LMFDB - Embedded newform 462.2.k.g.89.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("462.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 19 x^{18} - 42 x^{17} + 62 x^{16} - 42 x^{15} - 25 x^{14} + 6 x^{13} + 445 x^{12} + \cdots + 59049 $ x^20 - 6x^19 + 19x^18 - 42x^17 + 62x^16 - 42x^15 - 25x^14 + 6x^13 + 445x^12 - 1764x^11 + 3864x^10 - 5292x^9 + 4005x^8 + 162x^7 - 2025x^6 - 10206x^5 + 45198x^4 - 91854x^3 + 124659x^2 - 118098*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.3
Root			$1.69321 - 0.364755i$ of defining polynomial
Character	$\chi$	$=$	462.89
Dual form			462.2.k.g.353.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.530717 + 1.64874i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.417958 + 0.723925i) q^{5} +(1.28398 - 1.16249i) q^{6} +(-1.42670 + 2.22812i) q^{7} -1.00000i q^{8} +(-2.43668 - 1.75003i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.530717 + 1.64874i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.417958 + 0.723925i) q^{5} +(1.28398 - 1.16249i) q^{6} +(-1.42670 + 2.22812i) q^{7} -1.00000i q^{8} +(-2.43668 - 1.75003i) q^{9} +(0.723925 - 0.417958i) q^{10} +(0.866025 - 0.500000i) q^{11} +(-1.69321 + 0.364755i) q^{12} +3.86332i q^{13} +(2.34962 - 1.21626i) q^{14} +(-0.971746 - 1.07330i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.06563 - 1.84573i) q^{17} +(1.23521 + 2.73391i) q^{18} +(-2.35922 - 1.36210i) q^{19} -0.835917 q^{20} +(-2.91642 - 3.53475i) q^{21} -1.00000 q^{22} +(-6.08555 - 3.51349i) q^{23} +(1.64874 + 0.530717i) q^{24} +(2.15062 + 3.72499i) q^{25} +(1.93166 - 3.34573i) q^{26} +(4.17853 - 3.08868i) q^{27} +(-2.64296 - 0.121493i) q^{28} -7.25640i q^{29} +(0.304905 + 1.41538i) q^{30} +(-4.85360 + 2.80223i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.364755 + 1.69321i) q^{33} +2.13127i q^{34} +(-1.01670 - 1.96408i) q^{35} +(0.297229 - 2.98524i) q^{36} +(1.76131 - 3.05069i) q^{37} +(1.36210 + 2.35922i) q^{38} +(-6.36960 - 2.05033i) q^{39} +(0.723925 + 0.417958i) q^{40} +0.835917 q^{41} +(0.758320 + 4.51940i) q^{42} -9.85086 q^{43} +(0.866025 + 0.500000i) q^{44} +(2.28532 - 1.03253i) q^{45} +(3.51349 + 6.08555i) q^{46} +(-5.84290 + 10.1202i) q^{47} +(-1.16249 - 1.28398i) q^{48} +(-2.92908 - 6.35771i) q^{49} -4.30124i q^{50} +(3.60868 - 0.777390i) q^{51} +(-3.34573 + 1.93166i) q^{52} +(-7.26395 + 4.19384i) q^{53} +(-5.16305 + 0.585609i) q^{54} +0.835917i q^{55} +(2.22812 + 1.42670i) q^{56} +(3.49783 - 3.16686i) q^{57} +(-3.62820 + 6.28423i) q^{58} +(3.60897 + 6.25091i) q^{59} +(0.443635 - 1.37821i) q^{60} +(-2.31656 - 1.33746i) q^{61} +5.60445 q^{62} +(7.37568 - 2.93247i) q^{63} -1.00000 q^{64} +(-2.79675 - 1.61471i) q^{65} +(0.530717 - 1.64874i) q^{66} +(6.35213 + 11.0022i) q^{67} +(1.06563 - 1.84573i) q^{68} +(9.02254 - 8.16881i) q^{69} +(-0.101558 + 2.20930i) q^{70} +2.66448i q^{71} +(-1.75003 + 2.43668i) q^{72} +(10.7588 - 6.21158i) q^{73} +(-3.05069 + 1.76131i) q^{74} +(-7.28290 + 1.56890i) q^{75} -2.72420i q^{76} +(-0.121493 + 2.64296i) q^{77} +(4.49107 + 4.96044i) q^{78} +(2.81072 - 4.86831i) q^{79} +(-0.417958 - 0.723925i) q^{80} +(2.87481 + 8.52851i) q^{81} +(-0.723925 - 0.417958i) q^{82} -3.41567 q^{83} +(1.60297 - 4.29307i) q^{84} +1.78156 q^{85} +(8.53109 + 4.92543i) q^{86} +(11.9639 + 3.85110i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(0.355752 - 0.616180i) q^{89} +(-2.49541 - 0.248459i) q^{90} +(-8.60795 - 5.51178i) q^{91} -7.02699i q^{92} +(-2.04425 - 9.48951i) q^{93} +(10.1202 - 5.84290i) q^{94} +(1.97212 - 1.13860i) q^{95} +(0.364755 + 1.69321i) q^{96} +9.84612i q^{97} +(-0.642202 + 6.97048i) q^{98} +(-2.98524 - 0.297229i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9}+O(q^{10}) $ 20 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 2 * q^9	$ 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9} - 18 q^{10} - 6 q^{12} - 8 q^{15} - 10 q^{16} + 4 q^{18} + 36 q^{19} + 24 q^{21} - 20 q^{22} - 12 q^{25} - 22 q^{30} + 36 q^{31} - 4 q^{36} + 16 q^{37} + 4 q^{39} - 18 q^{40} + 32 q^{42} + 32 q^{43} + 24 q^{45} + 30 q^{46} - 42 q^{49} - 24 q^{52} - 36 q^{54} - 24 q^{57} + 32 q^{58} - 4 q^{60} + 42 q^{61} - 10 q^{63} - 20 q^{64} + 6 q^{66} - 10 q^{67} - 36 q^{70} - 4 q^{72} + 12 q^{73} - 108 q^{75} + 6 q^{79} + 42 q^{81} + 18 q^{82} + 18 q^{84} - 28 q^{85} + 36 q^{87} - 10 q^{88} - 112 q^{91} - 36 q^{93} + 42 q^{94} - 8 q^{99}+O(q^{100}) $ 20 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 2 * q^9 - 18 * q^10 - 6 * q^12 - 8 * q^15 - 10 * q^16 + 4 * q^18 + 36 * q^19 + 24 * q^21 - 20 * q^22 - 12 * q^25 - 22 * q^30 + 36 * q^31 - 4 * q^36 + 16 * q^37 + 4 * q^39 - 18 * q^40 + 32 * q^42 + 32 * q^43 + 24 * q^45 + 30 * q^46 - 42 * q^49 - 24 * q^52 - 36 * q^54 - 24 * q^57 + 32 * q^58 - 4 * q^60 + 42 * q^61 - 10 * q^63 - 20 * q^64 + 6 * q^66 - 10 * q^67 - 36 * q^70 - 4 * q^72 + 12 * q^73 - 108 * q^75 + 6 * q^79 + 42 * q^81 + 18 * q^82 + 18 * q^84 - 28 * q^85 + 36 * q^87 - 10 * q^88 - 112 * q^91 - 36 * q^93 + 42 * q^94 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.530717	+	1.64874i	−0.306410	+	0.951900i
$3$	−0.530717	+	1.64874i	−0.306410	+	0.951900i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.417958	+	0.723925i	−0.186917	+	0.323749i	−0.944221	−	0.329313i	$-0.893183\pi$
$5$	−0.417958	+	0.723925i	−0.186917	+	0.323749i	0.757304	+	0.653063i	$0.226516\pi$
$6$	1.28398	−	1.16249i	0.524184	−	0.474585i
$7$	−1.42670	+	2.22812i	−0.539240	+	0.842152i
$7$	−1.42670	+	2.22812i	−0.539240	+	0.842152i
$8$		−	1.00000i		−	0.353553i
$9$	−2.43668	−	1.75003i	−0.812226	−	0.583343i
$10$	0.723925	−	0.417958i	0.228925	−	0.132170i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$	−1.69321	+	0.364755i	−0.488787	+	0.105296i
$13$			3.86332i			1.07149i	0.844379	+	0.535746i	$0.179969\pi$
$13$			3.86332i			1.07149i	−0.844379	+	0.535746i	$0.820031\pi$
$14$	2.34962	−	1.21626i	0.627962	−	0.325060i
$15$	−0.971746	−	1.07330i	−0.250904	−	0.277126i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.06563	−	1.84573i	−0.258454	−	0.447656i	0.707374	−	0.706840i	$-0.249880\pi$
$17$	−1.06563	−	1.84573i	−0.258454	−	0.447656i	−0.965828	+	0.259184i	$0.916546\pi$
$18$	1.23521	+	2.73391i	0.291142	+	0.644388i
$19$	−2.35922	−	1.36210i	−0.541243	−	0.312487i	0.204339	−	0.978900i	$-0.434495\pi$
$19$	−2.35922	−	1.36210i	−0.541243	−	0.312487i	−0.745583	+	0.666413i	$0.767829\pi$
$20$	−0.835917			−0.186917
$21$	−2.91642	−	3.53475i	−0.636416	−	0.771346i
$22$	−1.00000			−0.213201
$23$	−6.08555	−	3.51349i	−1.26892	−	0.732614i	−0.294140	−	0.955762i	$-0.595033\pi$
$23$	−6.08555	−	3.51349i	−1.26892	−	0.732614i	−0.974785	+	0.223148i	$0.928367\pi$
$24$	1.64874	+	0.530717i	0.336547	+	0.108332i
$25$	2.15062	+	3.72499i	0.430124	+	0.744997i
$26$	1.93166	−	3.34573i	0.378829	−	0.656152i
$27$	4.17853	−	3.08868i	0.804158	−	0.594416i
$28$	−2.64296	−	0.121493i	−0.499473	−	0.0229600i
$29$		−	7.25640i		−	1.34748i	−0.738969	−	0.673740i	$-0.764687\pi$
$29$		−	7.25640i		−	1.34748i	0.738969	−	0.673740i	$-0.235313\pi$
$30$	0.304905	+	1.41538i	0.0556677	+	0.258412i
$31$	−4.85360	+	2.80223i	−0.871732	+	0.503295i	−0.867923	−	0.496698i	$-0.834546\pi$
$31$	−4.85360	+	2.80223i	−0.871732	+	0.503295i	−0.00380865	+	0.999993i	$0.501212\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	0.364755	+	1.69321i	0.0634957	+	0.294750i
$34$			2.13127i			0.365509i
$35$	−1.01670	−	1.96408i	−0.171853	−	0.331991i
$36$	0.297229	−	2.98524i	0.0495382	−	0.497540i
$37$	1.76131	−	3.05069i	0.289558	−	0.501530i	−0.684146	−	0.729345i	$-0.739825\pi$
$37$	1.76131	−	3.05069i	0.289558	−	0.501530i	0.973704	+	0.227815i	$0.0731583\pi$
$38$	1.36210	+	2.35922i	0.220962	+	0.382717i
$39$	−6.36960	−	2.05033i	−1.01995	−	0.328315i
$40$	0.723925	+	0.417958i	0.114463	+	0.0660850i
$41$	0.835917			0.130548			0.0652741	−	0.997867i	$-0.479208\pi$
$41$	0.835917			0.130548			0.0652741	+	0.997867i	$0.479208\pi$
$42$	0.758320	+	4.51940i	0.117011	+	0.697358i
$43$	−9.85086			−1.50224			−0.751121	−	0.660165i	$-0.770486\pi$
$43$	−9.85086			−1.50224			−0.751121	+	0.660165i	$0.770486\pi$
$44$	0.866025	+	0.500000i	0.130558	+	0.0753778i
$45$	2.28532	−	1.03253i	0.340675	−	0.153921i
$46$	3.51349	+	6.08555i	0.518036	+	0.897265i
$47$	−5.84290	+	10.1202i	−0.852274	+	1.47618i	0.0268770	+	0.999639i	$0.491444\pi$
$47$	−5.84290	+	10.1202i	−0.852274	+	1.47618i	−0.879151	+	0.476543i	$0.841890\pi$
$48$	−1.16249	−	1.28398i	−0.167791	−	0.185327i
$49$	−2.92908	−	6.35771i	−0.418440	−	0.908245i
$50$		−	4.30124i		−	0.608288i
$51$	3.60868	−	0.777390i	0.505316	−	0.108856i
$52$	−3.34573	+	1.93166i	−0.463969	+	0.267873i
$53$	−7.26395	+	4.19384i	−0.997780	+	0.576069i	−0.907591	−	0.419856i	$-0.862081\pi$
$53$	−7.26395	+	4.19384i	−0.997780	+	0.576069i	−0.0901894	+	0.995925i	$0.528747\pi$
$54$	−5.16305	+	0.585609i	−0.702602	+	0.0796914i
$55$			0.835917i			0.112715i
$56$	2.22812	+	1.42670i	0.297746	+	0.190650i
$57$	3.49783	−	3.16686i	0.463298	−	0.419460i
$58$	−3.62820	+	6.28423i	−0.476406	+	0.825159i
$59$	3.60897	+	6.25091i	0.469847	+	0.813799i	0.999406	−	0.0344741i	$-0.0109756\pi$
$59$	3.60897	+	6.25091i	0.469847	+	0.813799i	−0.529558	+	0.848274i	$0.677642\pi$
$60$	0.443635	−	1.37821i	0.0572731	−	0.177926i
$61$	−2.31656	−	1.33746i	−0.296605	−	0.171245i	0.344312	−	0.938855i	$-0.388112\pi$
$61$	−2.31656	−	1.33746i	−0.296605	−	0.171245i	−0.640917	+	0.767611i	$0.721446\pi$
$62$	5.60445			0.711766
$63$	7.37568	−	2.93247i	0.929248	−	0.369456i
$64$	−1.00000			−0.125000
$65$	−2.79675	−	1.61471i	−0.346895	−	0.200280i
$66$	0.530717	−	1.64874i	0.0653268	−	0.202946i
$67$	6.35213	+	11.0022i	0.776036	+	1.34413i	0.934211	+	0.356722i	$0.116106\pi$
$67$	6.35213	+	11.0022i	0.776036	+	1.34413i	−0.158175	+	0.987411i	$0.550561\pi$
$68$	1.06563	−	1.84573i	0.129227	−	0.223828i
$69$	9.02254	−	8.16881i	1.08619	−	0.983409i
$70$	−0.101558	+	2.20930i	−0.0121385	+	0.264061i
$71$			2.66448i			0.316215i	0.987422	+	0.158108i	$0.0505393\pi$
$71$			2.66448i			0.316215i	−0.987422	+	0.158108i	$0.949461\pi$
$72$	−1.75003	+	2.43668i	−0.206243	+	0.287165i
$73$	10.7588	−	6.21158i	1.25922	−	0.727011i	0.286297	−	0.958141i	$-0.407576\pi$
$73$	10.7588	−	6.21158i	1.25922	−	0.727011i	0.972923	+	0.231130i	$0.0742422\pi$
$74$	−3.05069	+	1.76131i	−0.354635	+	0.204749i
$75$	−7.28290	+	1.56890i	−0.840957	+	0.181161i
$76$		−	2.72420i		−	0.312487i
$77$	−0.121493	+	2.64296i	−0.0138454	+	0.301193i
$78$	4.49107	+	4.96044i	0.508514	+	0.561659i
$79$	2.81072	−	4.86831i	0.316231	−	0.547728i	−0.663467	−	0.748205i	$-0.730916\pi$
$79$	2.81072	−	4.86831i	0.316231	−	0.547728i	0.979698	+	0.200477i	$0.0642492\pi$
$80$	−0.417958	−	0.723925i	−0.0467292	−	0.0809373i
$81$	2.87481	+	8.52851i	0.319423	+	0.947612i
$82$	−0.723925	−	0.417958i	−0.0799442	−	0.0461558i
$83$	−3.41567			−0.374918			−0.187459	−	0.982272i	$-0.560025\pi$
$83$	−3.41567			−0.374918			−0.187459	+	0.982272i	$0.560025\pi$
$84$	1.60297	−	4.29307i	0.174899	−	0.468413i
$85$	1.78156			0.193238
$86$	8.53109	+	4.92543i	0.919931	+	0.531123i
$87$	11.9639	+	3.85110i	1.28267	+	0.412881i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	0.355752	−	0.616180i	0.0377096	−	0.0653150i	−0.846555	−	0.532302i	$-0.821327\pi$
$89$	0.355752	−	0.616180i	0.0377096	−	0.0653150i	0.884264	+	0.466987i	$0.154660\pi$
$90$	−2.49541	−	0.248459i	−0.263040	−	0.0261899i
$91$	−8.60795	−	5.51178i	−0.902359	−	0.577792i
$92$		−	7.02699i		−	0.732614i
$93$	−2.04425	−	9.48951i	−0.211979	−	0.984016i
$94$	10.1202	−	5.84290i	1.04382	−	0.602649i
$95$	1.97212	−	1.13860i	0.202335	−	0.116818i
$96$	0.364755	+	1.69321i	0.0372276	+	0.172812i
$97$			9.84612i			0.999722i	0.866106	+	0.499861i	$0.166616\pi$
$97$			9.84612i			0.999722i	−0.866106	+	0.499861i	$0.833384\pi$
$98$	−0.642202	+	6.97048i	−0.0648722	+	0.704125i
$99$	−2.98524	−	0.297229i	−0.300028	−	0.0298727i
$100$	−2.15062	+	3.72499i	−0.215062	+	0.372499i
$101$	3.31704	+	5.74529i	0.330058	+	0.571677i	0.982523	−	0.186142i	$-0.0595983\pi$
$101$	3.31704	+	5.74529i	0.330058	+	0.571677i	−0.652465	+	0.757819i	$0.726265\pi$
$102$	−3.51390	−	1.13110i	−0.347928	−	0.111996i
$103$	13.2128	+	7.62843i	1.30190	+	0.751651i	0.980729	−	0.195371i	$-0.0625910\pi$
$103$	13.2128	+	7.62843i	1.30190	+	0.751651i	0.321169	+	0.947022i	$0.395924\pi$
$104$	3.86332			0.378829
$105$	3.77784	−	0.633892i	0.368680	−	0.0618616i
$106$	8.38769			0.814684
$107$	3.22599	+	1.86253i	0.311868	+	0.180057i	0.647762	−	0.761843i	$-0.275705\pi$
$107$	3.22599	+	1.86253i	0.311868	+	0.180057i	−0.335894	+	0.941900i	$0.609038\pi$
$108$	4.76414	+	2.07437i	0.458429	+	0.199606i
$109$	−9.01132	−	15.6081i	−0.863128	−	1.49498i	−0.868894	−	0.494998i	$-0.835169\pi$
$109$	−9.01132	−	15.6081i	−0.863128	−	1.49498i	0.00576622	−	0.999983i	$-0.498165\pi$
$110$	0.417958	−	0.723925i	0.0398508	−	0.0690236i
$111$	4.09502	+	4.52300i	0.388682	+	0.429304i
$112$	−1.21626	−	2.34962i	−0.114926	−	0.222018i
$113$			13.9774i			1.31488i	0.753506	+	0.657441i	$0.228361\pi$
$113$			13.9774i			1.31488i	−0.753506	+	0.657441i	$0.771639\pi$
$114$	−4.61263	+	0.993664i	−0.432013	+	0.0930652i
$115$	5.08701	−	2.93699i	0.474366	−	0.273876i
$116$	6.28423	−	3.62820i	0.583476	−	0.336870i
$117$	6.76091	−	9.41366i	0.625047	−	0.870293i
$118$		−	7.21793i		−	0.664464i
$119$	5.63285	+	0.258934i	0.516363	+	0.0237364i
$120$	−1.07330	+	0.971746i	−0.0979788	+	0.0887079i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	1.33746	+	2.31656i	0.121088	+	0.209731i
$123$	−0.443635	+	1.37821i	−0.0400013	+	0.124269i
$124$	−4.85360	−	2.80223i	−0.435866	−	0.251647i
$125$	−7.77507			−0.695423
$126$	−7.85376	−	1.14825i	−0.699668	−	0.102294i
$127$	−10.4325			−0.925737			−0.462869	−	0.886427i	$-0.653180\pi$
$127$	−10.4325			−0.925737			−0.462869	+	0.886427i	$0.653180\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	5.22802	−	16.2415i	0.460301	−	1.42998i
$130$	1.61471	+	2.79675i	0.141619	+	0.245292i
$131$	5.20268	−	9.01131i	0.454561	−	0.787322i	−0.544102	−	0.839019i	$-0.683130\pi$
$131$	5.20268	−	9.01131i	0.454561	−	0.787322i	0.998663	+	0.0516968i	$0.0164629\pi$
$132$	−1.28398	+	1.16249i	−0.111756	+	0.101182i
$133$	6.40082	−	3.31334i	0.555022	−	0.287303i
$134$		−	12.7043i		−	1.09748i
$135$	0.489521	+	4.31588i	0.0421313	+	0.371452i
$136$	−1.84573	+	1.06563i	−0.158270	+	0.0913773i
$137$	5.61907	−	3.24417i	0.480070	−	0.277168i	−0.240376	−	0.970680i	$-0.577271\pi$
$137$	5.61907	−	3.24417i	0.480070	−	0.277168i	0.720446	+	0.693511i	$0.243937\pi$
$138$	−11.8982	+	2.56313i	−1.01284	+	0.218188i
$139$			15.0423i			1.27587i	0.770091	+	0.637934i	$0.220211\pi$
$139$			15.0423i			1.27587i	−0.770091	+	0.637934i	$0.779789\pi$
$140$	1.19260	−	1.86253i	0.100793	−	0.157412i
$141$	−13.5846	−	15.0044i	−1.14403	−	1.26360i
$142$	1.33224	−	2.30750i	0.111799	−	0.193641i
$143$	1.93166	+	3.34573i	0.161533	+	0.279784i
$144$	2.73391	−	1.23521i	0.227826	−	0.102934i
$145$	5.25309	+	3.03287i	0.436246	+	0.251866i
$146$	−12.4232			−1.02815
$147$	12.0367	−	1.45513i	0.992772	−	0.120017i
$148$	3.52263			0.289558
$149$	−4.20728	−	2.42908i	−0.344674	−	0.198998i	0.317663	−	0.948204i	$-0.397102\pi$
$149$	−4.20728	−	2.42908i	−0.344674	−	0.198998i	−0.662337	+	0.749206i	$0.730435\pi$
$150$	7.09163	+	2.28274i	0.579029	+	0.186385i
$151$	8.45368	+	14.6422i	0.687951	+	1.19157i	0.972500	+	0.232904i	$0.0748229\pi$
$151$	8.45368	+	14.6422i	0.687951	+	1.19157i	−0.284549	+	0.958662i	$0.591844\pi$
$152$	−1.36210	+	2.35922i	−0.110481	+	0.191358i
$153$	−0.633475	+	6.36234i	−0.0512134	+	0.514365i
$154$	1.42670	−	2.22812i	0.114966	−	0.179547i
$155$		−	4.68486i		−	0.376297i
$156$	−1.40916	−	6.54140i	−0.112823	−	0.523731i
$157$	3.28571	−	1.89701i	0.262229	−	0.151398i	−0.363122	−	0.931742i	$-0.618289\pi$
$157$	3.28571	−	1.89701i	0.262229	−	0.151398i	0.625351	+	0.780344i	$0.284956\pi$
$158$	−4.86831	+	2.81072i	−0.387302	+	0.223609i
$159$	−3.05945	−	14.2021i	−0.242630	−	1.12630i
$160$			0.835917i			0.0660850i
$161$	16.5107	−	8.54667i	1.30123	−	0.673572i
$162$	1.77460	−	8.82331i	0.139426	−	0.693225i
$163$	3.12271	−	5.40870i	0.244590	−	0.423642i	−0.717426	−	0.696634i	$-0.754680\pi$
$163$	3.12271	−	5.40870i	0.244590	−	0.423642i	0.962016	+	0.272992i	$0.0880134\pi$
$164$	0.417958	+	0.723925i	0.0326371	+	0.0565291i
$165$	−1.37821	−	0.443635i	−0.107293	−	0.0345370i
$166$	2.95806	+	1.70784i	0.229590	+	0.132554i
$167$	3.37801			0.261398			0.130699	−	0.991422i	$-0.458278\pi$
$167$	3.37801			0.261398			0.130699	+	0.991422i	$0.458278\pi$
$168$	−3.53475	+	2.91642i	−0.272712	+	0.225007i
$169$	−1.92522			−0.148094
$170$	−1.54288	−	0.890781i	−0.118333	−	0.0683198i
$171$	3.36496	+	7.44771i	0.257325	+	0.569540i
$172$	−4.92543	−	8.53109i	−0.375560	−	0.650490i
$173$	−5.09256	+	8.82057i	−0.387180	+	0.670615i	−0.992069	−	0.125694i	$-0.959884\pi$
$173$	−5.09256	+	8.82057i	−0.387180	+	0.670615i	0.604889	+	0.796310i	$0.293217\pi$
$174$	−8.43550	−	9.31710i	−0.639494	−	0.706328i
$175$	−11.3680	−	0.522570i	−0.859341	−	0.0395026i
$176$			1.00000i			0.0753778i
$177$	−12.2215	+	2.63278i	−0.918621	+	0.197892i
$178$	−0.616180	+	0.355752i	−0.0461846	+	0.0266647i
$179$	−16.5044	+	9.52883i	−1.23360	+	0.712218i	−0.967778	−	0.251805i	$-0.918976\pi$
$179$	−16.5044	+	9.52883i	−1.23360	+	0.712218i	−0.265820	+	0.964023i	$0.585643\pi$
$180$	2.03686	+	1.46288i	0.151819	+	0.109036i
$181$			21.3997i			1.59063i	0.606199	+	0.795313i	$0.292694\pi$
$181$			21.3997i			1.59063i	−0.606199	+	0.795313i	$0.707306\pi$
$182$	4.69882	+	9.07732i	0.348299	+	0.672856i
$183$	3.43456	−	3.10958i	0.253890	−	0.229867i
$184$	−3.51349	+	6.08555i	−0.259018	+	0.448633i
$185$	1.47231	+	2.55012i	0.108247	+	0.187489i
$186$	−2.97438	+	9.24028i	−0.218092	+	0.677530i
$187$	−1.84573	−	1.06563i	−0.134973	−	0.0779268i
$188$	−11.6858			−0.852274
$189$	0.920469	+	13.7169i	0.0669543	+	0.997756i
$190$	−2.27720			−0.165206
$191$	−7.70390	−	4.44785i	−0.557435	−	0.321835i	0.194680	−	0.980867i	$-0.437633\pi$
$191$	−7.70390	−	4.44785i	−0.557435	−	0.321835i	−0.752115	+	0.659032i	$0.770966\pi$
$192$	0.530717	−	1.64874i	0.0383012	−	0.118987i
$193$	3.07676	+	5.32910i	0.221470	+	0.383597i	0.955254	−	0.295785i	$-0.0955813\pi$
$193$	3.07676	+	5.32910i	0.221470	+	0.383597i	−0.733785	+	0.679382i	$0.762248\pi$
$194$	4.92306	−	8.52699i	0.353455	−	0.612202i
$195$	4.14651	−	3.75416i	0.296938	−	0.268841i
$196$	4.04140	−	5.71551i	0.288672	−	0.408251i
$197$			19.4741i			1.38748i	0.720228	+	0.693738i	$0.244037\pi$
$197$			19.4741i			1.38748i	−0.720228	+	0.693738i	$0.755963\pi$
$198$	2.43668	+	1.75003i	0.173167	+	0.124369i
$199$	−11.4944	+	6.63628i	−0.814815	+	0.470433i	−0.848625	−	0.528995i	$-0.822569\pi$
$199$	−11.4944	+	6.63628i	−0.814815	+	0.470433i	0.0338105	+	0.999428i	$0.489236\pi$
$200$	3.72499	−	2.15062i	0.263396	−	0.152072i
$201$	−21.5109	+	4.63394i	−1.51726	+	0.326853i
$202$		−	6.63409i		−	0.466773i
$203$	16.1682	+	10.3527i	1.13478	+	0.726615i
$204$	2.47758	+	2.73651i	0.173465	+	0.191594i
$205$	−0.349379	+	0.605141i	−0.0244017	+	0.0422649i
$206$	−7.62843	−	13.2128i	−0.531498	−	0.920581i
$207$	8.67982	+	19.2111i	0.603289	+	1.33527i
$208$	−3.34573	−	1.93166i	−0.231985	−	0.133936i
$209$	−2.72420			−0.188437
$210$	−3.58865	−	1.33995i	−0.247641	−	0.0924656i
$211$	−16.8085			−1.15715			−0.578574	−	0.815630i	$-0.696391\pi$
$211$	−16.8085			−1.15715			−0.578574	+	0.815630i	$0.696391\pi$
$212$	−7.26395	−	4.19384i	−0.498890	−	0.288034i
$213$	−4.39302	−	1.41408i	−0.301005	−	0.0968913i
$214$	−1.86253	−	3.22599i	−0.127320	−	0.220524i
$215$	4.11725	−	7.13129i	0.280794	−	0.486350i
$216$	−3.08868	−	4.17853i	−0.210158	−	0.284313i
$217$	0.680901	−	14.8123i	0.0462226	−	1.00553i
$218$			18.0226i			1.22065i
$219$	4.53141	+	21.0350i	0.306204	+	1.42141i
$220$	−0.723925	+	0.417958i	−0.0488070	+	0.0281788i
$221$	7.13065	−	4.11688i	0.479659	−	0.276931i
$222$	−1.28490	−	5.96454i	−0.0862365	−	0.400314i
$223$		−	5.99627i		−	0.401540i	−0.979638	−	0.200770i	$-0.935656\pi$
$223$		−	5.99627i		−	0.401540i	0.979638	−	0.200770i	$-0.0643444\pi$
$224$	−0.121493	+	2.64296i	−0.00811758	+	0.176590i
$225$	1.27846	−	12.8402i	0.0852303	−	0.856016i
$226$	6.98869	−	12.1048i	0.464881	−	0.805197i
$227$	−3.71163	−	6.42873i	−0.246350	−	0.426690i	0.716161	−	0.697935i	$-0.245898\pi$
$227$	−3.71163	−	6.42873i	−0.246350	−	0.426690i	−0.962510	+	0.271246i	$0.912564\pi$
$228$	4.49149	+	1.44578i	0.297456	+	0.0957490i
$229$	−10.1281	−	5.84744i	−0.669281	−	0.386410i	0.126523	−	0.991964i	$-0.459618\pi$
$229$	−10.1281	−	5.84744i	−0.669281	−	0.386410i	−0.795804	+	0.605554i	$0.792952\pi$
$230$	−5.87398			−0.387319
$231$	−4.29307	−	1.60297i	−0.282463	−	0.105468i
$232$	−7.25640			−0.476406
$233$	−12.0947	−	6.98286i	−0.792348	−	0.457462i	0.0484405	−	0.998826i	$-0.484575\pi$
$233$	−12.0947	−	6.98286i	−0.792348	−	0.457462i	−0.840788	+	0.541364i	$0.817908\pi$
$234$	−10.5620	+	4.77201i	−0.690457	+	0.311956i
$235$	−4.88418	−	8.45964i	−0.318609	−	0.551846i
$236$	−3.60897	+	6.25091i	−0.234924	+	0.406900i
$237$	6.53488	+	7.21785i	0.424486	+	0.468849i
$238$	−4.74873	−	3.04067i	−0.307814	−	0.197097i
$239$			9.25345i			0.598556i	0.954166	+	0.299278i	$0.0967458\pi$
$239$			9.25345i			0.598556i	−0.954166	+	0.299278i	$0.903254\pi$
$240$	1.41538	−	0.304905i	0.0913625	−	0.0196815i
$241$	−4.12181	+	2.37973i	−0.265509	+	0.153292i	−0.626845	−	0.779144i	$-0.715654\pi$
$241$	−4.12181	+	2.37973i	−0.265509	+	0.153292i	0.361336	+	0.932436i	$0.382321\pi$
$242$	−0.866025	+	0.500000i	−0.0556702	+	0.0321412i
$243$	−15.5870	+	0.213576i	−0.999906	+	0.0137009i
$244$		−	2.67493i		−	0.171245i
$245$	5.82674	+	0.536827i	0.372257	+	0.0342966i
$246$	1.07330	−	0.971746i	0.0684314	−	0.0619563i
$247$	5.26222	−	9.11443i	0.334827	−	0.579938i
$248$	2.80223	+	4.85360i	0.177942	+	0.308204i
$249$	1.81275	−	5.63155i	0.114879	−	0.356885i
$250$	6.73341	+	3.88753i	0.425858	+	0.245869i
$251$	−20.1964			−1.27478			−0.637392	−	0.770540i	$-0.719987\pi$
$251$	−20.1964			−1.27478			−0.637392	+	0.770540i	$0.719987\pi$
$252$	6.22743	+	4.92129i	0.392291	+	0.310012i
$253$	−7.02699			−0.441783
$254$	9.03483	+	5.21626i	0.566896	+	0.327298i
$255$	−0.945506	+	2.93733i	−0.0592099	+	0.183943i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	14.1698	−	24.5429i	0.883890	−	1.53094i	0.0369100	−	0.999319i	$-0.488249\pi$
$257$	14.1698	−	24.5429i	0.883890	−	1.53094i	0.846980	−	0.531624i	$-0.178418\pi$
$258$	−12.6483	+	11.4515i	−0.787451	+	0.712941i
$259$	4.28445	+	8.27683i	0.266223	+	0.514297i
$260$		−	3.22941i		−	0.200280i
$261$	−12.6989	+	17.6815i	−0.786042	+	1.09446i
$262$	−9.01131	+	5.20268i	−0.556721	+	0.321423i
$263$	−16.5761	+	9.57022i	−1.02213	+	0.590125i	−0.914719	−	0.404090i	$-0.867588\pi$
$263$	−16.5761	+	9.57022i	−1.02213	+	0.590125i	−0.107407	+	0.994215i	$0.534255\pi$
$264$	1.69321	−	0.364755i	0.104210	−	0.0224491i
$265$		−	7.01141i		−	0.430707i
$266$	−7.19995	−	0.330971i	−0.441457	−	0.0202931i
$267$	0.827116	+	0.913559i	0.0506187	+	0.0559089i
$268$	−6.35213	+	11.0022i	−0.388018	+	0.672067i
$269$	−4.24434	−	7.35142i	−0.258782	−	0.448224i	0.707134	−	0.707080i	$-0.249988\pi$
$269$	−4.24434	−	7.35142i	−0.258782	−	0.448224i	−0.965916	+	0.258856i	$0.916655\pi$
$270$	1.73400	−	3.98242i	0.105528	−	0.242362i
$271$	13.3069	+	7.68275i	0.808338	+	0.466694i	0.846378	−	0.532582i	$-0.178778\pi$
$271$	13.3069	+	7.68275i	0.808338	+	0.466694i	−0.0380407	+	0.999276i	$0.512112\pi$
$272$	2.13127			0.129227
$273$	13.6559	−	11.2671i	0.826491	−	0.681914i
$274$	−6.48835			−0.391975
$275$	3.72499	+	2.15062i	0.224625	+	0.129687i
$276$	11.5857	+	3.72934i	0.697375	+	0.224480i
$277$	10.1508	+	17.5818i	0.609904	+	1.05638i	0.991256	+	0.131955i	$0.0421254\pi$
$277$	10.1508	+	17.5818i	0.609904	+	1.05638i	−0.381352	+	0.924430i	$0.624541\pi$
$278$	7.52113	−	13.0270i	0.451088	−	0.781307i
$279$	16.7306	+	1.66581i	1.00164	+	0.0997293i
$280$	−1.96408	+	1.01670i	−0.117377	+	0.0607592i
$281$		−	11.7320i		−	0.699870i	−0.936774	−	0.349935i	$-0.886204\pi$
$281$		−	11.7320i		−	0.699870i	0.936774	−	0.349935i	$-0.113796\pi$
$282$	4.26245	+	19.7865i	0.253825	+	1.17827i
$283$	12.3521	−	7.13151i	0.734258	−	0.423924i	−0.0857197	−	0.996319i	$-0.527319\pi$
$283$	12.3521	−	7.13151i	0.734258	−	0.423924i	0.819978	+	0.572395i	$0.193986\pi$
$284$	−2.30750	+	1.33224i	−0.136925	+	0.0790538i
$285$	0.830621	+	3.85578i	0.0492017	+	0.228397i
$286$		−	3.86332i		−	0.228443i
$287$	−1.19260	+	1.86253i	−0.0703969	+	0.109941i
$288$	−2.98524	−	0.297229i	−0.175907	−	0.0175144i
$289$	6.22885	−	10.7887i	0.366403	−	0.634629i
$290$	−3.03287	−	5.25309i	−0.178096	−	0.308472i
$291$	−16.2337	−	5.22550i	−0.951635	−	0.306324i
$292$	10.7588	+	6.21158i	0.629610	+	0.363505i
$293$	−6.45384			−0.377038			−0.188519	−	0.982070i	$-0.560369\pi$
$293$	−6.45384			−0.377038			−0.188519	+	0.982070i	$0.560369\pi$
$294$	−11.1517	−	4.75818i	−0.650379	−	0.277502i
$295$	−6.03359			−0.351289
$296$	−3.05069	−	1.76131i	−0.177317	−	0.102374i
$297$	2.07437	−	4.76414i	0.120367	−	0.276443i
$298$	2.42908	+	4.20728i	0.140713	+	0.243721i
$299$	13.5737	−	23.5104i	0.784990	−	1.35964i
$300$	−5.00016	−	5.52273i	−0.288684	−	0.318855i
$301$	14.0542	−	21.9489i	0.810070	−	1.26512i
$302$		−	16.9074i		−	0.972910i
$303$	−11.2329	+	2.41981i	−0.645313	+	0.139015i
$304$	2.35922	−	1.36210i	0.135311	−	0.0781217i
$305$	1.93645	−	1.11801i	0.110881	−	0.0640170i
$306$	3.72978	−	5.19321i	0.213217	−	0.296876i
$307$		−	11.6367i		−	0.664141i	−0.943255	−	0.332071i	$-0.892253\pi$
$307$		−	11.6367i		−	0.664141i	0.943255	−	0.332071i	$-0.107747\pi$
$308$	−2.34962	+	1.21626i	−0.133882	+	0.0693031i
$309$	−19.5896	+	17.7360i	−1.11441	+	1.00896i
$310$	−2.34243	+	4.05721i	−0.133041	+	0.230434i
$311$	14.3269	+	24.8149i	0.812405	+	1.40713i	0.911177	+	0.412016i	$0.135175\pi$
$311$	14.3269	+	24.8149i	0.812405	+	1.40713i	−0.0987717	+	0.995110i	$0.531491\pi$
$312$	−2.05033	+	6.36960i	−0.116077	+	0.360608i
$313$	19.4240	+	11.2144i	1.09791	+	0.633878i	0.935671	−	0.352874i	$-0.114796\pi$
$313$	19.4240	+	11.2144i	1.09791	+	0.633878i	0.162238	+	0.986752i	$0.448129\pi$
$314$	−3.79402			−0.214109
$315$	−0.959842	+	6.56509i	−0.0540810	+	0.369901i
$316$	5.62145			0.316231
$317$	9.12201	+	5.26659i	0.512343	+	0.295801i	0.733796	−	0.679370i	$-0.237747\pi$
$317$	9.12201	+	5.26659i	0.512343	+	0.295801i	−0.221453	+	0.975171i	$0.571080\pi$
$318$	−4.45149	+	13.8291i	−0.249627	+	0.775498i
$319$	−3.62820	−	6.28423i	−0.203140	−	0.351849i
$320$	0.417958	−	0.723925i	0.0233646	−	0.0404687i
$321$	−4.78291	+	4.33034i	−0.266956	+	0.241696i
$322$	−18.5720	−	0.853729i	−1.03498	−	0.0475764i
$323$			5.80599i			0.323054i
$324$	−5.94850	+	6.75391i	−0.330472	+	0.375217i
$325$	−14.3908	+	8.30853i	−0.798258	+	0.460875i
$326$	−5.40870	+	3.12271i	−0.299560	+	0.172951i
$327$	30.5161	−	6.57384i	1.68754	−	0.363534i
$328$		−	0.835917i		−	0.0461558i
$329$	−14.2130	−	27.4571i	−0.783589	−	1.51376i
$330$	0.971746	+	1.07330i	0.0534929	+	0.0590834i
$331$	15.4645	−	26.7852i	0.850003	−	1.47225i	−0.0312013	−	0.999513i	$-0.509933\pi$
$331$	15.4645	−	26.7852i	0.850003	−	1.47225i	0.881204	−	0.472735i	$-0.156733\pi$
$332$	−1.70784	−	2.95806i	−0.0937296	−	0.162344i
$333$	−9.63054	+	4.35119i	−0.527750	+	0.238444i
$334$	−2.92544	−	1.68901i	−0.160073	−	0.0924183i
$335$	−10.6197			−0.580216
$336$	4.51940	−	0.758320i	0.246553	−	0.0413697i
$337$	8.74219			0.476217			0.238109	−	0.971239i	$-0.423473\pi$
$337$	8.74219			0.476217			0.238109	+	0.971239i	$0.423473\pi$
$338$	1.66729	+	0.962611i	0.0906887	+	0.0523591i
$339$	−23.0451	−	7.41804i	−1.25164	−	0.402892i
$340$	0.890781	+	1.54288i	0.0483094	+	0.0836743i
$341$	−2.80223	+	4.85360i	−0.151749	+	0.262837i
$342$	0.809711	−	8.13238i	0.0437842	−	0.439749i
$343$	18.3447	+	2.54418i	0.990519	+	0.137373i
$344$			9.85086i			0.531123i
$345$	2.14256	+	9.94587i	0.115352	+	0.535467i
$346$	8.82057	−	5.09256i	0.474197	−	0.273778i
$347$	1.10854	−	0.640018i	0.0595098	−	0.0343580i	−0.469950	−	0.882693i	$-0.655728\pi$
$347$	1.10854	−	0.640018i	0.0595098	−	0.0343580i	0.529460	+	0.848335i	$0.322395\pi$
$348$	2.64681	+	12.2866i	0.141884	+	0.658631i
$349$		−	13.1540i		−	0.704117i	−0.935978	−	0.352058i	$-0.885482\pi$
$349$		−	13.1540i		−	0.704117i	0.935978	−	0.352058i	$-0.114518\pi$
$350$	9.58370	+	6.13657i	0.512271	+	0.328013i
$351$	11.9325	+	16.1430i	0.636912	+	0.861648i
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	−7.51019	−	13.0080i	−0.399727	−	0.692347i	0.593965	−	0.804491i	$-0.297562\pi$
$353$	−7.51019	−	13.0080i	−0.399727	−	0.692347i	−0.993692	+	0.112143i	$0.964228\pi$
$354$	11.9005	+	3.83068i	0.632504	+	0.203598i
$355$	−1.92888	−	1.11364i	−0.102374	−	0.0591059i
$356$	0.711503			0.0377096
$357$	−3.41637	+	9.14968i	−0.180813	+	0.484253i
$358$	19.0577			1.00723
$359$	−27.0726	−	15.6304i	−1.42884	−	0.824940i	−0.431809	−	0.901965i	$-0.642125\pi$
$359$	−27.0726	−	15.6304i	−1.42884	−	0.824940i	−0.997029	+	0.0770249i	$0.975458\pi$
$360$	−1.03253	−	2.28532i	−0.0544193	−	0.120447i
$361$	−5.78937	−	10.0275i	−0.304704	−	0.527763i
$362$	10.6998	−	18.5327i	0.562371	−	0.974056i
$363$	1.16249	+	1.28398i	0.0610150	+	0.0673917i
$364$	0.469366	−	10.2106i	0.0246014	−	0.535181i
$365$			10.3847i			0.543562i
$366$	−4.52921	+	0.975693i	−0.236746	+	0.0510003i
$367$	−8.94931	+	5.16689i	−0.467150	+	0.269709i	−0.715046	−	0.699077i	$-0.753594\pi$
$367$	−8.94931	+	5.16689i	−0.467150	+	0.269709i	0.247896	+	0.968787i	$0.420261\pi$
$368$	6.08555	−	3.51349i	0.317231	−	0.183154i
$369$	−2.03686	−	1.46288i	−0.106035	−	0.0761544i
$370$		−	2.94462i		−	0.153084i
$371$	1.01904	−	22.1683i	0.0529061	−	1.15092i
$372$	7.19603	−	6.51513i	0.373097	−	0.337794i
$373$	−6.99037	+	12.1077i	−0.361947	+	0.626911i	−0.988281	−	0.152644i	$-0.951221\pi$
$373$	−6.99037	+	12.1077i	−0.361947	+	0.626911i	0.626334	+	0.779555i	$0.284555\pi$
$374$	1.06563	+	1.84573i	0.0551026	+	0.0954405i
$375$	4.12636	−	12.8191i	0.213084	−	0.661973i
$376$	10.1202	+	5.84290i	0.521909	+	0.301324i
$377$	28.0338			1.44381
$378$	6.06129	−	12.3394i	0.311759	−	0.634670i
$379$	−2.40372			−0.123471			−0.0617353	−	0.998093i	$-0.519663\pi$
$379$	−2.40372			−0.123471			−0.0617353	+	0.998093i	$0.519663\pi$
$380$	1.97212	+	1.13860i	0.101167	+	0.0584090i
$381$	5.53672	−	17.2005i	0.283655	−	0.881209i
$382$	4.44785	+	7.70390i	0.227572	+	0.394166i
$383$	−11.4425	+	19.8189i	−0.584683	+	1.01270i	0.410232	+	0.911981i	$0.365448\pi$
$383$	−11.4425	+	19.8189i	−0.584683	+	1.01270i	−0.994915	+	0.100720i	$0.967886\pi$
$384$	−1.28398	+	1.16249i	−0.0655230	+	0.0593231i
$385$	−1.86253	−	1.19260i	−0.0949232	−	0.0607805i
$386$		−	6.15351i		−	0.313206i
$387$	24.0034	+	17.2393i	1.22016	+	0.876322i
$388$	−8.52699	+	4.92306i	−0.432892	+	0.249930i
$389$	15.3333	−	8.85268i	0.777428	−	0.448849i	−0.0580897	−	0.998311i	$-0.518501\pi$
$389$	15.3333	−	8.85268i	0.777428	−	0.448849i	0.835518	+	0.549463i	$0.185168\pi$
$390$	−5.46807	+	1.17794i	−0.276886	+	0.0596475i
$391$			14.9764i			0.757388i
$392$	−6.35771	+	2.92908i	−0.321113	+	0.147941i
$393$	12.0961	+	13.3603i	0.610170	+	0.673939i
$394$	9.73707	−	16.8651i	0.490547	−	0.849652i
$395$	2.34953	+	4.06951i	0.118218	+	0.204759i
$396$	−1.23521	−	2.73391i	−0.0620717	−	0.137384i
$397$	−31.0739	−	17.9405i	−1.55955	−	0.900408i	−0.997299	−	0.0734435i	$-0.976601\pi$
$397$	−31.0739	−	17.9405i	−1.55955	−	0.900408i	−0.562254	−	0.826965i	$-0.690066\pi$
$398$	13.2726			0.665293
$399$	2.06581	+	12.3117i	0.103420	+	0.616358i
$400$	−4.30124			−0.215062
$401$	22.4661	+	12.9708i	1.12191	+	0.647733i	0.941887	−	0.335931i	$-0.109051\pi$
$401$	22.4661	+	12.9708i	1.12191	+	0.647733i	0.180019	+	0.983663i	$0.442384\pi$
$402$	20.9460	+	6.74236i	1.04469	+	0.336279i
$403$	−10.8259	−	18.7510i	−0.539276	−	0.934054i
$404$	−3.31704	+	5.74529i	−0.165029	+	0.285839i
$405$	−7.37555	−	1.48342i	−0.366494	−	0.0737117i
$406$	−8.82570	−	17.0498i	−0.438012	−	0.846165i
$407$		−	3.52263i		−	0.174610i
$408$	−0.777390	−	3.60868i	−0.0384865	−	0.178656i
$409$	8.55454	−	4.93897i	0.422995	−	0.244216i	−0.273363	−	0.961911i	$-0.588136\pi$
$409$	8.55454	−	4.93897i	0.422995	−	0.244216i	0.696358	+	0.717695i	$0.254803\pi$
$410$	0.605141	−	0.349379i	0.0298858	−	0.0172546i
$411$	2.36666	+	10.9861i	0.116739	+	0.541905i
$412$			15.2569i			0.751651i
$413$	−19.0767	−	0.876927i	−0.938703	−	0.0431508i
$414$	2.08863	−	20.9772i	0.102650	−	1.03098i
$415$	1.42761	−	2.47269i	0.0700785	−	0.121380i
$416$	1.93166	+	3.34573i	0.0947074	+	0.164038i
$417$	−24.8008	−	7.98319i	−1.21450	−	0.390939i
$418$	2.35922	+	1.36210i	0.115393	+	0.0666224i
$419$	7.14212			0.348916			0.174458	−	0.984665i	$-0.444183\pi$
$419$	7.14212			0.348916			0.174458	+	0.984665i	$0.444183\pi$
$420$	2.43789	+	2.95476i	0.118957	+	0.144178i
$421$	2.83262			0.138053			0.0690267	−	0.997615i	$-0.478011\pi$
$421$	2.83262			0.138053			0.0690267	+	0.997615i	$0.478011\pi$
$422$	14.5566	+	8.40427i	0.708606	+	0.409114i
$423$	31.9479	−	14.4344i	1.55336	−	0.701826i
$424$	4.19384	+	7.26395i	0.203671	+	0.352769i
$425$	4.58355	−	7.93894i	0.222335	−	0.385095i
$426$	3.09743	+	3.42114i	0.150071	+	0.165755i
$427$	6.28506	−	3.25342i	0.304155	−	0.157444i
$428$			3.72505i			0.180057i
$429$	−6.54140	+	1.40916i	−0.315822	+	0.0680351i
$430$	−7.13129	+	4.11725i	−0.343901	+	0.198551i
$431$	22.0931	−	12.7555i	1.06419	−	0.614410i	0.137601	−	0.990488i	$-0.456061\pi$
$431$	22.0931	−	12.7555i	1.06419	−	0.614410i	0.926588	+	0.376078i	$0.122728\pi$
$432$	0.585609	+	5.16305i	0.0281752	+	0.248407i
$433$		−	17.6085i		−	0.846213i	−0.906080	−	0.423106i	$-0.860940\pi$
$433$		−	17.6085i		−	0.846213i	0.906080	−	0.423106i	$-0.139060\pi$
$434$	−7.99585	+	12.4874i	−0.383813	+	0.599415i
$435$	−7.78832	+	7.05138i	−0.373421	+	0.338088i
$436$	9.01132	−	15.6081i	0.431564	−	0.747491i
$437$	9.57145	+	16.5782i	0.457865	+	0.793045i
$438$	6.59319	−	20.4826i	0.315035	−	0.978695i
$439$	20.3880	+	11.7710i	0.973068	+	0.561801i	0.900170	−	0.435538i	$-0.143442\pi$
$439$	20.3880	+	11.7710i	0.973068	+	0.561801i	0.0728977	+	0.997339i	$0.476775\pi$
$440$	0.835917			0.0398508
$441$	−3.98896	+	20.6177i	−0.189950	+	0.981794i
$442$	−8.23376			−0.391640
$443$	−8.86868	−	5.12033i	−0.421363	−	0.243274i	0.274297	−	0.961645i	$-0.411555\pi$
$443$	−8.86868	−	5.12033i	−0.421363	−	0.243274i	−0.695661	+	0.718371i	$0.744888\pi$
$444$	−1.86952	+	5.80789i	−0.0887235	+	0.275630i
$445$	0.297379	+	0.515075i	0.0140971	+	0.0244169i
$446$	−2.99814	+	5.19292i	−0.141966	+	0.245892i
$447$	6.23779	−	5.64756i	0.295037	−	0.267120i
$448$	1.42670	−	2.22812i	0.0674051	−	0.105269i
$449$			17.4205i			0.822123i	0.911608	+	0.411061i	$0.134842\pi$
$449$			17.4205i			0.822123i	−0.911608	+	0.411061i	$0.865158\pi$
$450$	−7.52729	+	10.4807i	−0.354840	+	0.494067i
$451$	0.723925	−	0.417958i	0.0340883	−	0.0196809i
$452$	−12.1048	+	6.98869i	−0.569360	+	0.328720i
$453$	−28.6277	+	6.16704i	−1.34505	+	0.289753i
$454$			7.42326i			0.348391i
$455$	7.58788	−	3.92782i	0.355725	−	0.184139i
$456$	−3.16686	−	3.49783i	−0.148302	−	0.163801i
$457$	−3.44330	+	5.96396i	−0.161071	+	0.278982i	−0.935253	−	0.353980i	$-0.884828\pi$
$457$	−3.44330	+	5.96396i	−0.161071	+	0.278982i	0.774182	+	0.632963i	$0.218161\pi$
$458$	5.84744	+	10.1281i	0.273233	+	0.473253i
$459$	−10.1536	−	4.42104i	−0.473931	−	0.206356i
$460$	5.08701	+	2.93699i	0.237183	+	0.136938i
$461$	6.62247			0.308439			0.154220	−	0.988037i	$-0.450714\pi$
$461$	6.62247			0.308439			0.154220	+	0.988037i	$0.450714\pi$
$462$	2.91642	+	3.53475i	0.135684	+	0.164452i
$463$	21.3829			0.993749			0.496874	−	0.867822i	$-0.334481\pi$
$463$	21.3829			0.993749			0.496874	+	0.867822i	$0.334481\pi$
$464$	6.28423	+	3.62820i	0.291738	+	0.168435i
$465$	7.72411	+	2.48633i	0.358197	+	0.115301i
$466$	6.98286	+	12.0947i	0.323475	+	0.560275i
$467$	−12.4871	+	21.6284i	−0.577836	+	1.00084i	0.417891	+	0.908497i	$0.362769\pi$
$467$	−12.4871	+	21.6284i	−0.577836	+	1.00084i	−0.995727	+	0.0923444i	$0.970564\pi$
$468$	11.5329	+	1.14829i	0.533110	+	0.0530798i
$469$	−33.5768	−	1.54348i	−1.55043	−	0.0712711i
$470$			9.76835i			0.450581i
$471$	1.38389	+	6.42406i	0.0637661	+	0.296005i
$472$	6.25091	−	3.60897i	0.287722	−	0.166116i
$473$	−8.53109	+	4.92543i	−0.392260	+	0.226471i
$474$	−2.05045	−	9.51828i	−0.0941803	−	0.437189i
$475$		−	11.7174i		−	0.537633i
$476$	2.59218	+	5.00766i	0.118813	+	0.229526i
$477$	25.0392	+	2.49307i	1.14647	+	0.114150i
$478$	4.62673	−	8.01372i	0.211622	−	0.366539i
$479$	−14.4998	−	25.1144i	−0.662512	−	1.14750i	−0.979954	−	0.199226i	$-0.936157\pi$
$479$	−14.4998	−	25.1144i	−0.662512	−	1.14750i	0.317442	−	0.948278i	$-0.397176\pi$
$480$	−1.37821	−	0.443635i	−0.0629063	−	0.0202491i
$481$	11.7858	+	6.80452i	0.537385	+	0.310259i
$482$	4.75945			0.216787
$483$	5.32870	+	31.7577i	0.242464	+	1.44503i
$484$	1.00000			0.0454545
$485$	−7.12785	−	4.11527i	−0.323659	−	0.186865i
$486$	13.6055	+	7.60853i	0.617159	+	0.345130i
$487$	−7.81129	−	13.5296i	−0.353963	−	0.613082i	0.632977	−	0.774171i	$-0.281833\pi$
$487$	−7.81129	−	13.5296i	−0.353963	−	0.613082i	−0.986940	+	0.161088i	$0.948500\pi$
$488$	−1.33746	+	2.31656i	−0.0605441	+	0.104866i
$489$	7.26025	+	8.01903i	0.328320	+	0.362633i
$490$	−4.77769	−	3.37828i	−0.215834	−	0.152615i
$491$			32.5285i			1.46799i	0.679154	+	0.733996i	$0.262347\pi$
$491$			32.5285i			1.46799i	−0.679154	+	0.733996i	$0.737653\pi$
$492$	−1.41538	+	0.304905i	−0.0638103	+	0.0137462i
$493$	−13.3934	+	7.73266i	−0.603207	+	0.348262i
$494$	−9.11443	+	5.26222i	−0.410078	+	0.236759i
$495$	1.46288	−	2.03686i	0.0657515	−	0.0915501i
$496$		−	5.60445i		−	0.251647i
$497$	−5.93678	−	3.80140i	−0.266301	−	0.170516i
$498$	−4.38567	+	3.97069i	−0.196526	+	0.177931i
$499$	7.65028	−	13.2507i	0.342473	−	0.593181i	−0.642418	−	0.766354i	$-0.722069\pi$
$499$	7.65028	−	13.2507i	0.342473	−	0.593181i	0.984891	+	0.173173i	$0.0554020\pi$
$500$	−3.88753	−	6.73341i	−0.173856	−	0.301127i
$501$	−1.79277	+	5.56946i	−0.0800950	+	0.248825i
$502$	17.4906	+	10.0982i	0.780642	+	0.450704i
$503$	31.3069			1.39590			0.697952	−	0.716145i	$-0.254095\pi$
$503$	31.3069			1.39590			0.697952	+	0.716145i	$0.254095\pi$
$504$	−2.93247	−	7.37568i	−0.130622	−	0.328539i
$505$	−5.54554			−0.246773
$506$	6.08555	+	3.51349i	0.270536	+	0.156194i
$507$	1.02175	−	3.17419i	0.0453774	−	0.140971i
$508$	−5.21626	−	9.03483i	−0.231434	−	0.400856i
$509$	−13.5445	+	23.4597i	−0.600348	+	1.03983i	0.392420	+	0.919786i	$0.371638\pi$
$509$	−13.5445	+	23.4597i	−0.600348	+	1.03983i	−0.992768	+	0.120048i	$0.961695\pi$
$510$	2.28750	−	2.07105i	0.101292	−	0.0917076i
$511$	−1.50933	+	32.8339i	−0.0667687	+	1.45249i
$512$			1.00000i			0.0441942i
$513$	−14.0652	+	1.59532i	−0.620992	+	0.0704349i
$514$	−24.5429	+	14.1698i	−1.08254	+	0.625005i
$515$	−11.0448	+	6.37673i	−0.486693	+	0.280992i
$516$	16.6796	−	3.59315i	0.734276	−	0.158180i
$517$			11.6858i			0.513941i
$518$	0.427974	−	9.31017i	0.0188041	−	0.409065i
$519$	−11.8401	−	13.0775i	−0.519723	−	0.574040i
$520$	−1.61471	+	2.79675i	−0.0708096	+	0.122646i
$521$	7.87689	+	13.6432i	0.345093	+	0.597718i	0.985371	−	0.170425i	$-0.0545142\pi$
$521$	7.87689	+	13.6432i	0.345093	+	0.597718i	−0.640278	+	0.768143i	$0.721181\pi$
$522$	19.8383	−	8.96319i	0.868300	−	0.392308i
$523$	15.4013	+	8.89196i	0.673453	+	0.388818i	0.797384	−	0.603473i	$-0.206217\pi$
$523$	15.4013	+	8.89196i	0.673453	+	0.388818i	−0.123931	+	0.992291i	$0.539550\pi$
$524$	10.4054			0.454561
$525$	6.89478	−	18.4655i	0.300913	−	0.805903i
$526$	19.1404			0.834563
$527$	10.3443	+	5.97229i	0.450605	+	0.260157i
$528$	−1.64874	−	0.530717i	−0.0717521	−	0.0230965i
$529$	13.1893	+	22.8445i	0.573447	+	0.993239i
$530$	−3.50570	+	6.07206i	−0.152278	+	0.263753i
$531$	2.14538	−	21.5473i	0.0931016	−	0.935071i
$532$	6.06985	+	3.88660i	0.263161	+	0.168506i
$533$			3.22941i			0.139881i
$534$	−0.259524	−	1.20472i	−0.0112307	−	0.0521335i
$535$	−2.69666	+	1.55692i	−0.116587	+	0.0673114i
$536$	11.0022	−	6.35213i	0.475223	−	0.274370i
$537$	−6.95137	−	32.2686i	−0.299974	−	1.39249i
$538$			8.48869i			0.365973i
$539$	−5.71551	−	4.04140i	−0.246184	−	0.174076i
$540$	−3.49290	+	2.58188i	−0.150311	+	0.111106i
$541$	17.3541	−	30.0582i	0.746111	−	1.29230i	−0.203563	−	0.979062i	$-0.565252\pi$
$541$	17.3541	−	30.0582i	0.746111	−	1.29230i	0.949674	−	0.313241i	$-0.101415\pi$
$542$	−7.68275	−	13.3069i	−0.330002	−	0.571581i
$543$	−35.2825	−	11.3572i	−1.51412	−	0.487383i
$544$	−1.84573	−	1.06563i	−0.0791351	−	0.0456887i
$545$	15.0654			0.645332
$546$	−17.4599	+	2.92963i	−0.747213	+	0.125377i
$547$	−9.06564			−0.387619			−0.193809	−	0.981039i	$-0.562084\pi$
$547$	−9.06564			−0.387619			−0.193809	+	0.981039i	$0.562084\pi$
$548$	5.61907	+	3.24417i	0.240035	+	0.138584i
$549$	3.30410	+	7.31301i	0.141016	+	0.312111i
$550$	−2.15062	−	3.72499i	−0.0917028	−	0.158834i
$551$	−9.88393	+	17.1195i	−0.421070	+	0.729314i
$552$	−8.16881	−	9.02254i	−0.347688	−	0.384025i
$553$	6.83716	+	13.2082i	0.290746	+	0.561672i
$554$		−	20.3017i		−	0.862535i
$555$	−4.98586	+	1.07407i	−0.211638	+	0.0455916i
$556$	−13.0270	+	7.52113i	−0.552467	+	0.318967i
$557$	−5.76379	+	3.32773i	−0.244220	+	0.141000i	−0.617115	−	0.786873i	$-0.711699\pi$
$557$	−5.76379	+	3.32773i	−0.244220	+	0.141000i	0.372895	+	0.927874i	$0.378365\pi$
$558$	−13.6563	−	9.80795i	−0.578115	−	0.415204i
$559$		−	38.0570i		−	1.60964i
$560$	2.20930	+	0.101558i	0.0933598	+	0.00429161i
$561$	2.73651	−	2.47758i	0.115536	−	0.104603i
$562$	−5.86598	+	10.1602i	−0.247441	+	0.428581i
$563$	−20.7720	−	35.9782i	−0.875435	−	1.51630i	−0.856298	−	0.516482i	$-0.827241\pi$
$563$	−20.7720	−	35.9782i	−0.875435	−	1.51630i	−0.0191372	−	0.999817i	$-0.506092\pi$
$564$	6.20185	−	19.2668i	0.261145	−	0.811279i
$565$	−10.1186	−	5.84197i	−0.425692	−	0.245773i
$566$	−14.2630			−0.599519
$567$	−23.1041	−	5.76217i	−0.970279	−	0.241988i
$568$	2.66448			0.111799
$569$	19.0011	+	10.9703i	0.796566	+	0.459898i	0.842269	−	0.539057i	$-0.181219\pi$
$569$	19.0011	+	10.9703i	0.796566	+	0.459898i	−0.0457028	+	0.998955i	$0.514553\pi$
$570$	1.20855	−	3.75451i	0.0506206	−	0.157259i
$571$	−12.8656	−	22.2839i	−0.538409	−	0.932551i	−0.998990	−	0.0449337i	$-0.985692\pi$
$571$	−12.8656	−	22.2839i	−0.538409	−	0.932551i	0.460581	−	0.887618i	$-0.347641\pi$
$572$	−1.93166	+	3.34573i	−0.0807667	+	0.139892i
$573$	11.4219	−	10.3412i	0.477158	−	0.432009i
$574$	1.96408	−	1.01670i	0.0819793	−	0.0424361i
$575$		−	30.2248i		−	1.26046i
$576$	2.43668	+	1.75003i	0.101528	+	0.0729178i
$577$	9.60562	−	5.54581i	0.399887	−	0.230875i	−0.286548	−	0.958066i	$-0.592508\pi$
$577$	9.60562	−	5.54581i	0.399887	−	0.230875i	0.686435	+	0.727191i	$0.259175\pi$
$578$	−10.7887	+	6.22885i	−0.448750	+	0.259086i
$579$	−10.4192	+	2.24452i	−0.433006	+	0.0932792i
$580$			6.06575i			0.251866i
$581$	4.87312	−	7.61054i	0.202171	−	0.315738i
$582$	11.4460	+	12.6423i	0.474453	+	0.524038i
$583$	−4.19384	+	7.26395i	−0.173691	+	0.300842i
$584$	−6.21158	−	10.7588i	−0.257037	−	0.445201i
$585$	3.98901	+	8.82892i	0.164925	+	0.365031i
$586$	5.58919	+	3.22692i	0.230887	+	0.133303i
$587$	−39.3634			−1.62470			−0.812351	−	0.583169i	$-0.801813\pi$
$587$	−39.3634			−1.62470			−0.812351	+	0.583169i	$0.801813\pi$
$588$	7.27854	+	9.69654i	0.300162	+	0.399878i
$589$	15.2676			0.629092
$590$	5.22524	+	3.01680i	0.215120	+	0.124200i
$591$	−32.1078	−	10.3353i	−1.32074	−	0.425136i
$592$	1.76131	+	3.05069i	0.0723896	+	0.125382i
$593$	4.17903	−	7.23829i	0.171612	−	0.297241i	−0.767371	−	0.641203i	$-0.778436\pi$
$593$	4.17903	−	7.23829i	0.171612	−	0.297241i	0.938984	+	0.343962i	$0.111769\pi$
$594$	−4.17853	+	3.08868i	−0.171447	+	0.126730i
$595$	−2.54175	+	3.96954i	−0.104201	+	0.162735i
$596$		−	4.85815i		−	0.198998i
$597$	−4.84123	−	22.4732i	−0.198138	−	0.919767i
$598$	−23.5104	+	13.5737i	−0.961412	+	0.555072i
$599$	10.5034	−	6.06417i	0.429159	−	0.247775i	−0.269829	−	0.962908i	$-0.586967\pi$
$599$	10.5034	−	6.06417i	0.429159	−	0.247775i	0.698988	+	0.715133i	$0.253634\pi$
$600$	1.56890	+	7.28290i	0.0640500	+	0.297323i
$601$			41.6196i			1.69770i	0.528634	+	0.848850i	$0.322705\pi$
$601$			41.6196i			1.69770i	−0.528634	+	0.848850i	$0.677295\pi$
$602$	−23.1457	+	11.9812i	−0.943350	+	0.488319i
$603$	3.77607	−	37.9252i	0.153774	−	1.54443i
$604$	−8.45368	+	14.6422i	−0.343975	+	0.595783i
$605$	0.417958	+	0.723925i	0.0169924	+	0.0294317i
$606$	10.9379	+	3.52082i	0.444321	+	0.143024i
$607$	−18.6709	−	10.7797i	−0.757830	−	0.437533i	0.0706862	−	0.997499i	$-0.477481\pi$
$607$	−18.6709	−	10.7797i	−0.757830	−	0.437533i	−0.828516	+	0.559965i	$0.810814\pi$
$608$	−2.72420			−0.110481
$609$	−25.6496	+	21.1627i	−1.03937	+	0.857557i
$610$	−2.23602			−0.0905337
$611$	−39.0975	−	22.5730i	−1.58172	−	0.913204i
$612$	−5.82669	+	2.63257i	−0.235530	+	0.106415i
$613$	2.42873	+	4.20669i	0.0980955	+	0.169906i	0.910896	−	0.412635i	$-0.135392\pi$
$613$	2.42873	+	4.20669i	0.0980955	+	0.169906i	−0.812801	+	0.582542i	$0.802058\pi$
$614$	−5.81835	+	10.0777i	−0.234809	+	0.406702i
$615$	−0.812299	−	0.897193i	−0.0327551	−	0.0361783i
$616$	2.64296	+	0.121493i	0.106488	+	0.00489509i
$617$		−	20.6685i		−	0.832084i	−0.909345	−	0.416042i	$-0.863417\pi$
$617$		−	20.6685i		−	0.832084i	0.909345	−	0.416042i	$-0.136583\pi$
$618$	25.8330	−	5.56501i	1.03916	−	0.223858i
$619$	−15.9542	+	9.21116i	−0.641253	+	0.370228i	−0.785097	−	0.619373i	$-0.787387\pi$
$619$	−15.9542	+	9.21116i	−0.641253	+	0.370228i	0.143844	+	0.989600i	$0.454054\pi$
$620$	4.05721	−	2.34243i	0.162941	−	0.0940742i
$621$	−36.2807	+	4.11507i	−1.45589	+	0.165132i
$622$		−	28.6538i		−	1.14891i
$623$	0.865376	+	1.67176i	0.0346706	+	0.0669777i
$624$	4.96044	−	4.49107i	0.198576	−	0.179787i
$625$	−7.50345	+	12.9964i	−0.300138	+	0.519854i
$626$	−11.2144	−	19.4240i	−0.448219	−	0.776338i
$627$	1.44578	−	4.49149i	0.0577388	−	0.179373i
$628$	3.28571	+	1.89701i	0.131114	+	0.0756989i
$629$	−7.50766			−0.299350
$630$	4.11379	−	5.20561i	0.163897	−	0.207397i
$631$	−21.1539			−0.842125			−0.421063	−	0.907032i	$-0.638343\pi$
$631$	−21.1539			−0.842125			−0.421063	+	0.907032i	$0.638343\pi$
$632$	−4.86831	−	2.81072i	−0.193651	−	0.111805i
$633$	8.92059	−	27.7129i	0.354561	−	1.10149i
$634$	−5.26659	−	9.12201i	−0.209163	−	0.362281i
$635$	4.36036	−	7.55237i	0.173036	−	0.299707i
$636$	10.7697	−	9.75061i	0.427045	−	0.386637i
$637$	24.5619	−	11.3160i	0.973176	−	0.448354i
$638$			7.25640i			0.287284i
$639$	4.66291	−	6.49247i	0.184462	−	0.256838i
$640$	−0.723925	+	0.417958i	−0.0286157	+	0.0165213i
$641$	29.6480	−	17.1173i	1.17102	−	0.676091i	0.217103	−	0.976149i	$-0.430339\pi$
$641$	29.6480	−	17.1173i	1.17102	−	0.676091i	0.953921	+	0.300058i	$0.0970059\pi$
$642$	6.30729	−	1.35873i	0.248929	−	0.0536248i
$643$			37.5930i			1.48252i	0.671215	+	0.741262i	$0.265773\pi$
$643$			37.5930i			1.48252i	−0.671215	+	0.741262i	$0.734227\pi$
$644$	15.6570	+	10.0254i	0.616972	+	0.395055i
$645$	9.57253	+	10.5730i	0.376918	+	0.416310i
$646$	2.90300	−	5.02814i	0.114217	−	0.197829i
$647$	20.3948	+	35.3248i	0.801802	+	1.38876i	0.918429	+	0.395585i	$0.129458\pi$
$647$	20.3948	+	35.3248i	0.801802	+	1.38876i	−0.116628	+	0.993176i	$0.537208\pi$
$648$	8.52851	−	2.87481i	0.335032	−	0.112933i
$649$	6.25091	+	3.60897i	0.245370	+	0.141664i
$650$	16.6171			0.651775
$651$	24.0603	+	8.98380i	0.942998	+	0.352103i
$652$	6.24543			0.244590
$653$	36.7047	+	21.1915i	1.43637	+	0.829286i	0.997595	−	0.0693127i	$-0.0220806\pi$
$653$	36.7047	+	21.1915i	1.43637	+	0.829286i	0.438771	+	0.898599i	$0.355414\pi$
$654$	−29.7146	−	9.56492i	−1.16193	−	0.374018i
$655$	4.34901	+	7.53271i	0.169930	+	0.294327i
$656$	−0.417958	+	0.723925i	−0.0163185	+	0.0282645i
$657$	−37.0861	−	3.69253i	−1.44687	−	0.144059i
$658$	−1.41974	+	30.8851i	−0.0553472	+	1.20403i
$659$		−	44.3754i		−	1.72862i	−0.502961	−	0.864309i	$-0.667756\pi$
$659$		−	44.3754i		−	1.72862i	0.502961	−	0.864309i	$-0.332244\pi$
$660$	−0.304905	−	1.41538i	−0.0118684	−	0.0550936i
$661$	−15.0119	+	8.66712i	−0.583895	+	0.337112i	−0.762680	−	0.646776i	$-0.776117\pi$
$661$	−15.0119	+	8.66712i	−0.583895	+	0.337112i	0.178785	+	0.983888i	$0.442783\pi$
$662$	−26.7852	+	15.4645i	−1.04104	+	0.601043i
$663$	3.00330	+	13.9415i	0.116639	+	0.541442i
$664$			3.41567i			0.132554i
$665$	−0.276664	+	6.01856i	−0.0107286	+	0.233390i
$666$	10.5159	+	1.04703i	0.407482	+	0.0405715i
$667$	−25.4953	+	44.1592i	−0.987182	+	1.70985i
$668$	1.68901	+	2.92544i	0.0653496	+	0.113189i
$669$	9.88629	+	3.18232i	0.382226	+	0.123036i
$670$	9.19693	+	5.30985i	0.355308	+	0.205137i
$671$	−2.67493			−0.103264
$672$	−4.29307	−	1.60297i	−0.165609	−	0.0618361i
$673$	8.22070			0.316885			0.158442	−	0.987368i	$-0.449353\pi$
$673$	8.22070			0.316885			0.158442	+	0.987368i	$0.449353\pi$
$674$	−7.57096	−	4.37109i	−0.291622	−	0.168368i
$675$	20.4917	+	8.92237i	0.788726	+	0.343422i
$676$	−0.962611	−	1.66729i	−0.0370235	−	0.0641266i
$677$	−9.52599	+	16.4995i	−0.366113	+	0.634127i	−0.988954	−	0.148222i	$-0.952645\pi$
$677$	−9.52599	+	16.4995i	−0.366113	+	0.634127i	0.622841	+	0.782349i	$0.285978\pi$
$678$	16.2486	+	17.9467i	0.624023	+	0.689240i
$679$	−21.9384	−	14.0474i	−0.841917	−	0.539090i
$680$		−	1.78156i		−	0.0683198i
$681$	12.5691	−	2.70767i	0.481650	−	0.103758i
$682$	4.85360	−	2.80223i	0.185854	−	0.107303i
$683$	41.1088	−	23.7342i	1.57299	−	0.908164i	0.577185	−	0.816613i	$-0.304151\pi$
$683$	41.1088	−	23.7342i	1.57299	−	0.908164i	0.995800	−	0.0915501i	$-0.0291822\pi$
$684$	−4.76742	+	6.63799i	−0.182287	+	0.253810i
$685$			5.42372i			0.207230i
$686$	−14.6149	−	11.3757i	−0.557998	−	0.434325i
$687$	15.0160	−	13.5952i	0.572897	−	0.518689i
$688$	4.92543	−	8.53109i	0.187780	−	0.325245i
$689$	−16.2021	−	28.0629i	−0.617253	−	1.06911i
$690$	3.11742	−	9.68465i	0.118678	−	0.368688i
$691$	18.7810	+	10.8432i	0.714464	+	0.412496i	0.812712	−	0.582666i	$-0.197991\pi$
$691$	18.7810	+	10.8432i	0.714464	+	0.412496i	−0.0982480	+	0.995162i	$0.531324\pi$
$692$	−10.1851			−0.387180
$693$	4.92129	−	6.22743i	0.186944	−	0.236560i
$694$	−1.28004			−0.0485895
$695$	−10.8895	−	6.28704i	−0.413061	−	0.238481i
$696$	3.85110	−	11.9639i	0.145975	−	0.453491i
$697$	−0.890781	−	1.54288i	−0.0337407	−	0.0584407i
$698$	−6.57699	+	11.3917i	−0.248943	+	0.431182i
$699$	17.9318	−	16.2350i	0.678241	−	0.614065i
$700$	−5.23145	−	10.1063i	−0.197730	−	0.381981i
$701$			51.9746i			1.96305i	0.191328	+	0.981526i	$0.438720\pi$
$701$			51.9746i			1.96305i	−0.191328	+	0.981526i	$0.561280\pi$
$702$	−2.26240	−	19.9465i	−0.0853886	−	0.752832i
$703$	−8.31067	+	4.79817i	−0.313443	+	0.180966i
$704$	−0.866025	+	0.500000i	−0.0326396	+	0.0188445i
$705$	16.5399	−	3.56305i	0.622927	−	0.134192i
$706$			15.0204i			0.565299i
$707$	−17.5336	−	0.805994i	−0.659420	−	0.0303125i
$708$	−8.39078	−	9.26771i	−0.315345	−	0.348302i
$709$	9.83314	−	17.0315i	0.369291	−	0.639632i	−0.620163	−	0.784473i	$-0.712934\pi$
$709$	9.83314	−	17.0315i	0.369291	−	0.639632i	0.989455	+	0.144841i	$0.0462671\pi$
$710$	1.11364	+	1.92888i	0.0417942	+	0.0723896i
$711$	−15.3685	+	6.94368i	−0.576364	+	0.260408i
$712$	−0.616180	−	0.355752i	−0.0230923	−	0.0133324i
$713$	39.3824			1.47488
$714$	7.53350	−	6.21567i	0.281934	−	0.232616i
$715$	−3.22941			−0.120773
$716$	−16.5044	−	9.52883i	−0.616799	−	0.356109i
$717$	−15.2565	−	4.91097i	−0.569765	−	0.183403i
$718$	15.6304	+	27.0726i	0.583321	+	1.01034i
$719$	7.00169	−	12.1273i	0.261119	−	0.452271i	−0.705421	−	0.708789i	$-0.749242\pi$
$719$	7.00169	−	12.1273i	0.261119	−	0.452271i	0.966540	+	0.256518i	$0.0825752\pi$
$720$	−0.248459	+	2.49541i	−0.00925952	+	0.0929985i
$721$	−35.8478	+	18.5564i	−1.33504	+	0.691075i
$722$			11.5787i			0.430916i
$723$	−1.73603	−	8.05874i	−0.0645638	−	0.299708i
$724$	−18.5327	+	10.6998i	−0.688761	+	0.397657i
$725$	27.0300	−	15.6058i	1.00387	−	0.579584i
$726$	−0.364755	−	1.69321i	−0.0135373	−	0.0628408i
$727$			11.1514i			0.413582i	0.978385	+	0.206791i	$0.0663020\pi$
$727$			11.1514i			0.413582i	−0.978385	+	0.206791i	$0.933698\pi$
$728$	−5.51178	+	8.60795i	−0.204280	+	0.319032i
$729$	7.92015	−	25.8122i	0.293339	−	0.956008i
$730$	5.19237	−	8.99345i	0.192178	−	0.332862i
$731$	10.4974	+	18.1820i	0.388260	+	0.672487i
$732$	4.41026	+	1.41963i	0.163008	+	0.0524710i
$733$	9.63547	+	5.56304i	0.355894	+	0.205476i	0.667278	−	0.744809i	$-0.267459\pi$
$733$	9.63547	+	5.56304i	0.355894	+	0.205476i	−0.311384	+	0.950284i	$0.600793\pi$
$734$	10.3338			0.381427
$735$	−3.97744	+	9.32187i	−0.146710	+	0.343842i
$736$	−7.02699			−0.259018
$737$	11.0022	+	6.35213i	0.405271	+	0.233984i
$738$	1.03253	+	2.28532i	0.0380081	+	0.0841238i
$739$	−19.4856	−	33.7501i	−0.716790	−	1.24152i	−0.962265	−	0.272113i	$-0.912277\pi$
$739$	−19.4856	−	33.7501i	−0.716790	−	1.24152i	0.245476	−	0.969403i	$-0.421056\pi$
$740$	−1.47231	+	2.55012i	−0.0541233	+	0.0937443i
$741$	12.2346	+	13.5132i	0.449448	+	0.496420i
$742$	−11.9667	+	18.6888i	−0.439311	+	0.686088i
$743$			6.23560i			0.228762i	0.993437	+	0.114381i	$0.0364884\pi$
$743$			6.23560i			0.228762i	−0.993437	+	0.114381i	$0.963512\pi$
$744$	−9.48951	+	2.04425i	−0.347902	+	0.0749459i
$745$	3.51694	−	2.03051i	0.128851	−	0.0743920i
$746$	12.1077	−	6.99037i	0.443293	−	0.255936i
$747$	8.32289	+	5.97752i	0.304519	+	0.218706i
$748$		−	2.13127i		−	0.0779268i
$749$	−8.75245	+	4.53065i	−0.319808	+	0.165546i
$750$	−9.98306	+	9.03845i	−0.364530	+	0.330037i
$751$	10.7770	−	18.6663i	0.393257	−	0.681142i	−0.599620	−	0.800285i	$-0.704681\pi$
$751$	10.7770	−	18.6663i	0.393257	−	0.681142i	0.992877	+	0.119143i	$0.0380148\pi$
$752$	−5.84290	−	10.1202i	−0.213069	−	0.369045i
$753$	10.7186	−	33.2985i	0.390606	−	1.21347i
$754$	−24.2780	−	14.0169i	−0.884151	−	0.510465i
$755$	−14.1332			−0.514358
$756$	−11.4189	+	7.65559i	−0.415302	+	0.278431i
$757$	−33.0536			−1.20135			−0.600676	−	0.799492i	$-0.705102\pi$
$757$	−33.0536			−1.20135			−0.600676	+	0.799492i	$0.705102\pi$
$758$	2.08168	+	1.20186i	0.0756100	+	0.0436535i
$759$	3.72934	−	11.5857i	0.135367	−	0.420533i
$760$	−1.13860	−	1.97212i	−0.0413014	−	0.0715362i
$761$	−14.3382	+	24.8345i	−0.519759	+	0.900249i	0.479977	+	0.877281i	$0.340645\pi$
$761$	−14.3382	+	24.8345i	−0.519759	+	0.900249i	−0.999736	+	0.0229682i	$0.992688\pi$
$762$	−13.3952	+	12.1277i	−0.485257	+	0.439341i
$763$	47.6331	+	2.18962i	1.72443	+	0.0792696i
$764$		−	8.89570i		−	0.321835i
$765$	−4.34109	−	3.11778i	−0.156953	−	0.112724i
$766$	19.8189	−	11.4425i	0.716088	−	0.413433i
$767$	−24.1493	+	13.9426i	−0.871979	+	0.503437i
$768$	1.69321	−	0.364755i	0.0610984	−	0.0131620i
$769$			41.1250i			1.48301i	0.670950	+	0.741503i	$0.265886\pi$
$769$			41.1250i			1.48301i	−0.670950	+	0.741503i	$0.734114\pi$
$770$	1.01670	+	1.96408i	0.0366392	+	0.0707807i
$771$	32.9446	+	36.3877i	1.18647	+	1.31047i
$772$	−3.07676	+	5.32910i	−0.110735	+	0.191798i
$773$	−4.24621	−	7.35464i	−0.152725	−	0.264528i	0.779503	−	0.626398i	$-0.215472\pi$
$773$	−4.24621	−	7.35464i	−0.152725	−	0.264528i	−0.932228	+	0.361870i	$0.882138\pi$
$774$	−12.1679	−	26.9313i	−0.437366	−	0.968027i
$775$	−20.8765	−	12.0531i	−0.749906	−	0.432959i
$776$	9.84612			0.353455
$777$	−15.9202	+	2.67128i	−0.571132	+	0.0958316i
$778$	−17.7054			−0.634768
$779$	−1.97212	−	1.13860i	−0.0706584	−	0.0407946i
$780$	5.32446	+	1.71390i	0.190646	+	0.0613676i
$781$	1.33224	+	2.30750i	0.0476712	+	0.0825690i
$782$	7.48819	−	12.9699i	0.267777	−	0.463804i
$783$	−22.4127	−	30.3211i	−0.800964	−	1.08359i
$784$	6.97048	+	0.642202i	0.248946	+	0.0229358i
$785$			3.17148i			0.113195i
$786$	−3.79541	−	17.6185i	−0.135378	−	0.628430i
$787$	−39.8454	+	23.0048i	−1.42034	+	0.820032i	−0.996327	−	0.0856262i	$-0.972711\pi$
$787$	−39.8454	+	23.0048i	−1.42034	+	0.820032i	−0.424009	+	0.905658i	$0.639378\pi$
$788$	−16.8651	+	9.73707i	−0.600795	+	0.346869i
$789$	−6.98157	−	32.4087i	−0.248550	−	1.15378i
$790$		−	4.69906i		−	0.167185i
$791$	−31.1433	−	19.9415i	−1.10733	−	0.709037i
$792$	−0.297229	+	2.98524i	−0.0105616	+	0.106076i
$793$	5.16705	−	8.94959i	0.183487	−	0.317809i
$794$	17.9405	+	31.0739i	0.636685	+	1.10277i
$795$	11.5600	+	3.72107i	0.409990	+	0.131973i
$796$	−11.4944	−	6.63628i	−0.407407	−	0.235217i
$797$	−29.2744			−1.03695			−0.518476	−	0.855092i	$-0.673500\pi$
$797$	−29.2744			−1.03695			−0.518476	+	0.855092i	$0.673500\pi$
$798$	4.36682	−	11.6952i	0.154584	−	0.414005i
$799$	24.9055			0.881095
$800$	3.72499	+	2.15062i	0.131698	+	0.0760359i
$801$	−1.94518	+	0.878857i	−0.0687297	+	0.0310529i
$802$	−12.9708	−	22.4661i	−0.458016	−	0.793307i
$803$	6.21158	−	10.7588i	0.219202	−	0.379669i
$804$	−14.7686	−	16.3121i	−0.520848	−	0.575282i
$805$	−0.713646	+	15.5247i	−0.0251527	+	0.547173i
$806$			21.6518i			0.762652i
$807$	14.3731	−	3.09629i	0.505958	−	0.108995i
$808$	5.74529	−	3.31704i	0.202118	−	0.116693i
$809$	37.5875	−	21.7011i	1.32151	−	0.762972i	0.337537	−	0.941312i	$-0.390406\pi$
$809$	37.5875	−	21.7011i	1.32151	−	0.762972i	0.983969	+	0.178341i	$0.0570729\pi$
$810$	5.64571	+	4.97246i	0.198370	+	0.174714i
$811$		−	3.75467i		−	0.131844i	−0.997825	−	0.0659221i	$-0.979001\pi$
$811$		−	3.75467i		−	0.131844i	0.997825	−	0.0659221i	$-0.0209989\pi$
$812$	−0.881601	+	19.1784i	−0.0309381	+	0.673029i
$813$	−19.7291	+	17.8623i	−0.691928	+	0.626457i
$814$	−1.76131	+	3.05069i	−0.0617340	+	0.106926i
$815$	2.61033	+	4.52122i	0.0914358	+	0.158371i
$816$	−1.13110	+	3.51390i	−0.0395964	+	0.123011i
$817$	23.2404	+	13.4178i	0.813078	+	0.469431i
$818$	−9.87793			−0.345374
$819$	11.3290	+	28.4946i	0.395869	+	0.995682i
$820$	−0.698757			−0.0244017
$821$	35.4502	+	20.4672i	1.23722	+	0.714310i	0.968525	−	0.248915i	$-0.0800741\pi$
$821$	35.4502	+	20.4672i	1.23722	+	0.714310i	0.268696	+	0.963225i	$0.413407\pi$
$822$	3.44348	−	10.6976i	0.120105	−	0.373121i
$823$	14.6468	+	25.3690i	0.510556	+	0.884309i	0.999925	+	0.0122325i	$0.00389383\pi$
$823$	14.6468	+	25.3690i	0.510556	+	0.884309i	−0.489369	+	0.872077i	$0.662773\pi$
$824$	7.62843	−	13.2128i	0.265749	−	0.460291i
$825$	−5.52273	+	5.00016i	−0.192277	+	0.174083i
$826$	16.0825	+	10.2978i	0.559580	+	0.358306i
$827$		−	41.9854i		−	1.45998i	−0.683460	−	0.729988i	$-0.739526\pi$
$827$		−	41.9854i		−	1.45998i	0.683460	−	0.729988i	$-0.260474\pi$
$828$	−12.2974	+	17.1225i	−0.427365	+	0.595048i
$829$	−33.3726	+	19.2677i	−1.15908	+	0.669195i	−0.951083	−	0.308935i	$-0.900027\pi$
$829$	−33.3726	+	19.2677i	−1.15908	+	0.669195i	−0.207996	+	0.978130i	$0.566694\pi$
$830$	−2.47269	+	1.42761i	−0.0858283	+	0.0495530i
$831$	−34.3749	+	7.40513i	−1.19245	+	0.256881i
$832$		−	3.86332i		−	0.133936i
$833$	−8.61331	+	12.1813i	−0.298433	+	0.422056i
$834$	17.4865	+	19.3140i	0.605508	+	0.668790i
$835$	−1.41187	+	2.44543i	−0.0488597	+	0.0846275i
$836$	−1.36210	−	2.35922i	−0.0471092	−	0.0815955i
$837$	−11.6257	+	26.7004i	−0.401844	+	0.922900i
$838$	−6.18526	−	3.57106i	−0.213666	−	0.123360i
$839$	19.4169			0.670345			0.335172	−	0.942157i	$-0.391205\pi$
$839$	19.4169			0.670345			0.335172	+	0.942157i	$0.391205\pi$
$840$	−0.633892	−	3.77784i	−0.0218714	−	0.130348i
$841$	−23.6553			−0.815701
$842$	−2.45312	−	1.41631i	−0.0845401	−	0.0488092i
$843$	19.3429	+	6.22635i	0.666206	+	0.214447i
$844$	−8.40427	−	14.5566i	−0.289287	−	0.501060i
$845$	0.804663	−	1.39372i	0.0276812	−	0.0479453i
$846$	−34.8849	−	3.47336i	−1.19937	−	0.119417i
$847$	1.21626	+	2.34962i	0.0417913	+	0.0807338i
$848$		−	8.38769i		−	0.288034i
$849$	5.20250	+	24.1503i	0.178549	+	0.828835i
$850$	−7.93894	+	4.58355i	−0.272303	+	0.157214i
$851$	−21.4371	+	12.3767i	−0.734855	+	0.424269i
$852$	−0.971880	−	4.51151i	−0.0332961	−	0.154562i
$853$		−	44.3922i		−	1.51996i	−0.649946	−	0.759980i	$-0.725209\pi$
$853$		−	44.3922i		−	1.51996i	0.649946	−	0.759980i	$-0.274791\pi$
$854$	−7.06973	−	0.324985i	−0.241921	−	0.0111207i
$855$	−6.79800	−	0.676851i	−0.232487	−	0.0231478i
$856$	1.86253	−	3.22599i	0.0636599	−	0.110262i
$857$	−19.3914	−	33.5868i	−0.662396	−	1.14730i	−0.979984	−	0.199075i	$-0.936206\pi$
$857$	−19.3914	−	33.5868i	−0.662396	−	1.14730i	0.317588	−	0.948229i	$-0.397127\pi$
$858$	6.36960	+	2.05033i	0.217455	+	0.0699971i
$859$	23.2887	+	13.4458i	0.794601	+	0.458763i	0.841580	−	0.540133i	$-0.181626\pi$
$859$	23.2887	+	13.4458i	0.794601	+	0.458763i	−0.0469785	+	0.998896i	$0.514959\pi$
$860$	8.23450			0.280794
$861$	−2.43789	−	2.95476i	−0.0830830	−	0.100698i
$862$	−25.5110			−0.868907
$863$	−25.5304	−	14.7400i	−0.869063	−	0.501754i	−0.00202656	−	0.999998i	$-0.500645\pi$
$863$	−25.5304	−	14.7400i	−0.869063	−	0.501754i	−0.867037	+	0.498244i	$0.833978\pi$
$864$	2.07437	−	4.76414i	0.0705715	−	0.162079i
$865$	−4.25696	−	7.37326i	−0.144741	−	0.250698i
$866$	−8.80427	+	15.2494i	−0.299181	+	0.518197i
$867$	14.4820	+	15.9955i	0.491833	+	0.543235i
$868$	13.1683	−	6.81650i	0.446962	−	0.231367i
$869$		−	5.62145i		−	0.190694i
$870$	10.2706	−	2.21251i	0.348205	−	0.0750111i
$871$	−42.5050	+	24.5403i	−1.44023	+	0.831516i
$872$	−15.6081	+	9.01132i	−0.528556	+	0.305162i
$873$	17.2310	−	23.9918i	0.583180	−	0.812000i
$874$		−	19.1429i		−	0.647518i
$875$	11.0927	−	17.3238i	0.375000	−	0.585652i
$876$	−15.9511	+	14.4418i	−0.538939	+	0.487944i
$877$	−6.00638	+	10.4034i	−0.202821	+	0.351296i	−0.949436	−	0.313960i	$-0.898344\pi$
$877$	−6.00638	+	10.4034i	−0.202821	+	0.351296i	0.746615	+	0.665256i	$0.231678\pi$
$878$	−11.7710	−	20.3880i	−0.397253	−	0.688063i
$879$	3.42517	−	10.6407i	0.115528	−	0.358902i
$880$	−0.723925	−	0.417958i	−0.0244035	−	0.0140894i
$881$	15.9253			0.536538			0.268269	−	0.963344i	$-0.413548\pi$
$881$	15.9253			0.536538			0.268269	+	0.963344i	$0.413548\pi$
$882$	13.7634	−	15.8609i	0.463437	−	0.534066i
$883$	29.0733			0.978396			0.489198	−	0.872173i	$-0.337290\pi$
$883$	29.0733			0.978396			0.489198	+	0.872173i	$0.337290\pi$
$884$	7.13065	+	4.11688i	0.239830	+	0.138466i
$885$	3.20213	−	9.94782i	0.107638	−	0.334392i
$886$	5.12033	+	8.86868i	0.172021	+	0.297949i
$887$	−2.94979	+	5.10919i	−0.0990443	+	0.171550i	−0.911289	−	0.411767i	$-0.864912\pi$
$887$	−2.94979	+	5.10919i	−0.0990443	+	0.171550i	0.812245	+	0.583316i	$0.198245\pi$
$888$	4.52300	−	4.09502i	0.151782	−	0.137420i
$889$	14.8840	−	23.2450i	0.499195	−	0.779611i
$890$		−	0.594758i		−	0.0199363i
$891$	6.75391	+	5.94850i	0.226264	+	0.199282i
$892$	5.19292	−	2.99814i	0.173872	−	0.100385i
$893$	27.5694	−	15.9172i	0.922575	−	0.532649i
$894$	−8.22586	+	1.77203i	−0.275114	+	0.0592657i
$895$		−	15.9306i		−	0.532502i
$896$	−2.34962	+	1.21626i	−0.0784952	+	0.0406325i
$897$	31.5587	+	34.8569i	1.05371	+	1.16384i
$898$	8.71024	−	15.0866i	0.290664	−	0.503445i
$899$	20.3341	+	35.2197i	0.678179	+	1.17464i
$900$	11.7592	−	5.31295i	0.391973	−	0.177098i
$901$	15.4814	+	8.93820i	0.515761	+	0.297775i
$902$	−0.835917			−0.0278330
$903$	28.7293	+	34.8203i	0.956050	+	1.15875i
$904$	13.9774			0.464881
$905$	−15.4918	−	8.94418i	−0.514964	−	0.297315i
$906$	27.8758	+	8.97303i	0.926112	+	0.298109i
$907$	9.72266	+	16.8401i	0.322836	+	0.559168i	0.981072	−	0.193644i	$-0.0620306\pi$
$907$	9.72266	+	16.8401i	0.322836	+	0.559168i	−0.658236	+	0.752811i	$0.728697\pi$
$908$	3.71163	−	6.42873i	0.123175	−	0.213345i
$909$	1.97184	−	19.8043i	0.0654019	−	0.656868i
$910$	−8.53521	−	0.392351i	−0.282939	−	0.0130063i
$911$			14.8351i			0.491510i	0.969332	+	0.245755i	$0.0790359\pi$
$911$			14.8351i			0.491510i	−0.969332	+	0.245755i	$0.920964\pi$
$912$	0.993664	+	4.61263i	0.0329035	+	0.152740i
$913$	−2.95806	+	1.70784i	−0.0978974	+	0.0565211i
$914$	5.96396	−	3.44330i	0.197270	−	0.113894i
$915$	0.815598	+	3.78604i	0.0269628	+	0.125163i
$916$		−	11.6949i		−	0.386410i
$917$	12.6557	+	24.4486i	0.417927	+	0.807365i
$918$	6.58279	+	8.90555i	0.217265	+	0.293927i
$919$	18.3711	−	31.8197i	0.606007	−	1.04964i	−0.385884	−	0.922547i	$-0.626104\pi$
$919$	18.3711	−	31.8197i	0.606007	−	1.04964i	0.991891	−	0.127088i	$-0.0405630\pi$
$920$	−2.93699	−	5.08701i	−0.0968297	−	0.167714i
$921$	19.1859	+	6.17579i	0.632196	+	0.203499i
$922$	−5.73523	−	3.31124i	−0.188880	−	0.109050i
$923$	−10.2937			−0.338822
$924$	−0.758320	−	4.51940i	−0.0249469	−	0.148677i
$925$	15.1517			0.498184
$926$	−18.5182	−	10.6915i	−0.608544	−	0.351343i
$927$	−18.8454	−	41.7108i	−0.618966	−	1.36996i
$928$	−3.62820	−	6.28423i	−0.119101	−	0.206290i
$929$	−10.2616	+	17.7737i	−0.336674	+	0.583136i	−0.983805	−	0.179243i	$-0.942635\pi$
$929$	−10.2616	+	17.7737i	−0.336674	+	0.583136i	0.647131	+	0.762379i	$0.275969\pi$
$930$	−5.44610	−	6.01528i	−0.178585	−	0.197249i
$931$	−1.74948	+	18.9890i	−0.0573370	+	0.622338i
$932$		−	13.9657i		−	0.457462i
$933$	−48.5169	+	10.4516i	−1.58837	+	0.342171i
$934$	21.6284	−	12.4871i	0.707702	−	0.408592i
$935$	1.54288	−	0.890781i	0.0504575	−	0.0291317i
$936$	−9.41366	−	6.76091i	−0.307695	−	0.220987i
$937$			36.6682i			1.19790i	0.800788	+	0.598948i	$0.204414\pi$
$937$			36.6682i			1.19790i	−0.800788	+	0.598948i	$0.795586\pi$
$938$	28.3066	+	18.1251i	0.924245	+	0.591806i
$939$	−28.7983	+	26.0734i	−0.939798	+	0.850872i
$940$	4.88418	−	8.45964i	0.159304	−	0.275923i
$941$	4.81705	+	8.34338i	0.157031	+	0.271987i	0.933797	−	0.357804i	$-0.116474\pi$
$941$	4.81705	+	8.34338i	0.157031	+	0.271987i	−0.776765	+	0.629790i	$0.783141\pi$
$942$	2.01355	−	6.25534i	0.0656050	−	0.203810i
$943$	−5.08701	−	2.93699i	−0.165656	−	0.0956415i
$944$	−7.21793			−0.234924
$945$	−10.3147	−	5.06673i	−0.335538	−	0.164821i
$946$	9.85086			0.320279
$947$	−9.23315	−	5.33076i	−0.300037	−	0.173227i	0.342422	−	0.939546i	$-0.388753\pi$
$947$	−9.23315	−	5.33076i	−0.300037	−	0.173227i	−0.642460	+	0.766320i	$0.722086\pi$
$948$	−2.98340	+	9.26829i	−0.0968962	+	0.301020i
$949$	23.9973	+	41.5646i	0.778986	+	1.34924i
$950$	−5.85872	+	10.1476i	−0.190082	+	0.329232i
$951$	−13.5244	+	12.2447i	−0.438560	+	0.397063i
$952$	0.258934	−	5.63285i	0.00839209	−	0.182562i
$953$			20.5160i			0.664579i	0.943177	+	0.332290i	$0.107821\pi$
$953$			20.5160i			0.664579i	−0.943177	+	0.332290i	$0.892179\pi$
$954$	−20.4381	−	14.6787i	−0.661708	−	0.475240i
$955$	6.43982	−	3.71803i	0.208388	−	0.120313i
$956$	−8.01372	+	4.62673i	−0.259182	+	0.149639i
$957$	12.2866	−	2.64681i	0.397169	−	0.0855591i
$958$			28.9996i			0.936933i
$959$	−0.788288	+	17.1484i	−0.0254551	+	0.553752i
$960$	0.971746	+	1.07330i	0.0313630	+	0.0346407i
$961$	0.204948	−	0.354981i	0.00661124	−	0.0114510i
$962$	−6.80452	−	11.7858i	−0.219386	−	0.379988i
$963$	−4.60123	−	10.1840i	−0.148273	−	0.328173i
$964$	−4.12181	−	2.37973i	−0.132754	−	0.0766458i
$965$	−5.14382			−0.165586
$966$	11.2641	−	30.1674i	0.362416	−	0.970619i
$967$	38.6686			1.24350			0.621749	−	0.783217i	$-0.286423\pi$
$967$	38.6686			1.24350			0.621749	+	0.783217i	$0.286423\pi$
$968$	−0.866025	−	0.500000i	−0.0278351	−	0.0160706i
$969$	−9.57256	−	3.08134i	−0.307515	−	0.0989869i
$970$	4.11527	+	7.12785i	0.132133	+	0.228862i
$971$	24.3770	−	42.2221i	0.782294	−	1.35497i	−0.148309	−	0.988941i	$-0.547383\pi$
$971$	24.3770	−	42.2221i	0.782294	−	1.35497i	0.930602	−	0.366032i	$-0.119284\pi$
$972$	−7.97846	−	13.3919i	−0.255909	−	0.429547i
$973$	−33.5160	−	21.4607i	−1.07448	−	0.688000i
$974$			15.6226i			0.500580i
$975$	−6.06116	−	28.1362i	−0.194112	−	0.901078i
$976$	2.31656	−	1.33746i	0.0741511	−	0.0428112i
$977$	14.6963	−	8.48489i	0.470175	−	0.271456i	−0.246138	−	0.969235i	$-0.579162\pi$
$977$	14.6963	−	8.48489i	0.470175	−	0.271456i	0.716313	+	0.697779i	$0.245828\pi$
$978$	−2.27805	−	10.5748i	−0.0728440	−	0.338145i
$979$		−	0.711503i		−	0.0227397i
$980$	2.44846	+	5.31452i	0.0782133	+	0.169766i
$981$	−5.35686	+	53.8019i	−0.171031	+	1.71776i
$982$	16.2643	−	28.1705i	0.519014	−	0.898958i
$983$	−11.3004	−	19.5728i	−0.360426	−	0.624276i	0.627605	−	0.778532i	$-0.284035\pi$
$983$	−11.3004	−	19.5728i	−0.360426	−	0.624276i	−0.988031	+	0.154256i	$0.950702\pi$
$984$	1.37821	+	0.443635i	0.0439357	+	0.0141426i
$985$	−14.0978	−	8.13939i	−0.449194	−	0.259342i
$986$	15.4653			0.492516
$987$	52.8127	−	8.86157i	1.68105	−	0.282067i
$988$	10.5244			0.334827
$989$	59.9479	+	34.6109i	1.90623	+	1.10056i
$990$	−2.28532	+	1.03253i	−0.0726322	+	0.0328161i
$991$	3.09848	+	5.36672i	0.0984264	+	0.170479i	0.911033	−	0.412332i	$-0.135286\pi$
$991$	3.09848	+	5.36672i	0.0984264	+	0.170479i	−0.812607	+	0.582812i	$0.801952\pi$
$992$	−2.80223	+	4.85360i	−0.0889708	+	0.154102i
$993$	35.9546	+	39.7122i	1.14098	+	1.26023i
$994$	3.24071	+	6.26050i	0.102789	+	0.198571i
$995$		−	11.0948i		−	0.351727i
$996$	5.78344	−	1.24588i	0.183255	−	0.0394773i
$997$	−36.9714	+	21.3455i	−1.17090	+	0.676017i	−0.953891	−	0.300153i	$-0.902962\pi$
$997$	−36.9714	+	21.3455i	−1.17090	+	0.676017i	−0.217005	+	0.976170i	$0.569629\pi$
$998$	−13.2507	+	7.65028i	−0.419443	+	0.242165i
$999$	−2.06288	−	18.1875i	−0.0652668	−	0.575427i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.k.g.89.3	✓	20
3.2	odd	2	inner	462.2.k.g.89.6	yes	20
7.3	odd	6	inner	462.2.k.g.353.6	yes	20
21.17	even	6	inner	462.2.k.g.353.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.k.g.89.3	✓	20	1.1	even	1	trivial
462.2.k.g.89.6	yes	20	3.2	odd	2	inner
462.2.k.g.353.3	yes	20	21.17	even	6	inner
462.2.k.g.353.6	yes	20	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.530717 + 1.64874i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.417958 + 0.723925i) q^{5} +(1.28398 - 1.16249i) q^{6} +(-1.42670 + 2.22812i) q^{7} -1.00000i q^{8} +(-2.43668 - 1.75003i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.530717 + 1.64874i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.417958 + 0.723925i) q^{5} +(1.28398 - 1.16249i) q^{6} +(-1.42670 + 2.22812i) q^{7} -1.00000i q^{8} +(-2.43668 - 1.75003i) q^{9} +(0.723925 - 0.417958i) q^{10} +(0.866025 - 0.500000i) q^{11} +(-1.69321 + 0.364755i) q^{12} +3.86332i q^{13} +(2.34962 - 1.21626i) q^{14} +(-0.971746 - 1.07330i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.06563 - 1.84573i) q^{17} +(1.23521 + 2.73391i) q^{18} +(-2.35922 - 1.36210i) q^{19} -0.835917 q^{20} +(-2.91642 - 3.53475i) q^{21} -1.00000 q^{22} +(-6.08555 - 3.51349i) q^{23} +(1.64874 + 0.530717i) q^{24} +(2.15062 + 3.72499i) q^{25} +(1.93166 - 3.34573i) q^{26} +(4.17853 - 3.08868i) q^{27} +(-2.64296 - 0.121493i) q^{28} -7.25640i q^{29} +(0.304905 + 1.41538i) q^{30} +(-4.85360 + 2.80223i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.364755 + 1.69321i) q^{33} +2.13127i q^{34} +(-1.01670 - 1.96408i) q^{35} +(0.297229 - 2.98524i) q^{36} +(1.76131 - 3.05069i) q^{37} +(1.36210 + 2.35922i) q^{38} +(-6.36960 - 2.05033i) q^{39} +(0.723925 + 0.417958i) q^{40} +0.835917 q^{41} +(0.758320 + 4.51940i) q^{42} -9.85086 q^{43} +(0.866025 + 0.500000i) q^{44} +(2.28532 - 1.03253i) q^{45} +(3.51349 + 6.08555i) q^{46} +(-5.84290 + 10.1202i) q^{47} +(-1.16249 - 1.28398i) q^{48} +(-2.92908 - 6.35771i) q^{49} -4.30124i q^{50} +(3.60868 - 0.777390i) q^{51} +(-3.34573 + 1.93166i) q^{52} +(-7.26395 + 4.19384i) q^{53} +(-5.16305 + 0.585609i) q^{54} +0.835917i q^{55} +(2.22812 + 1.42670i) q^{56} +(3.49783 - 3.16686i) q^{57} +(-3.62820 + 6.28423i) q^{58} +(3.60897 + 6.25091i) q^{59} +(0.443635 - 1.37821i) q^{60} +(-2.31656 - 1.33746i) q^{61} +5.60445 q^{62} +(7.37568 - 2.93247i) q^{63} -1.00000 q^{64} +(-2.79675 - 1.61471i) q^{65} +(0.530717 - 1.64874i) q^{66} +(6.35213 + 11.0022i) q^{67} +(1.06563 - 1.84573i) q^{68} +(9.02254 - 8.16881i) q^{69} +(-0.101558 + 2.20930i) q^{70} +2.66448i q^{71} +(-1.75003 + 2.43668i) q^{72} +(10.7588 - 6.21158i) q^{73} +(-3.05069 + 1.76131i) q^{74} +(-7.28290 + 1.56890i) q^{75} -2.72420i q^{76} +(-0.121493 + 2.64296i) q^{77} +(4.49107 + 4.96044i) q^{78} +(2.81072 - 4.86831i) q^{79} +(-0.417958 - 0.723925i) q^{80} +(2.87481 + 8.52851i) q^{81} +(-0.723925 - 0.417958i) q^{82} -3.41567 q^{83} +(1.60297 - 4.29307i) q^{84} +1.78156 q^{85} +(8.53109 + 4.92543i) q^{86} +(11.9639 + 3.85110i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(0.355752 - 0.616180i) q^{89} +(-2.49541 - 0.248459i) q^{90} +(-8.60795 - 5.51178i) q^{91} -7.02699i q^{92} +(-2.04425 - 9.48951i) q^{93} +(10.1202 - 5.84290i) q^{94} +(1.97212 - 1.13860i) q^{95} +(0.364755 + 1.69321i) q^{96} +9.84612i q^{97} +(-0.642202 + 6.97048i) q^{98} +(-2.98524 - 0.297229i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9}+O(q^{10}) \) 20 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 2 * q^9	\( 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9} - 18 q^{10} - 6 q^{12} - 8 q^{15} - 10 q^{16} + 4 q^{18} + 36 q^{19} + 24 q^{21} - 20 q^{22} - 12 q^{25} - 22 q^{30} + 36 q^{31} - 4 q^{36} + 16 q^{37} + 4 q^{39} - 18 q^{40} + 32 q^{42} + 32 q^{43} + 24 q^{45} + 30 q^{46} - 42 q^{49} - 24 q^{52} - 36 q^{54} - 24 q^{57} + 32 q^{58} - 4 q^{60} + 42 q^{61} - 10 q^{63} - 20 q^{64} + 6 q^{66} - 10 q^{67} - 36 q^{70} - 4 q^{72} + 12 q^{73} - 108 q^{75} + 6 q^{79} + 42 q^{81} + 18 q^{82} + 18 q^{84} - 28 q^{85} + 36 q^{87} - 10 q^{88} - 112 q^{91} - 36 q^{93} + 42 q^{94} - 8 q^{99}+O(q^{100}) \) 20 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 2 * q^9 - 18 * q^10 - 6 * q^12 - 8 * q^15 - 10 * q^16 + 4 * q^18 + 36 * q^19 + 24 * q^21 - 20 * q^22 - 12 * q^25 - 22 * q^30 + 36 * q^31 - 4 * q^36 + 16 * q^37 + 4 * q^39 - 18 * q^40 + 32 * q^42 + 32 * q^43 + 24 * q^45 + 30 * q^46 - 42 * q^49 - 24 * q^52 - 36 * q^54 - 24 * q^57 + 32 * q^58 - 4 * q^60 + 42 * q^61 - 10 * q^63 - 20 * q^64 + 6 * q^66 - 10 * q^67 - 36 * q^70 - 4 * q^72 + 12 * q^73 - 108 * q^75 + 6 * q^79 + 42 * q^81 + 18 * q^82 + 18 * q^84 - 28 * q^85 + 36 * q^87 - 10 * q^88 - 112 * q^91 - 36 * q^93 + 42 * q^94 - 8 * q^99

Introduction

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