LMFDB - Embedded newform 380.2.bj.a.327.28

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			327.28
Character	$\chi$	$=$	380.327
Dual form			380.2.bj.a.43.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.00173027 - 1.41421i) q^{2} +(-1.61369 + 2.30458i) q^{3} +(-1.99999 - 0.00489393i) q^{4} +(-2.13805 + 0.654777i) q^{5} +(3.25638 + 2.28608i) q^{6} +(0.0970781 + 0.362300i) q^{7} +(-0.0103816 + 2.82841i) q^{8} +(-1.68106 - 4.61866i) q^{9} +O(q^{10})$	\(q+(0.00173027 - 1.41421i) q^{2} +(-1.61369 + 2.30458i) q^{3} +(-1.99999 - 0.00489393i) q^{4} +(-2.13805 + 0.654777i) q^{5} +(3.25638 + 2.28608i) q^{6} +(0.0970781 + 0.362300i) q^{7} +(-0.0103816 + 2.82841i) q^{8} +(-1.68106 - 4.61866i) q^{9} +(0.922294 + 3.02479i) q^{10} +(3.54429 - 2.04630i) q^{11} +(3.23864 - 4.60125i) q^{12} +(-2.59396 - 3.70457i) q^{13} +(0.512538 - 0.136662i) q^{14} +(1.94116 - 5.98392i) q^{15} +(3.99995 + 0.0195756i) q^{16} +(-2.42094 - 5.19173i) q^{17} +(-6.53468 + 2.36938i) q^{18} +(3.79915 + 2.13692i) q^{19} +(4.27930 - 1.29909i) q^{20} +(-0.991604 - 0.360914i) q^{21} +(-2.88777 - 5.01592i) q^{22} +(0.0474495 + 0.542351i) q^{23} +(-6.50154 - 4.58809i) q^{24} +(4.14254 - 2.79989i) q^{25} +(-5.24353 + 3.66201i) q^{26} +(5.20424 + 1.39447i) q^{27} +(-0.192383 - 0.725074i) q^{28} +(-0.432355 - 1.18788i) q^{29} +(-8.45917 - 2.75556i) q^{30} +(-6.81842 - 3.93662i) q^{31} +(0.0346051 - 5.65675i) q^{32} +(-1.00351 + 11.4702i) q^{33} +(-7.34640 + 3.41474i) q^{34} +(-0.444784 - 0.711053i) q^{35} +(3.33950 + 9.24552i) q^{36} +(5.60448 + 5.60448i) q^{37} +(3.02863 - 5.36911i) q^{38} +12.7233 q^{39} +(-1.82978 - 6.05408i) q^{40} +(-1.53495 - 8.70514i) q^{41} +(-0.512125 + 1.40171i) q^{42} +(-6.17204 - 0.539983i) q^{43} +(-7.09857 + 4.07524i) q^{44} +(6.61838 + 8.77422i) q^{45} +(0.767081 - 0.0661653i) q^{46} +(0.622516 - 1.33499i) q^{47} +(-6.49978 + 9.18663i) q^{48} +(5.94034 - 3.42966i) q^{49} +(-3.95248 - 5.86327i) q^{50} +(15.8714 + 2.79856i) q^{51} +(5.16978 + 7.42180i) q^{52} +(-5.83962 + 0.510901i) q^{53} +(1.98109 - 7.35749i) q^{54} +(-6.23801 + 6.69581i) q^{55} +(-1.02574 + 0.270815i) q^{56} +(-11.0553 + 5.30714i) q^{57} +(-1.68067 + 0.609386i) q^{58} +(3.62767 + 1.32036i) q^{59} +(-3.91159 + 11.9583i) q^{60} +(3.14017 + 2.63491i) q^{61} +(-5.57901 + 9.63588i) q^{62} +(1.51015 - 1.05742i) q^{63} +(-7.99978 - 0.0587266i) q^{64} +(7.97169 + 6.22209i) q^{65} +(16.2195 + 1.43902i) q^{66} +(-1.94577 + 4.17272i) q^{67} +(4.81646 + 10.3953i) q^{68} +(-1.32646 - 0.765832i) q^{69} +(-1.00635 + 0.627789i) q^{70} +(-7.20741 - 8.58945i) q^{71} +(13.0809 - 4.70676i) q^{72} +(-8.29423 - 5.80768i) 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} +(0.0220147 - 17.9935i) q^{78} +(-0.240466 - 1.36375i) q^{79} +(-8.56492 + 2.57722i) q^{80} +(-0.316185 + 0.265310i) q^{81} +(-12.3136 + 2.15569i) q^{82} +(3.00216 - 0.804426i) q^{83} +(1.98144 + 0.726680i) q^{84} +(8.57553 + 9.51501i) q^{85} +(-0.774330 + 8.72764i) q^{86} +(3.43526 + 0.920475i) q^{87} +(5.75097 + 10.0459i) q^{88} +(-8.36016 - 1.47412i) q^{89} +(12.4201 - 9.34461i) q^{90} +(1.09035 - 1.29943i) q^{91} +(-0.0922445 - 1.08493i) q^{92} +(20.0750 - 9.36114i) q^{93} +(-1.88688 - 0.882680i) q^{94} +(-9.52200 - 2.08125i) q^{95} +(12.9806 + 9.20796i) q^{96} +(-1.09412 - 2.34635i) q^{97} +(-4.83999 - 8.40684i) 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.00173027	−	1.41421i	0.00122348	−	0.999999i
$2$	0.00173027	−	1.41421i	0.00122348	−	0.999999i
$3$	−1.61369	+	2.30458i	−0.931662	+	1.33055i	0.0121009	+	0.999927i	$0.496148\pi$
$3$	−1.61369	+	2.30458i	−0.931662	+	1.33055i	−0.943763	+	0.330624i	$0.892741\pi$
$4$	−1.99999	−	0.00489393i	−0.999997	−	0.00244696i
$5$	−2.13805	+	0.654777i	−0.956166	+	0.292825i
$5$	−2.13805	+	0.654777i	−0.956166	+	0.292825i
$6$	3.25638	+	2.28608i	1.32941	+	0.933289i
$7$	0.0970781	+	0.362300i	0.0366921	+	0.136937i	0.981842	−	0.189700i	$-0.0607514\pi$
$7$	0.0970781	+	0.362300i	0.0366921	+	0.136937i	−0.945150	+	0.326636i	$0.894085\pi$
$8$	−0.0103816	+	2.82841i	−0.00367044	+	0.999993i
$9$	−1.68106	−	4.61866i	−0.560352	−	1.53955i
$10$	0.922294	+	3.02479i	0.291655	+	0.956524i
$11$	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	$0.121689\pi$
$12$	3.23864	−	4.60125i	0.934915	−	1.32827i
$13$	−2.59396	−	3.70457i	−0.719436	−	1.02746i	−0.997755	−	0.0669726i	$-0.978666\pi$
$13$	−2.59396	−	3.70457i	−0.719436	−	1.02746i	0.278319	−	0.960489i	$-0.410223\pi$
$14$	0.512538	−	0.136662i	0.136981	−	0.0365245i
$15$	1.94116	−	5.98392i	0.501205	−	1.54504i
$16$	3.99995	+	0.0195756i	0.999988	+	0.00489391i
$17$	−2.42094	−	5.19173i	−0.587165	−	1.25918i	−0.945511	−	0.325590i	$-0.894437\pi$
$17$	−2.42094	−	5.19173i	−0.587165	−	1.25918i	0.358346	−	0.933589i	$-0.383341\pi$
$18$	−6.53468	+	2.36938i	−1.54024	+	0.558468i
$19$	3.79915	+	2.13692i	0.871586	+	0.490243i
$19$	3.79915	+	2.13692i	0.871586	+	0.490243i
$20$	4.27930	−	1.29909i	0.956880	−	0.290484i
$21$	−0.991604	−	0.360914i	−0.216386	−	0.0787580i
$22$	−2.88777	−	5.01592i	−0.615674	−	1.06940i
$23$	0.0474495	+	0.542351i	0.00989391	+	0.113088i	0.999536	−	0.0304713i	$-0.00970081\pi$
$23$	0.0474495	+	0.542351i	0.00989391	+	0.113088i	−0.989642	+	0.143559i	$0.954145\pi$
$24$	−6.50154	−	4.58809i	−1.32712	−	0.936539i
$25$	4.14254	−	2.79989i	0.828507	−	0.559979i
$26$	−5.24353	+	3.66201i	−1.02834	+	0.718179i
$27$	5.20424	+	1.39447i	1.00156	+	0.268366i
$28$	−0.192383	−	0.725074i	−0.0363569	−	0.137026i
$29$	−0.432355	−	1.18788i	−0.0802862	−	0.220585i	0.893055	−	0.449948i	$-0.148558\pi$
$29$	−0.432355	−	1.18788i	−0.0802862	−	0.220585i	−0.973341	+	0.229364i	$0.926335\pi$
$30$	−8.45917	−	2.75556i	−1.54443	−	0.503095i
$31$	−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	$0.916635\pi$
$32$	0.0346051	−	5.65675i	0.00611737	−	0.999981i
$33$	−1.00351	+	11.4702i	−0.174689	+	1.99670i
$34$	−7.34640	+	3.41474i	−1.25990	+	0.585624i
$35$	−0.444784	−	0.711053i	−0.0751822	−	0.120190i
$36$	3.33950	+	9.24552i	0.556583	+	1.54092i
$37$	5.60448	+	5.60448i	0.921371	+	0.921371i	0.997126	−	0.0757558i	$-0.0241370\pi$
$37$	5.60448	+	5.60448i	0.921371	+	0.921371i	−0.0757558	+	0.997126i	$0.524137\pi$
$38$	3.02863	−	5.36911i	0.491309	−	0.870985i
$39$	12.7233			2.03736
$40$	−1.82978	−	6.05408i	−0.289314	−	0.957234i
$41$	−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	$-0.298052\pi$
$42$	−0.512125	+	1.40171i	−0.0790227	+	0.216289i
$43$	−6.17204	−	0.539983i	−0.941227	−	0.0823467i	−0.393796	−	0.919198i	$-0.628838\pi$
$43$	−6.17204	−	0.539983i	−0.941227	−	0.0823467i	−0.547431	+	0.836851i	$0.684394\pi$
$44$	−7.09857	+	4.07524i	−1.07015	+	0.614365i
$45$	6.61838	+	8.77422i	0.986609	+	1.30798i
$46$	0.767081	−	0.0661653i	0.113100	−	0.00975554i
$47$	0.622516	−	1.33499i	0.0908033	−	0.194728i	−0.855661	−	0.517537i	$-0.826849\pi$
$47$	0.622516	−	1.33499i	0.0908033	−	0.194728i	0.946464	+	0.322808i	$0.104627\pi$
$48$	−6.49978	+	9.18663i	−0.938162	+	1.32598i
$49$	5.94034	−	3.42966i	0.848620	−	0.489951i
$50$	−3.95248	−	5.86327i	−0.558965	−	0.829192i
$51$	15.8714	+	2.79856i	2.22244	+	0.391876i
$52$	5.16978	+	7.42180i	0.716920	+	1.02922i
$53$	−5.83962	+	0.510901i	−0.802133	+	0.0701776i	−0.480847	−	0.876804i	$-0.659671\pi$
$53$	−5.83962	+	0.510901i	−0.802133	+	0.0701776i	−0.321286	+	0.946982i	$0.604115\pi$
$54$	1.98109	−	7.35749i	0.269592	−	1.00123i
$55$	−6.23801	+	6.69581i	−0.841133	+	0.902862i
$56$	−1.02574	+	0.270815i	−0.137070	+	0.0361892i
$57$	−11.0553	+	5.30714i	−1.46432	+	0.702948i
$58$	−1.68067	+	0.609386i	−0.220683	+	0.0800163i
$59$	3.62767	+	1.32036i	0.472283	+	0.171897i	0.567186	−	0.823590i	$-0.308032\pi$
$59$	3.62767	+	1.32036i	0.472283	+	0.171897i	−0.0949034	+	0.995486i	$0.530254\pi$
$60$	−3.91159	+	11.9583i	−0.504984	+	1.54381i
$61$	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	$0.637700\pi$
$62$	−5.57901	+	9.63588i	−0.708535	+	1.22376i
$63$	1.51015	−	1.05742i	0.190261	−	0.133222i
$64$	−7.99978	−	0.0587266i	−0.999973	−	0.00734083i
$65$	7.97169	+	6.22209i	0.988767	+	0.771755i
$66$	16.2195	+	1.43902i	1.99649	+	0.177132i
$67$	−1.94577	+	4.17272i	−0.237714	+	0.509779i	−0.988584	−	0.150671i	$-0.951857\pi$
$67$	−1.94577	+	4.17272i	−0.237714	+	0.509779i	0.750870	+	0.660450i	$0.229634\pi$
$68$	4.81646	+	10.3953i	0.584082	+	1.26061i
$69$	−1.32646	−	0.765832i	−0.159687	−	0.0921953i
$70$	−1.00635	+	0.627789i	−0.120282	+	0.0750351i
$71$	−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	$-0.453941\pi$
$72$	13.0809	−	4.70676i	1.54160	−	0.554697i
$73$	−8.29423	−	5.80768i	−0.970766	−	0.679738i	−0.0233452	−	0.999727i	$-0.507432\pi$
$73$	−8.29423	−	5.80768i	−0.970766	−	0.679738i	−0.947421	+	0.319990i	$0.896321\pi$
$74$	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
$78$	0.0220147	−	17.9935i	0.00249267	−	2.03736i
$79$	−0.240466	−	1.36375i	−0.0270545	−	0.153434i	0.968288	−	0.249837i	$-0.0803771\pi$
$79$	−0.240466	−	1.36375i	−0.0270545	−	0.153434i	−0.995342	+	0.0964037i	$0.969266\pi$
$80$	−8.56492	+	2.57722i	−0.957588	+	0.288142i
$81$	−0.316185	+	0.265310i	−0.0351316	+	0.0294789i
$82$	−12.3136	+	2.15569i	−1.35981	+	0.238056i
$83$	3.00216	−	0.804426i	0.329530	−	0.0882972i	−0.0902610	−	0.995918i	$-0.528770\pi$
$83$	3.00216	−	0.804426i	0.329530	−	0.0882972i	0.419791	+	0.907621i	$0.362103\pi$
$84$	1.98144	+	0.726680i	0.216192	+	0.0792872i
$85$	8.57553	+	9.51501i	0.930146	+	1.03205i
$86$	−0.774330	+	8.72764i	−0.0834982	+	0.941125i
$87$	3.43526	+	0.920475i	0.368299	+	0.0986853i
$88$	5.75097	+	10.0459i	0.613055	+	1.07090i
$89$	−8.36016	−	1.47412i	−0.886176	−	0.156257i	−0.288008	−	0.957628i	$-0.592993\pi$
$89$	−8.36016	−	1.47412i	−0.886176	−	0.156257i	−0.598167	+	0.801371i	$0.704104\pi$
$90$	12.4201	−	9.34461i	1.30919	−	0.985008i
$91$	1.09035	−	1.29943i	0.114300	−	0.136217i
$92$	−0.0922445	−	1.08493i	−0.00961716	−	0.113112i
$93$	20.0750	−	9.36114i	2.08168	−	0.970705i
$94$	−1.88688	−	0.882680i	−0.194617	−	0.0910415i
$95$	−9.52200	−	2.08125i	−0.976936	−	0.213532i
$96$	12.9806	+	9.20796i	1.32483	+	0.939784i
$97$	−1.09412	−	2.34635i	−0.111091	−	0.238236i	0.842900	−	0.538070i	$-0.180846\pi$
$97$	−1.09412	−	2.34635i	−0.111091	−	0.238236i	−0.953991	+	0.299834i	$0.903069\pi$
$98$	−4.83999	−	8.40684i	−0.488912	−	0.849219i
$99$	−15.4093	−	12.9299i	−1.54869	−	1.29951i
$100$	−8.29875	+	5.57950i	−0.829875	+	0.557950i
$101$	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	$-0.122636\pi$
$102$	3.98522	−	22.4407i	0.394595	−	2.22196i
$103$	−3.15903	+	11.7897i	−0.311268	+	1.16167i	0.616145	+	0.787633i	$0.288693\pi$
$103$	−3.15903	+	11.7897i	−0.311268	+	1.16167i	−0.927414	+	0.374037i	$0.877973\pi$
$104$	10.5050	−	7.29833i	1.03010	−	0.715660i
$105$	2.35642	+	0.122375i	0.229963	+	0.0119425i
$106$	0.712418	+	8.25935i	0.0691961	+	0.802219i
$107$	−3.86560	−	14.4266i	−0.373702	−	1.39467i	−0.855232	−	0.518245i	$-0.826586\pi$
$107$	−3.86560	−	14.4266i	−0.373702	−	1.39467i	0.481530	−	0.876429i	$-0.340081\pi$
$108$	−10.4016	−	2.81441i	−1.00090	−	0.270816i
$109$	2.92513	+	3.48603i	0.280176	+	0.333901i	0.887719	−	0.460386i	$-0.152289\pi$
$109$	2.92513	+	3.48603i	0.280176	+	0.333901i	−0.607543	+	0.794287i	$0.707845\pi$
$110$	9.45850	+	8.83346i	0.901833	+	0.842237i
$111$	−21.9598	+	3.87211i	−2.08434	+	0.367525i
$112$	0.381215	+	1.45108i	0.0360215	+	0.137115i
$113$	11.4010	−	11.4010i	1.07251	−	1.07251i	0.0753576	−	0.997157i	$-0.475990\pi$
$113$	11.4010	−	11.4010i	1.07251	−	1.07251i	0.997157	−	0.0753576i	$-0.0240098\pi$
$114$	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
$117$	−12.7495	+	18.2082i	−1.17869	+	1.68335i
$118$	1.87355	−	5.12802i	0.172475	−	0.472072i
$119$	1.64594	−	1.38111i	0.150884	−	0.126606i
$120$	16.9048	+	5.55251i	1.54319	+	0.506872i
$121$	2.87466	−	4.97905i	0.261333	−	0.452641i
$122$	3.73176	−	4.43631i	0.337858	−	0.401644i
$123$	22.5386	+	10.5099i	2.03224	+	0.947649i
$124$	13.6175	+	7.90658i	1.22289	+	0.710032i
$125$	−7.02365	+	8.69875i	−0.628215	+	0.778040i
$126$	−1.49280	−	2.13750i	−0.132989	−	0.190424i
$127$	8.18718	+	11.6925i	0.726494	+	1.03754i	0.997193	+	0.0748773i	$0.0238565\pi$
$127$	8.18718	+	11.6925i	0.726494	+	1.03754i	−0.270698	+	0.962664i	$0.587255\pi$
$128$	−0.0968937	+	11.3133i	−0.00856427	+	0.999963i
$129$	11.2042	−	13.3526i	0.986471	−	1.17563i
$130$	8.81315	−	11.2629i	0.772964	−	0.987822i
$131$	−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	$0.117885\pi$
$132$	2.06315	−	22.9354i	0.179574	−	1.99627i
$133$	−0.405393	+	1.58388i	−0.0351520	+	0.137340i
$134$	5.89774	+	2.75895i	0.509487	+	0.238337i
$135$	−12.0400	+	0.426161i	−1.03624	+	0.0366781i
$136$	14.7095	−	6.79352i	1.26133	−	0.582539i
$137$	−1.39754	−	15.9740i	−0.119400	−	1.36475i	−0.785489	−	0.618875i	$-0.787589\pi$
$137$	−1.39754	−	15.9740i	−0.119400	−	1.36475i	0.666089	−	0.745872i	$-0.267967\pi$
$138$	−1.08534	+	1.87457i	−0.0923906	+	0.159574i
$139$	−1.32481	+	7.51335i	−0.112369	+	0.637274i	0.875651	+	0.482945i	$0.160433\pi$
$139$	−1.32481	+	7.51335i	−0.112369	+	0.637274i	−0.988019	+	0.154329i	$0.950678\pi$
$140$	0.886085	+	1.42428i	0.0748879	+	0.120373i
$141$	2.07205	+	3.58889i	0.174498	+	0.302239i
$142$	−12.1598	+	10.1779i	−1.02043	+	0.854114i
$143$	−16.7744	−	7.82203i	−1.40275	−	0.654111i
$144$	−6.63373	−	18.5073i	−0.552811	−	1.54228i
$145$	1.70220	+	2.25666i	0.141360	+	0.187406i
$146$	−8.22765	+	11.7198i	−0.680925	+	0.969934i
$147$	−1.68192	+	19.2244i	−0.138722	+	1.58560i
$148$	−11.1815	−	11.2364i	−0.919113	−	0.923622i
$149$	−11.4052	+	2.01105i	−0.934352	+	0.164752i	−0.620042	−	0.784569i	$-0.712884\pi$
$149$	−11.4052	+	2.01105i	−0.934352	+	0.164752i	−0.314311	+	0.949320i	$0.601773\pi$
$150$	19.8904	+	0.352667i	1.62405	+	0.0287952i
$151$		−	0.496458i		−	0.0404012i	−0.999796	−	0.0202006i	$-0.993570\pi$
$151$		−	0.496458i		−	0.0404012i	0.999796	−	0.0202006i	$-0.00643048\pi$
$152$	−6.08353	+	10.7234i	−0.493439	+	0.869780i
$153$	−19.9091	+	19.9091i	−1.60956	+	1.60956i
$154$	1.53693	−	1.53317i	0.123849	−	0.123547i
$155$	17.1557	+	3.95215i	1.37798	+	0.317444i
$156$	−25.4466	−	0.0622670i	−2.03735	−	0.00498535i
$157$	−0.267312	−	0.0233867i	−0.0213338	−	0.00186646i	0.0764839	−	0.997071i	$-0.475631\pi$
$157$	−0.267312	−	0.0233867i	−0.0213338	−	0.00186646i	−0.0978176	+	0.995204i	$0.531186\pi$
$158$	−1.92905	+	0.337710i	−0.153467	+	0.0268667i
$159$	8.24590	−	14.2823i	0.653942	−	1.13266i
$160$	3.62992	+	12.1171i	0.286970	+	0.957939i
$161$	−0.191888	+	0.0698413i	−0.0151229	+	0.00550427i
$162$	0.374658	+	0.447611i	0.0294359	+	0.0351677i
$163$	4.86431	−	18.1538i	0.381002	−	1.42192i	−0.463372	−	0.886164i	$-0.653361\pi$
$163$	4.86431	−	18.1538i	0.381002	−	1.42192i	0.844374	−	0.535754i	$-0.179973\pi$
$164$	3.02729	+	17.4177i	0.236392	+	1.36010i
$165$	−5.36485	−	25.1809i	−0.417653	−	1.96033i
$166$	−1.13244	−	4.24708i	−0.0878940	−	0.329638i
$167$	−19.3181	+	1.69012i	−1.49488	+	0.130785i	−0.805059	−	0.593195i	$-0.797866\pi$
$167$	−19.3181	+	1.69012i	−1.49488	+	0.130785i	−0.689821	+	0.723980i	$0.742311\pi$
$168$	1.03111	−	2.80091i	0.0795517	−	0.216095i
$169$	−2.54889	+	7.00302i	−0.196068	+	0.538693i
$170$	13.4711	−	12.1112i	1.03319	−	0.928883i
$171$	3.48313	−	21.1393i	0.266361	−	1.61656i
$172$	12.3414	+	1.11017i	0.941023	+	0.0846496i
$173$	−12.6922	+	5.91847i	−0.964970	+	0.449973i	−0.840238	−	0.542217i	$-0.817585\pi$
$173$	−12.6922	+	5.91847i	−0.964970	+	0.449973i	−0.124732	+	0.992190i	$0.539807\pi$
$174$	1.30769	−	4.85660i	0.0991358	−	0.368178i
$175$	1.41655	+	1.22903i	0.107081	+	0.0929062i
$176$	14.2170	−	8.11571i	1.07165	−	0.611744i
$177$	−8.89681	+	6.22961i	−0.668725	+	0.468246i
$178$	−2.09919	+	11.8205i	−0.157341	+	0.885984i
$179$	2.25279	+	3.90194i	0.168381	+	0.291645i	0.937851	−	0.347039i	$-0.112813\pi$
$179$	2.25279	+	3.90194i	0.168381	+	0.291645i	−0.769470	+	0.638683i	$0.779479\pi$
$180$	−13.1938	−	17.5808i	−0.983406	−	1.31039i
$181$	−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	$0.987968\pi$
$182$	−1.83578	−	1.54423i	−0.136077	−	0.114466i
$183$	−11.1396	+	2.98485i	−0.823464	+	0.220647i
$184$	−1.53448	+	0.128576i	−0.113123	+	0.00947876i
$185$	−15.6523	−	8.31299i	−1.15078	−	0.611183i
$186$	−13.2039	−	28.4066i	−0.968158	−	2.08287i
$187$	−19.2043	−	13.4470i	−1.40436	−	0.983344i
$188$	−1.25156	+	2.66693i	−0.0912795	+	0.194506i
$189$			2.02087i			0.146997i
$190$	−2.95981	+	13.4625i	−0.214727	+	0.976674i
$191$		−	8.05621i		−	0.582927i	−0.956582	−	0.291463i	$-0.905858\pi$
$191$		−	8.05621i		−	0.582927i	0.956582	−	0.291463i	$-0.0941421\pi$
$192$	13.0445	−	18.3414i	0.941404	−	1.32368i
$193$	4.15379	+	2.90852i	0.298996	+	0.209360i	0.713442	−	0.700715i	$-0.247135\pi$
$193$	4.15379	+	2.90852i	0.298996	+	0.209360i	−0.414445	+	0.910074i	$0.636024\pi$
$194$	−3.32013	+	1.54326i	−0.238371	+	0.110799i
$195$	−27.2031	+	8.33093i	−1.94806	+	0.596590i
$196$	−11.8974	+	6.83022i	−0.849816	+	0.487873i
$197$	20.7284	−	5.55415i	1.47683	−	0.395717i	0.571566	−	0.820556i	$-0.306336\pi$
$197$	20.7284	−	5.55415i	1.47683	−	0.395717i	0.905269	+	0.424840i	$0.139669\pi$
$198$	−18.3123	+	21.7696i	−1.30140	+	1.54710i
$199$	−2.13778	+	0.778089i	−0.151543	+	0.0551572i	−0.416678	−	0.909054i	$-0.636806\pi$
$199$	−2.13778	+	0.778089i	−0.151543	+	0.0551572i	0.265135	+	0.964211i	$0.414584\pi$
$200$	7.87624	+	11.7458i	0.556934	+	0.830557i
$201$	−6.47651	−	11.2176i	−0.456818	−	0.791231i
$202$	−14.8619	−	2.63931i	−1.04568	−	0.185701i
$203$	0.388399	−	0.271960i	0.0272602	−	0.0190878i
$204$	−31.7290	−	5.67477i	−2.22148	−	0.397313i
$205$	8.98173	+	17.6070i	0.627311	+	1.22973i
$206$	16.6676	+	4.48794i	1.16129	+	0.312690i
$207$	2.42517	−	1.13087i	0.168561	−	0.0786012i
$208$	−10.3032	−	14.8689i	−0.714399	−	1.03097i
$209$	17.8381	−	0.200329i	1.23389	−	0.0138571i
$210$	0.177141	−	3.33227i	0.0122239	−	0.229948i
$211$	−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	$0.950780\pi$
$212$	11.6817	−	0.993219i	0.802303	−	0.0682146i
$213$	31.4256	−	2.74938i	2.15325	−	0.188385i
$214$	−20.4090	+	5.44182i	−1.39513	+	0.371995i
$215$	13.5497	−	2.88679i	0.924082	−	0.196878i
$216$	−3.99817	+	14.7052i	−0.272041	+	1.00057i
$217$	0.764318	−	2.85247i	0.0518853	−	0.193639i
$218$	4.93505	−	4.13072i	0.334244	−	0.279768i
$219$	26.7686	−	9.74296i	1.80885	−	0.658368i
$220$	12.5087	−	13.3610i	0.843340	−	0.900801i
$221$	−12.9533	+	22.4357i	−0.871330	+	1.50919i
$222$	5.43799	+	31.0626i	0.364974	+	2.08478i
$223$	26.7010	+	2.33604i	1.78803	+	0.156433i	0.932466	−	0.361258i	$-0.117653\pi$
$223$	26.7010	+	2.33604i	1.78803	+	0.156433i	0.855568	+	0.517691i	$0.173208\pi$
$224$	2.05280	−	0.536609i	0.137159	−	0.0358537i
$225$	−19.8956	−	14.4262i	−1.32637	−	0.961746i
$226$	−16.1037	−	16.1431i	−1.07120	−	1.07383i
$227$	−12.3218	+	12.3218i	−0.817826	+	0.817826i	−0.985793	−	0.167967i	$-0.946280\pi$
$227$	−12.3218	+	12.3218i	−0.817826	+	0.817826i	0.167967	+	0.985793i	$0.446280\pi$
$228$	22.1366	−	10.5601i	1.46603	−	0.699363i
$229$			4.06734i			0.268778i	0.990929	+	0.134389i	$0.0429071\pi$
$229$			4.06734i			0.268778i	−0.990929	+	0.134389i	$0.957093\pi$
$230$	−1.59674	+	0.643732i	−0.105286	+	0.0424464i
$231$	−4.25307	+	0.749931i	−0.279832	+	0.0493418i
$232$	3.36431	−	1.21054i	0.220878	−	0.0794760i
$233$	−0.775629	+	8.86548i	−0.0508132	+	0.580797i	0.927522	+	0.373769i	$0.121935\pi$
$233$	−0.775629	+	8.86548i	−0.0508132	+	0.580797i	−0.978335	+	0.207028i	$0.933621\pi$
$234$	25.7282	+	18.0621i	1.68191	+	1.18075i
$235$	−0.456852	+	3.26189i	−0.0298017	+	0.212782i
$236$	−7.24886	−	2.65848i	−0.471861	−	0.173052i
$237$	3.53090	+	1.64649i	0.229357	+	0.106951i
$238$	−1.95034	−	2.33011i	−0.126422	−	0.151038i
$239$	−3.52279	−	6.10165i	−0.227870	−	0.394683i	0.729306	−	0.684187i	$-0.239843\pi$
$239$	−3.52279	−	6.10165i	−0.227870	−	0.394683i	−0.957177	+	0.289504i	$0.906510\pi$
$240$	7.88168	−	23.8974i	0.508760	−	1.54257i
$241$	−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	$0.928799\pi$
$242$	−7.03647	−	4.07399i	−0.452321	−	0.261886i
$243$	1.30753	+	14.9452i	0.0838783	+	0.958734i
$244$	−6.26742	−	5.28518i	−0.401231	−	0.338349i
$245$	−10.4551	+	11.2224i	−0.667952	+	0.716972i
$246$	14.9023	−	31.8562i	0.950135	−	2.03108i
$247$	−1.93851	−	19.6173i	−0.123344	−	1.24822i
$248$	11.2051	−	19.2444i	0.711527	−	1.22202i
$249$	−2.99068	+	8.21681i	−0.189526	+	0.520719i
$250$	12.2897	+	9.94799i	0.777271	+	0.629166i
$251$	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	$0.00492857\pi$
$252$	−3.02546	+	2.10744i	−0.190586	+	0.132756i
$253$	1.27798	+	1.82515i	0.0803462	+	0.114746i
$254$	16.5498	−	11.5582i	1.03843	−	0.725224i
$255$	−35.7663	+	4.40876i	−2.23977	+	0.276088i
$256$	15.9992	+	0.156603i	0.999952	+	0.00978770i
$257$	21.5424	+	10.0454i	1.34378	+	0.626615i	0.955518	−	0.294934i	$-0.0952975\pi$
$257$	21.5424	+	10.0454i	1.34378	+	0.626615i	0.388263	+	0.921549i	$0.373075\pi$
$258$	−18.8640	−	15.8682i	−1.17442	−	0.987909i
$259$	−1.48643	+	2.57458i	−0.0923624	+	0.159976i
$260$	−15.9129	−	12.4831i	−0.986876	−	0.774172i
$261$	−4.75962	+	3.99380i	−0.294613	+	0.247210i
$262$	0.647041	+	0.236401i	0.0399744	+	0.0146049i
$263$	3.31663	−	4.73664i	0.204512	−	0.292074i	−0.703773	−	0.710425i	$-0.748503\pi$
$263$	3.31663	−	4.73664i	0.204512	−	0.292074i	0.908285	+	0.418351i	$0.137392\pi$
$264$	−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
$268$	3.91195	−	8.33589i	0.238960	−	0.509195i
$269$	17.0745	−	3.01069i	1.04105	−	0.183565i	0.373114	−	0.927785i	$-0.378290\pi$
$269$	17.0745	−	3.01069i	1.04105	−	0.183565i	0.667934	+	0.744221i	$0.267179\pi$
$270$	0.581850	+	17.0279i	0.0354103	+	1.03628i
$271$	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	$0.747791\pi$
$272$	−9.58203	−	20.8141i	−0.580996	−	1.26204i
$273$	1.23516	+	4.60966i	0.0747550	+	0.278989i
$274$	−22.5930	+	1.94878i	−1.36489	+	0.117730i
$275$	8.95293	−	18.4005i	0.539882	−	1.10959i
$276$	2.64916	+	1.53815i	0.159461	+	0.0925858i
$277$	5.40976	−	20.1895i	0.325041	−	1.21307i	−0.589229	−	0.807966i	$-0.700568\pi$
$277$	5.40976	−	20.1895i	0.325041	−	1.21307i	0.914270	−	0.405104i	$-0.132765\pi$
$278$	10.6232	+	1.88656i	0.637136	+	0.113148i
$279$	−6.71976	+	38.1096i	−0.402301	+	2.28156i
$280$	2.01576	−	1.25065i	0.120465	−	0.0747405i
$281$	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	$0.533737\pi$
$282$	5.07904	−	2.92411i	0.302453	−	0.174128i
$283$	−5.24607	−	11.2502i	−0.311846	−	0.668756i	0.686446	−	0.727181i	$-0.259170\pi$
$283$	−5.24607	−	11.2502i	−0.311846	−	0.668756i	−0.998292	+	0.0584247i	$0.981392\pi$
$284$	14.3727	+	17.2141i	0.852865	+	1.02147i
$285$	20.1619	−	18.5857i	1.19429	−	1.10092i
$286$	−11.0910	+	23.7090i	−0.655827	+	1.40194i
$287$	3.00487	−	1.40119i	0.177372	−	0.0827098i
$288$	−26.1848	+	9.34948i	−1.54295	+	0.550923i
$289$	−10.1657	+	12.1150i	−0.597982	+	0.712647i
$290$	3.19435	−	2.40336i	0.187578	−	0.141130i
$291$	7.17292	+	1.26478i	0.420484	+	0.0741426i
$292$	16.5600	+	11.6559i	0.969100	+	0.682111i
$293$	−16.0335	−	4.29615i	−0.936684	−	0.250984i	−0.241982	−	0.970281i	$-0.577797\pi$
$293$	−16.0335	−	4.29615i	−0.936684	−	0.250984i	−0.694703	+	0.719297i	$0.744464\pi$
$294$	27.1845	+	2.41185i	1.58543	+	0.140662i
$295$	−8.62070	−	0.447694i	−0.501916	−	0.0260657i
$296$	−15.9099	+	15.7936i	−0.924746	+	0.917983i
$297$	21.2988	−	5.70701i	1.23588	−	0.331154i
$298$	2.82432	+	16.1329i	0.163608	+	0.934553i
$299$	1.88609	−	1.58262i	0.109075	−	0.0915252i
$300$	0.533162	−	28.1287i	0.0307821	−	1.62401i
$301$	−0.403533	−	2.28855i	−0.0232593	−	0.131910i
$302$	−0.702097		0.000859004i	−0.0404011		4.94301e-5i
$303$	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
$307$	−4.90021	−	3.43116i	−0.279669	−	0.195827i	0.425323	−	0.905042i	$-0.360161\pi$
$307$	−4.90021	−	3.43116i	−0.279669	−	0.195827i	−0.704992	+	0.709215i	$0.749050\pi$
$308$	−2.16558	−	2.17620i	−0.123395	−	0.124000i
$309$	−22.0726	−	26.3050i	−1.25566	−	1.49644i
$310$	5.61886	−	24.2550i	0.319130	−	1.37759i
$311$	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	$0.474712\pi$
$312$	−0.132088	+	35.9867i	−0.00747801	+	2.03735i
$313$	4.63175	−	9.93281i	0.261802	−	0.561436i	−0.730837	−	0.682553i	$-0.760870\pi$
$313$	4.63175	−	9.93281i	0.261802	−	0.561436i	0.992638	+	0.121117i	$0.0386476\pi$
$314$	−0.0335363	+	0.377995i	−0.00189256	+	0.0213315i
$315$	−2.53641	+	3.24962i	−0.142910	+	0.183096i
$316$	0.474256	+	2.72866i	0.0266790	+	0.153499i
$317$	16.1074	−	11.2785i	0.904680	−	0.633464i	−0.0258553	−	0.999666i	$-0.508231\pi$
$317$	16.1074	−	11.2785i	0.904680	−	0.633464i	0.930535	+	0.366202i	$0.119342\pi$
$318$	−20.1840	−	11.6862i	−1.13186	−	0.655327i
$319$	−3.96315	−	3.32548i	−0.221894	−	0.186191i
$320$	17.1424	−	5.11251i	0.958290	−	0.285798i
$321$	39.4852	+	14.3714i	2.20385	+	0.802135i
$322$	0.0984385	+	0.271491i	0.00548576	+	0.0151296i
$323$	1.89678	−	24.8975i	0.105540	−	1.38534i
$324$	0.633666	−	0.529072i	0.0352037	−	0.0293929i
$325$	−21.1180	−	8.08347i	−1.17141	−	0.448390i
$326$	−25.6650	−	6.91057i	−1.42145	−	0.382741i
$327$	−12.7541	+	1.11584i	−0.705302	+	0.0617059i
$328$	24.6376	−	4.25110i	1.36039	−	0.234728i
$329$	0.544100	+	0.0959395i	0.0299972	+	0.00528932i
$330$	−35.6205	+	7.54347i	−1.96084	+	0.415254i
$331$	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	$0.141810\pi$
$332$	−6.00824	+	1.59416i	−0.329745	+	0.0874906i
$333$	16.4637	−	35.3066i	0.902208	−	1.93479i
$334$	2.35676	+	27.3228i	0.128956	+	1.49504i
$335$	1.42796	−	10.1955i	0.0780178	−	0.557041i
$336$	−3.95930	−	1.46305i	−0.215998	−	0.0798160i
$337$	−10.0804	−	0.881918i	−0.549113	−	0.0480412i	−0.190776	−	0.981634i	$-0.561100\pi$
$337$	−10.0804	−	0.881918i	−0.549113	−	0.0480412i	−0.358337	+	0.933592i	$0.616656\pi$
$338$	9.89934	+	3.61679i	0.538453	+	0.196727i
$339$	7.87690	+	44.6721i	0.427814	+	2.42626i
$340$	−17.1044	−	19.0719i	−0.927618	−	1.03432i
$341$	−32.2219			−1.74492
$342$	−29.8894	−	4.96246i	−1.61623	−	0.268339i
$343$	3.67580	+	3.67580i	0.198474	+	0.198474i
$344$	1.59137	−	17.4514i	0.0858008	−	0.940918i
$345$	3.33749	+	0.768854i	0.179684	+	0.0413937i
$346$	8.34802	+	17.9597i	0.448792	+	0.965520i
$347$	−1.67207	+	19.1118i	−0.0897612	+	1.02598i	0.809079	+	0.587700i	$0.199966\pi$
$347$	−1.67207	+	19.1118i	−0.0897612	+	1.02598i	−0.898840	+	0.438276i	$0.855589\pi$
$348$	−6.86600	−	1.85776i	−0.368056	−	0.0995862i
$349$	−18.5333	−	10.7002i	−0.992064	−	0.572768i	−0.0861733	−	0.996280i	$-0.527464\pi$
$349$	−18.5333	−	10.7002i	−0.992064	−	0.572768i	−0.905891	+	0.423512i	$0.860797\pi$
$350$	1.74057	−	2.00118i	0.0930372	−	0.106968i
$351$	−8.33371	−	22.8967i	−0.444820	−	1.22213i
$352$	−11.4527	−	20.1200i	−0.610433	−	1.07240i
$353$	12.6808	+	3.39781i	0.674931	+	0.180847i	0.579975	−	0.814634i	$-0.303062\pi$
$353$	12.6808	+	3.39781i	0.674931	+	0.180847i	0.0949561	+	0.995481i	$0.469729\pi$
$354$	8.79460	+	12.5928i	0.467428	+	0.669298i
$355$	21.0340	+	13.6455i	1.11637	+	0.724226i
$356$	16.7131	+	2.98915i	0.885791	+	0.158425i
$357$	0.526847	+	6.02189i	0.0278837	+	0.318712i
$358$	5.52207	−	3.17917i	0.291850	−	0.168024i
$359$	13.6389	+	4.96416i	0.719835	+	0.261999i	0.675856	−	0.737034i	$-0.263774\pi$
$359$	13.6389	+	4.96416i	0.719835	+	0.261999i	0.0439794	+	0.999032i	$0.485996\pi$
$360$	−24.8858	+	18.6284i	−1.31160	+	0.981802i
$361$	9.86714	+	16.2370i	0.519323	+	0.854578i
$362$	12.3477	+	34.0546i	0.648981	+	1.78987i
$363$	6.83584	+	14.6595i	0.358789	+	0.769425i
$364$	−2.18705	+	2.59351i	−0.114633	+	0.135937i
$365$	21.5362	+	6.98626i	1.12726	+	0.365678i
$366$	4.20194	+	15.7590i	0.219639	+	0.823734i
$367$	−0.977727	−	1.39634i	−0.0510369	−	0.0728883i	0.792822	−	0.609453i	$-0.208611\pi$
$367$	−0.977727	−	1.39634i	−0.0510369	−	0.0728883i	−0.843859	+	0.536564i	$0.819722\pi$
$368$	0.179179	+	2.17031i	0.00934035	+	0.113135i
$369$	−37.6258	+	21.7232i	−1.95872	+	1.13087i
$370$	−11.7834	+	22.1214i	−0.612590	+	1.15003i
$371$	−0.751999	−	2.06610i	−0.0390418	−	0.107267i
$372$	−40.1958	+	18.6240i	−2.08405	+	0.965609i
$373$	−7.13464	−	26.6269i	−0.369418	−	1.37869i	−0.861332	−	0.508042i	$-0.830369\pi$
$373$	−7.13464	−	26.6269i	−0.369418	−	1.37869i	0.491914	−	0.870644i	$-0.336297\pi$
$374$	−19.0502	+	27.1358i	−0.985061	+	1.40316i
$375$	−8.71302	−	30.2236i	−0.449939	−	1.56074i
$376$	3.76943	+	1.77459i	0.194394	+	0.0915174i
$377$	−3.27908	+	4.68301i	−0.168881	+	0.241188i
$378$	2.85794	+	0.00349664i	0.146997	+	0.000179848i
$379$	−32.7053			−1.67996			−0.839979	−	0.542619i	$-0.817433\pi$
$379$	−32.7053			−1.67996			−0.839979	+	0.542619i	$0.817433\pi$
$380$	19.0337	+	4.20909i	0.976411	+	0.215922i
$381$	−40.1578			−2.05735
$382$	−11.3932	−	0.0139394i	−0.582926	−	0.000713200i
$383$	−5.04021	+	7.19816i	−0.257543	+	0.367809i	−0.927013	−	0.375030i	$-0.877632\pi$
$383$	−5.04021	+	7.19816i	−0.257543	+	0.367809i	0.669470	+	0.742839i	$0.266521\pi$
$384$	−25.9161	−	18.4794i	−1.32252	−	0.943023i
$385$	−3.03147	−	1.61002i	−0.154498	−	0.0820541i
$386$	4.12045	−	5.86931i	0.209725	−	0.298740i
$387$	7.88154	+	29.4143i	0.400641	+	1.49521i
$388$	2.17675	+	4.69804i	0.110508	+	0.238507i
$389$	1.26316	+	3.47052i	0.0640450	+	0.175962i	0.967587	−	0.252537i	$-0.0812648\pi$
$389$	1.26316	+	3.47052i	0.0640450	+	0.175962i	−0.903542	+	0.428499i	$0.859043\pi$
$390$	11.7346	+	38.4854i	0.594206	+	1.94878i
$391$	2.70086	−	1.55935i	0.136589	−	0.0788595i
$392$	9.63880	+	16.8373i	0.486833	+	0.850413i
$393$	−0.786039	−	1.12258i	−0.0396504	−	0.0566267i
$394$	−7.81888	−	29.3239i	−0.393909	−	1.47732i
$395$	1.40708	+	2.75831i	0.0707978	+	0.138786i
$396$	30.7552	+	25.9352i	1.54551	+	1.30329i
$397$	−6.39040	−	13.7043i	−0.320725	−	0.687797i	0.678165	−	0.734910i	$-0.262776\pi$
$397$	−6.39040	−	13.7043i	−0.320725	−	0.687797i	−0.998890	+	0.0471133i	$0.984998\pi$
$398$	1.09668	+	3.02462i	0.0549718	+	0.151611i
$399$	−2.99601	−	3.49015i	−0.149988	−	0.174726i
$400$	16.6248	−	11.1183i	0.831238	−	0.555917i
$401$	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	$0.439071\pi$
$402$	−15.8753	+	9.13975i	−0.791790	+	0.455849i
$403$	3.10329	+	35.4707i	0.154586	+	1.76692i
$404$	−3.75826	+	21.0134i	−0.186981	+	1.04545i
$405$	0.502300	−	0.774278i	0.0249595	−	0.0384742i
$406$	−0.383937	−	0.549749i	−0.0190545	−	0.0272836i
$407$	31.3323	+	8.39547i	1.55309	+	0.416148i
$408$	−8.08023	+	44.8618i	−0.400031	+	2.22099i
$409$	4.01538	+	11.0322i	0.198548	+	0.545505i	0.998511	−	0.0545430i	$-0.0173702\pi$
$409$	4.01538	+	11.0322i	0.198548	+	0.545505i	−0.799964	+	0.600048i	$0.795148\pi$
$410$	24.9156	−	12.6716i	1.23049	−	0.625806i
$411$	39.0685	+	22.5562i	1.92711	+	1.11261i
$412$	6.37574	−	23.5638i	0.314110	−	1.16090i
$413$	−0.126201	+	1.44249i	−0.00620995	+	0.0709801i
$414$	−1.59510	−	3.43166i	−0.0783949	−	0.168657i
$415$	−5.89205	+	3.68565i	−0.289230	+	0.180921i
$416$	−21.0456	+	14.5452i	−1.03184	+	0.713137i
$417$	−15.1773	−	15.1773i	−0.743236	−	0.743236i
$418$	−0.252444	−	25.2272i	−0.0123474	−	1.23390i
$419$	−11.0090			−0.537826			−0.268913	−	0.963164i	$-0.586664\pi$
$419$	−11.0090			−0.537826			−0.268913	+	0.963164i	$0.586664\pi$
$420$	−4.71223	−	0.256281i	−0.229933	−	0.0125052i
$421$	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	$0.824625\pi$
$422$	18.6262	+	6.80519i	0.906708	+	0.331272i
$423$	−7.21235	−	0.630999i	−0.350677	−	0.0306802i
$424$	−1.38441	−	16.5221i	−0.0672329	−	0.802386i
$425$	−24.5651	−	14.7285i	−1.19158	−	0.714439i
$426$	−3.83384	−	44.4472i	−0.185750	−	2.15347i
$427$	−0.649789	+	1.39348i	−0.0314455	+	0.0674351i
$428$	7.66058	+	28.8721i	0.370288	+	1.39558i
$429$	45.0951	−	26.0357i	2.17721	−	1.25701i
$430$	−4.05909	−	19.1672i	−0.195747	−	0.924323i
$431$	−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	$0.770991\pi$
$432$	20.7894	+	5.67970i	1.00023	+	0.273265i
$433$	14.3543	−	1.25584i	0.689825	−	0.0603519i	0.263148	−	0.964756i	$-0.415239\pi$
$433$	14.3543	−	1.25584i	0.689825	−	0.0603519i	0.426678	+	0.904404i	$0.359684\pi$
$434$	−4.03268	−	1.08584i	−0.193575	−	0.0521222i
$435$	−7.94747	+	0.281304i	−0.381052	+	0.0134875i
$436$	−5.83317	−	6.98635i	−0.279358	−	0.334586i
$437$	−0.978692	+	2.16187i	−0.0468172	+	0.103416i
$438$	−13.7323	−	37.8733i	−0.656154	−	1.80966i
$439$	3.48934	+	1.27002i	0.166537	+	0.0606146i	0.423943	−	0.905689i	$-0.360646\pi$
$439$	3.48934	+	1.27002i	0.166537	+	0.0606146i	−0.257406	+	0.966303i	$0.582868\pi$
$440$	−18.8737	−	17.7131i	−0.899769	−	0.844441i
$441$	−25.8265	−	21.6710i	−1.22983	−	1.03195i
$442$	31.7064	+	18.3575i	1.50812	+	0.873176i
$443$	−29.2117	+	20.4542i	−1.38789	+	0.971810i	−0.389171	+	0.921165i	$0.627239\pi$
$443$	−29.2117	+	20.4542i	−1.38789	+	0.971810i	−0.998717	+	0.0506443i	$0.983873\pi$
$444$	43.9385	−	7.63673i	2.08523	−	0.362423i
$445$	18.8397	−	2.32229i	0.893087	−	0.110087i
$446$	3.34985	−	37.7569i	0.158620	−	1.78784i
$447$	13.7698	−	29.5295i	0.651290	−	1.39670i
$448$	−0.755327	−	2.90403i	−0.0356859	−	0.137202i
$449$	−10.4332	−	6.02361i	−0.492373	−	0.284272i	0.233185	−	0.972432i	$-0.425085\pi$
$449$	−10.4332	−	6.02361i	−0.492373	−	0.284272i	−0.725559	+	0.688160i	$0.758419\pi$
$450$	−20.4361	+	28.1116i	−0.963368	+	1.32520i
$451$	−23.2536	−	27.7126i	−1.09497	−	1.30493i
$452$	−22.8577	+	22.7461i	−1.07514	+	1.06989i
$453$	1.14413	+	0.801127i	0.0537558	+	0.0376402i
$454$	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	0.951163	−	0.308689i	$-0.0998903\pi$
$457$	13.7345	+	13.7345i	0.642474	+	0.642474i	−0.308689	+	0.951163i	$0.599890\pi$
$458$	5.75209	+	0.00703758i	0.268777	+	0.000328845i
$459$	−5.35945	−	30.3950i	−0.250158	−	1.41872i
$460$	0.907611	+	2.25924i	0.0423176	+	0.105338i
$461$	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	$0.259395\pi$
$462$	1.05320	+	6.01604i	0.0489994	+	0.279892i
$463$	18.3765	−	4.92398i	0.854031	−	0.228837i	0.194861	−	0.980831i	$-0.437574\pi$
$463$	18.3765	−	4.92398i	0.854031	−	0.228837i	0.659170	+	0.751994i	$0.270908\pi$
$464$	−1.70614	−	4.75994i	−0.0792057	−	0.220975i
$465$	−36.7920	+	33.1593i	−1.70619	+	1.53772i
$466$	12.5363	+	1.11224i	0.580735	+	0.0515237i
$467$	7.78451	+	2.08585i	0.360224	+	0.0965218i	0.434392	−	0.900724i	$-0.356963\pi$
$467$	7.78451	+	2.08585i	0.360224	+	0.0965218i	−0.0741677	+	0.997246i	$0.523630\pi$
$468$	25.5881	−	36.3539i	1.18281	−	1.68046i
$469$	−1.70067	−	0.299874i	−0.0785296	−	0.0138469i
$470$	4.61221	+	0.651729i	0.212745	+	0.0300620i
$471$	0.485253	−	0.578302i	0.0223593	−	0.0266468i
$472$	−3.77219	+	10.2468i	−0.173629	+	0.471649i
$473$	−22.9805	+	10.7160i	−1.05664	+	0.492720i
$474$	2.33459	−	4.99060i	0.107231	−	0.229226i
$475$	21.7213	−	1.78496i	0.996641	−	0.0818994i
$476$	−3.29864	+	2.75416i	−0.151193	+	0.126237i
$477$	12.1764	+	26.1124i	0.557519	+	1.19560i
$478$	−8.63513	+	4.97142i	−0.394962	+	0.227387i
$479$	−10.2787	−	8.62489i	−0.469648	−	0.394081i	0.377018	−	0.926206i	$-0.376949\pi$
$479$	−10.2787	−	8.62489i	−0.469648	−	0.394081i	−0.846666	+	0.532124i	$0.821394\pi$
$480$	−33.7824	−	11.1877i	−1.54195	−	0.510647i
$481$	6.22434	−	35.3000i	0.283805	−	1.60954i
$482$	16.7645	+	2.97719i	0.763603	+	0.135607i
$483$	0.148691	−	0.554922i	0.00676567	−	0.0252498i
$484$	−5.77367	+	9.94401i	−0.262439	+	0.452001i
$485$	3.87562	+	4.30021i	0.175983	+	0.195262i
$486$	21.1379	−	1.82327i	0.958836	−	0.0827053i
$487$	−3.93663	−	14.6917i	−0.178386	−	0.665745i	−0.995950	−	0.0899075i	$-0.971343\pi$
$487$	−3.93663	−	14.6917i	−0.178386	−	0.665745i	0.817564	−	0.575837i	$-0.195324\pi$
$488$	−7.48521	+	8.85432i	−0.338840	+	0.400816i
$489$	33.9875	+	40.5048i	1.53697	+	1.83169i
$490$	15.8527	+	14.8051i	0.716154	+	0.668828i
$491$	−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	$0.583284\pi$
$492$	−45.0257	−	21.1301i	−2.02992	−	0.952619i
$493$	−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
$497$	2.41228	−	3.44509i	0.108206	−	0.154534i
$498$	11.6151	+	4.24367i	0.520487	+	0.190163i
$499$	16.3365	−	13.7079i	0.731322	−	0.613652i	−0.199170	−	0.979965i	$-0.563825\pi$
$499$	16.3365	−	13.7079i	0.731322	−	0.613652i	0.930492	+	0.366313i	$0.119380\pi$
$500$	14.0898	−	17.3631i	0.630116	−	0.776501i
$501$	27.2783	−	47.2475i	1.21871	−	2.11086i
$502$	−21.6329	−	18.1973i	−0.965525	−	0.812187i
$503$	−34.7351	−	16.1973i	−1.54876	−	0.722200i	−0.554806	−	0.831980i	$-0.687208\pi$
$503$	−34.7351	−	16.1973i	−1.54876	−	0.722200i	−0.993956	+	0.109780i	$0.964985\pi$
$504$	2.97513	+	4.28230i	0.132523	+	0.190749i
$505$	2.91982	+	23.6872i	0.129930	+	1.05407i
$506$	2.58336	−	1.80418i	0.114845	−	0.0802058i
$507$	−12.0259	−	17.1748i	−0.534090	−	0.762759i
$508$	−16.3171	−	23.4250i	−0.723953	−	1.03932i
$509$	−2.35274	+	2.80389i	−0.104283	+	0.124280i	−0.815662	−	0.578529i	$-0.803627\pi$
$509$	−2.35274	+	2.80389i	−0.104283	+	0.124280i	0.711378	+	0.702809i	$0.248071\pi$
$510$	6.17304	+	50.5888i	0.273347	+	2.24011i
$511$	1.29894	−	3.56880i	0.0574616	−	0.157874i
$512$	0.249153	−	22.6260i	0.0110111	−	0.999939i
$513$	16.7918	+	16.4189i	0.741378	+	0.724911i
$514$	14.2436	−	30.4482i	0.628259	−	1.34301i
$515$	−0.965423	−	27.2754i	−0.0425416	−	1.20190i
$516$	−22.4736	+	26.6503i	−0.989345	+	1.17321i
$517$	−0.525408	−	6.00544i	−0.0231074	−	0.264119i
$518$	3.63843	+	2.10659i	0.159863	+	0.0925581i
$519$	6.84162	−	38.8008i	0.300314	−	1.70316i
$520$	−17.6814	+	22.4826i	−0.775379	+	0.985928i
$521$	−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	$-0.375209\pi$
$522$	5.63984	+	6.73803i	0.246849	+	0.294916i
$523$	20.6529	+	9.63059i	0.903087	+	0.421116i	0.817974	−	0.575255i	$-0.195097\pi$
$523$	20.6529	+	9.63059i	0.903087	+	0.421116i	0.0851127	+	0.996371i	$0.472875\pi$
$524$	0.335440	−	0.914645i	0.0146538	−	0.0399565i
$525$	−5.11828	+	1.28129i	−0.223380	+	0.0559199i
$526$	−6.69287	−	4.69861i	−0.291823	−	0.204869i
$527$	−3.93084	+	44.9297i	−0.171230	+	1.95717i
$528$	−4.23853	+	45.8605i	−0.184458	+	1.99582i
$529$	22.3587	−	3.94244i	0.972117	−	0.171410i
$530$	−6.93121	−	17.1924i	−0.301073	−	0.746792i
$531$		−	18.9746i		−	0.823427i
$532$	0.818534	−	3.16577i	0.0354880	−	0.137254i
$533$	−28.2672	+	28.2672i	−1.22439	+	1.22439i
$534$	−23.8539	−	23.9123i	−1.03226	−	1.03479i
$535$	17.7111	+	28.3138i	0.765717	+	1.22411i
$536$	−11.7819	−	5.54675i	−0.508903	−	0.239583i
$537$	−12.6276	−	1.10477i	−0.544922	−	0.0476745i
$538$	−4.22821	−	24.1521i	−0.182291	−	1.04127i
$539$	14.0362	−	24.3114i	0.604582	−	1.04717i
$540$	24.0820	−	0.793397i	1.03633	−	0.0341424i
$541$	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	$0.388571\pi$
$542$	3.35871	−	2.81129i	0.144269	−	0.120755i
$543$	18.6512	−	69.6071i	0.800398	−	2.98712i
$544$	−29.4521	+	13.5150i	−1.26275	+	0.579451i
$545$	−8.53664	−	5.53801i	−0.365670	−	0.237222i
$546$	6.52118	−	1.73880i	0.279081	−	0.0744136i
$547$	18.1454	−	1.58752i	0.775842	−	0.0678773i	0.307644	−	0.951501i	$-0.400459\pi$
$547$	18.1454	−	1.58752i	0.775842	−	0.0678773i	0.468197	+	0.883624i	$0.344904\pi$
$548$	2.71690	+	31.9547i	0.116060	+	1.36504i
$549$	6.89098	−	18.9328i	0.294100	−	0.808033i
$550$	−26.0067	−	12.6932i	−1.10893	−	0.541239i
$551$	0.895833	−	5.43686i	0.0381638	−	0.231618i
$552$	2.17986	−	3.74382i	0.0927808	−	0.159348i
$553$	0.470742	−	0.219511i	0.0200180	−	0.00933455i
$554$	−28.5429	−	7.68549i	−1.21267	−	0.326525i
$555$	44.4159	−	22.6576i	1.88535	−	0.961760i
$556$	2.68637	−	15.0202i	0.113928	−	0.636997i
$557$	−28.3136	+	19.8254i	−1.19969	+	0.840029i	−0.990455	−	0.137838i	$-0.955985\pi$
$557$	−28.3136	+	19.8254i	−1.19969	+	0.840029i	−0.209231	+	0.977866i	$0.567096\pi$
$558$	53.8835	+	9.56910i	2.28107	+	0.405093i
$559$	14.0096	+	24.2654i	0.592545	+	1.02632i
$560$	−1.76519	−	2.85288i	−0.0745931	−	0.120556i
$561$	61.9795	−	22.5587i	2.61678	−	0.952429i
$562$	17.0350	−	20.2512i	0.718579	−	0.854244i
$563$	5.56706	−	1.49169i	0.234623	−	0.0628672i	−0.139591	−	0.990209i	$-0.544579\pi$
$563$	5.56706	−	1.49169i	0.234623	−	0.0628672i	0.374215	+	0.927342i	$0.377912\pi$
$564$	−4.12652	−	7.18791i	−0.173758	−	0.302665i
$565$	−16.9108	+	31.8410i	−0.711443	+	1.33956i
$566$	−15.9193	+	7.39959i	−0.669138	+	0.311028i
$567$	−0.126817	−	0.0887980i	−0.00532580	−	0.00372917i
$568$	24.3693	−	20.2963i	1.02251	−	0.851615i
$569$			31.1948i			1.30775i	0.756601	+	0.653877i	$0.226859\pi$
$569$			31.1948i			1.30775i	−0.756601	+	0.653877i	$0.773141\pi$
$570$	−26.2493	−	28.5454i	−1.09946	−	1.19563i
$571$			43.7061i			1.82904i	0.404537	+	0.914522i	$0.367433\pi$
$571$			43.7061i			1.82904i	−0.404537	+	0.914522i	$0.632567\pi$
$572$	33.5104	+	15.7261i	1.40114	+	0.657542i
$573$	18.5662	+	13.0002i	0.775613	+	0.543090i
$574$	−1.97638	−	4.25194i	−0.0824927	−	0.177473i
$575$	1.71509	+	2.11385i	0.0715240	+	0.0881538i
$576$	13.1768	+	37.0470i	0.549035	+	1.54363i
$577$	11.9703	−	3.20743i	0.498329	−	0.133527i	−0.000895290	−	1.00000i	$-0.500285\pi$
$577$	11.9703	−	3.20743i	0.498329	−	0.133527i	0.499224	+	0.866473i	$0.333618\pi$
$578$	17.1156	+	14.3974i	0.711915	+	0.598854i
$579$	−13.4058	+	4.87932i	−0.557127	+	0.202778i
$580$	−3.39334	−	4.52164i	−0.140901	−	0.187751i
$581$	0.582888	+	1.00959i	0.0241823	+	0.0418849i
$582$	1.80108	−	10.1418i	0.0746570	−	0.420393i
$583$	−19.6518	+	13.7604i	−0.813896	+	0.569896i
$584$	16.5126	−	23.3992i	0.683296	−	0.968265i
$585$	15.3369	−	47.2782i	0.634101	−	1.95471i
$586$	−6.10341	+	22.6673i	−0.252130	+	0.936377i
$587$	12.1807	−	5.67994i	0.502750	−	0.234436i	−0.154662	−	0.987967i	$-0.549429\pi$
$587$	12.1807	−	5.67994i	0.502750	−	0.234436i	0.657412	+	0.753531i	$0.271651\pi$
$588$	3.45790	−	38.4404i	0.142602	−	1.58526i
$589$	−17.4920	−	29.5262i	−0.720745	−	1.21661i
$590$	−0.648050	+	12.1907i	−0.0266798	+	0.501884i
$591$	−20.6491	+	56.7328i	−0.849389	+	2.33368i
$592$	22.3079	+	22.5274i	0.916850	+	0.925869i
$593$	6.51969	−	0.570399i	0.267731	−	0.0234235i	0.0475004	−	0.998871i	$-0.484874\pi$
$593$	6.51969	−	0.570399i	0.267731	−	0.0234235i	0.220231	+	0.975448i	$0.429319\pi$
$594$	−8.03407	−	30.1310i	−0.329642	−	1.23629i
$595$	−2.61480	+	4.03062i	−0.107196	+	0.165239i
$596$	22.8202	−	3.96627i	0.934753	−	0.162465i
$597$	1.65654	−	6.18228i	0.0677976	−	0.253024i
$598$	−2.23489	−	2.67007i	−0.0913916	−	0.109187i
$599$	−20.8254	+	7.57984i	−0.850904	+	0.309704i	−0.730409	−	0.683010i	$-0.760670\pi$
$599$	−20.8254	+	7.57984i	−0.850904	+	0.309704i	−0.120495	+	0.992714i	$0.538448\pi$
$600$	−39.7790	−	0.802675i	−1.62397	−	0.0327691i
$601$	−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	$0.959943\pi$
$602$	−3.23720	+	0.566722i	−0.131938	+	0.0230979i
$603$	22.5433	+	1.97228i	0.918035	+	0.0803176i
$604$	−0.00242963	+	0.992913i	−9.88601e−5	+	0.0404010i
$605$	−2.88600	+	12.5277i	−0.117333	+	0.509325i
$606$	30.0650	−	29.9915i	1.22131	−	1.21832i
$607$	5.20830	−	5.20830i	0.211399	−	0.211399i	−0.593463	−	0.804861i	$-0.702240\pi$
$607$	5.20830	−	5.20830i	0.211399	−	0.211399i	0.804861	+	0.593463i	$0.202240\pi$
$608$	12.2195	−	21.4169i	0.495566	−	0.868570i
$609$			1.33395i			0.0540545i
$610$	−5.07391	+	11.9285i	−0.205437	+	0.482972i
$611$	−6.56034	+	1.15677i	−0.265403	+	0.0467977i
$612$	39.9155	−	39.7206i	1.61349	−	1.60561i
$613$	2.44048	−	27.8948i	0.0985701	−	1.12666i	−0.772337	−	0.635213i	$-0.780912\pi$
$613$	2.44048	−	27.8948i	0.0985701	−	1.12666i	0.870907	−	0.491448i	$-0.163532\pi$
$614$	−4.86087	+	6.92399i	−0.196169	+	0.279430i
$615$	−55.0705	−	7.71303i	−2.22066	−	0.311019i
$616$	−3.08136	+	3.05882i	−0.124151	+	0.123243i
$617$	9.57599	+	4.46536i	0.385515	+	0.179769i	0.605707	−	0.795688i	$-0.292891\pi$
$617$	9.57599	+	4.46536i	0.385515	+	0.179769i	−0.220192	+	0.975457i	$0.570668\pi$
$618$	−37.2391	+	31.1698i	−1.49798	+	1.25383i
$619$	14.7471	+	25.5427i	0.592736	+	1.02665i	0.993862	+	0.110626i	$0.0352854\pi$
$619$	14.7471	+	25.5427i	0.592736	+	1.02665i	−0.401127	+	0.916023i	$0.631381\pi$
$620$	−34.2920	−	7.98823i	−1.37720	−	0.320815i
$621$	−0.509354	+	2.88869i	−0.0204397	+	0.115919i
$622$	14.1747	−	24.4820i	0.568353	−	0.981640i
$623$	−0.277514	−	3.17200i	−0.0111183	−	0.127083i
$624$	50.8926	+	0.249067i	2.03734	+	0.00997066i
$625$	9.32119	−	23.1973i	0.372848	−	0.927893i
$626$	−14.0391	−	6.56746i	−0.561115	−	0.262488i
$627$	−28.3234	+	41.4326i	−1.13113	+	1.65466i
$628$	0.534507	+	0.0480815i	0.0213292	+	0.00191866i
$629$	15.5288	−	42.6651i	0.619174	−	1.70117i
$630$	4.59127	+	3.59264i	0.182921	+	0.143134i
$631$	−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	$0.362915\pi$
$632$	3.85973	−	0.665977i	0.153532	−	0.0264911i
$633$	−22.6274	−	32.3153i	−0.899360	−	1.28442i
$634$	−15.9223	−	22.7988i	−0.632357	−	0.905455i
$635$	−25.1606	−	19.6384i	−0.998467	−	0.779326i
$636$	−16.5616	+	28.5242i	−0.656712	+	1.13106i
$637$	−28.1144	−	13.1100i	−1.11393	−	0.519436i
$638$	−4.70979	+	5.59899i	−0.186462	+	0.221666i
$639$	−27.5557	+	47.7279i	−1.09009	+	1.88809i
$640$	−7.20052	−	24.2519i	−0.284625	−	0.958639i
$641$	−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	$0.472438\pi$
$642$	20.3926	−	55.8156i	0.804831	−	2.20287i
$643$	1.87568	−	2.67874i	0.0739695	−	0.105639i	−0.780463	−	0.625202i	$-0.785016\pi$
$643$	1.87568	−	2.67874i	0.0739695	−	0.105639i	0.854432	+	0.519563i	$0.173905\pi$
$644$	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	$-0.805238\pi$
$647$	−6.21119	+	6.21119i	−0.244187	+	0.244187i	0.574393	+	0.818580i	$0.305238\pi$
$648$	−0.747124	−	0.897054i	−0.0293498	−	0.0352396i
$649$	15.5594	−	2.74354i	0.610759	−	0.107693i
$650$	−11.4683	+	29.8513i	−0.449823	+	1.17087i
$651$	5.34039	+	6.36443i	0.209306	+	0.249442i
$652$	−9.81743	+	36.2838i	−0.384480	+	1.42098i
$653$	2.70611	+	10.0993i	0.105898	+	0.395217i	0.998446	−	0.0557363i	$-0.0177506\pi$
$653$	2.70611	+	10.0993i	0.105898	+	0.395217i	−0.892547	+	0.450954i	$0.851084\pi$
$654$	1.55596	+	18.0389i	0.0608429	+	0.705377i
$655$	0.0564890	−	1.08774i	0.00220721	−	0.0425015i
$656$	−5.96932	−	34.8502i	−0.233063	−	1.36067i
$657$	−12.8807	+	48.0713i	−0.502522	+	1.87544i
$658$	0.136620	−	0.769307i	0.00532602	−	0.0299907i
$659$	6.57770	−	37.3040i	0.256231	−	1.45316i	−0.536663	−	0.843797i	$-0.680315\pi$
$659$	6.57770	−	37.3040i	0.256231	−	1.45316i	0.792894	−	0.609360i	$-0.208574\pi$
$660$	10.6064	+	50.3880i	0.412855	+	1.96135i
$661$	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	$0.663798\pi$
$662$	−14.5328	−	25.2429i	−0.564834	−	0.981092i
$663$	−30.8024	−	66.0560i	−1.19627	−	2.56540i
$664$	2.24408	+	8.49968i	0.0870871	+	0.329852i
$665$	−0.170339	−	3.65187i	−0.00660547	−	0.141613i
$666$	−49.9026	−	23.3443i	−1.93369	−	0.904574i
$667$	0.623735	−	0.290852i	0.0241511	−	0.0112618i
$668$	38.6444	−	3.28568i	1.49520	−	0.127127i
$669$	−48.4707	+	57.7651i	−1.87398	+	2.23333i
$670$	−14.4162	−	2.03708i	−0.556946	−	0.0786993i
$671$	16.5215	+	2.91318i	0.637805	+	0.112462i
$672$	−2.07592	+	5.59677i	−0.0800802	+	0.215900i
$673$	−35.1323	−	9.41368i	−1.35425	−	0.362871i	−0.492549	−	0.870285i	$-0.663935\pi$
$673$	−35.1323	−	9.41368i	−1.35425	−	0.362871i	−0.861702	+	0.507414i	$0.830601\pi$
$674$	−1.26466	+	14.2543i	−0.0487130	+	0.549054i
$675$	25.4631	−	8.79467i	0.980076	−	0.338507i
$676$	5.13204	−	13.9935i	0.197386	−	0.538212i
$677$	4.50308	−	1.20660i	0.173067	−	0.0463733i	−0.171245	−	0.985229i	$-0.554779\pi$
$677$	4.50308	−	1.20660i	0.173067	−	0.0463733i	0.344312	+	0.938855i	$0.388112\pi$
$678$	63.1895	−	11.0623i	2.42678	−	0.424845i
$679$	0.743868	−	0.624179i	0.0285470	−	0.0239538i
$680$	−27.0014	+	24.1563i	−1.03546	+	0.926352i
$681$	−8.51308	−	48.2801i	−0.326222	−	1.85010i
$682$	−0.0557525	+	45.5687i	−0.00213487	+	1.74491i
$683$	13.6377	+	13.6377i	0.521832	+	0.521832i	0.918124	−	0.396292i	$-0.129703\pi$
$683$	13.6377	+	13.6377i	0.521832	+	0.521832i	−0.396292	+	0.918124i	$0.629703\pi$
$684$	−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
$687$	−9.37353	−	6.56341i	−0.357622	−	0.250410i
$688$	−24.6773	−	2.28073i	−0.940813	−	0.0869520i
$689$	17.0404	+	20.3080i	0.649189	+	0.773673i
$690$	1.09310	−	4.71859i	0.0416135	−	0.179634i
$691$	−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	$0.890507\pi$
$692$	25.4133	−	11.7748i	0.966069	−	0.447611i
$693$	3.18862	−	6.83801i	0.121125	−	0.259754i
$694$	27.0253	+	2.39773i	1.02587	+	0.0910164i
$695$	−2.08706	−	16.9314i	−0.0791668	−	0.642244i
$696$	−2.63914	+	9.70676i	−0.100036	+	0.367934i
$697$	−41.4787	+	29.0437i	−1.57112	+	1.10011i
$698$	−15.1644	+	26.1915i	−0.573982	+	0.991362i
$699$	−19.1796	−	16.0936i	−0.725439	−	0.608716i
$700$	−2.82708	−	2.46499i	−0.106854	−	0.0931680i
$701$	−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	$0.675320\pi$
$702$	−32.3952	+	11.7460i	−1.22268	+	0.443325i
$703$	9.31595	+	33.2686i	0.351358	+	1.25475i
$704$	−28.4737	+	16.1618i	−1.07314	+	0.609120i
$705$	−6.78007	−	6.31651i	−0.255352	−	0.237894i
$706$	4.82717	−	17.9275i	0.181673	−	0.674710i
$707$	3.98816	−	0.348918i	0.149990	−	0.0131224i
$708$	17.8241	−	12.4157i	0.669869	−	0.466609i
$709$	25.1895	+	4.44158i	0.946011	+	0.166807i	0.625313	−	0.780374i	$-0.284971\pi$
$709$	25.1895	+	4.44158i	0.946011	+	0.166807i	0.320698	+	0.947182i	$0.396083\pi$
$710$	19.3340	−	29.7229i	0.725591	−	1.11548i
$711$	−5.89445	+	3.40316i	−0.221059	+	0.127629i
$712$	4.25621	−	23.6307i	0.159508	−	0.885596i
$713$	1.81150	−	3.88476i	0.0678410	−	0.145486i
$714$	8.51715	−	0.734655i	0.318746	−	0.0274938i
$715$	40.9862	+	5.74043i	1.53280	+	0.214680i
$716$	−4.48646	−	7.81488i	−0.167667	−	0.292056i
$717$	19.7464	+	1.72759i	0.737444	+	0.0645180i
$718$	7.04398	−	19.2798i	0.262879	−	0.719514i
$719$	5.61705	+	31.8559i	0.209481	+	1.18802i	0.890231	+	0.455508i	$0.150542\pi$
$719$	5.61705	+	31.8559i	0.209481	+	1.18802i	−0.680751	+	0.732515i	$0.738346\pi$
$720$	26.3014	+	35.2260i	0.980196	+	1.31280i
$721$	−4.57807			−0.170496
$722$	22.9796	−	13.9261i	0.855213	−	0.518277i
$723$	−23.9514	−	23.9514i	−0.890763	−	0.890763i
$724$	48.1818	−	17.4033i	1.79066	−	0.646790i
$725$	−5.11699	−	3.71031i	−0.190040	−	0.137797i
$726$	20.7435	−	9.64197i	0.769863	−	0.357847i
$727$	3.19906	−	36.5655i	0.118647	−	1.35614i	−0.670489	−	0.741919i	$-0.733916\pi$
$727$	3.19906	−	36.5655i	0.118647	−	1.35614i	0.789136	−	0.614219i	$-0.210529\pi$
$728$	3.66399	+	3.09744i	0.135796	+	0.114799i
$729$	−37.6247	−	21.7226i	−1.39351	−	0.804542i
$730$	9.91732	−	30.4447i	0.367057	−	1.12681i
$731$	12.1387	+	33.3508i	0.448966	+	1.23352i
$732$	22.2938	−	5.91517i	0.824002	−	0.218631i
$733$	4.77784	+	1.28022i	0.176474	+	0.0472859i	0.345974	−	0.938244i	$-0.387549\pi$
$733$	4.77784	+	1.28022i	0.176474	+	0.0472859i	−0.169500	+	0.985530i	$0.554215\pi$
$734$	−1.97641	+	1.38030i	−0.0729507	+	0.0509477i
$735$	−8.99166	−	42.2040i	−0.331662	−	1.55672i
$736$	3.06958	−	0.249642i	0.113146	−	0.00920192i
$737$	1.64224	+	18.7709i	0.0604929	+	0.691436i
$738$	30.6562	+	53.2484i	1.12847	+	1.96010i
$739$	−45.7989	−	16.6694i	−1.68474	−	0.613195i	−0.690793	−	0.723053i	$-0.742738\pi$
$739$	−45.7989	−	16.6694i	−1.68474	−	0.613195i	−0.993947	+	0.109857i	$0.964961\pi$
$740$	31.2639	+	16.7025i	1.14928	+	0.613997i
$741$	48.3378	+	27.1887i	1.77573	+	0.998802i
$742$	−2.92320	+	1.05991i	−0.107314	+	0.0389106i
$743$	−11.3045	−	24.2425i	−0.414721	−	0.889372i	−0.997074	−	0.0764363i	$-0.975646\pi$
$743$	−11.3045	−	24.2425i	−0.414721	−	0.889372i	0.582353	−	0.812936i	$-0.302132\pi$
$744$	26.2687	+	56.8776i	0.963058	+	2.08523i
$745$	23.0682	−	11.7676i	0.845153	−	0.431132i
$746$	−37.6684	+	10.0438i	−1.37914	+	0.367731i
$747$	−8.76217	−	12.5137i	−0.320591	−	0.457851i
$748$	38.3428	+	26.9880i	1.40195	+	0.986777i
$749$	4.85151	−	2.80102i	0.177270	−	0.102347i
$750$	−42.7577	+	12.2698i	−1.56129	+	0.448029i
$751$	−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	$0.915762\pi$
$752$	2.51617	−	5.32771i	0.0917552	−	0.194282i
$753$	14.5552	+	54.3206i	0.530419	+	1.97955i
$754$	6.61710	+	4.64542i	0.240981	+	0.169176i
$755$	0.325069	+	1.06145i	0.0118305	+	0.0386302i
$756$	0.00989000	−	4.04173i	0.000359696	−	0.146996i
$757$	9.07388	−	12.9588i	0.329796	−	0.470997i	−0.619672	−	0.784861i	$-0.712735\pi$
$757$	9.07388	−	12.9588i	0.329796	−	0.470997i	0.949468	+	0.313863i	$0.101623\pi$
$758$	−0.0565888	+	46.2522i	−0.00205540	+	1.67996i
$759$	−6.26848			−0.227531
$760$	5.98548	−	26.9105i	0.217116	−	0.976146i
$761$	23.6303			0.856596			0.428298	−	0.903637i	$-0.359113\pi$
$761$	23.6303			0.856596			0.428298	+	0.903637i	$0.359113\pi$
$762$	−0.0694837	+	56.7917i	−0.00251713	+	2.05735i
$763$	−0.979024	+	1.39819i	−0.0354431	+	0.0506179i
$764$	−0.0394265	+	16.1124i	−0.00142640	+	0.582925i
$765$	29.5307	−	55.6027i	1.06768	−	2.01032i
$766$	10.1710	+	7.14038i	0.367494	+	0.257992i
$767$	−4.51868	−	16.8639i	−0.163160	−	0.608921i
$768$	−26.1786	+	36.6188i	−0.944640	+	1.32137i
$769$	−9.13192	−	25.0897i	−0.329305	−	0.904759i	−0.988288	−	0.152601i	$-0.951235\pi$
$769$	−9.13192	−	25.0897i	−0.329305	−	0.904759i	0.658982	−	0.752158i	$-0.270987\pi$
$770$	−2.28215	+	4.28435i	−0.0822430	+	0.154397i
$771$	−57.9132	+	33.4362i	−2.08569	+	1.20417i
$772$	−8.29332	−	5.83734i	−0.298483	−	0.210091i
$773$	−8.86228	−	12.6567i	−0.318754	−	0.455228i	0.627517	−	0.778603i	$-0.284071\pi$
$773$	−8.86228	−	12.6567i	−0.318754	−	0.455228i	−0.946271	+	0.323375i	$0.895183\pi$
$774$	41.6117	−	11.0953i	1.49570	−	0.398811i
$775$	−39.2676	+	2.78328i	−1.41054	+	0.0999782i
$776$	6.64779	−	3.07026i	0.238642	−	0.110216i
$777$	−3.53469	−	7.58016i	−0.126806	−	0.271937i
$778$	4.91023	−	1.78038i	0.176040	−	0.0638296i
$779$	12.7707	−	36.3522i	0.457557	−	1.30245i
$780$	54.4468	−	16.5287i	1.94951	−	0.591822i
$781$	−43.1217	−	15.6950i	−1.54302	−	0.561612i
$782$	−2.20057	−	3.82229i	−0.0786923	−	0.136685i
$783$	−0.593606	−	6.78494i	−0.0212137	−	0.242474i
$784$	23.8282	−	13.6022i	0.851008	−	0.485792i
$785$	0.586839	−	0.125027i	0.0209452	−	0.00446242i
$786$	−1.58893	+	1.10968i	−0.0566751	+	0.0395811i
$787$	28.5927	+	7.66138i	1.01922	+	0.273099i	0.729476	−	0.684006i	$-0.239764\pi$
$787$	28.5927	+	7.66138i	1.01922	+	0.273099i	0.289742	+	0.957105i	$0.406431\pi$
$788$	−41.4838	+	11.0068i	−1.47780	+	0.392102i
$789$	5.56397	+	15.2869i	0.198083	+	0.544227i
$790$	3.90328	−	1.98513i	0.138872	−	0.0706279i
$791$	5.23737	+	3.02379i	0.186219	+	0.107514i
$792$	36.7311	−	43.4495i	1.30518	−	1.54391i
$793$	1.61573	−	18.4678i	0.0573761	−	0.655812i
$794$	−19.3918	+	9.01367i	−0.688189	+	0.319883i
$795$	−8.27843	+	35.9356i	−0.293606	+	1.27450i
$796$	4.27936	−	1.54571i	0.151678	−	0.0547863i
$797$	8.17145	+	8.17145i	0.289448	+	0.289448i	0.836862	−	0.547414i	$-0.184388\pi$
$797$	8.17145	+	8.17145i	0.289448	+	0.289448i	−0.547414	+	0.836862i	$0.684388\pi$
$798$	−4.94100	+	4.23096i	−0.174909	+	0.149774i
$799$	−8.43798			−0.298514
$800$	−15.6949	−	23.5302i	−0.554900	−	0.831917i
$801$	7.24542	+	41.0908i	0.256005	+	1.45187i
$802$	10.0012	−	27.3738i	0.353155	−	0.966604i
$803$	−41.2814	−	3.61165i	−1.45679	−	0.127453i
$804$	12.8981	+	22.4669i	0.454880	+	0.792347i
$805$	0.364535	−	0.274968i	0.0128482	−	0.00969135i
$806$	50.1685	−	4.32733i	1.76711	−	0.152424i
$807$	−20.6144	+	44.2078i	−0.725662	+	1.55619i
$808$	29.7109	+	5.35134i	1.04522	+	0.188260i
$809$	−34.6928	+	20.0299i	−1.21973	+	0.704213i	−0.964861	−	0.262762i	$-0.915367\pi$
$809$	−34.6928	+	20.0299i	−1.21973	+	0.704213i	−0.254872	+	0.966975i	$0.582033\pi$
$810$	−1.09412	−	0.711699i	−0.0384436	−	0.0250066i
$811$	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	$0.496669\pi$
$812$	−0.778126	+	0.542017i	−0.0273069	+	0.0190211i
$813$	−8.68020	+	0.759419i	−0.304428	+	0.0266340i
$814$	11.9272	−	44.2960i	0.418048	−	1.55258i
$815$	1.48657	+	41.9989i	0.0520722	+	1.47116i
$816$	63.4301	+	11.5048i	2.22050	+	0.402748i
$817$	−22.2946	−	15.2406i	−0.779990	−	0.533202i
$818$	15.6088	−	5.65951i	0.545748	−	0.197880i
$819$	−7.83455	−	2.85154i	−0.273761	−	0.0996409i
$820$	−17.8772	−	35.2579i	−0.624300	−	1.23126i
$821$	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	$0.631046\pi$
$822$	31.9668	−	55.2121i	1.11497	−	1.92574i
$823$	−41.9049	+	29.3421i	−1.46071	+	1.02280i	−0.470627	+	0.882332i	$0.655972\pi$
$823$	−41.9049	+	29.3421i	−1.46071	+	1.02280i	−0.990085	+	0.140470i	$0.955139\pi$
$824$	−33.3132	−	9.05742i	−1.16052	−	0.315530i
$825$	27.9582	+	50.3254i	0.973380	+	1.75210i
$826$	2.03976	+	0.180971i	0.0709724	+	0.00629679i
$827$	−13.0238	+	27.9297i	−0.452883	+	0.971211i	0.538791	+	0.842439i	$0.318881\pi$
$827$	−13.0238	+	27.9297i	−0.452883	+	0.971211i	−0.991674	+	0.128772i	$0.958897\pi$
$828$	−4.85586	+	2.24987i	−0.168753	+	0.0781885i
$829$	11.6014	+	6.69809i	0.402935	+	0.232634i	0.687749	−	0.725948i	$-0.258599\pi$
$829$	11.6014	+	6.69809i	0.402935	+	0.232634i	−0.284815	+	0.958583i	$0.591932\pi$
$830$	5.20210	+	8.33899i	0.180567	+	0.289451i
$831$	37.7987	+	45.0468i	1.31122	+	1.56266i
$832$	20.5336	+	29.7881i	0.711874	+	1.03272i
$833$	−32.1871	−	22.5376i	−1.11522	−	0.780883i
$834$	−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
$838$	−0.0190485	+	15.5691i	−0.000658020	+	0.537825i
$839$	1.49838	+	8.49773i	0.0517298	+	0.293374i	0.999687	−	0.0250240i	$-0.00796622\pi$
$839$	1.49838	+	8.49773i	0.0517298	+	0.293374i	−0.947957	+	0.318398i	$0.896855\pi$
$840$	−0.370589	+	6.66365i	−0.0127865	+	0.229918i
$841$	20.9912	−	17.6137i	0.723833	−	0.607368i
$842$	21.0138	−	3.67879i	0.724182	−	0.126780i
$843$	−50.8509	+	13.6255i	−1.75140	+	0.469286i
$844$	9.65622	−	26.3296i	0.332381	−	0.906302i
$845$	0.864247	−	16.6418i	0.0297310	−	0.572494i
$846$	−0.904846	+	10.1987i	−0.0311092	+	0.350639i
$847$	2.08298	+	0.558133i	0.0715720	+	0.0191777i
$848$	−23.3682	+	1.92926i	−0.802467	+	0.0662512i
$849$	34.3926	+	6.06434i	1.18035	+	0.208127i
$850$	−20.8718	+	34.7148i	−0.715896	+	1.19071i
$851$	−2.77366	+	3.30552i	−0.0950799	+	0.113312i
$852$	−62.8644	+	5.34495i	−2.15370	+	0.183115i
$853$	6.90681	−	3.22070i	0.236485	−	0.110275i	−0.300764	−	0.953699i	$-0.597242\pi$
$853$	6.90681	−	3.22070i	0.236485	−	0.110275i	0.537248	+	0.843424i	$0.319464\pi$
$854$	1.96955	+	0.921351i	0.0673965	+	0.0315280i
$855$	6.39441	+	47.4776i	0.218684	+	1.62370i
$856$	40.8445	−	10.7837i	1.39604	−	0.368580i
$857$	−7.96744	−	17.0862i	−0.272163	−	0.583655i	0.721958	−	0.691937i	$-0.243243\pi$
$857$	−7.96744	−	17.0862i	−0.272163	−	0.583655i	−0.994120	+	0.108283i	$0.965465\pi$
$858$	−36.7419	−	63.8191i	−1.25435	−	2.17875i
$859$	−42.1020	−	35.3277i	−1.43650	−	1.20537i	−0.941742	−	0.336336i	$-0.890812\pi$
$859$	−42.1020	−	35.3277i	−1.43650	−	1.20537i	−0.494758	−	0.869031i	$-0.664743\pi$
$860$	−27.1135	+	5.70726i	−0.924561	+	0.194616i
$861$	−1.61975	+	9.18604i	−0.0552008	+	0.313060i
$862$	−6.43052	+	36.2102i	−0.219024	+	1.23332i
$863$	6.14893	−	22.9481i	0.209312	−	0.781163i	−0.778780	−	0.627298i	$-0.784161\pi$
$863$	6.14893	−	22.9481i	0.209312	−	0.781163i	0.988092	−	0.153866i	$-0.0491723\pi$
$864$	8.06827	−	29.3908i	0.274488	−	0.999897i
$865$	23.2613	−	20.9646i	0.790909	−	0.712817i
$866$	−1.75119	−	20.3023i	−0.0595079	−	0.689899i
$867$	−11.5158	−	42.9775i	−0.391097	−	1.45959i
$868$	−1.54259	+	5.70119i	−0.0523590	+	0.193511i
$869$	−3.64291	−	4.34145i	−0.123577	−	0.147274i
$870$	0.384073	+	11.2399i	0.0130213	+	0.381068i
$871$	20.5054	−	3.61565i	0.694798	−	0.122512i
$872$	−9.89028	+	8.23726i	−0.334927	+	0.278949i
$873$	−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
$877$	−16.9460	+	24.2014i	−0.572226	+	0.817223i	−0.996075	−	0.0885095i	$-0.971790\pi$
$877$	−16.9460	+	24.2014i	−0.572226	+	0.817223i	0.423850	+	0.905733i	$0.360679\pi$
$878$	1.80211	−	4.93248i	0.0608183	−	0.166463i
$879$	35.7738	−	30.0178i	1.20662	−	1.01247i
$880$	−25.0828	+	26.6608i	−0.845541	+	0.898735i
$881$	−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	$0.286451\pi$
$882$	−30.6921	+	36.4866i	−1.03346	+	1.22857i
$883$	40.2287	+	18.7589i	1.35380	+	0.631289i	0.957926	−	0.287015i	$-0.0926630\pi$
$883$	40.2287	+	18.7589i	1.35380	+	0.631289i	0.395877	+	0.918304i	$0.370441\pi$
$884$	26.0162	−	44.8079i	0.875021	−	1.50705i
$885$	14.9428	−	19.1447i	0.502298	−	0.643541i
$886$	28.8761	+	41.3469i	0.970111	+	1.38908i
$887$	−14.9622	−	21.3682i	−0.502381	−	0.717474i	0.485232	−	0.874386i	$-0.338735\pi$
$887$	−14.9622	−	21.3682i	−0.502381	−	0.717474i	−0.987613	+	0.156911i	$0.949846\pi$
$888$	−10.7239	−	62.1516i	−0.359872	−	2.08567i
$889$	−3.44140	+	4.10130i	−0.115421	+	0.137553i
$890$	−3.25161	−	26.6473i	−0.108994	−	0.893221i
$891$	−0.577746	+	1.58734i	−0.0193552	+	0.0531780i
$892$	−53.3905	−	4.80274i	−1.78765	−	0.160807i
$893$	5.21780	−	3.74157i	0.174607	−	0.125207i
$894$	−41.7371	−	19.5245i	−1.39590	−	0.652998i
$895$	−7.37147	−	6.86748i	−0.246401	−	0.229555i
$896$	−4.10822	+	1.06317i	−0.137246	+	0.0355180i
$897$	0.603715	+	6.90050i	0.0201575	+	0.230401i
$898$	−8.53672	+	14.7443i	−0.284874	+	0.492025i
$899$	−1.72827	+	9.80151i	−0.0576410	+	0.326899i
$900$	39.7205	+	28.9497i	1.32402	+	0.964989i
$901$	16.7898	+	29.0809i	0.559351	+	0.968824i
$902$	−39.2317	+	32.8376i	−1.30627	+	1.09337i
$903$	5.92533	+	2.76303i	0.197183	+	0.0919478i
$904$	32.1283	+	32.3650i	1.06857	+	1.07644i
$905$	45.7257	−	34.4908i	1.51997	−	1.14651i
$906$	1.13494	−	1.61665i	0.0377060	−	0.0537097i
$907$	3.87406	−	44.2807i	0.128636	−	1.47032i	−0.607951	−	0.793975i	$-0.708008\pi$
$907$	3.87406	−	44.2807i	0.128636	−	1.47032i	0.736587	−	0.676343i	$-0.236436\pi$
$908$	24.7038	−	24.5832i	0.819825	−	0.815822i
$909$	−51.6636	+	9.10969i	−1.71357	+	0.302149i
$910$	4.93612	+	2.09962i	0.163631	+	0.0696019i
$911$		−	49.0076i		−	1.62369i	−0.583870	−	0.811847i	$-0.698462\pi$
$911$		−	49.0076i		−	1.62369i	0.583870	−	0.811847i	$-0.301538\pi$
$912$	−44.3248	+	21.0119i	−1.46774	+	0.695773i
$913$	8.99443	−	8.99443i	0.297672	−	0.297672i
$914$	19.4473	−	19.3998i	0.643259	−	0.641687i
$915$	21.8627	−	13.6757i	0.722758	−	0.452106i
$916$	0.0199053	−	8.13466i	0.000657689	−	0.268777i
$917$	−0.182010	−	0.0159238i	−0.00601049	−	0.000525849i
$918$	−42.9942	+	7.52681i	−1.41902	+	0.248422i
$919$	−14.2751	+	24.7253i	−0.470894	+	0.815611i	−0.999446	−	0.0332893i	$-0.989402\pi$
$919$	−14.2751	+	24.7253i	−0.470894	+	0.815611i	0.528552	+	0.848901i	$0.322735\pi$
$920$	3.19661	−	1.27965i	0.105389	−	0.0421887i
$921$	15.8148	−	5.75611i	0.521115	−	0.189670i
$922$	−2.24981	−	2.68789i	−0.0740935	−	0.0885209i
$923$	−13.1244	+	48.9810i	−0.431996	+	1.61223i
$924$	8.50979	−	1.47904i	0.279951	−	0.0486570i
$925$	38.9087	+	7.52481i	1.27931	+	0.247414i
$926$	−6.93176	−	25.9969i	−0.227792	−	0.854310i
$927$	59.7630	−	5.22858i	1.96287	−	0.171729i
$928$	−6.73452	+	2.40461i	−0.221072	+	0.0789353i
$929$	18.9522	−	52.0706i	0.621800	−	1.70838i	−0.0807381	−	0.996735i	$-0.525728\pi$
$929$	18.9522	−	52.0706i	0.621800	−	1.70838i	0.702538	−	0.711646i	$-0.252050\pi$
$930$	46.8306	+	52.0891i	1.53564	+	1.70807i
$931$	29.8972	−	0.335758i	0.979840	−	0.0110040i
$932$	1.59464	−	17.7271i	0.0522342	−	0.580671i
$933$	−51.0050	+	23.7840i	−1.66983	+	0.778653i
$934$	2.96331	−	11.0053i	0.0969624	−	0.360106i
$935$	49.8647	+	16.1759i	1.63075	+	0.529008i
$936$	−51.3679	−	36.2499i	−1.67901	−	1.18487i
$937$	37.0107	−	25.9152i	1.20909	−	0.846612i	0.217501	−	0.976060i	$-0.430210\pi$
$937$	37.0107	−	25.9152i	1.20909	−	0.846612i	0.991586	+	0.129448i	$0.0413206\pi$
$938$	−0.427028	+	2.40459i	−0.0139430	+	0.0785126i
$939$	15.4168	+	26.7027i	0.503108	+	0.871409i
$940$	0.929664	−	6.52152i	0.0303223	−	0.212709i
$941$	−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	$0.390631\pi$
$942$	−0.817003	−	0.687252i	−0.0266194	−	0.0223919i
$943$	4.64841	−	1.24554i	0.151373	−	0.0405603i
$944$	14.4847	+	5.35241i	0.471436	+	0.174206i
$945$	−1.32322	−	4.32073i	−0.0430443	−	0.140553i
$946$	15.1149	+	32.5178i	0.491427	+	1.05724i
$947$	17.6398	+	12.3515i	0.573215	+	0.401370i	0.823930	−	0.566691i	$-0.191777\pi$
$947$	17.6398	+	12.3515i	0.573215	+	0.401370i	−0.250715	+	0.968061i	$0.580666\pi$
$948$	−7.05373	−	3.31025i	−0.229094	−	0.107512i
$949$			45.7914i			1.48645i
$950$	−2.48672	−	30.7216i	−0.0806800	−	0.996740i
$951$			55.3207i			1.79390i
$952$	3.88926	+	4.66974i	0.126052	+	0.151347i
$953$	20.7975	+	14.5626i	0.673698	+	0.471728i	0.859685	−	0.510824i	$-0.170660\pi$
$953$	20.7975	+	14.5626i	0.673698	+	0.471728i	−0.185988	+	0.982552i	$0.559548\pi$
$954$	36.9495	−	17.1748i	1.19628	−	0.556056i
$955$	5.27502	+	17.2246i	0.170695	+	0.557375i
$956$	7.01570	+	12.2205i	0.226904	+	0.395239i
$957$	14.0591	−	3.76713i	0.454467	−	0.121774i
$958$	−12.2152	+	14.5214i	−0.394656	+	0.469165i
$959$	5.65170	−	2.05705i	0.182503	−	0.0664256i
$960$	−15.8803	+	47.7561i	−0.512533	+	1.54132i
$961$	15.4939	+	26.8362i	0.499803	+	0.865684i
$962$	−49.9109	−	8.86361i	−1.60919	−	0.285774i
$963$	−60.1334	+	42.1059i	−1.93777	+	1.35684i
$964$	4.23939	−	23.7035i	0.136542	−	0.763437i
$965$	−10.7855	−	3.49875i	−0.347196	−	0.112629i
$966$	−0.784521	−	0.211241i	−0.0252415	−	0.00679656i
$967$	−0.786232	+	0.366626i	−0.0252835	+	0.0117899i	−0.435219	−	0.900325i	$-0.643329\pi$
$967$	−0.786232	+	0.366626i	−0.0252835	+	0.0117899i	0.409935	+	0.912115i	$0.365551\pi$
$968$	14.0530	+	8.18240i	0.451679	+	0.262992i
$969$	54.3176	+	44.5481i	1.74493	+	1.43109i
$970$	6.08812	−	5.47351i	0.195478	−	0.175744i
$971$	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	$-0.0587702\pi$
$972$	−2.54192	−	29.8967i	−0.0815321	−	0.958936i
$973$	−2.85070	+	0.249404i	−0.0913892	+	0.00799552i
$974$	−20.7840	+	5.54181i	−0.665962	+	0.177571i
$975$	52.7068	−	35.6239i	1.68797	−	1.14088i
$976$	12.5089	+	10.6010i	0.400401	+	0.339330i
$977$	5.29716	−	19.7693i	0.169471	−	0.632475i	−0.827956	−	0.560793i	$-0.810496\pi$
$977$	5.29716	−	19.7693i	0.169471	−	0.632475i	0.997427	−	0.0716827i	$-0.0228369\pi$
$978$	57.3412	−	47.9955i	1.83357	−	1.53473i
$979$	−32.6473	+	11.8827i	−1.04341	+	0.379771i
$980$	20.9651	−	22.3935i	0.669704	−	0.715335i
$981$	11.1835	−	19.3704i	0.357061	−	0.618449i
$982$	4.56600	+	26.0816i	0.145707	+	0.832299i
$983$	58.4765	+	5.11603i	1.86511	+	0.163176i	0.963207	−	0.268762i	$-0.0866144\pi$
$983$	58.4765	+	5.11603i	1.86511	+	0.163176i	0.901904	+	0.431938i	$0.142170\pi$
$984$	−29.9604	+	63.6394i	−0.955102	+	2.02875i
$985$	−40.6816	+	25.4475i	−1.29622	+	0.810825i
$986$	7.23257	+	7.25029i	0.230332	+	0.230896i
$987$	−1.09911	+	1.09911i	−0.0349850	+	0.0349850i
$988$	3.78100	+	39.2440i	0.120290	+	1.24852i
$989$		−	3.37303i		−	0.107256i
$990$	24.8985	−	58.5351i	0.791326	−	1.86037i
$991$	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	$0.375977\pi$
$992$	−22.5044	+	38.4339i	−0.714515	+	1.22028i
$993$	−5.05022	+	57.7243i	−0.160264	+	1.83182i
$994$	−4.86792	−	3.41744i	−0.154401	−	0.108395i
$995$	4.06121	−	3.06336i	0.128749	−	0.0971152i
$996$	6.02154	−	16.4189i	0.190800	−	0.520254i
$997$	15.2636	+	7.11752i	0.483402	+	0.225414i	0.649013	−	0.760777i	$-0.275182\pi$
$997$	15.2636	+	7.11752i	0.483402	+	0.225414i	−0.165611	+	0.986191i	$0.552960\pi$
$998$	−19.3577	−	23.1270i	−0.612756	−	0.732072i
$999$	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.327.28	yes	672
4.3	odd	2	inner	380.2.bj.a.327.14	yes	672
5.3	odd	4	inner	380.2.bj.a.23.1	✓	672
19.5	even	9	inner	380.2.bj.a.347.17	yes	672
20.3	even	4	inner	380.2.bj.a.23.17	yes	672
76.43	odd	18	inner	380.2.bj.a.347.1	yes	672
95.43	odd	36	inner	380.2.bj.a.43.14	yes	672
380.43	even	36	inner	380.2.bj.a.43.28	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bj.a.23.1	✓	672	5.3	odd	4	inner
380.2.bj.a.23.17	yes	672	20.3	even	4	inner
380.2.bj.a.43.14	yes	672	95.43	odd	36	inner
380.2.bj.a.43.28	yes	672	380.43	even	36	inner
380.2.bj.a.327.14	yes	672	4.3	odd	2	inner
380.2.bj.a.327.28	yes	672	1.1	even	1	trivial
380.2.bj.a.347.1	yes	672	76.43	odd	18	inner
380.2.bj.a.347.17	yes	672	19.5	even	9	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)

\(f(q)\)	\(=\)	\(q+(0.00173027 - 1.41421i) q^{2} +(-1.61369 + 2.30458i) q^{3} +(-1.99999 - 0.00489393i) q^{4} +(-2.13805 + 0.654777i) q^{5} +(3.25638 + 2.28608i) q^{6} +(0.0970781 + 0.362300i) q^{7} +(-0.0103816 + 2.82841i) q^{8} +(-1.68106 - 4.61866i) q^{9} +O(q^{10})\)	\(q+(0.00173027 - 1.41421i) q^{2} +(-1.61369 + 2.30458i) q^{3} +(-1.99999 - 0.00489393i) q^{4} +(-2.13805 + 0.654777i) q^{5} +(3.25638 + 2.28608i) q^{6} +(0.0970781 + 0.362300i) q^{7} +(-0.0103816 + 2.82841i) q^{8} +(-1.68106 - 4.61866i) q^{9} +(0.922294 + 3.02479i) q^{10} +(3.54429 - 2.04630i) q^{11} +(3.23864 - 4.60125i) q^{12} +(-2.59396 - 3.70457i) q^{13} +(0.512538 - 0.136662i) q^{14} +(1.94116 - 5.98392i) q^{15} +(3.99995 + 0.0195756i) q^{16} +(-2.42094 - 5.19173i) q^{17} +(-6.53468 + 2.36938i) q^{18} +(3.79915 + 2.13692i) q^{19} +(4.27930 - 1.29909i) q^{20} +(-0.991604 - 0.360914i) q^{21} +(-2.88777 - 5.01592i) q^{22} +(0.0474495 + 0.542351i) q^{23} +(-6.50154 - 4.58809i) q^{24} +(4.14254 - 2.79989i) q^{25} +(-5.24353 + 3.66201i) q^{26} +(5.20424 + 1.39447i) q^{27} +(-0.192383 - 0.725074i) q^{28} +(-0.432355 - 1.18788i) q^{29} +(-8.45917 - 2.75556i) q^{30} +(-6.81842 - 3.93662i) q^{31} +(0.0346051 - 5.65675i) q^{32} +(-1.00351 + 11.4702i) q^{33} +(-7.34640 + 3.41474i) q^{34} +(-0.444784 - 0.711053i) q^{35} +(3.33950 + 9.24552i) q^{36} +(5.60448 + 5.60448i) q^{37} +(3.02863 - 5.36911i) q^{38} +12.7233 q^{39} +(-1.82978 - 6.05408i) q^{40} +(-1.53495 - 8.70514i) q^{41} +(-0.512125 + 1.40171i) q^{42} +(-6.17204 - 0.539983i) q^{43} +(-7.09857 + 4.07524i) q^{44} +(6.61838 + 8.77422i) q^{45} +(0.767081 - 0.0661653i) q^{46} +(0.622516 - 1.33499i) q^{47} +(-6.49978 + 9.18663i) q^{48} +(5.94034 - 3.42966i) q^{49} +(-3.95248 - 5.86327i) q^{50} +(15.8714 + 2.79856i) q^{51} +(5.16978 + 7.42180i) q^{52} +(-5.83962 + 0.510901i) q^{53} +(1.98109 - 7.35749i) q^{54} +(-6.23801 + 6.69581i) q^{55} +(-1.02574 + 0.270815i) q^{56} +(-11.0553 + 5.30714i) q^{57} +(-1.68067 + 0.609386i) q^{58} +(3.62767 + 1.32036i) q^{59} +(-3.91159 + 11.9583i) q^{60} +(3.14017 + 2.63491i) q^{61} +(-5.57901 + 9.63588i) q^{62} +(1.51015 - 1.05742i) q^{63} +(-7.99978 - 0.0587266i) q^{64} +(7.97169 + 6.22209i) q^{65} +(16.2195 + 1.43902i) q^{66} +(-1.94577 + 4.17272i) q^{67} +(4.81646 + 10.3953i) q^{68} +(-1.32646 - 0.765832i) q^{69} +(-1.00635 + 0.627789i) q^{70} +(-7.20741 - 8.58945i) q^{71} +(13.0809 - 4.70676i) q^{72} +(-8.29423 - 5.80768i) 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} +(0.0220147 - 17.9935i) q^{78} +(-0.240466 - 1.36375i) q^{79} +(-8.56492 + 2.57722i) q^{80} +(-0.316185 + 0.265310i) q^{81} +(-12.3136 + 2.15569i) q^{82} +(3.00216 - 0.804426i) q^{83} +(1.98144 + 0.726680i) q^{84} +(8.57553 + 9.51501i) q^{85} +(-0.774330 + 8.72764i) q^{86} +(3.43526 + 0.920475i) q^{87} +(5.75097 + 10.0459i) q^{88} +(-8.36016 - 1.47412i) q^{89} +(12.4201 - 9.34461i) q^{90} +(1.09035 - 1.29943i) q^{91} +(-0.0922445 - 1.08493i) q^{92} +(20.0750 - 9.36114i) q^{93} +(-1.88688 - 0.882680i) q^{94} +(-9.52200 - 2.08125i) q^{95} +(12.9806 + 9.20796i) q^{96} +(-1.09412 - 2.34635i) q^{97} +(-4.83999 - 8.40684i) 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

Introduction

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