LMFDB - Embedded newform 462.2.n.e.263.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(65,462)]

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, 2, 3]))

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

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

chi := DirichletCharacter("462.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.n (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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			263.5
Character	$\chi$	$=$	462.263
Dual form			462.2.n.e.65.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.470476 + 1.66693i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.00577 - 0.580683i) q^{5} +(1.67884 - 0.426020i) q^{6} +(-2.19957 - 1.47034i) q^{7} +1.00000 q^{8} +(-2.55730 - 1.56850i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.470476 + 1.66693i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.00577 - 0.580683i) q^{5} +(1.67884 - 0.426020i) q^{6} +(-2.19957 - 1.47034i) q^{7} +1.00000 q^{8} +(-2.55730 - 1.56850i) q^{9} +(-1.00577 - 0.580683i) q^{10} +(2.34054 - 2.34986i) q^{11} +(-1.20836 - 1.24091i) q^{12} -3.56641i q^{13} +(-0.173570 + 2.64005i) q^{14} +(0.494765 + 1.94975i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.71320 + 2.96735i) q^{17} +(-0.0797091 + 2.99894i) q^{18} +(4.30482 - 2.48539i) q^{19} +1.16137i q^{20} +(3.48580 - 2.97476i) q^{21} +(-3.20531 - 0.852040i) q^{22} +(7.67576 - 4.43160i) q^{23} +(-0.470476 + 1.66693i) q^{24} +(-1.82562 + 3.16206i) q^{25} +(-3.08860 + 1.78320i) q^{26} +(3.81773 - 3.52490i) q^{27} +(2.37314 - 1.16971i) q^{28} +6.04247 q^{29} +(1.44115 - 1.40335i) q^{30} +(-0.547062 + 0.947540i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.81588 + 5.00708i) q^{33} +3.42640 q^{34} +(-3.06606 - 0.201578i) q^{35} +(2.63701 - 1.43044i) q^{36} +(-5.31249 - 9.20151i) q^{37} +(-4.30482 - 2.48539i) q^{38} +(5.94495 + 1.67791i) q^{39} +(1.00577 - 0.580683i) q^{40} -4.05294 q^{41} +(-4.31912 - 1.53141i) q^{42} -6.97962i q^{43} +(0.864767 + 3.20190i) q^{44} +(-3.48287 - 0.0925714i) q^{45} +(-7.67576 - 4.43160i) q^{46} +(4.23571 - 2.44549i) q^{47} +(1.67884 - 0.426020i) q^{48} +(2.67619 + 6.46823i) q^{49} +3.65123 q^{50} +(-4.14034 - 4.25185i) q^{51} +(3.08860 + 1.78320i) q^{52} +(-1.75416 - 1.01277i) q^{53} +(-4.96152 - 1.54380i) q^{54} +(0.989530 - 3.72254i) q^{55} +(-2.19957 - 1.47034i) q^{56} +(2.11765 + 8.34515i) q^{57} +(-3.02124 - 5.23293i) q^{58} +(8.87574 + 5.12441i) q^{59} +(-1.93591 - 0.546395i) q^{60} +(-8.96386 + 5.17529i) q^{61} +1.09412 q^{62} +(3.31873 + 7.21013i) q^{63} +1.00000 q^{64} +(-2.07095 - 3.58699i) q^{65} +(2.92831 - 4.94216i) q^{66} +(-0.911110 + 1.57809i) q^{67} +(-1.71320 - 2.96735i) q^{68} +(3.77590 + 14.8799i) q^{69} +(1.35846 + 2.75608i) q^{70} -13.9074i q^{71} +(-2.55730 - 1.56850i) q^{72} +(-8.95771 - 5.17174i) q^{73} +(-5.31249 + 9.20151i) q^{74} +(-4.41202 - 4.53084i) q^{75} +4.97078i q^{76} +(-8.60329 + 1.72728i) q^{77} +(-1.51936 - 5.98743i) q^{78} +(-8.06437 + 4.65597i) q^{79} +(-1.00577 - 0.580683i) q^{80} +(4.07961 + 8.02227i) q^{81} +(2.02647 + 3.50995i) q^{82} -6.21423 q^{83} +(0.833319 + 4.50617i) q^{84} +3.97930i q^{85} +(-6.04453 + 3.48981i) q^{86} +(-2.84284 + 10.0724i) q^{87} +(2.34054 - 2.34986i) q^{88} +(2.99218 - 1.72754i) q^{89} +(1.66126 + 3.06254i) q^{90} +(-5.24384 + 7.84455i) q^{91} +8.86320i q^{92} +(-1.32210 - 1.35771i) q^{93} +(-4.23571 - 2.44549i) q^{94} +(2.88644 - 4.99947i) q^{95} +(-1.20836 - 1.24091i) q^{96} +5.20989 q^{97} +(4.26356 - 5.55176i) q^{98} +(-9.67125 + 2.33817i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9}+O(q^{10}) $ 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 8 * q^9	$ 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9} - 4 q^{11} + 4 q^{15} - 12 q^{16} + 4 q^{17} - 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} + 40 q^{29} - 2 q^{30} - 28 q^{31} - 12 q^{32} + 32 q^{33} - 8 q^{34} - 32 q^{35} + 16 q^{36} - 16 q^{37} - 8 q^{41} + 6 q^{42} - 4 q^{44} - 28 q^{45} - 8 q^{49} - 40 q^{50} - 34 q^{51} + 6 q^{54} + 8 q^{55} + 40 q^{57} - 20 q^{58} - 2 q^{60} + 56 q^{62} - 14 q^{63} + 24 q^{64} - 44 q^{65} + 32 q^{66} + 4 q^{68} - 20 q^{69} + 64 q^{70} - 8 q^{72} - 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} + 144 q^{83} - 6 q^{84} + 8 q^{87} - 4 q^{88} + 56 q^{90} - 32 q^{91} - 22 q^{93} - 44 q^{95} + 64 q^{97} - 8 q^{98} - 52 q^{99}+O(q^{100}) $ 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 8 * q^9 - 4 * q^11 + 4 * q^15 - 12 * q^16 + 4 * q^17 - 8 * q^18 + 8 * q^22 + 20 * q^25 - 12 * q^27 + 40 * q^29 - 2 * q^30 - 28 * q^31 - 12 * q^32 + 32 * q^33 - 8 * q^34 - 32 * q^35 + 16 * q^36 - 16 * q^37 - 8 * q^41 + 6 * q^42 - 4 * q^44 - 28 * q^45 - 8 * q^49 - 40 * q^50 - 34 * q^51 + 6 * q^54 + 8 * q^55 + 40 * q^57 - 20 * q^58 - 2 * q^60 + 56 * q^62 - 14 * q^63 + 24 * q^64 - 44 * q^65 + 32 * q^66 + 4 * q^68 - 20 * q^69 + 64 * q^70 - 8 * q^72 - 16 * q^74 - 26 * q^75 + 24 * q^81 + 4 * q^82 + 144 * q^83 - 6 * q^84 + 8 * q^87 - 4 * q^88 + 56 * q^90 - 32 * q^91 - 22 * q^93 - 44 * q^95 + 64 * q^97 - 8 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.470476	+	1.66693i	−0.271630	+	0.962402i
$3$	−0.470476	+	1.66693i	−0.271630	+	0.962402i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.00577	−	0.580683i	0.449795	−	0.259689i	−0.257949	−	0.966159i	$-0.583047\pi$
$5$	1.00577	−	0.580683i	0.449795	−	0.259689i	0.707744	+	0.706469i	$0.249713\pi$
$6$	1.67884	−	0.426020i	0.685384	−	0.173922i
$7$	−2.19957	−	1.47034i	−0.831358	−	0.555737i
$7$	−2.19957	−	1.47034i	−0.831358	−	0.555737i
$8$	1.00000			0.353553
$9$	−2.55730	−	1.56850i	−0.852435	−	0.522834i
$10$	−1.00577	−	0.580683i	−0.318053	−	0.183628i
$11$	2.34054	−	2.34986i	0.705701	−	0.708510i
$11$	2.34054	−	2.34986i	0.705701	−	0.708510i
$12$	−1.20836	−	1.24091i	−0.348825	−	0.358220i
$13$		−	3.56641i		−	0.989143i	−0.869137	−	0.494572i	$-0.835325\pi$
$13$		−	3.56641i		−	0.989143i	0.869137	−	0.494572i	$-0.164675\pi$
$14$	−0.173570	+	2.64005i	−0.0463885	+	0.705584i
$15$	0.494765	+	1.94975i	0.127748	+	0.503423i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.71320	+	2.96735i	−0.415512	+	0.719687i	−0.995482	−	0.0949503i	$-0.969731\pi$
$17$	−1.71320	+	2.96735i	−0.415512	+	0.719687i	0.579970	+	0.814638i	$0.303064\pi$
$18$	−0.0797091	+	2.99894i	−0.0187876	+	0.706857i
$19$	4.30482	−	2.48539i	0.987594	−	0.570187i	0.0830395	−	0.996546i	$-0.473537\pi$
$19$	4.30482	−	2.48539i	0.987594	−	0.570187i	0.904554	+	0.426359i	$0.140204\pi$
$20$			1.16137i			0.259689i
$21$	3.48580	−	2.97476i	0.760664	−	0.649146i
$22$	−3.20531	−	0.852040i	−0.683375	−	0.181656i
$23$	7.67576	−	4.43160i	1.60051	−	0.924052i	0.609120	−	0.793078i	$-0.291523\pi$
$23$	7.67576	−	4.43160i	1.60051	−	0.924052i	0.991386	−	0.130974i	$-0.0418106\pi$
$24$	−0.470476	+	1.66693i	−0.0960355	+	0.340260i
$25$	−1.82562	+	3.16206i	−0.365123	+	0.632412i
$26$	−3.08860	+	1.78320i	−0.605724	+	0.349715i
$27$	3.81773	−	3.52490i	0.734722	−	0.678368i
$28$	2.37314	−	1.16971i	0.448481	−	0.221054i
$29$	6.04247			1.12206			0.561030	−	0.827796i	$-0.310405\pi$
$29$	6.04247			1.12206			0.561030	+	0.827796i	$0.310405\pi$
$30$	1.44115	−	1.40335i	0.263116	−	0.256216i
$31$	−0.547062	+	0.947540i	−0.0982553	+	0.170183i	−0.910963	−	0.412489i	$-0.864660\pi$
$31$	−0.547062	+	0.947540i	−0.0982553	+	0.170183i	0.812707	+	0.582672i	$0.197993\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.81588	+	5.00708i	0.490182	+	0.871620i
$34$	3.42640			0.587622
$35$	−3.06606	−	0.201578i	−0.518259	−	0.0340729i
$36$	2.63701	−	1.43044i	0.439502	−	0.238407i
$37$	−5.31249	−	9.20151i	−0.873369	−	1.51272i	−0.858490	−	0.512830i	$-0.828597\pi$
$37$	−5.31249	−	9.20151i	−0.873369	−	1.51272i	−0.0148784	−	0.999889i	$-0.504736\pi$
$38$	−4.30482	−	2.48539i	−0.698334	−	0.403183i
$39$	5.94495	+	1.67791i	0.951953	+	0.268680i
$40$	1.00577	−	0.580683i	0.159026	−	0.0918140i
$41$	−4.05294			−0.632963			−0.316482	−	0.948599i	$-0.602502\pi$
$41$	−4.05294			−0.632963			−0.316482	+	0.948599i	$0.602502\pi$
$42$	−4.31912	−	1.53141i	−0.666454	−	0.236302i
$43$		−	6.97962i		−	1.06438i	−0.846624	−	0.532191i	$-0.821369\pi$
$43$		−	6.97962i		−	1.06438i	0.846624	−	0.532191i	$-0.178631\pi$
$44$	0.864767	+	3.20190i	0.130369	+	0.482705i
$45$	−3.48287	−	0.0925714i	−0.519195	−	0.0137997i
$46$	−7.67576	−	4.43160i	−1.13173	−	0.653404i
$47$	4.23571	−	2.44549i	0.617842	−	0.356711i	−0.158187	−	0.987409i	$-0.550565\pi$
$47$	4.23571	−	2.44549i	0.617842	−	0.356711i	0.776028	+	0.630698i	$0.217231\pi$
$48$	1.67884	−	0.426020i	0.242320	−	0.0614907i
$49$	2.67619	+	6.46823i	0.382313	+	0.924033i
$50$	3.65123			0.516362
$51$	−4.14034	−	4.25185i	−0.579763	−	0.595377i
$52$	3.08860	+	1.78320i	0.428312	+	0.247286i
$53$	−1.75416	−	1.01277i	−0.240952	−	0.139114i	0.374662	−	0.927161i	$-0.377759\pi$
$53$	−1.75416	−	1.01277i	−0.240952	−	0.139114i	−0.615614	+	0.788048i	$0.711092\pi$
$54$	−4.96152	−	1.54380i	−0.675177	−	0.210084i
$55$	0.989530	−	3.72254i	0.133428	−	0.501947i
$56$	−2.19957	−	1.47034i	−0.293930	−	0.196483i
$57$	2.11765	+	8.34515i	0.280490	+	1.10534i
$58$	−3.02124	−	5.23293i	−0.396708	−	0.687118i
$59$	8.87574	+	5.12441i	1.15552	+	0.667142i	0.950227	−	0.311558i	$-0.100851\pi$
$59$	8.87574	+	5.12441i	1.15552	+	0.667142i	0.205296	+	0.978700i	$0.434184\pi$
$60$	−1.93591	−	0.546395i	−0.249925	−	0.0705392i
$61$	−8.96386	+	5.17529i	−1.14771	+	0.662628i	−0.948327	−	0.317295i	$-0.897226\pi$
$61$	−8.96386	+	5.17529i	−1.14771	+	0.662628i	−0.199378	+	0.979923i	$0.563892\pi$
$62$	1.09412			0.138954
$63$	3.31873	+	7.21013i	0.418121	+	0.908391i
$64$	1.00000			0.125000
$65$	−2.07095	−	3.58699i	−0.256870	−	0.444911i
$66$	2.92831	−	4.94216i	0.360451	−	0.608338i
$67$	−0.911110	+	1.57809i	−0.111310	+	0.192794i	−0.916299	−	0.400496i	$-0.868838\pi$
$67$	−0.911110	+	1.57809i	−0.111310	+	0.192794i	0.804989	+	0.593290i	$0.202171\pi$
$68$	−1.71320	−	2.96735i	−0.207756	−	0.359844i
$69$	3.77590	+	14.8799i	0.454565	+	1.79133i
$70$	1.35846	+	2.75608i	0.162367	+	0.329414i
$71$		−	13.9074i		−	1.65050i	−0.564767	−	0.825251i	$-0.691034\pi$
$71$		−	13.9074i		−	1.65050i	0.564767	−	0.825251i	$-0.308966\pi$
$72$	−2.55730	−	1.56850i	−0.301381	−	0.184850i
$73$	−8.95771	−	5.17174i	−1.04842	−	0.605306i	−0.126214	−	0.992003i	$-0.540283\pi$
$73$	−8.95771	−	5.17174i	−1.04842	−	0.605306i	−0.922207	+	0.386697i	$0.873616\pi$
$74$	−5.31249	+	9.20151i	−0.617565	+	1.06965i
$75$	−4.41202	−	4.53084i	−0.509456	−	0.523177i
$76$			4.97078i			0.570187i
$77$	−8.60329	+	1.72728i	−0.980435	+	0.196842i
$78$	−1.51936	−	5.98743i	−0.172034	−	0.677943i
$79$	−8.06437	+	4.65597i	−0.907312	+	0.523837i	−0.879565	−	0.475778i	$-0.842167\pi$
$79$	−8.06437	+	4.65597i	−0.907312	+	0.523837i	−0.0277469	+	0.999615i	$0.508833\pi$
$80$	−1.00577	−	0.580683i	−0.112449	−	0.0649223i
$81$	4.07961	+	8.02227i	0.453290	+	0.891363i
$82$	2.02647	+	3.50995i	0.223786	+	0.387609i
$83$	−6.21423			−0.682100			−0.341050	−	0.940045i	$-0.610783\pi$
$83$	−6.21423			−0.682100			−0.341050	+	0.940045i	$0.610783\pi$
$84$	0.833319	+	4.50617i	0.0909226	+	0.491664i
$85$			3.97930i			0.431615i
$86$	−6.04453	+	3.48981i	−0.651798	+	0.376316i
$87$	−2.84284	+	10.0724i	−0.304784	+	1.07987i
$88$	2.34054	−	2.34986i	0.249503	−	0.250496i
$89$	2.99218	−	1.72754i	0.317170	−	0.183118i	−0.332960	−	0.942941i	$-0.608047\pi$
$89$	2.99218	−	1.72754i	0.317170	−	0.183118i	0.650131	+	0.759822i	$0.274714\pi$
$90$	1.66126	+	3.06254i	0.175113	+	0.322820i
$91$	−5.24384	+	7.84455i	−0.549703	+	0.822332i
$92$			8.86320i			0.924052i
$93$	−1.32210	−	1.35771i	−0.137096	−	0.140788i
$94$	−4.23571	−	2.44549i	−0.436880	−	0.252233i
$95$	2.88644	−	4.99947i	0.296143	−	0.512935i
$96$	−1.20836	−	1.24091i	−0.123328	−	0.126650i
$97$	5.20989			0.528985			0.264492	−	0.964388i	$-0.414796\pi$
$97$	5.20989			0.528985			0.264492	+	0.964388i	$0.414796\pi$
$98$	4.26356	−	5.55176i	0.430684	−	0.560813i
$99$	−9.67125	+	2.33817i	−0.971997	+	0.234995i
$100$	−1.82562	−	3.16206i	−0.182562	−	0.316206i
$101$	2.11536	−	3.66391i	0.210486	−	0.364573i	−0.741381	−	0.671085i	$-0.765829\pi$
$101$	2.11536	−	3.66391i	0.210486	−	0.364573i	0.951867	+	0.306512i	$0.0991619\pi$
$102$	−1.61204	+	5.71156i	−0.159616	+	0.565529i
$103$	9.13694	+	15.8257i	0.900290	+	1.55935i	0.827118	+	0.562028i	$0.189979\pi$
$103$	9.13694	+	15.8257i	0.900290	+	1.55935i	0.0731719	+	0.997319i	$0.476688\pi$
$104$		−	3.56641i		−	0.349715i
$105$	1.77853	−	5.01607i	0.173566	−	0.489519i
$106$			2.02553i			0.196737i
$107$	−0.328629	−	0.569202i	−0.0317698	−	0.0550269i	0.849703	−	0.527261i	$-0.176781\pi$
$107$	−0.328629	−	0.569202i	−0.0317698	−	0.0550269i	−0.881473	+	0.472234i	$0.843448\pi$
$108$	1.14379	+	5.06870i	0.110061	+	0.487736i
$109$	8.44989	+	4.87855i	0.809353	+	0.467280i	0.846731	−	0.532021i	$-0.178567\pi$
$109$	8.44989	+	4.87855i	0.809353	+	0.467280i	−0.0373781	+	0.999301i	$0.511901\pi$
$110$	−3.71858	+	1.00431i	−0.354552	+	0.0957573i
$111$	17.8377	−	4.52646i	1.69308	−	0.429633i
$112$	−0.173570	+	2.64005i	−0.0164008	+	0.249461i
$113$			10.7159i			1.00807i	0.863684	+	0.504034i	$0.168151\pi$
$113$			10.7159i			1.00807i	−0.863684	+	0.504034i	$0.831849\pi$
$114$	6.16828	−	6.00651i	0.577713	−	0.562562i
$115$	5.14671	−	8.91435i	0.479933	−	0.831268i
$116$	−3.02124	+	5.23293i	−0.280515	+	0.485866i
$117$	−5.59391	+	9.12039i	−0.517157	+	0.843180i
$118$		−	10.2488i		−	0.943481i
$119$	8.13131	−	4.00789i	0.745396	−	0.367403i
$120$	0.494765	+	1.94975i	0.0451657	+	0.177987i
$121$	−0.0436998	−	10.9999i	−0.00397271	−	0.999992i
$122$	8.96386	+	5.17529i	0.811550	+	0.468549i
$123$	1.90681	−	6.75597i	0.171932	−	0.609165i
$124$	−0.547062	−	0.947540i	−0.0491277	−	0.0850916i
$125$			10.0472i			0.898652i
$126$	4.58479	−	6.47917i	0.408446	−	0.577211i
$127$			5.18041i			0.459687i	0.973228	+	0.229843i	$0.0738214\pi$
$127$			5.18041i			0.459687i	−0.973228	+	0.229843i	$0.926179\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	11.6345	+	3.28374i	1.02436	+	0.289118i
$130$	−2.07095	+	3.58699i	−0.181634	+	0.314600i
$131$	9.74600	+	16.8806i	0.851512	+	1.47486i	0.879843	+	0.475264i	$0.157647\pi$
$131$	9.74600	+	16.8806i	0.851512	+	1.47486i	−0.0283313	+	0.999599i	$0.509019\pi$
$132$	−5.74420	−	0.0649125i	−0.499968	−	0.00564991i
$133$	−13.1231	−	0.862777i	−1.13792	−	0.0748123i
$134$	1.82222			0.157416
$135$	1.79291	−	5.76214i	0.154310	−	0.495926i
$136$	−1.71320	+	2.96735i	−0.146906	+	0.254448i
$137$	−19.3338	−	11.1624i	−1.65180	−	0.953666i	−0.976333	−	0.216273i	$-0.930610\pi$
$137$	−19.3338	−	11.1624i	−1.65180	−	0.953666i	−0.675465	−	0.737393i	$-0.736057\pi$
$138$	10.9984	−	10.7100i	0.936248	−	0.911694i
$139$			10.5744i			0.896905i	0.893807	+	0.448453i	$0.148025\pi$
$139$			10.5744i			0.896905i	−0.893807	+	0.448453i	$0.851975\pi$
$140$	1.70760	−	2.55450i	0.144319	−	0.215895i
$141$	2.08365	+	8.21117i	0.175475	+	0.691505i
$142$	−12.0441	+	6.95368i	−1.01072	+	0.583540i
$143$	−8.38056	−	8.34733i	−0.700818	−	0.698039i
$144$	−0.0797091	+	2.99894i	−0.00664242	+	0.249912i
$145$	6.07735	−	3.50876i	0.504696	−	0.291387i
$146$			10.3435i			0.856032i
$147$	−12.0412	+	1.41787i	−0.993139	+	0.116944i
$148$	10.6250			0.873369
$149$	−2.22819	−	3.85935i	−0.182541	−	0.316170i	0.760204	−	0.649684i	$-0.225099\pi$
$149$	−2.22819	−	3.85935i	−0.182541	−	0.316170i	−0.942745	+	0.333514i	$0.891765\pi$
$150$	−1.71782	+	6.08634i	−0.140259	+	0.496948i
$151$	−3.45781	−	1.99637i	−0.281393	−	0.162462i	0.352661	−	0.935751i	$-0.385277\pi$
$151$	−3.45781	−	1.99637i	−0.281393	−	0.162462i	−0.634054	+	0.773289i	$0.718610\pi$
$152$	4.30482	−	2.48539i	0.349167	−	0.201592i
$153$	9.03545	−	4.90126i	0.730473	−	0.396243i
$154$	5.79751	+	6.58702i	0.467177	+	0.530798i
$155$			1.27068i			0.102063i
$156$	−4.42558	+	4.30952i	−0.354330	+	0.345038i
$157$	7.16830	−	12.4159i	0.572093	−	0.990894i	−0.424258	−	0.905541i	$-0.639465\pi$
$157$	7.16830	−	12.4159i	0.572093	−	0.990894i	0.996351	−	0.0853524i	$-0.0272016\pi$
$158$	8.06437	+	4.65597i	0.641567	+	0.370409i
$159$	2.51350	−	2.44758i	0.199333	−	0.194106i
$160$			1.16137i			0.0918140i
$161$	−23.3993	−	1.53838i	−1.84412	−	0.121242i
$162$	4.90768	−	7.54418i	0.385584	−	0.592727i
$163$	−4.45739	−	7.72043i	−0.349130	−	0.604711i	0.636965	−	0.770893i	$-0.280190\pi$
$163$	−4.45739	−	7.72043i	−0.349130	−	0.604711i	−0.986095	+	0.166182i	$0.946856\pi$
$164$	2.02647	−	3.50995i	0.158241	−	0.274081i
$165$	5.73966	+	3.40084i	0.446832	+	0.264755i
$166$	3.10711	+	5.38168i	0.241159	+	0.417699i
$167$	0.940338			0.0727655			0.0363828	−	0.999338i	$-0.488416\pi$
$167$	0.940338			0.0727655			0.0363828	+	0.999338i	$0.488416\pi$
$168$	3.48580	−	2.97476i	0.268935	−	0.229508i
$169$	0.280747			0.0215959
$170$	3.44617	−	1.98965i	0.264309	−	0.152599i
$171$	−14.9071	−	0.396216i	−1.13997	−	0.0302994i
$172$	6.04453	+	3.48981i	0.460891	+	0.266095i
$173$	6.09331	+	10.5539i	0.463266	+	0.802400i	0.999121	−	0.0419097i	$-0.0133442\pi$
$173$	6.09331	+	10.5539i	0.463266	+	0.802400i	−0.535856	+	0.844310i	$0.680011\pi$
$174$	10.1444	−	2.57422i	0.769041	−	0.195151i
$175$	8.66487	−	4.27088i	0.655003	−	0.322848i
$176$	−3.20531	−	0.852040i	−0.241610	−	0.0642250i
$177$	−12.7179	+	12.3843i	−0.955933	+	0.930862i
$178$	−2.99218	−	1.72754i	−0.224273	−	0.129484i
$179$	−2.72052	−	1.57070i	−0.203342	−	0.117399i	0.394872	−	0.918736i	$-0.370789\pi$
$179$	−2.72052	−	1.57070i	−0.203342	−	0.117399i	−0.598213	+	0.801337i	$0.704122\pi$
$180$	1.82160	−	2.96996i	0.135774	−	0.221368i
$181$	−3.05508			−0.227082			−0.113541	−	0.993533i	$-0.536219\pi$
$181$	−3.05508			−0.227082			−0.113541	+	0.993533i	$0.536219\pi$
$182$	9.41550	+	0.619021i	0.697923	+	0.0458849i
$183$	−4.40956	−	17.3770i	−0.325964	−	1.28454i
$184$	7.67576	−	4.43160i	0.565864	−	0.326702i
$185$	−10.6863	−	6.16975i	−0.785673	−	0.453609i
$186$	−0.514760	+	1.82383i	−0.0377440	+	0.133730i
$187$	2.96304	+	10.9710i	0.216679	+	0.802278i
$188$			4.89098i			0.356711i
$189$	−13.5802	+	2.13989i	−0.987812	+	0.155654i
$190$	−5.77289			−0.418809
$191$	−0.195655	+	0.112961i	−0.0141571	+	0.00817359i	−0.507062	−	0.861910i	$-0.669268\pi$
$191$	−0.195655	+	0.112961i	−0.0141571	+	0.00817359i	0.492905	+	0.870083i	$0.335935\pi$
$192$	−0.470476	+	1.66693i	−0.0339537	+	0.120300i
$193$	−10.4291	−	6.02127i	−0.750706	−	0.433420i	0.0752429	−	0.997165i	$-0.476027\pi$
$193$	−10.4291	−	6.02127i	−0.750706	−	0.433420i	−0.825949	+	0.563745i	$0.809360\pi$
$194$	−2.60495	−	4.51190i	−0.187024	−	0.323936i
$195$	6.95359	−	1.76453i	0.497957	−	0.126361i
$196$	−6.93975	−	0.916467i	−0.495696	−	0.0654619i
$197$	0.542181			0.0386288			0.0193144	−	0.999813i	$-0.493852\pi$
$197$	0.542181			0.0386288			0.0193144	+	0.999813i	$0.493852\pi$
$198$	6.86053	+	7.20646i	0.487557	+	0.512141i
$199$	2.12131	−	3.67422i	0.150376	−	0.260458i	−0.780990	−	0.624544i	$-0.785285\pi$
$199$	2.12131	−	3.67422i	0.150376	−	0.260458i	0.931366	+	0.364085i	$0.118618\pi$
$200$	−1.82562	+	3.16206i	−0.129091	+	0.223591i
$201$	−2.20191	−	2.26121i	−0.155311	−	0.159493i
$202$	−4.23072			−0.297673
$203$	−13.2908	−	8.88450i	−0.932833	−	0.623570i
$204$	5.75237	−	1.45971i	0.402747	−	0.102200i
$205$	−4.07633	+	2.35347i	−0.284704	+	0.164374i
$206$	9.13694	−	15.8257i	0.636601	−	1.10263i
$207$	−26.5802	−	0.706478i	−1.84745	−	0.0491036i
$208$	−3.08860	+	1.78320i	−0.214156	+	0.123643i
$209$	4.23530	−	15.9329i	0.292962	−	1.10210i
$210$	−5.23331	+	0.967788i	−0.361133	+	0.0667837i
$211$			0.145154i			0.00999278i	0.999988	+	0.00499639i	$0.00159041\pi$
$211$			0.145154i			0.00999278i	−0.999988	+	0.00499639i	$0.998410\pi$
$212$	1.75416	−	1.01277i	0.120476	−	0.0695570i
$213$	23.1826	+	6.54308i	1.58845	+	0.448325i
$214$	−0.328629	+	0.569202i	−0.0224646	+	0.0389099i
$215$	−4.05294	−	7.01990i	−0.276408	−	0.478753i
$216$	3.81773	−	3.52490i	0.259764	−	0.239839i
$217$	2.59651	−	1.27981i	0.176262	−	0.0868791i
$218$		−	9.75710i		−	0.660834i
$219$	12.8353	−	12.4987i	0.867329	−	0.844583i
$220$	2.72905	+	2.71823i	0.183992	+	0.183263i
$221$	10.5828	+	6.10996i	0.711874	+	0.411000i
$222$	−12.8389	−	13.1846i	−0.861688	−	0.884895i
$223$	−10.6002			−0.709840			−0.354920	−	0.934897i	$-0.615492\pi$
$223$	−10.6002			−0.709840			−0.354920	+	0.934897i	$0.615492\pi$
$224$	2.37314	−	1.16971i	0.158562	−	0.0781545i
$225$	9.62835	−	5.22287i	0.641890	−	0.348191i
$226$	9.28025	−	5.35795i	0.617313	−	0.356406i
$227$	−1.02424	+	1.77403i	−0.0679810	+	0.117746i	−0.898012	−	0.439970i	$-0.854989\pi$
$227$	−1.02424	+	1.77403i	−0.0679810	+	0.117746i	0.830031	+	0.557717i	$0.188322\pi$
$228$	−8.28594	−	2.33863i	−0.548749	−	0.154880i
$229$	6.97376	+	12.0789i	0.460839	+	0.798196i	0.999003	−	0.0446437i	$-0.0142153\pi$
$229$	6.97376	+	12.0789i	0.460839	+	0.798196i	−0.538164	+	0.842840i	$0.680882\pi$
$230$	−10.2934			−0.678727
$231$	1.16839	−	15.1537i	0.0768745	−	0.997041i
$232$	6.04247			0.396708
$233$	14.3840	+	24.9138i	0.942328	+	1.63216i	0.761015	+	0.648735i	$0.224702\pi$
$233$	14.3840	+	24.9138i	0.942328	+	1.63216i	0.181314	+	0.983425i	$0.441965\pi$
$234$	10.6954	+	0.284275i	0.699183	+	0.0185836i
$235$	2.84010	−	4.91920i	0.185268	−	0.320894i
$236$	−8.87574	+	5.12441i	−0.577762	+	0.333571i
$237$	−3.96707	−	15.6333i	−0.257689	−	1.01549i
$238$	−7.53659	−	5.03797i	−0.488524	−	0.326563i
$239$	−15.2538			−0.986685			−0.493342	−	0.869835i	$-0.664225\pi$
$239$	−15.2538			−0.986685			−0.493342	+	0.869835i	$0.664225\pi$
$240$	1.44115	−	1.40335i	0.0930257	−	0.0905860i
$241$	7.64351	+	4.41298i	0.492362	+	0.284265i	0.725554	−	0.688166i	$-0.241584\pi$
$241$	7.64351	+	4.41298i	0.492362	+	0.284265i	−0.233192	+	0.972431i	$0.574917\pi$
$242$	−9.50435	+	5.53780i	−0.610963	+	0.355983i
$243$	−15.2919	+	3.02614i	−0.980976	+	0.194127i
$244$		−	10.3506i		−	0.662628i
$245$	6.44762	+	4.95155i	0.411924	+	0.316343i
$246$	−6.80425	+	1.72664i	−0.433823	+	0.110086i
$247$	−8.86391	−	15.3527i	−0.563997	−	0.976871i
$248$	−0.547062	+	0.947540i	−0.0347385	+	0.0601688i
$249$	2.92364	−	10.3587i	0.185278	−	0.656454i
$250$	8.70116	−	5.02362i	0.550310	−	0.317722i
$251$		−	2.93497i		−	0.185254i	−0.995701	−	0.0926269i	$-0.970474\pi$
$251$		−	2.93497i		−	0.185254i	0.995701	−	0.0926269i	$-0.0295264\pi$
$252$	−7.90352	−	0.730962i	−0.497875	−	0.0460463i
$253$	7.55180	−	28.4093i	0.474778	−	1.78608i
$254$	4.48636	−	2.59020i	0.281500	−	0.162524i
$255$	−6.63321	−	1.87216i	−0.415387	−	0.117239i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−14.2919	+	8.25142i	−0.891503	+	0.514709i	−0.874434	−	0.485145i	$-0.838767\pi$
$257$	−14.2919	+	8.25142i	−0.891503	+	0.514709i	−0.0170691	+	0.999854i	$0.505434\pi$
$258$	−2.97346	−	11.7177i	−0.185119	−	0.729510i
$259$	−1.84418	+	28.0505i	−0.114592	+	1.74297i
$260$	4.14190			0.256870
$261$	−15.4524	−	9.47762i	−0.956482	−	0.586650i
$262$	9.74600	−	16.8806i	0.602110	−	1.04289i
$263$	7.63064	−	13.2167i	0.470525	−	0.814974i	−0.528906	−	0.848680i	$-0.677398\pi$
$263$	7.63064	−	13.2167i	0.470525	−	0.814974i	0.999432	+	0.0337062i	$0.0107311\pi$
$264$	2.81588	+	5.00708i	0.173306	+	0.308164i
$265$	−2.35238			−0.144506
$266$	5.81437	+	11.7963i	0.356502	+	0.723280i
$267$	1.47193	+	5.80051i	0.0900807	+	0.354986i
$268$	−0.911110	−	1.57809i	−0.0556549	−	0.0963971i
$269$	−6.26825	−	3.61898i	−0.382182	−	0.220653i	0.296585	−	0.955006i	$-0.404152\pi$
$269$	−6.26825	−	3.61898i	−0.382182	−	0.220653i	−0.678767	+	0.734353i	$0.737485\pi$
$270$	−5.88661	+	1.32836i	−0.358248	+	0.0808413i
$271$	20.4336	−	11.7973i	1.24125	−	0.716637i	0.271903	−	0.962325i	$-0.412347\pi$
$271$	20.4336	−	11.7973i	1.24125	−	0.716637i	0.969349	+	0.245687i	$0.0790137\pi$
$272$	3.42640			0.207756
$273$	−10.6092	−	12.4318i	−0.642098	−	0.752405i
$274$			22.3247i			1.34869i
$275$	3.15747	+	11.6909i	0.190402	+	0.704987i
$276$	−14.7743	−	4.16992i	−0.889310	−	0.251000i
$277$	17.1573	+	9.90578i	1.03088	+	0.595181i	0.917238	−	0.398340i	$-0.130414\pi$
$277$	17.1573	+	9.90578i	1.03088	+	0.595181i	0.113646	+	0.993521i	$0.463747\pi$
$278$	9.15766	−	5.28718i	0.549240	−	0.317104i
$279$	2.88522	−	1.56508i	0.172734	−	0.0936989i
$280$	−3.06606	−	0.201578i	−0.183232	−	0.0120466i
$281$	18.8950			1.12718			0.563591	−	0.826054i	$-0.309419\pi$
$281$	18.8950			1.12718			0.563591	+	0.826054i	$0.309419\pi$
$282$	6.06926	−	5.91008i	0.361419	−	0.351940i
$283$	−1.62416	−	0.937708i	−0.0965462	−	0.0557410i	0.450950	−	0.892549i	$-0.351085\pi$
$283$	−1.62416	−	0.937708i	−0.0965462	−	0.0557410i	−0.547496	+	0.836808i	$0.684419\pi$
$284$	12.0441	+	6.95368i	0.714688	+	0.412625i
$285$	6.97576	+	7.16363i	0.413208	+	0.424337i
$286$	−3.03872	+	11.4314i	−0.179683	+	0.675956i
$287$	8.91472	+	5.95921i	0.526219	+	0.351761i
$288$	2.63701	−	1.43044i	0.155388	−	0.0842895i
$289$	2.62990	+	4.55513i	0.154700	+	0.267949i
$290$	−6.07735	−	3.50876i	−0.356874	−	0.206041i
$291$	−2.45113	+	8.68452i	−0.143688	+	0.509096i
$292$	8.95771	−	5.17174i	0.524210	−	0.302653i
$293$	17.3941			1.01618			0.508088	−	0.861305i	$-0.330353\pi$
$293$	17.3941			1.01618			0.508088	+	0.861305i	$0.330353\pi$
$294$	7.24849	+	9.71902i	0.422741	+	0.566825i
$295$	11.9026			0.692998
$296$	−5.31249	−	9.20151i	−0.308782	−	0.534827i
$297$	0.652533	−	17.2213i	0.0378638	−	0.999283i
$298$	−2.22819	+	3.85935i	−0.129076	+	0.223566i
$299$	−15.8049	−	27.3749i	−0.914020	−	1.58313i
$300$	6.12984	−	1.55550i	0.353906	−	0.0898067i
$301$	−10.2624	+	15.3521i	−0.591516	+	0.884883i
$302$			3.99274i			0.229756i
$303$	5.11226	+	5.24994i	0.293691	+	0.301601i
$304$	−4.30482	−	2.48539i	−0.246898	−	0.142547i
$305$	−6.01040	+	10.4103i	−0.344155	+	0.596093i
$306$	−8.76234	−	5.37430i	−0.500910	−	0.307229i
$307$		−	21.0137i		−	1.19931i	−0.800258	−	0.599656i	$-0.795304\pi$
$307$		−	21.0137i		−	1.19931i	0.800258	−	0.599656i	$-0.204696\pi$
$308$	2.80578	−	8.31430i	0.159874	−	0.473751i
$309$	−30.6790	+	7.78505i	−1.74526	+	0.442876i
$310$	1.10044	−	0.635339i	0.0625008	−	0.0360848i
$311$	24.4322	+	14.1059i	1.38542	+	0.799873i	0.992795	−	0.119826i	$-0.0382336\pi$
$311$	24.4322	+	14.1059i	1.38542	+	0.799873i	0.392625	+	0.919699i	$0.371567\pi$
$312$	5.94495	+	1.67791i	0.336566	+	0.0949929i
$313$	−2.99806	−	5.19278i	−0.169460	−	0.293513i	0.768770	−	0.639525i	$-0.220869\pi$
$313$	−2.99806	−	5.19278i	−0.169460	−	0.293513i	−0.938230	+	0.346012i	$0.887536\pi$
$314$	−14.3366			−0.809061
$315$	7.52468	+	5.32462i	0.423968	+	0.300008i
$316$		−	9.31193i		−	0.523837i
$317$	8.91377	−	5.14637i	0.500647	−	0.289049i	−0.228333	−	0.973583i	$-0.573328\pi$
$317$	8.91377	−	5.14637i	0.500647	−	0.289049i	0.728981	+	0.684534i	$0.239994\pi$
$318$	−3.37641	−	0.952964i	−0.189340	−	0.0534395i
$319$	14.1427	−	14.1990i	0.791838	−	0.794990i
$320$	1.00577	−	0.580683i	0.0562243	−	0.0324611i
$321$	1.10343	−	0.280005i	0.0615876	−	0.0156284i
$322$	10.3674	+	21.0336i	0.577751	+	1.17216i
$323$			17.0319i			0.947678i
$324$	−8.98729	−	0.478086i	−0.499294	−	0.0265603i
$325$	11.2772	+	6.51089i	0.625546	+	0.361159i
$326$	−4.45739	+	7.72043i	−0.246872	+	0.427595i
$327$	−12.1077	+	11.7901i	−0.669556	+	0.651996i
$328$	−4.05294			−0.223786
$329$	−12.9124	−	0.848926i	−0.711885	−	0.0468028i
$330$	0.0753871	−	6.67111i	0.00414992	−	0.367232i
$331$	6.54105	+	11.3294i	0.359529	+	0.622722i	0.987882	−	0.155206i	$-0.0496042\pi$
$331$	6.54105	+	11.3294i	0.359529	+	0.622722i	−0.628354	+	0.777928i	$0.716271\pi$
$332$	3.10711	−	5.38168i	0.170525	−	0.295358i
$333$	−0.846908	+	31.8637i	−0.0464103	+	1.74612i
$334$	−0.470169	−	0.814356i	−0.0257265	−	0.0445596i
$335$			2.11626i			0.115624i
$336$	−4.31912	−	1.53141i	−0.235627	−	0.0835453i
$337$			17.0981i			0.931394i	0.884944	+	0.465697i	$0.154196\pi$
$337$			17.0981i			0.931394i	−0.884944	+	0.465697i	$0.845804\pi$
$338$	−0.140373	−	0.243134i	−0.00763530	−	0.0132247i
$339$	−17.8627	−	5.04158i	−0.970166	−	0.273821i
$340$	−3.44617	−	1.98965i	−0.186895	−	0.107904i
$341$	0.946164	+	3.50328i	0.0512376	+	0.189713i
$342$	7.11040	+	13.1080i	0.384487	+	0.708800i
$343$	3.62405	−	18.1622i	0.195680	−	0.980668i
$344$		−	6.97962i		−	0.376316i
$345$	12.4382	+	12.7732i	0.669650	+	0.687685i
$346$	6.09331	−	10.5539i	0.327578	−	0.567382i
$347$	6.90245	−	11.9554i	0.370543	−	0.641799i	−0.619106	−	0.785307i	$-0.712505\pi$
$347$	6.90245	−	11.9554i	0.370543	−	0.641799i	0.989649	+	0.143508i	$0.0458384\pi$
$348$	−7.30151	−	7.49816i	−0.391402	−	0.401943i
$349$			27.1071i			1.45101i	0.688217	+	0.725505i	$0.258394\pi$
$349$			27.1071i			1.45101i	−0.688217	+	0.725505i	$0.741606\pi$
$350$	−8.03113	−	5.36856i	−0.429282	−	0.286961i
$351$	−12.5712	−	13.6156i	−0.671003	−	0.726746i
$352$	0.864767	+	3.20190i	0.0460923	+	0.170662i
$353$	15.3515	+	8.86320i	0.817079	+	0.471741i	0.849408	−	0.527737i	$-0.176959\pi$
$353$	15.3515	+	8.86320i	0.817079	+	0.471741i	−0.0323294	+	0.999477i	$0.510293\pi$
$354$	17.0841	+	4.82183i	0.908008	+	0.256277i
$355$	−8.07577	−	13.9876i	−0.428617	−	0.742387i
$356$			3.45507i			0.183118i
$357$	2.85528	+	15.4399i	0.151118	+	0.817168i
$358$			3.14139i			0.166028i
$359$	10.3453	+	17.9186i	0.546006	+	0.945710i	0.998543	+	0.0539641i	$0.0171857\pi$
$359$	10.3453	+	17.9186i	0.546006	+	0.945710i	−0.452537	+	0.891746i	$0.649481\pi$
$360$	−3.48287	−	0.0925714i	−0.183563	−	0.00487894i
$361$	2.85432	−	4.94383i	0.150227	−	0.260202i
$362$	1.52754	+	2.64578i	0.0802857	+	0.139059i
$363$	18.3566	+	5.10235i	0.963473	+	0.267804i
$364$	−4.17166	−	8.46357i	−0.218654	−	0.443612i
$365$	−12.0125			−0.628765
$366$	−12.8441	+	12.5073i	−0.671373	+	0.653766i
$367$	2.95817	−	5.12371i	0.154415	−	0.267455i	−0.778431	−	0.627731i	$-0.783984\pi$
$367$	2.95817	−	5.12371i	0.154415	−	0.267455i	0.932846	+	0.360275i	$0.117317\pi$
$368$	−7.67576	−	4.43160i	−0.400126	−	0.231013i
$369$	10.3646	+	6.35704i	0.539560	+	0.330934i
$370$			12.3395i			0.641500i
$371$	2.36928	+	4.80686i	0.123007	+	0.249560i
$372$	1.83686	−	0.466119i	0.0952368	−	0.0241672i
$373$	−7.47599	+	4.31626i	−0.387092	+	0.223488i	−0.680899	−	0.732377i	$-0.738411\pi$
$373$	−7.47599	+	4.31626i	−0.387092	+	0.223488i	0.293807	+	0.955865i	$0.405078\pi$
$374$	8.01963	−	8.05156i	0.414685	−	0.416336i
$375$	−16.7480	−	4.72699i	−0.864865	−	0.244100i
$376$	4.23571	−	2.44549i	0.218440	−	0.126116i
$377$		−	21.5499i		−	1.10988i
$378$	8.64328	+	10.6908i	0.444563	+	0.549876i
$379$	−3.30027			−0.169523			−0.0847617	−	0.996401i	$-0.527013\pi$
$379$	−3.30027			−0.169523			−0.0847617	+	0.996401i	$0.527013\pi$
$380$	2.88644	+	4.99947i	0.148071	+	0.256467i
$381$	−8.63537	−	2.43726i	−0.442403	−	0.124864i
$382$	0.195655	+	0.112961i	0.0100106	+	0.00577960i
$383$	13.9230	−	8.03845i	0.711433	−	0.410746i	−0.100159	−	0.994971i	$-0.531935\pi$
$383$	13.9230	−	8.03845i	0.711433	−	0.410746i	0.811591	+	0.584226i	$0.198602\pi$
$384$	1.67884	−	0.426020i	0.0856730	−	0.0217403i
$385$	−7.64994	+	6.73302i	−0.389877	+	0.343147i
$386$			12.0425i			0.612949i
$387$	−10.9475	+	17.8490i	−0.556495	+	0.907316i
$388$	−2.60495	+	4.51190i	−0.132246	+	0.229057i
$389$	17.8525	+	10.3071i	0.905156	+	0.522592i	0.878870	−	0.477062i	$-0.158298\pi$
$389$	17.8525	+	10.3071i	0.905156	+	0.522592i	0.0262868	+	0.999654i	$0.491632\pi$
$390$	−5.00493	−	5.13972i	−0.253434	−	0.260260i
$391$			30.3688i			1.53582i
$392$	2.67619	+	6.46823i	0.135168	+	0.326695i
$393$	−32.7240	+	8.30399i	−1.65071	+	0.418881i
$394$	−0.271090	−	0.469542i	−0.0136573	−	0.0236552i
$395$	−5.40728	+	9.36568i	−0.272070	+	0.471238i
$396$	2.81071	−	9.54463i	0.141244	−	0.479636i
$397$	2.61119	+	4.52272i	0.131052	+	0.226989i	0.924082	−	0.382193i	$-0.124831\pi$
$397$	2.61119	+	4.52272i	0.131052	+	0.226989i	−0.793030	+	0.609182i	$0.791498\pi$
$398$	−4.24262			−0.212663
$399$	7.61230	−	21.4694i	0.381092	−	1.07481i
$400$	3.65123			0.182562
$401$	−1.61502	+	0.932434i	−0.0806504	+	0.0465635i	−0.539783	−	0.841804i	$-0.681494\pi$
$401$	−1.61502	+	0.932434i	−0.0806504	+	0.0465635i	0.459132	+	0.888368i	$0.348160\pi$
$402$	−0.857311	+	3.03751i	−0.0427588	+	0.151497i
$403$	3.37931	+	1.95105i	0.168336	+	0.0971886i
$404$	2.11536	+	3.66391i	0.105243	+	0.182286i
$405$	8.76155	+	5.69961i	0.435365	+	0.283216i
$406$	−1.04879	+	15.9524i	−0.0520506	+	0.791706i
$407$	−34.0564	−	9.05292i	−1.68811	−	0.448737i
$408$	−4.14034	−	4.25185i	−0.204977	−	0.210498i
$409$	12.2281	+	7.05988i	0.604639	+	0.349089i	0.770864	−	0.636999i	$-0.219825\pi$
$409$	12.2281	+	7.05988i	0.604639	+	0.349089i	−0.166225	+	0.986088i	$0.553158\pi$
$410$	4.07633	+	2.35347i	0.201316	+	0.116230i
$411$	27.7030	−	26.9764i	1.36649	−	1.33065i
$412$	−18.2739			−0.900290
$413$	−11.9882	−	24.3219i	−0.589898	−	1.19680i
$414$	12.6783	+	23.3724i	0.623103	+	1.14869i
$415$	−6.25009	+	3.60849i	−0.306805	+	0.177134i
$416$	3.08860	+	1.78320i	0.151431	+	0.0874287i
$417$	−17.6267	−	4.97498i	−0.863183	−	0.243626i
$418$	−15.9159	+	4.29857i	−0.778474	+	0.210250i
$419$			20.8437i			1.01828i	0.860683	+	0.509141i	$0.170037\pi$
$419$			20.8437i			1.01828i	−0.860683	+	0.509141i	$0.829963\pi$
$420$	3.45478	+	4.04829i	0.168576	+	0.197536i
$421$	20.3260			0.990629			0.495314	−	0.868714i	$-0.335053\pi$
$421$	20.3260			0.990629			0.495314	+	0.868714i	$0.335053\pi$
$422$	0.125707	−	0.0725768i	0.00611930	−	0.00353298i
$423$	−14.6677	−	0.389855i	−0.713170	−	0.0189554i
$424$	−1.75416	−	1.01277i	−0.0851896	−	0.0491842i
$425$	−6.25528	−	10.8345i	−0.303426	−	0.525549i
$426$	−5.92482	−	23.3483i	−0.287058	−	1.13123i
$427$	27.3261	+	1.79655i	1.32240	+	0.0869411i
$428$	0.657258			0.0317698
$429$	17.8573	−	10.0426i	0.862157	−	0.484860i
$430$	−4.05294	+	7.01990i	−0.195450	+	0.338530i
$431$	19.1899	−	33.2379i	0.924344	−	1.60101i	0.131732	−	0.991285i	$-0.457946\pi$
$431$	19.1899	−	33.2379i	0.924344	−	1.60101i	0.792613	−	0.609726i	$-0.208720\pi$
$432$	−4.96152	−	1.54380i	−0.238711	−	0.0742761i
$433$	−29.7374			−1.42909			−0.714545	−	0.699589i	$-0.753366\pi$
$433$	−29.7374			−1.42909			−0.714545	+	0.699589i	$0.753366\pi$
$434$	−2.40660	−	1.60874i	−0.115521	−	0.0772219i
$435$	2.98960	+	11.7813i	0.143341	+	0.564870i
$436$	−8.44989	+	4.87855i	−0.404677	+	0.233640i
$437$	22.0285	−	38.1545i	1.05377	−	1.82518i
$438$	−17.2418	−	4.86636i	−0.823847	−	0.232523i
$439$	−15.9159	+	9.18904i	−0.759624	+	0.438569i	−0.829161	−	0.559010i	$-0.811181\pi$
$439$	−15.9159	+	9.18904i	−0.759624	+	0.438569i	0.0695369	+	0.997579i	$0.477848\pi$
$440$	0.989530	−	3.72254i	0.0471740	−	0.177465i
$441$	3.30159	−	20.7388i	0.157219	−	0.987564i
$442$		−	12.2199i		−	0.581242i
$443$	0.869330	−	0.501908i	0.0413031	−	0.0238464i	−0.479206	−	0.877702i	$-0.659075\pi$
$443$	0.869330	−	0.501908i	0.0413031	−	0.0238464i	0.520509	+	0.853856i	$0.325742\pi$
$444$	−4.99880	+	17.7111i	−0.237233	+	0.840532i
$445$	2.00630	−	3.47501i	0.0951077	−	0.164731i
$446$	5.30008	+	9.18001i	0.250966	+	0.434686i
$447$	7.48157	−	1.89851i	0.353866	−	0.0897965i
$448$	−2.19957	−	1.47034i	−0.103920	−	0.0694671i
$449$		−	26.5910i		−	1.25491i	−0.778655	−	0.627453i	$-0.784098\pi$
$449$		−	26.5910i		−	1.25491i	0.778655	−	0.627453i	$-0.215902\pi$
$450$	−9.33731	−	5.72696i	−0.440165	−	0.269971i
$451$	−9.48609	+	9.52386i	−0.446683	+	0.448461i
$452$	−9.28025	−	5.35795i	−0.436506	−	0.252017i
$453$	4.95462	−	4.82468i	0.232788	−	0.226683i
$454$	2.04847			0.0961396
$455$	−0.718909	+	10.9348i	−0.0337030	+	0.512633i
$456$	2.11765	+	8.34515i	0.0991682	+	0.390797i
$457$	−9.69107	+	5.59514i	−0.453329	+	0.261730i	−0.709235	−	0.704972i	$-0.750960\pi$
$457$	−9.69107	+	5.59514i	−0.453329	+	0.261730i	0.255906	+	0.966702i	$0.417626\pi$
$458$	6.97376	−	12.0789i	0.325862	−	0.564410i
$459$	3.91908	+	17.3674i	0.182927	+	0.810640i
$460$	5.14671	+	8.91435i	0.239966	+	0.415634i
$461$	−1.38465			−0.0644895			−0.0322448	−	0.999480i	$-0.510266\pi$
$461$	−1.38465			−0.0644895			−0.0322448	+	0.999480i	$0.510266\pi$
$462$	−13.7077	+	6.56500i	−0.637740	+	0.305431i
$463$	−16.8511			−0.783138			−0.391569	−	0.920149i	$-0.628068\pi$
$463$	−16.8511			−0.783138			−0.391569	+	0.920149i	$0.628068\pi$
$464$	−3.02124	−	5.23293i	−0.140257	−	0.242933i
$465$	−2.11813	−	0.597824i	−0.0982259	−	0.0277234i
$466$	14.3840	−	24.9138i	0.666327	−	1.15411i
$467$	−24.2746	+	14.0149i	−1.12329	+	0.648533i	−0.942239	−	0.334940i	$-0.891284\pi$
$467$	−24.2746	+	14.0149i	−1.12329	+	0.648533i	−0.181053	+	0.983473i	$0.557951\pi$
$468$	−5.10153	−	9.40466i	−0.235818	−	0.434731i
$469$	4.32438	−	2.13147i	0.199681	−	0.0984221i
$470$	−5.68021			−0.262008
$471$	17.3238	+	17.7904i	0.798241	+	0.819739i
$472$	8.87574	+	5.12441i	0.408539	+	0.235870i
$473$	−16.4011	−	16.3361i	−0.754125	−	0.751135i
$474$	−11.5553	+	11.2522i	−0.530751	+	0.516831i
$475$			18.1495i			0.832755i
$476$	−0.594719	+	9.04586i	−0.0272589	+	0.414617i
$477$	2.89740	+	5.34135i	0.132663	+	0.244564i
$478$	7.62689	+	13.2102i	0.348846	+	0.604219i
$479$	−19.8918	+	34.4537i	−0.908882	+	1.57423i	−0.0932611	+	0.995642i	$0.529729\pi$
$479$	−19.8918	+	34.4537i	−0.908882	+	1.57423i	−0.815620	+	0.578587i	$0.803604\pi$
$480$	−1.93591	−	0.546395i	−0.0883619	−	0.0249394i
$481$	−32.8163	+	18.9465i	−1.49630	+	0.863887i
$482$		−	8.82596i		−	0.402012i
$483$	13.5732	−	38.2812i	0.617602	−	1.74186i
$484$	9.54805	+	5.46211i	0.434002	+	0.248278i
$485$	5.23996	−	3.02529i	0.237935	−	0.137372i
$486$	10.2667	+	11.7301i	0.465705	+	0.532089i
$487$	−4.24821	+	7.35811i	−0.192505	+	0.333428i	−0.946080	−	0.323934i	$-0.894994\pi$
$487$	−4.24821	+	7.35811i	−0.192505	+	0.333428i	0.753575	+	0.657362i	$0.228328\pi$
$488$	−8.96386	+	5.17529i	−0.405775	+	0.234274i
$489$	14.9665	−	3.79788i	0.676809	−	0.171746i
$490$	1.06435	−	8.05958i	0.0480825	−	0.364095i
$491$	20.7951			0.938470			0.469235	−	0.883073i	$-0.344530\pi$
$491$	20.7951			0.938470			0.469235	+	0.883073i	$0.344530\pi$
$492$	4.89743	+	5.02933i	0.220793	+	0.226740i
$493$	−10.3520	+	17.9301i	−0.466229	+	0.807532i
$494$	−8.86391	+	15.3527i	−0.398806	+	0.690752i
$495$	−8.36933	+	7.96758i	−0.376173	+	0.358116i
$496$	1.09412			0.0491277
$497$	−20.4486	+	30.5902i	−0.917244	+	1.37216i
$498$	−10.4327	+	2.64739i	−0.467500	+	0.118632i
$499$	−0.147787	−	0.255975i	−0.00661586	−	0.0114590i	0.862699	−	0.505719i	$-0.168773\pi$
$499$	−0.147787	−	0.255975i	−0.00661586	−	0.0114590i	−0.869314	+	0.494260i	$0.835439\pi$
$500$	−8.70116	−	5.02362i	−0.389128	−	0.224663i
$501$	−0.442406	+	1.56748i	−0.0197653	+	0.0700297i
$502$	−2.54176	+	1.46749i	−0.113444	+	0.0654971i
$503$	7.11469			0.317228			0.158614	−	0.987341i	$-0.449297\pi$
$503$	7.11469			0.317228			0.158614	+	0.987341i	$0.449297\pi$
$504$	3.31873	+	7.21013i	0.147828	+	0.321165i
$505$		−	4.91341i		−	0.218644i
$506$	−28.3791	+	7.66461i	−1.26160	+	0.340733i
$507$	−0.132085	+	0.467985i	−0.00586608	+	0.0207839i
$508$	−4.48636	−	2.59020i	−0.199050	−	0.114922i
$509$	−1.06636	+	0.615664i	−0.0472657	+	0.0272888i	−0.523447	−	0.852058i	$-0.675354\pi$
$509$	−1.06636	+	0.615664i	−0.0472657	+	0.0272888i	0.476181	+	0.879347i	$0.342021\pi$
$510$	1.69526	+	6.68061i	0.0750674	+	0.295822i
$511$	12.0989	+	24.5465i	0.535222	+	1.08587i
$512$	1.00000			0.0441942
$513$	7.67389	−	24.6626i	0.338810	−	1.08888i
$514$	14.2919	+	8.25142i	0.630388	+	0.363955i
$515$	18.3794	+	10.6113i	0.809891	+	0.467591i
$516$	−8.66107	+	8.43393i	−0.381282	+	0.371283i
$517$	4.16731	−	15.6771i	0.183278	−	0.689478i
$518$	25.2146	−	12.4282i	1.10786	−	0.546062i
$519$	−20.4594	+	5.19175i	−0.898068	+	0.227892i
$520$	−2.07095	−	3.58699i	−0.0908172	−	0.157300i
$521$	−37.3509	−	21.5645i	−1.63637	−	0.944759i	−0.982068	−	0.188526i	$-0.939629\pi$
$521$	−37.3509	−	21.5645i	−1.63637	−	0.944759i	−0.654303	−	0.756233i	$-0.727038\pi$
$522$	−0.481640	+	18.1210i	−0.0210808	+	0.793135i
$523$	−3.39607	+	1.96072i	−0.148500	+	0.0857364i	−0.572409	−	0.819968i	$-0.693991\pi$
$523$	−3.39607	+	1.96072i	−0.148500	+	0.0857364i	0.423909	+	0.905705i	$0.360658\pi$
$524$	−19.4920			−0.851512
$525$	3.04264	+	16.4531i	0.132792	+	0.718071i
$526$	−15.2613			−0.665423
$527$	−1.87445	−	3.24665i	−0.0816524	−	0.141426i
$528$	2.92831	−	4.94216i	0.127439	−	0.215080i
$529$	27.7782	−	48.1132i	1.20775	−	2.09188i
$530$	1.17619	+	2.03722i	0.0510904	+	0.0884912i
$531$	−14.6603	−	27.0263i	−0.636204	−	1.17284i
$532$	7.30874	−	10.9336i	0.316874	−	0.474030i
$533$			14.4544i			0.626091i
$534$	4.28743	−	4.17499i	0.185535	−	0.180669i
$535$	−0.661052	−	0.381658i	−0.0285798	−	0.0165005i
$536$	−0.911110	+	1.57809i	−0.0393540	+	0.0681631i
$537$	3.89818	−	3.79595i	0.168219	−	0.163807i
$538$			7.23796i			0.312050i
$539$	21.4632	+	8.85051i	0.924485	+	0.381218i
$540$	4.09370	+	4.43378i	0.176165	+	0.190799i
$541$	9.87581	−	5.70180i	0.424594	−	0.245140i	−0.272447	−	0.962171i	$-0.587833\pi$
$541$	9.87581	−	5.70180i	0.424594	−	0.245140i	0.697041	+	0.717031i	$0.254500\pi$
$542$	−20.4336	−	11.7973i	−0.877698	−	0.506739i
$543$	1.43734	−	5.09260i	0.0616823	−	0.218544i
$544$	−1.71320	−	2.96735i	−0.0734528	−	0.127224i
$545$	11.3316			0.485390
$546$	−5.46163	+	15.4037i	−0.233736	+	0.659219i
$547$		−	11.7537i		−	0.502553i	−0.967915	−	0.251276i	$-0.919150\pi$
$547$		−	11.7537i		−	0.502553i	0.967915	−	0.251276i	$-0.0808503\pi$
$548$	19.3338	−	11.1624i	0.825899	−	0.476833i
$549$	31.0408	+	0.825035i	1.32479	+	0.0352116i
$550$	8.54587	−	8.57989i	0.364397	−	0.365848i
$551$	26.0118	−	15.0179i	1.10814	−	0.639784i
$552$	3.77590	+	14.8799i	0.160713	+	0.633331i
$553$	24.5840	+	1.61627i	1.04542	+	0.0687308i
$554$		−	19.8116i		−	0.841713i
$555$	15.3122	−	14.9106i	0.649966	−	0.632920i
$556$	−9.15766	−	5.28718i	−0.388371	−	0.224226i
$557$	−14.9173	+	25.8375i	−0.632067	+	1.09477i	0.355062	+	0.934843i	$0.384460\pi$
$557$	−14.9173	+	25.8375i	−0.632067	+	1.09477i	−0.987128	+	0.159929i	$0.948873\pi$
$558$	−2.79801	−	1.71614i	−0.118449	−	0.0726498i
$559$	−24.8922			−1.05283
$560$	1.35846	+	2.75608i	0.0574054	+	0.116466i
$561$	−19.6819	−	0.222416i	−0.830970	−	0.00939041i
$562$	−9.44751	−	16.3636i	−0.398519	−	0.690255i
$563$	−15.1418	+	26.2264i	−0.638152	+	1.10531i	0.347686	+	0.937611i	$0.386967\pi$
$563$	−15.1418	+	26.2264i	−0.638152	+	1.10531i	−0.985838	+	0.167700i	$0.946366\pi$
$564$	−8.15291	−	2.30109i	−0.343299	−	0.0968933i
$565$	6.22254	+	10.7778i	0.261784	+	0.453424i
$566$			1.87542i			0.0788296i
$567$	2.82209	−	23.6439i	0.118517	−	0.992952i
$568$		−	13.9074i		−	0.583540i
$569$	−3.28407	−	5.68818i	−0.137675	−	0.238461i	0.788941	−	0.614469i	$-0.210630\pi$
$569$	−3.28407	−	5.68818i	−0.137675	−	0.238461i	−0.926616	+	0.376008i	$0.877296\pi$
$570$	2.71601	−	9.62300i	0.113761	−	0.403063i
$571$	−25.3943	−	14.6614i	−1.06272	−	0.613561i	−0.136536	−	0.990635i	$-0.543597\pi$
$571$	−25.3943	−	14.6614i	−1.06272	−	0.613561i	−0.926183	+	0.377074i	$0.876930\pi$
$572$	11.4193	−	3.08411i	0.477464	−	0.128953i
$573$	−0.0962476	−	0.379288i	−0.00402080	−	0.0158450i
$574$	0.703469	−	10.7000i	0.0293622	−	0.446608i
$575$			32.3616i			1.34957i
$576$	−2.55730	−	1.56850i	−0.106554	−	0.0653542i
$577$	−3.89280	+	6.74253i	−0.162060	+	0.280695i	−0.935607	−	0.353043i	$-0.885147\pi$
$577$	−3.89280	+	6.74253i	−0.162060	+	0.280695i	0.773548	+	0.633738i	$0.218480\pi$
$578$	2.62990	−	4.55513i	0.109390	−	0.189468i
$579$	14.9437	−	14.5518i	0.621038	−	0.604751i
$580$			7.01752i			0.291387i
$581$	13.6686	+	9.13704i	0.567069	+	0.379068i
$582$	8.74658	−	2.21952i	0.362558	−	0.0920021i
$583$	−6.48555	+	1.75161i	−0.268604	+	0.0725444i
$584$	−8.95771	−	5.17174i	−0.370673	−	0.214008i
$585$	−0.330147	+	12.4213i	−0.0136499	+	0.513558i
$586$	−8.69706	−	15.0638i	−0.359272	−	0.622278i
$587$			8.98728i			0.370945i	0.982649	+	0.185472i	$0.0593815\pi$
$587$			8.98728i			0.370945i	−0.982649	+	0.185472i	$0.940618\pi$
$588$	4.79267	−	11.1369i	0.197646	−	0.459278i
$589$			5.43865i			0.224096i
$590$	−5.95131	−	10.3080i	−0.245012	−	0.424373i
$591$	−0.255083	+	0.903777i	−0.0104927	+	0.0371764i
$592$	−5.31249	+	9.20151i	−0.218342	+	0.378180i
$593$	−0.812081	−	1.40657i	−0.0333482	−	0.0577608i	0.848870	−	0.528602i	$-0.177284\pi$
$593$	−0.812081	−	1.40657i	−0.0333482	−	0.0577608i	−0.882218	+	0.470842i	$0.843950\pi$
$594$	−15.2404	+	8.04555i	−0.625320	+	0.330113i
$595$	5.85093	−	8.75273i	0.239865	−	0.358827i
$596$	4.45639			0.182541
$597$	5.12664	+	5.26471i	0.209819	+	0.215470i
$598$	−15.8049	+	27.3749i	−0.646310	+	1.11944i
$599$	14.6927	+	8.48281i	0.600326	+	0.346598i	0.769170	−	0.639045i	$-0.220670\pi$
$599$	14.6927	+	8.48281i	0.600326	+	0.346598i	−0.168844	+	0.985643i	$0.554003\pi$
$600$	−4.41202	−	4.53084i	−0.180120	−	0.184971i
$601$		−	23.0019i		−	0.938269i	−0.883127	−	0.469134i	$-0.844566\pi$
$601$		−	23.0019i		−	0.938269i	0.883127	−	0.469134i	$-0.155434\pi$
$602$	18.4266	+	1.21145i	0.751010	+	0.0493751i
$603$	4.80522	−	2.60658i	0.195684	−	0.106148i
$604$	3.45781	−	1.99637i	0.140696	−	0.0812311i
$605$	−6.43141	−	11.0380i	−0.261474	−	0.448760i
$606$	1.99045	−	7.05231i	0.0808567	−	0.286481i
$607$	28.8610	−	16.6629i	1.17143	−	0.676328i	0.217416	−	0.976079i	$-0.430237\pi$
$607$	28.8610	−	16.6629i	1.17143	−	0.676328i	0.954017	+	0.299751i	$0.0969038\pi$
$608$			4.97078i			0.201592i
$609$	21.0628	−	17.9749i	0.853510	−	0.728380i
$610$	12.0208			0.486708
$611$	−8.72160	−	15.1063i	−0.352838	−	0.611134i
$612$	−0.273115	+	10.2756i	−0.0110400	+	0.415365i
$613$	−33.8680	−	19.5537i	−1.36792	−	0.789767i	−0.377255	−	0.926109i	$-0.623132\pi$
$613$	−33.8680	−	19.5537i	−1.36792	−	0.789767i	−0.990662	+	0.136342i	$0.956465\pi$
$614$	−18.1984	+	10.5068i	−0.734426	+	0.424021i
$615$	−2.00525	−	7.90221i	−0.0808597	−	0.318648i
$616$	−8.60329	+	1.72728i	−0.346636	+	0.0695940i
$617$		−	37.9007i		−	1.52583i	−0.646501	−	0.762913i	$-0.723768\pi$
$617$		−	37.9007i		−	1.52583i	0.646501	−	0.762913i	$-0.276232\pi$
$618$	22.0815	+	22.6762i	0.888249	+	0.912172i
$619$	−10.2068	+	17.6788i	−0.410247	+	0.710569i	−0.994917	−	0.100702i	$-0.967891\pi$
$619$	−10.2068	+	17.6788i	−0.410247	+	0.710569i	0.584669	+	0.811272i	$0.301224\pi$
$620$	−1.10044	−	0.635339i	−0.0441947	−	0.0255158i
$621$	13.6830	−	43.9749i	0.549080	−	1.76465i
$622$		−	28.2118i		−	1.13119i
$623$	−9.12157	−	0.599696i	−0.365448	−	0.0240263i
$624$	−1.51936	−	5.98743i	−0.0608231	−	0.239689i
$625$	−3.29382	−	5.70507i	−0.131753	−	0.228203i
$626$	−2.99806	+	5.19278i	−0.119826	+	0.207545i
$627$	24.5664	+	14.5560i	0.981088	+	0.581311i
$628$	7.16830	+	12.4159i	0.286046	+	0.495447i
$629$	36.4054			1.45158
$630$	0.848914	−	9.17888i	0.0338215	−	0.365695i
$631$	5.27676			0.210065			0.105032	−	0.994469i	$-0.466505\pi$
$631$	5.27676			0.210065			0.105032	+	0.994469i	$0.466505\pi$
$632$	−8.06437	+	4.65597i	−0.320783	+	0.185204i
$633$	−0.241961	−	0.0682913i	−0.00961707	−	0.00271433i
$634$	−8.91377	−	5.14637i	−0.354011	−	0.204388i
$635$	3.00817	+	5.21031i	0.119376	+	0.206765i
$636$	0.862917	+	3.40054i	0.0342169	+	0.134840i
$637$	23.0683	−	9.54438i	0.914001	−	0.378162i
$638$	−19.3680	−	5.14843i	−0.766787	−	0.203828i
$639$	−21.8137	+	35.5654i	−0.862937	+	1.40694i
$640$	−1.00577	−	0.580683i	−0.0397566	−	0.0229535i
$641$	−12.3614	−	7.13687i	−0.488247	−	0.281890i	0.235600	−	0.971850i	$-0.424295\pi$
$641$	−12.3614	−	7.13687i	−0.488247	−	0.281890i	−0.723847	+	0.689961i	$0.757628\pi$
$642$	−0.794208	−	0.815597i	−0.0313449	−	0.0321891i
$643$	−9.93134			−0.391654			−0.195827	−	0.980638i	$-0.562739\pi$
$643$	−9.93134			−0.391654			−0.195827	+	0.980638i	$0.562739\pi$
$644$	13.0319	−	19.4952i	0.513530	−	0.768219i
$645$	13.6085	−	3.45327i	0.535834	−	0.135972i
$646$	14.7500	−	8.51593i	0.580332	−	0.335055i
$647$	18.3282	+	10.5818i	0.720556	+	0.416013i	0.814957	−	0.579521i	$-0.196760\pi$
$647$	18.3282	+	10.5818i	0.720556	+	0.416013i	−0.0944013	+	0.995534i	$0.530094\pi$
$648$	4.07961	+	8.02227i	0.160262	+	0.315144i
$649$	32.8157	−	8.86285i	1.28813	−	0.347897i
$650$		−	13.0218i		−	0.510756i
$651$	0.911755	+	4.93031i	0.0357345	+	0.193234i
$652$	8.91479			0.349130
$653$	−26.3449	+	15.2102i	−1.03096	+	0.595222i	−0.917258	−	0.398293i	$-0.869603\pi$
$653$	−26.3449	+	15.2102i	−1.03096	+	0.595222i	−0.113697	+	0.993515i	$0.536269\pi$
$654$	16.2644	+	4.59048i	0.635988	+	0.179502i
$655$	19.6045	+	11.3187i	0.766011	+	0.442257i
$656$	2.02647	+	3.50995i	0.0791204	+	0.137041i
$657$	14.7957	+	27.2759i	0.577236	+	1.06413i
$658$	5.72102	+	11.6070i	0.223029	+	0.452486i
$659$	50.2839			1.95878			0.979391	−	0.201972i	$-0.0647351\pi$
$659$	50.2839			1.95878			0.979391	+	0.201972i	$0.0647351\pi$
$660$	−5.81504	+	3.27027i	−0.226350	+	0.127295i
$661$	−14.1421	+	24.4948i	−0.550062	+	0.952736i	0.448207	+	0.893930i	$0.352063\pi$
$661$	−14.1421	+	24.4948i	−0.550062	+	0.952736i	−0.998269	+	0.0588062i	$0.981271\pi$
$662$	6.54105	−	11.3294i	0.254225	−	0.440331i
$663$	−15.1638	+	14.7661i	−0.588914	+	0.573469i
$664$	−6.21423			−0.241159
$665$	−13.6999	+	6.75261i	−0.531258	+	0.261855i
$666$	28.0182	−	15.1984i	1.08568	−	0.588927i
$667$	46.3805	−	26.7778i	1.79586	−	1.03684i
$668$	−0.470169	+	0.814356i	−0.0181914	+	0.0315084i
$669$	4.98712	−	17.6697i	0.192813	−	0.683151i
$670$	1.83274	−	1.05813i	0.0708048	−	0.0408792i
$671$	−8.81911	+	33.1768i	−0.340458	+	1.28078i
$672$	0.833319	+	4.50617i	0.0321460	+	0.173829i
$673$			5.41647i			0.208790i	0.994536	+	0.104395i	$0.0332906\pi$
$673$			5.41647i			0.208790i	−0.994536	+	0.104395i	$0.966709\pi$
$674$	14.8074	−	8.54906i	0.570360	−	0.329298i
$675$	4.17624	+	18.5070i	0.160744	+	0.712335i
$676$	−0.140373	+	0.243134i	−0.00539897	+	0.00935130i
$677$	12.3437	+	21.3799i	0.474407	+	0.821698i	0.999571	−	0.0293038i	$-0.00932903\pi$
$677$	12.3437	+	21.3799i	0.474407	+	0.821698i	−0.525163	+	0.851002i	$0.675996\pi$
$678$	4.56519	+	17.9903i	0.175325	+	0.690914i
$679$	−11.4595	−	7.66033i	−0.439776	−	0.293976i
$680$			3.97930i			0.152599i
$681$	−2.47530	−	2.54197i	−0.0948538	−	0.0974084i
$682$	2.56085	−	2.57104i	0.0980599	−	0.0984503i
$683$	18.1930	+	10.5037i	0.696135	+	0.401914i	0.805906	−	0.592043i	$-0.201678\pi$
$683$	18.1930	+	10.5037i	0.696135	+	0.401914i	−0.109771	+	0.993957i	$0.535012\pi$
$684$	7.79667	−	12.7118i	0.298113	−	0.486048i
$685$	−25.9272			−0.990626
$686$	−17.5410	+	5.94259i	−0.669717	+	0.226889i
$687$	−23.4157	+	5.94192i	−0.893363	+	0.226699i
$688$	−6.04453	+	3.48981i	−0.230445	+	0.133048i
$689$	−3.61193	+	6.25605i	−0.137604	+	0.238336i
$690$	4.84280	−	17.1584i	0.184362	−	0.653209i
$691$	−16.6920	−	28.9114i	−0.634993	−	1.09984i	−0.986517	−	0.163661i	$-0.947670\pi$
$691$	−16.6920	−	28.9114i	−0.634993	−	1.09984i	0.351523	−	0.936179i	$-0.385664\pi$
$692$	−12.1866			−0.463266
$693$	24.7105	+	9.07708i	0.938673	+	0.344810i
$694$	−13.8049			−0.524027
$695$	6.14034	+	10.6354i	0.232916	+	0.403423i
$696$	−2.84284	+	10.0724i	−0.107758	+	0.381792i
$697$	6.94349	−	12.0265i	0.263004	−	0.455536i
$698$	23.4754	−	13.5535i	0.888558	−	0.513009i
$699$	−48.2969	+	12.2558i	−1.82676	+	0.463555i
$700$	−0.633744	+	9.63944i	−0.0239533	+	0.364337i
$701$	−26.5494			−1.00276			−0.501379	−	0.865228i	$-0.667174\pi$
$701$	−26.5494			−1.00276			−0.501379	+	0.865228i	$0.667174\pi$
$702$	−5.50582	+	17.6948i	−0.207804	+	0.667847i
$703$	−45.7387	−	26.4072i	−1.72507	−	0.995968i
$704$	2.34054	−	2.34986i	0.0882126	−	0.0885637i
$705$	6.86376	+	7.04862i	0.258504	+	0.265466i
$706$		−	17.7264i		−	0.667142i
$707$	−10.0401	+	4.94872i	−0.377596	+	0.186116i
$708$	−4.36621	−	17.2061i	−0.164092	−	0.646647i
$709$	8.41921	+	14.5825i	0.316190	+	0.547657i	0.979690	−	0.200519i	$-0.0642629\pi$
$709$	8.41921	+	14.5825i	0.316190	+	0.547657i	−0.663500	+	0.748177i	$0.730930\pi$
$710$	−8.07577	+	13.9876i	−0.303078	+	0.524947i
$711$	27.9259	+	0.742246i	1.04730	+	0.0278364i
$712$	2.99218	−	1.72754i	0.112137	−	0.0647421i
$713$			9.69745i			0.363172i
$714$	11.9437	−	10.1927i	0.446983	−	0.381453i
$715$	−13.2761	−	3.52907i	−0.496497	−	0.131980i
$716$	2.72052	−	1.57070i	0.101671	−	0.0586996i
$717$	7.17654	−	25.4270i	0.268013	−	0.949588i
$718$	10.3453	−	17.9186i	0.386084	−	0.668718i
$719$	−23.1897	+	13.3886i	−0.864830	+	0.499310i	−0.865627	−	0.500690i	$-0.833080\pi$
$719$	−23.1897	+	13.3886i	−0.864830	+	0.499310i	0.000796544		1.00000i	$0.499746\pi$
$720$	1.66126	+	3.06254i	0.0619116	+	0.114134i
$721$	3.17180	−	48.2440i	0.118124	−	1.79670i
$722$	−5.70864			−0.212454
$723$	−10.9522	+	10.6650i	−0.407317	+	0.396635i
$724$	1.52754	−	2.64578i	0.0567706	−	0.0983295i
$725$	−11.0312	+	19.1067i	−0.409690	+	0.709603i
$726$	−4.75955	−	18.4485i	−0.176643	−	0.684688i
$727$	−28.1484			−1.04396			−0.521982	−	0.852956i	$-0.674807\pi$
$727$	−28.1484			−1.04396			−0.521982	+	0.852956i	$0.674807\pi$
$728$	−5.24384	+	7.84455i	−0.194349	+	0.290738i
$729$	2.15012	−	26.9143i	0.0796341	−	0.996824i
$730$	6.00627	+	10.4032i	0.222302	+	0.385039i
$731$	20.7109	+	11.9575i	0.766022	+	0.442263i
$732$	17.2537	+	4.86970i	0.637714	+	0.179989i
$733$	−4.85268	+	2.80169i	−0.179238	+	0.103483i	−0.586934	−	0.809634i	$-0.699665\pi$
$733$	−4.85268	+	2.80169i	−0.179238	+	0.103483i	0.407697	+	0.913117i	$0.366332\pi$
$734$	−5.91635			−0.218376
$735$	−11.2873	+	8.41815i	−0.416339	+	0.310508i
$736$			8.86320i			0.326702i
$737$	1.57580	+	5.83457i	0.0580452	+	0.214919i
$738$	0.323056	−	12.1545i	0.0118919	−	0.447415i
$739$	−11.0876	−	6.40146i	−0.407866	−	0.235481i	0.282007	−	0.959412i	$-0.409000\pi$
$739$	−11.0876	−	6.40146i	−0.407866	−	0.235481i	−0.689872	+	0.723931i	$0.742333\pi$
$740$	10.6863	−	6.16975i	0.392837	−	0.226804i
$741$	29.7622	−	7.55241i	1.09334	−	0.277445i
$742$	2.97822	−	4.45529i	0.109334	−	0.163559i
$743$	34.7835			1.27608			0.638042	−	0.770001i	$-0.279744\pi$
$743$	34.7835			1.27608			0.638042	+	0.770001i	$0.279744\pi$
$744$	−1.32210	−	1.35771i	−0.0484706	−	0.0497760i
$745$	−4.48211	−	2.58775i	−0.164212	−	0.0948077i
$746$	7.47599	+	4.31626i	0.273715	+	0.158030i
$747$	15.8917	+	9.74702i	0.581446	+	0.356625i
$748$	−10.9827	−	2.91943i	−0.401566	−	0.106745i
$749$	−0.114080	+	1.73520i	−0.00416840	+	0.0634027i
$750$	4.28033	+	16.8677i	0.156295	+	0.615922i
$751$	11.6628	+	20.2006i	0.425583	+	0.737131i	0.996475	−	0.0838942i	$-0.0267358\pi$
$751$	11.6628	+	20.2006i	0.425583	+	0.737131i	−0.570892	+	0.821025i	$0.693402\pi$
$752$	−4.23571	−	2.44549i	−0.154460	−	0.0891778i
$753$	4.89239	+	1.38083i	0.178289	+	0.0503204i
$754$	−18.6628	+	10.7750i	−0.679658	+	0.392401i
$755$	−4.63702			−0.168759
$756$	4.93688	−	12.8307i	0.179553	−	0.466649i
$757$	−41.4821			−1.50769			−0.753846	−	0.657051i	$-0.771804\pi$
$757$	−41.4821			−1.50769			−0.753846	+	0.657051i	$0.771804\pi$
$758$	1.65013	+	2.85812i	0.0599356	+	0.103811i
$759$	43.8034	+	25.9542i	1.58996	+	0.942079i
$760$	2.88644	−	4.99947i	0.104702	−	0.181350i
$761$	−20.6464	−	35.7605i	−0.748430	−	1.29632i	−0.948575	−	0.316552i	$-0.897475\pi$
$761$	−20.6464	−	35.7605i	−0.748430	−	1.29632i	0.200145	−	0.979766i	$-0.435859\pi$
$762$	2.20696	+	8.69708i	0.0799497	+	0.315062i
$763$	−11.4130	−	23.1549i	−0.413177	−	0.838265i
$764$		−	0.225923i		−	0.00817359i
$765$	6.24153	−	10.1763i	0.225663	−	0.367924i
$766$	−13.9230	−	8.03845i	−0.503059	−	0.290441i
$767$	18.2757	−	31.6545i	0.659899	−	1.14298i
$768$	−1.20836	−	1.24091i	−0.0436031	−	0.0447774i
$769$			10.9384i			0.394448i	0.980358	+	0.197224i	$0.0631926\pi$
$769$			10.9384i			0.394448i	−0.980358	+	0.197224i	$0.936807\pi$
$770$	9.65594	+	3.25853i	0.347976	+	0.117429i
$771$	−7.03054	−	27.7056i	−0.253199	−	0.997794i
$772$	10.4291	−	6.02127i	0.375353	−	0.216710i
$773$	−0.123624	−	0.0713746i	−0.00444646	−	0.00256717i	0.497775	−	0.867306i	$-0.334150\pi$
$773$	−0.123624	−	0.0713746i	−0.00444646	−	0.00256717i	−0.502222	+	0.864739i	$0.667484\pi$
$774$	20.9315	+	0.556339i	0.752366	+	0.0199972i
$775$	−1.99745	−	3.45969i	−0.0717506	−	0.124276i
$776$	5.20989			0.187024
$777$	−45.8906	−	16.2712i	−1.64632	−	0.583727i
$778$		−	20.6143i		−	0.739057i
$779$	−17.4472	+	10.0731i	−0.625111	+	0.360908i
$780$	−1.94866	+	6.90425i	−0.0697734	+	0.247212i
$781$	−32.6804	−	32.5508i	−1.16940	−	1.16476i
$782$	26.3002	−	15.1844i	0.940493	−	0.542994i
$783$	23.0685	−	21.2991i	0.824402	−	0.761169i
$784$	4.26356	−	5.55176i	0.152270	−	0.198277i
$785$		−	16.6500i		−	0.594265i
$786$	23.5534	+	24.1878i	0.840124	+	0.862750i
$787$	−11.8429	−	6.83752i	−0.422155	−	0.243731i	0.273844	−	0.961774i	$-0.411705\pi$
$787$	−11.8429	−	6.83752i	−0.422155	−	0.243731i	−0.695999	+	0.718043i	$0.745038\pi$
$788$	−0.271090	+	0.469542i	−0.00965720	+	0.0167268i
$789$	18.4412	+	18.9379i	0.656524	+	0.674206i
$790$	10.8146			0.384764
$791$	15.7560	−	23.5704i	0.560221	−	0.838065i
$792$	−9.67125	+	2.33817i	−0.343653	+	0.0830831i
$793$	18.4572	+	31.9688i	0.655434	+	1.13524i
$794$	2.61119	−	4.52272i	0.0926678	−	0.160505i
$795$	1.10674	−	3.92125i	0.0392520	−	0.139072i
$796$	2.12131	+	3.67422i	0.0751879	+	0.130229i
$797$		−	6.59645i		−	0.233658i	−0.993152	−	0.116829i	$-0.962727\pi$
$797$		−	6.59645i		−	0.233658i	0.993152	−	0.116829i	$-0.0372730\pi$
$798$	−22.3992	+	4.14225i	−0.792922	+	0.146634i
$799$			16.7584i			0.592870i
$800$	−1.82562	−	3.16206i	−0.0645453	−	0.111796i
$801$	−10.3616	−	0.275401i	−0.366107	−	0.00973080i
$802$	1.61502	+	0.932434i	0.0570285	+	0.0329254i
$803$	−33.1188	+	8.94470i	−1.16874	+	0.315652i
$804$	3.05922	−	0.776303i	0.107890	−	0.0273781i
$805$	−24.4277	+	12.0403i	−0.860962	+	0.424365i
$806$		−	3.90209i		−	0.137445i
$807$	8.98164	−	8.74609i	0.316169	−	0.307877i
$808$	2.11536	−	3.66391i	0.0744181	−	0.128896i
$809$	−11.1559	+	19.3225i	−0.392220	+	0.679345i	−0.992742	−	0.120263i	$-0.961626\pi$
$809$	−11.1559	+	19.3225i	−0.392220	+	0.679345i	0.600522	+	0.799608i	$0.294959\pi$
$810$	0.555232	−	10.4375i	0.0195089	−	0.366737i
$811$		−	34.3916i		−	1.20765i	−0.797116	−	0.603827i	$-0.793642\pi$
$811$		−	34.3916i		−	1.20765i	0.797116	−	0.603827i	$-0.206358\pi$
$812$	14.3396	−	7.06794i	0.503222	−	0.248036i
$813$	10.0518	+	39.6117i	0.352532	+	1.38924i
$814$	9.18815	+	34.0202i	0.322044	+	1.19241i
$815$	−8.96624	−	5.17666i	−0.314074	−	0.181331i
$816$	−1.61204	+	5.71156i	−0.0564326	+	0.199945i
$817$	−17.3471	−	30.0460i	−0.606897	−	1.05118i
$818$		−	14.1198i		−	0.493686i
$819$	25.7143	−	11.8359i	0.898529	−	0.413581i
$820$		−	4.70695i		−	0.164374i
$821$	−3.99233	−	6.91491i	−0.139333	−	0.241332i	0.787911	−	0.615789i	$-0.211163\pi$
$821$	−3.99233	−	6.91491i	−0.139333	−	0.241332i	−0.927244	+	0.374457i	$0.877829\pi$
$822$	−37.2138	−	10.5033i	−1.29798	−	0.366343i
$823$	14.0547	−	24.3434i	0.489914	−	0.848557i	−0.510018	−	0.860164i	$-0.670361\pi$
$823$	14.0547	−	24.3434i	0.489914	−	0.848557i	0.999933	+	0.0116069i	$0.00369468\pi$
$824$	9.13694	+	15.8257i	0.318301	+	0.551313i
$825$	−20.9734	−	0.237010i	−0.730200	−	0.00825165i
$826$	−15.0693	+	22.5430i	−0.524327	+	0.784371i
$827$	1.47055			0.0511361			0.0255680	−	0.999673i	$-0.491861\pi$
$827$	1.47055			0.0511361			0.0255680	+	0.999673i	$0.491861\pi$
$828$	13.9019	−	22.6659i	0.483126	−	0.787694i
$829$	25.2928	−	43.8085i	0.878456	−	1.52153i	0.0254218	−	0.999677i	$-0.491907\pi$
$829$	25.2928	−	43.8085i	0.878456	−	1.52153i	0.853035	−	0.521854i	$-0.174760\pi$
$830$	6.25009	+	3.60849i	0.216944	+	0.125253i
$831$	−24.5843	+	23.9396i	−0.852822	+	0.830456i
$832$		−	3.56641i		−	0.123643i
$833$	−23.7783	−	3.14018i	−0.823870	−	0.108801i
$834$	4.50489	+	17.7527i	0.155992	+	0.614724i
$835$	0.945765	−	0.546038i	0.0327295	−	0.0188964i
$836$	11.6806	+	11.6343i	0.403983	+	0.402382i
$837$	1.25145	+	5.54579i	0.0432564	+	0.191691i
$838$	18.0512	−	10.4219i	0.623568	−	0.360017i
$839$		−	19.5188i		−	0.673862i	−0.941529	−	0.336931i	$-0.890611\pi$
$839$		−	19.5188i		−	0.673862i	0.941529	−	0.336931i	$-0.109389\pi$
$840$	1.77853	−	5.01607i	0.0613650	−	0.173071i
$841$	7.51148			0.259016
$842$	−10.1630	−	17.6028i	−0.350240	−	0.606634i
$843$	−8.88965	+	31.4966i	−0.306176	+	1.08480i
$844$	−0.125707	−	0.0725768i	−0.00432700	−	0.00249820i
$845$	0.282367	−	0.163025i	0.00971372	−	0.00560822i
$846$	6.99625	+	12.8976i	0.240536	+	0.443428i
$847$	−16.0775	+	24.2593i	−0.552430	+	0.833559i
$848$			2.02553i			0.0695570i
$849$	2.32722	−	2.26619i	0.0798700	−	0.0777753i
$850$	−6.25528	+	10.8345i	−0.214554	+	0.371619i
$851$	−81.5548	−	47.0857i	−2.79566	−	1.61408i
$852$	−17.2578	+	16.8052i	−0.591242	+	0.575736i
$853$			7.98283i			0.273327i	0.990618	+	0.136663i	$0.0436379\pi$
$853$			7.98283i			0.273327i	−0.990618	+	0.136663i	$0.956362\pi$
$854$	−12.1072	−	24.5633i	−0.414299	−	0.840540i
$855$	−15.2232	+	8.25777i	−0.520622	+	0.282410i
$856$	−0.328629	−	0.569202i	−0.0112323	−	0.0194549i
$857$	−14.1944	+	24.5854i	−0.484871	+	0.839821i	−0.999849	−	0.0173825i	$-0.994467\pi$
$857$	−14.1944	+	24.5854i	−0.484871	+	0.839821i	0.514978	+	0.857203i	$0.327800\pi$
$858$	−17.6258	−	10.4436i	−0.601734	−	0.356537i
$859$	18.7050	+	32.3981i	0.638208	+	1.10541i	0.985826	+	0.167772i	$0.0536572\pi$
$859$	18.7050	+	32.3981i	0.638208	+	1.10541i	−0.347618	+	0.937636i	$0.613009\pi$
$860$	8.10589			0.276408
$861$	−14.1277	+	12.0565i	−0.481472	+	0.410886i
$862$	−38.3798			−1.30722
$863$	−22.9893	+	13.2729i	−0.782565	+	0.451814i	−0.837339	−	0.546685i	$-0.815890\pi$
$863$	−22.9893	+	13.2729i	−0.782565	+	0.451814i	0.0547734	+	0.998499i	$0.482556\pi$
$864$	1.14379	+	5.06870i	0.0389125	+	0.172441i
$865$	12.2570	+	7.07656i	0.416749	+	0.240610i
$866$	14.8687	+	25.7534i	0.505260	+	0.875135i
$867$	−8.83038	+	2.24078i	−0.299895	+	0.0761010i
$868$	−0.189907	+	2.88855i	−0.00644587	+	0.0980436i
$869$	−7.93414	+	29.8476i	−0.269147	+	1.01251i
$870$	8.70810	−	8.47972i	0.295232	−	0.287489i
$871$	5.62811	+	3.24939i	0.190701	+	0.110101i
$872$	8.44989	+	4.87855i	0.286150	+	0.165209i
$873$	−13.3233	−	8.17172i	−0.450925	−	0.276571i
$874$	−44.0570			−1.49025
$875$	14.7729	−	22.0996i	0.499414	−	0.747102i
$876$	4.40653	+	17.3650i	0.148883	+	0.586710i
$877$	8.96606	−	5.17656i	0.302762	−	0.174800i	−0.340921	−	0.940092i	$-0.610739\pi$
$877$	8.96606	−	5.17656i	0.302762	−	0.174800i	0.643683	+	0.765292i	$0.277405\pi$
$878$	15.9159	+	9.18904i	0.537135	+	0.310115i
$879$	−8.18352	+	28.9948i	−0.276023	+	0.977970i
$880$	−3.71858	+	1.00431i	−0.125353	+	0.0338553i
$881$		−	39.0911i		−	1.31701i	−0.752576	−	0.658506i	$-0.771189\pi$
$881$		−	39.0911i		−	1.31701i	0.752576	−	0.658506i	$-0.228811\pi$
$882$	−19.6112	+	7.51016i	−0.660342	+	0.252880i
$883$	46.5389			1.56616			0.783080	−	0.621921i	$-0.213648\pi$
$883$	46.5389			1.56616			0.783080	+	0.621921i	$0.213648\pi$
$884$	−10.5828	+	6.10996i	−0.355937	+	0.205500i
$885$	−5.59990	+	19.8408i	−0.188239	+	0.666942i
$886$	−0.869330	−	0.501908i	−0.0292057	−	0.0168619i
$887$	−4.65016	−	8.05432i	−0.156137	−	0.270438i	0.777335	−	0.629086i	$-0.216571\pi$
$887$	−4.65016	−	8.05432i	−0.156137	−	0.270438i	−0.933473	+	0.358649i	$0.883238\pi$
$888$	17.8377	−	4.52646i	0.598593	−	0.151898i
$889$	7.61697	−	11.3947i	0.255465	−	0.382164i
$890$	−4.01260			−0.134503
$891$	28.3997	+	9.18995i	0.951427	+	0.307875i
$892$	5.30008	−	9.18001i	0.177460	−	0.307370i
$893$	12.1560	−	21.0548i	0.406784	−	0.704571i
$894$	−5.38494	−	5.52997i	−0.180099	−	0.184950i
$895$	−3.64830			−0.121949
$896$	−0.173570	+	2.64005i	−0.00579856	+	0.0881979i
$897$	53.0678	−	13.4664i	1.77188	−	0.449630i
$898$	−23.0285	+	13.2955i	−0.768469	+	0.443676i
$899$	−3.30561	+	5.72548i	−0.110248	+	0.190956i
$900$	−0.291036	+	10.9498i	−0.00970121	+	0.364994i
$901$	6.01045	−	3.47013i	0.200237	−	0.115607i
$902$	12.9909	+	3.45327i	0.432551	+	0.114981i
$903$	−20.7627	−	24.3296i	−0.690939	−	0.809637i
$904$			10.7159i			0.356406i
$905$	−3.07271	+	1.77403i	−0.102140	+	0.0589708i
$906$	−6.65561	−	1.87849i	−0.221118	−	0.0624085i
$907$	−8.66455	+	15.0074i	−0.287702	+	0.498314i	−0.973261	−	0.229703i	$-0.926225\pi$
$907$	−8.66455	+	15.0074i	−0.287702	+	0.498314i	0.685559	+	0.728017i	$0.259558\pi$
$908$	−1.02424	−	1.77403i	−0.0339905	−	0.0588732i
$909$	−11.1565	+	6.05180i	−0.370037	+	0.200725i
$910$	9.82929	−	4.84482i	0.325838	−	0.160604i
$911$			41.9798i			1.39085i	0.718598	+	0.695426i	$0.244784\pi$
$911$			41.9798i			1.39085i	−0.718598	+	0.695426i	$0.755216\pi$
$912$	6.16828	−	6.00651i	0.204252	−	0.198896i
$913$	−14.5447	+	14.6026i	−0.481358	+	0.483275i
$914$	9.69107	+	5.59514i	0.320552	+	0.185071i
$915$	−14.5255	−	14.9167i	−0.480199	−	0.493131i
$916$	−13.9475			−0.460839
$917$	3.38322	−	51.4599i	0.111724	−	1.69936i
$918$	13.0811	−	12.0777i	0.431739	−	0.398624i
$919$	−2.03187	+	1.17310i	−0.0670252	+	0.0386970i	−0.533138	−	0.846028i	$-0.678987\pi$
$919$	−2.03187	+	1.17310i	−0.0670252	+	0.0386970i	0.466113	+	0.884725i	$0.345654\pi$
$920$	5.14671	−	8.91435i	0.169682	−	0.293898i
$921$	35.0283	+	9.88642i	1.15422	+	0.325769i
$922$	0.692324	+	1.19914i	0.0228005	+	0.0394916i
$923$	−49.5993			−1.63258
$924$	12.5393	+	8.58871i	0.412513	+	0.282548i
$925$	38.7943			1.27555
$926$	8.42556	+	14.5935i	0.276881	+	0.479572i
$927$	1.45660	−	54.8023i	0.0478409	−	1.79994i
$928$	−3.02124	+	5.23293i	−0.0991769	+	0.171780i
$929$	27.2536	−	15.7349i	0.894163	−	0.516245i	0.0188609	−	0.999822i	$-0.493996\pi$
$929$	27.2536	−	15.7349i	0.894163	−	0.516245i	0.875302	+	0.483577i	$0.160663\pi$
$930$	0.541335	+	2.13327i	0.0177511	+	0.0699526i
$931$	27.5966	+	21.1932i	0.904442	+	0.694579i
$932$	−28.7680			−0.942328
$933$	−35.0083	+	34.0902i	−1.14612	+	1.11606i
$934$	24.2746	+	14.0149i	0.794288	+	0.458582i
$935$	9.35080	+	9.31372i	0.305804	+	0.304591i
$936$	−5.59391	+	9.12039i	−0.182843	+	0.298109i
$937$			42.5796i			1.39102i	0.718519	+	0.695508i	$0.244820\pi$
$937$			42.5796i			1.39102i	−0.718519	+	0.695508i	$0.755180\pi$
$938$	−4.00810	−	2.67929i	−0.130869	−	0.0874818i
$939$	10.0665	−	2.55446i	0.328508	−	0.0833618i
$940$	2.84010	+	4.91920i	0.0926340	+	0.160447i
$941$	−28.2503	+	48.9309i	−0.920932	+	1.59510i	−0.122956	+	0.992412i	$0.539238\pi$
$941$	−28.2503	+	48.9309i	−0.920932	+	1.59510i	−0.797976	+	0.602689i	$0.794096\pi$
$942$	6.74503	−	23.8981i	0.219765	−	0.778642i
$943$	−31.1094	+	17.9610i	−1.01306	+	0.584891i
$944$		−	10.2488i		−	0.333571i
$945$	−12.4159	+	10.0380i	−0.403891	+	0.326536i
$946$	−5.94692	+	22.3719i	−0.193351	+	0.727372i
$947$	23.9465	−	13.8255i	0.778158	−	0.449270i	−0.0576190	−	0.998339i	$-0.518351\pi$
$947$	23.9465	−	13.8255i	0.778158	−	0.449270i	0.835777	+	0.549069i	$0.185018\pi$
$948$	15.5223	+	4.38104i	0.504142	+	0.142290i
$949$	−18.4445	+	31.9468i	−0.598734	+	1.03704i
$950$	15.7179	−	9.07473i	0.509956	−	0.294423i
$951$	4.38492	+	17.2799i	0.142191	+	0.560338i
$952$	8.13131	−	4.00789i	0.263537	−	0.129896i
$953$	36.7018			1.18889			0.594444	−	0.804137i	$-0.297372\pi$
$953$	36.7018			1.18889			0.594444	+	0.804137i	$0.297372\pi$
$954$	3.17705	−	5.17990i	0.102861	−	0.167705i
$955$	−0.131189	+	0.227227i	−0.00424519	+	0.00735288i
$956$	7.62689	−	13.2102i	0.246671	−	0.427247i
$957$	17.0149	+	30.2551i	0.550013	+	0.978009i
$958$	39.7837			1.28535
$959$	26.1135	+	52.9797i	0.843248	+	1.71080i
$960$	0.494765	+	1.94975i	0.0159685	+	0.0629278i
$961$	14.9014	+	25.8101i	0.480692	+	0.832583i
$962$	32.8163	+	18.9465i	1.05804	+	0.610860i
$963$	−0.0523895	+	1.97108i	−0.00168823	+	0.0635171i
$964$	−7.64351	+	4.41298i	−0.246181	+	0.142133i
$965$	−13.9858			−0.450218
$966$	−39.9391	+	7.38588i	−1.28502	+	0.237637i
$967$		−	13.2759i		−	0.426923i	−0.976951	−	0.213461i	$-0.931526\pi$
$967$		−	13.2759i		−	0.426923i	0.976951	−	0.213461i	$-0.0684738\pi$
$968$	−0.0436998	−	10.9999i	−0.00140457	−	0.353551i
$969$	−28.3909	−	8.01308i	−0.912047	−	0.257417i
$970$	−5.23996	−	3.02529i	−0.168245	−	0.0971364i
$971$	−5.24145	+	3.02615i	−0.168206	+	0.0971139i	−0.581740	−	0.813375i	$-0.697628\pi$
$971$	−5.24145	+	3.02615i	−0.168206	+	0.0971139i	0.413534	+	0.910489i	$0.364294\pi$
$972$	5.02524	−	14.7563i	0.161185	−	0.473307i
$973$	15.5479	−	23.2590i	0.498443	−	0.745649i
$974$	8.49641			0.272243
$975$	−16.1588	+	15.7351i	−0.517497	+	0.503925i
$976$	8.96386	+	5.17529i	0.286926	+	0.165657i
$977$	2.31699	+	1.33771i	0.0741269	+	0.0427972i	0.536605	−	0.843833i	$-0.319706\pi$
$977$	2.31699	+	1.33771i	0.0741269	+	0.0427972i	−0.462478	+	0.886631i	$0.653040\pi$
$978$	−10.7723	−	11.0624i	−0.344461	−	0.353738i
$979$	2.94386	−	11.0746i	0.0940862	−	0.353945i
$980$	−7.51198	+	3.10803i	−0.239961	+	0.0992825i
$981$	−13.9569	−	25.7296i	−0.445611	−	0.821483i
$982$	−10.3976	−	18.0091i	−0.331799	−	0.574693i
$983$	2.94995	+	1.70316i	0.0940890	+	0.0543223i	0.546306	−	0.837586i	$-0.316033\pi$
$983$	2.94995	+	1.70316i	0.0940890	+	0.0543223i	−0.452217	+	0.891908i	$0.649367\pi$
$984$	1.90681	−	6.75597i	0.0607870	−	0.215372i
$985$	0.545310	−	0.314835i	0.0173750	−	0.0100315i
$986$	20.7039			0.659347
$987$	7.49009	−	21.1247i	0.238412	−	0.672407i
$988$	17.7278			0.563997
$989$	−30.9309	−	53.5739i	−0.983545	−	1.70355i
$990$	11.0848	+	3.26426i	0.352298	+	0.103745i
$991$	24.7571	−	42.8805i	0.786434	−	1.36214i	−0.141705	−	0.989909i	$-0.545259\pi$
$991$	24.7571	−	42.8805i	0.786434	−	1.36214i	0.928139	−	0.372234i	$-0.121408\pi$
$992$	−0.547062	−	0.947540i	−0.0173692	−	0.0300844i
$993$	−21.9628	+	5.57324i	−0.696967	+	0.176861i
$994$	36.7162	+	2.41390i	1.16457	+	0.0765643i
$995$		−	4.92723i		−	0.156204i
$996$	7.50905	+	7.71129i	0.237933	+	0.244341i
$997$	11.3409	+	6.54767i	0.359170	+	0.207367i	0.668716	−	0.743518i	$-0.266844\pi$
$997$	11.3409	+	6.54767i	0.359170	+	0.207367i	−0.309547	+	0.950884i	$0.600177\pi$
$998$	−0.147787	+	0.255975i	−0.00467812	+	0.00810274i
$999$	−52.7161	−	16.4029i	−1.66786	−	0.518963i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.n.e.263.5	yes	24
3.2	odd	2		462.2.n.f.263.3	yes	24
7.2	even	3	inner	462.2.n.e.65.3	✓	24
11.10	odd	2		462.2.n.f.263.5	yes	24
21.2	odd	6		462.2.n.f.65.5	yes	24
33.32	even	2	inner	462.2.n.e.263.3	yes	24
77.65	odd	6		462.2.n.f.65.3	yes	24
231.65	even	6	inner	462.2.n.e.65.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.n.e.65.3	✓	24	7.2	even	3	inner
462.2.n.e.65.5	yes	24	231.65	even	6	inner
462.2.n.e.263.3	yes	24	33.32	even	2	inner
462.2.n.e.263.5	yes	24	1.1	even	1	trivial
462.2.n.f.65.3	yes	24	77.65	odd	6
462.2.n.f.65.5	yes	24	21.2	odd	6
462.2.n.f.263.3	yes	24	3.2	odd	2
462.2.n.f.263.5	yes	24	11.10	odd	2

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.470476 + 1.66693i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.00577 - 0.580683i) q^{5} +(1.67884 - 0.426020i) q^{6} +(-2.19957 - 1.47034i) q^{7} +1.00000 q^{8} +(-2.55730 - 1.56850i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.470476 + 1.66693i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.00577 - 0.580683i) q^{5} +(1.67884 - 0.426020i) q^{6} +(-2.19957 - 1.47034i) q^{7} +1.00000 q^{8} +(-2.55730 - 1.56850i) q^{9} +(-1.00577 - 0.580683i) q^{10} +(2.34054 - 2.34986i) q^{11} +(-1.20836 - 1.24091i) q^{12} -3.56641i q^{13} +(-0.173570 + 2.64005i) q^{14} +(0.494765 + 1.94975i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.71320 + 2.96735i) q^{17} +(-0.0797091 + 2.99894i) q^{18} +(4.30482 - 2.48539i) q^{19} +1.16137i q^{20} +(3.48580 - 2.97476i) q^{21} +(-3.20531 - 0.852040i) q^{22} +(7.67576 - 4.43160i) q^{23} +(-0.470476 + 1.66693i) q^{24} +(-1.82562 + 3.16206i) q^{25} +(-3.08860 + 1.78320i) q^{26} +(3.81773 - 3.52490i) q^{27} +(2.37314 - 1.16971i) q^{28} +6.04247 q^{29} +(1.44115 - 1.40335i) q^{30} +(-0.547062 + 0.947540i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.81588 + 5.00708i) q^{33} +3.42640 q^{34} +(-3.06606 - 0.201578i) q^{35} +(2.63701 - 1.43044i) q^{36} +(-5.31249 - 9.20151i) q^{37} +(-4.30482 - 2.48539i) q^{38} +(5.94495 + 1.67791i) q^{39} +(1.00577 - 0.580683i) q^{40} -4.05294 q^{41} +(-4.31912 - 1.53141i) q^{42} -6.97962i q^{43} +(0.864767 + 3.20190i) q^{44} +(-3.48287 - 0.0925714i) q^{45} +(-7.67576 - 4.43160i) q^{46} +(4.23571 - 2.44549i) q^{47} +(1.67884 - 0.426020i) q^{48} +(2.67619 + 6.46823i) q^{49} +3.65123 q^{50} +(-4.14034 - 4.25185i) q^{51} +(3.08860 + 1.78320i) q^{52} +(-1.75416 - 1.01277i) q^{53} +(-4.96152 - 1.54380i) q^{54} +(0.989530 - 3.72254i) q^{55} +(-2.19957 - 1.47034i) q^{56} +(2.11765 + 8.34515i) q^{57} +(-3.02124 - 5.23293i) q^{58} +(8.87574 + 5.12441i) q^{59} +(-1.93591 - 0.546395i) q^{60} +(-8.96386 + 5.17529i) q^{61} +1.09412 q^{62} +(3.31873 + 7.21013i) q^{63} +1.00000 q^{64} +(-2.07095 - 3.58699i) q^{65} +(2.92831 - 4.94216i) q^{66} +(-0.911110 + 1.57809i) q^{67} +(-1.71320 - 2.96735i) q^{68} +(3.77590 + 14.8799i) q^{69} +(1.35846 + 2.75608i) q^{70} -13.9074i q^{71} +(-2.55730 - 1.56850i) q^{72} +(-8.95771 - 5.17174i) q^{73} +(-5.31249 + 9.20151i) q^{74} +(-4.41202 - 4.53084i) q^{75} +4.97078i q^{76} +(-8.60329 + 1.72728i) q^{77} +(-1.51936 - 5.98743i) q^{78} +(-8.06437 + 4.65597i) q^{79} +(-1.00577 - 0.580683i) q^{80} +(4.07961 + 8.02227i) q^{81} +(2.02647 + 3.50995i) q^{82} -6.21423 q^{83} +(0.833319 + 4.50617i) q^{84} +3.97930i q^{85} +(-6.04453 + 3.48981i) q^{86} +(-2.84284 + 10.0724i) q^{87} +(2.34054 - 2.34986i) q^{88} +(2.99218 - 1.72754i) q^{89} +(1.66126 + 3.06254i) q^{90} +(-5.24384 + 7.84455i) q^{91} +8.86320i q^{92} +(-1.32210 - 1.35771i) q^{93} +(-4.23571 - 2.44549i) q^{94} +(2.88644 - 4.99947i) q^{95} +(-1.20836 - 1.24091i) q^{96} +5.20989 q^{97} +(4.26356 - 5.55176i) q^{98} +(-9.67125 + 2.33817i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9}+O(q^{10}) \) 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 8 * q^9	\( 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9} - 4 q^{11} + 4 q^{15} - 12 q^{16} + 4 q^{17} - 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} + 40 q^{29} - 2 q^{30} - 28 q^{31} - 12 q^{32} + 32 q^{33} - 8 q^{34} - 32 q^{35} + 16 q^{36} - 16 q^{37} - 8 q^{41} + 6 q^{42} - 4 q^{44} - 28 q^{45} - 8 q^{49} - 40 q^{50} - 34 q^{51} + 6 q^{54} + 8 q^{55} + 40 q^{57} - 20 q^{58} - 2 q^{60} + 56 q^{62} - 14 q^{63} + 24 q^{64} - 44 q^{65} + 32 q^{66} + 4 q^{68} - 20 q^{69} + 64 q^{70} - 8 q^{72} - 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} + 144 q^{83} - 6 q^{84} + 8 q^{87} - 4 q^{88} + 56 q^{90} - 32 q^{91} - 22 q^{93} - 44 q^{95} + 64 q^{97} - 8 q^{98} - 52 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 8 * q^9 - 4 * q^11 + 4 * q^15 - 12 * q^16 + 4 * q^17 - 8 * q^18 + 8 * q^22 + 20 * q^25 - 12 * q^27 + 40 * q^29 - 2 * q^30 - 28 * q^31 - 12 * q^32 + 32 * q^33 - 8 * q^34 - 32 * q^35 + 16 * q^36 - 16 * q^37 - 8 * q^41 + 6 * q^42 - 4 * q^44 - 28 * q^45 - 8 * q^49 - 40 * q^50 - 34 * q^51 + 6 * q^54 + 8 * q^55 + 40 * q^57 - 20 * q^58 - 2 * q^60 + 56 * q^62 - 14 * q^63 + 24 * q^64 - 44 * q^65 + 32 * q^66 + 4 * q^68 - 20 * q^69 + 64 * q^70 - 8 * q^72 - 16 * q^74 - 26 * q^75 + 24 * q^81 + 4 * q^82 + 144 * q^83 - 6 * q^84 + 8 * q^87 - 4 * q^88 + 56 * q^90 - 32 * q^91 - 22 * q^93 - 44 * q^95 + 64 * q^97 - 8 * q^98 - 52 * q^99

Introduction

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