LMFDB - Embedded newform 380.2.bj.a.207.20

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			207.20
Character	$\chi$	$=$	380.207
Dual form			380.2.bj.a.123.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.601507 + 1.27992i) q^{2} +(0.216127 + 2.47035i) q^{3} +(-1.27638 - 1.53976i) q^{4} +(1.88630 - 1.20078i) q^{5} +(-3.29184 - 1.20931i) q^{6} +(4.44155 + 1.19011i) q^{7} +(2.73852 - 0.707482i) q^{8} +(-3.10148 + 0.546874i) q^{9} +O(q^{10})$	\(q+(-0.601507 + 1.27992i) q^{2} +(0.216127 + 2.47035i) q^{3} +(-1.27638 - 1.53976i) q^{4} +(1.88630 - 1.20078i) q^{5} +(-3.29184 - 1.20931i) q^{6} +(4.44155 + 1.19011i) q^{7} +(2.73852 - 0.707482i) q^{8} +(-3.10148 + 0.546874i) q^{9} +(0.402283 + 3.13659i) q^{10} +(1.86545 + 1.07702i) q^{11} +(3.52788 - 3.48588i) q^{12} +(0.0817278 - 0.934153i) q^{13} +(-4.19487 + 4.96896i) q^{14} +(3.37403 + 4.40029i) q^{15} +(-0.741719 + 3.93063i) q^{16} +(0.155329 - 0.108763i) q^{17} +(1.16561 - 4.29858i) q^{18} +(0.561196 - 4.32262i) q^{19} +(-4.25655 - 1.37179i) q^{20} +(-1.98004 + 11.2294i) q^{21} +(-2.50057 + 1.73979i) q^{22} +(-1.50393 - 3.22518i) q^{23} +(2.33959 + 6.61218i) q^{24} +(2.11624 - 4.53007i) q^{25} +(1.14648 + 0.666505i) q^{26} +(-0.0958362 - 0.357666i) q^{27} +(-3.83661 - 8.35795i) q^{28} +(-4.99504 + 0.880760i) q^{29} +(-7.66151 + 1.67168i) q^{30} +(-7.09998 + 4.09917i) q^{31} +(-4.58473 - 3.31364i) q^{32} +(-2.25743 + 4.84108i) q^{33} +(0.0457757 + 0.264231i) q^{34} +(9.80715 - 3.08844i) q^{35} +(4.80071 + 4.07751i) q^{36} +(-3.09503 - 3.09503i) q^{37} +(5.19504 + 3.31837i) q^{38} +2.32534 q^{39} +(4.31612 - 4.62289i) q^{40} +(-8.95787 - 7.51654i) q^{41} +(-13.1817 - 9.28885i) q^{42} +(-2.96995 - 1.38491i) q^{43} +(-0.722670 - 4.24702i) q^{44} +(-5.19363 + 4.75577i) q^{45} +(5.03259 + 0.0150678i) q^{46} +(-1.49024 - 1.04348i) q^{47} +(-9.87032 - 0.982785i) q^{48} +(12.2488 + 7.07186i) q^{49} +(4.52519 + 5.43348i) q^{50} +(0.302253 + 0.360211i) q^{51} +(-1.54269 + 1.06649i) q^{52} +(-9.89039 + 4.61196i) q^{53} +(0.515429 + 0.0924760i) q^{54} +(4.81206 - 0.208425i) q^{55} +(13.0052 + 0.116818i) q^{56} +(10.7997 + 0.452111i) q^{57} +(1.87725 - 6.92302i) q^{58} +(-0.0187453 + 0.106310i) q^{59} +(2.46884 - 10.8116i) q^{60} +(3.61244 + 1.31482i) q^{61} +(-0.975917 - 11.5531i) q^{62} +(-14.4262 - 1.26213i) q^{63} +(6.99894 - 3.87490i) q^{64} +(-0.967553 - 1.86023i) q^{65} +(-4.83832 - 5.80127i) q^{66} +(4.93535 + 3.45577i) q^{67} +(-0.365728 - 0.100348i) q^{68} +(7.64228 - 4.41227i) q^{69} +(-1.94612 + 14.4101i) q^{70} +(3.03459 + 8.33748i) q^{71} +(-8.10654 + 3.69186i) q^{72} +(10.0328 - 0.877760i) q^{73} +(5.82307 - 2.09970i) q^{74} +(11.6482 + 4.24876i) q^{75} +(-7.37210 + 4.65319i) q^{76} +(7.00371 + 7.00371i) q^{77} +(-1.39871 + 2.97625i) q^{78} +(1.87409 + 1.57255i) q^{79} +(3.32073 + 8.30498i) q^{80} +(-8.01534 + 2.91734i) q^{81} +(15.0088 - 6.94408i) q^{82} +(-4.13650 + 15.4376i) q^{83} +(19.8178 - 11.2841i) q^{84} +(0.162397 - 0.391676i) q^{85} +(3.55902 - 2.96826i) q^{86} +(-3.25535 - 12.1491i) q^{87} +(5.87053 + 1.62966i) q^{88} +(-1.23134 - 1.46745i) q^{89} +(-2.96299 - 9.50805i) q^{90} +(1.47474 - 4.05182i) q^{91} +(-3.04643 + 6.43224i) q^{92} +(-11.6609 - 16.6535i) q^{93} +(2.23196 - 1.27973i) q^{94} +(-4.13195 - 8.82763i) q^{95} +(7.19496 - 12.0420i) q^{96} +(13.6916 - 9.58695i) q^{97} +(-16.4192 + 11.4237i) q^{98} +(-6.37464 - 2.32018i) 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.601507	+	1.27992i	−0.425330	+	0.905038i
$2$	−0.601507	+	1.27992i	−0.425330	+	0.905038i
$3$	0.216127	+	2.47035i	0.124781	+	1.42625i	0.757986	+	0.652271i	$0.226183\pi$
$3$	0.216127	+	2.47035i	0.124781	+	1.42625i	−0.633205	+	0.773984i	$0.718261\pi$
$4$	−1.27638	−	1.53976i	−0.638189	−	0.769880i
$5$	1.88630	−	1.20078i	0.843578	−	0.537007i
$5$	1.88630	−	1.20078i	0.843578	−	0.537007i
$6$	−3.29184	−	1.20931i	−1.34389	−	0.493697i
$7$	4.44155	+	1.19011i	1.67875	+	0.449819i	0.967448	−	0.253070i	$-0.0814401\pi$
$7$	4.44155	+	1.19011i	1.67875	+	0.449819i	0.711300	+	0.702889i	$0.248107\pi$
$8$	2.73852	−	0.707482i	0.968212	−	0.250133i
$9$	−3.10148	+	0.546874i	−1.03383	+	0.182291i
$10$	0.402283	+	3.13659i	0.127213	+	0.991875i
$11$	1.86545	+	1.07702i	0.562454	+	0.324733i	0.754130	−	0.656725i	$-0.228059\pi$
$11$	1.86545	+	1.07702i	0.562454	+	0.324733i	−0.191676	+	0.981458i	$0.561392\pi$
$12$	3.52788	−	3.48588i	1.01841	−	1.00629i
$13$	0.0817278	−	0.934153i	0.0226672	−	0.259087i	−0.976402	−	0.215959i	$-0.930712\pi$
$13$	0.0817278	−	0.934153i	0.0226672	−	0.259087i	0.999070	−	0.0431280i	$-0.0137323\pi$
$14$	−4.19487	+	4.96896i	−1.12113	+	1.32801i
$15$	3.37403	+	4.40029i	0.871171	+	1.13615i
$16$	−0.741719	+	3.93063i	−0.185430	+	0.982658i
$17$	0.155329	−	0.108763i	0.0376729	−	0.0263789i	−0.554588	−	0.832125i	$-0.687124\pi$
$17$	0.155329	−	0.108763i	0.0376729	−	0.0263789i	0.592261	+	0.805746i	$0.298235\pi$
$18$	1.16561	−	4.29858i	0.274736	−	1.01319i
$19$	0.561196	−	4.32262i	0.128747	−	0.991677i
$19$	0.561196	−	4.32262i	0.128747	−	0.991677i
$20$	−4.25655	−	1.37179i	−0.951793	−	0.306742i
$21$	−1.98004	+	11.2294i	−0.432081	+	2.45045i
$22$	−2.50057	+	1.73979i	−0.533124	+	0.370924i
$23$	−1.50393	−	3.22518i	−0.313591	−	0.672497i	0.684829	−	0.728704i	$-0.259877\pi$
$23$	−1.50393	−	3.22518i	−0.313591	−	0.672497i	−0.998419	+	0.0562071i	$0.982099\pi$
$24$	2.33959	+	6.61218i	0.477567	+	1.34970i
$25$	2.11624	−	4.53007i	0.423247	−	0.906014i
$26$	1.14648	+	0.666505i	0.224843	+	0.130712i
$27$	−0.0958362	−	0.357666i	−0.0184437	−	0.0688328i
$28$	−3.83661	−	8.35795i	−0.725052	−	1.57950i
$29$	−4.99504	+	0.880760i	−0.927555	+	0.163553i	−0.616965	−	0.786991i	$-0.711638\pi$
$29$	−4.99504	+	0.880760i	−0.927555	+	0.163553i	−0.310590	+	0.950544i	$0.600527\pi$
$30$	−7.66151	+	1.67168i	−1.39879	+	0.305205i
$31$	−7.09998	+	4.09917i	−1.27519	+	0.736233i	−0.975961	−	0.217947i	$-0.930064\pi$
$31$	−7.09998	+	4.09917i	−1.27519	+	0.736233i	−0.299233	+	0.954180i	$0.596731\pi$
$32$	−4.58473	−	3.31364i	−0.810474	−	0.585775i
$33$	−2.25743	+	4.84108i	−0.392968	+	0.842723i
$34$	0.0457757	+	0.264231i	0.00785047	+	0.0453152i
$35$	9.80715	−	3.08844i	1.65771	−	0.522042i
$36$	4.80071	+	4.07751i	0.800118	+	0.679585i
$37$	−3.09503	−	3.09503i	−0.508821	−	0.508821i	0.405344	−	0.914164i	$-0.367152\pi$
$37$	−3.09503	−	3.09503i	−0.508821	−	0.508821i	−0.914164	+	0.405344i	$0.867152\pi$
$38$	5.19504	+	3.31837i	0.842746	+	0.538311i
$39$	2.32534			0.372353
$40$	4.31612	−	4.62289i	0.682439	−	0.730943i
$41$	−8.95787	−	7.51654i	−1.39898	−	1.17389i	−0.961548	−	0.274637i	$-0.911442\pi$
$41$	−8.95787	−	7.51654i	−1.39898	−	1.17389i	−0.437436	−	0.899250i	$-0.644113\pi$
$42$	−13.1817	−	9.28885i	−2.03398	−	1.43330i
$43$	−2.96995	−	1.38491i	−0.452913	−	0.211197i	0.182756	−	0.983158i	$-0.441498\pi$
$43$	−2.96995	−	1.38491i	−0.452913	−	0.211197i	−0.635669	+	0.771961i	$0.719276\pi$
$44$	−0.722670	−	4.24702i	−0.108947	−	0.640263i
$45$	−5.19363	+	4.75577i	−0.774220	+	0.708948i
$46$	5.03259	+	0.0150678i	0.742015	+	0.00222163i
$47$	−1.49024	−	1.04348i	−0.217374	−	0.152207i	0.459818	−	0.888013i	$-0.347915\pi$
$47$	−1.49024	−	1.04348i	−0.217374	−	0.152207i	−0.677192	+	0.735806i	$0.736803\pi$
$48$	−9.87032	−	0.982785i	−1.42466	−	0.141853i
$49$	12.2488	+	7.07186i	1.74983	+	1.01027i
$50$	4.52519	+	5.43348i	0.639958	+	0.768410i
$51$	0.302253	+	0.360211i	0.0423239	+	0.0504396i
$52$	−1.54269	+	1.06649i	−0.213932	+	0.147896i
$53$	−9.89039	+	4.61196i	−1.35855	+	0.633502i	−0.959051	−	0.283232i	$-0.908593\pi$
$53$	−9.89039	+	4.61196i	−1.35855	+	0.633502i	−0.399498	+	0.916734i	$0.630816\pi$
$54$	0.515429	+	0.0924760i	0.0701410	+	0.0125844i
$55$	4.81206	−	0.208425i	0.648857	−	0.0281041i
$56$	13.0052	+	0.116818i	1.73790	+	0.0156104i
$57$	10.7997	+	0.452111i	1.43045	+	0.0598836i
$58$	1.87725	−	6.92302i	0.246495	−	0.909037i
$59$	−0.0187453	+	0.106310i	−0.00244043	+	0.0138404i	−0.986004	−	0.166724i	$-0.946681\pi$
$59$	−0.0187453	+	0.106310i	−0.00244043	+	0.0138404i	0.983563	+	0.180564i	$0.0577923\pi$
$60$	2.46884	−	10.8116i	0.318726	−	1.39577i
$61$	3.61244	+	1.31482i	0.462526	+	0.168346i	0.562763	−	0.826618i	$-0.309738\pi$
$61$	3.61244	+	1.31482i	0.462526	+	0.168346i	−0.100238	+	0.994963i	$0.531960\pi$
$62$	−0.975917	−	11.5531i	−0.123942	−	1.46724i
$63$	−14.4262	−	1.26213i	−1.81753	−	0.159013i
$64$	6.99894	−	3.87490i	0.874867	−	0.484363i
$65$	−0.967553	−	1.86023i	−0.120010	−	0.230733i
$66$	−4.83832	−	5.80127i	−0.595556	−	0.714087i
$67$	4.93535	+	3.45577i	0.602949	+	0.422189i	0.834793	−	0.550564i	$-0.185587\pi$
$67$	4.93535	+	3.45577i	0.602949	+	0.422189i	−0.231844	+	0.972753i	$0.574476\pi$
$68$	−0.365728	−	0.100348i	−0.0443510	−	0.0121689i
$69$	7.64228	−	4.41227i	0.920022	−	0.531175i
$70$	−1.94612	+	14.4101i	−0.232606	+	1.72233i
$71$	3.03459	+	8.33748i	0.360140	+	0.989476i	0.978979	+	0.203959i	$0.0653809\pi$
$71$	3.03459	+	8.33748i	0.360140	+	0.989476i	−0.618839	+	0.785517i	$0.712397\pi$
$72$	−8.10654	+	3.69186i	−0.955364	+	0.435090i
$73$	10.0328	−	0.877760i	1.17426	−	0.102734i	0.516718	−	0.856156i	$-0.327154\pi$
$73$	10.0328	−	0.877760i	1.17426	−	0.102734i	0.657537	+	0.753422i	$0.271598\pi$
$74$	5.82307	−	2.09970i	0.676919	−	0.244086i
$75$	11.6482	+	4.24876i	1.34502	+	0.490605i
$76$	−7.37210	+	4.65319i	−0.845637	+	0.533758i
$77$	7.00371	+	7.00371i	0.798147	+	0.798147i
$78$	−1.39871	+	2.97625i	−0.158373	+	0.336994i
$79$	1.87409	+	1.57255i	0.210851	+	0.176925i	0.742097	−	0.670293i	$-0.233831\pi$
$79$	1.87409	+	1.57255i	0.210851	+	0.176925i	−0.531246	+	0.847218i	$0.678276\pi$
$80$	3.32073	+	8.30498i	0.371269	+	0.928525i
$81$	−8.01534	+	2.91734i	−0.890593	+	0.324149i
$82$	15.0088	−	6.94408i	1.65744	−	0.766845i
$83$	−4.13650	+	15.4376i	−0.454040	+	1.69450i	0.236854	+	0.971545i	$0.423884\pi$
$83$	−4.13650	+	15.4376i	−0.454040	+	1.69450i	−0.690894	+	0.722956i	$0.742783\pi$
$84$	19.8178	−	11.2841i	2.16230	−	1.23120i
$85$	0.162397	−	0.391676i	0.0176144	−	0.0424833i
$86$	3.55902	−	2.96826i	0.383779	−	0.320076i
$87$	−3.25535	−	12.1491i	−0.349010	−	1.30252i
$88$	5.87053	+	1.62966i	0.625801	+	0.173722i
$89$	−1.23134	−	1.46745i	−0.130522	−	0.155550i	0.696825	−	0.717241i	$-0.254595\pi$
$89$	−1.23134	−	1.46745i	−0.130522	−	0.155550i	−0.827347	+	0.561691i	$0.810151\pi$
$90$	−2.96299	−	9.50805i	−0.312326	−	1.00224i
$91$	1.47474	−	4.05182i	0.154595	−	0.424746i
$92$	−3.04643	+	6.43224i	−0.317612	+	0.670607i
$93$	−11.6609	−	16.6535i	−1.20918	−	1.72688i
$94$	2.23196	−	1.27973i	0.230209	−	0.131994i
$95$	−4.13195	−	8.82763i	−0.423929	−	0.905695i
$96$	7.19496	−	12.0420i	0.734332	−	1.22904i
$97$	13.6916	−	9.58695i	1.39017	−	0.973407i	0.391589	−	0.920140i	$-0.371925\pi$
$97$	13.6916	−	9.58695i	1.39017	−	0.973407i	0.998580	−	0.0532672i	$-0.0169635\pi$
$98$	−16.4192	+	11.4237i	−1.65859	+	1.15397i
$99$	−6.37464	−	2.32018i	−0.640675	−	0.233187i
$100$	−9.67634	+	2.52359i	−0.967634	+	0.252359i
$101$	−5.78870	+	4.85730i	−0.575997	+	0.483319i	−0.883630	−	0.468186i	$-0.844908\pi$
$101$	−5.78870	+	4.85730i	−0.575997	+	0.483319i	0.307633	+	0.951505i	$0.400463\pi$
$102$	−0.642848	+	0.170189i	−0.0636514	+	0.0168512i
$103$	1.79879	−	0.481985i	0.177240	−	0.0474914i	−0.169107	−	0.985598i	$-0.554088\pi$
$103$	1.79879	−	0.481985i	0.177240	−	0.0474914i	0.346348	+	0.938106i	$0.387422\pi$
$104$	−0.437084	−	2.61601i	−0.0428596	−	0.256521i
$105$	9.74911	+	23.5596i	0.951415	+	2.29918i
$106$	0.0462072	−	15.4330i	0.00448804	−	1.49899i
$107$	−13.4546	−	3.60515i	−1.30071	−	0.348523i	−0.458990	−	0.888442i	$-0.651788\pi$
$107$	−13.4546	−	3.60515i	−1.30071	−	0.348523i	−0.841717	+	0.539918i	$0.818455\pi$
$108$	−0.428396	+	0.604081i	−0.0412224	+	0.0581277i
$109$	−4.85586	−	13.3414i	−0.465107	−	1.27787i	−0.921599	−	0.388144i	$-0.873116\pi$
$109$	−4.85586	−	13.3414i	−0.465107	−	1.27787i	0.456491	−	0.889728i	$-0.349106\pi$
$110$	−2.62772	+	6.28440i	−0.250543	+	0.599194i
$111$	6.97688	−	8.31473i	0.662217	−	0.789199i
$112$	−7.97226	+	16.5754i	−0.753308	+	1.56622i
$113$	4.44621	−	4.44621i	0.418264	−	0.418264i	−0.466341	−	0.884605i	$-0.654428\pi$
$113$	4.44621	−	4.44621i	0.418264	−	0.418264i	0.884605	+	0.466341i	$0.154428\pi$
$114$	−7.07474	+	13.5507i	−0.662610	+	1.26914i
$115$	−6.70960	−	4.27776i	−0.625674	−	0.398903i
$116$	7.73171	+	6.56697i	0.717872	+	0.609728i
$117$	0.257387	+	2.94195i	0.0237954	+	0.271983i
$118$	−0.124793	−	0.0879387i	−0.0114881	−	0.00809542i
$119$	0.819343	−	0.298217i	0.0751091	−	0.0273375i
$120$	12.3530	+	9.66318i	1.12767	+	0.882124i
$121$	−3.18007	−	5.50804i	−0.289097	−	0.500731i
$122$	−3.85577	+	3.83275i	−0.349085	+	0.347001i
$123$	16.6324	−	23.7536i	1.49970	−	2.14179i
$124$	15.3740	+	5.70016i	1.38063	+	0.511890i
$125$	−1.44778	−	11.0862i	−0.129494	−	0.991580i
$126$	10.2929	−	17.7052i	0.916963	−	1.57730i
$127$	0.608231	−	6.95211i	0.0539717	−	0.616900i	−0.920254	−	0.391323i	$-0.872018\pi$
$127$	0.608231	−	6.95211i	0.0539717	−	0.616900i	0.974225	−	0.225577i	$-0.0724268\pi$
$128$	0.749642	+	11.2888i	0.0662596	+	0.997802i
$129$	2.77932	−	7.63612i	0.244706	−	0.672323i
$130$	2.96293	−	0.119447i	0.259866	−	0.0104762i
$131$	−6.36531	−	1.12238i	−0.556140	−	0.0980624i	−0.111488	−	0.993766i	$-0.535562\pi$
$131$	−6.36531	−	1.12238i	−0.556140	−	0.0980624i	−0.444652	+	0.895703i	$0.646673\pi$
$132$	10.3354	−	2.70314i	0.899584	−	0.235278i
$133$	7.63697	−	18.5313i	0.662210	−	1.60686i
$134$	−7.39175	+	4.23817i	−0.638550	+	0.366122i
$135$	−0.610255	−	0.559585i	−0.0525224	−	0.0481614i
$136$	0.348425	−	0.407742i	0.0298772	−	0.0349636i
$137$	0.525525	+	1.12699i	0.0448986	+	0.0962853i	0.927478	−	0.373879i	$-0.121972\pi$
$137$	0.525525	+	1.12699i	0.0448986	+	0.0962853i	−0.882579	+	0.470164i	$0.844195\pi$
$138$	1.05046	+	12.4355i	0.0894209	+	1.05858i
$139$	−17.8870	+	15.0090i	−1.51716	+	1.27304i	−0.669050	+	0.743217i	$0.733299\pi$
$139$	−17.8870	+	15.0090i	−1.51716	+	1.27304i	−0.848105	+	0.529827i	$0.822257\pi$
$140$	−17.2731	−	11.1586i	−1.45984	−	0.943077i
$141$	2.25567	−	3.90694i	0.189962	−	0.329023i
$142$	−12.4966	−	1.13102i	−1.04869	−	0.0949134i
$143$	1.15856	−	1.65459i	0.0968835	−	0.138364i
$144$	0.150864	−	12.5964i	0.0125720	−	1.04970i
$145$	−8.36452	+	7.65933i	−0.694636	+	0.636073i
$146$	−4.91137	+	13.3692i	−0.406468	+	1.10644i
$147$	−14.8226	+	31.7873i	−1.22255	+	2.62177i
$148$	−0.815175	+	8.71604i	−0.0670070	+	0.716454i
$149$	2.62066	−	3.12318i	0.214693	−	0.255861i	−0.647940	−	0.761691i	$-0.724369\pi$
$149$	2.62066	−	3.12318i	0.214693	−	0.255861i	0.862633	+	0.505830i	$0.168814\pi$
$150$	−12.4446	+	12.3531i	−1.01609	+	1.00863i
$151$			10.6771i			0.868888i	0.900699	+	0.434444i	$0.143055\pi$
$151$			10.6771i			0.868888i	−0.900699	+	0.434444i	$0.856945\pi$
$152$	−1.52133	−	12.2346i	−0.123396	−	0.992357i
$153$	−0.422271	+	0.422271i	−0.0341386	+	0.0341386i
$154$	−13.1770	+	4.75139i	−1.06183	+	0.382878i
$155$	−8.47045	+	16.2578i	−0.680363	+	1.30586i
$156$	−2.96802	−	3.58047i	−0.237632	−	0.286667i
$157$	−5.39636	−	2.51636i	−0.430676	−	0.200828i	0.195178	−	0.980768i	$-0.437472\pi$
$157$	−5.39636	−	2.51636i	−0.430676	−	0.200828i	−0.625854	+	0.779940i	$0.715249\pi$
$158$	−3.14001	+	1.45278i	−0.249805	+	0.115577i
$159$	−13.5307	−	23.4359i	−1.07306	−	1.85859i
$160$	−12.6271	−	0.745240i	−0.998263	−	0.0589164i
$161$	−2.84145	−	16.1146i	−0.223937	−	1.27001i
$162$	1.08732	−	12.0138i	0.0854282	−	0.943891i
$163$	6.24003	−	1.67201i	0.488757	−	0.130962i	−0.00602013	−	0.999982i	$-0.501916\pi$
$163$	6.24003	−	1.67201i	0.488757	−	0.130962i	0.494777	+	0.869020i	$0.335250\pi$
$164$	−0.140044	+	23.3869i	−0.0109356	+	1.82621i
$165$	1.55490	+	11.8424i	0.121049	+	0.921929i
$166$	−17.2708	−	14.5802i	−1.34047	−	1.13165i
$167$	21.2951	−	9.93008i	1.64787	−	0.768413i	0.647889	−	0.761735i	$-0.275652\pi$
$167$	21.2951	−	9.93008i	1.64787	−	0.768413i	0.999978	−	0.00667791i	$-0.00212566\pi$
$168$	2.52221	+	32.1527i	0.194592	+	2.48063i
$169$	11.9365	+	2.10473i	0.918195	+	0.161903i
$170$	0.403630	+	0.443451i	0.0309570	+	0.0340111i
$171$	0.623394	+	13.7134i	0.0476721	+	1.04869i
$172$	1.65835	+	6.34068i	0.126448	+	0.483472i
$173$	3.23630	+	4.62191i	0.246051	+	0.351397i	0.923113	−	0.384529i	$-0.125636\pi$
$173$	3.23630	+	4.62191i	0.246051	+	0.351397i	−0.677062	+	0.735926i	$0.736747\pi$
$174$	17.5080	+	3.14121i	1.32728	+	0.238134i
$175$	14.7907	−	17.6020i	1.11807	−	1.33058i
$176$	−5.61699	+	6.53354i	−0.423397	+	0.492484i
$177$	−0.266674	−	0.0233309i	−0.0200444	−	0.00175366i
$178$	2.61888	−	0.693329i	0.196293	−	0.0519672i
$179$	−4.24733	+	7.35659i	−0.317460	+	0.549857i	−0.979957	−	0.199207i	$-0.936163\pi$
$179$	−4.24733	+	7.35659i	−0.317460	+	0.549857i	0.662497	+	0.749064i	$0.269497\pi$
$180$	13.9518	+	1.92678i	1.03990	+	0.143614i
$181$	3.20537	+	18.1786i	0.238254	+	1.35120i	0.835652	+	0.549259i	$0.185090\pi$
$181$	3.20537	+	18.1786i	0.238254	+	1.35120i	−0.597399	+	0.801944i	$0.703799\pi$
$182$	4.29893	+	4.32475i	0.318658	+	0.320572i
$183$	−2.46732	+	9.20815i	−0.182389	+	0.680686i
$184$	−6.40029	−	7.76821i	−0.471836	−	0.572680i
$185$	−9.55462	−	2.12169i	−0.702470	−	0.155990i
$186$	28.3292	−	4.90779i	2.07719	−	0.359856i
$187$	0.406899	−	0.0355990i	0.0297554	−	0.00260326i
$188$	0.295406	+	3.62649i	0.0215447	+	0.264489i
$189$		−	1.70265i		−	0.123849i
$190$	13.7840	+	0.0213232i	0.999999	+	0.00154695i
$191$		−	8.06730i		−	0.583730i	−0.956460	−	0.291865i	$-0.905724\pi$
$191$		−	8.06730i		−	0.583730i	0.956460	−	0.291865i	$-0.0942757\pi$
$192$	11.0850	+	16.4523i	0.799992	+	1.18734i
$193$	20.9396	−	1.83198i	1.50727	−	0.131869i	0.696635	−	0.717426i	$-0.254680\pi$
$193$	20.9396	−	1.83198i	1.50727	−	0.131869i	0.810631	+	0.585557i	$0.199124\pi$
$194$	4.03492	+	23.2907i	0.289690	+	1.67218i
$195$	4.38629	−	2.79224i	0.314109	−	0.199956i
$196$	−4.74516	−	27.8866i	−0.338940	−	1.99190i
$197$	1.27706	−	4.76606i	0.0909869	−	0.339568i	−0.905394	−	0.424573i	$-0.860424\pi$
$197$	1.27706	−	4.76606i	0.0909869	−	0.339568i	0.996380	+	0.0850055i	$0.0270908\pi$
$198$	6.80403	−	6.76340i	0.483541	−	0.480654i
$199$	−2.01989	−	11.4554i	−0.143186	−	0.812049i	−0.968806	−	0.247822i	$-0.920285\pi$
$199$	−2.01989	−	11.4554i	−0.143186	−	0.812049i	0.825619	−	0.564228i	$-0.190826\pi$
$200$	2.59040	−	13.9029i	0.183169	−	0.983081i
$201$	−7.47028	+	12.9389i	−0.526913	+	0.912640i
$202$	−2.73499	−	10.3308i	−0.192433	−	0.726870i
$203$	−23.2339	−	2.03270i	−1.63070	−	0.142668i
$204$	0.168849	−	0.925162i	0.0118218	−	0.0647743i
$205$	−25.9229	−	3.42197i	−1.81054	−	0.239001i
$206$	−0.465086	+	2.59223i	−0.0324041	+	0.180609i
$207$	6.42816	+	9.18037i	0.446788	+	0.638080i
$208$	3.61119	+	1.01412i	0.250391	+	0.0703166i
$209$	5.70242	−	7.45921i	0.394445	−	0.515964i
$210$	−36.0184	−	1.69319i	−2.48551	−	0.116841i
$211$	21.1860	+	3.73566i	1.45850	+	0.257173i	0.845952	−	0.533259i	$-0.179033\pi$
$211$	21.1860	+	3.73566i	1.45850	+	0.257173i	0.612550	+	0.790432i	$0.290144\pi$
$212$	19.7252	+	9.34221i	1.35473	+	0.641626i
$213$	−19.9406	+	9.29845i	−1.36631	+	0.637119i
$214$	12.7074	−	15.0523i	0.868657	−	1.02895i
$215$	−7.26519	+	0.953915i	−0.495482	+	0.0650565i
$216$	−0.515491	−	0.911671i	−0.0350747	−	0.0620313i
$217$	−36.4134	+	9.75693i	−2.47190	+	0.662344i
$218$	19.9967	+	1.80983i	1.35435	+	0.122577i
$219$	4.33674	+	24.5949i	0.293050	+	1.66197i
$220$	−6.46293	−	7.14338i	−0.435730	−	0.481606i
$221$	−0.0889064	−	0.153990i	−0.00598049	−	0.0103585i
$222$	6.44552	+	13.9312i	0.432595	+	0.935001i
$223$	−8.95444	−	4.17553i	−0.599634	−	0.279614i	0.0990066	−	0.995087i	$-0.468433\pi$
$223$	−8.95444	−	4.17553i	−0.599634	−	0.279614i	−0.698640	+	0.715473i	$0.746211\pi$
$224$	−16.4197	−	20.1740i	−1.09709	−	1.34793i
$225$	−4.08608	+	15.2072i	−0.272405	+	1.01381i
$226$	3.01635	+	8.36520i	0.200645	+	0.556445i
$227$	8.88171	−	8.88171i	0.589500	−	0.589500i	−0.347996	−	0.937496i	$-0.613138\pi$
$227$	8.88171	−	8.88171i	0.589500	−	0.589500i	0.937496	+	0.347996i	$0.113138\pi$
$228$	−13.0883	−	17.2059i	−0.866794	−	1.13949i
$229$		−	4.86863i		−	0.321728i	−0.986977	−	0.160864i	$-0.948572\pi$
$229$		−	4.86863i		−	0.321728i	0.986977	−	0.160864i	$-0.0514281\pi$
$230$	9.51106	−	6.01463i	0.627141	−	0.396593i
$231$	−15.7879	+	18.8153i	−1.03877	+	1.23796i
$232$	−13.0559	+	5.94587i	−0.857160	+	0.390366i
$233$	−6.67350	+	14.3114i	−0.437196	+	0.937569i	0.557053	+	0.830477i	$0.311932\pi$
$233$	−6.67350	+	14.3114i	−0.437196	+	0.937569i	−0.994249	+	0.107093i	$0.965846\pi$
$234$	−3.92027	−	1.44017i	−0.256276	−	0.0941468i
$235$	−4.06403	−	0.178853i	−0.265108	−	0.0116671i
$236$	0.187618	−	0.106828i	0.0122129	−	0.00695394i
$237$	−3.47969	+	4.96951i	−0.226030	+	0.322805i
$238$	−0.111148	+	1.22807i	−0.00720468	+	0.0796041i
$239$	−3.75411	+	6.50231i	−0.242833	+	0.420600i	−0.961520	−	0.274734i	$-0.911410\pi$
$239$	−3.75411	+	6.50231i	−0.242833	+	0.420600i	0.718687	+	0.695334i	$0.244743\pi$
$240$	−19.7985	+	9.99830i	−1.27799	+	0.645387i
$241$	10.1729	−	8.53608i	0.655295	−	0.549858i	−0.253378	−	0.967367i	$-0.581542\pi$
$241$	10.1729	−	8.53608i	0.655295	−	0.549858i	0.908672	+	0.417510i	$0.137097\pi$
$242$	8.96267	−	0.757099i	0.576142	−	0.0486682i
$243$	−9.40864	−	20.1769i	−0.603565	−	1.29435i
$244$	−2.58633	−	7.24050i	−0.165573	−	0.463525i
$245$	31.5967	−	1.36855i	2.01864	−	0.0874337i
$246$	20.3981	+	35.5761i	1.30053	+	2.26825i
$247$	−3.99212	−	0.877521i	−0.254013	−	0.0558353i
$248$	−16.5433	+	16.2488i	−1.05050	+	1.03180i
$249$	−39.0303	−	6.88210i	−2.47345	−	0.436135i
$250$	15.0603	+	4.81539i	0.952496	+	0.304552i
$251$	−4.04989	+	11.1270i	−0.255627	+	0.702328i	0.743798	+	0.668405i	$0.233022\pi$
$251$	−4.04989	+	11.1270i	−0.255627	+	0.702328i	−0.999424	+	0.0339235i	$0.989200\pi$
$252$	16.4699	+	23.8238i	1.03751	+	1.50076i
$253$	0.668078	−	7.63617i	0.0420017	−	0.480082i
$254$	8.53227	+	4.96023i	0.535362	+	0.311232i
$255$	1.00267	+	0.316525i	0.0627899	+	0.0198215i
$256$	−14.8997	−	5.83084i	−0.931232	−	0.364428i
$257$	2.47301	−	3.53182i	0.154262	−	0.220309i	−0.734581	−	0.678521i	$-0.762621\pi$
$257$	2.47301	−	3.53182i	0.154262	−	0.220309i	0.888843	+	0.458212i	$0.151510\pi$
$258$	8.10183	+	8.15049i	0.504398	+	0.507427i
$259$	−10.0633	−	17.4302i	−0.625304	−	1.08306i
$260$	−1.62934	+	3.86415i	−0.101047	+	0.239645i
$261$	15.0103	−	5.46331i	0.929116	−	0.338170i
$262$	5.26533	−	7.47195i	0.325293	−	0.461619i
$263$	1.26462	+	14.4547i	0.0779797	+	0.891312i	0.929941	+	0.367708i	$0.119857\pi$
$263$	1.26462	+	14.4547i	0.0779797	+	0.891312i	−0.851962	+	0.523604i	$0.824587\pi$
$264$	−2.75704	+	14.8545i	−0.169684	+	0.914229i
$265$	−13.1182	+	20.5758i	−0.805847	+	1.26396i
$266$	19.1248	+	20.9214i	1.17262	+	1.28277i
$267$	3.35899	−	3.35899i	0.205567	−	0.205567i
$268$	−0.978318	−	12.0101i	−0.0597603	−	0.733635i
$269$	−2.20177	+	2.62396i	−0.134244	+	0.159986i	−0.828979	−	0.559280i	$-0.811077\pi$
$269$	−2.20177	+	2.62396i	−0.134244	+	0.159986i	0.694734	+	0.719266i	$0.255522\pi$
$270$	1.08330	−	0.444481i	0.0659273	−	0.0270503i
$271$	−4.58135	−	12.5872i	−0.278297	−	0.764615i	−0.997556	−	0.0698730i	$-0.977741\pi$
$271$	−4.58135	−	12.5872i	−0.278297	−	0.764615i	0.719259	−	0.694742i	$-0.244482\pi$
$272$	0.312296	+	0.691214i	0.0189357	+	0.0419110i
$273$	10.3281	+	2.76742i	0.625087	+	0.167492i
$274$	−1.75856	−	0.00526523i	−0.106239	−	0.000318084i
$275$	8.82669	−	6.17139i	0.532270	−	0.372149i
$276$	−16.5483	−	6.13554i	−0.996089	−	0.369316i
$277$	−12.0451	+	3.22747i	−0.723719	+	0.193920i	−0.601830	−	0.798624i	$-0.705562\pi$
$277$	−12.0451	+	3.22747i	−0.723719	+	0.193920i	−0.121888	+	0.992544i	$0.538895\pi$
$278$	−8.45109	−	31.9219i	−0.506863	−	1.91455i
$279$	19.7787	−	16.5963i	1.18412	−	0.993593i
$280$	24.6720	−	15.3961i	1.47443	−	0.920094i
$281$	28.7295	+	10.4567i	1.71386	+	0.623793i	0.997280	−	0.0737124i	$-0.0234847\pi$
$281$	28.7295	+	10.4567i	1.71386	+	0.623793i	0.716579	+	0.697506i	$0.245707\pi$
$282$	3.64375	+	5.23712i	0.216982	+	0.311866i
$283$	6.58865	−	4.61342i	0.391654	−	0.274239i	−0.361118	−	0.932520i	$-0.617605\pi$
$283$	6.58865	−	4.61342i	0.391654	−	0.274239i	0.752773	+	0.658281i	$0.228716\pi$
$284$	8.96442	−	15.3143i	0.531941	−	0.908737i
$285$	20.9143	−	12.1152i	1.23885	−	0.717645i
$286$	1.42086	+	2.47811i	0.0840172	+	0.146534i
$287$	−30.8413	−	44.0459i	−1.82050	−	2.59995i
$288$	16.0316	+	7.76991i	0.944670	+	0.457846i
$289$	−5.80204	+	15.9410i	−0.341297	+	0.937705i
$290$	−4.77199	−	15.3130i	−0.280221	−	0.899213i
$291$	26.6422	+	31.7509i	1.56179	+	1.86127i
$292$	−14.1572	−	14.3278i	−0.828490	−	0.838472i
$293$	0.996458	+	3.71883i	0.0582137	+	0.217257i	0.988905	−	0.148549i	$-0.0474602\pi$
$293$	0.996458	+	3.71883i	0.0582137	+	0.217257i	−0.930691	+	0.365805i	$0.880794\pi$
$294$	−31.7691	−	38.0920i	−1.85281	−	2.22157i
$295$	0.0922961	+	0.223041i	0.00537369	+	0.0129860i
$296$	−10.6655	−	6.28612i	−0.619919	−	0.365373i
$297$	0.206435	−	0.770424i	0.0119785	−	0.0447045i
$298$	2.42106	+	5.23284i	0.140248	+	0.303130i
$299$	−3.13573	+	1.14131i	−0.181344	+	0.0660037i
$300$	−8.32545	−	23.3585i	−0.480670	−	1.34860i
$301$	−11.5430	−	9.68572i	−0.665327	−	0.558275i
$302$	−13.6658	−	6.42233i	−0.786377	−	0.369564i
$303$	−13.2503	−	13.2503i	−0.761210	−	0.761210i
$304$	16.5744	+	5.41202i	0.950606	+	0.310401i
$305$	8.39295	−	1.85762i	0.480579	−	0.106367i
$306$	−0.286473	−	0.794471i	−0.0163766	−	0.0454169i
$307$	19.6867	−	1.72237i	1.12358	−	0.0983007i	0.489816	−	0.871826i	$-0.337064\pi$
$307$	19.6867	−	1.72237i	1.12358	−	0.0983007i	0.633766	+	0.773525i	$0.281508\pi$
$308$	1.84465	−	19.7234i	0.105109	−	1.12385i
$309$	1.57944	+	4.33947i	0.0898511	+	0.246864i
$310$	−15.7136	−	20.6207i	−0.892473	−	1.17117i
$311$	−3.00066	+	1.73243i	−0.170152	+	0.0982372i	−0.582657	−	0.812718i	$-0.697987\pi$
$311$	−3.00066	+	1.73243i	−0.170152	+	0.0982372i	0.412506	+	0.910955i	$0.364654\pi$
$312$	6.36799	−	1.64514i	0.360517	−	0.0931377i
$313$	8.55910	+	5.99315i	0.483789	+	0.338753i	0.789892	−	0.613246i	$-0.210136\pi$
$313$	8.55910	+	5.99315i	0.483789	+	0.338753i	−0.306103	+	0.951998i	$0.599025\pi$
$314$	6.46668	−	5.39328i	0.364936	−	0.304360i
$315$	−28.7276	+	14.9420i	−1.61862	+	0.841886i
$316$	0.0292989	−	4.89281i	0.00164819	−	0.275242i
$317$	24.2689	+	2.12326i	1.36308	+	0.119254i	0.745107	−	0.666945i	$-0.232399\pi$
$317$	24.2689	+	2.12326i	1.36308	+	0.119254i	0.617973	+	0.786199i	$0.287954\pi$
$318$	38.1349	−	3.22135i	2.13850	−	0.180644i
$319$	−10.2666	−	3.73673i	−0.574818	−	0.209217i
$320$	8.54916	−	15.7134i	0.477913	−	0.878407i
$321$	5.99807	−	34.0167i	0.334780	−	1.89863i
$322$	22.3346	+	6.05626i	1.24466	+	0.337502i
$323$	−0.382971	−	0.732468i	−0.0213091	−	0.0407556i
$324$	14.7226	+	8.61806i	0.817922	+	0.478781i
$325$	−4.05882	−	2.34712i	−0.225143	−	0.130195i
$326$	−1.61339	+	8.99246i	−0.0893573	+	0.498046i
$327$	31.9083	−	14.8791i	1.76453	−	0.822816i
$328$	−29.8491	−	14.2466i	−1.64814	−	0.786639i
$329$	−5.37713	−	6.40821i	−0.296451	−	0.353296i
$330$	−16.0926	−	5.13314i	−0.885867	−	0.282570i
$331$	6.05244	+	3.49438i	0.332672	+	0.192068i	0.657027	−	0.753867i	$-0.271814\pi$
$331$	6.05244	+	3.49438i	0.332672	+	0.192068i	−0.324355	+	0.945935i	$0.605147\pi$
$332$	29.0500	−	13.3350i	1.59433	−	0.731856i
$333$	11.2918	+	7.90658i	0.618785	+	0.433278i
$334$	−0.0994894	+	33.2290i	−0.00544382	+	1.81821i
$335$	13.4592	+	0.592320i	0.735353	+	0.0323619i
$336$	−42.6699	−	16.1119i	−2.32783	−	0.878974i
$337$	7.29955	+	3.40384i	0.397632	+	0.185419i	0.611140	−	0.791522i	$-0.290711\pi$
$337$	7.29955	+	3.40384i	0.397632	+	0.185419i	−0.213508	+	0.976941i	$0.568489\pi$
$338$	−9.87380	+	14.0118i	−0.537064	+	0.762140i
$339$	11.9446	+	10.0227i	0.648742	+	0.544359i
$340$	−0.810367	+	0.249875i	−0.0439483	+	0.0135514i
$341$	−17.6595			−0.956317
$342$	−17.9270	−	7.45082i	−0.969382	−	0.402894i
$343$	23.2274	+	23.2274i	1.25416	+	1.25416i
$344$	−9.11306	−	1.69141i	−0.491343	−	0.0911949i
$345$	9.11743	−	17.4996i	0.490866	−	0.942146i
$346$	−7.86232	+	1.36208i	−0.422681	+	0.0732259i
$347$	−7.91969	+	16.9838i	−0.425151	+	0.911740i	0.570735	+	0.821134i	$0.306658\pi$
$347$	−7.91969	+	16.9838i	−0.425151	+	0.911740i	−0.995887	+	0.0906062i	$0.971120\pi$
$348$	−14.5517	+	20.5193i	−0.780051	+	1.09995i
$349$	9.77343	−	5.64269i	0.523160	−	0.302047i	−0.215067	−	0.976599i	$-0.568997\pi$
$349$	9.77343	−	5.64269i	0.523160	−	0.302047i	0.738227	+	0.674553i	$0.235664\pi$
$350$	13.6324	+	29.5185i	0.728682	+	1.57783i
$351$	−0.341947	+	0.0602945i	−0.0182518	+	0.00321828i
$352$	−4.98374	−	11.1193i	−0.265634	−	0.592659i
$353$	−3.03973	−	11.3444i	−0.161789	−	0.603803i	−0.998428	−	0.0560493i	$-0.982150\pi$
$353$	−3.03973	−	11.3444i	−0.161789	−	0.603803i	0.836639	−	0.547754i	$-0.184517\pi$
$354$	0.190268	−	0.327287i	0.0101126	−	0.0173951i
$355$	15.7357	+	12.0831i	0.835162	+	0.641303i
$356$	−0.687870	+	3.76899i	−0.0364570	+	0.199756i
$357$	0.913781	+	1.95961i	0.0483624	+	0.103714i
$358$	−6.86103	−	9.86127i	−0.362617	−	0.521184i
$359$	−0.599756	+	3.40139i	−0.0316539	+	0.179518i	−0.996536	−	0.0831662i	$-0.973497\pi$
$359$	−0.599756	+	3.40139i	−0.0316539	+	0.179518i	0.964882	+	0.262685i	$0.0846079\pi$
$360$	−10.8582	+	16.6981i	−0.572278	+	0.880069i
$361$	−18.3701	−	4.85167i	−0.966848	−	0.255351i
$362$	−25.1951	−	6.83193i	−1.32423	−	0.359078i
$363$	12.9195	−	9.04631i	0.678096	−	0.474808i
$364$	−8.12116	+	2.90091i	−0.425664	+	0.152049i
$365$	17.8709	−	13.7030i	0.935407	−	0.717247i
$366$	−10.3016	−	8.69673i	−0.538471	−	0.454585i
$367$	−0.761870	+	8.70821i	−0.0397693	+	0.454565i	0.950036	+	0.312140i	$0.101046\pi$
$367$	−0.761870	+	8.70821i	−0.0397693	+	0.454565i	−0.989806	+	0.142425i	$0.954510\pi$
$368$	13.7925	−	3.51920i	0.718983	−	0.183451i
$369$	31.8932	+	18.4136i	1.66029	+	0.958571i
$370$	8.46276	−	10.9529i	0.439958	−	0.569415i
$371$	−49.4174	+	8.71362i	−2.56562	+	0.452389i
$372$	−10.7586	+	39.2111i	−0.557809	+	2.03300i
$373$	14.5947	+	3.91063i	0.755684	+	0.202485i	0.616038	−	0.787717i	$-0.288737\pi$
$373$	14.5947	+	3.91063i	0.755684	+	0.202485i	0.139646	+	0.990201i	$0.455404\pi$
$374$	−0.199189	+	0.542210i	−0.0102998	+	0.0280370i
$375$	27.0739	−	5.97256i	1.39809	−	0.308422i
$376$	−4.81929	−	1.80326i	−0.248536	−	0.0929962i
$377$	0.414531	+	4.73811i	0.0213494	+	0.244025i
$378$	2.17925	+	1.02415i	0.112088	+	0.0526768i
$379$	−8.27687			−0.425154			−0.212577	−	0.977144i	$-0.568186\pi$
$379$	−8.27687			−0.425154			−0.212577	+	0.977144i	$0.568186\pi$
$380$	−8.31849	+	17.6296i	−0.426729	+	0.904379i
$381$	17.3056			0.886591
$382$	10.3255	+	4.85254i	0.528298	+	0.248278i
$383$	−0.630877	−	7.21096i	−0.0322363	−	0.368463i	−0.995129	−	0.0985791i	$-0.968570\pi$
$383$	−0.630877	−	7.21096i	−0.0322363	−	0.368463i	0.962893	−	0.269884i	$-0.0869853\pi$
$384$	−27.7253	+	4.29170i	−1.41485	+	0.219010i
$385$	21.6210	+	4.80114i	1.10191	+	0.244689i
$386$	−10.2505	+	27.9029i	−0.521739	+	1.42022i
$387$	9.96860	+	2.67108i	0.506732	+	0.135779i
$388$	−32.2372	−	8.84517i	−1.63660	−	0.449046i
$389$	−14.5970	+	2.57384i	−0.740096	+	0.130499i	−0.530971	−	0.847390i	$-0.678173\pi$
$389$	−14.5970	+	2.57384i	−0.740096	+	0.130499i	−0.209125	+	0.977889i	$0.567062\pi$
$390$	0.935446	+	7.29364i	0.0473681	+	0.369328i
$391$	−0.584385	−	0.337395i	−0.0295536	−	0.0170628i
$392$	38.5468	+	10.7006i	1.94691	+	0.540461i
$393$	1.39694	−	15.9671i	0.0704663	−	0.805433i
$394$	5.33200	+	4.50136i	0.268622	+	0.226775i
$395$	5.42337	+	0.715916i	0.272880	+	0.0360216i
$396$	4.56393	+	12.7768i	0.229346	+	0.642060i
$397$	−21.6941	+	15.1904i	−1.08880	+	0.762383i	−0.972980	−	0.230887i	$-0.925837\pi$
$397$	−21.6941	+	15.1904i	−1.08880	+	0.762383i	−0.115816	+	0.993271i	$0.536948\pi$
$398$	15.8769	+	4.30519i	0.795837	+	0.215800i
$399$	47.4292	+	14.8609i	2.37443	+	0.743973i
$400$	16.2364	+	11.6782i	0.811819	+	0.583909i
$401$	3.76720	−	21.3648i	0.188125	−	1.06691i	−0.733749	−	0.679420i	$-0.762231\pi$
$401$	3.76720	−	21.3648i	0.188125	−	1.06691i	0.921874	−	0.387489i	$-0.126658\pi$
$402$	−12.0673	−	17.3442i	−0.601862	−	0.865049i
$403$	3.24899	+	6.96748i	0.161844	+	0.347075i
$404$	14.8676	+	2.71346i	0.739693	+	0.135000i
$405$	−11.6162	+	15.1277i	−0.577214	+	0.751700i
$406$	16.5771	−	28.5148i	0.822706	−	1.41517i
$407$	−2.44022	−	9.10703i	−0.120957	−	0.451419i
$408$	1.08257	+	0.772605i	0.0535951	+	0.0382496i
$409$	−31.1766	+	5.49727i	−1.54158	+	0.271822i	−0.878873	−	0.477055i	$-0.841704\pi$
$409$	−31.1766	+	5.49727i	−1.54158	+	0.271822i	−0.662708	+	0.748878i	$0.730593\pi$
$410$	19.9727	−	31.1209i	0.986381	−	1.53695i
$411$	−2.67048	+	1.54180i	−0.131725	+	0.0760514i
$412$	−3.03808	−	2.15451i	−0.149676	−	0.106145i
$413$	−0.209779	+	0.449872i	−0.0103225	+	0.0221368i
$414$	−15.6167	+	2.70546i	−0.767519	+	0.132966i
$415$	10.7346	+	34.0870i	0.526941	+	1.67327i
$416$	−3.47015	+	4.01203i	−0.170138	+	0.196706i
$417$	−40.9432	−	40.9432i	−2.00500	−	2.00500i
$418$	6.11713	+	11.7854i	0.299199	+	0.576443i
$419$	−13.4955			−0.659300			−0.329650	−	0.944103i	$-0.606931\pi$
$419$	−13.4955			−0.659300			−0.329650	+	0.944103i	$0.606931\pi$
$420$	23.8325	−	45.0822i	1.16291	−	2.19978i
$421$	22.3714	+	18.7718i	1.09031	+	0.914882i	0.996736	−	0.0807296i	$-0.0257250\pi$
$421$	22.3714	+	18.7718i	1.09031	+	0.914882i	0.0935782	+	0.995612i	$0.470169\pi$
$422$	−17.5248	+	24.8693i	−0.853096	+	1.21062i
$423$	5.19260	+	2.42135i	0.252473	+	0.117730i
$424$	−23.8221	+	19.6272i	−1.15690	+	0.953182i
$425$	−0.163990	−	0.933822i	−0.00795467	−	0.0452970i
$426$	0.0931611	−	31.1154i	0.00451367	−	1.50755i
$427$	14.4801	+	10.1390i	0.700739	+	0.490663i
$428$	11.6221	+	25.3184i	0.561776	+	1.22381i
$429$	4.33781	+	2.50444i	0.209431	+	0.120915i
$430$	3.14913	−	9.87263i	0.151865	−	0.476101i
$431$	−22.6156	−	26.9522i	−1.08935	−	1.29824i	−0.951453	−	0.307795i	$-0.900409\pi$
$431$	−22.6156	−	26.9522i	−1.08935	−	1.29824i	−0.137901	−	0.990446i	$-0.544036\pi$
$432$	1.47693	−	0.111409i	0.0710591	−	0.00536019i
$433$	−0.0563792	+	0.0262900i	−0.00270941	+	0.00126342i	−0.423972	−	0.905675i	$-0.639365\pi$
$433$	−0.0563792	+	0.0262900i	−0.00270941	+	0.00126342i	0.421263	+	0.906938i	$0.361587\pi$
$434$	9.41484	−	52.4750i	0.451927	−	2.51888i
$435$	−20.7290	−	19.0079i	−0.993880	−	0.911358i
$436$	−14.3446	+	24.5055i	−0.686981	+	1.17360i
$437$	−14.7852	+	4.69095i	−0.707274	+	0.224399i
$438$	−34.0880	−	9.24333i	−1.62879	−	0.441663i
$439$	−3.26549	+	18.5195i	−0.155853	+	0.883887i	0.802148	+	0.597125i	$0.203690\pi$
$439$	−3.26549	+	18.5195i	−0.155853	+	0.883887i	−0.958002	+	0.286763i	$0.907421\pi$
$440$	13.0304	−	3.97522i	0.621202	−	0.189511i
$441$	−41.8568	−	15.2346i	−1.99318	−	0.725459i
$442$	0.250573	−	0.0211665i	0.0119185	−	0.00100679i
$443$	25.8116	+	2.25822i	1.22635	+	0.107291i	0.681863	−	0.731480i	$-0.261170\pi$
$443$	25.8116	+	2.25822i	1.22635	+	0.107291i	0.544484	+	0.838771i	$0.316725\pi$
$444$	−21.7078	−	0.129990i	−1.03021	−	0.00616904i
$445$	−4.08476	−	1.28948i	−0.193636	−	0.0611272i
$446$	10.7305	−	8.94934i	0.508103	−	0.423764i
$447$	8.28172	+	5.79892i	0.391712	+	0.274280i
$448$	35.6977	−	8.88106i	1.68656	−	0.419591i
$449$	−10.7206	+	6.18954i	−0.505936	+	0.292102i	−0.731162	−	0.682204i	$-0.761021\pi$
$449$	−10.7206	+	6.18954i	−0.505936	+	0.292102i	0.225226	+	0.974307i	$0.427688\pi$
$450$	−17.0062	−	14.3771i	−0.801679	−	0.677743i
$451$	−8.61499	−	23.6695i	−0.405664	−	1.11455i
$452$	−12.5211	−	1.17105i	−0.588944	−	0.0550815i
$453$	−26.3761	+	2.30761i	−1.23926	+	0.108421i
$454$	6.02544	+	16.7103i	0.282788	+	0.784252i
$455$	−2.08356	−	9.41379i	−0.0976787	−	0.441325i
$456$	29.8949	−	6.40245i	1.39996	−	0.299822i
$457$	19.8842	+	19.8842i	0.930143	+	0.930143i	0.997714	−	0.0675717i	$-0.0215251\pi$
$457$	19.8842	+	19.8842i	0.930143	+	0.930143i	−0.0675717	+	0.997714i	$0.521525\pi$
$458$	6.23145	+	2.92852i	0.291176	+	0.136841i
$459$	−0.0537869	−	0.0451326i	−0.00251056	−	0.00210661i
$460$	1.97726	+	15.7912i	0.0921903	+	0.736269i
$461$	−23.0693	+	8.39654i	−1.07444	+	0.391066i	−0.817837	−	0.575450i	$-0.804827\pi$
$461$	−23.0693	+	8.39654i	−1.07444	+	0.391066i	−0.256607	+	0.966516i	$0.582605\pi$
$462$	−14.5855	−	31.5247i	−0.678578	−	1.46666i
$463$	−0.316501	+	1.18120i	−0.0147090	+	0.0548949i	−0.972890	−	0.231267i	$-0.925713\pi$
$463$	−0.316501	+	1.18120i	−0.0147090	+	0.0548949i	0.958181	+	0.286162i	$0.0923795\pi$
$464$	0.242971	−	20.2869i	0.0112797	−	0.941797i
$465$	−41.9931	−	17.4112i	−1.94738	−	0.807424i
$466$	−14.3032	−	17.1499i	−0.662584	−	0.794455i
$467$	−4.43296	−	16.5440i	−0.205133	−	0.765566i	−0.989409	−	0.145154i	$-0.953632\pi$
$467$	−4.43296	−	16.5440i	−0.205133	−	0.765566i	0.784276	−	0.620412i	$-0.213035\pi$
$468$	4.20137	−	4.15135i	0.194208	−	0.191896i
$469$	17.8079	+	21.2226i	0.822290	+	0.979967i
$470$	2.67346	−	5.09404i	0.123318	−	0.234971i
$471$	5.04998	−	13.8747i	0.232691	−	0.639313i
$472$	0.0238781	+	0.304394i	0.00109908	+	0.0140109i
$473$	−4.04872	−	5.78217i	−0.186160	−	0.265864i
$474$	−4.26751	−	7.44292i	−0.196013	−	0.341865i
$475$	−18.3942	−	11.6899i	−0.843982	−	0.536372i
$476$	−1.50497	−	0.880955i	−0.0689804	−	0.0403785i
$477$	28.1526	−	19.7127i	1.28902	−	0.902582i
$478$	−6.06430	−	8.71614i	−0.277374	−	0.398667i
$479$	−0.624119	−	0.227161i	−0.0285167	−	0.0103792i	0.327722	−	0.944774i	$-0.393719\pi$
$479$	−0.624119	−	0.227161i	−0.0285167	−	0.0103792i	−0.356239	+	0.934395i	$0.615941\pi$
$480$	−0.888068	−	31.3545i	−0.0405346	−	1.43113i
$481$	−3.14419	+	2.63829i	−0.143363	+	0.120295i
$482$	4.80641	+	18.1550i	0.218926	+	0.826938i
$483$	39.1946	−	10.5022i	1.78342	−	0.477865i
$484$	−4.42209	+	11.9269i	−0.201004	+	0.542131i
$485$	14.3145	−	34.5245i	0.649990	−	1.56768i
$486$	31.4841	+	0.0942651i	1.42815	+	0.00427595i
$487$	−3.84320	−	1.02978i	−0.174152	−	0.0466639i	0.170689	−	0.985325i	$-0.445401\pi$
$487$	−3.84320	−	1.02978i	−0.174152	−	0.0466639i	−0.344841	+	0.938661i	$0.612067\pi$
$488$	10.8229	+	1.04492i	0.489931	+	0.0473014i
$489$	5.47909	+	15.0537i	0.247773	+	0.680751i
$490$	−17.2540	+	41.2644i	−0.779457	+	1.86413i
$491$	16.9029	−	20.1441i	0.762817	−	0.909090i	−0.235206	−	0.971946i	$-0.575576\pi$
$491$	16.9029	−	20.1441i	0.762817	−	0.909090i	0.998023	+	0.0628558i	$0.0200208\pi$
$492$	−57.8040	+	4.70859i	−2.60601	+	0.212280i
$493$	−0.680083	+	0.680083i	−0.0306294	+	0.0306294i
$494$	3.52445	−	4.58176i	0.158572	−	0.206143i
$495$	−14.8105	+	3.27801i	−0.665682	+	0.147336i
$496$	−10.8462	−	30.9478i	−0.487007	−	1.38960i
$497$	3.55579	+	40.6428i	0.159499	+	1.82308i
$498$	32.2856	−	45.8160i	1.44675	−	2.05306i
$499$	−5.33382	+	1.94135i	−0.238774	+	0.0869068i	−0.458636	−	0.888624i	$-0.651662\pi$
$499$	−5.33382	+	1.94135i	−0.238774	+	0.0869068i	0.219861	+	0.975531i	$0.429440\pi$
$500$	−15.2222	+	16.3794i	−0.680756	+	0.732510i
$501$	29.1332	+	50.4602i	1.30158	+	2.25439i
$502$	−11.8056	−	11.8765i	−0.526908	−	0.530073i
$503$	18.5500	−	26.4922i	0.827105	−	1.18123i	−0.154061	−	0.988061i	$-0.549235\pi$
$503$	18.5500	−	26.4922i	0.827105	−	1.18123i	0.981166	−	0.193167i	$-0.0618759\pi$
$504$	−40.3993	+	6.74991i	−1.79953	+	0.300665i
$505$	−5.08665	+	16.1133i	−0.226353	+	0.717032i
$506$	9.37181	+	5.44830i	0.416628	+	0.242206i
$507$	−2.61961	+	29.9423i	−0.116341	+	1.32978i
$508$	−11.4809	+	7.93699i	−0.509383	+	0.352147i
$509$	−8.46424	+	23.2553i	−0.375171	+	1.03077i	0.598162	+	0.801375i	$0.295898\pi$
$509$	−8.46424	+	23.2553i	−0.375171	+	1.03077i	−0.973333	+	0.229398i	$0.926324\pi$
$510$	−1.00824	+	1.09295i	−0.0446457	+	0.0483966i
$511$	45.6060	+	8.04157i	2.01749	+	0.355738i
$512$	16.4253	−	15.5631i	0.725902	−	0.687798i
$513$	−1.59984	+	0.213543i	−0.0706345	+	0.00942817i
$514$	3.03291	+	5.28967i	0.133776	+	0.233317i
$515$	2.81430	−	3.06913i	0.124013	−	0.135242i
$516$	−15.3053	+	5.46709i	−0.673776	+	0.240675i
$517$	−1.65612	−	3.55157i	−0.0728363	−	0.156198i
$518$	28.3624	−	2.39584i	1.24617	−	0.105267i
$519$	−10.7183	+	8.99369i	−0.470480	+	0.394779i
$520$	−3.96574	−	4.40974i	−0.173909	−	0.193380i
$521$	5.34775	−	9.26257i	0.234289	−	0.405801i	−0.724777	−	0.688984i	$-0.758057\pi$
$521$	5.34775	−	9.26257i	0.234289	−	0.405801i	0.959066	+	0.283183i	$0.0913904\pi$
$522$	−2.03623	+	22.4982i	−0.0891234	+	0.984719i
$523$	−8.79194	+	12.5562i	−0.384445	+	0.549044i	−0.964005	−	0.265886i	$-0.914336\pi$
$523$	−8.79194	+	12.5562i	−0.384445	+	0.549044i	0.579560	+	0.814930i	$0.303225\pi$
$524$	6.39635	+	11.2336i	0.279426	+	0.490743i
$525$	46.6796	+	32.7338i	2.03727	+	1.42862i
$526$	−19.2614	−	7.07597i	−0.839839	−	0.308527i
$527$	−0.656998	+	1.40894i	−0.0286193	+	0.0613743i
$528$	−17.3541	−	12.4638i	−0.755240	−	0.542419i
$529$	6.64411	−	7.91814i	0.288874	−	0.344267i
$530$	−18.4446	−	29.1667i	−0.801180	−	1.26692i
$531$		−	0.339969i		−	0.0147534i
$532$	−38.2813	+	11.8938i	−1.65971	+	0.515661i
$533$	−7.75371	+	7.75371i	−0.335850	+	0.335850i
$534$	2.27877	+	6.31969i	0.0986121	+	0.273480i
$535$	−29.7084	+	9.35569i	−1.28441	+	0.404482i
$536$	15.9604	+	5.97201i	0.689385	+	0.257951i
$537$	−19.0913	−	8.90241i	−0.823850	−	0.384167i
$538$	−2.03408	−	4.39642i	−0.0876954	−	0.189543i
$539$	15.2330	+	26.3844i	0.656133	+	1.13646i
$540$	−0.0827110	+	1.65389i	−0.00355931	+	0.0711720i
$541$	−5.38065	−	30.5152i	−0.231332	−	1.31195i	−0.850202	−	0.526456i	$-0.823520\pi$
$541$	−5.38065	−	30.5152i	−0.231332	−	1.31195i	0.618870	−	0.785493i	$-0.287591\pi$
$542$	18.8662	+	1.70752i	0.810374	+	0.0733441i
$543$	−44.2146	+	11.8473i	−1.89743	+	0.508415i
$544$	−1.07255	−	0.0160574i	−0.0459850	−	0.000688457i
$545$	−25.1797	−	19.3350i	−1.07858	−	0.828219i
$546$	−9.75451	+	11.5545i	−0.417455	+	0.494489i
$547$	−16.3888	+	7.64224i	−0.700737	+	0.326759i	−0.740129	−	0.672465i	$-0.765236\pi$
$547$	−16.3888	+	7.64224i	−0.700737	+	0.326759i	0.0393924	+	0.999224i	$0.487458\pi$
$548$	1.06453	−	2.24765i	0.0454744	−	0.0960148i
$549$	−11.9229	−	2.10234i	−0.508858	−	0.0897255i
$550$	2.58955	+	15.0096i	0.110419	+	0.640011i
$551$	1.00400	+	22.0859i	0.0427717	+	0.940892i
$552$	17.8069	−	17.4898i	0.757912	−	0.744417i
$553$	6.45235	+	9.21491i	0.274382	+	0.391858i
$554$	3.11431	−	17.3581i	0.132314	−	0.737473i
$555$	3.17629	−	24.0618i	0.134826	−	1.02137i
$556$	45.9408	+	8.38455i	1.94832	+	0.355584i
$557$	24.2817	+	2.12437i	1.02885	+	0.0900125i	0.589060	−	0.808089i	$-0.299498\pi$
$557$	24.2817	+	2.12437i	1.02885	+	0.0900125i	0.439787	+	0.898102i	$0.355054\pi$
$558$	9.34485	+	35.2979i	0.395599	+	1.49428i
$559$	−1.53645	+	2.66120i	−0.0649847	+	0.112557i
$560$	4.86537	+	40.8390i	0.205599	+	1.72576i
$561$	0.175884	+	0.997487i	0.00742582	+	0.0421139i
$562$	−30.6647	+	30.4816i	−1.29351	+	1.28579i
$563$	−3.79164	+	14.1506i	−0.159799	+	0.596376i	0.838848	+	0.544366i	$0.183230\pi$
$563$	−3.79164	+	14.1506i	−0.159799	+	0.596376i	−0.998647	+	0.0520106i	$0.983437\pi$
$564$	−8.89483	+	1.51354i	−0.374540	+	0.0637314i
$565$	3.04793	−	13.7258i	0.128228	−	0.577449i
$566$	1.94168	+	11.2079i	0.0816148	+	0.471104i
$567$	−39.0725	+	3.41840i	−1.64089	+	0.143559i
$568$	14.2089	+	20.6854i	0.596192	+	0.867940i
$569$		−	7.39898i		−	0.310181i	−0.987900	−	0.155091i	$-0.950433\pi$
$569$		−	7.39898i		−	0.310181i	0.987900	−	0.155091i	$-0.0495670\pi$
$570$	2.92643	+	34.0559i	0.122575	+	1.42645i
$571$			0.238481i			0.00998013i	0.999988	+	0.00499007i	$0.00158839\pi$
$571$			0.238481i			0.00998013i	−0.999988	+	0.00499007i	$0.998412\pi$
$572$	−4.02643	+	0.327984i	−0.168354	+	0.0137137i
$573$	19.9290	−	1.74356i	0.832547	−	0.0728384i
$574$	74.9264	−	12.9804i	3.12737	−	0.541790i
$575$	−17.7930	−	0.0123518i	−0.742018	−	0.000515107i
$576$	−19.5880	+	15.8454i	−0.816165	+	0.660227i
$577$	−11.2258	+	41.8953i	−0.467336	+	1.74412i	0.181690	+	0.983356i	$0.441843\pi$
$577$	−11.2258	+	41.8953i	−0.467336	+	1.74412i	−0.649026	+	0.760766i	$0.724823\pi$
$578$	−16.9132	−	17.0148i	−0.703495	−	0.707721i
$579$	9.05124	+	51.3321i	0.376157	+	2.13329i
$580$	22.4698	+	3.10315i	0.933009	+	0.128851i
$581$	−36.7450	+	63.6442i	−1.52444	+	2.64040i
$582$	−56.6641	+	15.0014i	−2.34880	+	0.621828i
$583$	−23.4172	−	2.04874i	−0.969840	−	0.0848500i
$584$	26.8541	−	9.50181i	1.11123	−	0.393188i
$585$	4.01815	+	5.24032i	0.166130	+	0.216661i
$586$	−5.35918	−	0.961521i	−0.221386	−	0.0397201i
$587$	14.9595	+	21.3644i	0.617444	+	0.881802i	0.999096	−	0.0425043i	$-0.0135336\pi$
$587$	14.9595	+	21.3644i	0.617444	+	0.881802i	−0.381652	+	0.924306i	$0.624645\pi$
$588$	67.8640	−	17.7493i	2.79867	−	0.731967i
$589$	13.7347	+	32.9910i	0.565929	+	1.35937i
$590$	−0.340991	−	0.0160296i	−0.0140384	−	0.000659930i
$591$	12.0498	+	2.12471i	0.495664	+	0.0873989i
$592$	14.4611	−	9.86979i	0.594347	−	0.405646i
$593$	6.48593	−	3.02444i	0.266345	−	0.124199i	−0.284858	−	0.958570i	$-0.591947\pi$
$593$	6.48593	−	3.02444i	0.266345	−	0.124199i	0.551204	+	0.834371i	$0.314169\pi$
$594$	0.861907	+	0.727635i	0.0353645	+	0.0298552i
$595$	1.18743	−	1.54638i	0.0486800	−	0.0633954i
$596$	−8.15389	−	0.0488268i	−0.333996	−	0.00200002i
$597$	27.8622	−	7.46565i	1.14032	−	0.305549i
$598$	0.425378	−	4.69998i	0.0173950	−	0.192196i
$599$	−2.97615	−	16.8786i	−0.121602	−	0.689640i	−0.983268	−	0.182164i	$-0.941690\pi$
$599$	−2.97615	−	16.8786i	−0.121602	−	0.689640i	0.861666	−	0.507476i	$-0.169421\pi$
$600$	34.9048	+	3.39440i	1.42498	+	0.138576i
$601$	−3.16661	−	5.48472i	−0.129169	−	0.223726i	0.794186	−	0.607675i	$-0.207897\pi$
$601$	−3.16661	−	5.48472i	−0.129169	−	0.223726i	−0.923355	+	0.383948i	$0.874564\pi$
$602$	19.3401	−	8.94804i	0.788244	−	0.364695i
$603$	−17.1967	−	8.01897i	−0.700305	−	0.326558i
$604$	16.4401	−	13.6280i	0.668939	−	0.554514i
$605$	−12.6125	−	6.57123i	−0.512772	−	0.267158i
$606$	24.9294	−	8.98914i	1.01269	−	0.365159i
$607$	−14.6410	+	14.6410i	−0.594260	+	0.594260i	−0.938779	−	0.344519i	$-0.888042\pi$
$607$	−14.6410	+	14.6410i	−0.594260	+	0.594260i	0.344519	+	0.938779i	$0.388042\pi$
$608$	−16.8966	+	17.9585i	−0.685246	+	0.728312i
$609$		−	57.8351i		−	2.34360i
$610$	−2.67083	+	11.8597i	−0.108139	+	0.480183i
$611$	−1.09656	+	1.30683i	−0.0443622	+	0.0528688i
$612$	1.18917	+	0.111218i	0.0480695	+	0.00449574i
$613$	7.01290	−	15.0392i	0.283248	−	0.607428i	−0.712280	−	0.701896i	$-0.752337\pi$
$613$	7.01290	−	15.0392i	0.283248	−	0.607428i	0.995528	+	0.0944678i	$0.0301150\pi$
$614$	−9.63723	+	26.2334i	−0.388927	+	1.05869i
$615$	2.85081	−	64.7782i	0.114956	−	2.61211i
$616$	24.1348	+	14.2248i	0.972418	+	0.573133i
$617$	18.2039	−	25.9979i	0.732862	−	1.04664i	−0.263766	−	0.964587i	$-0.584965\pi$
$617$	18.2039	−	25.9979i	0.732862	−	1.04664i	0.996628	−	0.0820490i	$-0.0261464\pi$
$618$	−6.50421	−	0.588673i	−0.261638	−	0.0236799i
$619$	23.5787	−	40.8394i	0.947706	−	1.64148i	0.197466	−	0.980310i	$-0.436729\pi$
$619$	23.5787	−	40.8394i	0.947706	−	1.64148i	0.750240	−	0.661166i	$-0.229938\pi$
$620$	35.8446	−	7.70864i	1.43955	−	0.309587i
$621$	−1.00941	+	0.846993i	−0.0405061	+	0.0339886i
$622$	−0.412451	−	4.88267i	−0.0165378	−	0.195777i
$623$	−3.72262	−	7.98319i	−0.149144	−	0.319840i
$624$	−1.72475	+	9.14007i	−0.0690453	+	0.365896i
$625$	−16.0431	−	19.1734i	−0.641723	−	0.766936i
$626$	−12.8191	+	7.35002i	−0.512354	+	0.293766i
$627$	19.6593	+	12.4748i	0.785116	+	0.498196i
$628$	3.01320	+	11.5209i	0.120240	+	0.459735i
$629$	−0.817375	−	0.144125i	−0.0325909	−	0.00574665i
$630$	−1.84463	−	45.7567i	−0.0734919	−	1.82299i
$631$	8.76700	−	24.0871i	0.349009	−	0.958893i	−0.633675	−	0.773600i	$-0.718454\pi$
$631$	8.76700	−	24.0871i	0.349009	−	0.958893i	0.982683	−	0.185293i	$-0.0593236\pi$
$632$	6.24477	+	2.98056i	0.248403	+	0.118560i
$633$	−4.64950	+	53.1440i	−0.184801	+	2.11229i
$634$	−17.3155	+	29.7851i	−0.687688	+	1.18292i
$635$	−7.20068	−	13.8441i	−0.285750	−	0.549386i
$636$	−18.8153	+	50.7472i	−0.746077	+	2.01226i
$637$	7.60727	−	10.8643i	0.301411	−	0.430460i
$638$	10.9581	−	10.8927i	0.433836	−	0.431246i
$639$	−13.9713	−	24.1989i	−0.552695	−	0.957295i
$640$	14.9695	+	20.3940i	0.591722	+	0.806142i
$641$	−2.94122	+	1.07052i	−0.116171	+	0.0422829i	−0.399452	−	0.916754i	$-0.630799\pi$
$641$	−2.94122	+	1.07052i	−0.116171	+	0.0422829i	0.283280	+	0.959037i	$0.408577\pi$
$642$	39.9307	+	28.1383i	1.57594	+	1.11053i
$643$	2.83670	+	32.4236i	0.111868	+	1.27866i	0.819910	+	0.572492i	$0.194023\pi$
$643$	2.83670	+	32.4236i	0.111868	+	1.27866i	−0.708042	+	0.706170i	$0.750421\pi$
$644$	−21.1859	+	24.9435i	−0.834842	+	0.982913i
$645$	−3.92671	−	17.7414i	−0.154614	−	0.698566i
$646$	1.16786	−	0.0495859i	0.0459488	−	0.00195093i
$647$	−16.3084	+	16.3084i	−0.641148	+	0.641148i	−0.950838	−	0.309690i	$-0.899775\pi$
$647$	−16.3084	+	16.3084i	−0.641148	+	0.641148i	0.309690	+	0.950838i	$0.399775\pi$
$648$	−19.8862	+	13.6599i	−0.781202	+	0.536611i
$649$	−0.149466	+	0.178127i	−0.00586706	+	0.00699209i
$650$	5.44553	−	3.78315i	0.213591	−	0.148387i
$651$	−31.9729	−	87.8449i	−1.25312	−	3.44291i
$652$	−10.5391	−	7.47403i	−0.412745	−	0.292706i
$653$	2.30268	+	0.617000i	0.0901107	+	0.0241451i	0.303593	−	0.952802i	$-0.401814\pi$
$653$	2.30268	+	0.617000i	0.0901107	+	0.0241451i	−0.213482	+	0.976947i	$0.568480\pi$
$654$	−0.149074	+	49.7899i	−0.00582924	+	1.94694i
$655$	−13.3546	+	5.52623i	−0.521807	+	0.215927i
$656$	36.1890	−	29.6349i	1.41294	−	1.15705i
$657$	−30.6366	+	8.20905i	−1.19525	+	0.320265i
$658$	11.4364	−	3.02770i	0.445836	−	0.118032i
$659$	13.3997	−	11.2437i	0.521978	−	0.437992i	−0.343343	−	0.939210i	$-0.611559\pi$
$659$	13.3997	−	11.2437i	0.521978	−	0.437992i	0.865321	+	0.501219i	$0.167115\pi$
$660$	16.2498	−	17.5095i	0.632523	−	0.681558i
$661$	−21.3765	−	7.78041i	−0.831450	−	0.302623i	−0.108996	−	0.994042i	$-0.534764\pi$
$661$	−21.3765	−	7.78041i	−0.831450	−	0.302623i	−0.722454	+	0.691419i	$0.756986\pi$
$662$	−8.11310	+	5.64473i	−0.315324	+	0.219389i
$663$	0.361195	−	0.252911i	0.0140276	−	0.00982226i
$664$	−0.406028	+	45.2027i	−0.0157569	+	1.75421i
$665$	−7.84643	−	44.1258i	−0.304271	−	1.71113i
$666$	−16.9119	+	9.69666i	−0.655321	+	0.375738i
$667$	10.3528	+	14.7853i	0.400861	+	0.572489i
$668$	−42.4706	−	20.1148i	−1.64324	−	0.778267i
$669$	8.37969	−	23.0230i	0.323978	−	0.890121i
$670$	−8.85391	+	16.8703i	−0.342056	+	0.651758i
$671$	5.32274	+	6.34339i	0.205482	+	0.244884i
$672$	46.2881	−	44.9226i	1.78560	−	1.73293i
$673$	0.940555	+	3.51020i	0.0362557	+	0.135308i	0.981682	−	0.190529i	$-0.0610204\pi$
$673$	0.940555	+	3.51020i	0.0362557	+	0.135308i	−0.945426	+	0.325838i	$0.894354\pi$
$674$	−8.74737	+	7.29539i	−0.336936	+	0.281008i
$675$	−1.82306	−	0.322760i	−0.0701697	−	0.0124230i
$676$	−11.9948	−	21.0658i	−0.461337	−	0.810224i
$677$	4.76805	−	17.7946i	0.183251	−	0.683902i	−0.811747	−	0.584009i	$-0.801483\pi$
$677$	4.76805	−	17.7946i	0.183251	−	0.683902i	0.994998	−	0.0998929i	$-0.0318500\pi$
$678$	−20.0130	+	9.25938i	−0.768596	+	0.355604i
$679$	72.2214	−	26.2864i	2.77160	−	1.00878i
$680$	0.167623	−	1.18750i	0.00642804	−	0.0455387i
$681$	23.8605	+	20.0213i	0.914336	+	0.767219i
$682$	10.6223	−	22.6027i	0.406750	−	0.865504i
$683$	18.2392	+	18.2392i	0.697905	+	0.697905i	0.963958	−	0.266053i	$-0.0857197\pi$
$683$	18.2392	+	18.2392i	0.697905	+	0.697905i	−0.266053	+	0.963958i	$0.585720\pi$
$684$	20.3197	−	18.4634i	0.776942	−	0.705965i
$685$	2.34457	+	1.49480i	0.0895813	+	0.0571133i
$686$	−43.7006	+	15.7577i	−1.66850	+	0.601632i
$687$	12.0272	−	1.05224i	0.458867	−	0.0401456i
$688$	7.64644	−	10.6466i	0.291518	−	0.405896i
$689$	3.49996	+	9.61606i	0.133338	+	0.366343i
$690$	16.9138	+	22.1957i	0.643898	+	0.844975i
$691$	−18.0048	+	10.3951i	−0.684934	+	0.395447i	−0.801711	−	0.597711i	$-0.796077\pi$
$691$	−18.0048	+	10.3951i	−0.684934	+	0.395447i	0.116778	+	0.993158i	$0.462744\pi$
$692$	2.98589	−	10.8824i	0.113507	−	0.413688i
$693$	−25.5520	−	17.8917i	−0.970640	−	0.679649i
$694$	−16.9742	−	20.3525i	−0.644330	−	0.772569i
$695$	−15.7177	+	49.7898i	−0.596205	+	1.88864i
$696$	−17.5101	−	30.9674i	−0.663718	−	1.17382i
$697$	−2.20894	−	0.193257i	−0.0836696	−	0.00732015i
$698$	1.34339	+	15.9033i	0.0508481	+	0.601949i
$699$	−36.7964	−	13.3928i	−1.39177	−	0.506562i
$700$	−45.9813	−	0.307264i	−1.73793	−	0.0116135i
$701$	5.73514	−	32.5256i	0.216613	−	1.22847i	−0.661472	−	0.749970i	$-0.730068\pi$
$701$	5.73514	−	32.5256i	0.216613	−	1.22847i	0.878085	−	0.478504i	$-0.158821\pi$
$702$	0.128512	−	0.473931i	0.00485036	−	0.0178874i
$703$	−15.1156	+	11.6417i	−0.570095	+	0.439077i
$704$	17.2295	+	0.309548i	0.649361	+	0.0116665i
$705$	−0.436520	−	10.0782i	−0.0164403	−	0.379568i
$706$	16.3484	+	2.93315i	0.615279	+	0.110391i
$707$	−31.4915	+	14.6847i	−1.18436	+	0.552276i
$708$	0.304453	+	0.440393i	0.0114420	+	0.0165510i
$709$	−13.8714	−	16.5312i	−0.520950	−	0.620843i	0.439855	−	0.898069i	$-0.355030\pi$
$709$	−13.8714	−	16.5312i	−0.520950	−	0.620843i	−0.960805	+	0.277225i	$0.910585\pi$
$710$	−24.9304	+	12.8723i	−0.935623	+	0.483088i
$711$	−6.67242	−	3.85232i	−0.250235	−	0.144473i
$712$	−4.41024	−	3.14749i	−0.165281	−	0.117957i
$713$	23.8984	+	16.7339i	0.895004	+	0.626688i
$714$	−3.05778	−	0.00915516i	−0.114435	−	0.000342623i
$715$	0.198577	−	4.51223i	0.00742637	−	0.168748i
$716$	16.7486	−	2.84992i	0.625924	−	0.106507i
$717$	−16.8743	−	7.86863i	−0.630183	−	0.293859i
$718$	−3.99274	−	2.81360i	−0.149008	−	0.105003i
$719$	−21.6667	−	18.1806i	−0.808033	−	0.678021i	0.142104	−	0.989852i	$-0.454613\pi$
$719$	−21.6667	−	18.1806i	−0.808033	−	0.678021i	−0.950138	+	0.311831i	$0.899058\pi$
$720$	−14.8410	−	23.9417i	−0.553090	−	0.892253i
$721$	8.56305			0.318904
$722$	17.2595	−	20.5939i	0.642332	−	0.766426i
$723$	23.2857	+	23.2857i	0.866005	+	0.866005i
$724$	23.8994	−	28.1382i	0.888213	−	1.04575i
$725$	−6.58078	+	24.4918i	−0.244404	+	0.909601i
$726$	3.80737	+	21.9773i	0.141305	+	0.815653i
$727$	−6.19331	+	13.2816i	−0.229697	+	0.492587i	−0.987049	−	0.160420i	$-0.948715\pi$
$727$	−6.19331	+	13.2816i	−0.229697	+	0.492587i	0.757352	+	0.653007i	$0.226493\pi$
$728$	1.17201	−	12.1393i	0.0434378	−	0.449914i
$729$	25.6496	−	14.8088i	0.949983	−	0.548473i
$730$	6.78921	+	31.1158i	0.251280	+	1.15165i
$731$	−0.611948	+	0.107903i	−0.0226337	+	0.00399093i
$732$	17.3276	−	7.95400i	0.640445	−	0.293988i
$733$	9.19452	+	34.3144i	0.339607	+	1.26743i	0.898787	+	0.438386i	$0.144450\pi$
$733$	9.19452	+	34.3144i	0.339607	+	1.26743i	−0.559179	+	0.829047i	$0.688884\pi$
$734$	−10.6875	−	6.21318i	−0.394484	−	0.229333i
$735$	10.2097	+	77.7590i	0.376591	+	2.86818i
$736$	−3.79199	+	19.7701i	−0.139775	+	0.728735i
$737$	5.48472	+	11.7620i	0.202032	+	0.433259i
$738$	−42.7518	+	29.7448i	−1.57372	+	1.09492i
$739$	7.31133	−	41.4646i	0.268952	−	1.52530i	−0.488590	−	0.872514i	$-0.662488\pi$
$739$	7.31133	−	41.4646i	0.268952	−	1.52530i	0.757541	−	0.652787i	$-0.226400\pi$
$740$	8.92842	+	17.4199i	0.328215	+	0.640368i
$741$	1.30497	−	10.0516i	0.0479394	−	0.369254i
$742$	18.5722	−	68.4915i	0.681807	−	2.51440i
$743$	8.64425	−	6.05277i	0.317127	−	0.222055i	−0.404165	−	0.914686i	$-0.632438\pi$
$743$	8.64425	−	6.05277i	0.317127	−	0.222055i	0.721291	+	0.692632i	$0.243549\pi$
$744$	−43.7155	−	37.3559i	−1.60269	−	1.36953i
$745$	1.19308	−	9.03808i	0.0437110	−	0.331130i
$746$	−13.7841	+	16.3277i	−0.504671	+	0.597800i
$747$	4.38682	−	50.1416i	0.160505	−	1.83459i
$748$	−0.574170	−	0.581088i	−0.0209937	−	0.0212467i
$749$	−55.4688	−	32.0249i	−2.02679	−	1.17017i
$750$	−8.64074	+	38.2448i	−0.315515	+	1.39650i
$751$	−14.0195	+	2.47202i	−0.511579	+	0.0902051i	−0.423478	−	0.905906i	$-0.639191\pi$
$751$	−14.0195	+	2.47202i	−0.511579	+	0.0902051i	−0.0881008	+	0.996112i	$0.528080\pi$
$752$	5.20687	−	5.08362i	0.189875	−	0.185381i
$753$	−28.3628	−	7.59978i	−1.03360	−	0.276951i
$754$	−6.31374	−	2.31944i	−0.229933	−	0.0844691i
$755$	12.8209	+	20.1401i	0.466599	+	0.732974i
$756$	−2.62166	+	2.17322i	−0.0953490	+	0.0790392i
$757$	−3.05661	−	34.9372i	−0.111094	−	1.26981i	−0.823204	−	0.567745i	$-0.807816\pi$
$757$	−3.05661	−	34.9372i	−0.111094	−	1.26981i	0.712110	−	0.702068i	$-0.247740\pi$
$758$	4.97860	−	10.5937i	0.180831	−	0.384781i
$759$	19.0084			0.689960
$760$	−17.5608	−	21.2513i	−0.636997	−	0.770866i
$761$	26.1037			0.946259			0.473130	−	0.880993i	$-0.343124\pi$
$761$	26.1037			0.946259			0.473130	+	0.880993i	$0.343124\pi$
$762$	−10.4094	+	22.1497i	−0.377094	+	0.802399i
$763$	−5.68986	−	65.0354i	−0.205987	−	2.35444i
$764$	−12.4217	+	10.2969i	−0.449402	+	0.372530i
$765$	−0.289473	+	1.30359i	−0.0104659	+	0.0471312i
$766$	9.60891	+	3.52998i	0.347184	+	0.127543i
$767$	0.0977778	+	0.0261995i	0.00353055	+	0.000946009i
$768$	11.1840	−	38.0676i	0.403567	−	1.37365i
$769$	34.7624	−	6.12955i	1.25356	−	0.221037i	0.492844	−	0.870118i	$-0.335957\pi$
$769$	34.7624	−	6.12955i	1.25356	−	0.221037i	0.760720	+	0.649081i	$0.224846\pi$
$770$	−19.1503	+	24.7852i	−0.690128	+	0.893197i
$771$	9.25931	+	5.34587i	0.333466	+	0.192527i
$772$	−29.5477	−	29.9037i	−1.06344	−	1.07626i
$773$	1.62343	−	18.5559i	0.0583906	−	0.667408i	−0.909445	−	0.415824i	$-0.863493\pi$
$773$	1.62343	−	18.5559i	0.0583906	−	0.667408i	0.967836	−	0.251584i	$-0.0809513\pi$
$774$	−9.41495	+	11.1523i	−0.338413	+	0.400862i
$775$	3.54432	+	40.8382i	0.127316	+	1.46695i
$776$	30.7120	−	35.9406i	1.10250	−	1.29019i
$777$	40.8836	−	28.6270i	1.46669	−	1.02699i
$778$	5.48589	−	20.2311i	0.196679	−	0.725321i
$779$	−37.5183	+	34.5032i	−1.34423	+	1.23621i
$780$	−9.89794	−	3.18989i	−0.354403	−	0.114216i
$781$	−3.31873	+	18.8214i	−0.118753	+	0.673484i
$782$	0.783349	−	0.545019i	0.0280125	−	0.0194898i
$783$	0.793723	+	1.70214i	0.0283653	+	0.0608297i
$784$	−36.8821	+	42.9003i	−1.31722	+	1.53215i
$785$	−13.2007	+	1.73325i	−0.471155	+	0.0618623i
$786$	19.5963	+	11.3923i	0.698977	+	0.406350i
$787$	0.602579	+	2.24885i	0.0214796	+	0.0801630i	0.975834	−	0.218515i	$-0.0701211\pi$
$787$	0.602579	+	2.24885i	0.0214796	+	0.0801630i	−0.954354	+	0.298678i	$0.903454\pi$
$788$	−8.96860	+	4.11693i	−0.319493	+	0.146659i
$789$	−35.4347	+	6.24809i	−1.26151	+	0.222438i
$790$	−4.17851	+	6.51084i	−0.148665	+	0.231645i
$791$	25.0395	−	14.4566i	0.890303	−	0.514016i
$792$	−19.0985	−	1.84390i	−0.678636	−	0.0655203i
$793$	1.52348	−	3.26711i	0.0541004	−	0.116019i
$794$	−6.39327	−	36.9038i	−0.226889	−	1.30967i
$795$	−53.6645	−	27.9596i	−1.90328	−	0.991626i
$796$	−15.0604	+	17.7315i	−0.533801	+	0.628477i
$797$	22.6313	+	22.6313i	0.801643	+	0.801643i	0.983352	−	0.181709i	$-0.0581629\pi$
$797$	22.6313	+	22.6313i	0.801643	+	0.801643i	−0.181709	+	0.983352i	$0.558163\pi$
$798$	−47.5497	+	51.7665i	−1.68324	+	1.83251i
$799$	−0.344970			−0.0122042
$800$	−24.7134	+	13.7567i	−0.873751	+	0.486373i
$801$	4.62148	+	3.87788i	0.163292	+	0.137018i
$802$	25.0792	+	17.6728i	0.885579	+	0.624049i
$803$	19.6611	+	9.16813i	0.693825	+	0.323536i
$804$	29.4577	−	5.01250i	1.03889	−	0.176777i
$805$	−24.7100	−	26.9851i	−0.870914	−	0.951098i
$806$	−10.8721	−	0.0325516i	−0.382953	−	0.00114658i
$807$	−6.95796	−	4.87202i	−0.244932	−	0.171503i
$808$	−12.4160	+	17.3972i	−0.436793	+	0.612031i
$809$	37.2039	+	21.4797i	1.30802	+	0.755185i	0.981765	−	0.190098i	$-0.0608805\pi$
$809$	37.2039	+	21.4797i	1.30802	+	0.755185i	0.326253	+	0.945282i	$0.394214\pi$
$810$	−12.3749	−	23.9672i	−0.434811	−	0.842121i
$811$	19.2791	+	22.9760i	0.676982	+	0.806796i	0.989716	−	0.143045i	$-0.0456893\pi$
$811$	19.2791	+	22.9760i	0.676982	+	0.806796i	−0.312734	+	0.949841i	$0.601245\pi$
$812$	26.5254	+	38.3691i	0.930858	+	1.34649i
$813$	30.1045	−	14.0380i	1.05581	−	0.492332i
$814$	13.1241	+	2.35466i	0.459998	+	0.0825309i
$815$	9.76284	−	10.6468i	0.341977	−	0.372943i
$816$	−1.64004	+	0.920869i	−0.0574130	+	0.0322369i
$817$	−7.65317	+	12.0608i	−0.267751	+	0.421953i
$818$	11.7169	−	43.2101i	0.409671	−	1.51080i
$819$	−2.35804	+	13.3731i	−0.0823967	+	0.467295i
$820$	27.8185	+	44.2828i	0.971463	+	1.54642i
$821$	−23.7164	−	8.63208i	−0.827709	−	0.301262i	−0.106791	−	0.994282i	$-0.534058\pi$
$821$	−23.7164	−	8.63208i	−0.827709	−	0.301262i	−0.720918	+	0.693020i	$0.756280\pi$
$822$	−0.367066	−	4.34540i	−0.0128029	−	0.151563i
$823$	−35.0889	−	3.06989i	−1.22312	−	0.107009i	−0.542762	−	0.839886i	$-0.682622\pi$
$823$	−35.0889	−	3.06989i	−1.22312	−	0.107009i	−0.680361	+	0.732877i	$0.738177\pi$
$824$	4.58503	−	2.59254i	0.159727	−	0.0903154i
$825$	17.1532	+	20.4712i	0.597196	+	0.712715i
$826$	−0.449616	−	0.539101i	−0.0156441	−	0.0187577i
$827$	−8.22757	−	5.76101i	−0.286101	−	0.200330i	0.421712	−	0.906730i	$-0.361429\pi$
$827$	−8.22757	−	5.76101i	−0.286101	−	0.200330i	−0.707813	+	0.706400i	$0.750318\pi$
$828$	5.93079	−	21.6154i	0.206109	−	0.751189i
$829$	−27.5454	+	15.9033i	−0.956691	+	0.552346i	−0.895153	−	0.445759i	$-0.852934\pi$
$829$	−27.5454	+	15.9033i	−0.956691	+	0.552346i	−0.0615379	+	0.998105i	$0.519601\pi$
$830$	−50.0855	−	6.76420i	−1.73849	−	0.234789i
$831$	−10.5762	−	29.0580i	−0.366886	−	1.00801i
$832$	−3.04774	−	6.85477i	−0.105661	−	0.237646i
$833$	2.67176	−	0.233749i	0.0925710	−	0.00809891i
$834$	77.0316	−	27.7763i	2.66739	−	0.961815i
$835$	28.2451	−	44.3019i	0.977461	−	1.53313i
$836$	−18.7638	+	0.740417i	−0.648961	+	0.0256079i
$837$	2.14657	+	2.14657i	0.0741963	+	0.0741963i
$838$	8.11767	−	17.2732i	0.280420	−	0.596692i
$839$	−0.687018	−	0.576476i	−0.0237185	−	0.0199022i	0.630851	−	0.775904i	$-0.282706\pi$
$839$	−0.687018	−	0.576476i	−0.0237185	−	0.0199022i	−0.654570	+	0.756002i	$0.727150\pi$
$840$	43.3660	+	57.6209i	1.49627	+	1.98811i
$841$	−3.07643	+	1.11973i	−0.106084	+	0.0386113i
$842$	−37.4829	+	17.3421i	−1.29175	+	0.597649i
$843$	−19.6224	+	73.2318i	−0.675831	+	2.52224i
$844$	−21.2893	−	37.3894i	−0.732807	−	1.28700i
$845$	25.0432	−	10.3630i	0.861512	−	0.356500i
$846$	−6.22251	+	5.18964i	−0.213934	+	0.178424i
$847$	−7.56926	−	28.2489i	−0.260083	−	0.970642i
$848$	−10.7920	−	42.2962i	−0.370600	−	1.45246i
$849$	12.8207	+	15.2791i	0.440006	+	0.524379i
$850$	1.29386	+	0.351807i	0.0443789	+	0.0120669i
$851$	−5.32734	+	14.6368i	−0.182619	+	0.501742i
$852$	39.7691	+	18.8354i	1.36247	+	0.645289i
$853$	−4.13095	−	5.89961i	−0.141441	−	0.201999i	0.742181	−	0.670199i	$-0.233791\pi$
$853$	−4.13095	−	5.89961i	−0.141441	−	0.201999i	−0.883622	+	0.468201i	$0.844902\pi$
$854$	−21.6870	+	12.4346i	−0.742114	+	0.425502i
$855$	17.6427	+	25.1190i	0.603369	+	0.859052i
$856$	−39.3963	−	0.353872i	−1.34654	−	0.0120951i
$857$	1.47637	−	1.03377i	0.0504320	−	0.0353128i	−0.548089	−	0.836420i	$-0.684644\pi$
$857$	1.47637	−	1.03377i	0.0504320	−	0.0353128i	0.598521	+	0.801107i	$0.295755\pi$
$858$	−5.81470	+	4.04560i	−0.198510	+	0.138115i
$859$	−29.2991	−	10.6640i	−0.999671	−	0.363851i	−0.210214	−	0.977655i	$-0.567416\pi$
$859$	−29.2991	−	10.6640i	−0.999671	−	0.363851i	−0.789458	+	0.613805i	$0.789638\pi$
$860$	10.7419	+	9.96909i	0.366297	+	0.339943i
$861$	102.143	−	85.7082i	3.48103	−	2.92093i
$862$	48.1000	−	12.7341i	1.63829	−	0.433726i
$863$	−29.6183	+	7.93620i	−1.00822	+	0.270151i	−0.724885	−	0.688870i	$-0.758107\pi$
$863$	−29.6183	+	7.93620i	−1.00822	+	0.270151i	−0.283334	+	0.959021i	$0.591440\pi$
$864$	−0.745792	+	1.95737i	−0.0253724	+	0.0665910i
$865$	11.6545	+	4.83221i	0.396266	+	0.164300i
$866$	0.000263400	−	0.0879743i	8.95068e−6	−	0.00298949i
$867$	−40.6337	−	10.8878i	−1.37999	−	0.369768i
$868$	61.5006	+	43.6143i	2.08746	+	1.48037i
$869$	1.80235	+	4.95193i	0.0611407	+	0.167983i
$870$	36.7972	−	15.0980i	1.24754	−	0.511872i
$871$	3.63157	−	4.32794i	0.123051	−	0.146647i
$872$	−22.7366	−	33.1001i	−0.769960	−	1.12091i
$873$	−37.2213	+	37.2213i	−1.25975	+	1.25975i
$874$	2.88940	−	21.7455i	0.0977355	−	0.735554i
$875$	6.76339	−	50.9629i	0.228644	−	1.72286i
$876$	32.3349	−	38.0699i	1.09249	−	1.28626i
$877$	−3.96630	−	45.3350i	−0.133933	−	1.53086i	−0.704559	−	0.709646i	$-0.748855\pi$
$877$	−3.96630	−	45.3350i	−0.133933	−	1.53086i	0.570626	−	0.821210i	$-0.306701\pi$
$878$	−21.7392	−	15.3192i	−0.733663	−	0.516997i
$879$	−8.97144	+	3.26534i	−0.302599	+	0.110137i
$880$	−2.74995	+	19.0690i	−0.0927007	+	0.642816i
$881$	19.2620	+	33.3628i	0.648954	+	1.12402i	0.983373	+	0.181597i	$0.0581268\pi$
$881$	19.2620	+	33.3628i	0.648954	+	1.12402i	−0.334419	+	0.942425i	$0.608540\pi$
$882$	44.6763	−	44.4096i	1.50433	−	1.49535i
$883$	12.4514	−	17.7825i	0.419025	−	0.598429i	−0.553037	−	0.833157i	$-0.686531\pi$
$883$	12.4514	−	17.7825i	0.419025	−	0.598429i	0.972061	+	0.234728i	$0.0754199\pi$
$884$	−0.123630	+	0.333445i	−0.00415813	+	0.0112150i
$885$	−0.531042	+	0.276209i	−0.0178508	+	0.00928465i
$886$	−18.4162	+	31.6784i	−0.618705	+	1.06426i
$887$	1.80258	−	20.6036i	0.0605247	−	0.691801i	−0.903952	−	0.427634i	$-0.859347\pi$
$887$	1.80258	−	20.6036i	0.0605247	−	0.691801i	0.964477	−	0.264167i	$-0.0850971\pi$
$888$	13.2238	−	27.7060i	0.443761	−	0.929754i
$889$	10.9753	−	30.1543i	0.368098	−	1.01134i
$890$	4.10744	−	4.45253i	0.137682	−	0.149249i
$891$	−18.0942	−	3.19050i	−0.606179	−	0.106886i
$892$	4.99995	+	19.1172i	0.167411	+	0.640092i
$893$	−5.34688	+	5.85616i	−0.178927	+	0.195969i
$894$	−12.4037	+	7.11183i	−0.414840	+	0.237855i
$895$	0.821947	+	18.9768i	0.0274747	+	0.634326i
$896$	−10.1054	+	51.0321i	−0.337598	+	1.70486i
$897$	−3.49715	−	7.49966i	−0.116766	−	0.250406i
$898$	−1.47358	−	17.4445i	−0.0491741	−	0.582131i
$899$	31.8543	−	26.7289i	1.06240	−	0.891459i
$900$	28.6308	−	13.1186i	0.954361	−	0.437286i
$901$	−1.03466	+	1.79208i	−0.0344695	+	0.0597029i
$902$	35.4770	+	3.21090i	1.18125	+	0.106911i
$903$	21.4323	−	30.6085i	0.713223	−	1.01859i
$904$	9.03039	−	15.3216i	0.300346	−	0.509589i
$905$	27.8748	+	30.4412i	0.926591	+	1.01190i
$906$	12.9118	−	35.1472i	0.428967	−	1.16769i
$907$	−9.30212	+	19.9485i	−0.308872	+	0.662378i	−0.998064	−	0.0622010i	$-0.980188\pi$
$907$	−9.30212	+	19.9485i	−0.308872	+	0.662378i	0.689192	+	0.724579i	$0.257966\pi$
$908$	−25.0121	−	2.33928i	−0.830056	−	0.0776317i
$909$	15.2972	−	18.2305i	0.507376	−	0.604667i
$910$	13.3021	+	2.99568i	0.440962	+	0.0993058i
$911$		−	55.6682i		−	1.84437i	−0.386748	−	0.922185i	$-0.626402\pi$
$911$		−	55.6682i		−	1.84437i	0.386748	−	0.922185i	$-0.373598\pi$
$912$	−9.78739	+	42.1141i	−0.324093	+	1.39454i
$913$	−24.3430	+	24.3430i	−0.805637	+	0.805637i
$914$	−37.4106	+	13.4896i	−1.23743	+	0.446197i
$915$	6.40290	+	20.3320i	0.211673	+	0.672156i
$916$	−7.49652	+	6.21421i	−0.247692	+	0.205323i
$917$	−26.9361	−	12.5605i	−0.889508	−	0.414784i
$918$	0.0901192	−	0.0416953i	0.00297438	−	0.00137615i
$919$	11.0770	+	19.1859i	0.365396	+	0.632884i	0.988840	−	0.148984i	$-0.0476004\pi$
$919$	11.0770	+	19.1859i	0.365396	+	0.632884i	−0.623444	+	0.781868i	$0.714267\pi$
$920$	−21.4008	−	6.96780i	−0.705563	−	0.229722i
$921$	8.50968	+	48.2608i	0.280404	+	1.59025i
$922$	3.12947	−	34.5774i	0.103064	−	1.13875i
$923$	8.03649	−	2.15337i	0.264524	−	0.0708791i
$924$	49.1224	+	0.294152i	1.61601	+	0.00967690i
$925$	−20.5706	+	7.47090i	−0.676356	+	0.245642i
$926$	−1.32146	−	1.11559i	−0.0434258	−	0.0366607i
$927$	−5.31533	+	2.47858i	−0.174578	+	0.0814072i
$928$	25.8194	+	12.5137i	0.847565	+	0.410783i
$929$	−26.8608	−	4.73629i	−0.881275	−	0.155393i	−0.285341	−	0.958426i	$-0.592107\pi$
$929$	−26.8608	−	4.73629i	−0.881275	−	0.155393i	−0.595934	+	0.803033i	$0.703218\pi$
$930$	47.5440	−	43.2747i	1.55903	−	1.41903i
$931$	37.4430	−	48.9783i	1.22714	−	1.60520i
$932$	30.5540	−	7.99113i	1.00083	−	0.261758i
$933$	−4.92823	−	7.03824i	−0.161343	−	0.230422i
$934$	23.8414	+	4.27753i	0.780116	+	0.139965i
$935$	0.724785	−	0.555748i	0.0237030	−	0.0181749i
$936$	2.78623	+	7.87447i	0.0910709	+	0.257385i
$937$	52.2226	+	4.56888i	1.70604	+	0.149259i	0.898036	−	0.439922i	$-0.144994\pi$
$937$	52.2226	+	4.56888i	1.70604	+	0.149259i	0.808001	+	0.589181i	$0.200549\pi$
$938$	−37.8747	+	10.0271i	−1.23665	+	0.327395i
$939$	−12.9553	+	22.4392i	−0.422780	+	0.732276i
$940$	4.91185	+	6.48591i	0.160207	+	0.211547i
$941$	1.73731	+	9.85276i	0.0566346	+	0.321191i	0.999942	−	0.0107283i	$-0.00341500\pi$
$941$	1.73731	+	9.85276i	0.0566346	+	0.321191i	−0.943308	+	0.331919i	$0.892304\pi$
$942$	14.7209	+	14.8093i	0.479633	+	0.482513i
$943$	−10.7702	+	40.1951i	−0.350727	+	1.30893i
$944$	−0.403962	−	0.152533i	−0.0131478	−	0.00496453i
$945$	−2.04451	−	3.21170i	−0.0665079	−	0.104476i
$946$	9.83603	−	1.70401i	0.319797	−	0.0554021i
$947$	10.7326	−	0.938980i	0.348762	−	0.0305127i	0.0885710	−	0.996070i	$-0.471770\pi$
$947$	10.7326	−	0.938980i	0.348762	−	0.0305127i	0.260191	+	0.965557i	$0.416214\pi$
$948$	12.0933	−	0.985091i	0.392771	−	0.0319943i
$949$		−	9.44395i		−	0.306563i
$950$	26.0264	−	16.5114i	0.844408	−	0.535701i
$951$			60.4116i			1.95898i
$952$	2.03280	−	1.39634i	0.0658835	−	0.0452557i
$953$	32.1261	−	2.81067i	1.04067	−	0.0910467i	0.446012	−	0.895027i	$-0.352844\pi$
$953$	32.1261	−	2.81067i	1.04067	−	0.0910467i	0.594656	+	0.803980i	$0.297288\pi$
$954$	8.29660	+	47.8904i	0.268612	+	1.55051i
$955$	−9.68709	−	15.2173i	−0.313467	−	0.492421i
$956$	14.8037	−	2.51898i	0.478785	−	0.0814696i
$957$	7.01213	−	26.1696i	0.226670	−	0.845943i
$958$	0.666159	−	0.662182i	0.0215226	−	0.0213941i
$959$	0.992901	+	5.63102i	0.0320624	+	0.181835i
$960$	40.6653	+	17.7233i	1.31247	+	0.572017i
$961$	18.1065	−	31.3613i	0.584079	−	1.01166i
$962$	−1.48554	−	5.61125i	−0.0478956	−	0.180914i
$963$	43.7007	+	3.82332i	1.40824	+	0.123205i
$964$	−26.1280	−	4.76856i	−0.841526	−	0.153585i
$965$	37.2985	−	28.5996i	1.20068	−	0.920653i
$966$	−10.1339	+	56.4830i	−0.326054	+	1.81731i
$967$	−1.08129	−	1.54424i	−0.0347718	−	0.0496593i	0.801390	−	0.598143i	$-0.204094\pi$
$967$	−1.08129	−	1.54424i	−0.0347718	−	0.0496593i	−0.836162	+	0.548483i	$0.815205\pi$
$968$	−12.6055	−	12.8340i	−0.405156	−	0.412501i
$969$	1.72668	−	1.10438i	0.0554689	−	0.0354777i
$970$	35.5782	+	39.0882i	1.14235	+	1.25505i
$971$	−35.2740	−	6.21976i	−1.13200	−	0.199602i	−0.423895	−	0.905711i	$-0.639337\pi$
$971$	−35.2740	−	6.21976i	−1.13200	−	0.199602i	−0.708102	+	0.706110i	$0.750448\pi$
$972$	−19.0586	+	40.2404i	−0.611305	+	1.29071i
$973$	−97.3083	+	45.3756i	−3.11956	+	1.45468i
$974$	3.62975	−	4.29956i	0.116305	−	0.137767i
$975$	4.92098	−	10.5340i	0.157597	−	0.337357i
$976$	−7.84749	+	13.2239i	−0.251192	+	0.423288i
$977$	−4.97086	+	1.33194i	−0.159032	+	0.0426125i	−0.337457	−	0.941341i	$-0.609567\pi$
$977$	−4.97086	+	1.33194i	−0.159032	+	0.0426125i	0.178425	+	0.983954i	$0.442900\pi$
$978$	−22.5632	−	2.04211i	−0.721491	−	0.0652996i
$979$	−0.716528	−	4.06363i	−0.0229003	−	0.129874i
$980$	−42.4366	−	46.9045i	−1.35559	−	1.49831i
$981$	22.3564	+	38.7224i	0.713785	+	1.23631i
$982$	15.6156	+	33.7511i	0.498312	+	1.07704i
$983$	−12.3963	−	5.78049i	−0.395381	−	0.184369i	0.214751	−	0.976669i	$-0.431106\pi$
$983$	−12.3963	−	5.78049i	−0.395381	−	0.184369i	−0.610132	+	0.792300i	$0.708884\pi$
$984$	28.7429	−	76.8166i	0.916291	−	2.44883i
$985$	−3.31409	−	10.5237i	−0.105596	−	0.335313i
$986$	−0.461375	−	1.27952i	−0.0146932	−	0.0407484i
$987$	14.6684	−	14.6684i	0.466899	−	0.466899i
$988$	3.74429	+	7.26696i	0.119122	+	0.231193i
$989$			11.6614i			0.370812i
$990$	4.71303	−	20.9280i	0.149790	−	0.665134i
$991$	−6.18394	+	7.36974i	−0.196439	+	0.234107i	−0.855268	−	0.518185i	$-0.826608\pi$
$991$	−6.18394	+	7.36974i	−0.196439	+	0.234107i	0.658829	+	0.752293i	$0.271052\pi$
$992$	46.1347	+	4.73316i	1.46478	+	0.150278i
$993$	−7.32422	+	15.7068i	−0.232427	+	0.498442i
$994$	−54.1583	−	19.8958i	−1.71780	−	0.631058i
$995$	−17.5655	−	19.1828i	−0.556865	−	0.608135i
$996$	39.2207	+	68.8815i	1.24275	+	2.18259i
$997$	−21.0253	+	30.0272i	−0.665878	+	0.950972i	0.334086	+	0.942542i	$0.391572\pi$
$997$	−21.0253	+	30.0272i	−0.665878	+	0.950972i	−0.999964	+	0.00842991i	$0.997317\pi$
$998$	0.723561	−	7.99458i	0.0229039	−	0.253064i
$999$	−0.810371	+	1.40360i	−0.0256390	+	0.0444081i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bj.a.207.20	yes	672
4.3	odd	2	inner	380.2.bj.a.207.3	yes	672
5.3	odd	4	inner	380.2.bj.a.283.48	yes	672
19.9	even	9	inner	380.2.bj.a.47.31	✓	672
20.3	even	4	inner	380.2.bj.a.283.31	yes	672
76.47	odd	18	inner	380.2.bj.a.47.48	yes	672
95.28	odd	36	inner	380.2.bj.a.123.3	yes	672
380.123	even	36	inner	380.2.bj.a.123.20	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bj.a.47.31	✓	672	19.9	even	9	inner
380.2.bj.a.47.48	yes	672	76.47	odd	18	inner
380.2.bj.a.123.3	yes	672	95.28	odd	36	inner
380.2.bj.a.123.20	yes	672	380.123	even	36	inner
380.2.bj.a.207.3	yes	672	4.3	odd	2	inner
380.2.bj.a.207.20	yes	672	1.1	even	1	trivial
380.2.bj.a.283.31	yes	672	20.3	even	4	inner
380.2.bj.a.283.48	yes	672	5.3	odd	4	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)

\(f(q)\)	\(=\)	\(q+(-0.601507 + 1.27992i) q^{2} +(0.216127 + 2.47035i) q^{3} +(-1.27638 - 1.53976i) q^{4} +(1.88630 - 1.20078i) q^{5} +(-3.29184 - 1.20931i) q^{6} +(4.44155 + 1.19011i) q^{7} +(2.73852 - 0.707482i) q^{8} +(-3.10148 + 0.546874i) q^{9} +O(q^{10})\)	\(q+(-0.601507 + 1.27992i) q^{2} +(0.216127 + 2.47035i) q^{3} +(-1.27638 - 1.53976i) q^{4} +(1.88630 - 1.20078i) q^{5} +(-3.29184 - 1.20931i) q^{6} +(4.44155 + 1.19011i) q^{7} +(2.73852 - 0.707482i) q^{8} +(-3.10148 + 0.546874i) q^{9} +(0.402283 + 3.13659i) q^{10} +(1.86545 + 1.07702i) q^{11} +(3.52788 - 3.48588i) q^{12} +(0.0817278 - 0.934153i) q^{13} +(-4.19487 + 4.96896i) q^{14} +(3.37403 + 4.40029i) q^{15} +(-0.741719 + 3.93063i) q^{16} +(0.155329 - 0.108763i) q^{17} +(1.16561 - 4.29858i) q^{18} +(0.561196 - 4.32262i) q^{19} +(-4.25655 - 1.37179i) q^{20} +(-1.98004 + 11.2294i) q^{21} +(-2.50057 + 1.73979i) q^{22} +(-1.50393 - 3.22518i) q^{23} +(2.33959 + 6.61218i) q^{24} +(2.11624 - 4.53007i) q^{25} +(1.14648 + 0.666505i) q^{26} +(-0.0958362 - 0.357666i) q^{27} +(-3.83661 - 8.35795i) q^{28} +(-4.99504 + 0.880760i) q^{29} +(-7.66151 + 1.67168i) q^{30} +(-7.09998 + 4.09917i) q^{31} +(-4.58473 - 3.31364i) q^{32} +(-2.25743 + 4.84108i) q^{33} +(0.0457757 + 0.264231i) q^{34} +(9.80715 - 3.08844i) q^{35} +(4.80071 + 4.07751i) q^{36} +(-3.09503 - 3.09503i) q^{37} +(5.19504 + 3.31837i) q^{38} +2.32534 q^{39} +(4.31612 - 4.62289i) q^{40} +(-8.95787 - 7.51654i) q^{41} +(-13.1817 - 9.28885i) q^{42} +(-2.96995 - 1.38491i) q^{43} +(-0.722670 - 4.24702i) q^{44} +(-5.19363 + 4.75577i) q^{45} +(5.03259 + 0.0150678i) q^{46} +(-1.49024 - 1.04348i) q^{47} +(-9.87032 - 0.982785i) q^{48} +(12.2488 + 7.07186i) q^{49} +(4.52519 + 5.43348i) q^{50} +(0.302253 + 0.360211i) q^{51} +(-1.54269 + 1.06649i) q^{52} +(-9.89039 + 4.61196i) q^{53} +(0.515429 + 0.0924760i) q^{54} +(4.81206 - 0.208425i) q^{55} +(13.0052 + 0.116818i) q^{56} +(10.7997 + 0.452111i) q^{57} +(1.87725 - 6.92302i) q^{58} +(-0.0187453 + 0.106310i) q^{59} +(2.46884 - 10.8116i) q^{60} +(3.61244 + 1.31482i) q^{61} +(-0.975917 - 11.5531i) q^{62} +(-14.4262 - 1.26213i) q^{63} +(6.99894 - 3.87490i) q^{64} +(-0.967553 - 1.86023i) q^{65} +(-4.83832 - 5.80127i) q^{66} +(4.93535 + 3.45577i) q^{67} +(-0.365728 - 0.100348i) q^{68} +(7.64228 - 4.41227i) q^{69} +(-1.94612 + 14.4101i) q^{70} +(3.03459 + 8.33748i) q^{71} +(-8.10654 + 3.69186i) q^{72} +(10.0328 - 0.877760i) q^{73} +(5.82307 - 2.09970i) q^{74} +(11.6482 + 4.24876i) q^{75} +(-7.37210 + 4.65319i) q^{76} +(7.00371 + 7.00371i) q^{77} +(-1.39871 + 2.97625i) q^{78} +(1.87409 + 1.57255i) q^{79} +(3.32073 + 8.30498i) q^{80} +(-8.01534 + 2.91734i) q^{81} +(15.0088 - 6.94408i) q^{82} +(-4.13650 + 15.4376i) q^{83} +(19.8178 - 11.2841i) q^{84} +(0.162397 - 0.391676i) q^{85} +(3.55902 - 2.96826i) q^{86} +(-3.25535 - 12.1491i) q^{87} +(5.87053 + 1.62966i) q^{88} +(-1.23134 - 1.46745i) q^{89} +(-2.96299 - 9.50805i) q^{90} +(1.47474 - 4.05182i) q^{91} +(-3.04643 + 6.43224i) q^{92} +(-11.6609 - 16.6535i) q^{93} +(2.23196 - 1.27973i) q^{94} +(-4.13195 - 8.82763i) q^{95} +(7.19496 - 12.0420i) q^{96} +(13.6916 - 9.58695i) q^{97} +(-16.4192 + 11.4237i) q^{98} +(-6.37464 - 2.32018i) 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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