LMFDB - Embedded newform 126.2.e.a.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(25,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 4]))

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

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

chi := DirichletCharacter("126.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.e (of order $3$, 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:	$1.00611506547$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	126.25
Dual form			126.2.e.a.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.73205i q^{3} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} -1.73205i q^{6} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.73205i q^{3} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} -1.73205i q^{6} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} -3.00000 q^{9} +(1.50000 - 2.59808i) q^{10} +(1.50000 + 2.59808i) q^{11} +1.73205i q^{12} +(0.500000 + 0.866025i) q^{13} +(2.00000 + 1.73205i) q^{14} +(-4.50000 - 2.59808i) q^{15} +1.00000 q^{16} +(-1.50000 + 2.59808i) q^{17} +3.00000 q^{18} +(3.50000 + 6.06218i) q^{19} +(-1.50000 + 2.59808i) q^{20} +(3.00000 - 3.46410i) q^{21} +(-1.50000 - 2.59808i) q^{22} +(4.50000 - 7.79423i) q^{23} -1.73205i q^{24} +(-2.00000 - 3.46410i) q^{25} +(-0.500000 - 0.866025i) q^{26} -5.19615i q^{27} +(-2.00000 - 1.73205i) q^{28} +(-1.50000 + 2.59808i) q^{29} +(4.50000 + 2.59808i) q^{30} +8.00000 q^{31} -1.00000 q^{32} +(-4.50000 + 2.59808i) q^{33} +(1.50000 - 2.59808i) q^{34} +(7.50000 - 2.59808i) q^{35} -3.00000 q^{36} +(0.500000 + 0.866025i) q^{37} +(-3.50000 - 6.06218i) q^{38} +(-1.50000 + 0.866025i) q^{39} +(1.50000 - 2.59808i) q^{40} +(-1.50000 - 2.59808i) q^{41} +(-3.00000 + 3.46410i) q^{42} +(0.500000 - 0.866025i) q^{43} +(1.50000 + 2.59808i) q^{44} +(4.50000 - 7.79423i) q^{45} +(-4.50000 + 7.79423i) q^{46} +1.73205i q^{48} +(1.00000 + 6.92820i) q^{49} +(2.00000 + 3.46410i) q^{50} +(-4.50000 - 2.59808i) q^{51} +(0.500000 + 0.866025i) q^{52} +(-1.50000 + 2.59808i) q^{53} +5.19615i q^{54} -9.00000 q^{55} +(2.00000 + 1.73205i) q^{56} +(-10.5000 + 6.06218i) q^{57} +(1.50000 - 2.59808i) q^{58} +(-4.50000 - 2.59808i) q^{60} +2.00000 q^{61} -8.00000 q^{62} +(6.00000 + 5.19615i) q^{63} +1.00000 q^{64} -3.00000 q^{65} +(4.50000 - 2.59808i) q^{66} -4.00000 q^{67} +(-1.50000 + 2.59808i) q^{68} +(13.5000 + 7.79423i) q^{69} +(-7.50000 + 2.59808i) q^{70} +12.0000 q^{71} +3.00000 q^{72} +(-5.50000 + 9.52628i) q^{73} +(-0.500000 - 0.866025i) q^{74} +(6.00000 - 3.46410i) q^{75} +(3.50000 + 6.06218i) q^{76} +(1.50000 - 7.79423i) q^{77} +(1.50000 - 0.866025i) q^{78} -16.0000 q^{79} +(-1.50000 + 2.59808i) q^{80} +9.00000 q^{81} +(1.50000 + 2.59808i) q^{82} +(4.50000 - 7.79423i) q^{83} +(3.00000 - 3.46410i) q^{84} +(-4.50000 - 7.79423i) q^{85} +(-0.500000 + 0.866025i) q^{86} +(-4.50000 - 2.59808i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(-1.50000 - 2.59808i) q^{89} +(-4.50000 + 7.79423i) q^{90} +(0.500000 - 2.59808i) q^{91} +(4.50000 - 7.79423i) q^{92} +13.8564i q^{93} -21.0000 q^{95} -1.73205i q^{96} +(0.500000 - 0.866025i) q^{97} +(-1.00000 - 6.92820i) q^{98} +(-4.50000 - 7.79423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} - 3 q^{5} - 4 q^{7} - 2 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 - 3 * q^5 - 4 * q^7 - 2 * q^8 - 6 * q^9	$ 2 q - 2 q^{2} + 2 q^{4} - 3 q^{5} - 4 q^{7} - 2 q^{8} - 6 q^{9} + 3 q^{10} + 3 q^{11} + q^{13} + 4 q^{14} - 9 q^{15} + 2 q^{16} - 3 q^{17} + 6 q^{18} + 7 q^{19} - 3 q^{20} + 6 q^{21} - 3 q^{22} + 9 q^{23} - 4 q^{25} - q^{26} - 4 q^{28} - 3 q^{29} + 9 q^{30} + 16 q^{31} - 2 q^{32} - 9 q^{33} + 3 q^{34} + 15 q^{35} - 6 q^{36} + q^{37} - 7 q^{38} - 3 q^{39} + 3 q^{40} - 3 q^{41} - 6 q^{42} + q^{43} + 3 q^{44} + 9 q^{45} - 9 q^{46} + 2 q^{49} + 4 q^{50} - 9 q^{51} + q^{52} - 3 q^{53} - 18 q^{55} + 4 q^{56} - 21 q^{57} + 3 q^{58} - 9 q^{60} + 4 q^{61} - 16 q^{62} + 12 q^{63} + 2 q^{64} - 6 q^{65} + 9 q^{66} - 8 q^{67} - 3 q^{68} + 27 q^{69} - 15 q^{70} + 24 q^{71} + 6 q^{72} - 11 q^{73} - q^{74} + 12 q^{75} + 7 q^{76} + 3 q^{77} + 3 q^{78} - 32 q^{79} - 3 q^{80} + 18 q^{81} + 3 q^{82} + 9 q^{83} + 6 q^{84} - 9 q^{85} - q^{86} - 9 q^{87} - 3 q^{88} - 3 q^{89} - 9 q^{90} + q^{91} + 9 q^{92} - 42 q^{95} + q^{97} - 2 q^{98} - 9 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 - 3 * q^5 - 4 * q^7 - 2 * q^8 - 6 * q^9 + 3 * q^10 + 3 * q^11 + q^13 + 4 * q^14 - 9 * q^15 + 2 * q^16 - 3 * q^17 + 6 * q^18 + 7 * q^19 - 3 * q^20 + 6 * q^21 - 3 * q^22 + 9 * q^23 - 4 * q^25 - q^26 - 4 * q^28 - 3 * q^29 + 9 * q^30 + 16 * q^31 - 2 * q^32 - 9 * q^33 + 3 * q^34 + 15 * q^35 - 6 * q^36 + q^37 - 7 * q^38 - 3 * q^39 + 3 * q^40 - 3 * q^41 - 6 * q^42 + q^43 + 3 * q^44 + 9 * q^45 - 9 * q^46 + 2 * q^49 + 4 * q^50 - 9 * q^51 + q^52 - 3 * q^53 - 18 * q^55 + 4 * q^56 - 21 * q^57 + 3 * q^58 - 9 * q^60 + 4 * q^61 - 16 * q^62 + 12 * q^63 + 2 * q^64 - 6 * q^65 + 9 * q^66 - 8 * q^67 - 3 * q^68 + 27 * q^69 - 15 * q^70 + 24 * q^71 + 6 * q^72 - 11 * q^73 - q^74 + 12 * q^75 + 7 * q^76 + 3 * q^77 + 3 * q^78 - 32 * q^79 - 3 * q^80 + 18 * q^81 + 3 * q^82 + 9 * q^83 + 6 * q^84 - 9 * q^85 - q^86 - 9 * q^87 - 3 * q^88 - 3 * q^89 - 9 * q^90 + q^91 + 9 * q^92 - 42 * q^95 + q^97 - 2 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$			1.73205i			1.00000i
$3$			1.73205i			1.00000i
$4$	1.00000			0.500000
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$		−	1.73205i		−	0.707107i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$8$	−1.00000			−0.353553
$9$	−3.00000			−1.00000
$10$	1.50000	−	2.59808i	0.474342	−	0.821584i
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$			1.73205i			0.500000i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	0.926995	−	0.375073i	$-0.122382\pi$
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	−0.788320	+	0.615265i	$0.789049\pi$
$14$	2.00000	+	1.73205i	0.534522	+	0.462910i
$15$	−4.50000	−	2.59808i	−1.16190	−	0.670820i
$16$	1.00000			0.250000
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$	3.00000			0.707107
$19$	3.50000	+	6.06218i	0.802955	+	1.39076i	0.917663	+	0.397360i	$0.130073\pi$
$19$	3.50000	+	6.06218i	0.802955	+	1.39076i	−0.114708	+	0.993399i	$0.536593\pi$
$20$	−1.50000	+	2.59808i	−0.335410	+	0.580948i
$21$	3.00000	−	3.46410i	0.654654	−	0.755929i
$22$	−1.50000	−	2.59808i	−0.319801	−	0.553912i
$23$	4.50000	−	7.79423i	0.938315	−	1.62521i	0.169701	−	0.985496i	$-0.445720\pi$
$23$	4.50000	−	7.79423i	0.938315	−	1.62521i	0.768613	−	0.639713i	$-0.220947\pi$
$24$		−	1.73205i		−	0.353553i
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	−0.500000	−	0.866025i	−0.0980581	−	0.169842i
$27$		−	5.19615i		−	1.00000i
$28$	−2.00000	−	1.73205i	−0.377964	−	0.327327i
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$	4.50000	+	2.59808i	0.821584	+	0.474342i
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$	−1.00000			−0.176777
$33$	−4.50000	+	2.59808i	−0.783349	+	0.452267i
$34$	1.50000	−	2.59808i	0.257248	−	0.445566i
$35$	7.50000	−	2.59808i	1.26773	−	0.439155i
$36$	−3.00000			−0.500000
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	−3.50000	−	6.06218i	−0.567775	−	0.983415i
$39$	−1.50000	+	0.866025i	−0.240192	+	0.138675i
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$	−3.00000	+	3.46410i	−0.462910	+	0.534522i
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$	1.50000	+	2.59808i	0.226134	+	0.391675i
$45$	4.50000	−	7.79423i	0.670820	−	1.16190i
$46$	−4.50000	+	7.79423i	−0.663489	+	1.14920i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$			1.73205i			0.250000i
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$	−4.50000	−	2.59808i	−0.630126	−	0.363803i
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$			5.19615i			0.707107i
$55$	−9.00000			−1.21356
$56$	2.00000	+	1.73205i	0.267261	+	0.231455i
$57$	−10.5000	+	6.06218i	−1.39076	+	0.802955i
$58$	1.50000	−	2.59808i	0.196960	−	0.341144i
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$	−4.50000	−	2.59808i	−0.580948	−	0.335410i
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$	−8.00000			−1.01600
$63$	6.00000	+	5.19615i	0.755929	+	0.654654i
$64$	1.00000			0.125000
$65$	−3.00000			−0.372104
$66$	4.50000	−	2.59808i	0.553912	−	0.319801i
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$	−1.50000	+	2.59808i	−0.181902	+	0.315063i
$69$	13.5000	+	7.79423i	1.62521	+	0.938315i
$70$	−7.50000	+	2.59808i	−0.896421	+	0.310530i
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$	3.00000			0.353553
$73$	−5.50000	+	9.52628i	−0.643726	+	1.11497i	0.340868	+	0.940111i	$0.389279\pi$
$73$	−5.50000	+	9.52628i	−0.643726	+	1.11497i	−0.984594	+	0.174855i	$0.944054\pi$
$74$	−0.500000	−	0.866025i	−0.0581238	−	0.100673i
$75$	6.00000	−	3.46410i	0.692820	−	0.400000i
$76$	3.50000	+	6.06218i	0.401478	+	0.695379i
$77$	1.50000	−	7.79423i	0.170941	−	0.888235i
$78$	1.50000	−	0.866025i	0.169842	−	0.0980581i
$79$	−16.0000			−1.80014			−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000			−1.80014			−0.900070	+	0.435745i	$0.856485\pi$
$80$	−1.50000	+	2.59808i	−0.167705	+	0.290474i
$81$	9.00000			1.00000
$82$	1.50000	+	2.59808i	0.165647	+	0.286910i
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	−0.506036	−	0.862512i	$-0.668890\pi$
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	0.999976	+	0.00698436i	$0.00222321\pi$
$84$	3.00000	−	3.46410i	0.327327	−	0.377964i
$85$	−4.50000	−	7.79423i	−0.488094	−	0.845403i
$86$	−0.500000	+	0.866025i	−0.0539164	+	0.0933859i
$87$	−4.50000	−	2.59808i	−0.482451	−	0.278543i
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	−1.50000	−	2.59808i	−0.159000	−	0.275396i	0.775509	−	0.631337i	$-0.217494\pi$
$89$	−1.50000	−	2.59808i	−0.159000	−	0.275396i	−0.934508	+	0.355942i	$0.884160\pi$
$90$	−4.50000	+	7.79423i	−0.474342	+	0.821584i
$91$	0.500000	−	2.59808i	0.0524142	−	0.272352i
$92$	4.50000	−	7.79423i	0.469157	−	0.812605i
$93$			13.8564i			1.43684i
$94$		0			0
$95$	−21.0000			−2.15455
$96$		−	1.73205i		−	0.176777i
$97$	0.500000	−	0.866025i	0.0507673	−	0.0879316i	−0.839525	−	0.543321i	$-0.817167\pi$
$97$	0.500000	−	0.866025i	0.0507673	−	0.0879316i	0.890292	+	0.455389i	$0.150500\pi$
$98$	−1.00000	−	6.92820i	−0.101015	−	0.699854i
$99$	−4.50000	−	7.79423i	−0.452267	−	0.783349i
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	0.781697	−	0.623658i	$-0.214354\pi$
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	−0.930953	+	0.365140i	$0.881021\pi$
$102$	4.50000	+	2.59808i	0.445566	+	0.257248i
$103$	6.50000	−	11.2583i	0.640464	−	1.10932i	−0.344865	−	0.938652i	$-0.612075\pi$
$103$	6.50000	−	11.2583i	0.640464	−	1.10932i	0.985329	−	0.170664i	$-0.0545913\pi$
$104$	−0.500000	−	0.866025i	−0.0490290	−	0.0849208i
$105$	4.50000	+	12.9904i	0.439155	+	1.26773i
$106$	1.50000	−	2.59808i	0.145693	−	0.252347i
$107$	−4.50000	−	7.79423i	−0.435031	−	0.753497i	0.562267	−	0.826956i	$-0.309929\pi$
$107$	−4.50000	−	7.79423i	−0.435031	−	0.753497i	−0.997298	+	0.0734594i	$0.976596\pi$
$108$		−	5.19615i		−	0.500000i
$109$	6.50000	−	11.2583i	0.622587	−	1.07835i	−0.366415	−	0.930451i	$-0.619415\pi$
$109$	6.50000	−	11.2583i	0.622587	−	1.07835i	0.989002	−	0.147901i	$-0.0472517\pi$
$110$	9.00000			0.858116
$111$	−1.50000	+	0.866025i	−0.142374	+	0.0821995i
$112$	−2.00000	−	1.73205i	−0.188982	−	0.163663i
$113$	4.50000	+	7.79423i	0.423324	+	0.733219i	0.996262	−	0.0863794i	$-0.0275297\pi$
$113$	4.50000	+	7.79423i	0.423324	+	0.733219i	−0.572938	+	0.819599i	$0.694196\pi$
$114$	10.5000	−	6.06218i	0.983415	−	0.567775i
$115$	13.5000	+	23.3827i	1.25888	+	2.18045i
$116$	−1.50000	+	2.59808i	−0.139272	+	0.241225i
$117$	−1.50000	−	2.59808i	−0.138675	−	0.240192i
$118$		0			0
$119$	7.50000	−	2.59808i	0.687524	−	0.238165i
$120$	4.50000	+	2.59808i	0.410792	+	0.237171i
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−2.00000			−0.181071
$123$	4.50000	−	2.59808i	0.405751	−	0.234261i
$124$	8.00000			0.718421
$125$	−3.00000			−0.268328
$126$	−6.00000	−	5.19615i	−0.534522	−	0.462910i
$127$	−4.00000			−0.354943			−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000			−0.354943			−0.177471	+	0.984126i	$0.556792\pi$
$128$	−1.00000			−0.0883883
$129$	1.50000	+	0.866025i	0.132068	+	0.0762493i
$130$	3.00000			0.263117
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	0.326546	+	0.945181i	$0.394115\pi$
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	−0.981824	+	0.189794i	$0.939218\pi$
$132$	−4.50000	+	2.59808i	−0.391675	+	0.226134i
$133$	3.50000	−	18.1865i	0.303488	−	1.57697i
$134$	4.00000			0.345547
$135$	13.5000	+	7.79423i	1.16190	+	0.670820i
$136$	1.50000	−	2.59808i	0.128624	−	0.222783i
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	0.991694	−	0.128618i	$-0.0410540\pi$
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	−0.607233	+	0.794524i	$0.707721\pi$
$138$	−13.5000	−	7.79423i	−1.14920	−	0.663489i
$139$	3.50000	+	6.06218i	0.296866	+	0.514187i	0.975417	−	0.220366i	$-0.0707252\pi$
$139$	3.50000	+	6.06218i	0.296866	+	0.514187i	−0.678551	+	0.734553i	$0.737392\pi$
$140$	7.50000	−	2.59808i	0.633866	−	0.219578i
$141$		0			0
$142$	−12.0000			−1.00702
$143$	−1.50000	+	2.59808i	−0.125436	+	0.217262i
$144$	−3.00000			−0.250000
$145$	−4.50000	−	7.79423i	−0.373705	−	0.647275i
$146$	5.50000	−	9.52628i	0.455183	−	0.788400i
$147$	−12.0000	+	1.73205i	−0.989743	+	0.142857i
$148$	0.500000	+	0.866025i	0.0410997	+	0.0711868i
$149$	4.50000	−	7.79423i	0.368654	−	0.638528i	−0.620701	−	0.784047i	$-0.713152\pi$
$149$	4.50000	−	7.79423i	0.368654	−	0.638528i	0.989355	+	0.145519i	$0.0464853\pi$
$150$	−6.00000	+	3.46410i	−0.489898	+	0.282843i
$151$	3.50000	+	6.06218i	0.284826	+	0.493333i	0.972567	−	0.232623i	$-0.0747309\pi$
$151$	3.50000	+	6.06218i	0.284826	+	0.493333i	−0.687741	+	0.725956i	$0.741398\pi$
$152$	−3.50000	−	6.06218i	−0.283887	−	0.491708i
$153$	4.50000	−	7.79423i	0.363803	−	0.630126i
$154$	−1.50000	+	7.79423i	−0.120873	+	0.628077i
$155$	−12.0000	+	20.7846i	−0.963863	+	1.66946i
$156$	−1.50000	+	0.866025i	−0.120096	+	0.0693375i
$157$	−22.0000			−1.75579			−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000			−1.75579			−0.877896	+	0.478852i	$0.841053\pi$
$158$	16.0000			1.27289
$159$	−4.50000	−	2.59808i	−0.356873	−	0.206041i
$160$	1.50000	−	2.59808i	0.118585	−	0.205396i
$161$	−22.5000	+	7.79423i	−1.77325	+	0.614271i
$162$	−9.00000			−0.707107
$163$	9.50000	+	16.4545i	0.744097	+	1.28881i	0.950615	+	0.310372i	$0.100454\pi$
$163$	9.50000	+	16.4545i	0.744097	+	1.28881i	−0.206518	+	0.978443i	$0.566213\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$		−	15.5885i		−	1.21356i
$166$	−4.50000	+	7.79423i	−0.349268	+	0.604949i
$167$	7.50000	+	12.9904i	0.580367	+	1.00523i	0.995436	+	0.0954356i	$0.0304244\pi$
$167$	7.50000	+	12.9904i	0.580367	+	1.00523i	−0.415068	+	0.909790i	$0.636242\pi$
$168$	−3.00000	+	3.46410i	−0.231455	+	0.267261i
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$	4.50000	+	7.79423i	0.345134	+	0.597790i
$171$	−10.5000	−	18.1865i	−0.802955	−	1.39076i
$172$	0.500000	−	0.866025i	0.0381246	−	0.0660338i
$173$	−6.00000			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$	4.50000	+	2.59808i	0.341144	+	0.196960i
$175$	−2.00000	+	10.3923i	−0.151186	+	0.785584i
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$		0			0
$178$	1.50000	+	2.59808i	0.112430	+	0.194734i
$179$	10.5000	−	18.1865i	0.784807	−	1.35933i	−0.144308	−	0.989533i	$-0.546095\pi$
$179$	10.5000	−	18.1865i	0.784807	−	1.35933i	0.929114	−	0.369792i	$-0.120571\pi$
$180$	4.50000	−	7.79423i	0.335410	−	0.580948i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	−0.500000	+	2.59808i	−0.0370625	+	0.192582i
$183$			3.46410i			0.256074i
$184$	−4.50000	+	7.79423i	−0.331744	+	0.574598i
$185$	−3.00000			−0.220564
$186$		−	13.8564i		−	1.01600i
$187$	−9.00000			−0.658145
$188$		0			0
$189$	−9.00000	+	10.3923i	−0.654654	+	0.755929i
$190$	21.0000			1.52350
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$			1.73205i			0.125000i
$193$	14.0000			1.00774			0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000			1.00774			0.503871	+	0.863779i	$0.331909\pi$
$194$	−0.500000	+	0.866025i	−0.0358979	+	0.0621770i
$195$		−	5.19615i		−	0.372104i
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$	4.50000	+	7.79423i	0.319801	+	0.553912i
$199$	12.5000	−	21.6506i	0.886102	−	1.53477i	0.0416556	−	0.999132i	$-0.486737\pi$
$199$	12.5000	−	21.6506i	0.886102	−	1.53477i	0.844446	−	0.535641i	$-0.179930\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$		−	6.92820i		−	0.488678i
$202$	1.50000	+	2.59808i	0.105540	+	0.182800i
$203$	7.50000	−	2.59808i	0.526397	−	0.182349i
$204$	−4.50000	−	2.59808i	−0.315063	−	0.181902i
$205$	9.00000			0.628587
$206$	−6.50000	+	11.2583i	−0.452876	+	0.784405i
$207$	−13.5000	+	23.3827i	−0.938315	+	1.62521i
$208$	0.500000	+	0.866025i	0.0346688	+	0.0600481i
$209$	−10.5000	+	18.1865i	−0.726300	+	1.25799i
$210$	−4.50000	−	12.9904i	−0.310530	−	0.896421i
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	0.767049	−	0.641588i	$-0.221724\pi$
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	−0.939156	+	0.343490i	$0.888391\pi$
$212$	−1.50000	+	2.59808i	−0.103020	+	0.178437i
$213$			20.7846i			1.42414i
$214$	4.50000	+	7.79423i	0.307614	+	0.532803i
$215$	1.50000	+	2.59808i	0.102299	+	0.177187i
$216$			5.19615i			0.353553i
$217$	−16.0000	−	13.8564i	−1.08615	−	0.940634i
$218$	−6.50000	+	11.2583i	−0.440236	+	0.762510i
$219$	−16.5000	−	9.52628i	−1.11497	−	0.643726i
$220$	−9.00000			−0.606780
$221$	−3.00000			−0.201802
$222$	1.50000	−	0.866025i	0.100673	−	0.0581238i
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	−0.848799	−	0.528716i	$-0.822674\pi$
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	0.882281	+	0.470723i	$0.156007\pi$
$224$	2.00000	+	1.73205i	0.133631	+	0.115728i
$225$	6.00000	+	10.3923i	0.400000	+	0.692820i
$226$	−4.50000	−	7.79423i	−0.299336	−	0.518464i
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	0.911502	−	0.411296i	$-0.134924\pi$
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	−0.811943	+	0.583736i	$0.801590\pi$
$228$	−10.5000	+	6.06218i	−0.695379	+	0.401478i
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	−0.567300	−	0.823511i	$-0.692012\pi$
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	0.996832	+	0.0795401i	$0.0253452\pi$
$230$	−13.5000	−	23.3827i	−0.890164	−	1.54181i
$231$	13.5000	+	2.59808i	0.888235	+	0.170941i
$232$	1.50000	−	2.59808i	0.0984798	−	0.170572i
$233$	−1.50000	−	2.59808i	−0.0982683	−	0.170206i	0.812700	−	0.582683i	$-0.197997\pi$
$233$	−1.50000	−	2.59808i	−0.0982683	−	0.170206i	−0.910968	+	0.412477i	$0.864664\pi$
$234$	1.50000	+	2.59808i	0.0980581	+	0.169842i
$235$		0			0
$236$		0			0
$237$		−	27.7128i		−	1.80014i
$238$	−7.50000	+	2.59808i	−0.486153	+	0.168408i
$239$	1.50000	+	2.59808i	0.0970269	+	0.168056i	0.910453	−	0.413613i	$-0.135733\pi$
$239$	1.50000	+	2.59808i	0.0970269	+	0.168056i	−0.813426	+	0.581669i	$0.802400\pi$
$240$	−4.50000	−	2.59808i	−0.290474	−	0.167705i
$241$	6.50000	+	11.2583i	0.418702	+	0.725213i	0.995809	−	0.0914555i	$-0.0291519\pi$
$241$	6.50000	+	11.2583i	0.418702	+	0.725213i	−0.577107	+	0.816668i	$0.695819\pi$
$242$	−1.00000	+	1.73205i	−0.0642824	+	0.111340i
$243$			15.5885i			1.00000i
$244$	2.00000			0.128037
$245$	−19.5000	−	7.79423i	−1.24581	−	0.497955i
$246$	−4.50000	+	2.59808i	−0.286910	+	0.165647i
$247$	−3.50000	+	6.06218i	−0.222700	+	0.385727i
$248$	−8.00000			−0.508001
$249$	13.5000	+	7.79423i	0.855528	+	0.493939i
$250$	3.00000			0.189737
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$	6.00000	+	5.19615i	0.377964	+	0.327327i
$253$	27.0000			1.69748
$254$	4.00000			0.250982
$255$	13.5000	−	7.79423i	0.845403	−	0.488094i
$256$	1.00000			0.0625000
$257$	10.5000	−	18.1865i	0.654972	−	1.13444i	−0.326929	−	0.945049i	$-0.606014\pi$
$257$	10.5000	−	18.1865i	0.654972	−	1.13444i	0.981901	−	0.189396i	$-0.0606529\pi$
$258$	−1.50000	−	0.866025i	−0.0933859	−	0.0539164i
$259$	0.500000	−	2.59808i	0.0310685	−	0.161437i
$260$	−3.00000			−0.186052
$261$	4.50000	−	7.79423i	0.278543	−	0.482451i
$262$	7.50000	−	12.9904i	0.463352	−	0.802548i
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	0.693276	−	0.720672i	$-0.256167\pi$
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	−0.970758	+	0.240059i	$0.922833\pi$
$264$	4.50000	−	2.59808i	0.276956	−	0.159901i
$265$	−4.50000	−	7.79423i	−0.276433	−	0.478796i
$266$	−3.50000	+	18.1865i	−0.214599	+	1.11509i
$267$	4.50000	−	2.59808i	0.275396	−	0.159000i
$268$	−4.00000			−0.244339
$269$	−7.50000	+	12.9904i	−0.457283	+	0.792038i	−0.998816	−	0.0486418i	$-0.984511\pi$
$269$	−7.50000	+	12.9904i	−0.457283	+	0.792038i	0.541533	+	0.840679i	$0.317844\pi$
$270$	−13.5000	−	7.79423i	−0.821584	−	0.474342i
$271$	−2.50000	−	4.33013i	−0.151864	−	0.263036i	0.780049	−	0.625719i	$-0.215194\pi$
$271$	−2.50000	−	4.33013i	−0.151864	−	0.263036i	−0.931913	+	0.362682i	$0.881861\pi$
$272$	−1.50000	+	2.59808i	−0.0909509	+	0.157532i
$273$	4.50000	+	0.866025i	0.272352	+	0.0524142i
$274$	−4.50000	−	7.79423i	−0.271855	−	0.470867i
$275$	6.00000	−	10.3923i	0.361814	−	0.626680i
$276$	13.5000	+	7.79423i	0.812605	+	0.469157i
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	0.880656	−	0.473757i	$-0.157103\pi$
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	−0.850613	+	0.525792i	$0.823769\pi$
$278$	−3.50000	−	6.06218i	−0.209916	−	0.363585i
$279$	−24.0000			−1.43684
$280$	−7.50000	+	2.59808i	−0.448211	+	0.155265i
$281$	10.5000	−	18.1865i	0.626377	−	1.08492i	−0.361895	−	0.932219i	$-0.617870\pi$
$281$	10.5000	−	18.1865i	0.626377	−	1.08492i	0.988273	−	0.152699i	$-0.0487965\pi$
$282$		0			0
$283$	−4.00000			−0.237775			−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000			−0.237775			−0.118888	+	0.992908i	$0.537933\pi$
$284$	12.0000			0.712069
$285$		−	36.3731i		−	2.15455i
$286$	1.50000	−	2.59808i	0.0886969	−	0.153627i
$287$	−1.50000	+	7.79423i	−0.0885422	+	0.460079i
$288$	3.00000			0.176777
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	4.50000	+	7.79423i	0.264249	+	0.457693i
$291$	1.50000	+	0.866025i	0.0879316	+	0.0507673i
$292$	−5.50000	+	9.52628i	−0.321863	+	0.557483i
$293$	4.50000	+	7.79423i	0.262893	+	0.455344i	0.967009	−	0.254741i	$-0.0819901\pi$
$293$	4.50000	+	7.79423i	0.262893	+	0.455344i	−0.704117	+	0.710084i	$0.748657\pi$
$294$	12.0000	−	1.73205i	0.699854	−	0.101015i
$295$		0			0
$296$	−0.500000	−	0.866025i	−0.0290619	−	0.0503367i
$297$	13.5000	−	7.79423i	0.783349	−	0.452267i
$298$	−4.50000	+	7.79423i	−0.260678	+	0.451508i
$299$	9.00000			0.520483
$300$	6.00000	−	3.46410i	0.346410	−	0.200000i
$301$	−2.50000	+	0.866025i	−0.144098	+	0.0499169i
$302$	−3.50000	−	6.06218i	−0.201402	−	0.348839i
$303$	4.50000	−	2.59808i	0.258518	−	0.149256i
$304$	3.50000	+	6.06218i	0.200739	+	0.347690i
$305$	−3.00000	+	5.19615i	−0.171780	+	0.297531i
$306$	−4.50000	+	7.79423i	−0.257248	+	0.445566i
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	1.50000	−	7.79423i	0.0854704	−	0.444117i
$309$	19.5000	+	11.2583i	1.10932	+	0.640464i
$310$	12.0000	−	20.7846i	0.681554	−	1.18049i
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$	1.50000	−	0.866025i	0.0849208	−	0.0490290i
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$	22.0000			1.24153
$315$	−22.5000	+	7.79423i	−1.26773	+	0.439155i
$316$	−16.0000			−0.900070
$317$	18.0000			1.01098			0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000			1.01098			0.505490	+	0.862832i	$0.331312\pi$
$318$	4.50000	+	2.59808i	0.252347	+	0.145693i
$319$	−9.00000			−0.503903
$320$	−1.50000	+	2.59808i	−0.0838525	+	0.145237i
$321$	13.5000	−	7.79423i	0.753497	−	0.435031i
$322$	22.5000	−	7.79423i	1.25388	−	0.434355i
$323$	−21.0000			−1.16847
$324$	9.00000			0.500000
$325$	2.00000	−	3.46410i	0.110940	−	0.192154i
$326$	−9.50000	−	16.4545i	−0.526156	−	0.911330i
$327$	19.5000	+	11.2583i	1.07835	+	0.622587i
$328$	1.50000	+	2.59808i	0.0828236	+	0.143455i
$329$		0			0
$330$			15.5885i			0.858116i
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$	4.50000	−	7.79423i	0.246970	−	0.427764i
$333$	−1.50000	−	2.59808i	−0.0821995	−	0.142374i
$334$	−7.50000	−	12.9904i	−0.410382	−	0.710802i
$335$	6.00000	−	10.3923i	0.327815	−	0.567792i
$336$	3.00000	−	3.46410i	0.163663	−	0.188982i
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	0.986960	−	0.160968i	$-0.0514616\pi$
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	−0.632882	+	0.774248i	$0.718128\pi$
$338$	−6.00000	+	10.3923i	−0.326357	+	0.565267i
$339$	−13.5000	+	7.79423i	−0.733219	+	0.423324i
$340$	−4.50000	−	7.79423i	−0.244047	−	0.422701i
$341$	12.0000	+	20.7846i	0.649836	+	1.12555i
$342$	10.5000	+	18.1865i	0.567775	+	0.983415i
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−0.500000	+	0.866025i	−0.0269582	+	0.0466930i
$345$	−40.5000	+	23.3827i	−2.18045	+	1.25888i
$346$	6.00000			0.322562
$347$	12.0000			0.644194			0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000			0.644194			0.322097	+	0.946707i	$0.395612\pi$
$348$	−4.50000	−	2.59808i	−0.241225	−	0.139272i
$349$	−11.5000	+	19.9186i	−0.615581	+	1.06622i	0.374701	+	0.927146i	$0.377745\pi$
$349$	−11.5000	+	19.9186i	−0.615581	+	1.06622i	−0.990282	+	0.139072i	$0.955588\pi$
$350$	2.00000	−	10.3923i	0.106904	−	0.555492i
$351$	4.50000	−	2.59808i	0.240192	−	0.138675i
$352$	−1.50000	−	2.59808i	−0.0799503	−	0.138478i
$353$	−1.50000	−	2.59808i	−0.0798369	−	0.138282i	0.823343	−	0.567545i	$-0.192107\pi$
$353$	−1.50000	−	2.59808i	−0.0798369	−	0.138282i	−0.903179	+	0.429263i	$0.858773\pi$
$354$		0			0
$355$	−18.0000	+	31.1769i	−0.955341	+	1.65470i
$356$	−1.50000	−	2.59808i	−0.0794998	−	0.137698i
$357$	4.50000	+	12.9904i	0.238165	+	0.687524i
$358$	−10.5000	+	18.1865i	−0.554942	+	0.961188i
$359$	−4.50000	−	7.79423i	−0.237501	−	0.411364i	0.722496	−	0.691375i	$-0.242995\pi$
$359$	−4.50000	−	7.79423i	−0.237501	−	0.411364i	−0.959997	+	0.280012i	$0.909662\pi$
$360$	−4.50000	+	7.79423i	−0.237171	+	0.410792i
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$	−2.00000			−0.105118
$363$	3.00000	+	1.73205i	0.157459	+	0.0909091i
$364$	0.500000	−	2.59808i	0.0262071	−	0.136176i
$365$	−16.5000	−	28.5788i	−0.863649	−	1.49588i
$366$		−	3.46410i		−	0.181071i
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	0.554264	−	0.832341i	$-0.313000\pi$
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	−0.997960	+	0.0638362i	$0.979666\pi$
$368$	4.50000	−	7.79423i	0.234579	−	0.406302i
$369$	4.50000	+	7.79423i	0.234261	+	0.405751i
$370$	3.00000			0.155963
$371$	7.50000	−	2.59808i	0.389381	−	0.134885i
$372$			13.8564i			0.718421i
$373$	6.50000	−	11.2583i	0.336557	−	0.582934i	−0.647225	−	0.762299i	$-0.724071\pi$
$373$	6.50000	−	11.2583i	0.336557	−	0.582934i	0.983783	+	0.179364i	$0.0574041\pi$
$374$	9.00000			0.465379
$375$		−	5.19615i		−	0.268328i
$376$		0			0
$377$	−3.00000			−0.154508
$378$	9.00000	−	10.3923i	0.462910	−	0.534522i
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$	−21.0000			−1.07728
$381$		−	6.92820i		−	0.354943i
$382$		0			0
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	−0.991522	−	0.129937i	$-0.958522\pi$
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	0.608290	+	0.793715i	$0.291856\pi$
$384$		−	1.73205i		−	0.0883883i
$385$	18.0000	+	15.5885i	0.917365	+	0.794461i
$386$	−14.0000			−0.712581
$387$	−1.50000	+	2.59808i	−0.0762493	+	0.132068i
$388$	0.500000	−	0.866025i	0.0253837	−	0.0439658i
$389$	−13.5000	−	23.3827i	−0.684477	−	1.18555i	−0.973601	−	0.228257i	$-0.926697\pi$
$389$	−13.5000	−	23.3827i	−0.684477	−	1.18555i	0.289124	−	0.957292i	$-0.406636\pi$
$390$			5.19615i			0.263117i
$391$	13.5000	+	23.3827i	0.682724	+	1.18251i
$392$	−1.00000	−	6.92820i	−0.0505076	−	0.349927i
$393$	−22.5000	−	12.9904i	−1.13497	−	0.655278i
$394$	−18.0000			−0.906827
$395$	24.0000	−	41.5692i	1.20757	−	2.09157i
$396$	−4.50000	−	7.79423i	−0.226134	−	0.391675i
$397$	6.50000	+	11.2583i	0.326226	+	0.565039i	0.981760	−	0.190126i	$-0.0608897\pi$
$397$	6.50000	+	11.2583i	0.326226	+	0.565039i	−0.655534	+	0.755166i	$0.727556\pi$
$398$	−12.5000	+	21.6506i	−0.626568	+	1.08525i
$399$	31.5000	+	6.06218i	1.57697	+	0.303488i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	−13.5000	+	23.3827i	−0.674158	+	1.16768i	0.302556	+	0.953131i	$0.402160\pi$
$401$	−13.5000	+	23.3827i	−0.674158	+	1.16768i	−0.976714	+	0.214544i	$0.931173\pi$
$402$			6.92820i			0.345547i
$403$	4.00000	+	6.92820i	0.199254	+	0.345118i
$404$	−1.50000	−	2.59808i	−0.0746278	−	0.129259i
$405$	−13.5000	+	23.3827i	−0.670820	+	1.16190i
$406$	−7.50000	+	2.59808i	−0.372219	+	0.128940i
$407$	−1.50000	+	2.59808i	−0.0743522	+	0.128782i
$408$	4.50000	+	2.59808i	0.222783	+	0.128624i
$409$	−34.0000			−1.68119			−0.840596	−	0.541663i	$-0.817795\pi$
$409$	−34.0000			−1.68119			−0.840596	+	0.541663i	$0.817795\pi$
$410$	−9.00000			−0.444478
$411$	−13.5000	+	7.79423i	−0.665906	+	0.384461i
$412$	6.50000	−	11.2583i	0.320232	−	0.554658i
$413$		0			0
$414$	13.5000	−	23.3827i	0.663489	−	1.14920i
$415$	13.5000	+	23.3827i	0.662689	+	1.14781i
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	−10.5000	+	6.06218i	−0.514187	+	0.296866i
$418$	10.5000	−	18.1865i	0.513572	−	0.889532i
$419$	−4.50000	−	7.79423i	−0.219839	−	0.380773i	0.734919	−	0.678155i	$-0.237220\pi$
$419$	−4.50000	−	7.79423i	−0.219839	−	0.380773i	−0.954759	+	0.297382i	$0.903887\pi$
$420$	4.50000	+	12.9904i	0.219578	+	0.633866i
$421$	−17.5000	+	30.3109i	−0.852898	+	1.47726i	0.0256838	+	0.999670i	$0.491824\pi$
$421$	−17.5000	+	30.3109i	−0.852898	+	1.47726i	−0.878582	+	0.477592i	$0.841510\pi$
$422$	2.50000	+	4.33013i	0.121698	+	0.210787i
$423$		0			0
$424$	1.50000	−	2.59808i	0.0728464	−	0.126174i
$425$	12.0000			0.582086
$426$		−	20.7846i		−	1.00702i
$427$	−4.00000	−	3.46410i	−0.193574	−	0.167640i
$428$	−4.50000	−	7.79423i	−0.217516	−	0.376748i
$429$	−4.50000	−	2.59808i	−0.217262	−	0.125436i
$430$	−1.50000	−	2.59808i	−0.0723364	−	0.125290i
$431$	−13.5000	+	23.3827i	−0.650272	+	1.12630i	0.332785	+	0.943003i	$0.392012\pi$
$431$	−13.5000	+	23.3827i	−0.650272	+	1.12630i	−0.983057	+	0.183301i	$0.941322\pi$
$432$		−	5.19615i		−	0.250000i
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$	16.0000	+	13.8564i	0.768025	+	0.665129i
$435$	13.5000	−	7.79423i	0.647275	−	0.373705i
$436$	6.50000	−	11.2583i	0.311294	−	0.539176i
$437$	63.0000			3.01370
$438$	16.5000	+	9.52628i	0.788400	+	0.455183i
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$	9.00000			0.429058
$441$	−3.00000	−	20.7846i	−0.142857	−	0.989743i
$442$	3.00000			0.142695
$443$	36.0000			1.71041			0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000			1.71041			0.855206	+	0.518289i	$0.173431\pi$
$444$	−1.50000	+	0.866025i	−0.0711868	+	0.0410997i
$445$	9.00000			0.426641
$446$	−0.500000	+	0.866025i	−0.0236757	+	0.0410075i
$447$	13.5000	+	7.79423i	0.638528	+	0.368654i
$448$	−2.00000	−	1.73205i	−0.0944911	−	0.0818317i
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$	−6.00000	−	10.3923i	−0.282843	−	0.489898i
$451$	4.50000	−	7.79423i	0.211897	−	0.367016i
$452$	4.50000	+	7.79423i	0.211662	+	0.366610i
$453$	−10.5000	+	6.06218i	−0.493333	+	0.284826i
$454$	−1.50000	−	2.59808i	−0.0703985	−	0.121934i
$455$	6.00000	+	5.19615i	0.281284	+	0.243599i
$456$	10.5000	−	6.06218i	0.491708	−	0.283887i
$457$	−10.0000			−0.467780			−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000			−0.467780			−0.233890	+	0.972263i	$0.575146\pi$
$458$	−6.50000	+	11.2583i	−0.303725	+	0.526067i
$459$	13.5000	+	7.79423i	0.630126	+	0.363803i
$460$	13.5000	+	23.3827i	0.629441	+	1.09022i
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	−0.741998	−	0.670402i	$-0.766122\pi$
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	0.951584	+	0.307388i	$0.0994551\pi$
$462$	−13.5000	−	2.59808i	−0.628077	−	0.120873i
$463$	−20.5000	−	35.5070i	−0.952716	−	1.65015i	−0.739511	−	0.673145i	$-0.764943\pi$
$463$	−20.5000	−	35.5070i	−0.952716	−	1.65015i	−0.213205	−	0.977007i	$-0.568390\pi$
$464$	−1.50000	+	2.59808i	−0.0696358	+	0.120613i
$465$	−36.0000	−	20.7846i	−1.66946	−	0.963863i
$466$	1.50000	+	2.59808i	0.0694862	+	0.120354i
$467$	1.50000	+	2.59808i	0.0694117	+	0.120225i	0.898642	−	0.438682i	$-0.144554\pi$
$467$	1.50000	+	2.59808i	0.0694117	+	0.120225i	−0.829231	+	0.558906i	$0.811221\pi$
$468$	−1.50000	−	2.59808i	−0.0693375	−	0.120096i
$469$	8.00000	+	6.92820i	0.369406	+	0.319915i
$470$		0			0
$471$		−	38.1051i		−	1.75579i
$472$		0			0
$473$	3.00000			0.137940
$474$			27.7128i			1.27289i
$475$	14.0000	−	24.2487i	0.642364	−	1.11261i
$476$	7.50000	−	2.59808i	0.343762	−	0.119083i
$477$	4.50000	−	7.79423i	0.206041	−	0.356873i
$478$	−1.50000	−	2.59808i	−0.0686084	−	0.118833i
$479$	1.50000	+	2.59808i	0.0685367	+	0.118709i	0.898257	−	0.439470i	$-0.144834\pi$
$479$	1.50000	+	2.59808i	0.0685367	+	0.118709i	−0.829721	+	0.558179i	$0.811500\pi$
$480$	4.50000	+	2.59808i	0.205396	+	0.118585i
$481$	−0.500000	+	0.866025i	−0.0227980	+	0.0394874i
$482$	−6.50000	−	11.2583i	−0.296067	−	0.512803i
$483$	−13.5000	−	38.9711i	−0.614271	−	1.77325i
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	1.50000	+	2.59808i	0.0681115	+	0.117973i
$486$		−	15.5885i		−	0.707107i
$487$	12.5000	−	21.6506i	0.566429	−	0.981084i	−0.430486	−	0.902597i	$-0.641658\pi$
$487$	12.5000	−	21.6506i	0.566429	−	0.981084i	0.996915	−	0.0784867i	$-0.0250088\pi$
$488$	−2.00000			−0.0905357
$489$	−28.5000	+	16.4545i	−1.28881	+	0.744097i
$490$	19.5000	+	7.79423i	0.880920	+	0.352107i
$491$	−10.5000	−	18.1865i	−0.473858	−	0.820747i	0.525694	−	0.850674i	$-0.323806\pi$
$491$	−10.5000	−	18.1865i	−0.473858	−	0.820747i	−0.999552	+	0.0299272i	$0.990472\pi$
$492$	4.50000	−	2.59808i	0.202876	−	0.117130i
$493$	−4.50000	−	7.79423i	−0.202670	−	0.351034i
$494$	3.50000	−	6.06218i	0.157472	−	0.272750i
$495$	27.0000			1.21356
$496$	8.00000			0.359211
$497$	−24.0000	−	20.7846i	−1.07655	−	0.932317i
$498$	−13.5000	−	7.79423i	−0.604949	−	0.349268i
$499$	12.5000	−	21.6506i	0.559577	−	0.969216i	−0.437955	−	0.898997i	$-0.644297\pi$
$499$	12.5000	−	21.6506i	0.559577	−	0.969216i	0.997532	−	0.0702185i	$-0.0223697\pi$
$500$	−3.00000			−0.134164
$501$	−22.5000	+	12.9904i	−1.00523	+	0.580367i
$502$	−12.0000			−0.535586
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$	−6.00000	−	5.19615i	−0.267261	−	0.231455i
$505$	9.00000			0.400495
$506$	−27.0000			−1.20030
$507$	18.0000	+	10.3923i	0.799408	+	0.461538i
$508$	−4.00000			−0.177471
$509$	4.50000	−	7.79423i	0.199459	−	0.345473i	−0.748894	−	0.662690i	$-0.769415\pi$
$509$	4.50000	−	7.79423i	0.199459	−	0.345473i	0.948353	+	0.317217i	$0.102748\pi$
$510$	−13.5000	+	7.79423i	−0.597790	+	0.345134i
$511$	27.5000	−	9.52628i	1.21653	−	0.421418i
$512$	−1.00000			−0.0441942
$513$	31.5000	−	18.1865i	1.39076	−	0.802955i
$514$	−10.5000	+	18.1865i	−0.463135	+	0.802174i
$515$	19.5000	+	33.7750i	0.859273	+	1.48830i
$516$	1.50000	+	0.866025i	0.0660338	+	0.0381246i
$517$		0			0
$518$	−0.500000	+	2.59808i	−0.0219687	+	0.114153i
$519$		−	10.3923i		−	0.456172i
$520$	3.00000			0.131559
$521$	−1.50000	+	2.59808i	−0.0657162	+	0.113824i	−0.897011	−	0.442007i	$-0.854267\pi$
$521$	−1.50000	+	2.59808i	−0.0657162	+	0.113824i	0.831295	+	0.555831i	$0.187600\pi$
$522$	−4.50000	+	7.79423i	−0.196960	+	0.341144i
$523$	3.50000	+	6.06218i	0.153044	+	0.265081i	0.932345	−	0.361569i	$-0.117759\pi$
$523$	3.50000	+	6.06218i	0.153044	+	0.265081i	−0.779301	+	0.626650i	$0.784426\pi$
$524$	−7.50000	+	12.9904i	−0.327639	+	0.567487i
$525$	−18.0000	−	3.46410i	−0.785584	−	0.151186i
$526$	4.50000	+	7.79423i	0.196209	+	0.339845i
$527$	−12.0000	+	20.7846i	−0.522728	+	0.905392i
$528$	−4.50000	+	2.59808i	−0.195837	+	0.113067i
$529$	−29.0000	−	50.2295i	−1.26087	−	2.18389i
$530$	4.50000	+	7.79423i	0.195468	+	0.338560i
$531$		0			0
$532$	3.50000	−	18.1865i	0.151744	−	0.788486i
$533$	1.50000	−	2.59808i	0.0649722	−	0.112535i
$534$	−4.50000	+	2.59808i	−0.194734	+	0.112430i
$535$	27.0000			1.16731
$536$	4.00000			0.172774
$537$	31.5000	+	18.1865i	1.35933	+	0.784807i
$538$	7.50000	−	12.9904i	0.323348	−	0.560055i
$539$	−16.5000	+	12.9904i	−0.710705	+	0.559535i
$540$	13.5000	+	7.79423i	0.580948	+	0.335410i
$541$	−5.50000	−	9.52628i	−0.236463	−	0.409567i	0.723234	−	0.690604i	$-0.242655\pi$
$541$	−5.50000	−	9.52628i	−0.236463	−	0.409567i	−0.959697	+	0.281037i	$0.909322\pi$
$542$	2.50000	+	4.33013i	0.107384	+	0.185995i
$543$			3.46410i			0.148659i
$544$	1.50000	−	2.59808i	0.0643120	−	0.111392i
$545$	19.5000	+	33.7750i	0.835288	+	1.44676i
$546$	−4.50000	−	0.866025i	−0.192582	−	0.0370625i
$547$	−5.50000	+	9.52628i	−0.235163	+	0.407314i	−0.959320	−	0.282321i	$-0.908896\pi$
$547$	−5.50000	+	9.52628i	−0.235163	+	0.407314i	0.724157	+	0.689635i	$0.242229\pi$
$548$	4.50000	+	7.79423i	0.192230	+	0.332953i
$549$	−6.00000			−0.256074
$550$	−6.00000	+	10.3923i	−0.255841	+	0.443129i
$551$	−21.0000			−0.894630
$552$	−13.5000	−	7.79423i	−0.574598	−	0.331744i
$553$	32.0000	+	27.7128i	1.36078	+	1.17847i
$554$	−0.500000	−	0.866025i	−0.0212430	−	0.0367939i
$555$		−	5.19615i		−	0.220564i
$556$	3.50000	+	6.06218i	0.148433	+	0.257094i
$557$	4.50000	−	7.79423i	0.190671	−	0.330252i	−0.754802	−	0.655953i	$-0.772267\pi$
$557$	4.50000	−	7.79423i	0.190671	−	0.330252i	0.945473	+	0.325701i	$0.105600\pi$
$558$	24.0000			1.01600
$559$	1.00000			0.0422955
$560$	7.50000	−	2.59808i	0.316933	−	0.109789i
$561$		−	15.5885i		−	0.658145i
$562$	−10.5000	+	18.1865i	−0.442916	+	0.767153i
$563$	12.0000			0.505740			0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000			0.505740			0.252870	+	0.967500i	$0.418626\pi$
$564$		0			0
$565$	−27.0000			−1.13590
$566$	4.00000			0.168133
$567$	−18.0000	−	15.5885i	−0.755929	−	0.654654i
$568$	−12.0000			−0.503509
$569$	−18.0000			−0.754599			−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000			−0.754599			−0.377300	+	0.926091i	$0.623147\pi$
$570$			36.3731i			1.52350i
$571$	32.0000			1.33916			0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000			1.33916			0.669579	+	0.742741i	$0.266474\pi$
$572$	−1.50000	+	2.59808i	−0.0627182	+	0.108631i
$573$		0			0
$574$	1.50000	−	7.79423i	0.0626088	−	0.325325i
$575$	−36.0000			−1.50130
$576$	−3.00000			−0.125000
$577$	12.5000	−	21.6506i	0.520382	−	0.901328i	−0.479337	−	0.877631i	$-0.659123\pi$
$577$	12.5000	−	21.6506i	0.520382	−	0.901328i	0.999719	−	0.0236970i	$-0.00754370\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$			24.2487i			1.00774i
$580$	−4.50000	−	7.79423i	−0.186852	−	0.323638i
$581$	−22.5000	+	7.79423i	−0.933457	+	0.323359i
$582$	−1.50000	−	0.866025i	−0.0621770	−	0.0358979i
$583$	−9.00000			−0.372742
$584$	5.50000	−	9.52628i	0.227592	−	0.394200i
$585$	9.00000			0.372104
$586$	−4.50000	−	7.79423i	−0.185893	−	0.321977i
$587$	−1.50000	+	2.59808i	−0.0619116	+	0.107234i	−0.895320	−	0.445424i	$-0.853053\pi$
$587$	−1.50000	+	2.59808i	−0.0619116	+	0.107234i	0.833408	+	0.552658i	$0.186386\pi$
$588$	−12.0000	+	1.73205i	−0.494872	+	0.0714286i
$589$	28.0000	+	48.4974i	1.15372	+	1.99830i
$590$		0			0
$591$			31.1769i			1.28245i
$592$	0.500000	+	0.866025i	0.0205499	+	0.0355934i
$593$	−19.5000	−	33.7750i	−0.800769	−	1.38697i	−0.919111	−	0.394000i	$-0.871091\pi$
$593$	−19.5000	−	33.7750i	−0.800769	−	1.38697i	0.118342	−	0.992973i	$-0.462242\pi$
$594$	−13.5000	+	7.79423i	−0.553912	+	0.319801i
$595$	−4.50000	+	23.3827i	−0.184482	+	0.958597i
$596$	4.50000	−	7.79423i	0.184327	−	0.319264i
$597$	37.5000	+	21.6506i	1.53477	+	0.886102i
$598$	−9.00000			−0.368037
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$	−6.00000	+	3.46410i	−0.244949	+	0.141421i
$601$	12.5000	−	21.6506i	0.509886	−	0.883148i	−0.490049	−	0.871695i	$-0.663021\pi$
$601$	12.5000	−	21.6506i	0.509886	−	0.883148i	0.999934	−	0.0114528i	$-0.00364562\pi$
$602$	2.50000	−	0.866025i	0.101892	−	0.0352966i
$603$	12.0000			0.488678
$604$	3.50000	+	6.06218i	0.142413	+	0.246667i
$605$	3.00000	+	5.19615i	0.121967	+	0.211254i
$606$	−4.50000	+	2.59808i	−0.182800	+	0.105540i
$607$	6.50000	−	11.2583i	0.263827	−	0.456962i	−0.703429	−	0.710766i	$-0.748349\pi$
$607$	6.50000	−	11.2583i	0.263827	−	0.456962i	0.967256	+	0.253804i	$0.0816819\pi$
$608$	−3.50000	−	6.06218i	−0.141944	−	0.245854i
$609$	4.50000	+	12.9904i	0.182349	+	0.526397i
$610$	3.00000	−	5.19615i	0.121466	−	0.210386i
$611$		0			0
$612$	4.50000	−	7.79423i	0.181902	−	0.315063i
$613$	−11.5000	+	19.9186i	−0.464481	+	0.804504i	−0.999178	−	0.0405396i	$-0.987092\pi$
$613$	−11.5000	+	19.9186i	−0.464481	+	0.804504i	0.534697	+	0.845044i	$0.320426\pi$
$614$	28.0000			1.12999
$615$			15.5885i			0.628587i
$616$	−1.50000	+	7.79423i	−0.0604367	+	0.314038i
$617$	22.5000	+	38.9711i	0.905816	+	1.56892i	0.819818	+	0.572624i	$0.194074\pi$
$617$	22.5000	+	38.9711i	0.905816	+	1.56892i	0.0859976	+	0.996295i	$0.472592\pi$
$618$	−19.5000	−	11.2583i	−0.784405	−	0.452876i
$619$	−8.50000	−	14.7224i	−0.341644	−	0.591744i	0.643094	−	0.765787i	$-0.277650\pi$
$619$	−8.50000	−	14.7224i	−0.341644	−	0.591744i	−0.984738	+	0.174042i	$0.944317\pi$
$620$	−12.0000	+	20.7846i	−0.481932	+	0.834730i
$621$	−40.5000	−	23.3827i	−1.62521	−	0.938315i
$622$	24.0000			0.962312
$623$	−1.50000	+	7.79423i	−0.0600962	+	0.312269i
$624$	−1.50000	+	0.866025i	−0.0600481	+	0.0346688i
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	10.0000			0.399680
$627$	−31.5000	−	18.1865i	−1.25799	−	0.726300i
$628$	−22.0000			−0.877896
$629$	−3.00000			−0.119618
$630$	22.5000	−	7.79423i	0.896421	−	0.310530i
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	16.0000			0.636446
$633$	7.50000	−	4.33013i	0.298098	−	0.172107i
$634$	−18.0000			−0.714871
$635$	6.00000	−	10.3923i	0.238103	−	0.412406i
$636$	−4.50000	−	2.59808i	−0.178437	−	0.103020i
$637$	−5.50000	+	4.33013i	−0.217918	+	0.171566i
$638$	9.00000			0.356313
$639$	−36.0000			−1.42414
$640$	1.50000	−	2.59808i	0.0592927	−	0.102698i
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	0.982708	+	0.185164i	$0.0592817\pi$
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	−0.330997	+	0.943632i	$0.607385\pi$
$642$	−13.5000	+	7.79423i	−0.532803	+	0.307614i
$643$	−14.5000	−	25.1147i	−0.571824	−	0.990429i	−0.996379	−	0.0850262i	$-0.972903\pi$
$643$	−14.5000	−	25.1147i	−0.571824	−	0.990429i	0.424555	−	0.905402i	$-0.360431\pi$
$644$	−22.5000	+	7.79423i	−0.886624	+	0.307136i
$645$	−4.50000	+	2.59808i	−0.177187	+	0.102299i
$646$	21.0000			0.826234
$647$	10.5000	−	18.1865i	0.412798	−	0.714986i	−0.582397	−	0.812905i	$-0.697885\pi$
$647$	10.5000	−	18.1865i	0.412798	−	0.714986i	0.995194	+	0.0979182i	$0.0312184\pi$
$648$	−9.00000			−0.353553
$649$		0			0
$650$	−2.00000	+	3.46410i	−0.0784465	+	0.135873i
$651$	24.0000	−	27.7128i	0.940634	−	1.08615i
$652$	9.50000	+	16.4545i	0.372049	+	0.644407i
$653$	−7.50000	+	12.9904i	−0.293498	+	0.508353i	−0.974634	−	0.223803i	$-0.928153\pi$
$653$	−7.50000	+	12.9904i	−0.293498	+	0.508353i	0.681137	+	0.732156i	$0.261486\pi$
$654$	−19.5000	−	11.2583i	−0.762510	−	0.440236i
$655$	−22.5000	−	38.9711i	−0.879148	−	1.52273i
$656$	−1.50000	−	2.59808i	−0.0585652	−	0.101438i
$657$	16.5000	−	28.5788i	0.643726	−	1.11497i
$658$		0			0
$659$	−1.50000	+	2.59808i	−0.0584317	+	0.101207i	−0.893762	−	0.448542i	$-0.851943\pi$
$659$	−1.50000	+	2.59808i	−0.0584317	+	0.101207i	0.835330	+	0.549749i	$0.185277\pi$
$660$		−	15.5885i		−	0.606780i
$661$	−22.0000			−0.855701			−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000			−0.855701			−0.427850	+	0.903850i	$0.640729\pi$
$662$	−8.00000			−0.310929
$663$		−	5.19615i		−	0.201802i
$664$	−4.50000	+	7.79423i	−0.174634	+	0.302475i
$665$	42.0000	+	36.3731i	1.62869	+	1.41049i
$666$	1.50000	+	2.59808i	0.0581238	+	0.100673i
$667$	13.5000	+	23.3827i	0.522722	+	0.905381i
$668$	7.50000	+	12.9904i	0.290184	+	0.502613i
$669$	1.50000	+	0.866025i	0.0579934	+	0.0334825i
$670$	−6.00000	+	10.3923i	−0.231800	+	0.401490i
$671$	3.00000	+	5.19615i	0.115814	+	0.200595i
$672$	−3.00000	+	3.46410i	−0.115728	+	0.133631i
$673$	−17.5000	+	30.3109i	−0.674575	+	1.16840i	0.302017	+	0.953302i	$0.402340\pi$
$673$	−17.5000	+	30.3109i	−0.674575	+	1.16840i	−0.976593	+	0.215096i	$0.930993\pi$
$674$	−6.50000	−	11.2583i	−0.250371	−	0.433655i
$675$	−18.0000	+	10.3923i	−0.692820	+	0.400000i
$676$	6.00000	−	10.3923i	0.230769	−	0.399704i
$677$	−30.0000			−1.15299			−0.576497	−	0.817099i	$-0.695581\pi$
$677$	−30.0000			−1.15299			−0.576497	+	0.817099i	$0.695581\pi$
$678$	13.5000	−	7.79423i	0.518464	−	0.299336i
$679$	−2.50000	+	0.866025i	−0.0959412	+	0.0332350i
$680$	4.50000	+	7.79423i	0.172567	+	0.298895i
$681$	−4.50000	+	2.59808i	−0.172440	+	0.0995585i
$682$	−12.0000	−	20.7846i	−0.459504	−	0.795884i
$683$	4.50000	−	7.79423i	0.172188	−	0.298238i	−0.766997	−	0.641651i	$-0.778250\pi$
$683$	4.50000	−	7.79423i	0.172188	−	0.298238i	0.939184	+	0.343413i	$0.111583\pi$
$684$	−10.5000	−	18.1865i	−0.401478	−	0.695379i
$685$	−27.0000			−1.03162
$686$	−10.0000	+	15.5885i	−0.381802	+	0.595170i
$687$	19.5000	+	11.2583i	0.743971	+	0.429532i
$688$	0.500000	−	0.866025i	0.0190623	−	0.0330169i
$689$	−3.00000			−0.114291
$690$	40.5000	−	23.3827i	1.54181	−	0.890164i
$691$	44.0000			1.67384			0.836919	−	0.547326i	$-0.184354\pi$
$691$	44.0000			1.67384			0.836919	+	0.547326i	$0.184354\pi$
$692$	−6.00000			−0.228086
$693$	−4.50000	+	23.3827i	−0.170941	+	0.888235i
$694$	−12.0000			−0.455514
$695$	−21.0000			−0.796575
$696$	4.50000	+	2.59808i	0.170572	+	0.0984798i
$697$	9.00000			0.340899
$698$	11.5000	−	19.9186i	0.435281	−	0.753930i
$699$	4.50000	−	2.59808i	0.170206	−	0.0982683i
$700$	−2.00000	+	10.3923i	−0.0755929	+	0.392792i
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$	−4.50000	+	2.59808i	−0.169842	+	0.0980581i
$703$	−3.50000	+	6.06218i	−0.132005	+	0.228639i
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$		0			0
$706$	1.50000	+	2.59808i	0.0564532	+	0.0977799i
$707$	−1.50000	+	7.79423i	−0.0564133	+	0.293132i
$708$		0			0
$709$	26.0000			0.976450			0.488225	−	0.872718i	$-0.337644\pi$
$709$	26.0000			0.976450			0.488225	+	0.872718i	$0.337644\pi$
$710$	18.0000	−	31.1769i	0.675528	−	1.17005i
$711$	48.0000			1.80014
$712$	1.50000	+	2.59808i	0.0562149	+	0.0973670i
$713$	36.0000	−	62.3538i	1.34821	−	2.33517i
$714$	−4.50000	−	12.9904i	−0.168408	−	0.486153i
$715$	−4.50000	−	7.79423i	−0.168290	−	0.291488i
$716$	10.5000	−	18.1865i	0.392403	−	0.679663i
$717$	−4.50000	+	2.59808i	−0.168056	+	0.0970269i
$718$	4.50000	+	7.79423i	0.167939	+	0.290878i
$719$	7.50000	+	12.9904i	0.279703	+	0.484459i	0.971311	−	0.237814i	$-0.0764307\pi$
$719$	7.50000	+	12.9904i	0.279703	+	0.484459i	−0.691608	+	0.722273i	$0.743097\pi$
$720$	4.50000	−	7.79423i	0.167705	−	0.290474i
$721$	−32.5000	+	11.2583i	−1.21036	+	0.419282i
$722$	15.0000	−	25.9808i	0.558242	−	0.966904i
$723$	−19.5000	+	11.2583i	−0.725213	+	0.418702i
$724$	2.00000			0.0743294
$725$	12.0000			0.445669
$726$	−3.00000	−	1.73205i	−0.111340	−	0.0642824i
$727$	6.50000	−	11.2583i	0.241072	−	0.417548i	−0.719948	−	0.694028i	$-0.755834\pi$
$727$	6.50000	−	11.2583i	0.241072	−	0.417548i	0.961020	+	0.276479i	$0.0891678\pi$
$728$	−0.500000	+	2.59808i	−0.0185312	+	0.0962911i
$729$	−27.0000			−1.00000
$730$	16.5000	+	28.5788i	0.610692	+	1.05775i
$731$	1.50000	+	2.59808i	0.0554795	+	0.0960933i
$732$			3.46410i			0.128037i
$733$	0.500000	−	0.866025i	0.0184679	−	0.0319874i	−0.856644	−	0.515908i	$-0.827454\pi$
$733$	0.500000	−	0.866025i	0.0184679	−	0.0319874i	0.875112	+	0.483921i	$0.160788\pi$
$734$	8.50000	+	14.7224i	0.313741	+	0.543415i
$735$	13.5000	−	33.7750i	0.497955	−	1.24581i
$736$	−4.50000	+	7.79423i	−0.165872	+	0.287299i
$737$	−6.00000	−	10.3923i	−0.221013	−	0.382805i
$738$	−4.50000	−	7.79423i	−0.165647	−	0.286910i
$739$	−11.5000	+	19.9186i	−0.423034	+	0.732717i	−0.996235	−	0.0866983i	$-0.972368\pi$
$739$	−11.5000	+	19.9186i	−0.423034	+	0.732717i	0.573200	+	0.819415i	$0.305702\pi$
$740$	−3.00000			−0.110282
$741$	−10.5000	−	6.06218i	−0.385727	−	0.222700i
$742$	−7.50000	+	2.59808i	−0.275334	+	0.0953784i
$743$	−10.5000	−	18.1865i	−0.385208	−	0.667199i	0.606590	−	0.795015i	$-0.292537\pi$
$743$	−10.5000	−	18.1865i	−0.385208	−	0.667199i	−0.991798	+	0.127815i	$0.959204\pi$
$744$		−	13.8564i		−	0.508001i
$745$	13.5000	+	23.3827i	0.494602	+	0.856675i
$746$	−6.50000	+	11.2583i	−0.237982	+	0.412197i
$747$	−13.5000	+	23.3827i	−0.493939	+	0.855528i
$748$	−9.00000			−0.329073
$749$	−4.50000	+	23.3827i	−0.164426	+	0.854385i
$750$			5.19615i			0.189737i
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	−0.722718	−	0.691143i	$-0.757107\pi$
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	0.959906	+	0.280321i	$0.0904408\pi$
$752$		0			0
$753$			20.7846i			0.757433i
$754$	3.00000			0.109254
$755$	−21.0000			−0.764268
$756$	−9.00000	+	10.3923i	−0.327327	+	0.377964i
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	28.0000			1.01701
$759$			46.7654i			1.69748i
$760$	21.0000			0.761750
$761$	22.5000	−	38.9711i	0.815624	−	1.41270i	−0.0932544	−	0.995642i	$-0.529727\pi$
$761$	22.5000	−	38.9711i	0.815624	−	1.41270i	0.908879	−	0.417061i	$-0.136940\pi$
$762$			6.92820i			0.250982i
$763$	−32.5000	+	11.2583i	−1.17658	+	0.407579i
$764$		0			0
$765$	13.5000	+	23.3827i	0.488094	+	0.845403i
$766$	7.50000	−	12.9904i	0.270986	−	0.469362i
$767$		0			0
$768$			1.73205i			0.0625000i
$769$	−11.5000	−	19.9186i	−0.414701	−	0.718283i	0.580696	−	0.814120i	$-0.302780\pi$
$769$	−11.5000	−	19.9186i	−0.414701	−	0.718283i	−0.995397	+	0.0958377i	$0.969447\pi$
$770$	−18.0000	−	15.5885i	−0.648675	−	0.561769i
$771$	31.5000	+	18.1865i	1.13444	+	0.654972i
$772$	14.0000			0.503871
$773$	−13.5000	+	23.3827i	−0.485561	+	0.841017i	−0.999862	−	0.0165929i	$-0.994718\pi$
$773$	−13.5000	+	23.3827i	−0.485561	+	0.841017i	0.514301	+	0.857610i	$0.328051\pi$
$774$	1.50000	−	2.59808i	0.0539164	−	0.0933859i
$775$	−16.0000	−	27.7128i	−0.574737	−	0.995474i
$776$	−0.500000	+	0.866025i	−0.0179490	+	0.0310885i
$777$	4.50000	+	0.866025i	0.161437	+	0.0310685i
$778$	13.5000	+	23.3827i	0.483998	+	0.838310i
$779$	10.5000	−	18.1865i	0.376202	−	0.651600i
$780$		−	5.19615i		−	0.186052i
$781$	18.0000	+	31.1769i	0.644091	+	1.11560i
$782$	−13.5000	−	23.3827i	−0.482759	−	0.836163i
$783$	13.5000	+	7.79423i	0.482451	+	0.278543i
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$	33.0000	−	57.1577i	1.17782	−	2.04004i
$786$	22.5000	+	12.9904i	0.802548	+	0.463352i
$787$	−28.0000			−0.998092			−0.499046	−	0.866575i	$-0.666316\pi$
$787$	−28.0000			−0.998092			−0.499046	+	0.866575i	$0.666316\pi$
$788$	18.0000			0.641223
$789$	13.5000	−	7.79423i	0.480613	−	0.277482i
$790$	−24.0000	+	41.5692i	−0.853882	+	1.47897i
$791$	4.50000	−	23.3827i	0.160002	−	0.831393i
$792$	4.50000	+	7.79423i	0.159901	+	0.276956i
$793$	1.00000	+	1.73205i	0.0355110	+	0.0615069i
$794$	−6.50000	−	11.2583i	−0.230676	−	0.399543i
$795$	13.5000	−	7.79423i	0.478796	−	0.276433i
$796$	12.5000	−	21.6506i	0.443051	−	0.767386i
$797$	10.5000	+	18.1865i	0.371929	+	0.644200i	0.989862	−	0.142031i	$-0.0453631\pi$
$797$	10.5000	+	18.1865i	0.371929	+	0.644200i	−0.617933	+	0.786231i	$0.712030\pi$
$798$	−31.5000	−	6.06218i	−1.11509	−	0.214599i
$799$		0			0
$800$	2.00000	+	3.46410i	0.0707107	+	0.122474i
$801$	4.50000	+	7.79423i	0.159000	+	0.275396i
$802$	13.5000	−	23.3827i	0.476702	−	0.825671i
$803$	−33.0000			−1.16454
$804$		−	6.92820i		−	0.244339i
$805$	13.5000	−	70.1481i	0.475812	−	2.47239i
$806$	−4.00000	−	6.92820i	−0.140894	−	0.244036i
$807$	−22.5000	−	12.9904i	−0.792038	−	0.457283i
$808$	1.50000	+	2.59808i	0.0527698	+	0.0914000i
$809$	16.5000	−	28.5788i	0.580109	−	1.00478i	−0.415357	−	0.909659i	$-0.636343\pi$
$809$	16.5000	−	28.5788i	0.580109	−	1.00478i	0.995466	−	0.0951198i	$-0.0303234\pi$
$810$	13.5000	−	23.3827i	0.474342	−	0.821584i
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	7.50000	−	2.59808i	0.263198	−	0.0911746i
$813$	7.50000	−	4.33013i	0.263036	−	0.151864i
$814$	1.50000	−	2.59808i	0.0525750	−	0.0910625i
$815$	−57.0000			−1.99662
$816$	−4.50000	−	2.59808i	−0.157532	−	0.0909509i
$817$	7.00000			0.244899
$818$	34.0000			1.18878
$819$	−1.50000	+	7.79423i	−0.0524142	+	0.272352i
$820$	9.00000			0.314294
$821$	−42.0000			−1.46581			−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000			−1.46581			−0.732905	+	0.680331i	$0.761836\pi$
$822$	13.5000	−	7.79423i	0.470867	−	0.271855i
$823$	−40.0000			−1.39431			−0.697156	−	0.716919i	$-0.745552\pi$
$823$	−40.0000			−1.39431			−0.697156	+	0.716919i	$0.745552\pi$
$824$	−6.50000	+	11.2583i	−0.226438	+	0.392203i
$825$	18.0000	+	10.3923i	0.626680	+	0.361814i
$826$		0			0
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$	−13.5000	+	23.3827i	−0.469157	+	0.812605i
$829$	−5.50000	+	9.52628i	−0.191023	+	0.330861i	−0.945589	−	0.325362i	$-0.894514\pi$
$829$	−5.50000	+	9.52628i	−0.191023	+	0.330861i	0.754567	+	0.656223i	$0.227847\pi$
$830$	−13.5000	−	23.3827i	−0.468592	−	0.811625i
$831$	−1.50000	+	0.866025i	−0.0520344	+	0.0300421i
$832$	0.500000	+	0.866025i	0.0173344	+	0.0300240i
$833$	−19.5000	−	7.79423i	−0.675635	−	0.270054i
$834$	10.5000	−	6.06218i	0.363585	−	0.209916i
$835$	−45.0000			−1.55729
$836$	−10.5000	+	18.1865i	−0.363150	+	0.628994i
$837$		−	41.5692i		−	1.43684i
$838$	4.50000	+	7.79423i	0.155450	+	0.269247i
$839$	−7.50000	+	12.9904i	−0.258929	+	0.448478i	−0.965955	−	0.258709i	$-0.916703\pi$
$839$	−7.50000	+	12.9904i	−0.258929	+	0.448478i	0.707026	+	0.707187i	$0.250036\pi$
$840$	−4.50000	−	12.9904i	−0.155265	−	0.448211i
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	17.5000	−	30.3109i	0.603090	−	1.04458i
$843$	31.5000	+	18.1865i	1.08492	+	0.626377i
$844$	−2.50000	−	4.33013i	−0.0860535	−	0.149049i
$845$	18.0000	+	31.1769i	0.619219	+	1.07252i
$846$		0			0
$847$	−5.00000	+	1.73205i	−0.171802	+	0.0595140i
$848$	−1.50000	+	2.59808i	−0.0515102	+	0.0892183i
$849$		−	6.92820i		−	0.237775i
$850$	−12.0000			−0.411597
$851$	9.00000			0.308516
$852$			20.7846i			0.712069i
$853$	0.500000	−	0.866025i	0.0171197	−	0.0296521i	−0.857339	−	0.514753i	$-0.827884\pi$
$853$	0.500000	−	0.866025i	0.0171197	−	0.0296521i	0.874458	+	0.485101i	$0.161217\pi$
$854$	4.00000	+	3.46410i	0.136877	+	0.118539i
$855$	63.0000			2.15455
$856$	4.50000	+	7.79423i	0.153807	+	0.266401i
$857$	−1.50000	−	2.59808i	−0.0512390	−	0.0887486i	0.839268	−	0.543718i	$-0.182984\pi$
$857$	−1.50000	−	2.59808i	−0.0512390	−	0.0887486i	−0.890507	+	0.454969i	$0.849650\pi$
$858$	4.50000	+	2.59808i	0.153627	+	0.0886969i
$859$	12.5000	−	21.6506i	0.426494	−	0.738710i	−0.570064	−	0.821600i	$-0.693082\pi$
$859$	12.5000	−	21.6506i	0.426494	−	0.738710i	0.996559	+	0.0828900i	$0.0264150\pi$
$860$	1.50000	+	2.59808i	0.0511496	+	0.0885937i
$861$	−13.5000	−	2.59808i	−0.460079	−	0.0885422i
$862$	13.5000	−	23.3827i	0.459812	−	0.796417i
$863$	25.5000	+	44.1673i	0.868030	+	1.50347i	0.864007	+	0.503480i	$0.167947\pi$
$863$	25.5000	+	44.1673i	0.868030	+	1.50347i	0.00402340	+	0.999992i	$0.498719\pi$
$864$			5.19615i			0.176777i
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$	−2.00000			−0.0679628
$867$	−12.0000	+	6.92820i	−0.407541	+	0.235294i
$868$	−16.0000	−	13.8564i	−0.543075	−	0.470317i
$869$	−24.0000	−	41.5692i	−0.814144	−	1.41014i
$870$	−13.5000	+	7.79423i	−0.457693	+	0.264249i
$871$	−2.00000	−	3.46410i	−0.0677674	−	0.117377i
$872$	−6.50000	+	11.2583i	−0.220118	+	0.381255i
$873$	−1.50000	+	2.59808i	−0.0507673	+	0.0879316i
$874$	−63.0000			−2.13101
$875$	6.00000	+	5.19615i	0.202837	+	0.175662i
$876$	−16.5000	−	9.52628i	−0.557483	−	0.321863i
$877$	−23.5000	+	40.7032i	−0.793539	+	1.37445i	0.130224	+	0.991485i	$0.458430\pi$
$877$	−23.5000	+	40.7032i	−0.793539	+	1.37445i	−0.923763	+	0.382965i	$0.874903\pi$
$878$	−8.00000			−0.269987
$879$	−13.5000	+	7.79423i	−0.455344	+	0.262893i
$880$	−9.00000			−0.303390
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$	3.00000	+	20.7846i	0.101015	+	0.699854i
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	−3.00000			−0.100901
$885$		0			0
$886$	−36.0000			−1.20944
$887$	16.5000	−	28.5788i	0.554016	−	0.959583i	−0.443964	−	0.896045i	$-0.646428\pi$
$887$	16.5000	−	28.5788i	0.554016	−	0.959583i	0.997979	−	0.0635387i	$-0.0202386\pi$
$888$	1.50000	−	0.866025i	0.0503367	−	0.0290619i
$889$	8.00000	+	6.92820i	0.268311	+	0.232364i
$890$	−9.00000			−0.301681
$891$	13.5000	+	23.3827i	0.452267	+	0.783349i
$892$	0.500000	−	0.866025i	0.0167412	−	0.0289967i
$893$		0			0
$894$	−13.5000	−	7.79423i	−0.451508	−	0.260678i
$895$	31.5000	+	54.5596i	1.05293	+	1.82373i
$896$	2.00000	+	1.73205i	0.0668153	+	0.0578638i
$897$			15.5885i			0.520483i
$898$	−6.00000			−0.200223
$899$	−12.0000	+	20.7846i	−0.400222	+	0.693206i
$900$	6.00000	+	10.3923i	0.200000	+	0.346410i
$901$	−4.50000	−	7.79423i	−0.149917	−	0.259663i
$902$	−4.50000	+	7.79423i	−0.149834	+	0.259519i
$903$	−1.50000	−	4.33013i	−0.0499169	−	0.144098i
$904$	−4.50000	−	7.79423i	−0.149668	−	0.259232i
$905$	−3.00000	+	5.19615i	−0.0997234	+	0.172726i
$906$	10.5000	−	6.06218i	0.348839	−	0.201402i
$907$	21.5000	+	37.2391i	0.713896	+	1.23650i	0.963384	+	0.268126i	$0.0864043\pi$
$907$	21.5000	+	37.2391i	0.713896	+	1.23650i	−0.249488	+	0.968378i	$0.580262\pi$
$908$	1.50000	+	2.59808i	0.0497792	+	0.0862202i
$909$	4.50000	+	7.79423i	0.149256	+	0.258518i
$910$	−6.00000	−	5.19615i	−0.198898	−	0.172251i
$911$	−19.5000	+	33.7750i	−0.646064	+	1.11902i	0.337991	+	0.941149i	$0.390253\pi$
$911$	−19.5000	+	33.7750i	−0.646064	+	1.11902i	−0.984055	+	0.177866i	$0.943081\pi$
$912$	−10.5000	+	6.06218i	−0.347690	+	0.200739i
$913$	27.0000			0.893570
$914$	10.0000			0.330771
$915$	−9.00000	−	5.19615i	−0.297531	−	0.171780i
$916$	6.50000	−	11.2583i	0.214766	−	0.371986i
$917$	37.5000	−	12.9904i	1.23836	−	0.428980i
$918$	−13.5000	−	7.79423i	−0.445566	−	0.257248i
$919$	−26.5000	−	45.8993i	−0.874154	−	1.51408i	−0.857661	−	0.514216i	$-0.828083\pi$
$919$	−26.5000	−	45.8993i	−0.874154	−	1.51408i	−0.0164935	−	0.999864i	$-0.505250\pi$
$920$	−13.5000	−	23.3827i	−0.445082	−	0.770904i
$921$		−	48.4974i		−	1.59804i
$922$	−4.50000	+	7.79423i	−0.148200	+	0.256689i
$923$	6.00000	+	10.3923i	0.197492	+	0.342067i
$924$	13.5000	+	2.59808i	0.444117	+	0.0854704i
$925$	2.00000	−	3.46410i	0.0657596	−	0.113899i
$926$	20.5000	+	35.5070i	0.673672	+	1.16683i
$927$	−19.5000	+	33.7750i	−0.640464	+	1.10932i
$928$	1.50000	−	2.59808i	0.0492399	−	0.0852860i
$929$	18.0000			0.590561			0.295280	−	0.955411i	$-0.404587\pi$
$929$	18.0000			0.590561			0.295280	+	0.955411i	$0.404587\pi$
$930$	36.0000	+	20.7846i	1.18049	+	0.681554i
$931$	−38.5000	+	30.3109i	−1.26179	+	0.993399i
$932$	−1.50000	−	2.59808i	−0.0491341	−	0.0851028i
$933$		−	41.5692i		−	1.36092i
$934$	−1.50000	−	2.59808i	−0.0490815	−	0.0850117i
$935$	13.5000	−	23.3827i	0.441497	−	0.764696i
$936$	1.50000	+	2.59808i	0.0490290	+	0.0849208i
$937$	26.0000			0.849383			0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000			0.849383			0.424691	+	0.905338i	$0.360383\pi$
$938$	−8.00000	−	6.92820i	−0.261209	−	0.226214i
$939$		−	17.3205i		−	0.565233i
$940$		0			0
$941$	−6.00000			−0.195594			−0.0977972	−	0.995206i	$-0.531180\pi$
$941$	−6.00000			−0.195594			−0.0977972	+	0.995206i	$0.531180\pi$
$942$			38.1051i			1.24153i
$943$	−27.0000			−0.879241
$944$		0			0
$945$	−13.5000	−	38.9711i	−0.439155	−	1.26773i
$946$	−3.00000			−0.0975384
$947$	12.0000			0.389948			0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000			0.389948			0.194974	+	0.980808i	$0.437538\pi$
$948$		−	27.7128i		−	0.900070i
$949$	−11.0000			−0.357075
$950$	−14.0000	+	24.2487i	−0.454220	+	0.786732i
$951$			31.1769i			1.01098i
$952$	−7.50000	+	2.59808i	−0.243076	+	0.0842041i
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$	−4.50000	+	7.79423i	−0.145693	+	0.252347i
$955$		0			0
$956$	1.50000	+	2.59808i	0.0485135	+	0.0840278i
$957$		−	15.5885i		−	0.503903i
$958$	−1.50000	−	2.59808i	−0.0484628	−	0.0839400i
$959$	4.50000	−	23.3827i	0.145313	−	0.755066i
$960$	−4.50000	−	2.59808i	−0.145237	−	0.0838525i
$961$	33.0000			1.06452
$962$	0.500000	−	0.866025i	0.0161206	−	0.0279218i
$963$	13.5000	+	23.3827i	0.435031	+	0.753497i
$964$	6.50000	+	11.2583i	0.209351	+	0.362606i
$965$	−21.0000	+	36.3731i	−0.676014	+	1.17089i
$966$	13.5000	+	38.9711i	0.434355	+	1.25388i
$967$	−20.5000	−	35.5070i	−0.659236	−	1.14183i	−0.980814	−	0.194946i	$-0.937547\pi$
$967$	−20.5000	−	35.5070i	−0.659236	−	1.14183i	0.321578	−	0.946883i	$-0.395787\pi$
$968$	−1.00000	+	1.73205i	−0.0321412	+	0.0556702i
$969$		−	36.3731i		−	1.16847i
$970$	−1.50000	−	2.59808i	−0.0481621	−	0.0834192i
$971$	−16.5000	−	28.5788i	−0.529510	−	0.917139i	−0.999408	−	0.0344175i	$-0.989042\pi$
$971$	−16.5000	−	28.5788i	−0.529510	−	0.917139i	0.469897	−	0.882721i	$-0.344291\pi$
$972$			15.5885i			0.500000i
$973$	3.50000	−	18.1865i	0.112205	−	0.583033i
$974$	−12.5000	+	21.6506i	−0.400526	+	0.693731i
$975$	6.00000	+	3.46410i	0.192154	+	0.110940i
$976$	2.00000			0.0640184
$977$	−30.0000			−0.959785			−0.479893	−	0.877327i	$-0.659324\pi$
$977$	−30.0000			−0.959785			−0.479893	+	0.877327i	$0.659324\pi$
$978$	28.5000	−	16.4545i	0.911330	−	0.526156i
$979$	4.50000	−	7.79423i	0.143821	−	0.249105i
$980$	−19.5000	−	7.79423i	−0.622905	−	0.248978i
$981$	−19.5000	+	33.7750i	−0.622587	+	1.07835i
$982$	10.5000	+	18.1865i	0.335068	+	0.580356i
$983$	7.50000	+	12.9904i	0.239213	+	0.414329i	0.960489	−	0.278319i	$-0.0897773\pi$
$983$	7.50000	+	12.9904i	0.239213	+	0.414329i	−0.721276	+	0.692648i	$0.756444\pi$
$984$	−4.50000	+	2.59808i	−0.143455	+	0.0828236i
$985$	−27.0000	+	46.7654i	−0.860292	+	1.49007i
$986$	4.50000	+	7.79423i	0.143309	+	0.248219i
$987$		0			0
$988$	−3.50000	+	6.06218i	−0.111350	+	0.192864i
$989$	−4.50000	−	7.79423i	−0.143092	−	0.247842i
$990$	−27.0000			−0.858116
$991$	12.5000	−	21.6506i	0.397076	−	0.687755i	−0.596288	−	0.802771i	$-0.703358\pi$
$991$	12.5000	−	21.6506i	0.397076	−	0.687755i	0.993364	+	0.115015i	$0.0366917\pi$
$992$	−8.00000			−0.254000
$993$			13.8564i			0.439720i
$994$	24.0000	+	20.7846i	0.761234	+	0.659248i
$995$	37.5000	+	64.9519i	1.18883	+	2.05911i
$996$	13.5000	+	7.79423i	0.427764	+	0.246970i
$997$	6.50000	+	11.2583i	0.205857	+	0.356555i	0.950405	−	0.311014i	$-0.100668\pi$
$997$	6.50000	+	11.2583i	0.205857	+	0.356555i	−0.744548	+	0.667568i	$0.767335\pi$
$998$	−12.5000	+	21.6506i	−0.395681	+	0.685339i
$999$	4.50000	−	2.59808i	0.142374	−	0.0821995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.e.a.25.1	✓	2
3.2	odd	2		378.2.e.b.235.1		2
4.3	odd	2		1008.2.q.a.529.1		2
7.2	even	3		126.2.h.b.79.1	yes	2
7.3	odd	6		882.2.f.g.295.1		2
7.4	even	3		882.2.f.i.295.1		2
7.5	odd	6		882.2.h.i.79.1		2
7.6	odd	2		882.2.e.c.655.1		2
9.2	odd	6		1134.2.g.c.487.1		2
9.4	even	3		126.2.h.b.67.1	yes	2
9.5	odd	6		378.2.h.a.361.1		2
9.7	even	3		1134.2.g.e.487.1		2
12.11	even	2		3024.2.q.f.2881.1		2
21.2	odd	6		378.2.h.a.289.1		2
21.5	even	6		2646.2.h.d.667.1		2
21.11	odd	6		2646.2.f.d.883.1		2
21.17	even	6		2646.2.f.a.883.1		2
21.20	even	2		2646.2.e.g.2125.1		2
28.23	odd	6		1008.2.t.f.961.1		2
36.23	even	6		3024.2.t.a.1873.1		2
36.31	odd	6		1008.2.t.f.193.1		2
63.2	odd	6		1134.2.g.c.163.1		2
63.4	even	3		882.2.f.i.589.1		2
63.5	even	6		2646.2.e.g.1549.1		2
63.11	odd	6		7938.2.a.t.1.1		1
63.13	odd	6		882.2.h.i.67.1		2
63.16	even	3		1134.2.g.e.163.1		2
63.23	odd	6		378.2.e.b.37.1		2
63.25	even	3		7938.2.a.m.1.1		1
63.31	odd	6		882.2.f.g.589.1		2
63.32	odd	6		2646.2.f.d.1765.1		2
63.38	even	6		7938.2.a.be.1.1		1
63.40	odd	6		882.2.e.c.373.1		2
63.41	even	6		2646.2.h.d.361.1		2
63.52	odd	6		7938.2.a.b.1.1		1
63.58	even	3	inner	126.2.e.a.121.1	yes	2
63.59	even	6		2646.2.f.a.1765.1		2
84.23	even	6		3024.2.t.a.289.1		2
252.23	even	6		3024.2.q.f.2305.1		2
252.247	odd	6		1008.2.q.a.625.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.a.25.1	✓	2	1.1	even	1	trivial
126.2.e.a.121.1	yes	2	63.58	even	3	inner
126.2.h.b.67.1	yes	2	9.4	even	3
126.2.h.b.79.1	yes	2	7.2	even	3
378.2.e.b.37.1		2	63.23	odd	6
378.2.e.b.235.1		2	3.2	odd	2
378.2.h.a.289.1		2	21.2	odd	6
378.2.h.a.361.1		2	9.5	odd	6
882.2.e.c.373.1		2	63.40	odd	6
882.2.e.c.655.1		2	7.6	odd	2
882.2.f.g.295.1		2	7.3	odd	6
882.2.f.g.589.1		2	63.31	odd	6
882.2.f.i.295.1		2	7.4	even	3
882.2.f.i.589.1		2	63.4	even	3
882.2.h.i.67.1		2	63.13	odd	6
882.2.h.i.79.1		2	7.5	odd	6
1008.2.q.a.529.1		2	4.3	odd	2
1008.2.q.a.625.1		2	252.247	odd	6
1008.2.t.f.193.1		2	36.31	odd	6
1008.2.t.f.961.1		2	28.23	odd	6
1134.2.g.c.163.1		2	63.2	odd	6
1134.2.g.c.487.1		2	9.2	odd	6
1134.2.g.e.163.1		2	63.16	even	3
1134.2.g.e.487.1		2	9.7	even	3
2646.2.e.g.1549.1		2	63.5	even	6
2646.2.e.g.2125.1		2	21.20	even	2
2646.2.f.a.883.1		2	21.17	even	6
2646.2.f.a.1765.1		2	63.59	even	6
2646.2.f.d.883.1		2	21.11	odd	6
2646.2.f.d.1765.1		2	63.32	odd	6
2646.2.h.d.361.1		2	63.41	even	6
2646.2.h.d.667.1		2	21.5	even	6
3024.2.q.f.2305.1		2	252.23	even	6
3024.2.q.f.2881.1		2	12.11	even	2
3024.2.t.a.289.1		2	84.23	even	6
3024.2.t.a.1873.1		2	36.23	even	6
7938.2.a.b.1.1		1	63.52	odd	6
7938.2.a.m.1.1		1	63.25	even	3
7938.2.a.t.1.1		1	63.11	odd	6
7938.2.a.be.1.1		1	63.38	even	6

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.73205i q^{3} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} -1.73205i q^{6} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.73205i q^{3} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} -1.73205i q^{6} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} -3.00000 q^{9} +(1.50000 - 2.59808i) q^{10} +(1.50000 + 2.59808i) q^{11} +1.73205i q^{12} +(0.500000 + 0.866025i) q^{13} +(2.00000 + 1.73205i) q^{14} +(-4.50000 - 2.59808i) q^{15} +1.00000 q^{16} +(-1.50000 + 2.59808i) q^{17} +3.00000 q^{18} +(3.50000 + 6.06218i) q^{19} +(-1.50000 + 2.59808i) q^{20} +(3.00000 - 3.46410i) q^{21} +(-1.50000 - 2.59808i) q^{22} +(4.50000 - 7.79423i) q^{23} -1.73205i q^{24} +(-2.00000 - 3.46410i) q^{25} +(-0.500000 - 0.866025i) q^{26} -5.19615i q^{27} +(-2.00000 - 1.73205i) q^{28} +(-1.50000 + 2.59808i) q^{29} +(4.50000 + 2.59808i) q^{30} +8.00000 q^{31} -1.00000 q^{32} +(-4.50000 + 2.59808i) q^{33} +(1.50000 - 2.59808i) q^{34} +(7.50000 - 2.59808i) q^{35} -3.00000 q^{36} +(0.500000 + 0.866025i) q^{37} +(-3.50000 - 6.06218i) q^{38} +(-1.50000 + 0.866025i) q^{39} +(1.50000 - 2.59808i) q^{40} +(-1.50000 - 2.59808i) q^{41} +(-3.00000 + 3.46410i) q^{42} +(0.500000 - 0.866025i) q^{43} +(1.50000 + 2.59808i) q^{44} +(4.50000 - 7.79423i) q^{45} +(-4.50000 + 7.79423i) q^{46} +1.73205i q^{48} +(1.00000 + 6.92820i) q^{49} +(2.00000 + 3.46410i) q^{50} +(-4.50000 - 2.59808i) q^{51} +(0.500000 + 0.866025i) q^{52} +(-1.50000 + 2.59808i) q^{53} +5.19615i q^{54} -9.00000 q^{55} +(2.00000 + 1.73205i) q^{56} +(-10.5000 + 6.06218i) q^{57} +(1.50000 - 2.59808i) q^{58} +(-4.50000 - 2.59808i) q^{60} +2.00000 q^{61} -8.00000 q^{62} +(6.00000 + 5.19615i) q^{63} +1.00000 q^{64} -3.00000 q^{65} +(4.50000 - 2.59808i) q^{66} -4.00000 q^{67} +(-1.50000 + 2.59808i) q^{68} +(13.5000 + 7.79423i) q^{69} +(-7.50000 + 2.59808i) q^{70} +12.0000 q^{71} +3.00000 q^{72} +(-5.50000 + 9.52628i) q^{73} +(-0.500000 - 0.866025i) q^{74} +(6.00000 - 3.46410i) q^{75} +(3.50000 + 6.06218i) q^{76} +(1.50000 - 7.79423i) q^{77} +(1.50000 - 0.866025i) q^{78} -16.0000 q^{79} +(-1.50000 + 2.59808i) q^{80} +9.00000 q^{81} +(1.50000 + 2.59808i) q^{82} +(4.50000 - 7.79423i) q^{83} +(3.00000 - 3.46410i) q^{84} +(-4.50000 - 7.79423i) q^{85} +(-0.500000 + 0.866025i) q^{86} +(-4.50000 - 2.59808i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(-1.50000 - 2.59808i) q^{89} +(-4.50000 + 7.79423i) q^{90} +(0.500000 - 2.59808i) q^{91} +(4.50000 - 7.79423i) q^{92} +13.8564i q^{93} -21.0000 q^{95} -1.73205i q^{96} +(0.500000 - 0.866025i) q^{97} +(-1.00000 - 6.92820i) q^{98} +(-4.50000 - 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} - 3 q^{5} - 4 q^{7} - 2 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 - 3 * q^5 - 4 * q^7 - 2 * q^8 - 6 * q^9	\( 2 q - 2 q^{2} + 2 q^{4} - 3 q^{5} - 4 q^{7} - 2 q^{8} - 6 q^{9} + 3 q^{10} + 3 q^{11} + q^{13} + 4 q^{14} - 9 q^{15} + 2 q^{16} - 3 q^{17} + 6 q^{18} + 7 q^{19} - 3 q^{20} + 6 q^{21} - 3 q^{22} + 9 q^{23} - 4 q^{25} - q^{26} - 4 q^{28} - 3 q^{29} + 9 q^{30} + 16 q^{31} - 2 q^{32} - 9 q^{33} + 3 q^{34} + 15 q^{35} - 6 q^{36} + q^{37} - 7 q^{38} - 3 q^{39} + 3 q^{40} - 3 q^{41} - 6 q^{42} + q^{43} + 3 q^{44} + 9 q^{45} - 9 q^{46} + 2 q^{49} + 4 q^{50} - 9 q^{51} + q^{52} - 3 q^{53} - 18 q^{55} + 4 q^{56} - 21 q^{57} + 3 q^{58} - 9 q^{60} + 4 q^{61} - 16 q^{62} + 12 q^{63} + 2 q^{64} - 6 q^{65} + 9 q^{66} - 8 q^{67} - 3 q^{68} + 27 q^{69} - 15 q^{70} + 24 q^{71} + 6 q^{72} - 11 q^{73} - q^{74} + 12 q^{75} + 7 q^{76} + 3 q^{77} + 3 q^{78} - 32 q^{79} - 3 q^{80} + 18 q^{81} + 3 q^{82} + 9 q^{83} + 6 q^{84} - 9 q^{85} - q^{86} - 9 q^{87} - 3 q^{88} - 3 q^{89} - 9 q^{90} + q^{91} + 9 q^{92} - 42 q^{95} + q^{97} - 2 q^{98} - 9 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 - 3 * q^5 - 4 * q^7 - 2 * q^8 - 6 * q^9 + 3 * q^10 + 3 * q^11 + q^13 + 4 * q^14 - 9 * q^15 + 2 * q^16 - 3 * q^17 + 6 * q^18 + 7 * q^19 - 3 * q^20 + 6 * q^21 - 3 * q^22 + 9 * q^23 - 4 * q^25 - q^26 - 4 * q^28 - 3 * q^29 + 9 * q^30 + 16 * q^31 - 2 * q^32 - 9 * q^33 + 3 * q^34 + 15 * q^35 - 6 * q^36 + q^37 - 7 * q^38 - 3 * q^39 + 3 * q^40 - 3 * q^41 - 6 * q^42 + q^43 + 3 * q^44 + 9 * q^45 - 9 * q^46 + 2 * q^49 + 4 * q^50 - 9 * q^51 + q^52 - 3 * q^53 - 18 * q^55 + 4 * q^56 - 21 * q^57 + 3 * q^58 - 9 * q^60 + 4 * q^61 - 16 * q^62 + 12 * q^63 + 2 * q^64 - 6 * q^65 + 9 * q^66 - 8 * q^67 - 3 * q^68 + 27 * q^69 - 15 * q^70 + 24 * q^71 + 6 * q^72 - 11 * q^73 - q^74 + 12 * q^75 + 7 * q^76 + 3 * q^77 + 3 * q^78 - 32 * q^79 - 3 * q^80 + 18 * q^81 + 3 * q^82 + 9 * q^83 + 6 * q^84 - 9 * q^85 - q^86 - 9 * q^87 - 3 * q^88 - 3 * q^89 - 9 * q^90 + q^91 + 9 * q^92 - 42 * q^95 + q^97 - 2 * q^98 - 9 * q^99

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