LMFDB - Embedded newform 930.2.z.d.109.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(109,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 2]))

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

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

chi := DirichletCharacter("930.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.z (of order $10$, degree $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.10
Character	$\chi$	$=$	930.109
Dual form			930.2.z.d.529.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-2.20868 + 0.348916i) q^{5} +1.00000 q^{6} +(-0.804232 - 0.261311i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-2.20868 + 0.348916i) q^{5} +1.00000 q^{6} +(-0.804232 - 0.261311i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(-1.58051 - 1.58177i) q^{10} +(0.585657 - 1.80247i) q^{11} +(0.587785 + 0.809017i) q^{12} +(1.67733 - 2.30865i) q^{13} +(-0.261311 - 0.804232i) q^{14} +(-1.01595 + 1.99195i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.51407 - 1.46671i) q^{17} +(0.587785 - 0.809017i) q^{18} +(4.78801 - 3.47869i) q^{19} +(0.350680 - 2.20840i) q^{20} +(-0.684120 + 0.497043i) q^{21} +(1.80247 - 0.585657i) q^{22} +(1.30274 - 0.423287i) q^{23} +(-0.309017 + 0.951057i) q^{24} +(4.75651 - 1.54129i) q^{25} +2.85365 q^{26} +(-0.951057 - 0.309017i) q^{27} +(0.497043 - 0.684120i) q^{28} +(-2.00381 + 1.45586i) q^{29} +(-2.20868 + 0.348916i) q^{30} +(5.55383 - 0.393719i) q^{31} -1.00000i q^{32} +(-1.11399 - 1.53327i) q^{33} +(3.83989 + 2.78985i) q^{34} +(1.86746 + 0.296542i) q^{35} +1.00000 q^{36} +2.53362i q^{37} +(5.62864 + 1.82886i) q^{38} +(-0.881825 - 2.71398i) q^{39} +(1.99276 - 1.01436i) q^{40} +(8.14499 - 5.91768i) q^{41} +(-0.804232 - 0.261311i) q^{42} +(-4.57891 - 6.30234i) q^{43} +(1.53327 + 1.11399i) q^{44} +(1.01436 + 1.99276i) q^{45} +(1.10818 + 0.805140i) q^{46} +(-6.06043 + 8.34146i) q^{47} +(-0.951057 + 0.309017i) q^{48} +(-5.08461 - 3.69419i) q^{49} +(4.04274 + 2.94215i) q^{50} +(1.46671 - 4.51407i) q^{51} +(1.67733 + 2.30865i) q^{52} +(-11.0939 + 3.60462i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-0.664618 + 4.18542i) q^{55} +0.845619 q^{56} -5.91830i q^{57} +(-2.35562 - 0.765389i) q^{58} +(0.127522 + 0.0926499i) q^{59} +(-1.58051 - 1.58177i) q^{60} +14.3118 q^{61} +(3.58298 + 4.26172i) q^{62} +0.845619i q^{63} +(0.809017 - 0.587785i) q^{64} +(-2.89916 + 5.68431i) q^{65} +(0.585657 - 1.80247i) q^{66} -4.77411i q^{67} +4.74637i q^{68} +(0.423287 - 1.30274i) q^{69} +(0.857761 + 1.68511i) q^{70} +(-0.541896 - 1.66779i) q^{71} +(0.587785 + 0.809017i) q^{72} +(-1.40054 - 0.455063i) q^{73} +(-2.04974 + 1.48923i) q^{74} +(1.54888 - 4.75405i) q^{75} +(1.82886 + 5.62864i) q^{76} +(-0.942008 + 1.29656i) q^{77} +(1.67733 - 2.30865i) q^{78} +(-2.60153 - 8.00668i) q^{79} +(1.99195 + 1.01595i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(9.57501 + 3.11111i) q^{82} +(-5.51303 - 7.58804i) q^{83} +(-0.261311 - 0.804232i) q^{84} +(-9.45836 + 4.81452i) q^{85} +(2.40728 - 7.40884i) q^{86} +2.47685i q^{87} +1.89523i q^{88} +(-1.11491 + 3.43135i) q^{89} +(-1.01595 + 1.99195i) q^{90} +(-1.95224 + 1.41838i) q^{91} +1.36979i q^{92} +(2.94593 - 4.72456i) q^{93} -10.3106 q^{94} +(-9.36139 + 9.35392i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(-12.1108 - 3.93502i) q^{97} -6.28493i q^{98} -1.89523 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9}+O(q^{10}) $ 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9	$ 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9} - 6 q^{11} - 4 q^{14} - 18 q^{16} + 12 q^{19} - 4 q^{20} - 16 q^{21} + 18 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} + 4 q^{30} + 22 q^{31} + 14 q^{34} - 22 q^{35} + 72 q^{36} + 8 q^{39} - 28 q^{41} - 4 q^{44} - 4 q^{45} - 22 q^{46} + 42 q^{49} - 32 q^{50} - 4 q^{51} + 18 q^{54} + 14 q^{55} + 24 q^{56} - 28 q^{59} + 56 q^{61} + 18 q^{64} + 46 q^{65} - 6 q^{66} - 8 q^{69} + 46 q^{70} - 68 q^{71} + 8 q^{74} + 32 q^{75} - 12 q^{76} + 26 q^{79} - 6 q^{80} - 18 q^{81} - 4 q^{84} - 32 q^{85} + 80 q^{86} + 32 q^{89} - 44 q^{91} + 12 q^{94} + 74 q^{95} - 18 q^{96} - 4 q^{99}+O(q^{100}) $ 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9 - 6 * q^11 - 4 * q^14 - 18 * q^16 + 12 * q^19 - 4 * q^20 - 16 * q^21 + 18 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 + 4 * q^30 + 22 * q^31 + 14 * q^34 - 22 * q^35 + 72 * q^36 + 8 * q^39 - 28 * q^41 - 4 * q^44 - 4 * q^45 - 22 * q^46 + 42 * q^49 - 32 * q^50 - 4 * q^51 + 18 * q^54 + 14 * q^55 + 24 * q^56 - 28 * q^59 + 56 * q^61 + 18 * q^64 + 46 * q^65 - 6 * q^66 - 8 * q^69 + 46 * q^70 - 68 * q^71 + 8 * q^74 + 32 * q^75 - 12 * q^76 + 26 * q^79 - 6 * q^80 - 18 * q^81 - 4 * q^84 - 32 * q^85 + 80 * q^86 + 32 * q^89 - 44 * q^91 + 12 * q^94 + 74 * q^95 - 18 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−2.20868	+	0.348916i	−0.987751	+	0.156040i
$5$	−2.20868	+	0.348916i	−0.987751	+	0.156040i
$6$	1.00000			0.408248
$7$	−0.804232	−	0.261311i	−0.303971	−	0.0987662i	0.153060	−	0.988217i	$-0.451087\pi$
$7$	−0.804232	−	0.261311i	−0.303971	−	0.0987662i	−0.457031	+	0.889451i	$0.651087\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$	−1.58051	−	1.58177i	−0.499800	−	0.500200i
$11$	0.585657	−	1.80247i	0.176582	−	0.543464i	−0.823120	−	0.567868i	$-0.807769\pi$
$11$	0.585657	−	1.80247i	0.176582	−	0.543464i	0.999702	+	0.0244032i	$0.00776854\pi$
$12$	0.587785	+	0.809017i	0.169679	+	0.233543i
$13$	1.67733	−	2.30865i	0.465208	−	0.640304i	−0.510371	−	0.859955i	$-0.670492\pi$
$13$	1.67733	−	2.30865i	0.465208	−	0.640304i	0.975579	+	0.219651i	$0.0704918\pi$
$14$	−0.261311	−	0.804232i	−0.0698382	−	0.214940i
$15$	−1.01595	+	1.99195i	−0.262317	+	0.514318i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	4.51407	−	1.46671i	1.09482	−	0.355729i	0.294714	−	0.955585i	$-0.404776\pi$
$17$	4.51407	−	1.46671i	1.09482	−	0.355729i	0.800108	+	0.599856i	$0.204776\pi$
$18$	0.587785	−	0.809017i	0.138542	−	0.190687i
$19$	4.78801	−	3.47869i	1.09844	−	0.798066i	0.117639	−	0.993056i	$-0.462467\pi$
$19$	4.78801	−	3.47869i	1.09844	−	0.798066i	0.980805	+	0.194990i	$0.0624674\pi$
$20$	0.350680	−	2.20840i	0.0784144	−	0.493813i
$21$	−0.684120	+	0.497043i	−0.149287	+	0.108464i
$22$	1.80247	−	0.585657i	0.384287	−	0.124863i
$23$	1.30274	−	0.423287i	0.271641	−	0.0882615i	−0.170029	−	0.985439i	$-0.554386\pi$
$23$	1.30274	−	0.423287i	0.271641	−	0.0882615i	0.441670	+	0.897178i	$0.354386\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	4.75651	−	1.54129i	0.951303	−	0.308258i
$26$	2.85365			0.559646
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$	0.497043	−	0.684120i	0.0939322	−	0.129287i
$29$	−2.00381	+	1.45586i	−0.372099	+	0.270346i	−0.758081	−	0.652161i	$-0.773863\pi$
$29$	−2.00381	+	1.45586i	−0.372099	+	0.270346i	0.385982	+	0.922506i	$0.373863\pi$
$30$	−2.20868	+	0.348916i	−0.403248	+	0.0637031i
$31$	5.55383	−	0.393719i	0.997497	−	0.0707140i
$31$	5.55383	−	0.393719i	0.997497	−	0.0707140i
$32$		−	1.00000i		−	0.176777i
$33$	−1.11399	−	1.53327i	−0.193920	−	0.266908i
$34$	3.83989	+	2.78985i	0.658536	+	0.478455i
$35$	1.86746	+	0.296542i	0.315659	+	0.0501247i
$36$	1.00000			0.166667
$37$			2.53362i			0.416525i	0.978073	+	0.208263i	$0.0667809\pi$
$37$			2.53362i			0.416525i	−0.978073	+	0.208263i	$0.933219\pi$
$38$	5.62864	+	1.82886i	0.913086	+	0.296680i
$39$	−0.881825	−	2.71398i	−0.141205	−	0.434584i
$40$	1.99276	−	1.01436i	0.315082	−	0.160384i
$41$	8.14499	−	5.91768i	1.27203	−	0.924186i	0.272752	−	0.962084i	$-0.412066\pi$
$41$	8.14499	−	5.91768i	1.27203	−	0.924186i	0.999282	+	0.0378981i	$0.0120662\pi$
$42$	−0.804232	−	0.261311i	−0.124096	−	0.0403211i
$43$	−4.57891	−	6.30234i	−0.698278	−	0.961097i	−0.999970	−	0.00769185i	$-0.997552\pi$
$43$	−4.57891	−	6.30234i	−0.698278	−	0.961097i	0.301692	−	0.953405i	$-0.402448\pi$
$44$	1.53327	+	1.11399i	0.231149	+	0.167940i
$45$	1.01436	+	1.99276i	0.151212	+	0.297063i
$46$	1.10818	+	0.805140i	0.163392	+	0.118711i
$47$	−6.06043	+	8.34146i	−0.884004	+	1.21673i	0.0912917	+	0.995824i	$0.470900\pi$
$47$	−6.06043	+	8.34146i	−0.884004	+	1.21673i	−0.975296	+	0.220903i	$0.929100\pi$
$48$	−0.951057	+	0.309017i	−0.137273	+	0.0446028i
$49$	−5.08461	−	3.69419i	−0.726373	−	0.527741i
$50$	4.04274	+	2.94215i	0.571729	+	0.416084i
$51$	1.46671	−	4.51407i	0.205380	−	0.632096i
$52$	1.67733	+	2.30865i	0.232604	+	0.320152i
$53$	−11.0939	+	3.60462i	−1.52386	+	0.495133i	−0.946870	−	0.321616i	$-0.895774\pi$
$53$	−11.0939	+	3.60462i	−1.52386	+	0.495133i	−0.576993	+	0.816749i	$0.695774\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	−0.664618	+	4.18542i	−0.0896170	+	0.564361i
$56$	0.845619			0.113001
$57$		−	5.91830i		−	0.783898i
$58$	−2.35562	−	0.765389i	−0.309309	−	0.100500i
$59$	0.127522	+	0.0926499i	0.0166019	+	0.0120620i	0.596055	−	0.802943i	$-0.296734\pi$
$59$	0.127522	+	0.0926499i	0.0166019	+	0.0120620i	−0.579453	+	0.815005i	$0.696734\pi$
$60$	−1.58051	−	1.58177i	−0.204043	−	0.204206i
$61$	14.3118			1.83244			0.916222	−	0.400671i	$-0.131223\pi$
$61$	14.3118			1.83244			0.916222	+	0.400671i	$0.131223\pi$
$62$	3.58298	+	4.26172i	0.455039	+	0.541239i
$63$			0.845619i			0.106538i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−2.89916	+	5.68431i	−0.359596	+	0.705052i
$66$	0.585657	−	1.80247i	0.0720894	−	0.221868i
$67$		−	4.77411i		−	0.583250i	−0.956533	−	0.291625i	$-0.905804\pi$
$67$		−	4.77411i		−	0.583250i	0.956533	−	0.291625i	$-0.0941960\pi$
$68$			4.74637i			0.575582i
$69$	0.423287	−	1.30274i	0.0509578	−	0.156832i
$70$	0.857761	+	1.68511i	0.102522	+	0.201410i
$71$	−0.541896	−	1.66779i	−0.0643113	−	0.197930i	0.913738	−	0.406304i	$-0.133183\pi$
$71$	−0.541896	−	1.66779i	−0.0643113	−	0.197930i	−0.978049	+	0.208375i	$0.933183\pi$
$72$	0.587785	+	0.809017i	0.0692712	+	0.0953436i
$73$	−1.40054	−	0.455063i	−0.163921	−	0.0532611i	0.225907	−	0.974149i	$-0.427465\pi$
$73$	−1.40054	−	0.455063i	−0.163921	−	0.0532611i	−0.389828	+	0.920888i	$0.627465\pi$
$74$	−2.04974	+	1.48923i	−0.238278	+	0.173119i
$75$	1.54888	−	4.75405i	0.178849	−	0.548950i
$76$	1.82886	+	5.62864i	0.209784	+	0.645649i
$77$	−0.942008	+	1.29656i	−0.107352	+	0.147757i
$78$	1.67733	−	2.30865i	0.189920	−	0.261403i
$79$	−2.60153	−	8.00668i	−0.292695	−	0.900822i	−0.983986	−	0.178246i	$-0.942958\pi$
$79$	−2.60153	−	8.00668i	−0.292695	−	0.900822i	0.691291	−	0.722576i	$-0.257042\pi$
$80$	1.99195	+	1.01595i	0.222706	+	0.113587i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	9.57501	+	3.11111i	1.05738	+	0.343564i
$83$	−5.51303	−	7.58804i	−0.605134	−	0.832896i	0.391032	−	0.920377i	$-0.372118\pi$
$83$	−5.51303	−	7.58804i	−0.605134	−	0.832896i	−0.996166	+	0.0874814i	$0.972118\pi$
$84$	−0.261311	−	0.804232i	−0.0285113	−	0.0877489i
$85$	−9.45836	+	4.81452i	−1.02590	+	0.522208i
$86$	2.40728	−	7.40884i	0.259583	−	0.798916i
$87$			2.47685i			0.265546i
$88$			1.89523i			0.202032i
$89$	−1.11491	+	3.43135i	−0.118181	+	0.363722i	−0.992597	−	0.121454i	$-0.961244\pi$
$89$	−1.11491	+	3.43135i	−0.118181	+	0.363722i	0.874417	+	0.485176i	$0.161244\pi$
$90$	−1.01595	+	1.99195i	−0.107090	+	0.209970i
$91$	−1.95224	+	1.41838i	−0.204650	+	0.148687i
$92$			1.36979i			0.142810i
$93$	2.94593	−	4.72456i	0.305479	−	0.489914i
$94$	−10.3106			−1.06346
$95$	−9.36139	+	9.35392i	−0.960459	+	0.959692i
$96$	−0.809017	−	0.587785i	−0.0825700	−	0.0599906i
$97$	−12.1108	−	3.93502i	−1.22966	−	0.399541i	−0.379069	−	0.925368i	$-0.623756\pi$
$97$	−12.1108	−	3.93502i	−1.22966	−	0.399541i	−0.850591	+	0.525827i	$0.823756\pi$
$98$		−	6.28493i		−	0.634874i
$99$	−1.89523			−0.190477
$100$	−0.00399192	+	5.00000i	−0.000399192	+	0.500000i
$101$	−4.12337	−	12.6904i	−0.410291	−	1.26274i	−0.916396	−	0.400273i	$-0.868915\pi$
$101$	−4.12337	−	12.6904i	−0.410291	−	1.26274i	0.506105	−	0.862472i	$-0.331085\pi$
$102$	4.51407	−	1.46671i	0.446959	−	0.145226i
$103$	8.34501	+	11.4859i	0.822259	+	1.13174i	0.989315	+	0.145794i	$0.0465738\pi$
$103$	8.34501	+	11.4859i	0.822259	+	1.13174i	−0.167056	+	0.985947i	$0.553426\pi$
$104$	−0.881825	+	2.71398i	−0.0864701	+	0.266128i
$105$	1.33758	−	1.33651i	0.130534	−	0.130430i
$106$	−9.43703	−	6.85640i	−0.916605	−	0.665953i
$107$	−5.45330	+	1.77188i	−0.527190	+	0.171294i	−0.560506	−	0.828150i	$-0.689393\pi$
$107$	−5.45330	+	1.77188i	−0.527190	+	0.171294i	0.0333158	+	0.999445i	$0.489393\pi$
$108$	0.587785	−	0.809017i	0.0565597	−	0.0778477i
$109$	9.75859	+	7.09003i	0.934704	+	0.679102i	0.947140	−	0.320821i	$-0.103959\pi$
$109$	9.75859	+	7.09003i	0.934704	+	0.679102i	−0.0124363	+	0.999923i	$0.503959\pi$
$110$	−3.77672	+	1.92244i	−0.360097	+	0.183297i
$111$	2.04974	+	1.48923i	0.194553	+	0.141351i
$112$	0.497043	+	0.684120i	0.0469661	+	0.0646433i
$113$	13.7731	+	4.47514i	1.29566	+	0.420986i	0.874070	−	0.485800i	$-0.161472\pi$
$113$	13.7731	+	4.47514i	1.29566	+	0.420986i	0.421592	+	0.906786i	$0.361472\pi$
$114$	4.78801	−	3.47869i	0.448438	−	0.325809i
$115$	−2.72965	+	1.38945i	−0.254541	+	0.129567i
$116$	−0.765389	−	2.35562i	−0.0710646	−	0.218714i
$117$	−2.71398	−	0.881825i	−0.250907	−	0.0815248i
$118$			0.157625i			0.0145106i
$119$	−4.01362			−0.367928
$120$	0.350680	−	2.20840i	0.0320125	−	0.201598i
$121$	5.99329	+	4.35438i	0.544845	+	0.395853i
$122$	8.41229	+	11.5785i	0.761613	+	1.04827i
$123$		−	10.0678i		−	0.907779i
$124$	−1.34178	+	5.40367i	−0.120495	+	0.485264i
$125$	−9.96783	+	5.06383i	−0.891550	+	0.452923i
$126$	−0.684120	+	0.497043i	−0.0609463	+	0.0442801i
$127$	8.67252	−	11.9367i	0.769561	−	1.05921i	−0.226797	−	0.973942i	$-0.572825\pi$
$127$	8.67252	−	11.9367i	0.769561	−	1.05921i	0.996358	−	0.0852682i	$-0.0271747\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$	−7.79011			−0.685881
$130$	−6.30279	+	0.995684i	−0.552791	+	0.0873273i
$131$	−4.59393	+	14.1387i	−0.401373	+	1.23530i	0.522513	+	0.852632i	$0.324995\pi$
$131$	−4.59393	+	14.1387i	−0.401373	+	1.23530i	−0.923886	+	0.382668i	$0.875005\pi$
$132$	1.80247	−	0.585657i	0.156885	−	0.0509749i
$133$	−4.75969	+	1.54652i	−0.412717	+	0.134100i
$134$	3.86234	−	2.80615i	0.333655	−	0.242415i
$135$	2.20840	+	0.350680i	0.190069	+	0.0301817i
$136$	−3.83989	+	2.78985i	−0.329268	+	0.239227i
$137$	−6.11681	+	8.41907i	−0.522594	+	0.719289i	−0.985979	−	0.166868i	$-0.946635\pi$
$137$	−6.11681	+	8.41907i	−0.522594	+	0.719289i	0.463385	+	0.886157i	$0.346635\pi$
$138$	1.30274	−	0.423287i	0.110897	−	0.0360326i
$139$	−6.85282	−	4.97887i	−0.581249	−	0.422302i	0.257925	−	0.966165i	$-0.416961\pi$
$139$	−6.85282	−	4.97887i	−0.581249	−	0.422302i	−0.839174	+	0.543863i	$0.816961\pi$
$140$	−0.859106	+	1.68443i	−0.0726077	+	0.142360i
$141$	3.18615	+	9.80598i	0.268323	+	0.825812i
$142$	1.03075	−	1.41870i	0.0864985	−	0.119055i
$143$	−3.17892	−	4.37541i	−0.265835	−	0.365890i
$144$	−0.309017	+	0.951057i	−0.0257514	+	0.0792547i
$145$	3.91781	−	3.91468i	0.325356	−	0.325096i
$146$	−0.455063	−	1.40054i	−0.0376613	−	0.115910i
$147$	−5.97732	+	1.94215i	−0.493001	+	0.160186i
$148$	−2.40962	−	0.782933i	−0.198069	−	0.0643567i
$149$	6.68511			0.547665			0.273833	−	0.961777i	$-0.411709\pi$
$149$	6.68511			0.547665			0.273833	+	0.961777i	$0.411709\pi$
$150$	4.75651	−	1.54129i	0.388368	−	0.125846i
$151$	2.38680	−	7.34583i	0.194235	−	0.597795i	−0.805749	−	0.592257i	$-0.798237\pi$
$151$	2.38680	−	7.34583i	0.194235	−	0.597795i	0.999985	−	0.00553819i	$-0.00176287\pi$
$152$	−3.47869	+	4.78801i	−0.282159	+	0.388359i
$153$	−2.78985	−	3.83989i	−0.225546	−	0.310437i
$154$	−1.60264			−0.129144
$155$	−12.1292	+	2.80742i	−0.974244	+	0.225497i
$156$	2.85365			0.228475
$157$	10.5862	+	14.5706i	0.844868	+	1.16286i	0.984970	+	0.172725i	$0.0552571\pi$
$157$	10.5862	+	14.5706i	0.844868	+	1.16286i	−0.140102	+	0.990137i	$0.544743\pi$
$158$	4.94840	−	6.81089i	0.393674	−	0.541845i
$159$	−3.60462	+	11.0939i	−0.285865	+	0.879803i
$160$	0.348916	+	2.20868i	0.0275843	+	0.174611i
$161$	−1.15832			−0.0912882
$162$	−0.951057	−	0.309017i	−0.0747221	−	0.0242787i
$163$	3.87399	−	1.25874i	0.303434	−	0.0985918i	−0.153342	−	0.988173i	$-0.549004\pi$
$163$	3.87399	−	1.25874i	0.303434	−	0.0985918i	0.456777	+	0.889581i	$0.349004\pi$
$164$	3.11111	+	9.57501i	0.242937	+	0.747682i
$165$	2.99542	+	2.99781i	0.233193	+	0.233379i
$166$	2.89837	−	8.92028i	0.224957	−	0.692348i
$167$	4.87398	+	6.70845i	0.377160	+	0.519116i	0.954829	−	0.297155i	$-0.0960378\pi$
$167$	4.87398	+	6.70845i	0.377160	+	0.519116i	−0.577670	+	0.816271i	$0.696038\pi$
$168$	0.497043	−	0.684120i	0.0383477	−	0.0527810i
$169$	1.50080	+	4.61900i	0.115446	+	0.355308i
$170$	−9.45451	−	4.82207i	−0.725128	−	0.369836i
$171$	−4.78801	−	3.47869i	−0.366148	−	0.266022i
$172$	7.40884	−	2.40728i	0.564919	−	0.183553i
$173$	−3.18808	+	4.38801i	−0.242385	+	0.333614i	−0.912826	−	0.408348i	$-0.866105\pi$
$173$	−3.18808	+	4.38801i	−0.242385	+	0.333614i	0.670441	+	0.741963i	$0.266105\pi$
$174$	−2.00381	+	1.45586i	−0.151909	+	0.110368i
$175$	−4.22810	−	0.00337565i	−0.319614	−	0.000255175i
$176$	−1.53327	+	1.11399i	−0.115575	+	0.0839699i
$177$	0.149911	−	0.0487089i	0.0112680	−	0.00366119i
$178$	−3.43135	+	1.11491i	−0.257191	+	0.0835663i
$179$	−2.53087	+	7.78923i	−0.189166	+	0.582194i	−0.999995	−	0.00308907i	$-0.999017\pi$
$179$	−2.53087	+	7.78923i	−0.189166	+	0.582194i	0.810829	+	0.585283i	$0.199017\pi$
$180$	−2.20868	+	0.348916i	−0.164625	+	0.0260067i
$181$	−8.57911			−0.637680			−0.318840	−	0.947808i	$-0.603293\pi$
$181$	−8.57911			−0.637680			−0.318840	+	0.947808i	$0.603293\pi$
$182$	−2.29499	−	0.745689i	−0.170116	−	0.0552741i
$183$	8.41229	−	11.5785i	0.621854	−	0.855909i
$184$	−1.10818	+	0.805140i	−0.0816961	+	0.0593557i
$185$	−0.884023	−	5.59596i	−0.0649947	−	0.411423i
$186$	5.55383	−	0.393719i	0.407226	−	0.0288689i
$187$		−	8.99545i		−	0.657812i
$188$	−6.06043	−	8.34146i	−0.442002	−	0.608364i
$189$	0.684120	+	0.497043i	0.0497624	+	0.0361545i
$190$	−13.0700	−	2.07543i	−0.948195	−	0.150567i
$191$	9.84042			0.712028			0.356014	−	0.934481i	$-0.384136\pi$
$191$	9.84042			0.712028			0.356014	+	0.934481i	$0.384136\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	3.40501	+	1.10635i	0.245098	+	0.0796370i	0.428990	−	0.903309i	$-0.358870\pi$
$193$	3.40501	+	1.10635i	0.245098	+	0.0796370i	−0.183892	+	0.982946i	$0.558870\pi$
$194$	−3.93502	−	12.1108i	−0.282518	−	0.869502i
$195$	2.89462	+	5.68662i	0.207288	+	0.407227i
$196$	5.08461	−	3.69419i	0.363187	−	0.263871i
$197$	−4.74488	−	1.54171i	−0.338059	−	0.109842i	0.135068	−	0.990836i	$-0.456875\pi$
$197$	−4.74488	−	1.54171i	−0.338059	−	0.109842i	−0.473127	+	0.880994i	$0.656875\pi$
$198$	−1.11399	−	1.53327i	−0.0791676	−	0.108965i
$199$	−4.26402	−	3.09799i	−0.302268	−	0.219611i	0.426303	−	0.904580i	$-0.359816\pi$
$199$	−4.26402	−	3.09799i	−0.302268	−	0.219611i	−0.728572	+	0.684969i	$0.759816\pi$
$200$	−4.04743	+	2.93570i	−0.286197	+	0.207585i
$201$	−3.86234	−	2.80615i	−0.272428	−	0.197931i
$202$	7.84312	−	10.7951i	0.551840	−	0.759542i
$203$	1.99196	−	0.647228i	0.139808	−	0.0454265i
$204$	3.83989	+	2.78985i	0.268846	+	0.195328i
$205$	−15.9249	+	15.9122i	−1.11224	+	1.11135i
$206$	−4.38723	+	13.5025i	−0.305673	+	0.940765i
$207$	−0.805140	−	1.10818i	−0.0559611	−	0.0770239i
$208$	−2.71398	+	0.881825i	−0.188181	+	0.0611436i
$209$	−3.46610	−	10.6675i	−0.239755	−	0.737890i
$210$	1.86746	+	0.296542i	0.128867	+	0.0204633i
$211$	19.5813			1.34803			0.674016	−	0.738717i	$-0.264568\pi$
$211$	19.5813			1.34803			0.674016	+	0.738717i	$0.264568\pi$
$212$		−	11.6648i		−	0.801142i
$213$	−1.66779	−	0.541896i	−0.114275	−	0.0371301i
$214$	−4.63885	−	3.37032i	−0.317105	−	0.230391i
$215$	12.3123	+	12.3222i	0.839694	+	0.840365i
$216$	1.00000			0.0680414
$217$	−4.56945	−	1.13463i	−0.310194	−	0.0770239i
$218$			12.0623i			0.816961i
$219$	−1.19137	+	0.865581i	−0.0805053	+	0.0584906i
$220$	−3.77519	−	1.92545i	−0.254523	−	0.129814i
$221$	4.18547	−	12.8815i	0.281545	−	0.866507i
$222$			2.53362i			0.170046i
$223$		−	3.78739i		−	0.253623i	−0.991927	−	0.126811i	$-0.959526\pi$
$223$		−	3.78739i		−	0.253623i	0.991927	−	0.126811i	$-0.0404743\pi$
$224$	−0.261311	+	0.804232i	−0.0174596	+	0.0537350i
$225$	−2.93570	−	4.04743i	−0.195713	−	0.269829i
$226$	4.47514	+	13.7731i	0.297682	+	0.916171i
$227$	−0.0245134	−	0.0337398i	−0.00162701	−	0.00223939i	0.808203	−	0.588904i	$-0.200441\pi$
$227$	−0.0245134	−	0.0337398i	−0.00162701	−	0.00223939i	−0.809830	+	0.586665i	$0.800441\pi$
$228$	5.62864	+	1.82886i	0.372766	+	0.121119i
$229$	−15.7448	+	11.4393i	−1.04045	+	0.755930i	−0.970373	−	0.241612i	$-0.922324\pi$
$229$	−15.7448	+	11.4393i	−1.04045	+	0.755930i	−0.0700751	+	0.997542i	$0.522324\pi$
$230$	−2.72854	−	1.39163i	−0.179915	−	0.0917616i
$231$	0.495243	+	1.52420i	0.0325846	+	0.100285i
$232$	1.45586	−	2.00381i	0.0955816	−	0.131557i
$233$	−8.00051	+	11.0118i	−0.524131	+	0.721404i	−0.986222	−	0.165428i	$-0.947099\pi$
$233$	−8.00051	+	11.0118i	−0.524131	+	0.721404i	0.462091	+	0.886833i	$0.347099\pi$
$234$	−0.881825	−	2.71398i	−0.0576467	−	0.177418i
$235$	10.4751	−	20.5382i	0.683317	−	1.33976i
$236$	−0.127522	+	0.0926499i	−0.00830095	+	0.00603099i
$237$	−8.00668	−	2.60153i	−0.520090	−	0.168987i
$238$	−2.35915	−	3.24709i	−0.152921	−	0.210477i
$239$	6.60749	+	20.3358i	0.427403	+	1.31541i	0.900675	+	0.434494i	$0.143073\pi$
$239$	6.60749	+	20.3358i	0.427403	+	1.31541i	−0.473272	+	0.880917i	$0.656927\pi$
$240$	1.99276	−	1.01436i	0.128632	−	0.0654765i
$241$	0.664662	−	2.04562i	0.0428146	−	0.131770i	−0.927364	−	0.374160i	$-0.877931\pi$
$241$	0.664662	−	2.04562i	0.0428146	−	0.131770i	0.970179	+	0.242390i	$0.0779312\pi$
$242$			7.40812i			0.476212i
$243$			1.00000i			0.0641500i
$244$	−4.42260	+	13.6114i	−0.283128	+	0.871379i
$245$	12.5192	+	6.38517i	0.799825	+	0.407933i
$246$	8.14499	−	5.91768i	0.519305	−	0.377298i
$247$		−	16.8887i		−	1.07460i
$248$	−5.16034	+	2.09068i	−0.327682	+	0.132758i
$249$	−9.37933			−0.594391
$250$	−9.95567	−	5.08769i	−0.629652	−	0.321774i
$251$	10.4315	+	7.57896i	0.658433	+	0.478380i	0.866133	−	0.499813i	$-0.166598\pi$
$251$	10.4315	+	7.57896i	0.658433	+	0.478380i	−0.207700	+	0.978193i	$0.566598\pi$
$252$	−0.804232	−	0.261311i	−0.0506618	−	0.0164610i
$253$		−	2.59606i		−	0.163213i
$254$	14.7546			0.925784
$255$	−1.66446	+	10.4819i	−0.104232	+	0.656401i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−3.79665	+	1.23361i	−0.236828	+	0.0769502i	−0.425027	−	0.905181i	$-0.639735\pi$
$257$	−3.79665	+	1.23361i	−0.236828	+	0.0769502i	0.188198	+	0.982131i	$0.439735\pi$
$258$	−4.57891	−	6.30234i	−0.285071	−	0.392366i
$259$	0.662063	−	2.03762i	0.0411386	−	0.126612i
$260$	−4.51021	−	4.51381i	−0.279711	−	0.279935i
$261$	2.00381	+	1.45586i	0.124033	+	0.0901152i
$262$	−14.1387	+	4.59393i	−0.873489	+	0.283814i
$263$	12.3642	−	17.0179i	0.762411	−	1.04937i	−0.234599	−	0.972092i	$-0.575378\pi$
$263$	12.3642	−	17.0179i	0.762411	−	1.04937i	0.997010	−	0.0772759i	$-0.0246222\pi$
$264$	1.53327	+	1.11399i	0.0943663	+	0.0685611i
$265$	23.2451	−	11.8323i	1.42794	−	0.726852i
$266$	−4.04883	−	2.94165i	−0.248250	−	0.180364i
$267$	2.12069	+	2.91888i	0.129784	+	0.178633i
$268$	4.54045	+	1.47528i	0.277352	+	0.0901172i
$269$	−24.0492	+	17.4728i	−1.46631	+	1.06533i	−0.484644	+	0.874712i	$0.661051\pi$
$269$	−24.0492	+	17.4728i	−1.46631	+	1.06533i	−0.981663	+	0.190623i	$0.938949\pi$
$270$	1.01436	+	1.99276i	0.0617319	+	0.121275i
$271$	−8.87912	−	27.3271i	−0.539368	−	1.66000i	−0.734017	−	0.679131i	$-0.762357\pi$
$271$	−8.87912	−	27.3271i	−0.539368	−	1.66000i	0.194649	−	0.980873i	$-0.437643\pi$
$272$	−4.51407	−	1.46671i	−0.273705	−	0.0889323i
$273$			2.41310i			0.146047i
$274$	−10.4065			−0.628682
$275$	0.00756560	−	9.47613i	0.000456223	−	0.571432i
$276$	1.10818	+	0.805140i	0.0667046	+	0.0484637i
$277$	−6.73439	−	9.26909i	−0.404630	−	0.556926i	0.557268	−	0.830333i	$-0.311850\pi$
$277$	−6.73439	−	9.26909i	−0.404630	−	0.556926i	−0.961899	+	0.273407i	$0.911850\pi$
$278$		−	8.47056i		−	0.508030i
$279$	−2.09068	−	5.16034i	−0.125165	−	0.308941i
$280$	−1.86770	+	0.295051i	−0.111616	+	0.0176326i
$281$	−1.06677	+	0.775056i	−0.0636383	+	0.0462360i	−0.619150	−	0.785273i	$-0.712523\pi$
$281$	−1.06677	+	0.775056i	−0.0636383	+	0.0462360i	0.555511	+	0.831509i	$0.312523\pi$
$282$	−6.06043	+	8.34146i	−0.360893	+	0.496727i
$283$	−2.92755	−	0.951220i	−0.174025	−	0.0565441i	0.220708	−	0.975340i	$-0.429163\pi$
$283$	−2.92755	−	0.951220i	−0.174025	−	0.0565441i	−0.394733	+	0.918796i	$0.629163\pi$
$284$	1.75361			0.104058
$285$	2.06499	+	13.0716i	0.122320	+	0.774296i
$286$	1.67126	−	5.14361i	0.0988236	−	0.304148i
$287$	−8.09681	+	2.63081i	−0.477940	+	0.155292i
$288$	−0.951057	+	0.309017i	−0.0560415	+	0.0182090i
$289$	4.47227	−	3.24929i	0.263075	−	0.191135i
$290$	5.46987	+	0.868581i	0.321202	+	0.0510048i
$291$	−10.3020	+	7.48486i	−0.603915	+	0.438770i
$292$	0.865581	−	1.19137i	0.0506543	−	0.0697197i
$293$	−2.14476	+	0.696875i	−0.125298	+	0.0407118i	−0.370995	−	0.928635i	$-0.620983\pi$
$293$	−2.14476	+	0.696875i	−0.125298	+	0.0407118i	0.245697	+	0.969347i	$0.420983\pi$
$294$	−5.08461	−	3.69419i	−0.296541	−	0.215449i
$295$	−0.313981	−	0.160139i	−0.0182807	−	0.00932367i
$296$	−0.782933	−	2.40962i	−0.0455070	−	0.140056i
$297$	−1.11399	+	1.53327i	−0.0646400	+	0.0889694i
$298$	3.92941	+	5.40836i	0.227624	+	0.313298i
$299$	1.20791	−	3.71757i	0.0698554	−	0.214993i
$300$	4.04274	+	2.94215i	0.233408	+	0.169865i
$301$	2.03564	+	6.26506i	0.117332	+	0.361112i
$302$	7.34583	−	2.38680i	0.422705	−	0.137345i
$303$	−12.6904	−	4.12337i	−0.729046	−	0.236881i
$304$	−5.91830			−0.339438
$305$	−31.6103	+	4.99364i	−1.81000	+	0.285935i
$306$	1.46671	−	4.51407i	0.0838462	−	0.258052i
$307$	6.49798	−	8.94370i	0.370859	−	0.510444i	−0.582275	−	0.812992i	$-0.697837\pi$
$307$	6.49798	−	8.94370i	0.370859	−	0.510444i	0.953134	+	0.302548i	$0.0978373\pi$
$308$	−0.942008	−	1.29656i	−0.0536759	−	0.0738786i
$309$	14.1974			0.807661
$310$	−9.40064	−	8.16260i	−0.533920	−	0.463605i
$311$	−14.8683			−0.843102			−0.421551	−	0.906805i	$-0.638514\pi$
$311$	−14.8683			−0.843102			−0.421551	+	0.906805i	$0.638514\pi$
$312$	1.67733	+	2.30865i	0.0949602	+	0.130701i
$313$	−19.5833	+	26.9542i	−1.10692	+	1.52354i	−0.281033	+	0.959698i	$0.590677\pi$
$313$	−19.5833	+	26.9542i	−1.10692	+	1.52354i	−0.825883	+	0.563842i	$0.809323\pi$
$314$	−5.56548	+	17.1288i	−0.314078	+	0.966633i
$315$	−0.295051	−	1.86770i	−0.0166242	−	0.105233i
$316$	8.41872			0.473590
$317$	−19.9180	−	6.47175i	−1.11871	−	0.363490i	−0.309433	−	0.950921i	$-0.600139\pi$
$317$	−19.9180	−	6.47175i	−1.11871	−	0.363490i	−0.809274	+	0.587432i	$0.800139\pi$
$318$	−11.0939	+	3.60462i	−0.622115	+	0.202137i
$319$	1.45059	+	4.46444i	0.0812172	+	0.249961i
$320$	−1.58177	+	1.58051i	−0.0884236	+	0.0883531i
$321$	−1.77188	+	5.45330i	−0.0988969	+	0.304373i
$322$	−0.680842	−	0.937099i	−0.0379419	−	0.0522225i
$323$	16.5112	−	22.7257i	0.918705	−	1.26449i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	4.41996	−	13.5664i	0.245175	−	0.752527i
$326$	3.29541	+	2.39426i	0.182516	+	0.132606i
$327$	11.4719	−	3.72745i	0.634398	−	0.206128i
$328$	−5.91768	+	8.14499i	−0.326749	+	0.449732i
$329$	7.05370	−	5.12481i	0.388883	−	0.282540i
$330$	−0.664618	+	4.18542i	−0.0365860	+	0.230400i
$331$	−1.44180	+	1.04753i	−0.0792483	+	0.0575773i	−0.626704	−	0.779257i	$-0.715596\pi$
$331$	−1.44180	+	1.04753i	−0.0792483	+	0.0575773i	0.547456	+	0.836835i	$0.315596\pi$
$332$	8.92028	−	2.89837i	0.489564	−	0.159069i
$333$	2.40962	−	0.782933i	0.132046	−	0.0429044i
$334$	−2.56240	+	7.88626i	−0.140208	+	0.431517i
$335$	1.66577	+	10.5445i	0.0910105	+	0.576106i
$336$	0.845619			0.0461323
$337$	−25.0164	−	8.12831i	−1.36273	−	0.442777i	−0.465776	−	0.884903i	$-0.654225\pi$
$337$	−25.0164	−	8.12831i	−1.36273	−	0.442777i	−0.896953	+	0.442125i	$0.854225\pi$
$338$	−2.85470	+	3.92915i	−0.155275	+	0.213718i
$339$	11.7161	−	8.51223i	0.636330	−	0.462321i
$340$	−1.65609	−	10.4832i	−0.0898139	−	0.568531i
$341$	2.54297	−	10.2412i	0.137710	−	0.554591i
$342$		−	5.91830i		−	0.320025i
$343$	6.60318	+	9.08849i	0.356538	+	0.490732i
$344$	6.30234	+	4.57891i	0.339799	+	0.246879i
$345$	−0.480356	+	3.02503i	−0.0258615	+	0.162862i
$346$	−5.42388			−0.291589
$347$		−	21.4128i		−	1.14950i	−0.818329	−	0.574750i	$-0.805099\pi$
$347$		−	21.4128i		−	1.14950i	0.818329	−	0.574750i	$-0.194901\pi$
$348$	−2.35562	−	0.765389i	−0.126275	−	0.0410291i
$349$	−6.50759	−	20.0283i	−0.348343	−	1.07209i	−0.959770	−	0.280789i	$-0.909404\pi$
$349$	−6.50759	−	20.0283i	−0.348343	−	1.07209i	0.611426	−	0.791301i	$-0.290596\pi$
$350$	−2.48248	−	3.42259i	−0.132694	−	0.182945i
$351$	−2.30865	+	1.67733i	−0.123227	+	0.0895293i
$352$	−1.80247	−	0.585657i	−0.0960719	−	0.0312156i
$353$	11.7262	+	16.1397i	0.624123	+	0.859032i	0.997645	−	0.0685894i	$-0.0218498\pi$
$353$	11.7262	+	16.1397i	0.624123	+	0.859032i	−0.373522	+	0.927621i	$0.621850\pi$
$354$	0.127522	+	0.0926499i	0.00677770	+	0.00492429i
$355$	1.77879	+	3.49452i	0.0944085	+	0.185470i
$356$	−2.91888	−	2.12069i	−0.154700	−	0.112396i
$357$	−2.35915	+	3.24709i	−0.124859	+	0.171854i
$358$	−7.78923	+	2.53087i	−0.411674	+	0.133761i
$359$	21.8758	+	15.8937i	1.15456	+	0.838838i	0.989081	−	0.147376i	$-0.0470826\pi$
$359$	21.8758	+	15.8937i	1.15456	+	0.838838i	0.165480	+	0.986213i	$0.447083\pi$
$360$	−1.58051	−	1.58177i	−0.0833001	−	0.0833666i
$361$	4.95240	−	15.2419i	0.260653	−	0.802206i
$362$	−5.04268	−	6.94065i	−0.265037	−	0.364792i
$363$	7.04554	−	2.28923i	0.369795	−	0.120154i
$364$	−0.745689	−	2.29499i	−0.0390847	−	0.120290i
$365$	3.25212	+	0.516416i	0.170224	+	0.0270305i
$366$	14.3118			0.748092
$367$			19.3937i			1.01234i	0.862433	+	0.506171i	$0.168940\pi$
$367$			19.3937i			1.01234i	−0.862433	+	0.506171i	$0.831060\pi$
$368$	−1.30274	−	0.423287i	−0.0679102	−	0.0220654i
$369$	−8.14499	−	5.91768i	−0.424011	−	0.308062i
$370$	4.00761	−	4.00441i	0.208346	−	0.208179i
$371$	9.86399			0.512113
$372$	3.58298	+	4.26172i	0.185769	+	0.220960i
$373$			35.8766i			1.85762i	0.370559	+	0.928809i	$0.379166\pi$
$373$			35.8766i			1.85762i	−0.370559	+	0.928809i	$0.620834\pi$
$374$	7.27747	−	5.28739i	0.376309	−	0.273404i
$375$	−1.76221	+	11.0406i	−0.0910003	+	0.570134i
$376$	3.18615	−	9.80598i	0.164313	−	0.505705i
$377$			7.06805i			0.364023i
$378$			0.845619i			0.0434940i
$379$	5.86765	−	18.0588i	0.301401	−	0.927616i	−0.679595	−	0.733587i	$-0.737845\pi$
$379$	5.86765	−	18.0588i	0.301401	−	0.927616i	0.980996	−	0.194029i	$-0.0621555\pi$
$380$	−6.00328	−	11.7937i	−0.307962	−	0.605006i
$381$	−4.55941	−	14.0324i	−0.233586	−	0.718903i
$382$	5.78405	+	7.96107i	0.295938	+	0.407324i
$383$	30.8922	+	10.0375i	1.57852	+	0.512891i	0.961674	−	0.274195i	$-0.0884112\pi$
$383$	30.8922	+	10.0375i	1.57852	+	0.512891i	0.616843	+	0.787086i	$0.288411\pi$
$384$	0.809017	−	0.587785i	0.0412850	−	0.0299953i
$385$	1.62820	−	3.19237i	0.0829808	−	0.162698i
$386$	1.10635	+	3.40501i	0.0563119	+	0.173310i
$387$	−4.57891	+	6.30234i	−0.232759	+	0.320366i
$388$	7.48486	−	10.3020i	0.379986	−	0.523006i
$389$	−1.20795	−	3.71768i	−0.0612453	−	0.188494i	0.915753	−	0.401743i	$-0.131595\pi$
$389$	−1.20795	−	3.71768i	−0.0612453	−	0.188494i	−0.976998	+	0.213249i	$0.931595\pi$
$390$	−2.89916	+	5.68431i	−0.146805	+	0.287836i
$391$	5.25983	−	3.82149i	0.266001	−	0.193261i
$392$	5.97732	+	1.94215i	0.301900	+	0.0980934i
$393$	8.73817	+	12.0271i	0.440782	+	0.606685i
$394$	−1.54171	−	4.74488i	−0.0776700	−	0.239044i
$395$	8.53960	+	16.7765i	0.429674	+	0.844115i
$396$	0.585657	−	1.80247i	0.0294304	−	0.0905774i
$397$		−	3.78010i		−	0.189718i	−0.995491	−	0.0948588i	$-0.969760\pi$
$397$		−	3.78010i		−	0.189718i	0.995491	−	0.0948588i	$-0.0302400\pi$
$398$		−	5.27062i		−	0.264192i
$399$	−1.54652	+	4.75969i	−0.0774226	+	0.238282i
$400$	−4.75405	−	1.54888i	−0.237702	−	0.0774441i
$401$	31.1117	−	22.6040i	1.55364	−	1.12879i	0.612655	−	0.790351i	$-0.290102\pi$
$401$	31.1117	−	22.6040i	1.55364	−	1.12879i	0.940989	−	0.338438i	$-0.109898\pi$
$402$		−	4.77411i		−	0.238111i
$403$	8.40665	−	13.4822i	0.418765	−	0.671598i
$404$	13.3435			0.663864
$405$	1.58177	−	1.58051i	0.0785988	−	0.0785361i
$406$	1.69446	+	1.23110i	0.0840948	+	0.0610985i
$407$	4.56677	+	1.48383i	0.226367	+	0.0735510i
$408$			4.74637i			0.234980i
$409$	26.7931			1.32483			0.662416	−	0.749136i	$-0.269531\pi$
$409$	26.7931			1.32483			0.662416	+	0.749136i	$0.269531\pi$
$410$	−22.2336	−	3.53056i	−1.09804	−	0.174362i
$411$	3.21580	+	9.89720i	0.158624	+	0.488193i
$412$	−13.5025	+	4.38723i	−0.665221	+	0.216143i
$413$	−0.0783465	−	0.107835i	−0.00385518	−	0.00530620i
$414$	0.423287	−	1.30274i	0.0208034	−	0.0640264i
$415$	14.8241	+	14.8359i	0.727687	+	0.728268i
$416$	−2.30865	−	1.67733i	−0.113191	−	0.0822379i
$417$	−8.05598	+	2.61755i	−0.394503	+	0.128182i
$418$	6.59291	−	9.07436i	0.322470	−	0.443841i
$419$	5.36096	+	3.89496i	0.261900	+	0.190281i	0.710984	−	0.703208i	$-0.248250\pi$
$419$	5.36096	+	3.89496i	0.261900	+	0.190281i	−0.449084	+	0.893489i	$0.648250\pi$
$420$	0.857761	+	1.68511i	0.0418544	+	0.0822251i
$421$	17.9841	+	13.0662i	0.876493	+	0.636809i	0.932321	−	0.361631i	$-0.117780\pi$
$421$	17.9841	+	13.0662i	0.876493	+	0.636809i	−0.0558285	+	0.998440i	$0.517780\pi$
$422$	11.5096	+	15.8416i	0.560278	+	0.771157i
$423$	9.80598	+	3.18615i	0.476783	+	0.154916i
$424$	9.43703	−	6.85640i	0.458303	−	0.332976i
$425$	19.2106	−	13.9339i	0.931851	−	0.675893i
$426$	−0.541896	−	1.66779i	−0.0262550	−	0.0808045i
$427$	−11.5100	−	3.73984i	−0.557010	−	0.180983i
$428$		−	5.73394i		−	0.277160i
$429$	−5.40831			−0.261116
$430$	−2.73184	+	17.2037i	−0.131741	+	0.829635i
$431$	−22.1410	−	16.0864i	−1.06649	−	0.774854i	−0.0912156	−	0.995831i	$-0.529075\pi$
$431$	−22.1410	−	16.0864i	−1.06649	−	0.774854i	−0.975279	+	0.220978i	$0.929075\pi$
$432$	0.587785	+	0.809017i	0.0282798	+	0.0389238i
$433$			34.6114i			1.66332i	0.555286	+	0.831659i	$0.312609\pi$
$433$			34.6114i			1.66332i	−0.555286	+	0.831659i	$0.687391\pi$
$434$	−1.76792	−	4.36368i	−0.0848627	−	0.209463i
$435$	−0.864214	−	5.47056i	−0.0414359	−	0.262293i
$436$	−9.75859	+	7.09003i	−0.467352	+	0.339551i
$437$	4.76506	−	6.55855i	0.227944	−	0.313738i
$438$	−1.40054	−	0.455063i	−0.0669204	−	0.0217438i
$439$	−9.45065			−0.451055			−0.225528	−	0.974237i	$-0.572411\pi$
$439$	−9.45065			−0.451055			−0.225528	+	0.974237i	$0.572411\pi$
$440$	−0.661276	−	4.18594i	−0.0315251	−	0.199557i
$441$	−1.94215	+	5.97732i	−0.0924833	+	0.284634i
$442$	12.8815	−	4.18547i	0.612713	−	0.199082i
$443$	−13.1695	+	4.27903i	−0.625702	+	0.203303i	−0.604670	−	0.796476i	$-0.706695\pi$
$443$	−13.1695	+	4.27903i	−0.625702	+	0.203303i	−0.0210317	+	0.999779i	$0.506695\pi$
$444$	−2.04974	+	1.48923i	−0.0972766	+	0.0706756i
$445$	1.26523	−	7.96776i	0.0599776	−	0.377708i
$446$	3.06407	−	2.22617i	0.145088	−	0.105412i
$447$	3.92941	−	5.40836i	0.185855	−	0.255807i
$448$	−0.804232	+	0.261311i	−0.0379964	+	0.0123458i
$449$	−3.56153	−	2.58760i	−0.168079	−	0.122117i	0.500566	−	0.865698i	$-0.333125\pi$
$449$	−3.56153	−	2.58760i	−0.168079	−	0.122117i	−0.668645	+	0.743582i	$0.733125\pi$
$450$	1.54888	−	4.75405i	0.0730150	−	0.224108i
$451$	−5.89626	−	18.1468i	−0.277644	−	0.854500i
$452$	−8.51223	+	11.7161i	−0.400382	+	0.551078i
$453$	−4.53997	−	6.24873i	−0.213306	−	0.293591i
$454$	0.0128875	−	0.0396635i	0.000604839	−	0.00186150i
$455$	3.81697	−	3.81392i	0.178942	−	0.178799i
$456$	1.82886	+	5.62864i	0.0856440	+	0.263585i
$457$	−6.39411	+	2.07757i	−0.299104	+	0.0971848i	−0.454725	−	0.890632i	$-0.650262\pi$
$457$	−6.39411	+	2.07757i	−0.299104	+	0.0971848i	0.155621	+	0.987817i	$0.450262\pi$
$458$	−18.5092	−	6.01399i	−0.864877	−	0.281015i
$459$	−4.74637			−0.221542
$460$	−0.477941	−	3.02542i	−0.0222841	−	0.141061i
$461$	−4.35547	+	13.4048i	−0.202854	+	0.624322i	0.796940	+	0.604058i	$0.206451\pi$
$461$	−4.35547	+	13.4048i	−0.202854	+	0.624322i	−0.999795	+	0.0202636i	$0.993549\pi$
$462$	−0.942008	+	1.29656i	−0.0438262	+	0.0603216i
$463$	21.7856	+	29.9853i	1.01246	+	1.39354i	0.917356	+	0.398068i	$0.130319\pi$
$463$	21.7856	+	29.9853i	1.01246	+	1.39354i	0.0951070	+	0.995467i	$0.469681\pi$
$464$	2.47685			0.114985
$465$	−4.85814	+	11.4629i	−0.225291	+	0.531580i
$466$	−13.6113			−0.630530
$467$	−5.92609	−	8.15656i	−0.274227	−	0.377441i	0.649584	−	0.760290i	$-0.274943\pi$
$467$	−5.92609	−	8.15656i	−0.274227	−	0.377441i	−0.923811	+	0.382849i	$0.874943\pi$
$468$	1.67733	−	2.30865i	0.0775347	−	0.106717i
$469$	−1.24753	+	3.83949i	−0.0576054	+	0.177291i
$470$	22.7728	−	3.59754i	1.05043	−	0.165942i
$471$	18.0103			0.829869
$472$	−0.149911	−	0.0487089i	−0.00690020	−	0.00224201i
$473$	−14.0414	+	4.56234i	−0.645626	+	0.209776i
$474$	−2.60153	−	8.00668i	−0.119492	−	0.367759i
$475$	17.4126	−	23.9261i	0.798943	−	1.09781i
$476$	1.24028	−	3.81718i	0.0568480	−	0.174960i
$477$	6.85640	+	9.43703i	0.313933	+	0.432092i
$478$	−12.5682	+	17.2986i	−0.574856	+	0.791221i
$479$	−2.98217	−	9.17818i	−0.136259	−	0.419362i	0.859525	−	0.511094i	$-0.170760\pi$
$479$	−2.98217	−	9.17818i	−0.136259	−	0.419362i	−0.995784	+	0.0917323i	$0.970760\pi$
$480$	1.99195	+	1.01595i	0.0909195	+	0.0463715i
$481$	5.84925	+	4.24973i	0.266703	+	0.193771i
$482$	2.04562	−	0.664662i	0.0931753	−	0.0302745i
$483$	−0.680842	+	0.937099i	−0.0309794	+	0.0426395i
$484$	−5.99329	+	4.35438i	−0.272422	+	0.197926i
$485$	28.1217	+	4.46556i	1.27694	+	0.202770i
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	−7.91775	+	2.57263i	−0.358787	+	0.116577i	−0.482864	−	0.875696i	$-0.660403\pi$
$487$	−7.91775	+	2.57263i	−0.358787	+	0.116577i	0.124076	+	0.992273i	$0.460403\pi$
$488$	−13.6114	+	4.42260i	−0.616158	+	0.200202i
$489$	1.25874	−	3.87399i	0.0569220	−	0.175188i
$490$	2.19291	+	13.8814i	0.0990658	+	0.627097i
$491$	38.8773			1.75451			0.877254	−	0.480026i	$-0.159373\pi$
$491$	38.8773			1.75451			0.877254	+	0.480026i	$0.159373\pi$
$492$	9.57501	+	3.11111i	0.431675	+	0.140260i
$493$	−6.91003	+	9.51084i	−0.311212	+	0.428347i
$494$	13.6633	−	9.92695i	0.614740	−	0.446635i
$495$	4.18594	−	0.661276i	0.188144	−	0.0297221i
$496$	−4.72456	−	2.94593i	−0.212139	−	0.132276i
$497$			1.48289i			0.0665167i
$498$	−5.51303	−	7.58804i	−0.247045	−	0.340028i
$499$	13.3110	+	9.67098i	0.595881	+	0.432933i	0.844414	−	0.535691i	$-0.179949\pi$
$499$	13.3110	+	9.67098i	0.595881	+	0.432933i	−0.248534	+	0.968623i	$0.579949\pi$
$500$	−1.73576	−	11.0448i	−0.0776258	−	0.493937i
$501$	8.29210			0.370464
$502$			12.8941i			0.575492i
$503$	27.2130	+	8.84202i	1.21337	+	0.394246i	0.844662	−	0.535301i	$-0.179802\pi$
$503$	27.2130	+	8.84202i	1.21337	+	0.394246i	0.368704	+	0.929547i	$0.379802\pi$
$504$	−0.261311	−	0.804232i	−0.0116397	−	0.0358233i
$505$	13.5351	+	26.5904i	0.602304	+	1.18326i
$506$	2.10025	−	1.52592i	0.0933676	−	0.0678356i
$507$	4.61900	+	1.50080i	0.205137	+	0.0666530i
$508$	8.67252	+	11.9367i	0.384781	+	0.529605i
$509$	0.614916	+	0.446762i	0.0272557	+	0.0198024i	0.601330	−	0.799001i	$-0.294638\pi$
$509$	0.614916	+	0.446762i	0.0272557	+	0.0198024i	−0.574074	+	0.818803i	$0.694638\pi$
$510$	−9.45836	+	4.81452i	−0.418823	+	0.213190i
$511$	1.00745	+	0.731952i	0.0445668	+	0.0323797i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	−5.62864	+	1.82886i	−0.248511	+	0.0807460i
$514$	−3.22962	−	2.34646i	−0.142453	−	0.103498i
$515$	−22.4391	−	22.4570i	−0.988784	−	0.989573i
$516$	2.40728	−	7.40884i	0.105975	−	0.326156i
$517$	11.4859	+	15.8090i	0.505149	+	0.695277i
$518$	2.03762	−	0.662063i	0.0895279	−	0.0290894i
$519$	1.67607	+	5.15841i	0.0735713	+	0.226429i
$520$	1.00072	−	6.30199i	0.0438843	−	0.276360i
$521$	11.0857			0.485672			0.242836	−	0.970067i	$-0.421922\pi$
$521$	11.0857			0.485672			0.242836	+	0.970067i	$0.421922\pi$
$522$			2.47685i			0.108409i
$523$	13.6049	+	4.42050i	0.594901	+	0.193295i	0.590965	−	0.806697i	$-0.298747\pi$
$523$	13.6049	+	4.42050i	0.594901	+	0.193295i	0.00393615	+	0.999992i	$0.498747\pi$
$524$	−12.0271	−	8.73817i	−0.525404	−	0.381729i
$525$	−2.48794	+	3.41862i	−0.108583	+	0.149201i
$526$	21.0353			0.917181
$527$	24.4929	−	9.92312i	1.06693	−	0.432258i
$528$			1.89523i			0.0824792i
$529$	−17.0894	+	12.4162i	−0.743018	+	0.539834i
$530$	23.2357	+	11.8509i	1.00929	+	0.514768i
$531$	0.0487089	−	0.149911i	0.00211379	−	0.00650557i
$532$		−	5.00463i		−	0.216978i
$533$		−	28.7298i		−	1.24443i
$534$	−1.11491	+	3.43135i	−0.0482470	+	0.148489i
$535$	11.4263	−	5.81627i	0.494004	−	0.251459i
$536$	1.47528	+	4.54045i	0.0637225	+	0.196118i
$537$	4.81401	+	6.62591i	0.207740	+	0.285929i
$538$	−28.2716	−	9.18599i	−1.21887	−	0.396036i
$539$	−9.63650	+	7.00132i	−0.415073	+	0.301568i
$540$	−1.01595	+	1.99195i	−0.0437195	+	0.0857197i
$541$	7.39960	+	22.7736i	0.318134	+	0.979115i	0.974445	+	0.224625i	$0.0721157\pi$
$541$	7.39960	+	22.7736i	0.318134	+	0.979115i	−0.656312	+	0.754490i	$0.727884\pi$
$542$	16.8891	−	23.2458i	0.725449	−	0.998494i
$543$	−5.04268	+	6.94065i	−0.216402	+	0.297852i
$544$	−1.46671	−	4.51407i	−0.0628846	−	0.193539i
$545$	−24.0274	−	12.2547i	−1.02922	−	0.524932i
$546$	−1.95224	+	1.41838i	−0.0835481	+	0.0607012i
$547$	26.8938	+	8.73831i	1.14989	+	0.373623i	0.821103	−	0.570780i	$-0.193359\pi$
$547$	26.8938	+	8.73831i	1.14989	+	0.373623i	0.328791	+	0.944403i	$0.393359\pi$
$548$	−6.11681	−	8.41907i	−0.261297	−	0.359645i
$549$	−4.42260	−	13.6114i	−0.188752	−	0.580919i
$550$	7.67080	−	5.56381i	0.327084	−	0.237242i
$551$	−4.52980	+	13.9413i	−0.192976	+	0.593919i
$552$			1.36979i			0.0583020i
$553$			7.11903i			0.302732i
$554$	3.54048	−	10.8965i	0.150421	−	0.462947i
$555$	−5.04684	−	2.57403i	−0.214226	−	0.109262i
$556$	6.85282	−	4.97887i	0.290625	−	0.211151i
$557$		−	19.5997i		−	0.830466i	−0.909715	−	0.415233i	$-0.863700\pi$
$557$		−	19.5997i		−	0.830466i	0.909715	−	0.415233i	$-0.136300\pi$
$558$	2.94593	−	4.72456i	0.124711	−	0.200007i
$559$	−22.2302			−0.940239
$560$	−1.33651	−	1.33758i	−0.0564778	−	0.0565229i
$561$	−7.27747	−	5.28739i	−0.307255	−	0.223234i
$562$	−1.25407	−	0.407471i	−0.0528996	−	0.0171881i
$563$		−	24.3306i		−	1.02541i	−0.858565	−	0.512706i	$-0.828643\pi$
$563$		−	24.3306i		−	1.02541i	0.858565	−	0.512706i	$-0.171357\pi$
$564$	−10.3106			−0.434155
$565$	−31.9817	−	5.07850i	−1.34548	−	0.213654i
$566$	−0.951220	−	2.92755i	−0.0399827	−	0.123054i
$567$	0.804232	−	0.261311i	0.0337746	−	0.0109740i
$568$	1.03075	+	1.41870i	0.0432492	+	0.0595275i
$569$	−3.62076	+	11.1435i	−0.151790	+	0.467162i	−0.997822	−	0.0659713i	$-0.978985\pi$
$569$	−3.62076	+	11.1435i	−0.151790	+	0.467162i	0.846032	+	0.533133i	$0.178985\pi$
$570$	−9.36139	+	9.35392i	−0.392106	+	0.391793i
$571$	−24.2802	−	17.6406i	−1.01609	−	0.738235i	−0.0506146	−	0.998718i	$-0.516118\pi$
$571$	−24.2802	−	17.6406i	−1.01609	−	0.738235i	−0.965478	+	0.260484i	$0.916118\pi$
$572$	5.14361	−	1.67126i	0.215065	−	0.0698788i
$573$	5.78405	−	7.96107i	0.241632	−	0.332578i
$574$	−6.88756	−	5.00411i	−0.287481	−	0.208867i
$575$	5.54411	−	4.02128i	0.231206	−	0.167699i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	8.75638	+	12.0521i	0.364533	+	0.501736i	0.951405	−	0.307944i	$-0.0996408\pi$
$577$	8.75638	+	12.0521i	0.364533	+	0.501736i	−0.586872	+	0.809680i	$0.699641\pi$
$578$	5.25746	+	1.70825i	0.218682	+	0.0710540i
$579$	2.89647	−	2.10441i	0.120373	−	0.0874563i
$580$	2.51241	+	4.93576i	0.104322	+	0.204946i
$581$	2.45092	+	7.54316i	0.101681	+	0.312943i
$582$	−12.1108	−	3.93502i	−0.502007	−	0.163112i
$583$			22.1075i			0.915597i
$584$	1.47261			0.0609372
$585$	6.30199	+	1.00072i	0.260555	+	0.0413745i
$586$	−1.82444	−	1.32553i	−0.0753670	−	0.0547573i
$587$	−15.0887	−	20.7678i	−0.622777	−	0.857179i	0.374775	−	0.927116i	$-0.377720\pi$
$587$	−15.0887	−	20.7678i	−0.622777	−	0.857179i	−0.997551	+	0.0699373i	$0.977720\pi$
$588$		−	6.28493i		−	0.259186i
$589$	25.2221	−	21.2052i	1.03926	−	0.873744i
$590$	−0.0549981	−	0.348144i	−0.00226424	−	0.0143329i
$591$	−4.03624	+	2.93250i	−0.166029	+	0.120627i
$592$	1.48923	−	2.04974i	0.0612068	−	0.0842440i
$593$	−26.4179	−	8.58370i	−1.08485	−	0.352491i	−0.288598	−	0.957450i	$-0.593189\pi$
$593$	−26.4179	−	8.58370i	−1.08485	−	0.352491i	−0.796256	+	0.604960i	$0.793189\pi$
$594$	−1.89523			−0.0777621
$595$	8.86480	−	1.40042i	0.363421	−	0.0574116i
$596$	−2.06581	+	6.35791i	−0.0846189	+	0.260430i
$597$	−5.01266	+	1.62871i	−0.205154	+	0.0666587i
$598$	3.71757	−	1.20791i	0.152023	−	0.0493952i
$599$	−11.0652	+	8.03937i	−0.452114	+	0.328480i	−0.790430	−	0.612553i	$-0.790143\pi$
$599$	−11.0652	+	8.03937i	−0.452114	+	0.328480i	0.338316	+	0.941033i	$0.390143\pi$
$600$	−0.00399192	+	5.00000i	−0.000162970	+	0.204124i
$601$	−18.2137	+	13.2330i	−0.742953	+	0.539787i	−0.893635	−	0.448795i	$-0.851853\pi$
$601$	−18.2137	+	13.2330i	−0.742953	+	0.539787i	0.150681	+	0.988582i	$0.451853\pi$
$602$	−3.87202	+	5.32938i	−0.157812	+	0.217209i
$603$	−4.54045	+	1.47528i	−0.184901	+	0.0600781i
$604$	6.24873	+	4.53997i	0.254257	+	0.184729i
$605$	−14.7566	−	7.52627i	−0.599940	−	0.305986i
$606$	−4.12337	−	12.6904i	−0.167500	−	0.515513i
$607$	12.2332	−	16.8376i	0.496532	−	0.683418i	−0.485044	−	0.874490i	$-0.661196\pi$
$607$	12.2332	−	16.8376i	0.496532	−	0.683418i	0.981576	+	0.191072i	$0.0611964\pi$
$608$	−3.47869	−	4.78801i	−0.141080	−	0.194179i
$609$	0.647228	−	1.99196i	0.0262270	−	0.0807184i
$610$	−22.6200	−	22.6380i	−0.915856	−	0.916588i
$611$	9.09216	+	27.9828i	0.367829	+	1.13206i
$612$	4.51407	−	1.46671i	0.182470	−	0.0592882i
$613$	27.1290	+	8.81476i	1.09573	+	0.356025i	0.800458	−	0.599388i	$-0.204589\pi$
$613$	27.1290	+	8.81476i	1.09573	+	0.356025i	0.295273	+	0.955413i	$0.404589\pi$
$614$	11.0550			0.446144
$615$	3.51281	+	22.2364i	0.141650	+	0.896660i
$616$	0.495243	−	1.52420i	0.0199539	−	0.0614118i
$617$	4.49336	−	6.18458i	0.180896	−	0.248982i	−0.708933	−	0.705276i	$-0.750823\pi$
$617$	4.49336	−	6.18458i	0.180896	−	0.248982i	0.889829	+	0.456294i	$0.150823\pi$
$618$	8.34501	+	11.4859i	0.335686	+	0.462032i
$619$	27.8026			1.11748			0.558740	−	0.829343i	$-0.311285\pi$
$619$	27.8026			1.11748			0.558740	+	0.829343i	$0.311285\pi$
$620$	1.07813	−	12.4031i	0.0432986	−	0.498122i
$621$	−1.36979			−0.0549676
$622$	−8.73934	−	12.0287i	−0.350416	−	0.482306i
$623$	1.79330	−	2.46826i	0.0718470	−	0.0988889i
$624$	−0.881825	+	2.71398i	−0.0353013	+	0.108646i
$625$	20.2489	−	14.6623i	0.809955	−	0.586493i
$626$	−33.3172			−1.33162
$627$	−10.6675	−	3.46610i	−0.426021	−	0.138423i
$628$	−17.1288	+	5.56548i	−0.683513	+	0.222087i
$629$	3.71609	+	11.4369i	0.148170	+	0.456021i
$630$	1.33758	−	1.33651i	0.0532903	−	0.0532477i
$631$	−4.74276	+	14.5967i	−0.188806	+	0.581086i	−0.999993	−	0.00370126i	$-0.998822\pi$
$631$	−4.74276	+	14.5967i	−0.188806	+	0.581086i	0.811187	+	0.584787i	$0.198822\pi$
$632$	4.94840	+	6.81089i	0.196837	+	0.270923i
$633$	11.5096	−	15.8416i	0.457465	−	0.629647i
$634$	−6.47175	−	19.9180i	−0.257026	−	0.791045i
$635$	−14.9899	+	29.3903i	−0.594855	+	1.16632i
$636$	−9.43703	−	6.85640i	−0.374203	−	0.271874i
$637$	−17.0572	+	5.54221i	−0.675829	+	0.219590i
$638$	−2.75918	+	3.79768i	−0.109237	+	0.150352i
$639$	−1.41870	+	1.03075i	−0.0561230	+	0.0407758i
$640$	−2.20840	−	0.350680i	−0.0872946	−	0.0138618i
$641$	9.96219	−	7.23795i	0.393483	−	0.285882i	−0.373398	−	0.927671i	$-0.621808\pi$
$641$	9.96219	−	7.23795i	0.393483	−	0.285882i	0.766881	+	0.641789i	$0.221808\pi$
$642$	−5.45330	+	1.77188i	−0.215224	+	0.0699307i
$643$	−30.7728	+	9.99867i	−1.21356	+	0.394309i	−0.844732	−	0.535189i	$-0.820240\pi$
$643$	−30.7728	+	9.99867i	−1.21356	+	0.394309i	−0.368827	+	0.929498i	$0.620240\pi$
$644$	0.357940	−	1.10163i	0.0141048	−	0.0434101i
$645$	17.2059	−	2.71810i	0.677480	−	0.107025i
$646$	28.0905			1.10520
$647$	−28.4261	−	9.23619i	−1.11754	−	0.363112i	−0.308714	−	0.951155i	$-0.599899\pi$
$647$	−28.4261	−	9.23619i	−1.11754	−	0.363112i	−0.808830	+	0.588043i	$0.799899\pi$
$648$	0.587785	−	0.809017i	0.0230904	−	0.0317812i
$649$	0.241682	−	0.175593i	0.00948686	−	0.00689261i
$650$	13.5734	−	4.39829i	0.532393	−	0.172515i
$651$	−3.60379	+	3.02984i	−0.141244	+	0.118749i
$652$			4.07336i			0.159525i
$653$	−9.23460	−	12.7103i	−0.361378	−	0.497394i	0.589154	−	0.808021i	$-0.299461\pi$
$653$	−9.23460	−	12.7103i	−0.361378	−	0.497394i	−0.950532	+	0.310627i	$0.899461\pi$
$654$	9.75859	+	7.09003i	0.381591	+	0.277242i
$655$	5.21329	−	32.8306i	0.203700	−	1.28280i
$656$	−10.0678			−0.393080
$657$			1.47261i			0.0574522i
$658$	8.29212	+	2.69427i	0.323261	+	0.105034i
$659$	−12.4083	−	38.1887i	−0.483358	−	1.48762i	−0.834345	−	0.551242i	$-0.814154\pi$
$659$	−12.4083	−	38.1887i	−0.483358	−	1.48762i	0.350988	−	0.936380i	$-0.385846\pi$
$660$	−3.77672	+	1.92244i	−0.147009	+	0.0748308i
$661$	−25.5646	+	18.5738i	−0.994349	+	0.722437i	−0.960869	−	0.277003i	$-0.910659\pi$
$661$	−25.5646	+	18.5738i	−0.994349	+	0.722437i	−0.0334797	+	0.999439i	$0.510659\pi$
$662$	−1.69493	−	0.550717i	−0.0658755	−	0.0214042i
$663$	−7.96123	−	10.9577i	−0.309189	−	0.425562i
$664$	7.58804	+	5.51303i	0.294473	+	0.213947i
$665$	9.97301	−	5.07649i	0.386737	−	0.196858i
$666$	2.04974	+	1.48923i	0.0794260	+	0.0577064i
$667$	−1.99421	+	2.74480i	−0.0772162	+	0.106279i
$668$	−7.88626	+	2.56240i	−0.305129	+	0.0991423i
$669$	−3.06407	−	2.22617i	−0.118464	−	0.0860688i
$670$	−7.55154	+	7.54552i	−0.291742	+	0.291509i
$671$	8.38184	−	25.7966i	0.323577	−	0.995868i
$672$	0.497043	+	0.684120i	0.0191738	+	0.0263905i
$673$	−31.0826	+	10.0993i	−1.19815	+	0.389301i	−0.839079	−	0.544010i	$-0.816905\pi$
$673$	−31.0826	+	10.0993i	−1.19815	+	0.389301i	−0.359068	+	0.933312i	$0.616905\pi$
$674$	−8.12831	−	25.0164i	−0.313091	−	0.963595i
$675$	−5.00000	−	0.00399192i	−0.192450	−	0.000153649i
$676$	−4.85670			−0.186796
$677$			9.00976i			0.346273i	0.984898	+	0.173137i	$0.0553902\pi$
$677$			9.00976i			0.346273i	−0.984898	+	0.173137i	$0.944610\pi$
$678$	13.7731	+	4.47514i	0.528952	+	0.171867i
$679$	8.71159	+	6.32934i	0.334320	+	0.242898i
$680$	7.50766	−	7.50167i	0.287906	−	0.287676i
$681$	−0.0417047			−0.00159813
$682$	9.78001	−	3.96230i	0.374496	−	0.151724i
$683$		−	25.7267i		−	0.984403i	−0.870481	−	0.492202i	$-0.836192\pi$
$683$		−	25.7267i		−	0.984403i	0.870481	−	0.492202i	$-0.163808\pi$
$684$	4.78801	−	3.47869i	0.183074	−	0.133011i
$685$	10.5725	−	20.7293i	0.403955	−	0.792024i
$686$	−3.47149	+	10.6842i	−0.132542	+	0.407923i
$687$			19.4617i			0.742510i
$688$			7.79011i			0.296995i
$689$	−10.2863	+	31.6580i	−0.391878	+	1.20608i
$690$	−2.72965	+	1.38945i	−0.103916	+	0.0528956i
$691$	1.38132	+	4.25127i	0.0525479	+	0.161726i	0.973887	−	0.227035i	$-0.0729032\pi$
$691$	1.38132	+	4.25127i	0.0525479	+	0.161726i	−0.921339	+	0.388761i	$0.872903\pi$
$692$	−3.18808	−	4.38801i	−0.121192	−	0.166807i
$693$	1.52420	+	0.495243i	0.0578996	+	0.0188127i
$694$	17.3233	−	12.5861i	0.657585	−	0.477763i
$695$	16.8729	+	8.60565i	0.640025	+	0.326431i
$696$	−0.765389	−	2.35562i	−0.0290120	−	0.0892897i
$697$	28.0875	−	38.6591i	1.06389	−	1.46432i
$698$	12.3782	−	17.0371i	0.468521	−	0.644863i
$699$	4.20612	+	12.9451i	0.159090	+	0.489629i
$700$	1.30976	−	4.02011i	0.0495044	−	0.151946i
$701$	−10.4836	+	7.61682i	−0.395962	+	0.287683i	−0.767894	−	0.640577i	$-0.778695\pi$
$701$	−10.4836	+	7.61682i	−0.395962	+	0.287683i	0.371932	+	0.928260i	$0.378695\pi$
$702$	−2.71398	−	0.881825i	−0.102433	−	0.0332823i
$703$	8.81369	+	12.1310i	0.332415	+	0.457530i
$704$	−0.585657	−	1.80247i	−0.0220728	−	0.0679331i
$705$	−10.4587	−	20.5465i	−0.393896	−	0.773827i
$706$	−6.16483	+	18.9734i	−0.232017	+	0.714074i
$707$			11.2835i			0.424361i
$708$			0.157625i			0.00592393i
$709$	5.77429	−	17.7714i	0.216858	−	0.667421i	−0.782158	−	0.623080i	$-0.785881\pi$
$709$	5.77429	−	17.7714i	0.216858	−	0.667421i	0.999016	−	0.0443409i	$-0.0141188\pi$
$710$	−1.78158	+	3.49310i	−0.0668616	+	0.131094i
$711$	−6.81089	+	4.94840i	−0.255428	+	0.185580i
$712$		−	3.60794i		−	0.135213i
$713$	7.06856	−	2.86378i	0.264720	−	0.107249i
$714$	−4.01362			−0.150206
$715$	8.54787	+	8.55470i	0.319672	+	0.319928i
$716$	−6.62591	−	4.81401i	−0.247622	−	0.179908i
$717$	20.3358	+	6.60749i	0.759453	+	0.246761i
$718$			27.0400i			1.00912i
$719$	45.4082			1.69344			0.846720	−	0.532038i	$-0.178574\pi$
$719$	45.4082			1.69344			0.846720	+	0.532038i	$0.178574\pi$
$720$	0.350680	−	2.20840i	0.0130691	−	0.0823022i
$721$	−3.70993	−	11.4180i	−0.138165	−	0.425228i
$722$	15.2419	−	4.95240i	0.567246	−	0.184309i
$723$	−1.26426	−	1.74011i	−0.0470184	−	0.0647153i
$724$	2.65109	−	8.15922i	0.0985271	−	0.303235i
$725$	−7.28728	+	10.0133i	−0.270643	+	0.371883i
$726$	5.99329	+	4.35438i	0.222432	+	0.161606i
$727$	−49.7149	+	16.1534i	−1.84383	+	0.599095i	−0.846000	+	0.533183i	$0.820996\pi$
$727$	−49.7149	+	16.1534i	−1.84383	+	0.599095i	−0.997825	+	0.0659118i	$0.979004\pi$
$728$	1.41838	−	1.95224i	0.0525688	−	0.0723547i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	1.49376	+	2.93456i	0.0552865	+	0.108613i
$731$	−29.9132	−	21.7332i	−1.10638	−	0.803832i
$732$	8.41229	+	11.5785i	0.310927	+	0.427955i
$733$	2.67464	+	0.869044i	0.0987901	+	0.0320989i	0.357995	−	0.933724i	$-0.383460\pi$
$733$	2.67464	+	0.869044i	0.0987901	+	0.0320989i	−0.259205	+	0.965822i	$0.583460\pi$
$734$	−15.6898	+	11.3993i	−0.579122	+	0.420757i
$735$	12.5243	−	6.37517i	0.461967	−	0.235152i
$736$	−0.423287	−	1.30274i	−0.0156026	−	0.0480198i
$737$	−8.60518	−	2.79599i	−0.316976	−	0.102992i
$738$		−	10.0678i		−	0.370599i
$739$	−22.6570			−0.833450			−0.416725	−	0.909033i	$-0.636822\pi$
$739$	−22.6570			−0.833450			−0.416725	+	0.909033i	$0.636822\pi$
$740$	5.59525	+	0.888490i	0.205685	+	0.0326616i
$741$	−13.6633	−	9.92695i	−0.501933	−	0.364676i
$742$	5.79791	+	7.98014i	0.212848	+	0.292960i
$743$		−	10.1039i		−	0.370675i	−0.982675	−	0.185337i	$-0.940662\pi$
$743$		−	10.1039i		−	0.370675i	0.982675	−	0.185337i	$-0.0593378\pi$
$744$	−1.34178	+	5.40367i	−0.0491920	+	0.198108i
$745$	−14.7652	+	2.33254i	−0.540957	+	0.0854578i
$746$	−29.0247	+	21.0877i	−1.06267	+	0.772076i
$747$	−5.51303	+	7.58804i	−0.201711	+	0.277632i
$748$	8.55518	+	2.77975i	0.312808	+	0.101638i
$749$	4.84873			0.177169
$750$	−9.96783	+	5.06383i	−0.363974	+	0.184905i
$751$	−9.99155	+	30.7508i	−0.364597	+	1.12211i	0.585636	+	0.810574i	$0.300845\pi$
$751$	−9.99155	+	30.7508i	−0.364597	+	1.12211i	−0.950233	+	0.311540i	$0.899155\pi$
$752$	9.80598	−	3.18615i	0.357587	−	0.116187i
$753$	12.2630	−	3.98449i	0.446889	−	0.145203i
$754$	−5.71818	+	4.15450i	−0.208244	+	0.151298i
$755$	−2.70860	+	17.0574i	−0.0985761	+	0.620781i
$756$	−0.684120	+	0.497043i	−0.0248812	+	0.0180773i
$757$	23.1088	−	31.8065i	0.839904	−	1.15603i	−0.146094	−	0.989271i	$-0.546670\pi$
$757$	23.1088	−	31.8065i	0.839904	−	1.15603i	0.985998	−	0.166758i	$-0.0533297\pi$
$758$	18.0588	−	5.86765i	0.655924	−	0.213122i
$759$	−2.10025	−	1.52592i	−0.0762344	−	0.0553875i
$760$	6.01269	−	11.7889i	0.218103	−	0.427630i
$761$	−6.60332	−	20.3229i	−0.239370	−	0.736706i	−0.996512	−	0.0834549i	$-0.973405\pi$
$761$	−6.60332	−	20.3229i	−0.239370	−	0.736706i	0.757141	−	0.653251i	$-0.226595\pi$
$762$	8.67252	−	11.9367i	0.314172	−	0.432421i
$763$	−5.99547	−	8.25205i	−0.217051	−	0.298744i
$764$	−3.04086	+	9.35879i	−0.110014	+	0.338589i
$765$	7.50167	+	7.50766i	0.271224	+	0.271440i
$766$	10.0375	+	30.8922i	0.362669	+	1.11618i
$767$	0.427792	−	0.138998i	0.0154467	−	0.00501893i
$768$	0.951057	+	0.309017i	0.0343183	+	0.0111507i
$769$	2.69389			0.0971440			0.0485720	−	0.998820i	$-0.484533\pi$
$769$	2.69389			0.0971440			0.0485720	+	0.998820i	$0.484533\pi$
$770$	3.53972	−	0.559188i	0.127563	−	0.0201517i
$771$	−1.23361	+	3.79665i	−0.0444272	+	0.136733i
$772$	−2.10441	+	2.89647i	−0.0757393	+	0.104246i
$773$	−9.09956	−	12.5245i	−0.327288	−	0.450474i	0.613387	−	0.789783i	$-0.289807\pi$
$773$	−9.09956	−	12.5245i	−0.327288	−	0.450474i	−0.940675	+	0.339309i	$0.889807\pi$
$774$	−7.79011			−0.280010
$775$	25.8100	−	10.4328i	0.927123	−	0.374756i
$776$	12.7340			0.457124
$777$	−1.25932	−	1.73330i	−0.0451778	−	0.0621819i
$778$	2.29765	−	3.16244i	0.0823747	−	0.113379i
$779$	18.4125	−	56.6678i	0.659696	−	2.03033i
$780$	−6.30279	+	0.995684i	−0.225676	+	0.0356512i
$781$	−3.32350			−0.118924
$782$	6.18331	+	2.00908i	0.221115	+	0.0718445i
$783$	2.35562	−	0.765389i	0.0841831	−	0.0273528i
$784$	1.94215	+	5.97732i	0.0693625	+	0.213476i
$785$	−28.4654	−	28.4881i	−1.01597	−	1.01678i
$786$	−4.59393	+	14.1387i	−0.163860	+	0.504309i
$787$	−12.3416	−	16.9867i	−0.439929	−	0.605511i	0.530267	−	0.847831i	$-0.322092\pi$
$787$	−12.3416	−	16.9867i	−0.439929	−	0.605511i	−0.970196	+	0.242320i	$0.922092\pi$
$788$	2.93250	−	4.03624i	0.104466	−	0.143785i
$789$	−6.50026	−	20.0057i	−0.231415	−	0.712223i
$790$	−8.55299	+	16.7696i	−0.304302	+	0.596637i
$791$	−9.90734	−	7.19811i	−0.352265	−	0.255935i
$792$	1.80247	−	0.585657i	0.0640479	−	0.0208104i
$793$	24.0057	−	33.0410i	0.852468	−	1.17332i
$794$	3.05816	−	2.22189i	0.108530	−	0.0788518i
$795$	4.09061	−	25.7605i	0.145079	−	0.913633i
$796$	4.26402	−	3.09799i	0.151134	−	0.109805i
$797$	−14.9384	+	4.85379i	−0.529147	+	0.171930i	−0.561392	−	0.827550i	$-0.689734\pi$
$797$	−14.9384	+	4.85379i	−0.529147	+	0.171930i	0.0322456	+	0.999480i	$0.489734\pi$
$798$	−4.75969	+	1.54652i	−0.168491	+	0.0547461i
$799$	−15.1227	+	46.5428i	−0.535002	+	1.64657i
$800$	−1.54129	−	4.75651i	−0.0544928	−	0.168168i
$801$	3.60794			0.127480
$802$	36.5740	+	11.8836i	1.29147	+	0.419625i
$803$	−1.64047	+	2.25792i	−0.0578910	+	0.0796802i
$804$	3.86234	−	2.80615i	0.136214	−	0.0989653i
$805$	2.55835	−	0.404156i	0.0901700	−	0.0142446i
$806$	15.8487	−	1.12353i	0.558245	−	0.0395748i
$807$			29.7265i			1.04642i
$808$	7.84312	+	10.7951i	0.275920	+	0.379771i
$809$	20.5779	+	14.9507i	0.723481	+	0.525640i	0.887494	−	0.460818i	$-0.152444\pi$
$809$	20.5779	+	14.9507i	0.723481	+	0.525640i	−0.164013	+	0.986458i	$0.552444\pi$
$810$	2.20840	+	0.350680i	0.0775952	+	0.0123216i
$811$	1.21047			0.0425053			0.0212526	−	0.999774i	$-0.493235\pi$
$811$	1.21047			0.0425053			0.0212526	+	0.999774i	$0.493235\pi$
$812$			2.09447i			0.0735016i
$813$	−27.3271	−	8.87912i	−0.958404	−	0.311404i
$814$	1.48383	+	4.56677i	0.0520084	+	0.160065i
$815$	−8.11721	+	4.13184i	−0.284333	+	0.144732i
$816$	−3.83989	+	2.78985i	−0.134423	+	0.0976641i
$817$	−43.8478	−	14.2470i	−1.53404	−	0.498439i
$818$	15.7486	+	21.6760i	0.550636	+	0.757885i
$819$	1.95224	+	1.41838i	0.0682167	+	0.0495623i
$820$	−10.2123	−	20.0626i	−0.356629	−	0.700616i
$821$	−28.5909	−	20.7725i	−0.997829	−	0.724965i	−0.0362070	−	0.999344i	$-0.511528\pi$
$821$	−28.5909	−	20.7725i	−0.997829	−	0.724965i	−0.961622	+	0.274379i	$0.911528\pi$
$822$	−6.11681	+	8.41907i	−0.213348	+	0.293649i
$823$	18.5944	−	6.04167i	0.648158	−	0.210599i	0.0335565	−	0.999437i	$-0.489317\pi$
$823$	18.5944	−	6.04167i	0.648158	−	0.210599i	0.614602	+	0.788837i	$0.289317\pi$
$824$	−11.4859	−	8.34501i	−0.400131	−	0.290712i
$825$	−7.66190	−	5.57605i	−0.266753	−	0.194133i
$826$	0.0411892	−	0.126767i	0.00143316	−	0.00441080i
$827$	0.607721	+	0.836457i	0.0211325	+	0.0290864i	0.819453	−	0.573147i	$-0.194278\pi$
$827$	0.607721	+	0.836457i	0.0211325	+	0.0290864i	−0.798320	+	0.602233i	$0.794278\pi$
$828$	1.30274	−	0.423287i	0.0452735	−	0.0147102i
$829$	14.1261	+	43.4758i	0.490621	+	1.50998i	0.823672	+	0.567067i	$0.191922\pi$
$829$	14.1261	+	43.4758i	0.490621	+	1.50998i	−0.333051	+	0.942909i	$0.608078\pi$
$830$	−3.28914	+	20.7133i	−0.114168	+	0.718969i
$831$	−11.4572			−0.397447
$832$		−	2.85365i		−	0.0989324i
$833$	−28.3706	−	9.21816i	−0.982982	−	0.319390i
$834$	−6.85282	−	4.97887i	−0.237294	−	0.172404i
$835$	−13.1057	−	13.1162i	−0.453543	−	0.453905i
$836$	11.2165			0.387932
$837$	−5.40367	−	1.34178i	−0.186778	−	0.0463786i
$838$			6.62651i			0.228909i
$839$	−16.2368	+	11.7967i	−0.560557	+	0.407268i	−0.831663	−	0.555281i	$-0.812611\pi$
$839$	−16.2368	+	11.7967i	−0.560557	+	0.407268i	0.271106	+	0.962550i	$0.412611\pi$
$840$	−0.859106	+	1.68443i	−0.0296420	+	0.0581183i
$841$	−7.06574	+	21.7461i	−0.243646	+	0.749866i
$842$			22.2296i			0.766083i
$843$			1.31860i			0.0454151i
$844$	−6.05095	+	18.6229i	−0.208282	+	0.641027i
$845$	−4.92644	−	9.67822i	−0.169475	−	0.332941i
$846$	3.18615	+	9.80598i	0.109542	+	0.337136i
$847$	−3.68215	−	5.06804i	−0.126520	−	0.174140i
$848$	11.0939	+	3.60462i	0.380966	+	0.123783i
$849$	−2.49033	+	1.80933i	−0.0854678	+	0.0620960i
$850$	22.5645	+	7.35156i	0.773955	+	0.252156i
$851$	1.07245	+	3.30066i	0.0367631	+	0.113145i
$852$	1.03075	−	1.41870i	0.0353128	−	0.0486040i
$853$	−26.0309	+	35.8284i	−0.891281	+	1.22674i	0.0818860	+	0.996642i	$0.473906\pi$
$853$	−26.0309	+	35.8284i	−0.891281	+	1.22674i	−0.973167	+	0.230101i	$0.926094\pi$
$854$	−3.73984	−	11.5100i	−0.127975	−	0.393865i
$855$	11.7889	+	6.01269i	0.403173	+	0.205630i
$856$	4.63885	−	3.37032i	0.158553	−	0.115195i
$857$	43.5596	+	14.1534i	1.48797	+	0.483470i	0.936483	−	0.350714i	$-0.114061\pi$
$857$	43.5596	+	14.1534i	1.48797	+	0.483470i	0.551486	+	0.834184i	$0.314061\pi$
$858$	−3.17892	−	4.37541i	−0.108527	−	0.149374i
$859$	−0.334698	−	1.03009i	−0.0114197	−	0.0351463i	0.945184	−	0.326537i	$-0.105882\pi$
$859$	−0.334698	−	1.03009i	−0.0114197	−	0.0351463i	−0.956604	+	0.291391i	$0.905882\pi$
$860$	−15.5238	+	7.90197i	−0.529357	+	0.269455i
$861$	−2.63081	+	8.09681i	−0.0896579	+	0.275939i
$862$		−	27.3678i		−	0.932150i
$863$		−	36.7984i		−	1.25263i	−0.779569	−	0.626317i	$-0.784562\pi$
$863$		−	36.7984i		−	1.25263i	0.779569	−	0.626317i	$-0.215438\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	5.51038	−	10.8041i	0.187359	−	0.367349i
$866$	−28.0012	+	20.3441i	−0.951520	+	0.691320i
$867$		−	5.52803i		−	0.187742i
$868$	2.49114	−	3.99518i	0.0845547	−	0.135605i
$869$	−15.9554			−0.541249
$870$	3.91781	−	3.91468i	0.132826	−	0.132720i
$871$	−11.0217	−	8.00777i	−0.373458	−	0.271333i
$872$	−11.4719	−	3.72745i	−0.388488	−	0.126227i
$873$			12.7340i			0.430981i
$874$	8.10681			0.274217
$875$	9.33968	−	1.46780i	0.315739	−	0.0496206i
$876$	−0.455063	−	1.40054i	−0.0153752	−	0.0473199i
$877$	−46.2968	+	15.0427i	−1.56333	+	0.507957i	−0.957695	−	0.287785i	$-0.907081\pi$
$877$	−46.2968	+	15.0427i	−1.56333	+	0.507957i	−0.605636	+	0.795742i	$0.707081\pi$
$878$	−5.55495	−	7.64574i	−0.187471	−	0.258031i
$879$	−0.696875	+	2.14476i	−0.0235050	+	0.0723409i
$880$	2.99781	−	2.99542i	0.101056	−	0.100976i
$881$	19.4456	+	14.1280i	0.655137	+	0.475985i	0.865017	−	0.501742i	$-0.167307\pi$
$881$	19.4456	+	14.1280i	0.655137	+	0.475985i	−0.209880	+	0.977727i	$0.567307\pi$
$882$	−5.97732	+	1.94215i	−0.201267	+	0.0653956i
$883$	8.29080	−	11.4113i	0.279008	−	0.384021i	−0.646397	−	0.763001i	$-0.723725\pi$
$883$	8.29080	−	11.4113i	0.279008	−	0.384021i	0.925405	+	0.378980i	$0.123725\pi$
$884$	10.9577	+	7.96123i	0.368547	+	0.267765i
$885$	−0.314109	+	0.159889i	−0.0105587	+	0.00537460i
$886$	−11.2026	−	8.13920i	−0.376360	−	0.273442i
$887$	−4.35536	−	5.99465i	−0.146239	−	0.201280i	0.729613	−	0.683860i	$-0.239700\pi$
$887$	−4.35536	−	5.99465i	−0.146239	−	0.201280i	−0.875852	+	0.482579i	$0.839700\pi$
$888$	−2.40962	−	0.782933i	−0.0808615	−	0.0262735i
$889$	−10.0939	+	7.33365i	−0.338539	+	0.245963i
$890$	7.18974	−	3.65974i	0.241001	−	0.122675i
$891$	0.585657	+	1.80247i	0.0196203	+	0.0603849i
$892$	3.60202	+	1.17037i	0.120605	+	0.0391868i
$893$			61.0213i			2.04200i
$894$	6.68511			0.223583
$895$	2.87209	−	18.0870i	0.0960035	−	0.604580i
$896$	−0.684120	−	0.497043i	−0.0228549	−	0.0166050i
$897$	−2.29759	−	3.16236i	−0.0767141	−	0.105588i
$898$		−	4.40229i		−	0.146906i
$899$	−10.5556	+	8.87451i	−0.352050	+	0.295981i
$900$	4.75651	−	1.54129i	0.158550	−	0.0513763i
$901$	−44.7916	+	32.5430i	−1.49223	+	1.08417i
$902$	11.2153	−	15.4366i	0.373430	−	0.513983i
$903$	6.26506	+	2.03564i	0.208488	+	0.0677419i
$904$	−14.4819			−0.481660
$905$	18.9485	−	2.99339i	0.629869	−	0.0995038i
$906$	2.38680	−	7.34583i	0.0792962	−	0.244049i
$907$	−20.1131	+	6.53514i	−0.667844	+	0.216996i	−0.623266	−	0.782010i	$-0.714195\pi$
$907$	−20.1131	+	6.53514i	−0.667844	+	0.216996i	−0.0445786	+	0.999006i	$0.514195\pi$
$908$	0.0396635	−	0.0128875i	0.00131628	−	0.000427686i
$909$	−10.7951	+	7.84312i	−0.358052	+	0.260140i
$910$	5.32908	+	0.846225i	0.176657	+	0.0280521i
$911$	−23.9321	+	17.3877i	−0.792905	+	0.576079i	−0.908824	−	0.417179i	$-0.863019\pi$
$911$	−23.9321	+	17.3877i	−0.792905	+	0.576079i	0.115919	+	0.993259i	$0.463019\pi$
$912$	−3.47869	+	4.78801i	−0.115191	+	0.158547i
$913$	−16.9059	+	5.49308i	−0.559505	+	0.181794i
$914$	−5.43916	−	3.95178i	−0.179911	−	0.130713i
$915$	−14.5401	+	28.5084i	−0.480681	+	0.942459i
$916$	−6.01399	−	18.5092i	−0.198708	−	0.611560i
$917$	7.38916	−	10.1703i	0.244012	−	0.335853i
$918$	−2.78985	−	3.83989i	−0.0920786	−	0.126735i
$919$	0.448635	−	1.38076i	0.0147991	−	0.0455470i	−0.943384	−	0.331702i	$-0.892377\pi$
$919$	0.448635	−	1.38076i	0.0147991	−	0.0455470i	0.958183	+	0.286155i	$0.0923772\pi$
$920$	2.16669	−	2.16496i	0.0714336	−	0.0713765i
$921$	−3.41619	−	10.5139i	−0.112567	−	0.346446i
$922$	−13.4048	+	4.35547i	−0.441462	+	0.143440i
$923$	−4.75927	−	1.54638i	−0.156653	−	0.0508997i
$924$	−1.60264			−0.0527230
$925$	3.90504	+	12.0512i	0.128397	+	0.396242i
$926$	−11.4534	+	35.2498i	−0.376381	+	1.15838i
$927$	8.34501	−	11.4859i	0.274086	−	0.377247i
$928$	1.45586	+	2.00381i	0.0477908	+	0.0657784i
$929$	−13.4044			−0.439785			−0.219893	−	0.975524i	$-0.570571\pi$
$929$	−13.4044			−0.439785			−0.219893	+	0.975524i	$0.570571\pi$
$930$	−12.1292	+	2.80742i	−0.397733	+	0.0920589i
$931$	−37.1961			−1.21905
$932$	−8.00051	−	11.0118i	−0.262065	−	0.360702i
$933$	−8.73934	+	12.0287i	−0.286113	+	0.393801i
$934$	3.11553	−	9.58861i	0.101943	−	0.313749i
$935$	3.13866	+	19.8680i	0.102645	+	0.649754i
$936$	2.85365			0.0932743
$937$	46.2496	+	15.0274i	1.51091	+	0.490923i	0.943177	−	0.332291i	$-0.107822\pi$
$937$	46.2496	+	15.0274i	1.51091	+	0.490923i	0.567730	+	0.823215i	$0.307822\pi$
$938$	−3.83949	+	1.24753i	−0.125364	+	0.0407332i
$939$	10.2956	+	31.6865i	0.335983	+	1.03405i
$940$	16.2960	+	16.3090i	0.531517	+	0.531942i
$941$	−8.75149	+	26.9343i	−0.285290	+	0.878034i	0.701021	+	0.713141i	$0.252728\pi$
$941$	−8.75149	+	26.9343i	−0.285290	+	0.878034i	−0.986311	+	0.164893i	$0.947272\pi$
$942$	10.5862	+	14.5706i	0.344916	+	0.474736i
$943$	8.10596	−	11.1569i	0.263966	−	0.363318i
$944$	−0.0487089	−	0.149911i	−0.00158534	−	0.00487918i
$945$	−1.68443	−	0.859106i	−0.0547944	−	0.0279467i
$946$	−11.9444	−	8.67808i	−0.388344	−	0.282149i
$947$	43.8105	−	14.2349i	1.42365	−	0.462572i	0.506891	−	0.862010i	$-0.330795\pi$
$947$	43.8105	−	14.2349i	1.42365	−	0.462572i	0.916760	+	0.399438i	$0.130795\pi$
$948$	4.94840	−	6.81089i	0.160717	−	0.221207i
$949$	−3.39975	+	2.47006i	−0.110361	+	0.0801816i
$950$	29.5915	+	0.0236254i	0.960075	+	0.000766510i
$951$	−16.9433	+	12.3100i	−0.549423	+	0.399179i
$952$	3.81718	−	1.24028i	0.123716	−	0.0401976i
$953$	16.3359	−	5.30785i	0.529171	−	0.171938i	−0.0322325	−	0.999480i	$-0.510262\pi$
$953$	16.3359	−	5.30785i	0.529171	−	0.171938i	0.561403	+	0.827542i	$0.310262\pi$
$954$	−3.60462	+	11.0939i	−0.116704	+	0.359178i
$955$	−21.7343	+	3.43348i	−0.703306	+	0.111105i
$956$	−21.3823			−0.691552
$957$	4.46444	+	1.45059i	0.144315	+	0.0468908i
$958$	5.67243	−	7.80743i	0.183268	−	0.252247i
$959$	7.11932	−	5.17249i	0.229895	−	0.167028i
$960$	0.348916	+	2.20868i	0.0112612	+	0.0712848i
$961$	30.6900	−	4.37329i	0.989999	−	0.141074i
$962$			7.23007i			0.233107i
$963$	3.37032	+	4.63885i	0.108607	+	0.149485i
$964$	1.74011	+	1.26426i	0.0560451	+	0.0407191i
$965$	−7.90658	−	1.25552i	−0.254522	−	0.0404165i
$966$	−1.15832			−0.0372683
$967$			8.81140i			0.283355i	0.989913	+	0.141678i	$0.0452497\pi$
$967$			8.81140i			0.283355i	−0.989913	+	0.141678i	$0.954750\pi$
$968$	−7.04554	−	2.28923i	−0.226452	−	0.0735788i
$969$	−8.68043	−	26.7156i	−0.278855	−	0.858229i
$970$	12.9168	+	25.3758i	0.414735	+	0.814767i
$971$	−46.4191	+	33.7255i	−1.48966	+	1.08230i	−0.515380	+	0.856962i	$0.672349\pi$
$971$	−46.4191	+	33.7255i	−1.48966	+	1.08230i	−0.974280	+	0.225340i	$0.927651\pi$
$972$	−0.951057	−	0.309017i	−0.0305052	−	0.00991172i
$973$	4.21023	+	5.79488i	0.134974	+	0.185775i
$974$	−6.73524	−	4.89344i	−0.215811	−	0.156796i
$975$	−8.37744	−	11.5499i	−0.268293	−	0.369894i
$976$	−11.5785	−	8.41229i	−0.370620	−	0.269271i
$977$	−15.2882	+	21.0424i	−0.489112	+	0.673205i	−0.980224	−	0.197892i	$-0.936591\pi$
$977$	−15.2882	+	21.0424i	−0.489112	+	0.673205i	0.491112	+	0.871096i	$0.336591\pi$
$978$	3.87399	−	1.25874i	0.123877	−	0.0402499i
$979$	5.53194	+	4.01919i	0.176802	+	0.128454i
$980$	−9.94131	+	9.93338i	−0.317563	+	0.317310i
$981$	3.72745	−	11.4719i	0.119008	−	0.366270i
$982$	22.8515	+	31.4524i	0.729221	+	1.00369i
$983$	3.29215	−	1.06968i	0.105003	−	0.0341176i	−0.256044	−	0.966665i	$-0.582419\pi$
$983$	3.29215	−	1.06968i	0.105003	−	0.0341176i	0.361047	+	0.932547i	$0.382419\pi$
$984$	3.11111	+	9.57501i	0.0991785	+	0.305240i
$985$	11.0178	+	1.74956i	0.351058	+	0.0557457i
$986$	−11.7560			−0.374389
$987$		−	8.71885i		−	0.277524i
$988$	16.0621	+	5.21891i	0.511005	+	0.166036i
$989$	−8.63285	−	6.27214i	−0.274509	−	0.199442i
$990$	2.99542	+	2.99781i	0.0952007	+	0.0952767i
$991$	−0.976881			−0.0310316			−0.0155158	−	0.999880i	$-0.504939\pi$
$991$	−0.976881			−0.0310316			−0.0155158	+	0.999880i	$0.504939\pi$
$992$	−0.393719	−	5.55383i	−0.0125006	−	0.176334i
$993$			1.78216i			0.0565551i
$994$	−1.19968	+	0.871621i	−0.0380516	+	0.0276461i
$995$	10.4988	+	5.35468i	0.332834	+	0.169755i
$996$	2.89837	−	8.92028i	0.0918385	−	0.282650i
$997$		−	8.34420i		−	0.264263i	−0.991232	−	0.132132i	$-0.957818\pi$
$997$		−	8.34420i		−	0.264263i	0.991232	−	0.132132i	$-0.0421822\pi$
$998$			16.4533i			0.520819i
$999$	0.782933	−	2.40962i	0.0247709	−	0.0762370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.z.d.109.10	yes	72
5.4	even	2	inner	930.2.z.d.109.1	✓	72
31.2	even	5	inner	930.2.z.d.529.1	yes	72
155.64	even	10	inner	930.2.z.d.529.10	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.d.109.1	✓	72	5.4	even	2	inner
930.2.z.d.109.10	yes	72	1.1	even	1	trivial
930.2.z.d.529.1	yes	72	31.2	even	5	inner
930.2.z.d.529.10	yes	72	155.64	even	10	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-2.20868 + 0.348916i) q^{5} +1.00000 q^{6} +(-0.804232 - 0.261311i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-2.20868 + 0.348916i) q^{5} +1.00000 q^{6} +(-0.804232 - 0.261311i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(-1.58051 - 1.58177i) q^{10} +(0.585657 - 1.80247i) q^{11} +(0.587785 + 0.809017i) q^{12} +(1.67733 - 2.30865i) q^{13} +(-0.261311 - 0.804232i) q^{14} +(-1.01595 + 1.99195i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.51407 - 1.46671i) q^{17} +(0.587785 - 0.809017i) q^{18} +(4.78801 - 3.47869i) q^{19} +(0.350680 - 2.20840i) q^{20} +(-0.684120 + 0.497043i) q^{21} +(1.80247 - 0.585657i) q^{22} +(1.30274 - 0.423287i) q^{23} +(-0.309017 + 0.951057i) q^{24} +(4.75651 - 1.54129i) q^{25} +2.85365 q^{26} +(-0.951057 - 0.309017i) q^{27} +(0.497043 - 0.684120i) q^{28} +(-2.00381 + 1.45586i) q^{29} +(-2.20868 + 0.348916i) q^{30} +(5.55383 - 0.393719i) q^{31} -1.00000i q^{32} +(-1.11399 - 1.53327i) q^{33} +(3.83989 + 2.78985i) q^{34} +(1.86746 + 0.296542i) q^{35} +1.00000 q^{36} +2.53362i q^{37} +(5.62864 + 1.82886i) q^{38} +(-0.881825 - 2.71398i) q^{39} +(1.99276 - 1.01436i) q^{40} +(8.14499 - 5.91768i) q^{41} +(-0.804232 - 0.261311i) q^{42} +(-4.57891 - 6.30234i) q^{43} +(1.53327 + 1.11399i) q^{44} +(1.01436 + 1.99276i) q^{45} +(1.10818 + 0.805140i) q^{46} +(-6.06043 + 8.34146i) q^{47} +(-0.951057 + 0.309017i) q^{48} +(-5.08461 - 3.69419i) q^{49} +(4.04274 + 2.94215i) q^{50} +(1.46671 - 4.51407i) q^{51} +(1.67733 + 2.30865i) q^{52} +(-11.0939 + 3.60462i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-0.664618 + 4.18542i) q^{55} +0.845619 q^{56} -5.91830i q^{57} +(-2.35562 - 0.765389i) q^{58} +(0.127522 + 0.0926499i) q^{59} +(-1.58051 - 1.58177i) q^{60} +14.3118 q^{61} +(3.58298 + 4.26172i) q^{62} +0.845619i q^{63} +(0.809017 - 0.587785i) q^{64} +(-2.89916 + 5.68431i) q^{65} +(0.585657 - 1.80247i) q^{66} -4.77411i q^{67} +4.74637i q^{68} +(0.423287 - 1.30274i) q^{69} +(0.857761 + 1.68511i) q^{70} +(-0.541896 - 1.66779i) q^{71} +(0.587785 + 0.809017i) q^{72} +(-1.40054 - 0.455063i) q^{73} +(-2.04974 + 1.48923i) q^{74} +(1.54888 - 4.75405i) q^{75} +(1.82886 + 5.62864i) q^{76} +(-0.942008 + 1.29656i) q^{77} +(1.67733 - 2.30865i) q^{78} +(-2.60153 - 8.00668i) q^{79} +(1.99195 + 1.01595i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(9.57501 + 3.11111i) q^{82} +(-5.51303 - 7.58804i) q^{83} +(-0.261311 - 0.804232i) q^{84} +(-9.45836 + 4.81452i) q^{85} +(2.40728 - 7.40884i) q^{86} +2.47685i q^{87} +1.89523i q^{88} +(-1.11491 + 3.43135i) q^{89} +(-1.01595 + 1.99195i) q^{90} +(-1.95224 + 1.41838i) q^{91} +1.36979i q^{92} +(2.94593 - 4.72456i) q^{93} -10.3106 q^{94} +(-9.36139 + 9.35392i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(-12.1108 - 3.93502i) q^{97} -6.28493i q^{98} -1.89523 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9}+O(q^{10}) \) 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9	\( 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9} - 6 q^{11} - 4 q^{14} - 18 q^{16} + 12 q^{19} - 4 q^{20} - 16 q^{21} + 18 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} + 4 q^{30} + 22 q^{31} + 14 q^{34} - 22 q^{35} + 72 q^{36} + 8 q^{39} - 28 q^{41} - 4 q^{44} - 4 q^{45} - 22 q^{46} + 42 q^{49} - 32 q^{50} - 4 q^{51} + 18 q^{54} + 14 q^{55} + 24 q^{56} - 28 q^{59} + 56 q^{61} + 18 q^{64} + 46 q^{65} - 6 q^{66} - 8 q^{69} + 46 q^{70} - 68 q^{71} + 8 q^{74} + 32 q^{75} - 12 q^{76} + 26 q^{79} - 6 q^{80} - 18 q^{81} - 4 q^{84} - 32 q^{85} + 80 q^{86} + 32 q^{89} - 44 q^{91} + 12 q^{94} + 74 q^{95} - 18 q^{96} - 4 q^{99}+O(q^{100}) \) 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9 - 6 * q^11 - 4 * q^14 - 18 * q^16 + 12 * q^19 - 4 * q^20 - 16 * q^21 + 18 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 + 4 * q^30 + 22 * q^31 + 14 * q^34 - 22 * q^35 + 72 * q^36 + 8 * q^39 - 28 * q^41 - 4 * q^44 - 4 * q^45 - 22 * q^46 + 42 * q^49 - 32 * q^50 - 4 * q^51 + 18 * q^54 + 14 * q^55 + 24 * q^56 - 28 * q^59 + 56 * q^61 + 18 * q^64 + 46 * q^65 - 6 * q^66 - 8 * q^69 + 46 * q^70 - 68 * q^71 + 8 * q^74 + 32 * q^75 - 12 * q^76 + 26 * q^79 - 6 * q^80 - 18 * q^81 - 4 * q^84 - 32 * q^85 + 80 * q^86 + 32 * q^89 - 44 * q^91 + 12 * q^94 + 74 * q^95 - 18 * q^96 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more