LMFDB - Embedded newform 62.2.c.b.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [62,2,Mod(5,62)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(62, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("62.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	62.c (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:	$0.495072492532$
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	$\chi$	$=$	62.25
Dual form			62.2.c.b.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.50000 - 2.59808i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 2.59808i) q^{6} +(1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.50000 - 2.59808i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 2.59808i) q^{6} +(1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(1.50000 - 2.59808i) q^{11} +(-1.50000 - 2.59808i) q^{12} +(-2.50000 + 4.33013i) q^{13} +(1.50000 + 2.59808i) q^{14} +3.00000 q^{15} +1.00000 q^{16} +(-1.50000 - 2.59808i) q^{17} +(-3.00000 + 5.19615i) q^{18} +(-3.50000 - 6.06218i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(4.50000 - 7.79423i) q^{21} +(1.50000 - 2.59808i) q^{22} -4.00000 q^{23} +(-1.50000 - 2.59808i) q^{24} +(2.00000 + 3.46410i) q^{25} +(-2.50000 + 4.33013i) q^{26} +9.00000 q^{27} +(1.50000 + 2.59808i) q^{28} +2.00000 q^{29} +3.00000 q^{30} +(2.00000 + 5.19615i) q^{31} +1.00000 q^{32} -9.00000 q^{33} +(-1.50000 - 2.59808i) q^{34} -3.00000 q^{35} +(-3.00000 + 5.19615i) q^{36} +(-0.500000 - 0.866025i) q^{37} +(-3.50000 - 6.06218i) q^{38} +15.0000 q^{39} +(-0.500000 + 0.866025i) q^{40} +(4.50000 - 7.79423i) q^{41} +(4.50000 - 7.79423i) q^{42} +(0.500000 + 0.866025i) q^{43} +(1.50000 - 2.59808i) q^{44} +(-3.00000 - 5.19615i) q^{45} -4.00000 q^{46} -8.00000 q^{47} +(-1.50000 - 2.59808i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(2.00000 + 3.46410i) q^{50} +(-4.50000 + 7.79423i) q^{51} +(-2.50000 + 4.33013i) q^{52} +(1.50000 - 2.59808i) q^{53} +9.00000 q^{54} +(1.50000 + 2.59808i) q^{55} +(1.50000 + 2.59808i) q^{56} +(-10.5000 + 18.1865i) q^{57} +2.00000 q^{58} +(-1.50000 - 2.59808i) q^{59} +3.00000 q^{60} +6.00000 q^{61} +(2.00000 + 5.19615i) q^{62} -18.0000 q^{63} +1.00000 q^{64} +(-2.50000 - 4.33013i) q^{65} -9.00000 q^{66} +(1.50000 - 2.59808i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(6.00000 + 10.3923i) q^{69} -3.00000 q^{70} +(0.500000 - 0.866025i) q^{71} +(-3.00000 + 5.19615i) q^{72} +(-3.50000 + 6.06218i) q^{73} +(-0.500000 - 0.866025i) q^{74} +(6.00000 - 10.3923i) q^{75} +(-3.50000 - 6.06218i) q^{76} +9.00000 q^{77} +15.0000 q^{78} +(-0.500000 - 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(4.50000 - 7.79423i) q^{82} +(-2.50000 + 4.33013i) q^{83} +(4.50000 - 7.79423i) q^{84} +3.00000 q^{85} +(0.500000 + 0.866025i) q^{86} +(-3.00000 - 5.19615i) q^{87} +(1.50000 - 2.59808i) q^{88} +6.00000 q^{89} +(-3.00000 - 5.19615i) q^{90} -15.0000 q^{91} -4.00000 q^{92} +(10.5000 - 12.9904i) q^{93} -8.00000 q^{94} +7.00000 q^{95} +(-1.50000 - 2.59808i) q^{96} +14.0000 q^{97} +(-1.00000 + 1.73205i) q^{98} +(9.00000 + 15.5885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - q^{5} - 3 q^{6} + 3 q^{7} + 2 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - q^5 - 3 * q^6 + 3 * q^7 + 2 * q^8 - 6 * q^9	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - q^{5} - 3 q^{6} + 3 q^{7} + 2 q^{8} - 6 q^{9} - q^{10} + 3 q^{11} - 3 q^{12} - 5 q^{13} + 3 q^{14} + 6 q^{15} + 2 q^{16} - 3 q^{17} - 6 q^{18} - 7 q^{19} - q^{20} + 9 q^{21} + 3 q^{22} - 8 q^{23} - 3 q^{24} + 4 q^{25} - 5 q^{26} + 18 q^{27} + 3 q^{28} + 4 q^{29} + 6 q^{30} + 4 q^{31} + 2 q^{32} - 18 q^{33} - 3 q^{34} - 6 q^{35} - 6 q^{36} - q^{37} - 7 q^{38} + 30 q^{39} - q^{40} + 9 q^{41} + 9 q^{42} + q^{43} + 3 q^{44} - 6 q^{45} - 8 q^{46} - 16 q^{47} - 3 q^{48} - 2 q^{49} + 4 q^{50} - 9 q^{51} - 5 q^{52} + 3 q^{53} + 18 q^{54} + 3 q^{55} + 3 q^{56} - 21 q^{57} + 4 q^{58} - 3 q^{59} + 6 q^{60} + 12 q^{61} + 4 q^{62} - 36 q^{63} + 2 q^{64} - 5 q^{65} - 18 q^{66} + 3 q^{67} - 3 q^{68} + 12 q^{69} - 6 q^{70} + q^{71} - 6 q^{72} - 7 q^{73} - q^{74} + 12 q^{75} - 7 q^{76} + 18 q^{77} + 30 q^{78} - q^{79} - q^{80} - 9 q^{81} + 9 q^{82} - 5 q^{83} + 9 q^{84} + 6 q^{85} + q^{86} - 6 q^{87} + 3 q^{88} + 12 q^{89} - 6 q^{90} - 30 q^{91} - 8 q^{92} + 21 q^{93} - 16 q^{94} + 14 q^{95} - 3 q^{96} + 28 q^{97} - 2 q^{98} + 18 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - q^5 - 3 * q^6 + 3 * q^7 + 2 * q^8 - 6 * q^9 - q^10 + 3 * q^11 - 3 * q^12 - 5 * q^13 + 3 * q^14 + 6 * q^15 + 2 * q^16 - 3 * q^17 - 6 * q^18 - 7 * q^19 - q^20 + 9 * q^21 + 3 * q^22 - 8 * q^23 - 3 * q^24 + 4 * q^25 - 5 * q^26 + 18 * q^27 + 3 * q^28 + 4 * q^29 + 6 * q^30 + 4 * q^31 + 2 * q^32 - 18 * q^33 - 3 * q^34 - 6 * q^35 - 6 * q^36 - q^37 - 7 * q^38 + 30 * q^39 - q^40 + 9 * q^41 + 9 * q^42 + q^43 + 3 * q^44 - 6 * q^45 - 8 * q^46 - 16 * q^47 - 3 * q^48 - 2 * q^49 + 4 * q^50 - 9 * q^51 - 5 * q^52 + 3 * q^53 + 18 * q^54 + 3 * q^55 + 3 * q^56 - 21 * q^57 + 4 * q^58 - 3 * q^59 + 6 * q^60 + 12 * q^61 + 4 * q^62 - 36 * q^63 + 2 * q^64 - 5 * q^65 - 18 * q^66 + 3 * q^67 - 3 * q^68 + 12 * q^69 - 6 * q^70 + q^71 - 6 * q^72 - 7 * q^73 - q^74 + 12 * q^75 - 7 * q^76 + 18 * q^77 + 30 * q^78 - q^79 - q^80 - 9 * q^81 + 9 * q^82 - 5 * q^83 + 9 * q^84 + 6 * q^85 + q^86 - 6 * q^87 + 3 * q^88 + 12 * q^89 - 6 * q^90 - 30 * q^91 - 8 * q^92 + 21 * q^93 - 16 * q^94 + 14 * q^95 - 3 * q^96 + 28 * q^97 - 2 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

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

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
$2$	1.00000			0.707107
$3$	−1.50000	−	2.59808i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−1.50000	−	2.59808i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$4$	1.00000			0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$	−1.50000	−	2.59808i	−0.612372	−	1.06066i
$7$	1.50000	+	2.59808i	0.566947	+	0.981981i	0.996866	+	0.0791130i	$0.0252088\pi$
$7$	1.50000	+	2.59808i	0.566947	+	0.981981i	−0.429919	+	0.902867i	$0.641458\pi$
$8$	1.00000			0.353553
$9$	−3.00000	+	5.19615i	−1.00000	+	1.73205i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$	−1.50000	−	2.59808i	−0.433013	−	0.750000i
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	0.277350	+	0.960769i	$0.410544\pi$
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	1.50000	+	2.59808i	0.400892	+	0.694365i
$15$	3.00000			0.774597
$16$	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	+	5.19615i	−0.707107	+	1.22474i
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	0.114708	−	0.993399i	$-0.463407\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	4.50000	−	7.79423i	0.981981	−	1.70084i
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$	−4.00000			−0.834058			−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000			−0.834058			−0.417029	+	0.908893i	$0.636929\pi$
$24$	−1.50000	−	2.59808i	−0.306186	−	0.530330i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	−2.50000	+	4.33013i	−0.490290	+	0.849208i
$27$	9.00000			1.73205
$28$	1.50000	+	2.59808i	0.283473	+	0.490990i
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$	3.00000			0.547723
$31$	2.00000	+	5.19615i	0.359211	+	0.933257i
$31$	2.00000	+	5.19615i	0.359211	+	0.933257i
$32$	1.00000			0.176777
$33$	−9.00000			−1.56670
$34$	−1.50000	−	2.59808i	−0.257248	−	0.445566i
$35$	−3.00000			−0.507093
$36$	−3.00000	+	5.19615i	−0.500000	+	0.866025i
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i	0.821995	−	0.569495i	$-0.192861\pi$
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i	−0.904194	+	0.427121i	$0.859528\pi$
$38$	−3.50000	−	6.06218i	−0.567775	−	0.983415i
$39$	15.0000			2.40192
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	−0.264704	−	0.964330i	$-0.585274\pi$
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	0.967486	−	0.252924i	$-0.0813924\pi$
$42$	4.50000	−	7.79423i	0.694365	−	1.20268i
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	1.50000	−	2.59808i	0.226134	−	0.391675i
$45$	−3.00000	−	5.19615i	−0.447214	−	0.774597i
$46$	−4.00000			−0.589768
$47$	−8.00000			−1.16692			−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000			−1.16692			−0.583460	+	0.812142i	$0.698301\pi$
$48$	−1.50000	−	2.59808i	−0.216506	−	0.375000i
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$	−4.50000	+	7.79423i	−0.630126	+	1.09141i
$52$	−2.50000	+	4.33013i	−0.346688	+	0.600481i
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	−0.744423	−	0.667708i	$-0.767275\pi$
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	0.950464	+	0.310835i	$0.100609\pi$
$54$	9.00000			1.22474
$55$	1.50000	+	2.59808i	0.202260	+	0.350325i
$56$	1.50000	+	2.59808i	0.200446	+	0.347183i
$57$	−10.5000	+	18.1865i	−1.39076	+	2.40887i
$58$	2.00000			0.262613
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	0.751710	−	0.659494i	$-0.229229\pi$
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	−0.946993	+	0.321253i	$0.895896\pi$
$60$	3.00000			0.387298
$61$	6.00000			0.768221			0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000			0.768221			0.384111	+	0.923287i	$0.374508\pi$
$62$	2.00000	+	5.19615i	0.254000	+	0.659912i
$63$	−18.0000			−2.26779
$64$	1.00000			0.125000
$65$	−2.50000	−	4.33013i	−0.310087	−	0.537086i
$66$	−9.00000			−1.10782
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	−0.759733	−	0.650236i	$-0.774670\pi$
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	0.942987	+	0.332830i	$0.108004\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$	6.00000	+	10.3923i	0.722315	+	1.25109i
$70$	−3.00000			−0.358569
$71$	0.500000	−	0.866025i	0.0593391	−	0.102778i	−0.834830	−	0.550508i	$-0.814434\pi$
$71$	0.500000	−	0.866025i	0.0593391	−	0.102778i	0.894169	+	0.447730i	$0.147767\pi$
$72$	−3.00000	+	5.19615i	−0.353553	+	0.612372i
$73$	−3.50000	+	6.06218i	−0.409644	+	0.709524i	−0.994850	−	0.101361i	$-0.967680\pi$
$73$	−3.50000	+	6.06218i	−0.409644	+	0.709524i	0.585206	+	0.810885i	$0.301014\pi$
$74$	−0.500000	−	0.866025i	−0.0581238	−	0.100673i
$75$	6.00000	−	10.3923i	0.692820	−	1.20000i
$76$	−3.50000	−	6.06218i	−0.401478	−	0.695379i
$77$	9.00000			1.02565
$78$	15.0000			1.69842
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	0.836527	−	0.547926i	$-0.184582\pi$
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	−0.892781	+	0.450490i	$0.851249\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	4.50000	−	7.79423i	0.496942	−	0.860729i
$83$	−2.50000	+	4.33013i	−0.274411	+	0.475293i	−0.969986	−	0.243160i	$-0.921816\pi$
$83$	−2.50000	+	4.33013i	−0.274411	+	0.475293i	0.695576	+	0.718453i	$0.255149\pi$
$84$	4.50000	−	7.79423i	0.490990	−	0.850420i
$85$	3.00000			0.325396
$86$	0.500000	+	0.866025i	0.0539164	+	0.0933859i
$87$	−3.00000	−	5.19615i	−0.321634	−	0.557086i
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$	−3.00000	−	5.19615i	−0.316228	−	0.547723i
$91$	−15.0000			−1.57243
$92$	−4.00000			−0.417029
$93$	10.5000	−	12.9904i	1.08880	−	1.34704i
$94$	−8.00000			−0.825137
$95$	7.00000			0.718185
$96$	−1.50000	−	2.59808i	−0.153093	−	0.265165i
$97$	14.0000			1.42148			0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000			1.42148			0.710742	+	0.703452i	$0.248359\pi$
$98$	−1.00000	+	1.73205i	−0.101015	+	0.174964i
$99$	9.00000	+	15.5885i	0.904534	+	1.56670i
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	−10.0000			−0.995037			−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000			−0.995037			−0.497519	+	0.867453i	$0.665755\pi$
$102$	−4.50000	+	7.79423i	−0.445566	+	0.771744i
$103$	6.50000	−	11.2583i	0.640464	−	1.10932i	−0.344865	−	0.938652i	$-0.612075\pi$
$103$	6.50000	−	11.2583i	0.640464	−	1.10932i	0.985329	−	0.170664i	$-0.0545913\pi$
$104$	−2.50000	+	4.33013i	−0.245145	+	0.424604i
$105$	4.50000	+	7.79423i	0.439155	+	0.760639i
$106$	1.50000	−	2.59808i	0.145693	−	0.252347i
$107$	6.50000	+	11.2583i	0.628379	+	1.08838i	0.987877	+	0.155238i	$0.0496145\pi$
$107$	6.50000	+	11.2583i	0.628379	+	1.08838i	−0.359498	+	0.933146i	$0.617052\pi$
$108$	9.00000			0.866025
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	1.50000	+	2.59808i	0.143019	+	0.247717i
$111$	−1.50000	+	2.59808i	−0.142374	+	0.246598i
$112$	1.50000	+	2.59808i	0.141737	+	0.245495i
$113$	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	$0.151689\pi$
$114$	−10.5000	+	18.1865i	−0.983415	+	1.70332i
$115$	2.00000	−	3.46410i	0.186501	−	0.323029i
$116$	2.00000			0.185695
$117$	−15.0000	−	25.9808i	−1.38675	−	2.40192i
$118$	−1.50000	−	2.59808i	−0.138086	−	0.239172i
$119$	4.50000	−	7.79423i	0.412514	−	0.714496i
$120$	3.00000			0.273861
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	6.00000			0.543214
$123$	−27.0000			−2.43451
$124$	2.00000	+	5.19615i	0.179605	+	0.466628i
$125$	−9.00000			−0.804984
$126$	−18.0000			−1.60357
$127$	−6.50000	−	11.2583i	−0.576782	−	0.999015i	−0.995846	−	0.0910585i	$-0.970975\pi$
$127$	−6.50000	−	11.2583i	−0.576782	−	0.999015i	0.419064	−	0.907957i	$-0.362358\pi$
$128$	1.00000			0.0883883
$129$	1.50000	−	2.59808i	0.132068	−	0.228748i
$130$	−2.50000	−	4.33013i	−0.219265	−	0.379777i
$131$	10.5000	+	18.1865i	0.917389	+	1.58896i	0.803365	+	0.595487i	$0.203041\pi$
$131$	10.5000	+	18.1865i	0.917389	+	1.58896i	0.114024	+	0.993478i	$0.463626\pi$
$132$	−9.00000			−0.783349
$133$	10.5000	−	18.1865i	0.910465	−	1.57697i
$134$	1.50000	−	2.59808i	0.129580	−	0.224440i
$135$	−4.50000	+	7.79423i	−0.387298	+	0.670820i
$136$	−1.50000	−	2.59808i	−0.128624	−	0.222783i
$137$	−5.50000	+	9.52628i	−0.469897	+	0.813885i	−0.999408	−	0.0344182i	$-0.989042\pi$
$137$	−5.50000	+	9.52628i	−0.469897	+	0.813885i	0.529511	+	0.848303i	$0.322376\pi$
$138$	6.00000	+	10.3923i	0.510754	+	0.884652i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$	−3.00000			−0.253546
$141$	12.0000	+	20.7846i	1.01058	+	1.75038i
$142$	0.500000	−	0.866025i	0.0419591	−	0.0726752i
$143$	7.50000	+	12.9904i	0.627182	+	1.08631i
$144$	−3.00000	+	5.19615i	−0.250000	+	0.433013i
$145$	−1.00000	+	1.73205i	−0.0830455	+	0.143839i
$146$	−3.50000	+	6.06218i	−0.289662	+	0.501709i
$147$	6.00000			0.494872
$148$	−0.500000	−	0.866025i	−0.0410997	−	0.0711868i
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	0.844818	−	0.535054i	$-0.179709\pi$
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	−0.885779	+	0.464107i	$0.846375\pi$
$150$	6.00000	−	10.3923i	0.489898	−	0.848528i
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$	−3.50000	−	6.06218i	−0.283887	−	0.491708i
$153$	18.0000			1.45521
$154$	9.00000			0.725241
$155$	−5.50000	−	0.866025i	−0.441771	−	0.0695608i
$156$	15.0000			1.20096
$157$	−10.0000			−0.798087			−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000			−0.798087			−0.399043	+	0.916932i	$0.630658\pi$
$158$	−0.500000	−	0.866025i	−0.0397779	−	0.0688973i
$159$	−9.00000			−0.713746
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−6.00000	−	10.3923i	−0.472866	−	0.819028i
$162$	−4.50000	−	7.79423i	−0.353553	−	0.612372i
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$	4.50000	−	7.79423i	0.351391	−	0.608627i
$165$	4.50000	−	7.79423i	0.350325	−	0.606780i
$166$	−2.50000	+	4.33013i	−0.194038	+	0.336083i
$167$	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	$0.570453\pi$
$168$	4.50000	−	7.79423i	0.347183	−	0.601338i
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$	3.00000			0.230089
$171$	42.0000			3.21182
$172$	0.500000	+	0.866025i	0.0381246	+	0.0660338i
$173$	−0.500000	+	0.866025i	−0.0380143	+	0.0658427i	−0.884407	−	0.466717i	$-0.845437\pi$
$173$	−0.500000	+	0.866025i	−0.0380143	+	0.0658427i	0.846392	+	0.532560i	$0.178770\pi$
$174$	−3.00000	−	5.19615i	−0.227429	−	0.393919i
$175$	−6.00000	+	10.3923i	−0.453557	+	0.785584i
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$	−4.50000	+	7.79423i	−0.338241	+	0.585850i
$178$	6.00000			0.449719
$179$	−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	$-0.418000\pi$
$180$	−3.00000	−	5.19615i	−0.223607	−	0.387298i
$181$	−2.50000	+	4.33013i	−0.185824	+	0.321856i	−0.943854	−	0.330364i	$-0.892829\pi$
$181$	−2.50000	+	4.33013i	−0.185824	+	0.321856i	0.758030	+	0.652219i	$0.226162\pi$
$182$	−15.0000			−1.11187
$183$	−9.00000	−	15.5885i	−0.665299	−	1.15233i
$184$	−4.00000			−0.294884
$185$	1.00000			0.0735215
$186$	10.5000	−	12.9904i	0.769897	−	0.952501i
$187$	−9.00000			−0.658145
$188$	−8.00000			−0.583460
$189$	13.5000	+	23.3827i	0.981981	+	1.70084i
$190$	7.00000			0.507833
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	−0.915177	−	0.403051i	$-0.867950\pi$
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	0.806641	+	0.591041i	$0.201283\pi$
$192$	−1.50000	−	2.59808i	−0.108253	−	0.187500i
$193$	−9.50000	−	16.4545i	−0.683825	−	1.18442i	−0.973805	−	0.227387i	$-0.926982\pi$
$193$	−9.50000	−	16.4545i	−0.683825	−	1.18442i	0.289980	−	0.957033i	$-0.406351\pi$
$194$	14.0000			1.00514
$195$	−7.50000	+	12.9904i	−0.537086	+	0.930261i
$196$	−1.00000	+	1.73205i	−0.0714286	+	0.123718i
$197$	7.50000	−	12.9904i	0.534353	−	0.925526i	−0.464841	−	0.885394i	$-0.653889\pi$
$197$	7.50000	−	12.9904i	0.534353	−	0.925526i	0.999194	−	0.0401324i	$-0.0127780\pi$
$198$	9.00000	+	15.5885i	0.639602	+	1.10782i
$199$	10.5000	−	18.1865i	0.744325	−	1.28921i	−0.206184	−	0.978513i	$-0.566105\pi$
$199$	10.5000	−	18.1865i	0.744325	−	1.28921i	0.950509	−	0.310696i	$-0.100562\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$	−9.00000			−0.634811
$202$	−10.0000			−0.703598
$203$	3.00000	+	5.19615i	0.210559	+	0.364698i
$204$	−4.50000	+	7.79423i	−0.315063	+	0.545705i
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$	6.50000	−	11.2583i	0.452876	−	0.784405i
$207$	12.0000	−	20.7846i	0.834058	−	1.44463i
$208$	−2.50000	+	4.33013i	−0.173344	+	0.300240i
$209$	−21.0000			−1.45260
$210$	4.50000	+	7.79423i	0.310530	+	0.537853i
$211$	0.500000	+	0.866025i	0.0344214	+	0.0596196i	0.882723	−	0.469894i	$-0.155708\pi$
$211$	0.500000	+	0.866025i	0.0344214	+	0.0596196i	−0.848301	+	0.529514i	$0.822374\pi$
$212$	1.50000	−	2.59808i	0.103020	−	0.178437i
$213$	−3.00000			−0.205557
$214$	6.50000	+	11.2583i	0.444331	+	0.769604i
$215$	−1.00000			−0.0681994
$216$	9.00000			0.612372
$217$	−10.5000	+	12.9904i	−0.712786	+	0.881845i
$218$	−2.00000			−0.135457
$219$	21.0000			1.41905
$220$	1.50000	+	2.59808i	0.101130	+	0.175162i
$221$	15.0000			1.00901
$222$	−1.50000	+	2.59808i	−0.100673	+	0.174371i
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	0.986267	+	0.165161i	$0.0528144\pi$
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	−0.350100	+	0.936713i	$0.613852\pi$
$224$	1.50000	+	2.59808i	0.100223	+	0.173591i
$225$	−24.0000			−1.60000
$226$	0.500000	−	0.866025i	0.0332595	−	0.0576072i
$227$	−10.5000	+	18.1865i	−0.696909	+	1.20708i	0.272623	+	0.962121i	$0.412109\pi$
$227$	−10.5000	+	18.1865i	−0.696909	+	1.20708i	−0.969533	+	0.244962i	$0.921225\pi$
$228$	−10.5000	+	18.1865i	−0.695379	+	1.20443i
$229$	3.50000	+	6.06218i	0.231287	+	0.400600i	0.958187	−	0.286143i	$-0.0923732\pi$
$229$	3.50000	+	6.06218i	0.231287	+	0.400600i	−0.726900	+	0.686743i	$0.759040\pi$
$230$	2.00000	−	3.46410i	0.131876	−	0.228416i
$231$	−13.5000	−	23.3827i	−0.888235	−	1.53847i
$232$	2.00000			0.131306
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$	−15.0000	−	25.9808i	−0.980581	−	1.69842i
$235$	4.00000	−	6.92820i	0.260931	−	0.451946i
$236$	−1.50000	−	2.59808i	−0.0976417	−	0.169120i
$237$	−1.50000	+	2.59808i	−0.0974355	+	0.168763i
$238$	4.50000	−	7.79423i	0.291692	−	0.505225i
$239$	0.500000	−	0.866025i	0.0323423	−	0.0560185i	−0.849401	−	0.527748i	$-0.823037\pi$
$239$	0.500000	−	0.866025i	0.0323423	−	0.0560185i	0.881743	+	0.471729i	$0.156370\pi$
$240$	3.00000			0.193649
$241$	12.5000	+	21.6506i	0.805196	+	1.39464i	0.916159	+	0.400815i	$0.131273\pi$
$241$	12.5000	+	21.6506i	0.805196	+	1.39464i	−0.110963	+	0.993825i	$0.535394\pi$
$242$	1.00000	+	1.73205i	0.0642824	+	0.111340i
$243$		0			0
$244$	6.00000			0.384111
$245$	−1.00000	−	1.73205i	−0.0638877	−	0.110657i
$246$	−27.0000			−1.72146
$247$	35.0000			2.22700
$248$	2.00000	+	5.19615i	0.127000	+	0.329956i
$249$	15.0000			0.950586
$250$	−9.00000			−0.569210
$251$	−11.5000	−	19.9186i	−0.725874	−	1.25725i	−0.958613	−	0.284711i	$-0.908102\pi$
$251$	−11.5000	−	19.9186i	−0.725874	−	1.25725i	0.232740	−	0.972539i	$-0.425231\pi$
$252$	−18.0000			−1.13389
$253$	−6.00000	+	10.3923i	−0.377217	+	0.653359i
$254$	−6.50000	−	11.2583i	−0.407846	−	0.706410i
$255$	−4.50000	−	7.79423i	−0.281801	−	0.488094i
$256$	1.00000			0.0625000
$257$	6.50000	−	11.2583i	0.405459	−	0.702275i	−0.588916	−	0.808194i	$-0.700445\pi$
$257$	6.50000	−	11.2583i	0.405459	−	0.702275i	0.994375	+	0.105919i	$0.0337784\pi$
$258$	1.50000	−	2.59808i	0.0933859	−	0.161749i
$259$	1.50000	−	2.59808i	0.0932055	−	0.161437i
$260$	−2.50000	−	4.33013i	−0.155043	−	0.268543i
$261$	−6.00000	+	10.3923i	−0.371391	+	0.643268i
$262$	10.5000	+	18.1865i	0.648692	+	1.12357i
$263$	−16.0000			−0.986602			−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000			−0.986602			−0.493301	+	0.869859i	$0.664210\pi$
$264$	−9.00000			−0.553912
$265$	1.50000	+	2.59808i	0.0921443	+	0.159599i
$266$	10.5000	−	18.1865i	0.643796	−	1.11509i
$267$	−9.00000	−	15.5885i	−0.550791	−	0.953998i
$268$	1.50000	−	2.59808i	0.0916271	−	0.158703i
$269$	−10.5000	+	18.1865i	−0.640196	+	1.10885i	0.345192	+	0.938532i	$0.387814\pi$
$269$	−10.5000	+	18.1865i	−0.640196	+	1.10885i	−0.985389	+	0.170321i	$0.945520\pi$
$270$	−4.50000	+	7.79423i	−0.273861	+	0.474342i
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$	−1.50000	−	2.59808i	−0.0909509	−	0.157532i
$273$	22.5000	+	38.9711i	1.36176	+	2.35864i
$274$	−5.50000	+	9.52628i	−0.332267	+	0.575504i
$275$	12.0000			0.723627
$276$	6.00000	+	10.3923i	0.361158	+	0.625543i
$277$	−2.00000			−0.120168			−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000			−0.120168			−0.0600842	+	0.998193i	$0.519137\pi$
$278$		0			0
$279$	−33.0000	−	5.19615i	−1.97566	−	0.311086i
$280$	−3.00000			−0.179284
$281$	30.0000			1.78965			0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000			1.78965			0.894825	+	0.446417i	$0.147300\pi$
$282$	12.0000	+	20.7846i	0.714590	+	1.23771i
$283$	4.00000			0.237775			0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000			0.237775			0.118888	+	0.992908i	$0.462067\pi$
$284$	0.500000	−	0.866025i	0.0296695	−	0.0513892i
$285$	−10.5000	−	18.1865i	−0.621966	−	1.07728i
$286$	7.50000	+	12.9904i	0.443484	+	0.768137i
$287$	27.0000			1.59376
$288$	−3.00000	+	5.19615i	−0.176777	+	0.306186i
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	−1.00000	+	1.73205i	−0.0587220	+	0.101710i
$291$	−21.0000	−	36.3731i	−1.23104	−	2.13223i
$292$	−3.50000	+	6.06218i	−0.204822	+	0.354762i
$293$	9.50000	+	16.4545i	0.554996	+	0.961281i	0.997904	+	0.0647140i	$0.0206135\pi$
$293$	9.50000	+	16.4545i	0.554996	+	0.961281i	−0.442908	+	0.896567i	$0.646053\pi$
$294$	6.00000			0.349927
$295$	3.00000			0.174667
$296$	−0.500000	−	0.866025i	−0.0290619	−	0.0503367i
$297$	13.5000	−	23.3827i	0.783349	−	1.35680i
$298$	−0.500000	−	0.866025i	−0.0289642	−	0.0501675i
$299$	10.0000	−	17.3205i	0.578315	−	1.00167i
$300$	6.00000	−	10.3923i	0.346410	−	0.600000i
$301$	−1.50000	+	2.59808i	−0.0864586	+	0.149751i
$302$	−16.0000			−0.920697
$303$	15.0000	+	25.9808i	0.861727	+	1.49256i
$304$	−3.50000	−	6.06218i	−0.200739	−	0.347690i
$305$	−3.00000	+	5.19615i	−0.171780	+	0.297531i
$306$	18.0000			1.02899
$307$	2.50000	+	4.33013i	0.142683	+	0.247133i	0.928506	−	0.371318i	$-0.121094\pi$
$307$	2.50000	+	4.33013i	0.142683	+	0.247133i	−0.785823	+	0.618451i	$0.787761\pi$
$308$	9.00000			0.512823
$309$	−39.0000			−2.21863
$310$	−5.50000	−	0.866025i	−0.312379	−	0.0491869i
$311$	32.0000			1.81455			0.907277	−	0.420534i	$-0.138157\pi$
$311$	32.0000			1.81455			0.907277	+	0.420534i	$0.138157\pi$
$312$	15.0000			0.849208
$313$	−3.50000	−	6.06218i	−0.197832	−	0.342655i	0.749993	−	0.661445i	$-0.230057\pi$
$313$	−3.50000	−	6.06218i	−0.197832	−	0.342655i	−0.947825	+	0.318791i	$0.896723\pi$
$314$	−10.0000			−0.564333
$315$	9.00000	−	15.5885i	0.507093	−	0.878310i
$316$	−0.500000	−	0.866025i	−0.0281272	−	0.0487177i
$317$	−14.5000	−	25.1147i	−0.814401	−	1.41058i	−0.909757	−	0.415141i	$-0.863732\pi$
$317$	−14.5000	−	25.1147i	−0.814401	−	1.41058i	0.0953560	−	0.995443i	$-0.469601\pi$
$318$	−9.00000			−0.504695
$319$	3.00000	−	5.19615i	0.167968	−	0.290929i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	19.5000	−	33.7750i	1.08838	−	1.88514i
$322$	−6.00000	−	10.3923i	−0.334367	−	0.579141i
$323$	−10.5000	+	18.1865i	−0.584236	+	1.01193i
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	−20.0000			−1.10940
$326$	−4.00000			−0.221540
$327$	3.00000	+	5.19615i	0.165900	+	0.287348i
$328$	4.50000	−	7.79423i	0.248471	−	0.430364i
$329$	−12.0000	−	20.7846i	−0.661581	−	1.14589i
$330$	4.50000	−	7.79423i	0.247717	−	0.429058i
$331$	−8.50000	+	14.7224i	−0.467202	+	0.809218i	−0.999298	−	0.0374662i	$-0.988071\pi$
$331$	−8.50000	+	14.7224i	−0.467202	+	0.809218i	0.532096	+	0.846684i	$0.321405\pi$
$332$	−2.50000	+	4.33013i	−0.137205	+	0.237647i
$333$	6.00000			0.328798
$334$	9.50000	+	16.4545i	0.519817	+	0.900349i
$335$	1.50000	+	2.59808i	0.0819538	+	0.141948i
$336$	4.50000	−	7.79423i	0.245495	−	0.425210i
$337$	30.0000			1.63420			0.817102	−	0.576493i	$-0.195579\pi$
$337$	30.0000			1.63420			0.817102	+	0.576493i	$0.195579\pi$
$338$	−6.00000	−	10.3923i	−0.326357	−	0.565267i
$339$	−3.00000			−0.162938
$340$	3.00000			0.162698
$341$	16.5000	+	2.59808i	0.893525	+	0.140694i
$342$	42.0000			2.27110
$343$	15.0000			0.809924
$344$	0.500000	+	0.866025i	0.0269582	+	0.0466930i
$345$	−12.0000			−0.646058
$346$	−0.500000	+	0.866025i	−0.0268802	+	0.0465578i
$347$	4.50000	+	7.79423i	0.241573	+	0.418416i	0.961162	−	0.275983i	$-0.0890035\pi$
$347$	4.50000	+	7.79423i	0.241573	+	0.418416i	−0.719590	+	0.694399i	$0.755670\pi$
$348$	−3.00000	−	5.19615i	−0.160817	−	0.278543i
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$	−6.00000	+	10.3923i	−0.320713	+	0.555492i
$351$	−22.5000	+	38.9711i	−1.20096	+	2.08013i
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	−15.5000	−	26.8468i	−0.824982	−	1.42891i	−0.901933	−	0.431875i	$-0.857852\pi$
$353$	−15.5000	−	26.8468i	−0.824982	−	1.42891i	0.0769515	−	0.997035i	$-0.475481\pi$
$354$	−4.50000	+	7.79423i	−0.239172	+	0.414259i
$355$	0.500000	+	0.866025i	0.0265372	+	0.0459639i
$356$	6.00000			0.317999
$357$	−27.0000			−1.42899
$358$	−9.50000	−	16.4545i	−0.502091	−	0.869646i
$359$	−15.5000	+	26.8468i	−0.818059	+	1.41692i	0.0890519	+	0.996027i	$0.471616\pi$
$359$	−15.5000	+	26.8468i	−0.818059	+	1.41692i	−0.907111	+	0.420892i	$0.861717\pi$
$360$	−3.00000	−	5.19615i	−0.158114	−	0.273861i
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$	−2.50000	+	4.33013i	−0.131397	+	0.227586i
$363$	3.00000	−	5.19615i	0.157459	−	0.272727i
$364$	−15.0000			−0.786214
$365$	−3.50000	−	6.06218i	−0.183198	−	0.317309i
$366$	−9.00000	−	15.5885i	−0.470438	−	0.814822i
$367$	−3.50000	+	6.06218i	−0.182699	+	0.316443i	−0.942799	−	0.333363i	$-0.891817\pi$
$367$	−3.50000	+	6.06218i	−0.182699	+	0.316443i	0.760100	+	0.649806i	$0.225150\pi$
$368$	−4.00000			−0.208514
$369$	27.0000	+	46.7654i	1.40556	+	2.43451i
$370$	1.00000			0.0519875
$371$	9.00000			0.467257
$372$	10.5000	−	12.9904i	0.544400	−	0.673520i
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$	−9.00000			−0.465379
$375$	13.5000	+	23.3827i	0.697137	+	1.20748i
$376$	−8.00000			−0.412568
$377$	−5.00000	+	8.66025i	−0.257513	+	0.446026i
$378$	13.5000	+	23.3827i	0.694365	+	1.20268i
$379$	0.500000	+	0.866025i	0.0256833	+	0.0444847i	0.878581	−	0.477593i	$-0.158491\pi$
$379$	0.500000	+	0.866025i	0.0256833	+	0.0444847i	−0.852898	+	0.522077i	$0.825157\pi$
$380$	7.00000			0.359092
$381$	−19.5000	+	33.7750i	−0.999015	+	1.73035i
$382$	−1.50000	+	2.59808i	−0.0767467	+	0.132929i
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	−0.991522	−	0.129937i	$-0.958522\pi$
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	0.608290	+	0.793715i	$0.291856\pi$
$384$	−1.50000	−	2.59808i	−0.0765466	−	0.132583i
$385$	−4.50000	+	7.79423i	−0.229341	+	0.397231i
$386$	−9.50000	−	16.4545i	−0.483537	−	0.837511i
$387$	−6.00000			−0.304997
$388$	14.0000			0.710742
$389$	11.5000	+	19.9186i	0.583073	+	1.00991i	0.995113	+	0.0987463i	$0.0314832\pi$
$389$	11.5000	+	19.9186i	0.583073	+	1.00991i	−0.412039	+	0.911166i	$0.635183\pi$
$390$	−7.50000	+	12.9904i	−0.379777	+	0.657794i
$391$	6.00000	+	10.3923i	0.303433	+	0.525561i
$392$	−1.00000	+	1.73205i	−0.0505076	+	0.0874818i
$393$	31.5000	−	54.5596i	1.58896	−	2.75217i
$394$	7.50000	−	12.9904i	0.377845	−	0.654446i
$395$	1.00000			0.0503155
$396$	9.00000	+	15.5885i	0.452267	+	0.783349i
$397$	−10.5000	−	18.1865i	−0.526980	−	0.912756i	−0.999506	−	0.0314391i	$-0.989991\pi$
$397$	−10.5000	−	18.1865i	−0.526980	−	0.912756i	0.472526	−	0.881317i	$-0.343342\pi$
$398$	10.5000	−	18.1865i	0.526317	−	0.911609i
$399$	−63.0000			−3.15394
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	−18.0000			−0.898877			−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000			−0.898877			−0.449439	+	0.893311i	$0.648376\pi$
$402$	−9.00000			−0.448879
$403$	−27.5000	−	4.33013i	−1.36987	−	0.215699i
$404$	−10.0000			−0.497519
$405$	9.00000			0.447214
$406$	3.00000	+	5.19615i	0.148888	+	0.257881i
$407$	−3.00000			−0.148704
$408$	−4.50000	+	7.79423i	−0.222783	+	0.385872i
$409$	−15.5000	−	26.8468i	−0.766426	−	1.32749i	−0.939490	−	0.342578i	$-0.888700\pi$
$409$	−15.5000	−	26.8468i	−0.766426	−	1.32749i	0.173064	−	0.984911i	$-0.444633\pi$
$410$	4.50000	+	7.79423i	0.222239	+	0.384930i
$411$	33.0000			1.62777
$412$	6.50000	−	11.2583i	0.320232	−	0.554658i
$413$	4.50000	−	7.79423i	0.221431	−	0.383529i
$414$	12.0000	−	20.7846i	0.589768	−	1.02151i
$415$	−2.50000	−	4.33013i	−0.122720	−	0.212558i
$416$	−2.50000	+	4.33013i	−0.122573	+	0.212302i
$417$		0			0
$418$	−21.0000			−1.02714
$419$	−28.0000			−1.36789			−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000			−1.36789			−0.683945	+	0.729534i	$0.739737\pi$
$420$	4.50000	+	7.79423i	0.219578	+	0.380319i
$421$	7.50000	−	12.9904i	0.365528	−	0.633112i	−0.623333	−	0.781956i	$-0.714222\pi$
$421$	7.50000	−	12.9904i	0.365528	−	0.633112i	0.988861	+	0.148844i	$0.0475552\pi$
$422$	0.500000	+	0.866025i	0.0243396	+	0.0421575i
$423$	24.0000	−	41.5692i	1.16692	−	2.02116i
$424$	1.50000	−	2.59808i	0.0728464	−	0.126174i
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$	−3.00000			−0.145350
$427$	9.00000	+	15.5885i	0.435541	+	0.754378i
$428$	6.50000	+	11.2583i	0.314189	+	0.544192i
$429$	22.5000	−	38.9711i	1.08631	−	1.88154i
$430$	−1.00000			−0.0482243
$431$	−2.50000	−	4.33013i	−0.120421	−	0.208575i	0.799513	−	0.600649i	$-0.205091\pi$
$431$	−2.50000	−	4.33013i	−0.120421	−	0.208575i	−0.919934	+	0.392074i	$0.871758\pi$
$432$	9.00000			0.433013
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$	−10.5000	+	12.9904i	−0.504016	+	0.623558i
$435$	6.00000			0.287678
$436$	−2.00000			−0.0957826
$437$	14.0000	+	24.2487i	0.669711	+	1.15997i
$438$	21.0000			1.00342
$439$	6.50000	−	11.2583i	0.310228	−	0.537331i	−0.668184	−	0.743996i	$-0.732928\pi$
$439$	6.50000	−	11.2583i	0.310228	−	0.537331i	0.978412	+	0.206666i	$0.0662612\pi$
$440$	1.50000	+	2.59808i	0.0715097	+	0.123858i
$441$	−6.00000	−	10.3923i	−0.285714	−	0.494872i
$442$	15.0000			0.713477
$443$	5.50000	−	9.52628i	0.261313	−	0.452607i	−0.705278	−	0.708931i	$-0.749178\pi$
$443$	5.50000	−	9.52628i	0.261313	−	0.452607i	0.966591	+	0.256323i	$0.0825112\pi$
$444$	−1.50000	+	2.59808i	−0.0711868	+	0.123299i
$445$	−3.00000	+	5.19615i	−0.142214	+	0.246321i
$446$	9.50000	+	16.4545i	0.449838	+	0.779142i
$447$	−1.50000	+	2.59808i	−0.0709476	+	0.122885i
$448$	1.50000	+	2.59808i	0.0708683	+	0.122748i
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$	−24.0000			−1.13137
$451$	−13.5000	−	23.3827i	−0.635690	−	1.10105i
$452$	0.500000	−	0.866025i	0.0235180	−	0.0407344i
$453$	24.0000	+	41.5692i	1.12762	+	1.95309i
$454$	−10.5000	+	18.1865i	−0.492789	+	0.853536i
$455$	7.50000	−	12.9904i	0.351605	−	0.608998i
$456$	−10.5000	+	18.1865i	−0.491708	+	0.851662i
$457$	10.0000			0.467780			0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000			0.467780			0.233890	+	0.972263i	$0.424854\pi$
$458$	3.50000	+	6.06218i	0.163544	+	0.283267i
$459$	−13.5000	−	23.3827i	−0.630126	−	1.09141i
$460$	2.00000	−	3.46410i	0.0932505	−	0.161515i
$461$	−42.0000			−1.95614			−0.978068	−	0.208288i	$-0.933211\pi$
$461$	−42.0000			−1.95614			−0.978068	+	0.208288i	$0.933211\pi$
$462$	−13.5000	−	23.3827i	−0.628077	−	1.08786i
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	2.00000			0.0928477
$465$	6.00000	+	15.5885i	0.278243	+	0.722897i
$466$	−18.0000			−0.833834
$467$	−8.00000			−0.370196			−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000			−0.370196			−0.185098	+	0.982720i	$0.559260\pi$
$468$	−15.0000	−	25.9808i	−0.693375	−	1.20096i
$469$	9.00000			0.415581
$470$	4.00000	−	6.92820i	0.184506	−	0.319574i
$471$	15.0000	+	25.9808i	0.691164	+	1.19713i
$472$	−1.50000	−	2.59808i	−0.0690431	−	0.119586i
$473$	3.00000			0.137940
$474$	−1.50000	+	2.59808i	−0.0688973	+	0.119334i
$475$	14.0000	−	24.2487i	0.642364	−	1.11261i
$476$	4.50000	−	7.79423i	0.206257	−	0.357248i
$477$	9.00000	+	15.5885i	0.412082	+	0.713746i
$478$	0.500000	−	0.866025i	0.0228695	−	0.0396111i
$479$	5.50000	+	9.52628i	0.251301	+	0.435267i	0.963884	−	0.266321i	$-0.0858081\pi$
$479$	5.50000	+	9.52628i	0.251301	+	0.435267i	−0.712583	+	0.701588i	$0.752475\pi$
$480$	3.00000			0.136931
$481$	5.00000			0.227980
$482$	12.5000	+	21.6506i	0.569359	+	0.986159i
$483$	−18.0000	+	31.1769i	−0.819028	+	1.41860i
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	−7.00000	+	12.1244i	−0.317854	+	0.550539i
$486$		0			0
$487$	−5.50000	+	9.52628i	−0.249229	+	0.431677i	−0.963312	−	0.268384i	$-0.913510\pi$
$487$	−5.50000	+	9.52628i	−0.249229	+	0.431677i	0.714083	+	0.700061i	$0.246844\pi$
$488$	6.00000			0.271607
$489$	6.00000	+	10.3923i	0.271329	+	0.469956i
$490$	−1.00000	−	1.73205i	−0.0451754	−	0.0782461i
$491$	7.50000	−	12.9904i	0.338470	−	0.586248i	−0.645675	−	0.763612i	$-0.723424\pi$
$491$	7.50000	−	12.9904i	0.338470	−	0.586248i	0.984145	+	0.177365i	$0.0567572\pi$
$492$	−27.0000			−1.21725
$493$	−3.00000	−	5.19615i	−0.135113	−	0.234023i
$494$	35.0000			1.57472
$495$	−18.0000			−0.809040
$496$	2.00000	+	5.19615i	0.0898027	+	0.233314i
$497$	3.00000			0.134568
$498$	15.0000			0.672166
$499$	−7.50000	−	12.9904i	−0.335746	−	0.581529i	0.647882	−	0.761741i	$-0.275655\pi$
$499$	−7.50000	−	12.9904i	−0.335746	−	0.581529i	−0.983628	+	0.180212i	$0.942322\pi$
$500$	−9.00000			−0.402492
$501$	28.5000	−	49.3634i	1.27329	−	2.20540i
$502$	−11.5000	−	19.9186i	−0.513270	−	0.889010i
$503$	−4.50000	−	7.79423i	−0.200645	−	0.347527i	0.748091	−	0.663596i	$-0.230970\pi$
$503$	−4.50000	−	7.79423i	−0.200645	−	0.347527i	−0.948736	+	0.316068i	$0.897637\pi$
$504$	−18.0000			−0.801784
$505$	5.00000	−	8.66025i	0.222497	−	0.385376i
$506$	−6.00000	+	10.3923i	−0.266733	+	0.461994i
$507$	−18.0000	+	31.1769i	−0.799408	+	1.38462i
$508$	−6.50000	−	11.2583i	−0.288391	−	0.499508i
$509$	−0.500000	+	0.866025i	−0.0221621	+	0.0383859i	−0.876894	−	0.480684i	$-0.840388\pi$
$509$	−0.500000	+	0.866025i	−0.0221621	+	0.0383859i	0.854732	+	0.519070i	$0.173722\pi$
$510$	−4.50000	−	7.79423i	−0.199263	−	0.345134i
$511$	−21.0000			−0.928985
$512$	1.00000			0.0441942
$513$	−31.5000	−	54.5596i	−1.39076	−	2.40887i
$514$	6.50000	−	11.2583i	0.286703	−	0.496584i
$515$	6.50000	+	11.2583i	0.286424	+	0.496101i
$516$	1.50000	−	2.59808i	0.0660338	−	0.114374i
$517$	−12.0000	+	20.7846i	−0.527759	+	0.914106i
$518$	1.50000	−	2.59808i	0.0659062	−	0.114153i
$519$	3.00000			0.131685
$520$	−2.50000	−	4.33013i	−0.109632	−	0.189889i
$521$	−15.5000	−	26.8468i	−0.679067	−	1.17618i	−0.975262	−	0.221052i	$-0.929051\pi$
$521$	−15.5000	−	26.8468i	−0.679067	−	1.17618i	0.296195	−	0.955128i	$-0.404282\pi$
$522$	−6.00000	+	10.3923i	−0.262613	+	0.454859i
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$	10.5000	+	18.1865i	0.458695	+	0.794482i
$525$	36.0000			1.57117
$526$	−16.0000			−0.697633
$527$	10.5000	−	12.9904i	0.457387	−	0.565870i
$528$	−9.00000			−0.391675
$529$	−7.00000			−0.304348
$530$	1.50000	+	2.59808i	0.0651558	+	0.112853i
$531$	18.0000			0.781133
$532$	10.5000	−	18.1865i	0.455233	−	0.788486i
$533$	22.5000	+	38.9711i	0.974583	+	1.68803i
$534$	−9.00000	−	15.5885i	−0.389468	−	0.674579i
$535$	−13.0000			−0.562039
$536$	1.50000	−	2.59808i	0.0647901	−	0.112220i
$537$	−28.5000	+	49.3634i	−1.22987	+	2.13019i
$538$	−10.5000	+	18.1865i	−0.452687	+	0.784077i
$539$	3.00000	+	5.19615i	0.129219	+	0.223814i
$540$	−4.50000	+	7.79423i	−0.193649	+	0.335410i
$541$	−14.5000	−	25.1147i	−0.623404	−	1.07977i	−0.988847	−	0.148933i	$-0.952416\pi$
$541$	−14.5000	−	25.1147i	−0.623404	−	1.07977i	0.365444	−	0.930834i	$-0.380917\pi$
$542$	−8.00000			−0.343629
$543$	15.0000			0.643712
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$	1.00000	−	1.73205i	0.0428353	−	0.0741929i
$546$	22.5000	+	38.9711i	0.962911	+	1.66781i
$547$	−6.50000	+	11.2583i	−0.277920	+	0.481371i	−0.970868	−	0.239616i	$-0.922978\pi$
$547$	−6.50000	+	11.2583i	−0.277920	+	0.481371i	0.692948	+	0.720988i	$0.256312\pi$
$548$	−5.50000	+	9.52628i	−0.234948	+	0.406942i
$549$	−18.0000	+	31.1769i	−0.768221	+	1.33060i
$550$	12.0000			0.511682
$551$	−7.00000	−	12.1244i	−0.298210	−	0.516515i
$552$	6.00000	+	10.3923i	0.255377	+	0.442326i
$553$	1.50000	−	2.59808i	0.0637865	−	0.110481i
$554$	−2.00000			−0.0849719
$555$	−1.50000	−	2.59808i	−0.0636715	−	0.110282i
$556$		0			0
$557$	−2.00000			−0.0847427			−0.0423714	−	0.999102i	$-0.513491\pi$
$557$	−2.00000			−0.0847427			−0.0423714	+	0.999102i	$0.513491\pi$
$558$	−33.0000	−	5.19615i	−1.39700	−	0.219971i
$559$	−5.00000			−0.211477
$560$	−3.00000			−0.126773
$561$	13.5000	+	23.3827i	0.569970	+	0.987218i
$562$	30.0000			1.26547
$563$	−10.5000	+	18.1865i	−0.442522	+	0.766471i	−0.997876	−	0.0651433i	$-0.979250\pi$
$563$	−10.5000	+	18.1865i	−0.442522	+	0.766471i	0.555354	+	0.831614i	$0.312583\pi$
$564$	12.0000	+	20.7846i	0.505291	+	0.875190i
$565$	0.500000	+	0.866025i	0.0210352	+	0.0364340i
$566$	4.00000			0.168133
$567$	13.5000	−	23.3827i	0.566947	−	0.981981i
$568$	0.500000	−	0.866025i	0.0209795	−	0.0363376i
$569$	12.5000	−	21.6506i	0.524027	−	0.907642i	−0.475581	−	0.879672i	$-0.657762\pi$
$569$	12.5000	−	21.6506i	0.524027	−	0.907642i	0.999609	−	0.0279702i	$-0.00890434\pi$
$570$	−10.5000	−	18.1865i	−0.439797	−	0.761750i
$571$	−12.5000	+	21.6506i	−0.523109	+	0.906051i	0.476530	+	0.879158i	$0.341895\pi$
$571$	−12.5000	+	21.6506i	−0.523109	+	0.906051i	−0.999638	+	0.0268925i	$0.991439\pi$
$572$	7.50000	+	12.9904i	0.313591	+	0.543155i
$573$	9.00000			0.375980
$574$	27.0000			1.12696
$575$	−8.00000	−	13.8564i	−0.333623	−	0.577852i
$576$	−3.00000	+	5.19615i	−0.125000	+	0.216506i
$577$	−1.50000	−	2.59808i	−0.0624458	−	0.108159i	0.833112	−	0.553104i	$-0.186557\pi$
$577$	−1.50000	−	2.59808i	−0.0624458	−	0.108159i	−0.895558	+	0.444945i	$0.853223\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	−28.5000	+	49.3634i	−1.18442	+	2.05147i
$580$	−1.00000	+	1.73205i	−0.0415227	+	0.0719195i
$581$	−15.0000			−0.622305
$582$	−21.0000	−	36.3731i	−0.870478	−	1.50771i
$583$	−4.50000	−	7.79423i	−0.186371	−	0.322804i
$584$	−3.50000	+	6.06218i	−0.144831	+	0.250855i
$585$	30.0000			1.24035
$586$	9.50000	+	16.4545i	0.392441	+	0.679728i
$587$	−28.0000			−1.15568			−0.577842	−	0.816149i	$-0.696105\pi$
$587$	−28.0000			−1.15568			−0.577842	+	0.816149i	$0.696105\pi$
$588$	6.00000			0.247436
$589$	24.5000	−	30.3109i	1.00950	−	1.24894i
$590$	3.00000			0.123508
$591$	−45.0000			−1.85105
$592$	−0.500000	−	0.866025i	−0.0205499	−	0.0355934i
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$	13.5000	−	23.3827i	0.553912	−	0.959403i
$595$	4.50000	+	7.79423i	0.184482	+	0.319532i
$596$	−0.500000	−	0.866025i	−0.0204808	−	0.0354738i
$597$	−63.0000			−2.57842
$598$	10.0000	−	17.3205i	0.408930	−	0.708288i
$599$	8.50000	−	14.7224i	0.347301	−	0.601542i	−0.638468	−	0.769648i	$-0.720432\pi$
$599$	8.50000	−	14.7224i	0.347301	−	0.601542i	0.985769	+	0.168106i	$0.0537650\pi$
$600$	6.00000	−	10.3923i	0.244949	−	0.424264i
$601$	16.5000	+	28.5788i	0.673049	+	1.16576i	0.977035	+	0.213079i	$0.0683491\pi$
$601$	16.5000	+	28.5788i	0.673049	+	1.16576i	−0.303986	+	0.952676i	$0.598318\pi$
$602$	−1.50000	+	2.59808i	−0.0611354	+	0.105890i
$603$	9.00000	+	15.5885i	0.366508	+	0.634811i
$604$	−16.0000			−0.651031
$605$	−2.00000			−0.0813116
$606$	15.0000	+	25.9808i	0.609333	+	1.05540i
$607$	20.5000	−	35.5070i	0.832069	−	1.44119i	−0.0643251	−	0.997929i	$-0.520489\pi$
$607$	20.5000	−	35.5070i	0.832069	−	1.44119i	0.896394	−	0.443257i	$-0.146177\pi$
$608$	−3.50000	−	6.06218i	−0.141944	−	0.245854i
$609$	9.00000	−	15.5885i	0.364698	−	0.631676i
$610$	−3.00000	+	5.19615i	−0.121466	+	0.210386i
$611$	20.0000	−	34.6410i	0.809113	−	1.40143i
$612$	18.0000			0.727607
$613$	−2.50000	−	4.33013i	−0.100974	−	0.174892i	0.811112	−	0.584891i	$-0.198863\pi$
$613$	−2.50000	−	4.33013i	−0.100974	−	0.174892i	−0.912086	+	0.409998i	$0.865529\pi$
$614$	2.50000	+	4.33013i	0.100892	+	0.174750i
$615$	13.5000	−	23.3827i	0.544373	−	0.942881i
$616$	9.00000			0.362620
$617$	−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	$-0.349564\pi$
$618$	−39.0000			−1.56881
$619$	4.00000			0.160774			0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000			0.160774			0.0803868	+	0.996764i	$0.474384\pi$
$620$	−5.50000	−	0.866025i	−0.220885	−	0.0347804i
$621$	−36.0000			−1.44463
$622$	32.0000			1.28308
$623$	9.00000	+	15.5885i	0.360577	+	0.624538i
$624$	15.0000			0.600481
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	−3.50000	−	6.06218i	−0.139888	−	0.242293i
$627$	31.5000	+	54.5596i	1.25799	+	2.17890i
$628$	−10.0000			−0.399043
$629$	−1.50000	+	2.59808i	−0.0598089	+	0.103592i
$630$	9.00000	−	15.5885i	0.358569	−	0.621059i
$631$	−13.5000	+	23.3827i	−0.537427	+	0.930850i	0.461615	+	0.887080i	$0.347270\pi$
$631$	−13.5000	+	23.3827i	−0.537427	+	0.930850i	−0.999042	+	0.0437697i	$0.986063\pi$
$632$	−0.500000	−	0.866025i	−0.0198889	−	0.0344486i
$633$	1.50000	−	2.59808i	0.0596196	−	0.103264i
$634$	−14.5000	−	25.1147i	−0.575869	−	0.997434i
$635$	13.0000			0.515889
$636$	−9.00000			−0.356873
$637$	−5.00000	−	8.66025i	−0.198107	−	0.343132i
$638$	3.00000	−	5.19615i	0.118771	−	0.205718i
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−5.50000	+	9.52628i	−0.217237	+	0.376265i	−0.953962	−	0.299927i	$-0.903038\pi$
$641$	−5.50000	+	9.52628i	−0.217237	+	0.376265i	0.736725	+	0.676192i	$0.236371\pi$
$642$	19.5000	−	33.7750i	0.769604	−	1.33299i
$643$	28.0000			1.10421			0.552106	−	0.833774i	$-0.313824\pi$
$643$	28.0000			1.10421			0.552106	+	0.833774i	$0.313824\pi$
$644$	−6.00000	−	10.3923i	−0.236433	−	0.409514i
$645$	1.50000	+	2.59808i	0.0590624	+	0.102299i
$646$	−10.5000	+	18.1865i	−0.413117	+	0.715540i
$647$	4.00000			0.157256			0.0786281	−	0.996904i	$-0.474946\pi$
$647$	4.00000			0.157256			0.0786281	+	0.996904i	$0.474946\pi$
$648$	−4.50000	−	7.79423i	−0.176777	−	0.306186i
$649$	−9.00000			−0.353281
$650$	−20.0000			−0.784465
$651$	49.5000	+	7.79423i	1.94006	+	0.305480i
$652$	−4.00000			−0.156652
$653$	−18.0000			−0.704394			−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000			−0.704394			−0.352197	+	0.935926i	$0.614565\pi$
$654$	3.00000	+	5.19615i	0.117309	+	0.203186i
$655$	−21.0000			−0.820538
$656$	4.50000	−	7.79423i	0.175695	−	0.304314i
$657$	−21.0000	−	36.3731i	−0.819288	−	1.41905i
$658$	−12.0000	−	20.7846i	−0.467809	−	0.810268i
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$	4.50000	−	7.79423i	0.175162	−	0.303390i
$661$	−24.5000	+	42.4352i	−0.952940	+	1.65054i	−0.213925	+	0.976850i	$0.568625\pi$
$661$	−24.5000	+	42.4352i	−0.952940	+	1.65054i	−0.739014	+	0.673690i	$0.764708\pi$
$662$	−8.50000	+	14.7224i	−0.330362	+	0.572204i
$663$	−22.5000	−	38.9711i	−0.873828	−	1.51351i
$664$	−2.50000	+	4.33013i	−0.0970188	+	0.168042i
$665$	10.5000	+	18.1865i	0.407173	+	0.705244i
$666$	6.00000			0.232495
$667$	−8.00000			−0.309761
$668$	9.50000	+	16.4545i	0.367566	+	0.636643i
$669$	28.5000	−	49.3634i	1.10187	−	1.90850i
$670$	1.50000	+	2.59808i	0.0579501	+	0.100372i
$671$	9.00000	−	15.5885i	0.347441	−	0.601786i
$672$	4.50000	−	7.79423i	0.173591	−	0.300669i
$673$	−13.5000	+	23.3827i	−0.520387	+	0.901336i	0.479332	+	0.877633i	$0.340879\pi$
$673$	−13.5000	+	23.3827i	−0.520387	+	0.901336i	−0.999719	+	0.0237028i	$0.992454\pi$
$674$	30.0000			1.15556
$675$	18.0000	+	31.1769i	0.692820	+	1.20000i
$676$	−6.00000	−	10.3923i	−0.230769	−	0.399704i
$677$	13.5000	−	23.3827i	0.518847	−	0.898670i	−0.480913	−	0.876768i	$-0.659695\pi$
$677$	13.5000	−	23.3827i	0.518847	−	0.898670i	0.999760	−	0.0219013i	$-0.00697196\pi$
$678$	−3.00000			−0.115214
$679$	21.0000	+	36.3731i	0.805906	+	1.39587i
$680$	3.00000			0.115045
$681$	63.0000			2.41417
$682$	16.5000	+	2.59808i	0.631818	+	0.0994855i
$683$	−16.0000			−0.612223			−0.306111	−	0.951996i	$-0.599028\pi$
$683$	−16.0000			−0.612223			−0.306111	+	0.951996i	$0.599028\pi$
$684$	42.0000			1.60591
$685$	−5.50000	−	9.52628i	−0.210144	−	0.363980i
$686$	15.0000			0.572703
$687$	10.5000	−	18.1865i	0.400600	−	0.693860i
$688$	0.500000	+	0.866025i	0.0190623	+	0.0330169i
$689$	7.50000	+	12.9904i	0.285727	+	0.494894i
$690$	−12.0000			−0.456832
$691$	13.5000	−	23.3827i	0.513564	−	0.889519i	−0.486312	−	0.873785i	$-0.661658\pi$
$691$	13.5000	−	23.3827i	0.513564	−	0.889519i	0.999876	−	0.0157341i	$-0.00500851\pi$
$692$	−0.500000	+	0.866025i	−0.0190071	+	0.0329213i
$693$	−27.0000	+	46.7654i	−1.02565	+	1.77647i
$694$	4.50000	+	7.79423i	0.170818	+	0.295865i
$695$		0			0
$696$	−3.00000	−	5.19615i	−0.113715	−	0.196960i
$697$	−27.0000			−1.02270
$698$	−14.0000			−0.529908
$699$	27.0000	+	46.7654i	1.02123	+	1.76883i
$700$	−6.00000	+	10.3923i	−0.226779	+	0.392792i
$701$	7.50000	+	12.9904i	0.283271	+	0.490640i	0.972188	−	0.234200i	$-0.0752470\pi$
$701$	7.50000	+	12.9904i	0.283271	+	0.490640i	−0.688917	+	0.724840i	$0.741914\pi$
$702$	−22.5000	+	38.9711i	−0.849208	+	1.47087i
$703$	−3.50000	+	6.06218i	−0.132005	+	0.228639i
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$	−24.0000			−0.903892
$706$	−15.5000	−	26.8468i	−0.583350	−	1.01039i
$707$	−15.0000	−	25.9808i	−0.564133	−	0.977107i
$708$	−4.50000	+	7.79423i	−0.169120	+	0.292925i
$709$	38.0000			1.42712			0.713560	−	0.700594i	$-0.247082\pi$
$709$	38.0000			1.42712			0.713560	+	0.700594i	$0.247082\pi$
$710$	0.500000	+	0.866025i	0.0187647	+	0.0325014i
$711$	6.00000			0.225018
$712$	6.00000			0.224860
$713$	−8.00000	−	20.7846i	−0.299602	−	0.778390i
$714$	−27.0000			−1.01045
$715$	−15.0000			−0.560968
$716$	−9.50000	−	16.4545i	−0.355032	−	0.614933i
$717$	−3.00000			−0.112037
$718$	−15.5000	+	26.8468i	−0.578455	+	1.00191i
$719$	3.50000	+	6.06218i	0.130528	+	0.226081i	0.923880	−	0.382682i	$-0.124999\pi$
$719$	3.50000	+	6.06218i	0.130528	+	0.226081i	−0.793352	+	0.608763i	$0.791666\pi$
$720$	−3.00000	−	5.19615i	−0.111803	−	0.193649i
$721$	39.0000			1.45244
$722$	−15.0000	+	25.9808i	−0.558242	+	0.966904i
$723$	37.5000	−	64.9519i	1.39464	−	2.41559i
$724$	−2.50000	+	4.33013i	−0.0929118	+	0.160928i
$725$	4.00000	+	6.92820i	0.148556	+	0.257307i
$726$	3.00000	−	5.19615i	0.111340	−	0.192847i
$727$	−18.5000	−	32.0429i	−0.686127	−	1.18841i	−0.973081	−	0.230463i	$-0.925976\pi$
$727$	−18.5000	−	32.0429i	−0.686127	−	1.18841i	0.286954	−	0.957944i	$-0.407357\pi$
$728$	−15.0000			−0.555937
$729$	−27.0000			−1.00000
$730$	−3.50000	−	6.06218i	−0.129541	−	0.224371i
$731$	1.50000	−	2.59808i	0.0554795	−	0.0960933i
$732$	−9.00000	−	15.5885i	−0.332650	−	0.576166i
$733$	−0.500000	+	0.866025i	−0.0184679	+	0.0319874i	−0.875112	−	0.483921i	$-0.839212\pi$
$733$	−0.500000	+	0.866025i	−0.0184679	+	0.0319874i	0.856644	+	0.515908i	$0.172546\pi$
$734$	−3.50000	+	6.06218i	−0.129187	+	0.223759i
$735$	−3.00000	+	5.19615i	−0.110657	+	0.191663i
$736$	−4.00000			−0.147442
$737$	−4.50000	−	7.79423i	−0.165760	−	0.287104i
$738$	27.0000	+	46.7654i	0.993884	+	1.72146i
$739$	−12.5000	+	21.6506i	−0.459820	+	0.796431i	−0.998951	−	0.0457903i	$-0.985419\pi$
$739$	−12.5000	+	21.6506i	−0.459820	+	0.796431i	0.539131	+	0.842222i	$0.318753\pi$
$740$	1.00000			0.0367607
$741$	−52.5000	−	90.9327i	−1.92864	−	3.34050i
$742$	9.00000			0.330400
$743$	−40.0000			−1.46746			−0.733729	−	0.679442i	$-0.762222\pi$
$743$	−40.0000			−1.46746			−0.733729	+	0.679442i	$0.762222\pi$
$744$	10.5000	−	12.9904i	0.384949	−	0.476250i
$745$	1.00000			0.0366372
$746$	10.0000			0.366126
$747$	−15.0000	−	25.9808i	−0.548821	−	0.950586i
$748$	−9.00000			−0.329073
$749$	−19.5000	+	33.7750i	−0.712514	+	1.23411i
$750$	13.5000	+	23.3827i	0.492950	+	0.853815i
$751$	−14.5000	−	25.1147i	−0.529113	−	0.916450i	−0.999424	−	0.0339490i	$-0.989192\pi$
$751$	−14.5000	−	25.1147i	−0.529113	−	0.916450i	0.470311	−	0.882501i	$-0.344142\pi$
$752$	−8.00000			−0.291730
$753$	−34.5000	+	59.7558i	−1.25725	+	2.17762i
$754$	−5.00000	+	8.66025i	−0.182089	+	0.315388i
$755$	8.00000	−	13.8564i	0.291150	−	0.504286i
$756$	13.5000	+	23.3827i	0.490990	+	0.850420i
$757$	21.5000	−	37.2391i	0.781431	−	1.35348i	−0.149677	−	0.988735i	$-0.547824\pi$
$757$	21.5000	−	37.2391i	0.781431	−	1.35348i	0.931108	−	0.364743i	$-0.118843\pi$
$758$	0.500000	+	0.866025i	0.0181608	+	0.0314555i
$759$	36.0000			1.30672
$760$	7.00000			0.253917
$761$	−3.50000	−	6.06218i	−0.126875	−	0.219754i	0.795589	−	0.605836i	$-0.207161\pi$
$761$	−3.50000	−	6.06218i	−0.126875	−	0.219754i	−0.922464	+	0.386082i	$0.873828\pi$
$762$	−19.5000	+	33.7750i	−0.706410	+	1.22354i
$763$	−3.00000	−	5.19615i	−0.108607	−	0.188113i
$764$	−1.50000	+	2.59808i	−0.0542681	+	0.0939951i
$765$	−9.00000	+	15.5885i	−0.325396	+	0.563602i
$766$	−7.50000	+	12.9904i	−0.270986	+	0.469362i
$767$	15.0000			0.541619
$768$	−1.50000	−	2.59808i	−0.0541266	−	0.0937500i
$769$	16.5000	+	28.5788i	0.595005	+	1.03058i	0.993546	+	0.113429i	$0.0361834\pi$
$769$	16.5000	+	28.5788i	0.595005	+	1.03058i	−0.398541	+	0.917151i	$0.630483\pi$
$770$	−4.50000	+	7.79423i	−0.162169	+	0.280885i
$771$	−39.0000			−1.40455
$772$	−9.50000	−	16.4545i	−0.341912	−	0.592210i
$773$	46.0000			1.65451			0.827253	−	0.561830i	$-0.189903\pi$
$773$	46.0000			1.65451			0.827253	+	0.561830i	$0.189903\pi$
$774$	−6.00000			−0.215666
$775$	−14.0000	+	17.3205i	−0.502895	+	0.622171i
$776$	14.0000			0.502571
$777$	−9.00000			−0.322873
$778$	11.5000	+	19.9186i	0.412295	+	0.714116i
$779$	−63.0000			−2.25721
$780$	−7.50000	+	12.9904i	−0.268543	+	0.465130i
$781$	−1.50000	−	2.59808i	−0.0536742	−	0.0929665i
$782$	6.00000	+	10.3923i	0.214560	+	0.371628i
$783$	18.0000			0.643268
$784$	−1.00000	+	1.73205i	−0.0357143	+	0.0618590i
$785$	5.00000	−	8.66025i	0.178458	−	0.309098i
$786$	31.5000	−	54.5596i	1.12357	−	1.94608i
$787$	26.5000	+	45.8993i	0.944623	+	1.63614i	0.756504	+	0.653989i	$0.226906\pi$
$787$	26.5000	+	45.8993i	0.944623	+	1.63614i	0.188119	+	0.982146i	$0.439761\pi$
$788$	7.50000	−	12.9904i	0.267176	−	0.462763i
$789$	24.0000	+	41.5692i	0.854423	+	1.47990i
$790$	1.00000			0.0355784
$791$	3.00000			0.106668
$792$	9.00000	+	15.5885i	0.319801	+	0.553912i
$793$	−15.0000	+	25.9808i	−0.532666	+	0.922604i
$794$	−10.5000	−	18.1865i	−0.372631	−	0.645416i
$795$	4.50000	−	7.79423i	0.159599	−	0.276433i
$796$	10.5000	−	18.1865i	0.372163	−	0.644605i
$797$	−16.5000	+	28.5788i	−0.584460	+	1.01231i	0.410483	+	0.911868i	$0.365360\pi$
$797$	−16.5000	+	28.5788i	−0.584460	+	1.01231i	−0.994943	+	0.100446i	$0.967973\pi$
$798$	−63.0000			−2.23018
$799$	12.0000	+	20.7846i	0.424529	+	0.735307i
$800$	2.00000	+	3.46410i	0.0707107	+	0.122474i
$801$	−18.0000	+	31.1769i	−0.635999	+	1.10158i
$802$	−18.0000			−0.635602
$803$	10.5000	+	18.1865i	0.370537	+	0.641789i
$804$	−9.00000			−0.317406
$805$	12.0000			0.422944
$806$	−27.5000	−	4.33013i	−0.968646	−	0.152522i
$807$	63.0000			2.21771
$808$	−10.0000			−0.351799
$809$	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	$0.782761\pi$
$810$	9.00000			0.316228
$811$	−2.50000	+	4.33013i	−0.0877869	+	0.152051i	−0.906575	−	0.422044i	$-0.861313\pi$
$811$	−2.50000	+	4.33013i	−0.0877869	+	0.152051i	0.818788	+	0.574095i	$0.194646\pi$
$812$	3.00000	+	5.19615i	0.105279	+	0.182349i
$813$	12.0000	+	20.7846i	0.420858	+	0.728948i
$814$	−3.00000			−0.105150
$815$	2.00000	−	3.46410i	0.0700569	−	0.121342i
$816$	−4.50000	+	7.79423i	−0.157532	+	0.272853i
$817$	3.50000	−	6.06218i	0.122449	−	0.212089i
$818$	−15.5000	−	26.8468i	−0.541945	−	0.938676i
$819$	45.0000	−	77.9423i	1.57243	−	2.72352i
$820$	4.50000	+	7.79423i	0.157147	+	0.272186i
$821$	38.0000			1.32621			0.663105	−	0.748527i	$-0.269238\pi$
$821$	38.0000			1.32621			0.663105	+	0.748527i	$0.269238\pi$
$822$	33.0000			1.15101
$823$	−16.5000	−	28.5788i	−0.575154	−	0.996196i	−0.996025	−	0.0890752i	$-0.971609\pi$
$823$	−16.5000	−	28.5788i	−0.575154	−	0.996196i	0.420871	−	0.907120i	$-0.361724\pi$
$824$	6.50000	−	11.2583i	0.226438	−	0.392203i
$825$	−18.0000	−	31.1769i	−0.626680	−	1.08544i
$826$	4.50000	−	7.79423i	0.156575	−	0.271196i
$827$	21.5000	−	37.2391i	0.747628	−	1.29493i	−0.201328	−	0.979524i	$-0.564526\pi$
$827$	21.5000	−	37.2391i	0.747628	−	1.29493i	0.948957	−	0.315406i	$-0.102141\pi$
$828$	12.0000	−	20.7846i	0.417029	−	0.722315i
$829$	46.0000			1.59765			0.798823	−	0.601566i	$-0.205456\pi$
$829$	46.0000			1.59765			0.798823	+	0.601566i	$0.205456\pi$
$830$	−2.50000	−	4.33013i	−0.0867763	−	0.150301i
$831$	3.00000	+	5.19615i	0.104069	+	0.180253i
$832$	−2.50000	+	4.33013i	−0.0866719	+	0.150120i
$833$	6.00000			0.207888
$834$		0			0
$835$	−19.0000			−0.657522
$836$	−21.0000			−0.726300
$837$	18.0000	+	46.7654i	0.622171	+	1.61645i
$838$	−28.0000			−0.967244
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$	4.50000	+	7.79423i	0.155265	+	0.268926i
$841$	−25.0000			−0.862069
$842$	7.50000	−	12.9904i	0.258467	−	0.447678i
$843$	−45.0000	−	77.9423i	−1.54988	−	2.68447i
$844$	0.500000	+	0.866025i	0.0172107	+	0.0298098i
$845$	12.0000			0.412813
$846$	24.0000	−	41.5692i	0.825137	−	1.42918i
$847$	−3.00000	+	5.19615i	−0.103081	+	0.178542i
$848$	1.50000	−	2.59808i	0.0515102	−	0.0892183i
$849$	−6.00000	−	10.3923i	−0.205919	−	0.356663i
$850$	6.00000	−	10.3923i	0.205798	−	0.356453i
$851$	2.00000	+	3.46410i	0.0685591	+	0.118748i
$852$	−3.00000			−0.102778
$853$	14.0000			0.479351			0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000			0.479351			0.239675	+	0.970853i	$0.422959\pi$
$854$	9.00000	+	15.5885i	0.307974	+	0.533426i
$855$	−21.0000	+	36.3731i	−0.718185	+	1.24393i
$856$	6.50000	+	11.2583i	0.222165	+	0.384802i
$857$	10.5000	−	18.1865i	0.358673	−	0.621240i	−0.629066	−	0.777352i	$-0.716563\pi$
$857$	10.5000	−	18.1865i	0.358673	−	0.621240i	0.987739	+	0.156112i	$0.0498959\pi$
$858$	22.5000	−	38.9711i	0.768137	−	1.33045i
$859$	−0.500000	+	0.866025i	−0.0170598	+	0.0295484i	−0.874429	−	0.485153i	$-0.838764\pi$
$859$	−0.500000	+	0.866025i	−0.0170598	+	0.0295484i	0.857369	+	0.514701i	$0.172097\pi$
$860$	−1.00000			−0.0340997
$861$	−40.5000	−	70.1481i	−1.38024	−	2.39064i
$862$	−2.50000	−	4.33013i	−0.0851503	−	0.147485i
$863$	−1.50000	+	2.59808i	−0.0510606	+	0.0884395i	−0.890426	−	0.455128i	$-0.849593\pi$
$863$	−1.50000	+	2.59808i	−0.0510606	+	0.0884395i	0.839365	+	0.543568i	$0.182927\pi$
$864$	9.00000			0.306186
$865$	−0.500000	−	0.866025i	−0.0170005	−	0.0294457i
$866$	14.0000			0.475739
$867$	−24.0000			−0.815083
$868$	−10.5000	+	12.9904i	−0.356393	+	0.440922i
$869$	−3.00000			−0.101768
$870$	6.00000			0.203419
$871$	7.50000	+	12.9904i	0.254128	+	0.440162i
$872$	−2.00000			−0.0677285
$873$	−42.0000	+	72.7461i	−1.42148	+	2.46208i
$874$	14.0000	+	24.2487i	0.473557	+	0.820225i
$875$	−13.5000	−	23.3827i	−0.456383	−	0.790479i
$876$	21.0000			0.709524
$877$	5.50000	−	9.52628i	0.185722	−	0.321680i	−0.758098	−	0.652141i	$-0.773871\pi$
$877$	5.50000	−	9.52628i	0.185722	−	0.321680i	0.943820	+	0.330461i	$0.107204\pi$
$878$	6.50000	−	11.2583i	0.219364	−	0.379950i
$879$	28.5000	−	49.3634i	0.961281	−	1.66499i
$880$	1.50000	+	2.59808i	0.0505650	+	0.0875811i
$881$	−9.50000	+	16.4545i	−0.320063	+	0.554366i	−0.980501	−	0.196515i	$-0.937037\pi$
$881$	−9.50000	+	16.4545i	−0.320063	+	0.554366i	0.660438	+	0.750881i	$0.270371\pi$
$882$	−6.00000	−	10.3923i	−0.202031	−	0.349927i
$883$	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
$885$	−4.50000	−	7.79423i	−0.151266	−	0.262000i
$886$	5.50000	−	9.52628i	0.184776	−	0.320042i
$887$	−10.5000	−	18.1865i	−0.352555	−	0.610644i	0.634141	−	0.773217i	$-0.281354\pi$
$887$	−10.5000	−	18.1865i	−0.352555	−	0.610644i	−0.986696	+	0.162573i	$0.948021\pi$
$888$	−1.50000	+	2.59808i	−0.0503367	+	0.0871857i
$889$	19.5000	−	33.7750i	0.654009	−	1.13278i
$890$	−3.00000	+	5.19615i	−0.100560	+	0.174175i
$891$	−27.0000			−0.904534
$892$	9.50000	+	16.4545i	0.318084	+	0.550937i
$893$	28.0000	+	48.4974i	0.936984	+	1.62290i
$894$	−1.50000	+	2.59808i	−0.0501675	+	0.0868927i
$895$	19.0000			0.635100
$896$	1.50000	+	2.59808i	0.0501115	+	0.0867956i
$897$	−60.0000			−2.00334
$898$	30.0000			1.00111
$899$	4.00000	+	10.3923i	0.133407	+	0.346603i
$900$	−24.0000			−0.800000
$901$	−9.00000			−0.299833
$902$	−13.5000	−	23.3827i	−0.449501	−	0.778558i
$903$	9.00000			0.299501
$904$	0.500000	−	0.866025i	0.0166298	−	0.0288036i
$905$	−2.50000	−	4.33013i	−0.0831028	−	0.143938i
$906$	24.0000	+	41.5692i	0.797347	+	1.38104i
$907$	12.0000			0.398453			0.199227	−	0.979953i	$-0.436157\pi$
$907$	12.0000			0.398453			0.199227	+	0.979953i	$0.436157\pi$
$908$	−10.5000	+	18.1865i	−0.348455	+	0.603541i
$909$	30.0000	−	51.9615i	0.995037	−	1.72345i
$910$	7.50000	−	12.9904i	0.248623	−	0.430627i
$911$	7.50000	+	12.9904i	0.248486	+	0.430391i	0.963106	−	0.269122i	$-0.0867336\pi$
$911$	7.50000	+	12.9904i	0.248486	+	0.430391i	−0.714620	+	0.699513i	$0.753400\pi$
$912$	−10.5000	+	18.1865i	−0.347690	+	0.602216i
$913$	7.50000	+	12.9904i	0.248214	+	0.429919i
$914$	10.0000			0.330771
$915$	18.0000			0.595062
$916$	3.50000	+	6.06218i	0.115643	+	0.200300i
$917$	−31.5000	+	54.5596i	−1.04022	+	1.80172i
$918$	−13.5000	−	23.3827i	−0.445566	−	0.771744i
$919$	−29.5000	+	51.0955i	−0.973115	+	1.68548i	−0.287096	+	0.957902i	$0.592690\pi$
$919$	−29.5000	+	51.0955i	−0.973115	+	1.68548i	−0.686020	+	0.727583i	$0.740644\pi$
$920$	2.00000	−	3.46410i	0.0659380	−	0.114208i
$921$	7.50000	−	12.9904i	0.247133	−	0.428048i
$922$	−42.0000			−1.38320
$923$	2.50000	+	4.33013i	0.0822885	+	0.142528i
$924$	−13.5000	−	23.3827i	−0.444117	−	0.769234i
$925$	2.00000	−	3.46410i	0.0657596	−	0.113899i
$926$	16.0000			0.525793
$927$	39.0000	+	67.5500i	1.28093	+	2.21863i
$928$	2.00000			0.0656532
$929$	34.0000			1.11550			0.557752	−	0.830008i	$-0.311664\pi$
$929$	34.0000			1.11550			0.557752	+	0.830008i	$0.311664\pi$
$930$	6.00000	+	15.5885i	0.196748	+	0.511166i
$931$	14.0000			0.458831
$932$	−18.0000			−0.589610
$933$	−48.0000	−	83.1384i	−1.57145	−	2.72183i
$934$	−8.00000			−0.261768
$935$	4.50000	−	7.79423i	0.147166	−	0.254899i
$936$	−15.0000	−	25.9808i	−0.490290	−	0.849208i
$937$	−11.5000	−	19.9186i	−0.375689	−	0.650712i	0.614741	−	0.788729i	$-0.289260\pi$
$937$	−11.5000	−	19.9186i	−0.375689	−	0.650712i	−0.990430	+	0.138017i	$0.955927\pi$
$938$	9.00000			0.293860
$939$	−10.5000	+	18.1865i	−0.342655	+	0.593495i
$940$	4.00000	−	6.92820i	0.130466	−	0.225973i
$941$	−10.5000	+	18.1865i	−0.342290	+	0.592864i	−0.984858	−	0.173365i	$-0.944536\pi$
$941$	−10.5000	+	18.1865i	−0.342290	+	0.592864i	0.642567	+	0.766229i	$0.277869\pi$
$942$	15.0000	+	25.9808i	0.488726	+	0.846499i
$943$	−18.0000	+	31.1769i	−0.586161	+	1.01526i
$944$	−1.50000	−	2.59808i	−0.0488208	−	0.0845602i
$945$	−27.0000			−0.878310
$946$	3.00000			0.0975384
$947$	6.50000	+	11.2583i	0.211222	+	0.365847i	0.952097	−	0.305796i	$-0.0989225\pi$
$947$	6.50000	+	11.2583i	0.211222	+	0.365847i	−0.740875	+	0.671642i	$0.765589\pi$
$948$	−1.50000	+	2.59808i	−0.0487177	+	0.0843816i
$949$	−17.5000	−	30.3109i	−0.568074	−	0.983933i
$950$	14.0000	−	24.2487i	0.454220	−	0.786732i
$951$	−43.5000	+	75.3442i	−1.41058	+	2.44320i
$952$	4.50000	−	7.79423i	0.145846	−	0.252612i
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$	9.00000	+	15.5885i	0.291386	+	0.504695i
$955$	−1.50000	−	2.59808i	−0.0485389	−	0.0840718i
$956$	0.500000	−	0.866025i	0.0161712	−	0.0280093i
$957$	−18.0000			−0.581857
$958$	5.50000	+	9.52628i	0.177697	+	0.307780i
$959$	−33.0000			−1.06563
$960$	3.00000			0.0968246
$961$	−23.0000	+	20.7846i	−0.741935	+	0.670471i
$962$	5.00000			0.161206
$963$	−78.0000			−2.51351
$964$	12.5000	+	21.6506i	0.402598	+	0.697320i
$965$	19.0000			0.611632
$966$	−18.0000	+	31.1769i	−0.579141	+	1.00310i
$967$	−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	$0.900363\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$	63.0000			2.02385
$970$	−7.00000	+	12.1244i	−0.224756	+	0.389290i
$971$	−0.500000	+	0.866025i	−0.0160458	+	0.0277921i	−0.873937	−	0.486040i	$-0.838441\pi$
$971$	−0.500000	+	0.866025i	−0.0160458	+	0.0277921i	0.857891	+	0.513832i	$0.171774\pi$
$972$		0			0
$973$		0			0
$974$	−5.50000	+	9.52628i	−0.176231	+	0.305242i
$975$	30.0000	+	51.9615i	0.960769	+	1.66410i
$976$	6.00000			0.192055
$977$	54.0000			1.72761			0.863807	−	0.503824i	$-0.168074\pi$
$977$	54.0000			1.72761			0.863807	+	0.503824i	$0.168074\pi$
$978$	6.00000	+	10.3923i	0.191859	+	0.332309i
$979$	9.00000	−	15.5885i	0.287641	−	0.498209i
$980$	−1.00000	−	1.73205i	−0.0319438	−	0.0553283i
$981$	6.00000	−	10.3923i	0.191565	−	0.331801i
$982$	7.50000	−	12.9904i	0.239335	−	0.414540i
$983$	24.5000	−	42.4352i	0.781429	−	1.35347i	−0.149681	−	0.988734i	$-0.547825\pi$
$983$	24.5000	−	42.4352i	0.781429	−	1.35347i	0.931110	−	0.364740i	$-0.118842\pi$
$984$	−27.0000			−0.860729
$985$	7.50000	+	12.9904i	0.238970	+	0.413908i
$986$	−3.00000	−	5.19615i	−0.0955395	−	0.165479i
$987$	−36.0000	+	62.3538i	−1.14589	+	1.98474i
$988$	35.0000			1.11350
$989$	−2.00000	−	3.46410i	−0.0635963	−	0.110152i
$990$	−18.0000			−0.572078
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$	2.00000	+	5.19615i	0.0635001	+	0.164978i
$993$	51.0000			1.61844
$994$	3.00000			0.0951542
$995$	10.5000	+	18.1865i	0.332872	+	0.576552i
$996$	15.0000			0.475293
$997$	17.5000	−	30.3109i	0.554231	−	0.959955i	−0.443732	−	0.896159i	$-0.646346\pi$
$997$	17.5000	−	30.3109i	0.554231	−	0.959955i	0.997963	−	0.0637961i	$-0.0203207\pi$
$998$	−7.50000	−	12.9904i	−0.237408	−	0.411203i
$999$	−4.50000	−	7.79423i	−0.142374	−	0.246598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.2.c.b.25.1	yes	2
3.2	odd	2		558.2.e.b.397.1		2
4.3	odd	2		496.2.i.g.273.1		2
5.2	odd	4		1550.2.p.a.149.2		4
5.3	odd	4		1550.2.p.a.149.1		4
5.4	even	2		1550.2.e.d.1451.1		2
31.5	even	3	inner	62.2.c.b.5.1	✓	2
31.6	odd	6		1922.2.a.c.1.1		1
31.25	even	3		1922.2.a.e.1.1		1
93.5	odd	6		558.2.e.b.253.1		2
124.67	odd	6		496.2.i.g.129.1		2
155.67	odd	12		1550.2.p.a.749.2		4
155.98	odd	12		1550.2.p.a.749.1		4
155.129	even	6		1550.2.e.d.501.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.2.c.b.5.1	✓	2	31.5	even	3	inner
62.2.c.b.25.1	yes	2	1.1	even	1	trivial
496.2.i.g.129.1		2	124.67	odd	6
496.2.i.g.273.1		2	4.3	odd	2
558.2.e.b.253.1		2	93.5	odd	6
558.2.e.b.397.1		2	3.2	odd	2
1550.2.e.d.501.1		2	155.129	even	6
1550.2.e.d.1451.1		2	5.4	even	2
1550.2.p.a.149.1		4	5.3	odd	4
1550.2.p.a.149.2		4	5.2	odd	4
1550.2.p.a.749.1		4	155.98	odd	12
1550.2.p.a.749.2		4	155.67	odd	12
1922.2.a.c.1.1		1	31.6	odd	6
1922.2.a.e.1.1		1	31.25	even	3

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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	62.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.50000 - 2.59808i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 2.59808i) q^{6} +(1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.50000 - 2.59808i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 2.59808i) q^{6} +(1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(1.50000 - 2.59808i) q^{11} +(-1.50000 - 2.59808i) q^{12} +(-2.50000 + 4.33013i) q^{13} +(1.50000 + 2.59808i) q^{14} +3.00000 q^{15} +1.00000 q^{16} +(-1.50000 - 2.59808i) q^{17} +(-3.00000 + 5.19615i) q^{18} +(-3.50000 - 6.06218i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(4.50000 - 7.79423i) q^{21} +(1.50000 - 2.59808i) q^{22} -4.00000 q^{23} +(-1.50000 - 2.59808i) q^{24} +(2.00000 + 3.46410i) q^{25} +(-2.50000 + 4.33013i) q^{26} +9.00000 q^{27} +(1.50000 + 2.59808i) q^{28} +2.00000 q^{29} +3.00000 q^{30} +(2.00000 + 5.19615i) q^{31} +1.00000 q^{32} -9.00000 q^{33} +(-1.50000 - 2.59808i) q^{34} -3.00000 q^{35} +(-3.00000 + 5.19615i) q^{36} +(-0.500000 - 0.866025i) q^{37} +(-3.50000 - 6.06218i) q^{38} +15.0000 q^{39} +(-0.500000 + 0.866025i) q^{40} +(4.50000 - 7.79423i) q^{41} +(4.50000 - 7.79423i) q^{42} +(0.500000 + 0.866025i) q^{43} +(1.50000 - 2.59808i) q^{44} +(-3.00000 - 5.19615i) q^{45} -4.00000 q^{46} -8.00000 q^{47} +(-1.50000 - 2.59808i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(2.00000 + 3.46410i) q^{50} +(-4.50000 + 7.79423i) q^{51} +(-2.50000 + 4.33013i) q^{52} +(1.50000 - 2.59808i) q^{53} +9.00000 q^{54} +(1.50000 + 2.59808i) q^{55} +(1.50000 + 2.59808i) q^{56} +(-10.5000 + 18.1865i) q^{57} +2.00000 q^{58} +(-1.50000 - 2.59808i) q^{59} +3.00000 q^{60} +6.00000 q^{61} +(2.00000 + 5.19615i) q^{62} -18.0000 q^{63} +1.00000 q^{64} +(-2.50000 - 4.33013i) q^{65} -9.00000 q^{66} +(1.50000 - 2.59808i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(6.00000 + 10.3923i) q^{69} -3.00000 q^{70} +(0.500000 - 0.866025i) q^{71} +(-3.00000 + 5.19615i) q^{72} +(-3.50000 + 6.06218i) q^{73} +(-0.500000 - 0.866025i) q^{74} +(6.00000 - 10.3923i) q^{75} +(-3.50000 - 6.06218i) q^{76} +9.00000 q^{77} +15.0000 q^{78} +(-0.500000 - 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(4.50000 - 7.79423i) q^{82} +(-2.50000 + 4.33013i) q^{83} +(4.50000 - 7.79423i) q^{84} +3.00000 q^{85} +(0.500000 + 0.866025i) q^{86} +(-3.00000 - 5.19615i) q^{87} +(1.50000 - 2.59808i) q^{88} +6.00000 q^{89} +(-3.00000 - 5.19615i) q^{90} -15.0000 q^{91} -4.00000 q^{92} +(10.5000 - 12.9904i) q^{93} -8.00000 q^{94} +7.00000 q^{95} +(-1.50000 - 2.59808i) q^{96} +14.0000 q^{97} +(-1.00000 + 1.73205i) q^{98} +(9.00000 + 15.5885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - q^{5} - 3 q^{6} + 3 q^{7} + 2 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - q^5 - 3 * q^6 + 3 * q^7 + 2 * q^8 - 6 * q^9	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - q^{5} - 3 q^{6} + 3 q^{7} + 2 q^{8} - 6 q^{9} - q^{10} + 3 q^{11} - 3 q^{12} - 5 q^{13} + 3 q^{14} + 6 q^{15} + 2 q^{16} - 3 q^{17} - 6 q^{18} - 7 q^{19} - q^{20} + 9 q^{21} + 3 q^{22} - 8 q^{23} - 3 q^{24} + 4 q^{25} - 5 q^{26} + 18 q^{27} + 3 q^{28} + 4 q^{29} + 6 q^{30} + 4 q^{31} + 2 q^{32} - 18 q^{33} - 3 q^{34} - 6 q^{35} - 6 q^{36} - q^{37} - 7 q^{38} + 30 q^{39} - q^{40} + 9 q^{41} + 9 q^{42} + q^{43} + 3 q^{44} - 6 q^{45} - 8 q^{46} - 16 q^{47} - 3 q^{48} - 2 q^{49} + 4 q^{50} - 9 q^{51} - 5 q^{52} + 3 q^{53} + 18 q^{54} + 3 q^{55} + 3 q^{56} - 21 q^{57} + 4 q^{58} - 3 q^{59} + 6 q^{60} + 12 q^{61} + 4 q^{62} - 36 q^{63} + 2 q^{64} - 5 q^{65} - 18 q^{66} + 3 q^{67} - 3 q^{68} + 12 q^{69} - 6 q^{70} + q^{71} - 6 q^{72} - 7 q^{73} - q^{74} + 12 q^{75} - 7 q^{76} + 18 q^{77} + 30 q^{78} - q^{79} - q^{80} - 9 q^{81} + 9 q^{82} - 5 q^{83} + 9 q^{84} + 6 q^{85} + q^{86} - 6 q^{87} + 3 q^{88} + 12 q^{89} - 6 q^{90} - 30 q^{91} - 8 q^{92} + 21 q^{93} - 16 q^{94} + 14 q^{95} - 3 q^{96} + 28 q^{97} - 2 q^{98} + 18 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - q^5 - 3 * q^6 + 3 * q^7 + 2 * q^8 - 6 * q^9 - q^10 + 3 * q^11 - 3 * q^12 - 5 * q^13 + 3 * q^14 + 6 * q^15 + 2 * q^16 - 3 * q^17 - 6 * q^18 - 7 * q^19 - q^20 + 9 * q^21 + 3 * q^22 - 8 * q^23 - 3 * q^24 + 4 * q^25 - 5 * q^26 + 18 * q^27 + 3 * q^28 + 4 * q^29 + 6 * q^30 + 4 * q^31 + 2 * q^32 - 18 * q^33 - 3 * q^34 - 6 * q^35 - 6 * q^36 - q^37 - 7 * q^38 + 30 * q^39 - q^40 + 9 * q^41 + 9 * q^42 + q^43 + 3 * q^44 - 6 * q^45 - 8 * q^46 - 16 * q^47 - 3 * q^48 - 2 * q^49 + 4 * q^50 - 9 * q^51 - 5 * q^52 + 3 * q^53 + 18 * q^54 + 3 * q^55 + 3 * q^56 - 21 * q^57 + 4 * q^58 - 3 * q^59 + 6 * q^60 + 12 * q^61 + 4 * q^62 - 36 * q^63 + 2 * q^64 - 5 * q^65 - 18 * q^66 + 3 * q^67 - 3 * q^68 + 12 * q^69 - 6 * q^70 + q^71 - 6 * q^72 - 7 * q^73 - q^74 + 12 * q^75 - 7 * q^76 + 18 * q^77 + 30 * q^78 - q^79 - q^80 - 9 * q^81 + 9 * q^82 - 5 * q^83 + 9 * q^84 + 6 * q^85 + q^86 - 6 * q^87 + 3 * q^88 + 12 * q^89 - 6 * q^90 - 30 * q^91 - 8 * q^92 + 21 * q^93 - 16 * q^94 + 14 * q^95 - 3 * q^96 + 28 * q^97 - 2 * q^98 + 18 * q^99

Introduction

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