LMFDB - Embedded newform 57.2.f.a.50.4

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			50.4
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	57.50
Dual form			57.2.f.a.8.4

$q$-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 $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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	0.974057	+	0.226303i	$0.0726640\pi$
$2$	0.965926	+	1.67303i	0.683013	+	1.18301i	−0.291044	+	0.956710i	$0.594003\pi$
$3$	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	−0.748203	−	0.663470i	$-0.769083\pi$
$5$	−1.22474	+	0.707107i	−0.547723	+	0.316228i	0.200480	+	0.979698i	$0.435750\pi$
$6$	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	$-0.981806\pi$
$11$		−	0.378937i		−	0.114254i	0.998367	−	0.0571270i	$-0.0181940\pi$
$12$	2.44949	+	1.73205i	0.707107	+	0.500000i
$13$	3.23205	+	1.86603i	0.896410	+	0.517542i	0.876034	−	0.482250i	$-0.160180\pi$
$13$	3.23205	+	1.86603i	0.896410	+	0.517542i	0.0203760	+	0.999792i	$0.493514\pi$
$14$	−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	0.112296	−	0.993675i	$-0.464180\pi$
$17$	4.24264	−	2.44949i	1.02899	−	0.594089i	0.916696	+	0.399586i	$0.130846\pi$
$18$	−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	0.533824	−	0.845596i	$-0.320755\pi$
$23$	0.328169	+	0.189469i	0.0684280	+	0.0395070i	−0.465396	+	0.885103i	$0.654088\pi$
$24$	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	0.244527	+	0.969643i	$0.421367\pi$
$29$	−3.86370	+	6.69213i	−0.717472	+	1.24270i	−0.961998	+	0.273055i	$0.911966\pi$
$30$	−2.73205	+	3.86370i	−0.498802	+	0.705412i
$31$		−	4.46410i		−	0.801776i	−0.916127	−	0.400888i	$-0.868702\pi$
$31$		−	4.46410i		−	0.801776i	0.916127	−	0.400888i	$-0.131298\pi$
$32$	−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	$-0.885902\pi$
$37$		−	4.26795i		−	0.701647i	0.936442	−	0.350823i	$-0.114098\pi$
$38$	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	0.556092	−	0.831121i	$-0.312300\pi$
$41$	−2.82843	−	4.89898i	−0.441726	−	0.765092i	−0.997818	+	0.0660290i	$0.978967\pi$
$42$	−11.3419	+	5.22524i	−1.75010	+	0.806272i
$43$	−1.13397	−	1.96410i	−0.172930	−	0.299523i	0.766513	−	0.642228i	$-0.221990\pi$
$43$	−1.13397	−	1.96410i	−0.172930	−	0.299523i	−0.939443	+	0.342706i	$0.888657\pi$
$44$	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	0.985826	−	0.167773i	$-0.0536577\pi$
$47$	9.14162	+	5.27792i	1.33344	+	0.769863i	0.347617	+	0.937637i	$0.386991\pi$
$48$	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	−0.995380	−	0.0960135i	$-0.969391\pi$
$53$	−3.01790	+	5.22715i	−0.414540	+	0.718004i	0.580840	+	0.814018i	$0.302724\pi$
$54$	−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	−0.998560	−	0.0536419i	$-0.982917\pi$
$59$	−4.19187	−	7.26054i	−0.545735	−	0.945241i	0.452825	−	0.891599i	$-0.350416\pi$
$60$	−4.22474	−	0.389270i	−0.545412	−	0.0502545i
$61$	1.76795	−	3.06218i	0.226363	−	0.392072i	−0.730365	−	0.683057i	$-0.760650\pi$
$61$	1.76795	−	3.06218i	0.226363	−	0.392072i	0.956727	+	0.290986i	$0.0939832\pi$
$62$	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	0.551967	−	0.833866i	$-0.313877\pi$
$67$	0.866025	+	0.500000i	0.105802	+	0.0610847i	−0.446165	+	0.894951i	$0.647211\pi$
$68$			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	0.739784	−	0.672844i	$-0.234928\pi$
$71$	−1.79315	−	3.10583i	−0.212808	−	0.368594i	−0.952592	+	0.304250i	$0.901594\pi$
$72$	−1.52677	−	0.283763i	−0.179931	−	0.0334418i
$73$	1.50000	+	2.59808i	0.175562	+	0.304082i	0.940356	−	0.340193i	$-0.110493\pi$
$73$	1.50000	+	2.59808i	0.175562	+	0.304082i	−0.764794	+	0.644275i	$0.777159\pi$
$74$	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	−0.662270	−	0.749265i	$-0.730407\pi$
$79$	−3.06218	+	1.76795i	−0.344522	+	0.198910i	0.317748	+	0.948175i	$0.397073\pi$
$80$	−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	$-0.860592\pi$
$83$		−	7.72741i		−	0.848193i	0.905617	−	0.424097i	$-0.139408\pi$
$84$	−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	−0.992378	−	0.123231i	$-0.960674\pi$
$89$	−3.67423	+	6.36396i	−0.389468	+	0.674579i	0.602910	+	0.797809i	$0.294008\pi$
$90$	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	−0.134547	−	0.990907i	$-0.542958\pi$
$97$	6.46410	−	3.73205i	0.656330	−	0.378932i	0.790877	+	0.611975i	$0.209625\pi$
$98$	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	0.128626	−	0.991693i	$-0.458943\pi$
$101$	−6.69213	−	3.86370i	−0.665892	−	0.384453i	−0.794518	+	0.607240i	$0.792277\pi$
$102$	9.46410	−	13.3843i	0.937086	−	1.32524i
$103$			10.4641i			1.03106i	0.856872	+	0.515529i	$0.172405\pi$
$103$			10.4641i			1.03106i	−0.856872	+	0.515529i	$0.827595\pi$
$104$	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	−0.959176	−	0.282809i	$-0.908734\pi$
$109$	−12.4641	+	7.19615i	−1.19384	+	0.689266i	−0.234668	+	0.972076i	$0.575400\pi$
$110$	−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	0.770513	−	0.637424i	$-0.220000\pi$
$127$	6.80385	+	3.92820i	0.603744	+	0.348572i	−0.166769	+	0.985996i	$0.553333\pi$
$128$	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	−0.739936	−	0.672677i	$-0.765144\pi$
$131$	−6.03579	+	3.48477i	−0.527350	+	0.304465i	0.212587	+	0.977142i	$0.431811\pi$
$132$	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	0.471700	−	0.881759i	$-0.343640\pi$
$137$	−0.656339	−	0.378937i	−0.0560748	−	0.0323748i	−0.527775	+	0.849384i	$0.676974\pi$
$138$	1.26260	+	0.116337i	0.107480	+	0.00990322i
$139$	−6.59808	+	11.4282i	−0.559642	+	0.969328i	0.437885	+	0.899031i	$0.355728\pi$
$139$	−6.59808	+	11.4282i	−0.559642	+	0.969328i	−0.997526	+	0.0702964i	$0.977605\pi$
$140$			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	0.236972	−	0.971516i	$-0.423845\pi$
$149$	14.6090	−	8.43451i	1.19682	−	0.690982i	0.959844	+	0.280534i	$0.0905116\pi$
$150$	−0.921022	+	9.99585i	−0.0752011	+	0.816158i
$151$		−	2.00000i		−	0.162758i	−0.996683	−	0.0813788i	$-0.974068\pi$
$151$		−	2.00000i		−	0.162758i	0.996683	−	0.0813788i	$-0.0259324\pi$
$152$	−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	0.786813	−	0.617192i	$-0.211730\pi$
$157$	−1.76795	−	3.06218i	−0.141098	−	0.244388i	−0.927910	+	0.372804i	$0.878397\pi$
$158$	−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	−0.974997	−	0.222216i	$-0.928671\pi$
$167$	−3.81294	+	6.60420i	−0.295054	+	0.511048i	0.679944	+	0.733264i	$0.262004\pi$
$168$	−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	0.998459	−	0.0554909i	$-0.0176724\pi$
$173$	5.93426	+	10.2784i	0.451173	+	0.781455i	−0.547286	+	0.836946i	$0.684339\pi$
$174$	−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	0.384345	−	0.923190i	$-0.374427\pi$
$181$	−3.00000	−	1.73205i	−0.222988	−	0.128742i	−0.607333	+	0.794447i	$0.707761\pi$
$182$		−	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	$0.0194929\pi$
$191$			1.69161i			0.122401i	−0.998125	+	0.0612005i	$0.980507\pi$
$192$	−0.910930	+	9.88633i	−0.0657407	+	0.713484i
$193$	11.4282	−	6.59808i	0.822620	−	0.474940i	−0.0286991	−	0.999588i	$-0.509136\pi$
$193$	11.4282	−	6.59808i	0.822620	−	0.474940i	0.851319	+	0.524648i	$0.175803\pi$
$194$	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	$-0.894415\pi$
$197$		−	9.14162i		−	0.651313i	0.945488	−	0.325657i	$-0.105585\pi$
$198$	−2.07055	+	0.732051i	−0.147148	+	0.0520246i
$199$	6.40192	−	11.0885i	0.453820	−	0.786040i	−0.544799	−	0.838567i	$-0.683394\pi$
$199$	6.40192	−	11.0885i	0.453820	−	0.786040i	0.998620	+	0.0525267i	$0.0167275\pi$
$200$	−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	−0.790681	−	0.612228i	$-0.790273\pi$
$211$	−9.52628	+	5.50000i	−0.655816	+	0.378636i	0.134865	+	0.990864i	$0.456940\pi$
$212$	−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	−0.746978	−	0.664849i	$-0.768496\pi$
$223$	−8.13397	+	4.69615i	−0.544691	+	0.314478i	0.202287	+	0.979326i	$0.435163\pi$
$224$	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	−0.394803	−	0.918766i	$-0.629187\pi$
$233$	3.10583	−	1.79315i	0.203470	−	0.117473i	0.598273	+	0.801292i	$0.295854\pi$
$234$	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	$0.421168\pi$
$239$			29.9759i			1.93898i	−0.245133	+	0.969489i	$0.578832\pi$
$240$	−6.31319	+	8.92820i	−0.407515	+	0.576313i
$241$	−24.8205	−	14.3301i	−1.59883	−	0.923085i	−0.991713	−	0.128472i	$-0.958993\pi$
$241$	−24.8205	−	14.3301i	−1.59883	−	0.923085i	−0.607116	−	0.794613i	$-0.707674\pi$
$242$	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	0.844651	−	0.535317i	$-0.179808\pi$
$251$	12.7279	+	7.34847i	0.803379	+	0.463831i	−0.0412721	+	0.999148i	$0.513141\pi$
$252$	−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	−0.911699	−	0.410859i	$-0.865229\pi$
$257$	−1.60368	+	2.77766i	−0.100035	+	0.173266i	0.811664	+	0.584125i	$0.198562\pi$
$258$	−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	−0.485113	−	0.874451i	$-0.661222\pi$
$263$	0.480473	−	0.277401i	0.0296273	−	0.0171053i	0.514740	+	0.857346i	$0.327888\pi$
$264$	−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	0.759236	−	0.650815i	$-0.225573\pi$
$269$	−3.01790	−	5.22715i	−0.184004	−	0.318705i	−0.943241	+	0.332110i	$0.892239\pi$
$270$	10.1762	−	9.89828i	0.619303	−	0.602390i
$271$	3.46410	+	6.00000i	0.210429	+	0.364474i	0.951849	−	0.306568i	$-0.0991805\pi$
$271$	3.46410	+	6.00000i	0.210429	+	0.364474i	−0.741420	+	0.671042i	$0.765847\pi$
$272$	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	−0.548689	−	0.836027i	$-0.684873\pi$
$281$	7.53794	−	13.0561i	0.449676	−	0.778861i	0.998365	+	0.0571654i	$0.0182062\pi$
$282$	35.1715	+	3.24072i	2.09443	+	0.192982i
$283$	10.9282	+	18.9282i	0.649614	+	1.12516i	0.983215	+	0.182450i	$0.0584029\pi$
$283$	10.9282	+	18.9282i	0.649614	+	1.12516i	−0.333601	+	0.942714i	$0.608264\pi$
$284$	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	−0.801690	−	0.597740i	$-0.796065\pi$
$307$	−12.0000	+	6.92820i	−0.684876	+	0.395413i	0.116814	+	0.993154i	$0.462732\pi$
$308$	−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	$-0.720408\pi$
$311$		−	27.1475i		−	1.53939i	0.638411	−	0.769696i	$-0.279592\pi$
$312$	1.93185	−	2.73205i	0.109370	−	0.154672i
$313$	12.3923	−	21.4641i	0.700454	−	1.21322i	−0.267853	−	0.963460i	$-0.586314\pi$
$313$	12.3923	−	21.4641i	0.700454	−	1.21322i	0.968307	−	0.249763i	$-0.0803527\pi$
$314$	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	−0.605468	−	0.795870i	$-0.707014\pi$
$317$	6.88160	−	11.9193i	0.386509	−	0.669453i	0.991977	+	0.126416i	$0.0403474\pi$
$318$	−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	$-0.659232\pi$
$331$		−	31.9282i		−	1.75493i	0.479638	−	0.877466i	$-0.340768\pi$
$332$	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	−0.316779	−	0.948499i	$-0.602601\pi$
$337$	6.35641	−	3.66987i	0.346256	−	0.199911i	0.663035	+	0.748589i	$0.269268\pi$
$338$	−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	−0.950439	−	0.310911i	$-0.899366\pi$
$347$	−21.5414	+	12.4369i	−1.15640	+	0.667649i	−0.205963	+	0.978560i	$0.566032\pi$
$348$	−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	$0.103196\pi$
$353$			11.9700i			0.637101i	−0.947906	+	0.318551i	$0.896804\pi$
$354$	−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	0.257846	−	0.966186i	$-0.416987\pi$
$359$	23.1822	−	13.3843i	1.22351	−	0.706394i	0.965665	+	0.259792i	$0.0836539\pi$
$360$	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	−0.552989	−	0.833189i	$-0.686513\pi$
$367$	8.52628	−	14.7679i	0.445068	−	0.770881i	0.998057	+	0.0623080i	$0.0198461\pi$
$368$			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	$-0.894790\pi$
$373$		−	12.5359i		−	0.649084i	0.945871	−	0.324542i	$-0.105210\pi$
$374$	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	$-0.849007\pi$
$379$		−	17.7846i		−	0.913534i	0.889586	−	0.456767i	$-0.150993\pi$
$380$	−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	−0.974581	−	0.224034i	$-0.928077\pi$
$383$	−13.3335	−	23.0943i	−0.681310	−	1.18006i	0.293272	−	0.956029i	$-0.405256\pi$
$384$	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	0.386182	−	0.922423i	$-0.373794\pi$
$389$	−4.33057	−	2.50026i	−0.219569	−	0.126768i	−0.605751	+	0.795655i	$0.707127\pi$
$390$	−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	0.742539	−	0.669803i	$-0.233622\pi$
$397$	−4.16025	−	7.20577i	−0.208797	−	0.361647i	−0.951336	+	0.308156i	$0.900288\pi$
$398$	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	0.973064	−	0.230537i	$-0.0740482\pi$
$401$	5.74479	+	9.95026i	0.286881	+	0.496892i	−0.686183	+	0.727429i	$0.740715\pi$
$402$	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	0.962688	−	0.270615i	$-0.0872270\pi$
$409$	24.4641	+	14.1244i	1.20967	+	0.698404i	0.246984	+	0.969019i	$0.420560\pi$
$410$			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	$0.286202\pi$
$419$			32.0464i			1.56557i	−0.622292	+	0.782785i	$0.713798\pi$
$420$	15.7670	+	1.45277i	0.769349	+	0.0708881i
$421$	−30.7128	+	17.7321i	−1.49685	+	0.864207i	−0.999993	−	0.00362487i	$-0.998846\pi$
$421$	−30.7128	+	17.7321i	−1.49685	+	0.864207i	−0.496857	+	0.867832i	$0.665513\pi$
$422$	−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	0.377635	+	0.925954i	$0.376737\pi$
$431$	−12.7279	+	22.0454i	−0.613082	+	1.06189i	−0.990718	+	0.135935i	$0.956596\pi$
$432$	−22.4867	+	5.69287i	−1.08189	+	0.273898i
$433$	2.89230	+	1.66987i	0.138995	+	0.0802490i	0.567885	−	0.823108i	$-0.307762\pi$
$433$	2.89230	+	1.66987i	0.138995	+	0.0802490i	−0.428890	+	0.903357i	$0.641095\pi$
$434$	−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	0.0421712	−	0.999110i	$-0.486573\pi$
$439$	19.4545	−	11.2321i	0.928512	−	0.536077i	0.886341	+	0.463034i	$0.153239\pi$
$440$	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	0.993345	+	0.115177i	$0.0367435\pi$
$443$	33.4607	+	19.3185i	1.58976	+	0.917850i	0.596419	+	0.802674i	$0.296590\pi$
$444$	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	0.341452	−	0.939899i	$-0.389081\pi$
$461$	28.4737	−	16.4393i	1.32615	−	0.765656i	0.984703	+	0.174244i	$0.0557481\pi$
$462$	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	$-0.824613\pi$
$467$		−	22.6274i		−	1.04707i	0.852004	−	0.523536i	$-0.175387\pi$
$468$	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	0.246453	−	0.969155i	$-0.420735\pi$
$479$	−10.2784	−	5.93426i	−0.469634	−	0.271143i	−0.716086	+	0.698012i	$0.754068\pi$
$480$	−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	$0.191048\pi$
$487$			24.9282i			1.12960i	−0.825226	+	0.564802i	$0.808952\pi$
$488$	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	−0.291666	−	0.956520i	$-0.594210\pi$
$491$	8.66115	−	5.00052i	0.390872	−	0.225670i	0.682538	+	0.730850i	$0.260876\pi$
$492$	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	0.988111	−	0.153740i	$-0.0491319\pi$
$499$	8.06218	+	13.9641i	0.360913	+	0.625119i	−0.627199	+	0.778859i	$0.715799\pi$
$500$	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	0.103583	−	0.994621i	$-0.466969\pi$
$503$	−15.8338	−	9.14162i	−0.705992	−	0.407605i	−0.809575	+	0.587016i	$0.800303\pi$
$504$	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	−0.976391	−	0.216011i	$-0.930695\pi$
$509$	−6.79367	+	11.7670i	−0.301124	+	0.521562i	0.675267	+	0.737574i	$0.264028\pi$
$510$	−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	0.145641	−	0.989337i	$-0.453475\pi$
$523$	−14.5981	−	8.42820i	−0.638329	−	0.368540i	−0.783971	+	0.620798i	$0.786809\pi$
$524$		−	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	−0.613655	−	0.789574i	$-0.710302\pi$
$541$	8.76795	−	15.1865i	0.376964	−	0.652920i	0.990619	+	0.136654i	$0.0436349\pi$
$542$	−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	0.242716	−	0.970097i	$-0.421962\pi$
$547$	−11.1340	−	6.42820i	−0.476054	−	0.274850i	−0.718771	+	0.695247i	$0.755295\pi$
$548$	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	0.436641	−	0.899636i	$-0.356168\pi$
$557$	−2.92996	−	1.69161i	−0.124147	−	0.0716760i	−0.560787	+	0.827960i	$0.689501\pi$
$558$	−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	−0.295783	−	0.955255i	$-0.595580\pi$
$587$	9.29392	−	5.36585i	0.383601	−	0.221472i	0.679384	+	0.733783i	$0.262247\pi$
$588$	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	−0.0190636	−	0.999818i	$-0.506069\pi$
$593$	−21.7816	−	12.5756i	−0.894463	−	0.516419i	−0.875400	+	0.483400i	$0.839402\pi$
$594$	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	−0.985286	−	0.170916i	$-0.945327\pi$
$599$	−8.43451	+	14.6090i	−0.344625	+	0.596908i	0.640661	+	0.767824i	$0.278661\pi$
$600$	2.19615	+	1.55291i	0.0896575	+	0.0633975i
$601$			44.3731i			1.81002i	0.425395	+	0.905008i	$0.360135\pi$
$601$			44.3731i			1.81002i	−0.425395	+	0.905008i	$0.639865\pi$
$602$	−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	$-0.913348\pi$
$607$		−	13.2487i		−	0.537749i	0.963175	−	0.268874i	$-0.0866516\pi$
$608$	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	0.541582	−	0.840648i	$-0.317825\pi$
$613$	−11.3205	−	19.6077i	−0.457231	−	0.791947i	−0.998813	+	0.0487003i	$0.984492\pi$
$614$	−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	0.878275	−	0.478156i	$-0.158695\pi$
$617$	22.4379	+	12.9546i	0.903318	+	0.521531i	0.0250427	+	0.999686i	$0.492028\pi$
$618$	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	−0.301058	+	0.953606i	$0.597340\pi$
$631$	−24.5263	+	42.4808i	−0.976376	+	1.69113i	−0.675318	+	0.737526i	$0.735994\pi$
$632$	−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	0.711084	−	0.703107i	$-0.248205\pi$
$641$	−6.41473	−	11.1106i	−0.253367	−	0.438844i	−0.964451	+	0.264263i	$0.914871\pi$
$642$	−14.8883	+	6.85906i	−0.587594	+	0.270705i
$643$	21.7942	+	37.7487i	0.859480	+	1.48866i	0.872425	+	0.488748i	$0.162546\pi$
$643$	21.7942	+	37.7487i	0.859480	+	1.48866i	−0.0129447	+	0.999916i	$0.504121\pi$
$644$	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	$-0.867589\pi$
$647$		−	20.5569i		−	0.808174i	0.914721	−	0.404087i	$-0.132411\pi$
$648$	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	$0.373462\pi$
$653$			47.1223i			1.84404i	−0.387144	+	0.922019i	$0.626538\pi$
$654$	−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	0.340113	+	0.940385i	$0.389535\pi$
$659$	−16.5409	+	28.6496i	−0.644340	+	1.11603i	−0.984453	+	0.175646i	$0.943799\pi$
$660$	−0.147509	+	1.60091i	−0.00574177	+	0.0623155i
$661$	5.32051	+	3.07180i	0.206944	+	0.119479i	0.599890	−	0.800082i	$-0.295211\pi$
$661$	5.32051	+	3.07180i	0.206944	+	0.119479i	−0.392946	+	0.919561i	$0.628544\pi$
$662$	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	$-0.860749\pi$
$673$		−	21.9808i		−	0.847296i	0.905827	−	0.423648i	$-0.139251\pi$
$674$	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	−0.137881	−	0.990449i	$-0.544029\pi$
$701$	17.2344	−	9.95026i	0.650933	−	0.375816i	0.788814	+	0.614633i	$0.210696\pi$
$702$	−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	0.128346	+	0.991729i	$0.459033\pi$
$709$	−21.1603	+	36.6506i	−0.794690	+	1.37644i	−0.923036	+	0.384714i	$0.874300\pi$
$710$			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	−0.594293	−	0.804249i	$-0.702568\pi$
$719$	−5.22715	+	3.01790i	−0.194940	+	0.112549i	0.399353	+	0.916797i	$0.369235\pi$
$720$	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	0.964072	−	0.265641i	$-0.0855836\pi$
$727$	6.79423	+	11.7679i	0.251984	+	0.436449i	−0.712088	+	0.702090i	$0.752250\pi$
$728$	−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	0.985401	+	0.170249i	$0.0544570\pi$
$739$	17.4019	+	30.1410i	0.640140	+	1.10876i	−0.345261	+	0.938507i	$0.612210\pi$
$740$	−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	0.923563	−	0.383447i	$-0.125263\pi$
$743$	3.53553	+	6.12372i	0.129706	+	0.224658i	−0.793857	+	0.608105i	$0.791930\pi$
$744$	−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	0.357786	−	0.933803i	$-0.383532\pi$
$751$	−7.45448	−	4.30385i	−0.272018	−	0.157050i	−0.629804	+	0.776754i	$0.716865\pi$
$752$			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	0.821117	−	0.570760i	$-0.193352\pi$
$757$	−2.30385	−	3.99038i	−0.0837348	−	0.145033i	−0.904851	+	0.425728i	$0.860018\pi$
$758$	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	$-0.683425\pi$
$761$		−	46.2629i		−	1.67703i	0.544879	−	0.838514i	$-0.316575\pi$
$762$	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	−0.858201	−	0.513313i	$-0.828418\pi$
$769$	0.428203	−	0.741670i	0.0154414	−	0.0267453i	0.873643	+	0.486568i	$0.161751\pi$
$770$	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	−0.981543	−	0.191244i	$-0.938748\pi$
$773$	−9.04008	+	15.6579i	−0.325149	+	0.563175i	0.656393	+	0.754419i	$0.272081\pi$
$774$	−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	$0.141146\pi$
$787$			24.0718i			0.858067i	−0.903289	+	0.429033i	$0.858854\pi$
$788$	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	$-0.644020\pi$
$809$		−	51.1619i		−	1.79876i	0.437172	−	0.899378i	$-0.355980\pi$
$810$	−15.4548	−	19.1244i	−0.543027	−	0.671961i
$811$	18.8038	+	10.8564i	0.660292	+	0.381220i	0.792388	−	0.610017i	$-0.208837\pi$
$811$	18.8038	+	10.8564i	0.660292	+	0.381220i	−0.132096	+	0.991237i	$0.542171\pi$
$812$	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	0.920575	−	0.390566i	$-0.127721\pi$
$821$	29.8744	+	17.2480i	1.04262	+	0.601958i	0.122047	+	0.992524i	$0.461054\pi$
$822$	−2.52520	−	0.232673i	−0.0880765	−	0.00811540i
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	−0.787850	−	0.615867i	$-0.788806\pi$
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	0.927281	+	0.374365i	$0.122139\pi$
$824$			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	−0.996503	−	0.0835608i	$-0.973371\pi$
$827$	−12.2474	+	21.2132i	−0.425886	+	0.737655i	0.570617	+	0.821216i	$0.306704\pi$
$828$	1.85641	−	0.656339i	0.0645146	−	0.0228093i
$829$		−	38.6603i		−	1.34273i	−0.741129	−	0.671363i	$-0.765709\pi$
$829$		−	38.6603i		−	1.34273i	0.741129	−	0.671363i	$-0.234291\pi$
$830$	−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	0.911437	−	0.411440i	$-0.134974\pi$
$839$	2.87920	+	4.98691i	0.0994009	+	0.172167i	−0.812036	+	0.583607i	$0.801641\pi$
$840$	−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	0.646943	−	0.762539i	$-0.276047\pi$
$853$	−9.83975	−	17.0429i	−0.336906	−	0.583539i	−0.983849	+	0.178999i	$0.942714\pi$
$854$	−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	0.890752	−	0.454489i	$-0.150178\pi$
$857$	1.51575	+	2.62536i	0.0517770	+	0.0896804i	−0.838975	+	0.544170i	$0.816845\pi$
$858$	0.434174	−	4.71209i	0.0148224	−	0.160868i
$859$	2.33013	−	4.03590i	0.0795029	−	0.137703i	−0.823533	−	0.567269i	$-0.808000\pi$
$859$	2.33013	−	4.03590i	0.0795029	−	0.137703i	0.903036	+	0.429566i	$0.141333\pi$
$860$	−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	−0.553576	−	0.832799i	$-0.686737\pi$
$877$	−3.23205	+	1.86603i	−0.109139	+	0.0630112i	0.444437	+	0.895810i	$0.353404\pi$
$878$	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	$0.234246\pi$
$881$			39.8482i			1.34252i	−0.741222	+	0.671260i	$0.765754\pi$
$882$	−13.3843	−	37.8564i	−0.450672	−	1.27469i
$883$	11.1340	−	19.2846i	0.374688	−	0.648979i	−0.615592	−	0.788065i	$-0.711083\pi$
$883$	11.1340	−	19.2846i	0.374688	−	0.648979i	0.990280	+	0.139086i	$0.0444165\pi$
$884$	−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	−0.948837	−	0.315766i	$-0.897739\pi$
$887$	−5.98502	+	10.3664i	−0.200957	+	0.348068i	0.747880	+	0.663834i	$0.231072\pi$
$888$	−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	0.221626	−	0.975132i	$-0.428864\pi$
$907$	35.4449	−	20.4641i	1.17693	−	0.679499i	0.955302	+	0.295632i	$0.0955304\pi$
$908$	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	−0.180407	−	0.983592i	$-0.557742\pi$
$929$	17.7148	−	10.2277i	0.581205	−	0.335559i	0.761612	+	0.648033i	$0.224408\pi$
$930$	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	−0.909395	−	0.415934i	$-0.863455\pi$
$937$	−2.89230	+	5.00962i	−0.0944875	+	0.163657i	0.814907	+	0.579592i	$0.196788\pi$
$938$		−	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	−0.956977	−	0.290163i	$-0.906291\pi$
$941$	−6.96953	+	12.0716i	−0.227200	+	0.393522i	0.729777	+	0.683685i	$0.239624\pi$
$942$	−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	0.276107	−	0.961127i	$-0.410956\pi$
$947$	38.3596	−	22.1469i	1.24652	−	0.719679i	0.970414	+	0.241448i	$0.0776223\pi$
$948$	−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	0.971834	+	0.235668i	$0.0757279\pi$
$953$	21.3011	+	36.8947i	0.690011	+	1.19513i	−0.281822	+	0.959467i	$0.590939\pi$
$954$	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	0.928083	−	0.372374i	$-0.121456\pi$
$967$	4.40192	+	7.62436i	0.141556	+	0.245183i	−0.786527	+	0.617556i	$0.788123\pi$
$968$	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	0.727681	−	0.685916i	$-0.240598\pi$
$971$	−7.17260	−	12.4233i	−0.230180	−	0.398683i	−0.957861	+	0.287232i	$0.907265\pi$
$972$	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	0.999763	+	0.0217569i	$0.00692599\pi$
$983$	16.2635	+	28.1691i	0.518724	+	0.898456i	−0.481040	+	0.876699i	$0.659741\pi$
$984$	−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	−0.556352	−	0.830946i	$-0.687800\pi$
$991$	−3.61731	+	2.08846i	−0.114908	+	0.0663420i	0.441445	+	0.897289i	$0.354466\pi$
$992$	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	0.128559	+	0.991702i	$0.458965\pi$
$997$	−25.0885	+	43.4545i	−0.794559	+	1.37622i	−0.923119	+	0.384515i	$0.874369\pi$
$998$	−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.50.4	yes	8
3.2	odd	2	inner	57.2.f.a.50.1	yes	8
4.3	odd	2		912.2.bn.m.449.2		8
12.11	even	2		912.2.bn.m.449.1		8
19.7	even	3		1083.2.d.b.1082.2		8
19.8	odd	6	inner	57.2.f.a.8.1	✓	8
19.12	odd	6		1083.2.d.b.1082.7		8
57.8	even	6	inner	57.2.f.a.8.4	yes	8
57.26	odd	6		1083.2.d.b.1082.8		8
57.50	even	6		1083.2.d.b.1082.1		8
76.27	even	6		912.2.bn.m.65.1		8
228.179	odd	6		912.2.bn.m.65.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.f.a.8.1	✓	8	19.8	odd	6	inner
57.2.f.a.8.4	yes	8	57.8	even	6	inner
57.2.f.a.50.1	yes	8	3.2	odd	2	inner
57.2.f.a.50.4	yes	8	1.1	even	1	trivial
912.2.bn.m.65.1		8	76.27	even	6
912.2.bn.m.65.2		8	228.179	odd	6
912.2.bn.m.449.1		8	12.11	even	2
912.2.bn.m.449.2		8	4.3	odd	2
1083.2.d.b.1082.1		8	57.50	even	6
1083.2.d.b.1082.2		8	19.7	even	3
1083.2.d.b.1082.7		8	19.12	odd	6
1083.2.d.b.1082.8		8	57.26	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more