LMFDB - Embedded newform 462.2.n.f.65.3

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			65.3
Character	$\chi$	$=$	462.65
Dual form			462.2.n.f.263.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.20836 - 1.24091i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00577 - 0.580683i) q^{5} +(-1.67884 + 0.426020i) q^{6} +(-2.19957 + 1.47034i) q^{7} -1.00000 q^{8} +(-0.0797091 + 2.99894i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.20836 - 1.24091i) 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} +(-0.0797091 + 2.99894i) q^{9} +(-1.00577 + 0.580683i) q^{10} +(-2.34054 - 2.34986i) q^{11} +(-0.470476 + 1.66693i) 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} +(2.55730 + 1.56850i) q^{18} +(4.30482 + 2.48539i) q^{19} +1.16137i q^{20} +(4.48244 + 0.952753i) q^{21} +(-3.20531 + 0.852040i) q^{22} +(-7.67576 - 4.43160i) q^{23} +(1.20836 + 1.24091i) 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} +(1.93591 + 0.546395i) q^{30} +(-0.547062 - 0.947540i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.0877320 + 5.74389i) 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} +(4.42558 - 4.30952i) q^{39} +(1.00577 + 0.580683i) q^{40} +4.05294 q^{41} +(3.06633 - 3.40553i) q^{42} +6.97962i q^{43} +(-0.864767 + 3.20190i) q^{44} +(1.82160 - 2.96996i) 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} +(1.61204 - 5.71156i) q^{51} +(3.08860 - 1.78320i) q^{52} +(1.75416 - 1.01277i) q^{53} +(-1.14379 - 5.06870i) 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} +(1.44115 - 1.40335i) q^{60} +(-8.96386 - 5.17529i) q^{61} -1.09412 q^{62} +(-4.23414 - 6.71357i) q^{63} +1.00000 q^{64} +(2.07095 - 3.58699i) q^{65} +(4.93049 + 2.94792i) 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} +(0.0797091 - 2.99894i) q^{72} +(-8.95771 + 5.17174i) q^{73} +(5.31249 + 9.20151i) q^{74} +(-1.71782 + 6.08634i) 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} +(-8.98729 - 0.478086i) q^{81} +(2.02647 - 3.50995i) q^{82} +6.21423 q^{83} +(-1.41611 - 4.35828i) q^{84} -3.97930i q^{85} +(6.04453 + 3.48981i) q^{86} +(7.30151 + 7.49816i) 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} +(-0.514760 + 1.82383i) q^{93} +(-4.23571 + 2.44549i) q^{94} +(-2.88644 - 4.99947i) q^{95} +(0.470476 - 1.66693i) q^{96} +5.20989 q^{97} +(-4.26356 - 5.55176i) q^{98} +(7.23366 - 6.83185i) 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} + 24 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} - 24 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} + 28 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 + 24 * 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 - 24 * 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 + 28 * 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
$3$	−1.20836	−	1.24091i	−0.697650	−	0.716439i
$3$	−1.20836	−	1.24091i	−0.697650	−	0.716439i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.00577	−	0.580683i	−0.449795	−	0.259689i	0.257949	−	0.966159i	$-0.416953\pi$
$5$	−1.00577	−	0.580683i	−0.449795	−	0.259689i	−0.707744	+	0.706469i	$0.750287\pi$
$6$	−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
$9$	−0.0797091	+	2.99894i	−0.0265697	+	0.999647i
$10$	−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
$12$	−0.470476	+	1.66693i	−0.135815	+	0.481201i
$13$			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	0.995482	−	0.0949503i	$-0.0302692\pi$
$17$	1.71320	+	2.96735i	0.415512	+	0.719687i	−0.579970	+	0.814638i	$0.696936\pi$
$18$	2.55730	+	1.56850i	0.602762	+	0.369699i
$19$	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
$21$	4.48244	+	0.952753i	0.978148	+	0.207908i
$22$	−3.20531	+	0.852040i	−0.683375	+	0.181656i
$23$	−7.67576	−	4.43160i	−1.60051	−	0.924052i	−0.991386	−	0.130974i	$-0.958189\pi$
$23$	−7.67576	−	4.43160i	−1.60051	−	0.924052i	−0.609120	−	0.793078i	$-0.708477\pi$
$24$	1.20836	+	1.24091i	0.246656	+	0.253299i
$25$	−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	$-0.689595\pi$
$29$	−6.04247			−1.12206			−0.561030	+	0.827796i	$0.689595\pi$
$30$	1.93591	+	0.546395i	0.353448	+	0.0997575i
$31$	−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
$33$	−0.0877320	+	5.74389i	−0.0152722	+	0.999883i
$34$	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
$39$	4.42558	−	4.30952i	0.708661	−	0.690075i
$40$	1.00577	+	0.580683i	0.159026	+	0.0918140i
$41$	4.05294			0.632963			0.316482	−	0.948599i	$-0.397498\pi$
$41$	4.05294			0.632963			0.316482	+	0.948599i	$0.397498\pi$
$42$	3.06633	−	3.40553i	0.473145	−	0.525485i
$43$			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
$45$	1.82160	−	2.96996i	0.271548	−	0.442736i
$46$	−7.67576	+	4.43160i	−1.13173	+	0.653404i
$47$	−4.23571	−	2.44549i	−0.617842	−	0.356711i	0.158187	−	0.987409i	$-0.449435\pi$
$47$	−4.23571	−	2.44549i	−0.617842	−	0.356711i	−0.776028	+	0.630698i	$0.782769\pi$
$48$	1.67884	−	0.426020i	0.242320	−	0.0614907i
$49$	2.67619	−	6.46823i	0.382313	−	0.924033i
$50$	−3.65123			−0.516362
$51$	1.61204	−	5.71156i	0.225730	−	0.799778i
$52$	3.08860	−	1.78320i	0.428312	−	0.247286i
$53$	1.75416	−	1.01277i	0.240952	−	0.139114i	−0.374662	−	0.927161i	$-0.622241\pi$
$53$	1.75416	−	1.01277i	0.240952	−	0.139114i	0.615614	+	0.788048i	$0.288908\pi$
$54$	−1.14379	−	5.06870i	−0.155650	−	0.689763i
$55$	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	$-0.899149\pi$
$59$	−8.87574	+	5.12441i	−1.15552	+	0.667142i	−0.205296	+	0.978700i	$0.565816\pi$
$60$	1.44115	−	1.40335i	0.186051	−	0.181172i
$61$	−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
$63$	−4.23414	−	6.71357i	−0.533452	−	0.845830i
$64$	1.00000			0.125000
$65$	2.07095	−	3.58699i	0.256870	−	0.444911i
$66$	4.93049	+	2.94792i	0.606901	+	0.362864i
$67$	−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	$-0.691034\pi$
$71$		−	13.9074i		−	1.65050i	0.564767	−	0.825251i	$-0.308966\pi$
$72$	0.0797091	−	2.99894i	0.00939381	−	0.353429i
$73$	−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
$75$	−1.71782	+	6.08634i	−0.198356	+	0.702790i
$76$		−	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
$81$	−8.98729	−	0.478086i	−0.998588	−	0.0531206i
$82$	2.02647	−	3.50995i	0.223786	−	0.387609i
$83$	6.21423			0.682100			0.341050	−	0.940045i	$-0.389217\pi$
$83$	6.21423			0.682100			0.341050	+	0.940045i	$0.389217\pi$
$84$	−1.41611	−	4.35828i	−0.154510	−	0.475528i
$85$		−	3.97930i		−	0.431615i
$86$	6.04453	+	3.48981i	0.651798	+	0.376316i
$87$	7.30151	+	7.49816i	0.782804	+	0.803887i
$88$	2.34054	+	2.34986i	0.249503	+	0.250496i
$89$	−2.99218	−	1.72754i	−0.317170	−	0.183118i	0.332960	−	0.942941i	$-0.391953\pi$
$89$	−2.99218	−	1.72754i	−0.317170	−	0.183118i	−0.650131	+	0.759822i	$0.725286\pi$
$90$	−1.66126	−	3.06254i	−0.175113	−	0.322820i
$91$	−5.24384	−	7.84455i	−0.549703	−	0.822332i
$92$			8.86320i			0.924052i
$93$	−0.514760	+	1.82383i	−0.0533781	+	0.189122i
$94$	−4.23571	+	2.44549i	−0.436880	+	0.252233i
$95$	−2.88644	−	4.99947i	−0.296143	−	0.512935i
$96$	0.470476	−	1.66693i	0.0480178	−	0.170130i
$97$	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
$99$	7.23366	−	6.83185i	0.727010	−	0.686627i
$100$	−1.82562	+	3.16206i	−0.182562	+	0.316206i
$101$	−2.11536	−	3.66391i	−0.210486	−	0.364573i	0.741381	−	0.671085i	$-0.234171\pi$
$101$	−2.11536	−	3.66391i	−0.210486	−	0.364573i	−0.951867	+	0.306512i	$0.900838\pi$
$102$	−4.14034	−	4.25185i	−0.409954	−	0.420995i
$103$	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
$105$	−3.95506	−	3.56113i	−0.385975	−	0.347530i
$106$		−	2.02553i		−	0.196737i
$107$	0.328629	−	0.569202i	0.0317698	−	0.0550269i	−0.849703	−	0.527261i	$-0.823219\pi$
$107$	0.328629	−	0.569202i	0.0317698	−	0.0550269i	0.881473	+	0.472234i	$0.156552\pi$
$108$	−4.96152	−	1.54380i	−0.477423	−	0.148552i
$109$	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	$0.168151\pi$
$113$			10.7159i			1.00807i	−0.863684	+	0.504034i	$0.831849\pi$
$114$	−8.28594	−	2.33863i	−0.776049	−	0.219033i
$115$	5.14671	+	8.91435i	0.479933	+	0.831268i
$116$	3.02124	+	5.23293i	0.280515	+	0.485866i
$117$	−10.6954	−	0.284275i	−0.988794	−	0.0262812i
$118$			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
$123$	−4.89743	−	5.02933i	−0.441587	−	0.453480i
$124$	−0.547062	+	0.947540i	−0.0491277	+	0.0850916i
$125$			10.0472i			0.898652i
$126$	−7.93119	+	0.310090i	−0.706567	+	0.0276250i
$127$		−	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
$129$	8.66107	−	8.43393i	0.762565	−	0.742566i
$130$	−2.07095	−	3.58699i	−0.181634	−	0.314600i
$131$	−9.74600	+	16.8806i	−0.851512	+	1.47486i	0.0283313	+	0.999599i	$0.490981\pi$
$131$	−9.74600	+	16.8806i	−0.851512	+	1.47486i	−0.879843	+	0.475264i	$0.842353\pi$
$132$	5.01822	−	2.79597i	0.436780	−	0.243358i
$133$	−13.1231	+	0.862777i	−1.13792	+	0.0748123i
$134$	−1.82222			−0.157416
$135$	−5.88661	+	1.32836i	−0.506639	+	0.114327i
$136$	−1.71320	−	2.96735i	−0.146906	−	0.254448i
$137$	19.3338	−	11.1624i	1.65180	−	0.953666i	0.675465	−	0.737393i	$-0.263943\pi$
$137$	19.3338	−	11.1624i	1.65180	−	0.953666i	0.976333	−	0.216273i	$-0.0693902\pi$
$138$	14.7743	+	4.16992i	1.25767	+	0.354967i
$139$		−	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
$144$	−2.55730	−	1.56850i	−0.213109	−	0.130708i
$145$	6.07735	+	3.50876i	0.504696	+	0.291387i
$146$			10.3435i			0.856032i
$147$	−11.2603	+	4.49507i	−0.928734	+	0.370747i
$148$	10.6250			0.873369
$149$	2.22819	−	3.85935i	0.182541	−	0.316170i	−0.760204	−	0.649684i	$-0.774901\pi$
$149$	2.22819	−	3.85935i	0.182541	−	0.316170i	0.942745	+	0.333514i	$0.108235\pi$
$150$	4.41202	+	4.53084i	0.360240	+	0.369942i
$151$	−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
$156$	−5.94495	−	1.67791i	−0.475977	−	0.134340i
$157$	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
$159$	−3.37641	−	0.952964i	−0.267767	−	0.0755749i
$160$		−	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
$165$	3.42362	−	5.72610i	0.266528	−	0.445776i
$166$	3.10711	−	5.38168i	0.241159	−	0.417699i
$167$	−0.940338			−0.0727655			−0.0363828	−	0.999338i	$-0.511584\pi$
$167$	−0.940338			−0.0727655			−0.0363828	+	0.999338i	$0.511584\pi$
$168$	−4.48244	−	0.952753i	−0.345828	−	0.0735065i
$169$	0.280747			0.0215959
$170$	−3.44617	−	1.98965i	−0.264309	−	0.152599i
$171$	−7.79667	+	12.7118i	−0.596226	+	0.972095i
$172$	6.04453	−	3.48981i	0.460891	−	0.266095i
$173$	−6.09331	+	10.5539i	−0.463266	+	0.802400i	−0.999121	−	0.0419097i	$-0.986656\pi$
$173$	−6.09331	+	10.5539i	−0.463266	+	0.802400i	0.535856	+	0.844310i	$0.319989\pi$
$174$	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
$177$	17.0841	+	4.82183i	1.28412	+	0.362431i
$178$	−2.99218	+	1.72754i	−0.224273	+	0.129484i
$179$	2.72052	−	1.57070i	0.203342	−	0.117399i	−0.394872	−	0.918736i	$-0.629211\pi$
$179$	2.72052	−	1.57070i	0.203342	−	0.117399i	0.598213	+	0.801337i	$0.295878\pi$
$180$	−3.48287	−	0.0925714i	−0.259597	−	0.00689986i
$181$	−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
$186$	1.32210	+	1.35771i	0.0969412	+	0.0995521i
$187$	2.96304	−	10.9710i	0.216679	−	0.802278i
$188$			4.89098i			0.356711i
$189$	−3.21454	+	13.3666i	−0.233823	+	0.972279i
$190$	−5.77289			−0.418809
$191$	0.195655	+	0.112961i	0.0141571	+	0.00817359i	0.507062	−	0.861910i	$-0.330732\pi$
$191$	0.195655	+	0.112961i	0.0141571	+	0.00817359i	−0.492905	+	0.870083i	$0.664065\pi$
$192$	−1.20836	−	1.24091i	−0.0872062	−	0.0895549i
$193$	−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	$-0.506148\pi$
$197$	−0.542181			−0.0386288			−0.0193144	+	0.999813i	$0.506148\pi$
$198$	−2.29973	−	9.68046i	−0.163434	−	0.687960i
$199$	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
$201$	−0.857311	+	3.03751i	−0.0604701	+	0.214250i
$202$	−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
$207$	13.9019	−	22.6659i	0.966251	−	1.57539i
$208$	−3.08860	−	1.78320i	−0.214156	−	0.123643i
$209$	−4.23530	−	15.9329i	−0.292962	−	1.10210i
$210$	−5.06156	+	1.64462i	−0.349281	+	0.113490i
$211$		−	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
$213$	−17.2578	+	16.8052i	−1.18248	+	1.15147i
$214$	−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
$219$	17.2418	+	4.86636i	1.16510	+	0.328838i
$220$	2.72905	−	2.71823i	0.183992	−	0.183263i
$221$	−10.5828	+	6.10996i	−0.711874	+	0.411000i
$222$	4.99880	−	17.7111i	0.335498	−	1.18869i
$223$	−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	$-0.145011\pi$
$227$	1.02424	+	1.77403i	0.0679810	+	0.117746i	−0.830031	+	0.557717i	$0.811678\pi$
$228$	−6.16828	+	6.00651i	−0.408505	+	0.397791i
$229$	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
$231$	−8.25251	−	12.7631i	−0.542976	−	0.839749i
$232$	6.04247			0.396708
$233$	−14.3840	+	24.9138i	−0.942328	+	1.63216i	−0.181314	+	0.983425i	$0.558035\pi$
$233$	−14.3840	+	24.9138i	−0.942328	+	1.63216i	−0.761015	+	0.648735i	$0.775298\pi$
$234$	−5.59391	+	9.12039i	−0.365685	+	0.596218i
$235$	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	$-0.335775\pi$
$239$	15.2538			0.986685			0.493342	+	0.869835i	$0.335775\pi$
$240$	−1.93591	−	0.546395i	−0.124963	−	0.0352696i
$241$	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
$243$	10.2667	+	11.7301i	0.658607	+	0.752487i
$244$			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
$249$	−7.50905	−	7.71129i	−0.475867	−	0.488683i
$250$	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	$-0.0295264\pi$
$252$	−3.69705	+	7.02366i	−0.232892	+	0.442449i
$253$	7.55180	+	28.4093i	0.474778	+	1.78608i
$254$	−4.48636	−	2.59020i	−0.281500	−	0.162524i
$255$	−4.93794	+	4.80844i	−0.309226	+	0.301116i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	14.2919	+	8.25142i	0.891503	+	0.514709i	0.874434	−	0.485145i	$-0.161233\pi$
$257$	14.2919	+	8.25142i	0.891503	+	0.514709i	0.0170691	+	0.999854i	$0.494566\pi$
$258$	−2.97346	−	11.7177i	−0.185119	−	0.729510i
$259$	−1.84418	−	28.0505i	−0.114592	−	1.74297i
$260$	−4.14190			−0.256870
$261$	0.481640	−	18.1210i	0.0298128	−	1.12166i
$262$	9.74600	+	16.8806i	0.602110	+	1.04289i
$263$	−7.63064	−	13.2167i	−0.470525	−	0.814974i	0.528906	−	0.848680i	$-0.322602\pi$
$263$	−7.63064	−	13.2167i	−0.470525	−	0.814974i	−0.999432	+	0.0337062i	$0.989269\pi$
$264$	0.0877320	−	5.74389i	0.00539953	−	0.353512i
$265$	−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	$-0.595848\pi$
$269$	6.26825	−	3.61898i	0.382182	−	0.220653i	0.678767	+	0.734353i	$0.262515\pi$
$270$	−1.79291	+	5.76214i	−0.109113	+	0.350672i
$271$	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
$273$	−3.39790	+	15.9862i	−0.205650	+	0.967529i
$274$		−	22.3247i		−	1.34869i
$275$	−3.15747	+	11.6909i	−0.190402	+	0.704987i
$276$	10.9984	−	10.7100i	0.662027	−	0.644665i
$277$	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	$-0.690581\pi$
$281$	−18.8950			−1.12718			−0.563591	+	0.826054i	$0.690581\pi$
$282$	8.15291	+	2.30109i	0.485499	+	0.137028i
$283$	−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
$285$	−2.71601	+	9.62300i	−0.160882	+	0.570017i
$286$	−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
$291$	−6.29545	−	6.46500i	−0.369046	−	0.378985i
$292$	8.95771	+	5.17174i	0.524210	+	0.302653i
$293$	−17.3941			−1.01618			−0.508088	−	0.861305i	$-0.669647\pi$
$293$	−17.3941			−1.01618			−0.508088	+	0.861305i	$0.669647\pi$
$294$	−1.73730	+	11.9992i	−0.101321	+	0.699810i
$295$	11.9026			0.692998
$296$	5.31249	−	9.20151i	0.308782	−	0.534827i
$297$	−17.2186	−	0.720944i	−0.999125	−	0.0418334i
$298$	−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
$303$	−1.99045	+	7.05231i	−0.114349	+	0.405145i
$304$	−4.30482	+	2.48539i	−0.246898	+	0.142547i
$305$	6.01040	+	10.4103i	0.344155	+	0.596093i
$306$	−0.273115	+	10.2756i	−0.0156129	+	0.587415i
$307$			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	−0.992795	−	0.119826i	$-0.961766\pi$
$311$	−24.4322	+	14.1059i	−1.38542	+	0.799873i	−0.392625	+	0.919699i	$0.628433\pi$
$312$	−4.42558	+	4.30952i	−0.250549	+	0.243979i
$313$	−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
$315$	0.360127	+	9.21101i	0.0202909	+	0.518982i
$316$			9.31193i			0.523837i
$317$	−8.91377	−	5.14637i	−0.500647	−	0.289049i	0.228333	−	0.973583i	$-0.426672\pi$
$317$	−8.91377	−	5.14637i	−0.500647	−	0.289049i	−0.728981	+	0.684534i	$0.760006\pi$
$318$	−2.51350	+	2.44758i	−0.140950	+	0.137253i
$319$	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
$324$	4.07961	+	8.02227i	0.226645	+	0.445681i
$325$	11.2772	−	6.51089i	0.625546	−	0.361159i
$326$	4.45739	+	7.72043i	0.246872	+	0.427595i
$327$	−16.2644	−	4.59048i	−0.899423	−	0.253854i
$328$	−4.05294			−0.223786
$329$	12.9124	−	0.848926i	0.711885	−	0.0468028i
$330$	−3.24714	−	5.82799i	−0.178749	−	0.320820i
$331$	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
$333$	−27.1713	−	16.6653i	−1.48898	−	0.913253i
$334$	−0.470169	+	0.814356i	−0.0257265	+	0.0445596i
$335$			2.11626i			0.115624i
$336$	−3.06633	+	3.40553i	−0.167282	+	0.185787i
$337$		−	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
$339$	13.2975	−	12.9487i	0.722219	−	0.703278i
$340$	−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
$345$	4.84280	−	17.1584i	0.260728	−	0.923776i
$346$	6.09331	+	10.5539i	0.327578	+	0.567382i
$347$	−6.90245	−	11.9554i	−0.370543	−	0.641799i	0.619106	−	0.785307i	$-0.287495\pi$
$347$	−6.90245	−	11.9554i	−0.370543	−	0.641799i	−0.989649	+	0.143508i	$0.954162\pi$
$348$	2.84284	−	10.0724i	0.152392	−	0.539936i
$349$		−	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	−0.849408	−	0.527737i	$-0.823041\pi$
$353$	−15.3515	+	8.86320i	−0.817079	+	0.471741i	0.0323294	+	0.999477i	$0.489707\pi$
$354$	12.7179	−	12.3843i	0.675946	−	0.658219i
$355$	−8.07577	+	13.9876i	−0.428617	+	0.742387i
$356$			3.45507i			0.183118i
$357$	4.85216	+	14.9332i	0.256804	+	0.790349i
$358$		−	3.14139i		−	0.166028i
$359$	−10.3453	+	17.9186i	−0.546006	+	0.945710i	0.452537	+	0.891746i	$0.350519\pi$
$359$	−10.3453	+	17.9186i	−0.546006	+	0.945710i	−0.998543	+	0.0539641i	$0.982814\pi$
$360$	−1.82160	+	2.96996i	−0.0960068	+	0.156531i
$361$	2.85432	+	4.94383i	0.150227	+	0.260202i
$362$	−1.52754	+	2.64578i	−0.0802857	+	0.139059i
$363$	13.7027	−	13.2377i	0.719205	−	0.694798i
$364$	−4.17166	+	8.46357i	−0.218654	+	0.443612i
$365$	12.0125			0.628765
$366$	17.2537	+	4.86970i	0.901864	+	0.254543i
$367$	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
$369$	−0.323056	+	12.1545i	−0.0168176	+	0.632740i
$370$		−	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
$375$	12.4677	−	12.1407i	0.643830	−	0.626944i
$376$	4.23571	+	2.44549i	0.218440	+	0.126116i
$377$		−	21.5499i		−	1.10988i
$378$	9.96857	+	9.46719i	0.512728	+	0.486940i
$379$	−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
$381$	−6.42841	+	6.25982i	−0.329338	+	0.320700i
$382$	0.195655	−	0.112961i	0.0100106	−	0.00577960i
$383$	−13.9230	−	8.03845i	−0.711433	−	0.410746i	0.100159	−	0.994971i	$-0.468065\pi$
$383$	−13.9230	−	8.03845i	−0.711433	−	0.410746i	−0.811591	+	0.584226i	$0.801398\pi$
$384$	−1.67884	+	0.426020i	−0.0856730	+	0.0217403i
$385$	−7.64994	−	6.73302i	−0.389877	−	0.343147i
$386$			12.0425i			0.612949i
$387$	−20.9315	−	0.556339i	−1.06401	−	0.0282803i
$388$	−2.60495	−	4.51190i	−0.132246	−	0.229057i
$389$	−17.8525	+	10.3071i	−0.905156	+	0.522592i	−0.878870	−	0.477062i	$-0.841702\pi$
$389$	−17.8525	+	10.3071i	−0.905156	+	0.522592i	−0.0262868	+	0.999654i	$0.508368\pi$
$390$	−1.94866	+	6.90425i	−0.0986745	+	0.349610i
$391$		−	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
$396$	−9.53339	−	2.84861i	−0.479071	−	0.143148i
$397$	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
$399$	16.9281	+	15.2420i	0.847467	+	0.763056i
$400$	3.65123			0.182562
$401$	1.61502	+	0.932434i	0.0806504	+	0.0465635i	0.539783	−	0.841804i	$-0.318506\pi$
$401$	1.61502	+	0.932434i	0.0806504	+	0.0465635i	−0.459132	+	0.888368i	$0.651840\pi$
$402$	2.20191	+	2.26121i	0.109821	+	0.112779i
$403$	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
$408$	−1.61204	+	5.71156i	−0.0798078	+	0.282764i
$409$	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
$411$	−37.2138	−	10.5033i	−1.83562	−	0.518087i
$412$	−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
$417$	−13.1218	+	12.7777i	−0.642578	+	0.625726i
$418$	−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	$0.829963\pi$
$420$	−1.10649	+	5.20575i	−0.0539914	+	0.254015i
$421$	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
$423$	7.67150	−	12.5077i	0.373001	−	0.608146i
$424$	−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
$429$	−20.4851	−	0.312888i	−0.989028	−	0.0151064i
$430$	−4.05294	−	7.01990i	−0.195450	−	0.338530i
$431$	−19.1899	−	33.2379i	−0.924344	−	1.60101i	−0.792613	−	0.609726i	$-0.791280\pi$
$431$	−19.1899	−	33.2379i	−0.924344	−	1.60101i	−0.131732	−	0.991285i	$-0.542054\pi$
$432$	1.14379	+	5.06870i	0.0550306	+	0.243868i
$433$	−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
$438$	12.8353	−	12.4987i	0.613295	−	0.597210i
$439$	−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
$441$	19.1845	+	8.54131i	0.913549	+	0.406729i
$442$			12.2199i			0.581242i
$443$	−0.869330	−	0.501908i	−0.0413031	−	0.0238464i	0.479206	−	0.877702i	$-0.340925\pi$
$443$	−0.869330	−	0.501908i	−0.0413031	−	0.0238464i	−0.520509	+	0.853856i	$0.674258\pi$
$444$	−12.8389	−	13.1846i	−0.609305	−	0.625715i
$445$	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	$-0.215902\pi$
$450$	0.291036	−	10.9498i	0.0137196	−	0.516180i
$451$	−9.48609	−	9.52386i	−0.446683	−	0.448461i
$452$	9.28025	−	5.35795i	0.436506	−	0.252017i
$453$	6.65561	+	1.87849i	0.312708	+	0.0882590i
$454$	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
$459$	17.0001	+	5.28967i	0.793498	+	0.246901i
$460$	5.14671	−	8.91435i	0.239966	−	0.415634i
$461$	1.38465			0.0644895			0.0322448	−	0.999480i	$-0.489734\pi$
$461$	1.38465			0.0644895			0.0322448	+	0.999480i	$0.489734\pi$
$462$	−15.1794	+	0.765350i	−0.706210	+	0.0356073i
$463$	−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
$465$	1.57680	−	1.53544i	0.0731222	−	0.0712045i
$466$	14.3840	+	24.9138i	0.666327	+	1.15411i
$467$	24.2746	+	14.0149i	1.12329	+	0.648533i	0.942239	−	0.334940i	$-0.108716\pi$
$467$	24.2746	+	14.0149i	1.12329	+	0.648533i	0.181053	+	0.983473i	$0.442049\pi$
$468$	5.10153	+	9.40466i	0.235818	+	0.434731i
$469$	4.32438	+	2.13147i	0.199681	+	0.0984221i
$470$	5.68021			0.262008
$471$	6.74503	−	23.8981i	0.310795	−	1.10117i
$472$	8.87574	−	5.12441i	0.408539	−	0.235870i
$473$	16.4011	−	16.3361i	0.754125	−	0.751135i
$474$	15.5223	+	4.38104i	0.712964	+	0.201228i
$475$		−	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	$0.196396\pi$
$479$	19.8918	+	34.4537i	0.908882	+	1.57423i	0.0932611	+	0.995642i	$0.470271\pi$
$480$	−1.44115	+	1.40335i	−0.0657791	+	0.0640540i
$481$	−32.8163	−	18.9465i	−1.49630	−	0.863887i
$482$		−	8.82596i		−	0.402012i
$483$	−30.1839	−	27.1775i	−1.37341	−	1.23662i
$484$	9.54805	−	5.46211i	0.434002	−	0.248278i
$485$	−5.23996	−	3.02529i	−0.237935	−	0.137372i
$486$	15.2919	−	3.02614i	0.693655	−	0.137268i
$487$	−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	$-0.655470\pi$
$491$	−20.7951			−0.938470			−0.469235	+	0.883073i	$0.655470\pi$
$492$	−1.90681	+	6.75597i	−0.0859658	+	0.304583i
$493$	−10.3520	−	17.9301i	−0.466229	−	0.807532i
$494$	8.86391	+	15.3527i	0.398806	+	0.690752i
$495$	−11.2425	+	2.67082i	−0.505315	+	0.120045i
$496$	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
$501$	1.13627	+	1.16687i	0.0507648	+	0.0521320i
$502$	−2.54176	−	1.46749i	−0.113444	−	0.0654971i
$503$	−7.11469			−0.317228			−0.158614	−	0.987341i	$-0.550703\pi$
$503$	−7.11469			−0.317228			−0.158614	+	0.987341i	$0.550703\pi$
$504$	4.23414	+	6.71357i	0.188604	+	0.299046i
$505$			4.91341i			0.218644i
$506$	28.3791	+	7.66461i	1.26160	+	0.340733i
$507$	−0.339244	−	0.348381i	−0.0150664	−	0.0154721i
$508$	−4.48636	+	2.59020i	−0.199050	+	0.114922i
$509$	1.06636	+	0.615664i	0.0472657	+	0.0272888i	0.523447	−	0.852058i	$-0.324646\pi$
$509$	1.06636	+	0.615664i	0.0472657	+	0.0272888i	−0.476181	+	0.879347i	$0.657979\pi$
$510$	1.69526	+	6.68061i	0.0750674	+	0.295822i
$511$	12.0989	−	24.5465i	0.535222	−	1.08587i
$512$	−1.00000			−0.0441942
$513$	25.1954	−	5.68553i	1.11240	−	0.251022i
$514$	14.2919	−	8.25142i	0.630388	−	0.363955i
$515$	−18.3794	+	10.6113i	−0.809891	+	0.467591i
$516$	−11.6345	−	3.28374i	−0.512182	−	0.144559i
$517$	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	$-0.272962\pi$
$521$	37.3509	−	21.5645i	1.63637	−	0.944759i	0.982068	−	0.188526i	$-0.0603711\pi$
$522$	−15.4524	−	9.47762i	−0.676335	−	0.414824i
$523$	−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
$525$	−5.17055	−	15.9131i	−0.225661	−	0.694505i
$526$	−15.2613			−0.665423
$527$	1.87445	−	3.24665i	0.0816524	−	0.141426i
$528$	−4.93049	−	2.94792i	−0.214572	−	0.128292i
$529$	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
$534$	5.75936	+	1.62553i	0.249232	+	0.0703435i
$535$	−0.661052	+	0.381658i	−0.0285798	+	0.0165005i
$536$	0.911110	+	1.57809i	0.0393540	+	0.0681631i
$537$	−5.23648	−	1.47795i	−0.225971	−	0.0637782i
$538$		−	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
$543$	3.69165	+	3.79108i	0.158424	+	0.162691i
$544$	−1.71320	+	2.96735i	−0.0734528	+	0.127224i
$545$	−11.3316			−0.485390
$546$	12.1455	+	10.9358i	0.519780	+	0.468008i
$547$			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
$549$	16.2349	−	26.4696i	0.692888	−	1.12969i
$550$	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
$555$	−20.5691	−	5.80544i	−0.873108	−	0.246427i
$556$	−9.15766	+	5.28718i	−0.388371	+	0.224226i
$557$	14.9173	+	25.8375i	0.632067	+	1.09477i	0.987128	+	0.159929i	$0.0511266\pi$
$557$	14.9173	+	25.8375i	0.632067	+	1.09477i	−0.355062	+	0.934843i	$0.615540\pi$
$558$	0.0872117	−	3.28122i	0.00369197	−	0.138905i
$559$	−24.8922			−1.05283
$560$	−1.35846	+	2.75608i	−0.0574054	+	0.116466i
$561$	−17.1944	+	9.58010i	−0.725949	+	0.404472i
$562$	−9.44751	+	16.3636i	−0.398519	+	0.690255i
$563$	15.1418	+	26.2264i	0.638152	+	1.10531i	0.985838	+	0.167700i	$0.0536341\pi$
$563$	15.1418	+	26.2264i	0.638152	+	1.10531i	−0.347686	+	0.937611i	$0.613033\pi$
$564$	6.06926	−	5.91008i	0.255562	−	0.248859i
$565$	6.22254	−	10.7778i	0.261784	−	0.453424i
$566$			1.87542i			0.0788296i
$567$	20.4711	−	12.1628i	0.859705	−	0.510790i
$568$			13.9074i			0.583540i
$569$	3.28407	−	5.68818i	0.137675	−	0.238461i	−0.788941	−	0.614469i	$-0.789370\pi$
$569$	3.28407	−	5.68818i	0.137675	−	0.238461i	0.926616	+	0.376008i	$0.122704\pi$
$570$	6.97576	+	7.16363i	0.292182	+	0.300051i
$571$	−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
$576$	−0.0797091	+	2.99894i	−0.00332121	+	0.124956i
$577$	−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
$579$	20.0741	+	5.66573i	0.834249	+	0.235460i
$580$		−	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
$585$	10.5921	+	6.49657i	0.437929	+	0.268600i
$586$	−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	$0.940618\pi$
$588$	9.52300	+	7.50417i	0.392722	+	0.309467i
$589$		−	5.43865i		−	0.224096i
$590$	5.95131	−	10.3080i	0.245012	−	0.424373i
$591$	0.655152	+	0.672797i	0.0269494	+	0.0276752i
$592$	−5.31249	−	9.20151i	−0.218342	−	0.378180i
$593$	0.812081	−	1.40657i	0.0333482	−	0.0577608i	−0.848870	−	0.528602i	$-0.822716\pi$
$593$	0.812081	−	1.40657i	0.0333482	−	0.0577608i	0.882218	+	0.470842i	$0.156050\pi$
$594$	−9.23366	+	14.5513i	−0.378862	+	0.597046i
$595$	5.85093	+	8.75273i	0.239865	+	0.358827i
$596$	−4.45639			−0.182541
$597$	1.99605	−	7.07215i	0.0816930	−	0.289444i
$598$	−15.8049	−	27.3749i	−0.646310	−	1.11944i
$599$	−14.6927	+	8.48281i	−0.600326	+	0.346598i	−0.769170	−	0.639045i	$-0.779330\pi$
$599$	−14.6927	+	8.48281i	−0.600326	+	0.346598i	0.168844	+	0.985643i	$0.445997\pi$
$600$	1.71782	−	6.08634i	0.0701296	−	0.248474i
$601$			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
$606$	5.11226	+	5.24994i	0.207671	+	0.213264i
$607$	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
$609$	−27.0850	−	5.75698i	−1.09754	−	0.233285i
$610$	12.0208			0.486708
$611$	8.72160	−	15.1063i	0.352838	−	0.611134i
$612$	8.76234	+	5.37430i	0.354197	+	0.217243i
$613$	−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	$-0.723768\pi$
$617$		−	37.9007i		−	1.52583i	0.646501	−	0.762913i	$-0.276232\pi$
$618$	−8.59743	+	30.4613i	−0.345839	+	1.22533i
$619$	−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
$621$	−44.9249	+	10.1376i	−1.80277	+	0.406810i
$622$			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
$627$	−14.6535	+	24.5084i	−0.585204	+	0.978770i
$628$	7.16830	−	12.4159i	0.286046	−	0.495447i
$629$	−36.4054			−1.45158
$630$	8.15703	+	4.29363i	0.324984	+	0.171062i
$631$	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
$633$	−0.180122	+	0.175398i	−0.00715922	+	0.00697146i
$634$	−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
$639$	41.7074	+	1.10854i	1.64992	+	0.0438533i
$640$	−1.00577	+	0.580683i	−0.0397566	+	0.0229535i
$641$	12.3614	−	7.13687i	0.488247	−	0.281890i	−0.235600	−	0.971850i	$-0.575705\pi$
$641$	12.3614	−	7.13687i	0.488247	−	0.281890i	0.723847	+	0.689961i	$0.242372\pi$
$642$	−0.309224	+	1.09560i	−0.0122041	+	0.0432400i
$643$	−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	$-0.803240\pi$
$647$	−18.3282	+	10.5818i	−0.720556	+	0.416013i	0.0944013	+	0.995534i	$0.469906\pi$
$648$	8.98729	+	0.478086i	0.353054	+	0.0187810i
$649$	32.8157	+	8.86285i	1.28813	+	0.347897i
$650$		−	13.0218i		−	0.510756i
$651$	−1.54940	−	4.76850i	−0.0607259	−	0.186892i
$652$	8.91479			0.349130
$653$	26.3449	+	15.2102i	1.03096	+	0.595222i	0.917258	−	0.398293i	$-0.130397\pi$
$653$	26.3449	+	15.2102i	1.03096	+	0.595222i	0.113697	+	0.993515i	$0.463731\pi$
$654$	−12.1077	+	11.7901i	−0.473447	+	0.461031i
$655$	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	$-0.935265\pi$
$659$	−50.2839			−1.95878			−0.979391	+	0.201972i	$0.935265\pi$
$660$	−6.67076	−	0.101889i	−0.259659	−	0.00396602i
$661$	−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
$663$	20.3697	+	5.74918i	0.791095	+	0.223280i
$664$	−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
$669$	12.8089	+	13.1538i	0.495219	+	0.508557i
$670$	1.83274	+	1.05813i	0.0708048	+	0.0408792i
$671$	8.81911	+	33.1768i	0.340458	+	1.28078i
$672$	1.41611	+	4.35828i	0.0546277	+	0.168124i
$673$		−	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
$675$	−18.1157	−	5.63677i	−0.697272	−	0.216959i
$676$	−0.140373	−	0.243134i	−0.00539897	−	0.00935130i
$677$	−12.3437	+	21.3799i	−0.474407	+	0.821698i	−0.999571	−	0.0293038i	$-0.990671\pi$
$677$	−12.3437	+	21.3799i	−0.474407	+	0.821698i	0.525163	+	0.851002i	$0.324004\pi$
$678$	−4.56519	−	17.9903i	−0.175325	−	0.690914i
$679$	−11.4595	+	7.66033i	−0.439776	+	0.293976i
$680$			3.97930i			0.152599i
$681$	0.963758	−	3.41466i	0.0369313	−	0.130850i
$682$	2.56085	+	2.57104i	0.0980599	+	0.0984503i
$683$	−18.1930	+	10.5037i	−0.696135	+	0.401914i	−0.805906	−	0.592043i	$-0.798322\pi$
$683$	−18.1930	+	10.5037i	−0.696135	+	0.401914i	0.109771	+	0.993957i	$0.464988\pi$
$684$	14.9071	+	0.396216i	0.569986	+	0.0151497i
$685$	−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
$690$	−12.4382	−	12.7732i	−0.473514	−	0.486267i
$691$	−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
$693$	−5.86576	+	25.6631i	−0.222822	+	0.974859i
$694$	−13.8049			−0.524027
$695$	−6.14034	+	10.6354i	−0.232916	+	0.403423i
$696$	−7.30151	−	7.49816i	−0.276763	−	0.284217i
$697$	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	$-0.332826\pi$
$701$	26.5494			1.00276			0.501379	+	0.865228i	$0.332826\pi$
$702$	18.0771	−	4.07922i	0.682274	−	0.153960i
$703$	−45.7387	+	26.4072i	−1.72507	+	0.995968i
$704$	−2.34054	−	2.34986i	−0.0882126	−	0.0885637i
$705$	2.67240	−	9.46850i	0.100648	−	0.356605i
$706$			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
$711$	14.6058	−	23.8134i	0.547759	−	0.893074i
$712$	2.99218	+	1.72754i	0.112137	+	0.0647421i
$713$			9.69745i			0.363172i
$714$	15.3586	+	3.26451i	0.574782	+	0.122171i
$715$	−13.2761	+	3.52907i	−0.496497	+	0.131980i
$716$	−2.72052	−	1.57070i	−0.101671	−	0.0586996i
$717$	−18.4321	−	18.9285i	−0.688361	−	0.706900i
$718$	10.3453	+	17.9186i	0.386084	+	0.668718i
$719$	23.1897	+	13.3886i	0.864830	+	0.499310i	0.865627	−	0.500690i	$-0.166920\pi$
$719$	23.1897	+	13.3886i	0.864830	+	0.499310i	−0.000796544		1.00000i	$0.500254\pi$
$720$	1.66126	+	3.06254i	0.0619116	+	0.114134i
$721$	3.17180	+	48.2440i	0.118124	+	1.79670i
$722$	5.70864			0.212454
$723$	−14.7123	−	4.15240i	−0.547155	−	0.154430i
$724$	1.52754	+	2.64578i	0.0567706	+	0.0983295i
$725$	11.0312	+	19.1067i	0.409690	+	0.709603i
$726$	−4.61282	−	18.4857i	−0.171198	−	0.686069i
$727$	−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
$732$	12.8441	−	12.5073i	0.474733	−	0.462282i
$733$	−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
$735$	13.9355	+	2.01764i	0.514019	+	0.0744218i
$736$		−	8.86320i		−	0.326702i
$737$	−1.57580	+	5.83457i	−0.0580452	+	0.214919i
$738$	10.3646	+	6.35704i	0.381527	+	0.234006i
$739$	−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	$-0.720256\pi$
$743$	−34.7835			−1.27608			−0.638042	+	0.770001i	$0.720256\pi$
$744$	0.514760	−	1.82383i	0.0188720	−	0.0668648i
$745$	−4.48211	+	2.58775i	−0.164212	+	0.0948077i
$746$	−7.47599	+	4.31626i	−0.273715	+	0.158030i
$747$	−0.495330	+	18.6361i	−0.0181232	+	0.681859i
$748$	−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
$753$	−3.64203	+	3.54652i	−0.132723	+	0.129242i
$754$	−18.6628	−	10.7750i	−0.679658	−	0.392401i
$755$	4.63702			0.168759
$756$	13.1831	−	3.89944i	0.479465	−	0.141821i
$757$	−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
$759$	26.1280	−	43.6999i	0.948388	−	1.58621i
$760$	2.88644	+	4.99947i	0.104702	+	0.181350i
$761$	20.6464	−	35.7605i	0.748430	−	1.29632i	−0.200145	−	0.979766i	$-0.564141\pi$
$761$	20.6464	−	35.7605i	0.748430	−	1.29632i	0.948575	−	0.316552i	$-0.102525\pi$
$762$	2.20696	+	8.69708i	0.0799497	+	0.315062i
$763$	−11.4130	+	23.1549i	−0.413177	+	0.838265i
$764$		−	0.225923i		−	0.00817359i
$765$	11.9337	+	0.317186i	0.431463	+	0.0114679i
$766$	−13.9230	+	8.03845i	−0.503059	+	0.290441i
$767$	−18.2757	−	31.6545i	−0.659899	−	1.14298i
$768$	−0.470476	+	1.66693i	−0.0169768	+	0.0601501i
$769$		−	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	−0.497775	−	0.867306i	$-0.665850\pi$
$773$	0.123624	−	0.0713746i	0.00444646	−	0.00256717i	0.502222	+	0.864739i	$0.332516\pi$
$774$	−10.9475	+	17.8490i	−0.393501	+	0.641569i
$775$	−1.99745	+	3.45969i	−0.0717506	+	0.124276i
$776$	−5.20989			−0.187024
$777$	−32.5797	+	36.1837i	−1.16879	+	1.29808i
$778$			20.6143i			0.739057i
$779$	17.4472	+	10.0731i	0.625111	+	0.360908i
$780$	5.00493	+	5.13972i	0.179205	+	0.184031i
$781$	−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
$786$	9.17052	−	32.4918i	0.327102	−	1.15894i
$787$	−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
$789$	−7.18007	+	25.4395i	−0.255617	+	0.905669i
$790$	10.8146			0.384764
$791$	−15.7560	−	23.5704i	−0.560221	−	0.838065i
$792$	−7.23366	+	6.83185i	−0.257037	+	0.242759i
$793$	18.4572	−	31.9688i	0.655434	−	1.13524i
$794$	−2.61119	−	4.52272i	−0.0926678	−	0.160505i
$795$	2.84253	+	2.91909i	0.100814	+	0.103529i
$796$	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	$-0.0372730\pi$
$798$	21.6641	−	7.03918i	0.766899	−	0.249184i
$799$		−	16.7584i		−	0.592870i
$800$	1.82562	−	3.16206i	0.0645453	−	0.111796i
$801$	5.41928	−	8.83567i	0.191481	−	0.312193i
$802$	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
$807$	−12.0652	−	3.40529i	−0.424714	−	0.119872i
$808$	2.11536	+	3.66391i	0.0744181	+	0.128896i
$809$	11.1559	+	19.3225i	0.392220	+	0.679345i	0.992742	−	0.120263i	$-0.0383739\pi$
$809$	11.1559	+	19.3225i	0.392220	+	0.679345i	−0.600522	+	0.799608i	$0.705041\pi$
$810$	9.31678	−	4.73792i	0.327358	−	0.166473i
$811$			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
$816$	4.14034	+	4.25185i	0.144941	+	0.148844i
$817$	−17.3471	+	30.0460i	−0.606897	+	1.05118i
$818$		−	14.1198i		−	0.493686i
$819$	23.9433	−	15.1007i	0.836647	−	0.527660i
$820$			4.70695i			0.164374i
$821$	3.99233	−	6.91491i	0.139333	−	0.241332i	−0.787911	−	0.615789i	$-0.788837\pi$
$821$	3.99233	−	6.91491i	0.139333	−	0.241332i	0.927244	+	0.374457i	$0.122171\pi$
$822$	−27.7030	+	26.9764i	−0.966252	+	0.940911i
$823$	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
$825$	18.3227	−	10.2087i	0.637914	−	0.355422i
$826$	−15.0693	−	22.5430i	−0.524327	−	0.784371i
$827$	−1.47055			−0.0511361			−0.0255680	−	0.999673i	$-0.508139\pi$
$827$	−1.47055			−0.0511361			−0.0255680	+	0.999673i	$0.508139\pi$
$828$	−26.5802	−	0.706478i	−0.923726	−	0.0245518i
$829$	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
$831$	−33.0245	−	9.32087i	−1.14561	−	0.323337i
$832$			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
$837$	−5.42852	−	1.68911i	−0.187637	−	0.0583842i
$838$	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	$-0.109389\pi$
$840$	3.95506	+	3.56113i	0.136463	+	0.122871i
$841$	7.51148			0.259016
$842$	10.1630	−	17.6028i	0.350240	−	0.606634i
$843$	22.8321	+	23.4470i	0.786378	+	0.807557i
$844$	−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
$849$	3.12619	+	0.882339i	0.107290	+	0.0302818i
$850$	−6.25528	−	10.8345i	−0.214554	−	0.371619i
$851$	81.5548	−	47.0857i	2.79566	−	1.61408i
$852$	23.1826	+	6.54308i	0.794223	+	0.224162i
$853$		−	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	0.999849	−	0.0173825i	$-0.00553331\pi$
$857$	14.1944	+	24.5854i	0.484871	+	0.839821i	−0.514978	+	0.857203i	$0.672200\pi$
$858$	−10.5135	+	17.5841i	−0.358925	+	0.600312i
$859$	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
$861$	18.1671	+	3.86145i	0.619132	+	0.131598i
$862$	−38.3798			−1.30722
$863$	22.9893	+	13.2729i	0.782565	+	0.451814i	0.837339	−	0.546685i	$-0.184110\pi$
$863$	22.9893	+	13.2729i	0.782565	+	0.451814i	−0.0547734	+	0.998499i	$0.517444\pi$
$864$	4.96152	+	1.54380i	0.168794	+	0.0525211i
$865$	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
$870$	−11.6977	−	3.30157i	−0.396589	−	0.111934i
$871$	5.62811	−	3.24939i	0.190701	−	0.110101i
$872$	−8.44989	+	4.87855i	−0.286150	+	0.165209i
$873$	−0.415276	+	15.6242i	−0.0140550	+	0.528798i
$874$	−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
$879$	21.0185	+	21.5845i	0.708935	+	0.728028i
$880$	−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	$-0.228811\pi$
$882$	16.9893	−	12.3436i	0.572058	−	0.415632i
$883$	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
$885$	−14.3827	−	14.7701i	−0.483470	−	0.496491i
$886$	−0.869330	+	0.501908i	−0.0292057	+	0.0168619i
$887$	4.65016	−	8.05432i	0.156137	−	0.270438i	−0.777335	−	0.629086i	$-0.783429\pi$
$887$	4.65016	−	8.05432i	0.156137	−	0.270438i	0.933473	+	0.358649i	$0.116762\pi$
$888$	−17.8377	+	4.52646i	−0.598593	+	0.151898i
$889$	7.61697	+	11.3947i	0.255465	+	0.382164i
$890$	4.01260			0.134503
$891$	19.9117	+	22.2379i	0.667068	+	0.744997i
$892$	5.30008	+	9.18001i	0.177460	+	0.307370i
$893$	−12.1560	−	21.0548i	−0.406784	−	0.704571i
$894$	−2.09662	+	7.42848i	−0.0701216	+	0.248446i
$895$	−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
$900$	−9.33731	−	5.72696i	−0.311244	−	0.190899i
$901$	6.01045	+	3.47013i	0.200237	+	0.115607i
$902$	−12.9909	+	3.45327i	−0.432551	+	0.114981i
$903$	−6.64985	+	31.2857i	−0.221293	+	1.04112i
$904$		−	10.7159i		−	0.356406i
$905$	3.07271	+	1.77403i	0.102140	+	0.0589708i
$906$	4.95462	−	4.82468i	0.164606	−	0.160289i
$907$	−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	$0.244784\pi$
$911$			41.9798i			1.39085i	−0.718598	+	0.695426i	$0.755216\pi$
$912$	8.28594	+	2.33863i	0.274375	+	0.0774399i
$913$	−14.5447	−	14.6026i	−0.481358	−	0.483275i
$914$	−9.69107	+	5.59514i	−0.320552	+	0.185071i
$915$	5.65550	−	20.0378i	0.186965	−	0.662430i
$916$	−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
$921$	26.0760	−	25.3922i	0.859234	−	0.836700i
$922$	0.692324	−	1.19914i	0.0228005	−	0.0394916i
$923$	49.5993			1.63258
$924$	−6.92689	+	13.5284i	−0.227878	+	0.445052i
$925$	38.7943			1.27555
$926$	−8.42556	+	14.5935i	−0.276881	+	0.479572i
$927$	46.7319	+	28.6626i	1.53488	+	0.941403i
$928$	−3.02124	−	5.23293i	−0.0991769	−	0.171780i
$929$	−27.2536	−	15.7349i	−0.894163	−	0.516245i	−0.0188609	−	0.999822i	$-0.506004\pi$
$929$	−27.2536	−	15.7349i	−0.894163	−	0.516245i	−0.875302	+	0.483577i	$0.839337\pi$
$930$	−0.541335	−	2.13327i	−0.0177511	−	0.0699526i
$931$	27.5966	−	21.1932i	0.904442	−	0.694579i
$932$	28.7680			0.942328
$933$	47.0271	+	13.2730i	1.53960	+	0.434538i
$934$	24.2746	−	14.0149i	0.794288	−	0.458582i
$935$	−9.35080	+	9.31372i	−0.305804	+	0.304591i
$936$	10.6954	+	0.284275i	0.349591	+	0.00929182i
$937$		−	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	$0.205904\pi$
$941$	28.2503	+	48.9309i	0.920932	+	1.59510i	0.122956	+	0.992412i	$0.460762\pi$
$942$	−17.3238	−	17.7904i	−0.564441	−	0.579643i
$943$	−31.1094	−	17.9610i	−1.01306	−	0.584891i
$944$		−	10.2488i		−	0.333571i
$945$	10.9949	−	11.5771i	0.357663	−	0.376605i
$946$	−5.94692	−	22.3719i	−0.193351	−	0.727372i
$947$	−23.9465	−	13.8255i	−0.778158	−	0.449270i	0.0576190	−	0.998339i	$-0.481649\pi$
$947$	−23.9465	−	13.8255i	−0.778158	−	0.449270i	−0.835777	+	0.549069i	$0.814982\pi$
$948$	11.5553	−	11.2522i	0.375297	−	0.365455i
$949$	−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	$-0.702628\pi$
$953$	−36.7018			−1.18889			−0.594444	+	0.804137i	$0.702628\pi$
$954$	6.07445	+	0.161453i	0.196667	+	0.00522724i
$955$	−0.131189	−	0.227227i	−0.00424519	−	0.00735288i
$956$	−7.62689	−	13.2102i	−0.246671	−	0.427247i
$957$	0.530118	−	34.7073i	0.0171363	−	1.12193i
$958$	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
$963$	1.68081	+	1.03091i	0.0541633	+	0.0332206i
$964$	−7.64351	−	4.41298i	−0.246181	−	0.142133i
$965$	13.9858			0.450218
$966$	−38.6283	+	12.5513i	−1.24285	+	0.403831i
$967$			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
$969$	21.1350	−	20.5807i	0.678954	−	0.661147i
$970$	−5.23996	+	3.02529i	−0.168245	+	0.0971364i
$971$	5.24145	+	3.02615i	0.168206	+	0.0971139i	0.581740	−	0.813375i	$-0.302372\pi$
$971$	5.24145	+	3.02615i	0.168206	+	0.0971139i	−0.413534	+	0.910489i	$0.635706\pi$
$972$	5.02524	−	14.7563i	0.161185	−	0.473307i
$973$	15.5479	+	23.2590i	0.498443	+	0.745649i
$974$	−8.49641			−0.272243
$975$	−21.7064	−	6.12643i	−0.695160	−	0.196203i
$976$	8.96386	−	5.17529i	0.286926	−	0.165657i
$977$	−2.31699	+	1.33771i	−0.0741269	+	0.0427972i	−0.536605	−	0.843833i	$-0.680294\pi$
$977$	−2.31699	+	1.33771i	−0.0741269	+	0.0427972i	0.462478	+	0.886631i	$0.346960\pi$
$978$	4.19419	−	14.8603i	0.134116	−	0.475181i
$979$	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	$-0.683967\pi$
$983$	−2.94995	+	1.70316i	−0.0940890	+	0.0543223i	0.452217	+	0.891908i	$0.350633\pi$
$984$	4.89743	+	5.02933i	0.156124	+	0.160329i
$985$	0.545310	+	0.314835i	0.0173750	+	0.0100315i
$986$	−20.7039			−0.659347
$987$	−16.6564	−	14.9973i	−0.530178	−	0.477370i
$988$	17.7278			0.563997
$989$	30.9309	−	53.5739i	0.983545	−	1.70355i
$990$	−3.30827	+	11.0717i	−0.105144	+	0.351883i
$991$	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
$996$	−2.92364	+	10.3587i	−0.0926392	+	0.328227i
$997$	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
$999$	12.1528	+	53.8549i	0.384496	+	1.70389i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.20836 - 1.24091i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00577 - 0.580683i) q^{5} +(-1.67884 + 0.426020i) q^{6} +(-2.19957 + 1.47034i) q^{7} -1.00000 q^{8} +(-0.0797091 + 2.99894i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.20836 - 1.24091i) 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} +(-0.0797091 + 2.99894i) q^{9} +(-1.00577 + 0.580683i) q^{10} +(-2.34054 - 2.34986i) q^{11} +(-0.470476 + 1.66693i) 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} +(2.55730 + 1.56850i) q^{18} +(4.30482 + 2.48539i) q^{19} +1.16137i q^{20} +(4.48244 + 0.952753i) q^{21} +(-3.20531 + 0.852040i) q^{22} +(-7.67576 - 4.43160i) q^{23} +(1.20836 + 1.24091i) 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} +(1.93591 + 0.546395i) q^{30} +(-0.547062 - 0.947540i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.0877320 + 5.74389i) 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} +(4.42558 - 4.30952i) q^{39} +(1.00577 + 0.580683i) q^{40} +4.05294 q^{41} +(3.06633 - 3.40553i) q^{42} +6.97962i q^{43} +(-0.864767 + 3.20190i) q^{44} +(1.82160 - 2.96996i) 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} +(1.61204 - 5.71156i) q^{51} +(3.08860 - 1.78320i) q^{52} +(1.75416 - 1.01277i) q^{53} +(-1.14379 - 5.06870i) 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} +(1.44115 - 1.40335i) q^{60} +(-8.96386 - 5.17529i) q^{61} -1.09412 q^{62} +(-4.23414 - 6.71357i) q^{63} +1.00000 q^{64} +(2.07095 - 3.58699i) q^{65} +(4.93049 + 2.94792i) 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} +(0.0797091 - 2.99894i) q^{72} +(-8.95771 + 5.17174i) q^{73} +(5.31249 + 9.20151i) q^{74} +(-1.71782 + 6.08634i) 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} +(-8.98729 - 0.478086i) q^{81} +(2.02647 - 3.50995i) q^{82} +6.21423 q^{83} +(-1.41611 - 4.35828i) q^{84} -3.97930i q^{85} +(6.04453 + 3.48981i) q^{86} +(7.30151 + 7.49816i) 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} +(-0.514760 + 1.82383i) q^{93} +(-4.23571 + 2.44549i) q^{94} +(-2.88644 - 4.99947i) q^{95} +(0.470476 - 1.66693i) q^{96} +5.20989 q^{97} +(-4.26356 - 5.55176i) q^{98} +(7.23366 - 6.83185i) 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	\( 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} - 8 q^{9} + 4 q^{11} + 4 q^{15} - 12 q^{16} - 4 q^{17} + 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} - 40 q^{29} + 2 q^{30} - 28 q^{31} + 12 q^{32} + 24 q^{33} - 8 q^{34} + 32 q^{35} + 16 q^{36} - 16 q^{37} + 8 q^{41} + 6 q^{42} + 4 q^{44} - 28 q^{45} - 8 q^{49} + 40 q^{50} + 34 q^{51} - 6 q^{54} + 8 q^{55} - 40 q^{57} - 20 q^{58} - 2 q^{60} - 56 q^{62} + 14 q^{63} + 24 q^{64} + 44 q^{65} - 24 q^{66} - 4 q^{68} - 20 q^{69} + 64 q^{70} + 8 q^{72} + 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} - 144 q^{83} + 6 q^{84} - 8 q^{87} - 4 q^{88} - 56 q^{90} - 32 q^{91} - 22 q^{93} + 44 q^{95} + 64 q^{97} + 8 q^{98} + 28 q^{99}+O(q^{100}) \) 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 + 24 * 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 - 24 * 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 + 28 * q^99

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