LMFDB - Embedded newform 380.2.bj.a.23.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(23,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 4]))

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

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

chi := DirichletCharacter("380.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bj (of order $36$, degree $12$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$56$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			23.1
Character	$\chi$	$=$	380.23
Dual form			380.2.bj.a.347.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41421 - 0.00173027i) q^{2} +(-2.30458 - 1.61369i) q^{3} +(1.99999 + 0.00489393i) q^{4} +(-1.01610 + 1.99187i) q^{5} +(3.25638 + 2.28608i) q^{6} +(0.362300 - 0.0970781i) q^{7} +(-2.82841 - 0.0103816i) q^{8} +(1.68106 + 4.61866i) q^{9} +O(q^{10})$	\(q+(-1.41421 - 0.00173027i) q^{2} +(-2.30458 - 1.61369i) q^{3} +(1.99999 + 0.00489393i) q^{4} +(-1.01610 + 1.99187i) q^{5} +(3.25638 + 2.28608i) q^{6} +(0.362300 - 0.0970781i) q^{7} +(-2.82841 - 0.0103816i) q^{8} +(1.68106 + 4.61866i) q^{9} +(1.44042 - 2.81517i) q^{10} +(3.54429 - 2.04630i) q^{11} +(-4.60125 - 3.23864i) q^{12} +(3.70457 - 2.59396i) q^{13} +(-0.512538 + 0.136662i) q^{14} +(5.55593 - 2.95076i) q^{15} +(3.99995 + 0.0195756i) q^{16} +(-5.19173 + 2.42094i) q^{17} +(-2.36938 - 6.53468i) q^{18} +(-3.79915 - 2.13692i) q^{19} +(-2.04194 + 3.97875i) q^{20} +(-0.991604 - 0.360914i) q^{21} +(-5.01592 + 2.88777i) q^{22} +(-0.542351 + 0.0474495i) q^{23} +(6.50154 + 4.58809i) q^{24} +(-2.93509 - 4.04787i) q^{25} +(-5.24353 + 3.66201i) q^{26} +(1.39447 - 5.20424i) q^{27} +(0.725074 - 0.192383i) q^{28} +(0.432355 + 1.18788i) q^{29} +(-7.86237 + 4.16339i) q^{30} +(-6.81842 - 3.93662i) q^{31} +(-5.65675 - 0.0346051i) q^{32} +(-11.4702 - 1.00351i) q^{33} +(7.34640 - 3.41474i) q^{34} +(-0.174766 + 0.820296i) q^{35} +(3.33950 + 9.24552i) q^{36} +(5.60448 - 5.60448i) q^{37} +(5.36911 + 3.02863i) q^{38} -12.7233 q^{39} +(2.89462 - 5.62327i) q^{40} +(-1.53495 - 8.70514i) q^{41} +(1.40171 + 0.512125i) q^{42} +(0.539983 - 6.17204i) q^{43} +(7.09857 - 4.07524i) q^{44} +(-10.9079 - 1.34457i) q^{45} +(0.767081 - 0.0661653i) q^{46} +(-1.33499 - 0.622516i) q^{47} +(-9.18663 - 6.49978i) q^{48} +(-5.94034 + 3.42966i) q^{49} +(4.14384 + 5.72963i) q^{50} +(15.8714 + 2.79856i) q^{51} +(7.42180 - 5.16978i) q^{52} +(-0.510901 - 5.83962i) q^{53} +(-1.98109 + 7.35749i) q^{54} +(0.474610 + 9.13900i) q^{55} +(-1.02574 + 0.270815i) q^{56} +(5.30714 + 11.0553i) q^{57} +(-0.609386 - 1.68067i) q^{58} +(-3.62767 - 1.32036i) q^{59} +(11.1263 - 5.87432i) q^{60} +(3.14017 + 2.63491i) q^{61} +(9.63588 + 5.57901i) q^{62} +(1.05742 + 1.51015i) q^{63} +(7.99978 + 0.0587266i) q^{64} +(1.40264 + 10.0147i) q^{65} +(16.2195 + 1.43902i) q^{66} +(4.17272 + 1.94577i) q^{67} +(-10.3953 + 4.81646i) q^{68} +(1.32646 + 0.765832i) q^{69} +(0.248575 - 1.15977i) q^{70} +(-7.20741 - 8.58945i) q^{71} +(-4.70676 - 13.0809i) q^{72} +(5.80768 - 8.29423i) q^{73} +(-7.93562 + 7.91623i) q^{74} +(0.232165 + 14.0650i) q^{75} +(-7.58783 - 4.29242i) q^{76} +(1.08545 - 1.08545i) q^{77} +(17.9935 + 0.0220147i) q^{78} +(0.240466 + 1.36375i) q^{79} +(-4.10334 + 7.94749i) q^{80} +(-0.316185 + 0.265310i) q^{81} +(2.15569 + 12.3136i) q^{82} +(0.804426 + 3.00216i) q^{83} +(-1.98144 - 0.726680i) q^{84} +(0.453103 - 12.8012i) q^{85} +(-0.774330 + 8.72764i) q^{86} +(0.920475 - 3.43526i) q^{87} +(-10.0459 + 5.75097i) q^{88} +(8.36016 + 1.47412i) q^{89} +(15.4237 + 1.92038i) q^{90} +(1.09035 - 1.29943i) q^{91} +(-1.08493 + 0.0922445i) q^{92} +(9.36114 + 20.0750i) q^{93} +(1.88688 + 0.882680i) q^{94} +(8.11678 - 5.39610i) q^{95} +(12.9806 + 9.20796i) q^{96} +(-2.34635 + 1.09412i) q^{97} +(8.40684 - 4.83999i) q^{98} +(15.4093 + 12.9299i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.41421	−	0.00173027i	−0.999999	−	0.00122348i
$2$	−1.41421	−	0.00173027i	−0.999999	−	0.00122348i
$3$	−2.30458	−	1.61369i	−1.33055	−	0.931662i	−0.330624	−	0.943763i	$-0.607259\pi$
$3$	−2.30458	−	1.61369i	−1.33055	−	0.931662i	−0.999927	+	0.0121009i	$0.996148\pi$
$4$	1.99999	+	0.00489393i	0.999997	+	0.00244696i
$5$	−1.01610	+	1.99187i	−0.454413	+	0.890791i
$5$	−1.01610	+	1.99187i	−0.454413	+	0.890791i
$6$	3.25638	+	2.28608i	1.32941	+	0.933289i
$7$	0.362300	−	0.0970781i	0.136937	−	0.0366921i	−0.189700	−	0.981842i	$-0.560751\pi$
$7$	0.362300	−	0.0970781i	0.136937	−	0.0366921i	0.326636	+	0.945150i	$0.394085\pi$
$8$	−2.82841	−	0.0103816i	−0.999993	−	0.00367044i
$9$	1.68106	+	4.61866i	0.560352	+	1.53955i
$10$	1.44042	−	2.81517i	0.455502	−	0.890235i
$11$	3.54429	−	2.04630i	1.06864	−	0.616982i	0.140833	−	0.990033i	$-0.455022\pi$
$11$	3.54429	−	2.04630i	1.06864	−	0.616982i	0.927811	+	0.373052i	$0.121689\pi$
$12$	−4.60125	−	3.23864i	−1.32827	−	0.934915i
$13$	3.70457	−	2.59396i	1.02746	−	0.719436i	0.0669726	−	0.997755i	$-0.478666\pi$
$13$	3.70457	−	2.59396i	1.02746	−	0.719436i	0.960489	+	0.278319i	$0.0897771\pi$
$14$	−0.512538	+	0.136662i	−0.136981	+	0.0365245i
$15$	5.55593	−	2.95076i	1.43454	−	0.761884i
$16$	3.99995	+	0.0195756i	0.999988	+	0.00489391i
$17$	−5.19173	+	2.42094i	−1.25918	+	0.587165i	−0.933589	−	0.358346i	$-0.883341\pi$
$17$	−5.19173	+	2.42094i	−1.25918	+	0.587165i	−0.325590	+	0.945511i	$0.605563\pi$
$18$	−2.36938	−	6.53468i	−0.558468	−	1.54024i
$19$	−3.79915	−	2.13692i	−0.871586	−	0.490243i
$19$	−3.79915	−	2.13692i	−0.871586	−	0.490243i
$20$	−2.04194	+	3.97875i	−0.456591	+	0.889677i
$21$	−0.991604	−	0.360914i	−0.216386	−	0.0787580i
$22$	−5.01592	+	2.88777i	−1.06940	+	0.615674i
$23$	−0.542351	+	0.0474495i	−0.113088	+	0.00989391i	−0.143559	−	0.989642i	$-0.545855\pi$
$23$	−0.542351	+	0.0474495i	−0.113088	+	0.00989391i	0.0304713	+	0.999536i	$0.490299\pi$
$24$	6.50154	+	4.58809i	1.32712	+	0.936539i
$25$	−2.93509	−	4.04787i	−0.587018	−	0.809574i
$26$	−5.24353	+	3.66201i	−1.02834	+	0.718179i
$27$	1.39447	−	5.20424i	0.268366	−	1.00156i
$28$	0.725074	−	0.192383i	0.137026	−	0.0363569i
$29$	0.432355	+	1.18788i	0.0802862	+	0.220585i	0.973341	−	0.229364i	$-0.0736646\pi$
$29$	0.432355	+	1.18788i	0.0802862	+	0.220585i	−0.893055	+	0.449948i	$0.851442\pi$
$30$	−7.86237	+	4.16339i	−1.43547	+	0.760128i
$31$	−6.81842	−	3.93662i	−1.22462	−	0.707037i	−0.258724	−	0.965951i	$-0.583302\pi$
$31$	−6.81842	−	3.93662i	−1.22462	−	0.707037i	−0.965900	+	0.258914i	$0.916635\pi$
$32$	−5.65675	−	0.0346051i	−0.999981	−	0.00611737i
$33$	−11.4702	−	1.00351i	−1.99670	−	0.174689i
$34$	7.34640	−	3.41474i	1.25990	−	0.585624i
$35$	−0.174766	+	0.820296i	−0.0295408	+	0.138655i
$36$	3.33950	+	9.24552i	0.556583	+	1.54092i
$37$	5.60448	−	5.60448i	0.921371	−	0.921371i	−0.0757558	−	0.997126i	$-0.524137\pi$
$37$	5.60448	−	5.60448i	0.921371	−	0.921371i	0.997126	+	0.0757558i	$0.0241370\pi$
$38$	5.36911	+	3.02863i	0.870985	+	0.491309i
$39$	−12.7233			−2.03736
$40$	2.89462	−	5.62327i	0.457679	−	0.889117i
$41$	−1.53495	−	8.70514i	−0.239719	−	1.35951i	−0.832444	−	0.554110i	$-0.813059\pi$
$41$	−1.53495	−	8.70514i	−0.239719	−	1.35951i	0.592725	−	0.805405i	$-0.298052\pi$
$42$	1.40171	+	0.512125i	0.216289	+	0.0790227i
$43$	0.539983	−	6.17204i	0.0823467	−	0.941227i	−0.836851	−	0.547431i	$-0.815606\pi$
$43$	0.539983	−	6.17204i	0.0823467	−	0.941227i	0.919198	−	0.393796i	$-0.128838\pi$
$44$	7.09857	−	4.07524i	1.07015	−	0.614365i
$45$	−10.9079	−	1.34457i	−1.62605	−	0.200437i
$46$	0.767081	−	0.0661653i	0.113100	−	0.00975554i
$47$	−1.33499	−	0.622516i	−0.194728	−	0.0908033i	0.322808	−	0.946464i	$-0.395373\pi$
$47$	−1.33499	−	0.622516i	−0.194728	−	0.0908033i	−0.517537	+	0.855661i	$0.673151\pi$
$48$	−9.18663	−	6.49978i	−1.32598	−	0.938162i
$49$	−5.94034	+	3.42966i	−0.848620	+	0.489951i
$50$	4.14384	+	5.72963i	0.586027	+	0.810292i
$51$	15.8714	+	2.79856i	2.22244	+	0.391876i
$52$	7.42180	−	5.16978i	1.02922	−	0.716920i
$53$	−0.510901	−	5.83962i	−0.0701776	−	0.802133i	−0.946982	−	0.321286i	$-0.895885\pi$
$53$	−0.510901	−	5.83962i	−0.0701776	−	0.802133i	0.876804	−	0.480847i	$-0.159671\pi$
$54$	−1.98109	+	7.35749i	−0.269592	+	1.00123i
$55$	0.474610	+	9.13900i	0.0639965	+	1.23230i
$56$	−1.02574	+	0.270815i	−0.137070	+	0.0361892i
$57$	5.30714	+	11.0553i	0.702948	+	1.46432i
$58$	−0.609386	−	1.68067i	−0.0800163	−	0.220683i
$59$	−3.62767	−	1.32036i	−0.472283	−	0.171897i	0.0949034	−	0.995486i	$-0.469746\pi$
$59$	−3.62767	−	1.32036i	−0.472283	−	0.171897i	−0.567186	+	0.823590i	$0.691968\pi$
$60$	11.1263	−	5.87432i	1.43640	−	0.758371i
$61$	3.14017	+	2.63491i	0.402057	+	0.337366i	0.821288	−	0.570513i	$-0.193256\pi$
$61$	3.14017	+	2.63491i	0.402057	+	0.337366i	−0.419231	+	0.907880i	$0.637700\pi$
$62$	9.63588	+	5.57901i	1.22376	+	0.708535i
$63$	1.05742	+	1.51015i	0.133222	+	0.190261i
$64$	7.99978	+	0.0587266i	0.999973	+	0.00734083i
$65$	1.40264	+	10.0147i	0.173976	+	1.24217i
$66$	16.2195	+	1.43902i	1.99649	+	0.177132i
$67$	4.17272	+	1.94577i	0.509779	+	0.237714i	0.660450	−	0.750870i	$-0.270366\pi$
$67$	4.17272	+	1.94577i	0.509779	+	0.237714i	−0.150671	+	0.988584i	$0.548143\pi$
$68$	−10.3953	+	4.81646i	−1.26061	+	0.584082i
$69$	1.32646	+	0.765832i	0.159687	+	0.0921953i
$70$	0.248575	−	1.15977i	0.0297104	−	0.138619i
$71$	−7.20741	−	8.58945i	−0.855362	−	1.01938i	−0.999555	−	0.0298310i	$-0.990503\pi$
$71$	−7.20741	−	8.58945i	−0.855362	−	1.01938i	0.144193	−	0.989550i	$-0.453941\pi$
$72$	−4.70676	−	13.0809i	−0.554697	−	1.54160i
$73$	5.80768	−	8.29423i	0.679738	−	0.970766i	−0.319990	−	0.947421i	$-0.603679\pi$
$73$	5.80768	−	8.29423i	0.679738	−	0.970766i	0.999727	−	0.0233452i	$-0.00743168\pi$
$74$	−7.93562	+	7.91623i	−0.922497	+	0.920243i
$75$	0.232165	+	14.0650i	0.0268082	+	1.62408i
$76$	−7.58783	−	4.29242i	−0.870383	−	0.492375i
$77$	1.08545	−	1.08545i	0.123698	−	0.123698i
$78$	17.9935	+	0.0220147i	2.03736	+	0.00249267i
$79$	0.240466	+	1.36375i	0.0270545	+	0.153434i	0.995342	−	0.0964037i	$-0.0307340\pi$
$79$	0.240466	+	1.36375i	0.0270545	+	0.153434i	−0.968288	+	0.249837i	$0.919623\pi$
$80$	−4.10334	+	7.94749i	−0.458767	+	0.888557i
$81$	−0.316185	+	0.265310i	−0.0351316	+	0.0294789i
$82$	2.15569	+	12.3136i	0.238056	+	1.35981i
$83$	0.804426	+	3.00216i	0.0882972	+	0.329530i	0.995918	−	0.0902610i	$-0.0287701\pi$
$83$	0.804426	+	3.00216i	0.0882972	+	0.329530i	−0.907621	+	0.419791i	$0.862103\pi$
$84$	−1.98144	−	0.726680i	−0.216192	−	0.0792872i
$85$	0.453103	−	12.8012i	0.0491459	−	1.38848i
$86$	−0.774330	+	8.72764i	−0.0834982	+	0.941125i
$87$	0.920475	−	3.43526i	0.0986853	−	0.368299i
$88$	−10.0459	+	5.75097i	−1.07090	+	0.613055i
$89$	8.36016	+	1.47412i	0.886176	+	0.156257i	0.598167	−	0.801371i	$-0.295896\pi$
$89$	8.36016	+	1.47412i	0.886176	+	0.156257i	0.288008	+	0.957628i	$0.407007\pi$
$90$	15.4237	+	1.92038i	1.62581	+	0.202426i
$91$	1.09035	−	1.29943i	0.114300	−	0.136217i
$92$	−1.08493	+	0.0922445i	−0.113112	+	0.00961716i
$93$	9.36114	+	20.0750i	0.970705	+	2.08168i
$94$	1.88688	+	0.882680i	0.194617	+	0.0910415i
$95$	8.11678	−	5.39610i	0.832764	−	0.553628i
$96$	12.9806	+	9.20796i	1.32483	+	0.939784i
$97$	−2.34635	+	1.09412i	−0.238236	+	0.111091i	−0.538070	−	0.842900i	$-0.680846\pi$
$97$	−2.34635	+	1.09412i	−0.238236	+	0.111091i	0.299834	+	0.953991i	$0.403069\pi$
$98$	8.40684	−	4.83999i	0.849219	−	0.488912i
$99$	15.4093	+	12.9299i	1.54869	+	1.29951i
$100$	−5.85035	−	8.11008i	−0.585035	−	0.811008i
$101$	1.85342	−	10.5113i	0.184422	−	1.04591i	−0.742274	−	0.670097i	$-0.766253\pi$
$101$	1.85342	−	10.5113i	0.184422	−	1.04591i	0.926696	−	0.375812i	$-0.122636\pi$
$102$	−22.4407	−	3.98522i	−2.22196	−	0.394595i
$103$	−11.7897	−	3.15903i	−1.16167	−	0.311268i	−0.374037	−	0.927414i	$-0.622027\pi$
$103$	−11.7897	−	3.15903i	−1.16167	−	0.311268i	−0.787633	+	0.616145i	$0.788693\pi$
$104$	−10.5050	+	7.29833i	−1.03010	+	0.715660i
$105$	1.72646	−	1.60842i	0.168485	−	0.156966i
$106$	0.712418	+	8.25935i	0.0691961	+	0.802219i
$107$	−14.4266	+	3.86560i	−1.39467	+	0.373702i	−0.876429	−	0.481530i	$-0.840081\pi$
$107$	−14.4266	+	3.86560i	−1.39467	+	0.373702i	−0.518245	+	0.855232i	$0.673414\pi$
$108$	2.81441	−	10.4016i	0.270816	−	1.00090i
$109$	−2.92513	−	3.48603i	−0.280176	−	0.333901i	0.607543	−	0.794287i	$-0.292155\pi$
$109$	−2.92513	−	3.48603i	−0.280176	−	0.333901i	−0.887719	+	0.460386i	$0.847711\pi$
$110$	−0.655387	−	12.9253i	−0.0624887	−	1.23238i
$111$	−21.9598	+	3.87211i	−2.08434	+	0.367525i
$112$	1.45108	−	0.381215i	0.137115	−	0.0360215i
$113$	11.4010	+	11.4010i	1.07251	+	1.07251i	0.997157	+	0.0753576i	$0.0240098\pi$
$113$	11.4010	+	11.4010i	1.07251	+	1.07251i	0.0753576	+	0.997157i	$0.475990\pi$
$114$	−7.48630	−	15.6438i	−0.701156	−	1.46518i
$115$	0.456568	−	1.12851i	0.0425752	−	0.105234i
$116$	0.858893	+	2.37788i	0.0797462	+	0.220780i
$117$	18.2082	+	12.7495i	1.68335	+	1.17869i
$118$	5.12802	+	1.87355i	0.472072	+	0.172475i
$119$	−1.64594	+	1.38111i	−0.150884	+	0.126606i
$120$	−15.7451	+	8.28828i	−1.43732	+	0.756613i
$121$	2.87466	−	4.97905i	0.261333	−	0.452641i
$122$	−4.43631	−	3.73176i	−0.401644	−	0.337858i
$123$	−10.5099	+	22.5386i	−0.947649	+	2.03224i
$124$	−13.6175	−	7.90658i	−1.22289	−	0.710032i
$125$	11.0452	−	1.73328i	0.987910	−	0.155030i
$126$	−1.49280	−	2.13750i	−0.132989	−	0.190424i
$127$	11.6925	−	8.18718i	1.03754	−	0.726494i	0.0748773	−	0.997193i	$-0.476143\pi$
$127$	11.6925	−	8.18718i	1.03754	−	0.726494i	0.962664	+	0.270698i	$0.0872546\pi$
$128$	−11.3133	−	0.0968937i	−0.999963	−	0.00856427i
$129$	−11.2042	+	13.3526i	−0.986471	+	1.17563i
$130$	−1.96630	−	14.1654i	−0.172456	−	1.24239i
$131$	−0.166601	+	0.457732i	−0.0145560	+	0.0399922i	−0.946758	−	0.321947i	$-0.895663\pi$
$131$	−0.166601	+	0.457732i	−0.0145560	+	0.0399922i	0.932202	+	0.361939i	$0.117885\pi$
$132$	−22.9354	−	2.06315i	−1.99627	−	0.179574i
$133$	−1.58388	−	0.405393i	−0.137340	−	0.0351520i
$134$	−5.89774	−	2.75895i	−0.509487	−	0.238337i
$135$	8.94925	+	8.06563i	0.770229	+	0.694179i
$136$	14.7095	−	6.79352i	1.26133	−	0.582539i
$137$	−15.9740	+	1.39754i	−1.36475	+	0.119400i	−0.745872	−	0.666089i	$-0.767967\pi$
$137$	−15.9740	+	1.39754i	−1.36475	+	0.119400i	−0.618875	+	0.785489i	$0.712411\pi$
$138$	−1.87457	−	1.08534i	−0.159574	−	0.0923906i
$139$	1.32481	−	7.51335i	0.112369	−	0.637274i	−0.875651	−	0.482945i	$-0.839567\pi$
$139$	1.32481	−	7.51335i	0.112369	−	0.637274i	0.988019	−	0.154329i	$-0.0493217\pi$
$140$	−0.353545	+	1.63973i	−0.0298800	+	0.138583i
$141$	2.07205	+	3.58889i	0.174498	+	0.302239i
$142$	10.1779	+	12.1598i	0.854114	+	1.02043i
$143$	7.82203	−	16.7744i	0.654111	−	1.40275i
$144$	6.63373	+	18.5073i	0.552811	+	1.54228i
$145$	−2.80543	−	0.345813i	−0.232978	−	0.0287182i
$146$	−8.22765	+	11.7198i	−0.680925	+	0.969934i
$147$	19.2244	+	1.68192i	1.58560	+	0.138722i
$148$	11.2364	−	11.1815i	0.923622	−	0.919113i
$149$	11.4052	−	2.01105i	0.934352	−	0.164752i	0.314311	−	0.949320i	$-0.398227\pi$
$149$	11.4052	−	2.01105i	0.934352	−	0.164752i	0.620042	+	0.784569i	$0.287116\pi$
$150$	−0.303995	−	19.8912i	−0.0248211	−	1.62411i
$151$		−	0.496458i		−	0.0404012i	−0.999796	−	0.0202006i	$-0.993570\pi$
$151$		−	0.496458i		−	0.0404012i	0.999796	−	0.0202006i	$-0.00643048\pi$
$152$	10.7234	+	6.08353i	0.869780	+	0.493439i
$153$	−19.9091	−	19.9091i	−1.60956	−	1.60956i
$154$	−1.53693	+	1.53317i	−0.123849	+	0.123547i
$155$	14.7694	−	9.58141i	1.18631	−	0.769598i
$156$	−25.4466	−	0.0622670i	−2.03735	−	0.00498535i
$157$	−0.0233867	+	0.267312i	−0.00186646	+	0.0213338i	−0.997071	−	0.0764839i	$-0.975631\pi$
$157$	−0.0233867	+	0.267312i	−0.00186646	+	0.0213338i	0.995204	+	0.0978176i	$0.0311862\pi$
$158$	−0.337710	−	1.92905i	−0.0268667	−	0.153467i
$159$	−8.24590	+	14.2823i	−0.653942	+	1.13266i
$160$	5.81674	−	11.2323i	0.459854	−	0.887995i
$161$	−0.191888	+	0.0698413i	−0.0151229	+	0.00550427i
$162$	0.447611	−	0.374658i	0.0351677	−	0.0294359i
$163$	18.1538	+	4.86431i	1.42192	+	0.381002i	0.886164	−	0.463372i	$-0.153361\pi$
$163$	18.1538	+	4.86431i	1.42192	+	0.381002i	0.535754	+	0.844374i	$0.320027\pi$
$164$	−3.02729	−	17.4177i	−0.236392	−	1.36010i
$165$	13.6537	−	21.8274i	1.06294	−	1.69926i
$166$	−1.13244	−	4.24708i	−0.0878940	−	0.329638i
$167$	1.69012	+	19.3181i	0.130785	+	1.49488i	0.723980	+	0.689821i	$0.242311\pi$
$167$	1.69012	+	19.3181i	0.130785	+	1.49488i	−0.593195	+	0.805059i	$0.702134\pi$
$168$	2.80091	+	1.03111i	0.216095	+	0.0795517i
$169$	2.54889	−	7.00302i	0.196068	−	0.538693i
$170$	−0.662933	+	18.1028i	−0.0508446	+	1.38842i
$171$	3.48313	−	21.1393i	0.266361	−	1.61656i
$172$	1.11017	−	12.3414i	0.0846496	−	0.941023i
$173$	−5.91847	−	12.6922i	−0.449973	−	0.964970i	−0.992190	−	0.124732i	$-0.960193\pi$
$173$	−5.91847	−	12.6922i	−0.449973	−	0.964970i	0.542217	−	0.840238i	$-0.317585\pi$
$174$	−1.30769	+	4.85660i	−0.0991358	+	0.368178i
$175$	−1.45634	−	1.18161i	−0.110089	−	0.0893215i
$176$	14.2170	−	8.11571i	1.07165	−	0.611744i
$177$	6.22961	+	8.89681i	0.468246	+	0.668725i
$178$	−11.8205	−	2.09919i	−0.885984	−	0.157341i
$179$	−2.25279	−	3.90194i	−0.168381	−	0.291645i	0.769470	−	0.638683i	$-0.220521\pi$
$179$	−2.25279	−	3.90194i	−0.168381	−	0.291645i	−0.937851	+	0.347039i	$0.887187\pi$
$180$	−21.8091	−	2.74251i	−1.62556	−	0.204415i
$181$	−24.0695	+	8.76060i	−1.78907	+	0.651170i	−0.789789	+	0.613379i	$0.789810\pi$
$181$	−24.0695	+	8.76060i	−1.78907	+	0.651170i	−0.999286	+	0.0377912i	$0.987968\pi$
$182$	−1.54423	+	1.83578i	−0.114466	+	0.136077i
$183$	−2.98485	−	11.1396i	−0.220647	−	0.823464i
$184$	1.53448	−	0.128576i	0.113123	−	0.00947876i
$185$	5.46869	+	16.8581i	0.402066	+	1.23943i
$186$	−13.2039	−	28.4066i	−0.968158	−	2.08287i
$187$	−13.4470	+	19.2043i	−0.983344	+	1.40436i
$188$	−2.66693	−	1.25156i	−0.194506	−	0.0912795i
$189$		−	2.02087i		−	0.146997i
$190$	−11.4882	+	7.61719i	−0.833441	+	0.552609i
$191$		−	8.05621i		−	0.582927i	−0.956582	−	0.291463i	$-0.905858\pi$
$191$		−	8.05621i		−	0.582927i	0.956582	−	0.291463i	$-0.0941421\pi$
$192$	−18.3414	−	13.0445i	−1.32368	−	0.941404i
$193$	−2.90852	+	4.15379i	−0.209360	+	0.298996i	−0.910074	−	0.414445i	$-0.863976\pi$
$193$	−2.90852	+	4.15379i	−0.209360	+	0.298996i	0.700715	+	0.713442i	$0.252865\pi$
$194$	3.32013	−	1.54326i	0.238371	−	0.110799i
$195$	12.9281	−	25.3432i	0.925803	−	1.81486i
$196$	−11.8974	+	6.83022i	−0.849816	+	0.487873i
$197$	−5.55415	−	20.7284i	−0.395717	−	1.47683i	−0.820556	−	0.571566i	$-0.806336\pi$
$197$	−5.55415	−	20.7284i	−0.395717	−	1.47683i	0.424840	−	0.905269i	$-0.360331\pi$
$198$	−21.7696	−	18.3123i	−1.54710	−	1.30140i
$199$	2.13778	−	0.778089i	0.151543	−	0.0551572i	−0.265135	−	0.964211i	$-0.585416\pi$
$199$	2.13778	−	0.778089i	0.151543	−	0.0551572i	0.416678	+	0.909054i	$0.363194\pi$
$200$	8.25961	+	11.4795i	0.584042	+	0.811723i
$201$	−6.47651	−	11.2176i	−0.456818	−	0.791231i
$202$	−2.63931	+	14.8619i	−0.185701	+	1.04568i
$203$	0.271960	+	0.388399i	0.0190878	+	0.0272602i
$204$	31.7290	+	5.67477i	2.22148	+	0.397313i
$205$	18.8992	+	5.78786i	1.31998	+	0.404241i
$206$	16.6676	+	4.48794i	1.16129	+	0.312690i
$207$	−1.13087	−	2.42517i	−0.0786012	−	0.168561i
$208$	14.8689	−	10.3032i	1.03097	−	0.714399i
$209$	−17.8381	+	0.200329i	−1.23389	+	0.0138571i
$210$	−2.44437	+	2.27166i	−0.168677	+	0.156760i
$211$	−4.79588	+	13.1766i	−0.330162	+	0.907113i	0.657907	+	0.753099i	$0.271442\pi$
$211$	−4.79588	+	13.1766i	−0.330162	+	0.907113i	−0.988069	+	0.154013i	$0.950780\pi$
$212$	−0.993219	−	11.6817i	−0.0682146	−	0.802303i
$213$	2.74938	+	31.4256i	0.188385	+	2.15325i
$214$	20.4090	−	5.44182i	1.39513	−	0.371995i
$215$	11.7452	+	7.34697i	0.801017	+	0.501059i
$216$	−3.99817	+	14.7052i	−0.272041	+	1.00057i
$217$	−2.85247	−	0.764318i	−0.193639	−	0.0518853i
$218$	4.13072	+	4.93505i	0.279768	+	0.334244i
$219$	−26.7686	+	9.74296i	−1.80885	+	0.658368i
$220$	0.904492	+	18.2803i	0.0609809	+	1.23246i
$221$	−12.9533	+	22.4357i	−0.871330	+	1.50919i
$222$	31.0626	−	5.43799i	2.08478	−	0.364974i
$223$	−2.33604	+	26.7010i	−0.156433	+	1.78803i	0.361258	+	0.932466i	$0.382347\pi$
$223$	−2.33604	+	26.7010i	−0.156433	+	1.78803i	−0.517691	+	0.855568i	$0.673208\pi$
$224$	−2.05280	+	0.536609i	−0.137159	+	0.0358537i
$225$	13.7617	−	20.3609i	0.917446	−	1.35739i
$226$	−16.1037	−	16.1431i	−1.07120	−	1.07383i
$227$	12.3218	+	12.3218i	0.817826	+	0.817826i	0.985793	−	0.167967i	$-0.0537201\pi$
$227$	12.3218	+	12.3218i	0.817826	+	0.817826i	−0.167967	+	0.985793i	$0.553720\pi$
$228$	10.5601	+	22.1366i	0.699363	+	1.46603i
$229$		−	4.06734i		−	0.268778i	−0.990929	−	0.134389i	$-0.957093\pi$
$229$		−	4.06734i		−	0.268778i	0.990929	−	0.134389i	$-0.0429071\pi$
$230$	−0.647637	+	1.59516i	−0.0427039	+	0.105181i
$231$	−4.25307	+	0.749931i	−0.279832	+	0.0493418i
$232$	−1.21054	−	3.36431i	−0.0794760	−	0.220878i
$233$	−8.86548	−	0.775629i	−0.580797	−	0.0508132i	−0.207028	−	0.978335i	$-0.566379\pi$
$233$	−8.86548	−	0.775629i	−0.580797	−	0.0508132i	−0.373769	+	0.927522i	$0.621935\pi$
$234$	−25.7282	−	18.0621i	−1.68191	−	1.18075i
$235$	2.59645	−	2.02659i	0.169374	−	0.132200i
$236$	−7.24886	−	2.65848i	−0.471861	−	0.173052i
$237$	1.64649	−	3.53090i	0.106951	−	0.229357i
$238$	2.33011	−	1.95034i	0.151038	−	0.126422i
$239$	3.52279	+	6.10165i	0.227870	+	0.394683i	0.957177	−	0.289504i	$-0.0934904\pi$
$239$	3.52279	+	6.10165i	0.227870	+	0.394683i	−0.729306	+	0.684187i	$0.760157\pi$
$240$	22.2812	−	11.6942i	1.43825	−	0.754854i
$241$	−2.09069	+	11.8569i	−0.134673	+	0.763769i	0.840414	+	0.541945i	$0.182312\pi$
$241$	−2.09069	+	11.8569i	−0.134673	+	0.763769i	−0.975087	+	0.221824i	$0.928799\pi$
$242$	−4.07399	+	7.03647i	−0.261886	+	0.452321i
$243$	−14.9452	+	1.30753i	−0.958734	+	0.0838783i
$244$	6.26742	+	5.28518i	0.401231	+	0.338349i
$245$	−0.795462	−	15.3173i	−0.0508202	−	0.978583i
$246$	14.9023	−	31.8562i	0.950135	−	2.03108i
$247$	−19.6173	+	1.93851i	−1.24822	+	0.123344i
$248$	19.2444	+	11.2051i	1.22202	+	0.711527i
$249$	2.99068	−	8.21681i	0.189526	−	0.520719i
$250$	−15.6232	+	2.43212i	−0.988099	+	0.153821i
$251$	12.8487	−	15.3125i	0.811005	−	0.966518i	−0.188875	−	0.982001i	$-0.560484\pi$
$251$	12.8487	−	15.3125i	0.811005	−	0.966518i	0.999880	+	0.0154829i	$0.00492857\pi$
$252$	2.10744	+	3.02546i	0.132756	+	0.190586i
$253$	−1.82515	+	1.27798i	−0.114746	+	0.0803462i
$254$	−16.5498	+	11.5582i	−1.03843	+	0.725224i
$255$	−21.7013	+	28.7702i	−1.35899	+	1.80166i
$256$	15.9992	+	0.156603i	0.999952	+	0.00978770i
$257$	10.0454	−	21.5424i	0.626615	−	1.34378i	−0.294934	−	0.955518i	$-0.595298\pi$
$257$	10.0454	−	21.5424i	0.626615	−	1.34378i	0.921549	−	0.388263i	$-0.126925\pi$
$258$	15.8682	−	18.8640i	0.987909	−	1.17442i
$259$	1.48643	−	2.57458i	0.0923624	−	0.159976i
$260$	2.75626	+	20.0363i	0.170936	+	1.24260i
$261$	−4.75962	+	3.99380i	−0.294613	+	0.247210i
$262$	0.236401	−	0.647041i	0.0146049	−	0.0399744i
$263$	4.73664	+	3.31663i	0.292074	+	0.204512i	0.710425	−	0.703773i	$-0.248503\pi$
$263$	4.73664	+	3.31663i	0.292074	+	0.204512i	−0.418351	+	0.908285i	$0.637392\pi$
$264$	32.4319	+	2.95742i	1.99605	+	0.182016i
$265$	12.1509	+	4.91598i	0.746423	+	0.301986i
$266$	2.23925	+	0.576052i	0.137297	+	0.0353200i
$267$	−16.8879	−	16.8879i	−1.03352	−	1.03352i
$268$	8.33589	+	3.91195i	0.509195	+	0.238960i
$269$	−17.0745	+	3.01069i	−1.04105	+	0.183565i	−0.667934	−	0.744221i	$-0.732821\pi$
$269$	−17.0745	+	3.01069i	−1.04105	+	0.183565i	−0.373114	+	0.927785i	$0.621710\pi$
$270$	−12.6422	−	11.4220i	−0.769379	−	0.695121i
$271$	1.99079	+	2.37253i	0.120932	+	0.144121i	0.823114	−	0.567877i	$-0.192235\pi$
$271$	1.99079	+	2.37253i	0.120932	+	0.144121i	−0.702182	+	0.711998i	$0.747791\pi$
$272$	−20.8141	+	9.58203i	−1.26204	+	0.580996i
$273$	−4.60966	+	1.23516i	−0.278989	+	0.0747550i
$274$	22.5930	−	1.94878i	1.36489	−	0.117730i
$275$	−18.6859	−	8.34076i	−1.12681	−	0.502967i
$276$	2.64916	+	1.53815i	0.159461	+	0.0925858i
$277$	−20.1895	−	5.40976i	−1.21307	−	0.325041i	−0.405104	−	0.914270i	$-0.632765\pi$
$277$	−20.1895	−	5.40976i	−1.21307	−	0.325041i	−0.807966	+	0.589229i	$0.799432\pi$
$278$	−1.88656	+	10.6232i	−0.113148	+	0.637136i
$279$	6.71976	−	38.1096i	0.402301	−	2.28156i
$280$	0.502825	−	2.31832i	0.0300495	−	0.138546i
$281$	14.3345	+	12.0280i	0.855123	+	0.717533i	0.960912	−	0.276855i	$-0.0892923\pi$
$281$	14.3345	+	12.0280i	0.855123	+	0.717533i	−0.105789	+	0.994389i	$0.533737\pi$
$282$	−2.92411	−	5.07904i	−0.174128	−	0.302453i
$283$	11.2502	−	5.24607i	0.668756	−	0.311846i	−0.0584247	−	0.998292i	$-0.518608\pi$
$283$	11.2502	−	5.24607i	0.668756	−	0.311846i	0.727181	+	0.686446i	$0.240830\pi$
$284$	−14.3727	−	17.2141i	−0.852865	−	1.02147i
$285$	−27.4134	−	0.662181i	−1.62383	−	0.0392242i
$286$	−11.0910	+	23.7090i	−0.655827	+	1.40194i
$287$	−1.40119	−	3.00487i	−0.0827098	−	0.177372i
$288$	−9.34948	−	26.1848i	−0.550923	−	1.54295i
$289$	10.1657	−	12.1150i	0.597982	−	0.712647i
$290$	3.96687	+	0.493907i	0.232943	+	0.0290032i
$291$	7.17292	+	1.26478i	0.420484	+	0.0741426i
$292$	11.6559	−	16.5600i	0.682111	−	0.969100i
$293$	4.29615	−	16.0335i	0.250984	−	0.936684i	−0.719297	−	0.694703i	$-0.755536\pi$
$293$	4.29615	−	16.0335i	0.250984	−	0.936684i	0.970281	−	0.241982i	$-0.0777974\pi$
$294$	−27.1845	−	2.41185i	−1.58543	−	0.140662i
$295$	6.31607	−	5.88423i	0.367736	−	0.342593i
$296$	−15.9099	+	15.7936i	−0.924746	+	0.917983i
$297$	−5.70701	−	21.2988i	−0.331154	−	1.23588i
$298$	−16.1329	+	2.82432i	−0.934553	+	0.163608i
$299$	−1.88609	+	1.58262i	−0.109075	+	0.0915252i
$300$	0.395497	+	28.1310i	0.0228340	+	1.62414i
$301$	−0.403533	−	2.28855i	−0.0232593	−	0.131910i
$302$	−0.000859004		0.702097i	−4.94301e−5		0.0404011i
$303$	−21.2332	+	21.2332i	−1.21982	+	1.21982i
$304$	−15.1546	−	8.62195i	−0.869176	−	0.494503i
$305$	−8.43912	+	3.57748i	−0.483223	+	0.204846i
$306$	28.1213	+	28.1901i	1.60758	+	1.61152i
$307$	−3.43116	+	4.90021i	−0.195827	+	0.279669i	−0.905042	−	0.425323i	$-0.860161\pi$
$307$	−3.43116	+	4.90021i	−0.195827	+	0.279669i	0.709215	+	0.704992i	$0.249050\pi$
$308$	2.17620	−	2.16558i	0.124000	−	0.123395i
$309$	22.0726	+	26.3050i	1.25566	+	1.49644i
$310$	−20.9037	+	13.5246i	−1.18725	+	0.768146i
$311$	17.3237	+	10.0018i	0.982335	+	0.567151i	0.902974	−	0.429695i	$-0.141379\pi$
$311$	17.3237	+	10.0018i	0.982335	+	0.567151i	0.0793606	+	0.996846i	$0.474712\pi$
$312$	35.9867	+	0.132088i	2.03735	+	0.00747801i
$313$	9.93281	+	4.63175i	0.561436	+	0.261802i	0.682553	−	0.730837i	$-0.260870\pi$
$313$	9.93281	+	4.63175i	0.561436	+	0.261802i	−0.121117	+	0.992638i	$0.538648\pi$
$314$	0.0335363	−	0.377995i	0.00189256	−	0.0213315i
$315$	−4.08246	+	0.571779i	−0.230021	+	0.0322161i
$316$	0.474256	+	2.72866i	0.0266790	+	0.153499i
$317$	−11.2785	−	16.1074i	−0.633464	−	0.904680i	0.366202	−	0.930535i	$-0.380658\pi$
$317$	−11.2785	−	16.1074i	−0.633464	−	0.904680i	−0.999666	+	0.0258553i	$0.991769\pi$
$318$	11.6862	−	20.1840i	0.655327	−	1.13186i
$319$	3.96315	+	3.32548i	0.221894	+	0.186191i
$320$	−8.24554	+	15.8749i	−0.460940	+	0.887431i
$321$	39.4852	+	14.3714i	2.20385	+	0.802135i
$322$	0.271491	−	0.0984385i	0.0151296	−	0.00548576i
$323$	24.8975	+	1.89678i	1.38534	+	0.105540i
$324$	−0.633666	+	0.529072i	−0.0352037	+	0.0293929i
$325$	−21.3733	−	7.38208i	−1.18558	−	0.409484i
$326$	−25.6650	−	6.91057i	−1.42145	−	0.382741i
$327$	1.11584	+	12.7541i	0.0617059	+	0.705302i
$328$	4.25110	+	24.6376i	0.234728	+	1.36039i
$329$	−0.544100	−	0.0959395i	−0.0299972	−	0.00528932i
$330$	−19.3470	+	30.8450i	−1.06502	+	1.69796i
$331$	17.8368	−	10.2981i	0.980400	−	0.566034i	0.0780093	−	0.996953i	$-0.475144\pi$
$331$	17.8368	−	10.2981i	0.980400	−	0.566034i	0.902391	+	0.430918i	$0.141810\pi$
$332$	1.59416	+	6.00824i	0.0874906	+	0.329745i
$333$	35.3066	+	16.4637i	1.93479	+	0.902208i
$334$	−2.35676	−	27.3228i	−0.128956	−	1.49504i
$335$	−8.11561	+	6.33442i	−0.443403	+	0.346086i
$336$	−3.95930	−	1.46305i	−0.215998	−	0.0798160i
$337$	−0.881918	+	10.0804i	−0.0480412	+	0.549113i	0.933592	+	0.358337i	$0.116656\pi$
$337$	−0.881918	+	10.0804i	−0.0480412	+	0.549113i	−0.981634	+	0.190776i	$0.938900\pi$
$338$	−3.61679	+	9.89934i	−0.196727	+	0.538453i
$339$	−7.87690	−	44.6721i	−0.427814	−	2.42626i
$340$	0.968850	−	25.6000i	0.0525433	−	1.38836i
$341$	−32.2219			−1.74492
$342$	−4.96246	+	29.8894i	−0.268339	+	1.61623i
$343$	−3.67580	+	3.67580i	−0.198474	+	0.198474i
$344$	−1.59137	+	17.4514i	−0.0858008	+	0.940918i
$345$	−2.87325	+	1.86397i	−0.154691	+	0.100353i
$346$	8.34802	+	17.9597i	0.448792	+	0.965520i
$347$	19.1118	+	1.67207i	1.02598	+	0.0897612i	0.587700	−	0.809079i	$-0.300034\pi$
$347$	19.1118	+	1.67207i	1.02598	+	0.0897612i	0.438276	+	0.898840i	$0.355589\pi$
$348$	1.85776	−	6.86600i	0.0995862	−	0.368056i
$349$	18.5333	+	10.7002i	0.992064	+	0.572768i	0.905891	−	0.423512i	$-0.139203\pi$
$349$	18.5333	+	10.7002i	0.992064	+	0.572768i	0.0861733	+	0.996280i	$0.472536\pi$
$350$	2.05753	+	1.67357i	0.109980	+	0.0894561i
$351$	−8.33371	−	22.8967i	−0.444820	−	1.22213i
$352$	−20.1200	+	11.4527i	−1.07240	+	0.610433i
$353$	−3.39781	+	12.6808i	−0.180847	+	0.674931i	0.814634	+	0.579975i	$0.196938\pi$
$353$	−3.39781	+	12.6808i	−0.180847	+	0.674931i	−0.995481	+	0.0949561i	$0.969729\pi$
$354$	−8.79460	−	12.5928i	−0.467428	−	0.669298i
$355$	24.4325	−	5.62849i	1.29674	−	0.298729i
$356$	16.7131	+	2.98915i	0.885791	+	0.158425i
$357$	6.02189	−	0.526847i	0.318712	−	0.0278837i
$358$	3.17917	+	5.52207i	0.168024	+	0.291850i
$359$	−13.6389	−	4.96416i	−0.719835	−	0.261999i	−0.0439794	−	0.999032i	$-0.514004\pi$
$359$	−13.6389	−	4.96416i	−0.719835	−	0.261999i	−0.675856	+	0.737034i	$0.736226\pi$
$360$	30.8380	+	3.91623i	1.62531	+	0.206404i
$361$	9.86714	+	16.2370i	0.519323	+	0.854578i
$362$	34.0546	−	12.3477i	1.78987	−	0.648981i
$363$	−14.6595	+	6.83584i	−0.769425	+	0.358789i
$364$	2.18705	−	2.59351i	0.114633	−	0.135937i
$365$	10.6199	+	19.9959i	0.555868	+	1.04663i
$366$	4.20194	+	15.7590i	0.219639	+	0.823734i
$367$	−1.39634	+	0.977727i	−0.0728883	+	0.0510369i	−0.609453	−	0.792822i	$-0.708611\pi$
$367$	−1.39634	+	0.977727i	−0.0728883	+	0.0510369i	0.536564	+	0.843859i	$0.319722\pi$
$368$	−2.17031	+	0.179179i	−0.113135	+	0.00934035i
$369$	37.6258	−	21.7232i	1.95872	−	1.13087i
$370$	−7.70472	−	23.8504i	−0.400549	−	1.23992i
$371$	−0.751999	−	2.06610i	−0.0390418	−	0.107267i
$372$	18.6240	+	40.1958i	0.965609	+	2.08405i
$373$	26.6269	−	7.13464i	1.37869	−	0.369418i	0.508042	−	0.861332i	$-0.330369\pi$
$373$	26.6269	−	7.13464i	1.37869	−	0.369418i	0.870644	+	0.491914i	$0.163703\pi$
$374$	19.0502	−	27.1358i	0.985061	−	1.40316i
$375$	−28.2515	−	13.8289i	−1.45890	−	0.714123i
$376$	3.76943	+	1.77459i	0.194394	+	0.0915174i
$377$	4.68301	+	3.27908i	0.241188	+	0.168881i
$378$	−0.00349664	+	2.85794i	−0.000179848	+	0.146997i
$379$	32.7053			1.67996			0.839979	−	0.542619i	$-0.182567\pi$
$379$	32.7053			1.67996			0.839979	+	0.542619i	$0.182567\pi$
$380$	16.2599	−	10.7524i	0.834116	−	0.551589i
$381$	−40.1578			−2.05735
$382$	−0.0139394	+	11.3932i	−0.000713200	+	0.582926i
$383$	−7.19816	−	5.04021i	−0.367809	−	0.257543i	0.375030	−	0.927013i	$-0.377632\pi$
$383$	−7.19816	−	5.04021i	−0.367809	−	0.257543i	−0.742839	+	0.669470i	$0.766521\pi$
$384$	25.9161	+	18.4794i	1.32252	+	0.943023i
$385$	1.05915	+	3.26499i	0.0539792	+	0.166399i
$386$	4.12045	−	5.86931i	0.209725	−	0.298740i
$387$	29.4143	−	7.88154i	1.49521	−	0.400641i
$388$	−4.69804	+	2.17675i	−0.238507	+	0.110508i
$389$	−1.26316	−	3.47052i	−0.0640450	−	0.175962i	0.903542	−	0.428499i	$-0.140957\pi$
$389$	−1.26316	−	3.47052i	−0.0640450	−	0.175962i	−0.967587	+	0.252537i	$0.918735\pi$
$390$	−18.3270	+	35.8183i	−0.928023	+	1.81373i
$391$	2.70086	−	1.55935i	0.136589	−	0.0788595i
$392$	16.8373	−	9.63880i	0.850413	−	0.486833i
$393$	1.12258	−	0.786039i	0.0566267	−	0.0396504i
$394$	7.81888	+	29.3239i	0.393909	+	1.47732i
$395$	−2.96074	−	0.906725i	−0.148971	−	0.0456223i
$396$	30.7552	+	25.9352i	1.54551	+	1.30329i
$397$	−13.7043	+	6.39040i	−0.687797	+	0.320725i	−0.734910	−	0.678165i	$-0.762776\pi$
$397$	−13.7043	+	6.39040i	−0.687797	+	0.320725i	0.0471133	+	0.998890i	$0.484998\pi$
$398$	−3.02462	+	1.09668i	−0.151611	+	0.0549718i
$399$	2.99601	+	3.49015i	0.149988	+	0.174726i
$400$	−11.6610	−	16.2487i	−0.583049	−	0.812437i
$401$	19.3649	+	7.04823i	0.967035	+	0.351972i	0.776787	−	0.629764i	$-0.216848\pi$
$401$	19.3649	+	7.04823i	0.967035	+	0.351972i	0.190249	+	0.981736i	$0.439071\pi$
$402$	9.13975	+	15.8753i	0.455849	+	0.791790i
$403$	−35.4707	+	3.10329i	−1.76692	+	0.154586i
$404$	3.75826	−	21.0134i	0.186981	−	1.04545i
$405$	−0.207189	−	0.899380i	−0.0102953	−	0.0446906i
$406$	−0.383937	−	0.549749i	−0.0190545	−	0.0272836i
$407$	8.39547	−	31.3323i	0.416148	−	1.55309i
$408$	−44.8618	−	8.08023i	−2.22099	−	0.400031i
$409$	−4.01538	−	11.0322i	−0.198548	−	0.545505i	0.799964	−	0.600048i	$-0.204852\pi$
$409$	−4.01538	−	11.0322i	−0.198548	−	0.545505i	−0.998511	+	0.0545430i	$0.982630\pi$
$410$	−26.7174	−	8.21796i	−1.31948	−	0.405856i
$411$	39.0685	+	22.5562i	1.92711	+	1.11261i
$412$	−23.5638	−	6.37574i	−1.16090	−	0.314110i
$413$	−1.44249	−	0.126201i	−0.0709801	−	0.00620995i
$414$	1.59510	+	3.43166i	0.0783949	+	0.168657i
$415$	−6.79729	−	1.44818i	−0.333666	−	0.0710882i
$416$	−21.0456	+	14.5452i	−1.03184	+	0.713137i
$417$	−15.1773	+	15.1773i	−0.743236	+	0.743236i
$418$	25.2272	−	0.252444i	1.23390	−	0.0123474i
$419$	11.0090			0.537826			0.268913	−	0.963164i	$-0.413336\pi$
$419$	11.0090			0.537826			0.268913	+	0.963164i	$0.413336\pi$
$420$	3.46078	−	3.20839i	0.168869	−	0.156553i
$421$	2.61948	+	14.8558i	0.127665	+	0.724027i	0.979689	+	0.200523i	$0.0642642\pi$
$421$	2.61948	+	14.8558i	0.127665	+	0.724027i	−0.852023	+	0.523504i	$0.824625\pi$
$422$	6.80519	−	18.6262i	0.331272	−	0.906708i
$423$	0.630999	−	7.21235i	0.0306802	−	0.350677i
$424$	1.38441	+	16.5221i	0.0672329	+	0.802386i
$425$	25.0379	+	13.9098i	1.21451	+	0.674722i
$426$	−3.83384	−	44.4472i	−0.185750	−	2.15347i
$427$	1.39348	+	0.649789i	0.0674351	+	0.0314455i
$428$	−28.8721	+	7.66058i	−1.39558	+	0.370288i
$429$	−45.0951	+	26.0357i	−2.17721	+	1.25701i
$430$	−16.5975	−	10.4105i	−0.800404	−	0.502039i
$431$	−25.6100	−	4.51573i	−1.23359	−	0.217515i	−0.481424	−	0.876488i	$-0.659880\pi$
$431$	−25.6100	−	4.51573i	−1.23359	−	0.217515i	−0.752167	+	0.658973i	$0.770991\pi$
$432$	5.67970	−	20.7894i	0.273265	−	1.00023i
$433$	1.25584	+	14.3543i	0.0603519	+	0.689825i	0.964756	+	0.263148i	$0.0847606\pi$
$433$	1.25584	+	14.3543i	0.0603519	+	0.689825i	−0.904404	+	0.426678i	$0.859684\pi$
$434$	4.03268	+	1.08584i	0.193575	+	0.0521222i
$435$	5.90730	+	5.32403i	0.283233	+	0.255268i
$436$	−5.83317	−	6.98635i	−0.279358	−	0.334586i
$437$	2.16187	+	0.978692i	0.103416	+	0.0468172i
$438$	37.8733	−	13.7323i	1.80966	−	0.656154i
$439$	−3.48934	−	1.27002i	−0.166537	−	0.0606146i	0.257406	−	0.966303i	$-0.417132\pi$
$439$	−3.48934	−	1.27002i	−0.166537	−	0.0606146i	−0.423943	+	0.905689i	$0.639354\pi$
$440$	−1.24751	−	25.8538i	−0.0594729	−	1.23253i
$441$	−25.8265	−	21.6710i	−1.22983	−	1.03195i
$442$	18.3575	−	31.7064i	0.873176	−	1.50812i
$443$	−20.4542	−	29.2117i	−0.971810	−	1.38789i	−0.921165	−	0.389171i	$-0.872761\pi$
$443$	−20.4542	−	29.2117i	−0.971810	−	1.38789i	−0.0506443	−	0.998717i	$-0.516127\pi$
$444$	−43.9385	+	7.63673i	−2.08523	+	0.362423i
$445$	−11.4310	+	15.1545i	−0.541882	+	0.718392i
$446$	3.34985	−	37.7569i	0.158620	−	1.78784i
$447$	−29.5295	−	13.7698i	−1.39670	−	0.651290i
$448$	2.90403	−	0.755327i	0.137202	−	0.0356859i
$449$	10.4332	+	6.02361i	0.492373	+	0.284272i	0.725559	−	0.688160i	$-0.241581\pi$
$449$	10.4332	+	6.02361i	0.492373	+	0.284272i	−0.233185	+	0.972432i	$0.574915\pi$
$450$	−19.4972	+	28.7708i	−0.919106	+	1.35627i
$451$	−23.2536	−	27.7126i	−1.09497	−	1.30493i
$452$	22.7461	+	22.8577i	1.06989	+	1.07514i
$453$	−0.801127	+	1.14413i	−0.0376402	+	0.0537558i
$454$	−17.4043	−	17.4470i	−0.816825	−	0.818826i
$455$	1.48039	+	3.49218i	0.0694016	+	0.163716i
$456$	−14.8960	−	31.3241i	−0.697569	−	1.46689i
$457$	13.7345	−	13.7345i	0.642474	−	0.642474i	−0.308689	−	0.951163i	$-0.599890\pi$
$457$	13.7345	−	13.7345i	0.642474	−	0.642474i	0.951163	+	0.308689i	$0.0998903\pi$
$458$	−0.00703758	+	5.75209i	−0.000328845	+	0.268777i
$459$	5.35945	+	30.3950i	0.250158	+	1.41872i
$460$	0.918656	−	2.25477i	0.0428326	−	0.105129i
$461$	1.89868	−	1.59318i	0.0884302	−	0.0742017i	−0.597501	−	0.801868i	$-0.703840\pi$
$461$	1.89868	−	1.59318i	0.0884302	−	0.0742017i	0.685931	+	0.727666i	$0.259395\pi$
$462$	6.01604	−	1.05320i	0.279892	−	0.0489994i
$463$	4.92398	+	18.3765i	0.228837	+	0.854031i	0.980831	+	0.194861i	$0.0624255\pi$
$463$	4.92398	+	18.3765i	0.228837	+	0.854031i	−0.751994	+	0.659170i	$0.770908\pi$
$464$	1.70614	+	4.75994i	0.0792057	+	0.220975i
$465$	−49.4987	−	1.75203i	−2.29545	−	0.0812483i
$466$	12.5363	+	1.11224i	0.580735	+	0.0515237i
$467$	2.08585	−	7.78451i	0.0965218	−	0.360224i	−0.900724	−	0.434392i	$-0.856963\pi$
$467$	2.08585	−	7.78451i	0.0965218	−	0.360224i	0.997246	+	0.0741677i	$0.0236300\pi$
$468$	36.3539	+	25.5881i	1.68046	+	1.18281i
$469$	1.70067	+	0.299874i	0.0785296	+	0.0138469i
$470$	−3.67544	+	2.86154i	−0.169535	+	0.131993i
$471$	0.485253	−	0.578302i	0.0223593	−	0.0266468i
$472$	10.2468	+	3.77219i	0.471649	+	0.173629i
$473$	−10.7160	−	22.9805i	−0.492720	−	1.05664i
$474$	−2.33459	+	4.99060i	−0.107231	+	0.229226i
$475$	2.50088	+	21.6505i	0.114748	+	0.993395i
$476$	−3.29864	+	2.75416i	−0.151193	+	0.126237i
$477$	26.1124	−	12.1764i	1.19560	−	0.557519i
$478$	−4.97142	−	8.63513i	−0.227387	−	0.394962i
$479$	10.2787	+	8.62489i	0.469648	+	0.394081i	0.846666	−	0.532124i	$-0.178606\pi$
$479$	10.2787	+	8.62489i	0.469648	+	0.394081i	−0.377018	+	0.926206i	$0.623051\pi$
$480$	−31.5306	+	16.4995i	−1.43917	+	0.753094i
$481$	6.22434	−	35.3000i	0.283805	−	1.60954i
$482$	2.97719	−	16.7645i	0.135607	−	0.763603i
$483$	0.554922	+	0.148691i	0.0252498	+	0.00676567i
$484$	5.77367	−	9.94401i	0.262439	−	0.452001i
$485$	0.204775	−	5.78535i	0.00929835	−	0.262699i
$486$	21.1379	−	1.82327i	0.958836	−	0.0827053i
$487$	−14.6917	+	3.93663i	−0.665745	+	0.178386i	−0.575837	−	0.817564i	$-0.695324\pi$
$487$	−14.6917	+	3.93663i	−0.665745	+	0.178386i	−0.0899075	+	0.995950i	$0.528657\pi$
$488$	−8.85432	−	7.48521i	−0.400816	−	0.338840i
$489$	−33.9875	−	40.5048i	−1.53697	−	1.83169i
$490$	1.09845	+	21.6632i	0.0496229	+	0.978645i
$491$	−18.4385	+	3.25121i	−0.832120	+	0.146725i	−0.573450	−	0.819241i	$-0.694395\pi$
$491$	−18.4385	+	3.25121i	−0.832120	+	0.146725i	−0.258670	+	0.965966i	$0.583284\pi$
$492$	−21.1301	+	45.0257i	−0.952619	+	2.02992i
$493$	−5.12047	−	5.12047i	−0.230614	−	0.230614i
$494$	27.7464	−	2.70752i	1.24837	−	0.121817i
$495$	−41.4121	+	17.5552i	−1.86134	+	0.789049i
$496$	−27.1963	−	15.8798i	−1.22115	−	0.713022i
$497$	−3.44509	−	2.41228i	−0.154534	−	0.108206i
$498$	−4.24367	+	11.6151i	−0.190163	+	0.520487i
$499$	−16.3365	+	13.7079i	−0.731322	+	0.613652i	−0.930492	−	0.366313i	$-0.880620\pi$
$499$	−16.3365	+	13.7079i	−0.731322	+	0.613652i	0.199170	+	0.979965i	$0.436175\pi$
$500$	22.0988	−	3.41250i	0.988286	−	0.152612i
$501$	27.2783	−	47.2475i	1.21871	−	2.11086i
$502$	−18.1973	+	21.6329i	−0.812187	+	0.965525i
$503$	16.1973	−	34.7351i	0.722200	−	1.54876i	−0.109780	−	0.993956i	$-0.535015\pi$
$503$	16.1973	−	34.7351i	0.722200	−	1.54876i	0.831980	−	0.554806i	$-0.187208\pi$
$504$	−2.97513	−	4.28230i	−0.132523	−	0.190749i
$505$	19.0538	+	14.3722i	0.847883	+	0.639556i
$506$	2.58336	−	1.80418i	0.114845	−	0.0802058i
$507$	−17.1748	+	12.0259i	−0.762759	+	0.534090i
$508$	23.4250	−	16.3171i	1.03932	−	0.723953i
$509$	2.35274	−	2.80389i	0.104283	−	0.124280i	−0.711378	−	0.702809i	$-0.751929\pi$
$509$	2.35274	−	2.80389i	0.104283	−	0.124280i	0.815662	+	0.578529i	$0.196373\pi$
$510$	30.7400	−	40.6496i	1.36119	−	1.79999i
$511$	1.29894	−	3.56880i	0.0574616	−	0.157874i
$512$	−22.6260	−	0.249153i	−0.999939	−	0.0110111i
$513$	−16.4189	+	16.7918i	−0.724911	+	0.741378i
$514$	−14.2436	+	30.4482i	−0.628259	+	1.34301i
$515$	18.2718	−	20.2736i	0.805153	−	0.893361i
$516$	−22.4736	+	26.6503i	−0.989345	+	1.17321i
$517$	−6.00544	+	0.525408i	−0.264119	+	0.0231074i
$518$	−2.10659	+	3.63843i	−0.0925581	+	0.159863i
$519$	−6.84162	+	38.8008i	−0.300314	+	1.70316i
$520$	−3.86326	−	28.3403i	−0.169415	−	1.24280i
$521$	−13.9071	−	24.0878i	−0.609282	−	1.05531i	−0.991359	−	0.131177i	$-0.958124\pi$
$521$	−13.9071	−	24.0878i	−0.609282	−	1.05531i	0.382077	−	0.924130i	$-0.375209\pi$
$522$	6.73803	−	5.63984i	0.294916	−	0.246849i
$523$	−9.63059	+	20.6529i	−0.421116	+	0.903087i	0.575255	+	0.817974i	$0.304903\pi$
$523$	−9.63059	+	20.6529i	−0.421116	+	0.903087i	−0.996371	+	0.0851127i	$0.972875\pi$
$524$	−0.335440	+	0.914645i	−0.0146538	+	0.0399565i
$525$	1.44951	+	5.07320i	0.0632619	+	0.221413i
$526$	−6.69287	−	4.69861i	−0.291823	−	0.204869i
$527$	44.9297	+	3.93084i	1.95717	+	0.171230i
$528$	−45.8605	−	4.23853i	−1.99582	−	0.184458i
$529$	−22.3587	+	3.94244i	−0.972117	+	0.171410i
$530$	−17.1754	−	6.97326i	−0.746053	−	0.302899i
$531$		−	18.9746i		−	0.823427i
$532$	−3.16577	−	0.818534i	−0.137254	−	0.0354880i
$533$	−28.2672	−	28.2672i	−1.22439	−	1.22439i
$534$	23.8539	+	23.9123i	1.03226	+	1.03479i
$535$	6.95909	−	32.6638i	0.300868	−	1.41218i
$536$	−11.7819	−	5.54675i	−0.508903	−	0.239583i
$537$	−1.10477	+	12.6276i	−0.0476745	+	0.544922i
$538$	24.1521	−	4.22821i	1.04127	−	0.182291i
$539$	−14.0362	+	24.3114i	−0.604582	+	1.04717i
$540$	17.8590	+	16.1750i	0.768528	+	0.696061i
$541$	0.0436355	−	0.0158820i	0.00187604	−	0.000682822i	−0.341082	−	0.940034i	$-0.610793\pi$
$541$	0.0436355	−	0.0158820i	0.00187604	−	0.000682822i	0.342958	+	0.939351i	$0.388571\pi$
$542$	−2.81129	−	3.35871i	−0.120755	−	0.144269i
$543$	69.6071	+	18.6512i	2.98712	+	0.800398i
$544$	29.4521	−	13.5150i	1.26275	−	0.579451i
$545$	9.91593	−	2.28432i	0.424752	−	0.0978496i
$546$	6.52118	−	1.73880i	0.279081	−	0.0744136i
$547$	−1.58752	−	18.1454i	−0.0678773	−	0.775842i	−0.951501	−	0.307644i	$-0.900459\pi$
$547$	−1.58752	−	18.1454i	−0.0678773	−	0.775842i	0.883624	−	0.468197i	$-0.155096\pi$
$548$	−31.9547	+	2.71690i	−1.36504	+	0.116060i
$549$	−6.89098	+	18.9328i	−0.294100	+	0.808033i
$550$	26.4115	+	11.8279i	1.12619	+	0.504345i
$551$	0.895833	−	5.43686i	0.0381638	−	0.231618i
$552$	−3.74382	−	2.17986i	−0.159348	−	0.0927808i
$553$	0.219511	+	0.470742i	0.00933455	+	0.0200180i
$554$	28.5429	+	7.68549i	1.21267	+	0.326525i
$555$	14.6006	−	47.6756i	0.619761	−	2.02372i
$556$	2.68637	−	15.0202i	0.113928	−	0.636997i
$557$	19.8254	+	28.3136i	0.840029	+	1.19969i	0.977866	+	0.209231i	$0.0670959\pi$
$557$	19.8254	+	28.3136i	0.840029	+	1.19969i	−0.137838	+	0.990455i	$0.544015\pi$
$558$	−9.56910	+	53.8835i	−0.405093	+	2.28107i
$559$	−14.0096	−	24.2654i	−0.592545	−	1.02632i
$560$	−0.715113	+	3.27772i	−0.0302190	+	0.138509i
$561$	61.9795	−	22.5587i	2.61678	−	0.952429i
$562$	−20.2512	−	17.0350i	−0.854244	−	0.718579i
$563$	1.49169	+	5.56706i	0.0628672	+	0.234623i	0.990209	−	0.139591i	$-0.0445789\pi$
$563$	1.49169	+	5.56706i	0.0628672	+	0.234623i	−0.927342	+	0.374215i	$0.877912\pi$
$564$	4.12652	+	7.18791i	0.173758	+	0.302665i
$565$	−34.2938	+	11.1248i	−1.44275	+	0.468022i
$566$	−15.9193	+	7.39959i	−0.669138	+	0.311028i
$567$	−0.0887980	+	0.126817i	−0.00372917	+	0.00532580i
$568$	20.2963	+	24.3693i	0.851615	+	1.02251i
$569$		−	31.1948i		−	1.30775i	−0.756601	−	0.653877i	$-0.773141\pi$
$569$		−	31.1948i		−	1.30775i	0.756601	−	0.653877i	$-0.226859\pi$
$570$	38.7672	+	0.983897i	1.62378	+	0.0412109i
$571$			43.7061i			1.82904i	0.404537	+	0.914522i	$0.367433\pi$
$571$			43.7061i			1.82904i	−0.404537	+	0.914522i	$0.632567\pi$
$572$	15.7261	−	33.5104i	0.657542	−	1.40114i
$573$	−13.0002	+	18.5662i	−0.543090	+	0.775613i
$574$	1.97638	+	4.25194i	0.0824927	+	0.177473i
$575$	1.78392	+	2.05610i	0.0743945	+	0.0857451i
$576$	13.1768	+	37.0470i	0.549035	+	1.54363i
$577$	−3.20743	−	11.9703i	−0.133527	−	0.498329i	0.866473	−	0.499224i	$-0.166382\pi$
$577$	−3.20743	−	11.9703i	−0.133527	−	0.498329i	−1.00000		0.000895290i	$0.999715\pi$
$578$	−14.3974	+	17.1156i	−0.598854	+	0.711915i
$579$	13.4058	−	4.87932i	0.557127	−	0.202778i
$580$	−5.60914	−	0.705353i	−0.232907	−	0.0292882i
$581$	0.582888	+	1.00959i	0.0241823	+	0.0418849i
$582$	−10.1418	−	1.80108i	−0.420393	−	0.0746570i
$583$	−13.7604	−	19.6518i	−0.569896	−	0.813896i
$584$	−16.5126	+	23.3992i	−0.683296	+	0.968265i
$585$	−43.8967	+	23.3136i	−1.81491	+	0.963900i
$586$	−6.10341	+	22.6673i	−0.252130	+	0.936377i
$587$	−5.67994	−	12.1807i	−0.234436	−	0.502750i	0.753531	−	0.657412i	$-0.228349\pi$
$587$	−5.67994	−	12.1807i	−0.234436	−	0.502750i	−0.987967	+	0.154662i	$0.950571\pi$
$588$	38.4404	+	3.45790i	1.58526	+	0.142602i
$589$	17.4920	+	29.5262i	0.720745	+	1.21661i
$590$	−8.94244	+	8.31063i	−0.368154	+	0.342143i
$591$	−20.6491	+	56.7328i	−0.849389	+	2.33368i
$592$	22.5274	−	22.3079i	0.925869	−	0.916850i
$593$	0.570399	+	6.51969i	0.0234235	+	0.267731i	0.998871	+	0.0475004i	$0.0151255\pi$
$593$	0.570399	+	6.51969i	0.0234235	+	0.267731i	−0.975448	+	0.220231i	$0.929319\pi$
$594$	8.03407	+	30.1310i	0.329642	+	1.23629i
$595$	−1.07855	−	4.68185i	−0.0442164	−	0.191937i
$596$	22.8202	−	3.96627i	0.934753	−	0.162465i
$597$	−6.18228	−	1.65654i	−0.253024	−	0.0677976i
$598$	2.67007	−	2.23489i	0.109187	−	0.0913916i
$599$	20.8254	−	7.57984i	0.850904	−	0.309704i	0.120495	−	0.992714i	$-0.461552\pi$
$599$	20.8254	−	7.57984i	0.850904	−	0.309704i	0.730409	+	0.683010i	$0.239330\pi$
$600$	−0.510642	−	39.7838i	−0.0208469	−	1.62417i
$601$	−14.8254	+	25.6784i	−0.604741	+	1.04744i	0.387351	+	0.921932i	$0.373390\pi$
$601$	−14.8254	+	25.6784i	−0.604741	+	1.04744i	−0.992092	+	0.125510i	$0.959943\pi$
$602$	0.566722	+	3.23720i	0.0230979	+	0.131938i
$603$	−1.97228	+	22.5433i	−0.0803176	+	0.918035i
$604$	0.00242963	−	0.992913i	9.88601e−5	−	0.0404010i
$605$	6.99669	+	10.7852i	0.284456	+	0.438479i
$606$	30.0650	−	29.9915i	1.22131	−	1.21832i
$607$	−5.20830	−	5.20830i	−0.211399	−	0.211399i	0.593463	−	0.804861i	$-0.297760\pi$
$607$	−5.20830	−	5.20830i	−0.211399	−	0.211399i	−0.804861	+	0.593463i	$0.797760\pi$
$608$	21.4169	+	12.2195i	0.868570	+	0.495566i
$609$		−	1.33395i		−	0.0540545i
$610$	11.9409	−	5.04471i	0.483473	−	0.204254i
$611$	−6.56034	+	1.15677i	−0.265403	+	0.0467977i
$612$	−39.7206	−	39.9155i	−1.60561	−	1.61349i
$613$	27.8948	+	2.44048i	1.12666	+	0.0985701i	0.635213	−	0.772337i	$-0.280912\pi$
$613$	27.8948	+	2.44048i	1.12666	+	0.0985701i	0.491448	+	0.870907i	$0.336468\pi$
$614$	4.86087	−	6.92399i	0.196169	−	0.279430i
$615$	−34.2149	−	43.8359i	−1.37968	−	1.76763i
$616$	−3.08136	+	3.05882i	−0.124151	+	0.123243i
$617$	4.46536	−	9.57599i	0.179769	−	0.385515i	−0.795688	−	0.605707i	$-0.792891\pi$
$617$	4.46536	−	9.57599i	0.179769	−	0.385515i	0.975457	+	0.220192i	$0.0706683\pi$
$618$	−31.1698	−	37.2391i	−1.25383	−	1.49798i
$619$	−14.7471	−	25.5427i	−0.592736	−	1.02665i	−0.993862	−	0.110626i	$-0.964715\pi$
$619$	−14.7471	−	25.5427i	−0.592736	−	1.02665i	0.401127	−	0.916023i	$-0.368619\pi$
$620$	29.5856	−	19.0905i	1.18819	−	0.766693i
$621$	−0.509354	+	2.88869i	−0.0204397	+	0.115919i
$622$	−24.4820	−	14.1747i	−0.981640	−	0.568353i
$623$	3.17200	−	0.277514i	0.127083	−	0.0111183i
$624$	−50.8926	−	0.249067i	−2.03734	−	0.00997066i
$625$	−7.77050	+	23.7617i	−0.310820	+	0.950469i
$626$	−14.0391	−	6.56746i	−0.561115	−	0.262488i
$627$	41.4326	+	28.3234i	1.65466	+	1.13113i
$628$	−0.0480815	+	0.534507i	−0.00191866	+	0.0213292i
$629$	−15.5288	+	42.6651i	−0.619174	+	1.70117i
$630$	5.77446	−	0.801553i	0.230060	−	0.0319346i
$631$	−13.8134	+	16.4621i	−0.549902	+	0.655348i	−0.967377	−	0.253341i	$-0.918471\pi$
$631$	−13.8134	+	16.4621i	−0.549902	+	0.655348i	0.417475	+	0.908688i	$0.362915\pi$
$632$	−0.665977	−	3.85973i	−0.0264911	−	0.153532i
$633$	32.3153	−	22.6274i	1.28442	−	0.899360i
$634$	15.9223	+	22.7988i	0.632357	+	0.905455i
$635$	4.42706	+	31.6089i	0.175683	+	1.25436i
$636$	−16.5616	+	28.5242i	−0.656712	+	1.13106i
$637$	−13.1100	+	28.1144i	−0.519436	+	1.11393i
$638$	−5.59899	−	4.70979i	−0.221666	−	0.186462i
$639$	27.5557	−	47.7279i	1.09009	−	1.88809i
$640$	11.6884	−	22.4362i	0.462025	−	0.886867i
$641$	−22.2702	+	18.6869i	−0.879619	+	0.738088i	−0.966101	−	0.258165i	$-0.916882\pi$
$641$	−22.2702	+	18.6869i	−0.879619	+	0.738088i	0.0864816	+	0.996253i	$0.472438\pi$
$642$	−55.8156	−	20.3926i	−2.20287	−	0.804831i
$643$	2.67874	+	1.87568i	0.105639	+	0.0739695i	0.625202	−	0.780463i	$-0.285016\pi$
$643$	2.67874	+	1.87568i	0.105639	+	0.0739695i	−0.519563	+	0.854432i	$0.673905\pi$
$644$	−0.384116	+	0.138743i	−0.0151363	+	0.00546725i
$645$	−15.2121	−	35.8848i	−0.598976	−	1.41296i
$646$	−35.2071	−	2.72553i	−1.38521	−	0.107234i
$647$	6.21119	+	6.21119i	0.244187	+	0.244187i	0.818580	−	0.574393i	$-0.194762\pi$
$647$	6.21119	+	6.21119i	0.244187	+	0.244187i	−0.574393	+	0.818580i	$0.694762\pi$
$648$	0.897054	−	0.747124i	0.0352396	−	0.0293498i
$649$	−15.5594	+	2.74354i	−0.610759	+	0.107693i
$650$	30.2136	+	10.4768i	1.18507	+	0.410934i
$651$	5.34039	+	6.36443i	0.209306	+	0.249442i
$652$	36.2838	+	9.81743i	1.42098	+	0.384480i
$653$	−10.0993	+	2.70611i	−0.395217	+	0.105898i	−0.450954	−	0.892547i	$-0.648916\pi$
$653$	−10.0993	+	2.70611i	−0.395217	+	0.105898i	0.0557363	+	0.998446i	$0.482249\pi$
$654$	−1.55596	−	18.0389i	−0.0608429	−	0.705377i
$655$	−0.742459	−	0.796947i	−0.0290103	−	0.0311393i
$656$	−5.96932	−	34.8502i	−0.233063	−	1.36067i
$657$	48.0713	+	12.8807i	1.87544	+	0.502522i
$658$	0.769307	+	0.136620i	0.0299907	+	0.00532602i
$659$	−6.57770	+	37.3040i	−0.256231	+	1.45316i	0.536663	+	0.843797i	$0.319685\pi$
$659$	−6.57770	+	37.3040i	−0.256231	+	1.45316i	−0.792894	+	0.609360i	$0.791426\pi$
$660$	27.4141	−	43.5879i	1.06709	−	1.69666i
$661$	7.18929	+	6.03253i	0.279631	+	0.234638i	0.771806	−	0.635858i	$-0.219354\pi$
$661$	7.18929	+	6.03253i	0.279631	+	0.234638i	−0.492175	+	0.870496i	$0.663798\pi$
$662$	−25.2429	+	14.5328i	−0.981092	+	0.564834i
$663$	66.0560	−	30.8024i	2.56540	−	1.19627i
$664$	−2.24408	−	8.49968i	−0.0870871	−	0.329852i
$665$	2.41687	−	2.74297i	0.0937222	−	0.106368i
$666$	−49.9026	−	23.3443i	−1.93369	−	0.904574i
$667$	−0.290852	−	0.623735i	−0.0112618	−	0.0241511i
$668$	3.28568	+	38.6444i	0.127127	+	1.49520i
$669$	48.4707	−	57.7651i	1.87398	−	2.23333i
$670$	11.4882	−	8.94417i	0.443826	−	0.345543i
$671$	16.5215	+	2.91318i	0.637805	+	0.112462i
$672$	5.59677	+	2.07592i	0.215900	+	0.0800802i
$673$	9.41368	−	35.1323i	0.362871	−	1.35425i	−0.507414	−	0.861702i	$-0.669399\pi$
$673$	9.41368	−	35.1323i	0.362871	−	1.35425i	0.870285	−	0.492549i	$-0.163935\pi$
$674$	1.26466	−	14.2543i	0.0487130	−	0.549054i
$675$	−25.1590	+	9.63028i	−0.968370	+	0.370669i
$676$	5.13204	−	13.9935i	0.197386	−	0.538212i
$677$	−1.20660	−	4.50308i	−0.0463733	−	0.173067i	0.938855	−	0.344312i	$-0.111888\pi$
$677$	−1.20660	−	4.50308i	−0.0463733	−	0.173067i	−0.985229	+	0.171245i	$0.945221\pi$
$678$	11.0623	+	63.1895i	0.424845	+	2.42678i
$679$	−0.743868	+	0.624179i	−0.0285470	+	0.0239538i
$680$	−1.41446	+	36.2022i	−0.0542419	+	1.38829i
$681$	−8.51308	−	48.2801i	−0.326222	−	1.85010i
$682$	45.5687	+	0.0557525i	1.74491	+	0.00213487i
$683$	−13.6377	+	13.6377i	−0.521832	+	0.521832i	−0.918124	−	0.396292i	$-0.870297\pi$
$683$	−13.6377	+	13.6377i	−0.521832	+	0.521832i	0.396292	+	0.918124i	$0.370297\pi$
$684$	7.06968	−	42.2614i	0.270316	−	1.61591i
$685$	13.4474	−	33.2381i	0.513798	−	1.26996i
$686$	5.20472	−	5.19200i	0.198717	−	0.198232i
$687$	−6.56341	+	9.37353i	−0.250410	+	0.357622i
$688$	2.28073	−	24.6773i	0.0869520	−	0.940813i
$689$	−17.0404	−	20.3080i	−0.649189	−	0.773673i
$690$	4.06661	−	2.63108i	0.154813	−	0.100164i
$691$	−29.4432	−	16.9990i	−1.12007	−	0.646674i	−0.178653	−	0.983912i	$-0.557174\pi$
$691$	−29.4432	−	16.9990i	−1.12007	−	0.646674i	−0.941419	+	0.337238i	$0.890507\pi$
$692$	−11.7748	−	25.4133i	−0.447611	−	0.966069i
$693$	6.83801	+	3.18862i	0.259754	+	0.121125i
$694$	−27.0253	−	2.39773i	−1.02587	−	0.0910164i
$695$	13.6195	+	10.2731i	0.516616	+	0.389683i
$696$	−2.63914	+	9.70676i	−0.100036	+	0.367934i
$697$	29.0437	+	41.4787i	1.10011	+	1.57112i
$698$	−26.1915	−	15.1644i	−0.991362	−	0.573982i
$699$	19.1796	+	16.0936i	0.725439	+	0.608716i
$700$	−2.90690	−	2.37034i	−0.109870	−	0.0895906i
$701$	−9.96940	−	3.62856i	−0.376539	−	0.137049i	0.146816	−	0.989164i	$-0.453098\pi$
$701$	−9.96940	−	3.62856i	−0.376539	−	0.137049i	−0.523355	+	0.852115i	$0.675320\pi$
$702$	11.7460	+	32.3952i	0.443325	+	1.22268i
$703$	−33.2686	+	9.31595i	−1.25475	+	0.351358i
$704$	28.4737	−	16.1618i	1.07314	−	0.609120i
$705$	−9.25401	+	0.480583i	−0.348526	+	0.0180998i
$706$	4.82717	−	17.9275i	0.181673	−	0.674710i
$707$	−0.348918	−	3.98816i	−0.0131224	−	0.149990i
$708$	12.4157	+	17.8241i	0.466609	+	0.669869i
$709$	−25.1895	−	4.44158i	−0.946011	−	0.166807i	−0.320698	−	0.947182i	$-0.603917\pi$
$709$	−25.1895	−	4.44158i	−0.946011	−	0.166807i	−0.625313	+	0.780374i	$0.715029\pi$
$710$	−34.5625	+	7.91761i	−1.29711	+	0.297142i
$711$	−5.89445	+	3.40316i	−0.221059	+	0.127629i
$712$	−23.6307	−	4.25621i	−0.885596	−	0.159508i
$713$	3.88476	+	1.81150i	0.145486	+	0.0678410i
$714$	−8.51715	+	0.734655i	−0.318746	+	0.0274938i
$715$	25.4645	+	32.6249i	0.952317	+	1.22010i
$716$	−4.48646	−	7.81488i	−0.167667	−	0.292056i
$717$	1.72759	−	19.7464i	0.0645180	−	0.737444i
$718$	19.2798	+	7.04398i	0.719514	+	0.262879i
$719$	−5.61705	−	31.8559i	−0.209481	−	1.18802i	−0.890231	−	0.455508i	$-0.849458\pi$
$719$	−5.61705	−	31.8559i	−0.209481	−	1.18802i	0.680751	−	0.732515i	$-0.261654\pi$
$720$	−43.6047	−	5.59174i	−1.62505	−	0.208392i
$721$	−4.57807			−0.170496
$722$	−13.9261	−	22.9796i	−0.518277	−	0.855213i
$723$	23.9514	−	23.9514i	0.890763	−	0.890763i
$724$	−48.1818	+	17.4033i	−1.79066	+	0.646790i
$725$	3.53940	−	5.23666i	0.131450	−	0.194485i
$726$	20.7435	−	9.64197i	0.769863	−	0.357847i
$727$	−36.5655	−	3.19906i	−1.35614	−	0.118647i	−0.614219	−	0.789136i	$-0.710529\pi$
$727$	−36.5655	−	3.19906i	−1.35614	−	0.118647i	−0.741919	+	0.670489i	$0.766084\pi$
$728$	−3.09744	+	3.66399i	−0.114799	+	0.135796i
$729$	37.6247	+	21.7226i	1.39351	+	0.804542i
$730$	−14.9841	−	28.2968i	−0.554587	−	1.04731i
$731$	12.1387	+	33.3508i	0.448966	+	1.23352i
$732$	−5.91517	−	22.2938i	−0.218631	−	0.824002i
$733$	−1.28022	+	4.77784i	−0.0472859	+	0.176474i	−0.985530	−	0.169500i	$-0.945785\pi$
$733$	−1.28022	+	4.77784i	−0.0472859	+	0.176474i	0.938244	+	0.345974i	$0.112451\pi$
$734$	1.97641	−	1.38030i	0.0729507	−	0.0509477i
$735$	−22.8840	+	36.5835i	−0.844090	+	1.34940i
$736$	3.06958	−	0.249642i	0.113146	−	0.00920192i
$737$	18.7709	−	1.64224i	0.691436	−	0.0604929i
$738$	−53.2484	+	30.6562i	−1.96010	+	1.12847i
$739$	45.7989	+	16.6694i	1.68474	+	0.613195i	0.993947	−	0.109857i	$-0.0350394\pi$
$739$	45.7989	+	16.6694i	1.68474	+	0.613195i	0.690793	+	0.723053i	$0.257262\pi$
$740$	10.8548	+	33.7428i	0.399032	+	1.24041i
$741$	48.3378	+	27.1887i	1.77573	+	0.998802i
$742$	1.05991	+	2.92320i	0.0389106	+	0.107314i
$743$	24.2425	−	11.3045i	0.889372	−	0.414721i	0.0764363	−	0.997074i	$-0.475646\pi$
$743$	24.2425	−	11.3045i	0.889372	−	0.414721i	0.812936	+	0.582353i	$0.197868\pi$
$744$	−26.2687	−	56.8776i	−0.963058	−	2.08523i
$745$	−7.58308	+	24.7611i	−0.277823	+	0.907178i
$746$	−37.6684	+	10.0438i	−1.37914	+	0.367731i
$747$	−12.5137	+	8.76217i	−0.457851	+	0.320591i
$748$	−26.9880	+	38.3428i	−0.986777	+	1.40195i
$749$	−4.85151	+	2.80102i	−0.177270	+	0.102347i
$750$	39.9296	+	19.6059i	1.45802	+	0.715907i
$751$	−1.58071	−	4.34296i	−0.0576808	−	0.158477i	0.907505	−	0.420040i	$-0.137984\pi$
$751$	−1.58071	−	4.34296i	−0.0576808	−	0.158477i	−0.965186	+	0.261564i	$0.915762\pi$
$752$	−5.32771	−	2.51617i	−0.194282	−	0.0917552i
$753$	−54.3206	+	14.5552i	−1.97955	+	0.530419i
$754$	−6.61710	−	4.64542i	−0.240981	−	0.169176i
$755$	0.988879	+	0.504450i	0.0359890	+	0.0183588i
$756$	0.00989000	−	4.04173i	0.000359696	−	0.146996i
$757$	−12.9588	−	9.07388i	−0.470997	−	0.329796i	0.313863	−	0.949468i	$-0.398377\pi$
$757$	−12.9588	−	9.07388i	−0.470997	−	0.329796i	−0.784861	+	0.619672i	$0.787265\pi$
$758$	−46.2522	−	0.0565888i	−1.67996	−	0.00205540i
$759$	6.26848			0.227531
$760$	−23.0136	+	15.1781i	−0.834791	+	0.550568i
$761$	23.6303			0.856596			0.428298	−	0.903637i	$-0.359113\pi$
$761$	23.6303			0.856596			0.428298	+	0.903637i	$0.359113\pi$
$762$	56.7917	+	0.0694837i	2.05735	+	0.00251713i
$763$	−1.39819	−	0.979024i	−0.0506179	−	0.0354431i
$764$	0.0394265	−	16.1124i	0.00142640	−	0.582925i
$765$	59.8859	−	19.4267i	2.16518	−	0.702375i
$766$	10.1710	+	7.14038i	0.367494	+	0.257992i
$767$	−16.8639	+	4.51868i	−0.608921	+	0.163160i
$768$	−36.6188	−	26.1786i	−1.32137	−	0.944640i
$769$	9.13192	+	25.0897i	0.329305	+	0.904759i	0.988288	+	0.152601i	$0.0487649\pi$
$769$	9.13192	+	25.0897i	0.329305	+	0.904759i	−0.658982	+	0.752158i	$0.729013\pi$
$770$	−1.49221	−	4.61922i	−0.0537756	−	0.166465i
$771$	−57.9132	+	33.4362i	−2.08569	+	1.20417i
$772$	−5.83734	+	8.29332i	−0.210091	+	0.298483i
$773$	12.6567	−	8.86228i	0.455228	−	0.318754i	−0.323375	−	0.946271i	$-0.604817\pi$
$773$	12.6567	−	8.86228i	0.455228	−	0.318754i	0.778603	+	0.627517i	$0.215929\pi$
$774$	−41.6117	+	11.0953i	−1.49570	+	0.398811i
$775$	4.07776	+	39.1544i	0.146478	+	1.40647i
$776$	6.64779	−	3.07026i	0.238642	−	0.110216i
$777$	−7.58016	+	3.53469i	−0.271937	+	0.126806i
$778$	1.78038	+	4.91023i	0.0638296	+	0.176040i
$779$	−12.7707	+	36.3522i	−0.457557	+	1.30245i
$780$	25.9802	−	50.6229i	0.930241	−	1.81259i
$781$	−43.1217	−	15.6950i	−1.54302	−	0.561612i
$782$	−3.82229	+	2.20057i	−0.136685	+	0.0786923i
$783$	6.78494	−	0.593606i	0.242474	−	0.0212137i
$784$	−23.8282	+	13.6022i	−0.851008	+	0.485792i
$785$	−0.508687	−	0.318198i	−0.0181558	−	0.0113570i
$786$	−1.58893	+	1.10968i	−0.0566751	+	0.0395811i
$787$	7.66138	−	28.5927i	0.273099	−	1.01922i	−0.684006	−	0.729476i	$-0.739764\pi$
$787$	7.66138	−	28.5927i	0.273099	−	1.01922i	0.957105	−	0.289742i	$-0.0935695\pi$
$788$	−11.0068	−	41.4838i	−0.392102	−	1.47780i
$789$	−5.56397	−	15.2869i	−0.198083	−	0.544227i
$790$	4.18555	+	1.28743i	0.148915	+	0.0458045i
$791$	5.23737	+	3.02379i	0.186219	+	0.107514i
$792$	−43.4495	−	36.7311i	−1.54391	−	1.30518i
$793$	18.4678	+	1.61573i	0.655812	+	0.0573761i
$794$	19.3918	−	9.01367i	0.688189	−	0.319883i
$795$	−20.0699	−	30.9370i	−0.711805	−	1.09722i
$796$	4.27936	−	1.54571i	0.151678	−	0.0547863i
$797$	8.17145	−	8.17145i	0.289448	−	0.289448i	−0.547414	−	0.836862i	$-0.684388\pi$
$797$	8.17145	−	8.17145i	0.289448	−	0.289448i	0.836862	+	0.547414i	$0.184388\pi$
$798$	−4.23096	−	4.94100i	−0.149774	−	0.174909i
$799$	8.43798			0.298514
$800$	16.4630	+	22.9993i	0.582054	+	0.813150i
$801$	7.24542	+	41.0908i	0.256005	+	1.45187i
$802$	−27.3738	−	10.0012i	−0.966604	−	0.353155i
$803$	3.61165	−	41.2814i	0.127453	−	1.45679i
$804$	−12.8981	−	22.4669i	−0.454880	−	0.792347i
$805$	0.0558617	−	0.453181i	0.00196887	−	0.0159725i
$806$	50.1685	−	4.32733i	1.76711	−	0.152424i
$807$	44.2078	+	20.6144i	1.55619	+	0.725662i
$808$	−5.35134	+	29.7109i	−0.188260	+	1.04522i
$809$	34.6928	−	20.0299i	1.21973	−	0.704213i	0.254872	−	0.966975i	$-0.417967\pi$
$809$	34.6928	−	20.0299i	1.21973	−	0.704213i	0.964861	+	0.262762i	$0.0846334\pi$
$810$	0.291453	+	1.27227i	0.0102406	+	0.0447031i
$811$	10.3176	+	1.81928i	0.362301	+	0.0638834i	0.351836	−	0.936062i	$-0.385558\pi$
$811$	10.3176	+	1.81928i	0.362301	+	0.0638834i	0.0104654	+	0.999945i	$0.496669\pi$
$812$	0.542017	+	0.778126i	0.0190211	+	0.0273069i
$813$	−0.759419	−	8.68020i	−0.0266340	−	0.304428i
$814$	−11.9272	+	44.2960i	−0.418048	+	1.55258i
$815$	−28.1351	+	31.2175i	−0.985531	+	1.09350i
$816$	63.4301	+	11.5048i	2.22050	+	0.402748i
$817$	−15.2406	+	22.2946i	−0.533202	+	0.779990i
$818$	5.65951	+	15.6088i	0.197880	+	0.545748i
$819$	7.83455	+	2.85154i	0.273761	+	0.0996409i
$820$	37.7699	+	11.6682i	1.31898	+	0.407470i
$821$	12.4031	+	10.4074i	0.432872	+	0.363222i	0.833034	−	0.553222i	$-0.186602\pi$
$821$	12.4031	+	10.4074i	0.432872	+	0.363222i	−0.400162	+	0.916444i	$0.631046\pi$
$822$	−55.2121	−	31.9668i	−1.92574	−	1.11497i
$823$	−29.3421	−	41.9049i	−1.02280	−	1.46071i	−0.882332	−	0.470627i	$-0.844028\pi$
$823$	−29.3421	−	41.9049i	−1.02280	−	1.46071i	−0.140470	−	0.990085i	$-0.544861\pi$
$824$	33.3132	+	9.05742i	1.16052	+	0.315530i
$825$	29.6039	+	49.3752i	1.03068	+	1.71902i
$826$	2.03976	+	0.180971i	0.0709724	+	0.00629679i
$827$	27.9297	+	13.0238i	0.971211	+	0.452883i	0.842439	−	0.538791i	$-0.181119\pi$
$827$	27.9297	+	13.0238i	0.971211	+	0.452883i	0.128772	+	0.991674i	$0.458897\pi$
$828$	−2.24987	−	4.85586i	−0.0781885	−	0.168753i
$829$	−11.6014	−	6.69809i	−0.402935	−	0.232634i	0.284815	−	0.958583i	$-0.408068\pi$
$829$	−11.6014	−	6.69809i	−0.402935	−	0.232634i	−0.687749	+	0.725948i	$0.741401\pi$
$830$	9.61030	+	2.05979i	0.333578	+	0.0714963i
$831$	37.7987	+	45.0468i	1.31122	+	1.56266i
$832$	29.7881	−	20.5336i	1.03272	−	0.711874i
$833$	22.5376	−	32.1871i	0.780883	−	1.11522i
$834$	21.4902	−	21.4377i	0.744145	−	0.742326i
$835$	−40.1965	−	16.2626i	−1.39106	−	0.562790i
$836$	−35.6770	+	0.313359i	−1.23392	+	0.0108378i
$837$	−29.9952	+	29.9952i	−1.03679	+	1.03679i
$838$	−15.5691	−	0.0190485i	−0.537825	−	0.000658020i
$839$	−1.49838	−	8.49773i	−0.0517298	−	0.293374i	0.947957	−	0.318398i	$-0.103145\pi$
$839$	−1.49838	−	8.49773i	−0.0517298	−	0.293374i	−0.999687	+	0.0250240i	$0.992034\pi$
$840$	−4.89984	+	4.53135i	−0.169060	+	0.156346i
$841$	20.9912	−	17.6137i	0.723833	−	0.607368i
$842$	−3.67879	−	21.0138i	−0.126780	−	0.724182i
$843$	−13.6255	−	50.8509i	−0.469286	−	1.75140i
$844$	−9.65622	+	26.3296i	−0.332381	+	0.906302i
$845$	11.3592	+	12.1928i	0.390767	+	0.419445i
$846$	−0.904846	+	10.1987i	−0.0311092	+	0.350639i
$847$	0.558133	−	2.08298i	0.0191777	−	0.0715720i
$848$	−1.92926	−	23.3682i	−0.0662512	−	0.802467i
$849$	−34.3926	−	6.06434i	−1.18035	−	0.208127i
$850$	−35.3848	−	19.7147i	−1.21369	−	0.676208i
$851$	−2.77366	+	3.30552i	−0.0950799	+	0.113312i
$852$	5.34495	+	62.8644i	0.183115	+	2.15370i
$853$	3.22070	+	6.90681i	0.110275	+	0.236485i	0.953699	−	0.300764i	$-0.0972415\pi$
$853$	3.22070	+	6.90681i	0.110275	+	0.236485i	−0.843424	+	0.537248i	$0.819464\pi$
$854$	−1.96955	−	0.921351i	−0.0673965	−	0.0315280i
$855$	38.5675	+	28.4175i	1.31898	+	0.971859i
$856$	40.8445	−	10.7837i	1.39604	−	0.368580i
$857$	−17.0862	+	7.96744i	−0.583655	+	0.272163i	−0.691937	−	0.721958i	$-0.743243\pi$
$857$	−17.0862	+	7.96744i	−0.583655	+	0.272163i	0.108283	+	0.994120i	$0.465465\pi$
$858$	63.8191	−	36.7419i	2.17875	−	1.25435i
$859$	42.1020	+	35.3277i	1.43650	+	1.20537i	0.941742	+	0.336336i	$0.109188\pi$
$859$	42.1020	+	35.3277i	1.43650	+	1.20537i	0.494758	+	0.869031i	$0.335257\pi$
$860$	23.4544	+	14.7514i	0.799789	+	0.503018i
$861$	−1.61975	+	9.18604i	−0.0552008	+	0.313060i
$862$	36.2102	+	6.43052i	1.23332	+	0.219024i
$863$	22.9481	+	6.14893i	0.781163	+	0.209312i	0.627298	−	0.778780i	$-0.284161\pi$
$863$	22.9481	+	6.14893i	0.781163	+	0.209312i	0.153866	+	0.988092i	$0.450828\pi$
$864$	−8.06827	+	29.3908i	−0.274488	+	0.999897i
$865$	31.2950	+	1.10770i	1.06406	+	0.0376629i
$866$	−1.75119	−	20.3023i	−0.0595079	−	0.689899i
$867$	−42.9775	+	11.5158i	−1.45959	+	0.391097i
$868$	−5.70119	−	1.54259i	−0.193511	−	0.0523590i
$869$	3.64291	+	4.34145i	0.123577	+	0.147274i
$870$	−8.34496	−	7.53953i	−0.282921	−	0.255614i
$871$	20.5054	−	3.61565i	0.694798	−	0.122512i
$872$	8.23726	+	9.89028i	0.278949	+	0.334927i
$873$	−8.99771	−	8.99771i	−0.304526	−	0.304526i
$874$	−3.05565	−	1.38782i	−0.103359	−	0.0469437i
$875$	3.83340	−	1.70021i	0.129593	−	0.0574777i
$876$	−53.5846	+	19.3549i	−1.81046	+	0.653940i
$877$	24.2014	+	16.9460i	0.817223	+	0.572226i	0.905733	−	0.423850i	$-0.139321\pi$
$877$	24.2014	+	16.9460i	0.817223	+	0.572226i	−0.0885095	+	0.996075i	$0.528210\pi$
$878$	4.93248	+	1.80211i	0.166463	+	0.0608183i
$879$	−35.7738	+	30.0178i	−1.20662	+	1.01247i
$880$	1.71952	+	36.5649i	0.0579649	+	1.23260i
$881$	−10.9078	+	18.8929i	−0.367493	+	0.636517i	−0.989173	−	0.146755i	$-0.953117\pi$
$881$	−10.9078	+	18.8929i	−0.367493	+	0.636517i	0.621680	+	0.783272i	$0.286451\pi$
$882$	36.4866	+	30.6921i	1.22857	+	1.03346i
$883$	−18.7589	+	40.2287i	−0.631289	+	1.35380i	0.287015	+	0.957926i	$0.407337\pi$
$883$	−18.7589	+	40.2287i	−0.631289	+	1.35380i	−0.918304	+	0.395877i	$0.870441\pi$
$884$	−26.0162	+	44.8079i	−0.875021	+	1.50705i
$885$	−24.0512	+	3.36855i	−0.808472	+	0.113232i
$886$	28.8761	+	41.3469i	0.970111	+	1.38908i
$887$	−21.3682	+	14.9622i	−0.717474	+	0.502381i	−0.874386	−	0.485232i	$-0.838735\pi$
$887$	−21.3682	+	14.9622i	−0.717474	+	0.502381i	0.156911	+	0.987613i	$0.449846\pi$
$888$	62.1516	−	10.7239i	2.08567	−	0.359872i
$889$	3.44140	−	4.10130i	0.115421	−	0.137553i
$890$	16.1921	−	21.4119i	0.542760	−	0.717729i
$891$	−0.577746	+	1.58734i	−0.0193552	+	0.0531780i
$892$	−4.80274	+	53.3905i	−0.160807	+	1.78765i
$893$	3.74157	+	5.21780i	0.125207	+	0.174607i
$894$	41.7371	+	19.5245i	1.39590	+	0.652998i
$895$	10.0612	−	0.522503i	0.336309	−	0.0174653i
$896$	−4.10822	+	1.06317i	−0.137246	+	0.0355180i
$897$	6.90050	−	0.603715i	0.230401	−	0.0201575i
$898$	−14.7443	−	8.53672i	−0.492025	−	0.284874i
$899$	1.72827	−	9.80151i	0.0576410	−	0.326899i
$900$	27.6229	−	40.6543i	0.920765	−	1.35514i
$901$	16.7898	+	29.0809i	0.559351	+	0.968824i
$902$	32.8376	+	39.2317i	1.09337	+	1.30627i
$903$	−2.76303	+	5.92533i	−0.0919478	+	0.197183i
$904$	−32.1283	−	32.3650i	−1.06857	−	1.07644i
$905$	7.00704	−	56.8450i	0.232922	−	1.88959i
$906$	1.13494	−	1.61665i	0.0377060	−	0.0537097i
$907$	−44.2807	−	3.87406i	−1.47032	−	0.128636i	−0.676343	−	0.736587i	$-0.736436\pi$
$907$	−44.2807	−	3.87406i	−1.47032	−	0.128636i	−0.793975	+	0.607951i	$0.791992\pi$
$908$	24.5832	+	24.7038i	0.815822	+	0.819825i
$909$	51.6636	−	9.10969i	1.71357	−	0.302149i
$910$	−2.08754	−	4.94124i	−0.0692013	−	0.163801i
$911$		−	49.0076i		−	1.62369i	−0.583870	−	0.811847i	$-0.698462\pi$
$911$		−	49.0076i		−	1.62369i	0.583870	−	0.811847i	$-0.301538\pi$
$912$	21.0119	+	44.3248i	0.695773	+	1.46774i
$913$	8.99443	+	8.99443i	0.297672	+	0.297672i
$914$	−19.4473	+	19.3998i	−0.643259	+	0.641687i
$915$	25.2216	+	5.37351i	0.833799	+	0.177643i
$916$	0.0199053	−	8.13466i	0.000657689	−	0.268777i
$917$	−0.0159238	+	0.182010i	−0.000525849	+	0.00601049i
$918$	−7.52681	−	42.9942i	−0.248422	−	1.41902i
$919$	14.2751	−	24.7253i	0.470894	−	0.815611i	−0.528552	−	0.848901i	$-0.677265\pi$
$919$	14.2751	−	24.7253i	0.470894	−	0.815611i	0.999446	+	0.0332893i	$0.0105983\pi$
$920$	−1.30308	+	3.18713i	−0.0429612	+	0.105077i
$921$	15.8148	−	5.75611i	0.521115	−	0.189670i
$922$	−2.68789	+	2.24981i	−0.0885209	+	0.0740935i
$923$	−48.9810	−	13.1244i	−1.61223	−	0.431996i
$924$	−8.50979	+	1.47904i	−0.279951	+	0.0486570i
$925$	−39.1358	−	6.23655i	−1.28678	−	0.205057i
$926$	−6.93176	−	25.9969i	−0.227792	−	0.854310i
$927$	−5.22858	−	59.7630i	−0.171729	−	1.96287i
$928$	−2.40461	−	6.73452i	−0.0789353	−	0.221072i
$929$	−18.9522	+	52.0706i	−0.621800	+	1.70838i	0.0807381	+	0.996735i	$0.474272\pi$
$929$	−18.9522	+	52.0706i	−0.621800	+	1.70838i	−0.702538	+	0.711646i	$0.747950\pi$
$930$	69.9986	+	2.56338i	2.29535	+	0.0840567i
$931$	29.8972	−	0.335758i	0.979840	−	0.0110040i
$932$	−17.7271	−	1.59464i	−0.580671	−	0.0522342i
$933$	−23.7840	−	51.0050i	−0.778653	−	1.66983i
$934$	−2.96331	+	11.0053i	−0.0969624	+	0.360106i
$935$	−24.5890	−	46.2982i	−0.804148	−	1.51411i
$936$	−51.3679	−	36.2499i	−1.67901	−	1.18487i
$937$	−25.9152	−	37.0107i	−0.846612	−	1.20909i	−0.976060	−	0.217501i	$-0.930210\pi$
$937$	−25.9152	−	37.0107i	−0.846612	−	1.20909i	0.129448	−	0.991586i	$-0.458679\pi$
$938$	−2.40459	−	0.427028i	−0.0785126	−	0.0139430i
$939$	−15.4168	−	26.7027i	−0.503108	−	0.871409i
$940$	5.20281	−	4.04046i	0.169697	−	0.131785i
$941$	−0.315507	+	0.114835i	−0.0102852	+	0.00374352i	−0.347158	−	0.937807i	$-0.612853\pi$
$941$	−0.315507	+	0.114835i	−0.0102852	+	0.00374352i	0.336872	+	0.941550i	$0.390631\pi$
$942$	−0.687252	+	0.817003i	−0.0223919	+	0.0266194i
$943$	1.24554	+	4.64841i	0.0405603	+	0.151373i
$944$	−14.4847	−	5.35241i	−0.471436	−	0.174206i
$945$	4.02531	+	2.05340i	0.130943	+	0.0667972i
$946$	15.1149	+	32.5178i	0.491427	+	1.05724i
$947$	12.3515	−	17.6398i	0.401370	−	0.573215i	−0.566691	−	0.823930i	$-0.691777\pi$
$947$	12.3515	−	17.6398i	0.401370	−	0.573215i	0.968061	+	0.250715i	$0.0806657\pi$
$948$	3.31025	−	7.05373i	0.107512	−	0.229094i
$949$		−	45.7914i		−	1.48645i
$950$	−3.49932	−	30.6228i	−0.113533	−	0.993534i
$951$			55.3207i			1.79390i
$952$	4.66974	−	3.88926i	0.151347	−	0.126052i
$953$	−14.5626	+	20.7975i	−0.471728	+	0.673698i	−0.982552	−	0.185988i	$-0.940452\pi$
$953$	−14.5626	+	20.7975i	−0.471728	+	0.673698i	0.510824	+	0.859685i	$0.329340\pi$
$954$	−36.9495	+	17.1748i	−1.19628	+	0.556056i
$955$	16.0469	+	8.18589i	0.519266	+	0.264889i
$956$	7.01570	+	12.2205i	0.226904	+	0.395239i
$957$	−3.76713	−	14.0591i	−0.121774	−	0.454467i
$958$	−14.5214	−	12.2152i	−0.469165	−	0.394656i
$959$	−5.65170	+	2.05705i	−0.182503	+	0.0664256i
$960$	44.6195	−	23.2792i	1.44009	−	0.751333i
$961$	15.4939	+	26.8362i	0.499803	+	0.865684i
$962$	−8.86361	+	49.9109i	−0.285774	+	1.60919i
$963$	−42.1059	−	60.1334i	−1.35684	−	1.93777i
$964$	−4.23939	+	23.7035i	−0.136542	+	0.763437i
$965$	−5.31847	−	10.0140i	−0.171208	−	0.322364i
$966$	−0.784521	−	0.211241i	−0.0252415	−	0.00679656i
$967$	0.366626	+	0.786232i	0.0117899	+	0.0252835i	0.912115	−	0.409935i	$-0.134449\pi$
$967$	0.366626	+	0.786232i	0.0117899	+	0.0252835i	−0.900325	+	0.435219i	$0.856671\pi$
$968$	−8.18240	+	14.0530i	−0.262992	+	0.451679i
$969$	−54.3176	−	44.5481i	−1.74493	−	1.43109i
$970$	−0.299606	+	8.18136i	−0.00961975	+	0.262688i
$971$	10.8435	−	29.7923i	0.347985	−	0.956082i	−0.635019	−	0.772497i	$-0.719008\pi$
$971$	10.8435	−	29.7923i	0.347985	−	0.956082i	0.983004	−	0.183585i	$-0.0587702\pi$
$972$	−29.8967	+	2.54192i	−0.958936	+	0.0815321i
$973$	−0.249404	−	2.85070i	−0.00799552	−	0.0913892i
$974$	20.7840	−	5.54181i	0.665962	−	0.177571i
$975$	37.3441	+	51.5023i	1.19597	+	1.64939i
$976$	12.5089	+	10.6010i	0.400401	+	0.339330i
$977$	−19.7693	−	5.29716i	−0.632475	−	0.169471i	−0.0716827	−	0.997427i	$-0.522837\pi$
$977$	−19.7693	−	5.29716i	−0.632475	−	0.169471i	−0.560793	+	0.827956i	$0.689504\pi$
$978$	47.9955	+	57.3412i	1.53473	+	1.83357i
$979$	32.6473	−	11.8827i	1.04341	−	0.379771i
$980$	−1.51596	−	30.6383i	−0.0484255	−	0.978705i
$981$	11.1835	−	19.3704i	0.357061	−	0.618449i
$982$	26.0816	−	4.56600i	0.832299	−	0.145707i
$983$	−5.11603	+	58.4765i	−0.163176	+	1.86511i	0.268762	+	0.963207i	$0.413386\pi$
$983$	−5.11603	+	58.4765i	−0.163176	+	1.86511i	−0.431938	+	0.901904i	$0.642170\pi$
$984$	29.9604	−	63.6394i	0.955102	−	2.02875i
$985$	46.9318	+	9.99891i	1.49537	+	0.318592i
$986$	7.23257	+	7.25029i	0.230332	+	0.230896i
$987$	1.09911	+	1.09911i	0.0349850	+	0.0349850i
$988$	−39.2440	+	3.78100i	−1.24852	+	0.120290i
$989$			3.37303i			0.107256i
$990$	58.5959	−	24.7552i	1.86230	−	0.786771i
$991$	13.2341	−	2.33353i	0.420396	−	0.0741272i	0.0405514	−	0.999177i	$-0.487089\pi$
$991$	13.2341	−	2.33353i	0.420396	−	0.0741272i	0.379845	+	0.925050i	$0.375977\pi$
$992$	38.4339	+	22.5044i	1.22028	+	0.714515i
$993$	−57.7243	−	5.05022i	−1.83182	−	0.160264i
$994$	4.86792	+	3.41744i	0.154401	+	0.108395i
$995$	−0.622344	+	5.04880i	−0.0197296	+	0.160058i
$996$	6.02154	−	16.4189i	0.190800	−	0.520254i
$997$	7.11752	−	15.2636i	0.225414	−	0.483402i	−0.760777	−	0.649013i	$-0.775182\pi$
$997$	7.11752	−	15.2636i	0.225414	−	0.483402i	0.986191	+	0.165611i	$0.0529597\pi$
$998$	23.1270	−	19.3577i	0.732072	−	0.612756i
$999$	−21.3518	−	36.9824i	−0.675540	−	1.17007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bj.a.23.1	✓	672
4.3	odd	2	inner	380.2.bj.a.23.17	yes	672
5.2	odd	4	inner	380.2.bj.a.327.28	yes	672
19.5	even	9	inner	380.2.bj.a.43.14	yes	672
20.7	even	4	inner	380.2.bj.a.327.14	yes	672
76.43	odd	18	inner	380.2.bj.a.43.28	yes	672
95.62	odd	36	inner	380.2.bj.a.347.17	yes	672
380.347	even	36	inner	380.2.bj.a.347.1	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bj.a.23.1	✓	672	1.1	even	1	trivial
380.2.bj.a.23.17	yes	672	4.3	odd	2	inner
380.2.bj.a.43.14	yes	672	19.5	even	9	inner
380.2.bj.a.43.28	yes	672	76.43	odd	18	inner
380.2.bj.a.327.14	yes	672	20.7	even	4	inner
380.2.bj.a.327.28	yes	672	5.2	odd	4	inner
380.2.bj.a.347.1	yes	672	380.347	even	36	inner
380.2.bj.a.347.17	yes	672	95.62	odd	36	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bj (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 - 0.00173027i) q^{2} +(-2.30458 - 1.61369i) q^{3} +(1.99999 + 0.00489393i) q^{4} +(-1.01610 + 1.99187i) q^{5} +(3.25638 + 2.28608i) q^{6} +(0.362300 - 0.0970781i) q^{7} +(-2.82841 - 0.0103816i) q^{8} +(1.68106 + 4.61866i) q^{9} +O(q^{10})\)	\(q+(-1.41421 - 0.00173027i) q^{2} +(-2.30458 - 1.61369i) q^{3} +(1.99999 + 0.00489393i) q^{4} +(-1.01610 + 1.99187i) q^{5} +(3.25638 + 2.28608i) q^{6} +(0.362300 - 0.0970781i) q^{7} +(-2.82841 - 0.0103816i) q^{8} +(1.68106 + 4.61866i) q^{9} +(1.44042 - 2.81517i) q^{10} +(3.54429 - 2.04630i) q^{11} +(-4.60125 - 3.23864i) q^{12} +(3.70457 - 2.59396i) q^{13} +(-0.512538 + 0.136662i) q^{14} +(5.55593 - 2.95076i) q^{15} +(3.99995 + 0.0195756i) q^{16} +(-5.19173 + 2.42094i) q^{17} +(-2.36938 - 6.53468i) q^{18} +(-3.79915 - 2.13692i) q^{19} +(-2.04194 + 3.97875i) q^{20} +(-0.991604 - 0.360914i) q^{21} +(-5.01592 + 2.88777i) q^{22} +(-0.542351 + 0.0474495i) q^{23} +(6.50154 + 4.58809i) q^{24} +(-2.93509 - 4.04787i) q^{25} +(-5.24353 + 3.66201i) q^{26} +(1.39447 - 5.20424i) q^{27} +(0.725074 - 0.192383i) q^{28} +(0.432355 + 1.18788i) q^{29} +(-7.86237 + 4.16339i) q^{30} +(-6.81842 - 3.93662i) q^{31} +(-5.65675 - 0.0346051i) q^{32} +(-11.4702 - 1.00351i) q^{33} +(7.34640 - 3.41474i) q^{34} +(-0.174766 + 0.820296i) q^{35} +(3.33950 + 9.24552i) q^{36} +(5.60448 - 5.60448i) q^{37} +(5.36911 + 3.02863i) q^{38} -12.7233 q^{39} +(2.89462 - 5.62327i) q^{40} +(-1.53495 - 8.70514i) q^{41} +(1.40171 + 0.512125i) q^{42} +(0.539983 - 6.17204i) q^{43} +(7.09857 - 4.07524i) q^{44} +(-10.9079 - 1.34457i) q^{45} +(0.767081 - 0.0661653i) q^{46} +(-1.33499 - 0.622516i) q^{47} +(-9.18663 - 6.49978i) q^{48} +(-5.94034 + 3.42966i) q^{49} +(4.14384 + 5.72963i) q^{50} +(15.8714 + 2.79856i) q^{51} +(7.42180 - 5.16978i) q^{52} +(-0.510901 - 5.83962i) q^{53} +(-1.98109 + 7.35749i) q^{54} +(0.474610 + 9.13900i) q^{55} +(-1.02574 + 0.270815i) q^{56} +(5.30714 + 11.0553i) q^{57} +(-0.609386 - 1.68067i) q^{58} +(-3.62767 - 1.32036i) q^{59} +(11.1263 - 5.87432i) q^{60} +(3.14017 + 2.63491i) q^{61} +(9.63588 + 5.57901i) q^{62} +(1.05742 + 1.51015i) q^{63} +(7.99978 + 0.0587266i) q^{64} +(1.40264 + 10.0147i) q^{65} +(16.2195 + 1.43902i) q^{66} +(4.17272 + 1.94577i) q^{67} +(-10.3953 + 4.81646i) q^{68} +(1.32646 + 0.765832i) q^{69} +(0.248575 - 1.15977i) q^{70} +(-7.20741 - 8.58945i) q^{71} +(-4.70676 - 13.0809i) q^{72} +(5.80768 - 8.29423i) q^{73} +(-7.93562 + 7.91623i) q^{74} +(0.232165 + 14.0650i) q^{75} +(-7.58783 - 4.29242i) q^{76} +(1.08545 - 1.08545i) q^{77} +(17.9935 + 0.0220147i) q^{78} +(0.240466 + 1.36375i) q^{79} +(-4.10334 + 7.94749i) q^{80} +(-0.316185 + 0.265310i) q^{81} +(2.15569 + 12.3136i) q^{82} +(0.804426 + 3.00216i) q^{83} +(-1.98144 - 0.726680i) q^{84} +(0.453103 - 12.8012i) q^{85} +(-0.774330 + 8.72764i) q^{86} +(0.920475 - 3.43526i) q^{87} +(-10.0459 + 5.75097i) q^{88} +(8.36016 + 1.47412i) q^{89} +(15.4237 + 1.92038i) q^{90} +(1.09035 - 1.29943i) q^{91} +(-1.08493 + 0.0922445i) q^{92} +(9.36114 + 20.0750i) q^{93} +(1.88688 + 0.882680i) q^{94} +(8.11678 - 5.39610i) q^{95} +(12.9806 + 9.20796i) q^{96} +(-2.34635 + 1.09412i) q^{97} +(8.40684 - 4.83999i) q^{98} +(15.4093 + 12.9299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

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