LMFDB - Embedded newform 57.2.f.a.8.2

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			8.2
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	57.8
Dual form			57.2.f.a.50.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.448288i) q^{2} +(-1.57313 + 0.724745i) q^{3} +(0.866025 + 1.50000i) q^{4} +(1.22474 + 0.707107i) q^{5} +(0.0822623 - 0.892794i) q^{6} -0.267949 q^{7} -1.93185 q^{8} +(1.94949 - 2.28024i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.448288i) q^{2} +(-1.57313 + 0.724745i) q^{3} +(0.866025 + 1.50000i) q^{4} +(1.22474 + 0.707107i) q^{5} +(0.0822623 - 0.892794i) q^{6} -0.267949 q^{7} -1.93185 q^{8} +(1.94949 - 2.28024i) 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} +(-2.43916 - 0.224745i) 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} +(0.421519 - 0.194195i) q^{21} +(2.36603 + 1.36603i) q^{22} +(-4.57081 + 2.63896i) q^{23} +(3.03906 - 1.40010i) 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} +(3.82514 + 8.30286i) q^{33} +(-2.19615 + 1.26795i) q^{34} +(-0.328169 - 0.189469i) q^{35} +(5.10867 + 0.949490i) 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} +(-0.0220421 + 0.239223i) 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} +(0.391592 - 4.24995i) q^{48} -6.92820 q^{49} +1.55291 q^{50} +(-8.44949 - 0.778539i) q^{51} +(-0.401924 - 0.232051i) q^{52} +(-5.46739 - 9.46979i) q^{53} +(-1.87541 - 1.92807i) q^{54} +(3.73205 - 6.46410i) q^{55} +0.517638 q^{56} +(0.174235 + 7.54782i) q^{57} -1.07180 q^{58} +(5.60609 - 9.71003i) q^{59} +(-1.77526 - 3.85337i) q^{60} +(5.23205 + 9.06218i) q^{61} +(-1.10463 - 0.637756i) q^{62} +(-0.522364 + 0.610988i) q^{63} -2.26795 q^{64} -0.378937 q^{65} +(-4.71209 - 0.434174i) 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} +(-3.76612 + 4.40508i) 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} +(0.100523 + 0.218195i) q^{78} +(9.06218 + 5.23205i) q^{79} +(-3.01790 + 1.74238i) q^{80} +(-1.39898 - 8.89060i) 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} +(-0.401302 + 2.15918i) q^{90} +(0.0621778 - 0.0358984i) q^{91} +(-7.91688 - 4.57081i) q^{92} +(-1.78585 - 3.87636i) 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} +(-12.0349 - 10.2892i) 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	−0.942905	−	0.333062i	$-0.891918\pi$
$2$	−0.258819	+	0.448288i	−0.183013	+	0.316987i	0.759892	+	0.650049i	$0.225252\pi$
$3$	−1.57313	+	0.724745i	−0.908248	+	0.418432i
$3$	−1.57313	+	0.724745i	−0.908248	+	0.418432i
$4$	0.866025	+	1.50000i	0.433013	+	0.750000i
$5$	1.22474	+	0.707107i	0.547723	+	0.316228i	0.748203	−	0.663470i	$-0.230917\pi$
$5$	1.22474	+	0.707107i	0.547723	+	0.316228i	−0.200480	+	0.979698i	$0.564250\pi$
$6$	0.0822623	−	0.892794i	0.0335835	−	0.364481i
$7$	−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
$9$	1.94949	−	2.28024i	0.649830	−	0.760080i
$10$	−0.633975	+	0.366025i	−0.200480	+	0.115747i
$11$		−	5.27792i		−	1.59135i	−0.605723	−	0.795676i	$-0.707116\pi$
$11$		−	5.27792i		−	1.59135i	0.605723	−	0.795676i	$-0.292884\pi$
$12$	−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
$15$	−2.43916	−	0.224745i	−0.629788	−	0.0580289i
$16$	−1.23205	+	2.13397i	−0.308013	+	0.533494i
$17$	4.24264	+	2.44949i	1.02899	+	0.594089i	0.916696	−	0.399586i	$-0.130846\pi$
$17$	4.24264	+	2.44949i	1.02899	+	0.594089i	0.112296	+	0.993675i	$0.464180\pi$
$18$	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
$21$	0.421519	−	0.194195i	0.0919831	−	0.0423768i
$22$	2.36603	+	1.36603i	0.504438	+	0.291238i
$23$	−4.57081	+	2.63896i	−0.953080	+	0.550261i	−0.894036	−	0.447995i	$-0.852138\pi$
$23$	−4.57081	+	2.63896i	−0.953080	+	0.550261i	−0.0590435	+	0.998255i	$0.518805\pi$
$24$	3.03906	−	1.40010i	0.620345	−	0.285794i
$25$	−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	0.945994	−	0.324184i	$-0.105090\pi$
$29$	1.03528	+	1.79315i	0.192246	+	0.332980i	−0.753748	+	0.657163i	$0.771756\pi$
$30$	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
$33$	3.82514	+	8.30286i	0.665872	+	1.44534i
$34$	−2.19615	+	1.26795i	−0.376637	+	0.217451i
$35$	−0.328169	−	0.189469i	−0.0554708	−	0.0320261i
$36$	5.10867	+	0.949490i	0.851444	+	0.158248i
$37$		−	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	−0.997818	−	0.0660290i	$-0.978967\pi$
$41$	−2.82843	+	4.89898i	−0.441726	+	0.765092i	0.556092	+	0.831121i	$0.312300\pi$
$42$	−0.0220421	+	0.239223i	−0.00340117	+	0.0369130i
$43$	−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	−0.547104	−	0.837065i	$-0.684270\pi$
$47$	−0.656339	+	0.378937i	−0.0957369	+	0.0552737i	0.451367	+	0.892338i	$0.350936\pi$
$48$	0.391592	−	4.24995i	0.0565214	−	0.613427i
$49$	−6.92820			−0.989743
$50$	1.55291			0.219615
$51$	−8.44949	−	0.778539i	−1.18317	−	0.109017i
$52$	−0.401924	−	0.232051i	−0.0557368	−	0.0321797i
$53$	−5.46739	−	9.46979i	−0.751003	−	1.30078i	−0.947337	−	0.320239i	$-0.896237\pi$
$53$	−5.46739	−	9.46979i	−0.751003	−	1.30078i	0.196334	−	0.980537i	$-0.437096\pi$
$54$	−1.87541	−	1.92807i	−0.255211	−	0.262377i
$55$	3.73205	−	6.46410i	0.503230	−	0.871619i
$56$	0.517638			0.0691723
$57$	0.174235	+	7.54782i	0.0230779	+	0.999734i
$58$	−1.07180			−0.140734
$59$	5.60609	−	9.71003i	0.729850	−	1.26414i	−0.227096	−	0.973872i	$-0.572923\pi$
$59$	5.60609	−	9.71003i	0.729850	−	1.26414i	0.956946	−	0.290265i	$-0.0937436\pi$
$60$	−1.77526	−	3.85337i	−0.229184	−	0.497468i
$61$	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
$63$	−0.522364	+	0.610988i	−0.0658117	+	0.0769773i
$64$	−2.26795			−0.283494
$65$	−0.378937			−0.0470014
$66$	−4.71209	−	0.434174i	−0.580018	−	0.0534431i
$67$	−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	$0.458782\pi$
$71$	−6.69213	+	11.5911i	−0.794210	+	1.37561i	−0.923340	+	0.383984i	$0.874552\pi$
$72$	−3.76612	+	4.40508i	−0.443842	+	0.519144i
$73$	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
$78$	0.100523	+	0.218195i	0.0113819	+	0.0247057i
$79$	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
$81$	−1.39898	−	8.89060i	−0.155442	−	0.987845i
$82$	−1.46410	−	2.53590i	−0.161683	−	0.280043i
$83$			2.07055i			0.227273i	0.993522	+	0.113636i	$0.0362499\pi$
$83$			2.07055i			0.227273i	−0.993522	+	0.113636i	$0.963750\pi$
$84$	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	0.992378	−	0.123231i	$-0.0393255\pi$
$89$	3.67423	+	6.36396i	0.389468	+	0.674579i	−0.602910	+	0.797809i	$0.705992\pi$
$90$	−0.401302	+	2.15918i	−0.0423009	+	0.227597i
$91$	0.0621778	−	0.0358984i	0.00651801	−	0.00376317i
$92$	−7.91688	−	4.57081i	−0.825391	−	0.476540i
$93$	−1.78585	−	3.87636i	−0.185184	−	0.401960i
$94$		−	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
$99$	−12.0349	−	10.2892i	−1.20955	−	1.03411i
$100$	2.59808	−	4.50000i	0.259808	−	0.450000i
$101$	−1.79315	+	1.03528i	−0.178425	+	0.103014i	−0.586553	−	0.809911i	$-0.699515\pi$
$101$	−1.79315	+	1.03528i	−0.178425	+	0.103014i	0.408127	+	0.912925i	$0.366182\pi$
$102$	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
$105$	0.653570	+	0.0602202i	0.0637819	+	0.00587689i
$106$	5.66025			0.549772
$107$	4.89898			0.473602			0.236801	−	0.971558i	$-0.423901\pi$
$107$	4.89898			0.473602			0.236801	+	0.971558i	$0.423901\pi$
$108$	−8.72474	+	2.20881i	−0.839539	+	0.212543i
$109$	−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
$111$	5.60376	+	12.1635i	0.531886	+	1.15451i
$112$	0.330127	−	0.571797i	0.0311941	−	0.0540297i
$113$	3.96524			0.373018			0.186509	−	0.982453i	$-0.440283\pi$
$113$	3.96524			0.373018			0.186509	+	0.982453i	$0.440283\pi$
$114$	−3.42869	−	1.87541i	−0.321126	−	0.175649i
$115$	−7.46410			−0.696031
$116$	−1.79315	+	3.10583i	−0.166490	+	0.288369i
$117$	−0.146887	+	0.790313i	−0.0135797	+	0.0730645i
$118$	2.90192	+	5.02628i	0.267144	+	0.462707i
$119$	−1.13681	−	0.656339i	−0.104211	−	0.0601665i
$120$	4.71209	+	0.434174i	0.430153	+	0.0396345i
$121$	−16.8564			−1.53240
$122$	−5.41662			−0.490398
$123$	0.898979	−	9.75663i	0.0810583	−	0.879726i
$124$	−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
$129$	0.910930	−	9.88633i	0.0802029	−	0.870442i
$130$	0.0980762	−	0.169873i	0.00860185	−	0.0148988i
$131$	−10.9348	−	6.31319i	−0.955375	−	0.551586i	−0.0606288	−	0.998160i	$-0.519311\pi$
$131$	−10.9348	−	6.31319i	−0.955375	−	0.551586i	−0.894747	+	0.446574i	$0.852644\pi$
$132$	−9.14162	+	12.9282i	−0.795676	+	1.12526i
$133$	−0.464102	+	1.07180i	−0.0402427	+	0.0929366i
$134$		−	0.517638i		−	0.0447171i
$135$	−5.26758	+	5.12372i	−0.453362	+	0.440980i
$136$	−8.19615	−	4.73205i	−0.702814	−	0.405770i
$137$	9.14162	−	5.27792i	0.781021	−	0.450923i	−0.0557708	−	0.998444i	$-0.517762\pi$
$137$	9.14162	−	5.27792i	0.781021	−	0.450923i	0.836792	+	0.547521i	$0.184428\pi$
$138$	1.98004	+	4.29788i	0.168552	+	0.365860i
$139$	−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
$147$	10.8990	−	5.02118i	0.898933	−	0.414140i
$148$	11.5981	−	6.69615i	0.953356	−	0.550420i
$149$	2.36156	+	1.36345i	0.193466	+	0.111698i	0.593604	−	0.804757i	$-0.297704\pi$
$149$	2.36156	+	1.36345i	0.193466	+	0.111698i	−0.400138	+	0.916455i	$0.631038\pi$
$150$	−2.44294	+	1.12547i	−0.199465	+	0.0918940i
$151$		−	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
$156$	0.800457	+	0.0737544i	0.0640878	+	0.00590508i
$157$	−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
$162$	4.34763	+	1.67391i	0.341582	+	0.131515i
$163$	−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
$165$	−1.18618	+	12.8737i	−0.0923444	+	1.00221i
$166$	−0.928203	−	0.535898i	−0.0720425	−	0.0415938i
$167$	10.8840	+	18.8516i	0.842229	+	1.45878i	0.888006	+	0.459832i	$0.152091\pi$
$167$	10.8840	+	18.8516i	0.842229	+	1.45878i	−0.0457762	+	0.998952i	$0.514576\pi$
$168$	−0.814313	+	0.375156i	−0.0628256	+	0.0289439i
$169$	−6.46410	+	11.1962i	−0.497239	+	0.861242i
$170$	−3.58630			−0.275057
$171$	−5.74434	−	11.7474i	−0.439281	−	0.898350i
$172$	−9.92820			−0.757018
$173$	−8.76268	+	15.1774i	−0.666214	+	1.15392i	0.312740	+	0.949839i	$0.398753\pi$
$173$	−8.76268	+	15.1774i	−0.666214	+	1.15392i	−0.978955	+	0.204079i	$0.934580\pi$
$174$	1.68608	−	0.776779i	0.127821	−	0.0588875i
$175$	0.401924	+	0.696152i	0.0303826	+	0.0526242i
$176$	11.2629	+	6.50266i	0.848976	+	0.490157i
$177$	−1.78182	+	19.3381i	−0.133930	+	1.45354i
$178$	−3.80385			−0.285110
$179$	1.41421			0.105703			0.0528516	−	0.998602i	$-0.483169\pi$
$179$	1.41421			0.105703			0.0528516	+	0.998602i	$0.483169\pi$
$180$	5.58542	+	4.77526i	0.416313	+	0.355927i
$181$	−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
$186$	2.19993	+	0.202703i	0.161307	+	0.0148629i
$187$	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	$-0.844068\pi$
$191$		−	13.0053i		−	0.941032i	0.882391	−	0.470516i	$-0.155932\pi$
$192$	3.56778	−	1.64368i	0.257483	−	0.118623i
$193$	−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
$195$	0.596119	−	0.274633i	0.0426889	−	0.0196669i
$196$	−6.00000	−	10.3923i	−0.428571	−	0.742307i
$197$			0.656339i			0.0467622i	0.999727	+	0.0233811i	$0.00744311\pi$
$197$			0.656339i			0.0467622i	−0.999727	+	0.0233811i	$0.992557\pi$
$198$	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
$204$	−6.14966	−	13.3485i	−0.430563	−	0.934580i
$205$	−6.92820	+	4.00000i	−0.483887	+	0.279372i
$206$	−1.58510	−	0.915158i	−0.110439	−	0.0637621i
$207$	−2.89329	+	15.5672i	−0.201098	+	1.08199i
$208$		−	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
$213$	2.12701	−	23.0844i	0.145740	−	1.58172i
$214$	−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
$219$	−0.476756	+	5.17423i	−0.0322162	+	0.349642i
$220$	12.9282			0.871619
$221$	−1.31268			−0.0883003
$222$	−6.90313	−	0.636057i	−0.463307	−	0.0426893i
$223$	−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
$225$	−8.84847	−	1.64456i	−0.589898	−	0.109638i
$226$	−1.02628	+	1.77757i	−0.0682671	+	0.118242i
$227$	4.79744			0.318418			0.159209	−	0.987245i	$-0.449106\pi$
$227$	4.79744			0.318418			0.159209	+	0.987245i	$0.449106\pi$
$228$	−11.1708	+	6.79796i	−0.739807	+	0.450206i
$229$	−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
$231$	−1.02494	−	2.22474i	−0.0674364	−	0.146377i
$232$	−2.00000	−	3.46410i	−0.131306	−	0.227429i
$233$	−11.5911	−	6.69213i	−0.759359	−	0.438416i	0.0697066	−	0.997568i	$-0.477794\pi$
$233$	−11.5911	−	6.69213i	−0.759359	−	0.438416i	−0.829066	+	0.559151i	$0.811127\pi$
$234$	−0.316271	−	0.270396i	−0.0206753	−	0.0176763i
$235$	−1.07180			−0.0699163
$236$	19.4201			1.26414
$237$	−18.0479	−	1.66294i	−1.17234	−	0.108020i
$238$	0.588457	−	0.339746i	0.0381440	−	0.0220225i
$239$			15.2789i			0.988313i	0.869373	+	0.494156i	$0.164523\pi$
$239$			15.2789i			0.988313i	−0.869373	+	0.494156i	$0.835477\pi$
$240$	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
$243$	8.64420	+	12.9722i	0.554526	+	0.832167i
$244$	−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
$249$	−1.50062	−	3.25725i	−0.0950981	−	0.206420i
$250$	5.07180	+	2.92820i	0.320769	+	0.185196i
$251$	12.7279	−	7.34847i	0.803379	−	0.463831i	−0.0412721	−	0.999148i	$-0.513141\pi$
$251$	12.7279	−	7.34847i	0.803379	−	0.463831i	0.844651	+	0.535317i	$0.179808\pi$
$252$	−1.36886	−	0.254415i	−0.0862303	−	0.0160266i
$253$	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	0.711474	−	0.702713i	$-0.248028\pi$
$257$	−4.05317	−	7.02030i	−0.252830	−	0.437914i	−0.964304	+	0.264798i	$0.914695\pi$
$258$	4.19615	+	2.96713i	0.261241	+	0.184725i
$259$			2.07180i			0.128735i
$260$	−0.328169	−	0.568406i	−0.0203522	−	0.0352510i
$261$	6.10707	+	1.13505i	0.378018	+	0.0702580i
$262$	5.66025	−	3.26795i	0.349692	−	0.201895i
$263$	24.9754	+	14.4195i	1.54005	+	0.889147i	0.998835	+	0.0482609i	$0.0153679\pi$
$263$	24.9754	+	14.4195i	1.54005	+	0.889147i	0.541213	+	0.840886i	$0.317965\pi$
$264$	−7.38961	−	16.0399i	−0.454799	−	0.987187i
$265$		−	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	−0.983167	−	0.182710i	$-0.941513\pi$
$269$	−5.46739	+	9.46979i	−0.333352	+	0.577383i	0.649815	+	0.760093i	$0.274847\pi$
$270$	−0.933552	−	3.68751i	−0.0568141	−	0.224415i
$271$	−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
$276$	15.7670	+	1.45277i	0.949060	+	0.0874467i
$277$	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
$279$	5.61874	+	4.80374i	0.336385	+	0.287592i
$280$	0.633975	+	0.366025i	0.0378872	+	0.0218742i
$281$	−4.70951	−	8.15711i	−0.280946	−	0.486613i	0.690672	−	0.723168i	$-0.257315\pi$
$281$	−4.70951	−	8.15711i	−0.280946	−	0.486613i	−0.971618	+	0.236556i	$0.923981\pi$
$282$	0.284321	+	0.617147i	0.0169311	+	0.0367506i
$283$	−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
$285$	−5.12372	+	9.36736i	−0.303503	+	0.554875i
$286$	−0.732051			−0.0432871
$287$	0.757875	−	1.31268i	0.0447359	−	0.0774849i
$288$	−15.1581	−	2.81726i	−0.893198	−	0.166008i
$289$	3.50000	+	6.06218i	0.205882	+	0.356599i
$290$	−1.31268	−	0.757875i	−0.0770831	−	0.0445039i
$291$	0.924288	+	0.0851642i	0.0541827	+	0.00499242i
$292$	5.19615			0.304082
$293$	13.9391			0.814329			0.407164	−	0.913355i	$-0.366518\pi$
$293$	13.9391			0.814329			0.407164	+	0.913355i	$0.366518\pi$
$294$	−0.569930	+	6.18546i	−0.0332390	+	0.360743i
$295$	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
$300$	−0.825765	+	8.96204i	−0.0476756	+	0.517423i
$301$	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
$306$	−1.39015	+	7.47961i	−0.0794696	+	0.427581i
$307$	−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
$309$	−2.56262	−	5.56244i	−0.145783	−	0.316436i
$310$	−0.901924	−	1.56218i	−0.0512258	−	0.0887257i
$311$		−	12.4505i		−	0.706004i	−0.935623	−	0.353002i	$-0.885161\pi$
$311$		−	12.4505i		−	0.706004i	0.935623	−	0.353002i	$-0.114839\pi$
$312$	−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	0.963230	−	0.268679i	$-0.0865871\pi$
$317$	4.43211	+	7.67664i	0.248932	+	0.431163i	−0.714298	+	0.699842i	$0.753254\pi$
$318$	−8.90433	+	4.10224i	−0.499330	+	0.230042i
$319$	9.46410	−	5.46410i	0.529888	−	0.305931i
$320$	−2.77766	−	1.60368i	−0.155276	−	0.0896486i
$321$	−7.70674	+	3.55051i	−0.430148	+	0.198170i
$322$			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
$327$	11.0251	+	1.01586i	0.609689	+	0.0561770i
$328$	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
$333$	−17.6309	−	15.0736i	−0.966169	−	0.826026i
$334$	−11.2679			−0.616555
$335$	−1.41421			−0.0772667
$336$	−0.104927	+	1.13877i	−0.00572422	+	0.0621250i
$337$	−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
$339$	−6.23785	+	2.87379i	−0.338793	+	0.156083i
$340$	−6.00000	+	10.3923i	−0.325396	+	0.563602i
$341$	13.0053			0.704278
$342$	6.75298	+	0.465346i	0.365159	+	0.0251630i
$343$	3.73205			0.201512
$344$	5.53674	−	9.58991i	0.298521	−	0.517053i
$345$	11.7420	−	5.40957i	0.632169	−	0.291241i
$346$	−4.53590	−	7.85641i	−0.243851	−	0.422363i
$347$	−16.6424	−	9.60849i	−0.893410	−	0.515811i	−0.0183540	−	0.999832i	$-0.505843\pi$
$347$	−16.6424	−	9.60849i	−0.893410	−	0.515811i	−0.875057	+	0.484021i	$0.839176\pi$
$348$	0.569930	−	6.18546i	0.0305515	−	0.331575i
$349$	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
$351$	−0.341704	−	1.34972i	−0.0182388	−	0.0720429i
$352$	−23.4904	+	13.5622i	−1.25204	+	0.722867i
$353$			2.17209i			0.115609i	0.998328	+	0.0578043i	$0.0184099\pi$
$353$			2.17209i			0.115609i	−0.998328	+	0.0578043i	$0.981590\pi$
$354$	−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
$357$	2.26403	+	0.208609i	0.119825	+	0.0110408i
$358$	−0.366025	+	0.633975i	−0.0193450	+	0.0335066i
$359$	−6.21166	−	3.58630i	−0.327839	−	0.189278i	0.327042	−	0.945010i	$-0.393948\pi$
$359$	−6.21166	−	3.58630i	−0.327839	−	0.189278i	−0.654881	+	0.755732i	$0.727281\pi$
$360$	−7.72741	+	2.73205i	−0.407270	+	0.143992i
$361$	−13.0000	−	13.8564i	−0.684211	−	0.729285i
$362$		−	1.79315i		−	0.0942459i
$363$	26.5174	−	12.2166i	1.39180	−	0.641205i
$364$	0.107695	+	0.0621778i	0.00564476	+	0.00325900i
$365$	3.67423	−	2.12132i	0.192318	−	0.111035i
$366$	8.52106	−	3.92567i	0.445403	−	0.205198i
$367$	−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
$375$	8.19955	+	17.7980i	0.423423	+	0.919083i
$376$	1.26795	−	0.732051i	0.0653895	−	0.0377526i
$377$	−0.480473	−	0.277401i	−0.0247456	−	0.0142869i
$378$	0.502515	+	0.516625i	0.0258466	+	0.0265723i
$379$			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	−0.660492	−	0.750833i	$-0.729652\pi$
$383$	6.26243	−	10.8468i	0.319995	−	0.554248i	0.980487	+	0.196586i	$0.0629854\pi$
$384$	−1.82000	+	19.7525i	−0.0928765	+	1.00799i
$385$	−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	−0.138586	−	0.990350i	$-0.544256\pi$
$389$	12.8159	−	7.39924i	0.649790	−	0.375156i	0.788376	+	0.615194i	$0.210922\pi$
$390$	−0.0311723	+	0.338313i	−0.00157847	+	0.0171311i
$391$	−25.8564			−1.30761
$392$	13.3843			0.676007
$393$	21.7773	+	2.00657i	1.09852	+	0.101218i
$394$	−0.294229	−	0.169873i	−0.0148230	−	0.00855808i
$395$	7.39924	+	12.8159i	0.372296	+	0.644836i
$396$	5.01133	−	26.9631i	0.251829	−	1.35495i
$397$	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
$399$	−0.0466860	−	2.02243i	−0.00233722	−	0.101248i
$400$	7.39230			0.369615
$401$	−11.4016	+	19.7482i	−0.569371	+	0.986179i	0.427257	+	0.904130i	$0.359480\pi$
$401$	−11.4016	+	19.7482i	−0.569371	+	0.986179i	−0.996628	+	0.0820492i	$0.973854\pi$
$402$	0.375156	+	0.814313i	0.0187111	+	0.0406142i
$403$	−0.330127	−	0.571797i	−0.0164448	−	0.0284832i
$404$	−3.10583	−	1.79315i	−0.154521	−	0.0892126i
$405$	4.57321	−	11.8780i	0.227245	−	0.590220i
$406$	0.287187			0.0142529
$407$	−40.8091			−2.02283
$408$	16.3232	+	1.50402i	0.808117	+	0.0744602i
$409$	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
$414$	−6.22973	−	5.32611i	−0.306174	−	0.261764i
$415$	−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	$0.0590531\pi$
$419$			7.55154i			0.368917i	−0.982840	+	0.184458i	$0.940947\pi$
$420$	0.475678	+	1.03251i	0.0232107	+	0.0503812i
$421$	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
$423$	−0.415458	+	2.23534i	−0.0202003	+	0.108686i
$424$	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	$-0.956596\pi$
$431$	−12.7279	−	22.0454i	−0.613082	−	1.06189i	0.377635	−	0.925954i	$-0.376737\pi$
$432$	−8.92749	−	9.17815i	−0.429524	−	0.441584i
$433$	−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
$435$	−2.12220	−	4.60645i	−0.101752	−	0.220862i
$436$		−	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
$441$	−13.5065	+	15.7980i	−0.643165	+	0.752284i
$442$	0.339746	−	0.588457i	0.0161601	−	0.0279901i
$443$	8.96575	−	5.17638i	0.425976	−	0.245937i	−0.271655	−	0.962395i	$-0.587571\pi$
$443$	8.96575	−	5.17638i	0.425976	−	0.245937i	0.697631	+	0.716457i	$0.254238\pi$
$444$	−13.3923	+	18.9396i	−0.635571	+	0.898833i
$445$			10.3923i			0.492642i
$446$	5.10703	−	2.94855i	0.241825	−	0.139618i
$447$	−4.70319	−	0.433354i	−0.222453	−	0.0204969i
$448$	0.607695			0.0287109
$449$	5.10205			0.240781			0.120390	−	0.992727i	$-0.461585\pi$
$449$	5.10205			0.240781			0.120390	+	0.992727i	$0.461585\pi$
$450$	3.02739	−	3.54102i	0.142713	−	0.166925i
$451$	25.8564	+	14.9282i	1.21753	+	0.702942i
$452$	3.43400	+	5.94786i	0.161522	+	0.279764i
$453$	1.44949	+	3.14626i	0.0681030	+	0.147824i
$454$	−1.24167	+	2.15064i	−0.0582744	+	0.100934i
$455$	0.101536			0.00476008
$456$	−0.336595	−	14.5813i	−0.0157625	−	0.682831i
$457$	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
$459$	−18.2474	+	17.7491i	−0.851718	+	0.828457i
$460$	−6.46410	−	11.1962i	−0.301390	−	0.522023i
$461$	30.9232	+	17.8535i	1.44024	+	0.831522i	0.997865	−	0.0653090i	$-0.0208033\pi$
$461$	30.9232	+	17.8535i	1.44024	+	0.831522i	0.442373	+	0.896831i	$0.354137\pi$
$462$	1.26260	+	0.116337i	0.0587415	+	0.00541246i
$463$	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
$465$	0.553794	−	6.01033i	0.0256816	−	0.278722i
$466$	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	$-0.175387\pi$
$468$	−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
$471$	1.66294	−	18.0479i	0.0766243	−	0.831604i
$472$	−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
$477$	−32.2520	−	5.99431i	−1.47672	−	0.274461i
$478$	−6.84936	−	3.95448i	−0.313283	−	0.180874i
$479$	−15.1774	+	8.76268i	−0.693474	+	0.400377i	−0.804912	−	0.593394i	$-0.797788\pi$
$479$	−15.1774	+	8.76268i	−0.693474	+	0.400377i	0.111438	+	0.993771i	$0.464454\pi$
$480$	5.26741	+	11.4334i	0.240423	+	0.521863i
$481$	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
$489$	8.17423	−	3.76588i	0.369652	−	0.170299i
$490$	4.39230	−	2.53590i	0.198424	−	0.114560i
$491$	−25.6317	−	14.7985i	−1.15674	−	0.667846i	−0.206222	−	0.978505i	$-0.566117\pi$
$491$	−25.6317	−	14.7985i	−1.15674	−	0.667846i	−0.950521	+	0.310660i	$0.899450\pi$
$492$	15.4135	−	7.10102i	0.694894	−	0.320139i
$493$			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
$498$	1.84858	+	0.170328i	0.0828367	+	0.00763260i
$499$	−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	−0.525130	−	0.851022i	$-0.675983\pi$
$503$	−1.13681	+	0.656339i	−0.0506879	+	0.0292647i	0.474442	+	0.880287i	$0.342650\pi$
$504$	1.00913	−	1.18034i	0.0449502	−	0.0525765i
$505$	−2.92820			−0.130303
$506$	−14.4195			−0.641027
$507$	2.05453	−	22.2979i	0.0912450	−	0.990282i
$508$	29.7846	+	17.1962i	1.32148	+	0.762956i
$509$	−21.4906	−	37.2228i	−0.952554	−	1.64987i	−0.739868	−	0.672752i	$-0.765112\pi$
$509$	−21.4906	−	37.2228i	−0.952554	−	1.64987i	−0.212686	−	0.977121i	$-0.568221\pi$
$510$	5.64173	−	2.59915i	0.249820	−	0.115092i
$511$	−0.401924	+	0.696152i	−0.0177801	+	0.0307960i
$512$	22.1841			0.980408
$513$	17.5505	+	14.3171i	0.774874	+	0.632116i
$514$	4.19615			0.185084
$515$	−2.50026	+	4.33057i	−0.110175	+	0.190828i
$516$	15.6184	−	7.19541i	0.687561	−	0.316760i
$517$	2.00000	+	3.46410i	0.0879599	+	0.152351i
$518$	−0.928761	−	0.536220i	−0.0408074	−	0.0235602i
$519$	2.78511	−	30.2268i	0.122253	−	1.32681i
$520$	0.732051			0.0321026
$521$	10.1769			0.445858			0.222929	−	0.974835i	$-0.428438\pi$
$521$	10.1769			0.445858			0.222929	+	0.974835i	$0.428438\pi$
$522$	−2.08946	+	2.44395i	−0.0914530	+	0.106969i
$523$	−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
$528$	−22.4309	−	2.06679i	−0.976178	−	0.0899454i
$529$	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
$534$	5.98396	−	2.75682i	0.258951	−	0.119299i
$535$	6.00000	+	3.46410i	0.259403	+	0.149766i
$536$	1.67303	−	0.965926i	0.0722640	−	0.0417216i
$537$	−2.22474	+	1.02494i	−0.0960048	+	0.0442296i
$538$	−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
$546$	−0.0269350	−	0.0584651i	−0.00115271	−	0.00250207i
$547$	−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
$549$	30.8638	+	5.73630i	1.31723	+	0.244819i
$550$		−	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
$555$	−1.73774	+	18.8597i	−0.0737629	+	0.800549i
$556$	2.42820	−	4.20577i	0.102979	−	0.178364i
$557$	−22.5259	+	13.0053i	−0.954452	+	0.551053i	−0.894461	−	0.447146i	$-0.852441\pi$
$557$	−22.5259	+	13.0053i	−0.954452	+	0.551053i	−0.0599911	+	0.998199i	$0.519107\pi$
$558$	−3.60770	+	1.27551i	−0.152726	+	0.0539968i
$559$		−	1.53590i		−	0.0649616i
$560$	0.808643	−	0.466870i	0.0341714	−	0.0197289i
$561$	−4.10906	+	44.5957i	−0.173485	+	1.88283i
$562$	4.87564			0.205667
$563$	−26.0106			−1.09622			−0.548109	−	0.836407i	$-0.684652\pi$
$563$	−26.0106			−1.09622			−0.548109	+	0.836407i	$0.684652\pi$
$564$	2.26403	+	0.208609i	0.0953330	+	0.00878402i
$565$	4.85641	+	2.80385i	0.204311	+	0.117959i
$566$	−1.51575	−	2.62536i	−0.0637117	−	0.110352i
$567$	0.374855	+	2.38223i	0.0157424	+	0.100044i
$568$	12.9282	−	22.3923i	0.542455	−	0.939560i
$569$	25.2528			1.05865			0.529326	−	0.848419i	$-0.322445\pi$
$569$	25.2528			1.05865			0.529326	+	0.848419i	$0.322445\pi$
$570$	−2.87316	−	4.72135i	−0.120343	−	0.197756i
$571$	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
$573$	9.42554	+	20.4591i	0.393758	+	0.854691i
$574$	0.392305	+	0.679492i	0.0163745	+	0.0283614i
$575$	13.7124	+	7.91688i	0.571848	+	0.330157i
$576$	−4.42134	+	5.17147i	−0.184223	+	0.215478i
$577$	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
$579$	4.83592	+	0.445584i	0.200974	+	0.0185178i
$580$	−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
$585$	−0.738735	+	0.864068i	−0.0305429	+	0.0357248i
$586$	−3.60770	+	6.24871i	−0.149033	+	0.258132i
$587$	28.8898	+	16.6796i	1.19241	+	0.688439i	0.958853	−	0.283904i	$-0.0916296\pi$
$587$	28.8898	+	16.6796i	1.19241	+	0.688439i	0.233559	+	0.972343i	$0.424963\pi$
$588$	16.9706	+	12.0000i	0.699854	+	0.494872i
$589$	9.85641	+	4.26795i	0.406126	+	0.175858i
$590$			8.20788i			0.337913i
$591$	−0.475678	−	1.03251i	−0.0195668	−	0.0424717i
$592$	16.5000	+	9.52628i	0.678146	+	0.391528i
$593$	−29.1301	+	16.8183i	−1.19623	+	0.690643i	−0.959712	−	0.280984i	$-0.909339\pi$
$593$	−29.1301	+	16.8183i	−1.19623	+	0.690643i	−0.236517	+	0.971627i	$0.576006\pi$
$594$	−10.1762	+	9.89828i	−0.417534	+	0.406131i
$595$	−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	0.892535	−	0.450978i	$-0.148925\pi$
$599$	1.36345	+	2.36156i	0.0557089	+	0.0964906i	−0.836826	+	0.547469i	$0.815591\pi$
$600$	−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
$603$	−0.548188	+	2.94949i	−0.0223239	+	0.120113i
$604$	3.00000	−	1.73205i	0.122068	−	0.0704761i
$605$	−20.6448	−	11.9193i	−0.839330	−	0.484588i
$606$	0.776779	+	1.68608i	0.0315545	+	0.0684922i
$607$			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
$612$	19.3485	+	16.5420i	0.782116	+	0.668669i
$613$	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	−0.0404087	−	0.999183i	$-0.512866\pi$
$617$	19.9885	−	11.5403i	0.804705	−	0.464597i	0.845114	+	0.534587i	$0.179533\pi$
$618$	3.15683	+	0.290871i	0.126986	+	0.0117006i
$619$	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
$621$	−6.73069	−	26.5861i	−0.270093	−	1.06686i
$622$	5.58142	+	3.22243i	0.223794	+	0.129208i
$623$	−0.984508	−	1.70522i	−0.0394435	−	0.0683181i
$624$	0.478516	+	1.03867i	0.0191560	+	0.0415800i
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	8.68835			0.347256
$627$	39.8368	−	0.919596i	1.59093	−	0.0367251i
$628$	−18.1244			−0.723241
$629$	18.9396	−	32.8043i	0.755170	−	1.30799i
$630$	0.107528	−	0.578550i	0.00428404	−	0.0230500i
$631$	−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
$633$	−18.9722	−	1.74810i	−0.754077	−	0.0694809i
$634$	−4.58846			−0.182231
$635$	28.0812			1.11437
$636$	−3.00985	+	32.6659i	−0.119348	+	1.29529i
$637$	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	$0.387883\pi$
$641$	−16.2127	+	28.0812i	−0.640363	+	1.10914i	−0.985352	+	0.170534i	$0.945451\pi$
$642$	0.403001	−	4.37378i	0.0159052	−	0.172619i
$643$	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	$-0.796484\pi$
$647$		−	30.3548i		−	1.19337i	0.802475	−	0.596686i	$-0.203516\pi$
$648$	2.70262	+	17.1753i	0.106169	+	0.674711i
$649$	−51.2487	−	29.5885i	−2.01169	−	1.16145i
$650$	−0.360355	+	0.208051i	−0.0141343	+	0.00816043i
$651$	0.478516	+	1.03867i	0.0187545	+	0.0407086i
$652$	−4.50000	−	7.79423i	−0.176234	−	0.305246i
$653$		−	1.86748i		−	0.0730802i	−0.999332	−	0.0365401i	$-0.988366\pi$
$653$		−	1.86748i		−	0.0730802i	0.999332	−	0.0365401i	$-0.0116337\pi$
$654$	−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	0.827874	−	0.560914i	$-0.189550\pi$
$659$	−1.84392	−	3.19376i	−0.0718289	−	0.124411i	−0.899703	+	0.436503i	$0.856217\pi$
$660$	−20.3378	+	9.36965i	−0.791647	+	0.364713i
$661$	−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
$663$	2.06502	−	0.951356i	0.0801986	−	0.0369476i
$664$		−	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
$669$	19.6488	+	1.81045i	0.759667	+	0.0699960i
$670$	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
$675$	15.1117	−	3.82577i	0.581650	−	0.147254i
$676$	−22.3923			−0.861242
$677$	30.1518			1.15883			0.579413	−	0.815034i	$-0.303282\pi$
$677$	30.1518			1.15883			0.579413	+	0.815034i	$0.303282\pi$
$678$	0.326190	−	3.54014i	0.0125272	−	0.135958i
$679$	0.124356	+	0.0717968i	0.00477233	+	0.00275531i
$680$	−6.69213	−	11.5911i	−0.256631	−	0.444499i
$681$	−7.54701	+	3.47692i	−0.289202	+	0.133236i
$682$	−3.36603	+	5.83013i	−0.128892	+	0.223247i
$683$	−26.1122			−0.999155			−0.499577	−	0.866269i	$-0.666511\pi$
$683$	−26.1122			−0.999155			−0.499577	+	0.866269i	$0.666511\pi$
$684$	12.6464	−	18.7901i	0.483548	−	0.718457i
$685$	14.9282			0.570377
$686$	−0.965926	+	1.67303i	−0.0368792	+	0.0638767i
$687$	17.9216	−	8.25651i	0.683752	−	0.315006i
$688$	−7.06218	−	12.2321i	−0.269243	−	0.466343i
$689$	2.53742	+	1.46498i	0.0966681	+	0.0558114i
$690$	−0.614014	+	6.66390i	−0.0233751	+	0.253690i
$691$	−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
$693$	3.22474	+	2.75699i	0.122498	+	0.104730i
$694$	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
$699$	23.0844	+	2.12701i	0.873134	+	0.0804508i
$700$	−0.696152	+	1.20577i	−0.0263121	+	0.0455739i
$701$	−34.2049	−	19.7482i	−1.29190	−	0.745880i	−0.312911	−	0.949782i	$-0.601304\pi$
$701$	−34.2049	−	19.7482i	−1.29190	−	0.745880i	−0.978991	+	0.203902i	$0.934637\pi$
$702$	0.693504	+	0.196152i	0.0261746	+	0.00740330i
$703$	−30.9282	−	13.3923i	−1.16648	−	0.505100i
$704$			11.9700i			0.451138i
$705$	1.68608	−	0.776779i	0.0635014	−	0.0292552i
$706$	−0.973721	−	0.562178i	−0.0366465	−	0.0211578i
$707$	0.480473	−	0.277401i	0.0180701	−	0.0104328i
$708$	−30.5503	+	14.0746i	−1.14815	+	0.528955i
$709$	−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
$717$	−11.0733	−	24.0358i	−0.413541	−	0.897634i
$718$	3.21539	−	1.85641i	0.119997	−	0.0692805i
$719$	9.46979	+	5.46739i	0.353164	+	0.203899i	0.666078	−	0.745882i	$-0.267972\pi$
$719$	9.46979	+	5.46739i	0.353164	+	0.203899i	−0.312914	+	0.949781i	$0.601305\pi$
$720$	−1.91031	+	10.2783i	−0.0711930	+	0.383049i
$721$		−	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
$726$	−1.38665	+	15.0493i	−0.0514633	+	0.558532i
$727$	−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
$732$	2.88030	−	31.2599i	0.106459	−	1.15540i
$733$	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
$735$	16.8990	+	1.55708i	0.623328	+	0.0574337i
$736$	23.4904	+	13.5622i	0.865867	+	0.499909i
$737$	2.63896	+	4.57081i	0.0972073	+	0.168368i
$738$	−8.63671	−	1.60521i	−0.317922	−	0.0590885i
$739$	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
$741$	−1.05165	−	1.72814i	−0.0386333	−	0.0634846i
$742$	−1.51666			−0.0556784
$743$	3.53553	−	6.12372i	0.129706	−	0.224658i	−0.793857	−	0.608105i	$-0.791930\pi$
$743$	3.53553	−	6.12372i	0.129706	−	0.224658i	0.923563	+	0.383447i	$0.125263\pi$
$744$	3.44999	+	7.48855i	0.126483	+	0.274543i
$745$	1.92820	+	3.33975i	0.0706439	+	0.122359i
$746$	8.72552	+	5.03768i	0.319464	+	0.184443i
$747$	4.72135	+	4.03652i	0.172745	+	0.147689i
$748$	44.7846			1.63749
$749$	−1.31268			−0.0479642
$750$	−10.1008	−	0.930692i	−0.368829	−	0.0339841i
$751$	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
$756$	2.33779	−	0.591848i	0.0850245	−	0.0215253i
$757$	−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	$0.197803\pi$
$761$			32.1208i			1.16438i	−0.813054	+	0.582188i	$0.802197\pi$
$762$	−7.44924	−	16.1693i	−0.269858	−	0.585753i
$763$	1.48334	+	0.856406i	0.0537005	+	0.0310040i
$764$	19.5080	−	11.2629i	0.705774	−	0.407479i
$765$	20.4347	+	3.79796i	0.738817	+	0.137315i
$766$	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	$0.0947813\pi$
$773$	20.3538	+	35.2538i	0.732075	+	1.26799i	−0.223920	+	0.974608i	$0.571885\pi$
$774$	−8.75151	−	1.62654i	−0.314567	−	0.0584649i
$775$	6.40192	−	3.69615i	0.229964	−	0.132770i
$776$	0.896575	+	0.517638i	0.0321852	+	0.0185821i
$777$	−1.50152	−	3.25921i	−0.0538669	−	0.116924i
$778$			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
$783$	−10.4299	+	2.64048i	−0.372733	+	0.0943631i
$784$	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
$789$	−49.7400	−	4.58307i	−1.77079	−	0.163161i
$790$	−7.66025			−0.272540
$791$	−1.06248			−0.0377775
$792$	23.2497	+	19.8773i	0.826141	+	0.706309i
$793$	−2.42820	−	1.40192i	−0.0862280	−	0.0497838i
$794$	6.81225	+	11.7992i	0.241758	+	0.418737i
$795$	11.2075	+	24.3271i	0.397490	+	0.862792i
$796$	−20.0885	+	34.7942i	−0.712016	+	1.23325i
$797$	−54.0918			−1.91603			−0.958016	−	0.286716i	$-0.907437\pi$
$797$	−54.0918			−1.91603			−0.958016	+	0.286716i	$0.907437\pi$
$798$	0.918715	+	0.502515i	0.0325222	+	0.0177889i
$799$	−3.71281			−0.131350
$800$	−7.70882	+	13.3521i	−0.272548	+	0.472067i
$801$	21.6742	+	4.02834i	0.765821	+	0.142335i
$802$	−5.90192	−	10.2224i	−0.208404	−	0.360967i
$803$	−13.7124	−	7.91688i	−0.483901	−	0.279380i
$804$	2.98735	+	0.275255i	0.105356	+	0.00970750i
$805$	2.00000			0.0704907
$806$	0.341773			0.0120384
$807$	1.73774	−	18.8597i	0.0611713	−	0.663893i
$808$	3.46410	−	2.00000i	0.121867	−	0.0703598i
$809$			37.0197i			1.30155i	0.759273	+	0.650773i	$0.225555\pi$
$809$			37.0197i			1.30155i	−0.759273	+	0.650773i	$0.774445\pi$
$810$	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
$813$	1.10102	−	11.9494i	0.0386145	−	0.419083i
$814$	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
$819$	0.0393581	−	0.211764i	0.00137528	−	0.00739963i
$820$	−12.0000	−	6.92820i	−0.419058	−	0.241943i
$821$	−4.41851	+	2.55103i	−0.154207	+	0.0890314i	−0.575118	−	0.818071i	$-0.695044\pi$
$821$	−4.41851	+	2.55103i	−0.154207	+	0.0890314i	0.420911	+	0.907102i	$0.361710\pi$
$822$	−3.96008	−	8.59575i	−0.138124	−	0.299811i
$823$	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	0.996503	−	0.0835608i	$-0.0266293\pi$
$827$	12.2474	+	21.2132i	0.425886	+	0.737655i	−0.570617	+	0.821216i	$0.693296\pi$
$828$	−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
$831$	−28.0905	+	12.9413i	−0.974448	+	0.448930i
$832$	0.526279	−	0.303848i	0.0182455	−	0.0105340i
$833$	−29.3939	−	16.9706i	−1.01844	−	0.587995i
$834$	−2.28321	+	1.05188i	−0.0790611	+	0.0364236i
$835$			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	−0.559845	−	0.828597i	$-0.689139\pi$
$839$	12.6772	−	21.9575i	0.437664	−	0.758056i	0.997509	+	0.0705412i	$0.0224726\pi$
$840$	−1.26260	−	0.116337i	−0.0435639	−	0.00401399i
$841$	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
$846$	−0.894549	−	0.764794i	−0.0307552	−	0.0262942i
$847$	4.51666			0.155194
$848$	26.9444			0.925274
$849$	0.930692	−	10.1008i	0.0319413	−	0.346659i
$850$	6.58846	+	3.80385i	0.225982	+	0.130471i
$851$	20.4046	+	35.3417i	0.699459	+	1.21150i
$852$	36.4687	−	16.8012i	1.24940	−	0.575599i
$853$	−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
$855$	1.27135	−	18.4495i	0.0434792	−	0.630959i
$856$	−9.46410			−0.323476
$857$	21.1117	−	36.5665i	0.721161	−	1.24909i	−0.239374	−	0.970927i	$-0.576942\pi$
$857$	21.1117	−	36.5665i	0.721161	−	1.24909i	0.960535	−	0.278160i	$-0.0897245\pi$
$858$	1.15161	−	0.530550i	0.0393154	−	0.0181127i
$859$	−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
$861$	−0.240881	+	2.61428i	−0.00820920	+	0.0890945i
$862$	13.1769			0.448807
$863$	−1.31268			−0.0446841			−0.0223420	−	0.999750i	$-0.507112\pi$
$863$	−1.31268			−0.0446841			−0.0223420	+	0.999750i	$0.507112\pi$
$864$	25.8874	−	6.55381i	0.880708	−	0.222965i
$865$	−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
$870$	2.61428	+	0.240881i	0.0886324	+	0.00816662i
$871$	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
$876$	−8.17423	+	3.76588i	−0.276182	+	0.127237i
$877$	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
$879$	−21.9280	+	10.1023i	−0.739613	+	0.340741i
$880$	9.19615	+	15.9282i	0.310002	+	0.536940i
$881$		−	48.3335i		−	1.62840i	−0.580588	−	0.814198i	$-0.697177\pi$
$881$		−	48.3335i		−	1.62840i	0.580588	−	0.814198i	$-0.302823\pi$
$882$	−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	0.847217	−	0.531248i	$-0.178277\pi$
$887$	−1.08604	−	1.88108i	−0.0364658	−	0.0631606i	−0.883682	+	0.468087i	$0.844943\pi$
$888$	−10.8256	−	23.4982i	−0.363285	−	0.788546i
$889$	−4.60770	+	2.66025i	−0.154537	+	0.0892221i
$890$	−4.65874	−	2.68973i	−0.156161	−	0.0901598i
$891$	−46.9239	+	7.38370i	−1.57201	+	0.247363i
$892$		−	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
$897$	−0.224745	+	2.43916i	−0.00750401	+	0.0814411i
$898$	−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
$903$	−0.244083	+	2.64903i	−0.00812257	+	0.0881543i
$904$	−7.66025			−0.254776
$905$	−4.89898			−0.162848
$906$	−1.78559	−	0.164525i	−0.0593222	−	0.00546597i
$907$	−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
$909$	−1.13505	+	6.10707i	−0.0376473	+	0.202559i
$910$	−0.0262794	+	0.0455173i	−0.000871155	+	0.00150888i
$911$	−21.3147			−0.706189			−0.353094	−	0.935588i	$-0.614871\pi$
$911$	−21.3147			−0.706189			−0.353094	+	0.935588i	$0.614871\pi$
$912$	−16.3215	−	8.92749i	−0.540460	−	0.295619i
$913$	10.9282			0.361671
$914$	−8.98434	+	15.5613i	−0.297175	+	0.514723i
$915$	−10.7251	−	23.2800i	−0.354561	−	0.769612i
$916$	−9.86603	−	17.0885i	−0.325983	−	0.564619i
$917$	2.92996	+	1.69161i	0.0967559	+	0.0558620i
$918$	−3.23392	−	12.7739i	−0.106735	−	0.421602i
$919$	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
$921$	23.8988	+	2.20204i	0.787491	+	0.0725597i
$922$	−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
$927$	8.06269	+	6.89320i	0.264814	+	0.226402i
$928$	5.32051	−	9.21539i	0.174654	−	0.302510i
$929$	−9.22955	−	5.32868i	−0.302812	−	0.174828i	0.340894	−	0.940102i	$-0.389270\pi$
$929$	−9.22955	−	5.32868i	−0.302812	−	0.174828i	−0.643705	+	0.765273i	$0.722604\pi$
$930$	2.55103	+	1.80385i	0.0836514	+	0.0591505i
$931$	−12.0000	+	27.7128i	−0.393284	+	0.908251i
$932$		−	23.1822i		−	0.759359i
$933$	9.02345	+	19.5863i	0.295415	+	0.641227i
$934$	10.1436	+	5.85641i	0.331909	+	0.191627i
$935$	31.6675	−	18.2832i	1.03564	−	0.597926i
$936$	0.283763	−	1.52677i	0.00927509	−	0.0499040i
$937$	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	0.995066	−	0.0992170i	$-0.0316338\pi$
$941$	12.6264	+	21.8695i	0.411608	+	0.712927i	−0.583457	+	0.812144i	$0.698300\pi$
$942$	7.66025	+	5.41662i	0.249585	+	0.176483i
$943$		−	29.8564i		−	0.972258i
$944$	13.8140	+	23.9265i	0.449606	+	0.778741i
$945$	1.41145	−	1.37290i	0.0459143	−	0.0446604i
$946$	−13.5622	+	7.83013i	−0.440944	+	0.254579i
$947$	4.06678	+	2.34795i	0.132152	+	0.0762982i	0.564619	−	0.825352i	$-0.309023\pi$
$947$	4.06678	+	2.34795i	0.132152	+	0.0762982i	−0.432466	+	0.901650i	$0.642357\pi$
$948$	−13.1355	−	28.5120i	−0.426622	−	0.926027i
$949$			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	−0.790854	−	0.612004i	$-0.790363\pi$
$953$	4.15471	−	7.19617i	0.134584	−	0.233107i	0.925439	+	0.378898i	$0.123697\pi$
$954$	11.0346	−	12.9067i	0.357259	−	0.417871i
$955$	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
$960$	5.53189	+	0.509710i	0.178541	+	0.0164508i
$961$	24.9282			0.804136
$962$	−1.07244			−0.0345769
$963$	9.55051	−	11.1708i	0.307761	−	0.359975i
$964$	17.0096	+	9.82051i	0.547843	+	0.316297i
$965$	−1.98262	−	3.43400i	−0.0638228	−	0.110544i
$966$	−0.530550	−	1.15161i	−0.0170702	−	0.0370525i
$967$	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
$969$	−17.7491	+	32.4495i	−0.570183	+	1.04243i
$970$	0.392305			0.0125961
$971$	−26.7685	+	46.3644i	−0.859043	+	1.48791i	0.0138004	+	0.999905i	$0.495607\pi$
$971$	−26.7685	+	46.3644i	−0.859043	+	1.48791i	−0.872843	+	0.488001i	$0.837726\pi$
$972$	−11.9722	+	24.2005i	−0.384008	+	0.776233i
$973$	0.375644	+	0.650635i	0.0120426	+	0.0208584i
$974$	−4.96335	−	2.86559i	−0.159036	−	0.0918195i
$975$	−1.38643	−	0.127746i	−0.0444014	−	0.00409116i
$976$	−25.7846			−0.825345
$977$	−9.04008			−0.289218			−0.144609	−	0.989489i	$-0.546192\pi$
$977$	−9.04008			−0.289218			−0.144609	+	0.989489i	$0.546192\pi$
$978$	−0.427448	+	4.63909i	−0.0136683	+	0.148342i
$979$	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	$-0.659741\pi$
$983$	16.2635	−	28.1691i	0.518724	−	0.898456i	0.999763	−	0.0217569i	$-0.00692599\pi$
$984$	−1.73670	+	18.8484i	−0.0553638	+	0.600864i
$985$	−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
$990$	11.3960	+	2.11804i	0.362187	+	0.0673156i
$991$	−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
$993$	13.0974	+	28.4293i	0.415635	+	0.902177i
$994$	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.8.2	✓	8
3.2	odd	2	inner	57.2.f.a.8.3	yes	8
4.3	odd	2		912.2.bn.m.65.4		8
12.11	even	2		912.2.bn.m.65.3		8
19.8	odd	6		1083.2.d.b.1082.3		8
19.11	even	3		1083.2.d.b.1082.6		8
19.12	odd	6	inner	57.2.f.a.50.3	yes	8
57.8	even	6		1083.2.d.b.1082.5		8
57.11	odd	6		1083.2.d.b.1082.4		8
57.50	even	6	inner	57.2.f.a.50.2	yes	8
76.31	even	6		912.2.bn.m.449.3		8
228.107	odd	6		912.2.bn.m.449.4		8

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

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)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.448288i) q^{2} +(-1.57313 + 0.724745i) q^{3} +(0.866025 + 1.50000i) q^{4} +(1.22474 + 0.707107i) q^{5} +(0.0822623 - 0.892794i) q^{6} -0.267949 q^{7} -1.93185 q^{8} +(1.94949 - 2.28024i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.448288i) q^{2} +(-1.57313 + 0.724745i) q^{3} +(0.866025 + 1.50000i) q^{4} +(1.22474 + 0.707107i) q^{5} +(0.0822623 - 0.892794i) q^{6} -0.267949 q^{7} -1.93185 q^{8} +(1.94949 - 2.28024i) 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} +(-2.43916 - 0.224745i) 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} +(0.421519 - 0.194195i) q^{21} +(2.36603 + 1.36603i) q^{22} +(-4.57081 + 2.63896i) q^{23} +(3.03906 - 1.40010i) 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} +(3.82514 + 8.30286i) q^{33} +(-2.19615 + 1.26795i) q^{34} +(-0.328169 - 0.189469i) q^{35} +(5.10867 + 0.949490i) 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} +(-0.0220421 + 0.239223i) 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} +(0.391592 - 4.24995i) q^{48} -6.92820 q^{49} +1.55291 q^{50} +(-8.44949 - 0.778539i) q^{51} +(-0.401924 - 0.232051i) q^{52} +(-5.46739 - 9.46979i) q^{53} +(-1.87541 - 1.92807i) q^{54} +(3.73205 - 6.46410i) q^{55} +0.517638 q^{56} +(0.174235 + 7.54782i) q^{57} -1.07180 q^{58} +(5.60609 - 9.71003i) q^{59} +(-1.77526 - 3.85337i) q^{60} +(5.23205 + 9.06218i) q^{61} +(-1.10463 - 0.637756i) q^{62} +(-0.522364 + 0.610988i) q^{63} -2.26795 q^{64} -0.378937 q^{65} +(-4.71209 - 0.434174i) 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} +(-3.76612 + 4.40508i) 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} +(0.100523 + 0.218195i) q^{78} +(9.06218 + 5.23205i) q^{79} +(-3.01790 + 1.74238i) q^{80} +(-1.39898 - 8.89060i) 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} +(-0.401302 + 2.15918i) q^{90} +(0.0621778 - 0.0358984i) q^{91} +(-7.91688 - 4.57081i) q^{92} +(-1.78585 - 3.87636i) 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} +(-12.0349 - 10.2892i) 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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