LMFDB - Embedded newform 930.2.i.j.811.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(211,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("930.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.i (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			811.2
Root			$1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	930.811
Dual form			930.2.i.j.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-1.00000 - 1.73205i) q^{13} +(0.500000 - 0.866025i) q^{14} +1.00000 q^{15} +1.00000 q^{16} +(3.64575 - 6.31463i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-3.64575 + 6.31463i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-0.500000 - 0.866025i) q^{21} +(-0.500000 - 0.866025i) q^{22} +7.29150 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} +1.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} +4.29150 q^{29} -1.00000 q^{30} +(-4.14575 + 3.71655i) q^{31} -1.00000 q^{32} -1.00000 q^{33} +(-3.64575 + 6.31463i) q^{34} +1.00000 q^{35} +(-0.500000 - 0.866025i) q^{36} +(4.64575 - 8.04668i) q^{37} +(3.64575 - 6.31463i) q^{38} +2.00000 q^{39} +(0.500000 + 0.866025i) q^{40} +(2.64575 + 4.58258i) q^{41} +(0.500000 + 0.866025i) q^{42} +(2.00000 - 3.46410i) q^{43} +(0.500000 + 0.866025i) q^{44} +(-0.500000 + 0.866025i) q^{45} -7.29150 q^{46} -0.708497 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.00000 + 5.19615i) q^{49} +(0.500000 - 0.866025i) q^{50} +(3.64575 + 6.31463i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-1.50000 - 2.59808i) q^{53} -1.00000 q^{54} +(0.500000 - 0.866025i) q^{55} +(0.500000 - 0.866025i) q^{56} +(-3.64575 - 6.31463i) q^{57} -4.29150 q^{58} +(3.50000 - 6.06218i) q^{59} +1.00000 q^{60} +7.29150 q^{61} +(4.14575 - 3.71655i) q^{62} +1.00000 q^{63} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +1.00000 q^{66} +(4.64575 + 8.04668i) q^{67} +(3.64575 - 6.31463i) q^{68} +(-3.64575 + 6.31463i) q^{69} -1.00000 q^{70} +(3.29150 + 5.70105i) q^{71} +(0.500000 + 0.866025i) q^{72} +(8.29150 + 14.3613i) q^{73} +(-4.64575 + 8.04668i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(-3.64575 + 6.31463i) q^{76} -1.00000 q^{77} -2.00000 q^{78} +(4.00000 - 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.64575 - 4.58258i) q^{82} +(1.14575 + 1.98450i) q^{83} +(-0.500000 - 0.866025i) q^{84} -7.29150 q^{85} +(-2.00000 + 3.46410i) q^{86} +(-2.14575 + 3.71655i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(0.500000 - 0.866025i) q^{90} +2.00000 q^{91} +7.29150 q^{92} +(-1.14575 - 5.44860i) q^{93} +0.708497 q^{94} +7.29150 q^{95} +(0.500000 - 0.866025i) q^{96} +0.291503 q^{97} +(-3.00000 - 5.19615i) q^{98} +(0.500000 - 0.866025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9	\( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} - 2 q^{12} - 4 q^{13} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 4 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} - 2 q^{21} - 2 q^{22} + 8 q^{23} + 2 q^{24} - 2 q^{25} + 4 q^{26} + 4 q^{27} - 2 q^{28} - 4 q^{29} - 4 q^{30} - 6 q^{31} - 4 q^{32} - 4 q^{33} - 4 q^{34} + 4 q^{35} - 2 q^{36} + 8 q^{37} + 4 q^{38} + 8 q^{39} + 2 q^{40} + 2 q^{42} + 8 q^{43} + 2 q^{44} - 2 q^{45} - 8 q^{46} - 24 q^{47} - 2 q^{48} + 12 q^{49} + 2 q^{50} + 4 q^{51} - 4 q^{52} - 6 q^{53} - 4 q^{54} + 2 q^{55} + 2 q^{56} - 4 q^{57} + 4 q^{58} + 14 q^{59} + 4 q^{60} + 8 q^{61} + 6 q^{62} + 4 q^{63} + 4 q^{64} - 4 q^{65} + 4 q^{66} + 8 q^{67} + 4 q^{68} - 4 q^{69} - 4 q^{70} - 8 q^{71} + 2 q^{72} + 12 q^{73} - 8 q^{74} - 2 q^{75} - 4 q^{76} - 4 q^{77} - 8 q^{78} + 16 q^{79} - 2 q^{80} - 2 q^{81} - 6 q^{83} - 2 q^{84} - 8 q^{85} - 8 q^{86} + 2 q^{87} - 2 q^{88} + 2 q^{90} + 8 q^{91} + 8 q^{92} + 6 q^{93} + 24 q^{94} + 8 q^{95} + 2 q^{96} - 20 q^{97} - 12 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9 + 2 * q^10 + 2 * q^11 - 2 * q^12 - 4 * q^13 + 2 * q^14 + 4 * q^15 + 4 * q^16 + 4 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 - 2 * q^21 - 2 * q^22 + 8 * q^23 + 2 * q^24 - 2 * q^25 + 4 * q^26 + 4 * q^27 - 2 * q^28 - 4 * q^29 - 4 * q^30 - 6 * q^31 - 4 * q^32 - 4 * q^33 - 4 * q^34 + 4 * q^35 - 2 * q^36 + 8 * q^37 + 4 * q^38 + 8 * q^39 + 2 * q^40 + 2 * q^42 + 8 * q^43 + 2 * q^44 - 2 * q^45 - 8 * q^46 - 24 * q^47 - 2 * q^48 + 12 * q^49 + 2 * q^50 + 4 * q^51 - 4 * q^52 - 6 * q^53 - 4 * q^54 + 2 * q^55 + 2 * q^56 - 4 * q^57 + 4 * q^58 + 14 * q^59 + 4 * q^60 + 8 * q^61 + 6 * q^62 + 4 * q^63 + 4 * q^64 - 4 * q^65 + 4 * q^66 + 8 * q^67 + 4 * q^68 - 4 * q^69 - 4 * q^70 - 8 * q^71 + 2 * q^72 + 12 * q^73 - 8 * q^74 - 2 * q^75 - 4 * q^76 - 4 * q^77 - 8 * q^78 + 16 * q^79 - 2 * q^80 - 2 * q^81 - 6 * q^83 - 2 * q^84 - 8 * q^85 - 8 * q^86 + 2 * q^87 - 2 * q^88 + 2 * q^90 + 8 * q^91 + 8 * q^92 + 6 * q^93 + 24 * q^94 + 8 * q^95 + 2 * q^96 - 20 * q^97 - 12 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$2$	−1.00000			−0.707107
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	1.00000			0.500000
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i	0.755929	+	0.654654i	$0.227186\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$	1.00000			0.258199
$16$	1.00000			0.250000
$17$	3.64575	−	6.31463i	0.884225	−	1.53152i	0.0376247	−	0.999292i	$-0.488021\pi$
$17$	3.64575	−	6.31463i	0.884225	−	1.53152i	0.846600	−	0.532230i	$-0.178646\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−3.64575	+	6.31463i	−0.836393	+	1.44867i	0.0564987	+	0.998403i	$0.482006\pi$
$19$	−3.64575	+	6.31463i	−0.836393	+	1.44867i	−0.892891	+	0.450272i	$0.851327\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	−0.500000	−	0.866025i	−0.109109	−	0.188982i
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	7.29150			1.52038			0.760192	−	0.649699i	$-0.225105\pi$
$23$	7.29150			1.52038			0.760192	+	0.649699i	$0.225105\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.00000	+	1.73205i	0.196116	+	0.339683i
$27$	1.00000			0.192450
$28$	−0.500000	+	0.866025i	−0.0944911	+	0.163663i
$29$	4.29150			0.796912			0.398456	−	0.917187i	$-0.369546\pi$
$29$	4.29150			0.796912			0.398456	+	0.917187i	$0.369546\pi$
$30$	−1.00000			−0.182574
$31$	−4.14575	+	3.71655i	−0.744599	+	0.667512i
$31$	−4.14575	+	3.71655i	−0.744599	+	0.667512i
$32$	−1.00000			−0.176777
$33$	−1.00000			−0.174078
$34$	−3.64575	+	6.31463i	−0.625241	+	1.08295i
$35$	1.00000			0.169031
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	4.64575	−	8.04668i	0.763757	−	1.32287i	−0.177145	−	0.984185i	$-0.556686\pi$
$37$	4.64575	−	8.04668i	0.763757	−	1.32287i	0.940901	−	0.338681i	$-0.109981\pi$
$38$	3.64575	−	6.31463i	0.591419	−	1.02437i
$39$	2.00000			0.320256
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	2.64575	+	4.58258i	0.413197	+	0.715678i	0.995237	−	0.0974818i	$-0.0310788\pi$
$41$	2.64575	+	4.58258i	0.413197	+	0.715678i	−0.582040	+	0.813160i	$0.697745\pi$
$42$	0.500000	+	0.866025i	0.0771517	+	0.133631i
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	−0.672264	−	0.740312i	$-0.734678\pi$
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	0.977261	+	0.212041i	$0.0680112\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	−7.29150			−1.07507
$47$	−0.708497			−0.103345			−0.0516725	−	0.998664i	$-0.516455\pi$
$47$	−0.708497			−0.103345			−0.0516725	+	0.998664i	$0.516455\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	3.64575	+	6.31463i	0.510507	+	0.884225i
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	0.744423	−	0.667708i	$-0.232725\pi$
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	−0.950464	+	0.310835i	$0.899391\pi$
$54$	−1.00000			−0.136083
$55$	0.500000	−	0.866025i	0.0674200	−	0.116775i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$	−3.64575	−	6.31463i	−0.482892	−	0.836393i
$58$	−4.29150			−0.563502
$59$	3.50000	−	6.06218i	0.455661	−	0.789228i	−0.543065	−	0.839691i	$-0.682736\pi$
$59$	3.50000	−	6.06218i	0.455661	−	0.789228i	0.998726	+	0.0504625i	$0.0160695\pi$
$60$	1.00000			0.129099
$61$	7.29150			0.933581			0.466791	−	0.884368i	$-0.345410\pi$
$61$	7.29150			0.933581			0.466791	+	0.884368i	$0.345410\pi$
$62$	4.14575	−	3.71655i	0.526511	−	0.472002i
$63$	1.00000			0.125988
$64$	1.00000			0.125000
$65$	−1.00000	+	1.73205i	−0.124035	+	0.214834i
$66$	1.00000			0.123091
$67$	4.64575	+	8.04668i	0.567569	+	0.983058i	0.996806	+	0.0798661i	$0.0254493\pi$
$67$	4.64575	+	8.04668i	0.567569	+	0.983058i	−0.429237	+	0.903192i	$0.641217\pi$
$68$	3.64575	−	6.31463i	0.442112	−	0.765761i
$69$	−3.64575	+	6.31463i	−0.438897	+	0.760192i
$70$	−1.00000			−0.119523
$71$	3.29150	+	5.70105i	0.390629	+	0.676590i	0.992533	−	0.121979i	$-0.0389240\pi$
$71$	3.29150	+	5.70105i	0.390629	+	0.676590i	−0.601903	+	0.798569i	$0.705591\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	8.29150	+	14.3613i	0.970447	+	1.68086i	0.694208	+	0.719775i	$0.255755\pi$
$73$	8.29150	+	14.3613i	0.970447	+	1.68086i	0.276239	+	0.961089i	$0.410912\pi$
$74$	−4.64575	+	8.04668i	−0.540058	+	0.935407i
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$	−3.64575	+	6.31463i	−0.418196	+	0.724337i
$77$	−1.00000			−0.113961
$78$	−2.00000			−0.226455
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	−0.548352	−	0.836247i	$-0.684745\pi$
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	0.998388	+	0.0567635i	$0.0180781\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.64575	−	4.58258i	−0.292174	−	0.506061i
$83$	1.14575	+	1.98450i	0.125763	+	0.217827i	0.922031	−	0.387117i	$-0.126529\pi$
$83$	1.14575	+	1.98450i	0.125763	+	0.217827i	−0.796268	+	0.604944i	$0.793196\pi$
$84$	−0.500000	−	0.866025i	−0.0545545	−	0.0944911i
$85$	−7.29150			−0.790875
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$	−2.14575	+	3.71655i	−0.230049	+	0.398456i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$	0.500000	−	0.866025i	0.0527046	−	0.0912871i
$91$	2.00000			0.209657
$92$	7.29150			0.760192
$93$	−1.14575	−	5.44860i	−0.118809	−	0.564994i
$94$	0.708497			0.0730759
$95$	7.29150			0.748092
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	0.291503			0.0295976			0.0147988	−	0.999890i	$-0.495289\pi$
$97$	0.291503			0.0295976			0.0147988	+	0.999890i	$0.495289\pi$
$98$	−3.00000	−	5.19615i	−0.303046	−	0.524891i
$99$	0.500000	−	0.866025i	0.0502519	−	0.0870388i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	12.2915			1.22305			0.611525	−	0.791225i	$-0.290556\pi$
$101$	12.2915			1.22305			0.611525	+	0.791225i	$0.290556\pi$
$102$	−3.64575	−	6.31463i	−0.360983	−	0.625241i
$103$	8.79150	+	15.2273i	0.866252	+	1.50039i	0.865798	+	0.500393i	$0.166811\pi$
$103$	8.79150	+	15.2273i	0.866252	+	1.50039i	0.000454358		1.00000i	$0.499855\pi$
$104$	1.00000	+	1.73205i	0.0980581	+	0.169842i
$105$	−0.500000	+	0.866025i	−0.0487950	+	0.0845154i
$106$	1.50000	+	2.59808i	0.145693	+	0.252347i
$107$	5.14575	−	8.91270i	0.497459	−	0.861623i	−0.502537	−	0.864556i	$-0.667600\pi$
$107$	5.14575	−	8.91270i	0.497459	−	0.861623i	0.999996	+	0.00293213i	$0.000933326\pi$
$108$	1.00000			0.0962250
$109$	−15.2915			−1.46466			−0.732330	−	0.680950i	$-0.761567\pi$
$109$	−15.2915			−1.46466			−0.732330	+	0.680950i	$0.761567\pi$
$110$	−0.500000	+	0.866025i	−0.0476731	+	0.0825723i
$111$	4.64575	+	8.04668i	0.440955	+	0.763757i
$112$	−0.500000	+	0.866025i	−0.0472456	+	0.0818317i
$113$	6.29150	+	10.8972i	0.591855	+	1.02512i	0.993983	+	0.109539i	$0.0349374\pi$
$113$	6.29150	+	10.8972i	0.591855	+	1.02512i	−0.402128	+	0.915584i	$0.631729\pi$
$114$	3.64575	+	6.31463i	0.341456	+	0.591419i
$115$	−3.64575	−	6.31463i	−0.339968	−	0.588842i
$116$	4.29150			0.398456
$117$	−1.00000	+	1.73205i	−0.0924500	+	0.160128i
$118$	−3.50000	+	6.06218i	−0.322201	+	0.558069i
$119$	3.64575	+	6.31463i	0.334205	+	0.578861i
$120$	−1.00000			−0.0912871
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$	−7.29150			−0.660142
$123$	−5.29150			−0.477119
$124$	−4.14575	+	3.71655i	−0.372299	+	0.333756i
$125$	1.00000			0.0894427
$126$	−1.00000			−0.0890871
$127$	5.79150	−	10.0312i	0.513913	−	0.890123i	−0.485957	−	0.873983i	$-0.661529\pi$
$127$	5.79150	−	10.0312i	0.513913	−	0.890123i	0.999870	−	0.0161403i	$-0.00513783\pi$
$128$	−1.00000			−0.0883883
$129$	2.00000	+	3.46410i	0.176090	+	0.304997i
$130$	1.00000	−	1.73205i	0.0877058	−	0.151911i
$131$	4.00000	−	6.92820i	0.349482	−	0.605320i	−0.636676	−	0.771132i	$-0.719691\pi$
$131$	4.00000	−	6.92820i	0.349482	−	0.605320i	0.986157	+	0.165812i	$0.0530244\pi$
$132$	−1.00000			−0.0870388
$133$	−3.64575	−	6.31463i	−0.316127	−	0.547548i
$134$	−4.64575	−	8.04668i	−0.401332	−	0.695127i
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$	−3.64575	+	6.31463i	−0.312621	+	0.541475i
$137$	−7.93725	−	13.7477i	−0.678125	−	1.17455i	−0.975545	−	0.219801i	$-0.929459\pi$
$137$	−7.93725	−	13.7477i	−0.678125	−	1.17455i	0.297419	−	0.954747i	$-0.403874\pi$
$138$	3.64575	−	6.31463i	0.310347	−	0.537537i
$139$	1.29150			0.109544			0.0547719	−	0.998499i	$-0.482557\pi$
$139$	1.29150			0.109544			0.0547719	+	0.998499i	$0.482557\pi$
$140$	1.00000			0.0845154
$141$	0.354249	−	0.613577i	0.0298331	−	0.0516725i
$142$	−3.29150	−	5.70105i	−0.276217	−	0.478421i
$143$	1.00000	−	1.73205i	0.0836242	−	0.144841i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−2.14575	−	3.71655i	−0.178195	−	0.308643i
$146$	−8.29150	−	14.3613i	−0.686210	−	1.18855i
$147$	−6.00000			−0.494872
$148$	4.64575	−	8.04668i	0.381878	−	0.661433i
$149$	0.145751	−	0.252449i	0.0119404	−	0.0206814i	−0.859993	−	0.510305i	$-0.829532\pi$
$149$	0.145751	−	0.252449i	0.0119404	−	0.0206814i	0.871934	+	0.489624i	$0.162866\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	2.29150			0.186480			0.0932399	−	0.995644i	$-0.470278\pi$
$151$	2.29150			0.186480			0.0932399	+	0.995644i	$0.470278\pi$
$152$	3.64575	−	6.31463i	0.295709	−	0.512184i
$153$	−7.29150			−0.589483
$154$	1.00000			0.0805823
$155$	5.29150	+	1.73205i	0.425024	+	0.139122i
$156$	2.00000			0.160128
$157$	−19.2915			−1.53963			−0.769815	−	0.638267i	$-0.779651\pi$
$157$	−19.2915			−1.53963			−0.769815	+	0.638267i	$0.779651\pi$
$158$	−4.00000	+	6.92820i	−0.318223	+	0.551178i
$159$	3.00000			0.237915
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−3.64575	+	6.31463i	−0.287325	+	0.497662i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	−21.8745			−1.71334			−0.856672	−	0.515862i	$-0.827472\pi$
$163$	−21.8745			−1.71334			−0.856672	+	0.515862i	$0.827472\pi$
$164$	2.64575	+	4.58258i	0.206598	+	0.357839i
$165$	0.500000	+	0.866025i	0.0389249	+	0.0674200i
$166$	−1.14575	−	1.98450i	−0.0889275	−	0.154027i
$167$	−3.35425	+	5.80973i	−0.259560	+	0.449570i	−0.966124	−	0.258078i	$-0.916911\pi$
$167$	−3.35425	+	5.80973i	−0.259560	+	0.449570i	0.706564	+	0.707649i	$0.250244\pi$
$168$	0.500000	+	0.866025i	0.0385758	+	0.0668153i
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	7.29150			0.559233
$171$	7.29150			0.557595
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	5.50000	+	9.52628i	0.418157	+	0.724270i	0.995754	−	0.0920525i	$-0.0293428\pi$
$173$	5.50000	+	9.52628i	0.418157	+	0.724270i	−0.577597	+	0.816322i	$0.696009\pi$
$174$	2.14575	−	3.71655i	0.162669	−	0.281751i
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	0.500000	+	0.866025i	0.0376889	+	0.0652791i
$177$	3.50000	+	6.06218i	0.263076	+	0.455661i
$178$		0			0
$179$	−0.500000	+	0.866025i	−0.0373718	+	0.0647298i	−0.884106	−	0.467286i	$-0.845232\pi$
$179$	−0.500000	+	0.866025i	−0.0373718	+	0.0647298i	0.846735	+	0.532016i	$0.178565\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	−3.29150	−	5.70105i	−0.244655	−	0.423756i	0.717379	−	0.696683i	$-0.245342\pi$
$181$	−3.29150	−	5.70105i	−0.244655	−	0.423756i	−0.962035	+	0.272927i	$0.912008\pi$
$182$	−2.00000			−0.148250
$183$	−3.64575	+	6.31463i	−0.269502	+	0.466791i
$184$	−7.29150			−0.537537
$185$	−9.29150			−0.683125
$186$	1.14575	+	5.44860i	0.0840106	+	0.399511i
$187$	7.29150			0.533207
$188$	−0.708497			−0.0516725
$189$	−0.500000	+	0.866025i	−0.0363696	+	0.0629941i
$190$	−7.29150			−0.528981
$191$	−7.93725	−	13.7477i	−0.574320	−	0.994751i	−0.996115	−	0.0880597i	$-0.971933\pi$
$191$	−7.93725	−	13.7477i	−0.574320	−	0.994751i	0.421796	−	0.906691i	$-0.361400\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	4.14575	−	7.18065i	0.298418	−	0.516875i	−0.677356	−	0.735655i	$-0.736874\pi$
$193$	4.14575	−	7.18065i	0.298418	−	0.516875i	0.975774	+	0.218780i	$0.0702078\pi$
$194$	−0.291503			−0.0209287
$195$	−1.00000	−	1.73205i	−0.0716115	−	0.124035i
$196$	3.00000	+	5.19615i	0.214286	+	0.371154i
$197$	−11.5830	−	20.0624i	−0.825255	−	1.42938i	−0.901724	−	0.432312i	$-0.857698\pi$
$197$	−11.5830	−	20.0624i	−0.825255	−	1.42938i	0.0764693	−	0.997072i	$-0.475635\pi$
$198$	−0.500000	+	0.866025i	−0.0355335	+	0.0615457i
$199$	10.1458	+	17.5730i	0.719213	+	1.24571i	0.961312	+	0.275462i	$0.0888309\pi$
$199$	10.1458	+	17.5730i	0.719213	+	1.24571i	−0.242099	+	0.970252i	$0.577836\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−9.29150			−0.655372
$202$	−12.2915			−0.864827
$203$	−2.14575	+	3.71655i	−0.150602	+	0.260851i
$204$	3.64575	+	6.31463i	0.255254	+	0.442112i
$205$	2.64575	−	4.58258i	0.184787	−	0.320061i
$206$	−8.79150	−	15.2273i	−0.612533	−	1.06094i
$207$	−3.64575	−	6.31463i	−0.253397	−	0.438897i
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$	−7.29150			−0.504364
$210$	0.500000	−	0.866025i	0.0345033	−	0.0597614i
$211$	−7.64575	+	13.2428i	−0.526355	+	0.911674i	0.473173	+	0.880969i	$0.343108\pi$
$211$	−7.64575	+	13.2428i	−0.526355	+	0.911674i	−0.999529	+	0.0307046i	$0.990225\pi$
$212$	−1.50000	−	2.59808i	−0.103020	−	0.178437i
$213$	−6.58301			−0.451060
$214$	−5.14575	+	8.91270i	−0.351756	+	0.609260i
$215$	−4.00000			−0.272798
$216$	−1.00000			−0.0680414
$217$	−1.14575	−	5.44860i	−0.0777787	−	0.369875i
$218$	15.2915			1.03567
$219$	−16.5830			−1.12058
$220$	0.500000	−	0.866025i	0.0337100	−	0.0583874i
$221$	−14.5830			−0.980959
$222$	−4.64575	−	8.04668i	−0.311802	−	0.540058i
$223$	2.20850	−	3.82523i	0.147892	−	0.256156i	−0.782556	−	0.622580i	$-0.786085\pi$
$223$	2.20850	−	3.82523i	0.147892	−	0.256156i	0.930448	+	0.366424i	$0.119418\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$	1.00000			0.0666667
$226$	−6.29150	−	10.8972i	−0.418505	−	0.724871i
$227$	−11.4373	−	19.8099i	−0.759117	−	1.31483i	−0.943301	−	0.331938i	$-0.892298\pi$
$227$	−11.4373	−	19.8099i	−0.759117	−	1.31483i	0.184184	−	0.982892i	$-0.441036\pi$
$228$	−3.64575	−	6.31463i	−0.241446	−	0.418196i
$229$	11.9373	−	20.6759i	0.788836	−	1.36630i	−0.137845	−	0.990454i	$-0.544017\pi$
$229$	11.9373	−	20.6759i	0.788836	−	1.36630i	0.926680	−	0.375850i	$-0.122649\pi$
$230$	3.64575	+	6.31463i	0.240394	+	0.416374i
$231$	0.500000	−	0.866025i	0.0328976	−	0.0569803i
$232$	−4.29150			−0.281751
$233$	−19.8745			−1.30202			−0.651011	−	0.759068i	$-0.725655\pi$
$233$	−19.8745			−1.30202			−0.651011	+	0.759068i	$0.725655\pi$
$234$	1.00000	−	1.73205i	0.0653720	−	0.113228i
$235$	0.354249	+	0.613577i	0.0231086	+	0.0400253i
$236$	3.50000	−	6.06218i	0.227831	−	0.394614i
$237$	4.00000	+	6.92820i	0.259828	+	0.450035i
$238$	−3.64575	−	6.31463i	−0.236319	−	0.409316i
$239$	2.29150	+	3.96900i	0.148225	+	0.256733i	0.930571	−	0.366110i	$-0.119311\pi$
$239$	2.29150	+	3.96900i	0.148225	+	0.256733i	−0.782347	+	0.622843i	$0.785977\pi$
$240$	1.00000			0.0645497
$241$	−12.7915	+	22.1555i	−0.823973	+	1.42716i	0.0787285	+	0.996896i	$0.474914\pi$
$241$	−12.7915	+	22.1555i	−0.823973	+	1.42716i	−0.902702	+	0.430267i	$0.858419\pi$
$242$	−5.00000	+	8.66025i	−0.321412	+	0.556702i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	7.29150			0.466791
$245$	3.00000	−	5.19615i	0.191663	−	0.331970i
$246$	5.29150			0.337374
$247$	14.5830			0.927894
$248$	4.14575	−	3.71655i	0.263255	−	0.236001i
$249$	−2.29150			−0.145218
$250$	−1.00000			−0.0632456
$251$	−10.0000	+	17.3205i	−0.631194	+	1.09326i	0.356113	+	0.934443i	$0.384102\pi$
$251$	−10.0000	+	17.3205i	−0.631194	+	1.09326i	−0.987308	+	0.158818i	$0.949232\pi$
$252$	1.00000			0.0629941
$253$	3.64575	+	6.31463i	0.229206	+	0.396997i
$254$	−5.79150	+	10.0312i	−0.363391	+	0.629412i
$255$	3.64575	−	6.31463i	0.228306	−	0.395437i
$256$	1.00000			0.0625000
$257$	−10.9373	−	18.9439i	−0.682247	−	1.18169i	−0.974293	−	0.225283i	$-0.927669\pi$
$257$	−10.9373	−	18.9439i	−0.682247	−	1.18169i	0.292046	−	0.956404i	$-0.405664\pi$
$258$	−2.00000	−	3.46410i	−0.124515	−	0.215666i
$259$	4.64575	+	8.04668i	0.288673	+	0.499996i
$260$	−1.00000	+	1.73205i	−0.0620174	+	0.107417i
$261$	−2.14575	−	3.71655i	−0.132819	−	0.230049i
$262$	−4.00000	+	6.92820i	−0.247121	+	0.428026i
$263$	12.5830			0.775901			0.387951	−	0.921680i	$-0.373183\pi$
$263$	12.5830			0.775901			0.387951	+	0.921680i	$0.373183\pi$
$264$	1.00000			0.0615457
$265$	−1.50000	+	2.59808i	−0.0921443	+	0.159599i
$266$	3.64575	+	6.31463i	0.223535	+	0.387175i
$267$		0			0
$268$	4.64575	+	8.04668i	0.283784	+	0.491529i
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	0.942871	−	0.333157i	$-0.108114\pi$
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	−0.759958	+	0.649972i	$0.774781\pi$
$270$	0.500000	+	0.866025i	0.0304290	+	0.0527046i
$271$	−16.2915			−0.989638			−0.494819	−	0.868996i	$-0.664766\pi$
$271$	−16.2915			−0.989638			−0.494819	+	0.868996i	$0.664766\pi$
$272$	3.64575	−	6.31463i	0.221056	−	0.382880i
$273$	−1.00000	+	1.73205i	−0.0605228	+	0.104828i
$274$	7.93725	+	13.7477i	0.479507	+	0.830531i
$275$	−1.00000			−0.0603023
$276$	−3.64575	+	6.31463i	−0.219448	+	0.380096i
$277$	11.2915			0.678441			0.339220	−	0.940707i	$-0.389837\pi$
$277$	11.2915			0.678441			0.339220	+	0.940707i	$0.389837\pi$
$278$	−1.29150			−0.0774592
$279$	5.29150	+	1.73205i	0.316794	+	0.103695i
$280$	−1.00000			−0.0597614
$281$	−12.0000			−0.715860			−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000			−0.715860			−0.357930	+	0.933748i	$0.616517\pi$
$282$	−0.354249	+	0.613577i	−0.0210952	+	0.0365380i
$283$	14.0000			0.832214			0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000			0.832214			0.416107	+	0.909316i	$0.363394\pi$
$284$	3.29150	+	5.70105i	0.195315	+	0.338295i
$285$	−3.64575	+	6.31463i	−0.215956	+	0.374046i
$286$	−1.00000	+	1.73205i	−0.0591312	+	0.102418i
$287$	−5.29150			−0.312348
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−18.0830	−	31.3207i	−1.06371	−	1.84239i
$290$	2.14575	+	3.71655i	0.126003	+	0.218243i
$291$	−0.145751	+	0.252449i	−0.00854409	+	0.0147988i
$292$	8.29150	+	14.3613i	0.485223	+	0.840432i
$293$	1.20850	−	2.09318i	0.0706012	−	0.122285i	−0.828564	−	0.559895i	$-0.810842\pi$
$293$	1.20850	−	2.09318i	0.0706012	−	0.122285i	0.899165	+	0.437610i	$0.144175\pi$
$294$	6.00000			0.349927
$295$	−7.00000			−0.407556
$296$	−4.64575	+	8.04668i	−0.270029	+	0.467704i
$297$	0.500000	+	0.866025i	0.0290129	+	0.0502519i
$298$	−0.145751	+	0.252449i	−0.00844315	+	0.0146240i
$299$	−7.29150	−	12.6293i	−0.421678	−	0.730369i
$300$	−0.500000	−	0.866025i	−0.0288675	−	0.0500000i
$301$	2.00000	+	3.46410i	0.115278	+	0.199667i
$302$	−2.29150			−0.131861
$303$	−6.14575	+	10.6448i	−0.353064	+	0.611525i
$304$	−3.64575	+	6.31463i	−0.209098	+	0.362169i
$305$	−3.64575	−	6.31463i	−0.208755	−	0.361574i
$306$	7.29150			0.416827
$307$	14.6458	−	25.3672i	0.835877	−	1.44778i	−0.0574371	−	0.998349i	$-0.518293\pi$
$307$	14.6458	−	25.3672i	0.835877	−	1.44778i	0.893314	−	0.449433i	$-0.148374\pi$
$308$	−1.00000			−0.0569803
$309$	−17.5830			−1.00026
$310$	−5.29150	−	1.73205i	−0.300537	−	0.0983739i
$311$	18.0000			1.02069			0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000			1.02069			0.510343	+	0.859971i	$0.329518\pi$
$312$	−2.00000			−0.113228
$313$	−13.1458	+	22.7691i	−0.743042	+	1.28699i	0.208062	+	0.978116i	$0.433284\pi$
$313$	−13.1458	+	22.7691i	−0.743042	+	1.28699i	−0.951104	+	0.308871i	$0.900049\pi$
$314$	19.2915			1.08868
$315$	−0.500000	−	0.866025i	−0.0281718	−	0.0487950i
$316$	4.00000	−	6.92820i	0.225018	−	0.389742i
$317$	−14.7915	+	25.6196i	−0.830774	+	1.43894i	0.0666521	+	0.997776i	$0.478768\pi$
$317$	−14.7915	+	25.6196i	−0.830774	+	1.43894i	−0.897426	+	0.441166i	$0.854565\pi$
$318$	−3.00000			−0.168232
$319$	2.14575	+	3.71655i	0.120139	+	0.208087i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	5.14575	+	8.91270i	0.287208	+	0.497459i
$322$	3.64575	−	6.31463i	0.203170	−	0.351900i
$323$	26.5830	+	46.0431i	1.47912	+	2.56191i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	2.00000			0.110940
$326$	21.8745			1.21152
$327$	7.64575	−	13.2428i	0.422811	−	0.732330i
$328$	−2.64575	−	4.58258i	−0.146087	−	0.253030i
$329$	0.354249	−	0.613577i	0.0195304	−	0.0338276i
$330$	−0.500000	−	0.866025i	−0.0275241	−	0.0476731i
$331$	−10.9373	−	18.9439i	−0.601166	−	1.04125i	−0.992645	−	0.121063i	$-0.961370\pi$
$331$	−10.9373	−	18.9439i	−0.601166	−	1.04125i	0.391479	−	0.920187i	$-0.371964\pi$
$332$	1.14575	+	1.98450i	0.0628813	+	0.108914i
$333$	−9.29150			−0.509171
$334$	3.35425	−	5.80973i	0.183536	−	0.317894i
$335$	4.64575	−	8.04668i	0.253825	−	0.439637i
$336$	−0.500000	−	0.866025i	−0.0272772	−	0.0472456i
$337$	16.8745			0.919213			0.459607	−	0.888123i	$-0.347990\pi$
$337$	16.8745			0.919213			0.459607	+	0.888123i	$0.347990\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$	−12.5830			−0.683415
$340$	−7.29150			−0.395437
$341$	−5.29150	−	1.73205i	−0.286551	−	0.0937958i
$342$	−7.29150			−0.394279
$343$	−13.0000			−0.701934
$344$	−2.00000	+	3.46410i	−0.107833	+	0.186772i
$345$	7.29150			0.392561
$346$	−5.50000	−	9.52628i	−0.295682	−	0.512136i
$347$	2.14575	−	3.71655i	0.115190	−	0.199515i	−0.802666	−	0.596429i	$-0.796586\pi$
$347$	2.14575	−	3.71655i	0.115190	−	0.199515i	0.917856	+	0.396914i	$0.129919\pi$
$348$	−2.14575	+	3.71655i	−0.115024	+	0.199228i
$349$	28.4575			1.52330			0.761648	−	0.647991i	$-0.224391\pi$
$349$	28.4575			1.52330			0.761648	+	0.647991i	$0.224391\pi$
$350$	0.500000	+	0.866025i	0.0267261	+	0.0462910i
$351$	−1.00000	−	1.73205i	−0.0533761	−	0.0924500i
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	−5.58301	+	9.67005i	−0.297153	+	0.514685i	−0.975484	−	0.220072i	$-0.929371\pi$
$353$	−5.58301	+	9.67005i	−0.297153	+	0.514685i	0.678330	+	0.734757i	$0.262704\pi$
$354$	−3.50000	−	6.06218i	−0.186023	−	0.322201i
$355$	3.29150	−	5.70105i	0.174695	−	0.302580i
$356$		0			0
$357$	−7.29150			−0.385907
$358$	0.500000	−	0.866025i	0.0264258	−	0.0457709i
$359$	2.35425	+	4.07768i	0.124252	+	0.215212i	0.921441	−	0.388520i	$-0.127013\pi$
$359$	2.35425	+	4.07768i	0.124252	+	0.215212i	−0.797188	+	0.603731i	$0.793680\pi$
$360$	0.500000	−	0.866025i	0.0263523	−	0.0456435i
$361$	−17.0830	−	29.5886i	−0.899106	−	1.55730i
$362$	3.29150	+	5.70105i	0.172998	+	0.299641i
$363$	5.00000	+	8.66025i	0.262432	+	0.454545i
$364$	2.00000			0.104828
$365$	8.29150	−	14.3613i	0.433997	−	0.751705i
$366$	3.64575	−	6.31463i	0.190566	−	0.330071i
$367$	4.58301	+	7.93800i	0.239231	+	0.414360i	0.960494	−	0.278301i	$-0.0897714\pi$
$367$	4.58301	+	7.93800i	0.239231	+	0.414360i	−0.721263	+	0.692661i	$0.756438\pi$
$368$	7.29150			0.380096
$369$	2.64575	−	4.58258i	0.137732	−	0.238559i
$370$	9.29150			0.483042
$371$	3.00000			0.155752
$372$	−1.14575	−	5.44860i	−0.0594044	−	0.282497i
$373$	−16.7085			−0.865133			−0.432567	−	0.901602i	$-0.642392\pi$
$373$	−16.7085			−0.865133			−0.432567	+	0.901602i	$0.642392\pi$
$374$	−7.29150			−0.377035
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$	0.708497			0.0365380
$377$	−4.29150	−	7.43310i	−0.221024	−	0.382824i
$378$	0.500000	−	0.866025i	0.0257172	−	0.0445435i
$379$	−17.2915	+	29.9498i	−0.888205	+	1.53842i	−0.0462090	+	0.998932i	$0.514714\pi$
$379$	−17.2915	+	29.9498i	−0.888205	+	1.53842i	−0.841996	+	0.539484i	$0.818619\pi$
$380$	7.29150			0.374046
$381$	5.79150	+	10.0312i	0.296708	+	0.513913i
$382$	7.93725	+	13.7477i	0.406105	+	0.703395i
$383$	−11.3542	−	19.6661i	−0.580175	−	1.00489i	−0.995458	−	0.0952004i	$-0.969651\pi$
$383$	−11.3542	−	19.6661i	−0.580175	−	1.00489i	0.415283	−	0.909692i	$-0.363683\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	0.500000	+	0.866025i	0.0254824	+	0.0441367i
$386$	−4.14575	+	7.18065i	−0.211013	+	0.365486i
$387$	−4.00000			−0.203331
$388$	0.291503			0.0147988
$389$	−1.00000	+	1.73205i	−0.0507020	+	0.0878185i	−0.890263	−	0.455448i	$-0.849479\pi$
$389$	−1.00000	+	1.73205i	−0.0507020	+	0.0878185i	0.839561	+	0.543266i	$0.182813\pi$
$390$	1.00000	+	1.73205i	0.0506370	+	0.0877058i
$391$	26.5830	−	46.0431i	1.34436	−	2.32850i
$392$	−3.00000	−	5.19615i	−0.151523	−	0.262445i
$393$	4.00000	+	6.92820i	0.201773	+	0.349482i
$394$	11.5830	+	20.0624i	0.583543	+	1.01073i
$395$	−8.00000			−0.402524
$396$	0.500000	−	0.866025i	0.0251259	−	0.0435194i
$397$	14.5830	−	25.2585i	0.731900	−	1.26769i	−0.224170	−	0.974550i	$-0.571967\pi$
$397$	14.5830	−	25.2585i	0.731900	−	1.26769i	0.956070	−	0.293138i	$-0.0946996\pi$
$398$	−10.1458	−	17.5730i	−0.508561	−	0.880853i
$399$	7.29150			0.365032
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	35.1660			1.75611			0.878053	−	0.478563i	$-0.158842\pi$
$401$	35.1660			1.75611			0.878053	+	0.478563i	$0.158842\pi$
$402$	9.29150			0.463418
$403$	10.5830	+	3.46410i	0.527177	+	0.172559i
$404$	12.2915			0.611525
$405$	1.00000			0.0496904
$406$	2.14575	−	3.71655i	0.106492	−	0.184449i
$407$	9.29150			0.460563
$408$	−3.64575	−	6.31463i	−0.180492	−	0.312621i
$409$	4.50000	−	7.79423i	0.222511	−	0.385400i	−0.733059	−	0.680165i	$-0.761908\pi$
$409$	4.50000	−	7.79423i	0.222511	−	0.385400i	0.955570	+	0.294765i	$0.0952414\pi$
$410$	−2.64575	+	4.58258i	−0.130664	+	0.226317i
$411$	15.8745			0.783032
$412$	8.79150	+	15.2273i	0.433126	+	0.750197i
$413$	3.50000	+	6.06218i	0.172224	+	0.298300i
$414$	3.64575	+	6.31463i	0.179179	+	0.310347i
$415$	1.14575	−	1.98450i	0.0562427	−	0.0974152i
$416$	1.00000	+	1.73205i	0.0490290	+	0.0849208i
$417$	−0.645751	+	1.11847i	−0.0316226	+	0.0547719i
$418$	7.29150			0.356639
$419$	5.58301			0.272748			0.136374	−	0.990657i	$-0.456455\pi$
$419$	5.58301			0.272748			0.136374	+	0.990657i	$0.456455\pi$
$420$	−0.500000	+	0.866025i	−0.0243975	+	0.0422577i
$421$	15.6458	+	27.0992i	0.762527	+	1.32074i	0.941544	+	0.336890i	$0.109375\pi$
$421$	15.6458	+	27.0992i	0.762527	+	1.32074i	−0.179017	+	0.983846i	$0.557292\pi$
$422$	7.64575	−	13.2428i	0.372189	−	0.644651i
$423$	0.354249	+	0.613577i	0.0172242	+	0.0298331i
$424$	1.50000	+	2.59808i	0.0728464	+	0.126174i
$425$	3.64575	+	6.31463i	0.176845	+	0.306304i
$426$	6.58301			0.318948
$427$	−3.64575	+	6.31463i	−0.176430	+	0.305586i
$428$	5.14575	−	8.91270i	0.248729	−	0.430812i
$429$	1.00000	+	1.73205i	0.0482805	+	0.0836242i
$430$	4.00000			0.192897
$431$	4.64575	−	8.04668i	0.223778	−	0.387595i	−0.732174	−	0.681117i	$-0.761494\pi$
$431$	4.64575	−	8.04668i	0.223778	−	0.387595i	0.955952	+	0.293523i	$0.0948276\pi$
$432$	1.00000			0.0481125
$433$	22.0000			1.05725			0.528626	−	0.848855i	$-0.322707\pi$
$433$	22.0000			1.05725			0.528626	+	0.848855i	$0.322707\pi$
$434$	1.14575	+	5.44860i	0.0549978	+	0.261541i
$435$	4.29150			0.205762
$436$	−15.2915			−0.732330
$437$	−26.5830	+	46.0431i	−1.27164	+	2.20254i
$438$	16.5830			0.792367
$439$	2.14575	+	3.71655i	0.102411	+	0.177381i	0.912678	−	0.408680i	$-0.134011\pi$
$439$	2.14575	+	3.71655i	0.102411	+	0.177381i	−0.810266	+	0.586062i	$0.800678\pi$
$440$	−0.500000	+	0.866025i	−0.0238366	+	0.0412861i
$441$	3.00000	−	5.19615i	0.142857	−	0.247436i
$442$	14.5830			0.693643
$443$	−4.70850	−	8.15536i	−0.223707	−	0.387473i	0.732223	−	0.681065i	$-0.238483\pi$
$443$	−4.70850	−	8.15536i	−0.223707	−	0.387473i	−0.955931	+	0.293592i	$0.905149\pi$
$444$	4.64575	+	8.04668i	0.220478	+	0.381878i
$445$		0			0
$446$	−2.20850	+	3.82523i	−0.104575	+	0.181130i
$447$	0.145751	+	0.252449i	0.00689380	+	0.0119404i
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	−26.5830			−1.25453			−0.627265	−	0.778806i	$-0.715826\pi$
$449$	−26.5830			−1.25453			−0.627265	+	0.778806i	$0.715826\pi$
$450$	−1.00000			−0.0471405
$451$	−2.64575	+	4.58258i	−0.124584	+	0.215785i
$452$	6.29150	+	10.8972i	0.295927	+	0.512561i
$453$	−1.14575	+	1.98450i	−0.0538321	+	0.0932399i
$454$	11.4373	+	19.8099i	0.536777	+	0.929725i
$455$	−1.00000	−	1.73205i	−0.0468807	−	0.0811998i
$456$	3.64575	+	6.31463i	0.170728	+	0.295709i
$457$	7.16601			0.335212			0.167606	−	0.985854i	$-0.446396\pi$
$457$	7.16601			0.335212			0.167606	+	0.985854i	$0.446396\pi$
$458$	−11.9373	+	20.6759i	−0.557791	+	0.966123i
$459$	3.64575	−	6.31463i	0.170169	−	0.294742i
$460$	−3.64575	−	6.31463i	−0.169984	−	0.294421i
$461$	−4.29150			−0.199875			−0.0999376	−	0.994994i	$-0.531864\pi$
$461$	−4.29150			−0.199875			−0.0999376	+	0.994994i	$0.531864\pi$
$462$	−0.500000	+	0.866025i	−0.0232621	+	0.0402911i
$463$	15.0000			0.697109			0.348555	−	0.937288i	$-0.386673\pi$
$463$	15.0000			0.697109			0.348555	+	0.937288i	$0.386673\pi$
$464$	4.29150			0.199228
$465$	−4.14575	+	3.71655i	−0.192255	+	0.172351i
$466$	19.8745			0.920669
$467$	−6.29150			−0.291136			−0.145568	−	0.989348i	$-0.546501\pi$
$467$	−6.29150			−0.291136			−0.145568	+	0.989348i	$0.546501\pi$
$468$	−1.00000	+	1.73205i	−0.0462250	+	0.0800641i
$469$	−9.29150			−0.429042
$470$	−0.354249	−	0.613577i	−0.0163403	−	0.0283022i
$471$	9.64575	−	16.7069i	0.444453	−	0.769815i
$472$	−3.50000	+	6.06218i	−0.161101	+	0.279034i
$473$	4.00000			0.183920
$474$	−4.00000	−	6.92820i	−0.183726	−	0.318223i
$475$	−3.64575	−	6.31463i	−0.167279	−	0.289735i
$476$	3.64575	+	6.31463i	0.167103	+	0.289430i
$477$	−1.50000	+	2.59808i	−0.0686803	+	0.118958i
$478$	−2.29150	−	3.96900i	−0.104811	−	0.181538i
$479$	12.3542	−	21.3982i	0.564480	−	0.977708i	−0.432618	−	0.901577i	$-0.642410\pi$
$479$	12.3542	−	21.3982i	0.564480	−	0.977708i	0.997098	−	0.0761307i	$-0.0242566\pi$
$480$	−1.00000			−0.0456435
$481$	−18.5830			−0.847312
$482$	12.7915	−	22.1555i	0.582637	−	1.00916i
$483$	−3.64575	−	6.31463i	−0.165887	−	0.287325i
$484$	5.00000	−	8.66025i	0.227273	−	0.393648i
$485$	−0.145751	−	0.252449i	−0.00661823	−	0.0114631i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	8.08301	+	14.0002i	0.366276	+	0.634409i	0.988980	−	0.148049i	$-0.0472993\pi$
$487$	8.08301	+	14.0002i	0.366276	+	0.634409i	−0.622704	+	0.782457i	$0.713966\pi$
$488$	−7.29150			−0.330071
$489$	10.9373	−	18.9439i	0.494600	−	0.856672i
$490$	−3.00000	+	5.19615i	−0.135526	+	0.234738i
$491$	−6.20850	−	10.7534i	−0.280186	−	0.485296i	0.691245	−	0.722621i	$-0.257063\pi$
$491$	−6.20850	−	10.7534i	−0.280186	−	0.485296i	−0.971430	+	0.237325i	$0.923729\pi$
$492$	−5.29150			−0.238559
$493$	15.6458	−	27.0992i	0.704649	−	1.22049i
$494$	−14.5830			−0.656120
$495$	−1.00000			−0.0449467
$496$	−4.14575	+	3.71655i	−0.186150	+	0.166878i
$497$	−6.58301			−0.295288
$498$	2.29150			0.102685
$499$	4.64575	−	8.04668i	0.207972	−	0.360219i	−0.743103	−	0.669177i	$-0.766647\pi$
$499$	4.64575	−	8.04668i	0.207972	−	0.360219i	0.951076	+	0.308958i	$0.0999802\pi$
$500$	1.00000			0.0447214
$501$	−3.35425	−	5.80973i	−0.149857	−	0.259560i
$502$	10.0000	−	17.3205i	0.446322	−	0.773052i
$503$	10.6458	−	18.4390i	0.474671	−	0.822154i	−0.524909	−	0.851159i	$-0.675901\pi$
$503$	10.6458	−	18.4390i	0.474671	−	0.822154i	0.999579	+	0.0290050i	$0.00923386\pi$
$504$	−1.00000			−0.0445435
$505$	−6.14575	−	10.6448i	−0.273482	−	0.473685i
$506$	−3.64575	−	6.31463i	−0.162073	−	0.280719i
$507$	4.50000	+	7.79423i	0.199852	+	0.346154i
$508$	5.79150	−	10.0312i	0.256956	−	0.445062i
$509$	19.1458	+	33.1614i	0.848621	+	1.46985i	0.882440	+	0.470426i	$0.155900\pi$
$509$	19.1458	+	33.1614i	0.848621	+	1.46985i	−0.0338190	+	0.999428i	$0.510767\pi$
$510$	−3.64575	+	6.31463i	−0.161437	+	0.279616i
$511$	−16.5830			−0.733589
$512$	−1.00000			−0.0441942
$513$	−3.64575	+	6.31463i	−0.160964	+	0.278798i
$514$	10.9373	+	18.9439i	0.482422	+	0.835579i
$515$	8.79150	−	15.2273i	0.387400	−	0.670996i
$516$	2.00000	+	3.46410i	0.0880451	+	0.152499i
$517$	−0.354249	−	0.613577i	−0.0155798	−	0.0269851i
$518$	−4.64575	−	8.04668i	−0.204123	−	0.353551i
$519$	−11.0000			−0.482846
$520$	1.00000	−	1.73205i	0.0438529	−	0.0759555i
$521$	−18.8745	+	32.6916i	−0.826907	+	1.43225i	0.0735457	+	0.997292i	$0.476569\pi$
$521$	−18.8745	+	32.6916i	−0.826907	+	1.43225i	−0.900453	+	0.434953i	$0.856765\pi$
$522$	2.14575	+	3.71655i	0.0939170	+	0.162669i
$523$	−37.1660			−1.62516			−0.812578	−	0.582852i	$-0.801937\pi$
$523$	−37.1660			−1.62516			−0.812578	+	0.582852i	$0.801937\pi$
$524$	4.00000	−	6.92820i	0.174741	−	0.302660i
$525$	1.00000			0.0436436
$526$	−12.5830			−0.548645
$527$	8.35425	+	39.7285i	0.363917	+	1.73060i
$528$	−1.00000			−0.0435194
$529$	30.1660			1.31157
$530$	1.50000	−	2.59808i	0.0651558	−	0.112853i
$531$	−7.00000			−0.303774
$532$	−3.64575	−	6.31463i	−0.158063	−	0.273774i
$533$	5.29150	−	9.16515i	0.229200	−	0.396987i
$534$		0			0
$535$	−10.2915			−0.444940
$536$	−4.64575	−	8.04668i	−0.200666	−	0.347564i
$537$	−0.500000	−	0.866025i	−0.0215766	−	0.0373718i
$538$	−3.00000	−	5.19615i	−0.129339	−	0.224022i
$539$	−3.00000	+	5.19615i	−0.129219	+	0.223814i
$540$	−0.500000	−	0.866025i	−0.0215166	−	0.0372678i
$541$	−8.35425	+	14.4700i	−0.359177	+	0.622113i	−0.987824	−	0.155578i	$-0.950276\pi$
$541$	−8.35425	+	14.4700i	−0.359177	+	0.622113i	0.628646	+	0.777691i	$0.283609\pi$
$542$	16.2915			0.699780
$543$	6.58301			0.282504
$544$	−3.64575	+	6.31463i	−0.156310	+	0.270737i
$545$	7.64575	+	13.2428i	0.327508	+	0.567261i
$546$	1.00000	−	1.73205i	0.0427960	−	0.0741249i
$547$	14.5830	+	25.2585i	0.623524	+	1.07998i	0.988824	+	0.149086i	$0.0476331\pi$
$547$	14.5830	+	25.2585i	0.623524	+	1.07998i	−0.365300	+	0.930890i	$0.619034\pi$
$548$	−7.93725	−	13.7477i	−0.339063	−	0.587274i
$549$	−3.64575	−	6.31463i	−0.155597	−	0.269502i
$550$	1.00000			0.0426401
$551$	−15.6458	+	27.0992i	−0.666531	+	1.15447i
$552$	3.64575	−	6.31463i	0.155173	−	0.268768i
$553$	4.00000	+	6.92820i	0.170097	+	0.294617i
$554$	−11.2915			−0.479730
$555$	4.64575	−	8.04668i	0.197201	−	0.341562i
$556$	1.29150			0.0547719
$557$	−22.7490			−0.963907			−0.481953	−	0.876197i	$-0.660073\pi$
$557$	−22.7490			−0.963907			−0.481953	+	0.876197i	$0.660073\pi$
$558$	−5.29150	−	1.73205i	−0.224007	−	0.0733236i
$559$	−8.00000			−0.338364
$560$	1.00000			0.0422577
$561$	−3.64575	+	6.31463i	−0.153924	+	0.266604i
$562$	12.0000			0.506189
$563$	21.4373	+	37.1304i	0.903473	+	1.56486i	0.822955	+	0.568107i	$0.192324\pi$
$563$	21.4373	+	37.1304i	0.903473	+	1.56486i	0.0805180	+	0.996753i	$0.474343\pi$
$564$	0.354249	−	0.613577i	0.0149166	−	0.0258362i
$565$	6.29150	−	10.8972i	0.264686	−	0.458449i
$566$	−14.0000			−0.588464
$567$	−0.500000	−	0.866025i	−0.0209980	−	0.0363696i
$568$	−3.29150	−	5.70105i	−0.138108	−	0.239211i
$569$	1.70850	+	2.95920i	0.0716239	+	0.124056i	0.899613	−	0.436688i	$-0.143849\pi$
$569$	1.70850	+	2.95920i	0.0716239	+	0.124056i	−0.827989	+	0.560744i	$0.810515\pi$
$570$	3.64575	−	6.31463i	0.152704	−	0.264491i
$571$	8.70850	+	15.0836i	0.364439	+	0.631227i	0.988686	−	0.150000i	$-0.0479273\pi$
$571$	8.70850	+	15.0836i	0.364439	+	0.631227i	−0.624247	+	0.781227i	$0.714594\pi$
$572$	1.00000	−	1.73205i	0.0418121	−	0.0724207i
$573$	15.8745			0.663167
$574$	5.29150			0.220863
$575$	−3.64575	+	6.31463i	−0.152038	+	0.263338i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−18.8745	+	32.6916i	−0.785756	+	1.36097i	0.142790	+	0.989753i	$0.454393\pi$
$577$	−18.8745	+	32.6916i	−0.785756	+	1.36097i	−0.928546	+	0.371216i	$0.878941\pi$
$578$	18.0830	+	31.3207i	0.752154	+	1.30277i
$579$	4.14575	+	7.18065i	0.172292	+	0.298418i
$580$	−2.14575	−	3.71655i	−0.0890975	−	0.154321i
$581$	−2.29150			−0.0950675
$582$	0.145751	−	0.252449i	0.00604159	−	0.0104643i
$583$	1.50000	−	2.59808i	0.0621237	−	0.107601i
$584$	−8.29150	−	14.3613i	−0.343105	−	0.594275i
$585$	2.00000			0.0826898
$586$	−1.20850	+	2.09318i	−0.0499226	+	0.0864684i
$587$	−9.45751			−0.390353			−0.195177	−	0.980768i	$-0.562528\pi$
$587$	−9.45751			−0.390353			−0.195177	+	0.980768i	$0.562528\pi$
$588$	−6.00000			−0.247436
$589$	−8.35425	−	39.7285i	−0.344231	−	1.63698i
$590$	7.00000			0.288185
$591$	23.1660			0.952922
$592$	4.64575	−	8.04668i	0.190939	−	0.330716i
$593$	9.29150			0.381556			0.190778	−	0.981633i	$-0.438899\pi$
$593$	9.29150			0.381556			0.190778	+	0.981633i	$0.438899\pi$
$594$	−0.500000	−	0.866025i	−0.0205152	−	0.0355335i
$595$	3.64575	−	6.31463i	0.149461	−	0.258874i
$596$	0.145751	−	0.252449i	0.00597021	−	0.0103407i
$597$	−20.2915			−0.830476
$598$	7.29150	+	12.6293i	0.298172	+	0.516449i
$599$	15.8745	+	27.4955i	0.648615	+	1.12343i	0.983454	+	0.181158i	$0.0579847\pi$
$599$	15.8745	+	27.4955i	0.648615	+	1.12343i	−0.334839	+	0.942275i	$0.608682\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	−2.29150	+	3.96900i	−0.0934723	+	0.161899i	−0.908970	−	0.416862i	$-0.863130\pi$
$601$	−2.29150	+	3.96900i	−0.0934723	+	0.161899i	0.815498	+	0.578760i	$0.196463\pi$
$602$	−2.00000	−	3.46410i	−0.0815139	−	0.141186i
$603$	4.64575	−	8.04668i	0.189190	−	0.327686i
$604$	2.29150			0.0932399
$605$	−10.0000			−0.406558
$606$	6.14575	−	10.6448i	0.249654	−	0.432414i
$607$	10.5830	+	18.3303i	0.429551	+	0.744004i	0.996833	−	0.0795193i	$-0.0253385\pi$
$607$	10.5830	+	18.3303i	0.429551	+	0.744004i	−0.567282	+	0.823523i	$0.692005\pi$
$608$	3.64575	−	6.31463i	0.147855	−	0.256092i
$609$	−2.14575	−	3.71655i	−0.0869502	−	0.150602i
$610$	3.64575	+	6.31463i	0.147612	+	0.255672i
$611$	0.708497	+	1.22715i	0.0286627	+	0.0496453i
$612$	−7.29150			−0.294742
$613$	8.58301	−	14.8662i	0.346664	−	0.600440i	−0.638990	−	0.769215i	$-0.720648\pi$
$613$	8.58301	−	14.8662i	0.346664	−	0.600440i	0.985655	+	0.168775i	$0.0539810\pi$
$614$	−14.6458	+	25.3672i	−0.591054	+	1.02374i
$615$	2.64575	+	4.58258i	0.106687	+	0.184787i
$616$	1.00000			0.0402911
$617$	7.06275	−	12.2330i	0.284335	−	0.492483i	−0.688112	−	0.725604i	$-0.741560\pi$
$617$	7.06275	−	12.2330i	0.284335	−	0.492483i	0.972448	+	0.233121i	$0.0748937\pi$
$618$	17.5830			0.707292
$619$	16.0000			0.643094			0.321547	−	0.946894i	$-0.395797\pi$
$619$	16.0000			0.643094			0.321547	+	0.946894i	$0.395797\pi$
$620$	5.29150	+	1.73205i	0.212512	+	0.0695608i
$621$	7.29150			0.292598
$622$	−18.0000			−0.721734
$623$		0			0
$624$	2.00000			0.0800641
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	13.1458	−	22.7691i	0.525410	−	0.910037i
$627$	3.64575	−	6.31463i	0.145597	−	0.252182i
$628$	−19.2915			−0.769815
$629$	−33.8745	−	58.6724i	−1.35067	−	2.33942i
$630$	0.500000	+	0.866025i	0.0199205	+	0.0345033i
$631$	−4.43725	−	7.68555i	−0.176644	−	0.305957i	0.764085	−	0.645116i	$-0.223191\pi$
$631$	−4.43725	−	7.68555i	−0.176644	−	0.305957i	−0.940729	+	0.339159i	$0.889858\pi$
$632$	−4.00000	+	6.92820i	−0.159111	+	0.275589i
$633$	−7.64575	−	13.2428i	−0.303891	−	0.526355i
$634$	14.7915	−	25.6196i	0.587446	−	1.01749i
$635$	−11.5830			−0.459658
$636$	3.00000			0.118958
$637$	6.00000	−	10.3923i	0.237729	−	0.411758i
$638$	−2.14575	−	3.71655i	−0.0849511	−	0.147140i
$639$	3.29150	−	5.70105i	0.130210	−	0.225530i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	10.2288	+	17.7167i	0.404012	+	0.699769i	0.994206	−	0.107493i	$-0.0342822\pi$
$641$	10.2288	+	17.7167i	0.404012	+	0.699769i	−0.590194	+	0.807261i	$0.700949\pi$
$642$	−5.14575	−	8.91270i	−0.203087	−	0.351756i
$643$	−35.2915			−1.39176			−0.695881	−	0.718158i	$-0.744986\pi$
$643$	−35.2915			−1.39176			−0.695881	+	0.718158i	$0.744986\pi$
$644$	−3.64575	+	6.31463i	−0.143663	+	0.248831i
$645$	2.00000	−	3.46410i	0.0787499	−	0.136399i
$646$	−26.5830	−	46.0431i	−1.04589	−	1.81154i
$647$	−19.2915			−0.758427			−0.379214	−	0.925309i	$-0.623805\pi$
$647$	−19.2915			−0.758427			−0.379214	+	0.925309i	$0.623805\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	7.00000			0.274774
$650$	−2.00000			−0.0784465
$651$	5.29150	+	1.73205i	0.207390	+	0.0678844i
$652$	−21.8745			−0.856672
$653$	−15.0000			−0.586995			−0.293498	−	0.955960i	$-0.594819\pi$
$653$	−15.0000			−0.586995			−0.293498	+	0.955960i	$0.594819\pi$
$654$	−7.64575	+	13.2428i	−0.298973	+	0.517836i
$655$	−8.00000			−0.312586
$656$	2.64575	+	4.58258i	0.103299	+	0.178920i
$657$	8.29150	−	14.3613i	0.323482	−	0.560288i
$658$	−0.354249	+	0.613577i	−0.0138101	+	0.0239197i
$659$	−24.1660			−0.941374			−0.470687	−	0.882300i	$-0.655994\pi$
$659$	−24.1660			−0.941374			−0.470687	+	0.882300i	$0.655994\pi$
$660$	0.500000	+	0.866025i	0.0194625	+	0.0337100i
$661$	−0.354249	−	0.613577i	−0.0137787	−	0.0238654i	0.859054	−	0.511885i	$-0.171053\pi$
$661$	−0.354249	−	0.613577i	−0.0137787	−	0.0238654i	−0.872833	+	0.488020i	$0.837719\pi$
$662$	10.9373	+	18.9439i	0.425088	+	0.736275i
$663$	7.29150	−	12.6293i	0.283178	−	0.490480i
$664$	−1.14575	−	1.98450i	−0.0444638	−	0.0770135i
$665$	−3.64575	+	6.31463i	−0.141376	+	0.244871i
$666$	9.29150			0.360038
$667$	31.2915			1.21161
$668$	−3.35425	+	5.80973i	−0.129780	+	0.224785i
$669$	2.20850	+	3.82523i	0.0853854	+	0.147892i
$670$	−4.64575	+	8.04668i	−0.179481	+	0.310870i
$671$	3.64575	+	6.31463i	0.140743	+	0.243773i
$672$	0.500000	+	0.866025i	0.0192879	+	0.0334077i
$673$	−10.4373	−	18.0779i	−0.402327	−	0.696850i	0.591680	−	0.806173i	$-0.298465\pi$
$673$	−10.4373	−	18.0779i	−0.402327	−	0.696850i	−0.994006	+	0.109323i	$0.965132\pi$
$674$	−16.8745			−0.649982
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	−4.50000	−	7.79423i	−0.172949	−	0.299557i	0.766501	−	0.642244i	$-0.221996\pi$
$677$	−4.50000	−	7.79423i	−0.172949	−	0.299557i	−0.939450	+	0.342687i	$0.888663\pi$
$678$	12.5830			0.483247
$679$	−0.145751	+	0.252449i	−0.00559342	+	0.00968809i
$680$	7.29150			0.279616
$681$	22.8745			0.876553
$682$	5.29150	+	1.73205i	0.202622	+	0.0663237i
$683$	−14.8745			−0.569157			−0.284579	−	0.958653i	$-0.591854\pi$
$683$	−14.8745			−0.569157			−0.284579	+	0.958653i	$0.591854\pi$
$684$	7.29150			0.278798
$685$	−7.93725	+	13.7477i	−0.303267	+	0.525274i
$686$	13.0000			0.496342
$687$	11.9373	+	20.6759i	0.455435	+	0.788836i
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	−3.00000	+	5.19615i	−0.114291	+	0.197958i
$690$	−7.29150			−0.277583
$691$	−3.35425	−	5.80973i	−0.127602	−	0.221013i	0.795145	−	0.606419i	$-0.207395\pi$
$691$	−3.35425	−	5.80973i	−0.127602	−	0.221013i	−0.922747	+	0.385406i	$0.874061\pi$
$692$	5.50000	+	9.52628i	0.209079	+	0.362135i
$693$	0.500000	+	0.866025i	0.0189934	+	0.0328976i
$694$	−2.14575	+	3.71655i	−0.0814516	+	0.141078i
$695$	−0.645751	−	1.11847i	−0.0244947	−	0.0424261i
$696$	2.14575	−	3.71655i	0.0813345	−	0.140875i
$697$	38.5830			1.46144
$698$	−28.4575			−1.07713
$699$	9.93725	−	17.2118i	0.375861	−	0.651011i
$700$	−0.500000	−	0.866025i	−0.0188982	−	0.0327327i
$701$	13.8542	−	23.9963i	0.523268	−	0.906326i	−0.476366	−	0.879247i	$-0.658046\pi$
$701$	13.8542	−	23.9963i	0.523268	−	0.906326i	0.999633	−	0.0270790i	$-0.00862057\pi$
$702$	1.00000	+	1.73205i	0.0377426	+	0.0653720i
$703$	33.8745	+	58.6724i	1.27760	+	2.21287i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	−0.708497			−0.0266836
$706$	5.58301	−	9.67005i	0.210119	−	0.363937i
$707$	−6.14575	+	10.6448i	−0.231135	+	0.400337i
$708$	3.50000	+	6.06218i	0.131538	+	0.227831i
$709$	−9.29150			−0.348950			−0.174475	−	0.984662i	$-0.555823\pi$
$709$	−9.29150			−0.348950			−0.174475	+	0.984662i	$0.555823\pi$
$710$	−3.29150	+	5.70105i	−0.123528	+	0.213957i
$711$	−8.00000			−0.300023
$712$		0			0
$713$	−30.2288	+	27.0992i	−1.13208	+	1.01487i
$714$	7.29150			0.272878
$715$	−2.00000			−0.0747958
$716$	−0.500000	+	0.866025i	−0.0186859	+	0.0323649i
$717$	−4.58301			−0.171155
$718$	−2.35425	−	4.07768i	−0.0878598	−	0.152178i
$719$	13.9373	−	24.1400i	0.519772	−	0.900271i	−0.479964	−	0.877288i	$-0.659350\pi$
$719$	13.9373	−	24.1400i	0.519772	−	0.900271i	0.999736	−	0.0229831i	$-0.00731639\pi$
$720$	−0.500000	+	0.866025i	−0.0186339	+	0.0322749i
$721$	−17.5830			−0.654825
$722$	17.0830	+	29.5886i	0.635764	+	1.10117i
$723$	−12.7915	−	22.1555i	−0.475721	−	0.823973i
$724$	−3.29150	−	5.70105i	−0.122328	−	0.211878i
$725$	−2.14575	+	3.71655i	−0.0796912	+	0.138029i
$726$	−5.00000	−	8.66025i	−0.185567	−	0.321412i
$727$	−10.0830	+	17.4643i	−0.373958	+	0.647714i	−0.990170	−	0.139866i	$-0.955333\pi$
$727$	−10.0830	+	17.4643i	−0.373958	+	0.647714i	0.616213	+	0.787580i	$0.288666\pi$
$728$	−2.00000			−0.0741249
$729$	1.00000			0.0370370
$730$	−8.29150	+	14.3613i	−0.306882	+	0.531536i
$731$	−14.5830	−	25.2585i	−0.539372	−	0.934220i
$732$	−3.64575	+	6.31463i	−0.134751	+	0.233395i
$733$	−12.2915	−	21.2895i	−0.453997	−	0.786346i	0.544633	−	0.838675i	$-0.316669\pi$
$733$	−12.2915	−	21.2895i	−0.453997	−	0.786346i	−0.998630	+	0.0523287i	$0.983336\pi$
$734$	−4.58301	−	7.93800i	−0.169162	−	0.292997i
$735$	3.00000	+	5.19615i	0.110657	+	0.191663i
$736$	−7.29150			−0.268768
$737$	−4.64575	+	8.04668i	−0.171128	+	0.296403i
$738$	−2.64575	+	4.58258i	−0.0973915	+	0.168687i
$739$	−5.93725	−	10.2836i	−0.218405	−	0.378289i	0.735915	−	0.677074i	$-0.236752\pi$
$739$	−5.93725	−	10.2836i	−0.218405	−	0.378289i	−0.954321	+	0.298784i	$0.903419\pi$
$740$	−9.29150			−0.341562
$741$	−7.29150	+	12.6293i	−0.267860	+	0.463947i
$742$	−3.00000			−0.110133
$743$	39.7490			1.45825			0.729125	−	0.684381i	$-0.239927\pi$
$743$	39.7490			1.45825			0.729125	+	0.684381i	$0.239927\pi$
$744$	1.14575	+	5.44860i	0.0420053	+	0.199755i
$745$	−0.291503			−0.0106798
$746$	16.7085			0.611742
$747$	1.14575	−	1.98450i	0.0419208	−	0.0726090i
$748$	7.29150			0.266604
$749$	5.14575	+	8.91270i	0.188022	+	0.325663i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	−4.56275	+	7.90291i	−0.166497	+	0.288381i	−0.937186	−	0.348830i	$-0.886579\pi$
$751$	−4.56275	+	7.90291i	−0.166497	+	0.288381i	0.770689	+	0.637212i	$0.219912\pi$
$752$	−0.708497			−0.0258362
$753$	−10.0000	−	17.3205i	−0.364420	−	0.631194i
$754$	4.29150	+	7.43310i	0.156287	+	0.270698i
$755$	−1.14575	−	1.98450i	−0.0416982	−	0.0722233i
$756$	−0.500000	+	0.866025i	−0.0181848	+	0.0314970i
$757$	12.0000	+	20.7846i	0.436147	+	0.755429i	0.997389	−	0.0722229i	$-0.0230093\pi$
$757$	12.0000	+	20.7846i	0.436147	+	0.755429i	−0.561241	+	0.827652i	$0.689676\pi$
$758$	17.2915	−	29.9498i	0.628056	−	1.08782i
$759$	−7.29150			−0.264665
$760$	−7.29150			−0.264491
$761$	5.93725	−	10.2836i	0.215225	−	0.372781i	−0.738117	−	0.674673i	$-0.764285\pi$
$761$	5.93725	−	10.2836i	0.215225	−	0.372781i	0.953342	+	0.301892i	$0.0976181\pi$
$762$	−5.79150	−	10.0312i	−0.209804	−	0.363391i
$763$	7.64575	−	13.2428i	0.276795	−	0.479423i
$764$	−7.93725	−	13.7477i	−0.287160	−	0.497375i
$765$	3.64575	+	6.31463i	0.131812	+	0.228306i
$766$	11.3542	+	19.6661i	0.410246	+	0.710566i
$767$	−14.0000			−0.505511
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−20.5000	+	35.5070i	−0.739249	+	1.28042i	0.213585	+	0.976924i	$0.431486\pi$
$769$	−20.5000	+	35.5070i	−0.739249	+	1.28042i	−0.952834	+	0.303492i	$0.901847\pi$
$770$	−0.500000	−	0.866025i	−0.0180187	−	0.0312094i
$771$	21.8745			0.787791
$772$	4.14575	−	7.18065i	0.149209	−	0.258437i
$773$	−4.58301			−0.164839			−0.0824196	−	0.996598i	$-0.526265\pi$
$773$	−4.58301			−0.164839			−0.0824196	+	0.996598i	$0.526265\pi$
$774$	4.00000			0.143777
$775$	−1.14575	−	5.44860i	−0.0411566	−	0.195720i
$776$	−0.291503			−0.0104643
$777$	−9.29150			−0.333331
$778$	1.00000	−	1.73205i	0.0358517	−	0.0620970i
$779$	−38.5830			−1.38238
$780$	−1.00000	−	1.73205i	−0.0358057	−	0.0620174i
$781$	−3.29150	+	5.70105i	−0.117779	+	0.204000i
$782$	−26.5830	+	46.0431i	−0.950606	+	1.64650i
$783$	4.29150			0.153366
$784$	3.00000	+	5.19615i	0.107143	+	0.185577i
$785$	9.64575	+	16.7069i	0.344272	+	0.596296i
$786$	−4.00000	−	6.92820i	−0.142675	−	0.247121i
$787$	−10.2288	+	17.7167i	−0.364616	+	0.631533i	−0.988714	−	0.149812i	$-0.952133\pi$
$787$	−10.2288	+	17.7167i	−0.364616	+	0.631533i	0.624099	+	0.781346i	$0.285466\pi$
$788$	−11.5830	−	20.0624i	−0.412627	−	0.714692i
$789$	−6.29150	+	10.8972i	−0.223983	+	0.387951i
$790$	8.00000			0.284627
$791$	−12.5830			−0.447400
$792$	−0.500000	+	0.866025i	−0.0177667	+	0.0307729i
$793$	−7.29150	−	12.6293i	−0.258929	−	0.448478i
$794$	−14.5830	+	25.2585i	−0.517531	+	0.896391i
$795$	−1.50000	−	2.59808i	−0.0531995	−	0.0921443i
$796$	10.1458	+	17.5730i	0.359607	+	0.622857i
$797$	−11.0830	−	19.1963i	−0.392580	−	0.679969i	0.600209	−	0.799843i	$-0.295084\pi$
$797$	−11.0830	−	19.1963i	−0.392580	−	0.679969i	−0.992789	+	0.119874i	$0.961751\pi$
$798$	−7.29150			−0.258116
$799$	−2.58301	+	4.47390i	−0.0913802	+	0.158275i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$		0			0
$802$	−35.1660			−1.24175
$803$	−8.29150	+	14.3613i	−0.292601	+	0.506799i
$804$	−9.29150			−0.327686
$805$	7.29150			0.256992
$806$	−10.5830	−	3.46410i	−0.372770	−	0.122018i
$807$	−6.00000			−0.211210
$808$	−12.2915			−0.432414
$809$	6.22876	−	10.7885i	0.218991	−	0.379304i	−0.735508	−	0.677516i	$-0.763057\pi$
$809$	6.22876	−	10.7885i	0.218991	−	0.379304i	0.954500	+	0.298211i	$0.0963900\pi$
$810$	−1.00000			−0.0351364
$811$	−16.8745	−	29.2275i	−0.592544	−	1.02632i	−0.993888	−	0.110389i	$-0.964790\pi$
$811$	−16.8745	−	29.2275i	−0.592544	−	1.02632i	0.401344	−	0.915927i	$-0.368543\pi$
$812$	−2.14575	+	3.71655i	−0.0753011	+	0.130425i
$813$	8.14575	−	14.1089i	0.285684	−	0.494819i
$814$	−9.29150			−0.325667
$815$	10.9373	+	18.9439i	0.383115	+	0.663575i
$816$	3.64575	+	6.31463i	0.127627	+	0.221056i
$817$	14.5830	+	25.2585i	0.510195	+	0.883683i
$818$	−4.50000	+	7.79423i	−0.157339	+	0.272519i
$819$	−1.00000	−	1.73205i	−0.0349428	−	0.0605228i
$820$	2.64575	−	4.58258i	0.0923936	−	0.160030i
$821$	−10.2915			−0.359176			−0.179588	−	0.983742i	$-0.557476\pi$
$821$	−10.2915			−0.359176			−0.179588	+	0.983742i	$0.557476\pi$
$822$	−15.8745			−0.553687
$823$	5.79150	−	10.0312i	0.201879	−	0.349665i	−0.747255	−	0.664538i	$-0.768629\pi$
$823$	5.79150	−	10.0312i	0.201879	−	0.349665i	0.949134	+	0.314873i	$0.101962\pi$
$824$	−8.79150	−	15.2273i	−0.306267	−	0.530469i
$825$	0.500000	−	0.866025i	0.0174078	−	0.0301511i
$826$	−3.50000	−	6.06218i	−0.121781	−	0.210930i
$827$	−9.29150	−	16.0934i	−0.323097	−	0.559621i	0.658028	−	0.752993i	$-0.271391\pi$
$827$	−9.29150	−	16.0934i	−0.323097	−	0.559621i	−0.981125	+	0.193373i	$0.938057\pi$
$828$	−3.64575	−	6.31463i	−0.126699	−	0.219448i
$829$	−24.7085			−0.858162			−0.429081	−	0.903266i	$-0.641162\pi$
$829$	−24.7085			−0.858162			−0.429081	+	0.903266i	$0.641162\pi$
$830$	−1.14575	+	1.98450i	−0.0397696	+	0.0688830i
$831$	−5.64575	+	9.77873i	−0.195849	+	0.339220i
$832$	−1.00000	−	1.73205i	−0.0346688	−	0.0600481i
$833$	43.7490			1.51581
$834$	0.645751	−	1.11847i	0.0223605	−	0.0387296i
$835$	6.70850			0.232157
$836$	−7.29150			−0.252182
$837$	−4.14575	+	3.71655i	−0.143298	+	0.128463i
$838$	−5.58301			−0.192862
$839$	8.70850			0.300651			0.150325	−	0.988637i	$-0.451968\pi$
$839$	8.70850			0.300651			0.150325	+	0.988637i	$0.451968\pi$
$840$	0.500000	−	0.866025i	0.0172516	−	0.0298807i
$841$	−10.5830			−0.364931
$842$	−15.6458	−	27.0992i	−0.539188	−	0.933901i
$843$	6.00000	−	10.3923i	0.206651	−	0.357930i
$844$	−7.64575	+	13.2428i	−0.263178	+	0.455837i
$845$	−9.00000			−0.309609
$846$	−0.354249	−	0.613577i	−0.0121793	−	0.0210952i
$847$	5.00000	+	8.66025i	0.171802	+	0.297570i
$848$	−1.50000	−	2.59808i	−0.0515102	−	0.0892183i
$849$	−7.00000	+	12.1244i	−0.240239	+	0.416107i
$850$	−3.64575	−	6.31463i	−0.125048	−	0.216590i
$851$	33.8745	−	58.6724i	1.16120	−	2.01126i
$852$	−6.58301			−0.225530
$853$	46.3320			1.58638			0.793189	−	0.608975i	$-0.208419\pi$
$853$	46.3320			1.58638			0.793189	+	0.608975i	$0.208419\pi$
$854$	3.64575	−	6.31463i	0.124755	−	0.216082i
$855$	−3.64575	−	6.31463i	−0.124682	−	0.215956i
$856$	−5.14575	+	8.91270i	−0.175878	+	0.304630i
$857$	−5.29150	−	9.16515i	−0.180754	−	0.313076i	0.761383	−	0.648302i	$-0.224521\pi$
$857$	−5.29150	−	9.16515i	−0.180754	−	0.313076i	−0.942138	+	0.335226i	$0.891187\pi$
$858$	−1.00000	−	1.73205i	−0.0341394	−	0.0591312i
$859$	−19.8118	−	34.3150i	−0.675969	−	1.17081i	−0.976185	−	0.216941i	$-0.930392\pi$
$859$	−19.8118	−	34.3150i	−0.675969	−	1.17081i	0.300216	−	0.953871i	$-0.402941\pi$
$860$	−4.00000			−0.136399
$861$	2.64575	−	4.58258i	0.0901670	−	0.156174i
$862$	−4.64575	+	8.04668i	−0.158235	+	0.274071i
$863$	−26.5830	−	46.0431i	−0.904896	−	1.56733i	−0.821057	−	0.570847i	$-0.806615\pi$
$863$	−26.5830	−	46.0431i	−0.904896	−	1.56733i	−0.0838393	−	0.996479i	$-0.526718\pi$
$864$	−1.00000			−0.0340207
$865$	5.50000	−	9.52628i	0.187006	−	0.323903i
$866$	−22.0000			−0.747590
$867$	36.1660			1.22826
$868$	−1.14575	−	5.44860i	−0.0388893	−	0.184938i
$869$	8.00000			0.271381
$870$	−4.29150			−0.145496
$871$	9.29150	−	16.0934i	0.314831	−	0.545303i
$872$	15.2915			0.517836
$873$	−0.145751	−	0.252449i	−0.00493293	−	0.00854409i
$874$	26.5830	−	46.0431i	0.899184	−	1.55743i
$875$	−0.500000	+	0.866025i	−0.0169031	+	0.0292770i
$876$	−16.5830			−0.560288
$877$	−9.64575	−	16.7069i	−0.325714	−	0.564153i	0.655943	−	0.754811i	$-0.272271\pi$
$877$	−9.64575	−	16.7069i	−0.325714	−	0.564153i	−0.981657	+	0.190658i	$0.938938\pi$
$878$	−2.14575	−	3.71655i	−0.0724156	−	0.125427i
$879$	1.20850	+	2.09318i	0.0407616	+	0.0706012i
$880$	0.500000	−	0.866025i	0.0168550	−	0.0291937i
$881$	16.6458	+	28.8313i	0.560810	+	0.971351i	0.997426	+	0.0717030i	$0.0228434\pi$
$881$	16.6458	+	28.8313i	0.560810	+	0.971351i	−0.436616	+	0.899648i	$0.643823\pi$
$882$	−3.00000	+	5.19615i	−0.101015	+	0.174964i
$883$	−45.0405			−1.51573			−0.757867	−	0.652409i	$-0.773758\pi$
$883$	−45.0405			−1.51573			−0.757867	+	0.652409i	$0.773758\pi$
$884$	−14.5830			−0.490480
$885$	3.50000	−	6.06218i	0.117651	−	0.203778i
$886$	4.70850	+	8.15536i	0.158185	+	0.273985i
$887$	0.708497	−	1.22715i	0.0237890	−	0.0412038i	−0.853886	−	0.520460i	$-0.825760\pi$
$887$	0.708497	−	1.22715i	0.0237890	−	0.0412038i	0.877675	+	0.479257i	$0.159094\pi$
$888$	−4.64575	−	8.04668i	−0.155901	−	0.270029i
$889$	5.79150	+	10.0312i	0.194241	+	0.336435i
$890$		0			0
$891$	−1.00000			−0.0335013
$892$	2.20850	−	3.82523i	0.0739460	−	0.128078i
$893$	2.58301	−	4.47390i	0.0864370	−	0.149713i
$894$	−0.145751	−	0.252449i	−0.00487465	−	0.00844315i
$895$	1.00000			0.0334263
$896$	0.500000	−	0.866025i	0.0167038	−	0.0289319i
$897$	14.5830			0.486912
$898$	26.5830			0.887086
$899$	−17.7915	+	15.9496i	−0.593380	+	0.531948i
$900$	1.00000			0.0333333
$901$	−21.8745			−0.728746
$902$	2.64575	−	4.58258i	0.0880939	−	0.152583i
$903$	−4.00000			−0.133112
$904$	−6.29150	−	10.8972i	−0.209252	−	0.362436i
$905$	−3.29150	+	5.70105i	−0.109413	+	0.189509i
$906$	1.14575	−	1.98450i	0.0380650	−	0.0659306i
$907$	−40.5830			−1.34754			−0.673768	−	0.738943i	$-0.735325\pi$
$907$	−40.5830			−1.34754			−0.673768	+	0.738943i	$0.735325\pi$
$908$	−11.4373	−	19.8099i	−0.379559	−	0.657415i
$909$	−6.14575	−	10.6448i	−0.203842	−	0.353064i
$910$	1.00000	+	1.73205i	0.0331497	+	0.0574169i
$911$	5.22876	−	9.05647i	0.173236	−	0.300054i	−0.766313	−	0.642467i	$-0.777911\pi$
$911$	5.22876	−	9.05647i	0.173236	−	0.300054i	0.939550	+	0.342413i	$0.111244\pi$
$912$	−3.64575	−	6.31463i	−0.120723	−	0.209098i
$913$	−1.14575	+	1.98450i	−0.0379188	+	0.0656773i
$914$	−7.16601			−0.237031
$915$	7.29150			0.241050
$916$	11.9373	−	20.6759i	0.394418	−	0.683152i
$917$	4.00000	+	6.92820i	0.132092	+	0.228789i
$918$	−3.64575	+	6.31463i	−0.120328	+	0.208414i
$919$	−1.56275	−	2.70676i	−0.0515502	−	0.0892876i	0.839099	−	0.543979i	$-0.183083\pi$
$919$	−1.56275	−	2.70676i	−0.0515502	−	0.0892876i	−0.890649	+	0.454691i	$0.849750\pi$
$920$	3.64575	+	6.31463i	0.120197	+	0.208187i
$921$	14.6458	+	25.3672i	0.482594	+	0.835877i
$922$	4.29150			0.141333
$923$	6.58301	−	11.4021i	0.216682	−	0.375305i
$924$	0.500000	−	0.866025i	0.0164488	−	0.0284901i
$925$	4.64575	+	8.04668i	0.152751	+	0.264573i
$926$	−15.0000			−0.492931
$927$	8.79150	−	15.2273i	0.288751	−	0.500131i
$928$	−4.29150			−0.140875
$929$	48.4575			1.58984			0.794920	−	0.606715i	$-0.207513\pi$
$929$	48.4575			1.58984			0.794920	+	0.606715i	$0.207513\pi$
$930$	4.14575	−	3.71655i	0.135945	−	0.121870i
$931$	−43.7490			−1.43382
$932$	−19.8745			−0.651011
$933$	−9.00000	+	15.5885i	−0.294647	+	0.510343i
$934$	6.29150			0.205864
$935$	−3.64575	−	6.31463i	−0.119229	−	0.206510i
$936$	1.00000	−	1.73205i	0.0326860	−	0.0566139i
$937$	−1.70850	+	2.95920i	−0.0558142	+	0.0966730i	−0.892583	−	0.450884i	$-0.851109\pi$
$937$	−1.70850	+	2.95920i	−0.0558142	+	0.0966730i	0.836768	+	0.547557i	$0.184442\pi$
$938$	9.29150			0.303378
$939$	−13.1458	−	22.7691i	−0.428995	−	0.743042i
$940$	0.354249	+	0.613577i	0.0115543	+	0.0200127i
$941$	16.0203	+	27.7479i	0.522246	+	0.904556i	0.999665	+	0.0258803i	$0.00823888\pi$
$941$	16.0203	+	27.7479i	0.522246	+	0.904556i	−0.477420	+	0.878675i	$0.658428\pi$
$942$	−9.64575	+	16.7069i	−0.314276	+	0.544341i
$943$	19.2915	+	33.4139i	0.628218	+	1.08811i
$944$	3.50000	−	6.06218i	0.113915	−	0.197307i
$945$	1.00000			0.0325300
$946$	−4.00000			−0.130051
$947$	−8.58301	+	14.8662i	−0.278910	+	0.483087i	−0.971114	−	0.238615i	$-0.923307\pi$
$947$	−8.58301	+	14.8662i	−0.278910	+	0.483087i	0.692204	+	0.721702i	$0.256640\pi$
$948$	4.00000	+	6.92820i	0.129914	+	0.225018i
$949$	16.5830	−	28.7226i	0.538307	−	0.932375i
$950$	3.64575	+	6.31463i	0.118284	+	0.204874i
$951$	−14.7915	−	25.6196i	−0.479647	−	0.830774i
$952$	−3.64575	−	6.31463i	−0.118159	−	0.204658i
$953$	−4.70850			−0.152523			−0.0762616	−	0.997088i	$-0.524298\pi$
$953$	−4.70850			−0.152523			−0.0762616	+	0.997088i	$0.524298\pi$
$954$	1.50000	−	2.59808i	0.0485643	−	0.0841158i
$955$	−7.93725	+	13.7477i	−0.256844	+	0.444866i
$956$	2.29150	+	3.96900i	0.0741125	+	0.128367i
$957$	−4.29150			−0.138725
$958$	−12.3542	+	21.3982i	−0.399148	+	0.691344i
$959$	15.8745			0.512615
$960$	1.00000			0.0322749
$961$	3.37451	−	30.8158i	0.108855	−	0.994058i
$962$	18.5830			0.599140
$963$	−10.2915			−0.331639
$964$	−12.7915	+	22.1555i	−0.411987	+	0.713582i
$965$	−8.29150			−0.266913
$966$	3.64575	+	6.31463i	0.117300	+	0.203170i
$967$	−6.58301	+	11.4021i	−0.211695	+	0.366667i	−0.952245	−	0.305334i	$-0.901232\pi$
$967$	−6.58301	+	11.4021i	−0.211695	+	0.366667i	0.740550	+	0.672001i	$0.234565\pi$
$968$	−5.00000	+	8.66025i	−0.160706	+	0.278351i
$969$	−53.1660			−1.70794
$970$	0.145751	+	0.252449i	0.00467979	+	0.00810564i
$971$	−3.20850	−	5.55728i	−0.102966	−	0.178342i	0.809940	−	0.586513i	$-0.199500\pi$
$971$	−3.20850	−	5.55728i	−0.102966	−	0.178342i	−0.912905	+	0.408172i	$0.866166\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−0.645751	+	1.11847i	−0.0207018	+	0.0358566i
$974$	−8.08301	−	14.0002i	−0.258996	−	0.448595i
$975$	−1.00000	+	1.73205i	−0.0320256	+	0.0554700i
$976$	7.29150			0.233395
$977$	14.5830			0.466552			0.233276	−	0.972411i	$-0.425055\pi$
$977$	14.5830			0.466552			0.233276	+	0.972411i	$0.425055\pi$
$978$	−10.9373	+	18.9439i	−0.349735	+	0.605758i
$979$		0			0
$980$	3.00000	−	5.19615i	0.0958315	−	0.165985i
$981$	7.64575	+	13.2428i	0.244110	+	0.422811i
$982$	6.20850	+	10.7534i	0.198121	+	0.343156i
$983$	24.5830	+	42.5790i	0.784076	+	1.35806i	0.929549	+	0.368697i	$0.120196\pi$
$983$	24.5830	+	42.5790i	0.784076	+	1.35806i	−0.145473	+	0.989362i	$0.546471\pi$
$984$	5.29150			0.168687
$985$	−11.5830	+	20.0624i	−0.369065	+	0.639240i
$986$	−15.6458	+	27.0992i	−0.498262	+	0.863015i
$987$	0.354249	+	0.613577i	0.0112759	+	0.0195304i
$988$	14.5830			0.463947
$989$	14.5830	−	25.2585i	0.463713	−	0.803174i
$990$	1.00000			0.0317821
$991$	−27.7490			−0.881477			−0.440738	−	0.897636i	$-0.645283\pi$
$991$	−27.7490			−0.881477			−0.440738	+	0.897636i	$0.645283\pi$
$992$	4.14575	−	3.71655i	0.131628	−	0.118001i
$993$	21.8745			0.694167
$994$	6.58301			0.208800
$995$	10.1458	−	17.5730i	0.321642	−	0.557100i
$996$	−2.29150			−0.0726090
$997$	13.9373	+	24.1400i	0.441397	+	0.764522i	0.997793	−	0.0663947i	$-0.0211496\pi$
$997$	13.9373	+	24.1400i	0.441397	+	0.764522i	−0.556396	+	0.830917i	$0.687816\pi$
$998$	−4.64575	+	8.04668i	−0.147059	+	0.254713i
$999$	4.64575	−	8.04668i	0.146985	−	0.254586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.i.j.811.2	yes	4
31.25	even	3	inner	930.2.i.j.211.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.i.j.211.2	✓	4	31.25	even	3	inner
930.2.i.j.811.2	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-1.00000 - 1.73205i) q^{13} +(0.500000 - 0.866025i) q^{14} +1.00000 q^{15} +1.00000 q^{16} +(3.64575 - 6.31463i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-3.64575 + 6.31463i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-0.500000 - 0.866025i) q^{21} +(-0.500000 - 0.866025i) q^{22} +7.29150 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} +1.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} +4.29150 q^{29} -1.00000 q^{30} +(-4.14575 + 3.71655i) q^{31} -1.00000 q^{32} -1.00000 q^{33} +(-3.64575 + 6.31463i) q^{34} +1.00000 q^{35} +(-0.500000 - 0.866025i) q^{36} +(4.64575 - 8.04668i) q^{37} +(3.64575 - 6.31463i) q^{38} +2.00000 q^{39} +(0.500000 + 0.866025i) q^{40} +(2.64575 + 4.58258i) q^{41} +(0.500000 + 0.866025i) q^{42} +(2.00000 - 3.46410i) q^{43} +(0.500000 + 0.866025i) q^{44} +(-0.500000 + 0.866025i) q^{45} -7.29150 q^{46} -0.708497 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.00000 + 5.19615i) q^{49} +(0.500000 - 0.866025i) q^{50} +(3.64575 + 6.31463i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-1.50000 - 2.59808i) q^{53} -1.00000 q^{54} +(0.500000 - 0.866025i) q^{55} +(0.500000 - 0.866025i) q^{56} +(-3.64575 - 6.31463i) q^{57} -4.29150 q^{58} +(3.50000 - 6.06218i) q^{59} +1.00000 q^{60} +7.29150 q^{61} +(4.14575 - 3.71655i) q^{62} +1.00000 q^{63} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +1.00000 q^{66} +(4.64575 + 8.04668i) q^{67} +(3.64575 - 6.31463i) q^{68} +(-3.64575 + 6.31463i) q^{69} -1.00000 q^{70} +(3.29150 + 5.70105i) q^{71} +(0.500000 + 0.866025i) q^{72} +(8.29150 + 14.3613i) q^{73} +(-4.64575 + 8.04668i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(-3.64575 + 6.31463i) q^{76} -1.00000 q^{77} -2.00000 q^{78} +(4.00000 - 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.64575 - 4.58258i) q^{82} +(1.14575 + 1.98450i) q^{83} +(-0.500000 - 0.866025i) q^{84} -7.29150 q^{85} +(-2.00000 + 3.46410i) q^{86} +(-2.14575 + 3.71655i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(0.500000 - 0.866025i) q^{90} +2.00000 q^{91} +7.29150 q^{92} +(-1.14575 - 5.44860i) q^{93} +0.708497 q^{94} +7.29150 q^{95} +(0.500000 - 0.866025i) q^{96} +0.291503 q^{97} +(-3.00000 - 5.19615i) q^{98} +(0.500000 - 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9	\( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} - 2 q^{12} - 4 q^{13} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 4 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} - 2 q^{21} - 2 q^{22} + 8 q^{23} + 2 q^{24} - 2 q^{25} + 4 q^{26} + 4 q^{27} - 2 q^{28} - 4 q^{29} - 4 q^{30} - 6 q^{31} - 4 q^{32} - 4 q^{33} - 4 q^{34} + 4 q^{35} - 2 q^{36} + 8 q^{37} + 4 q^{38} + 8 q^{39} + 2 q^{40} + 2 q^{42} + 8 q^{43} + 2 q^{44} - 2 q^{45} - 8 q^{46} - 24 q^{47} - 2 q^{48} + 12 q^{49} + 2 q^{50} + 4 q^{51} - 4 q^{52} - 6 q^{53} - 4 q^{54} + 2 q^{55} + 2 q^{56} - 4 q^{57} + 4 q^{58} + 14 q^{59} + 4 q^{60} + 8 q^{61} + 6 q^{62} + 4 q^{63} + 4 q^{64} - 4 q^{65} + 4 q^{66} + 8 q^{67} + 4 q^{68} - 4 q^{69} - 4 q^{70} - 8 q^{71} + 2 q^{72} + 12 q^{73} - 8 q^{74} - 2 q^{75} - 4 q^{76} - 4 q^{77} - 8 q^{78} + 16 q^{79} - 2 q^{80} - 2 q^{81} - 6 q^{83} - 2 q^{84} - 8 q^{85} - 8 q^{86} + 2 q^{87} - 2 q^{88} + 2 q^{90} + 8 q^{91} + 8 q^{92} + 6 q^{93} + 24 q^{94} + 8 q^{95} + 2 q^{96} - 20 q^{97} - 12 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9 + 2 * q^10 + 2 * q^11 - 2 * q^12 - 4 * q^13 + 2 * q^14 + 4 * q^15 + 4 * q^16 + 4 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 - 2 * q^21 - 2 * q^22 + 8 * q^23 + 2 * q^24 - 2 * q^25 + 4 * q^26 + 4 * q^27 - 2 * q^28 - 4 * q^29 - 4 * q^30 - 6 * q^31 - 4 * q^32 - 4 * q^33 - 4 * q^34 + 4 * q^35 - 2 * q^36 + 8 * q^37 + 4 * q^38 + 8 * q^39 + 2 * q^40 + 2 * q^42 + 8 * q^43 + 2 * q^44 - 2 * q^45 - 8 * q^46 - 24 * q^47 - 2 * q^48 + 12 * q^49 + 2 * q^50 + 4 * q^51 - 4 * q^52 - 6 * q^53 - 4 * q^54 + 2 * q^55 + 2 * q^56 - 4 * q^57 + 4 * q^58 + 14 * q^59 + 4 * q^60 + 8 * q^61 + 6 * q^62 + 4 * q^63 + 4 * q^64 - 4 * q^65 + 4 * q^66 + 8 * q^67 + 4 * q^68 - 4 * q^69 - 4 * q^70 - 8 * q^71 + 2 * q^72 + 12 * q^73 - 8 * q^74 - 2 * q^75 - 4 * q^76 - 4 * q^77 - 8 * q^78 + 16 * q^79 - 2 * q^80 - 2 * q^81 - 6 * q^83 - 2 * q^84 - 8 * q^85 - 8 * q^86 + 2 * q^87 - 2 * q^88 + 2 * q^90 + 8 * q^91 + 8 * q^92 + 6 * q^93 + 24 * q^94 + 8 * q^95 + 2 * q^96 - 20 * q^97 - 12 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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