LMFDB - Embedded newform 462.2.n.e.65.5

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			65.5
Character	$\chi$	$=$	462.65
Dual form			462.2.n.e.263.5

$q$-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 $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.470476	−	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	0.707744	−	0.706469i	$-0.249713\pi$
$5$	1.00577	+	0.580683i	0.449795	+	0.259689i	−0.257949	+	0.966159i	$0.583047\pi$
$6$	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	$0.164675\pi$
$13$			3.56641i			0.989143i	−0.869137	+	0.494572i	$0.835325\pi$
$14$	−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	0.579970	−	0.814638i	$-0.303064\pi$
$17$	−1.71320	−	2.96735i	−0.415512	−	0.719687i	−0.995482	+	0.0949503i	$0.969731\pi$
$18$	−0.0797091	−	2.99894i	−0.0187876	−	0.706857i
$19$	4.30482	+	2.48539i	0.987594	+	0.570187i	0.904554	−	0.426359i	$-0.140204\pi$
$19$	4.30482	+	2.48539i	0.987594	+	0.570187i	0.0830395	+	0.996546i	$0.473537\pi$
$20$		−	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	0.991386	+	0.130974i	$0.0418106\pi$
$23$	7.67576	+	4.43160i	1.60051	+	0.924052i	0.609120	+	0.793078i	$0.291523\pi$
$24$	−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	0.812707	−	0.582672i	$-0.197993\pi$
$31$	−0.547062	−	0.947540i	−0.0982553	−	0.170183i	−0.910963	+	0.412489i	$0.864660\pi$
$32$	−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	−0.0148784	+	0.999889i	$0.504736\pi$
$37$	−5.31249	+	9.20151i	−0.873369	+	1.51272i	−0.858490	+	0.512830i	$0.828597\pi$
$38$	−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	$0.178631\pi$
$43$			6.97962i			1.06438i	−0.846624	+	0.532191i	$0.821369\pi$
$44$	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	0.776028	−	0.630698i	$-0.217231\pi$
$47$	4.23571	+	2.44549i	0.617842	+	0.356711i	−0.158187	+	0.987409i	$0.550565\pi$
$48$	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	−0.615614	−	0.788048i	$-0.711092\pi$
$53$	−1.75416	+	1.01277i	−0.240952	+	0.139114i	0.374662	+	0.927161i	$0.377759\pi$
$54$	−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	0.205296	−	0.978700i	$-0.434184\pi$
$59$	8.87574	−	5.12441i	1.15552	−	0.667142i	0.950227	+	0.311558i	$0.100851\pi$
$60$	−1.93591	+	0.546395i	−0.249925	+	0.0705392i
$61$	−8.96386	−	5.17529i	−1.14771	−	0.662628i	−0.199378	−	0.979923i	$-0.563892\pi$
$61$	−8.96386	−	5.17529i	−1.14771	−	0.662628i	−0.948327	+	0.317295i	$0.897226\pi$
$62$	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	0.804989	−	0.593290i	$-0.202171\pi$
$67$	−0.911110	−	1.57809i	−0.111310	−	0.192794i	−0.916299	+	0.400496i	$0.868838\pi$
$68$	−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	$0.308966\pi$
$71$			13.9074i			1.65050i	−0.564767	+	0.825251i	$0.691034\pi$
$72$	−2.55730	+	1.56850i	−0.301381	+	0.184850i
$73$	−8.95771	+	5.17174i	−1.04842	+	0.605306i	−0.922207	−	0.386697i	$-0.873616\pi$
$73$	−8.95771	+	5.17174i	−1.04842	+	0.605306i	−0.126214	+	0.992003i	$0.540283\pi$
$74$	−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	−0.0277469	−	0.999615i	$-0.508833\pi$
$79$	−8.06437	−	4.65597i	−0.907312	−	0.523837i	−0.879565	+	0.475778i	$0.842167\pi$
$80$	−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	0.650131	−	0.759822i	$-0.274714\pi$
$89$	2.99218	+	1.72754i	0.317170	+	0.183118i	−0.332960	+	0.942941i	$0.608047\pi$
$90$	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	0.951867	−	0.306512i	$-0.0991619\pi$
$101$	2.11536	+	3.66391i	0.210486	+	0.364573i	−0.741381	+	0.671085i	$0.765829\pi$
$102$	−1.61204	−	5.71156i	−0.159616	−	0.565529i
$103$	9.13694	−	15.8257i	0.900290	−	1.55935i	0.0731719	−	0.997319i	$-0.476688\pi$
$103$	9.13694	−	15.8257i	0.900290	−	1.55935i	0.827118	−	0.562028i	$-0.189979\pi$
$104$			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	−0.881473	−	0.472234i	$-0.843448\pi$
$107$	−0.328629	+	0.569202i	−0.0317698	+	0.0550269i	0.849703	+	0.527261i	$0.176781\pi$
$108$	1.14379	−	5.06870i	0.110061	−	0.487736i
$109$	8.44989	−	4.87855i	0.809353	−	0.467280i	−0.0373781	−	0.999301i	$-0.511901\pi$
$109$	8.44989	−	4.87855i	0.809353	−	0.467280i	0.846731	+	0.532021i	$0.178567\pi$
$110$	−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	$-0.831849\pi$
$113$		−	10.7159i		−	1.00807i	0.863684	−	0.504034i	$-0.168151\pi$
$114$	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	$-0.926179\pi$
$127$		−	5.18041i		−	0.459687i	0.973228	−	0.229843i	$-0.0738214\pi$
$128$	−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	−0.0283313	−	0.999599i	$-0.509019\pi$
$131$	9.74600	−	16.8806i	0.851512	−	1.47486i	0.879843	−	0.475264i	$-0.157647\pi$
$132$	−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	−0.675465	+	0.737393i	$0.736057\pi$
$137$	−19.3338	+	11.1624i	−1.65180	+	0.953666i	−0.976333	+	0.216273i	$0.930610\pi$
$138$	10.9984	+	10.7100i	0.936248	+	0.911694i
$139$		−	10.5744i		−	0.896905i	−0.893807	−	0.448453i	$-0.851975\pi$
$139$		−	10.5744i		−	0.896905i	0.893807	−	0.448453i	$-0.148025\pi$
$140$	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	−0.942745	−	0.333514i	$-0.891765\pi$
$149$	−2.22819	+	3.85935i	−0.182541	+	0.316170i	0.760204	+	0.649684i	$0.225099\pi$
$150$	−1.71782	−	6.08634i	−0.140259	−	0.496948i
$151$	−3.45781	+	1.99637i	−0.281393	+	0.162462i	−0.634054	−	0.773289i	$-0.718610\pi$
$151$	−3.45781	+	1.99637i	−0.281393	+	0.162462i	0.352661	+	0.935751i	$0.385277\pi$
$152$	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	0.996351	+	0.0853524i	$0.0272016\pi$
$157$	7.16830	+	12.4159i	0.572093	+	0.990894i	−0.424258	+	0.905541i	$0.639465\pi$
$158$	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	−0.986095	−	0.166182i	$-0.946856\pi$
$163$	−4.45739	+	7.72043i	−0.349130	+	0.604711i	0.636965	+	0.770893i	$0.280190\pi$
$164$	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	−0.535856	−	0.844310i	$-0.680011\pi$
$173$	6.09331	−	10.5539i	0.463266	−	0.802400i	0.999121	+	0.0419097i	$0.0133442\pi$
$174$	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	−0.598213	−	0.801337i	$-0.704122\pi$
$179$	−2.72052	+	1.57070i	−0.203342	+	0.117399i	0.394872	+	0.918736i	$0.370789\pi$
$180$	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	0.492905	−	0.870083i	$-0.335935\pi$
$191$	−0.195655	−	0.112961i	−0.0141571	−	0.00817359i	−0.507062	+	0.861910i	$0.669268\pi$
$192$	−0.470476	−	1.66693i	−0.0339537	−	0.120300i
$193$	−10.4291	+	6.02127i	−0.750706	+	0.433420i	−0.825949	−	0.563745i	$-0.809360\pi$
$193$	−10.4291	+	6.02127i	−0.750706	+	0.433420i	0.0752429	+	0.997165i	$0.476027\pi$
$194$	−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	0.931366	−	0.364085i	$-0.118618\pi$
$199$	2.12131	+	3.67422i	0.150376	+	0.260458i	−0.780990	+	0.624544i	$0.785285\pi$
$200$	−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	$-0.998410\pi$
$211$		−	0.145154i		−	0.00999278i	0.999988	−	0.00499639i	$-0.00159041\pi$
$212$	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	0.830031	−	0.557717i	$-0.188322\pi$
$227$	−1.02424	−	1.77403i	−0.0679810	−	0.117746i	−0.898012	+	0.439970i	$0.854989\pi$
$228$	−8.28594	+	2.33863i	−0.548749	+	0.154880i
$229$	6.97376	−	12.0789i	0.460839	−	0.798196i	−0.538164	−	0.842840i	$-0.680882\pi$
$229$	6.97376	−	12.0789i	0.460839	−	0.798196i	0.999003	+	0.0446437i	$0.0142153\pi$
$230$	−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	0.181314	−	0.983425i	$-0.441965\pi$
$233$	14.3840	−	24.9138i	0.942328	−	1.63216i	0.761015	−	0.648735i	$-0.224702\pi$
$234$	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	−0.233192	−	0.972431i	$-0.574917\pi$
$241$	7.64351	−	4.41298i	0.492362	−	0.284265i	0.725554	+	0.688166i	$0.241584\pi$
$242$	−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	$0.0295264\pi$
$251$			2.93497i			0.185254i	−0.995701	+	0.0926269i	$0.970474\pi$
$252$	−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	−0.0170691	−	0.999854i	$-0.505434\pi$
$257$	−14.2919	−	8.25142i	−0.891503	−	0.514709i	−0.874434	+	0.485145i	$0.838767\pi$
$258$	−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	0.999432	−	0.0337062i	$-0.0107311\pi$
$263$	7.63064	+	13.2167i	0.470525	+	0.814974i	−0.528906	+	0.848680i	$0.677398\pi$
$264$	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	−0.678767	−	0.734353i	$-0.737485\pi$
$269$	−6.26825	+	3.61898i	−0.382182	+	0.220653i	0.296585	+	0.955006i	$0.404152\pi$
$270$	−5.88661	−	1.32836i	−0.358248	−	0.0808413i
$271$	20.4336	+	11.7973i	1.24125	+	0.716637i	0.969349	−	0.245687i	$-0.0790137\pi$
$271$	20.4336	+	11.7973i	1.24125	+	0.716637i	0.271903	+	0.962325i	$0.412347\pi$
$272$	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	0.113646	−	0.993521i	$-0.463747\pi$
$277$	17.1573	−	9.90578i	1.03088	−	0.595181i	0.917238	+	0.398340i	$0.130414\pi$
$278$	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	−0.547496	−	0.836808i	$-0.684419\pi$
$283$	−1.62416	+	0.937708i	−0.0965462	+	0.0557410i	0.450950	+	0.892549i	$0.351085\pi$
$284$	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	$0.204696\pi$
$307$			21.0137i			1.19931i	−0.800258	+	0.599656i	$0.795304\pi$
$308$	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	0.392625	−	0.919699i	$-0.371567\pi$
$311$	24.4322	−	14.1059i	1.38542	−	0.799873i	0.992795	+	0.119826i	$0.0382336\pi$
$312$	5.94495	−	1.67791i	0.336566	−	0.0949929i
$313$	−2.99806	+	5.19278i	−0.169460	+	0.293513i	−0.938230	−	0.346012i	$-0.887536\pi$
$313$	−2.99806	+	5.19278i	−0.169460	+	0.293513i	0.768770	+	0.639525i	$0.220869\pi$
$314$	−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	0.728981	−	0.684534i	$-0.239994\pi$
$317$	8.91377	+	5.14637i	0.500647	+	0.289049i	−0.228333	+	0.973583i	$0.573328\pi$
$318$	−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	−0.628354	−	0.777928i	$-0.716271\pi$
$331$	6.54105	−	11.3294i	0.359529	−	0.622722i	0.987882	+	0.155206i	$0.0496042\pi$
$332$	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	$-0.845804\pi$
$337$		−	17.0981i		−	0.931394i	0.884944	−	0.465697i	$-0.154196\pi$
$338$	−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	0.989649	−	0.143508i	$-0.0458384\pi$
$347$	6.90245	+	11.9554i	0.370543	+	0.641799i	−0.619106	+	0.785307i	$0.712505\pi$
$348$	−7.30151	+	7.49816i	−0.391402	+	0.401943i
$349$		−	27.1071i		−	1.45101i	−0.688217	−	0.725505i	$-0.741606\pi$
$349$		−	27.1071i		−	1.45101i	0.688217	−	0.725505i	$-0.258394\pi$
$350$	−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	−0.0323294	−	0.999477i	$-0.510293\pi$
$353$	15.3515	−	8.86320i	0.817079	−	0.471741i	0.849408	+	0.527737i	$0.176959\pi$
$354$	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	−0.452537	−	0.891746i	$-0.649481\pi$
$359$	10.3453	−	17.9186i	0.546006	−	0.945710i	0.998543	−	0.0539641i	$-0.0171857\pi$
$360$	−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	0.932846	−	0.360275i	$-0.117317\pi$
$367$	2.95817	+	5.12371i	0.154415	+	0.267455i	−0.778431	+	0.627731i	$0.783984\pi$
$368$	−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	0.293807	−	0.955865i	$-0.405078\pi$
$373$	−7.47599	−	4.31626i	−0.387092	−	0.223488i	−0.680899	+	0.732377i	$0.738411\pi$
$374$	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	0.811591	−	0.584226i	$-0.198602\pi$
$383$	13.9230	+	8.03845i	0.711433	+	0.410746i	−0.100159	+	0.994971i	$0.531935\pi$
$384$	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	0.0262868	−	0.999654i	$-0.491632\pi$
$389$	17.8525	−	10.3071i	0.905156	−	0.522592i	0.878870	+	0.477062i	$0.158298\pi$
$390$	−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	−0.793030	−	0.609182i	$-0.791498\pi$
$397$	2.61119	−	4.52272i	0.131052	−	0.226989i	0.924082	+	0.382193i	$0.124831\pi$
$398$	−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	0.459132	−	0.888368i	$-0.348160\pi$
$401$	−1.61502	−	0.932434i	−0.0806504	−	0.0465635i	−0.539783	+	0.841804i	$0.681494\pi$
$402$	−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	−0.166225	−	0.986088i	$-0.553158\pi$
$409$	12.2281	−	7.05988i	0.604639	−	0.349089i	0.770864	+	0.636999i	$0.219825\pi$
$410$	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	$-0.829963\pi$
$419$		−	20.8437i		−	1.01828i	0.860683	−	0.509141i	$-0.170037\pi$
$420$	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	0.792613	+	0.609726i	$0.208720\pi$
$431$	19.1899	+	33.2379i	0.924344	+	1.60101i	0.131732	+	0.991285i	$0.457946\pi$
$432$	−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	0.0695369	−	0.997579i	$-0.477848\pi$
$439$	−15.9159	−	9.18904i	−0.759624	−	0.438569i	−0.829161	+	0.559010i	$0.811181\pi$
$440$	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	0.520509	−	0.853856i	$-0.325742\pi$
$443$	0.869330	+	0.501908i	0.0413031	+	0.0238464i	−0.479206	+	0.877702i	$0.659075\pi$
$444$	−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	$0.215902\pi$
$449$			26.5910i			1.25491i	−0.778655	+	0.627453i	$0.784098\pi$
$450$	−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	0.255906	−	0.966702i	$-0.417626\pi$
$457$	−9.69107	−	5.59514i	−0.453329	−	0.261730i	−0.709235	+	0.704972i	$0.750960\pi$
$458$	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	−0.181053	−	0.983473i	$-0.557951\pi$
$467$	−24.2746	−	14.0149i	−1.12329	−	0.648533i	−0.942239	+	0.334940i	$0.891284\pi$
$468$	−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	−0.815620	−	0.578587i	$-0.803604\pi$
$479$	−19.8918	−	34.4537i	−0.908882	−	1.57423i	−0.0932611	−	0.995642i	$-0.529729\pi$
$480$	−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	0.753575	−	0.657362i	$-0.228328\pi$
$487$	−4.24821	−	7.35811i	−0.192505	−	0.333428i	−0.946080	+	0.323934i	$0.894994\pi$
$488$	−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	−0.869314	−	0.494260i	$-0.835439\pi$
$499$	−0.147787	+	0.255975i	−0.00661586	+	0.0114590i	0.862699	+	0.505719i	$0.168773\pi$
$500$	−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	0.476181	−	0.879347i	$-0.342021\pi$
$509$	−1.06636	−	0.615664i	−0.0472657	−	0.0272888i	−0.523447	+	0.852058i	$0.675354\pi$
$510$	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	−0.654303	+	0.756233i	$0.727038\pi$
$521$	−37.3509	+	21.5645i	−1.63637	+	0.944759i	−0.982068	+	0.188526i	$0.939629\pi$
$522$	−0.481640	−	18.1210i	−0.0210808	−	0.793135i
$523$	−3.39607	−	1.96072i	−0.148500	−	0.0857364i	0.423909	−	0.905705i	$-0.360658\pi$
$523$	−3.39607	−	1.96072i	−0.148500	−	0.0857364i	−0.572409	+	0.819968i	$0.693991\pi$
$524$	−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	0.697041	−	0.717031i	$-0.254500\pi$
$541$	9.87581	+	5.70180i	0.424594	+	0.245140i	−0.272447	+	0.962171i	$0.587833\pi$
$542$	−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	$0.0808503\pi$
$547$			11.7537i			0.502553i	−0.967915	+	0.251276i	$0.919150\pi$
$548$	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	−0.987128	−	0.159929i	$-0.948873\pi$
$557$	−14.9173	−	25.8375i	−0.632067	−	1.09477i	0.355062	−	0.934843i	$-0.384460\pi$
$558$	−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	−0.985838	−	0.167700i	$-0.946366\pi$
$563$	−15.1418	−	26.2264i	−0.638152	−	1.10531i	0.347686	−	0.937611i	$-0.386967\pi$
$564$	−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	−0.926616	−	0.376008i	$-0.877296\pi$
$569$	−3.28407	+	5.68818i	−0.137675	+	0.238461i	0.788941	+	0.614469i	$0.210630\pi$
$570$	2.71601	+	9.62300i	0.113761	+	0.403063i
$571$	−25.3943	+	14.6614i	−1.06272	+	0.613561i	−0.926183	−	0.377074i	$-0.876930\pi$
$571$	−25.3943	+	14.6614i	−1.06272	+	0.613561i	−0.136536	+	0.990635i	$0.543597\pi$
$572$	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	0.773548	−	0.633738i	$-0.218480\pi$
$577$	−3.89280	−	6.74253i	−0.162060	−	0.280695i	−0.935607	+	0.353043i	$0.885147\pi$
$578$	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	$-0.940618\pi$
$587$		−	8.98728i		−	0.370945i	0.982649	−	0.185472i	$-0.0593815\pi$
$588$	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	−0.882218	−	0.470842i	$-0.843950\pi$
$593$	−0.812081	+	1.40657i	−0.0333482	+	0.0577608i	0.848870	+	0.528602i	$0.177284\pi$
$594$	−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	−0.168844	−	0.985643i	$-0.554003\pi$
$599$	14.6927	−	8.48281i	0.600326	−	0.346598i	0.769170	+	0.639045i	$0.220670\pi$
$600$	−4.41202	+	4.53084i	−0.180120	+	0.184971i
$601$			23.0019i			0.938269i	0.883127	+	0.469134i	$0.155434\pi$
$601$			23.0019i			0.938269i	−0.883127	+	0.469134i	$0.844566\pi$
$602$	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	0.954017	−	0.299751i	$-0.0969038\pi$
$607$	28.8610	+	16.6629i	1.17143	+	0.676328i	0.217416	+	0.976079i	$0.430237\pi$
$608$		−	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	−0.990662	−	0.136342i	$-0.956465\pi$
$613$	−33.8680	+	19.5537i	−1.36792	+	0.789767i	−0.377255	+	0.926109i	$0.623132\pi$
$614$	−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	$0.276232\pi$
$617$			37.9007i			1.52583i	−0.646501	+	0.762913i	$0.723768\pi$
$618$	22.0815	−	22.6762i	0.888249	−	0.912172i
$619$	−10.2068	−	17.6788i	−0.410247	−	0.710569i	0.584669	−	0.811272i	$-0.301224\pi$
$619$	−10.2068	−	17.6788i	−0.410247	−	0.710569i	−0.994917	+	0.100702i	$0.967891\pi$
$620$	−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	−0.723847	−	0.689961i	$-0.757628\pi$
$641$	−12.3614	+	7.13687i	−0.488247	+	0.281890i	0.235600	+	0.971850i	$0.424295\pi$
$642$	−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	−0.0944013	−	0.995534i	$-0.530094\pi$
$647$	18.3282	−	10.5818i	0.720556	−	0.416013i	0.814957	+	0.579521i	$0.196760\pi$
$648$	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	−0.113697	−	0.993515i	$-0.536269\pi$
$653$	−26.3449	−	15.2102i	−1.03096	−	0.595222i	−0.917258	+	0.398293i	$0.869603\pi$
$654$	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	−0.998269	−	0.0588062i	$-0.981271\pi$
$661$	−14.1421	−	24.4948i	−0.550062	−	0.952736i	0.448207	−	0.893930i	$-0.352063\pi$
$662$	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	$-0.966709\pi$
$673$		−	5.41647i		−	0.208790i	0.994536	−	0.104395i	$-0.0332906\pi$
$674$	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	−0.525163	−	0.851002i	$-0.675996\pi$
$677$	12.3437	−	21.3799i	0.474407	−	0.821698i	0.999571	+	0.0293038i	$0.00932903\pi$
$678$	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	−0.109771	−	0.993957i	$-0.535012\pi$
$683$	18.1930	−	10.5037i	0.696135	−	0.401914i	0.805906	+	0.592043i	$0.201678\pi$
$684$	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	0.351523	+	0.936179i	$0.385664\pi$
$691$	−16.6920	+	28.9114i	−0.634993	+	1.09984i	−0.986517	+	0.163661i	$0.947670\pi$
$692$	−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	−0.663500	−	0.748177i	$-0.730930\pi$
$709$	8.41921	−	14.5825i	0.316190	−	0.547657i	0.979690	+	0.200519i	$0.0642629\pi$
$710$	−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	0.000796544	−	1.00000i	$-0.499746\pi$
$719$	−23.1897	−	13.3886i	−0.864830	−	0.499310i	−0.865627	+	0.500690i	$0.833080\pi$
$720$	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	0.407697	−	0.913117i	$-0.366332\pi$
$733$	−4.85268	−	2.80169i	−0.179238	−	0.103483i	−0.586934	+	0.809634i	$0.699665\pi$
$734$	−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	−0.689872	−	0.723931i	$-0.742333\pi$
$739$	−11.0876	+	6.40146i	−0.407866	+	0.235481i	0.282007	+	0.959412i	$0.409000\pi$
$740$	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	−0.570892	−	0.821025i	$-0.693402\pi$
$751$	11.6628	−	20.2006i	0.425583	−	0.737131i	0.996475	+	0.0838942i	$0.0267358\pi$
$752$	−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	0.200145	+	0.979766i	$0.435859\pi$
$761$	−20.6464	+	35.7605i	−0.748430	+	1.29632i	−0.948575	+	0.316552i	$0.897475\pi$
$762$	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	$-0.936807\pi$
$769$		−	10.9384i		−	0.394448i	0.980358	−	0.197224i	$-0.0631926\pi$
$770$	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	−0.502222	−	0.864739i	$-0.667484\pi$
$773$	−0.123624	+	0.0713746i	−0.00444646	+	0.00256717i	0.497775	+	0.867306i	$0.334150\pi$
$774$	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	−0.695999	−	0.718043i	$-0.745038\pi$
$787$	−11.8429	+	6.83752i	−0.422155	+	0.243731i	0.273844	+	0.961774i	$0.411705\pi$
$788$	−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	$0.0372730\pi$
$797$			6.59645i			0.233658i	−0.993152	+	0.116829i	$0.962727\pi$
$798$	−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	0.600522	−	0.799608i	$-0.294959\pi$
$809$	−11.1559	−	19.3225i	−0.392220	−	0.679345i	−0.992742	+	0.120263i	$0.961626\pi$
$810$	0.555232	+	10.4375i	0.0195089	+	0.366737i
$811$			34.3916i			1.20765i	0.797116	+	0.603827i	$0.206358\pi$
$811$			34.3916i			1.20765i	−0.797116	+	0.603827i	$0.793642\pi$
$812$	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	−0.927244	−	0.374457i	$-0.877829\pi$
$821$	−3.99233	+	6.91491i	−0.139333	+	0.241332i	0.787911	+	0.615789i	$0.211163\pi$
$822$	−37.2138	+	10.5033i	−1.29798	+	0.366343i
$823$	14.0547	+	24.3434i	0.489914	+	0.848557i	0.999933	−	0.0116069i	$-0.00369468\pi$
$823$	14.0547	+	24.3434i	0.489914	+	0.848557i	−0.510018	+	0.860164i	$0.670361\pi$
$824$	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	0.853035	+	0.521854i	$0.174760\pi$
$829$	25.2928	+	43.8085i	0.878456	+	1.52153i	0.0254218	+	0.999677i	$0.491907\pi$
$830$	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	$0.109389\pi$
$839$			19.5188i			0.673862i	−0.941529	+	0.336931i	$0.890611\pi$
$840$	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	$-0.956362\pi$
$853$		−	7.98283i		−	0.273327i	0.990618	−	0.136663i	$-0.0436379\pi$
$854$	−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	0.514978	−	0.857203i	$-0.327800\pi$
$857$	−14.1944	−	24.5854i	−0.484871	−	0.839821i	−0.999849	+	0.0173825i	$0.994467\pi$
$858$	−17.6258	+	10.4436i	−0.601734	+	0.356537i
$859$	18.7050	−	32.3981i	0.638208	−	1.10541i	−0.347618	−	0.937636i	$-0.613009\pi$
$859$	18.7050	−	32.3981i	0.638208	−	1.10541i	0.985826	−	0.167772i	$-0.0536572\pi$
$860$	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	0.0547734	−	0.998499i	$-0.482556\pi$
$863$	−22.9893	−	13.2729i	−0.782565	−	0.451814i	−0.837339	+	0.546685i	$0.815890\pi$
$864$	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	0.643683	−	0.765292i	$-0.277405\pi$
$877$	8.96606	+	5.17656i	0.302762	+	0.174800i	−0.340921	+	0.940092i	$0.610739\pi$
$878$	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	$0.228811\pi$
$881$			39.0911i			1.31701i	−0.752576	+	0.658506i	$0.771189\pi$
$882$	−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	−0.933473	−	0.358649i	$-0.883238\pi$
$887$	−4.65016	+	8.05432i	−0.156137	+	0.270438i	0.777335	+	0.629086i	$0.216571\pi$
$888$	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	0.685559	−	0.728017i	$-0.259558\pi$
$907$	−8.66455	−	15.0074i	−0.287702	−	0.498314i	−0.973261	+	0.229703i	$0.926225\pi$
$908$	−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	$-0.755216\pi$
$911$		−	41.9798i		−	1.39085i	0.718598	−	0.695426i	$-0.244784\pi$
$912$	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	0.466113	−	0.884725i	$-0.345654\pi$
$919$	−2.03187	−	1.17310i	−0.0670252	−	0.0386970i	−0.533138	+	0.846028i	$0.678987\pi$
$920$	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	0.875302	−	0.483577i	$-0.160663\pi$
$929$	27.2536	+	15.7349i	0.894163	+	0.516245i	0.0188609	+	0.999822i	$0.493996\pi$
$930$	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	$-0.755180\pi$
$937$		−	42.5796i		−	1.39102i	0.718519	−	0.695508i	$-0.244820\pi$
$938$	−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	−0.797976	−	0.602689i	$-0.794096\pi$
$941$	−28.2503	−	48.9309i	−0.920932	−	1.59510i	−0.122956	−	0.992412i	$-0.539238\pi$
$942$	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	0.835777	−	0.549069i	$-0.185018\pi$
$947$	23.9465	+	13.8255i	0.778158	+	0.449270i	−0.0576190	+	0.998339i	$0.518351\pi$
$948$	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	$0.0684738\pi$
$967$			13.2759i			0.426923i	−0.976951	+	0.213461i	$0.931526\pi$
$968$	−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	0.413534	−	0.910489i	$-0.364294\pi$
$971$	−5.24145	−	3.02615i	−0.168206	−	0.0971139i	−0.581740	+	0.813375i	$0.697628\pi$
$972$	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	−0.462478	−	0.886631i	$-0.653040\pi$
$977$	2.31699	−	1.33771i	0.0741269	−	0.0427972i	0.536605	+	0.843833i	$0.319706\pi$
$978$	−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	−0.452217	−	0.891908i	$-0.649367\pi$
$983$	2.94995	−	1.70316i	0.0940890	−	0.0543223i	0.546306	+	0.837586i	$0.316033\pi$
$984$	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	0.928139	+	0.372234i	$0.121408\pi$
$991$	24.7571	+	42.8805i	0.786434	+	1.36214i	−0.141705	+	0.989909i	$0.545259\pi$
$992$	−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	−0.309547	−	0.950884i	$-0.600177\pi$
$997$	11.3409	−	6.54767i	0.359170	−	0.207367i	0.668716	+	0.743518i	$0.266844\pi$
$998$	−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.65.5	yes	24
3.2	odd	2		462.2.n.f.65.3	yes	24
7.4	even	3	inner	462.2.n.e.263.3	yes	24
11.10	odd	2		462.2.n.f.65.5	yes	24
21.11	odd	6		462.2.n.f.263.5	yes	24
33.32	even	2	inner	462.2.n.e.65.3	✓	24
77.32	odd	6		462.2.n.f.263.3	yes	24
231.32	even	6	inner	462.2.n.e.263.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.n.e.65.3	✓	24	33.32	even	2	inner
462.2.n.e.65.5	yes	24	1.1	even	1	trivial
462.2.n.e.263.3	yes	24	7.4	even	3	inner
462.2.n.e.263.5	yes	24	231.32	even	6	inner
462.2.n.f.65.3	yes	24	3.2	odd	2
462.2.n.f.65.5	yes	24	11.10	odd	2
462.2.n.f.263.3	yes	24	77.32	odd	6
462.2.n.f.263.5	yes	24	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.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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