LMFDB - Embedded newform 462.2.i.c.67.1

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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	462.67
Dual form			462.2.i.c.331.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} -1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} -1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} +2.00000 q^{13} +(0.500000 + 2.59808i) q^{14} -3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.00000 - 1.73205i) q^{19} -3.00000 q^{20} +(-2.00000 + 1.73205i) q^{21} +1.00000 q^{22} +(-1.50000 - 2.59808i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} +(1.00000 + 1.73205i) q^{26} +1.00000 q^{27} +(-2.00000 + 1.73205i) q^{28} -6.00000 q^{29} +(-1.50000 - 2.59808i) q^{30} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} -3.00000 q^{34} +(1.50000 + 7.79423i) q^{35} +1.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(1.00000 - 1.73205i) q^{38} +(-1.00000 + 1.73205i) q^{39} +(-1.50000 - 2.59808i) q^{40} -3.00000 q^{41} +(-2.50000 - 0.866025i) q^{42} +2.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(1.50000 - 2.59808i) q^{45} +(1.50000 - 2.59808i) q^{46} +(4.50000 + 7.79423i) q^{47} +1.00000 q^{48} +(5.50000 + 4.33013i) q^{49} -4.00000 q^{50} +(-1.50000 - 2.59808i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(0.500000 + 0.866025i) q^{54} +3.00000 q^{55} +(-2.50000 - 0.866025i) q^{56} +2.00000 q^{57} +(-3.00000 - 5.19615i) q^{58} +(6.00000 - 10.3923i) q^{59} +(1.50000 - 2.59808i) q^{60} +(-2.50000 - 4.33013i) q^{61} +4.00000 q^{62} +(-0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(3.00000 + 5.19615i) q^{65} +(-0.500000 + 0.866025i) q^{66} +(-2.50000 + 4.33013i) q^{67} +(-1.50000 - 2.59808i) q^{68} +3.00000 q^{69} +(-6.00000 + 5.19615i) q^{70} +12.0000 q^{71} +(0.500000 + 0.866025i) q^{72} +(8.00000 - 13.8564i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-2.00000 - 3.46410i) q^{75} +2.00000 q^{76} +(2.00000 - 1.73205i) q^{77} -2.00000 q^{78} +(-8.50000 - 14.7224i) q^{79} +(1.50000 - 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.50000 - 2.59808i) q^{82} +9.00000 q^{83} +(-0.500000 - 2.59808i) q^{84} -9.00000 q^{85} +(1.00000 + 1.73205i) q^{86} +(3.00000 - 5.19615i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(3.00000 + 5.19615i) q^{89} +3.00000 q^{90} +(5.00000 + 1.73205i) q^{91} +3.00000 q^{92} +(2.00000 + 3.46410i) q^{93} +(-4.50000 + 7.79423i) q^{94} +(3.00000 - 5.19615i) q^{95} +(0.500000 + 0.866025i) q^{96} +17.0000 q^{97} +(-1.00000 + 6.92820i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} + 3 q^{5} - 2 q^{6} + 5 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 + 3 * q^5 - 2 * q^6 + 5 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} + 3 q^{5} - 2 q^{6} + 5 q^{7} - 2 q^{8} - q^{9} - 3 q^{10} + q^{11} - q^{12} + 4 q^{13} + q^{14} - 6 q^{15} - q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - 6 q^{20} - 4 q^{21} + 2 q^{22} - 3 q^{23} + q^{24} - 4 q^{25} + 2 q^{26} + 2 q^{27} - 4 q^{28} - 12 q^{29} - 3 q^{30} + 4 q^{31} + q^{32} + q^{33} - 6 q^{34} + 3 q^{35} + 2 q^{36} - 2 q^{37} + 2 q^{38} - 2 q^{39} - 3 q^{40} - 6 q^{41} - 5 q^{42} + 4 q^{43} + q^{44} + 3 q^{45} + 3 q^{46} + 9 q^{47} + 2 q^{48} + 11 q^{49} - 8 q^{50} - 3 q^{51} - 2 q^{52} - 6 q^{53} + q^{54} + 6 q^{55} - 5 q^{56} + 4 q^{57} - 6 q^{58} + 12 q^{59} + 3 q^{60} - 5 q^{61} + 8 q^{62} - q^{63} + 2 q^{64} + 6 q^{65} - q^{66} - 5 q^{67} - 3 q^{68} + 6 q^{69} - 12 q^{70} + 24 q^{71} + q^{72} + 16 q^{73} + 2 q^{74} - 4 q^{75} + 4 q^{76} + 4 q^{77} - 4 q^{78} - 17 q^{79} + 3 q^{80} - q^{81} - 3 q^{82} + 18 q^{83} - q^{84} - 18 q^{85} + 2 q^{86} + 6 q^{87} - q^{88} + 6 q^{89} + 6 q^{90} + 10 q^{91} + 6 q^{92} + 4 q^{93} - 9 q^{94} + 6 q^{95} + q^{96} + 34 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 + 3 * q^5 - 2 * q^6 + 5 * q^7 - 2 * q^8 - q^9 - 3 * q^10 + q^11 - q^12 + 4 * q^13 + q^14 - 6 * q^15 - q^16 - 3 * q^17 + q^18 - 2 * q^19 - 6 * q^20 - 4 * q^21 + 2 * q^22 - 3 * q^23 + q^24 - 4 * q^25 + 2 * q^26 + 2 * q^27 - 4 * q^28 - 12 * q^29 - 3 * q^30 + 4 * q^31 + q^32 + q^33 - 6 * q^34 + 3 * q^35 + 2 * q^36 - 2 * q^37 + 2 * q^38 - 2 * q^39 - 3 * q^40 - 6 * q^41 - 5 * q^42 + 4 * q^43 + q^44 + 3 * q^45 + 3 * q^46 + 9 * q^47 + 2 * q^48 + 11 * q^49 - 8 * q^50 - 3 * q^51 - 2 * q^52 - 6 * q^53 + q^54 + 6 * q^55 - 5 * q^56 + 4 * q^57 - 6 * q^58 + 12 * q^59 + 3 * q^60 - 5 * q^61 + 8 * q^62 - q^63 + 2 * q^64 + 6 * q^65 - q^66 - 5 * q^67 - 3 * q^68 + 6 * q^69 - 12 * q^70 + 24 * q^71 + q^72 + 16 * q^73 + 2 * q^74 - 4 * q^75 + 4 * q^76 + 4 * q^77 - 4 * q^78 - 17 * q^79 + 3 * q^80 - q^81 - 3 * q^82 + 18 * q^83 - q^84 - 18 * q^85 + 2 * q^86 + 6 * q^87 - q^88 + 6 * q^89 + 6 * q^90 + 10 * q^91 + 6 * q^92 + 4 * q^93 - 9 * q^94 + 6 * q^95 + q^96 + 34 * q^97 - 2 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$	−1.00000			−0.408248
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$	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
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$	0.500000	+	2.59808i	0.133631	+	0.694365i
$15$	−3.00000			−0.774597
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$	−3.00000			−0.670820
$21$	−2.00000	+	1.73205i	−0.436436	+	0.377964i
$22$	1.00000			0.213201
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	1.00000	+	1.73205i	0.196116	+	0.339683i
$27$	1.00000			0.192450
$28$	−2.00000	+	1.73205i	−0.377964	+	0.327327i
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$	−1.50000	−	2.59808i	−0.273861	−	0.474342i
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$	−3.00000			−0.514496
$35$	1.50000	+	7.79423i	0.253546	+	1.31747i
$36$	1.00000			0.166667
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	1.00000	−	1.73205i	0.162221	−	0.280976i
$39$	−1.00000	+	1.73205i	−0.160128	+	0.277350i
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$	−2.50000	−	0.866025i	−0.385758	−	0.133631i
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$	1.50000	−	2.59808i	0.223607	−	0.387298i
$46$	1.50000	−	2.59808i	0.221163	−	0.383065i
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	0.981543	+	0.191243i	$0.0612518\pi$
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	−0.325150	+	0.945662i	$0.605415\pi$
$48$	1.00000			0.144338
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	−4.00000			−0.565685
$51$	−1.50000	−	2.59808i	−0.210042	−	0.363803i
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	−0.995117	−	0.0987002i	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	3.00000			0.404520
$56$	−2.50000	−	0.866025i	−0.334077	−	0.115728i
$57$	2.00000			0.264906
$58$	−3.00000	−	5.19615i	−0.393919	−	0.682288i
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$	1.50000	−	2.59808i	0.193649	−	0.335410i
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	0.660415	−	0.750901i	$-0.270381\pi$
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	−0.980507	+	0.196485i	$0.937047\pi$
$62$	4.00000			0.508001
$63$	−0.500000	−	2.59808i	−0.0629941	−	0.327327i
$64$	1.00000			0.125000
$65$	3.00000	+	5.19615i	0.372104	+	0.644503i
$66$	−0.500000	+	0.866025i	−0.0615457	+	0.106600i
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	0.671932	+	0.740613i	$0.265465\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$	3.00000			0.361158
$70$	−6.00000	+	5.19615i	−0.717137	+	0.621059i
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	8.00000	−	13.8564i	0.936329	−	1.62177i	0.164083	−	0.986447i	$-0.447534\pi$
$73$	8.00000	−	13.8564i	0.936329	−	1.62177i	0.772246	−	0.635323i	$-0.219133\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$	−2.00000	−	3.46410i	−0.230940	−	0.400000i
$76$	2.00000			0.229416
$77$	2.00000	−	1.73205i	0.227921	−	0.197386i
$78$	−2.00000			−0.226455
$79$	−8.50000	−	14.7224i	−0.956325	−	1.65640i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	−8.50000	−	14.7224i	−0.956325	−	1.65640i	−0.225018	−	0.974355i	$-0.572244\pi$
$80$	1.50000	−	2.59808i	0.167705	−	0.290474i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.50000	−	2.59808i	−0.165647	−	0.286910i
$83$	9.00000			0.987878			0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000			0.987878			0.493939	+	0.869496i	$0.335557\pi$
$84$	−0.500000	−	2.59808i	−0.0545545	−	0.283473i
$85$	−9.00000			−0.976187
$86$	1.00000	+	1.73205i	0.107833	+	0.186772i
$87$	3.00000	−	5.19615i	0.321634	−	0.557086i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$	3.00000			0.316228
$91$	5.00000	+	1.73205i	0.524142	+	0.181568i
$92$	3.00000			0.312772
$93$	2.00000	+	3.46410i	0.207390	+	0.359211i
$94$	−4.50000	+	7.79423i	−0.464140	+	0.803913i
$95$	3.00000	−	5.19615i	0.307794	−	0.533114i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	17.0000			1.72609			0.863044	−	0.505128i	$-0.168555\pi$
$97$	17.0000			1.72609			0.863044	+	0.505128i	$0.168555\pi$
$98$	−1.00000	+	6.92820i	−0.101015	+	0.699854i
$99$	−1.00000			−0.100504
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	0.396236	+	0.918149i	$0.370316\pi$
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	−0.993258	+	0.115924i	$0.963017\pi$
$102$	1.50000	−	2.59808i	0.148522	−	0.257248i
$103$	−7.00000	−	12.1244i	−0.689730	−	1.19465i	−0.971925	−	0.235291i	$-0.924396\pi$
$103$	−7.00000	−	12.1244i	−0.689730	−	1.19465i	0.282194	−	0.959357i	$-0.408938\pi$
$104$	−2.00000			−0.196116
$105$	−7.50000	−	2.59808i	−0.731925	−	0.253546i
$106$	−6.00000			−0.582772
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	0.784366	−	0.620298i	$-0.212988\pi$
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	−0.929377	+	0.369132i	$0.879655\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	0.472708	+	0.881219i	$0.343277\pi$
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	−0.999512	+	0.0312328i	$0.990057\pi$
$110$	1.50000	+	2.59808i	0.143019	+	0.247717i
$111$	2.00000			0.189832
$112$	−0.500000	−	2.59808i	−0.0472456	−	0.245495i
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$	1.00000	+	1.73205i	0.0936586	+	0.162221i
$115$	4.50000	−	7.79423i	0.419627	−	0.726816i
$116$	3.00000	−	5.19615i	0.278543	−	0.482451i
$117$	−1.00000	−	1.73205i	−0.0924500	−	0.160128i
$118$	12.0000			1.10469
$119$	−6.00000	+	5.19615i	−0.550019	+	0.476331i
$120$	3.00000			0.273861
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	2.50000	−	4.33013i	0.226339	−	0.392031i
$123$	1.50000	−	2.59808i	0.135250	−	0.234261i
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	3.00000			0.268328
$126$	2.00000	−	1.73205i	0.178174	−	0.154303i
$127$	11.0000			0.976092			0.488046	−	0.872818i	$-0.337710\pi$
$127$	11.0000			0.976092			0.488046	+	0.872818i	$0.337710\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−1.00000	+	1.73205i	−0.0880451	+	0.152499i
$130$	−3.00000	+	5.19615i	−0.263117	+	0.455733i
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	0.999602	+	0.0281993i	$0.00897729\pi$
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	−0.475380	+	0.879781i	$0.657689\pi$
$132$	−1.00000			−0.0870388
$133$	−1.00000	−	5.19615i	−0.0867110	−	0.450564i
$134$	−5.00000			−0.431934
$135$	1.50000	+	2.59808i	0.129099	+	0.223607i
$136$	1.50000	−	2.59808i	0.128624	−	0.222783i
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	0.169226	+	0.985577i	$0.445873\pi$
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	−0.938148	+	0.346235i	$0.887460\pi$
$138$	1.50000	+	2.59808i	0.127688	+	0.221163i
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$	−7.50000	−	2.59808i	−0.633866	−	0.219578i
$141$	−9.00000			−0.757937
$142$	6.00000	+	10.3923i	0.503509	+	0.872103i
$143$	1.00000	−	1.73205i	0.0836242	−	0.144841i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−9.00000	−	15.5885i	−0.747409	−	1.29455i
$146$	16.0000			1.32417
$147$	−6.50000	+	2.59808i	−0.536111	+	0.214286i
$148$	2.00000			0.164399
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$	2.00000	−	3.46410i	0.163299	−	0.282843i
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	−0.844963	−	0.534824i	$-0.820378\pi$
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	0.885653	+	0.464348i	$0.153711\pi$
$152$	1.00000	+	1.73205i	0.0811107	+	0.140488i
$153$	3.00000			0.242536
$154$	2.50000	+	0.866025i	0.201456	+	0.0697863i
$155$	12.0000			0.963863
$156$	−1.00000	−	1.73205i	−0.0800641	−	0.138675i
$157$	−10.0000	+	17.3205i	−0.798087	+	1.38233i	0.122774	+	0.992435i	$0.460821\pi$
$157$	−10.0000	+	17.3205i	−0.798087	+	1.38233i	−0.920860	+	0.389892i	$0.872512\pi$
$158$	8.50000	−	14.7224i	0.676224	−	1.17125i
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$	3.00000			0.237171
$161$	−1.50000	−	7.79423i	−0.118217	−	0.614271i
$162$	−1.00000			−0.0785674
$163$	0.500000	+	0.866025i	0.0391630	+	0.0678323i	0.884943	−	0.465700i	$-0.154198\pi$
$163$	0.500000	+	0.866025i	0.0391630	+	0.0678323i	−0.845780	+	0.533533i	$0.820864\pi$
$164$	1.50000	−	2.59808i	0.117130	−	0.202876i
$165$	−1.50000	+	2.59808i	−0.116775	+	0.202260i
$166$	4.50000	+	7.79423i	0.349268	+	0.604949i
$167$	−12.0000			−0.928588			−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000			−0.928588			−0.464294	+	0.885681i	$0.653692\pi$
$168$	2.00000	−	1.73205i	0.154303	−	0.133631i
$169$	−9.00000			−0.692308
$170$	−4.50000	−	7.79423i	−0.345134	−	0.597790i
$171$	−1.00000	+	1.73205i	−0.0764719	+	0.132453i
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	−6.00000	−	10.3923i	−0.456172	−	0.790112i	0.542583	−	0.840002i	$-0.317446\pi$
$173$	−6.00000	−	10.3923i	−0.456172	−	0.790112i	−0.998755	+	0.0498898i	$0.984113\pi$
$174$	6.00000			0.454859
$175$	−8.00000	+	6.92820i	−0.604743	+	0.523723i
$176$	−1.00000			−0.0753778
$177$	6.00000	+	10.3923i	0.450988	+	0.781133i
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	−0.998286	−	0.0585225i	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$	1.50000	+	2.59808i	0.111803	+	0.193649i
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	1.00000	+	5.19615i	0.0741249	+	0.385164i
$183$	5.00000			0.369611
$184$	1.50000	+	2.59808i	0.110581	+	0.191533i
$185$	3.00000	−	5.19615i	0.220564	−	0.382029i
$186$	−2.00000	+	3.46410i	−0.146647	+	0.254000i
$187$	1.50000	+	2.59808i	0.109691	+	0.189990i
$188$	−9.00000			−0.656392
$189$	2.50000	+	0.866025i	0.181848	+	0.0629941i
$190$	6.00000			0.435286
$191$	−12.0000	−	20.7846i	−0.868290	−	1.50392i	−0.863743	−	0.503932i	$-0.831886\pi$
$191$	−12.0000	−	20.7846i	−0.868290	−	1.50392i	−0.00454614	−	0.999990i	$-0.501447\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	0.827788	+	0.561041i	$0.189599\pi$
$194$	8.50000	+	14.7224i	0.610264	+	1.05701i
$195$	−6.00000			−0.429669
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$	12.0000			0.854965			0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000			0.854965			0.427482	+	0.904024i	$0.359401\pi$
$198$	−0.500000	−	0.866025i	−0.0355335	−	0.0615457i
$199$	−1.00000	+	1.73205i	−0.0708881	+	0.122782i	−0.899291	−	0.437351i	$-0.855917\pi$
$199$	−1.00000	+	1.73205i	−0.0708881	+	0.122782i	0.828403	+	0.560133i	$0.189250\pi$
$200$	2.00000	−	3.46410i	0.141421	−	0.244949i
$201$	−2.50000	−	4.33013i	−0.176336	−	0.305424i
$202$	−12.0000			−0.844317
$203$	−15.0000	−	5.19615i	−1.05279	−	0.364698i
$204$	3.00000			0.210042
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$	7.00000	−	12.1244i	0.487713	−	0.844744i
$207$	−1.50000	+	2.59808i	−0.104257	+	0.180579i
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$	−2.00000			−0.138343
$210$	−1.50000	−	7.79423i	−0.103510	−	0.537853i
$211$	−22.0000			−1.51454			−0.757271	−	0.653101i	$-0.773468\pi$
$211$	−22.0000			−1.51454			−0.757271	+	0.653101i	$0.773468\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$	−6.00000	+	10.3923i	−0.411113	+	0.712069i
$214$	1.50000	−	2.59808i	0.102538	−	0.177601i
$215$	3.00000	+	5.19615i	0.204598	+	0.354375i
$216$	−1.00000			−0.0680414
$217$	8.00000	−	6.92820i	0.543075	−	0.470317i
$218$	−11.0000			−0.745014
$219$	8.00000	+	13.8564i	0.540590	+	0.936329i
$220$	−1.50000	+	2.59808i	−0.101130	+	0.175162i
$221$	−3.00000	+	5.19615i	−0.201802	+	0.349531i
$222$	1.00000	+	1.73205i	0.0671156	+	0.116248i
$223$	20.0000			1.33930			0.669650	−	0.742677i	$-0.266444\pi$
$223$	20.0000			1.33930			0.669650	+	0.742677i	$0.266444\pi$
$224$	2.00000	−	1.73205i	0.133631	−	0.115728i
$225$	4.00000			0.266667
$226$	−3.00000	−	5.19615i	−0.199557	−	0.345643i
$227$	10.5000	−	18.1865i	0.696909	−	1.20708i	−0.272623	−	0.962121i	$-0.587891\pi$
$227$	10.5000	−	18.1865i	0.696909	−	1.20708i	0.969533	−	0.244962i	$-0.0787754\pi$
$228$	−1.00000	+	1.73205i	−0.0662266	+	0.114708i
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	0.982592	−	0.185776i	$-0.0594799\pi$
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	−0.652183	+	0.758062i	$0.726147\pi$
$230$	9.00000			0.593442
$231$	0.500000	+	2.59808i	0.0328976	+	0.170941i
$232$	6.00000			0.393919
$233$	−13.5000	−	23.3827i	−0.884414	−	1.53185i	−0.846383	−	0.532574i	$-0.821225\pi$
$233$	−13.5000	−	23.3827i	−0.884414	−	1.53185i	−0.0380310	−	0.999277i	$-0.512109\pi$
$234$	1.00000	−	1.73205i	0.0653720	−	0.113228i
$235$	−13.5000	+	23.3827i	−0.880643	+	1.52532i
$236$	6.00000	+	10.3923i	0.390567	+	0.676481i
$237$	17.0000			1.10427
$238$	−7.50000	−	2.59808i	−0.486153	−	0.168408i
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$	1.50000	+	2.59808i	0.0968246	+	0.167705i
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$	0.500000	−	0.866025i	0.0321412	−	0.0556702i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	5.00000			0.320092
$245$	−3.00000	+	20.7846i	−0.191663	+	1.32788i
$246$	3.00000			0.191273
$247$	−2.00000	−	3.46410i	−0.127257	−	0.220416i
$248$	−2.00000	+	3.46410i	−0.127000	+	0.219971i
$249$	−4.50000	+	7.79423i	−0.285176	+	0.493939i
$250$	1.50000	+	2.59808i	0.0948683	+	0.164317i
$251$	−24.0000			−1.51487			−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000			−1.51487			−0.757433	+	0.652913i	$0.773547\pi$
$252$	2.50000	+	0.866025i	0.157485	+	0.0545545i
$253$	−3.00000			−0.188608
$254$	5.50000	+	9.52628i	0.345101	+	0.597732i
$255$	4.50000	−	7.79423i	0.281801	−	0.488094i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	0.757159	−	0.653231i	$-0.226587\pi$
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	−0.944294	+	0.329104i	$0.893253\pi$
$258$	−2.00000			−0.124515
$259$	−1.00000	−	5.19615i	−0.0621370	−	0.322873i
$260$	−6.00000			−0.372104
$261$	3.00000	+	5.19615i	0.185695	+	0.321634i
$262$	−6.00000	+	10.3923i	−0.370681	+	0.642039i
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	−0.619586	−	0.784929i	$-0.712699\pi$
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	0.989561	+	0.144112i	$0.0460326\pi$
$264$	−0.500000	−	0.866025i	−0.0307729	−	0.0533002i
$265$	−18.0000			−1.10573
$266$	4.00000	−	3.46410i	0.245256	−	0.212398i
$267$	−6.00000			−0.367194
$268$	−2.50000	−	4.33013i	−0.152712	−	0.264505i
$269$	−4.50000	+	7.79423i	−0.274370	+	0.475223i	−0.969976	−	0.243201i	$-0.921803\pi$
$269$	−4.50000	+	7.79423i	−0.274370	+	0.475223i	0.695606	+	0.718423i	$0.255136\pi$
$270$	−1.50000	+	2.59808i	−0.0912871	+	0.158114i
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$	3.00000			0.181902
$273$	−4.00000	+	3.46410i	−0.242091	+	0.209657i
$274$	−18.0000			−1.08742
$275$	2.00000	+	3.46410i	0.120605	+	0.208893i
$276$	−1.50000	+	2.59808i	−0.0902894	+	0.156386i
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	−0.675810	−	0.737075i	$-0.736206\pi$
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	0.976231	+	0.216731i	$0.0695395\pi$
$278$	7.00000	+	12.1244i	0.419832	+	0.727171i
$279$	−4.00000			−0.239474
$280$	−1.50000	−	7.79423i	−0.0896421	−	0.465794i
$281$	3.00000			0.178965			0.0894825	−	0.995988i	$-0.471479\pi$
$281$	3.00000			0.178965			0.0894825	+	0.995988i	$0.471479\pi$
$282$	−4.50000	−	7.79423i	−0.267971	−	0.464140i
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	−0.995544	−	0.0942988i	$-0.969939\pi$
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	0.579437	+	0.815017i	$0.303272\pi$
$284$	−6.00000	+	10.3923i	−0.356034	+	0.616670i
$285$	3.00000	+	5.19615i	0.177705	+	0.307794i
$286$	2.00000			0.118262
$287$	−7.50000	−	2.59808i	−0.442711	−	0.153360i
$288$	−1.00000			−0.0589256
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	9.00000	−	15.5885i	0.528498	−	0.915386i
$291$	−8.50000	+	14.7224i	−0.498279	+	0.863044i
$292$	8.00000	+	13.8564i	0.468165	+	0.810885i
$293$	−24.0000			−1.40209			−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000			−1.40209			−0.701047	+	0.713115i	$0.747284\pi$
$294$	−5.50000	−	4.33013i	−0.320767	−	0.252538i
$295$	36.0000			2.09600
$296$	1.00000	+	1.73205i	0.0581238	+	0.100673i
$297$	0.500000	−	0.866025i	0.0290129	−	0.0502519i
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	−3.00000	−	5.19615i	−0.173494	−	0.300501i
$300$	4.00000			0.230940
$301$	5.00000	+	1.73205i	0.288195	+	0.0998337i
$302$	1.00000			0.0575435
$303$	−6.00000	−	10.3923i	−0.344691	−	0.597022i
$304$	−1.00000	+	1.73205i	−0.0573539	+	0.0993399i
$305$	7.50000	−	12.9904i	0.429449	−	0.743827i
$306$	1.50000	+	2.59808i	0.0857493	+	0.148522i
$307$	−22.0000			−1.25561			−0.627803	−	0.778372i	$-0.716046\pi$
$307$	−22.0000			−1.25561			−0.627803	+	0.778372i	$0.716046\pi$
$308$	0.500000	+	2.59808i	0.0284901	+	0.148039i
$309$	14.0000			0.796432
$310$	6.00000	+	10.3923i	0.340777	+	0.590243i
$311$	−10.5000	+	18.1865i	−0.595400	+	1.03126i	0.398090	+	0.917346i	$0.369673\pi$
$311$	−10.5000	+	18.1865i	−0.595400	+	1.03126i	−0.993490	+	0.113917i	$0.963660\pi$
$312$	1.00000	−	1.73205i	0.0566139	−	0.0980581i
$313$	−1.00000	−	1.73205i	−0.0565233	−	0.0979013i	0.836379	−	0.548151i	$-0.184668\pi$
$313$	−1.00000	−	1.73205i	−0.0565233	−	0.0979013i	−0.892903	+	0.450250i	$0.851335\pi$
$314$	−20.0000			−1.12867
$315$	6.00000	−	5.19615i	0.338062	−	0.292770i
$316$	17.0000			0.956325
$317$	16.5000	+	28.5788i	0.926732	+	1.60515i	0.788751	+	0.614713i	$0.210728\pi$
$317$	16.5000	+	28.5788i	0.926732	+	1.60515i	0.137981	+	0.990435i	$0.455939\pi$
$318$	3.00000	−	5.19615i	0.168232	−	0.291386i
$319$	−3.00000	+	5.19615i	−0.167968	+	0.290929i
$320$	1.50000	+	2.59808i	0.0838525	+	0.145237i
$321$	3.00000			0.167444
$322$	6.00000	−	5.19615i	0.334367	−	0.289570i
$323$	6.00000			0.333849
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−4.00000	+	6.92820i	−0.221880	+	0.384308i
$326$	−0.500000	+	0.866025i	−0.0276924	+	0.0479647i
$327$	−5.50000	−	9.52628i	−0.304151	−	0.526804i
$328$	3.00000			0.165647
$329$	4.50000	+	23.3827i	0.248093	+	1.28913i
$330$	−3.00000			−0.165145
$331$	−5.50000	−	9.52628i	−0.302307	−	0.523612i	0.674351	−	0.738411i	$-0.264424\pi$
$331$	−5.50000	−	9.52628i	−0.302307	−	0.523612i	−0.976658	+	0.214799i	$0.931090\pi$
$332$	−4.50000	+	7.79423i	−0.246970	+	0.427764i
$333$	−1.00000	+	1.73205i	−0.0547997	+	0.0949158i
$334$	−6.00000	−	10.3923i	−0.328305	−	0.568642i
$335$	−15.0000			−0.819538
$336$	2.50000	+	0.866025i	0.136386	+	0.0472456i
$337$	−22.0000			−1.19842			−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000			−1.19842			−0.599208	+	0.800593i	$0.704518\pi$
$338$	−4.50000	−	7.79423i	−0.244768	−	0.423950i
$339$	3.00000	−	5.19615i	0.162938	−	0.282216i
$340$	4.50000	−	7.79423i	0.244047	−	0.422701i
$341$	−2.00000	−	3.46410i	−0.108306	−	0.187592i
$342$	−2.00000			−0.108148
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	−2.00000			−0.107833
$345$	4.50000	+	7.79423i	0.242272	+	0.419627i
$346$	6.00000	−	10.3923i	0.322562	−	0.558694i
$347$	16.5000	−	28.5788i	0.885766	−	1.53419i	0.0409337	−	0.999162i	$-0.486967\pi$
$347$	16.5000	−	28.5788i	0.885766	−	1.53419i	0.844833	−	0.535031i	$-0.179700\pi$
$348$	3.00000	+	5.19615i	0.160817	+	0.278543i
$349$	11.0000			0.588817			0.294408	−	0.955680i	$-0.404877\pi$
$349$	11.0000			0.588817			0.294408	+	0.955680i	$0.404877\pi$
$350$	−10.0000	−	3.46410i	−0.534522	−	0.185164i
$351$	2.00000			0.106752
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	6.00000	−	10.3923i	0.319348	−	0.553127i	−0.661004	−	0.750382i	$-0.729870\pi$
$353$	6.00000	−	10.3923i	0.319348	−	0.553127i	0.980352	+	0.197256i	$0.0632029\pi$
$354$	−6.00000	+	10.3923i	−0.318896	+	0.552345i
$355$	18.0000	+	31.1769i	0.955341	+	1.65470i
$356$	−6.00000			−0.317999
$357$	−1.50000	−	7.79423i	−0.0793884	−	0.412514i
$358$	−12.0000			−0.634220
$359$	−15.0000	−	25.9808i	−0.791670	−	1.37121i	−0.924932	−	0.380131i	$-0.875879\pi$
$359$	−15.0000	−	25.9808i	−0.791670	−	1.37121i	0.133263	−	0.991081i	$-0.457455\pi$
$360$	−1.50000	+	2.59808i	−0.0790569	+	0.136931i
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	−5.00000	−	8.66025i	−0.262794	−	0.455173i
$363$	1.00000			0.0524864
$364$	−4.00000	+	3.46410i	−0.209657	+	0.181568i
$365$	48.0000			2.51243
$366$	2.50000	+	4.33013i	0.130677	+	0.226339i
$367$	5.00000	−	8.66025i	0.260998	−	0.452062i	−0.705509	−	0.708700i	$-0.749282\pi$
$367$	5.00000	−	8.66025i	0.260998	−	0.452062i	0.966507	+	0.256639i	$0.0826151\pi$
$368$	−1.50000	+	2.59808i	−0.0781929	+	0.135434i
$369$	1.50000	+	2.59808i	0.0780869	+	0.135250i
$370$	6.00000			0.311925
$371$	−12.0000	+	10.3923i	−0.623009	+	0.539542i
$372$	−4.00000			−0.207390
$373$	0.500000	+	0.866025i	0.0258890	+	0.0448411i	0.878680	−	0.477412i	$-0.158425\pi$
$373$	0.500000	+	0.866025i	0.0258890	+	0.0448411i	−0.852791	+	0.522253i	$0.825092\pi$
$374$	−1.50000	+	2.59808i	−0.0775632	+	0.134343i
$375$	−1.50000	+	2.59808i	−0.0774597	+	0.134164i
$376$	−4.50000	−	7.79423i	−0.232070	−	0.401957i
$377$	−12.0000			−0.618031
$378$	0.500000	+	2.59808i	0.0257172	+	0.133631i
$379$	29.0000			1.48963			0.744815	−	0.667271i	$-0.232538\pi$
$379$	29.0000			1.48963			0.744815	+	0.667271i	$0.232538\pi$
$380$	3.00000	+	5.19615i	0.153897	+	0.266557i
$381$	−5.50000	+	9.52628i	−0.281774	+	0.488046i
$382$	12.0000	−	20.7846i	0.613973	−	1.06343i
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	−0.990702	−	0.136047i	$-0.956560\pi$
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	0.377531	−	0.925997i	$-0.376773\pi$
$384$	−1.00000			−0.0510310
$385$	7.50000	+	2.59808i	0.382235	+	0.132410i
$386$	−2.00000			−0.101797
$387$	−1.00000	−	1.73205i	−0.0508329	−	0.0880451i
$388$	−8.50000	+	14.7224i	−0.431522	+	0.747418i
$389$	−10.5000	+	18.1865i	−0.532371	+	0.922094i	0.466915	+	0.884302i	$0.345366\pi$
$389$	−10.5000	+	18.1865i	−0.532371	+	0.922094i	−0.999286	+	0.0377914i	$0.987968\pi$
$390$	−3.00000	−	5.19615i	−0.151911	−	0.263117i
$391$	9.00000			0.455150
$392$	−5.50000	−	4.33013i	−0.277792	−	0.218704i
$393$	−12.0000			−0.605320
$394$	6.00000	+	10.3923i	0.302276	+	0.523557i
$395$	25.5000	−	44.1673i	1.28304	−	2.22230i
$396$	0.500000	−	0.866025i	0.0251259	−	0.0435194i
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	0.839840	−	0.542834i	$-0.182649\pi$
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	−0.890028	+	0.455905i	$0.849316\pi$
$398$	−2.00000			−0.100251
$399$	5.00000	+	1.73205i	0.250313	+	0.0867110i
$400$	4.00000			0.200000
$401$	−15.0000	−	25.9808i	−0.749064	−	1.29742i	−0.948272	−	0.317460i	$-0.897170\pi$
$401$	−15.0000	−	25.9808i	−0.749064	−	1.29742i	0.199207	−	0.979957i	$-0.436163\pi$
$402$	2.50000	−	4.33013i	0.124689	−	0.215967i
$403$	4.00000	−	6.92820i	0.199254	−	0.345118i
$404$	−6.00000	−	10.3923i	−0.298511	−	0.517036i
$405$	−3.00000			−0.149071
$406$	−3.00000	−	15.5885i	−0.148888	−	0.773642i
$407$	−2.00000			−0.0991363
$408$	1.50000	+	2.59808i	0.0742611	+	0.128624i
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	−0.985558	−	0.169338i	$-0.945837\pi$
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	0.639430	+	0.768849i	$0.279170\pi$
$410$	4.50000	−	7.79423i	0.222239	−	0.384930i
$411$	−9.00000	−	15.5885i	−0.443937	−	0.768922i
$412$	14.0000			0.689730
$413$	24.0000	−	20.7846i	1.18096	−	1.02274i
$414$	−3.00000			−0.147442
$415$	13.5000	+	23.3827i	0.662689	+	1.14781i
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$	−7.00000	+	12.1244i	−0.342791	+	0.593732i
$418$	−1.00000	−	1.73205i	−0.0489116	−	0.0847174i
$419$	−24.0000			−1.17248			−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000			−1.17248			−0.586238	+	0.810139i	$0.699392\pi$
$420$	6.00000	−	5.19615i	0.292770	−	0.253546i
$421$	20.0000			0.974740			0.487370	−	0.873195i	$-0.337956\pi$
$421$	20.0000			0.974740			0.487370	+	0.873195i	$0.337956\pi$
$422$	−11.0000	−	19.0526i	−0.535472	−	0.927464i
$423$	4.50000	−	7.79423i	0.218797	−	0.378968i
$424$	3.00000	−	5.19615i	0.145693	−	0.252347i
$425$	−6.00000	−	10.3923i	−0.291043	−	0.504101i
$426$	−12.0000			−0.581402
$427$	−2.50000	−	12.9904i	−0.120983	−	0.628649i
$428$	3.00000			0.145010
$429$	1.00000	+	1.73205i	0.0482805	+	0.0836242i
$430$	−3.00000	+	5.19615i	−0.144673	+	0.250581i
$431$	3.00000	−	5.19615i	0.144505	−	0.250290i	−0.784683	−	0.619897i	$-0.787174\pi$
$431$	3.00000	−	5.19615i	0.144505	−	0.250290i	0.929188	+	0.369607i	$0.120508\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	35.0000			1.68199			0.840996	−	0.541041i	$-0.181970\pi$
$433$	35.0000			1.68199			0.840996	+	0.541041i	$0.181970\pi$
$434$	10.0000	+	3.46410i	0.480015	+	0.166282i
$435$	18.0000			0.863034
$436$	−5.50000	−	9.52628i	−0.263402	−	0.456226i
$437$	−3.00000	+	5.19615i	−0.143509	+	0.248566i
$438$	−8.00000	+	13.8564i	−0.382255	+	0.662085i
$439$	9.50000	+	16.4545i	0.453410	+	0.785330i	0.998595	−	0.0529862i	$-0.0168739\pi$
$439$	9.50000	+	16.4545i	0.453410	+	0.785330i	−0.545185	+	0.838316i	$0.683541\pi$
$440$	−3.00000			−0.143019
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$	−6.00000			−0.285391
$443$	−9.00000	−	15.5885i	−0.427603	−	0.740630i	0.569057	−	0.822298i	$-0.307309\pi$
$443$	−9.00000	−	15.5885i	−0.427603	−	0.740630i	−0.996660	+	0.0816684i	$0.973975\pi$
$444$	−1.00000	+	1.73205i	−0.0474579	+	0.0821995i
$445$	−9.00000	+	15.5885i	−0.426641	+	0.738964i
$446$	10.0000	+	17.3205i	0.473514	+	0.820150i
$447$	6.00000			0.283790
$448$	2.50000	+	0.866025i	0.118114	+	0.0409159i
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$	2.00000	+	3.46410i	0.0942809	+	0.163299i
$451$	−1.50000	+	2.59808i	−0.0706322	+	0.122339i
$452$	3.00000	−	5.19615i	0.141108	−	0.244406i
$453$	0.500000	+	0.866025i	0.0234920	+	0.0406894i
$454$	21.0000			0.985579
$455$	3.00000	+	15.5885i	0.140642	+	0.730798i
$456$	−2.00000			−0.0936586
$457$	−19.0000	−	32.9090i	−0.888783	−	1.53942i	−0.841316	−	0.540544i	$-0.818219\pi$
$457$	−19.0000	−	32.9090i	−0.888783	−	1.53942i	−0.0474665	−	0.998873i	$-0.515115\pi$
$458$	−5.00000	+	8.66025i	−0.233635	+	0.404667i
$459$	−1.50000	+	2.59808i	−0.0700140	+	0.121268i
$460$	4.50000	+	7.79423i	0.209814	+	0.363408i
$461$	6.00000			0.279448			0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000			0.279448			0.139724	+	0.990190i	$0.455378\pi$
$462$	−2.00000	+	1.73205i	−0.0930484	+	0.0805823i
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$	3.00000	+	5.19615i	0.139272	+	0.241225i
$465$	−6.00000	+	10.3923i	−0.278243	+	0.481932i
$466$	13.5000	−	23.3827i	0.625375	−	1.08318i
$467$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$467$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$468$	2.00000			0.0924500
$469$	−10.0000	+	8.66025i	−0.461757	+	0.399893i
$470$	−27.0000			−1.24542
$471$	−10.0000	−	17.3205i	−0.460776	−	0.798087i
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$	1.00000	−	1.73205i	0.0459800	−	0.0796398i
$474$	8.50000	+	14.7224i	0.390418	+	0.676224i
$475$	8.00000			0.367065
$476$	−1.50000	−	7.79423i	−0.0687524	−	0.357248i
$477$	6.00000			0.274721
$478$	3.00000	+	5.19615i	0.137217	+	0.237666i
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	0.450098	+	0.892979i	$0.351389\pi$
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	−0.998392	+	0.0566937i	$0.981944\pi$
$480$	−1.50000	+	2.59808i	−0.0684653	+	0.118585i
$481$	−2.00000	−	3.46410i	−0.0911922	−	0.157949i
$482$	10.0000			0.455488
$483$	7.50000	+	2.59808i	0.341262	+	0.118217i
$484$	1.00000			0.0454545
$485$	25.5000	+	44.1673i	1.15790	+	2.00553i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−4.00000	+	6.92820i	−0.181257	+	0.313947i	−0.942309	−	0.334744i	$-0.891350\pi$
$487$	−4.00000	+	6.92820i	−0.181257	+	0.313947i	0.761052	+	0.648691i	$0.224683\pi$
$488$	2.50000	+	4.33013i	0.113170	+	0.196016i
$489$	−1.00000			−0.0452216
$490$	−19.5000	+	7.79423i	−0.880920	+	0.352107i
$491$	−3.00000			−0.135388			−0.0676941	−	0.997706i	$-0.521564\pi$
$491$	−3.00000			−0.135388			−0.0676941	+	0.997706i	$0.521564\pi$
$492$	1.50000	+	2.59808i	0.0676252	+	0.117130i
$493$	9.00000	−	15.5885i	0.405340	−	0.702069i
$494$	2.00000	−	3.46410i	0.0899843	−	0.155857i
$495$	−1.50000	−	2.59808i	−0.0674200	−	0.116775i
$496$	−4.00000			−0.179605
$497$	30.0000	+	10.3923i	1.34568	+	0.466159i
$498$	−9.00000			−0.403300
$499$	14.0000	+	24.2487i	0.626726	+	1.08552i	0.988204	+	0.153141i	$0.0489388\pi$
$499$	14.0000	+	24.2487i	0.626726	+	1.08552i	−0.361478	+	0.932381i	$0.617728\pi$
$500$	−1.50000	+	2.59808i	−0.0670820	+	0.116190i
$501$	6.00000	−	10.3923i	0.268060	−	0.464294i
$502$	−12.0000	−	20.7846i	−0.535586	−	0.927663i
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$	0.500000	+	2.59808i	0.0222718	+	0.115728i
$505$	−36.0000			−1.60198
$506$	−1.50000	−	2.59808i	−0.0666831	−	0.115499i
$507$	4.50000	−	7.79423i	0.199852	−	0.346154i
$508$	−5.50000	+	9.52628i	−0.244023	+	0.422660i
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	0.791849	−	0.610718i	$-0.209119\pi$
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	−0.924821	+	0.380402i	$0.875786\pi$
$510$	9.00000			0.398527
$511$	32.0000	−	27.7128i	1.41560	−	1.22594i
$512$	−1.00000			−0.0441942
$513$	−1.00000	−	1.73205i	−0.0441511	−	0.0764719i
$514$	3.00000	−	5.19615i	0.132324	−	0.229192i
$515$	21.0000	−	36.3731i	0.925371	−	1.60279i
$516$	−1.00000	−	1.73205i	−0.0440225	−	0.0762493i
$517$	9.00000			0.395820
$518$	4.00000	−	3.46410i	0.175750	−	0.152204i
$519$	12.0000			0.526742
$520$	−3.00000	−	5.19615i	−0.131559	−	0.227866i
$521$	−9.00000	+	15.5885i	−0.394297	+	0.682943i	−0.993011	−	0.118020i	$-0.962345\pi$
$521$	−9.00000	+	15.5885i	−0.394297	+	0.682943i	0.598714	+	0.800963i	$0.295679\pi$
$522$	−3.00000	+	5.19615i	−0.131306	+	0.227429i
$523$	−13.0000	−	22.5167i	−0.568450	−	0.984585i	−0.996719	−	0.0809336i	$-0.974210\pi$
$523$	−13.0000	−	22.5167i	−0.568450	−	0.984585i	0.428269	−	0.903651i	$-0.359124\pi$
$524$	−12.0000			−0.524222
$525$	−2.00000	−	10.3923i	−0.0872872	−	0.453557i
$526$	12.0000			0.523225
$527$	6.00000	+	10.3923i	0.261364	+	0.452696i
$528$	0.500000	−	0.866025i	0.0217597	−	0.0376889i
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	−9.00000	−	15.5885i	−0.390935	−	0.677119i
$531$	−12.0000			−0.520756
$532$	5.00000	+	1.73205i	0.216777	+	0.0750939i
$533$	−6.00000			−0.259889
$534$	−3.00000	−	5.19615i	−0.129823	−	0.224860i
$535$	4.50000	−	7.79423i	0.194552	−	0.336974i
$536$	2.50000	−	4.33013i	0.107984	−	0.187033i
$537$	−6.00000	−	10.3923i	−0.258919	−	0.448461i
$538$	−9.00000			−0.388018
$539$	6.50000	−	2.59808i	0.279975	−	0.111907i
$540$	−3.00000			−0.129099
$541$	−11.5000	−	19.9186i	−0.494424	−	0.856367i	0.505556	−	0.862794i	$-0.331288\pi$
$541$	−11.5000	−	19.9186i	−0.494424	−	0.856367i	−0.999979	+	0.00642713i	$0.997954\pi$
$542$	−8.00000	+	13.8564i	−0.343629	+	0.595184i
$543$	5.00000	−	8.66025i	0.214571	−	0.371647i
$544$	1.50000	+	2.59808i	0.0643120	+	0.111392i
$545$	−33.0000			−1.41356
$546$	−5.00000	−	1.73205i	−0.213980	−	0.0741249i
$547$	−46.0000			−1.96682			−0.983409	−	0.181402i	$-0.941936\pi$
$547$	−46.0000			−1.96682			−0.983409	+	0.181402i	$0.941936\pi$
$548$	−9.00000	−	15.5885i	−0.384461	−	0.665906i
$549$	−2.50000	+	4.33013i	−0.106697	+	0.184805i
$550$	−2.00000	+	3.46410i	−0.0852803	+	0.147710i
$551$	6.00000	+	10.3923i	0.255609	+	0.442727i
$552$	−3.00000			−0.127688
$553$	−8.50000	−	44.1673i	−0.361457	−	1.87818i
$554$	10.0000			0.424859
$555$	3.00000	+	5.19615i	0.127343	+	0.220564i
$556$	−7.00000	+	12.1244i	−0.296866	+	0.514187i
$557$	18.0000	−	31.1769i	0.762684	−	1.32101i	−0.178778	−	0.983890i	$-0.557214\pi$
$557$	18.0000	−	31.1769i	0.762684	−	1.32101i	0.941462	−	0.337119i	$-0.109452\pi$
$558$	−2.00000	−	3.46410i	−0.0846668	−	0.146647i
$559$	4.00000			0.169182
$560$	6.00000	−	5.19615i	0.253546	−	0.219578i
$561$	−3.00000			−0.126660
$562$	1.50000	+	2.59808i	0.0632737	+	0.109593i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$	4.50000	−	7.79423i	0.189484	−	0.328196i
$565$	−9.00000	−	15.5885i	−0.378633	−	0.655811i
$566$	−14.0000			−0.588464
$567$	−2.00000	+	1.73205i	−0.0839921	+	0.0727393i
$568$	−12.0000			−0.503509
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$	−3.00000	+	5.19615i	−0.125656	+	0.217643i
$571$	−19.0000	+	32.9090i	−0.795125	+	1.37720i	0.127634	+	0.991821i	$0.459262\pi$
$571$	−19.0000	+	32.9090i	−0.795125	+	1.37720i	−0.922760	+	0.385376i	$0.874072\pi$
$572$	1.00000	+	1.73205i	0.0418121	+	0.0724207i
$573$	24.0000			1.00261
$574$	−1.50000	−	7.79423i	−0.0626088	−	0.325325i
$575$	12.0000			0.500435
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−8.50000	+	14.7224i	−0.353860	+	0.612903i	−0.986922	−	0.161198i	$-0.948464\pi$
$577$	−8.50000	+	14.7224i	−0.353860	+	0.612903i	0.633062	+	0.774101i	$0.281798\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$	−1.00000	−	1.73205i	−0.0415586	−	0.0719816i
$580$	18.0000			0.747409
$581$	22.5000	+	7.79423i	0.933457	+	0.323359i
$582$	−17.0000			−0.704673
$583$	3.00000	+	5.19615i	0.124247	+	0.215203i
$584$	−8.00000	+	13.8564i	−0.331042	+	0.573382i
$585$	3.00000	−	5.19615i	0.124035	−	0.214834i
$586$	−12.0000	−	20.7846i	−0.495715	−	0.858604i
$587$	36.0000			1.48588			0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000			1.48588			0.742940	+	0.669359i	$0.233431\pi$
$588$	1.00000	−	6.92820i	0.0412393	−	0.285714i
$589$	−8.00000			−0.329634
$590$	18.0000	+	31.1769i	0.741048	+	1.28353i
$591$	−6.00000	+	10.3923i	−0.246807	+	0.427482i
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	0.797831	−	0.602881i	$-0.205981\pi$
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	−0.921026	+	0.389501i	$0.872647\pi$
$594$	1.00000			0.0410305
$595$	−22.5000	−	7.79423i	−0.922410	−	0.319532i
$596$	6.00000			0.245770
$597$	−1.00000	−	1.73205i	−0.0409273	−	0.0708881i
$598$	3.00000	−	5.19615i	0.122679	−	0.212486i
$599$	−13.5000	+	23.3827i	−0.551595	+	0.955391i	0.446565	+	0.894751i	$0.352647\pi$
$599$	−13.5000	+	23.3827i	−0.551595	+	0.955391i	−0.998160	+	0.0606393i	$0.980686\pi$
$600$	2.00000	+	3.46410i	0.0816497	+	0.141421i
$601$	−28.0000			−1.14214			−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000			−1.14214			−0.571072	+	0.820900i	$0.693472\pi$
$602$	1.00000	+	5.19615i	0.0407570	+	0.211779i
$603$	5.00000			0.203616
$604$	0.500000	+	0.866025i	0.0203447	+	0.0352381i
$605$	1.50000	−	2.59808i	0.0609837	−	0.105627i
$606$	6.00000	−	10.3923i	0.243733	−	0.422159i
$607$	0.500000	+	0.866025i	0.0202944	+	0.0351509i	0.875994	−	0.482322i	$-0.160206\pi$
$607$	0.500000	+	0.866025i	0.0202944	+	0.0351509i	−0.855700	+	0.517472i	$0.826873\pi$
$608$	−2.00000			−0.0811107
$609$	12.0000	−	10.3923i	0.486265	−	0.421117i
$610$	15.0000			0.607332
$611$	9.00000	+	15.5885i	0.364101	+	0.630641i
$612$	−1.50000	+	2.59808i	−0.0606339	+	0.105021i
$613$	15.5000	−	26.8468i	0.626039	−	1.08433i	−0.362300	−	0.932062i	$-0.618008\pi$
$613$	15.5000	−	26.8468i	0.626039	−	1.08433i	0.988339	−	0.152270i	$-0.0486583\pi$
$614$	−11.0000	−	19.0526i	−0.443924	−	0.768899i
$615$	9.00000			0.362915
$616$	−2.00000	+	1.73205i	−0.0805823	+	0.0697863i
$617$	30.0000			1.20775			0.603877	−	0.797077i	$-0.293622\pi$
$617$	30.0000			1.20775			0.603877	+	0.797077i	$0.293622\pi$
$618$	7.00000	+	12.1244i	0.281581	+	0.487713i
$619$	−5.50000	+	9.52628i	−0.221064	+	0.382893i	−0.955131	−	0.296183i	$-0.904286\pi$
$619$	−5.50000	+	9.52628i	−0.221064	+	0.382893i	0.734068	+	0.679076i	$0.237620\pi$
$620$	−6.00000	+	10.3923i	−0.240966	+	0.417365i
$621$	−1.50000	−	2.59808i	−0.0601929	−	0.104257i
$622$	−21.0000			−0.842023
$623$	3.00000	+	15.5885i	0.120192	+	0.624538i
$624$	2.00000			0.0800641
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	1.00000	−	1.73205i	0.0399680	−	0.0692267i
$627$	1.00000	−	1.73205i	0.0399362	−	0.0691714i
$628$	−10.0000	−	17.3205i	−0.399043	−	0.691164i
$629$	6.00000			0.239236
$630$	7.50000	+	2.59808i	0.298807	+	0.103510i
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$	8.50000	+	14.7224i	0.338112	+	0.585627i
$633$	11.0000	−	19.0526i	0.437211	−	0.757271i
$634$	−16.5000	+	28.5788i	−0.655299	+	1.13501i
$635$	16.5000	+	28.5788i	0.654783	+	1.13412i
$636$	6.00000			0.237915
$637$	11.0000	+	8.66025i	0.435836	+	0.343132i
$638$	−6.00000			−0.237542
$639$	−6.00000	−	10.3923i	−0.237356	−	0.411113i
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$641$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$642$	1.50000	+	2.59808i	0.0592003	+	0.102538i
$643$	−28.0000			−1.10421			−0.552106	−	0.833774i	$-0.686176\pi$
$643$	−28.0000			−1.10421			−0.552106	+	0.833774i	$0.686176\pi$
$644$	7.50000	+	2.59808i	0.295541	+	0.102379i
$645$	−6.00000			−0.236250
$646$	3.00000	+	5.19615i	0.118033	+	0.204440i
$647$	−19.5000	+	33.7750i	−0.766624	+	1.32783i	0.172760	+	0.984964i	$0.444732\pi$
$647$	−19.5000	+	33.7750i	−0.766624	+	1.32783i	−0.939384	+	0.342868i	$0.888602\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−6.00000	−	10.3923i	−0.235521	−	0.407934i
$650$	−8.00000			−0.313786
$651$	2.00000	+	10.3923i	0.0783862	+	0.407307i
$652$	−1.00000			−0.0391630
$653$	10.5000	+	18.1865i	0.410897	+	0.711694i	0.994988	−	0.0999939i	$-0.0318823\pi$
$653$	10.5000	+	18.1865i	0.410897	+	0.711694i	−0.584091	+	0.811688i	$0.698549\pi$
$654$	5.50000	−	9.52628i	0.215067	−	0.372507i
$655$	−18.0000	+	31.1769i	−0.703318	+	1.21818i
$656$	1.50000	+	2.59808i	0.0585652	+	0.101438i
$657$	−16.0000			−0.624219
$658$	−18.0000	+	15.5885i	−0.701713	+	0.607701i
$659$	−33.0000			−1.28550			−0.642749	−	0.766077i	$-0.722206\pi$
$659$	−33.0000			−1.28550			−0.642749	+	0.766077i	$0.722206\pi$
$660$	−1.50000	−	2.59808i	−0.0583874	−	0.101130i
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	0.366723	+	0.930330i	$0.380480\pi$
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	−0.989051	+	0.147573i	$0.952854\pi$
$662$	5.50000	−	9.52628i	0.213764	−	0.370249i
$663$	−3.00000	−	5.19615i	−0.116510	−	0.201802i
$664$	−9.00000			−0.349268
$665$	12.0000	−	10.3923i	0.465340	−	0.402996i
$666$	−2.00000			−0.0774984
$667$	9.00000	+	15.5885i	0.348481	+	0.603587i
$668$	6.00000	−	10.3923i	0.232147	−	0.402090i
$669$	−10.0000	+	17.3205i	−0.386622	+	0.669650i
$670$	−7.50000	−	12.9904i	−0.289750	−	0.501862i
$671$	−5.00000			−0.193023
$672$	0.500000	+	2.59808i	0.0192879	+	0.100223i
$673$	−34.0000			−1.31060			−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000			−1.31060			−0.655302	+	0.755367i	$0.727459\pi$
$674$	−11.0000	−	19.0526i	−0.423704	−	0.733877i
$675$	−2.00000	+	3.46410i	−0.0769800	+	0.133333i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	15.0000	+	25.9808i	0.576497	+	0.998522i	0.995877	+	0.0907112i	$0.0289140\pi$
$677$	15.0000	+	25.9808i	0.576497	+	0.998522i	−0.419380	+	0.907811i	$0.637753\pi$
$678$	6.00000			0.230429
$679$	42.5000	+	14.7224i	1.63100	+	0.564995i
$680$	9.00000			0.345134
$681$	10.5000	+	18.1865i	0.402361	+	0.696909i
$682$	2.00000	−	3.46410i	0.0765840	−	0.132647i
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$684$	−1.00000	−	1.73205i	−0.0382360	−	0.0662266i
$685$	−54.0000			−2.06323
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$	−10.0000			−0.381524
$688$	−1.00000	−	1.73205i	−0.0381246	−	0.0660338i
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$	−4.50000	+	7.79423i	−0.171312	+	0.296721i
$691$	9.50000	+	16.4545i	0.361397	+	0.625958i	0.988191	−	0.153227i	$-0.0489666\pi$
$691$	9.50000	+	16.4545i	0.361397	+	0.625958i	−0.626794	+	0.779185i	$0.715633\pi$
$692$	12.0000			0.456172
$693$	−2.50000	−	0.866025i	−0.0949671	−	0.0328976i
$694$	33.0000			1.25266
$695$	21.0000	+	36.3731i	0.796575	+	1.37971i
$696$	−3.00000	+	5.19615i	−0.113715	+	0.196960i
$697$	4.50000	−	7.79423i	0.170450	−	0.295227i
$698$	5.50000	+	9.52628i	0.208178	+	0.360575i
$699$	27.0000			1.02123
$700$	−2.00000	−	10.3923i	−0.0755929	−	0.392792i
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$	1.00000	+	1.73205i	0.0377426	+	0.0653720i
$703$	−2.00000	+	3.46410i	−0.0754314	+	0.130651i
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$	−13.5000	−	23.3827i	−0.508439	−	0.880643i
$706$	12.0000			0.451626
$707$	−24.0000	+	20.7846i	−0.902613	+	0.781686i
$708$	−12.0000			−0.450988
$709$	14.0000	+	24.2487i	0.525781	+	0.910679i	0.999549	+	0.0300298i	$0.00956021\pi$
$709$	14.0000	+	24.2487i	0.525781	+	0.910679i	−0.473768	+	0.880650i	$0.657106\pi$
$710$	−18.0000	+	31.1769i	−0.675528	+	1.17005i
$711$	−8.50000	+	14.7224i	−0.318775	+	0.552134i
$712$	−3.00000	−	5.19615i	−0.112430	−	0.194734i
$713$	−12.0000			−0.449404
$714$	6.00000	−	5.19615i	0.224544	−	0.194461i
$715$	6.00000			0.224387
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$	−3.00000	+	5.19615i	−0.112037	+	0.194054i
$718$	15.0000	−	25.9808i	0.559795	−	0.969593i
$719$	10.5000	+	18.1865i	0.391584	+	0.678243i	0.992659	−	0.120950i	$-0.0385939\pi$
$719$	10.5000	+	18.1865i	0.391584	+	0.678243i	−0.601075	+	0.799193i	$0.705261\pi$
$720$	−3.00000			−0.111803
$721$	−7.00000	−	36.3731i	−0.260694	−	1.35460i
$722$	15.0000			0.558242
$723$	5.00000	+	8.66025i	0.185952	+	0.322078i
$724$	5.00000	−	8.66025i	0.185824	−	0.321856i
$725$	12.0000	−	20.7846i	0.445669	−	0.771921i
$726$	0.500000	+	0.866025i	0.0185567	+	0.0321412i
$727$	14.0000			0.519231			0.259616	−	0.965712i	$-0.416404\pi$
$727$	14.0000			0.519231			0.259616	+	0.965712i	$0.416404\pi$
$728$	−5.00000	−	1.73205i	−0.185312	−	0.0641941i
$729$	1.00000			0.0370370
$730$	24.0000	+	41.5692i	0.888280	+	1.53855i
$731$	−3.00000	+	5.19615i	−0.110959	+	0.192187i
$732$	−2.50000	+	4.33013i	−0.0924027	+	0.160046i
$733$	24.5000	+	42.4352i	0.904928	+	1.56738i	0.821014	+	0.570909i	$0.193409\pi$
$733$	24.5000	+	42.4352i	0.904928	+	1.56738i	0.0839145	+	0.996473i	$0.473258\pi$
$734$	10.0000			0.369107
$735$	−16.5000	−	12.9904i	−0.608612	−	0.479157i
$736$	−3.00000			−0.110581
$737$	2.50000	+	4.33013i	0.0920887	+	0.159502i
$738$	−1.50000	+	2.59808i	−0.0552158	+	0.0956365i
$739$	−19.0000	+	32.9090i	−0.698926	+	1.21058i	0.269913	+	0.962885i	$0.413005\pi$
$739$	−19.0000	+	32.9090i	−0.698926	+	1.21058i	−0.968839	+	0.247691i	$0.920328\pi$
$740$	3.00000	+	5.19615i	0.110282	+	0.191014i
$741$	4.00000			0.146944
$742$	−15.0000	−	5.19615i	−0.550667	−	0.190757i
$743$	−30.0000			−1.10059			−0.550297	−	0.834969i	$-0.685485\pi$
$743$	−30.0000			−1.10059			−0.550297	+	0.834969i	$0.685485\pi$
$744$	−2.00000	−	3.46410i	−0.0733236	−	0.127000i
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$	−0.500000	+	0.866025i	−0.0183063	+	0.0317074i
$747$	−4.50000	−	7.79423i	−0.164646	−	0.285176i
$748$	−3.00000			−0.109691
$749$	−1.50000	−	7.79423i	−0.0548088	−	0.284795i
$750$	−3.00000			−0.109545
$751$	−1.00000	−	1.73205i	−0.0364905	−	0.0632034i	0.847203	−	0.531269i	$-0.178285\pi$
$751$	−1.00000	−	1.73205i	−0.0364905	−	0.0632034i	−0.883694	+	0.468065i	$0.844951\pi$
$752$	4.50000	−	7.79423i	0.164098	−	0.284226i
$753$	12.0000	−	20.7846i	0.437304	−	0.757433i
$754$	−6.00000	−	10.3923i	−0.218507	−	0.378465i
$755$	3.00000			0.109181
$756$	−2.00000	+	1.73205i	−0.0727393	+	0.0629941i
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$	14.5000	+	25.1147i	0.526664	+	0.912208i
$759$	1.50000	−	2.59808i	0.0544466	−	0.0943042i
$760$	−3.00000	+	5.19615i	−0.108821	+	0.188484i
$761$	−7.50000	−	12.9904i	−0.271875	−	0.470901i	0.697467	−	0.716617i	$-0.254310\pi$
$761$	−7.50000	−	12.9904i	−0.271875	−	0.470901i	−0.969342	+	0.245716i	$0.920977\pi$
$762$	−11.0000			−0.398488
$763$	−22.0000	+	19.0526i	−0.796453	+	0.689749i
$764$	24.0000			0.868290
$765$	4.50000	+	7.79423i	0.162698	+	0.281801i
$766$	12.0000	−	20.7846i	0.433578	−	0.750978i
$767$	12.0000	−	20.7846i	0.433295	−	0.750489i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	−46.0000			−1.65880			−0.829401	−	0.558653i	$-0.811318\pi$
$769$	−46.0000			−1.65880			−0.829401	+	0.558653i	$0.811318\pi$
$770$	1.50000	+	7.79423i	0.0540562	+	0.280885i
$771$	6.00000			0.216085
$772$	−1.00000	−	1.73205i	−0.0359908	−	0.0623379i
$773$	13.5000	−	23.3827i	0.485561	−	0.841017i	−0.514301	−	0.857610i	$-0.671949\pi$
$773$	13.5000	−	23.3827i	0.485561	−	0.841017i	0.999862	+	0.0165929i	$0.00528194\pi$
$774$	1.00000	−	1.73205i	0.0359443	−	0.0622573i
$775$	8.00000	+	13.8564i	0.287368	+	0.497737i
$776$	−17.0000			−0.610264
$777$	5.00000	+	1.73205i	0.179374	+	0.0621370i
$778$	−21.0000			−0.752886
$779$	3.00000	+	5.19615i	0.107486	+	0.186171i
$780$	3.00000	−	5.19615i	0.107417	−	0.186052i
$781$	6.00000	−	10.3923i	0.214697	−	0.371866i
$782$	4.50000	+	7.79423i	0.160920	+	0.278721i
$783$	−6.00000			−0.214423
$784$	1.00000	−	6.92820i	0.0357143	−	0.247436i
$785$	−60.0000			−2.14149
$786$	−6.00000	−	10.3923i	−0.214013	−	0.370681i
$787$	11.0000	−	19.0526i	0.392108	−	0.679150i	−0.600620	−	0.799535i	$-0.705079\pi$
$787$	11.0000	−	19.0526i	0.392108	−	0.679150i	0.992727	+	0.120384i	$0.0384127\pi$
$788$	−6.00000	+	10.3923i	−0.213741	+	0.370211i
$789$	6.00000	+	10.3923i	0.213606	+	0.369976i
$790$	51.0000			1.81450
$791$	−15.0000	−	5.19615i	−0.533339	−	0.184754i
$792$	1.00000			0.0355335
$793$	−5.00000	−	8.66025i	−0.177555	−	0.307535i
$794$	1.00000	−	1.73205i	0.0354887	−	0.0614682i
$795$	9.00000	−	15.5885i	0.319197	−	0.552866i
$796$	−1.00000	−	1.73205i	−0.0354441	−	0.0613909i
$797$	−27.0000			−0.956389			−0.478195	−	0.878254i	$-0.658709\pi$
$797$	−27.0000			−0.956389			−0.478195	+	0.878254i	$0.658709\pi$
$798$	1.00000	+	5.19615i	0.0353996	+	0.183942i
$799$	−27.0000			−0.955191
$800$	2.00000	+	3.46410i	0.0707107	+	0.122474i
$801$	3.00000	−	5.19615i	0.106000	−	0.183597i
$802$	15.0000	−	25.9808i	0.529668	−	0.917413i
$803$	−8.00000	−	13.8564i	−0.282314	−	0.488982i
$804$	5.00000			0.176336
$805$	18.0000	−	15.5885i	0.634417	−	0.549421i
$806$	8.00000			0.281788
$807$	−4.50000	−	7.79423i	−0.158408	−	0.274370i
$808$	6.00000	−	10.3923i	0.211079	−	0.365600i
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	−0.776012	−	0.630718i	$-0.782761\pi$
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	0.934224	+	0.356687i	$0.116094\pi$
$810$	−1.50000	−	2.59808i	−0.0527046	−	0.0912871i
$811$	26.0000			0.912983			0.456492	−	0.889728i	$-0.349106\pi$
$811$	26.0000			0.912983			0.456492	+	0.889728i	$0.349106\pi$
$812$	12.0000	−	10.3923i	0.421117	−	0.364698i
$813$	−16.0000			−0.561144
$814$	−1.00000	−	1.73205i	−0.0350500	−	0.0607083i
$815$	−1.50000	+	2.59808i	−0.0525427	+	0.0910066i
$816$	−1.50000	+	2.59808i	−0.0525105	+	0.0909509i
$817$	−2.00000	−	3.46410i	−0.0699711	−	0.121194i
$818$	−14.0000			−0.489499
$819$	−1.00000	−	5.19615i	−0.0349428	−	0.181568i
$820$	9.00000			0.314294
$821$	12.0000	+	20.7846i	0.418803	+	0.725388i	0.995819	−	0.0913446i	$-0.0291165\pi$
$821$	12.0000	+	20.7846i	0.418803	+	0.725388i	−0.577016	+	0.816733i	$0.695783\pi$
$822$	9.00000	−	15.5885i	0.313911	−	0.543710i
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	−0.961851	−	0.273573i	$-0.911795\pi$
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	0.717847	+	0.696201i	$0.245128\pi$
$824$	7.00000	+	12.1244i	0.243857	+	0.422372i
$825$	−4.00000			−0.139262
$826$	30.0000	+	10.3923i	1.04383	+	0.361595i
$827$	33.0000			1.14752			0.573761	−	0.819023i	$-0.305484\pi$
$827$	33.0000			1.14752			0.573761	+	0.819023i	$0.305484\pi$
$828$	−1.50000	−	2.59808i	−0.0521286	−	0.0902894i
$829$	17.0000	−	29.4449i	0.590434	−	1.02266i	−0.403739	−	0.914874i	$-0.632290\pi$
$829$	17.0000	−	29.4449i	0.590434	−	1.02266i	0.994174	−	0.107788i	$-0.0343769\pi$
$830$	−13.5000	+	23.3827i	−0.468592	+	0.811625i
$831$	5.00000	+	8.66025i	0.173448	+	0.300421i
$832$	2.00000			0.0693375
$833$	−19.5000	+	7.79423i	−0.675635	+	0.270054i
$834$	−14.0000			−0.484780
$835$	−18.0000	−	31.1769i	−0.622916	−	1.07892i
$836$	1.00000	−	1.73205i	0.0345857	−	0.0599042i
$837$	2.00000	−	3.46410i	0.0691301	−	0.119737i
$838$	−12.0000	−	20.7846i	−0.414533	−	0.717992i
$839$	33.0000			1.13929			0.569643	−	0.821892i	$-0.307081\pi$
$839$	33.0000			1.13929			0.569643	+	0.821892i	$0.307081\pi$
$840$	7.50000	+	2.59808i	0.258775	+	0.0896421i
$841$	7.00000			0.241379
$842$	10.0000	+	17.3205i	0.344623	+	0.596904i
$843$	−1.50000	+	2.59808i	−0.0516627	+	0.0894825i
$844$	11.0000	−	19.0526i	0.378636	−	0.655816i
$845$	−13.5000	−	23.3827i	−0.464414	−	0.804389i
$846$	9.00000			0.309426
$847$	−0.500000	−	2.59808i	−0.0171802	−	0.0892710i
$848$	6.00000			0.206041
$849$	−7.00000	−	12.1244i	−0.240239	−	0.416107i
$850$	6.00000	−	10.3923i	0.205798	−	0.356453i
$851$	−3.00000	+	5.19615i	−0.102839	+	0.178122i
$852$	−6.00000	−	10.3923i	−0.205557	−	0.356034i
$853$	17.0000			0.582069			0.291034	−	0.956713i	$-0.406001\pi$
$853$	17.0000			0.582069			0.291034	+	0.956713i	$0.406001\pi$
$854$	10.0000	−	8.66025i	0.342193	−	0.296348i
$855$	−6.00000			−0.205196
$856$	1.50000	+	2.59808i	0.0512689	+	0.0888004i
$857$	10.5000	−	18.1865i	0.358673	−	0.621240i	−0.629066	−	0.777352i	$-0.716563\pi$
$857$	10.5000	−	18.1865i	0.358673	−	0.621240i	0.987739	+	0.156112i	$0.0498959\pi$
$858$	−1.00000	+	1.73205i	−0.0341394	+	0.0591312i
$859$	−17.5000	−	30.3109i	−0.597092	−	1.03419i	−0.993248	−	0.116011i	$-0.962989\pi$
$859$	−17.5000	−	30.3109i	−0.597092	−	1.03419i	0.396156	−	0.918183i	$-0.370344\pi$
$860$	−6.00000			−0.204598
$861$	6.00000	−	5.19615i	0.204479	−	0.177084i
$862$	6.00000			0.204361
$863$	−19.5000	−	33.7750i	−0.663788	−	1.14971i	−0.979612	−	0.200897i	$-0.935615\pi$
$863$	−19.5000	−	33.7750i	−0.663788	−	1.14971i	0.315825	−	0.948818i	$-0.397719\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	18.0000	−	31.1769i	0.612018	−	1.06005i
$866$	17.5000	+	30.3109i	0.594674	+	1.03001i
$867$	−8.00000			−0.271694
$868$	2.00000	+	10.3923i	0.0678844	+	0.352738i
$869$	−17.0000			−0.576686
$870$	9.00000	+	15.5885i	0.305129	+	0.528498i
$871$	−5.00000	+	8.66025i	−0.169419	+	0.293442i
$872$	5.50000	−	9.52628i	0.186254	−	0.322601i
$873$	−8.50000	−	14.7224i	−0.287681	−	0.498279i
$874$	−6.00000			−0.202953
$875$	7.50000	+	2.59808i	0.253546	+	0.0878310i
$876$	−16.0000			−0.540590
$877$	18.5000	+	32.0429i	0.624701	+	1.08201i	0.988599	+	0.150574i	$0.0481123\pi$
$877$	18.5000	+	32.0429i	0.624701	+	1.08201i	−0.363898	+	0.931439i	$0.618554\pi$
$878$	−9.50000	+	16.4545i	−0.320609	+	0.555312i
$879$	12.0000	−	20.7846i	0.404750	−	0.701047i
$880$	−1.50000	−	2.59808i	−0.0505650	−	0.0875811i
$881$	6.00000			0.202145			0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000			0.202145			0.101073	+	0.994879i	$0.467773\pi$
$882$	6.50000	−	2.59808i	0.218866	−	0.0874818i
$883$	−13.0000			−0.437485			−0.218742	−	0.975783i	$-0.570195\pi$
$883$	−13.0000			−0.437485			−0.218742	+	0.975783i	$0.570195\pi$
$884$	−3.00000	−	5.19615i	−0.100901	−	0.174766i
$885$	−18.0000	+	31.1769i	−0.605063	+	1.04800i
$886$	9.00000	−	15.5885i	0.302361	−	0.523704i
$887$	−6.00000	−	10.3923i	−0.201460	−	0.348939i	0.747539	−	0.664218i	$-0.231235\pi$
$887$	−6.00000	−	10.3923i	−0.201460	−	0.348939i	−0.948999	+	0.315279i	$0.897902\pi$
$888$	−2.00000			−0.0671156
$889$	27.5000	+	9.52628i	0.922320	+	0.319501i
$890$	−18.0000			−0.603361
$891$	0.500000	+	0.866025i	0.0167506	+	0.0290129i
$892$	−10.0000	+	17.3205i	−0.334825	+	0.579934i
$893$	9.00000	−	15.5885i	0.301174	−	0.521648i
$894$	3.00000	+	5.19615i	0.100335	+	0.173785i
$895$	−36.0000			−1.20335
$896$	0.500000	+	2.59808i	0.0167038	+	0.0867956i
$897$	6.00000			0.200334
$898$	15.0000	+	25.9808i	0.500556	+	0.866989i
$899$	−12.0000	+	20.7846i	−0.400222	+	0.693206i
$900$	−2.00000	+	3.46410i	−0.0666667	+	0.115470i
$901$	−9.00000	−	15.5885i	−0.299833	−	0.519327i
$902$	−3.00000			−0.0998891
$903$	−4.00000	+	3.46410i	−0.133112	+	0.115278i
$904$	6.00000			0.199557
$905$	−15.0000	−	25.9808i	−0.498617	−	0.863630i
$906$	−0.500000	+	0.866025i	−0.0166114	+	0.0287718i
$907$	−23.5000	+	40.7032i	−0.780305	+	1.35153i	0.151460	+	0.988463i	$0.451603\pi$
$907$	−23.5000	+	40.7032i	−0.780305	+	1.35153i	−0.931764	+	0.363064i	$0.881731\pi$
$908$	10.5000	+	18.1865i	0.348455	+	0.603541i
$909$	12.0000			0.398015
$910$	−12.0000	+	10.3923i	−0.397796	+	0.344502i
$911$	−27.0000			−0.894550			−0.447275	−	0.894397i	$-0.647605\pi$
$911$	−27.0000			−0.894550			−0.447275	+	0.894397i	$0.647605\pi$
$912$	−1.00000	−	1.73205i	−0.0331133	−	0.0573539i
$913$	4.50000	−	7.79423i	0.148928	−	0.257951i
$914$	19.0000	−	32.9090i	0.628464	−	1.08853i
$915$	7.50000	+	12.9904i	0.247942	+	0.429449i
$916$	−10.0000			−0.330409
$917$	6.00000	+	31.1769i	0.198137	+	1.02955i
$918$	−3.00000			−0.0990148
$919$	3.50000	+	6.06218i	0.115454	+	0.199973i	0.917961	−	0.396670i	$-0.129834\pi$
$919$	3.50000	+	6.06218i	0.115454	+	0.199973i	−0.802507	+	0.596643i	$0.796501\pi$
$920$	−4.50000	+	7.79423i	−0.148361	+	0.256968i
$921$	11.0000	−	19.0526i	0.362462	−	0.627803i
$922$	3.00000	+	5.19615i	0.0987997	+	0.171126i
$923$	24.0000			0.789970
$924$	−2.50000	−	0.866025i	−0.0822440	−	0.0284901i
$925$	8.00000			0.263038
$926$	−8.00000	−	13.8564i	−0.262896	−	0.455350i
$927$	−7.00000	+	12.1244i	−0.229910	+	0.398216i
$928$	−3.00000	+	5.19615i	−0.0984798	+	0.170572i
$929$	−9.00000	−	15.5885i	−0.295280	−	0.511441i	0.679770	−	0.733426i	$-0.262080\pi$
$929$	−9.00000	−	15.5885i	−0.295280	−	0.511441i	−0.975050	+	0.221985i	$0.928746\pi$
$930$	−12.0000			−0.393496
$931$	2.00000	−	13.8564i	0.0655474	−	0.454125i
$932$	27.0000			0.884414
$933$	−10.5000	−	18.1865i	−0.343755	−	0.595400i
$934$		0			0
$935$	−4.50000	+	7.79423i	−0.147166	+	0.254899i
$936$	1.00000	+	1.73205i	0.0326860	+	0.0566139i
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$	−12.5000	−	4.33013i	−0.408139	−	0.141384i
$939$	2.00000			0.0652675
$940$	−13.5000	−	23.3827i	−0.440321	−	0.762659i
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	−0.681218	−	0.732081i	$-0.738549\pi$
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	0.974609	+	0.223912i	$0.0718827\pi$
$942$	10.0000	−	17.3205i	0.325818	−	0.564333i
$943$	4.50000	+	7.79423i	0.146540	+	0.253815i
$944$	−12.0000			−0.390567
$945$	1.50000	+	7.79423i	0.0487950	+	0.253546i
$946$	2.00000			0.0650256
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	0.681930	−	0.731417i	$-0.261141\pi$
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	−0.974391	+	0.224860i	$0.927807\pi$
$948$	−8.50000	+	14.7224i	−0.276067	+	0.478162i
$949$	16.0000	−	27.7128i	0.519382	−	0.899596i
$950$	4.00000	+	6.92820i	0.129777	+	0.224781i
$951$	−33.0000			−1.07010
$952$	6.00000	−	5.19615i	0.194461	−	0.168408i
$953$	27.0000			0.874616			0.437308	−	0.899312i	$-0.355932\pi$
$953$	27.0000			0.874616			0.437308	+	0.899312i	$0.355932\pi$
$954$	3.00000	+	5.19615i	0.0971286	+	0.168232i
$955$	36.0000	−	62.3538i	1.16493	−	2.01772i
$956$	−3.00000	+	5.19615i	−0.0970269	+	0.168056i
$957$	−3.00000	−	5.19615i	−0.0969762	−	0.167968i
$958$	−24.0000			−0.775405
$959$	−36.0000	+	31.1769i	−1.16250	+	1.00676i
$960$	−3.00000			−0.0968246
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	2.00000	−	3.46410i	0.0644826	−	0.111687i
$963$	−1.50000	+	2.59808i	−0.0483368	+	0.0837218i
$964$	5.00000	+	8.66025i	0.161039	+	0.278928i
$965$	−6.00000			−0.193147
$966$	1.50000	+	7.79423i	0.0482617	+	0.250775i
$967$	−43.0000			−1.38279			−0.691393	−	0.722478i	$-0.743003\pi$
$967$	−43.0000			−1.38279			−0.691393	+	0.722478i	$0.743003\pi$
$968$	0.500000	+	0.866025i	0.0160706	+	0.0278351i
$969$	−3.00000	+	5.19615i	−0.0963739	+	0.166924i
$970$	−25.5000	+	44.1673i	−0.818756	+	1.41813i
$971$	21.0000	+	36.3731i	0.673922	+	1.16727i	0.976783	+	0.214232i	$0.0687250\pi$
$971$	21.0000	+	36.3731i	0.673922	+	1.16727i	−0.302861	+	0.953035i	$0.597942\pi$
$972$	1.00000			0.0320750
$973$	35.0000	+	12.1244i	1.12205	+	0.388689i
$974$	−8.00000			−0.256337
$975$	−4.00000	−	6.92820i	−0.128103	−	0.221880i
$976$	−2.50000	+	4.33013i	−0.0800230	+	0.138604i
$977$	18.0000	−	31.1769i	0.575871	−	0.997438i	−0.420075	−	0.907489i	$-0.637996\pi$
$977$	18.0000	−	31.1769i	0.575871	−	0.997438i	0.995946	−	0.0899487i	$-0.0286703\pi$
$978$	−0.500000	−	0.866025i	−0.0159882	−	0.0276924i
$979$	6.00000			0.191761
$980$	−16.5000	−	12.9904i	−0.527073	−	0.414963i
$981$	11.0000			0.351203
$982$	−1.50000	−	2.59808i	−0.0478669	−	0.0829079i
$983$	22.5000	−	38.9711i	0.717639	−	1.24299i	−0.244294	−	0.969701i	$-0.578556\pi$
$983$	22.5000	−	38.9711i	0.717639	−	1.24299i	0.961933	−	0.273285i	$-0.0881103\pi$
$984$	−1.50000	+	2.59808i	−0.0478183	+	0.0828236i
$985$	18.0000	+	31.1769i	0.573528	+	0.993379i
$986$	18.0000			0.573237
$987$	−22.5000	−	7.79423i	−0.716183	−	0.248093i
$988$	4.00000			0.127257
$989$	−3.00000	−	5.19615i	−0.0953945	−	0.165228i
$990$	1.50000	−	2.59808i	0.0476731	−	0.0825723i
$991$	11.0000	−	19.0526i	0.349427	−	0.605224i	−0.636721	−	0.771094i	$-0.719710\pi$
$991$	11.0000	−	19.0526i	0.349427	−	0.605224i	0.986148	+	0.165870i	$0.0530431\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$	11.0000			0.349074
$994$	6.00000	+	31.1769i	0.190308	+	0.988872i
$995$	−6.00000			−0.190213
$996$	−4.50000	−	7.79423i	−0.142588	−	0.246970i
$997$	−13.0000	+	22.5167i	−0.411714	+	0.713110i	−0.995077	−	0.0991016i	$-0.968403\pi$
$997$	−13.0000	+	22.5167i	−0.411714	+	0.713110i	0.583363	+	0.812211i	$0.301736\pi$
$998$	−14.0000	+	24.2487i	−0.443162	+	0.767580i
$999$	−1.00000	−	1.73205i	−0.0316386	−	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.i.c.67.1	✓	2
3.2	odd	2		1386.2.k.c.991.1		2
7.2	even	3	inner	462.2.i.c.331.1	yes	2
7.3	odd	6		3234.2.a.g.1.1		1
7.4	even	3		3234.2.a.h.1.1		1
21.2	odd	6		1386.2.k.c.793.1		2
21.11	odd	6		9702.2.a.cf.1.1		1
21.17	even	6		9702.2.a.bd.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.i.c.67.1	✓	2	1.1	even	1	trivial
462.2.i.c.331.1	yes	2	7.2	even	3	inner
1386.2.k.c.793.1		2	21.2	odd	6
1386.2.k.c.991.1		2	3.2	odd	2
3234.2.a.g.1.1		1	7.3	odd	6
3234.2.a.h.1.1		1	7.4	even	3
9702.2.a.bd.1.1		1	21.17	even	6
9702.2.a.cf.1.1		1	21.11	odd	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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} -1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} -1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} +2.00000 q^{13} +(0.500000 + 2.59808i) q^{14} -3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.00000 - 1.73205i) q^{19} -3.00000 q^{20} +(-2.00000 + 1.73205i) q^{21} +1.00000 q^{22} +(-1.50000 - 2.59808i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} +(1.00000 + 1.73205i) q^{26} +1.00000 q^{27} +(-2.00000 + 1.73205i) q^{28} -6.00000 q^{29} +(-1.50000 - 2.59808i) q^{30} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} -3.00000 q^{34} +(1.50000 + 7.79423i) q^{35} +1.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(1.00000 - 1.73205i) q^{38} +(-1.00000 + 1.73205i) q^{39} +(-1.50000 - 2.59808i) q^{40} -3.00000 q^{41} +(-2.50000 - 0.866025i) q^{42} +2.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(1.50000 - 2.59808i) q^{45} +(1.50000 - 2.59808i) q^{46} +(4.50000 + 7.79423i) q^{47} +1.00000 q^{48} +(5.50000 + 4.33013i) q^{49} -4.00000 q^{50} +(-1.50000 - 2.59808i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(0.500000 + 0.866025i) q^{54} +3.00000 q^{55} +(-2.50000 - 0.866025i) q^{56} +2.00000 q^{57} +(-3.00000 - 5.19615i) q^{58} +(6.00000 - 10.3923i) q^{59} +(1.50000 - 2.59808i) q^{60} +(-2.50000 - 4.33013i) q^{61} +4.00000 q^{62} +(-0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(3.00000 + 5.19615i) q^{65} +(-0.500000 + 0.866025i) q^{66} +(-2.50000 + 4.33013i) q^{67} +(-1.50000 - 2.59808i) q^{68} +3.00000 q^{69} +(-6.00000 + 5.19615i) q^{70} +12.0000 q^{71} +(0.500000 + 0.866025i) q^{72} +(8.00000 - 13.8564i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-2.00000 - 3.46410i) q^{75} +2.00000 q^{76} +(2.00000 - 1.73205i) q^{77} -2.00000 q^{78} +(-8.50000 - 14.7224i) q^{79} +(1.50000 - 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.50000 - 2.59808i) q^{82} +9.00000 q^{83} +(-0.500000 - 2.59808i) q^{84} -9.00000 q^{85} +(1.00000 + 1.73205i) q^{86} +(3.00000 - 5.19615i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(3.00000 + 5.19615i) q^{89} +3.00000 q^{90} +(5.00000 + 1.73205i) q^{91} +3.00000 q^{92} +(2.00000 + 3.46410i) q^{93} +(-4.50000 + 7.79423i) q^{94} +(3.00000 - 5.19615i) q^{95} +(0.500000 + 0.866025i) q^{96} +17.0000 q^{97} +(-1.00000 + 6.92820i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} + 3 q^{5} - 2 q^{6} + 5 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 + 3 * q^5 - 2 * q^6 + 5 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} + 3 q^{5} - 2 q^{6} + 5 q^{7} - 2 q^{8} - q^{9} - 3 q^{10} + q^{11} - q^{12} + 4 q^{13} + q^{14} - 6 q^{15} - q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - 6 q^{20} - 4 q^{21} + 2 q^{22} - 3 q^{23} + q^{24} - 4 q^{25} + 2 q^{26} + 2 q^{27} - 4 q^{28} - 12 q^{29} - 3 q^{30} + 4 q^{31} + q^{32} + q^{33} - 6 q^{34} + 3 q^{35} + 2 q^{36} - 2 q^{37} + 2 q^{38} - 2 q^{39} - 3 q^{40} - 6 q^{41} - 5 q^{42} + 4 q^{43} + q^{44} + 3 q^{45} + 3 q^{46} + 9 q^{47} + 2 q^{48} + 11 q^{49} - 8 q^{50} - 3 q^{51} - 2 q^{52} - 6 q^{53} + q^{54} + 6 q^{55} - 5 q^{56} + 4 q^{57} - 6 q^{58} + 12 q^{59} + 3 q^{60} - 5 q^{61} + 8 q^{62} - q^{63} + 2 q^{64} + 6 q^{65} - q^{66} - 5 q^{67} - 3 q^{68} + 6 q^{69} - 12 q^{70} + 24 q^{71} + q^{72} + 16 q^{73} + 2 q^{74} - 4 q^{75} + 4 q^{76} + 4 q^{77} - 4 q^{78} - 17 q^{79} + 3 q^{80} - q^{81} - 3 q^{82} + 18 q^{83} - q^{84} - 18 q^{85} + 2 q^{86} + 6 q^{87} - q^{88} + 6 q^{89} + 6 q^{90} + 10 q^{91} + 6 q^{92} + 4 q^{93} - 9 q^{94} + 6 q^{95} + q^{96} + 34 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 + 3 * q^5 - 2 * q^6 + 5 * q^7 - 2 * q^8 - q^9 - 3 * q^10 + q^11 - q^12 + 4 * q^13 + q^14 - 6 * q^15 - q^16 - 3 * q^17 + q^18 - 2 * q^19 - 6 * q^20 - 4 * q^21 + 2 * q^22 - 3 * q^23 + q^24 - 4 * q^25 + 2 * q^26 + 2 * q^27 - 4 * q^28 - 12 * q^29 - 3 * q^30 + 4 * q^31 + q^32 + q^33 - 6 * q^34 + 3 * q^35 + 2 * q^36 - 2 * q^37 + 2 * q^38 - 2 * q^39 - 3 * q^40 - 6 * q^41 - 5 * q^42 + 4 * q^43 + q^44 + 3 * q^45 + 3 * q^46 + 9 * q^47 + 2 * q^48 + 11 * q^49 - 8 * q^50 - 3 * q^51 - 2 * q^52 - 6 * q^53 + q^54 + 6 * q^55 - 5 * q^56 + 4 * q^57 - 6 * q^58 + 12 * q^59 + 3 * q^60 - 5 * q^61 + 8 * q^62 - q^63 + 2 * q^64 + 6 * q^65 - q^66 - 5 * q^67 - 3 * q^68 + 6 * q^69 - 12 * q^70 + 24 * q^71 + q^72 + 16 * q^73 + 2 * q^74 - 4 * q^75 + 4 * q^76 + 4 * q^77 - 4 * q^78 - 17 * q^79 + 3 * q^80 - q^81 - 3 * q^82 + 18 * q^83 - q^84 - 18 * q^85 + 2 * q^86 + 6 * q^87 - q^88 + 6 * q^89 + 6 * q^90 + 10 * q^91 + 6 * q^92 + 4 * q^93 - 9 * q^94 + 6 * q^95 + q^96 + 34 * q^97 - 2 * q^98 - 2 * q^99

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