LMFDB - Embedded newform 462.2.k.g.89.6

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			89.6
Root			$0.530717 + 1.64874i$ of defining polynomial
Character	$\chi$	$=$	462.89
Dual form			462.2.k.g.353.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-1.69321 - 0.364755i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.417958 - 0.723925i) q^{5} +(-1.28398 - 1.16249i) q^{6} +(-1.42670 + 2.22812i) q^{7} +1.00000i q^{8} +(2.73391 + 1.23521i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-1.69321 - 0.364755i) 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} +(2.73391 + 1.23521i) q^{9} +(0.723925 - 0.417958i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(-0.530717 - 1.64874i) 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} +(1.75003 + 2.43668i) q^{18} +(-2.35922 - 1.36210i) q^{19} +0.835917 q^{20} +(3.22841 - 3.25228i) q^{21} -1.00000 q^{22} +(6.08555 + 3.51349i) q^{23} +(0.364755 - 1.69321i) 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} +(-1.37821 + 0.443635i) q^{30} +(-4.85360 + 2.80223i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.64874 - 0.530717i) 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} +(1.40916 - 6.54140i) q^{39} +(0.723925 + 0.417958i) q^{40} -0.835917 q^{41} +(4.42203 - 1.20235i) q^{42} -9.85086 q^{43} +(-0.866025 - 0.500000i) q^{44} +(2.03686 - 1.46288i) 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} +(-1.13110 - 3.51390i) q^{51} +(-3.34573 + 1.93166i) q^{52} +(7.26395 - 4.19384i) q^{53} +(-2.07437 - 4.76414i) 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} +(-1.41538 - 0.304905i) q^{60} +(-2.31656 - 1.33746i) q^{61} -5.60445 q^{62} +(-6.65266 + 4.32922i) q^{63} -1.00000 q^{64} +(2.79675 + 1.61471i) q^{65} +(1.69321 + 0.364755i) 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} +(-1.23521 + 2.73391i) q^{72} +(10.7588 - 6.21158i) q^{73} +(3.05069 - 1.76131i) q^{74} +(-2.28274 - 7.09163i) 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} +(5.94850 + 6.75391i) q^{81} +(-0.723925 - 0.417958i) q^{82} +3.41567 q^{83} +(4.43077 + 1.16975i) q^{84} +1.78156 q^{85} +(-8.53109 - 4.92543i) q^{86} +(2.64681 - 12.2866i) 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} +(9.24028 - 2.97438i) q^{93} +(10.1202 - 5.84290i) q^{94} +(-1.97212 + 1.13860i) q^{95} +(1.64874 - 0.530717i) 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
$3$	−1.69321	−	0.364755i	−0.977574	−	0.210591i
$3$	−1.69321	−	0.364755i	−0.977574	−	0.210591i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.417958	−	0.723925i	0.186917	−	0.323749i	−0.757304	−	0.653063i	$-0.773484\pi$
$5$	0.417958	−	0.723925i	0.186917	−	0.323749i	0.944221	+	0.329313i	$0.106817\pi$
$6$	−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
$9$	2.73391	+	1.23521i	0.911303	+	0.411737i
$10$	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
$12$	−0.530717	−	1.64874i	−0.153205	−	0.475950i
$13$			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	0.965828	−	0.259184i	$-0.0834536\pi$
$17$	1.06563	+	1.84573i	0.258454	+	0.447656i	−0.707374	+	0.706840i	$0.750120\pi$
$18$	1.75003	+	2.43668i	0.412486	+	0.574331i
$19$	−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
$21$	3.22841	−	3.25228i	0.704497	−	0.709707i
$22$	−1.00000			−0.213201
$23$	6.08555	+	3.51349i	1.26892	+	0.732614i	0.974785	−	0.223148i	$-0.0716334\pi$
$23$	6.08555	+	3.51349i	1.26892	+	0.732614i	0.294140	+	0.955762i	$0.404967\pi$
$24$	0.364755	−	1.69321i	0.0744553	−	0.345625i
$25$	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	$0.235313\pi$
$29$			7.25640i			1.34748i	−0.738969	+	0.673740i	$0.764687\pi$
$30$	−1.37821	+	0.443635i	−0.251625	+	0.0809964i
$31$	−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
$33$	1.64874	−	0.530717i	0.287009	−	0.0923860i
$34$			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
$39$	1.40916	−	6.54140i	0.225647	−	1.04746i
$40$	0.723925	+	0.417958i	0.114463	+	0.0660850i
$41$	−0.835917			−0.130548			−0.0652741	−	0.997867i	$-0.520792\pi$
$41$	−0.835917			−0.130548			−0.0652741	+	0.997867i	$0.520792\pi$
$42$	4.42203	−	1.20235i	0.682334	−	0.185527i
$43$	−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
$45$	2.03686	−	1.46288i	0.303637	−	0.218073i
$46$	3.51349	+	6.08555i	0.518036	+	0.897265i
$47$	5.84290	−	10.1202i	0.852274	−	1.47618i	−0.0268770	−	0.999639i	$-0.508556\pi$
$47$	5.84290	−	10.1202i	0.852274	−	1.47618i	0.879151	−	0.476543i	$-0.158110\pi$
$48$	1.16249	−	1.28398i	0.167791	−	0.185327i
$49$	−2.92908	−	6.35771i	−0.418440	−	0.908245i
$50$			4.30124i			0.608288i
$51$	−1.13110	−	3.51390i	−0.158386	−	0.492045i
$52$	−3.34573	+	1.93166i	−0.463969	+	0.267873i
$53$	7.26395	−	4.19384i	0.997780	−	0.576069i	0.0901894	−	0.995925i	$-0.471253\pi$
$53$	7.26395	−	4.19384i	0.997780	−	0.576069i	0.907591	+	0.419856i	$0.137919\pi$
$54$	−2.07437	−	4.76414i	−0.282286	−	0.648317i
$55$			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	0.529558	−	0.848274i	$-0.322358\pi$
$59$	−3.60897	−	6.25091i	−0.469847	−	0.813799i	−0.999406	+	0.0344741i	$0.989024\pi$
$60$	−1.41538	−	0.304905i	−0.182725	−	0.0393630i
$61$	−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
$63$	−6.65266	+	4.32922i	−0.838156	+	0.545430i
$64$	−1.00000			−0.125000
$65$	2.79675	+	1.61471i	0.346895	+	0.200280i
$66$	1.69321	+	0.364755i	0.208420	+	0.0448982i
$67$	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	$-0.949461\pi$
$71$		−	2.66448i		−	0.316215i	0.987422	−	0.158108i	$-0.0505393\pi$
$72$	−1.23521	+	2.73391i	−0.145571	+	0.322194i
$73$	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
$75$	−2.28274	−	7.09163i	−0.263588	−	0.818870i
$76$		−	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
$81$	5.94850	+	6.75391i	0.660945	+	0.750434i
$82$	−0.723925	−	0.417958i	−0.0799442	−	0.0461558i
$83$	3.41567			0.374918			0.187459	−	0.982272i	$-0.439975\pi$
$83$	3.41567			0.374918			0.187459	+	0.982272i	$0.439975\pi$
$84$	4.43077	+	1.16975i	0.483436	+	0.127630i
$85$	1.78156			0.193238
$86$	−8.53109	−	4.92543i	−0.919931	−	0.531123i
$87$	2.64681	−	12.2866i	0.283767	−	1.31726i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	−0.355752	+	0.616180i	−0.0377096	+	0.0653150i	−0.884264	−	0.466987i	$-0.845340\pi$
$89$	−0.355752	+	0.616180i	−0.0377096	+	0.0653150i	0.846555	+	0.532302i	$0.178673\pi$
$90$	2.49541	−	0.248459i	0.263040	−	0.0261899i
$91$	−8.60795	−	5.51178i	−0.902359	−	0.577792i
$92$			7.02699i			0.732614i
$93$	9.24028	−	2.97438i	0.958172	−	0.308429i
$94$	10.1202	−	5.84290i	1.04382	−	0.602649i
$95$	−1.97212	+	1.13860i	−0.202335	+	0.116818i
$96$	1.64874	−	0.530717i	0.168274	−	0.0541661i
$97$			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	0.652465	−	0.757819i	$-0.273735\pi$
$101$	−3.31704	−	5.74529i	−0.330058	−	0.571677i	−0.982523	+	0.186142i	$0.940402\pi$
$102$	0.777390	−	3.60868i	0.0769731	−	0.357312i
$103$	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
$105$	−1.00507	−	3.69645i	−0.0980846	−	0.360737i
$106$	8.38769			0.814684
$107$	−3.22599	−	1.86253i	−0.311868	−	0.180057i	0.335894	−	0.941900i	$-0.390962\pi$
$107$	−3.22599	−	1.86253i	−0.311868	−	0.180057i	−0.647762	+	0.761843i	$0.724295\pi$
$108$	0.585609	−	5.16305i	0.0563503	−	0.496814i
$109$	−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	$-0.771639\pi$
$113$		−	13.9774i		−	1.31488i	0.753506	−	0.657441i	$-0.228361\pi$
$114$	1.44578	+	4.49149i	0.135410	+	0.420667i
$115$	5.08701	−	2.93699i	0.474366	−	0.273876i
$116$	−6.28423	+	3.62820i	−0.583476	+	0.336870i
$117$	−4.77201	+	10.5620i	−0.441173	+	0.976453i
$118$		−	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
$123$	1.41538	+	0.304905i	0.127621	+	0.0274923i
$124$	−4.85360	−	2.80223i	−0.435866	−	0.251647i
$125$	7.77507			0.695423
$126$	−7.92598	+	0.422880i	−0.706102	+	0.0376731i
$127$	−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
$129$	16.6796	+	3.59315i	1.46855	+	0.316359i
$130$	1.61471	+	2.79675i	0.141619	+	0.245292i
$131$	−5.20268	+	9.01131i	−0.454561	+	0.787322i	−0.998663	−	0.0516968i	$-0.983537\pi$
$131$	−5.20268	+	9.01131i	−0.454561	+	0.787322i	0.544102	+	0.839019i	$0.316870\pi$
$132$	1.28398	+	1.16249i	0.111756	+	0.101182i
$133$	6.40082	−	3.31334i	0.555022	−	0.287303i
$134$			12.7043i			1.09748i
$135$	−3.98242	+	1.73400i	−0.342752	+	0.149239i
$136$	−1.84573	+	1.06563i	−0.158270	+	0.0913773i
$137$	−5.61907	+	3.24417i	−0.480070	+	0.277168i	−0.720446	−	0.693511i	$-0.756063\pi$
$137$	−5.61907	+	3.24417i	−0.480070	+	0.277168i	0.240376	+	0.970680i	$0.422729\pi$
$138$	−3.72934	−	11.5857i	−0.317463	−	0.986237i
$139$			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
$144$	−2.43668	+	1.75003i	−0.203057	+	0.145836i
$145$	5.25309	+	3.03287i	0.436246	+	0.251866i
$146$	12.4232			1.02815
$147$	2.64053	+	11.8333i	0.217787	+	0.975996i
$148$	3.52263			0.289558
$149$	4.20728	+	2.42908i	0.344674	+	0.198998i	0.662337	−	0.749206i	$-0.269565\pi$
$149$	4.20728	+	2.42908i	0.344674	+	0.198998i	−0.317663	+	0.948204i	$0.602898\pi$
$150$	1.56890	−	7.28290i	0.128100	−	0.594646i
$151$	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
$156$	6.36960	−	2.05033i	0.509976	−	0.164158i
$157$	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
$159$	−13.8291	+	4.45149i	−1.09672	+	0.353026i
$160$			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
$165$	0.304905	−	1.41538i	0.0237368	−	0.110187i
$166$	2.95806	+	1.70784i	0.229590	+	0.132554i
$167$	−3.37801			−0.261398			−0.130699	−	0.991422i	$-0.541722\pi$
$167$	−3.37801			−0.261398			−0.130699	+	0.991422i	$0.541722\pi$
$168$	3.25228	+	3.22841i	0.250919	+	0.249077i
$169$	−1.92522			−0.148094
$170$	1.54288	+	0.890781i	0.118333	+	0.0683198i
$171$	−4.76742	−	6.63799i	−0.364574	−	0.507620i
$172$	−4.92543	−	8.53109i	−0.375560	−	0.650490i
$173$	5.09256	−	8.82057i	0.387180	−	0.670615i	−0.604889	−	0.796310i	$-0.706783\pi$
$173$	5.09256	−	8.82057i	0.387180	−	0.670615i	0.992069	+	0.125694i	$0.0401159\pi$
$174$	8.43550	−	9.31710i	0.639494	−	0.706328i
$175$	−11.3680	−	0.522570i	−0.859341	−	0.0395026i
$176$		−	1.00000i		−	0.0753778i
$177$	3.83068	+	11.9005i	0.287932	+	0.894495i
$178$	−0.616180	+	0.355752i	−0.0461846	+	0.0266647i
$179$	16.5044	−	9.52883i	1.23360	−	0.712218i	0.265820	−	0.964023i	$-0.414357\pi$
$179$	16.5044	−	9.52883i	1.23360	−	0.712218i	0.967778	+	0.251805i	$0.0810241\pi$
$180$	2.28532	+	1.03253i	0.170338	+	0.0769606i
$181$			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
$186$	9.48951	+	2.04425i	0.695804	+	0.149892i
$187$	−1.84573	−	1.06563i	−0.134973	−	0.0779268i
$188$	11.6858			0.852274
$189$	12.8434	−	4.90367i	0.934223	−	0.356690i
$190$	−2.27720			−0.165206
$191$	7.70390	+	4.44785i	0.557435	+	0.321835i	0.752115	−	0.659032i	$-0.229034\pi$
$191$	7.70390	+	4.44785i	0.557435	+	0.321835i	−0.194680	+	0.980867i	$0.562367\pi$
$192$	1.69321	+	0.364755i	0.122197	+	0.0263239i
$193$	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	$-0.755963\pi$
$197$		−	19.4741i		−	1.38748i	0.720228	−	0.693738i	$-0.244037\pi$
$198$	−2.73391	−	1.23521i	−0.194290	−	0.0877827i
$199$	−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
$201$	−6.74236	−	20.9460i	−0.475570	−	1.47742i
$202$		−	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
$207$	12.2974	+	17.1225i	0.854730	+	1.19010i
$208$	−3.34573	−	1.93166i	−0.231985	−	0.133936i
$209$	2.72420			0.188437
$210$	0.977810	−	3.70375i	0.0674753	−	0.255583i
$211$	−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
$213$	−0.971880	+	4.51151i	−0.0665921	+	0.309124i
$214$	−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
$219$	−20.4826	+	6.59319i	−1.38408	+	0.445526i
$220$	−0.723925	+	0.417958i	−0.0488070	+	0.0281788i
$221$	−7.13065	+	4.11688i	−0.479659	+	0.276931i
$222$	−5.80789	+	1.86952i	−0.389800	+	0.125474i
$223$		−	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	0.962510	−	0.271246i	$-0.0874356\pi$
$227$	3.71163	+	6.42873i	0.246350	+	0.426690i	−0.716161	+	0.697935i	$0.754102\pi$
$228$	−0.993664	+	4.61263i	−0.0658070	+	0.305479i
$229$	−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
$231$	−1.16975	+	4.43077i	−0.0769636	+	0.291523i
$232$	−7.25640			−0.476406
$233$	12.0947	+	6.98286i	0.792348	+	0.457462i	0.840788	−	0.541364i	$-0.182092\pi$
$233$	12.0947	+	6.98286i	0.792348	+	0.457462i	−0.0484405	+	0.998826i	$0.515425\pi$
$234$	−9.41366	+	6.76091i	−0.615390	+	0.441975i
$235$	−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	$-0.903254\pi$
$239$		−	9.25345i		−	0.598556i	0.954166	−	0.299278i	$-0.0967458\pi$
$240$	−0.443635	−	1.37821i	−0.0286365	−	0.0889630i
$241$	−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
$243$	−7.60853	−	13.6055i	−0.488088	−	0.872795i
$244$		−	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
$249$	−5.78344	−	1.24588i	−0.366511	−	0.0789546i
$250$	6.73341	+	3.88753i	0.425858	+	0.245869i
$251$	20.1964			1.27478			0.637392	−	0.770540i	$-0.280013\pi$
$251$	20.1964			1.27478			0.637392	+	0.770540i	$0.280013\pi$
$252$	−7.07554	−	3.59677i	−0.445717	−	0.226575i
$253$	−7.02699			−0.441783
$254$	−9.03483	−	5.21626i	−0.566896	−	0.327298i
$255$	−3.01656	−	0.649833i	−0.188904	−	0.0406941i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−14.1698	+	24.5429i	−0.883890	+	1.53094i	−0.0369100	+	0.999319i	$0.511751\pi$
$257$	−14.1698	+	24.5429i	−0.883890	+	1.53094i	−0.846980	+	0.531624i	$0.821582\pi$
$258$	12.6483	+	11.4515i	0.787451	+	0.712941i
$259$	4.28445	+	8.27683i	0.266223	+	0.514297i
$260$			3.22941i			0.200280i
$261$	−8.96319	+	19.8383i	−0.554808	+	1.22796i
$262$	−9.01131	+	5.20268i	−0.556721	+	0.321423i
$263$	16.5761	−	9.57022i	1.02213	−	0.590125i	0.107407	−	0.994215i	$-0.465745\pi$
$263$	16.5761	−	9.57022i	1.02213	−	0.590125i	0.914719	+	0.404090i	$0.132412\pi$
$264$	0.530717	+	1.64874i	0.0326634	+	0.101473i
$265$		−	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	0.965916	−	0.258856i	$-0.0833455\pi$
$269$	4.24434	+	7.35142i	0.258782	+	0.448224i	−0.707134	+	0.707080i	$0.750012\pi$
$270$	−4.31588	−	0.489521i	−0.262656	−	0.0297913i
$271$	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
$273$	12.5646	+	12.4724i	0.760445	+	0.754863i
$274$	−6.48835			−0.391975
$275$	−3.72499	−	2.15062i	−0.224625	−	0.129687i
$276$	2.56313	−	11.8982i	0.154282	−	0.716185i
$277$	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	$0.113796\pi$
$281$			11.7320i			0.699870i	−0.936774	+	0.349935i	$0.886204\pi$
$282$	−19.2668	+	6.20185i	−1.14732	+	0.369315i
$283$	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
$285$	3.75451	−	1.20855i	0.222398	−	0.0715884i
$286$		−	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
$291$	3.59142	−	16.6715i	0.210533	−	0.977302i
$292$	10.7588	+	6.21158i	0.629610	+	0.363505i
$293$	6.45384			0.377038			0.188519	−	0.982070i	$-0.439631\pi$
$293$	6.45384			0.377038			0.188519	+	0.982070i	$0.439631\pi$
$294$	−3.62990	+	11.5682i	−0.211700	+	0.674673i
$295$	−6.03359			−0.351289
$296$	3.05069	+	1.76131i	0.177317	+	0.102374i
$297$	5.16305	+	0.585609i	0.299590	+	0.0339805i
$298$	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
$303$	3.52082	+	10.9379i	0.202266	+	0.628364i
$304$	2.35922	−	1.36210i	0.135311	−	0.0781217i
$305$	−1.93645	+	1.11801i	−0.110881	+	0.0640170i
$306$	−2.63257	+	5.82669i	−0.150494	+	0.333090i
$307$		−	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	$-0.864825\pi$
$311$	−14.3269	−	24.8149i	−0.812405	−	1.40713i	0.0987717	−	0.995110i	$-0.468509\pi$
$312$	6.54140	+	1.40916i	0.370334	+	0.0797782i
$313$	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
$315$	0.353492	+	6.62546i	0.0199170	+	0.373302i
$316$	5.62145			0.316231
$317$	−9.12201	−	5.26659i	−0.512343	−	0.295801i	0.221453	−	0.975171i	$-0.428920\pi$
$317$	−9.12201	−	5.26659i	−0.512343	−	0.295801i	−0.733796	+	0.679370i	$0.762253\pi$
$318$	−14.2021	−	3.05945i	−0.796414	−	0.171565i
$319$	−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
$324$	−2.87481	+	8.52851i	−0.159711	+	0.473806i
$325$	−14.3908	+	8.30853i	−0.798258	+	0.460875i
$326$	5.40870	−	3.12271i	0.299560	−	0.172951i
$327$	9.56492	+	29.7146i	0.528942	+	1.64322i
$328$		−	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
$333$	8.58351	−	6.16470i	0.470374	−	0.337823i
$334$	−2.92544	−	1.68901i	−0.160073	−	0.0924183i
$335$	10.6197			0.580216
$336$	1.20235	+	4.42203i	0.0655938	+	0.241241i
$337$	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
$339$	−5.09832	+	23.6666i	−0.276903	+	1.28539i
$340$	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
$345$	−9.68465	+	3.11742i	−0.521404	+	0.167836i
$346$	8.82057	−	5.09256i	0.474197	−	0.273778i
$347$	−1.10854	+	0.640018i	−0.0595098	+	0.0343580i	−0.529460	−	0.848335i	$-0.677605\pi$
$347$	−1.10854	+	0.640018i	−0.0595098	+	0.0343580i	0.469950	+	0.882693i	$0.344272\pi$
$348$	11.9639	−	3.85110i	0.641333	−	0.206440i
$349$		−	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	0.993692	−	0.112143i	$-0.0357716\pi$
$353$	7.51019	+	13.0080i	0.399727	+	0.692347i	−0.593965	+	0.804491i	$0.702438\pi$
$354$	−2.63278	+	12.2215i	−0.139930	+	0.649563i
$355$	−1.92888	−	1.11364i	−0.102374	−	0.0591059i
$356$	−0.711503			−0.0377096
$357$	9.44315	+	2.49304i	0.499784	+	0.131946i
$358$	19.0577			1.00723
$359$	27.0726	+	15.6304i	1.42884	+	0.824940i	0.997029	−	0.0770249i	$-0.0245421\pi$
$359$	27.0726	+	15.6304i	1.42884	+	0.824940i	0.431809	+	0.901965i	$0.357875\pi$
$360$	1.46288	+	2.03686i	0.0771004	+	0.107352i
$361$	−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
$366$	1.41963	+	4.41026i	0.0742052	+	0.230528i
$367$	−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
$369$	−2.28532	−	1.03253i	−0.118969	−	0.0537516i
$370$		−	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
$375$	−13.1648	−	2.83599i	−0.679828	−	0.146450i
$376$	10.1202	+	5.84290i	0.521909	+	0.301324i
$377$	−28.0338			−1.44381
$378$	13.5746	+	2.17502i	0.698201	+	0.111871i
$379$	−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
$381$	17.6644	+	3.80532i	0.904977	+	0.194952i
$382$	4.44785	+	7.70390i	0.227572	+	0.394166i
$383$	11.4425	−	19.8189i	0.584683	−	1.01270i	−0.410232	−	0.911981i	$-0.634552\pi$
$383$	11.4425	−	19.8189i	0.584683	−	1.01270i	0.994915	−	0.100720i	$-0.0321145\pi$
$384$	1.28398	+	1.16249i	0.0655230	+	0.0593231i
$385$	−1.86253	−	1.19260i	−0.0949232	−	0.0607805i
$386$			6.15351i			0.313206i
$387$	−26.9313	−	12.1679i	−1.36900	−	0.618529i
$388$	−8.52699	+	4.92306i	−0.432892	+	0.249930i
$389$	−15.3333	+	8.85268i	−0.777428	+	0.448849i	−0.835518	−	0.549463i	$-0.814832\pi$
$389$	−15.3333	+	8.85268i	−0.777428	+	0.448849i	0.0580897	+	0.998311i	$0.481499\pi$
$390$	−1.71390	−	5.32446i	−0.0867869	−	0.269614i
$391$			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
$396$	−1.75003	−	2.43668i	−0.0879422	−	0.122448i
$397$	−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
$399$	−12.0465	+	3.27545i	−0.603078	+	0.163978i
$400$	−4.30124			−0.215062
$401$	−22.4661	−	12.9708i	−1.12191	−	0.647733i	−0.180019	−	0.983663i	$-0.557616\pi$
$401$	−22.4661	−	12.9708i	−1.12191	−	0.647733i	−0.941887	+	0.335931i	$0.890949\pi$
$402$	4.63394	−	21.5109i	0.231120	−	1.07287i
$403$	−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
$408$	3.51390	−	1.13110i	0.173964	−	0.0559978i
$409$	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
$411$	10.6976	−	3.44348i	0.527673	−	0.169854i
$412$			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
$417$	5.48674	−	25.4697i	0.268687	−	1.24726i
$418$	2.35922	+	1.36210i	0.115393	+	0.0666224i
$419$	−7.14212			−0.348916			−0.174458	−	0.984665i	$-0.555817\pi$
$419$	−7.14212			−0.348916			−0.174458	+	0.984665i	$0.555817\pi$
$420$	2.69868	−	2.71864i	0.131682	−	0.132656i
$421$	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
$423$	28.4745	−	20.4505i	1.38448	−	0.994336i
$424$	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
$429$	2.05033	+	6.36960i	0.0989908	+	0.307527i
$430$	−7.13129	+	4.11725i	−0.343901	+	0.198551i
$431$	−22.0931	+	12.7555i	−1.06419	+	0.614410i	−0.926588	−	0.376078i	$-0.877272\pi$
$431$	−22.0931	+	12.7555i	−1.06419	+	0.614410i	−0.137601	+	0.990488i	$0.543939\pi$
$432$	4.76414	−	2.07437i	0.229215	−	0.0998032i
$433$		−	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
$438$	−21.0350	−	4.53141i	−1.00509	−	0.216519i
$439$	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
$441$	−0.154704	−	20.9994i	−0.00736688	−	0.999973i
$442$	−8.23376			−0.391640
$443$	8.86868	+	5.12033i	0.421363	+	0.243274i	0.695661	−	0.718371i	$-0.255112\pi$
$443$	8.86868	+	5.12033i	0.421363	+	0.243274i	−0.274297	+	0.961645i	$0.588445\pi$
$444$	−5.96454	−	1.28490i	−0.283065	−	0.0609784i
$445$	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	$-0.865158\pi$
$449$		−	17.4205i		−	0.822123i	0.911608	−	0.411061i	$-0.134842\pi$
$450$	−5.31295	+	11.7592i	−0.250455	+	0.554334i
$451$	0.723925	−	0.417958i	0.0340883	−	0.0196809i
$452$	12.1048	−	6.98869i	0.569360	−	0.328720i
$453$	−8.97303	−	27.8758i	−0.421590	−	1.30972i
$454$			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
$459$	1.24809	−	11.0038i	0.0582559	−	0.513615i
$460$	5.08701	+	2.93699i	0.237183	+	0.136938i
$461$	−6.62247			−0.308439			−0.154220	−	0.988037i	$-0.549286\pi$
$461$	−6.62247			−0.308439			−0.154220	+	0.988037i	$0.549286\pi$
$462$	−3.22841	+	3.25228i	−0.150199	+	0.151310i
$463$	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
$465$	1.70882	−	7.93244i	0.0792448	−	0.367858i
$466$	6.98286	+	12.0947i	0.323475	+	0.560275i
$467$	12.4871	−	21.6284i	0.577836	−	1.00084i	−0.417891	−	0.908497i	$-0.637231\pi$
$467$	12.4871	−	21.6284i	0.577836	−	1.00084i	0.995727	−	0.0923444i	$-0.0294361\pi$
$468$	−11.5329	+	1.14829i	−0.533110	+	0.0530798i
$469$	−33.5768	−	1.54348i	−1.55043	−	0.0712711i
$470$		−	9.76835i		−	0.450581i
$471$	−6.25534	+	2.01355i	−0.288231	+	0.0927794i
$472$	6.25091	−	3.60897i	0.287722	−	0.166116i
$473$	8.53109	−	4.92543i	0.392260	−	0.226471i
$474$	−9.26829	+	2.98340i	−0.425707	+	0.137032i
$475$		−	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	$0.0638429\pi$
$479$	14.4998	+	25.1144i	0.662512	+	1.14750i	−0.317442	+	0.948278i	$0.602824\pi$
$480$	0.304905	−	1.41538i	0.0139169	−	0.0646030i
$481$	11.7858	+	6.80452i	0.537385	+	0.310259i
$482$	−4.75945			−0.216787
$483$	31.0735	−	8.44893i	1.41390	−	0.384440i
$484$	1.00000			0.0454545
$485$	7.12785	+	4.11527i	0.323659	+	0.186865i
$486$	0.213576	−	15.5870i	0.00968800	−	0.707040i
$487$	−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	$-0.737653\pi$
$491$		−	32.5285i		−	1.46799i	0.679154	−	0.733996i	$-0.262347\pi$
$492$	0.443635	+	1.37821i	0.0200006	+	0.0621344i
$493$	−13.3934	+	7.73266i	−0.603207	+	0.348262i
$494$	9.11443	−	5.26222i	0.410078	−	0.236759i
$495$	−1.03253	+	2.28532i	−0.0464090	+	0.102717i
$496$		−	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
$501$	5.71968	+	1.23215i	0.255536	+	0.0550482i
$502$	17.4906	+	10.0982i	0.780642	+	0.450704i
$503$	−31.3069			−1.39590			−0.697952	−	0.716145i	$-0.745905\pi$
$503$	−31.3069			−1.39590			−0.697952	+	0.716145i	$0.745905\pi$
$504$	−4.32922	−	6.65266i	−0.192839	−	0.296333i
$505$	−5.54554			−0.246773
$506$	−6.08555	−	3.51349i	−0.270536	−	0.156194i
$507$	3.25980	+	0.702234i	0.144773	+	0.0311873i
$508$	−5.21626	−	9.03483i	−0.231434	−	0.400856i
$509$	13.5445	−	23.4597i	0.600348	−	1.03983i	−0.392420	−	0.919786i	$-0.628362\pi$
$509$	13.5445	−	23.4597i	0.600348	−	1.03983i	0.992768	−	0.120048i	$-0.0383047\pi$
$510$	−2.28750	−	2.07105i	−0.101292	−	0.0917076i
$511$	−1.50933	+	32.8339i	−0.0667687	+	1.45249i
$512$		−	1.00000i		−	0.0441942i
$513$	5.65100	+	12.9784i	0.249498	+	0.573012i
$514$	−24.5429	+	14.1698i	−1.08254	+	0.625005i
$515$	11.0448	−	6.37673i	0.486693	−	0.280992i
$516$	5.22802	+	16.2415i	0.230151	+	0.714992i
$517$			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	0.640278	−	0.768143i	$-0.278819\pi$
$521$	−7.87689	−	13.6432i	−0.345093	−	0.597718i	−0.985371	+	0.170425i	$0.945486\pi$
$522$	−17.6815	+	12.6989i	−0.773899	+	0.555816i
$523$	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
$525$	19.0578	+	5.03136i	0.831751	+	0.219586i
$526$	19.1404			0.834563
$527$	−10.3443	−	5.97229i	−0.450605	−	0.260157i
$528$	−0.364755	+	1.69321i	−0.0158739	+	0.0736874i
$529$	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
$534$	1.17308	−	0.377607i	0.0507643	−	0.0163407i
$535$	−2.69666	+	1.55692i	−0.116587	+	0.0673114i
$536$	−11.0022	+	6.35213i	−0.475223	+	0.274370i
$537$	−31.4211	+	10.1142i	−1.35592	+	0.436461i
$538$			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
$543$	7.80564	−	36.2341i	0.334972	−	1.55496i
$544$	−1.84573	−	1.06563i	−0.0791351	−	0.0456887i
$545$	−15.0654			−0.645332
$546$	4.64508	+	17.0837i	0.198791	+	0.731115i
$547$	−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
$549$	−4.68120	−	6.51794i	−0.199789	−	0.278179i
$550$	−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
$555$	1.56276	+	4.85492i	0.0663356	+	0.206080i
$556$	−13.0270	+	7.52113i	−0.552467	+	0.318967i
$557$	5.76379	−	3.32773i	0.244220	−	0.141000i	−0.372895	−	0.927874i	$-0.621635\pi$
$557$	5.76379	−	3.32773i	0.244220	−	0.141000i	0.617115	+	0.786873i	$0.288301\pi$
$558$	−15.3221	−	6.92269i	−0.648634	−	0.293061i
$559$		−	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	$0.172759\pi$
$563$	20.7720	+	35.9782i	0.875435	+	1.51630i	0.0191372	+	0.999817i	$0.493908\pi$
$564$	−19.7865	−	4.26245i	−0.833161	−	0.179481i
$565$	−10.1186	−	5.84197i	−0.425692	−	0.245773i
$566$	14.2630			0.599519
$567$	−23.5353	+	3.61823i	−0.988388	+	0.151951i
$568$	2.66448			0.111799
$569$	−19.0011	−	10.9703i	−0.796566	−	0.459898i	0.0457028	−	0.998955i	$-0.485447\pi$
$569$	−19.0011	−	10.9703i	−0.796566	−	0.459898i	−0.842269	+	0.539057i	$0.818781\pi$
$570$	3.85578	+	0.830621i	0.161501	+	0.0347909i
$571$	−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
$576$	−2.73391	−	1.23521i	−0.113913	−	0.0514672i
$577$	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
$579$	−3.26577	−	10.1455i	−0.135721	−	0.421634i
$580$			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
$585$	5.65156	+	7.86904i	0.233663	+	0.325345i
$586$	5.58919	+	3.22692i	0.230887	+	0.133303i
$587$	39.3634			1.62470			0.812351	−	0.583169i	$-0.198187\pi$
$587$	39.3634			1.62470			0.812351	+	0.583169i	$0.198187\pi$
$588$	−8.92770	+	8.20343i	−0.368172	+	0.338304i
$589$	15.2676			0.629092
$590$	−5.22524	−	3.01680i	−0.215120	−	0.124200i
$591$	−7.10329	+	32.9738i	−0.292190	+	1.35636i
$592$	1.76131	+	3.05069i	0.0723896	+	0.125382i
$593$	−4.17903	+	7.23829i	−0.171612	+	0.297241i	−0.938984	−	0.343962i	$-0.888231\pi$
$593$	−4.17903	+	7.23829i	−0.171612	+	0.297241i	0.767371	+	0.641203i	$0.221564\pi$
$594$	4.17853	+	3.08868i	0.171447	+	0.126730i
$595$	−2.54175	+	3.96954i	−0.104201	+	0.162735i
$596$			4.85815i			0.198998i
$597$	21.8830	−	7.04398i	0.895611	−	0.288291i
$598$	−23.5104	+	13.5737i	−0.961412	+	0.555072i
$599$	−10.5034	+	6.06417i	−0.429159	+	0.247775i	−0.698988	−	0.715133i	$-0.746366\pi$
$599$	−10.5034	+	6.06417i	−0.429159	+	0.247775i	0.269829	+	0.962908i	$0.413033\pi$
$600$	7.09163	−	2.28274i	0.289514	−	0.0931926i
$601$			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
$606$	−2.41981	+	11.2329i	−0.0982983	+	0.456305i
$607$	−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
$609$	23.5999	+	23.4267i	0.956315	+	0.949296i
$610$	−2.23602			−0.0905337
$611$	39.0975	+	22.5730i	1.58172	+	0.913204i
$612$	−5.19321	+	3.72978i	−0.209923	+	0.150767i
$613$	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	$0.136583\pi$
$617$			20.6685i			0.832084i	−0.909345	+	0.416042i	$0.863417\pi$
$618$	−8.09707	−	25.1546i	−0.325712	−	1.01187i
$619$	−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
$621$	−14.5766	−	33.4775i	−0.584938	−	1.34341i
$622$		−	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
$627$	−4.61263	−	0.993664i	−0.184211	−	0.0396831i
$628$	3.28571	+	1.89701i	0.131114	+	0.0756989i
$629$	7.50766			0.299350
$630$	−3.00660	+	5.91456i	−0.119786	+	0.235642i
$631$	−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
$633$	28.4604	+	6.13100i	1.13120	+	0.243685i
$634$	−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
$639$	3.29119	−	7.28443i	0.130197	−	0.288168i
$640$	−0.723925	+	0.417958i	−0.0286157	+	0.0165213i
$641$	−29.6480	+	17.1173i	−1.17102	+	0.676091i	−0.953921	−	0.300058i	$-0.902994\pi$
$641$	−29.6480	+	17.1173i	−1.17102	+	0.676091i	−0.217103	+	0.976149i	$0.569661\pi$
$642$	1.97695	+	6.14164i	0.0780240	+	0.242391i
$643$			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	$-0.870542\pi$
$647$	−20.3948	−	35.3248i	−0.801802	−	1.38876i	0.116628	−	0.993176i	$-0.462792\pi$
$648$	−6.75391	+	5.94850i	−0.265319	+	0.233679i
$649$	6.25091	+	3.60897i	0.245370	+	0.141664i
$650$	−16.6171			−0.651775
$651$	−6.55578	+	24.8320i	−0.256941	+	0.973244i
$652$	6.24543			0.244590
$653$	−36.7047	−	21.1915i	−1.43637	−	0.829286i	−0.438771	−	0.898599i	$-0.644586\pi$
$653$	−36.7047	−	21.1915i	−1.43637	−	0.829286i	−0.997595	+	0.0693127i	$0.977919\pi$
$654$	−6.57384	+	30.5161i	−0.257058	+	1.19327i
$655$	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	$0.332244\pi$
$659$			44.3754i			1.72862i	−0.502961	+	0.864309i	$0.667756\pi$
$660$	1.37821	−	0.443635i	0.0536467	−	0.0172685i
$661$	−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
$663$	13.5753	−	4.36980i	0.527222	−	0.169709i
$664$			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
$669$	−2.18717	+	10.1529i	−0.0845609	+	0.392535i
$670$	9.19693	+	5.30985i	0.355308	+	0.205137i
$671$	2.67493			0.103264
$672$	−1.16975	+	4.43077i	−0.0451239	+	0.170921i
$673$	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
$675$	2.51885	−	22.2075i	0.0969505	−	0.854768i
$676$	−0.962611	−	1.66729i	−0.0370235	−	0.0641266i
$677$	9.52599	−	16.4995i	0.366113	−	0.634127i	−0.622841	−	0.782349i	$-0.714022\pi$
$677$	9.52599	−	16.4995i	0.366113	−	0.634127i	0.988954	+	0.148222i	$0.0473549\pi$
$678$	−16.2486	+	17.9467i	−0.624023	+	0.689240i
$679$	−21.9384	−	14.0474i	−0.841917	−	0.539090i
$680$			1.78156i			0.0683198i
$681$	−3.93965	−	12.2390i	−0.150968	−	0.469000i
$682$	4.85360	−	2.80223i	0.185854	−	0.107303i
$683$	−41.1088	+	23.7342i	−1.57299	+	0.908164i	−0.577185	+	0.816613i	$0.695849\pi$
$683$	−41.1088	+	23.7342i	−1.57299	+	0.908164i	−0.995800	+	0.0915501i	$0.970818\pi$
$684$	3.36496	−	7.44771i	0.128663	−	0.284770i
$685$			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
$690$	−9.94587	−	2.14256i	−0.378633	−	0.0815659i
$691$	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
$693$	3.59677	−	7.07554i	0.136630	−	0.268778i
$694$	−1.28004			−0.0485895
$695$	10.8895	+	6.28704i	0.413061	+	0.238481i
$696$	12.2866	+	2.64681i	0.465722	+	0.100327i
$697$	−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	$-0.561280\pi$
$701$		−	51.9746i		−	1.96305i	0.191328	−	0.981526i	$-0.438720\pi$
$702$	18.4054	−	8.01395i	0.694666	−	0.302467i
$703$	−8.31067	+	4.79817i	−0.313443	+	0.180966i
$704$	0.866025	−	0.500000i	0.0326396	−	0.0188445i
$705$	5.18423	+	16.1055i	0.195249	+	0.606567i
$706$			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
$711$	13.6977	−	9.83769i	0.513702	−	0.368942i
$712$	−0.616180	−	0.355752i	−0.0230923	−	0.0133324i
$713$	−39.3824			−1.47488
$714$	6.93148	+	6.88061i	0.259404	+	0.257500i
$715$	−3.22941			−0.120773
$716$	16.5044	+	9.52883i	0.616799	+	0.356109i
$717$	−3.37524	+	15.6680i	−0.126051	+	0.585133i
$718$	15.6304	+	27.0726i	0.583321	+	1.01034i
$719$	−7.00169	+	12.1273i	−0.261119	+	0.452271i	−0.966540	−	0.256518i	$-0.917425\pi$
$719$	−7.00169	+	12.1273i	−0.261119	+	0.452271i	0.705421	+	0.708789i	$0.250758\pi$
$720$	0.248459	+	2.49541i	0.00925952	+	0.0929985i
$721$	−35.8478	+	18.5564i	−1.33504	+	0.691075i
$722$		−	11.5787i		−	0.430916i
$723$	7.84709	−	2.52592i	0.291836	−	0.0939401i
$724$	−18.5327	+	10.6998i	−0.688761	+	0.397657i
$725$	−27.0300	+	15.6058i	−1.00387	+	0.579584i
$726$	−1.64874	+	0.530717i	−0.0611904	+	0.0196968i
$727$			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
$732$	−0.975693	+	4.52921i	−0.0360626	+	0.167404i
$733$	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
$735$	9.67008	+	3.03429i	0.356686	+	0.111922i
$736$	−7.02699			−0.259018
$737$	−11.0022	−	6.35213i	−0.405271	−	0.233984i
$738$	−1.46288	−	2.03686i	−0.0538493	−	0.0749779i
$739$	−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	$-0.963512\pi$
$743$		−	6.23560i		−	0.228762i	0.993437	−	0.114381i	$-0.0364884\pi$
$744$	2.97438	+	9.24028i	0.109046	+	0.338765i
$745$	3.51694	−	2.03051i	0.128851	−	0.0743920i
$746$	−12.1077	+	6.99037i	−0.443293	+	0.255936i
$747$	9.33813	+	4.21908i	0.341664	+	0.154368i
$748$		−	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
$753$	−34.1967	−	7.36672i	−1.24620	−	0.268458i
$754$	−24.2780	−	14.0169i	−0.884151	−	0.510465i
$755$	14.1332			0.514358
$756$	10.6684	+	8.67091i	0.388007	+	0.315358i
$757$	−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
$759$	11.8982	+	2.56313i	0.431876	+	0.0930356i
$760$	−1.13860	−	1.97212i	−0.0413014	−	0.0715362i
$761$	14.3382	−	24.8345i	0.519759	−	0.900249i	−0.479977	−	0.877281i	$-0.659355\pi$
$761$	14.3382	−	24.8345i	0.519759	−	0.900249i	0.999736	−	0.0229682i	$-0.00731164\pi$
$762$	13.3952	+	12.1277i	0.485257	+	0.439341i
$763$	47.6331	+	2.18962i	1.72443	+	0.0792696i
$764$			8.89570i			0.321835i
$765$	4.87063	+	2.20061i	0.176098	+	0.0795631i
$766$	19.8189	−	11.4425i	0.716088	−	0.413433i
$767$	24.1493	−	13.9426i	0.871979	−	0.503437i
$768$	0.530717	+	1.64874i	0.0191506	+	0.0594937i
$769$			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	0.932228	−	0.361870i	$-0.117862\pi$
$773$	4.24621	+	7.35464i	0.152725	+	0.264528i	−0.779503	+	0.626398i	$0.784528\pi$
$774$	−17.2393	−	24.0034i	−0.619653	−	0.862784i
$775$	−20.8765	−	12.0531i	−0.749906	−	0.432959i
$776$	−9.84612			−0.353455
$777$	−4.23545	−	15.5772i	−0.151946	−	0.558828i
$778$	−17.7054			−0.634768
$779$	1.97212	+	1.13860i	0.0706584	+	0.0407946i
$780$	1.17794	−	5.46807i	0.0421772	−	0.195788i
$781$	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
$786$	17.1557	−	5.52231i	0.611925	−	0.196974i
$787$	−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
$789$	−31.5576	+	10.1582i	−1.12348	+	0.361640i
$790$		−	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
$795$	−2.55745	+	11.8718i	−0.0907032	+	0.421048i
$796$	−11.4944	−	6.63628i	−0.407407	−	0.235217i
$797$	29.2744			1.03695			0.518476	−	0.855092i	$-0.326500\pi$
$797$	29.2744			1.03695			0.518476	+	0.855092i	$0.326500\pi$
$798$	−12.0703	−	3.18662i	−0.427284	−	0.112805i
$799$	24.9055			0.881095
$800$	−3.72499	−	2.15062i	−0.131698	−	0.0760359i
$801$	−1.73371	+	1.24515i	−0.0612575	+	0.0439952i
$802$	−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
$807$	−4.50509	−	13.9956i	−0.158587	−	0.492669i
$808$	5.74529	−	3.31704i	0.202118	−	0.116693i
$809$	−37.5875	+	21.7011i	−1.32151	+	0.762972i	−0.983969	−	0.178341i	$-0.942927\pi$
$809$	−37.5875	+	21.7011i	−1.32151	+	0.762972i	−0.337537	+	0.941312i	$0.609594\pi$
$810$	7.12913	+	2.40310i	0.250492	+	0.0844363i
$811$		−	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
$816$	3.60868	+	0.777390i	0.126329	+	0.0272141i
$817$	23.2404	+	13.4178i	0.813078	+	0.469431i
$818$	9.87793			0.345374
$819$	−16.7251	−	25.7013i	−0.584423	−	0.898078i
$820$	−0.698757			−0.0244017
$821$	−35.4502	−	20.4672i	−1.23722	−	0.714310i	−0.268696	−	0.963225i	$-0.586593\pi$
$821$	−35.4502	−	20.4672i	−1.23722	−	0.714310i	−0.968525	+	0.248915i	$0.919926\pi$
$822$	10.9861	+	2.36666i	0.383185	+	0.0825466i
$823$	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	$0.260474\pi$
$827$			41.9854i			1.45998i	−0.683460	+	0.729988i	$0.739526\pi$
$828$	−8.67982	+	19.2111i	−0.301644	+	0.667633i
$829$	−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
$831$	−10.7744	−	33.4721i	−0.373761	−	1.16114i
$832$		−	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
$837$	28.9361	+	3.28202i	1.00018	+	0.113443i
$838$	−6.18526	−	3.57106i	−0.213666	−	0.123360i
$839$	−19.4169			−0.670345			−0.335172	−	0.942157i	$-0.608795\pi$
$839$	−19.4169			−0.670345			−0.335172	+	0.942157i	$0.608795\pi$
$840$	3.69645	−	1.00507i	0.127540	−	0.0346782i
$841$	−23.6553			−0.815701
$842$	2.45312	+	1.41631i	0.0845401	+	0.0488092i
$843$	4.27929	−	19.8646i	0.147387	−	0.684175i
$844$	−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
$849$	−23.5160	+	7.56963i	−0.807067	+	0.259789i
$850$	−7.93894	+	4.58355i	−0.272303	+	0.157214i
$851$	21.4371	−	12.3767i	0.734855	−	0.424269i
$852$	−4.39302	+	1.41408i	−0.150503	+	0.0484457i
$853$		−	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	$0.0637937\pi$
$857$	19.3914	+	33.5868i	0.662396	+	1.14730i	−0.317588	+	0.948229i	$0.602873\pi$
$858$	−1.40916	+	6.54140i	−0.0481081	+	0.223320i
$859$	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
$861$	−2.69868	+	2.71864i	−0.0919709	+	0.0926510i
$862$	−25.5110			−0.868907
$863$	25.5304	+	14.7400i	0.869063	+	0.501754i	0.867037	−	0.498244i	$-0.166022\pi$
$863$	25.5304	+	14.7400i	0.869063	+	0.501754i	0.00202656	+	0.999998i	$0.499355\pi$
$864$	5.16305	+	0.585609i	0.175650	+	0.0199228i
$865$	−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
$870$	−3.21920	−	10.0008i	−0.109141	−	0.339060i
$871$	−42.5050	+	24.5403i	−1.44023	+	0.831516i
$872$	15.6081	−	9.01132i	0.528556	−	0.305162i
$873$	−12.1620	+	26.9184i	−0.411623	+	0.911049i
$874$		−	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
$879$	−10.9277	−	2.35407i	−0.368582	−	0.0794008i
$880$	−0.723925	−	0.417958i	−0.0244035	−	0.0140894i
$881$	−15.9253			−0.536538			−0.268269	−	0.963344i	$-0.586452\pi$
$881$	−15.9253			−0.536538			−0.268269	+	0.963344i	$0.586452\pi$
$882$	10.3657	−	18.2634i	0.349033	−	0.614960i
$883$	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
$885$	10.2161	+	2.20078i	0.343411	+	0.0739785i
$886$	5.12033	+	8.86868i	0.172021	+	0.297949i
$887$	2.94979	−	5.10919i	0.0990443	−	0.171550i	−0.812245	−	0.583316i	$-0.801755\pi$
$887$	2.94979	−	5.10919i	0.0990443	−	0.171550i	0.911289	+	0.411767i	$0.135088\pi$
$888$	−4.52300	−	4.09502i	−0.151782	−	0.137420i
$889$	14.8840	−	23.2450i	0.499195	−	0.779611i
$890$			0.594758i			0.0199363i
$891$	−8.52851	−	2.87481i	−0.285716	−	0.0963096i
$892$	5.19292	−	2.99814i	0.173872	−	0.100385i
$893$	−27.5694	+	15.9172i	−0.922575	+	0.532649i
$894$	−2.57831	−	8.00983i	−0.0862314	−	0.267889i
$895$		−	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
$900$	−10.4807	+	7.52729i	−0.349358	+	0.250910i
$901$	15.4814	+	8.93820i	0.515761	+	0.297775i
$902$	0.835917			0.0278330
$903$	−31.8026	+	32.0378i	−1.05833	+	1.06615i
$904$	13.9774			0.464881
$905$	15.4918	+	8.94418i	0.514964	+	0.297315i
$906$	6.16704	−	28.6277i	0.204886	−	0.951091i
$907$	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	$-0.920964\pi$
$911$		−	14.8351i		−	0.491510i	0.969332	−	0.245755i	$-0.0790359\pi$
$912$	−4.49149	+	1.44578i	−0.148728	+	0.0478745i
$913$	−2.95806	+	1.70784i	−0.0978974	+	0.0565211i
$914$	−5.96396	+	3.44330i	−0.197270	+	0.113894i
$915$	3.68661	−	1.18669i	0.121876	−	0.0392309i
$916$		−	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
$921$	−4.24454	+	19.7033i	−0.139862	+	0.649247i
$922$	−5.73523	−	3.31124i	−0.188880	−	0.109050i
$923$	10.2937			0.338822
$924$	−4.42203	+	1.20235i	−0.145474	+	0.0395546i
$925$	15.1517			0.498184
$926$	18.5182	+	10.6915i	0.608544	+	0.351343i
$927$	26.6999	+	37.1761i	0.876940	+	1.22102i
$928$	−3.62820	−	6.28423i	−0.119101	−	0.206290i
$929$	10.2616	−	17.7737i	0.336674	−	0.583136i	−0.647131	−	0.762379i	$-0.724031\pi$
$929$	10.2616	−	17.7737i	0.336674	−	0.583136i	0.983805	+	0.179243i	$0.0573648\pi$
$930$	5.44610	−	6.01528i	0.178585	−	0.197249i
$931$	−1.74948	+	18.9890i	−0.0573370	+	0.622338i
$932$			13.9657i			0.457462i
$933$	15.2071	+	47.2427i	0.497857	+	1.54666i
$934$	21.6284	−	12.4871i	0.707702	−	0.408592i
$935$	−1.54288	+	0.890781i	−0.0504575	+	0.0291317i
$936$	−10.5620	−	4.77201i	−0.345228	−	0.155978i
$937$			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	0.776765	−	0.629790i	$-0.216859\pi$
$941$	−4.81705	−	8.34338i	−0.157031	−	0.271987i	−0.933797	+	0.357804i	$0.883526\pi$
$942$	−6.42406	−	1.38389i	−0.209307	−	0.0450894i
$943$	−5.08701	−	2.93699i	−0.165656	−	0.0956415i
$944$	7.21793			0.234924
$945$	1.81813	−	11.3472i	0.0591439	−	0.369125i
$946$	9.85086			0.320279
$947$	9.23315	+	5.33076i	0.300037	+	0.173227i	0.642460	−	0.766320i	$-0.277914\pi$
$947$	9.23315	+	5.33076i	0.300037	+	0.173227i	−0.342422	+	0.939546i	$0.611247\pi$
$948$	−9.51828	−	2.05045i	−0.309139	−	0.0665955i
$949$	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	$-0.892179\pi$
$953$		−	20.5160i		−	0.664579i	0.943177	−	0.332290i	$-0.107821\pi$
$954$	22.9312	+	10.3606i	0.742424	+	0.335436i
$955$	6.43982	−	3.71803i	0.208388	−	0.120313i
$956$	8.01372	−	4.62673i	0.259182	−	0.149639i
$957$	3.85110	+	11.9639i	0.124488	+	0.386738i
$958$			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
$963$	−6.51895	−	9.07676i	−0.210070	−	0.292494i
$964$	−4.12181	−	2.37973i	−0.132754	−	0.0766458i
$965$	5.14382			0.165586
$966$	31.1349	+	8.21978i	1.00175	+	0.264467i
$967$	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
$969$	−2.11776	+	9.83075i	−0.0680324	+	0.315809i
$970$	4.11527	+	7.12785i	0.132133	+	0.228862i
$971$	−24.3770	+	42.2221i	−0.782294	+	1.35497i	0.148309	+	0.988941i	$0.452617\pi$
$971$	−24.3770	+	42.2221i	−0.782294	+	1.35497i	−0.930602	+	0.366032i	$0.880716\pi$
$972$	7.97846	−	13.3919i	0.255909	−	0.429547i
$973$	−33.5160	−	21.4607i	−1.07448	−	0.688000i
$974$		−	15.6226i		−	0.500580i
$975$	27.3972	−	8.81896i	0.877413	−	0.282433i
$976$	2.31656	−	1.33746i	0.0741511	−	0.0428112i
$977$	−14.6963	+	8.48489i	−0.470175	+	0.271456i	−0.716313	−	0.697779i	$-0.754172\pi$
$977$	−14.6963	+	8.48489i	−0.470175	+	0.271456i	0.246138	+	0.969235i	$0.420838\pi$
$978$	−10.2971	+	3.31455i	−0.329264	+	0.105988i
$979$		−	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	0.988031	−	0.154256i	$-0.0492980\pi$
$983$	11.3004	+	19.5728i	0.360426	+	0.624276i	−0.627605	+	0.778532i	$0.715965\pi$
$984$	−0.304905	+	1.41538i	−0.00972001	+	0.0451207i
$985$	−14.0978	−	8.13939i	−0.449194	−	0.259342i
$986$	−15.4653			−0.492516
$987$	−14.0505	−	51.6749i	−0.447231	−	1.64483i
$988$	10.5244			0.334827
$989$	−59.9479	−	34.6109i	−1.90623	−	1.10056i
$990$	−2.03686	+	1.46288i	−0.0647357	+	0.0464933i
$991$	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
$996$	−1.81275	−	5.63155i	−0.0574393	−	0.178442i
$997$	−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
$999$	−16.7823	+	7.30724i	−0.530968	+	0.231191i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.69321 - 0.364755i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.417958 - 0.723925i) q^{5} +(-1.28398 - 1.16249i) q^{6} +(-1.42670 + 2.22812i) q^{7} +1.00000i q^{8} +(2.73391 + 1.23521i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.69321 - 0.364755i) 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} +(2.73391 + 1.23521i) q^{9} +(0.723925 - 0.417958i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(-0.530717 - 1.64874i) 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} +(1.75003 + 2.43668i) q^{18} +(-2.35922 - 1.36210i) q^{19} +0.835917 q^{20} +(3.22841 - 3.25228i) q^{21} -1.00000 q^{22} +(6.08555 + 3.51349i) q^{23} +(0.364755 - 1.69321i) 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} +(-1.37821 + 0.443635i) q^{30} +(-4.85360 + 2.80223i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.64874 - 0.530717i) 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} +(1.40916 - 6.54140i) q^{39} +(0.723925 + 0.417958i) q^{40} -0.835917 q^{41} +(4.42203 - 1.20235i) q^{42} -9.85086 q^{43} +(-0.866025 - 0.500000i) q^{44} +(2.03686 - 1.46288i) 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} +(-1.13110 - 3.51390i) q^{51} +(-3.34573 + 1.93166i) q^{52} +(7.26395 - 4.19384i) q^{53} +(-2.07437 - 4.76414i) 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} +(-1.41538 - 0.304905i) q^{60} +(-2.31656 - 1.33746i) q^{61} -5.60445 q^{62} +(-6.65266 + 4.32922i) q^{63} -1.00000 q^{64} +(2.79675 + 1.61471i) q^{65} +(1.69321 + 0.364755i) 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} +(-1.23521 + 2.73391i) q^{72} +(10.7588 - 6.21158i) q^{73} +(3.05069 - 1.76131i) q^{74} +(-2.28274 - 7.09163i) 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} +(5.94850 + 6.75391i) q^{81} +(-0.723925 - 0.417958i) q^{82} +3.41567 q^{83} +(4.43077 + 1.16975i) q^{84} +1.78156 q^{85} +(-8.53109 - 4.92543i) q^{86} +(2.64681 - 12.2866i) 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} +(9.24028 - 2.97438i) q^{93} +(10.1202 - 5.84290i) q^{94} +(-1.97212 + 1.13860i) q^{95} +(1.64874 - 0.530717i) 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

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