LMFDB - Embedded newform 63.2.h.a.58.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,2,Mod(25,63)]

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([4, 4]))

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

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

chi := DirichletCharacter("63.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	63.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:	$0.503057532734$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			58.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	63.58
Dual form			63.2.h.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.73205i q^{3} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} -1.73205i q^{6} +(2.00000 + 1.73205i) q^{7} -3.00000 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.73205i q^{3} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} -1.73205i q^{6} +(2.00000 + 1.73205i) q^{7} -3.00000 q^{8} -3.00000 q^{9} +(0.500000 + 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} +1.73205i q^{12} +(2.50000 - 4.33013i) q^{13} +(2.00000 + 1.73205i) q^{14} +(1.50000 - 0.866025i) q^{15} -1.00000 q^{16} +(-1.50000 - 2.59808i) q^{17} -3.00000 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} +(-1.50000 - 2.59808i) q^{23} +5.19615i q^{24} +(2.00000 - 3.46410i) q^{25} +(2.50000 - 4.33013i) q^{26} +5.19615i q^{27} +(-2.00000 - 1.73205i) q^{28} +(0.500000 + 0.866025i) q^{29} +(1.50000 - 0.866025i) q^{30} +5.00000 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} +(-0.500000 + 0.866025i) q^{38} +(-7.50000 - 4.33013i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(2.50000 - 4.33013i) q^{41} +(3.00000 - 3.46410i) 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} +(1.00000 + 6.92820i) q^{49} +(2.00000 - 3.46410i) q^{50} +(-4.50000 + 2.59808i) q^{51} +(-2.50000 + 4.33013i) q^{52} +(4.50000 + 7.79423i) q^{53} +5.19615i q^{54} -5.00000 q^{55} +(-6.00000 - 5.19615i) q^{56} +(1.50000 + 0.866025i) q^{57} +(0.500000 + 0.866025i) q^{58} +(-1.50000 + 0.866025i) q^{60} -14.0000 q^{61} +(-6.00000 - 5.19615i) q^{63} +7.00000 q^{64} +5.00000 q^{65} +(7.50000 + 4.33013i) q^{66} +4.00000 q^{67} +(1.50000 + 2.59808i) q^{68} +(-4.50000 + 2.59808i) q^{69} +(-0.500000 + 2.59808i) q^{70} -12.0000 q^{71} +9.00000 q^{72} +(-1.50000 - 2.59808i) q^{73} +(-1.50000 + 2.59808i) q^{74} +(-6.00000 - 3.46410i) q^{75} +(0.500000 - 0.866025i) q^{76} +(-12.5000 + 4.33013i) q^{77} +(-7.50000 - 4.33013i) q^{78} +8.00000 q^{79} +(-0.500000 - 0.866025i) q^{80} +9.00000 q^{81} +(2.50000 - 4.33013i) q^{82} +(4.50000 + 7.79423i) q^{83} +(-3.00000 + 3.46410i) q^{84} +(1.50000 - 2.59808i) q^{85} +(0.500000 + 0.866025i) q^{86} +(1.50000 - 0.866025i) q^{87} +(7.50000 - 12.9904i) 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} -1.00000 q^{95} -8.66025i 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 + 2 q^{2} - 2 q^{4} + q^{5} + 4 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^4 + q^5 + 4 * q^7 - 6 * q^8 - 6 * q^9	$ 2 q + 2 q^{2} - 2 q^{4} + q^{5} + 4 q^{7} - 6 q^{8} - 6 q^{9} + q^{10} - 5 q^{11} + 5 q^{13} + 4 q^{14} + 3 q^{15} - 2 q^{16} - 3 q^{17} - 6 q^{18} - q^{19} - q^{20} + 6 q^{21} - 5 q^{22} - 3 q^{23} + 4 q^{25} + 5 q^{26} - 4 q^{28} + q^{29} + 3 q^{30} + 10 q^{32} + 15 q^{33} - 3 q^{34} - q^{35} + 6 q^{36} - 3 q^{37} - q^{38} - 15 q^{39} - 3 q^{40} + 5 q^{41} + 6 q^{42} + q^{43} + 5 q^{44} - 3 q^{45} - 3 q^{46} + 2 q^{49} + 4 q^{50} - 9 q^{51} - 5 q^{52} + 9 q^{53} - 10 q^{55} - 12 q^{56} + 3 q^{57} + q^{58} - 3 q^{60} - 28 q^{61} - 12 q^{63} + 14 q^{64} + 10 q^{65} + 15 q^{66} + 8 q^{67} + 3 q^{68} - 9 q^{69} - q^{70} - 24 q^{71} + 18 q^{72} - 3 q^{73} - 3 q^{74} - 12 q^{75} + q^{76} - 25 q^{77} - 15 q^{78} + 16 q^{79} - q^{80} + 18 q^{81} + 5 q^{82} + 9 q^{83} - 6 q^{84} + 3 q^{85} + q^{86} + 3 q^{87} + 15 q^{88} + 13 q^{89} - 3 q^{90} + 25 q^{91} + 3 q^{92} - 2 q^{95} + 9 q^{97} + 2 q^{98} + 15 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^4 + q^5 + 4 * q^7 - 6 * q^8 - 6 * q^9 + q^10 - 5 * q^11 + 5 * q^13 + 4 * q^14 + 3 * q^15 - 2 * q^16 - 3 * q^17 - 6 * q^18 - q^19 - q^20 + 6 * q^21 - 5 * q^22 - 3 * q^23 + 4 * q^25 + 5 * q^26 - 4 * q^28 + q^29 + 3 * q^30 + 10 * q^32 + 15 * q^33 - 3 * q^34 - q^35 + 6 * q^36 - 3 * q^37 - q^38 - 15 * q^39 - 3 * q^40 + 5 * q^41 + 6 * q^42 + q^43 + 5 * q^44 - 3 * q^45 - 3 * q^46 + 2 * q^49 + 4 * q^50 - 9 * q^51 - 5 * q^52 + 9 * q^53 - 10 * q^55 - 12 * q^56 + 3 * q^57 + q^58 - 3 * q^60 - 28 * q^61 - 12 * q^63 + 14 * q^64 + 10 * q^65 + 15 * q^66 + 8 * q^67 + 3 * q^68 - 9 * q^69 - q^70 - 24 * q^71 + 18 * q^72 - 3 * q^73 - 3 * q^74 - 12 * q^75 + q^76 - 25 * q^77 - 15 * q^78 + 16 * q^79 - q^80 + 18 * q^81 + 5 * q^82 + 9 * q^83 - 6 * q^84 + 3 * q^85 + q^86 + 3 * q^87 + 15 * q^88 + 13 * q^89 - 3 * q^90 + 25 * q^91 + 3 * q^92 - 2 * q^95 + 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 $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.00000			0.707107			0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000			0.707107			0.353553	+	0.935414i	$0.384973\pi$
$3$		−	1.73205i		−	1.00000i
$3$		−	1.73205i		−	1.00000i
$4$	−1.00000			−0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	0.955901	−	0.293691i	$-0.0948835\pi$
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	−0.732294	+	0.680989i	$0.761550\pi$
$6$		−	1.73205i		−	0.707107i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$8$	−3.00000			−1.06066
$9$	−3.00000			−1.00000
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	0.192201	+	0.981356i	$0.438437\pi$
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	−0.945979	+	0.324227i	$0.894896\pi$
$12$			1.73205i			0.500000i
$13$	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	$-0.0772105\pi$
$14$	2.00000	+	1.73205i	0.534522	+	0.462910i
$15$	1.50000	−	0.866025i	0.387298	−	0.223607i
$16$	−1.00000			−0.250000
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$	−3.00000			−0.707107
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	0.802955	+	0.596040i	$0.203260\pi$
$20$	−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
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$			5.19615i			1.06066i
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	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	$0.803736\pi$
$30$	1.50000	−	0.866025i	0.273861	−	0.158114i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	5.00000			0.883883
$33$	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	−0.962580	−	0.270998i	$-0.912646\pi$
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	0.715981	+	0.698119i	$0.245980\pi$
$38$	−0.500000	+	0.866025i	−0.0811107	+	0.140488i
$39$	−7.50000	−	4.33013i	−1.20096	−	0.693375i
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	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	$0.0389915\pi$
$42$	3.00000	−	3.46410i	0.462910	−	0.534522i
$43$	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			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$			1.73205i			0.250000i
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	2.00000	−	3.46410i	0.282843	−	0.489898i
$51$	−4.50000	+	2.59808i	−0.630126	+	0.363803i
$52$	−2.50000	+	4.33013i	−0.346688	+	0.600481i
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	0.989828	+	0.142269i	$0.0454398\pi$
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	−0.371706	+	0.928351i	$0.621227\pi$
$54$			5.19615i			0.707107i
$55$	−5.00000			−0.674200
$56$	−6.00000	−	5.19615i	−0.801784	−	0.694365i
$57$	1.50000	+	0.866025i	0.198680	+	0.114708i
$58$	0.500000	+	0.866025i	0.0656532	+	0.113715i
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$	−1.50000	+	0.866025i	−0.193649	+	0.111803i
$61$	−14.0000			−1.79252			−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000			−1.79252			−0.896258	+	0.443533i	$0.853725\pi$
$62$		0			0
$63$	−6.00000	−	5.19615i	−0.755929	−	0.654654i
$64$	7.00000			0.875000
$65$	5.00000			0.620174
$66$	7.50000	+	4.33013i	0.923186	+	0.533002i
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$	−4.50000	+	2.59808i	−0.541736	+	0.312772i
$70$	−0.500000	+	2.59808i	−0.0597614	+	0.310530i
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$	9.00000			1.06066
$73$	−1.50000	−	2.59808i	−0.175562	−	0.304082i	0.764794	−	0.644275i	$-0.222841\pi$
$73$	−1.50000	−	2.59808i	−0.175562	−	0.304082i	−0.940356	+	0.340193i	$0.889507\pi$
$74$	−1.50000	+	2.59808i	−0.174371	+	0.302020i
$75$	−6.00000	−	3.46410i	−0.692820	−	0.400000i
$76$	0.500000	−	0.866025i	0.0573539	−	0.0993399i
$77$	−12.5000	+	4.33013i	−1.42451	+	0.493464i
$78$	−7.50000	−	4.33013i	−0.849208	−	0.490290i
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	9.00000			1.00000
$82$	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	$0.668890\pi$
$84$	−3.00000	+	3.46410i	−0.327327	+	0.377964i
$85$	1.50000	−	2.59808i	0.162698	−	0.281801i
$86$	0.500000	+	0.866025i	0.0539164	+	0.0933859i
$87$	1.50000	−	0.866025i	0.160817	−	0.0928477i
$88$	7.50000	−	12.9904i	0.799503	−	1.38478i
$89$	6.50000	−	11.2583i	0.688999	−	1.19338i	−0.283164	−	0.959072i	$-0.591384\pi$
$89$	6.50000	−	11.2583i	0.688999	−	1.19338i	0.972162	−	0.234309i	$-0.0752827\pi$
$90$	−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
$95$	−1.00000			−0.102598
$96$		−	8.66025i		−	0.883883i
$97$	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
$101$	8.50000	−	14.7224i	0.845782	−	1.46494i	−0.0391591	−	0.999233i	$-0.512468\pi$
$101$	8.50000	−	14.7224i	0.845782	−	1.46494i	0.884941	−	0.465704i	$-0.154199\pi$
$102$	−4.50000	+	2.59808i	−0.445566	+	0.257248i
$103$	0.500000	+	0.866025i	0.0492665	+	0.0853320i	0.889607	−	0.456727i	$-0.150978\pi$
$103$	0.500000	+	0.866025i	0.0492665	+	0.0853320i	−0.840341	+	0.542059i	$0.817645\pi$
$104$	−7.50000	+	12.9904i	−0.735436	+	1.27381i
$105$	4.50000	+	0.866025i	0.439155	+	0.0845154i
$106$	4.50000	+	7.79423i	0.437079	+	0.757042i
$107$	−8.50000	+	14.7224i	−0.821726	+	1.42327i	0.0826699	+	0.996577i	$0.473655\pi$
$107$	−8.50000	+	14.7224i	−0.821726	+	1.42327i	−0.904396	+	0.426694i	$0.859678\pi$
$108$		−	5.19615i		−	0.500000i
$109$	4.50000	+	7.79423i	0.431022	+	0.746552i	0.996962	−	0.0778949i	$-0.0248199\pi$
$109$	4.50000	+	7.79423i	0.431022	+	0.746552i	−0.565940	+	0.824447i	$0.691487\pi$
$110$	−5.00000			−0.476731
$111$	4.50000	+	2.59808i	0.427121	+	0.246598i
$112$	−2.00000	−	1.73205i	−0.188982	−	0.163663i
$113$	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
$115$	1.50000	−	2.59808i	0.139876	−	0.242272i
$116$	−0.500000	−	0.866025i	−0.0464238	−	0.0804084i
$117$	−7.50000	+	12.9904i	−0.693375	+	1.20096i
$118$		0			0
$119$	1.50000	−	7.79423i	0.137505	−	0.714496i
$120$	−4.50000	+	2.59808i	−0.410792	+	0.237171i
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$	−14.0000			−1.26750
$123$	−7.50000	−	4.33013i	−0.676252	−	0.390434i
$124$		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	$0.678715\pi$
$128$	−3.00000			−0.265165
$129$	1.50000	−	0.866025i	0.132068	−	0.0762493i
$130$	5.00000			0.438529
$131$	0.500000	+	0.866025i	0.0436852	+	0.0756650i	0.887041	−	0.461690i	$-0.152757\pi$
$131$	0.500000	+	0.866025i	0.0436852	+	0.0756650i	−0.843356	+	0.537355i	$0.819423\pi$
$132$	−7.50000	−	4.33013i	−0.652791	−	0.376889i
$133$	−2.50000	+	0.866025i	−0.216777	+	0.0750939i
$134$	4.00000			0.345547
$135$	−4.50000	+	2.59808i	−0.387298	+	0.223607i
$136$	4.50000	+	7.79423i	0.385872	+	0.668350i
$137$	4.50000	−	7.79423i	0.384461	−	0.665906i	−0.607233	−	0.794524i	$-0.707721\pi$
$137$	4.50000	−	7.79423i	0.384461	−	0.665906i	0.991694	+	0.128618i	$0.0410540\pi$
$138$	−4.50000	+	2.59808i	−0.383065	+	0.221163i
$139$	−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	$0.291323\pi$
$140$	0.500000	−	2.59808i	0.0422577	−	0.219578i
$141$		0			0
$142$	−12.0000			−1.00702
$143$	12.5000	+	21.6506i	1.04530	+	1.81052i
$144$	3.00000			0.250000
$145$	−0.500000	+	0.866025i	−0.0415227	+	0.0719195i
$146$	−1.50000	−	2.59808i	−0.124141	−	0.215018i
$147$	12.0000	−	1.73205i	0.989743	−	0.142857i
$148$	1.50000	−	2.59808i	0.123299	−	0.213561i
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	0.798019	−	0.602632i	$-0.205881\pi$
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	−0.920904	+	0.389789i	$0.872548\pi$
$150$	−6.00000	−	3.46410i	−0.489898	−	0.282843i
$151$	−2.50000	+	4.33013i	−0.203447	+	0.352381i	−0.949637	−	0.313353i	$-0.898548\pi$
$151$	−2.50000	+	4.33013i	−0.203447	+	0.352381i	0.746190	+	0.665733i	$0.231881\pi$
$152$	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
$157$	−14.0000			−1.11732			−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000			−1.11732			−0.558661	+	0.829396i	$0.688685\pi$
$158$	8.00000			0.636446
$159$	13.5000	−	7.79423i	1.07062	−	0.618123i
$160$	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	−0.566149	−	0.824303i	$-0.691567\pi$
$163$	5.50000	−	9.52628i	0.430793	−	0.746156i	0.996942	+	0.0781474i	$0.0249005\pi$
$164$	−2.50000	+	4.33013i	−0.195217	+	0.338126i
$165$			8.66025i			0.674200i
$166$	4.50000	+	7.79423i	0.349268	+	0.604949i
$167$	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
$171$	1.50000	−	2.59808i	0.114708	−	0.198680i
$172$	−0.500000	−	0.866025i	−0.0381246	−	0.0660338i
$173$	−14.0000			−1.06440			−0.532200	−	0.846619i	$-0.678635\pi$
$173$	−14.0000			−1.06440			−0.532200	+	0.846619i	$0.678635\pi$
$174$	1.50000	−	0.866025i	0.113715	−	0.0656532i
$175$	10.0000	−	3.46410i	0.755929	−	0.261861i
$176$	2.50000	−	4.33013i	0.188445	−	0.326396i
$177$		0			0
$178$	6.50000	−	11.2583i	0.487196	−	0.843848i
$179$	−9.50000	−	16.4545i	−0.710063	−	1.22987i	−0.964833	−	0.262864i	$-0.915333\pi$
$179$	−9.50000	−	16.4545i	−0.710063	−	1.22987i	0.254770	−	0.967002i	$-0.418000\pi$
$180$	1.50000	+	2.59808i	0.111803	+	0.193649i
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$	12.5000	−	4.33013i	0.926562	−	0.320970i
$183$			24.2487i			1.79252i
$184$	4.50000	+	7.79423i	0.331744	+	0.574598i
$185$	−3.00000			−0.220564
$186$		0			0
$187$	15.0000			1.09691
$188$		0			0
$189$	−9.00000	+	10.3923i	−0.654654	+	0.755929i
$190$	−1.00000			−0.0725476
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$		−	12.1244i		−	0.875000i
$193$	−10.0000			−0.719816			−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000			−0.719816			−0.359908	+	0.932988i	$0.617192\pi$
$194$	4.50000	+	7.79423i	0.323081	+	0.559593i
$195$		−	8.66025i		−	0.620174i
$196$	−1.00000	−	6.92820i	−0.0714286	−	0.494872i
$197$	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	0.807950	−	0.589252i	$-0.200577\pi$
$199$	−1.50000	−	2.59808i	−0.106332	−	0.184173i	−0.914282	+	0.405079i	$0.867244\pi$
$200$	−6.00000	+	10.3923i	−0.424264	+	0.734847i
$201$		−	6.92820i		−	0.488678i
$202$	8.50000	−	14.7224i	0.598058	−	1.03587i
$203$	−0.500000	+	2.59808i	−0.0350931	+	0.182349i
$204$	4.50000	−	2.59808i	0.315063	−	0.181902i
$205$	5.00000			0.349215
$206$	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	$0.314345\pi$
$212$	−4.50000	−	7.79423i	−0.309061	−	0.535310i
$213$			20.7846i			1.42414i
$214$	−8.50000	+	14.7224i	−0.581048	+	1.00640i
$215$	−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
$219$	−4.50000	+	2.59808i	−0.304082	+	0.175562i
$220$	5.00000			0.337100
$221$	−15.0000			−1.00901
$222$	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
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	−0.811943	−	0.583736i	$-0.801590\pi$
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	0.911502	+	0.411296i	$0.134924\pi$
$228$	−1.50000	−	0.866025i	−0.0993399	−	0.0573539i
$229$	0.500000	+	0.866025i	0.0330409	+	0.0572286i	0.882073	−	0.471113i	$-0.156147\pi$
$229$	0.500000	+	0.866025i	0.0330409	+	0.0572286i	−0.849032	+	0.528341i	$0.822814\pi$
$230$	1.50000	−	2.59808i	0.0989071	−	0.171312i
$231$	7.50000	+	21.6506i	0.493464	+	1.42451i
$232$	−1.50000	−	2.59808i	−0.0984798	−	0.170572i
$233$	−1.50000	+	2.59808i	−0.0982683	+	0.170206i	−0.910968	−	0.412477i	$-0.864664\pi$
$233$	−1.50000	+	2.59808i	−0.0982683	+	0.170206i	0.812700	+	0.582683i	$0.197997\pi$
$234$	−7.50000	+	12.9904i	−0.490290	+	0.849208i
$235$		0			0
$236$		0			0
$237$		−	13.8564i		−	0.900070i
$238$	1.50000	−	7.79423i	0.0972306	−	0.505225i
$239$	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	$0.00543724\pi$
$240$	−1.50000	+	0.866025i	−0.0968246	+	0.0559017i
$241$	−5.50000	+	9.52628i	−0.354286	+	0.613642i	−0.986996	−	0.160748i	$-0.948609\pi$
$241$	−5.50000	+	9.52628i	−0.354286	+	0.613642i	0.632709	+	0.774389i	$0.281943\pi$
$242$	−7.00000	−	12.1244i	−0.449977	−	0.779383i
$243$		−	15.5885i		−	1.00000i
$244$	14.0000			0.896258
$245$	−5.50000	+	4.33013i	−0.351382	+	0.276642i
$246$	−7.50000	−	4.33013i	−0.478183	−	0.276079i
$247$	2.50000	+	4.33013i	0.159071	+	0.275519i
$248$		0			0
$249$	13.5000	−	7.79423i	0.855528	−	0.493939i
$250$	9.00000			0.569210
$251$	−28.0000			−1.76734			−0.883672	−	0.468106i	$-0.844936\pi$
$251$	−28.0000			−1.76734			−0.883672	+	0.468106i	$0.844936\pi$
$252$	6.00000	+	5.19615i	0.377964	+	0.327327i
$253$	15.0000			0.943042
$254$	−12.0000			−0.752947
$255$	−4.50000	−	2.59808i	−0.281801	−	0.162698i
$256$	−17.0000			−1.06250
$257$	14.5000	+	25.1147i	0.904485	+	1.56661i	0.821607	+	0.570055i	$0.193078\pi$
$257$	14.5000	+	25.1147i	0.904485	+	1.56661i	0.0828783	+	0.996560i	$0.473589\pi$
$258$	1.50000	−	0.866025i	0.0933859	−	0.0539164i
$259$	−7.50000	+	2.59808i	−0.466027	+	0.161437i
$260$	−5.00000			−0.310087
$261$	−1.50000	−	2.59808i	−0.0928477	−	0.160817i
$262$	0.500000	+	0.866025i	0.0308901	+	0.0535032i
$263$	−2.50000	+	4.33013i	−0.154157	+	0.267007i	−0.932752	−	0.360520i	$-0.882599\pi$
$263$	−2.50000	+	4.33013i	−0.154157	+	0.267007i	0.778595	+	0.627527i	$0.215933\pi$
$264$	−22.5000	−	12.9904i	−1.38478	−	0.799503i
$265$	−4.50000	+	7.79423i	−0.276433	+	0.478796i
$266$	−2.50000	+	0.866025i	−0.153285	+	0.0530994i
$267$	−19.5000	−	11.2583i	−1.19338	−	0.688999i
$268$	−4.00000			−0.244339
$269$	−1.50000	−	2.59808i	−0.0914566	−	0.158408i	0.816668	−	0.577108i	$-0.195819\pi$
$269$	−1.50000	−	2.59808i	−0.0914566	−	0.158408i	−0.908124	+	0.418701i	$0.862486\pi$
$270$	−4.50000	+	2.59808i	−0.273861	+	0.158114i
$271$	−0.500000	+	0.866025i	−0.0303728	+	0.0526073i	−0.880812	−	0.473466i	$-0.843003\pi$
$271$	−0.500000	+	0.866025i	−0.0303728	+	0.0526073i	0.850439	+	0.526073i	$0.176336\pi$
$272$	1.50000	+	2.59808i	0.0909509	+	0.157532i
$273$	−7.50000	−	21.6506i	−0.453921	−	1.31036i
$274$	4.50000	−	7.79423i	0.271855	−	0.470867i
$275$	10.0000	+	17.3205i	0.603023	+	1.04447i
$276$	4.50000	−	2.59808i	0.270868	−	0.156386i
$277$	−9.50000	+	16.4545i	−0.570800	+	0.988654i	0.425684	+	0.904872i	$0.360033\pi$
$277$	−9.50000	+	16.4545i	−0.570800	+	0.988654i	−0.996484	+	0.0837823i	$0.973300\pi$
$278$	−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
$283$	28.0000			1.66443			0.832214	−	0.554455i	$-0.187073\pi$
$283$	28.0000			1.66443			0.832214	+	0.554455i	$0.187073\pi$
$284$	12.0000			0.712069
$285$			1.73205i			0.102598i
$286$	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
$290$	−0.500000	+	0.866025i	−0.0293610	+	0.0508548i
$291$	13.5000	−	7.79423i	0.791384	−	0.456906i
$292$	1.50000	+	2.59808i	0.0877809	+	0.152041i
$293$	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	$0.120010\pi$
$294$	12.0000	−	1.73205i	0.699854	−	0.101015i
$295$		0			0
$296$	4.50000	−	7.79423i	0.261557	−	0.453030i
$297$	−22.5000	−	12.9904i	−1.30558	−	0.753778i
$298$	−1.50000	−	2.59808i	−0.0868927	−	0.150503i
$299$	−15.0000			−0.867472
$300$	6.00000	+	3.46410i	0.346410	+	0.200000i
$301$	−0.500000	+	2.59808i	−0.0288195	+	0.149751i
$302$	−2.50000	+	4.33013i	−0.143859	+	0.249171i
$303$	−25.5000	−	14.7224i	−1.46494	−	0.845782i
$304$	0.500000	−	0.866025i	0.0286770	−	0.0496700i
$305$	−7.00000	−	12.1244i	−0.400819	−	0.694239i
$306$	4.50000	+	7.79423i	0.257248	+	0.445566i
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$	12.5000	−	4.33013i	0.712254	−	0.246732i
$309$	1.50000	−	0.866025i	0.0853320	−	0.0492665i
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$	22.5000	+	12.9904i	1.27381	+	0.735436i
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$	−14.0000			−0.790066
$315$	1.50000	−	7.79423i	0.0845154	−	0.439155i
$316$	−8.00000			−0.450035
$317$	−6.00000			−0.336994			−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000			−0.336994			−0.168497	+	0.985702i	$0.553891\pi$
$318$	13.5000	−	7.79423i	0.757042	−	0.437079i
$319$	−5.00000			−0.279946
$320$	3.50000	+	6.06218i	0.195656	+	0.338886i
$321$	25.5000	+	14.7224i	1.42327	+	0.821726i
$322$	1.50000	−	7.79423i	0.0835917	−	0.434355i
$323$	3.00000			0.166924
$324$	−9.00000			−0.500000
$325$	−10.0000	−	17.3205i	−0.554700	−	0.960769i
$326$	5.50000	−	9.52628i	0.304617	−	0.527612i
$327$	13.5000	−	7.79423i	0.746552	−	0.431022i
$328$	−7.50000	+	12.9904i	−0.414118	+	0.717274i
$329$		0			0
$330$			8.66025i			0.476731i
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$	−4.50000	−	7.79423i	−0.246970	−	0.427764i
$333$	4.50000	−	7.79423i	0.246598	−	0.427121i
$334$	9.50000	−	16.4545i	0.519817	−	0.900349i
$335$	2.00000	+	3.46410i	0.109272	+	0.189264i
$336$	−3.00000	+	3.46410i	−0.163663	+	0.188982i
$337$	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	$-0.123183\pi$
$338$	−6.00000	−	10.3923i	−0.326357	−	0.565267i
$339$	−1.50000	−	0.866025i	−0.0814688	−	0.0470360i
$340$	−1.50000	+	2.59808i	−0.0813489	+	0.140900i
$341$		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
$346$	−14.0000			−0.752645
$347$	4.00000			0.214731			0.107366	−	0.994220i	$-0.465758\pi$
$347$	4.00000			0.214731			0.107366	+	0.994220i	$0.465758\pi$
$348$	−1.50000	+	0.866025i	−0.0804084	+	0.0464238i
$349$	−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
$353$	−5.50000	+	9.52628i	−0.292735	+	0.507033i	−0.974456	−	0.224580i	$-0.927899\pi$
$353$	−5.50000	+	9.52628i	−0.292735	+	0.507033i	0.681720	+	0.731613i	$0.261232\pi$
$354$		0			0
$355$	−6.00000	−	10.3923i	−0.318447	−	0.551566i
$356$	−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	−0.683597	−	0.729860i	$-0.739585\pi$
$359$	5.50000	−	9.52628i	0.290279	−	0.502778i	0.973876	+	0.227082i	$0.0729186\pi$
$360$	4.50000	+	7.79423i	0.237171	+	0.410792i
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	−14.0000			−0.735824
$363$	−21.0000	+	12.1244i	−1.10221	+	0.636364i
$364$	−12.5000	+	4.33013i	−0.655178	+	0.226960i
$365$	1.50000	−	2.59808i	0.0785136	−	0.135990i
$366$			24.2487i			1.26750i
$367$	1.50000	−	2.59808i	0.0782994	−	0.135618i	−0.824217	−	0.566274i	$-0.808384\pi$
$367$	1.50000	−	2.59808i	0.0782994	−	0.135618i	0.902516	+	0.430656i	$0.141718\pi$
$368$	1.50000	+	2.59808i	0.0781929	+	0.135434i
$369$	−7.50000	+	12.9904i	−0.390434	+	0.676252i
$370$	−3.00000			−0.155963
$371$	−4.50000	+	23.3827i	−0.233628	+	1.21397i
$372$		0			0
$373$	12.5000	+	21.6506i	0.647225	+	1.12103i	0.983783	+	0.179364i	$0.0574041\pi$
$373$	12.5000	+	21.6506i	0.647225	+	1.12103i	−0.336557	+	0.941663i	$0.609263\pi$
$374$	15.0000			0.775632
$375$		−	15.5885i		−	0.804984i
$376$		0			0
$377$	5.00000			0.257513
$378$	−9.00000	+	10.3923i	−0.462910	+	0.534522i
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$	1.00000			0.0512989
$381$			20.7846i			1.06483i
$382$	8.00000			0.409316
$383$	−13.5000	−	23.3827i	−0.689818	−	1.19480i	−0.971897	−	0.235408i	$-0.924357\pi$
$383$	−13.5000	−	23.3827i	−0.689818	−	1.19480i	0.282079	−	0.959391i	$-0.408976\pi$
$384$			5.19615i			0.265165i
$385$	−10.0000	−	8.66025i	−0.509647	−	0.441367i
$386$	−10.0000			−0.508987
$387$	−1.50000	−	2.59808i	−0.0762493	−	0.132068i
$388$	−4.50000	−	7.79423i	−0.228453	−	0.395692i
$389$	4.50000	−	7.79423i	0.228159	−	0.395183i	−0.729103	−	0.684403i	$-0.760063\pi$
$389$	4.50000	−	7.79423i	0.228159	−	0.395183i	0.957263	+	0.289220i	$0.0933960\pi$
$390$		−	8.66025i		−	0.438529i
$391$	−4.50000	+	7.79423i	−0.227575	+	0.394171i
$392$	−3.00000	−	20.7846i	−0.151523	−	1.04978i
$393$	1.50000	−	0.866025i	0.0756650	−	0.0436852i
$394$	2.00000			0.100759
$395$	4.00000	+	6.92820i	0.201262	+	0.348596i
$396$	−7.50000	+	12.9904i	−0.376889	+	0.652791i
$397$	−7.50000	+	12.9904i	−0.376414	+	0.651969i	−0.990538	−	0.137241i	$-0.956176\pi$
$397$	−7.50000	+	12.9904i	−0.376414	+	0.651969i	0.614123	+	0.789210i	$0.289510\pi$
$398$	−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
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	0.826139	−	0.563466i	$-0.190532\pi$
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$402$		−	6.92820i		−	0.345547i
$403$		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
$408$	13.5000	−	7.79423i	0.668350	−	0.385872i
$409$	14.0000			0.692255			0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000			0.692255			0.346128	+	0.938187i	$0.387496\pi$
$410$	5.00000			0.246932
$411$	−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
$416$	12.5000	−	21.6506i	0.612863	−	1.06151i
$417$	13.5000	+	7.79423i	0.661098	+	0.381685i
$418$	−2.50000	−	4.33013i	−0.122279	−	0.211793i
$419$	−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	$0.237220\pi$
$420$	−4.50000	−	0.866025i	−0.219578	−	0.0422577i
$421$	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
$425$	−12.0000			−0.582086
$426$			20.7846i			1.00702i
$427$	−28.0000	−	24.2487i	−1.35501	−	1.17348i
$428$	8.50000	−	14.7224i	0.410863	−	0.711636i
$429$	37.5000	−	21.6506i	1.81052	−	1.04530i
$430$	−0.500000	+	0.866025i	−0.0241121	+	0.0417635i
$431$	4.50000	+	7.79423i	0.216757	+	0.375435i	0.953815	−	0.300395i	$-0.0971186\pi$
$431$	4.50000	+	7.79423i	0.216757	+	0.375435i	−0.737057	+	0.675830i	$0.763785\pi$
$432$		−	5.19615i		−	0.250000i
$433$	−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
$436$	−4.50000	−	7.79423i	−0.215511	−	0.373276i
$437$	3.00000			0.143509
$438$	−4.50000	+	2.59808i	−0.215018	+	0.124141i
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$	15.0000			0.715097
$441$	−3.00000	−	20.7846i	−0.142857	−	0.989743i
$442$	−15.0000			−0.713477
$443$	36.0000			1.71041			0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000			1.71041			0.855206	+	0.518289i	$0.173431\pi$
$444$	−4.50000	−	2.59808i	−0.213561	−	0.123299i
$445$	13.0000			0.616259
$446$	−9.50000	−	16.4545i	−0.449838	−	0.779142i
$447$	−4.50000	+	2.59808i	−0.212843	+	0.122885i
$448$	14.0000	+	12.1244i	0.661438	+	0.572822i
$449$	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
$452$	−0.500000	+	0.866025i	−0.0235180	+	0.0407344i
$453$	7.50000	+	4.33013i	0.352381	+	0.203447i
$454$	1.50000	−	2.59808i	0.0703985	−	0.121934i
$455$	10.0000	+	8.66025i	0.468807	+	0.405999i
$456$	−4.50000	−	2.59808i	−0.210732	−	0.121666i
$457$	22.0000			1.02912			0.514558	−	0.857455i	$-0.327956\pi$
$457$	22.0000			1.02912			0.514558	+	0.857455i	$0.327956\pi$
$458$	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	$0.979227\pi$
$462$	7.50000	+	21.6506i	0.348932	+	1.00728i
$463$	−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	$0.264348\pi$
$464$	−0.500000	−	0.866025i	−0.0232119	−	0.0402042i
$465$		0			0
$466$	−1.50000	+	2.59808i	−0.0694862	+	0.120354i
$467$	13.5000	−	23.3827i	0.624705	−	1.08202i	−0.363892	−	0.931441i	$-0.618552\pi$
$467$	13.5000	−	23.3827i	0.624705	−	1.08202i	0.988598	−	0.150581i	$-0.0481143\pi$
$468$	7.50000	−	12.9904i	0.346688	−	0.600481i
$469$	8.00000	+	6.92820i	0.369406	+	0.319915i
$470$		0			0
$471$			24.2487i			1.11732i
$472$		0			0
$473$	−5.00000			−0.229900
$474$		−	13.8564i		−	0.636446i
$475$	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
$479$	−12.5000	+	21.6506i	−0.571140	+	0.989243i	0.425310	+	0.905048i	$0.360165\pi$
$479$	−12.5000	+	21.6506i	−0.571140	+	0.989243i	−0.996449	+	0.0841949i	$0.973168\pi$
$480$	7.50000	−	4.33013i	0.342327	−	0.197642i
$481$	7.50000	+	12.9904i	0.341971	+	0.592310i
$482$	−5.50000	+	9.52628i	−0.250518	+	0.433910i
$483$	−13.5000	−	2.59808i	−0.614271	−	0.118217i
$484$	7.00000	+	12.1244i	0.318182	+	0.551107i
$485$	−4.50000	+	7.79423i	−0.204334	+	0.353918i
$486$		−	15.5885i		−	0.707107i
$487$	−9.50000	−	16.4545i	−0.430486	−	0.745624i	0.566429	−	0.824110i	$-0.308325\pi$
$487$	−9.50000	−	16.4545i	−0.430486	−	0.745624i	−0.996915	+	0.0784867i	$0.974991\pi$
$488$	42.0000			1.90125
$489$	−16.5000	−	9.52628i	−0.746156	−	0.430793i
$490$	−5.50000	+	4.33013i	−0.248465	+	0.195615i
$491$	−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
$493$	1.50000	−	2.59808i	0.0675566	−	0.117011i
$494$	2.50000	+	4.33013i	0.112480	+	0.194822i
$495$	15.0000			0.674200
$496$		0			0
$497$	−24.0000	−	20.7846i	−1.07655	−	0.932317i
$498$	13.5000	−	7.79423i	0.604949	−	0.349268i
$499$	−15.5000	−	26.8468i	−0.693875	−	1.20183i	−0.970558	−	0.240866i	$-0.922569\pi$
$499$	−15.5000	−	26.8468i	−0.693875	−	1.20183i	0.276683	−	0.960961i	$-0.410765\pi$
$500$	−9.00000			−0.402492
$501$	−28.5000	−	16.4545i	−1.27329	−	0.735132i
$502$	−28.0000			−1.24970
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	18.0000	+	15.5885i	0.801784	+	0.694365i
$505$	17.0000			0.756490
$506$	15.0000			0.666831
$507$	−18.0000	+	10.3923i	−0.799408	+	0.461538i
$508$	12.0000			0.532414
$509$	14.5000	+	25.1147i	0.642701	+	1.11319i	0.984827	+	0.173537i	$0.0555197\pi$
$509$	14.5000	+	25.1147i	0.642701	+	1.11319i	−0.342126	+	0.939654i	$0.611147\pi$
$510$	−4.50000	−	2.59808i	−0.199263	−	0.115045i
$511$	1.50000	−	7.79423i	0.0663561	−	0.344796i
$512$	−11.0000			−0.486136
$513$	−4.50000	−	2.59808i	−0.198680	−	0.114708i
$514$	14.5000	+	25.1147i	0.639568	+	1.10776i
$515$	−0.500000	+	0.866025i	−0.0220326	+	0.0381616i
$516$	−1.50000	+	0.866025i	−0.0660338	+	0.0381246i
$517$		0			0
$518$	−7.50000	+	2.59808i	−0.329531	+	0.114153i
$519$			24.2487i			1.06440i
$520$	−15.0000			−0.657794
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	0.831295	−	0.555831i	$-0.187600\pi$
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	−0.897011	+	0.442007i	$0.854267\pi$
$522$	−1.50000	−	2.59808i	−0.0656532	−	0.113715i
$523$	−0.500000	+	0.866025i	−0.0218635	+	0.0378686i	−0.876750	−	0.480946i	$-0.840293\pi$
$523$	−0.500000	+	0.866025i	−0.0218635	+	0.0378686i	0.854887	+	0.518815i	$0.173627\pi$
$524$	−0.500000	−	0.866025i	−0.0218426	−	0.0378325i
$525$	−6.00000	−	17.3205i	−0.261861	−	0.755929i
$526$	−2.50000	+	4.33013i	−0.109005	+	0.188803i
$527$		0			0
$528$	−7.50000	−	4.33013i	−0.326396	−	0.188445i
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	−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
$535$	−17.0000			−0.734974
$536$	−12.0000			−0.518321
$537$	−28.5000	+	16.4545i	−1.22987	+	0.710063i
$538$	−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	−0.461625	−	0.887075i	$-0.652733\pi$
$541$	12.5000	−	21.6506i	0.537417	−	0.930834i	0.999042	−	0.0437584i	$-0.0139332\pi$
$542$	−0.500000	+	0.866025i	−0.0214768	+	0.0371990i
$543$			24.2487i			1.04061i
$544$	−7.50000	−	12.9904i	−0.321560	−	0.556958i
$545$	−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
$549$	42.0000			1.79252
$550$	10.0000	+	17.3205i	0.426401	+	0.738549i
$551$	−1.00000			−0.0426014
$552$	13.5000	−	7.79423i	0.574598	−	0.331744i
$553$	16.0000	+	13.8564i	0.680389	+	0.589234i
$554$	−9.50000	+	16.4545i	−0.403616	+	0.699084i
$555$			5.19615i			0.220564i
$556$	4.50000	−	7.79423i	0.190843	−	0.330549i
$557$	18.5000	+	32.0429i	0.783870	+	1.35770i	0.929672	+	0.368389i	$0.120091\pi$
$557$	18.5000	+	32.0429i	0.783870	+	1.35770i	−0.145802	+	0.989314i	$0.546576\pi$
$558$		0			0
$559$	5.00000			0.211477
$560$	0.500000	−	2.59808i	0.0211289	−	0.109789i
$561$		−	25.9808i		−	1.09691i
$562$	14.5000	+	25.1147i	0.611646	+	1.05940i
$563$	−28.0000			−1.18006			−0.590030	−	0.807382i	$-0.700884\pi$
$563$	−28.0000			−1.18006			−0.590030	+	0.807382i	$0.700884\pi$
$564$		0			0
$565$	1.00000			0.0420703
$566$	28.0000			1.17693
$567$	18.0000	+	15.5885i	0.755929	+	0.654654i
$568$	36.0000			1.51053
$569$	−34.0000			−1.42535			−0.712677	−	0.701492i	$-0.752517\pi$
$569$	−34.0000			−1.42535			−0.712677	+	0.701492i	$0.752517\pi$
$570$			1.73205i			0.0725476i
$571$	32.0000			1.33916			0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000			1.33916			0.669579	+	0.742741i	$0.266474\pi$
$572$	−12.5000	−	21.6506i	−0.522651	−	0.905259i
$573$		−	13.8564i		−	0.578860i
$574$	12.5000	−	4.33013i	0.521740	−	0.180736i
$575$	−12.0000			−0.500435
$576$	−21.0000			−0.875000
$577$	−15.5000	−	26.8468i	−0.645273	−	1.11765i	−0.984238	−	0.176847i	$-0.943410\pi$
$577$	−15.5000	−	26.8468i	−0.645273	−	1.11765i	0.338965	−	0.940799i	$-0.389923\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$			17.3205i			0.719816i
$580$	0.500000	−	0.866025i	0.0207614	−	0.0359597i
$581$	−4.50000	+	23.3827i	−0.186691	+	0.970077i
$582$	13.5000	−	7.79423i	0.559593	−	0.323081i
$583$	−45.0000			−1.86371
$584$	4.50000	+	7.79423i	0.186211	+	0.322527i
$585$	−15.0000			−0.620174
$586$	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
$591$		−	3.46410i		−	0.142494i
$592$	1.50000	−	2.59808i	0.0616496	−	0.106780i
$593$	−7.50000	+	12.9904i	−0.307988	+	0.533451i	−0.977922	−	0.208970i	$-0.932989\pi$
$593$	−7.50000	+	12.9904i	−0.307988	+	0.533451i	0.669934	+	0.742421i	$0.266322\pi$
$594$	−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
$597$	−4.50000	+	2.59808i	−0.184173	+	0.106332i
$598$	−15.0000			−0.613396
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$	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
$605$	7.00000	−	12.1244i	0.284590	−	0.492925i
$606$	−25.5000	−	14.7224i	−1.03587	−	0.598058i
$607$	0.500000	+	0.866025i	0.0202944	+	0.0351509i	0.875994	−	0.482322i	$-0.160206\pi$
$607$	0.500000	+	0.866025i	0.0202944	+	0.0351509i	−0.855700	+	0.517472i	$0.826873\pi$
$608$	−2.50000	+	4.33013i	−0.101388	+	0.175610i
$609$	4.50000	+	0.866025i	0.182349	+	0.0350931i
$610$	−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	0.607887	−	0.794024i	$-0.292017\pi$
$613$	−9.50000	−	16.4545i	−0.383701	−	0.664590i	−0.991588	+	0.129433i	$0.958684\pi$
$614$	28.0000			1.12999
$615$		−	8.66025i		−	0.349215i
$616$	37.5000	−	12.9904i	1.51092	−	0.523397i
$617$	−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	$0.983769\pi$
$618$	1.50000	−	0.866025i	0.0603388	−	0.0348367i
$619$	−12.5000	+	21.6506i	−0.502417	+	0.870212i	0.497579	+	0.867419i	$0.334223\pi$
$619$	−12.5000	+	21.6506i	−0.502417	+	0.870212i	−0.999996	+	0.00279365i	$0.999111\pi$
$620$		0			0
$621$	13.5000	−	7.79423i	0.541736	−	0.312772i
$622$		0			0
$623$	32.5000	−	11.2583i	1.30209	−	0.451055i
$624$	7.50000	+	4.33013i	0.300240	+	0.173344i
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	14.0000			0.559553
$627$	−7.50000	+	4.33013i	−0.299521	+	0.172929i
$628$	14.0000			0.558661
$629$	9.00000			0.358854
$630$	1.50000	−	7.79423i	0.0597614	−	0.310530i
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$	−24.0000			−0.954669
$633$	19.5000	+	11.2583i	0.775055	+	0.447478i
$634$	−6.00000			−0.238290
$635$	−6.00000	−	10.3923i	−0.238103	−	0.412406i
$636$	−13.5000	+	7.79423i	−0.535310	+	0.309061i
$637$	32.5000	+	12.9904i	1.28770	+	0.514698i
$638$	−5.00000			−0.197952
$639$	36.0000			1.42414
$640$	−1.50000	−	2.59808i	−0.0592927	−	0.102698i
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	−0.763367	−	0.645966i	$-0.776455\pi$
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	0.941106	+	0.338112i	$0.109788\pi$
$642$	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	$0.0444318\pi$
$644$	−1.50000	+	7.79423i	−0.0591083	+	0.307136i
$645$	1.50000	+	0.866025i	0.0590624	+	0.0340997i
$646$	3.00000			0.118033
$647$	−15.5000	−	26.8468i	−0.609368	−	1.05546i	−0.991345	−	0.131284i	$-0.958090\pi$
$647$	−15.5000	−	26.8468i	−0.609368	−	1.05546i	0.381977	−	0.924172i	$-0.375243\pi$
$648$	−27.0000			−1.06066
$649$		0			0
$650$	−10.0000	−	17.3205i	−0.392232	−	0.679366i
$651$		0			0
$652$	−5.50000	+	9.52628i	−0.215397	+	0.373078i
$653$	−1.50000	−	2.59808i	−0.0586995	−	0.101671i	0.835182	−	0.549973i	$-0.185362\pi$
$653$	−1.50000	−	2.59808i	−0.0586995	−	0.101671i	−0.893882	+	0.448303i	$0.852029\pi$
$654$	13.5000	−	7.79423i	0.527892	−	0.304778i
$655$	−0.500000	+	0.866025i	−0.0195366	+	0.0338384i
$656$	−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	$-0.342933\pi$
$660$		−	8.66025i		−	0.337100i
$661$	−14.0000			−0.544537			−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000			−0.544537			−0.272268	+	0.962221i	$0.587774\pi$
$662$	8.00000			0.310929
$663$			25.9808i			1.00901i
$664$	−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
$668$	−9.50000	+	16.4545i	−0.367566	+	0.636643i
$669$	−28.5000	+	16.4545i	−1.10187	+	0.636167i
$670$	2.00000	+	3.46410i	0.0772667	+	0.133830i
$671$	35.0000	−	60.6218i	1.35116	−	2.34028i
$672$	15.0000	−	17.3205i	0.578638	−	0.668153i
$673$	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
$675$	18.0000	+	10.3923i	0.692820	+	0.400000i
$676$	6.00000	+	10.3923i	0.230769	+	0.399704i
$677$	42.0000			1.61419			0.807096	−	0.590421i	$-0.201038\pi$
$677$	42.0000			1.61419			0.807096	+	0.590421i	$0.201038\pi$
$678$	−1.50000	−	0.866025i	−0.0576072	−	0.0332595i
$679$	−4.50000	+	23.3827i	−0.172694	+	0.897345i
$680$	−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	0.939184	−	0.343413i	$-0.111583\pi$
$683$	4.50000	+	7.79423i	0.172188	+	0.298238i	−0.766997	+	0.641651i	$0.778250\pi$
$684$	−1.50000	+	2.59808i	−0.0573539	+	0.0993399i
$685$	9.00000			0.343872
$686$	−10.0000	+	15.5885i	−0.381802	+	0.595170i
$687$	1.50000	−	0.866025i	0.0572286	−	0.0330409i
$688$	−0.500000	−	0.866025i	−0.0190623	−	0.0330169i
$689$	45.0000			1.71436
$690$	−4.50000	−	2.59808i	−0.171312	−	0.0989071i
$691$	−28.0000			−1.06517			−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000			−1.06517			−0.532585	+	0.846376i	$0.678779\pi$
$692$	14.0000			0.532200
$693$	37.5000	−	12.9904i	1.42451	−	0.493464i
$694$	4.00000			0.151838
$695$	−9.00000			−0.341389
$696$	−4.50000	+	2.59808i	−0.170572	+	0.0984798i
$697$	−15.0000			−0.568166
$698$	−9.50000	−	16.4545i	−0.359580	−	0.622811i
$699$	4.50000	+	2.59808i	0.170206	+	0.0982683i
$700$	−10.0000	+	3.46410i	−0.377964	+	0.130931i
$701$	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
$704$	−17.5000	+	30.3109i	−0.659556	+	1.14238i
$705$		0			0
$706$	−5.50000	+	9.52628i	−0.206995	+	0.358526i
$707$	42.5000	−	14.7224i	1.59838	−	0.553694i
$708$		0			0
$709$	−6.00000			−0.225335			−0.112667	−	0.993633i	$-0.535939\pi$
$709$	−6.00000			−0.225335			−0.112667	+	0.993633i	$0.535939\pi$
$710$	−6.00000	−	10.3923i	−0.225176	−	0.390016i
$711$	−24.0000			−0.900070
$712$	−19.5000	+	33.7750i	−0.730793	+	1.26577i
$713$		0			0
$714$	−13.5000	−	2.59808i	−0.505225	−	0.0972306i
$715$	−12.5000	+	21.6506i	−0.467473	+	0.809688i
$716$	9.50000	+	16.4545i	0.355032	+	0.614933i
$717$	−22.5000	−	12.9904i	−0.840278	−	0.485135i
$718$	5.50000	−	9.52628i	0.205258	−	0.355518i
$719$	13.5000	−	23.3827i	0.503465	−	0.872027i	−0.496527	−	0.868021i	$-0.665392\pi$
$719$	13.5000	−	23.3827i	0.503465	−	0.872027i	0.999992	−	0.00400572i	$-0.00127506\pi$
$720$	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
$724$	14.0000			0.520306
$725$	4.00000			0.148556
$726$	−21.0000	+	12.1244i	−0.779383	+	0.449977i
$727$	−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
$731$	1.50000	−	2.59808i	0.0554795	−	0.0960933i
$732$		−	24.2487i		−	0.896258i
$733$	−13.5000	−	23.3827i	−0.498634	−	0.863659i	0.501365	−	0.865236i	$-0.332831\pi$
$733$	−13.5000	−	23.3827i	−0.498634	−	0.863659i	−0.999999	+	0.00157675i	$0.999498\pi$
$734$	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
$738$	−7.50000	+	12.9904i	−0.276079	+	0.478183i
$739$	4.50000	+	7.79423i	0.165535	+	0.286715i	0.936845	−	0.349744i	$-0.113732\pi$
$739$	4.50000	+	7.79423i	0.165535	+	0.286715i	−0.771310	+	0.636460i	$0.780398\pi$
$740$	3.00000			0.110282
$741$	7.50000	−	4.33013i	0.275519	−	0.159071i
$742$	−4.50000	+	23.3827i	−0.165200	+	0.858405i
$743$	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
$745$	1.50000	−	2.59808i	0.0549557	−	0.0951861i
$746$	12.5000	+	21.6506i	0.457658	+	0.792686i
$747$	−13.5000	−	23.3827i	−0.493939	−	0.855528i
$748$	−15.0000			−0.548454
$749$	−42.5000	+	14.7224i	−1.55292	+	0.537946i
$750$		−	15.5885i		−	0.569210i
$751$	−15.5000	−	26.8468i	−0.565603	−	0.979653i	−0.996993	−	0.0774878i	$-0.975310\pi$
$751$	−15.5000	−	26.8468i	−0.565603	−	0.979653i	0.431390	−	0.902165i	$-0.358023\pi$
$752$		0			0
$753$			48.4974i			1.76734i
$754$	5.00000			0.182089
$755$	−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	$0.488428\pi$
$758$	−12.0000			−0.435860
$759$		−	25.9808i		−	0.943042i
$760$	3.00000			0.108821
$761$	−13.5000	−	23.3827i	−0.489375	−	0.847622i	0.510551	−	0.859848i	$-0.329442\pi$
$761$	−13.5000	−	23.3827i	−0.489375	−	0.847622i	−0.999925	+	0.0122260i	$0.996108\pi$
$762$			20.7846i			0.752947i
$763$	−4.50000	+	23.3827i	−0.162911	+	0.846510i
$764$	−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
$768$			29.4449i			1.06250i
$769$	−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	$0.302780\pi$
$770$	−10.0000	−	8.66025i	−0.360375	−	0.312094i
$771$	43.5000	−	25.1147i	1.56661	−	0.904485i
$772$	10.0000			0.359908
$773$	−15.5000	−	26.8468i	−0.557496	−	0.965612i	−0.997705	−	0.0677162i	$-0.978429\pi$
$773$	−15.5000	−	26.8468i	−0.557496	−	0.965612i	0.440208	−	0.897896i	$-0.354905\pi$
$774$	−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
$779$	2.50000	+	4.33013i	0.0895718	+	0.155143i
$780$			8.66025i			0.310087i
$781$	30.0000	−	51.9615i	1.07348	−	1.85933i
$782$	−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
$786$	1.50000	−	0.866025i	0.0535032	−	0.0308901i
$787$	28.0000			0.998092			0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000			0.998092			0.499046	+	0.866575i	$0.333684\pi$
$788$	−2.00000			−0.0712470
$789$	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
$794$	−7.50000	+	12.9904i	−0.266165	+	0.461011i
$795$	13.5000	+	7.79423i	0.478796	+	0.276433i
$796$	1.50000	+	2.59808i	0.0531661	+	0.0920864i
$797$	−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	$0.300214\pi$
$798$	1.50000	+	4.33013i	0.0530994	+	0.153285i
$799$		0			0
$800$	10.0000	−	17.3205i	0.353553	−	0.612372i
$801$	−19.5000	+	33.7750i	−0.688999	+	1.19338i
$802$	−1.50000	−	2.59808i	−0.0529668	−	0.0917413i
$803$	15.0000			0.529339
$804$			6.92820i			0.244339i
$805$	7.50000	−	2.59808i	0.264340	−	0.0915702i
$806$		0			0
$807$	−4.50000	+	2.59808i	−0.158408	+	0.0914566i
$808$	−25.5000	+	44.1673i	−0.897087	+	1.55380i
$809$	4.50000	+	7.79423i	0.158212	+	0.274030i	0.934224	−	0.356687i	$-0.116094\pi$
$809$	4.50000	+	7.79423i	0.158212	+	0.274030i	−0.776012	+	0.630718i	$0.782761\pi$
$810$	4.50000	+	7.79423i	0.158114	+	0.273861i
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	0.500000	−	2.59808i	0.0175466	−	0.0911746i
$813$	1.50000	+	0.866025i	0.0526073	+	0.0303728i
$814$	−7.50000	−	12.9904i	−0.262875	−	0.455313i
$815$	11.0000			0.385313
$816$	4.50000	−	2.59808i	0.157532	−	0.0909509i
$817$	−1.00000			−0.0349856
$818$	14.0000			0.489499
$819$	−37.5000	+	12.9904i	−1.31036	+	0.453921i
$820$	−5.00000			−0.174608
$821$	22.0000			0.767805			0.383903	−	0.923374i	$-0.374580\pi$
$821$	22.0000			0.767805			0.383903	+	0.923374i	$0.374580\pi$
$822$	−13.5000	−	7.79423i	−0.470867	−	0.271855i
$823$	−24.0000			−0.836587			−0.418294	−	0.908312i	$-0.637372\pi$
$823$	−24.0000			−0.836587			−0.418294	+	0.908312i	$0.637372\pi$
$824$	−1.50000	−	2.59808i	−0.0522550	−	0.0905083i
$825$	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	$0.566904\pi$
$828$	−4.50000	−	7.79423i	−0.156386	−	0.270868i
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	0.997225	−	0.0744432i	$-0.0237179\pi$
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	−0.563082	+	0.826401i	$0.690385\pi$
$830$	−4.50000	+	7.79423i	−0.156197	+	0.270542i
$831$	28.5000	+	16.4545i	0.988654	+	0.570800i
$832$	17.5000	−	30.3109i	0.606703	−	1.05084i
$833$	16.5000	−	12.9904i	0.571691	−	0.450090i
$834$	13.5000	+	7.79423i	0.467467	+	0.269892i
$835$	19.0000			0.657522
$836$	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	$0.612810\pi$
$840$	−13.5000	−	2.59808i	−0.465794	−	0.0896421i
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	0.500000	+	0.866025i	0.0172311	+	0.0298452i
$843$	43.5000	−	25.1147i	1.49822	−	0.864997i
$844$	6.50000	−	11.2583i	0.223739	−	0.387528i
$845$	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
$849$		−	48.4974i		−	1.66443i
$850$	−12.0000			−0.411597
$851$	9.00000			0.308516
$852$		−	20.7846i		−	0.712069i
$853$	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
$857$	−5.50000	+	9.52628i	−0.187876	+	0.325412i	−0.944542	−	0.328391i	$-0.893494\pi$
$857$	−5.50000	+	9.52628i	−0.187876	+	0.325412i	0.756666	+	0.653802i	$0.226827\pi$
$858$	37.5000	−	21.6506i	1.28023	−	0.739140i
$859$	0.500000	+	0.866025i	0.0170598	+	0.0295484i	0.874429	−	0.485153i	$-0.161236\pi$
$859$	0.500000	+	0.866025i	0.0170598	+	0.0295484i	−0.857369	+	0.514701i	$0.827903\pi$
$860$	0.500000	−	0.866025i	0.0170499	−	0.0295312i
$861$	−7.50000	−	21.6506i	−0.255599	−	0.737852i
$862$	4.50000	+	7.79423i	0.153271	+	0.265472i
$863$	19.5000	−	33.7750i	0.663788	−	1.14971i	−0.315825	−	0.948818i	$-0.602281\pi$
$863$	19.5000	−	33.7750i	0.663788	−	1.14971i	0.979612	−	0.200897i	$-0.0643855\pi$
$864$			25.9808i			0.883883i
$865$	−7.00000	−	12.1244i	−0.238007	−	0.412240i
$866$	−14.0000			−0.475739
$867$	−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
$871$	10.0000	−	17.3205i	0.338837	−	0.586883i
$872$	−13.5000	−	23.3827i	−0.457168	−	0.791838i
$873$	−13.5000	−	23.3827i	−0.456906	−	0.791384i
$874$	3.00000			0.101477
$875$	18.0000	+	15.5885i	0.608511	+	0.526986i
$876$	4.50000	−	2.59808i	0.152041	−	0.0877809i
$877$	26.5000	+	45.8993i	0.894841	+	1.54991i	0.834001	+	0.551763i	$0.186045\pi$
$877$	26.5000	+	45.8993i	0.894841	+	1.54991i	0.0608407	+	0.998147i	$0.480622\pi$
$878$		0			0
$879$	−7.50000	−	4.33013i	−0.252969	−	0.146052i
$880$	5.00000			0.168550
$881$	−42.0000			−1.41502			−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$882$	−3.00000	−	20.7846i	−0.101015	−	0.699854i
$883$	44.0000			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$884$	15.0000			0.504505
$885$		0			0
$886$	36.0000			1.20944
$887$	14.5000	+	25.1147i	0.486862	+	0.843270i	0.999886	−	0.0151042i	$-0.00480800\pi$
$887$	14.5000	+	25.1147i	0.486862	+	0.843270i	−0.513024	+	0.858375i	$0.671475\pi$
$888$	−13.5000	−	7.79423i	−0.453030	−	0.261557i
$889$	−24.0000	−	20.7846i	−0.804934	−	0.697093i
$890$	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
$894$	−4.50000	+	2.59808i	−0.150503	+	0.0868927i
$895$	9.50000	−	16.4545i	0.317550	−	0.550013i
$896$	−6.00000	−	5.19615i	−0.200446	−	0.173591i
$897$			25.9808i			0.867472i
$898$	30.0000			1.00111
$899$		0			0
$900$	6.00000	−	10.3923i	0.200000	−	0.346410i
$901$	13.5000	−	23.3827i	0.449750	−	0.778990i
$902$	12.5000	+	21.6506i	0.416204	+	0.720887i
$903$	4.50000	+	0.866025i	0.149751	+	0.0288195i
$904$	−1.50000	+	2.59808i	−0.0498893	+	0.0864107i
$905$	−7.00000	−	12.1244i	−0.232688	−	0.403027i
$906$	7.50000	+	4.33013i	0.249171	+	0.143859i
$907$	−2.50000	+	4.33013i	−0.0830111	+	0.143780i	−0.904542	−	0.426385i	$-0.859787\pi$
$907$	−2.50000	+	4.33013i	−0.0830111	+	0.143780i	0.821531	+	0.570164i	$0.193120\pi$
$908$	−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
$913$	−45.0000			−1.48928
$914$	22.0000			0.727695
$915$	−21.0000	+	12.1244i	−0.694239	+	0.400819i
$916$	−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	−0.971481	−	0.237119i	$-0.923797\pi$
$919$	−8.50000	+	14.7224i	−0.280389	+	0.485648i	0.691091	+	0.722767i	$0.257130\pi$
$920$	−4.50000	+	7.79423i	−0.148361	+	0.256968i
$921$		−	48.4974i		−	1.59804i
$922$	−9.50000	−	16.4545i	−0.312866	−	0.541900i
$923$	−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
$929$	−14.0000			−0.459325			−0.229663	−	0.973270i	$-0.573762\pi$
$929$	−14.0000			−0.459325			−0.229663	+	0.973270i	$0.573762\pi$
$930$		0			0
$931$	−6.50000	−	2.59808i	−0.213029	−	0.0851485i
$932$	1.50000	−	2.59808i	0.0491341	−	0.0851028i
$933$		0			0
$934$	13.5000	−	23.3827i	0.441733	−	0.765105i
$935$	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	$0.259347\pi$
$938$	8.00000	+	6.92820i	0.261209	+	0.226214i
$939$		−	24.2487i		−	0.791327i
$940$		0			0
$941$	−14.0000			−0.456387			−0.228193	−	0.973616i	$-0.573282\pi$
$941$	−14.0000			−0.456387			−0.228193	+	0.973616i	$0.573282\pi$
$942$			24.2487i			0.790066i
$943$	−15.0000			−0.488467
$944$		0			0
$945$	−13.5000	−	2.59808i	−0.439155	−	0.0845154i
$946$	−5.00000			−0.162564
$947$	−20.0000			−0.649913			−0.324956	−	0.945729i	$-0.605350\pi$
$947$	−20.0000			−0.649913			−0.324956	+	0.945729i	$0.605350\pi$
$948$			13.8564i			0.450035i
$949$	−15.0000			−0.486921
$950$	2.00000	+	3.46410i	0.0648886	+	0.112390i
$951$			10.3923i			0.336994i
$952$	−4.50000	+	23.3827i	−0.145846	+	0.757837i
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$	−13.5000	−	23.3827i	−0.437079	−	0.757042i
$955$	4.00000	+	6.92820i	0.129437	+	0.224191i
$956$	−7.50000	+	12.9904i	−0.242567	+	0.420139i
$957$			8.66025i			0.279946i
$958$	−12.5000	+	21.6506i	−0.403857	+	0.699500i
$959$	22.5000	−	7.79423i	0.726563	−	0.251689i
$960$	10.5000	−	6.06218i	0.338886	−	0.195656i
$961$	−31.0000			−1.00000
$962$	7.50000	+	12.9904i	0.241810	+	0.418827i
$963$	25.5000	−	44.1673i	0.821726	−	1.42327i
$964$	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	$0.233696\pi$
$968$	21.0000	+	36.3731i	0.674966	+	1.16907i
$969$		−	5.19615i		−	0.166924i
$970$	−4.50000	+	7.79423i	−0.144486	+	0.250258i
$971$	−28.5000	+	49.3634i	−0.914609	+	1.58415i	−0.107135	+	0.994244i	$0.534168\pi$
$971$	−28.5000	+	49.3634i	−0.914609	+	1.58415i	−0.807473	+	0.589904i	$0.799166\pi$
$972$			15.5885i			0.500000i
$973$	−22.5000	+	7.79423i	−0.721317	+	0.249871i
$974$	−9.50000	−	16.4545i	−0.304400	−	0.527236i
$975$	−30.0000	+	17.3205i	−0.960769	+	0.554700i
$976$	14.0000			0.448129
$977$	18.0000			0.575871			0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000			0.575871			0.287936	+	0.957650i	$0.407031\pi$
$978$	−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
$983$	1.50000	−	2.59808i	0.0478426	−	0.0828658i	−0.841112	−	0.540860i	$-0.818099\pi$
$983$	1.50000	−	2.59808i	0.0478426	−	0.0828658i	0.888955	+	0.457995i	$0.151432\pi$
$984$	22.5000	+	12.9904i	0.717274	+	0.414118i
$985$	1.00000	+	1.73205i	0.0318626	+	0.0551877i
$986$	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
$990$	15.0000			0.476731
$991$	18.5000	+	32.0429i	0.587672	+	1.01788i	0.994537	+	0.104389i	$0.0332887\pi$
$991$	18.5000	+	32.0429i	0.587672	+	1.01788i	−0.406865	+	0.913488i	$0.633378\pi$
$992$		0			0
$993$		−	13.8564i		−	0.439720i
$994$	−24.0000	−	20.7846i	−0.761234	−	0.659248i
$995$	1.50000	−	2.59808i	0.0475532	−	0.0823646i
$996$	−13.5000	+	7.79423i	−0.427764	+	0.246970i
$997$	8.50000	−	14.7224i	0.269198	−	0.466264i	−0.699457	−	0.714675i	$-0.746575\pi$
$997$	8.50000	−	14.7224i	0.269198	−	0.466264i	0.968655	+	0.248410i	$0.0799082\pi$
$998$	−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.h.a.58.1	yes	2
3.2	odd	2		189.2.h.a.37.1		2
4.3	odd	2		1008.2.q.c.625.1		2
7.2	even	3		441.2.f.b.148.1		2
7.3	odd	6		441.2.g.a.67.1		2
7.4	even	3		63.2.g.a.4.1	✓	2
7.5	odd	6		441.2.f.a.148.1		2
7.6	odd	2		441.2.h.a.373.1		2
9.2	odd	6		189.2.g.a.100.1		2
9.4	even	3		567.2.e.a.163.1		2
9.5	odd	6		567.2.e.b.163.1		2
9.7	even	3		63.2.g.a.16.1	yes	2
12.11	even	2		3024.2.q.b.2305.1		2
21.2	odd	6		1323.2.f.a.442.1		2
21.5	even	6		1323.2.f.b.442.1		2
21.11	odd	6		189.2.g.a.172.1		2
21.17	even	6		1323.2.g.a.361.1		2
21.20	even	2		1323.2.h.a.226.1		2
28.11	odd	6		1008.2.t.d.193.1		2
36.7	odd	6		1008.2.t.d.961.1		2
36.11	even	6		3024.2.t.d.289.1		2
63.2	odd	6		1323.2.f.a.883.1		2
63.4	even	3		567.2.e.a.487.1		2
63.5	even	6		3969.2.a.a.1.1		1
63.11	odd	6		189.2.h.a.46.1		2
63.16	even	3		441.2.f.b.295.1		2
63.20	even	6		1323.2.g.a.667.1		2
63.23	odd	6		3969.2.a.c.1.1		1
63.25	even	3	inner	63.2.h.a.25.1	yes	2
63.32	odd	6		567.2.e.b.487.1		2
63.34	odd	6		441.2.g.a.79.1		2
63.38	even	6		1323.2.h.a.802.1		2
63.40	odd	6		3969.2.a.f.1.1		1
63.47	even	6		1323.2.f.b.883.1		2
63.52	odd	6		441.2.h.a.214.1		2
63.58	even	3		3969.2.a.d.1.1		1
63.61	odd	6		441.2.f.a.295.1		2
84.11	even	6		3024.2.t.d.1873.1		2
252.11	even	6		3024.2.q.b.2881.1		2
252.151	odd	6		1008.2.q.c.529.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.a.4.1	✓	2	7.4	even	3
63.2.g.a.16.1	yes	2	9.7	even	3
63.2.h.a.25.1	yes	2	63.25	even	3	inner
63.2.h.a.58.1	yes	2	1.1	even	1	trivial
189.2.g.a.100.1		2	9.2	odd	6
189.2.g.a.172.1		2	21.11	odd	6
189.2.h.a.37.1		2	3.2	odd	2
189.2.h.a.46.1		2	63.11	odd	6
441.2.f.a.148.1		2	7.5	odd	6
441.2.f.a.295.1		2	63.61	odd	6
441.2.f.b.148.1		2	7.2	even	3
441.2.f.b.295.1		2	63.16	even	3
441.2.g.a.67.1		2	7.3	odd	6
441.2.g.a.79.1		2	63.34	odd	6
441.2.h.a.214.1		2	63.52	odd	6
441.2.h.a.373.1		2	7.6	odd	2
567.2.e.a.163.1		2	9.4	even	3
567.2.e.a.487.1		2	63.4	even	3
567.2.e.b.163.1		2	9.5	odd	6
567.2.e.b.487.1		2	63.32	odd	6
1008.2.q.c.529.1		2	252.151	odd	6
1008.2.q.c.625.1		2	4.3	odd	2
1008.2.t.d.193.1		2	28.11	odd	6
1008.2.t.d.961.1		2	36.7	odd	6
1323.2.f.a.442.1		2	21.2	odd	6
1323.2.f.a.883.1		2	63.2	odd	6
1323.2.f.b.442.1		2	21.5	even	6
1323.2.f.b.883.1		2	63.47	even	6
1323.2.g.a.361.1		2	21.17	even	6
1323.2.g.a.667.1		2	63.20	even	6
1323.2.h.a.226.1		2	21.20	even	2
1323.2.h.a.802.1		2	63.38	even	6
3024.2.q.b.2305.1		2	12.11	even	2
3024.2.q.b.2881.1		2	252.11	even	6
3024.2.t.d.289.1		2	36.11	even	6
3024.2.t.d.1873.1		2	84.11	even	6
3969.2.a.a.1.1		1	63.5	even	6
3969.2.a.c.1.1		1	63.23	odd	6
3969.2.a.d.1.1		1	63.58	even	3
3969.2.a.f.1.1		1	63.40	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.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.73205i q^{3} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} -1.73205i q^{6} +(2.00000 + 1.73205i) q^{7} -3.00000 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.73205i q^{3} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} -1.73205i q^{6} +(2.00000 + 1.73205i) q^{7} -3.00000 q^{8} -3.00000 q^{9} +(0.500000 + 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} +1.73205i q^{12} +(2.50000 - 4.33013i) q^{13} +(2.00000 + 1.73205i) q^{14} +(1.50000 - 0.866025i) q^{15} -1.00000 q^{16} +(-1.50000 - 2.59808i) q^{17} -3.00000 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} +(-1.50000 - 2.59808i) q^{23} +5.19615i q^{24} +(2.00000 - 3.46410i) q^{25} +(2.50000 - 4.33013i) q^{26} +5.19615i q^{27} +(-2.00000 - 1.73205i) q^{28} +(0.500000 + 0.866025i) q^{29} +(1.50000 - 0.866025i) q^{30} +5.00000 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} +(-0.500000 + 0.866025i) q^{38} +(-7.50000 - 4.33013i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(2.50000 - 4.33013i) q^{41} +(3.00000 - 3.46410i) 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} +(1.00000 + 6.92820i) q^{49} +(2.00000 - 3.46410i) q^{50} +(-4.50000 + 2.59808i) q^{51} +(-2.50000 + 4.33013i) q^{52} +(4.50000 + 7.79423i) q^{53} +5.19615i q^{54} -5.00000 q^{55} +(-6.00000 - 5.19615i) q^{56} +(1.50000 + 0.866025i) q^{57} +(0.500000 + 0.866025i) q^{58} +(-1.50000 + 0.866025i) q^{60} -14.0000 q^{61} +(-6.00000 - 5.19615i) q^{63} +7.00000 q^{64} +5.00000 q^{65} +(7.50000 + 4.33013i) q^{66} +4.00000 q^{67} +(1.50000 + 2.59808i) q^{68} +(-4.50000 + 2.59808i) q^{69} +(-0.500000 + 2.59808i) q^{70} -12.0000 q^{71} +9.00000 q^{72} +(-1.50000 - 2.59808i) q^{73} +(-1.50000 + 2.59808i) q^{74} +(-6.00000 - 3.46410i) q^{75} +(0.500000 - 0.866025i) q^{76} +(-12.5000 + 4.33013i) q^{77} +(-7.50000 - 4.33013i) q^{78} +8.00000 q^{79} +(-0.500000 - 0.866025i) q^{80} +9.00000 q^{81} +(2.50000 - 4.33013i) q^{82} +(4.50000 + 7.79423i) q^{83} +(-3.00000 + 3.46410i) q^{84} +(1.50000 - 2.59808i) q^{85} +(0.500000 + 0.866025i) q^{86} +(1.50000 - 0.866025i) q^{87} +(7.50000 - 12.9904i) 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} -1.00000 q^{95} -8.66025i q^{96} +(4.50000 + 7.79423i) q^{97} +(1.00000 + 6.92820i) q^{98} +(7.50000 - 12.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{4} + q^{5} + 4 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^4 + q^5 + 4 * q^7 - 6 * q^8 - 6 * q^9	\( 2 q + 2 q^{2} - 2 q^{4} + q^{5} + 4 q^{7} - 6 q^{8} - 6 q^{9} + q^{10} - 5 q^{11} + 5 q^{13} + 4 q^{14} + 3 q^{15} - 2 q^{16} - 3 q^{17} - 6 q^{18} - q^{19} - q^{20} + 6 q^{21} - 5 q^{22} - 3 q^{23} + 4 q^{25} + 5 q^{26} - 4 q^{28} + q^{29} + 3 q^{30} + 10 q^{32} + 15 q^{33} - 3 q^{34} - q^{35} + 6 q^{36} - 3 q^{37} - q^{38} - 15 q^{39} - 3 q^{40} + 5 q^{41} + 6 q^{42} + q^{43} + 5 q^{44} - 3 q^{45} - 3 q^{46} + 2 q^{49} + 4 q^{50} - 9 q^{51} - 5 q^{52} + 9 q^{53} - 10 q^{55} - 12 q^{56} + 3 q^{57} + q^{58} - 3 q^{60} - 28 q^{61} - 12 q^{63} + 14 q^{64} + 10 q^{65} + 15 q^{66} + 8 q^{67} + 3 q^{68} - 9 q^{69} - q^{70} - 24 q^{71} + 18 q^{72} - 3 q^{73} - 3 q^{74} - 12 q^{75} + q^{76} - 25 q^{77} - 15 q^{78} + 16 q^{79} - q^{80} + 18 q^{81} + 5 q^{82} + 9 q^{83} - 6 q^{84} + 3 q^{85} + q^{86} + 3 q^{87} + 15 q^{88} + 13 q^{89} - 3 q^{90} + 25 q^{91} + 3 q^{92} - 2 q^{95} + 9 q^{97} + 2 q^{98} + 15 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^4 + q^5 + 4 * q^7 - 6 * q^8 - 6 * q^9 + q^10 - 5 * q^11 + 5 * q^13 + 4 * q^14 + 3 * q^15 - 2 * q^16 - 3 * q^17 - 6 * q^18 - q^19 - q^20 + 6 * q^21 - 5 * q^22 - 3 * q^23 + 4 * q^25 + 5 * q^26 - 4 * q^28 + q^29 + 3 * q^30 + 10 * q^32 + 15 * q^33 - 3 * q^34 - q^35 + 6 * q^36 - 3 * q^37 - q^38 - 15 * q^39 - 3 * q^40 + 5 * q^41 + 6 * q^42 + q^43 + 5 * q^44 - 3 * q^45 - 3 * q^46 + 2 * q^49 + 4 * q^50 - 9 * q^51 - 5 * q^52 + 9 * q^53 - 10 * q^55 - 12 * q^56 + 3 * q^57 + q^58 - 3 * q^60 - 28 * q^61 - 12 * q^63 + 14 * q^64 + 10 * q^65 + 15 * q^66 + 8 * q^67 + 3 * q^68 - 9 * q^69 - q^70 - 24 * q^71 + 18 * q^72 - 3 * q^73 - 3 * q^74 - 12 * q^75 + q^76 - 25 * q^77 - 15 * q^78 + 16 * q^79 - q^80 + 18 * q^81 + 5 * q^82 + 9 * q^83 - 6 * q^84 + 3 * q^85 + q^86 + 3 * q^87 + 15 * q^88 + 13 * q^89 - 3 * q^90 + 25 * q^91 + 3 * q^92 - 2 * q^95 + 9 * q^97 + 2 * q^98 + 15 * q^99

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