LMFDB - Embedded newform 57.2.f.a.8.3

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			8.3
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	57.8
Dual form			57.2.f.a.50.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.448288i) q^{2} +(-0.158919 - 1.72474i) q^{3} +(0.866025 + 1.50000i) q^{4} +(-1.22474 - 0.707107i) q^{5} +(-0.814313 - 0.375156i) q^{6} -0.267949 q^{7} +1.93185 q^{8} +(-2.94949 + 0.548188i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.448288i) q^{2} +(-0.158919 - 1.72474i) q^{3} +(0.866025 + 1.50000i) q^{4} +(-1.22474 - 0.707107i) q^{5} +(-0.814313 - 0.375156i) q^{6} -0.267949 q^{7} +1.93185 q^{8} +(-2.94949 + 0.548188i) q^{9} +(-0.633975 + 0.366025i) q^{10} +5.27792i q^{11} +(2.44949 - 1.73205i) q^{12} +(-0.232051 + 0.133975i) q^{13} +(-0.0693504 + 0.120118i) q^{14} +(-1.02494 + 2.22474i) q^{15} +(-1.23205 + 2.13397i) q^{16} +(-4.24264 - 2.44949i) q^{17} +(-0.517638 + 1.46410i) q^{18} +(1.73205 - 4.00000i) q^{19} -2.44949i q^{20} +(0.0425821 + 0.462144i) q^{21} +(2.36603 + 1.36603i) q^{22} +(4.57081 - 2.63896i) q^{23} +(-0.307007 - 3.33195i) q^{24} +(-1.50000 - 2.59808i) q^{25} +0.138701i q^{26} +(1.41421 + 5.00000i) q^{27} +(-0.232051 - 0.401924i) q^{28} +(-1.03528 - 1.79315i) q^{29} +(0.732051 + 1.03528i) q^{30} +2.46410i q^{31} +(2.56961 + 4.45069i) q^{32} +(9.10306 - 0.838759i) q^{33} +(-2.19615 + 1.26795i) q^{34} +(0.328169 + 0.189469i) q^{35} +(-3.37662 - 3.94949i) q^{36} -7.73205i q^{37} +(-1.34486 - 1.81173i) q^{38} +(0.267949 + 0.378937i) q^{39} +(-2.36603 - 1.36603i) q^{40} +(2.82843 - 4.89898i) q^{41} +(0.218195 + 0.100523i) q^{42} +(-2.86603 + 4.96410i) q^{43} +(-7.91688 + 4.57081i) q^{44} +(4.00000 + 1.41421i) q^{45} -2.73205i q^{46} +(0.656339 - 0.378937i) q^{47} +(3.87636 + 1.78585i) q^{48} -6.92820 q^{49} -1.55291 q^{50} +(-3.55051 + 7.70674i) q^{51} +(-0.401924 - 0.232051i) q^{52} +(5.46739 + 9.46979i) q^{53} +(2.60746 + 0.660121i) q^{54} +(3.73205 - 6.46410i) q^{55} -0.517638 q^{56} +(-7.17423 - 2.35167i) q^{57} -1.07180 q^{58} +(-5.60609 + 9.71003i) q^{59} +(-4.22474 + 0.389270i) q^{60} +(5.23205 + 9.06218i) q^{61} +(1.10463 + 0.637756i) q^{62} +(0.790313 - 0.146887i) q^{63} -2.26795 q^{64} +0.378937 q^{65} +(1.98004 - 4.29788i) q^{66} +(-0.866025 + 0.500000i) q^{67} -8.48528i q^{68} +(-5.27792 - 7.46410i) q^{69} +(0.169873 - 0.0980762i) q^{70} +(6.69213 - 11.5911i) q^{71} +(-5.69798 + 1.05902i) q^{72} +(1.50000 - 2.59808i) q^{73} +(-3.46618 - 2.00120i) q^{74} +(-4.24264 + 3.00000i) q^{75} +(7.50000 - 0.866025i) q^{76} -1.41421i q^{77} +(0.239223 - 0.0220421i) q^{78} +(9.06218 + 5.23205i) q^{79} +(3.01790 - 1.74238i) q^{80} +(8.39898 - 3.23375i) q^{81} +(-1.46410 - 2.53590i) q^{82} -2.07055i q^{83} +(-0.656339 + 0.464102i) q^{84} +(3.46410 + 6.00000i) q^{85} +(1.48356 + 2.56961i) q^{86} +(-2.92820 + 2.07055i) q^{87} +10.1962i q^{88} +(-3.67423 - 6.36396i) q^{89} +(1.66925 - 1.42713i) q^{90} +(0.0621778 - 0.0358984i) q^{91} +(7.91688 + 4.57081i) q^{92} +(4.24995 - 0.391592i) q^{93} -0.392305i q^{94} +(-4.94975 + 3.67423i) q^{95} +(7.26795 - 5.13922i) q^{96} +(-0.464102 - 0.267949i) q^{97} +(-1.79315 + 3.10583i) q^{98} +(-2.89329 - 15.5672i) 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 $

$2$	0.258819	−	0.448288i	0.183013	−	0.316987i	−0.759892	−	0.650049i	$-0.774748\pi$
$2$	0.258819	−	0.448288i	0.183013	−	0.316987i	0.942905	+	0.333062i	$0.108082\pi$
$3$	−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	$0.769083\pi$
$6$	−0.814313	−	0.375156i	−0.332442	−	0.153157i
$7$	−0.267949			−0.101275			−0.0506376	−	0.998717i	$-0.516125\pi$
$7$	−0.267949			−0.101275			−0.0506376	+	0.998717i	$0.516125\pi$
$8$	1.93185			0.683013
$9$	−2.94949	+	0.548188i	−0.983163	+	0.182729i
$10$	−0.633975	+	0.366025i	−0.200480	+	0.115747i
$11$			5.27792i			1.59135i	0.605723	+	0.795676i	$0.292884\pi$
$11$			5.27792i			1.59135i	−0.605723	+	0.795676i	$0.707116\pi$
$12$	2.44949	−	1.73205i	0.707107	−	0.500000i
$13$	−0.232051	+	0.133975i	−0.0643593	+	0.0371579i	−0.531834	−	0.846848i	$-0.678497\pi$
$13$	−0.232051	+	0.133975i	−0.0643593	+	0.0371579i	0.467475	+	0.884006i	$0.345164\pi$
$14$	−0.0693504	+	0.120118i	−0.0185347	+	0.0321030i
$15$	−1.02494	+	2.22474i	−0.264639	+	0.574427i
$16$	−1.23205	+	2.13397i	−0.308013	+	0.533494i
$17$	−4.24264	−	2.44949i	−1.02899	−	0.594089i	−0.112296	−	0.993675i	$-0.535820\pi$
$17$	−4.24264	−	2.44949i	−1.02899	−	0.594089i	−0.916696	+	0.399586i	$0.869154\pi$
$18$	−0.517638	+	1.46410i	−0.122008	+	0.345092i
$19$	1.73205	−	4.00000i	0.397360	−	0.917663i
$19$	1.73205	−	4.00000i	0.397360	−	0.917663i
$20$		−	2.44949i		−	0.547723i
$21$	0.0425821	+	0.462144i	0.00929218	+	0.100848i
$22$	2.36603	+	1.36603i	0.504438	+	0.291238i
$23$	4.57081	−	2.63896i	0.953080	−	0.550261i	0.0590435	−	0.998255i	$-0.481195\pi$
$23$	4.57081	−	2.63896i	0.953080	−	0.550261i	0.894036	+	0.447995i	$0.147862\pi$
$24$	−0.307007	−	3.33195i	−0.0626676	−	0.680132i
$25$	−1.50000	−	2.59808i	−0.300000	−	0.519615i
$26$			0.138701i			0.0272014i
$27$	1.41421	+	5.00000i	0.272166	+	0.962250i
$28$	−0.232051	−	0.401924i	−0.0438535	−	0.0759565i
$29$	−1.03528	−	1.79315i	−0.192246	−	0.332980i	0.753748	−	0.657163i	$-0.228244\pi$
$29$	−1.03528	−	1.79315i	−0.192246	−	0.332980i	−0.945994	+	0.324184i	$0.894910\pi$
$30$	0.732051	+	1.03528i	0.133654	+	0.189015i
$31$			2.46410i			0.442566i	0.975210	+	0.221283i	$0.0710244\pi$
$31$			2.46410i			0.442566i	−0.975210	+	0.221283i	$0.928976\pi$
$32$	2.56961	+	4.45069i	0.454247	+	0.786779i
$33$	9.10306	−	0.838759i	1.58464	−	0.146009i
$34$	−2.19615	+	1.26795i	−0.376637	+	0.217451i
$35$	0.328169	+	0.189469i	0.0554708	+	0.0320261i
$36$	−3.37662	−	3.94949i	−0.562769	−	0.658248i
$37$		−	7.73205i		−	1.27114i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$		−	7.73205i		−	1.27114i	0.772043	−	0.635571i	$-0.219235\pi$
$38$	−1.34486	−	1.81173i	−0.218166	−	0.293902i
$39$	0.267949	+	0.378937i	0.0429062	+	0.0606785i
$40$	−2.36603	−	1.36603i	−0.374101	−	0.215988i
$41$	2.82843	−	4.89898i	0.441726	−	0.765092i	−0.556092	−	0.831121i	$-0.687700\pi$
$41$	2.82843	−	4.89898i	0.441726	−	0.765092i	0.997818	+	0.0660290i	$0.0210330\pi$
$42$	0.218195	+	0.100523i	0.0336681	+	0.0155110i
$43$	−2.86603	+	4.96410i	−0.437065	+	0.757018i	−0.997462	−	0.0712058i	$-0.977315\pi$
$43$	−2.86603	+	4.96410i	−0.437065	+	0.757018i	0.560397	+	0.828224i	$0.310649\pi$
$44$	−7.91688	+	4.57081i	−1.19351	+	0.689076i
$45$	4.00000	+	1.41421i	0.596285	+	0.210819i
$46$		−	2.73205i		−	0.402819i
$47$	0.656339	−	0.378937i	0.0957369	−	0.0552737i	−0.451367	−	0.892338i	$-0.649064\pi$
$47$	0.656339	−	0.378937i	0.0957369	−	0.0552737i	0.547104	+	0.837065i	$0.315730\pi$
$48$	3.87636	+	1.78585i	0.559504	+	0.257765i
$49$	−6.92820			−0.989743
$50$	−1.55291			−0.219615
$51$	−3.55051	+	7.70674i	−0.497171	+	1.07916i
$52$	−0.401924	−	0.232051i	−0.0557368	−	0.0321797i
$53$	5.46739	+	9.46979i	0.751003	+	1.30078i	0.947337	+	0.320239i	$0.103763\pi$
$53$	5.46739	+	9.46979i	0.751003	+	1.30078i	−0.196334	+	0.980537i	$0.562904\pi$
$54$	2.60746	+	0.660121i	0.354831	+	0.0898310i
$55$	3.73205	−	6.46410i	0.503230	−	0.871619i
$56$	−0.517638			−0.0691723
$57$	−7.17423	−	2.35167i	−0.950251	−	0.311486i
$58$	−1.07180			−0.140734
$59$	−5.60609	+	9.71003i	−0.729850	+	1.26414i	0.227096	+	0.973872i	$0.427077\pi$
$59$	−5.60609	+	9.71003i	−0.729850	+	1.26414i	−0.956946	+	0.290265i	$0.906256\pi$
$60$	−4.22474	+	0.389270i	−0.545412	+	0.0502545i
$61$	5.23205	+	9.06218i	0.669895	+	1.16029i	0.977933	+	0.208919i	$0.0669944\pi$
$61$	5.23205	+	9.06218i	0.669895	+	1.16029i	−0.308038	+	0.951374i	$0.599672\pi$
$62$	1.10463	+	0.637756i	0.140288	+	0.0809951i
$63$	0.790313	−	0.146887i	0.0995701	−	0.0185060i
$64$	−2.26795			−0.283494
$65$	0.378937			0.0470014
$66$	1.98004	−	4.29788i	0.243726	−	0.529032i
$67$	−0.866025	+	0.500000i	−0.105802	+	0.0610847i	−0.551967	−	0.833866i	$-0.686123\pi$
$67$	−0.866025	+	0.500000i	−0.105802	+	0.0610847i	0.446165	+	0.894951i	$0.352789\pi$
$68$		−	8.48528i		−	1.02899i
$69$	−5.27792	−	7.46410i	−0.635387	−	0.898572i
$70$	0.169873	−	0.0980762i	0.0203037	−	0.0117223i
$71$	6.69213	−	11.5911i	0.794210	−	1.37561i	−0.129130	−	0.991628i	$-0.541218\pi$
$71$	6.69213	−	11.5911i	0.794210	−	1.37561i	0.923340	−	0.383984i	$-0.125448\pi$
$72$	−5.69798	+	1.05902i	−0.671513	+	0.124806i
$73$	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	$0.110493\pi$
$74$	−3.46618	−	2.00120i	−0.402936	−	0.232635i
$75$	−4.24264	+	3.00000i	−0.489898	+	0.346410i
$76$	7.50000	−	0.866025i	0.860309	−	0.0993399i
$77$		−	1.41421i		−	0.161165i
$78$	0.239223	−	0.0220421i	0.0270867	−	0.00249578i
$79$	9.06218	+	5.23205i	1.01957	+	0.588652i	0.913981	−	0.405758i	$-0.132992\pi$
$79$	9.06218	+	5.23205i	1.01957	+	0.588652i	0.105594	+	0.994409i	$0.466326\pi$
$80$	3.01790	−	1.74238i	0.337411	−	0.194804i
$81$	8.39898	−	3.23375i	0.933220	−	0.359306i
$82$	−1.46410	−	2.53590i	−0.161683	−	0.280043i
$83$		−	2.07055i		−	0.227273i	−0.993522	−	0.113636i	$-0.963750\pi$
$83$		−	2.07055i		−	0.227273i	0.993522	−	0.113636i	$-0.0362499\pi$
$84$	−0.656339	+	0.464102i	−0.0716124	+	0.0506376i
$85$	3.46410	+	6.00000i	0.375735	+	0.650791i
$86$	1.48356	+	2.56961i	0.159977	+	0.277088i
$87$	−2.92820	+	2.07055i	−0.313936	+	0.221987i
$88$			10.1962i			1.08691i
$89$	−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	$0.960674\pi$
$90$	1.66925	−	1.42713i	0.175954	−	0.150432i
$91$	0.0621778	−	0.0358984i	0.00651801	−	0.00376317i
$92$	7.91688	+	4.57081i	0.825391	+	0.476540i
$93$	4.24995	−	0.391592i	0.440699	−	0.0406062i
$94$		−	0.392305i		−	0.0404632i
$95$	−4.94975	+	3.67423i	−0.507833	+	0.376969i
$96$	7.26795	−	5.13922i	0.741782	−	0.524519i
$97$	−0.464102	−	0.267949i	−0.0471224	−	0.0272061i	0.476254	−	0.879308i	$-0.341994\pi$
$97$	−0.464102	−	0.267949i	−0.0471224	−	0.0272061i	−0.523376	+	0.852102i	$0.675328\pi$
$98$	−1.79315	+	3.10583i	−0.181136	+	0.313736i
$99$	−2.89329	−	15.5672i	−0.290787	−	1.56456i
$100$	2.59808	−	4.50000i	0.259808	−	0.450000i
$101$	1.79315	−	1.03528i	0.178425	−	0.103014i	−0.408127	−	0.912925i	$-0.633818\pi$
$101$	1.79315	−	1.03528i	0.178425	−	0.103014i	0.586553	+	0.809911i	$0.300485\pi$
$102$	2.53590	+	3.58630i	0.251091	+	0.355097i
$103$			3.53590i			0.348402i	0.984710	+	0.174201i	$0.0557343\pi$
$103$			3.53590i			0.348402i	−0.984710	+	0.174201i	$0.944266\pi$
$104$	−0.448288	+	0.258819i	−0.0439582	+	0.0253793i
$105$	0.274633	−	0.596119i	0.0268014	−	0.0581752i
$106$	5.66025			0.549772
$107$	−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
$109$	−5.53590	−	3.19615i	−0.530243	−	0.306136i	0.210872	−	0.977514i	$-0.432370\pi$
$109$	−5.53590	−	3.19615i	−0.530243	−	0.306136i	−0.741115	+	0.671378i	$0.765703\pi$
$110$	−1.93185	−	3.34607i	−0.184195	−	0.319035i
$111$	−13.3358	+	1.22877i	−1.26578	+	0.116629i
$112$	0.330127	−	0.571797i	0.0311941	−	0.0540297i
$113$	−3.96524			−0.373018			−0.186509	−	0.982453i	$-0.559717\pi$
$113$	−3.96524			−0.373018			−0.186509	+	0.982453i	$0.559717\pi$
$114$	−2.91105	+	2.60746i	−0.272645	+	0.244211i
$115$	−7.46410			−0.696031
$116$	1.79315	−	3.10583i	0.166490	−	0.288369i
$117$	0.610988	−	0.522364i	0.0564859	−	0.0482926i
$118$	2.90192	+	5.02628i	0.267144	+	0.462707i
$119$	1.13681	+	0.656339i	0.104211	+	0.0601665i
$120$	−1.98004	+	4.29788i	−0.180752	+	0.392341i
$121$	−16.8564			−1.53240
$122$	5.41662			0.490398
$123$	−8.89898	−	4.09978i	−0.802394	−	0.369664i
$124$	−3.69615	+	2.13397i	−0.331924	+	0.191637i
$125$			11.3137i			1.01193i
$126$	0.138701	−	0.392305i	0.0123564	−	0.0349493i
$127$	17.1962	−	9.92820i	1.52591	−	0.880986i	0.526384	−	0.850247i	$-0.323547\pi$
$127$	17.1962	−	9.92820i	1.52591	−	0.880986i	0.999527	−	0.0307388i	$-0.00978601\pi$
$128$	−5.72620	+	9.91808i	−0.506130	+	0.876642i
$129$	9.01727	+	4.15427i	0.793927	+	0.365763i
$130$	0.0980762	−	0.169873i	0.00860185	−	0.0148988i
$131$	10.9348	+	6.31319i	0.955375	+	0.551586i	0.894747	−	0.446574i	$-0.147356\pi$
$131$	10.9348	+	6.31319i	0.955375	+	0.551586i	0.0606288	+	0.998160i	$0.480689\pi$
$132$	9.14162	+	12.9282i	0.795676	+	1.12526i
$133$	−0.464102	+	1.07180i	−0.0402427	+	0.0929366i
$134$			0.517638i			0.0447171i
$135$	1.80348	−	7.12372i	0.155219	−	0.613113i
$136$	−8.19615	−	4.73205i	−0.702814	−	0.405770i
$137$	−9.14162	+	5.27792i	−0.781021	+	0.450923i	−0.836792	−	0.547521i	$-0.815572\pi$
$137$	−9.14162	+	5.27792i	−0.781021	+	0.450923i	0.0557708	+	0.998444i	$0.482238\pi$
$138$	−4.71209	+	0.434174i	−0.401120	+	0.0369593i
$139$	−1.40192	−	2.42820i	−0.118910	−	0.205958i	0.800426	−	0.599431i	$-0.204607\pi$
$139$	−1.40192	−	2.42820i	−0.118910	−	0.205958i	−0.919336	+	0.393474i	$0.871273\pi$
$140$			0.656339i			0.0554708i
$141$	−0.757875	−	1.07180i	−0.0638246	−	0.0902616i
$142$	−3.46410	−	6.00000i	−0.290701	−	0.503509i
$143$	−0.707107	−	1.22474i	−0.0591312	−	0.102418i
$144$	2.46410	−	6.96953i	0.205342	−	0.580794i
$145$			2.92820i			0.243174i
$146$	−0.776457	−	1.34486i	−0.0642600	−	0.111302i
$147$	1.10102	+	11.9494i	0.0908106	+	0.985568i
$148$	11.5981	−	6.69615i	0.953356	−	0.550420i
$149$	−2.36156	−	1.36345i	−0.193466	−	0.111698i	0.400138	−	0.916455i	$-0.368962\pi$
$149$	−2.36156	−	1.36345i	−0.193466	−	0.111698i	−0.593604	+	0.804757i	$0.702296\pi$
$150$	0.246787	+	2.67838i	0.0201501	+	0.218689i
$151$		−	2.00000i		−	0.162758i	−0.996683	−	0.0813788i	$-0.974068\pi$
$151$		−	2.00000i		−	0.162758i	0.996683	−	0.0813788i	$-0.0259324\pi$
$152$	3.34607	−	7.72741i	0.271402	−	0.626775i
$153$	13.8564	+	4.89898i	1.12022	+	0.396059i
$154$	−0.633975	−	0.366025i	−0.0510871	−	0.0294952i
$155$	1.74238	−	3.01790i	0.139952	−	0.242403i
$156$	−0.336355	+	0.730093i	−0.0269300	+	0.0584542i
$157$	−5.23205	+	9.06218i	−0.417563	+	0.723241i	−0.995694	−	0.0927037i	$-0.970449\pi$
$157$	−5.23205	+	9.06218i	−0.417563	+	0.723241i	0.578131	+	0.815944i	$0.303782\pi$
$158$	4.69093	−	2.70831i	0.373190	−	0.215461i
$159$	15.4641	−	10.9348i	1.22638	−	0.867184i
$160$		−	7.26795i		−	0.574582i
$161$	−1.22474	+	0.707107i	−0.0965234	+	0.0557278i
$162$	0.724165	−	4.60212i	0.0568958	−	0.361576i
$163$	−5.19615			−0.406994			−0.203497	−	0.979076i	$-0.565231\pi$
$163$	−5.19615			−0.406994			−0.203497	+	0.979076i	$0.565231\pi$
$164$	9.79796			0.765092
$165$	−11.7420	−	5.40957i	−0.914115	−	0.421134i
$166$	−0.928203	−	0.535898i	−0.0720425	−	0.0415938i
$167$	−10.8840	−	18.8516i	−0.842229	−	1.45878i	−0.888006	−	0.459832i	$-0.847909\pi$
$167$	−10.8840	−	18.8516i	−0.842229	−	1.45878i	0.0457762	−	0.998952i	$-0.485424\pi$
$168$	0.0822623	+	0.892794i	0.00634668	+	0.0688805i
$169$	−6.46410	+	11.1962i	−0.497239	+	0.861242i
$170$	3.58630			0.275057
$171$	−2.91591	+	12.7474i	−0.222985	+	0.974822i
$172$	−9.92820			−0.757018
$173$	8.76268	−	15.1774i	0.666214	−	1.15392i	−0.312740	−	0.949839i	$-0.601247\pi$
$173$	8.76268	−	15.1774i	0.666214	−	1.15392i	0.978955	−	0.204079i	$-0.0654198\pi$
$174$	0.170328	+	1.84858i	0.0129126	+	0.140140i
$175$	0.401924	+	0.696152i	0.0303826	+	0.0526242i
$176$	−11.2629	−	6.50266i	−0.848976	−	0.490157i
$177$	17.6382	+	8.12596i	1.32577	+	0.610785i
$178$	−3.80385			−0.285110
$179$	−1.41421			−0.105703			−0.0528516	−	0.998602i	$-0.516831\pi$
$179$	−1.41421			−0.105703			−0.0528516	+	0.998602i	$0.516831\pi$
$180$	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	$0.374427\pi$
$182$		−	0.0371647i		−	0.00275483i
$183$	14.7985	−	10.4641i	1.09393	−	0.773529i
$184$	8.83013	−	5.09808i	0.650966	−	0.375835i
$185$	−5.46739	+	9.46979i	−0.401970	+	0.696233i
$186$	0.924421	−	2.00655i	0.0677819	−	0.147127i
$187$	12.9282	−	22.3923i	0.945404	−	1.63749i
$188$	1.13681	+	0.656339i	0.0829105	+	0.0478684i
$189$	−0.378937	−	1.33975i	−0.0275636	−	0.0974522i
$190$	0.366025	+	3.16987i	0.0265543	+	0.229967i
$191$			13.0053i			0.941032i	0.882391	+	0.470516i	$0.155932\pi$
$191$			13.0053i			0.941032i	−0.882391	+	0.470516i	$0.844068\pi$
$192$	0.360419	+	3.91163i	0.0260110	+	0.282298i
$193$	−2.42820	−	1.40192i	−0.174786	−	0.100913i	0.410055	−	0.912061i	$-0.365510\pi$
$193$	−2.42820	−	1.40192i	−0.174786	−	0.100913i	−0.584841	+	0.811148i	$0.698843\pi$
$194$	−0.240237	+	0.138701i	−0.0172480	+	0.00995813i
$195$	−0.0602202	−	0.653570i	−0.00431246	−	0.0468031i
$196$	−6.00000	−	10.3923i	−0.428571	−	0.742307i
$197$		−	0.656339i		−	0.0467622i	−0.999727	−	0.0233811i	$-0.992557\pi$
$197$		−	0.656339i		−	0.0467622i	0.999727	−	0.0233811i	$-0.00744311\pi$
$198$	−7.72741	−	2.73205i	−0.549163	−	0.194158i
$199$	11.5981	+	20.0885i	0.822166	+	1.42403i	0.904066	+	0.427392i	$0.140568\pi$
$199$	11.5981	+	20.0885i	0.822166	+	1.42403i	−0.0819004	+	0.996641i	$0.526099\pi$
$200$	−2.89778	−	5.01910i	−0.204904	−	0.354904i
$201$	1.00000	+	1.41421i	0.0705346	+	0.0997509i
$202$		−	1.07180i		−	0.0754114i
$203$	0.277401	+	0.480473i	0.0194698	+	0.0337226i
$204$	−14.6349	+	1.34847i	−1.02465	+	0.0944117i
$205$	−6.92820	+	4.00000i	−0.483887	+	0.279372i
$206$	1.58510	+	0.915158i	0.110439	+	0.0637621i
$207$	−12.0349	+	10.2892i	−0.836484	+	0.715152i
$208$		−	0.660254i		−	0.0457804i
$209$	21.1117	+	9.14162i	1.46032	+	0.632339i
$210$	−0.196152	−	0.277401i	−0.0135358	−	0.0191425i
$211$	9.52628	+	5.50000i	0.655816	+	0.378636i	0.790681	−	0.612228i	$-0.209727\pi$
$211$	9.52628	+	5.50000i	0.655816	+	0.378636i	−0.134865	+	0.990864i	$0.543060\pi$
$212$	−9.46979	+	16.4022i	−0.650388	+	1.12650i
$213$	−21.0552	−	9.70017i	−1.44268	−	0.664645i
$214$	−1.26795	+	2.19615i	−0.0866752	+	0.150126i
$215$	7.02030	−	4.05317i	0.478780	−	0.276424i
$216$	2.73205	+	9.65926i	0.185893	+	0.657229i
$217$		−	0.660254i		−	0.0448210i
$218$	−2.86559	+	1.65445i	−0.194082	+	0.112054i
$219$	−4.71940	−	2.17423i	−0.318907	−	0.146921i
$220$	12.9282			0.871619
$221$	1.31268			0.0883003
$222$	−2.90072	+	6.29631i	−0.194684	+	0.422581i
$223$	−9.86603	−	5.69615i	−0.660678	−	0.381443i	0.131857	−	0.991269i	$-0.457906\pi$
$223$	−9.86603	−	5.69615i	−0.660678	−	0.381443i	−0.792535	+	0.609826i	$0.791239\pi$
$224$	−0.688524	−	1.19256i	−0.0460040	−	0.0796812i
$225$	5.84847	+	6.84072i	0.389898	+	0.456048i
$226$	−1.02628	+	1.77757i	−0.0682671	+	0.118242i
$227$	−4.79744			−0.318418			−0.159209	−	0.987245i	$-0.550894\pi$
$227$	−4.79744			−0.318418			−0.159209	+	0.987245i	$0.550894\pi$
$228$	−2.68556	−	12.7980i	−0.177856	−	0.847566i
$229$	−11.3923			−0.752825			−0.376412	−	0.926452i	$-0.622842\pi$
$229$	−11.3923			−0.752825			−0.376412	+	0.926452i	$0.622842\pi$
$230$	−1.93185	+	3.34607i	−0.127383	+	0.220633i
$231$	−2.43916	+	0.224745i	−0.160485	+	0.0147871i
$232$	−2.00000	−	3.46410i	−0.131306	−	0.227429i
$233$	11.5911	+	6.69213i	0.759359	+	0.438416i	0.829066	−	0.559151i	$-0.188873\pi$
$233$	11.5911	+	6.69213i	0.759359	+	0.438416i	−0.0697066	+	0.997568i	$0.522206\pi$
$234$	−0.0760341	−	0.409096i	−0.00497050	−	0.0267435i
$235$	−1.07180			−0.0699163
$236$	−19.4201			−1.26414
$237$	7.58380	−	16.4614i	0.492621	−	1.06928i
$238$	0.588457	−	0.339746i	0.0381440	−	0.0220225i
$239$		−	15.2789i		−	0.988313i	−0.869373	−	0.494156i	$-0.835477\pi$
$239$		−	15.2789i		−	0.988313i	0.869373	−	0.494156i	$-0.164523\pi$
$240$	−3.48477	−	4.92820i	−0.224941	−	0.318114i
$241$	9.82051	−	5.66987i	0.632595	−	0.365229i	−0.149162	−	0.988813i	$-0.547657\pi$
$241$	9.82051	−	5.66987i	0.632595	−	0.365229i	0.781756	+	0.623584i	$0.214324\pi$
$242$	−4.36276	+	7.55652i	−0.280449	+	0.485752i
$243$	−6.91215	−	13.9722i	−0.443415	−	0.896317i
$244$	−9.06218	+	15.6962i	−0.580146	+	1.00484i
$245$	8.48528	+	4.89898i	0.542105	+	0.312984i
$246$	−4.14110	+	2.92820i	−0.264027	+	0.186695i
$247$	0.133975	+	1.16025i	0.00852460	+	0.0738252i
$248$			4.76028i			0.302278i
$249$	−3.57117	+	0.329049i	−0.226314	+	0.0208527i
$250$	5.07180	+	2.92820i	0.320769	+	0.185196i
$251$	−12.7279	+	7.34847i	−0.803379	+	0.463831i	−0.844651	−	0.535317i	$-0.820192\pi$
$251$	−12.7279	+	7.34847i	−0.803379	+	0.463831i	0.0412721	+	0.999148i	$0.486859\pi$
$252$	0.904761	+	1.05826i	0.0569946	+	0.0666643i
$253$	13.9282	+	24.1244i	0.875659	+	1.51669i
$254$		−	10.2784i		−	0.644926i
$255$	9.79796	−	6.92820i	0.613572	−	0.433861i
$256$	0.696152	+	1.20577i	0.0435095	+	0.0753607i
$257$	4.05317	+	7.02030i	0.252830	+	0.437914i	0.964304	−	0.264798i	$-0.0853054\pi$
$257$	4.05317	+	7.02030i	0.252830	+	0.437914i	−0.711474	+	0.702713i	$0.751972\pi$
$258$	4.19615	−	2.96713i	0.261241	−	0.184725i
$259$			2.07180i			0.128735i
$260$	0.328169	+	0.568406i	0.0203522	+	0.0352510i
$261$	4.03652	+	4.72135i	0.249854	+	0.292244i
$262$	5.66025	−	3.26795i	0.349692	−	0.201895i
$263$	−24.9754	−	14.4195i	−1.54005	−	0.889147i	−0.998835	−	0.0482609i	$-0.984632\pi$
$263$	−24.9754	−	14.4195i	−1.54005	−	0.889147i	−0.541213	−	0.840886i	$-0.682035\pi$
$264$	17.5858	−	1.62036i	1.08233	−	0.0997262i
$265$		−	15.4641i		−	0.949952i
$266$	0.360355	+	0.485452i	0.0220948	+	0.0297650i
$267$	−10.3923	+	7.34847i	−0.635999	+	0.449719i
$268$	−1.50000	−	0.866025i	−0.0916271	−	0.0529009i
$269$	5.46739	−	9.46979i	0.333352	−	0.577383i	−0.649815	−	0.760093i	$-0.725153\pi$
$269$	5.46739	−	9.46979i	0.333352	−	0.577383i	0.983167	+	0.182710i	$0.0584868\pi$
$270$	−2.72670	−	2.65223i	−0.165942	−	0.161410i
$271$	−3.46410	+	6.00000i	−0.210429	+	0.364474i	−0.951849	−	0.306568i	$-0.900819\pi$
$271$	−3.46410	+	6.00000i	−0.210429	+	0.364474i	0.741420	+	0.671042i	$0.234153\pi$
$272$	10.4543	−	6.03579i	0.633885	−	0.365974i
$273$	−0.0717968	−	0.101536i	−0.00434534	−	0.00614524i
$274$			5.46410i			0.330098i
$275$	13.7124	−	7.91688i	0.826891	−	0.477406i
$276$	6.62534	−	14.3810i	0.398799	−	0.865633i
$277$	17.8564			1.07289			0.536444	−	0.843936i	$-0.319767\pi$
$277$	17.8564			1.07289			0.536444	+	0.843936i	$0.319767\pi$
$278$	−1.45138			−0.0870479
$279$	−1.35079	−	7.26784i	−0.0808698	−	0.435114i
$280$	0.633975	+	0.366025i	0.0378872	+	0.0218742i
$281$	4.70951	+	8.15711i	0.280946	+	0.486613i	0.971618	−	0.236556i	$-0.0760185\pi$
$281$	4.70951	+	8.15711i	0.280946	+	0.486613i	−0.690672	+	0.723168i	$0.742685\pi$
$282$	−0.676626	+	0.0623445i	−0.0402925	+	0.00371256i
$283$	−2.92820	+	5.07180i	−0.174064	+	0.301487i	−0.939837	−	0.341624i	$-0.889023\pi$
$283$	−2.92820	+	5.07180i	−0.174064	+	0.301487i	0.765773	+	0.643111i	$0.222357\pi$
$284$	23.1822			1.37561
$285$	7.12372	+	7.95315i	0.421973	+	0.471104i
$286$	−0.732051			−0.0432871
$287$	−0.757875	+	1.31268i	−0.0447359	+	0.0774849i
$288$	−10.0188	−	11.7186i	−0.590366	−	0.690528i
$289$	3.50000	+	6.06218i	0.205882	+	0.356599i
$290$	1.31268	+	0.757875i	0.0770831	+	0.0445039i
$291$	−0.388390	+	0.843039i	−0.0227678	+	0.0494198i
$292$	5.19615			0.304082
$293$	−13.9391			−0.814329			−0.407164	−	0.913355i	$-0.633482\pi$
$293$	−13.9391			−0.814329			−0.407164	+	0.913355i	$0.633482\pi$
$294$	5.64173	+	2.59915i	0.329032	+	0.151586i
$295$	13.7321	−	7.92820i	0.799511	−	0.461598i
$296$		−	14.9372i		−	0.868206i
$297$	−26.3896	+	7.46410i	−1.53128	+	0.433111i
$298$	−1.22243	+	0.705771i	−0.0708136	+	0.0408842i
$299$	−0.707107	+	1.22474i	−0.0408930	+	0.0708288i
$300$	−8.17423	−	3.76588i	−0.471940	−	0.217423i
$301$	0.767949	−	1.33013i	0.0442639	−	0.0766672i
$302$	−0.896575	−	0.517638i	−0.0515921	−	0.0297867i
$303$	−2.07055	−	2.92820i	−0.118950	−	0.168221i
$304$	6.40192	+	8.62436i	0.367176	+	0.494641i
$305$		−	14.7985i		−	0.847358i
$306$	5.78245	−	4.94371i	0.330561	−	0.282613i
$307$	−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
$309$	6.09852	−	0.561920i	0.346933	−	0.0319665i
$310$	−0.901924	−	1.56218i	−0.0512258	−	0.0887257i
$311$			12.4505i			0.706004i	0.935623	+	0.353002i	$0.114839\pi$
$311$			12.4505i			0.706004i	−0.935623	+	0.353002i	$0.885161\pi$
$312$	0.517638	+	0.732051i	0.0293055	+	0.0414442i
$313$	−8.39230	−	14.5359i	−0.474361	−	0.821618i	0.525208	−	0.850974i	$-0.323988\pi$
$313$	−8.39230	−	14.5359i	−0.474361	−	0.821618i	−0.999569	+	0.0293564i	$0.990654\pi$
$314$	2.70831	+	4.69093i	0.152839	+	0.264724i
$315$	−1.07180	−	0.378937i	−0.0603889	−	0.0213507i
$316$			18.1244i			1.01957i
$317$	−4.43211	−	7.67664i	−0.248932	−	0.431163i	0.714298	−	0.699842i	$-0.246746\pi$
$317$	−4.43211	−	7.67664i	−0.248932	−	0.431163i	−0.963230	+	0.268679i	$0.913413\pi$
$318$	−0.899520	−	9.76249i	−0.0504426	−	0.547453i
$319$	9.46410	−	5.46410i	0.529888	−	0.305931i
$320$	2.77766	+	1.60368i	0.155276	+	0.0896486i
$321$	0.778539	+	8.44949i	0.0434538	+	0.471605i
$322$			0.732051i			0.0407956i
$323$	−17.1464	+	12.7279i	−0.954053	+	0.708201i
$324$	12.1244	+	9.79796i	0.673575	+	0.544331i
$325$	0.696152	+	0.401924i	0.0386156	+	0.0222947i
$326$	−1.34486	+	2.32937i	−0.0744851	+	0.129012i
$327$	−4.63279	+	10.0559i	−0.256194	+	0.556095i
$328$	5.46410	−	9.46410i	0.301705	−	0.522568i
$329$	−0.175865	+	0.101536i	−0.00969578	+	0.00559786i
$330$	−5.46410	+	3.86370i	−0.300789	+	0.212690i
$331$		−	18.0718i		−	0.993316i	−0.867946	−	0.496658i	$-0.834560\pi$
$331$		−	18.0718i		−	0.993316i	0.867946	−	0.496658i	$-0.165440\pi$
$332$	3.10583	−	1.79315i	0.170454	−	0.0984119i
$333$	4.23862	+	22.8056i	0.232275	+	1.24974i
$334$	−11.2679			−0.616555
$335$	1.41421			0.0772667
$336$	−1.03867	−	0.478516i	−0.0566639	−	0.0261052i
$337$	−21.3564	−	12.3301i	−1.16336	−	0.671665i	−0.211251	−	0.977432i	$-0.567754\pi$
$337$	−21.3564	−	12.3301i	−1.16336	−	0.671665i	−0.952106	+	0.305767i	$0.901087\pi$
$338$	3.34607	+	5.79555i	0.182002	+	0.315237i
$339$	0.630150	+	6.83903i	0.0342251	+	0.371445i
$340$	−6.00000	+	10.3923i	−0.325396	+	0.563602i
$341$	−13.0053			−0.704278
$342$	4.95983	+	4.60645i	0.268197	+	0.249088i
$343$	3.73205			0.201512
$344$	−5.53674	+	9.58991i	−0.298521	+	0.517053i
$345$	1.18618	+	12.8737i	0.0638620	+	0.693095i
$346$	−4.53590	−	7.85641i	−0.243851	−	0.422363i
$347$	16.6424	+	9.60849i	0.893410	+	0.515811i	0.875057	−	0.484021i	$-0.160824\pi$
$347$	16.6424	+	9.60849i	0.893410	+	0.515811i	0.0183540	+	0.999832i	$0.494157\pi$
$348$	−5.64173	−	2.59915i	−0.302428	−	0.139329i
$349$	9.39230			0.502759			0.251379	−	0.967889i	$-0.419116\pi$
$349$	9.39230			0.502759			0.251379	+	0.967889i	$0.419116\pi$
$350$	0.416102			0.0222416
$351$	−0.998042	−	0.970785i	−0.0532716	−	0.0518167i
$352$	−23.4904	+	13.5622i	−1.25204	+	0.722867i
$353$		−	2.17209i		−	0.115609i	−0.998328	−	0.0578043i	$-0.981590\pi$
$353$		−	2.17209i		−	0.115609i	0.998328	−	0.0578043i	$-0.0184099\pi$
$354$	8.20788	−	5.80385i	0.436244	−	0.308471i
$355$	−16.3923	+	9.46410i	−0.870013	+	0.502302i
$356$	6.36396	−	11.0227i	0.337289	−	0.584202i
$357$	0.951356	−	2.06502i	0.0503511	−	0.109292i
$358$	−0.366025	+	0.633975i	−0.0193450	+	0.0335066i
$359$	6.21166	+	3.58630i	0.327839	+	0.189278i	0.654881	−	0.755732i	$-0.272719\pi$
$359$	6.21166	+	3.58630i	0.327839	+	0.189278i	−0.327042	+	0.945010i	$0.606052\pi$
$360$	7.72741	+	2.73205i	0.407270	+	0.143992i
$361$	−13.0000	−	13.8564i	−0.684211	−	0.729285i
$362$			1.79315i			0.0942459i
$363$	2.67880	+	29.0730i	0.140600	+	1.52594i
$364$	0.107695	+	0.0621778i	0.00564476	+	0.00325900i
$365$	−3.67423	+	2.12132i	−0.192318	+	0.111035i
$366$	−0.860801	−	9.34228i	−0.0449948	−	0.488329i
$367$	−10.5263	−	18.2321i	−0.549467	−	0.951705i	−0.998311	−	0.0580950i	$-0.981497\pi$
$367$	−10.5263	−	18.2321i	−0.549467	−	0.951705i	0.448844	−	0.893610i	$-0.351836\pi$
$368$			13.0053i			0.677949i
$369$	−5.65685	+	16.0000i	−0.294484	+	0.832927i
$370$	2.83013	+	4.90192i	0.147131	+	0.254839i
$371$	−1.46498	−	2.53742i	−0.0760581	−	0.131736i
$372$	4.26795	+	6.03579i	0.221283	+	0.312941i
$373$		−	19.4641i		−	1.00781i	−0.863758	−	0.503906i	$-0.831896\pi$
$373$		−	19.4641i		−	1.00781i	0.863758	−	0.503906i	$-0.168104\pi$
$374$	−6.69213	−	11.5911i	−0.346042	−	0.599362i
$375$	19.5133	−	1.79796i	1.00766	−	0.0928462i
$376$	1.26795	−	0.732051i	0.0653895	−	0.0377526i
$377$	0.480473	+	0.277401i	0.0247456	+	0.0142869i
$378$	−0.698668	−	0.176879i	−0.0359356	−	0.00909766i
$379$			23.7846i			1.22173i	0.791733	+	0.610867i	$0.209179\pi$
$379$			23.7846i			1.22173i	−0.791733	+	0.610867i	$0.790821\pi$
$380$	−9.79796	−	4.24264i	−0.502625	−	0.217643i
$381$	−19.8564	−	28.0812i	−1.01727	−	1.43864i
$382$	5.83013	+	3.36603i	0.298295	+	0.172221i
$383$	−6.26243	+	10.8468i	−0.319995	+	0.554248i	−0.980487	−	0.196586i	$-0.937015\pi$
$383$	−6.26243	+	10.8468i	−0.319995	+	0.554248i	0.660492	+	0.750833i	$0.270348\pi$
$384$	18.0162	+	8.30007i	0.919383	+	0.423561i
$385$	−1.00000	+	1.73205i	−0.0509647	+	0.0882735i
$386$	−1.25693	+	0.725689i	−0.0639761	+	0.0369366i
$387$	5.73205	−	16.2127i	0.291377	−	0.824137i
$388$		−	0.928203i		−	0.0471224i
$389$	−12.8159	+	7.39924i	−0.649790	+	0.375156i	−0.788376	−	0.615194i	$-0.789078\pi$
$389$	−12.8159	+	7.39924i	−0.649790	+	0.375156i	0.138586	+	0.990350i	$0.455744\pi$
$390$	−0.308574	−	0.142160i	−0.0156252	−	0.00719857i
$391$	−25.8564			−1.30761
$392$	−13.3843			−0.676007
$393$	9.15091	−	19.8630i	0.461602	−	1.00195i
$394$	−0.294229	−	0.169873i	−0.0148230	−	0.00855808i
$395$	−7.39924	−	12.8159i	−0.372296	−	0.644836i
$396$	20.8451	−	17.8215i	1.04750	−	0.895564i
$397$	13.1603	−	22.7942i	0.660494	−	1.14401i	−0.319992	−	0.947420i	$-0.603680\pi$
$397$	13.1603	−	22.7942i	0.660494	−	1.14401i	0.980486	−	0.196589i	$-0.0629865\pi$
$398$	12.0072			0.601867
$399$	1.92233	+	0.630128i	0.0962369	+	0.0315459i
$400$	7.39230			0.369615
$401$	11.4016	−	19.7482i	0.569371	−	0.986179i	−0.427257	−	0.904130i	$-0.640520\pi$
$401$	11.4016	−	19.7482i	0.569371	−	0.986179i	0.996628	−	0.0820492i	$-0.0261464\pi$
$402$	0.892794	−	0.0822623i	0.0445285	−	0.00410287i
$403$	−0.330127	−	0.571797i	−0.0164448	−	0.0284832i
$404$	3.10583	+	1.79315i	0.154521	+	0.0892126i
$405$	−12.5732	−	1.97846i	−0.624768	−	0.0983103i
$406$	0.287187			0.0142529
$407$	40.8091			2.02283
$408$	−6.85906	+	14.8883i	−0.339574	+	0.737080i
$409$	17.5359	−	10.1244i	0.867094	−	0.500617i	0.000712791	−	1.00000i	$-0.499773\pi$
$409$	17.5359	−	10.1244i	0.867094	−	0.500617i	0.866382	+	0.499383i	$0.166440\pi$
$410$			4.14110i			0.204515i
$411$	10.5558	+	14.9282i	0.520681	+	0.736354i
$412$	−5.30385	+	3.06218i	−0.261302	+	0.150863i
$413$	1.50215	−	2.60179i	0.0739158	−	0.128026i
$414$	1.49768	+	8.05816i	0.0736069	+	0.396037i
$415$	−1.46410	+	2.53590i	−0.0718699	+	0.124482i
$416$	−1.19256	−	0.688524i	−0.0584700	−	0.0337577i
$417$	−3.96524	+	2.80385i	−0.194179	+	0.137305i
$418$	9.56218	−	7.09808i	0.467701	−	0.347178i
$419$		−	7.55154i		−	0.368917i	−0.982840	−	0.184458i	$-0.940947\pi$
$419$		−	7.55154i		−	0.368917i	0.982840	−	0.184458i	$-0.0590531\pi$
$420$	1.13202	−	0.104304i	0.0552368	−	0.00508954i
$421$	24.7128	+	14.2679i	1.20443	+	0.695377i	0.961537	−	0.274676i	$-0.0885706\pi$
$421$	24.7128	+	14.2679i	1.20443	+	0.695377i	0.242892	+	0.970053i	$0.421904\pi$
$422$	4.93117	−	2.84701i	0.240045	−	0.138590i
$423$	−1.72814	+	1.47747i	−0.0840248	+	0.0718370i
$424$	10.5622	+	18.2942i	0.512945	+	0.888446i
$425$			14.6969i			0.712906i
$426$	−9.79796	+	6.92820i	−0.474713	+	0.335673i
$427$	−1.40192	−	2.42820i	−0.0678438	−	0.117509i
$428$	−4.24264	−	7.34847i	−0.205076	−	0.355202i
$429$	−2.00000	+	1.41421i	−0.0965609	+	0.0682789i
$430$		−	4.19615i		−	0.202356i
$431$	12.7279	+	22.0454i	0.613082	+	1.06189i	0.990718	+	0.135935i	$0.0434040\pi$
$431$	12.7279	+	22.0454i	0.613082	+	1.06189i	−0.377635	+	0.925954i	$0.623263\pi$
$432$	−12.4123	−	3.14236i	−0.597185	−	0.151187i
$433$	−17.8923	+	10.3301i	−0.859849	+	0.496434i	−0.863962	−	0.503557i	$-0.832024\pi$
$433$	−17.8923	+	10.3301i	−0.859849	+	0.496434i	0.00411252	+	0.999992i	$0.498691\pi$
$434$	−0.295984	−	0.170886i	−0.0142077	−	0.00820281i
$435$	5.05040	−	0.465346i	0.242148	−	0.0223116i
$436$		−	11.0718i		−	0.530243i
$437$	−2.63896	−	22.8541i	−0.126239	−	1.09326i
$438$	−2.19615	+	1.55291i	−0.104936	+	0.0742011i
$439$	−13.4545	−	7.76795i	−0.642147	−	0.370744i	0.143294	−	0.989680i	$-0.454231\pi$
$439$	−13.4545	−	7.76795i	−0.642147	−	0.370744i	−0.785441	+	0.618936i	$0.787564\pi$
$440$	7.20977	−	12.4877i	0.343712	−	0.595327i
$441$	20.4347	−	3.79796i	0.973079	−	0.180855i
$442$	0.339746	−	0.588457i	0.0161601	−	0.0279901i
$443$	−8.96575	+	5.17638i	−0.425976	+	0.245937i	−0.697631	−	0.716457i	$-0.745762\pi$
$443$	−8.96575	+	5.17638i	−0.425976	+	0.245937i	0.271655	+	0.962395i	$0.412429\pi$
$444$	−13.3923	−	18.9396i	−0.635571	−	0.898833i
$445$			10.3923i			0.492642i
$446$	−5.10703	+	2.94855i	−0.241825	+	0.139618i
$447$	−1.97630	+	4.28976i	−0.0934758	+	0.202899i
$448$	0.607695			0.0287109
$449$	−5.10205			−0.240781			−0.120390	−	0.992727i	$-0.538415\pi$
$449$	−5.10205			−0.240781			−0.120390	+	0.992727i	$0.538415\pi$
$450$	4.58030	−	0.851289i	0.215918	−	0.0401302i
$451$	25.8564	+	14.9282i	1.21753	+	0.702942i
$452$	−3.43400	−	5.94786i	−0.161522	−	0.279764i
$453$	−3.44949	+	0.317837i	−0.162071	+	0.0149333i
$454$	−1.24167	+	2.15064i	−0.0582744	+	0.100934i
$455$	−0.101536			−0.00476008
$456$	−13.8596	−	4.54308i	−0.649033	−	0.212749i
$457$	34.7128			1.62380			0.811898	−	0.583799i	$-0.198434\pi$
$457$	34.7128			1.62380			0.811898	+	0.583799i	$0.198434\pi$
$458$	−2.94855	+	5.10703i	−0.137776	+	0.238636i
$459$	6.24745	−	24.6773i	0.291606	−	1.15184i
$460$	−6.46410	−	11.1962i	−0.301390	−	0.522023i
$461$	−30.9232	−	17.8535i	−1.44024	−	0.831522i	−0.442373	−	0.896831i	$-0.645863\pi$
$461$	−30.9232	−	17.8535i	−1.44024	−	0.831522i	−0.997865	+	0.0653090i	$0.979197\pi$
$462$	−0.530550	+	1.15161i	−0.0246834	+	0.0535779i
$463$	1.58846			0.0738219			0.0369109	−	0.999319i	$-0.488248\pi$
$463$	1.58846			0.0738219			0.0369109	+	0.999319i	$0.488248\pi$
$464$	5.10205			0.236857
$465$	−5.48200	−	2.52557i	−0.254222	−	0.117120i
$466$	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	$0.824613\pi$
$468$	1.31268	+	0.464102i	0.0606785	+	0.0214531i
$469$	0.232051	−	0.133975i	0.0107151	−	0.00618637i
$470$	−0.277401	+	0.480473i	−0.0127956	+	0.0221626i
$471$	16.4614	+	7.58380i	0.758502	+	0.349443i
$472$	−10.8301	+	18.7583i	−0.498497	+	0.863422i
$473$	−26.2001	−	15.1266i	−1.20468	−	0.695524i
$474$	−5.41662	−	7.66025i	−0.248793	−	0.351847i
$475$	−12.9904	+	1.50000i	−0.596040	+	0.0688247i
$476$			2.27362i			0.104211i
$477$	−21.3172	−	24.9339i	−0.976049	−	1.14164i
$478$	−6.84936	−	3.95448i	−0.313283	−	0.180874i
$479$	15.1774	−	8.76268i	0.693474	−	0.400377i	−0.111438	−	0.993771i	$-0.535546\pi$
$479$	15.1774	−	8.76268i	0.693474	−	0.400377i	0.804912	+	0.593394i	$0.202212\pi$
$480$	−12.5354	+	1.15501i	−0.572158	+	0.0527189i
$481$	1.03590	+	1.79423i	0.0472329	+	0.0818098i
$482$		−	5.86988i		−	0.267366i
$483$	1.41421	+	2.00000i	0.0643489	+	0.0910032i
$484$	−14.5981	−	25.2846i	−0.663549	−	1.14930i
$485$	0.378937	+	0.656339i	0.0172067	+	0.0298028i
$486$	−8.05256	−	0.517638i	−0.365271	−	0.0234805i
$487$			11.0718i			0.501711i	0.968025	+	0.250856i	$0.0807119\pi$
$487$			11.0718i			0.501711i	−0.968025	+	0.250856i	$0.919288\pi$
$488$	10.1075	+	17.5068i	0.457547	+	0.792495i
$489$	0.825765	+	8.96204i	0.0373424	+	0.405277i
$490$	4.39230	−	2.53590i	0.198424	−	0.114560i
$491$	25.6317	+	14.7985i	1.15674	+	0.667846i	0.950521	−	0.310660i	$-0.100550\pi$
$491$	25.6317	+	14.7985i	1.15674	+	0.667846i	0.206222	+	0.978505i	$0.433883\pi$
$492$	−1.55708	−	16.8990i	−0.0701985	−	0.761865i
$493$			10.1436i			0.456844i
$494$	0.554803	+	0.240237i	0.0249618	+	0.0108088i
$495$	−7.46410	+	21.1117i	−0.335486	+	0.948899i
$496$	−5.25833	−	3.03590i	−0.236106	−	0.136316i
$497$	−1.79315	+	3.10583i	−0.0804338	+	0.139315i
$498$	−0.776779	+	1.68608i	−0.0348083	+	0.0755550i
$499$	−4.06218	+	7.03590i	−0.181848	+	0.314970i	−0.942510	−	0.334178i	$-0.891541\pi$
$499$	−4.06218	+	7.03590i	−0.181848	+	0.314970i	0.760662	+	0.649148i	$0.224875\pi$
$500$	−16.9706	+	9.79796i	−0.758947	+	0.438178i
$501$	−30.7846	+	21.7680i	−1.37535	+	0.972523i
$502$			7.60770i			0.339548i
$503$	1.13681	−	0.656339i	0.0506879	−	0.0292647i	−0.474442	−	0.880287i	$-0.657350\pi$
$503$	1.13681	−	0.656339i	0.0506879	−	0.0292647i	0.525130	+	0.851022i	$0.324017\pi$
$504$	1.52677	−	0.283763i	0.0680077	−	0.0126398i
$505$	−2.92820			−0.130303
$506$	14.4195			0.641027
$507$	20.3378	+	9.36965i	0.903232	+	0.416121i
$508$	29.7846	+	17.1962i	1.32148	+	0.762956i
$509$	21.4906	+	37.2228i	0.952554	+	1.64987i	0.739868	+	0.672752i	$0.234888\pi$
$509$	21.4906	+	37.2228i	0.952554	+	1.64987i	0.212686	+	0.977121i	$0.431779\pi$
$510$	−0.569930	−	6.18546i	−0.0252369	−	0.273897i
$511$	−0.401924	+	0.696152i	−0.0177801	+	0.0307960i
$512$	−22.1841			−0.980408
$513$	22.4495	+	3.00340i	0.991169	+	0.132603i
$514$	4.19615			0.185084
$515$	2.50026	−	4.33057i	0.110175	−	0.190828i
$516$	1.57778	+	17.1236i	0.0694577	+	0.753825i
$517$	2.00000	+	3.46410i	0.0879599	+	0.152351i
$518$	0.928761	+	0.536220i	0.0408074	+	0.0235602i
$519$	−27.5697	−	12.7014i	−1.21018	−	0.557530i
$520$	0.732051			0.0321026
$521$	−10.1769			−0.445858			−0.222929	−	0.974835i	$-0.571562\pi$
$521$	−10.1769			−0.445858			−0.222929	+	0.974835i	$0.571562\pi$
$522$	3.16125	−	0.587546i	0.138364	−	0.0257162i
$523$	−9.40192	+	5.42820i	−0.411117	+	0.237359i	−0.691270	−	0.722597i	$-0.742948\pi$
$523$	−9.40192	+	5.42820i	−0.411117	+	0.237359i	0.280152	+	0.959956i	$0.409615\pi$
$524$			21.8695i			0.955375i
$525$	1.13681	−	0.803848i	0.0496145	−	0.0350828i
$526$	−12.9282	+	7.46410i	−0.563696	+	0.325450i
$527$	6.03579	−	10.4543i	0.262923	−	0.455396i
$528$	−9.42554	+	20.4591i	−0.410194	+	0.890368i
$529$	2.42820	−	4.20577i	0.105574	−	0.182860i
$530$	−6.93237	−	4.00240i	−0.301123	−	0.173853i
$531$	11.2122	−	31.7128i	0.486567	−	1.37622i
$532$	−2.00962	+	0.232051i	−0.0871280	+	0.0100607i
$533$			1.51575i			0.0656544i
$534$	0.604502	+	6.56067i	0.0261594	+	0.283908i
$535$	6.00000	+	3.46410i	0.259403	+	0.149766i
$536$	−1.67303	+	0.965926i	−0.0722640	+	0.0417216i
$537$	0.224745	+	2.43916i	0.00969846	+	0.105257i
$538$	−2.83013	−	4.90192i	−0.122015	−	0.211337i
$539$		−	36.5665i		−	1.57503i
$540$	12.2474	−	3.46410i	0.527046	−	0.149071i
$541$	12.2321	+	21.1865i	0.525897	+	0.910880i	0.999545	+	0.0301660i	$0.00960358\pi$
$541$	12.2321	+	21.1865i	0.525897	+	0.910880i	−0.473648	+	0.880714i	$0.657063\pi$
$542$	1.79315	+	3.10583i	0.0770224	+	0.133407i
$543$	3.46410	+	4.89898i	0.148659	+	0.210235i
$544$		−	25.1769i		−	1.07945i
$545$	4.52004	+	7.82894i	0.193617	+	0.335355i
$546$	−0.0640997	+	0.00590617i	−0.00274321	+	0.000252761i
$547$	−12.8660	+	7.42820i	−0.550112	+	0.317607i	−0.749167	−	0.662381i	$-0.769546\pi$
$547$	−12.8660	+	7.42820i	−0.550112	+	0.317607i	0.199055	+	0.979988i	$0.436213\pi$
$548$	−15.8338	−	9.14162i	−0.676384	−	0.390511i
$549$	−20.3997	−	23.8607i	−0.870636	−	1.01835i
$550$		−	8.19615i		−	0.349485i
$551$	−8.96575	+	1.03528i	−0.381954	+	0.0441042i
$552$	−10.1962	−	14.4195i	−0.433977	−	0.613736i
$553$	−2.42820	−	1.40192i	−0.103258	−	0.0596159i
$554$	4.62158	−	8.00481i	0.196352	−	0.340092i
$555$	17.2018	+	7.92492i	0.730177	+	0.336394i
$556$	2.42820	−	4.20577i	0.102979	−	0.178364i
$557$	22.5259	−	13.0053i	0.954452	−	0.551053i	0.0599911	−	0.998199i	$-0.480893\pi$
$557$	22.5259	−	13.0053i	0.954452	−	0.551053i	0.894461	+	0.447146i	$0.147559\pi$
$558$	−3.60770	−	1.27551i	−0.152726	−	0.0539968i
$559$		−	1.53590i		−	0.0649616i
$560$	−0.808643	+	0.466870i	−0.0341714	+	0.0197289i
$561$	−40.6755	−	18.7393i	−1.71732	−	0.791174i
$562$	4.87564			0.205667
$563$	26.0106			1.09622			0.548109	−	0.836407i	$-0.315348\pi$
$563$	26.0106			1.09622			0.548109	+	0.836407i	$0.315348\pi$
$564$	0.951356	−	2.06502i	0.0400593	−	0.0869528i
$565$	4.85641	+	2.80385i	0.204311	+	0.117959i
$566$	1.51575	+	2.62536i	0.0637117	+	0.110352i
$567$	−2.25050	+	0.866481i	−0.0945121	+	0.0363888i
$568$	12.9282	−	22.3923i	0.542455	−	0.939560i
$569$	−25.2528			−1.05865			−0.529326	−	0.848419i	$-0.677555\pi$
$569$	−25.2528			−1.05865			−0.529326	+	0.848419i	$0.677555\pi$
$570$	5.40905	−	1.13505i	0.226560	−	0.0475421i
$571$	14.8038			0.619522			0.309761	−	0.950814i	$-0.399751\pi$
$571$	14.8038			0.619522			0.309761	+	0.950814i	$0.399751\pi$
$572$	1.22474	−	2.12132i	0.0512092	−	0.0886969i
$573$	22.4309	−	2.06679i	0.937063	−	0.0863413i
$574$	0.392305	+	0.679492i	0.0163745	+	0.0283614i
$575$	−13.7124	−	7.91688i	−0.571848	−	0.330157i
$576$	6.68929	−	1.24326i	0.278721	−	0.0518026i
$577$	29.0718			1.21027			0.605137	−	0.796121i	$-0.293118\pi$
$577$	29.0718			1.21027			0.605137	+	0.796121i	$0.293118\pi$
$578$	3.62347			0.150716
$579$	−2.03207	+	4.41082i	−0.0844501	+	0.183308i
$580$	−4.39230	+	2.53590i	−0.182381	+	0.105297i
$581$			0.554803i			0.0230171i
$582$	0.277401	+	0.392305i	0.0114987	+	0.0162616i
$583$	−49.9808	+	28.8564i	−2.06999	+	1.19511i
$584$	2.89778	−	5.01910i	0.119911	−	0.207692i
$585$	−1.11767	+	0.207729i	−0.0462100	+	0.00858854i
$586$	−3.60770	+	6.24871i	−0.149033	+	0.258132i
$587$	−28.8898	−	16.6796i	−1.19241	−	0.688439i	−0.233559	−	0.972343i	$-0.575037\pi$
$587$	−28.8898	−	16.6796i	−1.19241	−	0.688439i	−0.958853	+	0.283904i	$0.908370\pi$
$588$	−16.9706	+	12.0000i	−0.699854	+	0.494872i
$589$	9.85641	+	4.26795i	0.406126	+	0.175858i
$590$		−	8.20788i		−	0.337913i
$591$	−1.13202	+	0.104304i	−0.0465650	+	0.00429051i
$592$	16.5000	+	9.52628i	0.678146	+	0.391528i
$593$	29.1301	−	16.8183i	1.19623	−	0.690643i	0.236517	−	0.971627i	$-0.423994\pi$
$593$	29.1301	−	16.8183i	1.19623	−	0.690643i	0.959712	+	0.280984i	$0.0906609\pi$
$594$	−3.48406	+	13.7620i	−0.142953	+	0.564661i
$595$	−0.928203	−	1.60770i	−0.0380526	−	0.0659091i
$596$		−	4.72311i		−	0.193466i
$597$	32.8043	−	23.1962i	1.34259	−	0.949355i
$598$	0.366025	+	0.633975i	0.0149679	+	0.0259251i
$599$	−1.36345	−	2.36156i	−0.0557089	−	0.0964906i	0.836826	−	0.547469i	$-0.184409\pi$
$599$	−1.36345	−	2.36156i	−0.0557089	−	0.0964906i	−0.892535	+	0.450978i	$0.851075\pi$
$600$	−8.19615	+	5.79555i	−0.334607	+	0.236603i
$601$		−	28.3731i		−	1.15736i	−0.815554	−	0.578681i	$-0.803568\pi$
$601$		−	28.3731i		−	1.15736i	0.815554	−	0.578681i	$-0.196432\pi$
$602$	−0.397520	−	0.688524i	−0.0162017	−	0.0280622i
$603$	2.28024	−	1.94949i	0.0928585	−	0.0793894i
$604$	3.00000	−	1.73205i	0.122068	−	0.0704761i
$605$	20.6448	+	11.9193i	0.839330	+	0.484588i
$606$	−1.84858	+	0.170328i	−0.0750933	+	0.00691912i
$607$			35.2487i			1.43070i	0.698766	+	0.715351i	$0.253733\pi$
$607$			35.2487i			1.43070i	−0.698766	+	0.715351i	$0.746267\pi$
$608$	22.2535	−	2.56961i	0.902497	−	0.104211i
$609$	0.784610	−	0.554803i	0.0317940	−	0.0224817i
$610$	−6.63397	−	3.83013i	−0.268602	−	0.155077i
$611$	−0.101536	+	0.175865i	−0.00410771	+	0.00711475i
$612$	4.65153	+	25.0273i	0.188027	+	1.01167i
$613$	23.3205	−	40.3923i	0.941906	−	1.63143i	0.180077	−	0.983653i	$-0.442365\pi$
$613$	23.3205	−	40.3923i	0.941906	−	1.63143i	0.761830	−	0.647777i	$-0.224301\pi$
$614$	−6.21166	+	3.58630i	−0.250682	+	0.144731i
$615$	8.00000	+	11.3137i	0.322591	+	0.456213i
$616$		−	2.73205i		−	0.110077i
$617$	−19.9885	+	11.5403i	−0.804705	+	0.464597i	−0.845114	−	0.534587i	$-0.820467\pi$
$617$	−19.9885	+	11.5403i	−0.804705	+	0.464597i	0.0404087	+	0.999183i	$0.487134\pi$
$618$	1.32651	−	2.87933i	0.0533601	−	0.115824i
$619$	13.1962			0.530398			0.265199	−	0.964194i	$-0.414562\pi$
$619$	13.1962			0.530398			0.265199	+	0.964194i	$0.414562\pi$
$620$	6.03579			0.242403
$621$	19.6589	+	19.1220i	0.788884	+	0.767339i
$622$	5.58142	+	3.22243i	0.223794	+	0.129208i
$623$	0.984508	+	1.70522i	0.0394435	+	0.0683181i
$624$	−1.13877	+	0.104927i	−0.0455873	+	0.00420043i
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	−8.68835			−0.347256
$627$	12.4119	−	37.8650i	0.495685	−	1.51218i
$628$	−18.1244			−0.723241
$629$	−18.9396	+	32.8043i	−0.755170	+	1.30799i
$630$	−0.447274	+	0.382397i	−0.0178198	+	0.0152351i
$631$	−5.47372	−	9.48076i	−0.217905	−	0.377423i	0.736262	−	0.676697i	$-0.236589\pi$
$631$	−5.47372	−	9.48076i	−0.217905	−	0.377423i	−0.954167	+	0.299273i	$0.903256\pi$
$632$	17.5068	+	10.1075i	0.696382	+	0.402057i
$633$	7.97219	−	17.3045i	0.316866	−	0.687790i
$634$	−4.58846			−0.182231
$635$	−28.0812			−1.11437
$636$	29.7945	+	13.7264i	1.18143	+	0.544286i
$637$	1.60770	−	0.928203i	0.0636992	−	0.0367768i
$638$		−	5.65685i		−	0.223957i
$639$	−13.3843	+	37.8564i	−0.529473	+	1.49758i
$640$	14.0263	−	8.09808i	0.554437	−	0.320105i
$641$	16.2127	−	28.0812i	0.640363	−	1.10914i	−0.344989	−	0.938607i	$-0.612117\pi$
$641$	16.2127	−	28.0812i	0.640363	−	1.10914i	0.985352	−	0.170534i	$-0.0545493\pi$
$642$	3.98930	+	1.83788i	0.157445	+	0.0725353i
$643$	6.20577	−	10.7487i	0.244732	−	0.423888i	−0.717324	−	0.696739i	$-0.754633\pi$
$643$	6.20577	−	10.7487i	0.244732	−	0.423888i	0.962056	+	0.272852i	$0.0879668\pi$
$644$	−2.12132	−	1.22474i	−0.0835917	−	0.0482617i
$645$	−8.10634	−	11.4641i	−0.319187	−	0.451399i
$646$	1.26795	+	10.9808i	0.0498868	+	0.432032i
$647$			30.3548i			1.19337i	0.802475	+	0.596686i	$0.203516\pi$
$647$			30.3548i			1.19337i	−0.802475	+	0.596686i	$0.796484\pi$
$648$	16.2256	−	6.24713i	0.637401	−	0.245410i
$649$	−51.2487	−	29.5885i	−2.01169	−	1.16145i
$650$	0.360355	−	0.208051i	0.0141343	−	0.00816043i
$651$	−1.13877	+	0.104927i	−0.0446319	+	0.00411240i
$652$	−4.50000	−	7.79423i	−0.176234	−	0.305246i
$653$			1.86748i			0.0730802i	0.999332	+	0.0365401i	$0.0116337\pi$
$653$			1.86748i			0.0730802i	−0.999332	+	0.0365401i	$0.988366\pi$
$654$	3.30890	+	4.67949i	0.129388	+	0.182983i
$655$	−8.92820	−	15.4641i	−0.348854	−	0.604232i
$656$	6.96953	+	12.0716i	0.272115	+	0.471316i
$657$	−3.00000	+	8.48528i	−0.117041	+	0.331042i
$658$			0.105118i			0.00409792i
$659$	1.84392	+	3.19376i	0.0718289	+	0.124411i	0.899703	−	0.436503i	$-0.143783\pi$
$659$	1.84392	+	3.19376i	0.0718289	+	0.124411i	−0.827874	+	0.560914i	$0.810450\pi$
$660$	−2.05453	−	22.2979i	−0.0799726	−	0.867943i
$661$	−29.3205	+	16.9282i	−1.14044	+	0.658431i	−0.946538	−	0.322591i	$-0.895446\pi$
$661$	−29.3205	+	16.9282i	−1.14044	+	0.658431i	−0.193897	+	0.981022i	$0.562113\pi$
$662$	−8.10136	−	4.67733i	−0.314868	−	0.181789i
$663$	−0.208609	−	2.26403i	−0.00810170	−	0.0879278i
$664$		−	4.00000i		−	0.155230i
$665$	1.32628	−	0.984508i	0.0514310	−	0.0381776i
$666$	11.3205	+	4.00240i	0.438661	+	0.155090i
$667$	−9.46410	−	5.46410i	−0.366451	−	0.211571i
$668$	18.8516	−	32.6520i	0.729392	−	1.26334i
$669$	−8.25651	+	17.9216i	−0.319215	+	0.692889i
$670$	0.366025	−	0.633975i	0.0141408	−	0.0244926i
$671$	−47.8294	+	27.6143i	−1.84643	+	1.06604i
$672$	−1.94744	+	1.37705i	−0.0751242	+	0.0531208i
$673$			29.9808i			1.15567i	0.816152	+	0.577837i	$0.196103\pi$
$673$			29.9808i			1.15567i	−0.816152	+	0.577837i	$0.803897\pi$
$674$	−11.0549	+	6.38254i	−0.425818	+	0.245846i
$675$	10.8691	−	11.1742i	0.418350	−	0.430096i
$676$	−22.3923			−0.861242
$677$	−30.1518			−1.15883			−0.579413	−	0.815034i	$-0.696718\pi$
$677$	−30.1518			−1.15883			−0.579413	+	0.815034i	$0.696718\pi$
$678$	3.22895	+	1.48758i	0.124007	+	0.0571302i
$679$	0.124356	+	0.0717968i	0.00477233	+	0.00275531i
$680$	6.69213	+	11.5911i	0.256631	+	0.444499i
$681$	0.762403	+	8.27437i	0.0292154	+	0.317074i
$682$	−3.36603	+	5.83013i	−0.128892	+	0.223247i
$683$	26.1122			0.999155			0.499577	−	0.866269i	$-0.333489\pi$
$683$	26.1122			0.999155			0.499577	+	0.866269i	$0.333489\pi$
$684$	−21.6464	+	6.66574i	−0.827672	+	0.254871i
$685$	14.9282			0.570377
$686$	0.965926	−	1.67303i	0.0368792	−	0.0638767i
$687$	1.81045	+	19.6488i	0.0690730	+	0.749649i
$688$	−7.06218	−	12.2321i	−0.269243	−	0.466343i
$689$	−2.53742	−	1.46498i	−0.0966681	−	0.0558114i
$690$	6.07812	+	2.80020i	0.231390	+	0.106602i
$691$	−17.8564			−0.679290			−0.339645	−	0.940554i	$-0.610307\pi$
$691$	−17.8564			−0.679290			−0.339645	+	0.940554i	$0.610307\pi$
$692$	30.3548			1.15392
$693$	0.775255	+	4.17121i	0.0294495	+	0.158451i
$694$	8.61474	−	4.97372i	0.327011	−	0.188800i
$695$			3.96524i			0.150410i
$696$	−5.65685	+	4.00000i	−0.214423	+	0.151620i
$697$	−24.0000	+	13.8564i	−0.909065	+	0.524849i
$698$	2.43091	−	4.21046i	0.0920112	−	0.159368i
$699$	9.70017	−	21.0552i	0.366894	−	0.796381i
$700$	−0.696152	+	1.20577i	−0.0263121	+	0.0455739i
$701$	34.2049	+	19.7482i	1.29190	+	0.745880i	0.978991	−	0.203902i	$-0.0653625\pi$
$701$	34.2049	+	19.7482i	1.29190	+	0.745880i	0.312911	+	0.949782i	$0.398696\pi$
$702$	−0.693504	+	0.196152i	−0.0261746	+	0.00740330i
$703$	−30.9282	−	13.3923i	−1.16648	−	0.505100i
$704$		−	11.9700i		−	0.451138i
$705$	0.170328	+	1.84858i	0.00641494	+	0.0696214i
$706$	−0.973721	−	0.562178i	−0.0366465	−	0.0211578i
$707$	−0.480473	+	0.277401i	−0.0180701	+	0.0104328i
$708$	3.08621	+	33.4946i	0.115987	+	1.25881i
$709$	−3.83975	−	6.65064i	−0.144205	−	0.249770i	0.784871	−	0.619659i	$-0.212729\pi$
$709$	−3.83975	−	6.65064i	−0.144205	−	0.249770i	−0.929076	+	0.369889i	$0.879396\pi$
$710$			9.79796i			0.367711i
$711$	−29.5969	−	10.4641i	−1.10997	−	0.392434i
$712$	−7.09808	−	12.2942i	−0.266012	−	0.460746i
$713$	6.50266	+	11.2629i	0.243527	+	0.421800i
$714$	−0.679492	−	0.960947i	−0.0254293	−	0.0359625i
$715$			2.00000i			0.0747958i
$716$	−1.22474	−	2.12132i	−0.0457709	−	0.0792775i
$717$	−26.3523	+	2.42811i	−0.984144	+	0.0906794i
$718$	3.21539	−	1.85641i	0.119997	−	0.0692805i
$719$	−9.46979	−	5.46739i	−0.353164	−	0.203899i	0.312914	−	0.949781i	$-0.398695\pi$
$719$	−9.46979	−	5.46739i	−0.353164	−	0.203899i	−0.666078	+	0.745882i	$0.732028\pi$
$720$	−7.94610	+	6.79352i	−0.296134	+	0.253179i
$721$		−	0.947441i		−	0.0352846i
$722$	−9.57630	+	2.24144i	−0.356393	+	0.0834177i
$723$	−11.3397	−	16.0368i	−0.421730	−	0.596416i
$724$	−5.19615	−	3.00000i	−0.193113	−	0.111494i
$725$	−3.10583	+	5.37945i	−0.115348	+	0.199788i
$726$	13.7264	+	6.32377i	0.509434	+	0.234697i
$727$	−8.79423	+	15.2321i	−0.326160	+	0.564925i	−0.981746	−	0.190195i	$-0.939088\pi$
$727$	−8.79423	+	15.2321i	−0.326160	+	0.564925i	0.655587	+	0.755120i	$0.272421\pi$
$728$	0.120118	−	0.0693504i	0.00445188	−	0.00257030i
$729$	−23.0000	+	14.1421i	−0.851852	+	0.523783i
$730$			2.19615i			0.0812832i
$731$	24.3190	−	14.0406i	0.899472	−	0.519310i
$732$	28.5120	+	13.1355i	1.05383	+	0.485503i
$733$	19.7128			0.728109			0.364055	−	0.931378i	$-0.381392\pi$
$733$	19.7128			0.728109			0.364055	+	0.931378i	$0.381392\pi$
$734$	−10.8976			−0.402238
$735$	7.10102	−	15.4135i	0.261925	−	0.568535i
$736$	23.4904	+	13.5622i	0.865867	+	0.499909i
$737$	−2.63896	−	4.57081i	−0.0972073	−	0.168368i
$738$	5.70850	+	6.67700i	0.210133	+	0.245784i
$739$	22.5981	−	39.1410i	0.831284	−	1.43983i	−0.0657370	−	0.997837i	$-0.520940\pi$
$739$	22.5981	−	39.1410i	0.831284	−	1.43983i	0.897021	−	0.441989i	$-0.145727\pi$
$740$	−18.9396			−0.696233
$741$	1.97985	−	0.415458i	0.0727316	−	0.0152622i
$742$	−1.51666			−0.0556784
$743$	−3.53553	+	6.12372i	−0.129706	+	0.224658i	−0.923563	−	0.383447i	$-0.874737\pi$
$743$	−3.53553	+	6.12372i	−0.129706	+	0.224658i	0.793857	+	0.608105i	$0.208070\pi$
$744$	8.21027	−	0.756497i	0.301003	−	0.0277345i
$745$	1.92820	+	3.33975i	0.0706439	+	0.122359i
$746$	−8.72552	−	5.03768i	−0.319464	−	0.184443i
$747$	1.13505	+	6.10707i	0.0415294	+	0.223446i
$748$	44.7846			1.63749
$749$	1.31268			0.0479642
$750$	4.24440	−	9.21290i	0.154984	−	0.336408i
$751$	25.4545	−	14.6962i	0.928847	−	0.536270i	0.0424005	−	0.999101i	$-0.486499\pi$
$751$	25.4545	−	14.6962i	0.928847	−	0.536270i	0.886447	+	0.462830i	$0.153166\pi$
$752$			1.86748i			0.0681000i
$753$	14.6969	+	20.7846i	0.535586	+	0.757433i
$754$	0.248711	−	0.143594i	0.00905753	−	0.00522937i
$755$	−1.41421	+	2.44949i	−0.0514685	+	0.0891461i
$756$	1.68145	−	1.72866i	0.0611537	−	0.0628708i
$757$	−12.6962	+	21.9904i	−0.461450	+	0.799254i	−0.999033	−	0.0439562i	$-0.986004\pi$
$757$	−12.6962	+	21.9904i	−0.461450	+	0.799254i	0.537584	+	0.843210i	$0.319337\pi$
$758$	10.6623	+	6.15591i	0.387274	+	0.223593i
$759$	39.3949	−	27.8564i	1.42994	−	1.01112i
$760$	−9.56218	+	7.09808i	−0.346857	+	0.257474i
$761$		−	32.1208i		−	1.16438i	−0.813054	−	0.582188i	$-0.802197\pi$
$761$		−	32.1208i		−	1.16438i	0.813054	−	0.582188i	$-0.197803\pi$
$762$	−17.7277	+	1.63343i	−0.642206	+	0.0591731i
$763$	1.48334	+	0.856406i	0.0537005	+	0.0310040i
$764$	−19.5080	+	11.2629i	−0.705774	+	0.407479i
$765$	−13.5065	−	15.7980i	−0.488327	−	0.571176i
$766$	3.24167	+	5.61474i	0.117126	+	0.202869i
$767$		−	3.00429i		−	0.108479i
$768$	1.96902	−	1.39230i	0.0710508	−	0.0502405i
$769$	−13.4282	−	23.2583i	−0.484233	−	0.838717i	0.515603	−	0.856828i	$-0.327568\pi$
$769$	−13.4282	−	23.2583i	−0.484233	−	0.838717i	−0.999836	+	0.0181110i	$0.994235\pi$
$770$	0.517638	+	0.896575i	0.0186544	+	0.0323103i
$771$	11.4641	−	8.10634i	0.412870	−	0.291943i
$772$		−	4.85641i		−	0.174786i
$773$	−20.3538	−	35.2538i	−0.732075	−	1.26799i	−0.955995	−	0.293384i	$-0.905219\pi$
$773$	−20.3538	−	35.2538i	−0.732075	−	1.26799i	0.223920	−	0.974608i	$-0.428115\pi$
$774$	−5.78439	−	6.76576i	−0.207915	−	0.243190i
$775$	6.40192	−	3.69615i	0.229964	−	0.132770i
$776$	−0.896575	−	0.517638i	−0.0321852	−	0.0185821i
$777$	3.57332	−	0.329247i	0.128192	−	0.0118117i
$778$			7.66025i			0.274633i
$779$	−14.6969	−	19.7990i	−0.526572	−	0.709372i
$780$	0.928203	−	0.656339i	0.0332350	−	0.0235007i
$781$	61.1769	+	35.3205i	2.18908	+	1.26387i
$782$	−6.69213	+	11.5911i	−0.239310	+	0.414497i
$783$	7.50165	−	7.71228i	0.268087	−	0.275614i
$784$	8.53590	−	14.7846i	0.304854	−	0.528022i
$785$	12.8159	−	7.39924i	0.457417	−	0.264090i
$786$	−6.53590	−	9.24316i	−0.233128	−	0.329692i
$787$			37.9282i			1.35199i	0.736904	+	0.675997i	$0.236287\pi$
$787$			37.9282i			1.35199i	−0.736904	+	0.675997i	$0.763713\pi$
$788$	0.984508	−	0.568406i	0.0350717	−	0.0202486i
$789$	−20.9010	+	45.3677i	−0.744094	+	1.61513i
$790$	−7.66025			−0.272540
$791$	1.06248			0.0377775
$792$	−5.58941	−	30.0734i	−0.198611	−	1.06861i
$793$	−2.42820	−	1.40192i	−0.0862280	−	0.0497838i
$794$	−6.81225	−	11.7992i	−0.241758	−	0.418737i
$795$	−26.6716	+	2.45753i	−0.945945	+	0.0871597i
$796$	−20.0885	+	34.7942i	−0.712016	+	1.23325i
$797$	54.0918			1.91603			0.958016	−	0.286716i	$-0.0925635\pi$
$797$	54.0918			1.91603			0.958016	+	0.286716i	$0.0925635\pi$
$798$	0.780015	−	0.698668i	0.0276122	−	0.0247326i
$799$	−3.71281			−0.131350
$800$	7.70882	−	13.3521i	0.272548	−	0.472067i
$801$	14.3258	+	16.7563i	0.506176	+	0.592054i
$802$	−5.90192	−	10.2224i	−0.208404	−	0.360967i
$803$	13.7124	+	7.91688i	0.483901	+	0.279380i
$804$	−1.25529	+	2.72474i	−0.0442708	+	0.0960943i
$805$	2.00000			0.0704907
$806$	−0.341773			−0.0120384
$807$	−17.2018	−	7.92492i	−0.605533	−	0.278970i
$808$	3.46410	−	2.00000i	0.121867	−	0.0703598i
$809$		−	37.0197i		−	1.30155i	−0.759273	−	0.650773i	$-0.774445\pi$
$809$		−	37.0197i		−	1.30155i	0.759273	−	0.650773i	$-0.225555\pi$
$810$	−4.14110	+	5.12436i	−0.145504	+	0.180052i
$811$	29.1962	−	16.8564i	1.02522	−	0.591908i	0.109605	−	0.993975i	$-0.465041\pi$
$811$	29.1962	−	16.8564i	1.02522	−	0.591908i	0.915610	+	0.402067i	$0.131708\pi$
$812$	−0.480473	+	0.832204i	−0.0168613	+	0.0292046i
$813$	10.8990	+	5.02118i	0.382244	+	0.176100i
$814$	10.5622	−	18.2942i	0.370204	−	0.641212i
$815$	6.36396	+	3.67423i	0.222920	+	0.128703i
$816$	−12.0716	−	17.0718i	−0.422590	−	0.597632i
$817$	14.8923	+	20.0622i	0.521016	+	0.701887i
$818$		−	10.4815i		−	0.366477i
$819$	−0.163714	+	0.139967i	−0.00572062	+	0.00489085i
$820$	−12.0000	−	6.92820i	−0.419058	−	0.241943i
$821$	4.41851	−	2.55103i	0.154207	−	0.0890314i	−0.420911	−	0.907102i	$-0.638290\pi$
$821$	4.41851	−	2.55103i	0.154207	−	0.0890314i	0.575118	+	0.818071i	$0.304956\pi$
$822$	9.42418	−	0.868348i	0.328706	−	0.0302871i
$823$	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	$0.788806\pi$
$824$			6.83083i			0.237963i
$825$	−15.8338	−	22.3923i	−0.551260	−	0.779600i
$826$	−0.777568	−	1.34679i	−0.0270551	−	0.0468607i
$827$	−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	$0.973371\pi$
$828$	−25.8564	−	9.14162i	−0.898572	−	0.317693i
$829$		−	21.3397i		−	0.741160i	−0.928801	−	0.370580i	$-0.879159\pi$
$829$		−	21.3397i		−	0.741160i	0.928801	−	0.370580i	$-0.120841\pi$
$830$	0.757875	+	1.31268i	0.0263062	+	0.0455637i
$831$	−2.83772	−	30.7977i	−0.0984393	−	1.06836i
$832$	0.526279	−	0.303848i	0.0182455	−	0.0105340i
$833$	29.3939	+	16.9706i	1.01844	+	0.587995i
$834$	0.230651	+	2.50326i	0.00798679	+	0.0866807i
$835$			30.7846i			1.06535i
$836$	4.57081	+	39.5844i	0.158085	+	1.36905i
$837$	−12.3205	+	3.48477i	−0.425859	+	0.120451i
$838$	−3.38526	−	1.95448i	−0.116942	−	0.0675165i
$839$	−12.6772	+	21.9575i	−0.437664	+	0.758056i	−0.997509	−	0.0705412i	$-0.977527\pi$
$839$	−12.6772	+	21.9575i	−0.437664	+	0.758056i	0.559845	+	0.828597i	$0.310861\pi$
$840$	0.530550	−	1.15161i	0.0183057	−	0.0397344i
$841$	12.3564	−	21.4019i	0.426083	−	0.737997i
$842$	12.7923	−	7.38563i	0.440852	−	0.254526i
$843$	13.3205	−	9.41902i	0.458783	−	0.324408i
$844$			19.0526i			0.655816i
$845$	15.8338	−	9.14162i	0.544698	−	0.314481i
$846$	0.215057	+	1.15710i	0.00739381	+	0.0397819i
$847$	4.51666			0.155194
$848$	−26.9444			−0.925274
$849$	9.21290	+	4.24440i	0.316186	+	0.145667i
$850$	6.58846	+	3.80385i	0.225982	+	0.130471i
$851$	−20.4046	−	35.3417i	−0.699459	−	1.21150i
$852$	−3.68409	−	39.9834i	−0.126215	−	1.36981i
$853$	−27.1603	+	47.0429i	−0.929949	+	1.61072i	−0.146548	+	0.989204i	$0.546816\pi$
$853$	−27.1603	+	47.0429i	−0.929949	+	1.61072i	−0.783401	+	0.621516i	$0.786517\pi$
$854$	−1.45138			−0.0496651
$855$	12.5851	−	13.5505i	0.430400	−	0.463418i
$856$	−9.46410			−0.323476
$857$	−21.1117	+	36.5665i	−0.721161	+	1.24909i	0.239374	+	0.970927i	$0.423058\pi$
$857$	−21.1117	+	36.5665i	−0.721161	+	1.24909i	−0.960535	+	0.278160i	$0.910276\pi$
$858$	0.116337	+	1.26260i	0.00397166	+	0.0431045i
$859$	−6.33013	−	10.9641i	−0.215981	−	0.374090i	0.737594	−	0.675244i	$-0.235962\pi$
$859$	−6.33013	−	10.9641i	−0.215981	−	0.374090i	−0.953576	+	0.301154i	$0.902628\pi$
$860$	12.1595	+	7.02030i	0.414636	+	0.239390i
$861$	2.38447	+	1.09853i	0.0812627	+	0.0374379i
$862$	13.1769			0.448807
$863$	1.31268			0.0446841			0.0223420	−	0.999750i	$-0.492888\pi$
$863$	1.31268			0.0446841			0.0223420	+	0.999750i	$0.492888\pi$
$864$	−18.6195	+	19.1423i	−0.633448	+	0.651233i
$865$	−21.4641	+	12.3923i	−0.729801	+	0.421351i
$866$			10.6945i			0.363415i
$867$	9.89949	−	7.00000i	0.336204	−	0.237732i
$868$	0.990381	−	0.571797i	0.0336157	−	0.0194080i
$869$	−27.6143	+	47.8294i	−0.936752	+	1.62250i
$870$	1.09853	−	2.38447i	0.0372437	−	0.0808413i
$871$	0.133975	−	0.232051i	0.00453956	−	0.00786274i
$872$	−10.6945	−	6.17449i	−0.362163	−	0.209095i
$873$	1.51575	+	0.535898i	0.0513003	+	0.0181374i
$874$	−10.9282	−	4.73205i	−0.369652	−	0.160064i
$875$		−	3.03150i		−	0.102483i
$876$	−0.825765	−	8.96204i	−0.0279000	−	0.302799i
$877$	0.232051	+	0.133975i	0.00783580	+	0.00452400i	0.503913	−	0.863755i	$-0.331893\pi$
$877$	0.232051	+	0.133975i	0.00783580	+	0.00452400i	−0.496077	+	0.868279i	$0.665227\pi$
$878$	−6.96455	+	4.02099i	−0.235042	+	0.135702i
$879$	2.21518	+	24.0413i	0.0747161	+	0.810894i
$880$	9.19615	+	15.9282i	0.310002	+	0.536940i
$881$			48.3335i			1.62840i	0.580588	+	0.814198i	$0.302823\pi$
$881$			48.3335i			1.62840i	−0.580588	+	0.814198i	$0.697177\pi$
$882$	3.58630	−	10.1436i	0.120757	−	0.341553i
$883$	12.8660	+	22.2846i	0.432976	+	0.749937i	0.997128	−	0.0757343i	$-0.0241301\pi$
$883$	12.8660	+	22.2846i	0.432976	+	0.749937i	−0.564152	+	0.825671i	$0.690797\pi$
$884$	1.13681	+	1.96902i	0.0382351	+	0.0662252i
$885$	−15.8564	−	22.4243i	−0.533007	−	0.753786i
$886$			5.35898i			0.180039i
$887$	1.08604	+	1.88108i	0.0364658	+	0.0631606i	0.883682	−	0.468087i	$-0.155057\pi$
$887$	1.08604	+	1.88108i	0.0364658	+	0.0631606i	−0.847217	+	0.531248i	$0.821723\pi$
$888$	−25.7628	+	2.37380i	−0.864544	+	0.0796594i
$889$	−4.60770	+	2.66025i	−0.154537	+	0.0892221i
$890$	4.65874	+	2.68973i	0.156161	+	0.0901598i
$891$	17.0675	+	44.3291i	0.571782	+	1.48508i
$892$		−	19.7321i		−	0.660678i
$893$	−0.378937	−	3.28169i	−0.0126807	−	0.109818i
$894$	1.41154	+	1.99622i	0.0472091	+	0.0667637i
$895$	1.73205	+	1.00000i	0.0578961	+	0.0334263i
$896$	1.53433	−	2.65754i	0.0512584	−	0.0887822i
$897$	2.22474	+	1.02494i	0.0742821	+	0.0342219i
$898$	−1.32051	+	2.28719i	−0.0440659	+	0.0763244i
$899$	4.41851	−	2.55103i	0.147365	−	0.0850815i
$900$	−5.19615	+	14.6969i	−0.173205	+	0.489898i
$901$		−	53.5692i		−	1.78465i
$902$	13.3843	−	7.72741i	0.445647	−	0.257294i
$903$	−2.41617	−	1.11313i	−0.0804051	−	0.0370428i
$904$	−7.66025			−0.254776
$905$	4.89898			0.162848
$906$	−0.750311	+	1.62863i	−0.0249274	+	0.0541075i
$907$	−23.4449	−	13.5359i	−0.778474	−	0.449452i	0.0574152	−	0.998350i	$-0.481714\pi$
$907$	−23.4449	−	13.5359i	−0.778474	−	0.449452i	−0.835889	+	0.548898i	$0.815047\pi$
$908$	−4.15471	−	7.19617i	−0.137879	−	0.238813i
$909$	−4.72135	+	4.03652i	−0.156597	+	0.133883i
$910$	−0.0262794	+	0.0455173i	−0.000871155	+	0.00150888i
$911$	21.3147			0.706189			0.353094	−	0.935588i	$-0.385129\pi$
$911$	21.3147			0.706189			0.353094	+	0.935588i	$0.385129\pi$
$912$	13.8574	−	12.4123i	0.458865	−	0.411011i
$913$	10.9282			0.361671
$914$	8.98434	−	15.5613i	0.297175	−	0.514723i
$915$	−25.5236	+	2.35175i	−0.843784	+	0.0777466i
$916$	−9.86603	−	17.0885i	−0.325983	−	0.564619i
$917$	−2.92996	−	1.69161i	−0.0967559	−	0.0558620i
$918$	−9.44557	−	9.18761i	−0.311750	−	0.303236i
$919$	19.9808			0.659105			0.329552	−	0.944137i	$-0.393102\pi$
$919$	19.9808			0.659105			0.329552	+	0.944137i	$0.393102\pi$
$920$	−14.4195			−0.475398
$921$	−10.0424	+	21.7980i	−0.330907	+	0.718267i
$922$	−16.0070	+	9.24167i	−0.527164	+	0.304358i
$923$			3.58630i			0.118045i
$924$	−2.44949	−	3.46410i	−0.0805823	−	0.113961i
$925$	−20.0885	+	11.5981i	−0.660504	+	0.381342i
$926$	0.411123	−	0.712086i	0.0135103	−	0.0234006i
$927$	−1.93834	−	10.4291i	−0.0636634	−	0.342536i
$928$	5.32051	−	9.21539i	0.174654	−	0.302510i
$929$	9.22955	+	5.32868i	0.302812	+	0.174828i	0.643705	−	0.765273i	$-0.277396\pi$
$929$	9.22955	+	5.32868i	0.302812	+	0.174828i	−0.340894	+	0.940102i	$0.610730\pi$
$930$	−2.55103	+	1.80385i	−0.0836514	+	0.0591505i
$931$	−12.0000	+	27.7128i	−0.393284	+	0.908251i
$932$			23.1822i			0.759359i
$933$	21.4740	−	1.97862i	0.703026	−	0.0647771i
$934$	10.1436	+	5.85641i	0.331909	+	0.191627i
$935$	−31.6675	+	18.2832i	−1.03564	+	0.597926i
$936$	1.18034	−	1.00913i	0.0385806	−	0.0329845i
$937$	17.8923	+	30.9904i	0.584516	+	1.01241i	0.994936	+	0.100515i	$0.0320490\pi$
$937$	17.8923	+	30.9904i	0.584516	+	1.01241i	−0.410419	+	0.911897i	$0.634618\pi$
$938$		−	0.138701i		−	0.00452874i
$939$	−23.7370	+	16.7846i	−0.774628	+	0.547745i
$940$	−0.928203	−	1.60770i	−0.0302747	−	0.0524372i
$941$	−12.6264	−	21.8695i	−0.411608	−	0.712927i	0.583457	−	0.812144i	$-0.301700\pi$
$941$	−12.6264	−	21.8695i	−0.411608	−	0.712927i	−0.995066	+	0.0992170i	$0.968366\pi$
$942$	7.66025	−	5.41662i	0.249585	−	0.176483i
$943$		−	29.8564i		−	0.972258i
$944$	−13.8140	−	23.9265i	−0.449606	−	0.778741i
$945$	−0.483242	+	1.90880i	−0.0157199	+	0.0620931i
$946$	−13.5622	+	7.83013i	−0.440944	+	0.254579i
$947$	−4.06678	−	2.34795i	−0.132152	−	0.0762982i	0.432466	−	0.901650i	$-0.357643\pi$
$947$	−4.06678	−	2.34795i	−0.132152	−	0.0762982i	−0.564619	+	0.825352i	$0.690977\pi$
$948$	31.2599	−	2.88030i	1.01527	−	0.0935477i
$949$			0.803848i			0.0260940i
$950$	−2.68973	+	6.21166i	−0.0872662	+	0.201533i
$951$	−12.5359	+	8.86422i	−0.406504	+	0.287442i
$952$	2.19615	+	1.26795i	0.0711777	+	0.0410945i
$953$	−4.15471	+	7.19617i	−0.134584	+	0.233107i	−0.925439	−	0.378898i	$-0.876303\pi$
$953$	−4.15471	+	7.19617i	−0.134584	+	0.233107i	0.790854	+	0.612004i	$0.209637\pi$
$954$	−16.6949	+	3.10288i	−0.540516	+	0.100460i
$955$	9.19615	−	15.9282i	0.297581	−	0.515425i
$956$	22.9184	−	13.2320i	0.741235	−	0.427952i
$957$	−10.9282	−	15.4548i	−0.353259	−	0.499583i
$958$		−	9.07180i		−	0.293096i
$959$	2.44949	−	1.41421i	0.0790981	−	0.0456673i
$960$	2.32452	−	5.04561i	0.0750236	−	0.162846i
$961$	24.9282			0.804136
$962$	1.07244			0.0345769
$963$	14.4495	−	2.68556i	0.465628	−	0.0865410i
$964$	17.0096	+	9.82051i	0.547843	+	0.316297i
$965$	1.98262	+	3.43400i	0.0638228	+	0.110544i
$966$	1.26260	−	0.116337i	0.0406235	−	0.00374307i
$967$	9.59808	−	16.6244i	0.308653	−	0.534603i	−0.669415	−	0.742889i	$-0.733455\pi$
$967$	9.59808	−	16.6244i	0.308653	−	0.534603i	0.978068	+	0.208286i	$0.0667884\pi$
$968$	−32.5641			−1.04665
$969$	24.6773	+	27.5505i	0.792749	+	0.885050i
$970$	0.392305			0.0125961
$971$	26.7685	−	46.3644i	0.859043	−	1.48791i	−0.0138004	−	0.999905i	$-0.504393\pi$
$971$	26.7685	−	46.3644i	0.859043	−	1.48791i	0.872843	−	0.488001i	$-0.162274\pi$
$972$	14.9722	−	22.4685i	0.480233	−	0.720677i
$973$	0.375644	+	0.650635i	0.0120426	+	0.0208584i
$974$	4.96335	+	2.86559i	0.159036	+	0.0918195i
$975$	0.582584	−	1.26456i	0.0186576	−	0.0404983i
$976$	−25.7846			−0.825345
$977$	9.04008			0.289218			0.144609	−	0.989489i	$-0.453808\pi$
$977$	9.04008			0.289218			0.144609	+	0.989489i	$0.453808\pi$
$978$	4.23130	+	1.94937i	0.135302	+	0.0623338i
$979$	33.5885	−	19.3923i	1.07349	−	0.619781i
$980$			16.9706i			0.542105i
$981$	18.0802	+	6.39230i	0.577255	+	0.204091i
$982$	13.2679	−	7.66025i	0.423397	−	0.244449i
$983$	−16.2635	+	28.1691i	−0.518724	+	0.898456i	0.481040	+	0.876699i	$0.340259\pi$
$983$	−16.2635	+	28.1691i	−0.518724	+	0.898456i	−0.999763	+	0.0217569i	$0.993074\pi$
$984$	−17.1915	−	7.92016i	−0.548045	−	0.252485i
$985$	−0.464102	+	0.803848i	−0.0147875	+	0.0256127i
$986$	4.54725	+	2.62536i	0.144814	+	0.0836083i
$987$	0.203072	+	0.287187i	0.00646385	+	0.00914127i
$988$	−1.62436	+	1.20577i	−0.0516776	+	0.0383607i
$989$			30.2533i			0.961999i
$990$	7.53225	+	8.81017i	0.239391	+	0.280005i
$991$	−50.3827	−	29.0885i	−1.60046	−	0.924025i	−0.991395	−	0.130904i	$-0.958212\pi$
$991$	−50.3827	−	29.0885i	−1.60046	−	0.924025i	−0.609064	−	0.793121i	$-0.708455\pi$
$992$	−10.9670	+	6.33178i	−0.348201	+	0.201034i
$993$	−31.1692	+	2.87195i	−0.989126	+	0.0911384i
$994$	0.928203	+	1.60770i	0.0294408	+	0.0509930i
$995$		−	32.8043i		−	1.03997i
$996$	−3.58630	−	5.07180i	−0.113636	−	0.160706i
$997$	6.08846	+	10.5455i	0.192823	+	0.333980i	0.946185	−	0.323627i	$-0.104902\pi$
$997$	6.08846	+	10.5455i	0.192823	+	0.333980i	−0.753361	+	0.657607i	$0.771569\pi$
$998$	2.10274	+	3.64205i	0.0665610	+	0.115287i
$999$	38.6603	−	10.9348i	1.22316	−	0.345961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.2.f.a.8.3	yes	8
3.2	odd	2	inner	57.2.f.a.8.2	✓	8
4.3	odd	2		912.2.bn.m.65.3		8
12.11	even	2		912.2.bn.m.65.4		8
19.8	odd	6		1083.2.d.b.1082.5		8
19.11	even	3		1083.2.d.b.1082.4		8
19.12	odd	6	inner	57.2.f.a.50.2	yes	8
57.8	even	6		1083.2.d.b.1082.3		8
57.11	odd	6		1083.2.d.b.1082.6		8
57.50	even	6	inner	57.2.f.a.50.3	yes	8
76.31	even	6		912.2.bn.m.449.4		8
228.107	odd	6		912.2.bn.m.449.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.f.a.8.2	✓	8	3.2	odd	2	inner
57.2.f.a.8.3	yes	8	1.1	even	1	trivial
57.2.f.a.50.2	yes	8	19.12	odd	6	inner
57.2.f.a.50.3	yes	8	57.50	even	6	inner
912.2.bn.m.65.3		8	4.3	odd	2
912.2.bn.m.65.4		8	12.11	even	2
912.2.bn.m.449.3		8	228.107	odd	6
912.2.bn.m.449.4		8	76.31	even	6
1083.2.d.b.1082.3		8	57.8	even	6
1083.2.d.b.1082.4		8	19.11	even	3
1083.2.d.b.1082.5		8	19.8	odd	6
1083.2.d.b.1082.6		8	57.11	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)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.448288i) q^{2} +(-0.158919 - 1.72474i) q^{3} +(0.866025 + 1.50000i) q^{4} +(-1.22474 - 0.707107i) q^{5} +(-0.814313 - 0.375156i) q^{6} -0.267949 q^{7} +1.93185 q^{8} +(-2.94949 + 0.548188i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.448288i) q^{2} +(-0.158919 - 1.72474i) q^{3} +(0.866025 + 1.50000i) q^{4} +(-1.22474 - 0.707107i) q^{5} +(-0.814313 - 0.375156i) q^{6} -0.267949 q^{7} +1.93185 q^{8} +(-2.94949 + 0.548188i) q^{9} +(-0.633975 + 0.366025i) q^{10} +5.27792i q^{11} +(2.44949 - 1.73205i) q^{12} +(-0.232051 + 0.133975i) q^{13} +(-0.0693504 + 0.120118i) q^{14} +(-1.02494 + 2.22474i) q^{15} +(-1.23205 + 2.13397i) q^{16} +(-4.24264 - 2.44949i) q^{17} +(-0.517638 + 1.46410i) q^{18} +(1.73205 - 4.00000i) q^{19} -2.44949i q^{20} +(0.0425821 + 0.462144i) q^{21} +(2.36603 + 1.36603i) q^{22} +(4.57081 - 2.63896i) q^{23} +(-0.307007 - 3.33195i) q^{24} +(-1.50000 - 2.59808i) q^{25} +0.138701i q^{26} +(1.41421 + 5.00000i) q^{27} +(-0.232051 - 0.401924i) q^{28} +(-1.03528 - 1.79315i) q^{29} +(0.732051 + 1.03528i) q^{30} +2.46410i q^{31} +(2.56961 + 4.45069i) q^{32} +(9.10306 - 0.838759i) q^{33} +(-2.19615 + 1.26795i) q^{34} +(0.328169 + 0.189469i) q^{35} +(-3.37662 - 3.94949i) q^{36} -7.73205i q^{37} +(-1.34486 - 1.81173i) q^{38} +(0.267949 + 0.378937i) q^{39} +(-2.36603 - 1.36603i) q^{40} +(2.82843 - 4.89898i) q^{41} +(0.218195 + 0.100523i) q^{42} +(-2.86603 + 4.96410i) q^{43} +(-7.91688 + 4.57081i) q^{44} +(4.00000 + 1.41421i) q^{45} -2.73205i q^{46} +(0.656339 - 0.378937i) q^{47} +(3.87636 + 1.78585i) q^{48} -6.92820 q^{49} -1.55291 q^{50} +(-3.55051 + 7.70674i) q^{51} +(-0.401924 - 0.232051i) q^{52} +(5.46739 + 9.46979i) q^{53} +(2.60746 + 0.660121i) q^{54} +(3.73205 - 6.46410i) q^{55} -0.517638 q^{56} +(-7.17423 - 2.35167i) q^{57} -1.07180 q^{58} +(-5.60609 + 9.71003i) q^{59} +(-4.22474 + 0.389270i) q^{60} +(5.23205 + 9.06218i) q^{61} +(1.10463 + 0.637756i) q^{62} +(0.790313 - 0.146887i) q^{63} -2.26795 q^{64} +0.378937 q^{65} +(1.98004 - 4.29788i) q^{66} +(-0.866025 + 0.500000i) q^{67} -8.48528i q^{68} +(-5.27792 - 7.46410i) q^{69} +(0.169873 - 0.0980762i) q^{70} +(6.69213 - 11.5911i) q^{71} +(-5.69798 + 1.05902i) q^{72} +(1.50000 - 2.59808i) q^{73} +(-3.46618 - 2.00120i) q^{74} +(-4.24264 + 3.00000i) q^{75} +(7.50000 - 0.866025i) q^{76} -1.41421i q^{77} +(0.239223 - 0.0220421i) q^{78} +(9.06218 + 5.23205i) q^{79} +(3.01790 - 1.74238i) q^{80} +(8.39898 - 3.23375i) q^{81} +(-1.46410 - 2.53590i) q^{82} -2.07055i q^{83} +(-0.656339 + 0.464102i) q^{84} +(3.46410 + 6.00000i) q^{85} +(1.48356 + 2.56961i) q^{86} +(-2.92820 + 2.07055i) q^{87} +10.1962i q^{88} +(-3.67423 - 6.36396i) q^{89} +(1.66925 - 1.42713i) q^{90} +(0.0621778 - 0.0358984i) q^{91} +(7.91688 + 4.57081i) q^{92} +(4.24995 - 0.391592i) q^{93} -0.392305i q^{94} +(-4.94975 + 3.67423i) q^{95} +(7.26795 - 5.13922i) q^{96} +(-0.464102 - 0.267949i) q^{97} +(-1.79315 + 3.10583i) q^{98} +(-2.89329 - 15.5672i) 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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