0886278	+	0.996065i	$0.471752\pi$
$294$	−2.57883	−	1.87363i	−0.150400	−	0.109272i
$295$	−1.61586	−	4.97311i	−0.0940791	−	0.289546i
$296$	−11.6050			−0.674525
$297$	−43.9246	−	2.37242i	−2.54877	−	0.137662i
$298$	15.6247			0.905115
$299$	6.92914	+	21.3257i	0.400723	+	1.23330i
$300$	−2.57883	−	1.87363i	−0.148889	−	0.108174i
$301$	1.88780	−	1.37156i	0.108811	−	0.0790557i
$302$	−5.49586	+	16.9145i	−0.316251	+	0.973321i
$303$	−6.28926	+	19.3563i	−0.361308	+	1.11199i
$304$	−5.49296	+	3.99087i	−0.315043	+	0.228892i
$305$	6.21647	+	4.51653i	0.355954	+	0.258616i
$306$	−1.65745	−	5.10110i	−0.0947500	−	0.291610i
$307$	1.28791			0.0735047			0.0367524	−	0.999324i	$-0.488299\pi$
$307$	1.28791			0.0735047			0.0367524	+	0.999324i	$0.488299\pi$
$308$	3.31180	+	0.178874i	0.188707	+	0.0101923i
$309$	7.42298			0.422279
$310$	2.19696	+	6.76156i	0.124779	+	0.384031i
$311$	0.0401539	+	0.0291735i	0.00227692	+	0.00165428i	0.588923	−	0.808189i	$-0.299552\pi$
$311$	0.0401539	+	0.0291735i	0.00227692	+	0.00165428i	−0.586646	+	0.809843i	$0.699552\pi$
$312$	−14.6762	+	10.6629i	−0.830874	+	0.603665i
$313$	−8.55290	+	26.3231i	−0.483438	+	1.48787i	0.350792	+	0.936454i	$0.385913\pi$
$313$	−8.55290	+	26.3231i	−0.483438	+	1.48787i	−0.834230	+	0.551417i	$0.814087\pi$
$314$	−2.27913	+	7.01444i	−0.128619	+	0.395848i
$315$	−5.79323	+	4.20903i	−0.326412	+	0.237152i
$316$	−5.52947	−	4.01740i	−0.311057	−	0.225996i
$317$	2.85312	+	8.78101i	0.160247	+	0.493191i	0.998655	−	0.0518535i	$-0.0165129\pi$
$317$	2.85312	+	8.78101i	0.160247	+	0.493191i	−0.838407	+	0.545044i	$0.816513\pi$
$318$	−34.3212			−1.92464
$319$	−14.7715	−	12.0009i	−0.827044	−	0.671919i
$320$	−1.00000			−0.0559017
$321$	1.86047	+	5.72595i	0.103842	+	0.319591i
$322$	3.18761	+	2.31593i	0.177638	+	0.129062i
$323$	4.11434	−	2.98925i	0.228928	−	0.166326i
$324$	6.42600	−	19.7772i	0.357000	−	1.09873i
$325$	1.75862	−	5.41248i	0.0975508	−	0.300231i
$326$	8.46347	−	6.14907i	0.468749	−	0.340566i
$327$	−20.0260	−	14.5497i	−1.10744	−	0.804602i
$328$	3.53695	+	10.8856i	0.195295	+	0.601057i
$329$	5.00025			0.275673
$330$	3.80447	−	9.86383i	0.209429	−	0.542986i
$331$	16.5715			0.910851			0.455425	−	0.890274i	$-0.349487\pi$
$331$	16.5715			0.910851			0.455425	+	0.890274i	$0.349487\pi$
$332$	3.25248	+	10.0101i	0.178503	+	0.549376i
$333$	67.2303	+	48.8457i	3.68420	+	2.67673i
$334$	11.2395	−	8.16598i	0.614999	−	0.446823i
$335$	2.28545	−	7.03389i	0.124867	−	0.384303i
$336$	−0.985024	+	3.03159i	−0.0537375	+	0.165387i
$337$	5.23202	−	3.80128i	0.285006	−	0.207069i	−0.436092	−	0.899902i	$-0.643638\pi$
$337$	5.23202	−	3.80128i	0.285006	−	0.207069i	0.721098	+	0.692833i	$0.243638\pi$
$338$	−15.6850	−	11.3958i	−0.853151	−	0.619851i
$339$	7.63673	+	23.5034i	0.414770	+	1.27653i
$340$	0.749022			0.0406214
$341$	−19.7960	+	12.8107i	−1.07202	+	0.693741i
$342$	48.6196			2.62905
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$	−1.88780	−	1.37156i	−0.101783	−	0.0739498i
$345$	10.1608	−	7.38227i	0.547041	−	0.397448i
$346$	3.02704	−	9.31627i	0.162735	−	0.500846i
$347$	−9.13353	+	28.1101i	−0.490313	+	1.50903i	0.333822	+	0.942636i	$0.391662\pi$
$347$	−9.13353	+	28.1101i	−0.490313	+	1.50903i	−0.824135	+	0.566393i	$0.808338\pi$
$348$	14.7983	−	10.7516i	0.793270	−	0.576344i
$349$	20.5554	+	14.9344i	1.10031	+	0.799419i	0.981110	−	0.193451i	$-0.0619681\pi$
$349$	20.5554	+	14.9344i	1.10031	+	0.799419i	0.119197	+	0.992871i	$0.461968\pi$
$350$	−0.309017	−	0.951057i	−0.0165177	−	0.0508361i
$351$	75.4804			4.02885
$352$	−0.853282	−	3.20498i	−0.0454801	−	0.170826i
$353$	13.7939			0.734174			0.367087	−	0.930187i	$-0.380355\pi$
$353$	13.7939			0.734174			0.367087	+	0.930187i	$0.380355\pi$
$354$	5.15073	+	15.8523i	0.273758	+	0.842541i
$355$	−0.465339	−	0.338089i	−0.0246976	−	0.0179439i
$356$	−3.88706	+	2.82412i	−0.206014	+	0.149678i
$357$	0.737804	−	2.27073i	0.0390487	−	0.120180i
$358$	0.208909	−	0.642955i	0.0110412	−	0.0339812i
$359$	−18.4280	+	13.3887i	−0.972594	+	0.706631i	−0.956041	−	0.293232i	$-0.905269\pi$
$359$	−18.4280	+	13.3887i	−0.972594	+	0.706631i	−0.0165528	+	0.999863i	$0.505269\pi$
$360$	5.79323	+	4.20903i	0.305330	+	0.221835i
$361$	8.37424	+	25.7733i	0.440749	+	1.35649i
$362$	−5.50028			−0.289089
$363$	34.8597	+	3.77664i	1.82966	+	0.198222i
$364$	−5.69102			−0.298291
$365$	3.88447	+	11.9552i	0.203322	+	0.625762i
$366$	−19.8157	−	14.3969i	−1.03578	−	0.752539i
$367$	7.86279	−	5.71265i	0.410435	−	0.298198i	−0.363343	−	0.931655i	$-0.618365\pi$
$367$	7.86279	−	5.71265i	0.410435	−	0.298198i	0.773778	+	0.633457i	$0.218365\pi$
$368$	1.21756	−	3.74725i	0.0634695	−	0.195339i
$369$	25.3275	−	77.9500i	1.31850	−	4.05791i
$370$	−9.38862	+	6.82123i	−0.488091	+	0.354619i
$371$	−8.71076	−	6.32874i	−0.452240	−	0.328572i
$372$	−7.00305	−	21.5532i	−0.363091	−	1.11748i
$373$	−6.44329			−0.333621			−0.166811	−	0.985989i	$-0.553347\pi$
$373$	−6.44329			−0.333621			−0.166811	+	0.985989i	$0.553347\pi$
$374$	0.639127	+	2.40060i	0.0330485	+	0.124132i
$375$	−3.18761			−0.164607
$376$	−1.54516	−	4.75552i	−0.0796856	−	0.245247i
$377$	26.4202	+	19.1954i	1.36071	+	0.988613i
$378$	10.7301	−	7.79584i	0.551894	−	0.400975i
$379$	−8.90341	+	27.4019i	−0.457337	+	1.40754i	0.411032	+	0.911621i	$0.365169\pi$
$379$	−8.90341	+	27.4019i	−0.457337	+	1.40754i	−0.868369	+	0.495918i	$0.834831\pi$
$380$	−2.09812	+	6.45736i	−0.107631	+	0.331256i
$381$	40.0471	−	29.0959i	2.05167	−	1.49063i
$382$	10.1906	+	7.40390i	0.521396	+	0.378817i
$383$	5.93814	+	18.2757i	0.303425	+	0.933845i	0.980260	+	0.197711i	$0.0633508\pi$
$383$	5.93814	+	18.2757i	0.303425	+	0.933845i	−0.676836	+	0.736134i	$0.736649\pi$
$384$	3.18761			0.162667
$385$	2.78444	−	1.80191i	0.141908	−	0.0918340i
$386$	−2.47246			−0.125845
$387$	5.16349	+	15.8916i	0.262475	+	0.807815i
$388$	−13.1641	−	9.56427i	−0.668306	−	0.485552i
$389$	0.945541	−	0.686976i	0.0479409	−	0.0348311i	−0.563557	−	0.826077i	$-0.690567\pi$
$389$	0.945541	−	0.686976i	0.0479409	−	0.0348311i	0.611498	+	0.791246i	$0.290567\pi$
$390$	−5.60579	+	17.2529i	−0.283860	+	0.873632i
$391$	−0.911976	+	2.80677i	−0.0461206	+	0.141945i
$392$	−0.809017	+	0.587785i	−0.0408615	+	0.0296876i
$393$	−2.47041	−	1.79486i	−0.124616	−	0.0905386i
$394$	2.75374	+	8.47514i	0.138731	+	0.426971i
$395$	−6.83481			−0.343896
$396$	−8.54660	+	22.1587i	−0.429483	+	1.11352i
$397$	−34.1835			−1.71562			−0.857811	−	0.513966i	$-0.828176\pi$
$397$	−34.1835			−1.71562			−0.857811	+	0.513966i	$0.828176\pi$
$398$	8.17479	+	25.1594i	0.409765	+	1.26113i
$399$	17.5094	+	12.7213i	0.876565	+	0.636862i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	7.43016	−	22.8677i	0.371044	−	1.14196i	−0.575064	−	0.818108i	$-0.695023\pi$
$401$	7.43016	−	22.8677i	0.371044	−	1.14196i	0.946109	−	0.323849i	$-0.104977\pi$
$402$	−7.28511	+	22.4213i	−0.363348	+	1.11827i
$403$	32.7332	−	23.7821i	1.63056	−	1.18467i
$404$	5.16547	+	3.75294i	0.256992	+	0.186716i
$405$	−6.42600	−	19.7772i	−0.319310	−	0.982736i
$406$	5.73837			0.284790
$407$	−29.8731	−	24.2699i	−1.48075	−	1.20302i
$408$	−2.38759			−0.118203
$409$	−1.68752	−	5.19365i	−0.0834424	−	0.256809i	0.900627	−	0.434592i	$-0.143107\pi$
$409$	−1.68752	−	5.19365i	−0.0834424	−	0.256809i	−0.984070	+	0.177783i	$0.943107\pi$
$410$	9.25986	+	6.72768i	0.457312	+	0.332256i
$411$	12.0219	−	8.73440i	0.592995	−	0.430836i
$412$	0.719608	−	2.21473i	0.0354526	−	0.109112i
$413$	−1.61586	+	4.97311i	−0.0795113	+	0.244711i
$414$	−22.8259	+	16.5840i	−1.12183	+	0.815058i
$415$	8.51510	+	6.18659i	0.417990	+	0.303688i
$416$	1.75862	+	5.41248i	0.0862235	+	0.265369i
$417$	14.2304			0.696864
$418$	−22.4860	−	1.21450i	−1.09983	−	0.0594029i
$419$	−37.5281			−1.83337			−0.916684	−	0.399613i	$-0.869145\pi$
$419$	−37.5281			−1.83337			−0.916684	+	0.399613i	$0.869145\pi$
$420$	0.985024	+	3.03159i	0.0480643	+	0.147927i
$421$	−7.56720	−	5.49789i	−0.368803	−	0.267951i	0.387912	−	0.921697i	$-0.373197\pi$
$421$	−7.56720	−	5.49789i	−0.368803	−	0.267951i	−0.756714	+	0.653746i	$0.773197\pi$
$422$	6.70842	−	4.87395i	0.326561	−	0.237260i
$423$	−11.0646	+	34.0534i	−0.537981	+	1.65573i
$424$	−3.32721	+	10.2401i	−0.161584	+	0.497304i
$425$	0.605971	−	0.440264i	0.0293939	−	0.0213559i
$426$	1.48332	+	1.07769i	0.0718670	+	0.0522144i
$427$	−2.37448	−	7.30790i	−0.114909	−	0.353654i
$428$	1.88876			0.0912967
$429$	−60.0784	−	3.24491i	−2.90061	−	0.156666i
$430$	−2.33345			−0.112529
$431$	−1.57605	−	4.85057i	−0.0759155	−	0.233644i	0.905897	−	0.423499i	$-0.139198\pi$
$431$	−1.57605	−	4.85057i	−0.0759155	−	0.233644i	−0.981812	+	0.189855i	$0.939198\pi$
$432$	−10.7301	−	7.79584i	−0.516250	−	0.375078i
$433$	12.1991	−	8.86320i	0.586254	−	0.425938i	−0.254720	−	0.967015i	$-0.581983\pi$
$433$	12.1991	−	8.86320i	0.586254	−	0.425938i	0.840973	+	0.541077i	$0.181983\pi$
$434$	2.19696	−	6.76156i	0.105458	−	0.324565i
$435$	5.65243	−	17.3964i	0.271013	−	0.834093i
$436$	−6.28246	+	4.56447i	−0.300875	+	0.218599i
$437$	−21.6428	−	15.7244i	−1.03531	−	0.752200i
$438$	−12.3821	−	38.1083i	−0.591642	−	1.82089i
$439$	−8.35774			−0.398893			−0.199447	−	0.979909i	$-0.563914\pi$
$439$	−8.35774			−0.398893			−0.199447	+	0.979909i	$0.563914\pi$
$440$	−2.57416	−	2.09134i	−0.122718	−	0.0997006i
$441$	7.16083			0.340992
$442$	−1.31725	−	4.05407i	−0.0626550	−	0.192832i
$443$	−5.40848	−	3.92949i	−0.256964	−	0.186696i	0.451843	−	0.892097i	$-0.350767\pi$
$443$	−5.40848	−	3.92949i	−0.256964	−	0.186696i	−0.708808	+	0.705402i	$0.750767\pi$
$444$	29.9272	−	21.7434i	1.42028	−	1.03190i
$445$	−1.48473	+	4.56952i	−0.0703828	+	0.216616i
$446$	0.120706	−	0.371493i	0.00571557	−	0.0175907i
$447$	−40.2934	+	29.2749i	−1.90581	+	1.38465i
$448$	0.809017	+	0.587785i	0.0382225	+	0.0277702i
$449$	−2.46350	−	7.58187i	−0.116260	−	0.357811i	0.875948	−	0.482406i	$-0.160237\pi$
$449$	−2.46350	−	7.58187i	−0.116260	−	0.357811i	−0.992208	+	0.124595i	$0.960237\pi$
$450$	7.16083			0.337565
$451$	−13.6608	+	35.4183i	−0.643263	+	1.66778i
$452$	7.75283			0.364663
$453$	−17.5186	−	53.9168i	−0.823097	−	2.53323i
$454$	3.97833	+	2.89042i	0.186712	+	0.135654i
$455$	−4.60413	+	3.34510i	−0.215845	+	0.156821i
$456$	6.68799	−	20.5835i	0.313194	−	0.963911i
$457$	−0.723744	+	2.22746i	−0.0338553	+	0.104196i	−0.966556	−	0.256455i	$-0.917445\pi$
$457$	−0.723744	+	2.22746i	−0.0338553	+	0.104196i	0.932701	+	0.360651i	$0.117445\pi$
$458$	7.42969	−	5.39798i	0.347166	−	0.252231i
$459$	8.03704	+	5.83925i	0.375137	+	0.272553i
$460$	−1.21756	−	3.74725i	−0.0567689	−	0.174717i
$461$	−0.312762			−0.0145668			−0.00728340	−	0.999973i	$-0.502318\pi$
$461$	−0.312762			−0.0145668			−0.00728340	+	0.999973i	$0.502318\pi$
$462$	−8.87570	+	5.74379i	−0.412935	+	0.267225i
$463$	15.8769			0.737863			0.368931	−	0.929457i	$-0.379724\pi$
$463$	15.8769			0.737863			0.368931	+	0.929457i	$0.379724\pi$
$464$	−1.77325	−	5.45751i	−0.0823212	−	0.253359i
$465$	−18.3342	−	13.3206i	−0.850230	−	0.617728i
$466$	16.3097	−	11.8497i	0.755532	−	0.548926i
$467$	−0.239299	+	0.736485i	−0.0110734	+	0.0340805i	−0.956441	−	0.291927i	$-0.905704\pi$
$467$	−0.239299	+	0.736485i	−0.0110734	+	0.0340805i	0.945367	+	0.326008i	$0.105704\pi$
$468$	12.5932	−	38.7579i	0.582120	−	1.79158i
$469$	−5.98339	+	4.34718i	−0.276287	+	0.200734i
$470$	−4.04528	−	2.93907i	−0.186595	−	0.135569i
$471$	−7.26497	−	22.3593i	−0.334752	−	1.03026i
$472$	5.22904			0.240686
$473$	−1.99109	−	7.47865i	−0.0915503	−	0.343869i
$474$	21.7867			1.00069
$475$	2.09812	+	6.45736i	0.0962685	+	0.296284i
$476$	−0.605971	−	0.440264i	−0.0277746	−	0.0201795i
$477$	62.3762	−	45.3190i	2.85601	−	2.07501i
$478$	3.02173	−	9.29993i	0.138211	−	0.425369i
$479$	9.38754	−	28.8919i	0.428927	−	1.32010i	−0.470256	−	0.882530i	$-0.655838\pi$
$479$	9.38754	−	28.8919i	0.428927	−	1.32010i	0.899183	−	0.437573i	$-0.144162\pi$
$480$	2.57883	−	1.87363i	0.117707	−	0.0855190i
$481$	53.4308	+	38.8198i	2.43624	+	1.77003i
$482$	−3.80116	−	11.6988i	−0.173138	−	0.532865i
$483$	−12.5595			−0.571476
$484$	4.50621	−	10.0346i	0.204828	−	0.456120i
$485$	−16.2717			−0.738861
$486$	8.18800	+	25.2001i	0.371415	+	1.14310i
$487$	−7.63477	−	5.54699i	−0.345965	−	0.251358i	0.401210	−	0.915986i	$-0.368590\pi$
$487$	−7.63477	−	5.54699i	−0.345965	−	0.251358i	−0.747174	+	0.664628i	$0.768590\pi$
$488$	−6.21647	+	4.51653i	−0.281407	+	0.204454i
$489$	−10.3048	+	31.7148i	−0.465997	+	1.43419i
$490$	−0.309017	+	0.951057i	−0.0139600	+	0.0429644i
$491$	−23.2292	+	16.8770i	−1.04832	+	0.761648i	−0.971892	−	0.235427i	$-0.924351\pi$
$491$	−23.2292	+	16.8770i	−1.04832	+	0.761648i	−0.0764267	+	0.997075i	$0.524351\pi$
$492$	−29.5168	−	21.4452i	−1.33072	−	0.966824i
$493$	1.32820	+	4.08779i	0.0598193	+	0.184105i
$494$	38.6401			1.73850
$495$	6.11021	+	22.9503i	0.274633	+	1.03154i
$496$	−7.10952			−0.319227
$497$	0.177744	+	0.547039i	0.00797290	+	0.0245381i
$498$	−27.1428	−	19.7204i	−1.21630	−	0.883692i
$499$	−22.3776	+	16.2582i	−1.00176	+	0.727819i	−0.962464	−	0.271409i	$-0.912510\pi$
$499$	−22.3776	+	16.2582i	−1.00176	+	0.727819i	−0.0392927	+	0.999228i	$0.512510\pi$
$500$	−0.309017	+	0.951057i	−0.0138197	+	0.0425325i
$501$	−13.6847	+	42.1173i	−0.611389	+	1.88166i
$502$	16.8632	−	12.2518i	0.752641	−	0.546826i
$503$	1.33822	+	0.972272i	0.0596682	+	0.0433515i	0.617220	−	0.786791i	$-0.288259\pi$
$503$	1.33822	+	0.972272i	0.0596682	+	0.0433515i	−0.557551	+	0.830142i	$0.688259\pi$
$504$	−2.21282	−	6.81035i	−0.0985667	−	0.303357i
$505$	6.38488			0.284123
$506$	10.9710	−	7.09971i	0.487719	−	0.315621i
$507$	61.8004			2.74465
$508$	−4.79878	−	14.7691i	−0.212912	−	0.655274i
$509$	−8.92627	−	6.48532i	−0.395650	−	0.287457i	0.372117	−	0.928186i	$-0.378632\pi$
$509$	−8.92627	−	6.48532i	−0.395650	−	0.287457i	−0.767767	+	0.640729i	$0.778632\pi$
$510$	−1.93160	+	1.40339i	−0.0855325	+	0.0621430i
$511$	3.88447	−	11.9552i	0.171839	−	0.528865i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−72.8535	+	52.9312i	−3.21656	+	2.33697i
$514$	−6.09118	−	4.42550i	−0.268670	−	0.195200i
$515$	−0.719608	−	2.21473i	−0.0317097	−	0.0975925i
$516$	7.43810			0.327444
$517$	5.96790	−	15.4729i	0.262468	−	0.680498i
$518$	11.6050			0.509893
$519$	9.64901	+	29.6966i	0.423545	+	1.30354i
$520$	4.60413	+	3.34510i	0.201905	+	0.146692i
$521$	−15.5724	+	11.3140i	−0.682239	+	0.495676i	−0.874100	−	0.485746i	$-0.838548\pi$
$521$	−15.5724	+	11.3140i	−0.682239	+	0.495676i	0.191861	+	0.981422i	$0.438548\pi$
$522$	−12.6980	+	39.0803i	−0.555774	+	1.71050i
$523$	1.26555	−	3.89496i	0.0553385	−	0.170314i	−0.919567	−	0.392933i	$-0.871460\pi$
$523$	1.26555	−	3.89496i	0.0553385	−	0.170314i	0.974906	+	0.222619i	$0.0714604\pi$
$524$	−0.775005	+	0.563074i	−0.0338563	+	0.0245980i
$525$	2.57883	+	1.87363i	0.112549	+	0.0817718i
$526$	1.01237	+	3.11576i	0.0441415	+	0.135853i
$527$	5.32519			0.231969
$528$	8.20541	+	6.66636i	0.357095	+	0.290116i
$529$	−7.47564			−0.325028
$530$	3.32721	+	10.2401i	0.144525	+	0.444802i
$531$	−30.2930	−	22.0092i	−1.31461	−	0.955117i
$532$	5.49296	−	3.99087i	0.238150	−	0.173026i
$533$	20.1289	−	61.9502i	0.871878	−	2.68336i
$534$	4.73272	−	14.5658i	0.204805	−	0.630324i
$535$	1.52804	−	1.11019i	0.0660629	−	0.0479975i
$536$	5.98339	+	4.34718i	0.258443	+	0.187770i
$537$	0.665918	+	2.04949i	0.0287365	+	0.0884418i
$538$	1.12272			0.0484039
$539$	−3.31180	−	0.178874i	−0.142649	−	0.00770465i
$540$	−13.2631			−0.570752
$541$	−3.72769	−	11.4727i	−0.160266	−	0.493248i	0.838390	−	0.545070i	$-0.183497\pi$
$541$	−3.72769	−	11.4727i	−0.160266	−	0.493248i	−0.998656	+	0.0518223i	$0.983497\pi$
$542$	−7.94628	−	5.77331i	−0.341322	−	0.247985i
$543$	14.1843	−	10.3055i	0.608706	−	0.442251i
$544$	−0.231460	+	0.712362i	−0.00992378	+	0.0305423i
$545$	−2.39968	+	7.38547i	−0.102791	+	0.316359i
$546$	14.6762	−	10.6629i	0.628082	−	0.456328i
$547$	4.60958	+	3.34906i	0.197092	+	0.143195i	0.681954	−	0.731395i	$-0.261130\pi$
$547$	4.60958	+	3.34906i	0.197092	+	0.143195i	−0.484863	+	0.874590i	$0.661130\pi$
$548$	−1.44056	−	4.43359i	−0.0615378	−	0.189394i
$549$	55.0237			2.34835
$550$	−3.31180	−	0.178874i	−0.141216	−	0.00762722i
$551$	−38.9616			−1.65982
$552$	3.88109	+	11.9448i	0.165190	+	0.508403i
$553$	5.52947	+	4.01740i	0.235137	+	0.170837i
$554$	0.721011	−	0.523845i	0.0306328	−	0.0222560i
$555$	11.4312	−	35.1816i	0.485227	−	1.49337i
$556$	1.37954	−	4.24578i	0.0585055	−	0.180061i
$557$	−7.18236	+	5.21829i	−0.304327	+	0.221106i	−0.729458	−	0.684025i	$-0.760228\pi$
$557$	−7.18236	+	5.21829i	−0.304327	+	0.221106i	0.425132	+	0.905131i	$0.360228\pi$
$558$	41.1871	+	29.9242i	1.74359	+	1.26679i
$559$	4.10365	+	12.6297i	0.173566	+	0.534181i
$560$	1.00000			0.0422577
$561$	−6.14603	−	4.99325i	−0.259486	−	0.210815i
$562$	17.3571			0.732167
$563$	6.21989	+	19.1429i	0.262137	+	0.806775i	0.992339	+	0.123544i	$0.0394260\pi$
$563$	6.21989	+	19.1429i	0.262137	+	0.806775i	−0.730202	+	0.683231i	$0.760574\pi$
$564$	12.8948	+	9.36860i	0.542968	+	0.394489i
$565$	6.27217	−	4.55700i	0.263872	−	0.191714i
$566$	−0.923748	+	2.84300i	−0.0388280	+	0.119500i
$567$	−6.42600	+	19.7772i	−0.269867	+	0.830564i
$568$	0.465339	−	0.338089i	0.0195252	−	0.0141859i
$569$	−20.0925	−	14.5980i	−0.842321	−	0.611982i	0.0806973	−	0.996739i	$-0.474285\pi$
$569$	−20.0925	−	14.5980i	−0.842321	−	0.611982i	−0.923018	+	0.384757i	$0.874285\pi$
$570$	−6.68799	−	20.5835i	−0.280129	−	0.862148i
$571$	−28.6955			−1.20087			−0.600435	−	0.799674i	$-0.705006\pi$
$571$	−28.6955			−1.20087			−0.600435	+	0.799674i	$0.705006\pi$
$572$	−6.79235	+	17.6105i	−0.284003	+	0.736331i
$573$	−40.1520			−1.67737
$574$	−3.53695	−	10.8856i	−0.147629	−	0.454357i
$575$	−3.18761	−	2.31593i	−0.132932	−	0.0965810i
$576$	−5.79323	+	4.20903i	−0.241385	+	0.175376i
$577$	−4.75432	+	14.6323i	−0.197925	+	0.609150i	0.802005	+	0.597317i	$0.203767\pi$
$577$	−4.75432	+	14.6323i	−0.197925	+	0.609150i	−0.999930	+	0.0118330i	$0.996233\pi$
$578$	−5.07992	+	15.6344i	−0.211297	+	0.650305i
$579$	6.37604	−	4.63246i	0.264979	−	0.192519i
$580$	−4.64244	−	3.37293i	−0.192767	−	0.140053i
$581$	−3.25248	−	10.0101i	−0.134936	−	0.415289i
$582$	51.8678			2.14999
$583$	−29.9803	+	19.4014i	−1.24166	+	0.803522i
$584$	−12.5704			−0.520167
$585$	−12.5932	−	38.7579i	−0.520664	−	1.60244i
$586$	−14.2295	−	10.3384i	−0.587817	−	0.427074i
$587$	29.2682	−	21.2646i	1.20803	−	0.877685i	0.212979	−	0.977057i	$-0.431683\pi$
$587$	29.2682	−	21.2646i	1.20803	−	0.877685i	0.995050	+	0.0993723i	$0.0316835\pi$
$588$	0.985024	−	3.03159i	0.0406217	−	0.125021i
$589$	−14.9167	+	45.9087i	−0.614630	+	1.89164i
$590$	4.23038	−	3.07355i	0.174162	−	0.126536i
$591$	−22.9807	−	16.6964i	−0.945298	−	0.686799i
$592$	−3.58613	−	11.0370i	−0.147389	−	0.453617i
$593$	22.6239			0.929052			0.464526	−	0.885560i	$-0.346225\pi$
$593$	22.6239			0.929052			0.464526	+	0.885560i	$0.346225\pi$
$594$	−11.3171	−	42.5079i	−0.464348	−	1.74412i
$595$	−0.749022			−0.0307069
$596$	4.82830	+	14.8600i	0.197775	+	0.608689i
$597$	−68.2208	−	49.5653i	−2.79209	−	2.02857i
$598$	−18.1407	+	13.1800i	−0.741830	+	0.538971i
$599$	0.906849	−	2.79099i	0.0370528	−	0.114037i	−0.930819	−	0.365480i	$-0.880905\pi$
$599$	0.906849	−	2.79099i	0.0370528	−	0.114037i	0.967872	+	0.251443i	$0.0809050\pi$
$600$	0.985024	−	3.03159i	0.0402134	−	0.123764i
$601$	26.9466	−	19.5778i	1.09917	−	0.798597i	0.118249	−	0.992984i	$-0.462272\pi$
$601$	26.9466	−	19.5778i	1.09917	−	0.798597i	0.980925	+	0.194387i	$0.0622718\pi$
$602$	1.88780	+	1.37156i	0.0769409	+	0.0559008i
$603$	−16.3657	−	50.3685i	−0.666463	−	2.05116i
$604$	−17.7850			−0.723660
$605$	−2.25261	−	10.7669i	−0.0915816	−	0.437736i
$606$	−20.3525			−0.826762
$607$	8.63117	+	26.5640i	0.350328	+	1.07820i	0.958669	+	0.284524i	$0.0918355\pi$
$607$	8.63117	+	26.5640i	0.350328	+	1.07820i	−0.608341	+	0.793676i	$0.708165\pi$
$608$	−5.49296	−	3.99087i	−0.222769	−	0.161851i
$609$	−14.7983	+	10.7516i	−0.599655	+	0.435675i
$610$	−2.37448	+	7.30790i	−0.0961399	+	0.295888i
$611$	−8.79354	+	27.0637i	−0.355749	+	1.09488i
$612$	4.33925	−	3.15265i	0.175404	−	0.127438i
$613$	−10.7580	−	7.81616i	−0.434512	−	0.315692i	0.348938	−	0.937146i	$-0.386542\pi$
$613$	−10.7580	−	7.81616i	−0.434512	−	0.315692i	−0.783451	+	0.621454i	$0.786542\pi$
$614$	0.397985	+	1.22487i	0.0160614	+	0.0494318i
$615$	−36.4847			−1.47121
$616$	0.853282	+	3.20498i	0.0343797	+	0.129132i
$617$	−17.0581			−0.686735			−0.343368	−	0.939201i	$-0.611568\pi$
$617$	−17.0581			−0.686735			−0.343368	+	0.939201i	$0.611568\pi$
$618$	2.29383	+	7.05968i	0.0922713	+	0.283982i
$619$	23.4976	+	17.0720i	0.944447	+	0.686181i	0.949487	−	0.313807i	$-0.101604\pi$
$619$	23.4976	+	17.0720i	0.944447	+	0.686181i	−0.00504022	+	0.999987i	$0.501604\pi$
$620$	−5.75173	+	4.17887i	−0.230995	+	0.167828i
$621$	16.1485	−	49.7001i	0.648019	−	1.99440i
$622$	−0.0153374	+	0.0472038i	−0.000614975	+	0.00189270i
$623$	3.88706	−	2.82412i	0.155732	−	0.113146i
$624$	−14.6762	−	10.6629i	−0.587517	−	0.426856i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	−27.6778			−1.10623
$627$	60.2630	−	38.9984i	2.40667	−	1.55745i
$628$	−7.37542			−0.294311
$629$	2.68609	+	8.26694i	0.107101	+	0.329624i
$630$	−5.79323	−	4.20903i	−0.230808	−	0.167692i
$631$	−25.9180	+	18.8305i	−1.03178	+	0.749632i	−0.968664	−	0.248374i	$-0.920104\pi$
$631$	−25.9180	+	18.8305i	−1.03178	+	0.749632i	−0.0631161	+	0.998006i	$0.520104\pi$
$632$	2.11207	−	6.50029i	0.0840137	−	0.258568i
$633$	−8.16788	+	25.1381i	−0.324644	+	0.999151i
$634$	−7.46957	+	5.42696i	−0.296655	+	0.215532i
$635$	−12.5634	−	9.12783i	−0.498562	−	0.362227i
$636$	−10.6058	−	32.6414i	−0.420549	−	1.29432i
$637$	5.69102			0.225486
$638$	6.84886	−	17.7570i	0.271149	−	0.703006i
$639$	−4.11884			−0.162939
$640$	−0.309017	−	0.951057i	−0.0122150	−	0.0375938i
$641$	−6.27336	−	4.55787i	−0.247783	−	0.180025i	0.456961	−	0.889487i	$-0.348938\pi$
$641$	−6.27336	−	4.55787i	−0.247783	−	0.180025i	−0.704744	+	0.709462i	$0.748938\pi$
$642$	−4.87078	+	3.53883i	−0.192235	+	0.139667i
$643$	7.48141	−	23.0254i	0.295038	−	0.908034i	−0.688171	−	0.725549i	$-0.741586\pi$
$643$	7.48141	−	23.0254i	0.295038	−	0.908034i	0.983209	−	0.182485i	$-0.0584141\pi$
$644$	−1.21756	+	3.74725i	−0.0479785	+	0.147663i
$645$	6.01755	−	4.37201i	0.236941	−	0.172148i
$646$	4.11434	+	2.98925i	0.161877	+	0.117610i
$647$	−0.266227	−	0.819364i	−0.0104665	−	0.0322125i	0.945687	−	0.325079i	$-0.105391\pi$
$647$	−0.266227	−	0.819364i	−0.0104665	−	0.0322125i	−0.956153	+	0.292866i	$0.905391\pi$
$648$	20.7950			0.816903
$649$	13.4604	+	10.9357i	0.528366	+	0.429263i
$650$	5.69102			0.223220
$651$	7.00305	+	21.5532i	0.274471	+	0.844736i
$652$	8.46347	+	6.14907i	0.331455	+	0.240816i
$653$	17.5739	−	12.7682i	0.687720	−	0.499657i	−0.188190	−	0.982133i	$-0.560262\pi$
$653$	17.5739	−	12.7682i	0.687720	−	0.499657i	0.875910	+	0.482475i	$0.160262\pi$
$654$	7.64925	−	23.5420i	0.299109	−	0.920564i
$655$	−0.296026	+	0.911073i	−0.0115667	+	0.0355986i
$656$	−9.25986	+	6.72768i	−0.361537	+	0.262672i
$657$	72.8232	+	52.9092i	2.84110	+	2.06418i
$658$	1.54516	+	4.75552i	0.0602367	+	0.185389i
$659$	−35.0148			−1.36398			−0.681991	−	0.731360i	$-0.738886\pi$
$659$	−35.0148			−1.36398			−0.681991	+	0.731360i	$0.738886\pi$
$660$	10.5567	+	0.570180i	0.410919	+	0.0221942i
$661$	21.6301			0.841315			0.420657	−	0.907220i	$-0.361799\pi$
$661$	21.6301			0.841315			0.420657	+	0.907220i	$0.361799\pi$
$662$	5.12087	+	15.7604i	0.199028	+	0.612546i
$663$	10.9928	+	7.98671i	0.426923	+	0.310178i
$664$	−8.51510	+	6.18659i	−0.330450	+	0.240086i
$665$	2.09812	−	6.45736i	0.0813617	−	0.250406i
$666$	−25.6797	+	79.0339i	−0.995068	+	3.06250i
$667$	18.2916	−	13.2897i	0.708255	−	0.514578i
$668$	11.2395	+	8.16598i	0.434870	+	0.315951i
$669$	0.384762	+	1.18417i	0.0148757	+	0.0457828i
$670$	7.39587			0.285727
$671$	−25.4478	−	1.37447i	−0.982401	−	0.0530607i
$672$	−3.18761			−0.122965
$673$	−10.6531	−	32.7868i	−0.410646	−	1.26384i	−0.916087	−	0.400979i	$-0.868670\pi$
$673$	−10.6531	−	32.7868i	−0.410646	−	1.26384i	0.505441	−	0.862861i	$-0.331330\pi$
$674$	5.23202	+	3.80128i	0.201530	+	0.146420i
$675$	−10.7301	+	7.79584i	−0.413000	+	0.300062i
$676$	5.99114	−	18.4388i	0.230428	−	0.709185i
$677$	−4.18147	+	12.8692i	−0.160707	+	0.494605i	−0.998694	−	0.0510847i	$-0.983732\pi$
$677$	−4.18147	+	12.8692i	−0.160707	+	0.494605i	0.837987	+	0.545689i	$0.183732\pi$
$678$	−19.9932	+	14.5259i	−0.767835	+	0.557865i
$679$	13.1641	+	9.56427i	0.505192	+	0.367043i
$680$	0.231460	+	0.712362i	0.00887610	+	0.0273178i
$681$	−15.6750			−0.600667
$682$	−18.3011	−	14.8684i	−0.700784	−	0.569341i
$683$	19.6188			0.750694			0.375347	−	0.926884i	$-0.377524\pi$
$683$	19.6188			0.750694			0.375347	+	0.926884i	$0.377524\pi$
$684$	15.0243	+	46.2400i	0.574468	+	1.76803i
$685$	−3.77144	−	2.74011i	−0.144099	−	0.104694i
$686$	0.809017	−	0.587785i	0.0308884	−	0.0224417i
$687$	−9.04607	+	27.8409i	−0.345129	+	1.06220i
$688$	0.721074	−	2.21924i	0.0274907	−	0.0846077i
$689$	49.5731	−	36.0170i	1.88858	−	1.37214i
$690$	10.1608	+	7.38227i	0.386816	+	0.281038i
$691$	−8.47855	−	26.0943i	−0.322539	−	0.992674i	−0.972539	−	0.232740i	$-0.925231\pi$
$691$	−8.47855	−	26.0943i	−0.322539	−	0.992674i	0.650000	−	0.759934i	$-0.274769\pi$
$692$	9.79571			0.372377
$693$	8.54660	−	22.1587i	0.324658	−	0.841739i
$694$	−29.5567			−1.12196
$695$	−1.37954	−	4.24578i	−0.0523289	−	0.161052i
$696$	14.7983	+	10.7516i	0.560926	+	0.407537i
$697$	6.93583	−	5.03918i	0.262713	−	0.190872i
$698$	−7.85147	+	24.1643i	−0.297183	+	0.914634i
$699$	−19.8580	+	61.1165i	−0.751097	+	2.31164i
$700$	0.809017	−	0.587785i	0.0305780	−	0.0222162i
$701$	26.0864	+	18.9529i	0.985270	+	0.715840i	0.958880	−	0.283811i	$-0.0915989\pi$
$701$	26.0864	+	18.9529i	0.985270	+	0.715840i	0.0263897	+	0.999652i	$0.491599\pi$
$702$	23.3247	+	71.7862i	0.880336	+	2.70939i
$703$	−78.7939			−2.97177
$704$	2.78444	−	1.80191i	0.104943	−	0.0679122i
$705$	15.9388			0.600290
$706$	4.26254	+	13.1188i	0.160423	+	0.493731i
$707$	−5.16547	−	3.75294i	−0.194268	−	0.141144i
$708$	−13.4848	+	9.79727i	−0.506789	+	0.368204i
$709$	6.44254	−	19.8281i	0.241955	−	0.744660i	−0.754168	−	0.656682i	$-0.771959\pi$
$709$	6.44254	−	19.8281i	0.241955	−	0.744660i	0.996122	−	0.0879784i	$-0.0280406\pi$
$710$	0.177744	−	0.547039i	0.00667061	−	0.0205300i
$711$	−39.5956	+	28.7679i	−1.48495	+	1.07888i
$712$	−3.88706	−	2.82412i	−0.145674	−	0.105838i
$713$	−8.65625	−	26.6412i	−0.324179	−	0.997721i
$714$	2.38759			0.0893531
$715$	4.85605	+	18.2396i	0.181606	+	0.682123i
$716$	0.676043			0.0252649
$717$	9.63208	+	29.6445i	0.359717	+	1.10709i
$718$	−18.4280	−	13.3887i	−0.687728	−	0.499664i
$719$	32.6186	−	23.6988i	1.21647	−	0.883815i	0.220666	−	0.975350i	$-0.429177\pi$
$719$	32.6186	−	23.6988i	1.21647	−	0.883815i	0.995802	+	0.0915342i	$0.0291771\pi$
$720$	−2.21282	+	6.81035i	−0.0824668	+	0.253807i
$721$	−0.719608	+	2.21473i	−0.0267996	+	0.0824807i
$722$	−21.9240	+	15.9287i	−0.815928	+	0.592807i
$723$	31.7217	+	23.0472i	1.17974	+	0.857133i
$724$	−1.69968	−	5.23108i	−0.0631682	−	0.194412i
$725$	−5.73837			−0.213118
$726$	7.18043	+	34.3206i	0.266491	+	1.27376i
$727$	39.1899			1.45347			0.726736	−	0.686917i	$-0.241036\pi$
$727$	39.1899			1.45347			0.726736	+	0.686917i	$0.241036\pi$
$728$	−1.75862	−	5.41248i	−0.0651789	−	0.200600i
$729$	−17.8605	−	12.9764i	−0.661501	−	0.480608i
$730$	−10.1697	+	7.38869i	−0.376396	+	0.273468i
$731$	−0.540100	+	1.66226i	−0.0199763	+	0.0614808i
$732$	7.56891	−	23.2947i	0.279755	−	0.860997i
$733$	19.7462	−	14.3465i	0.729344	−	0.529899i	−0.160012	−	0.987115i	$-0.551153\pi$
$733$	19.7462	−	14.3465i	0.729344	−	0.529899i	0.889356	+	0.457216i	$0.151153\pi$
$734$	7.86279	+	5.71265i	0.290221	+	0.210858i
$735$	−0.985024	−	3.03159i	−0.0363332	−	0.111822i
$736$	3.94010			0.145234
$737$	6.31077	+	23.7036i	0.232460	+	0.873135i
$738$	81.9615			3.01704
$739$	−12.8334	−	39.4973i	−0.472086	−	1.45293i	−0.849848	−	0.527029i	$-0.823306\pi$
$739$	−12.8334	−	39.4973i	−0.472086	−	1.45293i	0.377762	−	0.925903i	$-0.376694\pi$
$740$	−9.38862	−	6.82123i	−0.345133	−	0.250753i
$741$	−99.6462	+	72.3972i	−3.66060	+	2.65958i
$742$	3.32721	−	10.2401i	0.122146	−	0.375926i
$743$	−6.98457	+	21.4963i	−0.256239	+	0.788622i	0.737344	+	0.675517i	$0.236080\pi$
$743$	−6.98457	+	21.4963i	−0.256239	+	0.788622i	−0.993583	+	0.113105i	$0.963920\pi$
$744$	18.3342	−	13.3206i	0.672166	−	0.488357i
$745$	12.6407	+	9.18398i	0.463118	+	0.336475i
$746$	−1.99109	−	6.12794i	−0.0728989	−	0.224360i
$747$	75.3695			2.75763
$748$	−2.08561	+	1.34967i	−0.0762573	+	0.0493489i
$749$	−1.88876			−0.0690138
$750$	−0.985024	−	3.03159i	−0.0359680	−	0.110698i
$751$	18.4296	+	13.3899i	0.672505	+	0.488604i	0.870863	−	0.491526i	$-0.163561\pi$
$751$	18.4296	+	13.3899i	0.672505	+	0.488604i	−0.198358	+	0.980130i	$0.563561\pi$
$752$	4.04528	−	2.93907i	0.147516	−	0.107177i
$753$	−20.5319	+	63.1907i	−0.748224	+	2.30280i
$754$	−10.0916	+	31.0588i	−0.367515	+	1.13110i
$755$	−14.3883	+	10.4537i	−0.523645	+	0.380451i
$756$	10.7301	+	7.79584i	0.390248	+	0.283532i
$757$	2.09304	+	6.44172i	0.0760729	+	0.234128i	0.981861	−	0.189603i	$-0.0607201\pi$
$757$	2.09304	+	6.44172i	0.0760729	+	0.234128i	−0.905788	+	0.423731i	$0.860720\pi$
$758$	−28.8120			−1.04650
$759$	−14.9900	+	38.8644i	−0.544102	+	1.41069i
$760$	−6.78967			−0.246287
$761$	2.23888	+	6.89055i	0.0811592	+	0.249782i	0.983400	−	0.181450i	$-0.0580790\pi$
$761$	2.23888	+	6.89055i	0.0811592	+	0.249782i	−0.902241	+	0.431232i	$0.858079\pi$
$762$	40.0471	+	29.0959i	1.45075	+	1.05403i
$763$	6.28246	−	4.56447i	0.227440	−	0.165245i
$764$	−3.89246	+	11.9798i	−0.140824	+	0.433413i
$765$	1.65745	−	5.10110i	0.0599252	−	0.184431i
$766$	−15.5462	+	11.2950i	−0.561709	+	0.408105i
$767$	−24.0752	−	17.4916i	−0.869304	−	0.631587i
$768$	0.985024	+	3.03159i	0.0355440	+	0.109393i
$769$	−1.45679			−0.0525333			−0.0262667	−	0.999655i	$-0.508362\pi$
$769$	−1.45679			−0.0525333			−0.0262667	+	0.999655i	$0.508362\pi$
$770$	2.57416	+	2.09134i	0.0927663	+	0.0753666i
$771$	23.9998			0.864333
$772$	−0.764031	−	2.35145i	−0.0274981	−	0.0846304i
$773$	20.5899	+	14.9594i	0.740566	+	0.538053i	0.892888	−	0.450278i	$-0.148675\pi$
$773$	20.5899	+	14.9594i	0.740566	+	0.538053i	−0.152322	+	0.988331i	$0.548675\pi$
$774$	−13.5182	+	9.82154i	−0.485901	+	0.353028i
$775$	−2.19696	+	6.76156i	−0.0789173	+	0.242882i
$776$	5.02824	−	15.4753i	0.180503	−	0.555532i
$777$	−29.9272	+	21.7434i	−1.07363	+	0.780040i
$778$	0.945541	+	0.686976i	0.0338993	+	0.0246293i
$779$	24.0147	+	73.9097i	0.860417	+	2.64809i
$780$	−18.1407			−0.649542
$781$	1.90492	+	0.102887i	0.0681633	+	0.00368158i
$782$	−2.95122			−0.105535
$783$	−23.5188	−	72.3834i	−0.840493	−	2.58677i
$784$	−0.809017	−	0.587785i	−0.0288935	−	0.0209923i
$785$	−5.96684	+	4.33516i	−0.212966	+	0.154729i
$786$	0.943613	−	2.90414i	0.0336576	−	0.103587i
$787$	5.86952	−	18.0645i	0.209226	−	0.643931i	−0.790287	−	0.612736i	$-0.790069\pi$
$787$	5.86952	−	18.0645i	0.209226	−	0.643931i	0.999513	−	0.0311947i	$-0.00993120\pi$
$788$	−7.20938	+	5.23792i	−0.256824	+	0.186593i
$789$	−8.44850	−	6.13819i	−0.300774	−	0.218525i
$790$	−2.11207	−	6.50029i	−0.0751441	−	0.231270i
$791$	−7.75283			−0.275659
$792$	−23.7152	−	1.28089i	−0.842683	−	0.0455143i
$793$	43.7297			1.55289
$794$	−10.5633	−	32.5104i	−0.374877	−	1.15375i
$795$	−27.7665	−	20.1735i	−0.984775	−	0.715481i
$796$	−21.4019	+	15.5494i	−0.758570	+	0.551133i
$797$	−13.9043	+	42.7930i	−0.492516	+	1.51581i	0.328277	+	0.944581i	$0.393532\pi$
$797$	−13.9043	+	42.7930i	−0.492516	+	1.51581i	−0.820793	+	0.571226i	$0.806468\pi$
$798$	−6.68799	+	20.5835i	−0.236752	+	0.728648i
$799$	−3.03001	+	2.20143i	−0.107194	+	0.0778809i
$800$	−0.809017	−	0.587785i	−0.0286031	−	0.0207813i
$801$	10.6319	+	32.7215i	0.375658	+	1.15616i
$802$	24.0445			0.849041
$803$	−32.3582	−	26.2889i	−1.14190	−	0.927717i
$804$	−23.5751			−0.831430
$805$	1.21756	+	3.74725i	0.0429132	+	0.132073i
$806$	32.7332	+	23.7821i	1.15298	+	0.837687i
$807$	−2.89530	+	2.10356i	−0.101919	+	0.0740488i
$808$	−1.97303	+	6.07238i	−0.0694111	+	0.213625i
$809$	−9.66014	+	29.7309i	−0.339632	+	1.04528i	0.624762	+	0.780815i	$0.285196\pi$
$809$	−9.66014	+	29.7309i	−0.339632	+	1.04528i	−0.964395	+	0.264466i	$0.914804\pi$
$810$	16.8235	−	12.2230i	0.591117	−	0.429472i
$811$	−22.3268	−	16.2214i	−0.784000	−	0.569610i	0.122177	−	0.992508i	$-0.461013\pi$
$811$	−22.3268	−	16.2214i	−0.784000	−	0.569610i	−0.906177	+	0.422899i	$0.861013\pi$
$812$	1.77325	+	5.45751i	0.0622290	+	0.191521i
$813$	31.3091			1.09806
$814$	13.8508	−	35.9108i	0.485470	−	1.25867i
$815$	10.4614			0.366448
$816$	−0.737804	−	2.27073i	−0.0258283	−	0.0794914i
$817$	−12.8175	−	9.31247i	−0.448428	−	0.325802i
$818$	4.41798	−	3.20985i	0.154471	−	0.112230i
$819$	−12.5932	+	38.7579i	−0.440042	+	1.35431i
$820$	−3.53695	+	10.8856i	−0.123516	+	0.380142i
$821$	17.2719	−	12.5488i	0.602795	−	0.437956i	−0.244075	−	0.969756i	$-0.578484\pi$
$821$	17.2719	−	12.5488i	0.602795	−	0.437956i	0.846870	+	0.531800i	$0.178484\pi$
$822$	12.0219	+	8.73440i	0.419311	+	0.304647i
$823$	−16.3321	−	50.2651i	−0.569301	−	1.75213i	−0.654811	−	0.755792i	$-0.727252\pi$
$823$	−16.3321	−	50.2651i	−0.569301	−	1.75213i	0.0855099	−	0.996337i	$-0.472748\pi$
$824$	2.32870			0.0811242
$825$	8.87570	−	5.74379i	0.309012	−	0.199973i
$826$	−5.22904			−0.181941
$827$	5.50960	+	16.9568i	0.191587	+	0.589646i	0.999999	+	0.00102854i	$0.000327395\pi$
$827$	5.50960	+	16.9568i	0.191587	+	0.589646i	−0.808412	+	0.588617i	$0.799673\pi$
$828$	−22.8259	−	16.5840i	−0.793255	−	0.576333i
$829$	37.3909	−	27.1661i	1.29864	−	0.943517i	0.298698	−	0.954348i	$-0.403448\pi$
$829$	37.3909	−	27.1661i	1.29864	−	0.943517i	0.999941	+	0.0108311i	$0.00344772\pi$
$830$	−3.25248	+	10.0101i	−0.112895	+	0.347456i
$831$	−0.877872	+	2.70181i	−0.0304530	+	0.0937248i
$832$	−4.60413	+	3.34510i	−0.159620	+	0.115970i
$833$	0.605971	+	0.440264i	0.0209957	+	0.0152542i
$834$	4.39742	+	13.5339i	0.152270	+	0.468640i
$835$	13.8928			0.480780
$836$	−5.79350	−	21.7608i	−0.200373	−	0.752612i
$837$	−94.2942			−3.25928
$838$	−11.5968	−	35.6914i	−0.400606	−	1.23294i
$839$	15.7067	+	11.4116i	0.542254	+	0.393971i	0.824921	−	0.565247i	$-0.191219\pi$
$839$	15.7067	+	11.4116i	0.542254	+	0.393971i	−0.282667	+	0.959218i	$0.591219\pi$
$840$	−2.57883	+	1.87363i	−0.0889780	+	0.0646463i
$841$	1.21408	−	3.73655i	0.0418648	−	0.128847i
$842$	2.89041	−	8.89578i	0.0996102	−	0.306569i
$843$	−44.7611	+	32.5208i	−1.54165	+	1.12008i
$844$	6.70842	+	4.87395i	0.230913	+	0.167768i
$845$	−5.99114	−	18.4388i	−0.206101	−	0.634315i
$846$	−35.8059			−1.23103
$847$	−4.50621	+	10.0346i	−0.154835	+	0.344794i
$848$	−10.7671			−0.369743
$849$	−2.94454	−	9.06238i	−0.101056	−	0.311020i
$850$	0.605971	+	0.440264i	0.0207846	+	0.0151009i
$851$	36.9921	−	26.8763i	1.26807	−	0.921308i
$852$	−0.566577	+	1.74374i	−0.0194106	+	0.0597397i
$853$	−7.22035	+	22.2220i	−0.247220	+	0.760866i	0.748043	+	0.663650i	$0.230994\pi$
$853$	−7.22035	+	22.2220i	−0.247220	+	0.760866i	−0.995263	+	0.0972154i	$0.969006\pi$
$854$	6.21647	−	4.51653i	0.212723	−	0.154553i
$855$	39.3341	+	28.5779i	1.34520	+	0.977344i
$856$	0.583659	+	1.79632i	0.0199491	+	0.0613969i
$857$	−32.8025			−1.12051			−0.560256	−	0.828320i	$-0.689297\pi$
$857$	−32.8025			−1.12051			−0.560256	+	0.828320i	$0.689297\pi$
$858$	−15.4792	−	58.1407i	−0.528450	−	1.98489i
$859$	−5.80773			−0.198157			−0.0990786	−	0.995080i	$-0.531590\pi$
$859$	−5.80773			−0.198157			−0.0990786	+	0.995080i	$0.531590\pi$
$860$	−0.721074	−	2.21924i	−0.0245884	−	0.0756754i
$861$	29.5168	+	21.4452i	1.00593	+	0.730850i
$862$	4.12614	−	2.99782i	0.140537	−	0.102106i
$863$	−13.7246	+	42.2400i	−0.467191	+	1.43787i	0.389015	+	0.921231i	$0.372815\pi$
$863$	−13.7246	+	42.2400i	−0.467191	+	1.43787i	−0.856206	+	0.516634i	$0.827185\pi$
$864$	4.09852	−	12.6139i	0.139434	−	0.429135i
$865$	7.92490	−	5.75777i	0.269455	−	0.195770i
$866$	12.1991	+	8.86320i	0.414544	+	0.301184i
$867$	−16.1928	−	49.8363i	−0.549936	−	1.69253i
$868$	7.10952			0.241313
$869$	19.0311	−	12.3157i	0.645586	−	0.417782i
$870$	18.2916			0.620145
$871$	−13.0065	−	40.0300i	−0.440710	−	1.35637i
$872$	−6.28246	−	4.56447i	−0.212751	−	0.154573i
$873$	−94.2658	+	68.4881i	−3.19041	+	2.31797i
$874$	8.26681	−	25.4426i	0.279629	−	0.860609i
$875$	0.309017	−	0.951057i	0.0104467	−	0.0321516i
$876$	32.4169	−	23.5522i	1.09526	−	0.795756i
$877$	14.0335	+	10.1959i	0.473878	+	0.344293i	0.798951	−	0.601396i	$-0.205389\pi$
$877$	14.0335	+	10.1959i	0.473878	+	0.344293i	−0.325073	+	0.945689i	$0.605389\pi$
$878$	−2.58268	−	7.94868i	−0.0871614	−	0.268255i
$879$	56.0658			1.89105
$880$	1.19352	−	3.09443i	0.0402336	−	0.104313i
$881$	2.06132			0.0694478			0.0347239	−	0.999397i	$-0.488945\pi$
$881$	2.06132			0.0694478			0.0347239	+	0.999397i	$0.488945\pi$
$882$	2.21282	+	6.81035i	0.0745094	+	0.229316i
$883$	37.6710	+	27.3696i	1.26773	+	0.921060i	0.999110	−	0.0421857i	$-0.0134321\pi$
$883$	37.6710	+	27.3696i	1.26773	+	0.921060i	0.268621	+	0.963246i	$0.413432\pi$
$884$	3.44859	−	2.50555i	0.115989	−	0.0842708i
$885$	−5.15073	+	15.8523i	−0.173140	+	0.532870i
$886$	2.06585	−	6.35804i	0.0694037	−	0.213603i
$887$	−22.5736	+	16.4007i	−0.757946	+	0.550680i	−0.898280	−	0.439424i	$-0.855183\pi$
$887$	−22.5736	+	16.4007i	−0.757946	+	0.550680i	0.140333	+	0.990104i	$0.455183\pi$
$888$	29.9272	+	21.7434i	1.00429	+	0.729661i
$889$	4.79878	+	14.7691i	0.160946	+	0.495341i
$890$	−4.80467			−0.161053
$891$	53.5296	+	43.4893i	1.79331	+	1.45695i
$892$	0.390611			0.0130786
$893$	−10.4911	−	32.2884i	−0.351072	−	1.08049i
$894$	−40.2934	−	29.2749i	−1.34761	−	0.979099i
$895$	0.546930	−	0.397368i	0.0182819	−	0.0132825i
$896$	−0.309017	+	0.951057i	−0.0103235	+	0.0317726i
$897$	22.0874	−	67.9779i	0.737476	−	2.26972i
$898$	6.44952	−	4.68585i	0.215223	−	0.156369i
$899$	−33.0055	−	23.9799i	−1.10080	−	0.799775i
$900$	2.21282	+	6.81035i	0.0737606	+	0.227012i
$901$	8.06478			0.268677
$902$	−37.9062	−	2.04736i	−1.26214	−	0.0681696i
$903$	−7.43810			−0.247525
$904$	2.39576	+	7.37338i	0.0796817	+	0.245235i
$905$	−4.44982	−	3.23299i	−0.147917	−	0.107468i
$906$	45.8644	−	33.3224i	1.52374	−	1.10706i
$907$	−2.25752	+	6.94794i	−0.0749598	+	0.230703i	−0.981515	−	0.191384i	$-0.938702\pi$
$907$	−2.25752	+	6.94794i	−0.0749598	+	0.230703i	0.906555	+	0.422087i	$0.138702\pi$
$908$	−1.51959	+	4.67680i	−0.0504292	+	0.155205i
$909$	36.9891	−	26.8741i	1.22685	−	0.891358i
$910$	−4.60413	−	3.34510i	−0.152626	−	0.110889i
$911$	−8.95554	−	27.5623i	−0.296710	−	0.913180i	−0.982642	−	0.185514i	$-0.940605\pi$
$911$	−8.95554	−	27.5623i	−0.296710	−	0.913180i	0.685931	−	0.727666i	$-0.259395\pi$
$912$	21.6428			0.716664
$913$	−34.8575	−	1.88269i	−1.15361	−	0.0623081i
$914$	−2.34209			−0.0774693
$915$	−7.56891	−	23.2947i	−0.250220	−	0.770099i
$916$	7.42969	+	5.39798i	0.245484	+	0.178354i
$917$	0.775005	−	0.563074i	0.0255929	−	0.0185943i
$918$	−3.06988	+	9.44811i	−0.101321	+	0.311834i
$919$	1.56507	−	4.81680i	0.0516270	−	0.158892i	−0.921919	−	0.387383i	$-0.873379\pi$
$919$	1.56507	−	4.81680i	0.0516270	−	0.158892i	0.973546	+	0.228491i	$0.0733792\pi$
$920$	3.18761	−	2.31593i	0.105092	−	0.0763540i
$921$	−3.32129	−	2.41306i	−0.109440	−	0.0795130i
$922$	−0.0966489	−	0.297455i	−0.00318296	−	0.00979615i
$923$	−3.27342			−0.107746
$924$	−8.20541	−	6.66636i	−0.269938	−	0.219307i
$925$	−11.6050			−0.381569
$926$	4.90624	+	15.0998i	0.161229	+	0.496212i
$927$	−13.4907	−	9.80157i	−0.443093	−	0.321926i
$928$	4.64244	−	3.37293i	0.152395	−	0.110722i
$929$	−7.30090	+	22.4699i	−0.239535	+	0.737212i	0.756953	+	0.653470i	$0.226687\pi$
$929$	−7.30090	+	22.4699i	−0.239535	+	0.737212i	−0.996487	+	0.0837426i	$0.973313\pi$
$930$	7.00305	−	21.5532i	0.229639	−	0.706757i
$931$	−5.49296	+	3.99087i	−0.180024	+	0.130795i
$932$	16.3097	+	11.8497i	0.534242	+	0.388149i
$933$	−0.0488897	−	0.150467i	−0.00160058	−	0.00492607i
$934$	−0.774386			−0.0253387
$935$	−0.893973	+	2.31780i	−0.0292360	+	0.0758000i
$936$	40.7524			1.33203
$937$	−12.2082	−	37.5730i	−0.398825	−	1.22746i	−0.925942	−	0.377665i	$-0.876727\pi$
$937$	−12.2082	−	37.5730i	−0.398825	−	1.22746i	0.527117	−	0.849793i	$-0.323273\pi$
$938$	−5.98339	−	4.34718i	−0.195364	−	0.141941i
$939$	71.3761	−	51.8578i	2.32927	−	1.69232i
$940$	1.54516	−	4.75552i	0.0503976	−	0.155108i
$941$	4.41085	−	13.5752i	0.143790	−	0.442539i	−0.853064	−	0.521807i	$-0.825258\pi$
$941$	4.41085	−	13.5752i	0.143790	−	0.442539i	0.996853	+	0.0792678i	$0.0252582\pi$
$942$	19.0199	−	13.8188i	0.619703	−	0.450241i
$943$	−36.4847	−	26.5077i	−1.18811	−	0.863210i
$944$	1.61586	+	4.97311i	0.0525918	+	0.161861i
$945$	13.2631			0.431448
$946$	6.49734	−	4.20467i	0.211247	−	0.136706i
$947$	15.8228			0.514171			0.257085	−	0.966389i	$-0.417238\pi$
$947$	15.8228			0.514171			0.257085	+	0.966389i	$0.417238\pi$
$948$	6.73245	+	20.7203i	0.218660	+	0.672966i
$949$	57.8758	+	42.0492i	1.87873	+	1.36498i
$950$	−5.49296	+	3.99087i	−0.178215	+	0.129481i
$951$	9.09463	−	27.9904i	0.294914	−	0.907651i
$952$	0.231460	−	0.712362i	0.00750167	−	0.0230878i
$953$	−25.8844	+	18.8061i	−0.838478	+	0.609190i	−0.921945	−	0.387320i	$-0.873401\pi$
$953$	−25.8844	+	18.8061i	−0.838478	+	0.609190i	0.0834669	+	0.996511i	$0.473401\pi$
$954$	62.3762	+	45.3190i	2.01950	+	1.46726i
$955$	3.89246	+	11.9798i	0.125957	+	0.387656i
$956$	9.77852			0.316260
$957$	15.6079	+	58.6244i	0.504533	+	1.89506i
$958$	30.3787			0.981491
$959$	1.44056	+	4.43359i	0.0465182	+	0.143168i
$960$	2.57883	+	1.87363i	0.0832313	+	0.0604711i
$961$	−15.8125	+	11.4885i	−0.510081	+	0.370596i
$962$	−20.4088	+	62.8117i	−0.658005	+	2.02513i
$963$	4.17948	−	12.8631i	0.134682	−	0.414508i
$964$	9.95158	−	7.23024i	0.320519	−	0.232871i
$965$	−2.00026	−	1.45327i	−0.0643907	−	0.0467825i
$966$	−3.88109	−	11.9448i	−0.124872	−	0.384317i
$967$	−24.1383			−0.776237			−0.388118	−	0.921610i	$-0.626875\pi$
$967$	−24.1383			−0.776237			−0.388118	+	0.921610i	$0.626875\pi$
$968$	10.9360	+	1.18479i	0.351497	+	0.0380806i
$969$	−16.2109			−0.520770
$970$	−5.02824	−	15.4753i	−0.161447	−	0.496883i
$971$	19.7288	+	14.3338i	0.633126	+	0.459993i	0.857482	−	0.514514i	$-0.172028\pi$
$971$	19.7288	+	14.3338i	0.633126	+	0.459993i	−0.224356	+	0.974507i	$0.572028\pi$
$972$	−21.4365	+	15.5745i	−0.687575	+	0.499552i
$973$	−1.37954	+	4.24578i	−0.0442260	+	0.136114i
$974$	2.91622	−	8.97521i	0.0934418	−	0.287584i
$975$	−14.6762	+	10.6629i	−0.470013	+	0.341485i
$976$	−6.21647	−	4.51653i	−0.198984	−	0.144571i
$977$	16.8285	+	51.7927i	0.538390	+	1.65699i	0.736208	+	0.676755i	$0.236615\pi$
$977$	16.8285	+	51.7927i	0.538390	+	1.65699i	−0.197818	+	0.980239i	$0.563385\pi$
$978$	−33.3469			−1.06632
$979$	−4.09974	−	15.3989i	−0.131028	−	0.492151i
$980$	−1.00000			−0.0319438
$981$	17.1837	+	52.8861i	0.548634	+	1.68852i
$982$	−23.2292	−	16.8770i	−0.741273	−	0.538567i
$983$	42.3935	−	30.8007i	1.35214	−	0.982390i	0.353242	−	0.935532i	$-0.385079\pi$
$983$	42.3935	−	30.8007i	1.35214	−	0.982390i	0.998902	−	0.0468574i	$-0.0149206\pi$
$984$	11.2744	−	34.6990i	0.359415	−	1.10616i
$985$	−2.75374	+	8.47514i	−0.0877414	+	0.270040i
$986$	−3.47728	+	2.52639i	−0.110739	+	0.0804568i
$987$	−12.8948	−	9.36860i	−0.410445	−	0.298206i
$988$	11.9405	+	36.7490i	0.379877	+	1.16914i
$989$	9.19400			0.292352
$990$	−19.9389	+	12.9032i	−0.633700	+	0.410090i
$991$	13.7527			0.436870			0.218435	−	0.975851i	$-0.429905\pi$
$991$	13.7527			0.436870			0.218435	+	0.975851i	$0.429905\pi$
$992$	−2.19696	−	6.76156i	−0.0697537	−	0.214680i
$993$	−42.7350	−	31.0488i	−1.35615	−	0.985303i
$994$	−0.465339	+	0.338089i	−0.0147597	+	0.0107235i
$995$	−8.17479	+	25.1594i	−0.259158	+	0.797607i
$996$	10.3676	−	31.9083i	0.328511	−	1.01105i
$997$	−31.3195	+	22.7549i	−0.991898	+	0.720656i	−0.960336	−	0.278846i	$-0.910048\pi$
$997$	−31.3195	+	22.7549i	−0.991898	+	0.720656i	−0.0315617	+	0.999502i	$0.510048\pi$
$998$	−22.3776	−	16.2582i	−0.708349	−	0.514646i
$999$	−47.5632	−	146.384i	−1.50483	−	4.63140i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.k.71.1	✓	16
11.3	even	5		8470.2.a.dh.1.8		8
11.8	odd	10		8470.2.a.dg.1.8		8
11.9	even	5	inner	770.2.n.k.141.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.k.71.1	✓	16	1.1	even	1	trivial
770.2.n.k.141.1	yes	16	11.9	even	5	inner
8470.2.a.dg.1.8		8	11.8	odd	10
8470.2.a.dh.1.8		8	11.3	even	5

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-2.57883 - 1.87363i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.985024 - 3.03159i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.21282 + 6.81035i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(-2.57883 - 1.87363i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.985024 - 3.03159i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.21282 + 6.81035i) q^{9} -1.00000 q^{10} +(-0.853282 - 3.20498i) q^{11} +3.18761 q^{12} +(1.75862 + 5.41248i) q^{13} +(0.809017 + 0.587785i) q^{14} +(2.57883 - 1.87363i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.231460 + 0.712362i) q^{17} +(-5.79323 + 4.20903i) q^{18} +(-5.49296 - 3.99087i) q^{19} +(-0.309017 - 0.951057i) q^{20} -3.18761 q^{21} +(2.78444 - 1.80191i) q^{22} +3.94010 q^{23} +(0.985024 + 3.03159i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-4.60413 + 3.34510i) q^{26} +(4.09852 - 12.6139i) q^{27} +(-0.309017 + 0.951057i) q^{28} +(4.64244 - 3.37293i) q^{29} +(2.57883 + 1.87363i) q^{30} +(-2.19696 - 6.76156i) q^{31} +1.00000 q^{32} +(-3.80447 + 9.86383i) q^{33} -0.749022 q^{34} +(0.309017 + 0.951057i) q^{35} +(-5.79323 - 4.20903i) q^{36} +(9.38862 - 6.82123i) q^{37} +(2.09812 - 6.45736i) q^{38} +(5.60579 - 17.2529i) q^{39} +(0.809017 - 0.587785i) q^{40} +(-9.25986 - 6.72768i) q^{41} +(-0.985024 - 3.03159i) q^{42} +2.33345 q^{43} +(2.57416 + 2.09134i) q^{44} -7.16083 q^{45} +(1.21756 + 3.74725i) q^{46} +(4.04528 + 2.93907i) q^{47} +(-2.57883 + 1.87363i) q^{48} +(0.309017 - 0.951057i) q^{49} +(0.309017 - 0.951057i) q^{50} +(1.93160 - 1.40339i) q^{51} +(-4.60413 - 3.34510i) q^{52} +(-3.32721 - 10.2401i) q^{53} +13.2631 q^{54} +(3.31180 + 0.178874i) q^{55} -1.00000 q^{56} +(6.68799 + 20.5835i) q^{57} +(4.64244 + 3.37293i) q^{58} +(-4.23038 + 3.07355i) q^{59} +(-0.985024 + 3.03159i) q^{60} +(2.37448 - 7.30790i) q^{61} +(5.75173 - 4.17887i) q^{62} +(5.79323 + 4.20903i) q^{63} +(0.309017 + 0.951057i) q^{64} -5.69102 q^{65} +(-10.5567 - 0.570180i) q^{66} -7.39587 q^{67} +(-0.231460 - 0.712362i) q^{68} +(-10.1608 - 7.38227i) q^{69} +(-0.809017 + 0.587785i) q^{70} +(-0.177744 + 0.547039i) q^{71} +(2.21282 - 6.81035i) q^{72} +(10.1697 - 7.38869i) q^{73} +(9.38862 + 6.82123i) q^{74} +(0.985024 + 3.03159i) q^{75} +6.78967 q^{76} +(-2.57416 - 2.09134i) q^{77} +18.1407 q^{78} +(2.11207 + 6.50029i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-16.8235 + 12.2230i) q^{81} +(3.53695 - 10.8856i) q^{82} +(3.25248 - 10.0101i) q^{83} +(2.57883 - 1.87363i) q^{84} +(-0.605971 - 0.440264i) q^{85} +(0.721074 + 2.21924i) q^{86} -18.2916 q^{87} +(-1.19352 + 3.09443i) q^{88} +4.80467 q^{89} +(-2.21282 - 6.81035i) q^{90} +(4.60413 + 3.34510i) q^{91} +(-3.18761 + 2.31593i) q^{92} +(-7.00305 + 21.5532i) q^{93} +(-1.54516 + 4.75552i) q^{94} +(5.49296 - 3.99087i) q^{95} +(-2.57883 - 1.87363i) q^{96} +(5.02824 + 15.4753i) q^{97} +1.00000 q^{98} +(19.9389 - 12.9032i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 5 q^{3} - 4 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{7} - 4 q^{8} + q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 5 * q^3 - 4 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^7 - 4 * q^8 + q^9	\( 16 q - 4 q^{2} - 5 q^{3} - 4 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{7} - 4 q^{8} + q^{9} - 16 q^{10} - 2 q^{11} + 8 q^{13} + 4 q^{14} + 5 q^{15} - 4 q^{16} - 13 q^{17} - 9 q^{18} + 15 q^{19} + 4 q^{20} - 2 q^{22} + 20 q^{23} + 5 q^{24} - 4 q^{25} - 7 q^{26} + 10 q^{27} + 4 q^{28} - 14 q^{29} + 5 q^{30} - 6 q^{31} + 16 q^{32} - 25 q^{33} + 12 q^{34} - 4 q^{35} - 9 q^{36} + 28 q^{37} - 20 q^{38} + 15 q^{39} + 4 q^{40} + 2 q^{41} - 5 q^{42} - 10 q^{43} + 3 q^{44} - 16 q^{45} - 10 q^{46} - 10 q^{47} - 5 q^{48} - 4 q^{49} - 4 q^{50} - 42 q^{51} - 7 q^{52} - 2 q^{53} - 3 q^{55} - 16 q^{56} + 21 q^{57} - 14 q^{58} + 7 q^{59} - 5 q^{60} + 4 q^{61} + 14 q^{62} + 9 q^{63} - 4 q^{64} + 2 q^{65} - 10 q^{66} + 66 q^{67} - 13 q^{68} - 64 q^{69} - 4 q^{70} + 2 q^{71} + q^{72} + 12 q^{73} + 28 q^{74} + 5 q^{75} + 10 q^{76} - 3 q^{77} + 70 q^{78} + 2 q^{79} + 4 q^{80} - 30 q^{81} - 13 q^{82} - 5 q^{83} + 5 q^{84} - 7 q^{85} + 5 q^{86} - 24 q^{87} - 2 q^{88} + 2 q^{89} - q^{90} + 7 q^{91} - 38 q^{93} + 25 q^{94} - 15 q^{95} - 5 q^{96} + 22 q^{97} + 16 q^{98} - 18 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 5 * q^3 - 4 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^7 - 4 * q^8 + q^9 - 16 * q^10 - 2 * q^11 + 8 * q^13 + 4 * q^14 + 5 * q^15 - 4 * q^16 - 13 * q^17 - 9 * q^18 + 15 * q^19 + 4 * q^20 - 2 * q^22 + 20 * q^23 + 5 * q^24 - 4 * q^25 - 7 * q^26 + 10 * q^27 + 4 * q^28 - 14 * q^29 + 5 * q^30 - 6 * q^31 + 16 * q^32 - 25 * q^33 + 12 * q^34 - 4 * q^35 - 9 * q^36 + 28 * q^37 - 20 * q^38 + 15 * q^39 + 4 * q^40 + 2 * q^41 - 5 * q^42 - 10 * q^43 + 3 * q^44 - 16 * q^45 - 10 * q^46 - 10 * q^47 - 5 * q^48 - 4 * q^49 - 4 * q^50 - 42 * q^51 - 7 * q^52 - 2 * q^53 - 3 * q^55 - 16 * q^56 + 21 * q^57 - 14 * q^58 + 7 * q^59 - 5 * q^60 + 4 * q^61 + 14 * q^62 + 9 * q^63 - 4 * q^64 + 2 * q^65 - 10 * q^66 + 66 * q^67 - 13 * q^68 - 64 * q^69 - 4 * q^70 + 2 * q^71 + q^72 + 12 * q^73 + 28 * q^74 + 5 * q^75 + 10 * q^76 - 3 * q^77 + 70 * q^78 + 2 * q^79 + 4 * q^80 - 30 * q^81 - 13 * q^82 - 5 * q^83 + 5 * q^84 - 7 * q^85 + 5 * q^86 - 24 * q^87 - 2 * q^88 + 2 * q^89 - q^90 + 7 * q^91 - 38 * q^93 + 25 * q^94 - 15 * q^95 - 5 * q^96 + 22 * q^97 + 16 * q^98 - 18 * q^99

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