LMFDB - Embedded newform 572.2.bn.a.459.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(95,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 21, 5]))

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

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

chi := DirichletCharacter("572.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bn (of order $30$, degree $8$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$80$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			459.27
Character	$\chi$	$=$	572.459
Dual form			572.2.bn.a.491.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.748680 - 1.19978i) q^{2} +(0.283140 - 1.33207i) q^{3} +(-0.878956 + 1.79651i) q^{4} +(-0.329599 + 0.453654i) q^{5} +(-1.81017 + 0.657587i) q^{6} +(-0.174143 - 0.819278i) q^{7} +(2.81347 - 0.290453i) q^{8} +(1.04640 + 0.465888i) q^{9} +O(q^{10})$	\(q+(-0.748680 - 1.19978i) q^{2} +(0.283140 - 1.33207i) q^{3} +(-0.878956 + 1.79651i) q^{4} +(-0.329599 + 0.453654i) q^{5} +(-1.81017 + 0.657587i) q^{6} +(-0.174143 - 0.819278i) q^{7} +(2.81347 - 0.290453i) q^{8} +(1.04640 + 0.465888i) q^{9} +(0.791051 + 0.0558053i) q^{10} +(2.09334 + 2.57254i) q^{11} +(2.14420 + 1.67949i) q^{12} +(3.07247 + 1.88677i) q^{13} +(-0.852578 + 0.822311i) q^{14} +(0.510976 + 0.567496i) q^{15} +(-2.45487 - 3.15810i) q^{16} +(5.40318 + 0.567897i) q^{17} +(-0.224456 - 1.60425i) q^{18} +(-1.49174 - 1.34317i) q^{19} +(-0.525290 - 0.990869i) q^{20} -1.14064 q^{21} +(1.51924 - 4.43756i) q^{22} +(-7.01090 - 4.04774i) q^{23} +(0.409703 - 3.82998i) q^{24} +(1.44792 + 4.45623i) q^{25} +(-0.0365797 - 5.09889i) q^{26} +(3.31826 - 4.56719i) q^{27} +(1.62490 + 0.407260i) q^{28} +(1.35149 - 1.21689i) q^{29} +(0.298314 - 1.03793i) q^{30} +(4.78001 - 3.47288i) q^{31} +(-1.95112 + 5.30972i) q^{32} +(4.01950 - 2.06008i) q^{33} +(-3.36390 - 6.90782i) q^{34} +(0.429067 + 0.191033i) q^{35} +(-1.75671 + 1.47037i) q^{36} +(0.880308 - 0.792633i) q^{37} +(-0.494674 + 2.79537i) q^{38} +(3.38325 - 3.55852i) q^{39} +(-0.795553 + 1.37208i) q^{40} +(-7.54001 - 1.60268i) q^{41} +(0.853975 + 1.36852i) q^{42} +(3.10539 + 5.37869i) q^{43} +(-6.46153 + 1.49955i) q^{44} +(-0.556245 + 0.321148i) q^{45} +(0.392509 + 11.4420i) q^{46} +(0.292632 + 0.900628i) q^{47} +(-4.90187 + 2.37587i) q^{48} +(5.75393 - 2.56181i) q^{49} +(4.26248 - 5.07348i) q^{50} +(2.28633 - 7.03661i) q^{51} +(-6.09017 + 3.86132i) q^{52} +(9.70361 - 7.05009i) q^{53} +(-7.96394 - 0.561822i) q^{54} +(-1.85700 + 0.101746i) q^{55} +(-0.727909 - 2.25444i) q^{56} +(-2.21156 + 1.60680i) q^{57} +(-2.47184 - 0.710437i) q^{58} +(0.0189921 - 0.00403689i) q^{59} +(-1.46864 + 0.419167i) q^{60} +(-12.1375 - 1.27570i) q^{61} +(-7.74540 - 3.13490i) q^{62} +(0.199468 - 0.938425i) q^{63} +(7.83127 - 1.63437i) q^{64} +(-1.86863 + 0.771961i) q^{65} +(-5.48097 - 3.28018i) q^{66} +(-1.89884 + 3.28888i) q^{67} +(-5.76939 + 9.20770i) q^{68} +(-7.37693 + 8.19291i) q^{69} +(-0.0920359 - 0.657809i) q^{70} +(1.02249 - 9.72834i) q^{71} +(3.07934 + 1.00683i) q^{72} +(-1.23344 + 3.79615i) q^{73} +(-1.61006 - 0.462749i) q^{74} +(6.34597 - 0.666988i) q^{75} +(3.72419 - 1.49934i) q^{76} +(1.74308 - 2.16302i) q^{77} +(-6.80242 - 1.39497i) q^{78} +(-3.38131 + 2.45667i) q^{79} +(2.24181 - 0.0727569i) q^{80} +(-2.84495 - 3.15964i) q^{81} +(3.72219 + 10.2463i) q^{82} +(-1.83934 + 2.53163i) q^{83} +(1.00257 - 2.04917i) q^{84} +(-2.03851 + 2.26400i) q^{85} +(4.12832 - 7.75271i) q^{86} +(-1.23832 - 2.14483i) q^{87} +(6.63675 + 6.62974i) q^{88} +(-6.41766 - 3.70524i) q^{89} +(0.801758 + 0.426936i) q^{90} +(1.01074 - 2.84578i) q^{91} +(13.4341 - 9.03734i) q^{92} +(-3.27270 - 7.35061i) q^{93} +(0.861470 - 1.02538i) q^{94} +(1.10101 - 0.234027i) q^{95} +(6.52047 + 4.10241i) q^{96} +(-7.43998 + 16.7105i) q^{97} +(-7.38147 - 4.98548i) q^{98} +(0.991958 + 3.66716i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 15 q^{2} - 3 q^{4} - 15 q^{6} - 78 q^{9}+O(q^{10}) $ 640 * q - 15 * q^2 - 3 * q^4 - 15 * q^6 - 78 * q^9	$ 640 q - 15 q^{2} - 3 q^{4} - 15 q^{6} - 78 q^{9} - 4 q^{12} - 20 q^{13} - 12 q^{14} - 19 q^{16} - 10 q^{17} - 45 q^{20} - 15 q^{22} - 15 q^{24} + 104 q^{25} - 20 q^{26} - 15 q^{28} - 10 q^{29} + 45 q^{30} - 24 q^{33} + 4 q^{36} - 18 q^{37} - 14 q^{38} - 20 q^{40} - 30 q^{41} - 13 q^{42} - 108 q^{45} - 15 q^{46} + 35 q^{48} - 74 q^{49} - 90 q^{50} + 15 q^{52} - 8 q^{53} + 50 q^{56} + 27 q^{58} - 10 q^{61} - 5 q^{62} - 84 q^{64} - 146 q^{66} - 70 q^{68} - 26 q^{69} - 15 q^{72} - 55 q^{74} + 44 q^{77} + 24 q^{78} - 39 q^{80} + 30 q^{81} - 29 q^{82} + 30 q^{84} - 30 q^{85} - 75 q^{88} - 24 q^{89} + 30 q^{90} + 14 q^{92} + 66 q^{93} - 5 q^{94} - 30 q^{97}+O(q^{100}) $ 640 * q - 15 * q^2 - 3 * q^4 - 15 * q^6 - 78 * q^9 - 4 * q^12 - 20 * q^13 - 12 * q^14 - 19 * q^16 - 10 * q^17 - 45 * q^20 - 15 * q^22 - 15 * q^24 + 104 * q^25 - 20 * q^26 - 15 * q^28 - 10 * q^29 + 45 * q^30 - 24 * q^33 + 4 * q^36 - 18 * q^37 - 14 * q^38 - 20 * q^40 - 30 * q^41 - 13 * q^42 - 108 * q^45 - 15 * q^46 + 35 * q^48 - 74 * q^49 - 90 * q^50 + 15 * q^52 - 8 * q^53 + 50 * q^56 + 27 * q^58 - 10 * q^61 - 5 * q^62 - 84 * q^64 - 146 * q^66 - 70 * q^68 - 26 * q^69 - 15 * q^72 - 55 * q^74 + 44 * q^77 + 24 * q^78 - 39 * q^80 + 30 * q^81 - 29 * q^82 + 30 * q^84 - 30 * q^85 - 75 * q^88 - 24 * q^89 + 30 * q^90 + 14 * q^92 + 66 * q^93 - 5 * q^94 - 30 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.748680	−	1.19978i	−0.529397	−	0.848374i
$2$	−0.748680	−	1.19978i	−0.529397	−	0.848374i
$3$	0.283140	−	1.33207i	0.163471	−	0.769069i	−0.817657	−	0.575706i	$-0.804727\pi$
$3$	0.283140	−	1.33207i	0.163471	−	0.769069i	0.981127	−	0.193363i	$-0.0619395\pi$
$4$	−0.878956	+	1.79651i	−0.439478	+	0.898253i
$5$	−0.329599	+	0.453654i	−0.147401	+	0.202880i	−0.876333	−	0.481706i	$-0.840017\pi$
$5$	−0.329599	+	0.453654i	−0.147401	+	0.202880i	0.728932	+	0.684587i	$0.240017\pi$
$6$	−1.81017	+	0.657587i	−0.739000	+	0.268459i
$7$	−0.174143	−	0.819278i	−0.0658199	−	0.309658i	0.932906	−	0.360120i	$-0.117264\pi$
$7$	−0.174143	−	0.819278i	−0.0658199	−	0.309658i	−0.998726	+	0.0504615i	$0.983931\pi$
$8$	2.81347	−	0.290453i	0.994713	−	0.102691i
$9$	1.04640	+	0.465888i	0.348800	+	0.155296i
$10$	0.791051	+	0.0558053i	0.250152	+	0.0176472i
$11$	2.09334	+	2.57254i	0.631165	+	0.775649i
$11$	2.09334	+	2.57254i	0.631165	+	0.775649i
$12$	2.14420	+	1.67949i	0.618977	+	0.484827i
$13$	3.07247	+	1.88677i	0.852150	+	0.523297i
$13$	3.07247	+	1.88677i	0.852150	+	0.523297i
$14$	−0.852578	+	0.822311i	−0.227861	+	0.219772i
$15$	0.510976	+	0.567496i	0.131933	+	0.146527i
$16$	−2.45487	−	3.15810i	−0.613718	−	0.789525i
$17$	5.40318	+	0.567897i	1.31046	+	0.137735i	0.733867	−	0.679293i	$-0.237713\pi$
$17$	5.40318	+	0.567897i	1.31046	+	0.137735i	0.576597	+	0.817028i	$0.304380\pi$
$18$	−0.224456	−	1.60425i	−0.0529047	−	0.378126i
$19$	−1.49174	−	1.34317i	−0.342229	−	0.308144i	0.480036	−	0.877249i	$-0.340623\pi$
$19$	−1.49174	−	1.34317i	−0.342229	−	0.308144i	−0.822265	+	0.569104i	$0.807290\pi$
$20$	−0.525290	−	0.990869i	−0.117458	−	0.221565i
$21$	−1.14064			−0.248908
$22$	1.51924	−	4.43756i	0.323903	−	0.946090i
$23$	−7.01090	−	4.04774i	−1.46187	−	0.844013i	−0.462775	−	0.886476i	$-0.653146\pi$
$23$	−7.01090	−	4.04774i	−1.46187	−	0.844013i	−0.999098	+	0.0424630i	$0.986480\pi$
$24$	0.409703	−	3.82998i	0.0836302	−	0.781791i
$25$	1.44792	+	4.45623i	0.289584	+	0.891247i
$26$	−0.0365797	−	5.09889i	−0.00717387	−	0.999974i
$27$	3.31826	−	4.56719i	0.638599	−	0.878956i
$28$	1.62490	+	0.407260i	0.307078	+	0.0769650i
$29$	1.35149	−	1.21689i	0.250966	−	0.225971i	−0.534039	−	0.845460i	$-0.679327\pi$
$29$	1.35149	−	1.21689i	0.250966	−	0.225971i	0.785006	+	0.619489i	$0.212660\pi$
$30$	0.298314	−	1.03793i	0.0544645	−	0.189500i
$31$	4.78001	−	3.47288i	0.858516	−	0.623748i	−0.0689651	−	0.997619i	$-0.521970\pi$
$31$	4.78001	−	3.47288i	0.858516	−	0.623748i	0.927481	+	0.373871i	$0.121970\pi$
$32$	−1.95112	+	5.30972i	−0.344912	+	0.938635i
$33$	4.01950	−	2.06008i	0.699705	−	0.358614i
$34$	−3.36390	−	6.90782i	−0.576905	−	1.18468i
$35$	0.429067	+	0.191033i	0.0725255	+	0.0322904i
$36$	−1.75671	+	1.47037i	−0.292785	+	0.245062i
$37$	0.880308	−	0.792633i	0.144722	−	0.130308i	−0.593590	−	0.804768i	$-0.702290\pi$
$37$	0.880308	−	0.792633i	0.144722	−	0.130308i	0.738312	+	0.674459i	$0.235623\pi$
$38$	−0.494674	+	2.79537i	−0.0802468	+	0.453469i
$39$	3.38325	−	3.55852i	0.541753	−	0.569819i
$40$	−0.795553	+	1.37208i	−0.125788	+	0.216945i
$41$	−7.54001	−	1.60268i	−1.17755	−	0.250296i	−0.422748	−	0.906247i	$-0.638935\pi$
$41$	−7.54001	−	1.60268i	−1.17755	−	0.250296i	−0.754804	+	0.655951i	$0.772268\pi$
$42$	0.853975	+	1.36852i	0.131771	+	0.211167i
$43$	3.10539	+	5.37869i	0.473568	+	0.820243i	0.999542	−	0.0302573i	$-0.00963266\pi$
$43$	3.10539	+	5.37869i	0.473568	+	0.820243i	−0.525975	+	0.850500i	$0.676299\pi$
$44$	−6.46153	+	1.49955i	−0.974112	+	0.226066i
$45$	−0.556245	+	0.321148i	−0.0829201	+	0.0478739i
$46$	0.392509	+	11.4420i	0.0578723	+	1.68703i
$47$	0.292632	+	0.900628i	0.0426847	+	0.131370i	0.970128	−	0.242594i	$-0.0779983\pi$
$47$	0.292632	+	0.900628i	0.0426847	+	0.131370i	−0.927443	+	0.373964i	$0.877998\pi$
$48$	−4.90187	+	2.37587i	−0.707525	+	0.342928i
$49$	5.75393	−	2.56181i	0.821990	−	0.365973i
$50$	4.26248	−	5.07348i	0.602806	−	0.717499i
$51$	2.28633	−	7.03661i	0.320151	−	0.985323i
$52$	−6.09017	+	3.86132i	−0.844555	+	0.535469i
$53$	9.70361	−	7.05009i	1.33289	−	0.968404i	0.333220	−	0.942849i	$-0.391865\pi$
$53$	9.70361	−	7.05009i	1.33289	−	0.968404i	0.999673	−	0.0255546i	$-0.00813517\pi$
$54$	−7.96394	−	0.561822i	−1.08376	−	0.0764543i
$55$	−1.85700	+	0.101746i	−0.250398	+	0.0137195i
$56$	−0.727909	−	2.25444i	−0.0972709	−	0.301262i
$57$	−2.21156	+	1.60680i	−0.292929	+	0.212825i
$58$	−2.47184	−	0.710437i	−0.324569	−	0.0932850i
$59$	0.0189921	−	0.00403689i	0.00247256	−	0.000525558i	−0.206675	−	0.978410i	$-0.566264\pi$
$59$	0.0189921	−	0.00403689i	0.00247256	−	0.000525558i	0.209148	+	0.977884i	$0.432931\pi$
$60$	−1.46864	+	0.419167i	−0.189600	+	0.0541143i
$61$	−12.1375	−	1.27570i	−1.55405	−	0.163337i	−0.711783	−	0.702400i	$-0.752112\pi$
$61$	−12.1375	−	1.27570i	−1.55405	−	0.163337i	−0.842266	+	0.539063i	$0.818779\pi$
$62$	−7.74540	−	3.13490i	−0.983667	−	0.398132i
$63$	0.199468	−	0.938425i	0.0251306	−	0.118230i
$64$	7.83127	−	1.63437i	0.978909	−	0.204296i
$65$	−1.86863	+	0.771961i	−0.231775	+	0.0957500i
$66$	−5.48097	−	3.28018i	−0.674660	−	0.403762i
$67$	−1.89884	+	3.28888i	−0.231980	+	0.401801i	−0.958391	−	0.285460i	$-0.907854\pi$
$67$	−1.89884	+	3.28888i	−0.231980	+	0.401801i	0.726411	+	0.687261i	$0.241187\pi$
$68$	−5.76939	+	9.20770i	−0.699641	+	1.11660i
$69$	−7.37693	+	8.19291i	−0.888078	+	0.986310i
$70$	−0.0920359	−	0.657809i	−0.0110004	−	0.0786232i
$71$	1.02249	−	9.72834i	0.121347	−	1.15454i	−0.749161	−	0.662388i	$-0.769543\pi$
$71$	1.02249	−	9.72834i	0.121347	−	1.15454i	0.870508	−	0.492154i	$-0.163790\pi$
$72$	3.07934	+	1.00683i	0.362904	+	0.118656i
$73$	−1.23344	+	3.79615i	−0.144364	+	0.444306i	−0.996929	−	0.0783154i	$-0.975046\pi$
$73$	−1.23344	+	3.79615i	−0.144364	+	0.444306i	0.852565	+	0.522621i	$0.175046\pi$
$74$	−1.61006	−	0.462749i	−0.187165	−	0.0537935i
$75$	6.34597	−	0.666988i	0.732769	−	0.0770171i
$76$	3.72419	−	1.49934i	0.427194	−	0.171986i
$77$	1.74308	−	2.16302i	0.198643	−	0.246498i
$78$	−6.80242	−	1.39497i	−0.770222	−	0.157949i
$79$	−3.38131	+	2.45667i	−0.380427	+	0.276396i	−0.761521	−	0.648140i	$-0.775547\pi$
$79$	−3.38131	+	2.45667i	−0.380427	+	0.276396i	0.381094	+	0.924536i	$0.375547\pi$
$80$	2.24181	−	0.0727569i	0.250642	−	0.00813446i
$81$	−2.84495	−	3.15964i	−0.316105	−	0.351071i
$82$	3.72219	+	10.2463i	0.411047	+	1.13151i
$83$	−1.83934	+	2.53163i	−0.201893	+	0.277882i	−0.897943	−	0.440111i	$-0.854939\pi$
$83$	−1.83934	+	2.53163i	−0.201893	+	0.277882i	0.696050	+	0.717993i	$0.254939\pi$
$84$	1.00257	−	2.04917i	0.109390	−	0.223583i
$85$	−2.03851	+	2.26400i	−0.221108	+	0.245565i
$86$	4.12832	−	7.75271i	0.445168	−	0.835997i
$87$	−1.23832	−	2.14483i	−0.132762	−	0.229950i
$88$	6.63675	+	6.62974i	0.707480	+	0.706733i
$89$	−6.41766	−	3.70524i	−0.680271	−	0.392754i	0.119686	−	0.992812i	$-0.461811\pi$
$89$	−6.41766	−	3.70524i	−0.680271	−	0.392754i	−0.799957	+	0.600057i	$0.795144\pi$
$90$	0.801758	+	0.426936i	0.0845127	+	0.0450030i
$91$	1.01074	−	2.84578i	0.105955	−	0.298319i
$92$	13.4341	−	9.03734i	1.40060	−	0.942207i
$93$	−3.27270	−	7.35061i	−0.339363	−	0.762223i
$94$	0.861470	−	1.02538i	0.0888538	−	0.105760i
$95$	1.10101	−	0.234027i	0.112961	−	0.0240107i
$96$	6.52047	+	4.10241i	0.665492	+	0.418701i
$97$	−7.43998	+	16.7105i	−0.755416	+	1.69669i	−0.0387760	+	0.999248i	$0.512346\pi$
$97$	−7.43998	+	16.7105i	−0.755416	+	1.69669i	−0.716640	+	0.697444i	$0.754321\pi$
$98$	−7.38147	−	4.98548i	−0.745641	−	0.503610i
$99$	0.991958	+	3.66716i	0.0996955	+	0.368564i
$100$	−9.27831	−	1.31564i	−0.927831	−	0.131564i
$101$	3.98270	−	0.418598i	0.396293	−	0.0416521i	0.0957137	−	0.995409i	$-0.469487\pi$
$101$	3.98270	−	0.418598i	0.396293	−	0.0416521i	0.300579	+	0.953757i	$0.402820\pi$
$102$	−10.1541	+	2.52507i	−1.00541	+	0.250019i
$103$	19.1859	+	6.23386i	1.89044	+	0.614241i	0.979403	+	0.201913i	$0.0647158\pi$
$103$	19.1859	+	6.23386i	1.89044	+	0.614241i	0.911036	+	0.412328i	$0.135284\pi$
$104$	9.19234	+	4.41598i	0.901383	+	0.433023i
$105$	0.375954	−	0.517457i	0.0366894	−	0.0504986i
$106$	−15.7235	−	6.36396i	−1.52720	−	0.618123i
$107$	13.6174	+	2.89447i	1.31644	+	0.279819i	0.812016	−	0.583635i	$-0.198370\pi$
$107$	13.6174	+	2.89447i	1.31644	+	0.279819i	0.504428	+	0.863454i	$0.331703\pi$
$108$	5.28838	+	9.97563i	0.508875	+	0.959905i
$109$	14.6283			1.40114			0.700569	−	0.713585i	$-0.252930\pi$
$109$	14.6283			1.40114			0.700569	+	0.713585i	$0.252930\pi$
$110$	1.51238	+	2.15183i	0.144199	+	0.205169i
$111$	−0.806590	−	1.39706i	−0.0765582	−	0.132603i
$112$	−2.15986	+	2.56119i	−0.204088	+	0.242009i
$113$	10.1960	−	11.3238i	0.959157	−	1.06525i	−0.0386625	−	0.999252i	$-0.512310\pi$
$113$	10.1960	−	11.3238i	0.959157	−	1.06525i	0.997820	−	0.0659996i	$-0.0210236\pi$
$114$	3.58356	+	1.45042i	0.335631	+	0.135844i
$115$	4.14706	−	1.84639i	0.386716	−	0.172177i
$116$	0.998249	+	3.49756i	0.0926851	+	0.324741i
$117$	2.33601	+	3.40575i	0.215964	+	0.314862i
$118$	−0.0190624	−	0.0197640i	−0.00175483	−	0.00181942i
$119$	−0.475660	−	4.52561i	−0.0436037	−	0.414862i
$120$	1.60245	+	1.44822i	0.146283	+	0.132204i
$121$	−2.23587	+	10.7704i	−0.203261	+	0.979125i
$122$	7.55655	+	15.5175i	0.684137	+	1.40488i
$123$	−4.26975	+	9.59002i	−0.384991	+	0.864703i
$124$	2.03764	+	11.6398i	0.182985	+	1.04529i
$125$	−5.16534	−	1.67832i	−0.462002	−	0.150113i
$126$	−1.27524	+	0.463261i	−0.113608	+	0.0412706i
$127$	−10.3120	+	4.59122i	−0.915046	+	0.407405i	−0.809574	−	0.587017i	$-0.800302\pi$
$127$	−10.3120	+	4.59122i	−0.915046	+	0.407405i	−0.105472	+	0.994422i	$0.533635\pi$
$128$	−7.82400	−	8.17221i	−0.691551	−	0.722328i
$129$	8.04404	−	2.61367i	0.708238	−	0.230121i
$130$	2.32519	+	1.66400i	0.203933	+	0.145942i
$131$	−19.8413			−1.73354			−0.866770	−	0.498708i	$-0.833808\pi$
$131$	−19.8413			−1.73354			−0.866770	+	0.498708i	$0.833808\pi$
$132$	0.167988	+	9.03177i	0.0146215	+	0.786115i
$133$	−0.840654	+	1.45606i	−0.0728939	+	0.126256i
$134$	5.36757	−	0.184130i	0.463687	−	0.0159064i
$135$	0.978230	+	3.01068i	0.0841927	+	0.259118i
$136$	15.3667	+	0.0283914i	1.31768	+	0.00243454i
$137$	−20.1315	−	2.11591i	−1.71995	−	0.180774i	−0.807476	−	0.589900i	$-0.799167\pi$
$137$	−20.1315	−	2.11591i	−1.71995	−	0.180774i	−0.912478	+	0.409126i	$0.865834\pi$
$138$	15.3527	+	2.71684i	1.30691	+	0.231273i
$139$	8.50886	−	1.80861i	0.721712	−	0.153405i	0.167610	−	0.985853i	$-0.446395\pi$
$139$	8.50886	−	1.80861i	0.721712	−	0.153405i	0.554102	+	0.832449i	$0.313062\pi$
$140$	−0.720322	+	0.602912i	−0.0608783	+	0.0509553i
$141$	1.28255	−	0.134802i	0.108010	−	0.0113524i
$142$	−12.4374	+	6.05665i	−1.04372	+	0.508263i
$143$	1.57793	+	11.8537i	0.131953	+	0.991256i
$144$	−1.09746	−	4.44833i	−0.0914552	−	0.370695i
$145$	0.106596	+	1.01420i	0.00885236	+	0.0842245i
$146$	5.47801	−	1.36224i	0.453364	−	0.112740i
$147$	−1.78334	−	8.38997i	−0.147088	−	0.691993i
$148$	0.650219	+	2.27817i	0.0534476	+	0.187264i
$149$	−0.420130	+	3.99727i	−0.0344184	+	0.327469i	0.963742	+	0.266836i	$0.0859784\pi$
$149$	−0.420130	+	3.99727i	−0.0344184	+	0.327469i	−0.998160	+	0.0606323i	$0.980688\pi$
$150$	−5.55134	−	7.11442i	−0.453265	−	0.580890i
$151$	−8.00230	+	2.60010i	−0.651218	+	0.211593i	−0.615951	−	0.787785i	$-0.711228\pi$
$151$	−8.00230	+	2.60010i	−0.651218	+	0.211593i	−0.0352666	+	0.999378i	$0.511228\pi$
$152$	−4.58710	−	3.34569i	−0.372063	−	0.271372i
$153$	5.38932	+	3.11153i	0.435701	+	0.251552i
$154$	−3.90016	−	0.471913i	−0.314284	−	0.0380278i
$155$			3.31313i			0.266117i
$156$	3.41918	+	9.20581i	0.273753	+	0.737055i
$157$	−0.138568	−	0.426468i	−0.0110589	−	0.0340358i	0.945375	−	0.325985i	$-0.105696\pi$
$157$	−0.138568	−	0.426468i	−0.0110589	−	0.0340358i	−0.956434	+	0.291950i	$0.905696\pi$
$158$	5.47898	+	2.21758i	0.435884	+	0.176421i
$159$	−6.64371	−	14.9220i	−0.526881	−	1.18339i
$160$	−1.76569	−	2.63521i	−0.139590	−	0.208332i
$161$	−2.09533	+	6.44876i	−0.165135	+	0.508234i
$162$	−1.66092	+	5.77888i	−0.130494	+	0.454031i
$163$	14.5371	+	6.47235i	1.13864	+	0.506953i	0.887413	−	0.460976i	$-0.152501\pi$
$163$	14.5371	+	6.47235i	1.13864	+	0.506953i	0.251223	+	0.967929i	$0.419167\pi$
$164$	9.50656	−	12.1370i	0.742338	−	0.947740i
$165$	−0.390259	+	2.50246i	−0.0303816	+	0.194817i
$166$	4.41448	+	0.311422i	0.342630	+	0.0241711i
$167$	−15.8422	+	1.66509i	−1.22591	+	0.128848i	−0.695269	−	0.718749i	$-0.744715\pi$
$167$	−15.8422	+	1.66509i	−1.22591	+	0.128848i	−0.530640	+	0.847597i	$0.678048\pi$
$168$	−3.20916	+	0.331303i	−0.247592	+	0.0255606i
$169$	5.88016	+	11.5941i	0.452320	+	0.891856i
$170$	4.24250	+	0.750762i	0.325385	+	0.0575808i
$171$	−0.935193	−	2.10048i	−0.0715160	−	0.160628i
$172$	−12.3924	+	0.851221i	−0.944909	+	0.0649050i
$173$	5.03412	+	4.53274i	0.382737	+	0.344618i	0.837933	−	0.545773i	$-0.183764\pi$
$173$	5.03412	+	4.53274i	0.382737	+	0.344618i	−0.455196	+	0.890391i	$0.650431\pi$
$174$	−1.64623	+	3.09151i	−0.124800	+	0.234367i
$175$	3.39875	−	1.96227i	0.256921	−	0.148334i
$176$	2.98544	−	12.9262i	0.225036	−	0.974350i
$177$		−	0.0264417i		−	0.00198748i
$178$	0.359296	+	10.4738i	0.0269304	+	0.785047i
$179$	−1.29174	+	6.07716i	−0.0965492	+	0.454228i	0.903141	+	0.429344i	$0.141255\pi$
$179$	−1.29174	+	6.07716i	−0.0965492	+	0.454228i	−0.999690	+	0.0248845i	$0.992078\pi$
$180$	−0.0880302	−	1.28157i	−0.00656138	−	0.0955228i
$181$	−11.1470	−	8.09874i	−0.828547	−	0.601975i	0.0906009	−	0.995887i	$-0.471121\pi$
$181$	−11.1470	−	8.09874i	−0.828547	−	0.601975i	−0.919148	+	0.393913i	$0.871121\pi$
$182$	−4.17104	+	0.917905i	−0.309178	+	0.0680396i
$183$	−5.13593	+	15.8068i	−0.379659	+	1.16847i
$184$	−20.9007	−	9.35188i	−1.54082	−	0.689430i
$185$	0.0694326	+	0.660607i	0.00510478	+	0.0485688i
$186$	−6.36892	+	9.42979i	−0.466992	+	0.691425i
$187$	9.84975	+	15.0887i	0.720285	+	1.10339i
$188$	−1.87519	−	0.265897i	−0.136763	−	0.0193925i
$189$	−4.31965	−	1.92323i	−0.314208	−	0.139895i
$190$	−1.10509	−	1.14576i	−0.0801715	−	0.0831224i
$191$	−1.86423	−	8.77052i	−0.134891	−	0.634612i	−0.992697	−	0.120638i	$-0.961506\pi$
$191$	−1.86423	−	8.77052i	−0.134891	−	0.634612i	0.857806	−	0.513974i	$-0.171827\pi$
$192$	0.0402576	−	10.8945i	0.00290534	−	0.786246i
$193$	−12.5480	+	5.58672i	−0.903223	+	0.402141i	−0.805173	−	0.593040i	$-0.797927\pi$
$193$	−12.5480	+	5.58672i	−0.903223	+	0.402141i	−0.0980507	+	0.995181i	$0.531261\pi$
$194$	25.6191	−	3.58444i	1.83934	−	0.257348i
$195$	0.499221	+	2.70771i	0.0357500	+	0.193903i
$196$	−0.455132	+	12.5887i	−0.0325094	+	0.899192i
$197$	9.00373	−	15.5949i	0.641489	−	1.11109i	−0.343611	−	0.939112i	$-0.611650\pi$
$197$	9.00373	−	15.5949i	0.641489	−	1.11109i	0.985100	−	0.171980i	$-0.0550164\pi$
$198$	3.65714	−	3.93567i	0.259902	−	0.279696i
$199$	1.78009	−	1.02774i	0.126187	−	0.0728543i	−0.435578	−	0.900151i	$-0.643456\pi$
$199$	1.78009	−	1.02774i	0.126187	−	0.0728543i	0.561765	+	0.827297i	$0.310123\pi$
$200$	5.36801	+	12.1169i	0.379576	+	0.856798i
$201$	3.84338	+	3.46059i	0.271091	+	0.244091i
$202$	−3.48399	−	4.46497i	−0.245133	−	0.314154i
$203$	−1.23233	−	0.895337i	−0.0864923	−	0.0628403i
$204$	10.6317	+	10.2923i	0.744370	+	0.720604i
$205$	3.21224	−	2.89232i	0.224353	−	0.202008i
$206$	−6.88479	−	27.6860i	−0.479686	−	1.92898i
$207$	−5.45042	−	7.50185i	−0.378830	−	0.521415i
$208$	−1.58391	−	14.3350i	−0.109824	−	0.993951i
$209$	0.332633	−	6.64927i	0.0230087	−	0.459939i
$210$	−0.902305	−	0.0636538i	−0.0622650	−	0.00439253i
$211$	0.786669	+	7.48465i	0.0541565	+	0.515265i	0.987651	+	0.156672i	$0.0500766\pi$
$211$	0.786669	+	7.48465i	0.0541565	+	0.515265i	−0.933494	+	0.358593i	$0.883257\pi$
$212$	4.13648	+	23.6293i	0.284095	+	1.62287i
$213$	−12.6693	−	4.11650i	−0.868086	−	0.282058i
$214$	−6.72235	−	18.5049i	−0.459530	−	1.26497i
$215$	−3.46360	−	0.364039i	−0.236216	−	0.0248273i
$216$	8.00927	−	13.8135i	0.544962	−	0.939887i
$217$	−3.67766	−	3.31138i	−0.249656	−	0.224791i
$218$	−10.9519	−	17.5508i	−0.741758	−	1.18869i
$219$	4.70749	+	2.71787i	0.318103	+	0.183657i
$220$	1.44944	−	3.42555i	0.0977210	−	0.230951i
$221$	15.5296	+	11.9394i	1.04464	+	0.803134i
$222$	−1.07228	+	2.01368i	−0.0719670	+	0.135149i
$223$	−26.1208	−	5.55215i	−1.74918	−	0.371799i	−0.781484	−	0.623925i	$-0.785537\pi$
$223$	−26.1208	−	5.55215i	−1.74918	−	0.371799i	−0.967694	+	0.252126i	$0.918870\pi$
$224$	4.68991	+	0.673858i	0.313358	+	0.0450240i
$225$	−0.561002	+	5.33758i	−0.0374001	+	0.355838i
$226$	−21.2196	−	3.75507i	−1.41151	−	0.249783i
$227$	−1.78002	−	8.37433i	−0.118144	−	0.555824i	−0.996909	−	0.0785685i	$-0.974965\pi$
$227$	−1.78002	−	8.37433i	−0.118144	−	0.555824i	0.878765	−	0.477255i	$-0.158368\pi$
$228$	−0.942752	−	5.38539i	−0.0624353	−	0.356656i
$229$	−1.41199	−	1.94343i	−0.0933066	−	0.128426i	0.759811	−	0.650144i	$-0.225291\pi$
$229$	−1.41199	−	1.94343i	−0.0933066	−	0.128426i	−0.853118	+	0.521718i	$0.825291\pi$
$230$	−5.32009	−	3.59322i	−0.350796	−	0.236930i
$231$	−2.38775	−	2.93434i	−0.157102	−	0.193065i
$232$	3.44894	−	3.81624i	0.226434	−	0.250548i
$233$	12.5086	+	17.2167i	0.819468	+	1.12790i	0.989793	+	0.142513i	$0.0455183\pi$
$233$	12.5086	+	17.2167i	0.819468	+	1.12790i	−0.170325	+	0.985388i	$0.554482\pi$
$234$	2.33723	−	5.35252i	0.152790	−	0.349905i
$235$	−0.505025	−	0.164093i	−0.0329442	−	0.0107042i
$236$	−0.00944089	+	0.0376676i	−0.000614549	+	0.00245195i
$237$	2.31506	+	5.19971i	0.150379	+	0.337758i
$238$	−5.07363	+	3.95892i	−0.328874	+	0.256619i
$239$	−15.3375	+	4.98346i	−0.992102	+	0.322353i	−0.759705	−	0.650268i	$-0.774657\pi$
$239$	−15.3375	+	4.98346i	−0.992102	+	0.322353i	−0.232397	+	0.972621i	$0.574657\pi$
$240$	0.537828	−	3.00684i	0.0347167	−	0.194091i
$241$	−11.1246	−	19.2684i	−0.716600	−	1.24119i	−0.962339	−	0.271852i	$-0.912364\pi$
$241$	−11.1246	−	19.2684i	−0.716600	−	1.24119i	0.245739	−	0.969336i	$-0.420969\pi$
$242$	14.5961	−	5.38100i	0.938270	−	0.345904i
$243$	9.65270	−	5.57299i	0.619221	−	0.357507i
$244$	12.9601	−	20.6838i	0.829688	−	1.32415i
$245$	−0.734312	+	3.45467i	−0.0469135	+	0.220711i
$246$	14.7026	−	2.05709i	0.937405	−	0.131155i
$247$	−2.04907	−	6.94143i	−0.130379	−	0.441673i
$248$	12.4397	−	11.1592i	0.789924	−	0.708612i
$249$	2.85151	+	3.16692i	0.180707	+	0.200696i
$250$	1.85357	+	7.45381i	0.117230	+	0.471420i
$251$	−0.762689	+	1.71303i	−0.0481405	+	0.108125i	−0.936015	−	0.351961i	$-0.885515\pi$
$251$	−0.762689	+	1.71303i	−0.0481405	+	0.108125i	0.887874	+	0.460086i	$0.152182\pi$
$252$	1.51056	+	1.18318i	0.0951565	+	0.0745333i
$253$	−4.26321	−	26.5091i	−0.268026	−	1.66661i
$254$	13.2289	+	8.93486i	0.830055	+	0.560623i
$255$	2.43862	+	3.35647i	0.152712	+	0.210190i
$256$	−3.94719	+	15.5055i	−0.246700	+	0.969092i
$257$	−3.16942	−	3.52000i	−0.197703	−	0.219572i	0.636139	−	0.771574i	$-0.280530\pi$
$257$	−3.16942	−	3.52000i	−0.197703	−	0.219572i	−0.833842	+	0.552003i	$0.813864\pi$
$258$	−9.15825	−	7.69430i	−0.570168	−	0.479026i
$259$	−0.802686	−	0.583186i	−0.0498765	−	0.0362374i
$260$	0.255608	−	4.03552i	0.0158522	−	0.250272i
$261$	1.98114	−	0.643711i	0.122629	−	0.0398447i
$262$	14.8548	+	23.8052i	0.917731	+	1.47069i
$263$	−10.4803	+	18.1523i	−0.646240	+	1.11932i	0.337774	+	0.941227i	$0.390326\pi$
$263$	−10.4803	+	18.1523i	−0.646240	+	1.11932i	−0.984014	+	0.178093i	$0.943007\pi$
$264$	10.7104	−	6.96346i	0.659179	−	0.428571i
$265$			6.72579i			0.413162i
$266$	2.37633	−	0.0815180i	0.145702	−	0.00499819i
$267$	−6.75272	+	7.49966i	−0.413260	+	0.458971i
$268$	−4.23951	−	6.30206i	−0.258969	−	0.384960i
$269$	2.86510	−	27.2596i	0.174688	−	1.66205i	−0.458982	−	0.888446i	$-0.651786\pi$
$269$	2.86510	−	27.2596i	0.174688	−	1.66205i	0.633670	−	0.773603i	$-0.281548\pi$
$270$	2.87978	−	3.42770i	0.175258	−	0.208603i
$271$	−5.78016	+	5.20448i	−0.351120	+	0.316150i	−0.825751	−	0.564035i	$-0.809248\pi$
$271$	−5.78016	+	5.20448i	−0.351120	+	0.316150i	0.474631	+	0.880185i	$0.342582\pi$
$272$	−11.4707	−	18.4579i	−0.695511	−	1.11918i
$273$	−3.50459	−	2.15213i	−0.212107	−	0.130253i
$274$	12.5335	+	25.7376i	0.757174	+	1.55487i
$275$	−8.43284	+	13.0532i	−0.508519	+	0.787139i
$276$	−8.23462	−	20.4539i	−0.495666	−	1.23118i
$277$	−2.62096	+	5.88678i	−0.157478	+	0.353702i	−0.975003	−	0.222191i	$-0.928679\pi$
$277$	−2.62096	+	5.88678i	−0.157478	+	0.353702i	0.817525	+	0.575894i	$0.195346\pi$
$278$	−8.54036	−	8.85471i	−0.512217	−	0.531070i
$279$	6.61978	−	1.40708i	0.396316	−	0.0842396i
$280$	1.26265	+	0.412842i	0.0754580	+	0.0246720i
$281$	−15.1460	−	11.0042i	−0.903535	−	0.656457i	0.0358362	−	0.999358i	$-0.488591\pi$
$281$	−15.1460	−	11.0042i	−0.903535	−	0.656457i	−0.939372	+	0.342901i	$0.888591\pi$
$282$	−1.12195	−	1.43786i	−0.0668114	−	0.0856234i
$283$	−9.27513	−	1.97149i	−0.551349	−	0.117193i	−0.0761911	−	0.997093i	$-0.524276\pi$
$283$	−9.27513	−	1.97149i	−0.551349	−	0.117193i	−0.475158	+	0.879900i	$0.657609\pi$
$284$	16.5783	+	10.3877i	0.983741	+	0.616396i
$285$		−	1.53288i		−	0.0908002i
$286$	13.0405	−	10.7678i	0.771101	−	0.636713i
$287$			6.45646i			0.381113i
$288$	−4.51539	+	4.64710i	−0.266072	+	0.273833i
$289$	12.2434	+	2.60241i	0.720199	+	0.153083i
$290$	1.13701	−	0.887202i	0.0667675	−	0.0520983i
$291$	20.1529	+	14.6420i	1.18139	+	0.858327i
$292$	−5.73567	−	5.55254i	−0.335655	−	0.324938i
$293$	4.88627	−	1.03861i	0.285459	−	0.0606762i	−0.0629569	−	0.998016i	$-0.520053\pi$
$293$	4.88627	−	1.03861i	0.285459	−	0.0606762i	0.348416	+	0.937340i	$0.386720\pi$
$294$	−8.73098	+	8.42103i	−0.509201	+	0.491124i
$295$	−0.00442842	+	0.00994639i	−0.000257832	+	0.000579101i
$296$	2.24650	−	2.48574i	0.130575	−	0.144481i
$297$	18.6955	−	1.02434i	1.08482	−	0.0594380i
$298$	5.11039	−	2.48861i	0.296037	−	0.144161i
$299$	−13.9036	−	25.6646i	−0.804066	−	1.48422i
$300$	−4.37958	+	11.9868i	−0.252855	+	0.692060i
$301$	3.86586	−	3.48084i	0.222825	−	0.200632i
$302$	9.11072	+	7.65437i	0.524263	+	0.440459i
$303$	0.570058	−	5.42374i	0.0327490	−	0.311586i
$304$	−0.579829	+	8.00838i	−0.0332555	+	0.459312i
$305$	4.57924	−	5.08576i	0.262207	−	0.291210i
$306$	−0.301724	−	8.79555i	−0.0172484	−	0.502808i
$307$			26.8687i			1.53348i	0.641958	+	0.766740i	$0.278123\pi$
$307$			26.8687i			1.53348i	−0.641958	+	0.766740i	$0.721877\pi$
$308$	2.35378	+	5.03265i	0.134119	+	0.286762i
$309$	13.7362	−	23.7918i	0.781425	−	1.35347i
$310$	3.97504	−	2.48048i	0.225767	−	0.140882i
$311$	−8.74538	+	2.84155i	−0.495905	+	0.161129i	−0.546283	−	0.837601i	$-0.683958\pi$
$311$	−8.74538	+	2.84155i	−0.495905	+	0.161129i	0.0503776	+	0.998730i	$0.483958\pi$
$312$	8.48510	−	10.9945i	0.480374	−	0.622440i
$313$	−15.8563	−	11.5203i	−0.896250	−	0.651164i	0.0412499	−	0.999149i	$-0.486866\pi$
$313$	−15.8563	−	11.5203i	−0.896250	−	0.651164i	−0.937500	+	0.347985i	$0.886866\pi$
$314$	−0.407925	+	0.485539i	−0.0230206	+	0.0274005i
$315$	0.359976	+	0.399794i	0.0202823	+	0.0225258i
$316$	−1.44139	−	8.23385i	−0.0810848	−	0.463190i
$317$	−6.94100	−	9.55347i	−0.389846	−	0.536576i	0.568314	−	0.822812i	$-0.307596\pi$
$317$	−6.94100	−	9.55347i	−0.389846	−	0.536576i	−0.958159	+	0.286236i	$0.907596\pi$
$318$	−12.9292	+	19.1428i	−0.725031	+	1.07348i
$319$	5.95963	+	0.929403i	0.333675	+	0.0520366i
$320$	−1.83974	+	4.09138i	−0.102845	+	0.228715i
$321$	7.71125	−	17.3198i	0.430400	−	0.966695i
$322$	9.30584	−	2.31412i	0.518594	−	0.128961i
$323$	−7.29737	−	8.10455i	−0.406037	−	0.450949i
$324$	8.17689	−	2.33379i	0.454272	−	0.129655i
$325$	−3.95922	+	16.4235i	−0.219618	+	0.911015i
$326$	−3.11825	−	22.2871i	−0.172704	−	1.23437i
$327$	4.14185	−	19.4859i	0.229045	−	1.07757i
$328$	−21.6791	−	2.31907i	−1.19703	−	0.128049i
$329$	0.686905	−	0.396585i	0.0378703	−	0.0218644i
$330$	3.29459	−	1.40532i	0.181361	−	0.0773603i
$331$	4.72156	+	8.17798i	0.259520	+	0.449503i	0.966114	−	0.258117i	$-0.0831022\pi$
$331$	4.72156	+	8.17798i	0.259520	+	0.449503i	−0.706593	+	0.707620i	$0.749769\pi$
$332$	−2.93139	−	5.52957i	−0.160881	−	0.303475i
$333$	1.29043	−	0.419287i	0.0707153	−	0.0229768i
$334$	13.8585	+	17.7606i	0.758304	+	0.971818i
$335$	−0.866161	−	1.94543i	−0.0473234	−	0.106290i
$336$	2.80013	+	3.60226i	0.152760	+	0.196519i
$337$	−4.83008	−	1.56939i	−0.263111	−	0.0854900i	0.174491	−	0.984659i	$-0.444172\pi$
$337$	−4.83008	−	1.56939i	−0.263111	−	0.0854900i	−0.437602	+	0.899169i	$0.644172\pi$
$338$	9.50806	−	15.7352i	0.517170	−	0.855882i
$339$	−12.1972	−	16.7879i	−0.662459	−	0.911796i
$340$	−2.27553	−	5.65216i	−0.123408	−	0.306531i
$341$	18.9403	+	5.02683i	1.02567	+	0.272218i
$342$	−1.81996	+	2.69462i	−0.0984120	+	0.145708i
$343$	−6.54707	−	9.01127i	−0.353509	−	0.486563i
$344$	10.2992	+	14.2308i	0.555295	+	0.767276i
$345$	−1.28532	−	6.04695i	−0.0691993	−	0.325557i
$346$	1.66936	−	9.43342i	0.0897452	−	0.507144i
$347$	−0.362175	+	3.44586i	−0.0194426	+	0.184984i	−0.999933	−	0.0115837i	$-0.996313\pi$
$347$	−0.362175	+	3.44586i	−0.0194426	+	0.184984i	0.980490	+	0.196567i	$0.0629794\pi$
$348$	4.94163	−	0.339437i	0.264899	−	0.0181957i
$349$	−1.24627	−	0.264903i	−0.0667113	−	0.0141799i	0.174435	−	0.984669i	$-0.444190\pi$
$349$	−1.24627	−	0.264903i	−0.0667113	−	0.0141799i	−0.241146	+	0.970489i	$0.577523\pi$
$350$	−4.89887	−	2.60865i	−0.261856	−	0.139438i
$351$	18.8125	−	7.77175i	1.00414	−	0.414825i
$352$	−17.7438	+	6.09572i	−0.945747	+	0.324903i
$353$	−13.0387	−	7.52788i	−0.693978	−	0.400668i	0.111123	−	0.993807i	$-0.464555\pi$
$353$	−13.0387	−	7.52788i	−0.693978	−	0.400668i	−0.805101	+	0.593138i	$0.797889\pi$
$354$	−0.0317243	+	0.0197964i	−0.00168613	+	0.00105217i
$355$	4.07629	+	3.67031i	0.216347	+	0.194800i
$356$	12.2973	−	8.27263i	0.651757	−	0.438448i
$357$	−6.16309	−	0.647767i	−0.326185	−	0.0342835i
$358$	8.25837	−	3.00004i	0.436468	−	0.158557i
$359$	−21.7267	−	7.05944i	−1.14669	−	0.372583i	−0.326796	−	0.945095i	$-0.605969\pi$
$359$	−21.7267	−	7.05944i	−1.14669	−	0.372583i	−0.819896	+	0.572512i	$0.805969\pi$
$360$	−1.47170	+	1.06511i	−0.0775655	+	0.0561360i
$361$	−1.56485	−	14.8886i	−0.0823607	−	0.783610i
$362$	−1.37122	+	19.4373i	−0.0720696	+	1.02160i
$363$	13.7138	+	6.02785i	0.719787	+	0.316380i
$364$	4.22406	+	4.31712i	0.221401	+	0.226279i
$365$	−1.31560	−	1.81077i	−0.0688616	−	0.0947799i
$366$	22.8099	−	5.67222i	1.19229	−	0.296492i
$367$	18.3037	−	16.4807i	0.955443	−	0.860285i	−0.0348344	−	0.999393i	$-0.511090\pi$
$367$	18.3037	−	16.4807i	0.955443	−	0.860285i	0.990277	+	0.139109i	$0.0444237\pi$
$368$	4.42769	+	32.0778i	0.230809	+	1.67217i
$369$	−7.14321	−	5.18984i	−0.371861	−	0.270172i
$370$	0.740602	−	0.577887i	0.0385020	−	0.0300429i
$371$	−7.46580	−	6.72223i	−0.387605	−	0.349001i
$372$	16.0820	+	0.581429i	0.833812	+	0.0301457i
$373$	−16.8491	+	9.72785i	−0.872415	+	0.503689i	−0.868150	−	0.496302i	$-0.834691\pi$
$373$	−16.8491	+	9.72785i	−0.872415	+	0.503689i	−0.00426520	+	0.999991i	$0.501358\pi$
$374$	10.7288	−	23.1142i	0.554774	−	1.19520i
$375$	−3.69815	+	6.40538i	−0.190971	+	0.330772i
$376$	1.08490	+	2.44890i	0.0559496	+	0.126292i
$377$	6.44843	−	1.18890i	0.332111	−	0.0612314i
$378$	0.926576	+	6.62252i	0.0476579	+	0.340626i
$379$	11.3706	−	5.06250i	0.584067	−	0.260043i	−0.0933613	−	0.995632i	$-0.529761\pi$
$379$	11.3706	−	5.06250i	0.584067	−	0.260043i	0.677428	+	0.735589i	$0.263095\pi$
$380$	−0.547309	+	2.18367i	−0.0280764	+	0.112020i
$381$	3.19606	+	15.0363i	0.163739	+	0.770333i
$382$	−9.12700	+	8.80298i	−0.466978	+	0.450400i
$383$	21.4702	+	9.55914i	1.09708	+	0.488449i	0.873790	−	0.486304i	$-0.161655\pi$
$383$	21.4702	+	9.55914i	1.09708	+	0.488449i	0.223285	+	0.974753i	$0.428322\pi$
$384$	−13.1012	+	8.10823i	−0.668569	+	0.413771i
$385$	0.406743	+	1.50369i	0.0207295	+	0.0766349i
$386$	16.0973	+	10.8722i	0.819330	+	0.553379i
$387$	0.743616	+	7.07503i	0.0378001	+	0.359644i
$388$	−23.4811	−	28.0537i	−1.19207	−	1.42421i
$389$	−9.35014	+	28.7768i	−0.474071	+	1.45904i	0.373136	+	0.927777i	$0.378283\pi$
$389$	−9.35014	+	28.7768i	−0.474071	+	1.45904i	−0.847207	+	0.531264i	$0.821717\pi$
$390$	2.87491	−	2.62617i	0.145577	−	0.132981i
$391$	−35.5825	−	25.8522i	−1.79948	−	1.30740i
$392$	15.4444	−	8.87884i	0.780062	−	0.448449i
$393$	−5.61785	+	26.4299i	−0.283383	+	1.33321i
$394$	−25.4514	+	0.873090i	−1.28222	+	0.0439856i
$395$		−	2.34366i		−	0.117922i
$396$	−7.45997	−	1.44122i	−0.374878	−	0.0724238i
$397$	−20.5488	+	11.8639i	−1.03132	+	0.595430i	−0.917361	−	0.398056i	$-0.869685\pi$
$397$	−20.5488	+	11.8639i	−1.03132	+	0.595430i	−0.113954	+	0.993486i	$0.536352\pi$
$398$	−2.56578	−	1.36628i	−0.128611	−	0.0684853i
$399$	1.70154	+	1.53207i	0.0851836	+	0.0766997i
$400$	10.5188	−	15.5122i	0.525939	−	0.775608i
$401$	−7.70794	−	17.3123i	−0.384916	−	0.864536i	−0.997262	−	0.0739464i	$-0.976441\pi$
$401$	−7.70794	−	17.3123i	−0.384916	−	0.864536i	0.612346	−	0.790590i	$-0.290226\pi$
$402$	1.27450	−	7.20210i	0.0635662	−	0.359208i
$403$	21.2390	−	1.65153i	1.05799	−	0.0822684i
$404$	−2.74860	+	7.52287i	−0.136748	+	0.374277i
$405$	2.37108	−	0.249210i	0.117820	−	0.0123833i
$406$	−0.151592	+	2.14884i	−0.00752337	+	0.106645i
$407$	3.88186	+	0.605375i	0.192417	+	0.0300073i
$408$	4.38873	−	20.4614i	0.217275	−	1.01299i
$409$	22.4581	+	9.99899i	1.11048	+	0.494418i	0.878231	−	0.478238i	$-0.158724\pi$
$409$	22.4581	+	9.99899i	1.11048	+	0.494418i	0.232251	+	0.972656i	$0.425391\pi$
$410$	−5.87510	−	1.68857i	−0.290150	−	0.0833927i
$411$	−8.51857	+	26.2175i	−0.420190	+	1.29321i
$412$	−28.0627	+	28.9882i	−1.38255	+	1.42815i
$413$	−0.00661467	−	0.0148568i	−0.000325487	−	0.000731055i
$414$	−4.91997	+	12.1558i	−0.241803	+	0.597425i
$415$	−0.542241	−	1.66885i	−0.0266176	−	0.0819204i
$416$	−16.0130	+	12.6326i	−0.785102	+	0.619367i
$417$		−	11.8465i		−	0.580124i
$418$	−8.22671	+	4.57909i	−0.402381	+	0.223970i
$419$	−1.61212	−	0.930759i	−0.0787573	−	0.0454705i	0.460104	−	0.887865i	$-0.347812\pi$
$419$	−1.61212	−	0.930759i	−0.0787573	−	0.0454705i	−0.538861	+	0.842394i	$0.681145\pi$
$420$	0.599167	+	1.13023i	0.0292364	+	0.0551494i
$421$	−16.1262	+	5.23972i	−0.785943	+	0.255368i	−0.674375	−	0.738389i	$-0.735587\pi$
$421$	−16.1262	+	5.23972i	−0.785943	+	0.255368i	−0.111567	+	0.993757i	$0.535587\pi$
$422$	8.39099	−	6.54744i	0.408467	−	0.318725i
$423$	−0.113381	+	1.07875i	−0.00551279	+	0.0524507i
$424$	25.2531	−	22.6537i	1.22640	−	1.10016i
$425$	5.29268	+	24.9001i	0.256733	+	1.20783i
$426$	4.54634	+	18.2823i	0.220271	+	0.885782i
$427$	1.06851	+	10.1662i	0.0517086	+	0.491975i
$428$	−17.1690	+	21.9196i	−0.829896	+	1.05953i
$429$	16.2367	+	1.25435i	0.783915	+	0.0605605i
$430$	2.15636	+	4.42812i	0.103989	+	0.213543i
$431$	−25.5510	+	2.68551i	−1.23075	+	0.129357i	−0.697489	−	0.716596i	$-0.745699\pi$
$431$	−25.5510	+	2.68551i	−1.23075	+	0.129357i	−0.533258	+	0.845953i	$0.679033\pi$
$432$	−22.5695	+	0.732483i	−1.08588	+	0.0352416i
$433$	−0.350019	+	0.0743989i	−0.0168209	+	0.00357538i	−0.216314	−	0.976324i	$-0.569404\pi$
$433$	−0.350019	+	0.0743989i	−0.0168209	+	0.00357538i	0.199494	+	0.979899i	$0.436070\pi$
$434$	−1.21954	+	6.89156i	−0.0585400	+	0.330806i
$435$	1.38116	+	0.145166i	0.0662216	+	0.00696017i
$436$	−12.8576	+	26.2799i	−0.615769	+	1.25858i
$437$	5.02164	+	15.4550i	0.240218	+	0.739314i
$438$	−0.263552	−	7.68279i	−0.0125930	−	0.367098i
$439$	6.79221	−	11.7645i	0.324175	−	0.561487i	−0.657170	−	0.753742i	$-0.728247\pi$
$439$	6.79221	−	11.7645i	0.324175	−	0.561487i	0.981345	+	0.192255i	$0.0615801\pi$
$440$	−5.19508	+	0.825634i	−0.247666	+	0.0393606i
$441$	7.21443			0.343544
$442$	2.69800	−	27.5710i	0.128331	−	1.31142i
$443$	−9.26341	+	3.00987i	−0.440118	+	0.143003i	−0.520690	−	0.853746i	$-0.674325\pi$
$443$	−9.26341	+	3.00987i	−0.440118	+	0.143003i	0.0805721	+	0.996749i	$0.474325\pi$
$444$	3.21878	−	0.221095i	0.152756	−	0.0104927i
$445$	3.79615	−	1.69016i	0.179955	−	0.0801211i
$446$	12.8948	+	35.4961i	0.610585	+	1.68079i
$447$	5.20567	+	1.69143i	0.246220	+	0.0800017i
$448$	−2.70276	−	6.13138i	−0.127694	−	0.289680i
$449$	−2.23442	+	5.01858i	−0.105449	+	0.236842i	−0.958562	−	0.284884i	$-0.908045\pi$
$449$	−2.23442	+	5.01858i	−0.105449	+	0.236842i	0.853113	+	0.521726i	$0.174712\pi$
$450$	6.82394	−	3.32306i	0.321684	−	0.156650i
$451$	−11.6608	−	22.7519i	−0.549088	−	1.07134i
$452$	11.3814	+	28.2703i	0.535338	+	1.32972i
$453$	1.19775	+	11.3958i	0.0562750	+	0.535421i
$454$	−8.71471	+	8.40533i	−0.409002	+	0.394482i
$455$	0.957859	+	1.39649i	0.0449051	+	0.0654687i
$456$	−5.75548	+	5.16303i	−0.269525	+	0.241781i
$457$	−7.33064	+	3.26381i	−0.342913	+	0.152675i	−0.570965	−	0.820974i	$-0.693431\pi$
$457$	−7.33064	+	3.26381i	−0.342913	+	0.152675i	0.228052	+	0.973649i	$0.426764\pi$
$458$	−1.27457	+	3.14908i	−0.0595567	+	0.147147i
$459$	20.5228	−	22.7929i	0.957924	−	1.06388i
$460$	−0.328030	+	9.07312i	−0.0152945	+	0.423037i
$461$	1.81373	+	3.14148i	0.0844740	+	0.146313i	0.905167	−	0.425056i	$-0.139746\pi$
$461$	1.81373	+	3.14148i	0.0844740	+	0.146313i	−0.820693	+	0.571369i	$0.806412\pi$
$462$	−1.73291	+	5.06166i	−0.0806222	+	0.235490i
$463$	0.0234358			0.00108915			0.000544576	−	1.00000i	$-0.499827\pi$
$463$	0.0234358			0.00108915			0.000544576		1.00000i	$0.499827\pi$
$464$	−7.16081	−	1.28084i	−0.332432	−	0.0594616i
$465$	4.41332	+	0.938079i	0.204663	+	0.0435024i
$466$	11.2913	−	27.8974i	0.523058	−	1.29232i
$467$	14.3397	−	19.7369i	0.663562	−	0.913315i	−0.336030	−	0.941851i	$-0.609085\pi$
$467$	14.3397	−	19.7369i	0.663562	−	0.913315i	0.999593	+	0.0285360i	$0.00908452\pi$
$468$	−8.17170	+	1.20316i	−0.377737	+	0.0556160i
$469$	3.02518	+	0.982941i	0.139690	+	0.0453880i
$470$	0.181227	+	0.728773i	0.00835937	+	0.0336158i
$471$	−0.607317	+	0.0638316i	−0.0279837	+	0.00294121i
$472$	0.0522612	−	0.0168740i	0.00240551	−	0.000776688i
$473$	−7.33625	+	19.2481i	−0.337321	+	0.885031i
$474$	4.50528	−	6.67049i	0.206934	−	0.306386i
$475$	3.82556	−	8.59235i	0.175529	−	0.394244i
$476$	8.54837	+	3.12328i	0.391814	+	0.143155i
$477$	13.4384	−	2.85642i	0.615303	−	0.130787i
$478$	17.4620	+	14.6707i	0.798692	+	0.671021i
$479$	13.1522	+	29.5404i	0.600941	+	1.34974i	0.916196	+	0.400729i	$0.131243\pi$
$479$	13.1522	+	29.5404i	0.600941	+	1.34974i	−0.315255	+	0.949007i	$0.602090\pi$
$480$	−4.01022	+	1.60589i	−0.183041	+	0.0732984i
$481$	4.20024	−	0.774399i	0.191514	−	0.0353096i
$482$	−14.7891	+	27.7730i	−0.673626	+	1.26503i
$483$	7.99691	+	4.61702i	0.363872	+	0.210082i
$484$	−17.3838	−	13.4834i	−0.790173	−	0.612884i
$485$	−5.12857	−	8.88294i	−0.232876	−	0.403354i
$486$	−13.9132	−	7.40875i	−0.631114	−	0.336068i
$487$	−0.512060	+	0.568701i	−0.0232037	+	0.0257703i	−0.754635	−	0.656145i	$-0.772186\pi$
$487$	−0.512060	+	0.568701i	−0.0232037	+	0.0257703i	0.731431	+	0.681915i	$0.238853\pi$
$488$	−34.5191	−	0.0637774i	−1.56261	−	0.00288707i
$489$	12.7376	−	17.5319i	0.576016	−	0.792818i
$490$	4.69461	−	1.70543i	0.212081	−	0.0770433i
$491$	9.22890	+	10.2497i	0.416494	+	0.462564i	0.914486	−	0.404618i	$-0.132596\pi$
$491$	9.22890	+	10.2497i	0.416494	+	0.462564i	−0.497991	+	0.867182i	$0.665929\pi$
$492$	−13.4756	−	16.0998i	−0.607528	−	0.725837i
$493$	7.99344	−	5.80758i	0.360007	−	0.261560i
$494$	−6.79411	+	7.65536i	−0.305681	+	0.344431i
$495$	−1.99057	−	0.758688i	−0.0894696	−	0.0341005i
$496$	−22.7020	−	6.57027i	−1.01935	−	0.295014i
$497$	−8.14827	+	0.856418i	−0.365500	+	0.0384156i
$498$	1.66475	−	5.79221i	0.0745992	−	0.259555i
$499$	−1.58678	+	4.88362i	−0.0710342	+	0.218621i	−0.980271	−	0.197659i	$-0.936666\pi$
$499$	−1.58678	+	4.88362i	−0.0710342	+	0.218621i	0.909237	+	0.416280i	$0.136666\pi$
$500$	7.55522	−	7.80439i	0.337880	−	0.349023i
$501$	−2.26756	+	21.5744i	−0.101307	+	0.963872i
$502$	2.62627	−	0.367449i	0.117216	−	0.0164001i
$503$	−14.2160	+	15.7885i	−0.633862	+	0.703975i	−0.971430	−	0.237326i	$-0.923729\pi$
$503$	−14.2160	+	15.7885i	−0.633862	+	0.703975i	0.337568	+	0.941301i	$0.390396\pi$
$504$	0.288630	−	2.69817i	0.0128566	−	0.120186i
$505$	−1.12279	+	1.94474i	−0.0499637	+	0.0865397i
$506$	−28.6133	+	24.9617i	−1.27202	+	1.10968i
$507$	17.1091	−	4.55002i	0.759840	−	0.202073i
$508$	0.815677	−	22.5611i	0.0361898	−	1.00099i
$509$	−0.125722	+	0.591478i	−0.00557255	+	0.0262168i	−0.980846	−	0.194785i	$-0.937599\pi$
$509$	−0.125722	+	0.591478i	−0.00557255	+	0.0262168i	0.975273	+	0.221001i	$0.0709325\pi$
$510$	2.20129	−	5.43873i	0.0974746	−	0.240831i
$511$	3.32490	+	0.349461i	0.147085	+	0.0154593i
$512$	21.5584	−	6.87287i	0.952755	−	0.303741i
$513$	−11.0845	+	2.35608i	−0.489392	+	0.104024i
$514$	−1.85035	+	6.43797i	−0.0816154	+	0.283967i
$515$	−9.15166	+	6.64907i	−0.403271	+	0.292993i
$516$	−2.37488	+	16.7485i	−0.104548	+	0.737310i
$517$	−1.70432	+	2.63812i	−0.0749559	+	0.116025i
$518$	−0.0987406	+	1.39967i	−0.00433841	+	0.0614979i
$519$	7.46327	−	5.42239i	0.327601	−	0.238016i
$520$	−5.03312	+	2.71464i	−0.220717	+	0.119045i
$521$	−0.657985	+	2.02507i	−0.0288269	+	0.0887199i	−0.964435	−	0.264321i	$-0.914852\pi$
$521$	−0.657985	+	2.02507i	−0.0288269	+	0.0887199i	0.935608	+	0.353041i	$0.114852\pi$
$522$	−2.25555	−	1.89500i	−0.0987229	−	0.0829420i
$523$	18.8225	−	8.38032i	0.823051	−	0.366446i	0.0483947	−	0.998828i	$-0.484589\pi$
$523$	18.8225	−	8.38032i	0.823051	−	0.366446i	0.774656	+	0.632382i	$0.217923\pi$
$524$	17.4396	−	35.6450i	0.761853	−	1.55716i
$525$	−1.65155	−	5.08296i	−0.0720797	−	0.221839i
$526$	29.6252	−	1.01627i	1.29172	−	0.0443114i
$527$	27.7995	−	16.0501i	1.21097	−	0.699152i
$528$	−16.3733	−	7.63674i	−0.712556	−	0.332346i
$529$	21.2684	+	36.8380i	0.924715	+	1.60165i
$530$	8.06948	−	5.03546i	0.350516	−	0.218727i
$531$	0.0217540	+	0.00462397i	0.000944045	+	0.000200663i
$532$	−1.87692	−	2.79005i	−0.0813746	−	0.120964i
$533$	−20.1426	−	19.1505i	−0.872472	−	0.829500i
$534$	14.0536	+	2.48695i	0.608158	+	0.107621i
$535$	−5.80137	+	5.22358i	−0.250815	+	0.225835i
$536$	−4.38706	+	9.80471i	−0.189492	+	0.423499i
$537$	7.72944	+	3.44137i	0.333550	+	0.148506i
$538$	−34.8507	+	16.9712i	−1.50252	+	0.731682i
$539$	18.6353	+	9.43944i	0.802678	+	0.406585i
$540$	−6.26853	−	0.888860i	−0.269755	−	0.0382504i
$541$	−12.6753	+	9.20915i	−0.544954	+	0.395932i	−0.825922	−	0.563785i	$-0.809345\pi$
$541$	−12.6753	+	9.20915i	−0.544954	+	0.395932i	0.280967	+	0.959717i	$0.409345\pi$
$542$	10.5717	+	3.03845i	0.454095	+	0.130512i
$543$	−13.9442	+	12.5554i	−0.598404	+	0.538805i
$544$	−13.5576	+	27.5814i	−0.581278	+	1.18254i
$545$	−4.82148	+	6.63620i	−0.206529	+	0.284263i
$546$	0.0417243	+	5.81600i	0.00178563	+	0.248902i
$547$	2.50988	+	7.72462i	0.107315	+	0.330281i	0.990267	−	0.139182i	$-0.0444474\pi$
$547$	2.50988	+	7.72462i	0.107315	+	0.330281i	−0.882952	+	0.469463i	$0.844447\pi$
$548$	21.4960	−	34.3067i	0.918263	−	1.46551i
$549$	−12.1064	−	6.98961i	−0.516687	−	0.298309i
$550$	21.9745	+	0.344879i	0.936997	+	0.0147057i
$551$	−3.65057			−0.155520
$552$	−18.3751	+	25.1932i	−0.782098	+	1.07229i
$553$	2.60152	+	2.34242i	0.110628	+	0.0996099i
$554$	9.02512	−	1.26273i	0.383441	−	0.0536483i
$555$	0.899632	+	0.0945551i	0.0381872	+	0.00401364i
$556$	−4.22973	+	16.8759i	−0.179380	+	0.715699i
$557$	−3.43256	−	3.81225i	−0.145442	−	0.161530i	0.666022	−	0.745932i	$-0.267996\pi$
$557$	−3.43256	−	3.81225i	−0.145442	−	0.161530i	−0.811464	+	0.584402i	$0.801329\pi$
$558$	−6.64429	−	6.88885i	−0.281275	−	0.291628i
$559$	−0.607160	+	22.3851i	−0.0256801	+	0.946787i
$560$	−0.450004	−	1.82400i	−0.0190161	−	0.0770779i
$561$	22.8880	−	8.84833i	0.966332	−	0.373577i
$562$	−1.86315	+	26.4106i	−0.0785923	+	1.11406i
$563$	20.7866	+	9.25478i	0.876050	+	0.390042i	0.794958	−	0.606664i	$-0.207493\pi$
$563$	20.7866	+	9.25478i	0.876050	+	0.390042i	0.0810914	+	0.996707i	$0.474159\pi$
$564$	−0.885135	+	2.42260i	−0.0372709	+	0.102010i
$565$	1.77650	+	8.35776i	0.0747378	+	0.351614i
$566$	4.57875	+	12.6042i	0.192459	+	0.529792i
$567$	−2.09319	+	2.88103i	−0.0879058	+	0.120992i
$568$	0.0511182	−	27.6674i	0.00214487	−	1.16090i
$569$	4.36903	−	20.5547i	0.183159	−	0.861697i	−0.786568	−	0.617504i	$-0.788144\pi$
$569$	4.36903	−	20.5547i	0.183159	−	0.861697i	0.969727	−	0.244192i	$-0.0785228\pi$
$570$	−1.83913	+	1.14764i	−0.0770326	+	0.0480694i
$571$	18.4563			0.772371			0.386186	−	0.922421i	$-0.373792\pi$
$571$	18.4563			0.772371			0.386186	+	0.922421i	$0.373792\pi$
$572$	−22.6822	−	7.58412i	−0.948389	−	0.317108i
$573$	−12.2108			−0.510112
$574$	7.74635	−	4.83383i	0.323326	−	0.201760i
$575$	7.88649	−	37.1030i	0.328889	−	1.54730i
$576$	8.95608	+	1.93829i	0.373170	+	0.0807621i
$577$	10.6171	−	14.6132i	0.441996	−	0.608356i	−0.528658	−	0.848835i	$-0.677305\pi$
$577$	10.6171	−	14.6132i	0.441996	−	0.608356i	0.970654	+	0.240479i	$0.0773046\pi$
$578$	−6.04405	−	16.6378i	−0.251399	−	0.692040i
$579$	3.88906	+	18.2966i	0.161624	+	0.760380i
$580$	−1.91571	−	0.699934i	−0.0795454	−	0.0290632i
$581$	2.39442	+	1.06606i	0.0993371	+	0.0442277i
$582$	2.47907	−	35.1413i	0.102761	−	1.45665i
$583$	38.4495	+	10.2047i	1.59242	+	0.422634i
$584$	−2.36766	+	11.0386i	−0.0979745	+	0.456782i
$585$	−2.31498	−	0.0627902i	−0.0957127	−	0.00259606i
$586$	−4.90436	−	5.08488i	−0.202597	−	0.210054i
$587$	−9.19808	−	10.2155i	−0.379645	−	0.421639i	0.522792	−	0.852460i	$-0.324891\pi$
$587$	−9.19808	−	10.2155i	−0.379645	−	0.421639i	−0.902437	+	0.430821i	$0.858224\pi$
$588$	16.6401	+	4.17062i	0.686227	+	0.171994i
$589$	−11.7952	−	1.23973i	−0.486013	−	0.0510821i
$590$	0.0152490	−	0.00213353i	0.000627790	−	8.78359e-5i
$591$	−18.2242	−	16.4091i	−0.749642	−	0.674981i
$592$	−4.66426	−	0.834287i	−0.191700	−	0.0342890i
$593$	7.14772			0.293522			0.146761	−	0.989172i	$-0.453115\pi$
$593$	7.14772			0.293522			0.146761	+	0.989172i	$0.453115\pi$
$594$	−15.2259	−	21.6636i	−0.624727	−	0.888869i
$595$	2.20984	+	1.27585i	0.0905946	+	0.0523048i
$596$	−6.81184	−	4.26819i	−0.279024	−	0.174832i
$597$	−0.865000	−	2.66219i	−0.0354021	−	0.108956i
$598$	−20.3825	+	35.8958i	−0.833504	+	1.46789i
$599$	−1.83713	+	2.52860i	−0.0750632	+	0.103316i	−0.844898	−	0.534928i	$-0.820339\pi$
$599$	−1.83713	+	2.52860i	−0.0750632	+	0.103316i	0.769834	+	0.638244i	$0.220339\pi$
$600$	17.6605	−	3.71976i	0.720986	−	0.151859i
$601$	29.7958	−	26.8282i	1.21539	−	1.09435i	0.222551	−	0.974921i	$-0.428562\pi$
$601$	29.7958	−	26.8282i	1.21539	−	1.09435i	0.992843	−	0.119425i	$-0.0381050\pi$
$602$	−7.07055	−	2.03216i	−0.288174	−	0.0828247i
$603$	−3.51920	+	2.55685i	−0.143313	+	0.104123i
$604$	2.36256	−	16.6616i	0.0961312	−	0.677949i
$605$	−4.14908	−	4.56422i	−0.168684	−	0.185562i
$606$	−6.93410	+	3.37670i	−0.281679	+	0.137169i
$607$	7.99949	+	3.56160i	0.324689	+	0.144561i	0.562607	−	0.826724i	$-0.309798\pi$
$607$	7.99949	+	3.56160i	0.324689	+	0.144561i	−0.237918	+	0.971285i	$0.576465\pi$
$608$	10.0424	−	5.30005i	0.407274	−	0.214945i
$609$	−1.54157	+	1.38804i	−0.0624676	+	0.0562460i
$610$	−9.53020	−	1.68648i	−0.385866	−	0.0682837i
$611$	−0.800179	+	3.31928i	−0.0323718	+	0.134284i
$612$	−10.3269	+	6.94706i	−0.417438	+	0.280818i
$613$	20.1062	+	4.27371i	0.812084	+	0.172614i	0.595194	−	0.803582i	$-0.297075\pi$
$613$	20.1062	+	4.27371i	0.812084	+	0.172614i	0.216890	+	0.976196i	$0.430409\pi$
$614$	32.2366	−	20.1161i	1.30097	−	0.811820i
$615$	−2.94325	−	5.09786i	−0.118683	−	0.205565i
$616$	4.27586	−	6.59187i	0.172279	−	0.265594i
$617$	33.2490	−	19.1963i	1.33855	−	0.772814i	0.351961	−	0.936015i	$-0.385515\pi$
$617$	33.2490	−	19.1963i	1.33855	−	0.772814i	0.986593	+	0.163201i	$0.0521818\pi$
$618$	−38.8290	+	1.33200i	−1.56193	+	0.0535808i
$619$	7.49375	+	23.0634i	0.301199	+	0.926997i	0.981068	+	0.193663i	$0.0620367\pi$
$619$	7.49375	+	23.0634i	0.301199	+	0.926997i	−0.679869	+	0.733334i	$0.737963\pi$
$620$	−5.95207	−	2.91210i	−0.239041	−	0.116953i
$621$	−41.7508	+	18.5886i	−1.67540	+	0.745936i
$622$	9.95673	+	8.36514i	0.399229	+	0.335412i
$623$	−1.91803	+	5.90309i	−0.0768443	+	0.236502i
$624$	−19.5436	−	1.94893i	−0.782370	−	0.0780196i
$625$	−16.4896	+	11.9804i	−0.659585	+	0.479217i
$626$	−1.95052	+	27.6491i	−0.0779586	+	1.10508i
$627$	−8.76309	−	2.32576i	−0.349964	−	0.0928820i
$628$	0.887947	+	0.125908i	0.0354329	+	0.00502429i
$629$	5.20660	−	3.78282i	0.207601	−	0.150831i
$630$	0.210159	−	0.731210i	0.00837292	−	0.0291321i
$631$	−32.6764	+	6.94559i	−1.30083	+	0.276500i	−0.805702	−	0.592321i	$-0.798212\pi$
$631$	−32.6764	+	6.94559i	−1.30083	+	0.276500i	−0.495127	+	0.868821i	$0.664878\pi$
$632$	−8.79968	+	7.89388i	−0.350032	+	0.314002i
$633$	10.1928	+	1.07131i	0.405127	+	0.0425806i
$634$	−6.26550	+	15.4802i	−0.248835	+	0.614797i
$635$	1.31602	−	6.19137i	0.0522245	−	0.245697i
$636$	32.6470	+	1.18032i	1.29454	+	0.0468029i
$637$	22.5123	+	2.98526i	0.891971	+	0.118281i
$638$	−3.34678	−	7.84608i	−0.132500	−	0.310629i
$639$	5.60225	−	9.70338i	0.221621	−	0.383860i
$640$	6.28614	−	0.855841i	0.248482	−	0.0338301i
$641$	−19.5527	+	21.7155i	−0.772285	+	0.857709i	−0.993059	−	0.117616i	$-0.962475\pi$
$641$	−19.5527	+	21.7155i	−0.772285	+	0.857709i	0.220774	+	0.975325i	$0.429142\pi$
$642$	−26.5532	+	3.71513i	−1.04797	+	0.146625i
$643$	5.05951	−	48.1381i	0.199528	−	1.89838i	−0.197073	−	0.980389i	$-0.563144\pi$
$643$	5.05951	−	48.1381i	0.199528	−	1.89838i	0.396601	−	0.917991i	$-0.370190\pi$
$644$	−9.74354	−	9.43245i	−0.383949	−	0.371691i
$645$	−1.46561	+	4.51068i	−0.0577083	+	0.177608i
$646$	−4.26030	+	14.8230i	−0.167619	+	0.583202i
$647$	−29.9296	+	3.14573i	−1.17665	+	0.123671i	−0.672604	−	0.740003i	$-0.734824\pi$
$647$	−29.9296	+	3.14573i	−1.17665	+	0.123671i	−0.504050	+	0.863674i	$0.668157\pi$
$648$	−8.92192	−	8.06323i	−0.350486	−	0.316753i
$649$	0.0501418	+	0.0404072i	0.00196824	+	0.00158612i
$650$	22.6689	−	7.54578i	0.889146	−	0.295970i
$651$	−5.45228	+	3.96131i	−0.213692	+	0.155256i
$652$	−24.4051	+	20.4271i	−0.955778	+	0.799989i
$653$	2.04046	+	2.26616i	0.0798494	+	0.0886817i	0.781746	−	0.623598i	$-0.214330\pi$
$653$	2.04046	+	2.26616i	0.0798494	+	0.0886817i	−0.701896	+	0.712279i	$0.747663\pi$
$654$	−26.4798	+	9.61938i	−1.03544	+	0.376147i
$655$	6.53967	−	9.00108i	0.255526	−	0.351701i
$656$	13.4484	+	27.7465i	0.525070	+	1.08332i
$657$	−3.05926	+	3.39765i	−0.119353	+	0.132555i
$658$	−0.990088	−	0.527221i	−0.0385976	−	0.0205532i
$659$	3.22623	+	5.58800i	0.125676	+	0.217677i	0.921997	−	0.387197i	$-0.126557\pi$
$659$	3.22623	+	5.58800i	0.125676	+	0.217677i	−0.796321	+	0.604874i	$0.793223\pi$
$660$	−4.15267	−	2.90066i	−0.161643	−	0.112908i
$661$	30.9679	+	17.8793i	1.20451	+	0.695426i	0.961555	−	0.274611i	$-0.0885492\pi$
$661$	30.9679	+	17.8793i	1.20451	+	0.695426i	0.242957	+	0.970037i	$0.421883\pi$
$662$	6.27686	−	11.7875i	0.243957	−	0.458136i
$663$	20.3012	−	17.3060i	0.788433	−	0.672109i
$664$	−4.43960	+	7.65691i	−0.172290	+	0.297146i
$665$	−0.383467	−	0.861281i	−0.0148702	−	0.0333990i
$666$	−1.46918	−	1.23433i	−0.0569294	−	0.0478292i
$667$	−14.4009	+	3.06100i	−0.557603	+	0.118522i
$668$	10.9333	−	29.9242i	0.423022	−	1.15780i
$669$	−14.7917	+	33.2226i	−0.571879	+	1.28446i
$670$	−1.68561	+	2.49571i	−0.0651210	+	0.0964177i
$671$	−22.1261	−	33.8946i	−0.854169	−	1.30849i
$672$	2.22552	−	6.05648i	0.0858515	−	0.233634i
$673$	−11.5925	+	1.21842i	−0.446858	+	0.0469666i	−0.325285	−	0.945616i	$-0.605460\pi$
$673$	−11.5925	+	1.21842i	−0.446858	+	0.0469666i	−0.121572	+	0.992583i	$0.538794\pi$
$674$	1.73326	+	6.97001i	0.0667627	+	0.268475i
$675$	25.1570	+	8.17401i	0.968294	+	0.314618i
$676$	−25.9973	+	0.373031i	−0.999897	+	0.0143474i
$677$	−1.27242	+	1.75133i	−0.0489030	+	0.0673092i	−0.832768	−	0.553622i	$-0.813245\pi$
$677$	−1.27242	+	1.75133i	−0.0489030	+	0.0673092i	0.783865	+	0.620931i	$0.213245\pi$
$678$	−11.0101	+	27.2027i	−0.422841	+	1.04471i
$679$	14.9861	+	3.18540i	0.575116	+	0.122245i
$680$	−5.07772	+	6.96180i	−0.194722	+	0.266973i
$681$	−11.6592			−0.446780
$682$	−8.14911	−	26.4877i	−0.312046	−	1.01427i
$683$	13.2275	+	22.9108i	0.506138	+	0.876656i	0.999975	+	0.00710192i	$0.00226063\pi$
$683$	13.2275	+	22.9108i	0.506138	+	0.876656i	−0.493837	+	0.869555i	$0.664406\pi$
$684$	4.59552	+	0.166147i	0.175714	+	0.00635277i
$685$	7.59523	−	8.43536i	0.290199	−	0.322299i
$686$	−5.90990	+	14.6016i	−0.225641	+	0.557492i
$687$	−2.98857	+	1.33060i	−0.114021	+	0.0507654i
$688$	9.36311	−	23.0111i	0.356965	−	0.877292i
$689$	43.1160	−	3.35266i	1.64259	−	0.127726i
$690$	−6.29274	+	6.06934i	−0.239560	+	0.231056i
$691$	−5.14279	−	48.9304i	−0.195641	−	1.86140i	−0.448350	−	0.893858i	$-0.647988\pi$
$691$	−5.14279	−	48.9304i	−0.195641	−	1.86140i	0.252709	−	0.967542i	$-0.418679\pi$
$692$	−12.5679	+	5.05975i	−0.477759	+	0.192343i
$693$	2.83168	−	1.45130i	0.107567	−	0.0551303i
$694$	4.40544	−	2.14532i	0.167228	−	0.0814352i
$695$	−1.98403	+	4.45620i	−0.0752585	+	0.169033i
$696$	−4.10695	−	5.67476i	−0.155674	−	0.215101i
$697$	−39.8299	−	12.9415i	−1.50867	−	0.490195i
$698$	0.615232	+	1.69358i	0.0232869	+	0.0641030i
$699$	26.4754	−	11.7876i	1.00139	−	0.445849i
$700$	0.537879	+	7.83063i	0.0203299	+	0.295970i
$701$	−36.1739	+	11.7536i	−1.36627	+	0.443927i	−0.898131	−	0.439729i	$-0.855075\pi$
$701$	−36.1739	+	11.7536i	−1.36627	+	0.443927i	−0.468137	+	0.883656i	$0.655075\pi$
$702$	−23.4090	−	16.7524i	−0.883514	−	0.632277i
$703$	−2.37783			−0.0896817
$704$	20.5980	+	16.7249i	0.776315	+	0.630345i
$705$	−0.361575	+	0.626266i	−0.0136177	+	0.0235865i
$706$	0.729977	+	21.2795i	0.0274730	+	0.800866i
$707$	−1.03651	−	3.19004i	−0.0389819	−	0.119974i
$708$	0.0475027	+	0.0232411i	0.00178526	+	0.000873454i
$709$	21.7752	+	2.28867i	0.817786	+	0.0859527i	0.504178	−	0.863600i	$-0.331796\pi$
$709$	21.7752	+	2.28867i	0.817786	+	0.0859527i	0.313608	+	0.949553i	$0.398462\pi$
$710$	1.35173	−	7.63855i	0.0507297	−	0.286670i
$711$	−4.68274	+	0.995346i	−0.175616	+	0.0373284i
$712$	−19.1321	−	8.56056i	−0.717006	−	0.320820i
$713$	−47.5695	+	4.99976i	−1.78149	+	0.187242i
$714$	3.83701	+	7.87934i	0.143596	+	0.294877i
$715$	−5.89757	−	3.19114i	−0.220556	−	0.119342i
$716$	−9.78228	−	7.66218i	−0.365581	−	0.286349i
$717$	2.29565	+	21.8416i	0.0857325	+	0.815691i
$718$	7.79658	+	31.3526i	0.290966	+	1.17007i
$719$	−6.45974	−	30.3907i	−0.240907	−	1.13338i	−0.917721	−	0.397226i	$-0.869973\pi$
$719$	−6.45974	−	30.3907i	−0.240907	−	1.13338i	0.676813	−	0.736155i	$-0.263360\pi$
$720$	2.37973	+	0.968299i	0.0886873	+	0.0360864i
$721$	1.76619	−	16.8041i	0.0657762	−	0.625819i
$722$	−16.6915	+	13.0243i	−0.621193	+	0.484713i
$723$	−28.8167	+	9.36310i	−1.07170	+	0.348217i
$724$	24.3471	−	12.9072i	0.904854	−	0.479691i
$725$	7.37961	+	4.26062i	0.274072	+	0.158235i
$726$	−3.03513	−	20.9665i	−0.112644	−	0.778140i
$727$		−	8.43605i		−	0.312876i	−0.987688	−	0.156438i	$-0.949999\pi$
$727$		−	8.43605i		−	0.312876i	0.987688	−	0.156438i	$-0.0500011\pi$
$728$	2.01714	−	8.30010i	0.0747601	−	0.307622i
$729$	−8.63208	−	26.5668i	−0.319707	−	0.983956i
$730$	−1.18756	+	2.93412i	−0.0439537	+	0.108597i
$731$	13.7244	+	30.8256i	0.507617	+	1.14013i
$732$	−23.8827	−	23.1202i	−0.882731	−	0.854547i
$733$	−2.81930	+	8.67692i	−0.104133	+	0.320489i	−0.989526	−	0.144354i	$-0.953889\pi$
$733$	−2.81930	+	8.67692i	−0.104133	+	0.320489i	0.885393	+	0.464844i	$0.153889\pi$
$734$	−33.4768	−	9.62164i	−1.23565	−	0.355141i
$735$	4.39394	+	1.95631i	0.162073	+	0.0721594i
$736$	35.1715	−	29.3283i	1.29644	−	1.08105i
$737$	−12.4357	+	1.99992i	−0.458074	+	0.0736679i
$738$	−0.878705	+	12.4558i	−0.0323456	+	0.458505i
$739$	39.9094	−	4.19465i	1.46809	−	0.154303i	0.663520	−	0.748158i	$-0.269062\pi$
$739$	39.9094	−	4.19465i	1.46809	−	0.154303i	0.804572	+	0.593856i	$0.202395\pi$
$740$	−1.24781	−	0.455908i	−0.0458705	−	0.0167595i
$741$	−9.82663	+	0.764110i	−0.360990	+	0.0280703i
$742$	−2.47572	+	13.9901i	−0.0908867	+	0.513594i
$743$	−11.0686	−	24.8604i	−0.406066	−	0.912040i	−0.994621	−	0.103583i	$-0.966969\pi$
$743$	−11.0686	−	24.8604i	−0.406066	−	0.912040i	0.588554	−	0.808458i	$-0.299697\pi$
$744$	−11.3427	−	19.7302i	−0.415843	−	0.723344i
$745$	−1.67490	−	1.50809i	−0.0613637	−	0.0552521i
$746$	24.2859	+	12.9322i	0.889171	+	0.473483i
$747$	−3.10414	+	1.79217i	−0.113574	+	0.0655722i
$748$	−35.7644	+	4.43286i	−1.30768	+	0.162082i
$749$		−	11.6605i		−	0.426065i
$750$	10.4538	−	0.358609i	0.381718	−	0.0130945i
$751$	−4.39183	+	20.6619i	−0.160260	+	0.753965i	0.822453	+	0.568833i	$0.192605\pi$
$751$	−4.39183	+	20.6619i	−0.160260	+	0.753965i	−0.982714	+	0.185133i	$0.940729\pi$
$752$	2.12590	−	3.13509i	0.0775236	−	0.114325i
$753$	2.06592	+	1.50098i	0.0752864	+	0.0546988i
$754$	−6.25423	−	6.84661i	−0.227766	−	0.249339i
$755$	1.45800	−	4.48727i	0.0530621	−	0.163308i
$756$	7.25188	−	6.06984i	0.263748	−	0.220758i
$757$	−3.27956	−	31.2030i	−0.119198	−	1.13409i	−0.876626	−	0.481172i	$-0.840211\pi$
$757$	−3.27956	−	31.2030i	−0.119198	−	1.13409i	0.757428	−	0.652918i	$-0.226456\pi$
$758$	−14.5868	−	9.85201i	−0.529817	−	0.357841i
$759$	−36.5190	−	1.82688i	−1.32555	−	0.0663116i
$760$	3.02969	−	0.978222i	0.109899	−	0.0354839i
$761$	13.1220	+	5.84229i	0.475672	+	0.211783i	0.630547	−	0.776151i	$-0.282831\pi$
$761$	13.1220	+	5.84229i	0.475672	+	0.211783i	−0.154875	+	0.987934i	$0.549497\pi$
$762$	15.6475	−	15.0920i	0.566848	−	0.546724i
$763$	−2.54742	−	11.9847i	−0.0922227	−	0.433874i
$764$	17.3949	+	4.35979i	0.629324	+	0.157732i
$765$	−3.18787	+	1.41933i	−0.115258	+	0.0513161i
$766$	−4.60541	−	32.9163i	−0.166400	−	1.18931i
$767$	0.0659693	+	0.0234305i	0.00238201	+	0.000846027i
$768$	19.5367	+	9.64814i	0.704971	+	0.348147i
$769$	20.0193	−	34.6745i	0.721916	−	1.25039i	−0.238315	−	0.971188i	$-0.576595\pi$
$769$	20.0193	−	34.6745i	0.721916	−	1.25039i	0.960231	−	0.279207i	$-0.0900715\pi$
$770$	1.49957	−	1.61378i	0.0540409	−	0.0581567i
$771$	−5.58627	+	3.22523i	−0.201184	+	0.116154i
$772$	0.992538	−	27.4530i	0.0357222	−	0.988056i
$773$	4.66770	+	4.20282i	0.167886	+	0.151165i	0.748791	−	0.662806i	$-0.230635\pi$
$773$	4.66770	+	4.20282i	0.167886	+	0.151165i	−0.580905	+	0.813971i	$0.697301\pi$
$774$	7.93177	−	6.18911i	0.285102	−	0.222463i
$775$	22.3970	+	16.2724i	0.804526	+	0.584522i
$776$	−16.0786	+	49.1755i	−0.577187	+	1.76530i
$777$	−1.00412	+	0.904109i	−0.0360224	+	0.0324347i
$778$	41.5261	−	10.3265i	1.48878	−	0.370222i
$779$	9.09508	+	12.5183i	0.325865	+	0.448515i
$780$	−5.30321	−	1.48310i	−0.189886	−	0.0531036i
$781$	27.1669	−	17.7343i	0.972108	−	0.634583i
$782$	−4.37709	+	62.0462i	−0.156525	+	2.21877i
$783$	−1.07317	−	10.2105i	−0.0383518	−	0.364893i
$784$	−22.2156	−	11.8825i	−0.793415	−	0.424377i
$785$	0.239141	+	0.0777015i	0.00853530	+	0.00277329i
$786$	35.9161	−	13.0474i	1.28109	−	0.465384i
$787$	−2.65643	−	0.279202i	−0.0946915	−	0.00995248i	0.0570642	−	0.998371i	$-0.481826\pi$
$787$	−2.65643	−	0.279202i	−0.0946915	−	0.00995248i	−0.151756	+	0.988418i	$0.548493\pi$
$788$	20.1025	+	29.8825i	0.716122	+	1.06452i
$789$	21.2128	+	19.1000i	0.755194	+	0.679980i
$790$	−2.81188	+	1.75465i	−0.100042	+	0.0624277i
$791$	−11.0529	−	6.38139i	−0.392995	−	0.226896i
$792$	3.85599	+	10.0294i	0.137017	+	0.356378i
$793$	−34.8852	−	26.8203i	−1.23881	−	0.952417i
$794$	29.6185	+	15.7719i	1.05112	+	0.559722i
$795$	8.95920	+	1.90434i	0.317750	+	0.0675399i
$796$	0.281714	+	4.10128i	0.00998507	+	0.145366i
$797$	2.21989	−	21.1208i	0.0786325	−	0.748138i	−0.882175	−	0.470922i	$-0.843921\pi$
$797$	2.21989	−	21.1208i	0.0786325	−	0.748138i	0.960807	−	0.277217i	$-0.0894120\pi$
$798$	0.564246	−	3.18851i	0.0199741	−	0.112872i
$799$	1.06968	+	5.03244i	0.0378425	+	0.178035i
$800$	−26.4864	−	1.00660i	−0.936436	−	0.0355885i
$801$	−4.98922	−	6.86707i	−0.176285	−	0.242636i
$802$	−15.0002	+	22.2093i	−0.529677	+	0.784236i
$803$	−12.3478	+	4.77355i	−0.435743	+	0.168455i
$804$	−9.59514	+	3.86295i	−0.338394	+	0.136236i
$805$	−2.23489	−	3.07606i	−0.0787695	−	0.108417i
$806$	−17.8827	−	24.2457i	−0.629891	−	0.854019i
$807$	−35.5004	−	11.5348i	−1.24967	−	0.406044i
$808$	11.0836	−	2.33450i	0.389921	−	0.0821275i
$809$	5.19639	+	11.6713i	0.182695	+	0.410340i	0.981556	−	0.191176i	$-0.0612302\pi$
$809$	5.19639	+	11.6713i	0.182695	+	0.410340i	−0.798861	+	0.601516i	$0.794563\pi$
$810$	−2.07417	−	2.65820i	−0.0728791	−	0.0933995i
$811$	−14.0431	+	4.56287i	−0.493119	+	0.160224i	−0.545011	−	0.838429i	$-0.683475\pi$
$811$	−14.0431	+	4.56287i	−0.493119	+	0.160224i	0.0518925	+	0.998653i	$0.483475\pi$
$812$	2.69164	−	1.42692i	0.0944580	−	0.0500751i
$813$	5.29613	+	9.17316i	0.185743	+	0.321717i
$814$	−2.17995	−	5.11062i	−0.0764073	−	0.179127i
$815$	−7.72763	+	4.46155i	−0.270687	+	0.156281i
$816$	−27.8350	+	10.0535i	−0.974419	+	0.351944i
$817$	2.59206	−	12.1947i	0.0906847	−	0.426638i
$818$	−4.81732	−	34.4309i	−0.168434	−	1.20385i
$819$	2.38346	−	2.50693i	0.0832847	−	0.0875993i
$820$	2.37265	+	8.31304i	0.0828565	+	0.290304i
$821$	2.80564	+	3.11598i	0.0979177	+	0.108749i	0.790112	−	0.612963i	$-0.210022\pi$
$821$	2.80564	+	3.11598i	0.0979177	+	0.108749i	−0.692194	+	0.721711i	$0.743356\pi$
$822$	37.8330	−	9.40807i	1.31958	−	0.328144i
$823$	−7.57368	+	17.0108i	−0.264002	+	0.592958i	−0.996099	−	0.0882425i	$-0.971875\pi$
$823$	−7.57368	+	17.0108i	−0.264002	+	0.592958i	0.732097	+	0.681200i	$0.238542\pi$
$824$	55.7896	+	11.9662i	1.94352	+	0.416863i
$825$	15.0001	+	14.9290i	0.522237	+	0.519761i
$826$	−0.0128726	+	0.0190591i	−0.000447897	+	0.000663153i
$827$	24.4557	+	33.6604i	0.850407	+	1.17049i	0.983773	+	0.179418i	$0.0574216\pi$
$827$	24.4557	+	33.6604i	0.850407	+	1.17049i	−0.133365	+	0.991067i	$0.542578\pi$
$828$	18.2678	−	3.19791i	0.634850	−	0.111135i
$829$	26.7076	+	29.6618i	0.927594	+	1.03020i	0.999462	+	0.0327835i	$0.0104372\pi$
$829$	26.7076	+	29.6618i	0.927594	+	1.03020i	−0.0718683	+	0.997414i	$0.522896\pi$
$830$	−1.59629	+	1.90000i	−0.0554079	+	0.0659501i
$831$	7.09949	+	5.15808i	0.246279	+	0.178932i
$832$	27.1450	+	9.75430i	0.941085	+	0.338170i
$833$	32.5444	−	10.5743i	1.12760	−	0.366378i
$834$	−14.2132	+	8.86922i	−0.492162	+	0.307116i
$835$	4.46622	−	7.73571i	0.154560	−	0.267705i
$836$	11.6531	+	6.44199i	0.403030	+	0.222801i
$837$		−	33.3551i		−	1.15292i
$838$	0.0902555	+	2.63104i	0.00311782	+	0.0908876i
$839$	37.5869	−	41.7444i	1.29764	−	1.44118i	0.467119	−	0.884195i	$-0.345292\pi$
$839$	37.5869	−	41.7444i	1.29764	−	1.44118i	0.830524	−	0.556983i	$-0.188041\pi$
$840$	0.907441	−	1.56505i	0.0313097	−	0.0539993i
$841$	−2.68561	+	25.5519i	−0.0926073	+	0.881100i
$842$	18.3599	+	15.4251i	0.632724	+	0.531583i
$843$	−18.9468	+	17.0598i	−0.652563	+	0.587570i
$844$	−14.1377	−	5.16542i	−0.486639	−	0.177801i
$845$	−7.19782	−	1.15385i	−0.247613	−	0.0396937i
$846$	1.37915	−	0.671607i	0.0474163	−	0.0230903i
$847$	9.21329	−	0.0437810i	0.316572	−	0.00150433i
$848$	−46.0860	−	13.3379i	−1.58260	−	0.458026i
$849$	−5.25232	+	11.7969i	−0.180259	+	0.404868i
$850$	25.9122	−	24.9923i	0.888781	−	0.857229i
$851$	−9.38012	+	1.99381i	−0.321546	+	0.0683468i
$852$	18.5311	−	19.1422i	0.634864	−	0.655803i
$853$	−2.23271	−	1.62216i	−0.0764467	−	0.0555418i	0.548906	−	0.835884i	$-0.315045\pi$
$853$	−2.23271	−	1.62216i	−0.0764467	−	0.0555418i	−0.625352	+	0.780343i	$0.715045\pi$
$854$	11.3972	−	8.89317i	0.390004	−	0.304318i
$855$	1.26113	+	0.268062i	0.0431297	+	0.00916751i
$856$	39.1529	+	4.18829i	1.33822	+	0.143153i
$857$		−	7.19831i		−	0.245889i	−0.992414	−	0.122945i	$-0.960766\pi$
$857$		−	7.19831i		−	0.245889i	0.992414	−	0.122945i	$-0.0392338\pi$
$858$	−10.6512	−	20.4196i	−0.363624	−	0.697114i
$859$		−	28.4529i		−	0.970801i	−0.874292	−	0.485401i	$-0.838674\pi$
$859$		−	28.4529i		−	0.970801i	0.874292	−	0.485401i	$-0.161326\pi$
$860$	3.69835	−	5.90241i	0.126113	−	0.201271i
$861$	8.60044	+	1.82808i	0.293102	+	0.0623008i
$862$	22.3515	+	28.6450i	0.761296	+	0.975653i
$863$	32.0274	+	23.2693i	1.09023	+	0.792096i	0.979438	−	0.201748i	$-0.0646621\pi$
$863$	32.0274	+	23.2693i	1.09023	+	0.792096i	0.110789	+	0.993844i	$0.464662\pi$
$864$	17.7762	+	26.5301i	0.604758	+	0.902574i
$865$	−3.71554	+	0.789762i	−0.126332	+	0.0268527i
$866$	0.351315	+	0.364246i	0.0119382	+	0.0123776i
$867$	6.93317	−	15.5722i	0.235463	−	0.528858i
$868$	9.18142	−	3.69639i	0.311638	−	0.125464i
$869$	−13.3981	−	3.55591i	−0.454499	−	0.120626i
$870$	−0.859881	−	1.76578i	−0.0291527	−	0.0598654i
$871$	−12.0395	+	6.52232i	−0.407943	+	0.221000i
$872$	41.1564	−	4.24884i	1.39373	−	0.143884i
$873$	−15.5704	+	14.0197i	−0.526978	+	0.474494i
$874$	14.7831	−	17.5957i	0.500044	−	0.595185i
$875$	−0.475504	+	4.52412i	−0.0160750	+	0.152943i
$876$	−9.02036	+	6.06816i	−0.304770	+	0.205024i
$877$	11.4456	−	12.7116i	0.386490	−	0.429241i	−0.518234	−	0.855239i	$-0.673410\pi$
$877$	11.4456	−	12.7116i	0.386490	−	0.429241i	0.904724	+	0.425998i	$0.140077\pi$
$878$	−19.2000	+	0.658639i	−0.647968	+	0.0222280i
$879$		−	6.80291i		−	0.229457i
$880$	4.88004	+	5.61483i	0.164506	+	0.189276i
$881$	−15.5930	+	27.0078i	−0.525340	+	0.909916i	0.474224	+	0.880404i	$0.342729\pi$
$881$	−15.5930	+	27.0078i	−0.525340	+	0.909916i	−0.999564	+	0.0295121i	$0.990605\pi$
$882$	−5.40130	−	8.65575i	−0.181871	−	0.291454i
$883$	−49.7033	+	16.1496i	−1.67265	+	0.543476i	−0.983463	−	0.181109i	$-0.942031\pi$
$883$	−49.7033	+	16.1496i	−1.67265	+	0.543476i	−0.689185	+	0.724585i	$0.742031\pi$
$884$	−35.0991	+	17.4049i	−1.18051	+	0.585389i
$885$	0.0119954	+	0.00871517i	0.000403221	+	0.000292957i
$886$	10.5465	+	8.86065i	0.354317	+	0.297679i
$887$	−28.2751	−	31.4026i	−0.949384	−	1.05440i	−0.998453	−	0.0556023i	$-0.982292\pi$
$887$	−28.2751	−	31.4026i	−0.949384	−	1.05440i	0.0490691	−	0.998795i	$-0.484375\pi$
$888$	−2.67510	−	3.69630i	−0.0897705	−	0.124040i
$889$	5.55726	+	7.64891i	0.186384	+	0.256536i
$890$	−4.86992	−	3.28917i	−0.163240	−	0.110253i
$891$	2.17283	−	13.9329i	0.0727927	−	0.466770i
$892$	32.9335	−	42.0461i	1.10270	−	1.40781i
$893$	0.773165	−	1.73656i	0.0258730	−	0.0581117i
$894$	−1.86804	−	7.51201i	−0.0624766	−	0.251239i
$895$	−2.33117	−	2.58903i	−0.0779226	−	0.0865418i
$896$	−5.33282	+	7.83317i	−0.178157	+	0.261688i
$897$	−38.1236	+	11.2539i	−1.27291	+	0.375756i
$898$	7.69407	−	1.07650i	0.256755	−	0.0359233i
$899$	2.23404	−	10.5103i	0.0745094	−	0.350539i
$900$	−9.09589	−	5.69934i	−0.303196	−	0.189978i
$901$	56.4341	−	32.5823i	1.88009	−	1.08547i
$902$	−18.5671	+	31.0244i	−0.618216	+	1.03300i
$903$	−3.54213	−	6.13516i	−0.117875	−	0.204165i
$904$	25.3971	−	34.8206i	0.844695	−	1.15812i
$905$	7.34806	−	2.38753i	0.244258	−	0.0793642i
$906$	12.7757	−	9.96884i	0.424446	−	0.331192i
$907$	−0.714692	−	1.60523i	−0.0237310	−	0.0533006i	0.901291	−	0.433214i	$-0.142621\pi$
$907$	−0.714692	−	1.60523i	−0.0237310	−	0.0533006i	−0.925022	+	0.379913i	$0.875954\pi$
$908$	16.6091	+	4.16285i	0.551192	+	0.138149i
$909$	4.36252	+	1.41747i	0.144696	+	0.0470144i
$910$	0.958360	−	2.19475i	0.0317693	−	0.0727553i
$911$	−2.29890	−	3.16417i	−0.0761661	−	0.104834i	0.769234	−	0.638967i	$-0.220638\pi$
$911$	−2.29890	−	3.16417i	−0.0761661	−	0.104834i	−0.845400	+	0.534133i	$0.820638\pi$
$912$	10.5035	+	3.03986i	0.347807	+	0.100660i
$913$	−10.3631	+	0.567798i	−0.342967	+	0.0187914i
$914$	9.40417	+	6.35162i	0.311062	+	0.210093i
$915$	−5.47801	−	7.53984i	−0.181098	−	0.249259i
$916$	4.73246	−	0.828451i	0.156365	−	0.0273728i
$917$	3.45522	+	16.2555i	0.114101	+	0.536805i
$918$	−42.7116	−	7.55833i	−1.40969	−	0.249462i
$919$	5.58354	−	53.1239i	0.184184	−	1.75239i	−0.378389	−	0.925647i	$-0.623522\pi$
$919$	5.58354	−	53.1239i	0.184184	−	1.75239i	0.562573	−	0.826748i	$-0.309811\pi$
$920$	11.1314	−	6.39930i	0.366990	−	0.210979i
$921$	35.7910	+	7.60761i	1.17935	+	0.250679i
$922$	2.41118	−	4.52805i	0.0794081	−	0.149123i
$923$	21.4967	−	27.9608i	0.707574	−	0.920342i
$924$	7.37028	−	1.71045i	0.242464	−	0.0562696i
$925$	4.80677	+	2.77519i	0.158046	+	0.0912477i
$926$	−0.0175459	−	0.0281178i	−0.000576594	−	0.000924008i
$927$	17.1718	+	15.4616i	0.563997	+	0.507825i
$928$	3.82443	+	9.55036i	0.125543	+	0.313506i
$929$	−10.3179	−	1.08446i	−0.338519	−	0.0355798i	−0.0662562	−	0.997803i	$-0.521105\pi$
$929$	−10.3179	−	1.08446i	−0.338519	−	0.0355798i	−0.272263	+	0.962223i	$0.587772\pi$
$930$	−2.17867	−	5.99734i	−0.0714415	−	0.196661i
$931$	−12.0243	−	3.90694i	−0.394081	−	0.128045i
$932$	−41.9244	+	7.33917i	−1.37328	+	0.240402i
$933$	1.30897	+	12.4540i	0.0428537	+	0.407725i
$934$	−34.4158	−	2.42789i	−1.12612	−	0.0794430i
$935$	−10.0915	−	0.504834i	−0.330028	−	0.0165098i
$936$	7.56152	+	8.90349i	0.247156	+	0.291020i
$937$	−2.89738	−	3.98790i	−0.0946532	−	0.130279i	0.759064	−	0.651016i	$-0.225657\pi$
$937$	−2.89738	−	3.98790i	−0.0946532	−	0.130279i	−0.853717	+	0.520737i	$0.825657\pi$
$938$	−1.08558	−	4.36547i	−0.0354454	−	0.142538i
$939$	−19.8353	+	17.8598i	−0.647301	+	0.582832i
$940$	0.738688	−	0.763051i	0.0240933	−	0.0248880i
$941$	−1.15668	−	0.840379i	−0.0377068	−	0.0273956i	0.568772	−	0.822495i	$-0.307419\pi$
$941$	−1.15668	−	0.840379i	−0.0377068	−	0.0273956i	−0.606479	+	0.795099i	$0.707419\pi$
$942$	0.531271	+	0.680859i	0.0173097	+	0.0221836i
$943$	46.3750	+	41.7563i	1.51018	+	1.35977i
$944$	−0.0593720	−	0.0500688i	−0.00193239	−	0.00162960i
$945$	2.29624	−	1.32573i	0.0746965	−	0.0431261i
$946$	28.5861	−	5.60881i	0.929414	−	0.182358i
$947$	−23.5408	+	40.7739i	−0.764974	+	1.32497i	0.175286	+	0.984518i	$0.443915\pi$
$947$	−23.5408	+	40.7739i	−0.764974	+	1.32497i	−0.940260	+	0.340457i	$0.889418\pi$
$948$	−11.3762	−	0.411294i	−0.369480	−	0.0133582i
$949$	−10.9522	+	9.33634i	−0.355524	+	0.303070i
$950$	−13.1731	+	1.84308i	−0.427391	+	0.0597975i
$951$	−14.6911	+	6.54092i	−0.476393	+	0.212104i
$952$	−2.65274	−	12.5945i	−0.0859757	−	0.408191i
$953$	−10.0808	−	47.4266i	−0.326550	−	1.53630i	−0.768850	−	0.639430i	$-0.779171\pi$
$953$	−10.0808	−	47.4266i	−0.326550	−	1.53630i	0.442300	−	0.896867i	$-0.354163\pi$
$954$	−13.4882	−	13.9846i	−0.436695	−	0.452769i
$955$	4.59323	+	2.04504i	0.148634	+	0.0661759i
$956$	4.52818	−	31.9342i	0.146452	−	1.03283i
$957$	2.92544	−	7.67548i	0.0945659	−	0.248113i
$958$	25.5953	−	37.8962i	0.826945	−	1.22437i
$959$	1.77225	+	16.8618i	0.0572289	+	0.544496i
$960$	4.92909	+	3.60909i	0.159086	+	0.116483i
$961$	1.20808	−	3.71809i	0.0389703	−	0.119938i
$962$	−4.07375	−	4.45960i	−0.131343	−	0.143783i
$963$	12.9008	+	9.37295i	0.415721	+	0.302039i
$964$	44.3939	−	3.04938i	1.42983	−	0.0982139i
$965$	1.60136	−	7.53383i	0.0515497	−	0.242522i
$966$	−0.447712	−	13.0512i	−0.0144049	−	0.419916i
$967$			18.0860i			0.581606i	0.956783	+	0.290803i	$0.0939225\pi$
$967$			18.0860i			0.581606i	−0.956783	+	0.290803i	$0.906078\pi$
$968$	−3.16228	+	30.9516i	−0.101640	+	0.994821i
$969$	−12.8620	+	7.42587i	−0.413186	+	0.238553i
$970$	−6.81794	+	12.8036i	−0.218911	+	0.411100i
$971$	12.2849	+	11.0613i	0.394240	+	0.354975i	0.842282	−	0.539037i	$-0.181212\pi$
$971$	12.2849	+	11.0613i	0.394240	+	0.354975i	−0.448042	+	0.894012i	$0.647879\pi$
$972$	1.52762	+	22.2395i	0.0489983	+	0.713334i
$973$	−2.96352	−	6.65617i	−0.0950060	−	0.213387i
$974$	1.06569	+	0.188586i	0.0341468	+	0.00604269i
$975$	20.7563	+	9.92411i	0.664732	+	0.317826i
$976$	25.7672	+	41.4632i	0.824789	+	1.32720i
$977$	36.6365	−	3.85065i	1.17211	−	0.123193i	0.501602	−	0.865099i	$-0.332744\pi$
$977$	36.6365	−	3.85065i	1.17211	−	0.123193i	0.670505	+	0.741905i	$0.266078\pi$
$978$	−30.5708	−	2.15664i	−0.977547	−	0.0689618i
$979$	−3.90248	−	24.2660i	−0.124724	−	0.775544i
$980$	−5.56090	−	4.35570i	−0.177637	−	0.139138i
$981$	15.3071	+	6.81515i	0.488717	+	0.217591i
$982$	5.38795	−	18.7464i	0.171937	−	0.598223i
$983$	−13.8617	+	42.6620i	−0.442121	+	1.36071i	0.443490	+	0.896279i	$0.353740\pi$
$983$	−13.8617	+	42.6620i	−0.442121	+	1.36071i	−0.885611	+	0.464428i	$0.846260\pi$
$984$	−9.22738	+	28.2214i	−0.294158	+	0.899667i
$985$	4.10708	+	9.22465i	0.130862	+	0.293922i
$986$	−12.9524	−	5.24237i	−0.412487	−	0.166951i
$987$	−0.333788	−	1.02729i	−0.0106246	−	0.0326991i
$988$	14.2714	+	2.42004i	0.454033	+	0.0769916i
$989$		−	50.2793i		−	1.59879i
$990$	0.580042	+	2.95627i	0.0184350	+	0.0939564i
$991$	−17.0788	−	9.86043i	−0.542525	−	0.313227i	0.203577	−	0.979059i	$-0.434743\pi$
$991$	−17.0788	−	9.86043i	−0.542525	−	0.313227i	−0.746102	+	0.665832i	$0.768077\pi$
$992$	9.11367	+	32.1565i	0.289359	+	1.02097i
$993$	12.2305	−	3.97393i	0.388123	−	0.126109i
$994$	7.12797	+	9.13497i	0.226085	+	0.289744i
$995$	−0.120480	+	1.14629i	−0.00381946	+	0.0363398i
$996$	−8.19575	+	2.33917i	−0.259692	+	0.0741195i
$997$	4.20326	+	19.7748i	0.133119	+	0.626273i	0.993230	+	0.116167i	$0.0370607\pi$
$997$	4.20326	+	19.7748i	0.133119	+	0.626273i	−0.860111	+	0.510107i	$0.829606\pi$
$998$	7.04728	−	1.75247i	0.223078	−	0.0554736i
$999$	−0.699016	−	6.65069i	−0.0221159	−	0.210419i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bn.a.459.27	yes	640
4.3	odd	2	inner	572.2.bn.a.459.50	yes	640
11.7	odd	10	inner	572.2.bn.a.95.24	yes	640
13.10	even	6	inner	572.2.bn.a.283.2	yes	640
44.7	even	10	inner	572.2.bn.a.95.2	✓	640
52.23	odd	6	inner	572.2.bn.a.283.24	yes	640
143.62	odd	30	inner	572.2.bn.a.491.50	yes	640
572.491	even	30	inner	572.2.bn.a.491.27	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bn.a.95.2	✓	640	44.7	even	10	inner
572.2.bn.a.95.24	yes	640	11.7	odd	10	inner
572.2.bn.a.283.2	yes	640	13.10	even	6	inner
572.2.bn.a.283.24	yes	640	52.23	odd	6	inner
572.2.bn.a.459.27	yes	640	1.1	even	1	trivial
572.2.bn.a.459.50	yes	640	4.3	odd	2	inner
572.2.bn.a.491.27	yes	640	572.491	even	30	inner
572.2.bn.a.491.50	yes	640	143.62	odd	30	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bn (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.748680 - 1.19978i) q^{2} +(0.283140 - 1.33207i) q^{3} +(-0.878956 + 1.79651i) q^{4} +(-0.329599 + 0.453654i) q^{5} +(-1.81017 + 0.657587i) q^{6} +(-0.174143 - 0.819278i) q^{7} +(2.81347 - 0.290453i) q^{8} +(1.04640 + 0.465888i) q^{9} +O(q^{10})\)	\(q+(-0.748680 - 1.19978i) q^{2} +(0.283140 - 1.33207i) q^{3} +(-0.878956 + 1.79651i) q^{4} +(-0.329599 + 0.453654i) q^{5} +(-1.81017 + 0.657587i) q^{6} +(-0.174143 - 0.819278i) q^{7} +(2.81347 - 0.290453i) q^{8} +(1.04640 + 0.465888i) q^{9} +(0.791051 + 0.0558053i) q^{10} +(2.09334 + 2.57254i) q^{11} +(2.14420 + 1.67949i) q^{12} +(3.07247 + 1.88677i) q^{13} +(-0.852578 + 0.822311i) q^{14} +(0.510976 + 0.567496i) q^{15} +(-2.45487 - 3.15810i) q^{16} +(5.40318 + 0.567897i) q^{17} +(-0.224456 - 1.60425i) q^{18} +(-1.49174 - 1.34317i) q^{19} +(-0.525290 - 0.990869i) q^{20} -1.14064 q^{21} +(1.51924 - 4.43756i) q^{22} +(-7.01090 - 4.04774i) q^{23} +(0.409703 - 3.82998i) q^{24} +(1.44792 + 4.45623i) q^{25} +(-0.0365797 - 5.09889i) q^{26} +(3.31826 - 4.56719i) q^{27} +(1.62490 + 0.407260i) q^{28} +(1.35149 - 1.21689i) q^{29} +(0.298314 - 1.03793i) q^{30} +(4.78001 - 3.47288i) q^{31} +(-1.95112 + 5.30972i) q^{32} +(4.01950 - 2.06008i) q^{33} +(-3.36390 - 6.90782i) q^{34} +(0.429067 + 0.191033i) q^{35} +(-1.75671 + 1.47037i) q^{36} +(0.880308 - 0.792633i) q^{37} +(-0.494674 + 2.79537i) q^{38} +(3.38325 - 3.55852i) q^{39} +(-0.795553 + 1.37208i) q^{40} +(-7.54001 - 1.60268i) q^{41} +(0.853975 + 1.36852i) q^{42} +(3.10539 + 5.37869i) q^{43} +(-6.46153 + 1.49955i) q^{44} +(-0.556245 + 0.321148i) q^{45} +(0.392509 + 11.4420i) q^{46} +(0.292632 + 0.900628i) q^{47} +(-4.90187 + 2.37587i) q^{48} +(5.75393 - 2.56181i) q^{49} +(4.26248 - 5.07348i) q^{50} +(2.28633 - 7.03661i) q^{51} +(-6.09017 + 3.86132i) q^{52} +(9.70361 - 7.05009i) q^{53} +(-7.96394 - 0.561822i) q^{54} +(-1.85700 + 0.101746i) q^{55} +(-0.727909 - 2.25444i) q^{56} +(-2.21156 + 1.60680i) q^{57} +(-2.47184 - 0.710437i) q^{58} +(0.0189921 - 0.00403689i) q^{59} +(-1.46864 + 0.419167i) q^{60} +(-12.1375 - 1.27570i) q^{61} +(-7.74540 - 3.13490i) q^{62} +(0.199468 - 0.938425i) q^{63} +(7.83127 - 1.63437i) q^{64} +(-1.86863 + 0.771961i) q^{65} +(-5.48097 - 3.28018i) q^{66} +(-1.89884 + 3.28888i) q^{67} +(-5.76939 + 9.20770i) q^{68} +(-7.37693 + 8.19291i) q^{69} +(-0.0920359 - 0.657809i) q^{70} +(1.02249 - 9.72834i) q^{71} +(3.07934 + 1.00683i) q^{72} +(-1.23344 + 3.79615i) q^{73} +(-1.61006 - 0.462749i) q^{74} +(6.34597 - 0.666988i) q^{75} +(3.72419 - 1.49934i) q^{76} +(1.74308 - 2.16302i) q^{77} +(-6.80242 - 1.39497i) q^{78} +(-3.38131 + 2.45667i) q^{79} +(2.24181 - 0.0727569i) q^{80} +(-2.84495 - 3.15964i) q^{81} +(3.72219 + 10.2463i) q^{82} +(-1.83934 + 2.53163i) q^{83} +(1.00257 - 2.04917i) q^{84} +(-2.03851 + 2.26400i) q^{85} +(4.12832 - 7.75271i) q^{86} +(-1.23832 - 2.14483i) q^{87} +(6.63675 + 6.62974i) q^{88} +(-6.41766 - 3.70524i) q^{89} +(0.801758 + 0.426936i) q^{90} +(1.01074 - 2.84578i) q^{91} +(13.4341 - 9.03734i) q^{92} +(-3.27270 - 7.35061i) q^{93} +(0.861470 - 1.02538i) q^{94} +(1.10101 - 0.234027i) q^{95} +(6.52047 + 4.10241i) q^{96} +(-7.43998 + 16.7105i) q^{97} +(-7.38147 - 4.98548i) q^{98} +(0.991958 + 3.66716i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 15 q^{2} - 3 q^{4} - 15 q^{6} - 78 q^{9}+O(q^{10}) \) 640 * q - 15 * q^2 - 3 * q^4 - 15 * q^6 - 78 * q^9	\( 640 q - 15 q^{2} - 3 q^{4} - 15 q^{6} - 78 q^{9} - 4 q^{12} - 20 q^{13} - 12 q^{14} - 19 q^{16} - 10 q^{17} - 45 q^{20} - 15 q^{22} - 15 q^{24} + 104 q^{25} - 20 q^{26} - 15 q^{28} - 10 q^{29} + 45 q^{30} - 24 q^{33} + 4 q^{36} - 18 q^{37} - 14 q^{38} - 20 q^{40} - 30 q^{41} - 13 q^{42} - 108 q^{45} - 15 q^{46} + 35 q^{48} - 74 q^{49} - 90 q^{50} + 15 q^{52} - 8 q^{53} + 50 q^{56} + 27 q^{58} - 10 q^{61} - 5 q^{62} - 84 q^{64} - 146 q^{66} - 70 q^{68} - 26 q^{69} - 15 q^{72} - 55 q^{74} + 44 q^{77} + 24 q^{78} - 39 q^{80} + 30 q^{81} - 29 q^{82} + 30 q^{84} - 30 q^{85} - 75 q^{88} - 24 q^{89} + 30 q^{90} + 14 q^{92} + 66 q^{93} - 5 q^{94} - 30 q^{97}+O(q^{100}) \) 640 * q - 15 * q^2 - 3 * q^4 - 15 * q^6 - 78 * q^9 - 4 * q^12 - 20 * q^13 - 12 * q^14 - 19 * q^16 - 10 * q^17 - 45 * q^20 - 15 * q^22 - 15 * q^24 + 104 * q^25 - 20 * q^26 - 15 * q^28 - 10 * q^29 + 45 * q^30 - 24 * q^33 + 4 * q^36 - 18 * q^37 - 14 * q^38 - 20 * q^40 - 30 * q^41 - 13 * q^42 - 108 * q^45 - 15 * q^46 + 35 * q^48 - 74 * q^49 - 90 * q^50 + 15 * q^52 - 8 * q^53 + 50 * q^56 + 27 * q^58 - 10 * q^61 - 5 * q^62 - 84 * q^64 - 146 * q^66 - 70 * q^68 - 26 * q^69 - 15 * q^72 - 55 * q^74 + 44 * q^77 + 24 * q^78 - 39 * q^80 + 30 * q^81 - 29 * q^82 + 30 * q^84 - 30 * q^85 - 75 * q^88 - 24 * q^89 + 30 * q^90 + 14 * q^92 + 66 * q^93 - 5 * q^94 - 30 * q^97

Introduction

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