LMFDB - Embedded newform 462.2.i.g.331.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("462.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$6$
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			331.2
Root			$0.500000 + 3.05087i$ of defining polynomial
Character	$\chi$	$=$	462.331
Dual form			462.2.i.g.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.806615 - 1.39710i) q^{5} -1.00000 q^{6} +(-0.806615 + 2.51980i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.806615 - 1.39710i) q^{5} -1.00000 q^{6} +(-0.806615 + 2.51980i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.806615 + 1.39710i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-1.77890 - 1.95845i) q^{14} +1.61323 q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.67103 + 6.35841i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.585515 + 1.01414i) q^{19} -1.61323 q^{20} +(-2.58551 + 0.561349i) q^{21} -1.00000 q^{22} +(-1.77890 + 3.08115i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.19874 + 2.07629i) q^{25} -1.00000 q^{27} +(2.58551 - 0.561349i) q^{28} +10.3975 q^{29} +(-0.806615 + 1.39710i) q^{30} +(-3.17103 - 5.49238i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} -7.34206 q^{34} +(2.86977 + 3.15943i) q^{35} +1.00000 q^{36} +(-1.41449 + 2.44996i) q^{37} +(-0.585515 - 1.01414i) q^{38} +(0.806615 - 1.39710i) q^{40} +4.94457 q^{41} +(0.806615 - 2.51980i) q^{42} -11.5131 q^{43} +(0.500000 - 0.866025i) q^{44} +(0.806615 + 1.39710i) q^{45} +(-1.77890 - 3.08115i) q^{46} +(-3.39213 + 5.87534i) q^{47} -1.00000 q^{48} +(-5.69874 - 4.06501i) q^{49} -2.39749 q^{50} +(-3.67103 + 6.35841i) q^{51} +(-4.00000 - 6.92820i) q^{53} +(0.500000 - 0.866025i) q^{54} +1.61323 q^{55} +(-0.806615 + 2.51980i) q^{56} -1.17103 q^{57} +(-5.19874 + 9.00449i) q^{58} +(-2.19874 - 3.80834i) q^{59} +(-0.806615 - 1.39710i) q^{60} +(5.97764 - 10.3536i) q^{61} +6.34206 q^{62} +(-1.77890 - 1.95845i) q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{66} +(-1.47229 - 2.55007i) q^{67} +(3.67103 - 6.35841i) q^{68} -3.55780 q^{69} +(-4.17103 + 0.905585i) q^{70} +15.5131 q^{71} +(-0.500000 + 0.866025i) q^{72} +(2.55780 + 4.43024i) q^{73} +(-1.41449 - 2.44996i) q^{74} +(-1.19874 + 2.07629i) q^{75} +1.17103 q^{76} +(-2.58551 + 0.561349i) q^{77} +(-2.80661 + 4.86120i) q^{79} +(0.806615 + 1.39710i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.47229 + 4.28212i) q^{82} +5.05543 q^{83} +(1.77890 + 1.95845i) q^{84} +11.8444 q^{85} +(5.75654 - 9.97063i) q^{86} +(5.19874 + 9.00449i) q^{87} +(0.500000 + 0.866025i) q^{88} +(0.386770 - 0.669906i) q^{89} -1.61323 q^{90} +3.55780 q^{92} +(3.17103 - 5.49238i) q^{93} +(-3.39213 - 5.87534i) q^{94} +(0.944570 + 1.63604i) q^{95} +(0.500000 - 0.866025i) q^{96} +7.00000 q^{97} +(6.36977 - 2.90275i) 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
$5$	0.806615	−	1.39710i	0.360729	−	0.624801i	−0.627352	−	0.778736i	$-0.715861\pi$
$5$	0.806615	−	1.39710i	0.360729	−	0.624801i	0.988081	+	0.153935i	$0.0491945\pi$
$6$	−1.00000			−0.408248
$7$	−0.806615	+	2.51980i	−0.304872	+	0.952393i
$7$	−0.806615	+	2.51980i	−0.304872	+	0.952393i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.806615	+	1.39710i	0.255074	+	0.441801i
$11$	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	$0.5\pi$
$14$	−1.77890	−	1.95845i	−0.475431	−	0.523417i
$15$	1.61323			0.416534
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.67103	+	6.35841i	0.890356	+	1.54214i	0.839450	+	0.543438i	$0.182878\pi$
$17$	3.67103	+	6.35841i	0.890356	+	1.54214i	0.0509059	+	0.998703i	$0.483789\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−0.585515	+	1.01414i	−0.134326	+	0.232660i	−0.925340	−	0.379139i	$-0.876220\pi$
$19$	−0.585515	+	1.01414i	−0.134326	+	0.232660i	0.791014	+	0.611799i	$0.209554\pi$
$20$	−1.61323			−0.360729
$21$	−2.58551	+	0.561349i	−0.564206	+	0.122496i
$22$	−1.00000			−0.213201
$23$	−1.77890	+	3.08115i	−0.370926	+	0.642463i	−0.989708	−	0.143100i	$-0.954293\pi$
$23$	−1.77890	+	3.08115i	−0.370926	+	0.642463i	0.618782	+	0.785563i	$0.287626\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	1.19874	+	2.07629i	0.239749	+	0.415257i
$26$		0			0
$27$	−1.00000			−0.192450
$28$	2.58551	−	0.561349i	0.488616	−	0.106085i
$29$	10.3975			1.93077			0.965383	−	0.260838i	$-0.0839988\pi$
$29$	10.3975			1.93077			0.965383	+	0.260838i	$0.0839988\pi$
$30$	−0.806615	+	1.39710i	−0.147267	+	0.255074i
$31$	−3.17103	−	5.49238i	−0.569534	−	0.986461i	−0.996612	−	0.0822467i	$-0.973790\pi$
$31$	−3.17103	−	5.49238i	−0.569534	−	0.986461i	0.427078	−	0.904215i	$-0.359543\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$	−7.34206			−1.25915
$35$	2.86977	+	3.15943i	0.485080	+	0.534040i
$36$	1.00000			0.166667
$37$	−1.41449	+	2.44996i	−0.232540	+	0.402771i	−0.958555	−	0.284908i	$-0.908037\pi$
$37$	−1.41449	+	2.44996i	−0.232540	+	0.402771i	0.726015	+	0.687679i	$0.241370\pi$
$38$	−0.585515	−	1.01414i	−0.0949831	−	0.164515i
$39$		0			0
$40$	0.806615	−	1.39710i	0.127537	−	0.220901i
$41$	4.94457			0.772212			0.386106	−	0.922454i	$-0.373820\pi$
$41$	4.94457			0.772212			0.386106	+	0.922454i	$0.373820\pi$
$42$	0.806615	−	2.51980i	0.124463	−	0.388813i
$43$	−11.5131			−1.75573			−0.877865	−	0.478908i	$-0.841033\pi$
$43$	−11.5131			−1.75573			−0.877865	+	0.478908i	$0.841033\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$	0.806615	+	1.39710i	0.120243	+	0.208267i
$46$	−1.77890	−	3.08115i	−0.262284	−	0.454290i
$47$	−3.39213	+	5.87534i	−0.494793	+	0.857007i	−0.999982	−	0.00600214i	$-0.998089\pi$
$47$	−3.39213	+	5.87534i	−0.494793	+	0.857007i	0.505189	+	0.863009i	$0.331423\pi$
$48$	−1.00000			−0.144338
$49$	−5.69874	−	4.06501i	−0.814106	−	0.580716i
$50$	−2.39749			−0.339056
$51$	−3.67103	+	6.35841i	−0.514047	+	0.890356i
$52$		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
$55$	1.61323			0.217528
$56$	−0.806615	+	2.51980i	−0.107788	+	0.336722i
$57$	−1.17103			−0.155107
$58$	−5.19874	+	9.00449i	−0.682629	+	1.18235i
$59$	−2.19874	−	3.80834i	−0.286252	−	0.495803i	0.686660	−	0.726979i	$-0.259076\pi$
$59$	−2.19874	−	3.80834i	−0.286252	−	0.495803i	−0.972912	+	0.231175i	$0.925743\pi$
$60$	−0.806615	−	1.39710i	−0.104134	−	0.180365i
$61$	5.97764	−	10.3536i	0.765359	−	1.32564i	−0.174698	−	0.984622i	$-0.555895\pi$
$61$	5.97764	−	10.3536i	0.765359	−	1.32564i	0.940057	−	0.341019i	$-0.110772\pi$
$62$	6.34206			0.805442
$63$	−1.77890	−	1.95845i	−0.224120	−	0.246741i
$64$	1.00000			0.125000
$65$		0			0
$66$	−0.500000	−	0.866025i	−0.0615457	−	0.106600i
$67$	−1.47229	−	2.55007i	−0.179868	−	0.311541i	0.761967	−	0.647616i	$-0.224234\pi$
$67$	−1.47229	−	2.55007i	−0.179868	−	0.311541i	−0.941835	+	0.336075i	$0.890900\pi$
$68$	3.67103	−	6.35841i	0.445178	−	0.771070i
$69$	−3.55780			−0.428309
$70$	−4.17103	+	0.905585i	−0.498533	+	0.108238i
$71$	15.5131			1.84106			0.920532	−	0.390666i	$-0.127755\pi$
$71$	15.5131			1.84106			0.920532	+	0.390666i	$0.127755\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	2.55780	+	4.43024i	0.299368	+	0.518520i	0.975991	−	0.217809i	$-0.0698909\pi$
$73$	2.55780	+	4.43024i	0.299368	+	0.518520i	−0.676624	+	0.736329i	$0.736558\pi$
$74$	−1.41449	−	2.44996i	−0.164431	−	0.284802i
$75$	−1.19874	+	2.07629i	−0.138419	+	0.239749i
$76$	1.17103			0.134326
$77$	−2.58551	+	0.561349i	−0.294647	+	0.0639717i
$78$		0			0
$79$	−2.80661	+	4.86120i	−0.315769	+	0.546928i	−0.979601	−	0.200954i	$-0.935596\pi$
$79$	−2.80661	+	4.86120i	−0.315769	+	0.546928i	0.663832	+	0.747882i	$0.268929\pi$
$80$	0.806615	+	1.39710i	0.0901823	+	0.156200i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.47229	+	4.28212i	−0.273018	+	0.472881i
$83$	5.05543			0.554906			0.277453	−	0.960739i	$-0.410510\pi$
$83$	5.05543			0.554906			0.277453	+	0.960739i	$0.410510\pi$
$84$	1.77890	+	1.95845i	0.194094	+	0.213684i
$85$	11.8444			1.28471
$86$	5.75654	−	9.97063i	0.620744	−	1.07516i
$87$	5.19874	+	9.00449i	0.557364	+	0.965383i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	0.386770	−	0.669906i	0.0409976	−	0.0710098i	−0.844799	−	0.535085i	$-0.820280\pi$
$89$	0.386770	−	0.669906i	0.0409976	−	0.0710098i	0.885796	+	0.464075i	$0.153613\pi$
$90$	−1.61323			−0.170049
$91$		0			0
$92$	3.55780			0.370926
$93$	3.17103	−	5.49238i	0.328820	−	0.569534i
$94$	−3.39213	−	5.87534i	−0.349871	−	0.605995i
$95$	0.944570	+	1.63604i	0.0969108	+	0.167855i
$96$	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	$0.384354\pi$
$98$	6.36977	−	2.90275i	0.643444	−	0.293222i
$99$	−1.00000			−0.100504
$100$	1.19874	−	2.07629i	0.119874	−	0.207629i
$101$	−6.81197	−	11.7987i	−0.677817	−	1.17401i	−0.975637	−	0.219391i	$-0.929593\pi$
$101$	−6.81197	−	11.7987i	−0.677817	−	1.17401i	0.297820	−	0.954622i	$-0.403740\pi$
$102$	−3.67103	−	6.35841i	−0.363486	−	0.629576i
$103$	6.17103	−	10.6885i	0.608050	−	1.05317i	−0.383512	−	0.923536i	$-0.625285\pi$
$103$	6.17103	−	10.6885i	0.608050	−	1.05317i	0.991562	−	0.129637i	$-0.0413812\pi$
$104$		0			0
$105$	−1.30126	+	4.06501i	−0.126990	+	0.396704i
$106$	8.00000			0.777029
$107$	7.86977	−	13.6308i	0.760800	−	1.31774i	−0.181639	−	0.983365i	$-0.558140\pi$
$107$	7.86977	−	13.6308i	0.760800	−	1.31774i	0.942439	−	0.334379i	$-0.108526\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−1.97764	−	3.42538i	−0.189424	−	0.328092i	0.755634	−	0.654994i	$-0.227329\pi$
$109$	−1.97764	−	3.42538i	−0.189424	−	0.328092i	−0.945058	+	0.326902i	$0.893995\pi$
$110$	−0.806615	+	1.39710i	−0.0769077	+	0.133208i
$111$	−2.82897			−0.268514
$112$	−1.77890	−	1.95845i	−0.168090	−	0.185056i
$113$	−4.34206			−0.408467			−0.204233	−	0.978922i	$-0.565470\pi$
$113$	−4.34206			−0.408467			−0.204233	+	0.978922i	$0.565470\pi$
$114$	0.585515	−	1.01414i	0.0548385	−	0.0949831i
$115$	2.86977	+	4.97060i	0.267608	+	0.463510i
$116$	−5.19874	−	9.00449i	−0.482691	−	0.836046i
$117$		0			0
$118$	4.39749			0.404822
$119$	−18.9830	+	4.12146i	−1.74017	+	0.377813i
$120$	1.61323			0.147267
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	5.97764	+	10.3536i	0.541191	+	0.937369i
$123$	2.47229	+	4.28212i	0.222918	+	0.386106i
$124$	−3.17103	+	5.49238i	−0.284767	+	0.493231i
$125$	11.9339			1.06740
$126$	2.58551	−	0.561349i	0.230336	−	0.0500089i
$127$	−0.442200			−0.0392389			−0.0196195	−	0.999808i	$-0.506245\pi$
$127$	−0.442200			−0.0392389			−0.0196195	+	0.999808i	$0.506245\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−5.75654	−	9.97063i	−0.506835	−	0.877865i
$130$		0			0
$131$	1.17103	−	2.02828i	0.102313	−	0.177212i	−0.810324	−	0.585982i	$-0.800709\pi$
$131$	1.17103	−	2.02828i	0.102313	−	0.177212i	0.912637	+	0.408770i	$0.134042\pi$
$132$	1.00000			0.0870388
$133$	−2.08314	−	2.29340i	−0.180632	−	0.198863i
$134$	2.94457			0.254372
$135$	−0.806615	+	1.39710i	−0.0694224	+	0.120243i
$136$	3.67103	+	6.35841i	0.314788	+	0.545229i
$137$	−1.61323	−	2.79420i	−0.137828	−	0.238724i	0.788847	−	0.614590i	$-0.210679\pi$
$137$	−1.61323	−	2.79420i	−0.137828	−	0.238724i	−0.926674	+	0.375866i	$0.877345\pi$
$138$	1.77890	−	3.08115i	0.151430	−	0.262284i
$139$	18.3975			1.56045			0.780227	−	0.625496i	$-0.215103\pi$
$139$	18.3975			1.56045			0.780227	+	0.625496i	$0.215103\pi$
$140$	1.30126	−	4.06501i	0.109976	−	0.343556i
$141$	−6.78426			−0.571338
$142$	−7.75654	+	13.4347i	−0.650915	+	1.12742i
$143$		0			0
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	8.38677	−	14.5263i	0.696483	−	1.20634i
$146$	−5.11560			−0.423370
$147$	0.671030	−	6.96776i	0.0553456	−	0.574691i
$148$	2.82897			0.232540
$149$	−9.81197	+	16.9948i	−0.803828	+	1.39227i	0.113251	+	0.993566i	$0.463874\pi$
$149$	−9.81197	+	16.9948i	−0.803828	+	1.39227i	−0.917079	+	0.398705i	$0.869460\pi$
$150$	−1.19874	−	2.07629i	−0.0978771	−	0.169528i
$151$	0.165670	+	0.286949i	0.0134820	+	0.0233516i	0.872688	−	0.488279i	$-0.162375\pi$
$151$	0.165670	+	0.286949i	0.0134820	+	0.0233516i	−0.859206	+	0.511630i	$0.829042\pi$
$152$	−0.585515	+	1.01414i	−0.0474915	+	0.0822577i
$153$	−7.34206			−0.593570
$154$	0.806615	−	2.51980i	0.0649989	−	0.203051i
$155$	−10.2312			−0.821790
$156$		0			0
$157$	−9.98300	−	17.2911i	−0.796730	−	1.37998i	−0.921735	−	0.387821i	$-0.873228\pi$
$157$	−9.98300	−	17.2911i	−0.796730	−	1.37998i	0.125004	−	0.992156i	$-0.460106\pi$
$158$	−2.80661	−	4.86120i	−0.223282	−	0.386736i
$159$	4.00000	−	6.92820i	0.317221	−	0.549442i
$160$	−1.61323			−0.127537
$161$	−6.32897	−	6.96776i	−0.498793	−	0.549137i
$162$	1.00000			0.0785674
$163$	−10.6433	+	18.4348i	−0.833649	+	1.44392i	0.0614771	+	0.998108i	$0.480419\pi$
$163$	−10.6433	+	18.4348i	−0.833649	+	1.44392i	−0.895126	+	0.445814i	$0.852914\pi$
$164$	−2.47229	−	4.28212i	−0.193053	−	0.334378i
$165$	0.806615	+	1.39710i	0.0627949	+	0.108764i
$166$	−2.52771	+	4.37813i	−0.196189	+	0.339809i
$167$	22.0214			1.70407			0.852035	−	0.523485i	$-0.175368\pi$
$167$	22.0214			1.70407			0.852035	+	0.523485i	$0.175368\pi$
$168$	−2.58551	+	0.561349i	−0.199477	+	0.0433090i
$169$	−13.0000			−1.00000
$170$	−5.92221	+	10.2576i	−0.454213	+	0.786720i
$171$	−0.585515	−	1.01414i	−0.0447754	−	0.0775533i
$172$	5.75654	+	9.97063i	0.438932	+	0.760253i
$173$	−0.828970	+	1.43582i	−0.0630254	+	0.109163i	−0.895816	−	0.444424i	$-0.853408\pi$
$173$	−0.828970	+	1.43582i	−0.0630254	+	0.109163i	0.832791	+	0.553588i	$0.186742\pi$
$174$	−10.3975			−0.788232
$175$	−6.19874	+	1.34583i	−0.468581	+	0.101735i
$176$	−1.00000			−0.0753778
$177$	2.19874	−	3.80834i	0.165268	−	0.286252i
$178$	0.386770	+	0.669906i	0.0289896	+	0.0502115i
$179$	−7.53008	−	13.0425i	−0.562825	−	0.974841i	−0.997248	−	0.0741327i	$-0.976381\pi$
$179$	−7.53008	−	13.0425i	−0.562825	−	0.974841i	0.434423	−	0.900709i	$-0.356952\pi$
$180$	0.806615	−	1.39710i	0.0601215	−	0.104134i
$181$	15.1156			1.12353			0.561767	−	0.827296i	$-0.310122\pi$
$181$	15.1156			1.12353			0.561767	+	0.827296i	$0.310122\pi$
$182$		0			0
$183$	11.9553			0.883760
$184$	−1.77890	+	3.08115i	−0.131142	+	0.227145i
$185$	2.28189	+	3.95235i	0.167768	+	0.290582i
$186$	3.17103	+	5.49238i	0.232511	+	0.402721i
$187$	−3.67103	+	6.35841i	−0.268452	+	0.464973i
$188$	6.78426			0.494793
$189$	0.806615	−	2.51980i	0.0586726	−	0.183288i
$190$	−1.88914			−0.137053
$191$	2.38677	−	4.13401i	0.172701	−	0.299126i	−0.766663	−	0.642050i	$-0.778084\pi$
$191$	2.38677	−	4.13401i	0.172701	−	0.299126i	0.939363	+	0.342924i	$0.111417\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−1.55780	−	2.69819i	−0.112133	−	0.194220i	0.804497	−	0.593957i	$-0.202435\pi$
$193$	−1.55780	−	2.69819i	−0.112133	−	0.194220i	−0.916630	+	0.399737i	$0.869102\pi$
$194$	−3.50000	+	6.06218i	−0.251285	+	0.435239i
$195$		0			0
$196$	−0.671030	+	6.96776i	−0.0479307	+	0.497697i
$197$	−4.82897			−0.344050			−0.172025	−	0.985093i	$-0.555031\pi$
$197$	−4.82897			−0.344050			−0.172025	+	0.985093i	$0.555031\pi$
$198$	0.500000	−	0.866025i	0.0355335	−	0.0615457i
$199$	−2.94457	−	5.10015i	−0.208735	−	0.361540i	0.742581	−	0.669756i	$-0.233601\pi$
$199$	−2.94457	−	5.10015i	−0.208735	−	0.361540i	−0.951316	+	0.308216i	$0.900268\pi$
$200$	1.19874	+	2.07629i	0.0847641	+	0.146816i
$201$	1.47229	−	2.55007i	0.103847	−	0.179868i
$202$	13.6239			0.958578
$203$	−8.38677	+	26.1996i	−0.588636	+	1.83885i
$204$	7.34206			0.514047
$205$	3.98836	−	6.90805i	0.278559	−	0.482479i
$206$	6.17103	+	10.6885i	0.429956	+	0.744706i
$207$	−1.77890	−	3.08115i	−0.123642	−	0.214154i
$208$		0			0
$209$	−1.17103			−0.0810018
$210$	−2.86977	−	3.15943i	−0.198033	−	0.218021i
$211$	−13.6794			−0.941727			−0.470864	−	0.882206i	$-0.656058\pi$
$211$	−13.6794			−0.941727			−0.470864	+	0.882206i	$0.656058\pi$
$212$	−4.00000	+	6.92820i	−0.274721	+	0.475831i
$213$	7.75654	+	13.4347i	0.531470	+	0.920532i
$214$	7.86977	+	13.6308i	0.537967	+	0.931786i
$215$	−9.28663	+	16.0849i	−0.633343	+	1.09698i
$216$	−1.00000			−0.0680414
$217$	16.3975	−	3.56011i	1.11313	−	0.241676i
$218$	3.95529			0.267886
$219$	−2.55780	+	4.43024i	−0.172840	+	0.299368i
$220$	−0.806615	−	1.39710i	−0.0543820	−	0.0941923i
$221$		0			0
$222$	1.41449	−	2.44996i	0.0949340	−	0.164431i
$223$	−5.11560			−0.342566			−0.171283	−	0.985222i	$-0.554791\pi$
$223$	−5.11560			−0.342566			−0.171283	+	0.985222i	$0.554791\pi$
$224$	2.58551	−	0.561349i	0.172752	−	0.0375067i
$225$	−2.39749			−0.159833
$226$	2.17103	−	3.76033i	0.144415	−	0.250134i
$227$	2.64331	+	4.57836i	0.175443	+	0.303876i	0.940314	−	0.340307i	$-0.110531\pi$
$227$	2.64331	+	4.57836i	0.175443	+	0.303876i	−0.764872	+	0.644183i	$0.777198\pi$
$228$	0.585515	+	1.01414i	0.0387767	+	0.0671632i
$229$	2.44220	−	4.23001i	0.161385	−	0.279527i	−0.773981	−	0.633209i	$-0.781737\pi$
$229$	2.44220	−	4.23001i	0.161385	−	0.279527i	0.935366	+	0.353682i	$0.115071\pi$
$230$	−5.73955			−0.378455
$231$	−1.77890	−	1.95845i	−0.117043	−	0.128856i
$232$	10.3975			0.682629
$233$	−4.89749	+	8.48270i	−0.320845	+	0.555720i	−0.980663	−	0.195706i	$-0.937300\pi$
$233$	−4.89749	+	8.48270i	−0.320845	+	0.555720i	0.659817	+	0.751426i	$0.270634\pi$
$234$		0			0
$235$	5.47229	+	9.47828i	0.356973	+	0.618295i
$236$	−2.19874	+	3.80834i	−0.143126	+	0.247902i
$237$	−5.61323			−0.364618
$238$	5.92221	−	18.5005i	0.383880	−	1.19921i
$239$	−23.9106			−1.54665			−0.773323	−	0.634012i	$-0.781407\pi$
$239$	−23.9106			−1.54665			−0.773323	+	0.634012i	$0.781407\pi$
$240$	−0.806615	+	1.39710i	−0.0520668	+	0.0901823i
$241$	−0.944570	−	1.63604i	−0.0608451	−	0.105387i	0.833998	−	0.551767i	$-0.186046\pi$
$241$	−0.944570	−	1.63604i	−0.0608451	−	0.105387i	−0.894843	+	0.446380i	$0.852713\pi$
$242$	−0.500000	−	0.866025i	−0.0321412	−	0.0556702i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−11.9553			−0.765359
$245$	−10.2759	+	4.68281i	−0.656504	+	0.299174i
$246$	−4.94457			−0.315254
$247$		0			0
$248$	−3.17103	−	5.49238i	−0.201361	−	0.348767i
$249$	2.52771	+	4.37813i	0.160187	+	0.277453i
$250$	−5.96693	+	10.3350i	−0.377381	+	0.653644i
$251$	0.939830			0.0593215			0.0296608	−	0.999560i	$-0.490557\pi$
$251$	0.939830			0.0593215			0.0296608	+	0.999560i	$0.490557\pi$
$252$	−0.806615	+	2.51980i	−0.0508120	+	0.158732i
$253$	−3.55780			−0.223677
$254$	0.221100	−	0.382956i	0.0138730	−	0.0240288i
$255$	5.92221	+	10.2576i	0.370863	+	0.642354i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.61323	−	9.72240i	0.350144	−	0.606467i	−0.636131	−	0.771581i	$-0.719466\pi$
$257$	5.61323	−	9.72240i	0.350144	−	0.606467i	0.986274	+	0.165115i	$0.0527994\pi$
$258$	11.5131			0.716774
$259$	−5.03246	−	5.54039i	−0.312702	−	0.344263i
$260$		0			0
$261$	−5.19874	+	9.00449i	−0.321794	+	0.557364i
$262$	1.17103	+	2.02828i	0.0723465	+	0.125308i
$263$	0.613230	+	1.06215i	0.0378134	+	0.0654947i	0.884313	−	0.466895i	$-0.154627\pi$
$263$	0.613230	+	1.06215i	0.0378134	+	0.0654947i	−0.846499	+	0.532390i	$0.821294\pi$
$264$	−0.500000	+	0.866025i	−0.0307729	+	0.0533002i
$265$	−12.9058			−0.792799
$266$	3.02771	−	0.657356i	0.185641	−	0.0403051i
$267$	0.773540			0.0473399
$268$	−1.47229	+	2.55007i	−0.0899341	+	0.155770i
$269$	−4.75119	−	8.22929i	−0.289685	−	0.501749i	0.684050	−	0.729435i	$-0.260217\pi$
$269$	−4.75119	−	8.22929i	−0.289685	−	0.501749i	−0.973734	+	0.227687i	$0.926884\pi$
$270$	−0.806615	−	1.39710i	−0.0490890	−	0.0850247i
$271$	−1.61323	+	2.79420i	−0.0979967	+	0.169735i	−0.910855	−	0.412726i	$-0.864577\pi$
$271$	−1.61323	+	2.79420i	−0.0979967	+	0.169735i	0.812859	+	0.582461i	$0.197910\pi$
$272$	−7.34206			−0.445178
$273$		0			0
$274$	3.22646			0.194918
$275$	−1.19874	+	2.07629i	−0.0722870	+	0.125205i
$276$	1.77890	+	3.08115i	0.107077	+	0.185463i
$277$	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	$0.673726\pi$
$278$	−9.19874	+	15.9327i	−0.551704	+	0.955579i
$279$	6.34206			0.379689
$280$	2.86977	+	3.15943i	0.171502	+	0.188812i
$281$	−11.2312			−0.669997			−0.334999	−	0.942219i	$-0.608736\pi$
$281$	−11.2312			−0.669997			−0.334999	+	0.942219i	$0.608736\pi$
$282$	3.39213	−	5.87534i	0.201998	−	0.349871i
$283$	12.7288	+	22.0470i	0.756650	+	1.31056i	0.944550	+	0.328369i	$0.106499\pi$
$283$	12.7288	+	22.0470i	0.756650	+	1.31056i	−0.187899	+	0.982188i	$0.560168\pi$
$284$	−7.75654	−	13.4347i	−0.460266	−	0.797205i
$285$	−0.944570	+	1.63604i	−0.0559515	+	0.0969108i
$286$		0			0
$287$	−3.98836	+	12.4593i	−0.235426	+	0.735450i
$288$	1.00000			0.0589256
$289$	−18.4529	+	31.9614i	−1.08547	+	1.88008i
$290$	8.38677	+	14.5263i	0.492488	+	0.853014i
$291$	3.50000	+	6.06218i	0.205174	+	0.355371i
$292$	2.55780	−	4.43024i	0.149684	−	0.259260i
$293$	17.9446			1.04833			0.524166	−	0.851616i	$-0.324377\pi$
$293$	17.9446			1.04833			0.524166	+	0.851616i	$0.324377\pi$
$294$	5.69874	+	4.06501i	0.332358	+	0.237076i
$295$	−7.09416			−0.413038
$296$	−1.41449	+	2.44996i	−0.0822153	+	0.142401i
$297$	−0.500000	−	0.866025i	−0.0290129	−	0.0502519i
$298$	−9.81197	−	16.9948i	−0.568392	−	0.984485i
$299$		0			0
$300$	2.39749			0.138419
$301$	9.28663	−	29.0106i	0.535272	−	1.67215i
$302$	−0.331340			−0.0190665
$303$	6.81197	−	11.7987i	0.391338	−	0.677817i
$304$	−0.585515	−	1.01414i	−0.0335816	−	0.0581650i
$305$	−9.64331	−	16.7027i	−0.552175	−	0.956394i
$306$	3.67103	−	6.35841i	0.209859	−	0.363486i
$307$	−33.0262			−1.88490			−0.942452	−	0.334342i	$-0.891486\pi$
$307$	−33.0262			−1.88490			−0.942452	+	0.334342i	$0.891486\pi$
$308$	1.77890	+	1.95845i	0.101362	+	0.111593i
$309$	12.3421			0.702115
$310$	5.11560	−	8.86048i	0.290547	−	0.503241i
$311$	0.165670	+	0.286949i	0.00939429	+	0.0162714i	0.870684	−	0.491842i	$-0.163676\pi$
$311$	0.165670	+	0.286949i	0.00939429	+	0.0162714i	−0.861290	+	0.508114i	$0.830343\pi$
$312$		0			0
$313$	7.19874	−	12.4686i	0.406897	−	0.704766i	−0.587643	−	0.809120i	$-0.699944\pi$
$313$	7.19874	−	12.4686i	0.406897	−	0.704766i	0.994540	+	0.104354i	$0.0332774\pi$
$314$	19.9660			1.12675
$315$	−4.17103	+	0.905585i	−0.235011	+	0.0510239i
$316$	5.61323			0.315769
$317$	−8.76190	+	15.1761i	−0.492118	+	0.852373i	−0.999959	−	0.00907805i	$-0.997110\pi$
$317$	−8.76190	+	15.1761i	−0.492118	+	0.852373i	0.507841	+	0.861451i	$0.330444\pi$
$318$	4.00000	+	6.92820i	0.224309	+	0.388514i
$319$	5.19874	+	9.00449i	0.291074	+	0.504155i
$320$	0.806615	−	1.39710i	0.0450911	−	0.0781002i
$321$	15.7395			0.878496
$322$	9.19874	−	1.99717i	0.512626	−	0.111298i
$323$	−8.59777			−0.478393
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$		0			0
$326$	−10.6433	−	18.4348i	−0.589479	−	1.02101i
$327$	1.97764	−	3.42538i	0.109364	−	0.189424i
$328$	4.94457			0.273018
$329$	−12.0685	−	13.2866i	−0.665359	−	0.732515i
$330$	−1.61323			−0.0888054
$331$	4.47229	−	7.74622i	0.245819	−	0.425771i	−0.716543	−	0.697543i	$-0.754276\pi$
$331$	4.47229	−	7.74622i	0.245819	−	0.425771i	0.962362	+	0.271772i	$0.0876098\pi$
$332$	−2.52771	−	4.37813i	−0.138726	−	0.240281i
$333$	−1.41449	−	2.44996i	−0.0775133	−	0.134257i
$334$	−11.0107	+	19.0711i	−0.602480	+	1.04353i
$335$	−4.75027			−0.259535
$336$	0.806615	−	2.51980i	0.0440045	−	0.137466i
$337$	−3.33732			−0.181795			−0.0908977	−	0.995860i	$-0.528974\pi$
$337$	−3.33732			−0.181795			−0.0908977	+	0.995860i	$0.528974\pi$
$338$	6.50000	−	11.2583i	0.353553	−	0.612372i
$339$	−2.17103	−	3.76033i	−0.117914	−	0.204233i
$340$	−5.92221	−	10.2576i	−0.321177	−	0.556295i
$341$	3.17103	−	5.49238i	0.171721	−	0.297429i
$342$	1.17103			0.0633220
$343$	14.8397	−	11.0808i	0.801268	−	0.598306i
$344$	−11.5131			−0.620744
$345$	−2.86977	+	4.97060i	−0.154503	+	0.267608i
$346$	−0.828970	−	1.43582i	−0.0445657	−	0.0771901i
$347$	15.2118	+	26.3477i	0.816614	+	1.41442i	0.908163	+	0.418616i	$0.137485\pi$
$347$	15.2118	+	26.3477i	0.816614	+	1.41442i	−0.0915491	+	0.995801i	$0.529182\pi$
$348$	5.19874	−	9.00449i	0.278682	−	0.482691i
$349$	17.5238			0.938028			0.469014	−	0.883191i	$-0.344609\pi$
$349$	17.5238			0.938028			0.469014	+	0.883191i	$0.344609\pi$
$350$	1.93385	−	6.04118i	0.103369	−	0.322915i
$351$		0			0
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	−2.55780	−	4.43024i	−0.136138	−	0.235798i	0.789894	−	0.613244i	$-0.210136\pi$
$353$	−2.55780	−	4.43024i	−0.136138	−	0.235798i	−0.926032	+	0.377446i	$0.876802\pi$
$354$	2.19874	+	3.80834i	0.116862	+	0.202411i
$355$	12.5131	−	21.6733i	0.664126	−	1.15030i
$356$	−0.773540			−0.0409976
$357$	−13.0608	−	14.3790i	−0.691250	−	0.761019i
$358$	15.0602			0.795955
$359$	15.3421	−	26.5732i	0.809723	−	1.40248i	−0.103333	−	0.994647i	$-0.532951\pi$
$359$	15.3421	−	26.5732i	0.809723	−	1.40248i	0.913056	−	0.407834i	$-0.133716\pi$
$360$	0.806615	+	1.39710i	0.0425123	+	0.0736335i
$361$	8.81434	+	15.2669i	0.463913	+	0.803521i
$362$	−7.55780	+	13.0905i	−0.397229	+	0.688021i
$363$	−1.00000			−0.0524864
$364$		0			0
$365$	8.25264			0.431963
$366$	−5.97764	+	10.3536i	−0.312456	+	0.541191i
$367$	−0.728830	−	1.26237i	−0.0380446	−	0.0658952i	0.846376	−	0.532586i	$-0.178780\pi$
$367$	−0.728830	−	1.26237i	−0.0380446	−	0.0658952i	−0.884421	+	0.466690i	$0.845446\pi$
$368$	−1.77890	−	3.08115i	−0.0927316	−	0.160616i
$369$	−2.47229	+	4.28212i	−0.128702	+	0.222918i
$370$	−4.56378			−0.237260
$371$	20.6841	−	4.49079i	1.07387	−	0.233150i
$372$	−6.34206			−0.328820
$373$	17.0932	−	29.6064i	0.885055	−	1.53296i	0.0394037	−	0.999223i	$-0.487454\pi$
$373$	17.0932	−	29.6064i	0.885055	−	1.53296i	0.845651	−	0.533736i	$-0.179212\pi$
$374$	−3.67103	−	6.35841i	−0.189824	−	0.328786i
$375$	5.96693	+	10.3350i	0.308131	+	0.533698i
$376$	−3.39213	+	5.87534i	−0.174936	+	0.302998i
$377$		0			0
$378$	1.77890	+	1.95845i	0.0914967	+	0.100732i
$379$	−9.28663			−0.477022			−0.238511	−	0.971140i	$-0.576659\pi$
$379$	−9.28663			−0.477022			−0.238511	+	0.971140i	$0.576659\pi$
$380$	0.944570	−	1.63604i	0.0484554	−	0.0839273i
$381$	−0.221100	−	0.382956i	−0.0113273	−	0.0196195i
$382$	2.38677	+	4.13401i	0.122118	+	0.211514i
$383$	1.81197	−	3.13843i	0.0925876	−	0.160366i	−0.816012	−	0.578035i	$-0.803820\pi$
$383$	1.81197	−	3.13843i	0.0925876	−	0.160366i	0.908599	+	0.417669i	$0.137153\pi$
$384$	−1.00000			−0.0510310
$385$	−1.30126	+	4.06501i	−0.0663181	+	0.207172i
$386$	3.11560			0.158580
$387$	5.75654	−	9.97063i	0.292622	−	0.506835i
$388$	−3.50000	−	6.06218i	−0.177686	−	0.307760i
$389$	−3.58016	−	6.20101i	−0.181521	−	0.314404i	0.760878	−	0.648895i	$-0.224769\pi$
$389$	−3.58016	−	6.20101i	−0.181521	−	0.314404i	−0.942399	+	0.334492i	$0.891435\pi$
$390$		0			0
$391$	−26.1216			−1.32103
$392$	−5.69874	−	4.06501i	−0.287830	−	0.205314i
$393$	2.34206			0.118141
$394$	2.41449	−	4.18201i	0.121640	−	0.210687i
$395$	4.52771	+	7.84223i	0.227814	+	0.394586i
$396$	0.500000	+	0.866025i	0.0251259	+	0.0435194i
$397$	15.1987	−	26.3250i	0.762803	−	1.32121i	−0.178597	−	0.983922i	$-0.557156\pi$
$397$	15.1987	−	26.3250i	0.762803	−	1.32121i	0.941400	−	0.337291i	$-0.109511\pi$
$398$	5.88914			0.295196
$399$	0.944570	−	2.95076i	0.0472877	−	0.147723i
$400$	−2.39749			−0.119874
$401$	6.01072	−	10.4109i	0.300161	−	0.519894i	−0.676011	−	0.736891i	$-0.736293\pi$
$401$	6.01072	−	10.4109i	0.300161	−	0.519894i	0.976172	+	0.216997i	$0.0696263\pi$
$402$	1.47229	+	2.55007i	0.0734309	+	0.127186i
$403$		0			0
$404$	−6.81197	+	11.7987i	−0.338908	+	0.587007i
$405$	−1.61323			−0.0801620
$406$	−18.4961	−	20.3629i	−0.917946	−	1.01060i
$407$	−2.82897			−0.140227
$408$	−3.67103	+	6.35841i	−0.181743	+	0.314788i
$409$	−8.78426	−	15.2148i	−0.434354	−	0.752323i	0.562889	−	0.826533i	$-0.309690\pi$
$409$	−8.78426	−	15.2148i	−0.434354	−	0.752323i	−0.997243	+	0.0742099i	$0.976357\pi$
$410$	3.98836	+	6.90805i	0.196971	+	0.341164i
$411$	1.61323	−	2.79420i	0.0795748	−	0.137828i
$412$	−12.3421			−0.608050
$413$	11.3698	−	2.46853i	0.559470	−	0.121468i
$414$	3.55780			0.174856
$415$	4.07779	−	7.06293i	0.200171	−	0.346706i
$416$		0			0
$417$	9.19874	+	15.9327i	0.450464	+	0.780227i
$418$	0.585515	−	1.01414i	0.0286385	−	0.0496033i
$419$	−27.1710			−1.32739			−0.663696	−	0.748003i	$-0.731013\pi$
$419$	−27.1710			−1.32739			−0.663696	+	0.748003i	$0.731013\pi$
$420$	4.17103	−	0.905585i	0.203525	−	0.0441880i
$421$	23.1710			1.12929			0.564643	−	0.825335i	$-0.309014\pi$
$421$	23.1710			1.12929			0.564643	+	0.825335i	$0.309014\pi$
$422$	6.83969	−	11.8467i	0.332951	−	0.576688i
$423$	−3.39213	−	5.87534i	−0.164931	−	0.285669i
$424$	−4.00000	−	6.92820i	−0.194257	−	0.336463i
$425$	−8.80126	+	15.2442i	−0.426924	+	0.739453i
$426$	−15.5131			−0.751612
$427$	21.2673	+	23.4138i	1.02920	+	1.13307i
$428$	−15.7395			−0.760800
$429$		0			0
$430$	−9.28663	−	16.0849i	−0.447841	−	0.775683i
$431$	8.38677	+	14.5263i	0.403977	+	0.699708i	0.994202	−	0.107531i	$-0.0342944\pi$
$431$	8.38677	+	14.5263i	0.403977	+	0.699708i	−0.590225	+	0.807239i	$0.700961\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	17.3421			0.833406			0.416703	−	0.909043i	$-0.363185\pi$
$433$	17.3421			0.833406			0.416703	+	0.909043i	$0.363185\pi$
$434$	−5.11560	+	15.9807i	−0.245557	+	0.767098i
$435$	16.7735			0.804230
$436$	−1.97764	+	3.42538i	−0.0947120	+	0.164046i
$437$	−2.08314	−	3.60811i	−0.0996503	−	0.172599i
$438$	−2.55780	−	4.43024i	−0.122216	−	0.211685i
$439$	−16.5739	+	28.7068i	−0.791028	+	1.37010i	0.134303	+	0.990940i	$0.457121\pi$
$439$	−16.5739	+	28.7068i	−0.791028	+	1.37010i	−0.925331	+	0.379160i	$0.876213\pi$
$440$	1.61323			0.0769077
$441$	6.36977	−	2.90275i	0.303323	−	0.138226i
$442$		0			0
$443$	6.02771	−	10.4403i	0.286385	−	0.496034i	−0.686559	−	0.727074i	$-0.740880\pi$
$443$	6.02771	−	10.4403i	0.286385	−	0.496034i	0.972944	+	0.231040i	$0.0742129\pi$
$444$	1.41449	+	2.44996i	0.0671285	+	0.116270i
$445$	−0.623949	−	1.08071i	−0.0295780	−	0.0512306i
$446$	2.55780	−	4.43024i	0.121115	−	0.209778i
$447$	−19.6239			−0.928181
$448$	−0.806615	+	2.51980i	−0.0381090	+	0.119049i
$449$	−36.5947			−1.72701			−0.863505	−	0.504340i	$-0.831736\pi$
$449$	−36.5947			−1.72701			−0.863505	+	0.504340i	$0.831736\pi$
$450$	1.19874	−	2.07629i	0.0565094	−	0.0978771i
$451$	2.47229	+	4.28212i	0.116415	+	0.201637i
$452$	2.17103	+	3.76033i	0.102117	+	0.176871i
$453$	−0.165670	+	0.286949i	−0.00778386	+	0.0134820i
$454$	−5.28663			−0.248114
$455$		0			0
$456$	−1.17103			−0.0548385
$457$	−18.9106	+	32.7541i	−0.884600	+	1.53217i	−0.0384276	+	0.999261i	$0.512235\pi$
$457$	−18.9106	+	32.7541i	−0.884600	+	1.53217i	−0.846172	+	0.532910i	$0.821098\pi$
$458$	2.44220	+	4.23001i	0.114117	+	0.197656i
$459$	−3.67103	−	6.35841i	−0.171349	−	0.296785i
$460$	2.86977	−	4.97060i	0.133804	−	0.231755i
$461$	34.9707			1.62875			0.814375	−	0.580339i	$-0.197080\pi$
$461$	34.9707			1.62875			0.814375	+	0.580339i	$0.197080\pi$
$462$	2.58551	−	0.561349i	0.120289	−	0.0261163i
$463$	7.56852			0.351739			0.175869	−	0.984413i	$-0.443726\pi$
$463$	7.56852			0.351739			0.175869	+	0.984413i	$0.443726\pi$
$464$	−5.19874	+	9.00449i	−0.241346	+	0.418023i
$465$	−5.11560	−	8.86048i	−0.237230	−	0.410895i
$466$	−4.89749	−	8.48270i	−0.226872	−	0.392954i
$467$	7.31434	−	12.6688i	0.338468	−	0.586243i	−0.645677	−	0.763610i	$-0.723425\pi$
$467$	7.31434	−	12.6688i	0.338468	−	0.586243i	0.984145	+	0.177368i	$0.0567581\pi$
$468$		0			0
$469$	7.61323	−	1.65293i	0.351546	−	0.0763253i
$470$	−10.9446			−0.504835
$471$	9.98300	−	17.2911i	0.459993	−	0.796730i
$472$	−2.19874	−	3.80834i	−0.101205	−	0.175293i
$473$	−5.75654	−	9.97063i	−0.264686	−	0.458450i
$474$	2.80661	−	4.86120i	0.128912	−	0.223282i
$475$	−2.80753			−0.128818
$476$	13.0608	+	14.3790i	0.598640	+	0.659062i
$477$	8.00000			0.366295
$478$	11.9553	−	20.7072i	0.546822	−	0.947124i
$479$	0.613230	+	1.06215i	0.0280192	+	0.0485307i	0.879695	−	0.475538i	$-0.157747\pi$
$479$	0.613230	+	1.06215i	0.0280192	+	0.0485307i	−0.851676	+	0.524069i	$0.824413\pi$
$480$	−0.806615	−	1.39710i	−0.0368168	−	0.0637685i
$481$		0			0
$482$	1.88914			0.0860480
$483$	2.86977	−	8.96493i	0.130579	−	0.407918i
$484$	1.00000			0.0454545
$485$	5.64630	−	9.77969i	0.256385	−	0.444073i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−15.3528	−	26.5918i	−0.695701	−	1.20499i	−0.969944	−	0.243329i	$-0.921761\pi$
$487$	−15.3528	−	26.5918i	−0.695701	−	1.20499i	0.274243	−	0.961660i	$-0.411573\pi$
$488$	5.97764	−	10.3536i	0.270595	−	0.468685i
$489$	−21.2866			−0.962615
$490$	1.08253	−	11.2406i	0.0489035	−	0.507799i
$491$	30.9446			1.39651			0.698254	−	0.715850i	$-0.253960\pi$
$491$	30.9446			1.39651			0.698254	+	0.715850i	$0.253960\pi$
$492$	2.47229	−	4.28212i	0.111459	−	0.193053i
$493$	38.1695	+	66.1115i	1.71907	+	2.97751i
$494$		0			0
$495$	−0.806615	+	1.39710i	−0.0362546	+	0.0627949i
$496$	6.34206			0.284767
$497$	−12.5131	+	39.0898i	−0.561289	+	1.75342i
$498$	−5.05543			−0.226539
$499$	5.17103	−	8.95649i	0.231487	−	0.400947i	−0.726759	−	0.686893i	$-0.758974\pi$
$499$	5.17103	−	8.95649i	0.231487	−	0.400947i	0.958246	+	0.285945i	$0.0923076\pi$
$500$	−5.96693	−	10.3350i	−0.266849	−	0.462196i
$501$	11.0107	+	19.0711i	0.491923	+	0.852035i
$502$	−0.469915	+	0.813917i	−0.0209733	+	0.0363269i
$503$	4.66268			0.207899			0.103949	−	0.994583i	$-0.466852\pi$
$503$	4.66268			0.207899			0.103949	+	0.994583i	$0.466852\pi$
$504$	−1.77890	−	1.95845i	−0.0792385	−	0.0872362i
$505$	−21.9786			−0.978033
$506$	1.77890	−	3.08115i	0.0790817	−	0.136974i
$507$	−6.50000	−	11.2583i	−0.288675	−	0.500000i
$508$	0.221100	+	0.382956i	0.00980973	+	0.0169909i
$509$	−12.7950	+	22.1616i	−0.567127	+	0.982294i	0.429721	+	0.902962i	$0.358612\pi$
$509$	−12.7950	+	22.1616i	−0.567127	+	0.982294i	−0.996848	+	0.0793318i	$0.974721\pi$
$510$	−11.8444			−0.524480
$511$	−13.2265	+	2.87164i	−0.585104	+	0.127034i
$512$	1.00000			0.0441942
$513$	0.585515	−	1.01414i	0.0258511	−	0.0447754i
$514$	5.61323	+	9.72240i	0.247589	+	0.428837i
$515$	−9.95529	−	17.2431i	−0.438682	−	0.759820i
$516$	−5.75654	+	9.97063i	−0.253418	+	0.438932i
$517$	−6.78426			−0.298371
$518$	7.31434	−	1.58804i	0.321374	−	0.0697745i
$519$	−1.65794			−0.0727755
$520$		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	$0.704321\pi$
$522$	−5.19874	−	9.00449i	−0.227543	−	0.394116i
$523$	−15.1817	+	26.2956i	−0.663852	+	1.14982i	0.315744	+	0.948844i	$0.397746\pi$
$523$	−15.1817	+	26.2956i	−0.663852	+	1.14982i	−0.979595	+	0.200980i	$0.935587\pi$
$524$	−2.34206			−0.102313
$525$	−4.26489	−	4.69536i	−0.186135	−	0.204922i
$526$	−1.22646			−0.0534762
$527$	23.2819	−	40.3254i	1.01418	−	1.75660i
$528$	−0.500000	−	0.866025i	−0.0217597	−	0.0376889i
$529$	5.17103	+	8.95649i	0.224827	+	0.389412i
$530$	6.45292	−	11.1768i	0.280297	−	0.485488i
$531$	4.39749			0.190835
$532$	−0.944570	+	2.95076i	−0.0409523	+	0.127932i
$533$		0			0
$534$	−0.386770	+	0.669906i	−0.0167372	+	0.0289896i
$535$	−12.6958	−	21.9897i	−0.548885	−	0.950697i
$536$	−1.47229	−	2.55007i	−0.0635930	−	0.110146i
$537$	7.53008	−	13.0425i	0.324947	−	0.562825i
$538$	9.50237			0.409676
$539$	0.671030	−	6.96776i	0.0289033	−	0.300123i
$540$	1.61323			0.0694224
$541$	−0.806615	+	1.39710i	−0.0346791	+	0.0600659i	−0.882844	−	0.469666i	$-0.844374\pi$
$541$	−0.806615	+	1.39710i	−0.0346791	+	0.0600659i	0.848165	+	0.529732i	$0.177708\pi$
$542$	−1.61323	−	2.79420i	−0.0692942	−	0.120021i
$543$	7.55780	+	13.0905i	0.324336	+	0.561767i
$544$	3.67103	−	6.35841i	0.157394	−	0.272615i
$545$	−6.38079			−0.273323
$546$		0			0
$547$	15.7348			0.672772			0.336386	−	0.941724i	$-0.390795\pi$
$547$	15.7348			0.672772			0.336386	+	0.941724i	$0.390795\pi$
$548$	−1.61323	+	2.79420i	−0.0689138	+	0.119362i
$549$	5.97764	+	10.3536i	0.255120	+	0.441880i
$550$	−1.19874	−	2.07629i	−0.0511146	−	0.0885332i
$551$	−6.08788	+	10.5445i	−0.259353	+	0.449212i
$552$	−3.55780			−0.151430
$553$	−9.98537	−	10.9932i	−0.424621	−	0.467479i
$554$	−16.0000			−0.679775
$555$	−2.28189	+	3.95235i	−0.0968608	+	0.167768i
$556$	−9.19874	−	15.9327i	−0.390114	−	0.675697i
$557$	−5.64094	−	9.77040i	−0.239015	−	0.413985i	0.721417	−	0.692501i	$-0.243491\pi$
$557$	−5.64094	−	9.77040i	−0.239015	−	0.413985i	−0.960432	+	0.278515i	$0.910158\pi$
$558$	−3.17103	+	5.49238i	−0.134240	+	0.232511i
$559$		0			0
$560$	−4.17103	+	0.905585i	−0.176258	+	0.0382680i
$561$	−7.34206			−0.309982
$562$	5.61560	−	9.72650i	0.236880	−	0.410288i
$563$	−10.4529	−	18.1050i	−0.440538	−	0.763034i	0.557191	−	0.830384i	$-0.311879\pi$
$563$	−10.4529	−	18.1050i	−0.440538	−	0.763034i	−0.997729	+	0.0673499i	$0.978546\pi$
$564$	3.39213	+	5.87534i	0.142834	+	0.247396i
$565$	−3.50237	+	6.06628i	−0.147346	+	0.255210i
$566$	−25.4577			−1.07007
$567$	2.58551	−	0.561349i	0.108581	−	0.0235744i
$568$	15.5131			0.650915
$569$	3.91686	−	6.78419i	0.164203	−	0.284408i	−0.772169	−	0.635417i	$-0.780828\pi$
$569$	3.91686	−	6.78419i	0.164203	−	0.284408i	0.936372	+	0.351009i	$0.114161\pi$
$570$	−0.944570	−	1.63604i	−0.0395637	−	0.0685263i
$571$	−1.19874	−	2.07629i	−0.0501659	−	0.0868899i	0.839852	−	0.542815i	$-0.182642\pi$
$571$	−1.19874	−	2.07629i	−0.0501659	−	0.0868899i	−0.890018	+	0.455926i	$0.849308\pi$
$572$		0			0
$573$	4.77354			0.199418
$574$	−8.79590	−	9.68368i	−0.367134	−	0.404189i
$575$	−8.52979			−0.355717
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−12.8143	−	22.1951i	−0.533468	−	0.923994i	−0.999236	−	0.0390869i	$-0.987555\pi$
$577$	−12.8143	−	22.1951i	−0.533468	−	0.923994i	0.465768	−	0.884907i	$-0.345778\pi$
$578$	−18.4529	−	31.9614i	−0.767540	−	1.32942i
$579$	1.55780	−	2.69819i	0.0647400	−	0.112133i
$580$	−16.7735			−0.696483
$581$	−4.07779	+	12.7387i	−0.169175	+	0.528488i
$582$	−7.00000			−0.290159
$583$	4.00000	−	6.92820i	0.165663	−	0.286937i
$584$	2.55780	+	4.43024i	0.105843	+	0.183325i
$585$		0			0
$586$	−8.97229	+	15.5405i	−0.370642	+	0.641970i
$587$	5.79972			0.239380			0.119690	−	0.992811i	$-0.461810\pi$
$587$	5.79972			0.239380			0.119690	+	0.992811i	$0.461810\pi$
$588$	−6.36977	+	2.90275i	−0.262685	+	0.119707i
$589$	7.42674			0.306014
$590$	3.54708	−	6.14372i	0.146031	−	0.252933i
$591$	−2.41449	−	4.18201i	−0.0993186	−	0.172025i
$592$	−1.41449	−	2.44996i	−0.0581350	−	0.100693i
$593$	−15.5962	+	27.0135i	−0.640461	+	1.10931i	0.344869	+	0.938651i	$0.387923\pi$
$593$	−15.5962	+	27.0135i	−0.640461	+	1.10931i	−0.985330	+	0.170660i	$0.945410\pi$
$594$	1.00000			0.0410305
$595$	−9.55389	+	29.8455i	−0.391671	+	1.22355i
$596$	19.6239			0.803828
$597$	2.94457	−	5.10015i	0.120513	−	0.208735i
$598$		0			0
$599$	15.6463	+	27.1002i	0.639291	+	1.10728i	0.985589	+	0.169159i	$0.0541053\pi$
$599$	15.6463	+	27.1002i	0.639291	+	1.10728i	−0.346298	+	0.938125i	$0.612561\pi$
$600$	−1.19874	+	2.07629i	−0.0489385	+	0.0847641i
$601$	−22.1203			−0.902307			−0.451154	−	0.892446i	$-0.648987\pi$
$601$	−22.1203			−0.902307			−0.451154	+	0.892446i	$0.648987\pi$
$602$	20.4806	+	22.5478i	0.834728	+	0.918979i
$603$	2.94457			0.119912
$604$	0.165670	−	0.286949i	0.00674102	−	0.0116758i
$605$	0.806615	+	1.39710i	0.0327936	+	0.0568001i
$606$	6.81197	+	11.7987i	0.276718	+	0.479289i
$607$	10.3090	−	17.8557i	0.418429	−	0.724740i	−0.577353	−	0.816495i	$-0.695914\pi$
$607$	10.3090	−	17.8557i	0.418429	−	0.724740i	0.995782	+	0.0917548i	$0.0292476\pi$
$608$	1.17103			0.0474915
$609$	−26.8829	+	5.83662i	−1.08935	+	0.236512i
$610$	19.2866			0.780893
$611$		0			0
$612$	3.67103	+	6.35841i	0.148393	+	0.257023i
$613$	7.87750	+	13.6442i	0.318169	+	0.551086i	0.980106	−	0.198474i	$-0.0635986\pi$
$613$	7.87750	+	13.6442i	0.318169	+	0.551086i	−0.661937	+	0.749560i	$0.730265\pi$
$614$	16.5131	−	28.6015i	0.666414	−	1.15426i
$615$	7.97673			0.321653
$616$	−2.58551	+	0.561349i	−0.104173	+	0.0226174i
$617$	34.2526			1.37896			0.689480	−	0.724305i	$-0.257839\pi$
$617$	34.2526			1.37896			0.689480	+	0.724305i	$0.257839\pi$
$618$	−6.17103	+	10.6885i	−0.248235	+	0.429956i
$619$	10.9854	+	19.0272i	0.441539	+	0.764769i	0.997804	−	0.0662365i	$-0.0210992\pi$
$619$	10.9854	+	19.0272i	0.441539	+	0.764769i	−0.556264	+	0.831005i	$0.687766\pi$
$620$	5.11560	+	8.86048i	0.205447	+	0.355845i
$621$	1.77890	−	3.08115i	0.0713848	−	0.123642i
$622$	−0.331340			−0.0132855
$623$	1.37605	+	1.51494i	0.0551303	+	0.0606947i
$624$		0			0
$625$	3.63230	−	6.29133i	0.145292	−	0.251653i
$626$	7.19874	+	12.4686i	0.287720	+	0.498345i
$627$	−0.585515	−	1.01414i	−0.0233832	−	0.0405009i
$628$	−9.98300	+	17.2911i	−0.398365	+	0.689989i
$629$	−20.7705			−0.828173
$630$	1.30126	−	4.06501i	0.0518433	−	0.161954i
$631$	−27.5685			−1.09749			−0.548743	−	0.835991i	$-0.684893\pi$
$631$	−27.5685			−1.09749			−0.548743	+	0.835991i	$0.684893\pi$
$632$	−2.80661	+	4.86120i	−0.111641	+	0.193368i
$633$	−6.83969	−	11.8467i	−0.271853	−	0.470864i
$634$	−8.76190	−	15.1761i	−0.347980	−	0.602718i
$635$	−0.356685	+	0.617797i	−0.0141546	+	0.0245165i
$636$	−8.00000			−0.317221
$637$		0			0
$638$	−10.3975			−0.411641
$639$	−7.75654	+	13.4347i	−0.306844	+	0.531470i
$640$	0.806615	+	1.39710i	0.0318843	+	0.0552251i
$641$	−2.82897	−	4.89992i	−0.111738	−	0.193535i	0.804733	−	0.593636i	$-0.202308\pi$
$641$	−2.82897	−	4.89992i	−0.111738	−	0.193535i	−0.916471	+	0.400101i	$0.868975\pi$
$642$	−7.86977	+	13.6308i	−0.310595	+	0.537967i
$643$	17.4791			0.689308			0.344654	−	0.938730i	$-0.387996\pi$
$643$	17.4791			0.689308			0.344654	+	0.938730i	$0.387996\pi$
$644$	−2.86977	+	8.96493i	−0.113085	+	0.353268i
$645$	−18.5733			−0.731321
$646$	4.29889	−	7.44589i	0.169137	−	0.292955i
$647$	4.41984	+	7.65540i	0.173762	+	0.300965i	0.939732	−	0.341912i	$-0.111074\pi$
$647$	4.41984	+	7.65540i	0.173762	+	0.300965i	−0.765970	+	0.642876i	$0.777741\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	2.19874	−	3.80834i	0.0863083	−	0.149490i
$650$		0			0
$651$	11.2819	+	12.4206i	0.442172	+	0.486801i
$652$	21.2866			0.833649
$653$	12.3751	−	21.4344i	0.484276	−	0.838791i	−0.515560	−	0.856853i	$-0.672416\pi$
$653$	12.3751	−	21.4344i	0.484276	−	0.838791i	0.999837	+	0.0180618i	$0.00574958\pi$
$654$	1.97764	+	3.42538i	0.0773320	+	0.133943i
$655$	−1.88914	−	3.27209i	−0.0738148	−	0.127851i
$656$	−2.47229	+	4.28212i	−0.0965265	+	0.167189i
$657$	−5.11560			−0.199579
$658$	17.5408	−	3.80834i	0.683812	−	0.148464i
$659$	5.62869			0.219263			0.109631	−	0.993972i	$-0.465033\pi$
$659$	5.62869			0.219263			0.109631	+	0.993972i	$0.465033\pi$
$660$	0.806615	−	1.39710i	0.0313974	−	0.0543820i
$661$	6.70111	+	11.6067i	0.260643	+	0.451447i	0.966413	−	0.256994i	$-0.0827321\pi$
$661$	6.70111	+	11.6067i	0.260643	+	0.451447i	−0.705770	+	0.708441i	$0.749399\pi$
$662$	4.47229	+	7.74622i	0.173820	+	0.301066i
$663$		0			0
$664$	5.05543			0.196189
$665$	−4.88440	+	1.06047i	−0.189409	+	0.0411231i
$666$	2.82897			0.109620
$667$	−18.4961	+	32.0362i	−0.716172	+	1.24045i
$668$	−11.0107	−	19.0711i	−0.426018	−	0.737884i
$669$	−2.55780	−	4.43024i	−0.0988903	−	0.171283i
$670$	2.37513	−	4.11385i	0.0917594	−	0.158932i
$671$	11.9553			0.461529
$672$	1.77890	+	1.95845i	0.0686226	+	0.0755487i
$673$	−29.0262			−1.11888			−0.559438	−	0.828872i	$-0.688983\pi$
$673$	−29.0262			−1.11888			−0.559438	+	0.828872i	$0.688983\pi$
$674$	1.66866	−	2.89020i	0.0642744	−	0.111326i
$675$	−1.19874	−	2.07629i	−0.0461397	−	0.0799163i
$676$	6.50000	+	11.2583i	0.250000	+	0.433013i
$677$	10.1540	−	17.5873i	0.390251	−	0.675935i	−0.602231	−	0.798322i	$-0.705721\pi$
$677$	10.1540	−	17.5873i	0.390251	−	0.675935i	0.992482	+	0.122387i	$0.0390548\pi$
$678$	4.34206			0.166756
$679$	−5.64630	+	17.6386i	−0.216685	+	0.676906i
$680$	11.8444			0.454213
$681$	−2.64331	+	4.57836i	−0.101292	+	0.175443i
$682$	3.17103	+	5.49238i	0.121425	+	0.210314i
$683$	5.36977	+	9.30072i	0.205469	+	0.355882i	0.950282	−	0.311391i	$-0.100795\pi$
$683$	5.36977	+	9.30072i	0.205469	+	0.355882i	−0.744813	+	0.667273i	$0.767461\pi$
$684$	−0.585515	+	1.01414i	−0.0223877	+	0.0387767i
$685$	−5.20502			−0.198874
$686$	2.17639	+	18.3919i	0.0830949	+	0.702207i
$687$	4.88440			0.186351
$688$	5.75654	−	9.97063i	0.219466	−	0.380127i
$689$		0			0
$690$	−2.86977	−	4.97060i	−0.109250	−	0.189227i
$691$	−2.98537	+	5.17082i	−0.113569	+	0.196707i	−0.917207	−	0.398411i	$-0.869562\pi$
$691$	−2.98537	+	5.17082i	−0.113569	+	0.196707i	0.803638	+	0.595119i	$0.202895\pi$
$692$	1.65794			0.0630254
$693$	0.806615	−	2.51980i	0.0306408	−	0.0957191i
$694$	−30.4237			−1.15487
$695$	14.8397	−	25.7031i	0.562902	−	0.974974i
$696$	5.19874	+	9.00449i	0.197058	+	0.341314i
$697$	18.1517	+	31.4396i	0.687543	+	1.19086i
$698$	−8.76190	+	15.1761i	−0.331643	+	0.574422i
$699$	−9.79498			−0.370480
$700$	4.26489	+	4.69536i	0.161198	+	0.177468i
$701$	−5.28189			−0.199494			−0.0997471	−	0.995013i	$-0.531803\pi$
$701$	−5.28189			−0.199494			−0.0997471	+	0.995013i	$0.531803\pi$
$702$		0			0
$703$	−1.65640	−	2.86898i	−0.0624725	−	0.108205i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	−5.47229	+	9.47828i	−0.206098	+	0.356973i
$706$	5.11560			0.192528
$707$	35.2249	−	7.64779i	1.32477	−	0.287625i
$708$	−4.39749			−0.165268
$709$	−19.6564	+	34.0459i	−0.738212	+	1.27862i	0.215088	+	0.976595i	$0.430996\pi$
$709$	−19.6564	+	34.0459i	−0.738212	+	1.27862i	−0.953300	+	0.302026i	$0.902337\pi$
$710$	12.5131	+	21.6733i	0.469608	+	0.813385i
$711$	−2.80661	−	4.86120i	−0.105256	−	0.182309i
$712$	0.386770	−	0.669906i	0.0144948	−	0.0251058i
$713$	22.5638			0.845020
$714$	18.9830	−	4.12146i	0.710421	−	0.154242i
$715$		0			0
$716$	−7.53008	+	13.0425i	−0.281412	+	0.487421i
$717$	−11.9553	−	20.7072i	−0.446478	−	0.773323i
$718$	15.3421	+	26.5732i	0.572561	+	0.991704i
$719$	17.6788	−	30.6205i	0.659306	−	1.14195i	−0.321489	−	0.946913i	$-0.604183\pi$
$719$	17.6788	−	30.6205i	0.659306	−	1.14195i	0.980795	−	0.195039i	$-0.0624833\pi$
$720$	−1.61323			−0.0601215
$721$	21.9553	+	24.1713i	0.817658	+	0.900185i
$722$	−17.6287			−0.656072
$723$	0.944570	−	1.63604i	0.0351289	−	0.0608451i
$724$	−7.55780	−	13.0905i	−0.280883	−	0.486504i
$725$	12.4639	+	21.5882i	0.462899	+	0.801765i
$726$	0.500000	−	0.866025i	0.0185567	−	0.0321412i
$727$	−40.2312			−1.49209			−0.746046	−	0.665894i	$-0.768050\pi$
$727$	−40.2312			−1.49209			−0.746046	+	0.665894i	$0.768050\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−4.12632	+	7.14699i	−0.152722	+	0.264522i
$731$	−42.2649	−	73.2049i	−1.56322	−	2.70758i
$732$	−5.97764	−	10.3536i	−0.220940	−	0.382679i
$733$	−14.3644	+	24.8799i	−0.530562	+	0.918960i	0.468802	+	0.883303i	$0.344686\pi$
$733$	−14.3644	+	24.8799i	−0.530562	+	0.918960i	−0.999364	+	0.0356568i	$0.988648\pi$
$734$	1.45766			0.0538032
$735$	−9.19339	−	6.55780i	−0.339103	−	0.241888i
$736$	3.55780			0.131142
$737$	1.47229	−	2.55007i	0.0542323	−	0.0939331i
$738$	−2.47229	−	4.28212i	−0.0910061	−	0.157627i
$739$	8.17103	+	14.1526i	0.300576	+	0.520613i	0.976267	−	0.216572i	$-0.0694877\pi$
$739$	8.17103	+	14.1526i	0.300576	+	0.520613i	−0.675690	+	0.737186i	$0.736154\pi$
$740$	2.28189	−	3.95235i	0.0838839	−	0.145291i
$741$		0			0
$742$	−6.45292	+	20.1584i	−0.236894	+	0.740037i
$743$	45.3897			1.66519			0.832593	−	0.553885i	$-0.186855\pi$
$743$	45.3897			1.66519			0.832593	+	0.553885i	$0.186855\pi$
$744$	3.17103	−	5.49238i	0.116256	−	0.201361i
$745$	15.8290	+	27.4166i	0.579929	+	1.00447i
$746$	17.0932	+	29.6064i	0.625828	+	1.08397i
$747$	−2.52771	+	4.37813i	−0.0924843	+	0.160187i
$748$	7.34206			0.268452
$749$	27.9991	+	30.8251i	1.02306	+	1.12632i
$750$	−11.9339			−0.435763
$751$	13.8999	−	24.0753i	0.507213	−	0.878519i	−0.492752	−	0.870170i	$-0.664009\pi$
$751$	13.8999	−	24.0753i	0.507213	−	0.878519i	0.999965	−	0.00834907i	$-0.00265762\pi$
$752$	−3.39213	−	5.87534i	−0.123698	−	0.214252i
$753$	0.469915	+	0.813917i	0.0171247	+	0.0296608i
$754$		0			0
$755$	0.534528			0.0194535
$756$	−2.58551	+	0.561349i	−0.0940343	+	0.0204161i
$757$	19.0816			0.693533			0.346766	−	0.937952i	$-0.387280\pi$
$757$	19.0816			0.693533			0.346766	+	0.937952i	$0.387280\pi$
$758$	4.64331	−	8.04246i	0.168653	−	0.292115i
$759$	−1.77890	−	3.08115i	−0.0645700	−	0.111838i
$760$	0.944570	+	1.63604i	0.0342632	+	0.0593455i
$761$	−23.6093	+	40.8925i	−0.855837	+	1.48235i	0.0200287	+	0.999799i	$0.493624\pi$
$761$	−23.6093	+	40.8925i	−0.855837	+	1.48235i	−0.875866	+	0.482554i	$0.839709\pi$
$762$	0.442200			0.0160192
$763$	10.2265	−	2.22030i	0.370223	−	0.0803802i
$764$	−4.77354			−0.172701
$765$	−5.92221	+	10.2576i	−0.214118	+	0.370863i
$766$	1.81197	+	3.13843i	0.0654693	+	0.113396i
$767$		0			0
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−9.56852			−0.345050			−0.172525	−	0.985005i	$-0.555192\pi$
$769$	−9.56852			−0.345050			−0.172525	+	0.985005i	$0.555192\pi$
$770$	−2.86977	−	3.15943i	−0.103419	−	0.113858i
$771$	11.2265			0.404311
$772$	−1.55780	+	2.69819i	−0.0560664	+	0.0971099i
$773$	−7.97764	−	13.8177i	−0.286936	−	0.496988i	0.686141	−	0.727469i	$-0.259303\pi$
$773$	−7.97764	−	13.8177i	−0.286936	−	0.496988i	−0.973077	+	0.230481i	$0.925970\pi$
$774$	5.75654	+	9.97063i	0.206915	+	0.358387i
$775$	7.60251	−	13.1679i	0.273090	−	0.473006i
$776$	7.00000			0.251285
$777$	2.28189	−	7.12843i	0.0818623	−	0.255731i
$778$	7.16031			0.256710
$779$	−2.89512	+	5.01449i	−0.103728	+	0.179663i
$780$		0			0
$781$	7.75654	+	13.4347i	0.277551	+	0.480732i
$782$	13.0608	−	22.6220i	0.467053	−	0.808959i
$783$	−10.3975			−0.371576
$784$	6.36977	−	2.90275i	0.227492	−	0.103670i
$785$	−32.2098			−1.14962
$786$	−1.17103	+	2.02828i	−0.0417692	+	0.0723465i
$787$	−24.9276	−	43.1758i	−0.888572	−	1.53905i	−0.841564	−	0.540157i	$-0.818365\pi$
$787$	−24.9276	−	43.1758i	−0.888572	−	1.53905i	−0.0470081	−	0.998895i	$-0.514969\pi$
$788$	2.41449	+	4.18201i	0.0860125	+	0.148978i
$789$	−0.613230	+	1.06215i	−0.0218316	+	0.0378134i
$790$	−9.05543			−0.322178
$791$	3.50237	−	10.9411i	0.124530	−	0.389021i
$792$	−1.00000			−0.0355335
$793$		0			0
$794$	15.1987	+	26.3250i	0.539383	+	0.934239i
$795$	−6.45292	−	11.1768i	−0.228861	−	0.396400i
$796$	−2.94457	+	5.10015i	−0.104368	+	0.180770i
$797$	36.4177			1.28998			0.644990	−	0.764191i	$-0.276861\pi$
$797$	36.4177			1.28998			0.644990	+	0.764191i	$0.276861\pi$
$798$	2.08314	+	2.29340i	0.0737425	+	0.0811855i
$799$	−49.8104			−1.76217
$800$	1.19874	−	2.07629i	0.0423820	−	0.0734078i
$801$	0.386770	+	0.669906i	0.0136659	+	0.0236699i
$802$	6.01072	+	10.4109i	0.212246	+	0.367621i
$803$	−2.55780	+	4.43024i	−0.0902628	+	0.156340i
$804$	−2.94457			−0.103847
$805$	−14.8397	+	3.22189i	−0.523030	+	0.113557i
$806$		0			0
$807$	4.75119	−	8.22929i	0.167250	−	0.289685i
$808$	−6.81197	−	11.7987i	−0.239644	−	0.415076i
$809$	−24.2118	−	41.9361i	−0.851243	−	1.47440i	−0.880087	−	0.474812i	$-0.842516\pi$
$809$	−24.2118	−	41.9361i	−0.851243	−	1.47440i	0.0288446	−	0.999584i	$-0.490817\pi$
$810$	0.806615	−	1.39710i	0.0283416	−	0.0490890i
$811$	−41.0262			−1.44062			−0.720312	−	0.693650i	$-0.756001\pi$
$811$	−41.0262			−1.44062			−0.720312	+	0.693650i	$0.756001\pi$
$812$	26.8829	−	5.83662i	0.943404	−	0.204825i
$813$	−3.22646			−0.113157
$814$	1.41449	−	2.44996i	0.0495777	−	0.0858711i
$815$	17.1701	+	29.7395i	0.601443	+	1.04173i
$816$	−3.67103	−	6.35841i	−0.128512	−	0.222589i
$817$	6.74109	−	11.6759i	0.235841	−	0.408488i
$818$	17.5685			0.614269
$819$		0			0
$820$	−7.97673			−0.278559
$821$	−19.9660	+	34.5821i	−0.696819	+	1.20693i	0.272745	+	0.962086i	$0.412068\pi$
$821$	−19.9660	+	34.5821i	−0.696819	+	1.20693i	−0.969564	+	0.244839i	$0.921265\pi$
$822$	1.61323	+	2.79420i	0.0562679	+	0.0974588i
$823$	7.89986	+	13.6830i	0.275372	+	0.476958i	0.970229	−	0.242190i	$-0.0778657\pi$
$823$	7.89986	+	13.6830i	0.275372	+	0.476958i	−0.694857	+	0.719148i	$0.744532\pi$
$824$	6.17103	−	10.6885i	0.214978	−	0.372353i
$825$	−2.39749			−0.0834699
$826$	−3.54708	+	11.0808i	−0.123419	+	0.385550i
$827$	−26.8766			−0.934591			−0.467295	−	0.884101i	$-0.654771\pi$
$827$	−26.8766			−0.934591			−0.467295	+	0.884101i	$0.654771\pi$
$828$	−1.77890	+	3.08115i	−0.0618210	+	0.107077i
$829$	4.15403	+	7.19500i	0.144276	+	0.249893i	0.929102	−	0.369822i	$-0.120581\pi$
$829$	4.15403	+	7.19500i	0.144276	+	0.249893i	−0.784827	+	0.619715i	$0.787248\pi$
$830$	4.07779	+	7.06293i	0.141542	+	0.245158i
$831$	−8.00000	+	13.8564i	−0.277517	+	0.480673i
$832$		0			0
$833$	4.92674	−	51.1577i	0.170701	−	1.77251i
$834$	−18.3975			−0.637053
$835$	17.7628	−	30.7661i	0.614708	−	1.06471i
$836$	0.585515	+	1.01414i	0.0202505	+	0.0350748i
$837$	3.17103	+	5.49238i	0.109607	+	0.189845i
$838$	13.5855	−	23.5308i	0.469304	−	0.812858i
$839$	−4.28787			−0.148034			−0.0740168	−	0.997257i	$-0.523582\pi$
$839$	−4.28787			−0.148034			−0.0740168	+	0.997257i	$0.523582\pi$
$840$	−1.30126	+	4.06501i	−0.0448976	+	0.140256i
$841$	79.1078			2.72785
$842$	−11.5855	+	20.0667i	−0.399263	+	0.691544i
$843$	−5.61560	−	9.72650i	−0.193412	−	0.334999i
$844$	6.83969	+	11.8467i	0.235432	+	0.407780i
$845$	−10.4860	+	18.1623i	−0.360729	+	0.624801i
$846$	6.78426			0.233248
$847$	−1.77890	−	1.95845i	−0.0611237	−	0.0672930i
$848$	8.00000			0.274721
$849$	−12.7288	+	22.0470i	−0.436852	+	0.756650i
$850$	−8.80126	−	15.2442i	−0.301881	−	0.522872i
$851$	−5.03246	−	8.71647i	−0.172510	−	0.298797i
$852$	7.75654	−	13.4347i	0.265735	−	0.460266i
$853$	−46.2973			−1.58519			−0.792596	−	0.609748i	$-0.791271\pi$
$853$	−46.2973			−1.58519			−0.792596	+	0.609748i	$0.791271\pi$
$854$	−30.9106	+	6.71109i	−1.05774	+	0.229649i
$855$	−1.88914			−0.0646072
$856$	7.86977	−	13.6308i	0.268983	−	0.465893i
$857$	13.7312	+	23.7831i	0.469049	+	0.812416i	0.999374	−	0.0353779i	$-0.0112635\pi$
$857$	13.7312	+	23.7831i	0.469049	+	0.812416i	−0.530325	+	0.847794i	$0.677930\pi$
$858$		0			0
$859$	6.09623	−	10.5590i	0.208001	−	0.360268i	−0.743084	−	0.669198i	$-0.766638\pi$
$859$	6.09623	−	10.5590i	0.208001	−	0.360268i	0.951085	+	0.308930i	$0.0999710\pi$
$860$	18.5733			0.633343
$861$	−12.7843	+	2.77563i	−0.435686	+	0.0945932i
$862$	−16.7735			−0.571309
$863$	−0.419845	+	0.727192i	−0.0142917	+	0.0247539i	−0.873083	−	0.487572i	$-0.837883\pi$
$863$	−0.419845	+	0.727192i	−0.0142917	+	0.0247539i	0.858791	+	0.512326i	$0.171216\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	1.33732	+	2.31631i	0.0454702	+	0.0787567i
$866$	−8.67103	+	15.0187i	−0.294654	+	0.510355i
$867$	−36.9058			−1.25339
$868$	−11.2819	−	12.4206i	−0.382932	−	0.421582i
$869$	−5.61323			−0.190416
$870$	−8.38677	+	14.5263i	−0.284338	+	0.492488i
$871$		0			0
$872$	−1.97764	−	3.42538i	−0.0669715	−	0.115998i
$873$	−3.50000	+	6.06218i	−0.118457	+	0.205174i
$874$	4.16629			0.140927
$875$	−9.62602	+	30.0709i	−0.325419	+	1.01658i
$876$	5.11560			0.172840
$877$	10.2643	−	17.7782i	0.346600	−	0.600329i	−0.639043	−	0.769171i	$-0.720669\pi$
$877$	10.2643	−	17.7782i	0.346600	−	0.600329i	0.985643	+	0.168842i	$0.0540028\pi$
$878$	−16.5739	−	28.7068i	−0.559341	−	0.968808i
$879$	8.97229	+	15.5405i	0.302628	+	0.524166i
$880$	−0.806615	+	1.39710i	−0.0271910	+	0.0470962i
$881$	1.88914			0.0636468			0.0318234	−	0.999494i	$-0.489869\pi$
$881$	1.88914			0.0636468			0.0318234	+	0.999494i	$0.489869\pi$
$882$	−0.671030	+	6.96776i	−0.0225947	+	0.234617i
$883$	26.5345			0.892958			0.446479	−	0.894794i	$-0.352678\pi$
$883$	26.5345			0.892958			0.446479	+	0.894794i	$0.352678\pi$
$884$		0			0
$885$	−3.54708	−	6.14372i	−0.119234	−	0.206519i
$886$	6.02771	+	10.4403i	0.202505	+	0.350749i
$887$	−8.55780	+	14.8225i	−0.287343	+	0.497692i	−0.973175	−	0.230068i	$-0.926105\pi$
$887$	−8.55780	+	14.8225i	−0.287343	+	0.497692i	0.685832	+	0.727760i	$0.259439\pi$
$888$	−2.82897			−0.0949340
$889$	0.356685	−	1.11425i	0.0119628	−	0.0373709i
$890$	1.24790			0.0418296
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	2.55780	+	4.43024i	0.0856415	+	0.148335i
$893$	−3.97229	−	6.88020i	−0.132927	−	0.230237i
$894$	9.81197	−	16.9948i	0.328162	−	0.568392i
$895$	−24.2955			−0.812110
$896$	−1.77890	−	1.95845i	−0.0594289	−	0.0654271i
$897$		0			0
$898$	18.2973	−	31.6919i	0.610590	−	1.05757i
$899$	−32.9707	−	57.1070i	−1.09964	−	1.90463i
$900$	1.19874	+	2.07629i	0.0399582	+	0.0692096i
$901$	29.3682	−	50.8673i	0.978398	−	1.69463i
$902$	−4.94457			−0.164636
$903$	29.7673	−	6.46286i	0.990593	−	0.215071i
$904$	−4.34206			−0.144415
$905$	12.1925	−	21.1180i	0.405291	−	0.701985i
$906$	−0.165670	−	0.286949i	−0.00550402	−	0.00953324i
$907$	−1.64331	−	2.84630i	−0.0545654	−	0.0945100i	0.837453	−	0.546510i	$-0.184044\pi$
$907$	−1.64331	−	2.84630i	−0.0545654	−	0.0945100i	−0.892018	+	0.452000i	$0.850711\pi$
$908$	2.64331	−	4.57836i	0.0877215	−	0.151938i
$909$	13.6239			0.451878
$910$		0			0
$911$	14.0107			0.464196			0.232098	−	0.972692i	$-0.425441\pi$
$911$	14.0107			0.464196			0.232098	+	0.972692i	$0.425441\pi$
$912$	0.585515	−	1.01414i	0.0193883	−	0.0335816i
$913$	2.52771	+	4.37813i	0.0836552	+	0.144895i
$914$	−18.9106	−	32.7541i	−0.625506	−	1.08341i
$915$	9.64331	−	16.7027i	0.318798	−	0.552175i
$916$	−4.88440			−0.161385
$917$	4.16629	+	4.58680i	0.137583	+	0.151469i
$918$	7.34206			0.242324
$919$	23.2580	−	40.2840i	0.767211	−	1.32885i	−0.171859	−	0.985121i	$-0.554977\pi$
$919$	23.2580	−	40.2840i	0.767211	−	1.32885i	0.939070	−	0.343726i	$-0.111689\pi$
$920$	2.86977	+	4.97060i	0.0946137	+	0.163876i
$921$	−16.5131	−	28.6015i	−0.544125	−	0.942452i
$922$	−17.4854	+	30.2856i	−0.575850	+	0.997402i
$923$		0			0
$924$	−0.806615	+	2.51980i	−0.0265357	+	0.0828952i
$925$	−6.78243			−0.223005
$926$	−3.78426	+	6.55453i	−0.124358	+	0.215395i
$927$	6.17103	+	10.6885i	0.202683	+	0.351058i
$928$	−5.19874	−	9.00449i	−0.170657	−	0.295587i
$929$	12.4422	−	21.5505i	0.408215	−	0.707050i	−0.586475	−	0.809968i	$-0.699485\pi$
$929$	12.4422	−	21.5505i	0.408215	−	0.707050i	0.994690	+	0.102918i	$0.0328179\pi$
$930$	10.2312			0.335494
$931$	7.45920	−	3.39921i	0.244465	−	0.111405i
$932$	9.79498			0.320845
$933$	−0.165670	+	0.286949i	−0.00542380	+	0.00939429i
$934$	7.31434	+	12.6688i	0.239333	+	0.414536i
$935$	5.92221	+	10.2576i	0.193677	+	0.335459i
$936$		0			0
$937$	−46.7950			−1.52873			−0.764363	−	0.644787i	$-0.776946\pi$
$937$	−46.7950			−1.52873			−0.764363	+	0.644787i	$0.776946\pi$
$938$	−2.37513	+	7.41972i	−0.0775509	+	0.242262i
$939$	14.3975			0.469844
$940$	5.47229	−	9.47828i	0.178486	−	0.309147i
$941$	−8.74583	−	15.1482i	−0.285106	−	0.493818i	0.687529	−	0.726157i	$-0.258695\pi$
$941$	−8.74583	−	15.1482i	−0.285106	−	0.493818i	−0.972635	+	0.232339i	$0.925362\pi$
$942$	9.98300	+	17.2911i	0.325264	+	0.563374i
$943$	−8.79590	+	15.2349i	−0.286434	+	0.496118i
$944$	4.39749			0.143126
$945$	−2.86977	−	3.15943i	−0.0933538	−	0.102776i
$946$	11.5131			0.374323
$947$	−7.30960	+	12.6606i	−0.237530	+	0.411414i	−0.960005	−	0.279983i	$-0.909671\pi$
$947$	−7.30960	+	12.6606i	−0.237530	+	0.411414i	0.722475	+	0.691397i	$0.243005\pi$
$948$	2.80661	+	4.86120i	0.0911546	+	0.157884i
$949$		0			0
$950$	1.40377	−	2.43139i	0.0455442	−	0.0788848i
$951$	−17.5238			−0.568248
$952$	−18.9830	+	4.12146i	−0.615243	+	0.133577i
$953$	−20.0816			−0.650507			−0.325254	−	0.945627i	$-0.605450\pi$
$953$	−20.0816			−0.650507			−0.325254	+	0.945627i	$0.605450\pi$
$954$	−4.00000	+	6.92820i	−0.129505	+	0.224309i
$955$	−3.85041	−	6.66910i	−0.124596	−	0.215807i
$956$	11.9553	+	20.7072i	0.386662	+	0.669718i
$957$	−5.19874	+	9.00449i	−0.168052	+	0.291074i
$958$	−1.22646			−0.0396251
$959$	8.34206	−	1.81117i	0.269379	−	0.0584857i
$960$	1.61323			0.0520668
$961$	−4.61086	+	7.98624i	−0.148737	+	0.257621i
$962$		0			0
$963$	7.86977	+	13.6308i	0.253600	+	0.439248i
$964$	−0.944570	+	1.63604i	−0.0304226	+	0.0526934i
$965$	−5.02618			−0.161798
$966$	6.32897	+	6.96776i	0.203631	+	0.224184i
$967$	−60.2634			−1.93794			−0.968969	−	0.247180i	$-0.920496\pi$
$967$	−60.2634			−1.93794			−0.968969	+	0.247180i	$0.920496\pi$
$968$	−0.500000	+	0.866025i	−0.0160706	+	0.0278351i
$969$	−4.29889	−	7.44589i	−0.138100	−	0.239196i
$970$	5.64630	+	9.77969i	0.181292	+	0.314007i
$971$	26.4237	−	45.7671i	0.847976	−	1.46874i	−0.0350357	−	0.999386i	$-0.511154\pi$
$971$	26.4237	−	45.7671i	0.847976	−	1.46874i	0.883012	−	0.469351i	$-0.155512\pi$
$972$	−1.00000			−0.0320750
$973$	−14.8397	+	46.3579i	−0.475739	+	1.48617i
$974$	30.7056			0.983870
$975$		0			0
$976$	5.97764	+	10.3536i	0.191340	+	0.331410i
$977$	−12.4529	−	21.5691i	−0.398404	−	0.690056i	0.595125	−	0.803633i	$-0.297103\pi$
$977$	−12.4529	−	21.5691i	−0.398404	−	0.690056i	−0.993529	+	0.113577i	$0.963769\pi$
$978$	10.6433	−	18.4348i	0.340336	−	0.589479i
$979$	0.773540			0.0247225
$980$	9.19339	+	6.55780i	0.293672	+	0.209481i
$981$	3.95529			0.126283
$982$	−15.4723	+	26.7988i	−0.493740	+	0.855184i
$983$	12.5632	+	21.7600i	0.400703	+	0.694037i	0.993811	−	0.111086i	$-0.0354327\pi$
$983$	12.5632	+	21.7600i	0.400703	+	0.694037i	−0.593108	+	0.805123i	$0.702099\pi$
$984$	2.47229	+	4.28212i	0.0788136	+	0.136509i
$985$	−3.89512	+	6.74654i	−0.124109	+	0.214963i
$986$	−76.3390			−2.43113
$987$	5.47229	−	17.0950i	0.174185	−	0.544138i
$988$		0			0
$989$	20.4806	−	35.4735i	0.651246	−	1.12799i
$990$	−0.806615	−	1.39710i	−0.0256359	−	0.0444027i
$991$	−28.9600	−	50.1602i	−0.919946	−	1.59339i	−0.799495	−	0.600673i	$-0.794899\pi$
$991$	−28.9600	−	50.1602i	−0.919946	−	1.59339i	−0.120451	−	0.992719i	$-0.538434\pi$
$992$	−3.17103	+	5.49238i	−0.100680	+	0.174383i
$993$	8.94457			0.283847
$994$	−27.5962	−	30.3816i	−0.875299	−	0.963645i
$995$	−9.50054			−0.301187
$996$	2.52771	−	4.37813i	0.0800937	−	0.138726i
$997$	−8.68412	−	15.0413i	−0.275029	−	0.476364i	0.695114	−	0.718900i	$-0.255354\pi$
$997$	−8.68412	−	15.0413i	−0.275029	−	0.476364i	−0.970142	+	0.242536i	$0.922021\pi$
$998$	5.17103	+	8.95649i	0.163686	+	0.283513i
$999$	1.41449	−	2.44996i	0.0447523	−	0.0775133i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.i.g.331.2	yes	6
3.2	odd	2		1386.2.k.v.793.2		6
7.2	even	3		3234.2.a.bf.1.2		3
7.4	even	3	inner	462.2.i.g.67.2	✓	6
7.5	odd	6		3234.2.a.bh.1.2		3
21.2	odd	6		9702.2.a.dv.1.2		3
21.5	even	6		9702.2.a.dw.1.2		3
21.11	odd	6		1386.2.k.v.991.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.i.g.67.2	✓	6	7.4	even	3	inner
462.2.i.g.331.2	yes	6	1.1	even	1	trivial
1386.2.k.v.793.2		6	3.2	odd	2
1386.2.k.v.991.2		6	21.11	odd	6
3234.2.a.bf.1.2		3	7.2	even	3
3234.2.a.bh.1.2		3	7.5	odd	6
9702.2.a.dv.1.2		3	21.2	odd	6
9702.2.a.dw.1.2		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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.806615 - 1.39710i) q^{5} -1.00000 q^{6} +(-0.806615 + 2.51980i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.806615 - 1.39710i) q^{5} -1.00000 q^{6} +(-0.806615 + 2.51980i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.806615 + 1.39710i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-1.77890 - 1.95845i) q^{14} +1.61323 q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.67103 + 6.35841i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.585515 + 1.01414i) q^{19} -1.61323 q^{20} +(-2.58551 + 0.561349i) q^{21} -1.00000 q^{22} +(-1.77890 + 3.08115i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.19874 + 2.07629i) q^{25} -1.00000 q^{27} +(2.58551 - 0.561349i) q^{28} +10.3975 q^{29} +(-0.806615 + 1.39710i) q^{30} +(-3.17103 - 5.49238i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} -7.34206 q^{34} +(2.86977 + 3.15943i) q^{35} +1.00000 q^{36} +(-1.41449 + 2.44996i) q^{37} +(-0.585515 - 1.01414i) q^{38} +(0.806615 - 1.39710i) q^{40} +4.94457 q^{41} +(0.806615 - 2.51980i) q^{42} -11.5131 q^{43} +(0.500000 - 0.866025i) q^{44} +(0.806615 + 1.39710i) q^{45} +(-1.77890 - 3.08115i) q^{46} +(-3.39213 + 5.87534i) q^{47} -1.00000 q^{48} +(-5.69874 - 4.06501i) q^{49} -2.39749 q^{50} +(-3.67103 + 6.35841i) q^{51} +(-4.00000 - 6.92820i) q^{53} +(0.500000 - 0.866025i) q^{54} +1.61323 q^{55} +(-0.806615 + 2.51980i) q^{56} -1.17103 q^{57} +(-5.19874 + 9.00449i) q^{58} +(-2.19874 - 3.80834i) q^{59} +(-0.806615 - 1.39710i) q^{60} +(5.97764 - 10.3536i) q^{61} +6.34206 q^{62} +(-1.77890 - 1.95845i) q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{66} +(-1.47229 - 2.55007i) q^{67} +(3.67103 - 6.35841i) q^{68} -3.55780 q^{69} +(-4.17103 + 0.905585i) q^{70} +15.5131 q^{71} +(-0.500000 + 0.866025i) q^{72} +(2.55780 + 4.43024i) q^{73} +(-1.41449 - 2.44996i) q^{74} +(-1.19874 + 2.07629i) q^{75} +1.17103 q^{76} +(-2.58551 + 0.561349i) q^{77} +(-2.80661 + 4.86120i) q^{79} +(0.806615 + 1.39710i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.47229 + 4.28212i) q^{82} +5.05543 q^{83} +(1.77890 + 1.95845i) q^{84} +11.8444 q^{85} +(5.75654 - 9.97063i) q^{86} +(5.19874 + 9.00449i) q^{87} +(0.500000 + 0.866025i) q^{88} +(0.386770 - 0.669906i) q^{89} -1.61323 q^{90} +3.55780 q^{92} +(3.17103 - 5.49238i) q^{93} +(-3.39213 - 5.87534i) q^{94} +(0.944570 + 1.63604i) q^{95} +(0.500000 - 0.866025i) q^{96} +7.00000 q^{97} +(6.36977 - 2.90275i) 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

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