LMFDB - Embedded newform 966.2.bd.a.59.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(59,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 11, 42]))

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

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

chi := DirichletCharacter("966.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.bd (of order $66$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$1280$
Relative dimension:	$64$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			59.15
Character	$\chi$	$=$	966.59
Dual form			966.2.bd.a.131.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.945001 - 0.327068i) q^{2} +(-0.0481888 - 1.73138i) q^{3} +(0.786053 + 0.618159i) q^{4} +(-1.37494 + 0.131291i) q^{5} +(-0.520741 + 1.65192i) q^{6} +(2.07811 + 1.63751i) q^{7} +(-0.540641 - 0.841254i) q^{8} +(-2.99536 + 0.166866i) q^{9} +O(q^{10})$	\(q+(-0.945001 - 0.327068i) q^{2} +(-0.0481888 - 1.73138i) q^{3} +(0.786053 + 0.618159i) q^{4} +(-1.37494 + 0.131291i) q^{5} +(-0.520741 + 1.65192i) q^{6} +(2.07811 + 1.63751i) q^{7} +(-0.540641 - 0.841254i) q^{8} +(-2.99536 + 0.166866i) q^{9} +(1.34226 + 0.325630i) q^{10} +(0.00401406 - 0.00138928i) q^{11} +(1.03239 - 1.39075i) q^{12} +(0.217392 + 0.740370i) q^{13} +(-1.42824 - 2.22714i) q^{14} +(0.293572 + 2.37422i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-0.139973 - 0.0560367i) q^{17} +(2.88519 + 0.821996i) q^{18} +(1.87752 + 4.68981i) q^{19} +(-1.16194 - 0.746732i) q^{20} +(2.73502 - 3.67691i) q^{21} -0.00424768 q^{22} +(4.64643 - 1.18772i) q^{23} +(-1.43048 + 0.976594i) q^{24} +(-3.03641 + 0.585220i) q^{25} +(0.0367155 - 0.770753i) q^{26} +(0.433251 + 5.17806i) q^{27} +(0.621262 + 2.57178i) q^{28} +(1.19152 - 0.171314i) q^{29} +(0.499107 - 2.33966i) q^{30} +(9.16139 - 0.436411i) q^{31} +(0.0950560 - 0.995472i) q^{32} +(-0.00259880 - 0.00688292i) q^{33} +(0.113947 + 0.0987354i) q^{34} +(-3.07228 - 1.97865i) q^{35} +(-2.45766 - 1.72044i) q^{36} +(0.376641 - 0.528918i) q^{37} +(-0.240368 - 5.04595i) q^{38} +(1.27139 - 0.412066i) q^{39} +(0.853800 + 1.08569i) q^{40} +(-4.07596 + 8.92510i) q^{41} +(-3.78719 + 2.58015i) q^{42} +(8.93155 + 5.73996i) q^{43} +(0.00401406 + 0.00138928i) q^{44} +(4.09654 - 0.622695i) q^{45} +(-4.77935 - 0.397300i) q^{46} +(-3.33265 - 5.77233i) q^{47} +(1.67121 - 0.455019i) q^{48} +(1.63710 + 6.80587i) q^{49} +(3.06082 + 0.440079i) q^{50} +(-0.0902757 + 0.245047i) q^{51} +(-0.286785 + 0.716353i) q^{52} +(5.73918 + 6.01908i) q^{53} +(1.28415 - 5.03497i) q^{54} +(-0.00533670 + 0.00243719i) q^{55} +(0.254052 - 2.63353i) q^{56} +(8.02937 - 3.47669i) q^{57} +(-1.18202 - 0.227815i) q^{58} +(2.87372 - 11.8456i) q^{59} +(-1.23688 + 2.04774i) q^{60} +(5.65179 - 10.9629i) q^{61} +(-8.80026 - 2.58399i) q^{62} +(-6.49793 - 4.55817i) q^{63} +(-0.415415 + 0.909632i) q^{64} +(-0.396106 - 0.989426i) q^{65} +(0.000204690 + 0.00735435i) q^{66} +(-4.41272 + 0.850481i) q^{67} +(-0.0753865 - 0.130573i) q^{68} +(-2.28030 - 7.98750i) q^{69} +(2.25615 + 2.87467i) q^{70} +(-5.65883 + 4.90340i) q^{71} +(1.75979 + 2.42964i) q^{72} +(7.75356 - 9.85946i) q^{73} +(-0.528918 + 0.376641i) q^{74} +(1.15956 + 5.22898i) q^{75} +(-1.42322 + 4.84704i) q^{76} +(0.0106166 + 0.00368600i) q^{77} +(-1.33624 - 0.0264268i) q^{78} +(-3.38673 - 3.22924i) q^{79} +(-0.451745 - 1.30523i) q^{80} +(8.94431 - 0.999647i) q^{81} +(6.77090 - 7.10111i) q^{82} +(5.88625 + 12.8891i) q^{83} +(4.42278 - 1.19957i) q^{84} +(0.199812 + 0.0586701i) q^{85} +(-6.56297 - 8.34549i) q^{86} +(-0.354028 - 2.05471i) q^{87} +(-0.00333890 - 0.00262574i) q^{88} +(0.456100 - 9.57472i) q^{89} +(-4.07489 - 0.751398i) q^{90} +(-0.760601 + 1.89456i) q^{91} +(4.38654 + 1.93862i) q^{92} +(-1.19707 - 15.8408i) q^{93} +(1.26142 + 6.54486i) q^{94} +(-3.19721 - 6.20172i) q^{95} +(-1.72812 - 0.116608i) q^{96} +(6.14348 + 2.80563i) q^{97} +(0.678925 - 6.96700i) q^{98} +(-0.0117917 + 0.00483120i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1280 q - 64 q^{4} + 4 q^{9}+O(q^{10}) $ 1280 * q - 64 * q^4 + 4 * q^9	$ 1280 q - 64 q^{4} + 4 q^{9} + 16 q^{15} + 64 q^{16} - 44 q^{18} + 120 q^{21} - 16 q^{22} - 12 q^{24} + 56 q^{25} + 32 q^{30} - 24 q^{33} + 8 q^{36} - 44 q^{37} - 20 q^{39} + 4 q^{42} + 136 q^{43} + 12 q^{45} + 12 q^{46} + 92 q^{49} + 4 q^{51} - 36 q^{54} - 56 q^{57} - 28 q^{58} + 8 q^{60} + 72 q^{61} - 134 q^{63} + 128 q^{64} + 24 q^{67} - 72 q^{70} - 44 q^{72} - 72 q^{73} + 48 q^{75} - 16 q^{78} - 72 q^{79} + 40 q^{81} + 48 q^{82} - 10 q^{84} - 32 q^{85} + 222 q^{87} - 8 q^{88} - 8 q^{91} - 16 q^{93} + 72 q^{94} - 12 q^{96} - 68 q^{99}+O(q^{100}) $ 1280 * q - 64 * q^4 + 4 * q^9 + 16 * q^15 + 64 * q^16 - 44 * q^18 + 120 * q^21 - 16 * q^22 - 12 * q^24 + 56 * q^25 + 32 * q^30 - 24 * q^33 + 8 * q^36 - 44 * q^37 - 20 * q^39 + 4 * q^42 + 136 * q^43 + 12 * q^45 + 12 * q^46 + 92 * q^49 + 4 * q^51 - 36 * q^54 - 56 * q^57 - 28 * q^58 + 8 * q^60 + 72 * q^61 - 134 * q^63 + 128 * q^64 + 24 * q^67 - 72 * q^70 - 44 * q^72 - 72 * q^73 + 48 * q^75 - 16 * q^78 - 72 * q^79 + 40 * q^81 + 48 * q^82 - 10 * q^84 - 32 * q^85 + 222 * q^87 - 8 * q^88 - 8 * q^91 - 16 * q^93 + 72 * q^94 - 12 * q^96 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{11}\right)$

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 $

$2$	−0.945001	−	0.327068i	−0.668216	−	0.231272i
$2$	−0.945001	−	0.327068i	−0.668216	−	0.231272i
$3$	−0.0481888	−	1.73138i	−0.0278218	−	0.999613i
$3$	−0.0481888	−	1.73138i	−0.0278218	−	0.999613i
$4$	0.786053	+	0.618159i	0.393027	+	0.309079i
$5$	−1.37494	+	0.131291i	−0.614893	+	0.0587152i	−0.397856	−	0.917448i	$-0.630246\pi$
$5$	−1.37494	+	0.131291i	−0.614893	+	0.0587152i	−0.217038	+	0.976163i	$0.569639\pi$
$6$	−0.520741	+	1.65192i	−0.212591	+	0.674392i
$7$	2.07811	+	1.63751i	0.785452	+	0.618922i
$7$	2.07811	+	1.63751i	0.785452	+	0.618922i
$8$	−0.540641	−	0.841254i	−0.191145	−	0.297428i
$9$	−2.99536	+	0.166866i	−0.998452	+	0.0556220i
$10$	1.34226	+	0.325630i	0.424461	+	0.102973i
$11$	0.00401406	−	0.00138928i	0.00121028	−	0.000418884i	−0.326463	−	0.945210i	$-0.605857\pi$
$11$	0.00401406	−	0.00138928i	0.00121028	−	0.000418884i	0.327673	+	0.944791i	$0.393736\pi$
$12$	1.03239	−	1.39075i	0.298025	−	0.401474i
$13$	0.217392	+	0.740370i	0.0602938	+	0.205342i	0.984131	−	0.177444i	$-0.0567829\pi$
$13$	0.217392	+	0.740370i	0.0602938	+	0.205342i	−0.923837	+	0.382786i	$0.874965\pi$
$14$	−1.42824	−	2.22714i	−0.381713	−	0.595227i
$15$	0.293572	+	2.37422i	0.0757999	+	0.613022i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	−0.139973	−	0.0560367i	−0.0339484	−	0.0135909i	0.354626	−	0.935008i	$-0.384608\pi$
$17$	−0.139973	−	0.0560367i	−0.0339484	−	0.0135909i	−0.388575	+	0.921417i	$0.627032\pi$
$18$	2.88519	+	0.821996i	0.680046	+	0.193746i
$19$	1.87752	+	4.68981i	0.430732	+	1.07592i	0.971982	+	0.235055i	$0.0755269\pi$
$19$	1.87752	+	4.68981i	0.430732	+	1.07592i	−0.541250	+	0.840862i	$0.682049\pi$
$20$	−1.16194	−	0.746732i	−0.259817	−	0.166974i
$21$	2.73502	−	3.67691i	0.596830	−	0.802368i
$22$	−0.00424768			−0.000905608
$23$	4.64643	−	1.18772i	0.968848	−	0.247657i
$23$	4.64643	−	1.18772i	0.968848	−	0.247657i
$24$	−1.43048	+	0.976594i	−0.291995	+	0.199346i
$25$	−3.03641	+	0.585220i	−0.607282	+	0.117044i
$26$	0.0367155	−	0.770753i	0.00720050	−	0.151157i
$27$	0.433251	+	5.17806i	0.0833792	+	0.996518i
$28$	0.621262	+	2.57178i	0.117408	+	0.486020i
$29$	1.19152	−	0.171314i	0.221259	−	0.0318123i	−0.0307936	−	0.999526i	$-0.509803\pi$
$29$	1.19152	−	0.171314i	0.221259	−	0.0318123i	0.252053	+	0.967713i	$0.418894\pi$
$30$	0.499107	−	2.33966i	0.0911240	−	0.427162i
$31$	9.16139	−	0.436411i	1.64543	−	0.0783817i	0.795734	−	0.605647i	$-0.207086\pi$
$31$	9.16139	−	0.436411i	1.64543	−	0.0783817i	0.849701	+	0.527265i	$0.176783\pi$
$32$	0.0950560	−	0.995472i	0.0168037	−	0.175976i
$33$	−0.00259880	−	0.00688292i	−0.000452394	−	0.00119816i
$34$	0.113947	+	0.0987354i	0.0195417	+	0.0169330i
$35$	−3.07228	−	1.97865i	−0.519310	−	0.334453i
$36$	−2.45766	−	1.72044i	−0.409610	−	0.286740i
$37$	0.376641	−	0.528918i	0.0619193	−	0.0869535i	−0.782455	−	0.622707i	$-0.786033\pi$
$37$	0.376641	−	0.528918i	0.0619193	−	0.0869535i	0.844375	+	0.535753i	$0.179972\pi$
$38$	−0.240368	−	5.04595i	−0.0389929	−	0.818561i
$39$	1.27139	−	0.412066i	0.203585	−	0.0659834i
$40$	0.853800	+	1.08569i	0.134998	+	0.171663i
$41$	−4.07596	+	8.92510i	−0.636558	+	1.39387i	0.266284	+	0.963895i	$0.414204\pi$
$41$	−4.07596	+	8.92510i	−0.636558	+	1.39387i	−0.902842	+	0.429972i	$0.858523\pi$
$42$	−3.78719	+	2.58015i	−0.584377	+	0.398125i
$43$	8.93155	+	5.73996i	1.36205	+	0.875336i	0.998419	−	0.0562078i	$-0.0179009\pi$
$43$	8.93155	+	5.73996i	1.36205	+	0.875336i	0.363630	+	0.931544i	$0.381537\pi$
$44$	0.00401406	+	0.00138928i	0.000605142	+	0.000209442i
$45$	4.09654	−	0.622695i	0.610676	−	0.0928259i
$46$	−4.77935	−	0.397300i	−0.704676	−	0.0585788i
$47$	−3.33265	−	5.77233i	−0.486118	−	0.841980i	0.513755	−	0.857937i	$-0.328254\pi$
$47$	−3.33265	−	5.77233i	−0.486118	−	0.841980i	−0.999873	+	0.0159566i	$0.994921\pi$
$48$	1.67121	−	0.455019i	0.241219	−	0.0656763i
$49$	1.63710	+	6.80587i	0.233871	+	0.972268i
$50$	3.06082	+	0.440079i	0.432865	+	0.0622366i
$51$	−0.0902757	+	0.245047i	−0.0126411	+	0.0343134i
$52$	−0.286785	+	0.716353i	−0.0397699	+	0.0993403i
$53$	5.73918	+	6.01908i	0.788337	+	0.826784i	0.988221	−	0.153036i	$-0.0489050\pi$
$53$	5.73918	+	6.01908i	0.788337	+	0.826784i	−0.199884	+	0.979820i	$0.564057\pi$
$54$	1.28415	−	5.03497i	0.174751	−	0.685173i
$55$	−0.00533670	+	0.00243719i	−0.000719601	+	0.000328631i
$56$	0.254052	−	2.63353i	0.0339492	−	0.351920i
$57$	8.02937	−	3.47669i	1.06352	−	0.460499i
$58$	−1.18202	−	0.227815i	−0.155206	−	0.0299136i
$59$	2.87372	−	11.8456i	0.374126	−	1.54217i	−0.404416	−	0.914575i	$-0.632525\pi$
$59$	2.87372	−	11.8456i	0.374126	−	1.54217i	0.778542	−	0.627593i	$-0.215960\pi$
$60$	−1.23688	+	2.04774i	−0.159681	+	0.264362i
$61$	5.65179	−	10.9629i	0.723637	−	1.40366i	−0.183583	−	0.983004i	$-0.558769\pi$
$61$	5.65179	−	10.9629i	0.723637	−	1.40366i	0.907220	−	0.420657i	$-0.138200\pi$
$62$	−8.80026	−	2.58399i	−1.11763	−	0.328167i
$63$	−6.49793	−	4.55817i	−0.818662	−	0.574275i
$64$	−0.415415	+	0.909632i	−0.0519269	+	0.113704i
$65$	−0.396106	−	0.989426i	−0.0491309	−	0.122723i
$66$	0.000204690		0.00735435i	2.51956e−5		0.000905257i
$67$	−4.41272	+	0.850481i	−0.539099	+	0.103903i	−0.451530	−	0.892256i	$-0.649122\pi$
$67$	−4.41272	+	0.850481i	−0.539099	+	0.103903i	−0.0875685	+	0.996159i	$0.527910\pi$
$68$	−0.0753865	−	0.130573i	−0.00914196	−	0.0158343i
$69$	−2.28030	−	7.98750i	−0.274516	−	0.961582i
$70$	2.25615	+	2.87467i	0.269662	+	0.343589i
$71$	−5.65883	+	4.90340i	−0.671579	+	0.581927i	−0.922461	−	0.386091i	$-0.873825\pi$
$71$	−5.65883	+	4.90340i	−0.671579	+	0.581927i	0.250881	+	0.968018i	$0.419280\pi$
$72$	1.75979	+	2.42964i	0.207393	+	0.286336i
$73$	7.75356	−	9.85946i	0.907486	−	1.15396i	−0.0800848	−	0.996788i	$-0.525519\pi$
$73$	7.75356	−	9.85946i	0.907486	−	1.15396i	0.987571	−	0.157174i	$-0.0502384\pi$
$74$	−0.528918	+	0.376641i	−0.0614854	+	0.0437836i
$75$	1.15956	+	5.22898i	0.133894	+	0.603791i
$76$	−1.42322	+	4.84704i	−0.163255	+	0.555994i
$77$	0.0106166	+	0.00368600i	0.00120988	+	0.000420059i
$78$	−1.33624	−	0.0264268i	−0.151299	−	0.00299225i
$79$	−3.38673	−	3.22924i	−0.381037	−	0.363318i	0.475221	−	0.879866i	$-0.342368\pi$
$79$	−3.38673	−	3.22924i	−0.381037	−	0.363318i	−0.856258	+	0.516548i	$0.827217\pi$
$80$	−0.451745	−	1.30523i	−0.0505067	−	0.145929i
$81$	8.94431	−	0.999647i	0.993812	−	0.111072i
$82$	6.77090	−	7.10111i	0.747721	−	0.784187i
$83$	5.88625	+	12.8891i	0.646100	+	1.41476i	0.894927	+	0.446213i	$0.147228\pi$
$83$	5.88625	+	12.8891i	0.646100	+	1.41476i	−0.248827	+	0.968548i	$0.580045\pi$
$84$	4.42278	−	1.19957i	0.482565	−	0.130884i
$85$	0.199812	+	0.0586701i	0.0216726	+	0.00636366i
$86$	−6.56297	−	8.34549i	−0.707703	−	0.899918i
$87$	−0.354028	−	2.05471i	−0.0379558	−	0.220288i
$88$	−0.00333890	−	0.00262574i	−0.000355928	−	0.000279905i
$89$	0.456100	−	9.57472i	0.0483465	−	1.01492i	−0.836188	−	0.548443i	$-0.815221\pi$
$89$	0.456100	−	9.57472i	0.0483465	−	1.01492i	0.884534	−	0.466475i	$-0.154476\pi$
$90$	−4.07489	−	0.751398i	−0.429532	−	0.0792043i
$91$	−0.760601	+	1.89456i	−0.0797327	+	0.198603i
$92$	4.38654	+	1.93862i	0.457329	+	0.202115i
$93$	−1.19707	−	15.8408i	−0.124130	−	1.64262i
$94$	1.26142	+	6.54486i	0.130105	+	0.675050i
$95$	−3.19721	−	6.20172i	−0.328027	−	0.636283i
$96$	−1.72812	−	0.116608i	−0.176376	−	0.0119012i
$97$	6.14348	+	2.80563i	0.623776	+	0.284869i	0.702121	−	0.712057i	$-0.252236\pi$
$97$	6.14348	+	2.80563i	0.623776	+	0.284869i	−0.0783453	+	0.996926i	$0.524964\pi$
$98$	0.678925	−	6.96700i	0.0685818	−	0.703773i
$99$	−0.0117917	+	0.00483120i	−0.00118511	+	0.000485554i
$100$	−2.74854	−	1.41697i	−0.274854	−	0.141697i
$101$	6.18247	+	0.590354i	0.615179	+	0.0587424i	0.397994	−	0.917388i	$-0.369707\pi$
$101$	6.18247	+	0.590354i	0.615179	+	0.0587424i	0.217185	+	0.976131i	$0.430313\pi$
$102$	0.165458	−	0.202043i	0.0163827	−	0.0200052i
$103$	0.236442	−	1.22678i	0.0232973	−	0.120878i	−0.968418	−	0.249331i	$-0.919789\pi$
$103$	0.236442	−	1.22678i	0.0232973	−	0.120878i	0.991716	+	0.128453i	$0.0410013\pi$
$104$	0.505308	−	0.583156i	0.0495495	−	0.0571832i
$105$	−3.27775	+	5.41463i	−0.319875	+	0.528414i
$106$	−3.45488	−	7.56513i	−0.335568	−	0.734791i
$107$	0.963863	−	1.86963i	0.0931802	−	0.180744i	−0.837639	−	0.546224i	$-0.816065\pi$
$107$	0.963863	−	1.86963i	0.0931802	−	0.180744i	0.930819	+	0.365480i	$0.119095\pi$
$108$	−2.86031	+	4.33805i	−0.275233	+	0.417429i
$109$	−2.97643	−	1.19158i	−0.285091	−	0.114133i	0.224710	−	0.974426i	$-0.427857\pi$
$109$	−2.97643	−	1.19158i	−0.285091	−	0.114133i	−0.509801	+	0.860293i	$0.670281\pi$
$110$	0.00584032		0.000557683i	0.000556852		5.31730e-5i
$111$	−0.933908	−	0.626620i	−0.0886426	−	0.0594762i
$112$	−1.10142	+	2.40559i	−0.104075	+	0.227307i
$113$	4.13719	−	3.58490i	0.389194	−	0.337239i	−0.438183	−	0.898886i	$-0.644378\pi$
$113$	4.13719	−	3.58490i	0.389194	−	0.337239i	0.827377	+	0.561647i	$0.189832\pi$
$114$	−8.72488	+	0.659327i	−0.817159	+	0.0617516i
$115$	−6.23264	+	2.24309i	−0.581197	+	0.209169i
$116$	1.04250	+	0.601885i	0.0967933	+	0.0558836i
$117$	−0.774710	−	2.18140i	−0.0716220	−	0.201670i
$118$	−6.58999	+	10.2542i	−0.606657	+	0.943977i
$119$	−0.199118	−	0.345658i	−0.0182532	−	0.0316864i
$120$	1.83861	−	1.53057i	0.167841	−	0.139721i
$121$	−8.64657	+	6.79974i	−0.786052	+	0.618158i
$122$	−8.92657	+	8.51147i	−0.808174	+	0.770592i
$123$	15.6492	+	6.62694i	1.41104	+	0.597531i
$124$	7.47111	+	5.32015i	0.670926	+	0.477764i
$125$	10.7243	−	3.14894i	0.959211	−	0.281650i
$126$	4.64972	+	6.43274i	0.414230	+	0.573074i
$127$	−5.92068	+	6.83283i	−0.525376	+	0.606316i	−0.954969	−	0.296707i	$-0.904112\pi$
$127$	−5.92068	+	6.83283i	−0.525376	+	0.606316i	0.429593	+	0.903023i	$0.358657\pi$
$128$	0.690079	−	0.723734i	0.0609949	−	0.0639697i
$129$	9.50765	−	15.7405i	0.837102	−	1.38588i
$130$	0.0507113	+	1.06456i	0.00444768	+	0.0933682i
$131$	2.32527	+	9.58488i	0.203159	+	0.837434i	0.978560	+	0.205964i	$0.0660331\pi$
$131$	2.32527	+	9.58488i	0.203159	+	0.837434i	−0.775400	+	0.631470i	$0.782452\pi$
$132$	0.00221194	−	0.00701681i	0.000192525	−	0.000610735i
$133$	−3.77794	+	12.8204i	−0.327589	+	1.11167i
$134$	4.44818	+	0.639552i	0.384265	+	0.0552489i
$135$	−1.27553	−	7.06266i	−0.109780	−	0.607857i
$136$	0.0285340	+	0.148048i	0.00244677	+	0.0126950i
$137$	4.82308	+	2.78461i	0.412064	+	0.237905i	0.691676	−	0.722208i	$-0.256873\pi$
$137$	4.82308	+	2.78461i	0.412064	+	0.237905i	−0.279612	+	0.960113i	$0.590206\pi$
$138$	−0.457567	+	8.29401i	−0.0389507	+	0.706033i
$139$		−	19.0794i		−	1.61830i	−0.587604	−	0.809149i	$-0.699929\pi$
$139$		−	19.0794i		−	1.61830i	0.587604	−	0.809149i	$-0.300071\pi$
$140$	−1.19185	−	3.45448i	−0.100730	−	0.291957i
$141$	−9.83350	+	6.04825i	−0.828130	+	0.509355i
$142$	6.95134	−	2.78290i	0.583344	−	0.233536i
$143$	0.00190121	+	0.00266987i	0.000158987	+	0.000223266i
$144$	−0.868344	−	2.87158i	−0.0723620	−	0.239298i
$145$	−1.61578	+	0.391983i	−0.134183	+	0.0325524i
$146$	−10.5518	+	6.78125i	−0.873276	+	0.561221i
$147$	11.7047	−	3.16240i	0.965385	−	0.260831i
$148$	0.623015	−	0.182934i	0.0512115	−	0.0150371i
$149$	−4.20767	+	21.8315i	−0.344706	+	1.78850i	0.233231	+	0.972421i	$0.425070\pi$
$149$	−4.20767	+	21.8315i	−0.344706	+	1.78850i	−0.577936	+	0.816082i	$0.696142\pi$
$150$	0.614447	−	5.32065i	0.0501694	−	0.434429i
$151$	−4.23163	+	17.4430i	−0.344365	+	1.41949i	0.491653	+	0.870791i	$0.336393\pi$
$151$	−4.23163	+	17.4430i	−0.344365	+	1.41949i	−0.836018	+	0.548701i	$0.815122\pi$
$152$	2.93026	−	4.11497i	0.237675	−	0.333768i
$153$	0.428619	+	0.144493i	0.0346518	+	0.0116816i
$154$	−0.00882715	−	0.00695563i	−0.000711312	−	0.000560501i
$155$	−12.5391	+	1.80285i	−1.00716	+	0.144808i
$156$	1.25410	+	0.462013i	0.100408	+	0.0369907i
$157$	−4.67974	+	5.95078i	−0.373484	+	0.474924i	−0.936069	−	0.351816i	$-0.885564\pi$
$157$	−4.67974	+	5.95078i	−0.373484	+	0.474924i	0.562585	+	0.826739i	$0.309807\pi$
$158$	2.14428	+	4.15933i	0.170590	+	0.330898i
$159$	10.1447	−	10.2267i	0.804531	−	0.811034i
$160$			1.38120i			0.109193i
$161$	11.6007	+	5.14038i	0.914264	+	0.405118i
$162$	−8.77933	−	1.98073i	−0.689770	−	0.155621i
$163$	1.76323	−	5.09451i	0.138106	−	0.399032i	−0.854646	−	0.519212i	$-0.826226\pi$
$163$	1.76323	−	5.09451i	0.138106	−	0.399032i	0.992752	+	0.120179i	$0.0383469\pi$
$164$	−8.72105	+	4.49602i	−0.681000	+	0.351080i
$165$	0.00447687	+	0.00912242i	0.000348524	+	0.000710179i
$166$	−1.34690	−	14.1054i	−0.104540	−	1.09479i
$167$	0.234337	+	1.62985i	0.0181335	+	0.126121i	0.996877	−	0.0789650i	$-0.0251615\pi$
$167$	0.234337	+	1.62985i	0.0181335	+	0.126121i	−0.978744	+	0.205086i	$0.934252\pi$
$168$	−4.57188	−	0.312955i	−0.352728	−	0.0241450i
$169$	10.4354	−	6.70643i	0.802724	−	0.515879i
$170$	−0.169633	−	0.120795i	−0.0130103	−	0.00926458i
$171$	−6.40640	−	13.7344i	−0.489910	−	1.05029i
$172$	3.47247	+	10.0330i	0.264773	+	0.765012i
$173$	16.0947	+	3.10200i	1.22366	+	0.235841i	0.759852	−	0.650096i	$-0.225271\pi$
$173$	16.0947	+	3.10200i	1.22366	+	0.235841i	0.463806	+	0.885937i	$0.346483\pi$
$174$	−0.337474	+	2.05750i	−0.0255839	+	0.155978i
$175$	−7.26831	−	3.75601i	−0.549432	−	0.283928i
$176$	0.00229647	+	0.00357337i	0.000173103	+	0.000269353i
$177$	−20.6478	−	4.40467i	−1.55198	−	0.331075i
$178$	−3.56260	+	8.89894i	−0.267028	+	0.667004i
$179$	−2.88267	+	2.05274i	−0.215461	+	0.153429i	−0.682692	−	0.730706i	$-0.739191\pi$
$179$	−2.88267	+	2.05274i	−0.215461	+	0.153429i	0.467231	+	0.884135i	$0.345252\pi$
$180$	3.60502	+	2.04284i	0.268702	+	0.152264i
$181$	4.15628	−	6.46730i	0.308934	−	0.480711i	−0.651720	−	0.758460i	$-0.725952\pi$
$181$	4.15628	−	6.46730i	0.308934	−	0.480711i	0.960654	+	0.277749i	$0.0895884\pi$
$182$	1.33842	−	1.54159i	0.0992101	−	0.114270i
$183$	−19.2534	−	9.25711i	−1.42325	−	0.684305i
$184$	−3.51123	−	3.26670i	−0.258851	−	0.240824i
$185$	−0.448417	+	0.776682i	−0.0329683	+	0.0571028i
$186$	−4.04979	+	15.3611i	−0.296945	+	1.12633i
$187$	−0.000639710	0	3.04731e-5i	−4.67802e−5	0	2.22842e-6i
$188$	0.948572	−	6.59746i	0.0691817	−	0.481170i
$189$	−7.57880	+	11.4700i	−0.551276	+	0.834323i
$190$	0.992981	+	6.90634i	0.0720384	+	0.501038i
$191$	5.91676	−	1.43539i	0.428121	−	0.103861i	−0.0159077	−	0.999873i	$-0.505064\pi$
$191$	5.91676	−	1.43539i	0.428121	−	0.103861i	0.444029	+	0.896012i	$0.353549\pi$
$192$	1.59494	+	0.675407i	0.115105	+	0.0487433i
$193$	−18.5226	−	1.76870i	−1.33329	−	0.127314i	−0.596050	−	0.802947i	$-0.703264\pi$
$193$	−18.5226	−	1.76870i	−1.33329	−	0.127314i	−0.737237	+	0.675634i	$0.763870\pi$
$194$	−4.88796	−	4.66066i	−0.350935	−	0.334616i
$195$	−1.69398	+	0.733490i	−0.121309	+	0.0525263i
$196$	−2.92027	+	6.36176i	−0.208590	+	0.454412i
$197$	7.23097	+	24.6264i	0.515185	+	1.75456i	0.646189	+	0.763177i	$0.276362\pi$
$197$	7.23097	+	24.6264i	0.515185	+	1.75456i	−0.131004	+	0.991382i	$0.541820\pi$
$198$	0.0127233		0.000708794i	0.000904206		5.03718e-5i
$199$	−15.7792	+	0.751656i	−1.11856	+	0.0532835i	−0.598703	−	0.800971i	$-0.704317\pi$
$199$	−15.7792	+	0.751656i	−1.11856	+	0.0532835i	−0.519855	+	0.854255i	$0.674014\pi$
$200$	2.13393	+	2.23800i	0.150891	+	0.158250i
$201$	1.68515	+	7.59910i	0.118861	+	0.536000i
$202$	−5.64935	−	2.57997i	−0.397487	−	0.181526i
$203$	2.75664	+	1.59512i	0.193478	+	0.111955i
$204$	−0.222439	+	0.136815i	−0.0155739	+	0.00957896i
$205$	4.43242	−	12.8066i	0.309574	−	0.894455i
$206$	−0.624677	+	1.08197i	−0.0435233	+	0.0753846i
$207$	−13.7195	+	4.33298i	−0.953573	+	0.301163i
$208$	−0.668248	+	0.385813i	−0.0463347	+	0.0267513i
$209$	0.0140519	+	0.0162168i	0.000971992	+	0.00112174i
$210$	4.86843	−	4.04478i	0.335953	−	0.279117i
$211$	−0.833098	+	5.79432i	−0.0573528	+	0.398898i	0.940842	+	0.338845i	$0.110036\pi$
$211$	−0.833098	+	5.79432i	−0.0573528	+	0.398898i	−0.998195	+	0.0600531i	$0.980873\pi$
$212$	0.790552	+	8.27904i	0.0542953	+	0.568607i
$213$	8.76235	+	9.56130i	0.600386	+	0.655129i
$214$	−1.52235	+	1.45156i	−0.104066	+	0.0992264i
$215$	−13.0340	−	6.71949i	−0.888910	−	0.458265i
$216$	4.12183	−	3.16394i	0.280455	−	0.215279i
$217$	19.7530	+	14.0950i	1.34092	+	0.956830i
$218$	2.42300	+	2.09955i	0.164107	+	0.142199i
$219$	−17.4441	−	12.9493i	−1.17876	−	0.875029i
$220$	−0.00570150	−	0.00138317i	−0.000384395	−	9.32533e-5i
$221$	0.0110589	−	0.115814i	0.000743900	−	0.00779047i
$222$	0.677596	+	0.897608i	0.0454773	+	0.0602435i
$223$	−5.87258	+	20.0002i	−0.393257	+	1.33931i	0.490531	+	0.871424i	$0.336803\pi$
$223$	−5.87258	+	20.0002i	−0.393257	+	1.33931i	−0.883788	+	0.467887i	$0.845015\pi$
$224$	1.82764	−	1.91305i	0.122114	−	0.127821i
$225$	8.99748	−	2.25962i	0.599832	−	0.150641i
$226$	−5.08215	+	2.03459i	−0.338060	+	0.135339i
$227$	0.352628	−	0.181793i	0.0234048	−	0.0120660i	−0.446484	−	0.894791i	$-0.647324\pi$
$227$	0.352628	−	0.181793i	0.0234048	−	0.0120660i	0.469889	+	0.882725i	$0.344294\pi$
$228$	8.46066	+	2.23056i	0.560321	+	0.147723i
$229$	7.22521	−	4.17148i	0.477455	−	0.275659i	−0.241900	−	0.970301i	$-0.577771\pi$
$229$	7.22521	−	4.17148i	0.477455	−	0.275659i	0.719355	+	0.694642i	$0.244437\pi$
$230$	6.62349	−	0.0812204i	0.436740	−	0.00535552i
$231$	0.00587027	−	0.0185590i	0.000386235	−	0.00122110i
$232$	−0.788302	−	0.909749i	−0.0517545	−	0.0597279i
$233$	−17.8967	−	0.852523i	−1.17245	−	0.0558506i	−0.547699	−	0.836675i	$-0.684496\pi$
$233$	−17.8967	−	0.852523i	−1.17245	−	0.0558506i	−0.624750	+	0.780825i	$0.714799\pi$
$234$	0.0186366	+	2.31480i	0.00121831	+	0.151324i
$235$	5.34007	+	7.49907i	0.348348	+	0.489186i
$236$	9.58137	−	7.53487i	0.623694	−	0.490478i
$237$	−5.42784	+	6.01933i	−0.352576	+	0.390998i
$238$	0.0751134	+	0.391772i	0.00486888	+	0.0253948i
$239$	−8.79732	+	4.01760i	−0.569051	+	0.259877i	−0.679096	−	0.734050i	$-0.737628\pi$
$239$	−8.79732	+	4.01760i	−0.569051	+	0.259877i	0.110044	+	0.993927i	$0.464901\pi$
$240$	−2.23809	+	0.845041i	−0.144468	+	0.0545471i
$241$	−4.50264	+	1.55838i	−0.290041	+	0.100384i	−0.468214	−	0.883615i	$-0.655102\pi$
$241$	−4.50264	+	1.55838i	−0.290041	+	0.100384i	0.178173	+	0.983999i	$0.442981\pi$
$242$	10.3950	−	3.59774i	0.668215	−	0.231272i
$243$	−2.16178	−	15.4378i	−0.138679	−	0.990337i
$244$	11.2194	−	5.12375i	0.718252	−	0.328014i
$245$	−3.14447	−	9.14275i	−0.200893	−	0.584109i
$246$	−12.6210	−	11.3808i	−0.804686	−	0.725614i
$247$	−3.06404	+	2.40959i	−0.194960	+	0.153318i
$248$	−5.32015	−	7.47111i	−0.337830	−	0.474416i
$249$	22.0323	−	10.8124i	1.39624	−	0.685211i
$250$	−11.1644	−	0.531826i	−0.706098	−	0.0336356i
$251$	−5.43826	−	6.27608i	−0.343260	−	0.396143i	0.557702	−	0.830041i	$-0.311683\pi$
$251$	−5.43826	−	6.27608i	−0.343260	−	0.396143i	−0.900962	+	0.433898i	$0.857138\pi$
$252$	−2.29004	−	7.59972i	−0.144259	−	0.478737i
$253$	0.0170010	−	0.0112228i	0.00106884	−	0.000705570i
$254$	7.82985	−	4.52057i	0.491289	−	0.283646i
$255$	0.0919515	−	0.348778i	0.00575823	−	0.0218413i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	−3.60538	+	1.44337i	−0.224897	+	0.0900352i	−0.481375	−	0.876515i	$-0.659862\pi$
$257$	−3.60538	+	1.44337i	−0.224897	+	0.0900352i	0.256477	+	0.966550i	$0.417438\pi$
$258$	−14.1330	+	11.7652i	−0.879880	+	0.732466i
$259$	1.64881	−	0.482396i	0.102452	−	0.0299746i
$260$	0.300262	−	1.02260i	0.0186214	−	0.0634188i
$261$	−3.54043	+	0.711971i	−0.219147	+	0.0440699i
$262$	0.937528	−	9.81823i	0.0579207	−	0.606573i
$263$	−10.6591	−	2.58588i	−0.657270	−	0.159452i	−0.106765	−	0.994284i	$-0.534049\pi$
$263$	−10.6591	−	2.58588i	−0.657270	−	0.159452i	−0.550504	+	0.834832i	$0.685565\pi$
$264$	−0.00438526	+	0.00590744i	−0.000269894	+	0.000363578i
$265$	−8.68130	−	7.52239i	−0.533288	−	0.462096i
$266$	7.76330	−	10.8797i	0.475999	−	0.667074i
$267$	−16.5995	−	0.328289i	−1.01587	−	0.0200910i
$268$	−3.99436	−	2.05924i	−0.243994	−	0.125788i
$269$	−16.4199	+	15.6564i	−1.00114	+	0.954585i	−0.998968	−	0.0454127i	$-0.985540\pi$
$269$	−16.4199	+	15.6564i	−1.00114	+	0.954585i	−0.00217158	+	0.999998i	$0.500691\pi$
$270$	−1.10459	+	7.09140i	−0.0672233	+	0.431569i
$271$	−0.259873	−	2.72151i	−0.0157862	−	0.165320i	0.984141	−	0.177388i	$-0.0567647\pi$
$271$	−0.259873	−	2.72151i	−0.0157862	−	0.165320i	−0.999927	+	0.0120677i	$0.996159\pi$
$272$	0.0214572	−	0.149238i	0.00130104	−	0.00904891i
$273$	3.31685	+	1.22559i	0.200745	+	0.0741763i
$274$	−3.64706	−	4.20893i	−0.220327	−	0.254271i
$275$	−0.0113753	+	0.00656753i	−0.000685956	+	0.000396037i
$276$	3.14511	−	7.68819i	0.189313	−	0.462775i
$277$	−8.58706	+	14.8732i	−0.515946	+	0.893645i	0.483882	+	0.875133i	$0.339226\pi$
$277$	−8.58706	+	14.8732i	−0.515946	+	0.893645i	−0.999829	+	0.0185123i	$0.994107\pi$
$278$	−6.24027	+	18.0301i	−0.374267	+	1.08137i
$279$	−27.3688	+	2.83593i	−1.63853	+	0.169783i
$280$	−0.00354880	+	3.65430i	−0.000212081	+	0.218386i
$281$	14.2772	+	6.52017i	0.851706	+	0.388961i	0.792932	−	0.609310i	$-0.208554\pi$
$281$	14.2772	+	6.52017i	0.851706	+	0.388961i	0.0587738	+	0.998271i	$0.481281\pi$
$282$	11.2709	−	2.49938i	0.671169	−	0.148836i
$283$	−4.02256	−	4.21874i	−0.239117	−	0.250778i	0.593231	−	0.805032i	$-0.297852\pi$
$283$	−4.02256	−	4.21874i	−0.239117	−	0.250778i	−0.832348	+	0.554254i	$0.813004\pi$
$284$	−7.47922	+	0.356279i	−0.443810	+	0.0211413i
$285$	−10.5835	+	5.83444i	−0.626911	+	0.345602i
$286$	−0.000923413	−	0.00314485i	−5.46025e−5	−	0.000185959i
$287$	−23.0853	+	11.8729i	−1.36268	+	0.700837i
$288$	−0.118616	+	2.99765i	−0.00698952	+	0.176638i
$289$	−12.2870	−	11.7157i	−0.722766	−	0.689156i
$290$	1.65512	+	0.158044i	0.0971917	+	0.00928068i
$291$	4.56157	−	10.7719i	0.267404	−	0.631460i
$292$	12.1894	−	2.95712i	0.713332	−	0.173053i
$293$	−0.525529	−	3.65514i	−0.0307017	−	0.213535i	0.968695	−	0.248252i	$-0.0798562\pi$
$293$	−0.525529	−	3.65514i	−0.0307017	−	0.213535i	−0.999397	+	0.0347168i	$0.988947\pi$
$294$	−12.0952	−	0.839747i	−0.705409	−	0.0489750i
$295$	−2.39597	+	16.6643i	−0.139499	+	0.970236i
$296$	−0.648581	−	0.0308957i	−0.0376980	−	0.00179578i
$297$	0.00893287	+	0.0201831i	0.000518337	+	0.00117114i
$298$	11.1166	−	19.2546i	0.643969	−	1.11539i
$299$	1.88945	+	3.18188i	0.109270	+	0.184013i
$300$	−2.32087	+	4.82705i	−0.133995	+	0.278690i
$301$	9.16150	+	26.5538i	0.528060	+	1.53054i
$302$	9.70394	−	15.0996i	0.558399	−	0.868886i
$303$	0.724202	−	10.7327i	0.0416043	−	0.616575i
$304$	−4.11497	+	2.93026i	−0.236010	+	0.168062i
$305$	−6.33155	+	15.8155i	−0.362544	+	0.905590i
$306$	−0.357786	−	0.276734i	−0.0204533	−	0.0158198i
$307$	4.26389	+	6.63475i	0.243353	+	0.378665i	0.941348	−	0.337438i	$-0.109560\pi$
$307$	4.26389	+	6.63475i	0.243353	+	0.378665i	−0.697994	+	0.716103i	$0.745924\pi$
$308$	0.00606670	+	0.00946016i	0.000345682	+	0.000539042i
$309$	−2.13541	−	0.350254i	−0.121479	−	0.0199252i
$310$	12.4391	+	2.39744i	0.706494	+	0.136166i
$311$	−7.03198	−	20.3176i	−0.398747	−	1.15210i	−0.948500	−	0.316777i	$-0.897399\pi$
$311$	−7.03198	−	20.3176i	−0.398747	−	1.15210i	0.549753	−	0.835327i	$-0.314722\pi$
$312$	−1.03402	−	0.846779i	−0.0585396	−	0.0479394i
$313$	−9.95446	−	7.08854i	−0.562659	−	0.400668i	0.263035	−	0.964786i	$-0.415277\pi$
$313$	−9.95446	−	7.08854i	−0.562659	−	0.400668i	−0.825694	+	0.564119i	$0.809216\pi$
$314$	6.36867	−	4.09290i	0.359405	−	0.230975i
$315$	9.53273	+	5.41410i	0.537109	+	0.305050i
$316$	−0.665966	−	4.63189i	−0.0374635	−	0.260564i
$317$	0.0995549	+	1.04259i	0.00559156	+	0.0585575i	0.997837	−	0.0657362i	$-0.0209396\pi$
$317$	0.0995549	+	1.04259i	0.00559156	+	0.0585575i	−0.992245	+	0.124294i	$0.960334\pi$
$318$	−12.9316	+	6.34627i	−0.725170	+	0.355881i
$319$	0.00454482	−	0.00234302i	0.000254461	−	0.000131184i
$320$	0.451745	−	1.30523i	0.0252533	−	0.0729647i
$321$	−3.28349	−	1.57872i	−0.183267	−	0.0881155i
$322$	−9.28143	−	8.65188i	−0.517234	−	0.482150i
$323$		−	0.761656i		−	0.0423797i
$324$	7.64864	+	4.74323i	0.424925	+	0.263513i
$325$	−1.09337	−	2.12085i	−0.0606494	−	0.117643i
$326$	−3.33250	+	4.23762i	−0.184570	+	0.234700i
$327$	−1.91966	+	5.21076i	−0.106157	+	0.288156i
$328$	9.71190	−	1.39636i	0.536250	−	0.0771011i
$329$	2.52664	−	17.4528i	0.139298	−	0.962204i
$330$	−0.00124700	−	0.0100849i	−6.86450e−5	−	0.000555157i
$331$	18.7024	−	26.2638i	1.02797	−	1.44359i	0.136433	−	0.990649i	$-0.456436\pi$
$331$	18.7024	−	26.2638i	1.02797	−	1.44359i	0.891542	−	0.452939i	$-0.149624\pi$
$332$	−3.34060	+	13.7701i	−0.183339	+	0.755735i
$333$	−1.03991	+	1.64715i	−0.0569869	+	0.0902630i
$334$	0.311623	−	1.61685i	0.0170512	−	0.0884702i
$335$	5.95557	−	1.74871i	0.325388	−	0.0955425i
$336$	4.21807	+	1.79106i	0.230115	+	0.0977102i
$337$	2.06639	−	1.32799i	0.112563	−	0.0723401i	−0.483148	−	0.875539i	$-0.660507\pi$
$337$	2.06639	−	1.32799i	0.112563	−	0.0723401i	0.595711	+	0.803199i	$0.296870\pi$
$338$	−12.0549	+	2.92449i	−0.655702	+	0.159071i
$339$	−6.40619	−	6.99030i	−0.347936	−	0.379661i
$340$	0.120795	+	0.169633i	0.00655105	+	0.00919966i
$341$	0.0361681	−	0.0144795i	0.00195861	−	0.000784109i
$342$	1.56199	+	15.0743i	0.0844626	+	0.815125i
$343$	−7.74264	+	16.8241i	−0.418063	+	0.908418i
$344$		−	10.6170i		−	0.572428i
$345$	4.18398	+	10.6830i	0.225258	+	0.575152i
$346$	−14.1950	−	8.19546i	−0.763125	−	0.440591i
$347$	−0.896248	−	4.65018i	−0.0481131	−	0.249635i	0.949907	−	0.312533i	$-0.101178\pi$
$347$	−0.896248	−	4.65018i	−0.0481131	−	0.249635i	−0.998020	+	0.0628987i	$0.979965\pi$
$348$	0.991855	−	1.83396i	0.0531690	−	0.0983106i
$349$	18.9347	+	2.72240i	1.01355	+	0.145726i	0.629022	−	0.777387i	$-0.283455\pi$
$349$	18.9347	+	2.72240i	1.01355	+	0.145726i	0.384527	+	0.923114i	$0.374364\pi$
$350$	5.64009	+	5.92667i	0.301475	+	0.316794i
$351$	−3.73950	+	1.44644i	−0.199599	+	0.0772051i
$352$	−0.00100143	−	0.00412794i	−5.33763e−5	−	0.000220020i
$353$	0.985391	+	20.6859i	0.0524471	+	1.10100i	0.859702	+	0.510796i	$0.170649\pi$
$353$	0.985391	+	20.6859i	0.0524471	+	1.10100i	−0.807255	+	0.590203i	$0.799048\pi$
$354$	18.0715	+	10.9156i	0.960490	+	0.580159i
$355$	7.13680	−	7.48486i	0.378782	−	0.397255i
$356$	6.27722	−	7.24429i	0.332692	−	0.383947i
$357$	−0.588870	+	0.361407i	−0.0311663	+	0.0191277i
$358$	3.39551	−	0.997012i	0.179458	−	0.0526937i
$359$	−18.4412	−	13.1319i	−0.973287	−	0.693075i	−0.0214793	−	0.999769i	$-0.506838\pi$
$359$	−18.4412	−	13.1319i	−0.973287	−	0.693075i	−0.951808	+	0.306695i	$0.900777\pi$
$360$	−2.73860	−	3.10957i	−0.144337	−	0.163889i
$361$	−4.71830	+	4.49889i	−0.248332	+	0.236784i
$362$	−6.04294	+	4.75222i	−0.317610	+	0.249771i
$363$	12.1896	+	14.6428i	0.639788	+	0.768549i
$364$	−1.76901	+	1.01905i	−0.0927213	+	0.0534127i
$365$	−9.36625	+	14.5742i	−0.490252	+	0.762847i
$366$	15.1668	+	15.0451i	0.792779	+	0.786422i
$367$	−16.0399	−	9.26063i	−0.837275	−	0.483401i	0.0190622	−	0.999818i	$-0.493932\pi$
$367$	−16.0399	−	9.26063i	−0.837275	−	0.483401i	−0.856337	+	0.516417i	$0.827265\pi$
$368$	2.24968	+	4.23544i	0.117273	+	0.220788i
$369$	10.7196	−	27.4140i	0.558043	−	1.42712i
$370$	0.677782	−	0.587302i	0.0352362	−	0.0305324i
$371$	2.07033	+	21.9063i	0.107486	+	1.13732i
$372$	8.85119	−	13.1917i	0.458913	−	0.683958i
$373$	22.5285	−	2.15121i	1.16648	−	0.111386i	0.506209	−	0.862411i	$-0.331046\pi$
$373$	22.5285	−	2.15121i	1.16648	−	0.111386i	0.660274	+	0.751025i	$0.270440\pi$
$374$	0.000594560	0	0.000238026i	3.07440e−5	0	1.23080e-5i
$375$	−5.96880	−	18.4161i	−0.308228	−	0.951004i
$376$	−3.05422	+	5.92436i	−0.157509	+	0.305526i
$377$	0.385863	+	0.844921i	0.0198729	+	0.0435157i
$378$	10.9135	−	8.36041i	0.561327	−	0.430013i
$379$	1.48965	−	1.71915i	0.0765182	−	0.0883067i	−0.716200	−	0.697896i	$-0.754120\pi$
$379$	1.48965	−	1.71915i	0.0765182	−	0.0883067i	0.792718	+	0.609589i	$0.208665\pi$
$380$	1.32047	−	6.85127i	0.0677389	−	0.351463i
$381$	12.1155	+	9.92169i	0.620698	+	0.508304i
$382$	−6.06081	−	0.578737i	−0.310098	−	0.0296108i
$383$	9.96415	+	5.13688i	0.509144	+	0.262482i	0.693602	−	0.720358i	$-0.256023\pi$
$383$	9.96415	+	5.13688i	0.509144	+	0.262482i	−0.184458	+	0.982840i	$0.559053\pi$
$384$	−1.28631	−	1.15991i	−0.0656419	−	0.0591916i
$385$	−0.0150812	−	0.00367417i	−0.000768609	−	0.000187253i
$386$	16.9254	+	7.72957i	0.861481	+	0.393425i
$387$	−27.7110	−	15.7028i	−1.40863	−	0.798221i
$388$	3.09478	+	6.00303i	0.157113	+	0.304757i
$389$	−4.02044	−	20.8600i	−0.203845	−	1.05765i	−0.929286	−	0.369362i	$-0.879576\pi$
$389$	−4.02044	−	20.8600i	−0.203845	−	1.05765i	0.725441	−	0.688284i	$-0.241636\pi$
$390$	1.84072	−	0.139100i	0.0932083	−	0.00704363i
$391$	−0.716930	−	0.0941217i	−0.0362567	−	0.00475994i
$392$	4.84038	−	5.05675i	0.244476	−	0.255404i
$393$	16.4830	−	4.48780i	0.831458	−	0.226380i
$394$	1.22124	−	25.6370i	0.0615252	−	1.29157i
$395$	5.08053	+	3.99538i	0.255629	+	0.201029i
$396$	−0.0122554	−	0.00349158i	−0.000615855	−	0.000175458i
$397$	−4.41209	−	5.61043i	−0.221437	−	0.281579i	0.662624	−	0.748953i	$-0.269443\pi$
$397$	−4.41209	−	5.61043i	−0.221437	−	0.281579i	−0.884060	+	0.467373i	$0.845200\pi$
$398$	15.1572	+	4.45056i	0.759762	+	0.223086i
$399$	22.3791	+	5.92325i	1.12035	+	0.296533i
$400$	−1.28459	−	2.81285i	−0.0642293	−	0.140642i
$401$	15.8153	−	16.5866i	0.789779	−	0.828297i	−0.198636	−	0.980073i	$-0.563651\pi$
$401$	15.8153	−	16.5866i	0.789779	−	0.828297i	0.988415	+	0.151777i	$0.0484995\pi$
$402$	0.892956	−	7.73232i	0.0445366	−	0.385653i
$403$	2.31472	+	6.68795i	0.115304	+	0.333150i
$404$	4.49482	+	4.28580i	0.223625	+	0.213226i
$405$	−12.1667	+	2.54877i	−0.604567	+	0.126649i
$406$	−2.08331	−	2.40899i	−0.103393	−	0.119556i
$407$	0.000777043	−	0.00264637i	3.85166e−5	−	0.000131175i
$408$	0.254953	−	0.0565375i	0.0126221	−	0.00279902i
$409$	11.6155	−	8.27134i	0.574348	−	0.408992i	−0.255640	−	0.966772i	$-0.582286\pi$
$409$	11.6155	−	8.27134i	0.574348	−	0.408992i	0.829989	+	0.557780i	$0.188347\pi$
$410$	−8.37729	+	10.6526i	−0.413725	+	0.526094i
$411$	4.58880	−	8.48477i	0.226349	−	0.418523i
$412$	0.944199	−	0.818153i	0.0465173	−	0.0403075i
$413$	25.3693	−	19.9108i	1.24834	−	0.979745i
$414$	14.3821	+	0.392545i	0.706844	+	0.0192925i
$415$	−9.78548	−	16.9490i	−0.480351	−	0.831992i
$416$	0.757682	−	0.146031i	0.0371484	−	0.00715977i
$417$	−33.0338	+	0.919415i	−1.61767	+	0.0450239i
$418$	−0.00797509	−	0.0199208i	−0.000390074	−	0.000974358i
$419$	−1.84500	+	4.03998i	−0.0901340	+	0.197366i	−0.949330	−	0.314280i	$-0.898237\pi$
$419$	−1.84500	+	4.03998i	−0.0901340	+	0.197366i	0.859196	+	0.511646i	$0.170964\pi$
$420$	−5.92359	+	2.23002i	−0.289041	+	0.108814i
$421$	13.5092	+	3.96666i	0.658398	+	0.193323i	0.593830	−	0.804590i	$-0.297615\pi$
$421$	13.5092	+	3.96666i	0.658398	+	0.193323i	0.0645675	+	0.997913i	$0.479433\pi$
$422$	2.68242	−	5.20316i	0.130578	−	0.253286i
$423$	10.9457	+	16.7341i	0.532198	+	0.813638i
$424$	1.96074	−	8.08226i	0.0952217	−	0.392509i
$425$	0.457809	+	0.0882355i	0.0222070	+	0.00428005i
$426$	−5.15323	−	11.9013i	−0.249675	−	0.576621i
$427$	29.6970	−	13.5273i	1.43714	−	0.654634i
$428$	1.91338	−	0.873811i	0.0924866	−	0.0422372i
$429$	0.00453095	−	0.00342037i	0.000218756	−	0.000165137i
$430$	10.1194	+	10.6129i	0.488001	+	0.511800i
$431$	12.1890	−	30.4468i	0.587126	−	1.46657i	−0.275788	−	0.961218i	$-0.588939\pi$
$431$	12.1890	−	30.4468i	0.587126	−	1.46657i	0.862914	−	0.505351i	$-0.168637\pi$
$432$	−4.92995	+	1.64181i	−0.237193	+	0.0789917i
$433$	−6.46494	−	0.929518i	−0.310685	−	0.0446698i	−0.0147912	−	0.999891i	$-0.504708\pi$
$433$	−6.46494	−	0.929518i	−0.310685	−	0.0446698i	−0.295894	+	0.955221i	$0.595617\pi$
$434$	−14.0566	−	19.7804i	−0.674738	−	0.949488i
$435$	0.756534	+	2.77863i	0.0362730	+	0.133225i
$436$	−1.60305	−	2.77656i	−0.0767720	−	0.132973i
$437$	14.2939	+	19.5609i	0.683772	+	0.935725i
$438$	12.2494	+	17.9425i	0.585299	+	0.857324i
$439$	33.8946	+	11.7310i	1.61770	+	0.559892i	0.977977	−	0.208712i	$-0.0669273\pi$
$439$	33.8946	+	11.7310i	1.61770	+	0.559892i	0.639724	+	0.768604i	$0.279048\pi$
$440$	0.00493554	+	0.00317188i	0.000235292	+	0.000151213i
$441$	−6.03936	−	20.1128i	−0.287588	−	0.957754i
$442$	−0.0483296	+	0.105827i	−0.00229880	+	0.00503368i
$443$	15.0986	+	19.1994i	0.717354	+	0.912190i	0.998878	−	0.0473640i	$-0.0150821\pi$
$443$	15.0986	+	19.1994i	0.717354	+	0.912190i	−0.281523	+	0.959554i	$0.590840\pi$
$444$	−0.346750	−	1.06986i	−0.0164560	−	0.0507733i
$445$	0.629964	+	13.2246i	0.0298632	+	0.626905i
$446$	12.0910	−	16.9794i	0.572526	−	0.804000i
$447$	38.0013	+	6.23305i	1.79740	+	0.294813i
$448$	−2.35281	+	1.21007i	−0.111160	+	0.0571704i
$449$	12.6594	+	10.9695i	0.597436	+	0.517681i	0.900253	−	0.435368i	$-0.143382\pi$
$449$	12.6594	+	10.9695i	0.597436	+	0.517681i	−0.302817	+	0.953049i	$0.597927\pi$
$450$	−9.24167	−	0.807447i	−0.435657	−	0.0380634i
$451$	−0.00396168	+	0.0414885i	−0.000186548	+	0.00195362i
$452$	5.46809	−	0.260477i	0.257197	−	0.0122518i
$453$	30.4044	+	6.48600i	1.42852	+	0.304739i
$454$	−0.392693	+	0.0564607i	−0.0184300	+	0.00264983i
$455$	0.797045	−	2.70477i	0.0373660	−	0.126801i
$456$	−7.26578	−	4.87509i	−0.340252	−	0.228297i
$457$	−1.62810	+	34.1780i	−0.0761592	+	1.59878i	0.560847	+	0.827919i	$0.310476\pi$
$457$	−1.62810	+	34.1780i	−0.0761592	+	1.59878i	−0.637006	+	0.770859i	$0.719827\pi$
$458$	−8.19219	+	1.57891i	−0.382796	+	0.0737778i
$459$	0.229518	−	0.749066i	0.0107130	−	0.0349634i
$460$	−6.28577	−	2.08958i	−0.293076	−	0.0974271i
$461$	28.3168			1.31884			0.659421	−	0.751774i	$-0.270801\pi$
$461$	28.3168			1.31884			0.659421	+	0.751774i	$0.270801\pi$
$462$	−0.0116175	+	0.0156183i	−0.000540494	+	0.000726631i
$463$	−21.0074	−	13.5007i	−0.976298	−	0.627428i	−0.0478355	−	0.998855i	$-0.515232\pi$
$463$	−21.0074	−	13.5007i	−0.976298	−	0.627428i	−0.928462	+	0.371427i	$0.878869\pi$
$464$	0.447396	+	1.11754i	0.0207698	+	0.0518806i
$465$	3.72566	+	21.6231i	0.172773	+	1.00275i
$466$	16.6335	+	6.65906i	0.770533	+	0.308475i
$467$	1.79510	+	7.39950i	0.0830673	+	0.342408i	0.998146	−	0.0608677i	$-0.0193868\pi$
$467$	1.79510	+	7.39950i	0.0830673	+	0.342408i	−0.915079	+	0.403276i	$0.867872\pi$
$468$	0.739487	−	2.19359i	0.0341828	−	0.101399i
$469$	−10.5628	−	5.45849i	−0.487744	−	0.252050i
$470$	−2.59366	−	8.83320i	−0.119637	−	0.407445i
$471$	10.5286	+	7.81565i	0.485131	+	0.360126i
$472$	−11.5188	+	3.98670i	−0.530196	+	0.183503i
$473$	0.0438262	+	0.0106321i	0.00201513	+	0.000488865i
$474$	7.09805	−	3.91300i	0.326024	−	0.179730i
$475$	−8.44549	−	13.1414i	−0.387505	−	0.602970i
$476$	0.0571540	−	0.394792i	0.00261965	−	0.0180953i
$477$	−18.1953	−	17.0716i	−0.833104	−	0.781655i
$478$	9.62750	−	0.919315i	0.440352	−	0.0420485i
$479$	14.6975	+	11.5583i	0.671547	+	0.528111i	0.894697	−	0.446674i	$-0.147391\pi$
$479$	14.6975	+	11.5583i	0.671547	+	0.528111i	−0.223150	+	0.974784i	$0.571634\pi$
$480$	2.39138	−	0.0665582i	0.109151	−	0.00303795i
$481$	0.473474	+	0.163871i	0.0215885	+	0.00747187i
$482$	4.76470			0.217026
$483$	8.34092	−	20.3330i	0.379525	−	0.925181i
$484$	−11.0000			−0.499999
$485$	−8.81530	−	3.05100i	−0.400282	−	0.138539i
$486$	−3.00633	+	15.2958i	−0.136370	+	0.693832i
$487$	−22.5050	−	17.6981i	−1.01980	−	0.801978i	−0.0394430	−	0.999222i	$-0.512558\pi$
$487$	−22.5050	−	17.6981i	−1.01980	−	0.801978i	−0.980354	+	0.197244i	$0.936801\pi$
$488$	−12.2782	+	1.17243i	−0.555808	+	0.0530732i
$489$	−8.90549	−	2.80732i	−0.402720	−	0.126951i
$490$	−0.0187785	+	9.66836i	−0.000848325	+	0.436772i
$491$	4.27600	+	6.65359i	0.192973	+	0.300272i	0.924235	−	0.381825i	$-0.124704\pi$
$491$	4.27600	+	6.65359i	0.192973	+	0.300272i	−0.731261	+	0.682097i	$0.761068\pi$
$492$	8.20457	+	14.8828i	0.369891	+	0.670969i
$493$	−0.176380	−	0.0427893i	−0.00794375	−	0.00192713i
$494$	3.68362	−	1.27491i	0.165734	−	0.0573610i
$495$	0.0155786	−	0.00819077i	0.000700208	−	0.000368148i
$496$	2.58399	+	8.80026i	0.116025	+	0.395143i
$497$	−19.7891	+	0.923409i	−0.887661	+	0.0414206i
$498$	−24.3569	+	3.01172i	−1.09146	+	0.134959i
$499$	1.72925	+	7.12807i	0.0774120	+	0.319096i	0.997331	−	0.0730117i	$-0.0232611\pi$
$499$	1.72925	+	7.12807i	0.0774120	+	0.319096i	−0.919919	+	0.392108i	$0.871746\pi$
$500$	10.3764	+	4.15409i	0.464048	+	0.185777i
$501$	2.81059	−	0.484266i	0.125568	−	0.0216354i
$502$	3.08645	+	7.70958i	0.137755	+	0.344095i
$503$	−29.6215	−	19.0366i	−1.32076	−	0.848798i	−0.325448	−	0.945560i	$-0.605515\pi$
$503$	−29.6215	−	19.0366i	−1.32076	−	0.848798i	−0.995308	+	0.0967622i	$0.969151\pi$
$504$	−0.321531	+	7.93074i	−0.0143221	+	0.353263i
$505$	−8.57805			−0.381718
$506$	−0.0197365	+	0.00504506i	−0.000877396	+	0.000224280i
$507$	−12.1142	−	17.7445i	−0.538013	−	0.788060i
$508$	−8.87775	+	1.71105i	−0.393886	+	0.0759154i
$509$	0.763199	−	16.0215i	0.0338282	−	0.710141i	−0.916714	−	0.399545i	$-0.869168\pi$
$509$	0.763199	−	16.0215i	0.0338282	−	0.710141i	0.950542	−	0.310596i	$-0.100529\pi$
$510$	−0.200968	+	0.299521i	−0.00889902	+	0.0132630i
$511$	32.2578	−	7.79249i	1.42700	−	0.344719i
$512$	0.989821	−	0.142315i	0.0437443	−	0.00628949i
$513$	−23.4707	+	11.7538i	−1.03626	+	0.518941i
$514$	3.87917	−	0.184787i	0.171103	−	0.00815062i
$515$	−0.164029	+	1.71779i	−0.00722799	+	0.0756949i
$516$	17.2037	−	6.49564i	0.757349	−	0.285955i
$517$	−0.0213968	−	0.0185405i	−0.000941032	−	0.000815409i
$518$	−1.71590	−	0.0834088i	−0.0753925	−	0.00366477i
$519$	4.59516	−	28.0156i	0.201705	−	1.22975i
$520$	−0.618207	+	0.868150i	−0.0271102	+	0.0380709i
$521$	−1.62944	−	34.2061i	−0.0713869	−	1.49860i	−0.696215	−	0.717833i	$-0.745134\pi$
$521$	−1.62944	−	34.2061i	−0.0713869	−	1.49860i	0.624828	−	0.780762i	$-0.285169\pi$
$522$	3.57857	+	0.485148i	0.156630	+	0.0212344i
$523$	−5.62579	−	7.15378i	−0.245999	−	0.312813i	0.647336	−	0.762205i	$-0.275883\pi$
$523$	−5.62579	−	7.15378i	−0.245999	−	0.312813i	−0.893335	+	0.449392i	$0.851641\pi$
$524$	−4.09719	+	8.97160i	−0.178987	+	0.391926i
$525$	−6.15284	+	12.7652i	−0.268532	+	0.557119i
$526$	9.22712	+	5.92991i	0.402322	+	0.258556i
$527$	−1.30680	−	0.452288i	−0.0569252	−	0.0197020i
$528$	0.00607621	−	0.00414826i	0.000264433	−	0.000180530i
$529$	20.1786	−	11.0373i	0.877332	−	0.479884i
$530$	5.74350	+	9.94803i	0.249482	+	0.432115i
$531$	−6.63117	+	35.9614i	−0.287768	+	1.56059i
$532$	−10.8947	+	7.74216i	−0.472346	+	0.335665i
$533$	−7.49396	−	1.07747i	−0.324600	−	0.0466704i
$534$	15.5791	+	5.73938i	0.674175	+	0.248367i
$535$	−1.07979	+	2.69719i	−0.0466834	+	0.116610i
$536$	3.10116	+	3.25241i	0.133950	+	0.140483i
$537$	3.69298	+	4.89208i	0.159364	+	0.211109i
$538$	20.6375	−	9.42484i	0.889747	−	0.406334i
$539$	0.0160267	+	0.0250448i	0.000690317	+	0.00107876i
$540$	3.36321	−	6.34010i	0.144730	−	0.272835i
$541$	−30.8074	−	5.93763i	−1.32451	−	0.255279i	−0.522527	−	0.852623i	$-0.675011\pi$
$541$	−30.8074	−	5.93763i	−1.32451	−	0.255279i	−0.801985	+	0.597344i	$0.796223\pi$
$542$	−0.644540	+	2.65683i	−0.0276854	+	0.114121i
$543$	−11.3976	−	6.88445i	−0.489120	−	0.295440i
$544$	−0.0690882	+	0.134012i	−0.00296213	+	0.00574574i
$545$	4.24887	+	1.24758i	0.182002	+	0.0534405i
$546$	−2.73357	−	2.24302i	−0.116986	−	0.0959925i
$547$	−4.95859	+	10.8578i	−0.212014	+	0.464246i	−0.985523	−	0.169539i	$-0.945772\pi$
$547$	−4.95859	+	10.8578i	−0.212014	+	0.464246i	0.773510	+	0.633785i	$0.218499\pi$
$548$	2.06987	+	5.17028i	0.0884204	+	0.220863i
$549$	−15.0998	+	33.7810i	−0.644443	+	1.44174i
$550$	0.0128977	−	0.00248583i	0.000549960	−	0.000105996i
$551$	3.04053	+	5.26634i	0.129531	+	0.224354i
$552$	−5.48669	+	6.23668i	−0.233529	+	0.265451i
$553$	−1.75008	−	12.2565i	−0.0744209	−	0.521201i
$554$	12.9793	−	11.2467i	0.551439	−	0.477825i
$555$	1.36634	+	0.738954i	0.0579979	+	0.0313668i
$556$	11.7941	−	14.9975i	0.500182	−	0.636034i
$557$	−32.7900	+	23.3497i	−1.38936	+	0.989357i	−0.391761	+	0.920067i	$0.628134\pi$
$557$	−32.7900	+	23.3497i	−1.38936	+	0.989357i	−0.997597	+	0.0692898i	$0.977927\pi$
$558$	26.7911	+	6.27150i	1.13416	+	0.265494i
$559$	−2.30804	+	7.86048i	−0.0976199	+	0.332463i
$560$	1.19856	−	3.45216i	0.0506484	−	0.145880i
$561$	−2.19338e−5		0.00110905i	−9.26045e−7		4.68241e-5i
$562$	−11.3594	−	10.8312i	−0.479168	−	0.456886i
$563$	11.1641	+	32.2566i	0.470511	+	1.35945i	0.891761	+	0.452508i	$0.149470\pi$
$563$	11.1641	+	32.2566i	0.470511	+	1.35945i	−0.421249	+	0.906945i	$0.638408\pi$
$564$	−11.4684	−	1.32442i	−0.482908	−	0.0557680i
$565$	−5.21774	+	5.47221i	−0.219512	+	0.230217i
$566$	2.42151	+	5.30237i	0.101784	+	0.222875i
$567$	20.2242	+	12.5691i	0.849337	+	0.527851i
$568$	7.18440	+	2.10953i	0.301451	+	0.0885139i
$569$	−3.27043	−	4.15869i	−0.137104	−	0.174342i	0.712653	−	0.701517i	$-0.247494\pi$
$569$	−3.27043	−	4.15869i	−0.137104	−	0.174342i	−0.849757	+	0.527175i	$0.823251\pi$
$570$	11.9096	−	2.05204i	0.498840	−	0.0859503i
$571$	−15.9370	−	12.5330i	−0.666941	−	0.524488i	0.226305	−	0.974056i	$-0.427335\pi$
$571$	−15.9370	−	12.5330i	−0.666941	−	0.524488i	−0.893246	+	0.449568i	$0.851578\pi$
$572$	−0.000155955		0.00327391i	−6.52083e−6		0.000136889i
$573$	−2.77033	−	10.1750i	−0.115732	−	0.425066i
$574$	25.6989	−	3.66947i	1.07265	−	0.153161i
$575$	−13.4134	+	6.32560i	−0.559377	+	0.263796i
$576$	1.09253	−	2.79399i	0.0455220	−	0.116416i
$577$	−4.80123	−	24.9111i	−0.199878	−	1.03706i	−0.933791	−	0.357820i	$-0.883520\pi$
$577$	−4.80123	−	24.9111i	−0.199878	−	1.03706i	0.733913	−	0.679244i	$-0.237692\pi$
$578$	7.77943	+	15.0900i	0.323582	+	0.627661i
$579$	−2.16970	+	32.1549i	−0.0901698	+	1.33631i
$580$	−1.51239	−	0.690687i	−0.0627987	−	0.0286792i
$581$	−8.87378	+	36.4238i	−0.368146	+	1.51111i
$582$	−7.83384	+	8.68751i	−0.324723	+	0.360109i
$583$	0.0313996	+	0.0161876i	0.00130044	+	0.000670422i
$584$	−12.4862	−	1.19229i	−0.516683	−	0.0493372i
$585$	1.35158	+	2.89758i	0.0558810	+	0.119800i
$586$	−0.698852	+	3.62599i	−0.0288693	+	0.149788i
$587$	13.0477	−	15.0578i	0.538536	−	0.621503i	−0.419638	−	0.907692i	$-0.637843\pi$
$587$	13.0477	−	15.0578i	0.538536	−	0.621503i	0.958173	+	0.286188i	$0.0923883\pi$
$588$	11.1554	+	4.74953i	0.460039	+	0.195867i
$589$	19.2473	+	42.1458i	0.793073	+	1.73659i
$590$	7.71457	−	14.9642i	0.317604	−	0.616065i
$591$	42.2892	−	13.7063i	1.73955	−	0.563801i
$592$	0.602805	+	0.241327i	0.0247751	+	0.00991846i
$593$	−1.01378	+	0.0968038i	−0.0416308	+	0.00397526i	−0.115851	−	0.993267i	$-0.536959\pi$
$593$	−1.01378	+	0.0968038i	−0.0416308	+	0.00397526i	0.0742199	+	0.997242i	$0.476353\pi$
$594$	−0.00184031	−	0.0219947i	−7.55089e−5	−	0.000902455i
$595$	0.319158	+	0.449118i	0.0130842	+	0.0184120i
$596$	−16.8028	+	14.5597i	−0.688268	+	0.596388i
$597$	2.06178	+	27.2836i	0.0843831	+	1.11664i
$598$	−0.744844	−	3.62486i	−0.0304589	−	0.148231i
$599$	−6.73821	−	3.89031i	−0.275316	−	0.158954i	0.355985	−	0.934492i	$-0.384145\pi$
$599$	−6.73821	−	3.89031i	−0.275316	−	0.158954i	−0.631301	+	0.775538i	$0.717479\pi$
$600$	3.77199	−	3.80248i	0.153991	−	0.155236i
$601$	19.3264	−	30.0724i	0.788339	−	1.22668i	−0.181609	−	0.983371i	$-0.558131\pi$
$601$	19.3264	−	30.0724i	0.788339	−	1.22668i	0.969949	−	0.243309i	$-0.0782330\pi$
$602$	0.0272788	−	28.0898i	0.00111180	−	1.14486i
$603$	13.0757	−	3.28383i	0.532485	−	0.133728i
$604$	−14.1088	+	11.0953i	−0.574081	+	0.451462i
$605$	10.9958	−	10.4845i	0.447043	−	0.426254i
$606$	−4.19468	+	9.90550i	−0.170397	+	0.402383i
$607$	−33.5368	−	23.8814i	−1.36122	−	0.969318i	−0.999311	−	0.0371033i	$-0.988187\pi$
$607$	−33.5368	−	23.8814i	−1.36122	−	0.969318i	−0.361905	−	0.932215i	$-0.617874\pi$
$608$	4.84704	−	1.42322i	0.196574	−	0.0577192i
$609$	2.62891	−	4.84965i	0.106529	−	0.196518i
$610$	11.1561	−	12.8748i	0.451695	−	0.521284i
$611$	3.54917	−	3.72226i	0.143584	−	0.150586i
$612$	0.247598	+	0.378534i	0.0100085	+	0.0153013i
$613$	−0.173824	−	3.64901i	−0.00702068	−	0.147382i	−0.999656	−	0.0262389i	$-0.991647\pi$
$613$	−0.173824	−	3.64901i	−0.00702068	−	0.147382i	0.992635	−	0.121143i	$-0.0386561\pi$
$614$	−1.85937	−	7.66443i	−0.0750381	−	0.309311i
$615$	−22.3868	−	7.05708i	−0.902722	−	0.284569i
$616$	−0.00263892	−	0.0109241i	−0.000106325	−	0.000440144i
$617$	−35.0261	−	5.03599i	−1.41010	−	0.202741i	−0.605161	−	0.796103i	$-0.706891\pi$
$617$	−35.0261	−	5.03599i	−1.41010	−	0.202741i	−0.804936	+	0.593362i	$0.797800\pi$
$618$	1.90341	+	1.02941i	0.0765663	+	0.0414091i
$619$	−0.254816	−	1.32211i	−0.0102419	−	0.0531402i	0.976448	−	0.215752i	$-0.0692203\pi$
$619$	−0.254816	−	1.32211i	−0.0102419	−	0.0531402i	−0.986690	+	0.162612i	$0.948008\pi$
$620$	−10.9708	−	6.33402i	−0.440600	−	0.254380i
$621$	8.16317	+	23.5449i	0.327577	+	0.944825i
$622$			21.5001i			0.862074i
$623$	16.6266	−	19.1505i	0.666129	−	0.767247i
$624$	0.700192	+	1.13840i	0.0280301	+	0.0455725i
$625$	0.0220427	−	0.00882458i	0.000881709	−	0.000352983i
$626$	7.08854	+	9.95446i	0.283315	+	0.397860i
$627$	0.0274003	−	0.0251107i	0.00109426	−	0.00100282i
$628$	−7.35705	+	1.78480i	−0.293578	+	0.0712213i
$629$	−0.0823583	+	0.0529284i	−0.00328384	+	0.00211040i
$630$	−7.23766	−	8.23419i	−0.288355	−	0.328058i
$631$	9.86148	−	2.89559i	0.392579	−	0.115272i	−0.0794843	−	0.996836i	$-0.525327\pi$
$631$	9.86148	−	2.89559i	0.392579	−	0.115272i	0.472064	+	0.881564i	$0.343509\pi$
$632$	−0.885606	+	4.59496i	−0.0352275	+	0.182778i
$633$	10.0723	+	1.16319i	0.400339	+	0.0462326i
$634$	0.246917	−	1.01781i	0.00980633	−	0.0404222i
$635$	7.24352	−	10.1721i	0.287450	−	0.403667i
$636$	14.2961	−	1.76770i	0.566876	−	0.0700940i
$637$	−4.68297	+	2.69160i	−0.185546	+	0.106645i
$638$	−0.00506118		0.000727688i	−0.000200374		2.88094e-5i
$639$	16.1320	−	15.6317i	0.638172	−	0.618381i
$640$	−0.853800	+	1.08569i	−0.0337494	+	0.0429158i
$641$	−16.9896	−	32.9553i	−0.671050	−	1.30166i	−0.940878	−	0.338747i	$-0.889997\pi$
$641$	−16.9896	−	32.9553i	−0.671050	−	1.30166i	0.269828	−	0.962909i	$-0.413033\pi$
$642$	2.58656	+	2.56582i	0.102083	+	0.101265i
$643$		−	1.37976i		−	0.0544125i	−0.999630	−	0.0272062i	$-0.991339\pi$
$643$		−	1.37976i		−	0.0544125i	0.999630	−	0.0272062i	$-0.00866108\pi$
$644$	5.94121	+	11.2117i	0.234116	+	0.441803i
$645$	−11.0059	+	22.8906i	−0.433357	+	0.901316i
$646$	−0.249113	+	0.719766i	−0.00980123	+	0.0283188i
$647$	−34.5324	+	17.8027i	−1.35761	+	0.699897i	−0.974622	−	0.223856i	$-0.928135\pi$
$647$	−34.5324	+	17.8027i	−1.35761	+	0.699897i	−0.382988	+	0.923753i	$0.625105\pi$
$648$	−5.67662	−	6.98398i	−0.222999	−	0.274357i
$649$	−0.00492161	−	0.0515414i	−0.000193190	−	0.00202318i
$650$	0.339577	+	2.36181i	0.0133193	+	0.0926378i
$651$	23.4519	−	34.8792i	0.919153	−	1.36702i
$652$	4.53520	−	2.91460i	0.177612	−	0.114144i
$653$	19.9267	+	14.1897i	0.779793	+	0.555288i	0.899190	−	0.437559i	$-0.144157\pi$
$653$	19.9267	+	14.1897i	0.779793	+	0.555288i	−0.119397	+	0.992847i	$0.538096\pi$
$654$	3.51835	−	4.29632i	0.137578	−	0.167999i
$655$	−4.45552	−	12.8734i	−0.174092	−	0.503004i
$656$	−9.63446	−	1.85689i	−0.376163	−	0.0724994i
$657$	−21.5795	+	30.8264i	−0.841895	+	1.20265i
$658$	−8.09593	+	15.6665i	−0.315612	+	0.610745i
$659$	−22.9057	−	35.6420i	−0.892281	−	1.38842i	−0.921306	−	0.388837i	$-0.872877\pi$
$659$	−22.9057	−	35.6420i	−0.892281	−	1.38842i	0.0290256	−	0.999579i	$-0.490760\pi$
$660$	−0.00212004	+	0.00993813i	−8.25226e−5	+	0.000386841i
$661$	10.9381	−	27.3221i	0.425444	−	1.06271i	−0.548547	−	0.836120i	$-0.684819\pi$
$661$	10.9381	−	27.3221i	0.425444	−	1.06271i	0.973991	−	0.226588i	$-0.0727570\pi$
$662$	−26.2638	+	18.7024i	−1.02077	+	0.726888i
$663$	−0.201050	−	0.0135662i	−0.00780815	−	0.000526867i
$664$	7.66065	−	11.9202i	0.297291	−	0.462593i
$665$	3.51125	−	18.1233i	0.136160	−	0.702793i
$666$	1.52145	−	1.21643i	0.0589549	−	0.0471357i
$667$	5.33283	−	2.21119i	0.206488	−	0.0856177i
$668$	−0.823304	+	1.42600i	−0.0318546	+	0.0551738i
$669$	34.9109	+	9.20389i	1.34973	+	0.355843i
$670$	−6.19997	−	0.295341i	−0.239526	−	0.0114100i
$671$	0.00745603	−	0.0518578i	0.000287837	−	0.00200195i
$672$	−3.40028	−	3.07215i	−0.131169	−	0.118511i
$673$	2.53091	+	17.6028i	0.0975593	+	0.678540i	0.978641	+	0.205576i	$0.0659068\pi$
$673$	2.53091	+	17.6028i	0.0975593	+	0.678540i	−0.881082	+	0.472964i	$0.843184\pi$
$674$	−2.38708	+	0.579099i	−0.0919469	+	0.0223061i
$675$	−4.34583	−	15.4692i	−0.167271	−	0.595409i
$676$	12.3484	+	1.17913i	0.474939	+	0.0453512i
$677$	−25.9182	−	24.7129i	−0.996117	−	0.949796i	0.00262200	−	0.999997i	$-0.499165\pi$
$677$	−25.9182	−	24.7129i	−0.996117	−	0.949796i	−0.998739	+	0.0502008i	$0.984014\pi$
$678$	3.76755	+	8.70110i	0.144692	+	0.334164i
$679$	8.17258	+	15.8905i	0.313635	+	0.609820i
$680$	−0.0586701	−	0.199812i	−0.00224989	−	0.00766244i
$681$	−0.331745	−	0.601773i	−0.0127125	−	0.0230600i
$682$	−0.0389146	+	0.00185373i	−0.00149012	+	7.09831e-5i
$683$	−3.08024	−	3.23046i	−0.117862	−	0.123610i	0.662159	−	0.749363i	$-0.269640\pi$
$683$	−3.08024	−	3.23046i	−0.117862	−	0.123610i	−0.780021	+	0.625753i	$0.784792\pi$
$684$	3.45424	−	14.7561i	0.132076	−	0.564214i
$685$	−6.99706	−	3.19545i	−0.267344	−	0.122092i
$686$	12.8194	−	13.3665i	0.489448	−	0.510333i
$687$	−7.57059	−	12.3086i	−0.288836	−	0.469601i
$688$	−3.47247	+	10.0330i	−0.132387	+	0.382506i
$689$	−3.20869	+	5.55762i	−0.122241	+	0.211728i
$690$	−0.459801	−	11.4639i	−0.0175043	−	0.436422i
$691$	21.6918	−	12.5238i	0.825196	−	0.476427i	−0.0270091	−	0.999635i	$-0.508598\pi$
$691$	21.6918	−	12.5238i	0.825196	−	0.476427i	0.852205	+	0.523208i	$0.175265\pi$
$692$	10.7338	+	12.3874i	0.408037	+	0.470899i
$693$	−0.0324156	−	0.00926932i	−0.00123137	−	0.000352113i
$694$	−0.673969	+	4.68756i	−0.0255835	+	0.177937i
$695$	2.50496	+	26.2332i	0.0950186	+	0.995080i
$696$	−1.53713	+	1.40869i	−0.0582649	+	0.0533962i
$697$	1.07066	−	1.02087i	0.0405540	−	0.0386682i
$698$	−17.0029	−	8.76559i	−0.643568	−	0.331782i
$699$	−0.613624	+	31.0270i	−0.0232094	+	1.17355i
$700$	−3.39146	−	7.44540i	−0.128185	−	0.281410i
$701$	−34.3689	−	29.7808i	−1.29809	−	1.12480i	−0.984526	−	0.175239i	$-0.943930\pi$
$701$	−34.3689	−	29.7808i	−1.29809	−	1.12480i	−0.313568	−	0.949566i	$-0.601524\pi$
$702$	4.00691	−	0.143815i	0.151231	−	0.00542793i
$703$	3.18767	+	0.773321i	0.120225	+	0.0291664i
$704$	−0.000403767		0.00422844i	−1.52176e−5		0.000159365i
$705$	12.7264	−	9.60706i	0.479305	−	0.361823i
$706$	5.83450	−	19.8705i	0.219584	−	0.747836i
$707$	11.8811	+	11.3507i	0.446836	+	0.426887i
$708$	−13.5074	−	16.2259i	−0.507641	−	0.609807i
$709$	16.5875	−	6.64061i	0.622955	−	0.249393i	−0.0386422	−	0.999253i	$-0.512303\pi$
$709$	16.5875	−	6.64061i	0.622955	−	0.249393i	0.661597	+	0.749860i	$0.269879\pi$
$710$	−9.19233	+	4.73898i	−0.344982	+	0.177851i
$711$	10.6833	+	9.10759i	0.400656	+	0.341561i
$712$	−8.30135	+	4.79279i	−0.311106	+	0.179617i
$713$	42.0494	−	12.9089i	1.57476	−	0.483443i
$714$	0.674687	−	0.148929i	0.0252495	−	0.00557352i
$715$	−0.00296458	−	0.00342131i	−0.000110869	−	0.000127950i
$716$	−3.53485	−	0.168386i	−0.132104	−	0.00629287i
$717$	7.37993	+	15.0379i	0.275608	+	0.561601i
$718$	13.1319	+	18.4412i	0.490078	+	0.688218i
$719$	−27.0579	+	21.2786i	−1.00909	+	0.793558i	−0.978557	−	0.205976i	$-0.933963\pi$
$719$	−27.0579	+	21.2786i	−1.00909	+	0.793558i	−0.0305336	+	0.999534i	$0.509721\pi$
$720$	1.57094	+	3.83426i	0.0585454	+	0.142894i
$721$	2.50022	−	2.16220i	0.0931129	−	0.0805246i
$722$	5.93024	−	2.70825i	0.220701	−	0.100791i
$723$	2.91513	+	7.72069i	0.108415	+	0.287136i
$724$	7.26488	−	2.51440i	0.269997	−	0.0934469i
$725$	−3.51768	+	1.21748i	−0.130643	+	0.0452161i
$726$	−6.72998	−	17.8243i	−0.249773	−	0.661522i
$727$	41.6262	−	19.0101i	1.54383	−	0.705044i	0.552147	−	0.833747i	$-0.313809\pi$
$727$	41.6262	−	19.0101i	1.54383	−	0.705044i	0.991683	+	0.128703i	$0.0410813\pi$
$728$	2.00501	−	0.384416i	0.0743107	−	0.0142474i
$729$	−26.6246	+	4.48680i	−0.986096	+	0.166178i
$730$	13.6179	−	10.7092i	0.504020	−	0.396365i
$731$	−0.928527	−	1.30393i	−0.0343428	−	0.0482277i
$732$	−9.41181	−	19.1782i	−0.347871	−	0.708848i
$733$	−32.4482	−	1.54570i	−1.19850	−	0.0570917i	−0.561183	−	0.827692i	$-0.689654\pi$
$733$	−32.4482	−	1.54570i	−1.19850	−	0.0570917i	−0.637319	+	0.770600i	$0.719957\pi$
$734$	12.1288	+	13.9974i	0.447684	+	0.516655i
$735$	−15.6781	+	5.88485i	−0.578294	+	0.217066i
$736$	−0.740672	−	4.73829i	−0.0273015	−	0.174656i
$737$	−0.0165313	+	0.00954438i	−0.000608940	+	0.000351572i
$738$	−19.0963	+	22.4002i	−0.702945	+	0.824563i
$739$	2.26420	−	1.16727i	0.0832898	−	0.0429389i	−0.416078	−	0.909329i	$-0.636596\pi$
$739$	2.26420	−	1.16727i	0.0832898	−	0.0429389i	0.499368	+	0.866390i	$0.333566\pi$
$740$	−0.832592	+	0.333320i	−0.0306067	+	0.0122531i
$741$	4.31956	+	5.18890i	0.158683	+	0.190619i
$742$	5.20838	−	21.3786i	0.191206	−	0.784833i
$743$	5.13614	−	17.4921i	0.188427	−	0.641722i	−0.810040	−	0.586374i	$-0.800555\pi$
$743$	5.13614	−	17.4921i	0.188427	−	0.641722i	0.998467	−	0.0553483i	$-0.0176269\pi$
$744$	−12.6790	+	9.57123i	−0.464833	+	0.350898i
$745$	2.91903	−	30.5695i	0.106945	−	1.11998i
$746$	−21.9931	−	5.33546i	−0.805223	−	0.195345i
$747$	−19.7822	−	37.6252i	−0.723792	−	1.37663i
$748$	−0.000484009	0	0.000419396i	−1.76971e−5	0	1.53346e-5i
$749$	5.06457	−	2.30697i	0.185055	−	0.0842948i
$750$	−0.382794	+	19.3554i	−0.0139777	+	0.706761i
$751$	−20.6555	−	10.6487i	−0.753731	−	0.388575i	0.0381334	−	0.999273i	$-0.487859\pi$
$751$	−20.6555	−	10.6487i	−0.753731	−	0.388575i	−0.791864	+	0.610698i	$0.790889\pi$
$752$	4.82391	−	4.59959i	0.175910	−	0.167730i
$753$	−10.6042	+	9.71812i	−0.386439	+	0.354148i
$754$	−0.0882938	−	0.924655i	−0.00321547	−	0.0336739i
$755$	3.52814	−	24.5387i	0.128402	−	0.893056i
$756$	−13.0476	+	4.33116i	−0.474538	+	0.157523i
$757$	4.98556	+	5.75364i	0.181203	+	0.209120i	0.839083	−	0.544003i	$-0.183092\pi$
$757$	4.98556	+	5.75364i	0.181203	+	0.209120i	−0.657880	+	0.753123i	$0.728547\pi$
$758$	−1.97000	+	1.13738i	−0.0715536	+	0.0413115i
$759$	−0.0202501	−	0.0288943i	−0.000735034	−	0.00104880i
$760$	−3.48868	+	6.04257i	−0.126548	+	0.219187i
$761$	3.52947	−	10.1977i	0.127943	−	0.369668i	−0.862777	−	0.505585i	$-0.831277\pi$
$761$	3.52947	−	10.1977i	0.127943	−	0.369668i	0.990720	+	0.135917i	$0.0433981\pi$
$762$	−8.20413	−	13.3386i	−0.297204	−	0.483207i
$763$	−4.23413	−	7.35020i	−0.153286	−	0.266095i
$764$	5.53818	+	2.52920i	0.200364	+	0.0915034i
$765$	−0.608298	−	0.142396i	−0.0219931	−	0.00514833i
$766$	−7.73602	−	8.11331i	−0.279514	−	0.293146i
$767$	9.39487	−	0.447533i	0.339229	−	0.0161595i
$768$	0.836196	+	1.51683i	0.0301736	+	0.0547339i
$769$	−6.57595	−	22.3956i	−0.237135	−	0.807607i	−0.988952	−	0.148235i	$-0.952641\pi$
$769$	−6.57595	−	22.3956i	−0.237135	−	0.807607i	0.751817	−	0.659371i	$-0.229178\pi$
$770$	0.0130500	+	0.00840467i	0.000470291	+	0.000302883i
$771$	2.67277	+	6.17272i	0.0962574	+	0.222305i
$772$	−13.4664	−	12.8402i	−0.484667	−	0.462129i
$773$	19.3523	+	1.84792i	0.696052	+	0.0664650i	0.437084	−	0.899421i	$-0.356011\pi$
$773$	19.3523	+	1.84792i	0.696052	+	0.0664650i	0.258969	+	0.965886i	$0.416617\pi$
$774$	21.0510	+	23.9026i	0.756663	+	0.859160i
$775$	−27.5624	+	6.68655i	−0.990069	+	0.240188i
$776$	−0.961167	−	6.68507i	−0.0345039	−	0.239980i
$777$	−0.914665	−	2.83147i	−0.0328134	−	0.101579i
$778$	−3.02333	+	21.0277i	−0.108392	+	0.753880i
$779$	−49.5097	−	2.35844i	−1.77387	−	0.0844998i
$780$	−1.78497	−	0.470590i	−0.0639123	−	0.0168498i
$781$	−0.0159027	+	0.0275442i	−0.000569042	+	0.000985610i
$782$	0.646715	+	0.323430i	0.0231265	+	0.0115658i
$783$	1.40330	+	6.09552i	0.0501499	+	0.217836i
$784$	−6.22807	+	3.19550i	−0.222431	+	0.114125i
$785$	5.65310	−	8.79639i	0.201768	−	0.313957i
$786$	−17.0443	−	1.15009i	−0.607949	−	0.0410223i
$787$	−15.0049	+	10.6849i	−0.534866	+	0.380876i	−0.815337	−	0.578986i	$-0.803449\pi$
$787$	−15.0049	+	10.6849i	−0.534866	+	0.380876i	0.280471	+	0.959862i	$0.409509\pi$
$788$	−9.53911	+	23.8276i	−0.339817	+	0.848822i
$789$	−3.96348	+	18.5796i	−0.141104	+	0.661452i
$790$	−3.49435	−	5.43731i	−0.124323	−	0.193451i
$791$	14.4679	−	0.675108i	0.514418	−	0.0240041i
$792$	0.0104393	+	0.00730788i	0.000370946	+	0.000259674i
$793$	9.34529	+	1.80116i	0.331861	+	0.0639610i
$794$	2.33444	+	6.74492i	0.0828461	+	0.239368i
$795$	−12.6058	+	15.3931i	−0.447081	+	0.545938i
$796$	−12.8679	−	9.16321i	−0.456092	−	0.324782i
$797$	38.0400	−	24.4468i	1.34745	−	0.865951i	0.349956	−	0.936766i	$-0.386196\pi$
$797$	38.0400	−	24.4468i	1.34745	−	0.865951i	0.997489	+	0.0708151i	$0.0225600\pi$
$798$	−19.2109	−	12.9169i	−0.680059	−	0.457255i
$799$	0.143019	+	0.994720i	0.00505965	+	0.0351907i
$800$	0.293941	+	3.07829i	0.0103924	+	0.108834i
$801$	0.231514	+	28.7558i	0.00818016	+	1.01604i
$802$	−20.3704	+	10.5017i	−0.719305	+	0.370828i
$803$	0.0174257	−	0.0503483i	0.000614940	−	0.00177675i
$804$	−3.37284	+	7.01499i	−0.118951	+	0.247400i
$805$	−16.6252	−	5.54465i	−0.585962	−	0.195423i
$806$		−	7.07719i		−	0.249283i
$807$	27.8984	+	27.6747i	0.982069	+	0.974194i
$808$	−2.84586	−	5.52019i	−0.100117	−	0.194200i
$809$	3.09280	−	3.93282i	0.108737	−	0.138271i	−0.728638	−	0.684899i	$-0.759846\pi$
$809$	3.09280	−	3.93282i	0.108737	−	0.138271i	0.837375	+	0.546628i	$0.184089\pi$
$810$	12.3311	+	1.57074i	0.433272	+	0.0551903i
$811$	14.7135	−	2.11549i	0.516662	−	0.0742848i	0.120948	−	0.992659i	$-0.461406\pi$
$811$	14.7135	−	2.11549i	0.516662	−	0.0742848i	0.395713	+	0.918374i	$0.370497\pi$
$812$	1.18083	+	2.95788i	0.0414389	+	0.103801i
$813$	−4.69945	+	0.581085i	−0.164817	+	0.0203796i
$814$	−0.00159985	+	0.00224667i	−5.60746e−5	+	7.87458e-5i
$815$	−1.75547	+	7.23615i	−0.0614915	+	0.253471i
$816$	−0.259422	−	0.0299590i	−0.00908160	−	0.00104878i
$817$	−10.1502	+	52.6642i	−0.355110	+	1.84249i
$818$	−13.6819	+	4.01738i	−0.478377	+	0.140464i
$819$	1.96213	−	5.80179i	0.0685625	−	0.202731i
$820$	11.4007	−	7.32676i	0.398129	−	0.255862i
$821$	−13.4778	+	3.26968i	−0.470379	+	0.114113i	−0.463940	−	0.885867i	$-0.653565\pi$
$821$	−13.4778	+	3.26968i	−0.470379	+	0.114113i	−0.00643899	+	0.999979i	$0.502050\pi$
$822$	−7.11151	+	6.51727i	−0.248043	+	0.227316i
$823$	−13.5120	−	18.9749i	−0.470998	−	0.661425i	0.508922	−	0.860812i	$-0.330044\pi$
$823$	−13.5120	−	18.9749i	−0.470998	−	0.661425i	−0.979921	+	0.199388i	$0.936105\pi$
$824$	−1.15986	+	0.464338i	−0.0404056	+	0.0161760i
$825$	0.0119191	+	0.0193785i	0.000414968	+	0.000674672i
$826$	−30.4862	+	10.5182i	−1.06075	+	0.365976i
$827$			5.23173i			0.181925i	0.995854	+	0.0909625i	$0.0289943\pi$
$827$			5.23173i			0.181925i	−0.995854	+	0.0909625i	$0.971006\pi$
$828$	−13.4627	−	5.07489i	−0.467863	−	0.176365i
$829$	−25.6142	−	14.7884i	−0.889619	−	0.513622i	−0.0158015	−	0.999875i	$-0.505030\pi$
$829$	−25.6142	−	14.7884i	−0.889619	−	0.513622i	−0.873818	+	0.486253i	$0.838363\pi$
$830$	3.70383	+	19.2173i	0.128562	+	0.667042i
$831$	26.1650	+	14.1507i	0.907654	+	0.490884i
$832$	−0.763773	−	0.109814i	−0.0264790	−	0.00380711i
$833$	0.152229	−	1.04438i	0.00527444	−	0.0361855i
$834$	31.5176	+	9.93544i	1.09137	+	0.344036i
$835$	−0.536184	−	2.21018i	−0.0185554	−	0.0764865i
$836$	0.00102101	+	0.0214336i	3.53123e−5	+	0.000741296i
$837$	6.22894	+	47.2491i	0.215304	+	1.63317i
$838$	3.06487	−	3.21435i	0.105874	−	0.111038i
$839$	−23.5533	+	27.1820i	−0.813151	+	0.938426i	−0.999025	−	0.0441471i	$-0.985943\pi$
$839$	−23.5533	+	27.1820i	−0.813151	+	0.938426i	0.185874	+	0.982574i	$0.440488\pi$
$840$	6.32716	−	0.169952i	0.218308	−	0.00586390i
$841$	−26.4349	+	7.76200i	−0.911549	+	0.267655i
$842$	−11.4688	−	8.16692i	−0.395242	−	0.281451i
$843$	10.6009	−	25.0334i	0.365114	−	0.862197i
$844$	−4.23667	+	4.03966i	−0.145832	+	0.139051i
$845$	−13.4676	+	10.5910i	−0.463300	+	0.364343i
$846$	−4.87051	−	19.3937i	−0.167452	−	0.666769i
$847$	−29.1032	−	0.0282630i	−0.999998	−	0.000971127i
$848$	−4.49635	+	6.99645i	−0.154405	+	0.240259i
$849$	−7.11041	+	7.16788i	−0.244028	+	0.246001i
$850$	−0.403771	−	0.233117i	−0.0138492	−	0.00799586i
$851$	1.12183	−	2.90492i	0.0384557	−	0.0995795i
$852$	0.977269	+	12.9322i	0.0334807	+	0.443050i
$853$	31.6997	−	27.4679i	1.08538	−	0.940483i	0.0869299	−	0.996214i	$-0.472294\pi$
$853$	31.6997	−	27.4679i	1.08538	−	0.940483i	0.998446	+	0.0557310i	$0.0177489\pi$
$854$	−32.4881	+	3.07040i	−1.11172	+	0.105067i
$855$	10.6116	+	18.0429i	0.362910	+	0.617053i
$856$	−2.09394	+	0.199947i	−0.0715694	+	0.00683405i
$857$	46.6276	+	18.6669i	1.59277	+	0.637649i	0.987393	−	0.158291i	$-0.0505983\pi$
$857$	46.6276	+	18.6669i	1.59277	+	0.637649i	0.605376	+	0.795939i	$0.293023\pi$
$858$	−0.00540044	+	0.00175033i	−0.000184368	+	5.97551e-5i
$859$	0.898345	−	1.74255i	0.0306511	−	0.0594549i	−0.873013	−	0.487698i	$-0.837837\pi$
$859$	0.898345	−	1.74255i	0.0306511	−	0.0594549i	0.903664	+	0.428243i	$0.140867\pi$
$860$	−6.09169	−	13.3389i	−0.207725	−	0.454854i
$861$	21.6690	+	39.3973i	0.738478	+	1.34265i
$862$	−21.4768	+	24.7856i	−0.731504	+	0.844200i
$863$	0.703336	−	3.64925i	0.0239418	−	0.124222i	−0.967991	−	0.250983i	$-0.919246\pi$
$863$	0.703336	−	3.64925i	0.0239418	−	0.124222i	0.991933	+	0.126761i	$0.0404582\pi$
$864$	5.19580	+	0.0609164i	0.176765	+	0.00207242i
$865$	−22.5366	−	2.15198i	−0.766267	−	0.0731696i
$866$	5.80536	+	2.99287i	0.197274	+	0.101702i
$867$	−19.6922	+	21.8381i	−0.668781	+	0.741660i
$868$	6.81398	+	23.2899i	0.231281	+	0.790511i
$869$	−0.0180809	−	0.00825725i	−0.000613351	−	0.000280108i
$870$	0.193877	−	2.87325i	0.00657304	−	0.0974123i
$871$	−1.58896	−	3.08216i	−0.0538399	−	0.104435i
$872$	0.606757	+	3.14816i	0.0205474	+	0.106610i
$873$	−18.8701	−	7.37873i	−0.638655	−	0.249732i
$874$	−7.11004	−	23.1602i	−0.240501	−	0.783404i
$875$	27.4427	+	11.0174i	0.927734	+	0.372454i
$876$	−5.70730	−	20.9620i	−0.192832	−	0.708241i
$877$	0.246460	−	5.17384i	0.00832238	−	0.174708i	−0.990879	−	0.134754i	$-0.956976\pi$
$877$	0.246460	−	5.17384i	0.00832238	−	0.174708i	0.999202	−	0.0399545i	$-0.0127213\pi$
$878$	−28.1936	−	22.1717i	−0.951488	−	0.748258i
$879$	−6.30311	+	1.08603i	−0.212598	+	0.0366308i
$880$	−0.00362667	−	0.00461168i	−0.000122255	−	0.000155460i
$881$	−35.9997	−	10.5705i	−1.21286	−	0.356128i	−0.388103	−	0.921616i	$-0.626870\pi$
$881$	−35.9997	−	10.5705i	−1.21286	−	0.356128i	−0.824756	+	0.565488i	$0.808688\pi$
$882$	−0.871067	+	20.9819i	−0.0293303	+	0.706498i
$883$	−8.50601	−	18.6256i	−0.286250	−	0.626800i	0.710813	−	0.703381i	$-0.248327\pi$
$883$	−8.50601	−	18.6256i	−0.286250	−	0.626800i	−0.997063	+	0.0765806i	$0.975600\pi$
$884$	0.0802841	−	0.0841996i	0.00270025	−	0.00283194i
$885$	28.9678	+	3.34530i	0.973741	+	0.112451i
$886$	−7.98865	−	23.0817i	−0.268384	−	0.775445i
$887$	40.1397	+	38.2731i	1.34776	+	1.28509i	0.925570	+	0.378578i	$0.123587\pi$
$887$	40.1397	+	38.2731i	1.34776	+	1.28509i	0.422189	+	0.906508i	$0.361262\pi$
$888$	−0.0222379	+	1.12443i	−0.000746256	+	0.0377334i
$889$	−23.4927	+	4.50419i	−0.787920	+	0.151066i
$890$	3.73002	−	12.7033i	0.125031	−	0.425815i
$891$	0.0345142	−	0.0164388i	0.00115627	−	0.000550720i
$892$	−16.9794	+	12.0910i	−0.568514	+	0.404837i
$893$	20.8140	−	26.4672i	0.696514	−	0.885690i
$894$	−33.8727	−	18.3193i	−1.13287	−	0.612687i
$895$	3.69400	−	3.20087i	0.123477	−	0.106993i
$896$	2.61919	−	0.373986i	0.0875009	−	0.0124940i
$897$	5.41799	−	3.42469i	0.180901	−	0.114347i
$898$	−8.37542	−	14.5066i	−0.279491	−	0.484093i
$899$	10.8412	−	2.08947i	0.361574	−	0.0696877i
$900$	8.46930	+	3.78569i	0.282310	+	0.126190i
$901$	−0.466040	−	1.16411i	−0.0155260	−	0.0387822i
$902$	0.0173134	−	0.0379110i	0.000576472	−	0.00126230i
$903$	45.5333	−	17.1416i	1.51525	−	0.570438i
$904$	−5.25254	−	1.54229i	−0.174697	−	0.0512957i
$905$	−4.86555	+	9.43786i	−0.161736	+	0.313725i
$906$	−26.6108	−	16.0736i	−0.884086	−	0.534009i
$907$	−11.8857	+	48.9933i	−0.394657	+	1.62680i	0.334461	+	0.942410i	$0.391446\pi$
$907$	−11.8857	+	48.9933i	−0.394657	+	1.62680i	−0.729118	+	0.684388i	$0.760069\pi$
$908$	0.389561	+	0.0750818i	0.0129280	+	0.00249168i
$909$	−18.6172	−	0.736676i	−0.617494	−	0.0244340i
$910$	−1.63785	+	2.29532i	−0.0542942	+	0.0760891i
$911$	−28.9733	+	13.2316i	−0.959927	+	0.438384i	−0.832844	−	0.553508i	$-0.813289\pi$
$911$	−28.9733	+	13.2316i	−0.959927	+	0.438384i	−0.127083	+	0.991892i	$0.540562\pi$
$912$	5.27168	+	6.98337i	0.174563	+	0.231243i
$913$	0.0415343	+	0.0435599i	0.00137458	+	0.00144162i
$914$	12.7171	−	31.7657i	0.420643	−	1.05072i
$915$	27.6877	+	10.2002i	0.915326	+	0.337208i
$916$	8.25804	+	1.18733i	0.272853	+	0.0392304i
$917$	−10.8632	+	23.7261i	−0.358735	+	0.783505i
$918$	−0.461890	+	0.632800i	−0.0152446	+	0.0208855i
$919$	7.14545	+	12.3763i	0.235707	+	0.408256i	0.959478	−	0.281784i	$-0.0909263\pi$
$919$	7.14545	+	12.3763i	0.235707	+	0.408256i	−0.723771	+	0.690040i	$0.757593\pi$
$920$	5.25662	+	4.03053i	0.173306	+	0.132883i
$921$	11.2818	−	7.70214i	0.371748	−	0.253794i
$922$	−26.7594	−	9.26150i	−0.881272	−	0.305011i
$923$	−4.86052	−	3.12367i	−0.159986	−	0.102817i
$924$	0.0160868	−	0.0109596i	0.000529216	−	0.000360546i
$925$	−0.834102	+	1.82643i	−0.0274251	+	0.0600526i
$926$	15.4364	+	19.6290i	0.507272	+	0.645048i
$927$	−0.503520	+	3.71409i	−0.0165378	+	0.121987i
$928$	−0.0572777	−	1.20241i	−0.00188023	−	0.0394709i
$929$	−0.316514	+	0.444482i	−0.0103845	+	0.0145830i	−0.819736	−	0.572742i	$-0.805880\pi$
$929$	−0.316514	+	0.444482i	−0.0103845	+	0.0145830i	0.809351	+	0.587325i	$0.199819\pi$
$930$	3.55146	−	21.6524i	0.116457	−	0.710009i
$931$	−28.8446	+	20.4558i	−0.945343	+	0.670412i
$932$	−13.5407	−	11.7331i	−0.443541	−	0.384331i
$933$	−34.8386	+	13.1541i	−1.14056	+	0.430646i
$934$	0.723769	−	7.57965i	0.0236824	−	0.248014i
$935$	0.000883566	0	4.20894e-5i	2.88957e−5	0	1.37647e-6i
$936$	−1.41627	+	1.83108i	−0.0462922	+	0.0598507i
$937$	−37.2373	+	5.35391i	−1.21649	+	0.174905i	−0.720519	−	0.693435i	$-0.756096\pi$
$937$	−37.2373	+	5.35391i	−1.21649	+	0.174905i	−0.495969	+	0.868340i	$0.665187\pi$
$938$	8.19655	+	8.61303i	0.267627	+	0.281225i
$939$	−11.7933	+	17.5765i	−0.384859	+	0.573589i
$940$	−0.438044	+	9.19568i	−0.0142874	+	0.299930i
$941$	−38.9960	+	7.51587i	−1.27123	+	0.245010i	−0.779869	−	0.625943i	$-0.784714\pi$
$941$	−38.9960	+	7.51587i	−1.27123	+	0.245010i	−0.491366	+	0.870953i	$0.663502\pi$
$942$	−7.39326	−	10.8294i	−0.240885	−	0.352840i
$943$	−8.33812	+	46.3110i	−0.271526	+	1.50809i
$944$	12.1892			0.396725
$945$	8.91450	−	16.7657i	0.289989	−	0.545388i
$946$	−0.0379384	−	0.0243815i	−0.00123348	−	0.000792711i
$947$	0.230335	+	0.575350i	0.00748489	+	0.0186964i	0.932063	−	0.362295i	$-0.118007\pi$
$947$	0.230335	+	0.575350i	0.00748489	+	0.0186964i	−0.924578	+	0.380992i	$0.875583\pi$
$948$	−7.98748	+	1.37624i	−0.259421	+	0.0446984i
$949$	8.98522	+	3.59714i	0.291672	+	0.116768i
$950$	3.68285	+	15.1809i	0.119487	+	0.492534i
$951$	1.80032	−	0.222608i	0.0583792	−	0.00721857i
$952$	−0.183134	+	0.354386i	−0.00593542	+	0.0114857i
$953$	5.94713	+	20.2541i	0.192646	+	0.656093i	0.997995	+	0.0632918i	$0.0201599\pi$
$953$	5.94713	+	20.2541i	0.192646	+	0.656093i	−0.805349	+	0.592801i	$0.798022\pi$
$954$	11.6110	+	22.0838i	0.375919	+	0.714988i
$955$	−7.94675	+	2.75040i	−0.257151	+	0.0890008i
$956$	−9.39868	−	2.28009i	−0.303975	−	0.0737435i
$957$	−0.00427566	−	0.00775590i	−0.000138212	−	0.000250713i
$958$	−10.1088	−	15.7297i	−0.326602	−	0.508202i
$959$	5.46307	+	13.6846i	0.176412	+	0.441898i
$960$	−2.28162	−	0.719246i	−0.0736391	−	0.0232136i
$961$	52.8810	−	5.04952i	1.70584	−	0.162888i
$962$	−0.393836	−	0.309716i	−0.0126978	−	0.00998565i
$963$	−2.57513	+	5.76105i	−0.0829825	+	0.185647i
$964$	−4.50264	−	1.55838i	−0.145020	−	0.0501920i
$965$	25.6998			0.827305
$966$	−14.5324	+	16.4866i	−0.467573	+	0.530448i
$967$	−16.0922			−0.517489			−0.258745	−	0.965946i	$-0.583309\pi$
$967$	−16.0922			−0.517489			−0.258745	+	0.965946i	$0.583309\pi$
$968$	10.3950	+	3.59774i	0.334108	+	0.115636i
$969$	−1.31872	+	0.0367033i	−0.0423633	+	0.00117908i
$970$	7.33258	+	5.76640i	0.235435	+	0.185148i
$971$	51.3800	−	4.90620i	1.64886	−	0.157447i	0.771156	−	0.636646i	$-0.219679\pi$
$971$	51.3800	−	4.90620i	1.64886	−	0.157447i	0.877707	+	0.479198i	$0.159073\pi$
$972$	7.84376	−	13.4713i	0.251589	−	0.432092i
$973$	31.2428	−	39.6492i	1.00160	−	1.27110i
$974$	15.4787	+	24.0854i	0.495970	+	0.771745i
$975$	−3.61930	+	1.99524i	−0.115910	+	0.0638990i
$976$	11.9864	+	2.90786i	0.383674	+	0.0930784i
$977$	47.8596	−	16.5644i	1.53116	−	0.529941i	0.573841	−	0.818966i	$-0.305453\pi$
$977$	47.8596	−	16.5644i	1.53116	−	0.529941i	0.957321	+	0.289026i	$0.0933313\pi$
$978$	7.49752	+	5.56562i	0.239744	+	0.177969i
$979$	−0.0114711	−	0.0390671i	−0.000366619	−	0.00124859i
$980$	3.17996	−	9.13047i	0.101580	−	0.291662i
$981$	9.11432	+	3.07255i	0.290998	+	0.0980991i
$982$	−1.86465	−	7.68619i	−0.0595034	−	0.245276i
$983$	−33.5840	−	13.4450i	−1.07116	−	0.428829i	−0.232004	−	0.972715i	$-0.574528\pi$
$983$	−33.5840	−	13.4450i	−1.07116	−	0.428829i	−0.839160	+	0.543885i	$0.816953\pi$
$984$	−2.88564	−	16.7477i	−0.0919907	−	0.533898i
$985$	−13.1754	−	32.9106i	−0.419803	−	1.04862i
$986$	0.152684	+	0.0981242i	0.00486246	+	0.00312491i
$987$	−30.3392	−	3.53354i	−0.965707	−	0.112474i
$988$	−3.89800			−0.124012
$989$	48.3173	+	16.0621i	1.53640	+	0.510746i
$990$	−0.0174008	+	0.00264501i	−0.000553033	+	8.40639e-5i
$991$	28.4894	−	5.49089i	0.904997	−	0.174424i	0.284540	−	0.958664i	$-0.408159\pi$
$991$	28.4894	−	5.49089i	0.904997	−	0.174424i	0.620457	+	0.784240i	$0.286947\pi$
$992$	0.436411	−	9.16139i	0.0138561	−	0.290874i
$993$	−46.3738	−	31.1153i	−1.47163	−	0.987413i
$994$	19.0027	+	5.59975i	0.602729	+	0.177613i
$995$	21.5968	−	3.10515i	0.684665	−	0.0984400i
$996$	24.0023	+	5.12029i	0.760543	+	0.162242i
$997$	27.6730	−	1.31823i	0.876413	−	0.0417487i	0.395448	−	0.918489i	$-0.370589\pi$
$997$	27.6730	−	1.31823i	0.876413	−	0.0417487i	0.480965	+	0.876740i	$0.340286\pi$
$998$	0.697220	−	7.30162i	0.0220701	−	0.231129i
$999$	2.90195	+	1.72111i	0.0918135	+	0.0544536i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.bd.a.59.15	✓	1280
3.2	odd	2	inner	966.2.bd.a.59.40	yes	1280
7.5	odd	6	inner	966.2.bd.a.887.37	yes	1280
21.5	even	6	inner	966.2.bd.a.887.4	yes	1280
23.16	even	11	inner	966.2.bd.a.269.4	yes	1280
69.62	odd	22	inner	966.2.bd.a.269.37	yes	1280
161.131	odd	66	inner	966.2.bd.a.131.40	yes	1280
483.131	even	66	inner	966.2.bd.a.131.15	yes	1280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.bd.a.59.15	✓	1280	1.1	even	1	trivial
966.2.bd.a.59.40	yes	1280	3.2	odd	2	inner
966.2.bd.a.131.15	yes	1280	483.131	even	66	inner
966.2.bd.a.131.40	yes	1280	161.131	odd	66	inner
966.2.bd.a.269.4	yes	1280	23.16	even	11	inner
966.2.bd.a.269.37	yes	1280	69.62	odd	22	inner
966.2.bd.a.887.4	yes	1280	21.5	even	6	inner
966.2.bd.a.887.37	yes	1280	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.bd (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.945001 - 0.327068i) q^{2} +(-0.0481888 - 1.73138i) q^{3} +(0.786053 + 0.618159i) q^{4} +(-1.37494 + 0.131291i) q^{5} +(-0.520741 + 1.65192i) q^{6} +(2.07811 + 1.63751i) q^{7} +(-0.540641 - 0.841254i) q^{8} +(-2.99536 + 0.166866i) q^{9} +O(q^{10})\)	\(q+(-0.945001 - 0.327068i) q^{2} +(-0.0481888 - 1.73138i) q^{3} +(0.786053 + 0.618159i) q^{4} +(-1.37494 + 0.131291i) q^{5} +(-0.520741 + 1.65192i) q^{6} +(2.07811 + 1.63751i) q^{7} +(-0.540641 - 0.841254i) q^{8} +(-2.99536 + 0.166866i) q^{9} +(1.34226 + 0.325630i) q^{10} +(0.00401406 - 0.00138928i) q^{11} +(1.03239 - 1.39075i) q^{12} +(0.217392 + 0.740370i) q^{13} +(-1.42824 - 2.22714i) q^{14} +(0.293572 + 2.37422i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-0.139973 - 0.0560367i) q^{17} +(2.88519 + 0.821996i) q^{18} +(1.87752 + 4.68981i) q^{19} +(-1.16194 - 0.746732i) q^{20} +(2.73502 - 3.67691i) q^{21} -0.00424768 q^{22} +(4.64643 - 1.18772i) q^{23} +(-1.43048 + 0.976594i) q^{24} +(-3.03641 + 0.585220i) q^{25} +(0.0367155 - 0.770753i) q^{26} +(0.433251 + 5.17806i) q^{27} +(0.621262 + 2.57178i) q^{28} +(1.19152 - 0.171314i) q^{29} +(0.499107 - 2.33966i) q^{30} +(9.16139 - 0.436411i) q^{31} +(0.0950560 - 0.995472i) q^{32} +(-0.00259880 - 0.00688292i) q^{33} +(0.113947 + 0.0987354i) q^{34} +(-3.07228 - 1.97865i) q^{35} +(-2.45766 - 1.72044i) q^{36} +(0.376641 - 0.528918i) q^{37} +(-0.240368 - 5.04595i) q^{38} +(1.27139 - 0.412066i) q^{39} +(0.853800 + 1.08569i) q^{40} +(-4.07596 + 8.92510i) q^{41} +(-3.78719 + 2.58015i) q^{42} +(8.93155 + 5.73996i) q^{43} +(0.00401406 + 0.00138928i) q^{44} +(4.09654 - 0.622695i) q^{45} +(-4.77935 - 0.397300i) q^{46} +(-3.33265 - 5.77233i) q^{47} +(1.67121 - 0.455019i) q^{48} +(1.63710 + 6.80587i) q^{49} +(3.06082 + 0.440079i) q^{50} +(-0.0902757 + 0.245047i) q^{51} +(-0.286785 + 0.716353i) q^{52} +(5.73918 + 6.01908i) q^{53} +(1.28415 - 5.03497i) q^{54} +(-0.00533670 + 0.00243719i) q^{55} +(0.254052 - 2.63353i) q^{56} +(8.02937 - 3.47669i) q^{57} +(-1.18202 - 0.227815i) q^{58} +(2.87372 - 11.8456i) q^{59} +(-1.23688 + 2.04774i) q^{60} +(5.65179 - 10.9629i) q^{61} +(-8.80026 - 2.58399i) q^{62} +(-6.49793 - 4.55817i) q^{63} +(-0.415415 + 0.909632i) q^{64} +(-0.396106 - 0.989426i) q^{65} +(0.000204690 + 0.00735435i) q^{66} +(-4.41272 + 0.850481i) q^{67} +(-0.0753865 - 0.130573i) q^{68} +(-2.28030 - 7.98750i) q^{69} +(2.25615 + 2.87467i) q^{70} +(-5.65883 + 4.90340i) q^{71} +(1.75979 + 2.42964i) q^{72} +(7.75356 - 9.85946i) q^{73} +(-0.528918 + 0.376641i) q^{74} +(1.15956 + 5.22898i) q^{75} +(-1.42322 + 4.84704i) q^{76} +(0.0106166 + 0.00368600i) q^{77} +(-1.33624 - 0.0264268i) q^{78} +(-3.38673 - 3.22924i) q^{79} +(-0.451745 - 1.30523i) q^{80} +(8.94431 - 0.999647i) q^{81} +(6.77090 - 7.10111i) q^{82} +(5.88625 + 12.8891i) q^{83} +(4.42278 - 1.19957i) q^{84} +(0.199812 + 0.0586701i) q^{85} +(-6.56297 - 8.34549i) q^{86} +(-0.354028 - 2.05471i) q^{87} +(-0.00333890 - 0.00262574i) q^{88} +(0.456100 - 9.57472i) q^{89} +(-4.07489 - 0.751398i) q^{90} +(-0.760601 + 1.89456i) q^{91} +(4.38654 + 1.93862i) q^{92} +(-1.19707 - 15.8408i) q^{93} +(1.26142 + 6.54486i) q^{94} +(-3.19721 - 6.20172i) q^{95} +(-1.72812 - 0.116608i) q^{96} +(6.14348 + 2.80563i) q^{97} +(0.678925 - 6.96700i) q^{98} +(-0.0117917 + 0.00483120i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1280 q - 64 q^{4} + 4 q^{9}+O(q^{10}) \) 1280 * q - 64 * q^4 + 4 * q^9	\( 1280 q - 64 q^{4} + 4 q^{9} + 16 q^{15} + 64 q^{16} - 44 q^{18} + 120 q^{21} - 16 q^{22} - 12 q^{24} + 56 q^{25} + 32 q^{30} - 24 q^{33} + 8 q^{36} - 44 q^{37} - 20 q^{39} + 4 q^{42} + 136 q^{43} + 12 q^{45} + 12 q^{46} + 92 q^{49} + 4 q^{51} - 36 q^{54} - 56 q^{57} - 28 q^{58} + 8 q^{60} + 72 q^{61} - 134 q^{63} + 128 q^{64} + 24 q^{67} - 72 q^{70} - 44 q^{72} - 72 q^{73} + 48 q^{75} - 16 q^{78} - 72 q^{79} + 40 q^{81} + 48 q^{82} - 10 q^{84} - 32 q^{85} + 222 q^{87} - 8 q^{88} - 8 q^{91} - 16 q^{93} + 72 q^{94} - 12 q^{96} - 68 q^{99}+O(q^{100}) \) 1280 * q - 64 * q^4 + 4 * q^9 + 16 * q^15 + 64 * q^16 - 44 * q^18 + 120 * q^21 - 16 * q^22 - 12 * q^24 + 56 * q^25 + 32 * q^30 - 24 * q^33 + 8 * q^36 - 44 * q^37 - 20 * q^39 + 4 * q^42 + 136 * q^43 + 12 * q^45 + 12 * q^46 + 92 * q^49 + 4 * q^51 - 36 * q^54 - 56 * q^57 - 28 * q^58 + 8 * q^60 + 72 * q^61 - 134 * q^63 + 128 * q^64 + 24 * q^67 - 72 * q^70 - 44 * q^72 - 72 * q^73 + 48 * q^75 - 16 * q^78 - 72 * q^79 + 40 * q^81 + 48 * q^82 - 10 * q^84 - 32 * q^85 + 222 * q^87 - 8 * q^88 - 8 * q^91 - 16 * q^93 + 72 * q^94 - 12 * q^96 - 68 * q^99

Introduction

L-functions

Modular forms

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