LMFDB - Embedded newform 520.2.by.c.61.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(61,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 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("520.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.by (of order $6$, degree $2$, 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:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$52$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			61.8
Character	$\chi$	$=$	520.61
Dual form			520.2.by.c.341.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17635 - 0.784979i) q^{2} +(-2.41200 - 1.39257i) q^{3} +(0.767616 + 1.84683i) q^{4} +1.00000i q^{5} +(1.74423 + 3.53152i) q^{6} +(-0.704365 - 1.22000i) q^{7} +(0.546731 - 2.77508i) q^{8} +(2.37849 + 4.11966i) q^{9} +O(q^{10})$	\(q+(-1.17635 - 0.784979i) q^{2} +(-2.41200 - 1.39257i) q^{3} +(0.767616 + 1.84683i) q^{4} +1.00000i q^{5} +(1.74423 + 3.53152i) q^{6} +(-0.704365 - 1.22000i) q^{7} +(0.546731 - 2.77508i) q^{8} +(2.37849 + 4.11966i) q^{9} +(0.784979 - 1.17635i) q^{10} +(0.726457 + 0.419420i) q^{11} +(0.720341 - 5.52350i) q^{12} +(2.44780 + 2.64732i) q^{13} +(-0.129089 + 1.98806i) q^{14} +(1.39257 - 2.41200i) q^{15} +(-2.82153 + 2.83531i) q^{16} +(-0.473218 - 0.819638i) q^{17} +(0.435904 - 6.71324i) q^{18} +(4.18051 - 2.41362i) q^{19} +(-1.84683 + 0.767616i) q^{20} +3.92350i q^{21} +(-0.525334 - 1.06364i) q^{22} +(4.11754 - 7.13179i) q^{23} +(-5.18320 + 5.93213i) q^{24} -1.00000 q^{25} +(-0.801391 - 5.03565i) q^{26} -4.89341i q^{27} +(1.71244 - 2.23733i) q^{28} +(-4.61109 - 2.66221i) q^{29} +(-3.53152 + 1.74423i) q^{30} -3.68658 q^{31} +(5.54477 - 1.12048i) q^{32} +(-1.16814 - 2.02328i) q^{33} +(-0.0867266 + 1.33565i) q^{34} +(1.22000 - 0.704365i) q^{35} +(-5.78253 + 7.55497i) q^{36} +(-2.22424 - 1.28417i) q^{37} +(-6.81240 - 0.442343i) q^{38} +(-2.21752 - 9.79404i) q^{39} +(2.77508 + 0.546731i) q^{40} +(-0.759646 + 1.31575i) q^{41} +(3.07987 - 4.61543i) q^{42} +(-4.82468 + 2.78553i) q^{43} +(-0.216956 + 1.66359i) q^{44} +(-4.11966 + 2.37849i) q^{45} +(-10.4420 + 5.15733i) q^{46} -12.2962 q^{47} +(10.7539 - 2.90958i) q^{48} +(2.50774 - 4.34353i) q^{49} +(1.17635 + 0.784979i) q^{50} +2.63595i q^{51} +(-3.01016 + 6.55278i) q^{52} -6.16214i q^{53} +(-3.84122 + 5.75638i) q^{54} +(-0.419420 + 0.726457i) q^{55} +(-3.77069 + 1.28766i) q^{56} -13.4445 q^{57} +(3.33449 + 6.75131i) q^{58} +(6.36256 - 3.67343i) q^{59} +(5.52350 + 0.720341i) q^{60} +(5.68689 - 3.28333i) q^{61} +(4.33672 + 2.89388i) q^{62} +(3.35064 - 5.80349i) q^{63} +(-7.40217 - 3.03445i) q^{64} +(-2.64732 + 2.44780i) q^{65} +(-0.214085 + 3.29706i) q^{66} +(-3.23239 - 1.86622i) q^{67} +(1.15048 - 1.50312i) q^{68} +(-19.8630 + 11.4679i) q^{69} +(-1.98806 - 0.129089i) q^{70} +(-3.60632 - 6.24634i) q^{71} +(12.7328 - 4.34815i) q^{72} +9.00792 q^{73} +(1.60845 + 3.25662i) q^{74} +(2.41200 + 1.39257i) q^{75} +(7.66657 + 5.86795i) q^{76} -1.18170i q^{77} +(-5.07953 + 13.2620i) q^{78} +7.20112 q^{79} +(-2.83531 - 2.82153i) q^{80} +(0.321063 - 0.556098i) q^{81} +(1.92644 - 0.951476i) q^{82} -17.9498i q^{83} +(-7.24602 + 3.01174i) q^{84} +(0.819638 - 0.473218i) q^{85} +(7.86212 + 0.510503i) q^{86} +(7.41462 + 12.8425i) q^{87} +(1.56110 - 1.78667i) q^{88} +(6.88440 - 11.9241i) q^{89} +(6.71324 + 0.435904i) q^{90} +(1.50557 - 4.85098i) q^{91} +(16.3319 + 2.12990i) q^{92} +(8.89201 + 5.13380i) q^{93} +(14.4647 + 9.65225i) q^{94} +(2.41362 + 4.18051i) q^{95} +(-14.9343 - 5.01887i) q^{96} +(4.14886 + 7.18604i) q^{97} +(-6.35957 + 3.14101i) q^{98} +3.99034i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q + 2 q^{6} - 4 q^{7} + 12 q^{8} + 60 q^{9}+O(q^{10}) $ 104 * q + 2 * q^6 - 4 * q^7 + 12 * q^8 + 60 * q^9	$ 104 q + 2 q^{6} - 4 q^{7} + 12 q^{8} + 60 q^{9} - 28 q^{12} - 24 q^{14} + 4 q^{15} - 20 q^{16} + 4 q^{17} - 40 q^{18} - 4 q^{20} + 24 q^{22} + 32 q^{23} + 24 q^{24} - 104 q^{25} - 10 q^{26} + 22 q^{28} - 12 q^{30} - 40 q^{31} + 30 q^{32} + 12 q^{33} - 4 q^{34} + 18 q^{36} + 56 q^{39} - 16 q^{41} - 20 q^{42} - 32 q^{44} - 30 q^{46} - 56 q^{47} - 24 q^{48} - 80 q^{49} - 6 q^{52} - 10 q^{54} + 16 q^{55} - 38 q^{56} + 104 q^{57} - 68 q^{58} - 12 q^{62} + 12 q^{63} - 108 q^{64} + 180 q^{66} - 6 q^{68} + 8 q^{70} - 72 q^{71} - 80 q^{72} + 24 q^{73} + 40 q^{74} - 20 q^{76} - 52 q^{78} - 40 q^{79} - 24 q^{80} - 60 q^{81} + 64 q^{82} - 70 q^{84} + 140 q^{86} - 8 q^{87} + 86 q^{88} + 36 q^{89} - 20 q^{90} + 76 q^{92} + 46 q^{94} - 32 q^{95} + 12 q^{96} + 12 q^{97} - 8 q^{98}+O(q^{100}) $ 104 * q + 2 * q^6 - 4 * q^7 + 12 * q^8 + 60 * q^9 - 28 * q^12 - 24 * q^14 + 4 * q^15 - 20 * q^16 + 4 * q^17 - 40 * q^18 - 4 * q^20 + 24 * q^22 + 32 * q^23 + 24 * q^24 - 104 * q^25 - 10 * q^26 + 22 * q^28 - 12 * q^30 - 40 * q^31 + 30 * q^32 + 12 * q^33 - 4 * q^34 + 18 * q^36 + 56 * q^39 - 16 * q^41 - 20 * q^42 - 32 * q^44 - 30 * q^46 - 56 * q^47 - 24 * q^48 - 80 * q^49 - 6 * q^52 - 10 * q^54 + 16 * q^55 - 38 * q^56 + 104 * q^57 - 68 * q^58 - 12 * q^62 + 12 * q^63 - 108 * q^64 + 180 * q^66 - 6 * q^68 + 8 * q^70 - 72 * q^71 - 80 * q^72 + 24 * q^73 + 40 * q^74 - 20 * q^76 - 52 * q^78 - 40 * q^79 - 24 * q^80 - 60 * q^81 + 64 * q^82 - 70 * q^84 + 140 * q^86 - 8 * q^87 + 86 * q^88 + 36 * q^89 - 20 * q^90 + 76 * q^92 + 46 * q^94 - 32 * q^95 + 12 * q^96 + 12 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$1$

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 $

$2$	−1.17635	−	0.784979i	−0.831808	−	0.555064i
$2$	−1.17635	−	0.784979i	−0.831808	−	0.555064i
$3$	−2.41200	−	1.39257i	−1.39257	−	0.803999i	−0.398968	−	0.916965i	$-0.630632\pi$
$3$	−2.41200	−	1.39257i	−1.39257	−	0.803999i	−0.993599	+	0.112966i	$0.963965\pi$
$4$	0.767616	+	1.84683i	0.383808	+	0.923413i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	1.74423	+	3.53152i	0.712077	+	1.44174i
$7$	−0.704365	−	1.22000i	−0.266225	−	0.461115i	0.701659	−	0.712513i	$-0.252443\pi$
$7$	−0.704365	−	1.22000i	−0.266225	−	0.461115i	−0.967884	+	0.251398i	$0.919110\pi$
$8$	0.546731	−	2.77508i	0.193299	−	0.981140i
$9$	2.37849	+	4.11966i	0.792829	+	1.37322i
$10$	0.784979	−	1.17635i	0.248232	−	0.371996i
$11$	0.726457	+	0.419420i	0.219035	+	0.126460i	0.605503	−	0.795843i	$-0.292972\pi$
$11$	0.726457	+	0.419420i	0.219035	+	0.126460i	−0.386468	+	0.922303i	$0.626305\pi$
$12$	0.720341	−	5.52350i	0.207944	−	1.59450i
$13$	2.44780	+	2.64732i	0.678897	+	0.734233i
$13$	2.44780	+	2.64732i	0.678897	+	0.734233i
$14$	−0.129089	+	1.98806i	−0.0345004	+	0.531331i
$15$	1.39257	−	2.41200i	0.359559	−	0.622775i
$16$	−2.82153	+	2.83531i	−0.705383	+	0.708827i
$17$	−0.473218	−	0.819638i	−0.114772	−	0.198792i	0.802916	−	0.596092i	$-0.203281\pi$
$17$	−0.473218	−	0.819638i	−0.114772	−	0.198792i	−0.917689	+	0.397300i	$0.869947\pi$
$18$	0.435904	−	6.71324i	0.102744	−	1.58233i
$19$	4.18051	−	2.41362i	0.959076	−	0.553723i	0.0631871	−	0.998002i	$-0.479873\pi$
$19$	4.18051	−	2.41362i	0.959076	−	0.553723i	0.895888	+	0.444279i	$0.146540\pi$
$20$	−1.84683	+	0.767616i	−0.412963	+	0.171644i
$21$			3.92350i			0.856178i
$22$	−0.525334	−	1.06364i	−0.112002	−	0.226769i
$23$	4.11754	−	7.13179i	0.858567	−	1.48708i	−0.0147293	−	0.999892i	$-0.504689\pi$
$23$	4.11754	−	7.13179i	0.858567	−	1.48708i	0.873296	−	0.487190i	$-0.161978\pi$
$24$	−5.18320	+	5.93213i	−1.05802	+	1.21089i
$25$	−1.00000			−0.200000
$26$	−0.801391	−	5.03565i	−0.157166	−	0.987572i
$27$		−	4.89341i		−	0.941736i
$28$	1.71244	−	2.23733i	0.323620	−	0.422815i
$29$	−4.61109	−	2.66221i	−0.856258	−	0.494361i	0.00649955	−	0.999979i	$-0.497931\pi$
$29$	−4.61109	−	2.66221i	−0.856258	−	0.494361i	−0.862757	+	0.505618i	$0.831264\pi$
$30$	−3.53152	+	1.74423i	−0.644764	+	0.318451i
$31$	−3.68658			−0.662129			−0.331064	−	0.943608i	$-0.607408\pi$
$31$	−3.68658			−0.662129			−0.331064	+	0.943608i	$0.607408\pi$
$32$	5.54477	−	1.12048i	0.980187	−	0.198075i
$33$	−1.16814	−	2.02328i	−0.203347	−	0.352208i
$34$	−0.0867266	+	1.33565i	−0.0148735	+	0.229062i
$35$	1.22000	−	0.704365i	0.206217	−	0.119059i
$36$	−5.78253	+	7.55497i	−0.963755	+	1.25916i
$37$	−2.22424	−	1.28417i	−0.365663	−	0.211116i	0.305899	−	0.952064i	$-0.401043\pi$
$37$	−2.22424	−	1.28417i	−0.365663	−	0.211116i	−0.671562	+	0.740948i	$0.734376\pi$
$38$	−6.81240	−	0.442343i	−1.10512	−	0.0717576i
$39$	−2.21752	−	9.79404i	−0.355087	−	1.56830i
$40$	2.77508	+	0.546731i	0.438779	+	0.0864458i
$41$	−0.759646	+	1.31575i	−0.118637	+	0.205485i	−0.919228	−	0.393726i	$-0.871186\pi$
$41$	−0.759646	+	1.31575i	−0.118637	+	0.205485i	0.800591	+	0.599211i	$0.204519\pi$
$42$	3.07987	−	4.61543i	0.475234	−	0.712176i
$43$	−4.82468	+	2.78553i	−0.735757	+	0.424790i	−0.820525	−	0.571611i	$-0.806319\pi$
$43$	−4.82468	+	2.78553i	−0.735757	+	0.424790i	0.0847674	+	0.996401i	$0.472985\pi$
$44$	−0.216956	+	1.66359i	−0.0327073	+	0.250796i
$45$	−4.11966	+	2.37849i	−0.614123	+	0.354564i
$46$	−10.4420	+	5.15733i	−1.53959	+	0.760406i
$47$	−12.2962			−1.79358			−0.896792	−	0.442453i	$-0.854108\pi$
$47$	−12.2962			−1.79358			−0.896792	+	0.442453i	$0.854108\pi$
$48$	10.7539	−	2.90958i	1.55219	−	0.419962i
$49$	2.50774	−	4.34353i	0.358249	−	0.620505i
$50$	1.17635	+	0.784979i	0.166362	+	0.111013i
$51$			2.63595i			0.369107i
$52$	−3.01016	+	6.55278i	−0.417434	+	0.908707i
$53$		−	6.16214i		−	0.846436i	−0.906028	−	0.423218i	$-0.860900\pi$
$53$		−	6.16214i		−	0.846436i	0.906028	−	0.423218i	$-0.139100\pi$
$54$	−3.84122	+	5.75638i	−0.522724	+	0.783344i
$55$	−0.419420	+	0.726457i	−0.0565546	+	0.0979554i
$56$	−3.77069	+	1.28766i	−0.503879	+	0.172071i
$57$	−13.4445			−1.78077
$58$	3.33449	+	6.75131i	0.437840	+	0.886491i
$59$	6.36256	−	3.67343i	0.828335	−	0.478239i	−0.0249472	−	0.999689i	$-0.507942\pi$
$59$	6.36256	−	3.67343i	0.828335	−	0.478239i	0.853282	+	0.521449i	$0.174608\pi$
$60$	5.52350	+	0.720341i	0.713080	+	0.0929956i
$61$	5.68689	−	3.28333i	0.728132	−	0.420387i	−0.0896067	−	0.995977i	$-0.528561\pi$
$61$	5.68689	−	3.28333i	0.728132	−	0.420387i	0.817738	+	0.575590i	$0.195228\pi$
$62$	4.33672	+	2.89388i	0.550764	+	0.367524i
$63$	3.35064	−	5.80349i	0.422142	−	0.731171i
$64$	−7.40217	−	3.03445i	−0.925271	−	0.379306i
$65$	−2.64732	+	2.44780i	−0.328359	+	0.303612i
$66$	−0.214085	+	3.29706i	−0.0263520	+	0.405840i
$67$	−3.23239	−	1.86622i	−0.394900	−	0.227995i	0.289381	−	0.957214i	$-0.406550\pi$
$67$	−3.23239	−	1.86622i	−0.394900	−	0.227995i	−0.684281	+	0.729219i	$0.739884\pi$
$68$	1.15048	−	1.50312i	0.139516	−	0.182280i
$69$	−19.8630	+	11.4679i	−2.39122	+	1.38057i
$70$	−1.98806	−	0.129089i	−0.237618	−	0.0154290i
$71$	−3.60632	−	6.24634i	−0.427992	−	0.741304i	0.568703	−	0.822543i	$-0.307446\pi$
$71$	−3.60632	−	6.24634i	−0.427992	−	0.741304i	−0.996695	+	0.0812394i	$0.974112\pi$
$72$	12.7328	−	4.34815i	1.50057	−	0.512435i
$73$	9.00792			1.05430			0.527149	−	0.849773i	$-0.323261\pi$
$73$	9.00792			1.05430			0.527149	+	0.849773i	$0.323261\pi$
$74$	1.60845	+	3.25662i	0.186979	+	0.378574i
$75$	2.41200	+	1.39257i	0.278513	+	0.160800i
$76$	7.66657	+	5.86795i	0.879415	+	0.673099i
$77$		−	1.18170i		−	0.134667i
$78$	−5.07953	+	13.2620i	−0.575143	+	1.50162i
$79$	7.20112			0.810189			0.405095	−	0.914275i	$-0.367239\pi$
$79$	7.20112			0.810189			0.405095	+	0.914275i	$0.367239\pi$
$80$	−2.83531	−	2.82153i	−0.316997	−	0.315457i
$81$	0.321063	−	0.556098i	0.0356737	−	0.0617887i
$82$	1.92644	−	0.951476i	0.212740	−	0.105073i
$83$		−	17.9498i		−	1.97025i	−0.171846	−	0.985124i	$-0.554973\pi$
$83$		−	17.9498i		−	1.97025i	0.171846	−	0.985124i	$-0.445027\pi$
$84$	−7.24602	+	3.01174i	−0.790606	+	0.328608i
$85$	0.819638	−	0.473218i	0.0889023	−	0.0513277i
$86$	7.86212	+	0.510503i	0.847794	+	0.0550490i
$87$	7.41462	+	12.8425i	0.794931	+	1.37686i
$88$	1.56110	−	1.78667i	0.166414	−	0.190459i
$89$	6.88440	−	11.9241i	0.729745	−	1.26396i	−0.227246	−	0.973837i	$-0.572972\pi$
$89$	6.88440	−	11.9241i	0.729745	−	1.26396i	0.956991	−	0.290118i	$-0.0936947\pi$
$90$	6.71324	+	0.435904i	0.707637	+	0.0459483i
$91$	1.50557	−	4.85098i	0.157827	−	0.508521i
$92$	16.3319	+	2.12990i	1.70271	+	0.222058i
$93$	8.89201	+	5.13380i	0.922058	+	0.532351i
$94$	14.4647	+	9.65225i	1.49192	+	0.995553i
$95$	2.41362	+	4.18051i	0.247632	+	0.428912i
$96$	−14.9343	−	5.01887i	−1.52423	−	0.512236i
$97$	4.14886	+	7.18604i	0.421253	+	0.729631i	0.996062	−	0.0886559i	$-0.0282571\pi$
$97$	4.14886	+	7.18604i	0.421253	+	0.729631i	−0.574809	+	0.818287i	$0.694924\pi$
$98$	−6.35957	+	3.14101i	−0.642414	+	0.317290i
$99$			3.99034i			0.401044i
$100$	−0.767616	−	1.84683i	−0.0767616	−	0.184683i
$101$	−0.0705030	−	0.0407049i	−0.00701531	−	0.00405029i	0.496488	−	0.868043i	$-0.334623\pi$
$101$	−0.0705030	−	0.0407049i	−0.00701531	−	0.00405029i	−0.503504	+	0.863993i	$0.667956\pi$
$102$	2.06917	−	3.10081i	0.204878	−	0.307026i
$103$	9.93823			0.979243			0.489622	−	0.871935i	$-0.337135\pi$
$103$	9.93823			0.979243			0.489622	+	0.871935i	$0.337135\pi$
$104$	8.68481	−	5.34548i	0.851615	−	0.524167i
$105$	−3.92350			−0.382895
$106$	−4.83715	+	7.24886i	−0.469826	+	0.704072i
$107$	1.38920	+	0.802053i	0.134299	+	0.0775374i	0.565644	−	0.824649i	$-0.308628\pi$
$107$	1.38920	+	0.802053i	0.134299	+	0.0775374i	−0.431345	+	0.902187i	$0.641961\pi$
$108$	9.03727	−	3.75626i	0.869611	−	0.361446i
$109$			4.99678i			0.478604i	0.970945	+	0.239302i	$0.0769187\pi$
$109$			4.99678i			0.478604i	−0.970945	+	0.239302i	$0.923081\pi$
$110$	1.06364	−	0.525334i	0.101414	−	0.0500887i
$111$	3.57658	+	6.19482i	0.339474	+	0.587986i
$112$	5.44645	+	1.44516i	0.514641	+	0.136555i
$113$	1.20744	+	2.09134i	0.113586	+	0.196737i	0.917214	−	0.398396i	$-0.130433\pi$
$113$	1.20744	+	2.09134i	0.113586	+	0.196737i	−0.803628	+	0.595132i	$0.797100\pi$
$114$	15.8155	+	10.5537i	1.48126	+	0.988441i
$115$	7.13179	+	4.11754i	0.665043	+	0.383963i
$116$	1.37710	−	10.5594i	0.127860	−	0.980419i
$117$	−5.08398	+	16.3807i	−0.470014	+	1.51440i
$118$	−10.3682	−	0.673227i	−0.954469	−	0.0619756i
$119$	−0.666637	+	1.15465i	−0.0611105	+	0.105847i
$120$	−5.93213	−	5.18320i	−0.541527	−	0.473160i
$121$	−5.14817	−	8.91690i	−0.468016	−	0.810627i
$122$	−9.26714	−	0.601734i	−0.839007	−	0.0544784i
$123$	3.66453	−	2.11572i	0.330419	−	0.190768i
$124$	−2.82988	−	6.80846i	−0.254130	−	0.611418i
$125$		−	1.00000i		−	0.0894427i
$126$	−8.49716	+	4.19677i	−0.756987	+	0.373878i
$127$	−6.04223	+	10.4655i	−0.536161	+	0.928659i	0.462945	+	0.886387i	$0.346793\pi$
$127$	−6.04223	+	10.4655i	−0.536161	+	0.928659i	−0.999106	+	0.0422717i	$0.986540\pi$
$128$	6.32559	+	9.38013i	0.559109	+	0.829094i
$129$	15.5162			1.36612
$130$	5.03565	−	0.801391i	0.441656	−	0.0702866i
$131$		−	21.5840i		−	1.88581i	−0.333068	−	0.942903i	$-0.608084\pi$
$131$		−	21.5840i		−	1.88581i	0.333068	−	0.942903i	$-0.391916\pi$
$132$	2.83996	−	3.71045i	0.247187	−	0.322954i
$133$	−5.88921	−	3.40014i	−0.510660	−	0.294829i
$134$	2.33749	+	4.73270i	0.201929	+	0.408843i
$135$	4.89341			0.421157
$136$	−2.53329	+	0.865099i	−0.217228	+	0.0741816i
$137$	−6.19845	−	10.7360i	−0.529569	−	0.917241i	−0.999405	−	0.0344871i	$-0.989020\pi$
$137$	−6.19845	−	10.7360i	−0.529569	−	0.917241i	0.469836	−	0.882754i	$-0.344313\pi$
$138$	32.3680	+	2.10172i	2.75535	+	0.178910i
$139$	0.662867	−	0.382706i	0.0562236	−	0.0324607i	−0.471625	−	0.881799i	$-0.656332\pi$
$139$	0.662867	−	0.382706i	0.0562236	−	0.0324607i	0.527848	+	0.849339i	$0.322999\pi$
$140$	2.23733	+	1.71244i	0.189089	+	0.144727i
$141$	29.6584	+	17.1233i	2.49769	+	1.44204i
$142$	−0.660930	+	10.1788i	−0.0554640	+	0.854185i
$143$	0.667883	+	2.94982i	0.0558512	+	0.246676i
$144$	−18.3915	−	4.88001i	−1.53262	−	0.406667i
$145$	2.66221	−	4.61109i	0.221085	−	0.382930i
$146$	−10.5965	−	7.07103i	−0.876973	−	0.585203i
$147$	−12.0973	+	6.98439i	−0.997770	+	0.576063i
$148$	0.664268	−	5.09354i	0.0546025	−	0.418686i
$149$	−14.3312	+	8.27411i	−1.17406	+	0.677841i	−0.954632	−	0.297788i	$-0.903751\pi$
$149$	−14.3312	+	8.27411i	−1.17406	+	0.677841i	−0.219424	+	0.975630i	$0.570418\pi$
$150$	−1.74423	−	3.53152i	−0.142415	−	0.288347i
$151$	−11.0999			−0.903293			−0.451647	−	0.892197i	$-0.649163\pi$
$151$	−11.0999			−0.903293			−0.451647	+	0.892197i	$0.649163\pi$
$152$	−4.41238	−	12.9209i	−0.357891	−	1.04802i
$153$	2.25109	−	3.89900i	0.181990	−	0.315215i
$154$	−0.927609	+	1.39010i	−0.0747488	+	0.112017i
$155$		−	3.68658i		−	0.296113i
$156$	16.3857	−	11.6134i	1.31190	−	0.929819i
$157$			11.3760i			0.907901i	0.891027	+	0.453951i	$0.149986\pi$
$157$			11.3760i			0.907901i	−0.891027	+	0.453951i	$0.850014\pi$
$158$	−8.47106	−	5.65273i	−0.673922	−	0.449707i
$159$	−8.58120	+	14.8631i	−0.680533	+	1.17872i
$160$	1.12048	+	5.54477i	0.0885819	+	0.438353i
$161$	−11.6010			−0.914288
$162$	−0.814210	+	0.402140i	−0.0639703	+	0.0315951i
$163$	−12.6902	+	7.32669i	−0.993974	+	0.573871i	−0.906460	−	0.422292i	$-0.861226\pi$
$163$	−12.6902	+	7.32669i	−0.993974	+	0.573871i	−0.0875139	+	0.996163i	$0.527892\pi$
$164$	−3.01307	−	0.392946i	−0.235281	−	0.0306839i
$165$	2.02328	−	1.16814i	0.157512	−	0.0909396i
$166$	−14.0902	+	21.1153i	−1.09361	+	1.63887i
$167$	−5.24065	+	9.07707i	−0.405534	+	0.702405i	−0.994383	−	0.105838i	$-0.966248\pi$
$167$	−5.24065	+	9.07707i	−0.405534	+	0.702405i	0.588850	+	0.808243i	$0.299581\pi$
$168$	10.8880	+	2.14510i	0.840031	+	0.165498i
$169$	−1.01656	+	12.9602i	−0.0781967	+	0.996938i
$170$	−1.33565	−	0.0867266i	−0.102440	−	0.00665162i
$171$	19.8866	+	11.4815i	1.52077	+	0.878014i
$172$	−8.84790	−	6.77213i	−0.674646	−	0.516370i
$173$	14.7580	−	8.52054i	1.12203	−	0.647805i	0.180112	−	0.983646i	$-0.442354\pi$
$173$	14.7580	−	8.52054i	1.12203	−	0.647805i	0.941919	+	0.335841i	$0.109021\pi$
$174$	1.35887	−	20.9276i	0.103016	−	1.58652i
$175$	0.704365	+	1.22000i	0.0532450	+	0.0922230i
$176$	−3.23890	+	0.876321i	−0.244142	+	0.0660552i
$177$	−20.4620			−1.53802
$178$	−17.4587	+	8.62289i	−1.30858	+	0.646313i
$179$	19.8001	+	11.4316i	1.47993	+	0.854438i	0.999742	−	0.0227268i	$-0.00723479\pi$
$179$	19.8001	+	11.4316i	1.47993	+	0.854438i	0.480189	+	0.877165i	$0.340568\pi$
$180$	−7.55497	−	5.78253i	−0.563114	−	0.431004i
$181$		−	3.51196i		−	0.261042i	−0.991446	−	0.130521i	$-0.958335\pi$
$181$		−	3.51196i		−	0.261042i	0.991446	−	0.130521i	$-0.0416649\pi$
$182$	−5.57900	+	4.52463i	−0.413543	+	0.335388i
$183$	−18.2890			−1.35196
$184$	−17.5401	−	15.3257i	−1.29308	−	1.12982i
$185$	1.28417	−	2.22424i	0.0944139	−	0.163530i
$186$	−6.43022	−	13.0192i	−0.471487	−	0.954615i
$187$		−	0.793909i		−	0.0580564i
$188$	−9.43875	−	22.7089i	−0.688392	−	1.65622i
$189$	−5.96993	+	3.44674i	−0.434249	+	0.250714i
$190$	0.442343	−	6.81240i	0.0320910	−	0.494224i
$191$	7.63900	+	13.2311i	0.552738	+	0.957371i	0.998076	+	0.0620080i	$0.0197504\pi$
$191$	7.63900	+	13.2311i	0.552738	+	0.957371i	−0.445337	+	0.895363i	$0.646916\pi$
$192$	13.6283	+	17.6271i	0.983541	+	1.27213i
$193$	10.9703	−	19.0012i	0.789662	−	1.36773i	−0.136512	−	0.990638i	$-0.543589\pi$
$193$	10.9703	−	19.0012i	0.789662	−	1.36773i	0.926174	−	0.377096i	$-0.123077\pi$
$194$	0.760360	−	11.7101i	0.0545907	−	0.840735i
$195$	9.79404	−	2.21752i	0.701366	−	0.158800i
$196$	9.94673	+	1.29719i	0.710481	+	0.0926566i
$197$	−12.4655	−	7.19698i	−0.888133	−	0.512764i	−0.0148018	−	0.999890i	$-0.504712\pi$
$197$	−12.4655	−	7.19698i	−0.888133	−	0.512764i	−0.873331	+	0.487127i	$0.838045\pi$
$198$	3.13233	−	4.69405i	0.222605	−	0.333592i
$199$	−6.44767	−	11.1677i	−0.457063	−	0.791657i	0.541741	−	0.840546i	$-0.317765\pi$
$199$	−6.44767	−	11.1677i	−0.457063	−	0.791657i	−0.998804	+	0.0488886i	$0.984432\pi$
$200$	−0.546731	+	2.77508i	−0.0386597	+	0.196228i
$201$	5.19768	+	9.00265i	0.366616	+	0.634998i
$202$	0.0509840	+	0.103227i	0.00358722	+	0.00726301i
$203$			7.50068i			0.526445i
$204$	−4.86815	+	2.02340i	−0.340839	+	0.141666i
$205$	−1.31575	−	0.759646i	−0.0918956	−	0.0530560i
$206$	−11.6909	−	7.80130i	−0.814542	−	0.543543i
$207$	39.1741			2.72279
$208$	−14.4125	−	0.529219i	−0.999327	−	0.0366948i
$209$	4.04928			0.280095
$210$	4.61543	+	3.07987i	0.318495	+	0.212531i
$211$	16.7535	+	9.67264i	1.15336	+	0.665892i	0.949703	−	0.313151i	$-0.101385\pi$
$211$	16.7535	+	9.67264i	1.15336	+	0.665892i	0.203655	+	0.979043i	$0.434718\pi$
$212$	11.3804	−	4.73016i	0.781610	−	0.324869i
$213$			20.0882i			1.37642i
$214$	−1.00459	−	2.03399i	−0.0686725	−	0.139041i
$215$	−2.78553	−	4.82468i	−0.189972	−	0.329041i
$216$	−13.5796	−	2.67538i	−0.923975	−	0.182036i
$217$	2.59669	+	4.49761i	0.176275	+	0.305317i
$218$	3.92236	−	5.87798i	0.265656	−	0.398107i
$219$	−21.7271	−	12.5441i	−1.46818	−	0.847654i
$220$	−1.66359	−	0.216956i	−0.112159	−	0.0146271i
$221$	1.01150	−	3.25907i	0.0680407	−	0.219229i
$222$	0.655478	−	10.0948i	0.0439928	−	0.677521i
$223$	−0.311995	+	0.540391i	−0.0208927	+	0.0361872i	−0.876283	−	0.481797i	$-0.839984\pi$
$223$	−0.311995	+	0.540391i	−0.0208927	+	0.0361872i	0.855390	+	0.517984i	$0.173318\pi$
$224$	−5.27253	−	5.97537i	−0.352286	−	0.399246i
$225$	−2.37849	−	4.11966i	−0.158566	−	0.274644i
$226$	0.221286	−	3.40797i	0.0147197	−	0.226695i
$227$	9.26146	−	5.34710i	0.614704	−	0.354900i	−0.160100	−	0.987101i	$-0.551182\pi$
$227$	9.26146	−	5.34710i	0.614704	−	0.354900i	0.774804	+	0.632201i	$0.217848\pi$
$228$	−10.3202	−	24.8297i	−0.683474	−	1.64439i
$229$		−	22.9566i		−	1.51702i	−0.651663	−	0.758509i	$-0.725928\pi$
$229$		−	22.9566i		−	1.51702i	0.651663	−	0.758509i	$-0.274072\pi$
$230$	−5.15733	−	10.4420i	−0.340064	−	0.688525i
$231$	−1.64559	+	2.85025i	−0.108272	+	0.187533i
$232$	−9.90889	+	11.3406i	−0.650550	+	0.744550i
$233$	22.2049			1.45469			0.727346	−	0.686271i	$-0.240753\pi$
$233$	22.2049			1.45469			0.727346	+	0.686271i	$0.240753\pi$
$234$	18.8391	−	15.2787i	1.23155	−	0.998799i
$235$		−	12.2962i		−	0.802115i
$236$	11.6682	+	8.93076i	0.759534	+	0.581343i
$237$	−17.3691	−	10.0280i	−1.12824	−	0.651391i
$238$	1.69058	−	0.834980i	0.109584	−	0.0541237i
$239$	−14.1393			−0.914598			−0.457299	−	0.889313i	$-0.651183\pi$
$239$	−14.1393			−0.914598			−0.457299	+	0.889313i	$0.651183\pi$
$240$	2.90958	+	10.7539i	0.187813	+	0.694160i
$241$	12.8223	+	22.2088i	0.825955	+	1.43060i	0.901187	+	0.433430i	$0.142697\pi$
$241$	12.8223	+	22.2088i	0.825955	+	1.43060i	−0.0752321	+	0.997166i	$0.523970\pi$
$242$	−0.943504	+	14.5306i	−0.0606507	+	0.934065i
$243$	−14.2622	+	8.23431i	−0.914924	+	0.528231i
$244$	10.4291	+	7.98236i	0.667654	+	0.511018i
$245$	4.34353	+	2.50774i	0.277498	+	0.160214i
$246$	−5.97157	−	0.387746i	−0.380734	−	0.0247218i
$247$	16.6227	+	5.15908i	1.05768	+	0.328264i
$248$	−2.01557	+	10.2306i	−0.127989	+	0.649641i
$249$	−24.9963	+	43.2949i	−1.58408	+	2.74370i
$250$	−0.784979	+	1.17635i	−0.0496464	+	0.0743991i
$251$	−5.74460	+	3.31665i	−0.362596	+	0.209345i	−0.670219	−	0.742163i	$-0.733800\pi$
$251$	−5.74460	+	3.31665i	−0.362596	+	0.209345i	0.307623	+	0.951508i	$0.400466\pi$
$252$	13.2900	+	1.73321i	0.837194	+	0.109182i
$253$	5.98243	−	3.45396i	0.376112	−	0.217149i
$254$	15.3230	−	7.56805i	0.961448	−	0.474862i
$255$	−2.63595			−0.165070
$256$	−0.0779303	−	15.9998i	−0.00487064	−	0.999988i
$257$	−3.12066	+	5.40515i	−0.194662	+	0.337164i	−0.946790	−	0.321853i	$-0.895694\pi$
$257$	−3.12066	+	5.40515i	−0.194662	+	0.337164i	0.752128	+	0.659017i	$0.229028\pi$
$258$	−18.2525	−	12.1799i	−1.13635	−	0.758285i
$259$			3.61809i			0.224817i
$260$	−6.55278	−	3.01016i	−0.406386	−	0.186682i
$261$		−	25.3282i		−	1.56777i
$262$	−16.9430	+	25.3905i	−1.04674	+	1.56863i
$263$	−13.0918	+	22.6757i	−0.807276	+	1.39824i	0.107468	+	0.994209i	$0.465726\pi$
$263$	−13.0918	+	22.6757i	−0.807276	+	1.39824i	−0.914744	+	0.404034i	$0.867608\pi$
$264$	−6.25343	+	2.13550i	−0.384872	+	0.131431i
$265$	6.16214			0.378538
$266$	4.25876	+	8.62268i	0.261121	+	0.528690i
$267$	−33.2103	+	19.1740i	−2.03244	+	1.17343i
$268$	0.965351	−	7.40221i	0.0589682	−	0.452162i
$269$	23.3150	−	13.4609i	1.42154	−	0.820728i	0.425111	−	0.905141i	$-0.360235\pi$
$269$	23.3150	−	13.4609i	1.42154	−	0.820728i	0.996431	+	0.0844135i	$0.0269017\pi$
$270$	−5.75638	−	3.84122i	−0.350322	−	0.233769i
$271$	6.37358	−	11.0394i	0.387168	−	0.670594i	−0.604900	−	0.796302i	$-0.706787\pi$
$271$	6.37358	−	11.0394i	0.387168	−	0.670594i	0.992067	+	0.125708i	$0.0401201\pi$
$272$	3.65913	+	0.970915i	0.221867	+	0.0588704i
$273$	−10.3867	+	9.60395i	−0.628635	+	0.581257i
$274$	−1.13599	+	17.4950i	−0.0686275	+	1.05691i
$275$	−0.726457	−	0.419420i	−0.0438070	−	0.0252920i
$276$	−36.4264	−	27.8805i	−2.19261	−	1.67821i
$277$	1.37891	−	0.796117i	0.0828510	−	0.0478340i	−0.458002	−	0.888951i	$-0.651435\pi$
$277$	1.37891	−	0.796117i	0.0828510	−	0.0478340i	0.540853	+	0.841117i	$0.318101\pi$
$278$	−1.08018	−	0.0701384i	−0.0647850	−	0.00420662i
$279$	−8.76847	−	15.1874i	−0.524955	−	0.909248i
$280$	−1.28766	−	3.77069i	−0.0769525	−	0.225342i
$281$	−16.8162			−1.00317			−0.501587	−	0.865107i	$-0.667250\pi$
$281$	−16.8162			−1.00317			−0.501587	+	0.865107i	$0.667250\pi$
$282$	−21.4473	−	43.4242i	−1.27717	−	2.58587i
$283$	−13.7650	−	7.94720i	−0.818242	−	0.472412i	0.0315679	−	0.999502i	$-0.489950\pi$
$283$	−13.7650	−	7.94720i	−0.818242	−	0.472412i	−0.849810	+	0.527089i	$0.823283\pi$
$284$	8.76762	−	11.4550i	0.520263	−	0.679732i
$285$		−	13.4445i		−	0.796384i
$286$	1.52988	−	3.99430i	0.0904635	−	0.236188i
$287$	2.14027			0.126336
$288$	17.8042	+	20.1775i	1.04912	+	1.18897i
$289$	8.05213	−	13.9467i	0.473655	−	0.820394i
$290$	−6.75131	+	3.33449i	−0.396451	+	0.195808i
$291$		−	23.1103i		−	1.35475i
$292$	6.91463	+	16.6361i	0.404648	+	0.973552i
$293$	−20.3057	+	11.7235i	−1.18627	+	0.684894i	−0.957457	−	0.288576i	$-0.906818\pi$
$293$	−20.3057	+	11.7235i	−1.18627	+	0.684894i	−0.228814	+	0.973470i	$0.573485\pi$
$294$	19.7133	+	1.28003i	1.14970	+	0.0746527i
$295$	3.67343	+	6.36256i	0.213875	+	0.370443i
$296$	−4.77974	+	5.47037i	−0.277816	+	0.317959i
$297$	2.05239	−	3.55485i	0.119092	−	0.206273i
$298$	23.3535	+	1.51639i	1.35283	+	0.0878423i
$299$	28.9590	−	6.55676i	1.67474	−	0.379187i
$300$	−0.720341	+	5.52350i	−0.0415889	+	0.318899i
$301$	6.79668	+	3.92406i	0.391754	+	0.226179i
$302$	13.0574	+	8.71315i	0.751366	+	0.501385i
$303$	0.113369	+	0.196360i	0.00651286	+	0.0112806i
$304$	−4.95209	+	18.6631i	−0.284022	+	1.07040i
$305$	3.28333	+	5.68689i	0.188003	+	0.325630i
$306$	−5.70871	+	2.81954i	−0.326345	+	0.161183i
$307$		−	8.81938i		−	0.503349i	−0.967812	−	0.251674i	$-0.919019\pi$
$307$		−	8.81938i		−	0.503349i	0.967812	−	0.251674i	$-0.0809812\pi$
$308$	2.18239	−	0.907091i	0.124353	−	0.0516863i
$309$	−23.9710	−	13.8397i	−1.36366	−	0.787311i
$310$	−2.89388	+	4.33672i	−0.164362	+	0.246309i
$311$	−11.2591			−0.638443			−0.319221	−	0.947680i	$-0.603421\pi$
$311$	−11.2591			−0.638443			−0.319221	+	0.947680i	$0.603421\pi$
$312$	−28.3917	+	0.799096i	−1.60736	+	0.0452399i
$313$	14.6983			0.830796			0.415398	−	0.909640i	$-0.363642\pi$
$313$	14.6983			0.830796			0.415398	+	0.909640i	$0.363642\pi$
$314$	8.92990	−	13.3822i	0.503943	−	0.755199i
$315$	5.80349	+	3.35064i	0.326989	+	0.188787i
$316$	5.52770	+	13.2992i	0.310957	+	0.748139i
$317$			9.23017i			0.518418i	0.965821	+	0.259209i	$0.0834619\pi$
$317$			9.23017i			0.518418i	−0.965821	+	0.259209i	$0.916538\pi$
$318$	21.7617	−	10.7482i	1.22034	−	0.602728i
$319$	−2.23317	−	3.86797i	−0.125034	−	0.216565i
$320$	3.03445	−	7.40217i	0.169631	−	0.413794i
$321$	−2.23383	−	3.86910i	−0.124680	−	0.215952i
$322$	13.6469	+	9.10655i	0.760511	+	0.507488i
$323$	−3.95659	−	2.28434i	−0.220151	−	0.127104i
$324$	1.27347	+	0.166078i	0.0707483	+	0.00922657i
$325$	−2.44780	−	2.64732i	−0.135779	−	0.146847i
$326$	20.6795	+	1.34276i	1.14533	+	0.0743686i
$327$	6.95835	−	12.0522i	0.384798	−	0.666489i
$328$	3.23598	+	2.82744i	0.178677	+	0.156119i
$329$	8.66100	+	15.0013i	0.477497	+	0.827048i
$330$	−3.29706	−	0.214085i	−0.181497	−	0.0117850i
$331$	−22.0255	+	12.7164i	−1.21063	+	0.698957i	−0.962896	−	0.269872i	$-0.913019\pi$
$331$	−22.0255	+	12.7164i	−1.21063	+	0.698957i	−0.247732	+	0.968828i	$0.579685\pi$
$332$	33.1502	−	13.7786i	1.81935	−	0.756197i
$333$		−	12.2175i		−	0.669515i
$334$	13.2902	−	6.56405i	0.727206	−	0.359169i
$335$	1.86622	−	3.23239i	0.101963	−	0.176604i
$336$	−11.1243	−	11.0703i	−0.606882	−	0.603933i
$337$	−10.8720			−0.592238			−0.296119	−	0.955151i	$-0.595693\pi$
$337$	−10.8720			−0.592238			−0.296119	+	0.955151i	$0.595693\pi$
$338$	11.3693	−	14.4478i	0.618409	−	0.785856i
$339$		−	6.72574i		−	0.365292i
$340$	1.50312	+	1.15048i	0.0815181	+	0.0623935i
$341$	−2.67814	−	1.54622i	−0.145029	−	0.0837327i
$342$	−14.3809	−	29.1169i	−0.777630	−	1.57446i
$343$	−16.9266			−0.913949
$344$	5.09228	+	14.9118i	0.274557	+	0.803992i
$345$	−11.4679	−	19.8630i	−0.617411	−	1.06939i
$346$	−24.0491	−	1.56156i	−1.29289	−	0.0839498i
$347$	12.5334	−	7.23619i	0.672830	−	0.388459i	−0.124318	−	0.992242i	$-0.539674\pi$
$347$	12.5334	−	7.23619i	0.672830	−	0.388459i	0.797148	+	0.603784i	$0.206341\pi$
$348$	−18.0263	+	23.5516i	−0.966310	+	1.26250i
$349$	3.05706	+	1.76499i	0.163640	+	0.0944779i	0.579584	−	0.814913i	$-0.303215\pi$
$349$	3.05706	+	1.76499i	0.163640	+	0.0944779i	−0.415943	+	0.909391i	$0.636549\pi$
$350$	0.129089	−	1.98806i	0.00690008	−	0.106266i
$351$	12.9544	−	11.9781i	0.691454	−	0.639342i
$352$	4.49799	+	1.51161i	0.239744	+	0.0805689i
$353$	−6.96359	+	12.0613i	−0.370635	+	0.641958i	−0.989663	−	0.143410i	$-0.954193\pi$
$353$	−6.96359	+	12.0613i	−0.370635	+	0.641958i	0.619029	+	0.785368i	$0.287526\pi$
$354$	24.0705	+	16.0622i	1.27933	+	0.853697i
$355$	6.24634	−	3.60632i	0.331521	−	0.191404i
$356$	27.3064	+	3.56113i	1.44724	+	0.188740i
$357$	3.21585	−	1.85667i	0.170201	−	0.0982656i
$358$	−14.3184	−	28.9903i	−0.756750	−	1.53218i
$359$	−23.3055			−1.23002			−0.615010	−	0.788519i	$-0.710848\pi$
$359$	−23.3055			−1.23002			−0.615010	+	0.788519i	$0.710848\pi$
$360$	4.34815	+	12.7328i	0.229168	+	0.671077i
$361$	2.15113	−	3.72586i	0.113217	−	0.196098i
$362$	−2.75681	+	4.13130i	−0.144895	+	0.217136i
$363$			28.6767i			1.50514i
$364$	10.1146	−	0.943167i	0.530150	−	0.0494354i
$365$			9.00792i			0.471496i
$366$	21.5144	+	14.3565i	1.12457	+	0.750426i
$367$	18.1432	−	31.4249i	0.947066	−	1.64037i	0.195506	−	0.980703i	$-0.437365\pi$
$367$	18.1432	−	31.4249i	0.947066	−	1.64037i	0.751560	−	0.659664i	$-0.229302\pi$
$368$	8.60305	+	31.7971i	0.448465	+	1.65754i
$369$	−7.22723			−0.376235
$370$	−3.25662	+	1.60845i	−0.169304	+	0.0836195i
$371$	−7.51779	+	4.34040i	−0.390304	+	0.225342i
$372$	−2.65559	+	20.3628i	−0.137686	+	1.05576i
$373$	14.7888	−	8.53833i	0.765736	−	0.442098i	−0.0656153	−	0.997845i	$-0.520901\pi$
$373$	14.7888	−	8.53833i	0.765736	−	0.442098i	0.831351	+	0.555747i	$0.187568\pi$
$374$	−0.623202	+	0.933918i	−0.0322250	+	0.0482917i
$375$	−1.39257	+	2.41200i	−0.0719119	+	0.124555i
$376$	−6.72271	+	34.1229i	−0.346697	+	1.75976i
$377$	−4.23930	−	18.7236i	−0.218335	−	0.964313i
$378$	9.72838	+	0.631683i	0.500374	+	0.0324903i
$379$	−29.0741	−	16.7860i	−1.49344	−	0.862237i	−0.493466	−	0.869765i	$-0.664270\pi$
$379$	−29.0741	−	16.7860i	−1.49344	−	0.862237i	−0.999972	+	0.00752812i	$0.997604\pi$
$380$	−5.86795	+	7.66657i	−0.301019	+	0.393287i
$381$	29.1477	−	16.8284i	1.49328	−	0.862147i
$382$	1.40000	−	21.5609i	0.0716300	−	1.10315i
$383$	9.07727	+	15.7223i	0.463827	+	0.803372i	0.999148	−	0.0412772i	$-0.0131427\pi$
$383$	9.07727	+	15.7223i	0.463827	+	0.803372i	−0.535321	+	0.844649i	$0.679809\pi$
$384$	−2.19485	−	31.4337i	−0.112005	−	1.60409i
$385$	1.18170			0.0602249
$386$	−27.8205	+	13.7406i	−1.41603	+	0.699379i
$387$	−22.9509	−	13.2507i	−1.16666	−	0.673571i
$388$	−10.0866	+	13.1783i	−0.512071	+	0.669029i
$389$		−	1.11349i		−	0.0564562i	−0.999602	−	0.0282281i	$-0.991014\pi$
$389$		−	1.11349i		−	0.0564562i	0.999602	−	0.0282281i	$-0.00898647\pi$
$390$	−13.2620	−	5.07953i	−0.671546	−	0.257212i
$391$	−7.79399			−0.394159
$392$	−10.6826	−	9.33393i	−0.539553	−	0.471435i
$393$	−30.0572	+	52.0606i	−1.51619	+	2.62611i
$394$	9.01441	+	18.2514i	0.454139	+	0.919492i
$395$			7.20112i			0.362328i
$396$	−7.36946	+	3.06305i	−0.370329	+	0.153924i
$397$	0.270926	−	0.156419i	0.0135974	−	0.00785047i	−0.493186	−	0.869924i	$-0.664168\pi$
$397$	0.270926	−	0.156419i	0.0135974	−	0.00785047i	0.506783	+	0.862073i	$0.330834\pi$
$398$	−1.18166	+	18.1984i	−0.0592314	+	0.912206i
$399$	9.46984	+	16.4023i	0.474085	+	0.821140i
$400$	2.82153	−	2.83531i	0.141077	−	0.141765i
$401$	7.54788	−	13.0733i	0.376923	−	0.652850i	−0.613690	−	0.789547i	$-0.710315\pi$
$401$	7.54788	−	13.0733i	0.376923	−	0.652850i	0.990613	+	0.136697i	$0.0436487\pi$
$402$	0.952577	−	14.6704i	0.0475102	−	0.731691i
$403$	−9.02400	−	9.75953i	−0.449517	−	0.486157i
$404$	0.0210557	−	0.161453i	0.00104756	−	0.00803256i
$405$	0.556098	+	0.321063i	0.0276327	+	0.0159538i
$406$	5.88788	−	8.82345i	0.292210	−	0.437901i
$407$	−1.07721	−	1.86578i	−0.0533954	−	0.0924835i
$408$	7.31499	+	1.44116i	0.362146	+	0.0713479i
$409$	−1.24789	−	2.16140i	−0.0617040	−	0.106874i	0.833523	−	0.552484i	$-0.186320\pi$
$409$	−1.24789	−	2.16140i	−0.0617040	−	0.106874i	−0.895227	+	0.445610i	$0.852987\pi$
$410$	0.951476	+	1.92644i	0.0469900	+	0.0951403i
$411$			34.5270i			1.70309i
$412$	7.62875	+	18.3542i	0.375842	+	0.904246i
$413$	−8.96313	−	5.17487i	−0.441047	−	0.254639i
$414$	−46.0826	−	30.7508i	−2.26483	−	1.51132i
$415$	17.9498			0.881122
$416$	16.5388	+	11.9361i	0.810880	+	0.585213i
$417$	−2.13178			−0.104394
$418$	−4.76339	−	3.17860i	−0.232985	−	0.155470i
$419$	15.3009	+	8.83396i	0.747496	+	0.431567i	0.824789	−	0.565441i	$-0.191294\pi$
$419$	15.3009	+	8.83396i	0.747496	+	0.431567i	−0.0772923	+	0.997008i	$0.524627\pi$
$420$	−3.01174	−	7.24602i	−0.146958	−	0.353570i
$421$			26.9453i			1.31323i	0.754225	+	0.656617i	$0.228013\pi$
$421$			26.9453i			1.31323i	−0.754225	+	0.656617i	$0.771987\pi$
$422$	−12.1152	−	24.5296i	−0.589760	−	1.19408i
$423$	−29.2463	−	50.6561i	−1.42200	−	2.46298i
$424$	−17.1005	−	3.36904i	−0.830472	−	0.163615i
$425$	0.473218	+	0.819638i	0.0229545	+	0.0397583i
$426$	15.7688	−	23.6308i	0.764001	−	1.14492i
$427$	−8.01129	−	4.62532i	−0.387694	−	0.223835i
$428$	−0.414882	+	3.18127i	−0.0200541	+	0.153773i
$429$	2.49688	−	8.04502i	0.120551	−	0.388417i
$430$	−0.510503	+	7.86212i	−0.0246187	+	0.379145i
$431$	−1.45788	+	2.52511i	−0.0702234	+	0.121630i	−0.898999	−	0.437950i	$-0.855705\pi$
$431$	−1.45788	+	2.52511i	−0.0702234	+	0.121630i	0.828776	+	0.559581i	$0.189038\pi$
$432$	13.8743	+	13.8069i	0.667528	+	0.664284i
$433$	7.20676	+	12.4825i	0.346335	+	0.599870i	0.985595	−	0.169121i	$-0.0540927\pi$
$433$	7.20676	+	12.4825i	0.346335	+	0.599870i	−0.639260	+	0.768990i	$0.720759\pi$
$434$	0.475895	−	7.32913i	0.0228437	−	0.351809i
$435$	−12.8425	+	7.41462i	−0.615751	+	0.355504i
$436$	−9.22818	+	3.83561i	−0.441950	+	0.183692i
$437$		−	39.7527i		−	1.90163i
$438$	15.7119	+	31.8116i	0.750741	+	1.52002i
$439$	−5.19605	+	8.99982i	−0.247994	+	0.429538i	−0.962969	−	0.269612i	$-0.913105\pi$
$439$	−5.19605	+	8.99982i	−0.247994	+	0.429538i	0.714975	+	0.699150i	$0.246438\pi$
$440$	1.78667	+	1.56110i	0.0851760	+	0.0744226i
$441$	23.8585			1.13612
$442$	−3.74818	+	3.03981i	−0.178283	+	0.144589i
$443$			7.61517i			0.361807i	0.983501	+	0.180904i	$0.0579022\pi$
$443$			7.61517i			0.361807i	−0.983501	+	0.180904i	$0.942098\pi$
$444$	−8.69531	+	11.3606i	−0.412661	+	0.539148i
$445$	11.9241	+	6.88440i	0.565258	+	0.326352i
$446$	0.791212	−	0.390781i	0.0374650	−	0.0185040i
$447$	46.0890			2.17994
$448$	1.51182	+	11.1680i	0.0714266	+	0.527637i
$449$	10.5130	+	18.2091i	0.496139	+	0.859339i	0.999990	−	0.00445211i	$-0.00141716\pi$
$449$	10.5130	+	18.2091i	0.496139	+	0.859339i	−0.503851	+	0.863791i	$0.668084\pi$
$450$	−0.435904	+	6.71324i	−0.0205487	+	0.316465i
$451$	−1.10370	+	0.637221i	−0.0519712	+	0.0300056i
$452$	−2.93549	+	3.83527i	−0.138074	+	0.180396i
$453$	26.7728	+	15.4573i	1.25790	+	0.726247i
$454$	−15.0921	−	0.979962i	−0.708308	−	0.0459919i
$455$	4.85098	+	1.50557i	0.227418	+	0.0705822i
$456$	−7.35053	+	37.3096i	−0.344220	+	1.74718i
$457$	17.5453	−	30.3894i	0.820735	−	1.42155i	−0.0844012	−	0.996432i	$-0.526898\pi$
$457$	17.5453	−	30.3894i	0.820735	−	1.42155i	0.905136	−	0.425122i	$-0.139769\pi$
$458$	−18.0205	+	27.0051i	−0.842041	+	1.26187i
$459$	−4.01082	+	2.31565i	−0.187209	+	0.108085i
$460$	−2.12990	+	16.3319i	−0.0993072	+	0.761477i
$461$	−26.5009	+	15.3003i	−1.23427	+	0.712607i	−0.967917	−	0.251269i	$-0.919152\pi$
$461$	−26.5009	+	15.3003i	−1.23427	+	0.712607i	−0.266353	+	0.963875i	$0.585819\pi$
$462$	4.17319	−	2.06115i	0.194154	−	0.0958934i
$463$	15.0620			0.699990			0.349995	−	0.936752i	$-0.386183\pi$
$463$	15.0620			0.699990			0.349995	+	0.936752i	$0.386183\pi$
$464$	20.5585	−	5.56234i	0.954405	−	0.258225i
$465$	−5.13380	+	8.89201i	−0.238074	+	0.412357i
$466$	−26.1208	−	17.4304i	−1.21002	−	0.807447i
$467$			36.6322i			1.69514i	0.530687	+	0.847568i	$0.321934\pi$
$467$			36.6322i			1.69514i	−0.530687	+	0.847568i	$0.678066\pi$
$468$	−34.1549	+	3.18487i	−1.57881	+	0.147221i
$469$			5.25801i			0.242792i
$470$	−9.65225	+	14.4647i	−0.445225	+	0.667205i
$471$	15.8418	−	27.4388i	0.729952	−	1.26431i
$472$	−6.71545	−	19.6650i	−0.309104	−	0.905156i
$473$	−4.67323			−0.214875
$474$	12.5604	+	25.4309i	0.576917	+	1.16808i
$475$	−4.18051	+	2.41362i	−0.191815	+	0.110745i
$476$	−2.64416	−	0.344835i	−0.121195	−	0.0158055i
$477$	25.3859	−	14.6566i	1.16234	−	0.671079i
$478$	16.6329	+	11.0991i	0.760770	+	0.507660i
$479$	11.5509	−	20.0068i	0.527774	−	0.914132i	−0.471701	−	0.881758i	$-0.656360\pi$
$479$	11.5509	−	20.0068i	0.527774	−	0.914132i	0.999476	−	0.0323738i	$-0.0103067\pi$
$480$	5.01887	−	14.9343i	0.229079	−	0.681656i
$481$	−2.04491	−	9.03166i	−0.0932397	−	0.411808i
$482$	2.34993	−	36.1906i	0.107036	−	1.64844i
$483$	27.9816	+	16.1552i	1.27321	+	0.735086i
$484$	12.5161	−	16.3525i	0.568915	−	0.743297i
$485$	−7.18604	+	4.14886i	−0.326301	+	0.188390i
$486$	23.2412	+	1.50910i	1.05424	+	0.0684541i
$487$	7.31159	+	12.6640i	0.331320	+	0.573863i	0.982771	−	0.184828i	$-0.0591728\pi$
$487$	7.31159	+	12.6640i	0.331320	+	0.573863i	−0.651451	+	0.758691i	$0.725839\pi$
$488$	−6.00231	−	17.5767i	−0.271712	−	0.795659i
$489$	40.8117			1.84557
$490$	−3.14101	−	6.35957i	−0.141896	−	0.287296i
$491$	19.5760	+	11.3022i	0.883454	+	0.510063i	0.871796	−	0.489869i	$-0.162956\pi$
$491$	19.5760	+	11.3022i	0.883454	+	0.510063i	0.0116586	+	0.999932i	$0.496289\pi$
$492$	6.72031	+	5.14369i	0.302975	+	0.231895i
$493$			5.03923i			0.226956i
$494$	−15.5044	−	19.1173i	−0.697575	−	0.860130i
$495$	−3.99034			−0.179352
$496$	10.4018	−	10.4526i	0.467054	−	0.469334i
$497$	−5.08034	+	8.79940i	−0.227884	+	0.394707i
$498$	63.3901	−	31.3085i	2.84058	−	1.40297i
$499$			35.4723i			1.58796i	0.607944	+	0.793980i	$0.291995\pi$
$499$			35.4723i			1.58796i	−0.607944	+	0.793980i	$0.708005\pi$
$500$	1.84683	−	0.767616i	0.0825926	−	0.0343288i
$501$	25.2809	−	14.5959i	1.12947	−	0.652097i
$502$	9.36118	+	0.607841i	0.417810	+	0.0271293i
$503$	0.288824	+	0.500258i	0.0128780	+	0.0223054i	0.872393	−	0.488806i	$-0.162567\pi$
$503$	0.288824	+	0.500258i	0.0128780	+	0.0223054i	−0.859515	+	0.511111i	$0.829234\pi$
$504$	−14.2733	−	12.4713i	−0.635781	−	0.555514i
$505$	0.0407049	−	0.0705030i	0.00181135	−	0.00313734i
$506$	−9.74874	−	0.633006i	−0.433384	−	0.0281405i
$507$	20.4999	−	29.8443i	0.910431	−	1.32543i
$508$	−23.9660	−	3.12550i	−1.06332	−	0.138672i
$509$	24.9951	+	14.4310i	1.10789	+	0.639641i	0.938282	−	0.345871i	$-0.112416\pi$
$509$	24.9951	+	14.4310i	1.10789	+	0.639641i	0.169608	+	0.985512i	$0.445750\pi$
$510$	3.10081	+	2.06917i	0.137306	+	0.0916243i
$511$	−6.34487	−	10.9896i	−0.280680	−	0.486153i
$512$	−12.4678	+	18.8826i	−0.551006	+	0.834501i
$513$	−11.8108	−	20.4569i	−0.521461	−	0.903196i
$514$	7.91393	−	3.90871i	0.349069	−	0.172406i
$515$			9.93823i			0.437931i
$516$	11.9105	+	28.6556i	0.524329	+	1.26149i
$517$	−8.93265	−	5.15727i	−0.392857	−	0.226816i
$518$	2.84013	−	4.25615i	0.124788	−	0.187005i
$519$	−47.4617			−2.08334
$520$	5.34548	+	8.68481i	0.234415	+	0.380854i
$521$	32.5741			1.42710			0.713548	−	0.700606i	$-0.247087\pi$
$521$	32.5741			1.42710			0.713548	+	0.700606i	$0.247087\pi$
$522$	−19.8821	+	29.7949i	−0.870215	+	1.30409i
$523$	32.6174	+	18.8317i	1.42626	+	0.823452i	0.996823	−	0.0796453i	$-0.0253788\pi$
$523$	32.6174	+	18.8317i	1.42626	+	0.823452i	0.429437	+	0.903097i	$0.358712\pi$
$524$	39.8619	−	16.5683i	1.74138	−	0.723787i
$525$		−	3.92350i		−	0.171236i
$526$	33.2005	−	16.3978i	1.44761	−	0.714979i
$527$	1.74456	+	3.02166i	0.0759940	+	0.131626i
$528$	9.03256	+	2.39671i	0.393092	+	0.104303i
$529$	−22.4083	−	38.8123i	−0.974274	−	1.68749i
$530$	−7.24886	−	4.83715i	−0.314870	−	0.210113i
$531$	30.2665	+	17.4744i	1.31346	+	0.758324i
$532$	1.75881	−	13.4864i	0.0762540	−	0.584708i
$533$	−5.34265	+	1.20966i	−0.231416	+	0.0523961i
$534$	54.1183	+	3.51401i	2.34193	+	0.152066i
$535$	−0.802053	+	1.38920i	−0.0346758	+	0.0600602i
$536$	−6.94617	+	7.94984i	−0.300029	+	0.343381i
$537$	−31.8386	−	55.1460i	−1.37394	−	2.37973i
$538$	−37.9933	−	2.46698i	−1.63801	−	0.106359i
$539$	3.64353	−	2.10359i	0.156938	−	0.0906081i
$540$	3.75626	+	9.03727i	0.161644	+	0.388902i
$541$			1.91059i			0.0821428i	0.999156	+	0.0410714i	$0.0130771\pi$
$541$			1.91059i			0.0821428i	−0.999156	+	0.0410714i	$0.986923\pi$
$542$	−16.1633	+	7.98308i	−0.694272	+	0.342903i
$543$	−4.89063	+	8.47083i	−0.209877	+	0.363518i
$544$	−3.54228	−	4.01448i	−0.151874	−	0.172119i
$545$	−4.99678			−0.214038
$546$	19.7574	−	3.14426i	0.845538	−	0.134562i
$547$			15.5224i			0.663690i	0.943334	+	0.331845i	$0.107671\pi$
$547$			15.5224i			0.663690i	−0.943334	+	0.331845i	$0.892329\pi$
$548$	15.0695	−	19.6886i	0.643739	−	0.841056i
$549$	27.0524	+	15.6187i	1.15457	+	0.666590i
$550$	0.525334	+	1.06364i	0.0224003	+	0.0453537i
$551$	−25.7023			−1.09495
$552$	20.9647	+	61.3913i	0.892316	+	2.61299i
$553$	−5.07222	−	8.78534i	−0.215693	−	0.373590i
$554$	−2.24703	−	0.145904i	−0.0954670	−	0.00619887i
$555$	−6.19482	+	3.57658i	−0.262955	+	0.151817i
$556$	1.21562	+	0.930428i	0.0515537	+	0.0394589i
$557$	−6.02676	−	3.47955i	−0.255362	−	0.147433i	0.366855	−	0.930278i	$-0.380435\pi$
$557$	−6.02676	−	3.47955i	−0.255362	−	0.147433i	−0.622217	+	0.782845i	$0.713768\pi$
$558$	−1.60699	+	24.7489i	−0.0680295	+	1.04770i
$559$	−19.1840	−	5.95403i	−0.811398	−	0.251829i
$560$	−1.44516	+	5.44645i	−0.0610694	+	0.230155i
$561$	−1.10557	+	1.91491i	−0.0466773	+	0.0808474i
$562$	19.7819	+	13.2004i	0.834447	+	0.556825i
$563$	0.131968	−	0.0761915i	0.00556177	−	0.00321109i	−0.497217	−	0.867626i	$-0.665645\pi$
$563$	0.131968	−	0.0761915i	0.00556177	−	0.00321109i	0.502778	+	0.864415i	$0.332311\pi$
$564$	−8.85745	+	67.9179i	−0.372966	+	2.85986i
$565$	−2.09134	+	1.20744i	−0.0879833	+	0.0507972i
$566$	9.95408	+	20.1539i	0.418401	+	0.847133i
$567$	−0.904583			−0.0379889
$568$	−19.3058	+	6.59278i	−0.810053	+	0.276627i
$569$	−10.6584	+	18.4609i	−0.446824	+	0.773923i	−0.998177	−	0.0603495i	$-0.980778\pi$
$569$	−10.6584	+	18.4609i	−0.446824	+	0.773923i	0.551353	+	0.834272i	$0.314112\pi$
$570$	−10.5537	+	15.8155i	−0.442044	+	0.662439i
$571$		−	16.4350i		−	0.687784i	−0.939009	−	0.343892i	$-0.888255\pi$
$571$		−	16.4350i		−	0.687784i	0.939009	−	0.343892i	$-0.111745\pi$
$572$	−4.93512	+	3.49779i	−0.206348	+	0.146250i
$573$		−	42.5513i		−	1.77760i
$574$	−2.51772	−	1.68007i	−0.105087	−	0.0701247i
$575$	−4.11754	+	7.13179i	−0.171713	+	0.297416i
$576$	−5.10507	−	37.7118i	−0.212711	−	1.57133i
$577$	7.77394			0.323633			0.161817	−	0.986821i	$-0.448265\pi$
$577$	7.77394			0.323633			0.161817	+	0.986821i	$0.448265\pi$
$578$	−20.4200	+	10.0855i	−0.849361	+	0.419501i
$579$	−52.9208	+	30.5538i	−2.19931	+	1.26977i
$580$	10.5594	+	1.37710i	0.438457	+	0.0571809i
$581$	−21.8987	+	12.6432i	−0.908511	+	0.524529i
$582$	−18.1411	+	27.1858i	−0.751972	+	1.12689i
$583$	2.58453	−	4.47653i	0.107040	−	0.185399i
$584$	4.92491	−	24.9977i	0.203794	−	1.03441i
$585$	−16.3807	−	5.08398i	−0.677259	−	0.210197i
$586$	33.0894	+	2.14856i	1.36691	+	0.0887562i
$587$	21.8724	+	12.6280i	0.902771	+	0.521215i	0.878098	−	0.478481i	$-0.158812\pi$
$587$	21.8724	+	12.6280i	0.902771	+	0.521215i	0.0246726	+	0.999696i	$0.492146\pi$
$588$	−22.1851	−	16.9803i	−0.914896	−	0.700256i
$589$	−15.4118	+	8.89799i	−0.635031	+	0.366635i
$590$	0.673227	−	10.3682i	0.0277163	−	0.426851i
$591$	20.0446	+	34.7182i	0.824523	+	1.42812i
$592$	9.91678	−	2.68310i	0.407577	−	0.110275i
$593$	−0.228182			−0.00937030			−0.00468515	−	0.999989i	$-0.501491\pi$
$593$	−0.228182			−0.00937030			−0.00468515	+	0.999989i	$0.501491\pi$
$594$	−5.20482	+	2.57067i	−0.213556	+	0.105476i
$595$	−1.15465	−	0.666637i	−0.0473360	−	0.0273295i
$596$	−26.2817	−	20.1158i	−1.07654	−	0.823977i
$597$			35.9153i			1.46991i
$598$	−39.2130	−	15.0191i	−1.60354	−	0.614179i
$599$	3.55855			0.145398			0.0726992	−	0.997354i	$-0.476839\pi$
$599$	3.55855			0.145398			0.0726992	+	0.997354i	$0.476839\pi$
$600$	5.18320	−	5.93213i	0.211603	−	0.242178i
$601$	12.0009	−	20.7862i	0.489527	−	0.847886i	−0.510400	−	0.859937i	$-0.670503\pi$
$601$	12.0009	−	20.7862i	0.489527	−	0.847886i	0.999927	+	0.0120508i	$0.00383599\pi$
$602$	−4.91499	−	9.95133i	−0.200320	−	0.405586i
$603$		−	17.7551i		−	0.723045i
$604$	−8.52043	−	20.4995i	−0.346691	−	0.834112i
$605$	8.91690	−	5.14817i	0.362523	−	0.209303i
$606$	0.0207770	−	0.319981i	0.000844009	−	0.0129983i
$607$	3.99567	+	6.92070i	0.162179	+	0.280902i	0.935650	−	0.352929i	$-0.114814\pi$
$607$	3.99567	+	6.92070i	0.162179	+	0.280902i	−0.773471	+	0.633832i	$0.781481\pi$
$608$	20.4756	−	18.0672i	0.830395	−	0.732720i
$609$	10.4452	−	18.0916i	0.423261	−	0.733109i
$610$	0.601734	−	9.26714i	0.0243635	−	0.375215i
$611$	−30.0986	−	32.5519i	−1.21766	−	1.31691i
$612$	8.92874	+	1.16443i	0.360923	+	0.0470694i
$613$	−29.6723	−	17.1313i	−1.19845	−	0.691927i	−0.238242	−	0.971206i	$-0.576571\pi$
$613$	−29.6723	−	17.1313i	−1.19845	−	0.691927i	−0.960210	+	0.279279i	$0.909905\pi$
$614$	−6.92303	+	10.3747i	−0.279391	+	0.418689i
$615$	2.11572	+	3.66453i	0.0853139	+	0.147768i
$616$	−3.27931	−	0.646071i	−0.132127	−	0.0260310i
$617$	−6.26932	−	10.8588i	−0.252393	−	0.437158i	0.711791	−	0.702392i	$-0.247884\pi$
$617$	−6.26932	−	10.8588i	−0.252393	−	0.437158i	−0.964184	+	0.265233i	$0.914551\pi$
$618$	17.3345	+	35.0971i	0.697297	+	1.41181i
$619$			22.1688i			0.891041i	0.895272	+	0.445520i	$0.146981\pi$
$619$			22.1688i			0.891041i	−0.895272	+	0.445520i	$0.853019\pi$
$620$	6.80846	−	2.82988i	0.273434	−	0.113651i
$621$	−34.8988	−	20.1488i	−1.40044	−	0.808544i
$622$	13.2446	+	8.83813i	0.531062	+	0.354377i
$623$	−19.3965			−0.777105
$624$	34.0259	+	21.3468i	1.36213	+	0.854557i
$625$	1.00000			0.0400000
$626$	−17.2904	−	11.5378i	−0.691062	−	0.461145i
$627$	−9.76686	−	5.63890i	−0.390051	−	0.225196i
$628$	−21.0094	+	8.73238i	−0.838368	+	0.348460i
$629$			2.43077i			0.0969211i
$630$	−4.19677	−	8.49716i	−0.167203	−	0.338535i
$631$	−7.03243	−	12.1805i	−0.279956	−	0.484899i	0.691417	−	0.722456i	$-0.256987\pi$
$631$	−7.03243	−	12.1805i	−0.279956	−	0.484899i	−0.971374	+	0.237557i	$0.923653\pi$
$632$	3.93707	−	19.9837i	0.156608	−	0.794909i
$633$	−26.9396	−	46.6607i	−1.07075	−	1.85460i
$634$	7.24549	−	10.8579i	0.287755	−	0.431224i
$635$	−10.4655	−	6.04223i	−0.415309	−	0.239779i
$636$	−34.0366	−	4.43884i	−1.34964	−	0.176012i
$637$	17.6371	−	3.99332i	0.698809	−	0.158221i
$638$	−0.409272	+	6.30309i	−0.0162032	+	0.249542i
$639$	17.1552	−	29.7137i	0.678649	−	1.17545i
$640$	−9.38013	+	6.32559i	−0.370782	+	0.250041i
$641$	−12.7774	−	22.1310i	−0.504675	−	0.874124i	−0.999985	−	0.00540718i	$-0.998279\pi$
$641$	−12.7774	−	22.1310i	−0.504675	−	0.874124i	0.495310	−	0.868716i	$-0.335055\pi$
$642$	−0.409392	+	6.30494i	−0.0161574	+	0.248836i
$643$	5.15223	−	2.97464i	0.203184	−	0.117308i	−0.394956	−	0.918700i	$-0.629240\pi$
$643$	5.15223	−	2.97464i	0.203184	−	0.117308i	0.598140	+	0.801392i	$0.295907\pi$
$644$	−8.90512	−	21.4250i	−0.350911	−	0.844265i
$645$			15.5162i			0.610948i
$646$	2.86119	+	5.79303i	0.112572	+	0.227924i
$647$	−8.20553	+	14.2124i	−0.322593	+	0.558747i	−0.981022	−	0.193896i	$-0.937888\pi$
$647$	−8.20553	+	14.2124i	−0.322593	+	0.558747i	0.658430	+	0.752642i	$0.271221\pi$
$648$	−1.36768	−	1.19501i	−0.0537277	−	0.0469446i
$649$	6.16283			0.241912
$650$	0.801391	+	5.03565i	0.0314331	+	0.197514i
$651$		−	14.4643i		−	0.566900i
$652$	−23.2723	−	17.8125i	−0.911415	−	0.697592i
$653$	−35.1085	−	20.2699i	−1.37390	−	0.793224i	−0.382487	−	0.923961i	$-0.624932\pi$
$653$	−35.1085	−	20.2699i	−1.37390	−	0.793224i	−0.991417	+	0.130737i	$0.958266\pi$
$654$	−17.6462	+	8.71551i	−0.690021	+	0.340803i
$655$	21.5840			0.843358
$656$	−1.58718	−	5.86624i	−0.0619689	−	0.229038i
$657$	21.4252	+	37.1096i	0.835878	+	1.44778i
$658$	1.58730	−	24.4455i	0.0618794	−	0.952986i
$659$	−25.0852	+	14.4829i	−0.977179	+	0.564174i	−0.901417	−	0.432952i	$-0.857472\pi$
$659$	−25.0852	+	14.4829i	−0.977179	+	0.564174i	−0.0757616	+	0.997126i	$0.524139\pi$
$660$	3.71045	+	2.83996i	0.144429	+	0.110545i
$661$	14.3624	+	8.29215i	0.558634	+	0.322527i	0.752597	−	0.658481i	$-0.228801\pi$
$661$	14.3624	+	8.29215i	0.558634	+	0.322527i	−0.193963	+	0.981009i	$0.562134\pi$
$662$	35.8918	+	2.33053i	1.39498	+	0.0905786i
$663$	−6.97820	+	6.45229i	−0.271011	+	0.250586i
$664$	−49.8122	−	9.81372i	−1.93309	−	0.380846i
$665$	3.40014	−	5.88921i	0.131852	−	0.228374i
$666$	−9.59048	+	14.3721i	−0.371624	+	0.556908i
$667$	−37.9727	+	21.9236i	−1.47031	+	0.848883i
$668$	−20.7866	−	2.71086i	−0.804257	−	0.104886i
$669$	1.50506	−	0.868947i	0.0581890	−	0.0335954i
$670$	−4.73270	+	2.33749i	−0.182840	+	0.0903052i
$671$	5.50837			0.212648
$672$	4.39621	+	21.7549i	0.169588	+	0.839215i
$673$	2.49000	−	4.31281i	0.0959826	−	0.166247i	−0.814036	−	0.580815i	$-0.802734\pi$
$673$	2.49000	−	4.31281i	0.0959826	−	0.166247i	0.910018	+	0.414568i	$0.136067\pi$
$674$	12.7894	+	8.53433i	0.492628	+	0.328730i
$675$			4.89341i			0.188347i
$676$	−24.7155	+	8.07105i	−0.950598	+	0.310425i
$677$		−	2.51791i		−	0.0967710i	−0.998829	−	0.0483855i	$-0.984592\pi$
$677$		−	2.51791i		−	0.0967710i	0.998829	−	0.0483855i	$-0.0154076\pi$
$678$	−5.27957	+	7.91185i	−0.202760	+	0.303853i
$679$	5.84462	−	10.1232i	0.224296	−	0.388492i
$680$	−0.865099	−	2.53329i	−0.0331750	−	0.0971472i
$681$	−29.7848			−1.14136
$682$	1.93668	+	3.92119i	0.0741595	+	0.150150i
$683$	21.0117	−	12.1311i	0.803990	−	0.464184i	−0.0408744	−	0.999164i	$-0.513014\pi$
$683$	21.0117	−	12.1311i	0.803990	−	0.464184i	0.844864	+	0.534980i	$0.179681\pi$
$684$	−5.93911	+	45.5405i	−0.227088	+	1.74128i
$685$	10.7360	−	6.19845i	0.410203	−	0.236831i
$686$	19.9116	+	13.2870i	0.760230	+	0.507300i
$687$	−31.9687	+	55.3713i	−1.21968	+	2.11255i
$688$	5.71515	−	21.5389i	0.217888	−	0.821164i
$689$	16.3131	−	15.0837i	0.621481	−	0.574643i
$690$	−2.10172	+	32.3680i	−0.0800111	+	1.23223i
$691$	−5.18155	−	2.99157i	−0.197115	−	0.113805i	0.398194	−	0.917301i	$-0.369637\pi$
$691$	−5.18155	−	2.99157i	−0.197115	−	0.113805i	−0.595309	+	0.803497i	$0.702970\pi$
$692$	27.0644	+	20.7150i	1.02884	+	0.787465i
$693$	4.86820	−	2.81065i	0.184928	−	0.106768i
$694$	−20.4240	−	1.32617i	−0.775285	−	0.0503408i
$695$	0.382706	+	0.662867i	0.0145169	+	0.0251440i
$696$	39.6928	−	13.5548i	1.50455	−	0.513793i
$697$	1.43791			0.0544649
$698$	−2.21070	−	4.47598i	−0.0836762	−	0.169418i
$699$	−53.5582	−	30.9218i	−2.02576	−	1.16957i
$700$	−1.71244	+	2.23733i	−0.0647241	+	0.0845630i
$701$		−	11.3524i		−	0.428773i	−0.976749	−	0.214386i	$-0.931225\pi$
$701$		−	11.3524i		−	0.428773i	0.976749	−	0.214386i	$-0.0687752\pi$
$702$	−24.6415	+	3.92153i	−0.930033	+	0.148009i
$703$	−12.3980			−0.467598
$704$	−4.10465	−	5.30901i	−0.154700	−	0.200091i
$705$	−17.1233	+	29.6584i	−0.644900	+	1.11700i
$706$	17.6595	−	8.72208i	0.664624	−	0.328260i
$707$			0.114684i			0.00431315i
$708$	−15.7069	−	37.7897i	−0.590303	−	1.42022i
$709$	29.3936	−	16.9704i	1.10390	−	0.637336i	0.166656	−	0.986015i	$-0.446703\pi$
$709$	29.3936	−	16.9704i	1.10390	−	0.637336i	0.937242	+	0.348679i	$0.113370\pi$
$710$	−10.1788	−	0.660930i	−0.382003	−	0.0248042i
$711$	17.1278	+	29.6662i	0.642341	+	1.11257i
$712$	−29.3265	−	25.6241i	−1.09906	−	0.960303i
$713$	−15.1796	+	26.2919i	−0.568482	+	0.984639i
$714$	−5.24043	−	0.340272i	−0.196118	−	0.0127344i
$715$	−2.94982	+	0.667883i	−0.110317	+	0.0249774i
$716$	−5.91329	+	45.3425i	−0.220990	+	1.69453i
$717$	34.1041	+	19.6900i	1.27364	+	0.735336i
$718$	27.4156	+	18.2944i	1.02314	+	0.682740i
$719$	9.37440	+	16.2369i	0.349606	+	0.605535i	0.986179	−	0.165681i	$-0.0529821\pi$
$719$	9.37440	+	16.2369i	0.349606	+	0.605535i	−0.636573	+	0.771216i	$0.719649\pi$
$720$	4.88001	−	18.3915i	0.181867	−	0.685410i
$721$	−7.00014	−	12.1246i	−0.260699	−	0.451544i
$722$	−5.45521	+	2.69434i	−0.203022	+	0.100273i
$723$		−	71.4235i		−	2.65627i
$724$	6.48597	−	2.69583i	0.241049	−	0.100190i
$725$	4.61109	+	2.66221i	0.171252	+	0.0988721i
$726$	22.5106	−	33.7340i	0.835447	−	1.25198i
$727$	23.5587			0.873744			0.436872	−	0.899524i	$-0.356086\pi$
$727$	23.5587			0.873744			0.436872	+	0.899524i	$0.356086\pi$
$728$	−12.6387	−	6.83026i	−0.468423	−	0.253146i
$729$	43.9410			1.62744
$730$	7.07103	−	10.5965i	0.261711	−	0.392194i
$731$	4.56626	+	2.63633i	0.168889	+	0.0975082i
$732$	−14.0389	−	33.7766i	−0.518894	−	1.24842i
$733$			45.0940i			1.66558i	0.553586	+	0.832792i	$0.313259\pi$
$733$			45.0940i			1.66558i	−0.553586	+	0.832792i	$0.686741\pi$
$734$	−46.0107	+	22.7248i	−1.69829	+	0.838788i
$735$	−6.98439	−	12.0973i	−0.257623	−	0.446216i
$736$	14.8398	−	44.1578i	0.547002	−	1.62768i
$737$	−1.56546	−	2.71146i	−0.0576645	−	0.0998779i
$738$	8.50178	+	5.67322i	0.312955	+	0.208834i
$739$	−17.9447	−	10.3604i	−0.660105	−	0.381112i	0.132212	−	0.991221i	$-0.457792\pi$
$739$	−17.9447	−	10.3604i	−0.660105	−	0.381112i	−0.792317	+	0.610110i	$0.791125\pi$
$740$	5.09354	+	0.664268i	0.187242	+	0.0244190i
$741$	−32.9095	−	35.5919i	−1.20896	−	1.30750i
$742$	12.2507	+	0.795463i	0.449737	+	0.0292024i
$743$	21.5045	−	37.2470i	0.788925	−	1.36646i	−0.137701	−	0.990474i	$-0.543971\pi$
$743$	21.5045	−	37.2470i	0.788925	−	1.36646i	0.926626	−	0.375984i	$-0.122695\pi$
$744$	19.1083	−	21.8693i	0.700543	−	0.801766i
$745$	−8.27411	−	14.3312i	−0.303140	−	0.525054i
$746$	−24.0993	−	1.56482i	−0.882338	−	0.0572920i
$747$	73.9471	−	42.6934i	2.70558	−	1.56207i
$748$	1.46621	−	0.609418i	0.0536100	−	0.0222825i
$749$		−	2.25975i		−	0.0825696i
$750$	3.53152	−	1.74423i	0.128953	−	0.0636901i
$751$	−1.18585	+	2.05396i	−0.0432724	+	0.0749501i	−0.886850	−	0.462057i	$-0.847112\pi$
$751$	−1.18585	+	2.05396i	−0.0432724	+	0.0749501i	0.843578	+	0.537007i	$0.180445\pi$
$752$	34.6941	−	34.8635i	1.26516	−	1.27134i
$753$	18.4746			0.673253
$754$	−9.71069	+	25.3533i	−0.353642	+	0.923313i
$755$		−	11.0999i		−	0.403965i
$756$	−10.9482	−	8.37965i	−0.398180	−	0.304765i
$757$	−37.8724	−	21.8657i	−1.37650	−	0.794721i	−0.384761	−	0.923016i	$-0.625716\pi$
$757$	−37.8724	−	21.8657i	−1.37650	−	0.794721i	−0.991736	+	0.128295i	$0.959050\pi$
$758$	21.0248	+	42.5688i	0.763657	+	1.54617i
$759$	−19.2395			−0.698349
$760$	12.9209	−	4.41238i	0.468689	−	0.160054i
$761$	6.53734	+	11.3230i	0.236979	+	0.410459i	0.959846	−	0.280528i	$-0.0905096\pi$
$761$	6.53734	+	11.3230i	0.236979	+	0.410459i	−0.722867	+	0.690987i	$0.757176\pi$
$762$	−47.4980	−	3.08414i	−1.72067	−	0.111727i
$763$	6.09605	−	3.51955i	0.220692	−	0.127416i
$764$	−18.5718	+	24.2643i	−0.671903	+	0.877852i
$765$	3.89900	+	2.25109i	0.140969	+	0.0813882i
$766$	1.66359	−	25.6204i	0.0601079	−	0.925704i
$767$	25.2990	+	7.85190i	0.913494	+	0.283516i
$768$	−22.0928	+	38.7000i	−0.797207	+	1.39647i
$769$	−5.35126	+	9.26866i	−0.192971	+	0.334236i	−0.946234	−	0.323484i	$-0.895146\pi$
$769$	−5.35126	+	9.26866i	−0.192971	+	0.334236i	0.753262	+	0.657720i	$0.228479\pi$
$770$	−1.39010	−	0.927609i	−0.0500956	−	0.0334287i
$771$	15.0541	−	8.69147i	0.542159	−	0.313016i
$772$	43.5129	+	5.67468i	1.56606	+	0.204236i
$773$	6.62059	−	3.82240i	0.238126	−	0.137482i	−0.376189	−	0.926543i	$-0.622766\pi$
$773$	6.62059	−	3.82240i	0.238126	−	0.137482i	0.614315	+	0.789061i	$0.289432\pi$
$774$	16.5968	+	33.6035i	0.596561	+	1.20785i
$775$	3.68658			0.132426
$776$	22.2102	−	7.58460i	0.797298	−	0.272271i
$777$	5.03843	−	8.72683i	0.180753	−	0.313073i
$778$	−0.874066	+	1.30986i	−0.0313368	+	0.0469607i
$779$			7.33399i			0.262767i
$780$	11.6134	+	16.3857i	0.415828	+	0.586702i
$781$		−	6.05026i		−	0.216495i
$782$	9.16849	+	6.11812i	0.327864	+	0.218783i
$783$	−13.0273	+	22.5639i	−0.465557	+	0.806369i
$784$	5.23958	+	19.3656i	0.187128	+	0.691629i
$785$	−11.3760			−0.406026
$786$	76.2244	−	37.6474i	2.71883	−	1.34284i
$787$	13.8708	−	8.00830i	0.494440	−	0.285465i	−0.231975	−	0.972722i	$-0.574519\pi$
$787$	13.8708	−	8.00830i	0.494440	−	0.285465i	0.726414	+	0.687257i	$0.241185\pi$
$788$	3.72282	−	28.5462i	0.132620	−	1.01692i
$789$	63.1548	−	36.4625i	2.24837	−	1.29810i
$790$	5.65273	−	8.47106i	0.201115	−	0.301387i
$791$	1.70095	−	2.94613i	0.0604789	−	0.104752i
$792$	11.0735	+	2.18164i	0.393480	+	0.0775213i
$793$	22.6124	+	7.01806i	0.802989	+	0.249219i
$794$	−0.441491	−	0.0286669i	−0.0156679	−	0.00101735i
$795$	−14.8631	−	8.58120i	−0.527139	−	0.304344i
$796$	15.6754	−	20.4802i	0.555602	−	0.725903i
$797$	−48.1940	+	27.8248i	−1.70712	+	0.985606i	−0.769031	+	0.639212i	$0.779261\pi$
$797$	−48.1940	+	27.8248i	−1.70712	+	0.985606i	−0.938089	+	0.346394i	$0.887406\pi$
$798$	1.73553	−	26.7285i	0.0614373	−	0.946178i
$799$	5.81878	+	10.0784i	0.205854	+	0.356549i
$800$	−5.54477	+	1.12048i	−0.196037	+	0.0396150i
$801$	65.4978			2.31425
$802$	−19.1413	+	9.45392i	−0.675901	+	0.333829i
$803$	6.54387	+	3.77810i	0.230928	+	0.133326i
$804$	−12.6365	+	16.5098i	−0.445655	+	0.582255i
$805$		−	11.6010i		−	0.408882i
$806$	2.95439	+	18.5643i	0.104064	+	0.653900i
$807$	−74.9810			−2.63946
$808$	−0.151506	+	0.173397i	−0.00532995	+	0.00610009i
$809$	3.59866	−	6.23306i	0.126522	−	0.219143i	−0.795805	−	0.605553i	$-0.792952\pi$
$809$	3.59866	−	6.23306i	0.126522	−	0.219143i	0.922327	+	0.386411i	$0.126285\pi$
$810$	−0.402140	−	0.814210i	−0.0141298	−	0.0286084i
$811$		−	6.96504i		−	0.244576i	−0.992495	−	0.122288i	$-0.960977\pi$
$811$		−	6.96504i		−	0.244576i	0.992495	−	0.122288i	$-0.0390231\pi$
$812$	−13.8524	+	5.75764i	−0.486126	+	0.202054i
$813$	−30.7461	+	17.7513i	−1.07831	+	0.622565i
$814$	−0.197420	+	3.04041i	−0.00691957	+	0.106566i
$815$	−7.32669	−	12.6902i	−0.256643	−	0.444519i
$816$	−7.47374	−	7.43742i	−0.261633	−	0.260362i
$817$	−13.4464	+	23.2899i	−0.470431	+	0.814811i
$818$	−0.228700	+	3.52214i	−0.00799629	+	0.123149i
$819$	23.5654	−	5.33556i	0.823441	−	0.186439i
$820$	0.392946	−	3.01307i	0.0137223	−	0.105221i
$821$	−26.2136	−	15.1344i	−0.914860	−	0.528195i	−0.0328682	−	0.999460i	$-0.510464\pi$
$821$	−26.2136	−	15.1344i	−0.914860	−	0.528195i	−0.881992	+	0.471265i	$0.843798\pi$
$822$	27.1030	−	40.6160i	0.945325	−	1.41665i
$823$	14.3321	+	24.8239i	0.499584	+	0.865305i	1.00000		0.000480053i	$-0.000152806\pi$
$823$	14.3321	+	24.8239i	0.499584	+	0.865305i	−0.500416	+	0.865785i	$0.666819\pi$
$824$	5.43354	−	27.5794i	0.189286	−	0.960775i
$825$	1.16814	+	2.02328i	0.0406694	+	0.0704415i
$826$	6.48165	+	13.1233i	0.225526	+	0.456619i
$827$		−	5.61334i		−	0.195195i	−0.995226	−	0.0975976i	$-0.968884\pi$
$827$		−	5.61334i		−	0.195195i	0.995226	−	0.0975976i	$-0.0311158\pi$
$828$	30.0707	+	72.3477i	1.04503	+	2.51426i
$829$	−11.5582	−	6.67312i	−0.401433	−	0.231767i	0.285669	−	0.958328i	$-0.407784\pi$
$829$	−11.5582	−	6.67312i	−0.401433	−	0.231767i	−0.687102	+	0.726561i	$0.741117\pi$
$830$	−21.1153	−	14.0902i	−0.732924	−	0.489079i
$831$	−4.43458			−0.153834
$832$	−10.0859	−	27.0236i	−0.349665	−	0.936875i
$833$	−4.74684			−0.164468
$834$	2.50772	+	1.67340i	0.0868354	+	0.0579451i
$835$	−9.07707	−	5.24065i	−0.314125	−	0.181360i
$836$	3.10829	+	7.47832i	0.107503	+	0.258643i
$837$			18.0399i			0.623550i
$838$	−11.0648	−	22.4027i	−0.382226	−	0.773889i
$839$	−0.117693	−	0.203850i	−0.00406321	−	0.00703769i	0.863987	−	0.503515i	$-0.167960\pi$
$839$	−0.117693	−	0.203850i	−0.00406321	−	0.00703769i	−0.868050	+	0.496477i	$0.834627\pi$
$840$	−2.14510	+	10.8880i	−0.0740130	+	0.375673i
$841$	−0.325237	−	0.563327i	−0.0112151	−	0.0194251i
$842$	21.1515	−	31.6972i	0.728928	−	1.09236i
$843$	40.5607	+	23.4178i	1.39699	+	0.806550i
$844$	−5.00342	+	38.3657i	−0.172225	+	1.32060i
$845$	−12.9602	−	1.01656i	−0.445844	−	0.0349706i
$846$	−5.35996	+	82.5473i	−0.184279	+	2.83803i
$847$	−7.25239	+	12.5615i	−0.249195	+	0.431618i
$848$	17.4716	+	17.3867i	0.599976	+	0.597061i
$849$	22.1340	+	38.3373i	0.759638	+	1.31573i
$850$	0.0867266	−	1.33565i	0.00297470	−	0.0458125i
$851$	−18.3168	+	10.5752i	−0.627893	+	0.362514i
$852$	−37.0994	+	15.4200i	−1.27100	+	0.528281i
$853$		−	10.5169i		−	0.360093i	−0.983658	−	0.180046i	$-0.942375\pi$
$853$		−	10.5169i		−	0.360093i	0.983658	−	0.180046i	$-0.0576248\pi$
$854$	5.79333	+	11.7297i	0.198244	+	0.401382i
$855$	−11.4815	+	19.8866i	−0.392660	+	0.680107i
$856$	2.98528	−	3.41663i	0.102035	−	0.116778i
$857$	−44.8066			−1.53057			−0.765283	−	0.643694i	$-0.777401\pi$
$857$	−44.8066			−1.53057			−0.765283	+	0.643694i	$0.777401\pi$
$858$	−9.25239	+	7.50379i	−0.315871	+	0.256175i
$859$		−	40.9808i		−	1.39825i	−0.715001	−	0.699123i	$-0.753574\pi$
$859$		−	40.9808i		−	1.39825i	0.715001	−	0.699123i	$-0.246426\pi$
$860$	6.77213	−	8.84790i	0.230928	−	0.301711i
$861$	−5.16233	−	2.98047i	−0.175932	−	0.101574i
$862$	3.69714	−	1.82603i	0.125925	−	0.0621947i
$863$	33.6948			1.14698			0.573492	−	0.819211i	$-0.305588\pi$
$863$	33.6948			1.14698			0.573492	+	0.819211i	$0.305588\pi$
$864$	−5.48297	−	27.1328i	−0.186535	−	0.923078i
$865$	8.52054	+	14.7580i	0.289707	+	0.501787i
$866$	1.32078	−	20.3410i	0.0448820	−	0.691214i
$867$	−38.8434	+	22.4263i	−1.31919	+	0.761636i
$868$	−6.31303	+	8.24808i	−0.214278	+	0.279958i
$869$	5.23130	+	3.02029i	0.177460	+	0.102456i
$870$	20.9276	+	1.35887i	0.709514	+	0.0460702i
$871$	−2.97177	−	13.1253i	−0.100695	−	0.444734i
$872$	13.8665	+	2.73189i	0.469578	+	0.0925136i
$873$	−19.7360	+	34.1838i	−0.667963	+	1.15695i
$874$	−31.2051	+	46.7633i	−1.05553	+	1.58179i
$875$	−1.22000	+	0.704365i	−0.0412434	+	0.0238119i
$876$	6.48877	−	49.7552i	0.219235	−	1.68107i
$877$	35.4453	−	20.4644i	1.19690	−	0.691032i	0.237040	−	0.971500i	$-0.423823\pi$
$877$	35.4453	−	20.4644i	1.19690	−	0.691032i	0.959863	+	0.280468i	$0.0904896\pi$
$878$	13.1771	−	6.50818i	0.444704	−	0.219640i
$879$	65.3030			2.20262
$880$	−0.876321	−	3.23890i	−0.0295408	−	0.109183i
$881$	−23.2290	+	40.2337i	−0.782603	+	1.35551i	0.147817	+	0.989015i	$0.452775\pi$
$881$	−23.2290	+	40.2337i	−0.782603	+	1.35551i	−0.930420	+	0.366494i	$0.880558\pi$
$882$	−28.0660	−	18.7284i	−0.945033	−	0.630619i
$883$			38.9850i			1.31195i	0.754782	+	0.655975i	$0.227742\pi$
$883$			38.9850i			1.31195i	−0.754782	+	0.655975i	$0.772258\pi$
$884$	6.79537	−	0.633654i	0.228553	−	0.0213121i
$885$		−	20.4620i		−	0.687822i
$886$	5.97774	−	8.95813i	0.200826	−	0.300954i
$887$	28.4476	−	49.2727i	0.955177	−	1.65442i	0.221216	−	0.975225i	$-0.428998\pi$
$887$	28.4476	−	49.2727i	0.955177	−	1.65442i	0.733962	−	0.679191i	$-0.237669\pi$
$888$	19.1466	−	6.53841i	0.642516	−	0.219415i
$889$	17.0237			0.570958
$890$	−8.62289	−	17.4587i	−0.289040	−	0.585217i
$891$	0.466477	−	0.269321i	0.0156276	−	0.00902259i
$892$	−1.23750	−	0.161387i	−0.0414346	−	0.00540364i
$893$	−51.4044	+	29.6783i	−1.72018	+	0.993148i
$894$	−54.2170	−	36.1789i	−1.81329	−	1.21000i
$895$	−11.4316	+	19.8001i	−0.382116	+	0.661845i
$896$	6.98820	−	14.3242i	0.233459	−	0.478539i
$897$	−78.9798	−	24.5125i	−2.63706	−	0.818448i
$898$	1.92671	−	29.6728i	0.0642953	−	0.990194i
$899$	16.9991	+	9.81445i	0.566953	+	0.327330i
$900$	5.78253	−	7.55497i	0.192751	−	0.251832i
$901$	−5.05073	+	2.91604i	−0.168264	+	0.0971474i
$902$	1.79855	+	0.116783i	0.0598850	+	0.00388846i
$903$	−10.9290	−	18.9297i	−0.363696	−	0.629939i
$904$	6.46379	−	2.20733i	0.214982	−	0.0734148i
$905$	3.51196			0.116741
$906$	−19.3606	−	39.1993i	−0.643214	−	1.30231i
$907$	9.41943	+	5.43831i	0.312767	+	0.180576i	0.648164	−	0.761501i	$-0.275537\pi$
$907$	9.41943	+	5.43831i	0.312767	+	0.180576i	−0.335397	+	0.942077i	$0.608870\pi$
$908$	16.9844	+	12.9998i	0.563648	+	0.431413i
$909$		−	0.387264i		−	0.0128448i
$910$	−4.52463	−	5.57900i	−0.149990	−	0.184942i
$911$	−21.2420			−0.703779			−0.351890	−	0.936041i	$-0.614461\pi$
$911$	−21.2420			−0.703779			−0.351890	+	0.936041i	$0.614461\pi$
$912$	37.9341	−	38.1193i	1.25612	−	1.26226i
$913$	7.52851	−	13.0398i	0.249157	−	0.431553i
$914$	−44.4945	+	21.9759i	−1.47175	+	0.726900i
$915$		−	18.2890i		−	0.604616i
$916$	42.3969	−	17.6219i	1.40083	−	0.582244i
$917$	−26.3324	+	15.2030i	−0.869573	+	0.502048i
$918$	6.53588	+	0.424388i	0.215716	+	0.0140069i
$919$	−1.54066	−	2.66850i	−0.0508216	−	0.0880256i	0.839495	−	0.543367i	$-0.182851\pi$
$919$	−1.54066	−	2.66850i	−0.0508216	−	0.0880256i	−0.890317	+	0.455341i	$0.849517\pi$
$920$	15.3257	−	17.5401i	0.505273	−	0.578281i
$921$	−12.2816	+	21.2723i	−0.404692	+	0.700947i
$922$	43.1849	+	2.80408i	1.42222	+	0.0923475i
$923$	7.70847	−	24.8369i	0.253727	−	0.817515i
$924$	−6.52711	−	0.851226i	−0.214726	−	0.0280033i
$925$	2.22424	+	1.28417i	0.0731327	+	0.0422232i
$926$	−17.7182	−	11.8233i	−0.582257	−	0.388539i
$927$	23.6380	+	40.9421i	0.776372	+	1.34472i
$928$	−28.5504	−	9.59473i	−0.937213	−	0.314962i
$929$	−24.1479	−	41.8254i	−0.792267	−	1.37225i	−0.924560	−	0.381036i	$-0.875567\pi$
$929$	−24.1479	−	41.8254i	−0.792267	−	1.37225i	0.132293	−	0.991211i	$-0.457766\pi$
$930$	13.0192	−	6.43022i	0.426917	−	0.210855i
$931$		−	24.2109i		−	0.793481i
$932$	17.0449	+	41.0086i	0.558323	+	1.34328i
$933$	27.1568	+	15.6790i	0.889074	+	0.513307i
$934$	28.7555	−	43.0924i	0.940909	−	1.41003i
$935$	0.793909			0.0259636
$936$	42.6782	+	23.0643i	1.39498	+	0.753880i
$937$	44.9307			1.46782			0.733910	−	0.679246i	$-0.237693\pi$
$937$	44.9307			1.46782			0.733910	+	0.679246i	$0.237693\pi$
$938$	4.12742	−	6.18528i	0.134765	−	0.201956i
$939$	−35.4522	−	20.4683i	−1.15694	−	0.667959i
$940$	22.7089	−	9.43875i	0.740683	−	0.307858i
$941$			29.6587i			0.966846i	0.875387	+	0.483423i	$0.160607\pi$
$941$			29.6587i			0.966846i	−0.875387	+	0.483423i	$0.839393\pi$
$942$	−40.1744	+	19.8423i	−1.30895	+	0.646496i
$943$	6.25575	+	10.8353i	0.203715	+	0.352845i
$944$	−7.53687	+	28.4045i	−0.245304	+	0.924488i
$945$	−3.44674	−	5.96993i	−0.112123	−	0.194202i
$946$	5.49737	+	3.66839i	0.178735	+	0.119270i
$947$	39.5738	+	22.8479i	1.28597	+	0.742458i	0.977934	−	0.208915i	$-0.0669933\pi$
$947$	39.5738	+	22.8479i	1.28597	+	0.742458i	0.308041	+	0.951373i	$0.400327\pi$
$948$	5.18726	−	39.7753i	0.168474	−	1.29184i
$949$	22.0496	+	23.8468i	0.715760	+	0.774100i
$950$	6.81240	+	0.442343i	0.221024	+	0.0143515i
$951$	12.8536	−	22.2631i	0.416808	−	0.721932i
$952$	2.83978	+	2.48126i	0.0920377	+	0.0804179i
$953$	24.6055	+	42.6179i	0.797049	+	1.38053i	0.921530	+	0.388307i	$0.126940\pi$
$953$	24.6055	+	42.6179i	0.797049	+	1.38053i	−0.124481	+	0.992222i	$0.539727\pi$
$954$	−41.3679	−	2.68611i	−1.33934	−	0.0869659i
$955$	−13.2311	+	7.63900i	−0.428149	+	0.247192i
$956$	−10.8536	−	26.1129i	−0.351030	−	0.844552i
$957$			12.4394i			0.402107i
$958$	−29.2928	+	14.4678i	−0.946409	+	0.467434i
$959$	−8.73194	+	15.1242i	−0.281969	+	0.488385i
$960$	−17.6271	+	13.6283i	−0.568912	+	0.439853i
$961$	−17.4092			−0.561586
$962$	−4.68413	+	12.2296i	−0.151022	+	0.394299i
$963$			7.63069i			0.245896i
$964$	−31.1732	+	40.7284i	−1.00402	+	1.31177i
$965$	19.0012	+	10.9703i	0.611669	+	0.353147i
$966$	−20.2348	−	40.9692i	−0.651043	−	1.31816i
$967$	2.78684			0.0896188			0.0448094	−	0.998996i	$-0.485732\pi$
$967$	2.78684			0.0896188			0.0448094	+	0.998996i	$0.485732\pi$
$968$	−27.5598	+	9.41146i	−0.885805	+	0.302496i
$969$	6.36219	+	11.0196i	0.204383	+	0.354002i
$970$	11.7101	+	0.760360i	0.375988	+	0.0244137i
$971$	−9.01116	+	5.20260i	−0.289182	+	0.166959i	−0.637573	−	0.770390i	$-0.720062\pi$
$971$	−9.01116	+	5.20260i	−0.289182	+	0.166959i	0.348391	+	0.937349i	$0.386728\pi$
$972$	−26.1553	−	20.0191i	−0.838931	−	0.642113i
$973$	−0.933800	−	0.539130i	−0.0299363	−	0.0172837i
$974$	1.33999	−	20.6368i	0.0429361	−	0.661247i
$975$	2.21752	+	9.79404i	0.0710175	+	0.313660i
$976$	−6.73649	+	25.3881i	−0.215630	+	0.812653i
$977$	−15.9698	+	27.6605i	−0.510919	+	0.884937i	0.489001	+	0.872283i	$0.337361\pi$
$977$	−15.9698	+	27.6605i	−0.510919	+	0.884937i	−0.999920	+	0.0126539i	$0.995972\pi$
$978$	−48.0089	−	32.0363i	−1.53516	−	1.02441i
$979$	10.0024	−	5.77491i	0.319679	−	0.184567i
$980$	−1.29719	+	9.94673i	−0.0414373	+	0.317737i
$981$	−20.5850	+	11.8848i	−0.657229	+	0.379451i
$982$	−14.1563	−	28.6622i	−0.451747	−	0.914648i
$983$	−30.7869			−0.981950			−0.490975	−	0.871174i	$-0.663359\pi$
$983$	−30.7869			−0.981950			−0.490975	+	0.871174i	$0.663359\pi$
$984$	−3.86778	−	11.3261i	−0.123300	−	0.361063i
$985$	7.19698	−	12.4655i	0.229315	−	0.397185i
$986$	3.95569	−	5.92792i	0.125975	−	0.188784i
$987$		−	48.2441i		−	1.53563i
$988$	3.23191	+	34.6594i	0.102821	+	1.10266i
$989$			45.8782i			1.45884i
$990$	4.69405	+	3.13233i	0.149187	+	0.0995520i
$991$	28.2028	−	48.8487i	0.895891	−	1.55173i	0.0631941	−	0.998001i	$-0.479871\pi$
$991$	28.2028	−	48.8487i	0.895891	−	1.55173i	0.832697	−	0.553728i	$-0.186795\pi$
$992$	−20.4412	+	4.13074i	−0.649010	+	0.131151i
$993$	70.8338			2.24784
$994$	12.8836	−	6.36325i	0.408644	−	0.201830i
$995$	11.1677	−	6.44767i	0.354040	−	0.204405i
$996$	−99.1457	−	12.9300i	−3.14155	−	0.409702i
$997$	16.3064	−	9.41450i	0.516429	−	0.298160i	−0.219044	−	0.975715i	$-0.570294\pi$
$997$	16.3064	−	9.41450i	0.516429	−	0.298160i	0.735472	+	0.677555i	$0.236960\pi$
$998$	27.8450	−	41.7280i	0.881419	−	1.32088i
$999$	−6.28395	+	10.8841i	−0.198816	+	0.344359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	520.2.by.c.61.8	✓	104
8.5	even	2	inner	520.2.by.c.61.45	yes	104
13.3	even	3	inner	520.2.by.c.341.45	yes	104
104.29	even	6	inner	520.2.by.c.341.8	yes	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.by.c.61.8	✓	104	1.1	even	1	trivial
520.2.by.c.61.45	yes	104	8.5	even	2	inner
520.2.by.c.341.8	yes	104	104.29	even	6	inner
520.2.by.c.341.45	yes	104	13.3	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.by (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17635 - 0.784979i) q^{2} +(-2.41200 - 1.39257i) q^{3} +(0.767616 + 1.84683i) q^{4} +1.00000i q^{5} +(1.74423 + 3.53152i) q^{6} +(-0.704365 - 1.22000i) q^{7} +(0.546731 - 2.77508i) q^{8} +(2.37849 + 4.11966i) q^{9} +O(q^{10})\)	\(q+(-1.17635 - 0.784979i) q^{2} +(-2.41200 - 1.39257i) q^{3} +(0.767616 + 1.84683i) q^{4} +1.00000i q^{5} +(1.74423 + 3.53152i) q^{6} +(-0.704365 - 1.22000i) q^{7} +(0.546731 - 2.77508i) q^{8} +(2.37849 + 4.11966i) q^{9} +(0.784979 - 1.17635i) q^{10} +(0.726457 + 0.419420i) q^{11} +(0.720341 - 5.52350i) q^{12} +(2.44780 + 2.64732i) q^{13} +(-0.129089 + 1.98806i) q^{14} +(1.39257 - 2.41200i) q^{15} +(-2.82153 + 2.83531i) q^{16} +(-0.473218 - 0.819638i) q^{17} +(0.435904 - 6.71324i) q^{18} +(4.18051 - 2.41362i) q^{19} +(-1.84683 + 0.767616i) q^{20} +3.92350i q^{21} +(-0.525334 - 1.06364i) q^{22} +(4.11754 - 7.13179i) q^{23} +(-5.18320 + 5.93213i) q^{24} -1.00000 q^{25} +(-0.801391 - 5.03565i) q^{26} -4.89341i q^{27} +(1.71244 - 2.23733i) q^{28} +(-4.61109 - 2.66221i) q^{29} +(-3.53152 + 1.74423i) q^{30} -3.68658 q^{31} +(5.54477 - 1.12048i) q^{32} +(-1.16814 - 2.02328i) q^{33} +(-0.0867266 + 1.33565i) q^{34} +(1.22000 - 0.704365i) q^{35} +(-5.78253 + 7.55497i) q^{36} +(-2.22424 - 1.28417i) q^{37} +(-6.81240 - 0.442343i) q^{38} +(-2.21752 - 9.79404i) q^{39} +(2.77508 + 0.546731i) q^{40} +(-0.759646 + 1.31575i) q^{41} +(3.07987 - 4.61543i) q^{42} +(-4.82468 + 2.78553i) q^{43} +(-0.216956 + 1.66359i) q^{44} +(-4.11966 + 2.37849i) q^{45} +(-10.4420 + 5.15733i) q^{46} -12.2962 q^{47} +(10.7539 - 2.90958i) q^{48} +(2.50774 - 4.34353i) q^{49} +(1.17635 + 0.784979i) q^{50} +2.63595i q^{51} +(-3.01016 + 6.55278i) q^{52} -6.16214i q^{53} +(-3.84122 + 5.75638i) q^{54} +(-0.419420 + 0.726457i) q^{55} +(-3.77069 + 1.28766i) q^{56} -13.4445 q^{57} +(3.33449 + 6.75131i) q^{58} +(6.36256 - 3.67343i) q^{59} +(5.52350 + 0.720341i) q^{60} +(5.68689 - 3.28333i) q^{61} +(4.33672 + 2.89388i) q^{62} +(3.35064 - 5.80349i) q^{63} +(-7.40217 - 3.03445i) q^{64} +(-2.64732 + 2.44780i) q^{65} +(-0.214085 + 3.29706i) q^{66} +(-3.23239 - 1.86622i) q^{67} +(1.15048 - 1.50312i) q^{68} +(-19.8630 + 11.4679i) q^{69} +(-1.98806 - 0.129089i) q^{70} +(-3.60632 - 6.24634i) q^{71} +(12.7328 - 4.34815i) q^{72} +9.00792 q^{73} +(1.60845 + 3.25662i) q^{74} +(2.41200 + 1.39257i) q^{75} +(7.66657 + 5.86795i) q^{76} -1.18170i q^{77} +(-5.07953 + 13.2620i) q^{78} +7.20112 q^{79} +(-2.83531 - 2.82153i) q^{80} +(0.321063 - 0.556098i) q^{81} +(1.92644 - 0.951476i) q^{82} -17.9498i q^{83} +(-7.24602 + 3.01174i) q^{84} +(0.819638 - 0.473218i) q^{85} +(7.86212 + 0.510503i) q^{86} +(7.41462 + 12.8425i) q^{87} +(1.56110 - 1.78667i) q^{88} +(6.88440 - 11.9241i) q^{89} +(6.71324 + 0.435904i) q^{90} +(1.50557 - 4.85098i) q^{91} +(16.3319 + 2.12990i) q^{92} +(8.89201 + 5.13380i) q^{93} +(14.4647 + 9.65225i) q^{94} +(2.41362 + 4.18051i) q^{95} +(-14.9343 - 5.01887i) q^{96} +(4.14886 + 7.18604i) q^{97} +(-6.35957 + 3.14101i) q^{98} +3.99034i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q + 2 q^{6} - 4 q^{7} + 12 q^{8} + 60 q^{9}+O(q^{10}) \) 104 * q + 2 * q^6 - 4 * q^7 + 12 * q^8 + 60 * q^9	\( 104 q + 2 q^{6} - 4 q^{7} + 12 q^{8} + 60 q^{9} - 28 q^{12} - 24 q^{14} + 4 q^{15} - 20 q^{16} + 4 q^{17} - 40 q^{18} - 4 q^{20} + 24 q^{22} + 32 q^{23} + 24 q^{24} - 104 q^{25} - 10 q^{26} + 22 q^{28} - 12 q^{30} - 40 q^{31} + 30 q^{32} + 12 q^{33} - 4 q^{34} + 18 q^{36} + 56 q^{39} - 16 q^{41} - 20 q^{42} - 32 q^{44} - 30 q^{46} - 56 q^{47} - 24 q^{48} - 80 q^{49} - 6 q^{52} - 10 q^{54} + 16 q^{55} - 38 q^{56} + 104 q^{57} - 68 q^{58} - 12 q^{62} + 12 q^{63} - 108 q^{64} + 180 q^{66} - 6 q^{68} + 8 q^{70} - 72 q^{71} - 80 q^{72} + 24 q^{73} + 40 q^{74} - 20 q^{76} - 52 q^{78} - 40 q^{79} - 24 q^{80} - 60 q^{81} + 64 q^{82} - 70 q^{84} + 140 q^{86} - 8 q^{87} + 86 q^{88} + 36 q^{89} - 20 q^{90} + 76 q^{92} + 46 q^{94} - 32 q^{95} + 12 q^{96} + 12 q^{97} - 8 q^{98}+O(q^{100}) \) 104 * q + 2 * q^6 - 4 * q^7 + 12 * q^8 + 60 * q^9 - 28 * q^12 - 24 * q^14 + 4 * q^15 - 20 * q^16 + 4 * q^17 - 40 * q^18 - 4 * q^20 + 24 * q^22 + 32 * q^23 + 24 * q^24 - 104 * q^25 - 10 * q^26 + 22 * q^28 - 12 * q^30 - 40 * q^31 + 30 * q^32 + 12 * q^33 - 4 * q^34 + 18 * q^36 + 56 * q^39 - 16 * q^41 - 20 * q^42 - 32 * q^44 - 30 * q^46 - 56 * q^47 - 24 * q^48 - 80 * q^49 - 6 * q^52 - 10 * q^54 + 16 * q^55 - 38 * q^56 + 104 * q^57 - 68 * q^58 - 12 * q^62 + 12 * q^63 - 108 * q^64 + 180 * q^66 - 6 * q^68 + 8 * q^70 - 72 * q^71 - 80 * q^72 + 24 * q^73 + 40 * q^74 - 20 * q^76 - 52 * q^78 - 40 * q^79 - 24 * q^80 - 60 * q^81 + 64 * q^82 - 70 * q^84 + 140 * q^86 - 8 * q^87 + 86 * q^88 + 36 * q^89 - 20 * q^90 + 76 * q^92 + 46 * q^94 - 32 * q^95 + 12 * q^96 + 12 * q^97 - 8 * q^98

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