LMFDB - Embedded newform 462.2.k.d.89.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(89,462)]

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([3, 5, 0]))

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

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

chi := DirichletCharacter("462.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.1
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	462.89
Dual form			462.2.k.d.353.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.358719 + 0.621320i) q^{5} +1.73205 q^{6} +(2.62132 + 0.358719i) q^{7} -1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.358719 + 0.621320i) q^{5} +1.73205 q^{6} +(2.62132 + 0.358719i) q^{7} -1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +(0.621320 - 0.358719i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(-1.50000 - 0.866025i) q^{12} +3.46410i q^{13} +(-2.09077 - 1.62132i) q^{14} -1.24264i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.31552 - 5.74264i) q^{17} +(-2.59808 + 1.50000i) q^{18} +(1.24264 + 0.717439i) q^{19} -0.717439 q^{20} +(-4.24264 + 1.73205i) q^{21} +1.00000 q^{22} +(6.27231 + 3.62132i) q^{23} +(0.866025 + 1.50000i) q^{24} +(2.24264 + 3.88437i) q^{25} +(1.73205 - 3.00000i) q^{26} +5.19615i q^{27} +(1.00000 + 2.44949i) q^{28} +8.48528i q^{29} +(-0.621320 + 1.07616i) q^{30} +(-7.24264 + 4.18154i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.866025 - 1.50000i) q^{33} +6.63103i q^{34} +(-1.16320 + 1.50000i) q^{35} +3.00000 q^{36} +(-2.00000 + 3.46410i) q^{37} +(-0.717439 - 1.24264i) q^{38} +(-3.00000 - 5.19615i) q^{39} +(0.621320 + 0.358719i) q^{40} -5.19615 q^{41} +(4.54026 + 0.621320i) q^{42} +12.4853 q^{43} +(-0.866025 - 0.500000i) q^{44} +(1.07616 + 1.86396i) q^{45} +(-3.62132 - 6.27231i) q^{46} +(-0.358719 + 0.621320i) q^{47} -1.73205i q^{48} +(6.74264 + 1.88064i) q^{49} -4.48528i q^{50} +(9.94655 + 5.74264i) q^{51} +(-3.00000 + 1.73205i) q^{52} +(-7.34847 + 4.24264i) q^{53} +(2.59808 - 4.50000i) q^{54} -0.717439i q^{55} +(0.358719 - 2.62132i) q^{56} -2.48528 q^{57} +(4.24264 - 7.34847i) q^{58} +(6.63103 + 11.4853i) q^{59} +(1.07616 - 0.621320i) q^{60} +(-3.62132 - 2.09077i) q^{61} +8.36308 q^{62} +(4.86396 - 6.27231i) q^{63} -1.00000 q^{64} +(-2.15232 - 1.24264i) q^{65} +(-1.50000 + 0.866025i) q^{66} +(-6.74264 - 11.6786i) q^{67} +(3.31552 - 5.74264i) q^{68} -12.5446 q^{69} +(1.75736 - 0.717439i) q^{70} -6.00000i q^{71} +(-2.59808 - 1.50000i) q^{72} +(1.24264 - 0.717439i) q^{73} +(3.46410 - 2.00000i) q^{74} +(-6.72792 - 3.88437i) q^{75} +1.43488i q^{76} +(-2.44949 + 1.00000i) q^{77} +6.00000i q^{78} +(-1.62132 + 2.80821i) q^{79} +(-0.358719 - 0.621320i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(4.50000 + 2.59808i) q^{82} +6.63103 q^{83} +(-3.62132 - 2.80821i) q^{84} +4.75736 q^{85} +(-10.8126 - 6.24264i) q^{86} +(-7.34847 - 12.7279i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-5.91359 + 10.2426i) q^{89} -2.15232i q^{90} +(-1.24264 + 9.08052i) q^{91} +7.24264i q^{92} +(7.24264 - 12.5446i) q^{93} +(0.621320 - 0.358719i) q^{94} +(-0.891519 + 0.514719i) q^{95} +(-0.866025 + 1.50000i) q^{96} -10.0951i q^{97} +(-4.89898 - 5.00000i) q^{98} +3.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{3} + 4 q^{4} + 4 q^{7} + 12 q^{9}+O(q^{10}) $ 8 * q - 12 * q^3 + 4 * q^4 + 4 * q^7 + 12 * q^9	$ 8 q - 12 q^{3} + 4 q^{4} + 4 q^{7} + 12 q^{9} - 12 q^{10} - 12 q^{12} - 4 q^{16} - 24 q^{19} + 8 q^{22} - 16 q^{25} + 8 q^{28} + 12 q^{30} - 24 q^{31} + 24 q^{36} - 16 q^{37} - 24 q^{39} - 12 q^{40} + 32 q^{43} - 12 q^{46} + 20 q^{49} - 24 q^{52} + 48 q^{57} - 12 q^{61} - 12 q^{63} - 8 q^{64} - 12 q^{66} - 20 q^{67} + 48 q^{70} - 24 q^{73} + 48 q^{75} + 4 q^{79} - 36 q^{81} + 36 q^{82} - 12 q^{84} + 72 q^{85} + 4 q^{88} + 24 q^{91} + 24 q^{93} - 12 q^{94}+O(q^{100}) $ 8 * q - 12 * q^3 + 4 * q^4 + 4 * q^7 + 12 * q^9 - 12 * q^10 - 12 * q^12 - 4 * q^16 - 24 * q^19 + 8 * q^22 - 16 * q^25 + 8 * q^28 + 12 * q^30 - 24 * q^31 + 24 * q^36 - 16 * q^37 - 24 * q^39 - 12 * q^40 + 32 * q^43 - 12 * q^46 + 20 * q^49 - 24 * q^52 + 48 * q^57 - 12 * q^61 - 12 * q^63 - 8 * q^64 - 12 * q^66 - 20 * q^67 + 48 * q^70 - 24 * q^73 + 48 * q^75 + 4 * q^79 - 36 * q^81 + 36 * q^82 - 12 * q^84 + 72 * q^85 + 4 * q^88 + 24 * q^91 + 24 * q^93 - 12 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.358719	+	0.621320i	−0.160424	+	0.277863i	−0.935021	−	0.354593i	$-0.884620\pi$
$5$	−0.358719	+	0.621320i	−0.160424	+	0.277863i	0.774597	+	0.632456i	$0.217953\pi$
$6$	1.73205			0.707107
$7$	2.62132	+	0.358719i	0.990766	+	0.135583i
$7$	2.62132	+	0.358719i	0.990766	+	0.135583i
$8$		−	1.00000i		−	0.353553i
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	0.621320	−	0.358719i	0.196479	−	0.113437i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$	−1.50000	−	0.866025i	−0.433013	−	0.250000i
$13$			3.46410i			0.960769i	0.877058	+	0.480384i	$0.159503\pi$
$13$			3.46410i			0.960769i	−0.877058	+	0.480384i	$0.840497\pi$
$14$	−2.09077	−	1.62132i	−0.558782	−	0.433316i
$15$		−	1.24264i		−	0.320848i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.31552	−	5.74264i	−0.804131	−	1.39279i	−0.916876	−	0.399171i	$-0.869298\pi$
$17$	−3.31552	−	5.74264i	−0.804131	−	1.39279i	0.112746	−	0.993624i	$-0.464035\pi$
$18$	−2.59808	+	1.50000i	−0.612372	+	0.353553i
$19$	1.24264	+	0.717439i	0.285081	+	0.164592i	0.635722	−	0.771918i	$-0.280703\pi$
$19$	1.24264	+	0.717439i	0.285081	+	0.164592i	−0.350640	+	0.936510i	$0.614036\pi$
$20$	−0.717439			−0.160424
$21$	−4.24264	+	1.73205i	−0.925820	+	0.377964i
$22$	1.00000			0.213201
$23$	6.27231	+	3.62132i	1.30787	+	0.755097i	0.981740	−	0.190228i	$-0.0609228\pi$
$23$	6.27231	+	3.62132i	1.30787	+	0.755097i	0.326127	+	0.945326i	$0.394256\pi$
$24$	0.866025	+	1.50000i	0.176777	+	0.306186i
$25$	2.24264	+	3.88437i	0.448528	+	0.776874i
$26$	1.73205	−	3.00000i	0.339683	−	0.588348i
$27$			5.19615i			1.00000i
$28$	1.00000	+	2.44949i	0.188982	+	0.462910i
$29$			8.48528i			1.57568i	0.615882	+	0.787839i	$0.288800\pi$
$29$			8.48528i			1.57568i	−0.615882	+	0.787839i	$0.711200\pi$
$30$	−0.621320	+	1.07616i	−0.113437	+	0.196479i
$31$	−7.24264	+	4.18154i	−1.30082	+	0.751027i	−0.980544	−	0.196299i	$-0.937108\pi$
$31$	−7.24264	+	4.18154i	−1.30082	+	0.751027i	−0.320273	+	0.947325i	$0.603774\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	0.866025	−	1.50000i	0.150756	−	0.261116i
$34$			6.63103i			1.13721i
$35$	−1.16320	+	1.50000i	−0.196616	+	0.253546i
$36$	3.00000			0.500000
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	−0.982274	−	0.187453i	$-0.939977\pi$
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	0.653476	+	0.756948i	$0.273310\pi$
$38$	−0.717439	−	1.24264i	−0.116384	−	0.201583i
$39$	−3.00000	−	5.19615i	−0.480384	−	0.832050i
$40$	0.621320	+	0.358719i	0.0982394	+	0.0567185i
$41$	−5.19615			−0.811503			−0.405751	−	0.913984i	$-0.632990\pi$
$41$	−5.19615			−0.811503			−0.405751	+	0.913984i	$0.632990\pi$
$42$	4.54026	+	0.621320i	0.700577	+	0.0958718i
$43$	12.4853			1.90399			0.951994	−	0.306117i	$-0.0990300\pi$
$43$	12.4853			1.90399			0.951994	+	0.306117i	$0.0990300\pi$
$44$	−0.866025	−	0.500000i	−0.130558	−	0.0753778i
$45$	1.07616	+	1.86396i	0.160424	+	0.277863i
$46$	−3.62132	−	6.27231i	−0.533935	−	0.924802i
$47$	−0.358719	+	0.621320i	−0.0523246	+	0.0906289i	−0.891001	−	0.454001i	$-0.849996\pi$
$47$	−0.358719	+	0.621320i	−0.0523246	+	0.0906289i	0.838677	+	0.544630i	$0.183330\pi$
$48$		−	1.73205i		−	0.250000i
$49$	6.74264	+	1.88064i	0.963234	+	0.268662i
$50$		−	4.48528i		−	0.634315i
$51$	9.94655	+	5.74264i	1.39279	+	0.804131i
$52$	−3.00000	+	1.73205i	−0.416025	+	0.240192i
$53$	−7.34847	+	4.24264i	−1.00939	+	0.582772i	−0.911013	−	0.412378i	$-0.864698\pi$
$53$	−7.34847	+	4.24264i	−1.00939	+	0.582772i	−0.0983769	+	0.995149i	$0.531365\pi$
$54$	2.59808	−	4.50000i	0.353553	−	0.612372i
$55$		−	0.717439i		−	0.0967394i
$56$	0.358719	−	2.62132i	0.0479359	−	0.350289i
$57$	−2.48528			−0.329184
$58$	4.24264	−	7.34847i	0.557086	−	0.964901i
$59$	6.63103	+	11.4853i	0.863287	+	1.49526i	0.868738	+	0.495271i	$0.164931\pi$
$59$	6.63103	+	11.4853i	0.863287	+	1.49526i	−0.00545184	+	0.999985i	$0.501735\pi$
$60$	1.07616	−	0.621320i	0.138931	−	0.0802121i
$61$	−3.62132	−	2.09077i	−0.463663	−	0.267696i	0.249920	−	0.968266i	$-0.419596\pi$
$61$	−3.62132	−	2.09077i	−0.463663	−	0.267696i	−0.713583	+	0.700571i	$0.752929\pi$
$62$	8.36308			1.06211
$63$	4.86396	−	6.27231i	0.612801	−	0.790237i
$64$	−1.00000			−0.125000
$65$	−2.15232	−	1.24264i	−0.266962	−	0.154131i
$66$	−1.50000	+	0.866025i	−0.184637	+	0.106600i
$67$	−6.74264	−	11.6786i	−0.823745	−	1.42677i	−0.902875	−	0.429903i	$-0.858548\pi$
$67$	−6.74264	−	11.6786i	−0.823745	−	1.42677i	0.0791303	−	0.996864i	$-0.474786\pi$
$68$	3.31552	−	5.74264i	0.402065	−	0.696397i
$69$	−12.5446			−1.51019
$70$	1.75736	−	0.717439i	0.210045	−	0.0857504i
$71$		−	6.00000i		−	0.712069i	−0.934473	−	0.356034i	$-0.884129\pi$
$71$		−	6.00000i		−	0.712069i	0.934473	−	0.356034i	$-0.115871\pi$
$72$	−2.59808	−	1.50000i	−0.306186	−	0.176777i
$73$	1.24264	−	0.717439i	0.145440	−	0.0839699i	−0.425514	−	0.904952i	$-0.639907\pi$
$73$	1.24264	−	0.717439i	0.145440	−	0.0839699i	0.570954	+	0.820982i	$0.306573\pi$
$74$	3.46410	−	2.00000i	0.402694	−	0.232495i
$75$	−6.72792	−	3.88437i	−0.776874	−	0.448528i
$76$			1.43488i			0.164592i
$77$	−2.44949	+	1.00000i	−0.279145	+	0.113961i
$78$			6.00000i			0.679366i
$79$	−1.62132	+	2.80821i	−0.182413	+	0.315948i	−0.942702	−	0.333637i	$-0.891724\pi$
$79$	−1.62132	+	2.80821i	−0.182413	+	0.315948i	0.760289	+	0.649585i	$0.225057\pi$
$80$	−0.358719	−	0.621320i	−0.0401061	−	0.0694657i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	4.50000	+	2.59808i	0.496942	+	0.286910i
$83$	6.63103			0.727850			0.363925	−	0.931428i	$-0.381436\pi$
$83$	6.63103			0.727850			0.363925	+	0.931428i	$0.381436\pi$
$84$	−3.62132	−	2.80821i	−0.395118	−	0.306401i
$85$	4.75736			0.516008
$86$	−10.8126	−	6.24264i	−1.16595	−	0.673161i
$87$	−7.34847	−	12.7279i	−0.787839	−	1.36458i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	−5.91359	+	10.2426i	−0.626839	+	1.08572i	0.361343	+	0.932433i	$0.382318\pi$
$89$	−5.91359	+	10.2426i	−0.626839	+	1.08572i	−0.988182	+	0.153285i	$0.951015\pi$
$90$		−	2.15232i		−	0.226874i
$91$	−1.24264	+	9.08052i	−0.130264	+	0.951897i
$92$			7.24264i			0.755097i
$93$	7.24264	−	12.5446i	0.751027	−	1.30082i
$94$	0.621320	−	0.358719i	0.0640843	−	0.0369991i
$95$	−0.891519	+	0.514719i	−0.0914679	+	0.0528090i
$96$	−0.866025	+	1.50000i	−0.0883883	+	0.153093i
$97$		−	10.0951i		−	1.02501i	−0.858686	−	0.512503i	$-0.828718\pi$
$97$		−	10.0951i		−	1.02501i	0.858686	−	0.512503i	$-0.171282\pi$
$98$	−4.89898	−	5.00000i	−0.494872	−	0.505076i
$99$			3.00000i			0.301511i
$100$	−2.24264	+	3.88437i	−0.224264	+	0.388437i
$101$	5.91359	+	10.2426i	0.588424	+	1.01918i	0.994439	+	0.105314i	$0.0335849\pi$
$101$	5.91359	+	10.2426i	0.588424	+	1.01918i	−0.406015	+	0.913867i	$0.633082\pi$
$102$	−5.74264	−	9.94655i	−0.568606	−	0.984855i
$103$	1.75736	+	1.01461i	0.173158	+	0.0999727i	0.584074	−	0.811700i	$-0.301458\pi$
$103$	1.75736	+	1.01461i	0.173158	+	0.0999727i	−0.410916	+	0.911673i	$0.634791\pi$
$104$	3.46410			0.339683
$105$	0.445759	−	3.25736i	0.0435017	−	0.317886i
$106$	8.48528			0.824163
$107$	12.9904	+	7.50000i	1.25583	+	0.725052i	0.972261	−	0.233900i	$-0.0751489\pi$
$107$	12.9904	+	7.50000i	1.25583	+	0.725052i	0.283567	+	0.958952i	$0.408482\pi$
$108$	−4.50000	+	2.59808i	−0.433013	+	0.250000i
$109$	−5.62132	−	9.73641i	−0.538425	−	0.932579i	−0.998989	−	0.0449528i	$-0.985686\pi$
$109$	−5.62132	−	9.73641i	−0.538425	−	0.932579i	0.460564	−	0.887626i	$-0.347647\pi$
$110$	−0.358719	+	0.621320i	−0.0342026	+	0.0592406i
$111$		−	6.92820i		−	0.657596i
$112$	−1.62132	+	2.09077i	−0.153200	+	0.197559i
$113$		−	18.0000i		−	1.69330i	−0.532152	−	0.846649i	$-0.678617\pi$
$113$		−	18.0000i		−	1.69330i	0.532152	−	0.846649i	$-0.321383\pi$
$114$	2.15232	+	1.24264i	0.201583	+	0.116384i
$115$	−4.50000	+	2.59808i	−0.419627	+	0.242272i
$116$	−7.34847	+	4.24264i	−0.682288	+	0.393919i
$117$	9.00000	+	5.19615i	0.832050	+	0.480384i
$118$		−	13.2621i		−	1.22087i
$119$	−6.63103	−	16.2426i	−0.607866	−	1.48896i
$120$	−1.24264			−0.113437
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	2.09077	+	3.62132i	0.189289	+	0.327859i
$123$	7.79423	−	4.50000i	0.702782	−	0.405751i
$124$	−7.24264	−	4.18154i	−0.650408	−	0.375513i
$125$	−6.80511			−0.608668
$126$	−7.34847	+	3.00000i	−0.654654	+	0.267261i
$127$	6.75736			0.599619			0.299809	−	0.953999i	$-0.403077\pi$
$127$	6.75736			0.599619			0.299809	+	0.953999i	$0.403077\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−18.7279	+	10.8126i	−1.64890	+	0.951994i
$130$	1.24264	+	2.15232i	0.108987	+	0.188771i
$131$	6.63103	−	11.4853i	0.579356	−	1.00347i	−0.416198	−	0.909274i	$-0.636638\pi$
$131$	6.63103	−	11.4853i	0.579356	−	1.00347i	0.995553	−	0.0941995i	$-0.0300291\pi$
$132$	1.73205			0.150756
$133$	3.00000	+	2.32640i	0.260133	+	0.201724i
$134$			13.4853i			1.16495i
$135$	−3.22848	−	1.86396i	−0.277863	−	0.160424i
$136$	−5.74264	+	3.31552i	−0.492427	+	0.284303i
$137$	−2.15232	+	1.24264i	−0.183885	+	0.106166i	−0.589117	−	0.808048i	$-0.700524\pi$
$137$	−2.15232	+	1.24264i	−0.183885	+	0.106166i	0.405232	+	0.914214i	$0.367191\pi$
$138$	10.8640	+	6.27231i	0.924802	+	0.533935i
$139$		−	3.46410i		−	0.293821i	−0.989150	−	0.146911i	$-0.953067\pi$
$139$		−	3.46410i		−	0.293821i	0.989150	−	0.146911i	$-0.0469330\pi$
$140$	−1.88064	−	0.257359i	−0.158943	−	0.0217508i
$141$		−	1.24264i		−	0.104649i
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	−1.73205	−	3.00000i	−0.144841	−	0.250873i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	−5.27208	−	3.04384i	−0.437822	−	0.252777i
$146$	−1.43488			−0.118751
$147$	−11.7426	+	3.01834i	−0.968517	+	0.248949i
$148$	−4.00000			−0.328798
$149$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$149$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$150$	3.88437	+	6.72792i	0.317157	+	0.549333i
$151$	4.62132	+	8.00436i	0.376078	+	0.651386i	0.990488	−	0.137601i	$-0.0439392\pi$
$151$	4.62132	+	8.00436i	0.376078	+	0.651386i	−0.614410	+	0.788987i	$0.710606\pi$
$152$	0.717439	−	1.24264i	0.0581920	−	0.100791i
$153$	−19.8931			−1.60826
$154$	2.62132	+	0.358719i	0.211232	+	0.0289064i
$155$		−	6.00000i		−	0.481932i
$156$	3.00000	−	5.19615i	0.240192	−	0.416025i
$157$	−7.75736	+	4.47871i	−0.619105	+	0.357440i	−0.776520	−	0.630092i	$-0.783017\pi$
$157$	−7.75736	+	4.47871i	−0.619105	+	0.357440i	0.157416	+	0.987532i	$0.449684\pi$
$158$	2.80821	−	1.62132i	0.223409	−	0.128985i
$159$	7.34847	−	12.7279i	0.582772	−	1.00939i
$160$			0.717439i			0.0567185i
$161$	15.1427	+	11.7426i	1.19341	+	0.925450i
$162$			9.00000i			0.707107i
$163$	6.50000	−	11.2583i	0.509119	−	0.881820i	−0.490825	−	0.871258i	$-0.663305\pi$
$163$	6.50000	−	11.2583i	0.509119	−	0.881820i	0.999944	−	0.0105623i	$-0.00336213\pi$
$164$	−2.59808	−	4.50000i	−0.202876	−	0.351391i
$165$	0.621320	+	1.07616i	0.0483697	+	0.0837788i
$166$	−5.74264	−	3.31552i	−0.445715	−	0.257334i
$167$	11.8272			0.915215			0.457607	−	0.889154i	$-0.348707\pi$
$167$	11.8272			0.915215			0.457607	+	0.889154i	$0.348707\pi$
$168$	1.73205	+	4.24264i	0.133631	+	0.327327i
$169$	1.00000			0.0769231
$170$	−4.11999	−	2.37868i	−0.315989	−	0.182436i
$171$	3.72792	−	2.15232i	0.285081	−	0.164592i
$172$	6.24264	+	10.8126i	0.475997	+	0.824451i
$173$	0.717439	−	1.24264i	0.0545459	−	0.0944762i	−0.837463	−	0.546494i	$-0.815962\pi$
$173$	0.717439	−	1.24264i	0.0545459	−	0.0944762i	0.892009	+	0.452018i	$0.149296\pi$
$174$			14.6969i			1.11417i
$175$	4.48528	+	10.9867i	0.339055	+	0.830513i
$176$		−	1.00000i		−	0.0753778i
$177$	−19.8931	−	11.4853i	−1.49526	−	0.863287i
$178$	10.2426	−	5.91359i	0.767718	−	0.443242i
$179$	−2.15232	+	1.24264i	−0.160872	+	0.0928793i	−0.578275	−	0.815842i	$-0.696274\pi$
$179$	−2.15232	+	1.24264i	−0.160872	+	0.0928793i	0.417403	+	0.908722i	$0.362940\pi$
$180$	−1.07616	+	1.86396i	−0.0802121	+	0.138931i
$181$			2.86976i			0.213307i	0.994296	+	0.106654i	$0.0340136\pi$
$181$			2.86976i			0.213307i	−0.994296	+	0.106654i	$0.965986\pi$
$182$	5.61642	−	7.24264i	0.416317	−	0.536860i
$183$	7.24264			0.535391
$184$	3.62132	−	6.27231i	0.266967	−	0.462401i
$185$	−1.43488	−	2.48528i	−0.105494	−	0.182722i
$186$	−12.5446	+	7.24264i	−0.919816	+	0.531056i
$187$	5.74264	+	3.31552i	0.419943	+	0.242454i
$188$	−0.717439			−0.0523246
$189$	−1.86396	+	13.6208i	−0.135583	+	0.990766i
$190$	1.02944			0.0746832
$191$	15.5885	+	9.00000i	1.12794	+	0.651217i	0.943416	−	0.331611i	$-0.107592\pi$
$191$	15.5885	+	9.00000i	1.12794	+	0.651217i	0.184525	+	0.982828i	$0.440925\pi$
$192$	1.50000	−	0.866025i	0.108253	−	0.0625000i
$193$	−0.242641	−	0.420266i	−0.0174657	−	0.0302514i	0.857160	−	0.515049i	$-0.172226\pi$
$193$	−0.242641	−	0.420266i	−0.0174657	−	0.0302514i	−0.874626	+	0.484798i	$0.838893\pi$
$194$	−5.04757	+	8.74264i	−0.362394	+	0.627685i
$195$	4.30463			0.308261
$196$	1.74264	+	6.77962i	0.124474	+	0.484258i
$197$		−	8.48528i		−	0.604551i	−0.953221	−	0.302276i	$-0.902254\pi$
$197$		−	8.48528i		−	0.604551i	0.953221	−	0.302276i	$-0.0977463\pi$
$198$	1.50000	−	2.59808i	0.106600	−	0.184637i
$199$	−5.48528	+	3.16693i	−0.388841	+	0.224498i	−0.681658	−	0.731671i	$-0.738741\pi$
$199$	−5.48528	+	3.16693i	−0.388841	+	0.224498i	0.292817	+	0.956169i	$0.405407\pi$
$200$	3.88437	−	2.24264i	0.274666	−	0.158579i
$201$	20.2279	+	11.6786i	1.42677	+	0.823745i
$202$		−	11.8272i		−	0.832158i
$203$	−3.04384	+	22.2426i	−0.213635	+	1.56113i
$204$			11.4853i			0.804131i
$205$	1.86396	−	3.22848i	0.130185	−	0.225486i
$206$	−1.01461	−	1.75736i	−0.0706914	−	0.122441i
$207$	18.8169	−	10.8640i	1.30787	−	0.755097i
$208$	−3.00000	−	1.73205i	−0.208013	−	0.120096i
$209$	−1.43488			−0.0992526
$210$	−2.01472	+	2.59808i	−0.139029	+	0.179284i
$211$	−4.48528			−0.308780			−0.154390	−	0.988010i	$-0.549341\pi$
$211$	−4.48528			−0.308780			−0.154390	+	0.988010i	$0.549341\pi$
$212$	−7.34847	−	4.24264i	−0.504695	−	0.291386i
$213$	5.19615	+	9.00000i	0.356034	+	0.616670i
$214$	−7.50000	−	12.9904i	−0.512689	−	0.888004i
$215$	−4.47871	+	7.75736i	−0.305446	+	0.529048i
$216$	5.19615			0.353553
$217$	−20.4853	+	8.36308i	−1.39063	+	0.567723i
$218$			11.2426i			0.761448i
$219$	−1.24264	+	2.15232i	−0.0839699	+	0.145440i
$220$	0.621320	−	0.358719i	0.0418894	−	0.0241849i
$221$	19.8931	−	11.4853i	1.33815	−	0.772584i
$222$	−3.46410	+	6.00000i	−0.232495	+	0.402694i
$223$		−	13.2621i		−	0.888093i	−0.896004	−	0.444047i	$-0.853542\pi$
$223$		−	13.2621i		−	0.888093i	0.896004	−	0.444047i	$-0.146458\pi$
$224$	2.44949	−	1.00000i	0.163663	−	0.0668153i
$225$	13.4558			0.897056
$226$	−9.00000	+	15.5885i	−0.598671	+	1.03693i
$227$	−1.16320	−	2.01472i	−0.0772042	−	0.133722i	0.824838	−	0.565368i	$-0.191266\pi$
$227$	−1.16320	−	2.01472i	−0.0772042	−	0.133722i	−0.902043	+	0.431647i	$0.857933\pi$
$228$	−1.24264	−	2.15232i	−0.0822959	−	0.142541i
$229$	6.00000	+	3.46410i	0.396491	+	0.228914i	0.684969	−	0.728572i	$-0.259816\pi$
$229$	6.00000	+	3.46410i	0.396491	+	0.228914i	−0.288478	+	0.957487i	$0.593149\pi$
$230$	5.19615			0.342624
$231$	2.80821	−	3.62132i	0.184767	−	0.238265i
$232$	8.48528			0.557086
$233$	6.90271	+	3.98528i	0.452212	+	0.261084i	0.708764	−	0.705446i	$-0.249253\pi$
$233$	6.90271	+	3.98528i	0.452212	+	0.261084i	−0.256552	+	0.966530i	$0.582587\pi$
$234$	−5.19615	−	9.00000i	−0.339683	−	0.588348i
$235$	−0.257359	−	0.445759i	−0.0167883	−	0.0290781i
$236$	−6.63103	+	11.4853i	−0.431643	+	0.747628i
$237$		−	5.61642i		−	0.364826i
$238$	−2.37868	+	17.3821i	−0.154187	+	1.12671i
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$	1.07616	+	0.621320i	0.0694657	+	0.0401061i
$241$	12.0000	−	6.92820i	0.772988	−	0.446285i	−0.0609515	−	0.998141i	$-0.519414\pi$
$241$	12.0000	−	6.92820i	0.772988	−	0.446285i	0.833939	+	0.551856i	$0.186080\pi$
$242$	−0.866025	+	0.500000i	−0.0556702	+	0.0321412i
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$		−	4.18154i		−	0.267696i
$245$	−3.58719	+	3.51472i	−0.229177	+	0.224547i
$246$	−9.00000			−0.573819
$247$	−2.48528	+	4.30463i	−0.158135	+	0.273897i
$248$	4.18154	+	7.24264i	0.265528	+	0.459908i
$249$	−9.94655	+	5.74264i	−0.630337	+	0.363925i
$250$	5.89340	+	3.40256i	0.372731	+	0.215196i
$251$	−14.6969			−0.927663			−0.463831	−	0.885924i	$-0.653526\pi$
$251$	−14.6969			−0.927663			−0.463831	+	0.885924i	$0.653526\pi$
$252$	7.86396	+	1.07616i	0.495383	+	0.0677916i
$253$	−7.24264			−0.455341
$254$	−5.85204	−	3.37868i	−0.367190	−	0.211997i
$255$	−7.13604	+	4.11999i	−0.446876	+	0.258004i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.91359	−	10.2426i	0.368880	−	0.638918i	−0.620511	−	0.784198i	$-0.713075\pi$
$257$	5.91359	−	10.2426i	0.368880	−	0.638918i	0.989391	+	0.145279i	$0.0464081\pi$
$258$	21.6251			1.34632
$259$	−6.48528	+	8.36308i	−0.402976	+	0.519657i
$260$		−	2.48528i		−	0.154131i
$261$	22.0454	+	12.7279i	1.36458	+	0.787839i
$262$	−11.4853	+	6.63103i	−0.709563	+	0.409666i
$263$	−19.8931	+	11.4853i	−1.22666	+	0.708213i	−0.966330	−	0.257307i	$-0.917165\pi$
$263$	−19.8931	+	11.4853i	−1.22666	+	0.708213i	−0.260331	+	0.965519i	$0.583832\pi$
$264$	−1.50000	−	0.866025i	−0.0923186	−	0.0533002i
$265$		−	6.08767i		−	0.373963i
$266$	−1.43488	−	3.51472i	−0.0879780	−	0.215501i
$267$		−	20.4853i		−	1.25368i
$268$	6.74264	−	11.6786i	0.411872	−	0.713384i
$269$	−4.11999	−	7.13604i	−0.251200	−	0.435092i	0.712656	−	0.701514i	$-0.247492\pi$
$269$	−4.11999	−	7.13604i	−0.251200	−	0.435092i	−0.963857	+	0.266422i	$0.914159\pi$
$270$	1.86396	+	3.22848i	0.113437	+	0.196479i
$271$	−18.7279	−	10.8126i	−1.13764	−	0.656817i	−0.191795	−	0.981435i	$-0.561431\pi$
$271$	−18.7279	−	10.8126i	−1.13764	−	0.656817i	−0.945845	+	0.324618i	$0.894764\pi$
$272$	6.63103			0.402065
$273$	−6.00000	−	14.6969i	−0.363137	−	0.889499i
$274$	2.48528			0.150141
$275$	−3.88437	−	2.24264i	−0.234236	−	0.135236i
$276$	−6.27231	−	10.8640i	−0.377549	−	0.653934i
$277$	−5.75736	−	9.97204i	−0.345926	−	0.599162i	0.639595	−	0.768712i	$-0.279102\pi$
$277$	−5.75736	−	9.97204i	−0.345926	−	0.599162i	−0.985522	+	0.169550i	$0.945769\pi$
$278$	−1.73205	+	3.00000i	−0.103882	+	0.179928i
$279$			25.0892i			1.50205i
$280$	1.50000	+	1.16320i	0.0896421	+	0.0695144i
$281$		−	0.514719i		−	0.0307055i	−0.999882	−	0.0153528i	$-0.995113\pi$
$281$		−	0.514719i		−	0.0307055i	0.999882	−	0.0153528i	$-0.00488713\pi$
$282$	−0.621320	+	1.07616i	−0.0369991	+	0.0640843i
$283$	21.2132	−	12.2474i	1.26099	−	0.728035i	0.287727	−	0.957712i	$-0.407100\pi$
$283$	21.2132	−	12.2474i	1.26099	−	0.728035i	0.973267	+	0.229677i	$0.0737670\pi$
$284$	5.19615	−	3.00000i	0.308335	−	0.178017i
$285$	0.891519	−	1.54416i	0.0528090	−	0.0914679i
$286$			3.46410i			0.204837i
$287$	−13.6208	−	1.86396i	−0.804009	−	0.110026i
$288$		−	3.00000i		−	0.176777i
$289$	−13.4853	+	23.3572i	−0.793252	+	1.37395i
$290$	3.04384	+	5.27208i	0.178740	+	0.309587i
$291$	8.74264	+	15.1427i	0.512503	+	0.887681i
$292$	1.24264	+	0.717439i	0.0727200	+	0.0419849i
$293$	22.2195			1.29808			0.649038	−	0.760756i	$-0.275172\pi$
$293$	22.2195			1.29808			0.649038	+	0.760756i	$0.275172\pi$
$294$	11.6786	+	3.25736i	0.681110	+	0.189973i
$295$	−9.51472			−0.553968
$296$	3.46410	+	2.00000i	0.201347	+	0.116248i
$297$	−2.59808	−	4.50000i	−0.150756	−	0.261116i
$298$		0			0
$299$	−12.5446	+	21.7279i	−0.725474	+	1.25656i
$300$		−	7.76874i		−	0.448528i
$301$	32.7279	+	4.47871i	1.88641	+	0.258149i
$302$		−	9.24264i		−	0.531854i
$303$	−17.7408	−	10.2426i	−1.01918	−	0.588424i
$304$	−1.24264	+	0.717439i	−0.0712703	+	0.0411479i
$305$	2.59808	−	1.50000i	0.148765	−	0.0858898i
$306$	17.2279	+	9.94655i	0.984855	+	0.568606i
$307$		−	4.05845i		−	0.231628i	−0.993271	−	0.115814i	$-0.963052\pi$
$307$		−	4.05845i		−	0.231628i	0.993271	−	0.115814i	$-0.0369476\pi$
$308$	−2.09077	−	1.62132i	−0.119133	−	0.0923833i
$309$	−3.51472			−0.199945
$310$	−3.00000	+	5.19615i	−0.170389	+	0.295122i
$311$	−14.3382	−	24.8345i	−0.813046	−	1.40824i	−0.910723	−	0.413018i	$-0.864474\pi$
$311$	−14.3382	−	24.8345i	−0.813046	−	1.40824i	0.0976768	−	0.995218i	$-0.468859\pi$
$312$	−5.19615	+	3.00000i	−0.294174	+	0.169842i
$313$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$313$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$314$	8.95743			0.505497
$315$	2.15232	+	5.27208i	0.121269	+	0.297048i
$316$	−3.24264			−0.182413
$317$	−14.5123	−	8.37868i	−0.815092	−	0.470594i	0.0336291	−	0.999434i	$-0.489294\pi$
$317$	−14.5123	−	8.37868i	−0.815092	−	0.470594i	−0.848721	+	0.528841i	$0.822627\pi$
$318$	−12.7279	+	7.34847i	−0.713746	+	0.412082i
$319$	−4.24264	−	7.34847i	−0.237542	−	0.411435i
$320$	0.358719	−	0.621320i	0.0200530	−	0.0347329i
$321$	−25.9808			−1.45010
$322$	−7.24264	−	17.7408i	−0.403617	−	0.988655i
$323$		−	9.51472i		−	0.529413i
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$	−13.4558	+	7.76874i	−0.746396	+	0.430932i
$326$	−11.2583	+	6.50000i	−0.623541	+	0.360002i
$327$	16.8640	+	9.73641i	0.932579	+	0.538425i
$328$			5.19615i			0.286910i
$329$	−1.16320	+	1.50000i	−0.0641292	+	0.0826977i
$330$		−	1.24264i		−	0.0684051i
$331$	−9.50000	+	16.4545i	−0.522167	+	0.904420i	0.477500	+	0.878632i	$0.341543\pi$
$331$	−9.50000	+	16.4545i	−0.522167	+	0.904420i	−0.999667	+	0.0257885i	$0.991790\pi$
$332$	3.31552	+	5.74264i	0.181963	+	0.315168i
$333$	6.00000	+	10.3923i	0.328798	+	0.569495i
$334$	−10.2426	−	5.91359i	−0.560452	−	0.323577i
$335$	9.67487			0.528594
$336$	0.621320	−	4.54026i	0.0338958	−	0.247691i
$337$	13.5147			0.736194			0.368097	−	0.929787i	$-0.380009\pi$
$337$	13.5147			0.736194			0.368097	+	0.929787i	$0.380009\pi$
$338$	−0.866025	−	0.500000i	−0.0471056	−	0.0271964i
$339$	15.5885	+	27.0000i	0.846649	+	1.46644i
$340$	2.37868	+	4.11999i	0.129002	+	0.223438i
$341$	4.18154	−	7.24264i	0.226443	−	0.392211i
$342$	−4.30463			−0.232768
$343$	17.0000	+	7.34847i	0.917914	+	0.396780i
$344$		−	12.4853i		−	0.673161i
$345$	4.50000	−	7.79423i	0.242272	−	0.419627i
$346$	−1.24264	+	0.717439i	−0.0668048	+	0.0385698i
$347$	15.1427	−	8.74264i	0.812903	−	0.469330i	−0.0350602	−	0.999385i	$-0.511162\pi$
$347$	15.1427	−	8.74264i	0.812903	−	0.469330i	0.847963	+	0.530056i	$0.177829\pi$
$348$	7.34847	−	12.7279i	0.393919	−	0.682288i
$349$			18.8785i			1.01054i	0.862961	+	0.505271i	$0.168607\pi$
$349$			18.8785i			1.01054i	−0.862961	+	0.505271i	$0.831393\pi$
$350$	1.60896	−	11.7574i	0.0860024	−	0.628457i
$351$	−18.0000			−0.960769
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	−2.15232	−	3.72792i	−0.114556	−	0.198417i	0.803046	−	0.595917i	$-0.203211\pi$
$353$	−2.15232	−	3.72792i	−0.114556	−	0.198417i	−0.917602	+	0.397500i	$0.869878\pi$
$354$	11.4853	+	19.8931i	0.610436	+	1.05731i
$355$	3.72792	+	2.15232i	0.197858	+	0.114233i
$356$	−11.8272			−0.626839
$357$	24.0131	+	18.6213i	1.27091	+	0.985545i
$358$	2.48528			0.131351
$359$	7.34847	+	4.24264i	0.387837	+	0.223918i	0.681223	−	0.732076i	$-0.261449\pi$
$359$	7.34847	+	4.24264i	0.387837	+	0.223918i	−0.293385	+	0.955994i	$0.594782\pi$
$360$	1.86396	−	1.07616i	0.0982394	−	0.0567185i
$361$	−8.47056	−	14.6714i	−0.445819	−	0.772181i
$362$	1.43488	−	2.48528i	0.0754155	−	0.130623i
$363$			1.73205i			0.0909091i
$364$	−8.48528	+	3.46410i	−0.444750	+	0.181568i
$365$			1.02944i			0.0538832i
$366$	−6.27231	−	3.62132i	−0.327859	−	0.189289i
$367$	3.72792	−	2.15232i	0.194596	−	0.112350i	−0.399536	−	0.916717i	$-0.630829\pi$
$367$	3.72792	−	2.15232i	0.194596	−	0.112350i	0.594132	+	0.804367i	$0.297496\pi$
$368$	−6.27231	+	3.62132i	−0.326967	+	0.188774i
$369$	−7.79423	+	13.5000i	−0.405751	+	0.702782i
$370$			2.86976i			0.149191i
$371$	−20.7846	+	8.48528i	−1.07908	+	0.440534i
$372$	14.4853			0.751027
$373$	3.86396	−	6.69258i	0.200068	−	0.346528i	−0.748482	−	0.663155i	$-0.769217\pi$
$373$	3.86396	−	6.69258i	0.200068	−	0.346528i	0.948550	+	0.316627i	$0.102550\pi$
$374$	−3.31552	−	5.74264i	−0.171441	−	0.296945i
$375$	10.2077	−	5.89340i	0.527122	−	0.304334i
$376$	0.621320	+	0.358719i	0.0320422	+	0.0184995i
$377$	−29.3939			−1.51386
$378$	8.42463	−	10.8640i	0.433316	−	0.558782i
$379$	−33.9706			−1.74495			−0.872475	−	0.488658i	$-0.837487\pi$
$379$	−33.9706			−1.74495			−0.872475	+	0.488658i	$0.837487\pi$
$380$	−0.891519	−	0.514719i	−0.0457340	−	0.0264045i
$381$	−10.1360	+	5.85204i	−0.519285	+	0.299809i
$382$	−9.00000	−	15.5885i	−0.460480	−	0.797575i
$383$	−8.78335	+	15.2132i	−0.448808	+	0.777358i	−0.998309	−	0.0581349i	$-0.981485\pi$
$383$	−8.78335	+	15.2132i	−0.448808	+	0.777358i	0.549501	+	0.835493i	$0.314818\pi$
$384$	−1.73205			−0.0883883
$385$	0.257359	−	1.88064i	0.0131162	−	0.0958462i
$386$			0.485281i			0.0247002i
$387$	18.7279	−	32.4377i	0.951994	−	1.64890i
$388$	8.74264	−	5.04757i	0.443840	−	0.256251i
$389$	−1.96768	+	1.13604i	−0.0997652	+	0.0575995i	−0.549052	−	0.835788i	$-0.685011\pi$
$389$	−1.96768	+	1.13604i	−0.0997652	+	0.0575995i	0.449287	+	0.893387i	$0.351678\pi$
$390$	−3.72792	−	2.15232i	−0.188771	−	0.108987i
$391$		−	48.0262i		−	2.42879i
$392$	1.88064	−	6.74264i	0.0949865	−	0.340555i
$393$			22.9706i			1.15871i
$394$	−4.24264	+	7.34847i	−0.213741	+	0.370211i
$395$	−1.16320	−	2.01472i	−0.0585269	−	0.101371i
$396$	−2.59808	+	1.50000i	−0.130558	+	0.0753778i
$397$	−21.2132	−	12.2474i	−1.06466	−	0.614682i	−0.137943	−	0.990440i	$-0.544049\pi$
$397$	−21.2132	−	12.2474i	−1.06466	−	0.614682i	−0.926718	+	0.375758i	$0.877382\pi$
$398$	6.33386			0.317488
$399$	−6.51472	−	0.891519i	−0.326144	−	0.0446318i
$400$	−4.48528			−0.224264
$401$	−7.34847	−	4.24264i	−0.366965	−	0.211867i	0.305167	−	0.952299i	$-0.401288\pi$
$401$	−7.34847	−	4.24264i	−0.366965	−	0.211867i	−0.672132	+	0.740432i	$0.734621\pi$
$402$	−11.6786	−	20.2279i	−0.582475	−	1.00888i
$403$	−14.4853	−	25.0892i	−0.721563	−	1.24978i
$404$	−5.91359	+	10.2426i	−0.294212	+	0.509590i
$405$	6.45695			0.320848
$406$	13.7574	−	17.7408i	0.682766	−	0.880460i
$407$		−	4.00000i		−	0.198273i
$408$	5.74264	−	9.94655i	0.284303	−	0.492427i
$409$	4.75736	−	2.74666i	0.235236	−	0.135814i	−0.377749	−	0.925908i	$-0.623302\pi$
$409$	4.75736	−	2.74666i	0.235236	−	0.135814i	0.612985	+	0.790094i	$0.289968\pi$
$410$	−3.22848	+	1.86396i	−0.159443	+	0.0920545i
$411$	2.15232	−	3.72792i	0.106166	−	0.183885i
$412$			2.02922i			0.0999727i
$413$	13.2621	+	32.4853i	0.652583	+	1.59850i
$414$	−21.7279			−1.06787
$415$	−2.37868	+	4.11999i	−0.116765	+	0.202243i
$416$	1.73205	+	3.00000i	0.0849208	+	0.147087i
$417$	3.00000	+	5.19615i	0.146911	+	0.254457i
$418$	1.24264	+	0.717439i	0.0607795	+	0.0350911i
$419$	−1.43488			−0.0700984			−0.0350492	−	0.999386i	$-0.511159\pi$
$419$	−1.43488			−0.0700984			−0.0350492	+	0.999386i	$0.511159\pi$
$420$	3.04384	−	1.24264i	0.148524	−	0.0606347i
$421$	−0.485281			−0.0236512			−0.0118256	−	0.999930i	$-0.503764\pi$
$421$	−0.485281			−0.0236512			−0.0118256	+	0.999930i	$0.503764\pi$
$422$	3.88437	+	2.24264i	0.189088	+	0.109170i
$423$	1.07616	+	1.86396i	0.0523246	+	0.0906289i
$424$	4.24264	+	7.34847i	0.206041	+	0.356873i
$425$	14.8710	−	25.7574i	0.721350	−	1.24942i
$426$		−	10.3923i		−	0.503509i
$427$	−8.74264	−	6.77962i	−0.423086	−	0.328089i
$428$			15.0000i			0.725052i
$429$	5.19615	+	3.00000i	0.250873	+	0.144841i
$430$	7.75736	−	4.47871i	0.374093	−	0.215983i
$431$	22.9369	−	13.2426i	1.10483	−	0.637876i	0.167347	−	0.985898i	$-0.446480\pi$
$431$	22.9369	−	13.2426i	1.10483	−	0.637876i	0.937486	+	0.348023i	$0.113147\pi$
$432$	−4.50000	−	2.59808i	−0.216506	−	0.125000i
$433$			9.25460i			0.444748i	0.974961	+	0.222374i	$0.0713805\pi$
$433$			9.25460i			0.444748i	−0.974961	+	0.222374i	$0.928619\pi$
$434$	21.9223	+	3.00000i	1.05230	+	0.144005i
$435$	10.5442			0.505554
$436$	5.62132	−	9.73641i	0.269212	−	0.466290i
$437$	5.19615	+	9.00000i	0.248566	+	0.430528i
$438$	2.15232	−	1.24264i	0.102842	−	0.0593757i
$439$	−13.3492	−	7.70719i	−0.637125	−	0.367844i	0.146381	−	0.989228i	$-0.453237\pi$
$439$	−13.3492	−	7.70719i	−0.637125	−	0.367844i	−0.783506	+	0.621384i	$0.786571\pi$
$440$	−0.717439			−0.0342026
$441$	15.0000	−	14.6969i	0.714286	−	0.699854i
$442$	−22.9706			−1.09260
$443$	−31.1769	−	18.0000i	−1.48126	−	0.855206i	−0.481486	−	0.876454i	$-0.659903\pi$
$443$	−31.1769	−	18.0000i	−1.48126	−	0.855206i	−0.999774	+	0.0212481i	$0.993236\pi$
$444$	6.00000	−	3.46410i	0.284747	−	0.164399i
$445$	−4.24264	−	7.34847i	−0.201120	−	0.348351i
$446$	−6.63103	+	11.4853i	−0.313988	+	0.543844i
$447$		0			0
$448$	−2.62132	−	0.358719i	−0.123846	−	0.0169479i
$449$		−	20.4853i		−	0.966760i	−0.875411	−	0.483380i	$-0.839409\pi$
$449$		−	20.4853i		−	0.966760i	0.875411	−	0.483380i	$-0.160591\pi$
$450$	−11.6531	−	6.72792i	−0.549333	−	0.317157i
$451$	4.50000	−	2.59808i	0.211897	−	0.122339i
$452$	15.5885	−	9.00000i	0.733219	−	0.423324i
$453$	−13.8640	−	8.00436i	−0.651386	−	0.376078i
$454$			2.32640i			0.109183i
$455$	−5.19615	−	4.02944i	−0.243599	−	0.188903i
$456$			2.48528i			0.116384i
$457$	6.48528	−	11.2328i	0.303369	−	0.525450i	−0.673528	−	0.739162i	$-0.735222\pi$
$457$	6.48528	−	11.2328i	0.303369	−	0.525450i	0.976897	+	0.213712i	$0.0685553\pi$
$458$	−3.46410	−	6.00000i	−0.161867	−	0.280362i
$459$	29.8396	−	17.2279i	1.39279	−	0.804131i
$460$	−4.50000	−	2.59808i	−0.209814	−	0.121136i
$461$	13.2621			0.617676			0.308838	−	0.951115i	$-0.400060\pi$
$461$	13.2621			0.617676			0.308838	+	0.951115i	$0.400060\pi$
$462$	−4.24264	+	1.73205i	−0.197386	+	0.0805823i
$463$	21.4558			0.997138			0.498569	−	0.866850i	$-0.333859\pi$
$463$	21.4558			0.997138			0.498569	+	0.866850i	$0.333859\pi$
$464$	−7.34847	−	4.24264i	−0.341144	−	0.196960i
$465$	5.19615	+	9.00000i	0.240966	+	0.417365i
$466$	−3.98528	−	6.90271i	−0.184615	−	0.319762i
$467$	−15.5885	+	27.0000i	−0.721348	+	1.24941i	0.239112	+	0.970992i	$0.423144\pi$
$467$	−15.5885	+	27.0000i	−0.721348	+	1.24941i	−0.960460	+	0.278419i	$0.910190\pi$
$468$			10.3923i			0.480384i
$469$	−13.4853	−	33.0321i	−0.622692	−	1.52528i
$470$			0.514719i			0.0237422i
$471$	7.75736	−	13.4361i	0.357440	−	0.619105i
$472$	11.4853	−	6.63103i	0.528653	−	0.305218i
$473$	−10.8126	+	6.24264i	−0.497163	+	0.287037i
$474$	−2.80821	+	4.86396i	−0.128985	+	0.223409i
$475$			6.43583i			0.295296i
$476$	10.7510	−	13.8640i	0.492772	−	0.635454i
$477$			25.4558i			1.16554i
$478$		0			0
$479$	8.78335	+	15.2132i	0.401321	+	0.695109i	0.993886	−	0.110414i	$-0.0352177\pi$
$479$	8.78335	+	15.2132i	0.401321	+	0.695109i	−0.592564	+	0.805523i	$0.701884\pi$
$480$	−0.621320	−	1.07616i	−0.0283593	−	0.0491197i
$481$	−12.0000	−	6.92820i	−0.547153	−	0.315899i
$482$	−13.8564			−0.631142
$483$	−32.8835	−	4.50000i	−1.49625	−	0.204757i
$484$	1.00000			0.0454545
$485$	6.27231	+	3.62132i	0.284811	+	0.164436i
$486$	−7.79423	−	13.5000i	−0.353553	−	0.612372i
$487$	9.48528	+	16.4290i	0.429819	+	0.744469i	0.996857	−	0.0792232i	$-0.0252440\pi$
$487$	9.48528	+	16.4290i	0.429819	+	0.744469i	−0.567038	+	0.823692i	$0.691911\pi$
$488$	−2.09077	+	3.62132i	−0.0946447	+	0.163929i
$489$			22.5167i			1.01824i
$490$	4.86396	−	1.25024i	0.219731	−	0.0564800i
$491$		−	13.9706i		−	0.630483i	−0.949012	−	0.315241i	$-0.897915\pi$
$491$		−	13.9706i		−	0.630483i	0.949012	−	0.315241i	$-0.102085\pi$
$492$	7.79423	+	4.50000i	0.351391	+	0.202876i
$493$	48.7279	−	28.1331i	2.19460	−	1.26705i
$494$	4.30463	−	2.48528i	0.193675	−	0.111818i
$495$	−1.86396	−	1.07616i	−0.0837788	−	0.0483697i
$496$		−	8.36308i		−	0.375513i
$497$	2.15232	−	15.7279i	0.0965446	−	0.705494i
$498$	11.4853			0.514668
$499$	−10.4853	+	18.1610i	−0.469386	+	0.813000i	−0.999387	−	0.0349967i	$-0.988858\pi$
$499$	−10.4853	+	18.1610i	−0.469386	+	0.813000i	0.530002	+	0.847997i	$0.322191\pi$
$500$	−3.40256	−	5.89340i	−0.152167	−	0.263561i
$501$	−17.7408	+	10.2426i	−0.792599	+	0.457607i
$502$	12.7279	+	7.34847i	0.568075	+	0.327978i
$503$	−2.86976			−0.127956			−0.0639780	−	0.997951i	$-0.520379\pi$
$503$	−2.86976			−0.127956			−0.0639780	+	0.997951i	$0.520379\pi$
$504$	−6.27231	−	4.86396i	−0.279391	−	0.216658i
$505$	−8.48528			−0.377590
$506$	6.27231	+	3.62132i	0.278838	+	0.160987i
$507$	−1.50000	+	0.866025i	−0.0666173	+	0.0384615i
$508$	3.37868	+	5.85204i	0.149905	+	0.259643i
$509$	6.63103	−	11.4853i	0.293915	−	0.509076i	−0.680817	−	0.732454i	$-0.738375\pi$
$509$	6.63103	−	11.4853i	0.293915	−	0.509076i	0.974732	+	0.223378i	$0.0717083\pi$
$510$	8.23999			0.364873
$511$	3.51472	−	1.43488i	0.155482	−	0.0634753i
$512$			1.00000i			0.0441942i
$513$	−3.72792	+	6.45695i	−0.164592	+	0.285081i
$514$	−10.2426	+	5.91359i	−0.451784	+	0.260837i
$515$	−1.26080	+	0.727922i	−0.0555574	+	0.0320761i
$516$	−18.7279	−	10.8126i	−0.824451	−	0.475997i
$517$		−	0.717439i		−	0.0315529i
$518$	9.79796	−	4.00000i	0.430498	−	0.175750i
$519$			2.48528i			0.109092i
$520$	−1.24264	+	2.15232i	−0.0544934	+	0.0943853i
$521$	18.4582	+	31.9706i	0.808669	+	1.40066i	0.913786	+	0.406196i	$0.133145\pi$
$521$	18.4582	+	31.9706i	0.808669	+	1.40066i	−0.105117	+	0.994460i	$0.533522\pi$
$522$	−12.7279	−	22.0454i	−0.557086	−	0.964901i
$523$	−31.2426	−	18.0379i	−1.36615	−	0.788744i	−0.375712	−	0.926736i	$-0.622602\pi$
$523$	−31.2426	−	18.0379i	−1.36615	−	0.788744i	−0.990433	+	0.137992i	$0.955935\pi$
$524$	13.2621			0.579356
$525$	−16.2426	−	12.5956i	−0.708887	−	0.549717i
$526$	22.9706			1.00156
$527$	48.0262	+	27.7279i	2.09205	+	1.20785i
$528$	0.866025	+	1.50000i	0.0376889	+	0.0652791i
$529$	14.7279	+	25.5095i	0.640344	+	1.10911i
$530$	−3.04384	+	5.27208i	−0.132216	+	0.229004i
$531$	39.7862			1.72657
$532$	−0.514719	+	3.76127i	−0.0223159	+	0.163072i
$533$		−	18.0000i		−	0.779667i
$534$	−10.2426	+	17.7408i	−0.443242	+	0.767718i
$535$	−9.31981	+	5.38079i	−0.402930	+	0.232632i
$536$	−11.6786	+	6.74264i	−0.504439	+	0.291238i
$537$	2.15232	−	3.72792i	0.0928793	−	0.160872i
$538$			8.23999i			0.355251i
$539$	−6.77962	+	1.74264i	−0.292019	+	0.0750608i
$540$		−	3.72792i		−	0.160424i
$541$	−7.62132	+	13.2005i	−0.327666	+	0.567534i	−0.982048	−	0.188630i	$-0.939595\pi$
$541$	−7.62132	+	13.2005i	−0.327666	+	0.567534i	0.654382	+	0.756164i	$0.272929\pi$
$542$	10.8126	+	18.7279i	0.464440	+	0.804433i
$543$	−2.48528	−	4.30463i	−0.106654	−	0.184730i
$544$	−5.74264	−	3.31552i	−0.246214	−	0.142152i
$545$	8.06591			0.345506
$546$	−2.15232	+	15.7279i	−0.0921107	+	0.673093i
$547$	39.4558			1.68701			0.843505	−	0.537121i	$-0.180488\pi$
$547$	39.4558			1.68701			0.843505	+	0.537121i	$0.180488\pi$
$548$	−2.15232	−	1.24264i	−0.0919424	−	0.0530830i
$549$	−10.8640	+	6.27231i	−0.463663	+	0.267696i
$550$	2.24264	+	3.88437i	0.0956265	+	0.165630i
$551$	−6.08767	+	10.5442i	−0.259344	+	0.449196i
$552$			12.5446i			0.533935i
$553$	−5.25736	+	6.77962i	−0.223566	+	0.288299i
$554$			11.5147i			0.489214i
$555$	4.30463	+	2.48528i	0.182722	+	0.105494i
$556$	3.00000	−	1.73205i	0.127228	−	0.0734553i
$557$	−38.5254	+	22.2426i	−1.63237	+	0.942451i	−0.649014	+	0.760776i	$0.724818\pi$
$557$	−38.5254	+	22.2426i	−1.63237	+	0.942451i	−0.983359	+	0.181675i	$0.941848\pi$
$558$	12.5446	−	21.7279i	0.531056	−	0.919816i
$559$			43.2503i			1.82929i
$560$	−0.717439	−	1.75736i	−0.0303173	−	0.0742620i
$561$	−11.4853			−0.484909
$562$	−0.257359	+	0.445759i	−0.0108560	+	0.0188032i
$563$	3.76127	+	6.51472i	0.158519	+	0.274563i	0.934335	−	0.356397i	$-0.115995\pi$
$563$	3.76127	+	6.51472i	0.158519	+	0.274563i	−0.775816	+	0.630959i	$0.782661\pi$
$564$	1.07616	−	0.621320i	0.0453144	−	0.0261623i
$565$	11.1838	+	6.45695i	0.470505	+	0.271646i
$566$	−24.4949			−1.02960
$567$	−9.00000	−	22.0454i	−0.377964	−	0.925820i
$568$	−6.00000			−0.251754
$569$	−34.5900	−	19.9706i	−1.45009	−	0.837210i	−0.451604	−	0.892219i	$-0.649148\pi$
$569$	−34.5900	−	19.9706i	−1.45009	−	0.837210i	−0.998486	+	0.0550091i	$0.982481\pi$
$570$	−1.54416	+	0.891519i	−0.0646776	+	0.0373416i
$571$	10.4853	+	18.1610i	0.438795	+	0.760016i	0.997597	−	0.0692856i	$-0.0220720\pi$
$571$	10.4853	+	18.1610i	0.438795	+	0.760016i	−0.558801	+	0.829301i	$0.688739\pi$
$572$	1.73205	−	3.00000i	0.0724207	−	0.125436i
$573$	−31.1769			−1.30243
$574$	10.8640	+	8.42463i	0.453453	+	0.351637i
$575$			32.4853i			1.35473i
$576$	−1.50000	+	2.59808i	−0.0625000	+	0.108253i
$577$	9.25736	−	5.34474i	0.385389	−	0.222504i	−0.294771	−	0.955568i	$-0.595243\pi$
$577$	9.25736	−	5.34474i	0.385389	−	0.222504i	0.680160	+	0.733063i	$0.261910\pi$
$578$	23.3572	−	13.4853i	0.971531	−	0.560914i
$579$	0.727922	+	0.420266i	0.0302514	+	0.0174657i
$580$		−	6.08767i		−	0.252777i
$581$	17.3821	+	2.37868i	0.721129	+	0.0986843i
$582$		−	17.4853i		−	0.724788i
$583$	4.24264	−	7.34847i	0.175712	−	0.304342i
$584$	−0.717439	−	1.24264i	−0.0296878	−	0.0514208i
$585$	−6.45695	+	3.72792i	−0.266962	+	0.154131i
$586$	−19.2426	−	11.1097i	−0.794906	−	0.458939i
$587$	−22.2195			−0.917096			−0.458548	−	0.888670i	$-0.651630\pi$
$587$	−22.2195			−0.917096			−0.458548	+	0.888670i	$0.651630\pi$
$588$	−8.48528	−	8.66025i	−0.349927	−	0.357143i
$589$	−12.0000			−0.494451
$590$	8.23999	+	4.75736i	0.339235	+	0.195857i
$591$	7.34847	+	12.7279i	0.302276	+	0.523557i
$592$	−2.00000	−	3.46410i	−0.0821995	−	0.142374i
$593$	22.2195	−	38.4853i	0.912445	−	1.58040i	0.101845	−	0.994800i	$-0.467525\pi$
$593$	22.2195	−	38.4853i	0.912445	−	1.58040i	0.810600	−	0.585601i	$-0.199141\pi$
$594$			5.19615i			0.213201i
$595$	12.4706	+	1.70656i	0.511243	+	0.0699620i
$596$		0			0
$597$	5.48528	−	9.50079i	0.224498	−	0.388841i
$598$	21.7279	−	12.5446i	0.888521	−	0.512988i
$599$	−1.96768	+	1.13604i	−0.0803971	+	0.0464173i	−0.539660	−	0.841883i	$-0.681447\pi$
$599$	−1.96768	+	1.13604i	−0.0803971	+	0.0464173i	0.459263	+	0.888301i	$0.348114\pi$
$600$	−3.88437	+	6.72792i	−0.158579	+	0.274666i
$601$		−	9.79796i		−	0.399667i	−0.979830	−	0.199834i	$-0.935960\pi$
$601$		−	9.79796i		−	0.399667i	0.979830	−	0.199834i	$-0.0640401\pi$
$602$	−26.1039	−	20.2426i	−1.06391	−	0.825028i
$603$	−40.4558			−1.64749
$604$	−4.62132	+	8.00436i	−0.188039	+	0.325693i
$605$	0.358719	+	0.621320i	0.0145840	+	0.0252603i
$606$	10.2426	+	17.7408i	0.416079	+	0.720670i
$607$	19.8640	+	11.4685i	0.806253	+	0.465491i	0.845653	−	0.533733i	$-0.179211\pi$
$607$	19.8640	+	11.4685i	0.806253	+	0.465491i	−0.0393998	+	0.999224i	$0.512545\pi$
$608$	1.43488			0.0581920
$609$	−14.6969	−	36.0000i	−0.595550	−	1.45879i
$610$	−3.00000			−0.121466
$611$	−2.15232	−	1.24264i	−0.0870734	−	0.0502719i
$612$	−9.94655	−	17.2279i	−0.402065	−	0.696397i
$613$	17.1066	+	29.6295i	0.690929	+	1.19672i	0.971534	+	0.236901i	$0.0761317\pi$
$613$	17.1066	+	29.6295i	0.690929	+	1.19672i	−0.280605	+	0.959823i	$0.590535\pi$
$614$	−2.02922	+	3.51472i	−0.0818928	+	0.141843i
$615$			6.45695i			0.260369i
$616$	1.00000	+	2.44949i	0.0402911	+	0.0986928i
$617$		−	8.48528i		−	0.341605i	−0.985305	−	0.170802i	$-0.945364\pi$
$617$		−	8.48528i		−	0.341605i	0.985305	−	0.170802i	$-0.0546359\pi$
$618$	3.04384	+	1.75736i	0.122441	+	0.0706914i
$619$	29.2279	−	16.8747i	1.17477	−	0.678253i	0.219971	−	0.975506i	$-0.429404\pi$
$619$	29.2279	−	16.8747i	1.17477	−	0.678253i	0.954799	+	0.297253i	$0.0960705\pi$
$620$	5.19615	−	3.00000i	0.208683	−	0.120483i
$621$	−18.8169	+	32.5919i	−0.755097	+	1.30787i
$622$			28.6764i			1.14982i
$623$	−19.1757	+	24.7279i	−0.768256	+	0.990703i
$624$	6.00000			0.240192
$625$	−8.77208	+	15.1937i	−0.350883	+	0.607747i
$626$		0			0
$627$	2.15232	−	1.24264i	0.0859553	−	0.0496263i
$628$	−7.75736	−	4.47871i	−0.309552	−	0.178720i
$629$	26.5241			1.05759
$630$	0.772078	−	5.64191i	0.0307603	−	0.224779i
$631$	6.97056			0.277494			0.138747	−	0.990328i	$-0.455693\pi$
$631$	6.97056			0.277494			0.138747	+	0.990328i	$0.455693\pi$
$632$	2.80821	+	1.62132i	0.111705	+	0.0644927i
$633$	6.72792	−	3.88437i	0.267411	−	0.154390i
$634$	8.37868	+	14.5123i	0.332760	+	0.576357i
$635$	−2.42400	+	4.19848i	−0.0961934	+	0.166612i
$636$	14.6969			0.582772
$637$	−6.51472	+	23.3572i	−0.258123	+	0.925446i
$638$			8.48528i			0.335936i
$639$	−15.5885	−	9.00000i	−0.616670	−	0.356034i
$640$	−0.621320	+	0.358719i	−0.0245598	+	0.0141796i
$641$	25.0892	−	14.4853i	0.990966	−	0.572134i	0.0854028	−	0.996347i	$-0.472782\pi$
$641$	25.0892	−	14.4853i	0.990966	−	0.572134i	0.905563	+	0.424212i	$0.139449\pi$
$642$	22.5000	+	12.9904i	0.888004	+	0.512689i
$643$			43.8446i			1.72906i	0.502578	+	0.864532i	$0.332385\pi$
$643$			43.8446i			1.72906i	−0.502578	+	0.864532i	$0.667615\pi$
$644$	−2.59808	+	18.9853i	−0.102379	+	0.748125i
$645$		−	15.5147i		−	0.610891i
$646$	−4.75736	+	8.23999i	−0.187176	+	0.324198i
$647$	−4.83743	−	8.37868i	−0.190179	−	0.329400i	0.755130	−	0.655575i	$-0.227574\pi$
$647$	−4.83743	−	8.37868i	−0.190179	−	0.329400i	−0.945309	+	0.326175i	$0.894240\pi$
$648$	−7.79423	+	4.50000i	−0.306186	+	0.176777i
$649$	−11.4853	−	6.63103i	−0.450837	−	0.260291i
$650$	15.5375			0.609430
$651$	23.4853	−	30.2854i	0.920461	−	1.18698i
$652$	13.0000			0.509119
$653$	−0.184640	−	0.106602i	−0.00722551	−	0.00417165i	0.496383	−	0.868104i	$-0.334661\pi$
$653$	−0.184640	−	0.106602i	−0.00722551	−	0.00417165i	−0.503608	+	0.863932i	$0.667995\pi$
$654$	−9.73641	−	16.8640i	−0.380724	−	0.659433i
$655$	4.75736	+	8.23999i	0.185885	+	0.321963i
$656$	2.59808	−	4.50000i	0.101438	−	0.175695i
$657$		−	4.30463i		−	0.167940i
$658$	1.75736	−	0.717439i	0.0685090	−	0.0279687i
$659$			25.9706i			1.01167i	0.862630	+	0.505835i	$0.168815\pi$
$659$			25.9706i			1.01167i	−0.862630	+	0.505835i	$0.831185\pi$
$660$	−0.621320	+	1.07616i	−0.0241849	+	0.0418894i
$661$	−6.51472	+	3.76127i	−0.253393	+	0.146297i	−0.621317	−	0.783559i	$-0.713402\pi$
$661$	−6.51472	+	3.76127i	−0.253393	+	0.146297i	0.367924	+	0.929856i	$0.380069\pi$
$662$	16.4545	−	9.50000i	0.639522	−	0.369228i
$663$	−19.8931	+	34.4558i	−0.772584	+	1.33815i
$664$		−	6.63103i		−	0.257334i
$665$	−2.52160	+	1.02944i	−0.0977833	+	0.0399199i
$666$		−	12.0000i		−	0.464991i
$667$	−30.7279	+	53.2223i	−1.18979	+	2.06078i
$668$	5.91359	+	10.2426i	0.228804	+	0.396300i
$669$	11.4853	+	19.8931i	0.444047	+	0.769111i
$670$	−8.37868	−	4.83743i	−0.323697	−	0.186886i
$671$	4.18154			0.161427
$672$	−2.80821	+	3.62132i	−0.108329	+	0.139695i
$673$	10.0000			0.385472			0.192736	−	0.981251i	$-0.438264\pi$
$673$	10.0000			0.385472			0.192736	+	0.981251i	$0.438264\pi$
$674$	−11.7041	−	6.75736i	−0.450825	−	0.260284i
$675$	−20.1838	+	11.6531i	−0.776874	+	0.448528i
$676$	0.500000	+	0.866025i	0.0192308	+	0.0333087i
$677$	25.8067	−	44.6985i	0.991831	−	1.71790i	0.385449	−	0.922729i	$-0.374047\pi$
$677$	25.8067	−	44.6985i	0.991831	−	1.71790i	0.606382	−	0.795173i	$-0.292620\pi$
$678$		−	31.1769i		−	1.19734i
$679$	3.62132	−	26.4626i	0.138974	−	1.01554i
$680$		−	4.75736i		−	0.182436i
$681$	3.48960	+	2.01472i	0.133722	+	0.0772042i
$682$	−7.24264	+	4.18154i	−0.277335	+	0.160119i
$683$	20.7846	−	12.0000i	0.795301	−	0.459167i	−0.0465244	−	0.998917i	$-0.514815\pi$
$683$	20.7846	−	12.0000i	0.795301	−	0.459167i	0.841825	+	0.539750i	$0.181481\pi$
$684$	3.72792	+	2.15232i	0.142541	+	0.0822959i
$685$		−	1.78304i		−	0.0681264i
$686$	−11.0482	−	14.8640i	−0.421822	−	0.567509i
$687$	−12.0000			−0.457829
$688$	−6.24264	+	10.8126i	−0.237998	+	0.412225i
$689$	−14.6969	−	25.4558i	−0.559909	−	0.969790i
$690$	−7.79423	+	4.50000i	−0.296721	+	0.171312i
$691$	8.74264	+	5.04757i	0.332586	+	0.192018i	0.656989	−	0.753901i	$-0.271830\pi$
$691$	8.74264	+	5.04757i	0.332586	+	0.192018i	−0.324403	+	0.945919i	$0.605163\pi$
$692$	1.43488			0.0545459
$693$	−1.07616	+	7.86396i	−0.0408799	+	0.298727i
$694$	−17.4853			−0.663732
$695$	2.15232	+	1.24264i	0.0816420	+	0.0471360i
$696$	−12.7279	+	7.34847i	−0.482451	+	0.278543i
$697$	17.2279	+	29.8396i	0.652554	+	1.13026i
$698$	9.43924	−	16.3492i	0.357280	−	0.618828i
$699$	−13.8054			−0.522169
$700$	−7.27208	+	9.37769i	−0.274859	+	0.354443i
$701$			2.48528i			0.0938678i	0.998898	+	0.0469339i	$0.0149450\pi$
$701$			2.48528i			0.0938678i	−0.998898	+	0.0469339i	$0.985055\pi$
$702$	15.5885	+	9.00000i	0.588348	+	0.339683i
$703$	−4.97056	+	2.86976i	−0.187468	+	0.108235i
$704$	0.866025	−	0.500000i	0.0326396	−	0.0188445i
$705$	0.772078	+	0.445759i	0.0290781	+	0.0167883i
$706$			4.30463i			0.162007i
$707$	11.8272	+	28.9706i	0.444807	+	1.08955i
$708$		−	22.9706i		−	0.863287i
$709$	2.75736	−	4.77589i	0.103555	−	0.179362i	−0.809592	−	0.586993i	$-0.800312\pi$
$709$	2.75736	−	4.77589i	0.103555	−	0.179362i	0.913147	+	0.407631i	$0.133645\pi$
$710$	−2.15232	−	3.72792i	−0.0807750	−	0.139906i
$711$	4.86396	+	8.42463i	0.182413	+	0.315948i
$712$	10.2426	+	5.91359i	0.383859	+	0.221621i
$713$	−60.5708			−2.26839
$714$	−11.4853	−	28.1331i	−0.429826	−	1.05285i
$715$	2.48528			0.0929443
$716$	−2.15232	−	1.24264i	−0.0804359	−	0.0464397i
$717$		0			0
$718$	−4.24264	−	7.34847i	−0.158334	−	0.274242i
$719$	16.6646	−	28.8640i	0.621485	−	1.07644i	−0.367724	−	0.929935i	$-0.619863\pi$
$719$	16.6646	−	28.8640i	0.621485	−	1.07644i	0.989209	−	0.146509i	$-0.0468038\pi$
$720$	−2.15232			−0.0802121
$721$	4.24264	+	3.29002i	0.158004	+	0.122527i
$722$			16.9411i			0.630483i
$723$	−12.0000	+	20.7846i	−0.446285	+	0.772988i
$724$	−2.48528	+	1.43488i	−0.0923648	+	0.0533268i
$725$	−32.9600	+	19.0294i	−1.22410	+	0.706736i
$726$	0.866025	−	1.50000i	0.0321412	−	0.0556702i
$727$			21.6251i			0.802032i	0.916071	+	0.401016i	$0.131343\pi$
$727$			21.6251i			0.802032i	−0.916071	+	0.401016i	$0.868657\pi$
$728$	9.08052	+	1.24264i	0.336546	+	0.0460553i
$729$	−27.0000			−1.00000
$730$	0.514719	−	0.891519i	0.0190506	−	0.0329966i
$731$	−41.3951	−	71.6985i	−1.53105	−	2.65186i
$732$	3.62132	+	6.27231i	0.133848	+	0.231831i
$733$	−7.86396	−	4.54026i	−0.290462	−	0.167698i	0.347688	−	0.937610i	$-0.386967\pi$
$733$	−7.86396	−	4.54026i	−0.290462	−	0.167698i	−0.638150	+	0.769912i	$0.720300\pi$
$734$	−4.30463			−0.158887
$735$	2.33696	−	8.37868i	0.0861999	−	0.309052i
$736$	7.24264			0.266967
$737$	11.6786	+	6.74264i	0.430187	+	0.248368i
$738$	13.5000	−	7.79423i	0.496942	−	0.286910i
$739$	−7.00000	−	12.1244i	−0.257499	−	0.446002i	0.708072	−	0.706140i	$-0.249565\pi$
$739$	−7.00000	−	12.1244i	−0.257499	−	0.446002i	−0.965571	+	0.260138i	$0.916232\pi$
$740$	1.43488	−	2.48528i	0.0527472	−	0.0913608i
$741$		−	8.60927i		−	0.316269i
$742$	22.2426	+	3.04384i	0.816553	+	0.111743i
$743$		−	12.0000i		−	0.440237i	−0.975473	−	0.220119i	$-0.929356\pi$
$743$		−	12.0000i		−	0.440237i	0.975473	−	0.220119i	$-0.0706445\pi$
$744$	−12.5446	−	7.24264i	−0.459908	−	0.265528i
$745$		0			0
$746$	−6.69258	+	3.86396i	−0.245033	+	0.141470i
$747$	9.94655	−	17.2279i	0.363925	−	0.630337i
$748$			6.63103i			0.242454i
$749$	31.3616	+	24.3198i	1.14593	+	0.888626i
$750$	−11.7868			−0.430393
$751$	1.72792	−	2.99285i	0.0630528	−	0.109211i	−0.832776	−	0.553610i	$-0.813250\pi$
$751$	1.72792	−	2.99285i	0.0630528	−	0.109211i	0.895829	+	0.444400i	$0.146583\pi$
$752$	−0.358719	−	0.621320i	−0.0130812	−	0.0226572i
$753$	22.0454	−	12.7279i	0.803379	−	0.463831i
$754$	25.4558	+	14.6969i	0.927047	+	0.535231i
$755$	−6.63103			−0.241328
$756$	−12.7279	+	5.19615i	−0.462910	+	0.188982i
$757$	19.9411			0.724773			0.362386	−	0.932028i	$-0.381962\pi$
$757$	19.9411			0.724773			0.362386	+	0.932028i	$0.381962\pi$
$758$	29.4194	+	16.9853i	1.06856	+	0.616933i
$759$	10.8640	−	6.27231i	0.394337	−	0.227670i
$760$	0.514719	+	0.891519i	0.0186708	+	0.0323388i
$761$	7.07679	−	12.2574i	0.256533	−	0.444329i	−0.708777	−	0.705432i	$-0.750753\pi$
$761$	7.07679	−	12.2574i	0.256533	−	0.444329i	0.965311	+	0.261103i	$0.0840863\pi$
$762$	11.7041			0.423994
$763$	−11.2426	−	27.5387i	−0.407011	−	0.996969i
$764$			18.0000i			0.651217i
$765$	7.13604	−	12.3600i	0.258004	−	0.446876i
$766$	15.2132	−	8.78335i	0.549675	−	0.317355i
$767$	−39.7862	+	22.9706i	−1.43660	+	0.829419i
$768$	1.50000	+	0.866025i	0.0541266	+	0.0312500i
$769$		−	27.9590i		−	1.00823i	−0.863637	−	0.504114i	$-0.831819\pi$
$769$		−	27.9590i		−	1.00823i	0.863637	−	0.504114i	$-0.168181\pi$
$770$	−1.16320	+	1.50000i	−0.0419188	+	0.0540562i
$771$			20.4853i			0.737759i
$772$	0.242641	−	0.420266i	0.00873283	−	0.0151257i
$773$	20.2518	+	35.0772i	0.728407	+	1.26164i	0.957556	+	0.288247i	$0.0930723\pi$
$773$	20.2518	+	35.0772i	0.728407	+	1.26164i	−0.229149	+	0.973391i	$0.573594\pi$
$774$	−32.4377	+	18.7279i	−1.16595	+	0.673161i
$775$	−32.4853	−	18.7554i	−1.16691	−	0.673713i
$776$	−10.0951			−0.362394
$777$	2.48528	−	18.1610i	0.0891590	−	0.651524i
$778$	2.27208			0.0814579
$779$	−6.45695	−	3.72792i	−0.231344	−	0.133567i
$780$	2.15232	+	3.72792i	0.0770653	+	0.133481i
$781$	3.00000	+	5.19615i	0.107348	+	0.185933i
$782$	−24.0131	+	41.5919i	−0.858706	+	1.48732i
$783$	−44.0908			−1.57568
$784$	−5.00000	+	4.89898i	−0.178571	+	0.174964i
$785$		−	6.42641i		−	0.229368i
$786$	11.4853	−	19.8931i	0.409666	−	0.709563i
$787$	9.72792	−	5.61642i	0.346763	−	0.200204i	−0.316496	−	0.948594i	$-0.602506\pi$
$787$	9.72792	−	5.61642i	0.346763	−	0.200204i	0.663259	+	0.748390i	$0.269173\pi$
$788$	7.34847	−	4.24264i	0.261778	−	0.151138i
$789$	19.8931	−	34.4558i	0.708213	−	1.22666i
$790$			2.32640i			0.0827695i
$791$	6.45695	−	47.1838i	0.229583	−	1.67766i
$792$	3.00000			0.106600
$793$	7.24264	−	12.5446i	0.257194	−	0.445473i
$794$	12.2474	+	21.2132i	0.434646	+	0.752828i
$795$	5.27208	+	9.13151i	0.186981	+	0.323861i
$796$	−5.48528	−	3.16693i	−0.194421	−	0.112249i
$797$	36.1990			1.28223			0.641117	−	0.767443i	$-0.278471\pi$
$797$	36.1990			1.28223			0.641117	+	0.767443i	$0.278471\pi$
$798$	5.19615	+	4.02944i	0.183942	+	0.142641i
$799$	4.75736			0.168303
$800$	3.88437	+	2.24264i	0.137333	+	0.0792893i
$801$	17.7408	+	30.7279i	0.626839	+	1.08572i
$802$	4.24264	+	7.34847i	0.149813	+	0.259483i
$803$	−0.717439	+	1.24264i	−0.0253179	+	0.0438518i
$804$			23.3572i			0.823745i
$805$	−12.7279	+	5.19615i	−0.448600	+	0.183140i
$806$			28.9706i			1.02044i
$807$	12.3600	+	7.13604i	0.435092	+	0.251200i
$808$	10.2426	−	5.91359i	0.360335	−	0.208039i
$809$	2.59808	−	1.50000i	0.0913435	−	0.0527372i	−0.453632	−	0.891189i	$-0.649872\pi$
$809$	2.59808	−	1.50000i	0.0913435	−	0.0527372i	0.544976	+	0.838452i	$0.316539\pi$
$810$	−5.59188	−	3.22848i	−0.196479	−	0.113437i
$811$		−	36.9164i		−	1.29631i	−0.761508	−	0.648156i	$-0.775541\pi$
$811$		−	36.9164i		−	1.29631i	0.761508	−	0.648156i	$-0.224459\pi$
$812$	−20.7846	+	8.48528i	−0.729397	+	0.297775i
$813$	37.4558			1.31363
$814$	−2.00000	+	3.46410i	−0.0701000	+	0.121417i
$815$	4.66335	+	8.07716i	0.163350	+	0.282931i
$816$	−9.94655	+	5.74264i	−0.348199	+	0.201033i
$817$	15.5147	+	8.95743i	0.542791	+	0.313381i
$818$	−5.49333			−0.192070
$819$	21.7279	+	16.8493i	0.759235	+	0.588761i
$820$	3.72792			0.130185
$821$	12.5446	+	7.24264i	0.437810	+	0.252770i	0.702668	−	0.711518i	$-0.251992\pi$
$821$	12.5446	+	7.24264i	0.437810	+	0.252770i	−0.264858	+	0.964287i	$0.585325\pi$
$822$	−3.72792	+	2.15232i	−0.130026	+	0.0750707i
$823$	15.2426	+	26.4010i	0.531325	+	0.920282i	0.999332	+	0.0365570i	$0.0116390\pi$
$823$	15.2426	+	26.4010i	0.531325	+	0.920282i	−0.468007	+	0.883725i	$0.655028\pi$
$824$	1.01461	−	1.75736i	0.0353457	−	0.0612205i
$825$	7.76874			0.270473
$826$	4.75736	−	34.7641i	0.165530	−	1.20960i
$827$		−	0.514719i		−	0.0178985i	−0.999960	−	0.00894926i	$-0.997151\pi$
$827$		−	0.514719i		−	0.0178985i	0.999960	−	0.00894926i	$-0.00284868\pi$
$828$	18.8169	+	10.8640i	0.653934	+	0.377549i
$829$	4.97056	−	2.86976i	0.172635	−	0.0996707i	−0.411193	−	0.911548i	$-0.634888\pi$
$829$	4.97056	−	2.86976i	0.172635	−	0.0996707i	0.583828	+	0.811878i	$0.301554\pi$
$830$	4.11999	−	2.37868i	0.143007	−	0.0825652i
$831$	17.2721	+	9.97204i	0.599162	+	0.345926i
$832$		−	3.46410i		−	0.120096i
$833$	−11.5555	−	44.9558i	−0.400374	−	1.55763i
$834$		−	6.00000i		−	0.207763i
$835$	−4.24264	+	7.34847i	−0.146823	+	0.254304i
$836$	−0.717439	−	1.24264i	−0.0248131	−	0.0429776i
$837$	−21.7279	−	37.6339i	−0.751027	−	1.30082i
$838$	1.24264	+	0.717439i	0.0429263	+	0.0247835i
$839$	39.0687			1.34880			0.674401	−	0.738365i	$-0.264402\pi$
$839$	39.0687			1.34880			0.674401	+	0.738365i	$0.264402\pi$
$840$	−3.25736	−	0.445759i	−0.112390	−	0.0153802i
$841$	−43.0000			−1.48276
$842$	0.420266	+	0.242641i	0.0144833	+	0.00836195i
$843$	0.445759	+	0.772078i	0.0153528	+	0.0265918i
$844$	−2.24264	−	3.88437i	−0.0771949	−	0.133705i
$845$	−0.358719	+	0.621320i	−0.0123403	+	0.0213741i
$846$		−	2.15232i		−	0.0739982i
$847$	1.62132	−	2.09077i	0.0557092	−	0.0718397i
$848$		−	8.48528i		−	0.291386i
$849$	−21.2132	+	36.7423i	−0.728035	+	1.26099i
$850$	−25.7574	+	14.8710i	−0.883470	+	0.510072i
$851$	−25.0892	+	14.4853i	−0.860048	+	0.496549i
$852$	−5.19615	+	9.00000i	−0.178017	+	0.308335i
$853$		−	13.9795i		−	0.478649i	−0.970940	−	0.239324i	$-0.923074\pi$
$853$		−	13.9795i		−	0.478649i	0.970940	−	0.239324i	$-0.0769260\pi$
$854$	4.18154	+	10.2426i	0.143089	+	0.350496i
$855$			3.08831i			0.105618i
$856$	7.50000	−	12.9904i	0.256345	−	0.444002i
$857$	11.5555	+	20.0147i	0.394728	+	0.683690i	0.993066	−	0.117554i	$-0.0375053\pi$
$857$	11.5555	+	20.0147i	0.394728	+	0.683690i	−0.598338	+	0.801244i	$0.704172\pi$
$858$	−3.00000	−	5.19615i	−0.102418	−	0.177394i
$859$	26.4411	+	15.2658i	0.902160	+	0.520862i	0.877900	−	0.478844i	$-0.158944\pi$
$859$	26.4411	+	15.2658i	0.902160	+	0.520862i	0.0242594	+	0.999706i	$0.492277\pi$
$860$	−8.95743			−0.305446
$861$	22.0454	−	9.00000i	0.751305	−	0.306719i
$862$	−26.4853			−0.902092
$863$	−28.3177	−	16.3492i	−0.963946	−	0.556535i	−0.0665610	−	0.997782i	$-0.521203\pi$
$863$	−28.3177	−	16.3492i	−0.963946	−	0.556535i	−0.897385	+	0.441248i	$0.854536\pi$
$864$	2.59808	+	4.50000i	0.0883883	+	0.153093i
$865$	0.514719	+	0.891519i	0.0175010	+	0.0303125i
$866$	4.62730	−	8.01472i	0.157242	−	0.272351i
$867$		−	46.7144i		−	1.58650i
$868$	−17.4853	−	13.5592i	−0.593489	−	0.460230i
$869$		−	3.24264i		−	0.109999i
$870$	−9.13151	−	5.27208i	−0.309587	−	0.178740i
$871$	40.4558	−	23.3572i	1.37079	−	0.791428i
$872$	−9.73641	+	5.62132i	−0.329717	+	0.190362i
$873$	−26.2279	−	15.1427i	−0.887681	−	0.512503i
$874$		−	10.3923i		−	0.351525i
$875$	−17.8384	−	2.44113i	−0.603047	−	0.0825251i
$876$	−2.48528			−0.0839699
$877$	−26.3492	+	45.6382i	−0.889751	+	1.54109i	−0.0495808	+	0.998770i	$0.515789\pi$
$877$	−26.3492	+	45.6382i	−0.889751	+	1.54109i	−0.840170	+	0.542323i	$0.817545\pi$
$878$	7.70719	+	13.3492i	0.260105	+	0.450515i
$879$	−33.3292	+	19.2426i	−1.12417	+	0.649038i
$880$	0.621320	+	0.358719i	0.0209447	+	0.0120924i
$881$	39.7862			1.34043			0.670215	−	0.742167i	$-0.266202\pi$
$881$	39.7862			1.34043			0.670215	+	0.742167i	$0.266202\pi$
$882$	−20.3389	+	5.22792i	−0.684845	+	0.176033i
$883$	−18.4558			−0.621089			−0.310544	−	0.950559i	$-0.600511\pi$
$883$	−18.4558			−0.621089			−0.310544	+	0.950559i	$0.600511\pi$
$884$	19.8931	+	11.4853i	0.669077	+	0.386292i
$885$	14.2721	−	8.23999i	0.479751	−	0.276984i
$886$	18.0000	+	31.1769i	0.604722	+	1.04741i
$887$	2.32640	−	4.02944i	0.0781128	−	0.135295i	−0.824323	−	0.566120i	$-0.808444\pi$
$887$	2.32640	−	4.02944i	0.0781128	−	0.135295i	0.902436	+	0.430825i	$0.141777\pi$
$888$	−6.92820			−0.232495
$889$	17.7132	+	2.42400i	0.594082	+	0.0812982i
$890$			8.48528i			0.284427i
$891$	7.79423	+	4.50000i	0.261116	+	0.150756i
$892$	11.4853	−	6.63103i	0.384556	−	0.222023i
$893$	−0.891519	+	0.514719i	−0.0298335	+	0.0172244i
$894$		0			0
$895$		−	1.78304i		−	0.0596004i
$896$	2.09077	+	1.62132i	0.0698477	+	0.0541645i
$897$		−	43.4558i		−	1.45095i
$898$	−10.2426	+	17.7408i	−0.341801	+	0.592017i
$899$	−35.4815	−	61.4558i	−1.18338	−	2.04967i
$900$	6.72792	+	11.6531i	0.224264	+	0.388437i
$901$	48.7279	+	28.1331i	1.62336	+	0.937249i
$902$	−5.19615			−0.173013
$903$	−52.9706	+	21.6251i	−1.76275	+	0.719640i
$904$	−18.0000			−0.598671
$905$	−1.78304	−	1.02944i	−0.0592702	−	0.0342197i
$906$	8.00436	+	13.8640i	0.265927	+	0.460599i
$907$	0.227922	+	0.394773i	0.00756803	+	0.0131082i	0.869785	−	0.493432i	$-0.164258\pi$
$907$	0.227922	+	0.394773i	0.00756803	+	0.0131082i	−0.862217	+	0.506540i	$0.830924\pi$
$908$	1.16320	−	2.01472i	0.0386021	−	0.0668608i
$909$	35.4815			1.17685
$910$	2.48528	+	6.08767i	0.0823863	+	0.201804i
$911$			27.7279i			0.918667i	0.888264	+	0.459334i	$0.151912\pi$
$911$			27.7279i			0.918667i	−0.888264	+	0.459334i	$0.848088\pi$
$912$	1.24264	−	2.15232i	0.0411479	−	0.0712703i
$913$	−5.74264	+	3.31552i	−0.190054	+	0.109728i
$914$	−11.2328	+	6.48528i	−0.371549	+	0.214514i
$915$	−2.59808	+	4.50000i	−0.0858898	+	0.148765i
$916$			6.92820i			0.228914i
$917$	21.5020	−	27.7279i	0.710060	−	0.915657i
$918$	−34.4558			−1.13721
$919$	−0.136039	+	0.235626i	−0.00448751	+	0.00777260i	−0.868260	−	0.496109i	$-0.834762\pi$
$919$	−0.136039	+	0.235626i	−0.00448751	+	0.00777260i	0.863773	+	0.503881i	$0.168095\pi$
$920$	2.59808	+	4.50000i	0.0856560	+	0.148361i
$921$	3.51472	+	6.08767i	0.115814	+	0.200596i
$922$	−11.4853	−	6.63103i	−0.378248	−	0.218381i
$923$	20.7846			0.684134
$924$	4.54026	+	0.621320i	0.149364	+	0.0204399i
$925$	−17.9411			−0.589901
$926$	−18.5813	−	10.7279i	−0.610620	−	0.352541i
$927$	5.27208	−	3.04384i	0.173158	−	0.0999727i
$928$	4.24264	+	7.34847i	0.139272	+	0.241225i
$929$	−0.717439	+	1.24264i	−0.0235384	+	0.0407697i	−0.877555	−	0.479477i	$-0.840827\pi$
$929$	−0.717439	+	1.24264i	−0.0235384	+	0.0407697i	0.854016	+	0.520246i	$0.174160\pi$
$930$		−	10.3923i		−	0.340777i
$931$	7.02944	+	7.17439i	0.230381	+	0.235131i
$932$			7.97056i			0.261084i
$933$	43.0147	+	24.8345i	1.40824	+	0.813046i
$934$	27.0000	−	15.5885i	0.883467	−	0.510070i
$935$	−4.11999	+	2.37868i	−0.134738	+	0.0777911i
$936$	5.19615	−	9.00000i	0.169842	−	0.294174i
$937$			52.4539i			1.71359i	0.515654	+	0.856797i	$0.327549\pi$
$937$			52.4539i			1.71359i	−0.515654	+	0.856797i	$0.672451\pi$
$938$	−4.83743	+	35.3492i	−0.157948	+	1.15419i
$939$		0			0
$940$	0.257359	−	0.445759i	0.00839414	−	0.0145391i
$941$	−5.19615	−	9.00000i	−0.169390	−	0.293392i	0.768816	−	0.639470i	$-0.220846\pi$
$941$	−5.19615	−	9.00000i	−0.169390	−	0.293392i	−0.938205	+	0.346079i	$0.887513\pi$
$942$	−13.4361	+	7.75736i	−0.437773	+	0.252748i
$943$	−32.5919	−	18.8169i	−1.06134	−	0.612764i
$944$	−13.2621			−0.431643
$945$	−7.79423	−	6.04416i	−0.253546	−	0.196616i
$946$	12.4853			0.405932
$947$	−0.891519	−	0.514719i	−0.0289705	−	0.0167261i	0.485445	−	0.874267i	$-0.338658\pi$
$947$	−0.891519	−	0.514719i	−0.0289705	−	0.0167261i	−0.514415	+	0.857541i	$0.671991\pi$
$948$	4.86396	−	2.80821i	0.157974	−	0.0912064i
$949$	2.48528	+	4.30463i	0.0806756	+	0.139734i
$950$	3.21792	−	5.57359i	0.104403	−	0.180831i
$951$	29.0246			0.941187
$952$	−16.2426	+	6.63103i	−0.526427	+	0.214913i
$953$		−	7.97056i		−	0.258192i	−0.991632	−	0.129096i	$-0.958792\pi$
$953$		−	7.97056i		−	0.258192i	0.991632	−	0.129096i	$-0.0412075\pi$
$954$	12.7279	−	22.0454i	0.412082	−	0.713746i
$955$	−11.1838	+	6.45695i	−0.361898	+	0.208942i
$956$		0			0
$957$	12.7279	+	7.34847i	0.411435	+	0.237542i
$958$		−	17.5667i		−	0.567554i
$959$	−6.08767	+	2.48528i	−0.196581	+	0.0802539i
$960$			1.24264i			0.0401061i
$961$	19.4706	−	33.7240i	0.628083	−	1.08787i
$962$	6.92820	+	12.0000i	0.223374	+	0.386896i
$963$	38.9711	−	22.5000i	1.25583	−	0.725052i
$964$	12.0000	+	6.92820i	0.386494	+	0.223142i
$965$	0.348160			0.0112077
$966$	26.2279	+	20.3389i	0.843870	+	0.654392i
$967$	−40.2132			−1.29317			−0.646585	−	0.762842i	$-0.723803\pi$
$967$	−40.2132			−1.29317			−0.646585	+	0.762842i	$0.723803\pi$
$968$	−0.866025	−	0.500000i	−0.0278351	−	0.0160706i
$969$	8.23999	+	14.2721i	0.264707	+	0.458485i
$970$	−3.62132	−	6.27231i	−0.116274	−	0.201392i
$971$	−2.32640	+	4.02944i	−0.0746576	+	0.129311i	−0.900937	−	0.433949i	$-0.857120\pi$
$971$	−2.32640	+	4.02944i	−0.0746576	+	0.129311i	0.826280	+	0.563260i	$0.190453\pi$
$972$			15.5885i			0.500000i
$973$	1.24264	−	9.08052i	0.0398372	−	0.291108i
$974$		−	18.9706i		−	0.607856i
$975$	13.4558	−	23.3062i	0.430932	−	0.746396i
$976$	3.62132	−	2.09077i	0.115916	−	0.0669239i
$977$	30.2854	−	17.4853i	0.968916	−	0.559404i	0.0700102	−	0.997546i	$-0.477697\pi$
$977$	30.2854	−	17.4853i	0.968916	−	0.559404i	0.898905	+	0.438143i	$0.144363\pi$
$978$	11.2583	−	19.5000i	0.360002	−	0.623541i
$979$		−	11.8272i		−	0.377998i
$980$	−4.83743	−	1.34924i	−0.154526	−	0.0431000i
$981$	−33.7279			−1.07685
$982$	−6.98528	+	12.0989i	−0.222909	+	0.386090i
$983$	−20.9692	−	36.3198i	−0.668815	−	1.15842i	−0.978236	−	0.207497i	$-0.933468\pi$
$983$	−20.9692	−	36.3198i	−0.668815	−	1.15842i	0.309421	−	0.950925i	$-0.399865\pi$
$984$	−4.50000	−	7.79423i	−0.143455	−	0.248471i
$985$	5.27208	+	3.04384i	0.167982	+	0.0969847i
$986$	−56.2662			−1.79188
$987$	0.445759	−	3.25736i	0.0141887	−	0.103683i
$988$	−4.97056			−0.158135
$989$	78.3116	+	45.2132i	2.49016	+	1.43770i
$990$	1.07616	+	1.86396i	0.0342026	+	0.0592406i
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	0.922538	−	0.385906i	$-0.126111\pi$
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	−0.795474	+	0.605988i	$0.792778\pi$
$992$	−4.18154	+	7.24264i	−0.132764	+	0.229954i
$993$		−	32.9090i		−	1.04433i
$994$	−9.72792	+	12.5446i	−0.308551	+	0.397891i
$995$		−	4.54416i		−	0.144059i
$996$	−9.94655	−	5.74264i	−0.315168	−	0.181963i
$997$	17.4853	−	10.0951i	0.553764	−	0.319716i	−0.196874	−	0.980429i	$-0.563079\pi$
$997$	17.4853	−	10.0951i	0.553764	−	0.319716i	0.750639	+	0.660713i	$0.229746\pi$
$998$	18.1610	−	10.4853i	0.574878	−	0.331906i
$999$	−18.0000	−	10.3923i	−0.569495	−	0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.k.d.89.1	✓	8
3.2	odd	2	inner	462.2.k.d.89.4	yes	8
7.3	odd	6	inner	462.2.k.d.353.4	yes	8
21.17	even	6	inner	462.2.k.d.353.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.k.d.89.1	✓	8	1.1	even	1	trivial
462.2.k.d.89.4	yes	8	3.2	odd	2	inner
462.2.k.d.353.1	yes	8	21.17	even	6	inner
462.2.k.d.353.4	yes	8	7.3	odd	6	inner

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.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.358719 + 0.621320i) q^{5} +1.73205 q^{6} +(2.62132 + 0.358719i) q^{7} -1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.358719 + 0.621320i) q^{5} +1.73205 q^{6} +(2.62132 + 0.358719i) q^{7} -1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +(0.621320 - 0.358719i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(-1.50000 - 0.866025i) q^{12} +3.46410i q^{13} +(-2.09077 - 1.62132i) q^{14} -1.24264i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.31552 - 5.74264i) q^{17} +(-2.59808 + 1.50000i) q^{18} +(1.24264 + 0.717439i) q^{19} -0.717439 q^{20} +(-4.24264 + 1.73205i) q^{21} +1.00000 q^{22} +(6.27231 + 3.62132i) q^{23} +(0.866025 + 1.50000i) q^{24} +(2.24264 + 3.88437i) q^{25} +(1.73205 - 3.00000i) q^{26} +5.19615i q^{27} +(1.00000 + 2.44949i) q^{28} +8.48528i q^{29} +(-0.621320 + 1.07616i) q^{30} +(-7.24264 + 4.18154i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.866025 - 1.50000i) q^{33} +6.63103i q^{34} +(-1.16320 + 1.50000i) q^{35} +3.00000 q^{36} +(-2.00000 + 3.46410i) q^{37} +(-0.717439 - 1.24264i) q^{38} +(-3.00000 - 5.19615i) q^{39} +(0.621320 + 0.358719i) q^{40} -5.19615 q^{41} +(4.54026 + 0.621320i) q^{42} +12.4853 q^{43} +(-0.866025 - 0.500000i) q^{44} +(1.07616 + 1.86396i) q^{45} +(-3.62132 - 6.27231i) q^{46} +(-0.358719 + 0.621320i) q^{47} -1.73205i q^{48} +(6.74264 + 1.88064i) q^{49} -4.48528i q^{50} +(9.94655 + 5.74264i) q^{51} +(-3.00000 + 1.73205i) q^{52} +(-7.34847 + 4.24264i) q^{53} +(2.59808 - 4.50000i) q^{54} -0.717439i q^{55} +(0.358719 - 2.62132i) q^{56} -2.48528 q^{57} +(4.24264 - 7.34847i) q^{58} +(6.63103 + 11.4853i) q^{59} +(1.07616 - 0.621320i) q^{60} +(-3.62132 - 2.09077i) q^{61} +8.36308 q^{62} +(4.86396 - 6.27231i) q^{63} -1.00000 q^{64} +(-2.15232 - 1.24264i) q^{65} +(-1.50000 + 0.866025i) q^{66} +(-6.74264 - 11.6786i) q^{67} +(3.31552 - 5.74264i) q^{68} -12.5446 q^{69} +(1.75736 - 0.717439i) q^{70} -6.00000i q^{71} +(-2.59808 - 1.50000i) q^{72} +(1.24264 - 0.717439i) q^{73} +(3.46410 - 2.00000i) q^{74} +(-6.72792 - 3.88437i) q^{75} +1.43488i q^{76} +(-2.44949 + 1.00000i) q^{77} +6.00000i q^{78} +(-1.62132 + 2.80821i) q^{79} +(-0.358719 - 0.621320i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(4.50000 + 2.59808i) q^{82} +6.63103 q^{83} +(-3.62132 - 2.80821i) q^{84} +4.75736 q^{85} +(-10.8126 - 6.24264i) q^{86} +(-7.34847 - 12.7279i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-5.91359 + 10.2426i) q^{89} -2.15232i q^{90} +(-1.24264 + 9.08052i) q^{91} +7.24264i q^{92} +(7.24264 - 12.5446i) q^{93} +(0.621320 - 0.358719i) q^{94} +(-0.891519 + 0.514719i) q^{95} +(-0.866025 + 1.50000i) q^{96} -10.0951i q^{97} +(-4.89898 - 5.00000i) q^{98} +3.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{3} + 4 q^{4} + 4 q^{7} + 12 q^{9}+O(q^{10}) \) 8 * q - 12 * q^3 + 4 * q^4 + 4 * q^7 + 12 * q^9	\( 8 q - 12 q^{3} + 4 q^{4} + 4 q^{7} + 12 q^{9} - 12 q^{10} - 12 q^{12} - 4 q^{16} - 24 q^{19} + 8 q^{22} - 16 q^{25} + 8 q^{28} + 12 q^{30} - 24 q^{31} + 24 q^{36} - 16 q^{37} - 24 q^{39} - 12 q^{40} + 32 q^{43} - 12 q^{46} + 20 q^{49} - 24 q^{52} + 48 q^{57} - 12 q^{61} - 12 q^{63} - 8 q^{64} - 12 q^{66} - 20 q^{67} + 48 q^{70} - 24 q^{73} + 48 q^{75} + 4 q^{79} - 36 q^{81} + 36 q^{82} - 12 q^{84} + 72 q^{85} + 4 q^{88} + 24 q^{91} + 24 q^{93} - 12 q^{94}+O(q^{100}) \) 8 * q - 12 * q^3 + 4 * q^4 + 4 * q^7 + 12 * q^9 - 12 * q^10 - 12 * q^12 - 4 * q^16 - 24 * q^19 + 8 * q^22 - 16 * q^25 + 8 * q^28 + 12 * q^30 - 24 * q^31 + 24 * q^36 - 16 * q^37 - 24 * q^39 - 12 * q^40 + 32 * q^43 - 12 * q^46 + 20 * q^49 - 24 * q^52 + 48 * q^57 - 12 * q^61 - 12 * q^63 - 8 * q^64 - 12 * q^66 - 20 * q^67 + 48 * q^70 - 24 * q^73 + 48 * q^75 + 4 * q^79 - 36 * q^81 + 36 * q^82 - 12 * q^84 + 72 * q^85 + 4 * q^88 + 24 * q^91 + 24 * q^93 - 12 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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