LMFDB - Embedded newform 380.2.bb.a.219.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(59,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 1]))

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

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

chi := DirichletCharacter("380.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bb (of order $18$, degree $6$, 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:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			219.34
Character	$\chi$	$=$	380.219
Dual form			380.2.bb.a.59.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.359549 + 1.36774i) q^{2} +(1.00908 + 1.20257i) q^{3} +(-1.74145 + 0.983541i) q^{4} +(-1.95513 + 1.08511i) q^{5} +(-1.28200 + 1.81254i) q^{6} +(-0.0550050 + 0.0952714i) q^{7} +(-1.97137 - 2.02823i) q^{8} +(0.0930035 - 0.527449i) q^{9} +O(q^{10})$	\(q+(0.359549 + 1.36774i) q^{2} +(1.00908 + 1.20257i) q^{3} +(-1.74145 + 0.983541i) q^{4} +(-1.95513 + 1.08511i) q^{5} +(-1.28200 + 1.81254i) q^{6} +(-0.0550050 + 0.0952714i) q^{7} +(-1.97137 - 2.02823i) q^{8} +(0.0930035 - 0.527449i) q^{9} +(-2.18712 - 2.28397i) q^{10} +(-5.05421 + 2.91805i) q^{11} +(-2.94004 - 1.10175i) q^{12} +(2.48633 + 2.08628i) q^{13} +(-0.150084 - 0.0409780i) q^{14} +(-3.27780 - 1.25622i) q^{15} +(2.06529 - 3.42557i) q^{16} +(-0.624519 + 0.110120i) q^{17} +(0.754854 - 0.0624385i) q^{18} +(2.31090 + 3.69591i) q^{19} +(2.33750 - 3.81262i) q^{20} +(-0.170075 + 0.0299888i) q^{21} +(-5.80838 - 5.86369i) q^{22} +(-3.43236 + 1.24928i) q^{23} +(0.449825 - 4.41735i) q^{24} +(2.64506 - 4.24307i) q^{25} +(-1.95954 + 4.15078i) q^{26} +(4.80672 - 2.77516i) q^{27} +(0.00208504 - 0.220010i) q^{28} +(5.65030 + 0.996301i) q^{29} +(0.539656 - 4.93487i) q^{30} +(-3.25751 + 5.64218i) q^{31} +(5.42788 + 1.59313i) q^{32} +(-8.60926 - 3.13351i) q^{33} +(-0.375161 - 0.814590i) q^{34} +(0.00416146 - 0.245954i) q^{35} +(0.356807 + 1.01000i) q^{36} +0.716369 q^{37} +(-4.22418 + 4.48958i) q^{38} +5.09521i q^{39} +(6.05514 + 1.82629i) q^{40} +(-4.84598 - 5.77522i) q^{41} +(-0.102167 - 0.221837i) q^{42} +(8.35823 + 3.04215i) q^{43} +(5.93163 - 10.0527i) q^{44} +(0.390508 + 1.13215i) q^{45} +(-2.94279 - 4.24542i) q^{46} +(-2.13567 + 12.1120i) q^{47} +(6.20354 - 0.973007i) q^{48} +(3.49395 + 6.05170i) q^{49} +(6.75447 + 2.09217i) q^{50} +(-0.762615 - 0.639910i) q^{51} +(-6.38176 - 1.18774i) q^{52} +(6.30930 - 2.29640i) q^{53} +(5.52396 + 5.57656i) q^{54} +(6.71522 - 11.1896i) q^{55} +(0.301667 - 0.0762525i) q^{56} +(-2.11272 + 6.50848i) q^{57} +(0.668874 + 8.08639i) q^{58} +(-2.21174 - 12.5434i) q^{59} +(6.94367 - 1.03621i) q^{60} +(-11.2741 + 4.10342i) q^{61} +(-8.88830 - 2.42681i) q^{62} +(0.0451351 + 0.0378729i) q^{63} +(-0.227411 + 7.99677i) q^{64} +(-7.12495 - 1.38099i) q^{65} +(1.19040 - 12.9019i) q^{66} +(7.89198 + 1.39157i) q^{67} +(0.979262 - 0.806008i) q^{68} +(-4.96586 - 2.86704i) q^{69} +(0.337899 - 0.0827408i) q^{70} +(-4.58464 - 1.66867i) q^{71} +(-1.25313 + 0.851164i) q^{72} +(0.0197371 + 0.0235218i) q^{73} +(0.257569 + 0.979810i) q^{74} +(7.77166 - 1.10072i) q^{75} +(-7.65940 - 4.16337i) q^{76} -0.642029i q^{77} +(-6.96894 + 1.83197i) q^{78} +(-1.17406 + 0.985156i) q^{79} +(-0.320775 + 8.93852i) q^{80} +(6.67782 + 2.43053i) q^{81} +(6.15665 - 8.70454i) q^{82} +(-2.11752 + 3.66765i) q^{83} +(0.266682 - 0.219500i) q^{84} +(1.10152 - 0.892973i) q^{85} +(-1.15569 + 12.5257i) q^{86} +(4.50347 + 7.80024i) q^{87} +(15.8822 + 4.49854i) q^{88} +(7.35130 - 8.76094i) q^{89} +(-1.40808 + 0.941178i) q^{90} +(-0.335523 + 0.122120i) q^{91} +(4.74857 - 5.55142i) q^{92} +(-10.0722 + 1.77600i) q^{93} +(-17.3339 + 1.43379i) q^{94} +(-8.52859 - 4.71838i) q^{95} +(3.56130 + 8.13501i) q^{96} +(0.749823 + 4.25245i) q^{97} +(-7.02093 + 6.95471i) q^{98} +(1.06906 + 2.93723i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.359549	+	1.36774i	0.254239	+	0.967141i
$2$	0.359549	+	1.36774i	0.254239	+	0.967141i
$3$	1.00908	+	1.20257i	0.582591	+	0.694305i	0.974164	−	0.225842i	$-0.0725134\pi$
$3$	1.00908	+	1.20257i	0.582591	+	0.694305i	−0.391573	+	0.920147i	$0.628069\pi$
$4$	−1.74145	+	0.983541i	−0.870725	+	0.491771i
$5$	−1.95513	+	1.08511i	−0.874360	+	0.485278i
$5$	−1.95513	+	1.08511i	−0.874360	+	0.485278i
$6$	−1.28200	+	1.81254i	−0.523373	+	0.739967i
$7$	−0.0550050	+	0.0952714i	−0.0207899	+	0.0360092i	−0.876233	−	0.481887i	$-0.839951\pi$
$7$	−0.0550050	+	0.0952714i	−0.0207899	+	0.0360092i	0.855443	+	0.517897i	$0.173285\pi$
$8$	−1.97137	−	2.02823i	−0.696984	−	0.717087i
$9$	0.0930035	−	0.527449i	0.0310012	−	0.175816i
$10$	−2.18712	−	2.28397i	−0.691629	−	0.722253i
$11$	−5.05421	+	2.91805i	−1.52390	+	0.879826i	−0.524303	+	0.851532i	$0.675674\pi$
$11$	−5.05421	+	2.91805i	−1.52390	+	0.879826i	−0.999600	+	0.0282938i	$0.990993\pi$
$12$	−2.94004	−	1.10175i	−0.848715	−	0.318047i
$13$	2.48633	+	2.08628i	0.689584	+	0.578630i	0.918789	−	0.394748i	$-0.129168\pi$
$13$	2.48633	+	2.08628i	0.689584	+	0.578630i	−0.229205	+	0.973378i	$0.573613\pi$
$14$	−0.150084	−	0.0409780i	−0.0401116	−	0.0109518i
$15$	−3.27780	−	1.25622i	−0.846325	−	0.324354i
$16$	2.06529	−	3.42557i	0.516323	−	0.856394i
$17$	−0.624519	+	0.110120i	−0.151468	+	0.0267079i	−0.248868	−	0.968537i	$-0.580059\pi$
$17$	−0.624519	+	0.110120i	−0.151468	+	0.0267079i	0.0973998	+	0.995245i	$0.468947\pi$
$18$	0.754854	−	0.0624385i	0.177921	−	0.0147169i
$19$	2.31090	+	3.69591i	0.530157	+	0.847899i
$19$	2.31090	+	3.69591i	0.530157	+	0.847899i
$20$	2.33750	−	3.81262i	0.522682	−	0.852528i
$21$	−0.170075	+	0.0299888i	−0.0371134	+	0.00654409i
$22$	−5.80838	−	5.86369i	−1.23835	−	1.25014i
$23$	−3.43236	+	1.24928i	−0.715697	+	0.260492i	−0.674098	−	0.738642i	$-0.735467\pi$
$23$	−3.43236	+	1.24928i	−0.715697	+	0.260492i	−0.0415990	+	0.999134i	$0.513245\pi$
$24$	0.449825	−	4.41735i	0.0918201	−	0.901688i
$25$	2.64506	−	4.24307i	0.529011	−	0.848615i
$26$	−1.95954	+	4.15078i	−0.384297	+	0.814036i
$27$	4.80672	−	2.77516i	0.925054	−	0.534080i
$28$	0.00208504	−	0.220010i	0.000394035	−	0.0415780i
$29$	5.65030	+	0.996301i	1.04924	+	0.185008i	0.671576	−	0.740936i	$-0.265618\pi$
$29$	5.65030	+	0.996301i	1.04924	+	0.185008i	0.377660	+	0.925945i	$0.376729\pi$
$30$	0.539656	−	4.93487i	0.0985272	−	0.900979i
$31$	−3.25751	+	5.64218i	−0.585067	+	1.01337i	0.409800	+	0.912175i	$0.365598\pi$
$31$	−3.25751	+	5.64218i	−0.585067	+	1.01337i	−0.994867	+	0.101190i	$0.967735\pi$
$32$	5.42788	+	1.59313i	0.959523	+	0.281629i
$33$	−8.60926	−	3.13351i	−1.49868	−	0.545475i
$34$	−0.375161	−	0.814590i	−0.0643395	−	0.139701i
$35$	0.00416146	−	0.245954i	0.000703415	−	0.0415739i
$36$	0.356807	+	1.01000i	0.0594678	+	0.168333i
$37$	0.716369			0.117770			0.0588852	−	0.998265i	$-0.481245\pi$
$37$	0.716369			0.117770			0.0588852	+	0.998265i	$0.481245\pi$
$38$	−4.22418	+	4.48958i	−0.685252	+	0.728306i
$39$			5.09521i			0.815886i
$40$	6.05514	+	1.82629i	0.957401	+	0.288761i
$41$	−4.84598	−	5.77522i	−0.756815	−	0.901937i	0.240827	−	0.970568i	$-0.422581\pi$
$41$	−4.84598	−	5.77522i	−0.756815	−	0.901937i	−0.997642	+	0.0686307i	$0.978137\pi$
$42$	−0.102167	−	0.221837i	−0.0157647	−	0.0342301i
$43$	8.35823	+	3.04215i	1.27462	+	0.463923i	0.888649	−	0.458589i	$-0.151645\pi$
$43$	8.35823	+	3.04215i	1.27462	+	0.463923i	0.385969	+	0.922512i	$0.373867\pi$
$44$	5.93163	−	10.0527i	0.894227	−	1.51550i
$45$	0.390508	+	1.13215i	0.0582135	+	0.168771i
$46$	−2.94279	−	4.24542i	−0.433891	−	0.625953i
$47$	−2.13567	+	12.1120i	−0.311519	+	1.76671i	0.279590	+	0.960119i	$0.409801\pi$
$47$	−2.13567	+	12.1120i	−0.311519	+	1.76671i	−0.591109	+	0.806592i	$0.701310\pi$
$48$	6.20354	−	0.973007i	0.895404	−	0.140441i
$49$	3.49395	+	6.05170i	0.499136	+	0.864528i
$50$	6.75447	+	2.09217i	0.955226	+	0.295877i
$51$	−0.762615	−	0.639910i	−0.106787	−	0.0896053i
$52$	−6.38176	−	1.18774i	−0.884991	−	0.164710i
$53$	6.30930	−	2.29640i	0.866649	−	0.315434i	0.129839	−	0.991535i	$-0.458554\pi$
$53$	6.30930	−	2.29640i	0.866649	−	0.315434i	0.736809	+	0.676101i	$0.236332\pi$
$54$	5.52396	+	5.57656i	0.751716	+	0.758874i
$55$	6.71522	−	11.1896i	0.905480	−	1.50880i
$56$	0.301667	−	0.0762525i	0.0403120	−	0.0101897i
$57$	−2.11272	+	6.50848i	−0.279836	+	0.862069i
$58$	0.668874	+	8.08639i	0.0878274	+	1.06180i
$59$	−2.21174	−	12.5434i	−0.287943	−	1.63301i	−0.694578	−	0.719417i	$-0.744409\pi$
$59$	−2.21174	−	12.5434i	−0.287943	−	1.63301i	0.406635	−	0.913591i	$-0.366702\pi$
$60$	6.94367	−	1.03621i	0.896424	−	0.133775i
$61$	−11.2741	+	4.10342i	−1.44350	+	0.525389i	−0.940767	−	0.339055i	$-0.889893\pi$
$61$	−11.2741	+	4.10342i	−1.44350	+	0.525389i	−0.502729	+	0.864444i	$0.667671\pi$
$62$	−8.88830	−	2.42681i	−1.12881	−	0.308205i
$63$	0.0451351	+	0.0378729i	0.00568649	+	0.00477153i
$64$	−0.227411	+	7.99677i	−0.0284263	+	0.999596i
$65$	−7.12495	−	1.38099i	−0.883741	−	0.171291i
$66$	1.19040	−	12.9019i	0.146528	−	1.58812i
$67$	7.89198	+	1.39157i	0.964159	+	0.170007i	0.633500	−	0.773743i	$-0.281618\pi$
$67$	7.89198	+	1.39157i	0.964159	+	0.170007i	0.330659	+	0.943750i	$0.392729\pi$
$68$	0.979262	−	0.806008i	0.118753	−	0.0977429i
$69$	−4.96586	−	2.86704i	−0.597820	−	0.345151i
$70$	0.337899	−	0.0827408i	0.0403867	−	0.00988941i
$71$	−4.58464	−	1.66867i	−0.544097	−	0.198035i	0.0553248	−	0.998468i	$-0.482381\pi$
$71$	−4.58464	−	1.66867i	−0.544097	−	0.198035i	−0.599422	+	0.800433i	$0.704603\pi$
$72$	−1.25313	+	0.851164i	−0.147683	+	0.100311i
$73$	0.0197371	+	0.0235218i	0.00231006	+	0.00275302i	0.767198	−	0.641410i	$-0.221650\pi$
$73$	0.0197371	+	0.0235218i	0.00231006	+	0.00275302i	−0.764888	+	0.644163i	$0.777206\pi$
$74$	0.257569	+	0.979810i	0.0299418	+	0.113901i
$75$	7.77166	−	1.10072i	0.897395	−	0.127100i
$76$	−7.65940	−	4.16337i	−0.878593	−	0.477571i
$77$		−	0.642029i		−	0.0731660i
$78$	−6.96894	+	1.83197i	−0.789077	+	0.207430i
$79$	−1.17406	+	0.985156i	−0.132092	+	0.110839i	−0.706440	−	0.707773i	$-0.749700\pi$
$79$	−1.17406	+	0.985156i	−0.132092	+	0.110839i	0.574348	+	0.818611i	$0.305256\pi$
$80$	−0.320775	+	8.93852i	−0.0358638	+	0.999357i
$81$	6.67782	+	2.43053i	0.741980	+	0.270059i
$82$	6.15665	−	8.70454i	0.679889	−	0.961255i
$83$	−2.11752	+	3.66765i	−0.232428	+	0.402577i	−0.958522	−	0.285018i	$-0.908000\pi$
$83$	−2.11752	+	3.66765i	−0.232428	+	0.402577i	0.726094	+	0.687595i	$0.241334\pi$
$84$	0.266682	−	0.219500i	0.0290973	−	0.0239494i
$85$	1.10152	−	0.892973i	0.119477	−	0.0968565i
$86$	−1.15569	+	12.5257i	−0.124621	+	1.35068i
$87$	4.50347	+	7.80024i	0.482823	+	0.836273i
$88$	15.8822	+	4.49854i	1.69305	+	0.479546i
$89$	7.35130	−	8.76094i	0.779237	−	0.928658i	−0.219662	−	0.975576i	$-0.570495\pi$
$89$	7.35130	−	8.76094i	0.779237	−	0.928658i	0.998899	+	0.0469179i	$0.0149399\pi$
$90$	−1.40808	+	0.941178i	−0.148425	+	0.0992089i
$91$	−0.335523	+	0.122120i	−0.0351724	+	0.0128017i
$92$	4.74857	−	5.55142i	0.495073	−	0.578776i
$93$	−10.0722	+	1.77600i	−1.04444	+	0.184163i
$94$	−17.3339	+	1.43379i	−1.78786	+	0.147885i
$95$	−8.52859	−	4.71838i	−0.875015	−	0.484096i
$96$	3.56130	+	8.13501i	0.363473	+	0.830276i
$97$	0.749823	+	4.25245i	0.0761329	+	0.431771i	0.998920	+	0.0464613i	$0.0147944\pi$
$97$	0.749823	+	4.25245i	0.0761329	+	0.431771i	−0.922787	+	0.385310i	$0.874094\pi$
$98$	−7.02093	+	6.95471i	−0.709221	+	0.702532i
$99$	1.06906	+	2.93723i	0.107445	+	0.295202i
$100$	−0.432992	+	9.99062i	−0.0432992	+	0.999062i
$101$	5.65192	+	4.74252i	0.562387	+	0.471899i	0.879110	−	0.476619i	$-0.158138\pi$
$101$	5.65192	+	4.74252i	0.562387	+	0.471899i	−0.316723	+	0.948518i	$0.602582\pi$
$102$	0.601036	−	1.27314i	0.0595114	−	0.126060i
$103$	0.955601	−	0.551717i	0.0941582	−	0.0543622i	−0.452182	−	0.891926i	$-0.649354\pi$
$103$	0.955601	−	0.551717i	0.0941582	−	0.0543622i	0.546340	+	0.837564i	$0.316021\pi$
$104$	−0.670027	−	9.15567i	−0.0657015	−	0.897787i
$105$	0.299977	−	0.243183i	0.0292748	−	0.0237322i
$106$	5.40938	+	7.80384i	0.525406	+	0.757976i
$107$	6.22369	+	3.59325i	0.601667	+	0.347372i	0.769697	−	0.638409i	$-0.220407\pi$
$107$	6.22369	+	3.59325i	0.601667	+	0.347372i	−0.168030	+	0.985782i	$0.553741\pi$
$108$	−5.64118	+	9.56041i	−0.542822	+	0.919951i
$109$	1.50104	−	4.12408i	0.143774	−	0.395015i	−0.846815	−	0.531888i	$-0.821483\pi$
$109$	1.50104	−	4.12408i	0.143774	−	0.395015i	0.990589	+	0.136873i	$0.0437051\pi$
$110$	17.7189	+	5.16151i	1.68943	+	0.492131i
$111$	0.722872	+	0.861485i	0.0686119	+	0.0817685i
$112$	0.212758	+	0.385187i	0.0201037	+	0.0363967i
$113$	14.1662			1.33264			0.666320	−	0.745666i	$-0.267868\pi$
$113$	14.1662			1.33264			0.666320	+	0.745666i	$0.267868\pi$
$114$	−9.66156	−	0.549540i	−0.904888	−	0.0514691i
$115$	5.35510	−	6.16700i	0.499366	−	0.575076i
$116$	−10.8196	+	3.82230i	−1.00458	+	0.354892i
$117$	1.33164	−	1.11738i	0.123110	−	0.103302i
$118$	16.3609	−	7.53504i	1.50614	−	0.693657i
$119$	0.0238604	−	0.0655560i	0.00218728	−	0.00600950i
$120$	3.91386	+	9.12460i	0.357285	+	0.832958i
$121$	11.5300	−	19.9706i	1.04819	−	1.81551i
$122$	−9.66600	−	13.9447i	−0.875119	−	1.26249i
$123$	2.05514	−	11.6553i	0.185306	−	1.05092i
$124$	0.123480	−	13.0295i	0.0110889	−	1.17008i
$125$	−0.567204	+	11.1659i	−0.0507323	+	0.998712i
$126$	−0.0355721	+	0.0753505i	−0.00316902	+	0.00671275i
$127$	1.41768	−	1.68953i	0.125799	−	0.149921i	−0.699469	−	0.714663i	$-0.746580\pi$
$127$	1.41768	−	1.68953i	0.125799	−	0.149921i	0.825267	+	0.564742i	$0.191024\pi$
$128$	−11.0193	+	2.56419i	−0.973978	+	0.226644i
$129$	4.77570	+	13.1211i	0.420477	+	1.15525i
$130$	−0.672921	−	10.2416i	−0.0590190	−	0.898251i
$131$	−2.87869	+	0.507592i	−0.251513	+	0.0443485i	−0.297983	−	0.954571i	$-0.596314\pi$
$131$	−2.87869	+	0.507592i	−0.251513	+	0.0443485i	0.0464702	+	0.998920i	$0.485203\pi$
$132$	18.0745	−	3.01070i	1.57319	−	0.262048i
$133$	−0.479225	+	0.0168695i	−0.0415541	+	0.00146277i
$134$	0.934240	+	11.2946i	0.0807060	+	0.975701i
$135$	−6.38639	+	10.6416i	−0.549653	+	0.915886i
$136$	1.45451	+	1.04958i	0.124723	+	0.0900008i
$137$	−2.70229	−	7.42448i	−0.230872	−	0.634316i	0.769116	−	0.639109i	$-0.220697\pi$
$137$	−2.70229	−	7.42448i	−0.230872	−	0.634316i	−0.999989	+	0.00479252i	$0.998474\pi$
$138$	2.13591	−	7.82287i	0.181821	−	0.665927i
$139$	7.37088	−	8.78427i	0.625190	−	0.745072i	−0.356764	−	0.934195i	$-0.616120\pi$
$139$	7.37088	−	8.78427i	0.625190	−	0.745072i	0.981954	+	0.189122i	$0.0605643\pi$
$140$	0.234659	+	0.432410i	0.0198323	+	0.0365453i
$141$	−16.7205	+	9.65361i	−1.40812	+	0.812981i
$142$	0.633917	−	6.87059i	0.0531971	−	0.576567i
$143$	−18.6543	−	3.28926i	−1.55995	−	0.275062i
$144$	−1.61474	−	1.40793i	−0.134561	−	0.117327i
$145$	−12.1282	+	4.18333i	−1.00719	+	0.347406i
$146$	−0.0250753	+	0.0354526i	−0.00207525	+	0.00293408i
$147$	−3.75193	+	10.3084i	−0.309454	+	0.850219i
$148$	−1.24752	+	0.704578i	−0.102546	+	0.0579160i
$149$	−4.18484	+	3.51150i	−0.342835	+	0.287673i	−0.797906	−	0.602783i	$-0.794059\pi$
$149$	−4.18484	+	3.51150i	−0.342835	+	0.287673i	0.455070	+	0.890456i	$0.349614\pi$
$150$	4.29980	+	10.2339i	0.351077	+	0.835593i
$151$	−2.34868			−0.191133			−0.0955666	−	0.995423i	$-0.530466\pi$
$151$	−2.34868			−0.191133			−0.0955666	+	0.995423i	$0.530466\pi$
$152$	2.94050	−	11.9730i	0.238506	−	0.971141i
$153$			0.339644i			0.0274586i
$154$	0.878132	−	0.230841i	0.0707619	−	0.0186017i
$155$	0.246451	−	14.5660i	0.0197954	−	1.16997i
$156$	−5.01135	−	8.87305i	−0.401229	−	0.710412i
$157$	1.92657	−	5.29320i	0.153757	−	0.422444i	−0.838768	−	0.544490i	$-0.816723\pi$
$157$	1.92657	−	5.29320i	0.153757	−	0.422444i	0.992524	+	0.122046i	$0.0389456\pi$
$158$	−1.76957	−	1.25161i	−0.140780	−	0.0995725i
$159$	9.12815	+	5.27014i	0.723909	+	0.417949i
$160$	−12.3409	+	2.77509i	−0.975637	+	0.219390i
$161$	0.0697765	−	0.395722i	0.00549916	−	0.0311873i
$162$	−0.923340	+	10.0074i	−0.0725445	+	0.786259i
$163$	−9.35037	−	16.1953i	−0.732378	−	1.26852i	−0.955864	−	0.293808i	$-0.905077\pi$
$163$	−9.35037	−	16.1953i	−0.732378	−	1.26852i	0.223487	−	0.974707i	$-0.428256\pi$
$164$	14.1192	+	5.29103i	1.10252	+	0.413160i
$165$	20.2324	−	3.21560i	1.57509	−	0.250334i
$166$	−5.77776	−	1.57753i	−0.448441	−	0.122440i
$167$	−2.04591	−	5.62109i	−0.158317	−	0.434973i	0.835020	−	0.550220i	$-0.185456\pi$
$167$	−2.04591	−	5.62109i	−0.158317	−	0.434973i	−0.993337	+	0.115247i	$0.963234\pi$
$168$	0.396104	+	0.285832i	0.0305601	+	0.0220524i
$169$	−0.428147	−	2.42814i	−0.0329344	−	0.186780i
$170$	1.61741	+	1.18554i	0.124050	+	0.0909264i
$171$	2.16432	−	0.875150i	0.165510	−	0.0669244i
$172$	−17.5475	+	2.92292i	−1.33798	+	0.222870i
$173$	2.84688	+	16.1455i	0.216444	+	1.22752i	0.878382	+	0.477959i	$0.158623\pi$
$173$	2.84688	+	16.1455i	0.216444	+	1.22752i	−0.661938	+	0.749559i	$0.730266\pi$
$174$	−9.04952	+	8.96416i	−0.686042	+	0.679571i
$175$	0.258752	+	0.485388i	0.0195598	+	0.0366919i
$176$	−0.442430	+	23.3402i	−0.0333494	+	1.75934i
$177$	12.8525	−	15.3170i	0.966052	−	1.15130i
$178$	14.6259	+	6.90472i	1.09626	+	0.517531i
$179$	−6.06351	−	10.5023i	−0.453208	−	0.784980i	0.545375	−	0.838192i	$-0.316387\pi$
$179$	−6.06351	−	10.5023i	−0.453208	−	0.784980i	−0.998583	+	0.0532125i	$0.983054\pi$
$180$	−1.79357	−	1.58750i	−0.133685	−	0.118325i
$181$	4.74997	+	0.837548i	0.353063	+	0.0622545i	0.347367	−	0.937729i	$-0.387076\pi$
$181$	4.74997	+	0.837548i	0.353063	+	0.0622545i	0.00569573	+	0.999984i	$0.498187\pi$
$182$	−0.287666	−	0.415002i	−0.0213233	−	0.0307620i
$183$	−16.3111	−	9.41719i	−1.20575	−	0.696139i
$184$	9.30027	+	4.49882i	0.685625	+	0.331658i
$185$	−1.40059	+	0.777342i	−0.102974	+	0.0571513i
$186$	−6.05057	−	13.1376i	−0.443649	−	0.963299i
$187$	2.83512	−	2.37895i	0.207324	−	0.173966i
$188$	−8.19346	−	23.1929i	−0.597569	−	1.69151i
$189$			0.610591i			0.0444139i
$190$	3.38710	−	13.3614i	0.245726	−	0.969339i
$191$		−	2.90191i		−	0.209975i	−0.994474	−	0.104988i	$-0.966520\pi$
$191$		−	2.90191i		−	0.209975i	0.994474	−	0.104988i	$-0.0334803\pi$
$192$	−9.84616	+	7.79588i	−0.710585	+	0.562619i
$193$	−12.1126	+	10.1637i	−0.871885	+	0.731598i	−0.964494	−	0.264104i	$-0.914924\pi$
$193$	−12.1126	+	10.1637i	−0.871885	+	0.731598i	0.0926091	+	0.995703i	$0.470479\pi$
$194$	−5.54667	+	2.55453i	−0.398228	+	0.183405i
$195$	−5.52888	−	9.96178i	−0.395931	−	0.713378i
$196$	−12.0366	−	7.10228i	−0.859759	−	0.507306i
$197$	−14.1694	−	8.18072i	−1.00953	−	0.582852i	−0.0984760	−	0.995139i	$-0.531397\pi$
$197$	−14.1694	−	8.18072i	−1.00953	−	0.582852i	−0.911054	+	0.412287i	$0.864730\pi$
$198$	−3.63300	+	2.51828i	−0.258186	+	0.178966i
$199$	6.27595	+	1.10662i	0.444890	+	0.0784462i	0.391606	−	0.920133i	$-0.371920\pi$
$199$	6.27595	+	1.10662i	0.444890	+	0.0784462i	0.0532847	+	0.998579i	$0.483031\pi$
$200$	−13.8203	+	2.99989i	−0.977243	+	0.212124i
$201$	6.29016	+	10.8949i	0.443674	+	0.768465i
$202$	−4.45442	+	9.43555i	−0.313412	+	0.663883i
$203$	−0.405714	+	0.483511i	−0.0284755	+	0.0339358i
$204$	1.95743	+	0.364308i	0.137048	+	0.0255066i
$205$	15.7413	+	6.03285i	1.09942	+	0.421352i
$206$	1.09819	+	1.10865i	0.0765147	+	0.0772432i
$207$	0.339708	+	1.92658i	0.0236114	+	0.133907i
$208$	12.2817	−	4.20833i	0.851583	−	0.291795i
$209$	−22.4646	−	11.9366i	−1.55391	−	0.825670i
$210$	0.440468	+	0.322856i	0.0303952	+	0.0222792i
$211$	−1.68973	−	9.58294i	−0.116326	−	0.659717i	−0.986085	−	0.166241i	$-0.946837\pi$
$211$	−1.68973	−	9.58294i	−0.116326	−	0.659717i	0.869759	−	0.493476i	$-0.164274\pi$
$212$	−8.72872	+	10.2045i	−0.599491	+	0.700849i
$213$	−2.61956	−	7.19718i	−0.179489	−	0.493143i
$214$	−2.67693	+	9.80436i	−0.182991	+	0.670212i
$215$	−19.6425	+	3.12184i	−1.33961	+	0.212908i
$216$	−15.1045	−	4.27825i	−1.02773	−	0.291098i
$217$	−0.358359	−	0.620696i	−0.0243270	−	0.0421356i
$218$	6.18038	+	0.570235i	0.418588	+	0.0386212i
$219$	−0.00837035	+	0.0474706i	−0.000565616	+	0.00320777i
$220$	−0.688819	+	26.0908i	−0.0464401	+	1.75904i
$221$	−1.78250	−	1.02913i	−0.119904	−	0.0692266i
$222$	−0.918384	+	1.29845i	−0.0616379	+	0.0871462i
$223$	9.23797	−	25.3811i	0.618620	−	1.69964i	−0.0917190	−	0.995785i	$-0.529236\pi$
$223$	9.23797	−	25.3811i	0.618620	−	1.69964i	0.710339	−	0.703860i	$-0.248542\pi$
$224$	−0.450341	+	0.429492i	−0.0300896	+	0.0286966i
$225$	−1.99201	−	1.78975i	−0.132800	−	0.119317i
$226$	5.09342	+	19.3757i	0.338810	+	1.28885i
$227$			24.1464i			1.60265i	0.598226	+	0.801327i	$0.295872\pi$
$227$			24.1464i			1.60265i	−0.598226	+	0.801327i	$0.704128\pi$
$228$	−2.72217	−	13.4121i	−0.180280	−	0.888240i
$229$	−6.65633			−0.439862			−0.219931	−	0.975515i	$-0.570583\pi$
$229$	−6.65633			−0.439862			−0.219931	+	0.975515i	$0.570583\pi$
$230$	10.3603	+	5.10707i	0.683138	+	0.336750i
$231$	0.772086	−	0.647857i	0.0507995	−	0.0426259i
$232$	−9.11811	−	13.4242i	−0.598633	−	0.881340i
$233$	8.83175	−	24.2650i	0.578587	−	1.58966i	−0.211976	−	0.977275i	$-0.567990\pi$
$233$	8.83175	−	24.2650i	0.578587	−	1.58966i	0.790563	−	0.612380i	$-0.209788\pi$
$234$	2.00708	+	1.41959i	0.131207	+	0.0928018i
$235$	−8.96736	−	25.9979i	−0.584966	−	1.69591i
$236$	16.1885	+	19.6683i	1.05378	+	1.28030i
$237$	−2.36944	−	0.417796i	−0.153912	−	0.0271388i
$238$	0.0982428	+	0.00906440i	0.00636813	+	0.000587558i
$239$	3.81137	−	2.20049i	0.246537	−	0.142338i	−0.371641	−	0.928377i	$-0.621205\pi$
$239$	3.81137	−	2.20049i	0.246537	−	0.142338i	0.618178	+	0.786039i	$0.287871\pi$
$240$	−11.0729	+	8.63390i	−0.714752	+	0.557316i
$241$	4.91997	−	5.86339i	0.316923	−	0.377694i	−0.583940	−	0.811797i	$-0.698490\pi$
$241$	4.91997	−	5.86339i	0.316923	−	0.377694i	0.900864	+	0.434102i	$0.142934\pi$
$242$	31.4603	+	8.58975i	2.02235	+	0.552170i
$243$	−1.87941	−	5.16364i	−0.120564	−	0.331248i
$244$	15.5973	−	18.2344i	0.998516	−	1.16734i
$245$	−13.3979	−	8.04051i	−0.855960	−	0.513690i
$246$	16.6804	−	1.37973i	1.06350	−	0.0879685i
$247$	−1.96503	+	14.0104i	−0.125032	+	0.891463i
$248$	17.8654	−	4.51584i	1.13445	−	0.286756i
$249$	−6.54736	+	1.15448i	−0.414922	+	0.0731619i
$250$	−15.4761	+	3.23891i	−0.978794	+	0.204847i
$251$	4.62074	+	12.6954i	0.291659	+	0.801325i	0.995824	+	0.0912897i	$0.0290989\pi$
$251$	4.62074	+	12.6954i	0.291659	+	0.801325i	−0.704166	+	0.710036i	$0.748679\pi$
$252$	−0.115850	−	0.0215614i	−0.00729787	−	0.00135824i
$253$	13.7024	−	16.3299i	0.861465	−	1.02665i
$254$	2.82056	+	1.33156i	0.176978	+	0.0835494i
$255$	2.18539	+	0.423582i	0.136854	+	0.0265257i
$256$	−7.46913	−	14.1496i	−0.466820	−	0.884352i
$257$	−3.61596	+	20.5071i	−0.225557	+	1.27920i	0.636059	+	0.771640i	$0.280563\pi$
$257$	−3.61596	+	20.5071i	−0.225557	+	1.27920i	−0.861617	+	0.507559i	$0.830548\pi$
$258$	−16.2292	+	11.2496i	−1.01039	+	0.700371i
$259$	−0.0394038	+	0.0682495i	−0.00244844	+	0.00424082i
$260$	13.7660	−	4.60275i	0.853731	−	0.285450i
$261$	1.05100	−	2.88759i	0.0650550	−	0.178737i
$262$	−1.72929	−	3.75482i	−0.106836	−	0.231973i
$263$	−2.41836	+	2.02925i	−0.149123	+	0.125129i	−0.714297	−	0.699843i	$-0.753253\pi$
$263$	−2.41836	+	2.02925i	−0.149123	+	0.125129i	0.565174	+	0.824971i	$0.308809\pi$
$264$	10.6165	+	23.6388i	0.653403	+	1.45487i
$265$	−9.84363	+	11.3361i	−0.604690	+	0.696368i
$266$	−0.195378	−	0.649392i	−0.0119794	−	0.0398168i
$267$	17.9537			1.09875
$268$	−15.1122	+	5.33874i	−0.923122	+	0.326116i
$269$	8.82420	+	10.5163i	0.538021	+	0.641188i	0.964743	−	0.263195i	$-0.0847761\pi$
$269$	8.82420	+	10.5163i	0.538021	+	0.641188i	−0.426722	+	0.904383i	$0.640332\pi$
$270$	−16.8513	−	4.90876i	−1.02553	−	0.298738i
$271$	4.46591	−	12.2700i	0.271285	−	0.745348i	−0.726991	−	0.686647i	$-0.759082\pi$
$271$	4.46591	−	12.2700i	0.271285	−	0.745348i	0.998276	−	0.0587013i	$-0.0186960\pi$
$272$	−0.912593	+	2.36677i	−0.0553341	+	0.143506i
$273$	−0.485427	−	0.280262i	−0.0293794	−	0.0169622i
$274$	9.18319	−	6.36551i	0.554777	−	0.384554i
$275$	−0.987165	+	29.1638i	−0.0595283	+	1.75864i
$276$	11.4677	+	0.108679i	0.690272	+	0.00654171i
$277$	−0.999718	+	0.577187i	−0.0600672	+	0.0346798i	−0.529733	−	0.848165i	$-0.677708\pi$
$277$	−0.999718	+	0.577187i	−0.0600672	+	0.0346798i	0.469666	+	0.882844i	$0.344374\pi$
$278$	14.6648	+	6.92311i	0.879538	+	0.415220i
$279$	2.67300	+	2.24291i	0.160028	+	0.134280i
$280$	−0.507055	+	0.476427i	−0.0303023	+	0.0284719i
$281$	0.737949	+	2.02750i	0.0440223	+	0.120950i	0.959756	−	0.280836i	$-0.0906117\pi$
$281$	0.737949	+	2.02750i	0.0440223	+	0.120950i	−0.915733	+	0.401786i	$0.868389\pi$
$282$	−19.2155	−	19.3985i	−1.14427	−	1.15516i
$283$	3.41967	+	19.3939i	0.203279	+	1.15285i	0.900126	+	0.435630i	$0.143474\pi$
$283$	3.41967	+	19.3939i	0.203279	+	1.15285i	−0.696847	+	0.717220i	$0.745414\pi$
$284$	9.62514	−	1.60327i	0.571147	−	0.0951368i
$285$	−2.93181	−	15.0175i	−0.173666	−	0.889557i
$286$	−2.20827	−	26.6970i	−0.130578	−	1.57863i
$287$	0.816766	−	0.144018i	0.0482122	−	0.00850111i
$288$	1.34511	−	2.71476i	0.0792613	−	0.159969i
$289$	−15.5969	+	5.67680i	−0.917463	+	0.333929i
$290$	−10.0824	−	15.0841i	−0.592058	−	0.885771i
$291$	−4.35725	+	5.19277i	−0.255427	+	0.304406i
$292$	−0.0575059	−	0.0215497i	−0.00336528	−	0.00126110i
$293$	5.32781	+	9.22803i	0.311254	+	0.539107i	0.978634	−	0.205610i	$-0.0659178\pi$
$293$	5.32781	+	9.22803i	0.311254	+	0.539107i	−0.667380	+	0.744717i	$0.732584\pi$
$294$	−15.4482	−	1.42533i	−0.900957	−	0.0831271i
$295$	17.9352	+	22.1239i	1.04423	+	1.28810i
$296$	−1.41223	−	1.45296i	−0.0820841	−	0.0844515i
$297$	−16.1961	+	28.0525i	−0.939795	+	1.62777i
$298$	−6.30748	−	4.46124i	−0.365383	−	0.258433i
$299$	−11.1403	−	4.05475i	−0.644262	−	0.234492i
$300$	−12.4514	+	9.56060i	−0.718879	+	0.551982i
$301$	−0.749573	+	0.628967i	−0.0432047	+	0.0362530i
$302$	−0.844466	−	3.21240i	−0.0485936	−	0.184853i
$303$			11.5824i			0.665392i
$304$	17.4333	−	0.283030i	0.999868	−	0.0162329i
$305$	17.5896	−	20.2564i	1.00717	−	1.15988i
$306$	−0.464546	+	0.122118i	−0.0265563	+	0.00698104i
$307$	−1.21249	−	1.44499i	−0.0692005	−	0.0824699i	0.730334	−	0.683091i	$-0.239365\pi$
$307$	−1.21249	−	1.44499i	−0.0692005	−	0.0824699i	−0.799534	+	0.600621i	$0.794920\pi$
$308$	0.631462	+	1.11806i	0.0359809	+	0.0637075i
$309$	1.62775	+	0.592454i	0.0925997	+	0.0337035i
$310$	20.0111	−	4.90009i	1.13656	−	0.278306i
$311$	20.9249	+	12.0810i	1.18654	+	0.685050i	0.957519	−	0.288371i	$-0.0931137\pi$
$311$	20.9249	+	12.0810i	1.18654	+	0.685050i	0.229023	+	0.973421i	$0.426447\pi$
$312$	10.3342	−	10.0445i	0.585061	−	0.568660i
$313$	−7.18564	−	1.26702i	−0.406156	−	0.0716163i	−0.0331622	−	0.999450i	$-0.510558\pi$
$313$	−7.18564	−	1.26702i	−0.406156	−	0.0716163i	−0.372994	+	0.927834i	$0.621669\pi$
$314$	7.93245	+	0.731890i	0.447654	+	0.0413029i
$315$	−0.129341	−	0.0250696i	−0.00728756	−	0.00141251i
$316$	1.07563	−	2.87034i	0.0605089	−	0.161469i
$317$	5.85224	+	4.91061i	0.328694	+	0.275807i	0.792168	−	0.610304i	$-0.208953\pi$
$317$	5.85224	+	4.91061i	0.328694	+	0.275807i	−0.463473	+	0.886111i	$0.653397\pi$
$318$	−3.92619	+	14.3798i	−0.220170	+	0.806382i
$319$	−31.4651	+	11.4524i	−1.76171	+	0.641209i
$320$	−8.23279	−	15.8815i	−0.460227	−	0.887801i
$321$	1.95904	+	11.1103i	0.109343	+	0.620116i
$322$	0.566335	−	0.0468450i	0.0315606	−	0.00261057i
$323$	−1.85019	−	2.05369i	−0.102948	−	0.114270i
$324$	−14.0196	+	2.33527i	−0.778868	+	0.129737i
$325$	15.4287	−	5.03136i	0.855831	−	0.279090i
$326$	18.7891	−	18.6119i	1.04063	−	1.03082i
$327$	6.47417	−	2.35640i	0.358022	−	0.130309i
$328$	−2.16023	+	21.2138i	−0.119279	+	1.17134i
$329$	−1.03645	−	0.869686i	−0.0571414	−	0.0479473i
$330$	11.6727	+	26.5166i	0.642559	+	1.45969i
$331$	−8.79684	−	15.2366i	−0.483518	−	0.837478i	0.516303	−	0.856406i	$-0.327308\pi$
$331$	−8.79684	−	15.2366i	−0.483518	−	0.837478i	−0.999821	+	0.0189284i	$0.993975\pi$
$332$	0.0802674	−	8.46970i	0.00440524	−	0.464835i
$333$	0.0666248	−	0.377848i	0.00365102	−	0.0207059i
$334$	6.95261	−	4.81934i	0.380430	−	0.263702i
$335$	−16.9399	+	5.84300i	−0.925523	+	0.319237i
$336$	−0.248526	+	0.644540i	−0.0135582	+	0.0351625i
$337$	14.5512	+	5.29620i	0.792654	+	0.288502i	0.706439	−	0.707774i	$-0.250301\pi$
$337$	14.5512	+	5.29620i	0.792654	+	0.288502i	0.0862150	+	0.996277i	$0.472523\pi$
$338$	3.16714	−	1.45863i	0.172270	−	0.0793390i
$339$	14.2948	+	17.0358i	0.776384	+	0.925259i
$340$	−1.03997	+	2.63846i	−0.0564004	+	0.143091i
$341$		−	38.0224i		−	2.05903i
$342$	1.97516	+	2.64558i	0.106804	+	0.143057i
$343$	−1.53881			−0.0830878
$344$	−10.3070	−	22.9496i	−0.555715	−	1.23736i
$345$	12.8200	+	0.216909i	0.690204	+	0.0116780i
$346$	−21.0593	+	9.69889i	−1.13215	+	0.521415i
$347$	15.2769	+	5.56034i	0.820108	+	0.298495i	0.717792	−	0.696257i	$-0.245153\pi$
$347$	15.2769	+	5.56034i	0.820108	+	0.298495i	0.102315	+	0.994752i	$0.467375\pi$
$348$	−15.5144	−	9.15437i	−0.831660	−	0.490726i
$349$	12.7774	−	22.1310i	0.683956	−	1.18465i	−0.289808	−	0.957085i	$-0.593591\pi$
$349$	12.7774	−	22.1310i	0.683956	−	1.18465i	0.973764	−	0.227562i	$-0.0730754\pi$
$350$	−0.570853	+	0.528428i	−0.0305134	+	0.0282457i
$351$	17.7409	+	3.12819i	0.946937	+	0.166971i
$352$	−32.0825	+	7.78681i	−1.71000	+	0.415038i
$353$	−8.84343	+	5.10576i	−0.470688	+	0.271752i	−0.716528	−	0.697559i	$-0.754270\pi$
$353$	−8.84343	+	5.10576i	−0.470688	+	0.271752i	0.245839	+	0.969311i	$0.420936\pi$
$354$	25.5708	+	12.0717i	1.35907	+	0.641604i
$355$	10.7743	−	1.71239i	0.571839	−	0.0908842i
$356$	−4.18518	+	22.4871i	−0.221814	+	1.19181i
$357$	0.102913	−	0.0374572i	0.00544672	−	0.00198244i
$358$	12.1844	−	12.0694i	0.643963	−	0.637889i
$359$	−14.7314	+	2.59755i	−0.777496	+	0.137093i	−0.548294	−	0.836285i	$-0.684723\pi$
$359$	−14.7314	+	2.59755i	−0.777496	+	0.137093i	−0.229202	+	0.973379i	$0.573611\pi$
$360$	1.52642	−	3.02392i	0.0804494	−	0.159375i
$361$	−8.31947	+	17.0818i	−0.437867	+	0.899040i
$362$	0.562294	+	6.79789i	0.0295535	+	0.357289i
$363$	35.6508	−	6.28620i	1.87118	−	0.329940i
$364$	0.464186	−	0.542668i	0.0243300	−	0.0284435i
$365$	−0.0641125	−	0.0245711i	−0.00335580	−	0.00128611i
$366$	7.01569	−	25.6953i	0.366716	−	1.34311i
$367$	1.76817	+	1.48367i	0.0922975	+	0.0774468i	0.687769	−	0.725930i	$-0.258590\pi$
$367$	1.76817	+	1.48367i	0.0922975	+	0.0774468i	−0.595471	+	0.803377i	$0.703035\pi$
$368$	−2.80934	+	14.3379i	−0.146447	+	0.747417i
$369$	−3.49682	+	2.01889i	−0.182037	+	0.105099i
$370$	−1.56679	−	1.63616i	−0.0814534	−	0.0850600i
$371$	−0.128262	+	0.727409i	−0.00665902	+	0.0377652i
$372$	15.7935	−	12.9992i	0.818853	−	0.673980i
$373$	−11.4118	+	19.7658i	−0.590880	+	1.02343i	0.403234	+	0.915097i	$0.367886\pi$
$373$	−11.4118	+	19.7658i	−0.590880	+	1.02343i	−0.994114	+	0.108337i	$0.965447\pi$
$374$	4.27316	+	3.02237i	0.220960	+	0.156283i
$375$	−14.0002	+	10.5852i	−0.722967	+	0.546617i
$376$	28.7760	−	19.5455i	1.48401	−	1.00798i
$377$	11.9700	+	14.2652i	0.616484	+	0.734698i
$378$	−0.835132	+	0.219537i	−0.0429545	+	0.0112918i
$379$	7.67928			0.394458			0.197229	−	0.980357i	$-0.436806\pi$
$379$	7.67928			0.394458			0.197229	+	0.980357i	$0.436806\pi$
$380$	19.4928	−	0.171391i	0.999961	−	0.00879219i
$381$	3.46232			0.177380
$382$	3.96908	−	1.04338i	0.203076	−	0.0533839i
$383$	17.0817	+	20.3571i	0.872832	+	1.04020i	0.998839	+	0.0481712i	$0.0153393\pi$
$383$	17.0817	+	20.3571i	0.872832	+	1.04020i	−0.126007	+	0.992029i	$0.540216\pi$
$384$	−14.2029	−	10.6640i	−0.724791	−	0.544197i
$385$	0.696675	+	1.25525i	0.0355058	+	0.0639734i
$386$	−18.2564	−	12.9126i	−0.929227	−	0.657235i
$387$	2.38192	−	4.12561i	0.121080	−	0.209716i
$388$	−5.48824	−	6.66795i	−0.278623	−	0.338514i
$389$	−3.41179	+	19.3492i	−0.172985	+	0.981046i	0.767459	+	0.641098i	$0.221521\pi$
$389$	−3.41179	+	19.3492i	−0.172985	+	0.981046i	−0.940444	+	0.339948i	$0.889590\pi$
$390$	11.6373	−	11.1438i	0.589276	−	0.564290i
$391$	2.00601	−	1.15817i	0.101448	−	0.0585711i
$392$	5.38635	−	19.0166i	0.272052	−	0.960486i
$393$	−3.51524	−	2.94964i	−0.177320	−	0.148789i
$394$	6.09454	−	22.3215i	0.307039	−	1.12454i
$395$	1.22644	−	3.20010i	0.0617088	−	0.161014i
$396$	−4.75060	−	4.06357i	−0.238727	−	0.204202i
$397$	−13.4420	+	2.37019i	−0.674634	+	0.118956i	−0.500461	−	0.865759i	$-0.666836\pi$
$397$	−13.4420	+	2.37019i	−0.674634	+	0.118956i	−0.174173	+	0.984715i	$0.555725\pi$
$398$	0.742937	+	8.98178i	0.0372400	+	0.450216i
$399$	−0.503862	−	0.559280i	−0.0252247	−	0.0279990i
$400$	−9.07215	−	17.8240i	−0.453608	−	0.891201i
$401$	−21.5172	+	3.79407i	−1.07452	+	0.189467i	−0.682791	−	0.730614i	$-0.739234\pi$
$401$	−21.5172	+	3.79407i	−1.07452	+	0.189467i	−0.391729	+	0.920081i	$0.628123\pi$
$402$	−12.6398	+	12.5206i	−0.630415	+	0.624469i
$403$	−19.8704	+	7.23224i	−0.989816	+	0.360264i
$404$	−14.5070	−	2.69997i	−0.721750	−	0.134329i
$405$	−15.6934	+	2.49420i	−0.779812	+	0.123938i
$406$	−0.807193	−	0.381067i	−0.0400603	−	0.0189120i
$407$	−3.62068	+	2.09040i	−0.179471	+	0.103617i
$408$	0.205513	+	2.80826i	0.0101744	+	0.139029i
$409$	−0.406034	−	0.0715947i	−0.0200771	−	0.00354013i	0.163601	−	0.986527i	$-0.447689\pi$
$409$	−0.406034	−	0.0715947i	−0.0200771	−	0.00354013i	−0.183678	+	0.982987i	$0.558800\pi$
$410$	−2.59164	+	23.6992i	−0.127992	+	1.17042i
$411$	6.20165	−	10.7416i	0.305905	−	0.529843i
$412$	−1.12150	+	1.90066i	−0.0552521	+	0.0936388i
$413$	1.31668	+	0.479233i	0.0647896	+	0.0235815i
$414$	−2.51293	+	1.15733i	−0.123504	+	0.0568799i
$415$	0.160203	−	9.46848i	0.00786407	−	0.464790i
$416$	10.1718	+	15.2851i	0.498713	+	0.749416i
$417$	18.0015			0.881537
$418$	8.24906	−	35.0177i	0.403475	−	1.71277i
$419$		−	28.4918i		−	1.39192i	−0.718083	−	0.695958i	$-0.754980\pi$
$419$		−	28.4918i		−	1.39192i	0.718083	−	0.695958i	$-0.245020\pi$
$420$	−0.283215	+	0.718530i	−0.0138195	+	0.0350607i
$421$	17.8710	+	21.2979i	0.870980	+	1.03799i	0.998932	+	0.0462133i	$0.0147154\pi$
$421$	17.8710	+	21.2979i	0.870980	+	1.03799i	−0.127951	+	0.991780i	$0.540840\pi$
$422$	12.4995	−	5.75665i	0.608465	−	0.280229i
$423$	6.18981	+	2.25291i	0.300959	+	0.109540i
$424$	−17.0956	−	8.26964i	−0.830234	−	0.401609i
$425$	−1.18464	+	2.94116i	−0.0574636	+	0.142667i
$426$	8.90205	−	6.17062i	0.431306	−	0.298968i
$427$	0.229190	−	1.29980i	0.0110913	−	0.0629019i
$428$	−14.3723	−	0.136207i	−0.694714	−	0.00658380i
$429$	−14.8681	−	25.7523i	−0.717837	−	1.24333i
$430$	−11.3323	−	25.7434i	−0.546493	−	1.24146i
$431$	−13.6989	−	11.4947i	−0.659851	−	0.553681i	0.250191	−	0.968196i	$-0.419506\pi$
$431$	−13.6989	−	11.4947i	−0.659851	−	0.553681i	−0.910042	+	0.414516i	$0.863951\pi$
$432$	0.420766	−	22.1973i	0.0202441	−	1.06797i
$433$	38.2149	−	13.9091i	1.83649	−	0.668428i	0.845591	−	0.533831i	$-0.179248\pi$
$433$	38.2149	−	13.9091i	1.83649	−	0.668428i	0.990900	−	0.134598i	$-0.0429743\pi$
$434$	0.720106	−	0.713314i	0.0345662	−	0.0342402i
$435$	−17.2690	−	10.3637i	−0.827986	−	0.496901i
$436$	1.44221	+	8.65821i	0.0690695	+	0.414653i
$437$	−12.5491	−	9.79874i	−0.600303	−	0.468737i
$438$	−0.0679372	+	0.00561949i	−0.00324617	+	0.000268510i
$439$	5.23922	+	29.7131i	0.250054	+	1.41813i	0.808455	+	0.588557i	$0.200304\pi$
$439$	5.23922	+	29.7131i	0.250054	+	1.41813i	−0.558401	+	0.829571i	$0.688585\pi$
$440$	−35.9331	+	8.43877i	−1.71305	+	0.402302i
$441$	3.51691	−	1.28005i	0.167472	−	0.0609548i
$442$	0.766688	−	2.80803i	0.0364676	−	0.133564i
$443$	22.5426	+	18.9155i	1.07103	+	0.898702i	0.995146	−	0.0984141i	$-0.0313770\pi$
$443$	22.5426	+	18.9155i	1.07103	+	0.898702i	0.0758863	+	0.997116i	$0.475821\pi$
$444$	−2.10615	−	0.789258i	−0.0999535	−	0.0374565i
$445$	−4.86612	+	25.1058i	−0.230676	+	1.19013i
$446$	38.0364	+	3.50944i	1.80107	+	0.166177i
$447$	−8.44565	−	1.48920i	−0.399466	−	0.0704366i
$448$	−0.749354	−	0.461528i	−0.0354037	−	0.0218051i
$449$	15.2890	+	8.82712i	0.721534	+	0.416578i	0.815317	−	0.579015i	$-0.196563\pi$
$449$	15.2890	+	8.82712i	0.721534	+	0.416578i	−0.0937832	+	0.995593i	$0.529896\pi$
$450$	1.73170	−	3.36806i	0.0816331	−	0.158772i
$451$	41.3450	+	15.0484i	1.94686	+	0.708599i
$452$	−24.6697	+	13.9330i	−1.16036	+	0.655353i
$453$	−2.37000	−	2.82446i	−0.111352	−	0.132705i
$454$	−33.0261	+	8.68181i	−1.54999	+	0.407458i
$455$	0.523476	−	0.602842i	0.0245410	−	0.0282617i
$456$	17.3656	−	8.54555i	0.813219	−	0.400182i
$457$			4.71555i			0.220584i	0.993899	+	0.110292i	$0.0351786\pi$
$457$			4.71555i			0.220584i	−0.993899	+	0.110292i	$0.964821\pi$
$458$	−2.39327	−	9.10415i	−0.111830	−	0.425409i
$459$	−2.69629	+	2.26246i	−0.125852	+	0.105602i
$460$	−3.26014	+	16.0065i	−0.152005	+	0.746306i
$461$	33.2691	+	12.1090i	1.54950	+	0.563971i	0.968300	−	0.249792i	$-0.0803621\pi$
$461$	33.2691	+	12.1090i	1.54950	+	0.563971i	0.581198	+	0.813763i	$0.302584\pi$
$462$	1.16371	+	0.823080i	0.0541405	+	0.0382932i
$463$	−14.3923	+	24.9282i	−0.668867	+	1.15851i	0.309354	+	0.950947i	$0.399887\pi$
$463$	−14.3923	+	24.9282i	−0.668867	+	1.15851i	−0.978221	+	0.207565i	$0.933446\pi$
$464$	15.0824	−	17.2979i	0.700185	−	0.803034i
$465$	17.7653	−	14.4018i	0.823846	−	0.667868i
$466$	36.3638	+	3.35512i	1.68452	+	0.155423i
$467$	−2.75312	−	4.76855i	−0.127399	−	0.220662i	0.795269	−	0.606257i	$-0.207330\pi$
$467$	−2.75312	−	4.76855i	−0.127399	−	0.220662i	−0.922668	+	0.385595i	$0.873996\pi$
$468$	−1.22000	+	3.25559i	−0.0563945	+	0.150490i
$469$	−0.566675	+	0.675337i	−0.0261666	+	0.0311842i
$470$	32.3343	−	21.6126i	1.49147	−	0.996913i
$471$	8.30951	−	3.02441i	0.382882	−	0.139358i
$472$	−21.0807	+	29.2135i	−0.970316	+	1.34466i
$473$	−51.1214	+	9.01408i	−2.35056	+	0.414468i
$474$	−0.280490	−	3.39101i	−0.0128834	−	0.155754i
$475$	21.7945	−	0.0294444i	0.999999	−	0.00135100i
$476$	0.0229253	+	0.137630i	0.00105078	+	0.00630827i
$477$	−0.624445	−	3.54140i	−0.0285914	−	0.162150i
$478$	4.38009	+	4.42179i	0.200340	+	0.202248i
$479$	−0.954896	−	2.62355i	−0.0436303	−	0.119873i	0.915964	−	0.401260i	$-0.131428\pi$
$479$	−0.954896	−	2.62355i	−0.0436303	−	0.119873i	−0.959594	+	0.281387i	$0.909206\pi$
$480$	−15.7902	−	12.0406i	−0.720721	−	0.549575i
$481$	1.78113	+	1.49455i	0.0812126	+	0.0681454i
$482$	9.78859	+	4.62109i	0.445858	+	0.210485i
$483$	0.546294	−	0.315403i	0.0248572	−	0.0143513i
$484$	−0.437062	+	46.1181i	−0.0198664	+	2.09628i
$485$	−6.08040	−	7.50045i	−0.276097	−	0.340578i
$486$	6.38680	−	4.42713i	0.289711	−	0.200819i
$487$	−17.7717	−	10.2605i	−0.805312	−	0.464947i	0.0400131	−	0.999199i	$-0.487260\pi$
$487$	−17.7717	−	10.2605i	−0.805312	−	0.464947i	−0.845325	+	0.534252i	$0.820593\pi$
$488$	30.5480	+	14.7770i	1.38284	+	0.668923i
$489$	10.0408	−	27.5868i	0.454060	−	1.24752i
$490$	6.18017	−	21.2159i	0.279192	−	0.958435i
$491$	−13.1646	−	15.6890i	−0.594112	−	0.708035i	0.382279	−	0.924047i	$-0.375139\pi$
$491$	−13.1646	−	15.6890i	−0.594112	−	0.708035i	−0.976391	+	0.216012i	$0.930695\pi$
$492$	7.88452	+	22.3184i	0.355462	+	1.00619i
$493$	−3.63844			−0.163867
$494$	−19.8692	+	2.34977i	−0.893958	+	0.105721i
$495$	−5.27738	−	4.58260i	−0.237201	−	0.205973i
$496$	12.6000	+	22.8116i	0.565756	+	1.02427i
$497$	0.411155	−	0.345000i	0.0184428	−	0.0154754i
$498$	−3.93312	−	8.54002i	−0.176247	−	0.382687i
$499$	−4.16587	+	11.4456i	−0.186490	+	0.512377i	−0.997341	−	0.0728753i	$-0.976782\pi$
$499$	−4.16587	+	11.4456i	−0.186490	+	0.512377i	0.810851	+	0.585253i	$0.199005\pi$
$500$	−9.99441	−	20.0028i	−0.446963	−	0.894552i
$501$	4.69528	−	8.13246i	0.209770	−	0.363332i
$502$	−15.7027	+	10.8846i	−0.700844	+	0.485803i
$503$	6.56917	−	37.2556i	0.292905	−	1.66114i	−0.382694	−	0.923875i	$-0.625004\pi$
$503$	6.56917	−	37.2556i	0.292905	−	1.66114i	0.675599	−	0.737270i	$-0.263885\pi$
$504$	−0.0121632	−	0.166206i	−0.000541792	−	0.00740339i
$505$	−16.1964	−	3.13927i	−0.720731	−	0.139696i
$506$	27.2619	+	12.8700i	1.21194	+	0.572142i
$507$	2.48798	−	2.96506i	0.110495	−	0.131683i
$508$	−0.807101	+	4.33657i	−0.0358093	+	0.192404i
$509$	9.31887	+	25.6034i	0.413052	+	1.13485i	0.955559	+	0.294799i	$0.0952528\pi$
$509$	9.31887	+	25.6034i	0.413052	+	1.13485i	−0.542508	+	0.840051i	$0.682525\pi$
$510$	0.206400	+	3.14135i	0.00913956	+	0.139101i
$511$	−0.00332659		0.000586568i	−0.000147160		2.59483e-5i
$512$	16.6676	−	15.3033i	0.736609	−	0.676318i
$513$	21.3646	+	11.3521i	0.943270	+	0.501206i
$514$	−29.3486	+	2.42760i	−1.29451	+	0.107077i
$515$	−1.26965	+	2.11561i	−0.0559474	+	0.0932250i
$516$	−21.2218	−	18.1527i	−0.934238	−	0.799127i
$517$	−24.5492	−	67.4484i	−1.07967	−	2.96638i
$518$	−0.107515	−	0.0293554i	−0.00472396	−	0.00128980i
$519$	−16.5434	+	19.7156i	−0.726173	+	0.865419i
$520$	11.2449	+	17.1735i	0.493123	+	0.753106i
$521$	−26.0441	+	15.0366i	−1.14101	+	0.658765i	−0.946681	−	0.322171i	$-0.895587\pi$
$521$	−26.0441	+	15.0366i	−1.14101	+	0.658765i	−0.194332	+	0.980936i	$0.562254\pi$
$522$	4.32736	+	0.399266i	0.189404	+	0.0174754i
$523$	−13.1517	−	2.31901i	−0.575085	−	0.101403i	−0.121461	−	0.992596i	$-0.538758\pi$
$523$	−13.1517	−	2.31901i	−0.575085	−	0.101403i	−0.453624	+	0.891193i	$0.649869\pi$
$524$	4.51386	−	3.71526i	0.197189	−	0.162302i
$525$	−0.322613	+	0.800962i	−0.0140800	+	0.0349569i
$526$	−3.64501	−	2.57809i	−0.158930	−	0.112410i
$527$	1.41307	−	3.88237i	0.0615541	−	0.169119i
$528$	−28.5147	+	23.0200i	−1.24094	+	1.00182i
$529$	−7.39861	+	6.20817i	−0.321679	+	0.269920i
$530$	−19.0441	−	9.38771i	−0.827222	−	0.407776i
$531$	−6.82169			−0.296036
$532$	0.817955	−	0.500715i	0.0354628	−	0.0217088i
$533$		−	24.4692i		−	1.05988i
$534$	6.45523	+	24.5561i	0.279345	+	1.06264i
$535$	−16.0672	−	0.271851i	−0.694645	−	0.0117531i
$536$	−12.7356	−	18.7500i	−0.550094	−	0.809878i
$537$	6.51123	−	17.8894i	0.280980	−	0.771987i
$538$	−11.2108	+	15.8504i	−0.483334	+	0.683358i
$539$	−35.3183	−	20.3910i	−1.52127	−	0.878304i
$540$	0.655089	−	24.8132i	0.0281905	−	1.06779i
$541$	4.67605	−	26.5192i	0.201039	−	1.14015i	−0.702513	−	0.711671i	$-0.747939\pi$
$541$	4.67605	−	26.5192i	0.201039	−	1.14015i	0.903552	−	0.428478i	$-0.140950\pi$
$542$	18.3879	+	1.69657i	0.789828	+	0.0728738i
$543$	3.78588	+	6.55733i	0.162467	+	0.281402i
$544$	−3.56525	−	0.397226i	−0.152859	−	0.0170309i
$545$	1.54037	+	9.69191i	0.0659820	+	0.415156i
$546$	0.208792	−	0.764708i	0.00893545	−	0.0327265i
$547$	1.65216	+	4.53927i	0.0706412	+	0.194085i	0.969989	−	0.243149i	$-0.0781803\pi$
$547$	1.65216	+	4.53927i	0.0706412	+	0.194085i	−0.899348	+	0.437234i	$0.855958\pi$
$548$	12.0082	+	10.2715i	0.512964	+	0.438779i
$549$	1.11582	+	6.32812i	0.0476220	+	0.270078i
$550$	−40.2436	+	9.13562i	−1.71599	+	0.389544i
$551$	9.37506	+	23.1854i	0.399391	+	0.987729i
$552$	3.97453	+	15.7239i	0.169167	+	0.669253i
$553$	−0.0292779	−	0.166043i	−0.00124502	−	0.00706087i
$554$	−1.14889	−	1.15983i	−0.0488118	−	0.0492765i
$555$	−2.34812	−	0.899916i	−0.0996720	−	0.0381993i
$556$	−4.19632	+	22.5469i	−0.177964	+	0.956203i
$557$	13.6941	−	16.3200i	0.580239	−	0.691501i	−0.393460	−	0.919342i	$-0.628722\pi$
$557$	13.6941	−	16.3200i	0.580239	−	0.691501i	0.973699	+	0.227840i	$0.0731664\pi$
$558$	−2.10666	+	4.46242i	−0.0891820	+	0.188909i
$559$	14.4346	+	25.0014i	0.610517	+	1.05745i
$560$	−0.833941	−	0.522224i	−0.0352404	−	0.0220680i
$561$	5.72171	+	1.00889i	0.241571	+	0.0425954i
$562$	−2.50777	+	1.73831i	−0.105784	+	0.0733262i
$563$	15.2545	+	8.80716i	0.642899	+	0.371178i	0.785730	−	0.618569i	$-0.212287\pi$
$563$	15.2545	+	8.80716i	0.642899	+	0.371178i	−0.142832	+	0.989747i	$0.545621\pi$
$564$	19.6233	−	33.2566i	0.826289	−	1.40036i
$565$	−27.6967	+	15.3719i	−1.16521	+	0.646701i
$566$	−25.2964	+	11.6503i	−1.06329	+	0.489699i
$567$	−0.598873	+	0.502514i	−0.0251503	+	0.0211036i
$568$	5.65357	+	12.5883i	0.237219	+	0.528192i
$569$		−	32.5554i		−	1.36479i	−0.730983	−	0.682396i	$-0.760938\pi$
$569$		−	32.5554i		−	1.36479i	0.730983	−	0.682396i	$-0.239062\pi$
$570$	19.4859	−	9.40947i	0.816175	−	0.394119i
$571$			44.6351i			1.86792i	0.357379	+	0.933960i	$0.383671\pi$
$571$			44.6351i			1.86792i	−0.357379	+	0.933960i	$0.616329\pi$
$572$	35.7207	−	12.6192i	1.49356	−	0.527636i
$573$	3.48976	−	2.92826i	0.145787	−	0.122330i
$574$	0.490647	+	1.06535i	0.0204792	+	0.0444667i
$575$	−3.77801	+	17.8682i	−0.157554	+	0.745154i
$576$	4.19674	+	0.863674i	0.174864	+	0.0359864i
$577$	−16.3595	−	9.44513i	−0.681053	−	0.393206i	0.119199	−	0.992870i	$-0.461967\pi$
$577$	−16.3595	−	9.44513i	−0.681053	−	0.393206i	−0.800252	+	0.599664i	$0.795301\pi$
$578$	−13.3722	−	19.2915i	−0.556212	−	0.802419i
$579$	−24.4451	−	4.31034i	−1.01590	−	0.179131i
$580$	17.0061	−	19.2136i	0.706141	−	0.797802i
$581$	−0.232948	−	0.403478i	−0.00966432	−	0.0167391i
$582$	−8.66903	−	4.09255i	−0.359343	−	0.169642i
$583$	−25.1875	+	30.0173i	−1.04316	+	1.24319i
$584$	0.00879838	−	0.0864015i	0.000364080	−	0.00357532i
$585$	−1.39105	+	3.62961i	−0.0575127	+	0.150066i
$586$	−10.7060	+	10.6050i	−0.442260	+	0.438089i
$587$	−3.26553	−	18.5197i	−0.134783	−	0.764391i	−0.975011	−	0.222157i	$-0.928690\pi$
$587$	−3.26553	−	18.5197i	−0.134783	−	0.764391i	0.840228	−	0.542233i	$-0.182421\pi$
$588$	−3.60489	−	21.6417i	−0.148663	−	0.892487i
$589$	−28.3808	+	0.999048i	−1.16941	+	0.0411651i
$590$	−23.8113	+	32.4854i	−0.980295	+	1.33740i
$591$	−4.46014	−	25.2947i	−0.183466	−	1.04049i
$592$	1.47951	−	2.45398i	0.0608076	−	0.100858i
$593$	13.3687	+	36.7303i	0.548987	+	1.50833i	0.835080	+	0.550129i	$0.185421\pi$
$593$	13.3687	+	36.7303i	0.548987	+	1.50833i	−0.286092	+	0.958202i	$0.592356\pi$
$594$	−44.1920	−	12.0659i	−1.81322	−	0.495071i
$595$	0.0244855	+	0.154062i	0.00100381	+	0.00631591i
$596$	3.83399	−	10.2311i	0.157046	−	0.419081i
$597$	5.00213	+	8.66394i	0.204723	+	0.354591i
$598$	1.54037	−	16.6950i	0.0629904	−	0.682709i
$599$	3.64027	−	20.6450i	0.148737	−	0.843532i	−0.815553	−	0.578683i	$-0.803567\pi$
$599$	3.64027	−	20.6450i	0.148737	−	0.843532i	0.964290	−	0.264849i	$-0.0853220\pi$
$600$	−17.5533	−	13.5928i	−0.716612	−	0.554923i
$601$	−31.8025	−	18.3612i	−1.29725	−	0.748968i	−0.317322	−	0.948318i	$-0.602784\pi$
$601$	−31.8025	−	18.3612i	−1.29725	−	0.748968i	−0.979928	+	0.199350i	$0.936117\pi$
$602$	−1.12977	−	0.799081i	−0.0460461	−	0.0325681i
$603$	1.46796	−	4.03320i	0.0597801	−	0.164244i
$604$	4.09011	−	2.31003i	0.166424	−	0.0939937i
$605$	−0.872318	+	51.5566i	−0.0354648	+	2.09607i
$606$	−15.8418	+	4.16444i	−0.643528	+	0.169169i
$607$		−	39.2383i		−	1.59263i	−0.604881	−	0.796316i	$-0.706779\pi$
$607$		−	39.2383i		−	1.59263i	0.604881	−	0.796316i	$-0.293221\pi$
$608$	6.65523	+	23.7425i	0.269905	+	0.962887i
$609$	−0.990853			−0.0401514
$610$	34.0298	+	16.7749i	1.37783	+	0.679195i
$611$	−30.5789	+	25.6587i	−1.23709	+	1.03804i
$612$	−0.334053	−	0.591472i	−0.0135033	−	0.0239088i
$613$	−10.1531	+	27.8955i	−0.410081	+	1.12669i	0.547067	+	0.837089i	$0.315744\pi$
$613$	−10.1531	+	27.8955i	−0.410081	+	1.12669i	−0.957148	+	0.289599i	$0.906478\pi$
$614$	1.54043	−	2.17792i	0.0621666	−	0.0878937i
$615$	8.62924	+	25.0176i	0.347965	+	1.00881i
$616$	−1.30218	+	1.26568i	−0.0524664	+	0.0509955i
$617$	36.8082	+	6.49028i	1.48184	+	0.261289i	0.855314	−	0.518110i	$-0.173364\pi$
$617$	36.8082	+	6.49028i	1.48184	+	0.261289i	0.626528	+	0.779399i	$0.284475\pi$
$618$	−0.225069	+	2.43937i	−0.00905360	+	0.0981257i
$619$	15.0887	−	8.71147i	0.606467	−	0.350144i	−0.165115	−	0.986274i	$-0.552799\pi$
$619$	15.0887	−	8.71147i	0.606467	−	0.350144i	0.771581	+	0.636131i	$0.219466\pi$
$620$	13.8970	+	25.6083i	0.558119	+	1.02845i
$621$	−13.0315	+	15.5303i	−0.522934	+	0.623209i
$622$	−9.00019	+	32.9636i	−0.360875	+	1.32172i
$623$	0.430309	+	1.18226i	0.0172400	+	0.0473664i
$624$	17.4540	+	10.5231i	0.698720	+	0.421261i
$625$	−11.0074	−	22.4463i	−0.440295	−	0.897853i
$626$	−0.850624	−	10.2837i	−0.0339978	−	0.411018i
$627$	−8.31396	−	39.0603i	−0.332028	−	1.55992i
$628$	1.85106	+	11.1127i	0.0738654	+	0.443445i
$629$	−0.447386	+	0.0788863i	−0.0178385	+	0.00314540i
$630$	−0.0122157	−	0.185920i	−0.000486687	−	0.00740722i
$631$	−14.2782	−	39.2290i	−0.568406	−	1.56168i	−0.806993	−	0.590561i	$-0.798906\pi$
$631$	−14.2782	−	39.2290i	−0.568406	−	1.56168i	0.238587	−	0.971121i	$-0.423316\pi$
$632$	4.31263	+	0.439161i	0.171547	+	0.0174689i
$633$	9.81910	−	11.7019i	0.390274	−	0.465111i
$634$	−4.61229	+	9.76997i	−0.183178	+	0.388015i
$635$	−0.938420	+	4.84159i	−0.0372400	+	0.192132i
$636$	−21.0796	−	0.199771i	−0.835861	−	0.00792145i
$637$	−3.93842	+	22.3359i	−0.156046	+	0.884980i
$638$	−26.9771	−	38.9185i	−1.06803	−	1.54080i
$639$	−1.30653	+	2.26297i	−0.0516854	+	0.0895218i
$640$	18.7617	−	16.9705i	0.741622	−	0.670818i
$641$	−0.968241	+	2.66022i	−0.0382432	+	0.105072i	−0.957344	−	0.288949i	$-0.906694\pi$
$641$	−0.968241	+	2.66022i	−0.0382432	+	0.105072i	0.919101	+	0.394021i	$0.128916\pi$
$642$	−14.4917	+	6.67416i	−0.571941	+	0.263408i
$643$	−13.4064	+	11.2493i	−0.528696	+	0.443629i	−0.867651	−	0.497174i	$-0.834371\pi$
$643$	−13.4064	+	11.2493i	−0.528696	+	0.443629i	0.338955	+	0.940803i	$0.389927\pi$
$644$	0.267697	+	0.757759i	0.0105487	+	0.0298599i
$645$	−23.5750	−	20.4713i	−0.928266	−	0.806057i
$646$	2.14369	−	3.26900i	0.0843423	−	0.128617i
$647$	−48.7259			−1.91561			−0.957807	−	0.287412i	$-0.907205\pi$
$647$	−48.7259			−1.91561			−0.957807	+	0.287412i	$0.907205\pi$
$648$	−8.23479	−	18.3356i	−0.323493	−	0.720291i
$649$	47.7808	+	56.9429i	1.87556	+	2.23521i
$650$	12.4290	+	19.2935i	0.487505	+	0.756754i
$651$	0.384819	−	1.05728i	0.0150823	−	0.0414382i
$652$	32.2120	+	19.0069i	1.26152	+	0.744366i
$653$	−25.6509	−	14.8095i	−1.00380	−	0.579542i	−0.0944265	−	0.995532i	$-0.530102\pi$
$653$	−25.6509	−	14.8095i	−1.00380	−	0.579542i	−0.909369	+	0.415990i	$0.863435\pi$
$654$	5.55074	+	8.00776i	0.217051	+	0.313128i
$655$	5.07742	−	4.11612i	0.198391	−	0.160830i
$656$	−29.7918	+	4.67276i	−1.16317	+	0.182441i
$657$	0.0142422	−	0.00822272i	0.000555640	−	0.000320799i
$658$	0.816853	−	1.73029i	0.0318443	−	0.0674539i
$659$	18.5550	+	15.5695i	0.722800	+	0.606501i	0.928158	−	0.372186i	$-0.121392\pi$
$659$	18.5550	+	15.5695i	0.722800	+	0.606501i	−0.205359	+	0.978687i	$0.565836\pi$
$660$	−32.0711	+	25.4992i	−1.24836	+	0.992556i
$661$	−5.92570	−	16.2807i	−0.230483	−	0.633247i	0.769502	−	0.638644i	$-0.220504\pi$
$661$	−5.92570	−	16.2807i	−0.230483	−	0.633247i	−0.999985	+	0.00539689i	$0.998282\pi$
$662$	17.6768	−	17.5101i	0.687030	−	0.680550i
$663$	−0.561082	−	3.18206i	−0.0217906	−	0.123581i
$664$	11.6132	−	2.93548i	0.450681	−	0.113919i
$665$	0.918642	−	0.552996i	0.0356234	−	0.0214443i
$666$	0.540754	−	0.0447290i	0.0209538	−	0.00173321i
$667$	−20.6385	+	3.63913i	−0.799128	+	0.140908i
$668$	9.09142	+	7.77661i	0.351758	+	0.300886i
$669$	39.8444	−	14.5022i	1.54047	−	0.560687i
$670$	−14.0824	−	21.0685i	−0.544052	−	0.813949i
$671$	45.0075	−	53.6378i	1.73750	−	2.07067i
$672$	−0.970923	−	0.108176i	−0.0374542	−	0.00417299i
$673$	−1.59245	−	2.75820i	−0.0613844	−	0.106321i	0.833700	−	0.552218i	$-0.186218\pi$
$673$	−1.59245	−	2.75820i	−0.0613844	−	0.106321i	−0.895084	+	0.445897i	$0.852885\pi$
$674$	−2.01199	+	21.8065i	−0.0774989	+	0.839957i
$675$	0.938826	−	27.7357i	0.0361354	−	1.06755i
$676$	3.13377	+	3.80739i	0.120530	+	0.146438i
$677$	5.42205	−	9.39127i	0.208386	−	0.360936i	−0.742820	−	0.669491i	$-0.766512\pi$
$677$	5.42205	−	9.39127i	0.208386	−	0.360936i	0.951206	+	0.308555i	$0.0998455\pi$
$678$	−18.1610	+	25.6768i	−0.697469	+	0.986111i
$679$	−0.446381	−	0.162469i	−0.0171305	−	0.00623501i
$680$	−3.98266	−	0.473761i	−0.152728	−	0.0181679i
$681$	−29.0378	+	24.3656i	−1.11273	+	0.933692i
$682$	52.0049	−	13.6709i	1.99137	−	0.523486i
$683$		−	31.1790i		−	1.19303i	−0.802602	−	0.596515i	$-0.796552\pi$
$683$		−	31.1790i		−	1.19303i	0.802602	−	0.596515i	$-0.203448\pi$
$684$	−2.90832	+	3.65273i	−0.111202	+	0.139666i
$685$	13.3397	+	11.5835i	0.509685	+	0.442584i
$686$	−0.553276	−	2.10470i	−0.0211242	−	0.0803576i
$687$	−6.71675	−	8.00471i	−0.256260	−	0.305399i
$688$	27.6833	−	22.3488i	1.05542	−	0.852040i
$689$	20.4779	+	7.45335i	0.780147	+	0.283950i
$690$	4.31273	+	17.6124i	0.164183	+	0.670494i
$691$	19.7997	+	11.4314i	0.753215	+	0.434869i	0.826855	−	0.562416i	$-0.190128\pi$
$691$	19.7997	+	11.4314i	0.753215	+	0.434869i	−0.0736391	+	0.997285i	$0.523461\pi$
$692$	−20.8374	−	25.3165i	−0.792120	−	0.962389i
$693$	−0.338638	−	0.0597109i	−0.0128638	−	0.00226823i
$694$	−2.11233	+	22.8941i	−0.0801831	+	0.869049i
$695$	−4.87908	+	25.1726i	−0.185074	+	0.954852i
$696$	6.94266	−	24.5112i	0.263161	−	0.929095i
$697$	3.66238	+	3.07310i	0.138722	+	0.116402i
$698$	34.8637	+	9.51898i	1.31961	+	0.360299i
$699$	38.0924	−	13.8645i	1.44079	−	0.524403i
$700$	−0.928004	−	0.590785i	−0.0350752	−	0.0223296i
$701$	−2.97140	−	16.8517i	−0.112228	−	0.636478i	−0.988085	−	0.153908i	$-0.950814\pi$
$701$	−2.97140	−	16.8517i	−0.112228	−	0.636478i	0.875857	−	0.482571i	$-0.160297\pi$
$702$	2.10013	+	25.3897i	0.0792644	+	0.958272i
$703$	1.65546	+	2.64763i	0.0624368	+	0.0998574i
$704$	−22.1856	−	41.0810i	−0.836151	−	1.54830i
$705$	22.2156	−	37.0178i	0.836686	−	1.39417i
$706$	−10.1630	−	10.2598i	−0.382490	−	0.386132i
$707$	−0.762711	+	0.277604i	−0.0286847	+	0.0104404i
$708$	−7.31706	+	39.3147i	−0.274992	+	1.47754i
$709$	6.48053	+	5.43781i	0.243382	+	0.204221i	0.756316	−	0.654206i	$-0.226997\pi$
$709$	6.48053	+	5.43781i	0.243382	+	0.204221i	−0.512935	+	0.858428i	$0.671442\pi$
$710$	6.21598	+	14.1208i	0.233282	+	0.529943i
$711$	0.410427	+	0.710881i	0.0153922	+	0.0266601i
$712$	−32.2613	+	2.36093i	−1.20904	+	0.0884798i
$713$	4.13232	−	23.4355i	0.154757	−	0.877668i
$714$	0.0882340	+	0.127291i	0.00330207	+	0.00476373i
$715$	40.0408	−	13.8111i	1.49744	−	0.516507i
$716$	20.8888	+	12.3255i	0.780650	+	0.460627i
$717$	6.49222	+	2.36297i	0.242456	+	0.0882469i
$718$	−8.84946	−	19.2149i	−0.330259	−	0.717094i
$719$	−22.5343	−	26.8553i	−0.840387	−	1.00153i	−0.999897	−	0.0143376i	$-0.995436\pi$
$719$	−22.5343	−	26.8553i	−0.840387	−	1.00153i	0.159511	−	0.987196i	$-0.449008\pi$
$720$	4.68478	+	1.00051i	0.174591	+	0.0372866i
$721$			0.121389i			0.00452075i
$722$	−26.3547	−	5.23719i	−0.980822	−	0.194908i
$723$	12.0158			0.446872
$724$	−9.09560	+	3.21324i	−0.338035	+	0.119419i
$725$	19.1727	−	21.3394i	0.712058	−	0.792525i
$726$	21.4161	+	46.5010i	0.794827	+	1.72581i
$727$	−25.0708	−	9.12503i	−0.929825	−	0.338429i	−0.167685	−	0.985841i	$-0.553629\pi$
$727$	−25.0708	−	9.12503i	−0.929825	−	0.338429i	−0.762140	+	0.647412i	$0.775851\pi$
$728$	0.909128	+	0.439773i	0.0336945	+	0.0162991i
$729$	14.9728	−	25.9336i	0.554547	−	0.960503i
$730$	0.0105554	−	0.0965240i	0.000390674	−	0.00357251i
$731$	−5.55488	−	0.979475i	−0.205455	−	0.0362272i
$732$	37.6671	+	0.356971i	1.39221	+	0.0131940i
$733$	19.6274	−	11.3319i	0.724953	−	0.418552i	−0.0916197	−	0.995794i	$-0.529204\pi$
$733$	19.6274	−	11.3319i	0.724953	−	0.418552i	0.816573	+	0.577242i	$0.195871\pi$
$734$	−1.39354	+	2.95185i	−0.0514364	+	0.108955i
$735$	−3.85022	−	24.2254i	−0.142018	−	0.893568i
$736$	−20.6207	+	1.31272i	−0.760090	+	0.0483877i
$737$	−43.9484	+	15.9959i	−1.61886	+	0.589217i
$738$	−4.01861	−	4.05687i	−0.147927	−	0.149336i
$739$	42.1479	−	7.43181i	1.55043	−	0.273384i	0.668124	−	0.744050i	$-0.267098\pi$
$739$	42.1479	−	7.43181i	1.55043	−	0.273384i	0.882311	+	0.470667i	$0.155987\pi$
$740$	1.67452	−	2.73124i	0.0615564	−	0.100403i
$741$	−18.8314	+	11.7745i	−0.691789	+	0.432548i
$742$	−1.04103	+	0.0861094i	−0.0382172	+	0.00316118i
$743$	−28.2872	+	4.98780i	−1.03776	+	0.182985i	−0.666469	−	0.745533i	$-0.732195\pi$
$743$	−28.2872	+	4.98780i	−1.03776	+	0.182985i	−0.371289	+	0.928517i	$0.621084\pi$
$744$	23.4582	+	16.9276i	0.860018	+	0.620595i
$745$	4.37153	−	11.4065i	0.160160	−	0.417900i
$746$	−31.1376	−	8.50164i	−1.14003	−	0.311267i
$747$	1.73756	+	1.45799i	0.0635741	+	0.0533450i
$748$	−2.59742	+	6.93128i	−0.0949713	+	0.253433i
$749$	−0.684667	+	0.395293i	−0.0250172	+	0.0144437i
$750$	−19.5116	−	15.3428i	−0.712463	−	0.560240i
$751$	6.13883	−	34.8151i	0.224009	−	1.27042i	−0.640561	−	0.767907i	$-0.721298\pi$
$751$	6.13883	−	34.8151i	0.224009	−	1.27042i	0.864570	−	0.502512i	$-0.167591\pi$
$752$	37.0797	+	32.3306i	1.35216	+	1.17898i
$753$	−10.6044	+	18.3674i	−0.386446	+	0.669345i
$754$	−15.2074	+	21.5009i	−0.553822	+	0.783017i
$755$	4.59198	−	2.54859i	0.167119	−	0.0927527i
$756$	−0.600541	−	1.06331i	−0.0218415	−	0.0386723i
$757$	28.7776	+	34.2958i	1.04594	+	1.24650i	0.968371	+	0.249515i	$0.0802713\pi$
$757$	28.7776	+	34.2958i	1.04594	+	1.24650i	0.0775688	+	0.996987i	$0.475284\pi$
$758$	2.76107	+	10.5033i	0.100287	+	0.381497i
$759$	33.4647			1.21469
$760$	7.24304	+	26.5996i	0.262733	+	0.964869i
$761$	36.6681			1.32922			0.664609	−	0.747192i	$-0.268598\pi$
$761$	36.6681			1.32922			0.664609	+	0.747192i	$0.268598\pi$
$762$	1.24487	+	4.73558i	0.0450970	+	0.171552i
$763$	0.310342	+	0.369851i	0.0112351	+	0.0133895i
$764$	2.85415	+	5.05354i	0.103260	+	0.182831i
$765$	−0.368552	−	0.664047i	−0.0133250	−	0.0240087i
$766$	−21.7017	+	30.6827i	−0.784113	+	1.10861i
$767$	20.6699	−	35.8013i	0.746346	−	1.29271i
$768$	9.47902	−	23.2602i	0.342045	−	0.839331i
$769$	−2.86217	+	16.2322i	−0.103213	+	0.585347i	0.888707	+	0.458476i	$0.151605\pi$
$769$	−2.86217	+	16.2322i	−0.103213	+	0.585347i	−0.991919	+	0.126871i	$0.959507\pi$
$770$	−1.46637	+	1.40420i	−0.0528444	+	0.0506037i
$771$	−28.3101	+	16.3448i	−1.01956	+	0.588644i
$772$	11.0971	−	29.6128i	0.399393	−	1.06579i
$773$	14.1813	+	11.8995i	0.510066	+	0.427996i	0.861152	−	0.508347i	$-0.169743\pi$
$773$	14.1813	+	11.8995i	0.510066	+	0.427996i	−0.351086	+	0.936343i	$0.614188\pi$
$774$	6.49919	+	1.77450i	0.233609	+	0.0637832i
$775$	15.3239	+	28.7458i	0.550450	+	1.03258i
$776$	7.14677	−	9.90397i	0.256554	−	0.355532i
$777$	−0.121836	+	0.0214830i	−0.00437086	+	0.000770700i
$778$	−27.6915	+	2.29053i	−0.992790	+	0.0821196i
$779$	10.1461	−	31.2563i	0.363521	−	1.11987i
$780$	19.4261	+	11.9101i	0.695566	+	0.426449i
$781$	28.0410	−	4.94439i	1.00339	−	0.176924i
$782$	2.30534	+	2.32729i	0.0824386	+	0.0832236i
$783$	29.9243	−	10.8916i	1.06941	−	0.389233i
$784$	27.9466	+	0.529747i	0.998092	+	0.0189195i
$785$	1.97704	+	12.4394i	0.0705636	+	0.443983i
$786$	2.77045	−	5.86849i	0.0988187	−	0.209322i
$787$	0.370908	−	0.214144i	0.0132215	−	0.00763341i	−0.493375	−	0.869817i	$-0.664237\pi$
$787$	0.370908	−	0.214144i	0.0132215	−	0.00763341i	0.506596	+	0.862183i	$0.330904\pi$
$788$	32.7214	+	0.310101i	1.16565	+	0.0110469i
$789$	−4.88062	−	0.860586i	−0.173755	−	0.0306377i
$790$	4.81788	+	0.526862i	0.171412	+	0.0187449i
$791$	−0.779209	+	1.34963i	−0.0277055	+	0.0479873i
$792$	3.84985	−	7.95866i	0.136798	−	0.282799i
$793$	−36.5919	−	13.3184i	−1.29942	−	0.472949i
$794$	−8.07486	−	17.5330i	−0.286566	−	0.622223i
$795$	−23.5654	−	0.398718i	−0.835779	−	0.0141411i
$796$	−12.0177	+	4.24553i	−0.425954	+	0.150479i
$797$	−6.48430			−0.229686			−0.114843	−	0.993384i	$-0.536636\pi$
$797$	−6.48430			−0.229686			−0.114843	+	0.993384i	$0.536636\pi$
$798$	0.583789	−	0.890243i	0.0206659	−	0.0315143i
$799$		−	7.79933i		−	0.275921i
$800$	21.1168	−	18.8170i	0.746593	−	0.665281i
$801$	−3.93725	−	4.69223i	−0.139116	−	0.165792i
$802$	−12.9258	−	28.0659i	−0.456426	−	0.991043i
$803$	−0.168393	−	0.0612902i	−0.00594248	−	0.00216288i
$804$	−21.6695	−	12.7862i	−0.764226	−	0.450936i
$805$	0.292982	+	0.849403i	0.0103262	+	0.0299375i
$806$	−17.0362	−	24.5773i	−0.600076	−	0.865699i
$807$	−3.74227	+	21.2235i	−0.131734	+	0.747101i
$808$	−1.52310	−	20.8126i	−0.0535826	−	0.732186i
$809$	−12.0846	−	20.9312i	−0.424873	−	0.735902i	0.571535	−	0.820578i	$-0.306348\pi$
$809$	−12.0846	−	20.9312i	−0.424873	−	0.735902i	−0.996409	+	0.0846751i	$0.973015\pi$
$810$	−9.05397	−	20.5678i	−0.318124	−	0.722678i
$811$	1.35905	+	1.14038i	0.0477226	+	0.0400440i	0.666337	−	0.745651i	$-0.267861\pi$
$811$	1.35905	+	1.14038i	0.0477226	+	0.0400440i	−0.618614	+	0.785695i	$0.712306\pi$
$812$	0.230977	−	1.24105i	0.00810571	−	0.0435522i
$813$	19.2620	−	7.01079i	0.675547	−	0.245879i
$814$	−4.16095	−	4.20057i	−0.145841	−	0.147230i
$815$	35.8550	+	21.5177i	1.25594	+	0.753733i
$816$	−3.76708	+	1.29079i	−0.131874	+	0.0451868i
$817$	8.07155	+	37.9213i	0.282388	+	1.32670i
$818$	−0.0480656	−	0.581092i	−0.00168057	−	0.0203174i
$819$	0.0332075	+	0.188329i	0.00116036	+	0.00658075i
$820$	−33.3462	+	4.97630i	−1.16450	+	0.173780i
$821$	28.1529	−	10.2468i	0.982543	−	0.357617i	0.199715	−	0.979854i	$-0.435998\pi$
$821$	28.1529	−	10.2468i	0.982543	−	0.357617i	0.782829	+	0.622237i	$0.213776\pi$
$822$	16.9215	+	4.62016i	0.590206	+	0.161146i
$823$	−12.9490	−	10.8655i	−0.451374	−	0.378748i	0.388571	−	0.921419i	$-0.372969\pi$
$823$	−12.9490	−	10.8655i	−0.451374	−	0.378748i	−0.839945	+	0.542671i	$0.817413\pi$
$824$	−3.00285	−	0.850539i	−0.104609	−	0.0296299i
$825$	−36.0677	+	28.2414i	−1.25572	+	0.983239i
$826$	−0.182057	+	1.97319i	−0.00633457	+	0.0686561i
$827$	−7.16550	−	1.26347i	−0.249169	−	0.0439352i	0.0476686	−	0.998863i	$-0.484821\pi$
$827$	−7.16550	−	1.26347i	−0.249169	−	0.0439352i	−0.296837	+	0.954928i	$0.595932\pi$
$828$	−2.48646	−	3.02093i	−0.0864104	−	0.104985i
$829$	−7.30736	−	4.21891i	−0.253795	−	0.146529i	0.367706	−	0.929942i	$-0.380143\pi$
$829$	−7.30736	−	4.21891i	−0.253795	−	0.146529i	−0.621501	+	0.783414i	$0.713477\pi$
$830$	13.0081	−	3.18526i	0.451517	−	0.110562i
$831$	−1.70290	−	0.619806i	−0.0590730	−	0.0215008i
$832$	−17.2489	+	19.4082i	−0.597998	+	0.672857i
$833$	−2.84845	−	3.39465i	−0.0986929	−	0.117618i
$834$	6.47241	+	24.6215i	0.224121	+	0.852571i
$835$	10.0995	+	8.76991i	0.349509	+	0.303495i
$836$	50.8611	−	1.30795i	1.75907	−	0.0452362i
$837$			36.1605i			1.24989i
$838$	38.9695	−	10.2442i	1.34618	−	0.353880i
$839$	23.5133	−	19.7300i	0.811769	−	0.681155i	−0.139261	−	0.990256i	$-0.544473\pi$
$839$	23.5133	−	19.7300i	0.811769	−	0.681155i	0.951029	+	0.309101i	$0.100028\pi$
$840$	−1.08459	−	0.129019i	−0.0374221	−	0.00445158i
$841$	3.68224	+	1.34022i	0.126974	+	0.0462146i
$842$	−22.7045	+	32.1006i	−0.782449	+	1.10626i
$843$	−1.69356	+	2.93334i	−0.0583294	+	0.101030i
$844$	12.3678	+	15.0263i	0.425717	+	0.517226i
$845$	3.47189	+	4.28274i	0.119437	+	0.147331i
$846$	−0.855864	+	9.27611i	−0.0294252	+	0.318919i
$847$	1.26842	+	2.19697i	0.0435834	+	0.0754887i
$848$	5.16407	−	26.3557i	0.177335	−	0.905058i
$849$	−19.8719	+	23.6824i	−0.682001	+	0.812777i
$850$	−4.44869	−	0.562800i	−0.152589	−	0.0193039i
$851$	−2.45884	+	0.894944i	−0.0842879	+	0.0306783i
$852$	11.6406	+	9.95708i	0.398799	+	0.341124i
$853$	40.4088	−	7.12517i	1.38357	−	0.243961i	0.568196	−	0.822893i	$-0.307641\pi$
$853$	40.4088	−	7.12517i	1.38357	−	0.243961i	0.815376	+	0.578932i	$0.196530\pi$
$854$	1.86020	−	0.153869i	0.0636549	−	0.00526528i
$855$	−3.28189	+	4.05957i	−0.112238	+	0.138834i
$856$	−4.98126	−	19.7067i	−0.170256	−	0.673560i
$857$	−4.20492	−	23.8473i	−0.143637	−	0.814608i	−0.968451	−	0.249204i	$-0.919831\pi$
$857$	−4.20492	−	23.8473i	−0.143637	−	0.814608i	0.824814	−	0.565405i	$-0.191280\pi$
$858$	29.8767	−	29.5949i	1.01997	−	1.01035i
$859$	0.426929	+	1.17298i	0.0145666	+	0.0400215i	0.946763	−	0.321932i	$-0.104332\pi$
$859$	0.426929	+	1.17298i	0.0145666	+	0.0400215i	−0.932196	+	0.361953i	$0.882110\pi$
$860$	31.1359	−	24.7557i	1.06173	−	0.844163i
$861$	0.997372	+	0.836894i	0.0339903	+	0.0285213i
$862$	10.7964	−	22.8694i	0.367727	−	0.778936i
$863$	18.2283	−	10.5241i	0.620498	−	0.358245i	−0.156565	−	0.987668i	$-0.550042\pi$
$863$	18.2283	−	10.5241i	0.620498	−	0.358245i	0.777063	+	0.629423i	$0.216709\pi$
$864$	30.5115	−	7.40551i	1.03802	−	0.251941i
$865$	−23.0857	−	28.4773i	−0.784937	−	0.968256i
$866$	32.7642	+	47.2672i	1.11337	+	1.60621i
$867$	−22.5652	−	13.0280i	−0.766355	−	0.442455i
$868$	1.23454	+	0.728450i	0.0419031	+	0.0247252i
$869$	3.05923	−	8.40516i	0.103777	−	0.285126i
$870$	7.96583	−	27.3458i	0.270067	−	0.927111i
$871$	16.7189	+	19.9248i	0.566498	+	0.675125i
$872$	−11.3237	+	5.08563i	−0.383468	+	0.172221i
$873$	2.31269			0.0782726
$874$	8.89017	−	20.6870i	0.300714	−	0.699749i
$875$	−1.03260	−	0.668221i	−0.0349081	−	0.0225900i
$876$	−0.0321128	−	0.0909003i	−0.00108499	−	0.00307124i
$877$	28.0664	−	23.5505i	0.947736	−	0.795245i	−0.0311789	−	0.999514i	$-0.509926\pi$
$877$	28.0664	−	23.5505i	0.947736	−	0.795245i	0.978915	+	0.204269i	$0.0654817\pi$
$878$	−38.7562	+	17.8492i	−1.30796	+	0.602382i
$879$	−5.72120	+	15.7189i	−0.192971	+	0.530184i
$880$	−24.4618	−	46.1132i	−0.824607	−	1.55448i
$881$	4.42421	−	7.66296i	0.149056	−	0.258172i	−0.781823	−	0.623500i	$-0.785710\pi$
$881$	4.42421	−	7.66296i	0.149056	−	0.258172i	0.930879	+	0.365328i	$0.119043\pi$
$882$	3.01528	+	4.34999i	0.101530	+	0.146472i
$883$	−0.786232	+	4.45894i	−0.0264588	+	0.150055i	−0.995175	−	0.0981158i	$-0.968718\pi$
$883$	−0.786232	+	4.45894i	−0.0264588	+	0.150055i	0.968716	+	0.248171i	$0.0798295\pi$
$884$	4.11633	+	0.0390105i	0.138447	+	0.00131206i
$885$	−8.50758	+	43.8931i	−0.285979	+	1.47545i
$886$	−17.7664	+	37.6336i	−0.596874	+	1.26432i
$887$	12.6974	−	15.1322i	0.426338	−	0.508090i	−0.509524	−	0.860457i	$-0.670178\pi$
$887$	12.6974	−	15.1322i	0.426338	−	0.508090i	0.935862	+	0.352366i	$0.114623\pi$
$888$	0.322240	−	3.16445i	0.0108137	−	0.106192i
$889$	0.0829840	+	0.227997i	0.00278319	+	0.00764676i
$890$	−36.0879	+	2.37113i	−1.20967	+	0.0794805i
$891$	−40.8436	+	7.20182i	−1.36831	+	0.241270i
$892$	8.87591	+	53.2858i	0.297187	+	1.78414i
$893$	−49.7000	+	20.0963i	−1.66315	+	0.672498i
$894$	−0.999783	−	12.0869i	−0.0334377	−	0.404248i
$895$	23.2512	+	13.9538i	0.777200	+	0.466423i
$896$	0.361822	−	1.19087i	0.0120876	−	0.0397841i
$897$	−6.36533	−	17.4886i	−0.212532	−	0.583927i
$898$	−6.57610	+	24.0853i	−0.219447	+	0.803735i
$899$	−24.0273	+	28.6346i	−0.801354	+	0.955016i
$900$	5.22927	+	1.15754i	0.174309	+	0.0385848i
$901$	−3.68740	+	2.12892i	−0.122845	+	0.0709247i
$902$	−5.71676	+	61.9600i	−0.190347	+	2.06304i
$903$	−1.51275	−	0.266739i	−0.0503413	−	0.00887653i
$904$	−27.9267	−	28.7322i	−0.928829	−	0.955619i
$905$	−10.1956	+	3.51675i	−0.338915	+	0.116901i
$906$	3.01101	−	4.25709i	0.100034	−	0.141432i
$907$	1.63351	−	4.48804i	0.0542399	−	0.149023i	−0.909614	−	0.415455i	$-0.863622\pi$
$907$	1.63351	−	4.48804i	0.0542399	−	0.149023i	0.963854	+	0.266432i	$0.0858447\pi$
$908$	−23.7490	−	42.0498i	−0.788138	−	1.39547i
$909$	3.02709	−	2.54003i	0.100402	−	0.0842474i
$910$	1.01275	+	0.499231i	0.0335723	+	0.0165493i
$911$	−52.7605			−1.74803			−0.874016	−	0.485897i	$-0.838493\pi$
$911$	−52.7605			−1.74803			−0.874016	+	0.485897i	$0.838493\pi$
$912$	17.9319	+	20.6792i	0.593785	+	0.684756i
$913$		−	24.7161i		−	0.817985i
$914$	−6.44967	+	1.69547i	−0.213336	+	0.0560812i
$915$	42.1089	+	0.712468i	1.39208	+	0.0235535i
$916$	11.5917	−	6.54677i	0.382999	−	0.216311i
$917$	0.109984	−	0.302177i	0.00363198	−	0.00997877i
$918$	−4.06391	−	2.87437i	−0.134129	−	0.0948685i
$919$	−12.2358	−	7.06437i	−0.403623	−	0.233032i	0.284423	−	0.958699i	$-0.408198\pi$
$919$	−12.2358	−	7.06437i	−0.403623	−	0.233032i	−0.688046	+	0.725667i	$0.741531\pi$
$920$	−23.0650	+	1.29608i	−0.760429	+	0.0427303i
$921$	0.514207	−	2.91621i	0.0169437	−	0.0960925i
$922$	−4.60011	+	49.8574i	−0.151497	+	1.64197i
$923$	−7.91762	−	13.7137i	−0.260612	−	0.451393i
$924$	−0.707355	+	1.88759i	−0.0232703	+	0.0620971i
$925$	1.89484	−	3.03961i	0.0623018	−	0.0999417i
$926$	−39.2701	−	10.7221i	−1.29050	−	0.352350i
$927$	−0.202128	−	0.555342i	−0.00663876	−	0.0182398i
$928$	29.0820	+	14.4095i	0.954662	+	0.473015i
$929$	0.810160	+	4.59464i	0.0265805	+	0.150745i	0.995209	−	0.0977661i	$-0.0311697\pi$
$929$	0.810160	+	4.59464i	0.0265805	+	0.150745i	−0.968629	+	0.248512i	$0.920059\pi$
$930$	26.0855	+	19.1202i	0.855376	+	0.626977i
$931$	−14.2923	+	26.8982i	−0.468413	+	0.881552i
$932$	8.48561	+	50.9427i	0.277955	+	1.66868i
$933$	6.58657	+	37.3543i	0.215635	+	1.22293i
$934$	5.53228	−	5.48010i	0.181022	−	0.179314i
$935$	−2.96159	+	7.72758i	−0.0968545	+	0.252719i
$936$	−4.89146	−	0.498104i	−0.159882	−	0.0162810i
$937$	−9.27234	+	11.0503i	−0.302914	+	0.360999i	−0.895933	−	0.444190i	$-0.853492\pi$
$937$	−9.27234	+	11.0503i	−0.302914	+	0.360999i	0.593019	+	0.805189i	$0.297936\pi$
$938$	−1.12744	−	0.532250i	−0.0368121	−	0.0173786i
$939$	−5.72718	−	9.91977i	−0.186900	−	0.323719i
$940$	41.1862	+	36.4542i	1.34335	+	1.18901i
$941$	−17.7522	−	3.13019i	−0.578705	−	0.102041i	−0.123369	−	0.992361i	$-0.539370\pi$
$941$	−17.7522	−	3.13019i	−0.578705	−	0.102041i	−0.455336	+	0.890320i	$0.650481\pi$
$942$	7.12430	+	10.2779i	0.232122	+	0.334871i
$943$	23.8480	+	13.7687i	0.776598	+	0.448369i
$944$	−47.5361	−	18.3293i	−1.54717	−	0.596567i
$945$	−0.662560	−	1.19378i	−0.0215531	−	0.0388338i
$946$	−30.7096	−	66.6800i	−0.998455	−	2.16795i
$947$	−38.6392	+	32.4221i	−1.25560	+	1.05358i	−0.259469	+	0.965752i	$0.583547\pi$
$947$	−38.6392	+	32.4221i	−1.25560	+	1.05358i	−0.996136	+	0.0878257i	$0.972008\pi$
$948$	4.53718	−	1.60287i	0.147361	−	0.0520588i
$949$			0.0996601i			0.00323510i
$950$	7.87645	+	29.7987i	0.255546	+	0.966797i
$951$			11.9929i			0.388897i
$952$	−0.180000	+	0.0808406i	−0.00583384	+	0.00262006i
$953$	7.04173	−	5.90872i	0.228104	−	0.191402i	−0.521571	−	0.853208i	$-0.674654\pi$
$953$	7.04173	−	5.90872i	0.228104	−	0.191402i	0.749676	+	0.661806i	$0.230210\pi$
$954$	4.61922	−	2.12739i	0.149553	−	0.0688767i
$955$	3.14891	+	5.67362i	0.101896	+	0.183594i
$956$	−4.47303	+	7.58069i	−0.144668	+	0.245177i
$957$	−45.5230	−	26.2827i	−1.47155	−	0.849599i
$958$	3.24502	−	2.24935i	0.104842	−	0.0726731i
$959$	0.855980	+	0.150932i	0.0276410	+	0.00487386i
$960$	10.7911	−	25.9261i	0.348281	−	0.836763i
$961$	−5.72280	−	9.91218i	−0.184607	−	0.319748i
$962$	−1.40375	+	2.97349i	−0.0452588	+	0.0958693i
$963$	2.47408	−	2.94849i	0.0797261	−	0.0950138i
$964$	−2.80099	+	15.0498i	−0.0902139	+	0.484721i
$965$	12.6530	−	33.0149i	0.407313	−	1.06279i
$966$	0.627810	+	0.633788i	0.0201995	+	0.0203918i
$967$	−0.360138	−	2.04244i	−0.0115813	−	0.0656806i	0.978469	−	0.206392i	$-0.0661722\pi$
$967$	−0.360138	−	2.04244i	−0.0115813	−	0.0656806i	−0.990051	+	0.140711i	$0.955061\pi$
$968$	−63.2349	+	15.9839i	−2.03245	+	0.513743i
$969$	0.602720	−	4.29732i	0.0193622	−	0.138050i
$970$	8.07250	−	11.0132i	0.259193	−	0.353613i
$971$	1.41294	+	8.01316i	0.0453433	+	0.257155i	0.999050	−	0.0435845i	$-0.0138778\pi$
$971$	1.41294	+	8.01316i	0.0453433	+	0.257155i	−0.953706	+	0.300739i	$0.902767\pi$
$972$	8.35155	+	7.14374i	0.267876	+	0.229136i
$973$	0.431455	+	1.18541i	0.0138318	+	0.0380026i
$974$	7.64394	−	27.9963i	0.244928	−	0.897059i
$975$	21.6193	+	13.4771i	0.692373	+	0.431613i
$976$	−9.22766	+	47.0949i	−0.295370	+	1.50747i
$977$	−4.46378	−	7.73149i	−0.142809	−	0.247352i	0.785744	−	0.618551i	$-0.212280\pi$
$977$	−4.46378	−	7.73149i	−0.142809	−	0.247352i	−0.928553	+	0.371199i	$0.878947\pi$
$978$	41.3419	+	3.81442i	1.32197	+	0.121972i
$979$	−11.5902	+	65.7312i	−0.370424	+	2.10078i
$980$	31.2399	+	0.824762i	0.997923	+	0.0263460i
$981$	−2.03564	−	1.17528i	−0.0649929	−	0.0375237i
$982$	16.7252	−	23.6468i	0.533723	−	0.754600i
$983$	−12.3434	+	33.9132i	−0.393693	+	1.08166i	0.571609	+	0.820526i	$0.306320\pi$
$983$	−12.3434	+	33.9132i	−0.393693	+	1.08166i	−0.965302	+	0.261137i	$0.915903\pi$
$984$	−27.6910	+	18.8086i	−0.882757	+	0.599595i
$985$	36.5801	+	0.618922i	1.16554	+	0.0197205i
$986$	−1.30820	−	4.97645i	−0.0416614	−	0.158483i
$987$		−	2.12399i		−	0.0676072i
$988$	−10.3578	−	26.3312i	−0.329527	−	0.837706i
$989$	−32.4889			−1.03309
$990$	4.37035	−	8.86578i	0.138899	−	0.281773i
$991$	−6.28025	+	5.26975i	−0.199499	+	0.167399i	−0.737064	−	0.675823i	$-0.763788\pi$
$991$	−6.28025	+	5.26975i	−0.199499	+	0.167399i	0.537566	+	0.843222i	$0.319344\pi$
$992$	−26.6702	+	25.4354i	−0.846778	+	0.807576i
$993$	9.44637	−	25.9537i	0.299772	−	0.823616i
$994$	0.619702	+	0.438311i	0.0196558	+	0.0139024i
$995$	−13.4711	+	4.64654i	−0.427062	+	0.147305i
$996$	10.2664	−	8.45005i	0.325304	−	0.267750i
$997$	−20.5849	−	3.62967i	−0.651931	−	0.114953i	−0.162105	−	0.986773i	$-0.551828\pi$
$997$	−20.5849	−	3.62967i	−0.651931	−	0.114953i	−0.489825	+	0.871821i	$0.662939\pi$
$998$	−17.1526	−	1.58259i	−0.542954	−	0.0500959i
$999$	3.44339	−	1.98804i	0.108944	−	0.0628988i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bb.a.219.34	yes	336
4.3	odd	2	inner	380.2.bb.a.219.29	yes	336
5.4	even	2	inner	380.2.bb.a.219.23	yes	336
19.2	odd	18	inner	380.2.bb.a.59.28	yes	336
20.19	odd	2	inner	380.2.bb.a.219.28	yes	336
76.59	even	18	inner	380.2.bb.a.59.23	✓	336
95.59	odd	18	inner	380.2.bb.a.59.29	yes	336
380.59	even	18	inner	380.2.bb.a.59.34	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bb.a.59.23	✓	336	76.59	even	18	inner
380.2.bb.a.59.28	yes	336	19.2	odd	18	inner
380.2.bb.a.59.29	yes	336	95.59	odd	18	inner
380.2.bb.a.59.34	yes	336	380.59	even	18	inner
380.2.bb.a.219.23	yes	336	5.4	even	2	inner
380.2.bb.a.219.28	yes	336	20.19	odd	2	inner
380.2.bb.a.219.29	yes	336	4.3	odd	2	inner
380.2.bb.a.219.34	yes	336	1.1	even	1	trivial

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.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.359549 + 1.36774i) q^{2} +(1.00908 + 1.20257i) q^{3} +(-1.74145 + 0.983541i) q^{4} +(-1.95513 + 1.08511i) q^{5} +(-1.28200 + 1.81254i) q^{6} +(-0.0550050 + 0.0952714i) q^{7} +(-1.97137 - 2.02823i) q^{8} +(0.0930035 - 0.527449i) q^{9} +O(q^{10})\)	\(q+(0.359549 + 1.36774i) q^{2} +(1.00908 + 1.20257i) q^{3} +(-1.74145 + 0.983541i) q^{4} +(-1.95513 + 1.08511i) q^{5} +(-1.28200 + 1.81254i) q^{6} +(-0.0550050 + 0.0952714i) q^{7} +(-1.97137 - 2.02823i) q^{8} +(0.0930035 - 0.527449i) q^{9} +(-2.18712 - 2.28397i) q^{10} +(-5.05421 + 2.91805i) q^{11} +(-2.94004 - 1.10175i) q^{12} +(2.48633 + 2.08628i) q^{13} +(-0.150084 - 0.0409780i) q^{14} +(-3.27780 - 1.25622i) q^{15} +(2.06529 - 3.42557i) q^{16} +(-0.624519 + 0.110120i) q^{17} +(0.754854 - 0.0624385i) q^{18} +(2.31090 + 3.69591i) q^{19} +(2.33750 - 3.81262i) q^{20} +(-0.170075 + 0.0299888i) q^{21} +(-5.80838 - 5.86369i) q^{22} +(-3.43236 + 1.24928i) q^{23} +(0.449825 - 4.41735i) q^{24} +(2.64506 - 4.24307i) q^{25} +(-1.95954 + 4.15078i) q^{26} +(4.80672 - 2.77516i) q^{27} +(0.00208504 - 0.220010i) q^{28} +(5.65030 + 0.996301i) q^{29} +(0.539656 - 4.93487i) q^{30} +(-3.25751 + 5.64218i) q^{31} +(5.42788 + 1.59313i) q^{32} +(-8.60926 - 3.13351i) q^{33} +(-0.375161 - 0.814590i) q^{34} +(0.00416146 - 0.245954i) q^{35} +(0.356807 + 1.01000i) q^{36} +0.716369 q^{37} +(-4.22418 + 4.48958i) q^{38} +5.09521i q^{39} +(6.05514 + 1.82629i) q^{40} +(-4.84598 - 5.77522i) q^{41} +(-0.102167 - 0.221837i) q^{42} +(8.35823 + 3.04215i) q^{43} +(5.93163 - 10.0527i) q^{44} +(0.390508 + 1.13215i) q^{45} +(-2.94279 - 4.24542i) q^{46} +(-2.13567 + 12.1120i) q^{47} +(6.20354 - 0.973007i) q^{48} +(3.49395 + 6.05170i) q^{49} +(6.75447 + 2.09217i) q^{50} +(-0.762615 - 0.639910i) q^{51} +(-6.38176 - 1.18774i) q^{52} +(6.30930 - 2.29640i) q^{53} +(5.52396 + 5.57656i) q^{54} +(6.71522 - 11.1896i) q^{55} +(0.301667 - 0.0762525i) q^{56} +(-2.11272 + 6.50848i) q^{57} +(0.668874 + 8.08639i) q^{58} +(-2.21174 - 12.5434i) q^{59} +(6.94367 - 1.03621i) q^{60} +(-11.2741 + 4.10342i) q^{61} +(-8.88830 - 2.42681i) q^{62} +(0.0451351 + 0.0378729i) q^{63} +(-0.227411 + 7.99677i) q^{64} +(-7.12495 - 1.38099i) q^{65} +(1.19040 - 12.9019i) q^{66} +(7.89198 + 1.39157i) q^{67} +(0.979262 - 0.806008i) q^{68} +(-4.96586 - 2.86704i) q^{69} +(0.337899 - 0.0827408i) q^{70} +(-4.58464 - 1.66867i) q^{71} +(-1.25313 + 0.851164i) q^{72} +(0.0197371 + 0.0235218i) q^{73} +(0.257569 + 0.979810i) q^{74} +(7.77166 - 1.10072i) q^{75} +(-7.65940 - 4.16337i) q^{76} -0.642029i q^{77} +(-6.96894 + 1.83197i) q^{78} +(-1.17406 + 0.985156i) q^{79} +(-0.320775 + 8.93852i) q^{80} +(6.67782 + 2.43053i) q^{81} +(6.15665 - 8.70454i) q^{82} +(-2.11752 + 3.66765i) q^{83} +(0.266682 - 0.219500i) q^{84} +(1.10152 - 0.892973i) q^{85} +(-1.15569 + 12.5257i) q^{86} +(4.50347 + 7.80024i) q^{87} +(15.8822 + 4.49854i) q^{88} +(7.35130 - 8.76094i) q^{89} +(-1.40808 + 0.941178i) q^{90} +(-0.335523 + 0.122120i) q^{91} +(4.74857 - 5.55142i) q^{92} +(-10.0722 + 1.77600i) q^{93} +(-17.3339 + 1.43379i) q^{94} +(-8.52859 - 4.71838i) q^{95} +(3.56130 + 8.13501i) q^{96} +(0.749823 + 4.25245i) q^{97} +(-7.02093 + 6.95471i) q^{98} +(1.06906 + 2.93723i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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