LMFDB - Embedded newform 462.2.i.e.331.2

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			331.2
Root			$-1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	462.331
Dual form			462.2.i.e.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(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} +(4.64575 - 8.04668i) 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} -1.29150 q^{43} +(-0.500000 + 0.866025i) q^{44} +(1.32288 + 2.29129i) q^{45} +(1.32288 + 2.29129i) q^{46} +(-5.96863 + 10.3380i) 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} +(7.29150 + 12.6293i) q^{59} +(-1.32288 - 2.29129i) q^{60} +(1.96863 - 3.40976i) 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} +(6.79150 + 11.7632i) q^{67} +(1.50000 - 2.59808i) q^{68} -2.64575 q^{69} -7.00000 q^{70} -13.2915 q^{71} +(0.500000 - 0.866025i) q^{72} +(2.35425 + 4.07768i) q^{73} +(-4.64575 - 8.04668i) q^{74} +(1.00000 - 1.73205i) q^{75} -5.29150 q^{76} -2.64575 q^{77} -4.00000 q^{78} +(-2.67712 + 4.63692i) q^{79} +(1.32288 + 2.29129i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.50000 - 7.79423i) q^{82} -5.58301 q^{83} +(-1.32288 - 2.29129i) q^{84} +7.93725 q^{85} +(-0.645751 + 1.11847i) q^{86} +(1.00000 + 1.73205i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-6.64575 + 11.5108i) q^{89} +2.64575 q^{90} +(-5.29150 + 9.16515i) q^{91} +2.64575 q^{92} +(-2.00000 + 3.46410i) q^{93} +(5.96863 + 10.3380i) q^{94} +(-7.00000 - 12.1244i) q^{95} +(-0.500000 + 0.866025i) q^{96} +9.58301 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} - 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}+ \cdots + 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

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	$-0.631827\pi$
$5$	1.32288	−	2.29129i	0.591608	−	1.02470i	0.994016	−	0.109235i	$-0.0348400\pi$
$6$	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	$-0.625715\pi$
$19$	2.64575	−	4.58258i	0.606977	−	1.05131i	0.991736	−	0.128298i	$-0.0409513\pi$
$20$	−2.64575			−0.591608
$21$	2.64575			0.577350
$22$	−1.00000			−0.213201
$23$	−1.32288	+	2.29129i	−0.275839	+	0.477767i	−0.970346	−	0.241719i	$-0.922289\pi$
$23$	−1.32288	+	2.29129i	−0.275839	+	0.477767i	0.694508	+	0.719485i	$0.255622\pi$
$24$	−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
$37$	4.64575	−	8.04668i	0.763757	−	1.32287i	−0.177145	−	0.984185i	$-0.556686\pi$
$37$	4.64575	−	8.04668i	0.763757	−	1.32287i	0.940901	−	0.338681i	$-0.109981\pi$
$38$	−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
$43$	−1.29150			−0.196952			−0.0984762	−	0.995139i	$-0.531397\pi$
$43$	−1.29150			−0.196952			−0.0984762	+	0.995139i	$0.531397\pi$
$44$	−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
$47$	−5.96863	+	10.3380i	−0.870614	+	1.50795i	−0.00925075	+	0.999957i	$0.502945\pi$
$47$	−5.96863	+	10.3380i	−0.870614	+	1.50795i	−0.861363	+	0.507990i	$0.830389\pi$
$48$	−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
$59$	7.29150	+	12.6293i	0.949273	+	1.64419i	0.746961	+	0.664867i	$0.231512\pi$
$59$	7.29150	+	12.6293i	0.949273	+	1.64419i	0.202311	+	0.979321i	$0.435155\pi$
$60$	−1.32288	−	2.29129i	−0.170783	−	0.295804i
$61$	1.96863	−	3.40976i	0.252057	−	0.436575i	−0.712035	−	0.702144i	$-0.752226\pi$
$61$	1.96863	−	3.40976i	0.252057	−	0.436575i	0.964092	+	0.265569i	$0.0855597\pi$
$62$	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
$67$	6.79150	+	11.7632i	0.829714	+	1.43711i	0.898263	+	0.439459i	$0.144830\pi$
$67$	6.79150	+	11.7632i	0.829714	+	1.43711i	−0.0685485	+	0.997648i	$0.521837\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$	−2.64575			−0.318511
$70$	−7.00000			−0.836660
$71$	−13.2915			−1.57741			−0.788706	−	0.614771i	$-0.789248\pi$
$71$	−13.2915			−1.57741			−0.788706	+	0.614771i	$0.789248\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	2.35425	+	4.07768i	0.275544	+	0.477256i	0.970272	−	0.242016i	$-0.0778087\pi$
$73$	2.35425	+	4.07768i	0.275544	+	0.477256i	−0.694728	+	0.719272i	$0.744475\pi$
$74$	−4.64575	−	8.04668i	−0.540058	−	0.935407i
$75$	1.00000	−	1.73205i	0.115470	−	0.200000i
$76$	−5.29150			−0.606977
$77$	−2.64575			−0.301511
$78$	−4.00000			−0.452911
$79$	−2.67712	+	4.63692i	−0.301200	+	0.521694i	−0.976408	−	0.215934i	$-0.930721\pi$
$79$	−2.67712	+	4.63692i	−0.301200	+	0.521694i	0.675208	+	0.737627i	$0.264054\pi$
$80$	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
$83$	−5.58301			−0.612814			−0.306407	−	0.951901i	$-0.599127\pi$
$83$	−5.58301			−0.612814			−0.306407	+	0.951901i	$0.599127\pi$
$84$	−1.32288	−	2.29129i	−0.144338	−	0.250000i
$85$	7.93725			0.860916
$86$	−0.645751	+	1.11847i	−0.0696332	+	0.120608i
$87$	1.00000	+	1.73205i	0.107211	+	0.185695i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	−6.64575	+	11.5108i	−0.704448	+	1.22014i	0.262442	+	0.964948i	$0.415472\pi$
$89$	−6.64575	+	11.5108i	−0.704448	+	1.22014i	−0.966890	+	0.255192i	$0.917861\pi$
$90$	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
$94$	5.96863	+	10.3380i	0.615617	+	1.06628i
$95$	−7.00000	−	12.1244i	−0.718185	−	1.24393i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	9.58301			0.973007			0.486503	−	0.873679i	$-0.338272\pi$
$97$	9.58301			0.973007			0.486503	+	0.873679i	$0.338272\pi$
$98$	−7.00000			−0.707107
$99$	1.00000			0.100504
$100$	−1.00000	+	1.73205i	−0.100000	+	0.173205i
$101$	1.64575	+	2.85052i	0.163758	+	0.283638i	0.936214	−	0.351431i	$-0.114305\pi$
$101$	1.64575	+	2.85052i	0.163758	+	0.283638i	−0.772455	+	0.635069i	$0.780972\pi$
$102$	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
$109$	−5.96863	−	10.3380i	−0.571691	−	0.990197i	−0.996393	−	0.0848642i	$-0.972954\pi$
$109$	−5.96863	−	10.3380i	−0.571691	−	0.990197i	0.424702	−	0.905333i	$-0.360379\pi$
$110$	−1.32288	+	2.29129i	−0.126131	+	0.218466i
$111$	9.29150			0.881910
$112$	1.32288	+	2.29129i	0.125000	+	0.216506i
$113$	−8.58301			−0.807421			−0.403711	−	0.914887i	$-0.632280\pi$
$113$	−8.58301			−0.807421			−0.403711	+	0.914887i	$0.632280\pi$
$114$	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
$118$	14.5830			1.34247
$119$	7.93725			0.727607
$120$	−2.64575			−0.241523
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−1.96863	−	3.40976i	−0.178231	−	0.308705i
$123$	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	$-0.537452\pi$
$127$	−2.64575			−0.234772			−0.117386	+	0.993086i	$0.537452\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−0.645751	−	1.11847i	−0.0568552	−	0.0984762i
$130$	5.29150	+	9.16515i	0.464095	+	0.803837i
$131$	−1.29150	+	2.23695i	−0.112839	+	0.195443i	−0.916914	−	0.399085i	$-0.869328\pi$
$131$	−1.29150	+	2.23695i	−0.112839	+	0.195443i	0.804075	+	0.594528i	$0.202661\pi$
$132$	−1.00000			−0.0870388
$133$	−7.00000	−	12.1244i	−0.606977	−	1.05131i
$134$	13.5830			1.17339
$135$	−1.32288	+	2.29129i	−0.113855	+	0.197203i
$136$	−1.50000	−	2.59808i	−0.128624	−	0.222783i
$137$	1.35425	+	2.34563i	0.115701	+	0.200400i	0.918060	−	0.396442i	$-0.129755\pi$
$137$	1.35425	+	2.34563i	0.115701	+	0.200400i	−0.802359	+	0.596842i	$0.796422\pi$
$138$	−1.32288	+	2.29129i	−0.112611	+	0.195047i
$139$	8.58301			0.728001			0.364001	−	0.931399i	$-0.381411\pi$
$139$	8.58301			0.728001			0.364001	+	0.931399i	$0.381411\pi$
$140$	−3.50000	+	6.06218i	−0.295804	+	0.512348i
$141$	−11.9373			−1.00530
$142$	−6.64575	+	11.5108i	−0.557699	+	0.965963i
$143$	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
$146$	4.70850			0.389678
$147$	3.50000	−	6.06218i	0.288675	−	0.500000i
$148$	−9.29150			−0.763757
$149$	5.93725	−	10.2836i	0.486399	−	0.842467i	−0.513479	−	0.858102i	$-0.671644\pi$
$149$	5.93725	−	10.2836i	0.486399	−	0.842467i	0.999878	+	0.0156348i	$0.00497690\pi$
$150$	−1.00000	−	1.73205i	−0.0816497	−	0.141421i
$151$	−8.67712	−	15.0292i	−0.706134	−	1.22306i	−0.966281	−	0.257491i	$-0.917104\pi$
$151$	−8.67712	−	15.0292i	−0.706134	−	1.22306i	0.260146	−	0.965569i	$-0.416229\pi$
$152$	−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
$157$	5.64575	+	9.77873i	0.450580	+	0.780427i	0.998422	−	0.0561543i	$-0.0178839\pi$
$157$	5.64575	+	9.77873i	0.450580	+	0.780427i	−0.547842	+	0.836582i	$0.684551\pi$
$158$	2.67712	+	4.63692i	0.212981	+	0.368893i
$159$	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
$163$	−7.79150	+	13.4953i	−0.610278	+	1.05703i	0.380916	+	0.924610i	$0.375609\pi$
$163$	−7.79150	+	13.4953i	−0.610278	+	1.05703i	−0.991193	+	0.132422i	$0.957725\pi$
$164$	−4.50000	−	7.79423i	−0.351391	−	0.608627i
$165$	−1.32288	−	2.29129i	−0.102986	−	0.178377i
$166$	−2.79150	+	4.83502i	−0.216663	+	0.375271i
$167$	19.2915			1.49282			0.746411	−	0.665486i	$-0.231776\pi$
$167$	19.2915			1.49282			0.746411	+	0.665486i	$0.231776\pi$
$168$	−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
$172$	0.645751	+	1.11847i	0.0492381	+	0.0852828i
$173$	−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
$177$	−7.29150	+	12.6293i	−0.548063	+	0.949273i
$178$	6.64575	+	11.5108i	0.498120	+	0.862769i
$179$	−7.64575	−	13.2428i	−0.571470	−	0.989816i	−0.996415	−	0.0845964i	$-0.973040\pi$
$179$	−7.64575	−	13.2428i	−0.571470	−	0.989816i	0.424945	−	0.905219i	$-0.360293\pi$
$180$	1.32288	−	2.29129i	0.0986013	−	0.170783i
$181$	5.29150			0.393314			0.196657	−	0.980472i	$-0.436991\pi$
$181$	5.29150			0.393314			0.196657	+	0.980472i	$0.436991\pi$
$182$	5.29150	+	9.16515i	0.392232	+	0.679366i
$183$	3.93725			0.291050
$184$	1.32288	−	2.29129i	0.0975237	−	0.168916i
$185$	−12.2915	−	21.2895i	−0.903689	−	1.56524i
$186$	2.00000	+	3.46410i	0.146647	+	0.254000i
$187$	1.50000	−	2.59808i	0.109691	−	0.189990i
$188$	11.9373			0.870614
$189$	−1.32288	+	2.29129i	−0.0962250	+	0.166667i
$190$	−14.0000			−1.01567
$191$	−8.64575	+	14.9749i	−0.625585	+	1.08354i	0.362843	+	0.931850i	$0.381806\pi$
$191$	−8.64575	+	14.9749i	−0.625585	+	1.08354i	−0.988428	+	0.151694i	$0.951527\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−7.93725	−	13.7477i	−0.571336	−	0.989583i	−0.996429	−	0.0844334i	$-0.973092\pi$
$193$	−7.93725	−	13.7477i	−0.571336	−	0.989583i	0.425093	−	0.905150i	$-0.360241\pi$
$194$	4.79150	−	8.29913i	0.344010	−	0.595843i
$195$	−10.5830			−0.757865
$196$	−3.50000	+	6.06218i	−0.250000	+	0.433013i
$197$	−9.87451			−0.703530			−0.351765	−	0.936088i	$-0.614418\pi$
$197$	−9.87451			−0.703530			−0.351765	+	0.936088i	$0.614418\pi$
$198$	0.500000	−	0.866025i	0.0355335	−	0.0615457i
$199$	−11.5830	−	20.0624i	−0.821097	−	1.42218i	−0.904866	−	0.425697i	$-0.860029\pi$
$199$	−11.5830	−	20.0624i	−0.821097	−	1.42218i	0.0837682	−	0.996485i	$-0.473304\pi$
$200$	1.00000	+	1.73205i	0.0707107	+	0.122474i
$201$	−6.79150	+	11.7632i	−0.479036	+	0.829714i
$202$	3.29150			0.231589
$203$	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
$211$	10.7085			0.737203			0.368602	−	0.929587i	$-0.379837\pi$
$211$	10.7085			0.737203			0.368602	+	0.929587i	$0.379837\pi$
$212$	−2.00000	+	3.46410i	−0.137361	+	0.237915i
$213$	−6.64575	−	11.5108i	−0.455359	−	0.788706i
$214$	4.50000	+	7.79423i	0.307614	+	0.532803i
$215$	−1.70850	+	2.95920i	−0.116519	+	0.201816i
$216$	1.00000			0.0680414
$217$	10.5830			0.718421
$218$	−11.9373			−0.808493
$219$	−2.35425	+	4.07768i	−0.159085	+	0.275544i
$220$	1.32288	+	2.29129i	0.0891883	+	0.154479i
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$	4.64575	−	8.04668i	0.311802	−	0.540058i
$223$	−24.4575			−1.63780			−0.818898	−	0.573939i	$-0.805415\pi$
$223$	−24.4575			−1.63780			−0.818898	+	0.573939i	$0.805415\pi$
$224$	2.64575			0.176777
$225$	2.00000			0.133333
$226$	−4.29150	+	7.43310i	−0.285467	+	0.494442i
$227$	−11.7915	−	20.4235i	−0.782630	−	1.35555i	−0.930405	−	0.366533i	$-0.880545\pi$
$227$	−11.7915	−	20.4235i	−0.782630	−	1.35555i	0.147775	−	0.989021i	$-0.452789\pi$
$228$	−2.64575	−	4.58258i	−0.175219	−	0.303488i
$229$	−8.64575	+	14.9749i	−0.571327	+	0.989568i	0.425103	+	0.905145i	$0.360238\pi$
$229$	−8.64575	+	14.9749i	−0.571327	+	0.989568i	−0.996430	+	0.0844228i	$0.973095\pi$
$230$	7.00000			0.461566
$231$	−1.32288	−	2.29129i	−0.0870388	−	0.150756i
$232$	−2.00000			−0.131306
$233$	11.0830	−	19.1963i	0.726072	−	1.25759i	−0.232460	−	0.972606i	$-0.574677\pi$
$233$	11.0830	−	19.1963i	0.726072	−	1.25759i	0.958531	−	0.284987i	$-0.0919894\pi$
$234$	−2.00000	−	3.46410i	−0.130744	−	0.226455i
$235$	15.7915	+	27.3517i	1.03012	+	1.78423i
$236$	7.29150	−	12.6293i	0.474636	−	0.822094i
$237$	−5.35425			−0.347796
$238$	3.96863	−	6.87386i	0.257248	−	0.445566i
$239$	13.2915			0.859756			0.429878	−	0.902887i	$-0.358557\pi$
$239$	13.2915			0.859756			0.429878	+	0.902887i	$0.358557\pi$
$240$	−1.32288	+	2.29129i	−0.0853913	+	0.147902i
$241$	−7.58301	−	13.1342i	−0.488464	−	0.846045i	0.511448	−	0.859314i	$-0.329109\pi$
$241$	−7.58301	−	13.1342i	−0.488464	−	0.846045i	−0.999912	+	0.0132694i	$0.995776\pi$
$242$	0.500000	+	0.866025i	0.0321412	+	0.0556702i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−3.93725			−0.252057
$245$	−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
$249$	−2.79150	−	4.83502i	−0.176904	−	0.306407i
$250$	3.96863	−	6.87386i	0.250998	−	0.434741i
$251$	12.7085			0.802153			0.401077	−	0.916045i	$-0.368636\pi$
$251$	12.7085			0.802153			0.401077	+	0.916045i	$0.368636\pi$
$252$	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
$257$	0.645751	−	1.11847i	0.0402809	−	0.0697685i	−0.845182	−	0.534478i	$-0.820508\pi$
$257$	0.645751	−	1.11847i	0.0402809	−	0.0697685i	0.885463	+	0.464710i	$0.153841\pi$
$258$	−1.29150			−0.0804054
$259$	−12.2915	−	21.2895i	−0.763757	−	1.32287i
$260$	10.5830			0.656330
$261$	−1.00000	+	1.73205i	−0.0618984	+	0.107211i
$262$	1.29150	+	2.23695i	0.0797893	+	0.138199i
$263$	4.93725	+	8.55157i	0.304444	+	0.527313i	0.977137	−	0.212609i	$-0.0681960\pi$
$263$	4.93725	+	8.55157i	0.304444	+	0.527313i	−0.672693	+	0.739921i	$0.734863\pi$
$264$	−0.500000	+	0.866025i	−0.0307729	+	0.0533002i
$265$	−10.5830			−0.650109
$266$	−14.0000			−0.858395
$267$	−13.2915			−0.813427
$268$	6.79150	−	11.7632i	0.414857	−	0.718553i
$269$	2.67712	+	4.63692i	0.163227	+	0.282718i	0.936024	−	0.351935i	$-0.114476\pi$
$269$	2.67712	+	4.63692i	0.163227	+	0.282718i	−0.772797	+	0.634653i	$0.781143\pi$
$270$	1.32288	+	2.29129i	0.0805076	+	0.139443i
$271$	0.645751	−	1.11847i	0.0392266	−	0.0679425i	−0.845746	−	0.533586i	$-0.820844\pi$
$271$	0.645751	−	1.11847i	0.0392266	−	0.0679425i	0.884972	+	0.465644i	$0.154177\pi$
$272$	−3.00000			−0.181902
$273$	−10.5830			−0.640513
$274$	2.70850			0.163626
$275$	−1.00000	+	1.73205i	−0.0603023	+	0.104447i
$276$	1.32288	+	2.29129i	0.0796278	+	0.137919i
$277$	−12.5830	−	21.7944i	−0.756040	−	1.30950i	−0.944856	−	0.327486i	$-0.893798\pi$
$277$	−12.5830	−	21.7944i	−0.756040	−	1.30950i	0.188816	−	0.982012i	$-0.439535\pi$
$278$	4.29150	−	7.43310i	0.257387	−	0.445808i
$279$	−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	$0.528521\pi$
$282$	−5.96863	+	10.3380i	−0.355427	+	0.615617i
$283$	11.2288	+	19.4488i	0.667480	+	1.15611i	0.978606	+	0.205741i	$0.0659605\pi$
$283$	11.2288	+	19.4488i	0.667480	+	1.15611i	−0.311126	+	0.950369i	$0.600706\pi$
$284$	6.64575	+	11.5108i	0.394353	+	0.683039i
$285$	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
$291$	4.79150	+	8.29913i	0.280883	+	0.486503i
$292$	2.35425	−	4.07768i	0.137772	−	0.238628i
$293$	6.58301			0.384583			0.192292	−	0.981338i	$-0.438408\pi$
$293$	6.58301			0.384583			0.192292	+	0.981338i	$0.438408\pi$
$294$	−3.50000	−	6.06218i	−0.204124	−	0.353553i
$295$	38.5830			2.24639
$296$	−4.64575	+	8.04668i	−0.270029	+	0.467704i
$297$	0.500000	+	0.866025i	0.0290129	+	0.0502519i
$298$	−5.93725	−	10.2836i	−0.343936	−	0.595714i
$299$	5.29150	−	9.16515i	0.306015	−	0.530034i
$300$	−2.00000			−0.115470
$301$	−1.70850	+	2.95920i	−0.0984762	+	0.170566i
$302$	−17.3542			−0.998625
$303$	−1.64575	+	2.85052i	−0.0945459	+	0.163758i
$304$	2.64575	+	4.58258i	0.151744	+	0.262829i
$305$	−5.20850	−	9.02138i	−0.298238	−	0.516563i
$306$	−1.50000	+	2.59808i	−0.0857493	+	0.148522i
$307$	−32.5830			−1.85961			−0.929805	−	0.368052i	$-0.880025\pi$
$307$	−32.5830			−1.85961			−0.929805	+	0.368052i	$0.880025\pi$
$308$	1.32288	+	2.29129i	0.0753778	+	0.130558i
$309$	10.0000			0.568880
$310$	5.29150	−	9.16515i	0.300537	−	0.520546i
$311$	7.26013	+	12.5749i	0.411684	+	0.713058i	0.995074	−	0.0991343i	$-0.0316074\pi$
$311$	7.26013	+	12.5749i	0.411684	+	0.713058i	−0.583390	+	0.812192i	$0.698274\pi$
$312$	2.00000	+	3.46410i	0.113228	+	0.196116i
$313$	−0.291503	+	0.504897i	−0.0164767	+	0.0285385i	−0.874146	−	0.485663i	$-0.838578\pi$
$313$	−0.291503	+	0.504897i	−0.0164767	+	0.0285385i	0.857669	+	0.514201i	$0.171912\pi$
$314$	11.2915			0.637216
$315$	7.00000			0.394405
$316$	5.35425			0.301200
$317$	8.61438	−	14.9205i	0.483832	−	0.838021i	−0.515996	−	0.856591i	$-0.672578\pi$
$317$	8.61438	−	14.9205i	0.483832	−	0.838021i	0.999828	+	0.0185700i	$0.00591136\pi$
$318$	−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
$326$	7.79150	+	13.4953i	0.431531	+	0.747434i
$327$	5.96863	−	10.3380i	0.330066	−	0.571691i
$328$	−9.00000			−0.496942
$329$	15.7915	+	27.3517i	0.870614	+	1.50795i
$330$	−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	$0.282960\pi$
$332$	2.79150	+	4.83502i	0.153204	+	0.265356i
$333$	4.64575	+	8.04668i	0.254586	+	0.440955i
$334$	9.64575	−	16.7069i	0.527792	−	0.914163i
$335$	35.9373			1.96346
$336$	−1.32288	+	2.29129i	−0.0721688	+	0.125000i
$337$	17.2915			0.941928			0.470964	−	0.882152i	$-0.343906\pi$
$337$	17.2915			0.941928			0.470964	+	0.882152i	$0.343906\pi$
$338$	1.50000	−	2.59808i	0.0815892	−	0.141317i
$339$	−4.29150	−	7.43310i	−0.233082	−	0.403711i
$340$	−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
$344$	1.29150			0.0696332
$345$	−3.50000	+	6.06218i	−0.188434	+	0.326377i
$346$	2.00000	+	3.46410i	0.107521	+	0.186231i
$347$	−4.20850	−	7.28933i	−0.225924	−	0.391312i	0.730672	−	0.682728i	$-0.239207\pi$
$347$	−4.20850	−	7.28933i	−0.225924	−	0.391312i	−0.956596	+	0.291417i	$0.905873\pi$
$348$	1.00000	−	1.73205i	0.0536056	−	0.0928477i
$349$	13.2288			0.708119			0.354060	−	0.935223i	$-0.384801\pi$
$349$	13.2288			0.708119			0.354060	+	0.935223i	$0.384801\pi$
$350$	−2.64575	+	4.58258i	−0.141421	+	0.244949i
$351$	4.00000			0.213504
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	6.35425	+	11.0059i	0.338203	+	0.585784i	0.984095	−	0.177645i	$-0.0568478\pi$
$353$	6.35425	+	11.0059i	0.338203	+	0.585784i	−0.645892	+	0.763429i	$0.723514\pi$
$354$	7.29150	+	12.6293i	0.387539	+	0.671237i
$355$	−17.5830	+	30.4547i	−0.933209	+	1.61637i
$356$	13.2915			0.704448
$357$	3.96863	+	6.87386i	0.210042	+	0.363803i
$358$	−15.2915			−0.808181
$359$	0.291503	−	0.504897i	0.0153849	−	0.0266475i	−0.858230	−	0.513265i	$-0.828436\pi$
$359$	0.291503	−	0.504897i	0.0153849	−	0.0266475i	0.873615	+	0.486617i	$0.161769\pi$
$360$	−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
$365$	12.4575			0.652056
$366$	1.96863	−	3.40976i	0.102902	−	0.178231i
$367$	−10.6458	−	18.4390i	−0.555704	−	0.962507i	−0.997848	−	0.0655633i	$-0.979116\pi$
$367$	−10.6458	−	18.4390i	−0.555704	−	0.962507i	0.442145	−	0.896944i	$-0.354218\pi$
$368$	−1.32288	−	2.29129i	−0.0689597	−	0.119442i
$369$	−4.50000	+	7.79423i	−0.234261	+	0.405751i
$370$	−24.5830			−1.27801
$371$	−10.5830			−0.549442
$372$	4.00000			0.207390
$373$	−15.9059	+	27.5498i	−0.823575	+	1.42647i	0.0794280	+	0.996841i	$0.474691\pi$
$373$	−15.9059	+	27.5498i	−0.823575	+	1.42647i	−0.903003	+	0.429634i	$0.858643\pi$
$374$	−1.50000	−	2.59808i	−0.0775632	−	0.134343i
$375$	3.96863	+	6.87386i	0.204939	+	0.354965i
$376$	5.96863	−	10.3380i	0.307808	−	0.533140i
$377$	−8.00000			−0.412021
$378$	1.32288	+	2.29129i	0.0680414	+	0.117851i
$379$	−6.41699			−0.329619			−0.164809	−	0.986325i	$-0.552701\pi$
$379$	−6.41699			−0.329619			−0.164809	+	0.986325i	$0.552701\pi$
$380$	−7.00000	+	12.1244i	−0.359092	+	0.621966i
$381$	−1.32288	−	2.29129i	−0.0677730	−	0.117386i
$382$	8.64575	+	14.9749i	0.442355	+	0.766182i
$383$	−14.6458	+	25.3672i	−0.748363	+	1.29620i	0.200244	+	0.979746i	$0.435826\pi$
$383$	−14.6458	+	25.3672i	−0.748363	+	1.29620i	−0.948607	+	0.316457i	$0.897507\pi$
$384$	1.00000			0.0510310
$385$	−3.50000	+	6.06218i	−0.178377	+	0.308957i
$386$	−15.8745			−0.807991
$387$	0.645751	−	1.11847i	0.0328254	−	0.0568552i
$388$	−4.79150	−	8.29913i	−0.243252	−	0.421324i
$389$	−8.03137	−	13.9107i	−0.407207	−	0.705303i	0.587369	−	0.809319i	$-0.300164\pi$
$389$	−8.03137	−	13.9107i	−0.407207	−	0.705303i	−0.994576	+	0.104017i	$0.966830\pi$
$390$	−5.29150	+	9.16515i	−0.267946	+	0.464095i
$391$	−7.93725			−0.401404
$392$	3.50000	+	6.06218i	0.176777	+	0.306186i
$393$	−2.58301			−0.130295
$394$	−4.93725	+	8.55157i	−0.248735	+	0.430822i
$395$	7.08301	+	12.2681i	0.356385	+	0.617276i
$396$	−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	$0.214776\pi$
$398$	−23.1660			−1.16121
$399$	7.00000	−	12.1244i	0.350438	−	0.606977i
$400$	2.00000			0.100000
$401$	2.06275	−	3.57278i	0.103009	−	0.178416i	−0.809914	−	0.586548i	$-0.800486\pi$
$401$	2.06275	−	3.57278i	0.103009	−	0.178416i	0.912923	+	0.408132i	$0.133820\pi$
$402$	6.79150	+	11.7632i	0.338729	+	0.586696i
$403$	−8.00000	−	13.8564i	−0.398508	−	0.690237i
$404$	1.64575	−	2.85052i	0.0818792	−	0.141819i
$405$	−2.64575			−0.131468
$406$	−2.64575	−	4.58258i	−0.131306	−	0.227429i
$407$	−9.29150			−0.460563
$408$	1.50000	−	2.59808i	0.0742611	−	0.128624i
$409$	−2.06275	−	3.57278i	−0.101996	−	0.176663i	0.810511	−	0.585724i	$-0.199190\pi$
$409$	−2.06275	−	3.57278i	−0.101996	−	0.176663i	−0.912507	+	0.409061i	$0.865856\pi$
$410$	−11.9059	−	20.6216i	−0.587990	−	1.01843i
$411$	−1.35425	+	2.34563i	−0.0668002	+	0.115701i
$412$	−10.0000			−0.492665
$413$	38.5830			1.89855
$414$	−2.64575			−0.130032
$415$	−7.38562	+	12.7923i	−0.362546	+	0.627948i
$416$	−2.00000	−	3.46410i	−0.0980581	−	0.169842i
$417$	4.29150	+	7.43310i	0.210156	+	0.364001i
$418$	−2.64575	+	4.58258i	−0.129408	+	0.224141i
$419$	21.8745			1.06864			0.534320	−	0.845282i	$-0.320568\pi$
$419$	21.8745			1.06864			0.534320	+	0.845282i	$0.320568\pi$
$420$	−7.00000			−0.341565
$421$	37.8745			1.84589			0.922945	−	0.384931i	$-0.125775\pi$
$421$	37.8745			1.84589			0.922945	+	0.384931i	$0.125775\pi$
$422$	5.35425	−	9.27383i	0.260641	−	0.451443i
$423$	−5.96863	−	10.3380i	−0.290205	−	0.502649i
$424$	2.00000	+	3.46410i	0.0971286	+	0.168232i
$425$	3.00000	−	5.19615i	0.145521	−	0.252050i
$426$	−13.2915			−0.643975
$427$	−5.20850	−	9.02138i	−0.252057	−	0.436575i
$428$	9.00000			0.435031
$429$	−2.00000	+	3.46410i	−0.0965609	+	0.167248i
$430$	1.70850	+	2.95920i	0.0823911	+	0.142706i
$431$	3.35425	+	5.80973i	0.161568	+	0.279845i	0.935431	−	0.353508i	$-0.115011\pi$
$431$	3.35425	+	5.80973i	0.161568	+	0.279845i	−0.773863	+	0.633353i	$0.781678\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−19.5830			−0.941099			−0.470550	−	0.882374i	$-0.655944\pi$
$433$	−19.5830			−0.941099			−0.470550	+	0.882374i	$0.655944\pi$
$434$	5.29150	−	9.16515i	0.254000	−	0.439941i
$435$	5.29150			0.253708
$436$	−5.96863	+	10.3380i	−0.285845	+	0.495099i
$437$	7.00000	+	12.1244i	0.334855	+	0.579987i
$438$	2.35425	+	4.07768i	0.112490	+	0.194839i
$439$	7.32288	−	12.6836i	0.349502	−	0.605355i	−0.636659	−	0.771145i	$-0.719684\pi$
$439$	7.32288	−	12.6836i	0.349502	−	0.605355i	0.986161	+	0.165790i	$0.0530175\pi$
$440$	2.64575			0.126131
$441$	7.00000			0.333333
$442$	−12.0000			−0.570782
$443$	−5.58301	+	9.67005i	−0.265257	+	0.459438i	−0.967631	−	0.252370i	$-0.918790\pi$
$443$	−5.58301	+	9.67005i	−0.265257	+	0.459438i	0.702374	+	0.711808i	$0.252123\pi$
$444$	−4.64575	−	8.04668i	−0.220478	−	0.381878i
$445$	17.5830	+	30.4547i	0.833514	+	1.44369i
$446$	−12.2288	+	21.1808i	−0.579048	+	1.00294i
$447$	11.8745			0.561645
$448$	1.32288	−	2.29129i	0.0625000	−	0.108253i
$449$	−22.4575			−1.05984			−0.529918	−	0.848049i	$-0.677777\pi$
$449$	−22.4575			−1.05984			−0.529918	+	0.848049i	$0.677777\pi$
$450$	1.00000	−	1.73205i	0.0471405	−	0.0816497i
$451$	−4.50000	−	7.79423i	−0.211897	−	0.367016i
$452$	4.29150	+	7.43310i	0.201855	+	0.349624i
$453$	8.67712	−	15.0292i	0.407687	−	0.706134i
$454$	−23.5830			−1.10681
$455$	14.0000	+	24.2487i	0.656330	+	1.13680i
$456$	−5.29150			−0.247797
$457$	9.70850	−	16.8156i	0.454144	−	0.786601i	−0.544494	−	0.838765i	$-0.683278\pi$
$457$	9.70850	−	16.8156i	0.454144	−	0.786601i	0.998639	+	0.0521635i	$0.0166117\pi$
$458$	8.64575	+	14.9749i	0.403989	+	0.699730i
$459$	−1.50000	−	2.59808i	−0.0700140	−	0.121268i
$460$	3.50000	−	6.06218i	0.163188	−	0.282650i
$461$	−3.41699			−0.159145			−0.0795727	−	0.996829i	$-0.525356\pi$
$461$	−3.41699			−0.159145			−0.0795727	+	0.996829i	$0.525356\pi$
$462$	−2.64575			−0.123091
$463$	−35.0405			−1.62847			−0.814235	−	0.580535i	$-0.802844\pi$
$463$	−35.0405			−1.62847			−0.814235	+	0.580535i	$0.802844\pi$
$464$	−1.00000	+	1.73205i	−0.0464238	+	0.0804084i
$465$	5.29150	+	9.16515i	0.245388	+	0.425024i
$466$	−11.0830	−	19.1963i	−0.513410	−	0.889253i
$467$	−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
$469$	35.9373			1.65943
$470$	31.5830			1.45682
$471$	−5.64575	+	9.77873i	−0.260142	+	0.450580i
$472$	−7.29150	−	12.6293i	−0.335619	−	0.581308i
$473$	0.645751	+	1.11847i	0.0296917	+	0.0514275i
$474$	−2.67712	+	4.63692i	−0.122964	+	0.212981i
$475$	−10.5830			−0.485582
$476$	−3.96863	−	6.87386i	−0.181902	−	0.315063i
$477$	4.00000			0.183147
$478$	6.64575	−	11.5108i	0.303970	−	0.526491i
$479$	1.06275	+	1.84073i	0.0485581	+	0.0841051i	0.889283	−	0.457358i	$-0.151204\pi$
$479$	1.06275	+	1.84073i	0.0485581	+	0.0841051i	−0.840725	+	0.541463i	$0.817871\pi$
$480$	1.32288	+	2.29129i	0.0603807	+	0.104583i
$481$	−18.5830	+	32.1867i	−0.847312	+	1.46759i
$482$	−15.1660			−0.690793
$483$	−3.50000	+	6.06218i	−0.159256	+	0.275839i
$484$	1.00000			0.0454545
$485$	12.6771	−	21.9574i	0.575639	−	0.997035i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	4.93725	+	8.55157i	0.223728	+	0.387509i	0.955937	−	0.293571i	$-0.0948438\pi$
$487$	4.93725	+	8.55157i	0.223728	+	0.387509i	−0.732209	+	0.681080i	$0.761510\pi$
$488$	−1.96863	+	3.40976i	−0.0891156	+	0.154353i
$489$	−15.5830			−0.704688
$490$	−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
$497$	−17.5830	+	30.4547i	−0.788706	+	1.36608i
$498$	−5.58301			−0.250180
$499$	−1.29150	+	2.23695i	−0.0578156	+	0.100140i	−0.893485	−	0.449094i	$-0.851747\pi$
$499$	−1.29150	+	2.23695i	−0.0578156	+	0.100140i	0.835669	+	0.549233i	$0.185080\pi$
$500$	−3.96863	−	6.87386i	−0.177482	−	0.307409i
$501$	9.64575	+	16.7069i	0.430940	+	0.746411i
$502$	6.35425	−	11.0059i	0.283604	−	0.491217i
$503$	9.29150			0.414288			0.207144	−	0.978311i	$-0.433583\pi$
$503$	9.29150			0.414288			0.207144	+	0.978311i	$0.433583\pi$
$504$	−1.32288	−	2.29129i	−0.0589256	−	0.102062i
$505$	8.70850			0.387523
$506$	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
$509$	8.58301	−	14.8662i	0.380435	−	0.658933i	−0.610689	−	0.791870i	$-0.709108\pi$
$509$	8.58301	−	14.8662i	0.380435	−	0.658933i	0.991124	+	0.132937i	$0.0424409\pi$
$510$	7.93725			0.351468
$511$	12.4575			0.551088
$512$	−1.00000			−0.0441942
$513$	−2.64575	+	4.58258i	−0.116813	+	0.202326i
$514$	−0.645751	−	1.11847i	−0.0284829	−	0.0493338i
$515$	−13.2288	−	22.9129i	−0.582929	−	1.00966i
$516$	−0.645751	+	1.11847i	−0.0284276	+	0.0492381i
$517$	11.9373			0.525000
$518$	−24.5830			−1.08012
$519$	−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
$523$	−6.64575	+	11.5108i	−0.290598	+	0.503331i	−0.973951	−	0.226757i	$-0.927188\pi$
$523$	−6.64575	+	11.5108i	−0.290598	+	0.503331i	0.683353	+	0.730088i	$0.260521\pi$
$524$	2.58301			0.112839
$525$	−2.64575	−	4.58258i	−0.115470	−	0.200000i
$526$	9.87451			0.430549
$527$	−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
$531$	−14.5830			−0.632849
$532$	−7.00000	+	12.1244i	−0.303488	+	0.525657i
$533$	−36.0000			−1.55933
$534$	−6.64575	+	11.5108i	−0.287590	+	0.498120i
$535$	11.9059	+	20.6216i	0.514736	+	0.891549i
$536$	−6.79150	−	11.7632i	−0.293348	−	0.508094i
$537$	7.64575	−	13.2428i	0.329939	−	0.571470i
$538$	5.35425			0.230838
$539$	−3.50000	+	6.06218i	−0.150756	+	0.261116i
$540$	2.64575			0.113855
$541$	21.9059	−	37.9421i	0.941807	−	1.63126i	0.179787	−	0.983706i	$-0.442459\pi$
$541$	21.9059	−	37.9421i	0.941807	−	1.63126i	0.762021	−	0.647553i	$-0.224207\pi$
$542$	−0.645751	−	1.11847i	−0.0277374	−	0.0480426i
$543$	2.64575	+	4.58258i	0.113540	+	0.196657i
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$	−31.5830			−1.35287
$546$	−5.29150	+	9.16515i	−0.226455	+	0.392232i
$547$	25.2915			1.08139			0.540693	−	0.841220i	$-0.318162\pi$
$547$	25.2915			1.08139			0.540693	+	0.841220i	$0.318162\pi$
$548$	1.35425	−	2.34563i	0.0578506	−	0.100200i
$549$	1.96863	+	3.40976i	0.0840190	+	0.145525i
$550$	1.00000	+	1.73205i	0.0426401	+	0.0738549i
$551$	5.29150	−	9.16515i	0.225426	−	0.390449i
$552$	2.64575			0.112611
$553$	7.08301	+	12.2681i	0.301200	+	0.521694i
$554$	−25.1660			−1.06920
$555$	12.2915	−	21.2895i	0.521745	−	0.903689i
$556$	−4.29150	−	7.43310i	−0.182000	−	0.315234i
$557$	4.35425	+	7.54178i	0.184495	+	0.319555i	0.943406	−	0.331639i	$-0.107602\pi$
$557$	4.35425	+	7.54178i	0.184495	+	0.319555i	−0.758911	+	0.651194i	$0.774268\pi$
$558$	−2.00000	+	3.46410i	−0.0846668	+	0.146647i
$559$	5.16601			0.218499
$560$	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	$0.833333\pi$
$564$	5.96863	+	10.3380i	0.251325	+	0.435307i
$565$	−11.3542	+	19.6661i	−0.477677	+	0.827361i
$566$	22.4575			0.943960
$567$	−2.64575			−0.111111
$568$	13.2915			0.557699
$569$	−13.5830	+	23.5265i	−0.569429	+	0.986280i	0.427193	+	0.904160i	$0.359502\pi$
$569$	−13.5830	+	23.5265i	−0.569429	+	0.986280i	−0.996622	+	0.0821200i	$0.973831\pi$
$570$	−7.00000	−	12.1244i	−0.293198	−	0.507833i
$571$	−16.8745	−	29.2275i	−0.706176	−	1.22313i	−0.966265	−	0.257548i	$-0.917085\pi$
$571$	−16.8745	−	29.2275i	−0.706176	−	1.22313i	0.260089	−	0.965585i	$-0.416248\pi$
$572$	2.00000	−	3.46410i	0.0836242	−	0.144841i
$573$	−17.2915			−0.722363
$574$	−11.9059	−	20.6216i	−0.496942	−	0.860729i
$575$	5.29150			0.220671
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	20.3745	+	35.2897i	0.848202	+	1.46913i	0.882811	+	0.469728i	$0.155648\pi$
$577$	20.3745	+	35.2897i	0.848202	+	1.46913i	−0.0346094	+	0.999401i	$0.511019\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$	7.93725	−	13.7477i	0.329861	−	0.571336i
$580$	−5.29150			−0.219718
$581$	−7.38562	+	12.7923i	−0.306407	+	0.530713i
$582$	9.58301			0.397228
$583$	−2.00000	+	3.46410i	−0.0828315	+	0.143468i
$584$	−2.35425	−	4.07768i	−0.0974195	−	0.168736i
$585$	−5.29150	−	9.16515i	−0.218777	−	0.378932i
$586$	3.29150	−	5.70105i	0.135971	−	0.235508i
$587$	−21.8745			−0.902858			−0.451429	−	0.892307i	$-0.649086\pi$
$587$	−21.8745			−0.902858			−0.451429	+	0.892307i	$0.649086\pi$
$588$	−7.00000			−0.288675
$589$	21.1660			0.872130
$590$	19.2915	−	33.4139i	0.794219	−	1.37563i
$591$	−4.93725	−	8.55157i	−0.203091	−	0.351765i
$592$	4.64575	+	8.04668i	0.190939	+	0.330716i
$593$	−18.8745	+	32.6916i	−0.775083	+	1.34248i	0.159665	+	0.987171i	$0.448959\pi$
$593$	−18.8745	+	32.6916i	−0.775083	+	1.34248i	−0.934748	+	0.355312i	$0.884375\pi$
$594$	1.00000			0.0410305
$595$	10.5000	−	18.1865i	0.430458	−	0.745575i
$596$	−11.8745			−0.486399
$597$	11.5830	−	20.0624i	0.474061	−	0.821097i
$598$	−5.29150	−	9.16515i	−0.216386	−	0.374791i
$599$	−17.3229	−	30.0041i	−0.707794	−	1.22593i	−0.965674	−	0.259757i	$-0.916357\pi$
$599$	−17.3229	−	30.0041i	−0.707794	−	1.22593i	0.257880	−	0.966177i	$-0.416976\pi$
$600$	−1.00000	+	1.73205i	−0.0408248	+	0.0707107i
$601$	−17.4170			−0.710454			−0.355227	−	0.934780i	$-0.615596\pi$
$601$	−17.4170			−0.710454			−0.355227	+	0.934780i	$0.615596\pi$
$602$	1.70850	+	2.95920i	0.0696332	+	0.120608i
$603$	−13.5830			−0.553143
$604$	−8.67712	+	15.0292i	−0.353067	+	0.611530i
$605$	1.32288	+	2.29129i	0.0537825	+	0.0931541i
$606$	1.64575	+	2.85052i	0.0668541	+	0.115795i
$607$	−22.5516	+	39.0606i	−0.915343	+	1.58542i	−0.108943	+	0.994048i	$0.534747\pi$
$607$	−22.5516	+	39.0606i	−0.915343	+	1.58542i	−0.806399	+	0.591372i	$0.798587\pi$
$608$	5.29150			0.214599
$609$	5.29150			0.214423
$610$	−10.4170			−0.421772
$611$	23.8745	−	41.3519i	0.965859	−	1.67292i
$612$	1.50000	+	2.59808i	0.0606339	+	0.105021i
$613$	19.9059	+	34.4780i	0.803991	+	1.39255i	0.916970	+	0.398956i	$0.130627\pi$
$613$	19.9059	+	34.4780i	0.803991	+	1.39255i	−0.112979	+	0.993597i	$0.536039\pi$
$614$	−16.2915	+	28.2177i	−0.657472	+	1.13877i
$615$	23.8118			0.960183
$616$	2.64575			0.106600
$617$	−25.2915			−1.01820			−0.509099	−	0.860708i	$-0.670021\pi$
$617$	−25.2915			−1.01820			−0.509099	+	0.860708i	$0.670021\pi$
$618$	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
$622$	14.5203			0.582209
$623$	17.5830	+	30.4547i	0.704448	+	1.22014i
$624$	4.00000			0.160128
$625$	15.5000	−	26.8468i	0.620000	−	1.07387i
$626$	0.291503	+	0.504897i	0.0116508	+	0.0201798i
$627$	−2.64575	−	4.58258i	−0.105661	−	0.183010i
$628$	5.64575	−	9.77873i	0.225290	−	0.390214i
$629$	27.8745			1.11143
$630$	3.50000	−	6.06218i	0.139443	−	0.241523i
$631$	10.1255			0.403089			0.201545	−	0.979479i	$-0.435404\pi$
$631$	10.1255			0.403089			0.201545	+	0.979479i	$0.435404\pi$
$632$	2.67712	−	4.63692i	0.106490	−	0.184447i
$633$	5.35425	+	9.27383i	0.212812	+	0.368602i
$634$	−8.61438	−	14.9205i	−0.342121	−	0.592570i
$635$	−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
$639$	6.64575	−	11.5108i	0.262902	−	0.455359i
$640$	−1.32288	−	2.29129i	−0.0522913	−	0.0905711i
$641$	2.70850	+	4.69126i	0.106979	+	0.185293i	0.914545	−	0.404484i	$-0.132549\pi$
$641$	2.70850	+	4.69126i	0.106979	+	0.185293i	−0.807566	+	0.589777i	$0.799216\pi$
$642$	−4.50000	+	7.79423i	−0.177601	+	0.307614i
$643$	41.1660			1.62343			0.811714	−	0.584054i	$-0.198535\pi$
$643$	41.1660			1.62343			0.811714	+	0.584054i	$0.198535\pi$
$644$	3.50000	−	6.06218i	0.137919	−	0.238883i
$645$	−3.41699			−0.134544
$646$	7.93725	−	13.7477i	0.312287	−	0.540897i
$647$	−21.1974	−	36.7149i	−0.833355	−	1.44341i	−0.895363	−	0.445338i	$-0.853084\pi$
$647$	−21.1974	−	36.7149i	−0.833355	−	1.44341i	0.0620075	−	0.998076i	$-0.480250\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	7.29150	−	12.6293i	0.286217	−	0.495742i
$650$	8.00000			0.313786
$651$	5.29150	+	9.16515i	0.207390	+	0.359211i
$652$	15.5830			0.610278
$653$	−6.55163	+	11.3478i	−0.256385	+	0.444072i	−0.965271	−	0.261251i	$-0.915865\pi$
$653$	−6.55163	+	11.3478i	−0.256385	+	0.444072i	0.708886	+	0.705323i	$0.249198\pi$
$654$	−5.96863	−	10.3380i	−0.233392	−	0.404246i
$655$	3.41699	+	5.91841i	0.133513	+	0.231251i
$656$	−4.50000	+	7.79423i	−0.175695	+	0.304314i
$657$	−4.70850			−0.183696
$658$	31.5830			1.23123
$659$	18.1660			0.707647			0.353824	−	0.935312i	$-0.384881\pi$
$659$	18.1660			0.707647			0.353824	+	0.935312i	$0.384881\pi$
$660$	−1.32288	+	2.29129i	−0.0514929	+	0.0891883i
$661$	−15.6458	−	27.0992i	−0.608549	−	1.05404i	−0.991480	−	0.130261i	$-0.958418\pi$
$661$	−15.6458	−	27.0992i	−0.608549	−	1.05404i	0.382931	−	0.923777i	$-0.374915\pi$
$662$	6.50000	+	11.2583i	0.252630	+	0.437567i
$663$	6.00000	−	10.3923i	0.233021	−	0.403604i
$664$	5.58301			0.216663
$665$	−37.0405			−1.43637
$666$	9.29150			0.360038
$667$	−2.64575	+	4.58258i	−0.102444	+	0.177438i
$668$	−9.64575	−	16.7069i	−0.373205	−	0.646411i
$669$	−12.2288	−	21.1808i	−0.472791	−	0.818898i
$670$	17.9686	−	31.1226i	0.694189	−	1.20237i
$671$	−3.93725			−0.151996
$672$	1.32288	+	2.29129i	0.0510310	+	0.0883883i
$673$	−40.5830			−1.56436			−0.782180	−	0.623053i	$-0.785892\pi$
$673$	−40.5830			−1.56436			−0.782180	+	0.623053i	$0.785892\pi$
$674$	8.64575	−	14.9749i	0.333022	−	0.576811i
$675$	1.00000	+	1.73205i	0.0384900	+	0.0666667i
$676$	−1.50000	−	2.59808i	−0.0576923	−	0.0999260i
$677$	19.9373	−	34.5323i	0.766251	−	1.32719i	−0.173332	−	0.984863i	$-0.555453\pi$
$677$	19.9373	−	34.5323i	0.766251	−	1.32719i	0.939583	−	0.342322i	$-0.111213\pi$
$678$	−8.58301			−0.329628
$679$	12.6771	−	21.9574i	0.486503	−	0.842649i
$680$	−7.93725			−0.304380
$681$	11.7915	−	20.4235i	0.451851	−	0.782630i
$682$	−2.00000	−	3.46410i	−0.0765840	−	0.132647i
$683$	−12.5830	−	21.7944i	−0.481475	−	0.833940i	0.518299	−	0.855200i	$-0.326566\pi$
$683$	−12.5830	−	21.7944i	−0.481475	−	0.833940i	−0.999774	+	0.0212600i	$0.993232\pi$
$684$	2.64575	−	4.58258i	0.101163	−	0.175219i
$685$	7.16601			0.273799
$686$	−9.26013	+	16.0390i	−0.353553	+	0.612372i
$687$	−17.2915			−0.659712
$688$	0.645751	−	1.11847i	0.0246190	−	0.0426414i
$689$	8.00000	+	13.8564i	0.304776	+	0.527887i
$690$	3.50000	+	6.06218i	0.133243	+	0.230783i
$691$	14.0830	−	24.3925i	0.535743	−	0.927934i	−0.463384	−	0.886157i	$-0.653365\pi$
$691$	14.0830	−	24.3925i	0.535743	−	0.927934i	0.999127	−	0.0417762i	$-0.0133017\pi$
$692$	4.00000			0.152057
$693$	1.32288	−	2.29129i	0.0502519	−	0.0870388i
$694$	−8.41699			−0.319505
$695$	11.3542	−	19.6661i	0.430691	−	0.745979i
$696$	−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
$699$	22.1660			0.838396
$700$	2.64575	+	4.58258i	0.100000	+	0.173205i
$701$	−10.4575			−0.394975			−0.197487	−	0.980305i	$-0.563278\pi$
$701$	−10.4575			−0.394975			−0.197487	+	0.980305i	$0.563278\pi$
$702$	2.00000	−	3.46410i	0.0754851	−	0.130744i
$703$	−24.5830	−	42.5790i	−0.927166	−	1.60590i
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$	−15.7915	+	27.3517i	−0.594742	+	1.03012i
$706$	12.7085			0.478291
$707$	8.70850			0.327517
$708$	14.5830			0.548063
$709$	23.8745	−	41.3519i	0.896626	−	1.55300i	0.0648467	−	0.997895i	$-0.479344\pi$
$709$	23.8745	−	41.3519i	0.896626	−	1.55300i	0.831779	−	0.555106i	$-0.187322\pi$
$710$	17.5830	+	30.4547i	0.659878	+	1.14294i
$711$	−2.67712	−	4.63692i	−0.100400	−	0.173898i
$712$	6.64575	−	11.5108i	0.249060	−	0.431385i
$713$	−10.5830			−0.396337
$714$	7.93725			0.297044
$715$	10.5830			0.395782
$716$	−7.64575	+	13.2428i	−0.285735	+	0.494908i
$717$	6.64575	+	11.5108i	0.248190	+	0.429878i
$718$	−0.291503	−	0.504897i	−0.0108788	−	0.0188426i
$719$	21.9686	−	38.0508i	0.819292	−	1.41905i	−0.0869134	−	0.996216i	$-0.527700\pi$
$719$	21.9686	−	38.0508i	0.819292	−	1.41905i	0.906205	−	0.422839i	$-0.138966\pi$
$720$	−2.64575			−0.0986013
$721$	−13.2288	−	22.9129i	−0.492665	−	0.853320i
$722$	−9.00000			−0.334945
$723$	7.58301	−	13.1342i	0.282015	−	0.488464i
$724$	−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
$730$	6.22876	−	10.7885i	0.230537	−	0.399301i
$731$	−1.93725	−	3.35542i	−0.0716519	−	0.124105i
$732$	−1.96863	−	3.40976i	−0.0727625	−	0.126028i
$733$	1.96863	−	3.40976i	0.0727129	−	0.125942i	−0.827377	−	0.561648i	$-0.810168\pi$
$733$	1.96863	−	3.40976i	0.0727129	−	0.125942i	0.900089	+	0.435705i	$0.143501\pi$
$734$	−21.2915			−0.785884
$735$	−9.26013	−	16.0390i	−0.341565	−	0.591608i
$736$	−2.64575			−0.0975237
$737$	6.79150	−	11.7632i	0.250168	−	0.433304i
$738$	4.50000	+	7.79423i	0.165647	+	0.286910i
$739$	1.70850	+	2.95920i	0.0628481	+	0.108856i	0.895737	−	0.444584i	$-0.146648\pi$
$739$	1.70850	+	2.95920i	0.0628481	+	0.108856i	−0.832889	+	0.553440i	$0.813315\pi$
$740$	−12.2915	+	21.2895i	−0.451845	+	0.782618i
$741$	−21.1660			−0.777553
$742$	−5.29150	+	9.16515i	−0.194257	+	0.336463i
$743$	−29.2915			−1.07460			−0.537301	−	0.843391i	$-0.680556\pi$
$743$	−29.2915			−1.07460			−0.537301	+	0.843391i	$0.680556\pi$
$744$	2.00000	−	3.46410i	0.0733236	−	0.127000i
$745$	−15.7085	−	27.2079i	−0.575515	−	0.996821i
$746$	15.9059	+	27.5498i	0.582356	+	1.00867i
$747$	2.79150	−	4.83502i	0.102136	−	0.176904i
$748$	−3.00000			−0.109691
$749$	11.9059	+	20.6216i	0.435031	+	0.753497i
$750$	7.93725			0.289828
$751$	9.35425	−	16.2020i	0.341341	−	0.591221i	−0.643341	−	0.765580i	$-0.722452\pi$
$751$	9.35425	−	16.2020i	0.341341	−	0.591221i	0.984682	+	0.174359i	$0.0557854\pi$
$752$	−5.96863	−	10.3380i	−0.217653	−	0.376987i
$753$	6.35425	+	11.0059i	0.231562	+	0.401077i
$754$	−4.00000	+	6.92820i	−0.145671	+	0.252310i
$755$	−45.9150			−1.67102
$756$	2.64575			0.0962250
$757$	−11.4170			−0.414958			−0.207479	−	0.978240i	$-0.566526\pi$
$757$	−11.4170			−0.414958			−0.207479	+	0.978240i	$0.566526\pi$
$758$	−3.20850	+	5.55728i	−0.116538	+	0.201850i
$759$	1.32288	+	2.29129i	0.0480173	+	0.0831685i
$760$	7.00000	+	12.1244i	0.253917	+	0.439797i
$761$	−13.2085	+	22.8778i	−0.478808	+	0.829319i	−0.999705	−	0.0243003i	$-0.992264\pi$
$761$	−13.2085	+	22.8778i	−0.478808	+	0.829319i	0.520897	+	0.853620i	$0.325598\pi$
$762$	−2.64575			−0.0958455
$763$	−31.5830			−1.14338
$764$	17.2915			0.625585
$765$	−3.96863	+	6.87386i	−0.143486	+	0.248525i
$766$	14.6458	+	25.3672i	0.529173	+	0.916554i
$767$	−29.1660	−	50.5170i	−1.05312	−	1.82406i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−41.2915			−1.48901			−0.744505	−	0.667617i	$-0.767314\pi$
$769$	−41.2915			−1.48901			−0.744505	+	0.667617i	$0.767314\pi$
$770$	3.50000	+	6.06218i	0.126131	+	0.218466i
$771$	1.29150			0.0465123
$772$	−7.93725	+	13.7477i	−0.285668	+	0.494792i
$773$	11.9686	+	20.7303i	0.430482	+	0.745616i	0.996915	−	0.0784917i	$-0.0250104\pi$
$773$	11.9686	+	20.7303i	0.430482	+	0.745616i	−0.566433	+	0.824108i	$0.691677\pi$
$774$	−0.645751	−	1.11847i	−0.0232111	−	0.0402027i
$775$	4.00000	−	6.92820i	0.143684	−	0.248868i
$776$	−9.58301			−0.344010
$777$	12.2915	−	21.2895i	0.440955	−	0.763757i
$778$	−16.0627			−0.575877
$779$	23.8118	−	41.2432i	0.853145	−	1.47769i
$780$	5.29150	+	9.16515i	0.189466	+	0.328165i
$781$	6.64575	+	11.5108i	0.237804	+	0.411888i
$782$	−3.96863	+	6.87386i	−0.141918	+	0.245809i
$783$	−2.00000			−0.0714742
$784$	7.00000			0.250000
$785$	29.8745			1.06627
$786$	−1.29150	+	2.23695i	−0.0460664	+	0.0797893i
$787$	0.645751	+	1.11847i	0.0230185	+	0.0398693i	0.877305	−	0.479933i	$-0.159339\pi$
$787$	0.645751	+	1.11847i	0.0230185	+	0.0398693i	−0.854287	+	0.519802i	$0.826006\pi$
$788$	4.93725	+	8.55157i	0.175882	+	0.304637i
$789$	−4.93725	+	8.55157i	−0.175771	+	0.304444i
$790$	14.1660			0.504004
$791$	−11.3542	+	19.6661i	−0.403711	+	0.699247i
$792$	−1.00000			−0.0355335
$793$	−7.87451	+	13.6390i	−0.279632	+	0.484337i
$794$	3.00000	+	5.19615i	0.106466	+	0.184405i
$795$	−5.29150	−	9.16515i	−0.187670	−	0.325054i
$796$	−11.5830	+	20.0624i	−0.410549	+	0.711091i
$797$	−13.1033			−0.464141			−0.232071	−	0.972699i	$-0.574550\pi$
$797$	−13.1033			−0.464141			−0.232071	+	0.972699i	$0.574550\pi$
$798$	−7.00000	−	12.1244i	−0.247797	−	0.429198i
$799$	−35.8118			−1.26693
$800$	1.00000	−	1.73205i	0.0353553	−	0.0612372i
$801$	−6.64575	−	11.5108i	−0.234816	−	0.406713i
$802$	−2.06275	−	3.57278i	−0.0728381	−	0.126159i
$803$	2.35425	−	4.07768i	0.0830796	−	0.143898i
$804$	13.5830			0.479036
$805$	18.5203			0.652753
$806$	−16.0000			−0.563576
$807$	−2.67712	+	4.63692i	−0.0942392	+	0.163227i
$808$	−1.64575	−	2.85052i	−0.0578973	−	0.100281i
$809$	19.6660	+	34.0625i	0.691420	+	1.19757i	0.971373	+	0.237561i	$0.0763479\pi$
$809$	19.6660	+	34.0625i	0.691420	+	1.19757i	−0.279953	+	0.960014i	$0.590319\pi$
$810$	−1.32288	+	2.29129i	−0.0464811	+	0.0805076i
$811$	−4.58301			−0.160931			−0.0804655	−	0.996757i	$-0.525641\pi$
$811$	−4.58301			−0.160931			−0.0804655	+	0.996757i	$0.525641\pi$
$812$	−5.29150			−0.185695
$813$	1.29150			0.0452950
$814$	−4.64575	+	8.04668i	−0.162833	+	0.282036i
$815$	20.6144	+	35.7052i	0.722090	+	1.25070i
$816$	−1.50000	−	2.59808i	−0.0525105	−	0.0909509i
$817$	−3.41699	+	5.91841i	−0.119546	+	0.207059i
$818$	−4.12549			−0.144244
$819$	−5.29150	−	9.16515i	−0.184900	−	0.320256i
$820$	−23.8118			−0.831543
$821$	−27.1660	+	47.0529i	−0.948100	+	1.64216i	−0.198679	+	0.980065i	$0.563665\pi$
$821$	−27.1660	+	47.0529i	−0.948100	+	1.64216i	−0.749421	+	0.662093i	$0.769668\pi$
$822$	1.35425	+	2.34563i	0.0472348	+	0.0818132i
$823$	21.9373	+	37.9964i	0.764685	+	1.32447i	0.940413	+	0.340034i	$0.110439\pi$
$823$	21.9373	+	37.9964i	0.764685	+	1.32447i	−0.175729	+	0.984439i	$0.556228\pi$
$824$	−5.00000	+	8.66025i	−0.174183	+	0.301694i
$825$	−2.00000			−0.0696311
$826$	19.2915	−	33.4139i	0.671237	−	1.16262i
$827$	−49.3320			−1.71544			−0.857721	−	0.514115i	$-0.828120\pi$
$827$	−49.3320			−1.71544			−0.857721	+	0.514115i	$0.828120\pi$
$828$	−1.32288	+	2.29129i	−0.0459731	+	0.0796278i
$829$	5.93725	+	10.2836i	0.206209	+	0.357165i	0.950517	−	0.310671i	$-0.100554\pi$
$829$	5.93725	+	10.2836i	0.206209	+	0.357165i	−0.744308	+	0.667836i	$0.767221\pi$
$830$	7.38562	+	12.7923i	0.256359	+	0.444026i
$831$	12.5830	−	21.7944i	0.436500	−	0.756040i
$832$	−4.00000			−0.138675
$833$	10.5000	−	18.1865i	0.363803	−	0.630126i
$834$	8.58301			0.297205
$835$	25.5203	−	44.2024i	0.883165	−	1.52969i
$836$	2.64575	+	4.58258i	0.0915052	+	0.158492i
$837$	−2.00000	−	3.46410i	−0.0691301	−	0.119737i
$838$	10.9373	−	18.9439i	0.377821	−	0.654405i
$839$	21.1033			0.728566			0.364283	−	0.931288i	$-0.381314\pi$
$839$	21.1033			0.728566			0.364283	+	0.931288i	$0.381314\pi$
$840$	−3.50000	+	6.06218i	−0.120761	+	0.209165i
$841$	−25.0000			−0.862069
$842$	18.9373	−	32.8003i	0.652621	−	1.13037i
$843$	−1.50000	−	2.59808i	−0.0516627	−	0.0894825i
$844$	−5.35425	−	9.27383i	−0.184301	−	0.319218i
$845$	3.96863	−	6.87386i	0.136525	−	0.236468i
$846$	−11.9373			−0.410411
$847$	1.32288	+	2.29129i	0.0454545	+	0.0787296i
$848$	4.00000			0.137361
$849$	−11.2288	+	19.4488i	−0.385370	+	0.667480i
$850$	−3.00000	−	5.19615i	−0.102899	−	0.178227i
$851$	12.2915	+	21.2895i	0.421347	+	0.729795i
$852$	−6.64575	+	11.5108i	−0.227680	+	0.394353i
$853$	−22.5203			−0.771079			−0.385539	−	0.922691i	$-0.625985\pi$
$853$	−22.5203			−0.771079			−0.385539	+	0.922691i	$0.625985\pi$
$854$	−10.4170			−0.356462
$855$	14.0000			0.478790
$856$	4.50000	−	7.79423i	0.153807	−	0.266401i
$857$	−26.0830	−	45.1771i	−0.890978	−	1.54322i	−0.838704	−	0.544587i	$-0.816686\pi$
$857$	−26.0830	−	45.1771i	−0.890978	−	1.54322i	−0.0522743	−	0.998633i	$-0.516647\pi$
$858$	2.00000	+	3.46410i	0.0682789	+	0.118262i
$859$	7.37451	−	12.7730i	0.251615	−	0.435810i	−0.712356	−	0.701819i	$-0.752372\pi$
$859$	7.37451	−	12.7730i	0.251615	−	0.435810i	0.963971	+	0.266009i	$0.0857050\pi$
$860$	3.41699			0.116519
$861$	23.8118			0.811503
$862$	6.70850			0.228492
$863$	−12.5516	+	21.7401i	−0.427263	+	0.740040i	−0.996629	−	0.0820436i	$-0.973855\pi$
$863$	−12.5516	+	21.7401i	−0.427263	+	0.740040i	0.569366	+	0.822084i	$0.307189\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	5.29150	+	9.16515i	0.179916	+	0.311624i
$866$	−9.79150	+	16.9594i	−0.332729	+	0.576303i
$867$	8.00000			0.271694
$868$	−5.29150	−	9.16515i	−0.179605	−	0.311086i
$869$	5.35425			0.181630
$870$	2.64575	−	4.58258i	0.0896994	−	0.155364i
$871$	−27.1660	−	47.0529i	−0.920485	−	1.59433i
$872$	5.96863	+	10.3380i	0.202123	+	0.350088i
$873$	−4.79150	+	8.29913i	−0.162168	+	0.280883i
$874$	14.0000			0.473557
$875$	10.5000	−	18.1865i	0.354965	−	0.614817i
$876$	4.70850			0.159085
$877$	−18.6144	+	32.2410i	−0.628563	+	1.08870i	0.359277	+	0.933231i	$0.383023\pi$
$877$	−18.6144	+	32.2410i	−0.628563	+	1.08870i	−0.987840	+	0.155472i	$0.950310\pi$
$878$	−7.32288	−	12.6836i	−0.247135	−	0.428051i
$879$	3.29150	+	5.70105i	0.111020	+	0.192292i
$880$	1.32288	−	2.29129i	0.0445941	−	0.0772393i
$881$	−19.1660			−0.645719			−0.322860	−	0.946447i	$-0.604644\pi$
$881$	−19.1660			−0.645719			−0.322860	+	0.946447i	$0.604644\pi$
$882$	3.50000	−	6.06218i	0.117851	−	0.204124i
$883$	−55.5830			−1.87052			−0.935259	−	0.353965i	$-0.884833\pi$
$883$	−55.5830			−1.87052			−0.935259	+	0.353965i	$0.884833\pi$
$884$	−6.00000	+	10.3923i	−0.201802	+	0.349531i
$885$	19.2915	+	33.4139i	0.648477	+	1.12319i
$886$	5.58301	+	9.67005i	0.187565	+	0.324872i
$887$	−21.5203	+	37.2742i	−0.722580	+	1.25154i	0.237383	+	0.971416i	$0.423710\pi$
$887$	−21.5203	+	37.2742i	−0.722580	+	1.25154i	−0.959963	+	0.280128i	$0.909623\pi$
$888$	−9.29150			−0.311802
$889$	−3.50000	+	6.06218i	−0.117386	+	0.203319i
$890$	35.1660			1.17877
$891$	−0.500000	+	0.866025i	−0.0167506	+	0.0290129i
$892$	12.2288	+	21.1808i	0.409449	+	0.709187i
$893$	31.5830	+	54.7034i	1.05688	+	1.83058i
$894$	5.93725	−	10.2836i	0.198571	−	0.343936i
$895$	−40.4575			−1.35235
$896$	−1.32288	−	2.29129i	−0.0441942	−	0.0765466i
$897$	10.5830			0.353356
$898$	−11.2288	+	19.4488i	−0.374708	+	0.649014i
$899$	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
$903$	−3.41699			−0.113710
$904$	8.58301			0.285467
$905$	7.00000	−	12.1244i	0.232688	−	0.403027i
$906$	−8.67712	−	15.0292i	−0.288278	−	0.499312i
$907$	29.0830	+	50.3732i	0.965685	+	1.67262i	0.707762	+	0.706451i	$0.249705\pi$
$907$	29.0830	+	50.3732i	0.965685	+	1.67262i	0.257923	+	0.966165i	$0.416962\pi$
$908$	−11.7915	+	20.4235i	−0.391315	+	0.677777i
$909$	−3.29150			−0.109172
$910$	28.0000			0.928191
$911$	50.3948			1.66965			0.834827	−	0.550513i	$-0.185568\pi$
$911$	50.3948			1.66965			0.834827	+	0.550513i	$0.185568\pi$
$912$	−2.64575	+	4.58258i	−0.0876096	+	0.151744i
$913$	2.79150	+	4.83502i	0.0923853	+	0.160016i
$914$	−9.70850	−	16.8156i	−0.321129	−	0.556211i
$915$	5.20850	−	9.02138i	0.172188	−	0.298238i
$916$	17.2915			0.571327
$917$	3.41699	+	5.91841i	0.112839	+	0.195443i
$918$	−3.00000			−0.0990148
$919$	−7.32288	+	12.6836i	−0.241559	+	0.418393i	−0.961159	−	0.275996i	$-0.910992\pi$
$919$	−7.32288	+	12.6836i	−0.241559	+	0.418393i	0.719599	+	0.694390i	$0.244326\pi$
$920$	−3.50000	−	6.06218i	−0.115392	−	0.199864i
$921$	−16.2915	−	28.2177i	−0.536823	−	0.929805i
$922$	−1.70850	+	2.95920i	−0.0562664	+	0.0974562i
$923$	53.1660			1.74998
$924$	−1.32288	+	2.29129i	−0.0435194	+	0.0753778i
$925$	−18.5830			−0.611005
$926$	−17.5203	+	30.3460i	−0.575751	+	0.997231i
$927$	5.00000	+	8.66025i	0.164222	+	0.284440i
$928$	1.00000	+	1.73205i	0.0328266	+	0.0568574i
$929$	−9.22876	+	15.9847i	−0.302786	+	0.524440i	−0.976766	−	0.214309i	$-0.931250\pi$
$929$	−9.22876	+	15.9847i	−0.302786	+	0.524440i	0.673980	+	0.738749i	$0.264583\pi$
$930$	10.5830			0.347030
$931$	−37.0405			−1.21395
$932$	−22.1660			−0.726072
$933$	−7.26013	+	12.5749i	−0.237686	+	0.411684i
$934$	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	$0.195793\pi$
$938$	17.9686	−	31.1226i	0.586696	−	1.01619i
$939$	−0.583005			−0.0190257
$940$	15.7915	−	27.3517i	0.515062	−	0.892114i
$941$	−12.2915	−	21.2895i	−0.400692	−	0.694018i	0.593118	−	0.805116i	$-0.297897\pi$
$941$	−12.2915	−	21.2895i	−0.400692	−	0.694018i	−0.993810	+	0.111097i	$0.964563\pi$
$942$	5.64575	+	9.77873i	0.183949	+	0.318608i
$943$	−11.9059	+	20.6216i	−0.387709	+	0.671531i
$944$	−14.5830			−0.474636
$945$	3.50000	+	6.06218i	0.113855	+	0.197203i
$946$	1.29150			0.0419904
$947$	18.2915	−	31.6818i	0.594394	−	1.02952i	−0.399238	−	0.916847i	$-0.630725\pi$
$947$	18.2915	−	31.6818i	0.594394	−	1.02952i	0.993632	−	0.112673i	$-0.0359413\pi$
$948$	2.67712	+	4.63692i	0.0869490	+	0.150600i
$949$	−9.41699	−	16.3107i	−0.305689	−	0.529468i
$950$	−5.29150	+	9.16515i	−0.171679	+	0.297357i
$951$	17.2288			0.558681
$952$	−7.93725			−0.257248
$953$	−36.7490			−1.19042			−0.595209	−	0.803571i	$-0.702931\pi$
$953$	−36.7490			−1.19042			−0.595209	+	0.803571i	$0.702931\pi$
$954$	2.00000	−	3.46410i	0.0647524	−	0.112154i
$955$	22.8745	+	39.6198i	0.740202	+	1.28207i
$956$	−6.64575	−	11.5108i	−0.214939	−	0.372285i
$957$	1.00000	−	1.73205i	0.0323254	−	0.0559893i
$958$	2.12549			0.0686715
$959$	7.16601			0.231403
$960$	2.64575			0.0853913
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	18.5830	+	32.1867i	0.599140	+	1.03774i
$963$	−4.50000	−	7.79423i	−0.145010	−	0.251166i
$964$	−7.58301	+	13.1342i	−0.244232	+	0.423022i
$965$	−42.0000			−1.35203
$966$	3.50000	+	6.06218i	0.112611	+	0.195047i
$967$	55.9373			1.79882			0.899410	−	0.437105i	$-0.143996\pi$
$967$	55.9373			1.79882			0.899410	+	0.437105i	$0.143996\pi$
$968$	0.500000	−	0.866025i	0.0160706	−	0.0278351i
$969$	7.93725	+	13.7477i	0.254981	+	0.441641i
$970$	−12.6771	−	21.9574i	−0.407038	−	0.705010i
$971$	−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
$973$	11.3542	−	19.6661i	0.364001	−	0.630467i
$974$	9.87451			0.316400
$975$	−4.00000	+	6.92820i	−0.128103	+	0.221880i
$976$	1.96863	+	3.40976i	0.0630142	+	0.109144i
$977$	14.5830	+	25.2585i	0.466552	+	0.808091i	0.999270	−	0.0382014i	$-0.0121628\pi$
$977$	14.5830	+	25.2585i	0.466552	+	0.808091i	−0.532718	+	0.846293i	$0.678830\pi$
$978$	−7.79150	+	13.4953i	−0.249145	+	0.431531i
$979$	13.2915			0.424798
$980$	9.26013	+	16.0390i	0.295804	+	0.512348i
$981$	11.9373			0.381127
$982$	−0.500000	+	0.866025i	−0.0159556	+	0.0276360i
$983$	−2.73987	−	4.74559i	−0.0873883	−	0.151361i	0.819018	−	0.573768i	$-0.194519\pi$
$983$	−2.73987	−	4.74559i	−0.0873883	−	0.151361i	−0.906406	+	0.422407i	$0.861185\pi$
$984$	−4.50000	−	7.79423i	−0.143455	−	0.248471i
$985$	−13.0627	+	22.6253i	−0.416214	+	0.720903i
$986$	6.00000			0.191079
$987$	−15.7915	+	27.3517i	−0.502649	+	0.870614i
$988$	21.1660			0.673380
$989$	1.70850	−	2.95920i	0.0543271	−	0.0940972i
$990$	−1.32288	−	2.29129i	−0.0420437	−	0.0728219i
$991$	6.06275	+	10.5010i	0.192589	+	0.333575i	0.946108	−	0.323852i	$-0.104978\pi$
$991$	6.06275	+	10.5010i	0.192589	+	0.333575i	−0.753518	+	0.657427i	$0.771645\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$	−13.0000			−0.412543
$994$	17.5830	+	30.4547i	0.557699	+	0.965963i
$995$	−61.2915			−1.94307
$996$	−2.79150	+	4.83502i	−0.0884521	+	0.153204i
$997$	−24.5830	−	42.5790i	−0.778552	−	1.34849i	−0.932777	−	0.360455i	$-0.882621\pi$
$997$	−24.5830	−	42.5790i	−0.778552	−	1.34849i	0.154225	−	0.988036i	$-0.450712\pi$
$998$	1.29150	+	2.23695i	0.0408818	+	0.0708094i
$999$	−4.64575	+	8.04668i	−0.146985	+	0.254586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.i.e.331.2	yes	4
3.2	odd	2		1386.2.k.r.793.1		4
7.2	even	3		3234.2.a.w.1.1		2
7.4	even	3	inner	462.2.i.e.67.2	✓	4
7.5	odd	6		3234.2.a.ba.1.2		2
21.2	odd	6		9702.2.a.db.1.2		2
21.5	even	6		9702.2.a.dm.1.1		2
21.11	odd	6		1386.2.k.r.991.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.i.e.67.2	✓	4	7.4	even	3	inner
462.2.i.e.331.2	yes	4	1.1	even	1	trivial
1386.2.k.r.793.1		4	3.2	odd	2
1386.2.k.r.991.1		4	21.11	odd	6
3234.2.a.w.1.1		2	7.2	even	3
3234.2.a.ba.1.2		2	7.5	odd	6
9702.2.a.db.1.2		2	21.2	odd	6
9702.2.a.dm.1.1		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} +(-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} +(4.64575 - 8.04668i) 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} -1.29150 q^{43} +(-0.500000 + 0.866025i) q^{44} +(1.32288 + 2.29129i) q^{45} +(1.32288 + 2.29129i) q^{46} +(-5.96863 + 10.3380i) 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} +(7.29150 + 12.6293i) q^{59} +(-1.32288 - 2.29129i) q^{60} +(1.96863 - 3.40976i) 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} +(6.79150 + 11.7632i) q^{67} +(1.50000 - 2.59808i) q^{68} -2.64575 q^{69} -7.00000 q^{70} -13.2915 q^{71} +(0.500000 - 0.866025i) q^{72} +(2.35425 + 4.07768i) q^{73} +(-4.64575 - 8.04668i) q^{74} +(1.00000 - 1.73205i) q^{75} -5.29150 q^{76} -2.64575 q^{77} -4.00000 q^{78} +(-2.67712 + 4.63692i) q^{79} +(1.32288 + 2.29129i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.50000 - 7.79423i) q^{82} -5.58301 q^{83} +(-1.32288 - 2.29129i) q^{84} +7.93725 q^{85} +(-0.645751 + 1.11847i) q^{86} +(1.00000 + 1.73205i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-6.64575 + 11.5108i) q^{89} +2.64575 q^{90} +(-5.29150 + 9.16515i) q^{91} +2.64575 q^{92} +(-2.00000 + 3.46410i) q^{93} +(5.96863 + 10.3380i) q^{94} +(-7.00000 - 12.1244i) q^{95} +(-0.500000 + 0.866025i) q^{96} +9.58301 q^{97} -7.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{6} - 4 q^{8} - 2 q^{9} - 2 q^{11} + 2 q^{12} - 16 q^{13} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{22} - 2 q^{24} - 4 q^{25} - 8 q^{26} - 4 q^{27} + 8 q^{29} + 8 q^{31}+ \cdots + 4 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

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