LMFDB - Embedded newform 63.2.g.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,2,Mod(4,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, 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("63.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	63.g (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:	$0.503057532734$
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			4.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	63.4
Dual form			63.2.g.a.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} -1.73205i q^{6} +(0.500000 + 2.59808i) q^{7} -3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} -1.73205i q^{6} +(0.500000 + 2.59808i) q^{7} -3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(0.500000 - 0.866025i) q^{10} +5.00000 q^{11} +(-1.50000 - 0.866025i) q^{12} +(2.50000 - 4.33013i) q^{13} +(-2.50000 - 0.866025i) q^{14} +(1.50000 - 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(1.50000 + 2.59808i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-3.00000 - 3.46410i) q^{21} +(-2.50000 + 4.33013i) q^{22} +3.00000 q^{23} +(4.50000 - 2.59808i) q^{24} -4.00000 q^{25} +(2.50000 + 4.33013i) q^{26} +5.19615i q^{27} +(-2.00000 + 1.73205i) q^{28} +(0.500000 + 0.866025i) q^{29} +1.73205i q^{30} +(-2.50000 - 4.33013i) q^{32} +(-7.50000 + 4.33013i) q^{33} +(-1.50000 - 2.59808i) q^{34} +(-0.500000 - 2.59808i) q^{35} +3.00000 q^{36} +(-1.50000 - 2.59808i) q^{37} +1.00000 q^{38} +8.66025i q^{39} +3.00000 q^{40} +(2.50000 - 4.33013i) q^{41} +(4.50000 - 0.866025i) q^{42} +(0.500000 + 0.866025i) q^{43} +(2.50000 + 4.33013i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(-1.50000 + 2.59808i) q^{46} +1.73205i q^{48} +(-6.50000 + 2.59808i) q^{49} +(2.00000 - 3.46410i) q^{50} -5.19615i q^{51} +5.00000 q^{52} +(4.50000 - 7.79423i) q^{53} +(-4.50000 - 2.59808i) q^{54} -5.00000 q^{55} +(-1.50000 - 7.79423i) q^{56} +(1.50000 + 0.866025i) q^{57} -1.00000 q^{58} +(1.50000 + 0.866025i) q^{60} +(7.00000 - 12.1244i) q^{61} +(7.50000 + 2.59808i) q^{63} +7.00000 q^{64} +(-2.50000 + 4.33013i) q^{65} -8.66025i q^{66} +(-2.00000 - 3.46410i) q^{67} -3.00000 q^{68} +(-4.50000 + 2.59808i) q^{69} +(2.50000 + 0.866025i) q^{70} -12.0000 q^{71} +(-4.50000 + 7.79423i) q^{72} +(-1.50000 + 2.59808i) q^{73} +3.00000 q^{74} +(6.00000 - 3.46410i) q^{75} +(0.500000 - 0.866025i) q^{76} +(2.50000 + 12.9904i) q^{77} +(-7.50000 - 4.33013i) q^{78} +(-4.00000 + 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(2.50000 + 4.33013i) q^{82} +(4.50000 + 7.79423i) q^{83} +(1.50000 - 4.33013i) q^{84} +(1.50000 - 2.59808i) q^{85} -1.00000 q^{86} +(-1.50000 - 0.866025i) q^{87} -15.0000 q^{88} +(6.50000 + 11.2583i) q^{89} +(-1.50000 - 2.59808i) q^{90} +(12.5000 + 4.33013i) q^{91} +(1.50000 + 2.59808i) q^{92} +(0.500000 + 0.866025i) q^{95} +(7.50000 + 4.33013i) q^{96} +(4.50000 + 7.79423i) q^{97} +(1.00000 - 6.92820i) q^{98} +(7.50000 - 12.9904i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 3 q^{3} + q^{4} - 2 q^{5} + q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - q^2 - 3 * q^3 + q^4 - 2 * q^5 + q^7 - 6 * q^8 + 3 * q^9	$ 2 q - q^{2} - 3 q^{3} + q^{4} - 2 q^{5} + q^{7} - 6 q^{8} + 3 q^{9} + q^{10} + 10 q^{11} - 3 q^{12} + 5 q^{13} - 5 q^{14} + 3 q^{15} + q^{16} - 3 q^{17} + 3 q^{18} - q^{19} - q^{20} - 6 q^{21} - 5 q^{22} + 6 q^{23} + 9 q^{24} - 8 q^{25} + 5 q^{26} - 4 q^{28} + q^{29} - 5 q^{32} - 15 q^{33} - 3 q^{34} - q^{35} + 6 q^{36} - 3 q^{37} + 2 q^{38} + 6 q^{40} + 5 q^{41} + 9 q^{42} + q^{43} + 5 q^{44} - 3 q^{45} - 3 q^{46} - 13 q^{49} + 4 q^{50} + 10 q^{52} + 9 q^{53} - 9 q^{54} - 10 q^{55} - 3 q^{56} + 3 q^{57} - 2 q^{58} + 3 q^{60} + 14 q^{61} + 15 q^{63} + 14 q^{64} - 5 q^{65} - 4 q^{67} - 6 q^{68} - 9 q^{69} + 5 q^{70} - 24 q^{71} - 9 q^{72} - 3 q^{73} + 6 q^{74} + 12 q^{75} + q^{76} + 5 q^{77} - 15 q^{78} - 8 q^{79} - q^{80} - 9 q^{81} + 5 q^{82} + 9 q^{83} + 3 q^{84} + 3 q^{85} - 2 q^{86} - 3 q^{87} - 30 q^{88} + 13 q^{89} - 3 q^{90} + 25 q^{91} + 3 q^{92} + q^{95} + 15 q^{96} + 9 q^{97} + 2 q^{98} + 15 q^{99}+O(q^{100}) $ 2 * q - q^2 - 3 * q^3 + q^4 - 2 * q^5 + q^7 - 6 * q^8 + 3 * q^9 + q^10 + 10 * q^11 - 3 * q^12 + 5 * q^13 - 5 * q^14 + 3 * q^15 + q^16 - 3 * q^17 + 3 * q^18 - q^19 - q^20 - 6 * q^21 - 5 * q^22 + 6 * q^23 + 9 * q^24 - 8 * q^25 + 5 * q^26 - 4 * q^28 + q^29 - 5 * q^32 - 15 * q^33 - 3 * q^34 - q^35 + 6 * q^36 - 3 * q^37 + 2 * q^38 + 6 * q^40 + 5 * q^41 + 9 * q^42 + q^43 + 5 * q^44 - 3 * q^45 - 3 * q^46 - 13 * q^49 + 4 * q^50 + 10 * q^52 + 9 * q^53 - 9 * q^54 - 10 * q^55 - 3 * q^56 + 3 * q^57 - 2 * q^58 + 3 * q^60 + 14 * q^61 + 15 * q^63 + 14 * q^64 - 5 * q^65 - 4 * q^67 - 6 * q^68 - 9 * q^69 + 5 * q^70 - 24 * q^71 - 9 * q^72 - 3 * q^73 + 6 * q^74 + 12 * q^75 + q^76 + 5 * q^77 - 15 * q^78 - 8 * q^79 - q^80 - 9 * q^81 + 5 * q^82 + 9 * q^83 + 3 * q^84 + 3 * q^85 - 2 * q^86 - 3 * q^87 - 30 * q^88 + 13 * q^89 - 3 * q^90 + 25 * q^91 + 3 * q^92 + q^95 + 15 * q^96 + 9 * q^97 + 2 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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	−0.986869	−	0.161521i	$-0.948360\pi$
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	0.633316	+	0.773893i	$0.281693\pi$
$3$	−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
$5$	−1.00000			−0.447214			−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000			−0.447214			−0.223607	+	0.974679i	$0.571783\pi$
$6$		−	1.73205i		−	0.707107i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$	−3.00000			−1.06066
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	5.00000			1.50756			0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000			1.50756			0.753778	+	0.657129i	$0.228229\pi$
$12$	−1.50000	−	0.866025i	−0.433013	−	0.250000i
$13$	2.50000	−	4.33013i	0.693375	−	1.20096i	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	2.50000	−	4.33013i	0.693375	−	1.20096i	0.970725	−	0.240192i	$-0.0772105\pi$
$14$	−2.50000	−	0.866025i	−0.668153	−	0.231455i
$15$	1.50000	−	0.866025i	0.387298	−	0.223607i
$16$	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
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	−3.00000	−	3.46410i	−0.654654	−	0.755929i
$22$	−2.50000	+	4.33013i	−0.533002	+	0.923186i
$23$	3.00000			0.625543			0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000			0.625543			0.312772	+	0.949828i	$0.398743\pi$
$24$	4.50000	−	2.59808i	0.918559	−	0.530330i
$25$	−4.00000			−0.800000
$26$	2.50000	+	4.33013i	0.490290	+	0.849208i
$27$			5.19615i			1.00000i
$28$	−2.00000	+	1.73205i	−0.377964	+	0.327327i
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	0.908708	−	0.417432i	$-0.137070\pi$
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	−0.815861	+	0.578249i	$0.803736\pi$
$30$			1.73205i			0.316228i
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	−2.50000	−	4.33013i	−0.441942	−	0.765466i
$33$	−7.50000	+	4.33013i	−1.30558	+	0.753778i
$34$	−1.50000	−	2.59808i	−0.257248	−	0.445566i
$35$	−0.500000	−	2.59808i	−0.0845154	−	0.439155i
$36$	3.00000			0.500000
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	0.715981	−	0.698119i	$-0.245980\pi$
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	−0.962580	+	0.270998i	$0.912646\pi$
$38$	1.00000			0.162221
$39$			8.66025i			1.38675i
$40$	3.00000			0.474342
$41$	2.50000	−	4.33013i	0.390434	−	0.676252i	−0.602072	−	0.798441i	$-0.705658\pi$
$41$	2.50000	−	4.33013i	0.390434	−	0.676252i	0.992507	+	0.122189i	$0.0389915\pi$
$42$	4.50000	−	0.866025i	0.694365	−	0.133631i
$43$	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	$0.809039\pi$
$44$	2.50000	+	4.33013i	0.376889	+	0.652791i
$45$	−1.50000	+	2.59808i	−0.223607	+	0.387298i
$46$	−1.50000	+	2.59808i	−0.221163	+	0.383065i
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$			1.73205i			0.250000i
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	2.00000	−	3.46410i	0.282843	−	0.489898i
$51$		−	5.19615i		−	0.727607i
$52$	5.00000			0.693375
$53$	4.50000	−	7.79423i	0.618123	−	1.07062i	−0.371706	−	0.928351i	$-0.621227\pi$
$53$	4.50000	−	7.79423i	0.618123	−	1.07062i	0.989828	−	0.142269i	$-0.0454398\pi$
$54$	−4.50000	−	2.59808i	−0.612372	−	0.353553i
$55$	−5.00000			−0.674200
$56$	−1.50000	−	7.79423i	−0.200446	−	1.04155i
$57$	1.50000	+	0.866025i	0.198680	+	0.114708i
$58$	−1.00000			−0.131306
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$	1.50000	+	0.866025i	0.193649	+	0.111803i
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.832240	−	0.554416i	$-0.187058\pi$
$62$		0			0
$63$	7.50000	+	2.59808i	0.944911	+	0.327327i
$64$	7.00000			0.875000
$65$	−2.50000	+	4.33013i	−0.310087	+	0.537086i
$66$		−	8.66025i		−	1.06600i
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	0.717607	−	0.696449i	$-0.245238\pi$
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	−0.961946	+	0.273241i	$0.911904\pi$
$68$	−3.00000			−0.363803
$69$	−4.50000	+	2.59808i	−0.541736	+	0.312772i
$70$	2.50000	+	0.866025i	0.298807	+	0.103510i
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$	−4.50000	+	7.79423i	−0.530330	+	0.918559i
$73$	−1.50000	+	2.59808i	−0.175562	+	0.304082i	−0.940356	−	0.340193i	$-0.889507\pi$
$73$	−1.50000	+	2.59808i	−0.175562	+	0.304082i	0.764794	+	0.644275i	$0.222841\pi$
$74$	3.00000			0.348743
$75$	6.00000	−	3.46410i	0.692820	−	0.400000i
$76$	0.500000	−	0.866025i	0.0573539	−	0.0993399i
$77$	2.50000	+	12.9904i	0.284901	+	1.48039i
$78$	−7.50000	−	4.33013i	−0.849208	−	0.490290i
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	2.50000	+	4.33013i	0.276079	+	0.478183i
$83$	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	$0.668890\pi$
$84$	1.50000	−	4.33013i	0.163663	−	0.472456i
$85$	1.50000	−	2.59808i	0.162698	−	0.281801i
$86$	−1.00000			−0.107833
$87$	−1.50000	−	0.866025i	−0.160817	−	0.0928477i
$88$	−15.0000			−1.59901
$89$	6.50000	+	11.2583i	0.688999	+	1.19338i	0.972162	+	0.234309i	$0.0752827\pi$
$89$	6.50000	+	11.2583i	0.688999	+	1.19338i	−0.283164	+	0.959072i	$0.591384\pi$
$90$	−1.50000	−	2.59808i	−0.158114	−	0.273861i
$91$	12.5000	+	4.33013i	1.31036	+	0.453921i
$92$	1.50000	+	2.59808i	0.156386	+	0.270868i
$93$		0			0
$94$		0			0
$95$	0.500000	+	0.866025i	0.0512989	+	0.0888523i
$96$	7.50000	+	4.33013i	0.765466	+	0.441942i
$97$	4.50000	+	7.79423i	0.456906	+	0.791384i	0.998796	−	0.0490655i	$-0.0156243\pi$
$97$	4.50000	+	7.79423i	0.456906	+	0.791384i	−0.541890	+	0.840450i	$0.682291\pi$
$98$	1.00000	−	6.92820i	0.101015	−	0.699854i
$99$	7.50000	−	12.9904i	0.753778	−	1.30558i
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	−17.0000			−1.69156			−0.845782	−	0.533529i	$-0.820865\pi$
$101$	−17.0000			−1.69156			−0.845782	+	0.533529i	$0.820865\pi$
$102$	4.50000	+	2.59808i	0.445566	+	0.257248i
$103$	−1.00000			−0.0985329			−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000			−0.0985329			−0.0492665	+	0.998786i	$0.515688\pi$
$104$	−7.50000	+	12.9904i	−0.735436	+	1.27381i
$105$	3.00000	+	3.46410i	0.292770	+	0.338062i
$106$	4.50000	+	7.79423i	0.437079	+	0.757042i
$107$	−8.50000	−	14.7224i	−0.821726	−	1.42327i	−0.904396	−	0.426694i	$-0.859678\pi$
$107$	−8.50000	−	14.7224i	−0.821726	−	1.42327i	0.0826699	−	0.996577i	$-0.473655\pi$
$108$	−4.50000	+	2.59808i	−0.433013	+	0.250000i
$109$	4.50000	−	7.79423i	0.431022	−	0.746552i	−0.565940	−	0.824447i	$-0.691487\pi$
$109$	4.50000	−	7.79423i	0.431022	−	0.746552i	0.996962	+	0.0778949i	$0.0248199\pi$
$110$	2.50000	−	4.33013i	0.238366	−	0.412861i
$111$	4.50000	+	2.59808i	0.427121	+	0.246598i
$112$	2.50000	+	0.866025i	0.236228	+	0.0818317i
$113$	0.500000	−	0.866025i	0.0470360	−	0.0814688i	−0.841549	−	0.540181i	$-0.818356\pi$
$113$	0.500000	−	0.866025i	0.0470360	−	0.0814688i	0.888585	+	0.458712i	$0.151689\pi$
$114$	−1.50000	+	0.866025i	−0.140488	+	0.0811107i
$115$	−3.00000			−0.279751
$116$	−0.500000	+	0.866025i	−0.0464238	+	0.0804084i
$117$	−7.50000	−	12.9904i	−0.693375	−	1.20096i
$118$		0			0
$119$	−7.50000	−	2.59808i	−0.687524	−	0.238165i
$120$	−4.50000	+	2.59808i	−0.410792	+	0.237171i
$121$	14.0000			1.27273
$122$	7.00000	+	12.1244i	0.633750	+	1.09769i
$123$			8.66025i			0.780869i
$124$		0			0
$125$	9.00000			0.804984
$126$	−6.00000	+	5.19615i	−0.534522	+	0.462910i
$127$	−12.0000			−1.06483			−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000			−1.06483			−0.532414	+	0.846484i	$0.678715\pi$
$128$	1.50000	−	2.59808i	0.132583	−	0.229640i
$129$	−1.50000	−	0.866025i	−0.132068	−	0.0762493i
$130$	−2.50000	−	4.33013i	−0.219265	−	0.379777i
$131$	−1.00000			−0.0873704			−0.0436852	−	0.999045i	$-0.513910\pi$
$131$	−1.00000			−0.0873704			−0.0436852	+	0.999045i	$0.513910\pi$
$132$	−7.50000	−	4.33013i	−0.652791	−	0.376889i
$133$	2.00000	−	1.73205i	0.173422	−	0.150188i
$134$	4.00000			0.345547
$135$		−	5.19615i		−	0.447214i
$136$	4.50000	−	7.79423i	0.385872	−	0.668350i
$137$	−9.00000			−0.768922			−0.384461	−	0.923141i	$-0.625613\pi$
$137$	−9.00000			−0.768922			−0.384461	+	0.923141i	$0.625613\pi$
$138$		−	5.19615i		−	0.442326i
$139$	−4.50000	+	7.79423i	−0.381685	+	0.661098i	−0.991303	−	0.131597i	$-0.957989\pi$
$139$	−4.50000	+	7.79423i	−0.381685	+	0.661098i	0.609618	+	0.792695i	$0.291323\pi$
$140$	2.00000	−	1.73205i	0.169031	−	0.146385i
$141$		0			0
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$	12.5000	−	21.6506i	1.04530	−	1.81052i
$144$	−1.50000	−	2.59808i	−0.125000	−	0.216506i
$145$	−0.500000	−	0.866025i	−0.0415227	−	0.0719195i
$146$	−1.50000	−	2.59808i	−0.124141	−	0.215018i
$147$	7.50000	−	9.52628i	0.618590	−	0.785714i
$148$	1.50000	−	2.59808i	0.123299	−	0.213561i
$149$	3.00000			0.245770			0.122885	−	0.992421i	$-0.460785\pi$
$149$	3.00000			0.245770			0.122885	+	0.992421i	$0.460785\pi$
$150$			6.92820i			0.565685i
$151$	5.00000			0.406894			0.203447	−	0.979086i	$-0.434786\pi$
$151$	5.00000			0.406894			0.203447	+	0.979086i	$0.434786\pi$
$152$	1.50000	+	2.59808i	0.121666	+	0.210732i
$153$	4.50000	+	7.79423i	0.363803	+	0.630126i
$154$	−12.5000	−	4.33013i	−1.00728	−	0.348932i
$155$		0			0
$156$	−7.50000	+	4.33013i	−0.600481	+	0.346688i
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	0.997609	+	0.0691164i	$0.0220180\pi$
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	−0.438948	+	0.898513i	$0.644649\pi$
$158$	−4.00000	−	6.92820i	−0.318223	−	0.551178i
$159$			15.5885i			1.23625i
$160$	2.50000	+	4.33013i	0.197642	+	0.342327i
$161$	1.50000	+	7.79423i	0.118217	+	0.614271i
$162$	9.00000			0.707107
$163$	5.50000	+	9.52628i	0.430793	+	0.746156i	0.996942	−	0.0781474i	$-0.0249005\pi$
$163$	5.50000	+	9.52628i	0.430793	+	0.746156i	−0.566149	+	0.824303i	$0.691567\pi$
$164$	5.00000			0.390434
$165$	7.50000	−	4.33013i	0.583874	−	0.337100i
$166$	−9.00000			−0.698535
$167$	9.50000	−	16.4545i	0.735132	−	1.27329i	−0.219533	−	0.975605i	$-0.570453\pi$
$167$	9.50000	−	16.4545i	0.735132	−	1.27329i	0.954665	−	0.297681i	$-0.0962132\pi$
$168$	9.00000	+	10.3923i	0.694365	+	0.801784i
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$	1.50000	+	2.59808i	0.115045	+	0.199263i
$171$	−3.00000			−0.229416
$172$	−0.500000	+	0.866025i	−0.0381246	+	0.0660338i
$173$	7.00000	−	12.1244i	0.532200	−	0.921798i	−0.467093	−	0.884208i	$-0.654699\pi$
$173$	7.00000	−	12.1244i	0.532200	−	0.921798i	0.999293	−	0.0375896i	$-0.0119679\pi$
$174$	1.50000	−	0.866025i	0.113715	−	0.0656532i
$175$	−2.00000	−	10.3923i	−0.151186	−	0.785584i
$176$	2.50000	−	4.33013i	0.188445	−	0.326396i
$177$		0			0
$178$	−13.0000			−0.974391
$179$	−9.50000	+	16.4545i	−0.710063	+	1.22987i	0.254770	+	0.967002i	$0.418000\pi$
$179$	−9.50000	+	16.4545i	−0.710063	+	1.22987i	−0.964833	+	0.262864i	$0.915333\pi$
$180$	−3.00000			−0.223607
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$	−10.0000	+	8.66025i	−0.741249	+	0.641941i
$183$			24.2487i			1.79252i
$184$	−9.00000			−0.663489
$185$	1.50000	+	2.59808i	0.110282	+	0.191014i
$186$		0			0
$187$	−7.50000	+	12.9904i	−0.548454	+	0.949951i
$188$		0			0
$189$	−13.5000	+	2.59808i	−0.981981	+	0.188982i
$190$	−1.00000			−0.0725476
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	−0.973674	−	0.227946i	$-0.926799\pi$
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	0.684244	+	0.729253i	$0.260132\pi$
$192$	−10.5000	+	6.06218i	−0.757772	+	0.437500i
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	0.987945	−	0.154805i	$-0.0494748\pi$
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	−0.628037	+	0.778183i	$0.716141\pi$
$194$	−9.00000			−0.646162
$195$		−	8.66025i		−	0.620174i
$196$	−5.50000	−	4.33013i	−0.392857	−	0.309295i
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$	7.50000	+	12.9904i	0.533002	+	0.923186i
$199$	−1.50000	+	2.59808i	−0.106332	+	0.184173i	−0.914282	−	0.405079i	$-0.867244\pi$
$199$	−1.50000	+	2.59808i	−0.106332	+	0.184173i	0.807950	+	0.589252i	$0.200577\pi$
$200$	12.0000			0.848528
$201$	6.00000	+	3.46410i	0.423207	+	0.244339i
$202$	8.50000	−	14.7224i	0.598058	−	1.03587i
$203$	−2.00000	+	1.73205i	−0.140372	+	0.121566i
$204$	4.50000	−	2.59808i	0.315063	−	0.181902i
$205$	−2.50000	+	4.33013i	−0.174608	+	0.302429i
$206$	0.500000	−	0.866025i	0.0348367	−	0.0603388i
$207$	4.50000	−	7.79423i	0.312772	−	0.541736i
$208$	−2.50000	−	4.33013i	−0.173344	−	0.300240i
$209$	−2.50000	−	4.33013i	−0.172929	−	0.299521i
$210$	−4.50000	+	0.866025i	−0.310530	+	0.0597614i
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	−0.998221	−	0.0596196i	$-0.981011\pi$
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	0.550743	+	0.834675i	$0.314345\pi$
$212$	9.00000			0.618123
$213$	18.0000	−	10.3923i	1.23334	−	0.712069i
$214$	17.0000			1.16210
$215$	−0.500000	−	0.866025i	−0.0340997	−	0.0590624i
$216$		−	15.5885i		−	1.06066i
$217$		0			0
$218$	4.50000	+	7.79423i	0.304778	+	0.527892i
$219$		−	5.19615i		−	0.351123i
$220$	−2.50000	−	4.33013i	−0.168550	−	0.291937i
$221$	7.50000	+	12.9904i	0.504505	+	0.873828i
$222$	−4.50000	+	2.59808i	−0.302020	+	0.174371i
$223$	−9.50000	−	16.4545i	−0.636167	−	1.10187i	−0.986267	−	0.165161i	$-0.947186\pi$
$223$	−9.50000	−	16.4545i	−0.636167	−	1.10187i	0.350100	−	0.936713i	$-0.386148\pi$
$224$	10.0000	−	8.66025i	0.668153	−	0.578638i
$225$	−6.00000	+	10.3923i	−0.400000	+	0.692820i
$226$	0.500000	+	0.866025i	0.0332595	+	0.0576072i
$227$	−3.00000			−0.199117			−0.0995585	−	0.995032i	$-0.531743\pi$
$227$	−3.00000			−0.199117			−0.0995585	+	0.995032i	$0.531743\pi$
$228$			1.73205i			0.114708i
$229$	−1.00000			−0.0660819			−0.0330409	−	0.999454i	$-0.510519\pi$
$229$	−1.00000			−0.0660819			−0.0330409	+	0.999454i	$0.510519\pi$
$230$	1.50000	−	2.59808i	0.0989071	−	0.171312i
$231$	−15.0000	−	17.3205i	−0.986928	−	1.13961i
$232$	−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	$0.864664\pi$
$234$	15.0000			0.980581
$235$		0			0
$236$		0			0
$237$		−	13.8564i		−	0.900070i
$238$	6.00000	−	5.19615i	0.388922	−	0.336817i
$239$	7.50000	−	12.9904i	0.485135	−	0.840278i	−0.514719	−	0.857359i	$-0.672104\pi$
$239$	7.50000	−	12.9904i	0.485135	−	0.840278i	0.999854	+	0.0170808i	$0.00543724\pi$
$240$		−	1.73205i		−	0.111803i
$241$	11.0000			0.708572			0.354286	−	0.935137i	$-0.384724\pi$
$241$	11.0000			0.708572			0.354286	+	0.935137i	$0.384724\pi$
$242$	−7.00000	+	12.1244i	−0.449977	+	0.779383i
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$	14.0000			0.896258
$245$	6.50000	−	2.59808i	0.415270	−	0.165985i
$246$	−7.50000	−	4.33013i	−0.478183	−	0.276079i
$247$	−5.00000			−0.318142
$248$		0			0
$249$	−13.5000	−	7.79423i	−0.855528	−	0.493939i
$250$	−4.50000	+	7.79423i	−0.284605	+	0.492950i
$251$	−28.0000			−1.76734			−0.883672	−	0.468106i	$-0.844936\pi$
$251$	−28.0000			−1.76734			−0.883672	+	0.468106i	$0.844936\pi$
$252$	1.50000	+	7.79423i	0.0944911	+	0.490990i
$253$	15.0000			0.943042
$254$	6.00000	−	10.3923i	0.376473	−	0.652071i
$255$			5.19615i			0.325396i
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	−29.0000			−1.80897			−0.904485	−	0.426505i	$-0.859745\pi$
$257$	−29.0000			−1.80897			−0.904485	+	0.426505i	$0.859745\pi$
$258$	1.50000	−	0.866025i	0.0933859	−	0.0539164i
$259$	6.00000	−	5.19615i	0.372822	−	0.322873i
$260$	−5.00000			−0.310087
$261$	3.00000			0.185695
$262$	0.500000	−	0.866025i	0.0308901	−	0.0535032i
$263$	5.00000			0.308313			0.154157	−	0.988046i	$-0.450734\pi$
$263$	5.00000			0.308313			0.154157	+	0.988046i	$0.450734\pi$
$264$	22.5000	−	12.9904i	1.38478	−	0.799503i
$265$	−4.50000	+	7.79423i	−0.276433	+	0.478796i
$266$	0.500000	+	2.59808i	0.0306570	+	0.159298i
$267$	−19.5000	−	11.2583i	−1.19338	−	0.688999i
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	−0.908124	−	0.418701i	$-0.862486\pi$
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	0.816668	+	0.577108i	$0.195819\pi$
$270$	4.50000	+	2.59808i	0.273861	+	0.158114i
$271$	−0.500000	−	0.866025i	−0.0303728	−	0.0526073i	0.850439	−	0.526073i	$-0.176336\pi$
$271$	−0.500000	−	0.866025i	−0.0303728	−	0.0526073i	−0.880812	+	0.473466i	$0.843003\pi$
$272$	1.50000	+	2.59808i	0.0909509	+	0.157532i
$273$	−22.5000	+	4.33013i	−1.36176	+	0.262071i
$274$	4.50000	−	7.79423i	0.271855	−	0.470867i
$275$	−20.0000			−1.20605
$276$	−4.50000	−	2.59808i	−0.270868	−	0.156386i
$277$	19.0000			1.14160			0.570800	−	0.821089i	$-0.306633\pi$
$277$	19.0000			1.14160			0.570800	+	0.821089i	$0.306633\pi$
$278$	−4.50000	−	7.79423i	−0.269892	−	0.467467i
$279$		0			0
$280$	1.50000	+	7.79423i	0.0896421	+	0.465794i
$281$	14.5000	+	25.1147i	0.864997	+	1.49822i	0.867050	+	0.498222i	$0.166013\pi$
$281$	14.5000	+	25.1147i	0.864997	+	1.49822i	−0.00205220	+	0.999998i	$0.500653\pi$
$282$		0			0
$283$	−14.0000	−	24.2487i	−0.832214	−	1.44144i	−0.896279	−	0.443491i	$-0.853740\pi$
$283$	−14.0000	−	24.2487i	−0.832214	−	1.44144i	0.0640654	−	0.997946i	$-0.479593\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$	−1.50000	−	0.866025i	−0.0888523	−	0.0512989i
$286$	12.5000	+	21.6506i	0.739140	+	1.28023i
$287$	12.5000	+	4.33013i	0.737852	+	0.255599i
$288$	−15.0000			−0.883883
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	1.00000			0.0587220
$291$	−13.5000	−	7.79423i	−0.791384	−	0.456906i
$292$	−3.00000			−0.175562
$293$	2.50000	−	4.33013i	0.146052	−	0.252969i	−0.783713	−	0.621123i	$-0.786677\pi$
$293$	2.50000	−	4.33013i	0.146052	−	0.252969i	0.929765	+	0.368154i	$0.120010\pi$
$294$	4.50000	+	11.2583i	0.262445	+	0.656599i
$295$		0			0
$296$	4.50000	+	7.79423i	0.261557	+	0.453030i
$297$			25.9808i			1.50756i
$298$	−1.50000	+	2.59808i	−0.0868927	+	0.150503i
$299$	7.50000	−	12.9904i	0.433736	−	0.751253i
$300$	6.00000	+	3.46410i	0.346410	+	0.200000i
$301$	−2.00000	+	1.73205i	−0.115278	+	0.0998337i
$302$	−2.50000	+	4.33013i	−0.143859	+	0.249171i
$303$	25.5000	−	14.7224i	1.46494	−	0.845782i
$304$	−1.00000			−0.0573539
$305$	−7.00000	+	12.1244i	−0.400819	+	0.694239i
$306$	−9.00000			−0.514496
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$	−10.0000	+	8.66025i	−0.569803	+	0.493464i
$309$	1.50000	−	0.866025i	0.0853320	−	0.0492665i
$310$		0			0
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$		−	25.9808i		−	1.47087i
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	−0.993186	−	0.116543i	$-0.962819\pi$
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	0.597522	+	0.801852i	$0.296152\pi$
$314$	−14.0000			−0.790066
$315$	−7.50000	−	2.59808i	−0.422577	−	0.146385i
$316$	−8.00000			−0.450035
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	−0.769395	−	0.638774i	$-0.779442\pi$
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	0.937892	+	0.346929i	$0.112775\pi$
$318$	−13.5000	−	7.79423i	−0.757042	−	0.437079i
$319$	2.50000	+	4.33013i	0.139973	+	0.242441i
$320$	−7.00000			−0.391312
$321$	25.5000	+	14.7224i	1.42327	+	0.821726i
$322$	−7.50000	−	2.59808i	−0.417959	−	0.144785i
$323$	3.00000			0.166924
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$	−10.0000	+	17.3205i	−0.554700	+	0.960769i
$326$	−11.0000			−0.609234
$327$			15.5885i			0.862044i
$328$	−7.50000	+	12.9904i	−0.414118	+	0.717274i
$329$		0			0
$330$			8.66025i			0.476731i
$331$	−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
$333$	−9.00000			−0.493197
$334$	9.50000	+	16.4545i	0.519817	+	0.900349i
$335$	2.00000	+	3.46410i	0.109272	+	0.189264i
$336$	−4.50000	+	0.866025i	−0.245495	+	0.0472456i
$337$	14.5000	−	25.1147i	0.789865	−	1.36809i	−0.136184	−	0.990684i	$-0.543484\pi$
$337$	14.5000	−	25.1147i	0.789865	−	1.36809i	0.926049	−	0.377403i	$-0.123183\pi$
$338$	12.0000			0.652714
$339$			1.73205i			0.0940721i
$340$	3.00000			0.162698
$341$		0			0
$342$	1.50000	−	2.59808i	0.0811107	−	0.140488i
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	−1.50000	−	2.59808i	−0.0808746	−	0.140079i
$345$	4.50000	−	2.59808i	0.242272	−	0.139876i
$346$	7.00000	+	12.1244i	0.376322	+	0.651809i
$347$	−2.00000	−	3.46410i	−0.107366	−	0.185963i	0.807337	−	0.590091i	$-0.200908\pi$
$347$	−2.00000	−	3.46410i	−0.107366	−	0.185963i	−0.914702	+	0.404128i	$0.867575\pi$
$348$		−	1.73205i		−	0.0928477i
$349$	−9.50000	−	16.4545i	−0.508523	−	0.880788i	−0.999951	−	0.00987003i	$-0.996858\pi$
$349$	−9.50000	−	16.4545i	−0.508523	−	0.880788i	0.491428	−	0.870918i	$-0.336475\pi$
$350$	10.0000	+	3.46410i	0.534522	+	0.185164i
$351$	22.5000	+	12.9904i	1.20096	+	0.693375i
$352$	−12.5000	−	21.6506i	−0.666252	−	1.15398i
$353$	11.0000			0.585471			0.292735	−	0.956193i	$-0.405434\pi$
$353$	11.0000			0.585471			0.292735	+	0.956193i	$0.405434\pi$
$354$		0			0
$355$	12.0000			0.636894
$356$	−6.50000	+	11.2583i	−0.344499	+	0.596690i
$357$	13.5000	−	2.59808i	0.714496	−	0.137505i
$358$	−9.50000	−	16.4545i	−0.502091	−	0.869646i
$359$	5.50000	+	9.52628i	0.290279	+	0.502778i	0.973876	−	0.227082i	$-0.0729186\pi$
$359$	5.50000	+	9.52628i	0.290279	+	0.502778i	−0.683597	+	0.729860i	$0.739585\pi$
$360$	4.50000	−	7.79423i	0.237171	−	0.410792i
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	7.00000	−	12.1244i	0.367912	−	0.637242i
$363$	−21.0000	+	12.1244i	−1.10221	+	0.636364i
$364$	2.50000	+	12.9904i	0.131036	+	0.680881i
$365$	1.50000	−	2.59808i	0.0785136	−	0.135990i
$366$	−21.0000	−	12.1244i	−1.09769	−	0.633750i
$367$	−3.00000			−0.156599			−0.0782994	−	0.996930i	$-0.524949\pi$
$367$	−3.00000			−0.156599			−0.0782994	+	0.996930i	$0.524949\pi$
$368$	1.50000	−	2.59808i	0.0781929	−	0.135434i
$369$	−7.50000	−	12.9904i	−0.390434	−	0.676252i
$370$	−3.00000			−0.155963
$371$	22.5000	+	7.79423i	1.16814	+	0.404656i
$372$		0			0
$373$	−25.0000			−1.29445			−0.647225	−	0.762299i	$-0.724071\pi$
$373$	−25.0000			−1.29445			−0.647225	+	0.762299i	$0.724071\pi$
$374$	−7.50000	−	12.9904i	−0.387816	−	0.671717i
$375$	−13.5000	+	7.79423i	−0.697137	+	0.402492i
$376$		0			0
$377$	5.00000			0.257513
$378$	4.50000	−	12.9904i	0.231455	−	0.668153i
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$	−0.500000	+	0.866025i	−0.0256495	+	0.0444262i
$381$	18.0000	−	10.3923i	0.922168	−	0.532414i
$382$	−4.00000	−	6.92820i	−0.204658	−	0.354478i
$383$	27.0000			1.37964			0.689818	−	0.723983i	$-0.257691\pi$
$383$	27.0000			1.37964			0.689818	+	0.723983i	$0.257691\pi$
$384$			5.19615i			0.265165i
$385$	−2.50000	−	12.9904i	−0.127412	−	0.662051i
$386$	−10.0000			−0.508987
$387$	3.00000			0.152499
$388$	−4.50000	+	7.79423i	−0.228453	+	0.395692i
$389$	−9.00000			−0.456318			−0.228159	−	0.973624i	$-0.573271\pi$
$389$	−9.00000			−0.456318			−0.228159	+	0.973624i	$0.573271\pi$
$390$	7.50000	+	4.33013i	0.379777	+	0.219265i
$391$	−4.50000	+	7.79423i	−0.227575	+	0.394171i
$392$	19.5000	−	7.79423i	0.984899	−	0.393668i
$393$	1.50000	−	0.866025i	0.0756650	−	0.0436852i
$394$	−1.00000	+	1.73205i	−0.0503793	+	0.0872595i
$395$	4.00000	−	6.92820i	0.201262	−	0.348596i
$396$	15.0000			0.753778
$397$	−7.50000	−	12.9904i	−0.376414	−	0.651969i	0.614123	−	0.789210i	$-0.289510\pi$
$397$	−7.50000	−	12.9904i	−0.376414	−	0.651969i	−0.990538	+	0.137241i	$0.956176\pi$
$398$	−1.50000	−	2.59808i	−0.0751882	−	0.130230i
$399$	−1.50000	+	4.33013i	−0.0750939	+	0.216777i
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	3.00000			0.149813			0.0749064	−	0.997191i	$-0.476134\pi$
$401$	3.00000			0.149813			0.0749064	+	0.997191i	$0.476134\pi$
$402$	−6.00000	+	3.46410i	−0.299253	+	0.172774i
$403$		0			0
$404$	−8.50000	−	14.7224i	−0.422891	−	0.732468i
$405$	4.50000	+	7.79423i	0.223607	+	0.387298i
$406$	−0.500000	−	2.59808i	−0.0248146	−	0.128940i
$407$	−7.50000	−	12.9904i	−0.371761	−	0.643909i
$408$			15.5885i			0.771744i
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	0.639430	−	0.768849i	$-0.279170\pi$
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	−0.985558	+	0.169338i	$0.945837\pi$
$410$	−2.50000	−	4.33013i	−0.123466	−	0.213850i
$411$	13.5000	−	7.79423i	0.665906	−	0.384461i
$412$	−0.500000	−	0.866025i	−0.0246332	−	0.0426660i
$413$		0			0
$414$	4.50000	+	7.79423i	0.221163	+	0.383065i
$415$	−4.50000	−	7.79423i	−0.220896	−	0.382604i
$416$	−25.0000			−1.22573
$417$		−	15.5885i		−	0.763370i
$418$	5.00000			0.244558
$419$	−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	$0.237220\pi$
$420$	−1.50000	+	4.33013i	−0.0731925	+	0.211289i
$421$	0.500000	+	0.866025i	0.0243685	+	0.0422075i	0.877952	−	0.478748i	$-0.158909\pi$
$421$	0.500000	+	0.866025i	0.0243685	+	0.0422075i	−0.853584	+	0.520955i	$0.825576\pi$
$422$	−6.50000	−	11.2583i	−0.316415	−	0.548047i
$423$		0			0
$424$	−13.5000	+	23.3827i	−0.655618	+	1.13556i
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$			20.7846i			1.00702i
$427$	35.0000	+	12.1244i	1.69377	+	0.586739i
$428$	8.50000	−	14.7224i	0.410863	−	0.711636i
$429$			43.3013i			2.09061i
$430$	1.00000			0.0482243
$431$	4.50000	−	7.79423i	0.216757	−	0.375435i	−0.737057	−	0.675830i	$-0.763785\pi$
$431$	4.50000	−	7.79423i	0.216757	−	0.375435i	0.953815	+	0.300395i	$0.0971186\pi$
$432$	4.50000	+	2.59808i	0.216506	+	0.125000i
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$	1.50000	+	0.866025i	0.0719195	+	0.0415227i
$436$	9.00000			0.431022
$437$	−1.50000	−	2.59808i	−0.0717547	−	0.124283i
$438$	4.50000	+	2.59808i	0.215018	+	0.124141i
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$	15.0000			0.715097
$441$	−3.00000	+	20.7846i	−0.142857	+	0.989743i
$442$	−15.0000			−0.713477
$443$	−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	$0.840097\pi$
$444$			5.19615i			0.246598i
$445$	−6.50000	−	11.2583i	−0.308130	−	0.533696i
$446$	19.0000			0.899676
$447$	−4.50000	+	2.59808i	−0.212843	+	0.122885i
$448$	3.50000	+	18.1865i	0.165359	+	0.859233i
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$	−6.00000	−	10.3923i	−0.282843	−	0.489898i
$451$	12.5000	−	21.6506i	0.588602	−	1.01949i
$452$	1.00000			0.0470360
$453$	−7.50000	+	4.33013i	−0.352381	+	0.203447i
$454$	1.50000	−	2.59808i	0.0703985	−	0.121934i
$455$	−12.5000	−	4.33013i	−0.586009	−	0.202999i
$456$	−4.50000	−	2.59808i	−0.210732	−	0.121666i
$457$	−11.0000	+	19.0526i	−0.514558	+	0.891241i	0.485299	+	0.874348i	$0.338711\pi$
$457$	−11.0000	+	19.0526i	−0.514558	+	0.891241i	−0.999857	+	0.0168929i	$0.994623\pi$
$458$	0.500000	−	0.866025i	0.0233635	−	0.0404667i
$459$	−13.5000	−	7.79423i	−0.630126	−	0.363803i
$460$	−1.50000	−	2.59808i	−0.0699379	−	0.121136i
$461$	−9.50000	−	16.4545i	−0.442459	−	0.766362i	0.555412	−	0.831575i	$-0.312560\pi$
$461$	−9.50000	−	16.4545i	−0.442459	−	0.766362i	−0.997871	+	0.0652135i	$0.979227\pi$
$462$	22.5000	−	4.33013i	1.04679	−	0.201456i
$463$	−6.50000	+	11.2583i	−0.302081	+	0.523219i	−0.976607	−	0.215032i	$-0.931015\pi$
$463$	−6.50000	+	11.2583i	−0.302081	+	0.523219i	0.674526	+	0.738251i	$0.264348\pi$
$464$	1.00000			0.0464238
$465$		0			0
$466$	3.00000			0.138972
$467$	13.5000	+	23.3827i	0.624705	+	1.08202i	0.988598	+	0.150581i	$0.0481143\pi$
$467$	13.5000	+	23.3827i	0.624705	+	1.08202i	−0.363892	+	0.931441i	$0.618552\pi$
$468$	7.50000	−	12.9904i	0.346688	−	0.600481i
$469$	8.00000	−	6.92820i	0.369406	−	0.319915i
$470$		0			0
$471$	−21.0000	−	12.1244i	−0.967629	−	0.558661i
$472$		0			0
$473$	2.50000	+	4.33013i	0.114950	+	0.199099i
$474$	12.0000	+	6.92820i	0.551178	+	0.318223i
$475$	2.00000	+	3.46410i	0.0917663	+	0.158944i
$476$	−1.50000	−	7.79423i	−0.0687524	−	0.357248i
$477$	−13.5000	−	23.3827i	−0.618123	−	1.07062i
$478$	7.50000	+	12.9904i	0.343042	+	0.594166i
$479$	25.0000			1.14228			0.571140	−	0.820853i	$-0.306501\pi$
$479$	25.0000			1.14228			0.571140	+	0.820853i	$0.306501\pi$
$480$	−7.50000	−	4.33013i	−0.342327	−	0.197642i
$481$	−15.0000			−0.683941
$482$	−5.50000	+	9.52628i	−0.250518	+	0.433910i
$483$	−9.00000	−	10.3923i	−0.409514	−	0.472866i
$484$	7.00000	+	12.1244i	0.318182	+	0.551107i
$485$	−4.50000	−	7.79423i	−0.204334	−	0.353918i
$486$	−13.5000	+	7.79423i	−0.612372	+	0.353553i
$487$	−9.50000	+	16.4545i	−0.430486	+	0.745624i	−0.996915	−	0.0784867i	$-0.974991\pi$
$487$	−9.50000	+	16.4545i	−0.430486	+	0.745624i	0.566429	+	0.824110i	$0.308325\pi$
$488$	−21.0000	+	36.3731i	−0.950625	+	1.64653i
$489$	−16.5000	−	9.52628i	−0.746156	−	0.430793i
$490$	−1.00000	+	6.92820i	−0.0451754	+	0.312984i
$491$	−6.50000	+	11.2583i	−0.293341	+	0.508081i	−0.974598	−	0.223963i	$-0.928100\pi$
$491$	−6.50000	+	11.2583i	−0.293341	+	0.508081i	0.681257	+	0.732045i	$0.261434\pi$
$492$	−7.50000	+	4.33013i	−0.338126	+	0.195217i
$493$	−3.00000			−0.135113
$494$	2.50000	−	4.33013i	0.112480	−	0.194822i
$495$	−7.50000	+	12.9904i	−0.337100	+	0.583874i
$496$		0			0
$497$	−6.00000	−	31.1769i	−0.269137	−	1.39848i
$498$	13.5000	−	7.79423i	0.604949	−	0.349268i
$499$	31.0000			1.38775			0.693875	−	0.720095i	$-0.255902\pi$
$499$	31.0000			1.38775			0.693875	+	0.720095i	$0.255902\pi$
$500$	4.50000	+	7.79423i	0.201246	+	0.348569i
$501$			32.9090i			1.47026i
$502$	14.0000	−	24.2487i	0.624851	−	1.08227i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	−22.5000	−	7.79423i	−1.00223	−	0.347183i
$505$	17.0000			0.756490
$506$	−7.50000	+	12.9904i	−0.333416	+	0.577493i
$507$	18.0000	+	10.3923i	0.799408	+	0.461538i
$508$	−6.00000	−	10.3923i	−0.266207	−	0.461084i
$509$	−29.0000			−1.28540			−0.642701	−	0.766117i	$-0.722186\pi$
$509$	−29.0000			−1.28540			−0.642701	+	0.766117i	$0.722186\pi$
$510$	−4.50000	−	2.59808i	−0.199263	−	0.115045i
$511$	−7.50000	−	2.59808i	−0.331780	−	0.114932i
$512$	−11.0000			−0.486136
$513$	4.50000	−	2.59808i	0.198680	−	0.114708i
$514$	14.5000	−	25.1147i	0.639568	−	1.10776i
$515$	1.00000			0.0440653
$516$		−	1.73205i		−	0.0762493i
$517$		0			0
$518$	1.50000	+	7.79423i	0.0659062	+	0.342459i
$519$			24.2487i			1.06440i
$520$	7.50000	−	12.9904i	0.328897	−	0.569666i
$521$	−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	$0.187600\pi$
$522$	−1.50000	+	2.59808i	−0.0656532	+	0.113715i
$523$	−0.500000	−	0.866025i	−0.0218635	−	0.0378686i	0.854887	−	0.518815i	$-0.173627\pi$
$523$	−0.500000	−	0.866025i	−0.0218635	−	0.0378686i	−0.876750	+	0.480946i	$0.840293\pi$
$524$	−0.500000	−	0.866025i	−0.0218426	−	0.0378325i
$525$	12.0000	+	13.8564i	0.523723	+	0.604743i
$526$	−2.50000	+	4.33013i	−0.109005	+	0.188803i
$527$		0			0
$528$			8.66025i			0.376889i
$529$	−14.0000			−0.608696
$530$	−4.50000	−	7.79423i	−0.195468	−	0.338560i
$531$		0			0
$532$	2.50000	+	0.866025i	0.108389	+	0.0375470i
$533$	−12.5000	−	21.6506i	−0.541435	−	0.937793i
$534$	19.5000	−	11.2583i	0.843848	−	0.487196i
$535$	8.50000	+	14.7224i	0.367487	+	0.636506i
$536$	6.00000	+	10.3923i	0.259161	+	0.448879i
$537$		−	32.9090i		−	1.42013i
$538$	−1.50000	−	2.59808i	−0.0646696	−	0.112011i
$539$	−32.5000	+	12.9904i	−1.39987	+	0.559535i
$540$	4.50000	−	2.59808i	0.193649	−	0.111803i
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	0.999042	+	0.0437584i	$0.0139332\pi$
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	−0.461625	+	0.887075i	$0.652733\pi$
$542$	1.00000			0.0429537
$543$	21.0000	−	12.1244i	0.901196	−	0.520306i
$544$	15.0000			0.643120
$545$	−4.50000	+	7.79423i	−0.192759	+	0.333868i
$546$	7.50000	−	21.6506i	0.320970	−	0.926562i
$547$	14.5000	+	25.1147i	0.619975	+	1.07383i	0.989490	+	0.144604i	$0.0461907\pi$
$547$	14.5000	+	25.1147i	0.619975	+	1.07383i	−0.369514	+	0.929225i	$0.620476\pi$
$548$	−4.50000	−	7.79423i	−0.192230	−	0.332953i
$549$	−21.0000	−	36.3731i	−0.896258	−	1.55236i
$550$	10.0000	−	17.3205i	0.426401	−	0.738549i
$551$	0.500000	−	0.866025i	0.0213007	−	0.0368939i
$552$	13.5000	−	7.79423i	0.574598	−	0.331744i
$553$	−20.0000	−	6.92820i	−0.850487	−	0.294617i
$554$	−9.50000	+	16.4545i	−0.403616	+	0.699084i
$555$	−4.50000	−	2.59808i	−0.191014	−	0.110282i
$556$	−9.00000			−0.381685
$557$	18.5000	−	32.0429i	0.783870	−	1.35770i	−0.145802	−	0.989314i	$-0.546576\pi$
$557$	18.5000	−	32.0429i	0.783870	−	1.35770i	0.929672	−	0.368389i	$-0.120091\pi$
$558$		0			0
$559$	5.00000			0.211477
$560$	−2.50000	−	0.866025i	−0.105644	−	0.0365963i
$561$		−	25.9808i		−	1.09691i
$562$	−29.0000			−1.22329
$563$	14.0000	+	24.2487i	0.590030	+	1.02196i	0.994228	+	0.107290i	$0.0342173\pi$
$563$	14.0000	+	24.2487i	0.590030	+	1.02196i	−0.404198	+	0.914671i	$0.632449\pi$
$564$		0			0
$565$	−0.500000	+	0.866025i	−0.0210352	+	0.0364340i
$566$	28.0000			1.17693
$567$	18.0000	−	15.5885i	0.755929	−	0.654654i
$568$	36.0000			1.51053
$569$	17.0000	−	29.4449i	0.712677	−	1.23439i	−0.251172	−	0.967943i	$-0.580816\pi$
$569$	17.0000	−	29.4449i	0.712677	−	1.23439i	0.963849	−	0.266450i	$-0.0858508\pi$
$570$	1.50000	−	0.866025i	0.0628281	−	0.0362738i
$571$	−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	$-0.400192\pi$
$572$	25.0000			1.04530
$573$		−	13.8564i		−	0.578860i
$574$	−10.0000	+	8.66025i	−0.417392	+	0.361472i
$575$	−12.0000			−0.500435
$576$	10.5000	−	18.1865i	0.437500	−	0.757772i
$577$	−15.5000	+	26.8468i	−0.645273	+	1.11765i	0.338965	+	0.940799i	$0.389923\pi$
$577$	−15.5000	+	26.8468i	−0.645273	+	1.11765i	−0.984238	+	0.176847i	$0.943410\pi$
$578$	−8.00000			−0.332756
$579$	−15.0000	−	8.66025i	−0.623379	−	0.359908i
$580$	0.500000	−	0.866025i	0.0207614	−	0.0359597i
$581$	−18.0000	+	15.5885i	−0.746766	+	0.646718i
$582$	13.5000	−	7.79423i	0.559593	−	0.323081i
$583$	22.5000	−	38.9711i	0.931855	−	1.61402i
$584$	4.50000	−	7.79423i	0.186211	−	0.322527i
$585$	7.50000	+	12.9904i	0.310087	+	0.537086i
$586$	2.50000	+	4.33013i	0.103274	+	0.178876i
$587$	18.5000	+	32.0429i	0.763577	+	1.32255i	0.940996	+	0.338418i	$0.109892\pi$
$587$	18.5000	+	32.0429i	0.763577	+	1.32255i	−0.177419	+	0.984135i	$0.556775\pi$
$588$	12.0000	+	1.73205i	0.494872	+	0.0714286i
$589$		0			0
$590$		0			0
$591$	−3.00000	+	1.73205i	−0.123404	+	0.0712470i
$592$	−3.00000			−0.123299
$593$	−7.50000	−	12.9904i	−0.307988	−	0.533451i	0.669934	−	0.742421i	$-0.266322\pi$
$593$	−7.50000	−	12.9904i	−0.307988	−	0.533451i	−0.977922	+	0.208970i	$0.932989\pi$
$594$	−22.5000	−	12.9904i	−0.923186	−	0.533002i
$595$	7.50000	+	2.59808i	0.307470	+	0.106511i
$596$	1.50000	+	2.59808i	0.0614424	+	0.106421i
$597$		−	5.19615i		−	0.212664i
$598$	7.50000	+	12.9904i	0.306698	+	0.531216i
$599$	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	$0.670218\pi$
$600$	−18.0000	+	10.3923i	−0.734847	+	0.424264i
$601$	4.50000	+	7.79423i	0.183559	+	0.317933i	0.943090	−	0.332538i	$-0.107905\pi$
$601$	4.50000	+	7.79423i	0.183559	+	0.317933i	−0.759531	+	0.650471i	$0.774572\pi$
$602$	−0.500000	−	2.59808i	−0.0203785	−	0.105890i
$603$	−12.0000			−0.488678
$604$	2.50000	+	4.33013i	0.101724	+	0.176190i
$605$	−14.0000			−0.569181
$606$			29.4449i			1.19612i
$607$	−1.00000			−0.0405887			−0.0202944	−	0.999794i	$-0.506460\pi$
$607$	−1.00000			−0.0405887			−0.0202944	+	0.999794i	$0.506460\pi$
$608$	−2.50000	+	4.33013i	−0.101388	+	0.175610i
$609$	1.50000	−	4.33013i	0.0607831	−	0.175466i
$610$	−7.00000	−	12.1244i	−0.283422	−	0.490901i
$611$		0			0
$612$	−4.50000	+	7.79423i	−0.181902	+	0.315063i
$613$	−9.50000	+	16.4545i	−0.383701	+	0.664590i	−0.991588	−	0.129433i	$-0.958684\pi$
$613$	−9.50000	+	16.4545i	−0.383701	+	0.664590i	0.607887	+	0.794024i	$0.292017\pi$
$614$	−14.0000	+	24.2487i	−0.564994	+	0.978598i
$615$		−	8.66025i		−	0.349215i
$616$	−7.50000	−	38.9711i	−0.302184	−	1.57019i
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	0.455211	+	0.890384i	$0.349564\pi$
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	−0.998700	+	0.0509678i	$0.983769\pi$
$618$			1.73205i			0.0696733i
$619$	25.0000			1.00483			0.502417	−	0.864625i	$-0.332444\pi$
$619$	25.0000			1.00483			0.502417	+	0.864625i	$0.332444\pi$
$620$		0			0
$621$			15.5885i			0.625543i
$622$		0			0
$623$	−26.0000	+	22.5167i	−1.04167	+	0.902111i
$624$	7.50000	+	4.33013i	0.300240	+	0.173344i
$625$	11.0000			0.440000
$626$	−7.00000	−	12.1244i	−0.279776	−	0.484587i
$627$	7.50000	+	4.33013i	0.299521	+	0.172929i
$628$	−7.00000	+	12.1244i	−0.279330	+	0.483814i
$629$	9.00000			0.358854
$630$	6.00000	−	5.19615i	0.239046	−	0.207020i
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$	12.0000	−	20.7846i	0.477334	−	0.826767i
$633$		−	22.5167i		−	0.894957i
$634$	3.00000	+	5.19615i	0.119145	+	0.206366i
$635$	12.0000			0.476205
$636$	−13.5000	+	7.79423i	−0.535310	+	0.309061i
$637$	−5.00000	+	34.6410i	−0.198107	+	1.37253i
$638$	−5.00000			−0.197952
$639$	−18.0000	+	31.1769i	−0.712069	+	1.23334i
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	−9.00000			−0.355479			−0.177739	−	0.984078i	$-0.556878\pi$
$641$	−9.00000			−0.355479			−0.177739	+	0.984078i	$0.556878\pi$
$642$	−25.5000	+	14.7224i	−1.00640	+	0.581048i
$643$	9.50000	−	16.4545i	0.374643	−	0.648901i	−0.615630	−	0.788035i	$-0.711098\pi$
$643$	9.50000	−	16.4545i	0.374643	−	0.648901i	0.990274	+	0.139134i	$0.0444318\pi$
$644$	−6.00000	+	5.19615i	−0.236433	+	0.204757i
$645$	1.50000	+	0.866025i	0.0590624	+	0.0340997i
$646$	−1.50000	+	2.59808i	−0.0590167	+	0.102220i
$647$	−15.5000	+	26.8468i	−0.609368	+	1.05546i	0.381977	+	0.924172i	$0.375243\pi$
$647$	−15.5000	+	26.8468i	−0.609368	+	1.05546i	−0.991345	+	0.131284i	$0.958090\pi$
$648$	13.5000	+	23.3827i	0.530330	+	0.918559i
$649$		0			0
$650$	−10.0000	−	17.3205i	−0.392232	−	0.679366i
$651$		0			0
$652$	−5.50000	+	9.52628i	−0.215397	+	0.373078i
$653$	3.00000			0.117399			0.0586995	−	0.998276i	$-0.481305\pi$
$653$	3.00000			0.117399			0.0586995	+	0.998276i	$0.481305\pi$
$654$	−13.5000	−	7.79423i	−0.527892	−	0.304778i
$655$	1.00000			0.0390732
$656$	−2.50000	−	4.33013i	−0.0976086	−	0.169063i
$657$	4.50000	+	7.79423i	0.175562	+	0.304082i
$658$		0			0
$659$	−13.5000	−	23.3827i	−0.525885	−	0.910860i	−0.999545	−	0.0301523i	$-0.990401\pi$
$659$	−13.5000	−	23.3827i	−0.525885	−	0.910860i	0.473660	−	0.880708i	$-0.342933\pi$
$660$	7.50000	+	4.33013i	0.291937	+	0.168550i
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	0.969442	−	0.245319i	$-0.0788928\pi$
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	−0.697174	+	0.716902i	$0.745559\pi$
$662$	−4.00000	−	6.92820i	−0.155464	−	0.269272i
$663$	−22.5000	−	12.9904i	−0.873828	−	0.504505i
$664$	−13.5000	−	23.3827i	−0.523902	−	0.907424i
$665$	−2.00000	+	1.73205i	−0.0775567	+	0.0671660i
$666$	4.50000	−	7.79423i	0.174371	−	0.302020i
$667$	1.50000	+	2.59808i	0.0580802	+	0.100598i
$668$	19.0000			0.735132
$669$	28.5000	+	16.4545i	1.10187	+	0.636167i
$670$	−4.00000			−0.154533
$671$	35.0000	−	60.6218i	1.35116	−	2.34028i
$672$	−7.50000	+	21.6506i	−0.289319	+	0.835191i
$673$	14.5000	+	25.1147i	0.558934	+	0.968102i	0.997586	+	0.0694449i	$0.0221228\pi$
$673$	14.5000	+	25.1147i	0.558934	+	0.968102i	−0.438652	+	0.898657i	$0.644544\pi$
$674$	14.5000	+	25.1147i	0.558519	+	0.967384i
$675$		−	20.7846i		−	0.800000i
$676$	6.00000	−	10.3923i	0.230769	−	0.399704i
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	0.107772	+	0.994176i	$0.465628\pi$
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	−0.914867	+	0.403755i	$0.867705\pi$
$678$	−1.50000	−	0.866025i	−0.0576072	−	0.0332595i
$679$	−18.0000	+	15.5885i	−0.690777	+	0.598230i
$680$	−4.50000	+	7.79423i	−0.172567	+	0.298895i
$681$	4.50000	−	2.59808i	0.172440	−	0.0995585i
$682$		0			0
$683$	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	$0.111583\pi$
$684$	−1.50000	−	2.59808i	−0.0573539	−	0.0993399i
$685$	9.00000			0.343872
$686$	18.5000	−	0.866025i	0.706333	−	0.0330650i
$687$	1.50000	−	0.866025i	0.0572286	−	0.0330409i
$688$	1.00000			0.0381246
$689$	−22.5000	−	38.9711i	−0.857182	−	1.48468i
$690$			5.19615i			0.197814i
$691$	14.0000	−	24.2487i	0.532585	−	0.922464i	−0.466691	−	0.884420i	$-0.654554\pi$
$691$	14.0000	−	24.2487i	0.532585	−	0.922464i	0.999276	−	0.0380440i	$-0.0121127\pi$
$692$	14.0000			0.532200
$693$	37.5000	+	12.9904i	1.42451	+	0.493464i
$694$	4.00000			0.151838
$695$	4.50000	−	7.79423i	0.170695	−	0.295652i
$696$	4.50000	+	2.59808i	0.170572	+	0.0984798i
$697$	7.50000	+	12.9904i	0.284083	+	0.492046i
$698$	19.0000			0.719161
$699$	4.50000	+	2.59808i	0.170206	+	0.0982683i
$700$	8.00000	−	6.92820i	0.302372	−	0.261861i
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$	−22.5000	+	12.9904i	−0.849208	+	0.490290i
$703$	−1.50000	+	2.59808i	−0.0565736	+	0.0979883i
$704$	35.0000			1.31911
$705$		0			0
$706$	−5.50000	+	9.52628i	−0.206995	+	0.358526i
$707$	−8.50000	−	44.1673i	−0.319675	−	1.66108i
$708$		0			0
$709$	3.00000	−	5.19615i	0.112667	−	0.195146i	−0.804178	−	0.594389i	$-0.797394\pi$
$709$	3.00000	−	5.19615i	0.112667	−	0.195146i	0.916845	+	0.399244i	$0.130727\pi$
$710$	−6.00000	+	10.3923i	−0.225176	+	0.390016i
$711$	12.0000	+	20.7846i	0.450035	+	0.779484i
$712$	−19.5000	−	33.7750i	−0.730793	−	1.26577i
$713$		0			0
$714$	−4.50000	+	12.9904i	−0.168408	+	0.486153i
$715$	−12.5000	+	21.6506i	−0.467473	+	0.809688i
$716$	−19.0000			−0.710063
$717$			25.9808i			0.970269i
$718$	−11.0000			−0.410516
$719$	13.5000	+	23.3827i	0.503465	+	0.872027i	0.999992	+	0.00400572i	$0.00127506\pi$
$719$	13.5000	+	23.3827i	0.503465	+	0.872027i	−0.496527	+	0.868021i	$0.665392\pi$
$720$	1.50000	+	2.59808i	0.0559017	+	0.0968246i
$721$	−0.500000	−	2.59808i	−0.0186210	−	0.0967574i
$722$	9.00000	+	15.5885i	0.334945	+	0.580142i
$723$	−16.5000	+	9.52628i	−0.613642	+	0.354286i
$724$	−7.00000	−	12.1244i	−0.260153	−	0.450598i
$725$	−2.00000	−	3.46410i	−0.0742781	−	0.128654i
$726$		−	24.2487i		−	0.899954i
$727$	−23.5000	−	40.7032i	−0.871567	−	1.50960i	−0.860376	−	0.509661i	$-0.829771\pi$
$727$	−23.5000	−	40.7032i	−0.871567	−	1.50960i	−0.0111912	−	0.999937i	$-0.503562\pi$
$728$	−37.5000	−	12.9904i	−1.38984	−	0.481456i
$729$	−27.0000			−1.00000
$730$	1.50000	+	2.59808i	0.0555175	+	0.0961591i
$731$	−3.00000			−0.110959
$732$	−21.0000	+	12.1244i	−0.776182	+	0.448129i
$733$	27.0000			0.997268			0.498634	−	0.866813i	$-0.333835\pi$
$733$	27.0000			0.997268			0.498634	+	0.866813i	$0.333835\pi$
$734$	1.50000	−	2.59808i	0.0553660	−	0.0958967i
$735$	−7.50000	+	9.52628i	−0.276642	+	0.351382i
$736$	−7.50000	−	12.9904i	−0.276454	−	0.478832i
$737$	−10.0000	−	17.3205i	−0.368355	−	0.638009i
$738$	15.0000			0.552158
$739$	4.50000	−	7.79423i	0.165535	−	0.286715i	−0.771310	−	0.636460i	$-0.780398\pi$
$739$	4.50000	−	7.79423i	0.165535	−	0.286715i	0.936845	+	0.349744i	$0.113732\pi$
$740$	−1.50000	+	2.59808i	−0.0551411	+	0.0955072i
$741$	7.50000	−	4.33013i	0.275519	−	0.159071i
$742$	−18.0000	+	15.5885i	−0.660801	+	0.572270i
$743$	7.50000	−	12.9904i	0.275148	−	0.476571i	−0.695024	−	0.718986i	$-0.744606\pi$
$743$	7.50000	−	12.9904i	0.275148	−	0.476571i	0.970173	+	0.242415i	$0.0779397\pi$
$744$		0			0
$745$	−3.00000			−0.109911
$746$	12.5000	−	21.6506i	0.457658	−	0.792686i
$747$	27.0000			0.987878
$748$	−15.0000			−0.548454
$749$	34.0000	−	29.4449i	1.24233	−	1.07589i
$750$		−	15.5885i		−	0.569210i
$751$	31.0000			1.13121			0.565603	−	0.824678i	$-0.308643\pi$
$751$	31.0000			1.13121			0.565603	+	0.824678i	$0.308643\pi$
$752$		0			0
$753$	42.0000	−	24.2487i	1.53057	−	0.883672i
$754$	−2.50000	+	4.33013i	−0.0910446	+	0.157694i
$755$	−5.00000			−0.181969
$756$	−9.00000	−	10.3923i	−0.327327	−	0.377964i
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	6.00000	−	10.3923i	0.217930	−	0.377466i
$759$	−22.5000	+	12.9904i	−0.816698	+	0.471521i
$760$	−1.50000	−	2.59808i	−0.0544107	−	0.0942421i
$761$	27.0000			0.978749			0.489375	−	0.872074i	$-0.337225\pi$
$761$	27.0000			0.978749			0.489375	+	0.872074i	$0.337225\pi$
$762$			20.7846i			0.752947i
$763$	22.5000	+	7.79423i	0.814555	+	0.282170i
$764$	−8.00000			−0.289430
$765$	−4.50000	−	7.79423i	−0.162698	−	0.281801i
$766$	−13.5000	+	23.3827i	−0.487775	+	0.844851i
$767$		0			0
$768$	−25.5000	−	14.7224i	−0.920152	−	0.531250i
$769$	−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	$0.302780\pi$
$770$	12.5000	+	4.33013i	0.450469	+	0.156047i
$771$	43.5000	−	25.1147i	1.56661	−	0.904485i
$772$	−5.00000	+	8.66025i	−0.179954	+	0.311689i
$773$	−15.5000	+	26.8468i	−0.557496	+	0.965612i	0.440208	+	0.897896i	$0.354905\pi$
$773$	−15.5000	+	26.8468i	−0.557496	+	0.965612i	−0.997705	+	0.0677162i	$0.978429\pi$
$774$	−1.50000	+	2.59808i	−0.0539164	+	0.0933859i
$775$		0			0
$776$	−13.5000	−	23.3827i	−0.484622	−	0.839390i
$777$	−4.50000	+	12.9904i	−0.161437	+	0.466027i
$778$	4.50000	−	7.79423i	0.161333	−	0.279437i
$779$	−5.00000			−0.179144
$780$	7.50000	−	4.33013i	0.268543	−	0.155043i
$781$	−60.0000			−2.14697
$782$	−4.50000	−	7.79423i	−0.160920	−	0.278721i
$783$	−4.50000	+	2.59808i	−0.160817	+	0.0928477i
$784$	−1.00000	+	6.92820i	−0.0357143	+	0.247436i
$785$	−7.00000	−	12.1244i	−0.249841	−	0.432737i
$786$			1.73205i			0.0617802i
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	0.500953	−	0.865474i	$-0.332983\pi$
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	−0.999999	+	0.00110111i	$0.999650\pi$
$788$	1.00000	+	1.73205i	0.0356235	+	0.0617018i
$789$	−7.50000	+	4.33013i	−0.267007	+	0.154157i
$790$	4.00000	+	6.92820i	0.142314	+	0.246494i
$791$	2.50000	+	0.866025i	0.0888898	+	0.0307923i
$792$	−22.5000	+	38.9711i	−0.799503	+	1.38478i
$793$	−35.0000	−	60.6218i	−1.24289	−	2.15274i
$794$	15.0000			0.532330
$795$		−	15.5885i		−	0.552866i
$796$	−3.00000			−0.106332
$797$	−11.5000	+	19.9186i	−0.407351	+	0.705552i	−0.994592	−	0.103860i	$-0.966881\pi$
$797$	−11.5000	+	19.9186i	−0.407351	+	0.705552i	0.587241	+	0.809412i	$0.300214\pi$
$798$	−3.00000	−	3.46410i	−0.106199	−	0.122628i
$799$		0			0
$800$	10.0000	+	17.3205i	0.353553	+	0.612372i
$801$	39.0000			1.37800
$802$	−1.50000	+	2.59808i	−0.0529668	+	0.0917413i
$803$	−7.50000	+	12.9904i	−0.264669	+	0.458421i
$804$			6.92820i			0.244339i
$805$	−1.50000	−	7.79423i	−0.0528681	−	0.274710i
$806$		0			0
$807$		−	5.19615i		−	0.182913i
$808$	51.0000			1.79417
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	−0.776012	−	0.630718i	$-0.782761\pi$
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	0.934224	+	0.356687i	$0.116094\pi$
$810$	−9.00000			−0.316228
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	−2.50000	−	0.866025i	−0.0877328	−	0.0303915i
$813$	1.50000	+	0.866025i	0.0526073	+	0.0303728i
$814$	15.0000			0.525750
$815$	−5.50000	−	9.52628i	−0.192657	−	0.333691i
$816$	−4.50000	−	2.59808i	−0.157532	−	0.0909509i
$817$	0.500000	−	0.866025i	0.0174928	−	0.0302984i
$818$	14.0000			0.489499
$819$	30.0000	−	25.9808i	1.04828	−	0.907841i
$820$	−5.00000			−0.174608
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	−0.991616	−	0.129217i	$-0.958754\pi$
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	0.607714	+	0.794156i	$0.292087\pi$
$822$			15.5885i			0.543710i
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	0.995768	−	0.0919029i	$-0.0292950\pi$
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	−0.577474	+	0.816409i	$0.695962\pi$
$824$	3.00000			0.104510
$825$	30.0000	−	17.3205i	1.04447	−	0.603023i
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$	9.00000			0.312772
$829$	12.5000	−	21.6506i	0.434143	−	0.751958i	−0.563082	−	0.826401i	$-0.690385\pi$
$829$	12.5000	−	21.6506i	0.434143	−	0.751958i	0.997225	+	0.0744432i	$0.0237179\pi$
$830$	9.00000			0.312395
$831$	−28.5000	+	16.4545i	−0.988654	+	0.570800i
$832$	17.5000	−	30.3109i	0.606703	−	1.05084i
$833$	3.00000	−	20.7846i	0.103944	−	0.720144i
$834$	13.5000	+	7.79423i	0.467467	+	0.269892i
$835$	−9.50000	+	16.4545i	−0.328761	+	0.569431i
$836$	2.50000	−	4.33013i	0.0864643	−	0.149761i
$837$		0			0
$838$	−4.50000	−	7.79423i	−0.155450	−	0.269247i
$839$	18.5000	+	32.0429i	0.638691	+	1.10625i	0.985720	+	0.168391i	$0.0538571\pi$
$839$	18.5000	+	32.0429i	0.638691	+	1.10625i	−0.347029	+	0.937854i	$0.612810\pi$
$840$	−9.00000	−	10.3923i	−0.310530	−	0.358569i
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	−1.00000			−0.0344623
$843$	−43.5000	−	25.1147i	−1.49822	−	0.864997i
$844$	−13.0000			−0.447478
$845$	6.00000	+	10.3923i	0.206406	+	0.357506i
$846$		0			0
$847$	7.00000	+	36.3731i	0.240523	+	1.24979i
$848$	−4.50000	−	7.79423i	−0.154531	−	0.267655i
$849$	42.0000	+	24.2487i	1.44144	+	0.832214i
$850$	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
$853$	18.5000	+	32.0429i	0.633428	+	1.09713i	0.986846	+	0.161664i	$0.0516860\pi$
$853$	18.5000	+	32.0429i	0.633428	+	1.09713i	−0.353418	+	0.935466i	$0.614981\pi$
$854$	−28.0000	+	24.2487i	−0.958140	+	0.829774i
$855$	3.00000			0.102598
$856$	25.5000	+	44.1673i	0.871572	+	1.50961i
$857$	11.0000			0.375753			0.187876	−	0.982193i	$-0.439840\pi$
$857$	11.0000			0.375753			0.187876	+	0.982193i	$0.439840\pi$
$858$	−37.5000	−	21.6506i	−1.28023	−	0.739140i
$859$	−1.00000			−0.0341196			−0.0170598	−	0.999854i	$-0.505431\pi$
$859$	−1.00000			−0.0341196			−0.0170598	+	0.999854i	$0.505431\pi$
$860$	0.500000	−	0.866025i	0.0170499	−	0.0295312i
$861$	−22.5000	+	4.33013i	−0.766798	+	0.147570i
$862$	4.50000	+	7.79423i	0.153271	+	0.265472i
$863$	19.5000	+	33.7750i	0.663788	+	1.14971i	0.979612	+	0.200897i	$0.0643855\pi$
$863$	19.5000	+	33.7750i	0.663788	+	1.14971i	−0.315825	+	0.948818i	$0.602281\pi$
$864$	22.5000	−	12.9904i	0.765466	−	0.441942i
$865$	−7.00000	+	12.1244i	−0.238007	+	0.412240i
$866$	7.00000	−	12.1244i	0.237870	−	0.412002i
$867$	−12.0000	−	6.92820i	−0.407541	−	0.235294i
$868$		0			0
$869$	−20.0000	+	34.6410i	−0.678454	+	1.17512i
$870$	−1.50000	+	0.866025i	−0.0508548	+	0.0293610i
$871$	−20.0000			−0.677674
$872$	−13.5000	+	23.3827i	−0.457168	+	0.791838i
$873$	27.0000			0.913812
$874$	3.00000			0.101477
$875$	4.50000	+	23.3827i	0.152128	+	0.790479i
$876$	4.50000	−	2.59808i	0.152041	−	0.0877809i
$877$	−53.0000			−1.78968			−0.894841	−	0.446384i	$-0.852711\pi$
$877$	−53.0000			−1.78968			−0.894841	+	0.446384i	$0.852711\pi$
$878$		0			0
$879$			8.66025i			0.292103i
$880$	−2.50000	+	4.33013i	−0.0842750	+	0.145969i
$881$	−42.0000			−1.41502			−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$882$	−16.5000	−	12.9904i	−0.555584	−	0.437409i
$883$	44.0000			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$884$	−7.50000	+	12.9904i	−0.252252	+	0.436914i
$885$		0			0
$886$	−18.0000	−	31.1769i	−0.604722	−	1.04741i
$887$	−29.0000			−0.973725			−0.486862	−	0.873479i	$-0.661859\pi$
$887$	−29.0000			−0.973725			−0.486862	+	0.873479i	$0.661859\pi$
$888$	−13.5000	−	7.79423i	−0.453030	−	0.261557i
$889$	−6.00000	−	31.1769i	−0.201234	−	1.04564i
$890$	13.0000			0.435761
$891$	−22.5000	−	38.9711i	−0.753778	−	1.30558i
$892$	9.50000	−	16.4545i	0.318084	−	0.550937i
$893$		0			0
$894$		−	5.19615i		−	0.173785i
$895$	9.50000	−	16.4545i	0.317550	−	0.550013i
$896$	7.50000	+	2.59808i	0.250557	+	0.0867956i
$897$			25.9808i			0.867472i
$898$	−15.0000	+	25.9808i	−0.500556	+	0.866989i
$899$		0			0
$900$	−12.0000			−0.400000
$901$	13.5000	+	23.3827i	0.449750	+	0.778990i
$902$	12.5000	+	21.6506i	0.416204	+	0.720887i
$903$	1.50000	−	4.33013i	0.0499169	−	0.144098i
$904$	−1.50000	+	2.59808i	−0.0498893	+	0.0864107i
$905$	14.0000			0.465376
$906$		−	8.66025i		−	0.287718i
$907$	5.00000			0.166022			0.0830111	−	0.996549i	$-0.473546\pi$
$907$	5.00000			0.166022			0.0830111	+	0.996549i	$0.473546\pi$
$908$	−1.50000	−	2.59808i	−0.0497792	−	0.0862202i
$909$	−25.5000	+	44.1673i	−0.845782	+	1.46494i
$910$	10.0000	−	8.66025i	0.331497	−	0.287085i
$911$	−13.5000	−	23.3827i	−0.447275	−	0.774703i	0.550933	−	0.834550i	$-0.314272\pi$
$911$	−13.5000	−	23.3827i	−0.447275	−	0.774703i	−0.998208	+	0.0598468i	$0.980939\pi$
$912$	1.50000	−	0.866025i	0.0496700	−	0.0286770i
$913$	22.5000	+	38.9711i	0.744641	+	1.28976i
$914$	−11.0000	−	19.0526i	−0.363848	−	0.630203i
$915$		−	24.2487i		−	0.801638i
$916$	−0.500000	−	0.866025i	−0.0165205	−	0.0286143i
$917$	−0.500000	−	2.59808i	−0.0165115	−	0.0857960i
$918$	13.5000	−	7.79423i	0.445566	−	0.257248i
$919$	−8.50000	−	14.7224i	−0.280389	−	0.485648i	0.691091	−	0.722767i	$-0.257130\pi$
$919$	−8.50000	−	14.7224i	−0.280389	−	0.485648i	−0.971481	+	0.237119i	$0.923797\pi$
$920$	9.00000			0.296721
$921$	−42.0000	+	24.2487i	−1.38395	+	0.799022i
$922$	19.0000			0.625732
$923$	−30.0000	+	51.9615i	−0.987462	+	1.71033i
$924$	7.50000	−	21.6506i	0.246732	−	0.712254i
$925$	6.00000	+	10.3923i	0.197279	+	0.341697i
$926$	−6.50000	−	11.2583i	−0.213603	−	0.369972i
$927$	−1.50000	+	2.59808i	−0.0492665	+	0.0853320i
$928$	2.50000	−	4.33013i	0.0820665	−	0.142143i
$929$	7.00000	−	12.1244i	0.229663	−	0.397787i	−0.728046	−	0.685529i	$-0.759571\pi$
$929$	7.00000	−	12.1244i	0.229663	−	0.397787i	0.957708	+	0.287742i	$0.0929044\pi$
$930$		0			0
$931$	5.50000	+	4.33013i	0.180255	+	0.141914i
$932$	1.50000	−	2.59808i	0.0491341	−	0.0851028i
$933$		0			0
$934$	−27.0000			−0.883467
$935$	7.50000	−	12.9904i	0.245276	−	0.424831i
$936$	22.5000	+	38.9711i	0.735436	+	1.27381i
$937$	42.0000			1.37208			0.686040	−	0.727564i	$-0.259347\pi$
$937$	42.0000			1.37208			0.686040	+	0.727564i	$0.259347\pi$
$938$	2.00000	+	10.3923i	0.0653023	+	0.339321i
$939$		−	24.2487i		−	0.791327i
$940$		0			0
$941$	7.00000	+	12.1244i	0.228193	+	0.395243i	0.957273	−	0.289187i	$-0.0933848\pi$
$941$	7.00000	+	12.1244i	0.228193	+	0.395243i	−0.729079	+	0.684429i	$0.760051\pi$
$942$	21.0000	−	12.1244i	0.684217	−	0.395033i
$943$	7.50000	−	12.9904i	0.244234	−	0.423025i
$944$		0			0
$945$	13.5000	−	2.59808i	0.439155	−	0.0845154i
$946$	−5.00000			−0.162564
$947$	10.0000	−	17.3205i	0.324956	−	0.562841i	−0.656547	−	0.754285i	$-0.727984\pi$
$947$	10.0000	−	17.3205i	0.324956	−	0.562841i	0.981504	+	0.191444i	$0.0613171\pi$
$948$	12.0000	−	6.92820i	0.389742	−	0.225018i
$949$	7.50000	+	12.9904i	0.243460	+	0.421686i
$950$	−4.00000			−0.129777
$951$			10.3923i			0.336994i
$952$	22.5000	+	7.79423i	0.729229	+	0.252612i
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$	27.0000			0.874157
$955$	4.00000	−	6.92820i	0.129437	−	0.224191i
$956$	15.0000			0.485135
$957$	−7.50000	−	4.33013i	−0.242441	−	0.139973i
$958$	−12.5000	+	21.6506i	−0.403857	+	0.699500i
$959$	−4.50000	−	23.3827i	−0.145313	−	0.755066i
$960$	10.5000	−	6.06218i	0.338886	−	0.195656i
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$	7.50000	−	12.9904i	0.241810	−	0.418827i
$963$	−51.0000			−1.64345
$964$	5.50000	+	9.52628i	0.177143	+	0.306821i
$965$	−5.00000	−	8.66025i	−0.160956	−	0.278783i
$966$	13.5000	−	2.59808i	0.434355	−	0.0835917i
$967$	−6.50000	+	11.2583i	−0.209026	+	0.362043i	−0.951408	−	0.307933i	$-0.900363\pi$
$967$	−6.50000	+	11.2583i	−0.209026	+	0.362043i	0.742382	+	0.669977i	$0.233696\pi$
$968$	−42.0000			−1.34993
$969$	−4.50000	+	2.59808i	−0.144561	+	0.0834622i
$970$	9.00000			0.288973
$971$	−28.5000	−	49.3634i	−0.914609	−	1.58415i	−0.807473	−	0.589904i	$-0.799166\pi$
$971$	−28.5000	−	49.3634i	−0.914609	−	1.58415i	−0.107135	−	0.994244i	$-0.534168\pi$
$972$			15.5885i			0.500000i
$973$	−22.5000	−	7.79423i	−0.721317	−	0.249871i
$974$	−9.50000	−	16.4545i	−0.304400	−	0.527236i
$975$		−	34.6410i		−	1.10940i
$976$	−7.00000	−	12.1244i	−0.224065	−	0.388091i
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	0.685381	−	0.728184i	$-0.259636\pi$
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	−0.973317	+	0.229465i	$0.926302\pi$
$978$	16.5000	−	9.52628i	0.527612	−	0.304617i
$979$	32.5000	+	56.2917i	1.03870	+	1.79909i
$980$	5.50000	+	4.33013i	0.175691	+	0.138321i
$981$	−13.5000	−	23.3827i	−0.431022	−	0.746552i
$982$	−6.50000	−	11.2583i	−0.207423	−	0.359268i
$983$	−3.00000			−0.0956851			−0.0478426	−	0.998855i	$-0.515235\pi$
$983$	−3.00000			−0.0956851			−0.0478426	+	0.998855i	$0.515235\pi$
$984$		−	25.9808i		−	0.828236i
$985$	−2.00000			−0.0637253
$986$	1.50000	−	2.59808i	0.0477697	−	0.0827396i
$987$		0			0
$988$	−2.50000	−	4.33013i	−0.0795356	−	0.137760i
$989$	1.50000	+	2.59808i	0.0476972	+	0.0826140i
$990$	−7.50000	−	12.9904i	−0.238366	−	0.412861i
$991$	18.5000	−	32.0429i	0.587672	−	1.01788i	−0.406865	−	0.913488i	$-0.633378\pi$
$991$	18.5000	−	32.0429i	0.587672	−	1.01788i	0.994537	−	0.104389i	$-0.0332887\pi$
$992$		0			0
$993$		−	13.8564i		−	0.439720i
$994$	30.0000	+	10.3923i	0.951542	+	0.329624i
$995$	1.50000	−	2.59808i	0.0475532	−	0.0823646i
$996$		−	15.5885i		−	0.493939i
$997$	−17.0000			−0.538395			−0.269198	−	0.963085i	$-0.586759\pi$
$997$	−17.0000			−0.538395			−0.269198	+	0.963085i	$0.586759\pi$
$998$	−15.5000	+	26.8468i	−0.490644	+	0.849820i
$999$	13.5000	−	7.79423i	0.427121	−	0.246598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.2.g.a.4.1	✓	2
3.2	odd	2		189.2.g.a.172.1		2
4.3	odd	2		1008.2.t.d.193.1		2
7.2	even	3		63.2.h.a.58.1	yes	2
7.3	odd	6		441.2.f.a.148.1		2
7.4	even	3		441.2.f.b.148.1		2
7.5	odd	6		441.2.h.a.373.1		2
7.6	odd	2		441.2.g.a.67.1		2
9.2	odd	6		189.2.h.a.46.1		2
9.4	even	3		567.2.e.a.487.1		2
9.5	odd	6		567.2.e.b.487.1		2
9.7	even	3		63.2.h.a.25.1	yes	2
12.11	even	2		3024.2.t.d.1873.1		2
21.2	odd	6		189.2.h.a.37.1		2
21.5	even	6		1323.2.h.a.226.1		2
21.11	odd	6		1323.2.f.a.442.1		2
21.17	even	6		1323.2.f.b.442.1		2
21.20	even	2		1323.2.g.a.361.1		2
28.23	odd	6		1008.2.q.c.625.1		2
36.7	odd	6		1008.2.q.c.529.1		2
36.11	even	6		3024.2.q.b.2881.1		2
63.2	odd	6		189.2.g.a.100.1		2
63.4	even	3		3969.2.a.d.1.1		1
63.11	odd	6		1323.2.f.a.883.1		2
63.16	even	3	inner	63.2.g.a.16.1	yes	2
63.20	even	6		1323.2.h.a.802.1		2
63.23	odd	6		567.2.e.b.163.1		2
63.25	even	3		441.2.f.b.295.1		2
63.31	odd	6		3969.2.a.f.1.1		1
63.32	odd	6		3969.2.a.c.1.1		1
63.34	odd	6		441.2.h.a.214.1		2
63.38	even	6		1323.2.f.b.883.1		2
63.47	even	6		1323.2.g.a.667.1		2
63.52	odd	6		441.2.f.a.295.1		2
63.58	even	3		567.2.e.a.163.1		2
63.59	even	6		3969.2.a.a.1.1		1
63.61	odd	6		441.2.g.a.79.1		2
84.23	even	6		3024.2.q.b.2305.1		2
252.79	odd	6		1008.2.t.d.961.1		2
252.191	even	6		3024.2.t.d.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.a.4.1	✓	2	1.1	even	1	trivial
63.2.g.a.16.1	yes	2	63.16	even	3	inner
63.2.h.a.25.1	yes	2	9.7	even	3
63.2.h.a.58.1	yes	2	7.2	even	3
189.2.g.a.100.1		2	63.2	odd	6
189.2.g.a.172.1		2	3.2	odd	2
189.2.h.a.37.1		2	21.2	odd	6
189.2.h.a.46.1		2	9.2	odd	6
441.2.f.a.148.1		2	7.3	odd	6
441.2.f.a.295.1		2	63.52	odd	6
441.2.f.b.148.1		2	7.4	even	3
441.2.f.b.295.1		2	63.25	even	3
441.2.g.a.67.1		2	7.6	odd	2
441.2.g.a.79.1		2	63.61	odd	6
441.2.h.a.214.1		2	63.34	odd	6
441.2.h.a.373.1		2	7.5	odd	6
567.2.e.a.163.1		2	63.58	even	3
567.2.e.a.487.1		2	9.4	even	3
567.2.e.b.163.1		2	63.23	odd	6
567.2.e.b.487.1		2	9.5	odd	6
1008.2.q.c.529.1		2	36.7	odd	6
1008.2.q.c.625.1		2	28.23	odd	6
1008.2.t.d.193.1		2	4.3	odd	2
1008.2.t.d.961.1		2	252.79	odd	6
1323.2.f.a.442.1		2	21.11	odd	6
1323.2.f.a.883.1		2	63.11	odd	6
1323.2.f.b.442.1		2	21.17	even	6
1323.2.f.b.883.1		2	63.38	even	6
1323.2.g.a.361.1		2	21.20	even	2
1323.2.g.a.667.1		2	63.47	even	6
1323.2.h.a.226.1		2	21.5	even	6
1323.2.h.a.802.1		2	63.20	even	6
3024.2.q.b.2305.1		2	84.23	even	6
3024.2.q.b.2881.1		2	36.11	even	6
3024.2.t.d.289.1		2	252.191	even	6
3024.2.t.d.1873.1		2	12.11	even	2
3969.2.a.a.1.1		1	63.59	even	6
3969.2.a.c.1.1		1	63.32	odd	6
3969.2.a.d.1.1		1	63.4	even	3
3969.2.a.f.1.1		1	63.31	odd	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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} -1.73205i q^{6} +(0.500000 + 2.59808i) q^{7} -3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} -1.73205i q^{6} +(0.500000 + 2.59808i) q^{7} -3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(0.500000 - 0.866025i) q^{10} +5.00000 q^{11} +(-1.50000 - 0.866025i) q^{12} +(2.50000 - 4.33013i) q^{13} +(-2.50000 - 0.866025i) q^{14} +(1.50000 - 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(1.50000 + 2.59808i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-3.00000 - 3.46410i) q^{21} +(-2.50000 + 4.33013i) q^{22} +3.00000 q^{23} +(4.50000 - 2.59808i) q^{24} -4.00000 q^{25} +(2.50000 + 4.33013i) q^{26} +5.19615i q^{27} +(-2.00000 + 1.73205i) q^{28} +(0.500000 + 0.866025i) q^{29} +1.73205i q^{30} +(-2.50000 - 4.33013i) q^{32} +(-7.50000 + 4.33013i) q^{33} +(-1.50000 - 2.59808i) q^{34} +(-0.500000 - 2.59808i) q^{35} +3.00000 q^{36} +(-1.50000 - 2.59808i) q^{37} +1.00000 q^{38} +8.66025i q^{39} +3.00000 q^{40} +(2.50000 - 4.33013i) q^{41} +(4.50000 - 0.866025i) q^{42} +(0.500000 + 0.866025i) q^{43} +(2.50000 + 4.33013i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(-1.50000 + 2.59808i) q^{46} +1.73205i q^{48} +(-6.50000 + 2.59808i) q^{49} +(2.00000 - 3.46410i) q^{50} -5.19615i q^{51} +5.00000 q^{52} +(4.50000 - 7.79423i) q^{53} +(-4.50000 - 2.59808i) q^{54} -5.00000 q^{55} +(-1.50000 - 7.79423i) q^{56} +(1.50000 + 0.866025i) q^{57} -1.00000 q^{58} +(1.50000 + 0.866025i) q^{60} +(7.00000 - 12.1244i) q^{61} +(7.50000 + 2.59808i) q^{63} +7.00000 q^{64} +(-2.50000 + 4.33013i) q^{65} -8.66025i q^{66} +(-2.00000 - 3.46410i) q^{67} -3.00000 q^{68} +(-4.50000 + 2.59808i) q^{69} +(2.50000 + 0.866025i) q^{70} -12.0000 q^{71} +(-4.50000 + 7.79423i) q^{72} +(-1.50000 + 2.59808i) q^{73} +3.00000 q^{74} +(6.00000 - 3.46410i) q^{75} +(0.500000 - 0.866025i) q^{76} +(2.50000 + 12.9904i) q^{77} +(-7.50000 - 4.33013i) q^{78} +(-4.00000 + 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(2.50000 + 4.33013i) q^{82} +(4.50000 + 7.79423i) q^{83} +(1.50000 - 4.33013i) q^{84} +(1.50000 - 2.59808i) q^{85} -1.00000 q^{86} +(-1.50000 - 0.866025i) q^{87} -15.0000 q^{88} +(6.50000 + 11.2583i) q^{89} +(-1.50000 - 2.59808i) q^{90} +(12.5000 + 4.33013i) q^{91} +(1.50000 + 2.59808i) q^{92} +(0.500000 + 0.866025i) q^{95} +(7.50000 + 4.33013i) q^{96} +(4.50000 + 7.79423i) q^{97} +(1.00000 - 6.92820i) q^{98} +(7.50000 - 12.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 3 q^{3} + q^{4} - 2 q^{5} + q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - q^2 - 3 * q^3 + q^4 - 2 * q^5 + q^7 - 6 * q^8 + 3 * q^9	\( 2 q - q^{2} - 3 q^{3} + q^{4} - 2 q^{5} + q^{7} - 6 q^{8} + 3 q^{9} + q^{10} + 10 q^{11} - 3 q^{12} + 5 q^{13} - 5 q^{14} + 3 q^{15} + q^{16} - 3 q^{17} + 3 q^{18} - q^{19} - q^{20} - 6 q^{21} - 5 q^{22} + 6 q^{23} + 9 q^{24} - 8 q^{25} + 5 q^{26} - 4 q^{28} + q^{29} - 5 q^{32} - 15 q^{33} - 3 q^{34} - q^{35} + 6 q^{36} - 3 q^{37} + 2 q^{38} + 6 q^{40} + 5 q^{41} + 9 q^{42} + q^{43} + 5 q^{44} - 3 q^{45} - 3 q^{46} - 13 q^{49} + 4 q^{50} + 10 q^{52} + 9 q^{53} - 9 q^{54} - 10 q^{55} - 3 q^{56} + 3 q^{57} - 2 q^{58} + 3 q^{60} + 14 q^{61} + 15 q^{63} + 14 q^{64} - 5 q^{65} - 4 q^{67} - 6 q^{68} - 9 q^{69} + 5 q^{70} - 24 q^{71} - 9 q^{72} - 3 q^{73} + 6 q^{74} + 12 q^{75} + q^{76} + 5 q^{77} - 15 q^{78} - 8 q^{79} - q^{80} - 9 q^{81} + 5 q^{82} + 9 q^{83} + 3 q^{84} + 3 q^{85} - 2 q^{86} - 3 q^{87} - 30 q^{88} + 13 q^{89} - 3 q^{90} + 25 q^{91} + 3 q^{92} + q^{95} + 15 q^{96} + 9 q^{97} + 2 q^{98} + 15 q^{99}+O(q^{100}) \) 2 * q - q^2 - 3 * q^3 + q^4 - 2 * q^5 + q^7 - 6 * q^8 + 3 * q^9 + q^10 + 10 * q^11 - 3 * q^12 + 5 * q^13 - 5 * q^14 + 3 * q^15 + q^16 - 3 * q^17 + 3 * q^18 - q^19 - q^20 - 6 * q^21 - 5 * q^22 + 6 * q^23 + 9 * q^24 - 8 * q^25 + 5 * q^26 - 4 * q^28 + q^29 - 5 * q^32 - 15 * q^33 - 3 * q^34 - q^35 + 6 * q^36 - 3 * q^37 + 2 * q^38 + 6 * q^40 + 5 * q^41 + 9 * q^42 + q^43 + 5 * q^44 - 3 * q^45 - 3 * q^46 - 13 * q^49 + 4 * q^50 + 10 * q^52 + 9 * q^53 - 9 * q^54 - 10 * q^55 - 3 * q^56 + 3 * q^57 - 2 * q^58 + 3 * q^60 + 14 * q^61 + 15 * q^63 + 14 * q^64 - 5 * q^65 - 4 * q^67 - 6 * q^68 - 9 * q^69 + 5 * q^70 - 24 * q^71 - 9 * q^72 - 3 * q^73 + 6 * q^74 + 12 * q^75 + q^76 + 5 * q^77 - 15 * q^78 - 8 * q^79 - q^80 - 9 * q^81 + 5 * q^82 + 9 * q^83 + 3 * q^84 + 3 * q^85 - 2 * q^86 - 3 * q^87 - 30 * q^88 + 13 * q^89 - 3 * q^90 + 25 * q^91 + 3 * q^92 + q^95 + 15 * q^96 + 9 * q^97 + 2 * q^98 + 15 * q^99

Introduction

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