LMFDB - Embedded newform 462.2.n.e.263.3

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			263.3
Character	$\chi$	$=$	462.263
Dual form			462.2.n.e.65.3

$q$-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} +(0.864767 - 3.20190i) 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} +(2.92831 + 4.94216i) 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} +(2.34054 + 2.34986i) 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} +(2.81588 - 5.00708i) 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} +(6.61000 - 5.77129i) 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} +(0.864767 - 3.20190i) 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} +(-9.67125 - 2.33817i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9}+O(q^{10}) $ 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 8 * q^9	$ 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9} - 4 q^{11} + 4 q^{15} - 12 q^{16} + 4 q^{17} - 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} + 40 q^{29} - 2 q^{30} - 28 q^{31} - 12 q^{32} + 32 q^{33} - 8 q^{34} - 32 q^{35} + 16 q^{36} - 16 q^{37} - 8 q^{41} + 6 q^{42} - 4 q^{44} - 28 q^{45} - 8 q^{49} - 40 q^{50} - 34 q^{51} + 6 q^{54} + 8 q^{55} + 40 q^{57} - 20 q^{58} - 2 q^{60} + 56 q^{62} - 14 q^{63} + 24 q^{64} - 44 q^{65} + 32 q^{66} + 4 q^{68} - 20 q^{69} + 64 q^{70} - 8 q^{72} - 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} + 144 q^{83} - 6 q^{84} + 8 q^{87} - 4 q^{88} + 56 q^{90} - 32 q^{91} - 22 q^{93} - 44 q^{95} + 64 q^{97} - 8 q^{98} - 52 q^{99}+O(q^{100}) $ 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 8 * q^9 - 4 * q^11 + 4 * q^15 - 12 * q^16 + 4 * q^17 - 8 * q^18 + 8 * q^22 + 20 * q^25 - 12 * q^27 + 40 * q^29 - 2 * q^30 - 28 * q^31 - 12 * q^32 + 32 * q^33 - 8 * q^34 - 32 * q^35 + 16 * q^36 - 16 * q^37 - 8 * q^41 + 6 * q^42 - 4 * q^44 - 28 * q^45 - 8 * q^49 - 40 * q^50 - 34 * q^51 + 6 * q^54 + 8 * q^55 + 40 * q^57 - 20 * q^58 - 2 * q^60 + 56 * q^62 - 14 * q^63 + 24 * q^64 - 44 * q^65 + 32 * q^66 + 4 * q^68 - 20 * q^69 + 64 * q^70 - 8 * q^72 - 16 * q^74 - 26 * q^75 + 24 * q^81 + 4 * q^82 + 144 * q^83 - 6 * q^84 + 8 * q^87 - 4 * q^88 + 56 * q^90 - 32 * q^91 - 22 * q^93 - 44 * q^95 + 64 * q^97 - 8 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−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	−0.707744	−	0.706469i	$-0.750287\pi$
$5$	−1.00577	+	0.580683i	−0.449795	+	0.259689i	0.257949	+	0.966159i	$0.416953\pi$
$6$	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
$11$	0.864767	−	3.20190i	0.260737	−	0.965410i
$11$	0.864767	−	3.20190i	0.260737	−	0.965410i
$12$	−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	$-0.969731\pi$
$17$	−1.71320	+	2.96735i	−0.415512	+	0.719687i	0.579970	+	0.814638i	$0.303064\pi$
$18$	−2.55730	+	1.56850i	−0.602762	+	0.369699i
$19$	−4.30482	+	2.48539i	−0.987594	+	0.570187i	−0.904554	−	0.426359i	$-0.859796\pi$
$19$	−4.30482	+	2.48539i	−0.987594	+	0.570187i	−0.0830395	+	0.996546i	$0.526463\pi$
$20$		−	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	−0.609120	+	0.793078i	$0.708477\pi$
$23$	−7.67576	+	4.43160i	−1.60051	+	0.924052i	−0.991386	+	0.130974i	$0.958189\pi$
$24$	−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	$-0.310405\pi$
$29$	6.04247			1.12206			0.561030	+	0.827796i	$0.310405\pi$
$30$	−1.93591	+	0.546395i	−0.353448	+	0.0997575i
$31$	−0.547062	+	0.947540i	−0.0982553	+	0.170183i	−0.910963	−	0.412489i	$-0.864660\pi$
$31$	−0.547062	+	0.947540i	−0.0982553	+	0.170183i	0.812707	+	0.582672i	$0.197993\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.92831	+	4.94216i	0.509754	+	0.860320i
$34$	3.42640			0.587622
$35$	−3.06606	−	0.201578i	−0.518259	−	0.0340729i
$36$	2.63701	+	1.43044i	0.439502	+	0.238407i
$37$	−5.31249	−	9.20151i	−0.873369	−	1.51272i	−0.858490	−	0.512830i	$-0.828597\pi$
$37$	−5.31249	−	9.20151i	−0.873369	−	1.51272i	−0.0148784	−	0.999889i	$-0.504736\pi$
$38$	4.30482	+	2.48539i	0.698334	+	0.403183i
$39$	−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	$-0.602502\pi$
$41$	−4.05294			−0.632963			−0.316482	+	0.948599i	$0.602502\pi$
$42$	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	$0.821369\pi$
$44$	2.34054	+	2.34986i	0.352850	+	0.354255i
$45$	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	−0.776028	−	0.630698i	$-0.782769\pi$
$47$	−4.23571	+	2.44549i	−0.617842	+	0.356711i	0.158187	+	0.987409i	$0.449435\pi$
$48$	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	0.615614	−	0.788048i	$-0.288908\pi$
$53$	1.75416	+	1.01277i	0.240952	+	0.139114i	−0.374662	+	0.927161i	$0.622241\pi$
$54$	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	−0.205296	−	0.978700i	$-0.565816\pi$
$59$	−8.87574	−	5.12441i	−1.15552	−	0.667142i	−0.950227	+	0.311558i	$0.899149\pi$
$60$	1.44115	+	1.40335i	0.186051	+	0.181172i
$61$	8.96386	−	5.17529i	1.14771	−	0.662628i	0.199378	−	0.979923i	$-0.436108\pi$
$61$	8.96386	−	5.17529i	1.14771	−	0.662628i	0.948327	+	0.317295i	$0.102774\pi$
$62$	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
$66$	2.81588	−	5.00708i	0.346611	−	0.616328i
$67$	−0.911110	+	1.57809i	−0.111310	+	0.192794i	−0.916299	−	0.400496i	$-0.868838\pi$
$67$	−0.911110	+	1.57809i	−0.111310	+	0.192794i	0.804989	+	0.593290i	$0.202171\pi$
$68$	−1.71320	−	2.96735i	−0.207756	−	0.359844i
$69$	3.77590	−	14.8799i	0.454565	−	1.79133i
$70$	1.35846	+	2.75608i	0.162367	+	0.329414i
$71$			13.9074i			1.65050i	0.564767	+	0.825251i	$0.308966\pi$
$71$			13.9074i			1.65050i	−0.564767	+	0.825251i	$0.691034\pi$
$72$	−0.0797091	−	2.99894i	−0.00939381	−	0.353429i
$73$	8.95771	+	5.17174i	1.04842	+	0.605306i	0.922207	−	0.386697i	$-0.126384\pi$
$73$	8.95771	+	5.17174i	1.04842	+	0.605306i	0.126214	+	0.992003i	$0.459717\pi$
$74$	−5.31249	+	9.20151i	−0.617565	+	1.06965i
$75$	−1.71782	−	6.08634i	−0.198356	−	0.702790i
$76$		−	4.97078i		−	0.570187i
$77$	6.61000	−	5.77129i	0.753280	−	0.657700i
$78$	−1.51936	+	5.98743i	−0.172034	+	0.677943i
$79$	8.06437	−	4.65597i	0.907312	−	0.523837i	0.0277469	−	0.999615i	$-0.491167\pi$
$79$	8.06437	−	4.65597i	0.907312	−	0.523837i	0.879565	+	0.475778i	$0.157833\pi$
$80$	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	$-0.610783\pi$
$83$	−6.21423			−0.682100			−0.341050	+	0.940045i	$0.610783\pi$
$84$	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
$88$	0.864767	−	3.20190i	0.0921845	−	0.341324i
$89$	−2.99218	+	1.72754i	−0.317170	+	0.183118i	−0.650131	−	0.759822i	$-0.725286\pi$
$89$	−2.99218	+	1.72754i	−0.317170	+	0.183118i	0.332960	+	0.942941i	$0.391953\pi$
$90$	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
$99$	−9.67125	−	2.33817i	−0.971997	−	0.234995i
$100$	−1.82562	−	3.16206i	−0.182562	−	0.316206i
$101$	2.11536	−	3.66391i	0.210486	−	0.364573i	−0.741381	−	0.671085i	$-0.765829\pi$
$101$	2.11536	−	3.66391i	0.210486	−	0.364573i	0.951867	+	0.306512i	$0.0991619\pi$
$102$	−4.14034	+	4.25185i	−0.409954	+	0.420995i
$103$	9.13694	+	15.8257i	0.900290	+	1.55935i	0.827118	+	0.562028i	$0.189979\pi$
$103$	9.13694	+	15.8257i	0.900290	+	1.55935i	0.0731719	+	0.997319i	$0.476688\pi$
$104$			3.56641i			0.349715i
$105$	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	$-0.176781\pi$
$107$	−0.328629	−	0.569202i	−0.0317698	−	0.0550269i	−0.881473	+	0.472234i	$0.843448\pi$
$108$	−4.96152	+	1.54380i	−0.477423	+	0.148552i
$109$	−8.44989	−	4.87855i	−0.809353	−	0.467280i	0.0373781	−	0.999301i	$-0.488099\pi$
$109$	−8.44989	−	4.87855i	−0.809353	−	0.467280i	−0.846731	+	0.532021i	$0.821433\pi$
$110$	2.72905	−	2.71823i	0.260204	−	0.259173i
$111$	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	$-0.168151\pi$
$114$	−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
$121$	−9.50435	−	5.53780i	−0.864032	−	0.503437i
$122$	−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	0.879843	+	0.475264i	$0.157647\pi$
$131$	9.74600	+	16.8806i	0.851512	+	1.47486i	−0.0283313	+	0.999599i	$0.509019\pi$
$132$	−5.74420	+	0.0649125i	−0.499968	+	0.00564991i
$133$	−13.1231	−	0.862777i	−1.13792	−	0.0748123i
$134$	1.82222			0.157416
$135$	−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	0.976333	+	0.216273i	$0.0693902\pi$
$137$	19.3338	+	11.1624i	1.65180	+	0.953666i	0.675465	+	0.737393i	$0.263943\pi$
$138$	−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
$143$	11.4193	+	3.08411i	0.954928	+	0.257906i
$144$	−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	$-0.225099\pi$
$149$	−2.22819	−	3.85935i	−0.182541	−	0.316170i	−0.942745	+	0.333514i	$0.891765\pi$
$150$	−4.41202	+	4.53084i	−0.360240	+	0.369942i
$151$	3.45781	+	1.99637i	0.281393	+	0.162462i	0.634054	−	0.773289i	$-0.281390\pi$
$151$	3.45781	+	1.99637i	0.281393	+	0.162462i	−0.352661	+	0.935751i	$0.614723\pi$
$152$	−4.30482	+	2.48539i	−0.349167	+	0.201592i
$153$	9.03545	+	4.90126i	0.730473	+	0.396243i
$154$	−8.30309	−	2.83878i	−0.669082	−	0.228756i
$155$		−	1.27068i		−	0.102063i
$156$	5.94495	−	1.67791i	0.475977	−	0.134340i
$157$	7.16830	−	12.4159i	0.572093	−	0.990894i	−0.424258	−	0.905541i	$-0.639465\pi$
$157$	7.16830	−	12.4159i	0.572093	−	0.990894i	0.996351	−	0.0853524i	$-0.0272016\pi$
$158$	−8.06437	−	4.65597i	−0.641567	−	0.370409i
$159$	−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	0.636965	−	0.770893i	$-0.280190\pi$
$163$	−4.45739	−	7.72043i	−0.349130	−	0.604711i	−0.986095	+	0.166182i	$0.946856\pi$
$164$	2.02647	−	3.50995i	0.158241	−	0.274081i
$165$	−5.81504	−	3.27027i	−0.452700	−	0.254590i
$166$	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	$0.488416\pi$
$168$	−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	$-0.0133442\pi$
$173$	6.09331	+	10.5539i	0.463266	+	0.802400i	−0.535856	+	0.844310i	$0.680011\pi$
$174$	10.1444	+	2.57422i	0.769041	+	0.195151i
$175$	−8.66487	+	4.27088i	−0.655003	+	0.322848i
$176$	−3.20531	+	0.852040i	−0.241610	+	0.0642250i
$177$	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	0.598213	−	0.801337i	$-0.295878\pi$
$179$	2.72052	+	1.57070i	0.203342	+	0.117399i	−0.394872	+	0.918736i	$0.629211\pi$
$180$	−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
$187$	8.01963	+	8.05156i	0.586454	+	0.588788i
$188$		−	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	−0.492905	−	0.870083i	$-0.664065\pi$
$191$	0.195655	−	0.112961i	0.0141571	−	0.00817359i	0.507062	+	0.861910i	$0.330732\pi$
$192$	−1.20836	+	1.24091i	−0.0872062	+	0.0895549i
$193$	10.4291	+	6.02127i	0.750706	+	0.433420i	0.825949	−	0.563745i	$-0.190640\pi$
$193$	10.4291	+	6.02127i	0.750706	+	0.433420i	−0.0752429	+	0.997165i	$0.523973\pi$
$194$	−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	$0.493852\pi$
$198$	2.81071	+	9.54463i	0.199749	+	0.678307i
$199$	2.12131	−	3.67422i	0.150376	−	0.260458i	−0.780990	−	0.624544i	$-0.785285\pi$
$199$	2.12131	−	3.67422i	0.150376	−	0.260458i	0.931366	+	0.364085i	$0.118618\pi$
$200$	−1.82562	+	3.16206i	−0.129091	+	0.223591i
$201$	−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
$220$	−3.71858	−	1.00431i	−0.250706	−	0.0677106i
$221$	−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	$-0.854989\pi$
$227$	−1.02424	+	1.77403i	−0.0679810	+	0.117746i	0.830031	+	0.557717i	$0.188322\pi$
$228$	6.16828	+	6.00651i	0.408505	+	0.397791i
$229$	6.97376	+	12.0789i	0.460839	+	0.798196i	0.999003	−	0.0446437i	$-0.0142153\pi$
$229$	6.97376	+	12.0789i	0.460839	+	0.798196i	−0.538164	+	0.842840i	$0.680882\pi$
$230$	−10.2934			−0.678727
$231$	−0.825647	+	15.1762i	−0.0543236	+	0.998523i
$232$	6.04247			0.396708
$233$	14.3840	+	24.9138i	0.942328	+	1.63216i	0.761015	+	0.648735i	$0.224702\pi$
$233$	14.3840	+	24.9138i	0.942328	+	1.63216i	0.181314	+	0.983425i	$0.441965\pi$
$234$	−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	$-0.664225\pi$
$239$	−15.2538			−0.986685			−0.493342	+	0.869835i	$0.664225\pi$
$240$	−1.93591	+	0.546395i	−0.124963	+	0.0352696i
$241$	−7.64351	−	4.41298i	−0.492362	−	0.284265i	0.233192	−	0.972431i	$-0.425083\pi$
$241$	−7.64351	−	4.41298i	−0.492362	−	0.284265i	−0.725554	+	0.688166i	$0.758416\pi$
$242$	−0.0436998	+	10.9999i	−0.00280913	+	0.707101i
$243$	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	$0.0295264\pi$
$251$			2.93497i			0.185254i	−0.995701	+	0.0926269i	$0.970474\pi$
$252$	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	0.0170691	−	0.999854i	$-0.494566\pi$
$257$	14.2919	−	8.25142i	0.891503	−	0.514709i	0.874434	+	0.485145i	$0.161233\pi$
$258$	−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	$-0.677398\pi$
$263$	7.63064	−	13.2167i	0.470525	−	0.814974i	0.999432	+	0.0337062i	$0.0107311\pi$
$264$	2.92831	+	4.94216i	0.180225	+	0.304169i
$265$	−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	$-0.262515\pi$
$269$	6.26825	+	3.61898i	0.382182	+	0.220653i	−0.296585	+	0.955006i	$0.595848\pi$
$270$	1.79291	+	5.76214i	0.109113	+	0.350672i
$271$	−20.4336	+	11.7973i	−1.24125	+	0.716637i	−0.969349	−	0.245687i	$-0.920986\pi$
$271$	−20.4336	+	11.7973i	−1.24125	+	0.716637i	−0.271903	+	0.962325i	$0.587653\pi$
$272$	3.42640			0.207756
$273$	−3.39790	−	15.9862i	−0.205650	−	0.967529i
$274$		−	22.3247i		−	1.34869i
$275$	8.54587	+	8.57989i	0.515335	+	0.517387i
$276$	10.9984	+	10.7100i	0.662027	+	0.644665i
$277$	−17.1573	−	9.90578i	−1.03088	−	0.595181i	−0.113646	−	0.993521i	$-0.536253\pi$
$277$	−17.1573	−	9.90578i	−1.03088	−	0.595181i	−0.917238	+	0.398340i	$0.869586\pi$
$278$	−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	$0.309419\pi$
$282$	−8.15291	+	2.30109i	−0.485499	+	0.137028i
$283$	1.62416	+	0.937708i	0.0965462	+	0.0557410i	0.547496	−	0.836808i	$-0.315581\pi$
$283$	1.62416	+	0.937708i	0.0965462	+	0.0557410i	−0.450950	+	0.892549i	$0.648915\pi$
$284$	−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	$-0.330353\pi$
$293$	17.3941			1.01618			0.508088	+	0.861305i	$0.330353\pi$
$294$	1.73730	+	11.9992i	0.101321	+	0.699810i
$295$	11.9026			0.692998
$296$	−5.31249	−	9.20151i	−0.308782	−	0.534827i
$297$	14.5878	−	9.17578i	0.846472	−	0.532432i
$298$	−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	$0.795304\pi$
$308$	1.69309	+	8.61008i	0.0964725	+	0.490605i
$309$	−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	$-0.628433\pi$
$311$	−24.4322	−	14.1059i	−1.38542	−	0.799873i	−0.992795	+	0.119826i	$0.961766\pi$
$312$	−4.42558	−	4.30952i	−0.250549	−	0.243979i
$313$	−2.99806	−	5.19278i	−0.169460	−	0.293513i	0.768770	−	0.639525i	$-0.220869\pi$
$313$	−2.99806	−	5.19278i	−0.169460	−	0.293513i	−0.938230	+	0.346012i	$0.887536\pi$
$314$	−14.3366			−0.809061
$315$	−0.360127	+	9.21101i	−0.0202909	+	0.518982i
$316$			9.31193i			0.523837i
$317$	−8.91377	+	5.14637i	−0.500647	+	0.289049i	−0.728981	−	0.684534i	$-0.760006\pi$
$317$	−8.91377	+	5.14637i	−0.500647	+	0.289049i	0.228333	+	0.973583i	$0.426672\pi$
$318$	2.51350	+	2.44758i	0.140950	+	0.137253i
$319$	5.22533	−	19.3474i	0.292563	−	1.08325i
$320$	−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
$330$	0.0753871	+	6.67111i	0.00414992	+	0.367232i
$331$	6.54105	+	11.3294i	0.359529	+	0.622722i	0.987882	−	0.155206i	$-0.0496042\pi$
$331$	6.54105	+	11.3294i	0.359529	+	0.622722i	−0.628354	+	0.777928i	$0.716271\pi$
$332$	3.10711	−	5.38168i	0.170525	−	0.295358i
$333$	−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
$341$	2.56085	+	2.57104i	0.138678	+	0.139230i
$342$	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	$-0.712505\pi$
$347$	6.90245	−	11.9554i	0.370543	−	0.641799i	0.989649	+	0.143508i	$0.0458384\pi$
$348$	−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
$352$	2.34054	+	2.34986i	0.124751	+	0.125248i
$353$	−15.3515	−	8.86320i	−0.817079	−	0.471741i	0.0323294	−	0.999477i	$-0.489707\pi$
$353$	−15.3515	−	8.86320i	−0.817079	−	0.471741i	−0.849408	+	0.527737i	$0.823041\pi$
$354$	−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	0.998543	+	0.0539641i	$0.0171857\pi$
$359$	10.3453	+	17.9186i	0.546006	+	0.945710i	−0.452537	+	0.891746i	$0.649481\pi$
$360$	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
$363$	18.3566	−	5.10235i	0.963473	−	0.267804i
$364$	−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	−0.778431	−	0.627731i	$-0.783984\pi$
$367$	2.95817	−	5.12371i	0.154415	−	0.267455i	0.932846	+	0.360275i	$0.117317\pi$
$368$	7.67576	+	4.43160i	0.400126	+	0.231013i
$369$	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	$-0.594922\pi$
$373$	7.47599	−	4.31626i	0.387092	−	0.223488i	0.680899	+	0.732377i	$0.261589\pi$
$374$	2.96304	−	10.9710i	0.153215	−	0.567296i
$375$	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	−0.811591	−	0.584226i	$-0.801398\pi$
$383$	−13.9230	+	8.03845i	−0.711433	+	0.410746i	0.100159	+	0.994971i	$0.468065\pi$
$384$	1.67884	+	0.426020i	0.0856730	+	0.0217403i
$385$	−3.29687	+	9.64292i	−0.168024	+	0.491449i
$386$		−	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	−0.0262868	−	0.999654i	$-0.508368\pi$
$389$	−17.8525	−	10.3071i	−0.905156	−	0.522592i	−0.878870	+	0.477062i	$0.841702\pi$
$390$	−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
$396$	6.86053	−	7.20646i	0.344755	−	0.362138i
$397$	2.61119	+	4.52272i	0.131052	+	0.226989i	0.924082	−	0.382193i	$-0.124831\pi$
$397$	2.61119	+	4.52272i	0.131052	+	0.226989i	−0.793030	+	0.609182i	$0.791498\pi$
$398$	−4.24262			−0.212663
$399$	16.9281	−	15.2420i	0.847467	−	0.763056i
$400$	3.65123			0.182562
$401$	1.61502	−	0.932434i	0.0806504	−	0.0465635i	−0.459132	−	0.888368i	$-0.651840\pi$
$401$	1.61502	−	0.932434i	0.0806504	−	0.0465635i	0.539783	+	0.841804i	$0.318506\pi$
$402$	−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	$-0.446842\pi$
$409$	−12.2281	−	7.05988i	−0.604639	−	0.349089i	−0.770864	+	0.636999i	$0.780175\pi$
$410$	−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
$418$	11.6806	−	11.6343i	0.571319	−	0.569054i
$419$		−	20.8437i		−	1.01828i	−0.860683	−	0.509141i	$-0.829963\pi$
$419$		−	20.8437i		−	1.01828i	0.860683	−	0.509141i	$-0.170037\pi$
$420$	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
$429$	−17.6258	+	10.4436i	−0.850980	+	0.504220i
$430$	−4.05294	+	7.01990i	−0.195450	+	0.338530i
$431$	19.1899	−	33.2379i	0.924344	−	1.60101i	0.131732	−	0.991285i	$-0.457946\pi$
$431$	19.1899	−	33.2379i	0.924344	−	1.60101i	0.792613	−	0.609726i	$-0.208720\pi$
$432$	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	$-0.522152\pi$
$439$	15.9159	−	9.18904i	0.759624	−	0.438569i	0.829161	+	0.559010i	$0.188819\pi$
$440$	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	−0.520509	−	0.853856i	$-0.674258\pi$
$443$	−0.869330	+	0.501908i	−0.0413031	+	0.0238464i	0.479206	+	0.877702i	$0.340925\pi$
$444$	−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	$0.215902\pi$
$449$			26.5910i			1.25491i	−0.778655	+	0.627453i	$0.784098\pi$
$450$	−0.291036	−	10.9498i	−0.0137196	−	0.516180i
$451$	−3.50485	+	12.9771i	−0.165037	+	0.611069i
$452$	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	$-0.582374\pi$
$457$	9.69107	−	5.59514i	0.453329	−	0.261730i	0.709235	+	0.704972i	$0.249040\pi$
$458$	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	$-0.510266\pi$
$461$	−1.38465			−0.0644895			−0.0322448	+	0.999480i	$0.510266\pi$
$462$	13.5558	−	6.87309i	0.630674	−	0.319765i
$463$	−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	0.181053	−	0.983473i	$-0.442049\pi$
$467$	24.2746	−	14.0149i	1.12329	−	0.648533i	0.942239	+	0.334940i	$0.108716\pi$
$468$	−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
$473$	22.3481	+	6.03575i	1.02756	+	0.277524i
$474$	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	−0.0932611	+	0.995642i	$0.529729\pi$
$479$	−19.8918	+	34.4537i	−0.908882	+	1.57423i	−0.815620	+	0.578587i	$0.803604\pi$
$480$	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	−0.946080	−	0.323934i	$-0.894994\pi$
$487$	−4.24821	+	7.35811i	−0.192505	+	0.333428i	0.753575	+	0.657362i	$0.228328\pi$
$488$	8.96386	−	5.17529i	0.405775	−	0.234274i
$489$	14.9665	+	3.79788i	0.676809	+	0.171746i
$490$	−1.06435	+	8.05958i	−0.0480825	+	0.364095i
$491$	20.7951			0.938470			0.469235	−	0.883073i	$-0.344530\pi$
$491$	20.7951			0.938470			0.469235	+	0.883073i	$0.344530\pi$
$492$	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
$495$	11.0848	−	3.26426i	0.498225	−	0.146718i
$496$	1.09412			0.0491277
$497$	−20.4486	+	30.5902i	−0.917244	+	1.37216i
$498$	−10.4327	−	2.64739i	−0.467500	−	0.118632i
$499$	−0.147787	−	0.255975i	−0.00661586	−	0.0114590i	0.862699	−	0.505719i	$-0.168773\pi$
$499$	−0.147787	−	0.255975i	−0.00661586	−	0.0114590i	−0.869314	+	0.494260i	$0.835439\pi$
$500$	8.70116	+	5.02362i	0.389128	+	0.224663i
$501$	−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	$-0.449297\pi$
$503$	7.11469			0.317228			0.158614	+	0.987341i	$0.449297\pi$
$504$	4.23414	−	6.71357i	0.188604	−	0.299046i
$505$			4.91341i			0.218644i
$506$	20.8273	−	20.7447i	0.925886	−	0.922215i
$507$	−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	−0.476181	−	0.879347i	$-0.657979\pi$
$509$	1.06636	−	0.615664i	0.0472657	−	0.0272888i	0.523447	+	0.852058i	$0.324646\pi$
$510$	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	0.982068	+	0.188526i	$0.0603711\pi$
$521$	37.3509	+	21.5645i	1.63637	+	0.944759i	0.654303	+	0.756233i	$0.272962\pi$
$522$	−15.4524	+	9.47762i	−0.676335	+	0.414824i
$523$	3.39607	−	1.96072i	0.148500	−	0.0857364i	−0.423909	−	0.905705i	$-0.639342\pi$
$523$	3.39607	−	1.96072i	0.148500	−	0.0857364i	0.572409	+	0.819968i	$0.306009\pi$
$524$	−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
$528$	2.81588	−	5.00708i	0.122546	−	0.217905i
$529$	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
$539$	23.0249	−	2.97538i	0.991754	−	0.128159i
$540$	4.09370	−	4.43378i	0.176165	−	0.190799i
$541$	−9.87581	+	5.70180i	−0.424594	+	0.245140i	−0.697041	−	0.717031i	$-0.745500\pi$
$541$	−9.87581	+	5.70180i	−0.424594	+	0.245140i	0.272447	+	0.962171i	$0.412167\pi$
$542$	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
$550$	3.15747	−	11.6909i	0.134635	−	0.498501i
$551$	−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	0.355062	+	0.934843i	$0.384460\pi$
$557$	−14.9173	+	25.8375i	−0.632067	+	1.09477i	−0.987128	+	0.159929i	$0.948873\pi$
$558$	−0.0872117	−	3.28122i	−0.00369197	−	0.138905i
$559$	−24.8922			−1.05283
$560$	1.35846	+	2.75608i	0.0574054	+	0.116466i
$561$	−19.6819	+	0.222416i	−0.830970	+	0.00939041i
$562$	−9.44751	−	16.3636i	−0.398519	−	0.690255i
$563$	−15.1418	+	26.2264i	−0.638152	+	1.10531i	0.347686	+	0.937611i	$0.386967\pi$
$563$	−15.1418	+	26.2264i	−0.638152	+	1.10531i	−0.985838	+	0.167700i	$0.946366\pi$
$564$	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	$-0.210630\pi$
$569$	−3.28407	−	5.68818i	−0.137675	−	0.238461i	−0.926616	+	0.376008i	$0.877296\pi$
$570$	6.97576	−	7.16363i	0.292182	−	0.300051i
$571$	25.3943	+	14.6614i	1.06272	+	0.613561i	0.926183	−	0.377074i	$-0.123070\pi$
$571$	25.3943	+	14.6614i	1.06272	+	0.613561i	0.136536	+	0.990635i	$0.456403\pi$
$572$	−8.38056	+	8.34733i	−0.350409	+	0.349020i
$573$	−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	−0.935607	−	0.353043i	$-0.885147\pi$
$577$	−3.89280	+	6.74253i	−0.162060	+	0.280695i	0.773548	+	0.633738i	$0.218480\pi$
$578$	2.62990	−	4.55513i	0.109390	−	0.189468i
$579$	−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
$583$	4.75972	−	4.74084i	0.197127	−	0.196346i
$584$	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	$-0.940618\pi$
$587$		−	8.98728i		−	0.370945i	0.982649	−	0.185472i	$-0.0593815\pi$
$588$	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	$-0.177284\pi$
$593$	−0.812081	−	1.40657i	−0.0333482	−	0.0577608i	−0.882218	+	0.470842i	$0.843950\pi$
$594$	−15.2404	−	8.04555i	−0.625320	−	0.330113i
$595$	5.85093	−	8.75273i	0.239865	−	0.358827i
$596$	4.45639			0.182541
$597$	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	0.168844	−	0.985643i	$-0.445997\pi$
$599$	−14.6927	−	8.48281i	−0.600326	−	0.346598i	−0.769170	+	0.639045i	$0.779330\pi$
$600$	−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
$605$	12.7749	+	0.0507514i	0.519374	+	0.00206334i
$606$	5.11226	−	5.24994i	0.207671	−	0.213264i
$607$	−28.8610	+	16.6629i	−1.17143	+	0.676328i	−0.954017	−	0.299751i	$-0.903096\pi$
$607$	−28.8610	+	16.6629i	−1.17143	+	0.676328i	−0.217416	+	0.976079i	$0.569763\pi$
$608$		−	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	$-0.0435348\pi$
$613$	33.8680	+	19.5537i	1.36792	+	0.789767i	0.377255	+	0.926109i	$0.376868\pi$
$614$	18.1984	−	10.5068i	0.734426	−	0.424021i
$615$	−2.00525	+	7.90221i	−0.0808597	+	0.318648i
$616$	6.61000	−	5.77129i	0.266325	−	0.232532i
$617$			37.9007i			1.52583i	0.646501	+	0.762913i	$0.276232\pi$
$617$			37.9007i			1.52583i	−0.646501	+	0.762913i	$0.723768\pi$
$618$	8.59743	+	30.4613i	0.345839	+	1.22533i
$619$	−10.2068	+	17.6788i	−0.410247	+	0.710569i	−0.994917	−	0.100702i	$-0.967891\pi$
$619$	−10.2068	+	17.6788i	−0.410247	+	0.710569i	0.584669	+	0.811272i	$0.301224\pi$
$620$	1.10044	+	0.635339i	0.0441947	+	0.0255158i
$621$	−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
$627$	−24.8891	−	13.9971i	−0.993974	−	0.558991i
$628$	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	0.723847	−	0.689961i	$-0.242372\pi$
$641$	12.3614	+	7.13687i	0.488247	+	0.281890i	−0.235600	+	0.971850i	$0.575705\pi$
$642$	−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	0.0944013	−	0.995534i	$-0.469906\pi$
$647$	−18.3282	−	10.5818i	−0.720556	−	0.416013i	−0.814957	+	0.579521i	$0.803240\pi$
$648$	−8.98729	+	0.478086i	−0.353054	+	0.0187810i
$649$	−24.0833	+	23.9878i	−0.945353	+	0.941605i
$650$			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	0.113697	−	0.993515i	$-0.463731\pi$
$653$	26.3449	−	15.2102i	1.03096	−	0.595222i	0.917258	+	0.398293i	$0.130397\pi$
$654$	−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	$-0.0647351\pi$
$659$	50.2839			1.95878			0.979391	+	0.201972i	$0.0647351\pi$
$660$	5.73966	−	3.40084i	0.223416	−	0.132378i
$661$	−14.1421	+	24.4948i	−0.550062	+	0.952736i	0.448207	+	0.893930i	$0.352063\pi$
$661$	−14.1421	+	24.4948i	−0.550062	+	0.952736i	−0.998269	+	0.0588062i	$0.981271\pi$
$662$	6.54105	−	11.3294i	0.254225	−	0.440331i
$663$	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	$-0.00932903\pi$
$677$	12.3437	+	21.3799i	0.474407	+	0.821698i	−0.525163	+	0.851002i	$0.675996\pi$
$678$	4.56519	−	17.9903i	0.175325	−	0.690914i
$679$	11.4595	+	7.66033i	0.439776	+	0.293976i
$680$		−	3.97930i		−	0.152599i
$681$	−0.963758	−	3.41466i	−0.0369313	−	0.130850i
$682$	0.946164	−	3.50328i	0.0362305	−	0.134148i
$683$	−18.1930	−	10.5037i	−0.696135	−	0.401914i	0.109771	−	0.993957i	$-0.464988\pi$
$683$	−18.1930	−	10.5037i	−0.696135	−	0.401914i	−0.805906	+	0.592043i	$0.798322\pi$
$684$	−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	−0.986517	−	0.163661i	$-0.947670\pi$
$691$	−16.6920	−	28.9114i	−0.634993	−	1.09984i	0.351523	−	0.936179i	$-0.385664\pi$
$692$	−12.1866			−0.463266
$693$	−17.8346	−	19.3630i	−0.677482	−	0.735539i
$694$	−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	$-0.667174\pi$
$701$	−26.5494			−1.00276			−0.501379	+	0.865228i	$0.667174\pi$
$702$	18.0771	+	4.07922i	0.682274	+	0.153960i
$703$	45.7387	+	26.4072i	1.72507	+	0.995968i
$704$	0.864767	−	3.20190i	0.0325922	−	0.120676i
$705$	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	0.979690	−	0.200519i	$-0.0642629\pi$
$709$	8.41921	+	14.5825i	0.316190	+	0.547657i	−0.663500	+	0.748177i	$0.730930\pi$
$710$	−8.07577	+	13.9876i	−0.303078	+	0.524947i
$711$	−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	−0.000796544	−	1.00000i	$-0.500254\pi$
$719$	23.1897	−	13.3886i	0.864830	−	0.499310i	0.865627	+	0.500690i	$0.166920\pi$
$720$	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
$726$	−13.5971	−	13.3461i	−0.504635	−	0.495322i
$727$	−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	$-0.633668\pi$
$733$	4.85268	−	2.80169i	0.179238	−	0.103483i	0.586934	+	0.809634i	$0.300335\pi$
$734$	−5.91635			−0.218376
$735$	13.9355	−	2.01764i	0.514019	−	0.0744218i
$736$		−	8.86320i		−	0.326702i
$737$	4.26499	+	4.28197i	0.157103	+	0.157728i
$738$	10.3646	−	6.35704i	0.381527	−	0.234006i
$739$	11.0876	+	6.40146i	0.407866	+	0.235481i	0.689872	−	0.723931i	$-0.257667\pi$
$739$	11.0876	+	6.40146i	0.407866	+	0.235481i	−0.282007	+	0.959412i	$0.591000\pi$
$740$	−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	$0.279744\pi$
$744$	−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	0.996475	−	0.0838942i	$-0.0267358\pi$
$751$	11.6628	+	20.2006i	0.425583	+	0.737131i	−0.570892	+	0.821025i	$0.693402\pi$
$752$	4.23571	+	2.44549i	0.154460	+	0.0891778i
$753$	−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
$759$	−44.3787	−	24.9577i	−1.61085	−	0.905908i
$760$	2.88644	−	4.99947i	0.104702	−	0.181350i
$761$	−20.6464	−	35.7605i	−0.748430	−	1.29632i	−0.948575	−	0.316552i	$-0.897475\pi$
$761$	−20.6464	−	35.7605i	−0.748430	−	1.29632i	0.200145	−	0.979766i	$-0.435859\pi$
$762$	2.20696	−	8.69708i	0.0799497	−	0.315062i
$763$	−11.4130	−	23.1549i	−0.413177	−	0.838265i
$764$			0.225923i			0.00817359i
$765$	−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	$-0.0631926\pi$
$770$	9.99944	−	1.96629i	0.360355	−	0.0708602i
$771$	−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	$-0.332516\pi$
$773$	0.123624	+	0.0713746i	0.00444646	+	0.00256717i	−0.497775	+	0.867306i	$0.665850\pi$
$774$	−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
$781$	44.5300	+	12.0266i	1.59341	+	0.430347i
$782$	−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	$-0.254962\pi$
$787$	11.8429	+	6.83752i	0.422155	+	0.243731i	−0.273844	+	0.961774i	$0.588295\pi$
$788$	−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
$792$	−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
$795$	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	$0.0372730\pi$
$797$			6.59645i			0.233658i	−0.993152	+	0.116829i	$0.962727\pi$
$798$	−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
$803$	24.3057	−	24.2094i	0.857730	−	0.854330i
$804$	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	$-0.961626\pi$
$809$	−11.1559	+	19.3225i	−0.392220	+	0.679345i	0.600522	+	0.799608i	$0.294959\pi$
$810$	−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
$814$	24.8683	+	24.9673i	0.871632	+	0.875102i
$815$	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	$-0.211163\pi$
$821$	−3.99233	−	6.91491i	−0.139333	−	0.241332i	−0.927244	+	0.374457i	$0.877829\pi$
$822$	27.7030	+	26.9764i	0.966252	+	0.940911i
$823$	14.0547	−	24.3434i	0.489914	−	0.848557i	−0.510018	−	0.860164i	$-0.670361\pi$
$823$	14.0547	−	24.3434i	0.489914	−	0.848557i	0.999933	+	0.0116069i	$0.00369468\pi$
$824$	9.13694	+	15.8257i	0.318301	+	0.551313i
$825$	−20.9734	+	0.237010i	−0.730200	+	0.00825165i
$826$	−15.0693	+	22.5430i	−0.524327	+	0.784371i
$827$	1.47055			0.0511361			0.0255680	−	0.999673i	$-0.491861\pi$
$827$	1.47055			0.0511361			0.0255680	+	0.999673i	$0.491861\pi$
$828$	−26.5802	+	0.706478i	−0.923726	+	0.0245518i
$829$	25.2928	−	43.8085i	0.878456	−	1.52153i	0.0254218	−	0.999677i	$-0.491907\pi$
$829$	25.2928	−	43.8085i	0.878456	−	1.52153i	0.853035	−	0.521854i	$-0.174760\pi$
$830$	−6.25009	−	3.60849i	−0.216944	−	0.125253i
$831$	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
$836$	−15.9159	−	4.29857i	−0.550465	−	0.148669i
$837$	−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	$0.109389\pi$
$839$			19.5188i			0.673862i	−0.941529	+	0.336931i	$0.890611\pi$
$840$	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
$847$	−12.7630	−	26.1554i	−0.438542	−	0.898711i
$848$		−	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	$-0.994467\pi$
$857$	−14.1944	+	24.5854i	−0.484871	+	0.839821i	0.514978	+	0.857203i	$0.327800\pi$
$858$	17.8573	+	10.0426i	0.609637	+	0.342848i
$859$	18.7050	+	32.3981i	0.638208	+	1.10541i	0.985826	+	0.167772i	$0.0536572\pi$
$859$	18.7050	+	32.3981i	0.638208	+	1.10541i	−0.347618	+	0.937636i	$0.613009\pi$
$860$	8.10589			0.276408
$861$	18.1671	−	3.86145i	0.619132	−	0.131598i
$862$	−38.3798			−1.30722
$863$	22.9893	−	13.2729i	0.782565	−	0.451814i	−0.0547734	−	0.998499i	$-0.517444\pi$
$863$	22.9893	−	13.2729i	0.782565	−	0.451814i	0.837339	+	0.546685i	$0.184110\pi$
$864$	−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	$-0.722595\pi$
$877$	−8.96606	+	5.17656i	−0.302762	+	0.174800i	0.340921	+	0.940092i	$0.389261\pi$
$878$	−15.9159	−	9.18904i	−0.537135	−	0.310115i
$879$	−21.0185	+	21.5845i	−0.708935	+	0.728028i
$880$	2.72905	−	2.71823i	0.0919962	−	0.0916314i
$881$			39.0911i			1.31701i	0.752576	+	0.658506i	$0.228811\pi$
$881$			39.0911i			1.31701i	−0.752576	+	0.658506i	$0.771189\pi$
$882$	−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	$-0.216571\pi$
$887$	−4.65016	−	8.05432i	−0.156137	−	0.270438i	−0.933473	+	0.358649i	$0.883238\pi$
$888$	17.8377	+	4.52646i	0.598593	+	0.151898i
$889$	7.61697	−	11.3947i	0.255465	−	0.382164i
$890$	−4.01260			−0.134503
$891$	−6.24114	+	29.1899i	−0.209086	+	0.977897i
$892$	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	−0.973261	−	0.229703i	$-0.926225\pi$
$907$	−8.66455	+	15.0074i	−0.287702	+	0.498314i	0.685559	+	0.728017i	$0.259558\pi$
$908$	−1.02424	−	1.77403i	−0.0339905	−	0.0588732i
$909$	−11.1565	−	6.05180i	−0.370037	−	0.200725i
$910$	−9.82929	+	4.84482i	−0.325838	+	0.160604i
$911$		−	41.9798i		−	1.39085i	−0.718598	−	0.695426i	$-0.755216\pi$
$911$		−	41.9798i		−	1.39085i	0.718598	−	0.695426i	$-0.244784\pi$
$912$	−8.28594	+	2.33863i	−0.274375	+	0.0774399i
$913$	−5.37386	+	19.8973i	−0.177849	+	0.658506i
$914$	−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	$-0.654346\pi$
$919$	2.03187	−	1.17310i	0.0670252	−	0.0386970i	0.533138	+	0.846028i	$0.321013\pi$
$920$	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
$924$	−12.7302	−	8.30315i	−0.418792	−	0.273154i
$925$	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	−0.875302	−	0.483577i	$-0.839337\pi$
$929$	−27.2536	+	15.7349i	−0.894163	+	0.516245i	−0.0188609	+	0.999822i	$0.506004\pi$
$930$	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
$935$	−12.7413	−	3.44117i	−0.416686	−	0.112538i
$936$	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	−0.122956	+	0.992412i	$0.539238\pi$
$941$	−28.2503	+	48.9309i	−0.920932	+	1.59510i	−0.797976	+	0.602689i	$0.794096\pi$
$942$	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	−0.835777	−	0.549069i	$-0.814982\pi$
$947$	−23.9465	+	13.8255i	−0.778158	+	0.449270i	0.0576190	+	0.998339i	$0.481649\pi$
$948$	−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	$-0.297372\pi$
$953$	36.7018			1.18889			0.594444	+	0.804137i	$0.297372\pi$
$954$	−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
$957$	17.6943	+	29.8629i	0.571974	+	0.965330i
$958$	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	$0.931526\pi$
$968$	−9.50435	−	5.53780i	−0.305482	−	0.177992i
$969$	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	−0.413534	−	0.910489i	$-0.635706\pi$
$971$	5.24145	−	3.02615i	0.168206	−	0.0971139i	0.581740	+	0.813375i	$0.302372\pi$
$972$	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	0.462478	−	0.886631i	$-0.346960\pi$
$977$	−2.31699	−	1.33771i	−0.0741269	−	0.0427972i	−0.536605	+	0.843833i	$0.680294\pi$
$978$	−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	0.452217	−	0.891908i	$-0.350633\pi$
$983$	−2.94995	−	1.70316i	−0.0940890	−	0.0543223i	−0.546306	+	0.837586i	$0.683967\pi$
$984$	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
$990$	−8.36933	−	7.96758i	−0.265995	−	0.253226i
$991$	24.7571	−	42.8805i	0.786434	−	1.36214i	−0.141705	−	0.989909i	$-0.545259\pi$
$991$	24.7571	−	42.8805i	0.786434	−	1.36214i	0.928139	−	0.372234i	$-0.121408\pi$
$992$	−0.547062	−	0.947540i	−0.0173692	−	0.0300844i
$993$	−21.9628	−	5.57324i	−0.696967	−	0.176861i
$994$	36.7162	+	2.41390i	1.16457	+	0.0765643i
$995$			4.92723i			0.156204i
$996$	2.92364	+	10.3587i	0.0926392	+	0.328227i
$997$	−11.3409	−	6.54767i	−0.359170	−	0.207367i	0.309547	−	0.950884i	$-0.399823\pi$
$997$	−11.3409	−	6.54767i	−0.359170	−	0.207367i	−0.668716	+	0.743518i	$0.733156\pi$
$998$	−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.e.263.3	yes	24
3.2	odd	2		462.2.n.f.263.5	yes	24
7.2	even	3	inner	462.2.n.e.65.5	yes	24
11.10	odd	2		462.2.n.f.263.3	yes	24
21.2	odd	6		462.2.n.f.65.3	yes	24
33.32	even	2	inner	462.2.n.e.263.5	yes	24
77.65	odd	6		462.2.n.f.65.5	yes	24
231.65	even	6	inner	462.2.n.e.65.3	✓	24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.20836 + 1.24091i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.00577 + 0.580683i) q^{5} +(1.67884 + 0.426020i) q^{6} +(2.19957 + 1.47034i) q^{7} +1.00000 q^{8} +(-0.0797091 - 2.99894i) q^{9} +O(q^{10})\)	\(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} +(0.864767 - 3.20190i) 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} +(2.92831 + 4.94216i) 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} +(2.34054 + 2.34986i) 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} +(2.81588 - 5.00708i) 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} +(6.61000 - 5.77129i) 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} +(0.864767 - 3.20190i) 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} +(-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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