LMFDB - Embedded newform 429.2.bm.a.17.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(17,429)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 27, 5]))

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

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

chi := DirichletCharacter("429.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bm (of order $30$, degree $8$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			17.13
Character	$\chi$	$=$	429.17
Dual form			429.2.bm.a.101.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.358071 + 1.68459i) q^{2} +(0.834638 + 1.51769i) q^{3} +(-0.882537 - 0.392931i) q^{4} +(-0.368818 + 1.13510i) q^{5} +(-2.85554 + 0.862583i) q^{6} +(1.13679 + 0.506130i) q^{7} +(-1.04666 + 1.44060i) q^{8} +(-1.60676 + 2.53344i) q^{9} +O(q^{10})$	\(q+(-0.358071 + 1.68459i) q^{2} +(0.834638 + 1.51769i) q^{3} +(-0.882537 - 0.392931i) q^{4} +(-0.368818 + 1.13510i) q^{5} +(-2.85554 + 0.862583i) q^{6} +(1.13679 + 0.506130i) q^{7} +(-1.04666 + 1.44060i) q^{8} +(-1.60676 + 2.53344i) q^{9} +(-1.78012 - 1.02775i) q^{10} +(3.13290 + 1.08855i) q^{11} +(-0.140253 - 1.66737i) q^{12} +(-0.202956 - 3.59983i) q^{13} +(-1.25967 + 1.73379i) q^{14} +(-2.03057 + 0.387651i) q^{15} +(-3.34488 - 3.71487i) q^{16} +(0.684027 - 0.145394i) q^{17} +(-3.69248 - 3.61388i) q^{18} +(-0.0731003 + 0.695503i) q^{19} +(0.771513 - 0.856852i) q^{20} +(0.180658 + 2.14772i) q^{21} +(-2.95556 + 4.88787i) q^{22} +(-2.00409 - 1.15706i) q^{23} +(-3.05997 - 0.386120i) q^{24} +(2.89265 + 2.10163i) q^{25} +(6.13692 + 0.947098i) q^{26} +(-5.18604 - 0.324050i) q^{27} +(-0.804382 - 0.893357i) q^{28} +(-0.322296 - 3.06644i) q^{29} +(0.0740524 - 3.55948i) q^{30} +(-0.786706 + 0.255616i) q^{31} +(4.37150 - 2.52389i) q^{32} +(0.962753 + 5.66331i) q^{33} +1.20437i q^{34} +(-0.993778 + 1.10370i) q^{35} +(2.41349 - 1.60451i) q^{36} +(0.496886 - 0.0522249i) q^{37} +(-1.14546 - 0.372183i) q^{38} +(5.29403 - 3.31258i) q^{39} +(-1.24921 - 1.71939i) q^{40} +(-1.76860 - 3.97234i) q^{41} +(-3.68272 - 0.464702i) q^{42} +(9.76151 - 5.63581i) q^{43} +(-2.33717 - 2.19170i) q^{44} +(-2.28312 - 2.75822i) q^{45} +(2.66678 - 2.96175i) q^{46} +(4.69563 + 3.41158i) q^{47} +(2.84625 - 8.17706i) q^{48} +(-3.64780 - 4.05129i) q^{49} +(-4.57616 + 4.12039i) q^{50} +(0.791579 + 0.916788i) q^{51} +(-1.23537 + 3.25673i) q^{52} +(-8.86976 + 2.88196i) q^{53} +(2.40286 - 8.62031i) q^{54} +(-2.39109 + 3.15469i) q^{55} +(-1.91896 + 1.10791i) q^{56} +(-1.11657 + 0.469550i) q^{57} +(5.28110 + 0.555066i) q^{58} +(4.87846 + 2.17203i) q^{59} +(1.94437 + 0.455755i) q^{60} +(1.29996 + 6.11582i) q^{61} +(-0.148912 - 1.41680i) q^{62} +(-3.10879 + 2.06676i) q^{63} +(-0.403051 - 1.24046i) q^{64} +(4.16104 + 1.09731i) q^{65} +(-9.88509 - 0.406021i) q^{66} +(6.76153 + 3.90377i) q^{67} +(-0.660809 - 0.140459i) q^{68} +(0.0833693 - 4.00731i) q^{69} +(-1.50344 - 2.06931i) q^{70} +(-1.06023 + 0.225359i) q^{71} +(-1.96796 - 4.96635i) q^{72} +(7.27022 - 5.28212i) q^{73} +(-0.0899429 + 0.855750i) q^{74} +(-0.775308 + 6.14424i) q^{75} +(0.337798 - 0.585083i) q^{76} +(3.01049 + 2.82311i) q^{77} +(3.68471 + 10.1044i) q^{78} +(-6.44207 + 2.09316i) q^{79} +(5.45042 - 2.42668i) q^{80} +(-3.83666 - 8.14126i) q^{81} +(7.32505 - 1.55699i) q^{82} +(7.61540 + 2.47439i) q^{83} +(0.684469 - 1.96643i) q^{84} +(-0.0872435 + 0.830066i) q^{85} +(5.99872 + 18.4622i) q^{86} +(4.38490 - 3.04852i) q^{87} +(-4.84725 + 3.37392i) q^{88} +(-7.39533 + 12.8091i) q^{89} +(5.46398 - 2.85849i) q^{90} +(1.59127 - 4.19497i) q^{91} +(1.31404 + 1.80861i) q^{92} +(-1.04456 - 0.980627i) q^{93} +(-7.42848 + 6.68863i) q^{94} +(-0.762508 - 0.339490i) q^{95} +(7.47909 + 4.52804i) q^{96} +(5.92170 + 5.33192i) q^{97} +(8.13093 - 4.69439i) q^{98} +(-7.79159 + 6.18798i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 3 q^{3} - 54 q^{4} - 15 q^{6} - 30 q^{7} - 9 q^{9}+O(q^{10}) $ 416 * q - 3 * q^3 - 54 * q^4 - 15 * q^6 - 30 * q^7 - 9 * q^9	$ 416 q - 3 q^{3} - 54 q^{4} - 15 q^{6} - 30 q^{7} - 9 q^{9} - 36 q^{12} - 20 q^{13} - 9 q^{15} + 14 q^{16} - 30 q^{19} - 28 q^{22} + 15 q^{24} - 84 q^{25} - 24 q^{27} - 30 q^{28} - 5 q^{30} - 27 q^{33} - 73 q^{36} - 18 q^{37} - 65 q^{39} - 120 q^{40} - 25 q^{42} + 36 q^{45} + 30 q^{46} - 41 q^{48} + 14 q^{49} + 60 q^{51} + 20 q^{52} + 18 q^{55} - 126 q^{58} - 30 q^{61} + 105 q^{63} - 56 q^{64} + 170 q^{66} - 33 q^{69} - 195 q^{72} + 77 q^{75} + 4 q^{78} - 13 q^{81} + 36 q^{82} - 60 q^{84} - 30 q^{85} + 38 q^{88} - 190 q^{90} - 56 q^{91} + 24 q^{93} - 90 q^{94} + 54 q^{97}+O(q^{100}) $ 416 * q - 3 * q^3 - 54 * q^4 - 15 * q^6 - 30 * q^7 - 9 * q^9 - 36 * q^12 - 20 * q^13 - 9 * q^15 + 14 * q^16 - 30 * q^19 - 28 * q^22 + 15 * q^24 - 84 * q^25 - 24 * q^27 - 30 * q^28 - 5 * q^30 - 27 * q^33 - 73 * q^36 - 18 * q^37 - 65 * q^39 - 120 * q^40 - 25 * q^42 + 36 * q^45 + 30 * q^46 - 41 * q^48 + 14 * q^49 + 60 * q^51 + 20 * q^52 + 18 * q^55 - 126 * q^58 - 30 * q^61 + 105 * q^63 - 56 * q^64 + 170 * q^66 - 33 * q^69 - 195 * q^72 + 77 * q^75 + 4 * q^78 - 13 * q^81 + 36 * q^82 - 60 * q^84 - 30 * q^85 + 38 * q^88 - 190 * q^90 - 56 * q^91 + 24 * q^93 - 90 * q^94 + 54 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{10}\right)$	$-1$

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 $

$2$	−0.358071	+	1.68459i	−0.253194	+	1.19118i	0.649317	+	0.760518i	$0.275055\pi$
$2$	−0.358071	+	1.68459i	−0.253194	+	1.19118i	−0.902511	+	0.430667i	$0.858278\pi$
$3$	0.834638	+	1.51769i	0.481879	+	0.876238i
$3$	0.834638	+	1.51769i	0.481879	+	0.876238i
$4$	−0.882537	−	0.392931i	−0.441268	−	0.196465i
$5$	−0.368818	+	1.13510i	−0.164940	+	0.507634i	−0.999032	−	0.0439918i	$-0.985992\pi$
$5$	−0.368818	+	1.13510i	−0.164940	+	0.507634i	0.834092	+	0.551626i	$0.185992\pi$
$6$	−2.85554	+	0.862583i	−1.16577	+	0.352148i
$7$	1.13679	+	0.506130i	0.429665	+	0.191299i	0.610163	−	0.792276i	$-0.291104\pi$
$7$	1.13679	+	0.506130i	0.429665	+	0.191299i	−0.180497	+	0.983575i	$0.557771\pi$
$8$	−1.04666	+	1.44060i	−0.370050	+	0.509330i
$9$	−1.60676	+	2.53344i	−0.535586	+	0.844481i
$10$	−1.78012	−	1.02775i	−0.562924	−	0.325004i
$11$	3.13290	+	1.08855i	0.944604	+	0.328211i
$11$	3.13290	+	1.08855i	0.944604	+	0.328211i
$12$	−0.140253	−	1.66737i	−0.0404874	−	0.481328i
$13$	−0.202956	−	3.59983i	−0.0562898	−	0.998414i
$13$	−0.202956	−	3.59983i	−0.0562898	−	0.998414i
$14$	−1.25967	+	1.73379i	−0.336661	+	0.463375i
$15$	−2.03057	+	0.387651i	−0.524290	+	0.100091i
$16$	−3.34488	−	3.71487i	−0.836221	−	0.928717i
$17$	0.684027	−	0.145394i	0.165901	−	0.0352633i	−0.124212	−	0.992256i	$-0.539640\pi$
$17$	0.684027	−	0.145394i	0.165901	−	0.0352633i	0.290113	+	0.956992i	$0.406307\pi$
$18$	−3.69248	−	3.61388i	−0.870325	−	0.851799i
$19$	−0.0731003	+	0.695503i	−0.0167704	+	0.159559i	−0.999702	−	0.0244119i	$-0.992229\pi$
$19$	−0.0731003	+	0.695503i	−0.0167704	+	0.159559i	0.982932	+	0.183971i	$0.0588953\pi$
$20$	0.771513	−	0.856852i	0.172515	−	0.191598i
$21$	0.180658	+	2.14772i	0.0394228	+	0.468672i
$22$	−2.95556	+	4.88787i	−0.630128	+	1.04210i
$23$	−2.00409	−	1.15706i	−0.417881	−	0.241264i	0.276289	−	0.961075i	$-0.410895\pi$
$23$	−2.00409	−	1.15706i	−0.417881	−	0.241264i	−0.694170	+	0.719811i	$0.744229\pi$
$24$	−3.05997	−	0.386120i	−0.624613	−	0.0788165i
$25$	2.89265	+	2.10163i	0.578530	+	0.420326i
$26$	6.13692	+	0.947098i	1.20355	+	0.185741i
$27$	−5.18604	−	0.324050i	−0.998054	−	0.0623634i
$28$	−0.804382	−	0.893357i	−0.152014	−	0.168829i
$29$	−0.322296	−	3.06644i	−0.0598489	−	0.569424i	−0.982822	−	0.184558i	$-0.940914\pi$
$29$	−0.322296	−	3.06644i	−0.0598489	−	0.569424i	0.922973	−	0.384866i	$-0.125752\pi$
$30$	0.0740524	−	3.55948i	0.0135201	−	0.649868i
$31$	−0.786706	+	0.255616i	−0.141297	+	0.0459100i	−0.378811	−	0.925474i	$-0.623667\pi$
$31$	−0.786706	+	0.255616i	−0.141297	+	0.0459100i	0.237515	+	0.971384i	$0.423667\pi$
$32$	4.37150	−	2.52389i	0.772779	−	0.446164i
$33$	0.962753	+	5.66331i	0.167594	+	0.985856i
$34$			1.20437i			0.206547i
$35$	−0.993778	+	1.10370i	−0.167979	+	0.186560i
$36$	2.41349	−	1.60451i	0.402248	−	0.267419i
$37$	0.496886	−	0.0522249i	0.0816876	−	0.00858571i	−0.0635965	−	0.997976i	$-0.520257\pi$
$37$	0.496886	−	0.0522249i	0.0816876	−	0.00858571i	0.145284	+	0.989390i	$0.453590\pi$
$38$	−1.14546	−	0.372183i	−0.185818	−	0.0603761i
$39$	5.29403	−	3.31258i	0.847724	−	0.530438i
$40$	−1.24921	−	1.71939i	−0.197517	−	0.271859i
$41$	−1.76860	−	3.97234i	−0.276209	−	0.620376i	0.721168	−	0.692761i	$-0.243606\pi$
$41$	−1.76860	−	3.97234i	−0.276209	−	0.620376i	−0.997377	+	0.0723848i	$0.976939\pi$
$42$	−3.68272	−	0.464702i	−0.568256	−	0.0717051i
$43$	9.76151	−	5.63581i	1.48862	−	0.859453i	0.488701	−	0.872451i	$-0.337471\pi$
$43$	9.76151	−	5.63581i	1.48862	−	0.859453i	0.999916	+	0.0129978i	$0.00413744\pi$
$44$	−2.33717	−	2.19170i	−0.352342	−	0.330411i
$45$	−2.28312	−	2.75822i	−0.340348	−	0.411171i
$46$	2.66678	−	2.96175i	0.393195	−	0.436687i
$47$	4.69563	+	3.41158i	0.684929	+	0.497630i	0.874989	−	0.484143i	$-0.160868\pi$
$47$	4.69563	+	3.41158i	0.684929	+	0.497630i	−0.190060	+	0.981772i	$0.560868\pi$
$48$	2.84625	−	8.17706i	0.410820	−	1.18026i
$49$	−3.64780	−	4.05129i	−0.521114	−	0.578756i
$50$	−4.57616	+	4.12039i	−0.647167	+	0.582712i
$51$	0.791579	+	0.916788i	0.110843	+	0.128376i
$52$	−1.23537	+	3.25673i	−0.171315	+	0.451628i
$53$	−8.86976	+	2.88196i	−1.21836	+	0.395868i	−0.846483	−	0.532416i	$-0.821284\pi$
$53$	−8.86976	+	2.88196i	−1.21836	+	0.395868i	−0.371872	+	0.928284i	$0.621284\pi$
$54$	2.40286	−	8.62031i	0.326988	−	1.17308i
$55$	−2.39109	+	3.15469i	−0.322415	+	0.425378i
$56$	−1.91896	+	1.10791i	−0.256432	+	0.148051i
$57$	−1.11657	+	0.469550i	−0.147893	+	0.0621934i
$58$	5.28110	+	0.555066i	0.693443	+	0.0728838i
$59$	4.87846	+	2.17203i	0.635121	+	0.282774i	0.698932	−	0.715188i	$-0.253659\pi$
$59$	4.87846	+	2.17203i	0.635121	+	0.282774i	−0.0638110	+	0.997962i	$0.520325\pi$
$60$	1.94437	+	0.455755i	0.251017	+	0.0588377i
$61$	1.29996	+	6.11582i	0.166442	+	0.783050i	0.979592	+	0.200996i	$0.0644177\pi$
$61$	1.29996	+	6.11582i	0.166442	+	0.783050i	−0.813150	+	0.582055i	$0.802249\pi$
$62$	−0.148912	−	1.41680i	−0.0189119	−	0.179934i
$63$	−3.10879	+	2.06676i	−0.391671	+	0.260387i
$64$	−0.403051	−	1.24046i	−0.0503814	−	0.155058i
$65$	4.16104	+	1.09731i	0.516114	+	0.136104i
$66$	−9.88509	−	0.406021i	−1.21677	−	0.0499777i
$67$	6.76153	+	3.90377i	0.826052	+	0.476921i	0.852499	−	0.522729i	$-0.175086\pi$
$67$	6.76153	+	3.90377i	0.826052	+	0.476921i	−0.0264469	+	0.999650i	$0.508419\pi$
$68$	−0.660809	−	0.140459i	−0.0801348	−	0.0170332i
$69$	0.0833693	−	4.00731i	0.0100365	−	0.482423i
$70$	−1.50344	−	2.06931i	−0.179696	−	0.247330i
$71$	−1.06023	+	0.225359i	−0.125826	+	0.0267452i	−0.270394	−	0.962750i	$-0.587154\pi$
$71$	−1.06023	+	0.225359i	−0.125826	+	0.0267452i	0.144568	+	0.989495i	$0.453821\pi$
$72$	−1.96796	−	4.96635i	−0.231926	−	0.585290i
$73$	7.27022	−	5.28212i	0.850915	−	0.618226i	−0.0744834	−	0.997222i	$-0.523731\pi$
$73$	7.27022	−	5.28212i	0.850915	−	0.618226i	0.925398	+	0.378997i	$0.123731\pi$
$74$	−0.0899429	+	0.855750i	−0.0104557	+	0.0994789i
$75$	−0.775308	+	6.14424i	−0.0895249	+	0.709476i
$76$	0.337798	−	0.585083i	0.0387481	−	0.0671137i
$77$	3.01049	+	2.82311i	0.343077	+	0.321723i
$78$	3.68471	+	10.1044i	0.417211	+	1.14410i
$79$	−6.44207	+	2.09316i	−0.724790	+	0.235498i	−0.648099	−	0.761556i	$-0.724436\pi$
$79$	−6.44207	+	2.09316i	−0.724790	+	0.235498i	−0.0766912	+	0.997055i	$0.524436\pi$
$80$	5.45042	−	2.42668i	0.609375	−	0.271311i
$81$	−3.83666	−	8.14126i	−0.426295	−	0.904584i
$82$	7.32505	−	1.55699i	0.808917	−	0.171941i
$83$	7.61540	+	2.47439i	0.835899	+	0.271600i	0.695528	−	0.718499i	$-0.255171\pi$
$83$	7.61540	+	2.47439i	0.835899	+	0.271600i	0.140371	+	0.990099i	$0.455171\pi$
$84$	0.684469	−	1.96643i	0.0746817	−	0.214555i
$85$	−0.0872435	+	0.830066i	−0.00946289	+	0.0900333i
$86$	5.99872	+	18.4622i	0.646859	+	1.99083i
$87$	4.38490	−	3.04852i	0.470111	−	0.326835i
$88$	−4.84725	+	3.37392i	−0.516718	+	0.359661i
$89$	−7.39533	+	12.8091i	−0.783903	+	1.35776i	0.145749	+	0.989322i	$0.453441\pi$
$89$	−7.39533	+	12.8091i	−0.783903	+	1.35776i	−0.929652	+	0.368438i	$0.879893\pi$
$90$	5.46398	−	2.85849i	0.575954	−	0.301311i
$91$	1.59127	−	4.19497i	0.166810	−	0.439752i
$92$	1.31404	+	1.80861i	0.136998	+	0.188561i
$93$	−1.04456	−	0.980627i	−0.108316	−	0.101686i
$94$	−7.42848	+	6.68863i	−0.766189	+	0.689880i
$95$	−0.762508	−	0.339490i	−0.0782317	−	0.0348310i
$96$	7.47909	+	4.52804i	0.763332	+	0.462141i
$97$	5.92170	+	5.33192i	0.601257	+	0.541375i	0.912563	−	0.408935i	$-0.134100\pi$
$97$	5.92170	+	5.33192i	0.601257	+	0.541375i	−0.311306	+	0.950310i	$0.600766\pi$
$98$	8.13093	−	4.69439i	0.821348	−	0.474205i
$99$	−7.79159	+	6.18798i	−0.783085	+	0.621915i
$100$	−1.72707	−	2.99138i	−0.172707	−	0.299138i
$101$	−7.99610	−	1.69962i	−0.795642	−	0.169119i	−0.207882	−	0.978154i	$-0.566657\pi$
$101$	−7.99610	−	1.69962i	−0.795642	−	0.169119i	−0.587760	+	0.809035i	$0.699990\pi$
$102$	−1.82785	+	1.00521i	−0.180984	+	0.0995307i
$103$	−10.4759	+	7.61119i	−1.03222	+	0.749952i	−0.968752	−	0.248031i	$-0.920216\pi$
$103$	−10.4759	+	7.61119i	−1.03222	+	0.749952i	−0.0634690	+	0.997984i	$0.520216\pi$
$104$	5.39836	+	3.47542i	0.529352	+	0.340793i
$105$	−2.50452	−	0.587053i	−0.244416	−	0.0572906i
$106$	−1.67892	−	15.9738i	−0.163071	−	1.55152i
$107$	9.68079	−	4.31017i	0.935877	−	0.416679i	0.118612	−	0.992941i	$-0.462156\pi$
$107$	9.68079	−	4.31017i	0.935877	−	0.416679i	0.817266	+	0.576261i	$0.195489\pi$
$108$	4.44954	+	2.32374i	0.428157	+	0.223602i
$109$	16.8727			1.61611			0.808055	−	0.589107i	$-0.200520\pi$
$109$	16.8727			1.61611			0.808055	+	0.589107i	$0.200520\pi$
$110$	−4.45818	−	5.15761i	−0.425071	−	0.491759i
$111$	0.493982	+	0.710530i	0.0468866	+	0.0674405i
$112$	−1.92221	−	5.91596i	−0.181632	−	0.559006i
$113$	1.70203	+	0.178890i	0.160113	+	0.0168286i	0.184246	−	0.982880i	$-0.441016\pi$
$113$	1.70203	+	0.178890i	0.160113	+	0.0168286i	−0.0241327	+	0.999709i	$0.507682\pi$
$114$	−0.391188	−	2.04909i	−0.0366381	−	0.191915i
$115$	2.05253	−	1.84810i	0.191399	−	0.172337i
$116$	−0.920461	+	2.83289i	−0.0854626	+	0.263027i
$117$	9.44607	+	5.26989i	0.873290	+	0.487201i
$118$	−5.40581	+	7.44046i	−0.497645	+	0.684950i
$119$	0.851182	+	0.180924i	0.0780277	+	0.0165853i
$120$	1.56686	−	3.33098i	0.143034	−	0.304075i
$121$	8.63011	+	6.82065i	0.784555	+	0.620059i
$122$	−10.7681			−0.974900
$123$	4.55264	−	5.99966i	0.410498	−	0.540971i
$124$	0.794736	+	0.0835301i	0.0713694	+	0.00750123i
$125$	−8.28032	+	6.01601i	−0.740615	+	0.538088i
$126$	−2.36847	−	5.97708i	−0.211000	−	0.532481i
$127$	3.51512	−	3.16503i	0.311916	−	0.280851i	−0.498271	−	0.867021i	$-0.666032\pi$
$127$	3.51512	−	3.16503i	0.311916	−	0.280851i	0.810188	+	0.586170i	$0.199365\pi$
$128$	12.2742	−	1.29007i	1.08490	−	0.114027i
$129$	16.7007	+	10.1111i	1.47042	+	0.890230i
$130$	−3.33846	+	6.61674i	−0.292802	+	0.580326i
$131$	−16.6274			−1.45274			−0.726371	−	0.687303i	$-0.758794\pi$
$131$	−16.6274			−1.45274			−0.726371	+	0.687303i	$0.758794\pi$
$132$	1.37562	−	5.37638i	0.119733	−	0.467953i
$133$	−0.435115	+	0.753640i	−0.0377292	+	0.0653489i
$134$	−8.99735	+	9.99257i	−0.777253	+	0.863227i
$135$	2.28053	−	5.76718i	0.196277	−	0.496360i
$136$	−0.506487	+	1.13759i	−0.0434309	+	0.0975475i
$137$	14.9889	−	3.18600i	1.28059	−	0.272198i	0.483120	−	0.875554i	$-0.339504\pi$
$137$	14.9889	−	3.18600i	1.28059	−	0.272198i	0.797472	+	0.603356i	$0.206170\pi$
$138$	6.72081	+	1.57534i	0.572114	+	0.134102i
$139$	−0.670199	+	1.50529i	−0.0568455	+	0.127677i	−0.939735	−	0.341904i	$-0.888928\pi$
$139$	−0.670199	+	1.50529i	−0.0568455	+	0.127677i	0.882889	+	0.469581i	$0.155595\pi$
$140$	1.31072	−	0.583572i	0.110776	−	0.0493208i
$141$	−1.25856	+	9.97395i	−0.105990	+	0.839958i
$142$		−	1.86675i		−	0.156654i
$143$	3.28277	−	11.4988i	0.274519	−	0.961582i
$144$	14.7858	−	2.50517i	1.23215	−	0.208764i
$145$	3.59960	+	0.765119i	0.298931	+	0.0635397i
$146$	6.29496	+	14.1387i	0.520974	+	1.17013i
$147$	3.10400	−	8.91758i	0.256014	−	0.735510i
$148$	−0.459041	−	0.149152i	−0.0377330	−	0.0122602i
$149$	0.392376	+	1.84598i	0.0321447	+	0.151229i	0.991293	−	0.131675i	$-0.0420356\pi$
$149$	0.392376	+	1.84598i	0.0321447	+	0.151229i	−0.959148	+	0.282904i	$0.908702\pi$
$150$	−10.0729	−	3.50615i	−0.822450	−	0.286276i
$151$	0.262337	+	0.190599i	0.0213487	+	0.0155107i	0.598408	−	0.801191i	$-0.295800\pi$
$151$	0.262337	+	0.190599i	0.0213487	+	0.0155107i	−0.577060	+	0.816702i	$0.695800\pi$
$152$	−0.925432	−	0.833263i	−0.0750625	−	0.0675865i
$153$	−0.730717	+	1.96656i	−0.0590750	+	0.158987i
$154$	−5.83374	+	4.06057i	−0.470096	+	0.327210i
$155$		−	0.987269i		−	0.0792994i
$156$	−5.97379	+	0.843288i	−0.478286	+	0.0675171i
$157$	6.95020	+	5.04962i	0.554686	+	0.403003i	0.829510	−	0.558491i	$-0.188620\pi$
$157$	6.95020	+	5.04962i	0.554686	+	0.403003i	−0.274824	+	0.961495i	$0.588620\pi$
$158$	−1.21939	−	11.6017i	−0.0970097	−	0.922985i
$159$	−11.7770	−	11.0561i	−0.933973	−	0.876809i
$160$	1.25259	+	5.89296i	0.0990258	+	0.465880i
$161$	−1.69260	−	2.32966i	−0.133395	−	0.183603i
$162$	15.0885	−	3.54805i	1.18546	−	0.278761i
$163$	−17.0527	−	15.3543i	−1.33567	−	1.20264i	−0.961346	−	0.275343i	$-0.911209\pi$
$163$	−17.0527	−	15.3543i	−1.33567	−	1.20264i	−0.374323	−	0.927299i	$-0.622125\pi$
$164$			4.20068i			0.328018i
$165$	−6.78353	−	0.995905i	−0.528097	−	0.0775311i
$166$	−6.89519	+	11.9428i	−0.535170	+	0.926942i
$167$	1.34506	−	6.32801i	0.104084	−	0.489677i	−0.894968	−	0.446131i	$-0.852801\pi$
$167$	1.34506	−	6.32801i	0.104084	−	0.489677i	0.999051	−	0.0435452i	$-0.0138652\pi$
$168$	−3.28310	−	1.98768i	−0.253297	−	0.153353i
$169$	−12.9176	+	1.46121i	−0.993663	+	0.112401i
$170$	−1.36708	−	0.444192i	−0.104850	−	0.0340680i
$171$	−1.64456	−	1.30270i	−0.125763	−	0.0996200i
$172$	−10.8294	+	1.13821i	−0.825732	+	0.0867879i
$173$	2.18733	−	20.8110i	0.166299	−	1.58223i	−0.519517	−	0.854460i	$-0.673888\pi$
$173$	2.18733	−	20.8110i	0.166299	−	1.58223i	0.685817	−	0.727774i	$-0.259445\pi$
$174$	3.56539	+	8.47835i	0.270292	+	0.642742i
$175$	2.22463	+	3.85317i	0.168166	+	0.291272i
$176$	−6.43535	−	15.2794i	−0.485083	−	1.15173i
$177$	0.775284	+	9.21684i	0.0582739	+	0.692780i
$178$	−18.9300	−	17.0446i	−1.41886	−	1.27755i
$179$	−6.48391	−	14.5631i	−0.484630	−	1.08850i	−0.976044	−	0.217572i	$-0.930186\pi$
$179$	−6.48391	−	14.5631i	−0.484630	−	1.08850i	0.491414	−	0.870926i	$-0.336480\pi$
$180$	0.931150	+	3.33134i	0.0694038	+	0.248303i
$181$	−0.370770	+	1.14111i	−0.0275591	+	0.0848183i	−0.963890	−	0.266300i	$-0.914199\pi$
$181$	−0.370770	+	1.14111i	−0.0275591	+	0.0848183i	0.936331	+	0.351119i	$0.114199\pi$
$182$	6.49701	+	4.18273i	0.481591	+	0.310044i
$183$	−8.19691	+	7.07743i	−0.605933	+	0.523178i
$184$	3.76446	−	1.67604i	0.277520	−	0.123560i
$185$	−0.123980	+	0.583280i	−0.00911518	+	0.0428836i
$186$	2.02598	−	1.40852i	0.148552	−	0.103278i
$187$	2.30126	+	0.289093i	0.168285	+	0.0211406i
$188$	−2.80356	−	4.85590i	−0.204470	−	0.354153i
$189$	−5.73141	−	2.99319i	−0.416899	−	0.217722i
$190$	0.844934	−	1.16295i	0.0612979	−	0.0843694i
$191$	3.73671	−	8.39279i	0.270379	−	0.607281i	−0.726418	−	0.687253i	$-0.758816\pi$
$191$	3.73671	−	8.39279i	0.270379	−	0.607281i	0.996797	+	0.0799718i	$0.0254830\pi$
$192$	1.54623	−	1.64704i	0.111590	−	0.118865i
$193$	15.0908	+	16.7600i	1.08626	+	1.20641i	0.977187	+	0.212380i	$0.0681213\pi$
$193$	15.0908	+	16.7600i	1.08626	+	1.20641i	0.109072	+	0.994034i	$0.465212\pi$
$194$	−11.1025	+	8.06643i	−0.797112	+	0.579136i
$195$	1.80759	+	7.23102i	0.129445	+	0.517824i
$196$	1.62744	+	5.00874i	0.116246	+	0.357767i
$197$	−21.5309	−	12.4309i	−1.53401	−	0.885664i	−0.999171	−	0.0407127i	$-0.987037\pi$
$197$	−21.5309	−	12.4309i	−1.53401	−	0.885664i	−0.534844	−	0.844951i	$-0.679630\pi$
$198$	−7.63426	−	15.3414i	−0.542543	−	1.09026i
$199$	−9.23559	−	15.9965i	−0.654694	−	1.13396i	−0.981971	−	0.189034i	$-0.939464\pi$
$199$	−9.23559	−	15.9965i	−0.654694	−	1.13396i	0.327277	−	0.944929i	$-0.393869\pi$
$200$	−6.05523	+	1.96746i	−0.428170	+	0.139121i
$201$	−0.281277	+	13.5201i	−0.0198398	+	0.953636i
$202$	5.72634	−	12.8616i	0.402904	−	0.904937i
$203$	1.18564	−	3.64902i	0.0832154	−	0.256111i
$204$	−0.338363	−	1.12013i	−0.0236901	−	0.0784251i
$205$	5.16132	−	0.542476i	0.360482	−	0.0378882i
$206$	−9.07061	−	20.3729i	−0.631980	−	1.41945i
$207$	6.15143	−	3.21812i	0.427554	−	0.223675i
$208$	−12.6940	+	12.7950i	−0.880174	+	0.887172i
$209$	−0.986107	+	2.09937i	−0.0682105	+	0.145216i
$210$	1.88574	−	4.00889i	0.130128	−	0.276639i
$211$	−1.74957	+	8.23109i	−0.120445	+	0.566651i	0.875993	+	0.482324i	$0.160207\pi$
$211$	−1.74957	+	8.23109i	−0.120445	+	0.566651i	−0.996438	+	0.0843270i	$0.973126\pi$
$212$	8.96030	+	0.941765i	0.615396	+	0.0646807i
$213$	−1.22693	−	1.42101i	−0.0840680	−	0.0973657i
$214$	3.79445	+	17.8515i	0.259384	+	1.22030i
$215$	2.79702	+	13.1589i	0.190755	+	0.897431i
$216$	5.89484	−	7.13185i	0.401093	−	0.485261i
$217$	−1.02369	−	0.107594i	−0.0694927	−	0.00730398i
$218$	−6.04161	+	28.4236i	−0.409190	+	1.92509i
$219$	14.0846	+	6.62527i	0.951750	+	0.447694i
$220$	3.34980	−	1.84460i	0.225843	−	0.124363i
$221$	−0.662223	−	2.43288i	−0.0445459	−	0.163653i
$222$	−1.37383	+	0.577736i	−0.0922055	+	0.0387751i
$223$	−4.21589	−	9.46905i	−0.282317	−	0.634094i	0.715607	−	0.698503i	$-0.246150\pi$
$223$	−4.21589	−	9.46905i	−0.282317	−	0.634094i	−0.997924	+	0.0644093i	$0.979484\pi$
$224$	6.24688	−	0.656573i	0.417387	−	0.0438692i
$225$	−9.97215	+	3.95154i	−0.664810	+	0.263436i
$226$	−0.910802	+	2.80316i	−0.0605857	+	0.186463i
$227$	−0.926614	+	2.08121i	−0.0615015	+	0.138135i	−0.941682	−	0.336505i	$-0.890755\pi$
$227$	−0.926614	+	2.08121i	−0.0615015	+	0.138135i	0.880180	+	0.474640i	$0.157422\pi$
$228$	1.16991	+	0.0243393i	0.0774794	+	0.00161191i
$229$	−17.6428	+	5.73248i	−1.16587	+	0.378813i	−0.827098	−	0.562057i	$-0.810010\pi$
$229$	−17.6428	+	5.73248i	−1.16587	+	0.378813i	−0.338768	+	0.940870i	$0.610010\pi$
$230$	2.37835	+	4.11942i	0.156824	+	0.271626i
$231$	−1.77193	+	6.92526i	−0.116584	+	0.455649i
$232$	4.75486	+	2.74522i	0.312172	+	0.180232i
$233$	−7.92740	−	24.3980i	−0.519342	−	1.59837i	−0.775241	−	0.631665i	$-0.782372\pi$
$233$	−7.92740	−	24.3980i	−0.519342	−	1.59837i	0.255900	−	0.966703i	$-0.417628\pi$
$234$	−12.2600	+	14.0258i	−0.801458	+	0.916893i
$235$	−5.60433	+	4.07179i	−0.365586	+	0.265614i
$236$	−3.45196	−	3.83379i	−0.224704	−	0.249559i
$237$	−8.55356	−	8.03003i	−0.555613	−	0.521607i
$238$	−0.609566	+	1.36911i	−0.0395123	+	0.0887461i
$239$	4.87376	−	6.70815i	0.315257	−	0.433914i	−0.621754	−	0.783212i	$-0.713580\pi$
$239$	4.87376	−	6.70815i	0.315257	−	0.433914i	0.937012	+	0.349298i	$0.113580\pi$
$240$	8.23207	+	6.24663i	0.531378	+	0.403218i
$241$	−6.95746	−	12.0507i	−0.448169	−	0.776252i	0.550098	−	0.835100i	$-0.314590\pi$
$241$	−6.95746	−	12.0507i	−0.448169	−	0.776252i	−0.998267	+	0.0588484i	$0.981257\pi$
$242$	−14.5802	+	12.0959i	−0.937250	+	0.777555i
$243$	9.15367	−	12.6179i	0.587208	−	0.809436i
$244$	1.25583	−	5.90823i	0.0803964	−	0.378235i
$245$	5.94401	−	2.64644i	0.379749	−	0.169075i
$246$	8.47679	+	9.81763i	0.540460	+	0.625949i
$247$	2.51853	+	0.121993i	0.160250	+	0.00776221i
$248$	0.455171	−	1.40087i	0.0289034	−	0.0889555i
$249$	2.60075	+	13.6230i	0.164816	+	0.863324i
$250$	−7.16956	−	16.1031i	−0.453443	−	1.01845i
$251$	−6.81701	−	6.13806i	−0.430286	−	0.387431i	0.425334	−	0.905037i	$-0.360157\pi$
$251$	−6.81701	−	6.13806i	−0.430286	−	0.387431i	−0.855619	+	0.517606i	$0.826823\pi$
$252$	3.55571	−	0.602448i	0.223989	−	0.0379506i
$253$	−5.01908	−	5.80650i	−0.315547	−	0.365052i
$254$	4.07311	+	7.05484i	0.255570	+	0.442660i
$255$	−1.33260	+	0.560397i	−0.0834506	+	0.0350934i
$256$	−1.94912	+	18.5447i	−0.121820	+	1.15904i
$257$	21.0203	−	2.20932i	1.31121	−	0.137813i	0.577003	−	0.816742i	$-0.304222\pi$
$257$	21.0203	−	2.20932i	1.31121	−	0.137813i	0.734205	+	0.678928i	$0.237555\pi$
$258$	−23.0131	+	24.5134i	−1.43273	+	1.52614i
$259$	0.591287	+	0.192121i	0.0367408	+	0.0119378i
$260$	−3.24111	−	2.60341i	−0.201005	−	0.161457i
$261$	8.28651	+	4.11051i	0.512922	+	0.254434i
$262$	5.95378	−	28.0103i	0.367826	−	1.73048i
$263$	13.2141	−	22.8874i	0.814814	−	1.41130i	−0.0946470	−	0.995511i	$-0.530172\pi$
$263$	13.2141	−	22.8874i	0.814814	−	1.41130i	0.909461	−	0.415789i	$-0.136494\pi$
$264$	−9.16626	−	4.54061i	−0.564144	−	0.279455i
$265$		−	11.1310i		−	0.683773i
$266$	−1.11377	−	1.00285i	−0.0682898	−	0.0614884i
$267$	−25.6126	−	0.532853i	−1.56747	−	0.0326101i
$268$	−4.43338	−	6.10203i	−0.270812	−	0.372741i
$269$	4.38876	+	20.6475i	0.267587	+	1.25890i	0.882503	+	0.470307i	$0.155857\pi$
$269$	4.38876	+	20.6475i	0.267587	+	1.25890i	−0.614915	+	0.788593i	$0.710810\pi$
$270$	8.89874	+	5.90682i	0.541560	+	0.359478i
$271$	−1.01326	−	9.64054i	−0.0615513	−	0.585621i	−0.981215	−	0.192915i	$-0.938206\pi$
$271$	−1.01326	−	9.64054i	−0.0615513	−	0.585621i	0.919664	−	0.392706i	$-0.128461\pi$
$272$	−2.82811	−	2.05474i	−0.171479	−	0.124587i
$273$	7.69479	−	1.08623i	0.465710	−	0.0657417i
$274$			26.3910i			1.59434i
$275$	6.77464	+	9.73300i	0.408526	+	0.586922i
$276$	−1.64817	+	3.50384i	−0.0992081	+	0.210906i
$277$	9.43758	+	8.49764i	0.567050	+	0.510574i	0.902043	−	0.431647i	$-0.142067\pi$
$277$	9.43758	+	8.49764i	0.567050	+	0.510574i	−0.334993	+	0.942221i	$0.608734\pi$
$278$	−2.29582	−	1.66801i	−0.137694	−	0.100041i
$279$	0.616457	−	2.40379i	0.0369063	−	0.143911i
$280$	−0.549850	−	2.58684i	−0.0328598	−	0.154593i
$281$	−5.63146	−	1.82977i	−0.335945	−	0.109155i	0.136187	−	0.990683i	$-0.456515\pi$
$281$	−5.63146	−	1.82977i	−0.335945	−	0.109155i	−0.472132	+	0.881528i	$0.656515\pi$
$282$	−16.3514	−	5.69153i	−0.973709	−	0.338926i
$283$	−10.6193	−	23.8514i	−0.631254	−	1.41782i	−0.891832	−	0.452367i	$-0.850580\pi$
$283$	−10.6193	−	23.8514i	−0.631254	−	1.41782i	0.260577	−	0.965453i	$-0.416087\pi$
$284$	1.02424	+	0.217709i	0.0607775	+	0.0129187i
$285$	−0.121178	−	1.44060i	−0.00717794	−	0.0853339i
$286$	18.1954	+	9.64752i	1.07591	+	0.570470i
$287$		−	5.41085i		−	0.319392i
$288$	−0.629820	+	15.1302i	−0.0371125	+	0.891556i
$289$	−15.0835	+	6.71562i	−0.887266	+	0.395036i
$290$	−2.57782	+	5.78988i	−0.151375	+	0.339994i
$291$	−3.14972	+	13.4375i	−0.184640	+	0.787721i
$292$	−8.49174	+	1.80498i	−0.496942	+	0.105628i
$293$	−3.25839	+	7.31846i	−0.190357	+	0.427549i	−0.983360	−	0.181669i	$-0.941850\pi$
$293$	−3.25839	+	7.31846i	−0.190357	+	0.427549i	0.793003	+	0.609218i	$0.208517\pi$
$294$	13.9110	+	8.42210i	0.811307	+	0.491187i
$295$	−4.26475	+	4.73648i	−0.248303	+	0.275768i
$296$	−0.444835	+	0.770477i	−0.0258555	+	0.0447831i
$297$	−15.8946	−	6.66049i	−0.922297	−	0.386481i
$298$	−3.25022			−0.188280
$299$	−3.75848	+	7.44921i	−0.217359	+	0.430799i
$300$	3.09850	−	5.11788i	0.178892	−	0.295481i
$301$	13.9492	−	1.46612i	0.804019	−	0.0845059i
$302$	−0.415016	+	0.373682i	−0.0238815	+	0.0215030i
$303$	−4.09435	−	13.5542i	−0.235214	−	0.778667i
$304$	2.82821	−	2.05482i	0.162209	−	0.117852i
$305$	−7.42154	−	0.780036i	−0.424956	−	0.0446647i
$306$	−3.05119	−	1.93512i	−0.174425	−	0.110624i
$307$	1.60054			0.0913475			0.0456738	−	0.998956i	$-0.485457\pi$
$307$	1.60054			0.0913475			0.0456738	+	0.998956i	$0.485457\pi$
$308$	−1.54758	−	3.67441i	−0.0881816	−	0.209369i
$309$	−20.2950	−	9.54657i	−1.15454	−	0.543085i
$310$	1.66314	+	0.353512i	0.0944602	+	0.0200781i
$311$	19.3328	−	26.6093i	1.09626	−	1.50887i	0.256009	−	0.966674i	$-0.417592\pi$
$311$	19.3328	−	26.6093i	1.09626	−	1.50887i	0.840251	−	0.542198i	$-0.182408\pi$
$312$	−0.768932	+	11.0937i	−0.0435322	+	0.628060i
$313$	2.88056	−	8.86546i	0.162819	−	0.501105i	−0.836050	−	0.548653i	$-0.815141\pi$
$313$	2.88056	−	8.86546i	0.162819	−	0.501105i	0.998869	+	0.0475480i	$0.0151407\pi$
$314$	−10.9952	+	9.90012i	−0.620495	+	0.558696i
$315$	−1.19941	−	4.29106i	−0.0675789	−	0.241774i
$316$	6.50783	+	0.684000i	0.366094	+	0.0384780i
$317$	8.49172	+	26.1348i	0.476942	+	1.46788i	0.843320	+	0.537412i	$0.180598\pi$
$317$	8.49172	+	26.1348i	0.476942	+	1.46788i	−0.366378	+	0.930466i	$0.619402\pi$
$318$	22.8420	−	15.8805i	1.28092	−	0.890532i
$319$	2.32826	−	9.95769i	0.130358	−	0.557524i
$320$	1.55671			0.0870226
$321$	14.6215	+	11.0950i	0.816090	+	0.619262i
$322$	4.53059	−	2.01715i	0.252480	−	0.112411i
$323$	0.0511197	+	0.486371i	0.00284438	+	0.0270624i
$324$	0.187044	+	8.69250i	0.0103913	+	0.482916i
$325$	6.97845	−	10.8396i	0.387095	−	0.601273i
$326$	31.9718	−	23.2288i	1.77075	−	1.28653i
$327$	14.0826	+	25.6075i	0.778769	+	1.41610i
$328$	7.57369	+	1.60984i	0.418187	+	0.0888884i
$329$	3.61123	+	6.25484i	0.199094	+	0.344841i
$330$	4.10667	−	11.0709i	0.226065	−	0.609431i
$331$	−12.7943	+	7.38678i	−0.703238	+	0.406014i	−0.808552	−	0.588425i	$-0.799748\pi$
$331$	−12.7943	+	7.38678i	−0.703238	+	0.406014i	0.105315	+	0.994439i	$0.466415\pi$
$332$	−5.74860	−	5.17607i	−0.315496	−	0.284073i
$333$	−0.666067	+	1.34275i	−0.0365003	+	0.0735820i
$334$	10.1785	+	4.53175i	0.556942	+	0.247966i
$335$	−6.92496	+	6.23526i	−0.378351	+	0.340669i
$336$	7.37423	−	7.85501i	0.402297	−	0.428526i
$337$	14.6333	+	20.1410i	0.797127	+	1.09715i	0.993184	+	0.116558i	$0.0371861\pi$
$337$	14.6333	+	20.1410i	0.797127	+	1.09715i	−0.196057	+	0.980592i	$0.562814\pi$
$338$	2.16387	−	22.2841i	0.117699	−	1.21210i
$339$	1.14908	+	2.73245i	0.0624093	+	0.148407i
$340$	0.403154	−	0.698283i	0.0218641	−	0.0378697i
$341$	−2.74292	−	0.0555509i	−0.148537	−	0.00300825i
$342$	2.78338	−	2.30395i	0.150508	−	0.124584i
$343$	−4.78801	−	14.7360i	−0.258528	−	0.795667i
$344$	−2.09801	+	19.9612i	−0.113117	+	1.07624i
$345$	4.51796	+	1.57260i	0.243239	+	0.0846659i
$346$	34.2748	+	11.1366i	1.84263	+	0.598706i
$347$	−6.45049	+	1.37109i	−0.346281	+	0.0736042i	−0.377769	−	0.925900i	$-0.623309\pi$
$347$	−6.45049	+	1.37109i	−0.346281	+	0.0736042i	0.0314883	+	0.999504i	$0.489975\pi$
$348$	−5.06769	+	0.967463i	−0.271657	+	0.0518615i
$349$	18.3877	−	8.18672i	0.984269	−	0.438225i	0.149462	−	0.988767i	$-0.452246\pi$
$349$	18.3877	−	8.18672i	0.984269	−	0.438225i	0.834807	+	0.550543i	$0.185579\pi$
$350$	−7.28758	+	2.36788i	−0.389537	+	0.126568i
$351$	−0.113990	+	18.7346i	−0.00608435	+	0.999981i
$352$	16.4428	−	3.14847i	0.876407	−	0.167814i
$353$	7.84030	−	13.5798i	0.417297	−	0.722779i	−0.578370	−	0.815775i	$-0.696311\pi$
$353$	7.84030	−	13.5798i	0.417297	−	0.722779i	0.995667	+	0.0929954i	$0.0296442\pi$
$354$	−15.8042	−	1.99425i	−0.839984	−	0.105993i
$355$	0.135226	−	1.28659i	0.00717704	−	0.0682850i
$356$	11.5597	−	8.39863i	0.612664	−	0.445127i
$357$	0.435842	+	1.44283i	0.0230672	+	0.0763629i
$358$	26.8546	−	5.70811i	1.41931	−	0.301683i
$359$	−14.1056	−	19.4146i	−0.744463	−	1.02467i	−0.998349	−	0.0574317i	$-0.981709\pi$
$359$	−14.1056	−	19.4146i	−0.744463	−	1.02467i	0.253886	−	0.967234i	$-0.418291\pi$
$360$	6.36314	−	0.402158i	0.335367	−	0.0211956i
$361$	18.1064	+	3.84864i	0.952970	+	0.202560i
$362$	−1.78955	−	1.03319i	−0.0940564	−	0.0543035i
$363$	−3.14860	+	18.7906i	−0.165259	+	0.986250i
$364$	−3.05268	+	3.07695i	−0.160004	+	0.161276i
$365$	3.31438	+	10.2006i	0.173482	+	0.533924i
$366$	−8.98749	−	16.3427i	−0.469783	−	0.854244i
$367$	1.93701	+	18.4294i	0.101111	+	0.962009i	0.921020	+	0.389515i	$0.127357\pi$
$367$	1.93701	+	18.4294i	0.101111	+	0.962009i	−0.819909	+	0.572494i	$0.805976\pi$
$368$	2.40511	+	11.3151i	0.125375	+	0.589843i
$369$	12.9054	+	1.90194i	0.671829	+	0.0990113i
$370$	−0.938193	−	0.417710i	−0.0487743	−	0.0217157i
$371$	−11.5417	−	1.21308i	−0.599214	−	0.0629799i
$372$	0.536544	+	1.27588i	0.0278185	+	0.0661512i
$373$	−27.2944	+	15.7584i	−1.41325	+	0.815940i	−0.995693	−	0.0927115i	$-0.970447\pi$
$373$	−27.2944	+	15.7584i	−1.41325	+	0.815940i	−0.417556	+	0.908651i	$0.637113\pi$
$374$	−1.31102	+	3.77316i	−0.0677910	+	0.195105i
$375$	−16.0415	−	7.54576i	−0.828379	−	0.389661i
$376$	−9.82946	+	3.19378i	−0.506915	+	0.164707i
$377$	−10.9733	+	1.78256i	−0.565152	+	0.0918067i
$378$	7.09454	−	8.58330i	0.364904	−	0.441477i
$379$	17.9935	−	16.2014i	0.924265	−	0.832212i	−0.0618820	−	0.998083i	$-0.519710\pi$
$379$	17.9935	−	16.2014i	0.924265	−	0.832212i	0.986147	+	0.165871i	$0.0530436\pi$
$380$	0.539545	+	0.599225i	0.0276781	+	0.0307396i
$381$	7.73738	+	2.69320i	0.396398	+	0.137977i
$382$	12.8004	+	9.30004i	0.654926	+	0.475831i
$383$	−12.9680	+	14.4024i	−0.662634	+	0.735930i	−0.976969	−	0.213383i	$-0.931552\pi$
$383$	−12.9680	+	14.4024i	−0.662634	+	0.735930i	0.314335	+	0.949312i	$0.398219\pi$
$384$	12.2025	+	17.5517i	0.622705	+	0.895682i
$385$	−4.31484	+	2.37601i	−0.219905	+	0.121093i
$386$	−33.6373	+	19.4205i	−1.71210	+	0.988479i
$387$	−1.40638	+	33.7856i	−0.0714904	+	1.71742i
$388$	−3.13104	−	7.03243i	−0.158954	−	0.357018i
$389$	2.44660	+	3.36745i	0.124047	+	0.170737i	0.866524	−	0.499135i	$-0.166349\pi$
$389$	2.44660	+	3.36745i	0.124047	+	0.170737i	−0.742477	+	0.669872i	$0.766349\pi$
$390$	−12.8286	+	0.455839i	−0.649599	+	0.0230823i
$391$	−1.53908	−	0.500077i	−0.0778346	−	0.0252900i
$392$	9.65430	−	1.01471i	0.487616	−	0.0512505i
$393$	−13.8779	−	25.2352i	−0.700045	−	1.27295i
$394$	28.6505	−	31.8196i	1.44339	−	1.60305i
$395$		−	8.08442i		−	0.406771i
$396$	9.30781	−	2.39956i	0.467735	−	0.120582i
$397$	10.0502	−	5.80247i	0.504403	−	0.291217i	−0.226127	−	0.974098i	$-0.572606\pi$
$397$	10.0502	−	5.80247i	0.504403	−	0.291217i	0.730530	+	0.682880i	$0.239273\pi$
$398$	30.2546	−	9.83030i	1.51652	−	0.492748i
$399$	−1.50695	−	0.0313512i	−0.0754421	−	0.00156952i
$400$	−1.86828	−	17.7755i	−0.0934141	−	0.888776i
$401$	−7.97315	−	8.85509i	−0.398160	−	0.442202i	0.510412	−	0.859930i	$-0.329493\pi$
$401$	−7.97315	−	8.85509i	−0.398160	−	0.442202i	−0.908572	+	0.417728i	$0.862826\pi$
$402$	−22.6752	−	5.31500i	−1.13093	−	0.265088i
$403$	1.07984	+	2.78013i	0.0537908	+	0.138488i
$404$	6.38902	+	4.64189i	0.317866	+	0.230943i
$405$	10.6562	−	1.35237i	0.529511	−	0.0671998i
$406$	5.72255	+	3.30392i	0.284005	+	0.163971i
$407$	1.61354	+	0.377272i	0.0799804	+	0.0187007i
$408$	−2.14924	+	0.180785i	−0.106403	+	0.00895022i
$409$	−16.1402	+	17.9255i	−0.798079	+	0.886357i	−0.995577	−	0.0939463i	$-0.970052\pi$
$409$	−16.1402	+	17.9255i	−0.798079	+	0.886357i	0.197498	+	0.980303i	$0.436718\pi$
$410$	−0.934266	+	8.88895i	−0.0461401	+	0.438994i
$411$	17.3457	+	20.0894i	0.855600	+	0.990937i
$412$	12.2360	−	2.60085i	0.602826	−	0.128135i
$413$	4.44644	+	4.93827i	0.218795	+	0.242996i
$414$	3.21857	+	11.5149i	0.158184	+	0.565929i
$415$	−5.61739	+	7.73167i	−0.275747	+	0.379533i
$416$	−9.97279	−	15.2244i	−0.488956	−	0.746439i
$417$	−2.84394	+	0.239221i	−0.139268	+	0.0117147i
$418$	−3.18348	−	2.41291i	−0.155709	−	0.118019i
$419$	6.66176	+	3.84617i	0.325448	+	0.187898i	0.653818	−	0.756651i	$-0.273166\pi$
$419$	6.66176	+	3.84617i	0.325448	+	0.187898i	−0.328370	+	0.944549i	$0.606499\pi$
$420$	1.97966	+	1.50220i	0.0965976	+	0.0732998i
$421$	−13.5147	+	18.6014i	−0.658668	+	0.906579i	−0.999436	−	0.0335687i	$-0.989313\pi$
$421$	−13.5147	+	18.6014i	−0.658668	+	0.906579i	0.340769	+	0.940147i	$0.389313\pi$
$422$	−13.2395	−	5.89462i	−0.644490	−	0.286946i
$423$	−16.1878	+	6.41454i	−0.787077	+	0.311886i
$424$	5.13185	−	15.7942i	0.249225	−	0.767035i
$425$	2.28422	+	1.01700i	0.110801	+	0.0493317i
$426$	2.83314	−	1.55806i	0.137266	−	0.0754881i
$427$	−1.61763	+	7.61033i	−0.0782824	+	0.368290i
$428$	−10.2372			−0.494836
$429$	20.1916	−	4.61515i	0.974859	−	0.222822i
$430$	−23.1689			−1.11730
$431$	−1.16985	+	5.50373i	−0.0563498	+	0.265105i	−0.997300	−	0.0734412i	$-0.976602\pi$
$431$	−1.16985	+	5.50373i	−0.0563498	+	0.265105i	0.940950	+	0.338546i	$0.109935\pi$
$432$	16.1429	+	20.3494i	0.776675	+	0.979059i
$433$	4.98341	+	2.21876i	0.239487	+	0.106627i	0.522971	−	0.852350i	$-0.324824\pi$
$433$	4.98341	+	2.21876i	0.239487	+	0.106627i	−0.283484	+	0.958977i	$0.591490\pi$
$434$	0.547806	−	1.68597i	0.0262955	−	0.0809293i
$435$	1.84315	+	6.10167i	0.0883724	+	0.292553i
$436$	−14.8908	−	6.62980i	−0.713138	−	0.317510i
$437$	0.951238	−	1.30927i	0.0455039	−	0.0626307i
$438$	−16.2041	+	21.3545i	−0.774264	+	1.02036i
$439$	−22.3055	−	12.8781i	−1.06458	−	0.614636i	−0.137886	−	0.990448i	$-0.544031\pi$
$439$	−22.3055	−	12.8781i	−1.06458	−	0.614636i	−0.926696	+	0.375812i	$0.877364\pi$
$440$	−2.04200	−	6.74650i	−0.0973485	−	0.321627i
$441$	16.1248	−	2.73204i	0.767849	−	0.130097i
$442$	4.33552	−	0.244433i	0.206220	−	0.0116265i
$443$	10.2486	−	14.1060i	0.486925	−	0.670194i	−0.492892	−	0.870090i	$-0.664060\pi$
$443$	10.2486	−	14.1060i	0.486925	−	0.670194i	0.979817	+	0.199896i	$0.0640604\pi$
$444$	−0.156768	−	0.821169i	−0.00743987	−	0.0389710i
$445$	−11.8121	−	13.1187i	−0.559948	−	0.621885i
$446$	17.4610	−	3.71146i	0.826804	−	0.175743i
$447$	−2.47414	+	2.13623i	−0.117023	+	0.101040i
$448$	0.169653	−	1.61414i	0.00801534	−	0.0762609i
$449$	−4.22205	+	4.68906i	−0.199251	+	0.221290i	−0.834487	−	0.551027i	$-0.814236\pi$
$449$	−4.22205	+	4.68906i	−0.199251	+	0.221290i	0.635236	+	0.772318i	$0.280903\pi$
$450$	−3.08600	−	18.2139i	−0.145475	−	0.858612i
$451$	−1.21674	−	14.3702i	−0.0572942	−	0.676665i
$452$	−1.43181	−	0.826655i	−0.0673466	−	0.0388826i
$453$	−0.0703133	+	0.557226i	−0.00330361	+	0.0261808i
$454$	−3.17419	−	2.30618i	−0.148972	−	0.108235i
$455$	4.17484	+	3.35343i	0.195719	+	0.157211i
$456$	0.492232	−	2.09999i	0.0230509	−	0.0983411i
$457$	−2.03884	−	2.26436i	−0.0953728	−	0.105922i	0.693569	−	0.720390i	$-0.256037\pi$
$457$	−2.03884	−	2.26436i	−0.0953728	−	0.105922i	−0.788942	+	0.614468i	$0.789371\pi$
$458$	−3.33952	−	31.7734i	−0.156046	−	1.48467i
$459$	−3.59451	+	0.532362i	−0.167777	+	0.0248485i
$460$	−2.53761	+	0.824518i	−0.118317	+	0.0384434i
$461$	−35.7971	+	20.6675i	−1.66724	+	0.962580i	−0.698119	+	0.715982i	$0.745979\pi$
$461$	−35.7971	+	20.6675i	−1.66724	+	0.962580i	−0.969118	+	0.246597i	$0.920687\pi$
$462$	−11.0317	−	5.46470i	−0.513243	−	0.254241i
$463$		−	29.4550i		−	1.36889i	−0.729065	−	0.684445i	$-0.760045\pi$
$463$		−	29.4550i		−	1.36889i	0.729065	−	0.684445i	$-0.239955\pi$
$464$	−10.3134	+	11.4542i	−0.478787	+	0.531747i
$465$	1.49837	−	0.824013i	0.0694851	−	0.0382127i
$466$	43.9393	−	4.61820i	2.03545	−	0.213934i
$467$	−31.0813	−	10.0989i	−1.43827	−	0.467322i	−0.516912	−	0.856039i	$-0.672919\pi$
$467$	−31.0813	−	10.0989i	−1.43827	−	0.467322i	−0.921357	+	0.388717i	$0.872919\pi$
$468$	−6.26581	−	8.36252i	−0.289637	−	0.386558i
$469$	5.71060	+	7.85997i	0.263691	+	0.362940i
$470$	−4.85254	−	10.8990i	−0.223831	−	0.502733i
$471$	−1.86284	+	14.7628i	−0.0858352	+	0.680236i
$472$	−8.23512	+	4.75455i	−0.379052	+	0.218846i
$473$	36.7167	−	7.03051i	1.68824	−	0.323263i
$474$	16.5901	−	11.5339i	0.762008	−	0.529771i
$475$	−1.67315	+	1.85822i	−0.0767692	+	0.0852608i
$476$	−0.680108	−	0.494128i	−0.0311727	−	0.0226483i
$477$	6.95028	−	27.1016i	0.318231	−	1.24090i
$478$	9.55534	+	10.6123i	0.437051	+	0.485394i
$479$	−2.81836	+	2.53766i	−0.128774	+	0.115949i	−0.731001	−	0.682376i	$-0.760947\pi$
$479$	−2.81836	+	2.53766i	−0.128774	+	0.115949i	0.602227	+	0.798325i	$0.294280\pi$
$480$	−7.89823	+	6.81953i	−0.360503	+	0.311268i
$481$	−0.288847	−	1.77811i	−0.0131703	−	0.0810748i
$482$	22.7917	−	7.40547i	1.03813	−	0.337310i
$483$	2.12299	−	4.51326i	0.0965995	−	0.205360i
$484$	−4.93634	−	9.41051i	−0.224379	−	0.427750i
$485$	−8.23632	+	4.75524i	−0.373992	+	0.215924i
$486$	17.9783	+	19.9383i	0.815510	+	0.904418i
$487$	−1.11520	−	0.117212i	−0.0505346	−	0.00531140i	0.0792274	−	0.996857i	$-0.474755\pi$
$487$	−1.11520	−	0.117212i	−0.0505346	−	0.00531140i	−0.129762	+	0.991545i	$0.541421\pi$
$488$	−10.1711	−	4.52845i	−0.460423	−	0.204993i
$489$	9.07023	−	38.6959i	0.410170	−	1.74989i
$490$	2.32980	+	10.9608i	0.105249	+	0.495160i
$491$	−0.697804	−	6.63916i	−0.0314914	−	0.299621i	−0.998919	−	0.0464748i	$-0.985201\pi$
$491$	−0.697804	−	6.63916i	−0.0314914	−	0.299621i	0.967428	−	0.253146i	$-0.0814654\pi$
$492$	−6.37532	+	3.50604i	−0.287422	+	0.158065i
$493$	−0.666303	−	2.05067i	−0.0300088	−	0.0923575i
$494$	−1.10732	+	4.19901i	−0.0498207	+	0.188922i
$495$	−4.15032	−	11.1265i	−0.186543	−	0.500100i
$496$	3.58102	+	2.06750i	0.160792	+	0.0928336i
$497$	−1.31932	−	0.280429i	−0.0591794	−	0.0125790i
$498$	−23.8805	−	0.496817i	−1.07011	−	0.0222629i
$499$	16.2082	+	22.3086i	0.725577	+	0.998672i	0.999320	+	0.0368687i	$0.0117383\pi$
$499$	16.2082	+	22.3086i	0.725577	+	0.998672i	−0.273743	+	0.961803i	$0.588262\pi$
$500$	9.67156	−	2.05575i	0.432525	−	0.0919361i
$501$	10.7266	−	3.24022i	0.479229	−	0.144762i
$502$	12.7811	−	9.28600i	0.570447	−	0.414454i
$503$	−1.72078	+	16.3721i	−0.0767258	+	0.729997i	0.886759	+	0.462233i	$0.152952\pi$
$503$	−1.72078	+	16.3721i	−0.0767258	+	0.729997i	−0.963484	+	0.267765i	$0.913715\pi$
$504$	0.276473	−	6.64172i	0.0123151	−	0.295846i
$505$	4.87836	−	8.44956i	0.217084	−	0.376001i
$506$	11.5788	−	6.37595i	0.514739	−	0.283446i
$507$	−12.9992	−	18.3853i	−0.577315	−	0.816521i
$508$	−4.34586	+	1.41205i	−0.192816	+	0.0626498i
$509$	15.6737	−	6.97840i	0.694727	−	0.309312i	−0.0288230	−	0.999585i	$-0.509176\pi$
$509$	15.6737	−	6.97840i	0.694727	−	0.309312i	0.723550	+	0.690272i	$0.242509\pi$
$510$	−0.466874	−	2.44554i	−0.0206735	−	0.108291i
$511$	10.9381	−	2.32497i	0.483874	−	0.102851i
$512$	−7.06666	−	2.29610i	−0.312305	−	0.101474i
$513$	0.604479	−	3.58322i	0.0266884	−	0.158203i
$514$	−3.80494	+	36.2016i	−0.167829	+	1.59678i
$515$	−4.77579	−	14.6984i	−0.210447	−	0.647688i
$516$	−10.7661	−	15.4856i	−0.473950	−	0.681717i
$517$	10.9973	+	15.7996i	0.483659	+	0.694864i
$518$	−0.535367	+	0.927282i	−0.0235227	+	0.0407425i
$519$	33.4103	−	14.0500i	1.46655	−	0.616727i
$520$	−5.93598	+	4.84590i	−0.260310	+	0.212507i
$521$	17.7339	+	24.4087i	0.776938	+	1.06936i	0.995613	+	0.0935653i	$0.0298264\pi$
$521$	17.7339	+	24.4087i	0.776938	+	1.06936i	−0.218676	+	0.975798i	$0.570174\pi$
$522$	−9.89168	+	12.4875i	−0.432947	+	0.546563i
$523$	−16.7823	+	15.1109i	−0.733839	+	0.660751i	−0.948802	−	0.315871i	$-0.897703\pi$
$523$	−16.7823	+	15.1109i	−0.733839	+	0.660751i	0.214963	+	0.976622i	$0.431037\pi$
$524$	14.6743	+	6.53341i	0.641049	+	0.285413i
$525$	−3.99115	+	6.59229i	−0.174188	+	0.287711i
$526$	33.8244	+	30.4556i	1.47481	+	1.32793i
$527$	−0.500963	+	0.289231i	−0.0218223	+	0.0125991i
$528$	17.8182	−	22.5196i	0.775436	−	0.980040i
$529$	−8.82242	−	15.2809i	−0.383584	−	0.664386i
$530$	18.7512	+	3.98569i	0.814500	+	0.173127i
$531$	−13.3412	+	8.86937i	−0.578959	+	0.384898i
$532$	0.680133	−	0.494145i	0.0294875	−	0.0214239i
$533$	−13.9408	+	7.17288i	−0.603844	+	0.310692i
$534$	10.0688	−	42.9560i	0.435718	−	1.85889i
$535$	1.32204	+	12.5784i	0.0571568	+	0.543811i
$536$	−12.7008	+	5.65476i	−0.548591	+	0.244248i
$537$	16.6905	−	21.9955i	0.720250	−	0.949175i
$538$	−36.3540			−1.56733
$539$	−7.01814	−	16.6631i	−0.302293	−	0.717730i
$540$	−4.27876	+	4.19366i	−0.184128	+	0.180466i
$541$	−3.16030	−	9.72640i	−0.135872	−	0.418171i	0.859853	−	0.510542i	$-0.170555\pi$
$541$	−3.16030	−	9.72640i	−0.135872	−	0.418171i	−0.995725	+	0.0923714i	$0.970555\pi$
$542$	16.6032	+	1.74506i	0.713167	+	0.0749569i
$543$	−2.04131	+	0.389703i	−0.0876011	+	0.0167238i
$544$	2.62326	−	2.36200i	0.112472	−	0.101270i
$545$	−6.22295	+	19.1523i	−0.266562	+	0.820393i
$546$	−0.925422	+	13.3515i	−0.0396044	+	0.571392i
$547$	−9.84070	+	13.5446i	−0.420758	+	0.579124i	−0.965801	−	0.259284i	$-0.916513\pi$
$547$	−9.84070	+	13.5446i	−0.420758	+	0.579124i	0.545043	+	0.838408i	$0.316513\pi$
$548$	−14.4802	−	3.07785i	−0.618562	−	0.131479i
$549$	−17.5828	−	6.53327i	−0.750415	−	0.278833i
$550$	−18.8219	+	7.92738i	−0.802569	+	0.338025i
$551$	2.15628			0.0918606
$552$	5.68568	+	4.31438i	0.241998	+	0.183632i
$553$	−8.38267	−	0.881055i	−0.356468	−	0.0374663i
$554$	−17.6944	+	12.8557i	−0.751761	+	0.546186i
$555$	−0.988715	+	0.298665i	−0.0419686	+	0.0126776i
$556$	1.18295	−	1.06513i	0.0501682	−	0.0451717i
$557$	11.4433	−	1.20274i	0.484869	−	0.0509618i	0.141060	−	0.990001i	$-0.454949\pi$
$557$	11.4433	−	1.20274i	0.484869	−	0.0509618i	0.343810	+	0.939039i	$0.388282\pi$
$558$	3.82866	+	1.89920i	0.162080	+	0.0803996i
$559$	−22.2691	−	33.9960i	−0.941885	−	1.43788i
$560$	7.42418			0.313729
$561$	1.48196	+	3.73388i	0.0625686	+	0.157645i
$562$	5.09888	−	8.83152i	0.215083	−	0.372535i
$563$	−15.8971	+	17.6555i	−0.669981	+	0.744089i	−0.978300	−	0.207194i	$-0.933567\pi$
$563$	−15.8971	+	17.6555i	−0.669981	+	0.744089i	0.308319	+	0.951283i	$0.400234\pi$
$564$	5.02979	−	8.30785i	0.211792	−	0.349823i
$565$	−0.830797	+	1.86600i	−0.0349519	+	0.0785032i
$566$	43.9823	−	9.34874i	1.84872	−	0.392957i
$567$	−0.240929	−	11.1967i	−0.0101181	−	0.470218i
$568$	0.785046	−	1.76324i	0.0329398	−	0.0739840i
$569$	18.4146	−	8.19871i	0.771980	−	0.343708i	0.0173427	−	0.999850i	$-0.494479\pi$
$569$	18.4146	−	8.19871i	0.771980	−	0.343708i	0.754638	+	0.656142i	$0.227813\pi$
$570$	2.47021	+	0.311702i	0.103466	+	0.0130558i
$571$			25.1474i			1.05238i	0.850366	+	0.526192i	$0.176381\pi$
$571$			25.1474i			1.05238i	−0.850366	+	0.526192i	$0.823619\pi$
$572$	−7.41541	+	8.85825i	−0.310054	+	0.370382i
$573$	15.8565	−	1.33378i	0.662413	−	0.0557195i
$574$	9.11506	+	1.93747i	0.380455	+	0.0808683i
$575$	−3.36540	−	7.55882i	−0.140347	−	0.315225i
$576$	3.79025	+	0.972017i	0.157927	+	0.0405007i
$577$	7.23072	+	2.34940i	0.301019	+	0.0978069i	0.455632	−	0.890168i	$-0.349413\pi$
$577$	7.23072	+	2.34940i	0.301019	+	0.0978069i	−0.154614	+	0.987975i	$0.549413\pi$
$578$	−5.91209	−	27.8142i	−0.245911	−	1.15692i
$579$	−12.8411	+	36.8917i	−0.533660	+	1.53317i
$580$	−2.87614	−	2.08964i	−0.119425	−	0.0867675i
$581$	7.40472	+	6.66724i	0.307200	+	0.276604i
$582$	−21.5089	−	10.1176i	−0.891572	−	0.419387i
$583$	−30.9252	−	0.626312i	−1.28079	−	0.0259392i
$584$			16.0021i			0.662171i
$585$	−9.46575	+	8.77865i	−0.391361	+	0.362953i
$586$	−11.1619	−	8.10957i	−0.461093	−	0.335003i
$587$	4.04201	+	38.4572i	0.166832	+	1.58730i	0.682745	+	0.730657i	$0.260786\pi$
$587$	4.04201	+	38.4572i	0.166832	+	1.58730i	−0.515913	+	0.856641i	$0.672547\pi$
$588$	−6.24339	+	6.65043i	−0.257473	+	0.274259i
$589$	−0.120273	−	0.565842i	−0.00495578	−	0.0233151i
$590$	−6.45194	−	8.88034i	−0.265622	−	0.365598i
$591$	0.895678	−	43.0525i	0.0368433	−	1.77094i
$592$	−1.85603	−	1.67118i	−0.0762826	−	0.0686851i
$593$		−	35.8539i		−	1.47234i	−0.676795	−	0.736171i	$-0.736632\pi$
$593$		−	35.8539i		−	1.47234i	0.676795	−	0.736171i	$-0.263368\pi$
$594$	16.9116	−	24.3909i	0.693890	−	1.00077i
$595$	−0.519299	+	0.899452i	−0.0212892	+	0.0368739i
$596$	0.379057	−	1.78332i	0.0155268	−	0.0730478i
$597$	16.5693	−	27.3681i	0.678138	−	1.12010i
$598$	−11.2031	−	8.99885i	−0.458127	−	0.367990i
$599$	22.7233	+	7.38326i	0.928450	+	0.301672i	0.733929	−	0.679226i	$-0.237685\pi$
$599$	22.7233	+	7.38326i	0.928450	+	0.301672i	0.194522	+	0.980898i	$0.437685\pi$
$600$	−8.03993	−	7.54784i	−0.328229	−	0.308139i
$601$	−7.10595	+	0.746866i	−0.289858	+	0.0304653i	−0.248341	−	0.968673i	$-0.579886\pi$
$601$	−7.10595	+	0.746866i	−0.289858	+	0.0304653i	−0.0415163	+	0.999138i	$0.513219\pi$
$602$	−2.52499	+	24.0237i	−0.102911	+	0.979132i
$603$	−20.7541	+	10.8575i	−0.845173	+	0.442153i
$604$	−0.156630	−	0.271290i	−0.00637317	−	0.0110387i
$605$	−10.9251	+	7.28050i	−0.444168	+	0.295994i
$606$	24.2993	−	2.04396i	0.987091	−	0.0830301i
$607$	−30.6880	−	27.6316i	−1.24559	−	1.12153i	−0.987865	−	0.155315i	$-0.950361\pi$
$607$	−30.6880	−	27.6316i	−1.24559	−	1.12153i	−0.257724	−	0.966219i	$-0.582972\pi$
$608$	1.43581	+	3.22489i	0.0582299	+	0.130786i
$609$	6.52765	−	1.24618i	0.264514	−	0.0504978i
$610$	3.97148	−	12.2229i	0.160800	−	0.494893i
$611$	11.3281	−	17.5959i	0.458286	−	0.711854i
$612$	1.41761	−	1.44844i	0.0573033	−	0.0585496i
$613$	−38.3552	+	17.0768i	−1.54915	+	0.689727i	−0.990224	−	0.139489i	$-0.955454\pi$
$613$	−38.3552	+	17.0768i	−1.54915	+	0.689727i	−0.558928	+	0.829216i	$0.688787\pi$
$614$	−0.573105	+	2.69625i	−0.0231287	+	0.108812i
$615$	5.13114	+	7.38050i	0.206908	+	0.297611i
$616$	−7.21793	+	1.38209i	−0.290819	+	0.0556859i
$617$	11.3559	+	19.6690i	0.457171	+	0.791844i	0.998810	−	0.0487672i	$-0.0155292\pi$
$617$	11.3559	+	19.6690i	0.457171	+	0.791844i	−0.541639	+	0.840611i	$0.682196\pi$
$618$	23.3491	−	30.7704i	0.939238	−	1.23777i
$619$	−17.8272	+	24.5371i	−0.716537	+	0.986228i	0.283095	+	0.959092i	$0.408639\pi$
$619$	−17.8272	+	24.5371i	−0.716537	+	0.986228i	−0.999632	+	0.0271363i	$0.991361\pi$
$620$	−0.387928	+	0.871301i	−0.0155796	+	0.0349923i
$621$	10.0183	+	6.64998i	0.402021	+	0.266855i
$622$	37.9032	+	42.0957i	1.51978	+	1.68789i
$623$	−14.8900	+	10.8182i	−0.596554	+	0.433422i
$624$	−30.0137	−	8.58643i	−1.20151	−	0.343732i
$625$	1.74960	+	5.38472i	0.0699841	+	0.215389i
$626$	13.9032	+	8.02702i	0.555684	+	0.320824i
$627$	−4.00923	+	0.255608i	−0.160113	+	0.0102080i
$628$	−4.14966	−	7.18742i	−0.165589	−	0.286809i
$629$	0.332291	−	0.107968i	0.0132493	−	0.00430496i
$630$	7.65815	−	0.484003i	0.305108	−	0.0192832i
$631$	−4.46458	+	10.0276i	−0.177732	+	0.399193i	−0.980340	−	0.197314i	$-0.936778\pi$
$631$	−4.46458	+	10.0276i	−0.177732	+	0.399193i	0.802608	+	0.596506i	$0.203445\pi$
$632$	3.72725	−	11.4713i	0.148262	−	0.456303i
$633$	−13.9525	+	4.21468i	−0.554562	+	0.167518i
$634$	−47.0671	+	4.94695i	−1.86927	+	0.196468i
$635$	2.29620	+	5.15735i	0.0911219	+	0.204663i
$636$	6.04930	+	14.3850i	0.239870	+	0.570401i
$637$	−13.8436	+	13.9537i	−0.548505	+	0.552866i
$638$	15.9409	+	7.48772i	0.631108	+	0.296442i
$639$	1.13260	−	3.04813i	0.0448049	−	0.120582i
$640$	−3.06259	+	14.4083i	−0.121059	+	0.569540i
$641$	−5.25228	−	0.552037i	−0.207453	−	0.0218041i	0.000232095	−	1.00000i	$-0.499926\pi$
$641$	−5.25228	−	0.552037i	−0.207453	−	0.0218041i	−0.207685	+	0.978196i	$0.566593\pi$
$642$	−23.9260	+	20.6584i	−0.944285	+	0.815320i
$643$	−4.89219	−	23.0160i	−0.192929	−	0.907661i	−0.962958	−	0.269651i	$-0.913092\pi$
$643$	−4.89219	−	23.0160i	−0.192929	−	0.907661i	0.770029	−	0.638009i	$-0.220242\pi$
$644$	0.578384	+	2.72108i	0.0227915	+	0.107226i
$645$	−17.6367	+	15.2279i	−0.694443	+	0.599600i
$646$	−0.837640	−	0.0880396i	−0.0329565	−	0.00346387i
$647$	6.90308	−	32.4765i	0.271388	−	1.27678i	−0.605407	−	0.795916i	$-0.706989\pi$
$647$	6.90308	−	32.4765i	0.271388	−	1.27678i	0.876795	−	0.480865i	$-0.159677\pi$
$648$	15.7440	+	2.99402i	0.618482	+	0.117616i
$649$	12.9194	+	12.1152i	0.507129	+	0.475564i
$650$	15.7615	+	15.6372i	0.618217	+	0.613340i
$651$	−0.691118	−	1.64345i	−0.0270870	−	0.0644118i
$652$	9.01644	+	20.2512i	0.353111	+	0.793100i
$653$	−26.1709	+	2.75067i	−1.02415	+	0.107642i	−0.601680	−	0.798737i	$-0.705502\pi$
$653$	−26.1709	+	2.75067i	−1.02415	+	0.107642i	−0.422465	+	0.906379i	$0.638835\pi$
$654$	−48.1807	+	14.5541i	−1.88401	+	0.569110i
$655$	6.13248	−	18.8738i	0.239616	−	0.737461i
$656$	−8.84097	+	19.8571i	−0.345182	+	0.775291i
$657$	1.70047	+	26.9058i	0.0663418	+	1.04969i
$658$	−11.8299	+	3.84377i	−0.461178	+	0.149846i
$659$	18.1801	+	31.4889i	0.708196	+	1.22663i	0.965526	+	0.260308i	$0.0838242\pi$
$659$	18.1801	+	31.4889i	0.708196	+	1.22663i	−0.257329	+	0.966324i	$0.582842\pi$
$660$	5.59539	+	3.54438i	0.217800	+	0.137965i
$661$	−35.9767	−	20.7712i	−1.39933	−	0.807904i	−0.405009	−	0.914313i	$-0.632732\pi$
$661$	−35.9767	−	20.7712i	−1.39933	−	0.807904i	−0.994322	+	0.106409i	$0.966065\pi$
$662$	−7.86244	−	24.1981i	−0.305583	−	0.940486i
$663$	3.13963	−	3.03562i	0.121933	−	0.117894i
$664$	−11.5353	+	8.38092i	−0.447658	+	0.325243i
$665$	−0.694983	−	0.771857i	−0.0269503	−	0.0299313i
$666$	−2.02348	−	1.60285i	−0.0784081	−	0.0621091i
$667$	−2.90215	+	6.51833i	−0.112372	+	0.252391i
$668$	−3.67354	+	5.05619i	−0.142133	+	0.195630i
$669$	10.8523	−	14.3016i	0.419575	−	0.552933i
$670$	−8.02423	−	13.8984i	−0.310003	−	0.536941i
$671$	−2.58476	+	20.5753i	−0.0997834	+	0.794301i
$672$	6.21036	+	8.93281i	0.239570	+	0.344591i
$673$	−5.90726	+	27.7915i	−0.227708	+	1.07128i	0.704596	+	0.709608i	$0.251128\pi$
$673$	−5.90726	+	27.7915i	−0.227708	+	1.07128i	−0.932304	+	0.361675i	$0.882205\pi$
$674$	−39.1691	+	17.4392i	−1.50874	+	0.671733i
$675$	−14.3204	−	11.8365i	−0.551191	−	0.455587i
$676$	11.9744	+	3.78615i	0.460555	+	0.145621i
$677$	−7.17343	+	22.0775i	−0.275697	+	0.848509i	0.713337	+	0.700821i	$0.247183\pi$
$677$	−7.17343	+	22.0775i	−0.275697	+	0.848509i	−0.989034	+	0.147687i	$0.952817\pi$
$678$	−5.01452	+	0.957311i	−0.192581	+	0.0367653i
$679$	4.03306	+	9.05841i	0.154775	+	0.347630i
$680$	−1.10448	−	0.994480i	−0.0423549	−	0.0381366i
$681$	−3.93201	+	0.330745i	−0.150675	+	0.0126742i
$682$	1.07574	−	4.60080i	0.0411922	−	0.176174i
$683$	3.07617	+	5.32808i	0.117706	+	0.203873i	0.918858	−	0.394588i	$-0.129113\pi$
$683$	3.07617	+	5.32808i	0.117706	+	0.203873i	−0.801152	+	0.598461i	$0.795779\pi$
$684$	0.939515	+	1.79588i	0.0359233	+	0.0686672i
$685$	−1.91175	+	18.1891i	−0.0730442	+	0.694969i
$686$	26.5385	−	2.78931i	1.01324	−	0.106496i
$687$	−23.4254	−	21.9917i	−0.893736	−	0.839034i
$688$	−53.5874	−	17.4116i	−2.04300	−	0.663811i
$689$	12.1747	+	31.3448i	0.463821	+	1.19414i
$690$	−4.26693	+	7.04781i	−0.162439	+	0.268306i
$691$	−0.648362	+	3.05031i	−0.0246649	+	0.116039i	−0.988758	−	0.149526i	$-0.952225\pi$
$691$	−0.648362	+	3.05031i	−0.0246649	+	0.116039i	0.964093	+	0.265565i	$0.0855585\pi$
$692$	−10.1077	+	17.5070i	−0.384237	+	0.665518i
$693$	−11.9893	+	3.09085i	−0.455436	+	0.117412i
$694$		−	11.3574i		−	0.431120i
$695$	−1.46148	−	1.31592i	−0.0554372	−	0.0499158i
$696$	−0.197800	+	9.50766i	−0.00749760	+	0.360387i
$697$	−1.78733	−	2.46005i	−0.0676999	−	0.0931809i
$698$	7.20718	+	33.9071i	0.272796	+	1.28340i
$699$	30.4121	−	32.3949i	1.15029	−	1.22529i
$700$	−0.449287	−	4.27468i	−0.0169815	−	0.161568i
$701$	18.2265	+	13.2423i	0.688404	+	0.500155i	0.876135	−	0.482066i	$-0.160113\pi$
$701$	18.2265	+	13.2423i	0.688404	+	0.500155i	−0.187731	+	0.982220i	$0.560113\pi$
$702$	−31.5194	−	6.90035i	−1.18962	−	0.260437i
$703$			0.349404i			0.0131780i
$704$	0.0875916	−	4.32499i	0.00330123	−	0.163004i
$705$	−10.8573	−	5.10716i	−0.408909	−	0.192347i
$706$	20.0690	+	18.0702i	0.755307	+	0.680081i
$707$	−8.22964	−	5.97918i	−0.309507	−	0.224870i
$708$	2.93736	−	8.43883i	0.110393	−	0.317151i
$709$	−1.85441	−	8.72431i	−0.0696438	−	0.327648i	0.929509	−	0.368799i	$-0.120231\pi$
$709$	−1.85441	−	8.72431i	−0.0696438	−	0.327648i	−0.999153	+	0.0411508i	$0.986898\pi$
$710$	2.11895	+	0.688489i	0.0795228	+	0.0258385i
$711$	5.04796	−	19.6838i	0.189313	−	0.738201i
$712$	−10.7124	−	24.0605i	−0.401465	−	0.901704i
$713$	1.87239	+	0.397989i	0.0701215	+	0.0149048i
$714$	−2.58665	+	0.217578i	−0.0968028	+	0.00814267i
$715$	11.8416	+	7.96727i	0.442853	+	0.297959i
$716$			15.4002i			0.575533i
$717$	14.2487	+	1.79797i	0.532128	+	0.0671463i
$718$	37.7565	−	16.8103i	1.40906	−	0.627354i
$719$	0.853833	−	1.91774i	0.0318426	−	0.0715196i	−0.896924	−	0.442185i	$-0.854204\pi$
$719$	0.853833	−	1.91774i	0.0318426	−	0.0715196i	0.928767	+	0.370665i	$0.120870\pi$
$720$	−2.60964	+	17.7074i	−0.0972556	+	0.659916i
$721$	−15.7611	+	3.35013i	−0.586975	+	0.124765i
$722$	−12.9668	+	29.1238i	−0.482573	+	1.08388i
$723$	12.4822	−	20.6172i	0.464218	−	0.766762i
$724$	0.775596	−	0.861387i	0.0288248	−	0.0320132i
$725$	5.51224	−	9.54749i	0.204720	−	0.354585i
$726$	−30.5270	−	12.0325i	−1.13296	−	0.446567i
$727$	27.7235			1.02821			0.514103	−	0.857728i	$-0.328125\pi$
$727$	27.7235			1.02821			0.514103	+	0.857728i	$0.328125\pi$
$728$	4.37777	+	6.68308i	0.162251	+	0.247692i
$729$	26.7900	+	3.36107i	0.992222	+	0.124484i
$730$	−18.3706	+	1.93083i	−0.679927	+	0.0714632i
$731$	5.85772	−	5.27432i	0.216656	−	0.195078i
$732$	10.0150	−	3.02527i	0.370166	−	0.111817i
$733$	24.6217	−	17.8887i	0.909423	−	0.660734i	−0.0314461	−	0.999505i	$-0.510011\pi$
$733$	24.6217	−	17.8887i	0.909423	−	0.660734i	0.940869	+	0.338771i	$0.110011\pi$
$734$	−31.7396	−	3.33597i	−1.17153	−	0.123133i
$735$	8.97758	+	6.81233i	0.331143	+	0.251277i
$736$	−11.6811			−0.430573
$737$	16.9337	+	19.5904i	0.623762	+	0.721621i
$738$	−7.82504	+	21.0593i	−0.288044	+	0.775203i
$739$	−4.85185	−	1.03129i	−0.178478	−	0.0379367i	0.117806	−	0.993037i	$-0.462414\pi$
$739$	−4.85185	−	1.03129i	−0.178478	−	0.0379367i	−0.296284	+	0.955100i	$0.595747\pi$
$740$	0.338605	−	0.466050i	0.0124474	−	0.0171323i
$741$	1.91692	+	3.92417i	0.0704197	+	0.144158i
$742$	6.17627	−	19.0086i	0.226738	−	0.697828i
$743$	2.71266	−	2.44249i	0.0995180	−	0.0896064i	−0.617870	−	0.786280i	$-0.712004\pi$
$743$	2.71266	−	2.44249i	0.0995180	−	0.0896064i	0.717388	+	0.696674i	$0.245338\pi$
$744$	2.50599	−	0.478414i	0.0918741	−	0.0175395i
$745$	−2.24010	−	0.235444i	−0.0820709	−	0.00862600i
$746$	−16.7731	−	51.6224i	−0.614109	−	1.89003i
$747$	−18.5048	+	15.3174i	−0.677056	+	0.560435i
$748$	−1.91735	−	1.15937i	−0.0701053	−	0.0423908i
$749$	13.1865			0.481824
$750$	18.4555	−	24.3214i	0.673900	−	0.888093i
$751$	39.0897	−	17.4038i	1.42640	−	0.635075i	0.459027	−	0.888423i	$-0.348198\pi$
$751$	39.0897	−	17.4038i	1.42640	−	0.635075i	0.967375	+	0.253348i	$0.0815316\pi$
$752$	−3.03278	−	28.8550i	−0.110594	−	1.05223i
$753$	3.62593	−	15.4692i	0.132136	−	0.563727i
$754$	0.926317	−	19.1237i	0.0337345	−	0.696446i
$755$	−0.313104	+	0.227483i	−0.0113950	+	0.00827897i
$756$	3.88206	+	4.89364i	0.141189	+	0.177980i
$757$	33.9231	+	7.21058i	1.23296	+	0.262073i	0.777899	−	0.628389i	$-0.216286\pi$
$757$	33.9231	+	7.21058i	1.23296	+	0.262073i	0.455057	+	0.890462i	$0.349619\pi$
$758$	20.8498	+	36.1130i	0.757300	+	1.31168i
$759$	4.62335	−	12.4637i	0.167817	−	0.452405i
$760$	1.28716	−	0.743140i	0.0466901	−	0.0269565i
$761$	−10.0263	−	9.02770i	−0.363452	−	0.327254i	0.467090	−	0.884210i	$-0.345303\pi$
$761$	−10.0263	−	9.02770i	−0.363452	−	0.327254i	−0.830542	+	0.556956i	$0.811969\pi$
$762$	−7.30747	+	12.0700i	−0.264722	+	0.437248i
$763$	19.1807	+	8.53978i	0.694386	+	0.309161i
$764$	−6.59557	+	5.93868i	−0.238619	+	0.214854i
$765$	−1.96275	−	1.55474i	−0.0709632	−	0.0562118i
$766$	−19.6187	−	27.0028i	−0.708853	−	0.975653i
$767$	6.82884	−	18.0025i	0.246575	−	0.650032i
$768$	−29.7718	+	12.5199i	−1.07430	+	0.451774i
$769$	−4.31818	+	7.47931i	−0.155718	+	0.269711i	−0.933320	−	0.359045i	$-0.883102\pi$
$769$	−4.31818	+	7.47931i	−0.155718	+	0.269711i	0.777602	+	0.628756i	$0.216436\pi$
$770$	−2.45758	−	8.11952i	−0.0885650	−	0.292607i
$771$	20.8974	+	30.0582i	0.752600	+	1.08252i
$772$	−6.73265	−	20.7210i	−0.242313	−	0.745764i
$773$	2.80588	−	26.6962i	0.100921	−	0.960196i	−0.820505	−	0.571640i	$-0.806307\pi$
$773$	2.80588	−	26.6962i	0.100921	−	0.960196i	0.921425	−	0.388556i	$-0.127026\pi$
$774$	−56.4113	−	14.4668i	−2.02766	−	0.519999i
$775$	−2.81287	−	0.913958i	−0.101041	−	0.0328304i
$776$	−13.8792	+	2.95011i	−0.498233	+	0.105903i
$777$	0.201931	+	1.05774i	0.00724424	+	0.0379462i
$778$	−6.54883	+	2.91573i	−0.234787	+	0.104534i
$779$	2.89206	−	0.939688i	0.103619	−	0.0336678i
$780$	1.24602	−	7.09190i	0.0446147	−	0.253931i
$781$	−3.56691	−	0.448089i	−0.127634	−	0.0160339i
$782$	1.39352	−	2.41365i	0.0498323	−	0.0863121i
$783$	0.677759	+	16.0071i	0.0242211	+	0.572048i
$784$	−2.84855	+	27.1022i	−0.101734	+	0.967935i
$785$	−8.29520	+	6.02682i	−0.296068	+	0.215106i
$786$	47.4802	−	14.3425i	1.69356	−	0.511580i
$787$	−11.3567	+	2.41395i	−0.404824	+	0.0860481i	−0.405824	−	0.913951i	$-0.633015\pi$
$787$	−11.3567	+	2.41395i	−0.404824	+	0.0860481i	0.000999287		1.00000i	$0.499682\pi$
$788$	14.1174	+	19.4309i	0.502910	+	0.692196i
$789$	45.7650	+	0.952109i	1.62928	+	0.0338960i
$790$	13.6189	+	2.89479i	0.484540	+	0.102992i
$791$	1.84430	+	1.06481i	0.0655757	+	0.0378602i
$792$	−0.759274	−	17.7013i	−0.0269796	−	0.628988i
$793$	21.7521	−	5.92087i	0.772440	−	0.210256i
$794$	6.17610	+	19.0081i	0.219182	+	0.674572i
$795$	16.8934	−	9.29038i	0.599148	−	0.329496i
$796$	1.86523	+	17.7465i	0.0661112	+	0.629006i
$797$	−8.41813	−	39.6042i	−0.298185	−	1.40285i	−0.830836	−	0.556517i	$-0.812137\pi$
$797$	−8.41813	−	39.6042i	−0.298185	−	1.40285i	0.532651	−	0.846335i	$-0.321196\pi$
$798$	0.592410	−	2.52737i	0.0209711	−	0.0894681i
$799$	3.70797	+	1.65089i	0.131178	+	0.0584044i
$800$	17.9495	+	1.88657i	0.634610	+	0.0667002i
$801$	−20.5686	−	39.3167i	−0.726755	−	1.38919i
$802$	17.7721	−	10.2607i	0.627556	−	0.362320i
$803$	28.5267	−	8.63434i	1.00669	−	0.304699i
$804$	5.56071	−	11.8215i	0.196111	−	0.416912i
$805$	3.26867	−	1.06205i	0.115205	−	0.0374325i
$806$	−5.07004	+	0.823608i	−0.178585	+	0.0290103i
$807$	−27.6734	+	23.8940i	−0.974151	+	0.841107i
$808$	10.8177	−	9.74028i	0.380565	−	0.342662i
$809$	6.57170	+	7.29861i	0.231049	+	0.256605i	0.847510	−	0.530780i	$-0.178101\pi$
$809$	6.57170	+	7.29861i	0.231049	+	0.256605i	−0.616461	+	0.787385i	$0.711434\pi$
$810$	−1.53749	+	18.4356i	−0.0540218	+	0.647760i
$811$	4.15964	+	3.02216i	0.146065	+	0.106122i	0.658418	−	0.752653i	$-0.271226\pi$
$811$	4.15964	+	3.02216i	0.146065	+	0.106122i	−0.512353	+	0.858775i	$0.671226\pi$
$812$	−2.48018	+	2.75452i	−0.0870372	+	0.0966646i
$813$	13.7856	−	9.58418i	0.483483	−	0.336132i
$814$	−1.21331	+	2.58307i	−0.0425265	+	0.0905365i
$815$	23.7181	−	13.6936i	0.830808	−	0.479667i
$816$	0.758010	−	6.00716i	0.0265357	−	0.210293i
$817$	3.20615	+	7.20114i	0.112169	+	0.251936i
$818$	−24.4177	−	33.6081i	−0.853746	−	1.17508i
$819$	8.07093	+	10.7717i	0.282021	+	0.376393i
$820$	−4.76821	−	1.54928i	−0.166513	−	0.0541034i
$821$	−7.53080	+	0.791519i	−0.262827	+	0.0276242i	−0.235025	−	0.971989i	$-0.575517\pi$
$821$	−7.53080	+	0.791519i	−0.262827	+	0.0276242i	−0.0278015	+	0.999613i	$0.508851\pi$
$822$	−40.0534	+	22.0270i	−1.39702	+	0.768279i
$823$	19.0383	−	21.1441i	0.663632	−	0.737038i	−0.313519	−	0.949582i	$-0.601508\pi$
$823$	19.0383	−	21.1441i	0.663632	−	0.737038i	0.977152	+	0.212543i	$0.0681747\pi$
$824$		−	23.0579i		−	0.803261i
$825$	−9.11729	+	18.4053i	−0.317423	+	0.640791i
$826$	−9.91110	+	5.72218i	−0.344851	+	0.199100i
$827$	−15.5834	+	5.06335i	−0.541888	+	0.176070i	−0.567156	−	0.823611i	$-0.691956\pi$
$827$	−15.5834	+	5.06335i	−0.541888	+	0.176070i	0.0252677	+	0.999681i	$0.491956\pi$
$828$	−6.69336	+	0.423027i	−0.232610	+	0.0147012i
$829$	−5.31249	−	50.5450i	−0.184511	−	1.75550i	−0.559833	−	0.828606i	$-0.689135\pi$
$829$	−5.31249	−	50.5450i	−0.184511	−	1.75550i	0.375322	−	0.926894i	$-0.377532\pi$
$830$	−11.0133	−	12.2315i	−0.382276	−	0.424561i
$831$	−5.01980	+	21.4158i	−0.174135	+	0.742905i
$832$	−4.38366	+	1.70268i	−0.151976	+	0.0590296i
$833$	−3.08423	−	2.24082i	−0.106862	−	0.0776399i
$834$	0.615342	−	4.87652i	0.0213075	−	0.168860i
$835$	6.68688	+	3.86067i	0.231409	+	0.133604i
$836$	1.69518	−	1.46530i	0.0586291	−	0.0506783i
$837$	4.16272	−	1.07070i	0.143885	−	0.0370089i
$838$	−8.86460	+	9.84513i	−0.306222	+	0.340095i
$839$	1.92133	−	18.2803i	0.0663318	−	0.631105i	−0.909967	−	0.414680i	$-0.863894\pi$
$839$	1.92133	−	18.2803i	0.0663318	−	0.631105i	0.976299	−	0.216425i	$-0.0694398\pi$
$840$	3.46709	−	2.99358i	0.119626	−	0.103288i
$841$	19.0671	−	4.05283i	0.657486	−	0.139753i
$842$	−26.4966	−	29.4274i	−0.913132	−	1.01414i
$843$	−1.92321	−	10.0740i	−0.0662388	−	0.346967i
$844$	4.77831	−	6.57678i	0.164476	−	0.226382i
$845$	3.10562	−	15.2018i	0.106836	−	0.522957i
$846$	−5.00950	−	29.5666i	−0.172230	−	1.01652i
$847$	6.35846	+	12.1216i	0.218479	+	0.416503i
$848$	40.3744	+	23.3102i	1.38646	+	0.800474i
$849$	27.3357	−	36.0242i	0.938160	−	1.23635i
$850$	−2.53114	+	3.48381i	−0.0868172	+	0.119494i
$851$	−1.05623	−	0.470264i	−0.0362071	−	0.0161204i
$852$	0.524456	+	1.73619i	0.0179676	+	0.0594808i
$853$	−17.1391	+	52.7487i	−0.586831	+	1.80608i	0.00495678	+	0.999988i	$0.498422\pi$
$853$	−17.1391	+	52.7487i	−0.586831	+	1.80608i	−0.591788	+	0.806094i	$0.701578\pi$
$854$	−12.2411	−	5.45007i	−0.418880	−	0.186498i
$855$	2.08525	−	1.38629i	0.0713139	−	0.0474102i
$856$	−3.92325	+	18.4574i	−0.134094	+	0.630863i
$857$	−17.9504			−0.613173			−0.306587	−	0.951843i	$-0.599187\pi$
$857$	−17.9504			−0.613173			−0.306587	+	0.951843i	$0.599187\pi$
$858$	0.544627	+	35.6671i	0.0185933	+	1.21765i
$859$	9.39050			0.320400			0.160200	−	0.987085i	$-0.448786\pi$
$859$	9.39050			0.320400			0.160200	+	0.987085i	$0.448786\pi$
$860$	2.70208	−	12.7123i	0.0921400	−	0.433485i
$861$	8.21199	−	4.51610i	0.279864	−	0.153908i
$862$	−8.85263	−	3.94144i	−0.301522	−	0.134246i
$863$	−4.90783	+	15.1047i	−0.167064	+	0.514171i	−0.999182	−	0.0404272i	$-0.987128\pi$
$863$	−4.90783	+	15.1047i	−0.167064	+	0.514171i	0.832118	+	0.554598i	$0.187128\pi$
$864$	−23.4886	+	11.6724i	−0.799099	+	0.397103i
$865$	22.8160	+	10.1583i	0.775767	+	0.345394i
$866$	−5.52211	+	7.60053i	−0.187649	+	0.258276i
$867$	−22.7815	−	17.2870i	−0.773700	−	0.587096i
$868$	0.861168	+	0.497196i	0.0292300	+	0.0168759i
$869$	−22.4609	−	0.454888i	−0.761933	−	0.0154310i
$870$	−10.9388	+	0.920127i	−0.370860	+	0.0311952i
$871$	12.6806	−	25.1327i	0.429667	−	0.851588i
$872$	−17.6600	+	24.3068i	−0.598041	+	0.823133i
$873$	−23.0228	+	6.43518i	−0.779205	+	0.217798i
$874$	1.86497	+	2.07126i	0.0630834	+	0.0700613i
$875$	−12.4578	+	2.64800i	−0.421152	+	0.0895186i
$876$	−9.82692	−	11.3813i	−0.332021	−	0.384539i
$877$	2.92307	−	27.8111i	0.0987050	−	0.939115i	−0.827340	−	0.561702i	$-0.810147\pi$
$877$	2.92307	−	27.8111i	0.0987050	−	0.939115i	0.926045	−	0.377414i	$-0.123186\pi$
$878$	29.6812	−	32.9643i	1.00169	−	1.11249i
$879$	−13.8267	+	1.16305i	−0.466364	+	0.0392287i
$880$	19.7172	−	1.66948i	0.664666	−	0.0562783i
$881$	−30.9363	−	17.8611i	−1.04227	−	0.601754i	−0.121794	−	0.992555i	$-0.538865\pi$
$881$	−30.9363	−	17.8611i	−1.04227	−	0.601754i	−0.920475	+	0.390801i	$0.872198\pi$
$882$	−1.17146	+	28.1420i	−0.0394450	+	0.947590i
$883$	30.6129	+	22.2415i	1.03020	+	0.748488i	0.968350	−	0.249598i	$-0.0802983\pi$
$883$	30.6129	+	22.2415i	1.03020	+	0.748488i	0.0618551	+	0.998085i	$0.480298\pi$
$884$	−0.371515	+	2.40731i	−0.0124954	+	0.0809666i
$885$	−10.7480	−	2.51931i	−0.361291	−	0.0846856i
$886$	20.0930	+	22.3156i	0.675039	+	0.749707i
$887$	−0.991114	−	9.42982i	−0.0332784	−	0.316622i	−0.998480	−	0.0551156i	$-0.982447\pi$
$887$	−0.991114	−	9.42982i	−0.0332784	−	0.316622i	0.965202	−	0.261507i	$-0.0842194\pi$
$888$	−1.54062	−	0.0320516i	−0.0516999	−	0.00107558i
$889$	5.59786	−	1.81885i	0.187746	−	0.0610024i
$890$	26.3292	−	15.2012i	0.882556	−	0.509544i
$891$	−3.15768	−	29.6821i	−0.105786	−	0.994389i
$892$			10.0133i			0.335271i
$893$	−2.71602	+	3.01644i	−0.0908880	+	0.100941i
$894$	−2.71276	−	4.93282i	−0.0907282	−	0.164978i
$895$	18.9220	−	1.98879i	0.632494	−	0.0664778i
$896$	14.6061	+	4.74582i	0.487957	+	0.158547i
$897$	−14.4426	+	0.513190i	−0.482223	+	0.0171349i
$898$	−6.38735	−	8.79143i	−0.213148	−	0.293374i
$899$	1.03738	+	2.33000i	0.0345987	+	0.0777100i
$900$	10.3535	+	0.430980i	0.345116	+	0.0143660i
$901$	−5.64813	+	3.26095i	−0.188167	+	0.108638i
$902$	24.6435	+	3.09582i	0.820539	+	0.103079i
$903$	13.8677	+	19.9469i	0.461487	+	0.663791i
$904$	−2.03915	+	2.26471i	−0.0678211	+	0.0753230i
$905$	−1.15854	−	0.841726i	−0.0385110	−	0.0279799i
$906$	−0.913521	−	0.317975i	−0.0303497	−	0.0105640i
$907$	15.9046	+	17.6638i	0.528103	+	0.586517i	0.946886	−	0.321569i	$-0.104210\pi$
$907$	15.9046	+	17.6638i	0.528103	+	0.586517i	−0.418784	+	0.908086i	$0.637543\pi$
$908$	1.63554	−	1.47265i	0.0542773	−	0.0488715i
$909$	17.1537	−	17.5268i	0.568952	−	0.581327i
$910$	−7.14405	+	5.83212i	−0.236823	+	0.193333i
$911$	9.95029	−	3.23304i	0.329668	−	0.107116i	−0.139507	−	0.990221i	$-0.544552\pi$
$911$	9.95029	−	3.23304i	0.329668	−	0.107116i	0.469174	+	0.883106i	$0.344552\pi$
$912$	5.47911	+	2.57732i	0.181431	+	0.0853435i
$913$	21.1648	+	16.0418i	0.700451	+	0.530906i
$914$	4.54456	−	2.62381i	0.150321	−	0.0867878i
$915$	−5.01045	−	11.9146i	−0.165640	−	0.393886i
$916$	17.8228	+	1.87326i	0.588883	+	0.0618941i
$917$	−18.9018	−	8.41562i	−0.624192	−	0.277908i
$918$	0.390275	−	6.24589i	0.0128810	−	0.206145i
$919$	−4.16694	−	19.6039i	−0.137455	−	0.646673i	−0.991888	−	0.127112i	$-0.959429\pi$
$919$	−4.16694	−	19.6039i	−0.137455	−	0.646673i	0.854434	−	0.519560i	$-0.173904\pi$
$920$	0.514087	+	4.89121i	0.0169489	+	0.161258i
$921$	1.33587	+	2.42912i	0.0440184	+	0.0800422i
$922$	−21.9983	−	67.7038i	−0.724475	−	2.22971i
$923$	1.02643	+	3.77091i	0.0337855	+	0.124121i
$924$	4.28494	−	5.41555i	0.140964	−	0.178158i
$925$	1.54708	+	0.893204i	0.0508675	+	0.0293684i
$926$	49.6196	+	10.5470i	1.63060	+	0.346595i
$927$	−2.45027	−	38.7694i	−0.0804774	−	1.27335i
$928$	−9.14827	−	12.5915i	−0.300307	−	0.413337i
$929$	−14.5886	+	3.10091i	−0.478637	+	0.101737i	−0.440911	−	0.897551i	$-0.645345\pi$
$929$	−14.5886	+	3.10091i	−0.478637	+	0.101737i	−0.0377259	+	0.999288i	$0.512011\pi$
$930$	0.851602	+	2.81919i	0.0279251	+	0.0924448i
$931$	3.08434	−	2.24090i	0.101085	−	0.0734426i
$932$	−2.59051	+	24.6471i	−0.0848551	+	0.807342i
$933$	56.5204	+	7.13200i	1.85040	+	0.233491i
$934$	28.1418	−	48.7430i	0.920828	−	1.59492i
$935$	−1.17690	+	2.50554i	−0.0384886	+	0.0819401i
$936$	−17.4786	+	8.09226i	−0.571307	+	0.264504i
$937$	27.0101	−	8.77611i	0.882381	−	0.286703i	0.167435	−	0.985883i	$-0.446451\pi$
$937$	27.0101	−	8.77611i	0.882381	−	0.286703i	0.714946	+	0.699180i	$0.246451\pi$
$938$	−15.2856	+	6.80560i	−0.499093	+	0.222211i
$939$	15.8592	−	3.02765i	0.517546	−	0.0988038i
$940$	6.54596	−	1.39139i	0.213506	−	0.0453820i
$941$	1.39876	+	0.454485i	0.0455983	+	0.0148158i	0.331727	−	0.943375i	$-0.392369\pi$
$941$	1.39876	+	0.454485i	0.0455983	+	0.0148158i	−0.286129	+	0.958191i	$0.592369\pi$
$942$	−24.2023	−	8.42426i	−0.788554	−	0.274477i
$943$	−1.05181	+	10.0073i	−0.0342516	+	0.325882i
$944$	−8.24907	−	25.3880i	−0.268484	−	0.826310i
$945$	5.51143	−	5.40181i	0.179287	−	0.175721i
$946$	−1.30365	+	64.3700i	−0.0423854	+	2.09285i
$947$	25.7583	−	44.6147i	0.837033	−	1.44978i	−0.0553317	−	0.998468i	$-0.517622\pi$
$947$	25.7583	−	44.6147i	0.837033	−	1.44978i	0.892365	−	0.451315i	$-0.149045\pi$
$948$	4.39358	+	10.4478i	0.142697	+	0.339327i
$949$	−20.4903	−	25.0995i	−0.665143	−	0.814766i
$950$	−2.53123	−	3.48394i	−0.0821239	−	0.113034i
$951$	−32.5770	+	34.7009i	−1.05638	+	1.12525i
$952$	−1.15154	+	1.03685i	−0.0373215	+	0.0336044i
$953$	25.4542	+	11.3329i	0.824542	+	0.367110i	0.775234	−	0.631674i	$-0.217632\pi$
$953$	25.4542	+	11.3329i	0.824542	+	0.367110i	0.0493079	+	0.998784i	$0.484298\pi$
$954$	43.1664	+	21.4127i	1.39757	+	0.693260i
$955$	8.14853	+	7.33697i	0.263680	+	0.237419i
$956$	−6.93711	+	4.00514i	−0.224362	+	0.129536i
$957$	17.0559	−	4.77749i	0.551340	−	0.154434i
$958$	−3.26575	−	5.65644i	−0.105512	−	0.182751i
$959$	18.6518	+	3.96455i	0.602297	+	0.128022i
$960$	1.29929	+	2.36260i	0.0419343	+	0.0762525i
$961$	−24.5260	+	17.8192i	−0.791160	+	0.574811i
$962$	3.09881	+	0.150100i	0.0999097	+	0.00483943i
$963$	−4.63513	+	31.4511i	−0.149365	+	1.01350i
$964$	1.40513	+	13.3690i	0.0452563	+	0.430585i
$965$	−24.5901	+	10.9482i	−0.791585	+	0.352436i
$966$	6.84281	+	5.19243i	0.220164	+	0.167064i
$967$	42.0622			1.35263			0.676315	−	0.736613i	$-0.263576\pi$
$967$	42.0622			1.35263			0.676315	+	0.736613i	$0.263576\pi$
$968$	−18.8586	+	5.29366i	−0.606139	+	0.170145i
$969$	−0.695494	+	0.483528i	−0.0223425	+	0.0155332i
$970$	−5.06144	−	15.5775i	−0.162513	−	0.500164i
$971$	20.7869	+	2.18479i	0.667082	+	0.0701132i	0.432016	−	0.901866i	$-0.357803\pi$
$971$	20.7869	+	2.18479i	0.667082	+	0.0701132i	0.235067	+	0.971979i	$0.424469\pi$
$972$	−13.0364	+	7.53896i	−0.418142	+	0.241812i
$973$	−1.52375	+	1.37199i	−0.0488491	+	0.0439839i
$974$	0.596776	−	1.83669i	0.0191219	−	0.0588512i
$975$	22.2756	+	1.54397i	0.713391	+	0.0494467i
$976$	18.3713	−	25.2859i	0.588050	−	0.809381i
$977$	29.7659	+	6.32694i	0.952296	+	0.202417i	0.657764	−	0.753224i	$-0.271503\pi$
$977$	29.7659	+	6.32694i	0.952296	+	0.202417i	0.294533	+	0.955641i	$0.404836\pi$
$978$	61.9390	+	29.1355i	1.98059	+	0.931650i
$979$	−37.1122	+	32.0794i	−1.18611	+	1.02526i
$980$	−6.28568			−0.200789
$981$	−27.1103	+	42.7460i	−0.865566	+	1.36477i
$982$	11.4341	+	1.20177i	0.364877	+	0.0383502i
$983$	−29.6666	+	21.5540i	−0.946216	+	0.687466i	−0.949909	−	0.312527i	$-0.898825\pi$
$983$	−29.6666	+	21.5540i	−0.946216	+	0.687466i	0.00369283	+	0.999993i	$0.498825\pi$
$984$	3.87806	+	12.8381i	0.123628	+	0.409265i
$985$	22.0513	−	19.8551i	0.702614	−	0.632637i
$986$	3.69312	−	0.388163i	0.117613	−	0.0123616i
$987$	−6.47883	+	10.7013i	−0.206223	+	0.340625i
$988$	−2.17476	−	1.09727i	−0.0691884	−	0.0349088i
$989$	−26.0839			−0.829419
$990$	20.2297	−	3.00751i	0.642943	−	0.0955851i
$991$	7.25232	−	12.5614i	0.230378	−	0.399026i	−0.727542	−	0.686064i	$-0.759337\pi$
$991$	7.25232	−	12.5614i	0.230378	−	0.399026i	0.957919	+	0.287038i	$0.0926705\pi$
$992$	−2.79394	+	3.10298i	−0.0887076	+	0.0985197i
$993$	−21.8894	−	13.2525i	−0.694640	−	0.420554i
$994$	0.944816	−	2.12209i	0.0299678	−	0.0673087i
$995$	21.5640	−	4.58356i	0.683624	−	0.145309i
$996$	3.05765	−	13.0447i	0.0968854	−	0.413338i
$997$	19.9000	−	44.6961i	0.630238	−	1.41554i	−0.262486	−	0.964936i	$-0.584542\pi$
$997$	19.9000	−	44.6961i	0.630238	−	1.41554i	0.892725	−	0.450603i	$-0.148791\pi$
$998$	−43.3846	+	19.3161i	−1.37331	+	0.611439i
$999$	−2.59380	+	0.109824i	−0.0820640	+	0.00347468i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bm.a.17.13	✓	416
3.2	odd	2	inner	429.2.bm.a.17.40	yes	416
11.2	odd	10	inner	429.2.bm.a.134.13	yes	416
13.10	even	6	inner	429.2.bm.a.413.40	yes	416
33.2	even	10	inner	429.2.bm.a.134.40	yes	416
39.23	odd	6	inner	429.2.bm.a.413.13	yes	416
143.101	odd	30	inner	429.2.bm.a.101.40	yes	416
429.101	even	30	inner	429.2.bm.a.101.13	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bm.a.17.13	✓	416	1.1	even	1	trivial
429.2.bm.a.17.40	yes	416	3.2	odd	2	inner
429.2.bm.a.101.13	yes	416	429.101	even	30	inner
429.2.bm.a.101.40	yes	416	143.101	odd	30	inner
429.2.bm.a.134.13	yes	416	11.2	odd	10	inner
429.2.bm.a.134.40	yes	416	33.2	even	10	inner
429.2.bm.a.413.13	yes	416	39.23	odd	6	inner
429.2.bm.a.413.40	yes	416	13.10	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bm (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.358071 + 1.68459i) q^{2} +(0.834638 + 1.51769i) q^{3} +(-0.882537 - 0.392931i) q^{4} +(-0.368818 + 1.13510i) q^{5} +(-2.85554 + 0.862583i) q^{6} +(1.13679 + 0.506130i) q^{7} +(-1.04666 + 1.44060i) q^{8} +(-1.60676 + 2.53344i) q^{9} +O(q^{10})\)	\(q+(-0.358071 + 1.68459i) q^{2} +(0.834638 + 1.51769i) q^{3} +(-0.882537 - 0.392931i) q^{4} +(-0.368818 + 1.13510i) q^{5} +(-2.85554 + 0.862583i) q^{6} +(1.13679 + 0.506130i) q^{7} +(-1.04666 + 1.44060i) q^{8} +(-1.60676 + 2.53344i) q^{9} +(-1.78012 - 1.02775i) q^{10} +(3.13290 + 1.08855i) q^{11} +(-0.140253 - 1.66737i) q^{12} +(-0.202956 - 3.59983i) q^{13} +(-1.25967 + 1.73379i) q^{14} +(-2.03057 + 0.387651i) q^{15} +(-3.34488 - 3.71487i) q^{16} +(0.684027 - 0.145394i) q^{17} +(-3.69248 - 3.61388i) q^{18} +(-0.0731003 + 0.695503i) q^{19} +(0.771513 - 0.856852i) q^{20} +(0.180658 + 2.14772i) q^{21} +(-2.95556 + 4.88787i) q^{22} +(-2.00409 - 1.15706i) q^{23} +(-3.05997 - 0.386120i) q^{24} +(2.89265 + 2.10163i) q^{25} +(6.13692 + 0.947098i) q^{26} +(-5.18604 - 0.324050i) q^{27} +(-0.804382 - 0.893357i) q^{28} +(-0.322296 - 3.06644i) q^{29} +(0.0740524 - 3.55948i) q^{30} +(-0.786706 + 0.255616i) q^{31} +(4.37150 - 2.52389i) q^{32} +(0.962753 + 5.66331i) q^{33} +1.20437i q^{34} +(-0.993778 + 1.10370i) q^{35} +(2.41349 - 1.60451i) q^{36} +(0.496886 - 0.0522249i) q^{37} +(-1.14546 - 0.372183i) q^{38} +(5.29403 - 3.31258i) q^{39} +(-1.24921 - 1.71939i) q^{40} +(-1.76860 - 3.97234i) q^{41} +(-3.68272 - 0.464702i) q^{42} +(9.76151 - 5.63581i) q^{43} +(-2.33717 - 2.19170i) q^{44} +(-2.28312 - 2.75822i) q^{45} +(2.66678 - 2.96175i) q^{46} +(4.69563 + 3.41158i) q^{47} +(2.84625 - 8.17706i) q^{48} +(-3.64780 - 4.05129i) q^{49} +(-4.57616 + 4.12039i) q^{50} +(0.791579 + 0.916788i) q^{51} +(-1.23537 + 3.25673i) q^{52} +(-8.86976 + 2.88196i) q^{53} +(2.40286 - 8.62031i) q^{54} +(-2.39109 + 3.15469i) q^{55} +(-1.91896 + 1.10791i) q^{56} +(-1.11657 + 0.469550i) q^{57} +(5.28110 + 0.555066i) q^{58} +(4.87846 + 2.17203i) q^{59} +(1.94437 + 0.455755i) q^{60} +(1.29996 + 6.11582i) q^{61} +(-0.148912 - 1.41680i) q^{62} +(-3.10879 + 2.06676i) q^{63} +(-0.403051 - 1.24046i) q^{64} +(4.16104 + 1.09731i) q^{65} +(-9.88509 - 0.406021i) q^{66} +(6.76153 + 3.90377i) q^{67} +(-0.660809 - 0.140459i) q^{68} +(0.0833693 - 4.00731i) q^{69} +(-1.50344 - 2.06931i) q^{70} +(-1.06023 + 0.225359i) q^{71} +(-1.96796 - 4.96635i) q^{72} +(7.27022 - 5.28212i) q^{73} +(-0.0899429 + 0.855750i) q^{74} +(-0.775308 + 6.14424i) q^{75} +(0.337798 - 0.585083i) q^{76} +(3.01049 + 2.82311i) q^{77} +(3.68471 + 10.1044i) q^{78} +(-6.44207 + 2.09316i) q^{79} +(5.45042 - 2.42668i) q^{80} +(-3.83666 - 8.14126i) q^{81} +(7.32505 - 1.55699i) q^{82} +(7.61540 + 2.47439i) q^{83} +(0.684469 - 1.96643i) q^{84} +(-0.0872435 + 0.830066i) q^{85} +(5.99872 + 18.4622i) q^{86} +(4.38490 - 3.04852i) q^{87} +(-4.84725 + 3.37392i) q^{88} +(-7.39533 + 12.8091i) q^{89} +(5.46398 - 2.85849i) q^{90} +(1.59127 - 4.19497i) q^{91} +(1.31404 + 1.80861i) q^{92} +(-1.04456 - 0.980627i) q^{93} +(-7.42848 + 6.68863i) q^{94} +(-0.762508 - 0.339490i) q^{95} +(7.47909 + 4.52804i) q^{96} +(5.92170 + 5.33192i) q^{97} +(8.13093 - 4.69439i) q^{98} +(-7.79159 + 6.18798i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 3 q^{3} - 54 q^{4} - 15 q^{6} - 30 q^{7} - 9 q^{9}+O(q^{10}) \) 416 * q - 3 * q^3 - 54 * q^4 - 15 * q^6 - 30 * q^7 - 9 * q^9	\( 416 q - 3 q^{3} - 54 q^{4} - 15 q^{6} - 30 q^{7} - 9 q^{9} - 36 q^{12} - 20 q^{13} - 9 q^{15} + 14 q^{16} - 30 q^{19} - 28 q^{22} + 15 q^{24} - 84 q^{25} - 24 q^{27} - 30 q^{28} - 5 q^{30} - 27 q^{33} - 73 q^{36} - 18 q^{37} - 65 q^{39} - 120 q^{40} - 25 q^{42} + 36 q^{45} + 30 q^{46} - 41 q^{48} + 14 q^{49} + 60 q^{51} + 20 q^{52} + 18 q^{55} - 126 q^{58} - 30 q^{61} + 105 q^{63} - 56 q^{64} + 170 q^{66} - 33 q^{69} - 195 q^{72} + 77 q^{75} + 4 q^{78} - 13 q^{81} + 36 q^{82} - 60 q^{84} - 30 q^{85} + 38 q^{88} - 190 q^{90} - 56 q^{91} + 24 q^{93} - 90 q^{94} + 54 q^{97}+O(q^{100}) \) 416 * q - 3 * q^3 - 54 * q^4 - 15 * q^6 - 30 * q^7 - 9 * q^9 - 36 * q^12 - 20 * q^13 - 9 * q^15 + 14 * q^16 - 30 * q^19 - 28 * q^22 + 15 * q^24 - 84 * q^25 - 24 * q^27 - 30 * q^28 - 5 * q^30 - 27 * q^33 - 73 * q^36 - 18 * q^37 - 65 * q^39 - 120 * q^40 - 25 * q^42 + 36 * q^45 + 30 * q^46 - 41 * q^48 + 14 * q^49 + 60 * q^51 + 20 * q^52 + 18 * q^55 - 126 * q^58 - 30 * q^61 + 105 * q^63 - 56 * q^64 + 170 * q^66 - 33 * q^69 - 195 * q^72 + 77 * q^75 + 4 * q^78 - 13 * q^81 + 36 * q^82 - 60 * q^84 - 30 * q^85 + 38 * q^88 - 190 * q^90 - 56 * q^91 + 24 * q^93 - 90 * q^94 + 54 * q^97

Introduction

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