LMFDB - Embedded newform 78.2.i.a.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,2,Mod(43,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("78.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	78.i (of order $6$, 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:	$0.622833135766$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	78.43
Dual form			78.2.i.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.73205i q^{5} +(0.866025 - 0.500000i) q^{6} +(2.36603 - 1.36603i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.73205i q^{5} +(0.866025 - 0.500000i) q^{6} +(2.36603 - 1.36603i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.86603 - 3.23205i) q^{10} +(1.09808 + 0.633975i) q^{11} -1.00000 q^{12} +(-2.59808 + 2.50000i) q^{13} -2.73205 q^{14} +(-3.23205 - 1.86603i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.86603 - 4.96410i) q^{17} +1.00000i q^{18} +(4.09808 - 2.36603i) q^{19} +(-3.23205 + 1.86603i) q^{20} +2.73205i q^{21} +(-0.633975 - 1.09808i) q^{22} +(2.09808 - 3.63397i) q^{23} +(0.866025 + 0.500000i) q^{24} -8.92820 q^{25} +(3.50000 - 0.866025i) q^{26} +1.00000 q^{27} +(2.36603 + 1.36603i) q^{28} +(2.23205 - 3.86603i) q^{29} +(1.86603 + 3.23205i) q^{30} +1.46410i q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.09808 + 0.633975i) q^{33} +5.73205i q^{34} +(5.09808 + 8.83013i) q^{35} +(0.500000 - 0.866025i) q^{36} +(3.06218 + 1.76795i) q^{37} -4.73205 q^{38} +(-0.866025 - 3.50000i) q^{39} +3.73205 q^{40} +(8.13397 + 4.69615i) q^{41} +(1.36603 - 2.36603i) q^{42} +(-4.83013 - 8.36603i) q^{43} +1.26795i q^{44} +(3.23205 - 1.86603i) q^{45} +(-3.63397 + 2.09808i) q^{46} -2.19615i q^{47} +(-0.500000 - 0.866025i) q^{48} +(0.232051 - 0.401924i) q^{49} +(7.73205 + 4.46410i) q^{50} +5.73205 q^{51} +(-3.46410 - 1.00000i) q^{52} -6.46410 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-2.36603 + 4.09808i) q^{55} +(-1.36603 - 2.36603i) q^{56} +4.73205i q^{57} +(-3.86603 + 2.23205i) q^{58} +(-6.92820 + 4.00000i) q^{59} -3.73205i q^{60} +(4.59808 + 7.96410i) q^{61} +(0.732051 - 1.26795i) q^{62} +(-2.36603 - 1.36603i) q^{63} -1.00000 q^{64} +(-9.33013 - 9.69615i) q^{65} +1.26795 q^{66} +(-11.3660 - 6.56218i) q^{67} +(2.86603 - 4.96410i) q^{68} +(2.09808 + 3.63397i) q^{69} -10.1962i q^{70} +(4.09808 - 2.36603i) q^{71} +(-0.866025 + 0.500000i) q^{72} +6.26795i q^{73} +(-1.76795 - 3.06218i) q^{74} +(4.46410 - 7.73205i) q^{75} +(4.09808 + 2.36603i) q^{76} +3.46410 q^{77} +(-1.00000 + 3.46410i) q^{78} -2.53590 q^{79} +(-3.23205 - 1.86603i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.69615 - 8.13397i) q^{82} -0.196152i q^{83} +(-2.36603 + 1.36603i) q^{84} +(18.5263 - 10.6962i) q^{85} +9.66025i q^{86} +(2.23205 + 3.86603i) q^{87} +(0.633975 - 1.09808i) q^{88} +(-8.19615 - 4.73205i) q^{89} -3.73205 q^{90} +(-2.73205 + 9.46410i) q^{91} +4.19615 q^{92} +(-1.26795 - 0.732051i) q^{93} +(-1.09808 + 1.90192i) q^{94} +(8.83013 + 15.2942i) q^{95} +1.00000i q^{96} +(-5.19615 + 3.00000i) q^{97} +(-0.401924 + 0.232051i) q^{98} -1.26795i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{4} + 6 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^7 - 2 * q^9	$ 4 q - 2 q^{3} + 2 q^{4} + 6 q^{7} - 2 q^{9} + 4 q^{10} - 6 q^{11} - 4 q^{12} - 4 q^{14} - 6 q^{15} - 2 q^{16} - 8 q^{17} + 6 q^{19} - 6 q^{20} - 6 q^{22} - 2 q^{23} - 8 q^{25} + 14 q^{26} + 4 q^{27} + 6 q^{28} + 2 q^{29} + 4 q^{30} + 6 q^{33} + 10 q^{35} + 2 q^{36} - 12 q^{37} - 12 q^{38} + 8 q^{40} + 36 q^{41} + 2 q^{42} - 2 q^{43} + 6 q^{45} - 18 q^{46} - 2 q^{48} - 6 q^{49} + 24 q^{50} + 16 q^{51} - 12 q^{53} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 8 q^{61} - 4 q^{62} - 6 q^{63} - 4 q^{64} - 20 q^{65} + 12 q^{66} - 42 q^{67} + 8 q^{68} - 2 q^{69} + 6 q^{71} - 14 q^{74} + 4 q^{75} + 6 q^{76} - 4 q^{78} - 24 q^{79} - 6 q^{80} - 2 q^{81} + 2 q^{82} - 6 q^{84} + 36 q^{85} + 2 q^{87} + 6 q^{88} - 12 q^{89} - 8 q^{90} - 4 q^{91} - 4 q^{92} - 12 q^{93} + 6 q^{94} + 18 q^{95} - 12 q^{98}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^7 - 2 * q^9 + 4 * q^10 - 6 * q^11 - 4 * q^12 - 4 * q^14 - 6 * q^15 - 2 * q^16 - 8 * q^17 + 6 * q^19 - 6 * q^20 - 6 * q^22 - 2 * q^23 - 8 * q^25 + 14 * q^26 + 4 * q^27 + 6 * q^28 + 2 * q^29 + 4 * q^30 + 6 * q^33 + 10 * q^35 + 2 * q^36 - 12 * q^37 - 12 * q^38 + 8 * q^40 + 36 * q^41 + 2 * q^42 - 2 * q^43 + 6 * q^45 - 18 * q^46 - 2 * q^48 - 6 * q^49 + 24 * q^50 + 16 * q^51 - 12 * q^53 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 8 * q^61 - 4 * q^62 - 6 * q^63 - 4 * q^64 - 20 * q^65 + 12 * q^66 - 42 * q^67 + 8 * q^68 - 2 * q^69 + 6 * q^71 - 14 * q^74 + 4 * q^75 + 6 * q^76 - 4 * q^78 - 24 * q^79 - 6 * q^80 - 2 * q^81 + 2 * q^82 - 6 * q^84 + 36 * q^85 + 2 * q^87 + 6 * q^88 - 12 * q^89 - 8 * q^90 - 4 * q^91 - 4 * q^92 - 12 * q^93 + 6 * q^94 + 18 * q^95 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$			3.73205i			1.66902i	0.550990	+	0.834512i	$0.314250\pi$
$5$			3.73205i			1.66902i	−0.550990	+	0.834512i	$0.685750\pi$
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	2.36603	−	1.36603i	0.894274	−	0.516309i	0.0189356	−	0.999821i	$-0.493972\pi$
$7$	2.36603	−	1.36603i	0.894274	−	0.516309i	0.875338	+	0.483512i	$0.160639\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.86603	−	3.23205i	0.590089	−	1.02206i
$11$	1.09808	+	0.633975i	0.331082	+	0.191151i	0.656322	−	0.754481i	$-0.272111\pi$
$11$	1.09808	+	0.633975i	0.331082	+	0.191151i	−0.325239	+	0.945632i	$0.605445\pi$
$12$	−1.00000			−0.288675
$13$	−2.59808	+	2.50000i	−0.720577	+	0.693375i
$13$	−2.59808	+	2.50000i	−0.720577	+	0.693375i
$14$	−2.73205			−0.730171
$15$	−3.23205	−	1.86603i	−0.834512	−	0.481806i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.86603	−	4.96410i	−0.695113	−	1.20397i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$	−2.86603	−	4.96410i	−0.695113	−	1.20397i	0.275029	−	0.961436i	$-0.411312\pi$
$18$			1.00000i			0.235702i
$19$	4.09808	−	2.36603i	0.940163	−	0.542803i	0.0501517	−	0.998742i	$-0.484030\pi$
$19$	4.09808	−	2.36603i	0.940163	−	0.542803i	0.890011	+	0.455938i	$0.150696\pi$
$20$	−3.23205	+	1.86603i	−0.722709	+	0.417256i
$21$			2.73205i			0.596182i
$22$	−0.633975	−	1.09808i	−0.135164	−	0.234111i
$23$	2.09808	−	3.63397i	0.437479	−	0.757736i	−0.560015	−	0.828482i	$-0.689205\pi$
$23$	2.09808	−	3.63397i	0.437479	−	0.757736i	0.997494	+	0.0707462i	$0.0225381\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−8.92820			−1.78564
$26$	3.50000	−	0.866025i	0.686406	−	0.169842i
$27$	1.00000			0.192450
$28$	2.36603	+	1.36603i	0.447137	+	0.258155i
$29$	2.23205	−	3.86603i	0.414481	−	0.717903i	−0.580892	−	0.813980i	$-0.697296\pi$
$29$	2.23205	−	3.86603i	0.414481	−	0.717903i	0.995374	+	0.0960774i	$0.0306296\pi$
$30$	1.86603	+	3.23205i	0.340688	+	0.590089i
$31$			1.46410i			0.262960i	0.991319	+	0.131480i	$0.0419730\pi$
$31$			1.46410i			0.262960i	−0.991319	+	0.131480i	$0.958027\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−1.09808	+	0.633975i	−0.191151	+	0.110361i
$34$			5.73205i			0.983039i
$35$	5.09808	+	8.83013i	0.861732	+	1.49256i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	3.06218	+	1.76795i	0.503419	+	0.290649i	0.730124	−	0.683314i	$-0.239462\pi$
$37$	3.06218	+	1.76795i	0.503419	+	0.290649i	−0.226705	+	0.973963i	$0.572795\pi$
$38$	−4.73205			−0.767640
$39$	−0.866025	−	3.50000i	−0.138675	−	0.560449i
$40$	3.73205			0.590089
$41$	8.13397	+	4.69615i	1.27031	+	0.733416i	0.975047	−	0.221999i	$-0.0712582\pi$
$41$	8.13397	+	4.69615i	1.27031	+	0.733416i	0.295267	+	0.955415i	$0.404592\pi$
$42$	1.36603	−	2.36603i	0.210782	−	0.365086i
$43$	−4.83013	−	8.36603i	−0.736587	−	1.27581i	−0.954023	−	0.299732i	$-0.903103\pi$
$43$	−4.83013	−	8.36603i	−0.736587	−	1.27581i	0.217436	−	0.976075i	$-0.430231\pi$
$44$			1.26795i			0.191151i
$45$	3.23205	−	1.86603i	0.481806	−	0.278171i
$46$	−3.63397	+	2.09808i	−0.535800	+	0.309344i
$47$		−	2.19615i		−	0.320342i	−0.987089	−	0.160171i	$-0.948795\pi$
$47$		−	2.19615i		−	0.320342i	0.987089	−	0.160171i	$-0.0512045\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	0.232051	−	0.401924i	0.0331501	−	0.0574177i
$50$	7.73205	+	4.46410i	1.09348	+	0.631319i
$51$	5.73205			0.802648
$52$	−3.46410	−	1.00000i	−0.480384	−	0.138675i
$53$	−6.46410			−0.887913			−0.443956	−	0.896048i	$-0.646425\pi$
$53$	−6.46410			−0.887913			−0.443956	+	0.896048i	$0.646425\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	−2.36603	+	4.09808i	−0.319035	+	0.552584i
$56$	−1.36603	−	2.36603i	−0.182543	−	0.316173i
$57$			4.73205i			0.626775i
$58$	−3.86603	+	2.23205i	−0.507634	+	0.293083i
$59$	−6.92820	+	4.00000i	−0.901975	+	0.520756i	−0.877841	−	0.478953i	$-0.841016\pi$
$59$	−6.92820	+	4.00000i	−0.901975	+	0.520756i	−0.0241347	+	0.999709i	$0.507683\pi$
$60$		−	3.73205i		−	0.481806i
$61$	4.59808	+	7.96410i	0.588723	+	1.01970i	0.994400	+	0.105682i	$0.0337026\pi$
$61$	4.59808	+	7.96410i	0.588723	+	1.01970i	−0.405677	+	0.914017i	$0.632964\pi$
$62$	0.732051	−	1.26795i	0.0929705	−	0.161030i
$63$	−2.36603	−	1.36603i	−0.298091	−	0.172103i
$64$	−1.00000			−0.125000
$65$	−9.33013	−	9.69615i	−1.15726	−	1.20266i
$66$	1.26795			0.156074
$67$	−11.3660	−	6.56218i	−1.38858	−	0.801698i	−0.395426	−	0.918498i	$-0.629403\pi$
$67$	−11.3660	−	6.56218i	−1.38858	−	0.801698i	−0.993155	+	0.116800i	$0.962736\pi$
$68$	2.86603	−	4.96410i	0.347557	−	0.601986i
$69$	2.09808	+	3.63397i	0.252579	+	0.437479i
$70$		−	10.1962i		−	1.21867i
$71$	4.09808	−	2.36603i	0.486352	−	0.280796i	−0.236708	−	0.971581i	$-0.576068\pi$
$71$	4.09808	−	2.36603i	0.486352	−	0.280796i	0.723060	+	0.690785i	$0.242735\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$			6.26795i			0.733608i	0.930298	+	0.366804i	$0.119548\pi$
$73$			6.26795i			0.733608i	−0.930298	+	0.366804i	$0.880452\pi$
$74$	−1.76795	−	3.06218i	−0.205520	−	0.355971i
$75$	4.46410	−	7.73205i	0.515470	−	0.892820i
$76$	4.09808	+	2.36603i	0.470082	+	0.271402i
$77$	3.46410			0.394771
$78$	−1.00000	+	3.46410i	−0.113228	+	0.392232i
$79$	−2.53590			−0.285311			−0.142655	−	0.989772i	$-0.545564\pi$
$79$	−2.53590			−0.285311			−0.142655	+	0.989772i	$0.545564\pi$
$80$	−3.23205	−	1.86603i	−0.361354	−	0.208628i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.69615	−	8.13397i	−0.518603	−	0.898247i
$83$		−	0.196152i		−	0.0215305i	−0.999942	−	0.0107653i	$-0.996573\pi$
$83$		−	0.196152i		−	0.0215305i	0.999942	−	0.0107653i	$-0.00342676\pi$
$84$	−2.36603	+	1.36603i	−0.258155	+	0.149046i
$85$	18.5263	−	10.6962i	2.00946	−	1.16016i
$86$			9.66025i			1.04169i
$87$	2.23205	+	3.86603i	0.239301	+	0.414481i
$88$	0.633975	−	1.09808i	0.0675819	−	0.117055i
$89$	−8.19615	−	4.73205i	−0.868790	−	0.501596i	−0.00184433	−	0.999998i	$-0.500587\pi$
$89$	−8.19615	−	4.73205i	−0.868790	−	0.501596i	−0.866946	+	0.498402i	$0.833920\pi$
$90$	−3.73205			−0.393393
$91$	−2.73205	+	9.46410i	−0.286397	+	0.992107i
$92$	4.19615			0.437479
$93$	−1.26795	−	0.732051i	−0.131480	−	0.0759101i
$94$	−1.09808	+	1.90192i	−0.113258	+	0.196168i
$95$	8.83013	+	15.2942i	0.905952	+	1.56915i
$96$			1.00000i			0.102062i
$97$	−5.19615	+	3.00000i	−0.527589	+	0.304604i	−0.740034	−	0.672569i	$-0.765191\pi$
$97$	−5.19615	+	3.00000i	−0.527589	+	0.304604i	0.212445	+	0.977173i	$0.431857\pi$
$98$	−0.401924	+	0.232051i	−0.0406004	+	0.0234407i
$99$		−	1.26795i		−	0.127434i
$100$	−4.46410	−	7.73205i	−0.446410	−	0.773205i
$101$	0.964102	−	1.66987i	0.0959317	−	0.166159i	−0.814065	−	0.580773i	$-0.802750\pi$
$101$	0.964102	−	1.66987i	0.0959317	−	0.166159i	0.909997	+	0.414615i	$0.136084\pi$
$102$	−4.96410	−	2.86603i	−0.491519	−	0.283779i
$103$	15.2679			1.50440			0.752198	−	0.658937i	$-0.228994\pi$
$103$	15.2679			1.50440			0.752198	+	0.658937i	$0.228994\pi$
$104$	2.50000	+	2.59808i	0.245145	+	0.254762i
$105$	−10.1962			−0.995043
$106$	5.59808	+	3.23205i	0.543733	+	0.313925i
$107$	−5.09808	+	8.83013i	−0.492850	+	0.853641i	−0.999966	−	0.00823695i	$-0.997378\pi$
$107$	−5.09808	+	8.83013i	−0.492850	+	0.853641i	0.507116	+	0.861878i	$0.330711\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$			1.46410i			0.140236i	0.997539	+	0.0701178i	$0.0223375\pi$
$109$			1.46410i			0.140236i	−0.997539	+	0.0701178i	$0.977662\pi$
$110$	4.09808	−	2.36603i	0.390736	−	0.225592i
$111$	−3.06218	+	1.76795i	−0.290649	+	0.167806i
$112$			2.73205i			0.258155i
$113$	0.669873	+	1.16025i	0.0630163	+	0.109148i	0.895812	−	0.444432i	$-0.146595\pi$
$113$	0.669873	+	1.16025i	0.0630163	+	0.109148i	−0.832796	+	0.553580i	$0.813261\pi$
$114$	2.36603	−	4.09808i	0.221599	−	0.383820i
$115$	13.5622	+	7.83013i	1.26468	+	0.730163i
$116$	4.46410			0.414481
$117$	3.46410	+	1.00000i	0.320256	+	0.0924500i
$118$	8.00000			0.736460
$119$	−13.5622	−	7.83013i	−1.24324	−	0.717787i
$120$	−1.86603	+	3.23205i	−0.170344	+	0.295045i
$121$	−4.69615	−	8.13397i	−0.426923	−	0.739452i
$122$		−	9.19615i		−	0.832581i
$123$	−8.13397	+	4.69615i	−0.733416	+	0.423438i
$124$	−1.26795	+	0.732051i	−0.113865	+	0.0657401i
$125$		−	14.6603i		−	1.31125i
$126$	1.36603	+	2.36603i	0.121695	+	0.210782i
$127$	−4.92820	+	8.53590i	−0.437307	+	0.757438i	−0.997481	−	0.0709368i	$-0.977401\pi$
$127$	−4.92820	+	8.53590i	−0.437307	+	0.757438i	0.560173	+	0.828375i	$0.310734\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	9.66025			0.850538
$130$	3.23205	+	13.0622i	0.283470	+	1.14563i
$131$	6.53590			0.571044			0.285522	−	0.958372i	$-0.407833\pi$
$131$	6.53590			0.571044			0.285522	+	0.958372i	$0.407833\pi$
$132$	−1.09808	−	0.633975i	−0.0955753	−	0.0551804i
$133$	6.46410	−	11.1962i	0.560509	−	0.970830i
$134$	6.56218	+	11.3660i	0.566886	+	0.981875i
$135$			3.73205i			0.321204i
$136$	−4.96410	+	2.86603i	−0.425668	+	0.245760i
$137$	−10.3301	+	5.96410i	−0.882562	+	0.509548i	−0.871502	−	0.490391i	$-0.836854\pi$
$137$	−10.3301	+	5.96410i	−0.882562	+	0.509548i	−0.0110599	+	0.999939i	$0.503521\pi$
$138$		−	4.19615i		−	0.357200i
$139$	−8.92820	−	15.4641i	−0.757280	−	1.31165i	−0.944233	−	0.329279i	$-0.893194\pi$
$139$	−8.92820	−	15.4641i	−0.757280	−	1.31165i	0.186952	−	0.982369i	$-0.440139\pi$
$140$	−5.09808	+	8.83013i	−0.430866	+	0.746282i
$141$	1.90192	+	1.09808i	0.160171	+	0.0924747i
$142$	−4.73205			−0.397105
$143$	−4.43782	+	1.09808i	−0.371109	+	0.0918257i
$144$	1.00000			0.0833333
$145$	14.4282	+	8.33013i	1.19820	+	0.691779i
$146$	3.13397	−	5.42820i	0.259370	−	0.449241i
$147$	0.232051	+	0.401924i	0.0191392	+	0.0331501i
$148$			3.53590i			0.290649i
$149$	11.4282	−	6.59808i	0.936235	−	0.540535i	0.0474568	−	0.998873i	$-0.484888\pi$
$149$	11.4282	−	6.59808i	0.936235	−	0.540535i	0.888778	+	0.458338i	$0.151555\pi$
$150$	−7.73205	+	4.46410i	−0.631319	+	0.364492i
$151$		−	6.73205i		−	0.547847i	−0.961752	−	0.273923i	$-0.911679\pi$
$151$		−	6.73205i		−	0.547847i	0.961752	−	0.273923i	$-0.0883214\pi$
$152$	−2.36603	−	4.09808i	−0.191910	−	0.332398i
$153$	−2.86603	+	4.96410i	−0.231704	+	0.401324i
$154$	−3.00000	−	1.73205i	−0.241747	−	0.139573i
$155$	−5.46410			−0.438887
$156$	2.59808	−	2.50000i	0.208013	−	0.200160i
$157$	7.58846			0.605625			0.302812	−	0.953050i	$-0.402074\pi$
$157$	7.58846			0.605625			0.302812	+	0.953050i	$0.402074\pi$
$158$	2.19615	+	1.26795i	0.174717	+	0.100873i
$159$	3.23205	−	5.59808i	0.256318	−	0.443956i
$160$	1.86603	+	3.23205i	0.147522	+	0.255516i
$161$		−	11.4641i		−	0.903498i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	11.6603	−	6.73205i	0.913302	−	0.527295i	0.0318096	−	0.999494i	$-0.489873\pi$
$163$	11.6603	−	6.73205i	0.913302	−	0.527295i	0.881492	+	0.472199i	$0.156540\pi$
$164$			9.39230i			0.733416i
$165$	−2.36603	−	4.09808i	−0.184195	−	0.319035i
$166$	−0.0980762	+	0.169873i	−0.00761219	+	0.0131847i
$167$	−8.19615	−	4.73205i	−0.634237	−	0.366177i	0.148154	−	0.988964i	$-0.452667\pi$
$167$	−8.19615	−	4.73205i	−0.634237	−	0.366177i	−0.782391	+	0.622787i	$0.786000\pi$
$168$	2.73205			0.210782
$169$	0.500000	−	12.9904i	0.0384615	−	0.999260i
$170$	−21.3923			−1.64071
$171$	−4.09808	−	2.36603i	−0.313388	−	0.180934i
$172$	4.83013	−	8.36603i	0.368294	−	0.637903i
$173$	2.19615	+	3.80385i	0.166970	+	0.289201i	0.937353	−	0.348380i	$-0.113268\pi$
$173$	2.19615	+	3.80385i	0.166970	+	0.289201i	−0.770383	+	0.637582i	$0.779935\pi$
$174$		−	4.46410i		−	0.338423i
$175$	−21.1244	+	12.1962i	−1.59685	+	0.921942i
$176$	−1.09808	+	0.633975i	−0.0827706	+	0.0477876i
$177$		−	8.00000i		−	0.601317i
$178$	4.73205	+	8.19615i	0.354682	+	0.614328i
$179$	−8.02628	+	13.9019i	−0.599912	+	1.03908i	0.392921	+	0.919572i	$0.371465\pi$
$179$	−8.02628	+	13.9019i	−0.599912	+	1.03908i	−0.992833	+	0.119506i	$0.961869\pi$
$180$	3.23205	+	1.86603i	0.240903	+	0.139085i
$181$	−19.1962			−1.42684			−0.713419	−	0.700737i	$-0.752855\pi$
$181$	−19.1962			−1.42684			−0.713419	+	0.700737i	$0.752855\pi$
$182$	7.09808	−	6.83013i	0.526144	−	0.506283i
$183$	−9.19615			−0.679799
$184$	−3.63397	−	2.09808i	−0.267900	−	0.154672i
$185$	−6.59808	+	11.4282i	−0.485100	+	0.840218i
$186$	0.732051	+	1.26795i	0.0536766	+	0.0929705i
$187$		−	7.26795i		−	0.531485i
$188$	1.90192	−	1.09808i	0.138712	−	0.0800854i
$189$	2.36603	−	1.36603i	0.172103	−	0.0993637i
$190$		−	17.6603i		−	1.28121i
$191$	3.46410	+	6.00000i	0.250654	+	0.434145i	0.963706	−	0.266966i	$-0.0860212\pi$
$191$	3.46410	+	6.00000i	0.250654	+	0.434145i	−0.713052	+	0.701111i	$0.752688\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−10.1603	−	5.86603i	−0.731351	−	0.422246i	0.0875652	−	0.996159i	$-0.472091\pi$
$193$	−10.1603	−	5.86603i	−0.731351	−	0.422246i	−0.818916	+	0.573913i	$0.805425\pi$
$194$	6.00000			0.430775
$195$	13.0622	−	3.23205i	0.935402	−	0.231452i
$196$	0.464102			0.0331501
$197$	15.4641	+	8.92820i	1.10177	+	0.636108i	0.936686	−	0.350171i	$-0.113877\pi$
$197$	15.4641	+	8.92820i	1.10177	+	0.636108i	0.165086	+	0.986279i	$0.447210\pi$
$198$	−0.633975	+	1.09808i	−0.0450546	+	0.0780369i
$199$	−7.09808	−	12.2942i	−0.503169	−	0.871515i	−0.999993	−	0.00366345i	$-0.998834\pi$
$199$	−7.09808	−	12.2942i	−0.503169	−	0.871515i	0.496824	−	0.867851i	$-0.334499\pi$
$200$			8.92820i			0.631319i
$201$	11.3660	−	6.56218i	0.801698	−	0.462860i
$202$	−1.66987	+	0.964102i	−0.117492	+	0.0678340i
$203$		−	12.1962i		−	0.856002i
$204$	2.86603	+	4.96410i	0.200662	+	0.347557i
$205$	−17.5263	+	30.3564i	−1.22409	+	2.12018i
$206$	−13.2224	−	7.63397i	−0.921250	−	0.531884i
$207$	−4.19615			−0.291653
$208$	−0.866025	−	3.50000i	−0.0600481	−	0.242681i
$209$	6.00000			0.415029
$210$	8.83013	+	5.09808i	0.609337	+	0.351801i
$211$	−8.19615	+	14.1962i	−0.564246	+	0.977303i	0.432873	+	0.901455i	$0.357500\pi$
$211$	−8.19615	+	14.1962i	−0.564246	+	0.977303i	−0.997119	+	0.0758485i	$0.975833\pi$
$212$	−3.23205	−	5.59808i	−0.221978	−	0.384477i
$213$			4.73205i			0.324235i
$214$	8.83013	−	5.09808i	0.603615	−	0.348497i
$215$	31.2224	−	18.0263i	2.12935	−	1.22938i
$216$		−	1.00000i		−	0.0680414i
$217$	2.00000	+	3.46410i	0.135769	+	0.235159i
$218$	0.732051	−	1.26795i	0.0495807	−	0.0858764i
$219$	−5.42820	−	3.13397i	−0.366804	−	0.211774i
$220$	−4.73205			−0.319035
$221$	19.8564	+	5.73205i	1.33569	+	0.385579i
$222$	3.53590			0.237314
$223$	23.3205	+	13.4641i	1.56166	+	0.901623i	0.997090	+	0.0762356i	$0.0242901\pi$
$223$	23.3205	+	13.4641i	1.56166	+	0.901623i	0.564567	+	0.825387i	$0.309043\pi$
$224$	1.36603	−	2.36603i	0.0912714	−	0.158087i
$225$	4.46410	+	7.73205i	0.297607	+	0.515470i
$226$		−	1.33975i		−	0.0891186i
$227$	−10.5622	+	6.09808i	−0.701036	+	0.404744i	−0.807733	−	0.589548i	$-0.799306\pi$
$227$	−10.5622	+	6.09808i	−0.701036	+	0.404744i	0.106697	+	0.994292i	$0.465973\pi$
$228$	−4.09808	+	2.36603i	−0.271402	+	0.156694i
$229$			11.8564i			0.783493i	0.920073	+	0.391747i	$0.128129\pi$
$229$			11.8564i			0.783493i	−0.920073	+	0.391747i	$0.871871\pi$
$230$	−7.83013	−	13.5622i	−0.516303	−	0.894264i
$231$	−1.73205	+	3.00000i	−0.113961	+	0.197386i
$232$	−3.86603	−	2.23205i	−0.253817	−	0.146541i
$233$	7.85641			0.514690			0.257345	−	0.966320i	$-0.417152\pi$
$233$	7.85641			0.514690			0.257345	+	0.966320i	$0.417152\pi$
$234$	−2.50000	−	2.59808i	−0.163430	−	0.169842i
$235$	8.19615			0.534658
$236$	−6.92820	−	4.00000i	−0.450988	−	0.260378i
$237$	1.26795	−	2.19615i	0.0823622	−	0.142655i
$238$	7.83013	+	13.5622i	0.507552	+	0.879105i
$239$			7.66025i			0.495501i	0.968824	+	0.247750i	$0.0796913\pi$
$239$			7.66025i			0.495501i	−0.968824	+	0.247750i	$0.920309\pi$
$240$	3.23205	−	1.86603i	0.208628	−	0.120451i
$241$	−11.7679	+	6.79423i	−0.758040	+	0.437655i	−0.828592	−	0.559853i	$-0.810857\pi$
$241$	−11.7679	+	6.79423i	−0.758040	+	0.437655i	0.0705514	+	0.997508i	$0.477524\pi$
$242$			9.39230i			0.603760i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−4.59808	+	7.96410i	−0.294362	+	0.509849i
$245$	1.50000	+	0.866025i	0.0958315	+	0.0553283i
$246$	9.39230			0.598831
$247$	−4.73205	+	16.3923i	−0.301093	+	1.04302i
$248$	1.46410			0.0929705
$249$	0.169873	+	0.0980762i	0.0107653	+	0.00621533i
$250$	−7.33013	+	12.6962i	−0.463598	+	0.802975i
$251$	6.73205	+	11.6603i	0.424923	+	0.735989i	0.996413	−	0.0846203i	$-0.0269677\pi$
$251$	6.73205	+	11.6603i	0.424923	+	0.735989i	−0.571490	+	0.820609i	$0.693634\pi$
$252$		−	2.73205i		−	0.172103i
$253$	4.60770	−	2.66025i	0.289683	−	0.167249i
$254$	8.53590	−	4.92820i	0.535590	−	0.309223i
$255$			21.3923i			1.33964i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.66987	−	8.08846i	0.291299	−	0.504544i	−0.682818	−	0.730588i	$-0.739246\pi$
$257$	4.66987	−	8.08846i	0.291299	−	0.504544i	0.974117	+	0.226044i	$0.0725793\pi$
$258$	−8.36603	−	4.83013i	−0.520846	−	0.300711i
$259$	9.66025			0.600259
$260$	3.73205	−	12.9282i	0.231452	−	0.801773i
$261$	−4.46410			−0.276321
$262$	−5.66025	−	3.26795i	−0.349692	−	0.201895i
$263$	5.02628	−	8.70577i	0.309934	−	0.536821i	−0.668414	−	0.743790i	$-0.733026\pi$
$263$	5.02628	−	8.70577i	0.309934	−	0.536821i	0.978348	+	0.206969i	$0.0663598\pi$
$264$	0.633975	+	1.09808i	0.0390184	+	0.0675819i
$265$		−	24.1244i		−	1.48195i
$266$	−11.1962	+	6.46410i	−0.686480	+	0.396339i
$267$	8.19615	−	4.73205i	0.501596	−	0.289597i
$268$		−	13.1244i		−	0.801698i
$269$	−2.73205	−	4.73205i	−0.166576	−	0.288518i	0.770638	−	0.637273i	$-0.219938\pi$
$269$	−2.73205	−	4.73205i	−0.166576	−	0.288518i	−0.937214	+	0.348755i	$0.886604\pi$
$270$	1.86603	−	3.23205i	0.113563	−	0.196696i
$271$	−18.9282	−	10.9282i	−1.14981	−	0.663841i	−0.200966	−	0.979598i	$-0.564408\pi$
$271$	−18.9282	−	10.9282i	−1.14981	−	0.663841i	−0.948840	+	0.315757i	$0.897742\pi$
$272$	5.73205			0.347557
$273$	−6.83013	−	7.09808i	−0.413378	−	0.429595i
$274$	11.9282			0.720609
$275$	−9.80385	−	5.66025i	−0.591194	−	0.341326i
$276$	−2.09808	+	3.63397i	−0.126289	+	0.218740i
$277$	−2.86603	−	4.96410i	−0.172203	−	0.298264i	0.766987	−	0.641663i	$-0.221755\pi$
$277$	−2.86603	−	4.96410i	−0.172203	−	0.298264i	−0.939190	+	0.343399i	$0.888422\pi$
$278$			17.8564i			1.07096i
$279$	1.26795	−	0.732051i	0.0759101	−	0.0438267i
$280$	8.83013	−	5.09808i	0.527701	−	0.304668i
$281$		−	12.3205i		−	0.734980i	−0.930027	−	0.367490i	$-0.880217\pi$
$281$		−	12.3205i		−	0.734980i	0.930027	−	0.367490i	$-0.119783\pi$
$282$	−1.09808	−	1.90192i	−0.0653895	−	0.113258i
$283$	12.8301	−	22.2224i	0.762672	−	1.32099i	−0.178797	−	0.983886i	$-0.557220\pi$
$283$	12.8301	−	22.2224i	0.762672	−	1.32099i	0.941469	−	0.337100i	$-0.109446\pi$
$284$	4.09808	+	2.36603i	0.243176	+	0.140398i
$285$	−17.6603			−1.04610
$286$	4.39230	+	1.26795i	0.259722	+	0.0749754i
$287$	25.6603			1.51468
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	−7.92820	+	13.7321i	−0.466365	+	0.807768i
$290$	−8.33013	−	14.4282i	−0.489162	−	0.847253i
$291$		−	6.00000i		−	0.351726i
$292$	−5.42820	+	3.13397i	−0.317662	+	0.183402i
$293$	−26.4282	+	15.2583i	−1.54395	+	0.891401i	−0.545368	+	0.838196i	$0.683610\pi$
$293$	−26.4282	+	15.2583i	−1.54395	+	0.891401i	−0.998584	+	0.0532048i	$0.983056\pi$
$294$		−	0.464102i		−	0.0270670i
$295$	−14.9282	−	25.8564i	−0.869154	−	1.50542i
$296$	1.76795	−	3.06218i	0.102760	−	0.177985i
$297$	1.09808	+	0.633975i	0.0637168	+	0.0367869i
$298$	−13.1962			−0.764433
$299$	3.63397	+	14.6865i	0.210158	+	0.849344i
$300$	8.92820			0.515470
$301$	−22.8564	−	13.1962i	−1.31742	−	0.760614i
$302$	−3.36603	+	5.83013i	−0.193693	+	0.335486i
$303$	0.964102	+	1.66987i	0.0553862	+	0.0959317i
$304$			4.73205i			0.271402i
$305$	−29.7224	+	17.1603i	−1.70190	+	0.982593i
$306$	4.96410	−	2.86603i	0.283779	−	0.163840i
$307$			22.5885i			1.28919i	0.764524	+	0.644596i	$0.222974\pi$
$307$			22.5885i			1.28919i	−0.764524	+	0.644596i	$0.777026\pi$
$308$	1.73205	+	3.00000i	0.0986928	+	0.170941i
$309$	−7.63397	+	13.2224i	−0.434282	+	0.752198i
$310$	4.73205	+	2.73205i	0.268762	+	0.155170i
$311$	1.66025			0.0941444			0.0470722	−	0.998891i	$-0.485011\pi$
$311$	1.66025			0.0941444			0.0470722	+	0.998891i	$0.485011\pi$
$312$	−3.50000	+	0.866025i	−0.198148	+	0.0490290i
$313$	6.53590			0.369431			0.184715	−	0.982792i	$-0.440864\pi$
$313$	6.53590			0.369431			0.184715	+	0.982792i	$0.440864\pi$
$314$	−6.57180	−	3.79423i	−0.370868	−	0.214121i
$315$	5.09808	−	8.83013i	0.287244	−	0.497521i
$316$	−1.26795	−	2.19615i	−0.0713277	−	0.123543i
$317$			20.6603i			1.16040i	0.814476	+	0.580198i	$0.197025\pi$
$317$			20.6603i			1.16040i	−0.814476	+	0.580198i	$0.802975\pi$
$318$	−5.59808	+	3.23205i	−0.313925	+	0.181244i
$319$	4.90192	−	2.83013i	0.274455	−	0.158457i
$320$		−	3.73205i		−	0.208628i
$321$	−5.09808	−	8.83013i	−0.284547	−	0.492850i
$322$	−5.73205	+	9.92820i	−0.319435	+	0.553277i
$323$	−23.4904	−	13.5622i	−1.30704	−	0.754620i
$324$	−1.00000			−0.0555556
$325$	23.1962	−	22.3205i	1.28669	−	1.23812i
$326$	−13.4641			−0.745708
$327$	−1.26795	−	0.732051i	−0.0701178	−	0.0404825i
$328$	4.69615	−	8.13397i	0.259302	−	0.449124i
$329$	−3.00000	−	5.19615i	−0.165395	−	0.286473i
$330$			4.73205i			0.260491i
$331$	17.3205	−	10.0000i	0.952021	−	0.549650i	0.0583130	−	0.998298i	$-0.481428\pi$
$331$	17.3205	−	10.0000i	0.952021	−	0.549650i	0.893708	+	0.448649i	$0.148095\pi$
$332$	0.169873	−	0.0980762i	0.00932299	−	0.00538263i
$333$		−	3.53590i		−	0.193766i
$334$	4.73205	+	8.19615i	0.258926	+	0.448474i
$335$	24.4904	−	42.4186i	1.33805	−	2.31757i
$336$	−2.36603	−	1.36603i	−0.129077	−	0.0745228i
$337$	20.8564			1.13612			0.568060	−	0.822987i	$-0.307694\pi$
$337$	20.8564			1.13612			0.568060	+	0.822987i	$0.307694\pi$
$338$	−6.92820	+	11.0000i	−0.376845	+	0.598321i
$339$	−1.33975			−0.0727650
$340$	18.5263	+	10.6962i	1.00473	+	0.580080i
$341$	−0.928203	+	1.60770i	−0.0502650	+	0.0870616i
$342$	2.36603	+	4.09808i	0.127940	+	0.221599i
$343$			17.8564i			0.964155i
$344$	−8.36603	+	4.83013i	−0.451066	+	0.260423i
$345$	−13.5622	+	7.83013i	−0.730163	+	0.421560i
$346$		−	4.39230i		−	0.236132i
$347$	−16.5622	−	28.6865i	−0.889104	−	1.53997i	−0.840936	−	0.541135i	$-0.817995\pi$
$347$	−16.5622	−	28.6865i	−0.889104	−	1.53997i	−0.0481683	−	0.998839i	$-0.515338\pi$
$348$	−2.23205	+	3.86603i	−0.119650	+	0.207241i
$349$	13.2679	+	7.66025i	0.710217	+	0.410044i	0.811141	−	0.584850i	$-0.198847\pi$
$349$	13.2679	+	7.66025i	0.710217	+	0.410044i	−0.100924	+	0.994894i	$0.532180\pi$
$350$	24.3923			1.30382
$351$	−2.59808	+	2.50000i	−0.138675	+	0.133440i
$352$	1.26795			0.0675819
$353$	18.8660	+	10.8923i	1.00414	+	0.579739i	0.909470	−	0.415770i	$-0.136488\pi$
$353$	18.8660	+	10.8923i	1.00414	+	0.579739i	0.0946674	+	0.995509i	$0.469821\pi$
$354$	−4.00000	+	6.92820i	−0.212598	+	0.368230i
$355$	8.83013	+	15.2942i	0.468654	+	0.811733i
$356$		−	9.46410i		−	0.501596i
$357$	13.5622	−	7.83013i	0.717787	−	0.414414i
$358$	13.9019	−	8.02628i	0.734740	−	0.424202i
$359$			1.12436i			0.0593412i	0.999560	+	0.0296706i	$0.00944584\pi$
$359$			1.12436i			0.0593412i	−0.999560	+	0.0296706i	$0.990554\pi$
$360$	−1.86603	−	3.23205i	−0.0983482	−	0.170344i
$361$	1.69615	−	2.93782i	0.0892712	−	0.154622i
$362$	16.6244	+	9.59808i	0.873757	+	0.504464i
$363$	9.39230			0.492968
$364$	−9.56218	+	2.36603i	−0.501194	+	0.124013i
$365$	−23.3923			−1.22441
$366$	7.96410	+	4.59808i	0.416290	+	0.240345i
$367$	5.63397	−	9.75833i	0.294091	−	0.509381i	−0.680682	−	0.732579i	$-0.738316\pi$
$367$	5.63397	−	9.75833i	0.294091	−	0.509381i	0.974773	+	0.223198i	$0.0716498\pi$
$368$	2.09808	+	3.63397i	0.109370	+	0.189434i
$369$		−	9.39230i		−	0.488944i
$370$	11.4282	−	6.59808i	0.594124	−	0.343018i
$371$	−15.2942	+	8.83013i	−0.794037	+	0.458437i
$372$		−	1.46410i		−	0.0759101i
$373$	6.86603	+	11.8923i	0.355509	+	0.615760i	0.987205	−	0.159456i	$-0.0509741\pi$
$373$	6.86603	+	11.8923i	0.355509	+	0.615760i	−0.631696	+	0.775216i	$0.717641\pi$
$374$	−3.63397	+	6.29423i	−0.187908	+	0.325467i
$375$	12.6962	+	7.33013i	0.655626	+	0.378526i
$376$	−2.19615			−0.113258
$377$	3.86603	+	15.6244i	0.199110	+	0.804695i
$378$	−2.73205			−0.140522
$379$	4.73205	+	2.73205i	0.243069	+	0.140336i	0.616587	−	0.787287i	$-0.288515\pi$
$379$	4.73205	+	2.73205i	0.243069	+	0.140336i	−0.373517	+	0.927623i	$0.621848\pi$
$380$	−8.83013	+	15.2942i	−0.452976	+	0.784577i
$381$	−4.92820	−	8.53590i	−0.252479	−	0.437307i
$382$		−	6.92820i		−	0.354478i
$383$	−1.26795	+	0.732051i	−0.0647892	+	0.0374060i	−0.532045	−	0.846716i	$-0.678576\pi$
$383$	−1.26795	+	0.732051i	−0.0647892	+	0.0374060i	0.467255	+	0.884122i	$0.345243\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$			12.9282i			0.658882i
$386$	5.86603	+	10.1603i	0.298573	+	0.517143i
$387$	−4.83013	+	8.36603i	−0.245529	+	0.425269i
$388$	−5.19615	−	3.00000i	−0.263795	−	0.152302i
$389$	−11.7846			−0.597503			−0.298752	−	0.954331i	$-0.596570\pi$
$389$	−11.7846			−0.597503			−0.298752	+	0.954331i	$0.596570\pi$
$390$	−12.9282	−	3.73205i	−0.654645	−	0.188980i
$391$	−24.0526			−1.21639
$392$	−0.401924	−	0.232051i	−0.0203002	−	0.0117203i
$393$	−3.26795	+	5.66025i	−0.164846	+	0.285522i
$394$	−8.92820	−	15.4641i	−0.449796	−	0.779070i
$395$		−	9.46410i		−	0.476191i
$396$	1.09808	−	0.633975i	0.0551804	−	0.0318584i
$397$	−17.6603	+	10.1962i	−0.886343	+	0.511730i	−0.872744	−	0.488177i	$-0.837662\pi$
$397$	−17.6603	+	10.1962i	−0.886343	+	0.511730i	−0.0135983	+	0.999908i	$0.504329\pi$
$398$			14.1962i			0.711589i
$399$	6.46410	+	11.1962i	0.323610	+	0.560509i
$400$	4.46410	−	7.73205i	0.223205	−	0.386603i
$401$	6.99038	+	4.03590i	0.349083	+	0.201543i	0.664281	−	0.747483i	$-0.268738\pi$
$401$	6.99038	+	4.03590i	0.349083	+	0.201543i	−0.315198	+	0.949026i	$0.602071\pi$
$402$	−13.1244			−0.654583
$403$	−3.66025	−	3.80385i	−0.182330	−	0.189483i
$404$	1.92820			0.0959317
$405$	−3.23205	−	1.86603i	−0.160602	−	0.0927235i
$406$	−6.09808	+	10.5622i	−0.302642	+	0.524192i
$407$	2.24167	+	3.88269i	0.111115	+	0.192458i
$408$		−	5.73205i		−	0.283779i
$409$	15.3564	−	8.86603i	0.759325	−	0.438397i	−0.0697281	−	0.997566i	$-0.522213\pi$
$409$	15.3564	−	8.86603i	0.759325	−	0.438397i	0.829053	+	0.559169i	$0.188880\pi$
$410$	30.3564	−	17.5263i	1.49920	−	0.865561i
$411$		−	11.9282i		−	0.588375i
$412$	7.63397	+	13.2224i	0.376099	+	0.651422i
$413$	−10.9282	+	18.9282i	−0.537742	+	0.931396i
$414$	3.63397	+	2.09808i	0.178600	+	0.103115i
$415$	0.732051			0.0359350
$416$	−1.00000	+	3.46410i	−0.0490290	+	0.169842i
$417$	17.8564			0.874432
$418$	−5.19615	−	3.00000i	−0.254152	−	0.146735i
$419$	8.73205	−	15.1244i	0.426589	−	0.738873i	−0.569979	−	0.821659i	$-0.693049\pi$
$419$	8.73205	−	15.1244i	0.426589	−	0.738873i	0.996567	+	0.0827863i	$0.0263819\pi$
$420$	−5.09808	−	8.83013i	−0.248761	−	0.430866i
$421$		−	22.7128i		−	1.10695i	−0.832864	−	0.553477i	$-0.813301\pi$
$421$		−	22.7128i		−	1.10695i	0.832864	−	0.553477i	$-0.186699\pi$
$422$	14.1962	−	8.19615i	0.691058	−	0.398982i
$423$	−1.90192	+	1.09808i	−0.0924747	+	0.0533903i
$424$			6.46410i			0.313925i
$425$	25.5885	+	44.3205i	1.24122	+	2.14986i
$426$	2.36603	−	4.09808i	0.114634	−	0.198552i
$427$	21.7583	+	12.5622i	1.05296	+	0.607926i
$428$	−10.1962			−0.492850
$429$	1.26795	−	4.39230i	0.0612172	−	0.212062i
$430$	−36.0526			−1.73861
$431$	−11.3660	−	6.56218i	−0.547482	−	0.316089i	0.200624	−	0.979668i	$-0.435703\pi$
$431$	−11.3660	−	6.56218i	−0.547482	−	0.316089i	−0.748106	+	0.663579i	$0.769036\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	6.42820	+	11.1340i	0.308920	+	0.535065i	0.978126	−	0.208012i	$-0.0666992\pi$
$433$	6.42820	+	11.1340i	0.308920	+	0.535065i	−0.669207	+	0.743076i	$0.733366\pi$
$434$		−	4.00000i		−	0.192006i
$435$	−14.4282	+	8.33013i	−0.691779	+	0.399399i
$436$	−1.26795	+	0.732051i	−0.0607238	+	0.0350589i
$437$		−	19.8564i		−	0.949861i
$438$	3.13397	+	5.42820i	0.149747	+	0.259370i
$439$	−0.169873	+	0.294229i	−0.00810760	+	0.0140428i	−0.870051	−	0.492962i	$-0.835914\pi$
$439$	−0.169873	+	0.294229i	−0.00810760	+	0.0140428i	0.861943	+	0.507005i	$0.169247\pi$
$440$	4.09808	+	2.36603i	0.195368	+	0.112796i
$441$	−0.464102			−0.0221001
$442$	−14.3301	−	14.8923i	−0.681615	−	0.708355i
$443$	15.6077			0.741544			0.370772	−	0.928724i	$-0.379093\pi$
$443$	15.6077			0.741544			0.370772	+	0.928724i	$0.379093\pi$
$444$	−3.06218	−	1.76795i	−0.145325	−	0.0839032i
$445$	17.6603	−	30.5885i	0.837176	−	1.45003i
$446$	−13.4641	−	23.3205i	−0.637544	−	1.10426i
$447$			13.1962i			0.624157i
$448$	−2.36603	+	1.36603i	−0.111784	+	0.0645386i
$449$	−9.80385	+	5.66025i	−0.462672	+	0.267124i	−0.713167	−	0.700994i	$-0.752740\pi$
$449$	−9.80385	+	5.66025i	−0.462672	+	0.267124i	0.250495	+	0.968118i	$0.419407\pi$
$450$		−	8.92820i		−	0.420880i
$451$	5.95448	+	10.3135i	0.280386	+	0.485642i
$452$	−0.669873	+	1.16025i	−0.0315082	+	0.0545738i
$453$	5.83013	+	3.36603i	0.273923	+	0.158150i
$454$	12.1962			0.572394
$455$	−35.3205	−	10.1962i	−1.65585	−	0.478003i
$456$	4.73205			0.221599
$457$	−1.16025	−	0.669873i	−0.0542744	−	0.0313353i	0.472617	−	0.881268i	$-0.343309\pi$
$457$	−1.16025	−	0.669873i	−0.0542744	−	0.0313353i	−0.526892	+	0.849932i	$0.676643\pi$
$458$	5.92820	−	10.2679i	0.277007	−	0.479790i
$459$	−2.86603	−	4.96410i	−0.133775	−	0.231704i
$460$			15.6603i			0.730163i
$461$	19.2846	−	11.1340i	0.898174	−	0.518561i	0.0215666	−	0.999767i	$-0.493135\pi$
$461$	19.2846	−	11.1340i	0.898174	−	0.518561i	0.876607	+	0.481207i	$0.159801\pi$
$462$	3.00000	−	1.73205i	0.139573	−	0.0805823i
$463$		−	10.0526i		−	0.467182i	−0.972335	−	0.233591i	$-0.924952\pi$
$463$		−	10.0526i		−	0.467182i	0.972335	−	0.233591i	$-0.0750477\pi$
$464$	2.23205	+	3.86603i	0.103620	+	0.179476i
$465$	2.73205	−	4.73205i	0.126696	−	0.219444i
$466$	−6.80385	−	3.92820i	−0.315182	−	0.181971i
$467$	−18.5885			−0.860171			−0.430086	−	0.902788i	$-0.641517\pi$
$467$	−18.5885			−0.860171			−0.430086	+	0.902788i	$0.641517\pi$
$468$	0.866025	+	3.50000i	0.0400320	+	0.161788i
$469$	−35.8564			−1.65570
$470$	−7.09808	−	4.09808i	−0.327410	−	0.189030i
$471$	−3.79423	+	6.57180i	−0.174829	+	0.302812i
$472$	4.00000	+	6.92820i	0.184115	+	0.318896i
$473$		−	12.2487i		−	0.563196i
$474$	−2.19615	+	1.26795i	−0.100873	+	0.0582388i
$475$	−36.5885	+	21.1244i	−1.67879	+	0.969252i
$476$		−	15.6603i		−	0.717787i
$477$	3.23205	+	5.59808i	0.147985	+	0.256318i
$478$	3.83013	−	6.63397i	0.175186	−	0.303431i
$479$	28.9808	+	16.7321i	1.32416	+	0.764507i	0.984390	−	0.176000i	$-0.0563159\pi$
$479$	28.9808	+	16.7321i	1.32416	+	0.764507i	0.339775	+	0.940507i	$0.389649\pi$
$480$	−3.73205			−0.170344
$481$	−12.3756	+	3.06218i	−0.564281	+	0.139623i
$482$	13.5885			0.618937
$483$	9.92820	+	5.73205i	0.451749	+	0.260817i
$484$	4.69615	−	8.13397i	0.213461	−	0.369726i
$485$	−11.1962	−	19.3923i	−0.508391	−	0.880559i
$486$			1.00000i			0.0453609i
$487$	−2.70577	+	1.56218i	−0.122610	+	0.0707890i	−0.560051	−	0.828458i	$-0.689218\pi$
$487$	−2.70577	+	1.56218i	−0.122610	+	0.0707890i	0.437441	+	0.899247i	$0.355885\pi$
$488$	7.96410	−	4.59808i	0.360518	−	0.208145i
$489$			13.4641i			0.608868i
$490$	−0.866025	−	1.50000i	−0.0391230	−	0.0677631i
$491$	4.36603	−	7.56218i	0.197036	−	0.341276i	−0.750530	−	0.660836i	$-0.770202\pi$
$491$	4.36603	−	7.56218i	0.197036	−	0.341276i	0.947566	+	0.319560i	$0.103535\pi$
$492$	−8.13397	−	4.69615i	−0.366708	−	0.211719i
$493$	−25.5885			−1.15245
$494$	12.2942	−	11.8301i	0.553143	−	0.532263i
$495$	4.73205			0.212690
$496$	−1.26795	−	0.732051i	−0.0569326	−	0.0328701i
$497$	6.46410	−	11.1962i	0.289955	−	0.502216i
$498$	−0.0980762	−	0.169873i	−0.00439490	−	0.00761219i
$499$			32.0000i			1.43252i	0.697835	+	0.716258i	$0.254147\pi$
$499$			32.0000i			1.43252i	−0.697835	+	0.716258i	$0.745853\pi$
$500$	12.6962	−	7.33013i	0.567789	−	0.327813i
$501$	8.19615	−	4.73205i	0.366177	−	0.211412i
$502$		−	13.4641i		−	0.600932i
$503$	−20.4904	−	35.4904i	−0.913621	−	1.58244i	−0.808908	−	0.587935i	$-0.799941\pi$
$503$	−20.4904	−	35.4904i	−0.913621	−	1.58244i	−0.104713	−	0.994502i	$-0.533392\pi$
$504$	−1.36603	+	2.36603i	−0.0608476	+	0.105391i
$505$	6.23205	+	3.59808i	0.277323	+	0.160112i
$506$	−5.32051			−0.236525
$507$	11.0000	+	6.92820i	0.488527	+	0.307692i
$508$	−9.85641			−0.437307
$509$	−11.8923	−	6.86603i	−0.527117	−	0.304331i	0.212725	−	0.977112i	$-0.431766\pi$
$509$	−11.8923	−	6.86603i	−0.527117	−	0.304331i	−0.739842	+	0.672781i	$0.765100\pi$
$510$	10.6962	−	18.5263i	0.473634	−	0.820357i
$511$	8.56218	+	14.8301i	0.378768	+	0.656046i
$512$			1.00000i			0.0441942i
$513$	4.09808	−	2.36603i	0.180934	−	0.104463i
$514$	−8.08846	+	4.66987i	−0.356767	+	0.205979i
$515$			56.9808i			2.51087i
$516$	4.83013	+	8.36603i	0.212634	+	0.368294i
$517$	1.39230	−	2.41154i	0.0612335	−	0.106060i
$518$	−8.36603	−	4.83013i	−0.367582	−	0.212224i
$519$	−4.39230			−0.192801
$520$	−9.69615	+	9.33013i	−0.425204	+	0.409153i
$521$	41.4449			1.81573			0.907866	−	0.419260i	$-0.137710\pi$
$521$	41.4449			1.81573			0.907866	+	0.419260i	$0.137710\pi$
$522$	3.86603	+	2.23205i	0.169211	+	0.0976942i
$523$	11.2224	−	19.4378i	0.490723	−	0.849957i	−0.509220	−	0.860636i	$-0.670066\pi$
$523$	11.2224	−	19.4378i	0.490723	−	0.849957i	0.999943	+	0.0106796i	$0.00339949\pi$
$524$	3.26795	+	5.66025i	0.142761	+	0.247269i
$525$		−	24.3923i		−	1.06457i
$526$	−8.70577	+	5.02628i	−0.379590	+	0.219156i
$527$	7.26795	−	4.19615i	0.316597	−	0.182787i
$528$		−	1.26795i		−	0.0551804i
$529$	2.69615	+	4.66987i	0.117224	+	0.203038i
$530$	−12.0622	+	20.8923i	−0.523948	+	0.907504i
$531$	6.92820	+	4.00000i	0.300658	+	0.173585i
$532$	12.9282			0.560509
$533$	−32.8731	+	8.13397i	−1.42389	+	0.352322i
$534$	−9.46410			−0.409552
$535$	−32.9545	−	19.0263i	−1.42475	−	0.822578i
$536$	−6.56218	+	11.3660i	−0.283443	+	0.490938i
$537$	−8.02628	−	13.9019i	−0.346360	−	0.599912i
$538$			5.46410i			0.235574i
$539$	0.509619	−	0.294229i	0.0219508	−	0.0126733i
$540$	−3.23205	+	1.86603i	−0.139085	+	0.0803009i
$541$		−	5.67949i		−	0.244180i	−0.992519	−	0.122090i	$-0.961040\pi$
$541$		−	5.67949i		−	0.244180i	0.992519	−	0.122090i	$-0.0389597\pi$
$542$	10.9282	+	18.9282i	0.469407	+	0.813036i
$543$	9.59808	−	16.6244i	0.411893	−	0.713419i
$544$	−4.96410	−	2.86603i	−0.212834	−	0.122880i
$545$	−5.46410			−0.234056
$546$	2.36603	+	9.56218i	0.101257	+	0.409223i
$547$	−4.19615			−0.179415			−0.0897073	−	0.995968i	$-0.528593\pi$
$547$	−4.19615			−0.179415			−0.0897073	+	0.995968i	$0.528593\pi$
$548$	−10.3301	−	5.96410i	−0.441281	−	0.254774i
$549$	4.59808	−	7.96410i	0.196241	−	0.339900i
$550$	5.66025	+	9.80385i	0.241354	+	0.418037i
$551$		−	21.1244i		−	0.899928i
$552$	3.63397	−	2.09808i	0.154672	−	0.0893001i
$553$	−6.00000	+	3.46410i	−0.255146	+	0.147309i
$554$			5.73205i			0.243532i
$555$	−6.59808	−	11.4282i	−0.280073	−	0.485100i
$556$	8.92820	−	15.4641i	0.378640	−	0.655824i
$557$	36.6962	+	21.1865i	1.55487	+	0.897702i	0.997734	+	0.0672780i	$0.0214314\pi$
$557$	36.6962	+	21.1865i	1.55487	+	0.897702i	0.557132	+	0.830424i	$0.311902\pi$
$558$	−1.46410			−0.0619804
$559$	33.4641	+	9.66025i	1.41538	+	0.408585i
$560$	−10.1962			−0.430866
$561$	6.29423	+	3.63397i	0.265743	+	0.153427i
$562$	−6.16025	+	10.6699i	−0.259855	+	0.450081i
$563$	17.4641	+	30.2487i	0.736024	+	1.27483i	0.954273	+	0.298938i	$0.0966324\pi$
$563$	17.4641	+	30.2487i	0.736024	+	1.27483i	−0.218248	+	0.975893i	$0.570034\pi$
$564$			2.19615i			0.0924747i
$565$	−4.33013	+	2.50000i	−0.182170	+	0.105176i
$566$	−22.2224	+	12.8301i	−0.934078	+	0.539290i
$567$			2.73205i			0.114735i
$568$	−2.36603	−	4.09808i	−0.0992762	−	0.171951i
$569$	15.3205	−	26.5359i	0.642269	−	1.11244i	−0.342656	−	0.939461i	$-0.611326\pi$
$569$	15.3205	−	26.5359i	0.642269	−	1.11244i	0.984925	−	0.172982i	$-0.0553402\pi$
$570$	15.2942	+	8.83013i	0.640605	+	0.369853i
$571$	−14.0526			−0.588081			−0.294041	−	0.955793i	$-0.595000\pi$
$571$	−14.0526			−0.588081			−0.294041	+	0.955793i	$0.595000\pi$
$572$	−3.16987	−	3.29423i	−0.132539	−	0.137739i
$573$	−6.92820			−0.289430
$574$	−22.2224	−	12.8301i	−0.927546	−	0.535519i
$575$	−18.7321	+	32.4449i	−0.781181	+	1.35304i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$			3.73205i			0.155367i	0.996978	+	0.0776837i	$0.0247524\pi$
$577$			3.73205i			0.155367i	−0.996978	+	0.0776837i	$0.975248\pi$
$578$	13.7321	−	7.92820i	0.571178	−	0.329770i
$579$	10.1603	−	5.86603i	0.422246	−	0.243784i
$580$			16.6603i			0.691779i
$581$	−0.267949	−	0.464102i	−0.0111164	−	0.0192542i
$582$	−3.00000	+	5.19615i	−0.124354	+	0.215387i
$583$	−7.09808	−	4.09808i	−0.293972	−	0.169725i
$584$	6.26795			0.259370
$585$	−3.73205	+	12.9282i	−0.154301	+	0.534515i
$586$	30.5167			1.26063
$587$	−13.8564	−	8.00000i	−0.571915	−	0.330195i	0.185999	−	0.982550i	$-0.440448\pi$
$587$	−13.8564	−	8.00000i	−0.571915	−	0.330195i	−0.757914	+	0.652355i	$0.773781\pi$
$588$	−0.232051	+	0.401924i	−0.00956961	+	0.0165751i
$589$	3.46410	+	6.00000i	0.142736	+	0.247226i
$590$			29.8564i			1.22917i
$591$	−15.4641	+	8.92820i	−0.636108	+	0.367257i
$592$	−3.06218	+	1.76795i	−0.125855	+	0.0726623i
$593$			9.14359i			0.375482i	0.982219	+	0.187741i	$0.0601166\pi$
$593$			9.14359i			0.375482i	−0.982219	+	0.187741i	$0.939883\pi$
$594$	−0.633975	−	1.09808i	−0.0260123	−	0.0450546i
$595$	29.2224	−	50.6147i	1.19800	−	2.07500i
$596$	11.4282	+	6.59808i	0.468117	+	0.270268i
$597$	14.1962			0.581010
$598$	4.19615	−	14.5359i	0.171593	−	0.594417i
$599$	−2.53590			−0.103614			−0.0518070	−	0.998657i	$-0.516498\pi$
$599$	−2.53590			−0.103614			−0.0518070	+	0.998657i	$0.516498\pi$
$600$	−7.73205	−	4.46410i	−0.315660	−	0.182246i
$601$	−3.96410	+	6.86603i	−0.161699	+	0.280071i	−0.935478	−	0.353385i	$-0.885031\pi$
$601$	−3.96410	+	6.86603i	−0.161699	+	0.280071i	0.773779	+	0.633456i	$0.218364\pi$
$602$	13.1962	+	22.8564i	0.537835	+	0.931558i
$603$			13.1244i			0.534465i
$604$	5.83013	−	3.36603i	0.237225	−	0.136962i
$605$	30.3564	−	17.5263i	1.23416	−	0.712545i
$606$		−	1.92820i		−	0.0783279i
$607$	20.3923	+	35.3205i	0.827698	+	1.43362i	0.899840	+	0.436221i	$0.143683\pi$
$607$	20.3923	+	35.3205i	0.827698	+	1.43362i	−0.0721415	+	0.997394i	$0.522983\pi$
$608$	2.36603	−	4.09808i	0.0959550	−	0.166199i
$609$	10.5622	+	6.09808i	0.428001	+	0.247107i
$610$	34.3205			1.38960
$611$	5.49038	+	5.70577i	0.222117	+	0.230831i
$612$	−5.73205			−0.231704
$613$	8.13397	+	4.69615i	0.328528	+	0.189676i	0.655187	−	0.755466i	$-0.272590\pi$
$613$	8.13397	+	4.69615i	0.328528	+	0.189676i	−0.326659	+	0.945142i	$0.605923\pi$
$614$	11.2942	−	19.5622i	0.455798	−	0.789465i
$615$	−17.5263	−	30.3564i	−0.706728	−	1.22409i
$616$		−	3.46410i		−	0.139573i
$617$	−11.4737	+	6.62436i	−0.461915	+	0.266687i	−0.712849	−	0.701318i	$-0.752596\pi$
$617$	−11.4737	+	6.62436i	−0.461915	+	0.266687i	0.250934	+	0.968004i	$0.419262\pi$
$618$	13.2224	−	7.63397i	0.531884	−	0.307083i
$619$		−	17.4641i		−	0.701942i	−0.936386	−	0.350971i	$-0.885852\pi$
$619$		−	17.4641i		−	0.701942i	0.936386	−	0.350971i	$-0.114148\pi$
$620$	−2.73205	−	4.73205i	−0.109722	−	0.190044i
$621$	2.09808	−	3.63397i	0.0841929	−	0.145826i
$622$	−1.43782	−	0.830127i	−0.0576514	−	0.0332851i
$623$	−25.8564			−1.03592
$624$	3.46410	+	1.00000i	0.138675	+	0.0400320i
$625$	10.0718			0.402872
$626$	−5.66025	−	3.26795i	−0.226229	−	0.130614i
$627$	−3.00000	+	5.19615i	−0.119808	+	0.207514i
$628$	3.79423	+	6.57180i	0.151406	+	0.262243i
$629$		−	20.2679i		−	0.808136i
$630$	−8.83013	+	5.09808i	−0.351801	+	0.203112i
$631$	6.67949	−	3.85641i	0.265906	−	0.153521i	−0.361119	−	0.932520i	$-0.617605\pi$
$631$	6.67949	−	3.85641i	0.265906	−	0.153521i	0.627026	+	0.778998i	$0.284272\pi$
$632$			2.53590i			0.100873i
$633$	−8.19615	−	14.1962i	−0.325768	−	0.564246i
$634$	10.3301	−	17.8923i	0.410262	−	0.710594i
$635$	−31.8564	−	18.3923i	−1.26418	−	0.729876i
$636$	6.46410			0.256318
$637$	0.401924	+	1.62436i	0.0159248	+	0.0643593i
$638$	−5.66025			−0.224092
$639$	−4.09808	−	2.36603i	−0.162117	−	0.0935985i
$640$	−1.86603	+	3.23205i	−0.0737611	+	0.127758i
$641$	−12.9904	−	22.5000i	−0.513089	−	0.888697i	−0.999885	−	0.0151806i	$-0.995168\pi$
$641$	−12.9904	−	22.5000i	−0.513089	−	0.888697i	0.486796	−	0.873516i	$-0.338166\pi$
$642$			10.1962i			0.402410i
$643$	−12.0000	+	6.92820i	−0.473234	+	0.273222i	−0.717592	−	0.696463i	$-0.754756\pi$
$643$	−12.0000	+	6.92820i	−0.473234	+	0.273222i	0.244359	+	0.969685i	$0.421423\pi$
$644$	9.92820	−	5.73205i	0.391226	−	0.225874i
$645$			36.0526i			1.41957i
$646$	13.5622	+	23.4904i	0.533597	+	0.924217i
$647$	−11.1244	+	19.2679i	−0.437344	+	0.757501i	−0.997484	−	0.0708966i	$-0.977414\pi$
$647$	−11.1244	+	19.2679i	−0.437344	+	0.757501i	0.560140	+	0.828398i	$0.310747\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−10.1436			−0.398171
$650$	−31.2487	+	7.73205i	−1.22568	+	0.303276i
$651$	−4.00000			−0.156772
$652$	11.6603	+	6.73205i	0.456651	+	0.263647i
$653$	8.73205	−	15.1244i	0.341712	−	0.591862i	−0.643039	−	0.765833i	$-0.722327\pi$
$653$	8.73205	−	15.1244i	0.341712	−	0.591862i	0.984751	+	0.173972i	$0.0556601\pi$
$654$	0.732051	+	1.26795i	0.0286255	+	0.0495807i
$655$			24.3923i			0.953086i
$656$	−8.13397	+	4.69615i	−0.317578	+	0.183354i
$657$	5.42820	−	3.13397i	0.211774	−	0.122268i
$658$			6.00000i			0.233904i
$659$	5.12436	+	8.87564i	0.199617	+	0.345746i	0.948404	−	0.317064i	$-0.102697\pi$
$659$	5.12436	+	8.87564i	0.199617	+	0.345746i	−0.748788	+	0.662810i	$0.769364\pi$
$660$	2.36603	−	4.09808i	0.0920974	−	0.159517i
$661$	9.86603	+	5.69615i	0.383744	+	0.221555i	0.679446	−	0.733726i	$-0.262220\pi$
$661$	9.86603	+	5.69615i	0.383744	+	0.221555i	−0.295702	+	0.955280i	$0.595554\pi$
$662$	−20.0000			−0.777322
$663$	−14.8923	+	14.3301i	−0.578369	+	0.556536i
$664$	−0.196152			−0.00761219
$665$	41.7846	+	24.1244i	1.62034	+	0.935502i
$666$	−1.76795	+	3.06218i	−0.0685066	+	0.118657i
$667$	−9.36603	−	16.2224i	−0.362654	−	0.628135i
$668$		−	9.46410i		−	0.366177i
$669$	−23.3205	+	13.4641i	−0.901623	+	0.520552i
$670$	−42.4186	+	24.4904i	−1.63877	+	0.946146i
$671$			11.6603i			0.450139i
$672$	1.36603	+	2.36603i	0.0526956	+	0.0912714i
$673$	13.9641	−	24.1865i	0.538277	−	0.932322i	−0.460720	−	0.887545i	$-0.652409\pi$
$673$	13.9641	−	24.1865i	0.538277	−	0.932322i	0.998997	−	0.0447770i	$-0.0142577\pi$
$674$	−18.0622	−	10.4282i	−0.695729	−	0.401679i
$675$	−8.92820			−0.343647
$676$	11.5000	−	6.06218i	0.442308	−	0.233161i
$677$	−45.4641			−1.74733			−0.873664	−	0.486530i	$-0.838262\pi$
$677$	−45.4641			−1.74733			−0.873664	+	0.486530i	$0.838262\pi$
$678$	1.16025	+	0.669873i	0.0445593	+	0.0257263i
$679$	−8.19615	+	14.1962i	−0.314539	+	0.544798i
$680$	−10.6962	−	18.5263i	−0.410179	−	0.710450i
$681$		−	12.1962i		−	0.467358i
$682$	1.60770	−	0.928203i	0.0615618	−	0.0355427i
$683$	8.78461	−	5.07180i	0.336134	−	0.194067i	−0.322427	−	0.946594i	$-0.604499\pi$
$683$	8.78461	−	5.07180i	0.336134	−	0.194067i	0.658561	+	0.752527i	$0.271165\pi$
$684$		−	4.73205i		−	0.180934i
$685$	−22.2583	−	38.5526i	−0.850447	−	1.47302i
$686$	8.92820	−	15.4641i	0.340880	−	0.590422i
$687$	−10.2679	−	5.92820i	−0.391747	−	0.226175i
$688$	9.66025			0.368294
$689$	16.7942	−	16.1603i	0.639809	−	0.615657i
$690$	15.6603			0.596176
$691$	−37.8109	−	21.8301i	−1.43839	−	0.830457i	−0.440656	−	0.897676i	$-0.645254\pi$
$691$	−37.8109	−	21.8301i	−1.43839	−	0.830457i	−0.997738	+	0.0672190i	$0.978587\pi$
$692$	−2.19615	+	3.80385i	−0.0834852	+	0.144601i
$693$	−1.73205	−	3.00000i	−0.0657952	−	0.113961i
$694$			33.1244i			1.25738i
$695$	57.7128	−	33.3205i	2.18917	−	1.26392i
$696$	3.86603	−	2.23205i	0.146541	−	0.0846057i
$697$		−	53.8372i		−	2.03923i
$698$	−7.66025	−	13.2679i	−0.289945	−	0.502199i
$699$	−3.92820	+	6.80385i	−0.148578	+	0.257345i
$700$	−21.1244	−	12.1962i	−0.798426	−	0.460971i
$701$	3.32051			0.125414			0.0627069	−	0.998032i	$-0.480027\pi$
$701$	3.32051			0.125414			0.0627069	+	0.998032i	$0.480027\pi$
$702$	3.50000	−	0.866025i	0.132099	−	0.0326860i
$703$	16.7321			0.631061
$704$	−1.09808	−	0.633975i	−0.0413853	−	0.0238938i
$705$	−4.09808	+	7.09808i	−0.154342	+	0.267329i
$706$	−10.8923	−	18.8660i	−0.409937	−	0.710032i
$707$		−	5.26795i		−	0.198122i
$708$	6.92820	−	4.00000i	0.260378	−	0.150329i
$709$	−11.3827	+	6.57180i	−0.427486	+	0.246809i	−0.698275	−	0.715830i	$-0.746049\pi$
$709$	−11.3827	+	6.57180i	−0.427486	+	0.246809i	0.270789	+	0.962639i	$0.412715\pi$
$710$		−	17.6603i		−	0.662778i
$711$	1.26795	+	2.19615i	0.0475518	+	0.0823622i
$712$	−4.73205	+	8.19615i	−0.177341	+	0.307164i
$713$	5.32051	+	3.07180i	0.199255	+	0.115040i
$714$	−15.6603			−0.586070
$715$	−4.09808	−	16.5622i	−0.153259	−	0.619390i
$716$	−16.0526			−0.599912
$717$	−6.63397	−	3.83013i	−0.247750	−	0.143039i
$718$	0.562178	−	0.973721i	0.0209803	−	0.0363389i
$719$	−14.7321	−	25.5167i	−0.549413	−	0.951611i	−0.998315	−	0.0580299i	$-0.981518\pi$
$719$	−14.7321	−	25.5167i	−0.549413	−	0.951611i	0.448902	−	0.893581i	$-0.351815\pi$
$720$			3.73205i			0.139085i
$721$	36.1244	−	20.8564i	1.34534	−	0.776733i
$722$	−2.93782	+	1.69615i	−0.109334	+	0.0631243i
$723$		−	13.5885i		−	0.505360i
$724$	−9.59808	−	16.6244i	−0.356710	−	0.617839i
$725$	−19.9282	+	34.5167i	−0.740115	+	1.28192i
$726$	−8.13397	−	4.69615i	−0.301880	−	0.174291i
$727$	30.9808			1.14901			0.574506	−	0.818500i	$-0.305194\pi$
$727$	30.9808			1.14901			0.574506	+	0.818500i	$0.305194\pi$
$728$	9.46410	+	2.73205i	0.350763	+	0.101257i
$729$	1.00000			0.0370370
$730$	20.2583	+	11.6962i	0.749794	+	0.432894i
$731$	−27.6865	+	47.9545i	−1.02402	+	1.77366i
$732$	−4.59808	−	7.96410i	−0.169950	−	0.294362i
$733$			19.0000i			0.701781i	0.936416	+	0.350891i	$0.114121\pi$
$733$			19.0000i			0.701781i	−0.936416	+	0.350891i	$0.885879\pi$
$734$	−9.75833	+	5.63397i	−0.360187	+	0.207954i
$735$	−1.50000	+	0.866025i	−0.0553283	+	0.0319438i
$736$		−	4.19615i		−	0.154672i
$737$	−8.32051	−	14.4115i	−0.306490	−	0.530856i
$738$	−4.69615	+	8.13397i	−0.172868	+	0.299416i
$739$	2.53590	+	1.46410i	0.0932845	+	0.0538578i	0.545917	−	0.837840i	$-0.316182\pi$
$739$	2.53590	+	1.46410i	0.0932845	+	0.0538578i	−0.452632	+	0.891697i	$0.649515\pi$
$740$	−13.1962			−0.485100
$741$	−11.8301	−	12.2942i	−0.434591	−	0.451640i
$742$	17.6603			0.648328
$743$	41.9090	+	24.1962i	1.53749	+	0.887671i	0.998985	+	0.0450491i	$0.0143444\pi$
$743$	41.9090	+	24.1962i	1.53749	+	0.887671i	0.538506	+	0.842622i	$0.318989\pi$
$744$	−0.732051	+	1.26795i	−0.0268383	+	0.0464853i
$745$	24.6244	+	42.6506i	0.902167	+	1.56260i
$746$		−	13.7321i		−	0.502766i
$747$	−0.169873	+	0.0980762i	−0.00621533	+	0.00358842i
$748$	6.29423	−	3.63397i	0.230140	−	0.132871i
$749$			27.8564i			1.01785i
$750$	−7.33013	−	12.6962i	−0.267658	−	0.463598i
$751$	−24.9545	+	43.2224i	−0.910602	+	1.57721i	−0.0973862	+	0.995247i	$0.531048\pi$
$751$	−24.9545	+	43.2224i	−0.910602	+	1.57721i	−0.813216	+	0.581962i	$0.802285\pi$
$752$	1.90192	+	1.09808i	0.0693560	+	0.0400427i
$753$	−13.4641			−0.490659
$754$	4.46410	−	15.4641i	0.162573	−	0.563169i
$755$	25.1244			0.914369
$756$	2.36603	+	1.36603i	0.0860515	+	0.0496819i
$757$	−10.4641	+	18.1244i	−0.380324	+	0.658741i	−0.991109	−	0.133056i	$-0.957521\pi$
$757$	−10.4641	+	18.1244i	−0.380324	+	0.658741i	0.610784	+	0.791797i	$0.290854\pi$
$758$	−2.73205	−	4.73205i	−0.0992326	−	0.171876i
$759$			5.32051i			0.193122i
$760$	15.2942	−	8.83013i	0.554780	−	0.320302i
$761$	−9.80385	+	5.66025i	−0.355389	+	0.205184i	−0.667056	−	0.745007i	$-0.732446\pi$
$761$	−9.80385	+	5.66025i	−0.355389	+	0.205184i	0.311667	+	0.950191i	$0.399113\pi$
$762$			9.85641i			0.357060i
$763$	2.00000	+	3.46410i	0.0724049	+	0.125409i
$764$	−3.46410	+	6.00000i	−0.125327	+	0.217072i
$765$	−18.5263	−	10.6962i	−0.669819	−	0.386720i
$766$	1.46410			0.0529001
$767$	8.00000	−	27.7128i	0.288863	−	1.00065i
$768$	1.00000			0.0360844
$769$	37.9808	+	21.9282i	1.36962	+	0.790751i	0.990879	−	0.134751i	$-0.0430235\pi$
$769$	37.9808	+	21.9282i	1.36962	+	0.790751i	0.378742	+	0.925502i	$0.376357\pi$
$770$	6.46410	−	11.1962i	0.232950	−	0.403481i
$771$	4.66987	+	8.08846i	0.168181	+	0.291299i
$772$		−	11.7321i		−	0.422246i
$773$	−42.3731	+	24.4641i	−1.52405	+	0.879913i	−0.524459	+	0.851436i	$0.675732\pi$
$773$	−42.3731	+	24.4641i	−1.52405	+	0.879913i	−0.999594	+	0.0284768i	$0.990934\pi$
$774$	8.36603	−	4.83013i	0.300711	−	0.173615i
$775$		−	13.0718i		−	0.469553i
$776$	3.00000	+	5.19615i	0.107694	+	0.186531i
$777$	−4.83013	+	8.36603i	−0.173280	+	0.300129i
$778$	10.2058	+	5.89230i	0.365895	+	0.211249i
$779$	44.4449			1.59240
$780$	9.33013	+	9.69615i	0.334072	+	0.347178i
$781$	6.00000			0.214697
$782$	20.8301	+	12.0263i	0.744884	+	0.430059i
$783$	2.23205	−	3.86603i	0.0797670	−	0.138160i
$784$	0.232051	+	0.401924i	0.00828753	+	0.0143544i
$785$			28.3205i			1.01080i
$786$	5.66025	−	3.26795i	0.201895	−	0.116564i
$787$	−4.05256	+	2.33975i	−0.144458	+	0.0834029i	−0.570487	−	0.821307i	$-0.693246\pi$
$787$	−4.05256	+	2.33975i	−0.144458	+	0.0834029i	0.426029	+	0.904710i	$0.359912\pi$
$788$			17.8564i			0.636108i
$789$	5.02628	+	8.70577i	0.178940	+	0.309934i
$790$	−4.73205	+	8.19615i	−0.168359	+	0.291606i
$791$	3.16987	+	1.83013i	0.112708	+	0.0650718i
$792$	−1.26795			−0.0450546
$793$	−31.8564	−	9.19615i	−1.13125	−	0.326565i
$794$	20.3923			0.723696
$795$	20.8923	+	12.0622i	0.740974	+	0.427801i
$796$	7.09808	−	12.2942i	0.251585	−	0.435757i
$797$	−17.0000	−	29.4449i	−0.602171	−	1.04299i	−0.992492	−	0.122312i	$-0.960969\pi$
$797$	−17.0000	−	29.4449i	−0.602171	−	1.04299i	0.390321	−	0.920679i	$-0.372364\pi$
$798$		−	12.9282i		−	0.457653i
$799$	−10.9019	+	6.29423i	−0.385682	+	0.222674i
$800$	−7.73205	+	4.46410i	−0.273369	+	0.157830i
$801$			9.46410i			0.334398i
$802$	−4.03590	−	6.99038i	−0.142513	−	0.246839i
$803$	−3.97372	+	6.88269i	−0.140230	+	0.242885i
$804$	11.3660	+	6.56218i	0.400849	+	0.231430i
$805$	42.7846			1.50796
$806$	1.26795	+	5.12436i	0.0446616	+	0.180498i
$807$	5.46410			0.192345
$808$	−1.66987	−	0.964102i	−0.0587459	−	0.0339170i
$809$	26.7942	−	46.4090i	0.942035	−	1.63165i	0.180453	−	0.983584i	$-0.442244\pi$
$809$	26.7942	−	46.4090i	0.942035	−	1.63165i	0.761582	−	0.648069i	$-0.224423\pi$
$810$	1.86603	+	3.23205i	0.0655654	+	0.113563i
$811$			17.1769i			0.603163i	0.953440	+	0.301582i	$0.0975145\pi$
$811$			17.1769i			0.603163i	−0.953440	+	0.301582i	$0.902485\pi$
$812$	10.5622	−	6.09808i	0.370660	−	0.214001i
$813$	18.9282	−	10.9282i	0.663841	−	0.383269i
$814$		−	4.48334i		−	0.157141i
$815$	25.1244	+	43.5167i	0.880068	+	1.52432i
$816$	−2.86603	+	4.96410i	−0.100331	+	0.173778i
$817$	−39.5885	−	22.8564i	−1.38502	−	0.799644i
$818$	−17.7321			−0.619987
$819$	9.56218	−	2.36603i	0.334130	−	0.0826756i
$820$	−35.0526			−1.22409
$821$	0.803848	+	0.464102i	0.0280545	+	0.0161973i	0.513962	−	0.857813i	$-0.328177\pi$
$821$	0.803848	+	0.464102i	0.0280545	+	0.0161973i	−0.485907	+	0.874010i	$0.661511\pi$
$822$	−5.96410	+	10.3301i	−0.208022	+	0.360305i
$823$	20.7846	+	36.0000i	0.724506	+	1.25488i	0.959177	+	0.282806i	$0.0912654\pi$
$823$	20.7846	+	36.0000i	0.724506	+	1.25488i	−0.234671	+	0.972075i	$0.575401\pi$
$824$		−	15.2679i		−	0.531884i
$825$	9.80385	−	5.66025i	0.341326	−	0.197065i
$826$	18.9282	−	10.9282i	0.658596	−	0.380241i
$827$		−	26.5359i		−	0.922744i	−0.887207	−	0.461372i	$-0.847357\pi$
$827$		−	26.5359i		−	0.922744i	0.887207	−	0.461372i	$-0.152643\pi$
$828$	−2.09808	−	3.63397i	−0.0729132	−	0.126289i
$829$	−6.06218	+	10.5000i	−0.210548	+	0.364680i	−0.951886	−	0.306452i	$-0.900858\pi$
$829$	−6.06218	+	10.5000i	−0.210548	+	0.364680i	0.741338	+	0.671132i	$0.234192\pi$
$830$	−0.633975	−	0.366025i	−0.0220056	−	0.0127049i
$831$	5.73205			0.198843
$832$	2.59808	−	2.50000i	0.0900721	−	0.0866719i
$833$	−2.66025			−0.0921723
$834$	−15.4641	−	8.92820i	−0.535478	−	0.309158i
$835$	17.6603	−	30.5885i	0.611158	−	1.05856i
$836$	3.00000	+	5.19615i	0.103757	+	0.179713i
$837$			1.46410i			0.0506068i
$838$	−15.1244	+	8.73205i	−0.522462	+	0.301644i
$839$	−36.2487	+	20.9282i	−1.25144	+	0.722522i	−0.971396	−	0.237464i	$-0.923684\pi$
$839$	−36.2487	+	20.9282i	−1.25144	+	0.722522i	−0.280048	+	0.959986i	$0.590350\pi$
$840$			10.1962i			0.351801i
$841$	4.53590	+	7.85641i	0.156410	+	0.270911i
$842$	−11.3564	+	19.6699i	−0.391368	+	0.677869i
$843$	10.6699	+	6.16025i	0.367490	+	0.212170i
$844$	−16.3923			−0.564246
$845$	48.4808	+	1.86603i	1.66779	+	0.0641932i
$846$	2.19615			0.0755053
$847$	−22.2224	−	12.8301i	−0.763572	−	0.440848i
$848$	3.23205	−	5.59808i	0.110989	−	0.192239i
$849$	12.8301	+	22.2224i	0.440329	+	0.762672i
$850$		−	51.1769i		−	1.75535i
$851$	12.8494	−	7.41858i	0.440471	−	0.254306i
$852$	−4.09808	+	2.36603i	−0.140398	+	0.0810587i
$853$			54.1769i			1.85498i	0.373845	+	0.927491i	$0.378039\pi$
$853$			54.1769i			1.85498i	−0.373845	+	0.927491i	$0.621961\pi$
$854$	−12.5622	−	21.7583i	−0.429869	−	0.744555i
$855$	8.83013	−	15.2942i	0.301984	−	0.523052i
$856$	8.83013	+	5.09808i	0.301808	+	0.174249i
$857$	−39.4449			−1.34741			−0.673705	−	0.739000i	$-0.735298\pi$
$857$	−39.4449			−1.34741			−0.673705	+	0.739000i	$0.735298\pi$
$858$	−3.29423	+	3.16987i	−0.112463	+	0.108218i
$859$	−47.1244			−1.60786			−0.803931	−	0.594722i	$-0.797262\pi$
$859$	−47.1244			−1.60786			−0.803931	+	0.594722i	$0.797262\pi$
$860$	31.2224	+	18.0263i	1.06468	+	0.614691i
$861$	−12.8301	+	22.2224i	−0.437250	+	0.757338i
$862$	6.56218	+	11.3660i	0.223509	+	0.387128i
$863$		−	17.1244i		−	0.582920i	−0.956583	−	0.291460i	$-0.905859\pi$
$863$		−	17.1244i		−	0.582920i	0.956583	−	0.291460i	$-0.0941410\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	−14.1962	+	8.19615i	−0.482684	+	0.278678i
$866$		−	12.8564i		−	0.436878i
$867$	−7.92820	−	13.7321i	−0.269256	−	0.466365i
$868$	−2.00000	+	3.46410i	−0.0678844	+	0.117579i
$869$	−2.78461	−	1.60770i	−0.0944614	−	0.0545373i
$870$	16.6603			0.564836
$871$	45.9352	−	11.3660i	1.55646	−	0.385123i
$872$	1.46410			0.0495807
$873$	5.19615	+	3.00000i	0.175863	+	0.101535i
$874$	−9.92820	+	17.1962i	−0.335826	+	0.581669i
$875$	−20.0263	−	34.6865i	−0.677012	−	1.17262i
$876$		−	6.26795i		−	0.211774i
$877$	20.7224	−	11.9641i	0.699747	−	0.403999i	−0.107506	−	0.994204i	$-0.534287\pi$
$877$	20.7224	−	11.9641i	0.699747	−	0.403999i	0.807253	+	0.590205i	$0.200953\pi$
$878$	0.294229	−	0.169873i	0.00992974	−	0.00573294i
$879$		−	30.5167i		−	1.02930i
$880$	−2.36603	−	4.09808i	−0.0797587	−	0.138146i
$881$	−13.9186	+	24.1077i	−0.468929	+	0.812209i	−0.999369	−	0.0355135i	$-0.988693\pi$
$881$	−13.9186	+	24.1077i	−0.468929	+	0.812209i	0.530440	+	0.847722i	$0.322027\pi$
$882$	0.401924	+	0.232051i	0.0135335	+	0.00781356i
$883$	−42.9282			−1.44465			−0.722325	−	0.691554i	$-0.756926\pi$
$883$	−42.9282			−1.44465			−0.722325	+	0.691554i	$0.756926\pi$
$884$	4.96410	+	20.0622i	0.166961	+	0.674764i
$885$	29.8564			1.00361
$886$	−13.5167	−	7.80385i	−0.454101	−	0.262175i
$887$	−18.9282	+	32.7846i	−0.635547	+	1.10080i	0.350852	+	0.936431i	$0.385892\pi$
$887$	−18.9282	+	32.7846i	−0.635547	+	1.10080i	−0.986399	+	0.164369i	$0.947441\pi$
$888$	1.76795	+	3.06218i	0.0593285	+	0.102760i
$889$			26.9282i			0.903143i
$890$	−30.5885	+	17.6603i	−1.02533	+	0.591973i
$891$	−1.09808	+	0.633975i	−0.0367869	+	0.0212389i
$892$			26.9282i			0.901623i
$893$	−5.19615	−	9.00000i	−0.173883	−	0.301174i
$894$	6.59808	−	11.4282i	0.220673	−	0.382216i
$895$	−51.8827	−	29.9545i	−1.73425	−	1.00127i
$896$	2.73205			0.0912714
$897$	−14.5359	−	4.19615i	−0.485340	−	0.140105i
$898$	11.3205			0.377770
$899$	5.66025	+	3.26795i	0.188780	+	0.108992i
$900$	−4.46410	+	7.73205i	−0.148803	+	0.257735i
$901$	18.5263	+	32.0885i	0.617200	+	1.06902i
$902$		−	11.9090i		−	0.396525i
$903$	22.8564	−	13.1962i	0.760614	−	0.439140i
$904$	1.16025	−	0.669873i	0.0385895	−	0.0222796i
$905$		−	71.6410i		−	2.38143i
$906$	−3.36603	−	5.83013i	−0.111829	−	0.193693i
$907$	18.1962	−	31.5167i	0.604193	−	1.04649i	−0.387985	−	0.921666i	$-0.626829\pi$
$907$	18.1962	−	31.5167i	0.604193	−	1.04649i	0.992178	−	0.124828i	$-0.0398379\pi$
$908$	−10.5622	−	6.09808i	−0.350518	−	0.202372i
$909$	−1.92820			−0.0639545
$910$	25.4904	+	26.4904i	0.844998	+	0.878148i
$911$	−2.53590			−0.0840181			−0.0420090	−	0.999117i	$-0.513376\pi$
$911$	−2.53590			−0.0840181			−0.0420090	+	0.999117i	$0.513376\pi$
$912$	−4.09808	−	2.36603i	−0.135701	−	0.0783469i
$913$	0.124356	−	0.215390i	0.00411557	−	0.00712838i
$914$	0.669873	+	1.16025i	0.0221574	+	0.0383778i
$915$		−	34.3205i		−	1.13460i
$916$	−10.2679	+	5.92820i	−0.339263	+	0.195873i
$917$	15.4641	−	8.92820i	0.510670	−	0.294835i
$918$			5.73205i			0.189186i
$919$	−22.9808	−	39.8038i	−0.758065	−	1.31301i	−0.943836	−	0.330415i	$-0.892811\pi$
$919$	−22.9808	−	39.8038i	−0.758065	−	1.31301i	0.185770	−	0.982593i	$-0.440522\pi$
$920$	7.83013	−	13.5622i	0.258152	−	0.447132i
$921$	−19.5622	−	11.2942i	−0.644596	−	0.372157i
$922$	−22.2679			−0.733356
$923$	−4.73205	+	16.3923i	−0.155757	+	0.539559i
$924$	−3.46410			−0.113961
$925$	−27.3397	−	15.7846i	−0.898925	−	0.518995i
$926$	−5.02628	+	8.70577i	−0.165174	+	0.286089i
$927$	−7.63397	−	13.2224i	−0.250733	−	0.434282i
$928$		−	4.46410i		−	0.146541i
$929$	−33.9904	+	19.6244i	−1.11519	+	0.643854i	−0.940168	−	0.340711i	$-0.889332\pi$
$929$	−33.9904	+	19.6244i	−1.11519	+	0.643854i	−0.175020	+	0.984565i	$0.555999\pi$
$930$	−4.73205	+	2.73205i	−0.155170	+	0.0895875i
$931$		−	2.19615i		−	0.0719760i
$932$	3.92820	+	6.80385i	0.128673	+	0.222867i
$933$	−0.830127	+	1.43782i	−0.0271771	+	0.0470722i
$934$	16.0981	+	9.29423i	0.526745	+	0.304116i
$935$	27.1244			0.887061
$936$	1.00000	−	3.46410i	0.0326860	−	0.113228i
$937$	−5.24871			−0.171468			−0.0857340	−	0.996318i	$-0.527324\pi$
$937$	−5.24871			−0.171468			−0.0857340	+	0.996318i	$0.527324\pi$
$938$	31.0526	+	17.9282i	1.01390	+	0.585377i
$939$	−3.26795	+	5.66025i	−0.106645	+	0.184715i
$940$	4.09808	+	7.09808i	0.133665	+	0.231514i
$941$			12.6410i			0.412085i	0.978543	+	0.206043i	$0.0660586\pi$
$941$			12.6410i			0.412085i	−0.978543	+	0.206043i	$0.933941\pi$
$942$	6.57180	−	3.79423i	0.214121	−	0.123623i
$943$	34.1314	−	19.7058i	1.11147	−	0.641708i
$944$		−	8.00000i		−	0.260378i
$945$	5.09808	+	8.83013i	0.165840	+	0.287244i
$946$	−6.12436	+	10.6077i	−0.199120	+	0.344886i
$947$	18.2487	+	10.5359i	0.593003	+	0.342371i	0.766284	−	0.642502i	$-0.222103\pi$
$947$	18.2487	+	10.5359i	0.593003	+	0.342371i	−0.173281	+	0.984872i	$0.555437\pi$
$948$	2.53590			0.0823622
$949$	−15.6699	−	16.2846i	−0.508666	−	0.528621i
$950$	42.2487			1.37073
$951$	−17.8923	−	10.3301i	−0.580198	−	0.334977i
$952$	−7.83013	+	13.5622i	−0.253776	+	0.439553i
$953$	20.7846	+	36.0000i	0.673280	+	1.16615i	0.976969	+	0.213383i	$0.0684483\pi$
$953$	20.7846	+	36.0000i	0.673280	+	1.16615i	−0.303689	+	0.952771i	$0.598218\pi$
$954$		−	6.46410i		−	0.209283i
$955$	−22.3923	+	12.9282i	−0.724598	+	0.418347i
$956$	−6.63397	+	3.83013i	−0.214558	+	0.123875i
$957$			5.66025i			0.182970i
$958$	−16.7321	−	28.9808i	−0.540588	−	0.936326i
$959$	−16.2942	+	28.2224i	−0.526168	+	0.911350i
$960$	3.23205	+	1.86603i	0.104314	+	0.0602257i
$961$	28.8564			0.930852
$962$	12.2487	+	3.53590i	0.394914	+	0.114002i
$963$	10.1962			0.328566
$964$	−11.7679	−	6.79423i	−0.379020	−	0.218827i
$965$	21.8923	−	37.9186i	0.704738	−	1.22064i
$966$	−5.73205	−	9.92820i	−0.184426	−	0.319435i
$967$		−	43.1244i		−	1.38679i	−0.720560	−	0.693393i	$-0.756115\pi$
$967$		−	43.1244i		−	1.38679i	0.720560	−	0.693393i	$-0.243885\pi$
$968$	−8.13397	+	4.69615i	−0.261436	+	0.150940i
$969$	23.4904	−	13.5622i	0.754620	−	0.435680i
$970$			22.3923i			0.718974i
$971$	−15.1244	−	26.1962i	−0.485364	−	0.840675i	0.514495	−	0.857493i	$-0.327979\pi$
$971$	−15.1244	−	26.1962i	−0.485364	−	0.840675i	−0.999859	+	0.0168189i	$0.994646\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−42.2487	−	24.3923i	−1.35443	−	0.781981i
$974$	3.12436			0.100111
$975$	7.73205	+	31.2487i	0.247624	+	1.00076i
$976$	−9.19615			−0.294362
$977$	−39.7750	−	22.9641i	−1.27251	−	0.734687i	−0.297054	−	0.954861i	$-0.596004\pi$
$977$	−39.7750	−	22.9641i	−1.27251	−	0.734687i	−0.975461	+	0.220174i	$0.929337\pi$
$978$	6.73205	−	11.6603i	0.215267	−	0.372854i
$979$	−6.00000	−	10.3923i	−0.191761	−	0.332140i
$980$			1.73205i			0.0553283i
$981$	1.26795	−	0.732051i	0.0404825	−	0.0233726i
$982$	−7.56218	+	4.36603i	−0.241319	+	0.139325i
$983$		−	20.7846i		−	0.662926i	−0.943468	−	0.331463i	$-0.892458\pi$
$983$		−	20.7846i		−	0.662926i	0.943468	−	0.331463i	$-0.107542\pi$
$984$	4.69615	+	8.13397i	0.149708	+	0.259302i
$985$	−33.3205	+	57.7128i	−1.06168	+	1.83888i
$986$	22.1603	+	12.7942i	0.705726	+	0.407451i
$987$	6.00000			0.190982
$988$	−16.5622	+	4.09808i	−0.526913	+	0.130377i
$989$	−40.5359			−1.28897
$990$	−4.09808	−	2.36603i	−0.130245	−	0.0751972i
$991$	−11.2942	+	19.5622i	−0.358773	+	0.621413i	−0.987756	−	0.156006i	$-0.950138\pi$
$991$	−11.2942	+	19.5622i	−0.358773	+	0.621413i	0.628983	+	0.777419i	$0.283471\pi$
$992$	0.732051	+	1.26795i	0.0232426	+	0.0402574i
$993$			20.0000i			0.634681i
$994$	−11.1962	+	6.46410i	−0.355120	+	0.205029i
$995$	45.8827	−	26.4904i	1.45458	−	0.839802i
$996$			0.196152i			0.00621533i
$997$	−10.6699	−	18.4808i	−0.337918	−	0.585292i	0.646123	−	0.763234i	$-0.276389\pi$
$997$	−10.6699	−	18.4808i	−0.337918	−	0.585292i	−0.984041	+	0.177942i	$0.943056\pi$
$998$	16.0000	−	27.7128i	0.506471	−	0.877234i
$999$	3.06218	+	1.76795i	0.0968830	+	0.0559354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.2.i.a.43.1	✓	4
3.2	odd	2		234.2.l.c.199.2		4
4.3	odd	2		624.2.bv.e.433.2		4
5.2	odd	4		1950.2.y.g.199.2		4
5.3	odd	4		1950.2.y.b.199.1		4
5.4	even	2		1950.2.bc.d.901.2		4
12.11	even	2		1872.2.by.h.433.1		4
13.2	odd	12		1014.2.e.g.991.2		4
13.3	even	3		1014.2.i.a.361.2		4
13.4	even	6		1014.2.b.e.337.1		4
13.5	odd	4		1014.2.e.g.529.2		4
13.6	odd	12		1014.2.a.k.1.2		2
13.7	odd	12		1014.2.a.i.1.1		2
13.8	odd	4		1014.2.e.i.529.1		4
13.9	even	3		1014.2.b.e.337.4		4
13.10	even	6	inner	78.2.i.a.49.1	yes	4
13.11	odd	12		1014.2.e.i.991.1		4
13.12	even	2		1014.2.i.a.823.2		4
39.17	odd	6		3042.2.b.i.1351.4		4
39.20	even	12		3042.2.a.y.1.2		2
39.23	odd	6		234.2.l.c.127.2		4
39.32	even	12		3042.2.a.p.1.1		2
39.35	odd	6		3042.2.b.i.1351.1		4
52.7	even	12		8112.2.a.bj.1.1		2
52.19	even	12		8112.2.a.bp.1.2		2
52.23	odd	6		624.2.bv.e.49.1		4
65.23	odd	12		1950.2.y.g.49.2		4
65.49	even	6		1950.2.bc.d.751.2		4
65.62	odd	12		1950.2.y.b.49.1		4
156.23	even	6		1872.2.by.h.1297.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.a.43.1	✓	4	1.1	even	1	trivial
78.2.i.a.49.1	yes	4	13.10	even	6	inner
234.2.l.c.127.2		4	39.23	odd	6
234.2.l.c.199.2		4	3.2	odd	2
624.2.bv.e.49.1		4	52.23	odd	6
624.2.bv.e.433.2		4	4.3	odd	2
1014.2.a.i.1.1		2	13.7	odd	12
1014.2.a.k.1.2		2	13.6	odd	12
1014.2.b.e.337.1		4	13.4	even	6
1014.2.b.e.337.4		4	13.9	even	3
1014.2.e.g.529.2		4	13.5	odd	4
1014.2.e.g.991.2		4	13.2	odd	12
1014.2.e.i.529.1		4	13.8	odd	4
1014.2.e.i.991.1		4	13.11	odd	12
1014.2.i.a.361.2		4	13.3	even	3
1014.2.i.a.823.2		4	13.12	even	2
1872.2.by.h.433.1		4	12.11	even	2
1872.2.by.h.1297.2		4	156.23	even	6
1950.2.y.b.49.1		4	65.62	odd	12
1950.2.y.b.199.1		4	5.3	odd	4
1950.2.y.g.49.2		4	65.23	odd	12
1950.2.y.g.199.2		4	5.2	odd	4
1950.2.bc.d.751.2		4	65.49	even	6
1950.2.bc.d.901.2		4	5.4	even	2
3042.2.a.p.1.1		2	39.32	even	12
3042.2.a.y.1.2		2	39.20	even	12
3042.2.b.i.1351.1		4	39.35	odd	6
3042.2.b.i.1351.4		4	39.17	odd	6
8112.2.a.bj.1.1		2	52.7	even	12
8112.2.a.bp.1.2		2	52.19	even	12

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:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	78.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.73205i q^{5} +(0.866025 - 0.500000i) q^{6} +(2.36603 - 1.36603i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.73205i q^{5} +(0.866025 - 0.500000i) q^{6} +(2.36603 - 1.36603i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.86603 - 3.23205i) q^{10} +(1.09808 + 0.633975i) q^{11} -1.00000 q^{12} +(-2.59808 + 2.50000i) q^{13} -2.73205 q^{14} +(-3.23205 - 1.86603i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.86603 - 4.96410i) q^{17} +1.00000i q^{18} +(4.09808 - 2.36603i) q^{19} +(-3.23205 + 1.86603i) q^{20} +2.73205i q^{21} +(-0.633975 - 1.09808i) q^{22} +(2.09808 - 3.63397i) q^{23} +(0.866025 + 0.500000i) q^{24} -8.92820 q^{25} +(3.50000 - 0.866025i) q^{26} +1.00000 q^{27} +(2.36603 + 1.36603i) q^{28} +(2.23205 - 3.86603i) q^{29} +(1.86603 + 3.23205i) q^{30} +1.46410i q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.09808 + 0.633975i) q^{33} +5.73205i q^{34} +(5.09808 + 8.83013i) q^{35} +(0.500000 - 0.866025i) q^{36} +(3.06218 + 1.76795i) q^{37} -4.73205 q^{38} +(-0.866025 - 3.50000i) q^{39} +3.73205 q^{40} +(8.13397 + 4.69615i) q^{41} +(1.36603 - 2.36603i) q^{42} +(-4.83013 - 8.36603i) q^{43} +1.26795i q^{44} +(3.23205 - 1.86603i) q^{45} +(-3.63397 + 2.09808i) q^{46} -2.19615i q^{47} +(-0.500000 - 0.866025i) q^{48} +(0.232051 - 0.401924i) q^{49} +(7.73205 + 4.46410i) q^{50} +5.73205 q^{51} +(-3.46410 - 1.00000i) q^{52} -6.46410 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-2.36603 + 4.09808i) q^{55} +(-1.36603 - 2.36603i) q^{56} +4.73205i q^{57} +(-3.86603 + 2.23205i) q^{58} +(-6.92820 + 4.00000i) q^{59} -3.73205i q^{60} +(4.59808 + 7.96410i) q^{61} +(0.732051 - 1.26795i) q^{62} +(-2.36603 - 1.36603i) q^{63} -1.00000 q^{64} +(-9.33013 - 9.69615i) q^{65} +1.26795 q^{66} +(-11.3660 - 6.56218i) q^{67} +(2.86603 - 4.96410i) q^{68} +(2.09808 + 3.63397i) q^{69} -10.1962i q^{70} +(4.09808 - 2.36603i) q^{71} +(-0.866025 + 0.500000i) q^{72} +6.26795i q^{73} +(-1.76795 - 3.06218i) q^{74} +(4.46410 - 7.73205i) q^{75} +(4.09808 + 2.36603i) q^{76} +3.46410 q^{77} +(-1.00000 + 3.46410i) q^{78} -2.53590 q^{79} +(-3.23205 - 1.86603i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.69615 - 8.13397i) q^{82} -0.196152i q^{83} +(-2.36603 + 1.36603i) q^{84} +(18.5263 - 10.6962i) q^{85} +9.66025i q^{86} +(2.23205 + 3.86603i) q^{87} +(0.633975 - 1.09808i) q^{88} +(-8.19615 - 4.73205i) q^{89} -3.73205 q^{90} +(-2.73205 + 9.46410i) q^{91} +4.19615 q^{92} +(-1.26795 - 0.732051i) q^{93} +(-1.09808 + 1.90192i) q^{94} +(8.83013 + 15.2942i) q^{95} +1.00000i q^{96} +(-5.19615 + 3.00000i) q^{97} +(-0.401924 + 0.232051i) q^{98} -1.26795i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{4} + 6 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^7 - 2 * q^9	\( 4 q - 2 q^{3} + 2 q^{4} + 6 q^{7} - 2 q^{9} + 4 q^{10} - 6 q^{11} - 4 q^{12} - 4 q^{14} - 6 q^{15} - 2 q^{16} - 8 q^{17} + 6 q^{19} - 6 q^{20} - 6 q^{22} - 2 q^{23} - 8 q^{25} + 14 q^{26} + 4 q^{27} + 6 q^{28} + 2 q^{29} + 4 q^{30} + 6 q^{33} + 10 q^{35} + 2 q^{36} - 12 q^{37} - 12 q^{38} + 8 q^{40} + 36 q^{41} + 2 q^{42} - 2 q^{43} + 6 q^{45} - 18 q^{46} - 2 q^{48} - 6 q^{49} + 24 q^{50} + 16 q^{51} - 12 q^{53} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 8 q^{61} - 4 q^{62} - 6 q^{63} - 4 q^{64} - 20 q^{65} + 12 q^{66} - 42 q^{67} + 8 q^{68} - 2 q^{69} + 6 q^{71} - 14 q^{74} + 4 q^{75} + 6 q^{76} - 4 q^{78} - 24 q^{79} - 6 q^{80} - 2 q^{81} + 2 q^{82} - 6 q^{84} + 36 q^{85} + 2 q^{87} + 6 q^{88} - 12 q^{89} - 8 q^{90} - 4 q^{91} - 4 q^{92} - 12 q^{93} + 6 q^{94} + 18 q^{95} - 12 q^{98}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^7 - 2 * q^9 + 4 * q^10 - 6 * q^11 - 4 * q^12 - 4 * q^14 - 6 * q^15 - 2 * q^16 - 8 * q^17 + 6 * q^19 - 6 * q^20 - 6 * q^22 - 2 * q^23 - 8 * q^25 + 14 * q^26 + 4 * q^27 + 6 * q^28 + 2 * q^29 + 4 * q^30 + 6 * q^33 + 10 * q^35 + 2 * q^36 - 12 * q^37 - 12 * q^38 + 8 * q^40 + 36 * q^41 + 2 * q^42 - 2 * q^43 + 6 * q^45 - 18 * q^46 - 2 * q^48 - 6 * q^49 + 24 * q^50 + 16 * q^51 - 12 * q^53 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 8 * q^61 - 4 * q^62 - 6 * q^63 - 4 * q^64 - 20 * q^65 + 12 * q^66 - 42 * q^67 + 8 * q^68 - 2 * q^69 + 6 * q^71 - 14 * q^74 + 4 * q^75 + 6 * q^76 - 4 * q^78 - 24 * q^79 - 6 * q^80 - 2 * q^81 + 2 * q^82 - 6 * q^84 + 36 * q^85 + 2 * q^87 + 6 * q^88 - 12 * q^89 - 8 * q^90 - 4 * q^91 - 4 * q^92 - 12 * q^93 + 6 * q^94 + 18 * q^95 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more