LMFDB - Embedded newform 546.2.q.h.251.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(251,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("546.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			251.1
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	546.251
Dual form			546.2.q.h.335.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 1.65831i) q^{3} +(-0.500000 - 0.866025i) q^{4} -0.792287i q^{5} +(-1.18614 - 1.26217i) q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-2.50000 - 1.65831i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 1.65831i) q^{3} +(-0.500000 - 0.866025i) q^{4} -0.792287i q^{5} +(-1.18614 - 1.26217i) q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-2.50000 - 1.65831i) q^{9} +(-0.686141 - 0.396143i) q^{10} +(2.18614 - 3.78651i) q^{11} +(-1.68614 + 0.396143i) q^{12} +(-3.50000 + 0.866025i) q^{13} +(2.00000 - 1.73205i) q^{14} +(-1.31386 - 0.396143i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.18614 - 3.78651i) q^{17} +(-2.68614 + 1.33591i) q^{18} +(1.18614 + 2.05446i) q^{19} +(-0.686141 + 0.396143i) q^{20} +(2.68614 - 3.71277i) q^{21} +(-2.18614 - 3.78651i) q^{22} +(3.68614 + 2.12819i) q^{23} +(-0.500000 + 1.65831i) q^{24} +4.37228 q^{25} +(-1.00000 + 3.46410i) q^{26} +(-4.00000 + 3.31662i) q^{27} +(-0.500000 - 2.59808i) q^{28} +(2.18614 + 1.26217i) q^{29} +(-1.00000 + 0.939764i) q^{30} -6.74456 q^{31} +(0.500000 + 0.866025i) q^{32} +(-5.18614 - 5.51856i) q^{33} -4.37228 q^{34} +(0.686141 - 1.98072i) q^{35} +(-0.186141 + 2.99422i) q^{36} +(-10.1168 - 5.84096i) q^{37} +2.37228 q^{38} +(-0.313859 + 6.23711i) q^{39} +0.792287i q^{40} +(8.18614 + 4.72627i) q^{41} +(-1.87228 - 4.18265i) q^{42} +(2.00000 + 3.46410i) q^{43} -4.37228 q^{44} +(-1.31386 + 1.98072i) q^{45} +(3.68614 - 2.12819i) q^{46} +0.939764i q^{47} +(1.18614 + 1.26217i) q^{48} +(5.50000 + 4.33013i) q^{49} +(2.18614 - 3.78651i) q^{50} +(-7.37228 + 1.73205i) q^{51} +(2.50000 + 2.59808i) q^{52} +2.22938i q^{53} +(0.872281 + 5.12241i) q^{54} +(-3.00000 - 1.73205i) q^{55} +(-2.50000 - 0.866025i) q^{56} +(4.00000 - 0.939764i) q^{57} +(2.18614 - 1.26217i) q^{58} +(5.31386 - 3.06796i) q^{59} +(0.313859 + 1.33591i) q^{60} +(-4.50000 + 2.59808i) q^{61} +(-3.37228 + 5.84096i) q^{62} +(-4.81386 - 6.31084i) q^{63} +1.00000 q^{64} +(0.686141 + 2.77300i) q^{65} +(-7.37228 + 1.73205i) q^{66} +(10.1168 + 5.84096i) q^{67} +(-2.18614 + 3.78651i) q^{68} +(5.37228 - 5.04868i) q^{69} +(-1.37228 - 1.58457i) q^{70} +(-8.05842 - 13.9576i) q^{71} +(2.50000 + 1.65831i) q^{72} +10.7446 q^{73} +(-10.1168 + 5.84096i) q^{74} +(2.18614 - 7.25061i) q^{75} +(1.18614 - 2.05446i) q^{76} +(8.74456 - 7.57301i) q^{77} +(5.24456 + 3.39036i) q^{78} +9.62772 q^{79} +(0.686141 + 0.396143i) q^{80} +(3.50000 + 8.29156i) q^{81} +(8.18614 - 4.72627i) q^{82} +1.58457i q^{83} +(-4.55842 - 0.469882i) q^{84} +(-3.00000 + 1.73205i) q^{85} +4.00000 q^{86} +(3.18614 - 2.99422i) q^{87} +(-2.18614 + 3.78651i) q^{88} +(9.30298 + 5.37108i) q^{89} +(1.05842 + 2.12819i) q^{90} +(-9.50000 - 0.866025i) q^{91} -4.25639i q^{92} +(-3.37228 + 11.1846i) q^{93} +(0.813859 + 0.469882i) q^{94} +(1.62772 - 0.939764i) q^{95} +(1.68614 - 0.396143i) q^{96} +(0.372281 + 0.644810i) q^{97} +(6.50000 - 2.59808i) q^{98} +(-11.7446 + 5.84096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + q^{6} + 10 q^{7} - 4 q^{8} - 10 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + q^6 + 10 * q^7 - 4 * q^8 - 10 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + q^{6} + 10 q^{7} - 4 q^{8} - 10 q^{9} + 3 q^{10} + 3 q^{11} - q^{12} - 14 q^{13} + 8 q^{14} - 11 q^{15} - 2 q^{16} - 3 q^{17} - 5 q^{18} - q^{19} + 3 q^{20} + 5 q^{21} - 3 q^{22} + 9 q^{23} - 2 q^{24} + 6 q^{25} - 4 q^{26} - 16 q^{27} - 2 q^{28} + 3 q^{29} - 4 q^{30} - 4 q^{31} + 2 q^{32} - 15 q^{33} - 6 q^{34} - 3 q^{35} + 5 q^{36} - 6 q^{37} - 2 q^{38} - 7 q^{39} + 27 q^{41} + 4 q^{42} + 8 q^{43} - 6 q^{44} - 11 q^{45} + 9 q^{46} - q^{48} + 22 q^{49} + 3 q^{50} - 18 q^{51} + 10 q^{52} - 8 q^{54} - 12 q^{55} - 10 q^{56} + 16 q^{57} + 3 q^{58} + 27 q^{59} + 7 q^{60} - 18 q^{61} - 2 q^{62} - 25 q^{63} + 4 q^{64} - 3 q^{65} - 18 q^{66} + 6 q^{67} - 3 q^{68} + 10 q^{69} + 6 q^{70} - 15 q^{71} + 10 q^{72} + 20 q^{73} - 6 q^{74} + 3 q^{75} - q^{76} + 12 q^{77} - 2 q^{78} + 50 q^{79} - 3 q^{80} + 14 q^{81} + 27 q^{82} - q^{84} - 12 q^{85} + 16 q^{86} + 7 q^{87} - 3 q^{88} - 3 q^{89} - 13 q^{90} - 38 q^{91} - 2 q^{93} + 9 q^{94} + 18 q^{95} + q^{96} - 10 q^{97} + 26 q^{98} - 24 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + q^6 + 10 * q^7 - 4 * q^8 - 10 * q^9 + 3 * q^10 + 3 * q^11 - q^12 - 14 * q^13 + 8 * q^14 - 11 * q^15 - 2 * q^16 - 3 * q^17 - 5 * q^18 - q^19 + 3 * q^20 + 5 * q^21 - 3 * q^22 + 9 * q^23 - 2 * q^24 + 6 * q^25 - 4 * q^26 - 16 * q^27 - 2 * q^28 + 3 * q^29 - 4 * q^30 - 4 * q^31 + 2 * q^32 - 15 * q^33 - 6 * q^34 - 3 * q^35 + 5 * q^36 - 6 * q^37 - 2 * q^38 - 7 * q^39 + 27 * q^41 + 4 * q^42 + 8 * q^43 - 6 * q^44 - 11 * q^45 + 9 * q^46 - q^48 + 22 * q^49 + 3 * q^50 - 18 * q^51 + 10 * q^52 - 8 * q^54 - 12 * q^55 - 10 * q^56 + 16 * q^57 + 3 * q^58 + 27 * q^59 + 7 * q^60 - 18 * q^61 - 2 * q^62 - 25 * q^63 + 4 * q^64 - 3 * q^65 - 18 * q^66 + 6 * q^67 - 3 * q^68 + 10 * q^69 + 6 * q^70 - 15 * q^71 + 10 * q^72 + 20 * q^73 - 6 * q^74 + 3 * q^75 - q^76 + 12 * q^77 - 2 * q^78 + 50 * q^79 - 3 * q^80 + 14 * q^81 + 27 * q^82 - q^84 - 12 * q^85 + 16 * q^86 + 7 * q^87 - 3 * q^88 - 3 * q^89 - 13 * q^90 - 38 * q^91 - 2 * q^93 + 9 * q^94 + 18 * q^95 + q^96 - 10 * q^97 + 26 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.500000	−	1.65831i	0.288675	−	0.957427i
$3$	0.500000	−	1.65831i	0.288675	−	0.957427i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		−	0.792287i		−	0.354322i	−0.984182	−	0.177161i	$-0.943309\pi$
$5$		−	0.792287i		−	0.354322i	0.984182	−	0.177161i	$-0.0566913\pi$
$6$	−1.18614	−	1.26217i	−0.484240	−	0.515278i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$	−1.00000			−0.353553
$9$	−2.50000	−	1.65831i	−0.833333	−	0.552771i
$10$	−0.686141	−	0.396143i	−0.216977	−	0.125272i
$11$	2.18614	−	3.78651i	0.659146	−	1.14167i	−0.321691	−	0.946845i	$-0.604251\pi$
$11$	2.18614	−	3.78651i	0.659146	−	1.14167i	0.980837	−	0.194830i	$-0.0624155\pi$
$12$	−1.68614	+	0.396143i	−0.486747	+	0.114357i
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$14$	2.00000	−	1.73205i	0.534522	−	0.462910i
$15$	−1.31386	−	0.396143i	−0.339237	−	0.102284i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.18614	−	3.78651i	−0.530217	−	0.918363i	−0.999379	−	0.0352504i	$-0.988777\pi$
$17$	−2.18614	−	3.78651i	−0.530217	−	0.918363i	0.469162	−	0.883112i	$-0.344556\pi$
$18$	−2.68614	+	1.33591i	−0.633129	+	0.314876i
$19$	1.18614	+	2.05446i	0.272119	+	0.471325i	0.969404	−	0.245470i	$-0.0789421\pi$
$19$	1.18614	+	2.05446i	0.272119	+	0.471325i	−0.697285	+	0.716794i	$0.745609\pi$
$20$	−0.686141	+	0.396143i	−0.153426	+	0.0885804i
$21$	2.68614	−	3.71277i	0.586164	−	0.810192i
$22$	−2.18614	−	3.78651i	−0.466087	−	0.807286i
$23$	3.68614	+	2.12819i	0.768613	+	0.443759i	0.832380	−	0.554206i	$-0.186978\pi$
$23$	3.68614	+	2.12819i	0.768613	+	0.443759i	−0.0637663	+	0.997965i	$0.520311\pi$
$24$	−0.500000	+	1.65831i	−0.102062	+	0.338502i
$25$	4.37228			0.874456
$26$	−1.00000	+	3.46410i	−0.196116	+	0.679366i
$27$	−4.00000	+	3.31662i	−0.769800	+	0.638285i
$28$	−0.500000	−	2.59808i	−0.0944911	−	0.490990i
$29$	2.18614	+	1.26217i	0.405956	+	0.234379i	0.689051	−	0.724713i	$-0.258028\pi$
$29$	2.18614	+	1.26217i	0.405956	+	0.234379i	−0.283095	+	0.959092i	$0.591361\pi$
$30$	−1.00000	+	0.939764i	−0.182574	+	0.171577i
$31$	−6.74456			−1.21136			−0.605680	−	0.795709i	$-0.707099\pi$
$31$	−6.74456			−1.21136			−0.605680	+	0.795709i	$0.707099\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−5.18614	−	5.51856i	−0.902791	−	0.960658i
$34$	−4.37228			−0.749840
$35$	0.686141	−	1.98072i	0.115979	−	0.334802i
$36$	−0.186141	+	2.99422i	−0.0310234	+	0.499037i
$37$	−10.1168	−	5.84096i	−1.66320	−	0.960248i	−0.971173	−	0.238376i	$-0.923385\pi$
$37$	−10.1168	−	5.84096i	−1.66320	−	0.960248i	−0.692026	−	0.721873i	$-0.743282\pi$
$38$	2.37228			0.384835
$39$	−0.313859	+	6.23711i	−0.0502577	+	0.998736i
$40$			0.792287i			0.125272i
$41$	8.18614	+	4.72627i	1.27846	+	0.738119i	0.976565	−	0.215222i	$-0.0690474\pi$
$41$	8.18614	+	4.72627i	1.27846	+	0.738119i	0.301895	+	0.953341i	$0.402381\pi$
$42$	−1.87228	−	4.18265i	−0.288899	−	0.645397i
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	0.977261	−	0.212041i	$-0.0680112\pi$
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	−0.672264	+	0.740312i	$0.734678\pi$
$44$	−4.37228			−0.659146
$45$	−1.31386	+	1.98072i	−0.195859	+	0.295268i
$46$	3.68614	−	2.12819i	0.543492	−	0.313785i
$47$			0.939764i			0.137079i	0.997648	+	0.0685393i	$0.0218339\pi$
$47$			0.939764i			0.137079i	−0.997648	+	0.0685393i	$0.978166\pi$
$48$	1.18614	+	1.26217i	0.171205	+	0.182178i
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	2.18614	−	3.78651i	0.309167	−	0.535493i
$51$	−7.37228	+	1.73205i	−1.03233	+	0.242536i
$52$	2.50000	+	2.59808i	0.346688	+	0.360288i
$53$			2.22938i			0.306229i	0.988208	+	0.153115i	$0.0489304\pi$
$53$			2.22938i			0.306229i	−0.988208	+	0.153115i	$0.951070\pi$
$54$	0.872281	+	5.12241i	0.118702	+	0.697072i
$55$	−3.00000	−	1.73205i	−0.404520	−	0.233550i
$56$	−2.50000	−	0.866025i	−0.334077	−	0.115728i
$57$	4.00000	−	0.939764i	0.529813	−	0.124475i
$58$	2.18614	−	1.26217i	0.287054	−	0.165731i
$59$	5.31386	−	3.06796i	0.691806	−	0.399414i	−0.112483	−	0.993654i	$-0.535880\pi$
$59$	5.31386	−	3.06796i	0.691806	−	0.399414i	0.804288	+	0.594240i	$0.202547\pi$
$60$	0.313859	+	1.33591i	0.0405191	+	0.172465i
$61$	−4.50000	+	2.59808i	−0.576166	+	0.332650i	−0.759608	−	0.650381i	$-0.774609\pi$
$61$	−4.50000	+	2.59808i	−0.576166	+	0.332650i	0.183442	+	0.983030i	$0.441276\pi$
$62$	−3.37228	+	5.84096i	−0.428280	+	0.741803i
$63$	−4.81386	−	6.31084i	−0.606489	−	0.795092i
$64$	1.00000			0.125000
$65$	0.686141	+	2.77300i	0.0851053	+	0.343949i
$66$	−7.37228	+	1.73205i	−0.907465	+	0.213201i
$67$	10.1168	+	5.84096i	1.23597	+	0.713587i	0.968268	−	0.249915i	$-0.0804026\pi$
$67$	10.1168	+	5.84096i	1.23597	+	0.713587i	0.267701	+	0.963502i	$0.413736\pi$
$68$	−2.18614	+	3.78651i	−0.265108	+	0.459181i
$69$	5.37228	−	5.04868i	0.646747	−	0.607789i
$70$	−1.37228	−	1.58457i	−0.164019	−	0.189393i
$71$	−8.05842	−	13.9576i	−0.956359	−	1.65646i	−0.731228	−	0.682133i	$-0.761052\pi$
$71$	−8.05842	−	13.9576i	−0.956359	−	1.65646i	−0.225131	−	0.974328i	$-0.572281\pi$
$72$	2.50000	+	1.65831i	0.294628	+	0.195434i
$73$	10.7446			1.25756			0.628778	−	0.777585i	$-0.283555\pi$
$73$	10.7446			1.25756			0.628778	+	0.777585i	$0.283555\pi$
$74$	−10.1168	+	5.84096i	−1.17606	+	0.678998i
$75$	2.18614	−	7.25061i	0.252434	−	0.837228i
$76$	1.18614	−	2.05446i	0.136060	−	0.235662i
$77$	8.74456	−	7.57301i	0.996535	−	0.863025i
$78$	5.24456	+	3.39036i	0.593830	+	0.383883i
$79$	9.62772			1.08320			0.541601	−	0.840635i	$-0.317818\pi$
$79$	9.62772			1.08320			0.541601	+	0.840635i	$0.317818\pi$
$80$	0.686141	+	0.396143i	0.0767129	+	0.0442902i
$81$	3.50000	+	8.29156i	0.388889	+	0.921285i
$82$	8.18614	−	4.72627i	0.904008	−	0.521929i
$83$			1.58457i			0.173930i	0.996211	+	0.0869648i	$0.0277168\pi$
$83$			1.58457i			0.173930i	−0.996211	+	0.0869648i	$0.972283\pi$
$84$	−4.55842	−	0.469882i	−0.497365	−	0.0512683i
$85$	−3.00000	+	1.73205i	−0.325396	+	0.187867i
$86$	4.00000			0.431331
$87$	3.18614	−	2.99422i	0.341590	−	0.321014i
$88$	−2.18614	+	3.78651i	−0.233043	+	0.403643i
$89$	9.30298	+	5.37108i	0.986114	+	0.569333i	0.904111	−	0.427299i	$-0.140535\pi$
$89$	9.30298	+	5.37108i	0.986114	+	0.569333i	0.0820038	+	0.996632i	$0.473868\pi$
$90$	1.05842	+	2.12819i	0.111567	+	0.224331i
$91$	−9.50000	−	0.866025i	−0.995871	−	0.0907841i
$92$		−	4.25639i		−	0.443759i
$93$	−3.37228	+	11.1846i	−0.349689	+	1.15979i
$94$	0.813859	+	0.469882i	0.0839432	+	0.0484646i
$95$	1.62772	−	0.939764i	0.167000	−	0.0964177i
$96$	1.68614	−	0.396143i	0.172091	−	0.0404312i
$97$	0.372281	+	0.644810i	0.0377994	+	0.0654706i	0.884306	−	0.466907i	$-0.154632\pi$
$97$	0.372281	+	0.644810i	0.0377994	+	0.0654706i	−0.846507	+	0.532378i	$0.821299\pi$
$98$	6.50000	−	2.59808i	0.656599	−	0.262445i
$99$	−11.7446	+	5.84096i	−1.18037	+	0.587039i
$100$	−2.18614	−	3.78651i	−0.218614	−	0.378651i
$101$	7.37228	−	12.7692i	0.733569	−	1.27058i	−0.221779	−	0.975097i	$-0.571186\pi$
$101$	7.37228	−	12.7692i	0.733569	−	1.27058i	0.955348	−	0.295482i	$-0.0954804\pi$
$102$	−2.18614	+	7.25061i	−0.216460	+	0.717917i
$103$		−	8.21782i		−	0.809726i	−0.914377	−	0.404863i	$-0.867319\pi$
$103$		−	8.21782i		−	0.809726i	0.914377	−	0.404863i	$-0.132681\pi$
$104$	3.50000	−	0.866025i	0.343203	−	0.0849208i
$105$	−2.94158	−	2.12819i	−0.287069	−	0.207690i
$106$	1.93070	+	1.11469i	0.187526	+	0.108268i
$107$	−0.813859	−	0.469882i	−0.0786788	−	0.0454252i	0.460144	−	0.887844i	$-0.347798\pi$
$107$	−0.813859	−	0.469882i	−0.0786788	−	0.0454252i	−0.538823	+	0.842419i	$0.681131\pi$
$108$	4.87228	+	1.80579i	0.468835	+	0.173762i
$109$			19.8997i			1.90605i	0.302891	+	0.953025i	$0.402048\pi$
$109$			19.8997i			1.90605i	−0.302891	+	0.953025i	$0.597952\pi$
$110$	−3.00000	+	1.73205i	−0.286039	+	0.165145i
$111$	−14.7446	+	13.8564i	−1.39949	+	1.31519i
$112$	−2.00000	+	1.73205i	−0.188982	+	0.163663i
$113$	3.25544	−	1.87953i	0.306246	−	0.176811i	−0.339000	−	0.940787i	$-0.610089\pi$
$113$	3.25544	−	1.87953i	0.306246	−	0.176811i	0.645245	+	0.763975i	$0.276755\pi$
$114$	1.18614	−	3.93398i	0.111092	−	0.368451i
$115$	1.68614	−	2.92048i	0.157233	−	0.272336i
$116$		−	2.52434i		−	0.234379i
$117$	10.1861	+	3.63903i	0.941709	+	0.336428i
$118$		−	6.13592i		−	0.564857i
$119$	−2.18614	−	11.3595i	−0.200403	−	1.04133i
$120$	1.31386	+	0.396143i	0.119938	+	0.0361628i
$121$	−4.05842	−	7.02939i	−0.368947	−	0.639036i
$122$			5.19615i			0.470438i
$123$	11.9307	−	11.2120i	1.07576	−	1.01096i
$124$	3.37228	+	5.84096i	0.302840	+	0.524534i
$125$		−	7.42554i		−	0.664160i
$126$	−7.87228	+	1.01350i	−0.701319	+	0.0902900i
$127$	1.05842	−	1.83324i	0.0939198	−	0.162674i	−0.815237	−	0.579127i	$-0.803394\pi$
$127$	1.05842	−	1.83324i	0.0939198	−	0.162674i	0.909157	+	0.416453i	$0.136727\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	6.74456	−	1.58457i	0.593826	−	0.139514i
$130$	2.74456	+	0.792287i	0.240714	+	0.0694882i
$131$	−21.6060			−1.88772			−0.943861	−	0.330342i	$-0.892836\pi$
$131$	−21.6060			−1.88772			−0.943861	+	0.330342i	$0.892836\pi$
$132$	−2.18614	+	7.25061i	−0.190279	+	0.631084i
$133$	1.18614	+	6.16337i	0.102851	+	0.534432i
$134$	10.1168	−	5.84096i	0.873962	−	0.504582i
$135$	2.62772	+	3.16915i	0.226158	+	0.272757i
$136$	2.18614	+	3.78651i	0.187460	+	0.324690i
$137$	3.68614	+	6.38458i	0.314928	+	0.545472i	0.979422	−	0.201822i	$-0.0646862\pi$
$137$	3.68614	+	6.38458i	0.314928	+	0.545472i	−0.664494	+	0.747294i	$0.731353\pi$
$138$	−1.68614	−	7.17687i	−0.143534	−	0.610936i
$139$	7.67527	−	4.43132i	0.651008	−	0.375859i	−0.137835	−	0.990455i	$-0.544014\pi$
$139$	7.67527	−	4.43132i	0.651008	−	0.375859i	0.788842	+	0.614596i	$0.210681\pi$
$140$	−2.05842	+	0.396143i	−0.173968	+	0.0334802i
$141$	1.55842	+	0.469882i	0.131243	+	0.0395712i
$142$	−16.1168			−1.35250
$143$	−4.37228	+	15.1460i	−0.365629	+	1.26657i
$144$	2.68614	−	1.33591i	0.223845	−	0.111326i
$145$	1.00000	−	1.73205i	0.0830455	−	0.143839i
$146$	5.37228	−	9.30506i	0.444613	−	0.770093i
$147$	9.93070	−	6.95565i	0.819071	−	0.573693i
$148$			11.6819i			0.960248i
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$	−5.18614	−	5.51856i	−0.423447	−	0.450588i
$151$			16.8781i			1.37352i	0.726885	+	0.686759i	$0.240967\pi$
$151$			16.8781i			1.37352i	−0.726885	+	0.686759i	$0.759033\pi$
$152$	−1.18614	−	2.05446i	−0.0962087	−	0.166638i
$153$	−0.813859	+	13.0916i	−0.0657966	+	1.05839i
$154$	−2.18614	−	11.3595i	−0.176164	−	0.915376i
$155$			5.34363i			0.429211i
$156$	5.55842	−	2.84674i	0.445030	−	0.227922i
$157$		0			0		1.00000			$0$
$157$		0			0		−1.00000			$\pi$
$158$	4.81386	−	8.33785i	0.382970	−	0.663324i
$159$	3.69702	+	1.11469i	0.293192	+	0.0884008i
$160$	0.686141	−	0.396143i	0.0542442	−	0.0313179i
$161$	7.37228	+	8.51278i	0.581017	+	0.670901i
$162$	8.93070	+	1.11469i	0.701662	+	0.0875785i
$163$	−9.00000	+	5.19615i	−0.704934	+	0.406994i	−0.809183	−	0.587557i	$-0.800090\pi$
$163$	−9.00000	+	5.19615i	−0.704934	+	0.406994i	0.104248	+	0.994551i	$0.466756\pi$
$164$		−	9.45254i		−	0.738119i
$165$	−4.37228	+	4.10891i	−0.340382	+	0.319878i
$166$	1.37228	+	0.792287i	0.106510	+	0.0614934i
$167$	5.74456	+	3.31662i	0.444528	+	0.256648i	0.705516	−	0.708694i	$-0.250715\pi$
$167$	5.74456	+	3.31662i	0.444528	+	0.256648i	−0.260989	+	0.965342i	$0.584049\pi$
$168$	−2.68614	+	3.71277i	−0.207240	+	0.286446i
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$			3.46410i			0.265684i
$171$	0.441578	−	7.10313i	0.0337683	−	0.543190i
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	−0.941578	−	1.63086i	−0.0715869	−	0.123992i	0.828010	−	0.560713i	$-0.189473\pi$
$173$	−0.941578	−	1.63086i	−0.0715869	−	0.123992i	−0.899597	+	0.436721i	$0.856140\pi$
$174$	−1.00000	−	4.25639i	−0.0758098	−	0.322676i
$175$	10.9307	+	3.78651i	0.826284	+	0.286233i
$176$	2.18614	+	3.78651i	0.164787	+	0.285419i
$177$	−2.43070	−	10.3460i	−0.182703	−	0.777654i
$178$	9.30298	−	5.37108i	0.697288	−	0.402580i
$179$	−4.37228	−	2.52434i	−0.326800	−	0.188678i	0.327620	−	0.944810i	$-0.393754\pi$
$179$	−4.37228	−	2.52434i	−0.326800	−	0.188678i	−0.654419	+	0.756132i	$0.727087\pi$
$180$	2.37228	+	0.147477i	0.176819	+	0.0109923i
$181$		−	12.1244i		−	0.901196i	−0.892727	−	0.450598i	$-0.851211\pi$
$181$		−	12.1244i		−	0.901196i	0.892727	−	0.450598i	$-0.148789\pi$
$182$	−5.50000	+	7.79423i	−0.407687	+	0.577747i
$183$	2.05842	+	8.76144i	0.152163	+	0.647665i
$184$	−3.68614	−	2.12819i	−0.271746	−	0.156893i
$185$	−4.62772	+	8.01544i	−0.340237	+	0.589307i
$186$	8.00000	+	8.51278i	0.586588	+	0.624187i
$187$	−19.1168			−1.39796
$188$	0.813859	−	0.469882i	0.0593568	−	0.0342697i
$189$	−12.8723	+	4.82746i	−0.936321	+	0.351146i
$190$		−	1.87953i		−	0.136355i
$191$	−10.6277	+	6.13592i	−0.768995	+	0.443979i	−0.832516	−	0.554001i	$-0.813100\pi$
$191$	−10.6277	+	6.13592i	−0.768995	+	0.443979i	0.0635211	+	0.997980i	$0.479767\pi$
$192$	0.500000	−	1.65831i	0.0360844	−	0.119678i
$193$	11.6168	+	6.70699i	0.836199	+	0.482780i	0.855970	−	0.517025i	$-0.172961\pi$
$193$	11.6168	+	6.70699i	0.836199	+	0.482780i	−0.0197716	+	0.999805i	$0.506294\pi$
$194$	0.744563			0.0534565
$195$	4.94158	+	0.248667i	0.353874	+	0.0178074i
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$	−12.3030	+	21.3094i	−0.876551	+	1.51823i	−0.0214504	+	0.999770i	$0.506828\pi$
$197$	−12.3030	+	21.3094i	−0.876551	+	1.51823i	−0.855101	+	0.518462i	$0.826505\pi$
$198$	−0.813859	+	13.0916i	−0.0578385	+	0.930377i
$199$	3.00000	−	1.73205i	0.212664	−	0.122782i	−0.389885	−	0.920864i	$-0.627485\pi$
$199$	3.00000	−	1.73205i	0.212664	−	0.122782i	0.602549	+	0.798082i	$0.294152\pi$
$200$	−4.37228			−0.309167
$201$	14.7446	−	13.8564i	1.04000	−	0.977356i
$202$	−7.37228	−	12.7692i	−0.518712	−	0.898435i
$203$	4.37228	+	5.04868i	0.306874	+	0.354348i
$204$	5.18614	+	5.51856i	0.363102	+	0.386376i
$205$	3.74456	−	6.48577i	0.261532	−	0.452986i
$206$	−7.11684	−	4.10891i	−0.495854	−	0.286281i
$207$	−5.68614	−	11.4333i	−0.395214	−	0.794666i
$208$	1.00000	−	3.46410i	0.0693375	−	0.240192i
$209$	10.3723			0.717466
$210$	−3.31386	+	1.48338i	−0.228678	+	0.102363i
$211$	−5.62772	+	9.74749i	−0.387428	+	0.671045i	−0.992103	−	0.125427i	$-0.959970\pi$
$211$	−5.62772	+	9.74749i	−0.387428	+	0.671045i	0.604675	+	0.796473i	$0.293303\pi$
$212$	1.93070	−	1.11469i	0.132601	−	0.0765574i
$213$	−27.1753	+	6.38458i	−1.86202	+	0.437464i
$214$	−0.813859	+	0.469882i	−0.0556343	+	0.0321205i
$215$	2.74456	−	1.58457i	0.187178	−	0.108067i
$216$	4.00000	−	3.31662i	0.272166	−	0.225668i
$217$	−16.8614	−	5.84096i	−1.14463	−	0.396510i
$218$	17.2337	+	9.94987i	1.16721	+	0.673891i
$219$	5.37228	−	17.8178i	0.363025	−	1.20402i
$220$			3.46410i			0.233550i
$221$	10.9307	+	11.3595i	0.735279	+	0.764124i
$222$	4.62772	+	19.6974i	0.310592	+	1.32200i
$223$	−14.1168	+	24.4511i	−0.945334	+	1.63737i	−0.190252	+	0.981735i	$0.560931\pi$
$223$	−14.1168	+	24.4511i	−0.945334	+	1.63737i	−0.755082	+	0.655631i	$0.772403\pi$
$224$	0.500000	+	2.59808i	0.0334077	+	0.173591i
$225$	−10.9307	−	7.25061i	−0.728714	−	0.483374i
$226$		−	3.75906i		−	0.250049i
$227$	−16.8030	+	9.70121i	−1.11525	+	0.643892i	−0.940185	−	0.340665i	$-0.889348\pi$
$227$	−16.8030	+	9.70121i	−1.11525	+	0.643892i	−0.175068	+	0.984556i	$0.556015\pi$
$228$	−2.81386	−	2.99422i	−0.186352	−	0.198297i
$229$	−5.11684			−0.338131			−0.169065	−	0.985605i	$-0.554075\pi$
$229$	−5.11684			−0.338131			−0.169065	+	0.985605i	$0.554075\pi$
$230$	−1.68614	−	2.92048i	−0.111181	−	0.192571i
$231$	−8.18614	−	18.2877i	−0.538609	−	1.20324i
$232$	−2.18614	−	1.26217i	−0.143527	−	0.0828654i
$233$			4.84630i			0.317491i	0.987320	+	0.158746i	$0.0507450\pi$
$233$			4.84630i			0.317491i	−0.987320	+	0.158746i	$0.949255\pi$
$234$	8.24456	−	7.00194i	0.538964	−	0.457731i
$235$	0.744563			0.0485699
$236$	−5.31386	−	3.06796i	−0.345903	−	0.199707i
$237$	4.81386	−	15.9658i	0.312694	−	1.03709i
$238$	−10.9307	−	3.78651i	−0.708532	−	0.245443i
$239$	−15.6060			−1.00947			−0.504733	−	0.863275i	$-0.668409\pi$
$239$	−15.6060			−1.00947			−0.504733	+	0.863275i	$0.668409\pi$
$240$	1.00000	−	0.939764i	0.0645497	−	0.0606615i
$241$	6.37228	+	11.0371i	0.410475	+	0.710963i	0.994942	−	0.100454i	$-0.0320297\pi$
$241$	6.37228	+	11.0371i	0.410475	+	0.710963i	−0.584467	+	0.811418i	$0.698696\pi$
$242$	−8.11684			−0.521770
$243$	15.5000	−	1.65831i	0.994325	−	0.106381i
$244$	4.50000	+	2.59808i	0.288083	+	0.166325i
$245$	3.43070	−	4.35758i	0.219180	−	0.278395i
$246$	−3.74456	−	15.9383i	−0.238745	−	1.01619i
$247$	−5.93070	−	6.16337i	−0.377362	−	0.392166i
$248$	6.74456			0.428280
$249$	2.62772	+	0.792287i	0.166525	+	0.0502091i
$250$	−6.43070	−	3.71277i	−0.406713	−	0.234816i
$251$	−8.05842	−	13.9576i	−0.508643	−	0.880996i	−0.999950	−	0.0100091i	$-0.996814\pi$
$251$	−8.05842	−	13.9576i	−0.508643	−	0.880996i	0.491307	−	0.870987i	$-0.336519\pi$
$252$	−3.05842	+	7.32435i	−0.192662	+	0.461390i
$253$	16.1168	−	9.30506i	1.01326	−	0.585004i
$254$	−1.05842	−	1.83324i	−0.0664113	−	0.115028i
$255$	1.37228	+	5.84096i	0.0859356	+	0.365775i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.44158	+	4.22894i	−0.152301	+	0.263794i	−0.932073	−	0.362270i	$-0.882002\pi$
$257$	−2.44158	+	4.22894i	−0.152301	+	0.263794i	0.779772	+	0.626064i	$0.215335\pi$
$258$	2.00000	−	6.63325i	0.124515	−	0.412968i
$259$	−20.2337	−	23.3639i	−1.25726	−	1.45176i
$260$	2.05842	−	1.98072i	0.127658	−	0.122839i
$261$	−3.37228	−	6.78073i	−0.208739	−	0.419716i
$262$	−10.8030	+	18.7113i	−0.667411	+	1.15599i
$263$	−19.5475	−	11.2858i	−1.20535	−	0.695911i	−0.243613	−	0.969873i	$-0.578333\pi$
$263$	−19.5475	−	11.2858i	−1.20535	−	0.695911i	−0.961741	+	0.273961i	$0.911666\pi$
$264$	5.18614	+	5.51856i	0.319185	+	0.339644i
$265$	1.76631			0.108504
$266$	5.93070	+	2.05446i	0.363635	+	0.125967i
$267$	13.5584	−	12.7417i	0.829762	−	0.779780i
$268$		−	11.6819i		−	0.713587i
$269$	0.430703	+	0.746000i	0.0262604	+	0.0454844i	0.878857	−	0.477085i	$-0.158307\pi$
$269$	0.430703	+	0.746000i	0.0262604	+	0.0454844i	−0.852597	+	0.522570i	$0.824973\pi$
$270$	4.05842	−	0.691097i	0.246988	−	0.0420588i
$271$	2.00000	−	3.46410i	0.121491	−	0.210429i	−0.798865	−	0.601511i	$-0.794566\pi$
$271$	2.00000	−	3.46410i	0.121491	−	0.210429i	0.920356	+	0.391082i	$0.127899\pi$
$272$	4.37228			0.265108
$273$	−6.18614	+	15.3210i	−0.374402	+	0.927266i
$274$	7.37228			0.445376
$275$	9.55842	−	16.5557i	0.576395	−	0.998345i
$276$	−7.05842	−	2.12819i	−0.424867	−	0.128102i
$277$	−6.74456	−	11.6819i	−0.405241	−	0.701899i	0.589108	−	0.808054i	$-0.299479\pi$
$277$	−6.74456	−	11.6819i	−0.405241	−	0.701899i	−0.994350	+	0.106155i	$0.966146\pi$
$278$		−	8.86263i		−	0.531545i
$279$	16.8614	+	11.1846i	1.00947	+	0.669604i
$280$	−0.686141	+	1.98072i	−0.0410047	+	0.118371i
$281$	−14.7446			−0.879587			−0.439793	−	0.898099i	$-0.644948\pi$
$281$	−14.7446			−0.879587			−0.439793	+	0.898099i	$0.644948\pi$
$282$	1.18614	−	1.11469i	0.0706336	−	0.0663789i
$283$	2.05842	+	1.18843i	0.122360	+	0.0706449i	0.559931	−	0.828539i	$-0.310828\pi$
$283$	2.05842	+	1.18843i	0.122360	+	0.0706449i	−0.437571	+	0.899184i	$0.644161\pi$
$284$	−8.05842	+	13.9576i	−0.478179	+	0.828231i
$285$	−0.744563	−	3.16915i	−0.0441041	−	0.187724i
$286$	10.9307	+	11.3595i	0.646346	+	0.671703i
$287$	16.3723	+	18.9051i	0.966425	+	1.11593i
$288$	0.186141	−	2.99422i	0.0109684	−	0.176436i
$289$	−1.05842	+	1.83324i	−0.0622601	+	0.107838i
$290$	−1.00000	−	1.73205i	−0.0587220	−	0.101710i
$291$	1.25544	−	0.294954i	0.0735950	−	0.0172905i
$292$	−5.37228	−	9.30506i	−0.314389	−	0.544538i
$293$	3.25544	−	1.87953i	0.190185	−	0.109803i	−0.401884	−	0.915690i	$-0.631645\pi$
$293$	3.25544	−	1.87953i	0.190185	−	0.109803i	0.592069	+	0.805887i	$0.298311\pi$
$294$	−1.05842	−	12.0781i	−0.0617284	−	0.704407i
$295$	−2.43070	−	4.21010i	−0.141521	−	0.245122i
$296$	10.1168	+	5.84096i	0.588030	+	0.339499i
$297$	3.81386	+	22.3966i	0.221303	+	1.29958i
$298$	−6.00000			−0.347571
$299$	−14.7446	−	4.25639i	−0.852700	−	0.246153i
$300$	−7.37228	+	1.73205i	−0.425639	+	0.100000i
$301$	2.00000	+	10.3923i	0.115278	+	0.599002i
$302$	14.6168	+	8.43904i	0.841105	+	0.485612i
$303$	−17.4891	−	18.6101i	−1.00472	−	1.06912i
$304$	−2.37228			−0.136060
$305$	2.05842	+	3.56529i	0.117865	+	0.204148i
$306$	10.9307	+	7.25061i	0.624867	+	0.414490i
$307$	−21.2337			−1.21187			−0.605935	−	0.795514i	$-0.707201\pi$
$307$	−21.2337			−1.21187			−0.605935	+	0.795514i	$0.707201\pi$
$308$	−10.9307	−	3.78651i	−0.622835	−	0.215756i
$309$	−13.6277	−	4.10891i	−0.775254	−	0.233748i
$310$	4.62772	+	2.67181i	0.262837	+	0.151749i
$311$	10.3723			0.588158			0.294079	−	0.955781i	$-0.404987\pi$
$311$	10.3723			0.588158			0.294079	+	0.955781i	$0.404987\pi$
$312$	0.313859	−	6.23711i	0.0177688	−	0.353107i
$313$			13.8564i			0.783210i	0.920133	+	0.391605i	$0.128080\pi$
$313$			13.8564i			0.783210i	−0.920133	+	0.391605i	$0.871920\pi$
$314$		0			0
$315$	−5.00000	+	3.81396i	−0.281718	+	0.214892i
$316$	−4.81386	−	8.33785i	−0.270801	−	0.469041i
$317$	−15.2554			−0.856831			−0.428415	−	0.903582i	$-0.640928\pi$
$317$	−15.2554			−0.856831			−0.428415	+	0.903582i	$0.640928\pi$
$318$	2.81386	−	2.64436i	0.157793	−	0.148289i
$319$	9.55842	−	5.51856i	0.535169	−	0.308980i
$320$		−	0.792287i		−	0.0442902i
$321$	−1.18614	+	1.11469i	−0.0662039	+	0.0622160i
$322$	11.0584	−	2.12819i	0.616262	−	0.118600i
$323$	5.18614	−	8.98266i	0.288565	−	0.499809i
$324$	5.43070	−	7.17687i	0.301706	−	0.398715i
$325$	−15.3030	+	3.78651i	−0.848857	+	0.210038i
$326$			10.3923i			0.575577i
$327$	33.0000	+	9.94987i	1.82490	+	0.550229i
$328$	−8.18614	−	4.72627i	−0.452004	−	0.260965i
$329$	−0.813859	+	2.34941i	−0.0448695	+	0.129527i
$330$	1.37228	+	5.84096i	0.0755416	+	0.321534i
$331$	−1.88316	+	1.08724i	−0.103508	+	0.0597602i	−0.550860	−	0.834598i	$-0.685700\pi$
$331$	−1.88316	+	1.08724i	−0.103508	+	0.0597602i	0.447353	+	0.894358i	$0.352367\pi$
$332$	1.37228	−	0.792287i	0.0753137	−	0.0434824i
$333$	15.6060	+	31.3793i	0.855202	+	1.71957i
$334$	5.74456	−	3.31662i	0.314328	−	0.181478i
$335$	4.62772	−	8.01544i	0.252839	−	0.437930i
$336$	1.87228	+	4.18265i	0.102141	+	0.228182i
$337$	−10.6060			−0.577744			−0.288872	−	0.957368i	$-0.593280\pi$
$337$	−10.6060			−0.577744			−0.288872	+	0.957368i	$0.593280\pi$
$338$	0.500000	−	12.9904i	0.0271964	−	0.706584i
$339$	−1.48913	−	6.33830i	−0.0808782	−	0.344249i
$340$	3.00000	+	1.73205i	0.162698	+	0.0939336i
$341$	−14.7446	+	25.5383i	−0.798463	+	1.38298i
$342$	−5.93070	−	3.93398i	−0.320696	−	0.212725i
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	−2.00000	−	3.46410i	−0.107833	−	0.186772i
$345$	−4.00000	−	4.25639i	−0.215353	−	0.229156i
$346$	−1.88316			−0.101239
$347$	18.0475	−	10.4198i	0.968843	−	0.559362i	0.0699597	−	0.997550i	$-0.477713\pi$
$347$	18.0475	−	10.4198i	0.968843	−	0.559362i	0.898883	+	0.438188i	$0.144380\pi$
$348$	−4.18614	−	1.26217i	−0.224401	−	0.0676594i
$349$	10.0584	−	17.4217i	0.538415	−	0.932562i	−0.460575	−	0.887621i	$-0.652357\pi$
$349$	10.0584	−	17.4217i	0.538415	−	0.932562i	0.998990	−	0.0449411i	$-0.0143100\pi$
$350$	8.74456	−	7.57301i	0.467417	−	0.404795i
$351$	11.1277	−	15.0723i	0.593954	−	0.804499i
$352$	4.37228			0.233043
$353$	−25.3723	−	14.6487i	−1.35043	−	0.779671i	−0.362121	−	0.932131i	$-0.617947\pi$
$353$	−25.3723	−	14.6487i	−1.35043	−	0.779671i	−0.988310	+	0.152460i	$0.951280\pi$
$354$	−10.1753	−	3.06796i	−0.540809	−	0.163060i
$355$	−11.0584	+	6.38458i	−0.586920	+	0.338858i
$356$		−	10.7422i		−	0.569333i
$357$	−19.9307	−	2.05446i	−1.05484	−	0.108733i
$358$	−4.37228	+	2.52434i	−0.231082	+	0.133415i
$359$	16.6277			0.877577			0.438789	−	0.898590i	$-0.355408\pi$
$359$	16.6277			0.877577			0.438789	+	0.898590i	$0.355408\pi$
$360$	1.31386	−	1.98072i	0.0692465	−	0.104393i
$361$	6.68614	−	11.5807i	0.351902	−	0.609512i
$362$	−10.5000	−	6.06218i	−0.551868	−	0.318621i
$363$	−13.6861	+	3.21543i	−0.718336	+	0.168767i
$364$	4.00000	+	8.66025i	0.209657	+	0.453921i
$365$		−	8.51278i		−	0.445579i
$366$	8.61684	+	2.59808i	0.450410	+	0.135804i
$367$	−26.2337	−	15.1460i	−1.36939	−	0.790616i	−0.378538	−	0.925586i	$-0.623573\pi$
$367$	−26.2337	−	15.1460i	−1.36939	−	0.790616i	−0.990850	+	0.134970i	$0.956906\pi$
$368$	−3.68614	+	2.12819i	−0.192153	+	0.110940i
$369$	−12.6277	−	25.3909i	−0.657373	−	1.32180i
$370$	4.62772	+	8.01544i	0.240584	+	0.416703i
$371$	−1.93070	+	5.57346i	−0.100237	+	0.289360i
$372$	11.3723	−	2.67181i	0.589625	−	0.138527i
$373$	−4.00000	−	6.92820i	−0.207112	−	0.358729i	0.743691	−	0.668523i	$-0.233073\pi$
$373$	−4.00000	−	6.92820i	−0.207112	−	0.358729i	−0.950804	+	0.309794i	$0.899740\pi$
$374$	−9.55842	+	16.5557i	−0.494254	+	0.856073i
$375$	−12.3139	−	3.71277i	−0.635885	−	0.191727i
$376$		−	0.939764i		−	0.0484646i
$377$	−8.74456	−	2.52434i	−0.450368	−	0.130010i
$378$	−2.25544	+	13.5615i	−0.116007	+	0.697526i
$379$	−4.88316	−	2.81929i	−0.250831	−	0.144817i	0.369314	−	0.929305i	$-0.379593\pi$
$379$	−4.88316	−	2.81929i	−0.250831	−	0.144817i	−0.620145	+	0.784487i	$0.712926\pi$
$380$	−1.62772	−	0.939764i	−0.0835002	−	0.0482089i
$381$	−2.51087	−	2.67181i	−0.128636	−	0.136881i
$382$			12.2718i			0.627882i
$383$	−13.0693	+	7.54556i	−0.667810	+	0.385560i	−0.795246	−	0.606287i	$-0.792658\pi$
$383$	−13.0693	+	7.54556i	−0.667810	+	0.385560i	0.127436	+	0.991847i	$0.459325\pi$
$384$	−1.18614	−	1.26217i	−0.0605300	−	0.0644098i
$385$	−6.00000	−	6.92820i	−0.305788	−	0.353094i
$386$	11.6168	−	6.70699i	0.591282	−	0.341377i
$387$	0.744563	−	11.9769i	0.0378482	−	0.608819i
$388$	0.372281	−	0.644810i	0.0188997	−	0.0327353i
$389$			29.2974i			1.48544i	0.669604	+	0.742718i	$0.266464\pi$
$389$			29.2974i			1.48544i	−0.669604	+	0.742718i	$0.733536\pi$
$390$	2.68614	−	4.15520i	0.136018	−	0.210407i
$391$		−	18.6101i		−	0.941155i
$392$	−5.50000	−	4.33013i	−0.277792	−	0.218704i
$393$	−10.8030	+	35.8294i	−0.544938	+	1.80736i
$394$	12.3030	+	21.3094i	0.619815	+	1.07355i
$395$		−	7.62792i		−	0.383802i
$396$	10.9307	+	7.25061i	0.549289	+	0.364357i
$397$	−1.12772	−	1.95327i	−0.0565986	−	0.0980316i	0.836338	−	0.548214i	$-0.184692\pi$
$397$	−1.12772	−	1.95327i	−0.0565986	−	0.0980316i	−0.892936	+	0.450183i	$0.851359\pi$
$398$		−	3.46410i		−	0.173640i
$399$	10.8139	+	1.11469i	0.541370	+	0.0558044i
$400$	−2.18614	+	3.78651i	−0.109307	+	0.189325i
$401$	5.74456	−	9.94987i	0.286870	−	0.496873i	−0.686191	−	0.727421i	$-0.740719\pi$
$401$	5.74456	−	9.94987i	0.286870	−	0.496873i	0.973061	+	0.230548i	$0.0740520\pi$
$402$	−4.62772	−	19.6974i	−0.230810	−	0.982415i
$403$	23.6060	−	5.84096i	1.17590	−	0.290959i
$404$	−14.7446			−0.733569
$405$	6.56930	−	2.77300i	0.326431	−	0.137792i
$406$	6.55842	−	1.26217i	0.325489	−	0.0626404i
$407$	−44.2337	+	25.5383i	−2.19258	+	1.26589i
$408$	7.37228	−	1.73205i	0.364982	−	0.0857493i
$409$	10.7446	+	18.6101i	0.531284	+	0.920212i	0.999333	+	0.0365091i	$0.0116238\pi$
$409$	10.7446	+	18.6101i	0.531284	+	0.920212i	−0.468049	+	0.883703i	$0.655043\pi$
$410$	−3.74456	−	6.48577i	−0.184931	−	0.320309i
$411$	12.4307	−	2.92048i	0.613161	−	0.144057i
$412$	−7.11684	+	4.10891i	−0.350622	+	0.202432i
$413$	15.9416	−	3.06796i	0.784434	−	0.150964i
$414$	−12.7446	−	0.792287i	−0.626361	−	0.0389388i
$415$	1.25544			0.0616270
$416$	−2.50000	−	2.59808i	−0.122573	−	0.127381i
$417$	−3.51087	−	14.9436i	−0.171928	−	0.731794i
$418$	5.18614	−	8.98266i	0.253662	−	0.439356i
$419$	2.74456	−	4.75372i	0.134081	−	0.232235i	−0.791165	−	0.611602i	$-0.790525\pi$
$419$	2.74456	−	4.75372i	0.134081	−	0.232235i	0.925246	+	0.379368i	$0.123859\pi$
$420$	−0.372281	+	3.61158i	−0.0181655	+	0.176227i
$421$			26.8280i			1.30751i	0.756704	+	0.653757i	$0.226808\pi$
$421$			26.8280i			1.30751i	−0.756704	+	0.653757i	$0.773192\pi$
$422$	5.62772	+	9.74749i	0.273953	+	0.474501i
$423$	1.55842	−	2.34941i	0.0757731	−	0.114232i
$424$		−	2.22938i		−	0.108268i
$425$	−9.55842	−	16.5557i	−0.463652	−	0.803068i
$426$	−8.05842	+	26.7268i	−0.390432	+	1.29492i
$427$	−13.5000	+	2.59808i	−0.653311	+	0.125730i
$428$			0.939764i			0.0454252i
$429$	22.9307	+	14.8236i	1.10710	+	0.715691i
$430$		−	3.16915i		−	0.152830i
$431$	12.6861	−	21.9730i	0.611070	−	1.05840i	−0.379991	−	0.924990i	$-0.624073\pi$
$431$	12.6861	−	21.9730i	0.611070	−	1.05840i	0.991060	−	0.133414i	$-0.0425939\pi$
$432$	−0.872281	−	5.12241i	−0.0419677	−	0.246452i
$433$	21.3505	−	12.3267i	1.02604	−	0.592385i	0.110193	−	0.993910i	$-0.464853\pi$
$433$	21.3505	−	12.3267i	1.02604	−	0.592385i	0.915848	+	0.401525i	$0.131520\pi$
$434$	−13.4891	+	11.6819i	−0.647499	+	0.560750i
$435$	−2.37228	−	2.52434i	−0.113742	−	0.121033i
$436$	17.2337	−	9.94987i	0.825344	−	0.476513i
$437$			10.0974i			0.483022i
$438$	−12.7446	−	13.5615i	−0.608959	−	0.647991i
$439$	21.3505	+	12.3267i	1.01901	+	0.588323i	0.913816	−	0.406129i	$-0.133122\pi$
$439$	21.3505	+	12.3267i	1.01901	+	0.588323i	0.105190	+	0.994452i	$0.466455\pi$
$440$	3.00000	+	1.73205i	0.143019	+	0.0825723i
$441$	−6.56930	−	19.9460i	−0.312824	−	0.949811i
$442$	15.3030	−	3.78651i	0.727889	−	0.180106i
$443$			7.86797i			0.373818i	0.982377	+	0.186909i	$0.0598470\pi$
$443$			7.86797i			0.373818i	−0.982377	+	0.186909i	$0.940153\pi$
$444$	19.3723	+	5.84096i	0.919368	+	0.277200i
$445$	4.25544	−	7.37063i	0.201727	−	0.349402i
$446$	14.1168	+	24.4511i	0.668452	+	1.15779i
$447$	−10.1168	+	2.37686i	−0.478510	+	0.112422i
$448$	2.50000	+	0.866025i	0.118114	+	0.0409159i
$449$	19.8030	+	34.2998i	0.934561	+	1.61871i	0.775416	+	0.631451i	$0.217540\pi$
$449$	19.8030	+	34.2998i	0.934561	+	1.61871i	0.159145	+	0.987255i	$0.449126\pi$
$450$	−11.7446	+	5.84096i	−0.553644	+	0.275346i
$451$	35.7921	−	20.6646i	1.68538	−	0.973057i
$452$	−3.25544	−	1.87953i	−0.153123	−	0.0884055i
$453$	27.9891	+	8.43904i	1.31504	+	0.396501i
$454$			19.4024i			0.910600i
$455$	−0.686141	+	7.52673i	−0.0321668	+	0.352858i
$456$	−4.00000	+	0.939764i	−0.187317	+	0.0440085i
$457$	9.17527	+	5.29734i	0.429201	+	0.247799i	0.699006	−	0.715116i	$-0.253626\pi$
$457$	9.17527	+	5.29734i	0.429201	+	0.247799i	−0.269805	+	0.962915i	$0.586959\pi$
$458$	−2.55842	+	4.43132i	−0.119547	+	0.207062i
$459$	21.3030	+	7.89542i	0.994338	+	0.368527i
$460$	−3.37228			−0.157233
$461$	27.4307	−	15.8371i	1.27758	−	0.737608i	0.301173	−	0.953569i	$-0.402622\pi$
$461$	27.4307	−	15.8371i	1.27758	−	0.737608i	0.976402	+	0.215961i	$0.0692884\pi$
$462$	−19.9307	−	2.05446i	−0.927260	−	0.0955819i
$463$		−	10.8347i		−	0.503533i	−0.967788	−	0.251766i	$-0.918989\pi$
$463$		−	10.8347i		−	0.503533i	0.967788	−	0.251766i	$-0.0810115\pi$
$464$	−2.18614	+	1.26217i	−0.101489	+	0.0585947i
$465$	8.86141	+	2.67181i	0.410938	+	0.123902i
$466$	4.19702	+	2.42315i	0.194423	+	0.112250i
$467$	−25.3723			−1.17409			−0.587045	−	0.809555i	$-0.699709\pi$
$467$	−25.3723			−1.17409			−0.587045	+	0.809555i	$0.699709\pi$
$468$	−1.94158	−	10.6410i	−0.0897495	−	0.491879i
$469$	20.2337	+	23.3639i	0.934305	+	1.07884i
$470$	0.372281	−	0.644810i	0.0171721	−	0.0297429i
$471$		0			0
$472$	−5.31386	+	3.06796i	−0.244590	+	0.141214i
$473$	17.4891			0.804151
$474$	−11.4198	−	12.1518i	−0.524530	−	0.558151i
$475$	5.18614	+	8.98266i	0.237956	+	0.412153i
$476$	−8.74456	+	7.57301i	−0.400806	+	0.347108i
$477$	3.69702	−	5.57346i	0.169275	−	0.255191i
$478$	−7.80298	+	13.5152i	−0.356900	+	0.618169i
$479$	−2.69702	−	1.55712i	−0.123230	−	0.0711467i	0.437118	−	0.899404i	$-0.355999\pi$
$479$	−2.69702	−	1.55712i	−0.123230	−	0.0711467i	−0.560348	+	0.828257i	$0.689333\pi$
$480$	−0.313859	−	1.33591i	−0.0143257	−	0.0609755i
$481$	40.4674	+	11.6819i	1.84515	+	0.532650i
$482$	12.7446			0.580499
$483$	17.8030	−	7.96916i	0.810064	−	0.362609i
$484$	−4.05842	+	7.02939i	−0.184474	+	0.319518i
$485$	0.510875	−	0.294954i	0.0231976	−	0.0133932i
$486$	6.31386	−	14.2525i	0.286402	−	0.646509i
$487$	−26.6168	+	15.3672i	−1.20612	+	0.696356i	−0.961910	−	0.273365i	$-0.911863\pi$
$487$	−26.6168	+	15.3672i	−1.20612	+	0.696356i	−0.244214	+	0.969721i	$0.578530\pi$
$488$	4.50000	−	2.59808i	0.203705	−	0.117609i
$489$	4.11684	+	17.5229i	0.186170	+	0.792412i
$490$	−2.05842	−	5.14987i	−0.0929900	−	0.232647i
$491$	−6.60597	−	3.81396i	−0.298123	−	0.172122i	0.343476	−	0.939161i	$-0.388396\pi$
$491$	−6.60597	−	3.81396i	−0.298123	−	0.172122i	−0.641599	+	0.767040i	$0.721729\pi$
$492$	−15.6753	−	4.72627i	−0.706696	−	0.213077i
$493$		−	11.0371i		−	0.497087i
$494$	−8.30298	+	2.05446i	−0.373569	+	0.0924343i
$495$	4.62772	+	9.30506i	0.208000	+	0.418232i
$496$	3.37228	−	5.84096i	0.151420	−	0.262267i
$497$	−8.05842	−	41.8728i	−0.361470	−	1.87825i
$498$	2.00000	−	1.87953i	0.0896221	−	0.0842236i
$499$			16.4356i			0.735761i	0.929873	+	0.367880i	$0.119916\pi$
$499$			16.4356i			0.735761i	−0.929873	+	0.367880i	$0.880084\pi$
$500$	−6.43070	+	3.71277i	−0.287590	+	0.166040i
$501$	8.37228	−	7.86797i	0.374046	−	0.351515i
$502$	−16.1168			−0.719330
$503$	11.4891	+	19.8997i	0.512275	+	0.887286i	0.999899	+	0.0142322i	$0.00453039\pi$
$503$	11.4891	+	19.8997i	0.512275	+	0.887286i	−0.487624	+	0.873054i	$0.662136\pi$
$504$	4.81386	+	6.31084i	0.214426	+	0.281107i
$505$	−10.1168	−	5.84096i	−0.450194	−	0.259919i
$506$		−	18.6101i		−	0.827321i
$507$	−4.30298	−	22.1017i	−0.191102	−	0.981570i
$508$	−2.11684			−0.0939198
$509$	−20.3139	−	11.7282i	−0.900396	−	0.519844i	−0.0230673	−	0.999734i	$-0.507343\pi$
$509$	−20.3139	−	11.7282i	−0.900396	−	0.519844i	−0.877329	+	0.479890i	$0.840677\pi$
$510$	5.74456	+	1.73205i	0.254374	+	0.0766965i
$511$	26.8614	+	9.30506i	1.18828	+	0.411632i
$512$	−1.00000			−0.0441942
$513$	−11.5584	−	4.28384i	−0.510317	−	0.189136i
$514$	2.44158	+	4.22894i	0.107693	+	0.186530i
$515$	−6.51087			−0.286903
$516$	−4.74456	−	5.04868i	−0.208868	−	0.222256i
$517$	3.55842	+	2.05446i	0.156499	+	0.0903549i
$518$	−30.3505	+	5.84096i	−1.33353	+	0.256637i
$519$	−3.17527	+	0.746000i	−0.139379	+	0.0327458i
$520$	−0.686141	−	2.77300i	−0.0300893	−	0.121604i
$521$	1.11684			0.0489298			0.0244649	−	0.999701i	$-0.492212\pi$
$521$	1.11684			0.0489298			0.0244649	+	0.999701i	$0.492212\pi$
$522$	−7.55842	−	0.469882i	−0.330823	−	0.0205662i
$523$	7.50000	+	4.33013i	0.327952	+	0.189343i	0.654932	−	0.755688i	$-0.272697\pi$
$523$	7.50000	+	4.33013i	0.327952	+	0.189343i	−0.326979	+	0.945031i	$0.606031\pi$
$524$	10.8030	+	18.7113i	0.471931	+	0.817408i
$525$	11.7446	−	16.2333i	0.512575	−	0.708478i
$526$	−19.5475	+	11.2858i	−0.852314	+	0.492083i
$527$	14.7446	+	25.5383i	0.642283	+	1.11247i
$528$	7.37228	−	1.73205i	0.320837	−	0.0753778i
$529$	−2.44158	−	4.22894i	−0.106156	−	0.183867i
$530$	0.883156	−	1.52967i	0.0383618	−	0.0664447i
$531$	−18.3723	−	1.14214i	−0.797289	−	0.0495648i
$532$	4.74456	−	4.10891i	0.205703	−	0.178144i
$533$	−32.7446	−	9.45254i	−1.41832	−	0.409435i
$534$	−4.25544	−	18.1128i	−0.184151	−	0.783817i
$535$	−0.372281	+	0.644810i	−0.0160951	+	0.0278776i
$536$	−10.1168	−	5.84096i	−0.436981	−	0.252291i
$537$	−6.37228	+	5.98844i	−0.274984	+	0.258420i
$538$	0.861407			0.0371379
$539$	28.4198	−	11.3595i	1.22413	−	0.489289i
$540$	1.43070	−	3.86025i	0.0615677	−	0.166119i
$541$			1.28962i			0.0554451i	0.999616	+	0.0277226i	$0.00882549\pi$
$541$			1.28962i			0.0554451i	−0.999616	+	0.0277226i	$0.991175\pi$
$542$	−2.00000	−	3.46410i	−0.0859074	−	0.148796i
$543$	−20.1060	−	6.06218i	−0.862830	−	0.260153i
$544$	2.18614	−	3.78651i	0.0937300	−	0.162345i
$545$	15.7663			0.675355
$546$	10.1753	+	13.0178i	0.435461	+	0.557112i
$547$	8.51087			0.363899			0.181949	−	0.983308i	$-0.441759\pi$
$547$	8.51087			0.363899			0.181949	+	0.983308i	$0.441759\pi$
$548$	3.68614	−	6.38458i	0.157464	−	0.272736i
$549$	15.5584	+	0.967215i	0.664017	+	0.0412797i
$550$	−9.55842	−	16.5557i	−0.407572	−	0.705936i
$551$			5.98844i			0.255116i
$552$	−5.37228	+	5.04868i	−0.228659	+	0.214886i
$553$	24.0693	+	8.33785i	1.02353	+	0.354561i
$554$	−13.4891			−0.573098
$555$	10.9783	+	11.6819i	0.466001	+	0.495870i
$556$	−7.67527	−	4.43132i	−0.325504	−	0.187930i
$557$	12.3030	−	21.3094i	0.521294	−	0.902908i	−0.478399	−	0.878143i	$-0.658783\pi$
$557$	12.3030	−	21.3094i	0.521294	−	0.902908i	0.999693	−	0.0247655i	$-0.00788391\pi$
$558$	18.1168	−	9.01011i	0.766947	−	0.381428i
$559$	−10.0000	−	10.3923i	−0.422955	−	0.439548i
$560$	1.37228	+	1.58457i	0.0579895	+	0.0669605i
$561$	−9.55842	+	31.7017i	−0.403557	+	1.33845i
$562$	−7.37228	+	12.7692i	−0.310981	+	0.538635i
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	0.943560	+	0.331202i	$0.107454\pi$
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	−0.184950	+	0.982748i	$0.559212\pi$
$564$	−0.372281	−	1.58457i	−0.0156759	−	0.0667226i
$565$	−1.48913	−	2.57924i	−0.0626480	−	0.108509i
$566$	2.05842	−	1.18843i	0.0865219	−	0.0499535i
$567$	1.56930	+	23.7600i	0.0659043	+	0.997826i
$568$	8.05842	+	13.9576i	0.338124	+	0.585648i
$569$	−29.6644	−	17.1267i	−1.24360	−	0.717990i	−0.273772	−	0.961795i	$-0.588271\pi$
$569$	−29.6644	−	17.1267i	−1.24360	−	0.717990i	−0.969824	+	0.243804i	$0.921605\pi$
$570$	−3.11684	−	0.939764i	−0.130550	−	0.0393624i
$571$	−9.48913			−0.397108			−0.198554	−	0.980090i	$-0.563624\pi$
$571$	−9.48913			−0.397108			−0.198554	+	0.980090i	$0.563624\pi$
$572$	15.3030	−	3.78651i	0.639850	−	0.158322i
$573$	4.86141	+	20.6920i	0.203088	+	0.864422i
$574$	24.5584	−	4.72627i	1.02505	−	0.197271i
$575$	16.1168	+	9.30506i	0.672119	+	0.388048i
$576$	−2.50000	−	1.65831i	−0.104167	−	0.0690963i
$577$	5.76631			0.240055			0.120027	−	0.992771i	$-0.461702\pi$
$577$	5.76631			0.240055			0.120027	+	0.992771i	$0.461702\pi$
$578$	1.05842	+	1.83324i	0.0440246	+	0.0762528i
$579$	16.9307	−	15.9109i	0.703616	−	0.661233i
$580$	−2.00000			−0.0830455
$581$	−1.37228	+	3.96143i	−0.0569318	+	0.164348i
$582$	0.372281	−	1.23472i	0.0154316	−	0.0511807i
$583$	8.44158	+	4.87375i	0.349614	+	0.201850i
$584$	−10.7446			−0.444613
$585$	2.88316	−	8.07035i	0.119204	−	0.333668i
$586$		−	3.75906i		−	0.155285i
$587$	−37.5475	−	21.6781i	−1.54975	−	0.894750i	−0.998160	−	0.0606372i	$-0.980687\pi$
$587$	−37.5475	−	21.6781i	−1.54975	−	0.894750i	−0.551593	−	0.834113i	$-0.685980\pi$
$588$	−10.9891	−	5.12241i	−0.453184	−	0.211245i
$589$	−8.00000	−	13.8564i	−0.329634	−	0.570943i
$590$	−4.86141			−0.200141
$591$	29.1861	+	31.0569i	1.20056	+	1.27751i
$592$	10.1168	−	5.84096i	0.415800	−	0.240062i
$593$			3.11425i			0.127887i	0.997954	+	0.0639434i	$0.0203677\pi$
$593$			3.11425i			0.127887i	−0.997954	+	0.0639434i	$0.979632\pi$
$594$	21.3030	+	7.89542i	0.874072	+	0.323953i
$595$	−9.00000	+	1.73205i	−0.368964	+	0.0710072i
$596$	−3.00000	+	5.19615i	−0.122885	+	0.212843i
$597$	−1.37228	−	5.84096i	−0.0561637	−	0.239055i
$598$	−11.0584	+	10.6410i	−0.452213	+	0.435142i
$599$			22.5716i			0.922249i	0.887335	+	0.461125i	$0.152554\pi$
$599$			22.5716i			0.922249i	−0.887335	+	0.461125i	$0.847446\pi$
$600$	−2.18614	+	7.25061i	−0.0892488	+	0.296005i
$601$	−37.1168	−	21.4294i	−1.51403	−	0.874124i	−0.999865	−	0.0164316i	$-0.994769\pi$
$601$	−37.1168	−	21.4294i	−1.51403	−	0.874124i	−0.514163	−	0.857693i	$-0.671897\pi$
$602$	10.0000	+	3.46410i	0.407570	+	0.141186i
$603$	−15.6060	−	31.3793i	−0.635524	−	1.27786i
$604$	14.6168	−	8.43904i	0.594751	−	0.343380i
$605$	−5.56930	+	3.21543i	−0.226424	+	0.130726i
$606$	−24.8614	+	5.84096i	−1.00993	+	0.237273i
$607$	−30.3505	+	17.5229i	−1.23189	+	0.711232i	−0.967424	−	0.253163i	$-0.918529\pi$
$607$	−30.3505	+	17.5229i	−1.23189	+	0.711232i	−0.264466	+	0.964395i	$0.585196\pi$
$608$	−1.18614	+	2.05446i	−0.0481044	+	0.0833192i
$609$	10.5584	−	4.72627i	0.427849	−	0.191518i
$610$	4.11684			0.166686
$611$	−0.813859	−	3.28917i	−0.0329252	−	0.133066i
$612$	11.7446	−	5.84096i	0.474746	−	0.236107i
$613$	−8.23369	−	4.75372i	−0.332556	−	0.192001i	0.324420	−	0.945913i	$-0.394831\pi$
$613$	−8.23369	−	4.75372i	−0.332556	−	0.192001i	−0.656975	+	0.753912i	$0.728164\pi$
$614$	−10.6168	+	18.3889i	−0.428461	+	0.742116i
$615$	−8.88316	−	9.45254i	−0.358203	−	0.381163i
$616$	−8.74456	+	7.57301i	−0.352328	+	0.305125i
$617$	16.8030	+	29.1036i	0.676463	+	1.17167i	0.976039	+	0.217595i	$0.0698213\pi$
$617$	16.8030	+	29.1036i	0.676463	+	1.17167i	−0.299576	+	0.954072i	$0.596845\pi$
$618$	−10.3723	+	9.74749i	−0.417234	+	0.392102i
$619$	33.4674			1.34517			0.672584	−	0.740021i	$-0.265184\pi$
$619$	33.4674			1.34517			0.672584	+	0.740021i	$0.265184\pi$
$620$	4.62772	−	2.67181i	0.185854	−	0.107303i
$621$	−21.8030	+	3.71277i	−0.874924	+	0.148988i
$622$	5.18614	−	8.98266i	0.207945	−	0.360172i
$623$	18.6060	+	21.4843i	0.745432	+	0.860751i
$624$	−5.24456	−	3.39036i	−0.209951	−	0.135723i
$625$	15.9783			0.639130
$626$	12.0000	+	6.92820i	0.479616	+	0.276907i
$627$	5.18614	−	17.2005i	0.207115	−	0.686921i
$628$		0			0
$629$			51.0767i			2.03656i
$630$	0.802985	+	6.23711i	0.0319917	+	0.248492i
$631$	−28.5000	+	16.4545i	−1.13457	+	0.655043i	−0.945080	−	0.326841i	$-0.894016\pi$
$631$	−28.5000	+	16.4545i	−1.13457	+	0.655043i	−0.189488	+	0.981883i	$0.560683\pi$
$632$	−9.62772			−0.382970
$633$	13.3505	+	14.2063i	0.530636	+	0.564648i
$634$	−7.62772	+	13.2116i	−0.302935	+	0.524700i
$635$	−1.45245	−	0.838574i	−0.0576388	−	0.0332778i
$636$	−0.883156	−	3.75906i	−0.0350194	−	0.149056i
$637$	−23.0000	−	10.3923i	−0.911293	−	0.411758i
$638$		−	11.0371i		−	0.436964i
$639$	−3.00000	+	48.2574i	−0.118678	+	1.90903i
$640$	−0.686141	−	0.396143i	−0.0271221	−	0.0156589i
$641$	23.6644	−	13.6626i	0.934687	−	0.539642i	0.0463963	−	0.998923i	$-0.485226\pi$
$641$	23.6644	−	13.6626i	0.934687	−	0.539642i	0.888291	+	0.459281i	$0.151893\pi$
$642$	0.372281	+	1.58457i	0.0146928	+	0.0625381i
$643$	1.61684	+	2.80046i	0.0637621	+	0.110439i	0.896144	−	0.443763i	$-0.146357\pi$
$643$	1.61684	+	2.80046i	0.0637621	+	0.110439i	−0.832382	+	0.554202i	$0.813023\pi$
$644$	3.68614	−	10.6410i	0.145254	−	0.419313i
$645$	−1.25544	−	5.34363i	−0.0494328	−	0.210405i
$646$	−5.18614	−	8.98266i	−0.204046	−	0.353418i
$647$	19.9307	−	34.5210i	0.783557	−	1.35716i	−0.146301	−	0.989240i	$-0.546737\pi$
$647$	19.9307	−	34.5210i	0.783557	−	1.35716i	0.929857	−	0.367920i	$-0.119930\pi$
$648$	−3.50000	−	8.29156i	−0.137493	−	0.325723i
$649$		−	26.8280i		−	1.05309i
$650$	−4.37228	+	15.1460i	−0.171495	+	0.594076i
$651$	−18.1168	+	25.0410i	−0.710055	+	0.981434i
$652$	9.00000	+	5.19615i	0.352467	+	0.203497i
$653$	−9.04755	−	5.22360i	−0.354058	−	0.204415i	0.312413	−	0.949946i	$-0.398863\pi$
$653$	−9.04755	−	5.22360i	−0.354058	−	0.204415i	−0.666471	+	0.745531i	$0.732196\pi$
$654$	25.1168	−	23.6039i	0.982146	−	0.922986i
$655$			17.1181i			0.668861i
$656$	−8.18614	+	4.72627i	−0.319615	+	0.184530i
$657$	−26.8614	−	17.8178i	−1.04796	−	0.695140i
$658$	1.62772	+	1.87953i	0.0634551	+	0.0732716i
$659$	37.1644	−	21.4569i	1.44772	−	0.835841i	0.449374	−	0.893344i	$-0.351647\pi$
$659$	37.1644	−	21.4569i	1.44772	−	0.835841i	0.998345	+	0.0575028i	$0.0183138\pi$
$660$	5.74456	+	1.73205i	0.223607	+	0.0674200i
$661$	10.5693	−	18.3066i	0.411098	−	0.712043i	−0.583912	−	0.811817i	$-0.698479\pi$
$661$	10.5693	−	18.3066i	0.411098	−	0.712043i	0.995010	+	0.0997743i	$0.0318121\pi$
$662$			2.17448i			0.0845136i
$663$	24.3030	−	12.4468i	0.943850	−	0.483392i
$664$		−	1.58457i		−	0.0614934i
$665$	4.88316	−	0.939764i	0.189361	−	0.0364425i
$666$	34.9783	+	2.17448i	1.35538	+	0.0842594i
$667$	5.37228	+	9.30506i	0.208016	+	0.360294i
$668$		−	6.63325i		−	0.256648i
$669$	33.4891	+	35.6357i	1.29476	+	1.37776i
$670$	−4.62772	−	8.01544i	−0.178784	−	0.309664i
$671$			22.7190i			0.877059i
$672$	4.55842	+	0.469882i	0.175845	+	0.0181261i
$673$	4.18614	−	7.25061i	0.161364	−	0.279490i	−0.773994	−	0.633193i	$-0.781744\pi$
$673$	4.18614	−	7.25061i	0.161364	−	0.279490i	0.935358	+	0.353702i	$0.115077\pi$
$674$	−5.30298	+	9.18504i	−0.204263	+	0.353794i
$675$	−17.4891	+	14.5012i	−0.673157	+	0.558152i
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	1.37228			0.0527411			0.0263705	−	0.999652i	$-0.491605\pi$
$677$	1.37228			0.0527411			0.0263705	+	0.999652i	$0.491605\pi$
$678$	−6.23369	−	1.87953i	−0.239403	−	0.0721828i
$679$	0.372281	+	1.93443i	0.0142868	+	0.0742366i
$680$	3.00000	−	1.73205i	0.115045	−	0.0664211i
$681$	7.68614	+	32.7152i	0.294534	+	1.25365i
$682$	14.7446	+	25.5383i	0.564598	+	0.977913i
$683$	−6.86141	−	11.8843i	−0.262544	−	0.454740i	0.704373	−	0.709830i	$-0.251228\pi$
$683$	−6.86141	−	11.8843i	−0.262544	−	0.454740i	−0.966917	+	0.255090i	$0.917895\pi$
$684$	−6.37228	+	3.16915i	−0.243650	+	0.121175i
$685$	5.05842	−	2.92048i	0.193272	−	0.111586i
$686$	18.5000	−	0.866025i	0.706333	−	0.0330650i
$687$	−2.55842	+	8.48533i	−0.0976099	+	0.323735i
$688$	−4.00000			−0.152499
$689$	−1.93070	−	7.80284i	−0.0735539	−	0.297265i
$690$	−5.68614	+	1.33591i	−0.216468	+	0.0508571i
$691$	−10.9416	+	18.9514i	−0.416237	+	0.720944i	−0.995557	−	0.0941560i	$-0.969985\pi$
$691$	−10.9416	+	18.9514i	−0.416237	+	0.720944i	0.579320	+	0.815100i	$0.303318\pi$
$692$	−0.941578	+	1.63086i	−0.0357934	+	0.0619960i
$693$	−34.4198	+	4.43132i	−1.30750	+	0.168332i
$694$		−	20.8395i		−	0.791057i
$695$	−3.51087	−	6.08101i	−0.133175	−	0.230666i
$696$	−3.18614	+	2.99422i	−0.120770	+	0.113496i
$697$		−	41.3292i		−	1.56545i
$698$	−10.0584	−	17.4217i	−0.380717	−	0.659421i
$699$	8.03667	+	2.42315i	0.303975	+	0.0916519i
$700$	−2.18614	−	11.3595i	−0.0826284	−	0.429350i
$701$		−	45.3832i		−	1.71410i	−0.515234	−	0.857049i	$-0.672295\pi$
$701$		−	45.3832i		−	1.71410i	0.515234	−	0.857049i	$-0.327705\pi$
$702$	−7.48913	−	17.1730i	−0.282659	−	0.648154i
$703$		−	27.7128i		−	1.04521i
$704$	2.18614	−	3.78651i	0.0823933	−	0.142709i
$705$	0.372281	−	1.23472i	0.0140209	−	0.0465022i
$706$	−25.3723	+	14.6487i	−0.954898	+	0.551311i
$707$	29.4891	−	25.5383i	1.10905	−	0.960468i
$708$	−7.74456	+	7.27806i	−0.291058	+	0.273526i
$709$	−22.8832	+	13.2116i	−0.859395	+	0.496172i	−0.863810	−	0.503818i	$-0.831928\pi$
$709$	−22.8832	+	13.2116i	−0.859395	+	0.496172i	0.00441467	+	0.999990i	$0.498595\pi$
$710$			12.7692i			0.479218i
$711$	−24.0693	−	15.9658i	−0.902669	−	0.598763i
$712$	−9.30298	−	5.37108i	−0.348644	−	0.201290i
$713$	−24.8614	−	14.3537i	−0.931067	−	0.537552i
$714$	−11.7446	+	16.2333i	−0.439529	+	0.607515i
$715$	12.0000	+	3.46410i	0.448775	+	0.129550i
$716$			5.04868i			0.188678i
$717$	−7.80298	+	25.8796i	−0.291408	+	0.966490i
$718$	8.31386	−	14.4000i	0.310270	−	0.537404i
$719$	12.5584	+	21.7518i	0.468350	+	0.811206i	0.999346	−	0.0361684i	$-0.0115153\pi$
$719$	12.5584	+	21.7518i	0.468350	+	0.811206i	−0.530996	+	0.847375i	$0.678182\pi$
$720$	−1.05842	−	2.12819i	−0.0394451	−	0.0793131i
$721$	7.11684	−	20.5446i	0.265045	−	0.765119i
$722$	−6.68614	−	11.5807i	−0.248832	−	0.430990i
$723$	21.4891	−	5.04868i	0.799189	−	0.187762i
$724$	−10.5000	+	6.06218i	−0.390229	+	0.225299i
$725$	9.55842	+	5.51856i	0.354991	+	0.204954i
$726$	−4.05842	+	13.4603i	−0.150622	+	0.499557i
$727$			28.1176i			1.04282i	0.853305	+	0.521412i	$0.174594\pi$
$727$			28.1176i			1.04282i	−0.853305	+	0.521412i	$0.825406\pi$
$728$	9.50000	+	0.866025i	0.352093	+	0.0320970i
$729$	5.00000	−	26.5330i	0.185185	−	0.982704i
$730$	−7.37228	−	4.25639i	−0.272860	−	0.157536i
$731$	8.74456	−	15.1460i	0.323429	−	0.560196i
$732$	6.55842	−	6.16337i	0.242406	−	0.227805i
$733$	43.7446			1.61574			0.807871	−	0.589359i	$-0.200620\pi$
$733$	43.7446			1.61574			0.807871	+	0.589359i	$0.200620\pi$
$734$	−26.2337	+	15.1460i	−0.968303	+	0.559050i
$735$	−5.51087	−	7.86797i	−0.203272	−	0.290214i
$736$			4.25639i			0.156893i
$737$	44.2337	−	25.5383i	1.62937	−	0.940717i
$738$	−28.3030	−	1.75950i	−1.04185	−	0.0647682i
$739$	−34.1168	−	19.6974i	−1.25501	−	0.724579i	−0.282909	−	0.959147i	$-0.591299\pi$
$739$	−34.1168	−	19.6974i	−1.25501	−	0.724579i	−0.972100	+	0.234567i	$0.924633\pi$
$740$	9.25544			0.340237
$741$	−13.1861	+	6.75327i	−0.484405	+	0.248088i
$742$	3.86141	+	4.45877i	0.141757	+	0.163687i
$743$	1.62772	−	2.81929i	0.0597152	−	0.103430i	−0.834622	−	0.550823i	$-0.814314\pi$
$743$	1.62772	−	2.81929i	0.0597152	−	0.103430i	0.894338	+	0.447393i	$0.147647\pi$
$744$	3.37228	−	11.1846i	0.123634	−	0.410047i
$745$	−4.11684	+	2.37686i	−0.150829	+	0.0870814i
$746$	−8.00000			−0.292901
$747$	2.62772	−	3.96143i	0.0961432	−	0.144941i
$748$	9.55842	+	16.5557i	0.349491	+	0.605335i
$749$	−1.62772	−	1.87953i	−0.0594755	−	0.0686764i
$750$	−9.37228	+	8.80773i	−0.342227	+	0.321613i
$751$	0.500000	−	0.866025i	0.0182453	−	0.0316017i	−0.856759	−	0.515718i	$-0.827525\pi$
$751$	0.500000	−	0.866025i	0.0182453	−	0.0316017i	0.875004	+	0.484116i	$0.160859\pi$
$752$	−0.813859	−	0.469882i	−0.0296784	−	0.0171348i
$753$	−27.1753	+	6.38458i	−0.990322	+	0.232667i
$754$	−6.55842	+	6.31084i	−0.238844	+	0.229827i
$755$	13.3723			0.486667
$756$	10.6168	+	8.73399i	0.386131	+	0.317652i
$757$	8.86141	−	15.3484i	0.322073	−	0.557847i	−0.658842	−	0.752281i	$-0.728954\pi$
$757$	8.86141	−	15.3484i	0.322073	−	0.557847i	0.980916	+	0.194434i	$0.0622869\pi$
$758$	−4.88316	+	2.81929i	−0.177364	+	0.102401i
$759$	−7.37228	−	31.3793i	−0.267597	−	1.13900i
$760$	−1.62772	+	0.939764i	−0.0590436	+	0.0340888i
$761$	3.25544	−	1.87953i	0.118010	−	0.0681328i	−0.439833	−	0.898079i	$-0.644963\pi$
$761$	3.25544	−	1.87953i	0.118010	−	0.0681328i	0.557843	+	0.829947i	$0.311629\pi$
$762$	−3.56930	+	0.838574i	−0.129302	+	0.0303783i
$763$	−17.2337	+	49.7494i	−0.623901	+	1.80105i
$764$	10.6277	+	6.13592i	0.384497	+	0.221990i
$765$	10.3723	+	0.644810i	0.375011	+	0.0233132i
$766$			15.0911i			0.545264i
$767$	−15.9416	+	15.3398i	−0.575617	+	0.553888i
$768$	−1.68614	+	0.396143i	−0.0608434	+	0.0142946i
$769$	12.1168	−	20.9870i	0.436945	−	0.756810i	−0.560508	−	0.828149i	$-0.689394\pi$
$769$	12.1168	−	20.9870i	0.436945	−	0.756810i	0.997452	+	0.0713391i	$0.0227273\pi$
$770$	−9.00000	+	1.73205i	−0.324337	+	0.0624188i
$771$	5.79211	+	6.16337i	0.208598	+	0.221968i
$772$		−	13.4140i		−	0.482780i
$773$	−18.0951	+	10.4472i	−0.650835	+	0.375760i	−0.788776	−	0.614681i	$-0.789285\pi$
$773$	−18.0951	+	10.4472i	−0.650835	+	0.375760i	0.137941	+	0.990440i	$0.455952\pi$
$774$	−10.0000	−	6.63325i	−0.359443	−	0.238427i
$775$	−29.4891			−1.05928
$776$	−0.372281	−	0.644810i	−0.0133641	−	0.0231473i
$777$	−48.8614	+	21.8719i	−1.75289	+	0.784648i
$778$	25.3723	+	14.6487i	0.909640	+	0.525181i
$779$			22.4241i			0.803426i
$780$	−2.25544	−	4.40387i	−0.0807576	−	0.157684i
$781$	−70.4674			−2.52152
$782$	−16.1168	−	9.30506i	−0.576337	−	0.332748i
$783$	−12.9307	+	2.20193i	−0.462106	+	0.0786907i
$784$	−6.50000	+	2.59808i	−0.232143	+	0.0927884i
$785$		0			0
$786$	25.6277	+	27.2704i	0.914110	+	0.972702i
$787$	−21.3614	−	36.9990i	−0.761452	−	1.31887i	−0.942102	−	0.335326i	$-0.891154\pi$
$787$	−21.3614	−	36.9990i	−0.761452	−	1.31887i	0.180650	−	0.983547i	$-0.442180\pi$
$788$	24.6060			0.876551
$789$	−28.4891	+	26.7730i	−1.01424	+	0.953146i
$790$	−6.60597	−	3.81396i	−0.235030	−	0.135695i
$791$	9.76631	−	1.87953i	0.347250	−	0.0668283i
$792$	11.7446	−	5.84096i	0.417325	−	0.207550i
$793$	13.5000	−	12.9904i	0.479399	−	0.461302i
$794$	−2.25544			−0.0800425
$795$	0.883156	−	2.92910i	0.0313223	−	0.103884i
$796$	−3.00000	−	1.73205i	−0.106332	−	0.0613909i
$797$	11.5693	+	20.0386i	0.409806	+	0.709804i	0.994868	−	0.101184i	$-0.0322632\pi$
$797$	11.5693	+	20.0386i	0.409806	+	0.709804i	−0.585062	+	0.810988i	$0.698930\pi$
$798$	6.37228	−	8.80773i	0.225576	−	0.311790i
$799$	3.55842	−	2.05446i	0.125888	−	0.0726814i
$800$	2.18614	+	3.78651i	0.0772917	+	0.133873i
$801$	−14.3505	−	28.8550i	−0.507051	−	1.01954i
$802$	−5.74456	−	9.94987i	−0.202848	−	0.351342i
$803$	23.4891	−	40.6844i	0.828913	−	1.43572i
$804$	−19.3723	−	5.84096i	−0.683208	−	0.205995i
$805$	6.74456	−	5.84096i	0.237715	−	0.205867i
$806$	6.74456	−	23.3639i	0.237567	−	0.822957i
$807$	1.45245	−	0.341241i	0.0511288	−	0.0120122i
$808$	−7.37228	+	12.7692i	−0.259356	+	0.449218i
$809$	−21.2554	−	12.2718i	−0.747301	−	0.431455i	0.0774166	−	0.996999i	$-0.475333\pi$
$809$	−21.2554	−	12.2718i	−0.747301	−	0.431455i	−0.824718	+	0.565544i	$0.808666\pi$
$810$	0.883156	−	7.07568i	0.0310309	−	0.248614i
$811$	−14.1168			−0.495709			−0.247855	−	0.968797i	$-0.579726\pi$
$811$	−14.1168			−0.495709			−0.247855	+	0.968797i	$0.579726\pi$
$812$	2.18614	−	6.31084i	0.0767185	−	0.221467i
$813$	−4.74456	−	5.04868i	−0.166399	−	0.177065i
$814$			51.0767i			1.79024i
$815$	4.11684	+	7.13058i	0.144207	+	0.249773i
$816$	2.18614	−	7.25061i	0.0765302	−	0.253822i
$817$	−4.74456	+	8.21782i	−0.165991	+	0.287505i
$818$	21.4891			0.751350
$819$	22.3139	+	17.9190i	0.779709	+	0.626142i
$820$	−7.48913			−0.261532
$821$	−10.4198	+	18.0477i	−0.363655	+	0.629868i	−0.988559	−	0.150833i	$-0.951804\pi$
$821$	−10.4198	+	18.0477i	−0.363655	+	0.629868i	0.624905	+	0.780701i	$0.285138\pi$
$822$	3.68614	−	12.2255i	0.128569	−	0.426415i
$823$	−17.2921	−	29.9508i	−0.602765	−	1.04402i	−0.992400	−	0.123050i	$-0.960732\pi$
$823$	−17.2921	−	29.9508i	−0.602765	−	1.04402i	0.389635	−	0.920969i	$-0.372601\pi$
$824$			8.21782i			0.286281i
$825$	−22.6753	−	24.1287i	−0.789451	−	0.840053i
$826$	5.31386	−	15.3398i	0.184893	−	0.533740i
$827$	8.23369			0.286313			0.143157	−	0.989700i	$-0.454275\pi$
$827$	8.23369			0.286313			0.143157	+	0.989700i	$0.454275\pi$
$828$	−7.05842	+	10.6410i	−0.245297	+	0.369799i
$829$	−13.5000	−	7.79423i	−0.468874	−	0.270705i	0.246894	−	0.969042i	$-0.420590\pi$
$829$	−13.5000	−	7.79423i	−0.468874	−	0.270705i	−0.715768	+	0.698338i	$0.753923\pi$
$830$	0.627719	−	1.08724i	0.0217884	−	0.0377387i
$831$	−22.7446	+	5.34363i	−0.789000	+	0.185368i
$832$	−3.50000	+	0.866025i	−0.121341	+	0.0300240i
$833$	4.37228	−	30.2921i	0.151491	−	1.04956i
$834$	−14.6970	−	4.43132i	−0.508916	−	0.153444i
$835$	2.62772	−	4.55134i	0.0909360	−	0.157506i
$836$	−5.18614	−	8.98266i	−0.179366	−	0.310672i
$837$	26.9783	−	22.3692i	0.932505	−	0.773192i
$838$	−2.74456	−	4.75372i	−0.0948093	−	0.164215i
$839$	42.6060	−	24.5986i	1.47092	−	0.849237i	0.471455	−	0.881890i	$-0.343729\pi$
$839$	42.6060	−	24.5986i	1.47092	−	0.849237i	0.999467	+	0.0326534i	$0.0103958\pi$
$840$	2.94158	+	2.12819i	0.101494	+	0.0734297i
$841$	−11.3139	−	19.5962i	−0.390133	−	0.675730i
$842$	23.2337	+	13.4140i	0.800686	+	0.462276i
$843$	−7.37228	+	24.4511i	−0.253915	+	0.842140i
$844$	11.2554			0.387428
$845$	−4.80298	−	9.11130i	−0.165228	−	0.313438i
$846$	−1.25544	−	2.52434i	−0.0431628	−	0.0867885i
$847$	−4.05842	−	21.0882i	−0.139449	−	0.724598i
$848$	−1.93070	−	1.11469i	−0.0663006	−	0.0382787i
$849$	3.00000	−	2.81929i	0.102960	−	0.0967578i
$850$	−19.1168			−0.655702
$851$	−24.8614	−	43.0612i	−0.852238	−	1.47612i
$852$	19.1168	+	20.3422i	0.654932	+	0.696912i
$853$	−14.7228			−0.504100			−0.252050	−	0.967714i	$-0.581105\pi$
$853$	−14.7228			−0.504100			−0.252050	+	0.967714i	$0.581105\pi$
$854$	−4.50000	+	12.9904i	−0.153987	+	0.444522i
$855$	−5.62772	−	0.349857i	−0.192464	−	0.0119648i
$856$	0.813859	+	0.469882i	0.0278171	+	0.0160602i
$857$	−19.7228			−0.673718			−0.336859	−	0.941555i	$-0.609365\pi$
$857$	−19.7228			−0.673718			−0.336859	+	0.941555i	$0.609365\pi$
$858$	24.3030	−	12.4468i	0.829690	−	0.424925i
$859$		−	6.28339i		−	0.214387i	−0.994238	−	0.107193i	$-0.965814\pi$
$859$		−	6.28339i		−	0.214387i	0.994238	−	0.107193i	$-0.0341864\pi$
$860$	−2.74456	−	1.58457i	−0.0935888	−	0.0540335i
$861$	39.5367	−	17.6978i	1.34741	−	0.603140i
$862$	−12.6861	−	21.9730i	−0.432092	−	0.748405i
$863$	−43.3723			−1.47641			−0.738205	−	0.674577i	$-0.764326\pi$
$863$	−43.3723			−1.47641			−0.738205	+	0.674577i	$0.764326\pi$
$864$	−4.87228	−	1.80579i	−0.165758	−	0.0614342i
$865$	−1.29211	+	0.746000i	−0.0439331	+	0.0253648i
$866$		−	24.6535i		−	0.837759i
$867$	2.51087	+	2.67181i	0.0852738	+	0.0907396i
$868$	3.37228	+	17.5229i	0.114463	+	0.594766i
$869$	21.0475	−	36.4554i	0.713989	−	1.23667i
$870$	−3.37228	+	0.792287i	−0.114331	+	0.0268610i
$871$	−40.4674	−	11.6819i	−1.37118	−	0.395827i
$872$		−	19.8997i		−	0.673891i
$873$	0.138593	−	2.22938i	0.00469068	−	0.0754532i
$874$	8.74456	+	5.04868i	0.295789	+	0.170774i
$875$	6.43070	−	18.5638i	0.217397	−	0.627572i
$876$	−18.1168	+	4.25639i	−0.612111	+	0.143810i
$877$	15.0000	−	8.66025i	0.506514	−	0.292436i	−0.224886	−	0.974385i	$-0.572201\pi$
$877$	15.0000	−	8.66025i	0.506514	−	0.292436i	0.731400	+	0.681949i	$0.238867\pi$
$878$	21.3505	−	12.3267i	0.720546	−	0.416007i
$879$	−1.48913	−	6.33830i	−0.0502269	−	0.213785i
$880$	3.00000	−	1.73205i	0.101130	−	0.0583874i
$881$	23.7446	−	41.1268i	0.799975	−	1.38560i	−0.119657	−	0.992815i	$-0.538180\pi$
$881$	23.7446	−	41.1268i	0.799975	−	1.38560i	0.919632	−	0.392781i	$-0.128487\pi$
$882$	−20.5584	−	4.28384i	−0.692238	−	0.144244i
$883$	−10.0000			−0.336527			−0.168263	−	0.985742i	$-0.553816\pi$
$883$	−10.0000			−0.336527			−0.168263	+	0.985742i	$0.553816\pi$
$884$	4.37228	−	15.1460i	0.147056	−	0.509416i
$885$	−8.19702	+	1.92581i	−0.275540	+	0.0647355i
$886$	6.81386	+	3.93398i	0.228916	+	0.132165i
$887$	−12.5584	+	21.7518i	−0.421671	+	0.730355i	−0.996103	−	0.0881972i	$-0.971889\pi$
$887$	−12.5584	+	21.7518i	−0.421671	+	0.730355i	0.574432	+	0.818552i	$0.305223\pi$
$888$	14.7446	−	13.8564i	0.494795	−	0.464991i
$889$	4.23369	−	3.66648i	0.141993	−	0.122970i
$890$	−4.25544	−	7.37063i	−0.142643	−	0.247064i
$891$	39.0475	+	4.87375i	1.30814	+	0.163277i
$892$	28.2337			0.945334
$893$	−1.93070	+	1.11469i	−0.0646085	+	0.0373017i
$894$	−3.00000	+	9.94987i	−0.100335	+	0.332774i
$895$	−2.00000	+	3.46410i	−0.0668526	+	0.115792i
$896$	2.00000	−	1.73205i	0.0668153	−	0.0578638i
$897$	−14.4307	+	22.3229i	−0.481827	+	0.745340i
$898$	39.6060			1.32167
$899$	−14.7446	−	8.51278i	−0.491759	−	0.283917i
$900$	−0.813859	+	13.0916i	−0.0271286	+	0.436386i
$901$	8.44158	−	4.87375i	0.281230	−	0.162368i
$902$		−	41.3292i		−	1.37611i
$903$	18.2337	+	1.87953i	0.606779	+	0.0625468i
$904$	−3.25544	+	1.87953i	−0.108274	+	0.0625122i
$905$	−9.60597			−0.319313
$906$	21.3030	−	20.0198i	0.707744	−	0.665112i
$907$	10.4891	−	18.1677i	0.348286	−	0.603249i	−0.637659	−	0.770318i	$-0.720097\pi$
$907$	10.4891	−	18.1677i	0.348286	−	0.603249i	0.985945	+	0.167070i	$0.0534306\pi$
$908$	16.8030	+	9.70121i	0.557627	+	0.321946i
$909$	−39.6060	+	19.6974i	−1.31365	+	0.653320i
$910$	6.17527	+	4.35758i	0.204708	+	0.144452i
$911$		−	11.1846i		−	0.370562i	−0.982686	−	0.185281i	$-0.940680\pi$
$911$		−	11.1846i		−	0.370562i	0.982686	−	0.185281i	$-0.0593195\pi$
$912$	−1.18614	+	3.93398i	−0.0392770	+	0.130267i
$913$	6.00000	+	3.46410i	0.198571	+	0.114645i
$914$	9.17527	−	5.29734i	0.303491	−	0.175221i
$915$	6.94158	−	1.63086i	0.229481	−	0.0539146i
$916$	2.55842	+	4.43132i	0.0845326	+	0.146415i
$917$	−54.0149	−	18.7113i	−1.78373	−	0.617902i
$918$	17.4891	−	14.5012i	0.577227	−	0.478611i
$919$	17.7337	+	30.7156i	0.584980	+	1.01322i	0.994878	+	0.101084i	$0.0322311\pi$
$919$	17.7337	+	30.7156i	0.584980	+	1.01322i	−0.409897	+	0.912132i	$0.634436\pi$
$920$	−1.68614	+	2.92048i	−0.0555904	+	0.0962854i
$921$	−10.6168	+	35.2121i	−0.349837	+	1.16028i
$922$		−	31.6742i		−	1.04314i
$923$	40.2921	+	41.8728i	1.32623	+	1.37826i
$924$	−11.7446	+	16.2333i	−0.386368	+	0.534035i
$925$	−44.2337	−	25.5383i	−1.45439	−	0.839695i
$926$	−9.38316	−	5.41737i	−0.308350	−	0.178026i
$927$	−13.6277	+	20.5446i	−0.447593	+	0.674772i
$928$			2.52434i			0.0828654i
$929$	−34.4198	+	19.8723i	−1.12928	+	0.651989i	−0.943753	−	0.330651i	$-0.892732\pi$
$929$	−34.4198	+	19.8723i	−1.12928	+	0.651989i	−0.185525	+	0.982640i	$0.559398\pi$
$930$	6.74456	−	6.33830i	0.221163	−	0.207841i
$931$	−2.37228	+	16.4356i	−0.0777484	+	0.538657i
$932$	4.19702	−	2.42315i	0.137478	−	0.0793729i
$933$	5.18614	−	17.2005i	0.169787	−	0.563119i
$934$	−12.6861	+	21.9730i	−0.415103	+	0.718980i
$935$			15.1460i			0.495328i
$936$	−10.1861	−	3.63903i	−0.332944	−	0.118945i
$937$			35.9306i			1.17380i	0.809658	+	0.586901i	$0.199652\pi$
$937$			35.9306i			1.17380i	−0.809658	+	0.586901i	$0.800348\pi$
$938$	30.3505	−	5.84096i	0.990980	−	0.190714i
$939$	22.9783	+	6.92820i	0.749867	+	0.226093i
$940$	−0.372281	−	0.644810i	−0.0121425	−	0.0210314i
$941$			13.0641i			0.425878i	0.977065	+	0.212939i	$0.0683036\pi$
$941$			13.0641i			0.425878i	−0.977065	+	0.212939i	$0.931696\pi$
$942$		0			0
$943$	20.1168	+	34.8434i	0.655095	+	1.13466i
$944$			6.13592i			0.199707i
$945$	3.82473	+	10.1985i	0.124419	+	0.331759i
$946$	8.74456	−	15.1460i	0.284310	−	0.492440i
$947$	−16.9307	+	29.3248i	−0.550174	+	0.952929i	0.448088	+	0.893990i	$0.352105\pi$
$947$	−16.9307	+	29.3248i	−0.550174	+	0.952929i	−0.998262	+	0.0589396i	$0.981228\pi$
$948$	−16.2337	+	3.81396i	−0.527246	+	0.123872i
$949$	−37.6060	+	9.30506i	−1.22074	+	0.302055i
$950$	10.3723			0.336521
$951$	−7.62772	+	25.2983i	−0.247346	+	0.820353i
$952$	2.18614	+	11.3595i	0.0708532	+	0.368164i
$953$	−32.9198	+	19.0063i	−1.06638	+	0.615674i	−0.927190	−	0.374592i	$-0.877783\pi$
$953$	−32.9198	+	19.0063i	−1.06638	+	0.615674i	−0.139188	+	0.990266i	$0.544449\pi$
$954$	−2.97825	−	5.98844i	−0.0964244	−	0.193883i
$955$	4.86141	+	8.42020i	0.157311	+	0.272471i
$956$	7.80298	+	13.5152i	0.252367	+	0.437112i
$957$	−4.37228	−	18.6101i	−0.141336	−	0.601580i
$958$	−2.69702	+	1.55712i	−0.0871366	+	0.0503083i
$959$	3.68614	+	19.1537i	0.119032	+	0.618507i
$960$	−1.31386	−	0.396143i	−0.0424046	−	0.0127855i
$961$	14.4891			0.467391
$962$	30.3505	−	29.2048i	0.978540	−	0.941601i
$963$	1.25544	+	2.52434i	0.0404559	+	0.0813456i
$964$	6.37228	−	11.0371i	0.205237	−	0.355482i
$965$	5.31386	−	9.20387i	0.171059	−	0.296283i
$966$	2.00000	−	19.4024i	0.0643489	−	0.624262i
$967$		−	40.6844i		−	1.30832i	−0.756356	−	0.654160i	$-0.773022\pi$
$967$		−	40.6844i		−	1.30832i	0.756356	−	0.654160i	$-0.226978\pi$
$968$	4.05842	+	7.02939i	0.130443	+	0.225933i
$969$	−12.3030	−	13.0916i	−0.395229	−	0.420562i
$970$		−	0.589907i		−	0.0189408i
$971$	6.94158	+	12.0232i	0.222766	+	0.385842i	0.955647	−	0.294515i	$-0.0951581\pi$
$971$	6.94158	+	12.0232i	0.222766	+	0.385842i	−0.732881	+	0.680357i	$0.761825\pi$
$972$	−9.18614	−	12.5942i	−0.294646	−	0.403960i
$973$	23.0258	−	4.43132i	0.738173	−	0.142061i
$974$			30.7345i			0.984796i
$975$	−1.37228	+	27.2704i	−0.0439482	+	0.873351i
$976$		−	5.19615i		−	0.166325i
$977$	9.43070	−	16.3345i	0.301715	−	0.522586i	−0.674810	−	0.737992i	$-0.735774\pi$
$977$	9.43070	−	16.3345i	0.301715	−	0.522586i	0.976525	+	0.215406i	$0.0691076\pi$
$978$	17.2337	+	5.19615i	0.551073	+	0.166155i
$979$	40.6753	−	23.4839i	1.29999	−	0.750548i
$980$	−5.48913	−	0.792287i	−0.175344	−	0.0253087i
$981$	33.0000	−	49.7494i	1.05361	−	1.58838i
$982$	−6.60597	+	3.81396i	−0.210805	+	0.121708i
$983$			37.9200i			1.20946i	0.796431	+	0.604730i	$0.206719\pi$
$983$			37.9200i			1.20946i	−0.796431	+	0.604730i	$0.793281\pi$
$984$	−11.9307	+	11.2120i	−0.380337	+	0.357427i
$985$	16.8832	+	9.74749i	0.537942	+	0.310581i
$986$	−9.55842	−	5.51856i	−0.304402	−	0.175747i
$987$	3.48913	+	2.52434i	0.111060	+	0.0803506i
$988$	−2.37228	+	8.21782i	−0.0754723	+	0.261444i
$989$			17.0256i			0.541381i
$990$	10.3723	+	0.644810i	0.329653	+	0.0204934i
$991$	10.6168	−	18.3889i	0.337255	−	0.584143i	−0.646660	−	0.762778i	$-0.723835\pi$
$991$	10.6168	−	18.3889i	0.337255	−	0.584143i	0.983915	+	0.178635i	$0.0571682\pi$
$992$	−3.37228	−	5.84096i	−0.107070	−	0.185451i
$993$	0.861407	+	3.66648i	0.0273359	+	0.116352i
$994$	−40.2921	−	13.9576i	−1.27799	−	0.442708i
$995$	−1.37228	−	2.37686i	−0.0435042	−	0.0753516i
$996$	−0.627719	−	2.67181i	−0.0198900	−	0.0846597i
$997$	39.7337	−	22.9403i	1.25838	−	0.726525i	0.285619	−	0.958343i	$-0.407801\pi$
$997$	39.7337	−	22.9403i	1.25838	−	0.726525i	0.972759	+	0.231818i	$0.0744674\pi$
$998$	14.2337	+	8.21782i	0.450560	+	0.260131i
$999$	59.8397	−	10.1899i	1.89324	−	0.322395i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.q.h.251.1	yes	4
3.2	odd	2		546.2.q.f.251.1	yes	4
7.6	odd	2		546.2.q.g.251.2	yes	4
13.10	even	6		546.2.q.e.335.2	yes	4
21.20	even	2		546.2.q.e.251.2	✓	4
39.23	odd	6		546.2.q.g.335.1	yes	4
91.62	odd	6		546.2.q.f.335.1	yes	4
273.62	even	6	inner	546.2.q.h.335.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.q.e.251.2	✓	4	21.20	even	2
546.2.q.e.335.2	yes	4	13.10	even	6
546.2.q.f.251.1	yes	4	3.2	odd	2
546.2.q.f.335.1	yes	4	91.62	odd	6
546.2.q.g.251.2	yes	4	7.6	odd	2
546.2.q.g.335.1	yes	4	39.23	odd	6
546.2.q.h.251.1	yes	4	1.1	even	1	trivial
546.2.q.h.335.2	yes	4	273.62	even	6	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 1.65831i) q^{3} +(-0.500000 - 0.866025i) q^{4} -0.792287i q^{5} +(-1.18614 - 1.26217i) q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-2.50000 - 1.65831i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 1.65831i) q^{3} +(-0.500000 - 0.866025i) q^{4} -0.792287i q^{5} +(-1.18614 - 1.26217i) q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-2.50000 - 1.65831i) q^{9} +(-0.686141 - 0.396143i) q^{10} +(2.18614 - 3.78651i) q^{11} +(-1.68614 + 0.396143i) q^{12} +(-3.50000 + 0.866025i) q^{13} +(2.00000 - 1.73205i) q^{14} +(-1.31386 - 0.396143i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.18614 - 3.78651i) q^{17} +(-2.68614 + 1.33591i) q^{18} +(1.18614 + 2.05446i) q^{19} +(-0.686141 + 0.396143i) q^{20} +(2.68614 - 3.71277i) q^{21} +(-2.18614 - 3.78651i) q^{22} +(3.68614 + 2.12819i) q^{23} +(-0.500000 + 1.65831i) q^{24} +4.37228 q^{25} +(-1.00000 + 3.46410i) q^{26} +(-4.00000 + 3.31662i) q^{27} +(-0.500000 - 2.59808i) q^{28} +(2.18614 + 1.26217i) q^{29} +(-1.00000 + 0.939764i) q^{30} -6.74456 q^{31} +(0.500000 + 0.866025i) q^{32} +(-5.18614 - 5.51856i) q^{33} -4.37228 q^{34} +(0.686141 - 1.98072i) q^{35} +(-0.186141 + 2.99422i) q^{36} +(-10.1168 - 5.84096i) q^{37} +2.37228 q^{38} +(-0.313859 + 6.23711i) q^{39} +0.792287i q^{40} +(8.18614 + 4.72627i) q^{41} +(-1.87228 - 4.18265i) q^{42} +(2.00000 + 3.46410i) q^{43} -4.37228 q^{44} +(-1.31386 + 1.98072i) q^{45} +(3.68614 - 2.12819i) q^{46} +0.939764i q^{47} +(1.18614 + 1.26217i) q^{48} +(5.50000 + 4.33013i) q^{49} +(2.18614 - 3.78651i) q^{50} +(-7.37228 + 1.73205i) q^{51} +(2.50000 + 2.59808i) q^{52} +2.22938i q^{53} +(0.872281 + 5.12241i) q^{54} +(-3.00000 - 1.73205i) q^{55} +(-2.50000 - 0.866025i) q^{56} +(4.00000 - 0.939764i) q^{57} +(2.18614 - 1.26217i) q^{58} +(5.31386 - 3.06796i) q^{59} +(0.313859 + 1.33591i) q^{60} +(-4.50000 + 2.59808i) q^{61} +(-3.37228 + 5.84096i) q^{62} +(-4.81386 - 6.31084i) q^{63} +1.00000 q^{64} +(0.686141 + 2.77300i) q^{65} +(-7.37228 + 1.73205i) q^{66} +(10.1168 + 5.84096i) q^{67} +(-2.18614 + 3.78651i) q^{68} +(5.37228 - 5.04868i) q^{69} +(-1.37228 - 1.58457i) q^{70} +(-8.05842 - 13.9576i) q^{71} +(2.50000 + 1.65831i) q^{72} +10.7446 q^{73} +(-10.1168 + 5.84096i) q^{74} +(2.18614 - 7.25061i) q^{75} +(1.18614 - 2.05446i) q^{76} +(8.74456 - 7.57301i) q^{77} +(5.24456 + 3.39036i) q^{78} +9.62772 q^{79} +(0.686141 + 0.396143i) q^{80} +(3.50000 + 8.29156i) q^{81} +(8.18614 - 4.72627i) q^{82} +1.58457i q^{83} +(-4.55842 - 0.469882i) q^{84} +(-3.00000 + 1.73205i) q^{85} +4.00000 q^{86} +(3.18614 - 2.99422i) q^{87} +(-2.18614 + 3.78651i) q^{88} +(9.30298 + 5.37108i) q^{89} +(1.05842 + 2.12819i) q^{90} +(-9.50000 - 0.866025i) q^{91} -4.25639i q^{92} +(-3.37228 + 11.1846i) q^{93} +(0.813859 + 0.469882i) q^{94} +(1.62772 - 0.939764i) q^{95} +(1.68614 - 0.396143i) q^{96} +(0.372281 + 0.644810i) q^{97} +(6.50000 - 2.59808i) q^{98} +(-11.7446 + 5.84096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + q^{6} + 10 q^{7} - 4 q^{8} - 10 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + q^6 + 10 * q^7 - 4 * q^8 - 10 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + q^{6} + 10 q^{7} - 4 q^{8} - 10 q^{9} + 3 q^{10} + 3 q^{11} - q^{12} - 14 q^{13} + 8 q^{14} - 11 q^{15} - 2 q^{16} - 3 q^{17} - 5 q^{18} - q^{19} + 3 q^{20} + 5 q^{21} - 3 q^{22} + 9 q^{23} - 2 q^{24} + 6 q^{25} - 4 q^{26} - 16 q^{27} - 2 q^{28} + 3 q^{29} - 4 q^{30} - 4 q^{31} + 2 q^{32} - 15 q^{33} - 6 q^{34} - 3 q^{35} + 5 q^{36} - 6 q^{37} - 2 q^{38} - 7 q^{39} + 27 q^{41} + 4 q^{42} + 8 q^{43} - 6 q^{44} - 11 q^{45} + 9 q^{46} - q^{48} + 22 q^{49} + 3 q^{50} - 18 q^{51} + 10 q^{52} - 8 q^{54} - 12 q^{55} - 10 q^{56} + 16 q^{57} + 3 q^{58} + 27 q^{59} + 7 q^{60} - 18 q^{61} - 2 q^{62} - 25 q^{63} + 4 q^{64} - 3 q^{65} - 18 q^{66} + 6 q^{67} - 3 q^{68} + 10 q^{69} + 6 q^{70} - 15 q^{71} + 10 q^{72} + 20 q^{73} - 6 q^{74} + 3 q^{75} - q^{76} + 12 q^{77} - 2 q^{78} + 50 q^{79} - 3 q^{80} + 14 q^{81} + 27 q^{82} - q^{84} - 12 q^{85} + 16 q^{86} + 7 q^{87} - 3 q^{88} - 3 q^{89} - 13 q^{90} - 38 q^{91} - 2 q^{93} + 9 q^{94} + 18 q^{95} + q^{96} - 10 q^{97} + 26 q^{98} - 24 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + q^6 + 10 * q^7 - 4 * q^8 - 10 * q^9 + 3 * q^10 + 3 * q^11 - q^12 - 14 * q^13 + 8 * q^14 - 11 * q^15 - 2 * q^16 - 3 * q^17 - 5 * q^18 - q^19 + 3 * q^20 + 5 * q^21 - 3 * q^22 + 9 * q^23 - 2 * q^24 + 6 * q^25 - 4 * q^26 - 16 * q^27 - 2 * q^28 + 3 * q^29 - 4 * q^30 - 4 * q^31 + 2 * q^32 - 15 * q^33 - 6 * q^34 - 3 * q^35 + 5 * q^36 - 6 * q^37 - 2 * q^38 - 7 * q^39 + 27 * q^41 + 4 * q^42 + 8 * q^43 - 6 * q^44 - 11 * q^45 + 9 * q^46 - q^48 + 22 * q^49 + 3 * q^50 - 18 * q^51 + 10 * q^52 - 8 * q^54 - 12 * q^55 - 10 * q^56 + 16 * q^57 + 3 * q^58 + 27 * q^59 + 7 * q^60 - 18 * q^61 - 2 * q^62 - 25 * q^63 + 4 * q^64 - 3 * q^65 - 18 * q^66 + 6 * q^67 - 3 * q^68 + 10 * q^69 + 6 * q^70 - 15 * q^71 + 10 * q^72 + 20 * q^73 - 6 * q^74 + 3 * q^75 - q^76 + 12 * q^77 - 2 * q^78 + 50 * q^79 - 3 * q^80 + 14 * q^81 + 27 * q^82 - q^84 - 12 * q^85 + 16 * q^86 + 7 * q^87 - 3 * q^88 - 3 * q^89 - 13 * q^90 - 38 * q^91 - 2 * q^93 + 9 * q^94 + 18 * q^95 + q^96 - 10 * q^97 + 26 * q^98 - 24 * q^99

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