LMFDB - Embedded newform 378.2.u.c.337.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (of order $9$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			337.1
Character	$\chi$	$=$	378.337
Dual form			378.2.u.c.295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{2} +(-1.63475 - 0.572349i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.789233 + 0.662245i) q^{5} +(-0.279782 + 1.70930i) q^{6} +(0.939693 + 0.342020i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.34483 + 1.87130i) q^{9} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{2} +(-1.63475 - 0.572349i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.789233 + 0.662245i) q^{5} +(-0.279782 + 1.70930i) q^{6} +(0.939693 + 0.342020i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.34483 + 1.87130i) q^{9} +(0.515135 - 0.892241i) q^{10} +(0.883571 - 0.741404i) q^{11} +(1.73192 - 0.0212861i) q^{12} +(1.14079 - 6.46977i) q^{13} +(0.173648 - 0.984808i) q^{14} +(-0.911165 - 1.53432i) q^{15} +(0.766044 - 0.642788i) q^{16} +(2.30658 - 3.99511i) q^{17} +(1.43569 - 2.63416i) q^{18} +(1.93090 + 3.34441i) q^{19} +(-0.968138 - 0.352373i) q^{20} +(-1.34041 - 1.09695i) q^{21} +(-0.883571 - 0.741404i) q^{22} +(-8.49003 + 3.09012i) q^{23} +(-0.321707 - 1.70191i) q^{24} +(-0.683921 - 3.87871i) q^{25} -6.56958 q^{26} +(-2.76219 - 4.40117i) q^{27} -1.00000 q^{28} +(-0.0227420 - 0.128977i) q^{29} +(-1.35279 + 1.16376i) q^{30} +(7.92820 - 2.88563i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-1.86876 + 0.706302i) q^{33} +(-4.33494 - 1.57779i) q^{34} +(0.515135 + 0.892241i) q^{35} +(-2.84344 - 0.956465i) q^{36} +(2.22493 - 3.85369i) q^{37} +(2.95831 - 2.48231i) q^{38} +(-5.56788 + 9.92354i) q^{39} +(-0.178905 + 1.01462i) q^{40} +(0.799066 - 4.53173i) q^{41} +(-0.847526 + 1.51053i) q^{42} +(4.97428 - 4.17391i) q^{43} +(-0.576710 + 0.998891i) q^{44} +(0.611361 + 3.02975i) q^{45} +(4.51745 + 7.82446i) q^{46} +(9.80491 + 3.56870i) q^{47} +(-1.62019 + 0.612354i) q^{48} +(0.766044 + 0.642788i) q^{49} +(-3.70102 + 1.34706i) q^{50} +(-6.05728 + 5.21084i) q^{51} +(1.14079 + 6.46977i) q^{52} -3.66401 q^{53} +(-3.85466 + 3.48448i) q^{54} +1.18834 q^{55} +(0.173648 + 0.984808i) q^{56} +(-1.24237 - 6.57243i) q^{57} +(-0.123068 + 0.0447931i) q^{58} +(-6.97889 - 5.85598i) q^{59} +(1.38099 + 1.13016i) q^{60} +(6.63281 + 2.41414i) q^{61} +(-4.21851 - 7.30667i) q^{62} +(1.56340 + 2.56043i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(5.18493 - 4.35067i) q^{65} +(1.02008 + 1.71772i) q^{66} +(-0.691750 + 3.92311i) q^{67} +(-0.801065 + 4.54307i) q^{68} +(15.6477 - 0.192318i) q^{69} +(0.789233 - 0.662245i) q^{70} +(-7.62588 + 13.2084i) q^{71} +(-0.448176 + 2.96633i) q^{72} +(5.07655 + 8.79285i) q^{73} +(-4.18149 - 1.52194i) q^{74} +(-1.10193 + 6.73217i) q^{75} +(-2.95831 - 2.48231i) q^{76} +(1.08386 - 0.394493i) q^{77} +(10.7396 + 3.76009i) q^{78} +(0.154845 + 0.878171i) q^{79} +1.03027 q^{80} +(1.99648 + 8.77577i) q^{81} -4.60164 q^{82} +(-0.537199 - 3.04660i) q^{83} +(1.63475 + 0.572349i) q^{84} +(4.46617 - 1.62555i) q^{85} +(-4.97428 - 4.17391i) q^{86} +(-0.0366420 + 0.223861i) q^{87} +(1.08386 + 0.394493i) q^{88} +(6.10257 + 10.5700i) q^{89} +(2.87755 - 1.12818i) q^{90} +(3.28479 - 5.68942i) q^{91} +(6.92114 - 5.80752i) q^{92} +(-14.6122 + 0.179591i) q^{93} +(1.81187 - 10.2757i) q^{94} +(-0.690893 + 3.91825i) q^{95} +(0.884394 + 1.48924i) q^{96} +(-5.22702 + 4.38599i) q^{97} +(0.500000 - 0.866025i) q^{98} +(3.45922 - 0.0850437i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9}+O(q^{10}) $ 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9	$ 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9} + 3 q^{10} - 9 q^{13} - 6 q^{18} + 15 q^{19} - 6 q^{20} - 3 q^{21} + 6 q^{23} + 3 q^{24} + 33 q^{25} + 18 q^{26} - 18 q^{27} - 24 q^{28} - 30 q^{29} + 15 q^{30} - 6 q^{33} - 3 q^{34} + 3 q^{35} - 12 q^{36} - 3 q^{37} + 15 q^{38} - 18 q^{39} - 3 q^{40} + 27 q^{41} + 18 q^{43} - 3 q^{44} + 12 q^{45} + 15 q^{46} + 3 q^{48} + 3 q^{50} + 24 q^{51} - 9 q^{52} + 6 q^{53} + 45 q^{54} - 66 q^{55} - 6 q^{57} + 3 q^{58} - 30 q^{59} - 30 q^{60} - 57 q^{61} - 18 q^{62} + 12 q^{63} - 12 q^{64} + 24 q^{65} - 54 q^{66} + 39 q^{67} + 3 q^{68} + 36 q^{69} + 3 q^{70} - 24 q^{71} - 6 q^{72} + 36 q^{73} - 12 q^{74} + 15 q^{75} - 15 q^{76} - 9 q^{77} + 18 q^{78} - 33 q^{79} + 6 q^{80} + 9 q^{81} - 15 q^{83} + 3 q^{84} + 36 q^{85} - 18 q^{86} - 84 q^{87} - 9 q^{88} - 3 q^{89} - 30 q^{90} - 9 q^{91} - 30 q^{92} - 45 q^{93} + 45 q^{94} + 63 q^{95} - 30 q^{97} + 12 q^{98} - 57 q^{99}+O(q^{100}) $ 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9 + 3 * q^10 - 9 * q^13 - 6 * q^18 + 15 * q^19 - 6 * q^20 - 3 * q^21 + 6 * q^23 + 3 * q^24 + 33 * q^25 + 18 * q^26 - 18 * q^27 - 24 * q^28 - 30 * q^29 + 15 * q^30 - 6 * q^33 - 3 * q^34 + 3 * q^35 - 12 * q^36 - 3 * q^37 + 15 * q^38 - 18 * q^39 - 3 * q^40 + 27 * q^41 + 18 * q^43 - 3 * q^44 + 12 * q^45 + 15 * q^46 + 3 * q^48 + 3 * q^50 + 24 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 - 66 * q^55 - 6 * q^57 + 3 * q^58 - 30 * q^59 - 30 * q^60 - 57 * q^61 - 18 * q^62 + 12 * q^63 - 12 * q^64 + 24 * q^65 - 54 * q^66 + 39 * q^67 + 3 * q^68 + 36 * q^69 + 3 * q^70 - 24 * q^71 - 6 * q^72 + 36 * q^73 - 12 * q^74 + 15 * q^75 - 15 * q^76 - 9 * q^77 + 18 * q^78 - 33 * q^79 + 6 * q^80 + 9 * q^81 - 15 * q^83 + 3 * q^84 + 36 * q^85 - 18 * q^86 - 84 * q^87 - 9 * q^88 - 3 * q^89 - 30 * q^90 - 9 * q^91 - 30 * q^92 - 45 * q^93 + 45 * q^94 + 63 * q^95 - 30 * q^97 + 12 * q^98 - 57 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

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 $

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$	−1.63475	−	0.572349i	−0.943825	−	0.330446i
$3$	−1.63475	−	0.572349i	−0.943825	−	0.330446i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	0.789233	+	0.662245i	0.352956	+	0.296165i	0.801976	−	0.597357i	$-0.203782\pi$
$5$	0.789233	+	0.662245i	0.352956	+	0.296165i	−0.449020	+	0.893522i	$0.648227\pi$
$6$	−0.279782	+	1.70930i	−0.114221	+	0.697821i
$7$	0.939693	+	0.342020i	0.355170	+	0.129271i
$7$	0.939693	+	0.342020i	0.355170	+	0.129271i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	2.34483	+	1.87130i	0.781611	+	0.623766i
$10$	0.515135	−	0.892241i	0.162900	−	0.282151i
$11$	0.883571	−	0.741404i	0.266407	−	0.223542i	−0.499792	−	0.866145i	$-0.666590\pi$
$11$	0.883571	−	0.741404i	0.266407	−	0.223542i	0.766199	+	0.642604i	$0.222146\pi$
$12$	1.73192	−	0.0212861i	0.499962	−	0.00614478i
$13$	1.14079	−	6.46977i	0.316400	−	1.79439i	−0.247862	−	0.968795i	$-0.579728\pi$
$13$	1.14079	−	6.46977i	0.316400	−	1.79439i	0.564262	−	0.825596i	$-0.309161\pi$
$14$	0.173648	−	0.984808i	0.0464094	−	0.263201i
$15$	−0.911165	−	1.53432i	−0.235262	−	0.396161i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	2.30658	−	3.99511i	0.559427	−	0.968955i	−0.438118	−	0.898918i	$-0.644355\pi$
$17$	2.30658	−	3.99511i	0.559427	−	0.968955i	0.997544	−	0.0700378i	$-0.0223120\pi$
$18$	1.43569	−	2.63416i	0.338396	−	0.620877i
$19$	1.93090	+	3.34441i	0.442978	+	0.767261i	0.997909	−	0.0646359i	$-0.0205886\pi$
$19$	1.93090	+	3.34441i	0.442978	+	0.767261i	−0.554931	+	0.831897i	$0.687255\pi$
$20$	−0.968138	−	0.352373i	−0.216482	−	0.0787931i
$21$	−1.34041	−	1.09695i	−0.292501	−	0.239374i
$22$	−0.883571	−	0.741404i	−0.188378	−	0.158068i
$23$	−8.49003	+	3.09012i	−1.77029	+	0.644334i	−0.770316	+	0.637662i	$0.779902\pi$
$23$	−8.49003	+	3.09012i	−1.77029	+	0.644334i	−0.999978	+	0.00667220i	$0.997876\pi$
$24$	−0.321707	−	1.70191i	−0.0656683	−	0.347401i
$25$	−0.683921	−	3.87871i	−0.136784	−	0.775741i
$26$	−6.56958			−1.28840
$27$	−2.76219	−	4.40117i	−0.531583	−	0.847006i
$28$	−1.00000			−0.188982
$29$	−0.0227420	−	0.128977i	−0.00422309	−	0.0239503i	0.982623	−	0.185611i	$-0.0594263\pi$
$29$	−0.0227420	−	0.128977i	−0.00422309	−	0.0239503i	−0.986846	+	0.161660i	$0.948315\pi$
$30$	−1.35279	+	1.16376i	−0.246985	+	0.212472i
$31$	7.92820	−	2.88563i	1.42395	−	0.518274i	0.488756	−	0.872420i	$-0.337451\pi$
$31$	7.92820	−	2.88563i	1.42395	−	0.518274i	0.935190	+	0.354146i	$0.115229\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	−1.86876	+	0.706302i	−0.325310	+	0.122951i
$34$	−4.33494	−	1.57779i	−0.743437	−	0.270589i
$35$	0.515135	+	0.892241i	0.0870738	+	0.150816i
$36$	−2.84344	−	0.956465i	−0.473907	−	0.159411i
$37$	2.22493	−	3.85369i	0.365776	−	0.633542i	−0.623125	−	0.782123i	$-0.714137\pi$
$37$	2.22493	−	3.85369i	0.365776	−	0.633542i	0.988900	+	0.148581i	$0.0474704\pi$
$38$	2.95831	−	2.48231i	0.479901	−	0.402684i
$39$	−5.56788	+	9.92354i	−0.891575	+	1.58904i
$40$	−0.178905	+	1.01462i	−0.0282873	+	0.160425i
$41$	0.799066	−	4.53173i	0.124793	−	0.707737i	−0.856637	−	0.515919i	$-0.827451\pi$
$41$	0.799066	−	4.53173i	0.124793	−	0.707737i	0.981430	−	0.191818i	$-0.0614384\pi$
$42$	−0.847526	+	1.51053i	−0.130776	+	0.233080i
$43$	4.97428	−	4.17391i	0.758570	−	0.636516i	−0.179184	−	0.983816i	$-0.557346\pi$
$43$	4.97428	−	4.17391i	0.758570	−	0.636516i	0.937754	+	0.347300i	$0.112901\pi$
$44$	−0.576710	+	0.998891i	−0.0869423	+	0.150589i
$45$	0.611361	+	3.02975i	0.0911364	+	0.451648i
$46$	4.51745	+	7.82446i	0.666062	+	1.15365i
$47$	9.80491	+	3.56870i	1.43019	+	0.520548i	0.936987	−	0.349364i	$-0.113602\pi$
$47$	9.80491	+	3.56870i	1.43019	+	0.520548i	0.493206	+	0.869912i	$0.335825\pi$
$48$	−1.62019	+	0.612354i	−0.233855	+	0.0883857i
$49$	0.766044	+	0.642788i	0.109435	+	0.0918268i
$50$	−3.70102	+	1.34706i	−0.523403	+	0.190503i
$51$	−6.05728	+	5.21084i	−0.848188	+	0.729664i
$52$	1.14079	+	6.46977i	0.158200	+	0.897195i
$53$	−3.66401			−0.503290			−0.251645	−	0.967820i	$-0.580972\pi$
$53$	−3.66401			−0.503290			−0.251645	+	0.967820i	$0.580972\pi$
$54$	−3.85466	+	3.48448i	−0.524553	+	0.474177i
$55$	1.18834			0.160235
$56$	0.173648	+	0.984808i	0.0232047	+	0.131600i
$57$	−1.24237	−	6.57243i	−0.164556	−	0.870540i
$58$	−0.123068	+	0.0447931i	−0.0161596	+	0.00588162i
$59$	−6.97889	−	5.85598i	−0.908574	−	0.762384i	0.0632733	−	0.997996i	$-0.479846\pi$
$59$	−6.97889	−	5.85598i	−0.908574	−	0.762384i	−0.971847	+	0.235612i	$0.924290\pi$
$60$	1.38099	+	1.13016i	0.178284	+	0.145903i
$61$	6.63281	+	2.41414i	0.849244	+	0.309100i	0.729732	−	0.683733i	$-0.239645\pi$
$61$	6.63281	+	2.41414i	0.849244	+	0.309100i	0.119512	+	0.992833i	$0.461867\pi$
$62$	−4.21851	−	7.30667i	−0.535751	−	0.927947i
$63$	1.56340	+	2.56043i	0.196970	+	0.322583i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	5.18493	−	4.35067i	0.643111	−	0.539634i
$66$	1.02008	+	1.71772i	0.125563	+	0.211437i
$67$	−0.691750	+	3.92311i	−0.0845107	+	0.479284i	0.912950	+	0.408071i	$0.133798\pi$
$67$	−0.691750	+	3.92311i	−0.0845107	+	0.479284i	−0.997461	+	0.0712134i	$0.977313\pi$
$68$	−0.801065	+	4.54307i	−0.0971434	+	0.550928i
$69$	15.6477	−	0.192318i	1.88377	−	0.0231524i
$70$	0.789233	−	0.662245i	0.0943314	−	0.0791534i
$71$	−7.62588	+	13.2084i	−0.905026	+	1.56755i	−0.0841436	+	0.996454i	$0.526815\pi$
$71$	−7.62588	+	13.2084i	−0.905026	+	1.56755i	−0.820882	+	0.571097i	$0.806518\pi$
$72$	−0.448176	+	2.96633i	−0.0528180	+	0.349586i
$73$	5.07655	+	8.79285i	0.594166	+	1.02913i	0.993664	+	0.112391i	$0.0358510\pi$
$73$	5.07655	+	8.79285i	0.594166	+	1.02913i	−0.399498	+	0.916734i	$0.630816\pi$
$74$	−4.18149	−	1.52194i	−0.486089	−	0.176922i
$75$	−1.10193	+	6.73217i	−0.127240	+	0.777364i
$76$	−2.95831	−	2.48231i	−0.339341	−	0.284741i
$77$	1.08386	−	0.394493i	0.123517	−	0.0449567i
$78$	10.7396	+	3.76009i	1.21602	+	0.425746i
$79$	0.154845	+	0.878171i	0.0174215	+	0.0988020i	0.992279	−	0.124029i	$-0.0395814\pi$
$79$	0.154845	+	0.878171i	0.0174215	+	0.0988020i	−0.974857	+	0.222831i	$0.928470\pi$
$80$	1.03027			0.115188
$81$	1.99648	+	8.77577i	0.221832	+	0.975085i
$82$	−4.60164			−0.508166
$83$	−0.537199	−	3.04660i	−0.0589652	−	0.334408i	0.941027	−	0.338331i	$-0.109862\pi$
$83$	−0.537199	−	3.04660i	−0.0589652	−	0.334408i	−0.999992	+	0.00392288i	$0.998751\pi$
$84$	1.63475	+	0.572349i	0.178366	+	0.0624484i
$85$	4.46617	−	1.62555i	0.484424	−	0.176316i
$86$	−4.97428	−	4.17391i	−0.536390	−	0.450085i
$87$	−0.0366420	+	0.223861i	−0.00392843	+	0.0240004i
$88$	1.08386	+	0.394493i	0.115540	+	0.0420531i
$89$	6.10257	+	10.5700i	0.646871	+	1.12041i	0.983866	+	0.178907i	$0.0572562\pi$
$89$	6.10257	+	10.5700i	0.646871	+	1.12041i	−0.336995	+	0.941507i	$0.609410\pi$
$90$	2.87755	−	1.12818i	0.303321	−	0.118921i
$91$	3.28479	−	5.68942i	0.344339	−	0.596413i
$92$	6.92114	−	5.80752i	0.721578	−	0.605476i
$93$	−14.6122	+	0.179591i	−1.51522	+	0.0186228i
$94$	1.81187	−	10.2757i	0.186881	−	1.05985i
$95$	−0.690893	+	3.91825i	−0.0708841	+	0.402004i
$96$	0.884394	+	1.48924i	0.0902631	+	0.151995i
$97$	−5.22702	+	4.38599i	−0.530723	+	0.445330i	−0.868351	−	0.495950i	$-0.834820\pi$
$97$	−5.22702	+	4.38599i	−0.530723	+	0.445330i	0.337628	+	0.941280i	$0.390375\pi$
$98$	0.500000	−	0.866025i	0.0505076	−	0.0874818i
$99$	3.45922	−	0.0850437i	0.347664	−	0.00854721i
$100$	1.96927	+	3.41088i	0.196927	+	0.341088i
$101$	−6.10235	−	2.22107i	−0.607207	−	0.221005i	0.0200739	−	0.999798i	$-0.493610\pi$
$101$	−6.10235	−	2.22107i	−0.607207	−	0.221005i	−0.627281	+	0.778793i	$0.715832\pi$
$102$	6.18351	+	5.06040i	0.612259	+	0.501054i
$103$	−13.9358	−	11.6935i	−1.37313	−	1.15219i	−0.971676	−	0.236317i	$-0.924060\pi$
$103$	−13.9358	−	11.6935i	−1.37313	−	1.15219i	−0.401456	−	0.915878i	$-0.631496\pi$
$104$	6.17338	−	2.24693i	0.605350	−	0.220329i
$105$	−0.331446	−	1.75343i	−0.0323458	−	0.171117i
$106$	0.636248	+	3.60834i	0.0617979	+	0.350473i
$107$	2.70078			0.261094			0.130547	−	0.991442i	$-0.458327\pi$
$107$	2.70078			0.261094			0.130547	+	0.991442i	$0.458327\pi$
$108$	4.10090	+	3.19103i	0.394609	+	0.307057i
$109$	12.4288			1.19046			0.595229	−	0.803556i	$-0.297061\pi$
$109$	12.4288			1.19046			0.595229	+	0.803556i	$0.297061\pi$
$110$	−0.206352	−	1.17028i	−0.0196749	−	0.111582i
$111$	−5.84286	+	5.02639i	−0.554580	+	0.477084i
$112$	0.939693	−	0.342020i	0.0887926	−	0.0323179i
$113$	−5.50385	−	4.61828i	−0.517758	−	0.434451i	0.346091	−	0.938201i	$-0.387509\pi$
$113$	−5.50385	−	4.61828i	−0.517758	−	0.434451i	−0.863849	+	0.503750i	$0.831953\pi$
$114$	−6.25685	+	2.36478i	−0.586008	+	0.221482i
$115$	−8.74703	−	3.18366i	−0.815665	−	0.296878i
$116$	0.0654831	+	0.113420i	0.00607995	+	0.0105308i
$117$	14.7818	−	13.0358i	1.36658	−	1.20516i
$118$	−4.55515	+	7.88974i	−0.419335	+	0.726310i
$119$	3.53388	−	2.96528i	0.323950	−	0.271826i
$120$	0.873181	−	1.55625i	0.0797101	−	0.142066i
$121$	−1.67911	+	9.52272i	−0.152647	+	0.865702i
$122$	1.22569	−	6.95125i	0.110969	−	0.629337i
$123$	−3.90001	+	6.95091i	−0.351652	+	0.626743i
$124$	−6.46313	+	5.42321i	−0.580406	+	0.487018i
$125$	4.60456	−	7.97533i	0.411844	−	0.713335i
$126$	2.25005	−	1.98426i	0.200450	−	0.176772i
$127$	−1.16837	−	2.02367i	−0.103676	−	0.179572i	0.809521	−	0.587092i	$-0.199727\pi$
$127$	−1.16837	−	2.02367i	−0.103676	−	0.179572i	−0.913196	+	0.407520i	$0.866394\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	−10.5206	+	3.97629i	−0.926291	+	0.350093i
$130$	−5.18493	−	4.35067i	−0.454748	−	0.381579i
$131$	−5.07973	+	1.84887i	−0.443818	+	0.161537i	−0.554256	−	0.832346i	$-0.686997\pi$
$131$	−5.07973	+	1.84887i	−0.443818	+	0.161537i	0.110437	+	0.993883i	$0.464775\pi$
$132$	1.51449	−	1.30286i	0.131820	−	0.113399i
$133$	0.670593	+	3.80312i	0.0581478	+	0.329773i
$134$	3.98363			0.344133
$135$	0.734647	−	5.30280i	0.0632284	−	0.456392i
$136$	4.61315			0.395574
$137$	2.85315	+	16.1810i	0.243761	+	1.38244i	0.823353	+	0.567530i	$0.192101\pi$
$137$	2.85315	+	16.1810i	0.243761	+	1.38244i	−0.579592	+	0.814907i	$0.696788\pi$
$138$	−2.90660	−	15.3766i	−0.247426	−	1.30894i
$139$	−3.29154	+	1.19802i	−0.279185	+	0.101615i	−0.477818	−	0.878459i	$-0.658572\pi$
$139$	−3.29154	+	1.19802i	−0.279185	+	0.101615i	0.198633	+	0.980074i	$0.436350\pi$
$140$	−0.789233	−	0.662245i	−0.0667024	−	0.0559699i
$141$	−13.9861	−	11.4458i	−1.17784	−	0.963908i
$142$	14.3320	+	5.21641i	1.20271	+	0.437752i
$143$	−3.78874	−	6.56229i	−0.316830	−	0.548766i
$144$	2.99909	−	0.0737317i	0.249924	−	0.00614431i
$145$	0.0674653	−	0.116853i	0.00560269	−	0.00970414i
$146$	7.77773	−	6.52629i	0.643690	−	0.540120i
$147$	−0.884394	−	1.48924i	−0.0729436	−	0.122831i
$148$	−0.772709	+	4.38225i	−0.0635163	+	0.360219i
$149$	0.840332	−	4.76576i	0.0688427	−	0.390426i	−0.930845	−	0.365416i	$-0.880927\pi$
$149$	0.840332	−	4.76576i	0.0688427	−	0.390426i	0.999687	−	0.0250107i	$-0.00796199\pi$
$150$	6.82124	−	0.0838363i	0.556952	−	0.00684521i
$151$	−18.0407	+	15.1379i	−1.46813	+	1.23191i	−0.550275	+	0.834983i	$0.685477\pi$
$151$	−18.0407	+	15.1379i	−1.46813	+	1.23191i	−0.917852	+	0.396922i	$0.870078\pi$
$152$	−1.93090	+	3.34441i	−0.156616	+	0.271268i
$153$	12.8846	−	5.05156i	1.04166	−	0.408395i
$154$	−0.576710	−	0.998891i	−0.0464726	−	0.0804930i
$155$	8.16819	+	2.97298i	0.656085	+	0.238795i
$156$	1.83805	−	11.2294i	0.147162	−	0.899072i
$157$	−8.90157	−	7.46930i	−0.710422	−	0.596115i	0.214295	−	0.976769i	$-0.431255\pi$
$157$	−8.90157	−	7.46930i	−0.710422	−	0.596115i	−0.924718	+	0.380654i	$0.875699\pi$
$158$	0.837941	−	0.304986i	0.0666630	−	0.0242634i
$159$	5.98975	+	2.09709i	0.475018	+	0.166310i
$160$	−0.178905	−	1.01462i	−0.0141437	−	0.0802126i
$161$	−9.03490			−0.712050
$162$	8.29576	−	3.49005i	0.651776	−	0.274204i
$163$	10.3326			0.809310			0.404655	−	0.914469i	$-0.367392\pi$
$163$	10.3326			0.809310			0.404655	+	0.914469i	$0.367392\pi$
$164$	0.799066	+	4.53173i	0.0623966	+	0.353869i
$165$	−1.94263	−	0.680143i	−0.151234	−	0.0529490i
$166$	−2.90704	+	1.05807i	−0.225630	+	0.0821225i
$167$	8.55680	+	7.18001i	0.662145	+	0.555606i	0.910729	−	0.413005i	$-0.135521\pi$
$167$	8.55680	+	7.18001i	0.662145	+	0.555606i	−0.248584	+	0.968610i	$0.579965\pi$
$168$	0.279782	−	1.70930i	0.0215857	−	0.131876i
$169$	−28.3405	−	10.3151i	−2.18004	−	0.793469i
$170$	−2.37640	−	4.11604i	−0.182261	−	0.315686i
$171$	−1.73076	+	11.4554i	−0.132355	+	0.876014i
$172$	−3.24673	+	5.62350i	−0.247561	+	0.428788i
$173$	−8.26469	+	6.93490i	−0.628353	+	0.527250i	−0.900417	−	0.435029i	$-0.856738\pi$
$173$	−8.26469	+	6.93490i	−0.628353	+	0.527250i	0.272064	+	0.962279i	$0.412294\pi$
$174$	0.226823	−	0.00278776i	0.0171954	−	0.000211340i
$175$	0.683921	−	3.87871i	0.0516995	−	0.293203i
$176$	0.200289	−	1.13590i	0.0150974	−	0.0856215i
$177$	8.05709	+	13.5674i	0.605608	+	1.01979i
$178$	9.34968	−	7.84531i	0.700788	−	0.588031i
$179$	3.31139	−	5.73550i	0.247505	−	0.428691i	−0.715328	−	0.698789i	$-0.753723\pi$
$179$	3.31139	−	5.73550i	0.247505	−	0.428691i	0.962833	+	0.270098i	$0.0870560\pi$
$180$	−1.61073	−	2.63793i	−0.120056	−	0.196620i
$181$	−5.63569	−	9.76130i	−0.418898	−	0.725552i	0.576931	−	0.816793i	$-0.304250\pi$
$181$	−5.63569	−	9.76130i	−0.418898	−	0.725552i	−0.995829	+	0.0912408i	$0.970917\pi$
$182$	−6.17338	−	2.24693i	−0.457601	−	0.166553i
$183$	−9.46127	−	7.74281i	−0.699397	−	0.572365i
$184$	−6.92114	−	5.80752i	−0.510233	−	0.428136i
$185$	4.30807	−	1.56801i	0.316736	−	0.115282i
$186$	2.71425	+	14.3590i	0.199018	+	1.05286i
$187$	−0.923965	−	5.24007i	−0.0675670	−	0.383192i
$188$	−10.4342			−0.760990
$189$	−1.09032	−	5.08047i	−0.0793088	−	0.369550i
$190$	3.97869			0.288645
$191$	1.52470	+	8.64699i	0.110323	+	0.625674i	0.988960	+	0.148183i	$0.0473426\pi$
$191$	1.52470	+	8.64699i	0.110323	+	0.625674i	−0.878637	+	0.477491i	$0.841546\pi$
$192$	1.31305	−	1.12956i	0.0947609	−	0.0815192i
$193$	1.91665	−	0.697602i	0.137963	−	0.0502145i	−0.272116	−	0.962265i	$-0.587723\pi$
$193$	1.91665	−	0.697602i	0.137963	−	0.0502145i	0.410079	+	0.912050i	$0.365501\pi$
$194$	5.22702	+	4.38599i	0.375278	+	0.314896i
$195$	−10.9662	+	4.14468i	−0.785304	+	0.296807i
$196$	−0.939693	−	0.342020i	−0.0671209	−	0.0244300i
$197$	10.6683	+	18.4781i	0.760087	+	1.31651i	0.942805	+	0.333344i	$0.108177\pi$
$197$	10.6683	+	18.4781i	0.760087	+	1.31651i	−0.182719	+	0.983165i	$0.558490\pi$
$198$	−0.684438	−	3.39190i	−0.0486409	−	0.241051i
$199$	2.50824	−	4.34439i	0.177804	−	0.307966i	−0.763324	−	0.646016i	$-0.776434\pi$
$199$	2.50824	−	4.34439i	0.177804	−	0.307966i	0.941128	+	0.338050i	$0.109767\pi$
$200$	3.01710	−	2.53165i	0.213341	−	0.179014i
$201$	3.37623	−	6.01739i	0.238141	−	0.424434i
$202$	−1.12767	+	6.39533i	−0.0793425	+	0.449974i
$203$	0.0227420	−	0.128977i	0.00159618	−	0.00905238i
$204$	3.90976	−	6.96830i	0.273738	−	0.487879i
$205$	3.63177	−	3.04741i	0.253653	−	0.212841i
$206$	−9.09593	+	15.7546i	−0.633743	+	1.09768i
$207$	−25.6902	−	8.64157i	−1.78560	−	0.600631i
$208$	−3.28479	−	5.68942i	−0.227759	−	0.394490i
$209$	4.18565	+	1.52345i	0.289527	+	0.105379i
$210$	−1.66924	+	0.630890i	−0.115188	+	0.0435356i
$211$	−2.90923	−	2.44113i	−0.200280	−	0.168054i	0.537132	−	0.843498i	$-0.319508\pi$
$211$	−2.90923	−	2.44113i	−0.200280	−	0.168054i	−0.737412	+	0.675444i	$0.763952\pi$
$212$	3.44304	−	1.25316i	0.236469	−	0.0860677i
$213$	20.0263	−	17.2278i	1.37218	−	1.18043i
$214$	−0.468985	−	2.65975i	−0.0320592	−	0.181816i
$215$	6.69002			0.456255
$216$	2.43043	−	4.59271i	0.165370	−	0.312494i
$217$	8.43701			0.572742
$218$	−2.15823	−	12.2399i	−0.146174	−	0.828993i
$219$	−3.26633	−	17.2797i	−0.220718	−	1.16765i
$220$	−1.11667	+	0.406435i	−0.0752859	+	0.0274018i
$221$	−23.2161	−	19.4806i	−1.56168	−	1.31041i
$222$	5.96463	+	4.88127i	0.400320	+	0.327609i
$223$	−8.67221	−	3.15643i	−0.580734	−	0.211370i	0.0349149	−	0.999390i	$-0.488884\pi$
$223$	−8.67221	−	3.15643i	−0.580734	−	0.211370i	−0.615649	+	0.788020i	$0.711106\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	5.65454	−	10.3747i	0.376969	−	0.691649i
$226$	−3.59238	+	6.22219i	−0.238962	+	0.413894i
$227$	19.8230	−	16.6334i	1.31570	−	1.10400i	0.328497	−	0.944505i	$-0.393458\pi$
$227$	19.8230	−	16.6334i	1.31570	−	1.10400i	0.987199	−	0.159495i	$-0.0509865\pi$
$228$	3.41535	+	5.75115i	0.226187	+	0.380879i
$229$	−2.22519	+	12.6197i	−0.147045	+	0.833931i	0.818658	+	0.574281i	$0.194718\pi$
$229$	−2.22519	+	12.6197i	−0.147045	+	0.833931i	−0.965703	+	0.259650i	$0.916393\pi$
$230$	−1.61639	+	9.16698i	−0.106581	+	0.604453i
$231$	−1.99763	+	0.0245519i	−0.131435	+	0.00161539i
$232$	0.100326	−	0.0841835i	0.00658672	−	0.00552691i
$233$	−0.202007	+	0.349886i	−0.0132339	+	0.0229218i	−0.872567	−	0.488495i	$-0.837546\pi$
$233$	−0.202007	+	0.349886i	−0.0132339	+	0.0229218i	0.859333	+	0.511417i	$0.170879\pi$
$234$	−15.4046	−	12.2936i	−1.00703	−	0.803660i
$235$	5.37501	+	9.30979i	0.350627	+	0.607304i
$236$	8.56087	+	3.11590i	0.557265	+	0.202828i
$237$	0.249487	−	1.52422i	0.0162059	−	0.0990086i
$238$	−3.53388	−	2.96528i	−0.229067	−	0.192210i
$239$	−9.77292	+	3.55705i	−0.632158	+	0.230087i	−0.638170	−	0.769895i	$-0.720308\pi$
$239$	−9.77292	+	3.55705i	−0.632158	+	0.230087i	0.00601251	+	0.999982i	$0.498086\pi$
$240$	−1.68424	−	0.589674i	−0.108717	−	0.0380633i
$241$	1.90986	+	10.8313i	0.123025	+	0.697707i	0.982462	+	0.186465i	$0.0597032\pi$
$241$	1.90986	+	10.8313i	0.123025	+	0.697707i	−0.859437	+	0.511242i	$0.829186\pi$
$242$	9.66962			0.621587
$243$	1.75904	−	15.4889i	0.112843	−	0.993613i
$244$	−7.05849			−0.451873
$245$	0.178905	+	1.01462i	0.0114298	+	0.0648216i
$246$	7.52254	+	2.63374i	0.479620	+	0.167921i
$247$	23.8403	−	8.67717i	1.51692	−	0.552115i
$248$	6.46313	+	5.42321i	0.410409	+	0.344374i
$249$	−0.865535	+	5.28791i	−0.0548510	+	0.335108i
$250$	−8.65374	−	3.14970i	−0.547311	−	0.199205i
$251$	11.1392	+	19.2937i	0.703103	+	1.21781i	0.967372	+	0.253360i	$0.0815359\pi$
$251$	11.1392	+	19.2937i	0.703103	+	1.21781i	−0.264269	+	0.964449i	$0.585131\pi$
$252$	−2.34483	−	1.87130i	−0.147711	−	0.117881i
$253$	−5.21052	+	9.02489i	−0.327583	+	0.567390i
$254$	−1.79004	+	1.50203i	−0.112317	+	0.0942455i
$255$	−8.23146	+	0.101169i	−0.515474	+	0.00633542i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	2.53535	−	14.3787i	0.158151	−	0.896919i	−0.797697	−	0.603058i	$-0.793949\pi$
$257$	2.53535	−	14.3787i	0.158151	−	0.896919i	0.955848	−	0.293861i	$-0.0949403\pi$
$258$	5.74278	+	9.67034i	0.357530	+	0.602049i
$259$	3.40879	−	2.86031i	0.211812	−	0.177731i
$260$	−3.38422	+	5.86164i	−0.209880	+	0.363524i
$261$	0.188027	−	0.344986i	0.0116386	−	0.0213541i
$262$	2.70287	+	4.68151i	0.166984	+	0.289225i
$263$	−8.13334	−	2.96029i	−0.501523	−	0.182540i	0.0788557	−	0.996886i	$-0.474873\pi$
$263$	−8.13334	−	2.96029i	−0.501523	−	0.182540i	−0.580379	+	0.814346i	$0.697096\pi$
$264$	−1.54606	−	1.26525i	−0.0951532	−	0.0778705i
$265$	−2.89176	−	2.42647i	−0.177639	−	0.149057i
$266$	3.62890	−	1.32081i	0.222502	−	0.0809841i
$267$	−3.92649	−	20.7721i	−0.240297	−	1.27123i
$268$	−0.691750	−	3.92311i	−0.0422553	−	0.239642i
$269$	−5.73906			−0.349917			−0.174958	−	0.984576i	$-0.555979\pi$
$269$	−5.73906			−0.349917			−0.174958	+	0.984576i	$0.555979\pi$
$270$	−5.34980	+	0.197335i	−0.325579	+	0.0120094i
$271$	−8.43854			−0.512605			−0.256302	−	0.966597i	$-0.582504\pi$
$271$	−8.43854			−0.512605			−0.256302	+	0.966597i	$0.582504\pi$
$272$	−0.801065	−	4.54307i	−0.0485717	−	0.275464i
$273$	−8.62615	+	7.42075i	−0.522078	+	0.449124i
$274$	15.4397	−	5.61961i	0.932749	−	0.339493i
$275$	−3.47998	−	2.92005i	−0.209851	−	0.176086i
$276$	−14.6383	+	5.53256i	−0.881121	+	0.333021i
$277$	24.6156	+	8.95935i	1.47901	+	0.538315i	0.950530	−	0.310632i	$-0.100541\pi$
$277$	24.6156	+	8.95935i	1.47901	+	0.538315i	0.528478	+	0.848947i	$0.322763\pi$
$278$	1.75139	+	3.03350i	0.105042	+	0.181937i
$279$	23.9902	+	8.06971i	1.43625	+	0.483121i
$280$	−0.515135	+	0.892241i	−0.0307852	+	0.0533216i
$281$	−1.66074	+	1.39352i	−0.0990712	+	0.0831306i	−0.690978	−	0.722876i	$-0.742820\pi$
$281$	−1.66074	+	1.39352i	−0.0990712	+	0.0831306i	0.591907	+	0.806006i	$0.298375\pi$
$282$	−8.84323	+	15.7611i	−0.526606	+	0.938561i
$283$	−1.13318	+	6.42660i	−0.0673607	+	0.382022i	0.932426	+	0.361361i	$0.117688\pi$
$283$	−1.13318	+	6.42660i	−0.0673607	+	0.382022i	−0.999787	+	0.0206603i	$0.993423\pi$
$284$	2.64844	−	15.0201i	0.157156	−	0.891277i
$285$	3.37204	−	6.00993i	0.199743	−	0.355998i
$286$	−5.80469	+	4.87071i	−0.343238	+	0.288011i
$287$	2.30082	−	3.98514i	0.135813	−	0.235235i
$288$	−0.593399	−	2.94073i	−0.0349664	−	0.173284i
$289$	−2.14058	−	3.70759i	−0.125916	−	0.218094i
$290$	−0.126793	−	0.0461490i	−0.00744556	−	0.00270996i
$291$	11.0552	−	4.17833i	0.648067	−	0.244938i
$292$	−7.77773	−	6.52629i	−0.455157	−	0.381922i
$293$	4.71220	−	1.71510i	0.275290	−	0.100197i	−0.200686	−	0.979656i	$-0.564317\pi$
$293$	4.71220	−	1.71510i	0.275290	−	0.100197i	0.475976	+	0.879458i	$0.342095\pi$
$294$	−1.31305	+	1.12956i	−0.0765784	+	0.0658774i
$295$	−1.62987	−	9.24347i	−0.0948949	−	0.538176i
$296$	4.44985			0.258642
$297$	−5.70364	−	1.84085i	−0.330959	−	0.106817i
$298$	−4.83928			−0.280332
$299$	10.3070	+	58.4537i	0.596067	+	3.38047i
$300$	−1.26706	−	6.70305i	−0.0731537	−	0.387001i
$301$	6.10185	−	2.22089i	0.351705	−	0.128010i
$302$	18.0407	+	15.1379i	1.03812	+	0.871089i
$303$	8.70461	+	7.12358i	0.500067	+	0.409239i
$304$	3.62890	+	1.32081i	0.208132	+	0.0757537i
$305$	3.63608	+	6.29787i	0.208201	+	0.360615i
$306$	−7.21220	−	11.8116i	−0.412294	−	0.675226i
$307$	13.0433	−	22.5917i	0.744422	−	1.28938i	−0.206042	−	0.978543i	$-0.566058\pi$
$307$	13.0433	−	22.5917i	0.744422	−	1.28938i	0.950464	−	0.310834i	$-0.100608\pi$
$308$	−0.883571	+	0.741404i	−0.0503461	+	0.0422454i
$309$	16.0888	+	27.0921i	0.915258	+	1.54122i
$310$	1.50942	−	8.56035i	0.0857293	−	0.486195i
$311$	0.454703	−	2.57875i	0.0257839	−	0.146228i	−0.969198	−	0.246283i	$-0.920791\pi$
$311$	0.454703	−	2.57875i	0.0257839	−	0.146228i	0.994982	+	0.100055i	$0.0319019\pi$
$312$	−11.3780	+	0.139841i	−0.644151	+	0.00791693i
$313$	−20.0297	+	16.8069i	−1.13214	+	0.949982i	−0.999154	−	0.0411358i	$-0.986902\pi$
$313$	−20.0297	+	16.8069i	−1.13214	+	0.949982i	−0.132990	+	0.991117i	$0.542458\pi$
$314$	−5.81009	+	10.0634i	−0.327882	+	0.567909i
$315$	−0.461742	+	3.05613i	−0.0260162	+	0.172193i
$316$	−0.445859	−	0.772251i	−0.0250815	−	0.0434425i
$317$	−13.5511	−	4.93219i	−0.761105	−	0.277019i	−0.0678339	−	0.997697i	$-0.521609\pi$
$317$	−13.5511	−	4.93219i	−0.761105	−	0.277019i	−0.693271	+	0.720677i	$0.743831\pi$
$318$	1.02512	−	6.26291i	0.0574861	−	0.351206i
$319$	−0.115718	−	0.0970989i	−0.00647896	−	0.00543650i
$320$	−0.968138	+	0.352373i	−0.0541205	+	0.0196983i
$321$	−4.41510	−	1.54579i	−0.246427	−	0.0862774i
$322$	1.56889	+	8.89764i	0.0874311	+	0.495846i
$323$	17.8150			0.991255
$324$	−4.87757	−	7.56368i	−0.270976	−	0.420205i
$325$	−25.8746			−1.43526
$326$	−1.79423	−	10.1756i	−0.0993734	−	0.563574i
$327$	−20.3179	−	7.11359i	−1.12358	−	0.393382i
$328$	4.32413	−	1.57385i	0.238760	−	0.0869015i
$329$	7.99304	+	6.70695i	0.440670	+	0.369766i
$330$	−0.332475	+	2.03123i	−0.0183021	+	0.111815i
$331$	−0.721220	−	0.262503i	−0.0396418	−	0.0144284i	0.322123	−	0.946698i	$-0.395603\pi$
$331$	−0.721220	−	0.262503i	−0.0396418	−	0.0144284i	−0.361765	+	0.932269i	$0.617826\pi$
$332$	1.54680	+	2.67914i	0.0848918	+	0.147037i
$333$	12.4285	−	4.87275i	0.681076	−	0.267025i
$334$	5.58505	−	9.67360i	0.305601	−	0.529316i
$335$	−3.14401	+	2.63814i	−0.171776	+	0.144137i
$336$	−1.73192	+	0.0212861i	−0.0944840	+	0.00116125i
$337$	1.13674	−	6.44680i	0.0619224	−	0.351180i	−0.938066	−	0.346456i	$-0.887385\pi$
$337$	1.13674	−	6.44680i	0.0619224	−	0.351180i	0.999989	−	0.00472408i	$-0.00150373\pi$
$338$	−5.23711	+	29.7011i	−0.284861	+	1.61553i
$339$	6.35416	+	10.6999i	0.345111	+	0.581137i
$340$	−3.64085	+	3.05504i	−0.197453	+	0.165683i
$341$	4.86571	−	8.42766i	0.263493	−	0.456383i
$342$	11.5819	−	0.284737i	0.626276	−	0.0153968i
$343$	0.500000	+	0.866025i	0.0269975	+	0.0467610i
$344$	6.10185	+	2.22089i	0.328990	+	0.119743i
$345$	12.4771	+	10.2108i	0.671743	+	0.549734i
$346$	8.26469	+	6.93490i	0.444312	+	0.372822i
$347$	−4.15176	+	1.51112i	−0.222878	+	0.0811210i	−0.451046	−	0.892501i	$-0.648949\pi$
$347$	−4.15176	+	1.51112i	−0.222878	+	0.0811210i	0.228168	+	0.973622i	$0.426727\pi$
$348$	−0.0421328	−	0.222893i	−0.00225856	−	0.0119483i
$349$	5.06954	+	28.7508i	0.271366	+	1.53899i	0.750273	+	0.661128i	$0.229922\pi$
$349$	5.06954	+	28.7508i	0.271366	+	1.53899i	−0.478907	+	0.877865i	$0.658967\pi$
$350$	−3.93854			−0.210524
$351$	−31.6257	+	12.8499i	−1.68805	+	0.685875i
$352$	−1.15342			−0.0614775
$353$	−2.00841	−	11.3903i	−0.106897	−	0.606244i	−0.990446	−	0.137904i	$-0.955963\pi$
$353$	−2.00841	−	11.3903i	−0.106897	−	0.606244i	0.883549	−	0.468340i	$-0.155148\pi$
$354$	11.9622	−	10.2906i	0.635785	−	0.546942i
$355$	−14.7658	+	5.37432i	−0.783688	+	0.285239i
$356$	−9.34968	−	7.84531i	−0.495532	−	0.415801i
$357$	−7.47419	+	2.82488i	−0.395576	+	0.149509i
$358$	−6.22338	−	2.26512i	−0.328916	−	0.119716i
$359$	0.0765248	+	0.132545i	0.00403882	+	0.00699545i	0.868038	−	0.496498i	$-0.165381\pi$
$359$	0.0765248	+	0.132545i	0.00403882	+	0.00699545i	−0.863999	+	0.503494i	$0.832048\pi$
$360$	−2.31816	+	2.04433i	−0.122178	+	0.107745i
$361$	2.04327	−	3.53905i	0.107541	−	0.186266i
$362$	−8.63438	+	7.24510i	−0.453813	+	0.380794i
$363$	8.19525	−	14.6063i	0.430139	−	0.766629i
$364$	−1.14079	+	6.46977i	−0.0597939	+	0.339108i
$365$	−1.81644	+	10.3015i	−0.0950767	+	0.539207i
$366$	−5.98225	+	10.6621i	−0.312697	+	0.557315i
$367$	−18.6132	+	15.6184i	−0.971603	+	0.815271i	−0.982801	−	0.184666i	$-0.940880\pi$
$367$	−18.6132	+	15.6184i	−0.971603	+	0.815271i	0.0111988	+	0.999937i	$0.496435\pi$
$368$	−4.51745	+	7.82446i	−0.235488	+	0.407878i
$369$	10.3539	−	9.13086i	0.539002	−	0.475333i
$370$	−2.29228	−	3.97034i	−0.119170	−	0.206408i
$371$	−3.44304	−	1.25316i	−0.178754	−	0.0650611i
$372$	13.6696	−	5.16644i	0.708735	−	0.267867i
$373$	8.87050	+	7.44324i	0.459297	+	0.385396i	0.842872	−	0.538114i	$-0.180863\pi$
$373$	8.87050	+	7.44324i	0.459297	+	0.385396i	−0.383575	+	0.923510i	$0.625307\pi$
$374$	−5.00001	+	1.81986i	−0.258545	+	0.0941025i
$375$	−12.0920	+	10.4023i	−0.624428	+	0.537171i
$376$	1.81187	+	10.2757i	0.0934403	+	0.529926i
$377$	−0.860392			−0.0443125
$378$	−4.81396	+	1.95597i	−0.247603	+	0.100604i
$379$	6.33623			0.325470			0.162735	−	0.986670i	$-0.447968\pi$
$379$	6.33623			0.325470			0.162735	+	0.986670i	$0.447968\pi$
$380$	−0.690893	−	3.91825i	−0.0354421	−	0.201002i
$381$	0.751746	+	3.97692i	0.0385131	+	0.203744i
$382$	8.25086	−	3.00307i	0.422151	−	0.153650i
$383$	23.3389	+	19.5836i	1.19256	+	1.00068i	0.999811	+	0.0194297i	$0.00618505\pi$
$383$	23.3389	+	19.5836i	1.19256	+	1.00068i	0.192750	+	0.981248i	$0.438259\pi$
$384$	−1.34041	−	1.09695i	−0.0684025	−	0.0559785i
$385$	1.11667	+	0.406435i	0.0569108	+	0.0207138i
$386$	−1.01983	−	1.76639i	−0.0519078	−	0.0899069i
$387$	19.4745	−	0.478774i	0.989944	−	0.0243374i
$388$	3.41169	−	5.90923i	0.173203	−	0.299996i
$389$	18.8731	−	15.8364i	0.956905	−	0.802939i	−0.0235415	−	0.999723i	$-0.507494\pi$
$389$	18.8731	−	15.8364i	0.956905	−	0.802939i	0.980447	+	0.196784i	$0.0630498\pi$
$390$	5.98597	+	10.0799i	0.303111	+	0.510413i
$391$	−7.23755	+	41.0462i	−0.366018	+	2.07579i
$392$	−0.173648	+	0.984808i	−0.00877056	+	0.0497403i
$393$	9.36231	−	0.115067i	0.472266	−	0.00580438i
$394$	16.3448	−	13.7149i	0.823440	−	0.690948i
$395$	−0.459356	+	0.795627i	−0.0231127	+	0.0400324i
$396$	−3.22151	+	1.26304i	−0.161887	+	0.0634700i
$397$	4.80000	+	8.31385i	0.240905	+	0.417260i	0.960972	−	0.276644i	$-0.0892224\pi$
$397$	4.80000	+	8.31385i	0.240905	+	0.417260i	−0.720067	+	0.693904i	$0.755889\pi$
$398$	−4.71394	−	1.71574i	−0.236289	−	0.0860020i
$399$	1.08046	−	6.60098i	0.0540907	−	0.330462i
$400$	−3.01710	−	2.53165i	−0.150855	−	0.126582i
$401$	18.8006	−	6.84286i	0.938858	−	0.341716i	0.173143	−	0.984897i	$-0.444608\pi$
$401$	18.8006	−	6.84286i	0.938858	−	0.341716i	0.765715	+	0.643180i	$0.222385\pi$
$402$	−6.51225	−	2.28003i	−0.324801	−	0.113717i
$403$	−9.62490	−	54.5855i	−0.479450	−	2.71910i
$404$	6.49399			0.323088
$405$	−4.23602	+	8.24829i	−0.210489	+	0.409861i
$406$	−0.130966			−0.00649974
$407$	−0.891258	−	5.05458i	−0.0441780	−	0.250546i
$408$	−7.54136	−	2.64033i	−0.373353	−	0.130716i
$409$	16.6083	−	6.04494i	0.821230	−	0.298903i	0.102976	−	0.994684i	$-0.467164\pi$
$409$	16.6083	−	6.04494i	0.821230	−	0.298903i	0.718254	+	0.695781i	$0.244941\pi$
$410$	−3.63177	−	3.04741i	−0.179360	−	0.150501i
$411$	4.59700	−	28.0850i	0.226753	−	1.38533i
$412$	17.0948	+	6.22198i	0.842198	+	0.306535i
$413$	−4.55515	−	7.88974i	−0.224144	−	0.388229i
$414$	−4.04922	+	26.8005i	−0.199008	+	1.31717i
$415$	1.59362	−	2.76024i	0.0782279	−	0.135495i
$416$	−5.03259	+	4.22284i	−0.246743	+	0.207042i
$417$	6.06655	−	0.0745608i	0.297080	−	0.00365126i
$418$	0.773476	−	4.38660i	0.0378320	−	0.214556i
$419$	0.570196	−	3.23374i	0.0278559	−	0.157979i	−0.967707	−	0.252078i	$-0.918886\pi$
$419$	0.570196	−	3.23374i	0.0278559	−	0.157979i	0.995563	+	0.0940994i	$0.0299972\pi$
$420$	0.911165	+	1.53432i	0.0444603	+	0.0748673i
$421$	−27.3078	+	22.9140i	−1.33090	+	1.11676i	−0.347034	+	0.937853i	$0.612811\pi$
$421$	−27.3078	+	22.9140i	−1.33090	+	1.11676i	−0.983866	+	0.178905i	$0.942744\pi$
$422$	−1.89886	+	3.28893i	−0.0924352	+	0.160103i
$423$	16.3128	+	26.7159i	0.793155	+	1.29897i
$424$	−1.83200	−	3.17312i	−0.0889700	−	0.154101i
$425$	−17.0734	−	6.21419i	−0.828180	−	0.301433i
$426$	−20.4436	−	16.7304i	−0.990497	−	0.810592i
$427$	5.40711	+	4.53711i	0.261669	+	0.219566i
$428$	−2.53790	+	0.923720i	−0.122674	+	0.0446497i
$429$	2.43773	+	12.8962i	0.117695	+	0.622635i
$430$	−1.16171	−	6.58838i	−0.0560226	−	0.317720i
$431$	0.614921			0.0296197			0.0148098	−	0.999890i	$-0.495286\pi$
$431$	0.614921			0.0296197			0.0148098	+	0.999890i	$0.495286\pi$
$432$	−4.94498	−	1.59600i	−0.237915	−	0.0767874i
$433$	−15.6218			−0.750738			−0.375369	−	0.926876i	$-0.622484\pi$
$433$	−15.6218			−0.750738			−0.375369	+	0.926876i	$0.622484\pi$
$434$	−1.46507	−	8.30883i	−0.0703257	−	0.398837i
$435$	−0.177170	+	0.152413i	−0.00849465	+	0.00730763i
$436$	−11.6792	+	4.25088i	−0.559333	+	0.203580i
$437$	−26.7280	−	22.4275i	−1.27857	−	1.07285i
$438$	−16.4500	+	6.21730i	−0.786011	+	0.297074i
$439$	−17.6912	−	6.43907i	−0.844354	−	0.307320i	−0.116618	−	0.993177i	$-0.537205\pi$
$439$	−17.6912	−	6.43907i	−0.844354	−	0.307320i	−0.727736	+	0.685857i	$0.759428\pi$
$440$	0.594168	+	1.02913i	0.0283258	+	0.0490618i
$441$	0.593399	+	2.94073i	0.0282571	+	0.140035i
$442$	−15.1532	+	26.2461i	−0.720765	+	1.24840i
$443$	−20.0991	+	16.8651i	−0.954936	+	0.801286i	−0.980122	−	0.198397i	$-0.936427\pi$
$443$	−20.0991	+	16.8651i	−0.954936	+	0.801286i	0.0251861	+	0.999683i	$0.491982\pi$
$444$	3.77136	−	6.72164i	0.178981	−	0.318995i
$445$	−2.18356	+	12.3836i	−0.103510	+	0.587037i
$446$	−1.60256	+	9.08857i	−0.0758834	+	0.430356i
$447$	−4.10141	+	7.30988i	−0.193990	+	0.345745i
$448$	−0.766044	+	0.642788i	−0.0361922	+	0.0303689i
$449$	−6.47136	+	11.2087i	−0.305403	+	0.528973i	−0.977351	−	0.211625i	$-0.932124\pi$
$449$	−6.47136	+	11.2087i	−0.305403	+	0.528973i	0.671948	+	0.740598i	$0.265458\pi$
$450$	−11.1990	−	3.76708i	−0.527927	−	0.177582i
$451$	−2.65381	−	4.59654i	−0.124963	−	0.216442i
$452$	6.75147	+	2.45733i	0.317562	+	0.115583i
$453$	38.1562	−	14.4212i	1.79273	−	0.677566i
$454$	−19.8230	−	16.6334i	−0.930337	−	0.780646i
$455$	6.36025	−	2.31494i	0.298173	−	0.108526i
$456$	5.07071	−	4.36214i	0.237458	−	0.204276i
$457$	3.67098	+	20.8191i	0.171721	+	0.973879i	0.941861	+	0.336003i	$0.109075\pi$
$457$	3.67098	+	20.8191i	0.171721	+	0.973879i	−0.770140	+	0.637875i	$0.779814\pi$
$458$	12.8144			0.598775
$459$	−23.9543	+	0.883587i	−1.11809	+	0.0412423i
$460$	9.30839			0.434006
$461$	−2.50688	−	14.2172i	−0.116757	−	0.662162i	−0.985865	−	0.167540i	$-0.946418\pi$
$461$	−2.50688	−	14.2172i	−0.116757	−	0.662162i	0.869108	−	0.494622i	$-0.164694\pi$
$462$	0.371064	+	1.96302i	0.0172635	+	0.0913280i
$463$	37.7513	−	13.7404i	1.75445	−	0.638569i	0.754608	−	0.656176i	$-0.227827\pi$
$463$	37.7513	−	13.7404i	1.75445	−	0.638569i	0.999845	+	0.0176079i	$0.00560504\pi$
$464$	−0.100326	−	0.0841835i	−0.00465751	−	0.00390812i
$465$	−11.6514	−	9.53514i	−0.540320	−	0.442181i
$466$	0.379649	+	0.138181i	0.0175869	+	0.00640111i
$467$	−13.8938	−	24.0648i	−0.642930	−	1.11359i	−0.984775	−	0.173831i	$-0.944385\pi$
$467$	−13.8938	−	24.0648i	−0.642930	−	1.11359i	0.341845	−	0.939756i	$-0.388948\pi$
$468$	−9.43190	+	17.3053i	−0.435990	+	0.799938i
$469$	−1.99181	+	3.44992i	−0.0919734	+	0.159303i
$470$	8.23499	−	6.90998i	0.379852	−	0.318734i
$471$	10.2768	+	17.3053i	0.473531	+	0.797385i
$472$	1.58199	−	8.97189i	0.0728168	−	0.412965i
$473$	1.30057	−	7.37590i	0.0598003	−	0.339144i
$474$	−1.54439	+	0.0189812i	−0.0709360	+	0.000871837i
$475$	11.6514	−	9.77670i	0.534604	−	0.448586i
$476$	−2.30658	+	3.99511i	−0.105722	+	0.183115i
$477$	−8.59149	−	6.85645i	−0.393377	−	0.313935i
$478$	5.20006	+	9.00677i	0.237845	+	0.411960i
$479$	2.45366	+	0.893058i	0.112110	+	0.0408049i	0.397466	−	0.917617i	$-0.369890\pi$
$479$	2.45366	+	0.893058i	0.112110	+	0.0408049i	−0.285356	+	0.958422i	$0.592112\pi$
$480$	−0.288251	+	1.76105i	−0.0131568	+	0.0803804i
$481$	−22.3943	−	18.7910i	−1.02109	−	0.856797i
$482$	10.3351	−	3.76168i	0.470752	−	0.171340i
$483$	14.7698	+	5.17112i	0.672051	+	0.235294i
$484$	−1.67911	−	9.52272i	−0.0763233	−	0.432851i
$485$	−7.02994			−0.319213
$486$	−15.5590	+	0.957297i	−0.705772	+	0.0434239i
$487$	40.1397			1.81890			0.909452	−	0.415808i	$-0.136501\pi$
$487$	40.1397			1.81890			0.909452	+	0.415808i	$0.136501\pi$
$488$	1.22569	+	6.95125i	0.0554845	+	0.314668i
$489$	−16.8912	−	5.91384i	−0.763847	−	0.267433i
$490$	0.968138	−	0.352373i	0.0437360	−	0.0159186i
$491$	−9.72442	−	8.15976i	−0.438857	−	0.368245i	0.396424	−	0.918067i	$-0.370251\pi$
$491$	−9.72442	−	8.15976i	−0.438857	−	0.368245i	−0.835281	+	0.549823i	$0.814695\pi$
$492$	1.28746	−	7.86560i	0.0580430	−	0.354609i
$493$	−0.567731	−	0.206637i	−0.0255693	−	0.00930647i
$494$	−12.6852	−	21.9714i	−0.570733	−	0.988538i
$495$	2.78645	+	2.22373i	0.125242	+	0.0999492i
$496$	4.21851	−	7.30667i	0.189416	−	0.328079i
$497$	−11.6835	+	9.80365i	−0.524078	+	0.439754i
$498$	5.35787	−	0.0658509i	0.240092	−	0.00295085i
$499$	−3.81329	+	21.6263i	−0.170706	+	0.968124i	0.772277	+	0.635286i	$0.219118\pi$
$499$	−3.81329	+	21.6263i	−0.170706	+	0.968124i	−0.942984	+	0.332839i	$0.891994\pi$
$500$	−1.59915	+	9.06921i	−0.0715160	+	0.405587i
$501$	−9.87878	−	16.6350i	−0.441351	−	0.743198i
$502$	17.0663	−	14.3203i	0.761706	−	0.639148i
$503$	−7.19505	+	12.4622i	−0.320812	+	0.555662i	−0.980656	−	0.195741i	$-0.937289\pi$
$503$	−7.19505	+	12.4622i	−0.320812	+	0.555662i	0.659844	+	0.751403i	$0.270622\pi$
$504$	−1.43569	+	2.63416i	−0.0639509	+	0.117335i
$505$	−3.34528	−	5.79420i	−0.148863	−	0.257838i
$506$	9.79258	+	3.56421i	0.435333	+	0.158448i
$507$	40.4259	+	33.0833i	1.79538	+	1.46928i
$508$	1.79004	+	1.50203i	0.0794204	+	0.0666416i
$509$	1.72266	−	0.626996i	0.0763555	−	0.0277911i	−0.303560	−	0.952812i	$-0.598175\pi$
$509$	1.72266	−	0.626996i	0.0763555	−	0.0277911i	0.379915	+	0.925021i	$0.375953\pi$
$510$	1.52901	+	8.08884i	0.0677057	+	0.358180i
$511$	1.76307	+	9.99886i	0.0779936	+	0.442324i
$512$	−1.00000			−0.0441942
$513$	9.38584	−	17.7361i	0.414395	−	0.783068i
$514$	−14.6005			−0.644001
$515$	−3.25461	−	18.4578i	−0.143415	−	0.813348i
$516$	8.52620	−	7.33477i	0.375345	−	0.322895i
$517$	11.3092	−	4.11621i	0.497377	−	0.181031i
$518$	−3.40879	−	2.86031i	−0.149773	−	0.125675i
$519$	17.4799	−	6.60655i	0.767283	−	0.289996i
$520$	6.36025	+	2.31494i	0.278916	+	0.101517i
$521$	−3.18211	−	5.51157i	−0.139411	−	0.241466i	0.787863	−	0.615851i	$-0.211187\pi$
$521$	−3.18211	−	5.51157i	−0.139411	−	0.241466i	−0.927274	+	0.374384i	$0.877854\pi$
$522$	−0.372395	−	0.125265i	−0.0162993	−	0.00548268i
$523$	13.4600	−	23.3135i	0.588566	−	1.01943i	−0.405854	−	0.913938i	$-0.633026\pi$
$523$	13.4600	−	23.3135i	0.588566	−	1.01943i	0.994420	−	0.105489i	$-0.0336408\pi$
$524$	4.14104	−	3.47474i	0.180902	−	0.151795i
$525$	−3.33802	+	5.94929i	−0.145683	+	0.259648i
$526$	−1.50298	+	8.52383i	−0.0655331	+	0.371657i
$527$	6.75860	−	38.3299i	0.294409	−	1.66968i
$528$	−0.977553	+	1.74228i	−0.0425426	+	0.0758228i
$529$	44.9128	−	37.6863i	1.95273	−	1.63853i
$530$	−1.88746	+	3.26918i	−0.0819860	+	0.142004i
$531$	−5.40604	−	26.7909i	−0.234602	−	1.16263i
$532$	−1.93090	−	3.34441i	−0.0837150	−	0.144999i
$533$	−28.4077	−	10.3395i	−1.23047	−	0.447855i
$534$	−19.7747	+	7.47387i	−0.855734	+	0.323426i
$535$	2.13154	+	1.78858i	0.0921546	+	0.0773269i
$536$	−3.74339	+	1.36248i	−0.161690	+	0.0588502i
$537$	−8.69601	+	7.48085i	−0.375261	+	0.322822i
$538$	0.996578	+	5.65187i	0.0429655	+	0.243670i
$539$	1.15342			0.0496813
$540$	1.12332	+	5.23426i	0.0483400	+	0.225247i
$541$	−11.4263			−0.491255			−0.245627	−	0.969364i	$-0.578994\pi$
$541$	−11.4263			−0.491255			−0.245627	+	0.969364i	$0.578994\pi$
$542$	1.46534	+	8.31034i	0.0629416	+	0.356960i
$543$	3.62609	+	19.1829i	0.155610	+	0.823217i
$544$	−4.33494	+	1.57779i	−0.185859	+	0.0676472i
$545$	9.80918	+	8.23088i	0.420179	+	0.352572i
$546$	8.80593	+	7.20650i	0.376859	+	0.308410i
$547$	−11.3414	−	4.12793i	−0.484923	−	0.176497i	0.0879776	−	0.996122i	$-0.471960\pi$
$547$	−11.3414	−	4.12793i	−0.484923	−	0.176497i	−0.572900	+	0.819625i	$0.694182\pi$
$548$	−8.21532	−	14.2293i	−0.350941	−	0.607848i
$549$	11.0352	+	18.0727i	0.470973	+	0.771325i
$550$	−2.27140	+	3.93418i	−0.0968527	+	0.167754i
$551$	0.387438	−	0.325099i	0.0165054	−	0.0138497i
$552$	7.99042	+	13.4552i	0.340095	+	0.572690i
$553$	−0.154845	+	0.878171i	−0.00658469	+	0.0373436i
$554$	4.54878	−	25.7974i	0.193259	−	1.09603i
$555$	−7.94008	+	0.0975874i	−0.337038	+	0.00414235i
$556$	2.68329	−	2.25155i	0.113797	−	0.0954869i
$557$	19.4405	−	33.6720i	0.823722	−	1.42673i	−0.0791706	−	0.996861i	$-0.525227\pi$
$557$	19.4405	−	33.6720i	0.823722	−	1.42673i	0.902892	−	0.429867i	$-0.141439\pi$
$558$	3.78126	−	25.0270i	0.160074	−	1.05948i
$559$	−21.3296	−	36.9440i	−0.902147	−	1.56256i
$560$	0.968138	+	0.352373i	0.0409113	+	0.0148905i
$561$	−1.48869	+	9.09504i	−0.0628527	+	0.383993i
$562$	1.66074	+	1.39352i	0.0700539	+	0.0587822i
$563$	−13.0775	+	4.75983i	−0.551152	+	0.200603i	−0.602558	−	0.798075i	$-0.705852\pi$
$563$	−13.0775	+	4.75983i	−0.551152	+	0.200603i	0.0514064	+	0.998678i	$0.483630\pi$
$564$	17.0573	+	5.97199i	0.718241	+	0.251466i
$565$	−1.28539	−	7.28979i	−0.0540766	−	0.306684i
$566$	6.52574			0.274297
$567$	−1.12541	+	8.92936i	−0.0472627	+	0.374998i
$568$	−15.2518			−0.639950
$569$	−5.91781	−	33.5616i	−0.248088	−	1.40698i	−0.813211	−	0.581969i	$-0.802283\pi$
$569$	−5.91781	−	33.5616i	−0.248088	−	1.40698i	0.565123	−	0.825006i	$-0.308829\pi$
$570$	−6.50418	−	2.27720i	−0.272430	−	0.0953815i
$571$	1.25220	−	0.455763i	0.0524029	−	0.0190731i	−0.315686	−	0.948864i	$-0.602235\pi$
$571$	1.25220	−	0.455763i	0.0524029	−	0.0190731i	0.368089	+	0.929791i	$0.380012\pi$
$572$	5.80469	+	4.87071i	0.242706	+	0.203655i
$573$	2.45659	−	15.0084i	0.102626	−	0.626983i
$574$	−4.32413	−	1.57385i	−0.180486	−	0.0656914i
$575$	17.7922	+	30.8169i	0.741985	+	1.28516i
$576$	−2.79301	+	1.09504i	−0.116375	+	0.0456265i
$577$	−11.5142	+	19.9432i	−0.479343	+	0.830246i	−0.999719	−	0.0236908i	$-0.992458\pi$
$577$	−11.5142	+	19.9432i	−0.479343	+	0.830246i	0.520377	+	0.853937i	$0.325792\pi$
$578$	−3.27956	+	2.75188i	−0.136412	+	0.114463i
$579$	−3.53251	+	0.0434163i	−0.146806	+	0.00180432i
$580$	−0.0234305	+	0.132881i	−0.000972897	+	0.00551757i
$581$	0.537199	−	3.04660i	0.0222868	−	0.126394i
$582$	−6.03457	−	10.1617i	−0.250141	−	0.421215i
$583$	−3.23741	+	2.71651i	−0.134080	+	0.112506i
$584$	−5.07655	+	8.79285i	−0.210069	+	0.363851i
$585$	20.2992	−	0.499049i	0.839268	−	0.0206331i
$586$	−2.50731	−	4.34279i	−0.103576	−	0.179399i
$587$	−10.8799	−	3.95997i	−0.449063	−	0.163445i	0.107582	−	0.994196i	$-0.465689\pi$
$587$	−10.8799	−	3.95997i	−0.449063	−	0.163445i	−0.556645	+	0.830751i	$0.687911\pi$
$588$	1.34041	+	1.09695i	0.0552776	+	0.0452375i
$589$	24.9593	+	20.9433i	1.02843	+	0.862954i
$590$	−8.82002	+	3.21022i	−0.363114	+	0.132163i
$591$	−6.86416	−	36.3131i	−0.282354	−	1.49372i
$592$	−0.772709	−	4.38225i	−0.0317581	−	0.180109i
$593$	−8.49072			−0.348672			−0.174336	−	0.984686i	$-0.555778\pi$
$593$	−8.49072			−0.348672			−0.174336	+	0.984686i	$0.555778\pi$
$594$	−0.822461	+	5.93665i	−0.0337460	+	0.243584i
$595$	4.75279			0.194846
$596$	0.840332	+	4.76576i	0.0344213	+	0.195213i
$597$	−6.58686	+	5.66642i	−0.269582	+	0.231911i
$598$	55.7759	−	20.3008i	2.28085	−	0.830160i
$599$	−17.2971	−	14.5140i	−0.706741	−	0.593026i	0.216942	−	0.976185i	$-0.430392\pi$
$599$	−17.2971	−	14.5140i	−0.706741	−	0.593026i	−0.923683	+	0.383159i	$0.874836\pi$
$600$	−6.38120	+	2.41178i	−0.260511	+	0.0984606i
$601$	36.6516	+	13.3401i	1.49505	+	0.544154i	0.954774	−	0.297334i	$-0.0960974\pi$
$601$	36.6516	+	13.3401i	1.49505	+	0.544154i	0.540277	+	0.841488i	$0.318320\pi$
$602$	−3.24673	−	5.62350i	−0.132327	−	0.229197i
$603$	−8.96335	+	7.90456i	−0.365016	+	0.321899i
$604$	11.7752	−	20.3952i	0.479126	−	0.829871i
$605$	−7.63158	+	6.40366i	−0.310268	+	0.260346i
$606$	5.50382	−	9.80936i	0.223577	−	0.398478i
$607$	−3.78788	+	21.4821i	−0.153745	+	0.871933i	0.806178	+	0.591672i	$0.201532\pi$
$607$	−3.78788	+	21.4821i	−0.153745	+	0.871933i	−0.959924	+	0.280261i	$0.909579\pi$
$608$	0.670593	−	3.80312i	0.0271962	−	0.154237i
$609$	−0.110997	+	0.197828i	−0.00449783	+	0.00801641i
$610$	5.57079	−	4.67445i	0.225555	−	0.189263i
$611$	34.2740	−	59.3644i	1.38658	−	2.40163i
$612$	−10.3798	+	9.15370i	−0.419578	+	0.370016i
$613$	−1.86759	−	3.23475i	−0.0754311	−	0.130650i	0.825843	−	0.563901i	$-0.190700\pi$
$613$	−1.86759	−	3.23475i	−0.0754311	−	0.130650i	−0.901274	+	0.433250i	$0.857367\pi$
$614$	−24.5134	−	8.92216i	−0.989282	−	0.360069i
$615$	−7.68122	+	2.90313i	−0.309737	+	0.117065i
$616$	0.883571	+	0.741404i	0.0356001	+	0.0298720i
$617$	−13.9306	+	5.07033i	−0.560825	+	0.204124i	−0.606850	−	0.794817i	$-0.707567\pi$
$617$	−13.9306	+	5.07033i	−0.560825	+	0.204124i	0.0460245	+	0.998940i	$0.485345\pi$
$618$	23.8867	−	20.5488i	0.960865	−	0.826596i
$619$	−0.806539	−	4.57411i	−0.0324175	−	0.183849i	0.964299	−	0.264815i	$-0.0853107\pi$
$619$	−0.806539	−	4.57411i	−0.0324175	−	0.183849i	−0.996717	+	0.0809656i	$0.974200\pi$
$620$	−8.69240			−0.349095
$621$	37.0512	+	28.8306i	1.48681	+	1.15693i
$622$	−2.61853			−0.104994
$623$	2.11940	+	12.0197i	0.0849120	+	0.481560i
$624$	2.11348	+	11.1808i	0.0846070	+	0.447592i
$625$	−9.58940	+	3.49026i	−0.383576	+	0.139610i
$626$	20.0297	+	16.8069i	0.800547	+	0.671738i
$627$	−5.97055	−	4.88612i	−0.238441	−	0.195133i
$628$	10.9194	+	3.97433i	0.435731	+	0.158593i
$629$	−10.2639	−	17.7776i	−0.409249	−	0.708841i
$630$	3.08988	−	0.0759637i	0.123104	−	0.00302646i
$631$	−22.1965	+	38.4455i	−0.883629	+	1.53049i	−0.0363521	+	0.999339i	$0.511574\pi$
$631$	−22.1965	+	38.4455i	−0.883629	+	1.53049i	−0.847277	+	0.531151i	$0.821760\pi$
$632$	−0.683096	+	0.573186i	−0.0271721	+	0.0228001i
$633$	3.35869	+	5.65574i	0.133496	+	0.224796i
$634$	−2.50414	+	14.2017i	−0.0994521	+	0.564021i
$635$	0.418053	−	2.37090i	0.0165899	−	0.0940861i
$636$	−6.34577	+	0.0779926i	−0.251626	+	0.00309261i
$637$	5.03259	−	4.22284i	0.199398	−	0.167315i
$638$	−0.0755296	+	0.130821i	−0.00299024	+	0.00517925i
$639$	−42.5983	+	16.7012i	−1.68516	+	0.660690i
$640$	0.515135	+	0.892241i	0.0203625	+	0.0352689i
$641$	8.52533	+	3.10297i	0.336730	+	0.122560i	0.504851	−	0.863207i	$-0.331548\pi$
$641$	8.52533	+	3.10297i	0.336730	+	0.122560i	−0.168120	+	0.985766i	$0.553770\pi$
$642$	−0.755629	+	4.61645i	−0.0298223	+	0.182197i
$643$	14.4053	+	12.0874i	0.568088	+	0.476682i	0.881011	−	0.473096i	$-0.156864\pi$
$643$	14.4053	+	12.0874i	0.568088	+	0.476682i	−0.312923	+	0.949779i	$0.601308\pi$
$644$	8.49003	−	3.09012i	0.334554	−	0.121768i
$645$	−10.9365	−	3.82902i	−0.430625	−	0.150768i
$646$	−3.09355	−	17.5444i	−0.121714	−	0.690275i
$647$	4.81470			0.189285			0.0946427	−	0.995511i	$-0.469829\pi$
$647$	4.81470			0.189285			0.0946427	+	0.995511i	$0.469829\pi$
$648$	−6.60179	+	6.11689i	−0.259343	+	0.240294i
$649$	−10.5080			−0.412475
$650$	4.49307	+	25.4815i	0.176233	+	0.999465i
$651$	−13.7924	−	4.82892i	−0.540568	−	0.189260i
$652$	−9.70945	+	3.53395i	−0.380251	+	0.138400i
$653$	−10.9729	−	9.20734i	−0.429402	−	0.360311i	0.402324	−	0.915497i	$-0.368203\pi$
$653$	−10.9729	−	9.20734i	−0.429402	−	0.360311i	−0.831726	+	0.555186i	$0.812647\pi$
$654$	−3.47734	+	21.2445i	−0.135975	+	0.830727i
$655$	−5.23350	−	1.90484i	−0.204490	−	0.0744282i
$656$	−2.30082	−	3.98514i	−0.0898319	−	0.155593i
$657$	−4.55038	+	30.1175i	−0.177527	+	1.17500i
$658$	5.21708	−	9.03626i	0.203383	−	0.352270i
$659$	34.3621	−	28.8332i	1.33856	−	1.12318i	0.356561	−	0.934272i	$-0.383949\pi$
$659$	34.3621	−	28.8332i	1.33856	−	1.12318i	0.981994	−	0.188910i	$-0.0604954\pi$
$660$	2.05810	−	0.0252951i	0.0801115	−	0.000984609i
$661$	−5.28663	+	29.9820i	−0.205626	+	1.16616i	0.690825	+	0.723022i	$0.257247\pi$
$661$	−5.28663	+	29.9820i	−0.205626	+	1.16616i	−0.896451	+	0.443142i	$0.853864\pi$
$662$	−0.133276	+	0.755846i	−0.00517992	+	0.0293768i
$663$	26.8028	+	45.1337i	1.04094	+	1.75285i
$664$	2.36984	−	1.98853i	0.0919675	−	0.0771699i
$665$	−1.98935	+	3.44565i	−0.0771435	+	0.133617i
$666$	−6.95690	−	11.3935i	−0.269574	−	0.441490i
$667$	0.591633	+	1.02474i	0.0229081	+	0.0396781i
$668$	−10.4965	−	3.82040i	−0.406121	−	0.147816i
$669$	12.3703	+	10.1235i	0.478265	+	0.391398i
$670$	3.14401	+	2.63814i	0.121464	+	0.101920i
$671$	7.65042	−	2.78452i	0.295341	−	0.107495i
$672$	0.321707	+	1.70191i	0.0124101	+	0.0656527i
$673$	−0.412726	−	2.34069i	−0.0159094	−	0.0902268i	0.975819	−	0.218579i	$-0.0701422\pi$
$673$	−0.412726	−	2.34069i	−0.0159094	−	0.0902268i	−0.991729	+	0.128352i	$0.959031\pi$
$674$	−6.54625			−0.252152
$675$	−15.1817	+	13.7238i	−0.584346	+	0.528228i
$676$	30.1593			1.15997
$677$	−1.17088	−	6.64040i	−0.0450006	−	0.255211i	0.954005	−	0.299790i	$-0.0969166\pi$
$677$	−1.17088	−	6.64040i	−0.0450006	−	0.255211i	−0.999006	+	0.0445786i	$0.985805\pi$
$678$	9.43392	−	8.11564i	0.362307	−	0.311679i
$679$	−6.41189	+	2.33374i	−0.246066	+	0.0895606i
$680$	3.64085	+	3.05504i	0.139620	+	0.117155i
$681$	−41.9258	+	15.8459i	−1.60660	+	0.607216i
$682$	−9.14454	−	3.32834i	−0.350163	−	0.127449i
$683$	−6.87943	−	11.9155i	−0.263234	−	0.455935i	0.703865	−	0.710333i	$-0.251456\pi$
$683$	−6.87943	−	11.9155i	−0.263234	−	0.455935i	−0.967099	+	0.254399i	$0.918122\pi$
$684$	−2.29158	−	11.3565i	−0.0876209	−	0.434226i
$685$	−8.46400	+	14.6601i	−0.323393	+	0.560133i
$686$	0.766044	−	0.642788i	0.0292477	−	0.0245417i
$687$	10.8605	−	19.3565i	0.414354	−	0.738495i
$688$	1.12758	−	6.39481i	0.0429885	−	0.243800i
$689$	−4.17988	+	23.7053i	−0.159241	+	0.903100i
$690$	7.88910	−	14.0606i	0.300333	−	0.535278i
$691$	32.3293	−	27.1275i	1.22986	−	1.03198i	0.231616	−	0.972807i	$-0.425599\pi$
$691$	32.3293	−	27.1275i	1.22986	−	1.03198i	0.998248	−	0.0591712i	$-0.0188458\pi$
$692$	5.39439	−	9.34336i	0.205064	−	0.355181i
$693$	3.27969	+	1.10321i	0.124585	+	0.0419074i
$694$	2.20911	+	3.82628i	0.0838565	+	0.145244i
$695$	−3.39118	−	1.23429i	−0.128635	−	0.0468192i
$696$	−0.212190	+	0.0801977i	−0.00804306	+	0.00303989i
$697$	−16.2616	−	13.6451i	−0.615953	−	0.516846i
$698$	27.4337	−	9.98504i	1.03838	−	0.377939i
$699$	0.530489	−	0.456359i	0.0200649	−	0.0172611i
$700$	0.683921	+	3.87871i	0.0258498	+	0.146601i
$701$	−32.8412			−1.24040			−0.620198	−	0.784446i	$-0.712948\pi$
$701$	−32.8412			−1.24040			−0.620198	+	0.784446i	$0.712948\pi$
$702$	18.1464	+	28.9138i	0.684891	+	1.09128i
$703$	17.1844			0.648122
$704$	0.200289	+	1.13590i	0.00754869	+	0.0428107i
$705$	−3.45836	−	18.2956i	−0.130249	−	0.689052i
$706$	−10.8685	+	3.95580i	−0.409041	+	0.148879i
$707$	−4.97468	−	4.17425i	−0.187092	−	0.156989i
$708$	−12.2115	−	9.99354i	−0.458937	−	0.375580i
$709$	−17.3881	−	6.32875i	−0.653023	−	0.237681i	−0.00580197	−	0.999983i	$-0.501847\pi$
$709$	−17.3881	−	6.32875i	−0.653023	−	0.237681i	−0.647221	+	0.762302i	$0.724069\pi$
$710$	7.85672	+	13.6082i	0.294858	+	0.510708i
$711$	−1.28023	+	2.34893i	−0.0480125	+	0.0880916i
$712$	−6.10257	+	10.5700i	−0.228704	+	0.396126i
$713$	−58.3937	+	48.9981i	−2.18686	+	1.83499i
$714$	4.07984	+	6.87011i	0.152684	+	0.257107i
$715$	1.35565	−	7.68825i	0.0506983	−	0.287524i
$716$	−1.15003	+	6.52217i	−0.0429788	+	0.243745i
$717$	18.0122	−	0.221378i	0.672677	−	0.00826753i
$718$	0.117243	−	0.0983784i	0.00437546	−	0.00367145i
$719$	14.8037	−	25.6408i	0.552085	−	0.956239i	−0.446039	−	0.895014i	$-0.647166\pi$
$719$	14.8037	−	25.6408i	0.552085	−	0.956239i	0.998124	−	0.0612256i	$-0.0195009\pi$
$720$	2.41581	+	1.92794i	0.0900320	+	0.0718502i
$721$	−9.09593	−	15.7546i	−0.338750	−	0.586732i
$722$	−3.84010	−	1.39768i	−0.142914	−	0.0520163i
$723$	3.07716	−	18.7996i	0.114441	−	0.699166i
$724$	8.63438	+	7.24510i	0.320894	+	0.269262i
$725$	−0.484708	+	0.176419i	−0.0180016	+	0.00655205i
$726$	−15.8074	−	5.53440i	−0.586669	−	0.205401i
$727$	−1.71502	−	9.72638i	−0.0636067	−	0.360731i	−0.999953	−	0.00965476i	$-0.996927\pi$
$727$	−1.71502	−	9.72638i	−0.0636067	−	0.360731i	0.936347	−	0.351077i	$-0.114184\pi$
$728$	6.56958			0.243485
$729$	−11.7407	+	24.3137i	−0.434839	+	0.900508i
$730$	10.4604			0.387159
$731$	−5.20168	−	29.5002i	−0.192391	−	1.09110i
$732$	11.5389	+	4.03992i	0.426489	+	0.149320i
$733$	−35.1122	+	12.7798i	−1.29690	+	0.472032i	−0.895985	−	0.444084i	$-0.853529\pi$
$733$	−35.1122	+	12.7798i	−1.29690	+	0.472032i	−0.400913	+	0.916116i	$0.631307\pi$
$734$	18.6132	+	15.6184i	0.687027	+	0.576484i
$735$	0.288251	−	1.76105i	0.0106323	−	0.0649572i
$736$	8.49003	+	3.09012i	0.312947	+	0.113903i
$737$	2.29740	+	3.97921i	0.0846258	+	0.146576i
$738$	−10.7901	−	8.61104i	−0.397188	−	0.316977i
$739$	−14.9345	+	25.8672i	−0.549373	+	0.951542i	0.448945	+	0.893560i	$0.351800\pi$
$739$	−14.9345	+	25.8672i	−0.549373	+	0.951542i	−0.998318	+	0.0579824i	$0.981533\pi$
$740$	−3.51197	+	2.94689i	−0.129103	+	0.108330i
$741$	−43.9394	+	0.540036i	−1.61415	+	0.0198387i
$742$	−0.636248	+	3.60834i	−0.0233574	+	0.132466i
$743$	−7.20949	+	40.8871i	−0.264491	+	1.50000i	0.505991	+	0.862539i	$0.331127\pi$
$743$	−7.20949	+	40.8871i	−0.264491	+	1.50000i	−0.770482	+	0.637462i	$0.779984\pi$
$744$	−7.46164	−	12.5648i	−0.273557	−	0.460647i
$745$	3.81932	−	3.20479i	0.139929	−	0.117414i
$746$	5.78981	−	10.0282i	0.211980	−	0.367160i
$747$	4.44147	−	8.14904i	0.162505	−	0.298158i
$748$	2.66045	+	4.60804i	0.0972757	+	0.168487i
$749$	2.53790	+	0.923720i	0.0927328	+	0.0337520i
$750$	12.3440	+	10.1019i	0.450739	+	0.368871i
$751$	−21.0175	−	17.6358i	−0.766939	−	0.643538i	0.172984	−	0.984925i	$-0.444659\pi$
$751$	−21.0175	−	17.6358i	−0.766939	−	0.643538i	−0.939923	+	0.341387i	$0.889103\pi$
$752$	9.80491	−	3.56870i	0.357548	−	0.130137i
$753$	−7.16715	−	37.9160i	−0.261186	−	1.38174i
$754$	0.149406	+	0.847321i	0.00544103	+	0.0308576i
$755$	−24.2633			−0.883031
$756$	2.76219	+	4.40117i	0.100460	+	0.160069i
$757$	−26.8298			−0.975146			−0.487573	−	0.873082i	$-0.662118\pi$
$757$	−26.8298			−0.975146			−0.487573	+	0.873082i	$0.662118\pi$
$758$	−1.10027	−	6.23997i	−0.0399638	−	0.226646i
$759$	13.6833	−	11.7712i	0.496672	−	0.427268i
$760$	−3.73875	+	1.36079i	−0.135619	+	0.0493612i
$761$	36.4938	+	30.6219i	1.32290	+	1.11004i	0.985681	+	0.168618i	$0.0539305\pi$
$761$	36.4938	+	30.6219i	1.32290	+	1.11004i	0.337218	+	0.941427i	$0.390514\pi$
$762$	3.78596	−	1.43091i	0.137151	−	0.0518364i
$763$	11.6792	+	4.25088i	0.422816	+	0.153892i
$764$	−4.39019	−	7.60404i	−0.158832	−	0.275104i
$765$	13.5143	+	4.54588i	0.488611	+	0.164357i
$766$	15.2334	−	26.3850i	0.550404	−	0.953328i
$767$	−45.8483	+	38.4713i	−1.65549	+	1.38912i
$768$	−0.847526	+	1.51053i	−0.0305824	+	0.0545065i
$769$	0.935372	−	5.30476i	0.0337304	−	0.191294i	−0.963287	−	0.268474i	$-0.913481\pi$
$769$	0.935372	−	5.30476i	0.0337304	−	0.191294i	0.997017	+	0.0771800i	$0.0245916\pi$
$770$	0.206352	−	1.17028i	0.00743642	−	0.0421740i
$771$	−12.3743	+	22.0545i	−0.445650	+	0.794274i
$772$	−1.56246	+	1.31106i	−0.0562343	+	0.0471862i
$773$	−6.28414	+	10.8845i	−0.226025	+	0.391487i	−0.956626	−	0.291317i	$-0.905906\pi$
$773$	−6.28414	+	10.8845i	−0.226025	+	0.391487i	0.730601	+	0.682804i	$0.239240\pi$
$774$	−3.85321	−	19.0955i	−0.138501	−	0.686373i
$775$	−16.6148	−	28.7776i	−0.596820	−	1.03372i
$776$	−6.41189	−	2.33374i	−0.230173	−	0.0837762i
$777$	−7.20962	+	2.72488i	−0.258644	+	0.0977547i
$778$	−18.8731	−	15.8364i	−0.676634	−	0.567764i
$779$	16.6989	−	6.07790i	0.598300	−	0.217763i
$780$	8.88727	−	7.64538i	0.318215	−	0.273748i
$781$	3.05477	+	17.3244i	0.109308	+	0.619917i
$782$	41.6794			1.49045
$783$	−0.504830	+	0.456349i	−0.0180412	+	0.0163086i
$784$	1.00000			0.0357143
$785$	−2.07890	−	11.7900i	−0.0741992	−	0.420805i
$786$	−1.73907	−	9.20009i	−0.0620305	−	0.328157i
$787$	−15.2752	+	5.55971i	−0.544501	+	0.198182i	−0.599601	−	0.800299i	$-0.704674\pi$
$787$	−15.2752	+	5.55971i	−0.544501	+	0.198182i	0.0551007	+	0.998481i	$0.482452\pi$
$788$	−16.3448	−	13.7149i	−0.582260	−	0.488574i
$789$	11.6017	+	9.49446i	0.413031	+	0.338012i
$790$	0.863306	+	0.314218i	0.0307151	+	0.0111794i
$791$	−3.59238	−	6.22219i	−0.127730	−	0.221235i
$792$	1.80326	+	2.95325i	0.0640760	+	0.104939i
$793$	23.1856	−	40.1587i	0.823346	−	1.42608i
$794$	7.35403	−	6.17076i	0.260985	−	0.218992i
$795$	3.33852	+	5.62178i	0.118405	+	0.199384i
$796$	−0.871102	+	4.94026i	−0.0308754	+	0.175103i
$797$	−5.62939	+	31.9259i	−0.199403	+	1.13087i	0.706604	+	0.707609i	$0.250226\pi$
$797$	−5.62939	+	31.9259i	−0.199403	+	1.13087i	−0.906007	+	0.423263i	$0.860885\pi$
$798$	−6.68832	+	0.0822026i	−0.236764	+	0.00290994i
$799$	36.8731	−	30.9402i	1.30448	−	1.09459i
$800$	−1.96927	+	3.41088i	−0.0696243	+	0.120593i
$801$	−5.47005	+	36.2045i	−0.193275	+	1.27922i
$802$	−10.0036	−	17.3267i	−0.353239	−	0.611829i
$803$	11.0046	+	4.00533i	0.388342	+	0.141345i
$804$	−1.11455	+	6.80923i	−0.0393071	+	0.240143i
$805$	−7.13064	−	5.98332i	−0.251322	−	0.210884i
$806$	−52.0849	+	18.9573i	−1.83461	+	0.667744i
$807$	9.38195	+	3.28475i	0.330260	+	0.115629i
$808$	−1.12767	−	6.39533i	−0.0396713	−	0.224987i
$809$	36.1098			1.26955			0.634777	−	0.772695i	$-0.281092\pi$
$809$	36.1098			1.26955			0.634777	+	0.772695i	$0.281092\pi$
$810$	8.85855	+	2.73936i	0.311258	+	0.0962514i
$811$	44.1305			1.54963			0.774815	−	0.632188i	$-0.217843\pi$
$811$	44.1305			1.54963			0.774815	+	0.632188i	$0.217843\pi$
$812$	0.0227420	+	0.128977i	0.000798089	+	0.00452619i
$813$	13.7949	+	4.82979i	0.483809	+	0.169388i
$814$	−4.82302	+	1.75544i	−0.169047	+	0.0615280i
$815$	8.15481	+	6.84270i	0.285651	+	0.239689i
$816$	−1.29068	+	7.88528i	−0.0451827	+	0.276040i
$817$	23.5641	+	8.57663i	0.824403	+	0.300058i
$818$	−8.83712	−	15.3063i	−0.308983	−	0.535174i
$819$	18.3489	−	7.19392i	0.641162	−	0.251376i
$820$	−2.37047	+	4.10577i	−0.0827803	+	0.143380i
$821$	−35.1959	+	29.5329i	−1.22835	+	1.03070i	−0.230000	+	0.973191i	$0.573873\pi$
$821$	−35.1959	+	29.5329i	−1.22835	+	1.03070i	−0.998345	+	0.0575134i	$0.981683\pi$
$822$	−28.4565	+	0.349745i	−0.992536	+	0.0121987i
$823$	−1.06228	+	6.02448i	−0.0370287	+	0.210000i	−0.997709	−	0.0676582i	$-0.978447\pi$
$823$	−1.06228	+	6.02448i	−0.0370287	+	0.210000i	0.960680	+	0.277658i	$0.0895584\pi$
$824$	3.15898	−	17.9155i	0.110048	−	0.624115i
$825$	4.01762	+	6.76533i	0.139876	+	0.235539i
$826$	−6.97889	+	5.85598i	−0.242827	+	0.203756i
$827$	14.4460	−	25.0212i	0.502337	−	0.870073i	−0.497660	−	0.867372i	$-0.665807\pi$
$827$	14.4460	−	25.0212i	0.502337	−	0.870073i	0.999996	−	0.00270043i	$-0.000859576\pi$
$828$	27.0965	−	0.666159i	0.941669	−	0.0231506i
$829$	23.2267	+	40.2298i	0.806697	+	1.39724i	0.915139	+	0.403138i	$0.132080\pi$
$829$	23.2267	+	40.2298i	0.806697	+	1.39724i	−0.108442	+	0.994103i	$0.534586\pi$
$830$	−2.99503	−	1.09010i	−0.103959	−	0.0378380i
$831$	−35.1125	−	28.7350i	−1.21804	−	0.996807i
$832$	5.03259	+	4.22284i	0.174474	+	0.146401i
$833$	4.33494	−	1.57779i	0.150197	−	0.0546672i
$834$	−1.12687	−	5.96144i	−0.0390204	−	0.206428i
$835$	1.99838	+	11.3334i	0.0691569	+	0.392208i
$836$	−4.45427			−0.154054
$837$	−34.5993	−	26.9227i	−1.19593	−	0.930586i
$838$	−3.28363			−0.113431
$839$	5.38782	+	30.5558i	0.186008	+	1.05490i	0.924653	+	0.380810i	$0.124355\pi$
$839$	5.38782	+	30.5558i	0.186008	+	1.05490i	−0.738645	+	0.674095i	$0.764534\pi$
$840$	1.35279	−	1.16376i	0.0466758	−	0.0401534i
$841$	27.2350	−	9.91272i	0.939137	−	0.341818i
$842$	27.3078	+	22.9140i	0.941089	+	0.789667i
$843$	3.51248	−	1.32755i	0.120976	−	0.0457231i
$844$	3.56870	+	1.29890i	0.122840	+	0.0447100i
$845$	−15.5361	−	26.9094i	−0.534459	−	0.925710i
$846$	23.4774	−	20.7041i	0.807168	−	0.711823i
$847$	−4.83481	+	8.37414i	−0.166126	+	0.287739i
$848$	−2.80679	+	2.35518i	−0.0963857	+	0.0808772i
$849$	5.53073	−	9.85733i	0.189814	−	0.338303i
$850$	−3.15503	+	17.8931i	−0.108217	+	0.613727i
$851$	−6.98135	+	39.5932i	−0.239318	+	1.35724i
$852$	−12.9263	+	23.0383i	−0.442847	+	0.789277i
$853$	−26.7269	+	22.4265i	−0.915110	+	0.767869i	−0.973084	−	0.230450i	$-0.925980\pi$
$853$	−26.7269	+	22.4265i	−0.915110	+	0.767869i	0.0579742	+	0.998318i	$0.481536\pi$
$854$	3.52924	−	6.11283i	0.120768	−	0.209177i
$855$	−8.95224	+	7.89477i	−0.306160	+	0.269995i
$856$	1.35039	+	2.33894i	0.0461553	+	0.0799434i
$857$	5.06600	+	1.84387i	0.173051	+	0.0629855i	0.427093	−	0.904208i	$-0.359538\pi$
$857$	5.06600	+	1.84387i	0.173051	+	0.0629855i	−0.254042	+	0.967193i	$0.581760\pi$
$858$	12.2770	−	4.64010i	0.419129	−	0.158410i
$859$	−6.09062	−	5.11064i	−0.207809	−	0.174373i	0.532943	−	0.846151i	$-0.321086\pi$
$859$	−6.09062	−	5.11064i	−0.207809	−	0.174373i	−0.740752	+	0.671779i	$0.765531\pi$
$860$	−6.28656	+	2.28812i	−0.214370	+	0.0780243i
$861$	−6.04216	+	5.19784i	−0.205916	+	0.177142i
$862$	−0.106780	−	0.605578i	−0.00363694	−	0.0206261i
$863$	−14.2055			−0.483561			−0.241781	−	0.970331i	$-0.577731\pi$
$863$	−14.2055			−0.483561			−0.241781	+	0.970331i	$0.577731\pi$
$864$	−0.713062	+	5.14699i	−0.0242589	+	0.175104i
$865$	−11.1154			−0.377934
$866$	2.71270	+	15.3845i	0.0921814	+	0.522787i
$867$	1.37728	+	7.28616i	0.0467749	+	0.247451i
$868$	−7.92820	+	2.88563i	−0.269101	+	0.0979446i
$869$	0.787897	+	0.661124i	0.0267276	+	0.0224271i
$870$	0.180862	+	0.148012i	0.00613181	+	0.00501808i
$871$	24.5925	+	8.95092i	0.833284	+	0.303290i
$872$	6.21438	+	10.7636i	0.210445	+	0.364502i
$873$	−20.4640	+	0.503100i	−0.692601	+	0.0170274i
$874$	−17.4455	+	30.2164i	−0.590102	+	1.02209i
$875$	7.05459	−	5.91951i	0.238489	−	0.200116i
$876$	8.97935	+	15.1205i	0.303384	+	0.510873i
$877$	−3.93725	+	22.3292i	−0.132951	+	0.754005i	0.843313	+	0.537423i	$0.180602\pi$
$877$	−3.93725	+	22.3292i	−0.132951	+	0.754005i	−0.976264	+	0.216582i	$0.930509\pi$
$878$	−3.26920	+	18.5406i	−0.110330	+	0.625713i
$879$	−8.68492	+	0.106742i	−0.292935	+	0.00360032i
$880$	0.910318	−	0.763847i	0.0306868	−	0.0257493i
$881$	5.49562	−	9.51869i	0.185152	−	0.320693i	−0.758476	−	0.651701i	$-0.774056\pi$
$881$	5.49562	−	9.51869i	0.185152	−	0.320693i	0.943628	+	0.331009i	$0.107389\pi$
$882$	2.79301	−	1.09504i	0.0940455	−	0.0368718i
$883$	−7.67418	−	13.2921i	−0.258257	−	0.447314i	0.707518	−	0.706695i	$-0.249815\pi$
$883$	−7.67418	−	13.2921i	−0.258257	−	0.447314i	−0.965775	+	0.259381i	$0.916481\pi$
$884$	28.4787	+	10.3654i	0.957844	+	0.348627i
$885$	−2.62605	+	16.0436i	−0.0882738	+	0.539301i
$886$	20.0991	+	16.8651i	0.675242	+	0.566595i
$887$	−40.9884	+	14.9186i	−1.37626	+	0.500916i	−0.921041	−	0.389465i	$-0.872660\pi$
$887$	−40.9884	+	14.9186i	−1.37626	+	0.500916i	−0.455215	+	0.890382i	$0.650438\pi$
$888$	−7.27441	−	2.54687i	−0.244113	−	0.0854673i
$889$	−0.405770	−	2.30124i	−0.0136091	−	0.0771810i
$890$	12.5746			0.421501
$891$	8.27043	+	6.27381i	0.277070	+	0.210181i
$892$	9.22878			0.309002
$893$	6.99709	+	39.6824i	0.234149	+	1.32792i
$894$	7.91102	+	2.76976i	0.264584	+	0.0926345i
$895$	6.41176	−	2.33369i	0.214322	−	0.0780067i
$896$	0.766044	+	0.642788i	0.0255917	+	0.0214740i
$897$	16.6066	−	101.457i	0.554478	−	3.38754i
$898$	12.1622	+	4.42667i	0.405857	+	0.147720i
$899$	−0.552482	−	0.956926i	−0.0184263	−	0.0319153i
$900$	−1.76516	+	11.6830i	−0.0588386	+	0.389434i
$901$	−8.45131	+	14.6381i	−0.281554	+	0.487666i
$902$	−4.06588	+	3.41167i	−0.135379	+	0.113596i
$903$	−11.2461	+	0.138221i	−0.374248	+	0.00459969i
$904$	1.24762	−	7.07561i	0.0414953	−	0.235331i
$905$	2.01650	−	11.4362i	0.0670308	−	0.380151i
$906$	−20.8278	−	35.0723i	−0.691959	−	1.16520i
$907$	15.0900	−	12.6620i	0.501055	−	0.420435i	−0.356913	−	0.934138i	$-0.616171\pi$
$907$	15.0900	−	12.6620i	0.501055	−	0.420435i	0.857969	+	0.513702i	$0.171726\pi$
$908$	−12.9385	+	22.4102i	−0.429380	+	0.743708i
$909$	−10.1527	−	16.6274i	−0.336744	−	0.551495i
$910$	−3.38422	−	5.86164i	−0.112186	−	0.194312i
$911$	52.0843	+	18.9571i	1.72563	+	0.628078i	0.998304	−	0.0582144i	$-0.0185407\pi$
$911$	52.0843	+	18.9571i	1.72563	+	0.628078i	0.727326	+	0.686292i	$0.240763\pi$
$912$	−5.17639	−	4.23620i	−0.171407	−	0.140275i
$913$	−2.73342	−	2.29361i	−0.0904630	−	0.0759075i
$914$	19.8654	−	7.23041i	0.657089	−	0.239161i
$915$	−2.33951	−	12.3766i	−0.0773417	−	0.409157i
$916$	−2.22519	−	12.6197i	−0.0735223	−	0.416966i
$917$	−5.40574			−0.178513
$918$	5.02979	+	23.4370i	0.166008	+	0.773536i
$919$	−56.6733			−1.86948			−0.934740	−	0.355332i	$-0.884368\pi$
$919$	−56.6733			−1.86948			−0.934740	+	0.355332i	$0.884368\pi$
$920$	−1.61639	−	9.16698i	−0.0532907	−	0.302226i
$921$	−34.2530	+	29.4665i	−1.12867	+	0.970955i
$922$	−13.5659	+	4.93759i	−0.446770	+	0.162611i
$923$	76.7558	+	64.4058i	2.52645	+	2.11994i
$924$	1.86876	−	0.706302i	0.0614778	−	0.0232356i
$925$	−16.4690	−	5.99422i	−0.541497	−	0.197089i
$926$	−20.0871	−	34.7918i	−0.660102	−	1.14333i
$927$	−10.7950	−	53.4973i	−0.354555	−	1.75708i
$928$	−0.0654831	+	0.113420i	−0.00214959	+	0.00372320i
$929$	32.9765	−	27.6706i	1.08193	−	0.907843i	0.0858461	−	0.996308i	$-0.472641\pi$
$929$	32.9765	−	27.6706i	1.08193	−	0.907843i	0.996079	+	0.0884653i	$0.0281962\pi$
$930$	−7.36704	+	13.1301i	−0.241575	+	0.430554i
$931$	−0.670593	+	3.80312i	−0.0219778	+	0.124642i
$932$	0.0701563	−	0.397876i	0.00229805	−	0.0130329i
$933$	−2.21927	+	3.95537i	−0.0726558	+	0.129493i
$934$	−21.2866	+	17.8616i	−0.696519	+	0.584448i
$935$	2.74098	−	4.74752i	0.0896398	−	0.155261i
$936$	18.6802	+	6.28357i	0.610582	+	0.205385i
$937$	−1.75121	−	3.03319i	−0.0572096	−	0.0990900i	0.836002	−	0.548726i	$-0.184887\pi$
$937$	−1.75121	−	3.03319i	−0.0572096	−	0.0990900i	−0.893212	+	0.449636i	$0.851554\pi$
$938$	3.74339	+	1.36248i	0.122226	+	0.0444866i
$939$	42.3630	−	16.0111i	1.38246	−	0.522504i
$940$	−8.23499	−	6.90998i	−0.268596	−	0.225379i
$941$	30.1477	−	10.9729i	0.982786	−	0.357705i	0.199863	−	0.979824i	$-0.435950\pi$
$941$	30.1477	−	10.9729i	0.982786	−	0.357705i	0.782923	+	0.622119i	$0.213728\pi$
$942$	15.2578	−	13.1257i	0.497126	−	0.427659i
$943$	7.21948	+	40.9437i	0.235099	+	1.33331i
$944$	−9.11029			−0.296515
$945$	2.50401	−	4.73173i	0.0814553	−	0.153923i
$946$	−7.48968			−0.243511
$947$	1.24418	+	7.05609i	0.0404304	+	0.229292i	0.998327	−	0.0578215i	$-0.0184154\pi$
$947$	1.24418	+	7.05609i	0.0404304	+	0.229292i	−0.957897	+	0.287114i	$0.907304\pi$
$948$	0.286873	+	1.51763i	0.00931719	+	0.0492902i
$949$	62.6790	−	22.8133i	2.03465	−	0.740551i
$950$	−11.6514	−	9.77670i	−0.378022	−	0.317198i
$951$	19.3297	+	15.8189i	0.626810	+	0.512962i
$952$	4.33494	+	1.57779i	0.140496	+	0.0511365i
$953$	28.3993	+	49.1891i	0.919944	+	1.59339i	0.799497	+	0.600671i	$0.205100\pi$
$953$	28.3993	+	49.1891i	0.919944	+	1.59339i	0.120448	+	0.992720i	$0.461567\pi$
$954$	−5.26039	+	9.65158i	−0.170312	+	0.312481i
$955$	−4.52309	+	7.83422i	−0.146364	+	0.253509i
$956$	7.96696	−	6.68507i	0.257670	−	0.216211i
$957$	0.133596	+	0.224964i	0.00431854	+	0.00727205i
$958$	0.453417	−	2.57146i	0.0146493	−	0.0830800i
$959$	−2.85315	+	16.1810i	−0.0921330	+	0.522512i
$960$	1.78435	−	0.0219305i	0.0575895	−	0.000707803i
$961$	30.7821	−	25.8292i	0.992970	−	0.833201i
$962$	−14.6168	+	25.3171i	−0.471265	+	0.816255i
$963$	6.33287	+	5.05396i	0.204074	+	0.162862i
$964$	−5.49921	−	9.52491i	−0.177118	−	0.306777i
$965$	1.97466	+	0.718719i	0.0635667	+	0.0231364i
$966$	2.52780	−	15.4434i	0.0813307	−	0.496883i
$967$	22.9732	+	19.2768i	0.738769	+	0.619901i	0.932507	−	0.361152i	$-0.117617\pi$
$967$	22.9732	+	19.2768i	0.738769	+	0.619901i	−0.193738	+	0.981053i	$0.562061\pi$
$968$	−9.08647	+	3.30721i	−0.292050	+	0.106298i
$969$	−29.1232	−	10.1964i	−0.935571	−	0.327556i
$970$	1.22074	+	6.92314i	0.0391955	+	0.222288i
$971$	−14.8931			−0.477943			−0.238972	−	0.971027i	$-0.576810\pi$
$971$	−14.8931			−0.477943			−0.238972	+	0.971027i	$0.576810\pi$
$972$	3.64455	+	15.1564i	0.116899	+	0.486143i
$973$	−3.50279			−0.112294
$974$	−6.97019	−	39.5299i	−0.223339	−	1.26662i
$975$	42.2985	+	14.8093i	1.35464	+	0.474276i
$976$	6.63281	−	2.41414i	0.212311	−	0.0772749i
$977$	12.0572	+	10.1172i	0.385745	+	0.323678i	0.814953	−	0.579527i	$-0.196763\pi$
$977$	12.0572	+	10.1172i	0.385745	+	0.323678i	−0.429208	+	0.903206i	$0.641207\pi$
$978$	−2.89087	+	17.6615i	−0.0924398	+	0.564753i
$979$	13.2287	+	4.81484i	0.422790	+	0.153883i
$980$	−0.515135	−	0.892241i	−0.0164554	−	0.0285016i
$981$	29.1433	+	23.2579i	0.930476	+	0.742568i
$982$	−6.34717	+	10.9936i	−0.202546	+	0.350820i
$983$	17.4066	−	14.6059i	0.555184	−	0.465854i	−0.321508	−	0.946907i	$-0.604190\pi$
$983$	17.4066	−	14.6059i	0.555184	−	0.465854i	0.876692	+	0.481052i	$0.159745\pi$
$984$	−7.96967	+	0.0979511i	−0.254064	+	0.00312257i
$985$	−3.81723	+	21.6486i	−0.121627	+	0.689780i
$986$	−0.104912	+	0.594988i	−0.00334109	+	0.0189483i
$987$	−9.22792	−	15.5390i	−0.293728	−	0.494612i
$988$	−19.4348	+	16.3077i	−0.618304	+	0.518818i
$989$	−29.3339	+	50.8078i	−0.932763	+	1.61559i
$990$	1.70608	−	3.13026i	0.0542229	−	0.0994862i
$991$	3.69736	+	6.40402i	0.117451	+	0.203430i	0.918757	−	0.394824i	$-0.129194\pi$
$991$	3.69736	+	6.40402i	0.117451	+	0.203430i	−0.801306	+	0.598255i	$0.795861\pi$
$992$	−7.92820	−	2.88563i	−0.251720	−	0.0916188i
$993$	1.02877	+	0.841917i	0.0326471	+	0.0267174i
$994$	11.6835	+	9.80365i	0.370579	+	0.310953i
$995$	4.85664	−	1.76767i	0.153966	−	0.0560390i
$996$	−0.995236	−	5.26504i	−0.0315352	−	0.166829i
$997$	−10.1280	−	57.4385i	−0.320756	−	1.81910i	−0.537961	−	0.842970i	$-0.680805\pi$
$997$	−10.1280	−	57.4385i	−0.320756	−	1.81910i	0.217205	−	0.976126i	$-0.430306\pi$
$998$	21.9599			0.695128
$999$	−23.1064	+	0.852310i	−0.731054	+	0.0269659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.c.337.1	yes	24
27.25	even	9	inner	378.2.u.c.295.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.c.295.1	✓	24	27.25	even	9	inner
378.2.u.c.337.1	yes	24	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-1.63475 - 0.572349i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.789233 + 0.662245i) q^{5} +(-0.279782 + 1.70930i) q^{6} +(0.939693 + 0.342020i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.34483 + 1.87130i) q^{9} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-1.63475 - 0.572349i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.789233 + 0.662245i) q^{5} +(-0.279782 + 1.70930i) q^{6} +(0.939693 + 0.342020i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.34483 + 1.87130i) q^{9} +(0.515135 - 0.892241i) q^{10} +(0.883571 - 0.741404i) q^{11} +(1.73192 - 0.0212861i) q^{12} +(1.14079 - 6.46977i) q^{13} +(0.173648 - 0.984808i) q^{14} +(-0.911165 - 1.53432i) q^{15} +(0.766044 - 0.642788i) q^{16} +(2.30658 - 3.99511i) q^{17} +(1.43569 - 2.63416i) q^{18} +(1.93090 + 3.34441i) q^{19} +(-0.968138 - 0.352373i) q^{20} +(-1.34041 - 1.09695i) q^{21} +(-0.883571 - 0.741404i) q^{22} +(-8.49003 + 3.09012i) q^{23} +(-0.321707 - 1.70191i) q^{24} +(-0.683921 - 3.87871i) q^{25} -6.56958 q^{26} +(-2.76219 - 4.40117i) q^{27} -1.00000 q^{28} +(-0.0227420 - 0.128977i) q^{29} +(-1.35279 + 1.16376i) q^{30} +(7.92820 - 2.88563i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-1.86876 + 0.706302i) q^{33} +(-4.33494 - 1.57779i) q^{34} +(0.515135 + 0.892241i) q^{35} +(-2.84344 - 0.956465i) q^{36} +(2.22493 - 3.85369i) q^{37} +(2.95831 - 2.48231i) q^{38} +(-5.56788 + 9.92354i) q^{39} +(-0.178905 + 1.01462i) q^{40} +(0.799066 - 4.53173i) q^{41} +(-0.847526 + 1.51053i) q^{42} +(4.97428 - 4.17391i) q^{43} +(-0.576710 + 0.998891i) q^{44} +(0.611361 + 3.02975i) q^{45} +(4.51745 + 7.82446i) q^{46} +(9.80491 + 3.56870i) q^{47} +(-1.62019 + 0.612354i) q^{48} +(0.766044 + 0.642788i) q^{49} +(-3.70102 + 1.34706i) q^{50} +(-6.05728 + 5.21084i) q^{51} +(1.14079 + 6.46977i) q^{52} -3.66401 q^{53} +(-3.85466 + 3.48448i) q^{54} +1.18834 q^{55} +(0.173648 + 0.984808i) q^{56} +(-1.24237 - 6.57243i) q^{57} +(-0.123068 + 0.0447931i) q^{58} +(-6.97889 - 5.85598i) q^{59} +(1.38099 + 1.13016i) q^{60} +(6.63281 + 2.41414i) q^{61} +(-4.21851 - 7.30667i) q^{62} +(1.56340 + 2.56043i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(5.18493 - 4.35067i) q^{65} +(1.02008 + 1.71772i) q^{66} +(-0.691750 + 3.92311i) q^{67} +(-0.801065 + 4.54307i) q^{68} +(15.6477 - 0.192318i) q^{69} +(0.789233 - 0.662245i) q^{70} +(-7.62588 + 13.2084i) q^{71} +(-0.448176 + 2.96633i) q^{72} +(5.07655 + 8.79285i) q^{73} +(-4.18149 - 1.52194i) q^{74} +(-1.10193 + 6.73217i) q^{75} +(-2.95831 - 2.48231i) q^{76} +(1.08386 - 0.394493i) q^{77} +(10.7396 + 3.76009i) q^{78} +(0.154845 + 0.878171i) q^{79} +1.03027 q^{80} +(1.99648 + 8.77577i) q^{81} -4.60164 q^{82} +(-0.537199 - 3.04660i) q^{83} +(1.63475 + 0.572349i) q^{84} +(4.46617 - 1.62555i) q^{85} +(-4.97428 - 4.17391i) q^{86} +(-0.0366420 + 0.223861i) q^{87} +(1.08386 + 0.394493i) q^{88} +(6.10257 + 10.5700i) q^{89} +(2.87755 - 1.12818i) q^{90} +(3.28479 - 5.68942i) q^{91} +(6.92114 - 5.80752i) q^{92} +(-14.6122 + 0.179591i) q^{93} +(1.81187 - 10.2757i) q^{94} +(-0.690893 + 3.91825i) q^{95} +(0.884394 + 1.48924i) q^{96} +(-5.22702 + 4.38599i) q^{97} +(0.500000 - 0.866025i) q^{98} +(3.45922 - 0.0850437i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9	\( 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9} + 3 q^{10} - 9 q^{13} - 6 q^{18} + 15 q^{19} - 6 q^{20} - 3 q^{21} + 6 q^{23} + 3 q^{24} + 33 q^{25} + 18 q^{26} - 18 q^{27} - 24 q^{28} - 30 q^{29} + 15 q^{30} - 6 q^{33} - 3 q^{34} + 3 q^{35} - 12 q^{36} - 3 q^{37} + 15 q^{38} - 18 q^{39} - 3 q^{40} + 27 q^{41} + 18 q^{43} - 3 q^{44} + 12 q^{45} + 15 q^{46} + 3 q^{48} + 3 q^{50} + 24 q^{51} - 9 q^{52} + 6 q^{53} + 45 q^{54} - 66 q^{55} - 6 q^{57} + 3 q^{58} - 30 q^{59} - 30 q^{60} - 57 q^{61} - 18 q^{62} + 12 q^{63} - 12 q^{64} + 24 q^{65} - 54 q^{66} + 39 q^{67} + 3 q^{68} + 36 q^{69} + 3 q^{70} - 24 q^{71} - 6 q^{72} + 36 q^{73} - 12 q^{74} + 15 q^{75} - 15 q^{76} - 9 q^{77} + 18 q^{78} - 33 q^{79} + 6 q^{80} + 9 q^{81} - 15 q^{83} + 3 q^{84} + 36 q^{85} - 18 q^{86} - 84 q^{87} - 9 q^{88} - 3 q^{89} - 30 q^{90} - 9 q^{91} - 30 q^{92} - 45 q^{93} + 45 q^{94} + 63 q^{95} - 30 q^{97} + 12 q^{98} - 57 q^{99}+O(q^{100}) \) 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9 + 3 * q^10 - 9 * q^13 - 6 * q^18 + 15 * q^19 - 6 * q^20 - 3 * q^21 + 6 * q^23 + 3 * q^24 + 33 * q^25 + 18 * q^26 - 18 * q^27 - 24 * q^28 - 30 * q^29 + 15 * q^30 - 6 * q^33 - 3 * q^34 + 3 * q^35 - 12 * q^36 - 3 * q^37 + 15 * q^38 - 18 * q^39 - 3 * q^40 + 27 * q^41 + 18 * q^43 - 3 * q^44 + 12 * q^45 + 15 * q^46 + 3 * q^48 + 3 * q^50 + 24 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 - 66 * q^55 - 6 * q^57 + 3 * q^58 - 30 * q^59 - 30 * q^60 - 57 * q^61 - 18 * q^62 + 12 * q^63 - 12 * q^64 + 24 * q^65 - 54 * q^66 + 39 * q^67 + 3 * q^68 + 36 * q^69 + 3 * q^70 - 24 * q^71 - 6 * q^72 + 36 * q^73 - 12 * q^74 + 15 * q^75 - 15 * q^76 - 9 * q^77 + 18 * q^78 - 33 * q^79 + 6 * q^80 + 9 * q^81 - 15 * q^83 + 3 * q^84 + 36 * q^85 - 18 * q^86 - 84 * q^87 - 9 * q^88 - 3 * q^89 - 30 * q^90 - 9 * q^91 - 30 * q^92 - 45 * q^93 + 45 * q^94 + 63 * q^95 - 30 * q^97 + 12 * q^98 - 57 * q^99

Introduction

L-functions

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