LMFDB - Embedded newform 726.2.h.f.233.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [726,2,Mod(161,726)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(726, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7]))

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

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

chi := DirichletCharacter("726.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.h (of order $10$, degree $4$, not 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:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.185640625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + x^{6} + x^{5} + 4x^{4} + 3x^{3} + 9x^{2} - 81x + 81 $ x^8 - 3x^7 + x^6 + x^5 + 4x^4 + 3x^3 + 9x^2 - 81*x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			233.2
Root			$-1.52536 - 0.820539i$ of defining polynomial
Character	$\chi$	$=$	726.233
Dual form			726.2.h.f.215.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(1.52536 - 0.820539i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(2.52536 - 0.820539i) q^{5} +(0.309017 + 1.70426i) q^{6} +(0.964601 - 1.32766i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.65343 - 2.50323i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(1.52536 - 0.820539i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(2.52536 - 0.820539i) q^{5} +(0.309017 + 1.70426i) q^{6} +(0.964601 - 1.32766i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.65343 - 2.50323i) q^{9} +2.65532i q^{10} +(-1.71634 - 0.232753i) q^{12} +(-1.43268 - 0.465507i) q^{13} +(0.964601 + 1.32766i) q^{14} +(3.17879 - 3.32377i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.09831 + 6.45792i) q^{17} +(1.86977 + 2.34605i) q^{18} +(-3.22603 - 4.44024i) q^{19} +(-2.52536 - 0.820539i) q^{20} +(0.381966 - 2.81665i) q^{21} -4.78856i q^{23} +(0.751740 - 1.56041i) q^{24} +(1.65906 - 1.20538i) q^{25} +(0.885446 - 1.21871i) q^{26} +(0.468081 - 5.17503i) q^{27} +(-1.56076 + 0.507121i) q^{28} +(0.375405 + 0.272747i) q^{29} +(2.17879 + 4.05031i) q^{30} +(-1.60451 + 4.93818i) q^{31} -1.00000 q^{32} -6.79026 q^{34} +(1.34657 - 4.14431i) q^{35} +(-2.80902 + 1.05329i) q^{36} +(-0.814648 - 0.591876i) q^{37} +(5.21982 - 1.69602i) q^{38} +(-2.56732 + 0.465507i) q^{39} +(1.56076 - 2.14820i) q^{40} +(-1.27362 + 0.925338i) q^{41} +(2.56076 + 1.23366i) q^{42} -3.42500i q^{43} +(2.12151 - 7.67826i) q^{45} +(4.55420 + 1.47975i) q^{46} +(5.88545 + 8.10062i) q^{47} +(1.25174 + 1.19714i) q^{48} +(1.33089 + 4.09607i) q^{49} +(0.633706 + 1.95035i) q^{50} +(8.49964 + 8.12890i) q^{51} +(0.885446 + 1.21871i) q^{52} +(-9.34406 - 3.03607i) q^{53} +(4.77710 + 2.04434i) q^{54} -1.64108i q^{56} +(-8.56424 - 4.12588i) q^{57} +(-0.375405 + 0.272747i) q^{58} +(-3.59268 + 4.94489i) q^{59} +(-4.52536 + 0.820539i) q^{60} +(13.2229 - 4.29640i) q^{61} +(-4.20067 - 3.05196i) q^{62} +(-1.72853 - 4.60981i) q^{63} +(0.309017 - 0.951057i) q^{64} -4.00000 q^{65} +11.7972 q^{67} +(2.09831 - 6.45792i) q^{68} +(-3.92920 - 7.30427i) q^{69} +(3.52536 + 2.56132i) q^{70} +(-0.854102 + 0.277515i) q^{71} +(-0.133706 - 2.99702i) q^{72} +(-2.71982 + 3.74351i) q^{73} +(0.814648 - 0.591876i) q^{74} +(1.54160 - 3.19996i) q^{75} +5.48844i q^{76} +(0.350622 - 2.58551i) q^{78} +(3.02188 + 0.981868i) q^{79} +(1.56076 + 2.14820i) q^{80} +(-3.53232 - 8.27785i) q^{81} +(-0.486479 - 1.49723i) q^{82} +(0.579155 + 1.78246i) q^{83} +(-1.96460 + 2.05420i) q^{84} +(10.5980 + 14.5868i) q^{85} +(3.25737 + 1.05838i) q^{86} +(0.796426 + 0.108003i) q^{87} +12.8092i q^{89} +(6.64687 + 4.39039i) q^{90} +(-2.00000 + 1.45309i) q^{91} +(-2.81465 + 3.87403i) q^{92} +(1.60451 + 8.84906i) q^{93} +(-9.52285 + 3.09416i) q^{94} +(-11.7903 - 8.56613i) q^{95} +(-1.52536 + 0.820539i) q^{96} +(-1.10968 + 3.41524i) q^{97} -4.30687 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 3 q^{3} - 2 q^{4} + 5 q^{5} - 2 q^{6} + 5 q^{7} + 2 q^{8} + 7 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 + 5 * q^5 - 2 * q^6 + 5 * q^7 + 2 * q^8 + 7 * q^9	$ 8 q + 2 q^{2} - 3 q^{3} - 2 q^{4} + 5 q^{5} - 2 q^{6} + 5 q^{7} + 2 q^{8} + 7 q^{9} - 3 q^{12} + 10 q^{13} + 5 q^{14} + 4 q^{15} - 2 q^{16} + 15 q^{17} - 2 q^{18} + 10 q^{19} - 5 q^{20} + 12 q^{21} - 2 q^{24} - q^{25} - 15 q^{27} - 22 q^{29} - 4 q^{30} - 2 q^{31} - 8 q^{32} + 10 q^{34} + 17 q^{35} - 18 q^{36} + 6 q^{37} + 15 q^{38} - 42 q^{39} - 3 q^{41} + 8 q^{42} - 8 q^{45} - 10 q^{46} + 40 q^{47} + 2 q^{48} + 7 q^{49} + 6 q^{50} + 25 q^{51} - 30 q^{53} + 15 q^{54} - 40 q^{57} + 22 q^{58} - 35 q^{59} - 21 q^{60} + 20 q^{61} - 13 q^{62} - 29 q^{63} - 2 q^{64} - 32 q^{65} - 2 q^{67} + 15 q^{68} - 26 q^{69} + 13 q^{70} + 20 q^{71} - 2 q^{72} + 5 q^{73} - 6 q^{74} + 6 q^{75} - 8 q^{78} + 25 q^{79} + 19 q^{81} - 2 q^{82} + 9 q^{83} - 13 q^{84} + 40 q^{85} + 10 q^{86} + 42 q^{87} + 13 q^{90} - 16 q^{91} - 10 q^{92} + 2 q^{93} - 10 q^{94} - 30 q^{95} + 3 q^{96} - q^{97} - 22 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 + 5 * q^5 - 2 * q^6 + 5 * q^7 + 2 * q^8 + 7 * q^9 - 3 * q^12 + 10 * q^13 + 5 * q^14 + 4 * q^15 - 2 * q^16 + 15 * q^17 - 2 * q^18 + 10 * q^19 - 5 * q^20 + 12 * q^21 - 2 * q^24 - q^25 - 15 * q^27 - 22 * q^29 - 4 * q^30 - 2 * q^31 - 8 * q^32 + 10 * q^34 + 17 * q^35 - 18 * q^36 + 6 * q^37 + 15 * q^38 - 42 * q^39 - 3 * q^41 + 8 * q^42 - 8 * q^45 - 10 * q^46 + 40 * q^47 + 2 * q^48 + 7 * q^49 + 6 * q^50 + 25 * q^51 - 30 * q^53 + 15 * q^54 - 40 * q^57 + 22 * q^58 - 35 * q^59 - 21 * q^60 + 20 * q^61 - 13 * q^62 - 29 * q^63 - 2 * q^64 - 32 * q^65 - 2 * q^67 + 15 * q^68 - 26 * q^69 + 13 * q^70 + 20 * q^71 - 2 * q^72 + 5 * q^73 - 6 * q^74 + 6 * q^75 - 8 * q^78 + 25 * q^79 + 19 * q^81 - 2 * q^82 + 9 * q^83 - 13 * q^84 + 40 * q^85 + 10 * q^86 + 42 * q^87 + 13 * q^90 - 16 * q^91 - 10 * q^92 + 2 * q^93 - 10 * q^94 - 30 * q^95 + 3 * q^96 - q^97 - 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/726\mathbb{Z}\right)^\times$.

$n$	$485$	$607$
$\chi(n)$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	1.52536	−	0.820539i	0.880666	−	0.473738i
$3$	1.52536	−	0.820539i	0.880666	−	0.473738i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	2.52536	−	0.820539i	1.12937	−	0.366956i	0.316036	−	0.948747i	$-0.397648\pi$
$5$	2.52536	−	0.820539i	1.12937	−	0.366956i	0.813338	+	0.581791i	$0.197648\pi$
$6$	0.309017	+	1.70426i	0.126156	+	0.695762i
$7$	0.964601	−	1.32766i	0.364585	−	0.501808i	−0.586834	−	0.809707i	$-0.699626\pi$
$7$	0.964601	−	1.32766i	0.364585	−	0.501808i	0.951419	+	0.307899i	$0.0996259\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	1.65343	−	2.50323i	0.551144	−	0.834410i
$10$			2.65532i			0.839685i
$11$		0			0
$11$		0			0
$12$	−1.71634	−	0.232753i	−0.495465	−	0.0671901i
$13$	−1.43268	−	0.465507i	−0.397354	−	0.129108i	0.103522	−	0.994627i	$-0.466989\pi$
$13$	−1.43268	−	0.465507i	−0.397354	−	0.129108i	−0.500876	+	0.865519i	$0.666989\pi$
$14$	0.964601	+	1.32766i	0.257800	+	0.354832i
$15$	3.17879	−	3.32377i	0.820760	−	0.858193i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	2.09831	+	6.45792i	0.508914	+	1.56628i	0.794089	+	0.607801i	$0.207948\pi$
$17$	2.09831	+	6.45792i	0.508914	+	1.56628i	−0.285175	+	0.958475i	$0.592052\pi$
$18$	1.86977	+	2.34605i	0.440710	+	0.552969i
$19$	−3.22603	−	4.44024i	−0.740101	−	1.01866i	−0.998613	−	0.0526539i	$-0.983232\pi$
$19$	−3.22603	−	4.44024i	−0.740101	−	1.01866i	0.258512	−	0.966008i	$-0.416768\pi$
$20$	−2.52536	−	0.820539i	−0.564687	−	0.183478i
$21$	0.381966	−	2.81665i	0.0833518	−	0.614643i
$22$		0			0
$23$		−	4.78856i		−	0.998485i	−0.866462	−	0.499242i	$-0.833612\pi$
$23$		−	4.78856i		−	0.998485i	0.866462	−	0.499242i	$-0.166388\pi$
$24$	0.751740	−	1.56041i	0.153448	−	0.318518i
$25$	1.65906	−	1.20538i	0.331813	−	0.241076i
$26$	0.885446	−	1.21871i	0.173650	−	0.239009i
$27$	0.468081	−	5.17503i	0.0900822	−	0.995934i
$28$	−1.56076	+	0.507121i	−0.294955	+	0.0958368i
$29$	0.375405	+	0.272747i	0.0697109	+	0.0506479i	0.622095	−	0.782942i	$-0.286282\pi$
$29$	0.375405	+	0.272747i	0.0697109	+	0.0506479i	−0.552384	+	0.833590i	$0.686282\pi$
$30$	2.17879	+	4.05031i	0.397791	+	0.739482i
$31$	−1.60451	+	4.93818i	−0.288179	+	0.886924i	0.697249	+	0.716829i	$0.254407\pi$
$31$	−1.60451	+	4.93818i	−0.288179	+	0.886924i	−0.985428	+	0.170094i	$0.945593\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−6.79026			−1.16452
$35$	1.34657	−	4.14431i	0.227611	−	0.700516i
$36$	−2.80902	+	1.05329i	−0.468169	+	0.175549i
$37$	−0.814648	−	0.591876i	−0.133927	−	0.0973038i	0.518805	−	0.854893i	$-0.326377\pi$
$37$	−0.814648	−	0.591876i	−0.133927	−	0.0973038i	−0.652732	+	0.757589i	$0.726377\pi$
$38$	5.21982	−	1.69602i	0.846767	−	0.275131i
$39$	−2.56732	+	0.465507i	−0.411100	+	0.0745407i
$40$	1.56076	−	2.14820i	0.246777	−	0.339660i
$41$	−1.27362	+	0.925338i	−0.198906	+	0.144513i	−0.682780	−	0.730624i	$-0.739229\pi$
$41$	−1.27362	+	0.925338i	−0.198906	+	0.144513i	0.483874	+	0.875138i	$0.339229\pi$
$42$	2.56076	+	1.23366i	0.395133	+	0.190358i
$43$		−	3.42500i		−	0.522308i	−0.965297	−	0.261154i	$-0.915897\pi$
$43$		−	3.42500i		−	0.522308i	0.965297	−	0.261154i	$-0.0841030\pi$
$44$		0			0
$45$	2.12151	−	7.67826i	0.316257	−	1.14461i
$46$	4.55420	+	1.47975i	0.671480	+	0.218177i
$47$	5.88545	+	8.10062i	0.858481	+	1.18160i	0.981930	+	0.189246i	$0.0606044\pi$
$47$	5.88545	+	8.10062i	0.858481	+	1.18160i	−0.123449	+	0.992351i	$0.539396\pi$
$48$	1.25174	+	1.19714i	0.180673	+	0.172792i
$49$	1.33089	+	4.09607i	0.190128	+	0.585153i
$50$	0.633706	+	1.95035i	0.0896196	+	0.275821i
$51$	8.49964	+	8.12890i	1.19019	+	1.13827i
$52$	0.885446	+	1.21871i	0.122789	+	0.169005i
$53$	−9.34406	−	3.03607i	−1.28351	−	0.417036i	−0.413692	−	0.910417i	$-0.635761\pi$
$53$	−9.34406	−	3.03607i	−1.28351	−	0.417036i	−0.869813	+	0.493381i	$0.835761\pi$
$54$	4.77710	+	2.04434i	0.650081	+	0.278200i
$55$		0			0
$56$		−	1.64108i		−	0.219298i
$57$	−8.56424	−	4.12588i	−1.13436	−	0.546487i
$58$	−0.375405	+	0.272747i	−0.0492931	+	0.0358135i
$59$	−3.59268	+	4.94489i	−0.467727	+	0.643770i	−0.976089	−	0.217373i	$-0.930251\pi$
$59$	−3.59268	+	4.94489i	−0.467727	+	0.643770i	0.508362	+	0.861143i	$0.330251\pi$
$60$	−4.52536	+	0.820539i	−0.584221	+	0.105931i
$61$	13.2229	−	4.29640i	1.69302	−	0.550097i	0.705658	−	0.708552i	$-0.250651\pi$
$61$	13.2229	−	4.29640i	1.69302	−	0.550097i	0.987366	+	0.158455i	$0.0506513\pi$
$62$	−4.20067	−	3.05196i	−0.533485	−	0.387600i
$63$	−1.72853	−	4.60981i	−0.217775	−	0.580782i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−4.00000			−0.496139
$66$		0			0
$67$	11.7972			1.44126			0.720630	−	0.693320i	$-0.243853\pi$
$67$	11.7972			1.44126			0.720630	+	0.693320i	$0.243853\pi$
$68$	2.09831	−	6.45792i	0.254457	−	0.783138i
$69$	−3.92920	−	7.30427i	−0.473020	−	0.879331i
$70$	3.52536	+	2.56132i	0.421361	+	0.306137i
$71$	−0.854102	+	0.277515i	−0.101363	+	0.0329349i	−0.359260	−	0.933238i	$-0.616971\pi$
$71$	−0.854102	+	0.277515i	−0.101363	+	0.0329349i	0.257896	+	0.966173i	$0.416971\pi$
$72$	−0.133706	−	2.99702i	−0.0157574	−	0.353202i
$73$	−2.71982	+	3.74351i	−0.318331	+	0.438145i	−0.937957	−	0.346752i	$-0.887284\pi$
$73$	−2.71982	+	3.74351i	−0.318331	+	0.438145i	0.619626	+	0.784897i	$0.287284\pi$
$74$	0.814648	−	0.591876i	0.0947009	−	0.0688042i
$75$	1.54160	−	3.19996i	0.178009	−	0.369500i
$76$			5.48844i			0.629568i
$77$		0			0
$78$	0.350622	−	2.58551i	0.0397001	−	0.292752i
$79$	3.02188	+	0.981868i	0.339988	+	0.110469i	0.474034	−	0.880506i	$-0.342797\pi$
$79$	3.02188	+	0.981868i	0.339988	+	0.110469i	−0.134047	+	0.990975i	$0.542797\pi$
$80$	1.56076	+	2.14820i	0.174498	+	0.240176i
$81$	−3.53232	−	8.27785i	−0.392480	−	0.919761i
$82$	−0.486479	−	1.49723i	−0.0537226	−	0.165341i
$83$	0.579155	+	1.78246i	0.0635705	+	0.195650i	0.977797	−	0.209553i	$-0.0672009\pi$
$83$	0.579155	+	1.78246i	0.0635705	+	0.195650i	−0.914227	+	0.405203i	$0.867201\pi$
$84$	−1.96460	+	2.05420i	−0.214356	+	0.224132i
$85$	10.5980	+	14.5868i	1.14951	+	1.58216i
$86$	3.25737	+	1.05838i	0.351251	+	0.114128i
$87$	0.796426	+	0.108003i	0.0853859	+	0.0115792i
$88$		0			0
$89$			12.8092i			1.35777i	0.734244	+	0.678886i	$0.237537\pi$
$89$			12.8092i			1.35777i	−0.734244	+	0.678886i	$0.762463\pi$
$90$	6.64687	+	4.39039i	0.700642	+	0.462788i
$91$	−2.00000	+	1.45309i	−0.209657	+	0.152325i
$92$	−2.81465	+	3.87403i	−0.293447	+	0.403896i
$93$	1.60451	+	8.84906i	0.166380	+	0.917605i
$94$	−9.52285	+	3.09416i	−0.982207	+	0.319138i
$95$	−11.7903	−	8.56613i	−1.20966	−	0.878866i
$96$	−1.52536	+	0.820539i	−0.155681	+	0.0837459i
$97$	−1.10968	+	3.41524i	−0.112671	+	0.346765i	−0.991454	−	0.130456i	$-0.958356\pi$
$97$	−1.10968	+	3.41524i	−0.112671	+	0.346765i	0.878783	+	0.477221i	$0.158356\pi$
$98$	−4.30687			−0.435059
$99$		0			0
$100$	−2.05072			−0.205072
$101$	−3.76143	+	11.5765i	−0.374276	+	1.15190i	0.569690	+	0.821860i	$0.307063\pi$
$101$	−3.76143	+	11.5765i	−0.374276	+	1.15190i	−0.943966	+	0.330043i	$0.892937\pi$
$102$	−10.3576	+	5.57167i	−1.02555	+	0.551678i
$103$	−0.717271	−	0.521128i	−0.0706749	−	0.0513483i	0.551887	−	0.833919i	$-0.313908\pi$
$103$	−0.717271	−	0.521128i	−0.0706749	−	0.0513483i	−0.622562	+	0.782571i	$0.713908\pi$
$104$	−1.43268	+	0.465507i	−0.140486	+	0.0456467i
$105$	−1.34657	−	7.42646i	−0.131411	−	0.724748i
$106$	5.77495	−	7.94853i	0.560912	−	0.772030i
$107$	1.80554	−	1.31180i	0.174548	−	0.126816i	−0.497081	−	0.867704i	$-0.665595\pi$
$107$	1.80554	−	1.31180i	0.174548	−	0.126816i	0.671629	+	0.740888i	$0.265595\pi$
$108$	−3.42049	+	3.91155i	−0.329137	+	0.376389i
$109$		−	4.73524i		−	0.453554i	−0.973947	−	0.226777i	$-0.927181\pi$
$109$		−	4.73524i		−	0.453554i	0.973947	−	0.226777i	$-0.0728188\pi$
$110$		0			0
$111$	−1.72829	−	0.234373i	−0.164042	−	0.0222457i
$112$	1.56076	+	0.507121i	0.147478	+	0.0479184i
$113$	2.28987	+	3.15173i	0.215412	+	0.296490i	0.903025	−	0.429588i	$-0.141341\pi$
$113$	2.28987	+	3.15173i	0.215412	+	0.296490i	−0.687613	+	0.726078i	$0.741341\pi$
$114$	6.57044	−	6.87011i	0.615378	−	0.643444i
$115$	−3.92920	−	12.0928i	−0.366400	−	1.12766i
$116$	−0.143392	−	0.441315i	−0.0133136	−	0.0409750i
$117$	−3.53411	+	2.81665i	−0.326729	+	0.260399i
$118$	−3.59268	−	4.94489i	−0.330733	−	0.455214i
$119$	10.5980	+	3.44348i	0.971513	+	0.315664i
$120$	0.618034	−	4.55743i	0.0564185	−	0.416035i
$121$		0			0
$122$			13.9034i			1.25876i
$123$	−1.18345	+	2.45652i	−0.106708	+	0.221497i
$124$	4.20067	−	3.05196i	0.377231	−	0.274075i
$125$	−4.60312	+	6.33565i	−0.411715	+	0.566677i
$126$	4.91834	−	0.219422i	0.438160	−	0.0195477i
$127$	0.224807	−	0.0730441i	0.0199484	−	0.00648161i	−0.299026	−	0.954245i	$-0.596662\pi$
$127$	0.224807	−	0.0730441i	0.0199484	−	0.00648161i	0.318974	+	0.947763i	$0.396662\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−2.81035	−	5.22435i	−0.247437	−	0.459979i
$130$	1.23607	−	3.80423i	0.108410	−	0.333653i
$131$	−5.26741			−0.460216			−0.230108	−	0.973165i	$-0.573908\pi$
$131$	−5.26741			−0.460216			−0.230108	+	0.973165i	$0.573908\pi$
$132$		0			0
$133$	−9.00696			−0.781002
$134$	−3.64554	+	11.2198i	−0.314927	+	0.969245i
$135$	−3.06424	−	13.4529i	−0.263728	−	1.15784i
$136$	5.49344	+	3.99122i	0.471058	+	0.342244i
$137$	−0.882365	+	0.286698i	−0.0753855	+	0.0244942i	−0.346467	−	0.938062i	$-0.612619\pi$
$137$	−0.882365	+	0.286698i	−0.0753855	+	0.0244942i	0.271081	+	0.962556i	$0.412619\pi$
$138$	8.16097	−	1.47975i	0.694708	−	0.125965i
$139$	−4.96866	+	6.83877i	−0.421436	+	0.580057i	−0.965961	−	0.258688i	$-0.916710\pi$
$139$	−4.96866	+	6.83877i	−0.421436	+	0.580057i	0.544525	+	0.838745i	$0.316710\pi$
$140$	−3.52536	+	2.56132i	−0.297947	+	0.216471i
$141$	15.6243	+	7.52711i	1.31580	+	0.633897i
$142$		−	0.898056i		−	0.0753632i
$143$		0			0
$144$	2.89165	+	0.798968i	0.240971	+	0.0665807i
$145$	1.17183	+	0.380751i	0.0973153	+	0.0316196i
$146$	−2.71982	−	3.74351i	−0.225094	−	0.309815i
$147$	5.39108	+	5.15593i	0.444649	+	0.425254i
$148$	0.311168	+	0.957676i	0.0255778	+	0.0787205i
$149$	−5.58443	−	17.1871i	−0.457494	−	1.40802i	−0.868182	−	0.496247i	$-0.834711\pi$
$149$	−5.58443	−	17.1871i	−0.457494	−	1.40802i	0.410687	−	0.911776i	$-0.365289\pi$
$150$	2.56696	+	2.45500i	0.209592	+	0.200450i
$151$	−7.83513	−	10.7841i	−0.637614	−	0.877600i	0.360872	−	0.932615i	$-0.382479\pi$
$151$	−7.83513	−	10.7841i	−0.637614	−	0.877600i	−0.998486	+	0.0550154i	$0.982479\pi$
$152$	−5.21982	−	1.69602i	−0.423383	−	0.137566i
$153$	19.6351	+	5.42520i	1.58740	+	0.438602i
$154$		0			0
$155$			13.7872i			1.10742i
$156$	2.35062	+	1.13243i	0.188200	+	0.0906669i
$157$	−7.85410	+	5.70634i	−0.626826	+	0.455415i	−0.855299	−	0.518135i	$-0.826627\pi$
$157$	−7.85410	+	5.70634i	−0.626826	+	0.455415i	0.228473	+	0.973550i	$0.426627\pi$
$158$	−1.86762	+	2.57056i	−0.148580	+	0.204503i
$159$	−16.7442	+	3.03607i	−1.32791	+	0.240776i
$160$	−2.52536	+	0.820539i	−0.199647	+	0.0648693i
$161$	−6.35758	−	4.61905i	−0.501048	−	0.364032i
$162$	8.96425	−	0.801439i	0.704298	−	0.0629670i
$163$	2.18848	−	6.73544i	0.171415	−	0.527560i	−0.828037	−	0.560674i	$-0.810542\pi$
$163$	2.18848	−	6.73544i	0.171415	−	0.527560i	0.999452	+	0.0331133i	$0.0105422\pi$
$164$	1.57428			0.122930
$165$		0			0
$166$	−1.87418			−0.145465
$167$	−0.783304	+	2.41076i	−0.0606139	+	0.186550i	−0.976778	−	0.214252i	$-0.931269\pi$
$167$	−0.783304	+	2.41076i	−0.0606139	+	0.186550i	0.916165	+	0.400802i	$0.131269\pi$
$168$	−1.34657	−	2.50323i	−0.103890	−	0.193128i
$169$	−8.68134	−	6.30736i	−0.667795	−	0.485182i
$170$	−17.1478	+	5.57167i	−1.31518	+	0.427328i
$171$	−16.4490	+	0.733838i	−1.25788	+	0.0561180i
$172$	−2.01317	+	2.77089i	−0.153502	+	0.211278i
$173$	−0.767987	+	0.557975i	−0.0583890	+	0.0424221i	−0.616597	−	0.787279i	$-0.711489\pi$
$173$	−0.767987	+	0.557975i	−0.0583890	+	0.0424221i	0.558208	+	0.829701i	$0.311489\pi$
$174$	−0.348827	+	0.724072i	−0.0264445	+	0.0548917i
$175$		−	3.36538i		−	0.254399i
$176$		0			0
$177$	−1.42264	+	10.4907i	−0.106932	+	0.788526i
$178$	−12.1823	−	3.95826i	−0.913100	−	0.296684i
$179$	−10.9126	−	15.0199i	−0.815646	−	1.12264i	−0.990428	−	0.138033i	$-0.955922\pi$
$179$	−10.9126	−	15.0199i	−0.815646	−	1.12264i	0.174782	−	0.984607i	$-0.444078\pi$
$180$	−6.22951	+	4.96485i	−0.464320	+	0.370058i
$181$	3.97992	+	12.2489i	0.295825	+	0.910456i	0.982943	+	0.183910i	$0.0588755\pi$
$181$	3.97992	+	12.2489i	0.295825	+	0.910456i	−0.687118	+	0.726546i	$0.741125\pi$
$182$	−0.763932	−	2.35114i	−0.0566264	−	0.174278i
$183$	16.6444	−	17.4035i	1.23039	−	1.28650i
$184$	−2.81465	−	3.87403i	−0.207499	−	0.285597i
$185$	−2.54293	−	0.826249i	−0.186960	−	0.0607471i
$186$	−8.91178	−	1.20853i	−0.653443	−	0.0886135i
$187$		0			0
$188$		−	10.0129i		−	0.730267i
$189$	−6.41916	−	5.61329i	−0.466925	−	0.408307i
$190$	11.7903	−	8.56613i	0.855356	−	0.621452i
$191$	−1.89786	+	2.61218i	−0.137324	+	0.189010i	−0.872140	−	0.489256i	$-0.837268\pi$
$191$	−1.89786	+	2.61218i	−0.137324	+	0.189010i	0.734816	+	0.678266i	$0.237268\pi$
$192$	−0.309017	−	1.70426i	−0.0223014	−	0.122995i
$193$	−9.28718	+	3.01759i	−0.668506	+	0.217211i	−0.623556	−	0.781778i	$-0.714313\pi$
$193$	−9.28718	+	3.01759i	−0.668506	+	0.217211i	−0.0449498	+	0.998989i	$0.514313\pi$
$194$	−2.90517	−	2.11073i	−0.208579	−	0.151542i
$195$	−6.10143	+	3.28215i	−0.436933	+	0.235040i
$196$	1.33089	−	4.09607i	0.0950639	−	0.292577i
$197$	−13.9679			−0.995175			−0.497587	−	0.867414i	$-0.665781\pi$
$197$	−13.9679			−0.995175			−0.497587	+	0.867414i	$0.665781\pi$
$198$		0			0
$199$	15.9679			1.13194			0.565969	−	0.824427i	$-0.308502\pi$
$199$	15.9679			1.13194			0.565969	+	0.824427i	$0.308502\pi$
$200$	0.633706	−	1.95035i	0.0448098	−	0.137910i
$201$	17.9950	−	9.68008i	1.26927	−	0.682780i
$202$	−9.84754	−	7.15466i	−0.692871	−	0.503400i
$203$	0.724231	−	0.235317i	0.0508311	−	0.0165160i
$204$	−2.09831	−	11.5724i	−0.146911	−	0.810229i
$205$	−2.45707	+	3.38186i	−0.171609	+	0.236199i
$206$	0.717271	−	0.521128i	0.0499747	−	0.0363087i
$207$	−11.9869	−	7.91757i	−0.833146	−	0.550309i
$208$		−	1.50641i		−	0.104451i
$209$		0			0
$210$	7.47910	+	1.01424i	0.516107	+	0.0699893i
$211$	−2.15709	−	0.700881i	−0.148500	−	0.0482506i	0.233824	−	0.972279i	$-0.424876\pi$
$211$	−2.15709	−	0.700881i	−0.148500	−	0.0482506i	−0.382324	+	0.924028i	$0.624876\pi$
$212$	5.77495	+	7.94853i	0.396625	+	0.545907i
$213$	−1.07510	+	1.12413i	−0.0736646	+	0.0770243i
$214$	0.689654	+	2.12254i	0.0471438	+	0.145094i
$215$	−2.81035	−	8.64936i	−0.191664	−	0.589881i
$216$	−2.66312	−	4.46182i	−0.181202	−	0.303588i
$217$	5.00851	+	6.89362i	0.340000	+	0.467969i
$218$	4.50348	+	1.46327i	0.305014	+	0.0991051i
$219$	−1.07700	+	7.94191i	−0.0727772	+	0.536665i
$220$		0			0
$221$		−	10.2289i		−	0.688072i
$222$	0.756972	−	1.57127i	0.0508046	−	0.105457i
$223$	−3.56076	+	2.58704i	−0.238446	+	0.173241i	−0.700591	−	0.713563i	$-0.747080\pi$
$223$	−3.56076	+	2.58704i	−0.238446	+	0.173241i	0.462145	+	0.886805i	$0.347080\pi$
$224$	−0.964601	+	1.32766i	−0.0644501	+	0.0887080i
$225$	−0.274193	−	6.14603i	−0.0182795	−	0.409736i
$226$	−3.70508	+	1.20385i	−0.246458	+	0.0800791i
$227$	−10.3015	−	7.48450i	−0.683736	−	0.496763i	0.190859	−	0.981617i	$-0.438873\pi$
$227$	−10.3015	−	7.48450i	−0.683736	−	0.496763i	−0.874595	+	0.484854i	$0.838873\pi$
$228$	4.50348	+	8.37184i	0.298250	+	0.554439i
$229$	1.98493	−	6.10899i	0.131168	−	0.403693i	−0.863806	−	0.503824i	$-0.831926\pi$
$229$	1.98493	−	6.10899i	0.131168	−	0.403693i	0.994974	+	0.100131i	$0.0319261\pi$
$230$	12.7152			0.838413
$231$		0			0
$232$	0.464026			0.0304648
$233$	5.19468	−	15.9876i	0.340315	−	1.04738i	−0.623729	−	0.781640i	$-0.714383\pi$
$233$	5.19468	−	15.9876i	0.340315	−	1.04738i	0.964044	−	0.265741i	$-0.0856167\pi$
$234$	−1.58669	−	4.23153i	−0.103725	−	0.276624i
$235$	21.5097	+	15.6277i	1.40314	+	1.01944i
$236$	5.81307	−	1.88878i	0.378399	−	0.122949i
$237$	5.41511	−	0.981868i	0.351749	−	0.0637792i
$238$	−6.54989	+	9.01516i	−0.424567	+	0.584366i
$239$	−9.73955	+	7.07620i	−0.629999	+	0.457721i	−0.856400	−	0.516313i	$-0.827304\pi$
$239$	−9.73955	+	7.07620i	−0.629999	+	0.457721i	0.226401	+	0.974034i	$0.427304\pi$
$240$	4.14339	+	1.99611i	0.267455	+	0.128848i
$241$			20.5642i			1.32466i	0.749214	+	0.662328i	$0.230432\pi$
$241$			20.5642i			1.32466i	−0.749214	+	0.662328i	$0.769568\pi$
$242$		0			0
$243$	−12.1803	−	9.72827i	−0.781369	−	0.624069i
$244$	−13.2229	−	4.29640i	−0.846512	−	0.275049i
$245$	6.72197	+	9.25200i	0.429451	+	0.591089i
$246$	−1.97059	−	1.88463i	−0.125640	−	0.120160i
$247$	2.55491	+	7.86319i	0.162565	+	0.500323i
$248$	1.60451	+	4.93818i	0.101887	+	0.313575i
$249$	2.34599	+	2.24366i	0.148671	+	0.142186i
$250$	−4.60312	−	6.33565i	−0.291127	−	0.400701i
$251$	−15.5648	−	5.05731i	−0.982442	−	0.319215i	−0.226614	−	0.973985i	$-0.572766\pi$
$251$	−15.5648	−	5.05731i	−0.982442	−	0.319215i	−0.755828	+	0.654770i	$0.772766\pi$
$252$	−1.31117	+	4.74542i	−0.0825958	+	0.298934i
$253$		0			0
$254$			0.236376i			0.0148315i
$255$	28.1347	+	13.5541i	1.76186	+	0.848791i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−5.01747	+	6.90595i	−0.312981	+	0.430781i	−0.936308	−	0.351180i	$-0.885781\pi$
$257$	−5.01747	+	6.90595i	−0.312981	+	0.430781i	0.623327	+	0.781961i	$0.285781\pi$
$258$	5.83710	−	1.05838i	0.363402	−	0.0658921i
$259$	−1.57162	+	0.510650i	−0.0976557	+	0.0317303i
$260$	3.23607	+	2.35114i	0.200692	+	0.145812i
$261$	1.30346	−	0.488754i	0.0806819	−	0.0302531i
$262$	1.62772	−	5.00961i	0.100561	−	0.309495i
$263$	13.5666			0.836553			0.418276	−	0.908320i	$-0.362634\pi$
$263$	13.5666			0.836553			0.418276	+	0.908320i	$0.362634\pi$
$264$		0			0
$265$	−26.0883			−1.60259
$266$	2.78330	−	8.56613i	0.170655	−	0.525223i
$267$	10.5104	+	19.5386i	0.643228	+	1.19574i
$268$	−9.54415	−	6.93423i	−0.583002	−	0.423576i
$269$	−11.2686	+	3.66138i	−0.687056	+	0.223238i	−0.631682	−	0.775228i	$-0.717635\pi$
$269$	−11.2686	+	3.66138i	−0.687056	+	0.223238i	−0.0553743	+	0.998466i	$0.517635\pi$
$270$	13.7413	+	1.24290i	0.836272	+	0.0756407i
$271$	12.7264	−	17.5164i	0.773075	−	1.06405i	−0.222937	−	0.974833i	$-0.571564\pi$
$271$	12.7264	−	17.5164i	0.773075	−	1.06405i	0.996012	−	0.0892140i	$-0.0284355\pi$
$272$	−5.49344	+	3.99122i	−0.333089	+	0.242003i
$273$	−1.85840	+	3.85755i	−0.112476	+	0.233470i
$274$		−	0.927773i		−	0.0560488i
$275$		0			0
$276$	−1.11455	+	8.21881i	−0.0670883	+	0.494714i
$277$	3.87418	+	1.25880i	0.232777	+	0.0756339i	0.423083	−	0.906091i	$-0.360948\pi$
$277$	3.87418	+	1.25880i	0.232777	+	0.0756339i	−0.190306	+	0.981725i	$0.560948\pi$
$278$	−4.96866	−	6.83877i	−0.298000	−	0.410162i
$279$	9.70845	+	12.1814i	0.581230	+	0.729282i
$280$	−1.34657	−	4.14431i	−0.0804728	−	0.247670i
$281$	5.52048	+	16.9903i	0.329324	+	1.01356i	0.969451	+	0.245286i	$0.0788820\pi$
$281$	5.52048	+	16.9903i	0.329324	+	1.01356i	−0.640126	+	0.768270i	$0.721118\pi$
$282$	−11.9869	+	12.5336i	−0.713808	+	0.746363i
$283$	1.78667	+	2.45914i	0.106207	+	0.146181i	0.858812	−	0.512291i	$-0.171203\pi$
$283$	1.78667	+	2.45914i	0.106207	+	0.146181i	−0.752605	+	0.658472i	$0.771203\pi$
$284$	0.854102	+	0.277515i	0.0506816	+	0.0164675i
$285$	−25.0132	−	3.39205i	−1.48165	−	0.200927i
$286$		0			0
$287$			2.58351i			0.152500i
$288$	−1.65343	+	2.50323i	−0.0974295	+	0.147504i
$289$	−23.5486	+	17.1091i	−1.38521	+	1.00642i
$290$	−0.724231	+	0.996819i	−0.0425283	+	0.0585352i
$291$	1.10968	+	6.11999i	0.0650504	+	0.358760i
$292$	4.40076	−	1.42989i	0.257535	−	0.0836782i
$293$	18.8833	+	13.7195i	1.10318	+	0.801505i	0.981576	−	0.191075i	$-0.0611972\pi$
$293$	18.8833	+	13.7195i	1.10318	+	0.801505i	0.121601	+	0.992579i	$0.461197\pi$
$294$	−6.56951	+	3.53395i	−0.383142	+	0.206104i
$295$	−5.01532	+	15.4356i	−0.292003	+	0.898693i
$296$	−1.00696			−0.0585284
$297$		0			0
$298$	18.0716			1.04686
$299$	−2.22911	+	6.86049i	−0.128913	+	0.396752i
$300$	−3.12808	+	1.68269i	−0.180600	+	0.0971502i
$301$	−4.54724	−	3.30376i	−0.262098	−	0.190426i
$302$	12.6775	−	4.11917i	0.729508	−	0.237032i
$303$	3.76143	+	20.7447i	0.216088	+	1.19175i
$304$	3.22603	−	4.44024i	0.185025	−	0.254666i
$305$	29.8673	−	21.6999i	1.71020	−	1.24253i
$306$	−11.2272	+	16.9976i	−0.641819	+	0.971688i
$307$		−	30.0216i		−	1.71342i	−0.515794	−	0.856712i	$-0.672503\pi$
$307$		−	30.0216i		−	1.71342i	0.515794	−	0.856712i	$-0.327497\pi$
$308$		0			0
$309$	−1.52170	−	0.206358i	−0.0865666	−	0.0117393i
$310$	−13.1124	−	4.26049i	−0.744737	−	0.241980i
$311$	0.291085	+	0.400644i	0.0165059	+	0.0227185i	0.817190	−	0.576368i	$-0.195531\pi$
$311$	0.291085	+	0.400644i	0.0165059	+	0.0227185i	−0.800684	+	0.599087i	$0.795531\pi$
$312$	−1.80339	+	1.88563i	−0.102097	+	0.106753i
$313$	−8.76956	−	26.9899i	−0.495685	−	1.52556i	−0.815887	−	0.578212i	$-0.803751\pi$
$313$	−8.76956	−	26.9899i	−0.495685	−	1.52556i	0.320202	−	0.947349i	$-0.396249\pi$
$314$	−3.00000	−	9.23305i	−0.169300	−	0.521051i
$315$	−8.14769	−	10.2231i	−0.459071	−	0.576006i
$316$	−1.86762	−	2.57056i	−0.105062	−	0.144605i
$317$	6.31569	+	2.05209i	0.354724	+	0.115257i	0.480958	−	0.876744i	$-0.340289\pi$
$317$	6.31569	+	2.05209i	0.354724	+	0.115257i	−0.126234	+	0.992001i	$0.540289\pi$
$318$	2.28678	−	16.8629i	0.128236	−	0.945626i
$319$		0			0
$320$		−	2.65532i		−	0.148437i
$321$	1.67771	−	3.48248i	0.0936405	−	0.194373i
$322$	6.35758	−	4.61905i	0.354294	−	0.257410i
$323$	21.9056	−	30.1504i	1.21886	−	1.67761i
$324$	−2.00789	+	8.77316i	−0.111549	+	0.487398i
$325$	−2.93802	+	0.954621i	−0.162972	+	0.0529529i
$326$	5.72951	+	4.16273i	0.317328	+	0.230552i
$327$	−3.88545	−	7.22293i	−0.214866	−	0.399429i
$328$	−0.486479	+	1.49723i	−0.0268613	+	0.0826706i
$329$	16.4320			0.905924
$330$		0			0
$331$	7.41016			0.407299			0.203650	−	0.979044i	$-0.434720\pi$
$331$	7.41016			0.407299			0.203650	+	0.979044i	$0.434720\pi$
$332$	0.579155	−	1.78246i	0.0317853	−	0.0978250i
$333$	−2.82857	+	1.06062i	−0.155005	+	0.0581218i
$334$	−2.05072	−	1.48993i	−0.112210	−	0.0815255i
$335$	29.7922	−	9.68008i	1.62772	−	0.528879i
$336$	2.79682	−	0.507121i	0.152579	−	0.0276657i
$337$	−20.1103	+	27.6795i	−1.09548	+	1.50780i	−0.254235	+	0.967143i	$0.581824\pi$
$337$	−20.1103	+	27.6795i	−1.09548	+	1.50780i	−0.841244	+	0.540655i	$0.818176\pi$
$338$	8.68134	−	6.30736i	0.472203	−	0.343075i
$339$	6.07898	+	2.92859i	0.330165	+	0.159059i
$340$		−	18.0303i		−	0.977831i
$341$		0			0
$342$	4.38509	−	15.8707i	0.237119	−	0.858188i
$343$	17.6473	+	5.73395i	0.952863	+	0.309604i
$344$	−2.01317	−	2.77089i	−0.108543	−	0.149396i
$345$	−15.9161	−	15.2218i	−0.856893	−	0.819517i
$346$	−0.293345	−	0.902823i	−0.0157703	−	0.0485361i
$347$	6.46604	+	19.9004i	0.347115	+	1.06831i	0.960442	+	0.278481i	$0.0898310\pi$
$347$	6.46604	+	19.9004i	0.347115	+	1.06831i	−0.613326	+	0.789830i	$0.710169\pi$
$348$	−0.580840	−	0.555504i	−0.0311363	−	0.0297782i
$349$	17.3120	+	23.8279i	0.926688	+	1.27548i	0.961137	+	0.276070i	$0.0890323\pi$
$349$	17.3120	+	23.8279i	0.926688	+	1.27548i	−0.0344491	+	0.999406i	$0.510968\pi$
$350$	3.20067	+	1.03996i	0.171083	+	0.0555882i
$351$	−3.07962	+	7.19627i	−0.164378	+	0.384109i
$352$		0			0
$353$		−	24.3265i		−	1.29477i	−0.762163	−	0.647385i	$-0.775863\pi$
$353$		−	24.3265i		−	1.29477i	0.762163	−	0.647385i	$-0.224137\pi$
$354$	−9.53759	−	4.59480i	−0.506917	−	0.244211i
$355$	−1.92920	+	1.40165i	−0.102391	+	0.0743917i
$356$	7.52906	−	10.3629i	0.399039	−	0.549230i
$357$	18.9912	−	3.44348i	1.00512	−	0.182248i
$358$	17.6570	−	5.73709i	0.933199	−	0.303215i
$359$	26.4772	+	19.2368i	1.39742	+	1.01528i	0.995005	+	0.0998217i	$0.0318272\pi$
$359$	26.4772	+	19.2368i	1.39742	+	1.01528i	0.402410	+	0.915460i	$0.368173\pi$
$360$	−2.79682	−	7.45883i	−0.147406	−	0.393115i
$361$	−3.43720	+	10.5786i	−0.180905	+	0.556770i
$362$	−12.8793			−0.676920
$363$		0			0
$364$	2.47214			0.129575
$365$	−3.79682	+	11.6854i	−0.198735	+	0.611643i
$366$	11.4083	+	21.2077i	0.596321	+	1.10854i
$367$	9.62969	+	6.99638i	0.502666	+	0.365208i	0.810034	−	0.586382i	$-0.199448\pi$
$367$	9.62969	+	6.99638i	0.502666	+	0.365208i	−0.307368	+	0.951591i	$0.599448\pi$
$368$	4.55420	−	1.47975i	0.237404	−	0.0771372i
$369$	0.210490	+	4.71814i	0.0109577	+	0.245617i
$370$	1.57162	−	2.16315i	0.0817046	−	0.112457i
$371$	−13.0442	+	9.47713i	−0.677219	+	0.492028i
$372$	3.90327	−	8.10215i	0.202375	−	0.420077i
$373$			27.7804i			1.43841i	0.694796	+	0.719207i	$0.255495\pi$
$373$			27.7804i			1.43841i	−0.694796	+	0.719207i	$0.744505\pi$
$374$		0			0
$375$	−1.82276	+	13.4412i	−0.0941268	+	0.694099i
$376$	9.52285	+	3.09416i	0.491104	+	0.159569i
$377$	−0.410870	−	0.565514i	−0.0211609	−	0.0291254i
$378$	7.32218	−	4.37038i	0.376612	−	0.224788i
$379$	−2.43031	−	7.47973i	−0.124837	−	0.384208i	0.869035	−	0.494751i	$-0.164741\pi$
$379$	−2.43031	−	7.47973i	−0.124837	−	0.384208i	−0.993871	+	0.110543i	$0.964741\pi$
$380$	4.50348	+	13.8603i	0.231024	+	0.711018i
$381$	0.282975	−	0.295881i	0.0144972	−	0.0151584i
$382$	−1.89786	−	2.61218i	−0.0971028	−	0.133651i
$383$	12.3219	+	4.00364i	0.629622	+	0.204576i	0.606407	−	0.795154i	$-0.292610\pi$
$383$	12.3219	+	4.00364i	0.629622	+	0.204576i	0.0232141	+	0.999731i	$0.492610\pi$
$384$	1.71634	+	0.232753i	0.0875867	+	0.0118776i
$385$		0			0
$386$		−	9.76512i		−	0.497032i
$387$	−8.57357	−	5.66301i	−0.435819	−	0.287867i
$388$	2.90517	−	2.11073i	0.147488	−	0.107156i
$389$	15.2222	−	20.9516i	0.771798	−	1.06229i	−0.224342	−	0.974510i	$-0.572023\pi$
$389$	15.2222	−	20.9516i	0.771798	−	1.06229i	0.996140	−	0.0877783i	$-0.0279767\pi$
$390$	−1.23607	−	6.81705i	−0.0625907	−	0.345195i
$391$	30.9242	−	10.0479i	1.56390	−	0.508143i
$392$	3.48433	+	2.53151i	0.175985	+	0.127861i
$393$	−8.03469	+	4.32211i	−0.405296	+	0.218022i
$394$	4.31633	−	13.2843i	0.217454	−	0.669254i
$395$	8.43698			0.424511
$396$		0			0
$397$	−17.9986			−0.903323			−0.451661	−	0.892189i	$-0.649168\pi$
$397$	−17.9986			−0.903323			−0.451661	+	0.892189i	$0.649168\pi$
$398$	−4.93437	+	15.1864i	−0.247337	+	0.761226i
$399$	−13.7388	+	7.39056i	−0.687802	+	0.369991i
$400$	1.65906	+	1.20538i	0.0829532	+	0.0602690i
$401$	3.58361	−	1.16439i	0.178957	−	0.0581466i	−0.218168	−	0.975911i	$-0.570008\pi$
$401$	3.58361	−	1.16439i	0.178957	−	0.0581466i	0.397125	+	0.917765i	$0.370008\pi$
$402$	3.64554	+	20.1056i	0.181823	+	1.00277i
$403$	4.59751	−	6.32793i	0.229018	−	0.315217i
$404$	9.84754	−	7.15466i	0.489933	−	0.355957i
$405$	−15.7127	−	18.0061i	−0.780768	−	0.894731i
$406$			0.761502i			0.0377927i
$407$		0			0
$408$	11.6544	+	1.58046i	0.576979	+	0.0782442i
$409$	13.6705	+	4.44183i	0.675965	+	0.219634i	0.626828	−	0.779158i	$-0.284353\pi$
$409$	13.6705	+	4.44183i	0.675965	+	0.219634i	0.0491370	+	0.998792i	$0.484353\pi$
$410$	−2.45707	−	3.38186i	−0.121346	−	0.167018i
$411$	−1.11068	+	1.16133i	−0.0547856	+	0.0572842i
$412$	0.273973	+	0.843203i	0.0134977	+	0.0415416i
$413$	3.09964	+	9.53970i	0.152523	+	0.469418i
$414$	11.2342	−	8.95353i	0.552131	−	0.440042i
$415$	2.92515	+	4.02612i	0.143590	+	0.197634i
$416$	1.43268	+	0.465507i	0.0702430	+	0.0228233i
$417$	−1.96751	+	14.5085i	−0.0963492	+	0.710486i
$418$		0			0
$419$		−	31.1601i		−	1.52227i	−0.648595	−	0.761134i	$-0.724643\pi$
$419$		−	31.1601i		−	1.52227i	0.648595	−	0.761134i	$-0.275357\pi$
$420$	−3.27577	+	6.79963i	−0.159841	+	0.331788i
$421$	8.75081	−	6.35784i	0.426488	−	0.309862i	−0.353755	−	0.935338i	$-0.615095\pi$
$421$	8.75081	−	6.35784i	0.426488	−	0.309862i	0.780243	+	0.625476i	$0.215095\pi$
$422$	1.33315	−	1.83493i	0.0648970	−	0.0893230i
$423$	30.0089	−	1.33879i	1.45908	−	0.0650941i
$424$	−9.34406	+	3.03607i	−0.453788	+	0.147445i
$425$	11.2655	+	8.18485i	0.546456	+	0.397024i
$426$	−0.736889	−	1.36986i	−0.0357024	−	0.0663698i
$427$	7.05072	−	21.6999i	0.341208	−	1.05013i
$428$	−2.23177			−0.107877
$429$		0			0
$430$	9.09447			0.438574
$431$	12.3088	−	37.8826i	0.592895	−	1.82474i	0.0279563	−	0.999609i	$-0.491100\pi$
$431$	12.3088	−	37.8826i	0.592895	−	1.82474i	0.564938	−	0.825133i	$-0.308900\pi$
$432$	5.06639	−	1.15400i	0.243757	−	0.0555218i
$433$	−13.0699	−	9.49585i	−0.628100	−	0.456341i	0.227642	−	0.973745i	$-0.426899\pi$
$433$	−13.0699	−	9.49585i	−0.628100	−	0.456341i	−0.855741	+	0.517404i	$0.826899\pi$
$434$	−8.10394	+	2.63313i	−0.389001	+	0.126394i
$435$	2.09988	−	0.380751i	0.100682	−	0.0182556i
$436$	−2.78330	+	3.83089i	−0.133296	+	0.183466i
$437$	−21.2624	+	15.4480i	−1.01712	+	0.738980i
$438$	−7.22040	−	3.47848i	−0.345004	−	0.166208i
$439$		−	6.13994i		−	0.293043i	−0.989207	−	0.146522i	$-0.953192\pi$
$439$		−	6.13994i		−	0.293043i	0.989207	−	0.146522i	$-0.0468078\pi$
$440$		0			0
$441$	12.4540	+	3.44105i	0.593046	+	0.163859i
$442$	9.72829	+	3.16091i	0.462727	+	0.150349i
$443$	−0.962696	−	1.32504i	−0.0457391	−	0.0629545i	0.785535	−	0.618817i	$-0.212388\pi$
$443$	−0.962696	−	1.32504i	−0.0457391	−	0.0629545i	−0.831274	+	0.555863i	$0.812388\pi$
$444$	1.26045	+	1.20547i	0.0598184	+	0.0572092i
$445$	10.5104	+	32.3478i	0.498243	+	1.53343i
$446$	−1.36009	−	4.18592i	−0.0644020	−	0.198209i
$447$	−22.6209	−	21.6343i	−1.06993	−	1.02326i
$448$	−0.964601	−	1.32766i	−0.0455731	−	0.0627260i
$449$	17.3870	+	5.64939i	0.820545	+	0.266611i	0.689058	−	0.724707i	$-0.258025\pi$
$449$	17.3870	+	5.64939i	0.820545	+	0.266611i	0.131487	+	0.991318i	$0.458025\pi$
$450$	5.92996	+	1.63846i	0.279541	+	0.0772376i
$451$		0			0
$452$		−	3.89575i		−	0.183241i
$453$	−20.8002	−	10.0206i	−0.977277	−	0.470810i
$454$	10.3015	−	7.48450i	0.483475	−	0.351265i
$455$	−3.85840	+	5.31064i	−0.180885	+	0.248966i
$456$	−9.35375	+	1.69602i	−0.438029	+	0.0794235i
$457$	−26.6151	+	8.64777i	−1.24500	+	0.404526i	−0.856127	−	0.516765i	$-0.827136\pi$
$457$	−26.6151	+	8.64777i	−1.24500	+	0.404526i	−0.388875	+	0.921291i	$0.627136\pi$
$458$	5.19661	+	3.77556i	0.242822	+	0.176420i
$459$	34.4021	−	7.83596i	1.60575	−	0.365751i
$460$	−3.92920	+	12.0928i	−0.183200	+	0.563832i
$461$	30.3359			1.41288			0.706441	−	0.707772i	$-0.250300\pi$
$461$	30.3359			1.41288			0.706441	+	0.707772i	$0.250300\pi$
$462$		0			0
$463$	−10.9632			−0.509503			−0.254752	−	0.967007i	$-0.581994\pi$
$463$	−10.9632			−0.509503			−0.254752	+	0.967007i	$0.581994\pi$
$464$	−0.143392	+	0.441315i	−0.00665680	+	0.0204875i
$465$	11.3130	+	21.0305i	0.524626	+	0.975265i
$466$	13.5999	+	9.88087i	0.630001	+	0.457723i
$467$	−30.6416	+	9.95606i	−1.41792	+	0.460712i	−0.914942	−	0.403585i	$-0.867764\pi$
$467$	−30.6416	+	9.95606i	−1.41792	+	0.460712i	−0.502983	+	0.864297i	$0.667764\pi$
$468$	4.51474	−	0.201416i	0.208694	−	0.00931046i
$469$	11.3796	−	15.6627i	0.525462	−	0.723236i
$470$	−21.5097	+	15.6277i	−0.992170	+	0.720854i
$471$	−7.29805	+	15.1488i	−0.336276	+	0.698020i
$472$			6.11223i			0.281338i
$473$		0			0
$474$	−0.739548	+	5.45348i	−0.0339686	+	0.250487i
$475$	−10.7044	−	3.47806i	−0.491150	−	0.159584i
$476$	−6.54989	−	9.01516i	−0.300214	−	0.413209i
$477$	−23.0498	+	18.3704i	−1.05538	+	0.841122i
$478$	−3.72018	−	11.4495i	−0.170157	−	0.523689i
$479$	−5.81966	−	17.9111i	−0.265907	−	0.818378i	−0.991483	−	0.130236i	$-0.958427\pi$
$479$	−5.81966	−	17.9111i	−0.265907	−	0.818378i	0.725576	−	0.688142i	$-0.241573\pi$
$480$	−3.17879	+	3.32377i	−0.145091	+	0.151709i
$481$	0.891609	+	1.22719i	0.0406539	+	0.0559552i
$482$	−19.5577	−	6.35469i	−0.890830	−	0.289448i
$483$	−13.4877	−	1.82907i	−0.613712	−	0.0832255i
$484$		0			0
$485$			9.53523i			0.432972i
$486$	13.0161	−	8.57799i	0.590421	−	0.389106i
$487$	21.7305	−	15.7881i	0.984702	−	0.715428i	0.0259475	−	0.999663i	$-0.491740\pi$
$487$	21.7305	−	15.7881i	0.984702	−	0.715428i	0.958755	+	0.284235i	$0.0917397\pi$
$488$	8.17223	−	11.2481i	0.369939	−	0.509178i
$489$	−2.18848	−	12.0697i	−0.0989663	−	0.545810i
$490$	−10.8764	+	3.53395i	−0.491345	+	0.159648i
$491$	15.4032	+	11.1911i	0.695139	+	0.505048i	0.878345	−	0.478027i	$-0.158648\pi$
$491$	15.4032	+	11.1911i	0.695139	+	0.505048i	−0.183207	+	0.983074i	$0.558648\pi$
$492$	2.40134	−	1.29176i	0.108261	−	0.0582369i
$493$	−0.973668	+	2.99664i	−0.0438518	+	0.134962i
$494$	−8.26785			−0.371988
$495$		0			0
$496$	−5.19231			−0.233142
$497$	−0.455423	+	1.40165i	−0.0204285	+	0.0628725i
$498$	−2.85880	+	1.53784i	−0.128106	+	0.0689123i
$499$	−8.59175	−	6.24227i	−0.384619	−	0.279442i	0.378628	−	0.925549i	$-0.376396\pi$
$499$	−8.59175	−	6.24227i	−0.384619	−	0.279442i	−0.763247	+	0.646107i	$0.776396\pi$
$500$	7.44800	−	2.42000i	0.333085	−	0.108226i
$501$	0.783304	+	4.32000i	0.0349954	+	0.193004i
$502$	9.61958	−	13.2402i	0.429343	−	0.590940i
$503$	25.0545	−	18.2032i	1.11713	−	0.811640i	0.133355	−	0.991068i	$-0.457425\pi$
$503$	25.0545	−	18.2032i	1.11713	−	0.811640i	0.983771	+	0.179429i	$0.0574249\pi$
$504$	−4.10799	−	2.71341i	−0.182985	−	0.120865i
$505$			32.3211i			1.43827i
$506$		0			0
$507$	−18.4176	−	2.49761i	−0.817954	−	0.110923i
$508$	−0.224807	−	0.0730441i	−0.00997418	−	0.00324081i
$509$	−12.0940	−	16.6460i	−0.536057	−	0.737820i	0.451981	−	0.892028i	$-0.350717\pi$
$509$	−12.0940	−	16.6460i	−0.536057	−	0.737820i	−0.988038	+	0.154208i	$0.950717\pi$
$510$	−21.5848	+	22.5693i	−0.955792	+	0.999384i
$511$	2.34657	+	7.22199i	0.103806	+	0.319482i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−24.4884	+	14.6164i	−1.08119	+	0.645329i
$514$	−5.01747	−	6.90595i	−0.221311	−	0.304608i
$515$	−2.23897	−	0.727486i	−0.0986609	−	0.0320569i
$516$	−0.797180	+	5.87847i	−0.0350939	+	0.258785i
$517$		0			0
$518$		−	1.65250i		−	0.0726066i
$519$	−0.713615	+	1.48128i	−0.0313242	+	0.0650208i
$520$	−3.23607	+	2.35114i	−0.141911	+	0.103104i
$521$	2.25112	−	3.09840i	0.0986234	−	0.135744i	−0.756853	−	0.653585i	$-0.773264\pi$
$521$	2.25112	−	3.09840i	0.0986234	−	0.135744i	0.855477	+	0.517841i	$0.173264\pi$
$522$	0.0620430	+	1.39069i	0.00271555	+	0.0608690i
$523$	−9.16028	+	2.97636i	−0.400551	+	0.130147i	−0.502363	−	0.864657i	$-0.667536\pi$
$523$	−9.16028	+	2.97636i	−0.400551	+	0.130147i	0.101812	+	0.994804i	$0.467536\pi$
$524$	4.26143	+	3.09611i	0.186161	+	0.135254i
$525$	−2.76143	−	5.13341i	−0.120519	−	0.224040i
$526$	−4.19231	+	12.9026i	−0.182794	+	0.562581i
$527$	−35.2572			−1.53583
$528$		0			0
$529$	0.0696480			0.00302817
$530$	8.06173	−	24.8115i	0.350179	−	1.07774i
$531$	6.43796	+	17.1693i	0.279384	+	0.745086i
$532$	7.28678	+	5.29416i	0.315922	+	0.229531i
$533$	2.25544	−	0.732837i	0.0976939	−	0.0317427i
$534$	−21.8302	+	3.95826i	−0.944686	+	0.171291i
$535$	3.48325	−	4.79428i	0.150594	−	0.207275i
$536$	9.54415	−	6.93423i	0.412245	−	0.299513i
$537$	−28.9700	−	13.9565i	−1.25015	−	0.602268i
$538$		−	11.8485i		−	0.510824i
$539$		0			0
$540$	−5.42838	+	12.6847i	−0.233600	+	0.545863i
$541$	−2.65253	−	0.861859i	−0.114041	−	0.0370542i	0.251441	−	0.967873i	$-0.419096\pi$
$541$	−2.65253	−	0.861859i	−0.114041	−	0.0370542i	−0.365482	+	0.930819i	$0.619096\pi$
$542$	12.7264	+	17.5164i	0.546647	+	0.752395i
$543$	16.1215	+	15.4183i	0.691840	+	0.661663i
$544$	−2.09831	−	6.45792i	−0.0899642	−	0.276881i
$545$	−3.88545	−	11.9582i	−0.166434	−	0.512232i
$546$	−3.09447	−	2.95950i	−0.132431	−	0.126655i
$547$	−19.4691	−	26.7969i	−0.832437	−	1.14575i	−0.987465	−	0.157841i	$-0.949547\pi$
$547$	−19.4691	−	26.7969i	−0.832437	−	1.14575i	0.155028	−	0.987910i	$-0.450453\pi$
$548$	0.882365	+	0.286698i	0.0376928	+	0.0122471i
$549$	11.1084	−	40.2039i	0.474095	−	1.71586i
$550$		0			0
$551$		−	2.54678i		−	0.108496i
$552$	−7.47214	−	3.59976i	−0.318035	−	0.153216i
$553$	4.21849	−	3.06491i	0.179389	−	0.130333i
$554$	−2.39438	+	3.29558i	−0.101727	+	0.140016i
$555$	−4.55685	+	0.826249i	−0.193428	+	0.0350723i
$556$	8.03945	−	2.61218i	0.340949	−	0.110781i
$557$	−22.1683	−	16.1062i	−0.939299	−	0.682441i	0.00895255	−	0.999960i	$-0.497150\pi$
$557$	−22.1683	−	16.1062i	−0.939299	−	0.682441i	−0.948252	+	0.317519i	$0.897150\pi$
$558$	−14.5853	+	5.46902i	−0.617445	+	0.231522i
$559$	−1.59436	+	4.90694i	−0.0674343	+	0.207541i
$560$	4.35758			0.184141
$561$		0			0
$562$	−17.8647			−0.753575
$563$	−6.56854	+	20.2159i	−0.276831	+	0.851998i	0.711898	+	0.702283i	$0.247836\pi$
$563$	−6.56854	+	20.2159i	−0.276831	+	0.851998i	−0.988729	+	0.149715i	$0.952164\pi$
$564$	−8.21599	−	15.2733i	−0.345955	−	0.643121i
$565$	8.36884	+	6.08032i	0.352080	+	0.255801i
$566$	−2.89090	+	0.939310i	−0.121513	+	0.0394821i
$567$	−14.3974	−	3.29510i	−0.604635	−	0.138381i
$568$	−0.527864	+	0.726543i	−0.0221487	+	0.0304850i
$569$	−29.8591	+	21.6939i	−1.25176	+	0.909457i	−0.998323	−	0.0578950i	$-0.981561\pi$
$569$	−29.8591	+	21.6939i	−1.25176	+	0.909457i	−0.253437	+	0.967352i	$0.581561\pi$
$570$	10.9555	−	22.7408i	0.458877	−	0.952506i
$571$		−	26.4505i		−	1.10692i	−0.832876	−	0.553460i	$-0.813307\pi$
$571$		−	26.4505i		−	1.10692i	0.832876	−	0.553460i	$-0.186693\pi$
$572$		0			0
$573$	−0.751520	+	5.54177i	−0.0313952	+	0.231511i
$574$	−2.45707	−	0.798349i	−0.102556	−	0.0333224i
$575$	−5.77204	−	7.94453i	−0.240711	−	0.331310i
$576$	−1.86977	−	2.34605i	−0.0779072	−	0.0977520i
$577$	−7.56818	−	23.2925i	−0.315068	−	0.969678i	−0.975727	−	0.218992i	$-0.929723\pi$
$577$	−7.56818	−	23.2925i	−0.315068	−	0.969678i	0.660659	−	0.750686i	$-0.270277\pi$
$578$	−8.99477	−	27.6830i	−0.374133	−	1.15146i
$579$	−11.6902	+	12.2234i	−0.485829	+	0.507987i
$580$	−0.724231	−	0.996819i	−0.0300721	−	0.0413907i
$581$	2.92515	+	0.950438i	0.121356	+	0.0394308i
$582$	−6.16337	−	0.835815i	−0.255480	−	0.0346456i
$583$		0			0
$584$			4.62724i			0.191476i
$585$	−6.61373	+	10.0129i	−0.273444	+	0.413983i
$586$	−18.8833	+	13.7195i	−0.780064	+	0.566749i
$587$	−24.3468	+	33.5105i	−1.00490	+	1.38313i	−0.0826291	+	0.996580i	$0.526332\pi$
$587$	−24.3468	+	33.5105i	−1.00490	+	1.38313i	−0.922270	+	0.386545i	$0.873668\pi$
$588$	−1.33089	−	7.34003i	−0.0548852	−	0.302698i
$589$	27.1029	−	8.80628i	1.11676	−	0.362856i
$590$	−13.1303	−	9.53970i	−0.540565	−	0.392743i
$591$	−21.3061	+	11.4612i	−0.876416	+	0.471452i
$592$	0.311168	−	0.957676i	0.0127889	−	0.0393602i
$593$	−2.94808			−0.121063			−0.0605316	−	0.998166i	$-0.519280\pi$
$593$	−2.94808			−0.121063			−0.0605316	+	0.998166i	$0.519280\pi$
$594$		0			0
$595$	29.5891			1.21304
$596$	−5.58443	+	17.1871i	−0.228747	+	0.704011i
$597$	24.3568	−	13.1023i	0.996859	−	0.536242i
$598$	−5.83588	−	4.24002i	−0.238647	−	0.173387i
$599$	−26.3852	+	8.57307i	−1.07807	+	0.350286i	−0.793626	−	0.608406i	$-0.791809\pi$
$599$	−26.3852	+	8.57307i	−1.07807	+	0.350286i	−0.284444	+	0.958693i	$0.591809\pi$
$600$	−0.633706	−	3.49496i	−0.0258709	−	0.142681i
$601$	2.61057	−	3.59314i	0.106487	−	0.146567i	−0.752447	−	0.658652i	$-0.771127\pi$
$601$	2.61057	−	3.59314i	0.106487	−	0.146567i	0.858935	+	0.512085i	$0.171127\pi$
$602$	4.54724	−	3.30376i	0.185331	−	0.134651i
$603$	19.5059	−	29.5312i	0.794342	−	1.20260i
$604$			13.3299i			0.542387i
$605$		0			0
$606$	−20.8917	−	2.83313i	−0.848667	−	0.115088i
$607$	−38.6506	−	12.5583i	−1.56878	−	0.509728i	−0.609645	−	0.792675i	$-0.708688\pi$
$607$	−38.6506	−	12.5583i	−1.56878	−	0.509728i	−0.959135	+	0.282947i	$0.908688\pi$
$608$	3.22603	+	4.44024i	0.130833	+	0.180076i
$609$	0.911625	−	0.953202i	0.0369409	−	0.0386257i
$610$	11.4083	+	35.1111i	0.461908	+	1.42161i
$611$	−4.66108	−	14.3453i	−0.188567	−	0.580350i
$612$	−12.6963	−	15.9303i	−0.513216	−	0.643944i
$613$	−16.9702	−	23.3574i	−0.685418	−	0.943398i	0.314564	−	0.949236i	$-0.398142\pi$
$613$	−16.9702	−	23.3574i	−0.685418	−	0.943398i	−0.999983	+	0.00583851i	$0.998142\pi$
$614$	28.5523	+	9.27719i	1.15228	+	0.374397i
$615$	−0.972957	+	7.17467i	−0.0392334	+	0.289310i
$616$		0			0
$617$			31.6428i			1.27389i	0.770909	+	0.636946i	$0.219802\pi$
$617$			31.6428i			1.27389i	−0.770909	+	0.636946i	$0.780198\pi$
$618$	0.666490	−	1.38346i	0.0268102	−	0.0556508i
$619$	−0.772112	+	0.560972i	−0.0310338	+	0.0225474i	−0.603194	−	0.797594i	$-0.706106\pi$
$619$	−0.772112	+	0.560972i	−0.0310338	+	0.0225474i	0.572160	+	0.820142i	$0.306106\pi$
$620$	8.10394	−	11.1541i	0.325462	−	0.447960i
$621$	−24.7809	−	2.24144i	−0.994425	−	0.0899457i
$622$	−0.470986	+	0.153033i	−0.0188848	+	0.00613605i
$623$	17.0062	+	12.3558i	0.681341	+	0.495023i
$624$	−1.23607	−	2.29782i	−0.0494823	−	0.0919862i
$625$	−9.59440	+	29.5285i	−0.383776	+	1.18114i
$626$	28.3789			1.13425
$627$		0			0
$628$	9.70820			0.387400
$629$	2.11291	−	6.50287i	0.0842473	−	0.259286i
$630$	12.2405	−	4.58981i	0.487674	−	0.182862i
$631$	−5.75737	−	4.18297i	−0.229197	−	0.166522i	0.467260	−	0.884120i	$-0.345241\pi$
$631$	−5.75737	−	4.18297i	−0.229197	−	0.166522i	−0.696457	+	0.717599i	$0.745241\pi$
$632$	3.02188	−	0.981868i	0.120204	−	0.0390566i
$633$	−3.86543	+	0.700881i	−0.153637	+	0.0278575i
$634$	−3.90331	+	5.37244i	−0.155020	+	0.213367i
$635$	0.507781	−	0.368925i	0.0201507	−	0.0146403i
$636$	15.3309	+	7.38579i	0.607911	+	0.292866i
$637$		−	6.48791i		−	0.257060i
$638$		0			0
$639$	−0.717518	+	2.59687i	−0.0283846	+	0.102730i
$640$	2.52536	+	0.820539i	0.0998235	+	0.0324346i
$641$	−19.3058	−	26.5721i	−0.762532	−	1.04953i	−0.996999	−	0.0774108i	$-0.975335\pi$
$641$	−19.3058	−	26.5721i	−0.762532	−	1.04953i	0.234468	−	0.972124i	$-0.424665\pi$
$642$	2.79359	+	2.67174i	0.110254	+	0.105445i
$643$	1.01864	+	3.13506i	0.0401714	+	0.123635i	0.969131	−	0.246546i	$-0.0792957\pi$
$643$	1.01864	+	3.13506i	0.0401714	+	0.123635i	−0.928960	+	0.370181i	$0.879296\pi$
$644$	2.42838	+	7.47379i	0.0956916	+	0.294508i
$645$	−11.3839	−	10.8874i	−0.448241	−	0.428690i
$646$	21.9056	+	30.1504i	0.861863	+	1.18625i
$647$	−5.53748	−	1.79924i	−0.217701	−	0.0707353i	0.198136	−	0.980175i	$-0.436511\pi$
$647$	−5.53748	−	1.79924i	−0.217701	−	0.0707353i	−0.415837	+	0.909439i	$0.636511\pi$
$648$	−7.72330	−	4.62067i	−0.303400	−	0.181517i
$649$		0			0
$650$		−	3.08922i		−	0.121169i
$651$	13.2962	+	6.40556i	0.521121	+	0.251054i
$652$	−5.72951	+	4.16273i	−0.224385	+	0.163025i
$653$	2.57317	−	3.54166i	0.100696	−	0.138596i	−0.755696	−	0.654923i	$-0.772701\pi$
$653$	2.57317	−	3.54166i	0.100696	−	0.138596i	0.856392	+	0.516327i	$0.172701\pi$
$654$	8.07009	−	1.46327i	0.315565	−	0.0572184i
$655$	−13.3021	+	4.32211i	−0.519756	+	0.168879i
$656$	−1.27362	−	0.925338i	−0.0497264	−	0.0361284i
$657$	4.87383	+	12.9980i	0.190146	+	0.507100i
$658$	−5.07776	+	15.6277i	−0.197952	+	0.609232i
$659$	15.3805			0.599141			0.299570	−	0.954074i	$-0.403157\pi$
$659$	15.3805			0.599141			0.299570	+	0.954074i	$0.403157\pi$
$660$		0			0
$661$	12.6047			0.490266			0.245133	−	0.969489i	$-0.421168\pi$
$661$	12.6047			0.490266			0.245133	+	0.969489i	$0.421168\pi$
$662$	−2.28987	+	7.04748i	−0.0889981	+	0.273908i
$663$	−8.39323	−	15.6028i	−0.325966	−	0.605961i
$664$	1.51625	+	1.10162i	0.0588418	+	0.0427511i
$665$	−22.7458	+	7.39056i	−0.882044	+	0.286594i
$666$	−0.134637	−	3.01788i	−0.00521706	−	0.116940i
$667$	1.30607	−	1.79765i	0.0505712	−	0.0696053i
$668$	2.05072	−	1.48993i	0.0793446	−	0.0576472i
$669$	−3.30866	+	6.86790i	−0.127920	+	0.265528i
$670$			31.3254i			1.21021i
$671$		0			0
$672$	−0.381966	+	2.81665i	−0.0147347	+	0.108655i
$673$	30.6554	+	9.96056i	1.18168	+	0.383951i	0.832991	−	0.553287i	$-0.186627\pi$
$673$	30.6554	+	9.96056i	1.18168	+	0.383951i	0.348690	+	0.937238i	$0.386627\pi$
$674$	−20.1103	−	27.6795i	−0.774621	−	1.06617i
$675$	−5.46130	−	9.14992i	−0.210206	−	0.352180i
$676$	3.31598	+	10.2055i	0.127538	+	0.392520i
$677$	−2.81576	−	8.66601i	−0.108218	−	0.333062i	0.882254	−	0.470774i	$-0.156025\pi$
$677$	−2.81576	−	8.66601i	−0.108218	−	0.333062i	−0.990472	+	0.137712i	$0.956025\pi$
$678$	−4.66376	+	4.87647i	−0.179111	+	0.187280i
$679$	3.46387	+	4.76761i	0.132931	+	0.182964i
$680$	17.1478	+	5.57167i	0.657590	+	0.213664i
$681$	−21.8548	−	2.96374i	−0.837479	−	0.113571i
$682$		0			0
$683$			28.1535i			1.07726i	0.842541	+	0.538632i	$0.181059\pi$
$683$			28.1535i			1.07726i	−0.842541	+	0.538632i	$0.818941\pi$
$684$	13.7388	+	9.07478i	0.525318	+	0.346983i
$685$	−1.99304	+	1.44803i	−0.0761501	+	0.0553263i
$686$	−10.9066	+	15.0117i	−0.416416	+	0.573148i
$687$	−1.98493	−	10.9471i	−0.0757298	−	0.417658i
$688$	3.25737	−	1.05838i	0.124186	−	0.0403505i
$689$	11.9738	+	8.69944i	0.456164	+	0.331422i
$690$	19.3952	−	10.4333i	0.738362	−	0.397188i
$691$	3.31810	−	10.2121i	0.126227	−	0.388485i	−0.867896	−	0.496746i	$-0.834528\pi$
$691$	3.31810	−	10.2121i	0.126227	−	0.388485i	0.994123	+	0.108261i	$0.0345281\pi$
$692$	0.949284			0.0360864
$693$		0			0
$694$	−20.9245			−0.794285
$695$	−6.93616	+	21.3473i	−0.263104	+	0.809750i
$696$	0.707805	−	0.380751i	0.0268293	−	0.0144323i
$697$	−8.64820	−	6.28329i	−0.327574	−	0.237996i
$698$	−28.0113	+	9.10144i	−1.06025	+	0.344495i
$699$	−5.19468	−	28.6492i	−0.196481	−	1.08361i
$700$	−1.97812	+	2.72265i	−0.0747660	+	0.102907i
$701$	33.6018	−	24.4131i	1.26912	−	0.922070i	0.269954	−	0.962873i	$-0.412992\pi$
$701$	33.6018	−	24.4131i	1.26912	−	0.922070i	0.999167	+	0.0408029i	$0.0129916\pi$
$702$	−5.89241	−	5.15266i	−0.222395	−	0.194475i
$703$			5.52664i			0.208441i
$704$		0			0
$705$	45.6332	+	6.18832i	1.71865	+	0.233066i
$706$	23.1359	+	7.51731i	0.870731	+	0.282918i
$707$	11.7413	+	16.1606i	0.441579	+	0.607781i
$708$	7.31720	−	7.65092i	0.274997	−	0.287539i
$709$	9.33679	+	28.7357i	0.350650	+	1.07919i	0.958489	+	0.285130i	$0.0920369\pi$
$709$	9.33679	+	28.7357i	0.350650	+	1.07919i	−0.607838	+	0.794061i	$0.707963\pi$
$710$	−0.736889	−	2.26791i	−0.0276550	−	0.0851132i
$711$	7.45431	−	5.94100i	0.279559	−	0.222805i
$712$	7.52906	+	10.3629i	0.282163	+	0.388365i
$713$	23.6468	+	7.68331i	0.885580	+	0.287742i
$714$	−2.59365	+	19.1258i	−0.0970649	+	0.715764i
$715$		0			0
$716$			18.5656i			0.693830i
$717$	−9.05000	+	18.7854i	−0.337979	+	0.701554i
$718$	−26.4772	+	19.2368i	−0.988122	+	0.717912i
$719$	29.5264	−	40.6397i	1.10115	−	1.51560i	0.267300	−	0.963613i	$-0.413869\pi$
$719$	29.5264	−	40.6397i	1.10115	−	1.51560i	0.833851	−	0.551990i	$-0.186131\pi$
$720$	7.95804	−	0.355032i	0.296579	−	0.0132313i
$721$	−1.38376	+	0.449611i	−0.0515340	+	0.0167444i
$722$	−8.99871	−	6.53795i	−0.334897	−	0.243317i
$723$	16.8737	+	31.3678i	0.627540	+	1.16658i
$724$	3.97992	−	12.2489i	0.147912	−	0.455228i
$725$	0.951585			0.0353410
$726$		0			0
$727$	42.9707			1.59369			0.796847	−	0.604181i	$-0.206499\pi$
$727$	42.9707			1.59369			0.796847	+	0.604181i	$0.206499\pi$
$728$	−0.763932	+	2.35114i	−0.0283132	+	0.0871391i
$729$	−26.5618	−	4.84466i	−0.983770	−	0.179432i
$730$	−9.94022	−	7.22199i	−0.367904	−	0.267298i
$731$	22.1184	−	7.18671i	0.818079	−	0.265810i
$732$	−23.6951	+	4.29640i	−0.875795	+	0.158799i
$733$	20.2596	−	27.8850i	0.748306	−	1.02995i	−0.249792	−	0.968300i	$-0.580362\pi$
$733$	20.2596	−	27.8850i	0.748306	−	1.02995i	0.998098	−	0.0616548i	$-0.0196378\pi$
$734$	−9.62969	+	6.99638i	−0.355438	+	0.258241i
$735$	17.8450	+	8.59697i	0.658224	+	0.317104i
$736$			4.78856i			0.176509i
$737$		0			0
$738$	−4.55226	−	1.25780i	−0.167571	−	0.0463002i
$739$	1.08368	+	0.352108i	0.0398637	+	0.0129525i	0.328881	−	0.944371i	$-0.393329\pi$
$739$	1.08368	+	0.352108i	0.0398637	+	0.0129525i	−0.289017	+	0.957324i	$0.593329\pi$
$740$	1.57162	+	2.16315i	0.0577739	+	0.0795189i
$741$	10.3492	+	9.89779i	0.380187	+	0.363604i
$742$	−4.98242	−	15.3343i	−0.182911	−	0.562941i
$743$	−4.53145	−	13.9464i	−0.166243	−	0.511643i	0.832883	−	0.553449i	$-0.186689\pi$
$743$	−4.53145	−	13.9464i	−0.166243	−	0.511643i	−0.999126	+	0.0418062i	$0.986689\pi$
$744$	6.49942	+	6.21593i	0.238280	+	0.227887i
$745$	−28.2054	−	38.8214i	−1.03336	−	1.42230i
$746$	−26.4207	−	8.58461i	−0.967331	−	0.314305i
$747$	5.41949	+	1.49741i	0.198289	+	0.0547875i
$748$		0			0
$749$		−	3.66250i		−	0.133825i
$750$	−12.2200	−	5.88709i	−0.446213	−	0.214966i
$751$	24.8491	−	18.0539i	0.906756	−	0.658797i	−0.0334362	−	0.999441i	$-0.510645\pi$
$751$	24.8491	−	18.0539i	0.906756	−	0.658797i	0.940192	+	0.340644i	$0.110645\pi$
$752$	−5.88545	+	8.10062i	−0.214620	+	0.295399i
$753$	−27.8916	+	5.05731i	−1.01643	+	0.184299i
$754$	0.664801	−	0.216007i	0.0242106	−	0.00786651i
$755$	−28.6353	−	20.8048i	−1.04215	−	0.757163i
$756$	1.89380	+	8.31433i	0.0688769	+	0.302389i
$757$	11.3743	−	35.0065i	0.413406	−	1.27233i	−0.500263	−	0.865873i	$-0.666763\pi$
$757$	11.3743	−	35.0065i	0.413406	−	1.27233i	0.913669	−	0.406459i	$-0.133237\pi$
$758$	7.86465			0.285657
$759$		0			0
$760$	−14.5736			−0.528639
$761$	−5.50036	+	16.9284i	−0.199388	+	0.613652i	0.800510	+	0.599320i	$0.204562\pi$
$761$	−5.50036	+	16.9284i	−0.199388	+	0.613652i	−0.999897	+	0.0143323i	$0.995438\pi$
$762$	0.193955	+	0.360557i	0.00702626	+	0.0130616i
$763$	−6.28678	−	4.56762i	−0.227597	−	0.165359i
$764$	3.07080	−	0.997763i	0.111098	−	0.0360978i
$765$	54.0372	−	2.41076i	1.95372	−	0.0871612i
$766$	−7.61538	+	10.4817i	−0.275155	+	0.378718i
$767$	7.44904	−	5.41205i	0.268969	−	0.195418i
$768$	−0.751740	+	1.56041i	−0.0271261	+	0.0563065i
$769$		−	15.5249i		−	0.559841i	−0.960023	−	0.279920i	$-0.909692\pi$
$769$		−	15.5249i		−	0.559841i	0.960023	−	0.279920i	$-0.0903081\pi$
$770$		0			0
$771$	−1.98683	+	14.6511i	−0.0715541	+	0.527645i
$772$	9.28718	+	3.01759i	0.334253	+	0.108605i
$773$	−20.4579	−	28.1579i	−0.735820	−	1.01277i	−0.998848	−	0.0479808i	$-0.984721\pi$
$773$	−20.4579	−	28.1579i	−0.735820	−	1.01277i	0.263029	−	0.964788i	$-0.415279\pi$
$774$	8.03522	−	6.40398i	0.288820	−	0.230186i
$775$	3.29040	+	10.1268i	0.118195	+	0.363766i
$776$	1.10968	+	3.41524i	0.0398351	+	0.122600i
$777$	−1.97827	+	2.06850i	−0.0709702	+	0.0742070i
$778$	15.2222	+	20.9516i	0.545744	+	0.751152i
$779$	8.21745	+	2.67001i	0.294421	+	0.0956631i
$780$	6.86536	+	0.931013i	0.245819	+	0.0333356i
$781$		0			0
$782$			32.5156i			1.16276i
$783$	1.58720	−	1.81506i	0.0567217	−	0.0648650i
$784$	−3.48433	+	2.53151i	−0.124440	+	0.0904112i
$785$	−15.1521	+	20.8551i	−0.540803	+	0.744352i
$786$	−1.62772	−	8.97705i	−0.0580588	−	0.320201i
$787$	17.9656	−	5.83738i	0.640405	−	0.208080i	0.0292263	−	0.999573i	$-0.490696\pi$
$787$	17.9656	−	5.83738i	0.640405	−	0.208080i	0.611179	+	0.791493i	$0.290696\pi$
$788$	11.3003	+	8.21015i	0.402557	+	0.292475i
$789$	20.6939	−	11.1319i	0.736723	−	0.396307i
$790$	−2.60717	+	8.02405i	−0.0927590	+	0.285483i
$791$	6.39323			0.227317
$792$		0			0
$793$	−20.9443			−0.743753
$794$	5.56187	−	17.1177i	0.197383	−	0.607483i
$795$	−39.7940	+	21.4065i	−1.41135	+	0.759209i
$796$	−12.9183	−	9.38572i	−0.457878	−	0.332668i
$797$	43.0416	−	13.9851i	1.52461	−	0.495376i	0.577530	−	0.816370i	$-0.304017\pi$
$797$	43.0416	−	13.9851i	1.52461	−	0.495376i	0.947081	+	0.320994i	$0.104017\pi$
$798$	−2.78330	−	15.3502i	−0.0985279	−	0.543392i
$799$	−39.9637	+	55.0054i	−1.41382	+	1.94595i
$800$	−1.65906	+	1.20538i	−0.0586568	+	0.0426166i
$801$	32.0644	+	21.1792i	1.13294	+	0.748329i
$802$			3.76803i			0.133054i
$803$		0			0
$804$	−20.2481	−	2.74584i	−0.714094	−	0.0968384i
$805$	−19.8453	−	6.44812i	−0.699454	−	0.227266i
$806$	4.59751	+	6.32793i	0.161940	+	0.222892i
$807$	−14.1843	+	14.8312i	−0.499311	+	0.522083i
$808$	3.76143	+	11.5765i	0.132326	+	0.407259i
$809$	−7.56069	−	23.2694i	−0.265820	−	0.818109i	−0.991503	−	0.130080i	$-0.958476\pi$
$809$	−7.56069	−	23.2694i	−0.265820	−	0.818109i	0.725684	−	0.688028i	$-0.241524\pi$
$810$	21.9803	−	9.37943i	0.772310	−	0.329560i
$811$	−7.12457	−	9.80613i	−0.250177	−	0.344340i	0.665396	−	0.746491i	$-0.268263\pi$
$811$	−7.12457	−	9.80613i	−0.250177	−	0.344340i	−0.915573	+	0.402151i	$0.868263\pi$
$812$	−0.724231	−	0.235317i	−0.0254155	−	0.00825801i
$813$	5.03945	−	37.1613i	0.176741	−	1.30330i
$814$		0			0
$815$		−	18.8051i		−	0.658715i
$816$	−5.10451	+	10.5956i	−0.178694	+	0.370921i
$817$	−15.2078	+	11.0491i	−0.532055	+	0.386561i
$818$	−8.44886	+	11.6289i	−0.295408	+	0.406594i
$819$	0.330539	+	7.40904i	0.0115500	+	0.258893i
$820$	3.97562	−	1.29176i	0.138835	−	0.0451101i
$821$	−31.2340	−	22.6928i	−1.09007	−	0.791984i	−0.110661	−	0.993858i	$-0.535297\pi$
$821$	−31.2340	−	22.6928i	−1.09007	−	0.791984i	−0.979412	+	0.201874i	$0.935297\pi$
$822$	−0.761274	−	1.41519i	−0.0265525	−	0.0493603i
$823$	−2.20652	+	6.79097i	−0.0769144	+	0.236718i	−0.982120	−	0.188256i	$-0.939717\pi$
$823$	−2.20652	+	6.79097i	−0.0769144	+	0.236718i	0.905206	+	0.424974i	$0.139717\pi$
$824$	−0.886596			−0.0308860
$825$		0			0
$826$	−10.0306			−0.349010
$827$	−4.45966	+	13.7254i	−0.155077	+	0.477279i	−0.998169	−	0.0604911i	$-0.980733\pi$
$827$	−4.45966	+	13.7254i	−0.155077	+	0.477279i	0.843091	+	0.537770i	$0.180733\pi$
$828$	5.04376	+	13.4512i	0.175283	+	0.467460i
$829$	45.0465	+	32.7282i	1.56453	+	1.13670i	0.932169	+	0.362023i	$0.117914\pi$
$829$	45.0465	+	32.7282i	1.56453	+	1.13670i	0.632360	+	0.774674i	$0.282086\pi$
$830$	−4.73299	+	1.53784i	−0.164284	+	0.0533792i
$831$	6.94241	−	1.25880i	0.240830	−	0.0436672i
$832$	−0.885446	+	1.21871i	−0.0306973	+	0.0422512i
$833$	−23.6595	+	17.1896i	−0.819753	+	0.595586i
$834$	−13.1905	−	6.35460i	−0.456748	−	0.220042i
$835$			6.73076i			0.232928i
$836$		0			0
$837$	24.8042	+	10.6149i	0.857358	+	0.366903i
$838$	29.6350	+	9.62899i	1.02372	+	0.332628i
$839$	24.3332	+	33.4918i	0.840075	+	1.15626i	0.985963	+	0.166963i	$0.0533961\pi$
$839$	24.3332	+	33.4918i	0.840075	+	1.15626i	−0.145888	+	0.989301i	$0.546604\pi$
$840$	−5.45456	−	5.21664i	−0.188200	−	0.179991i
$841$	−8.89496	−	27.3759i	−0.306723	−	0.943995i
$842$	3.34251	+	10.2872i	0.115191	+	0.354520i
$843$	22.3619	+	21.3865i	0.770185	+	0.736591i
$844$	1.33315	+	1.83493i	0.0458891	+	0.0631609i
$845$	−27.0989	−	8.80497i	−0.932231	−	0.302900i
$846$	−8.00000	+	28.9539i	−0.275046	+	0.995455i
$847$		0			0
$848$		−	9.82493i		−	0.337389i
$849$	4.74314	+	2.28504i	0.162784	+	0.0784224i
$850$	−11.2655	+	8.18485i	−0.386403	+	0.280738i
$851$	−2.83424	+	3.90099i	−0.0971564	+	0.133724i
$852$	1.53052	−	0.277515i	0.0524348	−	0.00950749i
$853$	−35.5391	+	11.5473i	−1.21683	+	0.395374i	−0.845928	−	0.533297i	$-0.820953\pi$
$853$	−35.5391	+	11.5473i	−1.21683	+	0.395374i	−0.370906	+	0.928670i	$0.620953\pi$
$854$	18.4590	+	13.4113i	0.631654	+	0.458924i
$855$	−40.9374	+	15.3502i	−1.40003	+	0.524966i
$856$	0.689654	−	2.12254i	0.0235719	−	0.0725468i
$857$	−34.9831			−1.19500			−0.597499	−	0.801869i	$-0.703839\pi$
$857$	−34.9831			−1.19500			−0.597499	+	0.801869i	$0.703839\pi$
$858$		0			0
$859$	3.21505			0.109696			0.0548481	−	0.998495i	$-0.482533\pi$
$859$	3.21505			0.109696			0.0548481	+	0.998495i	$0.482533\pi$
$860$	−2.81035	+	8.64936i	−0.0958320	+	0.294941i
$861$	2.11987	+	3.94078i	0.0722450	+	0.134301i
$862$	32.2249	+	23.4128i	1.09758	+	0.797442i
$863$	−43.0565	+	13.9899i	−1.46566	+	0.476222i	−0.929794	−	0.368082i	$-0.880015\pi$
$863$	−43.0565	+	13.9899i	−1.46566	+	0.476222i	−0.535866	+	0.844303i	$0.680015\pi$
$864$	−0.468081	+	5.17503i	−0.0159244	+	0.176058i
$865$	−1.48160	+	2.03925i	−0.0503760	+	0.0693366i
$866$	13.0699	−	9.49585i	0.444134	−	0.322682i
$867$	−21.8814	+	45.4200i	−0.743132	+	1.54254i
$868$		−	8.52098i		−	0.289221i
$869$		0			0
$870$	−0.286784	+	2.11477i	−0.00972288	+	0.0716973i
$871$	−16.9017	−	5.49168i	−0.572691	−	0.186079i
$872$	−2.78330	−	3.83089i	−0.0942546	−	0.129730i
$873$	6.71434	+	8.42464i	0.227246	+	0.285131i
$874$	−8.12151	−	24.9954i	−0.274714	−	0.845484i
$875$	3.97141	+	12.2227i	0.134258	+	0.413204i
$876$	5.53945	−	5.79210i	0.187161	−	0.195697i
$877$	28.0818	+	38.6513i	0.948255	+	1.30516i	0.952298	+	0.305169i	$0.0987128\pi$
$877$	28.0818	+	38.6513i	0.948255	+	1.30516i	−0.00404370	+	0.999992i	$0.501287\pi$
$878$	5.83943	+	1.89735i	0.197071	+	0.0640323i
$879$	40.0613	+	5.43271i	1.35123	+	0.183241i
$880$		0			0
$881$		−	34.4685i		−	1.16127i	−0.814163	−	0.580636i	$-0.802804\pi$
$881$		−	34.4685i		−	1.16127i	0.814163	−	0.580636i	$-0.197196\pi$
$882$	−7.12112	+	10.7811i	−0.239780	+	0.363018i
$883$	30.0307	−	21.8186i	1.01061	−	0.734253i	0.0462752	−	0.998929i	$-0.485265\pi$
$883$	30.0307	−	21.8186i	1.01061	−	0.734253i	0.964338	+	0.264676i	$0.0852649\pi$
$884$	−6.01241	+	8.27537i	−0.202219	+	0.278331i
$885$	5.01532	+	27.6600i	0.168588	+	0.929781i
$886$	1.55768	−	0.506119i	0.0523311	−	0.0170034i
$887$	−34.7710	−	25.2626i	−1.16750	−	0.848235i	−0.176788	−	0.984249i	$-0.556571\pi$
$887$	−34.7710	−	25.2626i	−1.16750	−	0.848235i	−0.990707	+	0.136014i	$0.956571\pi$
$888$	−1.53597	+	0.826249i	−0.0515439	+	0.0277271i
$889$	0.119871	−	0.368925i	0.00402034	−	0.0123733i
$890$	−34.0125			−1.14010
$891$		0			0
$892$	4.40134			0.147368
$893$	16.9821	−	52.2656i	0.568286	−	1.74900i
$894$	27.5657	−	14.8284i	0.921933	−	0.495937i
$895$	−39.8826	−	28.9764i	−1.33313	−	0.968575i
$896$	1.56076	−	0.507121i	0.0521412	−	0.0169417i
$897$	2.22911	+	12.2938i	0.0744278	+	0.410477i
$898$	−10.7458	+	14.7903i	−0.358591	+	0.493559i
$899$	−1.94922	+	1.41619i	−0.0650101	+	0.0472326i
$900$	−3.39072	+	5.13341i	−0.113024	+	0.171114i
$901$		−	66.7138i		−	2.22256i
$902$		0			0
$903$	−9.64702	−	1.30823i	−0.321033	−	0.0435353i
$904$	3.70508	+	1.20385i	0.123229	+	0.0400396i
$905$	20.1014	+	27.6672i	0.668194	+	0.919690i
$906$	15.9578	−	16.6856i	0.530162	−	0.554342i
$907$	−11.6924	−	35.9855i	−0.388240	−	1.19488i	−0.934103	−	0.357004i	$-0.883798\pi$
$907$	−11.6924	−	35.9855i	−0.388240	−	1.19488i	0.545863	−	0.837874i	$-0.316202\pi$
$908$	3.93483	+	12.1102i	0.130582	+	0.401890i
$909$	22.7593	+	28.5566i	0.754879	+	0.947164i
$910$	−3.85840	−	5.31064i	−0.127905	−	0.176046i
$911$	−19.3212	−	6.27785i	−0.640141	−	0.207994i	−0.0290788	−	0.999577i	$-0.509257\pi$
$911$	−19.3212	−	6.27785i	−0.640141	−	0.207994i	−0.611062	+	0.791583i	$0.709257\pi$
$912$	1.27745	−	9.42004i	0.0423007	−	0.311929i
$913$		0			0
$914$		−	27.9848i		−	0.925654i
$915$	27.7528	−	57.6073i	0.917478	−	1.90444i
$916$	−5.19661	+	3.77556i	−0.171701	+	0.124748i
$917$	−5.08095	+	6.99333i	−0.167788	+	0.230940i
$918$	−3.17839	+	35.1398i	−0.104903	+	1.15979i
$919$	31.7507	−	10.3164i	1.04736	−	0.340308i	0.265728	−	0.964048i	$-0.414388\pi$
$919$	31.7507	−	10.3164i	1.04736	−	0.340308i	0.781632	+	0.623740i	$0.214388\pi$
$920$	−10.2868	−	7.47379i	−0.339145	−	0.246403i
$921$	−24.6339	−	45.7937i	−0.811715	−	1.50895i
$922$	−9.37430	+	28.8511i	−0.308726	+	0.950161i
$923$	1.35284			0.0445293
$924$		0			0
$925$	−2.06499			−0.0678964
$926$	3.38782	−	10.4266i	0.111331	−	0.342640i
$927$	−2.49046	+	0.933845i	−0.0817976	+	0.0306715i
$928$	−0.375405	−	0.272747i	−0.0123233	−	0.00895337i
$929$	22.3896	−	7.27483i	0.734579	−	0.238679i	0.0822466	−	0.996612i	$-0.473790\pi$
$929$	22.3896	−	7.27483i	0.734579	−	0.238679i	0.652333	+	0.757933i	$0.273790\pi$
$930$	−23.4971	+	4.26049i	−0.770499	+	0.139707i
$931$	13.8941	−	19.1235i	0.455360	−	0.626749i
$932$	−13.5999	+	9.88087i	−0.445478	+	0.323659i
$933$	0.772753	+	0.372279i	0.0252988	+	0.0121879i
$934$		−	32.2185i		−	1.05422i
$935$		0			0
$936$	−1.20357	+	4.35602i	−0.0393400	+	0.142381i
$937$	−23.6413	−	7.68152i	−0.772327	−	0.250944i	−0.103766	−	0.994602i	$-0.533089\pi$
$937$	−23.6413	−	7.68152i	−0.772327	−	0.250944i	−0.668561	+	0.743657i	$0.733089\pi$
$938$	11.3796	+	15.6627i	0.371558	+	0.511405i
$939$	−35.5230	−	33.9736i	−1.15925	−	1.10868i
$940$	−8.21599	−	25.2862i	−0.267976	−	0.824745i
$941$	−2.18371	−	6.72077i	−0.0711869	−	0.219091i	0.909133	−	0.416506i	$-0.136745\pi$
$941$	−2.18371	−	6.72077i	−0.0711869	−	0.219091i	−0.980320	+	0.197415i	$0.936745\pi$
$942$	−12.1521	−	11.6221i	−0.395938	−	0.378668i
$943$	4.43104	+	6.09880i	0.144294	+	0.198604i
$944$	−5.81307	−	1.88878i	−0.189199	−	0.0614746i
$945$	−20.8166	−	8.90839i	−0.677164	−	0.289790i
$946$		0			0
$947$			11.7619i			0.382210i	0.981570	+	0.191105i	$0.0612071\pi$
$947$			11.7619i			0.382210i	−0.981570	+	0.191105i	$0.938793\pi$
$948$	−4.95804	−	2.38857i	−0.161030	−	0.0775772i
$949$	5.63927	−	4.09717i	0.183058	−	0.133000i
$950$	6.61566	−	9.10568i	0.214640	−	0.295427i
$951$	11.3175	−	2.05209i	0.366995	−	0.0665436i
$952$	10.5980	−	3.44348i	0.343482	−	0.111604i
$953$	−2.20038	−	1.59867i	−0.0712773	−	0.0517860i	0.551576	−	0.834125i	$-0.314027\pi$
$953$	−2.20038	−	1.59867i	−0.0712773	−	0.0517860i	−0.622853	+	0.782339i	$0.714027\pi$
$954$	−10.3485	−	27.5984i	−0.335046	−	0.893531i
$955$	−2.64938	+	8.15395i	−0.0857319	+	0.263856i
$956$	12.0387			0.389361
$957$		0			0
$958$	18.8328			0.608461
$959$	−0.470493	+	1.44803i	−0.0151930	+	0.0467593i
$960$	−2.17879	−	4.05031i	−0.0703202	−	0.130723i
$961$	3.26834	+	2.37459i	0.105430	+	0.0765997i
$962$	−1.44265	+	0.468746i	−0.0465130	+	0.0151130i
$963$	−0.298401	−	6.68865i	−0.00961582	−	0.215539i
$964$	12.0873	−	16.6368i	0.389307	−	0.535835i
$965$	−20.9774	+	15.2410i	−0.675287	+	0.490625i
$966$	5.90748	−	12.2624i	0.190070	−	0.394535i
$967$			21.8182i			0.701625i	0.936446	+	0.350812i	$0.114095\pi$
$967$			21.8182i			0.701625i	−0.936446	+	0.350812i	$0.885905\pi$
$968$		0			0
$969$	8.67424	−	63.9646i	0.278657	−	2.05484i
$970$	−9.06854	−	2.94655i	−0.291173	−	0.0946079i
$971$	−26.0801	−	35.8962i	−0.836952	−	1.15197i	−0.986589	−	0.163224i	$-0.947811\pi$
$971$	−26.0801	−	35.8962i	−0.836952	−	1.15197i	0.149637	−	0.988741i	$-0.452189\pi$
$972$	4.13597	+	15.0298i	0.132661	+	0.482080i
$973$	4.28678	+	13.1934i	0.137428	+	0.422960i
$974$	8.30030	+	25.5457i	0.265959	+	0.818537i
$975$	−3.69823	+	3.86690i	−0.118438	+	0.123840i
$976$	8.17223	+	11.2481i	0.261587	+	0.360043i
$977$	−29.7942	−	9.68073i	−0.953201	−	0.309714i	−0.209186	−	0.977876i	$-0.567081\pi$
$977$	−29.7942	−	9.68073i	−0.953201	−	0.309714i	−0.744016	+	0.668162i	$0.767081\pi$
$978$	12.1552	+	1.64837i	0.388681	+	0.0527091i
$979$		0			0
$980$		−	11.4361i		−	0.365313i
$981$	−11.8534	−	7.82940i	−0.378450	−	0.249974i
$982$	−15.4032	+	11.1911i	−0.491537	+	0.357123i
$983$	−22.5840	+	31.0843i	−0.720319	+	0.991434i	0.279194	+	0.960235i	$0.409933\pi$
$983$	−22.5840	+	31.0843i	−0.720319	+	0.991434i	−0.999513	+	0.0311991i	$0.990067\pi$
$984$	0.486479	+	2.68298i	0.0155084	+	0.0855304i
$985$	−35.2741	+	11.4612i	−1.12392	+	0.365185i
$986$	−2.54910	−	1.85203i	−0.0811798	−	0.0589806i
$987$	25.0646	−	13.4831i	0.797816	−	0.429171i
$988$	2.55491	−	7.86319i	0.0812824	−	0.250162i
$989$	−16.4008			−0.521517
$990$		0			0
$991$	−28.2808			−0.898371			−0.449185	−	0.893439i	$-0.648286\pi$
$991$	−28.2808			−0.898371			−0.449185	+	0.893439i	$0.648286\pi$
$992$	1.60451	−	4.93818i	0.0509433	−	0.156787i
$993$	11.3031	−	6.08032i	0.358694	−	0.192953i
$994$	−1.19231	−	0.866266i	−0.0378178	−	0.0274763i
$995$	40.3248	−	13.1023i	1.27838	−	0.415371i
$996$	−0.579155	−	3.19410i	−0.0183512	−	0.101209i
$997$	13.8910	−	19.1193i	0.439932	−	0.605514i	−0.530265	−	0.847832i	$-0.677908\pi$
$997$	13.8910	−	19.1193i	0.439932	−	0.605514i	0.970197	+	0.242318i	$0.0779076\pi$
$998$	8.59175	−	6.24227i	0.271967	−	0.197596i
$999$	−3.44430	+	3.93878i	−0.108973	+	0.124617i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.h.f.233.2		8
3.2	odd	2		726.2.h.c.233.2		8
11.2	odd	10		726.2.h.d.239.1		8
11.3	even	5		726.2.h.j.161.1		8
11.4	even	5		726.2.b.c.725.1		8
11.5	even	5		726.2.h.h.215.2		8
11.6	odd	10		726.2.h.c.215.2		8
11.7	odd	10		726.2.b.e.725.1		8
11.8	odd	10		66.2.h.a.29.1	✓	8
11.9	even	5		66.2.h.b.41.1	yes	8
11.10	odd	2		726.2.h.a.233.2		8
33.2	even	10		726.2.h.j.239.1		8
33.5	odd	10		726.2.h.a.215.2		8
33.8	even	10		66.2.h.b.29.2	yes	8
33.14	odd	10		726.2.h.d.161.2		8
33.17	even	10	inner	726.2.h.f.215.2		8
33.20	odd	10		66.2.h.a.41.1	yes	8
33.26	odd	10		726.2.b.e.725.2		8
33.29	even	10		726.2.b.c.725.2		8
33.32	even	2		726.2.h.h.233.2		8
44.19	even	10		528.2.bn.b.161.2		8
44.31	odd	10		528.2.bn.a.305.2		8
132.107	odd	10		528.2.bn.a.161.1		8
132.119	even	10		528.2.bn.b.305.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.h.a.29.1	✓	8	11.8	odd	10
66.2.h.a.41.1	yes	8	33.20	odd	10
66.2.h.b.29.2	yes	8	33.8	even	10
66.2.h.b.41.1	yes	8	11.9	even	5
528.2.bn.a.161.1		8	132.107	odd	10
528.2.bn.a.305.2		8	44.31	odd	10
528.2.bn.b.161.2		8	44.19	even	10
528.2.bn.b.305.2		8	132.119	even	10
726.2.b.c.725.1		8	11.4	even	5
726.2.b.c.725.2		8	33.29	even	10
726.2.b.e.725.1		8	11.7	odd	10
726.2.b.e.725.2		8	33.26	odd	10
726.2.h.a.215.2		8	33.5	odd	10
726.2.h.a.233.2		8	11.10	odd	2
726.2.h.c.215.2		8	11.6	odd	10
726.2.h.c.233.2		8	3.2	odd	2
726.2.h.d.161.2		8	33.14	odd	10
726.2.h.d.239.1		8	11.2	odd	10
726.2.h.f.215.2		8	33.17	even	10	inner
726.2.h.f.233.2		8	1.1	even	1	trivial
726.2.h.h.215.2		8	11.5	even	5
726.2.h.h.233.2		8	33.32	even	2
726.2.h.j.161.1		8	11.3	even	5
726.2.h.j.239.1		8	33.2	even	10

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:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(1.52536 - 0.820539i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(2.52536 - 0.820539i) q^{5} +(0.309017 + 1.70426i) q^{6} +(0.964601 - 1.32766i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.65343 - 2.50323i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(1.52536 - 0.820539i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(2.52536 - 0.820539i) q^{5} +(0.309017 + 1.70426i) q^{6} +(0.964601 - 1.32766i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.65343 - 2.50323i) q^{9} +2.65532i q^{10} +(-1.71634 - 0.232753i) q^{12} +(-1.43268 - 0.465507i) q^{13} +(0.964601 + 1.32766i) q^{14} +(3.17879 - 3.32377i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.09831 + 6.45792i) q^{17} +(1.86977 + 2.34605i) q^{18} +(-3.22603 - 4.44024i) q^{19} +(-2.52536 - 0.820539i) q^{20} +(0.381966 - 2.81665i) q^{21} -4.78856i q^{23} +(0.751740 - 1.56041i) q^{24} +(1.65906 - 1.20538i) q^{25} +(0.885446 - 1.21871i) q^{26} +(0.468081 - 5.17503i) q^{27} +(-1.56076 + 0.507121i) q^{28} +(0.375405 + 0.272747i) q^{29} +(2.17879 + 4.05031i) q^{30} +(-1.60451 + 4.93818i) q^{31} -1.00000 q^{32} -6.79026 q^{34} +(1.34657 - 4.14431i) q^{35} +(-2.80902 + 1.05329i) q^{36} +(-0.814648 - 0.591876i) q^{37} +(5.21982 - 1.69602i) q^{38} +(-2.56732 + 0.465507i) q^{39} +(1.56076 - 2.14820i) q^{40} +(-1.27362 + 0.925338i) q^{41} +(2.56076 + 1.23366i) q^{42} -3.42500i q^{43} +(2.12151 - 7.67826i) q^{45} +(4.55420 + 1.47975i) q^{46} +(5.88545 + 8.10062i) q^{47} +(1.25174 + 1.19714i) q^{48} +(1.33089 + 4.09607i) q^{49} +(0.633706 + 1.95035i) q^{50} +(8.49964 + 8.12890i) q^{51} +(0.885446 + 1.21871i) q^{52} +(-9.34406 - 3.03607i) q^{53} +(4.77710 + 2.04434i) q^{54} -1.64108i q^{56} +(-8.56424 - 4.12588i) q^{57} +(-0.375405 + 0.272747i) q^{58} +(-3.59268 + 4.94489i) q^{59} +(-4.52536 + 0.820539i) q^{60} +(13.2229 - 4.29640i) q^{61} +(-4.20067 - 3.05196i) q^{62} +(-1.72853 - 4.60981i) q^{63} +(0.309017 - 0.951057i) q^{64} -4.00000 q^{65} +11.7972 q^{67} +(2.09831 - 6.45792i) q^{68} +(-3.92920 - 7.30427i) q^{69} +(3.52536 + 2.56132i) q^{70} +(-0.854102 + 0.277515i) q^{71} +(-0.133706 - 2.99702i) q^{72} +(-2.71982 + 3.74351i) q^{73} +(0.814648 - 0.591876i) q^{74} +(1.54160 - 3.19996i) q^{75} +5.48844i q^{76} +(0.350622 - 2.58551i) q^{78} +(3.02188 + 0.981868i) q^{79} +(1.56076 + 2.14820i) q^{80} +(-3.53232 - 8.27785i) q^{81} +(-0.486479 - 1.49723i) q^{82} +(0.579155 + 1.78246i) q^{83} +(-1.96460 + 2.05420i) q^{84} +(10.5980 + 14.5868i) q^{85} +(3.25737 + 1.05838i) q^{86} +(0.796426 + 0.108003i) q^{87} +12.8092i q^{89} +(6.64687 + 4.39039i) q^{90} +(-2.00000 + 1.45309i) q^{91} +(-2.81465 + 3.87403i) q^{92} +(1.60451 + 8.84906i) q^{93} +(-9.52285 + 3.09416i) q^{94} +(-11.7903 - 8.56613i) q^{95} +(-1.52536 + 0.820539i) q^{96} +(-1.10968 + 3.41524i) q^{97} -4.30687 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 3 q^{3} - 2 q^{4} + 5 q^{5} - 2 q^{6} + 5 q^{7} + 2 q^{8} + 7 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 + 5 * q^5 - 2 * q^6 + 5 * q^7 + 2 * q^8 + 7 * q^9	\( 8 q + 2 q^{2} - 3 q^{3} - 2 q^{4} + 5 q^{5} - 2 q^{6} + 5 q^{7} + 2 q^{8} + 7 q^{9} - 3 q^{12} + 10 q^{13} + 5 q^{14} + 4 q^{15} - 2 q^{16} + 15 q^{17} - 2 q^{18} + 10 q^{19} - 5 q^{20} + 12 q^{21} - 2 q^{24} - q^{25} - 15 q^{27} - 22 q^{29} - 4 q^{30} - 2 q^{31} - 8 q^{32} + 10 q^{34} + 17 q^{35} - 18 q^{36} + 6 q^{37} + 15 q^{38} - 42 q^{39} - 3 q^{41} + 8 q^{42} - 8 q^{45} - 10 q^{46} + 40 q^{47} + 2 q^{48} + 7 q^{49} + 6 q^{50} + 25 q^{51} - 30 q^{53} + 15 q^{54} - 40 q^{57} + 22 q^{58} - 35 q^{59} - 21 q^{60} + 20 q^{61} - 13 q^{62} - 29 q^{63} - 2 q^{64} - 32 q^{65} - 2 q^{67} + 15 q^{68} - 26 q^{69} + 13 q^{70} + 20 q^{71} - 2 q^{72} + 5 q^{73} - 6 q^{74} + 6 q^{75} - 8 q^{78} + 25 q^{79} + 19 q^{81} - 2 q^{82} + 9 q^{83} - 13 q^{84} + 40 q^{85} + 10 q^{86} + 42 q^{87} + 13 q^{90} - 16 q^{91} - 10 q^{92} + 2 q^{93} - 10 q^{94} - 30 q^{95} + 3 q^{96} - q^{97} - 22 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 + 5 * q^5 - 2 * q^6 + 5 * q^7 + 2 * q^8 + 7 * q^9 - 3 * q^12 + 10 * q^13 + 5 * q^14 + 4 * q^15 - 2 * q^16 + 15 * q^17 - 2 * q^18 + 10 * q^19 - 5 * q^20 + 12 * q^21 - 2 * q^24 - q^25 - 15 * q^27 - 22 * q^29 - 4 * q^30 - 2 * q^31 - 8 * q^32 + 10 * q^34 + 17 * q^35 - 18 * q^36 + 6 * q^37 + 15 * q^38 - 42 * q^39 - 3 * q^41 + 8 * q^42 - 8 * q^45 - 10 * q^46 + 40 * q^47 + 2 * q^48 + 7 * q^49 + 6 * q^50 + 25 * q^51 - 30 * q^53 + 15 * q^54 - 40 * q^57 + 22 * q^58 - 35 * q^59 - 21 * q^60 + 20 * q^61 - 13 * q^62 - 29 * q^63 - 2 * q^64 - 32 * q^65 - 2 * q^67 + 15 * q^68 - 26 * q^69 + 13 * q^70 + 20 * q^71 - 2 * q^72 + 5 * q^73 - 6 * q^74 + 6 * q^75 - 8 * q^78 + 25 * q^79 + 19 * q^81 - 2 * q^82 + 9 * q^83 - 13 * q^84 + 40 * q^85 + 10 * q^86 + 42 * q^87 + 13 * q^90 - 16 * q^91 - 10 * q^92 + 2 * q^93 - 10 * q^94 - 30 * q^95 + 3 * q^96 - q^97 - 22 * q^98

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