LMFDB - Embedded newform 546.2.q.f.335.1

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			335.1
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	546.335
Dual form			546.2.q.f.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.18614 - 1.26217i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.792287i q^{5} +(-0.500000 + 1.65831i) q^{6} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.186141 + 2.99422i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.18614 - 1.26217i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.792287i q^{5} +(-0.500000 + 1.65831i) q^{6} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.186141 + 2.99422i) 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} +(-1.00000 + 0.939764i) 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} +(-4.05842 - 2.12819i) q^{21} +(-2.18614 + 3.78651i) q^{22} +(-3.68614 + 2.12819i) q^{23} +(-1.18614 - 1.26217i) 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} +(1.31386 + 0.396143i) q^{30} -6.74456 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.18614 + 7.25061i) q^{33} -4.37228 q^{34} +(-0.686141 - 1.98072i) q^{35} +(-2.50000 - 1.65831i) q^{36} +(-10.1168 + 5.84096i) q^{37} -2.37228 q^{38} +(3.05842 + 5.44482i) q^{39} -0.792287i q^{40} +(-8.18614 + 4.72627i) q^{41} +(0.186141 + 4.57879i) q^{42} +(2.00000 - 3.46410i) q^{43} +4.37228 q^{44} +(2.37228 + 0.147477i) q^{45} +(3.68614 + 2.12819i) q^{46} +0.939764i q^{47} +(-0.500000 + 1.65831i) 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} +(-4.87228 - 1.80579i) 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} +(2.12772 + 7.64675i) 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} +(7.05842 + 2.12819i) q^{69} +(-1.37228 + 1.58457i) q^{70} +(8.05842 - 13.9576i) q^{71} +(-0.186141 + 2.99422i) q^{72} +10.7446 q^{73} +(10.1168 + 5.84096i) q^{74} +(-5.18614 - 5.51856i) q^{75} +(1.18614 + 2.05446i) q^{76} +(-8.74456 - 7.57301i) q^{77} +(3.18614 - 5.37108i) q^{78} +9.62772 q^{79} +(-0.686141 + 0.396143i) q^{80} +(-8.93070 - 1.11469i) q^{81} +(8.18614 + 4.72627i) q^{82} +1.58457i q^{83} +(3.87228 - 2.45060i) q^{84} +(-3.00000 - 1.73205i) q^{85} -4.00000 q^{86} +(4.18614 + 1.26217i) 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} +(8.00000 + 8.51278i) 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} + q^{3} - 2 q^{4} - 2 q^{6} + 10 q^{7} + 4 q^{8} + 5 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + q^3 - 2 * q^4 - 2 * q^6 + 10 * q^7 + 4 * q^8 + 5 * q^9	\( 4 q - 2 q^{2} + q^{3} - 2 q^{4} - 2 q^{6} + 10 q^{7} + 4 q^{8} + 5 q^{9} + 3 q^{10} - 3 q^{11} + q^{12} - 14 q^{13} - 8 q^{14} - 4 q^{15} - 2 q^{16} + 3 q^{17} + 5 q^{18} - q^{19} - 3 q^{20} + q^{21} - 3 q^{22} - 9 q^{23} + q^{24} + 6 q^{25} + 4 q^{26} + 16 q^{27} - 2 q^{28} - 3 q^{29} + 11 q^{30} - 4 q^{31} - 2 q^{32} - 3 q^{33} - 6 q^{34} + 3 q^{35} - 10 q^{36} - 6 q^{37} + 2 q^{38} - 5 q^{39} - 27 q^{41} - 5 q^{42} + 8 q^{43} + 6 q^{44} - 2 q^{45} + 9 q^{46} - 2 q^{48} + 22 q^{49} - 3 q^{50} - 18 q^{51} + 10 q^{52} - 8 q^{54} - 12 q^{55} + 10 q^{56} - 16 q^{57} + 3 q^{58} - 27 q^{59} - 7 q^{60} - 18 q^{61} + 2 q^{62} + 20 q^{63} + 4 q^{64} + 3 q^{65} + 18 q^{66} + 6 q^{67} + 3 q^{68} + 11 q^{69} + 6 q^{70} + 15 q^{71} + 5 q^{72} + 20 q^{73} + 6 q^{74} - 15 q^{75} - q^{76} - 12 q^{77} + 7 q^{78} + 50 q^{79} + 3 q^{80} - 7 q^{81} + 27 q^{82} + 4 q^{84} - 12 q^{85} - 16 q^{86} + 11 q^{87} - 3 q^{88} + 3 q^{89} + 13 q^{90} - 38 q^{91} + 32 q^{93} + 9 q^{94} - 18 q^{95} + q^{96} - 10 q^{97} - 26 q^{98} + 24 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + q^3 - 2 * q^4 - 2 * q^6 + 10 * q^7 + 4 * q^8 + 5 * q^9 + 3 * q^10 - 3 * q^11 + q^12 - 14 * q^13 - 8 * q^14 - 4 * q^15 - 2 * q^16 + 3 * q^17 + 5 * q^18 - q^19 - 3 * q^20 + q^21 - 3 * q^22 - 9 * q^23 + q^24 + 6 * q^25 + 4 * q^26 + 16 * q^27 - 2 * q^28 - 3 * q^29 + 11 * q^30 - 4 * q^31 - 2 * q^32 - 3 * q^33 - 6 * q^34 + 3 * q^35 - 10 * q^36 - 6 * q^37 + 2 * q^38 - 5 * q^39 - 27 * q^41 - 5 * q^42 + 8 * q^43 + 6 * q^44 - 2 * q^45 + 9 * q^46 - 2 * 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 + 20 * q^63 + 4 * q^64 + 3 * q^65 + 18 * q^66 + 6 * q^67 + 3 * q^68 + 11 * q^69 + 6 * q^70 + 15 * q^71 + 5 * q^72 + 20 * q^73 + 6 * q^74 - 15 * q^75 - q^76 - 12 * q^77 + 7 * q^78 + 50 * q^79 + 3 * q^80 - 7 * q^81 + 27 * q^82 + 4 * q^84 - 12 * q^85 - 16 * q^86 + 11 * q^87 - 3 * q^88 + 3 * q^89 + 13 * q^90 - 38 * q^91 + 32 * 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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
$3$	−1.18614	−	1.26217i	−0.684819	−	0.728714i
$3$	−1.18614	−	1.26217i	−0.684819	−	0.728714i
$4$	−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	$-0.0566913\pi$
$6$	−0.500000	+	1.65831i	−0.204124	+	0.677003i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$	1.00000			0.353553
$9$	−0.186141	+	2.99422i	−0.0620469	+	0.998073i
$10$	−0.686141	+	0.396143i	−0.216977	+	0.125272i
$11$	−2.18614	−	3.78651i	−0.659146	−	1.14167i	−0.980837	−	0.194830i	$-0.937584\pi$
$11$	−2.18614	−	3.78651i	−0.659146	−	1.14167i	0.321691	−	0.946845i	$-0.395749\pi$
$12$	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
$15$	−1.00000	+	0.939764i	−0.258199	+	0.242646i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.18614	−	3.78651i	0.530217	−	0.918363i	−0.469162	−	0.883112i	$-0.655444\pi$
$17$	2.18614	−	3.78651i	0.530217	−	0.918363i	0.999379	−	0.0352504i	$-0.0112229\pi$
$18$	2.68614	−	1.33591i	0.633129	−	0.314876i
$19$	1.18614	−	2.05446i	0.272119	−	0.471325i	−0.697285	−	0.716794i	$-0.745609\pi$
$19$	1.18614	−	2.05446i	0.272119	−	0.471325i	0.969404	+	0.245470i	$0.0789421\pi$
$20$	0.686141	+	0.396143i	0.153426	+	0.0885804i
$21$	−4.05842	−	2.12819i	−0.885620	−	0.464410i
$22$	−2.18614	+	3.78651i	−0.466087	+	0.807286i
$23$	−3.68614	+	2.12819i	−0.768613	+	0.443759i	−0.832380	−	0.554206i	$-0.813022\pi$
$23$	−3.68614	+	2.12819i	−0.768613	+	0.443759i	0.0637663	+	0.997965i	$0.479689\pi$
$24$	−1.18614	−	1.26217i	−0.242120	−	0.257639i
$25$	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	$-0.741972\pi$
$29$	−2.18614	+	1.26217i	−0.405956	+	0.234379i	0.283095	+	0.959092i	$0.408639\pi$
$30$	1.31386	+	0.396143i	0.239877	+	0.0723256i
$31$	−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
$33$	−2.18614	+	7.25061i	−0.380558	+	1.26217i
$34$	−4.37228			−0.749840
$35$	−0.686141	−	1.98072i	−0.115979	−	0.334802i
$36$	−2.50000	−	1.65831i	−0.416667	−	0.276385i
$37$	−10.1168	+	5.84096i	−1.66320	+	0.960248i	−0.692026	+	0.721873i	$0.743282\pi$
$37$	−10.1168	+	5.84096i	−1.66320	+	0.960248i	−0.971173	+	0.238376i	$0.923385\pi$
$38$	−2.37228			−0.384835
$39$	3.05842	+	5.44482i	0.489739	+	0.871869i
$40$		−	0.792287i		−	0.125272i
$41$	−8.18614	+	4.72627i	−1.27846	+	0.738119i	−0.976565	−	0.215222i	$-0.930953\pi$
$41$	−8.18614	+	4.72627i	−1.27846	+	0.738119i	−0.301895	+	0.953341i	$0.597619\pi$
$42$	0.186141	+	4.57879i	0.0287221	+	0.706523i
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	−0.672264	−	0.740312i	$-0.734678\pi$
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	0.977261	+	0.212041i	$0.0680112\pi$
$44$	4.37228			0.659146
$45$	2.37228	+	0.147477i	0.353639	+	0.0219845i
$46$	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	$0.978166\pi$
$48$	−0.500000	+	1.65831i	−0.0721688	+	0.239357i
$49$	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	$0.951070\pi$
$54$	−4.87228	−	1.80579i	−0.663034	−	0.245737i
$55$	−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	$-0.464120\pi$
$59$	−5.31386	−	3.06796i	−0.691806	−	0.399414i	−0.804288	+	0.594240i	$0.797453\pi$
$60$	−0.313859	−	1.33591i	−0.0405191	−	0.172465i
$61$	−4.50000	−	2.59808i	−0.576166	−	0.332650i	0.183442	−	0.983030i	$-0.441276\pi$
$61$	−4.50000	−	2.59808i	−0.576166	−	0.332650i	−0.759608	+	0.650381i	$0.774609\pi$
$62$	3.37228	+	5.84096i	0.428280	+	0.741803i
$63$	2.12772	+	7.64675i	0.268067	+	0.963400i
$64$	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	0.267701	−	0.963502i	$-0.413736\pi$
$67$	10.1168	−	5.84096i	1.23597	−	0.713587i	0.968268	+	0.249915i	$0.0804026\pi$
$68$	2.18614	+	3.78651i	0.265108	+	0.459181i
$69$	7.05842	+	2.12819i	0.849734	+	0.256204i
$70$	−1.37228	+	1.58457i	−0.164019	+	0.189393i
$71$	8.05842	−	13.9576i	0.956359	−	1.65646i	0.225131	−	0.974328i	$-0.427719\pi$
$71$	8.05842	−	13.9576i	0.956359	−	1.65646i	0.731228	−	0.682133i	$-0.238948\pi$
$72$	−0.186141	+	2.99422i	−0.0219369	+	0.352872i
$73$	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
$75$	−5.18614	−	5.51856i	−0.598844	−	0.637228i
$76$	1.18614	+	2.05446i	0.136060	+	0.235662i
$77$	−8.74456	−	7.57301i	−0.996535	−	0.863025i
$78$	3.18614	−	5.37108i	0.360759	−	0.608155i
$79$	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
$81$	−8.93070	−	1.11469i	−0.992300	−	0.123855i
$82$	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	$0.972283\pi$
$84$	3.87228	−	2.45060i	0.422501	−	0.267382i
$85$	−3.00000	−	1.73205i	−0.325396	−	0.187867i
$86$	−4.00000			−0.431331
$87$	4.18614	+	1.26217i	0.448801	+	0.135319i
$88$	−2.18614	−	3.78651i	−0.233043	−	0.403643i
$89$	−9.30298	+	5.37108i	−0.986114	+	0.569333i	−0.904111	−	0.427299i	$-0.859465\pi$
$89$	−9.30298	+	5.37108i	−0.986114	+	0.569333i	−0.0820038	+	0.996632i	$0.526132\pi$
$90$	−1.05842	−	2.12819i	−0.111567	−	0.224331i
$91$	−9.50000	+	0.866025i	−0.995871	+	0.0907841i
$92$		−	4.25639i		−	0.443759i
$93$	8.00000	+	8.51278i	0.829561	+	0.882734i
$94$	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	−0.846507	−	0.532378i	$-0.821299\pi$
$97$	0.372281	−	0.644810i	0.0377994	−	0.0654706i	0.884306	+	0.466907i	$0.154632\pi$
$98$	−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	−0.955348	−	0.295482i	$-0.904520\pi$
$101$	−7.37228	−	12.7692i	−0.733569	−	1.27058i	0.221779	−	0.975097i	$-0.428814\pi$
$102$	5.18614	+	5.51856i	0.513504	+	0.546419i
$103$			8.21782i			0.809726i	0.914377	+	0.404863i	$0.132681\pi$
$103$			8.21782i			0.809726i	−0.914377	+	0.404863i	$0.867319\pi$
$104$	−3.50000	−	0.866025i	−0.343203	−	0.0849208i
$105$	−1.68614	+	3.21543i	−0.164550	+	0.313794i
$106$	1.93070	−	1.11469i	0.187526	−	0.108268i
$107$	0.813859	−	0.469882i	0.0786788	−	0.0454252i	−0.460144	−	0.887844i	$-0.652202\pi$
$107$	0.813859	−	0.469882i	0.0786788	−	0.0454252i	0.538823	+	0.842419i	$0.318869\pi$
$108$	0.872281	+	5.12241i	0.0839353	+	0.492905i
$109$		−	19.8997i		−	1.90605i	−0.302891	−	0.953025i	$-0.597952\pi$
$109$		−	19.8997i		−	1.90605i	0.302891	−	0.953025i	$-0.402048\pi$
$110$	3.00000	+	1.73205i	0.286039	+	0.165145i
$111$	19.3723	+	5.84096i	1.83874	+	0.554400i
$112$	−2.00000	−	1.73205i	−0.188982	−	0.163663i
$113$	−3.25544	−	1.87953i	−0.306246	−	0.176811i	0.339000	−	0.940787i	$-0.389911\pi$
$113$	−3.25544	−	1.87953i	−0.306246	−	0.176811i	−0.645245	+	0.763975i	$0.723245\pi$
$114$	2.81386	+	2.99422i	0.263542	+	0.280434i
$115$	1.68614	+	2.92048i	0.157233	+	0.272336i
$116$		−	2.52434i		−	0.234379i
$117$	3.24456	−	10.3186i	0.299960	−	0.953952i
$118$			6.13592i			0.564857i
$119$	2.18614	−	11.3595i	0.200403	−	1.04133i
$120$	−1.00000	+	0.939764i	−0.0912871	+	0.0857883i
$121$	−4.05842	+	7.02939i	−0.368947	+	0.639036i
$122$			5.19615i			0.470438i
$123$	15.6753	+	4.72627i	1.41339	+	0.426153i
$124$	3.37228	−	5.84096i	0.302840	−	0.524534i
$125$		−	7.42554i		−	0.664160i
$126$	5.55842	−	5.66603i	0.495184	−	0.504770i
$127$	1.05842	+	1.83324i	0.0939198	+	0.162674i	0.909157	−	0.416453i	$-0.136727\pi$
$127$	1.05842	+	1.83324i	0.0939198	+	0.162674i	−0.815237	+	0.579127i	$0.803394\pi$
$128$	−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	$-0.107164\pi$
$131$	21.6060			1.88772			0.943861	+	0.330342i	$0.107164\pi$
$132$	−5.18614	−	5.51856i	−0.451396	−	0.480329i
$133$	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	$-0.935314\pi$
$137$	−3.68614	+	6.38458i	−0.314928	+	0.545472i	0.664494	+	0.747294i	$0.268647\pi$
$138$	−1.68614	−	7.17687i	−0.143534	−	0.610936i
$139$	7.67527	+	4.43132i	0.651008	+	0.375859i	0.788842	−	0.614596i	$-0.210681\pi$
$139$	7.67527	+	4.43132i	0.651008	+	0.375859i	−0.137835	+	0.990455i	$0.544014\pi$
$140$	2.05842	+	0.396143i	0.173968	+	0.0334802i
$141$	1.18614	−	1.11469i	0.0998911	−	0.0938740i
$142$	−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
$147$	−11.9891	−	1.80579i	−0.988846	−	0.148939i
$148$		−	11.6819i		−	0.960248i
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	−2.18614	+	7.25061i	−0.178498	+	0.592010i
$151$		−	16.8781i		−	1.37352i	−0.726885	−	0.686759i	$-0.759033\pi$
$151$		−	16.8781i		−	1.37352i	0.726885	−	0.686759i	$-0.240967\pi$
$152$	1.18614	−	2.05446i	0.0962087	−	0.166638i
$153$	10.9307	+	7.25061i	0.883695	+	0.586177i
$154$	−2.18614	+	11.3595i	−0.176164	+	0.915376i
$155$			5.34363i			0.429211i
$156$	−6.24456	−	0.0737384i	−0.499965	−	0.00590380i
$157$		0			0		1.00000			$0$
$157$		0			0		−1.00000			$\pi$
$158$	−4.81386	−	8.33785i	−0.382970	−	0.663324i
$159$	2.81386	−	2.64436i	0.223154	−	0.209712i
$160$	0.686141	+	0.396143i	0.0542442	+	0.0313179i
$161$	−7.37228	+	8.51278i	−0.581017	+	0.670901i
$162$	3.50000	+	8.29156i	0.274986	+	0.651447i
$163$	−9.00000	−	5.19615i	−0.704934	−	0.406994i	0.104248	−	0.994551i	$-0.466756\pi$
$163$	−9.00000	−	5.19615i	−0.704934	−	0.406994i	−0.809183	+	0.587557i	$0.800090\pi$
$164$		−	9.45254i		−	0.738119i
$165$	5.74456	+	1.73205i	0.447214	+	0.134840i
$166$	1.37228	−	0.792287i	0.106510	−	0.0614934i
$167$	−5.74456	+	3.31662i	−0.444528	+	0.256648i	−0.705516	−	0.708694i	$-0.749285\pi$
$167$	−5.74456	+	3.31662i	−0.444528	+	0.256648i	0.260989	+	0.965342i	$0.415951\pi$
$168$	−4.05842	−	2.12819i	−0.313114	−	0.164194i
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$			3.46410i			0.265684i
$171$	5.93070	+	3.93398i	0.453532	+	0.300839i
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	0.941578	−	1.63086i	0.0715869	−	0.123992i	−0.828010	−	0.560713i	$-0.810527\pi$
$173$	0.941578	−	1.63086i	0.0715869	−	0.123992i	0.899597	+	0.436721i	$0.143860\pi$
$174$	−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	$-0.606246\pi$
$179$	4.37228	−	2.52434i	0.326800	−	0.188678i	0.654419	+	0.756132i	$0.272913\pi$
$180$	−1.31386	+	1.98072i	−0.0979293	+	0.147634i
$181$			12.1244i			0.901196i	0.892727	+	0.450598i	$0.148789\pi$
$181$			12.1244i			0.901196i	−0.892727	+	0.450598i	$0.851211\pi$
$182$	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
$186$	3.37228	−	11.1846i	0.247268	−	0.820094i
$187$	−19.1168			−1.39796
$188$	−0.813859	−	0.469882i	−0.0593568	−	0.0342697i
$189$	7.12772	−	11.7557i	0.518465	−	0.855099i
$190$			1.87953i			0.136355i
$191$	10.6277	+	6.13592i	0.768995	+	0.443979i	0.832516	−	0.554001i	$-0.186900\pi$
$191$	10.6277	+	6.13592i	0.768995	+	0.443979i	−0.0635211	+	0.997980i	$0.520233\pi$
$192$	−1.18614	−	1.26217i	−0.0856023	−	0.0910892i
$193$	11.6168	−	6.70699i	0.836199	−	0.482780i	−0.0197716	−	0.999805i	$-0.506294\pi$
$193$	11.6168	−	6.70699i	0.836199	−	0.482780i	0.855970	+	0.517025i	$0.172961\pi$
$194$	−0.744563			−0.0534565
$195$	4.31386	−	2.42315i	0.308922	−	0.173525i
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$	12.3030	+	21.3094i	0.876551	+	1.51823i	0.855101	+	0.518462i	$0.173495\pi$
$197$	12.3030	+	21.3094i	0.876551	+	1.51823i	0.0214504	+	0.999770i	$0.493172\pi$
$198$	−10.9307	−	7.25061i	−0.776811	−	0.515278i
$199$	3.00000	+	1.73205i	0.212664	+	0.122782i	0.602549	−	0.798082i	$-0.294152\pi$
$199$	3.00000	+	1.73205i	0.212664	+	0.122782i	−0.389885	+	0.920864i	$0.627485\pi$
$200$	4.37228			0.309167
$201$	−19.3723	−	5.84096i	−1.36642	−	0.411990i
$202$	−7.37228	+	12.7692i	−0.518712	+	0.898435i
$203$	−4.37228	+	5.04868i	−0.306874	+	0.354348i
$204$	2.18614	−	7.25061i	0.153060	−	0.507644i
$205$	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
$210$	3.62772	−	0.147477i	0.250336	−	0.0101769i
$211$	−5.62772	−	9.74749i	−0.387428	−	0.671045i	0.604675	−	0.796473i	$-0.293303\pi$
$211$	−5.62772	−	9.74749i	−0.387428	−	0.671045i	−0.992103	+	0.125427i	$0.959970\pi$
$212$	−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
$219$	−12.7446	−	13.5615i	−0.861198	−	0.916398i
$220$		−	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	−0.755082	−	0.655631i	$-0.772403\pi$
$223$	−14.1168	−	24.4511i	−0.945334	−	1.63737i	−0.190252	−	0.981735i	$-0.560931\pi$
$224$	−0.500000	+	2.59808i	−0.0334077	+	0.173591i
$225$	−0.813859	+	13.0916i	−0.0542573	+	0.872771i
$226$			3.75906i			0.250049i
$227$	16.8030	+	9.70121i	1.11525	+	0.643892i	0.940185	−	0.340665i	$-0.110652\pi$
$227$	16.8030	+	9.70121i	1.11525	+	0.643892i	0.175068	+	0.984556i	$0.443985\pi$
$228$	1.18614	−	3.93398i	0.0785541	−	0.260534i
$229$	−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
$231$	0.813859	+	20.0198i	0.0535480	+	1.31720i
$232$	−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	$0.949255\pi$
$234$	−10.5584	+	2.34941i	−0.690226	+	0.153586i
$235$	0.744563			0.0485699
$236$	5.31386	−	3.06796i	0.345903	−	0.199707i
$237$	−11.4198	−	12.1518i	−0.741798	−	0.789345i
$238$	−10.9307	+	3.78651i	−0.708532	+	0.245443i
$239$	15.6060			1.00947			0.504733	−	0.863275i	$-0.331591\pi$
$239$	15.6060			1.00947			0.504733	+	0.863275i	$0.331591\pi$
$240$	1.31386	+	0.396143i	0.0848093	+	0.0255710i
$241$	6.37228	−	11.0371i	0.410475	−	0.710963i	−0.584467	−	0.811418i	$-0.698696\pi$
$241$	6.37228	−	11.0371i	0.410475	−	0.710963i	0.994942	+	0.100454i	$0.0320297\pi$
$242$	8.11684			0.521770
$243$	9.18614	+	12.5942i	0.589291	+	0.807921i
$244$	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
$249$	2.00000	−	1.87953i	0.126745	−	0.119110i
$250$	−6.43070	+	3.71277i	−0.406713	+	0.234816i
$251$	8.05842	−	13.9576i	0.508643	−	0.880996i	−0.491307	−	0.870987i	$-0.663481\pi$
$251$	8.05842	−	13.9576i	0.508643	−	0.880996i	0.999950	−	0.0100091i	$-0.00318605\pi$
$252$	−7.68614	−	1.98072i	−0.484181	−	0.124773i
$253$	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	$-0.117998\pi$
$257$	2.44158	+	4.22894i	0.152301	+	0.263794i	−0.779772	+	0.626064i	$0.784665\pi$
$258$	4.74456	+	5.04868i	0.295384	+	0.314317i
$259$	−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	$-0.421667\pi$
$263$	19.5475	−	11.2858i	1.20535	−	0.695911i	0.961741	+	0.273961i	$0.0883341\pi$
$264$	−2.18614	+	7.25061i	−0.134548	+	0.446244i
$265$	1.76631			0.108504
$266$	−5.93070	+	2.05446i	−0.363635	+	0.125967i
$267$	17.8139	+	5.37108i	1.09019	+	0.328705i
$268$			11.6819i			0.713587i
$269$	−0.430703	+	0.746000i	−0.0262604	+	0.0454844i	−0.878857	−	0.477085i	$-0.841693\pi$
$269$	−0.430703	+	0.746000i	−0.0262604	+	0.0454844i	0.852597	+	0.522570i	$0.175027\pi$
$270$	−1.43070	+	3.86025i	−0.0870698	+	0.234927i
$271$	2.00000	+	3.46410i	0.121491	+	0.210429i	0.920356	−	0.391082i	$-0.127899\pi$
$271$	2.00000	+	3.46410i	0.121491	+	0.210429i	−0.798865	+	0.601511i	$0.794566\pi$
$272$	−4.37228			−0.265108
$273$	12.3614	+	10.9634i	0.748146	+	0.663534i
$274$	7.37228			0.445376
$275$	−9.55842	−	16.5557i	−0.576395	−	0.998345i
$276$	−5.37228	+	5.04868i	−0.323373	+	0.303895i
$277$	−6.74456	+	11.6819i	−0.405241	+	0.701899i	−0.994350	−	0.106155i	$-0.966146\pi$
$277$	−6.74456	+	11.6819i	−0.405241	+	0.701899i	0.589108	+	0.808054i	$0.299479\pi$
$278$		−	8.86263i		−	0.531545i
$279$	1.25544	−	20.1947i	0.0751611	−	1.20903i
$280$	−0.686141	−	1.98072i	−0.0410047	−	0.118371i
$281$	14.7446			0.879587			0.439793	−	0.898099i	$-0.355052\pi$
$281$	14.7446			0.879587			0.439793	+	0.898099i	$0.355052\pi$
$282$	−1.55842	−	0.469882i	−0.0928027	−	0.0279811i
$283$	2.05842	−	1.18843i	0.122360	−	0.0706449i	−0.437571	−	0.899184i	$-0.644161\pi$
$283$	2.05842	−	1.18843i	0.122360	−	0.0706449i	0.559931	+	0.828539i	$0.310828\pi$
$284$	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
$288$	−2.50000	−	1.65831i	−0.147314	−	0.0977170i
$289$	−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	$-0.368355\pi$
$293$	−3.25544	−	1.87953i	−0.190185	−	0.109803i	−0.592069	+	0.805887i	$0.701689\pi$
$294$	4.43070	+	11.2858i	0.258404	+	0.658200i
$295$	−2.43070	+	4.21010i	−0.141521	+	0.245122i
$296$	−10.1168	+	5.84096i	−0.588030	+	0.339499i
$297$	−21.3030	−	7.89542i	−1.23612	−	0.458139i
$298$	−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
$303$	−7.37228	+	24.4511i	−0.423526	+	1.40468i
$304$	−2.37228			−0.136060
$305$	−2.05842	+	3.56529i	−0.117865	+	0.204148i
$306$	0.813859	−	13.0916i	0.0465252	−	0.748395i
$307$	−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
$309$	10.3723	−	9.74749i	0.590058	−	0.554516i
$310$	4.62772	−	2.67181i	0.262837	−	0.151749i
$311$	−10.3723			−0.588158			−0.294079	−	0.955781i	$-0.595013\pi$
$311$	−10.3723			−0.588158			−0.294079	+	0.955781i	$0.595013\pi$
$312$	3.05842	+	5.44482i	0.173149	+	0.308252i
$313$		−	13.8564i		−	0.783210i	−0.920133	−	0.391605i	$-0.871920\pi$
$313$		−	13.8564i		−	0.783210i	0.920133	−	0.391605i	$-0.128080\pi$
$314$		0			0
$315$	6.05842	−	1.68576i	0.341353	−	0.0949820i
$316$	−4.81386	+	8.33785i	−0.270801	+	0.469041i
$317$	15.2554			0.856831			0.428415	−	0.903582i	$-0.359072\pi$
$317$	15.2554			0.856831			0.428415	+	0.903582i	$0.359072\pi$
$318$	−3.69702	−	1.11469i	−0.207318	−	0.0625088i
$319$	9.55842	+	5.51856i	0.535169	+	0.308980i
$320$		−	0.792287i		−	0.0442902i
$321$	−1.55842	−	0.469882i	−0.0869826	−	0.0262263i
$322$	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
$327$	−25.1168	+	23.6039i	−1.38896	+	1.30530i
$328$	−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	0.447353	−	0.894358i	$-0.352367\pi$
$331$	−1.88316	−	1.08724i	−0.103508	−	0.0597602i	−0.550860	+	0.834598i	$0.685700\pi$
$332$	−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
$336$	0.186141	+	4.57879i	0.0101548	+	0.249794i
$337$	−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
$342$	0.441578	−	7.10313i	0.0238778	−	0.384093i
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	2.00000	−	3.46410i	0.107833	−	0.186772i
$345$	1.68614	−	5.59230i	0.0907788	−	0.301079i
$346$	−1.88316			−0.101239
$347$	−18.0475	−	10.4198i	−0.968843	−	0.559362i	−0.0699597	−	0.997550i	$-0.522287\pi$
$347$	−18.0475	−	10.4198i	−0.968843	−	0.559362i	−0.898883	+	0.438188i	$0.855620\pi$
$348$	−3.18614	+	2.99422i	−0.170795	+	0.160507i
$349$	10.0584	+	17.4217i	0.538415	+	0.932562i	0.998990	+	0.0449411i	$0.0143100\pi$
$349$	10.0584	+	17.4217i	0.538415	+	0.932562i	−0.460575	+	0.887621i	$0.652357\pi$
$350$	−8.74456	−	7.57301i	−0.467417	−	0.404795i
$351$	−16.8723	+	8.14409i	−0.900576	+	0.434699i
$352$	4.37228			0.233043
$353$	25.3723	−	14.6487i	1.35043	−	0.779671i	0.362121	−	0.932131i	$-0.382053\pi$
$353$	25.3723	−	14.6487i	1.35043	−	0.779671i	0.988310	+	0.152460i	$0.0487195\pi$
$354$	7.74456	−	7.27806i	0.411619	−	0.386825i
$355$	−11.0584	−	6.38458i	−0.586920	−	0.338858i
$356$		−	10.7422i		−	0.569333i
$357$	−16.9307	+	10.7147i	−0.896068	+	0.567083i
$358$	−4.37228	−	2.52434i	−0.231082	−	0.133415i
$359$	−16.6277			−0.877577			−0.438789	−	0.898590i	$-0.644592\pi$
$359$	−16.6277			−0.877577			−0.438789	+	0.898590i	$0.644592\pi$
$360$	2.37228	+	0.147477i	0.125030	+	0.00777271i
$361$	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
$366$	6.55842	−	6.16337i	0.342814	−	0.322164i
$367$	−26.2337	+	15.1460i	−1.36939	+	0.790616i	−0.990850	−	0.134970i	$-0.956906\pi$
$367$	−26.2337	+	15.1460i	−1.36939	+	0.790616i	−0.378538	+	0.925586i	$0.623573\pi$
$368$	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	−0.950804	−	0.309794i	$-0.899740\pi$
$373$	−4.00000	+	6.92820i	−0.207112	+	0.358729i	0.743691	+	0.668523i	$0.233073\pi$
$374$	9.55842	+	16.5557i	0.494254	+	0.856073i
$375$	−9.37228	+	8.80773i	−0.483983	+	0.454829i
$376$			0.939764i			0.0484646i
$377$	8.74456	−	2.52434i	0.450368	−	0.130010i
$378$	−13.7446	−	0.294954i	−0.706944	−	0.0151708i
$379$	−4.88316	+	2.81929i	−0.250831	+	0.144817i	−0.620145	−	0.784487i	$-0.712926\pi$
$379$	−4.88316	+	2.81929i	−0.250831	+	0.144817i	0.369314	+	0.929305i	$0.379593\pi$
$380$	1.62772	−	0.939764i	0.0835002	−	0.0482089i
$381$	1.05842	−	3.51039i	0.0542246	−	0.179843i
$382$		−	12.2718i		−	0.627882i
$383$	13.0693	+	7.54556i	0.667810	+	0.385560i	0.795246	−	0.606287i	$-0.207342\pi$
$383$	13.0693	+	7.54556i	0.667810	+	0.385560i	−0.127436	+	0.991847i	$0.540675\pi$
$384$	−0.500000	+	1.65831i	−0.0255155	+	0.0846254i
$385$	−6.00000	+	6.92820i	−0.305788	+	0.353094i
$386$	−11.6168	−	6.70699i	−0.591282	−	0.341377i
$387$	10.0000	+	6.63325i	0.508329	+	0.337187i
$388$	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	$0.733536\pi$
$390$	−4.25544	−	2.52434i	−0.215482	−	0.127825i
$391$			18.6101i			0.941155i
$392$	5.50000	−	4.33013i	0.277792	−	0.218704i
$393$	−25.6277	−	27.2704i	−1.29275	−	1.37561i
$394$	12.3030	−	21.3094i	0.619815	−	1.07355i
$395$		−	7.62792i		−	0.383802i
$396$	−0.813859	+	13.0916i	−0.0408980	+	0.657876i
$397$	−1.12772	+	1.95327i	−0.0565986	+	0.0980316i	−0.892936	−	0.450183i	$-0.851359\pi$
$397$	−1.12772	+	1.95327i	−0.0565986	+	0.0980316i	0.836338	+	0.548214i	$0.184692\pi$
$398$		−	3.46410i		−	0.173640i
$399$	−9.18614	+	5.81351i	−0.459882	+	0.291040i
$400$	−2.18614	−	3.78651i	−0.109307	−	0.189325i
$401$	−5.74456	−	9.94987i	−0.286870	−	0.496873i	0.686191	−	0.727421i	$-0.259281\pi$
$401$	−5.74456	−	9.94987i	−0.286870	−	0.496873i	−0.973061	+	0.230548i	$0.925948\pi$
$402$	4.62772	+	19.6974i	0.230810	+	0.982415i
$403$	23.6060	+	5.84096i	1.17590	+	0.290959i
$404$	14.7446			0.733569
$405$	−0.883156	+	7.07568i	−0.0438844	+	0.351593i
$406$	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	−0.468049	−	0.883703i	$-0.655043\pi$
$409$	10.7446	−	18.6101i	0.531284	−	0.920212i	0.999333	−	0.0365091i	$-0.0116238\pi$
$410$	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
$414$	−7.05842	+	10.6410i	−0.346903	+	0.522975i
$415$	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	$-0.209475\pi$
$419$	−2.74456	−	4.75372i	−0.134081	−	0.232235i	−0.925246	+	0.379368i	$0.876141\pi$
$420$	−1.94158	−	3.06796i	−0.0947393	−	0.149701i
$421$		−	26.8280i		−	1.30751i	−0.756704	−	0.653757i	$-0.773192\pi$
$421$		−	26.8280i		−	1.30751i	0.756704	−	0.653757i	$-0.226808\pi$
$422$	−5.62772	+	9.74749i	−0.273953	+	0.474501i
$423$	−2.81386	−	0.174928i	−0.136815	−	0.00850530i
$424$			2.22938i			0.108268i
$425$	9.55842	−	16.5557i	0.463652	−	0.803068i
$426$	19.1168	+	20.3422i	0.926214	+	0.985582i
$427$	−13.5000	−	2.59808i	−0.653311	−	0.125730i
$428$			0.939764i			0.0454252i
$429$	13.9307	−	23.4839i	0.672581	−	1.13381i
$430$			3.16915i			0.152830i
$431$	−12.6861	−	21.9730i	−0.611070	−	1.05840i	−0.991060	−	0.133414i	$-0.957406\pi$
$431$	−12.6861	−	21.9730i	−0.611070	−	1.05840i	0.379991	−	0.924990i	$-0.375927\pi$
$432$	−4.87228	−	1.80579i	−0.234418	−	0.0868811i
$433$	21.3505	+	12.3267i	1.02604	+	0.592385i	0.915848	−	0.401525i	$-0.131520\pi$
$433$	21.3505	+	12.3267i	1.02604	+	0.592385i	0.110193	+	0.993910i	$0.464853\pi$
$434$	13.4891	+	11.6819i	0.647499	+	0.560750i
$435$	1.00000	−	3.31662i	0.0479463	−	0.159020i
$436$	17.2337	+	9.94987i	0.825344	+	0.476513i
$437$			10.0974i			0.483022i
$438$	−5.37228	+	17.8178i	−0.256698	+	0.851369i
$439$	21.3505	−	12.3267i	1.01901	−	0.588323i	0.105190	−	0.994452i	$-0.466455\pi$
$439$	21.3505	−	12.3267i	1.01901	−	0.588323i	0.913816	+	0.406129i	$0.133122\pi$
$440$	−3.00000	+	1.73205i	−0.143019	+	0.0825723i
$441$	11.9416	+	17.2742i	0.568647	+	0.822582i
$442$	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	$0.940153\pi$
$444$	−14.7446	+	13.8564i	−0.699746	+	0.657596i
$445$	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	−0.159145	+	0.987255i	$0.550874\pi$
$449$	−19.8030	+	34.2998i	−0.934561	+	1.61871i	−0.775416	+	0.631451i	$0.782460\pi$
$450$	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
$453$	−21.3030	+	20.0198i	−1.00090	+	0.940611i
$454$		−	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	−0.269805	−	0.962915i	$-0.586959\pi$
$457$	9.17527	−	5.29734i	0.429201	−	0.247799i	0.699006	+	0.715116i	$0.253626\pi$
$458$	2.55842	+	4.43132i	0.119547	+	0.207062i
$459$	−3.81386	−	22.3966i	−0.178016	−	1.04539i
$460$	−3.37228			−0.157233
$461$	−27.4307	−	15.8371i	−1.27758	−	0.737608i	−0.301173	−	0.953569i	$-0.597378\pi$
$461$	−27.4307	−	15.8371i	−1.27758	−	0.737608i	−0.976402	+	0.215961i	$0.930712\pi$
$462$	16.9307	−	10.7147i	0.787688	−	0.498493i
$463$			10.8347i			0.503533i	0.967788	+	0.251766i	$0.0810115\pi$
$463$			10.8347i			0.503533i	−0.967788	+	0.251766i	$0.918989\pi$
$464$	2.18614	+	1.26217i	0.101489	+	0.0585947i
$465$	6.74456	−	6.33830i	0.312772	−	0.293931i
$466$	4.19702	−	2.42315i	0.194423	−	0.112250i
$467$	25.3723			1.17409			0.587045	−	0.809555i	$-0.300291\pi$
$467$	25.3723			1.17409			0.587045	+	0.809555i	$0.300291\pi$
$468$	7.31386	+	7.96916i	0.338083	+	0.368374i
$469$	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
$474$	−4.81386	+	15.9658i	−0.221108	+	0.733332i
$475$	5.18614	−	8.98266i	0.237956	−	0.412153i
$476$	8.74456	+	7.57301i	0.400806	+	0.347108i
$477$	−6.67527	−	0.414979i	−0.305639	−	0.0190006i
$478$	−7.80298	−	13.5152i	−0.356900	−	0.618169i
$479$	2.69702	−	1.55712i	0.123230	−	0.0711467i	−0.437118	−	0.899404i	$-0.644001\pi$
$479$	2.69702	−	1.55712i	0.123230	−	0.0711467i	0.560348	+	0.828257i	$0.310667\pi$
$480$	−0.313859	−	1.33591i	−0.0143257	−	0.0609755i
$481$	40.4674	−	11.6819i	1.84515	−	0.532650i
$482$	−12.7446			−0.580499
$483$	19.4891	−	0.792287i	0.886786	−	0.0360503i
$484$	−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	−0.244214	−	0.969721i	$-0.578530\pi$
$487$	−26.6168	−	15.3672i	−1.20612	−	0.696356i	−0.961910	+	0.273365i	$0.911863\pi$
$488$	−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	$-0.611604\pi$
$491$	6.60597	−	3.81396i	0.298123	−	0.172122i	0.641599	+	0.767040i	$0.278271\pi$
$492$	−11.9307	+	11.2120i	−0.537878	+	0.505478i
$493$			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
$498$	−2.62772	−	0.792287i	−0.117751	−	0.0355032i
$499$		−	16.4356i		−	0.735761i	−0.929873	−	0.367880i	$-0.880084\pi$
$499$		−	16.4356i		−	0.735761i	0.929873	−	0.367880i	$-0.119916\pi$
$500$	6.43070	+	3.71277i	0.287590	+	0.166040i
$501$	11.0000	+	3.31662i	0.491444	+	0.148176i
$502$	−16.1168			−0.719330
$503$	−11.4891	+	19.8997i	−0.512275	+	0.887286i	0.487624	+	0.873054i	$0.337864\pi$
$503$	−11.4891	+	19.8997i	−0.512275	+	0.887286i	−0.999899	+	0.0142322i	$0.995470\pi$
$504$	2.12772	+	7.64675i	0.0947761	+	0.340613i
$505$	−10.1168	+	5.84096i	−0.450194	+	0.259919i
$506$		−	18.6101i		−	0.827321i
$507$	−5.98913	−	21.7055i	−0.265986	−	0.963977i
$508$	−2.11684			−0.0939198
$509$	20.3139	−	11.7282i	0.900396	−	0.519844i	0.0230673	−	0.999734i	$-0.492657\pi$
$509$	20.3139	−	11.7282i	0.900396	−	0.519844i	0.877329	+	0.479890i	$0.159323\pi$
$510$	4.37228	−	4.10891i	0.193608	−	0.181946i
$511$	26.8614	−	9.30506i	1.18828	−	0.411632i
$512$	1.00000			0.0441942
$513$	−2.06930	−	12.1518i	−0.0913617	−	0.536515i
$514$	2.44158	−	4.22894i	0.107693	−	0.186530i
$515$	6.51087			0.286903
$516$	2.00000	−	6.63325i	0.0880451	−	0.292013i
$517$	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	$-0.507788\pi$
$521$	−1.11684			−0.0489298			−0.0244649	+	0.999701i	$0.507788\pi$
$522$	−4.18614	+	6.31084i	−0.183222	+	0.276218i
$523$	7.50000	−	4.33013i	0.327952	−	0.189343i	−0.326979	−	0.945031i	$-0.606031\pi$
$523$	7.50000	−	4.33013i	0.327952	−	0.189343i	0.654932	+	0.755688i	$0.272697\pi$
$524$	−10.8030	+	18.7113i	−0.471931	+	0.817408i
$525$	−17.7446	−	9.30506i	−0.774436	−	0.406106i
$526$	−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
$531$	10.1753	−	15.3398i	0.441569	−	0.665690i
$532$	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
$537$	−8.37228	−	2.52434i	−0.361291	−	0.108933i
$538$	0.861407			0.0371379
$539$	−28.4198	−	11.3595i	−1.22413	−	0.489289i
$540$	4.05842	−	0.691097i	0.174647	−	0.0297401i
$541$		−	1.28962i		−	0.0554451i	−0.999616	−	0.0277226i	$-0.991175\pi$
$541$		−	1.28962i		−	0.0554451i	0.999616	−	0.0277226i	$-0.00882549\pi$
$542$	2.00000	−	3.46410i	0.0859074	−	0.148796i
$543$	15.3030	−	14.3812i	0.656714	−	0.617156i
$544$	2.18614	+	3.78651i	0.0937300	+	0.162345i
$545$	−15.7663			−0.675355
$546$	3.31386	−	16.1870i	0.141820	−	0.692739i
$547$	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
$549$	8.61684	−	12.9904i	0.367758	−	0.554416i
$550$	−9.55842	+	16.5557i	−0.407572	+	0.705936i
$551$			5.98844i			0.255116i
$552$	7.05842	+	2.12819i	0.300426	+	0.0905820i
$553$	24.0693	−	8.33785i	1.02353	−	0.354561i
$554$	13.4891			0.573098
$555$	4.62772	−	15.3484i	0.196436	−	0.651504i
$556$	−7.67527	+	4.43132i	−0.325504	+	0.187930i
$557$	−12.3030	−	21.3094i	−0.521294	−	0.902908i	−0.999693	−	0.0247655i	$-0.992116\pi$
$557$	−12.3030	−	21.3094i	−0.521294	−	0.902908i	0.478399	−	0.878143i	$-0.341217\pi$
$558$	−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
$561$	22.6753	+	24.1287i	0.957350	+	1.01871i
$562$	−7.37228	−	12.7692i	−0.310981	−	0.538635i
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	0.184950	+	0.982748i	$0.440788\pi$
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	−0.943560	+	0.331202i	$0.892546\pi$
$564$	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
$567$	−23.2921	+	4.94749i	−0.978177	+	0.207775i
$568$	8.05842	−	13.9576i	0.338124	−	0.585648i
$569$	29.6644	−	17.1267i	1.24360	−	0.717990i	0.273772	−	0.961795i	$-0.411729\pi$
$569$	29.6644	−	17.1267i	1.24360	−	0.717990i	0.969824	+	0.243804i	$0.0783955\pi$
$570$	2.37228	−	2.22938i	0.0993639	−	0.0933786i
$571$	−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
$576$	−0.186141	+	2.99422i	−0.00775586	+	0.124759i
$577$	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
$579$	−22.2446	−	6.70699i	−0.924452	−	0.278733i
$580$	−2.00000			−0.0830455
$581$	1.37228	+	3.96143i	0.0569318	+	0.164348i
$582$	0.883156	+	0.939764i	0.0366080	+	0.0389545i
$583$	8.44158	−	4.87375i	0.349614	−	0.201850i
$584$	10.7446			0.444613
$585$	−8.17527	−	2.57062i	−0.338006	−	0.106282i
$586$			3.75906i			0.155285i
$587$	37.5475	−	21.6781i	1.54975	−	0.894750i	0.551593	−	0.834113i	$-0.314020\pi$
$587$	37.5475	−	21.6781i	1.54975	−	0.894750i	0.998160	−	0.0606372i	$-0.0193133\pi$
$588$	7.55842	−	9.47999i	0.311704	−	0.390948i
$589$	−8.00000	+	13.8564i	−0.329634	+	0.570943i
$590$	4.86141			0.200141
$591$	12.3030	−	40.8044i	0.506077	−	1.67847i
$592$	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	$0.979632\pi$
$594$	3.81386	+	22.3966i	0.156485	+	0.918945i
$595$	−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	$0.847446\pi$
$600$	−5.18614	−	5.51856i	−0.211723	−	0.225294i
$601$	−37.1168	+	21.4294i	−1.51403	+	0.874124i	−0.514163	+	0.857693i	$0.671897\pi$
$601$	−37.1168	+	21.4294i	−1.51403	+	0.874124i	−0.999865	+	0.0164316i	$0.994769\pi$
$602$	−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	−0.264466	−	0.964395i	$-0.585196\pi$
$607$	−30.3505	−	17.5229i	−1.23189	−	0.711232i	−0.967424	+	0.253163i	$0.918529\pi$
$608$	1.18614	+	2.05446i	0.0481044	+	0.0833192i
$609$	11.5584	−	0.469882i	0.468371	−	0.0190406i
$610$	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	−0.656975	−	0.753912i	$-0.728164\pi$
$613$	−8.23369	+	4.75372i	−0.332556	+	0.192001i	0.324420	+	0.945913i	$0.394831\pi$
$614$	10.6168	+	18.3889i	0.428461	+	0.742116i
$615$	3.74456	−	12.4193i	0.150995	−	0.500795i
$616$	−8.74456	−	7.57301i	−0.352328	−	0.305125i
$617$	−16.8030	+	29.1036i	−0.676463	+	1.17167i	0.299576	+	0.954072i	$0.403155\pi$
$617$	−16.8030	+	29.1036i	−0.676463	+	1.17167i	−0.976039	+	0.217595i	$0.930179\pi$
$618$	−13.6277	−	4.10891i	−0.548187	−	0.165285i
$619$	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
$621$	−7.68614	+	20.7383i	−0.308434	+	0.832200i
$622$	5.18614	+	8.98266i	0.207945	+	0.360172i
$623$	−18.6060	+	21.4843i	−0.745432	+	0.860751i
$624$	3.18614	−	5.37108i	0.127548	−	0.215015i
$625$	15.9783			0.639130
$626$	−12.0000	+	6.92820i	−0.479616	+	0.276907i
$627$	12.3030	+	13.0916i	0.491334	+	0.522827i
$628$		0			0
$629$			51.0767i			2.03656i
$630$	−4.48913	−	4.40387i	−0.178851	−	0.175454i
$631$	−28.5000	−	16.4545i	−1.13457	−	0.655043i	−0.189488	−	0.981883i	$-0.560683\pi$
$631$	−28.5000	−	16.4545i	−1.13457	−	0.655043i	−0.945080	+	0.326841i	$0.894016\pi$
$632$	9.62772			0.382970
$633$	−5.62772	+	18.6650i	−0.223682	+	0.741868i
$634$	−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
$639$	40.2921	+	26.7268i	1.59393	+	1.05729i
$640$	−0.686141	+	0.396143i	−0.0271221	+	0.0156589i
$641$	−23.6644	−	13.6626i	−0.934687	−	0.539642i	−0.0463963	−	0.998923i	$-0.514774\pi$
$641$	−23.6644	−	13.6626i	−0.934687	−	0.539642i	−0.888291	+	0.459281i	$0.848107\pi$
$642$	0.372281	+	1.58457i	0.0146928	+	0.0625381i
$643$	1.61684	−	2.80046i	0.0637621	−	0.110439i	−0.832382	−	0.554202i	$-0.813023\pi$
$643$	1.61684	−	2.80046i	0.0637621	−	0.110439i	0.896144	+	0.443763i	$0.146357\pi$
$644$	−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	−0.929857	−	0.367920i	$-0.880070\pi$
$647$	−19.9307	−	34.5210i	−0.783557	−	1.35716i	0.146301	−	0.989240i	$-0.453263\pi$
$648$	−8.93070	−	1.11469i	−0.350831	−	0.0437892i
$649$			26.8280i			1.05309i
$650$	4.37228	+	15.1460i	0.171495	+	0.594076i
$651$	27.3723	+	14.3537i	1.07280	+	0.562567i
$652$	9.00000	−	5.19615i	0.352467	−	0.203497i
$653$	9.04755	−	5.22360i	0.354058	−	0.204415i	−0.312413	−	0.949946i	$-0.601137\pi$
$653$	9.04755	−	5.22360i	0.354058	−	0.204415i	0.666471	+	0.745531i	$0.267804\pi$
$654$	33.0000	+	9.94987i	1.29040	+	0.389071i
$655$		−	17.1181i		−	0.668861i
$656$	8.18614	+	4.72627i	0.319615	+	0.184530i
$657$	−2.00000	+	32.1716i	−0.0780274	+	1.25513i
$658$	1.62772	−	1.87953i	0.0634551	−	0.0732716i
$659$	−37.1644	−	21.4569i	−1.44772	−	0.835841i	−0.449374	−	0.893344i	$-0.648353\pi$
$659$	−37.1644	−	21.4569i	−1.44772	−	0.835841i	−0.998345	+	0.0575028i	$0.981686\pi$
$660$	−4.37228	+	4.10891i	−0.170191	+	0.159939i
$661$	10.5693	+	18.3066i	0.411098	+	0.712043i	0.995010	−	0.0997743i	$-0.0318121\pi$
$661$	10.5693	+	18.3066i	0.411098	+	0.712043i	−0.583912	+	0.811817i	$0.698479\pi$
$662$			2.17448i			0.0845136i
$663$	27.3030	+	0.322405i	1.06036	+	0.0125212i
$664$			1.58457i			0.0614934i
$665$	−4.88316	−	0.939764i	−0.189361	−	0.0364425i
$666$	−19.3723	+	29.2048i	−0.750661	+	1.13166i
$667$	5.37228	−	9.30506i	0.208016	−	0.360294i
$668$		−	6.63325i		−	0.256648i
$669$	−14.1168	+	46.8203i	−0.545789	+	1.81018i
$670$	−4.62772	+	8.01544i	−0.178784	+	0.309664i
$671$			22.7190i			0.877059i
$672$	3.87228	−	2.45060i	0.149376	−	0.0945339i
$673$	4.18614	+	7.25061i	0.161364	+	0.279490i	0.935358	−	0.353702i	$-0.115077\pi$
$673$	4.18614	+	7.25061i	0.161364	+	0.279490i	−0.773994	+	0.633193i	$0.781744\pi$
$674$	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	$-0.508395\pi$
$677$	−1.37228			−0.0527411			−0.0263705	+	0.999652i	$0.508395\pi$
$678$	4.74456	−	4.45877i	0.182214	−	0.171238i
$679$	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	$-0.748772\pi$
$683$	6.86141	−	11.8843i	0.262544	−	0.454740i	0.966917	+	0.255090i	$0.0821050\pi$
$684$	−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
$687$	6.06930	+	6.45832i	0.231558	+	0.246400i
$688$	−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	0.579320	−	0.815100i	$-0.303318\pi$
$691$	−10.9416	−	18.9514i	−0.416237	−	0.720944i	−0.995557	+	0.0941560i	$0.969985\pi$
$692$	0.941578	+	1.63086i	0.0357934	+	0.0619960i
$693$	24.3030	−	24.7735i	0.923194	−	0.941067i
$694$			20.8395i			0.791057i
$695$	3.51087	−	6.08101i	0.133175	−	0.230666i
$696$	4.18614	+	1.26217i	0.158675	+	0.0478424i
$697$			41.3292i			1.56545i
$698$	10.0584	−	17.4217i	0.380717	−	0.659421i
$699$	6.11684	−	5.74839i	0.231360	−	0.217424i
$700$	−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	$-0.327705\pi$
$702$	15.4891	+	10.5398i	0.584599	+	0.397798i
$703$			27.7128i			1.04521i
$704$	−2.18614	−	3.78651i	−0.0823933	−	0.142709i
$705$	−0.883156	−	0.939764i	−0.0332616	−	0.0353936i
$706$	−25.3723	−	14.6487i	−0.954898	−	0.551311i
$707$	−29.4891	−	25.5383i	−1.10905	−	0.960468i
$708$	−10.1753	−	3.06796i	−0.382410	−	0.115301i
$709$	−22.8832	−	13.2116i	−0.859395	−	0.496172i	0.00441467	−	0.999990i	$-0.498595\pi$
$709$	−22.8832	−	13.2116i	−0.859395	−	0.496172i	−0.863810	+	0.503818i	$0.831928\pi$
$710$			12.7692i			0.479218i
$711$	−1.79211	+	28.8275i	−0.0672094	+	1.08112i
$712$	−9.30298	+	5.37108i	−0.348644	+	0.201290i
$713$	24.8614	−	14.3537i	0.931067	−	0.537552i
$714$	17.7446	+	9.30506i	0.664074	+	0.348233i
$715$	12.0000	−	3.46410i	0.448775	−	0.129550i
$716$			5.04868i			0.188678i
$717$	−18.5109	−	19.6974i	−0.691301	−	0.735612i
$718$	8.31386	+	14.4000i	0.310270	+	0.537404i
$719$	−12.5584	+	21.7518i	−0.468350	+	0.811206i	−0.999346	−	0.0361684i	$-0.988485\pi$
$719$	−12.5584	+	21.7518i	−0.468350	+	0.811206i	0.530996	+	0.847375i	$0.321818\pi$
$720$	−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
$726$	−9.62772	−	10.2448i	−0.357318	−	0.380221i
$727$		−	28.1176i		−	1.04282i	−0.853305	−	0.521412i	$-0.825406\pi$
$727$		−	28.1176i		−	1.04282i	0.853305	−	0.521412i	$-0.174594\pi$
$728$	−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
$732$	−8.61684	−	2.59808i	−0.318488	−	0.0960277i
$733$	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
$735$	−1.43070	+	9.49883i	−0.0527723	+	0.350370i
$736$		−	4.25639i		−	0.156893i
$737$	−44.2337	−	25.5383i	−1.62937	−	0.940717i
$738$	−15.6753	+	23.6314i	−0.577015	+	0.869882i
$739$	−34.1168	+	19.6974i	−1.25501	+	0.724579i	−0.972100	−	0.234567i	$-0.924633\pi$
$739$	−34.1168	+	19.6974i	−1.25501	+	0.724579i	−0.282909	+	0.959147i	$0.591299\pi$
$740$	−9.25544			−0.340237
$741$	14.8139	+	0.174928i	0.544201	+	0.00642615i
$742$	3.86141	−	4.45877i	0.141757	−	0.163687i
$743$	−1.62772	−	2.81929i	−0.0597152	−	0.103430i	0.834622	−	0.550823i	$-0.185686\pi$
$743$	−1.62772	−	2.81929i	−0.0597152	−	0.103430i	−0.894338	+	0.447393i	$0.852353\pi$
$744$	8.00000	+	8.51278i	0.293294	+	0.312094i
$745$	−4.11684	−	2.37686i	−0.150829	−	0.0870814i
$746$	8.00000			0.292901
$747$	−4.74456	−	0.294954i	−0.173594	−	0.0107918i
$748$	9.55842	−	16.5557i	0.349491	−	0.605335i
$749$	1.62772	−	1.87953i	0.0594755	−	0.0686764i
$750$	12.3139	+	3.71277i	0.449639	+	0.135571i
$751$	0.500000	+	0.866025i	0.0182453	+	0.0316017i	0.875004	−	0.484116i	$-0.160859\pi$
$751$	0.500000	+	0.866025i	0.0182453	+	0.0316017i	−0.856759	+	0.515718i	$0.827525\pi$
$752$	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
$756$	6.61684	+	12.0506i	0.240652	+	0.438277i
$757$	8.86141	+	15.3484i	0.322073	+	0.557847i	0.980916	−	0.194434i	$-0.0622869\pi$
$757$	8.86141	+	15.3484i	0.322073	+	0.557847i	−0.658842	+	0.752281i	$0.728954\pi$
$758$	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	$-0.355037\pi$
$761$	−3.25544	−	1.87953i	−0.118010	−	0.0681328i	−0.557843	+	0.829947i	$0.688371\pi$
$762$	−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
$765$	5.74456	−	8.66025i	0.207695	−	0.313112i
$766$		−	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	0.997452	−	0.0713391i	$-0.0227273\pi$
$769$	12.1168	+	20.9870i	0.436945	+	0.756810i	−0.560508	+	0.828149i	$0.689394\pi$
$770$	9.00000	+	1.73205i	0.324337	+	0.0624188i
$771$	2.44158	−	8.09780i	0.0879313	−	0.291635i
$772$			13.4140i			0.482780i
$773$	18.0951	+	10.4472i	0.650835	+	0.375760i	0.788776	−	0.614681i	$-0.210715\pi$
$773$	18.0951	+	10.4472i	0.650835	+	0.375760i	−0.137941	+	0.990440i	$0.544048\pi$
$774$	0.744563	−	11.9769i	0.0267628	−	0.430500i
$775$	−29.4891			−1.05928
$776$	0.372281	−	0.644810i	0.0133641	−	0.0231473i
$777$	53.4891	−	2.17448i	1.91891	−	0.0780091i
$778$	25.3723	−	14.6487i	0.909640	−	0.525181i
$779$			22.4241i			0.803426i
$780$	−0.0584220	+	4.94749i	−0.00209184	+	0.177148i
$781$	−70.4674			−2.52152
$782$	16.1168	−	9.30506i	0.576337	−	0.332748i
$783$	−4.55842	+	12.2993i	−0.162905	+	0.439541i
$784$	−6.50000	−	2.59808i	−0.232143	−	0.0927884i
$785$		0			0
$786$	−10.8030	+	35.8294i	−0.385330	+	1.27799i
$787$	−21.3614	+	36.9990i	−0.761452	+	1.31887i	0.180650	+	0.983547i	$0.442180\pi$
$787$	−21.3614	+	36.9990i	−0.761452	+	1.31887i	−0.942102	+	0.335326i	$0.891154\pi$
$788$	−24.6060			−0.876551
$789$	−37.4307	−	11.2858i	−1.33257	−	0.401784i
$790$	−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
$795$	−2.09509	−	2.22938i	−0.0743053	−	0.0790681i
$796$	−3.00000	+	1.73205i	−0.106332	+	0.0613909i
$797$	−11.5693	+	20.0386i	−0.409806	+	0.709804i	−0.994868	−	0.101184i	$-0.967737\pi$
$797$	−11.5693	+	20.0386i	−0.409806	+	0.709804i	0.585062	+	0.810988i	$0.301070\pi$
$798$	9.62772	+	5.04868i	0.340818	+	0.178721i
$799$	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
$804$	14.7446	−	13.8564i	0.520001	−	0.488678i
$805$	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	$-0.524667\pi$
$809$	21.2554	−	12.2718i	0.747301	−	0.431455i	0.824718	+	0.565544i	$0.191334\pi$
$810$	6.56930	−	2.77300i	0.230822	−	0.0974334i
$811$	−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
$813$	2.00000	−	6.63325i	0.0701431	−	0.232638i
$814$		−	51.0767i		−	1.79024i
$815$	−4.11684	+	7.13058i	−0.144207	+	0.249773i
$816$	5.18614	+	5.51856i	0.181551	+	0.193188i
$817$	−4.74456	−	8.21782i	−0.165991	−	0.287505i
$818$	−21.4891			−0.751350
$819$	−0.824734	−	28.6063i	−0.0288185	−	0.999585i
$820$	−7.48913			−0.261532
$821$	10.4198	+	18.0477i	0.363655	+	0.629868i	0.988559	−	0.150833i	$-0.0481955\pi$
$821$	10.4198	+	18.0477i	0.363655	+	0.629868i	−0.624905	+	0.780701i	$0.714862\pi$
$822$	−8.74456	−	9.30506i	−0.305002	−	0.324551i
$823$	−17.2921	+	29.9508i	−0.602765	+	1.04402i	0.389635	+	0.920969i	$0.372601\pi$
$823$	−17.2921	+	29.9508i	−0.602765	+	1.04402i	−0.992400	+	0.123050i	$0.960732\pi$
$824$			8.21782i			0.286281i
$825$	−9.55842	+	31.7017i	−0.332782	+	1.10371i
$826$	5.31386	+	15.3398i	0.184893	+	0.533740i
$827$	−8.23369			−0.286313			−0.143157	−	0.989700i	$-0.545725\pi$
$827$	−8.23369			−0.286313			−0.143157	+	0.989700i	$0.545725\pi$
$828$	12.7446	+	0.792287i	0.442904	+	0.0275339i
$829$	−13.5000	+	7.79423i	−0.468874	+	0.270705i	−0.715768	−	0.698338i	$-0.753923\pi$
$829$	−13.5000	+	7.79423i	−0.468874	+	0.270705i	0.246894	+	0.969042i	$0.420590\pi$
$830$	−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
$834$	−11.1861	+	10.5123i	−0.387344	+	0.364012i
$835$	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	$-0.656271\pi$
$839$	−42.6060	−	24.5986i	−1.47092	−	0.849237i	−0.999467	+	0.0326534i	$0.989604\pi$
$840$	−1.68614	+	3.21543i	−0.0581774	+	0.110943i
$841$	−11.3139	+	19.5962i	−0.390133	+	0.675730i
$842$	−23.2337	+	13.4140i	−0.800686	+	0.462276i
$843$	−17.4891	−	18.6101i	−0.602357	−	0.640967i
$844$	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
$849$	−3.94158	−	1.18843i	−0.135275	−	0.0407868i
$850$	−19.1168			−0.655702
$851$	24.8614	−	43.0612i	0.852238	−	1.47612i
$852$	8.05842	−	26.7268i	0.276077	−	0.915644i
$853$	−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
$855$	3.11684	−	4.69882i	0.106594	−	0.160696i
$856$	0.813859	−	0.469882i	0.0278171	−	0.0160602i
$857$	19.7228			0.673718			0.336859	−	0.941555i	$-0.390635\pi$
$857$	19.7228			0.673718			0.336859	+	0.941555i	$0.390635\pi$
$858$	−27.3030	−	0.322405i	−0.932109	−	0.0110067i
$859$			6.28339i			0.214387i	0.994238	+	0.107193i	$0.0341864\pi$
$859$			6.28339i			0.214387i	−0.994238	+	0.107193i	$0.965814\pi$
$860$	2.74456	−	1.58457i	0.0935888	−	0.0540335i
$861$	43.2812	−	1.75950i	1.47502	−	0.0599637i
$862$	−12.6861	+	21.9730i	−0.432092	+	0.748405i
$863$	43.3723			1.47641			0.738205	−	0.674577i	$-0.235674\pi$
$863$	43.3723			1.47641			0.738205	+	0.674577i	$0.235674\pi$
$864$	0.872281	+	5.12241i	0.0296756	+	0.174268i
$865$	−1.29211	−	0.746000i	−0.0439331	−	0.0253648i
$866$		−	24.6535i		−	0.837759i
$867$	−1.05842	+	3.51039i	−0.0359459	+	0.119219i
$868$	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
$873$	1.86141	+	1.23472i	0.0629991	+	0.0417889i
$874$	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	0.731400	−	0.681949i	$-0.238867\pi$
$877$	15.0000	+	8.66025i	0.506514	+	0.292436i	−0.224886	+	0.974385i	$0.572201\pi$
$878$	−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	−0.919632	−	0.392781i	$-0.871513\pi$
$881$	−23.7446	−	41.1268i	−0.799975	−	1.38560i	0.119657	−	0.992815i	$-0.461820\pi$
$882$	8.98913	−	18.9788i	0.302680	−	0.639050i
$883$	−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	$-0.0281106\pi$
$887$	12.5584	+	21.7518i	0.421671	+	0.730355i	−0.574432	+	0.818552i	$0.694777\pi$
$888$	19.3723	+	5.84096i	0.650091	+	0.196010i
$889$	4.23369	+	3.66648i	0.141993	+	0.122970i
$890$	4.25544	−	7.37063i	0.142643	−	0.247064i
$891$	15.3030	+	36.2530i	0.512669	+	1.21452i
$892$	28.2337			0.945334
$893$	1.93070	+	1.11469i	0.0646085	+	0.0373017i
$894$	7.11684	+	7.57301i	0.238023	+	0.253279i
$895$	−2.00000	−	3.46410i	−0.0668526	−	0.115792i
$896$	−2.00000	−	1.73205i	−0.0668153	−	0.0578638i
$897$	−22.8614	−	13.5615i	−0.763320	−	0.452804i
$898$	39.6060			1.32167
$899$	14.7446	−	8.51278i	0.491759	−	0.283917i
$900$	−10.9307	−	7.25061i	−0.364357	−	0.241687i
$901$	8.44158	+	4.87375i	0.281230	+	0.162368i
$902$		−	41.3292i		−	1.37611i
$903$	−15.4891	+	9.80240i	−0.515446	+	0.326203i
$904$	−3.25544	−	1.87953i	−0.108274	−	0.0625122i
$905$	9.60597			0.319313
$906$	27.9891	+	8.43904i	0.929876	+	0.280368i
$907$	10.4891	+	18.1677i	0.348286	+	0.603249i	0.985945	−	0.167070i	$-0.0534306\pi$
$907$	10.4891	+	18.1677i	0.348286	+	0.603249i	−0.637659	+	0.770318i	$0.720097\pi$
$908$	−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	$-0.0593195\pi$
$912$	2.81386	+	2.99422i	0.0931762	+	0.0991485i
$913$	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	−0.409897	−	0.912132i	$-0.634436\pi$
$919$	17.7337	−	30.7156i	0.584980	−	1.01322i	0.994878	−	0.101084i	$-0.0322311\pi$
$920$	1.68614	+	2.92048i	0.0555904	+	0.0962854i
$921$	25.1861	+	26.8005i	0.829912	+	0.883107i
$922$			31.6742i			1.04314i
$923$	−40.2921	+	41.8728i	−1.32623	+	1.37826i
$924$	−17.7446	−	9.30506i	−0.583753	−	0.306114i
$925$	−44.2337	+	25.5383i	−1.45439	+	0.839695i
$926$	9.38316	−	5.41737i	0.308350	−	0.178026i
$927$	−24.6060	−	1.52967i	−0.808166	−	0.0502410i
$928$		−	2.52434i		−	0.0828654i
$929$	34.4198	+	19.8723i	1.12928	+	0.651989i	0.943753	−	0.330651i	$-0.107268\pi$
$929$	34.4198	+	19.8723i	1.12928	+	0.651989i	0.185525	+	0.982640i	$0.440602\pi$
$930$	−8.86141	−	2.67181i	−0.290577	−	0.0876123i
$931$	−2.37228	−	16.4356i	−0.0777484	−	0.538657i
$932$	−4.19702	−	2.42315i	−0.137478	−	0.0793729i
$933$	12.3030	+	13.0916i	0.402782	+	0.428599i
$934$	−12.6861	−	21.9730i	−0.415103	−	0.718980i
$935$			15.1460i			0.495328i
$936$	3.24456	−	10.3186i	0.106052	−	0.337273i
$937$		−	35.9306i		−	1.17380i	−0.809658	−	0.586901i	$-0.800348\pi$
$937$		−	35.9306i		−	1.17380i	0.809658	−	0.586901i	$-0.199652\pi$
$938$	−30.3505	−	5.84096i	−0.990980	−	0.190714i
$939$	−17.4891	+	16.4356i	−0.570736	+	0.536357i
$940$	−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
$945$	−9.31386	−	5.64720i	−0.302980	−	0.183703i
$946$	8.74456	+	15.1460i	0.284310	+	0.492440i
$947$	16.9307	+	29.3248i	0.550174	+	0.952929i	0.998262	+	0.0589396i	$0.0187719\pi$
$947$	16.9307	+	29.3248i	0.550174	+	0.952929i	−0.448088	+	0.893990i	$0.647895\pi$
$948$	16.2337	−	3.81396i	0.527246	−	0.123872i
$949$	−37.6060	−	9.30506i	−1.22074	−	0.302055i
$950$	−10.3723			−0.336521
$951$	−18.0951	−	19.2549i	−0.586774	−	0.624384i
$952$	2.18614	−	11.3595i	0.0708532	−	0.368164i
$953$	32.9198	+	19.0063i	1.06638	+	0.615674i	0.927190	−	0.374592i	$-0.122217\pi$
$953$	32.9198	+	19.0063i	1.06638	+	0.615674i	0.139188	+	0.990266i	$0.455551\pi$
$954$	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
$960$	−1.00000	+	0.939764i	−0.0322749	+	0.0303307i
$961$	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
$966$	−10.4307	−	16.4819i	−0.335602	−	0.530298i
$967$			40.6844i			1.30832i	0.756356	+	0.654160i	$0.226978\pi$
$967$			40.6844i			1.30832i	−0.756356	+	0.654160i	$0.773022\pi$
$968$	−4.05842	+	7.02939i	−0.130443	+	0.225933i
$969$	−5.18614	+	17.2005i	−0.166603	+	0.552559i
$970$			0.589907i			0.0189408i
$971$	−6.94158	+	12.0232i	−0.222766	+	0.385842i	−0.955647	−	0.294515i	$-0.904842\pi$
$971$	−6.94158	+	12.0232i	−0.222766	+	0.385842i	0.732881	+	0.680357i	$0.238175\pi$
$972$	−15.5000	+	1.65831i	−0.497163	+	0.0531904i
$973$	23.0258	+	4.43132i	0.738173	+	0.142061i
$974$			30.7345i			0.984796i
$975$	13.3723	+	23.8063i	0.428256	+	0.762411i
$976$			5.19615i			0.166325i
$977$	−9.43070	−	16.3345i	−0.301715	−	0.522586i	0.674810	−	0.737992i	$-0.264226\pi$
$977$	−9.43070	−	16.3345i	−0.301715	−	0.522586i	−0.976525	+	0.215406i	$0.930892\pi$
$978$	13.1168	−	12.3267i	0.419430	−	0.394166i
$979$	40.6753	+	23.4839i	1.29999	+	0.750548i
$980$	5.48913	−	0.792287i	0.175344	−	0.0253087i
$981$	59.5842	+	3.70415i	1.90238	+	0.118264i
$982$	−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	$0.793281\pi$
$984$	15.6753	+	4.72627i	0.499709	+	0.150668i
$985$	16.8832	−	9.74749i	0.537942	−	0.310581i
$986$	9.55842	−	5.51856i	0.304402	−	0.175747i
$987$	2.00000	−	3.81396i	0.0636607	−	0.121400i
$988$	−2.37228	−	8.21782i	−0.0754723	−	0.261444i
$989$			17.0256i			0.541381i
$990$	−5.74456	+	8.66025i	−0.182574	+	0.275241i
$991$	10.6168	+	18.3889i	0.337255	+	0.584143i	0.983915	−	0.178635i	$-0.0571682\pi$
$991$	10.6168	+	18.3889i	0.337255	+	0.584143i	−0.646660	+	0.762778i	$0.723835\pi$
$992$	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	0.972759	−	0.231818i	$-0.0744674\pi$
$997$	39.7337	+	22.9403i	1.25838	+	0.726525i	0.285619	+	0.958343i	$0.407801\pi$
$998$	−14.2337	+	8.21782i	−0.450560	+	0.260131i
$999$	−21.0951	+	56.9176i	−0.667419	+	1.80079i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.q.e.251.2	✓	4	39.17	odd	6
546.2.q.e.335.2	yes	4	7.6	odd	2
546.2.q.f.251.1	yes	4	273.251	even	6	inner
546.2.q.f.335.1	yes	4	1.1	even	1	trivial
546.2.q.g.251.2	yes	4	13.4	even	6
546.2.q.g.335.1	yes	4	21.20	even	2
546.2.q.h.251.1	yes	4	91.69	odd	6
546.2.q.h.335.2	yes	4	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.18614 - 1.26217i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.792287i q^{5} +(-0.500000 + 1.65831i) q^{6} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.186141 + 2.99422i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.18614 - 1.26217i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.792287i q^{5} +(-0.500000 + 1.65831i) q^{6} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.186141 + 2.99422i) 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} +(-1.00000 + 0.939764i) 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} +(-4.05842 - 2.12819i) q^{21} +(-2.18614 + 3.78651i) q^{22} +(-3.68614 + 2.12819i) q^{23} +(-1.18614 - 1.26217i) 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} +(1.31386 + 0.396143i) q^{30} -6.74456 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.18614 + 7.25061i) q^{33} -4.37228 q^{34} +(-0.686141 - 1.98072i) q^{35} +(-2.50000 - 1.65831i) q^{36} +(-10.1168 + 5.84096i) q^{37} -2.37228 q^{38} +(3.05842 + 5.44482i) q^{39} -0.792287i q^{40} +(-8.18614 + 4.72627i) q^{41} +(0.186141 + 4.57879i) q^{42} +(2.00000 - 3.46410i) q^{43} +4.37228 q^{44} +(2.37228 + 0.147477i) q^{45} +(3.68614 + 2.12819i) q^{46} +0.939764i q^{47} +(-0.500000 + 1.65831i) 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} +(-4.87228 - 1.80579i) 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} +(2.12772 + 7.64675i) 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} +(7.05842 + 2.12819i) q^{69} +(-1.37228 + 1.58457i) q^{70} +(8.05842 - 13.9576i) q^{71} +(-0.186141 + 2.99422i) q^{72} +10.7446 q^{73} +(10.1168 + 5.84096i) q^{74} +(-5.18614 - 5.51856i) q^{75} +(1.18614 + 2.05446i) q^{76} +(-8.74456 - 7.57301i) q^{77} +(3.18614 - 5.37108i) q^{78} +9.62772 q^{79} +(-0.686141 + 0.396143i) q^{80} +(-8.93070 - 1.11469i) q^{81} +(8.18614 + 4.72627i) q^{82} +1.58457i q^{83} +(3.87228 - 2.45060i) q^{84} +(-3.00000 - 1.73205i) q^{85} -4.00000 q^{86} +(4.18614 + 1.26217i) 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} +(8.00000 + 8.51278i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + q^{3} - 2 q^{4} - 2 q^{6} + 10 q^{7} + 4 q^{8} + 5 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + q^3 - 2 * q^4 - 2 * q^6 + 10 * q^7 + 4 * q^8 + 5 * q^9	\( 4 q - 2 q^{2} + q^{3} - 2 q^{4} - 2 q^{6} + 10 q^{7} + 4 q^{8} + 5 q^{9} + 3 q^{10} - 3 q^{11} + q^{12} - 14 q^{13} - 8 q^{14} - 4 q^{15} - 2 q^{16} + 3 q^{17} + 5 q^{18} - q^{19} - 3 q^{20} + q^{21} - 3 q^{22} - 9 q^{23} + q^{24} + 6 q^{25} + 4 q^{26} + 16 q^{27} - 2 q^{28} - 3 q^{29} + 11 q^{30} - 4 q^{31} - 2 q^{32} - 3 q^{33} - 6 q^{34} + 3 q^{35} - 10 q^{36} - 6 q^{37} + 2 q^{38} - 5 q^{39} - 27 q^{41} - 5 q^{42} + 8 q^{43} + 6 q^{44} - 2 q^{45} + 9 q^{46} - 2 q^{48} + 22 q^{49} - 3 q^{50} - 18 q^{51} + 10 q^{52} - 8 q^{54} - 12 q^{55} + 10 q^{56} - 16 q^{57} + 3 q^{58} - 27 q^{59} - 7 q^{60} - 18 q^{61} + 2 q^{62} + 20 q^{63} + 4 q^{64} + 3 q^{65} + 18 q^{66} + 6 q^{67} + 3 q^{68} + 11 q^{69} + 6 q^{70} + 15 q^{71} + 5 q^{72} + 20 q^{73} + 6 q^{74} - 15 q^{75} - q^{76} - 12 q^{77} + 7 q^{78} + 50 q^{79} + 3 q^{80} - 7 q^{81} + 27 q^{82} + 4 q^{84} - 12 q^{85} - 16 q^{86} + 11 q^{87} - 3 q^{88} + 3 q^{89} + 13 q^{90} - 38 q^{91} + 32 q^{93} + 9 q^{94} - 18 q^{95} + q^{96} - 10 q^{97} - 26 q^{98} + 24 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + q^3 - 2 * q^4 - 2 * q^6 + 10 * q^7 + 4 * q^8 + 5 * q^9 + 3 * q^10 - 3 * q^11 + q^12 - 14 * q^13 - 8 * q^14 - 4 * q^15 - 2 * q^16 + 3 * q^17 + 5 * q^18 - q^19 - 3 * q^20 + q^21 - 3 * q^22 - 9 * q^23 + q^24 + 6 * q^25 + 4 * q^26 + 16 * q^27 - 2 * q^28 - 3 * q^29 + 11 * q^30 - 4 * q^31 - 2 * q^32 - 3 * q^33 - 6 * q^34 + 3 * q^35 - 10 * q^36 - 6 * q^37 + 2 * q^38 - 5 * q^39 - 27 * q^41 - 5 * q^42 + 8 * q^43 + 6 * q^44 - 2 * q^45 + 9 * q^46 - 2 * 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 + 20 * q^63 + 4 * q^64 + 3 * q^65 + 18 * q^66 + 6 * q^67 + 3 * q^68 + 11 * q^69 + 6 * q^70 + 15 * q^71 + 5 * q^72 + 20 * q^73 + 6 * q^74 - 15 * q^75 - q^76 - 12 * q^77 + 7 * q^78 + 50 * q^79 + 3 * q^80 - 7 * q^81 + 27 * q^82 + 4 * q^84 - 12 * q^85 - 16 * q^86 + 11 * q^87 - 3 * q^88 + 3 * q^89 + 13 * q^90 - 38 * q^91 + 32 * q^93 + 9 * q^94 - 18 * q^95 + q^96 - 10 * q^97 - 26 * q^98 + 24 * q^99

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