LMFDB - Embedded newform 875.2.bb.a.593.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			593.8
Character	$\chi$	$=$	875.593
Dual form			875.2.bb.a.332.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.637685 - 0.516387i) q^{2} +(-0.0764752 + 0.117761i) q^{3} +(-0.275837 - 1.29771i) q^{4} +(0.109578 - 0.0356039i) q^{6} +(-2.34165 - 1.23154i) q^{7} +(-1.23927 + 2.43220i) q^{8} +(1.21219 + 2.72262i) q^{9} +(0.422943 + 0.188306i) q^{11} +(0.173915 + 0.0667597i) q^{12} +(2.81849 - 0.446405i) q^{13} +(0.857282 + 1.99453i) q^{14} +(-0.377790 + 0.168203i) q^{16} +(-6.66164 + 0.349122i) q^{17} +(0.632933 - 2.36214i) q^{18} +(-1.22155 - 0.259649i) q^{19} +(0.324106 - 0.181574i) q^{21} +(-0.172465 - 0.338482i) q^{22} +(-3.30320 + 4.07911i) q^{23} +(-0.191646 - 0.331940i) q^{24} +(-2.02783 - 1.17077i) q^{26} +(-0.829380 - 0.131361i) q^{27} +(-0.952270 + 3.37848i) q^{28} +(-2.85581 - 0.927907i) q^{29} +(8.01719 + 7.21871i) q^{31} +(5.60118 + 1.50083i) q^{32} +(-0.0545199 + 0.0354056i) q^{33} +(4.42831 + 3.21736i) q^{34} +(3.19881 - 2.32407i) q^{36} +(-2.02695 + 5.28038i) q^{37} +(0.644885 + 0.796367i) q^{38} +(-0.162975 + 0.366049i) q^{39} +(1.91768 - 2.63945i) q^{41} +(-0.300440 - 0.0515774i) q^{42} +(6.03422 + 6.03422i) q^{43} +(0.127704 - 0.600799i) q^{44} +(4.21280 - 0.895458i) q^{46} +(-0.0866332 + 1.65306i) q^{47} +(0.00908374 - 0.0573524i) q^{48} +(3.96662 + 5.76766i) q^{49} +(0.468337 - 0.811184i) q^{51} +(-1.35675 - 3.53445i) q^{52} +(-6.01286 - 3.90480i) q^{53} +(0.461050 + 0.512048i) q^{54} +(5.89727 - 4.16914i) q^{56} +(0.123995 - 0.123995i) q^{57} +(1.34194 + 2.06641i) q^{58} +(-0.255341 + 2.42941i) q^{59} +(0.751418 - 0.0789772i) q^{61} +(-1.38479 - 8.74324i) q^{62} +(0.514499 - 7.86829i) q^{63} +(-2.31063 - 3.18031i) q^{64} +(0.0530495 + 0.00557573i) q^{66} +(0.124434 + 2.37433i) q^{67} +(2.29059 + 8.54858i) q^{68} +(-0.227749 - 0.700940i) q^{69} +(-2.47456 + 7.61592i) q^{71} +(-8.12418 - 0.425770i) q^{72} +(-5.93202 + 2.27709i) q^{73} +(4.01928 - 2.32053i) q^{74} +1.65684i q^{76} +(-0.758476 - 0.961818i) q^{77} +(0.292950 - 0.149265i) q^{78} +(7.41534 - 6.67680i) q^{79} +(-5.90370 + 6.55672i) q^{81} +(-2.58585 + 0.692877i) q^{82} +(8.96119 + 4.56596i) q^{83} +(-0.325030 - 0.370511i) q^{84} +(-0.731939 - 6.96393i) q^{86} +(0.327670 - 0.265342i) q^{87} +(-0.982136 + 0.795318i) q^{88} +(0.971014 + 9.23858i) q^{89} +(-7.14968 - 2.42576i) q^{91} +(6.20465 + 3.16143i) q^{92} +(-1.46320 + 0.392064i) q^{93} +(0.908864 - 1.00940i) q^{94} +(-0.605091 + 0.544826i) q^{96} +(7.70801 - 3.92743i) q^{97} +(0.448893 - 5.72626i) q^{98} +1.37978i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) $ 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.637685	−	0.516387i	−0.450911	−	0.365141i	0.376800	−	0.926295i	$-0.377024\pi$
$2$	−0.637685	−	0.516387i	−0.450911	−	0.365141i	−0.827712	+	0.561154i	$0.810358\pi$
$3$	−0.0764752	+	0.117761i	−0.0441530	+	0.0679896i	−0.860058	−	0.510197i	$-0.829573\pi$
$3$	−0.0764752	+	0.117761i	−0.0441530	+	0.0679896i	0.815905	+	0.578186i	$0.196239\pi$
$4$	−0.275837	−	1.29771i	−0.137918	−	0.648855i
$5$		0			0
$5$		0			0
$6$	0.109578	−	0.0356039i	0.0447349	−	0.0145352i
$7$	−2.34165	−	1.23154i	−0.885059	−	0.465478i
$7$	−2.34165	−	1.23154i	−0.885059	−	0.465478i
$8$	−1.23927	+	2.43220i	−0.438146	+	0.859911i
$9$	1.21219	+	2.72262i	0.404064	+	0.907542i
$10$		0			0
$11$	0.422943	+	0.188306i	0.127522	+	0.0567765i	0.469506	−	0.882929i	$-0.344432\pi$
$11$	0.422943	+	0.188306i	0.127522	+	0.0567765i	−0.341984	+	0.939706i	$0.611099\pi$
$12$	0.173915	+	0.0667597i	0.0502049	+	0.0192719i
$13$	2.81849	−	0.446405i	0.781709	−	0.123811i	0.247190	−	0.968967i	$-0.420493\pi$
$13$	2.81849	−	0.446405i	0.781709	−	0.123811i	0.534519	+	0.845156i	$0.320493\pi$
$14$	0.857282	+	1.99453i	0.229118	+	0.533061i
$15$		0			0
$16$	−0.377790	+	0.168203i	−0.0944475	+	0.0420507i
$17$	−6.66164	+	0.349122i	−1.61569	+	0.0846745i	−0.838610	−	0.544733i	$-0.816631\pi$
$17$	−6.66164	+	0.349122i	−1.61569	+	0.0846745i	−0.777076	+	0.629407i	$0.783298\pi$
$18$	0.632933	−	2.36214i	0.149184	−	0.556761i
$19$	−1.22155	−	0.259649i	−0.280243	−	0.0595675i	0.0656459	−	0.997843i	$-0.479089\pi$
$19$	−1.22155	−	0.259649i	−0.280243	−	0.0595675i	−0.345889	+	0.938276i	$0.612423\pi$
$20$		0			0
$21$	0.324106	−	0.181574i	0.0707257	−	0.0396226i
$22$	−0.172465	−	0.338482i	−0.0367697	−	0.0721647i
$23$	−3.30320	+	4.07911i	−0.688764	+	0.850553i	−0.994840	−	0.101454i	$-0.967651\pi$
$23$	−3.30320	+	4.07911i	−0.688764	+	0.850553i	0.306076	+	0.952007i	$0.400984\pi$
$24$	−0.191646	−	0.331940i	−0.0391195	−	0.0677570i
$25$		0			0
$26$	−2.02783	−	1.17077i	−0.397690	−	0.229606i
$27$	−0.829380	−	0.131361i	−0.159614	−	0.0252804i
$28$	−0.952270	+	3.37848i	−0.179962	+	0.638473i
$29$	−2.85581	−	0.927907i	−0.530310	−	0.172308i	0.0316093	−	0.999500i	$-0.489937\pi$
$29$	−2.85581	−	0.927907i	−0.530310	−	0.172308i	−0.561919	+	0.827192i	$0.689937\pi$
$30$		0			0
$31$	8.01719	+	7.21871i	1.43993	+	1.29652i	0.885783	+	0.464099i	$0.153622\pi$
$31$	8.01719	+	7.21871i	1.43993	+	1.29652i	0.554146	+	0.832420i	$0.313045\pi$
$32$	5.60118	+	1.50083i	0.990157	+	0.265312i
$33$	−0.0545199	+	0.0354056i	−0.00949069	+	0.00616332i
$34$	4.42831	+	3.21736i	0.759449	+	0.551772i
$35$		0			0
$36$	3.19881	−	2.32407i	0.533135	−	0.387345i
$37$	−2.02695	+	5.28038i	−0.333228	+	0.868089i	0.659931	+	0.751326i	$0.270585\pi$
$37$	−2.02695	+	5.28038i	−0.333228	+	0.868089i	−0.993160	+	0.116764i	$0.962748\pi$
$38$	0.644885	+	0.796367i	0.104614	+	0.129188i
$39$	−0.162975	+	0.366049i	−0.0260970	+	0.0586147i
$40$		0			0
$41$	1.91768	−	2.63945i	0.299491	−	0.412213i	−0.632577	−	0.774497i	$-0.718003\pi$
$41$	1.91768	−	2.63945i	0.299491	−	0.412213i	0.932068	+	0.362284i	$0.118003\pi$
$42$	−0.300440	−	0.0515774i	−0.0463589	−	0.00795856i
$43$	6.03422	+	6.03422i	0.920211	+	0.920211i	0.997044	−	0.0768333i	$-0.0244809\pi$
$43$	6.03422	+	6.03422i	0.920211	+	0.920211i	−0.0768333	+	0.997044i	$0.524481\pi$
$44$	0.127704	−	0.600799i	0.0192521	−	0.0905739i
$45$		0			0
$46$	4.21280	−	0.895458i	0.621143	−	0.132028i
$47$	−0.0866332	+	1.65306i	−0.0126368	+	0.241124i	0.985007	+	0.172515i	$0.0551893\pi$
$47$	−0.0866332	+	1.65306i	−0.0126368	+	0.241124i	−0.997644	+	0.0686086i	$0.978144\pi$
$48$	0.00908374	−	0.0573524i	0.00131112	−	0.00827811i
$49$	3.96662	+	5.76766i	0.566660	+	0.823952i
$50$		0			0
$51$	0.468337	−	0.811184i	0.0655803	−	0.113588i
$52$	−1.35675	−	3.53445i	−0.188147	−	0.490140i
$53$	−6.01286	−	3.90480i	−0.825929	−	0.536365i	0.0610710	−	0.998133i	$-0.480548\pi$
$53$	−6.01286	−	3.90480i	−0.825929	−	0.536365i	−0.887000	+	0.461769i	$0.847215\pi$
$54$	0.461050	+	0.512048i	0.0627410	+	0.0696809i
$55$		0			0
$56$	5.89727	−	4.16914i	0.788055	−	0.557124i
$57$	0.123995	−	0.123995i	0.0164235	−	0.0164235i
$58$	1.34194	+	2.06641i	0.176206	+	0.271333i
$59$	−0.255341	+	2.42941i	−0.0332426	+	0.316282i	0.965247	+	0.261339i	$0.0841642\pi$
$59$	−0.255341	+	2.42941i	−0.0332426	+	0.316282i	−0.998490	+	0.0549424i	$0.982502\pi$
$60$		0			0
$61$	0.751418	−	0.0789772i	0.0962092	−	0.0101120i	−0.0563015	−	0.998414i	$-0.517931\pi$
$61$	0.751418	−	0.0789772i	0.0962092	−	0.0101120i	0.152511	+	0.988302i	$0.451264\pi$
$62$	−1.38479	−	8.74324i	−0.175869	−	1.11039i
$63$	0.514499	−	7.86829i	0.0648207	−	0.991311i
$64$	−2.31063	−	3.18031i	−0.288829	−	0.397538i
$65$		0			0
$66$	0.0530495	+	0.00557573i	0.00652994	+	0.000686325i
$67$	0.124434	+	2.37433i	0.0152020	+	0.290071i	0.995642	+	0.0932545i	$0.0297270\pi$
$67$	0.124434	+	2.37433i	0.0152020	+	0.290071i	−0.980440	+	0.196817i	$0.936940\pi$
$68$	2.29059	+	8.54858i	0.277774	+	1.03667i
$69$	−0.227749	−	0.700940i	−0.0274178	−	0.0843833i
$70$		0			0
$71$	−2.47456	+	7.61592i	−0.293676	+	0.903843i	0.689986	+	0.723822i	$0.257617\pi$
$71$	−2.47456	+	7.61592i	−0.293676	+	0.903843i	−0.983663	+	0.180021i	$0.942383\pi$
$72$	−8.12418	−	0.425770i	−0.957444	−	0.0501775i
$73$	−5.93202	+	2.27709i	−0.694291	+	0.266513i	−0.679817	−	0.733382i	$-0.737941\pi$
$73$	−5.93202	+	2.27709i	−0.694291	+	0.266513i	−0.0144739	+	0.999895i	$0.504607\pi$
$74$	4.01928	−	2.32053i	0.467231	−	0.269756i
$75$		0			0
$76$			1.65684i			0.190052i
$77$	−0.758476	−	0.961818i	−0.0864363	−	0.109609i
$78$	0.292950	−	0.149265i	0.0331700	−	0.0169010i
$79$	7.41534	−	6.67680i	0.834291	−	0.751199i	−0.136624	−	0.990623i	$-0.543625\pi$
$79$	7.41534	−	6.67680i	0.834291	−	0.751199i	0.970915	+	0.239424i	$0.0769585\pi$
$80$		0			0
$81$	−5.90370	+	6.55672i	−0.655967	+	0.728525i
$82$	−2.58585	+	0.692877i	−0.285560	+	0.0765155i
$83$	8.96119	+	4.56596i	0.983619	+	0.501179i	0.870375	−	0.492389i	$-0.163876\pi$
$83$	8.96119	+	4.56596i	0.983619	+	0.501179i	0.113243	+	0.993567i	$0.463876\pi$
$84$	−0.325030	−	0.370511i	−0.0354637	−	0.0404261i
$85$		0			0
$86$	−0.731939	−	6.96393i	−0.0789270	−	0.750940i
$87$	0.327670	−	0.265342i	0.0351299	−	0.0284476i
$88$	−0.982136	+	0.795318i	−0.104696	+	0.0847812i
$89$	0.971014	+	9.23858i	0.102927	+	0.979287i	0.917098	+	0.398662i	$0.130525\pi$
$89$	0.971014	+	9.23858i	0.102927	+	0.979287i	−0.814171	+	0.580626i	$0.802808\pi$
$90$		0			0
$91$	−7.14968	−	2.42576i	−0.749490	−	0.254289i
$92$	6.20465	+	3.16143i	0.646879	+	0.329601i
$93$	−1.46320	+	0.392064i	−0.151727	+	0.0406551i
$94$	0.908864	−	1.00940i	0.0937421	−	0.104111i
$95$		0			0
$96$	−0.605091	+	0.544826i	−0.0617569	+	0.0556061i
$97$	7.70801	−	3.92743i	0.782630	−	0.398770i	−0.0165492	−	0.999863i	$-0.505268\pi$
$97$	7.70801	−	3.92743i	0.782630	−	0.398770i	0.799179	+	0.601093i	$0.205268\pi$
$98$	0.448893	−	5.72626i	0.0453451	−	0.578440i
$99$			1.37978i			0.138673i
$100$		0			0
$101$	−15.3672	+	8.87223i	−1.52909	+	0.882820i	−0.529688	+	0.848192i	$0.677691\pi$
$101$	−15.3672	+	8.87223i	−1.52909	+	0.882820i	−0.999400	+	0.0346276i	$0.988975\pi$
$102$	−0.717537	+	0.275437i	−0.0710467	+	0.0272723i
$103$	11.0967	+	0.581553i	1.09339	+	0.0573021i	0.590492	−	0.807044i	$-0.298934\pi$
$103$	11.0967	+	0.581553i	1.09339	+	0.0573021i	0.502898	+	0.864346i	$0.332267\pi$
$104$	−2.40712	+	7.40834i	−0.236037	+	0.726448i
$105$		0			0
$106$	1.81792	+	5.59499i	0.176572	+	0.543434i
$107$	0.622945	+	2.32486i	0.0602223	+	0.224753i	0.989478	−	0.144685i	$-0.0462169\pi$
$107$	0.622945	+	2.32486i	0.0602223	+	0.224753i	−0.929255	+	0.369438i	$0.879550\pi$
$108$	0.0583052	+	1.11253i	0.00561042	+	0.107053i
$109$	−18.4112	−	1.93510i	−1.76347	−	0.185349i	−0.833388	−	0.552689i	$-0.813602\pi$
$109$	−18.4112	−	1.93510i	−1.76347	−	0.185349i	−0.930087	+	0.367340i	$0.880268\pi$
$110$		0			0
$111$	−0.466814	−	0.642515i	−0.0443081	−	0.0609848i
$112$	1.09180	+	0.0713915i	0.103165	+	0.00674587i
$113$	−1.54166	−	9.73363i	−0.145027	−	0.915663i	−0.947681	−	0.319219i	$-0.896580\pi$
$113$	−1.54166	−	9.73363i	−0.145027	−	0.915663i	0.802654	−	0.596444i	$-0.203420\pi$
$114$	−0.143099	+	0.0150403i	−0.0134025	+	0.00140865i
$115$		0			0
$116$	−0.416419	+	3.96196i	−0.0386635	+	0.367859i
$117$	4.63195	+	7.13257i	0.428223	+	0.659406i
$118$	1.41734	−	1.41734i	0.130477	−	0.130477i
$119$	16.0292	+	7.38656i	1.46939	+	0.677125i
$120$		0			0
$121$	−7.21702	−	8.01531i	−0.656092	−	0.728664i
$122$	−0.519951	−	0.337660i	−0.0470741	−	0.0305703i
$123$	0.164171	+	0.427681i	0.0148028	+	0.0385627i
$124$	7.15636	−	12.3952i	0.642660	−	1.11312i
$125$		0			0
$126$	−4.39117	+	4.75181i	−0.391197	+	0.423325i
$127$	−1.02863	+	6.49451i	−0.0912761	+	0.576294i	0.899084	+	0.437776i	$0.144234\pi$
$127$	−1.02863	+	6.49451i	−0.0912761	+	0.576294i	−0.990360	+	0.138518i	$0.955766\pi$
$128$	0.438151	−	8.36042i	0.0387275	−	0.738964i
$129$	−1.17207	+	0.249131i	−0.103195	+	0.0219347i
$130$		0			0
$131$	−2.29581	+	10.8009i	−0.200586	+	0.943681i	0.756526	+	0.653963i	$0.226895\pi$
$131$	−2.29581	+	10.8009i	−0.200586	+	0.943681i	−0.957112	+	0.289718i	$0.906438\pi$
$132$	0.0609848	+	0.0609848i	0.00530805	+	0.00530805i
$133$	2.54067	+	2.11239i	0.220304	+	0.183168i
$134$	1.14673	−	1.57833i	0.0990621	−	0.136347i
$135$		0			0
$136$	7.40641	−	16.6351i	0.635094	−	1.42645i
$137$	0.864790	+	1.06793i	0.0738840	+	0.0912391i	0.812748	−	0.582616i	$-0.197971\pi$
$137$	0.864790	+	1.06793i	0.0738840	+	0.0912391i	−0.738864	+	0.673855i	$0.764637\pi$
$138$	−0.216724	+	0.564586i	−0.0184488	+	0.0480607i
$139$	−2.70776	+	1.96730i	−0.229669	+	0.166865i	−0.696668	−	0.717393i	$-0.745335\pi$
$139$	−2.70776	+	1.96730i	−0.229669	+	0.166865i	0.466999	+	0.884258i	$0.345335\pi$
$140$		0			0
$141$	−0.188041	−	0.136620i	−0.0158360	−	0.0115055i
$142$	5.51075	−	3.57873i	0.462452	−	0.300320i
$143$	1.27612	+	0.341936i	0.106715	+	0.0285941i
$144$	−0.915907	−	0.824686i	−0.0763256	−	0.0687238i
$145$		0			0
$146$	4.95862	+	1.61115i	0.410378	+	0.133340i
$147$	−0.982556	+	0.0260318i	−0.0810399	+	0.00214707i
$148$	7.41151	+	1.17387i	0.609223	+	0.0964914i
$149$	−16.1916	−	9.34825i	−1.32647	−	0.765838i	−0.341719	−	0.939802i	$-0.611009\pi$
$149$	−16.1916	−	9.34825i	−1.32647	−	0.765838i	−0.984752	+	0.173964i	$0.944342\pi$
$150$		0			0
$151$	−5.55298	−	9.61804i	−0.451895	−	0.782705i	0.546609	−	0.837388i	$-0.315919\pi$
$151$	−5.55298	−	9.61804i	−0.451895	−	0.782705i	−0.998504	+	0.0546830i	$0.982585\pi$
$152$	2.14534	−	2.64928i	0.174010	−	0.214885i
$153$	−9.02571	−	17.7139i	−0.729685	−	1.43209i
$154$	−0.0130015	+	1.00500i	−0.00104769	+	0.0809855i
$155$		0			0
$156$	0.519980	+	0.110525i	0.0416317	+	0.00884910i
$157$	−0.202009	+	0.753908i	−0.0161221	+	0.0601684i	−0.973518	−	0.228609i	$-0.926582\pi$
$157$	−0.202009	+	0.753908i	−0.0161221	+	0.0601684i	0.957396	+	0.288778i	$0.0932488\pi$
$158$	−8.17647	+	0.428511i	−0.650485	+	0.0340905i
$159$	0.919669	−	0.409463i	0.0729345	−	0.0324725i
$160$		0			0
$161$	12.7585	−	5.48381i	1.00551	−	0.432185i
$162$	7.15051	−	1.13253i	0.561797	−	0.0889799i
$163$	−20.2100	−	7.75789i	−1.58297	−	0.607645i	−0.601434	−	0.798923i	$-0.705404\pi$
$163$	−20.2100	−	7.75789i	−1.58297	−	0.607645i	−0.981536	+	0.191277i	$0.938737\pi$
$164$	−3.95421	−	1.76053i	−0.308772	−	0.137474i
$165$		0			0
$166$	−3.35662	−	7.53909i	−0.260524	−	0.585147i
$167$	4.06888	−	7.98564i	0.314860	−	0.617947i	−0.678290	−	0.734794i	$-0.737279\pi$
$167$	4.06888	−	7.98564i	0.314860	−	0.617947i	0.993150	+	0.116847i	$0.0372787\pi$
$168$	0.0399691	+	1.01331i	0.00308368	+	0.0781783i
$169$	−4.61911	+	1.50084i	−0.355316	+	0.115449i
$170$		0			0
$171$	−0.773826	−	3.64057i	−0.0591760	−	0.278401i
$172$	6.16621	−	9.49514i	0.470169	−	0.723997i
$173$	−11.2942	−	9.14584i	−0.858680	−	0.695345i	0.0952246	−	0.995456i	$-0.469643\pi$
$173$	−11.2942	−	9.14584i	−0.858680	−	0.695345i	−0.953904	+	0.300111i	$0.902976\pi$
$174$	−0.345969			−0.0262279
$175$		0			0
$176$	−0.191457			−0.0144316
$177$	−0.266563	−	0.215859i	−0.0200361	−	0.0162249i
$178$	4.15148	−	6.39272i	0.311167	−	0.479155i
$179$	−2.01032	−	9.45779i	−0.150258	−	0.706909i	−0.987183	−	0.159591i	$-0.948982\pi$
$179$	−2.01032	−	9.45779i	−0.150258	−	0.706909i	0.836925	−	0.547317i	$-0.184351\pi$
$180$		0			0
$181$	19.1189	−	6.21211i	1.42110	−	0.461742i	0.505146	−	0.863034i	$-0.331439\pi$
$181$	19.1189	−	6.21211i	1.42110	−	0.461742i	0.915950	+	0.401292i	$0.131439\pi$
$182$	3.30661	+	5.23888i	0.245102	+	0.388331i
$183$	−0.0481643	+	0.0945278i	−0.00356041	+	0.00698770i
$184$	−5.82765	−	13.0891i	−0.429620	−	0.964943i
$185$		0			0
$186$	1.13552	+	0.505565i	0.0832603	+	0.0370699i
$187$	−2.88324	−	1.10677i	−0.210843	−	0.0809351i
$188$	2.16909	−	0.343550i	0.158197	−	0.0250560i
$189$	1.78034	+	1.32902i	0.129501	+	0.0966716i
$190$		0			0
$191$	−22.6790	+	10.0973i	−1.64099	+	0.730617i	−0.999338	−	0.0363766i	$-0.988418\pi$
$191$	−22.6790	+	10.0973i	−1.64099	+	0.730617i	−0.641655	+	0.766994i	$0.721752\pi$
$192$	0.551223	−	0.0288884i	0.0397811	−	0.00208484i
$193$	−3.66243	+	13.6684i	−0.263627	+	0.983870i	0.699458	+	0.714674i	$0.253425\pi$
$193$	−3.66243	+	13.6684i	−0.263627	+	0.983870i	−0.963085	+	0.269196i	$0.913242\pi$
$194$	−6.94335	−	1.47586i	−0.498504	−	0.105960i
$195$		0			0
$196$	6.39062	−	6.73846i	0.456473	−	0.481318i
$197$	9.45216	+	18.5509i	0.673439	+	1.32170i	0.934357	+	0.356337i	$0.115975\pi$
$197$	9.45216	+	18.5509i	0.673439	+	1.32170i	−0.260919	+	0.965361i	$0.584025\pi$
$198$	0.712499	−	0.879863i	0.0506351	−	0.0625292i
$199$	7.89655	+	13.6772i	0.559772	+	0.969553i	0.997515	+	0.0704529i	$0.0224444\pi$
$199$	7.89655	+	13.6772i	0.559772	+	0.969553i	−0.437744	+	0.899100i	$0.644222\pi$
$200$		0			0
$201$	−0.289121	−	0.166924i	−0.0203930	−	0.0117739i
$202$	14.3809	+	2.27771i	1.01184	+	0.160259i
$203$	5.54453	+	5.68987i	0.389150	+	0.399351i
$204$	−1.18187	−	0.384012i	−0.0827472	−	0.0268862i
$205$		0			0
$206$	−6.77589	−	6.10104i	−0.472099	−	0.425080i
$207$	−15.1100	−	4.04871i	−1.05022	−	0.281405i
$208$	−0.989712	+	0.642726i	−0.0686241	+	0.0445650i
$209$	−0.467752	−	0.339842i	−0.0323551	−	0.0235074i
$210$		0			0
$211$	3.76604	−	2.73619i	0.259265	−	0.188367i	−0.450558	−	0.892747i	$-0.648775\pi$
$211$	3.76604	−	2.73619i	0.259265	−	0.188367i	0.709823	+	0.704380i	$0.248775\pi$
$212$	−3.40873	+	8.88003i	−0.234112	+	0.609883i
$213$	−0.707619	−	0.873837i	−0.0484853	−	0.0598743i
$214$	0.803286	−	1.80421i	0.0549115	−	0.123333i
$215$		0			0
$216$	1.34732	−	1.85442i	0.0916733	−	0.126178i
$217$	−9.88329	−	26.7772i	−0.670922	−	1.81775i
$218$	10.7413	+	10.7413i	0.727492	+	0.727492i
$219$	0.185499	−	0.872705i	0.0125349	−	0.0589719i
$220$		0			0
$221$	−18.6199	+	3.95779i	−1.25251	+	0.266230i
$222$	−0.0341059	+	0.650779i	−0.00228904	+	0.0436774i
$223$	0.346137	−	2.18542i	0.0231790	−	0.146347i	−0.973385	−	0.229178i	$-0.926396\pi$
$223$	0.346137	−	2.18542i	0.0231790	−	0.146347i	0.996564	+	0.0828312i	$0.0263962\pi$
$224$	−11.2676	−	10.4125i	−0.752851	−	0.695714i
$225$		0			0
$226$	−4.04323	+	7.00308i	−0.268952	+	0.465838i
$227$	2.39249	+	6.23265i	0.158795	+	0.413676i	0.989777	−	0.142624i	$-0.0455540\pi$
$227$	2.39249	+	6.23265i	0.158795	+	0.413676i	−0.830982	+	0.556300i	$0.812221\pi$
$228$	−0.195112	−	0.126707i	−0.0129216	−	0.00839138i
$229$	−7.58996	−	8.42951i	−0.501559	−	0.557038i	0.438199	−	0.898878i	$-0.355616\pi$
$229$	−7.58996	−	8.42951i	−0.501559	−	0.557038i	−0.939758	+	0.341840i	$0.888950\pi$
$230$		0			0
$231$	0.171270	−	0.0157641i	0.0112687	−	0.00103720i
$232$	5.79595	−	5.79595i	0.380523	−	0.380523i
$233$	−1.41071	−	2.17230i	−0.0924187	−	0.142312i	0.789437	−	0.613831i	$-0.210373\pi$
$233$	−1.41071	−	2.17230i	−0.0924187	−	0.142312i	−0.881856	+	0.471519i	$0.843706\pi$
$234$	0.729446	−	6.94021i	0.0476853	−	0.453696i
$235$		0			0
$236$	3.22310	−	0.338761i	0.209806	−	0.0220515i
$237$	0.219181	+	1.38385i	0.0142373	+	0.0898908i
$238$	−6.40724	−	12.9876i	−0.415320	−	0.841858i
$239$	−9.58977	−	13.1992i	−0.620311	−	0.853784i	0.377065	−	0.926187i	$-0.376933\pi$
$239$	−9.58977	−	13.1992i	−0.620311	−	0.853784i	−0.997375	+	0.0724026i	$0.976933\pi$
$240$		0			0
$241$	−7.88029	−	0.828252i	−0.507614	−	0.0533524i	−0.152740	−	0.988266i	$-0.548810\pi$
$241$	−7.88029	−	0.828252i	−0.507614	−	0.0533524i	−0.354874	+	0.934914i	$0.615476\pi$
$242$	0.463181	+	8.83802i	0.0297744	+	0.568129i
$243$	−0.972648	−	3.62997i	−0.0623954	−	0.232863i
$244$	−0.309758	−	0.953338i	−0.0198302	−	0.0610312i
$245$		0			0
$246$	0.116159	−	0.357502i	0.00740605	−	0.0227935i
$247$	−3.55884	−	0.186511i	−0.226444	−	0.0118674i
$248$	−27.4927	+	10.5535i	−1.74579	+	0.670146i
$249$	−1.22300	+	0.706101i	−0.0775046	+	0.0447473i
$250$		0			0
$251$			13.1248i			0.828427i	0.910180	+	0.414214i	$0.135943\pi$
$251$			13.1248i			0.828427i	−0.910180	+	0.414214i	$0.864057\pi$
$252$	−10.3527	+	1.50269i	−0.652157	+	0.0946608i
$253$	−2.16519	+	1.10322i	−0.136124	+	0.0693587i
$254$	4.00962	−	3.61028i	0.251586	−	0.226529i
$255$		0			0
$256$	−9.85742	+	10.9478i	−0.616089	+	0.684236i
$257$	1.90875	−	0.511448i	0.119065	−	0.0319033i	−0.198795	−	0.980041i	$-0.563703\pi$
$257$	1.90875	−	0.511448i	0.119065	−	0.0319033i	0.317859	+	0.948138i	$0.397036\pi$
$258$	0.876058	+	0.446374i	0.0545410	+	0.0277900i
$259$	11.2494	−	9.86852i	0.699004	−	0.613200i
$260$		0			0
$261$	−0.935437	−	8.90009i	−0.0579021	−	0.550902i
$262$	7.04146	−	5.70206i	0.435023	−	0.352275i
$263$	8.54697	−	6.92120i	0.527029	−	0.426779i	−0.328524	−	0.944496i	$-0.606551\pi$
$263$	8.54697	−	6.92120i	0.527029	−	0.426779i	0.855552	+	0.517716i	$0.173218\pi$
$264$	−0.0185488	−	0.176480i	−0.00114160	−	0.0108616i
$265$		0			0
$266$	−0.529336	−	2.65901i	−0.0324557	−	0.163034i
$267$	−1.16221	−	0.592174i	−0.0711259	−	0.0362405i
$268$	3.04688	−	0.816408i	0.186118	−	0.0498700i
$269$	3.77103	−	4.18815i	0.229924	−	0.255356i	−0.617133	−	0.786859i	$-0.711706\pi$
$269$	3.77103	−	4.18815i	0.229924	−	0.255356i	0.847056	+	0.531503i	$0.178373\pi$
$270$		0			0
$271$	20.4059	−	18.3735i	1.23957	−	1.11611i	0.250583	−	0.968095i	$-0.419378\pi$
$271$	20.4059	−	18.3735i	1.23957	−	1.11611i	0.988985	−	0.148017i	$-0.0472891\pi$
$272$	2.45798	−	1.25240i	0.149037	−	0.0759380i
$273$	0.832435	−	0.656446i	0.0503812	−	0.0397299i
$274$		−	1.12757i		−	0.0681188i
$275$		0			0
$276$	−0.846796	+	0.488898i	−0.0509711	+	0.0294282i
$277$	12.1760	−	4.67394i	0.731586	−	0.280830i	0.0360792	−	0.999349i	$-0.488513\pi$
$277$	12.1760	−	4.67394i	0.731586	−	0.280830i	0.695507	+	0.718519i	$0.255180\pi$
$278$	2.74259	+	0.143733i	0.164490	+	0.00862053i
$279$	−9.93547	+	30.5782i	−0.594821	+	1.83067i
$280$		0			0
$281$	7.07687	+	21.7804i	0.422171	+	1.29931i	0.905677	+	0.423968i	$0.139363\pi$
$281$	7.07687	+	21.7804i	0.422171	+	1.29931i	−0.483506	+	0.875341i	$0.660637\pi$
$282$	0.0493624	+	0.184223i	0.00293949	+	0.0109703i
$283$	−0.0356048	−	0.679380i	−0.00211649	−	0.0403850i	0.997367	−	0.0725177i	$-0.0231034\pi$
$283$	−0.0356048	−	0.679380i	−0.00211649	−	0.0403850i	−0.999484	+	0.0321328i	$0.989770\pi$
$284$	10.5658	+	1.11051i	0.626967	+	0.0658969i
$285$		0			0
$286$	−0.637193	−	0.877020i	−0.0376780	−	0.0518593i
$287$	−7.74111	+	3.81897i	−0.456943	+	0.225427i
$288$	2.70349	+	17.0692i	0.159305	+	1.00581i
$289$	27.3487	−	2.87447i	1.60875	−	0.169086i
$290$		0			0
$291$	−0.126972	+	1.20806i	−0.00744323	+	0.0708176i
$292$	4.59127	+	7.06994i	0.268684	+	0.413737i
$293$	17.9628	−	17.9628i	1.04940	−	1.04940i	0.0506858	−	0.998715i	$-0.483859\pi$
$293$	17.9628	−	17.9628i	1.04940	−	1.04940i	0.998715	−	0.0506858i	$-0.0161407\pi$
$294$	0.640004	+	0.490779i	0.0373258	+	0.0286228i
$295$		0			0
$296$	−10.3310	−	11.4737i	−0.600477	−	0.666897i
$297$	−0.326044	−	0.211736i	−0.0189190	−	0.0122861i
$298$	5.49785	+	14.3224i	0.318482	+	0.829674i
$299$	−7.48910	+	12.9715i	−0.433106	+	0.750162i
$300$		0			0
$301$	−6.69863	−	21.5614i	−0.386103	−	1.24278i
$302$	−1.42558	+	9.00077i	−0.0820330	+	0.517936i
$303$	0.130399	−	2.48816i	0.00749124	−	0.142941i
$304$	0.505163	−	0.107376i	0.0289731	−	0.00615842i
$305$		0			0
$306$	−3.39170	+	15.9567i	−0.193890	+	0.912183i
$307$	−10.5853	−	10.5853i	−0.604135	−	0.604135i	0.337272	−	0.941407i	$-0.390496\pi$
$307$	−10.5853	−	10.5853i	−0.604135	−	0.604135i	−0.941407	+	0.337272i	$0.890496\pi$
$308$	−1.03895	+	1.24959i	−0.0591994	+	0.0712018i
$309$	−0.917107	+	1.26229i	−0.0521724	+	0.0718091i
$310$		0			0
$311$	0.167744	−	0.376759i	0.00951188	−	0.0213640i	−0.908727	−	0.417391i	$-0.862945\pi$
$311$	0.167744	−	0.376759i	0.00951188	−	0.0213640i	0.918239	+	0.396027i	$0.129611\pi$
$312$	−0.688332	−	0.850020i	−0.0389692	−	0.0481229i
$313$	−0.769705	+	2.00515i	−0.0435063	+	0.113338i	−0.953612	−	0.301038i	$-0.902667\pi$
$313$	−0.769705	+	2.00515i	−0.0435063	+	0.113338i	0.910106	+	0.414376i	$0.136000\pi$
$314$	0.518126	−	0.376441i	0.0292396	−	0.0212438i
$315$		0			0
$316$	−10.7100	−	7.78126i	−0.602484	−	0.437730i
$317$	5.11358	−	3.32080i	0.287207	−	0.186515i	−0.392992	−	0.919542i	$-0.628560\pi$
$317$	5.11358	−	3.32080i	0.287207	−	0.186515i	0.680199	+	0.733027i	$0.261893\pi$
$318$	−0.797901	−	0.213797i	−0.0447440	−	0.0119891i
$319$	−1.03311	−	0.930218i	−0.0578431	−	0.0520822i
$320$		0			0
$321$	−0.321419	−	0.104435i	−0.0179399	−	0.00582901i
$322$	−10.9677	−	3.09138i	−0.611205	−	0.172276i
$323$	8.22818	+	1.30322i	0.457828	+	0.0725129i
$324$	10.1372	+	5.85271i	0.563177	+	0.325150i
$325$		0			0
$326$	8.88154	+	15.3833i	0.491903	+	0.852001i
$327$	1.63588	−	2.02014i	0.0904644	−	0.111714i
$328$	4.04316	+	7.93514i	0.223246	+	0.438145i
$329$	2.23867	−	3.76419i	0.123422	−	0.207527i
$330$		0			0
$331$	16.6187	+	3.53241i	0.913446	+	0.194159i	0.640578	−	0.767893i	$-0.278695\pi$
$331$	16.6187	+	3.53241i	0.913446	+	0.194159i	0.272867	+	0.962052i	$0.412028\pi$
$332$	3.45346	−	12.8885i	0.189533	−	0.707348i
$333$	−16.8335	+	0.882209i	−0.922473	+	0.0483447i
$334$	−6.71835	+	2.99120i	−0.367612	+	0.163671i
$335$		0			0
$336$	−0.0919027	+	0.123112i	−0.00501370	+	0.00671632i
$337$	19.0087	−	3.01068i	1.03547	−	0.164002i	0.384515	−	0.923119i	$-0.374369\pi$
$337$	19.0087	−	3.01068i	1.03547	−	0.164002i	0.650955	+	0.759116i	$0.274369\pi$
$338$	3.72055	+	1.42819i	0.202371	+	0.0776831i
$339$	1.26415	+	0.562834i	0.0686589	+	0.0305689i
$340$		0			0
$341$	2.03148	+	4.56279i	0.110011	+	0.247089i
$342$	−1.38648	+	2.72113i	−0.0749725	+	0.147142i
$343$	−2.18531	−	18.3909i	−0.117996	−	0.993014i
$344$	−22.1544	+	7.19841i	−1.19449	+	0.388112i
$345$		0			0
$346$	2.47933	+	11.6643i	0.133290	+	0.627078i
$347$	−12.0760	+	18.5954i	−0.648272	+	0.998251i	0.349839	+	0.936810i	$0.386236\pi$
$347$	−12.0760	+	18.5954i	−0.648272	+	0.998251i	−0.998111	+	0.0614415i	$0.980430\pi$
$348$	−0.434721	−	0.352030i	−0.0233035	−	0.0188708i
$349$	−17.0829			−0.914426			−0.457213	−	0.889357i	$-0.651152\pi$
$349$	−17.0829			−0.914426			−0.457213	+	0.889357i	$0.651152\pi$
$350$		0			0
$351$	−2.39624			−0.127902
$352$	2.08636	+	1.68950i	0.111203	+	0.0900508i
$353$	9.70354	−	14.9421i	0.516467	−	0.795290i	−0.480175	−	0.877173i	$-0.659427\pi$
$353$	9.70354	−	14.9421i	0.516467	−	0.795290i	0.996642	+	0.0818829i	$0.0260933\pi$
$354$	0.0585168	+	0.275300i	0.00311013	+	0.0146320i
$355$		0			0
$356$	11.7212	−	3.80844i	0.621220	−	0.201847i
$357$	−2.09569	+	1.32273i	−0.110915	+	0.0700063i
$358$	−3.60193	+	7.06919i	−0.190368	+	0.373619i
$359$	5.75875	+	12.9344i	0.303935	+	0.682649i	0.999353	−	0.0359558i	$-0.0114476\pi$
$359$	5.75875	+	12.9344i	0.303935	+	0.682649i	−0.695418	+	0.718605i	$0.744781\pi$
$360$		0			0
$361$	−15.9326	−	7.09365i	−0.838558	−	0.373350i
$362$	−15.3997	−	5.91139i	−0.809390	−	0.310696i
$363$	1.49582	−	0.236914i	0.0785100	−	0.0124348i
$364$	−1.17579	+	9.94733i	−0.0616282	+	0.521382i
$365$		0			0
$366$	0.0795267	−	0.0354075i	0.00415692	−	0.00185078i
$367$	−20.4318	+	1.07079i	−1.06653	+	0.0558946i	−0.577516	−	0.816380i	$-0.695978\pi$
$367$	−20.4318	+	1.07079i	−1.06653	+	0.0558946i	−0.489017	+	0.872274i	$0.662644\pi$
$368$	0.561797	−	2.09665i	0.0292857	−	0.109296i
$369$	9.51083	+	2.02159i	0.495114	+	0.105240i
$370$		0			0
$371$	9.27108	+	16.5487i	0.481330	+	0.859167i
$372$	0.912390	+	1.79067i	0.0473052	+	0.0928417i
$373$	−4.58452	+	5.66141i	−0.237378	+	0.293137i	−0.881888	−	0.471458i	$-0.843728\pi$
$373$	−4.58452	+	5.66141i	−0.237378	+	0.293137i	0.644511	+	0.764595i	$0.277061\pi$
$374$	1.26707	+	2.19464i	0.0655188	+	0.113482i
$375$		0			0
$376$	−3.91320	−	2.25929i	−0.201808	−	0.116514i
$377$	−8.46329	−	1.34045i	−0.435882	−	0.0690369i
$378$	−0.449009	−	1.76684i	−0.0230945	−	0.0908763i
$379$	−3.99729	−	1.29880i	−0.205327	−	0.0667147i	0.204548	−	0.978857i	$-0.434428\pi$
$379$	−3.99729	−	1.29880i	−0.205327	−	0.0667147i	−0.409875	+	0.912142i	$0.634428\pi$
$380$		0			0
$381$	−0.686138	−	0.617802i	−0.0351519	−	0.0316509i
$382$	19.6762	+	5.27221i	1.00672	+	0.269750i
$383$	−18.7224	+	12.1585i	−0.956671	+	0.621269i	−0.925703	−	0.378251i	$-0.876526\pi$
$383$	−18.7224	+	12.1585i	−0.956671	+	0.621269i	−0.0309678	+	0.999520i	$0.509859\pi$
$384$	0.951028	+	0.690962i	0.0485319	+	0.0352605i
$385$		0			0
$386$	9.39364	−	6.82488i	0.478124	−	0.347377i
$387$	−9.11430	+	23.7436i	−0.463306	+	1.20695i
$388$	−7.22282	−	8.91943i	−0.366683	−	0.452816i
$389$	−2.73737	+	6.14824i	−0.138790	+	0.311728i	−0.969546	−	0.244909i	$-0.921242\pi$
$389$	−2.73737	+	6.14824i	−0.138790	+	0.311728i	0.830756	+	0.556637i	$0.187909\pi$
$390$		0			0
$391$	20.5806	−	28.3268i	1.04081	−	1.43255i
$392$	−18.9438	+	2.49993i	−0.956805	+	0.126265i
$393$	−1.09636	−	1.09636i	−0.0553041	−	0.0553041i
$394$	3.55195	−	16.7106i	0.178945	−	0.841869i
$395$		0			0
$396$	1.79055	−	0.380593i	0.0899786	−	0.0191255i
$397$	0.856195	−	16.3372i	0.0429712	−	0.819939i	−0.889111	−	0.457692i	$-0.848676\pi$
$397$	0.856195	−	16.3372i	0.0429712	−	0.819939i	0.932082	−	0.362247i	$-0.117990\pi$
$398$	2.02723	−	12.7994i	0.101616	−	0.641578i
$399$	−0.443057	+	0.137648i	−0.0221806	+	0.00689100i
$400$		0			0
$401$	−3.19866	+	5.54023i	−0.159733	+	0.276666i	−0.934772	−	0.355247i	$-0.884397\pi$
$401$	−3.19866	+	5.54023i	−0.159733	+	0.276666i	0.775039	+	0.631913i	$0.217730\pi$
$402$	0.0981707	+	0.255744i	0.00489631	+	0.0127553i
$403$	25.8189	+	16.7670i	1.28613	+	0.835222i
$404$	15.7524	+	17.4948i	0.783712	+	0.870400i
$405$		0			0
$406$	−0.597490	−	6.49147i	−0.0296529	−	0.322166i
$407$	−1.85161	+	1.85161i	−0.0917810	+	0.0917810i
$408$	1.39256	+	2.14436i	0.0689422	+	0.106162i
$409$	−0.493540	+	4.69572i	−0.0244040	+	0.232189i	0.975521	+	0.219908i	$0.0705758\pi$
$409$	−0.493540	+	4.69572i	−0.0244040	+	0.232189i	−0.999925	+	0.0122805i	$0.996091\pi$
$410$		0			0
$411$	−0.191896	+	0.0201690i	−0.00946551	+	0.000994865i
$412$	−2.30619	−	14.5607i	−0.113618	−	0.717355i
$413$	3.58983	−	5.37435i	0.176644	−	0.264454i
$414$	7.54471	+	10.3844i	0.370802	+	0.510366i
$415$		0			0
$416$	16.4569	+	1.72969i	0.806864	+	0.0848048i
$417$	−0.0245960	−	0.469320i	−0.00120447	−	0.0229827i
$418$	0.122789	+	0.458253i	0.00600579	+	0.0224139i
$419$	4.91344	+	15.1220i	0.240037	+	0.738759i	0.996413	+	0.0846218i	$0.0269682\pi$
$419$	4.91344	+	15.1220i	0.240037	+	0.738759i	−0.756376	+	0.654137i	$0.773032\pi$
$420$		0			0
$421$	−8.87472	+	27.3136i	−0.432527	+	1.33118i	0.463072	+	0.886321i	$0.346747\pi$
$421$	−8.87472	+	27.3136i	−0.432527	+	1.33118i	−0.895599	+	0.444862i	$0.853253\pi$
$422$	−3.81448	−	0.199909i	−0.185686	−	0.00973140i
$423$	−4.60568	+	1.76795i	−0.223936	+	0.0859609i
$424$	16.9487	−	9.78537i	0.823104	−	0.475219i
$425$		0			0
$426$			0.922638i			0.0447020i
$427$	−1.85682	−	0.740464i	−0.0898577	−	0.0358336i
$428$	2.84517	−	1.44968i	0.137526	−	0.0700731i
$429$	−0.137859	+	0.124128i	−0.00665587	+	0.00599298i
$430$		0			0
$431$	17.2952	−	19.2083i	0.833083	−	0.925232i	−0.165052	−	0.986285i	$-0.552779\pi$
$431$	17.2952	−	19.2083i	0.833083	−	0.925232i	0.998135	+	0.0610529i	$0.0194458\pi$
$432$	0.335427	−	0.0898773i	0.0161382	−	0.00432422i
$433$	23.4750	+	11.9611i	1.12814	+	0.574815i	0.915501	−	0.402316i	$-0.131795\pi$
$433$	23.4750	+	11.9611i	1.12814	+	0.574815i	0.212638	+	0.977131i	$0.431795\pi$
$434$	−7.52495	+	22.1790i	−0.361209	+	1.06463i
$435$		0			0
$436$	2.56730	+	24.4262i	0.122951	+	1.16980i
$437$	5.09416	−	4.12517i	0.243687	−	0.197333i
$438$	−0.568943	+	0.460721i	−0.0271852	+	0.0220141i
$439$	−3.80227	−	36.1762i	−0.181473	−	1.72660i	−0.584487	−	0.811403i	$-0.698704\pi$
$439$	−3.80227	−	36.1762i	−0.181473	−	1.72660i	0.403015	−	0.915194i	$-0.367962\pi$
$440$		0			0
$441$	−10.8949	+	17.7911i	−0.518804	+	0.847196i
$442$	13.9174	+	7.09128i	0.661984	+	0.337298i
$443$	−17.2080	+	4.61086i	−0.817575	+	0.219069i	−0.643286	−	0.765626i	$-0.722429\pi$
$443$	−17.2080	+	4.61086i	−0.817575	+	0.219069i	−0.174289	+	0.984695i	$0.555763\pi$
$444$	−0.705034	+	0.783019i	−0.0334594	+	0.0371604i
$445$		0			0
$446$	−1.34925	+	1.21487i	−0.0638889	+	0.0575258i
$447$	2.33912	−	1.19184i	0.110637	−	0.0563722i
$448$	1.49400	+	10.2928i	0.0705849	+	0.486288i
$449$			8.68138i			0.409699i	0.978793	+	0.204850i	$0.0656706\pi$
$449$			8.68138i			0.409699i	−0.978793	+	0.204850i	$0.934329\pi$
$450$		0			0
$451$	1.30809	−	0.755227i	0.0615957	−	0.0355623i
$452$	−12.2062	+	4.68552i	−0.574131	+	0.220388i
$453$	1.55730	+	0.0816146i	0.0731683	+	0.00383459i
$454$	1.69281	−	5.20992i	0.0794473	−	0.244514i
$455$		0			0
$456$	0.147917	+	0.455242i	0.00692686	+	0.0213187i
$457$	6.91837	+	25.8197i	0.323628	+	1.20780i	0.915684	+	0.401899i	$0.131650\pi$
$457$	6.91837	+	25.8197i	0.323628	+	1.20780i	−0.592056	+	0.805896i	$0.701684\pi$
$458$	0.487116	+	9.29473i	0.0227615	+	0.434314i
$459$	5.57089	+	0.585525i	0.260027	+	0.0273299i
$460$		0			0
$461$	0.325458	+	0.447954i	0.0151581	+	0.0208633i	0.816529	−	0.577305i	$-0.195896\pi$
$461$	0.325458	+	0.447954i	0.0151581	+	0.0208633i	−0.801371	+	0.598168i	$0.795896\pi$
$462$	−0.117356	−	0.0783889i	−0.00545992	−	0.00364698i
$463$	5.44624	+	34.3862i	0.253108	+	1.59806i	0.707138	+	0.707075i	$0.249986\pi$
$463$	5.44624	+	34.3862i	0.253108	+	1.59806i	−0.454030	+	0.890986i	$0.650014\pi$
$464$	1.23497	−	0.129801i	0.0573321	−	0.00602585i
$465$		0			0
$466$	−0.222161	+	2.11372i	−0.0102914	+	0.0979161i
$467$	17.2371	+	26.5428i	0.797638	+	1.22826i	0.969972	+	0.243217i	$0.0782027\pi$
$467$	17.2371	+	26.5428i	0.797638	+	1.22826i	−0.172333	+	0.985039i	$0.555131\pi$
$468$	7.97835	−	7.97835i	0.368799	−	0.368799i
$469$	2.63271	−	5.71310i	0.121567	−	0.263806i
$470$		0			0
$471$	−0.0733326	−	0.0814441i	−0.00337899	−	0.00375275i
$472$	−5.59236	−	3.63172i	−0.257409	−	0.167163i
$473$	1.41585	+	3.68841i	0.0651008	+	0.169593i
$474$	0.574835	−	0.995644i	0.0264031	−	0.0457314i
$475$		0			0
$476$	5.16418	−	22.8387i	0.236700	−	1.04681i
$477$	3.34256	−	21.1041i	0.153045	−	0.966291i
$478$	−0.700637	+	13.3690i	−0.0320464	+	0.611482i
$479$	21.0843	−	4.48161i	0.963366	−	0.204770i	0.300728	−	0.953710i	$-0.402770\pi$
$479$	21.0843	−	4.48161i	0.963366	−	0.204770i	0.662638	+	0.748940i	$0.269437\pi$
$480$		0			0
$481$	−3.35575	+	15.7876i	−0.153009	+	0.719851i
$482$	4.59744	+	4.59744i	0.209408	+	0.209408i
$483$	−0.329927	+	1.92184i	−0.0150122	+	0.0874466i
$484$	−8.41083	+	11.5765i	−0.382310	+	0.526205i
$485$		0			0
$486$	−1.25423	+	2.81704i	−0.0568929	+	0.127784i
$487$	11.1857	+	13.8132i	0.506874	+	0.625937i	0.964778	−	0.263064i	$-0.0847332\pi$
$487$	11.1857	+	13.8132i	0.506874	+	0.625937i	−0.457905	+	0.889001i	$0.651400\pi$
$488$	−0.739118	+	1.92547i	−0.0334583	+	0.0871618i
$489$	2.45915	−	1.78667i	0.111206	−	0.0807962i
$490$		0			0
$491$	16.3613	+	11.8872i	0.738374	+	0.536460i	0.892201	−	0.451638i	$-0.149160\pi$
$491$	16.3613	+	11.8872i	0.738374	+	0.536460i	−0.153828	+	0.988098i	$0.549160\pi$
$492$	0.509722	−	0.331017i	0.0229800	−	0.0149234i
$493$	19.3483	+	5.18436i	0.871404	+	0.233492i
$494$	2.17311	+	1.95667i	0.0977727	+	0.0880349i
$495$		0			0
$496$	−4.24302	−	1.37864i	−0.190517	−	0.0619028i
$497$	15.1739	−	14.7863i	0.680641	−	0.663255i
$498$	1.14451	+	0.181273i	0.0512868	+	0.00812303i
$499$	20.1816	+	11.6518i	0.903450	+	0.521607i	0.878318	−	0.478077i	$-0.158666\pi$
$499$	20.1816	+	11.6518i	0.903450	+	0.521607i	0.0251324	+	0.999684i	$0.491999\pi$
$500$		0			0
$501$	0.629232	+	1.08986i	0.0281120	+	0.0486914i
$502$	6.77745	−	8.36946i	0.302493	−	0.373547i
$503$	12.9561	+	25.4278i	0.577684	+	1.13377i	0.976254	+	0.216631i	$0.0695068\pi$
$503$	12.9561	+	25.4278i	0.577684	+	1.13377i	−0.398569	+	0.917138i	$0.630493\pi$
$504$	18.4996	+	11.0023i	0.824038	+	0.490079i
$505$		0			0
$506$	1.95039	+	0.414569i	0.0867056	+	0.0184298i
$507$	0.176506	−	0.658730i	0.00783892	−	0.0292552i
$508$	8.71172	−	0.456562i	0.386520	−	0.0202567i
$509$	13.9211	−	6.19808i	0.617043	−	0.274725i	−0.0743181	−	0.997235i	$-0.523678\pi$
$509$	13.9211	−	6.19808i	0.617043	−	0.274725i	0.691361	+	0.722509i	$0.257011\pi$
$510$		0			0
$511$	16.6950	+	1.97338i	0.738545	+	0.0872972i
$512$	−4.59842	+	0.728319i	−0.203224	+	0.0321874i
$513$	0.979022	+	0.375811i	0.0432249	+	0.0165925i
$514$	−1.48129	−	0.659511i	−0.0653368	−	0.0290898i
$515$		0			0
$516$	0.646599	+	1.45229i	0.0284649	+	0.0639333i
$517$	−0.347922	+	0.682836i	−0.0153016	+	0.0300311i
$518$	−12.2696	+	0.483963i	−0.539093	+	0.0212641i
$519$	1.94075	−	0.630588i	0.0851895	−	0.0276798i
$520$		0			0
$521$	−2.61108	−	12.2842i	−0.114393	−	0.538179i	−0.997603	−	0.0691998i	$-0.977955\pi$
$521$	−2.61108	−	12.2842i	−0.114393	−	0.538179i	0.883209	−	0.468979i	$-0.155378\pi$
$522$	−3.99938	+	6.15850i	−0.175048	+	0.269550i
$523$	−7.84099	−	6.34951i	−0.342863	−	0.277645i	0.442387	−	0.896824i	$-0.354132\pi$
$523$	−7.84099	−	6.34951i	−0.342863	−	0.277645i	−0.785249	+	0.619180i	$0.787465\pi$
$524$	14.6497			0.639977
$525$		0			0
$526$	−9.02429			−0.393478
$527$	−55.9278	−	45.2895i	−2.43626	−	1.97284i
$528$	0.0146417	−	0.0225463i	0.000637199	−	0.000981201i
$529$	−0.946049	−	4.45081i	−0.0411326	−	0.193514i
$530$		0			0
$531$	−6.92388	+	2.24971i	−0.300471	+	0.0976289i
$532$	2.04046	−	3.87973i	0.0884653	−	0.168208i
$533$	4.22669	−	8.29534i	0.183078	−	0.359311i
$534$	0.435331	+	0.977769i	0.0188386	+	0.0423122i
$535$		0			0
$536$	−5.92905	−	2.63978i	−0.256096	−	0.114021i
$537$	1.26750	+	0.486549i	0.0546968	+	0.0209961i
$538$	−4.56744	+	0.723411i	−0.196916	+	0.0311884i
$539$	0.591566	+	3.18633i	0.0254806	+	0.137245i
$540$		0			0
$541$	6.70459	−	2.98507i	0.288253	−	0.128338i	−0.257517	−	0.966274i	$-0.582904\pi$
$541$	6.70459	−	2.98507i	0.288253	−	0.128338i	0.545769	+	0.837936i	$0.316238\pi$
$542$	−22.5004	+	1.17919i	−0.966474	+	0.0506507i
$543$	−0.730575	+	2.72654i	−0.0313520	+	0.117007i
$544$	−37.8370	−	8.04250i	−1.62225	−	0.344819i
$545$		0			0
$546$	−0.869812	−	0.0112526i	−0.0372245	−	0.000481565i
$547$	−14.3950	−	28.2518i	−0.615487	−	1.20796i	−0.962801	−	0.270212i	$-0.912906\pi$
$547$	−14.3950	−	28.2518i	−0.615487	−	1.20796i	0.347314	−	0.937749i	$-0.387094\pi$
$548$	1.14732	−	1.41682i	0.0490110	−	0.0605236i
$549$	1.12589	+	1.95009i	0.0480517	+	0.0832279i
$550$		0			0
$551$	3.24758	+	1.87499i	0.138352	+	0.0798773i
$552$	1.98706	+	0.314720i	0.0845751	+	0.0133954i
$553$	−25.5869	+	6.50243i	−1.08806	+	0.276511i
$554$	−10.1780	−	3.30704i	−0.432423	−	0.140503i
$555$		0			0
$556$	3.29989	+	2.97124i	0.139947	+	0.126008i
$557$	−17.9755	−	4.81653i	−0.761648	−	0.204083i	−0.142970	−	0.989727i	$-0.545665\pi$
$557$	−17.9755	−	4.81653i	−0.761648	−	0.204083i	−0.618679	+	0.785644i	$0.712332\pi$
$558$	22.1259	−	14.3687i	0.936665	−	0.608277i
$559$	19.7011	+	14.3137i	0.833269	+	0.605405i
$560$		0			0
$561$	0.350831	−	0.254894i	0.0148121	−	0.0107616i
$562$	6.73429	−	17.5434i	0.284069	−	0.740025i
$563$	11.2303	+	13.8682i	0.473299	+	0.584475i	0.956756	−	0.290893i	$-0.0939523\pi$
$563$	11.2303	+	13.8682i	0.473299	+	0.584475i	−0.483457	+	0.875368i	$0.660619\pi$
$564$	−0.125425	+	0.281708i	−0.00528133	+	0.0118621i
$565$		0			0
$566$	−0.328119	+	0.451617i	−0.0137919	+	0.0189829i
$567$	21.8992	−	8.08289i	0.919682	−	0.339449i
$568$	−15.4568	−	15.4568i	−0.648551	−	0.648551i
$569$	−2.43038	+	11.4341i	−0.101887	+	0.479340i	0.897387	+	0.441244i	$0.145463\pi$
$569$	−2.43038	+	11.4341i	−0.101887	+	0.479340i	−0.999274	+	0.0380963i	$0.987871\pi$
$570$		0			0
$571$	32.5444	−	6.91753i	1.36194	−	0.289490i	0.531719	−	0.846921i	$-0.321546\pi$
$571$	32.5444	−	6.91753i	1.36194	−	0.289490i	0.830223	+	0.557431i	$0.188213\pi$
$572$	0.0917322	−	1.75036i	0.00383552	−	0.0731860i
$573$	0.545303	−	3.44290i	0.0227803	−	0.143829i
$574$	6.90846	+	1.56211i	0.288354	+	0.0652011i
$575$		0			0
$576$	5.85786	−	10.1461i	0.244078	−	0.422755i
$577$	15.0945	+	39.3226i	0.628394	+	1.63702i	0.763209	+	0.646151i	$0.223622\pi$
$577$	15.0945	+	39.3226i	0.628394	+	1.63702i	−0.134816	+	0.990871i	$0.543044\pi$
$578$	−18.9242	−	12.2895i	−0.787143	−	0.511177i
$579$	−1.32952	−	1.47658i	−0.0552530	−	0.0613647i
$580$		0			0
$581$	−15.3608	−	21.7279i	−0.637273	−	0.901426i
$582$	0.704793	−	0.704793i	0.0292146	−	0.0292146i
$583$	−1.80780	−	2.78376i	−0.0748713	−	0.115292i
$584$	1.81302	−	17.2498i	0.0750234	−	0.713800i
$585$		0			0
$586$	−20.7304	+	2.17885i	−0.856366	+	0.0900077i
$587$	−1.86295	−	11.7622i	−0.0768923	−	0.485479i	−0.995841	−	0.0911028i	$-0.970961\pi$
$587$	−1.86295	−	11.7622i	−0.0768923	−	0.485479i	0.918949	−	0.394376i	$-0.129039\pi$
$588$	0.304807	+	1.26789i	0.0125700	+	0.0522870i
$589$	−7.91907	−	10.8997i	−0.326300	−	0.449113i
$590$		0			0
$591$	−2.90744	−	0.305584i	−0.119596	−	0.0125701i
$592$	−0.122415	−	2.33581i	−0.00503122	−	0.0960014i
$593$	2.18171	+	8.14227i	0.0895922	+	0.334363i	0.996144	−	0.0877316i	$-0.0279618\pi$
$593$	2.18171	+	8.14227i	0.0895922	+	0.334363i	−0.906552	+	0.422094i	$0.861295\pi$
$594$	0.0985760	+	0.303386i	0.00404462	+	0.0124481i
$595$		0			0
$596$	−7.66507	+	23.5906i	−0.313973	+	0.966311i
$597$	−2.21454	−	0.116059i	−0.0906351	−	0.00474998i
$598$	11.4740	−	4.40446i	0.469207	−	0.180112i
$599$	−31.0038	+	17.9000i	−1.26678	+	0.731376i	−0.974377	−	0.224919i	$-0.927788\pi$
$599$	−31.0038	+	17.9000i	−1.26678	+	0.731376i	−0.292403	+	0.956295i	$0.594455\pi$
$600$		0			0
$601$			12.5021i			0.509971i	0.966945	+	0.254985i	$0.0820706\pi$
$601$			12.5021i			0.509971i	−0.966945	+	0.254985i	$0.917929\pi$
$602$	−6.86242	+	17.2085i	−0.279691	+	0.701365i
$603$	−6.31358	+	3.21693i	−0.257109	+	0.131004i
$604$	−10.9497	+	9.85917i	−0.445538	+	0.401164i
$605$		0			0
$606$	−1.36801	+	1.51933i	−0.0555716	+	0.0617185i
$607$	−30.0359	+	8.04810i	−1.21912	+	0.326662i	−0.810334	−	0.585968i	$-0.800715\pi$
$607$	−30.0359	+	8.04810i	−1.21912	+	0.326662i	−0.408786	+	0.912630i	$0.634048\pi$
$608$	−6.45243	−	3.28768i	−0.261681	−	0.133333i
$609$	−1.09407	+	0.217798i	−0.0443338	+	0.00882564i
$610$		0			0
$611$	0.493760	+	4.69781i	0.0199754	+	0.190053i
$612$	−20.4980	+	16.5989i	−0.828581	+	0.670971i
$613$	−3.62060	+	2.93190i	−0.146235	+	0.118418i	−0.699646	−	0.714490i	$-0.746659\pi$
$613$	−3.62060	+	2.93190i	−0.146235	+	0.118418i	0.553412	+	0.832908i	$0.313326\pi$
$614$	1.28397	+	12.2162i	0.0518170	+	0.493006i
$615$		0			0
$616$	3.27928	−	0.652814i	0.132126	−	0.0263026i
$617$	−22.0504	−	11.2353i	−0.887717	−	0.452314i	−0.0502084	−	0.998739i	$-0.515989\pi$
$617$	−22.0504	−	11.2353i	−0.887717	−	0.452314i	−0.837508	+	0.546424i	$0.815989\pi$
$618$	1.23666	−	0.331361i	0.0497456	−	0.0133293i
$619$	−3.10323	+	3.44649i	−0.124729	+	0.138526i	−0.802275	−	0.596955i	$-0.796377\pi$
$619$	−3.10323	+	3.44649i	−0.124729	+	0.138526i	0.677545	+	0.735481i	$0.263044\pi$
$620$		0			0
$621$	3.27544	−	2.94922i	0.131439	−	0.118348i
$622$	−0.301521	+	0.153633i	−0.0120899	+	0.00616011i
$623$	9.10391	−	22.8293i	0.364740	−	0.914638i
$624$		−	0.165703i		−	0.00663341i
$625$		0			0
$626$	1.52626	−	0.881189i	0.0610018	−	0.0352194i
$627$	0.0757918	−	0.0290937i	0.00302683	−	0.00116189i
$628$	1.03408	+	0.0541936i	0.0412641	+	0.00216256i
$629$	11.6593	−	35.8837i	0.464887	−	1.43078i
$630$		0			0
$631$	−8.92894	−	27.4805i	−0.355456	−	1.09398i	−0.955745	−	0.294197i	$-0.904948\pi$
$631$	−8.92894	−	27.4805i	−0.355456	−	1.09398i	0.600289	−	0.799783i	$-0.295052\pi$
$632$	7.04972	+	26.3099i	0.280423	+	1.04655i
$633$	0.0342090	+	0.652746i	0.00135968	+	0.0259443i
$634$	−4.97567	−	0.522964i	−0.197609	−	0.0207696i
$635$		0			0
$636$	−0.785043	−	1.08052i	−0.0311290	−	0.0428454i
$637$	13.7546	+	14.4854i	0.544977	+	0.573932i
$638$	0.178447	+	1.12667i	0.00706479	+	0.0446053i
$639$	−23.7349	+	2.49464i	−0.938939	+	0.0986865i
$640$		0			0
$641$	1.38534	−	13.1806i	0.0547175	−	0.520602i	−0.932494	−	0.361186i	$-0.882372\pi$
$641$	1.38534	−	13.1806i	0.0547175	−	0.520602i	0.987211	−	0.159416i	$-0.0509612\pi$
$642$	0.151035	+	0.232573i	0.00596088	+	0.00917894i
$643$	−11.0712	+	11.0712i	−0.436605	+	0.436605i	−0.890868	−	0.454263i	$-0.849903\pi$
$643$	−11.0712	+	11.0712i	−0.436605	+	0.436605i	0.454263	+	0.890868i	$0.349903\pi$
$644$	−10.6357	−	15.0442i	−0.419104	−	0.592825i
$645$		0			0
$646$	−4.57402	−	5.07997i	−0.179963	−	0.199869i
$647$	16.5451	+	10.7445i	0.650453	+	0.422409i	0.827247	−	0.561839i	$-0.189906\pi$
$647$	16.5451	+	10.7445i	0.650453	+	0.422409i	−0.176794	+	0.984248i	$0.556573\pi$
$648$	−8.63098	−	22.4845i	−0.339057	−	0.883274i
$649$	−0.565467	+	0.979418i	−0.0221965	+	0.0384455i
$650$		0			0
$651$	3.90914	+	0.883916i	0.153211	+	0.0346434i
$652$	−4.49284	+	28.3666i	−0.175953	+	1.11092i
$653$	−0.126284	+	2.40963i	−0.00494186	+	0.0942963i	−0.999987	−	0.00512946i	$-0.998367\pi$
$653$	−0.126284	+	2.40963i	−0.00494186	+	0.0942963i	0.995045	+	0.0994257i	$0.0317006\pi$
$654$	−2.08635	+	0.443468i	−0.0815829	+	0.0173410i
$655$		0			0
$656$	−0.280515	+	1.31972i	−0.0109523	+	0.0515263i
$657$	−13.3904	−	13.3904i	−0.522409	−	0.522409i
$658$	−3.37135	+	1.24435i	−0.131429	+	0.0485096i
$659$	8.37171	−	11.5227i	0.326116	−	0.448859i	−0.614207	−	0.789145i	$-0.710524\pi$
$659$	8.37171	−	11.5227i	0.326116	−	0.448859i	0.940322	+	0.340286i	$0.110524\pi$
$660$		0			0
$661$	2.90913	−	6.53401i	0.113152	−	0.254144i	−0.848089	−	0.529854i	$-0.822247\pi$
$661$	2.90913	−	6.53401i	0.113152	−	0.254144i	0.961241	+	0.275711i	$0.0889132\pi$
$662$	−8.77340	−	10.8342i	−0.340988	−	0.421085i
$663$	0.957888	−	2.49538i	0.0372013	−	0.0969127i
$664$	−22.2106	+	16.1369i	−0.861938	+	0.626235i
$665$		0			0
$666$	11.1901	+	8.13006i	0.433606	+	0.315033i
$667$	13.2183	−	8.58408i	0.511816	−	0.332377i
$668$	−11.4854	−	3.07750i	−0.444383	−	0.119072i
$669$	0.230888	+	0.207892i	0.00892663	+	0.00803758i
$670$		0			0
$671$	0.332679	+	0.108094i	0.0128429	+	0.00417292i
$672$	2.08789	−	0.530597i	0.0805419	−	0.0204682i
$673$	−11.9953	−	1.89988i	−0.462386	−	0.0732348i	−0.0791047	−	0.996866i	$-0.525206\pi$
$673$	−11.9953	−	1.89988i	−0.462386	−	0.0732348i	−0.383282	+	0.923631i	$0.625206\pi$
$674$	−13.6762	−	7.89599i	−0.526789	−	0.304142i
$675$		0			0
$676$	3.22178	+	5.58028i	0.123914	+	0.214626i
$677$	32.0258	−	39.5485i	1.23085	−	1.51997i	0.453018	−	0.891501i	$-0.350347\pi$
$677$	32.0258	−	39.5485i	1.23085	−	1.51997i	0.777832	−	0.628472i	$-0.216319\pi$
$678$	−0.515486	−	1.01170i	−0.0197971	−	0.0388541i
$679$	−22.8862	−	0.296074i	−0.878292	−	0.0113623i
$680$		0			0
$681$	−0.916933	−	0.194900i	−0.0351369	−	0.00746859i
$682$	1.06072	−	3.95865i	0.0406170	−	0.151585i
$683$	−9.20064	+	0.482185i	−0.352053	+	0.0184503i	−0.227543	−	0.973768i	$-0.573069\pi$
$683$	−9.20064	+	0.482185i	−0.352053	+	0.0184503i	−0.124510	+	0.992218i	$0.539736\pi$
$684$	−4.51095	+	2.00840i	−0.172481	+	0.0767933i
$685$		0			0
$686$	−8.10327	+	12.8561i	−0.309384	+	0.490847i
$687$	1.57312	−	0.249157i	0.0600181	−	0.00950593i
$688$	−3.29464	−	1.26470i	−0.125607	−	0.0482160i
$689$	−18.6903	−	8.32147i	−0.712044	−	0.317023i
$690$		0			0
$691$	0.160128	+	0.359653i	0.00609156	+	0.0136819i	0.916566	−	0.399884i	$-0.130950\pi$
$691$	0.160128	+	0.359653i	0.00609156	+	0.0136819i	−0.910474	+	0.413566i	$0.864283\pi$
$692$	−8.75330	+	17.1793i	−0.332751	+	0.653060i
$693$	1.69925	−	3.23095i	0.0645492	−	0.122734i
$694$	17.3031	−	5.62211i	0.656816	−	0.213412i
$695$		0			0
$696$	0.239293	+	1.12579i	0.00907039	+	0.0426728i
$697$	−11.8534	+	18.2526i	−0.448979	+	0.691366i
$698$	10.8935	+	8.82139i	0.412325	+	0.333894i
$699$	0.363698			0.0137563
$700$		0			0
$701$	46.4699			1.75515			0.877573	−	0.479443i	$-0.159161\pi$
$701$	46.4699			1.75515			0.877573	+	0.479443i	$0.159161\pi$
$702$	1.52805	+	1.23739i	0.0576724	+	0.0467022i
$703$	3.84706	−	5.92396i	0.145095	−	0.223426i
$704$	−0.378392	−	1.78019i	−0.0142612	−	0.0670936i
$705$		0			0
$706$	−13.9037	+	4.51760i	−0.523274	+	0.170022i
$707$	46.9109	−	1.85037i	1.76427	−	0.0695902i
$708$	−0.206594	+	0.405464i	−0.00776428	+	0.0152383i
$709$	−14.0994	−	31.6677i	−0.529513	−	1.18931i	−0.958264	−	0.285883i	$-0.907713\pi$
$709$	−14.0994	−	31.6677i	−0.529513	−	1.18931i	0.428752	−	0.903422i	$-0.358954\pi$
$710$		0			0
$711$	27.1672	+	12.0956i	1.01885	+	0.453622i
$712$	−23.6734	−	9.08736i	−0.887197	−	0.340563i
$713$	−55.9283	+	8.85817i	−2.09453	+	0.331741i
$714$	2.01943	+	0.238700i	0.0755752	+	0.00893312i
$715$		0			0
$716$	−11.7190	+	5.21762i	−0.437958	+	0.194991i
$717$	2.28773	−	0.119895i	0.0854370	−	0.00447756i
$718$	3.00687	−	11.2218i	0.112215	−	0.418793i
$719$	35.7822	+	7.60574i	1.33445	+	0.283646i	0.819257	−	0.573427i	$-0.194386\pi$
$719$	35.7822	+	7.60574i	1.33445	+	0.283646i	0.515194	+	0.857073i	$0.327720\pi$
$720$		0			0
$721$	−25.2683	−	15.0278i	−0.941042	−	0.559665i
$722$	6.49691	+	12.7509i	0.241790	+	0.474539i
$723$	0.700183	−	0.864654i	0.0260401	−	0.0321568i
$724$	−13.3352	−	23.0973i	−0.495599	−	0.858403i
$725$		0			0
$726$	−1.07620	−	0.621344i	−0.0399415	−	0.0230602i
$727$	36.2364	+	5.73928i	1.34393	+	0.212858i	0.786616	−	0.617442i	$-0.211831\pi$
$727$	36.2364	+	5.73928i	1.34393	+	0.212858i	0.557316	+	0.830300i	$0.311831\pi$
$728$	14.7603	−	14.3833i	0.547052	−	0.533079i
$729$	−24.6715	−	8.01626i	−0.913759	−	0.296898i
$730$		0			0
$731$	−42.3045	−	38.0912i	−1.56469	−	1.40885i
$732$	0.135955	+	0.0364291i	0.00502505	+	0.00134646i
$733$	−14.2128	+	9.22991i	−0.524963	+	0.340915i	−0.779759	−	0.626080i	$-0.784658\pi$
$733$	−14.2128	+	9.22991i	−0.524963	+	0.340915i	0.254796	+	0.966995i	$0.417992\pi$
$734$	13.5820	+	9.86791i	0.501321	+	0.364231i
$735$		0			0
$736$	−24.6238	+	17.8903i	−0.907647	+	0.659444i
$737$	−0.394474	+	1.02764i	−0.0145306	+	0.0378536i
$738$	−5.02099	−	6.20041i	−0.184825	−	0.228240i
$739$	−3.74205	+	8.40479i	−0.137654	+	0.309175i	−0.969198	−	0.246283i	$-0.920791\pi$
$739$	−3.74205	+	8.40479i	−0.137654	+	0.309175i	0.831544	+	0.555459i	$0.187457\pi$
$740$		0			0
$741$	0.294127	−	0.404831i	0.0108050	−	0.0148718i
$742$	2.63352	−	15.3403i	0.0966796	−	0.563162i
$743$	−28.0230	−	28.0230i	−1.02806	−	1.02806i	−0.999595	−	0.0284701i	$-0.990936\pi$
$743$	−28.0230	−	28.0230i	−1.02806	−	1.02806i	−0.0284701	−	0.999595i	$-0.509064\pi$
$744$	0.859720	−	4.04466i	0.0315189	−	0.148285i
$745$		0			0
$746$	5.84696	−	1.24281i	0.214073	−	0.0455025i
$747$	−1.56871	+	29.9328i	−0.0573961	+	1.09518i
$748$	−0.640965	+	4.04689i	−0.0234360	+	0.147969i
$749$	1.40444	−	6.21119i	0.0513172	−	0.226952i
$750$		0			0
$751$	21.1806	−	36.6859i	0.772892	−	1.33869i	−0.163080	−	0.986613i	$-0.552143\pi$
$751$	21.1806	−	36.6859i	0.772892	−	1.33869i	0.935972	−	0.352075i	$-0.114524\pi$
$752$	−0.245320	−	0.639081i	−0.00894591	−	0.0233049i
$753$	−1.54559	−	1.00372i	−0.0563244	−	0.0365775i
$754$	4.70472	+	5.22512i	0.171336	+	0.190288i
$755$		0			0
$756$	1.23359	−	2.67696i	0.0448654	−	0.0973599i
$757$	21.6112	−	21.6112i	0.785474	−	0.785474i	−0.195275	−	0.980749i	$-0.562560\pi$
$757$	21.6112	−	21.6112i	0.785474	−	0.785474i	0.980749	+	0.195275i	$0.0625599\pi$
$758$	1.87833	+	2.89237i	0.0682239	+	0.105056i
$759$	0.0356665	−	0.339344i	0.00129461	−	0.0123174i
$760$		0			0
$761$	−39.3434	+	4.13516i	−1.42620	+	0.149899i	−0.785960	−	0.618277i	$-0.787831\pi$
$761$	−39.3434	+	4.13516i	−1.42620	+	0.149899i	−0.640238	+	0.768177i	$0.721164\pi$
$762$	0.118515	+	0.748276i	0.00429335	+	0.0271072i
$763$	40.7294	+	27.2055i	1.47450	+	0.984904i
$764$	19.3591	+	26.6455i	0.700388	+	0.964001i
$765$		0			0
$766$	18.2175	+	1.91474i	0.658225	+	0.0691822i
$767$	0.364824	+	6.96125i	0.0131730	+	0.251356i
$768$	−0.535378	−	1.99806i	−0.0193188	−	0.0720987i
$769$	−0.678119	−	2.08704i	−0.0244536	−	0.0752604i	0.938085	−	0.346405i	$-0.112598\pi$
$769$	−0.678119	−	2.08704i	−0.0244536	−	0.0752604i	−0.962539	+	0.271145i	$0.912598\pi$
$770$		0			0
$771$	−0.0857432	+	0.263890i	−0.00308796	+	0.00950378i
$772$	18.7478	+	0.982531i	0.674748	+	0.0353620i
$773$	43.6415	−	16.7524i	1.56968	−	0.602542i	0.590768	−	0.806842i	$-0.298825\pi$
$773$	43.6415	−	16.7524i	1.56968	−	0.602542i	0.978908	+	0.204299i	$0.0654915\pi$
$774$	18.0729	−	10.4344i	0.649618	−	0.375057i
$775$		0			0
$776$			23.6145i			0.847711i
$777$	0.301832	+	2.07944i	0.0108282	+	0.0745996i
$778$	4.92045	−	2.50710i	0.176407	−	0.0898837i
$779$	−3.02787	+	2.72630i	−0.108485	+	0.0976800i
$780$		0			0
$781$	−2.48072	+	2.75512i	−0.0887673	+	0.0985860i
$782$	−27.7515	+	7.43600i	−0.992393	+	0.265911i
$783$	2.24666	+	1.14473i	0.0802890	+	0.0409093i
$784$	−2.46869	−	1.51177i	−0.0881674	−	0.0539917i
$785$		0			0
$786$	0.132986	+	1.26528i	0.00474346	+	0.0451310i
$787$	29.8811	−	24.1972i	1.06515	−	0.862538i	0.0742593	−	0.997239i	$-0.476341\pi$
$787$	29.8811	−	24.1972i	1.06515	−	0.862538i	0.990886	+	0.134701i	$0.0430074\pi$
$788$	21.4665	−	17.3832i	0.764711	−	0.619251i
$789$	0.161419	+	1.53580i	0.00574668	+	0.0546761i
$790$		0			0
$791$	−8.37734	+	24.6913i	−0.297864	+	0.877923i
$792$	−3.35589	−	1.70991i	−0.119246	−	0.0607590i
$793$	2.08261	−	0.558034i	0.0739556	−	0.0198164i
$794$	−8.98229	+	9.97584i	−0.318770	+	0.354029i
$795$		0			0
$796$	15.5709	−	14.0201i	0.551897	−	0.496930i
$797$	8.48456	−	4.32310i	0.300539	−	0.153132i	−0.297218	−	0.954810i	$-0.596059\pi$
$797$	8.48456	−	4.32310i	0.300539	−	0.153132i	0.597757	+	0.801678i	$0.296059\pi$
$798$	0.353610	+	0.141013i	0.0125177	+	0.00499181i
$799$		−	11.0423i		−	0.390650i
$800$		0			0
$801$	−23.9761	+	13.8426i	−0.847155	+	0.489105i
$802$	4.90064	−	1.88118i	0.173048	−	0.0664268i
$803$	−2.93770	−	0.153958i	−0.103669	−	0.00543306i
$804$	−0.136869	+	0.421239i	−0.00482700	+	0.0148560i
$805$		0			0
$806$	−7.80606	−	24.0246i	−0.274957	−	0.846229i
$807$	0.204813	+	0.764371i	0.00720975	+	0.0269071i
$808$	−2.53501	−	48.3710i	−0.0891815	−	1.70168i
$809$	10.2584	+	1.07820i	0.360666	+	0.0379075i	0.283129	−	0.959082i	$-0.408628\pi$
$809$	10.2584	+	1.07820i	0.360666	+	0.0379075i	0.0775373	+	0.996989i	$0.475294\pi$
$810$		0			0
$811$	2.44836	+	3.36987i	0.0859734	+	0.118332i	0.849837	−	0.527045i	$-0.176700\pi$
$811$	2.44836	+	3.36987i	0.0859734	+	0.118332i	−0.763864	+	0.645377i	$0.776700\pi$
$812$	5.85442	−	8.76467i	0.205450	−	0.307580i
$813$	0.603151	+	3.80814i	0.0211534	+	0.133557i
$814$	2.13689	−	0.224597i	0.0748981	−	0.00787211i
$815$		0			0
$816$	−0.0404896	+	0.385233i	−0.00141742	+	0.0134858i
$817$	−5.80433	−	8.93789i	−0.203068	−	0.312697i
$818$	2.73953	−	2.73953i	0.0957856	−	0.0957856i
$819$	−2.06234	−	22.4064i	−0.0720638	−	0.782942i
$820$		0			0
$821$	−21.6998	−	24.1000i	−0.757328	−	0.841098i	0.234038	−	0.972228i	$-0.424806\pi$
$821$	−21.6998	−	24.1000i	−0.757328	−	0.841098i	−0.991365	+	0.131130i	$0.958139\pi$
$822$	0.132784	+	0.0862309i	0.00463137	+	0.00300765i
$823$	15.4955	+	40.3671i	0.540139	+	1.40711i	0.883733	+	0.467992i	$0.155022\pi$
$823$	15.4955	+	40.3671i	0.540139	+	1.40711i	−0.343594	+	0.939118i	$0.611644\pi$
$824$	−15.1662	+	26.2686i	−0.528340	+	0.915111i
$825$		0			0
$826$	−5.06443	+	1.57340i	−0.176214	+	0.0547456i
$827$	−0.940691	+	5.93929i	−0.0327110	+	0.206529i	−0.998631	−	0.0523125i	$-0.983341\pi$
$827$	−0.940691	+	5.93929i	−0.0327110	+	0.206529i	0.965920	+	0.258842i	$0.0833408\pi$
$828$	−1.08616	+	20.7252i	−0.0377467	+	0.720250i
$829$	9.42367	−	2.00306i	0.327297	−	0.0695692i	−0.0413325	−	0.999145i	$-0.513160\pi$
$829$	9.42367	−	2.00306i	0.327297	−	0.0695692i	0.368630	+	0.929576i	$0.379827\pi$
$830$		0			0
$831$	−0.380754	+	1.79131i	−0.0132082	+	0.0621397i
$832$	−7.93220	−	7.93220i	−0.274999	−	0.274999i
$833$	−28.4378	−	37.0373i	−0.985312	−	1.28327i
$834$	−0.226666	+	0.311979i	−0.00784881	+	0.0108030i
$835$		0			0
$836$	−0.311993	+	0.700748i	−0.0107905	+	0.0242359i
$837$	−5.70104	−	7.04020i	−0.197057	−	0.243345i
$838$	4.67559	−	12.1803i	0.161516	−	0.420762i
$839$	32.1825	−	23.3819i	1.11106	−	0.807234i	0.128232	−	0.991744i	$-0.459070\pi$
$839$	32.1825	−	23.3819i	1.11106	−	0.807234i	0.982831	+	0.184510i	$0.0590698\pi$
$840$		0			0
$841$	−16.1669	−	11.7459i	−0.557479	−	0.405032i
$842$	19.7637	−	12.8347i	0.681101	−	0.442312i
$843$	−3.10610	−	0.832276i	−0.106980	−	0.0286651i
$844$	−4.58960	−	4.13249i	−0.157980	−	0.142246i
$845$		0			0
$846$	3.84992	+	1.25092i	0.132363	+	0.0430073i
$847$	7.02853	+	27.6571i	0.241503	+	0.950308i
$848$	2.92839	+	0.463812i	0.100561	+	0.0159274i
$849$	0.0827277	+	0.0477629i	0.00283921	+	0.00163922i
$850$		0			0
$851$	−14.8438	−	25.7103i	−0.508840	−	0.881337i
$852$	−0.938800	+	1.15932i	−0.0321628	+	0.0397177i
$853$	−11.8947	−	23.3447i	−0.407267	−	0.799307i	0.592714	−	0.805413i	$-0.298056\pi$
$853$	−11.8947	−	23.3447i	−0.407267	−	0.799307i	−0.999981	+	0.00610592i	$0.998056\pi$
$854$	0.801699	+	1.43102i	0.0274336	+	0.0489685i
$855$		0			0
$856$	−6.42651	−	1.36600i	−0.219654	−	0.0466888i
$857$	2.16145	−	8.06662i	0.0738336	−	0.275551i	−0.919133	−	0.393948i	$-0.871109\pi$
$857$	2.16145	−	8.06662i	0.0738336	−	0.275551i	0.992966	+	0.118397i	$0.0377757\pi$
$858$	0.152009	−	0.00796644i	0.00518949	−	0.000271970i
$859$	−4.68878	+	2.08758i	−0.159979	+	0.0712273i	−0.485164	−	0.874423i	$-0.661240\pi$
$859$	−4.68878	+	2.08758i	−0.159979	+	0.0712273i	0.325185	+	0.945650i	$0.394573\pi$
$860$		0			0
$861$	0.142275	−	1.20366i	0.00484871	−	0.0410207i
$862$	−20.9478	+	3.31781i	−0.713486	+	0.113005i
$863$	1.58461	+	0.608273i	0.0539406	+	0.0207059i	0.385189	−	0.922838i	$-0.374136\pi$
$863$	1.58461	+	0.608273i	0.0539406	+	0.0207059i	−0.331248	+	0.943544i	$0.607470\pi$
$864$	−4.44835	−	1.98053i	−0.151336	−	0.0673791i
$865$		0			0
$866$	−8.79311	−	19.7497i	−0.298802	−	0.671120i
$867$	−1.75300	+	3.44045i	−0.0595349	+	0.116844i
$868$	−32.0228	+	20.2118i	−1.08693	+	0.686033i
$869$	4.39355	−	1.42755i	0.149041	−	0.0484263i
$870$		0			0
$871$	1.41063	+	6.63650i	0.0477974	+	0.224869i
$872$	27.5229	−	42.3816i	0.932043	−	1.43522i
$873$	20.0365	+	16.2252i	0.678132	+	0.549141i
$874$	−5.37865			−0.181936
$875$		0			0
$876$	−1.18369			−0.0399930
$877$	−8.68941	−	7.03655i	−0.293421	−	0.237607i	0.471294	−	0.881976i	$-0.343787\pi$
$877$	−8.68941	−	7.03655i	−0.293421	−	0.237607i	−0.764715	+	0.644369i	$0.777120\pi$
$878$	−16.2563	+	25.0325i	−0.548623	+	0.844805i
$879$	0.741619	+	3.48904i	0.0250142	+	0.117682i
$880$		0			0
$881$	−19.9227	+	6.47328i	−0.671213	+	0.218090i	−0.624744	−	0.780829i	$-0.714797\pi$
$881$	−19.9227	+	6.47328i	−0.671213	+	0.218090i	−0.0464689	+	0.998920i	$0.514797\pi$
$882$	16.1346	−	5.71916i	0.543281	−	0.192574i
$883$	20.5259	−	40.2843i	0.690751	−	1.35567i	−0.232923	−	0.972495i	$-0.574829\pi$
$883$	20.5259	−	40.2843i	0.690751	−	1.35567i	0.923674	−	0.383180i	$-0.125171\pi$
$884$	10.2721	+	23.0716i	0.345489	+	0.775982i
$885$		0			0
$886$	13.3543	+	5.94570i	0.448645	+	0.199750i
$887$	32.7322	+	12.5647i	1.09904	+	0.421881i	0.839229	−	0.543778i	$-0.183007\pi$
$887$	32.7322	+	12.5647i	1.09904	+	0.421881i	0.259810	+	0.965660i	$0.416340\pi$
$888$	2.14123	−	0.339137i	0.0718549	−	0.0113807i
$889$	10.4069	−	13.9410i	0.349037	−	0.467568i
$890$		0			0
$891$	−3.73160	+	1.66142i	−0.125013	+	0.0556595i
$892$	−2.93152	+	0.153635i	−0.0981547	+	0.00514407i
$893$	0.535041	−	1.99680i	0.0179045	−	0.0668204i
$894$	−2.10708	−	0.447873i	−0.0704711	−	0.0149791i
$895$		0			0
$896$	−11.3222	+	19.0376i	−0.378248	+	0.636000i
$897$	−0.954813	−	1.87393i	−0.0318803	−	0.0625686i
$898$	4.48295	−	5.53598i	0.149598	−	0.184738i
$899$	−16.1972	−	28.0544i	−0.540208	−	0.935668i
$900$		0			0
$901$	41.4188	+	23.9131i	1.37986	+	0.796662i
$902$	−1.22414	−	0.193885i	−0.0407594	−	0.00645566i
$903$	3.05138	+	0.860072i	0.101544	+	0.0286214i
$904$	25.5846	+	8.31294i	0.850932	+	0.276484i
$905$		0			0
$906$	−0.950922	−	0.856214i	−0.0315923	−	0.0284458i
$907$	−17.0051	−	4.55651i	−0.564646	−	0.151296i	−0.0348060	−	0.999394i	$-0.511081\pi$
$907$	−17.0051	−	4.55651i	−0.564646	−	0.151296i	−0.529840	+	0.848098i	$0.677748\pi$
$908$	7.42824	−	4.82396i	0.246515	−	0.160089i
$909$	−42.7837	−	31.0842i	−1.41904	−	1.03100i
$910$		0			0
$911$	−17.7761	+	12.9151i	−0.588949	+	0.427897i	−0.841939	−	0.539572i	$-0.818586\pi$
$911$	−17.7761	+	12.9151i	−0.588949	+	0.427897i	0.252990	+	0.967469i	$0.418586\pi$
$912$	−0.0259877	+	0.0677003i	−0.000860539	+	0.00224178i
$913$	2.93027	+	3.61859i	0.0969779	+	0.119758i
$914$	8.92123	−	20.0374i	0.295088	−	0.662778i
$915$		0			0
$916$	−8.84547	+	12.1747i	−0.292263	+	0.402265i
$917$	18.6777	−	22.4646i	0.616793	−	0.741846i
$918$	−3.25012	−	3.25012i	−0.107270	−	0.107270i
$919$	3.37742	−	15.8895i	0.111411	−	0.524147i	−0.886680	−	0.462384i	$-0.846994\pi$
$919$	3.37742	−	15.8895i	0.111411	−	0.524147i	0.998091	−	0.0617633i	$-0.0196724\pi$
$920$		0			0
$921$	2.05605	−	0.437028i	0.0677493	−	0.0144006i
$922$	0.0237782	−	0.453716i	0.000783095	−	0.0149423i
$923$	−3.57475	+	22.5701i	−0.117664	+	0.742903i
$924$	−0.0676997	−	0.217910i	−0.00222716	−	0.00716872i
$925$		0			0
$926$	14.2836	−	24.7399i	0.469388	−	0.813004i
$927$	11.8680	+	30.9171i	0.389795	+	1.01545i
$928$	−14.6032	−	9.48345i	−0.479375	−	0.311310i
$929$	−12.6320	−	14.0292i	−0.414441	−	0.460283i	0.499391	−	0.866377i	$-0.333557\pi$
$929$	−12.6320	−	14.0292i	−0.414441	−	0.460283i	−0.913831	+	0.406094i	$0.866891\pi$
$930$		0			0
$931$	−3.34786	−	8.07542i	−0.109722	−	0.264661i
$932$	−2.42989	+	2.42989i	−0.0795939	+	0.0795939i
$933$	0.0315394	+	0.0485665i	0.00103255	+	0.00158999i
$934$	2.71453	−	25.8270i	0.0888220	−	0.845085i
$935$		0			0
$936$	−23.0880	+	2.42665i	−0.754655	+	0.0793175i
$937$	5.52877	+	34.9073i	0.180617	+	1.14037i	0.896792	+	0.442451i	$0.145891\pi$
$937$	5.52877	+	34.9073i	0.180617	+	1.14037i	−0.716175	+	0.697920i	$0.754109\pi$
$938$	−4.62901	+	2.28366i	−0.151142	+	0.0745641i
$939$	−0.177266	−	0.243986i	−0.00578486	−	0.00796218i
$940$		0			0
$941$	41.6382	+	4.37635i	1.35737	+	0.142665i	0.755089	−	0.655623i	$-0.227594\pi$
$941$	41.6382	+	4.37635i	1.35737	+	0.142665i	0.602277	+	0.798287i	$0.294260\pi$
$942$	0.00470641	+	0.0898037i	0.000153343	+	0.00292596i
$943$	4.43216	+	16.5410i	0.144331	+	0.538650i
$944$	−0.312168	−	0.960754i	−0.0101602	−	0.0312699i
$945$		0			0
$946$	1.00178	−	3.08317i	0.0325708	−	0.100243i
$947$	−0.712534	−	0.0373423i	−0.0231542	−	0.00121346i	0.0407553	−	0.999169i	$-0.487024\pi$
$947$	−0.712534	−	0.0373423i	−0.0231542	−	0.00121346i	−0.0639096	+	0.997956i	$0.520357\pi$
$948$	1.73538	−	0.666150i	0.0563625	−	0.0216356i
$949$	−15.7029	+	9.06605i	−0.509736	+	0.294296i
$950$		0			0
$951$			0.856142i			0.0277623i
$952$	−37.8299	+	29.8322i	−1.22608	+	0.966866i
$953$	−19.8369	+	10.1074i	−0.642581	+	0.327411i	−0.744738	−	0.667357i	$-0.767426\pi$
$953$	−19.8369	+	10.1074i	−0.642581	+	0.327411i	0.102157	+	0.994768i	$0.467426\pi$
$954$	−13.0294	+	11.7317i	−0.421842	+	0.379828i
$955$		0			0
$956$	−14.4835	+	16.0856i	−0.468430	+	0.520244i
$957$	0.188551	−	0.0505221i	0.00609500	−	0.00163315i
$958$	−15.7594	−	8.02981i	−0.509163	−	0.259431i
$959$	−0.709838	−	3.56573i	−0.0229219	−	0.115143i
$960$		0			0
$961$	8.92517	+	84.9173i	0.287909	+	2.73927i
$962$	10.2924	−	8.33463i	0.331840	−	0.268719i
$963$	−5.57460	+	4.51422i	−0.179639	+	0.145469i
$964$	1.09884	+	10.4548i	0.0353914	+	0.336726i
$965$		0			0
$966$	1.20280	−	1.05516i	0.0386995	−	0.0339491i
$967$	−24.2914	−	12.3771i	−0.781158	−	0.398020i	0.0174683	−	0.999847i	$-0.494439\pi$
$967$	−24.2914	−	12.3771i	−0.781158	−	0.398020i	−0.798626	+	0.601828i	$0.794439\pi$
$968$	28.4386	−	7.62010i	0.914051	−	0.244919i
$969$	−0.782720	+	0.869299i	−0.0251446	+	0.0279259i
$970$		0			0
$971$	18.6304	−	16.7749i	0.597879	−	0.538332i	−0.313666	−	0.949533i	$-0.601557\pi$
$971$	18.6304	−	16.7749i	0.597879	−	0.538332i	0.911545	+	0.411201i	$0.134891\pi$
$972$	−4.44236	+	2.26350i	−0.142489	+	0.0726017i
$973$	8.76343	−	1.27201i	0.280943	−	0.0407789i
$974$		−	14.5847i		−	0.467322i
$975$		0			0
$976$	−0.270594	+	0.156227i	−0.00866150	+	0.00500072i
$977$	15.6621	−	6.01214i	0.501077	−	0.192345i	−0.0946840	−	0.995507i	$-0.530184\pi$
$977$	15.6621	−	6.01214i	0.501077	−	0.192345i	0.595761	+	0.803162i	$0.296851\pi$
$978$	−2.49078	−	0.130536i	−0.0796462	−	0.00417408i
$979$	−1.32900	+	4.09024i	−0.0424750	+	0.130725i
$980$		0			0
$981$	−17.0494	−	52.4725i	−0.544344	−	1.67532i
$982$	−4.29496	−	16.0290i	−0.137058	−	0.511506i
$983$	−0.837455	−	15.9796i	−0.0267107	−	0.509670i	−0.978923	−	0.204232i	$-0.934530\pi$
$983$	−0.837455	−	15.9796i	−0.0267107	−	0.509670i	0.952212	−	0.305438i	$-0.0988029\pi$
$984$	−1.24366	−	0.130713i	−0.0396463	−	0.00416699i
$985$		0			0
$986$	−9.66099	−	13.2972i	−0.307669	−	0.423469i
$987$	0.272074	+	0.551497i	0.00866020	+	0.0175543i
$988$	0.739622	+	4.66979i	0.0235305	+	0.148566i
$989$	−44.5465	+	4.68203i	−1.41650	+	0.148880i
$990$		0			0
$991$	−2.76479	+	26.3052i	−0.0878264	+	0.835612i	0.858590	+	0.512663i	$0.171341\pi$
$991$	−2.76479	+	26.3052i	−0.0878264	+	0.835612i	−0.946416	+	0.322949i	$0.895326\pi$
$992$	34.0716	+	52.4657i	1.08178	+	1.66579i
$993$	−1.68690	+	1.68690i	−0.0535321	+	0.0535321i
$994$	−17.3116	+	1.59340i	−0.549090	+	0.0505395i
$995$		0			0
$996$	1.25366	+	1.39233i	0.0397239	+	0.0441178i
$997$	7.75776	+	5.03795i	0.245691	+	0.159553i	0.661610	−	0.749848i	$-0.269873\pi$
$997$	7.75776	+	5.03795i	0.245691	+	0.159553i	−0.415919	+	0.909402i	$0.636540\pi$
$998$	−6.85262	−	17.8517i	−0.216916	−	0.565085i
$999$	2.37475	−	4.11318i	0.0751337	−	0.130135i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.a.593.8		288
5.2	odd	4		875.2.bb.c.782.11		288
5.3	odd	4		175.2.x.a.152.8	yes	288
5.4	even	2		875.2.bb.b.593.11		288
7.3	odd	6	inner	875.2.bb.a.843.11		288
25.9	even	10		175.2.x.a.138.8	yes	288
25.12	odd	20	inner	875.2.bb.a.82.11		288
25.13	odd	20		875.2.bb.b.82.8		288
25.16	even	5		875.2.bb.c.418.11		288
35.3	even	12		175.2.x.a.52.8	yes	288
35.17	even	12		875.2.bb.c.157.11		288
35.24	odd	6		875.2.bb.b.843.8		288
175.38	even	60		875.2.bb.b.332.11		288
175.59	odd	30		175.2.x.a.38.8	✓	288
175.66	odd	30		875.2.bb.c.668.11		288
175.87	even	60	inner	875.2.bb.a.332.8		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.38.8	✓	288	175.59	odd	30
175.2.x.a.52.8	yes	288	35.3	even	12
175.2.x.a.138.8	yes	288	25.9	even	10
175.2.x.a.152.8	yes	288	5.3	odd	4
875.2.bb.a.82.11		288	25.12	odd	20	inner
875.2.bb.a.332.8		288	175.87	even	60	inner
875.2.bb.a.593.8		288	1.1	even	1	trivial
875.2.bb.a.843.11		288	7.3	odd	6	inner
875.2.bb.b.82.8		288	25.13	odd	20
875.2.bb.b.332.11		288	175.38	even	60
875.2.bb.b.593.11		288	5.4	even	2
875.2.bb.b.843.8		288	35.24	odd	6
875.2.bb.c.157.11		288	35.17	even	12
875.2.bb.c.418.11		288	25.16	even	5
875.2.bb.c.668.11		288	175.66	odd	30
875.2.bb.c.782.11		288	5.2	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.637685 - 0.516387i) q^{2} +(-0.0764752 + 0.117761i) q^{3} +(-0.275837 - 1.29771i) q^{4} +(0.109578 - 0.0356039i) q^{6} +(-2.34165 - 1.23154i) q^{7} +(-1.23927 + 2.43220i) q^{8} +(1.21219 + 2.72262i) q^{9} +(0.422943 + 0.188306i) q^{11} +(0.173915 + 0.0667597i) q^{12} +(2.81849 - 0.446405i) q^{13} +(0.857282 + 1.99453i) q^{14} +(-0.377790 + 0.168203i) q^{16} +(-6.66164 + 0.349122i) q^{17} +(0.632933 - 2.36214i) q^{18} +(-1.22155 - 0.259649i) q^{19} +(0.324106 - 0.181574i) q^{21} +(-0.172465 - 0.338482i) q^{22} +(-3.30320 + 4.07911i) q^{23} +(-0.191646 - 0.331940i) q^{24} +(-2.02783 - 1.17077i) q^{26} +(-0.829380 - 0.131361i) q^{27} +(-0.952270 + 3.37848i) q^{28} +(-2.85581 - 0.927907i) q^{29} +(8.01719 + 7.21871i) q^{31} +(5.60118 + 1.50083i) q^{32} +(-0.0545199 + 0.0354056i) q^{33} +(4.42831 + 3.21736i) q^{34} +(3.19881 - 2.32407i) q^{36} +(-2.02695 + 5.28038i) q^{37} +(0.644885 + 0.796367i) q^{38} +(-0.162975 + 0.366049i) q^{39} +(1.91768 - 2.63945i) q^{41} +(-0.300440 - 0.0515774i) q^{42} +(6.03422 + 6.03422i) q^{43} +(0.127704 - 0.600799i) q^{44} +(4.21280 - 0.895458i) q^{46} +(-0.0866332 + 1.65306i) q^{47} +(0.00908374 - 0.0573524i) q^{48} +(3.96662 + 5.76766i) q^{49} +(0.468337 - 0.811184i) q^{51} +(-1.35675 - 3.53445i) q^{52} +(-6.01286 - 3.90480i) q^{53} +(0.461050 + 0.512048i) q^{54} +(5.89727 - 4.16914i) q^{56} +(0.123995 - 0.123995i) q^{57} +(1.34194 + 2.06641i) q^{58} +(-0.255341 + 2.42941i) q^{59} +(0.751418 - 0.0789772i) q^{61} +(-1.38479 - 8.74324i) q^{62} +(0.514499 - 7.86829i) q^{63} +(-2.31063 - 3.18031i) q^{64} +(0.0530495 + 0.00557573i) q^{66} +(0.124434 + 2.37433i) q^{67} +(2.29059 + 8.54858i) q^{68} +(-0.227749 - 0.700940i) q^{69} +(-2.47456 + 7.61592i) q^{71} +(-8.12418 - 0.425770i) q^{72} +(-5.93202 + 2.27709i) q^{73} +(4.01928 - 2.32053i) q^{74} +1.65684i q^{76} +(-0.758476 - 0.961818i) q^{77} +(0.292950 - 0.149265i) q^{78} +(7.41534 - 6.67680i) q^{79} +(-5.90370 + 6.55672i) q^{81} +(-2.58585 + 0.692877i) q^{82} +(8.96119 + 4.56596i) q^{83} +(-0.325030 - 0.370511i) q^{84} +(-0.731939 - 6.96393i) q^{86} +(0.327670 - 0.265342i) q^{87} +(-0.982136 + 0.795318i) q^{88} +(0.971014 + 9.23858i) q^{89} +(-7.14968 - 2.42576i) q^{91} +(6.20465 + 3.16143i) q^{92} +(-1.46320 + 0.392064i) q^{93} +(0.908864 - 1.00940i) q^{94} +(-0.605091 + 0.544826i) q^{96} +(7.70801 - 3.92743i) q^{97} +(0.448893 - 5.72626i) q^{98} +1.37978i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) \) 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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