LMFDB - Embedded newform 462.2.i.g.331.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("462.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.21870000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 24x^{4} - 43x^{3} + 138x^{2} - 117x + 73 $ x^6 - 3x^5 + 24x^4 - 43x^3 + 138x^2 - 117*x + 73
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.1
Root			$0.500000 - 3.23735i$ of defining polynomial
Character	$\chi$	$=$	462.331
Dual form			462.2.i.g.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.20942 + 3.82682i) q^{5} -1.00000 q^{6} +(2.20942 + 1.45550i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.20942 + 3.82682i) q^{5} -1.00000 q^{6} +(2.20942 + 1.45550i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.20942 - 3.82682i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-2.36521 + 1.18566i) q^{14} -4.41883 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.18842 - 2.05840i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.84421 - 3.19426i) q^{19} +4.41883 q^{20} +(-0.155792 + 2.64116i) q^{21} -1.00000 q^{22} +(-2.36521 + 4.09666i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-7.26304 - 12.5800i) q^{25} -1.00000 q^{27} +(0.155792 - 2.64116i) q^{28} -6.52608 q^{29} +(2.20942 - 3.82682i) q^{30} +(1.68842 + 2.92442i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +2.37683 q^{34} +(-10.4515 + 5.23924i) q^{35} +1.00000 q^{36} +(-3.84421 + 6.65836i) q^{37} +(1.84421 + 3.19426i) q^{38} +(-2.20942 + 3.82682i) q^{40} +12.1492 q^{41} +(-2.20942 - 1.45550i) q^{42} +3.06525 q^{43} +(0.500000 - 0.866025i) q^{44} +(-2.20942 - 3.82682i) q^{45} +(-2.36521 - 4.09666i) q^{46} +(2.05362 - 3.55698i) q^{47} -1.00000 q^{48} +(2.76304 + 6.43161i) q^{49} +14.5261 q^{50} +(1.18842 - 2.05840i) q^{51} +(-4.00000 - 6.92820i) q^{53} +(0.500000 - 0.866025i) q^{54} -4.41883 q^{55} +(2.20942 + 1.45550i) q^{56} +3.68842 q^{57} +(3.26304 - 5.65175i) q^{58} +(6.26304 + 10.8479i) q^{59} +(2.20942 + 3.82682i) q^{60} +(-1.89783 + 3.28714i) q^{61} -3.37683 q^{62} +(-2.36521 + 1.18566i) q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{66} +(-5.07462 - 8.78951i) q^{67} +(-1.18842 + 2.05840i) q^{68} -4.73042 q^{69} +(0.688417 - 11.6708i) q^{70} +0.934749 q^{71} +(-0.500000 + 0.866025i) q^{72} +(3.73042 + 6.46127i) q^{73} +(-3.84421 - 6.65836i) q^{74} +(7.26304 - 12.5800i) q^{75} -3.68842 q^{76} +(-0.155792 + 2.64116i) q^{77} +(0.209416 - 0.362720i) q^{79} +(-2.20942 - 3.82682i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.07462 + 10.5216i) q^{82} -2.14925 q^{83} +(2.36521 - 1.18566i) q^{84} +10.5028 q^{85} +(-1.53263 + 2.65458i) q^{86} +(-3.26304 - 5.65175i) q^{87} +(0.500000 + 0.866025i) q^{88} +(6.41883 - 11.1177i) q^{89} +4.41883 q^{90} +4.73042 q^{92} +(-1.68842 + 2.92442i) q^{93} +(2.05362 + 3.55698i) q^{94} +(8.14925 + 14.1149i) q^{95} +(0.500000 - 0.866025i) q^{96} +7.00000 q^{97} +(-6.95146 - 0.822941i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 - 3 * q^9	$ 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} - 3 q^{9} + 3 q^{11} + 3 q^{12} - 3 q^{14} - 3 q^{16} - 3 q^{17} - 3 q^{18} + 9 q^{19} - 3 q^{21} - 6 q^{22} - 3 q^{23} + 3 q^{24} - 15 q^{25} - 6 q^{27} + 3 q^{28} + 18 q^{29} + 6 q^{31} - 3 q^{32} - 3 q^{33} + 6 q^{34} - 30 q^{35} + 6 q^{36} - 21 q^{37} + 9 q^{38} + 24 q^{41} + 6 q^{43} + 3 q^{44} - 3 q^{46} - 3 q^{47} - 6 q^{48} - 12 q^{49} + 30 q^{50} + 3 q^{51} - 24 q^{53} + 3 q^{54} + 18 q^{57} - 9 q^{58} + 9 q^{59} + 6 q^{61} - 12 q^{62} - 3 q^{63} + 6 q^{64} - 3 q^{66} - 6 q^{67} - 3 q^{68} - 6 q^{69} + 18 q^{71} - 3 q^{72} - 21 q^{74} + 15 q^{75} - 18 q^{76} - 3 q^{77} - 12 q^{79} - 3 q^{81} - 12 q^{82} + 36 q^{83} + 3 q^{84} - 3 q^{86} + 9 q^{87} + 3 q^{88} + 12 q^{89} + 6 q^{92} - 6 q^{93} - 3 q^{94} + 3 q^{96} + 42 q^{97} - 9 q^{98} - 6 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 - 3 * q^9 + 3 * q^11 + 3 * q^12 - 3 * q^14 - 3 * q^16 - 3 * q^17 - 3 * q^18 + 9 * q^19 - 3 * q^21 - 6 * q^22 - 3 * q^23 + 3 * q^24 - 15 * q^25 - 6 * q^27 + 3 * q^28 + 18 * q^29 + 6 * q^31 - 3 * q^32 - 3 * q^33 + 6 * q^34 - 30 * q^35 + 6 * q^36 - 21 * q^37 + 9 * q^38 + 24 * q^41 + 6 * q^43 + 3 * q^44 - 3 * q^46 - 3 * q^47 - 6 * q^48 - 12 * q^49 + 30 * q^50 + 3 * q^51 - 24 * q^53 + 3 * q^54 + 18 * q^57 - 9 * q^58 + 9 * q^59 + 6 * q^61 - 12 * q^62 - 3 * q^63 + 6 * q^64 - 3 * q^66 - 6 * q^67 - 3 * q^68 - 6 * q^69 + 18 * q^71 - 3 * q^72 - 21 * q^74 + 15 * q^75 - 18 * q^76 - 3 * q^77 - 12 * q^79 - 3 * q^81 - 12 * q^82 + 36 * q^83 + 3 * q^84 - 3 * q^86 + 9 * q^87 + 3 * q^88 + 12 * q^89 + 6 * q^92 - 6 * q^93 - 3 * q^94 + 3 * q^96 + 42 * q^97 - 9 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.20942	+	3.82682i	−0.988081	+	1.71141i	−0.360729	+	0.932671i	$0.617472\pi$
$5$	−2.20942	+	3.82682i	−0.988081	+	1.71141i	−0.627352	+	0.778736i	$0.715861\pi$
$6$	−1.00000			−0.408248
$7$	2.20942	+	1.45550i	0.835081	+	0.550127i
$7$	2.20942	+	1.45550i	0.835081	+	0.550127i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−2.20942	−	3.82682i	−0.698679	−	1.21015i
$11$	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
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	−2.36521	+	1.18566i	−0.632128	+	0.316881i
$15$	−4.41883			−1.14094
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.18842	−	2.05840i	−0.288233	−	0.499235i	0.685155	−	0.728398i	$-0.259735\pi$
$17$	−1.18842	−	2.05840i	−0.288233	−	0.499235i	−0.973388	+	0.229163i	$0.926401\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	1.84421	−	3.19426i	0.423090	−	0.732814i	−0.573150	−	0.819451i	$-0.694279\pi$
$19$	1.84421	−	3.19426i	0.423090	−	0.732814i	0.996240	+	0.0866367i	$0.0276119\pi$
$20$	4.41883			0.988081
$21$	−0.155792	+	2.64116i	−0.0339965	+	0.576348i
$22$	−1.00000			−0.213201
$23$	−2.36521	+	4.09666i	−0.493180	+	0.854213i	−0.999969	−	0.00785730i	$-0.997499\pi$
$23$	−2.36521	+	4.09666i	−0.493180	+	0.854213i	0.506789	+	0.862070i	$0.330832\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−7.26304	−	12.5800i	−1.45261	−	2.51599i
$26$		0			0
$27$	−1.00000			−0.192450
$28$	0.155792	−	2.64116i	0.0294418	−	0.499132i
$29$	−6.52608			−1.21186			−0.605932	−	0.795517i	$-0.707199\pi$
$29$	−6.52608			−1.21186			−0.605932	+	0.795517i	$0.707199\pi$
$30$	2.20942	−	3.82682i	0.403382	−	0.698679i
$31$	1.68842	+	2.92442i	0.303249	+	0.525242i	0.976870	−	0.213835i	$-0.0685954\pi$
$31$	1.68842	+	2.92442i	0.303249	+	0.525242i	−0.673621	+	0.739077i	$0.735262\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$	2.37683			0.407624
$35$	−10.4515	+	5.23924i	−1.76662	+	0.885593i
$36$	1.00000			0.166667
$37$	−3.84421	+	6.65836i	−0.631984	+	1.09463i	0.355162	+	0.934805i	$0.384426\pi$
$37$	−3.84421	+	6.65836i	−0.631984	+	1.09463i	−0.987146	+	0.159823i	$0.948908\pi$
$38$	1.84421	+	3.19426i	0.299170	+	0.518178i
$39$		0			0
$40$	−2.20942	+	3.82682i	−0.349339	+	0.605074i
$41$	12.1492			1.89739			0.948697	−	0.316187i	$-0.102403\pi$
$41$	12.1492			1.89739			0.948697	+	0.316187i	$0.102403\pi$
$42$	−2.20942	−	1.45550i	−0.340920	−	0.224588i
$43$	3.06525			0.467446			0.233723	−	0.972303i	$-0.424909\pi$
$43$	3.06525			0.467446			0.233723	+	0.972303i	$0.424909\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$	−2.20942	−	3.82682i	−0.329360	−	0.570469i
$46$	−2.36521	−	4.09666i	−0.348731	−	0.604020i
$47$	2.05362	−	3.55698i	0.299552	−	0.518839i	−0.676482	−	0.736460i	$-0.736496\pi$
$47$	2.05362	−	3.55698i	0.299552	−	0.518839i	0.976033	+	0.217620i	$0.0698295\pi$
$48$	−1.00000			−0.144338
$49$	2.76304	+	6.43161i	0.394720	+	0.918801i
$50$	14.5261			2.05430
$51$	1.18842	−	2.05840i	0.166412	−	0.288233i
$52$		0			0
$53$	−4.00000	−	6.92820i	−0.549442	−	0.951662i	−0.998313	−	0.0580651i	$-0.981507\pi$
$53$	−4.00000	−	6.92820i	−0.549442	−	0.951662i	0.448871	−	0.893597i	$-0.351826\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−4.41883			−0.595835
$56$	2.20942	+	1.45550i	0.295246	+	0.194499i
$57$	3.68842			0.488543
$58$	3.26304	−	5.65175i	0.428458	−	0.742112i
$59$	6.26304	+	10.8479i	0.815379	+	1.41228i	0.909056	+	0.416674i	$0.136804\pi$
$59$	6.26304	+	10.8479i	0.815379	+	1.41228i	−0.0936773	+	0.995603i	$0.529862\pi$
$60$	2.20942	+	3.82682i	0.285234	+	0.494041i
$61$	−1.89783	+	3.28714i	−0.242993	+	0.420876i	−0.961565	−	0.274576i	$-0.911462\pi$
$61$	−1.89783	+	3.28714i	−0.242993	+	0.420876i	0.718573	+	0.695452i	$0.244796\pi$
$62$	−3.37683			−0.428858
$63$	−2.36521	+	1.18566i	−0.297988	+	0.149379i
$64$	1.00000			0.125000
$65$		0			0
$66$	−0.500000	−	0.866025i	−0.0615457	−	0.106600i
$67$	−5.07462	−	8.78951i	−0.619964	−	1.07381i	−0.989492	−	0.144589i	$-0.953814\pi$
$67$	−5.07462	−	8.78951i	−0.619964	−	1.07381i	0.369528	−	0.929220i	$-0.379519\pi$
$68$	−1.18842	+	2.05840i	−0.144117	+	0.249617i
$69$	−4.73042			−0.569475
$70$	0.688417	−	11.6708i	0.0822816	−	1.39493i
$71$	0.934749			0.110934			0.0554672	−	0.998461i	$-0.482335\pi$
$71$	0.934749			0.110934			0.0554672	+	0.998461i	$0.482335\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	3.73042	+	6.46127i	0.436612	+	0.756234i	0.997426	−	0.0717077i	$-0.0228449\pi$
$73$	3.73042	+	6.46127i	0.436612	+	0.756234i	−0.560814	+	0.827942i	$0.689512\pi$
$74$	−3.84421	−	6.65836i	−0.446880	−	0.774019i
$75$	7.26304	−	12.5800i	0.838664	−	1.45261i
$76$	−3.68842			−0.423090
$77$	−0.155792	+	2.64116i	−0.0177541	+	0.300988i
$78$		0			0
$79$	0.209416	−	0.362720i	0.0235612	−	0.0408092i	−0.854004	−	0.520266i	$-0.825833\pi$
$79$	0.209416	−	0.362720i	0.0235612	−	0.0408092i	0.877566	+	0.479457i	$0.159166\pi$
$80$	−2.20942	−	3.82682i	−0.247020	−	0.427852i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.07462	+	10.5216i	−0.670830	+	1.16191i
$83$	−2.14925			−0.235911			−0.117955	−	0.993019i	$-0.537634\pi$
$83$	−2.14925			−0.235911			−0.117955	+	0.993019i	$0.537634\pi$
$84$	2.36521	−	1.18566i	0.258065	−	0.129366i
$85$	10.5028			1.13919
$86$	−1.53263	+	2.65458i	−0.165267	+	0.286251i
$87$	−3.26304	−	5.65175i	−0.349835	−	0.605932i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	6.41883	−	11.1177i	0.680395	−	1.17848i	−0.294466	−	0.955662i	$-0.595142\pi$
$89$	6.41883	−	11.1177i	0.680395	−	1.17848i	0.974860	−	0.222816i	$-0.0715251\pi$
$90$	4.41883			0.465786
$91$		0			0
$92$	4.73042			0.493180
$93$	−1.68842	+	2.92442i	−0.175081	+	0.303249i
$94$	2.05362	+	3.55698i	0.211815	+	0.366875i
$95$	8.14925	+	14.1149i	0.836095	+	1.44816i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	7.00000			0.710742			0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000			0.710742			0.355371	+	0.934725i	$0.384354\pi$
$98$	−6.95146	−	0.822941i	−0.702203	−	0.0831296i
$99$	−1.00000			−0.100504
$100$	−7.26304	+	12.5800i	−0.726304	+	1.25800i
$101$	7.68187	+	13.3054i	0.764375	+	1.32394i	0.940576	+	0.339582i	$0.110286\pi$
$101$	7.68187	+	13.3054i	0.764375	+	1.32394i	−0.176201	+	0.984354i	$0.556381\pi$
$102$	1.18842	+	2.05840i	0.117671	+	0.203812i
$103$	1.31158	−	2.27173i	0.129234	−	0.223840i	−0.794146	−	0.607727i	$-0.792081\pi$
$103$	1.31158	−	2.27173i	0.129234	−	0.223840i	0.923380	+	0.383887i	$0.125415\pi$
$104$		0			0
$105$	−9.76304	−	6.43161i	−0.952775	−	0.627661i
$106$	8.00000			0.777029
$107$	−5.45146	+	9.44220i	−0.527012	+	0.912812i	0.472492	+	0.881335i	$0.343355\pi$
$107$	−5.45146	+	9.44220i	−0.527012	+	0.912812i	−0.999504	+	0.0314773i	$0.989979\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	5.89783	+	10.2153i	0.564910	+	0.978453i	0.997058	+	0.0766501i	$0.0244224\pi$
$109$	5.89783	+	10.2153i	0.564910	+	0.978453i	−0.432148	+	0.901803i	$0.642244\pi$
$110$	2.20942	−	3.82682i	0.210660	−	0.364873i
$111$	−7.68842			−0.729752
$112$	−2.36521	+	1.18566i	−0.223491	+	0.112034i
$113$	5.37683			0.505810			0.252905	−	0.967491i	$-0.418614\pi$
$113$	5.37683			0.505810			0.252905	+	0.967491i	$0.418614\pi$
$114$	−1.84421	+	3.19426i	−0.172726	+	0.299170i
$115$	−10.4515	−	18.1025i	−0.974603	−	1.68806i
$116$	3.26304	+	5.65175i	0.302966	+	0.524752i
$117$		0			0
$118$	−12.5261			−1.15312
$119$	0.370291	−	6.27760i	0.0339445	−	0.575467i
$120$	−4.41883			−0.403382
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−1.89783	−	3.28714i	−0.171822	−	0.297604i
$123$	6.07462	+	10.5216i	0.547730	+	0.948697i
$124$	1.68842	−	2.92442i	0.151624	−	0.262621i
$125$	42.0942			3.76502
$126$	0.155792	−	2.64116i	0.0138790	−	0.235293i
$127$	0.730416			0.0648139			0.0324070	−	0.999475i	$-0.489683\pi$
$127$	0.730416			0.0648139			0.0324070	+	0.999475i	$0.489683\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	1.53263	+	2.65458i	0.134940	+	0.233723i
$130$		0			0
$131$	−3.68842	+	6.38853i	−0.322258	+	0.558168i	−0.980954	−	0.194242i	$-0.937775\pi$
$131$	−3.68842	+	6.38853i	−0.322258	+	0.558168i	0.658695	+	0.752410i	$0.271109\pi$
$132$	1.00000			0.0870388
$133$	8.72387	−	4.37321i	0.756456	−	0.379206i
$134$	10.1492			0.876762
$135$	2.20942	−	3.82682i	0.190156	−	0.329360i
$136$	−1.18842	−	2.05840i	−0.101906	−	0.176506i
$137$	4.41883	+	7.65364i	0.377526	+	0.653895i	0.990702	−	0.136052i	$-0.0434414\pi$
$137$	4.41883	+	7.65364i	0.377526	+	0.653895i	−0.613175	+	0.789947i	$0.710108\pi$
$138$	2.36521	−	4.09666i	0.201340	−	0.348731i
$139$	1.47392			0.125016			0.0625080	−	0.998044i	$-0.480090\pi$
$139$	1.47392			0.125016			0.0625080	+	0.998044i	$0.480090\pi$
$140$	9.76304	+	6.43161i	0.825128	+	0.543570i
$141$	4.10725			0.345893
$142$	−0.467375	+	0.809517i	−0.0392212	+	0.0679331i
$143$		0			0
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	14.4188	−	24.9742i	1.19742	−	2.07399i
$146$	−7.46083			−0.617463
$147$	−4.18842	+	5.60867i	−0.345455	+	0.462595i
$148$	7.68842			0.631984
$149$	4.68187	−	8.10924i	0.383554	−	0.664335i	−0.608013	−	0.793927i	$-0.708033\pi$
$149$	4.68187	−	8.10924i	0.383554	−	0.664335i	0.991567	+	0.129592i	$0.0413667\pi$
$150$	7.26304	+	12.5800i	0.593025	+	1.02715i
$151$	6.78404	+	11.7503i	0.552077	+	0.956226i	0.998125	+	0.0612166i	$0.0194980\pi$
$151$	6.78404	+	11.7503i	0.552077	+	0.956226i	−0.446047	+	0.895009i	$0.647169\pi$
$152$	1.84421	−	3.19426i	0.149585	−	0.259089i
$153$	2.37683			0.192156
$154$	−2.20942	−	1.45550i	−0.178040	−	0.117288i
$155$	−14.9217			−1.19854
$156$		0			0
$157$	9.37029	+	16.2298i	0.747831	+	1.29528i	0.948861	+	0.315696i	$0.102238\pi$
$157$	9.37029	+	16.2298i	0.747831	+	1.29528i	−0.201030	+	0.979585i	$0.564429\pi$
$158$	0.209416	+	0.362720i	0.0166603	+	0.0288564i
$159$	4.00000	−	6.92820i	0.317221	−	0.549442i
$160$	4.41883			0.349339
$161$	−11.1884	+	5.60867i	−0.881771	+	0.442025i
$162$	1.00000			0.0785674
$163$	−9.38621	+	16.2574i	−0.735185	+	1.27338i	0.219458	+	0.975622i	$0.429571\pi$
$163$	−9.38621	+	16.2574i	−0.735185	+	1.27338i	−0.954642	+	0.297755i	$0.903762\pi$
$164$	−6.07462	−	10.5216i	−0.474348	−	0.821596i
$165$	−2.20942	−	3.82682i	−0.172003	−	0.297918i
$166$	1.07462	−	1.86130i	0.0834070	−	0.144465i
$167$	−23.8898			−1.84865			−0.924325	−	0.381606i	$-0.875371\pi$
$167$	−23.8898			−1.84865			−0.924325	+	0.381606i	$0.875371\pi$
$168$	−0.155792	+	2.64116i	−0.0120196	+	0.203770i
$169$	−13.0000			−1.00000
$170$	−5.25142	+	9.09572i	−0.402765	+	0.697610i
$171$	1.84421	+	3.19426i	0.141030	+	0.244271i
$172$	−1.53263	−	2.65458i	−0.116862	−	0.202410i
$173$	−5.68842	+	9.85263i	−0.432482	+	0.749081i	−0.997086	−	0.0762805i	$-0.975696\pi$
$173$	−5.68842	+	9.85263i	−0.432482	+	0.749081i	0.564604	+	0.825362i	$0.309029\pi$
$174$	6.52608			0.494741
$175$	2.26304	−	38.3657i	0.171070	−	2.90018i
$176$	−1.00000			−0.0753778
$177$	−6.26304	+	10.8479i	−0.470759	+	0.815379i
$178$	6.41883	+	11.1177i	0.481112	+	0.833310i
$179$	−12.3050	−	21.3130i	−0.919722	−	1.59301i	−0.799837	−	0.600217i	$-0.795081\pi$
$179$	−12.3050	−	21.3130i	−0.919722	−	1.59301i	−0.119885	−	0.992788i	$-0.538253\pi$
$180$	−2.20942	+	3.82682i	−0.164680	+	0.285234i
$181$	17.4608			1.29785			0.648927	−	0.760851i	$-0.275218\pi$
$181$	17.4608			1.29785			0.648927	+	0.760851i	$0.275218\pi$
$182$		0			0
$183$	−3.79567			−0.280584
$184$	−2.36521	+	4.09666i	−0.174365	+	0.302010i
$185$	−16.9869	−	29.4222i	−1.24890	−	2.16316i
$186$	−1.68842	−	2.92442i	−0.123801	−	0.214429i
$187$	1.18842	−	2.05840i	0.0869056	−	0.150525i
$188$	−4.10725			−0.299552
$189$	−2.20942	−	1.45550i	−0.160711	−	0.105872i
$190$	−16.2985			−1.18242
$191$	8.41883	−	14.5818i	0.609165	−	1.05511i	−0.382213	−	0.924074i	$-0.624838\pi$
$191$	8.41883	−	14.5818i	0.609165	−	1.05511i	0.991378	−	0.131031i	$-0.0418288\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−2.73042	−	4.72922i	−0.196540	−	0.340417i	0.750865	−	0.660456i	$-0.229637\pi$
$193$	−2.73042	−	4.72922i	−0.196540	−	0.340417i	−0.947404	+	0.320040i	$0.896304\pi$
$194$	−3.50000	+	6.06218i	−0.251285	+	0.435239i
$195$		0			0
$196$	4.18842	−	5.60867i	0.299173	−	0.400619i
$197$	−9.68842			−0.690271			−0.345136	−	0.938553i	$-0.612167\pi$
$197$	−9.68842			−0.690271			−0.345136	+	0.938553i	$0.612167\pi$
$198$	0.500000	−	0.866025i	0.0355335	−	0.0615457i
$199$	−10.1492	−	17.5790i	−0.719461	−	1.24614i	−0.961214	−	0.275805i	$-0.911056\pi$
$199$	−10.1492	−	17.5790i	−0.719461	−	1.24614i	0.241752	−	0.970338i	$-0.422278\pi$
$200$	−7.26304	−	12.5800i	−0.513575	−	0.889537i
$201$	5.07462	−	8.78951i	0.357936	−	0.619964i
$202$	−15.3637			−1.08099
$203$	−14.4188	−	9.49871i	−1.01200	−	0.666679i
$204$	−2.37683			−0.166412
$205$	−26.8427	+	46.4930i	−1.87478	+	3.24721i
$206$	1.31158	+	2.27173i	0.0913823	+	0.158279i
$207$	−2.36521	−	4.09666i	−0.164393	−	0.284738i
$208$		0			0
$209$	3.68842			0.255133
$210$	10.4515	−	5.23924i	0.721219	−	0.361542i
$211$	22.5130			1.54986			0.774929	−	0.632048i	$-0.217785\pi$
$211$	22.5130			1.54986			0.774929	+	0.632048i	$0.217785\pi$
$212$	−4.00000	+	6.92820i	−0.274721	+	0.475831i
$213$	0.467375	+	0.809517i	0.0320240	+	0.0554672i
$214$	−5.45146	−	9.44220i	−0.372654	−	0.645456i
$215$	−6.77241	+	11.7302i	−0.461875	+	0.799991i
$216$	−1.00000			−0.0680414
$217$	−0.526082	+	8.91876i	−0.0357128	+	0.605445i
$218$	−11.7957			−0.798903
$219$	−3.73042	+	6.46127i	−0.252078	+	0.436612i
$220$	2.20942	+	3.82682i	0.148959	+	0.258004i
$221$		0			0
$222$	3.84421	−	6.65836i	0.258006	−	0.446880i
$223$	−7.46083			−0.499614			−0.249807	−	0.968296i	$-0.580367\pi$
$223$	−7.46083			−0.499614			−0.249807	+	0.968296i	$0.580367\pi$
$224$	0.155792	−	2.64116i	0.0104093	−	0.176470i
$225$	14.5261			0.968405
$226$	−2.68842	+	4.65647i	−0.178831	+	0.309744i
$227$	1.38621	+	2.40098i	0.0920058	+	0.159359i	0.908355	−	0.418200i	$-0.137339\pi$
$227$	1.38621	+	2.40098i	0.0920058	+	0.159359i	−0.816349	+	0.577559i	$0.804005\pi$
$228$	−1.84421	−	3.19426i	−0.122136	−	0.211545i
$229$	1.26958	−	2.19898i	0.0838965	−	0.145313i	−0.821024	−	0.570894i	$-0.806597\pi$
$229$	1.26958	−	2.19898i	0.0838965	−	0.145313i	0.904920	+	0.425581i	$0.139930\pi$
$230$	20.9029			1.37830
$231$	−2.36521	+	1.18566i	−0.155619	+	0.0780108i
$232$	−6.52608			−0.428458
$233$	12.0261	−	20.8298i	0.787855	−	1.36460i	−0.139424	−	0.990233i	$-0.544525\pi$
$233$	12.0261	−	20.8298i	0.787855	−	1.36460i	0.927279	−	0.374372i	$-0.122142\pi$
$234$		0			0
$235$	9.07462	+	15.7177i	0.591963	+	1.02531i
$236$	6.26304	−	10.8479i	0.407689	−	0.706138i
$237$	0.418833			0.0272061
$238$	5.25142	+	3.45948i	0.340399	+	0.224245i
$239$	7.59133			0.491042			0.245521	−	0.969391i	$-0.421041\pi$
$239$	7.59133			0.491042			0.245521	+	0.969391i	$0.421041\pi$
$240$	2.20942	−	3.82682i	0.142617	−	0.247020i
$241$	−8.14925	−	14.1149i	−0.524939	−	0.909221i	−0.999578	−	0.0290409i	$-0.990755\pi$
$241$	−8.14925	−	14.1149i	−0.524939	−	0.909221i	0.474639	−	0.880181i	$-0.342579\pi$
$242$	−0.500000	−	0.866025i	−0.0321412	−	0.0556702i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	3.79567			0.242993
$245$	−30.7173	−	3.63644i	−1.96246	−	0.232324i
$246$	−12.1492			−0.774608
$247$		0			0
$248$	1.68842	+	2.92442i	0.107215	+	0.185701i
$249$	−1.07462	−	1.86130i	−0.0681015	−	0.117955i
$250$	−21.0471	+	36.4546i	−1.33113	+	2.30559i
$251$	−8.61008			−0.543463			−0.271732	−	0.962373i	$-0.587596\pi$
$251$	−8.61008			−0.543463			−0.271732	+	0.962373i	$0.587596\pi$
$252$	2.20942	+	1.45550i	0.139180	+	0.0916879i
$253$	−4.73042			−0.297399
$254$	−0.365208	+	0.632559i	−0.0229152	+	0.0396903i
$255$	5.25142	+	9.09572i	0.328856	+	0.569596i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.418833	+	0.725439i	−0.0261261	+	0.0452517i	−0.878793	−	0.477203i	$-0.841650\pi$
$257$	−0.418833	+	0.725439i	−0.0261261	+	0.0452517i	0.852667	+	0.522455i	$0.174984\pi$
$258$	−3.06525			−0.190834
$259$	−18.1847	+	9.11585i	−1.12994	+	0.566432i
$260$		0			0
$261$	3.26304	−	5.65175i	0.201977	−	0.349835i
$262$	−3.68842	−	6.38853i	−0.227871	−	0.394684i
$263$	−5.41883	−	9.38569i	−0.334140	−	0.578747i	0.649180	−	0.760635i	$-0.275112\pi$
$263$	−5.41883	−	9.38569i	−0.334140	−	0.578747i	−0.983319	+	0.181888i	$0.941779\pi$
$264$	−0.500000	+	0.866025i	−0.0307729	+	0.0533002i
$265$	35.3507			2.17157
$266$	−0.574624	+	9.74170i	−0.0352325	+	0.597302i
$267$	12.8377			0.785652
$268$	−5.07462	+	8.78951i	−0.309982	+	0.536905i
$269$	−8.93983	−	15.4842i	−0.545071	−	0.944091i	−0.998602	−	0.0528506i	$-0.983169\pi$
$269$	−8.93983	−	15.4842i	−0.545071	−	0.944091i	0.453531	−	0.891240i	$-0.350164\pi$
$270$	2.20942	+	3.82682i	0.134461	+	0.232893i
$271$	4.41883	−	7.65364i	0.268425	−	0.464926i	−0.700030	−	0.714113i	$-0.746830\pi$
$271$	4.41883	−	7.65364i	0.268425	−	0.464926i	0.968455	+	0.249187i	$0.0801635\pi$
$272$	2.37683			0.144117
$273$		0			0
$274$	−8.83767			−0.533903
$275$	7.26304	−	12.5800i	0.437978	−	0.758600i
$276$	2.36521	+	4.09666i	0.142369	+	0.246590i
$277$	8.00000	+	13.8564i	0.480673	+	0.832551i	0.999754	−	0.0221745i	$-0.00705893\pi$
$277$	8.00000	+	13.8564i	0.480673	+	0.832551i	−0.519081	+	0.854725i	$0.673726\pi$
$278$	−0.736959	+	1.27645i	−0.0441999	+	0.0765564i
$279$	−3.37683			−0.202166
$280$	−10.4515	+	5.23924i	−0.624594	+	0.313104i
$281$	−15.9217			−0.949807			−0.474903	−	0.880038i	$-0.657517\pi$
$281$	−15.9217			−0.949807			−0.474903	+	0.880038i	$0.657517\pi$
$282$	−2.05362	+	3.55698i	−0.122292	+	0.211815i
$283$	9.04200	+	15.6612i	0.537491	+	0.930962i	0.999038	+	0.0438462i	$0.0139611\pi$
$283$	9.04200	+	15.6612i	0.537491	+	0.930962i	−0.461547	+	0.887116i	$0.652706\pi$
$284$	−0.467375	−	0.809517i	−0.0277336	−	0.0480360i
$285$	−8.14925	+	14.1149i	−0.482720	+	0.836095i
$286$		0			0
$287$	26.8427	+	17.6832i	1.58448	+	1.04381i
$288$	1.00000			0.0589256
$289$	5.67533	−	9.82996i	0.333843	−	0.578233i
$290$	14.4188	+	24.9742i	0.846703	+	1.46653i
$291$	3.50000	+	6.06218i	0.205174	+	0.355371i
$292$	3.73042	−	6.46127i	0.218306	−	0.378117i
$293$	25.1492			1.46923			0.734617	−	0.678482i	$-0.237362\pi$
$293$	25.1492			1.46923			0.734617	+	0.678482i	$0.237362\pi$
$294$	−2.76304	−	6.43161i	−0.161144	−	0.375099i
$295$	−55.3507			−3.22264
$296$	−3.84421	+	6.65836i	−0.223440	+	0.387010i
$297$	−0.500000	−	0.866025i	−0.0290129	−	0.0502519i
$298$	4.68187	+	8.10924i	0.271214	+	0.469756i
$299$		0			0
$300$	−14.5261			−0.838664
$301$	6.77241	+	4.46147i	0.390355	+	0.257155i
$302$	−13.5681			−0.780755
$303$	−7.68187	+	13.3054i	−0.441312	+	0.764375i
$304$	1.84421	+	3.19426i	0.105773	+	0.183204i
$305$	−8.38621	−	14.5253i	−0.480193	−	0.831718i
$306$	−1.18842	+	2.05840i	−0.0679373	+	0.117671i
$307$	−3.86950			−0.220844			−0.110422	−	0.993885i	$-0.535220\pi$
$307$	−3.86950			−0.220844			−0.110422	+	0.993885i	$0.535220\pi$
$308$	2.36521	−	1.18566i	0.134770	−	0.0675593i
$309$	2.62317			0.149227
$310$	7.46083	−	12.9225i	0.423747	−	0.733951i
$311$	6.78404	+	11.7503i	0.384688	+	0.666299i	0.991726	−	0.128374i	$-0.0409758\pi$
$311$	6.78404	+	11.7503i	0.384688	+	0.666299i	−0.607038	+	0.794673i	$0.707642\pi$
$312$		0			0
$313$	−1.26304	+	2.18765i	−0.0713913	+	0.123653i	−0.899511	−	0.436898i	$-0.856077\pi$
$313$	−1.26304	+	2.18765i	−0.0713913	+	0.123653i	0.828120	+	0.560551i	$0.189411\pi$
$314$	−18.7406			−1.05759
$315$	0.688417	−	11.6708i	0.0387879	−	0.657578i
$316$	−0.418833			−0.0235612
$317$	10.0051	−	17.3293i	0.561941	−	0.973311i	−0.435386	−	0.900244i	$-0.643388\pi$
$317$	10.0051	−	17.3293i	0.561941	−	0.973311i	0.997327	−	0.0730670i	$-0.0232787\pi$
$318$	4.00000	+	6.92820i	0.224309	+	0.388514i
$319$	−3.26304	−	5.65175i	−0.182695	−	0.316437i
$320$	−2.20942	+	3.82682i	−0.123510	+	0.213926i
$321$	−10.9029			−0.608541
$322$	0.736959	−	12.4938i	0.0410691	−	0.696252i
$323$	−8.76675			−0.487795
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$		0			0
$326$	−9.38621	−	16.2574i	−0.519854	−	0.900413i
$327$	−5.89783	+	10.2153i	−0.326151	+	0.564910i
$328$	12.1492			0.670830
$329$	9.71450	−	4.86980i	0.535578	−	0.268481i
$330$	4.41883			0.243249
$331$	8.07462	−	13.9857i	0.443821	−	0.768721i	−0.554148	−	0.832418i	$-0.686956\pi$
$331$	8.07462	−	13.9857i	0.443821	−	0.768721i	0.997969	+	0.0636969i	$0.0202891\pi$
$332$	1.07462	+	1.86130i	0.0589777	+	0.102152i
$333$	−3.84421	−	6.65836i	−0.210661	−	0.364876i
$334$	11.9449	−	20.6892i	0.653597	−	1.13206i
$335$	44.8478			2.45030
$336$	−2.20942	−	1.45550i	−0.120534	−	0.0794040i
$337$	23.1362			1.26031			0.630154	−	0.776471i	$-0.282992\pi$
$337$	23.1362			1.26031			0.630154	+	0.776471i	$0.282992\pi$
$338$	6.50000	−	11.2583i	0.353553	−	0.612372i
$339$	2.68842	+	4.65647i	0.146015	+	0.252905i
$340$	−5.25142	−	9.09572i	−0.284798	−	0.493285i
$341$	−1.68842	+	2.92442i	−0.0914329	+	0.158366i
$342$	−3.68842			−0.199447
$343$	−3.25650	+	18.2317i	−0.175834	+	0.984420i
$344$	3.06525			0.165267
$345$	10.4515	−	18.1025i	0.562688	−	0.974603i
$346$	−5.68842	−	9.85263i	−0.305811	−	0.529681i
$347$	−7.82829	−	13.5590i	−0.420245	−	0.727885i	0.575718	−	0.817648i	$-0.304722\pi$
$347$	−7.82829	−	13.5590i	−0.420245	−	0.727885i	−0.995963	+	0.0897628i	$0.971389\pi$
$348$	−3.26304	+	5.65175i	−0.174917	+	0.302966i
$349$	−20.0102			−1.07112			−0.535560	−	0.844497i	$-0.679899\pi$
$349$	−20.0102			−1.07112			−0.535560	+	0.844497i	$0.679899\pi$
$350$	32.0942	+	21.1427i	1.71551	+	1.13013i
$351$		0			0
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	−3.73042	−	6.46127i	−0.198550	−	0.343899i	0.749508	−	0.661995i	$-0.230290\pi$
$353$	−3.73042	−	6.46127i	−0.198550	−	0.343899i	−0.948058	+	0.318096i	$0.896957\pi$
$354$	−6.26304	−	10.8479i	−0.332877	−	0.576560i
$355$	−2.06525	+	3.57712i	−0.109612	+	0.189854i
$356$	−12.8377			−0.680395
$357$	5.62171	−	2.81812i	0.297532	−	0.149151i
$358$	24.6101			1.30068
$359$	5.62317	−	9.73961i	0.296779	−	0.514037i	−0.678618	−	0.734492i	$-0.737421\pi$
$359$	5.62317	−	9.73961i	0.296779	−	0.514037i	0.975397	+	0.220455i	$0.0707541\pi$
$360$	−2.20942	−	3.82682i	−0.116446	−	0.201691i
$361$	2.69779	+	4.67271i	0.141989	+	0.245932i
$362$	−8.73042	+	15.1215i	−0.458860	+	0.794770i
$363$	−1.00000			−0.0524864
$364$		0			0
$365$	−32.9682			−1.72563
$366$	1.89783	−	3.28714i	0.0992013	−	0.171822i
$367$	2.95800	+	5.12341i	0.154406	+	0.267440i	0.932843	−	0.360284i	$-0.117320\pi$
$367$	2.95800	+	5.12341i	0.154406	+	0.267440i	−0.778436	+	0.627724i	$0.783987\pi$
$368$	−2.36521	−	4.09666i	−0.123295	−	0.213553i
$369$	−6.07462	+	10.5216i	−0.316232	+	0.547730i
$370$	33.9738			1.76622
$371$	1.24633	−	21.1293i	0.0647064	−	1.09698i
$372$	3.37683			0.175081
$373$	11.5630	−	20.0277i	0.598709	−	1.03700i	−0.394303	−	0.918981i	$-0.629014\pi$
$373$	11.5630	−	20.0277i	0.598709	−	1.03700i	0.993012	−	0.118014i	$-0.0376529\pi$
$374$	1.18842	+	2.05840i	0.0614516	+	0.106437i
$375$	21.0471	+	36.4546i	1.08687	+	1.88251i
$376$	2.05362	−	3.55698i	0.105908	−	0.183437i
$377$		0			0
$378$	2.36521	−	1.18566i	0.121653	−	0.0609838i
$379$	−6.77241			−0.347876			−0.173938	−	0.984757i	$-0.555649\pi$
$379$	−6.77241			−0.347876			−0.173938	+	0.984757i	$0.555649\pi$
$380$	8.14925	−	14.1149i	0.418048	−	0.724080i
$381$	0.365208	+	0.632559i	0.0187102	+	0.0324070i
$382$	8.41883	+	14.5818i	0.430745	+	0.746072i
$383$	−12.6819	+	21.9656i	−0.648013	+	1.12239i	0.335583	+	0.942011i	$0.391067\pi$
$383$	−12.6819	+	21.9656i	−0.648013	+	1.12239i	−0.983597	+	0.180382i	$0.942267\pi$
$384$	−1.00000			−0.0510310
$385$	−9.76304	−	6.43161i	−0.497571	−	0.327785i
$386$	5.46083			0.277949
$387$	−1.53263	+	2.65458i	−0.0779077	+	0.134940i
$388$	−3.50000	−	6.06218i	−0.177686	−	0.307760i
$389$	−12.6282	−	21.8728i	−0.640278	−	1.10899i	−0.985371	−	0.170425i	$-0.945486\pi$
$389$	−12.6282	−	21.8728i	−0.640278	−	1.10899i	0.345093	−	0.938568i	$-0.387847\pi$
$390$		0			0
$391$	11.2434			0.568604
$392$	2.76304	+	6.43161i	0.139555	+	0.324845i
$393$	−7.37683			−0.372112
$394$	4.84421	−	8.39042i	0.244048	−	0.422703i
$395$	0.925376	+	1.60280i	0.0465607	+	0.0806455i
$396$	0.500000	+	0.866025i	0.0251259	+	0.0435194i
$397$	6.73696	−	11.6688i	0.338118	−	0.585638i	−0.645961	−	0.763371i	$-0.723543\pi$
$397$	6.73696	−	11.6688i	0.338118	−	0.585638i	0.984079	+	0.177733i	$0.0568763\pi$
$398$	20.2985			1.01747
$399$	8.14925	+	5.36849i	0.407973	+	0.268761i
$400$	14.5261			0.726304
$401$	−16.9449	+	29.3495i	−0.846189	+	1.46564i	0.0383962	+	0.999263i	$0.487775\pi$
$401$	−16.9449	+	29.3495i	−0.846189	+	1.46564i	−0.884585	+	0.466379i	$0.845558\pi$
$402$	5.07462	+	8.78951i	0.253099	+	0.438381i
$403$		0			0
$404$	7.68187	−	13.3054i	0.382188	−	0.661968i
$405$	4.41883			0.219574
$406$	15.4355	−	7.73772i	0.766053	−	0.384017i
$407$	−7.68842			−0.381101
$408$	1.18842	−	2.05840i	0.0588354	−	0.101906i
$409$	2.10725	+	3.64986i	0.104197	+	0.180474i	0.913410	−	0.407041i	$-0.133439\pi$
$409$	2.10725	+	3.64986i	0.104197	+	0.180474i	−0.809213	+	0.587515i	$0.800106\pi$
$410$	−26.8427	−	46.4930i	−1.32567	−	2.29613i
$411$	−4.41883	+	7.65364i	−0.217965	+	0.377526i
$412$	−2.62317			−0.129234
$413$	−1.95146	+	33.0834i	−0.0960250	+	1.62793i
$414$	4.73042			0.232487
$415$	4.74858	−	8.22479i	0.233099	−	0.403739i
$416$		0			0
$417$	0.736959	+	1.27645i	0.0360890	+	0.0625080i
$418$	−1.84421	+	3.19426i	−0.0902032	+	0.156236i
$419$	−22.3116			−1.08999			−0.544996	−	0.838439i	$-0.683469\pi$
$419$	−22.3116			−1.08999			−0.544996	+	0.838439i	$0.683469\pi$
$420$	−0.688417	+	11.6708i	−0.0335913	+	0.569479i
$421$	18.3116			0.892452			0.446226	−	0.894920i	$-0.352768\pi$
$421$	18.3116			0.892452			0.446226	+	0.894920i	$0.352768\pi$
$422$	−11.2565	+	19.4968i	−0.547958	+	0.949091i
$423$	2.05362	+	3.55698i	0.0998507	+	0.172946i
$424$	−4.00000	−	6.92820i	−0.194257	−	0.336463i
$425$	−17.2630	+	29.9005i	−0.837380	+	1.45039i
$426$	−0.934749			−0.0452888
$427$	−8.97754	+	4.50037i	−0.434454	+	0.217788i
$428$	10.9029			0.527012
$429$		0			0
$430$	−6.77241	−	11.7302i	−0.326595	−	0.565679i
$431$	14.4188	+	24.9742i	0.694531	+	1.20296i	0.970339	+	0.241750i	$0.0777213\pi$
$431$	14.4188	+	24.9742i	0.694531	+	1.20296i	−0.275808	+	0.961213i	$0.588945\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	7.62317			0.366346			0.183173	−	0.983081i	$-0.441363\pi$
$433$	7.62317			0.366346			0.183173	+	0.983081i	$0.441363\pi$
$434$	−7.46083	−	4.91498i	−0.358131	−	0.235927i
$435$	28.8377			1.38266
$436$	5.89783	−	10.2153i	0.282455	−	0.489226i
$437$	8.72387	+	15.1102i	0.417319	+	0.722818i
$438$	−3.73042	−	6.46127i	−0.178246	−	0.308731i
$439$	16.6870	−	28.9027i	0.796425	−	1.37945i	−0.125505	−	0.992093i	$-0.540055\pi$
$439$	16.6870	−	28.9027i	0.796425	−	1.37945i	0.921930	−	0.387356i	$-0.126611\pi$
$440$	−4.41883			−0.210660
$441$	−6.95146	−	0.822941i	−0.331022	−	0.0391877i
$442$		0			0
$443$	2.42538	−	4.20087i	0.115233	−	0.199590i	−0.802640	−	0.596464i	$-0.796572\pi$
$443$	2.42538	−	4.20087i	0.115233	−	0.199590i	0.917873	+	0.396874i	$0.129905\pi$
$444$	3.84421	+	6.65836i	0.182438	+	0.315992i
$445$	28.3637	+	49.1275i	1.34457	+	2.32886i
$446$	3.73042	−	6.46127i	0.176640	−	0.305950i
$447$	9.36375			0.442890
$448$	2.20942	+	1.45550i	0.104385	+	0.0687659i
$449$	14.3450			0.676982			0.338491	−	0.940970i	$-0.390083\pi$
$449$	14.3450			0.676982			0.338491	+	0.940970i	$0.390083\pi$
$450$	−7.26304	+	12.5800i	−0.342383	+	0.593025i
$451$	6.07462	+	10.5216i	0.286043	+	0.495441i
$452$	−2.68842	−	4.65647i	−0.126452	−	0.219022i
$453$	−6.78404	+	11.7503i	−0.318742	+	0.552077i
$454$	−2.77241			−0.130116
$455$		0			0
$456$	3.68842			0.172726
$457$	12.5913	−	21.8088i	0.588998	−	1.02017i	−0.405366	−	0.914154i	$-0.632856\pi$
$457$	12.5913	−	21.8088i	0.588998	−	1.02017i	0.994364	−	0.106020i	$-0.0338106\pi$
$458$	1.26958	+	2.19898i	0.0593238	+	0.102752i
$459$	1.18842	+	2.05840i	0.0554705	+	0.0960778i
$460$	−10.4515	+	18.1025i	−0.487302	+	0.844031i
$461$	13.0187			0.606344			0.303172	−	0.952936i	$-0.401954\pi$
$461$	13.0187			0.606344			0.303172	+	0.952936i	$0.401954\pi$
$462$	0.155792	−	2.64116i	0.00724808	−	0.122878i
$463$	−14.2145			−0.660604			−0.330302	−	0.943875i	$-0.607151\pi$
$463$	−14.2145			−0.660604			−0.330302	+	0.943875i	$0.607151\pi$
$464$	3.26304	−	5.65175i	0.151483	−	0.262376i
$465$	−7.46083	−	12.9225i	−0.345988	−	0.599268i
$466$	12.0261	+	20.8298i	0.557098	+	0.964921i
$467$	1.19779	−	2.07463i	0.0554271	−	0.0960026i	−0.836981	−	0.547233i	$-0.815681\pi$
$467$	1.19779	−	2.07463i	0.0554271	−	0.0960026i	0.892408	+	0.451230i	$0.149015\pi$
$468$		0			0
$469$	1.58117	−	26.8058i	0.0730115	−	1.23778i
$470$	−18.1492			−0.837162
$471$	−9.37029	+	16.2298i	−0.431760	+	0.747831i
$472$	6.26304	+	10.8479i	0.288280	+	0.499315i
$473$	1.53263	+	2.65458i	0.0704702	+	0.122058i
$474$	−0.209416	+	0.362720i	−0.00961881	+	0.0166603i
$475$	−53.5782			−2.45834
$476$	−5.62171	+	2.81812i	−0.257670	+	0.129168i
$477$	8.00000			0.366295
$478$	−3.79567	+	6.57429i	−0.173610	+	0.300701i
$479$	−5.41883	−	9.38569i	−0.247593	−	0.428843i	0.715265	−	0.698854i	$-0.246306\pi$
$479$	−5.41883	−	9.38569i	−0.247593	−	0.428843i	−0.962857	+	0.270010i	$0.912973\pi$
$480$	2.20942	+	3.82682i	0.100846	+	0.174670i
$481$		0			0
$482$	16.2985			0.742376
$483$	−10.4515	−	6.88512i	−0.475558	−	0.313284i
$484$	1.00000			0.0454545
$485$	−15.4659	+	26.7877i	−0.702271	+	1.21637i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	17.3217	+	30.0021i	0.784923	+	1.35953i	0.929045	+	0.369967i	$0.120631\pi$
$487$	17.3217	+	30.0021i	0.784923	+	1.35953i	−0.144121	+	0.989560i	$0.546036\pi$
$488$	−1.89783	+	3.28714i	−0.0859109	+	0.148802i
$489$	−18.7724			−0.848918
$490$	18.5079	−	24.7838i	0.836102	−	1.11962i
$491$	38.1492			1.72165			0.860826	−	0.508900i	$-0.169948\pi$
$491$	38.1492			1.72165			0.860826	+	0.508900i	$0.169948\pi$
$492$	6.07462	−	10.5216i	0.273865	−	0.474348i
$493$	7.75571	+	13.4333i	0.349299	+	0.605004i
$494$		0			0
$495$	2.20942	−	3.82682i	0.0993059	−	0.172003i
$496$	−3.37683			−0.151624
$497$	2.06525	+	1.36053i	0.0926392	+	0.0610280i
$498$	2.14925			0.0963101
$499$	0.311583	−	0.539678i	0.0139484	−	0.0241593i	−0.858967	−	0.512031i	$-0.828893\pi$
$499$	0.311583	−	0.539678i	0.0139484	−	0.0241593i	0.872915	+	0.487872i	$0.162227\pi$
$500$	−21.0471	−	36.4546i	−0.941254	−	1.63030i
$501$	−11.9449	−	20.6892i	−0.533659	−	0.924325i
$502$	4.30504	−	7.45655i	0.192143	−	0.332802i
$503$	31.1362			1.38829			0.694146	−	0.719834i	$-0.255782\pi$
$503$	31.1362			1.38829			0.694146	+	0.719834i	$0.255782\pi$
$504$	−2.36521	+	1.18566i	−0.105355	+	0.0528135i
$505$	−67.8898			−3.02106
$506$	2.36521	−	4.09666i	0.105146	−	0.182119i
$507$	−6.50000	−	11.2583i	−0.288675	−	0.500000i
$508$	−0.365208	−	0.632559i	−0.0162035	−	0.0280653i
$509$	21.0522	−	36.4634i	0.933121	−	1.61621i	0.155170	−	0.987888i	$-0.450408\pi$
$509$	21.0522	−	36.4634i	0.933121	−	1.61621i	0.777951	−	0.628325i	$-0.216259\pi$
$510$	−10.5028			−0.465073
$511$	−1.16233	+	19.7053i	−0.0514187	+	0.871709i
$512$	1.00000			0.0441942
$513$	−1.84421	+	3.19426i	−0.0814238	+	0.141030i
$514$	−0.418833	−	0.725439i	−0.0184739	−	0.0319978i
$515$	5.79567	+	10.0384i	0.255388	+	0.442344i
$516$	1.53263	−	2.65458i	0.0674701	−	0.116862i
$517$	4.10725			0.180637
$518$	1.19779	−	20.3063i	0.0526279	−	0.892209i
$519$	−11.3768			−0.499388
$520$		0			0
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	0.993011	−	0.118020i	$-0.0376547\pi$
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	−0.598714	+	0.800963i	$0.704321\pi$
$522$	3.26304	+	5.65175i	0.142819	+	0.247371i
$523$	12.6333	−	21.8816i	0.552417	−	0.956814i	−0.445682	−	0.895191i	$-0.647039\pi$
$523$	12.6333	−	21.8816i	0.552417	−	0.956814i	0.998099	−	0.0616232i	$-0.0196277\pi$
$524$	7.37683			0.322258
$525$	34.3572	−	17.2230i	1.49947	−	0.751674i
$526$	10.8377			0.472545
$527$	4.01309	−	6.95087i	0.174813	−	0.302785i
$528$	−0.500000	−	0.866025i	−0.0217597	−	0.0376889i
$529$	0.311583	+	0.539678i	0.0135471	+	0.0234643i
$530$	−17.6753	+	30.6146i	−0.767767	+	1.32981i
$531$	−12.5261			−0.543586
$532$	−8.14925	−	5.36849i	−0.353315	−	0.232754i
$533$		0			0
$534$	−6.41883	+	11.1177i	−0.277770	+	0.481112i
$535$	−24.0891	−	41.7235i	−1.04146	−	1.80386i
$536$	−5.07462	−	8.78951i	−0.219190	−	0.379649i
$537$	12.3050	−	21.3130i	0.531002	−	0.919722i
$538$	17.8797			0.770847
$539$	−4.18842	+	5.60867i	−0.180408	+	0.241582i
$540$	−4.41883			−0.190156
$541$	2.20942	−	3.82682i	0.0949902	−	0.164528i	−0.814614	−	0.580003i	$-0.803051\pi$
$541$	2.20942	−	3.82682i	0.0949902	−	0.164528i	0.909605	+	0.415475i	$0.136385\pi$
$542$	4.41883	+	7.65364i	0.189805	+	0.328752i
$543$	8.73042	+	15.1215i	0.374658	+	0.648927i
$544$	−1.18842	+	2.05840i	−0.0509530	+	0.0882531i
$545$	−52.1231			−2.23271
$546$		0			0
$547$	−27.6622			−1.18275			−0.591376	−	0.806396i	$-0.701415\pi$
$547$	−27.6622			−1.18275			−0.591376	+	0.806396i	$0.701415\pi$
$548$	4.41883	−	7.65364i	0.188763	−	0.326947i
$549$	−1.89783	−	3.28714i	−0.0809975	−	0.140292i
$550$	7.26304	+	12.5800i	0.309697	+	0.536411i
$551$	−12.0355	+	20.8460i	−0.512728	+	0.888070i
$552$	−4.73042			−0.201340
$553$	0.990626	−	0.496593i	0.0421257	−	0.0211173i
$554$	−16.0000			−0.679775
$555$	16.9869	−	29.4222i	0.721054	−	1.24890i
$556$	−0.736959	−	1.27645i	−0.0312540	−	0.0541335i
$557$	3.99346	+	6.91687i	0.169208	+	0.293077i	0.938142	−	0.346252i	$-0.112546\pi$
$557$	3.99346	+	6.91687i	0.169208	+	0.293077i	−0.768934	+	0.639329i	$0.779212\pi$
$558$	1.68842	−	2.92442i	0.0714764	−	0.123801i
$559$		0			0
$560$	0.688417	−	11.6708i	0.0290909	−	0.493183i
$561$	2.37683			0.100350
$562$	7.96083	−	13.7886i	0.335807	−	0.581636i
$563$	13.6753	+	23.6864i	0.576346	+	0.998261i	0.995894	+	0.0905280i	$0.0288555\pi$
$563$	13.6753	+	23.6864i	0.576346	+	0.998261i	−0.419547	+	0.907733i	$0.637811\pi$
$564$	−2.05362	−	3.55698i	−0.0864732	−	0.149776i
$565$	−11.8797	+	20.5762i	−0.499781	+	0.865646i
$566$	−18.0840			−0.760127
$567$	0.155792	−	2.64116i	0.00654263	−	0.110918i
$568$	0.934749			0.0392212
$569$	14.7239	−	25.5025i	0.617257	−	1.06912i	−0.372727	−	0.927941i	$-0.621577\pi$
$569$	14.7239	−	25.5025i	0.617257	−	1.06912i	0.989984	−	0.141179i	$-0.0450894\pi$
$570$	−8.14925	−	14.1149i	−0.341334	−	0.591209i
$571$	7.26304	+	12.5800i	0.303949	+	0.526455i	0.977027	−	0.213117i	$-0.0683615\pi$
$571$	7.26304	+	12.5800i	0.303949	+	0.526455i	−0.673078	+	0.739572i	$0.735028\pi$
$572$		0			0
$573$	16.8377			0.703404
$574$	−28.7355	+	14.4049i	−1.19940	+	0.601248i
$575$	68.7144			2.86559
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−6.69779	−	11.6009i	−0.278833	−	0.482952i	0.692262	−	0.721646i	$-0.256614\pi$
$577$	−6.69779	−	11.6009i	−0.278833	−	0.482952i	−0.971095	+	0.238694i	$0.923281\pi$
$578$	5.67533	+	9.82996i	0.236063	+	0.408872i
$579$	2.73042	−	4.72922i	0.113472	−	0.196540i
$580$	−28.8377			−1.19742
$581$	−4.74858	−	3.12823i	−0.197004	−	0.129781i
$582$	−7.00000			−0.290159
$583$	4.00000	−	6.92820i	0.165663	−	0.286937i
$584$	3.73042	+	6.46127i	0.154366	+	0.267369i
$585$		0			0
$586$	−12.5746	+	21.7799i	−0.519453	+	0.899719i
$587$	−11.2928			−0.466105			−0.233053	−	0.972464i	$-0.574871\pi$
$587$	−11.2928			−0.466105			−0.233053	+	0.972464i	$0.574871\pi$
$588$	6.95146	+	0.822941i	0.286673	+	0.0339375i
$589$	12.4552			0.513206
$590$	27.6753	−	47.9351i	1.13938	−	1.97346i
$591$	−4.84421	−	8.39042i	−0.199264	−	0.345136i
$592$	−3.84421	−	6.65836i	−0.157996	−	0.273657i
$593$	9.78912	−	16.9553i	0.401991	−	0.696269i	−0.591975	−	0.805956i	$-0.701652\pi$
$593$	9.78912	−	16.9553i	0.401991	−	0.696269i	0.993966	+	0.109687i	$0.0349849\pi$
$594$	1.00000			0.0410305
$595$	23.2051	+	15.2869i	0.951317	+	0.626700i
$596$	−9.36375			−0.383554
$597$	10.1492	−	17.5790i	0.415381	−	0.719461i
$598$		0			0
$599$	−5.46591	−	9.46724i	−0.223331	−	0.386821i	0.732486	−	0.680782i	$-0.238360\pi$
$599$	−5.46591	−	9.46724i	−0.223331	−	0.386821i	−0.955817	+	0.293961i	$0.905026\pi$
$600$	7.26304	−	12.5800i	0.296512	−	0.513575i
$601$	−41.2202			−1.68141			−0.840703	−	0.541497i	$-0.817858\pi$
$601$	−41.2202			−1.68141			−0.840703	+	0.541497i	$0.817858\pi$
$602$	−7.24995	+	3.63435i	−0.295486	+	0.148125i
$603$	10.1492			0.413309
$604$	6.78404	−	11.7503i	0.276039	−	0.478113i
$605$	−2.20942	−	3.82682i	−0.0898255	−	0.155582i
$606$	−7.68187	−	13.3054i	−0.312055	−	0.540495i
$607$	15.6702	−	27.1417i	0.636036	−	1.10165i	−0.350259	−	0.936653i	$-0.613906\pi$
$607$	15.6702	−	27.1417i	0.636036	−	1.10165i	0.986295	−	0.164993i	$-0.0527603\pi$
$608$	−3.68842			−0.149585
$609$	1.01671	−	17.2364i	0.0411991	−	0.698455i
$610$	16.7724			0.679095
$611$		0			0
$612$	−1.18842	−	2.05840i	−0.0480389	−	0.0832058i
$613$	−8.54425	−	14.7991i	−0.345099	−	0.597729i	0.640273	−	0.768148i	$-0.278821\pi$
$613$	−8.54425	−	14.7991i	−0.345099	−	0.597729i	−0.985372	+	0.170419i	$0.945488\pi$
$614$	1.93475	−	3.35108i	0.0780801	−	0.135239i
$615$	−53.6855			−2.16481
$616$	−0.155792	+	2.64116i	−0.00627702	+	0.106415i
$617$	−6.96817			−0.280528			−0.140264	−	0.990114i	$-0.544795\pi$
$617$	−6.96817			−0.280528			−0.140264	+	0.990114i	$0.544795\pi$
$618$	−1.31158	+	2.27173i	−0.0527596	+	0.0913823i
$619$	0.00937364	+	0.0162356i	0.000376759	+	0.000652565i	0.866214	−	0.499674i	$-0.166547\pi$
$619$	0.00937364	+	0.0162356i	0.000376759	+	0.000652565i	−0.865837	+	0.500326i	$0.833213\pi$
$620$	7.46083	+	12.9225i	0.299634	+	0.518982i
$621$	2.36521	−	4.09666i	0.0949125	−	0.164393i
$622$	−13.5681			−0.544030
$623$	30.3637	−	15.2211i	1.21650	−	0.609821i
$624$		0			0
$625$	−56.6883	+	98.1871i	−2.26753	+	3.92748i
$626$	−1.26304	−	2.18765i	−0.0504813	−	0.0874361i
$627$	1.84421	+	3.19426i	0.0736506	+	0.127567i
$628$	9.37029	−	16.2298i	0.373915	−	0.647640i
$629$	18.2741			0.728636
$630$	9.76304	+	6.43161i	0.388969	+	0.256241i
$631$	−5.78550			−0.230317			−0.115159	−	0.993347i	$-0.536738\pi$
$631$	−5.78550			−0.230317			−0.115159	+	0.993347i	$0.536738\pi$
$632$	0.209416	−	0.362720i	0.00833013	−	0.0144282i
$633$	11.2565	+	19.4968i	0.447406	+	0.774929i
$634$	10.0051	+	17.3293i	0.397353	+	0.688235i
$635$	−1.61379	+	2.79517i	−0.0640414	+	0.110923i
$636$	−8.00000			−0.317221
$637$		0			0
$638$	6.52608			0.258370
$639$	−0.467375	+	0.809517i	−0.0184891	+	0.0320240i
$640$	−2.20942	−	3.82682i	−0.0873348	−	0.151268i
$641$	−7.68842	−	13.3167i	−0.303674	−	0.525979i	0.673291	−	0.739378i	$-0.264880\pi$
$641$	−7.68842	−	13.3167i	−0.303674	−	0.525979i	−0.976965	+	0.213398i	$0.931547\pi$
$642$	5.45146	−	9.44220i	0.215152	−	0.372654i
$643$	−35.8058			−1.41204			−0.706022	−	0.708190i	$-0.749512\pi$
$643$	−35.8058			−1.41204			−0.706022	+	0.708190i	$0.749512\pi$
$644$	10.4515	+	6.88512i	0.411845	+	0.271312i
$645$	−13.5448			−0.533327
$646$	4.38338	−	7.59223i	0.172462	−	0.298712i
$647$	−4.62825	−	8.01636i	−0.181955	−	0.315156i	0.760591	−	0.649231i	$-0.224909\pi$
$647$	−4.62825	−	8.01636i	−0.181955	−	0.315156i	−0.942546	+	0.334076i	$0.891576\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−6.26304	+	10.8479i	−0.245846	+	0.425818i
$650$		0			0
$651$	−7.98691	+	4.00378i	−0.313032	+	0.156920i
$652$	18.7724			0.735185
$653$	−12.4239	+	21.5189i	−0.486185	+	0.842098i	−0.999874	−	0.0158790i	$-0.994945\pi$
$653$	−12.4239	+	21.5189i	−0.486185	+	0.842098i	0.513689	+	0.857977i	$0.328279\pi$
$654$	−5.89783	−	10.2153i	−0.230624	−	0.399452i
$655$	−16.2985	−	28.2298i	−0.636835	−	1.10303i
$656$	−6.07462	+	10.5216i	−0.237174	+	0.410798i
$657$	−7.46083			−0.291075
$658$	−0.639875	+	10.8479i	−0.0249449	+	0.422895i
$659$	−6.60442			−0.257272			−0.128636	−	0.991692i	$-0.541060\pi$
$659$	−6.60442			−0.257272			−0.128636	+	0.991692i	$0.541060\pi$
$660$	−2.20942	+	3.82682i	−0.0860014	+	0.148959i
$661$	6.61662	+	11.4603i	0.257357	+	0.445755i	0.965533	−	0.260281i	$-0.0838151\pi$
$661$	6.61662	+	11.4603i	0.257357	+	0.445755i	−0.708176	+	0.706036i	$0.750482\pi$
$662$	8.07462	+	13.9857i	0.313829	+	0.543568i
$663$		0			0
$664$	−2.14925			−0.0834070
$665$	−2.53917	+	43.0469i	−0.0984647	+	1.66929i
$666$	7.68842			0.297920
$667$	15.4355	−	26.7351i	0.597667	−	1.03519i
$668$	11.9449	+	20.6892i	0.462163	+	0.800489i
$669$	−3.73042	−	6.46127i	−0.144226	−	0.249807i
$670$	−22.4239	+	38.8394i	−0.866311	+	1.50050i
$671$	−3.79567			−0.146530
$672$	2.36521	−	1.18566i	0.0912399	−	0.0457379i
$673$	0.130501			0.00503045			0.00251523	−	0.999997i	$-0.499199\pi$
$673$	0.130501			0.00503045			0.00251523	+	0.999997i	$0.499199\pi$
$674$	−11.5681	+	20.0365i	−0.445586	+	0.771777i
$675$	7.26304	+	12.5800i	0.279555	+	0.484203i
$676$	6.50000	+	11.2583i	0.250000	+	0.433013i
$677$	−14.0587	+	24.3504i	−0.540320	+	0.935862i	0.458565	+	0.888661i	$0.348363\pi$
$677$	−14.0587	+	24.3504i	−0.540320	+	0.935862i	−0.998885	+	0.0472011i	$0.984970\pi$
$678$	−5.37683			−0.206496
$679$	15.4659	+	10.1885i	0.593527	+	0.390999i
$680$	10.5028			0.402765
$681$	−1.38621	+	2.40098i	−0.0531196	+	0.0920058i
$682$	−1.68842	−	2.92442i	−0.0646528	−	0.111982i
$683$	−7.95146	−	13.7723i	−0.304254	−	0.526984i	0.672841	−	0.739787i	$-0.265074\pi$
$683$	−7.95146	−	13.7723i	−0.304254	−	0.526984i	−0.977095	+	0.212804i	$0.931741\pi$
$684$	1.84421	−	3.19426i	0.0705151	−	0.122136i
$685$	−39.0522			−1.49211
$686$	−14.1609	−	11.9361i	−0.540665	−	0.455721i
$687$	2.53917			0.0968753
$688$	−1.53263	+	2.65458i	−0.0584308	+	0.101205i
$689$		0			0
$690$	10.4515	+	18.1025i	0.397880	+	0.689149i
$691$	7.99063	−	13.8402i	0.303978	−	0.526505i	−0.673055	−	0.739592i	$-0.735018\pi$
$691$	7.99063	−	13.8402i	0.303978	−	0.526505i	0.977033	+	0.213087i	$0.0683518\pi$
$692$	11.3768			0.432482
$693$	−2.20942	−	1.45550i	−0.0839288	−	0.0552899i
$694$	15.6566			0.594316
$695$	−3.25650	+	5.64042i	−0.123526	+	0.213953i
$696$	−3.26304	−	5.65175i	−0.123685	−	0.214229i
$697$	−14.4384	−	25.0080i	−0.546892	−	0.947245i
$698$	10.0051	−	17.3293i	0.378698	−	0.655924i
$699$	24.0522			0.909736
$700$	−34.3572	+	17.2230i	−1.29858	+	0.650968i
$701$	13.9869			0.528278			0.264139	−	0.964485i	$-0.414912\pi$
$701$	13.9869			0.528278			0.264139	+	0.964485i	$0.414912\pi$
$702$		0			0
$703$	14.1790	+	24.5588i	0.534773	+	0.926254i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	−9.07462	+	15.7177i	−0.341770	+	0.591963i
$706$	7.46083			0.280792
$707$	−2.39354	+	40.5781i	−0.0900184	+	1.52610i
$708$	12.5261			0.470759
$709$	−3.82096	+	6.61809i	−0.143499	+	0.248548i	−0.928812	−	0.370551i	$-0.879169\pi$
$709$	−3.82096	+	6.61809i	−0.143499	+	0.248548i	0.785313	+	0.619099i	$0.212502\pi$
$710$	−2.06525	−	3.57712i	−0.0775075	−	0.134247i
$711$	0.209416	+	0.362720i	0.00785373	+	0.0136031i
$712$	6.41883	−	11.1177i	0.240556	−	0.416655i
$713$	−15.9738			−0.598225
$714$	−0.370291	+	6.27760i	−0.0138578	+	0.234933i
$715$		0			0
$716$	−12.3050	+	21.3130i	−0.459861	+	0.796503i
$717$	3.79567	+	6.57429i	0.141752	+	0.245521i
$718$	5.62317	+	9.73961i	0.209855	+	0.363479i
$719$	9.71879	−	16.8334i	0.362450	−	0.627781i	−0.625914	−	0.779892i	$-0.715274\pi$
$719$	9.71879	−	16.8334i	0.362450	−	0.627781i	0.988363	+	0.152111i	$0.0486071\pi$
$720$	4.41883			0.164680
$721$	6.20433	−	3.11019i	0.231061	−	0.115829i
$722$	−5.39558			−0.200803
$723$	8.14925	−	14.1149i	0.303074	−	0.524939i
$724$	−8.73042	−	15.1215i	−0.324463	−	0.561987i
$725$	47.3992	+	82.0978i	1.76036	+	3.04904i
$726$	0.500000	−	0.866025i	0.0185567	−	0.0321412i
$727$	−44.9217			−1.66605			−0.833026	−	0.553234i	$-0.813394\pi$
$727$	−44.9217			−1.66605			−0.833026	+	0.553234i	$0.813394\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	16.4841	−	28.5513i	0.610103	−	1.05673i
$731$	−3.64280	−	6.30951i	−0.134734	−	0.233366i
$732$	1.89783	+	3.28714i	0.0701459	+	0.121496i
$733$	−12.5210	+	21.6870i	−0.462474	+	0.801028i	−0.999084	−	0.0428026i	$-0.986371\pi$
$733$	−12.5210	+	21.6870i	−0.462474	+	0.801028i	0.536610	+	0.843830i	$0.319705\pi$
$734$	−5.91600			−0.218364
$735$	−12.2094	−	28.4202i	−0.450351	−	1.04830i
$736$	4.73042			0.174365
$737$	5.07462	−	8.78951i	0.186926	−	0.323766i
$738$	−6.07462	−	10.5216i	−0.223610	−	0.387304i
$739$	3.31158	+	5.73583i	0.121819	+	0.210996i	0.920485	−	0.390778i	$-0.127794\pi$
$739$	3.31158	+	5.73583i	0.121819	+	0.210996i	−0.798666	+	0.601774i	$0.794461\pi$
$740$	−16.9869	+	29.4222i	−0.624451	+	1.08158i
$741$		0			0
$742$	17.6753	+	11.6440i	0.648882	+	0.427465i
$743$	−39.3972			−1.44534			−0.722671	−	0.691192i	$-0.757086\pi$
$743$	−39.3972			−1.44534			−0.722671	+	0.691192i	$0.757086\pi$
$744$	−1.68842	+	2.92442i	−0.0619004	+	0.107215i
$745$	20.6884	+	35.8334i	0.757965	+	1.31283i
$746$	11.5630	+	20.0277i	0.423351	+	0.733266i
$747$	1.07462	−	1.86130i	0.0393184	−	0.0681015i
$748$	−2.37683			−0.0869056
$749$	−25.7877	+	12.9272i	−0.942261	+	0.472348i
$750$	−42.0942			−1.53706
$751$	5.35358	−	9.27268i	0.195355	−	0.338365i	−0.751662	−	0.659549i	$-0.770747\pi$
$751$	5.35358	−	9.27268i	0.195355	−	0.338365i	0.947017	+	0.321184i	$0.104081\pi$
$752$	2.05362	+	3.55698i	0.0748880	+	0.129710i
$753$	−4.30504	−	7.45655i	−0.156884	−	0.271732i
$754$		0			0
$755$	−59.9551			−2.18199
$756$	−0.155792	+	2.64116i	−0.00566608	+	0.0960581i
$757$	−17.2797			−0.628043			−0.314022	−	0.949416i	$-0.601676\pi$
$757$	−17.2797			−0.628043			−0.314022	+	0.949416i	$0.601676\pi$
$758$	3.38621	−	5.86508i	0.122993	−	0.213029i
$759$	−2.36521	−	4.09666i	−0.0858516	−	0.148699i
$760$	8.14925	+	14.1149i	0.295604	+	0.512002i
$761$	16.3544	−	28.3266i	0.592846	−	1.02684i	−0.401001	−	0.916077i	$-0.631338\pi$
$761$	16.3544	−	28.3266i	0.592846	−	1.02684i	0.993847	−	0.110761i	$-0.0353289\pi$
$762$	−0.730416			−0.0264602
$763$	−1.83767	+	31.1542i	−0.0665280	+	1.12786i
$764$	−16.8377			−0.609165
$765$	−5.25142	+	9.09572i	−0.189865	+	0.328856i
$766$	−12.6819	−	21.9656i	−0.458215	−	0.793651i
$767$		0			0
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	12.2145			0.440466			0.220233	−	0.975447i	$-0.429318\pi$
$769$	12.2145			0.440466			0.220233	+	0.975447i	$0.429318\pi$
$770$	10.4515	−	5.23924i	0.376644	−	0.188809i
$771$	−0.837665			−0.0301678
$772$	−2.73042	+	4.72922i	−0.0982698	+	0.170208i
$773$	−0.102167	−	0.176958i	−0.00367468	−	0.00636474i	0.864182	−	0.503179i	$-0.167836\pi$
$773$	−0.102167	−	0.176958i	−0.00367468	−	0.00636474i	−0.867857	+	0.496814i	$0.834503\pi$
$774$	−1.53263	−	2.65458i	−0.0550891	−	0.0954171i
$775$	24.5261	−	42.4804i	0.881003	−	1.52594i
$776$	7.00000			0.251285
$777$	−16.9869	−	11.1905i	−0.609402	−	0.401457i
$778$	25.2565			0.905489
$779$	22.4057	−	38.8079i	0.802769	−	1.39044i
$780$		0			0
$781$	0.467375	+	0.809517i	0.0167240	+	0.0289668i
$782$	−5.62171	+	9.73708i	−0.201032	+	0.348197i
$783$	6.52608			0.233223
$784$	−6.95146	−	0.822941i	−0.248266	−	0.0293908i
$785$	−82.8115			−2.95567
$786$	3.68842	−	6.38853i	0.131561	−	0.227871i
$787$	−12.7790	−	22.1338i	−0.455521	−	0.788985i	0.543197	−	0.839605i	$-0.317214\pi$
$787$	−12.7790	−	22.1338i	−0.455521	−	0.788985i	−0.998718	+	0.0506202i	$0.983880\pi$
$788$	4.84421	+	8.39042i	0.172568	+	0.298896i
$789$	5.41883	−	9.38569i	0.192916	−	0.334140i
$790$	−1.85075			−0.0658468
$791$	11.8797	+	7.82598i	0.422392	+	0.278260i
$792$	−1.00000			−0.0355335
$793$		0			0
$794$	6.73696	+	11.6688i	0.239086	+	0.414109i
$795$	17.6753	+	30.6146i	0.626879	+	1.08579i
$796$	−10.1492	+	17.5790i	−0.359731	+	0.623072i
$797$	30.0477			1.06434			0.532171	−	0.846637i	$-0.321376\pi$
$797$	30.0477			1.06434			0.532171	+	0.846637i	$0.321376\pi$
$798$	−8.72387	+	4.37321i	−0.308822	+	0.154810i
$799$	−9.76225			−0.345364
$800$	−7.26304	+	12.5800i	−0.256787	+	0.444769i
$801$	6.41883	+	11.1177i	0.226798	+	0.392826i
$802$	−16.9449	−	29.3495i	−0.598346	−	1.03637i
$803$	−3.73042	+	6.46127i	−0.131644	+	0.228013i
$804$	−10.1492			−0.357936
$805$	3.25650	−	55.2080i	0.114776	−	1.94582i
$806$		0			0
$807$	8.93983	−	15.4842i	0.314697	−	0.545071i
$808$	7.68187	+	13.3054i	0.270247	+	0.468082i
$809$	−1.17171	−	2.02946i	−0.0411951	−	0.0713520i	0.844693	−	0.535252i	$-0.179783\pi$
$809$	−1.17171	−	2.02946i	−0.0411951	−	0.0713520i	−0.885888	+	0.463900i	$0.846450\pi$
$810$	−2.20942	+	3.82682i	−0.0776310	+	0.134461i
$811$	−11.8695			−0.416794			−0.208397	−	0.978044i	$-0.566825\pi$
$811$	−11.8695			−0.416794			−0.208397	+	0.978044i	$0.566825\pi$
$812$	−1.01671	+	17.2364i	−0.0356795	+	0.604880i
$813$	8.83767			0.309950
$814$	3.84421	−	6.65836i	0.134739	−	0.233376i
$815$	−41.4761	−	71.8387i	−1.45284	−	2.51640i
$816$	1.18842	+	2.05840i	0.0416029	+	0.0720584i
$817$	5.65296	−	9.79122i	0.197772	−	0.342551i
$818$	−4.21450			−0.147357
$819$		0			0
$820$	53.6855			1.87478
$821$	18.7406	−	32.4596i	0.654051	−	1.13285i	−0.328080	−	0.944650i	$-0.606402\pi$
$821$	18.7406	−	32.4596i	0.654051	−	1.13285i	0.982131	−	0.188199i	$-0.0602651\pi$
$822$	−4.41883	−	7.65364i	−0.154124	−	0.266951i
$823$	−0.646418	−	1.11963i	−0.0225327	−	0.0390278i	0.854539	−	0.519387i	$-0.173840\pi$
$823$	−0.646418	−	1.11963i	−0.0225327	−	0.0390278i	−0.877072	+	0.480359i	$0.840506\pi$
$824$	1.31158	−	2.27173i	0.0456912	−	0.0791394i
$825$	14.5261			0.505733
$826$	−27.6753	−	18.2317i	−0.962948	−	0.634362i
$827$	43.3319			1.50680			0.753399	−	0.657563i	$-0.228413\pi$
$827$	43.3319			1.50680			0.753399	+	0.657563i	$0.228413\pi$
$828$	−2.36521	+	4.09666i	−0.0821967	+	0.142369i
$829$	−20.0587	−	34.7427i	−0.696668	−	1.20666i	−0.969615	−	0.244635i	$-0.921332\pi$
$829$	−20.0587	−	34.7427i	−0.696668	−	1.20666i	0.272948	−	0.962029i	$-0.412001\pi$
$830$	4.74858	+	8.22479i	0.164826	+	0.285487i
$831$	−8.00000	+	13.8564i	−0.277517	+	0.480673i
$832$		0			0
$833$	9.95517	−	13.3309i	0.344926	−	0.461887i
$834$	−1.47392			−0.0510376
$835$	52.7826	−	91.4221i	1.82662	−	3.16379i
$836$	−1.84421	−	3.19426i	−0.0637833	−	0.110476i
$837$	−1.68842	−	2.92442i	−0.0583602	−	0.101083i
$838$	11.1558	−	19.3224i	0.385370	−	0.667481i
$839$	54.6912			1.88815			0.944074	−	0.329733i	$-0.106959\pi$
$839$	54.6912			1.88815			0.944074	+	0.329733i	$0.106959\pi$
$840$	−9.76304	−	6.43161i	−0.336857	−	0.221912i
$841$	13.5897			0.468612
$842$	−9.15579	+	15.8583i	−0.315529	+	0.546513i
$843$	−7.96083	−	13.7886i	−0.274186	−	0.474903i
$844$	−11.2565	−	19.4968i	−0.387465	−	0.671108i
$845$	28.7224	−	49.7487i	0.988081	−	1.71141i
$846$	−4.10725			−0.141210
$847$	−2.36521	+	1.18566i	−0.0812695	+	0.0407398i
$848$	8.00000			0.274721
$849$	−9.04200	+	15.6612i	−0.310321	+	0.537491i
$850$	−17.2630	−	29.9005i	−0.592117	−	1.02558i
$851$	−18.1847	−	31.4968i	−0.623364	−	1.07970i
$852$	0.467375	−	0.809517i	0.0160120	−	0.0277336i
$853$	−20.8275			−0.713120			−0.356560	−	0.934272i	$-0.616050\pi$
$853$	−20.8275			−0.713120			−0.356560	+	0.934272i	$0.616050\pi$
$854$	0.591333	−	10.0250i	0.0202350	−	0.343047i
$855$	−16.2985			−0.557397
$856$	−5.45146	+	9.44220i	−0.186327	+	0.322728i
$857$	18.4217	+	31.9073i	0.629272	+	1.08993i	0.987698	+	0.156373i	$0.0499802\pi$
$857$	18.4217	+	31.9073i	0.629272	+	1.08993i	−0.358426	+	0.933558i	$0.616686\pi$
$858$		0			0
$859$	−19.2891	+	33.4097i	−0.658136	+	1.13993i	0.322961	+	0.946412i	$0.395322\pi$
$859$	−19.2891	+	33.4097i	−0.658136	+	1.13993i	−0.981098	+	0.193513i	$0.938012\pi$
$860$	13.5448			0.461875
$861$	−1.89275	+	32.0881i	−0.0645048	+	1.09356i
$862$	−28.8377			−0.982215
$863$	8.62825	−	14.9446i	0.293709	−	0.508719i	−0.680975	−	0.732307i	$-0.738444\pi$
$863$	8.62825	−	14.9446i	0.293709	−	0.508719i	0.974684	+	0.223588i	$0.0717770\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−25.1362	−	43.5371i	−0.854655	−	1.48031i
$866$	−3.81158	+	6.60186i	−0.129523	+	0.224340i
$867$	11.3507			0.385489
$868$	7.98691	−	4.00378i	0.271094	−	0.135897i
$869$	0.418833			0.0142079
$870$	−14.4188	+	24.9742i	−0.488844	+	0.846703i
$871$		0			0
$872$	5.89783	+	10.2153i	0.199726	+	0.345935i
$873$	−3.50000	+	6.06218i	−0.118457	+	0.205174i
$874$	−17.4477			−0.590179
$875$	93.0035	+	61.2680i	3.14409	+	2.07124i
$876$	7.46083			0.252078
$877$	−0.125418	+	0.217231i	−0.00423508	+	0.00733537i	−0.868135	−	0.496328i	$-0.834681\pi$
$877$	−0.125418	+	0.217231i	−0.00423508	+	0.00733537i	0.863900	+	0.503663i	$0.168015\pi$
$878$	16.6870	+	28.9027i	0.563158	+	0.975417i
$879$	12.5746	+	21.7799i	0.424132	+	0.734617i
$880$	2.20942	−	3.82682i	0.0744794	−	0.129002i
$881$	16.2985			0.549110			0.274555	−	0.961571i	$-0.411469\pi$
$881$	16.2985			0.549110			0.274555	+	0.961571i	$0.411469\pi$
$882$	4.18842	−	5.60867i	0.141031	−	0.188854i
$883$	−33.9551			−1.14268			−0.571340	−	0.820714i	$-0.693576\pi$
$883$	−33.9551			−1.14268			−0.571340	+	0.820714i	$0.693576\pi$
$884$		0			0
$885$	−27.6753	−	47.9351i	−0.930296	−	1.61132i
$886$	2.42538	+	4.20087i	0.0814821	+	0.141131i
$887$	−9.73042	+	16.8536i	−0.326715	+	0.565888i	−0.981858	−	0.189618i	$-0.939275\pi$
$887$	−9.73042	+	16.8536i	−0.326715	+	0.565888i	0.655143	+	0.755505i	$0.272609\pi$
$888$	−7.68842			−0.258006
$889$	1.61379	+	1.06312i	0.0541249	+	0.0356559i
$890$	−56.7275			−1.90151
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	3.73042	+	6.46127i	0.124904	+	0.216339i
$893$	−7.57462	−	13.1196i	−0.253475	−	0.439032i
$894$	−4.68187	+	8.10924i	−0.156585	+	0.271214i
$895$	108.748			3.63504
$896$	−2.36521	+	1.18566i	−0.0790161	+	0.0396101i
$897$		0			0
$898$	−7.17250	+	12.4231i	−0.239349	+	0.414565i
$899$	−11.0187	−	19.0850i	−0.367496	−	0.636521i
$900$	−7.26304	−	12.5800i	−0.242101	−	0.419332i
$901$	−9.50733	+	16.4672i	−0.316735	+	0.548602i
$902$	−12.1492			−0.404526
$903$	−0.477540	+	8.09582i	−0.0158915	+	0.269412i
$904$	5.37683			0.178831
$905$	−38.5782	+	66.8195i	−1.28238	+	2.22115i
$906$	−6.78404	−	11.7503i	−0.225385	−	0.390378i
$907$	−0.386207	−	0.668931i	−0.0128238	−	0.0222115i	0.859542	−	0.511065i	$-0.170749\pi$
$907$	−0.386207	−	0.668931i	−0.0128238	−	0.0222115i	−0.872366	+	0.488853i	$0.837415\pi$
$908$	1.38621	−	2.40098i	0.0460029	−	0.0796794i
$909$	−15.3637			−0.509583
$910$		0			0
$911$	−8.94491			−0.296358			−0.148179	−	0.988961i	$-0.547341\pi$
$911$	−8.94491			−0.296358			−0.148179	+	0.988961i	$0.547341\pi$
$912$	−1.84421	+	3.19426i	−0.0610678	+	0.105773i
$913$	−1.07462	−	1.86130i	−0.0355649	−	0.0616002i
$914$	12.5913	+	21.8088i	0.416484	+	0.721372i
$915$	8.38621	−	14.5253i	0.277239	−	0.480193i
$916$	−2.53917			−0.0838965
$917$	−17.4477	+	8.74642i	−0.576175	+	0.288832i
$918$	−2.37683			−0.0784472
$919$	−29.4406	+	50.9927i	−0.971157	+	1.68209i	−0.279081	+	0.960268i	$0.590030\pi$
$919$	−29.4406	+	50.9927i	−0.971157	+	1.68209i	−0.692076	+	0.721825i	$0.743304\pi$
$920$	−10.4515	−	18.1025i	−0.344574	−	0.596820i
$921$	−1.93475	−	3.35108i	−0.0637522	−	0.110422i
$922$	−6.50937	+	11.2746i	−0.214375	+	0.371308i
$923$		0			0
$924$	2.20942	+	1.45550i	0.0726845	+	0.0478824i
$925$	111.683			3.67210
$926$	7.10725	−	12.3101i	0.233559	−	0.404536i
$927$	1.31158	+	2.27173i	0.0430780	+	0.0746134i
$928$	3.26304	+	5.65175i	0.107115	+	0.185528i
$929$	11.2696	−	19.5195i	0.369743	−	0.640414i	−0.619782	−	0.784774i	$-0.712779\pi$
$929$	11.2696	−	19.5195i	0.369743	−	0.640414i	0.989525	+	0.144360i	$0.0461124\pi$
$930$	14.9217			0.489301
$931$	25.6399	+	3.03535i	0.840313	+	0.0994796i
$932$	−24.0522			−0.787855
$933$	−6.78404	+	11.7503i	−0.222100	+	0.384688i
$934$	1.19779	+	2.07463i	0.0391929	+	0.0678841i
$935$	5.25142	+	9.09572i	0.171740	+	0.297462i
$936$		0			0
$937$	−12.9478			−0.422987			−0.211494	−	0.977379i	$-0.567833\pi$
$937$	−12.9478			−0.422987			−0.211494	+	0.977379i	$0.567833\pi$
$938$	22.4239	+	14.7722i	0.732167	+	0.482330i
$939$	−2.52608			−0.0824356
$940$	9.07462	−	15.7177i	0.295982	−	0.512655i
$941$	−24.4123	−	42.2833i	−0.795818	−	1.37840i	−0.922319	−	0.386431i	$-0.873708\pi$
$941$	−24.4123	−	42.2833i	−0.795818	−	1.37840i	0.126501	−	0.991967i	$-0.459625\pi$
$942$	−9.37029	−	16.2298i	−0.305301	−	0.528796i
$943$	−28.7355	+	49.7713i	−0.935757	+	1.62078i
$944$	−12.5261			−0.407689
$945$	10.4515	−	5.23924i	0.339986	−	0.170432i
$946$	−3.06525			−0.0996599
$947$	15.5615	−	26.9534i	0.505682	−	0.875867i	−0.494296	−	0.869293i	$-0.664574\pi$
$947$	15.5615	−	26.9534i	0.505682	−	0.875867i	0.999978	−	0.00657353i	$-0.00209243\pi$
$948$	−0.209416	−	0.362720i	−0.00680153	−	0.0117806i
$949$		0			0
$950$	26.7891	−	46.4001i	0.869154	−	1.50542i
$951$	20.0102			0.648874
$952$	0.370291	−	6.27760i	0.0120012	−	0.203458i
$953$	16.2797			0.527353			0.263676	−	0.964611i	$-0.415065\pi$
$953$	16.2797			0.527353			0.263676	+	0.964611i	$0.415065\pi$
$954$	−4.00000	+	6.92820i	−0.129505	+	0.224309i
$955$	37.2014	+	64.4347i	1.20381	+	2.08506i
$956$	−3.79567	−	6.57429i	−0.122761	−	0.212628i
$957$	3.26304	−	5.65175i	0.105479	−	0.182695i
$958$	10.8377			0.350149
$959$	−1.37683	+	23.3417i	−0.0444603	+	0.753743i
$960$	−4.41883			−0.142617
$961$	9.79850	−	16.9715i	0.316081	−	0.547468i
$962$		0			0
$963$	−5.45146	−	9.44220i	−0.175671	−	0.304271i
$964$	−8.14925	+	14.1149i	−0.262470	+	0.454611i
$965$	24.1305			0.776788
$966$	11.1884	−	5.60867i	0.359981	−	0.180456i
$967$	3.91308			0.125836			0.0629181	−	0.998019i	$-0.479959\pi$
$967$	3.91308			0.125836			0.0629181	+	0.998019i	$0.479959\pi$
$968$	−0.500000	+	0.866025i	−0.0160706	+	0.0278351i
$969$	−4.38338	−	7.59223i	−0.140814	−	0.243898i
$970$	−15.4659	−	26.7877i	−0.496581	−	0.860103i
$971$	−19.6566	+	34.0462i	−0.630810	+	1.09259i	0.356577	+	0.934266i	$0.383944\pi$
$971$	−19.6566	+	34.0462i	−0.630810	+	1.09259i	−0.987386	+	0.158329i	$0.949389\pi$
$972$	−1.00000			−0.0320750
$973$	3.25650	+	2.14529i	0.104399	+	0.0687747i
$974$	−34.6435			−1.11005
$975$		0			0
$976$	−1.89783	−	3.28714i	−0.0607482	−	0.105219i
$977$	11.6753	+	20.2223i	0.373527	+	0.646968i	0.990105	−	0.140326i	$-0.0448150\pi$
$977$	11.6753	+	20.2223i	0.373527	+	0.646968i	−0.616578	+	0.787293i	$0.711482\pi$
$978$	9.38621	−	16.2574i	0.300138	−	0.519854i
$979$	12.8377			0.410294
$980$	12.2094	+	28.4202i	0.390015	+	0.907850i
$981$	−11.7957			−0.376607
$982$	−19.0746	+	33.0382i	−0.608696	+	1.05429i
$983$	2.25796	+	3.91090i	0.0720177	+	0.124738i	0.899785	−	0.436333i	$-0.143723\pi$
$983$	2.25796	+	3.91090i	0.0720177	+	0.124738i	−0.827768	+	0.561071i	$0.810390\pi$
$984$	6.07462	+	10.5216i	0.193652	+	0.335415i
$985$	21.4057	−	37.0758i	0.682044	−	1.18133i
$986$	−15.5114			−0.493984
$987$	9.07462	+	5.97810i	0.288848	+	0.190285i
$988$		0			0
$989$	−7.24995	+	12.5573i	−0.230535	+	0.399299i
$990$	2.20942	+	3.82682i	0.0702199	+	0.121624i
$991$	−29.9637	−	51.8986i	−0.951827	−	1.64861i	−0.741467	−	0.670989i	$-0.765870\pi$
$991$	−29.9637	−	51.8986i	−0.951827	−	1.64861i	−0.210360	−	0.977624i	$-0.567463\pi$
$992$	1.68842	−	2.92442i	0.0536073	−	0.0928505i
$993$	16.1492			0.512481
$994$	−2.21088	+	1.10830i	−0.0701247	+	0.0351530i
$995$	89.6957			2.84354
$996$	−1.07462	+	1.86130i	−0.0340508	+	0.0589777i
$997$	10.7537	+	18.6259i	0.340572	+	0.589888i	0.984539	−	0.175165i	$-0.0560459\pi$
$997$	10.7537	+	18.6259i	0.340572	+	0.589888i	−0.643967	+	0.765053i	$0.722713\pi$
$998$	0.311583	+	0.539678i	0.00986299	+	0.0170832i
$999$	3.84421	−	6.65836i	0.121625	−	0.210661i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.i.g.331.1	yes	6
3.2	odd	2		1386.2.k.v.793.3		6
7.2	even	3		3234.2.a.bf.1.3		3
7.4	even	3	inner	462.2.i.g.67.1	✓	6
7.5	odd	6		3234.2.a.bh.1.1		3
21.2	odd	6		9702.2.a.dv.1.1		3
21.5	even	6		9702.2.a.dw.1.3		3
21.11	odd	6		1386.2.k.v.991.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.i.g.67.1	✓	6	7.4	even	3	inner
462.2.i.g.331.1	yes	6	1.1	even	1	trivial
1386.2.k.v.793.3		6	3.2	odd	2
1386.2.k.v.991.3		6	21.11	odd	6
3234.2.a.bf.1.3		3	7.2	even	3
3234.2.a.bh.1.1		3	7.5	odd	6
9702.2.a.dv.1.1		3	21.2	odd	6
9702.2.a.dw.1.3		3	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.20942 + 3.82682i) q^{5} -1.00000 q^{6} +(2.20942 + 1.45550i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.20942 + 3.82682i) q^{5} -1.00000 q^{6} +(2.20942 + 1.45550i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.20942 - 3.82682i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-2.36521 + 1.18566i) q^{14} -4.41883 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.18842 - 2.05840i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.84421 - 3.19426i) q^{19} +4.41883 q^{20} +(-0.155792 + 2.64116i) q^{21} -1.00000 q^{22} +(-2.36521 + 4.09666i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-7.26304 - 12.5800i) q^{25} -1.00000 q^{27} +(0.155792 - 2.64116i) q^{28} -6.52608 q^{29} +(2.20942 - 3.82682i) q^{30} +(1.68842 + 2.92442i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +2.37683 q^{34} +(-10.4515 + 5.23924i) q^{35} +1.00000 q^{36} +(-3.84421 + 6.65836i) q^{37} +(1.84421 + 3.19426i) q^{38} +(-2.20942 + 3.82682i) q^{40} +12.1492 q^{41} +(-2.20942 - 1.45550i) q^{42} +3.06525 q^{43} +(0.500000 - 0.866025i) q^{44} +(-2.20942 - 3.82682i) q^{45} +(-2.36521 - 4.09666i) q^{46} +(2.05362 - 3.55698i) q^{47} -1.00000 q^{48} +(2.76304 + 6.43161i) q^{49} +14.5261 q^{50} +(1.18842 - 2.05840i) q^{51} +(-4.00000 - 6.92820i) q^{53} +(0.500000 - 0.866025i) q^{54} -4.41883 q^{55} +(2.20942 + 1.45550i) q^{56} +3.68842 q^{57} +(3.26304 - 5.65175i) q^{58} +(6.26304 + 10.8479i) q^{59} +(2.20942 + 3.82682i) q^{60} +(-1.89783 + 3.28714i) q^{61} -3.37683 q^{62} +(-2.36521 + 1.18566i) q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{66} +(-5.07462 - 8.78951i) q^{67} +(-1.18842 + 2.05840i) q^{68} -4.73042 q^{69} +(0.688417 - 11.6708i) q^{70} +0.934749 q^{71} +(-0.500000 + 0.866025i) q^{72} +(3.73042 + 6.46127i) q^{73} +(-3.84421 - 6.65836i) q^{74} +(7.26304 - 12.5800i) q^{75} -3.68842 q^{76} +(-0.155792 + 2.64116i) q^{77} +(0.209416 - 0.362720i) q^{79} +(-2.20942 - 3.82682i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.07462 + 10.5216i) q^{82} -2.14925 q^{83} +(2.36521 - 1.18566i) q^{84} +10.5028 q^{85} +(-1.53263 + 2.65458i) q^{86} +(-3.26304 - 5.65175i) q^{87} +(0.500000 + 0.866025i) q^{88} +(6.41883 - 11.1177i) q^{89} +4.41883 q^{90} +4.73042 q^{92} +(-1.68842 + 2.92442i) q^{93} +(2.05362 + 3.55698i) q^{94} +(8.14925 + 14.1149i) q^{95} +(0.500000 - 0.866025i) q^{96} +7.00000 q^{97} +(-6.95146 - 0.822941i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 - 3 * q^9	\( 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} - 3 q^{9} + 3 q^{11} + 3 q^{12} - 3 q^{14} - 3 q^{16} - 3 q^{17} - 3 q^{18} + 9 q^{19} - 3 q^{21} - 6 q^{22} - 3 q^{23} + 3 q^{24} - 15 q^{25} - 6 q^{27} + 3 q^{28} + 18 q^{29} + 6 q^{31} - 3 q^{32} - 3 q^{33} + 6 q^{34} - 30 q^{35} + 6 q^{36} - 21 q^{37} + 9 q^{38} + 24 q^{41} + 6 q^{43} + 3 q^{44} - 3 q^{46} - 3 q^{47} - 6 q^{48} - 12 q^{49} + 30 q^{50} + 3 q^{51} - 24 q^{53} + 3 q^{54} + 18 q^{57} - 9 q^{58} + 9 q^{59} + 6 q^{61} - 12 q^{62} - 3 q^{63} + 6 q^{64} - 3 q^{66} - 6 q^{67} - 3 q^{68} - 6 q^{69} + 18 q^{71} - 3 q^{72} - 21 q^{74} + 15 q^{75} - 18 q^{76} - 3 q^{77} - 12 q^{79} - 3 q^{81} - 12 q^{82} + 36 q^{83} + 3 q^{84} - 3 q^{86} + 9 q^{87} + 3 q^{88} + 12 q^{89} + 6 q^{92} - 6 q^{93} - 3 q^{94} + 3 q^{96} + 42 q^{97} - 9 q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 - 3 * q^9 + 3 * q^11 + 3 * q^12 - 3 * q^14 - 3 * q^16 - 3 * q^17 - 3 * q^18 + 9 * q^19 - 3 * q^21 - 6 * q^22 - 3 * q^23 + 3 * q^24 - 15 * q^25 - 6 * q^27 + 3 * q^28 + 18 * q^29 + 6 * q^31 - 3 * q^32 - 3 * q^33 + 6 * q^34 - 30 * q^35 + 6 * q^36 - 21 * q^37 + 9 * q^38 + 24 * q^41 + 6 * q^43 + 3 * q^44 - 3 * q^46 - 3 * q^47 - 6 * q^48 - 12 * q^49 + 30 * q^50 + 3 * q^51 - 24 * q^53 + 3 * q^54 + 18 * q^57 - 9 * q^58 + 9 * q^59 + 6 * q^61 - 12 * q^62 - 3 * q^63 + 6 * q^64 - 3 * q^66 - 6 * q^67 - 3 * q^68 - 6 * q^69 + 18 * q^71 - 3 * q^72 - 21 * q^74 + 15 * q^75 - 18 * q^76 - 3 * q^77 - 12 * q^79 - 3 * q^81 - 12 * q^82 + 36 * q^83 + 3 * q^84 - 3 * q^86 + 9 * q^87 + 3 * q^88 + 12 * q^89 + 6 * q^92 - 6 * q^93 - 3 * q^94 + 3 * q^96 + 42 * q^97 - 9 * q^98 - 6 * q^99

Introduction

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