LMFDB - Embedded newform 63.2.h.a.25.1

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			25.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	63.25
Dual form			63.2.h.a.58.1

$q$-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} +(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} + 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}+ \cdots + 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

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000			0.707107			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	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$			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	−0.945979	−	0.324227i	$-0.894896\pi$
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	0.192201	−	0.981356i	$-0.438437\pi$
$12$		−	1.73205i		−	0.500000i
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	0.970725	+	0.240192i	$0.0772105\pi$
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	−0.277350	+	0.960769i	$0.589456\pi$
$14$	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	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$	−3.00000			−0.707107
$19$	−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
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$		−	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	−0.815861	−	0.578249i	$-0.803736\pi$
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	0.908708	+	0.417432i	$0.137070\pi$
$30$	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	0.715981	−	0.698119i	$-0.245980\pi$
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	−0.962580	+	0.270998i	$0.912646\pi$
$38$	−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	0.992507	−	0.122189i	$-0.0389915\pi$
$41$	2.50000	+	4.33013i	0.390434	+	0.676252i	−0.602072	+	0.798441i	$0.705658\pi$
$42$	3.00000	+	3.46410i	0.462910	+	0.534522i
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$	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	−0.371706	−	0.928351i	$-0.621227\pi$
$53$	4.50000	−	7.79423i	0.618123	−	1.07062i	0.989828	−	0.142269i	$-0.0454398\pi$
$54$		−	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	−0.940356	−	0.340193i	$-0.889507\pi$
$73$	−1.50000	+	2.59808i	−0.175562	+	0.304082i	0.764794	+	0.644275i	$0.222841\pi$
$74$	−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	−0.506036	−	0.862512i	$-0.668890\pi$
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	0.999976	+	0.00698436i	$0.00222321\pi$
$84$	−3.00000	−	3.46410i	−0.327327	−	0.377964i
$85$	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	0.972162	+	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
$95$	−1.00000			−0.102598
$96$			8.66025i			0.883883i
$97$	4.50000	−	7.79423i	0.456906	−	0.791384i	−0.541890	−	0.840450i	$-0.682291\pi$
$97$	4.50000	−	7.79423i	0.456906	−	0.791384i	0.998796	+	0.0490655i	$0.0156243\pi$
$98$	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	0.884941	+	0.465704i	$0.154199\pi$
$101$	8.50000	+	14.7224i	0.845782	+	1.46494i	−0.0391591	+	0.999233i	$0.512468\pi$
$102$	−4.50000	−	2.59808i	−0.445566	−	0.257248i
$103$	0.500000	−	0.866025i	0.0492665	−	0.0853320i	−0.840341	−	0.542059i	$-0.817645\pi$
$103$	0.500000	−	0.866025i	0.0492665	−	0.0853320i	0.889607	+	0.456727i	$0.150978\pi$
$104$	−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	−0.904396	−	0.426694i	$-0.859678\pi$
$107$	−8.50000	−	14.7224i	−0.821726	−	1.42327i	0.0826699	−	0.996577i	$-0.473655\pi$
$108$			5.19615i			0.500000i
$109$	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	$0.0248199\pi$
$110$	−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	0.888585	−	0.458712i	$-0.151689\pi$
$113$	0.500000	+	0.866025i	0.0470360	+	0.0814688i	−0.841549	+	0.540181i	$0.818356\pi$
$114$	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	−0.843356	−	0.537355i	$-0.819423\pi$
$131$	0.500000	−	0.866025i	0.0436852	−	0.0756650i	0.887041	+	0.461690i	$0.152757\pi$
$132$	−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	0.991694	−	0.128618i	$-0.0410540\pi$
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	−0.607233	+	0.794524i	$0.707721\pi$
$138$	−4.50000	−	2.59808i	−0.383065	−	0.221163i
$139$	−4.50000	−	7.79423i	−0.381685	−	0.661098i	0.609618	−	0.792695i	$-0.291323\pi$
$139$	−4.50000	−	7.79423i	−0.381685	−	0.661098i	−0.991303	+	0.131597i	$0.957989\pi$
$140$	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	−0.920904	−	0.389789i	$-0.872548\pi$
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	0.798019	+	0.602632i	$0.205881\pi$
$150$	−6.00000	+	3.46410i	−0.489898	+	0.282843i
$151$	−2.50000	−	4.33013i	−0.203447	−	0.352381i	0.746190	−	0.665733i	$-0.231881\pi$
$151$	−2.50000	−	4.33013i	−0.203447	−	0.352381i	−0.949637	+	0.313353i	$0.898548\pi$
$152$	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	0.996942	−	0.0781474i	$-0.0249005\pi$
$163$	5.50000	+	9.52628i	0.430793	+	0.746156i	−0.566149	+	0.824303i	$0.691567\pi$
$164$	−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	0.954665	+	0.297681i	$0.0962132\pi$
$167$	9.50000	+	16.4545i	0.735132	+	1.27329i	−0.219533	+	0.975605i	$0.570453\pi$
$168$	−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	0.254770	+	0.967002i	$0.418000\pi$
$179$	−9.50000	+	16.4545i	−0.710063	+	1.22987i	−0.964833	+	0.262864i	$0.915333\pi$
$180$	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	−0.914282	−	0.405079i	$-0.867244\pi$
$199$	−1.50000	+	2.59808i	−0.106332	+	0.184173i	0.807950	+	0.589252i	$0.200577\pi$
$200$	−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	0.550743	−	0.834675i	$-0.314345\pi$
$211$	−6.50000	−	11.2583i	−0.447478	−	0.775055i	−0.998221	+	0.0596196i	$0.981011\pi$
$212$	−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	0.350100	+	0.936713i	$0.386148\pi$
$223$	−9.50000	+	16.4545i	−0.636167	+	1.10187i	−0.986267	+	0.165161i	$0.947186\pi$
$224$	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	0.911502	−	0.411296i	$-0.134924\pi$
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	−0.811943	+	0.583736i	$0.801590\pi$
$228$	−1.50000	+	0.866025i	−0.0993399	+	0.0573539i
$229$	0.500000	−	0.866025i	0.0330409	−	0.0572286i	−0.849032	−	0.528341i	$-0.822814\pi$
$229$	0.500000	−	0.866025i	0.0330409	−	0.0572286i	0.882073	+	0.471113i	$0.156147\pi$
$230$	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	0.812700	−	0.582683i	$-0.197997\pi$
$233$	−1.50000	−	2.59808i	−0.0982683	−	0.170206i	−0.910968	+	0.412477i	$0.864664\pi$
$234$	−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	0.999854	−	0.0170808i	$-0.00543724\pi$
$239$	7.50000	+	12.9904i	0.485135	+	0.840278i	−0.514719	+	0.857359i	$0.672104\pi$
$240$	−1.50000	−	0.866025i	−0.0968246	−	0.0559017i
$241$	−5.50000	−	9.52628i	−0.354286	−	0.613642i	0.632709	−	0.774389i	$-0.281943\pi$
$241$	−5.50000	−	9.52628i	−0.354286	−	0.613642i	−0.986996	+	0.160748i	$0.948609\pi$
$242$	−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	0.0828783	−	0.996560i	$-0.473589\pi$
$257$	14.5000	−	25.1147i	0.904485	−	1.56661i	0.821607	−	0.570055i	$-0.193078\pi$
$258$	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	0.778595	−	0.627527i	$-0.215933\pi$
$263$	−2.50000	−	4.33013i	−0.154157	−	0.267007i	−0.932752	+	0.360520i	$0.882599\pi$
$264$	−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	−0.908124	−	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
$273$	−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	−0.996484	−	0.0837823i	$-0.973300\pi$
$277$	−9.50000	−	16.4545i	−0.570800	−	0.988654i	0.425684	−	0.904872i	$-0.360033\pi$
$278$	−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	−0.00205220	−	0.999998i	$-0.500653\pi$
$281$	14.5000	−	25.1147i	0.864997	−	1.49822i	0.867050	−	0.498222i	$-0.166013\pi$
$282$		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	0.929765	−	0.368154i	$-0.120010\pi$
$293$	2.50000	+	4.33013i	0.146052	+	0.252969i	−0.783713	+	0.621123i	$0.786677\pi$
$294$	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	0.926049	+	0.377403i	$0.123183\pi$
$337$	14.5000	+	25.1147i	0.789865	+	1.36809i	−0.136184	+	0.990684i	$0.543484\pi$
$338$	−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	0.491428	+	0.870918i	$0.336475\pi$
$349$	−9.50000	+	16.4545i	−0.508523	+	0.880788i	−0.999951	+	0.00987003i	$0.996858\pi$
$350$	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	0.681720	−	0.731613i	$-0.261232\pi$
$353$	−5.50000	−	9.52628i	−0.292735	−	0.507033i	−0.974456	+	0.224580i	$0.927899\pi$
$354$		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	0.973876	−	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
$362$	−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	0.902516	−	0.430656i	$-0.141718\pi$
$367$	1.50000	+	2.59808i	0.0782994	+	0.135618i	−0.824217	+	0.566274i	$0.808384\pi$
$368$	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	−0.336557	−	0.941663i	$-0.609263\pi$
$373$	12.5000	−	21.6506i	0.647225	−	1.12103i	0.983783	−	0.179364i	$-0.0574041\pi$
$374$	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	0.282079	+	0.959391i	$0.408976\pi$
$383$	−13.5000	+	23.3827i	−0.689818	+	1.19480i	−0.971897	+	0.235408i	$0.924357\pi$
$384$		−	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	0.957263	−	0.289220i	$-0.0933960\pi$
$389$	4.50000	+	7.79423i	0.228159	+	0.395183i	−0.729103	+	0.684403i	$0.760063\pi$
$390$			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	0.614123	−	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
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	−0.901046	−	0.433724i	$-0.857199\pi$
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	0.826139	+	0.563466i	$0.190532\pi$
$402$			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	0.734919	−	0.678155i	$-0.237220\pi$
$419$	−4.50000	−	7.79423i	−0.219839	−	0.380773i	−0.954759	+	0.297382i	$0.903887\pi$
$420$	−4.50000	+	0.866025i	−0.219578	+	0.0422577i
$421$	0.500000	−	0.866025i	0.0243685	−	0.0422075i	−0.853584	−	0.520955i	$-0.825576\pi$
$421$	0.500000	−	0.866025i	0.0243685	−	0.0422075i	0.877952	+	0.478748i	$0.158909\pi$
$422$	−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	−0.737057	−	0.675830i	$-0.763785\pi$
$431$	4.50000	−	7.79423i	0.216757	−	0.375435i	0.953815	+	0.300395i	$0.0971186\pi$
$432$			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	−0.997871	−	0.0652135i	$-0.979227\pi$
$461$	−9.50000	+	16.4545i	−0.442459	+	0.766362i	0.555412	+	0.831575i	$0.312560\pi$
$462$	7.50000	−	21.6506i	0.348932	−	1.00728i
$463$	−6.50000	−	11.2583i	−0.302081	−	0.523219i	0.674526	−	0.738251i	$-0.264348\pi$
$463$	−6.50000	−	11.2583i	−0.302081	−	0.523219i	−0.976607	+	0.215032i	$0.931015\pi$
$464$	−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	0.988598	+	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
$471$		−	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	−0.996449	−	0.0841949i	$-0.973168\pi$
$479$	−12.5000	−	21.6506i	−0.571140	−	0.989243i	0.425310	−	0.905048i	$-0.360165\pi$
$480$	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	−0.996915	−	0.0784867i	$-0.974991\pi$
$487$	−9.50000	+	16.4545i	−0.430486	+	0.745624i	0.566429	+	0.824110i	$0.308325\pi$
$488$	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	0.681257	−	0.732045i	$-0.261434\pi$
$491$	−6.50000	−	11.2583i	−0.293341	−	0.508081i	−0.974598	+	0.223963i	$0.928100\pi$
$492$	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	0.276683	+	0.960961i	$0.410765\pi$
$499$	−15.5000	+	26.8468i	−0.693875	+	1.20183i	−0.970558	+	0.240866i	$0.922569\pi$
$500$	−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	−0.342126	−	0.939654i	$-0.611147\pi$
$509$	14.5000	−	25.1147i	0.642701	−	1.11319i	0.984827	−	0.173537i	$-0.0555197\pi$
$510$	−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	−0.897011	−	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
$525$	−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	0.999042	+	0.0437584i	$0.0139332\pi$
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	−0.461625	+	0.887075i	$0.652733\pi$
$542$	−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	−0.369514	−	0.929225i	$-0.620476\pi$
$547$	14.5000	−	25.1147i	0.619975	−	1.07383i	0.989490	−	0.144604i	$-0.0461907\pi$
$548$	−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	−0.145802	−	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
$560$	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	0.338965	+	0.940799i	$0.389923\pi$
$577$	−15.5000	+	26.8468i	−0.645273	+	1.11765i	−0.984238	+	0.176847i	$0.943410\pi$
$578$	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	−0.177419	−	0.984135i	$-0.556775\pi$
$587$	18.5000	−	32.0429i	0.763577	−	1.32255i	0.940996	−	0.338418i	$-0.109892\pi$
$588$	−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	0.669934	−	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
$597$	−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	−0.759531	−	0.650471i	$-0.774572\pi$
$601$	4.50000	−	7.79423i	0.183559	−	0.317933i	0.943090	+	0.332538i	$0.107905\pi$
$602$	−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	−0.855700	−	0.517472i	$-0.826873\pi$
$607$	0.500000	−	0.866025i	0.0202944	−	0.0351509i	0.875994	+	0.482322i	$0.160206\pi$
$608$	−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	−0.991588	−	0.129433i	$-0.958684\pi$
$613$	−9.50000	+	16.4545i	−0.383701	+	0.664590i	0.607887	+	0.794024i	$0.292017\pi$
$614$	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	−0.998700	−	0.0509678i	$-0.983769\pi$
$617$	−13.5000	−	23.3827i	−0.543490	−	0.941351i	0.455211	−	0.890384i	$-0.349564\pi$
$618$	1.50000	+	0.866025i	0.0603388	+	0.0348367i
$619$	−12.5000	−	21.6506i	−0.502417	−	0.870212i	−0.999996	−	0.00279365i	$-0.999111\pi$
$619$	−12.5000	−	21.6506i	−0.502417	−	0.870212i	0.497579	−	0.867419i	$-0.334223\pi$
$620$		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	0.941106	−	0.338112i	$-0.109788\pi$
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	−0.763367	+	0.645966i	$0.776455\pi$
$642$	25.5000	−	14.7224i	1.00640	−	0.581048i
$643$	9.50000	+	16.4545i	0.374643	+	0.648901i	0.990274	−	0.139134i	$-0.0444318\pi$
$643$	9.50000	+	16.4545i	0.374643	+	0.648901i	−0.615630	+	0.788035i	$0.711098\pi$
$644$	−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	0.381977	+	0.924172i	$0.375243\pi$
$647$	−15.5000	+	26.8468i	−0.609368	+	1.05546i	−0.991345	+	0.131284i	$0.958090\pi$
$648$	−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	−0.893882	−	0.448303i	$-0.852029\pi$
$653$	−1.50000	+	2.59808i	−0.0586995	+	0.101671i	0.835182	+	0.549973i	$0.185362\pi$
$654$	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	0.473660	+	0.880708i	$0.342933\pi$
$659$	−13.5000	+	23.3827i	−0.525885	+	0.910860i	−0.999545	+	0.0301523i	$0.990401\pi$
$660$			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	−0.438652	−	0.898657i	$-0.644544\pi$
$673$	14.5000	−	25.1147i	0.558934	−	0.968102i	0.997586	−	0.0694449i	$-0.0221228\pi$
$674$	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	−0.766997	−	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
$686$	−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	0.999992	+	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
$724$	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	−0.0111912	+	0.999937i	$0.503562\pi$
$727$	−23.5000	+	40.7032i	−0.871567	+	1.50960i	−0.860376	+	0.509661i	$0.829771\pi$
$728$	−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	−0.999999	−	0.00157675i	$-0.999498\pi$
$733$	−13.5000	+	23.3827i	−0.498634	+	0.863659i	0.501365	+	0.865236i	$0.332831\pi$
$734$	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	−0.771310	−	0.636460i	$-0.780398\pi$
$739$	4.50000	−	7.79423i	0.165535	−	0.286715i	0.936845	+	0.349744i	$0.113732\pi$
$740$	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	0.970173	−	0.242415i	$-0.0779397\pi$
$743$	7.50000	+	12.9904i	0.275148	+	0.476571i	−0.695024	+	0.718986i	$0.744606\pi$
$744$		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	0.431390	+	0.902165i	$0.358023\pi$
$751$	−15.5000	+	26.8468i	−0.565603	+	0.979653i	−0.996993	+	0.0774878i	$0.975310\pi$
$752$		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	−0.999925	−	0.0122260i	$-0.996108\pi$
$761$	−13.5000	+	23.3827i	−0.489375	+	0.847622i	0.510551	+	0.859848i	$0.329442\pi$
$762$		−	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	0.580696	−	0.814120i	$-0.302780\pi$
$769$	−11.5000	−	19.9186i	−0.414701	−	0.718283i	−0.995397	+	0.0958377i	$0.969447\pi$
$770$	−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	0.440208	+	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
$779$	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	0.587241	−	0.809412i	$-0.300214\pi$
$797$	−11.5000	−	19.9186i	−0.407351	−	0.705552i	−0.994592	+	0.103860i	$0.966881\pi$
$798$	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	−0.776012	−	0.630718i	$-0.782761\pi$
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	0.934224	+	0.356687i	$0.116094\pi$
$810$	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	−0.563082	−	0.826401i	$-0.690385\pi$
$829$	12.5000	−	21.6506i	0.434143	−	0.751958i	0.997225	+	0.0744432i	$0.0237179\pi$
$830$	−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	−0.347029	−	0.937854i	$-0.612810\pi$
$839$	18.5000	−	32.0429i	0.638691	−	1.10625i	0.985720	−	0.168391i	$-0.0538571\pi$
$840$	−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	−0.353418	−	0.935466i	$-0.614981\pi$
$853$	18.5000	−	32.0429i	0.633428	−	1.09713i	0.986846	−	0.161664i	$-0.0516860\pi$
$854$	−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	0.756666	−	0.653802i	$-0.226827\pi$
$857$	−5.50000	−	9.52628i	−0.187876	−	0.325412i	−0.944542	+	0.328391i	$0.893494\pi$
$858$	37.5000	+	21.6506i	1.28023	+	0.739140i
$859$	0.500000	−	0.866025i	0.0170598	−	0.0295484i	−0.857369	−	0.514701i	$-0.827903\pi$
$859$	0.500000	−	0.866025i	0.0170598	−	0.0295484i	0.874429	+	0.485153i	$0.161236\pi$
$860$	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	0.979612	+	0.200897i	$0.0643855\pi$
$863$	19.5000	+	33.7750i	0.663788	+	1.14971i	−0.315825	+	0.948818i	$0.602281\pi$
$864$		−	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	0.0608407	−	0.998147i	$-0.480622\pi$
$877$	26.5000	−	45.8993i	0.894841	−	1.54991i	0.834001	−	0.551763i	$-0.186045\pi$
$878$		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	−0.513024	−	0.858375i	$-0.671475\pi$
$887$	14.5000	−	25.1147i	0.486862	−	0.843270i	0.999886	+	0.0151042i	$0.00480800\pi$
$888$	−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	0.821531	−	0.570164i	$-0.193120\pi$
$907$	−2.50000	−	4.33013i	−0.0830111	−	0.143780i	−0.904542	+	0.426385i	$0.859787\pi$
$908$	−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	−0.998208	−	0.0598468i	$-0.980939\pi$
$911$	−13.5000	+	23.3827i	−0.447275	+	0.774703i	0.550933	+	0.834550i	$0.314272\pi$
$912$	−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	0.691091	−	0.722767i	$-0.257130\pi$
$919$	−8.50000	−	14.7224i	−0.280389	−	0.485648i	−0.971481	+	0.237119i	$0.923797\pi$
$920$	−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	0.742382	−	0.669977i	$-0.233696\pi$
$967$	−6.50000	−	11.2583i	−0.209026	−	0.362043i	−0.951408	+	0.307933i	$0.900363\pi$
$968$	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	−0.807473	−	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
$975$	−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	0.888955	−	0.457995i	$-0.151432\pi$
$983$	1.50000	+	2.59808i	0.0478426	+	0.0828658i	−0.841112	+	0.540860i	$0.818099\pi$
$984$	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	−0.406865	−	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
$994$	−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	0.968655	−	0.248410i	$-0.0799082\pi$
$997$	8.50000	+	14.7224i	0.269198	+	0.466264i	−0.699457	+	0.714675i	$0.746575\pi$
$998$	−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.25.1	yes	2
3.2	odd	2		189.2.h.a.46.1		2
4.3	odd	2		1008.2.q.c.529.1		2
7.2	even	3		63.2.g.a.16.1	yes	2
7.3	odd	6		441.2.f.a.295.1		2
7.4	even	3		441.2.f.b.295.1		2
7.5	odd	6		441.2.g.a.79.1		2
7.6	odd	2		441.2.h.a.214.1		2
9.2	odd	6		567.2.e.b.487.1		2
9.4	even	3		63.2.g.a.4.1	✓	2
9.5	odd	6		189.2.g.a.172.1		2
9.7	even	3		567.2.e.a.487.1		2
12.11	even	2		3024.2.q.b.2881.1		2
21.2	odd	6		189.2.g.a.100.1		2
21.5	even	6		1323.2.g.a.667.1		2
21.11	odd	6		1323.2.f.a.883.1		2
21.17	even	6		1323.2.f.b.883.1		2
21.20	even	2		1323.2.h.a.802.1		2
28.23	odd	6		1008.2.t.d.961.1		2
36.23	even	6		3024.2.t.d.1873.1		2
36.31	odd	6		1008.2.t.d.193.1		2
63.2	odd	6		567.2.e.b.163.1		2
63.4	even	3		441.2.f.b.148.1		2
63.5	even	6		1323.2.h.a.226.1		2
63.11	odd	6		3969.2.a.c.1.1		1
63.13	odd	6		441.2.g.a.67.1		2
63.16	even	3		567.2.e.a.163.1		2
63.23	odd	6		189.2.h.a.37.1		2
63.25	even	3		3969.2.a.d.1.1		1
63.31	odd	6		441.2.f.a.148.1		2
63.32	odd	6		1323.2.f.a.442.1		2
63.38	even	6		3969.2.a.a.1.1		1
63.40	odd	6		441.2.h.a.373.1		2
63.41	even	6		1323.2.g.a.361.1		2
63.52	odd	6		3969.2.a.f.1.1		1
63.58	even	3	inner	63.2.h.a.58.1	yes	2
63.59	even	6		1323.2.f.b.442.1		2
84.23	even	6		3024.2.t.d.289.1		2
252.23	even	6		3024.2.q.b.2305.1		2
252.247	odd	6		1008.2.q.c.625.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.a.4.1	✓	2	9.4	even	3
63.2.g.a.16.1	yes	2	7.2	even	3
63.2.h.a.25.1	yes	2	1.1	even	1	trivial
63.2.h.a.58.1	yes	2	63.58	even	3	inner
189.2.g.a.100.1		2	21.2	odd	6
189.2.g.a.172.1		2	9.5	odd	6
189.2.h.a.37.1		2	63.23	odd	6
189.2.h.a.46.1		2	3.2	odd	2
441.2.f.a.148.1		2	63.31	odd	6
441.2.f.a.295.1		2	7.3	odd	6
441.2.f.b.148.1		2	63.4	even	3
441.2.f.b.295.1		2	7.4	even	3
441.2.g.a.67.1		2	63.13	odd	6
441.2.g.a.79.1		2	7.5	odd	6
441.2.h.a.214.1		2	7.6	odd	2
441.2.h.a.373.1		2	63.40	odd	6
567.2.e.a.163.1		2	63.16	even	3
567.2.e.a.487.1		2	9.7	even	3
567.2.e.b.163.1		2	63.2	odd	6
567.2.e.b.487.1		2	9.2	odd	6
1008.2.q.c.529.1		2	4.3	odd	2
1008.2.q.c.625.1		2	252.247	odd	6
1008.2.t.d.193.1		2	36.31	odd	6
1008.2.t.d.961.1		2	28.23	odd	6
1323.2.f.a.442.1		2	63.32	odd	6
1323.2.f.a.883.1		2	21.11	odd	6
1323.2.f.b.442.1		2	63.59	even	6
1323.2.f.b.883.1		2	21.17	even	6
1323.2.g.a.361.1		2	63.41	even	6
1323.2.g.a.667.1		2	21.5	even	6
1323.2.h.a.226.1		2	63.5	even	6
1323.2.h.a.802.1		2	21.20	even	2
3024.2.q.b.2305.1		2	252.23	even	6
3024.2.q.b.2881.1		2	12.11	even	2
3024.2.t.d.289.1		2	84.23	even	6
3024.2.t.d.1873.1		2	36.23	even	6
3969.2.a.a.1.1		1	63.38	even	6
3969.2.a.c.1.1		1	63.11	odd	6
3969.2.a.d.1.1		1	63.25	even	3
3969.2.a.f.1.1		1	63.52	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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{4} + q^{5} + 4 q^{7} - 6 q^{8} - 6 q^{9} + q^{10} - 5 q^{11} + 5 q^{13} + 4 q^{14} + 3 q^{15} - 2 q^{16} - 3 q^{17} - 6 q^{18} - q^{19} - q^{20} + 6 q^{21} - 5 q^{22} - 3 q^{23}+ \cdots + 15 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

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