LMFDB - Embedded newform 462.2.i.e.331.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(67,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("462.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.1
Root			$1.32288 + 2.29129i$ of defining polynomial
Character	$\chi$	$=$	462.331
Dual form			462.2.i.e.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.32288 + 2.29129i) q^{5} +1.00000 q^{6} +(-1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.32288 + 2.29129i) q^{5} +1.00000 q^{6} +(-1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.32288 + 2.29129i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} -4.00000 q^{13} +(1.32288 + 2.29129i) q^{14} -2.64575 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-2.64575 + 4.58258i) q^{19} +2.64575 q^{20} -2.64575 q^{21} -1.00000 q^{22} +(1.32288 - 2.29129i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(-2.00000 + 3.46410i) q^{26} -1.00000 q^{27} +2.64575 q^{28} +2.00000 q^{29} +(-1.32288 + 2.29129i) q^{30} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.500000 - 0.866025i) q^{33} +3.00000 q^{34} +(-3.50000 - 6.06218i) q^{35} +1.00000 q^{36} +(-0.645751 + 1.11847i) q^{37} +(2.64575 + 4.58258i) q^{38} +(-2.00000 - 3.46410i) q^{39} +(1.32288 - 2.29129i) q^{40} +9.00000 q^{41} +(-1.32288 + 2.29129i) q^{42} +9.29150 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-1.32288 - 2.29129i) q^{45} +(-1.32288 - 2.29129i) q^{46} +(1.96863 - 3.40976i) q^{47} -1.00000 q^{48} +(-3.50000 - 6.06218i) q^{49} -2.00000 q^{50} +(-1.50000 + 2.59808i) q^{51} +(2.00000 + 3.46410i) q^{52} +(-2.00000 - 3.46410i) q^{53} +(-0.500000 + 0.866025i) q^{54} +2.64575 q^{55} +(1.32288 - 2.29129i) q^{56} -5.29150 q^{57} +(1.00000 - 1.73205i) q^{58} +(-3.29150 - 5.70105i) q^{59} +(1.32288 + 2.29129i) q^{60} +(-5.96863 + 10.3380i) q^{61} +4.00000 q^{62} +(-1.32288 - 2.29129i) q^{63} +1.00000 q^{64} +(5.29150 - 9.16515i) q^{65} +(-0.500000 - 0.866025i) q^{66} +(-3.79150 - 6.56708i) q^{67} +(1.50000 - 2.59808i) q^{68} +2.64575 q^{69} -7.00000 q^{70} -2.70850 q^{71} +(0.500000 - 0.866025i) q^{72} +(7.64575 + 13.2428i) q^{73} +(0.645751 + 1.11847i) q^{74} +(1.00000 - 1.73205i) q^{75} +5.29150 q^{76} +2.64575 q^{77} -4.00000 q^{78} +(-5.32288 + 9.21949i) q^{79} +(-1.32288 - 2.29129i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.50000 - 7.79423i) q^{82} +15.5830 q^{83} +(1.32288 + 2.29129i) q^{84} -7.93725 q^{85} +(4.64575 - 8.04668i) q^{86} +(1.00000 + 1.73205i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-1.35425 + 2.34563i) q^{89} -2.64575 q^{90} +(5.29150 - 9.16515i) q^{91} -2.64575 q^{92} +(-2.00000 + 3.46410i) q^{93} +(-1.96863 - 3.40976i) q^{94} +(-7.00000 - 12.1244i) q^{95} +(-0.500000 + 0.866025i) q^{96} -11.5830 q^{97} -7.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{6} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^6 - 4 * q^8 - 2 * q^9	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{6} - 4 q^{8} - 2 q^{9} - 2 q^{11} + 2 q^{12} - 16 q^{13} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{22} - 2 q^{24} - 4 q^{25} - 8 q^{26} - 4 q^{27} + 8 q^{29} + 8 q^{31} + 2 q^{32} + 2 q^{33} + 12 q^{34} - 14 q^{35} + 4 q^{36} + 8 q^{37} - 8 q^{39} + 36 q^{41} + 16 q^{43} - 2 q^{44} - 8 q^{47} - 4 q^{48} - 14 q^{49} - 8 q^{50} - 6 q^{51} + 8 q^{52} - 8 q^{53} - 2 q^{54} + 4 q^{58} + 8 q^{59} - 8 q^{61} + 16 q^{62} + 4 q^{64} - 2 q^{66} + 6 q^{67} + 6 q^{68} - 28 q^{70} - 32 q^{71} + 2 q^{72} + 20 q^{73} - 8 q^{74} + 4 q^{75} - 16 q^{78} - 16 q^{79} - 2 q^{81} + 18 q^{82} + 20 q^{83} + 8 q^{86} + 4 q^{87} + 2 q^{88} - 16 q^{89} - 8 q^{93} + 8 q^{94} - 28 q^{95} - 2 q^{96} - 4 q^{97} - 28 q^{98} + 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^6 - 4 * q^8 - 2 * q^9 - 2 * q^11 + 2 * q^12 - 16 * q^13 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 4 * q^22 - 2 * q^24 - 4 * q^25 - 8 * q^26 - 4 * q^27 + 8 * q^29 + 8 * q^31 + 2 * q^32 + 2 * q^33 + 12 * q^34 - 14 * q^35 + 4 * q^36 + 8 * q^37 - 8 * q^39 + 36 * q^41 + 16 * q^43 - 2 * q^44 - 8 * q^47 - 4 * q^48 - 14 * q^49 - 8 * q^50 - 6 * q^51 + 8 * q^52 - 8 * q^53 - 2 * q^54 + 4 * q^58 + 8 * q^59 - 8 * q^61 + 16 * q^62 + 4 * q^64 - 2 * q^66 + 6 * q^67 + 6 * q^68 - 28 * q^70 - 32 * q^71 + 2 * q^72 + 20 * q^73 - 8 * q^74 + 4 * q^75 - 16 * q^78 - 16 * q^79 - 2 * q^81 + 18 * q^82 + 20 * q^83 + 8 * q^86 + 4 * q^87 + 2 * q^88 - 16 * q^89 - 8 * q^93 + 8 * q^94 - 28 * q^95 - 2 * q^96 - 4 * q^97 - 28 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	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
$5$	−1.32288	+	2.29129i	−0.591608	+	1.02470i	0.402408	+	0.915460i	$0.368173\pi$
$5$	−1.32288	+	2.29129i	−0.591608	+	1.02470i	−0.994016	+	0.109235i	$0.965160\pi$
$6$	1.00000			0.408248
$7$	−1.32288	+	2.29129i	−0.500000	+	0.866025i
$7$	−1.32288	+	2.29129i	−0.500000	+	0.866025i
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.32288	+	2.29129i	0.418330	+	0.724569i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$	1.32288	+	2.29129i	0.353553	+	0.612372i
$15$	−2.64575			−0.683130
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−2.64575	+	4.58258i	−0.606977	+	1.05131i	0.384759	+	0.923017i	$0.374285\pi$
$19$	−2.64575	+	4.58258i	−0.606977	+	1.05131i	−0.991736	+	0.128298i	$0.959049\pi$
$20$	2.64575			0.591608
$21$	−2.64575			−0.577350
$22$	−1.00000			−0.213201
$23$	1.32288	−	2.29129i	0.275839	−	0.477767i	−0.694508	−	0.719485i	$-0.744378\pi$
$23$	1.32288	−	2.29129i	0.275839	−	0.477767i	0.970346	+	0.241719i	$0.0777111\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−1.00000	−	1.73205i	−0.200000	−	0.346410i
$26$	−2.00000	+	3.46410i	−0.392232	+	0.679366i
$27$	−1.00000			−0.192450
$28$	2.64575			0.500000
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$	−1.32288	+	2.29129i	−0.241523	+	0.418330i
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.500000	−	0.866025i	0.0870388	−	0.150756i
$34$	3.00000			0.514496
$35$	−3.50000	−	6.06218i	−0.591608	−	1.02470i
$36$	1.00000			0.166667
$37$	−0.645751	+	1.11847i	−0.106161	+	0.183876i	−0.914212	−	0.405236i	$-0.867189\pi$
$37$	−0.645751	+	1.11847i	−0.106161	+	0.183876i	0.808051	+	0.589112i	$0.200523\pi$
$38$	2.64575	+	4.58258i	0.429198	+	0.743392i
$39$	−2.00000	−	3.46410i	−0.320256	−	0.554700i
$40$	1.32288	−	2.29129i	0.209165	−	0.362284i
$41$	9.00000			1.40556			0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000			1.40556			0.702782	+	0.711405i	$0.251941\pi$
$42$	−1.32288	+	2.29129i	−0.204124	+	0.353553i
$43$	9.29150			1.41694			0.708470	−	0.705740i	$-0.249386\pi$
$43$	9.29150			1.41694			0.708470	+	0.705740i	$0.249386\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$	−1.32288	−	2.29129i	−0.197203	−	0.341565i
$46$	−1.32288	−	2.29129i	−0.195047	−	0.337832i
$47$	1.96863	−	3.40976i	0.287154	−	0.497365i	−0.685975	−	0.727625i	$-0.740624\pi$
$47$	1.96863	−	3.40976i	0.287154	−	0.497365i	0.973129	+	0.230260i	$0.0739576\pi$
$48$	−1.00000			−0.144338
$49$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$50$	−2.00000			−0.282843
$51$	−1.50000	+	2.59808i	−0.210042	+	0.363803i
$52$	2.00000	+	3.46410i	0.277350	+	0.480384i
$53$	−2.00000	−	3.46410i	−0.274721	−	0.475831i	0.695344	−	0.718677i	$-0.255252\pi$
$53$	−2.00000	−	3.46410i	−0.274721	−	0.475831i	−0.970065	+	0.242846i	$0.921919\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	2.64575			0.356753
$56$	1.32288	−	2.29129i	0.176777	−	0.306186i
$57$	−5.29150			−0.700877
$58$	1.00000	−	1.73205i	0.131306	−	0.227429i
$59$	−3.29150	−	5.70105i	−0.428517	−	0.742213i	0.568225	−	0.822874i	$-0.307631\pi$
$59$	−3.29150	−	5.70105i	−0.428517	−	0.742213i	−0.996742	+	0.0806601i	$0.974297\pi$
$60$	1.32288	+	2.29129i	0.170783	+	0.295804i
$61$	−5.96863	+	10.3380i	−0.764204	+	1.32364i	0.176462	+	0.984307i	$0.443535\pi$
$61$	−5.96863	+	10.3380i	−0.764204	+	1.32364i	−0.940666	+	0.339333i	$0.889799\pi$
$62$	4.00000			0.508001
$63$	−1.32288	−	2.29129i	−0.166667	−	0.288675i
$64$	1.00000			0.125000
$65$	5.29150	−	9.16515i	0.656330	−	1.13680i
$66$	−0.500000	−	0.866025i	−0.0615457	−	0.106600i
$67$	−3.79150	−	6.56708i	−0.463206	−	0.802296i	0.535913	−	0.844273i	$-0.319968\pi$
$67$	−3.79150	−	6.56708i	−0.463206	−	0.802296i	−0.999119	+	0.0419774i	$0.986634\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$	2.64575			0.318511
$70$	−7.00000			−0.836660
$71$	−2.70850			−0.321440			−0.160720	−	0.987000i	$-0.551382\pi$
$71$	−2.70850			−0.321440			−0.160720	+	0.987000i	$0.551382\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	7.64575	+	13.2428i	0.894868	+	1.54996i	0.833969	+	0.551812i	$0.186063\pi$
$73$	7.64575	+	13.2428i	0.894868	+	1.54996i	0.0608990	+	0.998144i	$0.480603\pi$
$74$	0.645751	+	1.11847i	0.0750671	+	0.130020i
$75$	1.00000	−	1.73205i	0.115470	−	0.200000i
$76$	5.29150			0.606977
$77$	2.64575			0.301511
$78$	−4.00000			−0.452911
$79$	−5.32288	+	9.21949i	−0.598870	+	1.03727i	0.394118	+	0.919060i	$0.371050\pi$
$79$	−5.32288	+	9.21949i	−0.598870	+	1.03727i	−0.992988	+	0.118214i	$0.962283\pi$
$80$	−1.32288	−	2.29129i	−0.147902	−	0.256174i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.50000	−	7.79423i	0.496942	−	0.860729i
$83$	15.5830			1.71046			0.855229	−	0.518251i	$-0.173417\pi$
$83$	15.5830			1.71046			0.855229	+	0.518251i	$0.173417\pi$
$84$	1.32288	+	2.29129i	0.144338	+	0.250000i
$85$	−7.93725			−0.860916
$86$	4.64575	−	8.04668i	0.500964	−	0.867696i
$87$	1.00000	+	1.73205i	0.107211	+	0.185695i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	−1.35425	+	2.34563i	−0.143550	+	0.248636i	−0.928831	−	0.370504i	$-0.879185\pi$
$89$	−1.35425	+	2.34563i	−0.143550	+	0.248636i	0.785281	+	0.619140i	$0.212518\pi$
$90$	−2.64575			−0.278887
$91$	5.29150	−	9.16515i	0.554700	−	0.960769i
$92$	−2.64575			−0.275839
$93$	−2.00000	+	3.46410i	−0.207390	+	0.359211i
$94$	−1.96863	−	3.40976i	−0.203048	−	0.351690i
$95$	−7.00000	−	12.1244i	−0.718185	−	1.24393i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−11.5830			−1.17608			−0.588038	−	0.808833i	$-0.700099\pi$
$97$	−11.5830			−1.17608			−0.588038	+	0.808833i	$0.700099\pi$
$98$	−7.00000			−0.707107
$99$	1.00000			0.100504
$100$	−1.00000	+	1.73205i	−0.100000	+	0.173205i
$101$	−3.64575	−	6.31463i	−0.362766	−	0.628329i	0.625649	−	0.780105i	$-0.284834\pi$
$101$	−3.64575	−	6.31463i	−0.362766	−	0.628329i	−0.988415	+	0.151776i	$0.951501\pi$
$102$	1.50000	+	2.59808i	0.148522	+	0.257248i
$103$	5.00000	−	8.66025i	0.492665	−	0.853320i	−0.507300	−	0.861770i	$-0.669356\pi$
$103$	5.00000	−	8.66025i	0.492665	−	0.853320i	0.999964	+	0.00844953i	$0.00268960\pi$
$104$	4.00000			0.392232
$105$	3.50000	−	6.06218i	0.341565	−	0.591608i
$106$	−4.00000			−0.388514
$107$	−4.50000	+	7.79423i	−0.435031	+	0.753497i	−0.997298	−	0.0734594i	$-0.976596\pi$
$107$	−4.50000	+	7.79423i	−0.435031	+	0.753497i	0.562267	+	0.826956i	$0.309929\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	1.96863	+	3.40976i	0.188560	+	0.326596i	0.944770	−	0.327733i	$-0.106285\pi$
$109$	1.96863	+	3.40976i	0.188560	+	0.326596i	−0.756210	+	0.654329i	$0.772951\pi$
$110$	1.32288	−	2.29129i	0.126131	−	0.218466i
$111$	−1.29150			−0.122584
$112$	−1.32288	−	2.29129i	−0.125000	−	0.216506i
$113$	12.5830			1.18371			0.591855	−	0.806045i	$-0.298396\pi$
$113$	12.5830			1.18371			0.591855	+	0.806045i	$0.298396\pi$
$114$	−2.64575	+	4.58258i	−0.247797	+	0.429198i
$115$	3.50000	+	6.06218i	0.326377	+	0.565301i
$116$	−1.00000	−	1.73205i	−0.0928477	−	0.160817i
$117$	2.00000	−	3.46410i	0.184900	−	0.320256i
$118$	−6.58301			−0.606015
$119$	−7.93725			−0.727607
$120$	2.64575			0.241523
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	5.96863	+	10.3380i	0.540374	+	0.935955i
$123$	4.50000	+	7.79423i	0.405751	+	0.702782i
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	−7.93725			−0.709930
$126$	−2.64575			−0.235702
$127$	2.64575			0.234772			0.117386	−	0.993086i	$-0.462548\pi$
$127$	2.64575			0.234772			0.117386	+	0.993086i	$0.462548\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	4.64575	+	8.04668i	0.409036	+	0.708470i
$130$	−5.29150	−	9.16515i	−0.464095	−	0.803837i
$131$	9.29150	−	16.0934i	0.811802	−	1.40608i	−0.0997990	−	0.995008i	$-0.531820\pi$
$131$	9.29150	−	16.0934i	0.811802	−	1.40608i	0.911601	−	0.411075i	$-0.134847\pi$
$132$	−1.00000			−0.0870388
$133$	−7.00000	−	12.1244i	−0.606977	−	1.05131i
$134$	−7.58301			−0.655072
$135$	1.32288	−	2.29129i	0.113855	−	0.197203i
$136$	−1.50000	−	2.59808i	−0.128624	−	0.222783i
$137$	6.64575	+	11.5108i	0.567785	+	0.983432i	0.996785	+	0.0801276i	$0.0255328\pi$
$137$	6.64575	+	11.5108i	0.567785	+	0.983432i	−0.429000	+	0.903305i	$0.641134\pi$
$138$	1.32288	−	2.29129i	0.112611	−	0.195047i
$139$	−12.5830			−1.06728			−0.533638	−	0.845713i	$-0.679176\pi$
$139$	−12.5830			−1.06728			−0.533638	+	0.845713i	$0.679176\pi$
$140$	−3.50000	+	6.06218i	−0.295804	+	0.512348i
$141$	3.93725			0.331577
$142$	−1.35425	+	2.34563i	−0.113646	+	0.196841i
$143$	2.00000	+	3.46410i	0.167248	+	0.289683i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−2.64575	+	4.58258i	−0.219718	+	0.380562i
$146$	15.2915			1.26553
$147$	3.50000	−	6.06218i	0.288675	−	0.500000i
$148$	1.29150			0.106161
$149$	−9.93725	+	17.2118i	−0.814092	+	1.41005i	0.0958868	+	0.995392i	$0.469431\pi$
$149$	−9.93725	+	17.2118i	−0.814092	+	1.41005i	−0.909978	+	0.414656i	$0.863902\pi$
$150$	−1.00000	−	1.73205i	−0.0816497	−	0.141421i
$151$	−11.3229	−	19.6118i	−0.921443	−	1.59599i	−0.797185	−	0.603735i	$-0.793678\pi$
$151$	−11.3229	−	19.6118i	−0.921443	−	1.59599i	−0.124258	−	0.992250i	$-0.539655\pi$
$152$	2.64575	−	4.58258i	0.214599	−	0.371696i
$153$	−3.00000			−0.242536
$154$	1.32288	−	2.29129i	0.106600	−	0.184637i
$155$	−10.5830			−0.850047
$156$	−2.00000	+	3.46410i	−0.160128	+	0.277350i
$157$	0.354249	+	0.613577i	0.0282721	+	0.0489688i	0.879815	−	0.475316i	$-0.157666\pi$
$157$	0.354249	+	0.613577i	0.0282721	+	0.0489688i	−0.851543	+	0.524285i	$0.824333\pi$
$158$	5.32288	+	9.21949i	0.423465	+	0.733463i
$159$	2.00000	−	3.46410i	0.158610	−	0.274721i
$160$	−2.64575			−0.209165
$161$	3.50000	+	6.06218i	0.275839	+	0.477767i
$162$	−1.00000			−0.0785674
$163$	2.79150	−	4.83502i	0.218647	−	0.378708i	−0.735747	−	0.677256i	$-0.763169\pi$
$163$	2.79150	−	4.83502i	0.218647	−	0.378708i	0.954395	+	0.298548i	$0.0965022\pi$
$164$	−4.50000	−	7.79423i	−0.351391	−	0.608627i
$165$	1.32288	+	2.29129i	0.102986	+	0.178377i
$166$	7.79150	−	13.4953i	0.604738	−	1.04744i
$167$	8.70850			0.673884			0.336942	−	0.941525i	$-0.390607\pi$
$167$	8.70850			0.673884			0.336942	+	0.941525i	$0.390607\pi$
$168$	2.64575			0.204124
$169$	3.00000			0.230769
$170$	−3.96863	+	6.87386i	−0.304380	+	0.527201i
$171$	−2.64575	−	4.58258i	−0.202326	−	0.350438i
$172$	−4.64575	−	8.04668i	−0.354235	−	0.613553i
$173$	−2.00000	+	3.46410i	−0.152057	+	0.263371i	−0.931984	−	0.362500i	$-0.881923\pi$
$173$	−2.00000	+	3.46410i	−0.152057	+	0.263371i	0.779926	+	0.625871i	$0.215256\pi$
$174$	2.00000			0.151620
$175$	5.29150			0.400000
$176$	1.00000			0.0753778
$177$	3.29150	−	5.70105i	0.247404	−	0.428517i
$178$	1.35425	+	2.34563i	0.101505	+	0.175812i
$179$	−2.35425	−	4.07768i	−0.175965	−	0.304780i	0.764530	−	0.644588i	$-0.222971\pi$
$179$	−2.35425	−	4.07768i	−0.175965	−	0.304780i	−0.940495	+	0.339808i	$0.889638\pi$
$180$	−1.32288	+	2.29129i	−0.0986013	+	0.170783i
$181$	−5.29150			−0.393314			−0.196657	−	0.980472i	$-0.563009\pi$
$181$	−5.29150			−0.393314			−0.196657	+	0.980472i	$0.563009\pi$
$182$	−5.29150	−	9.16515i	−0.392232	−	0.679366i
$183$	−11.9373			−0.882427
$184$	−1.32288	+	2.29129i	−0.0975237	+	0.168916i
$185$	−1.70850	−	2.95920i	−0.125611	−	0.217565i
$186$	2.00000	+	3.46410i	0.146647	+	0.254000i
$187$	1.50000	−	2.59808i	0.109691	−	0.189990i
$188$	−3.93725			−0.287154
$189$	1.32288	−	2.29129i	0.0962250	−	0.166667i
$190$	−14.0000			−1.01567
$191$	−3.35425	+	5.80973i	−0.242705	+	0.420377i	−0.961484	−	0.274861i	$-0.911368\pi$
$191$	−3.35425	+	5.80973i	−0.242705	+	0.420377i	0.718779	+	0.695239i	$0.244701\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	7.93725	+	13.7477i	0.571336	+	0.989583i	0.996429	+	0.0844334i	$0.0269080\pi$
$193$	7.93725	+	13.7477i	0.571336	+	0.989583i	−0.425093	+	0.905150i	$0.639759\pi$
$194$	−5.79150	+	10.0312i	−0.415806	+	0.720197i
$195$	10.5830			0.757865
$196$	−3.50000	+	6.06218i	−0.250000	+	0.433013i
$197$	21.8745			1.55849			0.779247	−	0.626717i	$-0.215602\pi$
$197$	21.8745			1.55849			0.779247	+	0.626717i	$0.215602\pi$
$198$	0.500000	−	0.866025i	0.0355335	−	0.0615457i
$199$	9.58301	+	16.5983i	0.679321	+	1.17662i	0.975186	+	0.221389i	$0.0710590\pi$
$199$	9.58301	+	16.5983i	0.679321	+	1.17662i	−0.295864	+	0.955230i	$0.595608\pi$
$200$	1.00000	+	1.73205i	0.0707107	+	0.122474i
$201$	3.79150	−	6.56708i	0.267432	−	0.463206i
$202$	−7.29150			−0.513028
$203$	−2.64575	+	4.58258i	−0.185695	+	0.321634i
$204$	3.00000			0.210042
$205$	−11.9059	+	20.6216i	−0.831543	+	1.44027i
$206$	−5.00000	−	8.66025i	−0.348367	−	0.603388i
$207$	1.32288	+	2.29129i	0.0919462	+	0.159256i
$208$	2.00000	−	3.46410i	0.138675	−	0.240192i
$209$	5.29150			0.366021
$210$	−3.50000	−	6.06218i	−0.241523	−	0.418330i
$211$	21.2915			1.46577			0.732884	−	0.680354i	$-0.238174\pi$
$211$	21.2915			1.46577			0.732884	+	0.680354i	$0.238174\pi$
$212$	−2.00000	+	3.46410i	−0.137361	+	0.237915i
$213$	−1.35425	−	2.34563i	−0.0927916	−	0.160720i
$214$	4.50000	+	7.79423i	0.307614	+	0.532803i
$215$	−12.2915	+	21.2895i	−0.838274	+	1.45193i
$216$	1.00000			0.0680414
$217$	−10.5830			−0.718421
$218$	3.93725			0.266664
$219$	−7.64575	+	13.2428i	−0.516652	+	0.894868i
$220$	−1.32288	−	2.29129i	−0.0891883	−	0.154479i
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$	−0.645751	+	1.11847i	−0.0433400	+	0.0750671i
$223$	28.4575			1.90566			0.952828	−	0.303511i	$-0.0981588\pi$
$223$	28.4575			1.90566			0.952828	+	0.303511i	$0.0981588\pi$
$224$	−2.64575			−0.176777
$225$	2.00000			0.133333
$226$	6.29150	−	10.8972i	0.418505	−	0.724871i
$227$	−1.20850	−	2.09318i	−0.0802108	−	0.138929i	0.823130	−	0.567854i	$-0.192226\pi$
$227$	−1.20850	−	2.09318i	−0.0802108	−	0.138929i	−0.903340	+	0.428924i	$0.858893\pi$
$228$	2.64575	+	4.58258i	0.175219	+	0.303488i
$229$	−3.35425	+	5.80973i	−0.221655	+	0.383918i	−0.955311	−	0.295604i	$-0.904479\pi$
$229$	−3.35425	+	5.80973i	−0.221655	+	0.383918i	0.733656	+	0.679521i	$0.237813\pi$
$230$	7.00000			0.461566
$231$	1.32288	+	2.29129i	0.0870388	+	0.150756i
$232$	−2.00000			−0.131306
$233$	−10.0830	+	17.4643i	−0.660560	+	1.14412i	0.319909	+	0.947448i	$0.396348\pi$
$233$	−10.0830	+	17.4643i	−0.660560	+	1.14412i	−0.980469	+	0.196675i	$0.936986\pi$
$234$	−2.00000	−	3.46410i	−0.130744	−	0.226455i
$235$	5.20850	+	9.02138i	0.339765	+	0.588490i
$236$	−3.29150	+	5.70105i	−0.214259	+	0.371107i
$237$	−10.6458			−0.691516
$238$	−3.96863	+	6.87386i	−0.257248	+	0.445566i
$239$	2.70850			0.175198			0.0875991	−	0.996156i	$-0.472081\pi$
$239$	2.70850			0.175198			0.0875991	+	0.996156i	$0.472081\pi$
$240$	1.32288	−	2.29129i	0.0853913	−	0.147902i
$241$	13.5830	+	23.5265i	0.874958	+	1.51547i	0.856807	+	0.515637i	$0.172445\pi$
$241$	13.5830	+	23.5265i	0.874958	+	1.51547i	0.0181511	+	0.999835i	$0.494222\pi$
$242$	0.500000	+	0.866025i	0.0321412	+	0.0556702i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	11.9373			0.764204
$245$	18.5203			1.18322
$246$	9.00000			0.573819
$247$	10.5830	−	18.3303i	0.673380	−	1.16633i
$248$	−2.00000	−	3.46410i	−0.127000	−	0.219971i
$249$	7.79150	+	13.4953i	0.493766	+	0.855229i
$250$	−3.96863	+	6.87386i	−0.250998	+	0.434741i
$251$	23.2915			1.47015			0.735073	−	0.677988i	$-0.237148\pi$
$251$	23.2915			1.47015			0.735073	+	0.677988i	$0.237148\pi$
$252$	−1.32288	+	2.29129i	−0.0833333	+	0.144338i
$253$	−2.64575			−0.166337
$254$	1.32288	−	2.29129i	0.0830046	−	0.143768i
$255$	−3.96863	−	6.87386i	−0.248525	−	0.430458i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.64575	+	8.04668i	−0.289794	+	0.501938i	−0.973760	−	0.227576i	$-0.926920\pi$
$257$	−4.64575	+	8.04668i	−0.289794	+	0.501938i	0.683966	+	0.729513i	$0.260253\pi$
$258$	9.29150			0.578464
$259$	−1.70850	−	2.95920i	−0.106161	−	0.183876i
$260$	−10.5830			−0.656330
$261$	−1.00000	+	1.73205i	−0.0618984	+	0.107211i
$262$	−9.29150	−	16.0934i	−0.574031	−	0.994251i
$263$	−10.9373	−	18.9439i	−0.674420	−	1.16813i	−0.976638	−	0.214891i	$-0.931060\pi$
$263$	−10.9373	−	18.9439i	−0.674420	−	1.16813i	0.302218	−	0.953239i	$-0.402273\pi$
$264$	−0.500000	+	0.866025i	−0.0307729	+	0.0533002i
$265$	10.5830			0.650109
$266$	−14.0000			−0.858395
$267$	−2.70850			−0.165757
$268$	−3.79150	+	6.56708i	−0.231603	+	0.401148i
$269$	5.32288	+	9.21949i	0.324541	+	0.562122i	0.981419	−	0.191875i	$-0.0614567\pi$
$269$	5.32288	+	9.21949i	0.324541	+	0.562122i	−0.656878	+	0.753997i	$0.728123\pi$
$270$	−1.32288	−	2.29129i	−0.0805076	−	0.139443i
$271$	−4.64575	+	8.04668i	−0.282209	+	0.488801i	−0.971929	−	0.235276i	$-0.924401\pi$
$271$	−4.64575	+	8.04668i	−0.282209	+	0.488801i	0.689719	+	0.724077i	$0.257734\pi$
$272$	−3.00000			−0.181902
$273$	10.5830			0.640513
$274$	13.2915			0.802969
$275$	−1.00000	+	1.73205i	−0.0603023	+	0.104447i
$276$	−1.32288	−	2.29129i	−0.0796278	−	0.137919i
$277$	8.58301	+	14.8662i	0.515703	+	0.893223i	0.999834	+	0.0182280i	$0.00580246\pi$
$277$	8.58301	+	14.8662i	0.515703	+	0.893223i	−0.484131	+	0.874995i	$0.660864\pi$
$278$	−6.29150	+	10.8972i	−0.377339	+	0.653571i
$279$	−4.00000			−0.239474
$280$	3.50000	+	6.06218i	0.209165	+	0.362284i
$281$	−3.00000			−0.178965			−0.0894825	−	0.995988i	$-0.528521\pi$
$281$	−3.00000			−0.178965			−0.0894825	+	0.995988i	$0.528521\pi$
$282$	1.96863	−	3.40976i	0.117230	−	0.203048i
$283$	−15.2288	−	26.3770i	−0.905256	−	1.56795i	−0.820574	−	0.571541i	$-0.806346\pi$
$283$	−15.2288	−	26.3770i	−0.905256	−	1.56795i	−0.0846819	−	0.996408i	$-0.526987\pi$
$284$	1.35425	+	2.34563i	0.0803599	+	0.139187i
$285$	7.00000	−	12.1244i	0.414644	−	0.718185i
$286$	4.00000			0.236525
$287$	−11.9059	+	20.6216i	−0.702782	+	1.21725i
$288$	−1.00000			−0.0589256
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	2.64575	+	4.58258i	0.155364	+	0.269098i
$291$	−5.79150	−	10.0312i	−0.339504	−	0.588038i
$292$	7.64575	−	13.2428i	0.447434	−	0.774978i
$293$	−14.5830			−0.851948			−0.425974	−	0.904735i	$-0.640069\pi$
$293$	−14.5830			−0.851948			−0.425974	+	0.904735i	$0.640069\pi$
$294$	−3.50000	−	6.06218i	−0.204124	−	0.353553i
$295$	17.4170			1.01406
$296$	0.645751	−	1.11847i	0.0375335	−	0.0650100i
$297$	0.500000	+	0.866025i	0.0290129	+	0.0502519i
$298$	9.93725	+	17.2118i	0.575650	+	0.997054i
$299$	−5.29150	+	9.16515i	−0.306015	+	0.530034i
$300$	−2.00000			−0.115470
$301$	−12.2915	+	21.2895i	−0.708470	+	1.22711i
$302$	−22.6458			−1.30312
$303$	3.64575	−	6.31463i	0.209443	−	0.362766i
$304$	−2.64575	−	4.58258i	−0.151744	−	0.262829i
$305$	−15.7915	−	27.3517i	−0.904219	−	1.56615i
$306$	−1.50000	+	2.59808i	−0.0857493	+	0.148522i
$307$	−11.4170			−0.651602			−0.325801	−	0.945438i	$-0.605634\pi$
$307$	−11.4170			−0.651602			−0.325801	+	0.945438i	$0.605634\pi$
$308$	−1.32288	−	2.29129i	−0.0753778	−	0.130558i
$309$	10.0000			0.568880
$310$	−5.29150	+	9.16515i	−0.300537	+	0.520546i
$311$	−11.2601	−	19.5031i	−0.638503	−	1.10592i	−0.985761	−	0.168151i	$-0.946221\pi$
$311$	−11.2601	−	19.5031i	−0.638503	−	1.10592i	0.347258	−	0.937770i	$-0.387113\pi$
$312$	2.00000	+	3.46410i	0.113228	+	0.196116i
$313$	10.2915	−	17.8254i	0.581710	−	1.00755i	−0.413567	−	0.910474i	$-0.635717\pi$
$313$	10.2915	−	17.8254i	0.581710	−	1.00755i	0.995277	−	0.0970777i	$-0.0309495\pi$
$314$	0.708497			0.0399828
$315$	7.00000			0.394405
$316$	10.6458			0.598870
$317$	−4.61438	+	7.99234i	−0.259169	+	0.448894i	−0.966020	−	0.258469i	$-0.916782\pi$
$317$	−4.61438	+	7.99234i	−0.259169	+	0.448894i	0.706850	+	0.707363i	$0.250115\pi$
$318$	−2.00000	−	3.46410i	−0.112154	−	0.194257i
$319$	−1.00000	−	1.73205i	−0.0559893	−	0.0969762i
$320$	−1.32288	+	2.29129i	−0.0739510	+	0.128087i
$321$	−9.00000			−0.502331
$322$	7.00000			0.390095
$323$	−15.8745			−0.883281
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	4.00000	+	6.92820i	0.221880	+	0.384308i
$326$	−2.79150	−	4.83502i	−0.154607	−	0.267787i
$327$	−1.96863	+	3.40976i	−0.108865	+	0.188560i
$328$	−9.00000			−0.496942
$329$	5.20850	+	9.02138i	0.287154	+	0.497365i
$330$	2.64575			0.145644
$331$	−6.50000	+	11.2583i	−0.357272	+	0.618814i	−0.987504	−	0.157593i	$-0.949627\pi$
$331$	−6.50000	+	11.2583i	−0.357272	+	0.618814i	0.630232	+	0.776407i	$0.282960\pi$
$332$	−7.79150	−	13.4953i	−0.427614	−	0.740650i
$333$	−0.645751	−	1.11847i	−0.0353870	−	0.0612920i
$334$	4.35425	−	7.54178i	0.238254	−	0.412668i
$335$	20.0627			1.09614
$336$	1.32288	−	2.29129i	0.0721688	−	0.125000i
$337$	6.70850			0.365435			0.182718	−	0.983165i	$-0.441511\pi$
$337$	6.70850			0.365435			0.182718	+	0.983165i	$0.441511\pi$
$338$	1.50000	−	2.59808i	0.0815892	−	0.141317i
$339$	6.29150	+	10.8972i	0.341708	+	0.591855i
$340$	3.96863	+	6.87386i	0.215229	+	0.372788i
$341$	2.00000	−	3.46410i	0.108306	−	0.187592i
$342$	−5.29150			−0.286132
$343$	18.5203			1.00000
$344$	−9.29150			−0.500964
$345$	−3.50000	+	6.06218i	−0.188434	+	0.326377i
$346$	2.00000	+	3.46410i	0.107521	+	0.186231i
$347$	−14.7915	−	25.6196i	−0.794049	−	1.37533i	−0.923441	−	0.383740i	$-0.874636\pi$
$347$	−14.7915	−	25.6196i	−0.794049	−	1.37533i	0.129392	−	0.991594i	$-0.458698\pi$
$348$	1.00000	−	1.73205i	0.0536056	−	0.0928477i
$349$	−13.2288			−0.708119			−0.354060	−	0.935223i	$-0.615199\pi$
$349$	−13.2288			−0.708119			−0.354060	+	0.935223i	$0.615199\pi$
$350$	2.64575	−	4.58258i	0.141421	−	0.244949i
$351$	4.00000			0.213504
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	11.6458	+	20.1710i	0.619841	+	1.07360i	0.989514	+	0.144434i	$0.0461362\pi$
$353$	11.6458	+	20.1710i	0.619841	+	1.07360i	−0.369674	+	0.929162i	$0.620531\pi$
$354$	−3.29150	−	5.70105i	−0.174941	−	0.303007i
$355$	3.58301	−	6.20595i	0.190166	−	0.329377i
$356$	2.70850			0.143550
$357$	−3.96863	−	6.87386i	−0.210042	−	0.363803i
$358$	−4.70850			−0.248852
$359$	−10.2915	+	17.8254i	−0.543165	+	0.940789i	0.455555	+	0.890208i	$0.349441\pi$
$359$	−10.2915	+	17.8254i	−0.543165	+	0.940789i	−0.998720	+	0.0505814i	$0.983893\pi$
$360$	1.32288	+	2.29129i	0.0697217	+	0.120761i
$361$	−4.50000	−	7.79423i	−0.236842	−	0.410223i
$362$	−2.64575	+	4.58258i	−0.139058	+	0.240855i
$363$	−1.00000			−0.0524864
$364$	−10.5830			−0.554700
$365$	−40.4575			−2.11764
$366$	−5.96863	+	10.3380i	−0.311985	+	0.540374i
$367$	−5.35425	−	9.27383i	−0.279490	−	0.484090i	0.691768	−	0.722119i	$-0.256832\pi$
$367$	−5.35425	−	9.27383i	−0.279490	−	0.484090i	−0.971258	+	0.238029i	$0.923499\pi$
$368$	1.32288	+	2.29129i	0.0689597	+	0.119442i
$369$	−4.50000	+	7.79423i	−0.234261	+	0.405751i
$370$	−3.41699			−0.177641
$371$	10.5830			0.549442
$372$	4.00000			0.207390
$373$	7.90588	−	13.6934i	0.409351	−	0.709017i	−0.585466	−	0.810697i	$-0.699088\pi$
$373$	7.90588	−	13.6934i	0.409351	−	0.709017i	0.994817	+	0.101680i	$0.0324218\pi$
$374$	−1.50000	−	2.59808i	−0.0775632	−	0.134343i
$375$	−3.96863	−	6.87386i	−0.204939	−	0.354965i
$376$	−1.96863	+	3.40976i	−0.101524	+	0.175845i
$377$	−8.00000			−0.412021
$378$	−1.32288	−	2.29129i	−0.0680414	−	0.117851i
$379$	−27.5830			−1.41684			−0.708422	−	0.705789i	$-0.750593\pi$
$379$	−27.5830			−1.41684			−0.708422	+	0.705789i	$0.750593\pi$
$380$	−7.00000	+	12.1244i	−0.359092	+	0.621966i
$381$	1.32288	+	2.29129i	0.0677730	+	0.117386i
$382$	3.35425	+	5.80973i	0.171618	+	0.297252i
$383$	−9.35425	+	16.2020i	−0.477980	+	0.827885i	−0.999681	−	0.0252428i	$-0.991964\pi$
$383$	−9.35425	+	16.2020i	−0.477980	+	0.827885i	0.521702	+	0.853128i	$0.325297\pi$
$384$	1.00000			0.0510310
$385$	−3.50000	+	6.06218i	−0.178377	+	0.308957i
$386$	15.8745			0.807991
$387$	−4.64575	+	8.04668i	−0.236157	+	0.409036i
$388$	5.79150	+	10.0312i	0.294019	+	0.509256i
$389$	−15.9686	−	27.6585i	−0.809642	−	1.40234i	−0.913112	−	0.407708i	$-0.866328\pi$
$389$	−15.9686	−	27.6585i	−0.809642	−	1.40234i	0.103471	−	0.994632i	$-0.467005\pi$
$390$	5.29150	−	9.16515i	0.267946	−	0.464095i
$391$	7.93725			0.401404
$392$	3.50000	+	6.06218i	0.176777	+	0.306186i
$393$	18.5830			0.937389
$394$	10.9373	−	18.9439i	0.551011	−	0.954379i
$395$	−14.0830	−	24.3925i	−0.708593	−	1.22732i
$396$	−0.500000	−	0.866025i	−0.0251259	−	0.0435194i
$397$	−3.00000	+	5.19615i	−0.150566	+	0.260787i	−0.931436	−	0.363906i	$-0.881443\pi$
$397$	−3.00000	+	5.19615i	−0.150566	+	0.260787i	0.780870	+	0.624694i	$0.214776\pi$
$398$	19.1660			0.960705
$399$	7.00000	−	12.1244i	0.350438	−	0.606977i
$400$	2.00000			0.100000
$401$	17.9373	−	31.0682i	0.895744	−	1.55147i	0.0628623	−	0.998022i	$-0.479977\pi$
$401$	17.9373	−	31.0682i	0.895744	−	1.55147i	0.832881	−	0.553451i	$-0.186690\pi$
$402$	−3.79150	−	6.56708i	−0.189103	−	0.327536i
$403$	−8.00000	−	13.8564i	−0.398508	−	0.690237i
$404$	−3.64575	+	6.31463i	−0.181383	+	0.314164i
$405$	2.64575			0.131468
$406$	2.64575	+	4.58258i	0.131306	+	0.227429i
$407$	1.29150			0.0640174
$408$	1.50000	−	2.59808i	0.0742611	−	0.128624i
$409$	−17.9373	−	31.0682i	−0.886940	−	1.53623i	−0.843474	−	0.537170i	$-0.819493\pi$
$409$	−17.9373	−	31.0682i	−0.886940	−	1.53623i	−0.0434664	−	0.999055i	$-0.513840\pi$
$410$	11.9059	+	20.6216i	0.587990	+	1.01843i
$411$	−6.64575	+	11.5108i	−0.327811	+	0.567785i
$412$	−10.0000			−0.492665
$413$	17.4170			0.857034
$414$	2.64575			0.130032
$415$	−20.6144	+	35.7052i	−1.01192	+	1.75270i
$416$	−2.00000	−	3.46410i	−0.0980581	−	0.169842i
$417$	−6.29150	−	10.8972i	−0.308096	−	0.533638i
$418$	2.64575	−	4.58258i	0.129408	−	0.224141i
$419$	−9.87451			−0.482401			−0.241201	−	0.970475i	$-0.577541\pi$
$419$	−9.87451			−0.482401			−0.241201	+	0.970475i	$0.577541\pi$
$420$	−7.00000			−0.341565
$421$	6.12549			0.298538			0.149269	−	0.988797i	$-0.452308\pi$
$421$	6.12549			0.298538			0.149269	+	0.988797i	$0.452308\pi$
$422$	10.6458	−	18.4390i	0.518227	−	0.897596i
$423$	1.96863	+	3.40976i	0.0957179	+	0.165788i
$424$	2.00000	+	3.46410i	0.0971286	+	0.168232i
$425$	3.00000	−	5.19615i	0.145521	−	0.252050i
$426$	−2.70850			−0.131227
$427$	−15.7915	−	27.3517i	−0.764204	−	1.32364i
$428$	9.00000			0.435031
$429$	−2.00000	+	3.46410i	−0.0965609	+	0.167248i
$430$	12.2915	+	21.2895i	0.592749	+	1.02667i
$431$	8.64575	+	14.9749i	0.416451	+	0.721315i	0.995580	−	0.0939217i	$-0.0299403\pi$
$431$	8.64575	+	14.9749i	0.416451	+	0.721315i	−0.579128	+	0.815236i	$0.696607\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	1.58301			0.0760744			0.0380372	−	0.999276i	$-0.487889\pi$
$433$	1.58301			0.0760744			0.0380372	+	0.999276i	$0.487889\pi$
$434$	−5.29150	+	9.16515i	−0.254000	+	0.439941i
$435$	−5.29150			−0.253708
$436$	1.96863	−	3.40976i	0.0942801	−	0.163298i
$437$	7.00000	+	12.1244i	0.334855	+	0.579987i
$438$	7.64575	+	13.2428i	0.365328	+	0.632767i
$439$	4.67712	−	8.10102i	0.223227	−	0.386640i	−0.732559	−	0.680703i	$-0.761674\pi$
$439$	4.67712	−	8.10102i	0.223227	−	0.386640i	0.955786	+	0.294063i	$0.0950076\pi$
$440$	−2.64575			−0.126131
$441$	7.00000			0.333333
$442$	−12.0000			−0.570782
$443$	15.5830	−	26.9906i	0.740371	−	1.28236i	−0.211956	−	0.977279i	$-0.567983\pi$
$443$	15.5830	−	26.9906i	0.740371	−	1.28236i	0.952326	−	0.305081i	$-0.0986835\pi$
$444$	0.645751	+	1.11847i	0.0306460	+	0.0530804i
$445$	−3.58301	−	6.20595i	−0.169851	−	0.294190i
$446$	14.2288	−	24.6449i	0.673751	−	1.16697i
$447$	−19.8745			−0.940032
$448$	−1.32288	+	2.29129i	−0.0625000	+	0.108253i
$449$	30.4575			1.43738			0.718689	−	0.695331i	$-0.244742\pi$
$449$	30.4575			1.43738			0.718689	+	0.695331i	$0.244742\pi$
$450$	1.00000	−	1.73205i	0.0471405	−	0.0816497i
$451$	−4.50000	−	7.79423i	−0.211897	−	0.367016i
$452$	−6.29150	−	10.8972i	−0.295927	−	0.512561i
$453$	11.3229	−	19.6118i	0.531995	−	0.921443i
$454$	−2.41699			−0.113435
$455$	14.0000	+	24.2487i	0.656330	+	1.13680i
$456$	5.29150			0.247797
$457$	20.2915	−	35.1459i	0.949196	−	1.64406i	0.202074	−	0.979370i	$-0.435232\pi$
$457$	20.2915	−	35.1459i	0.949196	−	1.64406i	0.747123	−	0.664686i	$-0.231435\pi$
$458$	3.35425	+	5.80973i	0.156734	+	0.271471i
$459$	−1.50000	−	2.59808i	−0.0700140	−	0.121268i
$460$	3.50000	−	6.06218i	0.163188	−	0.282650i
$461$	−24.5830			−1.14494			−0.572472	−	0.819924i	$-0.694016\pi$
$461$	−24.5830			−1.14494			−0.572472	+	0.819924i	$0.694016\pi$
$462$	2.64575			0.123091
$463$	39.0405			1.81437			0.907183	−	0.420735i	$-0.138228\pi$
$463$	39.0405			1.81437			0.907183	+	0.420735i	$0.138228\pi$
$464$	−1.00000	+	1.73205i	−0.0464238	+	0.0804084i
$465$	−5.29150	−	9.16515i	−0.245388	−	0.425024i
$466$	10.0830	+	17.4643i	0.467086	+	0.809017i
$467$	−4.00000	+	6.92820i	−0.185098	+	0.320599i	−0.943610	−	0.331061i	$-0.892594\pi$
$467$	−4.00000	+	6.92820i	−0.185098	+	0.320599i	0.758512	+	0.651660i	$0.225927\pi$
$468$	−4.00000			−0.184900
$469$	20.0627			0.926412
$470$	10.4170			0.480500
$471$	−0.354249	+	0.613577i	−0.0163229	+	0.0282721i
$472$	3.29150	+	5.70105i	0.151504	+	0.262412i
$473$	−4.64575	−	8.04668i	−0.213612	−	0.369987i
$474$	−5.32288	+	9.21949i	−0.244488	+	0.423465i
$475$	10.5830			0.485582
$476$	3.96863	+	6.87386i	0.181902	+	0.315063i
$477$	4.00000			0.183147
$478$	1.35425	−	2.34563i	0.0619419	−	0.107287i
$479$	16.9373	+	29.3362i	0.773883	+	1.34040i	0.935420	+	0.353538i	$0.115021\pi$
$479$	16.9373	+	29.3362i	0.773883	+	1.34040i	−0.161537	+	0.986867i	$0.551645\pi$
$480$	−1.32288	−	2.29129i	−0.0603807	−	0.104583i
$481$	2.58301	−	4.47390i	0.117775	−	0.203992i
$482$	27.1660			1.23738
$483$	−3.50000	+	6.06218i	−0.159256	+	0.275839i
$484$	1.00000			0.0454545
$485$	15.3229	−	26.5400i	0.695776	−	1.20512i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−10.9373	−	18.9439i	−0.495614	−	0.858429i	0.504373	−	0.863486i	$-0.331724\pi$
$487$	−10.9373	−	18.9439i	−0.495614	−	0.858429i	−0.999987	+	0.00505681i	$0.998390\pi$
$488$	5.96863	−	10.3380i	0.270187	−	0.467978i
$489$	5.58301			0.252472
$490$	9.26013	−	16.0390i	0.418330	−	0.724569i
$491$	−1.00000			−0.0451294			−0.0225647	−	0.999745i	$-0.507183\pi$
$491$	−1.00000			−0.0451294			−0.0225647	+	0.999745i	$0.507183\pi$
$492$	4.50000	−	7.79423i	0.202876	−	0.351391i
$493$	3.00000	+	5.19615i	0.135113	+	0.234023i
$494$	−10.5830	−	18.3303i	−0.476152	−	0.824719i
$495$	−1.32288	+	2.29129i	−0.0594588	+	0.102986i
$496$	−4.00000			−0.179605
$497$	3.58301	−	6.20595i	0.160720	−	0.278375i
$498$	15.5830			0.698291
$499$	9.29150	−	16.0934i	0.415945	−	0.720437i	−0.579582	−	0.814914i	$-0.696784\pi$
$499$	9.29150	−	16.0934i	0.415945	−	0.720437i	0.995527	+	0.0944762i	$0.0301176\pi$
$500$	3.96863	+	6.87386i	0.177482	+	0.307409i
$501$	4.35425	+	7.54178i	0.194533	+	0.336942i
$502$	11.6458	−	20.1710i	0.519775	−	0.900277i
$503$	−1.29150			−0.0575853			−0.0287926	−	0.999585i	$-0.509166\pi$
$503$	−1.29150			−0.0575853			−0.0287926	+	0.999585i	$0.509166\pi$
$504$	1.32288	+	2.29129i	0.0589256	+	0.102062i
$505$	19.2915			0.858461
$506$	−1.32288	+	2.29129i	−0.0588090	+	0.101860i
$507$	1.50000	+	2.59808i	0.0666173	+	0.115385i
$508$	−1.32288	−	2.29129i	−0.0586931	−	0.101659i
$509$	−12.5830	+	21.7944i	−0.557732	+	0.966020i	0.439953	+	0.898021i	$0.354995\pi$
$509$	−12.5830	+	21.7944i	−0.557732	+	0.966020i	−0.997685	+	0.0679994i	$0.978338\pi$
$510$	−7.93725			−0.351468
$511$	−40.4575			−1.78974
$512$	−1.00000			−0.0441942
$513$	2.64575	−	4.58258i	0.116813	−	0.202326i
$514$	4.64575	+	8.04668i	0.204915	+	0.354924i
$515$	13.2288	+	22.9129i	0.582929	+	1.00966i
$516$	4.64575	−	8.04668i	0.204518	−	0.354235i
$517$	−3.93725			−0.173160
$518$	−3.41699			−0.150134
$519$	−4.00000			−0.175581
$520$	−5.29150	+	9.16515i	−0.232048	+	0.401918i
$521$	−21.0000	−	36.3731i	−0.920027	−	1.59353i	−0.799370	−	0.600839i	$-0.794833\pi$
$521$	−21.0000	−	36.3731i	−0.920027	−	1.59353i	−0.120656	−	0.992694i	$-0.538500\pi$
$522$	1.00000	+	1.73205i	0.0437688	+	0.0758098i
$523$	−1.35425	+	2.34563i	−0.0592172	+	0.102567i	−0.894114	−	0.447839i	$-0.852194\pi$
$523$	−1.35425	+	2.34563i	−0.0592172	+	0.102567i	0.834897	+	0.550406i	$0.185527\pi$
$524$	−18.5830			−0.811802
$525$	2.64575	+	4.58258i	0.115470	+	0.200000i
$526$	−21.8745			−0.953774
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$	0.500000	+	0.866025i	0.0217597	+	0.0376889i
$529$	8.00000	+	13.8564i	0.347826	+	0.602452i
$530$	5.29150	−	9.16515i	0.229848	−	0.398109i
$531$	6.58301			0.285678
$532$	−7.00000	+	12.1244i	−0.303488	+	0.525657i
$533$	−36.0000			−1.55933
$534$	−1.35425	+	2.34563i	−0.0586041	+	0.101505i
$535$	−11.9059	−	20.6216i	−0.514736	−	0.891549i
$536$	3.79150	+	6.56708i	0.163768	+	0.283654i
$537$	2.35425	−	4.07768i	0.101593	−	0.175965i
$538$	10.6458			0.458971
$539$	−3.50000	+	6.06218i	−0.150756	+	0.261116i
$540$	−2.64575			−0.113855
$541$	−1.90588	+	3.30108i	−0.0819402	+	0.141925i	−0.904083	−	0.427356i	$-0.859445\pi$
$541$	−1.90588	+	3.30108i	−0.0819402	+	0.141925i	0.822143	+	0.569281i	$0.192778\pi$
$542$	4.64575	+	8.04668i	0.199552	+	0.345634i
$543$	−2.64575	−	4.58258i	−0.113540	−	0.196657i
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$	−10.4170			−0.446215
$546$	5.29150	−	9.16515i	0.226455	−	0.392232i
$547$	14.7085			0.628890			0.314445	−	0.949276i	$-0.398182\pi$
$547$	14.7085			0.628890			0.314445	+	0.949276i	$0.398182\pi$
$548$	6.64575	−	11.5108i	0.283892	−	0.491716i
$549$	−5.96863	−	10.3380i	−0.254735	−	0.441214i
$550$	1.00000	+	1.73205i	0.0426401	+	0.0738549i
$551$	−5.29150	+	9.16515i	−0.225426	+	0.390449i
$552$	−2.64575			−0.112611
$553$	−14.0830	−	24.3925i	−0.598870	−	1.03727i
$554$	17.1660			0.729314
$555$	1.70850	−	2.95920i	0.0725217	−	0.125611i
$556$	6.29150	+	10.8972i	0.266819	+	0.462144i
$557$	9.64575	+	16.7069i	0.408704	+	0.707895i	0.994745	−	0.102386i	$-0.0326477\pi$
$557$	9.64575	+	16.7069i	0.408704	+	0.707895i	−0.586041	+	0.810281i	$0.699314\pi$
$558$	−2.00000	+	3.46410i	−0.0846668	+	0.146647i
$559$	−37.1660			−1.57195
$560$	7.00000			0.295804
$561$	3.00000			0.126660
$562$	−1.50000	+	2.59808i	−0.0632737	+	0.109593i
$563$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$563$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$564$	−1.96863	−	3.40976i	−0.0828941	−	0.143577i
$565$	−16.6458	+	28.8313i	−0.700292	+	1.21294i
$566$	−30.4575			−1.28022
$567$	2.64575			0.111111
$568$	2.70850			0.113646
$569$	7.58301	−	13.1342i	0.317896	−	0.550612i	−0.662153	−	0.749369i	$-0.730357\pi$
$569$	7.58301	−	13.1342i	0.317896	−	0.550612i	0.980049	+	0.198757i	$0.0636903\pi$
$570$	−7.00000	−	12.1244i	−0.293198	−	0.507833i
$571$	14.8745	+	25.7634i	0.622479	+	1.07816i	0.989023	+	0.147764i	$0.0472076\pi$
$571$	14.8745	+	25.7634i	0.622479	+	1.07816i	−0.366544	+	0.930401i	$0.619459\pi$
$572$	2.00000	−	3.46410i	0.0836242	−	0.144841i
$573$	−6.70850			−0.280251
$574$	11.9059	+	20.6216i	0.496942	+	0.860729i
$575$	−5.29150			−0.220671
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−11.3745	−	19.7012i	−0.473527	−	0.820173i	0.526014	−	0.850476i	$-0.323686\pi$
$577$	−11.3745	−	19.7012i	−0.473527	−	0.820173i	−0.999541	+	0.0303033i	$0.990353\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$	−7.93725	+	13.7477i	−0.329861	+	0.571336i
$580$	5.29150			0.219718
$581$	−20.6144	+	35.7052i	−0.855229	+	1.48130i
$582$	−11.5830			−0.480131
$583$	−2.00000	+	3.46410i	−0.0828315	+	0.143468i
$584$	−7.64575	−	13.2428i	−0.316383	−	0.547992i
$585$	5.29150	+	9.16515i	0.218777	+	0.378932i
$586$	−7.29150	+	12.6293i	−0.301209	+	0.521710i
$587$	9.87451			0.407565			0.203782	−	0.979016i	$-0.434677\pi$
$587$	9.87451			0.407565			0.203782	+	0.979016i	$0.434677\pi$
$588$	−7.00000			−0.288675
$589$	−21.1660			−0.872130
$590$	8.70850	−	15.0836i	0.358523	−	0.620980i
$591$	10.9373	+	18.9439i	0.449899	+	0.779247i
$592$	−0.645751	−	1.11847i	−0.0265402	−	0.0459690i
$593$	12.8745	−	22.2993i	0.528693	−	0.915723i	−0.470748	−	0.882268i	$-0.656016\pi$
$593$	12.8745	−	22.2993i	0.528693	−	0.915723i	0.999440	−	0.0334546i	$-0.0106509\pi$
$594$	1.00000			0.0410305
$595$	10.5000	−	18.1865i	0.430458	−	0.745575i
$596$	19.8745			0.814092
$597$	−9.58301	+	16.5983i	−0.392206	+	0.679321i
$598$	5.29150	+	9.16515i	0.216386	+	0.374791i
$599$	−14.6771	−	25.4215i	−0.599691	−	1.03870i	−0.992866	−	0.119232i	$-0.961957\pi$
$599$	−14.6771	−	25.4215i	−0.599691	−	1.03870i	0.393175	−	0.919463i	$-0.371377\pi$
$600$	−1.00000	+	1.73205i	−0.0408248	+	0.0707107i
$601$	−38.5830			−1.57383			−0.786917	−	0.617059i	$-0.788324\pi$
$601$	−38.5830			−1.57383			−0.786917	+	0.617059i	$0.788324\pi$
$602$	12.2915	+	21.2895i	0.500964	+	0.867696i
$603$	7.58301			0.308804
$604$	−11.3229	+	19.6118i	−0.460721	+	0.797993i
$605$	−1.32288	−	2.29129i	−0.0537825	−	0.0931541i
$606$	−3.64575	−	6.31463i	−0.148099	−	0.256514i
$607$	6.55163	−	11.3478i	0.265923	−	0.460591i	−0.701882	−	0.712293i	$-0.747657\pi$
$607$	6.55163	−	11.3478i	0.265923	−	0.460591i	0.967805	+	0.251702i	$0.0809901\pi$
$608$	−5.29150			−0.214599
$609$	−5.29150			−0.214423
$610$	−31.5830			−1.27876
$611$	−7.87451	+	13.6390i	−0.318568	+	0.551777i
$612$	1.50000	+	2.59808i	0.0606339	+	0.105021i
$613$	−3.90588	−	6.76518i	−0.157757	−	0.273243i	0.776302	−	0.630361i	$-0.217093\pi$
$613$	−3.90588	−	6.76518i	−0.157757	−	0.273243i	−0.934060	+	0.357117i	$0.883760\pi$
$614$	−5.70850	+	9.88741i	−0.230376	+	0.399023i
$615$	−23.8118			−0.960183
$616$	−2.64575			−0.106600
$617$	−14.7085			−0.592142			−0.296071	−	0.955166i	$-0.595676\pi$
$617$	−14.7085			−0.592142			−0.296071	+	0.955166i	$0.595676\pi$
$618$	5.00000	−	8.66025i	0.201129	−	0.348367i
$619$	20.5000	+	35.5070i	0.823965	+	1.42715i	0.902708	+	0.430254i	$0.141576\pi$
$619$	20.5000	+	35.5070i	0.823965	+	1.42715i	−0.0787435	+	0.996895i	$0.525091\pi$
$620$	5.29150	+	9.16515i	0.212512	+	0.368081i
$621$	−1.32288	+	2.29129i	−0.0530852	+	0.0919462i
$622$	−22.5203			−0.902980
$623$	−3.58301	−	6.20595i	−0.143550	−	0.248636i
$624$	4.00000			0.160128
$625$	15.5000	−	26.8468i	0.620000	−	1.07387i
$626$	−10.2915	−	17.8254i	−0.411331	−	0.712446i
$627$	2.64575	+	4.58258i	0.105661	+	0.183010i
$628$	0.354249	−	0.613577i	0.0141361	−	0.0244844i
$629$	−3.87451			−0.154487
$630$	3.50000	−	6.06218i	0.139443	−	0.241523i
$631$	41.8745			1.66700			0.833499	−	0.552521i	$-0.186334\pi$
$631$	41.8745			1.66700			0.833499	+	0.552521i	$0.186334\pi$
$632$	5.32288	−	9.21949i	0.211733	−	0.366732i
$633$	10.6458	+	18.4390i	0.423131	+	0.732884i
$634$	4.61438	+	7.99234i	0.183260	+	0.317416i
$635$	−3.50000	+	6.06218i	−0.138893	+	0.240570i
$636$	−4.00000			−0.158610
$637$	14.0000	+	24.2487i	0.554700	+	0.960769i
$638$	−2.00000			−0.0791808
$639$	1.35425	−	2.34563i	0.0535733	−	0.0927916i
$640$	1.32288	+	2.29129i	0.0522913	+	0.0905711i
$641$	13.2915	+	23.0216i	0.524983	+	0.909297i	0.999577	+	0.0290920i	$0.00926158\pi$
$641$	13.2915	+	23.0216i	0.524983	+	0.909297i	−0.474594	+	0.880205i	$0.657405\pi$
$642$	−4.50000	+	7.79423i	−0.177601	+	0.307614i
$643$	−1.16601			−0.0459830			−0.0229915	−	0.999736i	$-0.507319\pi$
$643$	−1.16601			−0.0459830			−0.0229915	+	0.999736i	$0.507319\pi$
$644$	3.50000	−	6.06218i	0.137919	−	0.238883i
$645$	−24.5830			−0.967955
$646$	−7.93725	+	13.7477i	−0.312287	+	0.540897i
$647$	13.1974	+	22.8585i	0.518843	+	0.898662i	0.999760	+	0.0218961i	$0.00697029\pi$
$647$	13.1974	+	22.8585i	0.518843	+	0.898662i	−0.480918	+	0.876766i	$0.659696\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−3.29150	+	5.70105i	−0.129203	+	0.223786i
$650$	8.00000			0.313786
$651$	−5.29150	−	9.16515i	−0.207390	−	0.359211i
$652$	−5.58301			−0.218647
$653$	22.5516	−	39.0606i	0.882514	−	1.52856i	0.0339763	−	0.999423i	$-0.489183\pi$
$653$	22.5516	−	39.0606i	0.882514	−	1.52856i	0.848537	−	0.529136i	$-0.177484\pi$
$654$	1.96863	+	3.40976i	0.0769794	+	0.133332i
$655$	24.5830	+	42.5790i	0.960537	+	1.66370i
$656$	−4.50000	+	7.79423i	−0.175695	+	0.304314i
$657$	−15.2915			−0.596578
$658$	10.4170			0.406097
$659$	−24.1660			−0.941374			−0.470687	−	0.882300i	$-0.655994\pi$
$659$	−24.1660			−0.941374			−0.470687	+	0.882300i	$0.655994\pi$
$660$	1.32288	−	2.29129i	0.0514929	−	0.0891883i
$661$	−10.3542	−	17.9341i	−0.402734	−	0.697555i	0.591321	−	0.806436i	$-0.298607\pi$
$661$	−10.3542	−	17.9341i	−0.402734	−	0.697555i	−0.994055	+	0.108881i	$0.965273\pi$
$662$	6.50000	+	11.2583i	0.252630	+	0.437567i
$663$	6.00000	−	10.3923i	0.233021	−	0.403604i
$664$	−15.5830			−0.604738
$665$	37.0405			1.43637
$666$	−1.29150			−0.0500447
$667$	2.64575	−	4.58258i	0.102444	−	0.177438i
$668$	−4.35425	−	7.54178i	−0.168471	−	0.291800i
$669$	14.2288	+	24.6449i	0.550116	+	0.952828i
$670$	10.0314	−	17.3748i	0.387546	−	0.671249i
$671$	11.9373			0.460833
$672$	−1.32288	−	2.29129i	−0.0510310	−	0.0883883i
$673$	−19.4170			−0.748470			−0.374235	−	0.927334i	$-0.622095\pi$
$673$	−19.4170			−0.748470			−0.374235	+	0.927334i	$0.622095\pi$
$674$	3.35425	−	5.80973i	0.129201	−	0.223782i
$675$	1.00000	+	1.73205i	0.0384900	+	0.0666667i
$676$	−1.50000	−	2.59808i	−0.0576923	−	0.0999260i
$677$	4.06275	−	7.03688i	0.156144	−	0.270449i	−0.777331	−	0.629092i	$-0.783427\pi$
$677$	4.06275	−	7.03688i	0.156144	−	0.270449i	0.933475	+	0.358642i	$0.116760\pi$
$678$	12.5830			0.483247
$679$	15.3229	−	26.5400i	0.588038	−	1.01851i
$680$	7.93725			0.304380
$681$	1.20850	−	2.09318i	0.0463097	−	0.0802108i
$682$	−2.00000	−	3.46410i	−0.0765840	−	0.132647i
$683$	8.58301	+	14.8662i	0.328420	+	0.568839i	0.982198	−	0.187846i	$-0.0601507\pi$
$683$	8.58301	+	14.8662i	0.328420	+	0.568839i	−0.653779	+	0.756686i	$0.726817\pi$
$684$	−2.64575	+	4.58258i	−0.101163	+	0.175219i
$685$	−35.1660			−1.34362
$686$	9.26013	−	16.0390i	0.353553	−	0.612372i
$687$	−6.70850			−0.255945
$688$	−4.64575	+	8.04668i	−0.177118	+	0.306777i
$689$	8.00000	+	13.8564i	0.304776	+	0.527887i
$690$	3.50000	+	6.06218i	0.133243	+	0.230783i
$691$	−7.08301	+	12.2681i	−0.269450	+	0.466701i	−0.968720	−	0.248156i	$-0.920175\pi$
$691$	−7.08301	+	12.2681i	−0.269450	+	0.466701i	0.699270	+	0.714858i	$0.253509\pi$
$692$	4.00000			0.152057
$693$	−1.32288	+	2.29129i	−0.0502519	+	0.0870388i
$694$	−29.5830			−1.12296
$695$	16.6458	−	28.8313i	0.631409	−	1.09363i
$696$	−1.00000	−	1.73205i	−0.0379049	−	0.0656532i
$697$	13.5000	+	23.3827i	0.511349	+	0.885682i
$698$	−6.61438	+	11.4564i	−0.250358	+	0.433633i
$699$	−20.1660			−0.762749
$700$	−2.64575	−	4.58258i	−0.100000	−	0.173205i
$701$	42.4575			1.60360			0.801799	−	0.597594i	$-0.203876\pi$
$701$	42.4575			1.60360			0.801799	+	0.597594i	$0.203876\pi$
$702$	2.00000	−	3.46410i	0.0754851	−	0.130744i
$703$	−3.41699	−	5.91841i	−0.128874	−	0.223217i
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$	−5.20850	+	9.02138i	−0.196163	+	0.339765i
$706$	23.2915			0.876587
$707$	19.2915			0.725532
$708$	−6.58301			−0.247404
$709$	−7.87451	+	13.6390i	−0.295733	+	0.512225i	−0.975155	−	0.221523i	$-0.928897\pi$
$709$	−7.87451	+	13.6390i	−0.295733	+	0.512225i	0.679422	+	0.733748i	$0.262231\pi$
$710$	−3.58301	−	6.20595i	−0.134468	−	0.232905i
$711$	−5.32288	−	9.21949i	−0.199623	−	0.345758i
$712$	1.35425	−	2.34563i	0.0507526	−	0.0879061i
$713$	10.5830			0.396337
$714$	−7.93725			−0.297044
$715$	−10.5830			−0.395782
$716$	−2.35425	+	4.07768i	−0.0879824	+	0.152390i
$717$	1.35425	+	2.34563i	0.0505753	+	0.0875991i
$718$	10.2915	+	17.8254i	0.384075	+	0.665238i
$719$	14.0314	−	24.3031i	0.523282	−	0.906351i	−0.476351	−	0.879255i	$-0.658041\pi$
$719$	14.0314	−	24.3031i	0.523282	−	0.906351i	0.999633	−	0.0270956i	$-0.00862586\pi$
$720$	2.64575			0.0986013
$721$	13.2288	+	22.9129i	0.492665	+	0.853320i
$722$	−9.00000			−0.334945
$723$	−13.5830	+	23.5265i	−0.505157	+	0.874958i
$724$	2.64575	+	4.58258i	0.0983286	+	0.170310i
$725$	−2.00000	−	3.46410i	−0.0742781	−	0.128654i
$726$	−0.500000	+	0.866025i	−0.0185567	+	0.0321412i
$727$	−2.00000			−0.0741759			−0.0370879	−	0.999312i	$-0.511808\pi$
$727$	−2.00000			−0.0741759			−0.0370879	+	0.999312i	$0.511808\pi$
$728$	−5.29150	+	9.16515i	−0.196116	+	0.339683i
$729$	1.00000			0.0370370
$730$	−20.2288	+	35.0372i	−0.748700	+	1.29679i
$731$	13.9373	+	24.1400i	0.515488	+	0.892851i
$732$	5.96863	+	10.3380i	0.220607	+	0.382102i
$733$	−5.96863	+	10.3380i	−0.220456	+	0.381841i	−0.954947	−	0.296778i	$-0.904088\pi$
$733$	−5.96863	+	10.3380i	−0.220456	+	0.381841i	0.734490	+	0.678619i	$0.237421\pi$
$734$	−10.7085			−0.395258
$735$	9.26013	+	16.0390i	0.341565	+	0.591608i
$736$	2.64575			0.0975237
$737$	−3.79150	+	6.56708i	−0.139662	+	0.241901i
$738$	4.50000	+	7.79423i	0.165647	+	0.286910i
$739$	12.2915	+	21.2895i	0.452150	+	0.783147i	0.998519	−	0.0543973i	$-0.0173238\pi$
$739$	12.2915	+	21.2895i	0.452150	+	0.783147i	−0.546369	+	0.837544i	$0.683990\pi$
$740$	−1.70850	+	2.95920i	−0.0628056	+	0.108783i
$741$	21.1660			0.777553
$742$	5.29150	−	9.16515i	0.194257	−	0.336463i
$743$	−18.7085			−0.686348			−0.343174	−	0.939272i	$-0.611502\pi$
$743$	−18.7085			−0.686348			−0.343174	+	0.939272i	$0.611502\pi$
$744$	2.00000	−	3.46410i	0.0733236	−	0.127000i
$745$	−26.2915	−	45.5382i	−0.963246	−	1.66839i
$746$	−7.90588	−	13.6934i	−0.289455	−	0.501351i
$747$	−7.79150	+	13.4953i	−0.285076	+	0.493766i
$748$	−3.00000			−0.109691
$749$	−11.9059	−	20.6216i	−0.435031	−	0.753497i
$750$	−7.93725			−0.289828
$751$	14.6458	−	25.3672i	0.534431	−	0.925662i	−0.464760	−	0.885437i	$-0.653859\pi$
$751$	14.6458	−	25.3672i	0.534431	−	0.925662i	0.999191	−	0.0402248i	$-0.0128074\pi$
$752$	1.96863	+	3.40976i	0.0717884	+	0.124341i
$753$	11.6458	+	20.1710i	0.424395	+	0.735073i
$754$	−4.00000	+	6.92820i	−0.145671	+	0.252310i
$755$	59.9150			2.18053
$756$	−2.64575			−0.0962250
$757$	−32.5830			−1.18425			−0.592125	−	0.805846i	$-0.701711\pi$
$757$	−32.5830			−1.18425			−0.592125	+	0.805846i	$0.701711\pi$
$758$	−13.7915	+	23.8876i	−0.500930	+	0.867636i
$759$	−1.32288	−	2.29129i	−0.0480173	−	0.0831685i
$760$	7.00000	+	12.1244i	0.253917	+	0.439797i
$761$	−23.7915	+	41.2081i	−0.862441	+	1.49379i	0.00712426	+	0.999975i	$0.497732\pi$
$761$	−23.7915	+	41.2081i	−0.862441	+	1.49379i	−0.869566	+	0.493818i	$0.835601\pi$
$762$	2.64575			0.0958455
$763$	−10.4170			−0.377121
$764$	6.70850			0.242705
$765$	3.96863	−	6.87386i	0.143486	−	0.248525i
$766$	9.35425	+	16.2020i	0.337983	+	0.585403i
$767$	13.1660	+	22.8042i	0.475397	+	0.823412i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−30.7085			−1.10738			−0.553688	−	0.832724i	$-0.686780\pi$
$769$	−30.7085			−1.10738			−0.553688	+	0.832724i	$0.686780\pi$
$770$	3.50000	+	6.06218i	0.126131	+	0.218466i
$771$	−9.29150			−0.334625
$772$	7.93725	−	13.7477i	0.285668	−	0.494792i
$773$	4.03137	+	6.98254i	0.144998	+	0.251145i	0.929372	−	0.369144i	$-0.120349\pi$
$773$	4.03137	+	6.98254i	0.144998	+	0.251145i	−0.784374	+	0.620288i	$0.787016\pi$
$774$	4.64575	+	8.04668i	0.166988	+	0.289232i
$775$	4.00000	−	6.92820i	0.143684	−	0.248868i
$776$	11.5830			0.415806
$777$	1.70850	−	2.95920i	0.0612920	−	0.106161i
$778$	−31.9373			−1.14501
$779$	−23.8118	+	41.2432i	−0.853145	+	1.47769i
$780$	−5.29150	−	9.16515i	−0.189466	−	0.328165i
$781$	1.35425	+	2.34563i	0.0484588	+	0.0839332i
$782$	3.96863	−	6.87386i	0.141918	−	0.245809i
$783$	−2.00000			−0.0714742
$784$	7.00000			0.250000
$785$	−1.87451			−0.0669041
$786$	9.29150	−	16.0934i	0.331417	−	0.574031i
$787$	−4.64575	−	8.04668i	−0.165603	−	0.286833i	0.771266	−	0.636513i	$-0.219624\pi$
$787$	−4.64575	−	8.04668i	−0.165603	−	0.286833i	−0.936869	+	0.349680i	$0.886290\pi$
$788$	−10.9373	−	18.9439i	−0.389624	−	0.674848i
$789$	10.9373	−	18.9439i	0.389377	−	0.674420i
$790$	−28.1660			−1.00210
$791$	−16.6458	+	28.8313i	−0.591855	+	1.02512i
$792$	−1.00000			−0.0355335
$793$	23.8745	−	41.3519i	0.847809	−	1.46845i
$794$	3.00000	+	5.19615i	0.106466	+	0.184405i
$795$	5.29150	+	9.16515i	0.187670	+	0.325054i
$796$	9.58301	−	16.5983i	0.339661	−	0.588309i
$797$	45.1033			1.59764			0.798820	−	0.601570i	$-0.205458\pi$
$797$	45.1033			1.59764			0.798820	+	0.601570i	$0.205458\pi$
$798$	−7.00000	−	12.1244i	−0.247797	−	0.429198i
$799$	11.8118			0.417870
$800$	1.00000	−	1.73205i	0.0353553	−	0.0612372i
$801$	−1.35425	−	2.34563i	−0.0478500	−	0.0828787i
$802$	−17.9373	−	31.0682i	−0.633386	−	1.09706i
$803$	7.64575	−	13.2428i	0.269813	−	0.467329i
$804$	−7.58301			−0.267432
$805$	−18.5203			−0.652753
$806$	−16.0000			−0.563576
$807$	−5.32288	+	9.21949i	−0.187374	+	0.324541i
$808$	3.64575	+	6.31463i	0.128257	+	0.222148i
$809$	−22.6660	−	39.2587i	−0.796894	−	1.38026i	−0.921629	−	0.388072i	$-0.873141\pi$
$809$	−22.6660	−	39.2587i	−0.796894	−	1.38026i	0.124735	−	0.992190i	$-0.460192\pi$
$810$	1.32288	−	2.29129i	0.0464811	−	0.0805076i
$811$	16.5830			0.582308			0.291154	−	0.956676i	$-0.405961\pi$
$811$	16.5830			0.582308			0.291154	+	0.956676i	$0.405961\pi$
$812$	5.29150			0.185695
$813$	−9.29150			−0.325867
$814$	0.645751	−	1.11847i	0.0226336	−	0.0392025i
$815$	7.38562	+	12.7923i	0.258707	+	0.448094i
$816$	−1.50000	−	2.59808i	−0.0525105	−	0.0909509i
$817$	−24.5830	+	42.5790i	−0.860050	+	1.48965i
$818$	−35.8745			−1.25432
$819$	5.29150	+	9.16515i	0.184900	+	0.320256i
$820$	23.8118			0.831543
$821$	15.1660	−	26.2683i	0.529297	−	0.916770i	−0.470119	−	0.882603i	$-0.655789\pi$
$821$	15.1660	−	26.2683i	0.529297	−	0.916770i	0.999416	−	0.0341668i	$-0.0108778\pi$
$822$	6.64575	+	11.5108i	0.231797	+	0.401485i
$823$	6.06275	+	10.5010i	0.211334	+	0.366041i	0.952132	−	0.305686i	$-0.0988859\pi$
$823$	6.06275	+	10.5010i	0.211334	+	0.366041i	−0.740798	+	0.671728i	$0.765553\pi$
$824$	−5.00000	+	8.66025i	−0.174183	+	0.301694i
$825$	−2.00000			−0.0696311
$826$	8.70850	−	15.0836i	0.303007	−	0.524824i
$827$	35.3320			1.22861			0.614307	−	0.789067i	$-0.289435\pi$
$827$	35.3320			1.22861			0.614307	+	0.789067i	$0.289435\pi$
$828$	1.32288	−	2.29129i	0.0459731	−	0.0796278i
$829$	−9.93725	−	17.2118i	−0.345135	−	0.597792i	0.640243	−	0.768172i	$-0.278834\pi$
$829$	−9.93725	−	17.2118i	−0.345135	−	0.597792i	−0.985378	+	0.170381i	$0.945500\pi$
$830$	20.6144	+	35.7052i	0.715536	+	1.23934i
$831$	−8.58301	+	14.8662i	−0.297741	+	0.515703i
$832$	−4.00000			−0.138675
$833$	10.5000	−	18.1865i	0.363803	−	0.630126i
$834$	−12.5830			−0.435714
$835$	−11.5203	+	19.9537i	−0.398675	+	0.690525i
$836$	−2.64575	−	4.58258i	−0.0915052	−	0.158492i
$837$	−2.00000	−	3.46410i	−0.0691301	−	0.119737i
$838$	−4.93725	+	8.55157i	−0.170555	+	0.295409i
$839$	−37.1033			−1.28095			−0.640473	−	0.767980i	$-0.721262\pi$
$839$	−37.1033			−1.28095			−0.640473	+	0.767980i	$0.721262\pi$
$840$	−3.50000	+	6.06218i	−0.120761	+	0.209165i
$841$	−25.0000			−0.862069
$842$	3.06275	−	5.30483i	0.105549	−	0.182817i
$843$	−1.50000	−	2.59808i	−0.0516627	−	0.0894825i
$844$	−10.6458	−	18.4390i	−0.366442	−	0.634696i
$845$	−3.96863	+	6.87386i	−0.136525	+	0.236468i
$846$	3.93725			0.135366
$847$	−1.32288	−	2.29129i	−0.0454545	−	0.0787296i
$848$	4.00000			0.137361
$849$	15.2288	−	26.3770i	0.522650	−	0.905256i
$850$	−3.00000	−	5.19615i	−0.102899	−	0.178227i
$851$	1.70850	+	2.95920i	0.0585665	+	0.101440i
$852$	−1.35425	+	2.34563i	−0.0463958	+	0.0803599i
$853$	14.5203			0.497164			0.248582	−	0.968611i	$-0.420035\pi$
$853$	14.5203			0.497164			0.248582	+	0.968611i	$0.420035\pi$
$854$	−31.5830			−1.08075
$855$	14.0000			0.478790
$856$	4.50000	−	7.79423i	0.153807	−	0.266401i
$857$	−4.91699	−	8.51648i	−0.167961	−	0.290918i	0.769742	−	0.638356i	$-0.220385\pi$
$857$	−4.91699	−	8.51648i	−0.167961	−	0.290918i	−0.937703	+	0.347438i	$0.887052\pi$
$858$	2.00000	+	3.46410i	0.0682789	+	0.118262i
$859$	−24.3745	+	42.2179i	−0.831647	+	1.44046i	0.0650836	+	0.997880i	$0.479269\pi$
$859$	−24.3745	+	42.2179i	−0.831647	+	1.44046i	−0.896731	+	0.442576i	$0.854065\pi$
$860$	24.5830			0.838274
$861$	−23.8118			−0.811503
$862$	17.2915			0.588951
$863$	16.5516	−	28.6683i	0.563424	−	0.975879i	−0.433770	−	0.901024i	$-0.642817\pi$
$863$	16.5516	−	28.6683i	0.563424	−	0.975879i	0.997194	−	0.0748557i	$-0.0238496\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−5.29150	−	9.16515i	−0.179916	−	0.311624i
$866$	0.791503	−	1.37092i	0.0268964	−	0.0465859i
$867$	8.00000			0.271694
$868$	5.29150	+	9.16515i	0.179605	+	0.311086i
$869$	10.6458			0.361132
$870$	−2.64575	+	4.58258i	−0.0896994	+	0.155364i
$871$	15.1660	+	26.2683i	0.513881	+	0.890067i
$872$	−1.96863	−	3.40976i	−0.0666661	−	0.115469i
$873$	5.79150	−	10.0312i	0.196013	−	0.339504i
$874$	14.0000			0.473557
$875$	10.5000	−	18.1865i	0.354965	−	0.614817i
$876$	15.2915			0.516652
$877$	−5.38562	+	9.32817i	−0.181860	+	0.314990i	−0.942514	−	0.334167i	$-0.891545\pi$
$877$	−5.38562	+	9.32817i	−0.181860	+	0.314990i	0.760654	+	0.649157i	$0.224878\pi$
$878$	−4.67712	−	8.10102i	−0.157845	−	0.273396i
$879$	−7.29150	−	12.6293i	−0.245936	−	0.425974i
$880$	−1.32288	+	2.29129i	−0.0445941	+	0.0772393i
$881$	23.1660			0.780483			0.390241	−	0.920713i	$-0.372392\pi$
$881$	23.1660			0.780483			0.390241	+	0.920713i	$0.372392\pi$
$882$	3.50000	−	6.06218i	0.117851	−	0.204124i
$883$	−34.4170			−1.15822			−0.579112	−	0.815248i	$-0.696601\pi$
$883$	−34.4170			−1.15822			−0.579112	+	0.815248i	$0.696601\pi$
$884$	−6.00000	+	10.3923i	−0.201802	+	0.349531i
$885$	8.70850	+	15.0836i	0.292733	+	0.507028i
$886$	−15.5830	−	26.9906i	−0.523521	−	0.906765i
$887$	15.5203	−	26.8819i	0.521119	−	0.902605i	−0.478579	−	0.878044i	$-0.658848\pi$
$887$	15.5203	−	26.8819i	0.521119	−	0.902605i	0.999698	−	0.0245606i	$-0.00781868\pi$
$888$	1.29150			0.0433400
$889$	−3.50000	+	6.06218i	−0.117386	+	0.203319i
$890$	−7.16601			−0.240205
$891$	−0.500000	+	0.866025i	−0.0167506	+	0.0290129i
$892$	−14.2288	−	24.6449i	−0.476414	−	0.825173i
$893$	10.4170	+	18.0428i	0.348591	+	0.603778i
$894$	−9.93725	+	17.2118i	−0.332351	+	0.575650i
$895$	12.4575			0.416409
$896$	1.32288	+	2.29129i	0.0441942	+	0.0765466i
$897$	−10.5830			−0.353356
$898$	15.2288	−	26.3770i	0.508190	−	0.880211i
$899$	4.00000	+	6.92820i	0.133407	+	0.231069i
$900$	−1.00000	−	1.73205i	−0.0333333	−	0.0577350i
$901$	6.00000	−	10.3923i	0.199889	−	0.346218i
$902$	−9.00000			−0.299667
$903$	−24.5830			−0.818071
$904$	−12.5830			−0.418505
$905$	7.00000	−	12.1244i	0.232688	−	0.403027i
$906$	−11.3229	−	19.6118i	−0.376177	−	0.651558i
$907$	7.91699	+	13.7126i	0.262879	+	0.455321i	0.967006	−	0.254754i	$-0.0819945\pi$
$907$	7.91699	+	13.7126i	0.262879	+	0.455321i	−0.704126	+	0.710075i	$0.748661\pi$
$908$	−1.20850	+	2.09318i	−0.0401054	+	0.0694646i
$909$	7.29150			0.241844
$910$	28.0000			0.928191
$911$	−18.3948			−0.609446			−0.304723	−	0.952441i	$-0.598564\pi$
$911$	−18.3948			−0.609446			−0.304723	+	0.952441i	$0.598564\pi$
$912$	2.64575	−	4.58258i	0.0876096	−	0.151744i
$913$	−7.79150	−	13.4953i	−0.257861	−	0.446629i
$914$	−20.2915	−	35.1459i	−0.671183	−	1.16252i
$915$	15.7915	−	27.3517i	0.522051	−	0.904219i
$916$	6.70850			0.221655
$917$	24.5830	+	42.5790i	0.811802	+	1.40608i
$918$	−3.00000			−0.0990148
$919$	−4.67712	+	8.10102i	−0.154284	+	0.267228i	−0.932798	−	0.360399i	$-0.882640\pi$
$919$	−4.67712	+	8.10102i	−0.154284	+	0.267228i	0.778514	+	0.627627i	$0.215974\pi$
$920$	−3.50000	−	6.06218i	−0.115392	−	0.199864i
$921$	−5.70850	−	9.88741i	−0.188101	−	0.325801i
$922$	−12.2915	+	21.2895i	−0.404799	+	0.701133i
$923$	10.8340			0.356605
$924$	1.32288	−	2.29129i	0.0435194	−	0.0753778i
$925$	2.58301			0.0849287
$926$	19.5203	−	33.8101i	0.641476	−	1.11107i
$927$	5.00000	+	8.66025i	0.164222	+	0.284440i
$928$	1.00000	+	1.73205i	0.0328266	+	0.0568574i
$929$	17.2288	−	29.8411i	0.565257	−	0.979054i	−0.431769	−	0.901984i	$-0.642110\pi$
$929$	17.2288	−	29.8411i	0.565257	−	0.979054i	0.997026	−	0.0770697i	$-0.0245564\pi$
$930$	−10.5830			−0.347030
$931$	37.0405			1.21395
$932$	20.1660			0.660560
$933$	11.2601	−	19.5031i	0.368640	−	0.638503i
$934$	4.00000	+	6.92820i	0.130884	+	0.226698i
$935$	3.96863	+	6.87386i	0.129788	+	0.224799i
$936$	−2.00000	+	3.46410i	−0.0653720	+	0.113228i
$937$	50.0000			1.63343			0.816714	−	0.577042i	$-0.195793\pi$
$937$	50.0000			1.63343			0.816714	+	0.577042i	$0.195793\pi$
$938$	10.0314	−	17.3748i	0.327536	−	0.567309i
$939$	20.5830			0.671701
$940$	5.20850	−	9.02138i	0.169882	−	0.294245i
$941$	−1.70850	−	2.95920i	−0.0556954	−	0.0964673i	0.836833	−	0.547458i	$-0.184404\pi$
$941$	−1.70850	−	2.95920i	−0.0556954	−	0.0964673i	−0.892529	+	0.450990i	$0.851071\pi$
$942$	0.354249	+	0.613577i	0.0115420	+	0.0199914i
$943$	11.9059	−	20.6216i	0.387709	−	0.671531i
$944$	6.58301			0.214259
$945$	3.50000	+	6.06218i	0.113855	+	0.197203i
$946$	−9.29150			−0.302093
$947$	7.70850	−	13.3515i	0.250493	−	0.433866i	−0.713169	−	0.700992i	$-0.752741\pi$
$947$	7.70850	−	13.3515i	0.250493	−	0.433866i	0.963662	+	0.267126i	$0.0860741\pi$
$948$	5.32288	+	9.21949i	0.172879	+	0.299435i
$949$	−30.5830	−	52.9713i	−0.992766	−	1.71952i
$950$	5.29150	−	9.16515i	0.171679	−	0.297357i
$951$	−9.22876			−0.299263
$952$	7.93725			0.257248
$953$	26.7490			0.866486			0.433243	−	0.901277i	$-0.357369\pi$
$953$	26.7490			0.866486			0.433243	+	0.901277i	$0.357369\pi$
$954$	2.00000	−	3.46410i	0.0647524	−	0.112154i
$955$	−8.87451	−	15.3711i	−0.287172	−	0.497397i
$956$	−1.35425	−	2.34563i	−0.0437995	−	0.0758630i
$957$	1.00000	−	1.73205i	0.0323254	−	0.0559893i
$958$	33.8745			1.09444
$959$	−35.1660			−1.13557
$960$	−2.64575			−0.0853913
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	−2.58301	−	4.47390i	−0.0832794	−	0.144244i
$963$	−4.50000	−	7.79423i	−0.145010	−	0.251166i
$964$	13.5830	−	23.5265i	0.437479	−	0.757736i
$965$	−42.0000			−1.35203
$966$	3.50000	+	6.06218i	0.112611	+	0.195047i
$967$	40.0627			1.28833			0.644166	−	0.764886i	$-0.277205\pi$
$967$	40.0627			1.28833			0.644166	+	0.764886i	$0.277205\pi$
$968$	0.500000	−	0.866025i	0.0160706	−	0.0278351i
$969$	−7.93725	−	13.7477i	−0.254981	−	0.441641i
$970$	−15.3229	−	26.5400i	−0.491988	−	0.852148i
$971$	−3.00000	+	5.19615i	−0.0962746	+	0.166752i	−0.910140	−	0.414301i	$-0.864026\pi$
$971$	−3.00000	+	5.19615i	−0.0962746	+	0.166752i	0.813865	+	0.581054i	$0.197359\pi$
$972$	−1.00000			−0.0320750
$973$	16.6458	−	28.8313i	0.533638	−	0.924289i
$974$	−21.8745			−0.700904
$975$	−4.00000	+	6.92820i	−0.128103	+	0.221880i
$976$	−5.96863	−	10.3380i	−0.191051	−	0.330910i
$977$	−6.58301	−	11.4021i	−0.210609	−	0.364785i	0.741296	−	0.671178i	$-0.234211\pi$
$977$	−6.58301	−	11.4021i	−0.210609	−	0.364785i	−0.951905	+	0.306392i	$0.900878\pi$
$978$	2.79150	−	4.83502i	0.0892624	−	0.154607i
$979$	2.70850			0.0865640
$980$	−9.26013	−	16.0390i	−0.295804	−	0.512348i
$981$	−3.93725			−0.125707
$982$	−0.500000	+	0.866025i	−0.0159556	+	0.0276360i
$983$	−21.2601	−	36.8236i	−0.678093	−	1.17449i	−0.975555	−	0.219757i	$-0.929473\pi$
$983$	−21.2601	−	36.8236i	−0.678093	−	1.17449i	0.297462	−	0.954734i	$-0.403860\pi$
$984$	−4.50000	−	7.79423i	−0.143455	−	0.248471i
$985$	−28.9373	+	50.1208i	−0.922018	+	1.59698i
$986$	6.00000			0.191079
$987$	−5.20850	+	9.02138i	−0.165788	+	0.287154i
$988$	−21.1660			−0.673380
$989$	12.2915	−	21.2895i	0.390847	−	0.676967i
$990$	1.32288	+	2.29129i	0.0420437	+	0.0728219i
$991$	21.9373	+	37.9964i	0.696860	+	1.20700i	0.969550	+	0.244895i	$0.0787534\pi$
$991$	21.9373	+	37.9964i	0.696860	+	1.20700i	−0.272690	+	0.962102i	$0.587913\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$	−13.0000			−0.412543
$994$	−3.58301	−	6.20595i	−0.113646	−	0.196841i
$995$	−50.7085			−1.60757
$996$	7.79150	−	13.4953i	0.246883	−	0.427614i
$997$	−3.41699	−	5.91841i	−0.108217	−	0.187438i	0.806831	−	0.590783i	$-0.201181\pi$
$997$	−3.41699	−	5.91841i	−0.108217	−	0.187438i	−0.915048	+	0.403345i	$0.867848\pi$
$998$	−9.29150	−	16.0934i	−0.294117	−	0.509426i
$999$	0.645751	−	1.11847i	0.0204307	−	0.0353870i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.i.e.331.1	yes	4
3.2	odd	2		1386.2.k.r.793.2		4
7.2	even	3		3234.2.a.w.1.2		2
7.4	even	3	inner	462.2.i.e.67.1	✓	4
7.5	odd	6		3234.2.a.ba.1.1		2
21.2	odd	6		9702.2.a.db.1.1		2
21.5	even	6		9702.2.a.dm.1.2		2
21.11	odd	6		1386.2.k.r.991.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.i.e.67.1	✓	4	7.4	even	3	inner
462.2.i.e.331.1	yes	4	1.1	even	1	trivial
1386.2.k.r.793.2		4	3.2	odd	2
1386.2.k.r.991.2		4	21.11	odd	6
3234.2.a.w.1.2		2	7.2	even	3
3234.2.a.ba.1.1		2	7.5	odd	6
9702.2.a.db.1.1		2	21.2	odd	6
9702.2.a.dm.1.2		2	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.32288 + 2.29129i) q^{5} +1.00000 q^{6} +(-1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.32288 + 2.29129i) q^{5} +1.00000 q^{6} +(-1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.32288 + 2.29129i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} -4.00000 q^{13} +(1.32288 + 2.29129i) q^{14} -2.64575 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-2.64575 + 4.58258i) q^{19} +2.64575 q^{20} -2.64575 q^{21} -1.00000 q^{22} +(1.32288 - 2.29129i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(-2.00000 + 3.46410i) q^{26} -1.00000 q^{27} +2.64575 q^{28} +2.00000 q^{29} +(-1.32288 + 2.29129i) q^{30} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.500000 - 0.866025i) q^{33} +3.00000 q^{34} +(-3.50000 - 6.06218i) q^{35} +1.00000 q^{36} +(-0.645751 + 1.11847i) q^{37} +(2.64575 + 4.58258i) q^{38} +(-2.00000 - 3.46410i) q^{39} +(1.32288 - 2.29129i) q^{40} +9.00000 q^{41} +(-1.32288 + 2.29129i) q^{42} +9.29150 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-1.32288 - 2.29129i) q^{45} +(-1.32288 - 2.29129i) q^{46} +(1.96863 - 3.40976i) q^{47} -1.00000 q^{48} +(-3.50000 - 6.06218i) q^{49} -2.00000 q^{50} +(-1.50000 + 2.59808i) q^{51} +(2.00000 + 3.46410i) q^{52} +(-2.00000 - 3.46410i) q^{53} +(-0.500000 + 0.866025i) q^{54} +2.64575 q^{55} +(1.32288 - 2.29129i) q^{56} -5.29150 q^{57} +(1.00000 - 1.73205i) q^{58} +(-3.29150 - 5.70105i) q^{59} +(1.32288 + 2.29129i) q^{60} +(-5.96863 + 10.3380i) q^{61} +4.00000 q^{62} +(-1.32288 - 2.29129i) q^{63} +1.00000 q^{64} +(5.29150 - 9.16515i) q^{65} +(-0.500000 - 0.866025i) q^{66} +(-3.79150 - 6.56708i) q^{67} +(1.50000 - 2.59808i) q^{68} +2.64575 q^{69} -7.00000 q^{70} -2.70850 q^{71} +(0.500000 - 0.866025i) q^{72} +(7.64575 + 13.2428i) q^{73} +(0.645751 + 1.11847i) q^{74} +(1.00000 - 1.73205i) q^{75} +5.29150 q^{76} +2.64575 q^{77} -4.00000 q^{78} +(-5.32288 + 9.21949i) q^{79} +(-1.32288 - 2.29129i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.50000 - 7.79423i) q^{82} +15.5830 q^{83} +(1.32288 + 2.29129i) q^{84} -7.93725 q^{85} +(4.64575 - 8.04668i) q^{86} +(1.00000 + 1.73205i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-1.35425 + 2.34563i) q^{89} -2.64575 q^{90} +(5.29150 - 9.16515i) q^{91} -2.64575 q^{92} +(-2.00000 + 3.46410i) q^{93} +(-1.96863 - 3.40976i) q^{94} +(-7.00000 - 12.1244i) q^{95} +(-0.500000 + 0.866025i) q^{96} -11.5830 q^{97} -7.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{6} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^6 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{6} - 4 q^{8} - 2 q^{9} - 2 q^{11} + 2 q^{12} - 16 q^{13} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{22} - 2 q^{24} - 4 q^{25} - 8 q^{26} - 4 q^{27} + 8 q^{29} + 8 q^{31} + 2 q^{32} + 2 q^{33} + 12 q^{34} - 14 q^{35} + 4 q^{36} + 8 q^{37} - 8 q^{39} + 36 q^{41} + 16 q^{43} - 2 q^{44} - 8 q^{47} - 4 q^{48} - 14 q^{49} - 8 q^{50} - 6 q^{51} + 8 q^{52} - 8 q^{53} - 2 q^{54} + 4 q^{58} + 8 q^{59} - 8 q^{61} + 16 q^{62} + 4 q^{64} - 2 q^{66} + 6 q^{67} + 6 q^{68} - 28 q^{70} - 32 q^{71} + 2 q^{72} + 20 q^{73} - 8 q^{74} + 4 q^{75} - 16 q^{78} - 16 q^{79} - 2 q^{81} + 18 q^{82} + 20 q^{83} + 8 q^{86} + 4 q^{87} + 2 q^{88} - 16 q^{89} - 8 q^{93} + 8 q^{94} - 28 q^{95} - 2 q^{96} - 4 q^{97} - 28 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^6 - 4 * q^8 - 2 * q^9 - 2 * q^11 + 2 * q^12 - 16 * q^13 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 4 * q^22 - 2 * q^24 - 4 * q^25 - 8 * q^26 - 4 * q^27 + 8 * q^29 + 8 * q^31 + 2 * q^32 + 2 * q^33 + 12 * q^34 - 14 * q^35 + 4 * q^36 + 8 * q^37 - 8 * q^39 + 36 * q^41 + 16 * q^43 - 2 * q^44 - 8 * q^47 - 4 * q^48 - 14 * q^49 - 8 * q^50 - 6 * q^51 + 8 * q^52 - 8 * q^53 - 2 * q^54 + 4 * q^58 + 8 * q^59 - 8 * q^61 + 16 * q^62 + 4 * q^64 - 2 * q^66 + 6 * q^67 + 6 * q^68 - 28 * q^70 - 32 * q^71 + 2 * q^72 + 20 * q^73 - 8 * q^74 + 4 * q^75 - 16 * q^78 - 16 * q^79 - 2 * q^81 + 18 * q^82 + 20 * q^83 + 8 * q^86 + 4 * q^87 + 2 * q^88 - 16 * q^89 - 8 * q^93 + 8 * q^94 - 28 * q^95 - 2 * q^96 - 4 * q^97 - 28 * q^98 + 4 * q^99

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