LMFDB - Embedded newform 735.2.p.g.509.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(374,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("735.374");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.p (of order $6$, degree $2$, not 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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			509.14
Character	$\chi$	$=$	735.509
Dual form			735.2.p.g.374.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.173233 + 0.300049i) q^{2} +(-0.124909 + 1.72754i) q^{3} +(0.939980 + 1.62809i) q^{4} +(-0.145835 - 2.23131i) q^{5} +(-0.496709 - 0.336746i) q^{6} -1.34428 q^{8} +(-2.96880 - 0.431570i) q^{9} +(0.694765 + 0.342779i) q^{10} +(-0.465604 + 0.268817i) q^{11} +(-2.93001 + 1.42049i) q^{12} -3.81157 q^{13} +(3.87289 + 0.0267743i) q^{15} +(-1.64709 + 2.85284i) q^{16} +(-3.35855 + 1.93906i) q^{17} +(0.643786 - 0.816022i) q^{18} +(-2.69962 - 1.55862i) q^{19} +(3.49570 - 2.33482i) q^{20} -0.186272i q^{22} +(-3.87516 + 6.71198i) q^{23} +(0.167912 - 2.32229i) q^{24} +(-4.95746 + 0.650804i) q^{25} +(0.660291 - 1.14366i) q^{26} +(1.11638 - 5.07481i) q^{27} +8.42000i q^{29} +(-0.678947 + 1.15742i) q^{30} +(-2.61715 + 1.51101i) q^{31} +(-1.91494 - 3.31677i) q^{32} +(-0.406234 - 0.837928i) q^{33} -1.34364i q^{34} +(-2.08797 - 5.23915i) q^{36} +(9.01516 + 5.20491i) q^{37} +(0.935327 - 0.540011i) q^{38} +(0.476098 - 6.58464i) q^{39} +(0.196042 + 2.99950i) q^{40} +8.56674 q^{41} -4.12561i q^{43} +(-0.875318 - 0.505365i) q^{44} +(-0.530012 + 6.68723i) q^{45} +(-1.34262 - 2.32548i) q^{46} +(-0.360706 - 0.208254i) q^{47} +(-4.72266 - 3.20176i) q^{48} +(0.663525 - 1.60022i) q^{50} +(-2.93029 - 6.04423i) q^{51} +(-3.58280 - 6.20559i) q^{52} +(-2.14239 - 3.71072i) q^{53} +(1.32930 + 1.21410i) q^{54} +(0.667714 + 0.999703i) q^{55} +(3.02979 - 4.46901i) q^{57} +(-2.52641 - 1.45862i) q^{58} +(-5.14940 - 8.91903i) q^{59} +(3.59685 + 6.33060i) q^{60} +(0.244494 + 0.141159i) q^{61} -1.04703i q^{62} -5.26142 q^{64} +(0.555859 + 8.50478i) q^{65} +(0.321793 + 0.0232670i) q^{66} +(8.38926 - 4.84354i) q^{67} +(-6.31394 - 3.64535i) q^{68} +(-11.1112 - 7.53289i) q^{69} +1.01073i q^{71} +(3.99088 + 0.580149i) q^{72} +(3.33943 + 5.78405i) q^{73} +(-3.12345 + 1.80333i) q^{74} +(-0.505060 - 8.64551i) q^{75} -5.86030i q^{76} +(1.89324 + 1.28353i) q^{78} +(1.93907 - 3.35858i) q^{79} +(6.60576 + 3.25911i) q^{80} +(8.62749 + 2.56249i) q^{81} +(-1.48404 + 2.57044i) q^{82} +10.8216i q^{83} +(4.81643 + 7.21117i) q^{85} +(1.23789 + 0.714694i) q^{86} +(-14.5459 - 1.05173i) q^{87} +(0.625901 - 0.361364i) q^{88} +(-3.08421 + 5.34201i) q^{89} +(-1.91468 - 1.31748i) q^{90} -14.5703 q^{92} +(-2.28343 - 4.70997i) q^{93} +(0.124972 - 0.0721529i) q^{94} +(-3.08407 + 6.25097i) q^{95} +(5.96905 - 2.89384i) q^{96} +8.00908 q^{97} +(1.49830 - 0.597121i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 16 q^{4} - 40 q^{9} + 32 q^{15} + 16 q^{16} - 64 q^{25} - 56 q^{30} - 32 q^{36} + 56 q^{39} + 32 q^{46} + 40 q^{51} - 8 q^{60} - 352 q^{64} - 48 q^{79} + 40 q^{81} - 128 q^{85} + 80 q^{99}+O(q^{100}) $ 64 * q - 16 * q^4 - 40 * q^9 + 32 * q^15 + 16 * q^16 - 64 * q^25 - 56 * q^30 - 32 * q^36 + 56 * q^39 + 32 * q^46 + 40 * q^51 - 8 * q^60 - 352 * q^64 - 48 * q^79 + 40 * q^81 - 128 * q^85 + 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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 $

$2$	−0.173233	+	0.300049i	−0.122494	+	0.212167i	−0.920751	−	0.390151i	$-0.872423\pi$
$2$	−0.173233	+	0.300049i	−0.122494	+	0.212167i	0.798256	+	0.602318i	$0.205756\pi$
$3$	−0.124909	+	1.72754i	−0.0721161	+	0.997396i
$3$	−0.124909	+	1.72754i	−0.0721161	+	0.997396i
$4$	0.939980	+	1.62809i	0.469990	+	0.814047i
$5$	−0.145835	−	2.23131i	−0.0652192	−	0.997871i
$5$	−0.145835	−	2.23131i	−0.0652192	−	0.997871i
$6$	−0.496709	−	0.336746i	−0.202780	−	0.137476i
$7$		0			0
$7$		0			0
$8$	−1.34428			−0.475274
$9$	−2.96880	−	0.431570i	−0.989599	−	0.143857i
$10$	0.694765	+	0.342779i	0.219704	+	0.108396i
$11$	−0.465604	+	0.268817i	−0.140385	+	0.0810513i	−0.568547	−	0.822650i	$-0.692494\pi$
$11$	−0.465604	+	0.268817i	−0.140385	+	0.0810513i	0.428162	+	0.903702i	$0.359161\pi$
$12$	−2.93001	+	1.42049i	−0.845821	+	0.410061i
$13$	−3.81157			−1.05714			−0.528570	−	0.848890i	$-0.677271\pi$
$13$	−3.81157			−1.05714			−0.528570	+	0.848890i	$0.677271\pi$
$14$		0			0
$15$	3.87289	+	0.0267743i	0.999976	+	0.00691311i
$16$	−1.64709	+	2.85284i	−0.411772	+	0.713210i
$17$	−3.35855	+	1.93906i	−0.814567	+	0.470291i	−0.848539	−	0.529132i	$-0.822518\pi$
$17$	−3.35855	+	1.93906i	−0.814567	+	0.470291i	0.0339722	+	0.999423i	$0.489184\pi$
$18$	0.643786	−	0.816022i	0.151742	−	0.192338i
$19$	−2.69962	−	1.55862i	−0.619334	−	0.357573i	0.157276	−	0.987555i	$-0.449729\pi$
$19$	−2.69962	−	1.55862i	−0.619334	−	0.357573i	−0.776610	+	0.629982i	$0.783062\pi$
$20$	3.49570	−	2.33482i	0.781661	−	0.522081i
$21$		0			0
$22$		−	0.186272i		−	0.0397133i
$23$	−3.87516	+	6.71198i	−0.808027	+	1.39954i	0.106201	+	0.994345i	$0.466131\pi$
$23$	−3.87516	+	6.71198i	−0.808027	+	1.39954i	−0.914228	+	0.405200i	$0.867202\pi$
$24$	0.167912	−	2.32229i	0.0342749	−	0.474036i
$25$	−4.95746	+	0.650804i	−0.991493	+	0.130161i
$26$	0.660291	−	1.14366i	0.129494	−	0.224290i
$27$	1.11638	−	5.07481i	0.214848	−	0.976647i
$28$		0			0
$29$			8.42000i			1.56355i	0.623558	+	0.781777i	$0.285687\pi$
$29$			8.42000i			1.56355i	−0.623558	+	0.781777i	$0.714313\pi$
$30$	−0.678947	+	1.15742i	−0.123958	+	0.211315i
$31$	−2.61715	+	1.51101i	−0.470054	+	0.271386i	−0.716262	−	0.697831i	$-0.754149\pi$
$31$	−2.61715	+	1.51101i	−0.470054	+	0.271386i	0.246208	+	0.969217i	$0.420815\pi$
$32$	−1.91494	−	3.31677i	−0.338516	−	0.586328i
$33$	−0.406234	−	0.837928i	−0.0707162	−	0.145865i
$34$		−	1.34364i		−	0.230432i
$35$		0			0
$36$	−2.08797	−	5.23915i	−0.347996	−	0.873191i
$37$	9.01516	+	5.20491i	1.48208	+	0.855681i	0.999793	−	0.0203301i	$-0.00647171\pi$
$37$	9.01516	+	5.20491i	1.48208	+	0.855681i	0.482290	+	0.876011i	$0.339805\pi$
$38$	0.935327	−	0.540011i	0.151730	−	0.0876014i
$39$	0.476098	−	6.58464i	0.0762367	−	1.05439i
$40$	0.196042	+	2.99950i	0.0309970	+	0.474262i
$41$	8.56674			1.33790			0.668950	−	0.743307i	$-0.266744\pi$
$41$	8.56674			1.33790			0.668950	+	0.743307i	$0.266744\pi$
$42$		0			0
$43$		−	4.12561i		−	0.629150i	−0.949233	−	0.314575i	$-0.898138\pi$
$43$		−	4.12561i		−	0.629150i	0.949233	−	0.314575i	$-0.101862\pi$
$44$	−0.875318	−	0.505365i	−0.131959	−	0.0761866i
$45$	−0.530012	+	6.68723i	−0.0790095	+	0.996874i
$46$	−1.34262	−	2.32548i	−0.197958	−	0.342873i
$47$	−0.360706	−	0.208254i	−0.0526143	−	0.0303769i	0.473462	−	0.880814i	$-0.343004\pi$
$47$	−0.360706	−	0.208254i	−0.0526143	−	0.0303769i	−0.526076	+	0.850437i	$0.676337\pi$
$48$	−4.72266	−	3.20176i	−0.681657	−	0.462134i
$49$		0			0
$50$	0.663525	−	1.60022i	0.0938366	−	0.226306i
$51$	−2.93029	−	6.04423i	−0.410323	−	0.846362i
$52$	−3.58280	−	6.20559i	−0.496845	−	0.860561i
$53$	−2.14239	−	3.71072i	−0.294279	−	0.509707i	0.680538	−	0.732713i	$-0.261746\pi$
$53$	−2.14239	−	3.71072i	−0.294279	−	0.509707i	−0.974817	+	0.223006i	$0.928413\pi$
$54$	1.32930	+	1.21410i	0.180894	+	0.165218i
$55$	0.667714	+	0.999703i	0.0900345	+	0.134800i
$56$		0			0
$57$	3.02979	−	4.46901i	0.401306	−	0.591935i
$58$	−2.52641	−	1.45862i	−0.331734	−	0.191527i
$59$	−5.14940	−	8.91903i	−0.670395	−	1.16116i	−0.977792	−	0.209577i	$-0.932791\pi$
$59$	−5.14940	−	8.91903i	−0.670395	−	1.16116i	0.307397	−	0.951581i	$-0.400542\pi$
$60$	3.59685	+	6.33060i	0.464351	+	0.817277i
$61$	0.244494	+	0.141159i	0.0313043	+	0.0180735i	0.515570	−	0.856847i	$-0.327580\pi$
$61$	0.244494	+	0.141159i	0.0313043	+	0.0180735i	−0.484266	+	0.874921i	$0.660913\pi$
$62$		−	1.04703i		−	0.132973i
$63$		0			0
$64$	−5.26142			−0.657678
$65$	0.555859	+	8.50478i	0.0689458	+	1.05489i
$66$	0.321793	+	0.0232670i	0.0396099	+	0.00286397i
$67$	8.38926	−	4.84354i	1.02491	−	0.591733i	0.109389	−	0.993999i	$-0.465111\pi$
$67$	8.38926	−	4.84354i	1.02491	−	0.591733i	0.915523	+	0.402266i	$0.131777\pi$
$68$	−6.31394	−	3.64535i	−0.765677	−	0.442064i
$69$	−11.1112	−	7.53289i	−1.33763	−	0.906853i
$70$		0			0
$71$			1.01073i			0.119952i	0.998200	+	0.0599758i	$0.0191023\pi$
$71$			1.01073i			0.119952i	−0.998200	+	0.0599758i	$0.980898\pi$
$72$	3.99088	+	0.580149i	0.470330	+	0.0683713i
$73$	3.33943	+	5.78405i	0.390850	+	0.676972i	0.992562	−	0.121741i	$-0.0388477\pi$
$73$	3.33943	+	5.78405i	0.390850	+	0.676972i	−0.601712	+	0.798713i	$0.705514\pi$
$74$	−3.12345	+	1.80333i	−0.363094	+	0.209632i
$75$	−0.505060	−	8.64551i	−0.0583193	−	0.998298i
$76$		−	5.86030i		−	0.672223i
$77$		0			0
$78$	1.89324	+	1.28353i	0.214367	+	0.145331i
$79$	1.93907	−	3.35858i	0.218163	−	0.377869i	−0.736083	−	0.676891i	$-0.763327\pi$
$79$	1.93907	−	3.35858i	0.218163	−	0.377869i	0.954246	+	0.299022i	$0.0966602\pi$
$80$	6.60576	+	3.25911i	0.738547	+	0.364380i
$81$	8.62749	+	2.56249i	0.958611	+	0.284721i
$82$	−1.48404	+	2.57044i	−0.163885	+	0.283858i
$83$			10.8216i			1.18783i	0.804528	+	0.593914i	$0.202418\pi$
$83$			10.8216i			1.18783i	−0.804528	+	0.593914i	$0.797582\pi$
$84$		0			0
$85$	4.81643	+	7.21117i	0.522415	+	0.782161i
$86$	1.23789	+	0.714694i	0.133485	+	0.0770674i
$87$	−14.5459	−	1.05173i	−1.55948	−	0.112757i
$88$	0.625901	−	0.361364i	0.0667213	−	0.0385215i
$89$	−3.08421	+	5.34201i	−0.326926	+	0.566252i	−0.981900	−	0.189399i	$-0.939346\pi$
$89$	−3.08421	+	5.34201i	−0.326926	+	0.566252i	0.654975	+	0.755651i	$0.272679\pi$
$90$	−1.91468	−	1.31748i	−0.201825	−	0.138875i
$91$		0			0
$92$	−14.5703			−1.51906
$93$	−2.28343	−	4.70997i	−0.236781	−	0.488402i
$94$	0.124972	−	0.0721529i	0.0128899	−	0.00744200i
$95$	−3.08407	+	6.25097i	−0.316419	+	0.641336i
$96$	5.96905	−	2.89384i	0.609213	−	0.295351i
$97$	8.00908			0.813199			0.406600	−	0.913606i	$-0.366714\pi$
$97$	8.00908			0.813199			0.406600	+	0.913606i	$0.366714\pi$
$98$		0			0
$99$	1.49830	−	0.597121i	0.150585	−	0.0600129i
$100$	−5.71949	−	7.45947i	−0.571949	−	0.745947i
$101$	0.0677581	+	0.117360i	0.00674218	+	0.0116778i	0.869377	−	0.494150i	$-0.164521\pi$
$101$	0.0677581	+	0.117360i	0.00674218	+	0.0116778i	−0.862635	+	0.505828i	$0.831187\pi$
$102$	2.32119	+	0.167832i	0.229832	+	0.0166179i
$103$	−0.593833	+	1.02855i	−0.0585121	+	0.101346i	−0.893798	−	0.448470i	$-0.851969\pi$
$103$	−0.593833	+	1.02855i	−0.0585121	+	0.101346i	0.835286	+	0.549816i	$0.185302\pi$
$104$	5.12381			0.502431
$105$		0			0
$106$	1.48453			0.144190
$107$	6.57437	−	11.3871i	0.635568	−	1.10084i	−0.350826	−	0.936441i	$-0.614099\pi$
$107$	6.57437	−	11.3871i	0.635568	−	1.10084i	0.986394	−	0.164396i	$-0.0525674\pi$
$108$	9.31164	−	2.95264i	0.896013	−	0.284118i
$109$	4.35638	+	7.54547i	0.417266	+	0.722725i	0.995663	−	0.0930296i	$-0.0296551\pi$
$109$	4.35638	+	7.54547i	0.417266	+	0.722725i	−0.578398	+	0.815755i	$0.696322\pi$
$110$	−0.415630	+	0.0271649i	−0.0396288	+	0.00259007i
$111$	−10.1178	+	14.9239i	−0.960335	+	1.41652i
$112$		0			0
$113$	5.82398			0.547874			0.273937	−	0.961748i	$-0.411674\pi$
$113$	5.82398			0.547874			0.273937	+	0.961748i	$0.411674\pi$
$114$	0.816061	+	1.68327i	0.0764311	+	0.157652i
$115$	15.5416	+	7.66784i	1.44926	+	0.715030i
$116$	−13.7085	+	7.91463i	−1.27281	+	0.734855i
$117$	11.3158	+	1.64496i	1.04614	+	0.152076i
$118$	3.56819			0.328479
$119$		0			0
$120$	−5.20624	−	0.0359921i	−0.475262	−	0.00328562i
$121$	−5.35548	+	9.27596i	−0.486861	+	0.843269i
$122$	−0.0847091	+	0.0489068i	−0.00766921	+	0.00442782i
$123$	−1.07006	+	14.7994i	−0.0964841	+	1.33442i
$124$	−4.92014	−	2.84064i	−0.441842	−	0.255097i
$125$	2.17511	+	10.9667i	0.194548	+	0.980893i
$126$		0			0
$127$		−	14.2361i		−	1.26325i	−0.775276	−	0.631623i	$-0.782389\pi$
$127$		−	14.2361i		−	1.26325i	0.775276	−	0.631623i	$-0.217611\pi$
$128$	4.74133	−	8.21222i	0.419078	−	0.725865i
$129$	7.12717	+	0.515325i	0.627512	+	0.0453718i
$130$	−2.64814	−	1.30653i	−0.232258	−	0.114590i
$131$	−8.48152	+	14.6904i	−0.741034	+	1.28351i	0.210991	+	0.977488i	$0.432331\pi$
$131$	−8.48152	+	14.6904i	−0.741034	+	1.28351i	−0.952025	+	0.306020i	$0.901003\pi$
$132$	0.982373	−	1.44902i	0.0855046	−	0.126121i
$133$		0			0
$134$			3.35625i			0.289936i
$135$	−11.4863	−	1.75091i	−0.988580	−	0.150694i
$136$	4.51482	−	2.60663i	0.387142	−	0.223517i
$137$	−6.22790	−	10.7870i	−0.532085	−	0.921599i	−0.999298	−	0.0374542i	$-0.988075\pi$
$137$	−6.22790	−	10.7870i	−0.532085	−	0.921599i	0.467213	−	0.884145i	$-0.345258\pi$
$138$	4.18506	−	2.02895i	0.356256	−	0.172716i
$139$			19.0259i			1.61375i	0.590719	+	0.806877i	$0.298844\pi$
$139$			19.0259i			1.61375i	−0.590719	+	0.806877i	$0.701156\pi$
$140$		0			0
$141$	0.404822	−	0.597121i	0.0340921	−	0.0502867i
$142$	−0.303268	−	0.175092i	−0.0254497	−	0.0146934i
$143$	1.77468	−	1.02461i	0.148406	−	0.0856825i
$144$	6.12106	−	7.75866i	0.510089	−	0.646555i
$145$	18.7876	−	1.22793i	1.56023	−	0.101974i
$146$	−2.31400			−0.191508
$147$		0			0
$148$			19.5700i			1.60865i
$149$	9.38114	+	5.41621i	0.768533	+	0.443713i	0.832351	−	0.554249i	$-0.186994\pi$
$149$	9.38114	+	5.41621i	0.768533	+	0.443713i	−0.0638179	+	0.997962i	$0.520328\pi$
$150$	2.68157	+	1.34615i	0.218949	+	0.109913i
$151$	−1.59774	−	2.76737i	−0.130022	−	0.225205i	0.793663	−	0.608358i	$-0.208172\pi$
$151$	−1.59774	−	2.76737i	−0.130022	−	0.225205i	−0.923685	+	0.383153i	$0.874838\pi$
$152$	3.62903	+	2.09522i	0.294353	+	0.169945i
$153$	10.8077	−	4.30722i	0.873749	−	0.348218i
$154$		0			0
$155$	3.75320	+	5.61931i	0.301465	+	0.451354i
$156$	11.1679	−	5.41430i	0.894151	−	0.433491i
$157$	−12.0457	−	20.8638i	−0.961355	−	1.66512i	−0.719104	−	0.694903i	$-0.755447\pi$
$157$	−12.0457	−	20.8638i	−0.961355	−	1.66512i	−0.242252	−	0.970213i	$-0.577886\pi$
$158$	0.671825	+	1.16363i	0.0534475	+	0.0925738i
$159$	6.67803	−	3.23756i	0.529602	−	0.256755i
$160$	−7.12147	+	4.75652i	−0.563002	+	0.376036i
$161$		0			0
$162$	−2.26344	+	2.14476i	−0.177833	+	0.168508i
$163$	−9.59705	−	5.54086i	−0.751699	−	0.433994i	0.0746084	−	0.997213i	$-0.476229\pi$
$163$	−9.59705	−	5.54086i	−0.751699	−	0.433994i	−0.826308	+	0.563219i	$0.809563\pi$
$164$	8.05257	+	13.9475i	0.628800	+	1.08911i
$165$	−1.81043	+	1.02863i	−0.140942	+	0.0800789i
$166$	−3.24702	−	1.87467i	−0.252018	−	0.145502i
$167$			12.2802i			0.950270i	0.879913	+	0.475135i	$0.157601\pi$
$167$			12.2802i			0.950270i	−0.879913	+	0.475135i	$0.842399\pi$
$168$		0			0
$169$	1.52807			0.117544
$170$	−2.99807	+	0.195949i	−0.229941	+	0.0150286i
$171$	7.34195	+	5.79231i	0.561453	+	0.442949i
$172$	6.71689	−	3.87800i	0.512158	−	0.295694i
$173$	17.5358	+	10.1243i	1.33322	+	0.769735i	0.985792	−	0.167971i	$-0.0537215\pi$
$173$	17.5358	+	10.1243i	1.33322	+	0.769735i	0.347429	+	0.937706i	$0.387055\pi$
$174$	2.83540	−	4.18229i	0.214951	−	0.317058i
$175$		0			0
$176$		−	1.77106i		−	0.133499i
$177$	16.0512	−	7.78174i	1.20648	−	0.584912i
$178$	−1.06858	−	1.85083i	−0.0800931	−	0.138725i
$179$	−5.59923	+	3.23271i	−0.418506	+	0.241624i	−0.694438	−	0.719553i	$-0.744347\pi$
$179$	−5.59923	+	3.23271i	−0.418506	+	0.241624i	0.275932	+	0.961177i	$0.411014\pi$
$180$	−11.3856	+	5.42296i	−0.848636	+	0.404204i
$181$		−	16.5297i		−	1.22864i	−0.789056	−	0.614322i	$-0.789430\pi$
$181$		−	16.5297i		−	1.22864i	0.789056	−	0.614322i	$-0.210570\pi$
$182$		0			0
$183$	−0.274397	+	0.404742i	−0.0202840	+	0.0299194i
$184$	5.20929	−	9.02276i	0.384034	−	0.665167i
$185$	10.2990	−	20.8747i	0.757199	−	1.53474i
$186$	1.80879	+	0.130783i	0.132627	+	0.00958950i
$187$	1.04250	−	1.80567i	0.0762353	−	0.132043i
$188$		−	0.783017i		−	0.0571074i
$189$		0			0
$190$	−1.34133	−	2.00825i	−0.0973106	−	0.145694i
$191$	8.88161	+	5.12780i	0.642650	+	0.371034i	0.785635	−	0.618691i	$-0.212337\pi$
$191$	8.88161	+	5.12780i	0.642650	+	0.371034i	−0.142984	+	0.989725i	$0.545670\pi$
$192$	0.657198	−	9.08933i	0.0474292	−	0.655966i
$193$	−14.2293	+	8.21529i	−1.02425	+	0.591350i	−0.915331	−	0.402701i	$-0.868071\pi$
$193$	−14.2293	+	8.21529i	−1.02425	+	0.591350i	−0.108916	+	0.994051i	$0.534738\pi$
$194$	−1.38744	+	2.40312i	−0.0996124	+	0.172534i
$195$	−14.7618	−	0.102052i	−1.05711	−	0.00730812i
$196$		0			0
$197$	−0.0212992			−0.00151751			−0.000758753	−	1.00000i	$-0.500242\pi$
$197$	−0.0212992			−0.00151751			−0.000758753		1.00000i	$0.500242\pi$
$198$	−0.0803894	+	0.553004i	−0.00571303	+	0.0393003i
$199$	−9.63950	+	5.56537i	−0.683326	+	0.394518i	−0.801107	−	0.598521i	$-0.795755\pi$
$199$	−9.63950	+	5.56537i	−0.683326	+	0.394518i	0.117781	+	0.993040i	$0.462422\pi$
$200$	6.66421	−	0.874861i	0.471231	−	0.0618620i
$201$	7.31953	+	15.0978i	0.516280	+	1.06492i
$202$	−0.0469519			−0.00330352
$203$		0			0
$204$	7.08616	−	10.4522i	0.496131	−	0.731804i
$205$	−1.24933	−	19.1150i	−0.0872568	−	1.33505i
$206$	−0.205743	−	0.356358i	−0.0143348	−	0.0248286i
$207$	14.4013	−	18.2541i	1.00096	−	1.26875i
$208$	6.27799	−	10.8738i	0.435300	−	0.753962i
$209$	1.67594			0.115927
$210$		0			0
$211$	−4.75289			−0.327203			−0.163601	−	0.986527i	$-0.552311\pi$
$211$	−4.75289			−0.327203			−0.163601	+	0.986527i	$0.552311\pi$
$212$	4.02760	−	6.97601i	0.276617	−	0.479114i
$213$	−1.74608	−	0.126249i	−0.119639	−	0.00865044i
$214$	2.27780	+	3.94526i	0.155707	+	0.269693i
$215$	−9.20551	+	0.601658i	−0.627811	+	0.0410327i
$216$	−1.50073	+	6.82195i	−0.102112	+	0.464175i
$217$		0			0
$218$	−3.01868			−0.204451
$219$	−10.4093	+	5.04651i	−0.703396	+	0.341012i
$220$	−0.999973	+	2.02680i	−0.0674181	+	0.136647i
$221$	12.8013	−	7.39085i	0.861111	−	0.497163i
$222$	−2.72517	−	5.62115i	−0.182902	−	0.377267i
$223$	9.93727			0.665449			0.332724	−	0.943024i	$-0.392032\pi$
$223$	9.93727			0.665449			0.332724	+	0.943024i	$0.392032\pi$
$224$		0			0
$225$	14.9986	+	0.207388i	0.999904	+	0.0138259i
$226$	−1.00891	+	1.74748i	−0.0671115	+	0.116241i
$227$	−12.3035	+	7.10345i	−0.816614	+	0.471472i	−0.849247	−	0.527995i	$-0.822944\pi$
$227$	−12.3035	+	7.10345i	−0.816614	+	0.471472i	0.0326333	+	0.999467i	$0.489611\pi$
$228$	10.1239	+	0.732003i	0.670472	+	0.0484781i
$229$	13.5128	+	7.80161i	0.892950	+	0.515545i	0.874906	−	0.484292i	$-0.160923\pi$
$229$	13.5128	+	7.80161i	0.892950	+	0.515545i	0.0180437	+	0.999837i	$0.494256\pi$
$230$	−4.99306	+	3.33492i	−0.329232	+	0.219898i
$231$		0			0
$232$		−	11.3188i		−	0.743117i
$233$	−5.32462	+	9.22251i	−0.348827	+	0.604186i	−0.986041	−	0.166500i	$-0.946753\pi$
$233$	−5.32462	+	9.22251i	−0.348827	+	0.604186i	0.637214	+	0.770687i	$0.280087\pi$
$234$	−2.45384	+	3.11032i	−0.160412	+	0.203328i
$235$	−0.412074	+	0.835216i	−0.0268808	+	0.0544835i
$236$	9.68068	−	16.7674i	0.630158	−	1.09147i
$237$	5.55987	+	3.76935i	0.361152	+	0.244845i
$238$		0			0
$239$		−	24.4443i		−	1.58117i	−0.612354	−	0.790584i	$-0.709777\pi$
$239$		−	24.4443i		−	1.58117i	0.612354	−	0.790584i	$-0.290223\pi$
$240$	−6.45537	+	11.0046i	−0.416692	+	0.710346i
$241$	−16.3507	+	9.44010i	−1.05324	+	0.608090i	−0.923556	−	0.383465i	$-0.874731\pi$
$241$	−16.3507	+	9.44010i	−1.05324	+	0.608090i	−0.129688	+	0.991555i	$0.541397\pi$
$242$	−1.85549	−	3.21381i	−0.119276	−	0.206591i
$243$	−5.50445	+	14.5843i	−0.353110	+	0.935582i
$244$			0.530746i			0.0339776i
$245$		0			0
$246$	−4.25517	−	2.88482i	−0.271300	−	0.183929i
$247$	10.2898	+	5.94080i	0.654723	+	0.378004i
$248$	3.51818	−	2.03122i	0.223404	−	0.128983i
$249$	−18.6948	−	1.35172i	−1.18474	−	0.0856616i
$250$	−3.66735	−	1.24716i	−0.231944	−	0.0788774i
$251$	−3.44293			−0.217316			−0.108658	−	0.994079i	$-0.534655\pi$
$251$	−3.44293			−0.217316			−0.108658	+	0.994079i	$0.534655\pi$
$252$		0			0
$253$		−	4.16683i		−	0.261967i
$254$	4.27152	+	2.46616i	0.268019	+	0.154741i
$255$	−13.0592	+	7.41984i	−0.817799	+	0.464648i
$256$	−3.61871	−	6.26779i	−0.226169	−	0.391737i
$257$	−3.27669	−	1.89180i	−0.204395	−	0.118007i	0.394309	−	0.918978i	$-0.370984\pi$
$257$	−3.27669	−	1.89180i	−0.204395	−	0.118007i	−0.598704	+	0.800971i	$0.704317\pi$
$258$	−1.38929	+	2.04923i	−0.0864932	+	0.127579i
$259$		0			0
$260$	−13.3241	+	8.89932i	−0.826325	+	0.551912i
$261$	3.63382	−	24.9973i	0.224928	−	1.54729i
$262$	−2.93856	−	5.08974i	−0.181545	−	0.314445i
$263$	12.8674	+	22.2870i	0.793437	+	1.37427i	0.923827	+	0.382810i	$0.125044\pi$
$263$	12.8674	+	22.2870i	0.793437	+	1.37427i	−0.130390	+	0.991463i	$0.541623\pi$
$264$	0.546091	+	1.12641i	0.0336096	+	0.0693256i
$265$	−7.96733	+	5.32147i	−0.489429	+	0.326896i
$266$		0			0
$267$	−8.84329	−	5.99536i	−0.541201	−	0.366910i
$268$	15.7715	+	9.10567i	0.963397	+	0.556217i
$269$	3.67674	+	6.36830i	0.224175	+	0.388282i	0.956072	−	0.293133i	$-0.0946980\pi$
$269$	3.67674	+	6.36830i	0.224175	+	0.388282i	−0.731897	+	0.681416i	$0.761365\pi$
$270$	2.51516	−	3.14313i	0.153068	−	0.191285i
$271$	−21.0330	−	12.1434i	−1.27767	−	0.737660i	−0.301247	−	0.953546i	$-0.597403\pi$
$271$	−21.0330	−	12.1434i	−1.27767	−	0.737660i	−0.976419	+	0.215886i	$0.930736\pi$
$272$		−	12.7752i		−	0.774610i
$273$		0			0
$274$	4.31552			0.260710
$275$	2.13327	−	1.63567i	0.128641	−	0.0986344i
$276$	1.81996	−	25.1708i	0.109549	−	1.51510i
$277$	5.24526	−	3.02835i	0.315157	−	0.181956i	−0.334075	−	0.942547i	$-0.608424\pi$
$277$	5.24526	−	3.02835i	0.315157	−	0.181956i	0.649232	+	0.760590i	$0.275090\pi$
$278$	−5.70870	−	3.29592i	−0.342385	−	0.197676i
$279$	8.42189	−	3.35640i	0.504206	−	0.200943i
$280$		0			0
$281$			18.8983i			1.12738i	0.825987	+	0.563689i	$0.190618\pi$
$281$			18.8983i			1.12738i	−0.825987	+	0.563689i	$0.809382\pi$
$282$	0.109037	+	0.224908i	0.00649306	+	0.0133931i
$283$	4.12883	+	7.15134i	0.245433	+	0.425103i	0.962253	−	0.272155i	$-0.0877364\pi$
$283$	4.12883	+	7.15134i	0.245433	+	0.425103i	−0.716820	+	0.697258i	$0.754403\pi$
$284$	−1.64556	+	0.950066i	−0.0976462	+	0.0563761i
$285$	−10.4136	−	6.10866i	−0.616847	−	0.361846i
$286$			0.709989i			0.0419825i
$287$		0			0
$288$	4.25364	+	10.6732i	0.250648	+	0.628927i
$289$	−0.980110	+	1.69760i	−0.0576535	+	0.0998588i
$290$	−2.88620	+	5.84992i	−0.169484	+	0.343519i
$291$	−1.00040	+	13.8360i	−0.0586447	+	0.811082i
$292$	−6.27799	+	10.8738i	−0.367391	+	0.636341i
$293$		−	5.23650i		−	0.305919i	−0.988232	−	0.152960i	$-0.951120\pi$
$293$		−	5.23650i		−	0.305919i	0.988232	−	0.152960i	$-0.0488805\pi$
$294$		0			0
$295$	−19.1501	+	12.7906i	−1.11496	+	0.744698i
$296$	−12.1189	−	6.99684i	−0.704395	−	0.406683i
$297$	0.844401	+	2.66295i	0.0489971	+	0.154520i
$298$	−3.25025	+	1.87653i	−0.188282	+	0.108705i
$299$	14.7705	−	25.5832i	0.854198	−	1.47951i
$300$	13.6010	−	8.94890i	0.785252	−	0.516665i
$301$		0			0
$302$	1.10713			0.0637080
$303$	−0.211209	+	0.102396i	−0.0121336	+	0.00588247i
$304$	8.89300	−	5.13438i	0.510049	−	0.294477i
$305$	0.279313	−	0.566128i	0.0159934	−	0.0324164i
$306$	−0.579874	+	3.98899i	−0.0331492	+	0.228035i
$307$	−1.12127			−0.0639940			−0.0319970	−	0.999488i	$-0.510187\pi$
$307$	−1.12127			−0.0639940			−0.0319970	+	0.999488i	$0.510187\pi$
$308$		0			0
$309$	−1.70269	−	1.15435i	−0.0968624	−	0.0656684i
$310$	−2.33625	+	0.152693i	−0.132690	+	0.00867240i
$311$	−6.48408	−	11.2308i	−0.367678	−	0.636838i	0.621524	−	0.783395i	$-0.286514\pi$
$311$	−6.48408	−	11.2308i	−0.367678	−	0.636838i	−0.989202	+	0.146558i	$0.953181\pi$
$312$	−0.640008	+	8.85159i	−0.0362333	+	0.501122i
$313$	−6.87182	+	11.9023i	−0.388418	+	0.672760i	−0.992237	−	0.124361i	$-0.960312\pi$
$313$	−6.87182	+	11.9023i	−0.388418	+	0.672760i	0.603819	+	0.797122i	$0.293645\pi$
$314$	8.34690			0.471043
$315$		0			0
$316$	7.29077			0.410138
$317$	−9.07954	+	15.7262i	−0.509958	+	0.883273i	0.489975	+	0.871736i	$0.337006\pi$
$317$	−9.07954	+	15.7262i	−0.509958	+	0.883273i	−0.999933	+	0.0115369i	$0.996328\pi$
$318$	−0.185431	+	2.56459i	−0.0103984	+	0.143815i
$319$	−2.26344	−	3.92039i	−0.126728	−	0.219500i
$320$	0.767298	+	11.7399i	0.0428933	+	0.656278i
$321$	18.8506	+	12.7798i	1.05214	+	0.713301i
$322$		0			0
$323$	12.0890			0.672652
$324$	3.93771	+	16.4551i	0.218762	+	0.914170i
$325$	18.8957	−	2.48058i	1.04815	−	0.137598i
$326$	3.32506	−	1.91972i	0.184158	−	0.106324i
$327$	−13.5793	+	6.58333i	−0.750935	+	0.364059i
$328$	−11.5161			−0.635869
$329$		0			0
$330$	0.00498731	−	0.721411i	0.000274543	−	0.0397124i
$331$	−15.4952	+	26.8384i	−0.851691	+	1.47517i	0.0279904	+	0.999608i	$0.491089\pi$
$331$	−15.4952	+	26.8384i	−0.851691	+	1.47517i	−0.879681	+	0.475564i	$0.842244\pi$
$332$	−17.6186	+	10.1721i	−0.966948	+	0.558268i
$333$	−24.5179	−	19.3430i	−1.34357	−	1.05999i
$334$	−3.68466	−	2.12734i	−0.201616	−	0.116403i
$335$	−12.0309	−	18.0127i	−0.657317	−	0.984137i
$336$		0			0
$337$			10.6732i			0.581409i	0.956813	+	0.290704i	$0.0938896\pi$
$337$			10.6732i			0.581409i	−0.956813	+	0.290704i	$0.906110\pi$
$338$	−0.264712	+	0.458495i	−0.0143984	+	0.0249388i
$339$	−0.727466	+	10.0612i	−0.0395105	+	0.546448i
$340$	−7.21311	+	14.6200i	−0.391186	+	0.792878i
$341$	0.812371	−	1.40707i	0.0439923	−	0.0761970i
$342$	−3.00985	+	1.19952i	−0.162754	+	0.0648628i
$343$		0			0
$344$			5.54597i			0.299019i
$345$	−15.1878	+	25.8910i	−0.817683	+	1.39393i
$346$	−6.07556	+	3.50773i	−0.326624	+	0.188577i
$347$	1.16875	+	2.02434i	0.0627420	+	0.108672i	0.895690	−	0.444679i	$-0.146682\pi$
$347$	1.16875	+	2.02434i	0.0627420	+	0.108672i	−0.832948	+	0.553351i	$0.813349\pi$
$348$	−11.9605	−	24.6707i	−0.641152	−	1.32249i
$349$		−	4.60715i		−	0.246615i	−0.992368	−	0.123308i	$-0.960650\pi$
$349$		−	4.60715i		−	0.246615i	0.992368	−	0.123308i	$-0.0393502\pi$
$350$		0			0
$351$	−4.25517	+	19.3430i	−0.227124	+	1.03245i
$352$	1.78321	+	1.02953i	0.0950452	+	0.0548744i
$353$	−5.20325	+	3.00410i	−0.276941	+	0.159892i	−0.632038	−	0.774938i	$-0.717781\pi$
$353$	−5.20325	+	3.00410i	−0.276941	+	0.159892i	0.355097	+	0.934830i	$0.384448\pi$
$354$	−0.445699	+	6.16420i	−0.0236886	+	0.327624i
$355$	2.25525	−	0.147399i	0.119696	−	0.00782315i
$356$	−11.5964			−0.614607
$357$		0			0
$358$		−	2.24006i		−	0.118391i
$359$	−16.9218	−	9.76982i	−0.893100	−	0.515631i	−0.0181447	−	0.999835i	$-0.505776\pi$
$359$	−16.9218	−	9.76982i	−0.893100	−	0.515631i	−0.874955	+	0.484204i	$0.839109\pi$
$360$	0.712482	−	8.98950i	0.0375511	−	0.473788i
$361$	−4.64139	−	8.03911i	−0.244283	−	0.423111i
$362$	4.95972	+	2.86350i	0.260677	+	0.150502i
$363$	−15.3556	−	10.4105i	−0.805962	−	0.546407i
$364$		0			0
$365$	12.4190	−	8.29480i	0.650040	−	0.434170i
$366$	−0.0739077	−	0.152447i	−0.00386322	−	0.00796855i
$367$	9.51920	+	16.4877i	0.496898	+	0.860653i	0.999994	−	0.00357789i	$-0.00113888\pi$
$367$	9.51920	+	16.4877i	0.496898	+	0.860653i	−0.503095	+	0.864231i	$0.667806\pi$
$368$	−12.7655	−	22.1104i	−0.665446	−	1.15259i
$369$	−25.4329	−	3.69715i	−1.32398	−	0.192466i
$370$	4.47928	+	6.70640i	0.232867	+	0.348649i
$371$		0			0
$372$	5.52190	−	8.14492i	0.286297	−	0.422295i
$373$	−17.4796	−	10.0918i	−0.905057	−	0.522535i	−0.0262197	−	0.999656i	$-0.508347\pi$
$373$	−17.4796	−	10.0918i	−0.905057	−	0.522535i	−0.878837	+	0.477121i	$0.841680\pi$
$374$	0.361192	+	0.625603i	0.0186768	+	0.0323492i
$375$	−19.2171	+	2.38776i	−0.992369	+	0.123303i
$376$	0.484888	+	0.279950i	0.0250062	+	0.0144373i
$377$		−	32.0934i		−	1.65290i
$378$		0			0
$379$	6.25621			0.321360			0.160680	−	0.987007i	$-0.448631\pi$
$379$	6.25621			0.321360			0.160680	+	0.987007i	$0.448631\pi$
$380$	−13.0761	+	0.854635i	−0.670792	+	0.0438419i
$381$	24.5934	+	1.77821i	1.25996	+	0.0911004i
$382$	−3.07718	+	1.77661i	−0.157442	+	0.0908993i
$383$	−13.9988	−	8.08223i	−0.715307	−	0.412982i	0.0977162	−	0.995214i	$-0.468846\pi$
$383$	−13.9988	−	8.08223i	−0.715307	−	0.412982i	−0.813023	+	0.582232i	$0.802180\pi$
$384$	13.5947	+	9.21662i	0.693753	+	0.470334i
$385$		0			0
$386$		−	5.69265i		−	0.289748i
$387$	−1.78049	+	12.2481i	−0.0905074	+	0.622606i
$388$	7.52838	+	13.0395i	0.382196	+	0.661982i
$389$	27.4829	−	15.8673i	1.39344	−	0.804503i	0.399746	−	0.916626i	$-0.369098\pi$
$389$	27.4829	−	15.8673i	1.39344	−	0.804503i	0.993694	+	0.112123i	$0.0357652\pi$
$390$	2.58786	−	4.41158i	0.131041	−	0.223389i
$391$		−	30.0567i		−	1.52003i
$392$		0			0
$393$	−24.3189	−	16.4871i	−1.22673	−	0.831666i
$394$	0.00368974	−	0.00639081i	0.000185886	−	0.000321964i
$395$	−7.77680	−	3.83687i	−0.391293	−	0.193054i
$396$	2.38054	+	1.87809i	0.119627	+	0.0943774i
$397$	4.56777	−	7.91161i	0.229250	−	0.397072i	−0.728336	−	0.685220i	$-0.759706\pi$
$397$	4.56777	−	7.91161i	0.229250	−	0.397072i	0.957586	+	0.288148i	$0.0930394\pi$
$398$		−	3.85643i		−	0.193305i
$399$		0			0
$400$	6.30874	−	15.2148i	0.315437	−	0.760739i
$401$	−6.94015	−	4.00690i	−0.346574	−	0.200095i	0.316601	−	0.948559i	$-0.397458\pi$
$401$	−6.94015	−	4.00690i	−0.346574	−	0.200095i	−0.663175	+	0.748464i	$0.730792\pi$
$402$	−5.79806	−	0.419225i	−0.289181	−	0.0209091i
$403$	9.97545	−	5.75933i	0.496913	−	0.286893i
$404$	−0.127383	+	0.220633i	−0.00633752	+	0.0109769i
$405$	4.45950	−	19.6243i	0.221595	−	0.975139i
$406$		0			0
$407$	−5.59666			−0.277416
$408$	3.93912	+	8.12512i	0.195016	+	0.402254i
$409$	6.66703	−	3.84921i	0.329663	−	0.190331i	−0.326028	−	0.945360i	$-0.605710\pi$
$409$	6.66703	−	3.84921i	0.329663	−	0.190331i	0.655692	+	0.755029i	$0.272377\pi$
$410$	5.95187	+	2.93650i	0.293942	+	0.145023i
$411$	19.4130	−	9.41156i	0.957571	−	0.464238i
$412$	−2.23277			−0.110000
$413$		0			0
$414$	2.98234	+	7.48330i	0.146574	+	0.367784i
$415$	24.1464	−	1.57817i	1.18530	−	0.0774693i
$416$	7.29892	+	12.6421i	0.357859	+	0.619830i
$417$	−32.8680	−	2.37650i	−1.60955	−	0.116378i
$418$	−0.290328	+	0.502863i	−0.0142004	+	0.0245958i
$419$	−0.801768			−0.0391689			−0.0195845	−	0.999808i	$-0.506234\pi$
$419$	−0.801768			−0.0391689			−0.0195845	+	0.999808i	$0.506234\pi$
$420$		0			0
$421$	19.7801			0.964022			0.482011	−	0.876165i	$-0.339907\pi$
$421$	19.7801			0.964022			0.482011	+	0.876165i	$0.339907\pi$
$422$	0.823359	−	1.42610i	0.0400805	−	0.0694215i
$423$	0.980985	+	0.773932i	0.0476971	+	0.0376299i
$424$	2.87996	+	4.98824i	0.139863	+	0.242250i
$425$	15.3879	−	11.7986i	0.746424	−	0.572314i
$426$	0.340360	−	0.502038i	0.0164905	−	0.0243238i
$427$		0			0
$428$	24.7191			1.19484
$429$	1.54839	+	3.19382i	0.0747569	+	0.154199i
$430$	1.41417	−	2.86633i	0.0681976	−	0.138227i
$431$	15.4013	−	8.89192i	0.741852	−	0.428309i	−0.0808900	−	0.996723i	$-0.525776\pi$
$431$	15.4013	−	8.89192i	0.741852	−	0.428309i	0.822742	+	0.568414i	$0.192443\pi$
$432$	12.6388	+	11.5435i	0.608086	+	0.555388i
$433$	−20.1791			−0.969746			−0.484873	−	0.874584i	$-0.661134\pi$
$433$	−20.1791			−0.969746			−0.484873	+	0.874584i	$0.661134\pi$
$434$		0			0
$435$	−0.225440	+	32.6097i	−0.0108090	+	1.56352i
$436$	−8.18983	+	14.1852i	−0.392222	+	0.679348i
$437$	20.9229	−	12.0798i	1.00088	−	0.577857i
$438$	0.289039	−	3.99753i	0.0138108	−	0.191009i
$439$	14.7323	+	8.50568i	0.703133	+	0.405954i	0.808513	−	0.588478i	$-0.200273\pi$
$439$	14.7323	+	8.50568i	0.703133	+	0.405954i	−0.105380	+	0.994432i	$0.533606\pi$
$440$	−0.897593	−	1.34388i	−0.0427910	−	0.0640669i
$441$		0			0
$442$			5.12137i			0.243599i
$443$	−7.87183	+	13.6344i	−0.374002	+	0.647790i	−0.990177	−	0.139819i	$-0.955348\pi$
$443$	−7.87183	+	13.6344i	−0.374002	+	0.647790i	0.616175	+	0.787609i	$0.288681\pi$
$444$	−33.8080	−	2.44447i	−1.60446	−	0.116009i
$445$	12.3694	+	6.10277i	0.586368	+	0.289299i
$446$	−1.72147	+	2.98167i	−0.0815138	+	0.141186i
$447$	−10.5285	+	15.5298i	−0.497981	+	0.734533i
$448$		0			0
$449$		−	17.8876i		−	0.844166i	−0.906557	−	0.422083i	$-0.861299\pi$
$449$		−	17.8876i		−	0.844166i	0.906557	−	0.422083i	$-0.138701\pi$
$450$	−2.66048	+	4.46438i	−0.125416	+	0.210453i
$451$	−3.98871	+	2.30288i	−0.187821	+	0.108439i
$452$	5.47443	+	9.48199i	0.257495	+	0.445995i
$453$	4.98031	−	2.41449i	0.233996	−	0.113443i
$454$		−	4.92222i		−	0.231011i
$455$		0			0
$456$	−4.07288	+	6.00759i	−0.190730	+	0.281331i
$457$	10.6207	+	6.13187i	0.496816	+	0.286837i	0.727398	−	0.686216i	$-0.240730\pi$
$457$	10.6207	+	6.13187i	0.496816	+	0.286837i	−0.230582	+	0.973053i	$0.574063\pi$
$458$	−4.68173	+	2.70300i	−0.218763	+	0.126303i
$459$	6.09092	+	19.2087i	0.284300	+	0.896586i
$460$	2.12486	+	32.5108i	0.0990720	+	1.51583i
$461$	−4.02980			−0.187687			−0.0938433	−	0.995587i	$-0.529915\pi$
$461$	−4.02980			−0.187687			−0.0938433	+	0.995587i	$0.529915\pi$
$462$		0			0
$463$		−	19.2199i		−	0.893223i	−0.894728	−	0.446611i	$-0.852631\pi$
$463$		−	19.2199i		−	0.893223i	0.894728	−	0.446611i	$-0.147369\pi$
$464$	−24.0209	−	13.8685i	−1.11514	−	0.643828i
$465$	−10.1764	+	5.78191i	−0.471919	+	0.268130i
$466$	−1.84480	−	3.19529i	−0.0854588	−	0.148019i
$467$	−22.3200	−	12.8864i	−1.03285	−	0.596314i	−0.115047	−	0.993360i	$-0.536702\pi$
$467$	−22.3200	−	12.8864i	−1.03285	−	0.596314i	−0.917799	+	0.397046i	$0.870035\pi$
$468$	7.95846	+	19.9694i	0.367880	+	0.923084i
$469$		0			0
$470$	−0.179221	−	0.268330i	−0.00826683	−	0.0123771i
$471$	37.5478	−	18.2034i	1.73011	−	0.838771i
$472$	6.92223	+	11.9896i	0.318621	+	0.551868i
$473$	1.10903	+	1.92090i	0.0509934	+	0.0883232i
$474$	−2.09414	+	1.01526i	−0.0961872	+	0.0466323i
$475$	14.3976	+	5.96990i	0.660607	+	0.273918i
$476$		0			0
$477$	4.75887	+	11.9410i	0.217894	+	0.546739i
$478$	7.33447	+	4.23456i	0.335471	+	0.193684i
$479$	−11.2070	−	19.4111i	−0.512061	−	0.886916i	−0.999902	−	0.0139833i	$-0.995549\pi$
$479$	−11.2070	−	19.4111i	−0.512061	−	0.886916i	0.487841	−	0.872932i	$-0.337785\pi$
$480$	−7.32754	−	12.8968i	−0.334455	−	0.588654i
$481$	−34.3619	−	19.8389i	−1.56677	−	0.904574i
$482$		−	6.54136i		−	0.297951i
$483$		0			0
$484$	−20.1362			−0.915280
$485$	−1.16800	−	17.8707i	−0.0530362	−	0.811468i
$486$	−3.42244	−	4.17809i	−0.155245	−	0.189522i
$487$	4.02571	−	2.32425i	0.182423	−	0.105322i	−0.406008	−	0.913870i	$-0.633079\pi$
$487$	4.02571	−	2.32425i	0.182423	−	0.105322i	0.588430	+	0.808548i	$0.299746\pi$
$488$	−0.328668	−	0.189757i	−0.0148781	−	0.00858988i
$489$	10.7708	−	15.8872i	0.487073	−	0.718444i
$490$		0			0
$491$		−	38.5971i		−	1.74186i	−0.491406	−	0.870931i	$-0.663517\pi$
$491$		−	38.5971i		−	1.74186i	0.491406	−	0.870931i	$-0.336483\pi$
$492$	−25.1006	+	12.1690i	−1.13162	+	0.548620i
$493$	−16.3269	−	28.2790i	−0.735325	−	1.27362i
$494$	−3.56506	+	2.05829i	−0.160400	+	0.0926069i
$495$	−1.55086	−	3.25608i	−0.0697062	−	0.146350i
$496$		−	9.95508i		−	0.446996i
$497$		0			0
$498$	3.64415	−	5.37520i	0.163298	−	0.240868i
$499$	5.51346	−	9.54959i	0.246816	−	0.427498i	−0.715824	−	0.698280i	$-0.753949\pi$
$499$	5.51346	−	9.54959i	0.246816	−	0.427498i	0.962641	+	0.270782i	$0.0872823\pi$
$500$	−15.8103	+	13.8498i	−0.707057	+	0.619381i
$501$	−21.2145	−	1.53390i	−0.947796	−	0.0685297i
$502$	0.596431	−	1.03305i	0.0266200	−	0.0461072i
$503$		−	3.76757i		−	0.167988i	−0.996466	−	0.0839939i	$-0.973232\pi$
$503$		−	3.76757i		−	0.167988i	0.996466	−	0.0839939i	$-0.0267676\pi$
$504$		0			0
$505$	0.251986	−	0.168304i	0.0112132	−	0.00748945i
$506$	1.25025	+	0.721835i	0.0555806	+	0.0320895i
$507$	−0.190869	+	2.63980i	−0.00847678	+	0.117238i
$508$	23.1776	−	13.3816i	1.02834	−	0.593713i
$509$	−14.7985	+	25.6318i	−0.655933	+	1.13611i	0.325726	+	0.945464i	$0.394391\pi$
$509$	−14.7985	+	25.6318i	−0.655933	+	1.13611i	−0.981659	+	0.190645i	$0.938942\pi$
$510$	0.0359750	−	5.20376i	0.00159300	−	0.230426i
$511$		0			0
$512$	21.4728			0.948975
$513$	−10.9235	+	11.9600i	−0.482285	+	0.528047i
$514$	1.13527	−	0.655446i	0.0500744	−	0.0289105i
$515$	2.38161	+	1.17503i	0.104946	+	0.0517778i
$516$	5.86040	+	12.0881i	0.257990	+	0.532149i
$517$	0.223928			0.00984835
$518$		0			0
$519$	−19.6805	+	29.0292i	−0.863878	+	1.27424i
$520$	−0.747229	−	11.4328i	−0.0327681	−	0.501361i
$521$	4.00301	+	6.93341i	0.175375	+	0.303758i	0.940291	−	0.340372i	$-0.110553\pi$
$521$	4.00301	+	6.93341i	0.175375	+	0.303758i	−0.764916	+	0.644130i	$0.777220\pi$
$522$	6.87090	+	5.42068i	0.300731	+	0.237257i
$523$	−10.1669	+	17.6096i	−0.444567	+	0.770013i	−0.998022	−	0.0628663i	$-0.979976\pi$
$523$	−10.1669	+	17.6096i	−0.444567	+	0.770013i	0.553455	+	0.832879i	$0.313309\pi$
$524$	−31.8898			−1.39311
$525$		0			0
$526$	−8.91624			−0.388767
$527$	5.85988	−	10.1496i	0.255260	−	0.442124i
$528$	3.05958	+	0.221221i	0.133151	+	0.00962739i
$529$	−18.5338	−	32.1015i	−0.805817	−	1.39572i
$530$	−0.216496	−	3.31244i	−0.00940399	−	0.143883i
$531$	11.4383	+	28.7011i	0.496382	+	1.24552i
$532$		0			0
$533$	−32.6527			−1.41435
$534$	3.33085	−	1.61482i	0.144140	−	0.0698803i
$535$	−26.3670	−	13.0088i	−1.13994	−	0.562419i
$536$	−11.2775	+	6.51106i	−0.487114	+	0.281235i
$537$	−4.88525	−	10.0767i	−0.210814	−	0.434841i
$538$	−2.54774			−0.109841
$539$		0			0
$540$	−7.94622	−	20.3465i	−0.341951	−	0.875576i
$541$	−5.50977	+	9.54320i	−0.236883	+	0.410294i	−0.959818	−	0.280622i	$-0.909459\pi$
$541$	−5.50977	+	9.54320i	−0.236883	+	0.410294i	0.722935	+	0.690916i	$0.242793\pi$
$542$	7.28724	−	4.20729i	0.313014	−	0.180719i
$543$	28.5557	+	2.06470i	1.22544	+	0.0886049i
$544$	12.8628	+	7.42635i	0.551489	+	0.318402i
$545$	16.2010	−	10.8208i	0.693973	−	0.463513i
$546$		0			0
$547$			32.5977i			1.39378i	0.717179	+	0.696889i	$0.245433\pi$
$547$			32.5977i			1.39378i	−0.717179	+	0.696889i	$0.754567\pi$
$548$	11.7082	−	20.2792i	0.500150	−	0.866285i
$549$	−0.664934	−	0.524588i	−0.0283787	−	0.0223889i
$550$	0.121227	+	0.923437i	0.00516912	+	0.0393755i
$551$	13.1236	−	22.7308i	0.559085	−	0.968363i
$552$	14.9365	+	10.1263i	0.635740	+	0.431004i
$553$		0			0
$554$			2.09845i			0.0891545i
$555$	34.7754	+	20.3994i	1.47613	+	0.865907i
$556$	−30.9759	+	17.8840i	−1.31367	+	0.758449i
$557$	15.3057	+	26.5103i	0.648524	+	1.12328i	0.983475	+	0.181041i	$0.0579468\pi$
$557$	15.3057	+	26.5103i	0.648524	+	1.12328i	−0.334951	+	0.942235i	$0.608720\pi$
$558$	−0.451867	+	3.10842i	−0.0191291	+	0.131590i
$559$			15.7251i			0.665099i
$560$		0			0
$561$	2.98915	+	2.02651i	0.126202	+	0.0855593i
$562$	−5.67041	−	3.27381i	−0.239192	−	0.138098i
$563$	−4.24449	+	2.45056i	−0.178884	+	0.103279i	−0.586768	−	0.809755i	$-0.699600\pi$
$563$	−4.24449	+	2.45056i	−0.178884	+	0.103279i	0.407884	+	0.913034i	$0.366267\pi$
$564$	1.35269	+	0.0978056i	0.0569587	+	0.00411836i
$565$	−0.849338	−	12.9951i	−0.0357319	−	0.546708i
$566$	−2.86100			−0.120257
$567$		0			0
$568$		−	1.35870i		−	0.0570098i
$569$	26.1233	+	15.0823i	1.09515	+	0.632283i	0.934942	−	0.354801i	$-0.115451\pi$
$569$	26.1233	+	15.0823i	1.09515	+	0.632283i	0.160205	+	0.987084i	$0.448785\pi$
$570$	3.63688	−	2.06636i	0.152332	−	0.0865504i
$571$	6.06919	+	10.5121i	0.253988	+	0.439920i	0.964620	−	0.263644i	$-0.0849244\pi$
$571$	6.06919	+	10.5121i	0.253988	+	0.439920i	−0.710632	+	0.703564i	$0.751591\pi$
$572$	3.33633	+	1.92623i	0.139499	+	0.0805399i
$573$	−9.96787	+	14.7028i	−0.416414	+	0.614220i
$574$		0			0
$575$	14.8428	−	35.7964i	0.618988	−	1.49281i
$576$	15.6201	+	2.27067i	0.650837	+	0.0946113i
$577$	0.280029	+	0.485025i	0.0116578	+	0.0201918i	0.871795	−	0.489870i	$-0.162956\pi$
$577$	0.280029	+	0.485025i	0.0116578	+	0.0201918i	−0.860138	+	0.510062i	$0.829622\pi$
$578$	−0.339575	−	0.588162i	−0.0141245	−	0.0244643i
$579$	−12.4149	−	25.6079i	−0.515945	−	1.06423i
$580$	19.6592	+	29.4338i	0.816302	+	1.22217i
$581$		0			0
$582$	−3.97818	−	2.69703i	−0.164901	−	0.111795i
$583$	1.99501	+	1.15182i	0.0826248	+	0.0477034i
$584$	−4.48911	−	7.77537i	−0.185761	−	0.321747i
$585$	2.02018	−	25.4889i	0.0835240	−	1.05383i
$586$	1.57121	+	0.907136i	0.0649059	+	0.0374734i
$587$			20.4166i			0.842683i	0.906902	+	0.421342i	$0.138441\pi$
$587$			20.4166i			0.842683i	−0.906902	+	0.421342i	$0.861559\pi$
$588$		0			0
$589$	9.42040			0.388161
$590$	−0.520366	−	7.96174i	−0.0214231	−	0.327780i
$591$	0.00266046	−	0.0367953i	0.000109437	−	0.00151356i
$592$	−29.6975	+	17.1459i	−1.22056	+	0.704691i
$593$	28.1524	+	16.2538i	1.15608	+	0.667463i	0.950361	−	0.311148i	$-0.100714\pi$
$593$	28.1524	+	16.2538i	1.15608	+	0.667463i	0.205718	+	0.978611i	$0.434047\pi$
$594$	−0.945295	−	0.207951i	−0.0387859	−	0.00853233i
$595$		0			0
$596$			20.3645i			0.834163i
$597$	−8.41034	−	17.3478i	−0.344212	−	0.709998i
$598$	5.11747	+	8.86372i	0.209269	+	0.362464i
$599$	−7.74433	+	4.47119i	−0.316425	+	0.182688i	−0.649798	−	0.760107i	$-0.725146\pi$
$599$	−7.74433	+	4.47119i	−0.316425	+	0.182688i	0.333373	+	0.942795i	$0.391813\pi$
$600$	0.678941	+	11.6220i	0.0277176	+	0.474465i
$601$			9.31473i			0.379956i	0.981788	+	0.189978i	$0.0608417\pi$
$601$			9.31473i			0.379956i	−0.981788	+	0.189978i	$0.939158\pi$
$602$		0			0
$603$	−26.9963	+	10.7589i	−1.09938	+	0.438138i
$604$	3.00369	−	5.20254i	0.122218	−	0.211688i
$605$	21.4785	+	10.5970i	0.873226	+	0.430827i
$606$	0.00586470	−	0.0811112i	0.000238237	−	0.00329492i
$607$	6.89530	−	11.9430i	0.279871	−	0.484752i	−0.691481	−	0.722395i	$-0.743041\pi$
$607$	6.89530	−	11.9430i	0.279871	−	0.484752i	0.971353	+	0.237643i	$0.0763748\pi$
$608$			11.9387i			0.484177i
$609$		0			0
$610$	0.121480	+	0.181880i	0.00491857	+	0.00736410i
$611$	1.37485	+	0.793773i	0.0556207	+	0.0321126i
$612$	17.1716	+	13.5472i	0.694119	+	0.547614i
$613$	−5.54509	+	3.20146i	−0.223964	+	0.129306i	−0.607784	−	0.794102i	$-0.707941\pi$
$613$	−5.54509	+	3.20146i	−0.223964	+	0.129306i	0.383820	+	0.923408i	$0.374608\pi$
$614$	0.194241	−	0.336435i	0.00783892	−	0.0135774i
$615$	33.1780	+	0.229369i	1.33787	+	0.00924904i
$616$		0			0
$617$	26.2321			1.05607			0.528033	−	0.849224i	$-0.322930\pi$
$617$	26.2321			1.05607			0.528033	+	0.849224i	$0.322930\pi$
$618$	0.641322	−	0.310918i	0.0257978	−	0.0125070i
$619$	33.4262	−	19.2987i	1.34351	−	0.775678i	0.356193	−	0.934412i	$-0.384075\pi$
$619$	33.4262	−	19.2987i	1.34351	−	0.775678i	0.987321	+	0.158734i	$0.0507413\pi$
$620$	−5.62082	+	11.3926i	−0.225738	+	0.457538i
$621$	29.7359	+	27.1589i	1.19326	+	1.08985i
$622$	4.49304			0.180154
$623$		0			0
$624$	18.0008	+	12.2037i	0.720607	+	0.488540i
$625$	24.1529	−	6.45267i	0.966116	−	0.258107i
$626$	−2.38086	−	4.12377i	−0.0951582	−	0.164819i
$627$	−0.209339	+	2.89525i	−0.00836020	+	0.115625i
$628$	22.6455	−	39.2232i	0.903655	−	1.56518i
$629$	−40.3705			−1.60968
$630$		0			0
$631$	−11.8214			−0.470602			−0.235301	−	0.971923i	$-0.575608\pi$
$631$	−11.8214			−0.470602			−0.235301	+	0.971923i	$0.575608\pi$
$632$	−2.60665	+	4.51486i	−0.103687	+	0.179591i
$633$	0.593678	−	8.21082i	0.0235966	−	0.326351i
$634$	−3.14576	−	5.44861i	−0.124934	−	0.216392i
$635$	−31.7650	+	2.07611i	−1.26056	+	0.0823880i
$636$	11.5483	+	7.82921i	0.457918	+	0.310448i
$637$		0			0
$638$	1.56841			0.0620940
$639$	0.436200	−	3.00065i	0.0172558	−	0.118704i
$640$	−19.0154	−	9.38174i	−0.751652	−	0.370846i
$641$	22.3042	−	12.8773i	0.880963	−	0.508624i	0.00998712	−	0.999950i	$-0.496821\pi$
$641$	22.3042	−	12.8773i	0.880963	−	0.508624i	0.870976	+	0.491326i	$0.163488\pi$
$642$	−7.10012	+	3.44219i	−0.280219	+	0.135853i
$643$	33.0845			1.30472			0.652362	−	0.757907i	$-0.273778\pi$
$643$	33.0845			1.30472			0.652362	+	0.757907i	$0.273778\pi$
$644$		0			0
$645$	0.110461	−	15.9781i	0.00434938	−	0.629135i
$646$	−2.09423	+	3.62731i	−0.0823962	+	0.142714i
$647$	33.2497	−	19.1967i	1.30718	−	0.754700i	0.325555	−	0.945523i	$-0.394449\pi$
$647$	33.2497	−	19.1967i	1.30718	−	0.754700i	0.981625	+	0.190823i	$0.0611156\pi$
$648$	−11.5977	−	3.44469i	−0.455602	−	0.135320i
$649$	4.79517	+	2.76849i	0.188227	+	0.108673i
$650$	−2.52907	+	6.09936i	−0.0991984	+	0.239237i
$651$		0			0
$652$		−	20.8332i		−	0.815891i
$653$	14.5375	−	25.1797i	0.568896	−	0.985356i	−0.427780	−	0.903883i	$-0.640704\pi$
$653$	14.5375	−	25.1797i	0.568896	−	0.985356i	0.996676	−	0.0814732i	$-0.0259625\pi$
$654$	0.377060	−	5.21490i	0.0147442	−	0.203919i
$655$	34.0157	+	16.7825i	1.32910	+	0.655747i
$656$	−14.1102	+	24.4395i	−0.550909	+	0.954203i
$657$	−7.41785	−	18.6129i	−0.289398	−	0.726157i
$658$		0			0
$659$			29.3766i			1.14435i	0.820132	+	0.572175i	$0.193900\pi$
$659$			29.3766i			1.14435i	−0.820132	+	0.572175i	$0.806100\pi$
$660$	−3.37648	−	1.98066i	−0.131429	−	0.0770970i
$661$	17.0023	−	9.81629i	0.661313	−	0.381809i	−0.131464	−	0.991321i	$-0.541968\pi$
$661$	17.0023	−	9.81629i	0.661313	−	0.381809i	0.792777	+	0.609512i	$0.208634\pi$
$662$	−5.36856	−	9.29861i	−0.208655	−	0.361401i
$663$	11.1690	+	23.0380i	0.433768	+	0.894722i
$664$		−	14.5473i		−	0.564544i
$665$		0			0
$666$	10.0512	−	4.00572i	0.389474	−	0.155219i
$667$	−56.5149	−	32.6289i	−2.18826	−	1.26340i
$668$	−19.9933	+	11.5431i	−0.773564	+	0.446618i
$669$	−1.24125	+	17.1670i	−0.0479896	+	0.663716i
$670$	7.48883	−	0.489458i	0.289319	−	0.0189094i
$671$	−0.151783			−0.00585954
$672$		0			0
$673$		−	7.40581i		−	0.285473i	−0.989761	−	0.142736i	$-0.954410\pi$
$673$		−	7.40581i		−	0.285473i	0.989761	−	0.142736i	$-0.0455901\pi$
$674$	−3.20250	−	1.84896i	−0.123355	−	0.0712193i
$675$	−2.23172	+	25.8847i	−0.0858991	+	0.996304i
$676$	1.43635	+	2.48784i	0.0552443	+	0.0956860i
$677$	39.4283	+	22.7639i	1.51535	+	0.874890i	0.999838	+	0.0180093i	$0.00573286\pi$
$677$	39.4283	+	22.7639i	1.51535	+	0.874890i	0.515515	+	0.856880i	$0.327600\pi$
$678$	−2.89282	−	1.96121i	−0.111098	−	0.0753196i
$679$		0			0
$680$	−6.47461	−	9.69381i	−0.248290	−	0.371741i
$681$	−10.7347	−	22.1421i	−0.411354	−	0.848489i
$682$	0.281459	+	0.487502i	0.0107776	+	0.0186674i
$683$	3.71705	+	6.43812i	0.142229	+	0.246348i	0.928336	−	0.371743i	$-0.121240\pi$
$683$	3.71705	+	6.43812i	0.142229	+	0.246348i	−0.786107	+	0.618091i	$0.787906\pi$
$684$	−2.52913	+	17.3980i	−0.0967037	+	0.665231i
$685$	−23.1610	+	15.4695i	−0.884935	+	0.591059i
$686$		0			0
$687$	−15.1655	+	22.3694i	−0.578599	+	0.853446i
$688$	11.7697	+	6.79525i	0.448716	+	0.259066i
$689$	8.16585	+	14.1437i	0.311094	+	0.538831i
$690$	−5.13754	−	9.04227i	−0.195583	−	0.344233i
$691$	−2.52569	−	1.45821i	−0.0960819	−	0.0554729i	0.451189	−	0.892428i	$-0.351000\pi$
$691$	−2.52569	−	1.45821i	−0.0960819	−	0.0554729i	−0.547271	+	0.836955i	$0.684333\pi$
$692$			38.0665i			1.44707i
$693$		0			0
$694$	−0.809869			−0.0307422
$695$	42.4526	−	2.77463i	1.61032	−	0.105248i
$696$	19.5537	+	1.41382i	0.741182	+	0.0535907i
$697$	−28.7718	+	16.6114i	−1.08981	+	0.629202i
$698$	1.38237	+	0.798112i	0.0523235	+	0.0302090i
$699$	−15.2672	−	10.3505i	−0.577457	−	0.391491i
$700$		0			0
$701$		−	25.2600i		−	0.954057i	−0.878888	−	0.477029i	$-0.841714\pi$
$701$		−	25.2600i		−	0.954057i	0.878888	−	0.477029i	$-0.158286\pi$
$702$	−5.06671	−	4.62761i	−0.191231	−	0.174658i
$703$	−16.2250	−	28.1025i	−0.611937	−	1.05991i
$704$	2.44974	−	1.41436i	0.0923281	−	0.0533057i
$705$	−1.39140	−	0.816201i	−0.0524031	−	0.0307399i
$706$		−	2.08164i		−	0.0783435i
$707$		0			0
$708$	27.7572	+	18.8182i	1.04318	+	0.707230i
$709$	−0.882570	+	1.52866i	−0.0331456	+	0.0574099i	−0.882122	−	0.471020i	$-0.843886\pi$
$709$	−0.882570	+	1.52866i	−0.0331456	+	0.0574099i	0.848977	+	0.528430i	$0.177219\pi$
$710$	−0.346457	+	0.702220i	−0.0130023	+	0.0263538i
$711$	−7.20618	+	9.13408i	−0.270253	+	0.342555i
$712$	4.14603	−	7.18114i	0.155379	−	0.269125i
$713$		−	23.4217i		−	0.877149i
$714$		0			0
$715$	−2.54504	−	3.81044i	−0.0951790	−	0.142502i
$716$	−10.5263	−	6.07738i	−0.393387	−	0.227122i
$717$	42.2285	+	3.05330i	1.57705	+	0.114028i
$718$	5.86285	−	3.38492i	0.218800	−	0.126324i
$719$	−7.00072	+	12.1256i	−0.261083	+	0.452209i	−0.966530	−	0.256554i	$-0.917413\pi$
$719$	−7.00072	+	12.1256i	−0.261083	+	0.452209i	0.705447	+	0.708763i	$0.250746\pi$
$720$	−18.2046	−	12.5265i	−0.678446	−	0.466835i
$721$		0			0
$722$	3.21617			0.119693
$723$	−14.2658	−	29.4257i	−0.530551	−	1.09435i
$724$	26.9119	−	15.5376i	1.00017	−	0.577450i
$725$	−5.47977	−	41.7418i	−0.203514	−	1.55025i
$726$	5.78375	−	2.80401i	0.214655	−	0.104067i
$727$	−32.1893			−1.19383			−0.596917	−	0.802303i	$-0.703608\pi$
$727$	−32.1893			−1.19383			−0.596917	+	0.802303i	$0.703608\pi$
$728$		0			0
$729$	−24.5074	−	11.3309i	−0.907681	−	0.419662i
$730$	0.337461	+	5.16324i	0.0124900	+	0.191100i
$731$	7.99980	+	13.8561i	0.295883	+	0.512485i
$732$	−0.916886	−	0.0662948i	−0.0338891	−	0.00245033i
$733$	−1.23440	+	2.13804i	−0.0455935	+	0.0789703i	−0.887922	−	0.459995i	$-0.847851\pi$
$733$	−1.23440	+	2.13804i	−0.0455935	+	0.0789703i	0.842328	+	0.538965i	$0.181185\pi$
$734$	−6.59617			−0.243469
$735$		0			0
$736$	29.6828			1.09412
$737$	−2.60405	+	4.51035i	−0.0959214	+	0.166141i
$738$	5.51515	−	6.99065i	0.203016	−	0.257329i
$739$	19.5506	+	33.8627i	0.719182	+	1.24566i	0.961324	+	0.275419i	$0.0888167\pi$
$739$	19.5506	+	33.8627i	0.719182	+	1.24566i	−0.242142	+	0.970241i	$0.577850\pi$
$740$	43.6668	−	2.85399i	1.60522	−	0.104915i
$741$	−11.5483	+	17.0339i	−0.424236	+	0.625758i
$742$		0			0
$743$	−23.3132			−0.855280			−0.427640	−	0.903949i	$-0.640655\pi$
$743$	−23.3132			−0.855280			−0.427640	+	0.903949i	$0.640655\pi$
$744$	3.06956	+	6.33151i	0.112536	+	0.232124i
$745$	10.7171	−	21.7221i	0.392645	−	0.795836i
$746$	6.05608	−	3.49648i	0.221729	−	0.128015i
$747$	4.67029	−	32.1272i	0.170877	−	1.17547i
$748$	3.91973			0.143319
$749$		0			0
$750$	2.61261	−	6.17972i	0.0953989	−	0.225652i
$751$	−0.654492	+	1.13361i	−0.0238828	+	0.0413662i	−0.877720	−	0.479174i	$-0.840936\pi$
$751$	−0.654492	+	1.13361i	−0.0238828	+	0.0413662i	0.853837	+	0.520540i	$0.174270\pi$
$752$	1.18823	−	0.686023i	0.0433302	−	0.0250167i
$753$	0.430052	−	5.94781i	0.0156720	−	0.216750i
$754$	9.62960	+	5.55965i	0.350689	+	0.202471i
$755$	−5.94184	+	3.96863i	−0.216246	+	0.144433i
$756$		0			0
$757$			16.4529i			0.597992i	0.954254	+	0.298996i	$0.0966518\pi$
$757$			16.4529i			0.597992i	−0.954254	+	0.298996i	$0.903348\pi$
$758$	−1.08378	+	1.87717i	−0.0393648	+	0.0681818i
$759$	7.19838	+	0.520474i	0.261285	+	0.0188920i
$760$	4.14585	−	8.40304i	0.150386	−	0.304810i
$761$	2.93936	−	5.09113i	0.106552	−	0.184553i	−0.807819	−	0.589430i	$-0.799352\pi$
$761$	2.93936	−	5.09113i	0.106552	−	0.184553i	0.914371	+	0.404877i	$0.132686\pi$
$762$	−4.79394	+	7.07117i	−0.173666	+	0.256162i
$763$		0			0
$764$			19.2801i			0.697530i
$765$	−11.1869	−	23.4871i	−0.404462	−	0.849178i
$766$	4.85013	−	2.80022i	0.175242	−	0.101176i
$767$	19.6273	+	33.9955i	0.708701	+	1.22751i
$768$	11.2799	−	5.46857i	0.407027	−	0.197330i
$769$			3.63344i			0.131025i	0.997852	+	0.0655127i	$0.0208683\pi$
$769$			3.63344i			0.131025i	−0.997852	+	0.0655127i	$0.979132\pi$
$770$		0			0
$771$	3.67745	−	5.42432i	0.132440	−	0.195352i
$772$	−26.7505	−	15.4444i	−0.962773	−	0.555857i
$773$	26.1680	−	15.1081i	0.941198	−	0.543401i	0.0508627	−	0.998706i	$-0.483803\pi$
$773$	26.1680	−	15.1081i	0.941198	−	0.543401i	0.890336	+	0.455304i	$0.150470\pi$
$774$	−3.36659	−	2.65601i	−0.121010	−	0.0954685i
$775$	11.9911	−	9.19404i	0.430732	−	0.330260i
$776$	−10.7664			−0.386492
$777$		0			0
$778$			10.9950i			0.394189i
$779$	−23.1269	−	13.3523i	−0.828607	−	0.478397i
$780$	−13.7096	−	24.1295i	−0.490884	−	0.863975i
$781$	−0.271701	−	0.470600i	−0.00972223	−	0.0168394i
$782$	9.01847	+	5.20682i	0.322500	+	0.186195i
$783$	42.7299	+	9.39994i	1.52704	+	0.335927i
$784$		0			0
$785$	−44.7970	+	29.9204i	−1.59887	+	1.06791i
$786$	9.15979	−	4.44074i	0.326719	−	0.158396i
$787$	25.4243	+	44.0362i	0.906279	+	1.56972i	0.819191	+	0.573521i	$0.194423\pi$
$787$	25.4243	+	44.0362i	0.906279	+	1.56972i	0.0870888	+	0.996201i	$0.472244\pi$
$788$	−0.0200209	−	0.0346771i	−0.000713213	−	0.00123532i
$789$	−40.1089	+	19.4451i	−1.42791	+	0.692264i
$790$	2.49845	−	1.66875i	0.0888909	−	0.0593713i
$791$		0			0
$792$	−2.01413	+	0.802696i	−0.0715689	+	0.0285226i
$793$	−0.931907	−	0.538037i	−0.0330930	−	0.0191063i
$794$	1.58258	+	2.74111i	0.0561637	+	0.0972784i
$795$	−8.19788	−	14.4286i	−0.290749	−	0.511729i
$796$	−18.1219	−	10.4627i	−0.642313	−	0.370839i
$797$			10.1940i			0.361089i	0.983567	+	0.180545i	$0.0577860\pi$
$797$			10.1940i			0.361089i	−0.983567	+	0.180545i	$0.942214\pi$
$798$		0			0
$799$	1.61526			0.0571439
$800$	11.6518	+	15.1965i	0.411953	+	0.537278i
$801$	11.4618	−	14.5283i	0.404984	−	0.513331i
$802$	2.40453	−	1.38826i	0.0849069	−	0.0490210i
$803$	−3.10970	−	1.79539i	−0.109739	−	0.0633578i
$804$	−17.7004	+	26.1085i	−0.624245	+	0.920776i
$805$		0			0
$806$			3.99083i			0.140571i
$807$	−11.4608	+	5.55627i	−0.403438	+	0.195590i
$808$	−0.0910857	−	0.157765i	−0.00320438	−	0.00555015i
$809$	10.9158	−	6.30222i	0.383778	−	0.221574i	−0.295683	−	0.955286i	$-0.595547\pi$
$809$	10.9158	−	6.30222i	0.383778	−	0.221574i	0.679461	+	0.733712i	$0.262214\pi$
$810$	5.11571	+	4.73765i	0.179748	+	0.166464i
$811$		−	40.1743i		−	1.41071i	−0.708853	−	0.705356i	$-0.750787\pi$
$811$		−	40.1743i		−	1.41071i	0.708853	−	0.705356i	$-0.249213\pi$
$812$		0			0
$813$	23.6055	−	34.8186i	0.827880	−	1.22114i
$814$	0.969529	−	1.67927i	0.0339820	−	0.0588585i
$815$	−10.9638	+	22.2220i	−0.384044	+	0.778403i
$816$	22.0697	+	1.59573i	0.772593	+	0.0558618i
$817$	−6.43028	+	11.1376i	−0.224967	+	0.389654i
$818$			2.66725i			0.0932581i
$819$		0			0
$820$	29.9467	−	20.0018i	1.04578	−	0.698492i
$821$	37.3677	+	21.5743i	1.30414	+	0.752947i	0.981112	−	0.193441i	$-0.0619649\pi$
$821$	37.3677	+	21.5743i	1.30414	+	0.752947i	0.323031	+	0.946388i	$0.395298\pi$
$822$	−0.539046	+	7.45524i	−0.0188014	+	0.260031i
$823$	−25.5070	+	14.7265i	−0.889120	+	0.513333i	−0.873654	−	0.486547i	$-0.838256\pi$
$823$	−25.5070	+	14.7265i	−0.889120	+	0.513333i	−0.0154652	+	0.999880i	$0.504923\pi$
$824$	0.798276	−	1.38266i	0.0278093	−	0.0481671i
$825$	2.55922	+	3.88962i	0.0891005	+	0.135419i
$826$		0			0
$827$	−4.77349			−0.165991			−0.0829953	−	0.996550i	$-0.526449\pi$
$827$	−4.77349			−0.165991			−0.0829953	+	0.996550i	$0.526449\pi$
$828$	43.2563	+	6.28811i	1.50326	+	0.218527i
$829$	−30.2779	+	17.4809i	−1.05159	+	0.607138i	−0.923095	−	0.384571i	$-0.874349\pi$
$829$	−30.2779	+	17.4809i	−1.05159	+	0.607138i	−0.128499	+	0.991710i	$0.541016\pi$
$830$	−3.70943	+	7.51849i	−0.128756	+	0.260971i
$831$	4.57643	+	9.43967i	0.158754	+	0.327459i
$832$	20.0543			0.695257
$833$		0			0
$834$	6.40690	−	9.45032i	0.221853	−	0.327238i
$835$	27.4009	−	1.79088i	0.948247	−	0.0619759i
$836$	1.57535	+	2.72858i	0.0544845	+	0.0943700i
$837$	4.74636	+	14.9684i	0.164058	+	0.517384i
$838$	0.138893	−	0.240570i	0.00479798	−	0.00831034i
$839$	35.3328			1.21982			0.609911	−	0.792470i	$-0.291205\pi$
$839$	35.3328			1.21982			0.609911	+	0.792470i	$0.291205\pi$
$840$		0			0
$841$	−41.8964			−1.44470
$842$	−3.42657	+	5.93499i	−0.118087	+	0.204533i
$843$	−32.6476	−	2.36056i	−1.12444	−	0.0813020i
$844$	−4.46763	−	7.73815i	−0.153782	−	0.266358i
$845$	−0.222845	−	3.40959i	−0.00766610	−	0.117293i
$846$	−0.402157	+	0.160273i	−0.0138264	+	0.00551029i
$847$		0			0
$848$	14.1148			0.484704
$849$	−12.8700	+	6.23945i	−0.441696	+	0.214137i
$850$	0.874445	+	6.66104i	0.0299932	+	0.228472i
$851$	−69.8705	+	40.3397i	−2.39513	+	1.38283i
$852$	−1.43573	−	2.96145i	−0.0491874	−	0.101458i
$853$	14.5110			0.496846			0.248423	−	0.968652i	$-0.420088\pi$
$853$	14.5110			0.496846			0.248423	+	0.968652i	$0.420088\pi$
$854$		0			0
$855$	11.8537	−	17.2269i	0.405388	−	0.589146i
$856$	−8.83777	+	15.3075i	−0.302069	+	0.523199i
$857$	8.15972	−	4.71102i	0.278731	−	0.160925i	−0.354118	−	0.935201i	$-0.615219\pi$
$857$	8.15972	−	4.71102i	0.278731	−	0.160925i	0.632849	+	0.774275i	$0.281886\pi$
$858$	−1.22654	−	0.0886838i	−0.0418732	−	0.00302762i
$859$	8.09305	+	4.67252i	0.276131	+	0.159424i	0.631671	−	0.775237i	$-0.282370\pi$
$859$	8.09305	+	4.67252i	0.276131	+	0.159424i	−0.355539	+	0.934661i	$0.615703\pi$
$860$	−9.63256	−	14.4219i	−0.328467	−	0.491782i
$861$		0			0
$862$			6.16151i			0.209862i
$863$	6.19173	−	10.7244i	0.210769	−	0.365063i	−0.741186	−	0.671299i	$-0.765737\pi$
$863$	6.19173	−	10.7244i	0.210769	−	0.365063i	0.951955	+	0.306237i	$0.0990699\pi$
$864$	−18.9698	+	6.01516i	−0.645365	+	0.204640i
$865$	20.0331	−	40.6042i	0.681145	−	1.38058i
$866$	3.49570	−	6.05472i	0.118789	−	0.205748i
$867$	−2.81025	−	1.90523i	−0.0954411	−	0.0647048i
$868$		0			0
$869$			2.08502i			0.0707295i
$870$	−9.74546	−	5.71674i	−0.330402	−	0.193816i
$871$	−31.9763	+	18.4615i	−1.08347	+	0.625544i
$872$	−5.85618	−	10.1432i	−0.198315	−	0.343492i
$873$	−23.7773	−	3.45648i	−0.804741	−	0.116984i
$874$			8.37053i			0.283137i
$875$		0			0
$876$	−18.0008	−	12.2037i	−0.608189	−	0.412325i
$877$	−9.34124	−	5.39317i	−0.315431	−	0.182114i	0.333923	−	0.942600i	$-0.391627\pi$
$877$	−9.34124	−	5.39317i	−0.315431	−	0.182114i	−0.649354	+	0.760486i	$0.724961\pi$
$878$	−5.10424	+	2.94694i	−0.172260	+	0.0994543i
$879$	9.04626	+	0.654084i	0.305123	+	0.0220617i
$880$	−3.95178	+	0.258282i	−0.133214	+	0.00870667i
$881$	16.5184			0.556520			0.278260	−	0.960506i	$-0.410242\pi$
$881$	16.5184			0.556520			0.278260	+	0.960506i	$0.410242\pi$
$882$		0			0
$883$			16.5025i			0.555352i	0.960675	+	0.277676i	$0.0895641\pi$
$883$			16.5025i			0.555352i	−0.960675	+	0.277676i	$0.910436\pi$
$884$	24.0660	+	13.8945i	0.809427	+	0.467323i
$885$	−19.7043	−	34.6803i	−0.662352	−	1.16577i
$886$	−2.72733	−	4.72387i	−0.0916263	−	0.158701i
$887$	−38.9737	−	22.5015i	−1.30861	−	0.755525i	−0.326744	−	0.945113i	$-0.605952\pi$
$887$	−38.9737	−	22.5015i	−1.30861	−	0.755525i	−0.981864	+	0.189587i	$0.939285\pi$
$888$	13.6011	−	20.0619i	0.456422	−	0.673233i
$889$		0			0
$890$	−3.97393	+	2.65424i	−0.133206	+	0.0889702i
$891$	−4.70584	+	1.12611i	−0.157651	+	0.0377261i
$892$	9.34084	+	16.1788i	0.312754	+	0.541706i
$893$	0.649178	+	1.12441i	0.0217239	+	0.0376269i
$894$	−2.83581	−	5.84934i	−0.0948435	−	0.195631i
$895$	8.02974	+	12.0222i	0.268405	+	0.401856i
$896$		0			0
$897$	42.3510	+	28.7121i	1.41406	+	0.958670i
$898$	5.36714	+	3.09872i	0.179104	+	0.103406i
$899$	−12.7227	−	22.0364i	−0.424327	−	0.734955i
$900$	13.7607	+	24.6140i	0.458690	+	0.820467i
$901$	14.3906	+	8.30842i	0.479421	+	0.276794i
$902$		−	1.59574i		−	0.0531325i
$903$		0			0
$904$	−7.82905			−0.260390
$905$	−36.8828	+	2.41060i	−1.22603	+	0.0801312i
$906$	−0.138290	+	1.91261i	−0.00459437	+	0.0635422i
$907$	6.72520	−	3.88280i	0.223307	−	0.128926i	−0.384174	−	0.923261i	$-0.625514\pi$
$907$	6.72520	−	3.88280i	0.223307	−	0.128926i	0.607480	+	0.794335i	$0.292180\pi$
$908$	−23.1302	−	13.3542i	−0.767601	−	0.443175i
$909$	−0.150511	−	0.377662i	−0.00499213	−	0.0125262i
$910$		0			0
$911$			12.5284i			0.415085i	0.978226	+	0.207543i	$0.0665466\pi$
$911$			12.5284i			0.415085i	−0.978226	+	0.207543i	$0.933453\pi$
$912$	7.75903	+	16.0044i	0.256927	+	0.529957i
$913$	−2.90904	−	5.03860i	−0.0962751	−	0.166753i
$914$	−3.67973	+	2.12449i	−0.121714	+	0.0702719i
$915$	0.943120	+	0.553239i	0.0311786	+	0.0182895i
$916$			29.3334i			0.969204i
$917$		0			0
$918$	−6.81871	−	1.50001i	−0.225051	−	0.0495079i
$919$	17.1363	−	29.6809i	0.565274	−	0.979084i	−0.431750	−	0.901993i	$-0.642104\pi$
$919$	17.1363	−	29.6809i	0.565274	−	0.979084i	0.997024	−	0.0770906i	$-0.0245631\pi$
$920$	−20.8922	−	10.3077i	−0.688797	−	0.339835i
$921$	0.140056	−	1.93703i	0.00461500	−	0.0638274i
$922$	0.698096	−	1.20914i	0.0229906	−	0.0398208i
$923$		−	3.85247i		−	0.126806i
$924$		0			0
$925$	−48.0797	−	19.9360i	−1.58085	−	0.655493i
$926$	5.76690	+	3.32952i	0.189512	+	0.109415i
$927$	2.20686	−	2.79727i	0.0724828	−	0.0918745i
$928$	27.9272	−	16.1238i	0.916755	−	0.529289i
$929$	22.7821	−	39.4597i	0.747455	−	1.29463i	−0.201584	−	0.979471i	$-0.564609\pi$
$929$	22.7821	−	39.4597i	0.747455	−	1.29463i	0.949039	−	0.315159i	$-0.102058\pi$
$930$	0.0280336	−	4.05504i	0.000919257	−	0.132970i
$931$		0			0
$932$	−20.0201			−0.655781
$933$	20.2115	−	9.79870i	0.661695	−	0.320795i
$934$	7.73313	−	4.46473i	0.253036	−	0.146090i
$935$	−4.18103	−	2.06281i	−0.136734	−	0.0674612i
$936$	−15.2115	−	2.21128i	−0.497205	−	0.0722780i
$937$	−15.5172			−0.506924			−0.253462	−	0.967345i	$-0.581569\pi$
$937$	−15.5172			−0.506924			−0.253462	+	0.967345i	$0.581569\pi$
$938$		0			0
$939$	−19.7034	−	13.3581i	−0.642997	−	0.435924i
$940$	−1.74715	+	0.114191i	−0.0569858	+	0.00372450i
$941$	−9.61292	−	16.6501i	−0.313372	−	0.542777i	0.665718	−	0.746203i	$-0.268125\pi$
$941$	−9.61292	−	16.6501i	−0.313372	−	0.542777i	−0.979090	+	0.203427i	$0.934792\pi$
$942$	−1.04260	+	14.4196i	−0.0339698	+	0.469816i
$943$	−33.1975	+	57.4998i	−1.08106	+	1.87245i
$944$	33.9261			1.10420
$945$		0			0
$946$	−0.768487			−0.0249857
$947$	−18.6530	+	32.3080i	−0.606142	+	1.04987i	0.385728	+	0.922613i	$0.373950\pi$
$947$	−18.6530	+	32.3080i	−0.606142	+	1.04987i	−0.991870	+	0.127256i	$0.959383\pi$
$948$	−0.910680	+	12.5951i	−0.0295775	+	0.409070i
$949$	−12.7285	−	22.0463i	−0.413183	−	0.715654i
$950$	−4.28541	+	3.28580i	−0.139037	+	0.106605i
$951$	−26.0336	−	17.6496i	−0.844197	−	0.572328i
$952$		0			0
$953$	10.1356			0.328326			0.164163	−	0.986433i	$-0.447508\pi$
$953$	10.1356			0.328326			0.164163	+	0.986433i	$0.447508\pi$
$954$	−4.40727	−	0.640679i	−0.142691	−	0.0207427i
$955$	10.1464	−	20.5654i	0.328331	−	0.665481i
$956$	39.7975	−	22.9771i	1.28714	−	0.743133i
$957$	7.05535	−	3.42049i	0.228067	−	0.110569i
$958$	7.76571			0.250899
$959$		0			0
$960$	−20.3769	−	0.140871i	−0.657662	−	0.00454660i
$961$	−10.9337	+	18.9377i	−0.352699	+	0.610893i
$962$	11.9053	−	6.87351i	0.383841	−	0.221611i
$963$	−24.4323	+	30.9688i	−0.787320	+	0.997955i
$964$	−30.7387	−	17.7470i	−0.990028	−	0.571593i
$965$	20.4060	+	30.5519i	0.656891	+	0.983500i
$966$		0			0
$967$		−	7.96860i		−	0.256253i	−0.991758	−	0.128126i	$-0.959104\pi$
$967$		−	7.96860i		−	0.256253i	0.991758	−	0.128126i	$-0.0408963\pi$
$968$	7.19924	−	12.4695i	0.231392	−	0.400783i
$969$	−1.51003	+	20.8843i	−0.0485091	+	0.670901i
$970$	5.56443	+	2.74535i	0.178663	+	0.0881478i
$971$	−12.8317	+	22.2252i	−0.411790	+	0.713242i	−0.995086	−	0.0990185i	$-0.968430\pi$
$971$	−12.8317	+	22.2252i	−0.411790	+	0.713242i	0.583295	+	0.812260i	$0.301763\pi$
$972$	−28.9186	+	4.74717i	−0.927566	+	0.152266i
$973$		0			0
$974$			1.61055i			0.0516053i
$975$	1.92507	+	32.9530i	0.0616516	+	1.05534i
$976$	−0.805407	+	0.465002i	−0.0257805	+	0.0148843i
$977$	−0.810100	−	1.40313i	−0.0259174	−	0.0448902i	0.852776	−	0.522277i	$-0.174917\pi$
$977$	−0.810100	−	1.40313i	−0.0259174	−	0.0448902i	−0.878693	+	0.477387i	$0.841584\pi$
$978$	2.90107	+	5.98397i	0.0927661	+	0.191346i
$979$		−	3.31635i		−	0.105991i
$980$		0			0
$981$	−9.67681	−	24.2811i	−0.308957	−	0.775234i
$982$	11.5810	+	6.68630i	0.369565	+	0.213368i
$983$	−11.0789	+	6.39643i	−0.353363	+	0.204014i	−0.666166	−	0.745804i	$-0.732066\pi$
$983$	−11.0789	+	6.39643i	−0.353363	+	0.204014i	0.312802	+	0.949818i	$0.398732\pi$
$984$	1.43846	−	19.8945i	0.0458564	−	0.634213i
$985$	0.00310617	+	0.0475251i	9.89707e−5	+	0.00151428i
$986$	11.3134			0.360293
$987$		0			0
$988$			22.3370i			0.710633i
$989$	27.6910	+	15.9874i	0.880524	+	0.508371i
$990$	1.24564	+	0.0987264i	0.0395892	+	0.00313773i
$991$	−15.1502	−	26.2409i	−0.481262	−	0.833570i	0.518507	−	0.855073i	$-0.326488\pi$
$991$	−15.1502	−	26.2409i	−0.481262	−	0.833570i	−0.999769	+	0.0215033i	$0.993155\pi$
$992$	10.0234	+	5.78699i	0.318242	+	0.183737i
$993$	−44.4290	−	30.1209i	−1.40991	−	0.955857i
$994$		0			0
$995$	13.8238	+	20.6971i	0.438244	+	0.656141i
$996$	−15.3720	−	31.7075i	−0.487082	−	1.00469i
$997$	14.1419	+	24.4945i	0.447879	+	0.775749i	0.998248	−	0.0591728i	$-0.0188463\pi$
$997$	14.1419	+	24.4945i	0.447879	+	0.775749i	−0.550369	+	0.834921i	$0.685513\pi$
$998$	1.91023	+	3.30861i	0.0604672	+	0.104732i
$999$	36.4783	−	39.9396i	1.15412	−	1.26363i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.p.g.509.14		64
3.2	odd	2	inner	735.2.p.g.509.20		64
5.4	even	2	inner	735.2.p.g.509.19		64
7.2	even	3		735.2.g.c.734.17	yes	32
7.3	odd	6	inner	735.2.p.g.374.13		64
7.4	even	3	inner	735.2.p.g.374.16		64
7.5	odd	6		735.2.g.c.734.20	yes	32
7.6	odd	2	inner	735.2.p.g.509.15		64
15.14	odd	2	inner	735.2.p.g.509.13		64
21.2	odd	6		735.2.g.c.734.14	yes	32
21.5	even	6		735.2.g.c.734.15	yes	32
21.11	odd	6	inner	735.2.p.g.374.18		64
21.17	even	6	inner	735.2.p.g.374.19		64
21.20	even	2	inner	735.2.p.g.509.17		64
35.4	even	6	inner	735.2.p.g.374.17		64
35.9	even	6		735.2.g.c.734.16	yes	32
35.19	odd	6		735.2.g.c.734.13	✓	32
35.24	odd	6	inner	735.2.p.g.374.20		64
35.34	odd	2	inner	735.2.p.g.509.18		64
105.44	odd	6		735.2.g.c.734.19	yes	32
105.59	even	6	inner	735.2.p.g.374.14		64
105.74	odd	6	inner	735.2.p.g.374.15		64
105.89	even	6		735.2.g.c.734.18	yes	32
105.104	even	2	inner	735.2.p.g.509.16		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.g.c.734.13	✓	32	35.19	odd	6
735.2.g.c.734.14	yes	32	21.2	odd	6
735.2.g.c.734.15	yes	32	21.5	even	6
735.2.g.c.734.16	yes	32	35.9	even	6
735.2.g.c.734.17	yes	32	7.2	even	3
735.2.g.c.734.18	yes	32	105.89	even	6
735.2.g.c.734.19	yes	32	105.44	odd	6
735.2.g.c.734.20	yes	32	7.5	odd	6
735.2.p.g.374.13		64	7.3	odd	6	inner
735.2.p.g.374.14		64	105.59	even	6	inner
735.2.p.g.374.15		64	105.74	odd	6	inner
735.2.p.g.374.16		64	7.4	even	3	inner
735.2.p.g.374.17		64	35.4	even	6	inner
735.2.p.g.374.18		64	21.11	odd	6	inner
735.2.p.g.374.19		64	21.17	even	6	inner
735.2.p.g.374.20		64	35.24	odd	6	inner
735.2.p.g.509.13		64	15.14	odd	2	inner
735.2.p.g.509.14		64	1.1	even	1	trivial
735.2.p.g.509.15		64	7.6	odd	2	inner
735.2.p.g.509.16		64	105.104	even	2	inner
735.2.p.g.509.17		64	21.20	even	2	inner
735.2.p.g.509.18		64	35.34	odd	2	inner
735.2.p.g.509.19		64	5.4	even	2	inner
735.2.p.g.509.20		64	3.2	odd	2	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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.173233 + 0.300049i) q^{2} +(-0.124909 + 1.72754i) q^{3} +(0.939980 + 1.62809i) q^{4} +(-0.145835 - 2.23131i) q^{5} +(-0.496709 - 0.336746i) q^{6} -1.34428 q^{8} +(-2.96880 - 0.431570i) q^{9} +(0.694765 + 0.342779i) q^{10} +(-0.465604 + 0.268817i) q^{11} +(-2.93001 + 1.42049i) q^{12} -3.81157 q^{13} +(3.87289 + 0.0267743i) q^{15} +(-1.64709 + 2.85284i) q^{16} +(-3.35855 + 1.93906i) q^{17} +(0.643786 - 0.816022i) q^{18} +(-2.69962 - 1.55862i) q^{19} +(3.49570 - 2.33482i) q^{20} -0.186272i q^{22} +(-3.87516 + 6.71198i) q^{23} +(0.167912 - 2.32229i) q^{24} +(-4.95746 + 0.650804i) q^{25} +(0.660291 - 1.14366i) q^{26} +(1.11638 - 5.07481i) q^{27} +8.42000i q^{29} +(-0.678947 + 1.15742i) q^{30} +(-2.61715 + 1.51101i) q^{31} +(-1.91494 - 3.31677i) q^{32} +(-0.406234 - 0.837928i) q^{33} -1.34364i q^{34} +(-2.08797 - 5.23915i) q^{36} +(9.01516 + 5.20491i) q^{37} +(0.935327 - 0.540011i) q^{38} +(0.476098 - 6.58464i) q^{39} +(0.196042 + 2.99950i) q^{40} +8.56674 q^{41} -4.12561i q^{43} +(-0.875318 - 0.505365i) q^{44} +(-0.530012 + 6.68723i) q^{45} +(-1.34262 - 2.32548i) q^{46} +(-0.360706 - 0.208254i) q^{47} +(-4.72266 - 3.20176i) q^{48} +(0.663525 - 1.60022i) q^{50} +(-2.93029 - 6.04423i) q^{51} +(-3.58280 - 6.20559i) q^{52} +(-2.14239 - 3.71072i) q^{53} +(1.32930 + 1.21410i) q^{54} +(0.667714 + 0.999703i) q^{55} +(3.02979 - 4.46901i) q^{57} +(-2.52641 - 1.45862i) q^{58} +(-5.14940 - 8.91903i) q^{59} +(3.59685 + 6.33060i) q^{60} +(0.244494 + 0.141159i) q^{61} -1.04703i q^{62} -5.26142 q^{64} +(0.555859 + 8.50478i) q^{65} +(0.321793 + 0.0232670i) q^{66} +(8.38926 - 4.84354i) q^{67} +(-6.31394 - 3.64535i) q^{68} +(-11.1112 - 7.53289i) q^{69} +1.01073i q^{71} +(3.99088 + 0.580149i) q^{72} +(3.33943 + 5.78405i) q^{73} +(-3.12345 + 1.80333i) q^{74} +(-0.505060 - 8.64551i) q^{75} -5.86030i q^{76} +(1.89324 + 1.28353i) q^{78} +(1.93907 - 3.35858i) q^{79} +(6.60576 + 3.25911i) q^{80} +(8.62749 + 2.56249i) q^{81} +(-1.48404 + 2.57044i) q^{82} +10.8216i q^{83} +(4.81643 + 7.21117i) q^{85} +(1.23789 + 0.714694i) q^{86} +(-14.5459 - 1.05173i) q^{87} +(0.625901 - 0.361364i) q^{88} +(-3.08421 + 5.34201i) q^{89} +(-1.91468 - 1.31748i) q^{90} -14.5703 q^{92} +(-2.28343 - 4.70997i) q^{93} +(0.124972 - 0.0721529i) q^{94} +(-3.08407 + 6.25097i) q^{95} +(5.96905 - 2.89384i) q^{96} +8.00908 q^{97} +(1.49830 - 0.597121i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 16 q^{4} - 40 q^{9} + 32 q^{15} + 16 q^{16} - 64 q^{25} - 56 q^{30} - 32 q^{36} + 56 q^{39} + 32 q^{46} + 40 q^{51} - 8 q^{60} - 352 q^{64} - 48 q^{79} + 40 q^{81} - 128 q^{85} + 80 q^{99}+O(q^{100}) \) 64 * q - 16 * q^4 - 40 * q^9 + 32 * q^15 + 16 * q^16 - 64 * q^25 - 56 * q^30 - 32 * q^36 + 56 * q^39 + 32 * q^46 + 40 * q^51 - 8 * q^60 - 352 * q^64 - 48 * q^79 + 40 * q^81 - 128 * q^85 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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