LMFDB - Embedded newform 57.2.f.a.8.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,2,Mod(8,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("57.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	57.f (of order $6$, degree $2$, 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:	$0.455147291521$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			8.4
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	57.8
Dual form			57.2.f.a.50.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 1.67303i) q^{2} +(0.158919 + 1.72474i) q^{3} +(-0.866025 - 1.50000i) q^{4} +(-1.22474 - 0.707107i) q^{5} +(3.03906 + 1.40010i) q^{6} -3.73205 q^{7} +0.517638 q^{8} +(-2.94949 + 0.548188i) q^{9} +O(q^{10})$	\(q+(0.965926 - 1.67303i) q^{2} +(0.158919 + 1.72474i) q^{3} +(-0.866025 - 1.50000i) q^{4} +(-1.22474 - 0.707107i) q^{5} +(3.03906 + 1.40010i) q^{6} -3.73205 q^{7} +0.517638 q^{8} +(-2.94949 + 0.548188i) q^{9} +(-2.36603 + 1.36603i) q^{10} +0.378937i q^{11} +(2.44949 - 1.73205i) q^{12} +(3.23205 - 1.86603i) q^{13} +(-3.60488 + 6.24384i) q^{14} +(1.02494 - 2.22474i) q^{15} +(2.23205 - 3.86603i) q^{16} +(4.24264 + 2.44949i) q^{17} +(-1.93185 + 5.46410i) q^{18} +(-1.73205 + 4.00000i) q^{19} +2.44949i q^{20} +(-0.593092 - 6.43684i) q^{21} +(0.633975 + 0.366025i) q^{22} +(0.328169 - 0.189469i) q^{23} +(0.0822623 + 0.892794i) q^{24} +(-1.50000 - 2.59808i) q^{25} -7.20977i q^{26} +(-1.41421 - 5.00000i) q^{27} +(3.23205 + 5.59808i) q^{28} +(-3.86370 - 6.69213i) q^{29} +(-2.73205 - 3.86370i) q^{30} +4.46410i q^{31} +(-3.79435 - 6.57201i) q^{32} +(-0.653570 + 0.0602202i) q^{33} +(8.19615 - 4.73205i) q^{34} +(4.57081 + 2.63896i) q^{35} +(3.37662 + 3.94949i) q^{36} +4.26795i q^{37} +(5.01910 + 6.76148i) q^{38} +(3.73205 + 5.27792i) q^{39} +(-0.633975 - 0.366025i) q^{40} +(-2.82843 + 4.89898i) q^{41} +(-11.3419 - 5.22524i) q^{42} +(-1.13397 + 1.96410i) q^{43} +(0.568406 - 0.328169i) q^{44} +(4.00000 + 1.41421i) q^{45} -0.732051i q^{46} +(9.14162 - 5.27792i) q^{47} +(7.02262 + 3.23533i) q^{48} +6.92820 q^{49} -5.79555 q^{50} +(-3.55051 + 7.70674i) q^{51} +(-5.59808 - 3.23205i) q^{52} +(-3.01790 - 5.22715i) q^{53} +(-9.73119 - 2.46360i) q^{54} +(0.267949 - 0.464102i) q^{55} -1.93185 q^{56} +(-7.17423 - 2.35167i) q^{57} -14.9282 q^{58} +(-4.19187 + 7.26054i) q^{59} +(-4.22474 + 0.389270i) q^{60} +(1.76795 + 3.06218i) q^{61} +(7.46859 + 4.31199i) q^{62} +(11.0076 - 2.04587i) q^{63} -5.73205 q^{64} -5.27792 q^{65} +(-0.530550 + 1.15161i) q^{66} +(0.866025 - 0.500000i) q^{67} -8.48528i q^{68} +(0.378937 + 0.535898i) q^{69} +(8.83013 - 5.09808i) q^{70} +(-1.79315 + 3.10583i) q^{71} +(-1.52677 + 0.283763i) q^{72} +(1.50000 - 2.59808i) q^{73} +(7.14042 + 4.12252i) q^{74} +(4.24264 - 3.00000i) q^{75} +(7.50000 - 0.866025i) q^{76} -1.41421i q^{77} +(12.4350 - 1.14577i) q^{78} +(-3.06218 - 1.76795i) q^{79} +(-5.46739 + 3.15660i) q^{80} +(8.39898 - 3.23375i) q^{81} +(5.46410 + 9.46410i) q^{82} +7.72741i q^{83} +(-9.14162 + 6.46410i) q^{84} +(-3.46410 - 6.00000i) q^{85} +(2.19067 + 3.79435i) q^{86} +(10.9282 - 7.72741i) q^{87} +0.196152i q^{88} +(-3.67423 - 6.36396i) q^{89} +(6.22973 - 5.32611i) q^{90} +(-12.0622 + 6.96410i) q^{91} +(-0.568406 - 0.328169i) q^{92} +(-7.69944 + 0.709429i) q^{93} -20.3923i q^{94} +(4.94975 - 3.67423i) q^{95} +(10.7321 - 7.58871i) q^{96} +(6.46410 + 3.73205i) q^{97} +(6.69213 - 11.5911i) q^{98} +(-0.207729 - 1.11767i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{6} - 16 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^6 - 16 * q^7 - 4 * q^9	$ 8 q + 4 q^{6} - 16 q^{7} - 4 q^{9} - 12 q^{10} + 12 q^{13} + 4 q^{16} - 12 q^{21} + 12 q^{22} + 4 q^{24} - 12 q^{25} + 12 q^{28} - 8 q^{30} + 24 q^{33} + 24 q^{34} + 16 q^{39} - 12 q^{40} - 20 q^{42} - 16 q^{43} + 32 q^{45} + 24 q^{48} - 48 q^{51} - 24 q^{52} - 4 q^{54} + 16 q^{55} - 28 q^{57} - 64 q^{58} - 24 q^{60} + 28 q^{61} + 8 q^{63} - 32 q^{64} - 4 q^{66} + 36 q^{70} - 24 q^{72} + 12 q^{73} + 60 q^{76} + 36 q^{78} + 24 q^{79} + 28 q^{81} + 16 q^{82} + 32 q^{87} + 12 q^{90} - 48 q^{91} - 4 q^{93} + 72 q^{96} + 24 q^{97} - 32 q^{99}+O(q^{100}) $ 8 * q + 4 * q^6 - 16 * q^7 - 4 * q^9 - 12 * q^10 + 12 * q^13 + 4 * q^16 - 12 * q^21 + 12 * q^22 + 4 * q^24 - 12 * q^25 + 12 * q^28 - 8 * q^30 + 24 * q^33 + 24 * q^34 + 16 * q^39 - 12 * q^40 - 20 * q^42 - 16 * q^43 + 32 * q^45 + 24 * q^48 - 48 * q^51 - 24 * q^52 - 4 * q^54 + 16 * q^55 - 28 * q^57 - 64 * q^58 - 24 * q^60 + 28 * q^61 + 8 * q^63 - 32 * q^64 - 4 * q^66 + 36 * q^70 - 24 * q^72 + 12 * q^73 + 60 * q^76 + 36 * q^78 + 24 * q^79 + 28 * q^81 + 16 * q^82 + 32 * q^87 + 12 * q^90 - 48 * q^91 - 4 * q^93 + 72 * q^96 + 24 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.965926	−	1.67303i	0.683013	−	1.18301i	−0.291044	−	0.956710i	$-0.594003\pi$
$2$	0.965926	−	1.67303i	0.683013	−	1.18301i	0.974057	−	0.226303i	$-0.0726640\pi$
$3$	0.158919	+	1.72474i	0.0917517	+	0.995782i
$3$	0.158919	+	1.72474i	0.0917517	+	0.995782i
$4$	−0.866025	−	1.50000i	−0.433013	−	0.750000i
$5$	−1.22474	−	0.707107i	−0.547723	−	0.316228i	0.200480	−	0.979698i	$-0.435750\pi$
$5$	−1.22474	−	0.707107i	−0.547723	−	0.316228i	−0.748203	+	0.663470i	$0.769083\pi$
$6$	3.03906	+	1.40010i	1.24069	+	0.571588i
$7$	−3.73205			−1.41058			−0.705291	−	0.708918i	$-0.749184\pi$
$7$	−3.73205			−1.41058			−0.705291	+	0.708918i	$0.749184\pi$
$8$	0.517638			0.183013
$9$	−2.94949	+	0.548188i	−0.983163	+	0.182729i
$10$	−2.36603	+	1.36603i	−0.748203	+	0.431975i
$11$			0.378937i			0.114254i	0.998367	+	0.0571270i	$0.0181940\pi$
$11$			0.378937i			0.114254i	−0.998367	+	0.0571270i	$0.981806\pi$
$12$	2.44949	−	1.73205i	0.707107	−	0.500000i
$13$	3.23205	−	1.86603i	0.896410	−	0.517542i	0.0203760	−	0.999792i	$-0.493514\pi$
$13$	3.23205	−	1.86603i	0.896410	−	0.517542i	0.876034	+	0.482250i	$0.160180\pi$
$14$	−3.60488	+	6.24384i	−0.963446	+	1.66874i
$15$	1.02494	−	2.22474i	0.264639	−	0.574427i
$16$	2.23205	−	3.86603i	0.558013	−	0.966506i
$17$	4.24264	+	2.44949i	1.02899	+	0.594089i	0.916696	−	0.399586i	$-0.130846\pi$
$17$	4.24264	+	2.44949i	1.02899	+	0.594089i	0.112296	+	0.993675i	$0.464180\pi$
$18$	−1.93185	+	5.46410i	−0.455342	+	1.28790i
$19$	−1.73205	+	4.00000i	−0.397360	+	0.917663i
$19$	−1.73205	+	4.00000i	−0.397360	+	0.917663i
$20$			2.44949i			0.547723i
$21$	−0.593092	−	6.43684i	−0.129423	−	1.40463i
$22$	0.633975	+	0.366025i	0.135164	+	0.0780369i
$23$	0.328169	−	0.189469i	0.0684280	−	0.0395070i	−0.465396	−	0.885103i	$-0.654088\pi$
$23$	0.328169	−	0.189469i	0.0684280	−	0.0395070i	0.533824	+	0.845596i	$0.320755\pi$
$24$	0.0822623	+	0.892794i	0.0167917	+	0.182241i
$25$	−1.50000	−	2.59808i	−0.300000	−	0.519615i
$26$		−	7.20977i		−	1.41395i
$27$	−1.41421	−	5.00000i	−0.272166	−	0.962250i
$28$	3.23205	+	5.59808i	0.610800	+	1.05794i
$29$	−3.86370	−	6.69213i	−0.717472	−	1.24270i	−0.961998	−	0.273055i	$-0.911966\pi$
$29$	−3.86370	−	6.69213i	−0.717472	−	1.24270i	0.244527	−	0.969643i	$-0.421367\pi$
$30$	−2.73205	−	3.86370i	−0.498802	−	0.705412i
$31$			4.46410i			0.801776i	0.916127	+	0.400888i	$0.131298\pi$
$31$			4.46410i			0.801776i	−0.916127	+	0.400888i	$0.868702\pi$
$32$	−3.79435	−	6.57201i	−0.670753	−	1.16178i
$33$	−0.653570	+	0.0602202i	−0.113772	+	0.0104830i
$34$	8.19615	−	4.73205i	1.40563	−	0.811540i
$35$	4.57081	+	2.63896i	0.772608	+	0.446065i
$36$	3.37662	+	3.94949i	0.562769	+	0.658248i
$37$			4.26795i			0.701647i	0.936442	+	0.350823i	$0.114098\pi$
$37$			4.26795i			0.701647i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	5.01910	+	6.76148i	0.814205	+	1.09686i
$39$	3.73205	+	5.27792i	0.597606	+	0.845143i
$40$	−0.633975	−	0.366025i	−0.100240	−	0.0578737i
$41$	−2.82843	+	4.89898i	−0.441726	+	0.765092i	−0.997818	−	0.0660290i	$-0.978967\pi$
$41$	−2.82843	+	4.89898i	−0.441726	+	0.765092i	0.556092	+	0.831121i	$0.312300\pi$
$42$	−11.3419	−	5.22524i	−1.75010	−	0.806272i
$43$	−1.13397	+	1.96410i	−0.172930	+	0.299523i	−0.939443	−	0.342706i	$-0.888657\pi$
$43$	−1.13397	+	1.96410i	−0.172930	+	0.299523i	0.766513	+	0.642228i	$0.221990\pi$
$44$	0.568406	−	0.328169i	0.0856904	−	0.0494734i
$45$	4.00000	+	1.41421i	0.596285	+	0.210819i
$46$		−	0.732051i		−	0.107935i
$47$	9.14162	−	5.27792i	1.33344	−	0.769863i	0.347617	−	0.937637i	$-0.386991\pi$
$47$	9.14162	−	5.27792i	1.33344	−	0.769863i	0.985826	+	0.167773i	$0.0536577\pi$
$48$	7.02262	+	3.23533i	1.01363	+	0.466980i
$49$	6.92820			0.989743
$50$	−5.79555			−0.819615
$51$	−3.55051	+	7.70674i	−0.497171	+	1.07916i
$52$	−5.59808	−	3.23205i	−0.776313	−	0.448205i
$53$	−3.01790	−	5.22715i	−0.414540	−	0.718004i	0.580840	−	0.814018i	$-0.302724\pi$
$53$	−3.01790	−	5.22715i	−0.414540	−	0.718004i	−0.995380	+	0.0960135i	$0.969391\pi$
$54$	−9.73119	−	2.46360i	−1.32425	−	0.335254i
$55$	0.267949	−	0.464102i	0.0361303	−	0.0625794i
$56$	−1.93185			−0.258155
$57$	−7.17423	−	2.35167i	−0.950251	−	0.311486i
$58$	−14.9282			−1.96017
$59$	−4.19187	+	7.26054i	−0.545735	+	0.945241i	0.452825	+	0.891599i	$0.350416\pi$
$59$	−4.19187	+	7.26054i	−0.545735	+	0.945241i	−0.998560	+	0.0536419i	$0.982917\pi$
$60$	−4.22474	+	0.389270i	−0.545412	+	0.0502545i
$61$	1.76795	+	3.06218i	0.226363	+	0.392072i	0.956727	−	0.290986i	$-0.0939832\pi$
$61$	1.76795	+	3.06218i	0.226363	+	0.392072i	−0.730365	+	0.683057i	$0.760650\pi$
$62$	7.46859	+	4.31199i	0.948512	+	0.547623i
$63$	11.0076	−	2.04587i	1.38683	−	0.257755i
$64$	−5.73205			−0.716506
$65$	−5.27792			−0.654645
$66$	−0.530550	+	1.15161i	−0.0653062	+	0.141754i
$67$	0.866025	−	0.500000i	0.105802	−	0.0610847i	−0.446165	−	0.894951i	$-0.647211\pi$
$67$	0.866025	−	0.500000i	0.105802	−	0.0610847i	0.551967	+	0.833866i	$0.313877\pi$
$68$		−	8.48528i		−	1.02899i
$69$	0.378937	+	0.535898i	0.0456187	+	0.0645146i
$70$	8.83013	−	5.09808i	1.05540	−	0.609337i
$71$	−1.79315	+	3.10583i	−0.212808	+	0.368594i	−0.952592	−	0.304250i	$-0.901594\pi$
$71$	−1.79315	+	3.10583i	−0.212808	+	0.368594i	0.739784	+	0.672844i	$0.234928\pi$
$72$	−1.52677	+	0.283763i	−0.179931	+	0.0334418i
$73$	1.50000	−	2.59808i	0.175562	−	0.304082i	−0.764794	−	0.644275i	$-0.777159\pi$
$73$	1.50000	−	2.59808i	0.175562	−	0.304082i	0.940356	+	0.340193i	$0.110493\pi$
$74$	7.14042	+	4.12252i	0.830057	+	0.479233i
$75$	4.24264	−	3.00000i	0.489898	−	0.346410i
$76$	7.50000	−	0.866025i	0.860309	−	0.0993399i
$77$		−	1.41421i		−	0.161165i
$78$	12.4350	−	1.14577i	1.40799	−	0.129733i
$79$	−3.06218	−	1.76795i	−0.344522	−	0.198910i	0.317748	−	0.948175i	$-0.397073\pi$
$79$	−3.06218	−	1.76795i	−0.344522	−	0.198910i	−0.662270	+	0.749265i	$0.730407\pi$
$80$	−5.46739	+	3.15660i	−0.611272	+	0.352918i
$81$	8.39898	−	3.23375i	0.933220	−	0.359306i
$82$	5.46410	+	9.46410i	0.603409	+	1.04514i
$83$			7.72741i			0.848193i	0.905617	+	0.424097i	$0.139408\pi$
$83$			7.72741i			0.848193i	−0.905617	+	0.424097i	$0.860592\pi$
$84$	−9.14162	+	6.46410i	−0.997433	+	0.705291i
$85$	−3.46410	−	6.00000i	−0.375735	−	0.650791i
$86$	2.19067	+	3.79435i	0.236226	+	0.409156i
$87$	10.9282	−	7.72741i	1.17163	−	0.828465i
$88$			0.196152i			0.0209099i
$89$	−3.67423	−	6.36396i	−0.389468	−	0.674579i	0.602910	−	0.797809i	$-0.294008\pi$
$89$	−3.67423	−	6.36396i	−0.389468	−	0.674579i	−0.992378	+	0.123231i	$0.960674\pi$
$90$	6.22973	−	5.32611i	0.656671	−	0.561421i
$91$	−12.0622	+	6.96410i	−1.26446	+	0.730036i
$92$	−0.568406	−	0.328169i	−0.0592604	−	0.0342140i
$93$	−7.69944	+	0.709429i	−0.798394	+	0.0735643i
$94$		−	20.3923i		−	2.10331i
$95$	4.94975	−	3.67423i	0.507833	−	0.376969i
$96$	10.7321	−	7.58871i	1.09534	−	0.774519i
$97$	6.46410	+	3.73205i	0.656330	+	0.378932i	0.790877	−	0.611975i	$-0.209625\pi$
$97$	6.46410	+	3.73205i	0.656330	+	0.378932i	−0.134547	+	0.990907i	$0.542958\pi$
$98$	6.69213	−	11.5911i	0.676007	−	1.17088i
$99$	−0.207729	−	1.11767i	−0.0208775	−	0.112330i
$100$	−2.59808	+	4.50000i	−0.259808	+	0.450000i
$101$	−6.69213	+	3.86370i	−0.665892	+	0.384453i	−0.794518	−	0.607240i	$-0.792277\pi$
$101$	−6.69213	+	3.86370i	−0.665892	+	0.384453i	0.128626	+	0.991693i	$0.458943\pi$
$102$	9.46410	+	13.3843i	0.937086	+	1.32524i
$103$		−	10.4641i		−	1.03106i	−0.856872	−	0.515529i	$-0.827595\pi$
$103$		−	10.4641i		−	1.03106i	0.856872	−	0.515529i	$-0.172405\pi$
$104$	1.67303	−	0.965926i	0.164054	−	0.0947168i
$105$	−3.82514	+	8.30286i	−0.373296	+	0.810276i
$106$	−11.6603			−1.13254
$107$	−4.89898			−0.473602			−0.236801	−	0.971558i	$-0.576099\pi$
$107$	−4.89898			−0.473602			−0.236801	+	0.971558i	$0.576099\pi$
$108$	−6.27526	+	6.45145i	−0.603837	+	0.620791i
$109$	−12.4641	−	7.19615i	−1.19384	−	0.689266i	−0.234668	−	0.972076i	$-0.575400\pi$
$109$	−12.4641	−	7.19615i	−1.19384	−	0.689266i	−0.959176	+	0.282809i	$0.908734\pi$
$110$	−0.517638	−	0.896575i	−0.0493549	−	0.0854851i
$111$	−7.36112	+	0.678257i	−0.698687	+	0.0643773i
$112$	−8.33013	+	14.4282i	−0.787123	+	1.36334i
$113$	18.6622			1.75559			0.877795	−	0.479036i	$-0.159014\pi$
$113$	18.6622			1.75559			0.877795	+	0.479036i	$0.159014\pi$
$114$	−10.8642	+	9.73119i	−1.01753	+	0.911409i
$115$	−0.535898			−0.0499728
$116$	−6.69213	+	11.5911i	−0.621349	+	1.07621i
$117$	−8.50997	+	7.27559i	−0.786747	+	0.672629i
$118$	8.09808	+	14.0263i	0.745488	+	1.29122i
$119$	−15.8338	−	9.14162i	−1.45148	−	0.838011i
$120$	0.530550	−	1.15161i	0.0484324	−	0.105127i
$121$	10.8564			0.986946
$122$	6.83083			0.618434
$123$	−8.89898	−	4.09978i	−0.802394	−	0.369664i
$124$	6.69615	−	3.86603i	0.601332	−	0.347179i
$125$			11.3137i			1.01193i
$126$	7.20977	−	20.3923i	0.642297	−	1.81669i
$127$	6.80385	−	3.92820i	0.603744	−	0.348572i	−0.166769	−	0.985996i	$-0.553333\pi$
$127$	6.80385	−	3.92820i	0.603744	−	0.348572i	0.770513	+	0.637424i	$0.220000\pi$
$128$	2.05197	−	3.55412i	0.181370	−	0.314142i
$129$	−3.56778	−	1.64368i	−0.314126	−	0.144718i
$130$	−5.09808	+	8.83013i	−0.447131	+	0.774453i
$131$	−6.03579	−	3.48477i	−0.527350	−	0.304465i	0.212587	−	0.977142i	$-0.431811\pi$
$131$	−6.03579	−	3.48477i	−0.527350	−	0.304465i	−0.739936	+	0.672677i	$0.765144\pi$
$132$	0.656339	+	0.928203i	0.0571270	+	0.0807897i
$133$	6.46410	−	14.9282i	0.560509	−	1.29444i
$134$		−	1.93185i		−	0.166887i
$135$	−1.80348	+	7.12372i	−0.155219	+	0.613113i
$136$	2.19615	+	1.26795i	0.188319	+	0.108726i
$137$	−0.656339	+	0.378937i	−0.0560748	+	0.0323748i	−0.527775	−	0.849384i	$-0.676974\pi$
$137$	−0.656339	+	0.378937i	−0.0560748	+	0.0323748i	0.471700	+	0.881759i	$0.343640\pi$
$138$	1.26260	−	0.116337i	0.107480	−	0.00990322i
$139$	−6.59808	−	11.4282i	−0.559642	−	0.969328i	−0.997526	−	0.0702964i	$-0.977605\pi$
$139$	−6.59808	−	11.4282i	−0.559642	−	0.969328i	0.437885	−	0.899031i	$-0.355728\pi$
$140$		−	9.14162i		−	0.772608i
$141$	10.5558	+	14.9282i	0.888962	+	1.25718i
$142$	3.46410	+	6.00000i	0.290701	+	0.503509i
$143$	0.707107	+	1.22474i	0.0591312	+	0.102418i
$144$	−4.46410	+	12.6264i	−0.372008	+	1.05220i
$145$			10.9282i			0.907538i
$146$	−2.89778	−	5.01910i	−0.239822	−	0.415383i
$147$	1.10102	+	11.9494i	0.0908106	+	0.985568i
$148$	6.40192	−	3.69615i	0.526235	−	0.303822i
$149$	14.6090	+	8.43451i	1.19682	+	0.690982i	0.959844	−	0.280534i	$-0.0905116\pi$
$149$	14.6090	+	8.43451i	1.19682	+	0.690982i	0.236972	+	0.971516i	$0.423845\pi$
$150$	−0.921022	−	9.99585i	−0.0752011	−	0.816158i
$151$			2.00000i			0.162758i	0.996683	+	0.0813788i	$0.0259324\pi$
$151$			2.00000i			0.162758i	−0.996683	+	0.0813788i	$0.974068\pi$
$152$	−0.896575	+	2.07055i	−0.0727219	+	0.167944i
$153$	−13.8564	−	4.89898i	−1.12022	−	0.396059i
$154$	−2.36603	−	1.36603i	−0.190660	−	0.110077i
$155$	3.15660	−	5.46739i	0.253544	−	0.439151i
$156$	4.68482	−	10.1689i	0.375086	−	0.814162i
$157$	−1.76795	+	3.06218i	−0.141098	+	0.244388i	−0.927910	−	0.372804i	$-0.878397\pi$
$157$	−1.76795	+	3.06218i	−0.141098	+	0.244388i	0.786813	+	0.617192i	$0.211730\pi$
$158$	−5.91567	+	3.41542i	−0.470626	+	0.271716i
$159$	8.53590	−	6.03579i	0.676941	−	0.478669i
$160$			10.7321i			0.848443i
$161$	−1.22474	+	0.707107i	−0.0965234	+	0.0557278i
$162$	2.70262	−	17.1753i	0.212338	−	1.34942i
$163$	5.19615			0.406994			0.203497	−	0.979076i	$-0.434769\pi$
$163$	5.19615			0.406994			0.203497	+	0.979076i	$0.434769\pi$
$164$	9.79796			0.765092
$165$	0.843039	+	0.388390i	0.0656305	+	0.0302361i
$166$	12.9282	+	7.46410i	1.00342	+	0.579327i
$167$	−3.81294	−	6.60420i	−0.295054	−	0.511048i	0.679944	−	0.733264i	$-0.262004\pi$
$167$	−3.81294	−	6.60420i	−0.295054	−	0.511048i	−0.974997	+	0.222216i	$0.928671\pi$
$168$	−0.307007	−	3.33195i	−0.0236861	−	0.257066i
$169$	0.464102	−	0.803848i	0.0357001	−	0.0618344i
$170$	−13.3843			−1.02653
$171$	2.91591	−	12.7474i	0.222985	−	0.974822i
$172$	3.92820			0.299523
$173$	5.93426	−	10.2784i	0.451173	−	0.781455i	−0.547286	−	0.836946i	$-0.684339\pi$
$173$	5.93426	−	10.2784i	0.451173	−	0.781455i	0.998459	+	0.0554909i	$0.0176724\pi$
$174$	−2.37237	−	25.7473i	−0.179849	−	1.95190i
$175$	5.59808	+	9.69615i	0.423175	+	0.732960i
$176$	1.46498	+	0.845807i	0.110427	+	0.0637551i
$177$	−13.1887	−	6.07608i	−0.991326	−	0.456706i
$178$	−14.1962			−1.06405
$179$	1.41421			0.105703			0.0528516	−	0.998602i	$-0.483169\pi$
$179$	1.41421			0.105703			0.0528516	+	0.998602i	$0.483169\pi$
$180$	−1.34278	−	7.22474i	−0.100085	−	0.538501i
$181$	−3.00000	+	1.73205i	−0.222988	+	0.128742i	−0.607333	−	0.794447i	$-0.707761\pi$
$181$	−3.00000	+	1.73205i	−0.222988	+	0.128742i	0.384345	+	0.923190i	$0.374427\pi$
$182$			26.9072i			1.99450i
$183$	−5.00052	+	3.53590i	−0.369649	+	0.261381i
$184$	0.169873	−	0.0980762i	0.0125232	−	0.00723027i
$185$	3.01790	−	5.22715i	0.221880	−	0.384308i
$186$	−6.25019	+	13.5667i	−0.458286	+	0.994756i
$187$	−0.928203	+	1.60770i	−0.0678769	+	0.117566i
$188$	−15.8338	−	9.14162i	−1.15479	−	0.666721i
$189$	5.27792	+	18.6603i	0.383912	+	1.35733i
$190$	−1.36603	−	11.8301i	−0.0991019	−	0.858248i
$191$		−	1.69161i		−	0.122401i	−0.998125	−	0.0612005i	$-0.980507\pi$
$191$		−	1.69161i		−	0.122401i	0.998125	−	0.0612005i	$-0.0194929\pi$
$192$	−0.910930	−	9.88633i	−0.0657407	−	0.713484i
$193$	11.4282	+	6.59808i	0.822620	+	0.474940i	0.851319	−	0.524648i	$-0.175803\pi$
$193$	11.4282	+	6.59808i	0.822620	+	0.474940i	−0.0286991	+	0.999588i	$0.509136\pi$
$194$	12.4877	−	7.20977i	0.896564	−	0.517631i
$195$	−0.838759	−	9.10306i	−0.0600648	−	0.651884i
$196$	−6.00000	−	10.3923i	−0.428571	−	0.742307i
$197$			9.14162i			0.651313i	0.945488	+	0.325657i	$0.105585\pi$
$197$			9.14162i			0.651313i	−0.945488	+	0.325657i	$0.894415\pi$
$198$	−2.07055	−	0.732051i	−0.147148	−	0.0520246i
$199$	6.40192	+	11.0885i	0.453820	+	0.786040i	0.998620	−	0.0525267i	$-0.0167275\pi$
$199$	6.40192	+	11.0885i	0.453820	+	0.786040i	−0.544799	+	0.838567i	$0.683394\pi$
$200$	−0.776457	−	1.34486i	−0.0549038	−	0.0950962i
$201$	1.00000	+	1.41421i	0.0705346	+	0.0997509i
$202$			14.9282i			1.05034i
$203$	14.4195	+	24.9754i	1.01205	+	1.75293i
$204$	14.6349	−	1.34847i	1.02465	−	0.0944117i
$205$	6.92820	−	4.00000i	0.483887	−	0.279372i
$206$	−17.5068	−	10.1075i	−1.21976	−	0.704226i
$207$	−0.864068	+	0.738735i	−0.0600569	+	0.0513456i
$208$		−	16.6603i		−	1.15518i
$209$	−1.51575	−	0.656339i	−0.104847	−	0.0453999i
$210$	10.1962	+	14.4195i	0.703601	+	0.995043i
$211$	−9.52628	−	5.50000i	−0.655816	−	0.378636i	0.134865	−	0.990864i	$-0.456940\pi$
$211$	−9.52628	−	5.50000i	−0.655816	−	0.378636i	−0.790681	+	0.612228i	$0.790273\pi$
$212$	−5.22715	+	9.05369i	−0.359002	+	0.621810i
$213$	−5.64173	−	2.59915i	−0.386565	−	0.178091i
$214$	−4.73205	+	8.19615i	−0.323476	+	0.560277i
$215$	2.77766	−	1.60368i	0.189435	−	0.109370i
$216$	−0.732051	−	2.58819i	−0.0498097	−	0.176104i
$217$		−	16.6603i		−	1.13097i
$218$	−24.0788	+	13.9019i	−1.63082	+	0.941555i
$219$	4.71940	+	2.17423i	0.318907	+	0.146921i
$220$	−0.928203			−0.0625794
$221$	18.2832			1.22986
$222$	−5.97555	+	12.9705i	−0.401053	+	0.870526i
$223$	−8.13397	−	4.69615i	−0.544691	−	0.314478i	0.202287	−	0.979326i	$-0.435163\pi$
$223$	−8.13397	−	4.69615i	−0.544691	−	0.314478i	−0.746978	+	0.664849i	$0.768496\pi$
$224$	14.1607	+	24.5271i	0.946153	+	1.63878i
$225$	5.84847	+	6.84072i	0.389898	+	0.456048i
$226$	18.0263	−	31.2224i	1.19909	−	2.07689i
$227$	−24.5964			−1.63252			−0.816261	−	0.577683i	$-0.803957\pi$
$227$	−24.5964			−1.63252			−0.816261	+	0.577683i	$0.803957\pi$
$228$	2.68556	+	12.7980i	0.177856	+	0.847566i
$229$	9.39230			0.620661			0.310330	−	0.950629i	$-0.399560\pi$
$229$	9.39230			0.620661			0.310330	+	0.950629i	$0.399560\pi$
$230$	−0.517638	+	0.896575i	−0.0341320	+	0.0591184i
$231$	2.43916	−	0.224745i	0.160485	−	0.0147871i
$232$	−2.00000	−	3.46410i	−0.131306	−	0.227429i
$233$	3.10583	+	1.79315i	0.203470	+	0.117473i	0.598273	−	0.801292i	$-0.295854\pi$
$233$	3.10583	+	1.79315i	0.203470	+	0.117473i	−0.394803	+	0.918766i	$0.629187\pi$
$234$	3.95231	+	21.2651i	0.258371	+	1.39015i
$235$	−14.9282			−0.973809
$236$	14.5211			0.945241
$237$	2.56262	−	5.56244i	0.166460	−	0.361319i
$238$	−30.5885	+	17.6603i	−1.98276	+	1.14474i
$239$		−	29.9759i		−	1.93898i	−0.245133	−	0.969489i	$-0.578832\pi$
$239$		−	29.9759i		−	1.93898i	0.245133	−	0.969489i	$-0.421168\pi$
$240$	−6.31319	−	8.92820i	−0.407515	−	0.576313i
$241$	−24.8205	+	14.3301i	−1.59883	+	0.923085i	−0.607116	+	0.794613i	$0.707674\pi$
$241$	−24.8205	+	14.3301i	−1.59883	+	0.923085i	−0.991713	+	0.128472i	$0.958993\pi$
$242$	10.4865	−	18.1631i	0.674097	−	1.16757i
$243$	6.91215	+	13.9722i	0.443415	+	0.896317i
$244$	3.06218	−	5.30385i	0.196036	−	0.339544i
$245$	−8.48528	−	4.89898i	−0.542105	−	0.312984i
$246$	−15.4548	+	10.9282i	−0.985363	+	0.696757i
$247$	1.86603	+	16.1603i	0.118732	+	1.02825i
$248$			2.31079i			0.146735i
$249$	−13.3278	+	1.22803i	−0.844615	+	0.0778232i
$250$	18.9282	+	10.9282i	1.19712	+	0.691160i
$251$	12.7279	−	7.34847i	0.803379	−	0.463831i	−0.0412721	−	0.999148i	$-0.513141\pi$
$251$	12.7279	−	7.34847i	0.803379	−	0.463831i	0.844651	+	0.535317i	$0.179808\pi$
$252$	−12.6017	−	14.7397i	−0.793832	−	0.928514i
$253$	0.0717968	+	0.124356i	0.00451382	+	0.00781817i
$254$		−	15.1774i		−	0.952316i
$255$	9.79796	−	6.92820i	0.613572	−	0.433861i
$256$	−9.69615	−	16.7942i	−0.606010	−	1.04964i
$257$	−1.60368	−	2.77766i	−0.100035	−	0.173266i	0.811664	−	0.584125i	$-0.198562\pi$
$257$	−1.60368	−	2.77766i	−0.100035	−	0.173266i	−0.911699	+	0.410859i	$0.865229\pi$
$258$	−6.19615	+	4.38134i	−0.385756	+	0.272770i
$259$		−	15.9282i		−	0.989730i
$260$	4.57081	+	7.91688i	0.283470	+	0.490984i
$261$	15.0645	+	17.6203i	0.932469	+	1.09067i
$262$	−11.6603	+	6.73205i	−0.720373	+	0.415907i
$263$	0.480473	+	0.277401i	0.0296273	+	0.0171053i	0.514740	−	0.857346i	$-0.327888\pi$
$263$	0.480473	+	0.277401i	0.0296273	+	0.0171053i	−0.485113	+	0.874451i	$0.661222\pi$
$264$	−0.338313	+	0.0311723i	−0.0208217	+	0.00191852i
$265$			8.53590i			0.524356i
$266$	−18.7315	−	25.2342i	−1.14850	−	1.54721i
$267$	10.3923	−	7.34847i	0.635999	−	0.449719i
$268$	−1.50000	−	0.866025i	−0.0916271	−	0.0529009i
$269$	−3.01790	+	5.22715i	−0.184004	+	0.318705i	−0.943241	−	0.332110i	$-0.892239\pi$
$269$	−3.01790	+	5.22715i	−0.184004	+	0.318705i	0.759236	+	0.650815i	$0.225573\pi$
$270$	10.1762	+	9.89828i	0.619303	+	0.602390i
$271$	3.46410	−	6.00000i	0.210429	−	0.364474i	−0.741420	−	0.671042i	$-0.765847\pi$
$271$	3.46410	−	6.00000i	0.210429	−	0.364474i	0.951849	+	0.306568i	$0.0991805\pi$
$272$	18.9396	−	10.9348i	1.14838	−	0.663018i
$273$	−13.9282	−	19.6975i	−0.842973	−	1.19214i
$274$			1.46410i			0.0884496i
$275$	0.984508	−	0.568406i	0.0593681	−	0.0342762i
$276$	0.475678	−	1.03251i	0.0286325	−	0.0621497i
$277$	−9.85641			−0.592214			−0.296107	−	0.955155i	$-0.595689\pi$
$277$	−9.85641			−0.592214			−0.296107	+	0.955155i	$0.595689\pi$
$278$	−25.4930			−1.52897
$279$	−2.44717	−	13.1668i	−0.146508	−	0.788277i
$280$	2.36603	+	1.36603i	0.141397	+	0.0816356i
$281$	7.53794	+	13.0561i	0.449676	+	0.778861i	0.998365	−	0.0571654i	$-0.0182062\pi$
$281$	7.53794	+	13.0561i	0.449676	+	0.778861i	−0.548689	+	0.836027i	$0.684873\pi$
$282$	35.1715	−	3.24072i	2.09443	−	0.192982i
$283$	10.9282	−	18.9282i	0.649614	−	1.12516i	−0.333601	−	0.942714i	$-0.608264\pi$
$283$	10.9282	−	18.9282i	0.649614	−	1.12516i	0.983215	−	0.182450i	$-0.0584029\pi$
$284$	6.21166			0.368594
$285$	7.12372	+	7.95315i	0.421973	+	0.471104i
$286$	2.73205			0.161550
$287$	10.5558	−	18.2832i	0.623091	−	1.07923i
$288$	14.7941	+	17.3041i	0.871751	+	1.01965i
$289$	3.50000	+	6.06218i	0.205882	+	0.356599i
$290$	18.2832	+	10.5558i	1.07363	+	0.619860i
$291$	−5.40957	+	11.7420i	−0.317115	+	0.688329i
$292$	−5.19615			−0.304082
$293$	−25.2528			−1.47528			−0.737641	−	0.675193i	$-0.764060\pi$
$293$	−25.2528			−1.47528			−0.737641	+	0.675193i	$0.764060\pi$
$294$	21.0552	+	9.70017i	1.22796	+	0.565726i
$295$	10.2679	−	5.92820i	0.597823	−	0.345153i
$296$			2.20925i			0.128410i
$297$	1.89469	−	0.535898i	0.109941	−	0.0310960i
$298$	28.2224	−	16.2942i	1.63488	−	0.943899i
$299$	0.707107	−	1.22474i	0.0408930	−	0.0708288i
$300$	−8.17423	−	3.76588i	−0.471940	−	0.217423i
$301$	4.23205	−	7.33013i	0.243931	−	0.422501i
$302$	3.34607	+	1.93185i	0.192544	+	0.111166i
$303$	−7.72741	−	10.9282i	−0.443928	−	0.627809i
$304$	11.5981	+	15.6244i	0.665195	+	0.896118i
$305$		−	5.00052i		−	0.286329i
$306$	−21.5804	+	18.4502i	−1.23367	+	1.05473i
$307$	−12.0000	−	6.92820i	−0.684876	−	0.395413i	0.116814	−	0.993154i	$-0.462732\pi$
$307$	−12.0000	−	6.92820i	−0.684876	−	0.395413i	−0.801690	+	0.597740i	$0.796065\pi$
$308$	−2.12132	+	1.22474i	−0.120873	+	0.0697863i
$309$	18.0479	−	1.66294i	1.02671	−	0.0946014i
$310$	−6.09808	−	10.5622i	−0.346347	−	0.599891i
$311$			27.1475i			1.53939i	0.638411	+	0.769696i	$0.279592\pi$
$311$			27.1475i			1.53939i	−0.638411	+	0.769696i	$0.720408\pi$
$312$	1.93185	+	2.73205i	0.109370	+	0.154672i
$313$	12.3923	+	21.4641i	0.700454	+	1.21322i	0.968307	+	0.249763i	$0.0803527\pi$
$313$	12.3923	+	21.4641i	0.700454	+	1.21322i	−0.267853	+	0.963460i	$0.586314\pi$
$314$	3.41542	+	5.91567i	0.192743	+	0.333841i
$315$	−14.9282	−	5.27792i	−0.841109	−	0.297377i
$316$			6.12436i			0.344522i
$317$	6.88160	+	11.9193i	0.386509	+	0.669453i	0.991977	−	0.126416i	$-0.0403474\pi$
$317$	6.88160	+	11.9193i	0.386509	+	0.669453i	−0.605468	+	0.795870i	$0.707014\pi$
$318$	−1.85303	−	20.1110i	−0.103913	−	1.12777i
$319$	2.53590	−	1.46410i	0.141983	−	0.0819740i
$320$	7.02030	+	4.05317i	0.392447	+	0.226579i
$321$	−0.778539	−	8.44949i	−0.0434538	−	0.471605i
$322$			2.73205i			0.152251i
$323$	−17.1464	+	12.7279i	−0.954053	+	0.708201i
$324$	−12.1244	−	9.79796i	−0.673575	−	0.544331i
$325$	−9.69615	−	5.59808i	−0.537846	−	0.310525i
$326$	5.01910	−	8.69333i	0.277982	−	0.481479i
$327$	10.4307	−	22.6410i	0.576822	−	1.25205i
$328$	−1.46410	+	2.53590i	−0.0808415	+	0.140022i
$329$	−34.1170	+	19.6975i	−1.88093	+	1.08596i
$330$	1.46410	−	1.03528i	0.0805961	−	0.0569901i
$331$			31.9282i			1.75493i	0.479638	+	0.877466i	$0.340768\pi$
$331$			31.9282i			1.75493i	−0.479638	+	0.877466i	$0.659232\pi$
$332$	11.5911	−	6.69213i	0.636145	−	0.367278i
$333$	−2.33964	−	12.5883i	−0.128211	−	0.689833i
$334$	−14.7321			−0.806102
$335$	−1.41421			−0.0772667
$336$	−26.2088	−	12.0744i	−1.42981	−	0.658714i
$337$	6.35641	+	3.66987i	0.346256	+	0.199911i	0.663035	−	0.748589i	$-0.269268\pi$
$337$	6.35641	+	3.66987i	0.346256	+	0.199911i	−0.316779	+	0.948499i	$0.602601\pi$
$338$	−0.896575	−	1.55291i	−0.0487673	−	0.0844674i
$339$	2.96577	+	32.1875i	0.161078	+	1.74818i
$340$	−6.00000	+	10.3923i	−0.325396	+	0.563602i
$341$	−1.69161			−0.0916061
$342$	−18.5103	−	17.1915i	−1.00092	−	0.929610i
$343$	0.267949			0.0144679
$344$	−0.586988	+	1.01669i	−0.0316483	+	0.0548165i
$345$	−0.0851642	−	0.924288i	−0.00458509	−	0.0497620i
$346$	−11.4641	−	19.8564i	−0.616314	−	1.06749i
$347$	−21.5414	−	12.4369i	−1.15640	−	0.667649i	−0.205963	−	0.978560i	$-0.566032\pi$
$347$	−21.5414	−	12.4369i	−1.15640	−	0.667649i	−0.950439	+	0.310911i	$0.899366\pi$
$348$	−21.0552	−	9.70017i	−1.12868	−	0.519984i
$349$	−11.3923			−0.609816			−0.304908	−	0.952382i	$-0.598626\pi$
$349$	−11.3923			−0.609816			−0.304908	+	0.952382i	$0.598626\pi$
$350$	21.6293			1.15614
$351$	−13.9009	−	13.5213i	−0.741977	−	0.721713i
$352$	2.49038	−	1.43782i	0.132738	−	0.0766362i
$353$		−	11.9700i		−	0.637101i	−0.947906	−	0.318551i	$-0.896804\pi$
$353$		−	11.9700i		−	0.637101i	0.947906	−	0.318551i	$-0.103196\pi$
$354$	−22.9048	+	16.1962i	−1.21738	+	0.860816i
$355$	4.39230	−	2.53590i	0.233119	−	0.134592i
$356$	−6.36396	+	11.0227i	−0.337289	+	0.584202i
$357$	13.2507	−	28.7620i	0.701301	−	1.52224i
$358$	1.36603	−	2.36603i	0.0721967	−	0.125048i
$359$	23.1822	+	13.3843i	1.22351	+	0.706394i	0.965665	−	0.259792i	$-0.0836539\pi$
$359$	23.1822	+	13.3843i	1.22351	+	0.706394i	0.257846	+	0.966186i	$0.416987\pi$
$360$	2.07055	+	0.732051i	0.109128	+	0.0385825i
$361$	−13.0000	−	13.8564i	−0.684211	−	0.729285i
$362$			6.69213i			0.351731i
$363$	1.72529	+	18.7245i	0.0905540	+	0.982783i
$364$	20.8923	+	12.0622i	1.09505	+	0.632230i
$365$	−3.67423	+	2.12132i	−0.192318	+	0.111035i
$366$	1.08555	+	11.7814i	0.0567424	+	0.615826i
$367$	8.52628	+	14.7679i	0.445068	+	0.770881i	0.998057	−	0.0623080i	$-0.0198461\pi$
$367$	8.52628	+	14.7679i	0.445068	+	0.770881i	−0.552989	+	0.833189i	$0.686513\pi$
$368$		−	1.69161i		−	0.0881815i
$369$	5.65685	−	16.0000i	0.294484	−	0.832927i
$370$	−5.83013	−	10.0981i	−0.303094	−	0.524974i
$371$	11.2629	+	19.5080i	0.584743	+	1.01280i
$372$	7.73205	+	10.9348i	0.400888	+	0.566941i
$373$			12.5359i			0.649084i	0.945871	+	0.324542i	$0.105210\pi$
$373$			12.5359i			0.649084i	−0.945871	+	0.324542i	$0.894790\pi$
$374$	1.79315	+	3.10583i	0.0927216	+	0.160599i
$375$	−19.5133	+	1.79796i	−1.00766	+	0.0928462i
$376$	4.73205	−	2.73205i	0.244037	−	0.140895i
$377$	−24.9754	−	14.4195i	−1.28630	−	0.742644i
$378$	36.3173	+	9.19429i	1.86796	+	0.472903i
$379$			17.7846i			0.913534i	0.889586	+	0.456767i	$0.150993\pi$
$379$			17.7846i			0.913534i	−0.889586	+	0.456767i	$0.849007\pi$
$380$	−9.79796	−	4.24264i	−0.502625	−	0.217643i
$381$	7.85641	+	11.1106i	0.402496	+	0.569215i
$382$	−2.83013	−	1.63397i	−0.144802	−	0.0836014i
$383$	−13.3335	+	23.0943i	−0.681310	+	1.18006i	0.293272	+	0.956029i	$0.405256\pi$
$383$	−13.3335	+	23.0943i	−0.681310	+	1.18006i	−0.974581	+	0.224034i	$0.928077\pi$
$384$	6.45604	+	2.97431i	0.329458	+	0.151782i
$385$	−1.00000	+	1.73205i	−0.0509647	+	0.0882735i
$386$	22.0776	−	12.7465i	1.12372	−	0.648780i
$387$	2.26795	−	6.41473i	0.115286	−	0.326079i
$388$		−	12.9282i		−	0.656330i
$389$	−4.33057	+	2.50026i	−0.219569	+	0.126768i	−0.605751	−	0.795655i	$-0.707127\pi$
$389$	−4.33057	+	2.50026i	−0.219569	+	0.126768i	0.386182	+	0.922423i	$0.373794\pi$
$390$	−16.0399	−	7.38961i	−0.812212	−	0.374187i
$391$	1.85641			0.0938825
$392$	3.58630			0.181136
$393$	5.05113	−	10.9640i	0.254796	−	0.553060i
$394$	15.2942	+	8.83013i	0.770512	+	0.444855i
$395$	2.50026	+	4.33057i	0.125802	+	0.217895i
$396$	−1.49661	+	1.27953i	−0.0752074	+	0.0642986i
$397$	−4.16025	+	7.20577i	−0.208797	+	0.361647i	−0.951336	−	0.308156i	$-0.900288\pi$
$397$	−4.16025	+	7.20577i	−0.208797	+	0.361647i	0.742539	+	0.669803i	$0.233622\pi$
$398$	24.7351			1.23986
$399$	26.7746	+	8.77656i	1.34041	+	0.439377i
$400$	−13.3923			−0.669615
$401$	5.74479	−	9.95026i	0.286881	−	0.496892i	−0.686183	−	0.727429i	$-0.740715\pi$
$401$	5.74479	−	9.95026i	0.286881	−	0.496892i	0.973064	+	0.230537i	$0.0740482\pi$
$402$	3.33195	−	0.307007i	0.166183	−	0.0153121i
$403$	8.33013	+	14.4282i	0.414953	+	0.718720i
$404$	11.5911	+	6.69213i	0.576679	+	0.332946i
$405$	−12.5732	−	1.97846i	−0.624768	−	0.0983103i
$406$	55.7128			2.76498
$407$	−1.61729			−0.0801659
$408$	−1.83788	+	3.98930i	−0.0909886	+	0.197500i
$409$	24.4641	−	14.1244i	1.20967	−	0.698404i	0.246984	−	0.969019i	$-0.420560\pi$
$409$	24.4641	−	14.1244i	1.20967	−	0.698404i	0.962688	+	0.270615i	$0.0872270\pi$
$410$		−	15.4548i		−	0.763259i
$411$	−0.757875	−	1.07180i	−0.0373832	−	0.0528678i
$412$	−15.6962	+	9.06218i	−0.773294	+	0.446461i
$413$	15.6443	−	27.0967i	0.769805	−	1.33334i
$414$	0.401302	+	2.15918i	0.0197229	+	0.106118i
$415$	5.46410	−	9.46410i	0.268222	−	0.464574i
$416$	−24.5271	−	14.1607i	−1.20254	−	0.694286i
$417$	18.6622	−	13.1962i	0.913891	−	0.646218i
$418$	−2.56218	+	1.90192i	−0.125320	+	0.0930261i
$419$		−	32.0464i		−	1.56557i	−0.622292	−	0.782785i	$-0.713798\pi$
$419$		−	32.0464i		−	1.56557i	0.622292	−	0.782785i	$-0.286202\pi$
$420$	15.7670	−	1.45277i	0.769349	−	0.0708881i
$421$	−30.7128	−	17.7321i	−1.49685	−	0.864207i	−0.496857	−	0.867832i	$-0.665513\pi$
$421$	−30.7128	−	17.7321i	−1.49685	−	0.864207i	−0.999993	+	0.00362487i	$0.998846\pi$
$422$	−18.4034	+	10.6252i	−0.895861	+	0.517226i
$423$	−24.0698	+	20.5785i	−1.17031	+	1.00056i
$424$	−1.56218	−	2.70577i	−0.0758661	−	0.131404i
$425$		−	14.6969i		−	0.712906i
$426$	−9.79796	+	6.92820i	−0.474713	+	0.335673i
$427$	−6.59808	−	11.4282i	−0.319303	−	0.553050i
$428$	4.24264	+	7.34847i	0.205076	+	0.355202i
$429$	−2.00000	+	1.41421i	−0.0965609	+	0.0682789i
$430$		−	6.19615i		−	0.298805i
$431$	−12.7279	−	22.0454i	−0.613082	−	1.06189i	−0.990718	−	0.135935i	$-0.956596\pi$
$431$	−12.7279	−	22.0454i	−0.613082	−	1.06189i	0.377635	−	0.925954i	$-0.376737\pi$
$432$	−22.4867	−	5.69287i	−1.08189	−	0.273898i
$433$	2.89230	−	1.66987i	0.138995	−	0.0802490i	−0.428890	−	0.903357i	$-0.641095\pi$
$433$	2.89230	−	1.66987i	0.138995	−	0.0802490i	0.567885	+	0.823108i	$0.307762\pi$
$434$	−27.8731	−	16.0926i	−1.33795	−	0.772468i
$435$	−18.8484	+	1.73670i	−0.903710	+	0.0832682i
$436$			24.9282i			1.19384i
$437$	0.189469	+	1.64085i	0.00906352	+	0.0784924i
$438$	8.19615	−	5.79555i	0.391627	−	0.276922i
$439$	19.4545	+	11.2321i	0.928512	+	0.536077i	0.886341	−	0.463034i	$-0.153239\pi$
$439$	19.4545	+	11.2321i	0.928512	+	0.536077i	0.0421712	+	0.999110i	$0.486573\pi$
$440$	0.138701	−	0.240237i	0.00661230	−	0.0114528i
$441$	−20.4347	+	3.79796i	−0.973079	+	0.180855i
$442$	17.6603	−	30.5885i	0.840013	−	1.45494i
$443$	33.4607	−	19.3185i	1.58976	−	0.917850i	0.596419	−	0.802674i	$-0.296590\pi$
$443$	33.4607	−	19.3185i	1.58976	−	0.917850i	0.993345	−	0.115177i	$-0.0367435\pi$
$444$	7.39230	+	10.4543i	0.350823	+	0.496139i
$445$			10.3923i			0.492642i
$446$	−15.7136	+	9.07227i	−0.744062	+	0.429584i
$447$	−12.2257	+	26.5372i	−0.578258	+	1.25517i
$448$	21.3923			1.01069
$449$	34.4959			1.62796			0.813982	−	0.580890i	$-0.197296\pi$
$449$	34.4959			1.62796			0.813982	+	0.580890i	$0.197296\pi$
$450$	17.0939	−	3.17705i	0.805816	−	0.149768i
$451$	−1.85641	−	1.07180i	−0.0874148	−	0.0504689i
$452$	−16.1619	−	27.9933i	−0.760193	−	1.31669i
$453$	−3.44949	+	0.317837i	−0.162071	+	0.0149333i
$454$	−23.7583	+	41.1506i	−1.11503	+	1.93129i
$455$	19.6975			0.923431
$456$	−3.71366	−	1.21731i	−0.173908	−	0.0570060i
$457$	−20.7128			−0.968905			−0.484452	−	0.874818i	$-0.660981\pi$
$457$	−20.7128			−0.968905			−0.484452	+	0.874818i	$0.660981\pi$
$458$	9.07227	−	15.7136i	0.423919	−	0.734250i
$459$	6.24745	−	24.6773i	0.291606	−	1.15184i
$460$	0.464102	+	0.803848i	0.0216388	+	0.0374796i
$461$	28.4737	+	16.4393i	1.32615	+	0.765656i	0.984703	−	0.174244i	$-0.0557481\pi$
$461$	28.4737	+	16.4393i	1.32615	+	0.765656i	0.341452	+	0.939899i	$0.389081\pi$
$462$	1.98004	−	4.29788i	0.0921198	−	0.199955i
$463$	−29.5885			−1.37509			−0.687546	−	0.726141i	$-0.741312\pi$
$463$	−29.5885			−1.37509			−0.687546	+	0.726141i	$0.741312\pi$
$464$	−34.4959			−1.60143
$465$	9.93149	+	4.57545i	0.460562	+	0.212182i
$466$	6.00000	−	3.46410i	0.277945	−	0.160471i
$467$			22.6274i			1.04707i	0.852004	+	0.523536i	$0.175387\pi$
$467$			22.6274i			1.04707i	−0.852004	+	0.523536i	$0.824613\pi$
$468$	18.2832	+	6.46410i	0.845143	+	0.298803i
$469$	−3.23205	+	1.86603i	−0.149242	+	0.0861650i
$470$	−14.4195	+	24.9754i	−0.665124	+	1.15203i
$471$	−5.56244	−	2.56262i	−0.256304	−	0.118079i
$472$	−2.16987	+	3.75833i	−0.0998765	+	0.172991i
$473$	−0.744272	−	0.429705i	−0.0342216	−	0.0197579i
$474$	−6.83083	−	9.66025i	−0.313750	−	0.443710i
$475$	12.9904	−	1.50000i	0.596040	−	0.0688247i
$476$			31.6675i			1.45148i
$477$	11.7667	+	13.7630i	0.538761	+	0.630167i
$478$	−50.1506	−	28.9545i	−2.29384	−	1.32435i
$479$	−10.2784	+	5.93426i	−0.469634	+	0.271143i	−0.716086	−	0.698012i	$-0.754068\pi$
$479$	−10.2784	+	5.93426i	−0.469634	+	0.271143i	0.246453	+	0.969155i	$0.420735\pi$
$480$	−18.5100	+	1.70552i	−0.844864	+	0.0778461i
$481$	7.96410	+	13.7942i	0.363132	+	0.628963i
$482$			55.3674i			2.52191i
$483$	−1.41421	−	2.00000i	−0.0643489	−	0.0910032i
$484$	−9.40192	−	16.2846i	−0.427360	−	0.740210i
$485$	−5.27792	−	9.14162i	−0.239658	−	0.415100i
$486$	30.0526	+	1.93185i	1.36321	+	0.0876306i
$487$		−	24.9282i		−	1.12960i	−0.825226	−	0.564802i	$-0.808952\pi$
$487$		−	24.9282i		−	1.12960i	0.825226	−	0.564802i	$-0.191048\pi$
$488$	0.915158	+	1.58510i	0.0414272	+	0.0717541i
$489$	0.825765	+	8.96204i	0.0373424	+	0.405277i
$490$	−16.3923	+	9.46410i	−0.740529	+	0.427545i
$491$	8.66115	+	5.00052i	0.390872	+	0.225670i	0.682538	−	0.730850i	$-0.260876\pi$
$491$	8.66115	+	5.00052i	0.390872	+	0.225670i	−0.291666	+	0.956520i	$0.594210\pi$
$492$	1.55708	+	16.8990i	0.0701985	+	0.761865i
$493$		−	37.8564i		−	1.70497i
$494$	28.8391	+	12.4877i	1.29753	+	0.561848i
$495$	−0.535898	+	1.51575i	−0.0240868	+	0.0681279i
$496$	17.2583	+	9.96410i	0.774922	+	0.447401i
$497$	6.69213	−	11.5911i	0.300183	−	0.519932i
$498$	−10.8191	+	23.4840i	−0.484817	+	1.05234i
$499$	8.06218	−	13.9641i	0.360913	−	0.625119i	−0.627199	−	0.778859i	$-0.715799\pi$
$499$	8.06218	−	13.9641i	0.360913	−	0.625119i	0.988111	+	0.153740i	$0.0491319\pi$
$500$	16.9706	−	9.79796i	0.758947	−	0.438178i
$501$	10.7846	−	7.62587i	0.481821	−	0.340699i
$502$		−	28.3923i		−	1.26721i
$503$	−15.8338	+	9.14162i	−0.705992	+	0.407605i	−0.809575	−	0.587016i	$-0.800303\pi$
$503$	−15.8338	+	9.14162i	−0.705992	+	0.407605i	0.103583	+	0.994621i	$0.466969\pi$
$504$	5.69798	−	1.05902i	0.253808	−	0.0471724i
$505$	10.9282			0.486299
$506$	0.277401			0.0123320
$507$	1.46019	+	0.672711i	0.0648492	+	0.0298761i
$508$	−11.7846	−	6.80385i	−0.522858	−	0.301872i
$509$	−6.79367	−	11.7670i	−0.301124	−	0.521562i	0.675267	−	0.737574i	$-0.264028\pi$
$509$	−6.79367	−	11.7670i	−0.301124	−	0.521562i	−0.976391	+	0.216011i	$0.930695\pi$
$510$	−2.12701	−	23.0844i	−0.0941855	−	1.02220i
$511$	−5.59808	+	9.69615i	−0.247644	+	0.428933i
$512$	−29.2552			−1.29291
$513$	22.4495	+	3.00340i	0.991169	+	0.132603i
$514$	−6.19615			−0.273301
$515$	−7.39924	+	12.8159i	−0.326049	+	0.564734i
$516$	0.624265	+	6.77515i	0.0274817	+	0.298259i
$517$	2.00000	+	3.46410i	0.0879599	+	0.152351i
$518$	−26.6484	−	15.3855i	−1.17086	−	0.675998i
$519$	18.6707	+	8.60164i	0.819554	+	0.377570i
$520$	−2.73205			−0.119808
$521$	−4.52004			−0.198027			−0.0990133	−	0.995086i	$-0.531569\pi$
$521$	−4.52004			−0.198027			−0.0990133	+	0.995086i	$0.531569\pi$
$522$	44.0306	−	8.18346i	1.92717	−	0.358180i
$523$	−14.5981	+	8.42820i	−0.638329	+	0.368540i	−0.783971	−	0.620798i	$-0.786809\pi$
$523$	−14.5981	+	8.42820i	−0.638329	+	0.368540i	0.145641	+	0.989337i	$0.453475\pi$
$524$			12.0716i			0.527350i
$525$	−15.8338	+	11.1962i	−0.691042	+	0.488640i
$526$	0.928203	−	0.535898i	0.0404716	−	0.0233663i
$527$	−10.9348	+	18.9396i	−0.476326	+	0.825021i
$528$	−1.22599	+	2.66113i	−0.0533543	+	0.115811i
$529$	−11.4282	+	19.7942i	−0.496878	+	0.860619i
$530$	14.2808	+	8.24504i	0.620320	+	0.358142i
$531$	8.38375	−	23.7128i	0.363824	−	1.02905i
$532$	−27.9904	+	3.23205i	−1.21354	+	0.140127i
$533$			21.1117i			0.914448i
$534$	−2.25603	−	24.4847i	−0.0976281	−	1.05956i
$535$	6.00000	+	3.46410i	0.259403	+	0.149766i
$536$	0.448288	−	0.258819i	0.0193631	−	0.0111793i
$537$	0.224745	+	2.43916i	0.00969846	+	0.105257i
$538$	5.83013	+	10.0981i	0.251355	+	0.435359i
$539$			2.62536i			0.113082i
$540$	12.2474	−	3.46410i	0.527046	−	0.149071i
$541$	8.76795	+	15.1865i	0.376964	+	0.652920i	0.990619	−	0.136654i	$-0.0436349\pi$
$541$	8.76795	+	15.1865i	0.376964	+	0.652920i	−0.613655	+	0.789574i	$0.710302\pi$
$542$	−6.69213	−	11.5911i	−0.287452	−	0.497881i
$543$	−3.46410	−	4.89898i	−0.148659	−	0.210235i
$544$		−	37.1769i		−	1.59395i
$545$	10.1769	+	17.6269i	0.435930	+	0.755054i
$546$	−46.4081	+	4.27606i	−1.98608	+	0.182998i
$547$	−11.1340	+	6.42820i	−0.476054	+	0.274850i	−0.718771	−	0.695247i	$-0.755295\pi$
$547$	−11.1340	+	6.42820i	−0.476054	+	0.274850i	0.242716	+	0.970097i	$0.421962\pi$
$548$	1.13681	+	0.656339i	0.0485622	+	0.0280374i
$549$	−6.89320	−	8.06269i	−0.294195	−	0.344107i
$550$		−	2.19615i		−	0.0936443i
$551$	33.4607	−	3.86370i	1.42547	−	0.164599i
$552$	0.196152	+	0.277401i	0.00834880	+	0.0118070i
$553$	11.4282	+	6.59808i	0.485977	+	0.280579i
$554$	−9.52056	+	16.4901i	−0.404490	+	0.700597i
$555$	9.49510	+	4.37441i	0.403044	+	0.185683i
$556$	−11.4282	+	19.7942i	−0.484664	+	0.839462i
$557$	−2.92996	+	1.69161i	−0.124147	+	0.0716760i	−0.560787	−	0.827960i	$-0.689501\pi$
$557$	−2.92996	+	1.69161i	−0.124147	+	0.0716760i	0.436641	+	0.899636i	$0.356168\pi$
$558$	−24.3923	−	8.62398i	−1.03261	−	0.365082i
$559$			8.46410i			0.357993i
$560$	20.4046	−	11.7806i	0.862250	−	0.497820i
$561$	−2.92037	−	1.34542i	−0.123298	−	0.0568037i
$562$	29.1244			1.22854
$563$	3.38323			0.142586			0.0712931	−	0.997455i	$-0.477287\pi$
$563$	3.38323			0.142586			0.0712931	+	0.997455i	$0.477287\pi$
$564$	13.2507	−	28.7620i	0.557954	−	1.21110i
$565$	−22.8564	−	13.1962i	−0.961576	−	0.555166i
$566$	−21.1117	−	36.5665i	−0.887390	−	1.53700i
$567$	−31.3454	+	12.0685i	−1.31638	+	0.506830i
$568$	−0.928203	+	1.60770i	−0.0389465	+	0.0674574i
$569$	−13.9391			−0.584356			−0.292178	−	0.956364i	$-0.594380\pi$
$569$	−13.9391			−0.584356			−0.292178	+	0.956364i	$0.594380\pi$
$570$	20.1869	−	4.23607i	0.845535	−	0.177430i
$571$	25.1962			1.05443			0.527213	−	0.849733i	$-0.323237\pi$
$571$	25.1962			1.05443			0.527213	+	0.849733i	$0.323237\pi$
$572$	1.22474	−	2.12132i	0.0512092	−	0.0886969i
$573$	2.91760	−	0.268829i	0.121885	−	0.0112305i
$574$	−20.3923	−	35.3205i	−0.851158	−	1.47425i
$575$	−0.984508	−	0.568406i	−0.0410568	−	0.0237042i
$576$	16.9066	−	3.14224i	0.704443	−	0.130927i
$577$	42.9282			1.78712			0.893562	−	0.448939i	$-0.148198\pi$
$577$	42.9282			1.78712			0.893562	+	0.448939i	$0.148198\pi$
$578$	13.5230			0.562481
$579$	−9.56384	+	20.7593i	−0.397460	+	0.862727i
$580$	16.3923	−	9.46410i	0.680653	−	0.392975i
$581$		−	28.8391i		−	1.19645i
$582$	14.4195	+	20.3923i	0.597709	+	0.845288i
$583$	1.98076	−	1.14359i	0.0820348	−	0.0473628i
$584$	0.776457	−	1.34486i	0.0321300	−	0.0556508i
$585$	15.5672	−	2.89329i	0.643623	−	0.119623i
$586$	−24.3923	+	42.2487i	−1.00764	+	1.74528i
$587$	9.29392	+	5.36585i	0.383601	+	0.221472i	0.679384	−	0.733783i	$-0.262247\pi$
$587$	9.29392	+	5.36585i	0.383601	+	0.221472i	−0.295783	+	0.955255i	$0.595580\pi$
$588$	16.9706	−	12.0000i	0.699854	−	0.494872i
$589$	−17.8564	−	7.73205i	−0.735760	−	0.318594i
$590$		−	22.9048i		−	0.942976i
$591$	−15.7670	+	1.45277i	−0.648566	+	0.0597591i
$592$	16.5000	+	9.52628i	0.678146	+	0.391528i
$593$	−21.7816	+	12.5756i	−0.894463	+	0.516419i	−0.875400	−	0.483400i	$-0.839402\pi$
$593$	−21.7816	+	12.5756i	−0.894463	+	0.516419i	−0.0190636	+	0.999818i	$0.506069\pi$
$594$	0.933552	−	3.68751i	0.0383041	−	0.151300i
$595$	12.9282	+	22.3923i	0.530005	+	0.917995i
$596$		−	29.2180i		−	1.19682i
$597$	−18.1074	+	12.8038i	−0.741086	+	0.524027i
$598$	−1.36603	−	2.36603i	−0.0558609	−	0.0967540i
$599$	−8.43451	−	14.6090i	−0.344625	−	0.596908i	0.640661	−	0.767824i	$-0.278661\pi$
$599$	−8.43451	−	14.6090i	−0.344625	−	0.596908i	−0.985286	+	0.170916i	$0.945327\pi$
$600$	2.19615	−	1.55291i	0.0896575	−	0.0633975i
$601$		−	44.3731i		−	1.81002i	−0.425395	−	0.905008i	$-0.639865\pi$
$601$		−	44.3731i		−	1.81002i	0.425395	−	0.905008i	$-0.360135\pi$
$602$	−8.17569	−	14.1607i	−0.333216	−	0.577148i
$603$	−2.28024	+	1.94949i	−0.0928585	+	0.0793894i
$604$	3.00000	−	1.73205i	0.122068	−	0.0704761i
$605$	−13.2963	−	7.67664i	−0.540573	−	0.312100i
$606$	−25.7473	+	2.37237i	−1.04591	+	0.0963709i
$607$			13.2487i			0.537749i	0.963175	+	0.268874i	$0.0866516\pi$
$607$			13.2487i			0.537749i	−0.963175	+	0.268874i	$0.913348\pi$
$608$	32.8601	−	3.79435i	1.33265	−	0.153881i
$609$	−40.7846	+	28.8391i	−1.65268	+	1.16862i
$610$	−8.36603	−	4.83013i	−0.338730	−	0.195566i
$611$	19.6975	−	34.1170i	0.796874	−	1.38023i
$612$	4.65153	+	25.0273i	0.188027	+	1.01167i
$613$	−11.3205	+	19.6077i	−0.457231	+	0.791947i	−0.998813	−	0.0487003i	$-0.984492\pi$
$613$	−11.3205	+	19.6077i	−0.457231	+	0.791947i	0.541582	+	0.840648i	$0.317825\pi$
$614$	−23.1822	+	13.3843i	−0.935558	+	0.540145i
$615$	8.00000	+	11.3137i	0.322591	+	0.456213i
$616$		−	0.732051i		−	0.0294952i
$617$	22.4379	−	12.9546i	0.903318	−	0.521531i	0.0250427	−	0.999686i	$-0.492028\pi$
$617$	22.4379	−	12.9546i	0.903318	−	0.521531i	0.878275	+	0.478156i	$0.158695\pi$
$618$	14.6508	−	31.8010i	0.589341	−	1.27922i
$619$	2.80385			0.112696			0.0563481	−	0.998411i	$-0.482054\pi$
$619$	2.80385			0.112696			0.0563481	+	0.998411i	$0.482054\pi$
$620$	−10.9348			−0.439151
$621$	−1.41145	−	1.37290i	−0.0566393	−	0.0550925i
$622$	45.4186	+	26.2224i	1.82112	+	1.05142i
$623$	13.7124	+	23.7506i	0.549377	+	0.951549i
$624$	28.7347	−	2.64762i	1.15031	−	0.105990i
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	47.8802			1.91368
$627$	0.891136	−	2.71859i	0.0355885	−	0.108570i
$628$	6.12436			0.244388
$629$	−10.4543	+	18.1074i	−0.416840	+	0.721988i
$630$	−23.2497	+	19.8773i	−0.926289	+	0.791930i
$631$	−24.5263	−	42.4808i	−0.976376	−	1.69113i	−0.675318	−	0.737526i	$-0.735994\pi$
$631$	−24.5263	−	42.4808i	−0.976376	−	1.69113i	−0.301058	−	0.953606i	$-0.597340\pi$
$632$	−1.58510	−	0.915158i	−0.0630519	−	0.0364030i
$633$	7.97219	−	17.3045i	0.316866	−	0.687790i
$634$	26.5885			1.05596
$635$	−11.1106			−0.440912
$636$	−16.4460	−	7.57670i	−0.652126	−	0.300436i
$637$	22.3923	−	12.9282i	0.887215	−	0.512234i
$638$		−	5.65685i		−	0.223957i
$639$	3.58630	−	10.1436i	0.141872	−	0.401274i
$640$	−5.02628	+	2.90192i	−0.198681	+	0.114709i
$641$	−6.41473	+	11.1106i	−0.253367	+	0.438844i	−0.964451	−	0.264263i	$-0.914871\pi$
$641$	−6.41473	+	11.1106i	−0.253367	+	0.438844i	0.711084	+	0.703107i	$0.248205\pi$
$642$	−14.8883	−	6.85906i	−0.587594	−	0.270705i
$643$	21.7942	−	37.7487i	0.859480	−	1.48866i	−0.0129447	−	0.999916i	$-0.504121\pi$
$643$	21.7942	−	37.7487i	0.859480	−	1.48866i	0.872425	−	0.488748i	$-0.162546\pi$
$644$	2.12132	+	1.22474i	0.0835917	+	0.0482617i
$645$	3.20736	+	4.53590i	0.126290	+	0.178601i
$646$	4.73205	+	40.9808i	0.186180	+	1.61237i
$647$			20.5569i			0.808174i	0.914721	+	0.404087i	$0.132411\pi$
$647$			20.5569i			0.808174i	−0.914721	+	0.404087i	$0.867589\pi$
$648$	4.34763	−	1.67391i	0.170791	−	0.0657575i
$649$	−2.75129	−	1.58846i	−0.107998	−	0.0623524i
$650$	−18.7315	+	10.8147i	−0.734711	+	0.424186i
$651$	28.7347	−	2.64762i	1.12620	−	0.103769i
$652$	−4.50000	−	7.79423i	−0.176234	−	0.305246i
$653$		−	47.1223i		−	1.84404i	−0.387144	−	0.922019i	$-0.626538\pi$
$653$		−	47.1223i		−	1.84404i	0.387144	−	0.922019i	$-0.373462\pi$
$654$	−27.8038	−	39.3205i	−1.08721	−	1.53755i
$655$	4.92820	+	8.53590i	0.192561	+	0.333525i
$656$	12.6264	+	21.8695i	0.492978	+	0.853862i
$657$	−3.00000	+	8.48528i	−0.117041	+	0.331042i
$658$			76.1051i			2.96689i
$659$	−16.5409	−	28.6496i	−0.644340	−	1.11603i	−0.984453	−	0.175646i	$-0.943799\pi$
$659$	−16.5409	−	28.6496i	−0.644340	−	1.11603i	0.340113	−	0.940385i	$-0.389535\pi$
$660$	−0.147509	−	1.60091i	−0.00574177	−	0.0623155i
$661$	5.32051	−	3.07180i	0.206944	−	0.119479i	−0.392946	−	0.919561i	$-0.628544\pi$
$661$	5.32051	−	3.07180i	0.206944	−	0.119479i	0.599890	+	0.800082i	$0.295211\pi$
$662$	53.4169	+	30.8403i	2.07611	+	1.19864i
$663$	2.90555	+	31.5339i	0.112842	+	1.22468i
$664$			4.00000i			0.155230i
$665$	−18.4727	+	13.7124i	−0.716341	+	0.531745i
$666$	−23.3205	−	8.24504i	−0.903651	−	0.319489i
$667$	−2.53590	−	1.46410i	−0.0981904	−	0.0566902i
$668$	−6.60420	+	11.4388i	−0.255524	+	0.442581i
$669$	6.80702	−	14.7753i	0.263175	−	0.571248i
$670$	−1.36603	+	2.36603i	−0.0527742	+	0.0914075i
$671$	−1.16037	+	0.669942i	−0.0447957	+	0.0258628i
$672$	−40.0526	+	28.3214i	−1.54506	+	1.09252i
$673$			21.9808i			0.847296i	0.905827	+	0.423648i	$0.139251\pi$
$673$			21.9808i			0.847296i	−0.905827	+	0.423648i	$0.860749\pi$
$674$	12.2796	−	7.08965i	0.472994	−	0.273083i
$675$	−10.8691	+	11.1742i	−0.418350	+	0.430096i
$676$	−1.60770			−0.0618344
$677$	−18.8380			−0.724005			−0.362002	−	0.932177i	$-0.617907\pi$
$677$	−18.8380			−0.724005			−0.362002	+	0.932177i	$0.617907\pi$
$678$	56.7154	+	26.1289i	2.17814	+	1.00347i
$679$	−24.1244	−	13.9282i	−0.925808	−	0.534515i
$680$	−1.79315	−	3.10583i	−0.0687642	−	0.119103i
$681$	−3.90883	−	42.4226i	−0.149787	−	1.62564i
$682$	−1.63397	+	2.83013i	−0.0625681	+	0.108371i
$683$	−16.3142			−0.624246			−0.312123	−	0.950042i	$-0.601040\pi$
$683$	−16.3142			−0.624246			−0.312123	+	0.950042i	$0.601040\pi$
$684$	−21.6464	+	6.66574i	−0.827672	+	0.254871i
$685$	1.07180			0.0409512
$686$	0.258819	−	0.448288i	0.00988176	−	0.0171157i
$687$	1.49261	+	16.1993i	0.0569467	+	0.618043i
$688$	5.06218	+	8.76795i	0.192994	+	0.334275i
$689$	−19.5080	−	11.2629i	−0.743195	−	0.429084i
$690$	−1.62863	−	0.750311i	−0.0620007	−	0.0285639i
$691$	9.85641			0.374955			0.187478	−	0.982269i	$-0.439969\pi$
$691$	9.85641			0.374955			0.187478	+	0.982269i	$0.439969\pi$
$692$	−20.5569			−0.781455
$693$	0.775255	+	4.17121i	0.0294495	+	0.158451i
$694$	−41.6147	+	24.0263i	−1.57967	+	0.912025i
$695$			18.6622i			0.707897i
$696$	5.65685	−	4.00000i	0.214423	−	0.151620i
$697$	−24.0000	+	13.8564i	−0.909065	+	0.524849i
$698$	−11.0041	+	19.0597i	−0.416512	+	0.721420i
$699$	−2.59915	+	5.64173i	−0.0983090	+	0.213390i
$700$	9.69615	−	16.7942i	0.366480	−	0.634762i
$701$	17.2344	+	9.95026i	0.650933	+	0.375816i	0.788814	−	0.614633i	$-0.210696\pi$
$701$	17.2344	+	9.95026i	0.650933	+	0.375816i	−0.137881	+	0.990449i	$0.544029\pi$
$702$	−36.0488	+	10.1962i	−1.36058	+	0.384829i
$703$	−17.0718	−	7.39230i	−0.643875	−	0.278806i
$704$		−	2.17209i		−	0.0818637i
$705$	−2.37237	−	25.7473i	−0.0893486	−	0.969701i
$706$	−20.0263	−	11.5622i	−0.753699	−	0.435148i
$707$	24.9754	−	14.4195i	0.939295	−	0.542303i
$708$	2.30767	+	25.0451i	0.0867275	+	0.941254i
$709$	−21.1603	−	36.6506i	−0.794690	−	1.37644i	−0.923036	−	0.384714i	$-0.874300\pi$
$709$	−21.1603	−	36.6506i	−0.794690	−	1.37644i	0.128346	−	0.991729i	$-0.459033\pi$
$710$		−	9.79796i		−	0.367711i
$711$	10.0010	+	3.53590i	0.375068	+	0.132607i
$712$	−1.90192	−	3.29423i	−0.0712776	−	0.123456i
$713$	0.845807	+	1.46498i	0.0316757	+	0.0548640i
$714$	−35.3205	−	49.9507i	−1.32184	−	1.86936i
$715$		−	2.00000i		−	0.0747958i
$716$	−1.22474	−	2.12132i	−0.0457709	−	0.0792775i
$717$	51.7008	−	4.76373i	1.93080	−	0.177905i
$718$	44.7846	−	25.8564i	1.67135	−	0.964953i
$719$	−5.22715	−	3.01790i	−0.194940	−	0.112549i	0.399353	−	0.916797i	$-0.369235\pi$
$719$	−5.22715	−	3.01790i	−0.194940	−	0.112549i	−0.594293	+	0.804249i	$0.702568\pi$
$720$	14.3956	−	12.3075i	0.536492	−	0.458674i
$721$			39.0526i			1.45439i
$722$	−35.7393	+	8.36516i	−1.33008	+	0.311319i
$723$	−28.6603	−	40.5317i	−1.06589	−	1.50739i
$724$	5.19615	+	3.00000i	0.193113	+	0.111494i
$725$	−11.5911	+	20.0764i	−0.430483	+	0.745618i
$726$	32.9932	+	15.2001i	1.22449	+	0.564127i
$727$	6.79423	−	11.7679i	0.251984	−	0.436449i	−0.712088	−	0.702090i	$-0.752250\pi$
$727$	6.79423	−	11.7679i	0.251984	−	0.436449i	0.964072	+	0.265641i	$0.0855836\pi$
$728$	−6.24384	+	3.60488i	−0.231412	+	0.133606i
$729$	−23.0000	+	14.1421i	−0.851852	+	0.523783i
$730$			8.19615i			0.303353i
$731$	−9.62209	+	5.55532i	−0.355886	+	0.205471i
$732$	9.63442	+	4.43860i	0.356098	+	0.164055i
$733$	−35.7128			−1.31908			−0.659541	−	0.751668i	$-0.729249\pi$
$733$	−35.7128			−1.31908			−0.659541	+	0.751668i	$0.729249\pi$
$734$	32.9430			1.21595
$735$	7.10102	−	15.4135i	0.261925	−	0.568535i
$736$	−2.49038	−	1.43782i	−0.0917967	−	0.0529988i
$737$	0.189469	+	0.328169i	0.00697917	+	0.0120883i
$738$	−21.3044	−	24.9189i	−0.784227	−	0.917278i
$739$	17.4019	−	30.1410i	0.640140	−	1.10876i	−0.345261	−	0.938507i	$-0.612210\pi$
$739$	17.4019	−	30.1410i	0.640140	−	1.10876i	0.985401	−	0.170249i	$-0.0544570\pi$
$740$	−10.4543			−0.384308
$741$	−27.5758	+	5.78658i	−1.01302	+	0.212575i
$742$	43.5167			1.59755
$743$	3.53553	−	6.12372i	0.129706	−	0.224658i	−0.793857	−	0.608105i	$-0.791930\pi$
$743$	3.53553	−	6.12372i	0.129706	−	0.224658i	0.923563	+	0.383447i	$0.125263\pi$
$744$	−3.98552	+	0.367227i	−0.146116	+	0.0134632i
$745$	−11.9282	−	20.6603i	−0.437016	−	0.756933i
$746$	20.9730	+	12.1087i	0.767875	+	0.443333i
$747$	−4.23607	−	22.7919i	−0.154990	−	0.833912i
$748$	3.21539			0.117566
$749$	18.2832			0.668055
$750$	−15.8403	+	34.3830i	−0.578407	+	1.25549i
$751$	−7.45448	+	4.30385i	−0.272018	+	0.157050i	−0.629804	−	0.776754i	$-0.716865\pi$
$751$	−7.45448	+	4.30385i	−0.272018	+	0.157050i	0.357786	+	0.933803i	$0.383532\pi$
$752$		−	47.1223i		−	1.71837i
$753$	14.6969	+	20.7846i	0.535586	+	0.757433i
$754$	−48.2487	+	27.8564i	−1.75711	+	1.01447i
$755$	1.41421	−	2.44949i	0.0514685	−	0.0891461i
$756$	23.4196	−	24.0771i	0.851762	−	0.875677i
$757$	−2.30385	+	3.99038i	−0.0837348	+	0.145033i	−0.904851	−	0.425728i	$-0.860018\pi$
$757$	−2.30385	+	3.99038i	−0.0837348	+	0.145033i	0.821117	+	0.570760i	$0.193352\pi$
$758$	29.7542	+	17.1786i	1.08072	+	0.623955i
$759$	−0.203072	+	0.143594i	−0.00737104	+	0.00521212i
$760$	2.56218	−	1.90192i	0.0929400	−	0.0689900i
$761$			46.2629i			1.67703i	0.544879	+	0.838514i	$0.316575\pi$
$761$			46.2629i			1.67703i	−0.544879	+	0.838514i	$0.683425\pi$
$762$	26.1772	−	2.41197i	0.948299	−	0.0873766i
$763$	46.5167	+	26.8564i	1.68402	+	0.972267i
$764$	−2.53742	+	1.46498i	−0.0918007	+	0.0530012i
$765$	13.5065	+	15.7980i	0.488327	+	0.571176i
$766$	25.7583	+	44.6147i	0.930686	+	1.61200i
$767$			31.2886i			1.12976i
$768$	27.4249	−	19.3923i	0.989609	−	0.699760i
$769$	0.428203	+	0.741670i	0.0154414	+	0.0267453i	0.873643	−	0.486568i	$-0.161751\pi$
$769$	0.428203	+	0.741670i	0.0154414	+	0.0267453i	−0.858201	+	0.513313i	$0.828418\pi$
$770$	1.93185	+	3.34607i	0.0696191	+	0.120584i
$771$	4.53590	−	3.20736i	0.163356	−	0.115510i
$772$		−	22.8564i		−	0.822620i
$773$	−9.04008	−	15.6579i	−0.325149	−	0.563175i	0.656393	−	0.754419i	$-0.272081\pi$
$773$	−9.04008	−	15.6579i	−0.325149	−	0.563175i	−0.981543	+	0.191244i	$0.938748\pi$
$774$	−8.54138	−	9.99051i	−0.307014	−	0.359101i
$775$	11.5981	−	6.69615i	0.416615	−	0.240533i
$776$	3.34607	+	1.93185i	0.120117	+	0.0693494i
$777$	27.4721	−	2.53129i	0.985556	−	0.0908095i
$778$			9.66025i			0.346337i
$779$	−14.6969	−	19.7990i	−0.526572	−	0.709372i
$780$	−12.9282	+	9.14162i	−0.462904	+	0.327323i
$781$	−1.17691	−	0.679492i	−0.0421133	−	0.0243141i
$782$	1.79315	−	3.10583i	0.0641229	−	0.111064i
$783$	−27.9966	+	28.7826i	−1.00052	+	1.02861i
$784$	15.4641	−	26.7846i	0.552289	−	0.956593i
$785$	4.33057	−	2.50026i	0.154565	−	0.0892380i
$786$	−13.4641	−	19.0411i	−0.480249	−	0.679174i
$787$		−	24.0718i		−	0.858067i	−0.903289	−	0.429033i	$-0.858854\pi$
$787$		−	24.0718i		−	0.858067i	0.903289	−	0.429033i	$-0.141146\pi$
$788$	13.7124	−	7.91688i	0.488485	−	0.282027i
$789$	−0.402091	+	0.872778i	−0.0143148	+	0.0310717i
$790$	9.66025			0.343696
$791$	−69.6482			−2.47640
$792$	−0.107528	−	0.578550i	−0.00382086	−	0.0205579i
$793$	11.4282	+	6.59808i	0.405827	+	0.234305i
$794$	8.03699	+	13.9205i	0.285222	+	0.494019i
$795$	−14.7222	+	1.35651i	−0.522144	+	0.0481106i
$796$	11.0885	−	19.2058i	0.393020	−	0.680731i
$797$	14.4939			0.513399			0.256700	−	0.966491i	$-0.417365\pi$
$797$	14.4939			0.513399			0.256700	+	0.966491i	$0.417365\pi$
$798$	40.5458	−	36.3173i	1.43530	−	1.28562i
$799$	51.7128			1.82947
$800$	−11.3831	+	19.7160i	−0.402452	+	0.697067i
$801$	14.3258	+	16.7563i	0.506176	+	0.592054i
$802$	−11.0981	−	19.2224i	−0.391887	−	0.678768i
$803$	0.984508	+	0.568406i	0.0347425	+	0.0200586i
$804$	1.25529	−	2.72474i	0.0442708	−	0.0960943i
$805$	2.00000			0.0704907
$806$	32.1851			1.13367
$807$	−9.49510	−	4.37441i	−0.334243	−	0.153986i
$808$	−3.46410	+	2.00000i	−0.121867	+	0.0703598i
$809$			51.1619i			1.79876i	0.437172	+	0.899378i	$0.355980\pi$
$809$			51.1619i			1.79876i	−0.437172	+	0.899378i	$0.644020\pi$
$810$	−15.4548	+	19.1244i	−0.543027	+	0.671961i
$811$	18.8038	−	10.8564i	0.660292	−	0.381220i	−0.132096	−	0.991237i	$-0.542171\pi$
$811$	18.8038	−	10.8564i	0.660292	−	0.381220i	0.792388	+	0.610017i	$0.208837\pi$
$812$	24.9754	−	43.2586i	0.876464	−	1.51808i
$813$	10.8990	+	5.02118i	0.382244	+	0.176100i
$814$	−1.56218	+	2.70577i	−0.0547543	+	0.0948372i
$815$	−6.36396	−	3.67423i	−0.222920	−	0.128703i
$816$	21.8695	+	30.9282i	0.765587	+	1.08270i
$817$	−5.89230	−	7.93782i	−0.206146	−	0.277709i
$818$		−	54.5723i		−	1.90808i
$819$	31.7596	−	27.1529i	1.10977	−	0.948799i
$820$	−12.0000	−	6.92820i	−0.419058	−	0.241943i
$821$	29.8744	−	17.2480i	1.04262	−	0.601958i	0.122047	−	0.992524i	$-0.461054\pi$
$821$	29.8744	−	17.2480i	1.04262	−	0.601958i	0.920575	+	0.390566i	$0.127721\pi$
$822$	−2.52520	+	0.232673i	−0.0880765	+	0.00811540i
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	0.927281	−	0.374365i	$-0.122139\pi$
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	−0.787850	+	0.615867i	$0.788806\pi$
$824$		−	5.41662i		−	0.188697i
$825$	1.13681	+	1.60770i	0.0395787	+	0.0559728i
$826$	−30.2224	−	52.3468i	−1.05157	−	1.82138i
$827$	−12.2474	−	21.2132i	−0.425886	−	0.737655i	0.570617	−	0.821216i	$-0.306704\pi$
$827$	−12.2474	−	21.2132i	−0.425886	−	0.737655i	−0.996503	+	0.0835608i	$0.973371\pi$
$828$	1.85641	+	0.656339i	0.0645146	+	0.0228093i
$829$			38.6603i			1.34273i	0.741129	+	0.671363i	$0.234291\pi$
$829$			38.6603i			1.34273i	−0.741129	+	0.671363i	$0.765709\pi$
$830$	−10.5558	−	18.2832i	−0.366398	−	0.634621i
$831$	−1.56637	−	16.9998i	−0.0543367	−	0.589716i
$832$	−18.5263	+	10.6962i	−0.642283	+	0.370822i
$833$	29.3939	+	16.9706i	1.01844	+	0.587995i
$834$	−4.05131	−	43.9689i	−0.140286	−	1.52252i
$835$			10.7846i			0.373217i
$836$	0.328169	+	2.84203i	0.0113500	+	0.0982937i
$837$	22.3205	−	6.31319i	0.771510	−	0.218216i
$838$	−53.6147	−	30.9545i	−1.85209	−	1.06930i
$839$	2.87920	−	4.98691i	0.0994009	−	0.172167i	−0.812036	−	0.583607i	$-0.801641\pi$
$839$	2.87920	−	4.98691i	0.0994009	−	0.172167i	0.911437	+	0.411440i	$0.134974\pi$
$840$	−1.98004	+	4.29788i	−0.0683179	+	0.148291i
$841$	−15.3564	+	26.5981i	−0.529531	+	0.917175i
$842$	−59.3326	+	34.2557i	−2.04474	+	1.18053i
$843$	−21.3205	+	15.0759i	−0.734317	+	0.519241i
$844$			19.0526i			0.655816i
$845$	−1.13681	+	0.656339i	−0.0391075	+	0.0225787i
$846$	11.1788	+	60.1469i	0.384336	+	2.06789i
$847$	−40.5167			−1.39217
$848$	−26.9444			−0.925274
$849$	34.3830	+	15.8403i	1.18002	+	0.543638i
$850$	−24.5885	−	14.1962i	−0.843377	−	0.486924i
$851$	0.808643	+	1.40061i	0.0277199	+	0.0480123i
$852$	0.987148	+	10.7135i	0.0338191	+	0.367039i
$853$	−9.83975	+	17.0429i	−0.336906	+	0.583539i	−0.983849	−	0.178999i	$-0.942714\pi$
$853$	−9.83975	+	17.0429i	−0.336906	+	0.583539i	0.646943	+	0.762539i	$0.276047\pi$
$854$	−25.4930			−0.872353
$855$	−12.5851	+	13.5505i	−0.430400	+	0.463418i
$856$	−2.53590			−0.0866752
$857$	1.51575	−	2.62536i	0.0517770	−	0.0896804i	−0.838975	−	0.544170i	$-0.816845\pi$
$857$	1.51575	−	2.62536i	0.0517770	−	0.0896804i	0.890752	+	0.454489i	$0.150178\pi$
$858$	0.434174	+	4.71209i	0.0148224	+	0.160868i
$859$	2.33013	+	4.03590i	0.0795029	+	0.137703i	0.903036	−	0.429566i	$-0.141333\pi$
$859$	2.33013	+	4.03590i	0.0795029	+	0.137703i	−0.823533	+	0.567269i	$0.808000\pi$
$860$	−4.81105	−	2.77766i	−0.164055	−	0.0947174i
$861$	33.2114	+	15.3006i	1.13184	+	0.521442i
$862$	−49.1769			−1.67497
$863$	18.2832			0.622369			0.311184	−	0.950350i	$-0.399274\pi$
$863$	18.2832			0.622369			0.311184	+	0.950350i	$0.399274\pi$
$864$	−27.4940	+	28.2660i	−0.935366	+	0.961629i
$865$	−14.5359	+	8.39230i	−0.494235	+	0.285347i
$866$		−	6.45189i		−	0.219244i
$867$	−9.89949	+	7.00000i	−0.336204	+	0.237732i
$868$	−24.9904	+	14.4282i	−0.848229	+	0.489725i
$869$	0.669942	−	1.16037i	0.0227262	−	0.0393630i
$870$	−15.3006	+	33.2114i	−0.518738	+	1.12597i
$871$	1.86603	−	3.23205i	0.0632279	−	0.109514i
$872$	−6.45189	−	3.72500i	−0.218489	−	0.126145i
$873$	−21.1117	−	7.46410i	−0.714522	−	0.252622i
$874$	2.92820	+	1.26795i	0.0990480	+	0.0428890i
$875$		−	42.2233i		−	1.42741i
$876$	−0.825765	−	8.96204i	−0.0279000	−	0.302799i
$877$	−3.23205	−	1.86603i	−0.109139	−	0.0630112i	0.444437	−	0.895810i	$-0.353404\pi$
$877$	−3.23205	−	1.86603i	−0.109139	−	0.0630112i	−0.553576	+	0.832799i	$0.686737\pi$
$878$	37.5832	−	21.6987i	1.26837	−	0.732294i
$879$	−4.01314	−	43.5546i	−0.135360	−	1.46906i
$880$	−1.19615	−	2.07180i	−0.0403223	−	0.0698403i
$881$		−	39.8482i		−	1.34252i	−0.741222	−	0.671260i	$-0.765754\pi$
$881$		−	39.8482i		−	1.34252i	0.741222	−	0.671260i	$-0.234246\pi$
$882$	−13.3843	+	37.8564i	−0.450672	+	1.27469i
$883$	11.1340	+	19.2846i	0.374688	+	0.648979i	0.990280	−	0.139086i	$-0.0444165\pi$
$883$	11.1340	+	19.2846i	0.374688	+	0.648979i	−0.615592	+	0.788065i	$0.711083\pi$
$884$	−15.8338	−	27.4249i	−0.532547	−	0.922398i
$885$	11.8564	+	16.7675i	0.398549	+	0.563633i
$886$		−	74.6410i		−	2.50761i
$887$	−5.98502	−	10.3664i	−0.200957	−	0.348068i	0.747880	−	0.663834i	$-0.231072\pi$
$887$	−5.98502	−	10.3664i	−0.200957	−	0.348068i	−0.948837	+	0.315766i	$0.897739\pi$
$888$	−3.81040	+	0.351091i	−0.127869	+	0.0117819i
$889$	−25.3923	+	14.6603i	−0.851631	+	0.491689i
$890$	17.3867	+	10.0382i	0.582802	+	0.336481i
$891$	1.22539	+	3.18269i	0.0410521	+	0.106624i
$892$			16.2679i			0.544691i
$893$	5.27792	+	45.7081i	0.176619	+	1.52956i
$894$	32.5885	+	46.0870i	1.08992	+	1.54138i
$895$	−1.73205	−	1.00000i	−0.0578961	−	0.0334263i
$896$	−7.65806	+	13.2641i	−0.255838	+	0.443124i
$897$	2.22474	+	1.02494i	0.0742821	+	0.0342219i
$898$	33.3205	−	57.7128i	1.11192	−	1.92590i
$899$	29.8744	−	17.2480i	0.996365	−	0.575252i
$900$	5.19615	−	14.6969i	0.173205	−	0.489898i
$901$		−	29.5692i		−	0.985094i
$902$	−3.58630	+	2.07055i	−0.119411	+	0.0689419i
$903$	13.3152	+	6.13431i	0.443100	+	0.204137i
$904$	9.66025			0.321295
$905$	4.89898			0.162848
$906$	−2.80020	+	6.07812i	−0.0930304	+	0.201932i
$907$	35.4449	+	20.4641i	1.17693	+	0.679499i	0.955302	−	0.295632i	$-0.0955304\pi$
$907$	35.4449	+	20.4641i	1.17693	+	0.679499i	0.221626	+	0.975132i	$0.428864\pi$
$908$	21.3011	+	36.8947i	0.706903	+	1.22439i
$909$	17.6203	−	15.0645i	0.584430	−	0.499658i
$910$	19.0263	−	32.9545i	0.630715	−	1.09243i
$911$	−40.9107			−1.35543			−0.677715	−	0.735324i	$-0.737030\pi$
$911$	−40.9107			−1.35543			−0.677715	+	0.735324i	$0.737030\pi$
$912$	−25.1049	+	22.4867i	−0.831306	+	0.744610i
$913$	−2.92820			−0.0969094
$914$	−20.0070	+	34.6532i	−0.661774	+	1.14623i
$915$	8.62461	−	0.794675i	0.285121	−	0.0262711i
$916$	−8.13397	−	14.0885i	−0.268754	−	0.465496i
$917$	22.5259	+	13.0053i	0.743870	+	0.429474i
$918$	−35.2514	−	34.2886i	−1.16347	−	1.13169i
$919$	−31.9808			−1.05495			−0.527474	−	0.849571i	$-0.676861\pi$
$919$	−31.9808			−1.05495			−0.527474	+	0.849571i	$0.676861\pi$
$920$	−0.277401			−0.00914565
$921$	10.0424	−	21.7980i	0.330907	−	0.718267i
$922$	55.0070	−	31.7583i	1.81156	−	1.04590i
$923$			13.3843i			0.440548i
$924$	−2.44949	−	3.46410i	−0.0805823	−	0.113961i
$925$	11.0885	−	6.40192i	0.364586	−	0.210494i
$926$	−28.5803	+	49.5025i	−0.939205	+	1.62675i
$927$	5.73630	+	30.8638i	0.188405	+	1.01370i
$928$	−29.3205	+	50.7846i	−0.962493	+	1.66709i
$929$	17.7148	+	10.2277i	0.581205	+	0.335559i	0.761612	−	0.648033i	$-0.224408\pi$
$929$	17.7148	+	10.2277i	0.581205	+	0.335559i	−0.180407	+	0.983592i	$0.557742\pi$
$930$	17.2480	−	12.1962i	0.565583	−	0.399928i
$931$	−12.0000	+	27.7128i	−0.393284	+	0.908251i
$932$		−	6.21166i		−	0.203470i
$933$	−46.8224	+	4.31424i	−1.53290	+	0.141242i
$934$	37.8564	+	21.8564i	1.23870	+	0.715163i
$935$	2.27362	−	1.31268i	0.0743555	−	0.0429291i
$936$	−4.40508	+	3.76612i	−0.143985	+	0.123100i
$937$	−2.89230	−	5.00962i	−0.0944875	−	0.163657i	0.814907	−	0.579592i	$-0.196788\pi$
$937$	−2.89230	−	5.00962i	−0.0944875	−	0.163657i	−0.909395	+	0.415934i	$0.863455\pi$
$938$			7.20977i			0.235407i
$939$	−35.0507	+	24.7846i	−1.14384	+	0.808815i
$940$	12.9282	+	22.3923i	0.421671	+	0.730356i
$941$	−6.96953	−	12.0716i	−0.227200	−	0.393522i	0.729777	−	0.683685i	$-0.239624\pi$
$941$	−6.96953	−	12.0716i	−0.227200	−	0.393522i	−0.956977	+	0.290163i	$0.906291\pi$
$942$	−9.66025	+	6.83083i	−0.314748	+	0.222561i
$943$			2.14359i			0.0698050i
$944$	18.7129	+	32.4118i	0.609055	+	1.05491i
$945$	6.73069	−	26.5861i	0.218949	−	0.864846i
$946$	−1.43782	+	0.830127i	−0.0467476	+	0.0269898i
$947$	38.3596	+	22.1469i	1.24652	+	0.719679i	0.970414	−	0.241448i	$-0.0776223\pi$
$947$	38.3596	+	22.1469i	1.24652	+	0.719679i	0.276107	+	0.961127i	$0.410956\pi$
$948$	−10.5630	+	0.973274i	−0.343069	+	0.0316105i
$949$		−	11.1962i		−	0.363442i
$950$	10.0382	−	23.1822i	0.325682	−	0.752131i
$951$	−19.4641	+	13.7632i	−0.631167	+	0.446302i
$952$	−8.19615	−	4.73205i	−0.265639	−	0.153367i
$953$	21.3011	−	36.8947i	0.690011	−	1.19513i	−0.281822	−	0.959467i	$-0.590939\pi$
$953$	21.3011	−	36.8947i	0.690011	−	1.19513i	0.971834	−	0.235668i	$-0.0757279\pi$
$954$	34.3918	−	6.39201i	1.11348	−	0.206949i
$955$	−1.19615	+	2.07180i	−0.0387066	+	0.0670418i
$956$	−44.9638	+	25.9599i	−1.45423	+	0.839602i
$957$	2.92820	+	4.14110i	0.0946554	+	0.133863i
$958$			22.9282i			0.740777i
$959$	2.44949	−	1.41421i	0.0790981	−	0.0456673i
$960$	−5.87503	+	12.7524i	−0.189616	+	0.411580i
$961$	11.0718			0.357155
$962$	30.7709			0.992094
$963$	14.4495	−	2.68556i	0.465628	−	0.0865410i
$964$	42.9904	+	24.8205i	1.38463	+	0.799415i
$965$	−9.33109	−	16.1619i	−0.300378	−	0.520271i
$966$	−4.71209	+	0.434174i	−0.151609	+	0.0139693i
$967$	4.40192	−	7.62436i	0.141556	−	0.245183i	−0.786527	−	0.617556i	$-0.788123\pi$
$967$	4.40192	−	7.62436i	0.141556	−	0.245183i	0.928083	+	0.372374i	$0.121456\pi$
$968$	5.61969			0.180624
$969$	−24.6773	−	27.5505i	−0.792749	−	0.885050i
$970$	−20.3923			−0.654757
$971$	−7.17260	+	12.4233i	−0.230180	+	0.398683i	−0.957861	−	0.287232i	$-0.907265\pi$
$971$	−7.17260	+	12.4233i	−0.230180	+	0.398683i	0.727681	+	0.685916i	$0.240598\pi$
$972$	14.9722	−	22.4685i	0.480233	−	0.720677i
$973$	24.6244	+	42.6506i	0.789421	+	1.36732i
$974$	−41.7057	−	24.0788i	−1.33634	−	0.771534i
$975$	8.11435	−	17.6130i	0.259867	−	0.564068i
$976$	15.7846			0.505253
$977$	20.3538			0.651176			0.325588	−	0.945512i	$-0.394438\pi$
$977$	20.3538			0.651176			0.325588	+	0.945512i	$0.394438\pi$
$978$	15.7914	+	7.27513i	0.504954	+	0.232633i
$979$	2.41154	−	1.39230i	0.0770732	−	0.0444983i
$980$			16.9706i			0.542105i
$981$	40.7076	+	14.3923i	1.29969	+	0.459511i
$982$	16.7321	−	9.66025i	0.533941	−	0.308271i
$983$	16.2635	−	28.1691i	0.518724	−	0.898456i	−0.481040	−	0.876699i	$-0.659741\pi$
$983$	16.2635	−	28.1691i	0.518724	−	0.898456i	0.999763	−	0.0217569i	$-0.00692599\pi$
$984$	−4.60645	−	2.12220i	−0.146848	−	0.0676533i
$985$	6.46410	−	11.1962i	0.205963	−	0.356739i
$986$	−63.3350	−	36.5665i	−2.01700	−	1.16451i
$987$	−39.3949	−	55.7128i	−1.25395	−	1.77336i
$988$	22.6244	−	16.7942i	0.719777	−	0.534296i
$989$			0.859411i			0.0273277i
$990$	2.01826	+	2.36068i	0.0641445	+	0.0750272i
$991$	−3.61731	−	2.08846i	−0.114908	−	0.0663420i	0.441445	−	0.897289i	$-0.354466\pi$
$991$	−3.61731	−	2.08846i	−0.114908	−	0.0663420i	−0.556352	+	0.830946i	$0.687800\pi$
$992$	29.3381	−	16.9384i	0.931487	−	0.537794i
$993$	−55.0680	+	5.07399i	−1.74753	+	0.161018i
$994$	−12.9282	−	22.3923i	−0.410058	−	0.710241i
$995$		−	18.1074i		−	0.574042i
$996$	13.3843	+	18.9282i	0.424097	+	0.599763i
$997$	−25.0885	−	43.4545i	−0.794559	−	1.37622i	−0.923119	−	0.384515i	$-0.874369\pi$
$997$	−25.0885	−	43.4545i	−0.794559	−	1.37622i	0.128559	−	0.991702i	$-0.458965\pi$
$998$	−15.5749	−	26.9766i	−0.493016	−	0.853928i
$999$	21.3397	−	6.03579i	0.675160	−	0.190964i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.2.f.a.8.4	yes	8
3.2	odd	2	inner	57.2.f.a.8.1	✓	8
4.3	odd	2		912.2.bn.m.65.2		8
12.11	even	2		912.2.bn.m.65.1		8
19.8	odd	6		1083.2.d.b.1082.8		8
19.11	even	3		1083.2.d.b.1082.1		8
19.12	odd	6	inner	57.2.f.a.50.1	yes	8
57.8	even	6		1083.2.d.b.1082.2		8
57.11	odd	6		1083.2.d.b.1082.7		8
57.50	even	6	inner	57.2.f.a.50.4	yes	8
76.31	even	6		912.2.bn.m.449.1		8
228.107	odd	6		912.2.bn.m.449.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.f.a.8.1	✓	8	3.2	odd	2	inner
57.2.f.a.8.4	yes	8	1.1	even	1	trivial
57.2.f.a.50.1	yes	8	19.12	odd	6	inner
57.2.f.a.50.4	yes	8	57.50	even	6	inner
912.2.bn.m.65.1		8	12.11	even	2
912.2.bn.m.65.2		8	4.3	odd	2
912.2.bn.m.449.1		8	76.31	even	6
912.2.bn.m.449.2		8	228.107	odd	6
1083.2.d.b.1082.1		8	19.11	even	3
1083.2.d.b.1082.2		8	57.8	even	6
1083.2.d.b.1082.7		8	57.11	odd	6
1083.2.d.b.1082.8		8	19.8	odd	6

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:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 1.67303i) q^{2} +(0.158919 + 1.72474i) q^{3} +(-0.866025 - 1.50000i) q^{4} +(-1.22474 - 0.707107i) q^{5} +(3.03906 + 1.40010i) q^{6} -3.73205 q^{7} +0.517638 q^{8} +(-2.94949 + 0.548188i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 1.67303i) q^{2} +(0.158919 + 1.72474i) q^{3} +(-0.866025 - 1.50000i) q^{4} +(-1.22474 - 0.707107i) q^{5} +(3.03906 + 1.40010i) q^{6} -3.73205 q^{7} +0.517638 q^{8} +(-2.94949 + 0.548188i) q^{9} +(-2.36603 + 1.36603i) q^{10} +0.378937i q^{11} +(2.44949 - 1.73205i) q^{12} +(3.23205 - 1.86603i) q^{13} +(-3.60488 + 6.24384i) q^{14} +(1.02494 - 2.22474i) q^{15} +(2.23205 - 3.86603i) q^{16} +(4.24264 + 2.44949i) q^{17} +(-1.93185 + 5.46410i) q^{18} +(-1.73205 + 4.00000i) q^{19} +2.44949i q^{20} +(-0.593092 - 6.43684i) q^{21} +(0.633975 + 0.366025i) q^{22} +(0.328169 - 0.189469i) q^{23} +(0.0822623 + 0.892794i) q^{24} +(-1.50000 - 2.59808i) q^{25} -7.20977i q^{26} +(-1.41421 - 5.00000i) q^{27} +(3.23205 + 5.59808i) q^{28} +(-3.86370 - 6.69213i) q^{29} +(-2.73205 - 3.86370i) q^{30} +4.46410i q^{31} +(-3.79435 - 6.57201i) q^{32} +(-0.653570 + 0.0602202i) q^{33} +(8.19615 - 4.73205i) q^{34} +(4.57081 + 2.63896i) q^{35} +(3.37662 + 3.94949i) q^{36} +4.26795i q^{37} +(5.01910 + 6.76148i) q^{38} +(3.73205 + 5.27792i) q^{39} +(-0.633975 - 0.366025i) q^{40} +(-2.82843 + 4.89898i) q^{41} +(-11.3419 - 5.22524i) q^{42} +(-1.13397 + 1.96410i) q^{43} +(0.568406 - 0.328169i) q^{44} +(4.00000 + 1.41421i) q^{45} -0.732051i q^{46} +(9.14162 - 5.27792i) q^{47} +(7.02262 + 3.23533i) q^{48} +6.92820 q^{49} -5.79555 q^{50} +(-3.55051 + 7.70674i) q^{51} +(-5.59808 - 3.23205i) q^{52} +(-3.01790 - 5.22715i) q^{53} +(-9.73119 - 2.46360i) q^{54} +(0.267949 - 0.464102i) q^{55} -1.93185 q^{56} +(-7.17423 - 2.35167i) q^{57} -14.9282 q^{58} +(-4.19187 + 7.26054i) q^{59} +(-4.22474 + 0.389270i) q^{60} +(1.76795 + 3.06218i) q^{61} +(7.46859 + 4.31199i) q^{62} +(11.0076 - 2.04587i) q^{63} -5.73205 q^{64} -5.27792 q^{65} +(-0.530550 + 1.15161i) q^{66} +(0.866025 - 0.500000i) q^{67} -8.48528i q^{68} +(0.378937 + 0.535898i) q^{69} +(8.83013 - 5.09808i) q^{70} +(-1.79315 + 3.10583i) q^{71} +(-1.52677 + 0.283763i) q^{72} +(1.50000 - 2.59808i) q^{73} +(7.14042 + 4.12252i) q^{74} +(4.24264 - 3.00000i) q^{75} +(7.50000 - 0.866025i) q^{76} -1.41421i q^{77} +(12.4350 - 1.14577i) q^{78} +(-3.06218 - 1.76795i) q^{79} +(-5.46739 + 3.15660i) q^{80} +(8.39898 - 3.23375i) q^{81} +(5.46410 + 9.46410i) q^{82} +7.72741i q^{83} +(-9.14162 + 6.46410i) q^{84} +(-3.46410 - 6.00000i) q^{85} +(2.19067 + 3.79435i) q^{86} +(10.9282 - 7.72741i) q^{87} +0.196152i q^{88} +(-3.67423 - 6.36396i) q^{89} +(6.22973 - 5.32611i) q^{90} +(-12.0622 + 6.96410i) q^{91} +(-0.568406 - 0.328169i) q^{92} +(-7.69944 + 0.709429i) q^{93} -20.3923i q^{94} +(4.94975 - 3.67423i) q^{95} +(10.7321 - 7.58871i) q^{96} +(6.46410 + 3.73205i) q^{97} +(6.69213 - 11.5911i) q^{98} +(-0.207729 - 1.11767i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{6} - 16 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^6 - 16 * q^7 - 4 * q^9	\( 8 q + 4 q^{6} - 16 q^{7} - 4 q^{9} - 12 q^{10} + 12 q^{13} + 4 q^{16} - 12 q^{21} + 12 q^{22} + 4 q^{24} - 12 q^{25} + 12 q^{28} - 8 q^{30} + 24 q^{33} + 24 q^{34} + 16 q^{39} - 12 q^{40} - 20 q^{42} - 16 q^{43} + 32 q^{45} + 24 q^{48} - 48 q^{51} - 24 q^{52} - 4 q^{54} + 16 q^{55} - 28 q^{57} - 64 q^{58} - 24 q^{60} + 28 q^{61} + 8 q^{63} - 32 q^{64} - 4 q^{66} + 36 q^{70} - 24 q^{72} + 12 q^{73} + 60 q^{76} + 36 q^{78} + 24 q^{79} + 28 q^{81} + 16 q^{82} + 32 q^{87} + 12 q^{90} - 48 q^{91} - 4 q^{93} + 72 q^{96} + 24 q^{97} - 32 q^{99}+O(q^{100}) \) 8 * q + 4 * q^6 - 16 * q^7 - 4 * q^9 - 12 * q^10 + 12 * q^13 + 4 * q^16 - 12 * q^21 + 12 * q^22 + 4 * q^24 - 12 * q^25 + 12 * q^28 - 8 * q^30 + 24 * q^33 + 24 * q^34 + 16 * q^39 - 12 * q^40 - 20 * q^42 - 16 * q^43 + 32 * q^45 + 24 * q^48 - 48 * q^51 - 24 * q^52 - 4 * q^54 + 16 * q^55 - 28 * q^57 - 64 * q^58 - 24 * q^60 + 28 * q^61 + 8 * q^63 - 32 * q^64 - 4 * q^66 + 36 * q^70 - 24 * q^72 + 12 * q^73 + 60 * q^76 + 36 * q^78 + 24 * q^79 + 28 * q^81 + 16 * q^82 + 32 * q^87 + 12 * q^90 - 48 * q^91 - 4 * q^93 + 72 * q^96 + 24 * q^97 - 32 * q^99

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