LMFDB - Embedded newform 390.2.y.c.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(139,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("390.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.y (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:	$3.11416567883$
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			289.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	390.289
Dual form			390.2.y.c.139.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.23205 - 0.133975i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.36603 + 1.36603i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.23205 - 0.133975i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.36603 + 1.36603i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.00000 - 1.00000i) q^{10} +(-0.366025 - 0.633975i) q^{11} -1.00000i q^{12} +(3.59808 + 0.232051i) q^{13} -2.73205 q^{14} +(-2.00000 + 1.00000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.86603 + 2.23205i) q^{17} +1.00000i q^{18} +(0.633975 - 1.09808i) q^{19} +(-1.23205 + 1.86603i) q^{20} +2.73205 q^{21} +(0.633975 + 0.366025i) q^{22} +(5.36603 - 3.09808i) q^{23} +(0.500000 + 0.866025i) q^{24} +(4.96410 + 0.598076i) q^{25} +(-3.23205 + 1.59808i) q^{26} -1.00000i q^{27} +(2.36603 - 1.36603i) q^{28} +(-3.23205 - 5.59808i) q^{29} +(1.23205 - 1.86603i) q^{30} +4.00000 q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.633975 - 0.366025i) q^{33} -4.46410 q^{34} +(-5.09808 - 3.36603i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-6.86603 + 3.96410i) q^{37} +1.26795i q^{38} +(3.23205 - 1.59808i) q^{39} +(0.133975 - 2.23205i) q^{40} +(4.59808 + 7.96410i) q^{41} +(-2.36603 + 1.36603i) q^{42} +(2.83013 + 1.63397i) q^{43} -0.732051 q^{44} +(-1.23205 + 1.86603i) q^{45} +(-3.09808 + 5.36603i) q^{46} -7.66025i q^{47} +(-0.866025 - 0.500000i) q^{48} +(0.232051 + 0.401924i) q^{49} +(-4.59808 + 1.96410i) q^{50} +4.46410 q^{51} +(2.00000 - 3.00000i) q^{52} +7.73205i q^{53} +(0.500000 + 0.866025i) q^{54} +(0.732051 + 1.46410i) q^{55} +(-1.36603 + 2.36603i) q^{56} -1.26795i q^{57} +(5.59808 + 3.23205i) q^{58} +(-6.19615 + 10.7321i) q^{59} +(-0.133975 + 2.23205i) q^{60} +(5.06218 - 8.76795i) q^{61} +(-3.46410 + 2.00000i) q^{62} +(2.36603 - 1.36603i) q^{63} -1.00000 q^{64} +(-8.00000 - 1.00000i) q^{65} +0.732051 q^{66} +(-6.63397 + 3.83013i) q^{67} +(3.86603 - 2.23205i) q^{68} +(3.09808 - 5.36603i) q^{69} +(6.09808 + 0.366025i) q^{70} +(-0.633975 + 1.09808i) q^{71} +(0.866025 + 0.500000i) q^{72} -4.66025i q^{73} +(3.96410 - 6.86603i) q^{74} +(4.59808 - 1.96410i) q^{75} +(-0.633975 - 1.09808i) q^{76} -2.00000i q^{77} +(-2.00000 + 3.00000i) q^{78} -12.0000 q^{79} +(1.00000 + 2.00000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-7.96410 - 4.59808i) q^{82} +5.26795i q^{83} +(1.36603 - 2.36603i) q^{84} +(-8.33013 - 5.50000i) q^{85} -3.26795 q^{86} +(-5.59808 - 3.23205i) q^{87} +(0.633975 - 0.366025i) q^{88} +(-2.46410 - 4.26795i) q^{89} +(0.133975 - 2.23205i) q^{90} +(8.19615 + 5.46410i) q^{91} -6.19615i q^{92} +(3.46410 - 2.00000i) q^{93} +(3.83013 + 6.63397i) q^{94} +(-1.56218 + 2.36603i) q^{95} +1.00000 q^{96} +(-8.66025 - 5.00000i) q^{97} +(-0.401924 - 0.232051i) q^{98} -0.732051 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 2 q^{5} - 2 q^{6} + 6 q^{7} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 2 * q^5 - 2 * q^6 + 6 * q^7 + 2 * q^9	$ 4 q + 2 q^{4} - 2 q^{5} - 2 q^{6} + 6 q^{7} + 2 q^{9} + 8 q^{10} + 2 q^{11} + 4 q^{13} - 4 q^{14} - 8 q^{15} - 2 q^{16} + 12 q^{17} + 6 q^{19} + 2 q^{20} + 4 q^{21} + 6 q^{22} + 18 q^{23} + 2 q^{24} + 6 q^{25} - 6 q^{26} + 6 q^{28} - 6 q^{29} - 2 q^{30} + 16 q^{31} - 6 q^{33} - 4 q^{34} - 10 q^{35} - 2 q^{36} - 24 q^{37} + 6 q^{39} + 4 q^{40} + 8 q^{41} - 6 q^{42} - 6 q^{43} + 4 q^{44} + 2 q^{45} - 2 q^{46} - 6 q^{49} - 8 q^{50} + 4 q^{51} + 8 q^{52} + 2 q^{54} - 4 q^{55} - 2 q^{56} + 12 q^{58} - 4 q^{59} - 4 q^{60} - 4 q^{61} + 6 q^{63} - 4 q^{64} - 32 q^{65} - 4 q^{66} - 30 q^{67} + 12 q^{68} + 2 q^{69} + 14 q^{70} - 6 q^{71} + 2 q^{74} + 8 q^{75} - 6 q^{76} - 8 q^{78} - 48 q^{79} + 4 q^{80} - 2 q^{81} - 18 q^{82} + 2 q^{84} - 16 q^{85} - 20 q^{86} - 12 q^{87} + 6 q^{88} + 4 q^{89} + 4 q^{90} + 12 q^{91} - 2 q^{94} + 18 q^{95} + 4 q^{96} - 12 q^{98} + 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 2 * q^5 - 2 * q^6 + 6 * q^7 + 2 * q^9 + 8 * q^10 + 2 * q^11 + 4 * q^13 - 4 * q^14 - 8 * q^15 - 2 * q^16 + 12 * q^17 + 6 * q^19 + 2 * q^20 + 4 * q^21 + 6 * q^22 + 18 * q^23 + 2 * q^24 + 6 * q^25 - 6 * q^26 + 6 * q^28 - 6 * q^29 - 2 * q^30 + 16 * q^31 - 6 * q^33 - 4 * q^34 - 10 * q^35 - 2 * q^36 - 24 * q^37 + 6 * q^39 + 4 * q^40 + 8 * q^41 - 6 * q^42 - 6 * q^43 + 4 * q^44 + 2 * q^45 - 2 * q^46 - 6 * q^49 - 8 * q^50 + 4 * q^51 + 8 * q^52 + 2 * q^54 - 4 * q^55 - 2 * q^56 + 12 * q^58 - 4 * q^59 - 4 * q^60 - 4 * q^61 + 6 * q^63 - 4 * q^64 - 32 * q^65 - 4 * q^66 - 30 * q^67 + 12 * q^68 + 2 * q^69 + 14 * q^70 - 6 * q^71 + 2 * q^74 + 8 * q^75 - 6 * q^76 - 8 * q^78 - 48 * q^79 + 4 * q^80 - 2 * q^81 - 18 * q^82 + 2 * q^84 - 16 * q^85 - 20 * q^86 - 12 * q^87 + 6 * q^88 + 4 * q^89 + 4 * q^90 + 12 * q^91 - 2 * q^94 + 18 * q^95 + 4 * q^96 - 12 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.23205	−	0.133975i	−0.998203	−	0.0599153i
$5$	−2.23205	−	0.133975i	−0.998203	−	0.0599153i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	2.36603	+	1.36603i	0.894274	+	0.516309i	0.875338	−	0.483512i	$-0.160639\pi$
$7$	2.36603	+	1.36603i	0.894274	+	0.516309i	0.0189356	+	0.999821i	$0.493972\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	2.00000	−	1.00000i	0.632456	−	0.316228i
$11$	−0.366025	−	0.633975i	−0.110361	−	0.191151i	0.805555	−	0.592521i	$-0.201867\pi$
$11$	−0.366025	−	0.633975i	−0.110361	−	0.191151i	−0.915916	+	0.401371i	$0.868534\pi$
$12$		−	1.00000i		−	0.288675i
$13$	3.59808	+	0.232051i	0.997927	+	0.0643593i
$13$	3.59808	+	0.232051i	0.997927	+	0.0643593i
$14$	−2.73205			−0.730171
$15$	−2.00000	+	1.00000i	−0.516398	+	0.258199i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.86603	+	2.23205i	0.937649	+	0.541352i	0.889223	−	0.457475i	$-0.151246\pi$
$17$	3.86603	+	2.23205i	0.937649	+	0.541352i	0.0484264	+	0.998827i	$0.484579\pi$
$18$			1.00000i			0.235702i
$19$	0.633975	−	1.09808i	0.145444	−	0.251916i	−0.784095	−	0.620641i	$-0.786872\pi$
$19$	0.633975	−	1.09808i	0.145444	−	0.251916i	0.929538	+	0.368725i	$0.120206\pi$
$20$	−1.23205	+	1.86603i	−0.275495	+	0.417256i
$21$	2.73205			0.596182
$22$	0.633975	+	0.366025i	0.135164	+	0.0780369i
$23$	5.36603	−	3.09808i	1.11889	−	0.645994i	0.177775	−	0.984071i	$-0.443110\pi$
$23$	5.36603	−	3.09808i	1.11889	−	0.645994i	0.941118	+	0.338078i	$0.109777\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	4.96410	+	0.598076i	0.992820	+	0.119615i
$26$	−3.23205	+	1.59808i	−0.633857	+	0.313409i
$27$		−	1.00000i		−	0.192450i
$28$	2.36603	−	1.36603i	0.447137	−	0.258155i
$29$	−3.23205	−	5.59808i	−0.600177	−	1.03954i	−0.992794	−	0.119835i	$-0.961764\pi$
$29$	−3.23205	−	5.59808i	−0.600177	−	1.03954i	0.392617	−	0.919702i	$-0.371570\pi$
$30$	1.23205	−	1.86603i	0.224941	−	0.340688i
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−0.633975	−	0.366025i	−0.110361	−	0.0637168i
$34$	−4.46410			−0.765587
$35$	−5.09808	−	3.36603i	−0.861732	−	0.568962i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−6.86603	+	3.96410i	−1.12877	+	0.651694i	−0.943625	−	0.331017i	$-0.892608\pi$
$37$	−6.86603	+	3.96410i	−1.12877	+	0.651694i	−0.185143	+	0.982712i	$0.559275\pi$
$38$			1.26795i			0.205689i
$39$	3.23205	−	1.59808i	0.517542	−	0.255897i
$40$	0.133975	−	2.23205i	0.0211832	−	0.352918i
$41$	4.59808	+	7.96410i	0.718099	+	1.24378i	0.961752	+	0.273921i	$0.0883208\pi$
$41$	4.59808	+	7.96410i	0.718099	+	1.24378i	−0.243653	+	0.969862i	$0.578346\pi$
$42$	−2.36603	+	1.36603i	−0.365086	+	0.210782i
$43$	2.83013	+	1.63397i	0.431590	+	0.249179i	0.700024	−	0.714119i	$-0.253173\pi$
$43$	2.83013	+	1.63397i	0.431590	+	0.249179i	−0.268434	+	0.963298i	$0.586506\pi$
$44$	−0.732051			−0.110361
$45$	−1.23205	+	1.86603i	−0.183663	+	0.278171i
$46$	−3.09808	+	5.36603i	−0.456786	+	0.791177i
$47$		−	7.66025i		−	1.11736i	−0.829382	−	0.558681i	$-0.811307\pi$
$47$		−	7.66025i		−	1.11736i	0.829382	−	0.558681i	$-0.188693\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	0.232051	+	0.401924i	0.0331501	+	0.0574177i
$50$	−4.59808	+	1.96410i	−0.650266	+	0.277766i
$51$	4.46410			0.625099
$52$	2.00000	−	3.00000i	0.277350	−	0.416025i
$53$			7.73205i			1.06208i	0.847347	+	0.531039i	$0.178198\pi$
$53$			7.73205i			1.06208i	−0.847347	+	0.531039i	$0.821802\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	0.732051	+	1.46410i	0.0987097	+	0.197419i
$56$	−1.36603	+	2.36603i	−0.182543	+	0.316173i
$57$		−	1.26795i		−	0.167944i
$58$	5.59808	+	3.23205i	0.735063	+	0.424389i
$59$	−6.19615	+	10.7321i	−0.806670	+	1.39719i	0.108487	+	0.994098i	$0.465399\pi$
$59$	−6.19615	+	10.7321i	−0.806670	+	1.39719i	−0.915158	+	0.403096i	$0.867934\pi$
$60$	−0.133975	+	2.23205i	−0.0172960	+	0.288157i
$61$	5.06218	−	8.76795i	0.648145	−	1.12262i	−0.335420	−	0.942069i	$-0.608878\pi$
$61$	5.06218	−	8.76795i	0.648145	−	1.12262i	0.983565	−	0.180552i	$-0.0577885\pi$
$62$	−3.46410	+	2.00000i	−0.439941	+	0.254000i
$63$	2.36603	−	1.36603i	0.298091	−	0.172103i
$64$	−1.00000			−0.125000
$65$	−8.00000	−	1.00000i	−0.992278	−	0.124035i
$66$	0.732051			0.0901092
$67$	−6.63397	+	3.83013i	−0.810469	+	0.467924i	−0.847119	−	0.531404i	$-0.821665\pi$
$67$	−6.63397	+	3.83013i	−0.810469	+	0.467924i	0.0366497	+	0.999328i	$0.488331\pi$
$68$	3.86603	−	2.23205i	0.468824	−	0.270676i
$69$	3.09808	−	5.36603i	0.372965	−	0.645994i
$70$	6.09808	+	0.366025i	0.728860	+	0.0437484i
$71$	−0.633975	+	1.09808i	−0.0752389	+	0.130318i	−0.901190	−	0.433424i	$-0.857305\pi$
$71$	−0.633975	+	1.09808i	−0.0752389	+	0.130318i	0.825951	+	0.563742i	$0.190639\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$		−	4.66025i		−	0.545441i	−0.962093	−	0.272721i	$-0.912076\pi$
$73$		−	4.66025i		−	0.545441i	0.962093	−	0.272721i	$-0.0879235\pi$
$74$	3.96410	−	6.86603i	0.460817	−	0.798159i
$75$	4.59808	−	1.96410i	0.530940	−	0.226795i
$76$	−0.633975	−	1.09808i	−0.0727219	−	0.125958i
$77$		−	2.00000i		−	0.227921i
$78$	−2.00000	+	3.00000i	−0.226455	+	0.339683i
$79$	−12.0000			−1.35011			−0.675053	−	0.737769i	$-0.735879\pi$
$79$	−12.0000			−1.35011			−0.675053	+	0.737769i	$0.735879\pi$
$80$	1.00000	+	2.00000i	0.111803	+	0.223607i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−7.96410	−	4.59808i	−0.879488	−	0.507773i
$83$			5.26795i			0.578233i	0.957294	+	0.289116i	$0.0933614\pi$
$83$			5.26795i			0.578233i	−0.957294	+	0.289116i	$0.906639\pi$
$84$	1.36603	−	2.36603i	0.149046	−	0.258155i
$85$	−8.33013	−	5.50000i	−0.903529	−	0.596559i
$86$	−3.26795			−0.352392
$87$	−5.59808	−	3.23205i	−0.600177	−	0.346512i
$88$	0.633975	−	0.366025i	0.0675819	−	0.0390184i
$89$	−2.46410	−	4.26795i	−0.261194	−	0.452402i	0.705365	−	0.708844i	$-0.250783\pi$
$89$	−2.46410	−	4.26795i	−0.261194	−	0.452402i	−0.966560	+	0.256442i	$0.917450\pi$
$90$	0.133975	−	2.23205i	0.0141222	−	0.235279i
$91$	8.19615	+	5.46410i	0.859190	+	0.572793i
$92$		−	6.19615i		−	0.645994i
$93$	3.46410	−	2.00000i	0.359211	−	0.207390i
$94$	3.83013	+	6.63397i	0.395047	+	0.684242i
$95$	−1.56218	+	2.36603i	−0.160276	+	0.242749i
$96$	1.00000			0.102062
$97$	−8.66025	−	5.00000i	−0.879316	−	0.507673i	−0.00888289	−	0.999961i	$-0.502828\pi$
$97$	−8.66025	−	5.00000i	−0.879316	−	0.507673i	−0.870433	+	0.492287i	$0.836161\pi$
$98$	−0.401924	−	0.232051i	−0.0406004	−	0.0234407i
$99$	−0.732051			−0.0735739
$100$	3.00000	−	4.00000i	0.300000	−	0.400000i
$101$	−6.96410	−	12.0622i	−0.692954	−	1.20023i	−0.970866	−	0.239625i	$-0.922976\pi$
$101$	−6.96410	−	12.0622i	−0.692954	−	1.20023i	0.277912	−	0.960607i	$-0.410358\pi$
$102$	−3.86603	+	2.23205i	−0.382794	+	0.221006i
$103$			9.26795i			0.913198i	0.889673	+	0.456599i	$0.150933\pi$
$103$			9.26795i			0.913198i	−0.889673	+	0.456599i	$0.849067\pi$
$104$	−0.232051	+	3.59808i	−0.0227545	+	0.352820i
$105$	−6.09808	−	0.366025i	−0.595111	−	0.0357204i
$106$	−3.86603	−	6.69615i	−0.375502	−	0.650388i
$107$	−1.09808	+	0.633975i	−0.106155	+	0.0612886i	−0.552138	−	0.833753i	$-0.686188\pi$
$107$	−1.09808	+	0.633975i	−0.106155	+	0.0612886i	0.445983	+	0.895042i	$0.352854\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$	−1.36603	−	0.901924i	−0.130245	−	0.0859951i
$111$	−3.96410	+	6.86603i	−0.376256	+	0.651694i
$112$		−	2.73205i		−	0.258155i
$113$	−7.79423	−	4.50000i	−0.733219	−	0.423324i	0.0863794	−	0.996262i	$-0.472470\pi$
$113$	−7.79423	−	4.50000i	−0.733219	−	0.423324i	−0.819599	+	0.572938i	$0.805804\pi$
$114$	0.633975	+	1.09808i	0.0593772	+	0.102844i
$115$	−12.3923	+	6.19615i	−1.15559	+	0.577794i
$116$	−6.46410			−0.600177
$117$	2.00000	−	3.00000i	0.184900	−	0.277350i
$118$		−	12.3923i		−	1.14080i
$119$	6.09808	+	10.5622i	0.559010	+	0.968233i
$120$	−1.00000	−	2.00000i	−0.0912871	−	0.182574i
$121$	5.23205	−	9.06218i	0.475641	−	0.823834i
$122$			10.1244i			0.916616i
$123$	7.96410	+	4.59808i	0.718099	+	0.414595i
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$	−1.36603	+	2.36603i	−0.121695	+	0.210782i
$127$	−3.46410	+	2.00000i	−0.307389	+	0.177471i	−0.645758	−	0.763542i	$-0.723458\pi$
$127$	−3.46410	+	2.00000i	−0.307389	+	0.177471i	0.338368	+	0.941014i	$0.390125\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	3.26795			0.287727
$130$	7.42820	−	3.13397i	0.651497	−	0.274868i
$131$	−13.8564			−1.21064			−0.605320	−	0.795982i	$-0.706955\pi$
$131$	−13.8564			−1.21064			−0.605320	+	0.795982i	$0.706955\pi$
$132$	−0.633975	+	0.366025i	−0.0551804	+	0.0318584i
$133$	3.00000	−	1.73205i	0.260133	−	0.150188i
$134$	3.83013	−	6.63397i	0.330873	−	0.573088i
$135$	−0.133975	+	2.23205i	−0.0115307	+	0.192104i
$136$	−2.23205	+	3.86603i	−0.191397	+	0.331509i
$137$	15.9904	+	9.23205i	1.36615	+	0.788747i	0.990434	−	0.137987i	$-0.0440633\pi$
$137$	15.9904	+	9.23205i	1.36615	+	0.788747i	0.375716	+	0.926735i	$0.377397\pi$
$138$			6.19615i			0.527452i
$139$	−0.535898	+	0.928203i	−0.0454543	+	0.0787292i	−0.887857	−	0.460119i	$-0.847807\pi$
$139$	−0.535898	+	0.928203i	−0.0454543	+	0.0787292i	0.842403	+	0.538848i	$0.181140\pi$
$140$	−5.46410	+	2.73205i	−0.461801	+	0.230900i
$141$	−3.83013	−	6.63397i	−0.322555	−	0.558681i
$142$		−	1.26795i		−	0.106404i
$143$	−1.16987	−	2.36603i	−0.0978297	−	0.197857i
$144$	−1.00000			−0.0833333
$145$	6.46410	+	12.9282i	0.536814	+	1.07363i
$146$	2.33013	+	4.03590i	0.192843	+	0.334013i
$147$	0.401924	+	0.232051i	0.0331501	+	0.0191392i
$148$			7.92820i			0.651694i
$149$	9.96410	−	17.2583i	0.816291	−	1.41386i	−0.0921062	−	0.995749i	$-0.529360\pi$
$149$	9.96410	−	17.2583i	0.816291	−	1.41386i	0.908397	−	0.418108i	$-0.137307\pi$
$150$	−3.00000	+	4.00000i	−0.244949	+	0.326599i
$151$	−5.12436			−0.417014			−0.208507	−	0.978021i	$-0.566860\pi$
$151$	−5.12436			−0.417014			−0.208507	+	0.978021i	$0.566860\pi$
$152$	1.09808	+	0.633975i	0.0890657	+	0.0514221i
$153$	3.86603	−	2.23205i	0.312550	−	0.180451i
$154$	1.00000	+	1.73205i	0.0805823	+	0.139573i
$155$	−8.92820	−	0.535898i	−0.717131	−	0.0430444i
$156$	0.232051	−	3.59808i	0.0185789	−	0.288077i
$157$		−	9.39230i		−	0.749588i	−0.927108	−	0.374794i	$-0.877714\pi$
$157$		−	9.39230i		−	0.749588i	0.927108	−	0.374794i	$-0.122286\pi$
$158$	10.3923	−	6.00000i	0.826767	−	0.477334i
$159$	3.86603	+	6.69615i	0.306596	+	0.531039i
$160$	−1.86603	−	1.23205i	−0.147522	−	0.0974022i
$161$	16.9282			1.33413
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	11.6603	+	6.73205i	0.913302	+	0.527295i	0.881492	−	0.472199i	$-0.156540\pi$
$163$	11.6603	+	6.73205i	0.913302	+	0.527295i	0.0318096	+	0.999494i	$0.489873\pi$
$164$	9.19615			0.718099
$165$	1.36603	+	0.901924i	0.106345	+	0.0702147i
$166$	−2.63397	−	4.56218i	−0.204436	−	0.354094i
$167$	12.0000	−	6.92820i	0.928588	−	0.536120i	0.0422232	−	0.999108i	$-0.486556\pi$
$167$	12.0000	−	6.92820i	0.928588	−	0.536120i	0.886365	+	0.462988i	$0.153223\pi$
$168$			2.73205i			0.210782i
$169$	12.8923	+	1.66987i	0.991716	+	0.128452i
$170$	9.96410	+	0.598076i	0.764212	+	0.0458704i
$171$	−0.633975	−	1.09808i	−0.0484812	−	0.0839720i
$172$	2.83013	−	1.63397i	0.215795	−	0.124589i
$173$	16.2679	+	9.39230i	1.23683	+	0.714084i	0.968445	−	0.249228i	$-0.0801769\pi$
$173$	16.2679	+	9.39230i	1.23683	+	0.714084i	0.268384	+	0.963312i	$0.413510\pi$
$174$	6.46410			0.490042
$175$	10.9282	+	8.19615i	0.826095	+	0.619571i
$176$	−0.366025	+	0.633975i	−0.0275902	+	0.0477876i
$177$			12.3923i			0.931463i
$178$	4.26795	+	2.46410i	0.319896	+	0.184692i
$179$	9.09808	+	15.7583i	0.680022	+	1.17783i	0.974974	+	0.222321i	$0.0713632\pi$
$179$	9.09808	+	15.7583i	0.680022	+	1.17783i	−0.294951	+	0.955512i	$0.595303\pi$
$180$	1.00000	+	2.00000i	0.0745356	+	0.149071i
$181$	−16.1244			−1.19851			−0.599257	−	0.800557i	$-0.704537\pi$
$181$	−16.1244			−1.19851			−0.599257	+	0.800557i	$0.704537\pi$
$182$	−9.83013	−	0.633975i	−0.728657	−	0.0469933i
$183$		−	10.1244i		−	0.748414i
$184$	3.09808	+	5.36603i	0.228393	+	0.395589i
$185$	15.8564	−	7.92820i	1.16579	−	0.582893i
$186$	−2.00000	+	3.46410i	−0.146647	+	0.254000i
$187$		−	3.26795i		−	0.238976i
$188$	−6.63397	−	3.83013i	−0.483832	−	0.279341i
$189$	1.36603	−	2.36603i	0.0993637	−	0.172103i
$190$	0.169873	−	2.83013i	0.0123239	−	0.205319i
$191$	4.73205	−	8.19615i	0.342399	−	0.593053i	−0.642479	−	0.766304i	$-0.722094\pi$
$191$	4.73205	−	8.19615i	0.342399	−	0.593053i	0.984878	+	0.173251i	$0.0554272\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−9.23205	+	5.33013i	−0.664538	+	0.383671i	−0.794004	−	0.607913i	$-0.792007\pi$
$193$	−9.23205	+	5.33013i	−0.664538	+	0.383671i	0.129466	+	0.991584i	$0.458674\pi$
$194$	10.0000			0.717958
$195$	−7.42820	+	3.13397i	−0.531945	+	0.224429i
$196$	0.464102			0.0331501
$197$	−8.53590	+	4.92820i	−0.608158	+	0.351120i	−0.772244	−	0.635326i	$-0.780866\pi$
$197$	−8.53590	+	4.92820i	−0.608158	+	0.351120i	0.164086	+	0.986446i	$0.447532\pi$
$198$	0.633975	−	0.366025i	0.0450546	−	0.0260123i
$199$	−14.0263	+	24.2942i	−0.994297	+	1.72217i	−0.404786	+	0.914411i	$0.632654\pi$
$199$	−14.0263	+	24.2942i	−0.994297	+	1.72217i	−0.589510	+	0.807761i	$0.700679\pi$
$200$	−0.598076	+	4.96410i	−0.0422904	+	0.351015i
$201$	−3.83013	+	6.63397i	−0.270156	+	0.467924i
$202$	12.0622	+	6.96410i	0.848692	+	0.489992i
$203$		−	17.6603i		−	1.23951i
$204$	2.23205	−	3.86603i	0.156275	−	0.270676i
$205$	−9.19615	−	18.3923i	−0.642287	−	1.28457i
$206$	−4.63397	−	8.02628i	−0.322864	−	0.559217i
$207$		−	6.19615i		−	0.430662i
$208$	−1.59808	−	3.23205i	−0.110807	−	0.224102i
$209$	−0.928203			−0.0642052
$210$	5.46410	−	2.73205i	0.377059	−	0.188529i
$211$	10.7321	+	18.5885i	0.738825	+	1.27968i	0.953025	+	0.302892i	$0.0979523\pi$
$211$	10.7321	+	18.5885i	0.738825	+	1.27968i	−0.214200	+	0.976790i	$0.568714\pi$
$212$	6.69615	+	3.86603i	0.459894	+	0.265520i
$213$			1.26795i			0.0868784i
$214$	0.633975	−	1.09808i	0.0433376	−	0.0750629i
$215$	−6.09808	−	4.02628i	−0.415885	−	0.274590i
$216$	1.00000			0.0680414
$217$	9.46410	+	5.46410i	0.642465	+	0.370927i
$218$	8.66025	−	5.00000i	0.586546	−	0.338643i
$219$	−2.33013	−	4.03590i	−0.157455	−	0.272721i
$220$	1.63397	+	0.0980762i	0.110163	+	0.00661230i
$221$	13.3923	+	8.92820i	0.900864	+	0.600576i
$222$		−	7.92820i		−	0.532106i
$223$	−0.339746	+	0.196152i	−0.0227511	+	0.0131353i	−0.511332	−	0.859383i	$-0.670848\pi$
$223$	−0.339746	+	0.196152i	−0.0227511	+	0.0131353i	0.488581	+	0.872518i	$0.337515\pi$
$224$	1.36603	+	2.36603i	0.0912714	+	0.158087i
$225$	3.00000	−	4.00000i	0.200000	−	0.266667i
$226$	9.00000			0.598671
$227$	−3.63397	−	2.09808i	−0.241195	−	0.139254i	0.374531	−	0.927215i	$-0.377804\pi$
$227$	−3.63397	−	2.09808i	−0.241195	−	0.139254i	−0.615726	+	0.787960i	$0.711137\pi$
$228$	−1.09808	−	0.633975i	−0.0727219	−	0.0419860i
$229$	−28.7846			−1.90214			−0.951070	−	0.308975i	$-0.900014\pi$
$229$	−28.7846			−1.90214			−0.951070	+	0.308975i	$0.900014\pi$
$230$	7.63397	−	11.5622i	0.503369	−	0.762387i
$231$	−1.00000	−	1.73205i	−0.0657952	−	0.113961i
$232$	5.59808	−	3.23205i	0.367532	−	0.212195i
$233$			12.3923i			0.811847i	0.913907	+	0.405923i	$0.133050\pi$
$233$			12.3923i			0.811847i	−0.913907	+	0.405923i	$0.866950\pi$
$234$	−0.232051	+	3.59808i	−0.0151696	+	0.235214i
$235$	−1.02628	+	17.0981i	−0.0669471	+	1.11536i
$236$	6.19615	+	10.7321i	0.403335	+	0.698597i
$237$	−10.3923	+	6.00000i	−0.675053	+	0.389742i
$238$	−10.5622	−	6.09808i	−0.684644	−	0.395280i
$239$	4.58846			0.296803			0.148401	−	0.988927i	$-0.452587\pi$
$239$	4.58846			0.296803			0.148401	+	0.988927i	$0.452587\pi$
$240$	1.86603	+	1.23205i	0.120451	+	0.0795285i
$241$	4.69615	−	8.13397i	0.302506	−	0.523955i	−0.674197	−	0.738551i	$-0.735510\pi$
$241$	4.69615	−	8.13397i	0.302506	−	0.523955i	0.976703	+	0.214596i	$0.0688435\pi$
$242$			10.4641i			0.672658i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−5.06218	−	8.76795i	−0.324073	−	0.561310i
$245$	−0.464102	−	0.928203i	−0.0296504	−	0.0593007i
$246$	−9.19615			−0.586325
$247$	2.53590	−	3.80385i	0.161355	−	0.242033i
$248$			4.00000i			0.254000i
$249$	2.63397	+	4.56218i	0.166921	+	0.289116i
$250$	10.5263	−	3.76795i	0.665740	−	0.238306i
$251$	10.7321	−	18.5885i	0.677401	−	1.17329i	−0.298360	−	0.954453i	$-0.596440\pi$
$251$	10.7321	−	18.5885i	0.677401	−	1.17329i	0.975761	−	0.218840i	$-0.0702271\pi$
$252$		−	2.73205i		−	0.172103i
$253$	−3.92820	−	2.26795i	−0.246964	−	0.142585i
$254$	2.00000	−	3.46410i	0.125491	−	0.217357i
$255$	−9.96410	−	0.598076i	−0.623976	−	0.0374530i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.59808	−	1.50000i	0.162064	−	0.0935674i	−0.416775	−	0.909010i	$-0.636840\pi$
$257$	2.59808	−	1.50000i	0.162064	−	0.0935674i	0.578838	+	0.815442i	$0.303506\pi$
$258$	−2.83013	+	1.63397i	−0.176196	+	0.101727i
$259$	−21.6603			−1.34590
$260$	−4.86603	+	6.42820i	−0.301778	+	0.398660i
$261$	−6.46410			−0.400118
$262$	12.0000	−	6.92820i	0.741362	−	0.428026i
$263$	−14.8301	+	8.56218i	−0.914465	+	0.527967i	−0.881865	−	0.471502i	$-0.843712\pi$
$263$	−14.8301	+	8.56218i	−0.914465	+	0.527967i	−0.0325998	+	0.999468i	$0.510379\pi$
$264$	0.366025	−	0.633975i	0.0225273	−	0.0390184i
$265$	1.03590	−	17.2583i	0.0636347	−	1.06017i
$266$	−1.73205	+	3.00000i	−0.106199	+	0.183942i
$267$	−4.26795	−	2.46410i	−0.261194	−	0.150801i
$268$			7.66025i			0.467924i
$269$	2.19615	−	3.80385i	0.133902	−	0.231925i	−0.791276	−	0.611460i	$-0.790583\pi$
$269$	2.19615	−	3.80385i	0.133902	−	0.231925i	0.925177	+	0.379535i	$0.123916\pi$
$270$	−1.00000	−	2.00000i	−0.0608581	−	0.121716i
$271$	−2.92820	−	5.07180i	−0.177876	−	0.308090i	0.763277	−	0.646071i	$-0.223589\pi$
$271$	−2.92820	−	5.07180i	−0.177876	−	0.308090i	−0.941153	+	0.337982i	$0.890256\pi$
$272$		−	4.46410i		−	0.270676i
$273$	9.83013	+	0.633975i	0.594946	+	0.0383699i
$274$	−18.4641			−1.11546
$275$	−1.43782	−	3.36603i	−0.0867039	−	0.202979i
$276$	−3.09808	−	5.36603i	−0.186482	−	0.322997i
$277$	10.6699	+	6.16025i	0.641091	+	0.370134i	0.785034	−	0.619452i	$-0.212645\pi$
$277$	10.6699	+	6.16025i	0.641091	+	0.370134i	−0.143944	+	0.989586i	$0.545979\pi$
$278$		−	1.07180i		−	0.0642821i
$279$	2.00000	−	3.46410i	0.119737	−	0.207390i
$280$	3.36603	−	5.09808i	0.201158	−	0.304668i
$281$	1.73205			0.103325			0.0516627	−	0.998665i	$-0.483548\pi$
$281$	1.73205			0.103325			0.0516627	+	0.998665i	$0.483548\pi$
$282$	6.63397	+	3.83013i	0.395047	+	0.228081i
$283$	6.63397	−	3.83013i	0.394349	−	0.227677i	−0.289694	−	0.957119i	$-0.593553\pi$
$283$	6.63397	−	3.83013i	0.394349	−	0.227677i	0.684043	+	0.729442i	$0.260220\pi$
$284$	0.633975	+	1.09808i	0.0376195	+	0.0651588i
$285$	−0.169873	+	2.83013i	−0.0100624	+	0.167642i
$286$	2.19615	+	1.46410i	0.129861	+	0.0865741i
$287$			25.1244i			1.48304i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	1.46410	+	2.53590i	0.0861236	+	0.149170i
$290$	−12.0622	−	7.96410i	−0.708315	−	0.467668i
$291$	−10.0000			−0.586210
$292$	−4.03590	−	2.33013i	−0.236183	−	0.136360i
$293$	−11.8923	−	6.86603i	−0.694756	−	0.401117i	0.110635	−	0.993861i	$-0.464711\pi$
$293$	−11.8923	−	6.86603i	−0.694756	−	0.401117i	−0.805391	+	0.592744i	$0.798045\pi$
$294$	−0.464102			−0.0270670
$295$	15.2679	−	23.1244i	0.888934	−	1.34635i
$296$	−3.96410	−	6.86603i	−0.230409	−	0.399080i
$297$	−0.633975	+	0.366025i	−0.0367869	+	0.0212389i
$298$			19.9282i			1.15441i
$299$	20.0263	−	9.90192i	1.15815	−	0.572643i
$300$	0.598076	−	4.96410i	0.0345299	−	0.286603i
$301$	4.46410	+	7.73205i	0.257307	+	0.445668i
$302$	4.43782	−	2.56218i	0.255368	−	0.147437i
$303$	−12.0622	−	6.96410i	−0.692954	−	0.400077i
$304$	−1.26795			−0.0727219
$305$	−12.4737	+	18.8923i	−0.714243	+	1.08177i
$306$	−2.23205	+	3.86603i	−0.127598	+	0.221006i
$307$			19.2679i			1.09968i	0.835270	+	0.549840i	$0.185311\pi$
$307$			19.2679i			1.09968i	−0.835270	+	0.549840i	$0.814689\pi$
$308$	−1.73205	−	1.00000i	−0.0986928	−	0.0569803i
$309$	4.63397	+	8.02628i	0.263618	+	0.456599i
$310$	8.00000	−	4.00000i	0.454369	−	0.227185i
$311$	3.12436			0.177166			0.0885830	−	0.996069i	$-0.471766\pi$
$311$	3.12436			0.177166			0.0885830	+	0.996069i	$0.471766\pi$
$312$	1.59808	+	3.23205i	0.0904732	+	0.182979i
$313$		−	14.0000i		−	0.791327i	−0.918396	−	0.395663i	$-0.870515\pi$
$313$		−	14.0000i		−	0.791327i	0.918396	−	0.395663i	$-0.129485\pi$
$314$	4.69615	+	8.13397i	0.265019	+	0.459027i
$315$	−5.46410	+	2.73205i	−0.307867	+	0.153934i
$316$	−6.00000	+	10.3923i	−0.337526	+	0.584613i
$317$		−	29.7321i		−	1.66992i	−0.550312	−	0.834959i	$-0.685491\pi$
$317$		−	29.7321i		−	1.66992i	0.550312	−	0.834959i	$-0.314509\pi$
$318$	−6.69615	−	3.86603i	−0.375502	−	0.216796i
$319$	−2.36603	+	4.09808i	−0.132472	+	0.229448i
$320$	2.23205	+	0.133975i	0.124775	+	0.00748941i
$321$	−0.633975	+	1.09808i	−0.0353850	+	0.0612886i
$322$	−14.6603	+	8.46410i	−0.816984	+	0.471686i
$323$	4.90192	−	2.83013i	0.272750	−	0.157472i
$324$	−1.00000			−0.0555556
$325$	17.7224	+	3.30385i	0.983064	+	0.183264i
$326$	−13.4641			−0.745708
$327$	−8.66025	+	5.00000i	−0.478913	+	0.276501i
$328$	−7.96410	+	4.59808i	−0.439744	+	0.253886i
$329$	10.4641	−	18.1244i	0.576905	−	0.999228i
$330$	−1.63397	−	0.0980762i	−0.0899473	−	0.00539892i
$331$	14.3923	−	24.9282i	0.791073	−	1.37018i	−0.134231	−	0.990950i	$-0.542856\pi$
$331$	14.3923	−	24.9282i	0.791073	−	1.37018i	0.925303	−	0.379228i	$-0.123810\pi$
$332$	4.56218	+	2.63397i	0.250382	+	0.144558i
$333$			7.92820i			0.434463i
$334$	−6.92820	+	12.0000i	−0.379094	+	0.656611i
$335$	15.3205	−	7.66025i	0.837049	−	0.418524i
$336$	−1.36603	−	2.36603i	−0.0745228	−	0.129077i
$337$		−	11.0526i		−	0.602071i	−0.953613	−	0.301036i	$-0.902668\pi$
$337$		−	11.0526i		−	0.602071i	0.953613	−	0.301036i	$-0.0973323\pi$
$338$	−12.0000	+	5.00000i	−0.652714	+	0.271964i
$339$	−9.00000			−0.488813
$340$	−8.92820	+	4.46410i	−0.484200	+	0.242100i
$341$	−1.46410	−	2.53590i	−0.0792855	−	0.137327i
$342$	1.09808	+	0.633975i	0.0593772	+	0.0342814i
$343$		−	17.8564i		−	0.964155i
$344$	−1.63397	+	2.83013i	−0.0880980	+	0.152590i
$345$	−7.63397	+	11.5622i	−0.410999	+	0.622487i
$346$	−18.7846			−1.00987
$347$	−4.90192	−	2.83013i	−0.263149	−	0.151929i	0.362621	−	0.931937i	$-0.381882\pi$
$347$	−4.90192	−	2.83013i	−0.263149	−	0.151929i	−0.625770	+	0.780007i	$0.715215\pi$
$348$	−5.59808	+	3.23205i	−0.300088	+	0.173256i
$349$	−9.53590	−	16.5167i	−0.510445	−	0.884117i	−0.999927	−	0.0121031i	$-0.996147\pi$
$349$	−9.53590	−	16.5167i	−0.510445	−	0.884117i	0.489482	−	0.872014i	$-0.337186\pi$
$350$	−13.5622	−	1.63397i	−0.724929	−	0.0873396i
$351$	0.232051	−	3.59808i	0.0123860	−	0.192051i
$352$		−	0.732051i		−	0.0390184i
$353$	−21.8660	+	12.6244i	−1.16381	+	0.671927i	−0.952214	−	0.305430i	$-0.901200\pi$
$353$	−21.8660	+	12.6244i	−1.16381	+	0.671927i	−0.211597	+	0.977357i	$0.567866\pi$
$354$	−6.19615	−	10.7321i	−0.329322	−	0.570402i
$355$	1.56218	−	2.36603i	0.0829118	−	0.125576i
$356$	−4.92820			−0.261194
$357$	10.5622	+	6.09808i	0.559010	+	0.322744i
$358$	−15.7583	−	9.09808i	−0.832854	−	0.480848i
$359$	−8.87564			−0.468439			−0.234219	−	0.972184i	$-0.575253\pi$
$359$	−8.87564			−0.468439			−0.234219	+	0.972184i	$0.575253\pi$
$360$	−1.86603	−	1.23205i	−0.0983482	−	0.0649348i
$361$	8.69615	+	15.0622i	0.457692	+	0.792746i
$362$	13.9641	−	8.06218i	0.733937	−	0.423739i
$363$		−	10.4641i		−	0.549223i
$364$	8.83013	−	4.36603i	0.462824	−	0.228842i
$365$	−0.624356	+	10.4019i	−0.0326803	+	0.544462i
$366$	5.06218	+	8.76795i	0.264604	+	0.458308i
$367$	−28.5622	+	16.4904i	−1.49093	+	0.860791i	−0.999946	−	0.0103758i	$-0.996697\pi$
$367$	−28.5622	+	16.4904i	−1.49093	+	0.860791i	−0.490987	+	0.871167i	$0.663364\pi$
$368$	−5.36603	−	3.09808i	−0.279723	−	0.161498i
$369$	9.19615			0.478733
$370$	−9.76795	+	14.7942i	−0.507811	+	0.769115i
$371$	−10.5622	+	18.2942i	−0.548361	+	0.949789i
$372$		−	4.00000i		−	0.207390i
$373$	−20.3827	−	11.7679i	−1.05538	−	0.609321i	−0.131226	−	0.991352i	$-0.541891\pi$
$373$	−20.3827	−	11.7679i	−1.05538	−	0.609321i	−0.924149	+	0.382031i	$0.875225\pi$
$374$	1.63397	+	2.83013i	0.0844908	+	0.146342i
$375$	−10.5263	+	3.76795i	−0.543575	+	0.194576i
$376$	7.66025			0.395047
$377$	−10.3301	−	20.8923i	−0.532029	−	1.07601i
$378$			2.73205i			0.140522i
$379$	13.1244	+	22.7321i	0.674153	+	1.16767i	0.976716	+	0.214538i	$0.0688244\pi$
$379$	13.1244	+	22.7321i	0.674153	+	1.16767i	−0.302563	+	0.953129i	$0.597842\pi$
$380$	1.26795	+	2.53590i	0.0650444	+	0.130089i
$381$	−2.00000	+	3.46410i	−0.102463	+	0.177471i
$382$			9.46410i			0.484226i
$383$	−23.3205	−	13.4641i	−1.19162	−	0.687983i	−0.232948	−	0.972489i	$-0.574837\pi$
$383$	−23.3205	−	13.4641i	−1.19162	−	0.687983i	−0.958674	+	0.284506i	$0.908171\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	−0.267949	+	4.46410i	−0.0136560	+	0.227512i
$386$	5.33013	−	9.23205i	0.271296	−	0.469899i
$387$	2.83013	−	1.63397i	0.143863	−	0.0830596i
$388$	−8.66025	+	5.00000i	−0.439658	+	0.253837i
$389$	24.0718			1.22049			0.610244	−	0.792213i	$-0.291071\pi$
$389$	24.0718			1.22049			0.610244	+	0.792213i	$0.291071\pi$
$390$	4.86603	−	6.42820i	0.246401	−	0.325505i
$391$	27.6603			1.39884
$392$	−0.401924	+	0.232051i	−0.0203002	+	0.0117203i
$393$	−12.0000	+	6.92820i	−0.605320	+	0.349482i
$394$	4.92820	−	8.53590i	0.248279	−	0.430032i
$395$	26.7846	+	1.60770i	1.34768	+	0.0808919i
$396$	−0.366025	+	0.633975i	−0.0183935	+	0.0318584i
$397$	−16.7321	−	9.66025i	−0.839758	−	0.484834i	0.0174242	−	0.999848i	$-0.494453\pi$
$397$	−16.7321	−	9.66025i	−0.839758	−	0.484834i	−0.857182	+	0.515014i	$0.827787\pi$
$398$		−	28.0526i		−	1.40615i
$399$	1.73205	−	3.00000i	0.0867110	−	0.150188i
$400$	−1.96410	−	4.59808i	−0.0982051	−	0.229904i
$401$	4.52628	+	7.83975i	0.226032	+	0.391498i	0.956628	−	0.291311i	$-0.0940914\pi$
$401$	4.52628	+	7.83975i	0.226032	+	0.391498i	−0.730597	+	0.682809i	$0.760758\pi$
$402$		−	7.66025i		−	0.382059i
$403$	14.3923	+	0.928203i	0.716932	+	0.0462371i
$404$	−13.9282			−0.692954
$405$	1.00000	+	2.00000i	0.0496904	+	0.0993808i
$406$	8.83013	+	15.2942i	0.438232	+	0.759040i
$407$	5.02628	+	2.90192i	0.249143	+	0.143843i
$408$			4.46410i			0.221006i
$409$	8.03590	−	13.9186i	0.397350	−	0.688230i	−0.596048	−	0.802949i	$-0.703263\pi$
$409$	8.03590	−	13.9186i	0.397350	−	0.688230i	0.993398	+	0.114719i	$0.0365967\pi$
$410$	17.1603	+	11.3301i	0.847485	+	0.559555i
$411$	18.4641			0.910767
$412$	8.02628	+	4.63397i	0.395426	+	0.228300i
$413$	−29.3205	+	16.9282i	−1.44277	+	0.832982i
$414$	3.09808	+	5.36603i	0.152262	+	0.263726i
$415$	0.705771	−	11.7583i	0.0346450	−	0.577194i
$416$	3.00000	+	2.00000i	0.147087	+	0.0980581i
$417$			1.07180i			0.0524861i
$418$	0.803848	−	0.464102i	0.0393175	−	0.0227000i
$419$	−3.26795	−	5.66025i	−0.159650	−	0.276522i	0.775093	−	0.631848i	$-0.217703\pi$
$419$	−3.26795	−	5.66025i	−0.159650	−	0.276522i	−0.934742	+	0.355326i	$0.884370\pi$
$420$	−3.36603	+	5.09808i	−0.164245	+	0.248761i
$421$	17.0526			0.831091			0.415545	−	0.909572i	$-0.363591\pi$
$421$	17.0526			0.831091			0.415545	+	0.909572i	$0.363591\pi$
$422$	−18.5885	−	10.7321i	−0.904872	−	0.522428i
$423$	−6.63397	−	3.83013i	−0.322555	−	0.186227i
$424$	−7.73205			−0.375502
$425$	17.8564	+	13.3923i	0.866163	+	0.649622i
$426$	−0.633975	−	1.09808i	−0.0307162	−	0.0532020i
$427$	23.9545	−	13.8301i	1.15924	−	0.669287i
$428$			1.26795i			0.0612886i
$429$	−2.19615	−	1.46410i	−0.106031	−	0.0706875i
$430$	7.29423	+	0.437822i	0.351759	+	0.0211137i
$431$	3.90192	+	6.75833i	0.187949	+	0.325537i	0.944566	−	0.328321i	$-0.106483\pi$
$431$	3.90192	+	6.75833i	0.187949	+	0.325537i	−0.756617	+	0.653858i	$0.773149\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	12.8205	+	7.40192i	0.616114	+	0.355714i	0.775355	−	0.631526i	$-0.217571\pi$
$433$	12.8205	+	7.40192i	0.616114	+	0.355714i	−0.159240	+	0.987240i	$0.550904\pi$
$434$	−10.9282			−0.524571
$435$	12.0622	+	7.96410i	0.578337	+	0.381849i
$436$	−5.00000	+	8.66025i	−0.239457	+	0.414751i
$437$		−	7.85641i		−	0.375823i
$438$	4.03590	+	2.33013i	0.192843	+	0.111338i
$439$	4.90192	+	8.49038i	0.233956	+	0.405224i	0.958969	−	0.283512i	$-0.0914995\pi$
$439$	4.90192	+	8.49038i	0.233956	+	0.405224i	−0.725013	+	0.688735i	$0.758166\pi$
$440$	−1.46410	+	0.732051i	−0.0697983	+	0.0348992i
$441$	0.464102			0.0221001
$442$	−16.0622	−	1.03590i	−0.764000	−	0.0492727i
$443$			34.6410i			1.64584i	0.568154	+	0.822922i	$0.307658\pi$
$443$			34.6410i			1.64584i	−0.568154	+	0.822922i	$0.692342\pi$
$444$	3.96410	+	6.86603i	0.188128	+	0.325847i
$445$	4.92820	+	9.85641i	0.233619	+	0.467238i
$446$	0.196152	−	0.339746i	0.00928809	−	0.0160874i
$447$		−	19.9282i		−	0.942572i
$448$	−2.36603	−	1.36603i	−0.111784	−	0.0645386i
$449$	−3.92820	+	6.80385i	−0.185383	+	0.321093i	−0.943706	−	0.330786i	$-0.892686\pi$
$449$	−3.92820	+	6.80385i	−0.185383	+	0.321093i	0.758322	+	0.651880i	$0.226019\pi$
$450$	−0.598076	+	4.96410i	−0.0281936	+	0.234010i
$451$	3.36603	−	5.83013i	0.158500	−	0.274530i
$452$	−7.79423	+	4.50000i	−0.366610	+	0.211662i
$453$	−4.43782	+	2.56218i	−0.208507	+	0.120382i
$454$	4.19615			0.196935
$455$	−17.5622	−	13.2942i	−0.823328	−	0.623243i
$456$	1.26795			0.0593772
$457$	7.62436	−	4.40192i	0.356652	−	0.205913i	−0.310959	−	0.950423i	$-0.600650\pi$
$457$	7.62436	−	4.40192i	0.356652	−	0.205913i	0.667611	+	0.744510i	$0.267317\pi$
$458$	24.9282	−	14.3923i	1.16482	−	0.672508i
$459$	2.23205	−	3.86603i	0.104183	−	0.180451i
$460$	−0.830127	+	13.8301i	−0.0387049	+	0.644833i
$461$	−13.0359	+	22.5788i	−0.607142	+	1.05160i	0.384567	+	0.923097i	$0.374351\pi$
$461$	−13.0359	+	22.5788i	−0.607142	+	1.05160i	−0.991709	+	0.128504i	$0.958982\pi$
$462$	1.73205	+	1.00000i	0.0805823	+	0.0465242i
$463$		−	6.33975i		−	0.294633i	−0.989089	−	0.147316i	$-0.952936\pi$
$463$		−	6.33975i		−	0.294633i	0.989089	−	0.147316i	$-0.0470636\pi$
$464$	−3.23205	+	5.59808i	−0.150044	+	0.259884i
$465$	−8.00000	+	4.00000i	−0.370991	+	0.185496i
$466$	−6.19615	−	10.7321i	−0.287031	−	0.497153i
$467$			22.0526i			1.02047i	0.860035	+	0.510235i	$0.170442\pi$
$467$			22.0526i			1.02047i	−0.860035	+	0.510235i	$0.829558\pi$
$468$	−1.59808	−	3.23205i	−0.0738711	−	0.149402i
$469$	−20.9282			−0.966375
$470$	−7.66025	−	15.3205i	−0.353341	−	0.706682i
$471$	−4.69615	−	8.13397i	−0.216387	−	0.374794i
$472$	−10.7321	−	6.19615i	−0.493983	−	0.285201i
$473$		−	2.39230i		−	0.109998i
$474$	6.00000	−	10.3923i	0.275589	−	0.477334i
$475$	3.80385	−	5.07180i	0.174532	−	0.232710i
$476$	12.1962			0.559010
$477$	6.69615	+	3.86603i	0.306596	+	0.177013i
$478$	−3.97372	+	2.29423i	−0.181754	+	0.104936i
$479$	−8.00000	−	13.8564i	−0.365529	−	0.633115i	0.623332	−	0.781958i	$-0.285779\pi$
$479$	−8.00000	−	13.8564i	−0.365529	−	0.633115i	−0.988861	+	0.148842i	$0.952445\pi$
$480$	−2.23205	−	0.133975i	−0.101879	−	0.00611508i
$481$	−25.6244	+	12.6699i	−1.16837	+	0.577696i
$482$			9.39230i			0.427808i
$483$	14.6603	−	8.46410i	0.667065	−	0.385130i
$484$	−5.23205	−	9.06218i	−0.237820	−	0.411917i
$485$	18.6603	+	12.3205i	0.847318	+	0.559445i
$486$	1.00000			0.0453609
$487$	33.2942	+	19.2224i	1.50871	+	0.871052i	0.999949	+	0.0101413i	$0.00322814\pi$
$487$	33.2942	+	19.2224i	1.50871	+	0.871052i	0.508757	+	0.860910i	$0.330105\pi$
$488$	8.76795	+	5.06218i	0.396906	+	0.229154i
$489$	13.4641			0.608868
$490$	0.866025	+	0.571797i	0.0391230	+	0.0258311i
$491$	−10.9019	−	18.8827i	−0.491997	−	0.852164i	0.507961	−	0.861380i	$-0.330400\pi$
$491$	−10.9019	−	18.8827i	−0.491997	−	0.852164i	−0.999958	+	0.00921662i	$0.997066\pi$
$492$	7.96410	−	4.59808i	0.359049	−	0.207297i
$493$		−	28.8564i		−	1.29963i
$494$	−0.294229	+	4.56218i	−0.0132380	+	0.205262i
$495$	1.63397	+	0.0980762i	0.0734417	+	0.00440820i
$496$	−2.00000	−	3.46410i	−0.0898027	−	0.155543i
$497$	−3.00000	+	1.73205i	−0.134568	+	0.0776931i
$498$	−4.56218	−	2.63397i	−0.204436	−	0.118031i
$499$	−40.3923			−1.80821			−0.904104	−	0.427313i	$-0.859460\pi$
$499$	−40.3923			−1.80821			−0.904104	+	0.427313i	$0.859460\pi$
$500$	−7.23205	+	8.52628i	−0.323427	+	0.381307i
$501$	6.92820	−	12.0000i	0.309529	−	0.536120i
$502$			21.4641i			0.957990i
$503$	−18.8827	−	10.9019i	−0.841937	−	0.486093i	0.0159849	−	0.999872i	$-0.494912\pi$
$503$	−18.8827	−	10.9019i	−0.841937	−	0.486093i	−0.857922	+	0.513779i	$0.828245\pi$
$504$	1.36603	+	2.36603i	0.0608476	+	0.105391i
$505$	13.9282	+	27.8564i	0.619797	+	1.23959i
$506$	4.53590			0.201645
$507$	12.0000	−	5.00000i	0.532939	−	0.222058i
$508$			4.00000i			0.177471i
$509$	−15.3564	−	26.5981i	−0.680661	−	1.17894i	−0.974780	−	0.223170i	$-0.928359\pi$
$509$	−15.3564	−	26.5981i	−0.680661	−	1.17894i	0.294119	−	0.955769i	$-0.404974\pi$
$510$	8.92820	−	4.46410i	0.395347	−	0.197674i
$511$	6.36603	−	11.0263i	0.281616	−	0.487774i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.09808	−	0.633975i	−0.0484812	−	0.0279907i
$514$	−1.50000	+	2.59808i	−0.0661622	+	0.114596i
$515$	1.24167	−	20.6865i	0.0547145	−	0.911558i
$516$	1.63397	−	2.83013i	0.0719317	−	0.124589i
$517$	−4.85641	+	2.80385i	−0.213585	+	0.123313i
$518$	18.7583	−	10.8301i	0.824194	−	0.475848i
$519$	18.7846			0.824553
$520$	1.00000	−	8.00000i	0.0438529	−	0.350823i
$521$	−19.4449			−0.851895			−0.425947	−	0.904748i	$-0.640059\pi$
$521$	−19.4449			−0.851895			−0.425947	+	0.904748i	$0.640059\pi$
$522$	5.59808	−	3.23205i	0.245021	−	0.141463i
$523$	−31.5622	+	18.2224i	−1.38012	+	0.796811i	−0.992173	−	0.124871i	$-0.960148\pi$
$523$	−31.5622	+	18.2224i	−1.38012	+	0.796811i	−0.387945	+	0.921683i	$0.626815\pi$
$524$	−6.92820	+	12.0000i	−0.302660	+	0.524222i
$525$	13.5622	+	1.63397i	0.591902	+	0.0713125i
$526$	8.56218	−	14.8301i	0.373329	−	0.646624i
$527$	15.4641	+	8.92820i	0.673627	+	0.388919i
$528$			0.732051i			0.0318584i
$529$	7.69615	−	13.3301i	0.334615	−	0.579571i
$530$	7.73205	+	15.4641i	0.335859	+	0.671718i
$531$	6.19615	+	10.7321i	0.268890	+	0.465731i
$532$		−	3.46410i		−	0.150188i
$533$	14.6962	+	29.7224i	0.636561	+	1.28742i
$534$	4.92820			0.213264
$535$	2.53590	−	1.26795i	0.109636	−	0.0548182i
$536$	−3.83013	−	6.63397i	−0.165436	−	0.286544i
$537$	15.7583	+	9.09808i	0.680022	+	0.392611i
$538$			4.39230i			0.189366i
$539$	0.169873	−	0.294229i	0.00731695	−	0.0126733i
$540$	1.86603	+	1.23205i	0.0803009	+	0.0530190i
$541$	−1.19615			−0.0514266			−0.0257133	−	0.999669i	$-0.508186\pi$
$541$	−1.19615			−0.0514266			−0.0257133	+	0.999669i	$0.508186\pi$
$542$	5.07180	+	2.92820i	0.217852	+	0.125777i
$543$	−13.9641	+	8.06218i	−0.599257	+	0.345981i
$544$	2.23205	+	3.86603i	0.0956984	+	0.165754i
$545$	22.3205	+	1.33975i	0.956106	+	0.0573884i
$546$	−8.83013	+	4.36603i	−0.377895	+	0.186849i
$547$		−	25.8038i		−	1.10329i	−0.834078	−	0.551646i	$-0.814000\pi$
$547$		−	25.8038i		−	1.10329i	0.834078	−	0.551646i	$-0.186000\pi$
$548$	15.9904	−	9.23205i	0.683075	−	0.394374i
$549$	−5.06218	−	8.76795i	−0.216048	−	0.374207i
$550$	2.92820	+	2.19615i	0.124859	+	0.0936443i
$551$	−8.19615			−0.349168
$552$	5.36603	+	3.09808i	0.228393	+	0.131863i
$553$	−28.3923	−	16.3923i	−1.20736	−	0.697072i
$554$	−12.3205			−0.523448
$555$	9.76795	−	14.7942i	0.414626	−	0.627980i
$556$	0.535898	+	0.928203i	0.0227272	+	0.0393646i
$557$	12.6962	−	7.33013i	0.537953	−	0.310587i	−0.206296	−	0.978490i	$-0.566141\pi$
$557$	12.6962	−	7.33013i	0.537953	−	0.310587i	0.744249	+	0.667902i	$0.232808\pi$
$558$			4.00000i			0.169334i
$559$	9.80385	+	6.53590i	0.414659	+	0.276439i
$560$	−0.366025	+	6.09808i	−0.0154674	+	0.257691i
$561$	−1.63397	−	2.83013i	−0.0689865	−	0.119488i
$562$	−1.50000	+	0.866025i	−0.0632737	+	0.0365311i
$563$	−6.92820	−	4.00000i	−0.291989	−	0.168580i	0.346850	−	0.937921i	$-0.387251\pi$
$563$	−6.92820	−	4.00000i	−0.291989	−	0.168580i	−0.638838	+	0.769341i	$0.720585\pi$
$564$	−7.66025			−0.322555
$565$	16.7942	+	11.0885i	0.706539	+	0.466495i
$566$	−3.83013	+	6.63397i	−0.160992	+	0.278847i
$567$		−	2.73205i		−	0.114735i
$568$	−1.09808	−	0.633975i	−0.0460743	−	0.0266010i
$569$	9.07180	+	15.7128i	0.380310	+	0.658715i	0.991106	−	0.133072i	$-0.0424841\pi$
$569$	9.07180	+	15.7128i	0.380310	+	0.658715i	−0.610797	+	0.791787i	$0.709151\pi$
$570$	−1.26795	−	2.53590i	−0.0531085	−	0.106217i
$571$	−25.6603			−1.07385			−0.536924	−	0.843631i	$-0.680414\pi$
$571$	−25.6603			−1.07385			−0.536924	+	0.843631i	$0.680414\pi$
$572$	−2.63397	−	0.169873i	−0.110132	−	0.00710275i
$573$		−	9.46410i		−	0.395369i
$574$	−12.5622	−	21.7583i	−0.524335	−	0.908175i
$575$	28.4904	−	12.1699i	1.18813	−	0.507519i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$		−	23.9808i		−	0.998332i	−0.866506	−	0.499166i	$-0.833640\pi$
$577$		−	23.9808i		−	0.998332i	0.866506	−	0.499166i	$-0.166360\pi$
$578$	−2.53590	−	1.46410i	−0.105479	−	0.0608986i
$579$	−5.33013	+	9.23205i	−0.221513	+	0.383671i
$580$	14.4282	+	0.866025i	0.599099	+	0.0359597i
$581$	−7.19615	+	12.4641i	−0.298547	+	0.517098i
$582$	8.66025	−	5.00000i	0.358979	−	0.207257i
$583$	4.90192	−	2.83013i	0.203017	−	0.117212i
$584$	4.66025			0.192843
$585$	−4.86603	+	6.42820i	−0.201185	+	0.265773i
$586$	13.7321			0.567266
$587$	−8.78461	+	5.07180i	−0.362580	+	0.209335i	−0.670212	−	0.742170i	$-0.733797\pi$
$587$	−8.78461	+	5.07180i	−0.362580	+	0.209335i	0.307632	+	0.951505i	$0.400463\pi$
$588$	0.401924	−	0.232051i	0.0165751	−	0.00956961i
$589$	2.53590	−	4.39230i	0.104490	−	0.180982i
$590$	−1.66025	+	27.6603i	−0.0683516	+	1.13875i
$591$	−4.92820	+	8.53590i	−0.202719	+	0.351120i
$592$	6.86603	+	3.96410i	0.282192	+	0.162924i
$593$			19.3923i			0.796347i	0.917310	+	0.398173i	$0.130356\pi$
$593$			19.3923i			0.796347i	−0.917310	+	0.398173i	$0.869644\pi$
$594$	0.366025	−	0.633975i	0.0150182	−	0.0260123i
$595$	−12.1962	−	24.3923i	−0.499994	−	0.999987i
$596$	−9.96410	−	17.2583i	−0.408146	−	0.706929i
$597$			28.0526i			1.14811i
$598$	−12.3923	+	18.5885i	−0.506759	+	0.760139i
$599$	−8.78461			−0.358929			−0.179465	−	0.983764i	$-0.557437\pi$
$599$	−8.78461			−0.358929			−0.179465	+	0.983764i	$0.557437\pi$
$600$	1.96410	+	4.59808i	0.0801841	+	0.187716i
$601$	−8.50000	−	14.7224i	−0.346722	−	0.600541i	0.638943	−	0.769254i	$-0.279372\pi$
$601$	−8.50000	−	14.7224i	−0.346722	−	0.600541i	−0.985665	+	0.168714i	$0.946039\pi$
$602$	−7.73205	−	4.46410i	−0.315135	−	0.181943i
$603$			7.66025i			0.311950i
$604$	−2.56218	+	4.43782i	−0.104254	+	0.180572i
$605$	−12.8923	+	19.5263i	−0.524147	+	0.793856i
$606$	13.9282			0.565795
$607$	41.9090	+	24.1962i	1.70103	+	0.982092i	0.944718	+	0.327883i	$0.106335\pi$
$607$	41.9090	+	24.1962i	1.70103	+	0.982092i	0.756314	+	0.654209i	$0.226998\pi$
$608$	1.09808	−	0.633975i	0.0445329	−	0.0257111i
$609$	−8.83013	−	15.2942i	−0.357815	−	0.619753i
$610$	1.35641	−	22.5981i	0.0549193	−	0.914969i
$611$	1.77757	−	27.5622i	0.0719127	−	1.11505i
$612$		−	4.46410i		−	0.180451i
$613$	18.8660	−	10.8923i	0.761992	−	0.439936i	−0.0680188	−	0.997684i	$-0.521668\pi$
$613$	18.8660	−	10.8923i	0.761992	−	0.439936i	0.830010	+	0.557748i	$0.188334\pi$
$614$	−9.63397	−	16.6865i	−0.388796	−	0.673414i
$615$	−17.1603	−	11.3301i	−0.691968	−	0.456875i
$616$	2.00000			0.0805823
$617$	−28.3301	−	16.3564i	−1.14053	−	0.658484i	−0.193967	−	0.981008i	$-0.562135\pi$
$617$	−28.3301	−	16.3564i	−1.14053	−	0.658484i	−0.946561	+	0.322524i	$0.895469\pi$
$618$	−8.02628	−	4.63397i	−0.322864	−	0.186406i
$619$	36.1051			1.45119			0.725594	−	0.688123i	$-0.241565\pi$
$619$	36.1051			1.45119			0.725594	+	0.688123i	$0.241565\pi$
$620$	−4.92820	+	7.46410i	−0.197921	+	0.299766i
$621$	−3.09808	−	5.36603i	−0.124322	−	0.215331i
$622$	−2.70577	+	1.56218i	−0.108492	+	0.0626376i
$623$		−	13.4641i		−	0.539428i
$624$	−3.00000	−	2.00000i	−0.120096	−	0.0800641i
$625$	24.2846	+	5.93782i	0.971384	+	0.237513i
$626$	7.00000	+	12.1244i	0.279776	+	0.484587i
$627$	−0.803848	+	0.464102i	−0.0321026	+	0.0185344i
$628$	−8.13397	−	4.69615i	−0.324581	−	0.187397i
$629$	−35.3923			−1.41118
$630$	3.36603	−	5.09808i	0.134106	−	0.203112i
$631$	−4.92820	+	8.53590i	−0.196189	+	0.339809i	−0.947290	−	0.320379i	$-0.896190\pi$
$631$	−4.92820	+	8.53590i	−0.196189	+	0.339809i	0.751101	+	0.660187i	$0.229523\pi$
$632$		−	12.0000i		−	0.477334i
$633$	18.5885	+	10.7321i	0.738825	+	0.426561i
$634$	14.8660	+	25.7487i	0.590405	+	1.02261i
$635$	8.00000	−	4.00000i	0.317470	−	0.158735i
$636$	7.73205			0.306596
$637$	0.741670	+	1.50000i	0.0293860	+	0.0594322i
$638$		−	4.73205i		−	0.187344i
$639$	0.633975	+	1.09808i	0.0250796	+	0.0434392i
$640$	−2.00000	+	1.00000i	−0.0790569	+	0.0395285i
$641$	−4.52628	+	7.83975i	−0.178777	+	0.309651i	−0.941462	−	0.337119i	$-0.890547\pi$
$641$	−4.52628	+	7.83975i	−0.178777	+	0.309651i	0.762685	+	0.646770i	$0.223881\pi$
$642$		−	1.26795i		−	0.0500420i
$643$	7.60770	+	4.39230i	0.300018	+	0.173216i	0.642451	−	0.766327i	$-0.277918\pi$
$643$	7.60770	+	4.39230i	0.300018	+	0.173216i	−0.342433	+	0.939542i	$0.611251\pi$
$644$	8.46410	−	14.6603i	0.333532	−	0.577695i
$645$	−7.29423	−	0.437822i	−0.287210	−	0.0172392i
$646$	−2.83013	+	4.90192i	−0.111350	+	0.192864i
$647$	20.1962	−	11.6603i	0.793993	−	0.458412i	−0.0473736	−	0.998877i	$-0.515085\pi$
$647$	20.1962	−	11.6603i	0.793993	−	0.458412i	0.841366	+	0.540465i	$0.181752\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	9.07180			0.356099
$650$	−17.0000	+	6.00000i	−0.666795	+	0.235339i
$651$	10.9282			0.428310
$652$	11.6603	−	6.73205i	0.456651	−	0.263647i
$653$	28.2679	−	16.3205i	1.10621	−	0.638671i	0.168365	−	0.985725i	$-0.446151\pi$
$653$	28.2679	−	16.3205i	1.10621	−	0.638671i	0.937845	+	0.347054i	$0.112818\pi$
$654$	5.00000	−	8.66025i	0.195515	−	0.338643i
$655$	30.9282	+	1.85641i	1.20846	+	0.0725358i
$656$	4.59808	−	7.96410i	0.179525	−	0.310946i
$657$	−4.03590	−	2.33013i	−0.157455	−	0.0909069i
$658$			20.9282i			0.815866i
$659$	−20.7321	+	35.9090i	−0.807606	+	1.39881i	0.106912	+	0.994269i	$0.465904\pi$
$659$	−20.7321	+	35.9090i	−0.807606	+	1.39881i	−0.914518	+	0.404546i	$0.867430\pi$
$660$	1.46410	−	0.732051i	0.0569901	−	0.0284950i
$661$	19.2583	+	33.3564i	0.749062	+	1.29741i	0.948273	+	0.317457i	$0.102829\pi$
$661$	19.2583	+	33.3564i	0.749062	+	1.29741i	−0.199210	+	0.979957i	$0.563838\pi$
$662$			28.7846i			1.11875i
$663$	16.0622	+	1.03590i	0.623803	+	0.0402310i
$664$	−5.26795			−0.204436
$665$	−6.92820	+	3.46410i	−0.268664	+	0.134332i
$666$	−3.96410	−	6.86603i	−0.153606	−	0.266053i
$667$	−34.6865	−	20.0263i	−1.34307	−	0.775421i
$668$		−	13.8564i		−	0.536120i
$669$	−0.196152	+	0.339746i	−0.00758369	+	0.0131353i
$670$	−9.43782	+	14.2942i	−0.364615	+	0.552234i
$671$	−7.41154			−0.286119
$672$	2.36603	+	1.36603i	0.0912714	+	0.0526956i
$673$	8.89230	−	5.13397i	0.342773	−	0.197900i	−0.318725	−	0.947847i	$-0.603254\pi$
$673$	8.89230	−	5.13397i	0.342773	−	0.197900i	0.661498	+	0.749947i	$0.269921\pi$
$674$	5.52628	+	9.57180i	0.212864	+	0.368692i
$675$	0.598076	−	4.96410i	0.0230200	−	0.191068i
$676$	7.89230	−	10.3301i	0.303550	−	0.397313i
$677$			48.6410i			1.86943i	0.355403	+	0.934713i	$0.384344\pi$
$677$			48.6410i			1.86943i	−0.355403	+	0.934713i	$0.615656\pi$
$678$	7.79423	−	4.50000i	0.299336	−	0.172821i
$679$	−13.6603	−	23.6603i	−0.524232	−	0.907997i
$680$	5.50000	−	8.33013i	0.210915	−	0.319446i
$681$	−4.19615			−0.160797
$682$	2.53590	+	1.46410i	0.0971046	+	0.0560633i
$683$	23.3205	+	13.4641i	0.892334	+	0.515190i	0.874705	−	0.484655i	$-0.161055\pi$
$683$	23.3205	+	13.4641i	0.892334	+	0.515190i	0.0176291	+	0.999845i	$0.494388\pi$
$684$	−1.26795			−0.0484812
$685$	−34.4545	−	22.7487i	−1.31644	−	0.869184i
$686$	8.92820	+	15.4641i	0.340880	+	0.590422i
$687$	−24.9282	+	14.3923i	−0.951070	+	0.549101i
$688$		−	3.26795i		−	0.124589i
$689$	−1.79423	+	27.8205i	−0.0683547	+	1.05988i
$690$	0.830127	−	13.8301i	0.0316024	−	0.526504i
$691$	−20.2942	−	35.1506i	−0.772029	−	1.33719i	−0.936449	−	0.350803i	$-0.885909\pi$
$691$	−20.2942	−	35.1506i	−0.772029	−	1.33719i	0.164420	−	0.986390i	$-0.447425\pi$
$692$	16.2679	−	9.39230i	0.618415	−	0.357042i
$693$	−1.73205	−	1.00000i	−0.0657952	−	0.0379869i
$694$	5.66025			0.214860
$695$	1.32051	−	2.00000i	0.0500897	−	0.0758643i
$696$	3.23205	−	5.59808i	0.122511	−	0.212195i
$697$			41.0526i			1.55498i
$698$	16.5167	+	9.53590i	0.625165	+	0.360939i
$699$	6.19615	+	10.7321i	0.234360	+	0.405923i
$700$	12.5622	−	5.36603i	0.474806	−	0.202817i
$701$	−13.4641			−0.508532			−0.254266	−	0.967134i	$-0.581834\pi$
$701$	−13.4641			−0.508532			−0.254266	+	0.967134i	$0.581834\pi$
$702$	1.59808	+	3.23205i	0.0603155	+	0.121986i
$703$			10.0526i			0.379139i
$704$	0.366025	+	0.633975i	0.0137951	+	0.0238938i
$705$	7.66025	+	15.3205i	0.288502	+	0.577004i
$706$	12.6244	−	21.8660i	0.475124	−	0.822939i
$707$		−	38.0526i		−	1.43111i
$708$	10.7321	+	6.19615i	0.403335	+	0.232866i
$709$	18.5263	−	32.0885i	0.695769	−	1.20511i	−0.274152	−	0.961686i	$-0.588397\pi$
$709$	18.5263	−	32.0885i	0.695769	−	1.20511i	0.969921	−	0.243421i	$-0.0782696\pi$
$710$	−0.169873	+	2.83013i	−0.00637522	+	0.106213i
$711$	−6.00000	+	10.3923i	−0.225018	+	0.389742i
$712$	4.26795	−	2.46410i	0.159948	−	0.0923461i
$713$	21.4641	−	12.3923i	0.803837	−	0.464095i
$714$	−12.1962			−0.456430
$715$	2.29423	+	5.43782i	0.0857993	+	0.203363i
$716$	18.1962			0.680022
$717$	3.97372	−	2.29423i	0.148401	−	0.0856795i
$718$	7.68653	−	4.43782i	0.286859	−	0.165618i
$719$	−16.1962	+	28.0526i	−0.604015	+	1.04618i	0.388192	+	0.921579i	$0.373100\pi$
$719$	−16.1962	+	28.0526i	−0.604015	+	1.04618i	−0.992206	+	0.124605i	$0.960234\pi$
$720$	2.23205	+	0.133975i	0.0831836	+	0.00499294i
$721$	−12.6603	+	21.9282i	−0.471492	+	0.816649i
$722$	−15.0622	−	8.69615i	−0.560556	−	0.323637i
$723$		−	9.39230i		−	0.349304i
$724$	−8.06218	+	13.9641i	−0.299628	+	0.518972i
$725$	−12.6962	−	29.7224i	−0.471523	−	1.10386i
$726$	5.23205	+	9.06218i	0.194180	+	0.336329i
$727$			13.2679i			0.492081i	0.969260	+	0.246040i	$0.0791296\pi$
$727$			13.2679i			0.492081i	−0.969260	+	0.246040i	$0.920870\pi$
$728$	−5.46410	+	8.19615i	−0.202513	+	0.303770i
$729$	−1.00000			−0.0370370
$730$	−4.66025	−	9.32051i	−0.172484	−	0.344967i
$731$	7.29423	+	12.6340i	0.269787	+	0.467284i
$732$	−8.76795	−	5.06218i	−0.324073	−	0.187103i
$733$			45.3923i			1.67660i	0.545207	+	0.838302i	$0.316451\pi$
$733$			45.3923i			1.67660i	−0.545207	+	0.838302i	$0.683549\pi$
$734$	16.4904	−	28.5622i	0.608671	−	1.05425i
$735$	−0.866025	−	0.571797i	−0.0319438	−	0.0210910i
$736$	6.19615			0.228393
$737$	4.85641	+	2.80385i	0.178888	+	0.103281i
$738$	−7.96410	+	4.59808i	−0.293163	+	0.169258i
$739$	1.07180	+	1.85641i	0.0394267	+	0.0682890i	0.885065	−	0.465467i	$-0.154114\pi$
$739$	1.07180	+	1.85641i	0.0394267	+	0.0682890i	−0.845639	+	0.533756i	$0.820780\pi$
$740$	1.06218	−	17.6962i	0.0390464	−	0.650524i
$741$	0.294229	−	4.56218i	0.0108088	−	0.167596i
$742$		−	21.1244i		−	0.775499i
$743$	−18.5885	+	10.7321i	−0.681944	+	0.393721i	−0.800587	−	0.599216i	$-0.795479\pi$
$743$	−18.5885	+	10.7321i	−0.681944	+	0.393721i	0.118643	+	0.992937i	$0.462146\pi$
$744$	2.00000	+	3.46410i	0.0733236	+	0.127000i
$745$	−24.5526	+	37.1865i	−0.899536	+	1.36241i
$746$	23.5359			0.861710
$747$	4.56218	+	2.63397i	0.166921	+	0.0963721i
$748$	−2.83013	−	1.63397i	−0.103480	−	0.0597440i
$749$	−3.46410			−0.126576
$750$	7.23205	−	8.52628i	0.264077	−	0.311336i
$751$	−18.0263	−	31.2224i	−0.657788	−	1.13932i	−0.981187	−	0.193060i	$-0.938159\pi$
$751$	−18.0263	−	31.2224i	−0.657788	−	1.13932i	0.323399	−	0.946263i	$-0.395175\pi$
$752$	−6.63397	+	3.83013i	−0.241916	+	0.139670i
$753$		−	21.4641i		−	0.782195i
$754$	19.3923	+	12.9282i	0.706226	+	0.470817i
$755$	11.4378	+	0.686533i	0.416265	+	0.0249855i
$756$	−1.36603	−	2.36603i	−0.0496819	−	0.0860515i
$757$	34.7321	−	20.0526i	1.26236	−	0.728823i	0.288828	−	0.957381i	$-0.406735\pi$
$757$	34.7321	−	20.0526i	1.26236	−	0.728823i	0.973530	+	0.228558i	$0.0734012\pi$
$758$	−22.7321	−	13.1244i	−0.825665	−	0.476698i
$759$	−4.53590			−0.164643
$760$	−2.36603	−	1.56218i	−0.0858248	−	0.0566661i
$761$	−11.5359	+	19.9808i	−0.418176	+	0.724302i	−0.995756	−	0.0920320i	$-0.970664\pi$
$761$	−11.5359	+	19.9808i	−0.418176	+	0.724302i	0.577580	+	0.816334i	$0.303997\pi$
$762$		−	4.00000i		−	0.144905i
$763$	−23.6603	−	13.6603i	−0.856559	−	0.494534i
$764$	−4.73205	−	8.19615i	−0.171200	−	0.296526i
$765$	−8.92820	+	4.46410i	−0.322800	+	0.161400i
$766$	26.9282			0.972956
$767$	−24.7846	+	37.1769i	−0.894920	+	1.34238i
$768$			1.00000i			0.0360844i
$769$	22.7321	+	39.3731i	0.819739	+	1.41983i	0.905875	+	0.423546i	$0.139215\pi$
$769$	22.7321	+	39.3731i	0.819739	+	1.41983i	−0.0861360	+	0.996283i	$0.527452\pi$
$770$	−2.00000	−	4.00000i	−0.0720750	−	0.144150i
$771$	1.50000	−	2.59808i	0.0540212	−	0.0935674i
$772$			10.6603i			0.383671i
$773$	−35.1962	−	20.3205i	−1.26592	−	0.730878i	−0.291705	−	0.956508i	$-0.594222\pi$
$773$	−35.1962	−	20.3205i	−1.26592	−	0.730878i	−0.974213	+	0.225631i	$0.927556\pi$
$774$	−1.63397	+	2.83013i	−0.0587320	+	0.101727i
$775$	19.8564	+	2.39230i	0.713263	+	0.0859341i
$776$	5.00000	−	8.66025i	0.179490	−	0.310885i
$777$	−18.7583	+	10.8301i	−0.672951	+	0.388529i
$778$	−20.8468	+	12.0359i	−0.747394	+	0.431508i
$779$	11.6603			0.417772
$780$	−1.00000	+	8.00000i	−0.0358057	+	0.286446i
$781$	0.928203			0.0332137
$782$	−23.9545	+	13.8301i	−0.856611	+	0.494564i
$783$	−5.59808	+	3.23205i	−0.200059	+	0.115504i
$784$	0.232051	−	0.401924i	0.00828753	−	0.0143544i
$785$	−1.25833	+	20.9641i	−0.0449117	+	0.748241i
$786$	6.92820	−	12.0000i	0.247121	−	0.428026i
$787$	−16.7321	−	9.66025i	−0.596433	−	0.344351i	0.171204	−	0.985236i	$-0.445234\pi$
$787$	−16.7321	−	9.66025i	−0.596433	−	0.344351i	−0.767637	+	0.640885i	$0.778568\pi$
$788$			9.85641i			0.351120i
$789$	−8.56218	+	14.8301i	−0.304822	+	0.527967i
$790$	−24.0000	+	12.0000i	−0.853882	+	0.426941i
$791$	−12.2942	−	21.2942i	−0.437132	−	0.757136i
$792$		−	0.732051i		−	0.0260123i
$793$	20.2487	−	30.3731i	0.719053	−	1.07858i
$794$	19.3205			0.685659
$795$	−7.73205	−	15.4641i	−0.274228	−	0.548455i
$796$	14.0263	+	24.2942i	0.497148	+	0.861086i
$797$	−0.928203	−	0.535898i	−0.0328786	−	0.0189825i	0.483471	−	0.875361i	$-0.339376\pi$
$797$	−0.928203	−	0.535898i	−0.0328786	−	0.0189825i	−0.516349	+	0.856378i	$0.672709\pi$
$798$			3.46410i			0.122628i
$799$	17.0981	−	29.6147i	0.604886	−	1.04769i
$800$	4.00000	+	3.00000i	0.141421	+	0.106066i
$801$	−4.92820			−0.174129
$802$	−7.83975	−	4.52628i	−0.276831	−	0.159828i
$803$	−2.95448	+	1.70577i	−0.104261	+	0.0601954i
$804$	3.83013	+	6.63397i	0.135078	+	0.233962i
$805$	−37.7846	−	2.26795i	−1.33173	−	0.0799347i
$806$	−12.9282	+	6.39230i	−0.455377	+	0.225159i
$807$		−	4.39230i		−	0.154616i
$808$	12.0622	−	6.96410i	0.424346	−	0.244996i
$809$	0.990381	+	1.71539i	0.0348199	+	0.0603099i	0.882910	−	0.469542i	$-0.155581\pi$
$809$	0.990381	+	1.71539i	0.0348199	+	0.0603099i	−0.848090	+	0.529852i	$0.822248\pi$
$810$	−1.86603	−	1.23205i	−0.0655654	−	0.0432899i
$811$	−33.8564			−1.18886			−0.594430	−	0.804148i	$-0.702622\pi$
$811$	−33.8564			−1.18886			−0.594430	+	0.804148i	$0.702622\pi$
$812$	−15.2942	−	8.83013i	−0.536722	−	0.309877i
$813$	−5.07180	−	2.92820i	−0.177876	−	0.102697i
$814$	−5.80385			−0.203425
$815$	−25.1244	−	16.5885i	−0.880068	−	0.581068i
$816$	−2.23205	−	3.86603i	−0.0781374	−	0.135338i
$817$	3.58846	−	2.07180i	0.125544	−	0.0724830i
$818$			16.0718i			0.561937i
$819$	8.83013	−	4.36603i	0.308550	−	0.152561i
$820$	−20.5263	−	1.23205i	−0.716809	−	0.0430251i
$821$	−5.12436	−	8.87564i	−0.178841	−	0.309762i	0.762643	−	0.646820i	$-0.223902\pi$
$821$	−5.12436	−	8.87564i	−0.178841	−	0.309762i	−0.941484	+	0.337058i	$0.890568\pi$
$822$	−15.9904	+	9.23205i	−0.557729	+	0.322005i
$823$	34.9808	+	20.1962i	1.21935	+	0.703994i	0.964780	−	0.263060i	$-0.0847317\pi$
$823$	34.9808	+	20.1962i	1.21935	+	0.703994i	0.254573	+	0.967054i	$0.418065\pi$
$824$	−9.26795			−0.322864
$825$	−2.92820	−	2.19615i	−0.101947	−	0.0764602i
$826$	16.9282	−	29.3205i	0.589008	−	1.02019i
$827$		−	48.7846i		−	1.69641i	−0.529670	−	0.848204i	$-0.677684\pi$
$827$		−	48.7846i		−	1.69641i	0.529670	−	0.848204i	$-0.322316\pi$
$828$	−5.36603	−	3.09808i	−0.186482	−	0.107666i
$829$	8.93782	+	15.4808i	0.310423	+	0.537669i	0.978454	−	0.206465i	$-0.0661958\pi$
$829$	8.93782	+	15.4808i	0.310423	+	0.537669i	−0.668031	+	0.744134i	$0.732863\pi$
$830$	5.26795	+	10.5359i	0.182853	+	0.365706i
$831$	12.3205			0.427394
$832$	−3.59808	−	0.232051i	−0.124741	−	0.00804491i
$833$			2.07180i			0.0717835i
$834$	−0.535898	−	0.928203i	−0.0185566	−	0.0321410i
$835$	−27.7128	+	13.8564i	−0.959041	+	0.479521i
$836$	−0.464102	+	0.803848i	−0.0160513	+	0.0278016i
$837$		−	4.00000i		−	0.138260i
$838$	5.66025	+	3.26795i	0.195530	+	0.112889i
$839$	24.0526	−	41.6603i	0.830387	−	1.43827i	−0.0673455	−	0.997730i	$-0.521453\pi$
$839$	24.0526	−	41.6603i	0.830387	−	1.43827i	0.897732	−	0.440542i	$-0.145214\pi$
$840$	0.366025	−	6.09808i	0.0126291	−	0.210404i
$841$	−6.39230	+	11.0718i	−0.220424	+	0.381786i
$842$	−14.7679	+	8.52628i	−0.508937	+	0.293835i
$843$	1.50000	−	0.866025i	0.0516627	−	0.0298275i
$844$	21.4641			0.738825
$845$	−28.5526	−	5.45448i	−0.982238	−	0.187640i
$846$	7.66025			0.263365
$847$	24.7583	−	14.2942i	0.850706	−	0.491156i
$848$	6.69615	−	3.86603i	0.229947	−	0.132760i
$849$	3.83013	−	6.63397i	0.131450	−	0.227677i
$850$	−22.1603	−	2.66987i	−0.760090	−	0.0915759i
$851$	−24.5622	+	42.5429i	−0.841981	+	1.45835i
$852$	1.09808	+	0.633975i	0.0376195	+	0.0217196i
$853$		−	12.0718i		−	0.413330i	−0.978412	−	0.206665i	$-0.933739\pi$
$853$		−	12.0718i		−	0.413330i	0.978412	−	0.206665i	$-0.0662611\pi$
$854$	−13.8301	+	23.9545i	−0.473257	+	0.819706i
$855$	1.26795	+	2.53590i	0.0433629	+	0.0867259i
$856$	−0.633975	−	1.09808i	−0.0216688	−	0.0375315i
$857$		−	3.92820i		−	0.134185i	−0.997747	−	0.0670924i	$-0.978628\pi$
$857$		−	3.92820i		−	0.134185i	0.997747	−	0.0670924i	$-0.0213722\pi$
$858$	2.63397	+	0.169873i	0.0899224	+	0.00579937i
$859$	44.3013			1.51154			0.755770	−	0.654837i	$-0.227263\pi$
$859$	44.3013			1.51154			0.755770	+	0.654837i	$0.227263\pi$
$860$	−6.53590	+	3.26795i	−0.222872	+	0.111436i
$861$	12.5622	+	21.7583i	0.428118	+	0.741522i
$862$	−6.75833	−	3.90192i	−0.230190	−	0.132900i
$863$			21.1244i			0.719081i	0.933129	+	0.359541i	$0.117067\pi$
$863$			21.1244i			0.719081i	−0.933129	+	0.359541i	$0.882933\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−35.0526	−	23.1436i	−1.19182	−	0.786906i
$866$	−14.8038			−0.503055
$867$	2.53590	+	1.46410i	0.0861236	+	0.0497235i
$868$	9.46410	−	5.46410i	0.321233	−	0.185464i
$869$	4.39230	+	7.60770i	0.148999	+	0.258073i
$870$	−14.4282	−	0.866025i	−0.489162	−	0.0293610i
$871$	−24.7583	+	12.2417i	−0.838904	+	0.414793i
$872$		−	10.0000i		−	0.338643i
$873$	−8.66025	+	5.00000i	−0.293105	+	0.169224i
$874$	3.92820	+	6.80385i	0.132873	+	0.230144i
$875$	−23.2942	−	19.7583i	−0.787489	−	0.667953i
$876$	−4.66025			−0.157455
$877$	−8.25833	−	4.76795i	−0.278864	−	0.161002i	0.354045	−	0.935228i	$-0.384806\pi$
$877$	−8.25833	−	4.76795i	−0.278864	−	0.161002i	−0.632909	+	0.774226i	$0.718139\pi$
$878$	−8.49038	−	4.90192i	−0.286536	−	0.165432i
$879$	−13.7321			−0.463171
$880$	0.901924	−	1.36603i	0.0304038	−	0.0460487i
$881$	−8.93782	−	15.4808i	−0.301123	−	0.521560i	0.675268	−	0.737573i	$-0.264028\pi$
$881$	−8.93782	−	15.4808i	−0.301123	−	0.521560i	−0.976391	+	0.216013i	$0.930695\pi$
$882$	−0.401924	+	0.232051i	−0.0135335	+	0.00781356i
$883$		−	18.2487i		−	0.614118i	−0.951690	−	0.307059i	$-0.900655\pi$
$883$		−	18.2487i		−	0.614118i	0.951690	−	0.307059i	$-0.0993449\pi$
$884$	14.4282	−	7.13397i	0.485273	−	0.239942i
$885$	1.66025	−	27.6603i	0.0558088	−	0.929789i
$886$	−17.3205	−	30.0000i	−0.581894	−	1.00787i
$887$	−25.1769	+	14.5359i	−0.845358	+	0.488068i	−0.859082	−	0.511838i	$-0.828965\pi$
$887$	−25.1769	+	14.5359i	−0.845358	+	0.488068i	0.0137239	+	0.999906i	$0.495631\pi$
$888$	−6.86603	−	3.96410i	−0.230409	−	0.133027i
$889$	−10.9282			−0.366520
$890$	−9.19615	−	6.07180i	−0.308256	−	0.203527i
$891$	−0.366025	+	0.633975i	−0.0122623	+	0.0212389i
$892$			0.392305i			0.0131353i
$893$	−8.41154	−	4.85641i	−0.281482	−	0.162513i
$894$	9.96410	+	17.2583i	0.333249	+	0.577205i
$895$	−18.1962	−	36.3923i	−0.608230	−	1.21646i
$896$	2.73205			0.0912714
$897$	12.3923	−	18.5885i	0.413767	−	0.620651i
$898$		−	7.85641i		−	0.262172i
$899$	−12.9282	−	22.3923i	−0.431180	−	0.746825i
$900$	−1.96410	−	4.59808i	−0.0654701	−	0.153269i
$901$	−17.2583	+	29.8923i	−0.574958	+	0.995857i
$902$			6.73205i			0.224153i
$903$	7.73205	+	4.46410i	0.257307	+	0.148556i
$904$	4.50000	−	7.79423i	0.149668	−	0.259232i
$905$	35.9904	+	2.16025i	1.19636	+	0.0718093i
$906$	2.56218	−	4.43782i	0.0851227	−	0.147437i
$907$	−6.00000	+	3.46410i	−0.199227	+	0.115024i	−0.596295	−	0.802766i	$-0.703361\pi$
$907$	−6.00000	+	3.46410i	−0.199227	+	0.115024i	0.397068	+	0.917789i	$0.370028\pi$
$908$	−3.63397	+	2.09808i	−0.120598	+	0.0696271i
$909$	−13.9282			−0.461969
$910$	21.8564	+	2.73205i	0.724533	+	0.0905666i
$911$	44.1051			1.46127			0.730634	−	0.682769i	$-0.239225\pi$
$911$	44.1051			1.46127			0.730634	+	0.682769i	$0.239225\pi$
$912$	−1.09808	+	0.633975i	−0.0363609	+	0.0209930i
$913$	3.33975	−	1.92820i	0.110529	−	0.0638142i
$914$	−4.40192	+	7.62436i	−0.145603	+	0.252191i
$915$	−1.35641	+	22.5981i	−0.0448414	+	0.747069i
$916$	−14.3923	+	24.9282i	−0.475535	+	0.823651i
$917$	−32.7846	−	18.9282i	−1.08264	−	0.625064i
$918$			4.46410i			0.147337i
$919$	−28.7321	+	49.7654i	−0.947783	+	1.64161i	−0.197702	+	0.980262i	$0.563348\pi$
$919$	−28.7321	+	49.7654i	−0.947783	+	1.64161i	−0.750081	+	0.661346i	$0.769986\pi$
$920$	−6.19615	−	12.3923i	−0.204281	−	0.408562i
$921$	9.63397	+	16.6865i	0.317450	+	0.549840i
$922$		−	26.0718i		−	0.858629i
$923$	−2.53590	+	3.80385i	−0.0834701	+	0.125205i
$924$	−2.00000			−0.0657952
$925$	−36.4545	+	15.5718i	−1.19862	+	0.511998i
$926$	3.16987	+	5.49038i	0.104168	+	0.180425i
$927$	8.02628	+	4.63397i	0.263618	+	0.152200i
$928$		−	6.46410i		−	0.212195i
$929$	19.7942	−	34.2846i	0.649428	−	1.12484i	−0.333832	−	0.942633i	$-0.608342\pi$
$929$	19.7942	−	34.2846i	0.649428	−	1.12484i	0.983260	−	0.182209i	$-0.0583248\pi$
$930$	4.92820	−	7.46410i	0.161602	−	0.244758i
$931$	0.588457			0.0192859
$932$	10.7321	+	6.19615i	0.351540	+	0.202962i
$933$	2.70577	−	1.56218i	0.0885830	−	0.0511434i
$934$	−11.0263	−	19.0981i	−0.360791	−	0.624908i
$935$	−0.437822	+	7.29423i	−0.0143183	+	0.238547i
$936$	3.00000	+	2.00000i	0.0980581	+	0.0653720i
$937$			17.0526i			0.557083i	0.960424	+	0.278541i	$0.0898509\pi$
$937$			17.0526i			0.557083i	−0.960424	+	0.278541i	$0.910149\pi$
$938$	18.1244	−	10.4641i	0.591781	−	0.341665i
$939$	−7.00000	−	12.1244i	−0.228436	−	0.395663i
$940$	14.2942	+	9.43782i	0.466226	+	0.307828i
$941$	12.3923			0.403978			0.201989	−	0.979388i	$-0.435260\pi$
$941$	12.3923			0.403978			0.201989	+	0.979388i	$0.435260\pi$
$942$	8.13397	+	4.69615i	0.265019	+	0.153009i
$943$	49.3468	+	28.4904i	1.60695	+	0.927774i
$944$	12.3923			0.403335
$945$	−3.36603	+	5.09808i	−0.109497	+	0.165840i
$946$	1.19615	+	2.07180i	0.0388903	+	0.0673599i
$947$	−24.0000	+	13.8564i	−0.779895	+	0.450273i	−0.836393	−	0.548130i	$-0.815340\pi$
$947$	−24.0000	+	13.8564i	−0.779895	+	0.450273i	0.0564979	+	0.998403i	$0.482007\pi$
$948$			12.0000i			0.389742i
$949$	1.08142	−	16.7679i	0.0351042	−	0.544311i
$950$	−0.758330	+	6.29423i	−0.0246035	+	0.204212i
$951$	−14.8660	−	25.7487i	−0.482064	−	0.834959i
$952$	−10.5622	+	6.09808i	−0.342322	+	0.197640i
$953$	32.6603	+	18.8564i	1.05797	+	0.610819i	0.924870	−	0.380284i	$-0.124174\pi$
$953$	32.6603	+	18.8564i	1.05797	+	0.610819i	0.133100	+	0.991103i	$0.457507\pi$
$954$	−7.73205			−0.250334
$955$	−11.6603	+	17.6603i	−0.377317	+	0.571472i
$956$	2.29423	−	3.97372i	0.0742007	−	0.128519i
$957$			4.73205i			0.152965i
$958$	13.8564	+	8.00000i	0.447680	+	0.258468i
$959$	25.2224	+	43.6865i	0.814475	+	1.41071i
$960$	2.00000	−	1.00000i	0.0645497	−	0.0322749i
$961$	−15.0000			−0.483871
$962$	15.8564	−	23.7846i	0.511231	−	0.766847i
$963$			1.26795i			0.0408591i
$964$	−4.69615	−	8.13397i	−0.151253	−	0.261978i
$965$	21.3205	−	10.6603i	0.686331	−	0.343166i
$966$	−8.46410	+	14.6603i	−0.272328	+	0.471686i
$967$			16.5885i			0.533449i	0.963773	+	0.266724i	$0.0859413\pi$
$967$			16.5885i			0.533449i	−0.963773	+	0.266724i	$0.914059\pi$
$968$	9.06218	+	5.23205i	0.291269	+	0.168164i
$969$	2.83013	−	4.90192i	0.0909168	−	0.157472i
$970$	−22.3205	−	1.33975i	−0.716668	−	0.0430167i
$971$	27.4641	−	47.5692i	0.881365	−	1.52657i	0.0315409	−	0.999502i	$-0.489959\pi$
$971$	27.4641	−	47.5692i	0.881365	−	1.52657i	0.849824	−	0.527066i	$-0.176708\pi$
$972$	−0.866025	+	0.500000i	−0.0277778	+	0.0160375i
$973$	−2.53590	+	1.46410i	−0.0812972	+	0.0469369i
$974$	−38.4449			−1.23185
$975$	17.0000	−	6.00000i	0.544436	−	0.192154i
$976$	−10.1244			−0.324073
$977$	−18.4019	+	10.6244i	−0.588730	+	0.339903i	−0.764595	−	0.644511i	$-0.777061\pi$
$977$	−18.4019	+	10.6244i	−0.588730	+	0.339903i	0.175865	+	0.984414i	$0.443728\pi$
$978$	−11.6603	+	6.73205i	−0.372854	+	0.215267i
$979$	−1.80385	+	3.12436i	−0.0576512	+	0.0998548i
$980$	−1.03590	−	0.0621778i	−0.0330906	−	0.00198620i
$981$	−5.00000	+	8.66025i	−0.159638	+	0.276501i
$982$	18.8827	+	10.9019i	0.602571	+	0.347894i
$983$		−	31.7128i		−	1.01148i	−0.862685	−	0.505741i	$-0.831219\pi$
$983$		−	31.7128i		−	1.01148i	0.862685	−	0.505741i	$-0.168781\pi$
$984$	−4.59808	+	7.96410i	−0.146581	+	0.253886i
$985$	19.7128	−	9.85641i	0.628102	−	0.314051i
$986$	14.4282	+	24.9904i	0.459488	+	0.795856i
$987$		−	20.9282i		−	0.666152i
$988$	−2.02628	−	4.09808i	−0.0644645	−	0.130377i
$989$	20.2487			0.643872
$990$	−1.46410	+	0.732051i	−0.0465322	+	0.0232661i
$991$	−4.02628	−	6.97372i	−0.127899	−	0.221528i	0.794963	−	0.606657i	$-0.207490\pi$
$991$	−4.02628	−	6.97372i	−0.127899	−	0.221528i	−0.922862	+	0.385130i	$0.874157\pi$
$992$	3.46410	+	2.00000i	0.109985	+	0.0635001i
$993$		−	28.7846i		−	0.913452i
$994$	1.73205	−	3.00000i	0.0549373	−	0.0951542i
$995$	34.5622	−	52.3468i	1.09569	−	1.65950i
$996$	5.26795			0.166921
$997$	−13.7942	−	7.96410i	−0.436868	−	0.252226i	0.265400	−	0.964138i	$-0.414496\pi$
$997$	−13.7942	−	7.96410i	−0.436868	−	0.252226i	−0.702268	+	0.711913i	$0.747829\pi$
$998$	34.9808	−	20.1962i	1.10730	−	0.639298i
$999$	3.96410	+	6.86603i	0.125419	+	0.217231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.y.c.289.1	yes	4
3.2	odd	2		1170.2.bp.e.289.2		4
5.2	odd	4		1950.2.i.y.601.1		4
5.3	odd	4		1950.2.i.bh.601.2		4
5.4	even	2		390.2.y.b.289.2	yes	4
13.9	even	3		390.2.y.b.139.2	✓	4
15.14	odd	2		1170.2.bp.d.289.1		4
39.35	odd	6		1170.2.bp.d.919.1		4
65.9	even	6	inner	390.2.y.c.139.1	yes	4
65.22	odd	12		1950.2.i.y.451.1		4
65.48	odd	12		1950.2.i.bh.451.2		4
195.74	odd	6		1170.2.bp.e.919.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.y.b.139.2	✓	4	13.9	even	3
390.2.y.b.289.2	yes	4	5.4	even	2
390.2.y.c.139.1	yes	4	65.9	even	6	inner
390.2.y.c.289.1	yes	4	1.1	even	1	trivial
1170.2.bp.d.289.1		4	15.14	odd	2
1170.2.bp.d.919.1		4	39.35	odd	6
1170.2.bp.e.289.2		4	3.2	odd	2
1170.2.bp.e.919.2		4	195.74	odd	6
1950.2.i.y.451.1		4	65.22	odd	12
1950.2.i.y.601.1		4	5.2	odd	4
1950.2.i.bh.451.2		4	65.48	odd	12
1950.2.i.bh.601.2		4	5.3	odd	4

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.y (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.23205 - 0.133975i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.36603 + 1.36603i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.23205 - 0.133975i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.36603 + 1.36603i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.00000 - 1.00000i) q^{10} +(-0.366025 - 0.633975i) q^{11} -1.00000i q^{12} +(3.59808 + 0.232051i) q^{13} -2.73205 q^{14} +(-2.00000 + 1.00000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.86603 + 2.23205i) q^{17} +1.00000i q^{18} +(0.633975 - 1.09808i) q^{19} +(-1.23205 + 1.86603i) q^{20} +2.73205 q^{21} +(0.633975 + 0.366025i) q^{22} +(5.36603 - 3.09808i) q^{23} +(0.500000 + 0.866025i) q^{24} +(4.96410 + 0.598076i) q^{25} +(-3.23205 + 1.59808i) q^{26} -1.00000i q^{27} +(2.36603 - 1.36603i) q^{28} +(-3.23205 - 5.59808i) q^{29} +(1.23205 - 1.86603i) q^{30} +4.00000 q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.633975 - 0.366025i) q^{33} -4.46410 q^{34} +(-5.09808 - 3.36603i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-6.86603 + 3.96410i) q^{37} +1.26795i q^{38} +(3.23205 - 1.59808i) q^{39} +(0.133975 - 2.23205i) q^{40} +(4.59808 + 7.96410i) q^{41} +(-2.36603 + 1.36603i) q^{42} +(2.83013 + 1.63397i) q^{43} -0.732051 q^{44} +(-1.23205 + 1.86603i) q^{45} +(-3.09808 + 5.36603i) q^{46} -7.66025i q^{47} +(-0.866025 - 0.500000i) q^{48} +(0.232051 + 0.401924i) q^{49} +(-4.59808 + 1.96410i) q^{50} +4.46410 q^{51} +(2.00000 - 3.00000i) q^{52} +7.73205i q^{53} +(0.500000 + 0.866025i) q^{54} +(0.732051 + 1.46410i) q^{55} +(-1.36603 + 2.36603i) q^{56} -1.26795i q^{57} +(5.59808 + 3.23205i) q^{58} +(-6.19615 + 10.7321i) q^{59} +(-0.133975 + 2.23205i) q^{60} +(5.06218 - 8.76795i) q^{61} +(-3.46410 + 2.00000i) q^{62} +(2.36603 - 1.36603i) q^{63} -1.00000 q^{64} +(-8.00000 - 1.00000i) q^{65} +0.732051 q^{66} +(-6.63397 + 3.83013i) q^{67} +(3.86603 - 2.23205i) q^{68} +(3.09808 - 5.36603i) q^{69} +(6.09808 + 0.366025i) q^{70} +(-0.633975 + 1.09808i) q^{71} +(0.866025 + 0.500000i) q^{72} -4.66025i q^{73} +(3.96410 - 6.86603i) q^{74} +(4.59808 - 1.96410i) q^{75} +(-0.633975 - 1.09808i) q^{76} -2.00000i q^{77} +(-2.00000 + 3.00000i) q^{78} -12.0000 q^{79} +(1.00000 + 2.00000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-7.96410 - 4.59808i) q^{82} +5.26795i q^{83} +(1.36603 - 2.36603i) q^{84} +(-8.33013 - 5.50000i) q^{85} -3.26795 q^{86} +(-5.59808 - 3.23205i) q^{87} +(0.633975 - 0.366025i) q^{88} +(-2.46410 - 4.26795i) q^{89} +(0.133975 - 2.23205i) q^{90} +(8.19615 + 5.46410i) q^{91} -6.19615i q^{92} +(3.46410 - 2.00000i) q^{93} +(3.83013 + 6.63397i) q^{94} +(-1.56218 + 2.36603i) q^{95} +1.00000 q^{96} +(-8.66025 - 5.00000i) q^{97} +(-0.401924 - 0.232051i) q^{98} -0.732051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 2 q^{5} - 2 q^{6} + 6 q^{7} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 2 * q^5 - 2 * q^6 + 6 * q^7 + 2 * q^9	\( 4 q + 2 q^{4} - 2 q^{5} - 2 q^{6} + 6 q^{7} + 2 q^{9} + 8 q^{10} + 2 q^{11} + 4 q^{13} - 4 q^{14} - 8 q^{15} - 2 q^{16} + 12 q^{17} + 6 q^{19} + 2 q^{20} + 4 q^{21} + 6 q^{22} + 18 q^{23} + 2 q^{24} + 6 q^{25} - 6 q^{26} + 6 q^{28} - 6 q^{29} - 2 q^{30} + 16 q^{31} - 6 q^{33} - 4 q^{34} - 10 q^{35} - 2 q^{36} - 24 q^{37} + 6 q^{39} + 4 q^{40} + 8 q^{41} - 6 q^{42} - 6 q^{43} + 4 q^{44} + 2 q^{45} - 2 q^{46} - 6 q^{49} - 8 q^{50} + 4 q^{51} + 8 q^{52} + 2 q^{54} - 4 q^{55} - 2 q^{56} + 12 q^{58} - 4 q^{59} - 4 q^{60} - 4 q^{61} + 6 q^{63} - 4 q^{64} - 32 q^{65} - 4 q^{66} - 30 q^{67} + 12 q^{68} + 2 q^{69} + 14 q^{70} - 6 q^{71} + 2 q^{74} + 8 q^{75} - 6 q^{76} - 8 q^{78} - 48 q^{79} + 4 q^{80} - 2 q^{81} - 18 q^{82} + 2 q^{84} - 16 q^{85} - 20 q^{86} - 12 q^{87} + 6 q^{88} + 4 q^{89} + 4 q^{90} + 12 q^{91} - 2 q^{94} + 18 q^{95} + 4 q^{96} - 12 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 2 * q^5 - 2 * q^6 + 6 * q^7 + 2 * q^9 + 8 * q^10 + 2 * q^11 + 4 * q^13 - 4 * q^14 - 8 * q^15 - 2 * q^16 + 12 * q^17 + 6 * q^19 + 2 * q^20 + 4 * q^21 + 6 * q^22 + 18 * q^23 + 2 * q^24 + 6 * q^25 - 6 * q^26 + 6 * q^28 - 6 * q^29 - 2 * q^30 + 16 * q^31 - 6 * q^33 - 4 * q^34 - 10 * q^35 - 2 * q^36 - 24 * q^37 + 6 * q^39 + 4 * q^40 + 8 * q^41 - 6 * q^42 - 6 * q^43 + 4 * q^44 + 2 * q^45 - 2 * q^46 - 6 * q^49 - 8 * q^50 + 4 * q^51 + 8 * q^52 + 2 * q^54 - 4 * q^55 - 2 * q^56 + 12 * q^58 - 4 * q^59 - 4 * q^60 - 4 * q^61 + 6 * q^63 - 4 * q^64 - 32 * q^65 - 4 * q^66 - 30 * q^67 + 12 * q^68 + 2 * q^69 + 14 * q^70 - 6 * q^71 + 2 * q^74 + 8 * q^75 - 6 * q^76 - 8 * q^78 - 48 * q^79 + 4 * q^80 - 2 * q^81 - 18 * q^82 + 2 * q^84 - 16 * q^85 - 20 * q^86 - 12 * q^87 + 6 * q^88 + 4 * q^89 + 4 * q^90 + 12 * q^91 - 2 * q^94 + 18 * q^95 + 4 * q^96 - 12 * q^98 + 4 * q^99

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