LMFDB - Embedded newform 126.2.h.b.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(67,126)]

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([2, 4]))

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

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

chi := DirichletCharacter("126.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.h (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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	126.67
Dual form			126.2.h.b.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +1.73205i q^{6} +(2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +1.73205i q^{6} +(2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(1.50000 - 2.59808i) q^{10} -3.00000 q^{11} +(1.50000 + 0.866025i) q^{12} +(0.500000 - 0.866025i) q^{13} +(0.500000 - 2.59808i) q^{14} +(-4.50000 + 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-1.50000 - 2.59808i) 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} -9.00000 q^{23} +(1.50000 - 0.866025i) q^{24} +4.00000 q^{25} +(-0.500000 - 0.866025i) q^{26} +5.19615i q^{27} +(-2.00000 - 1.73205i) q^{28} +(-1.50000 - 2.59808i) q^{29} +5.19615i q^{30} +(-4.00000 - 6.92820i) q^{31} +(0.500000 + 0.866025i) 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} +7.00000 q^{38} +1.73205i q^{39} -3.00000 q^{40} +(-1.50000 + 2.59808i) q^{41} +(1.50000 + 4.33013i) 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} +(5.50000 - 4.33013i) q^{49} +(2.00000 - 3.46410i) q^{50} -5.19615i q^{51} -1.00000 q^{52} +(-1.50000 + 2.59808i) q^{53} +(4.50000 + 2.59808i) q^{54} -9.00000 q^{55} +(-2.50000 + 0.866025i) q^{56} +(-10.5000 - 6.06218i) q^{57} -3.00000 q^{58} +(4.50000 + 2.59808i) q^{60} +(-1.00000 + 1.73205i) q^{61} -8.00000 q^{62} +(1.50000 - 7.79423i) q^{63} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{65} -5.19615i q^{66} +(2.00000 + 3.46410i) q^{67} +3.00000 q^{68} +(13.5000 - 7.79423i) q^{69} +(1.50000 - 7.79423i) q^{70} +12.0000 q^{71} +(-1.50000 + 2.59808i) q^{72} +(-5.50000 + 9.52628i) q^{73} +1.00000 q^{74} +(-6.00000 + 3.46410i) q^{75} +(3.50000 - 6.06218i) q^{76} +(-7.50000 + 2.59808i) q^{77} +(1.50000 + 0.866025i) q^{78} +(8.00000 - 13.8564i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(1.50000 + 2.59808i) q^{82} +(4.50000 + 7.79423i) q^{83} +(4.50000 + 0.866025i) q^{84} +(-4.50000 + 7.79423i) q^{85} +1.00000 q^{86} +(4.50000 + 2.59808i) q^{87} +3.00000 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} +(12.0000 + 6.92820i) q^{93} +(10.5000 + 18.1865i) q^{95} +(-1.50000 - 0.866025i) 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 + q^{2} - 3 q^{3} - q^{4} + 6 q^{5} + 5 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + q^2 - 3 * q^3 - q^4 + 6 * q^5 + 5 * q^7 - 2 * q^8 + 3 * q^9	$ 2 q + q^{2} - 3 q^{3} - q^{4} + 6 q^{5} + 5 q^{7} - 2 q^{8} + 3 q^{9} + 3 q^{10} - 6 q^{11} + 3 q^{12} + q^{13} + q^{14} - 9 q^{15} - q^{16} - 3 q^{17} - 3 q^{18} + 7 q^{19} - 3 q^{20} - 6 q^{21} - 3 q^{22} - 18 q^{23} + 3 q^{24} + 8 q^{25} - q^{26} - 4 q^{28} - 3 q^{29} - 8 q^{31} + q^{32} + 9 q^{33} + 3 q^{34} + 15 q^{35} - 6 q^{36} + q^{37} + 14 q^{38} - 6 q^{40} - 3 q^{41} + 3 q^{42} + q^{43} + 3 q^{44} + 9 q^{45} - 9 q^{46} + 11 q^{49} + 4 q^{50} - 2 q^{52} - 3 q^{53} + 9 q^{54} - 18 q^{55} - 5 q^{56} - 21 q^{57} - 6 q^{58} + 9 q^{60} - 2 q^{61} - 16 q^{62} + 3 q^{63} + 2 q^{64} + 3 q^{65} + 4 q^{67} + 6 q^{68} + 27 q^{69} + 3 q^{70} + 24 q^{71} - 3 q^{72} - 11 q^{73} + 2 q^{74} - 12 q^{75} + 7 q^{76} - 15 q^{77} + 3 q^{78} + 16 q^{79} - 3 q^{80} - 9 q^{81} + 3 q^{82} + 9 q^{83} + 9 q^{84} - 9 q^{85} + 2 q^{86} + 9 q^{87} + 6 q^{88} - 3 q^{89} - 9 q^{90} + q^{91} + 9 q^{92} + 24 q^{93} + 21 q^{95} - 3 q^{96} + q^{97} - 2 q^{98} - 9 q^{99}+O(q^{100}) $ 2 * q + q^2 - 3 * q^3 - q^4 + 6 * q^5 + 5 * q^7 - 2 * q^8 + 3 * q^9 + 3 * q^10 - 6 * q^11 + 3 * q^12 + q^13 + q^14 - 9 * q^15 - q^16 - 3 * q^17 - 3 * q^18 + 7 * q^19 - 3 * q^20 - 6 * q^21 - 3 * q^22 - 18 * q^23 + 3 * q^24 + 8 * q^25 - q^26 - 4 * q^28 - 3 * q^29 - 8 * q^31 + q^32 + 9 * q^33 + 3 * q^34 + 15 * q^35 - 6 * q^36 + q^37 + 14 * q^38 - 6 * q^40 - 3 * q^41 + 3 * q^42 + q^43 + 3 * q^44 + 9 * q^45 - 9 * q^46 + 11 * q^49 + 4 * q^50 - 2 * q^52 - 3 * q^53 + 9 * q^54 - 18 * q^55 - 5 * q^56 - 21 * q^57 - 6 * q^58 + 9 * q^60 - 2 * q^61 - 16 * q^62 + 3 * q^63 + 2 * q^64 + 3 * q^65 + 4 * q^67 + 6 * q^68 + 27 * q^69 + 3 * q^70 + 24 * q^71 - 3 * q^72 - 11 * q^73 + 2 * q^74 - 12 * q^75 + 7 * q^76 - 15 * q^77 + 3 * q^78 + 16 * q^79 - 3 * q^80 - 9 * q^81 + 3 * q^82 + 9 * q^83 + 9 * q^84 - 9 * q^85 + 2 * q^86 + 9 * q^87 + 6 * q^88 - 3 * q^89 - 9 * q^90 + q^91 + 9 * q^92 + 24 * q^93 + 21 * q^95 - 3 * q^96 + q^97 - 2 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	3.00000			1.34164			0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000			1.34164			0.670820	+	0.741620i	$0.265942\pi$
$6$			1.73205i			0.707107i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$	−1.00000			−0.353553
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	1.50000	−	2.59808i	0.474342	−	0.821584i
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$	1.50000	+	0.866025i	0.433013	+	0.250000i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	−0.788320	−	0.615265i	$-0.789049\pi$
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	0.926995	+	0.375073i	$0.122382\pi$
$14$	0.500000	−	2.59808i	0.133631	−	0.694365i
$15$	−4.50000	+	2.59808i	−1.16190	+	0.670820i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−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	$0.285189\pi$
$18$	−1.50000	−	2.59808i	−0.353553	−	0.612372i
$19$	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
$23$	−9.00000			−1.87663			−0.938315	−	0.345782i	$-0.887614\pi$
$23$	−9.00000			−1.87663			−0.938315	+	0.345782i	$0.887614\pi$
$24$	1.50000	−	0.866025i	0.306186	−	0.176777i
$25$	4.00000			0.800000
$26$	−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	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$			5.19615i			0.948683i
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	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	$0.807139\pi$
$38$	7.00000			1.13555
$39$			1.73205i			0.277350i
$40$	−3.00000			−0.474342
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$	1.50000	+	4.33013i	0.231455	+	0.668153i
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	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		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		−	1.73205i		−	0.250000i
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	2.00000	−	3.46410i	0.282843	−	0.489898i
$51$		−	5.19615i		−	0.727607i
$52$	−1.00000			−0.138675
$53$	−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	$0.232725\pi$
$54$	4.50000	+	2.59808i	0.612372	+	0.353553i
$55$	−9.00000			−1.21356
$56$	−2.50000	+	0.866025i	−0.334077	+	0.115728i
$57$	−10.5000	−	6.06218i	−1.39076	−	0.802955i
$58$	−3.00000			−0.393919
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$	4.50000	+	2.59808i	0.580948	+	0.335410i
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$	−8.00000			−1.01600
$63$	1.50000	−	7.79423i	0.188982	−	0.981981i
$64$	1.00000			0.125000
$65$	1.50000	−	2.59808i	0.186052	−	0.322252i
$66$		−	5.19615i		−	0.639602i
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	3.00000			0.363803
$69$	13.5000	−	7.79423i	1.62521	−	0.938315i
$70$	1.50000	−	7.79423i	0.179284	−	0.931589i
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$	−1.50000	+	2.59808i	−0.176777	+	0.306186i
$73$	−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	$0.944054\pi$
$74$	1.00000			0.116248
$75$	−6.00000	+	3.46410i	−0.692820	+	0.400000i
$76$	3.50000	−	6.06218i	0.401478	−	0.695379i
$77$	−7.50000	+	2.59808i	−0.854704	+	0.296078i
$78$	1.50000	+	0.866025i	0.169842	+	0.0980581i
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.0726692	−	0.997356i	$-0.476848\pi$
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.827401	−	0.561611i	$-0.189818\pi$
$80$	−1.50000	+	2.59808i	−0.167705	+	0.290474i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	1.50000	+	2.59808i	0.165647	+	0.286910i
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	0.999976	−	0.00698436i	$-0.00222321\pi$
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	−0.506036	+	0.862512i	$0.668890\pi$
$84$	4.50000	+	0.866025i	0.490990	+	0.0944911i
$85$	−4.50000	+	7.79423i	−0.488094	+	0.845403i
$86$	1.00000			0.107833
$87$	4.50000	+	2.59808i	0.482451	+	0.278543i
$88$	3.00000			0.319801
$89$	−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
$93$	12.0000	+	6.92820i	1.24434	+	0.718421i
$94$		0			0
$95$	10.5000	+	18.1865i	1.07728	+	1.86590i
$96$	−1.50000	−	0.866025i	−0.153093	−	0.0883883i
$97$	0.500000	+	0.866025i	0.0507673	+	0.0879316i	0.890292	−	0.455389i	$-0.150500\pi$
$97$	0.500000	+	0.866025i	0.0507673	+	0.0879316i	−0.839525	+	0.543321i	$0.817167\pi$
$98$	−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
$101$	3.00000			0.298511			0.149256	−	0.988799i	$-0.452312\pi$
$101$	3.00000			0.298511			0.149256	+	0.988799i	$0.452312\pi$
$102$	−4.50000	−	2.59808i	−0.445566	−	0.257248i
$103$	−13.0000			−1.28093			−0.640464	−	0.767988i	$-0.721258\pi$
$103$	−13.0000			−1.28093			−0.640464	+	0.767988i	$0.721258\pi$
$104$	−0.500000	+	0.866025i	−0.0490290	+	0.0849208i
$105$	−9.00000	+	10.3923i	−0.878310	+	1.01419i
$106$	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	$0.976596\pi$
$108$	4.50000	−	2.59808i	0.433013	−	0.250000i
$109$	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	$-0.0472517\pi$
$110$	−4.50000	+	7.79423i	−0.429058	+	0.743151i
$111$	−1.50000	−	0.866025i	−0.142374	−	0.0821995i
$112$	−0.500000	+	2.59808i	−0.0472456	+	0.245495i
$113$	4.50000	−	7.79423i	0.423324	−	0.733219i	−0.572938	−	0.819599i	$-0.694196\pi$
$113$	4.50000	−	7.79423i	0.423324	−	0.733219i	0.996262	+	0.0863794i	$0.0275297\pi$
$114$	−10.5000	+	6.06218i	−0.983415	+	0.567775i
$115$	−27.0000			−2.51776
$116$	−1.50000	+	2.59808i	−0.139272	+	0.241225i
$117$	−1.50000	−	2.59808i	−0.138675	−	0.240192i
$118$		0			0
$119$	−1.50000	+	7.79423i	−0.137505	+	0.714496i
$120$	4.50000	−	2.59808i	0.410792	−	0.237171i
$121$	−2.00000			−0.181818
$122$	1.00000	+	1.73205i	0.0905357	+	0.156813i
$123$		−	5.19615i		−	0.468521i
$124$	−4.00000	+	6.92820i	−0.359211	+	0.622171i
$125$	−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	$0.556792\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−1.50000	−	0.866025i	−0.132068	−	0.0762493i
$130$	−1.50000	−	2.59808i	−0.131559	−	0.227866i
$131$	15.0000			1.31056			0.655278	−	0.755388i	$-0.272551\pi$
$131$	15.0000			1.31056			0.655278	+	0.755388i	$0.272551\pi$
$132$	−4.50000	−	2.59808i	−0.391675	−	0.226134i
$133$	14.0000	+	12.1244i	1.21395	+	1.05131i
$134$	4.00000			0.345547
$135$			15.5885i			1.34164i
$136$	1.50000	−	2.59808i	0.128624	−	0.222783i
$137$	−9.00000			−0.768922			−0.384461	−	0.923141i	$-0.625613\pi$
$137$	−9.00000			−0.768922			−0.384461	+	0.923141i	$0.625613\pi$
$138$		−	15.5885i		−	1.32698i
$139$	3.50000	−	6.06218i	0.296866	−	0.514187i	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	3.50000	−	6.06218i	0.296866	−	0.514187i	0.975417	+	0.220366i	$0.0707252\pi$
$140$	−6.00000	−	5.19615i	−0.507093	−	0.439155i
$141$		0			0
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$	−1.50000	+	2.59808i	−0.125436	+	0.217262i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	−4.50000	−	7.79423i	−0.373705	−	0.647275i
$146$	5.50000	+	9.52628i	0.455183	+	0.788400i
$147$	−4.50000	+	11.2583i	−0.371154	+	0.928571i
$148$	0.500000	−	0.866025i	0.0410997	−	0.0711868i
$149$	−9.00000			−0.737309			−0.368654	−	0.929567i	$-0.620181\pi$
$149$	−9.00000			−0.737309			−0.368654	+	0.929567i	$0.620181\pi$
$150$			6.92820i			0.565685i
$151$	−7.00000			−0.569652			−0.284826	−	0.958579i	$-0.591936\pi$
$151$	−7.00000			−0.569652			−0.284826	+	0.958579i	$0.591936\pi$
$152$	−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
$157$	11.0000	+	19.0526i	0.877896	+	1.52056i	0.853646	+	0.520854i	$0.174386\pi$
$157$	11.0000	+	19.0526i	0.877896	+	1.52056i	0.0242497	+	0.999706i	$0.492280\pi$
$158$	−8.00000	−	13.8564i	−0.636446	−	1.10236i
$159$		−	5.19615i		−	0.412082i
$160$	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	$0.566213\pi$
$164$	3.00000			0.234261
$165$	13.5000	−	7.79423i	1.05097	−	0.606780i
$166$	9.00000			0.698535
$167$	7.50000	−	12.9904i	0.580367	−	1.00523i	−0.415068	−	0.909790i	$-0.636242\pi$
$167$	7.50000	−	12.9904i	0.580367	−	1.00523i	0.995436	−	0.0954356i	$-0.0304244\pi$
$168$	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
$171$	21.0000			1.60591
$172$	0.500000	−	0.866025i	0.0381246	−	0.0660338i
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$	4.50000	−	2.59808i	0.341144	−	0.196960i
$175$	10.0000	−	3.46410i	0.755929	−	0.261861i
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$		0			0
$178$	−3.00000			−0.224860
$179$	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	$-0.120571\pi$
$180$	−9.00000			−0.670820
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	−2.00000	−	1.73205i	−0.148250	−	0.128388i
$183$		−	3.46410i		−	0.256074i
$184$	9.00000			0.663489
$185$	1.50000	+	2.59808i	0.110282	+	0.191014i
$186$	12.0000	−	6.92820i	0.879883	−	0.508001i
$187$	4.50000	−	7.79423i	0.329073	−	0.569970i
$188$		0			0
$189$	4.50000	+	12.9904i	0.327327	+	0.944911i
$190$	21.0000			1.52350
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	−1.50000	+	0.866025i	−0.108253	+	0.0625000i
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	0.496119	−	0.868255i	$-0.334758\pi$
$194$	1.00000			0.0717958
$195$			5.19615i			0.372104i
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$	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	$-0.179930\pi$
$200$	−4.00000			−0.282843
$201$	−6.00000	−	3.46410i	−0.423207	−	0.244339i
$202$	1.50000	−	2.59808i	0.105540	−	0.182800i
$203$	−6.00000	−	5.19615i	−0.421117	−	0.364698i
$204$	−4.50000	+	2.59808i	−0.315063	+	0.181902i
$205$	−4.50000	+	7.79423i	−0.314294	+	0.544373i
$206$	−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	−0.939156	−	0.343490i	$-0.888391\pi$
$211$	−2.50000	+	4.33013i	−0.172107	+	0.298098i	0.767049	+	0.641588i	$0.221724\pi$
$212$	3.00000			0.206041
$213$	−18.0000	+	10.3923i	−1.23334	+	0.712069i
$214$	−9.00000			−0.615227
$215$	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
$219$		−	19.0526i		−	1.28745i
$220$	4.50000	+	7.79423i	0.303390	+	0.525487i
$221$	1.50000	+	2.59808i	0.100901	+	0.174766i
$222$	−1.50000	+	0.866025i	−0.100673	+	0.0581238i
$223$	0.500000	+	0.866025i	0.0334825	+	0.0579934i	0.882281	−	0.470723i	$-0.156007\pi$
$223$	0.500000	+	0.866025i	0.0334825	+	0.0579934i	−0.848799	+	0.528716i	$0.822674\pi$
$224$	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
$227$	−3.00000			−0.199117			−0.0995585	−	0.995032i	$-0.531743\pi$
$227$	−3.00000			−0.199117			−0.0995585	+	0.995032i	$0.531743\pi$
$228$			12.1244i			0.802955i
$229$	−13.0000			−0.859064			−0.429532	−	0.903052i	$-0.641321\pi$
$229$	−13.0000			−0.859064			−0.429532	+	0.903052i	$0.641321\pi$
$230$	−13.5000	+	23.3827i	−0.890164	+	1.54181i
$231$	9.00000	−	10.3923i	0.592157	−	0.683763i
$232$	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	$0.864664\pi$
$234$	−3.00000			−0.196116
$235$		0			0
$236$		0			0
$237$			27.7128i			1.80014i
$238$	6.00000	+	5.19615i	0.388922	+	0.336817i
$239$	1.50000	−	2.59808i	0.0970269	−	0.168056i	−0.813426	−	0.581669i	$-0.802400\pi$
$239$	1.50000	−	2.59808i	0.0970269	−	0.168056i	0.910453	+	0.413613i	$0.135733\pi$
$240$		−	5.19615i		−	0.335410i
$241$	−13.0000			−0.837404			−0.418702	−	0.908124i	$-0.637515\pi$
$241$	−13.0000			−0.837404			−0.418702	+	0.908124i	$0.637515\pi$
$242$	−1.00000	+	1.73205i	−0.0642824	+	0.111340i
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$	2.00000			0.128037
$245$	16.5000	−	12.9904i	1.05415	−	0.829925i
$246$	−4.50000	−	2.59808i	−0.286910	−	0.165647i
$247$	7.00000			0.445399
$248$	4.00000	+	6.92820i	0.254000	+	0.439941i
$249$	−13.5000	−	7.79423i	−0.855528	−	0.493939i
$250$	−1.50000	+	2.59808i	−0.0948683	+	0.164317i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$	−7.50000	+	2.59808i	−0.472456	+	0.163663i
$253$	27.0000			1.69748
$254$	−2.00000	+	3.46410i	−0.125491	+	0.217357i
$255$		−	15.5885i		−	0.976187i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−21.0000			−1.30994			−0.654972	−	0.755653i	$-0.727320\pi$
$257$	−21.0000			−1.30994			−0.654972	+	0.755653i	$0.727320\pi$
$258$	−1.50000	+	0.866025i	−0.0933859	+	0.0539164i
$259$	2.00000	+	1.73205i	0.124274	+	0.107624i
$260$	−3.00000			−0.186052
$261$	−9.00000			−0.557086
$262$	7.50000	−	12.9904i	0.463352	−	0.802548i
$263$	9.00000			0.554964			0.277482	−	0.960731i	$-0.410500\pi$
$263$	9.00000			0.554964			0.277482	+	0.960731i	$0.410500\pi$
$264$	−4.50000	+	2.59808i	−0.276956	+	0.159901i
$265$	−4.50000	+	7.79423i	−0.276433	+	0.478796i
$266$	17.5000	−	6.06218i	1.07299	−	0.371696i
$267$	4.50000	+	2.59808i	0.275396	+	0.159000i
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	−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
$273$	1.50000	+	4.33013i	0.0907841	+	0.262071i
$274$	−4.50000	+	7.79423i	−0.271855	+	0.470867i
$275$	−12.0000			−0.723627
$276$	−13.5000	−	7.79423i	−0.812605	−	0.469157i
$277$	−1.00000			−0.0600842			−0.0300421	−	0.999549i	$-0.509564\pi$
$277$	−1.00000			−0.0600842			−0.0300421	+	0.999549i	$0.509564\pi$
$278$	−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	0.988273	+	0.152699i	$0.0487965\pi$
$281$	10.5000	+	18.1865i	0.626377	+	1.08492i	−0.361895	+	0.932219i	$0.617870\pi$
$282$		0			0
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$	−31.5000	−	18.1865i	−1.86590	−	1.07728i
$286$	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
$290$	−9.00000			−0.528498
$291$	−1.50000	−	0.866025i	−0.0879316	−	0.0507673i
$292$	11.0000			0.643726
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	−0.704117	−	0.710084i	$-0.748657\pi$
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	0.967009	+	0.254741i	$0.0819901\pi$
$294$	7.50000	+	9.52628i	0.437409	+	0.555584i
$295$		0			0
$296$	−0.500000	−	0.866025i	−0.0290619	−	0.0503367i
$297$		−	15.5885i		−	0.904534i
$298$	−4.50000	+	7.79423i	−0.260678	+	0.451508i
$299$	−4.50000	+	7.79423i	−0.260242	+	0.450752i
$300$	6.00000	+	3.46410i	0.346410	+	0.200000i
$301$	2.00000	+	1.73205i	0.115278	+	0.0998337i
$302$	−3.50000	+	6.06218i	−0.201402	+	0.348839i
$303$	−4.50000	+	2.59808i	−0.258518	+	0.149256i
$304$	−7.00000			−0.401478
$305$	−3.00000	+	5.19615i	−0.171780	+	0.297531i
$306$	9.00000			0.514496
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	6.00000	+	5.19615i	0.341882	+	0.296078i
$309$	19.5000	−	11.2583i	1.10932	−	0.640464i
$310$	−24.0000			−1.36311
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	0.974841	+	0.222900i	$0.0715523\pi$
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	−0.294384	+	0.955687i	$0.595114\pi$
$312$		−	1.73205i		−	0.0980581i
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	−0.689412	−	0.724370i	$-0.742131\pi$
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	0.972028	+	0.234863i	$0.0754642\pi$
$314$	22.0000			1.24153
$315$	4.50000	−	23.3827i	0.253546	−	1.31747i
$316$	−16.0000			−0.900070
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	0.494489	+	0.869184i	$0.335355\pi$
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	−0.999980	+	0.00635137i	$0.997978\pi$
$318$	−4.50000	−	2.59808i	−0.252347	−	0.145693i
$319$	4.50000	+	7.79423i	0.251952	+	0.436393i
$320$	3.00000			0.167705
$321$	13.5000	+	7.79423i	0.753497	+	0.435031i
$322$	−4.50000	+	23.3827i	−0.250775	+	1.30307i
$323$	−21.0000			−1.16847
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	2.00000	−	3.46410i	0.110940	−	0.192154i
$326$	19.0000			1.05231
$327$			22.5167i			1.24517i
$328$	1.50000	−	2.59808i	0.0828236	−	0.143455i
$329$		0			0
$330$		−	15.5885i		−	0.858116i
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	−0.954765	−	0.297361i	$-0.903893\pi$
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	0.734905	+	0.678170i	$0.237227\pi$
$332$	4.50000	−	7.79423i	0.246970	−	0.427764i
$333$	3.00000			0.164399
$334$	−7.50000	−	12.9904i	−0.410382	−	0.710802i
$335$	6.00000	+	10.3923i	0.327815	+	0.567792i
$336$	−1.50000	−	4.33013i	−0.0818317	−	0.236228i
$337$	6.50000	−	11.2583i	0.354078	−	0.613280i	−0.632882	−	0.774248i	$-0.718128\pi$
$337$	6.50000	−	11.2583i	0.354078	−	0.613280i	0.986960	+	0.160968i	$0.0514616\pi$
$338$	12.0000			0.652714
$339$			15.5885i			0.846649i
$340$	9.00000			0.488094
$341$	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
$346$	−3.00000	−	5.19615i	−0.161281	−	0.279347i
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$		−	5.19615i		−	0.278543i
$349$	−11.5000	−	19.9186i	−0.615581	−	1.06622i	−0.990282	−	0.139072i	$-0.955588\pi$
$349$	−11.5000	−	19.9186i	−0.615581	−	1.06622i	0.374701	−	0.927146i	$-0.377745\pi$
$350$	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
$353$	3.00000			0.159674			0.0798369	−	0.996808i	$-0.474560\pi$
$353$	3.00000			0.159674			0.0798369	+	0.996808i	$0.474560\pi$
$354$		0			0
$355$	36.0000			1.91068
$356$	−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
$362$	1.00000	−	1.73205i	0.0525588	−	0.0910346i
$363$	3.00000	−	1.73205i	0.157459	−	0.0909091i
$364$	−2.50000	+	0.866025i	−0.131036	+	0.0453921i
$365$	−16.5000	+	28.5788i	−0.863649	+	1.49588i
$366$	−3.00000	−	1.73205i	−0.156813	−	0.0905357i
$367$	17.0000			0.887393			0.443696	−	0.896177i	$-0.353667\pi$
$367$	17.0000			0.887393			0.443696	+	0.896177i	$0.353667\pi$
$368$	4.50000	−	7.79423i	0.234579	−	0.406302i
$369$	4.50000	+	7.79423i	0.234261	+	0.405751i
$370$	3.00000			0.155963
$371$	−1.50000	+	7.79423i	−0.0778761	+	0.404656i
$372$		−	13.8564i		−	0.718421i
$373$	−13.0000			−0.673114			−0.336557	−	0.941663i	$-0.609263\pi$
$373$	−13.0000			−0.673114			−0.336557	+	0.941663i	$0.609263\pi$
$374$	−4.50000	−	7.79423i	−0.232689	−	0.403030i
$375$	4.50000	−	2.59808i	0.232379	−	0.134164i
$376$		0			0
$377$	−3.00000			−0.154508
$378$	13.5000	+	2.59808i	0.694365	+	0.133631i
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$	10.5000	−	18.1865i	0.538639	−	0.932949i
$381$	6.00000	−	3.46410i	0.307389	−	0.177471i
$382$		0			0
$383$	15.0000			0.766464			0.383232	−	0.923652i	$-0.374811\pi$
$383$	15.0000			0.766464			0.383232	+	0.923652i	$0.374811\pi$
$384$			1.73205i			0.0883883i
$385$	−22.5000	+	7.79423i	−1.14671	+	0.397231i
$386$	−14.0000			−0.712581
$387$	3.00000			0.152499
$388$	0.500000	−	0.866025i	0.0253837	−	0.0439658i
$389$	27.0000			1.36895			0.684477	−	0.729034i	$-0.260031\pi$
$389$	27.0000			1.36895			0.684477	+	0.729034i	$0.260031\pi$
$390$	4.50000	+	2.59808i	0.227866	+	0.131559i
$391$	13.5000	−	23.3827i	0.682724	−	1.18251i
$392$	−5.50000	+	4.33013i	−0.277792	+	0.218704i
$393$	−22.5000	+	12.9904i	−1.13497	+	0.655278i
$394$	9.00000	−	15.5885i	0.453413	−	0.785335i
$395$	24.0000	−	41.5692i	1.20757	−	2.09157i
$396$	9.00000			0.452267
$397$	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
$401$	27.0000			1.34832			0.674158	−	0.738587i	$-0.264507\pi$
$401$	27.0000			1.34832			0.674158	+	0.738587i	$0.264507\pi$
$402$	−6.00000	+	3.46410i	−0.299253	+	0.172774i
$403$	−8.00000			−0.398508
$404$	−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
$408$			5.19615i			0.257248i
$409$	17.0000	+	29.4449i	0.840596	+	1.45595i	0.889392	+	0.457146i	$0.151128\pi$
$409$	17.0000	+	29.4449i	0.840596	+	1.45595i	−0.0487958	+	0.998809i	$0.515538\pi$
$410$	4.50000	+	7.79423i	0.222239	+	0.384930i
$411$	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
$416$	1.00000			0.0490290
$417$			12.1244i			0.593732i
$418$	−21.0000			−1.02714
$419$	−4.50000	+	7.79423i	−0.219839	+	0.380773i	−0.954759	−	0.297382i	$-0.903887\pi$
$419$	−4.50000	+	7.79423i	−0.219839	+	0.380773i	0.734919	+	0.678155i	$0.237220\pi$
$420$	13.5000	+	2.59808i	0.658733	+	0.126773i
$421$	−17.5000	−	30.3109i	−0.852898	−	1.47726i	−0.878582	−	0.477592i	$-0.841510\pi$
$421$	−17.5000	−	30.3109i	−0.852898	−	1.47726i	0.0256838	−	0.999670i	$-0.491824\pi$
$422$	2.50000	+	4.33013i	0.121698	+	0.210787i
$423$		0			0
$424$	1.50000	−	2.59808i	0.0728464	−	0.126174i
$425$	−6.00000	+	10.3923i	−0.291043	+	0.504101i
$426$			20.7846i			1.00702i
$427$	−1.00000	+	5.19615i	−0.0483934	+	0.251459i
$428$	−4.50000	+	7.79423i	−0.217516	+	0.376748i
$429$		−	5.19615i		−	0.250873i
$430$	3.00000			0.144673
$431$	−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	$0.941322\pi$
$432$	−4.50000	−	2.59808i	−0.216506	−	0.125000i
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$	−20.0000	+	6.92820i	−0.960031	+	0.332564i
$435$	13.5000	+	7.79423i	0.647275	+	0.373705i
$436$	−13.0000			−0.622587
$437$	−31.5000	−	54.5596i	−1.50685	−	2.60994i
$438$	−16.5000	−	9.52628i	−0.788400	−	0.455183i
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$	9.00000			0.429058
$441$	−3.00000	−	20.7846i	−0.142857	−	0.989743i
$442$	3.00000			0.142695
$443$	−18.0000	+	31.1769i	−0.855206	+	1.48126i	0.0212481	+	0.999774i	$0.493236\pi$
$443$	−18.0000	+	31.1769i	−0.855206	+	1.48126i	−0.876454	+	0.481486i	$0.840097\pi$
$444$			1.73205i			0.0821995i
$445$	−4.50000	−	7.79423i	−0.213320	−	0.369482i
$446$	1.00000			0.0473514
$447$	13.5000	−	7.79423i	0.638528	−	0.368654i
$448$	2.50000	−	0.866025i	0.118114	−	0.0409159i
$449$	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
$452$	−9.00000			−0.423324
$453$	10.5000	−	6.06218i	0.493333	−	0.284826i
$454$	−1.50000	+	2.59808i	−0.0703985	+	0.121934i
$455$	1.50000	−	7.79423i	0.0703211	−	0.365399i
$456$	10.5000	+	6.06218i	0.491708	+	0.283887i
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	0.958950	+	0.283577i	$0.0915211\pi$
$458$	−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	0.951584	−	0.307388i	$-0.0994551\pi$
$461$	4.50000	+	7.79423i	0.209586	+	0.363013i	−0.741998	+	0.670402i	$0.766122\pi$
$462$	−4.50000	−	12.9904i	−0.209359	−	0.604367i
$463$	−20.5000	+	35.5070i	−0.952716	+	1.65015i	−0.213205	+	0.977007i	$0.568390\pi$
$463$	−20.5000	+	35.5070i	−0.952716	+	1.65015i	−0.739511	+	0.673145i	$0.764943\pi$
$464$	3.00000			0.139272
$465$	36.0000	+	20.7846i	1.66946	+	0.963863i
$466$	−3.00000			−0.138972
$467$	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
$471$	−33.0000	−	19.0526i	−1.52056	−	0.877896i
$472$		0			0
$473$	−1.50000	−	2.59808i	−0.0689701	−	0.119460i
$474$	24.0000	+	13.8564i	1.10236	+	0.636446i
$475$	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
$479$	−3.00000			−0.137073			−0.0685367	−	0.997649i	$-0.521833\pi$
$479$	−3.00000			−0.137073			−0.0685367	+	0.997649i	$0.521833\pi$
$480$	−4.50000	−	2.59808i	−0.205396	−	0.118585i
$481$	1.00000			0.0455961
$482$	−6.50000	+	11.2583i	−0.296067	+	0.512803i
$483$	27.0000	−	31.1769i	1.22854	−	1.41860i
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	1.50000	+	2.59808i	0.0681115	+	0.117973i
$486$	13.5000	−	7.79423i	0.612372	−	0.353553i
$487$	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	$-0.0250088\pi$
$488$	1.00000	−	1.73205i	0.0452679	−	0.0784063i
$489$	−28.5000	−	16.4545i	−1.28881	−	0.744097i
$490$	−3.00000	−	20.7846i	−0.135526	−	0.938953i
$491$	−10.5000	+	18.1865i	−0.473858	+	0.820747i	−0.999552	−	0.0299272i	$-0.990472\pi$
$491$	−10.5000	+	18.1865i	−0.473858	+	0.820747i	0.525694	+	0.850674i	$0.323806\pi$
$492$	−4.50000	+	2.59808i	−0.202876	+	0.117130i
$493$	9.00000			0.405340
$494$	3.50000	−	6.06218i	0.157472	−	0.272750i
$495$	−13.5000	+	23.3827i	−0.606780	+	1.05097i
$496$	8.00000			0.359211
$497$	30.0000	−	10.3923i	1.34568	−	0.466159i
$498$	−13.5000	+	7.79423i	−0.604949	+	0.349268i
$499$	−25.0000			−1.11915			−0.559577	−	0.828778i	$-0.689036\pi$
$499$	−25.0000			−1.11915			−0.559577	+	0.828778i	$0.689036\pi$
$500$	1.50000	+	2.59808i	0.0670820	+	0.116190i
$501$			25.9808i			1.16073i
$502$	6.00000	−	10.3923i	0.267793	−	0.463831i
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$	−1.50000	+	7.79423i	−0.0668153	+	0.347183i
$505$	9.00000			0.400495
$506$	13.5000	−	23.3827i	0.600148	−	1.03949i
$507$	−18.0000	−	10.3923i	−0.799408	−	0.461538i
$508$	2.00000	+	3.46410i	0.0887357	+	0.153695i
$509$	−9.00000			−0.398918			−0.199459	−	0.979906i	$-0.563918\pi$
$509$	−9.00000			−0.398918			−0.199459	+	0.979906i	$0.563918\pi$
$510$	−13.5000	−	7.79423i	−0.597790	−	0.345134i
$511$	−5.50000	+	28.5788i	−0.243306	+	1.26425i
$512$	−1.00000			−0.0441942
$513$	−31.5000	+	18.1865i	−1.39076	+	0.802955i
$514$	−10.5000	+	18.1865i	−0.463135	+	0.802174i
$515$	−39.0000			−1.71855
$516$			1.73205i			0.0762493i
$517$		0			0
$518$	2.50000	−	0.866025i	0.109844	−	0.0380510i
$519$			10.3923i			0.456172i
$520$	−1.50000	+	2.59808i	−0.0657794	+	0.113933i
$521$	−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
$525$	−12.0000	+	13.8564i	−0.523723	+	0.604743i
$526$	4.50000	−	7.79423i	0.196209	−	0.339845i
$527$	24.0000			1.04546
$528$			5.19615i			0.226134i
$529$	58.0000			2.52174
$530$	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
$535$	−13.5000	−	23.3827i	−0.583656	−	1.01092i
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$			36.3731i			1.56961i
$538$	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	$0.909322\pi$
$542$	−5.00000			−0.214768
$543$	−3.00000	+	1.73205i	−0.128742	+	0.0743294i
$544$	−3.00000			−0.128624
$545$	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	0.724157	−	0.689635i	$-0.242229\pi$
$547$	−5.50000	−	9.52628i	−0.235163	−	0.407314i	−0.959320	+	0.282321i	$0.908896\pi$
$548$	4.50000	+	7.79423i	0.192230	+	0.332953i
$549$	3.00000	+	5.19615i	0.128037	+	0.221766i
$550$	−6.00000	+	10.3923i	−0.255841	+	0.443129i
$551$	10.5000	−	18.1865i	0.447315	−	0.774772i
$552$	−13.5000	+	7.79423i	−0.574598	+	0.331744i
$553$	8.00000	−	41.5692i	0.340195	−	1.76770i
$554$	−0.500000	+	0.866025i	−0.0212430	+	0.0367939i
$555$	−4.50000	−	2.59808i	−0.191014	−	0.110282i
$556$	−7.00000			−0.296866
$557$	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	$0.105600\pi$
$558$	−12.0000	+	20.7846i	−0.508001	+	0.879883i
$559$	1.00000			0.0422955
$560$	−1.50000	+	7.79423i	−0.0633866	+	0.329366i
$561$			15.5885i			0.658145i
$562$	21.0000			0.885832
$563$	−6.00000	−	10.3923i	−0.252870	−	0.437983i	0.711445	−	0.702742i	$-0.248041\pi$
$563$	−6.00000	−	10.3923i	−0.252870	−	0.437983i	−0.964315	+	0.264758i	$0.914708\pi$
$564$		0			0
$565$	13.5000	−	23.3827i	0.567949	−	0.983717i
$566$	4.00000			0.168133
$567$	−18.0000	−	15.5885i	−0.755929	−	0.654654i
$568$	−12.0000			−0.503509
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	−0.613369	−	0.789797i	$-0.710186\pi$
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	0.990668	+	0.136295i	$0.0435194\pi$
$570$	−31.5000	+	18.1865i	−1.31939	+	0.761750i
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	0.308443	−	0.951243i	$-0.400192\pi$
$572$	3.00000			0.125436
$573$		0			0
$574$	6.00000	+	5.19615i	0.250435	+	0.216883i
$575$	−36.0000			−1.50130
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	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	$-0.00754370\pi$
$578$	8.00000			0.332756
$579$	21.0000	+	12.1244i	0.872730	+	0.503871i
$580$	−4.50000	+	7.79423i	−0.186852	+	0.323638i
$581$	18.0000	+	15.5885i	0.746766	+	0.646718i
$582$	−1.50000	+	0.866025i	−0.0621770	+	0.0358979i
$583$	4.50000	−	7.79423i	0.186371	−	0.322804i
$584$	5.50000	−	9.52628i	0.227592	−	0.394200i
$585$	−4.50000	−	7.79423i	−0.186052	−	0.322252i
$586$	−4.50000	−	7.79423i	−0.185893	−	0.321977i
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	0.833408	−	0.552658i	$-0.186386\pi$
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	−0.895320	+	0.445424i	$0.853053\pi$
$588$	12.0000	−	1.73205i	0.494872	−	0.0714286i
$589$	28.0000	−	48.4974i	1.15372	−	1.99830i
$590$		0			0
$591$	−27.0000	+	15.5885i	−1.11063	+	0.641223i
$592$	−1.00000			−0.0410997
$593$	−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
$597$			43.3013i			1.77220i
$598$	4.50000	+	7.79423i	0.184019	+	0.318730i
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	0.999938	−	0.0111569i	$-0.00355143\pi$
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	−0.509631	+	0.860393i	$0.670218\pi$
$600$	6.00000	−	3.46410i	0.244949	−	0.141421i
$601$	12.5000	+	21.6506i	0.509886	+	0.883148i	0.999934	+	0.0114528i	$0.00364562\pi$
$601$	12.5000	+	21.6506i	0.509886	+	0.883148i	−0.490049	+	0.871695i	$0.663021\pi$
$602$	2.50000	−	0.866025i	0.101892	−	0.0352966i
$603$	12.0000			0.488678
$604$	3.50000	+	6.06218i	0.142413	+	0.246667i
$605$	−6.00000			−0.243935
$606$			5.19615i			0.211079i
$607$	−13.0000			−0.527654			−0.263827	−	0.964570i	$-0.584985\pi$
$607$	−13.0000			−0.527654			−0.263827	+	0.964570i	$0.584985\pi$
$608$	−3.50000	+	6.06218i	−0.141944	+	0.245854i
$609$	13.5000	+	2.59808i	0.547048	+	0.105279i
$610$	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	$0.320426\pi$
$614$	−14.0000	+	24.2487i	−0.564994	+	0.978598i
$615$		−	15.5885i		−	0.628587i
$616$	7.50000	−	2.59808i	0.302184	−	0.104679i
$617$	22.5000	−	38.9711i	0.905816	−	1.56892i	0.0859976	−	0.996295i	$-0.472592\pi$
$617$	22.5000	−	38.9711i	0.905816	−	1.56892i	0.819818	−	0.572624i	$-0.194074\pi$
$618$		−	22.5167i		−	0.905753i
$619$	17.0000			0.683288			0.341644	−	0.939829i	$-0.389016\pi$
$619$	17.0000			0.683288			0.341644	+	0.939829i	$0.389016\pi$
$620$	−12.0000	+	20.7846i	−0.481932	+	0.834730i
$621$		−	46.7654i		−	1.87663i
$622$	24.0000			0.962312
$623$	−6.00000	−	5.19615i	−0.240385	−	0.208179i
$624$	−1.50000	−	0.866025i	−0.0600481	−	0.0346688i
$625$	−29.0000			−1.16000
$626$	−5.00000	−	8.66025i	−0.199840	−	0.346133i
$627$	31.5000	+	18.1865i	1.25799	+	0.726300i
$628$	11.0000	−	19.0526i	0.438948	−	0.760280i
$629$	−3.00000			−0.119618
$630$	−18.0000	−	15.5885i	−0.717137	−	0.621059i
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	−8.00000	+	13.8564i	−0.318223	+	0.551178i
$633$		−	8.66025i		−	0.344214i
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	−12.0000			−0.476205
$636$	−4.50000	+	2.59808i	−0.178437	+	0.103020i
$637$	−1.00000	−	6.92820i	−0.0396214	−	0.274505i
$638$	9.00000			0.356313
$639$	18.0000	−	31.1769i	0.712069	−	1.23334i
$640$	1.50000	−	2.59808i	0.0592927	−	0.102698i
$641$	−33.0000			−1.30342			−0.651711	−	0.758468i	$-0.725948\pi$
$641$	−33.0000			−1.30342			−0.651711	+	0.758468i	$0.725948\pi$
$642$	13.5000	−	7.79423i	0.532803	−	0.307614i
$643$	−14.5000	+	25.1147i	−0.571824	+	0.990429i	0.424555	+	0.905402i	$0.360431\pi$
$643$	−14.5000	+	25.1147i	−0.571824	+	0.990429i	−0.996379	+	0.0850262i	$0.972903\pi$
$644$	18.0000	+	15.5885i	0.709299	+	0.614271i
$645$	−4.50000	−	2.59808i	−0.177187	−	0.102299i
$646$	−10.5000	+	18.1865i	−0.413117	+	0.715540i
$647$	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	$0.0312184\pi$
$648$	4.50000	+	7.79423i	0.176777	+	0.306186i
$649$		0			0
$650$	−2.00000	−	3.46410i	−0.0784465	−	0.135873i
$651$	36.0000	+	6.92820i	1.41095	+	0.271538i
$652$	9.50000	−	16.4545i	0.372049	−	0.644407i
$653$	15.0000			0.586995			0.293498	−	0.955960i	$-0.405181\pi$
$653$	15.0000			0.586995			0.293498	+	0.955960i	$0.405181\pi$
$654$	19.5000	+	11.2583i	0.762510	+	0.440236i
$655$	45.0000			1.75830
$656$	−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	0.835330	−	0.549749i	$-0.185277\pi$
$659$	−1.50000	−	2.59808i	−0.0584317	−	0.101207i	−0.893762	+	0.448542i	$0.851943\pi$
$660$	−13.5000	−	7.79423i	−0.525487	−	0.303390i
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	0.996682	−	0.0813955i	$-0.0259377\pi$
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	−0.568831	+	0.822454i	$0.692604\pi$
$662$	4.00000	+	6.92820i	0.155464	+	0.269272i
$663$	−4.50000	−	2.59808i	−0.174766	−	0.100901i
$664$	−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
$668$	−15.0000			−0.580367
$669$	−1.50000	−	0.866025i	−0.0579934	−	0.0334825i
$670$	12.0000			0.463600
$671$	3.00000	−	5.19615i	0.115814	−	0.200595i
$672$	−4.50000	−	0.866025i	−0.173591	−	0.0334077i
$673$	−17.5000	−	30.3109i	−0.674575	−	1.16840i	−0.976593	−	0.215096i	$-0.930993\pi$
$673$	−17.5000	−	30.3109i	−0.674575	−	1.16840i	0.302017	−	0.953302i	$-0.402340\pi$
$674$	−6.50000	−	11.2583i	−0.250371	−	0.433655i
$675$			20.7846i			0.800000i
$676$	6.00000	−	10.3923i	0.230769	−	0.399704i
$677$	15.0000	−	25.9808i	0.576497	−	0.998522i	−0.419380	−	0.907811i	$-0.637753\pi$
$677$	15.0000	−	25.9808i	0.576497	−	0.998522i	0.995877	−	0.0907112i	$-0.0289140\pi$
$678$	13.5000	+	7.79423i	0.518464	+	0.299336i
$679$	2.00000	+	1.73205i	0.0767530	+	0.0664700i
$680$	4.50000	−	7.79423i	0.172567	−	0.298895i
$681$	4.50000	−	2.59808i	0.172440	−	0.0995585i
$682$	24.0000			0.919007
$683$	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
$686$	−8.50000	−	16.4545i	−0.324532	−	0.628235i
$687$	19.5000	−	11.2583i	0.743971	−	0.429532i
$688$	−1.00000			−0.0381246
$689$	1.50000	+	2.59808i	0.0571454	+	0.0989788i
$690$		−	46.7654i		−	1.78033i
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	0.0555386	+	0.998457i	$0.482312\pi$
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	−0.892458	+	0.451130i	$0.851021\pi$
$692$	−6.00000			−0.228086
$693$	−4.50000	+	23.3827i	−0.170941	+	0.888235i
$694$	−12.0000			−0.455514
$695$	10.5000	−	18.1865i	0.398288	−	0.689855i
$696$	−4.50000	−	2.59808i	−0.170572	−	0.0984798i
$697$	−4.50000	−	7.79423i	−0.170450	−	0.295227i
$698$	−23.0000			−0.870563
$699$	4.50000	+	2.59808i	0.170206	+	0.0982683i
$700$	−8.00000	−	6.92820i	−0.302372	−	0.261861i
$701$	−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
$704$	−3.00000			−0.113067
$705$		0			0
$706$	1.50000	−	2.59808i	0.0564532	−	0.0977799i
$707$	7.50000	−	2.59808i	0.282067	−	0.0977107i
$708$		0			0
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	−0.999908	−	0.0135434i	$-0.995689\pi$
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	0.511683	+	0.859174i	$0.329022\pi$
$710$	18.0000	−	31.1769i	0.675528	−	1.17005i
$711$	−24.0000	−	41.5692i	−0.900070	−	1.55897i
$712$	1.50000	+	2.59808i	0.0562149	+	0.0973670i
$713$	36.0000	+	62.3538i	1.34821	+	2.33517i
$714$	−13.5000	−	2.59808i	−0.505225	−	0.0972306i
$715$	−4.50000	+	7.79423i	−0.168290	+	0.291488i
$716$	−21.0000			−0.784807
$717$			5.19615i			0.194054i
$718$	−9.00000			−0.335877
$719$	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
$724$	−1.00000	−	1.73205i	−0.0371647	−	0.0643712i
$725$	−6.00000	−	10.3923i	−0.222834	−	0.385961i
$726$		−	3.46410i		−	0.128565i
$727$	6.50000	+	11.2583i	0.241072	+	0.417548i	0.961020	−	0.276479i	$-0.0891678\pi$
$727$	6.50000	+	11.2583i	0.241072	+	0.417548i	−0.719948	+	0.694028i	$0.755834\pi$
$728$	−0.500000	+	2.59808i	−0.0185312	+	0.0962911i
$729$	−27.0000			−1.00000
$730$	16.5000	+	28.5788i	0.610692	+	1.05775i
$731$	−3.00000			−0.110959
$732$	−3.00000	+	1.73205i	−0.110883	+	0.0640184i
$733$	−1.00000			−0.0369358			−0.0184679	−	0.999829i	$-0.505879\pi$
$733$	−1.00000			−0.0369358			−0.0184679	+	0.999829i	$0.505879\pi$
$734$	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
$738$	9.00000			0.331295
$739$	−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	$0.305702\pi$
$740$	1.50000	−	2.59808i	0.0551411	−	0.0955072i
$741$	−10.5000	+	6.06218i	−0.385727	+	0.222700i
$742$	6.00000	+	5.19615i	0.220267	+	0.190757i
$743$	−10.5000	+	18.1865i	−0.385208	+	0.667199i	−0.991798	−	0.127815i	$-0.959204\pi$
$743$	−10.5000	+	18.1865i	−0.385208	+	0.667199i	0.606590	+	0.795015i	$0.292537\pi$
$744$	−12.0000	−	6.92820i	−0.439941	−	0.254000i
$745$	−27.0000			−0.989203
$746$	−6.50000	+	11.2583i	−0.237982	+	0.412197i
$747$	27.0000			0.987878
$748$	−9.00000			−0.329073
$749$	−18.0000	−	15.5885i	−0.657706	−	0.569590i
$750$		−	5.19615i		−	0.189737i
$751$	−13.0000			−0.474377			−0.237188	−	0.971464i	$-0.576226\pi$
$751$	−13.0000			−0.474377			−0.237188	+	0.971464i	$0.576226\pi$
$752$		0			0
$753$	−18.0000	+	10.3923i	−0.655956	+	0.378717i
$754$	−1.50000	+	2.59808i	−0.0546268	+	0.0946164i
$755$	−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	$0.630921\pi$
$758$	−14.0000	+	24.2487i	−0.508503	+	0.880753i
$759$	−40.5000	+	23.3827i	−1.47006	+	0.848738i
$760$	−10.5000	−	18.1865i	−0.380875	−	0.659695i
$761$	−45.0000			−1.63125			−0.815624	−	0.578582i	$-0.803606\pi$
$761$	−45.0000			−1.63125			−0.815624	+	0.578582i	$0.803606\pi$
$762$		−	6.92820i		−	0.250982i
$763$	6.50000	−	33.7750i	0.235316	−	1.22274i
$764$		0			0
$765$	13.5000	+	23.3827i	0.488094	+	0.845403i
$766$	7.50000	−	12.9904i	0.270986	−	0.469362i
$767$		0			0
$768$	1.50000	+	0.866025i	0.0541266	+	0.0312500i
$769$	−11.5000	+	19.9186i	−0.414701	+	0.718283i	−0.995397	−	0.0958377i	$-0.969447\pi$
$769$	−11.5000	+	19.9186i	−0.414701	+	0.718283i	0.580696	+	0.814120i	$0.302780\pi$
$770$	−4.50000	+	23.3827i	−0.162169	+	0.842654i
$771$	31.5000	−	18.1865i	1.13444	−	0.654972i
$772$	−7.00000	+	12.1244i	−0.251936	+	0.436365i
$773$	−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
$779$	−21.0000			−0.752403
$780$	4.50000	−	2.59808i	0.161126	−	0.0930261i
$781$	−36.0000			−1.28818
$782$	−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
$786$			25.9808i			0.926703i
$787$	14.0000	+	24.2487i	0.499046	+	0.864373i	0.999999	−	0.00110111i	$-0.000350496\pi$
$787$	14.0000	+	24.2487i	0.499046	+	0.864373i	−0.500953	+	0.865474i	$0.667017\pi$
$788$	−9.00000	−	15.5885i	−0.320612	−	0.555316i
$789$	−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
$794$	13.0000			0.461353
$795$		−	15.5885i		−	0.552866i
$796$	−25.0000			−0.886102
$797$	10.5000	−	18.1865i	0.371929	−	0.644200i	−0.617933	−	0.786231i	$-0.712030\pi$
$797$	10.5000	−	18.1865i	0.371929	−	0.644200i	0.989862	+	0.142031i	$0.0453631\pi$
$798$	−21.0000	+	24.2487i	−0.743392	+	0.858395i
$799$		0			0
$800$	2.00000	+	3.46410i	0.0707107	+	0.122474i
$801$	−9.00000			−0.317999
$802$	13.5000	−	23.3827i	0.476702	−	0.825671i
$803$	16.5000	−	28.5788i	0.582272	−	1.00853i
$804$			6.92820i			0.244339i
$805$	−67.5000	+	23.3827i	−2.37906	+	0.824131i
$806$	−4.00000	+	6.92820i	−0.140894	+	0.244036i
$807$		−	25.9808i		−	0.914566i
$808$	−3.00000			−0.105540
$809$	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	$-0.0303234\pi$
$810$	−27.0000			−0.948683
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	−1.50000	+	7.79423i	−0.0526397	+	0.273524i
$813$	7.50000	+	4.33013i	0.263036	+	0.151864i
$814$	−3.00000			−0.105150
$815$	28.5000	+	49.3634i	0.998311	+	1.72913i
$816$	4.50000	+	2.59808i	0.157532	+	0.0909509i
$817$	−3.50000	+	6.06218i	−0.122449	+	0.212089i
$818$	34.0000			1.18878
$819$	−6.00000	−	5.19615i	−0.209657	−	0.181568i
$820$	9.00000			0.314294
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	−0.222731	−	0.974880i	$-0.571497\pi$
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	0.955636	−	0.294549i	$-0.0951694\pi$
$822$		−	15.5885i		−	0.543710i
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	0.969448	+	0.245295i	$0.0788849\pi$
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	−0.272292	+	0.962215i	$0.587782\pi$
$824$	13.0000			0.452876
$825$	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	$0.284723\pi$
$828$	27.0000			0.938315
$829$	−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	$0.227847\pi$
$830$	27.0000			0.937184
$831$	1.50000	−	0.866025i	0.0520344	−	0.0300421i
$832$	0.500000	−	0.866025i	0.0173344	−	0.0300240i
$833$	3.00000	+	20.7846i	0.103944	+	0.720144i
$834$	10.5000	+	6.06218i	0.363585	+	0.209916i
$835$	22.5000	−	38.9711i	0.778645	−	1.34865i
$836$	−10.5000	+	18.1865i	−0.363150	+	0.628994i
$837$	36.0000	−	20.7846i	1.24434	−	0.718421i
$838$	4.50000	+	7.79423i	0.155450	+	0.269247i
$839$	−7.50000	−	12.9904i	−0.258929	−	0.448478i	0.707026	−	0.707187i	$-0.250036\pi$
$839$	−7.50000	−	12.9904i	−0.258929	−	0.448478i	−0.965955	+	0.258709i	$0.916703\pi$
$840$	9.00000	−	10.3923i	0.310530	−	0.358569i
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−35.0000			−1.20618
$843$	−31.5000	−	18.1865i	−1.08492	−	0.626377i
$844$	5.00000			0.172107
$845$	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
$849$	−6.00000	−	3.46410i	−0.205919	−	0.118888i
$850$	6.00000	+	10.3923i	0.205798	+	0.356453i
$851$	−4.50000	−	7.79423i	−0.154258	−	0.267183i
$852$	18.0000	+	10.3923i	0.616670	+	0.356034i
$853$	0.500000	+	0.866025i	0.0171197	+	0.0296521i	0.874458	−	0.485101i	$-0.161217\pi$
$853$	0.500000	+	0.866025i	0.0171197	+	0.0296521i	−0.857339	+	0.514753i	$0.827884\pi$
$854$	4.00000	+	3.46410i	0.136877	+	0.118539i
$855$	63.0000			2.15455
$856$	4.50000	+	7.79423i	0.153807	+	0.266401i
$857$	3.00000			0.102478			0.0512390	−	0.998686i	$-0.483683\pi$
$857$	3.00000			0.102478			0.0512390	+	0.998686i	$0.483683\pi$
$858$	−4.50000	−	2.59808i	−0.153627	−	0.0886969i
$859$	−25.0000			−0.852989			−0.426494	−	0.904490i	$-0.640252\pi$
$859$	−25.0000			−0.852989			−0.426494	+	0.904490i	$0.640252\pi$
$860$	1.50000	−	2.59808i	0.0511496	−	0.0885937i
$861$	−4.50000	−	12.9904i	−0.153360	−	0.442711i
$862$	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	$0.498719\pi$
$864$	−4.50000	+	2.59808i	−0.153093	+	0.0883883i
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$	1.00000	−	1.73205i	0.0339814	−	0.0588575i
$867$	−12.0000	−	6.92820i	−0.407541	−	0.235294i
$868$	−4.00000	+	20.7846i	−0.135769	+	0.705476i
$869$	−24.0000	+	41.5692i	−0.814144	+	1.41014i
$870$	13.5000	−	7.79423i	0.457693	−	0.264249i
$871$	4.00000			0.135535
$872$	−6.50000	+	11.2583i	−0.220118	+	0.381255i
$873$	3.00000			0.101535
$874$	−63.0000			−2.13101
$875$	−7.50000	+	2.59808i	−0.253546	+	0.0878310i
$876$	−16.5000	+	9.52628i	−0.557483	+	0.321863i
$877$	47.0000			1.58708			0.793539	−	0.608520i	$-0.208236\pi$
$877$	47.0000			1.58708			0.793539	+	0.608520i	$0.208236\pi$
$878$	4.00000	+	6.92820i	0.134993	+	0.233816i
$879$			15.5885i			0.525786i
$880$	4.50000	−	7.79423i	0.151695	−	0.262743i
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$	−19.5000	−	7.79423i	−0.656599	−	0.262445i
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	1.50000	−	2.59808i	0.0504505	−	0.0873828i
$885$		0			0
$886$	18.0000	+	31.1769i	0.604722	+	1.04741i
$887$	−33.0000			−1.10803			−0.554016	−	0.832506i	$-0.686905\pi$
$887$	−33.0000			−1.10803			−0.554016	+	0.832506i	$0.686905\pi$
$888$	1.50000	+	0.866025i	0.0503367	+	0.0290619i
$889$	−10.0000	+	3.46410i	−0.335389	+	0.116182i
$890$	−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
$894$		−	15.5885i		−	0.521356i
$895$	31.5000	−	54.5596i	1.05293	−	1.82373i
$896$	0.500000	−	2.59808i	0.0167038	−	0.0867956i
$897$		−	15.5885i		−	0.520483i
$898$	3.00000	−	5.19615i	0.100111	−	0.173398i
$899$	−12.0000	+	20.7846i	−0.400222	+	0.693206i
$900$	−12.0000			−0.400000
$901$	−4.50000	−	7.79423i	−0.149917	−	0.259663i
$902$	−4.50000	−	7.79423i	−0.149834	−	0.259519i
$903$	−4.50000	−	0.866025i	−0.149751	−	0.0288195i
$904$	−4.50000	+	7.79423i	−0.149668	+	0.259232i
$905$	6.00000			0.199447
$906$		−	12.1244i		−	0.402805i
$907$	−43.0000			−1.42779			−0.713896	−	0.700252i	$-0.753071\pi$
$907$	−43.0000			−1.42779			−0.713896	+	0.700252i	$0.753071\pi$
$908$	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	−0.984055	−	0.177866i	$-0.943081\pi$
$911$	−19.5000	−	33.7750i	−0.646064	−	1.11902i	0.337991	−	0.941149i	$-0.390253\pi$
$912$	10.5000	−	6.06218i	0.347690	−	0.200739i
$913$	−13.5000	−	23.3827i	−0.446785	−	0.773854i
$914$	−5.00000	−	8.66025i	−0.165385	−	0.286456i
$915$		−	10.3923i		−	0.343559i
$916$	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	$-0.505250\pi$
$920$	27.0000			0.890164
$921$	42.0000	−	24.2487i	1.38395	−	0.799022i
$922$	9.00000			0.296399
$923$	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
$929$	−9.00000	+	15.5885i	−0.295280	+	0.511441i	−0.975050	−	0.221985i	$-0.928746\pi$
$929$	−9.00000	+	15.5885i	−0.295280	+	0.511441i	0.679770	+	0.733426i	$0.262080\pi$
$930$	36.0000	−	20.7846i	1.18049	−	0.681554i
$931$	45.5000	+	18.1865i	1.49120	+	0.596040i
$932$	−1.50000	+	2.59808i	−0.0491341	+	0.0851028i
$933$	−36.0000	−	20.7846i	−1.17859	−	0.680458i
$934$	3.00000			0.0981630
$935$	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	$0.360383\pi$
$938$	10.0000	−	3.46410i	0.326512	−	0.113107i
$939$			17.3205i			0.565233i
$940$		0			0
$941$	3.00000	+	5.19615i	0.0977972	+	0.169390i	0.910773	−	0.412908i	$-0.135487\pi$
$941$	3.00000	+	5.19615i	0.0977972	+	0.169390i	−0.812975	+	0.582298i	$0.802154\pi$
$942$	−33.0000	+	19.0526i	−1.07520	+	0.620766i
$943$	13.5000	−	23.3827i	0.439620	−	0.761445i
$944$		0			0
$945$	13.5000	+	38.9711i	0.439155	+	1.26773i
$946$	−3.00000			−0.0975384
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	−0.946892	−	0.321552i	$-0.895796\pi$
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	0.751918	+	0.659256i	$0.229129\pi$
$948$	24.0000	−	13.8564i	0.779484	−	0.450035i
$949$	5.50000	+	9.52628i	0.178538	+	0.309236i
$950$	28.0000			0.908440
$951$		−	31.1769i		−	1.01098i
$952$	1.50000	−	7.79423i	0.0486153	−	0.252612i
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$	9.00000			0.291386
$955$		0			0
$956$	−3.00000			−0.0970269
$957$	−13.5000	−	7.79423i	−0.436393	−	0.251952i
$958$	−1.50000	+	2.59808i	−0.0484628	+	0.0839400i
$959$	−22.5000	+	7.79423i	−0.726563	+	0.251689i
$960$	−4.50000	+	2.59808i	−0.145237	+	0.0838525i
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	0.500000	−	0.866025i	0.0161206	−	0.0279218i
$963$	−27.0000			−0.870063
$964$	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	0.321578	+	0.946883i	$0.395787\pi$
$967$	−20.5000	+	35.5070i	−0.659236	+	1.14183i	−0.980814	+	0.194946i	$0.937547\pi$
$968$	2.00000			0.0642824
$969$	31.5000	−	18.1865i	1.01193	−	0.584236i
$970$	3.00000			0.0963242
$971$	−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
$975$			6.92820i			0.221880i
$976$	−1.00000	−	1.73205i	−0.0320092	−	0.0554416i
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	0.999734	−	0.0230645i	$-0.00734232\pi$
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	−0.519841	+	0.854263i	$0.674009\pi$
$978$	−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
$983$	−15.0000			−0.478426			−0.239213	−	0.970967i	$-0.576889\pi$
$983$	−15.0000			−0.478426			−0.239213	+	0.970967i	$0.576889\pi$
$984$			5.19615i			0.165647i
$985$	54.0000			1.72058
$986$	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
$990$	13.5000	+	23.3827i	0.429058	+	0.743151i
$991$	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	$0.0366917\pi$
$992$	4.00000	−	6.92820i	0.127000	−	0.219971i
$993$		−	13.8564i		−	0.439720i
$994$	6.00000	−	31.1769i	0.190308	−	0.988872i
$995$	37.5000	−	64.9519i	1.18883	−	2.05911i
$996$			15.5885i			0.493939i
$997$	−13.0000			−0.411714			−0.205857	−	0.978582i	$-0.565998\pi$
$997$	−13.0000			−0.411714			−0.205857	+	0.978582i	$0.565998\pi$
$998$	−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.h.b.67.1	yes	2
3.2	odd	2		378.2.h.a.361.1		2
4.3	odd	2		1008.2.t.f.193.1		2
7.2	even	3		126.2.e.a.121.1	yes	2
7.3	odd	6		882.2.f.g.589.1		2
7.4	even	3		882.2.f.i.589.1		2
7.5	odd	6		882.2.e.c.373.1		2
7.6	odd	2		882.2.h.i.67.1		2
9.2	odd	6		378.2.e.b.235.1		2
9.4	even	3		1134.2.g.e.487.1		2
9.5	odd	6		1134.2.g.c.487.1		2
9.7	even	3		126.2.e.a.25.1	✓	2
12.11	even	2		3024.2.t.a.1873.1		2
21.2	odd	6		378.2.e.b.37.1		2
21.5	even	6		2646.2.e.g.1549.1		2
21.11	odd	6		2646.2.f.d.1765.1		2
21.17	even	6		2646.2.f.a.1765.1		2
21.20	even	2		2646.2.h.d.361.1		2
28.23	odd	6		1008.2.q.a.625.1		2
36.7	odd	6		1008.2.q.a.529.1		2
36.11	even	6		3024.2.q.f.2881.1		2
63.2	odd	6		378.2.h.a.289.1		2
63.4	even	3		7938.2.a.m.1.1		1
63.11	odd	6		2646.2.f.d.883.1		2
63.16	even	3	inner	126.2.h.b.79.1	yes	2
63.20	even	6		2646.2.e.g.2125.1		2
63.23	odd	6		1134.2.g.c.163.1		2
63.25	even	3		882.2.f.i.295.1		2
63.31	odd	6		7938.2.a.b.1.1		1
63.32	odd	6		7938.2.a.t.1.1		1
63.34	odd	6		882.2.e.c.655.1		2
63.38	even	6		2646.2.f.a.883.1		2
63.47	even	6		2646.2.h.d.667.1		2
63.52	odd	6		882.2.f.g.295.1		2
63.58	even	3		1134.2.g.e.163.1		2
63.59	even	6		7938.2.a.be.1.1		1
63.61	odd	6		882.2.h.i.79.1		2
84.23	even	6		3024.2.q.f.2305.1		2
252.79	odd	6		1008.2.t.f.961.1		2
252.191	even	6		3024.2.t.a.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.a.25.1	✓	2	9.7	even	3
126.2.e.a.121.1	yes	2	7.2	even	3
126.2.h.b.67.1	yes	2	1.1	even	1	trivial
126.2.h.b.79.1	yes	2	63.16	even	3	inner
378.2.e.b.37.1		2	21.2	odd	6
378.2.e.b.235.1		2	9.2	odd	6
378.2.h.a.289.1		2	63.2	odd	6
378.2.h.a.361.1		2	3.2	odd	2
882.2.e.c.373.1		2	7.5	odd	6
882.2.e.c.655.1		2	63.34	odd	6
882.2.f.g.295.1		2	63.52	odd	6
882.2.f.g.589.1		2	7.3	odd	6
882.2.f.i.295.1		2	63.25	even	3
882.2.f.i.589.1		2	7.4	even	3
882.2.h.i.67.1		2	7.6	odd	2
882.2.h.i.79.1		2	63.61	odd	6
1008.2.q.a.529.1		2	36.7	odd	6
1008.2.q.a.625.1		2	28.23	odd	6
1008.2.t.f.193.1		2	4.3	odd	2
1008.2.t.f.961.1		2	252.79	odd	6
1134.2.g.c.163.1		2	63.23	odd	6
1134.2.g.c.487.1		2	9.5	odd	6
1134.2.g.e.163.1		2	63.58	even	3
1134.2.g.e.487.1		2	9.4	even	3
2646.2.e.g.1549.1		2	21.5	even	6
2646.2.e.g.2125.1		2	63.20	even	6
2646.2.f.a.883.1		2	63.38	even	6
2646.2.f.a.1765.1		2	21.17	even	6
2646.2.f.d.883.1		2	63.11	odd	6
2646.2.f.d.1765.1		2	21.11	odd	6
2646.2.h.d.361.1		2	21.20	even	2
2646.2.h.d.667.1		2	63.47	even	6
3024.2.q.f.2305.1		2	84.23	even	6
3024.2.q.f.2881.1		2	36.11	even	6
3024.2.t.a.289.1		2	252.191	even	6
3024.2.t.a.1873.1		2	12.11	even	2
7938.2.a.b.1.1		1	63.31	odd	6
7938.2.a.m.1.1		1	63.4	even	3
7938.2.a.t.1.1		1	63.32	odd	6
7938.2.a.be.1.1		1	63.59	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.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +1.73205i q^{6} +(2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +1.73205i q^{6} +(2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(1.50000 - 2.59808i) q^{10} -3.00000 q^{11} +(1.50000 + 0.866025i) q^{12} +(0.500000 - 0.866025i) q^{13} +(0.500000 - 2.59808i) q^{14} +(-4.50000 + 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-1.50000 - 2.59808i) 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} -9.00000 q^{23} +(1.50000 - 0.866025i) q^{24} +4.00000 q^{25} +(-0.500000 - 0.866025i) q^{26} +5.19615i q^{27} +(-2.00000 - 1.73205i) q^{28} +(-1.50000 - 2.59808i) q^{29} +5.19615i q^{30} +(-4.00000 - 6.92820i) q^{31} +(0.500000 + 0.866025i) 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} +7.00000 q^{38} +1.73205i q^{39} -3.00000 q^{40} +(-1.50000 + 2.59808i) q^{41} +(1.50000 + 4.33013i) 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} +(5.50000 - 4.33013i) q^{49} +(2.00000 - 3.46410i) q^{50} -5.19615i q^{51} -1.00000 q^{52} +(-1.50000 + 2.59808i) q^{53} +(4.50000 + 2.59808i) q^{54} -9.00000 q^{55} +(-2.50000 + 0.866025i) q^{56} +(-10.5000 - 6.06218i) q^{57} -3.00000 q^{58} +(4.50000 + 2.59808i) q^{60} +(-1.00000 + 1.73205i) q^{61} -8.00000 q^{62} +(1.50000 - 7.79423i) q^{63} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{65} -5.19615i q^{66} +(2.00000 + 3.46410i) q^{67} +3.00000 q^{68} +(13.5000 - 7.79423i) q^{69} +(1.50000 - 7.79423i) q^{70} +12.0000 q^{71} +(-1.50000 + 2.59808i) q^{72} +(-5.50000 + 9.52628i) q^{73} +1.00000 q^{74} +(-6.00000 + 3.46410i) q^{75} +(3.50000 - 6.06218i) q^{76} +(-7.50000 + 2.59808i) q^{77} +(1.50000 + 0.866025i) q^{78} +(8.00000 - 13.8564i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(1.50000 + 2.59808i) q^{82} +(4.50000 + 7.79423i) q^{83} +(4.50000 + 0.866025i) q^{84} +(-4.50000 + 7.79423i) q^{85} +1.00000 q^{86} +(4.50000 + 2.59808i) q^{87} +3.00000 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} +(12.0000 + 6.92820i) q^{93} +(10.5000 + 18.1865i) q^{95} +(-1.50000 - 0.866025i) q^{96} +(0.500000 + 0.866025i) q^{97} +(-1.00000 - 6.92820i) q^{98} +(-4.50000 + 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 3 q^{3} - q^{4} + 6 q^{5} + 5 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + q^2 - 3 * q^3 - q^4 + 6 * q^5 + 5 * q^7 - 2 * q^8 + 3 * q^9	\( 2 q + q^{2} - 3 q^{3} - q^{4} + 6 q^{5} + 5 q^{7} - 2 q^{8} + 3 q^{9} + 3 q^{10} - 6 q^{11} + 3 q^{12} + q^{13} + q^{14} - 9 q^{15} - q^{16} - 3 q^{17} - 3 q^{18} + 7 q^{19} - 3 q^{20} - 6 q^{21} - 3 q^{22} - 18 q^{23} + 3 q^{24} + 8 q^{25} - q^{26} - 4 q^{28} - 3 q^{29} - 8 q^{31} + q^{32} + 9 q^{33} + 3 q^{34} + 15 q^{35} - 6 q^{36} + q^{37} + 14 q^{38} - 6 q^{40} - 3 q^{41} + 3 q^{42} + q^{43} + 3 q^{44} + 9 q^{45} - 9 q^{46} + 11 q^{49} + 4 q^{50} - 2 q^{52} - 3 q^{53} + 9 q^{54} - 18 q^{55} - 5 q^{56} - 21 q^{57} - 6 q^{58} + 9 q^{60} - 2 q^{61} - 16 q^{62} + 3 q^{63} + 2 q^{64} + 3 q^{65} + 4 q^{67} + 6 q^{68} + 27 q^{69} + 3 q^{70} + 24 q^{71} - 3 q^{72} - 11 q^{73} + 2 q^{74} - 12 q^{75} + 7 q^{76} - 15 q^{77} + 3 q^{78} + 16 q^{79} - 3 q^{80} - 9 q^{81} + 3 q^{82} + 9 q^{83} + 9 q^{84} - 9 q^{85} + 2 q^{86} + 9 q^{87} + 6 q^{88} - 3 q^{89} - 9 q^{90} + q^{91} + 9 q^{92} + 24 q^{93} + 21 q^{95} - 3 q^{96} + q^{97} - 2 q^{98} - 9 q^{99}+O(q^{100}) \) 2 * q + q^2 - 3 * q^3 - q^4 + 6 * q^5 + 5 * q^7 - 2 * q^8 + 3 * q^9 + 3 * q^10 - 6 * q^11 + 3 * q^12 + q^13 + q^14 - 9 * q^15 - q^16 - 3 * q^17 - 3 * q^18 + 7 * q^19 - 3 * q^20 - 6 * q^21 - 3 * q^22 - 18 * q^23 + 3 * q^24 + 8 * q^25 - q^26 - 4 * q^28 - 3 * q^29 - 8 * q^31 + q^32 + 9 * q^33 + 3 * q^34 + 15 * q^35 - 6 * q^36 + q^37 + 14 * q^38 - 6 * q^40 - 3 * q^41 + 3 * q^42 + q^43 + 3 * q^44 + 9 * q^45 - 9 * q^46 + 11 * q^49 + 4 * q^50 - 2 * q^52 - 3 * q^53 + 9 * q^54 - 18 * q^55 - 5 * q^56 - 21 * q^57 - 6 * q^58 + 9 * q^60 - 2 * q^61 - 16 * q^62 + 3 * q^63 + 2 * q^64 + 3 * q^65 + 4 * q^67 + 6 * q^68 + 27 * q^69 + 3 * q^70 + 24 * q^71 - 3 * q^72 - 11 * q^73 + 2 * q^74 - 12 * q^75 + 7 * q^76 - 15 * q^77 + 3 * q^78 + 16 * q^79 - 3 * q^80 - 9 * q^81 + 3 * q^82 + 9 * q^83 + 9 * q^84 - 9 * q^85 + 2 * q^86 + 9 * q^87 + 6 * q^88 - 3 * q^89 - 9 * q^90 + q^91 + 9 * q^92 + 24 * q^93 + 21 * q^95 - 3 * q^96 + q^97 - 2 * q^98 - 9 * q^99

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