LMFDB - Embedded newform 552.2.bb.a.469.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(13,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 0, 14]))

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

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

chi := DirichletCharacter("552.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			469.29
Character	$\chi$	$=$	552.469
Dual form			552.2.bb.a.133.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.447692 - 1.34148i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(-1.59914 - 1.20114i) q^{4} +(-0.994303 + 0.142959i) q^{5} +(0.540141 + 1.30700i) q^{6} +(1.86030 - 4.07350i) q^{7} +(-2.32723 + 1.60748i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(0.447692 - 1.34148i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(-1.59914 - 1.20114i) q^{4} +(-0.994303 + 0.142959i) q^{5} +(0.540141 + 1.30700i) q^{6} +(1.86030 - 4.07350i) q^{7} +(-2.32723 + 1.60748i) q^{8} +(0.142315 - 0.989821i) q^{9} +(-0.253364 + 1.39784i) q^{10} +(-0.868601 + 2.95818i) q^{11} +(1.99513 - 0.139456i) q^{12} +(-0.420961 + 0.192246i) q^{13} +(-4.63168 - 4.31923i) q^{14} +(0.657826 - 0.759171i) q^{15} +(1.11453 + 3.84159i) q^{16} +(-5.27716 - 3.39142i) q^{17} +(-1.26411 - 0.634047i) q^{18} +(-4.49564 - 6.99535i) q^{19} +(1.76175 + 0.965685i) q^{20} +(1.26165 + 4.29678i) q^{21} +(3.57948 + 2.48957i) q^{22} +(0.616760 + 4.75601i) q^{23} +(0.706126 - 2.73887i) q^{24} +(-3.82926 + 1.12437i) q^{25} +(0.0694343 + 0.650778i) q^{26} +(0.540641 + 0.841254i) q^{27} +(-7.86774 + 4.27963i) q^{28} +(1.75814 - 2.73572i) q^{29} +(-0.723911 - 1.22234i) q^{30} +(-2.99299 + 3.45409i) q^{31} +(5.65239 + 0.224732i) q^{32} +(-1.28075 - 2.80446i) q^{33} +(-6.91207 + 5.56089i) q^{34} +(-1.26736 + 4.31624i) q^{35} +(-1.41650 + 1.41193i) q^{36} +(-7.54673 - 1.08506i) q^{37} +(-11.3968 + 2.89906i) q^{38} +(0.192246 - 0.420961i) q^{39} +(2.08417 - 1.93102i) q^{40} +(0.0346364 + 0.240901i) q^{41} +(6.32889 + 0.231155i) q^{42} +(5.26279 - 4.56024i) q^{43} +(4.94221 - 3.68725i) q^{44} +1.00453i q^{45} +(6.65621 + 1.30185i) q^{46} +0.826720 q^{47} +(-3.35801 - 2.17342i) q^{48} +(-8.54863 - 9.86565i) q^{49} +(-0.206003 + 5.64026i) q^{50} +(6.20912 - 0.892736i) q^{51} +(0.904092 + 0.198203i) q^{52} +(-3.02032 - 1.37933i) q^{53} +(1.37057 - 0.348637i) q^{54} +(0.440753 - 3.06551i) q^{55} +(2.21872 + 12.4704i) q^{56} +(7.97856 + 2.34272i) q^{57} +(-2.88281 - 3.58327i) q^{58} +(5.22030 - 2.38403i) q^{59} +(-1.96383 + 0.423884i) q^{60} +(-5.24148 - 4.54177i) q^{61} +(3.29366 + 5.56140i) q^{62} +(-3.76729 - 2.42109i) q^{63} +(2.83200 - 7.48196i) q^{64} +(0.391079 - 0.251332i) q^{65} +(-4.33551 + 0.462574i) q^{66} +(1.44928 + 4.93578i) q^{67} +(4.36536 + 11.7620i) q^{68} +(-3.58064 - 3.19046i) q^{69} +(5.22277 + 3.63249i) q^{70} +(3.91182 - 1.14861i) q^{71} +(1.25992 + 2.53231i) q^{72} +(10.4806 - 6.73545i) q^{73} +(-4.83419 + 9.63802i) q^{74} +(2.15766 - 3.35738i) q^{75} +(-1.21322 + 16.5865i) q^{76} +(10.4343 + 9.04137i) q^{77} +(-0.478644 - 0.446356i) q^{78} +(1.04626 + 2.29099i) q^{79} +(-1.65737 - 3.66038i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(0.338671 + 0.0613854i) q^{82} +(17.5497 + 2.52327i) q^{83} +(3.14348 - 8.38660i) q^{84} +(5.73193 + 2.61768i) q^{85} +(-3.76136 - 9.10152i) q^{86} +(0.462802 + 3.21886i) q^{87} +(-2.73379 - 8.28063i) q^{88} +(-9.73176 - 11.2311i) q^{89} +(1.34756 + 0.449719i) q^{90} +2.07242i q^{91} +(4.72634 - 8.34636i) q^{92} -4.57042i q^{93} +(0.370116 - 1.10903i) q^{94} +(5.47008 + 6.31281i) q^{95} +(-4.41896 + 3.53169i) q^{96} +(-1.54914 - 10.7745i) q^{97} +(-17.0617 + 7.05106i) q^{98} +(2.80446 + 1.28075i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.447692	−	1.34148i	0.316566	−	0.948571i
$2$	0.447692	−	1.34148i	0.316566	−	0.948571i
$3$	−0.755750	+	0.654861i	−0.436332	+	0.378084i
$3$	−0.755750	+	0.654861i	−0.436332	+	0.378084i
$4$	−1.59914	−	1.20114i	−0.799572	−	0.600570i
$5$	−0.994303	+	0.142959i	−0.444666	+	0.0639333i	−0.361011	−	0.932561i	$-0.617568\pi$
$5$	−0.994303	+	0.142959i	−0.444666	+	0.0639333i	−0.0836547	+	0.996495i	$0.526659\pi$
$6$	0.540141	+	1.30700i	0.220512	+	0.533580i
$7$	1.86030	−	4.07350i	0.703129	−	1.53964i	−0.133007	−	0.991115i	$-0.542463\pi$
$7$	1.86030	−	4.07350i	0.703129	−	1.53964i	0.836136	−	0.548523i	$-0.184809\pi$
$8$	−2.32723	+	1.60748i	−0.822800	+	0.568331i
$9$	0.142315	−	0.989821i	0.0474383	−	0.329940i
$10$	−0.253364	+	1.39784i	−0.0801207	+	0.442036i
$11$	−0.868601	+	2.95818i	−0.261893	+	0.891926i	0.718609	+	0.695415i	$0.244779\pi$
$11$	−0.868601	+	2.95818i	−0.261893	+	0.891926i	−0.980502	+	0.196511i	$0.937039\pi$
$12$	1.99513	−	0.139456i	0.575945	−	0.0402575i
$13$	−0.420961	+	0.192246i	−0.116754	+	0.0533196i	−0.472935	−	0.881097i	$-0.656806\pi$
$13$	−0.420961	+	0.192246i	−0.116754	+	0.0533196i	0.356182	+	0.934417i	$0.384078\pi$
$14$	−4.63168	−	4.31923i	−1.23787	−	1.15436i
$15$	0.657826	−	0.759171i	0.169850	−	0.196017i
$16$	1.11453	+	3.84159i	0.278632	+	0.960398i
$17$	−5.27716	−	3.39142i	−1.27990	−	0.822541i	−0.289023	−	0.957322i	$-0.593330\pi$
$17$	−5.27716	−	3.39142i	−1.27990	−	0.822541i	−0.990875	+	0.134782i	$0.956967\pi$
$18$	−1.26411	−	0.634047i	−0.297954	−	0.149446i
$19$	−4.49564	−	6.99535i	−1.03137	−	1.60484i	−0.768325	−	0.640060i	$-0.778910\pi$
$19$	−4.49564	−	6.99535i	−1.03137	−	1.60484i	−0.263045	−	0.964784i	$-0.584727\pi$
$20$	1.76175	+	0.965685i	0.393939	+	0.215934i
$21$	1.26165	+	4.29678i	0.275315	+	0.937635i
$22$	3.57948	+	2.48957i	0.763148	+	0.530777i
$23$	0.616760	+	4.75601i	0.128603	+	0.991696i
$23$	0.616760	+	4.75601i	0.128603	+	0.991696i
$24$	0.706126	−	2.73887i	0.144137	−	0.559069i
$25$	−3.82926	+	1.12437i	−0.765853	+	0.224875i
$26$	0.0694343	+	0.650778i	0.0136172	+	0.127628i
$27$	0.540641	+	0.841254i	0.104046	+	0.161899i
$28$	−7.86774	+	4.27963i	−1.48686	+	0.808773i
$29$	1.75814	−	2.73572i	0.326479	−	0.508010i	−0.638751	−	0.769413i	$-0.720549\pi$
$29$	1.75814	−	2.73572i	0.326479	−	0.508010i	0.965230	+	0.261403i	$0.0841851\pi$
$30$	−0.723911	−	1.22234i	−0.132168	−	0.223167i
$31$	−2.99299	+	3.45409i	−0.537556	+	0.620373i	−0.957938	−	0.286974i	$-0.907351\pi$
$31$	−2.99299	+	3.45409i	−0.537556	+	0.620373i	0.420382	+	0.907347i	$0.361896\pi$
$32$	5.65239	+	0.224732i	0.999211	+	0.0397274i
$33$	−1.28075	−	2.80446i	−0.222951	−	0.488194i
$34$	−6.91207	+	5.56089i	−1.18541	+	0.953686i
$35$	−1.26736	+	4.31624i	−0.214223	+	0.729578i
$36$	−1.41650	+	1.41193i	−0.236083	+	0.235321i
$37$	−7.54673	−	1.08506i	−1.24067	−	0.178382i	−0.509439	−	0.860507i	$-0.670147\pi$
$37$	−7.54673	−	1.08506i	−1.24067	−	0.178382i	−0.731236	+	0.682125i	$0.761056\pi$
$38$	−11.3968	+	2.89906i	−1.84880	+	0.470289i
$39$	0.192246	−	0.420961i	0.0307841	−	0.0674077i
$40$	2.08417	−	1.93102i	0.329536	−	0.305322i
$41$	0.0346364	+	0.240901i	0.00540929	+	0.0376224i	0.992347	−	0.123478i	$-0.0394048\pi$
$41$	0.0346364	+	0.240901i	0.00540929	+	0.0376224i	−0.986938	+	0.161100i	$0.948496\pi$
$42$	6.32889	+	0.231155i	0.976568	+	0.0356679i
$43$	5.26279	−	4.56024i	0.802568	−	0.695429i	−0.153637	−	0.988127i	$-0.549099\pi$
$43$	5.26279	−	4.56024i	0.802568	−	0.695429i	0.956205	+	0.292698i	$0.0945531\pi$
$44$	4.94221	−	3.68725i	0.745066	−	0.555874i
$45$			1.00453i			0.149746i
$46$	6.65621	+	1.30185i	0.981405	+	0.191948i
$47$	0.826720			0.120590			0.0602948	−	0.998181i	$-0.480796\pi$
$47$	0.826720			0.120590			0.0602948	+	0.998181i	$0.480796\pi$
$48$	−3.35801	−	2.17342i	−0.484687	−	0.313706i
$49$	−8.54863	−	9.86565i	−1.22123	−	1.40938i
$50$	−0.206003	+	5.64026i	−0.0291333	+	0.797653i
$51$	6.20912	−	0.892736i	0.869450	−	0.125008i
$52$	0.904092	+	0.198203i	0.125375	+	0.0274858i
$53$	−3.02032	−	1.37933i	−0.414872	−	0.189466i	0.197033	−	0.980397i	$-0.436869\pi$
$53$	−3.02032	−	1.37933i	−0.414872	−	0.189466i	−0.611905	+	0.790931i	$0.709597\pi$
$54$	1.37057	−	0.348637i	0.186510	−	0.0474435i
$55$	0.440753	−	3.06551i	0.0594311	−	0.413353i
$56$	2.21872	+	12.4704i	0.296489	+	1.66642i
$57$	7.97856	+	2.34272i	1.05679	+	0.310300i
$58$	−2.88281	−	3.58327i	−0.378532	−	0.470507i
$59$	5.22030	−	2.38403i	0.679626	−	0.310375i	−0.0455266	−	0.998963i	$-0.514497\pi$
$59$	5.22030	−	2.38403i	0.679626	−	0.310375i	0.725152	+	0.688588i	$0.241769\pi$
$60$	−1.96383	+	0.423884i	−0.253529	+	0.0547232i
$61$	−5.24148	−	4.54177i	−0.671103	−	0.581514i	0.251222	−	0.967930i	$-0.419168\pi$
$61$	−5.24148	−	4.54177i	−0.671103	−	0.581514i	−0.922325	+	0.386415i	$0.873713\pi$
$62$	3.29366	+	5.56140i	0.418296	+	0.706299i
$63$	−3.76729	−	2.42109i	−0.474634	−	0.305028i
$64$	2.83200	−	7.48196i	0.354000	−	0.935245i
$65$	0.391079	−	0.251332i	0.0485074	−	0.0311738i
$66$	−4.33551	+	0.462574i	−0.533664	+	0.0569389i
$67$	1.44928	+	4.93578i	0.177057	+	0.603001i	0.999421	+	0.0340387i	$0.0108369\pi$
$67$	1.44928	+	4.93578i	0.177057	+	0.603001i	−0.822363	+	0.568963i	$0.807345\pi$
$68$	4.36536	+	11.7620i	0.529378	+	1.42635i
$69$	−3.58064	−	3.19046i	−0.431058	−	0.384086i
$70$	5.22277	+	3.63249i	0.624240	+	0.434165i
$71$	3.91182	−	1.14861i	0.464248	−	0.136315i	−0.0412399	−	0.999149i	$-0.513131\pi$
$71$	3.91182	−	1.14861i	0.464248	−	0.136315i	0.505488	+	0.862834i	$0.331313\pi$
$72$	1.25992	+	2.53231i	0.148483	+	0.298436i
$73$	10.4806	−	6.73545i	1.22666	−	0.788325i	0.243290	−	0.969954i	$-0.421773\pi$
$73$	10.4806	−	6.73545i	1.22666	−	0.788325i	0.983367	+	0.181629i	$0.0581369\pi$
$74$	−4.83419	+	9.63802i	−0.561963	+	1.12040i
$75$	2.15766	−	3.35738i	0.249145	−	0.387677i
$76$	−1.21322	+	16.5865i	−0.139166	+	1.90260i
$77$	10.4343	+	9.04137i	1.18910	+	1.03036i
$78$	−0.478644	−	0.446356i	−0.0541958	−	0.0505398i
$79$	1.04626	+	2.29099i	0.117713	+	0.257756i	0.959313	−	0.282346i	$-0.0911128\pi$
$79$	1.04626	+	2.29099i	0.117713	+	0.257756i	−0.841599	+	0.540102i	$0.818385\pi$
$80$	−1.65737	−	3.66038i	−0.185299	−	0.409242i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	0.338671	+	0.0613854i	0.0373999	+	0.00677888i
$83$	17.5497	+	2.52327i	1.92633	+	0.276965i	0.995971	−	0.0896796i	$-0.0285843\pi$
$83$	17.5497	+	2.52327i	1.92633	+	0.276965i	0.930361	+	0.366644i	$0.119493\pi$
$84$	3.14348	−	8.38660i	0.342982	−	0.915053i
$85$	5.73193	+	2.61768i	0.621715	+	0.283928i
$86$	−3.76136	−	9.10152i	−0.405598	−	0.981442i
$87$	0.462802	+	3.21886i	0.0496176	+	0.345098i
$88$	−2.73379	−	8.28063i	−0.291423	−	0.882719i
$89$	−9.73176	−	11.2311i	−1.03156	−	1.19049i	−0.981445	−	0.191746i	$-0.938585\pi$
$89$	−9.73176	−	11.2311i	−1.03156	−	1.19049i	−0.0501201	−	0.998743i	$-0.515960\pi$
$90$	1.34756	+	0.449719i	0.142045	+	0.0474045i
$91$			2.07242i			0.217249i
$92$	4.72634	−	8.34636i	0.492755	−	0.870168i
$93$		−	4.57042i		−	0.473930i
$94$	0.370116	−	1.10903i	0.0381745	−	0.114388i
$95$	5.47008	+	6.31281i	0.561218	+	0.647680i
$96$	−4.41896	+	3.53169i	−0.451008	+	0.360451i
$97$	−1.54914	−	10.7745i	−0.157291	−	1.09398i	−0.903598	−	0.428381i	$-0.859084\pi$
$97$	−1.54914	−	10.7745i	−0.157291	−	1.09398i	0.746308	−	0.665601i	$-0.231825\pi$
$98$	−17.0617	+	7.05106i	−1.72350	+	0.712265i
$99$	2.80446	+	1.28075i	0.281859	+	0.128721i
$100$	7.47407	+	2.80145i	0.747407	+	0.280145i
$101$	8.86055	+	1.27395i	0.881657	+	0.126763i	0.568250	−	0.822856i	$-0.307621\pi$
$101$	8.86055	+	1.27395i	0.881657	+	0.126763i	0.313407	+	0.949619i	$0.398530\pi$
$102$	1.58218	−	8.72908i	0.156659	−	0.864308i
$103$	19.3008	+	5.66722i	1.90176	+	0.558408i	0.988543	+	0.150938i	$0.0482293\pi$
$103$	19.3008	+	5.66722i	1.90176	+	0.558408i	0.913219	+	0.407470i	$0.133589\pi$
$104$	0.670640	−	1.12409i	0.0657617	−	0.110226i
$105$	−1.86873	−	4.09194i	−0.182369	−	0.399333i
$106$	−3.20252	+	3.43418i	−0.311056	+	0.333557i
$107$	−6.04773	−	5.24039i	−0.584657	−	0.506608i	0.311559	−	0.950227i	$-0.399149\pi$
$107$	−6.04773	−	5.24039i	−0.584657	−	0.506608i	−0.896215	+	0.443619i	$0.853694\pi$
$108$	0.145900	−	1.99467i	0.0140393	−	0.191937i
$109$	3.36856	−	5.24159i	0.322650	−	0.502053i	−0.641603	−	0.767037i	$-0.721730\pi$
$109$	3.36856	−	5.24159i	0.322650	−	0.502053i	0.964253	+	0.264984i	$0.0853667\pi$
$110$	−3.91500	−	1.96366i	−0.373280	−	0.187228i
$111$	6.41399	−	4.12202i	0.608789	−	0.391245i
$112$	17.7221	+	2.60651i	1.67458	+	0.246292i
$113$	−4.27019	+	1.25384i	−0.401705	+	0.117951i	−0.476343	−	0.879259i	$-0.658038\pi$
$113$	−4.27019	+	1.25384i	−0.401705	+	0.117951i	0.0746380	+	0.997211i	$0.476220\pi$
$114$	6.71464	−	9.65427i	0.628884	−	0.904205i
$115$	−1.29316	−	4.64074i	−0.120588	−	0.432751i
$116$	−6.09750	+	2.26304i	−0.566139	+	0.210118i
$117$	0.130381	+	0.444036i	0.0120537	+	0.0410511i
$118$	−0.861050	−	8.07025i	−0.0792661	−	0.742927i
$119$	−23.6321	+	15.1874i	−2.16635	+	1.39223i
$120$	−0.310557	+	2.82421i	−0.0283499	+	0.257814i
$121$	1.25741	+	0.808088i	0.114310	+	0.0734625i
$122$	−8.43927	+	4.99804i	−0.764056	+	0.452501i
$123$	−0.183933	−	0.159379i	−0.0165847	−	0.0143707i
$124$	8.93507	−	1.92860i	0.802393	−	0.173193i
$125$	8.21546	−	3.75188i	0.734813	−	0.335578i
$126$	−4.93443	+	3.96984i	−0.439594	+	0.353662i
$127$	2.37953	+	0.698694i	0.211149	+	0.0619990i	0.385597	−	0.922667i	$-0.373996\pi$
$127$	2.37953	+	0.698694i	0.211149	+	0.0619990i	−0.174447	+	0.984667i	$0.555814\pi$
$128$	−8.76905	−	7.14869i	−0.775082	−	0.631861i
$129$	−0.991034	+	6.89279i	−0.0872557	+	0.606877i
$130$	−0.162074	−	0.637145i	−0.0142148	−	0.0558813i
$131$	−13.1291	−	5.99586i	−1.14710	−	0.523861i	−0.251116	−	0.967957i	$-0.580798\pi$
$131$	−13.1291	−	5.99586i	−1.14710	−	0.523861i	−0.895979	+	0.444096i	$0.853525\pi$
$132$	−1.32044	+	6.02310i	−0.114929	+	0.524243i
$133$	−36.8588	+	5.29950i	−3.19606	+	0.459525i
$134$	7.27008	+	0.265531i	0.628040	+	0.0229384i
$135$	−0.657826	−	0.759171i	−0.0566166	−	0.0653391i
$136$	17.7328	−	0.590315i	1.52058	−	0.0506191i
$137$	−15.4862			−1.32307			−0.661536	−	0.749913i	$-0.730095\pi$
$137$	−15.4862			−1.32307			−0.661536	+	0.749913i	$0.730095\pi$
$138$	−5.88296	+	3.37502i	−0.500791	+	0.287301i
$139$		−	2.64999i		−	0.224769i	−0.993665	−	0.112385i	$-0.964151\pi$
$139$		−	2.64999i		−	0.224769i	0.993665	−	0.112385i	$-0.0358489\pi$
$140$	7.21110	−	5.38001i	0.609449	−	0.454694i
$141$	−0.624794	+	0.541387i	−0.0526171	+	0.0455930i
$142$	0.210445	−	5.76186i	0.0176601	−	0.483525i
$143$	−0.203053	−	1.41227i	−0.0169802	−	0.118100i
$144$	3.96110	−	0.556466i	0.330092	−	0.0463722i
$145$	−1.35703	+	2.97148i	−0.112695	+	0.246768i
$146$	−4.34342	−	17.0749i	−0.359464	−	1.41313i
$147$	12.9212	+	1.85780i	1.06573	+	0.153228i
$148$	10.7650	+	10.7998i	0.884878	+	0.887741i
$149$	−2.54984	+	8.68396i	−0.208891	+	0.711418i	0.786676	+	0.617366i	$0.211800\pi$
$149$	−2.54984	+	8.68396i	−0.208891	+	0.711418i	−0.995567	+	0.0940520i	$0.970018\pi$
$150$	−3.53790	−	4.39753i	−0.288868	−	0.359056i
$151$	−9.39703	−	20.5766i	−0.764719	−	1.67450i	−0.737945	−	0.674860i	$-0.764204\pi$
$151$	−9.39703	−	20.5766i	−0.764719	−	1.67450i	−0.0267739	−	0.999642i	$-0.508523\pi$
$152$	21.7073	+	9.05313i	1.76069	+	0.734306i
$153$	−4.10792	+	4.74079i	−0.332106	+	0.383270i
$154$	16.8002	−	9.94966i	1.35380	−	0.801767i
$155$	2.48214	−	3.86229i	0.199370	−	0.310226i
$156$	−0.813063	+	0.442263i	−0.0650971	+	0.0354094i
$157$	6.73028	+	10.4725i	0.537135	+	0.835798i	0.998682	−	0.0513171i	$-0.0163419\pi$
$157$	6.73028	+	10.4725i	0.537135	+	0.835798i	−0.461547	+	0.887116i	$0.652706\pi$
$158$	3.54172	−	0.377881i	0.281764	−	0.0300626i
$159$	3.18587	−	0.935457i	0.252656	−	0.0741865i
$160$	−5.65232	+	0.584609i	−0.446855	+	0.0462174i
$161$	20.5209	+	6.33525i	1.61728	+	0.499288i
$162$	−0.807496	+	1.16101i	−0.0634429	+	0.0912178i
$163$	0.474558	+	1.61620i	0.0371703	+	0.126590i	0.975988	−	0.217824i	$-0.0698958\pi$
$163$	0.474558	+	1.61620i	0.0371703	+	0.126590i	−0.938818	+	0.344414i	$0.888078\pi$
$164$	0.233967	−	0.426839i	0.0182698	−	0.0333305i
$165$	1.67438	+	2.60539i	0.130350	+	0.202829i
$166$	11.2418	−	22.4130i	0.872531	−	1.73958i
$167$	0.343546	+	0.220784i	0.0265844	+	0.0170848i	0.553866	−	0.832606i	$-0.313152\pi$
$167$	0.343546	+	0.220784i	0.0265844	+	0.0170848i	−0.527281	+	0.849691i	$0.676789\pi$
$168$	−9.84316	−	7.97153i	−0.759416	−	0.615017i
$169$	−8.37294	+	9.66289i	−0.644072	+	0.743299i
$170$	6.07771	−	6.51736i	0.466139	−	0.499859i
$171$	−7.56394	+	3.45434i	−0.578429	+	0.264160i
$172$	−13.8934	+	0.971126i	−1.05937	+	0.0740477i
$173$	−3.48988	+	11.8854i	−0.265331	+	0.903634i	0.713791	+	0.700359i	$0.246977\pi$
$173$	−3.48988	+	11.8854i	−0.265331	+	0.903634i	−0.979122	+	0.203275i	$0.934841\pi$
$174$	4.52523	+	0.820215i	0.343057	+	0.0621803i
$175$	−2.54346	+	17.6902i	−0.192268	+	1.33725i
$176$	−12.3322	−	0.0398376i	−0.929575	−	0.00300287i
$177$	−2.38403	+	5.22030i	−0.179195	+	0.392382i
$178$	−19.4231	+	8.02693i	−1.45582	+	0.601644i
$179$	−3.46934	+	0.498816i	−0.259311	+	0.0372832i	−0.270744	−	0.962651i	$-0.587270\pi$
$179$	−3.46934	+	0.498816i	−0.259311	+	0.0372832i	0.0114333	+	0.999935i	$0.496361\pi$
$180$	1.20658	−	1.60639i	0.0899330	−	0.119733i
$181$	−2.00929	+	1.74106i	−0.149350	+	0.129412i	−0.726331	−	0.687345i	$-0.758776\pi$
$181$	−2.00929	+	1.74106i	−0.149350	+	0.129412i	0.576981	+	0.816757i	$0.304231\pi$
$182$	2.78011	+	0.927805i	0.206076	+	0.0687735i
$183$	6.93548			0.512685
$184$	−9.08054	−	10.0769i	−0.669426	−	0.742878i
$185$	7.65885			0.563090
$186$	−6.13113	−	2.04614i	−0.449556	−	0.150030i
$187$	14.6162	−	12.6650i	1.06884	−	0.926156i
$188$	−1.32205	−	0.993007i	−0.0964201	−	0.0724225i
$189$	4.43260	−	0.637312i	0.322424	−	0.0463576i
$190$	10.9174	−	4.51182i	0.792033	−	0.327322i
$191$	0.104504	−	0.228832i	0.00756166	−	0.0165577i	−0.905813	−	0.423677i	$-0.860739\pi$
$191$	0.104504	−	0.228832i	0.00756166	−	0.0165577i	0.913375	+	0.407119i	$0.133467\pi$
$192$	2.75936	+	7.50906i	0.199140	+	0.541919i
$193$	0.990142	−	6.88659i	0.0712720	−	0.495707i	−0.922652	−	0.385635i	$-0.873983\pi$
$193$	0.990142	−	6.88659i	0.0712720	−	0.495707i	0.993924	−	0.110073i	$-0.0351084\pi$
$194$	−15.1473	−	2.74550i	−1.08751	−	0.197116i
$195$	−0.130971	+	0.446046i	−0.00937903	+	0.0319420i
$196$	1.82048	+	26.0447i	0.130034	+	1.86034i
$197$	−2.19988	+	1.00465i	−0.156735	+	0.0715784i	−0.492238	−	0.870461i	$-0.663821\pi$
$197$	−2.19988	+	1.00465i	−0.156735	+	0.0715784i	0.335503	+	0.942039i	$0.391094\pi$
$198$	2.97364	−	3.18875i	0.211327	−	0.226614i
$199$	14.8353	−	17.1209i	1.05165	−	1.21367i	0.0753689	−	0.997156i	$-0.475987\pi$
$199$	14.8353	−	17.1209i	1.05165	−	1.21367i	0.976280	−	0.216512i	$-0.0694680\pi$
$200$	7.10417	−	8.77215i	0.502340	−	0.620285i
$201$	−4.32754	−	2.78114i	−0.305241	−	0.196166i
$202$	5.67578	−	11.3159i	0.399346	−	0.796185i
$203$	−7.87327	−	12.2511i	−0.552596	−	0.859855i
$204$	−11.0016	−	6.03040i	−0.770264	−	0.422213i
$205$	−0.0688781	−	0.234577i	−0.00481065	−	0.0163836i
$206$	16.2433	−	23.3545i	1.13172	−	1.62718i
$207$	4.79537	+	0.0663685i	0.333301	+	0.00461293i
$208$	−1.20770	−	1.40290i	−0.0837393	−	0.0972734i
$209$	24.5984	−	7.22275i	1.70151	−	0.499608i
$210$	−6.32588	+	0.674935i	−0.436527	+	0.0465749i
$211$	0.528939	+	0.823045i	0.0364136	+	0.0566607i	0.858983	−	0.512004i	$-0.171097\pi$
$211$	0.528939	+	0.823045i	0.0364136	+	0.0566607i	−0.822570	+	0.568665i	$0.807460\pi$
$212$	3.17315	+	5.83357i	0.217933	+	0.400651i
$213$	−2.20417	+	3.42976i	−0.151028	+	0.235003i
$214$	−9.73741	+	5.76684i	−0.665635	+	0.394213i
$215$	−4.58088	+	5.28662i	−0.312414	+	0.360545i
$216$	−2.61050	−	1.08872i	−0.177622	−	0.0740780i
$217$	8.50237	+	18.6176i	0.577178	+	1.26384i
$218$	−5.52341	−	6.86548i	−0.374093	−	0.464989i
$219$	−3.50990	+	11.9536i	−0.237177	+	0.807751i
$220$	−4.38693	+	4.37278i	−0.295767	+	0.294813i
$221$	2.87347	+	0.413142i	0.193290	+	0.0277909i
$222$	−2.65813	−	10.4496i	−0.178402	−	0.701335i
$223$	1.76143	−	3.85700i	0.117954	−	0.258284i	−0.841441	−	0.540349i	$-0.818292\pi$
$223$	1.76143	−	3.85700i	0.117954	−	0.258284i	0.959395	+	0.282065i	$0.0910195\pi$
$224$	11.4306	−	22.6069i	0.763740	−	1.51049i
$225$	0.567968	+	3.95030i	0.0378645	+	0.263353i
$226$	−0.229724	+	6.28971i	−0.0152810	+	0.418385i
$227$	−15.3325	+	13.2857i	−1.01766	+	0.881803i	−0.993026	−	0.117894i	$-0.962386\pi$
$227$	−15.3325	+	13.2857i	−1.01766	+	0.881803i	−0.0246289	+	0.999697i	$0.507840\pi$
$228$	−9.94494	−	13.3297i	−0.658620	−	0.882781i
$229$		−	15.8161i		−	1.04516i	−0.852590	−	0.522580i	$-0.824970\pi$
$229$		−	15.8161i		−	1.04516i	0.852590	−	0.522580i	$-0.175030\pi$
$230$	−6.80441	−	0.342869i	−0.448669	−	0.0226081i
$231$	−13.8065			−0.908404
$232$	0.306024	+	9.19283i	0.0200915	+	0.603539i
$233$	−13.4842	−	15.5616i	−0.883381	−	1.01948i	−0.999655	−	0.0262586i	$-0.991641\pi$
$233$	−13.4842	−	15.5616i	−0.883381	−	1.01948i	0.116274	−	0.993217i	$-0.462905\pi$
$234$	0.654036	+	0.0238878i	0.0427557	+	0.00156160i
$235$	−0.822011	+	0.118187i	−0.0536221	+	0.00770969i
$236$	−11.2116	−	2.45790i	−0.729812	−	0.159996i
$237$	−2.29099	−	1.04626i	−0.148815	−	0.0679618i
$238$	9.79375	+	38.5012i	0.634834	+	2.49567i
$239$	−2.89894	+	20.1626i	−0.187517	+	1.30421i	0.650893	+	0.759169i	$0.274395\pi$
$239$	−2.89894	+	20.1626i	−0.187517	+	1.30421i	−0.838410	+	0.545040i	$0.816515\pi$
$240$	3.64959	+	1.68098i	0.235580	+	0.108507i
$241$	8.41341	+	2.47040i	0.541955	+	0.159132i	0.541241	−	0.840867i	$-0.317955\pi$
$241$	8.41341	+	2.47040i	0.541955	+	0.159132i	0.000713989		1.00000i	$0.499773\pi$
$242$	1.64697	−	1.32502i	0.105871	−	0.0851753i
$243$	0.909632	−	0.415415i	0.0583529	−	0.0266489i
$244$	2.92659	+	13.5587i	0.187356	+	0.868007i
$245$	9.91032	+	8.58734i	0.633147	+	0.548625i
$246$	−0.296149	+	0.175390i	−0.0188818	+	0.0111825i
$247$	3.23732	+	2.08050i	0.205986	+	0.132379i
$248$	1.41298	−	12.8496i	0.0897243	−	0.815953i
$249$	−14.9156	+	9.58566i	−0.945237	+	0.607467i
$250$	−1.35508	−	12.7006i	−0.0857027	−	0.803255i
$251$	−8.67497	−	29.5442i	−0.547559	−	1.86482i	−0.500147	−	0.865941i	$-0.666721\pi$
$251$	−8.67497	−	29.5442i	−0.547559	−	1.86482i	−0.0474126	−	0.998875i	$-0.515098\pi$
$252$	3.11637	+	8.39671i	0.196313	+	0.528943i
$253$	−14.6049	−	2.30658i	−0.918200	−	0.145014i
$254$	2.00258	−	2.87930i	0.125653	−	0.180663i
$255$	−6.04612	+	1.77530i	−0.378623	+	0.111174i
$256$	−13.5157	+	8.56311i	−0.844729	+	0.535194i
$257$	1.66938	−	1.07285i	0.104133	−	0.0669224i	−0.487538	−	0.873102i	$-0.662105\pi$
$257$	1.66938	−	1.07285i	0.104133	−	0.0669224i	0.591671	+	0.806180i	$0.298468\pi$
$258$	8.80287	+	4.41530i	0.548043	+	0.274884i
$259$	−18.4592	+	28.7230i	−1.14700	+	1.78476i
$260$	−0.927277	−	0.0678257i	−0.0575073	−	0.00420637i
$261$	−2.45766	−	2.12958i	−0.152126	−	0.131818i
$262$	−13.9211	+	14.9282i	−0.860050	+	0.922264i
$263$	11.2958	+	24.7344i	0.696531	+	1.52519i	0.844127	+	0.536143i	$0.180119\pi$
$263$	11.2958	+	24.7344i	0.696531	+	1.52519i	−0.147596	+	0.989048i	$0.547153\pi$
$264$	7.48872	+	4.46783i	0.460899	+	0.274976i
$265$	3.20030	+	0.939692i	0.196593	+	0.0577248i
$266$	−9.39220	+	51.8179i	−0.575873	+	3.17716i
$267$	14.7096	+	2.11491i	0.900210	+	0.129431i
$268$	3.61096	−	9.63381i	0.220574	−	0.588478i
$269$	20.2243	+	9.23612i	1.23310	+	0.563136i	0.921981	−	0.387236i	$-0.126570\pi$
$269$	20.2243	+	9.23612i	1.23310	+	0.563136i	0.311115	+	0.950372i	$0.399298\pi$
$270$	−1.31292	+	0.542586i	−0.0799016	+	0.0330208i
$271$	1.72497	+	11.9974i	0.104785	+	0.728792i	0.972698	+	0.232076i	$0.0745519\pi$
$271$	1.72497	+	11.9974i	0.104785	+	0.728792i	−0.867913	+	0.496716i	$0.834539\pi$
$272$	7.14693	−	24.0525i	0.433346	−	1.45840i
$273$	−1.35715	−	1.56623i	−0.0821383	−	0.0947926i
$274$	−6.93303	+	20.7744i	−0.418839	+	1.25503i
$275$		−	12.3043i		−	0.741977i
$276$	1.89377	+	9.40285i	0.113992	+	0.565985i
$277$			4.79030i			0.287821i	0.989591	+	0.143910i	$0.0459677\pi$
$277$			4.79030i			0.287821i	−0.989591	+	0.143910i	$0.954032\pi$
$278$	−3.55491	−	1.18638i	−0.213210	−	0.0711543i
$279$	2.99299	+	3.45409i	0.179185	+	0.206791i
$280$	−3.98884	−	12.0821i	−0.238379	−	0.722046i
$281$	1.27097	+	8.83982i	0.0758200	+	0.527340i	0.991967	+	0.126497i	$0.0403735\pi$
$281$	1.27097	+	8.83982i	0.0758200	+	0.527340i	−0.916147	+	0.400843i	$0.868717\pi$
$282$	0.446545	+	1.08052i	0.0265914	+	0.0643442i
$283$	−17.3787	−	7.93658i	−1.03306	−	0.471781i	−0.174584	−	0.984642i	$-0.555858\pi$
$283$	−17.3787	−	7.93658i	−1.03306	−	0.471781i	−0.858471	+	0.512862i	$0.828585\pi$
$284$	−7.63521	−	2.86184i	−0.453067	−	0.169819i
$285$	−8.26802	−	1.18876i	−0.489755	−	0.0704161i
$286$	−1.98543	−	0.359867i	−0.117401	−	0.0212794i
$287$	1.04574	+	0.307058i	0.0617283	+	0.0181251i
$288$	1.02686	−	5.56287i	0.0605085	−	0.327795i
$289$	9.28457	+	20.3304i	0.546151	+	1.19590i
$290$	3.37865	+	3.15073i	0.198401	+	0.185017i
$291$	8.22654	+	7.12833i	0.482248	+	0.417870i
$292$	−24.8502	−	1.81767i	−1.45425	−	0.106371i
$293$	−3.53862	+	5.50619i	−0.206728	+	0.321675i	−0.929099	−	0.369830i	$-0.879416\pi$
$293$	−3.53862	+	5.50619i	−0.206728	+	0.321675i	0.722371	+	0.691505i	$0.243052\pi$
$294$	8.27693	−	16.5019i	0.482720	−	0.962410i
$295$	−4.84975	+	3.11674i	−0.282363	+	0.181464i
$296$	19.3072	−	9.60605i	1.12221	−	0.558341i
$297$	−2.95818	+	0.868601i	−0.171651	+	0.0504013i
$298$	10.5078	+	7.30830i	0.608702	+	0.423359i
$299$	−1.17396	−	1.88352i	−0.0678917	−	0.108927i
$300$	−7.48309	+	2.77729i	−0.432036	+	0.160347i
$301$	−8.78572	−	29.9214i	−0.506400	−	1.72464i
$302$	−31.8101	+	3.39396i	−1.83047	+	0.195300i
$303$	−7.53062	+	4.83963i	−0.432623	+	0.278030i
$304$	21.8628	−	25.0669i	1.25392	−	1.43769i
$305$	5.86091	+	3.76658i	0.335595	+	0.215674i
$306$	4.52060	+	7.63311i	0.258426	+	0.436356i
$307$	12.0060	+	10.4033i	0.685221	+	0.593747i	0.926313	−	0.376755i	$-0.122960\pi$
$307$	12.0060	+	10.4033i	0.685221	+	0.593747i	−0.241092	+	0.970502i	$0.577506\pi$
$308$	−5.82600	−	26.9915i	−0.331967	−	1.53798i
$309$	−18.2978	+	8.35632i	−1.04092	+	0.475375i
$310$	−4.06995	−	5.05886i	−0.231158	−	0.287324i
$311$	5.57147	+	1.63593i	0.315929	+	0.0927652i	0.435853	−	0.900018i	$-0.356447\pi$
$311$	5.57147	+	1.63593i	0.315929	+	0.0927652i	−0.119924	+	0.992783i	$0.538265\pi$
$312$	0.229286	+	1.28871i	0.0129807	+	0.0729586i
$313$	1.47877	−	10.2851i	0.0835853	−	0.581349i	−0.904386	−	0.426714i	$-0.859671\pi$
$313$	1.47877	−	10.2851i	0.0835853	−	0.581349i	0.987972	−	0.154634i	$-0.0494199\pi$
$314$	17.0618	−	4.34009i	0.962852	−	0.244925i
$315$	4.09194	+	1.86873i	0.230555	+	0.105291i
$316$	1.07868	−	4.92032i	0.0606803	−	0.276790i
$317$	5.91142	−	0.849934i	0.332018	−	0.0477371i	0.0257103	−	0.999669i	$-0.491815\pi$
$317$	5.91142	−	0.849934i	0.332018	−	0.0477371i	0.306308	+	0.951932i	$0.400906\pi$
$318$	0.171391	−	4.69258i	0.00961111	−	0.263147i
$319$	6.56564	+	7.57715i	0.367605	+	0.424239i
$320$	−1.74625	+	7.84420i	−0.0976184	+	0.438504i
$321$	8.00230			0.446645
$322$	17.6857	−	24.6922i	0.985584	−	1.37604i
$323$			52.1622i			2.90238i
$324$	1.19597	+	1.60302i	0.0664427	+	0.0890565i
$325$	1.39581	−	1.20948i	0.0774258	−	0.0670899i
$326$	2.38055	+	0.0869467i	0.131847	+	0.00481553i
$327$	0.886719	+	6.16727i	0.0490357	+	0.341051i
$328$	−0.467851	−	0.504955i	−0.0258328	−	0.0278815i
$329$	1.53795	−	3.36764i	0.0847900	−	0.185664i
$330$	4.24468	−	1.07974i	0.233662	−	0.0594377i
$331$	−0.418444	−	0.0601631i	−0.0229998	−	0.00330686i	0.130805	−	0.991408i	$-0.458244\pi$
$331$	−0.418444	−	0.0601631i	−0.0229998	−	0.00330686i	−0.153805	+	0.988101i	$0.549153\pi$
$332$	−25.0337	−	25.1147i	−1.37390	−	1.37835i
$333$	−2.14802	+	7.31549i	−0.117711	+	0.400886i
$334$	0.449980	−	0.362018i	0.0246218	−	0.0198087i
$335$	−2.14663	−	4.70047i	−0.117283	−	0.256814i
$336$	−15.1004	+	9.63562i	−0.823792	+	0.525666i
$337$	−2.09633	+	2.41930i	−0.114195	+	0.131788i	−0.809969	−	0.586473i	$-0.800516\pi$
$337$	−2.09633	+	2.41930i	−0.114195	+	0.131788i	0.695774	+	0.718261i	$0.255061\pi$
$338$	9.21409	+	15.5581i	0.501180	+	0.846251i
$339$	2.40610	−	3.74397i	0.130681	−	0.203344i
$340$	−6.02198	−	11.0709i	−0.326588	−	0.600404i
$341$	−7.61812	−	11.8540i	−0.412544	−	0.641932i
$342$	1.24762	+	11.6934i	0.0674633	+	0.632305i
$343$	−26.0133	+	7.63818i	−1.40458	+	0.412423i
$344$	−4.91723	+	19.0726i	−0.265119	+	1.02832i
$345$	4.01635	+	2.66040i	0.216233	+	0.143231i
$346$	14.3817	+	10.0026i	0.773166	+	0.537745i
$347$	−3.67684	−	12.5222i	−0.197383	−	0.672225i	−0.997388	−	0.0722314i	$-0.976988\pi$
$347$	−3.67684	−	12.5222i	−0.197383	−	0.672225i	0.800005	−	0.599994i	$-0.204830\pi$
$348$	3.12621	−	5.70331i	0.167582	−	0.305729i
$349$	−15.1913	−	23.6381i	−0.813171	−	1.26532i	−0.961067	−	0.276316i	$-0.910886\pi$
$349$	−15.1913	−	23.6381i	−0.813171	−	1.26532i	0.147896	−	0.989003i	$-0.452750\pi$
$350$	22.5924	+	11.3318i	1.20761	+	0.605708i
$351$	−0.389317	−	0.250199i	−0.0207802	−	0.0133546i
$352$	−5.57447	+	16.5256i	−0.297120	+	0.880817i
$353$	5.79527	−	6.68810i	0.308451	−	0.355972i	−0.580266	−	0.814427i	$-0.697052\pi$
$353$	5.79527	−	6.68810i	0.308451	−	0.355972i	0.888718	+	0.458455i	$0.151597\pi$
$354$	5.93563	+	5.53522i	0.315475	+	0.294194i
$355$	−3.72533	+	1.70130i	−0.197720	+	0.0902957i
$356$	2.07243	+	29.6493i	0.109839	+	1.57141i
$357$	7.91429	−	26.9536i	0.418868	−	1.42654i
$358$	−0.884042	+	4.87737i	−0.0467231	+	0.257777i
$359$	4.17357	−	29.0278i	0.220272	−	1.53203i	−0.516736	−	0.856145i	$-0.672853\pi$
$359$	4.17357	−	29.0278i	0.220272	−	1.53203i	0.737008	−	0.675884i	$-0.236238\pi$
$360$	−1.61476	−	2.33777i	−0.0851054	−	0.123211i
$361$	−20.8313	+	45.6141i	−1.09638	+	2.40074i
$362$	1.43606	+	3.47489i	0.0754776	+	0.182636i
$363$	−1.47947	+	0.212716i	−0.0776521	+	0.0111647i
$364$	2.48927	−	3.31410i	0.130473	−	0.173706i
$365$	−9.45796	+	8.19537i	−0.495052	+	0.428965i
$366$	3.10495	−	9.30381i	0.162299	−	0.486318i
$367$	−26.5166			−1.38415			−0.692077	−	0.721824i	$-0.743304\pi$
$367$	−26.5166			−1.38415			−0.692077	+	0.721824i	$0.743304\pi$
$368$	−17.5832	+	7.67003i	−0.916590	+	0.399828i
$369$	0.243378			0.0126698
$370$	3.42880	−	10.2742i	0.178255	−	0.534131i
$371$	−11.2374	+	9.73727i	−0.583417	+	0.505534i
$372$	−5.48971	+	7.30876i	−0.284628	+	0.378941i
$373$	23.1814	−	3.33298i	1.20029	−	0.172575i	0.486971	−	0.873418i	$-0.338102\pi$
$373$	23.1814	−	3.33298i	1.20029	−	0.172575i	0.713316	+	0.700843i	$0.247192\pi$
$374$	−10.4463	−	25.2774i	−0.540166	−	1.30706i
$375$	−3.75188	+	8.21546i	−0.193746	+	0.424245i
$376$	−1.92397	+	1.32894i	−0.0992211	+	0.0685348i
$377$	−0.214176	+	1.48963i	−0.0110306	+	0.0767197i
$378$	1.12950	−	6.23157i	0.0580950	−	0.320517i
$379$	4.18452	−	14.2512i	0.214944	−	0.732033i	−0.779466	−	0.626445i	$-0.784509\pi$
$379$	4.18452	−	14.2512i	0.214944	−	0.732033i	0.994410	−	0.105588i	$-0.0336724\pi$
$380$	−1.16488	−	16.6654i	−0.0597572	−	0.854918i
$381$	−2.25588	+	1.03022i	−0.115572	+	0.0527800i
$382$	−0.260189	−	0.242637i	−0.0133124	−	0.0124144i
$383$	6.11134	−	7.05286i	0.312275	−	0.360384i	−0.577816	−	0.816167i	$-0.696095\pi$
$383$	6.11134	−	7.05286i	0.312275	−	0.360384i	0.890091	+	0.455783i	$0.150641\pi$
$384$	11.3086	−	0.339889i	0.577090	−	0.0173449i
$385$	−11.6674	−	7.49818i	−0.594626	−	0.382143i
$386$	−8.79495	−	4.41132i	−0.447651	−	0.224531i
$387$	−3.76485	−	5.85821i	−0.191378	−	0.297790i
$388$	−10.4644	+	19.0907i	−0.531247	+	0.969182i
$389$	−3.88581	−	13.2339i	−0.197019	−	0.670984i	−0.997438	−	0.0715427i	$-0.977208\pi$
$389$	−3.88581	−	13.2339i	−0.197019	−	0.670984i	0.800419	−	0.599441i	$-0.204610\pi$
$390$	0.539728	+	0.375386i	0.0273302	+	0.0190084i
$391$	12.8749	−	27.1899i	0.651111	−	1.37505i
$392$	35.7535	+	9.21786i	1.80582	+	0.465572i
$393$	13.8488	−	4.06637i	0.698578	−	0.205121i
$394$	0.362853	+	3.40087i	0.0182803	+	0.171333i
$395$	−1.36782	−	2.12836i	−0.0688222	−	0.107090i
$396$	−2.94637	−	5.41666i	−0.148061	−	0.272197i
$397$	−8.32764	+	12.9581i	−0.417953	+	0.650347i	−0.984843	−	0.173446i	$-0.944510\pi$
$397$	−8.32764	+	12.9581i	−0.417953	+	0.650347i	0.566891	+	0.823793i	$0.308146\pi$
$398$	−16.3257	−	27.5662i	−0.818333	−	1.38177i
$399$	24.3856	−	28.1425i	1.22081	−	1.40889i
$400$	−8.58720	−	13.4573i	−0.429360	−	0.672866i
$401$	−5.85572	−	12.8222i	−0.292421	−	0.640312i	0.705218	−	0.708991i	$-0.250849\pi$
$401$	−5.85572	−	12.8222i	−0.292421	−	0.640312i	−0.997639	+	0.0686781i	$0.978122\pi$
$402$	−5.66825	+	4.56022i	−0.282707	+	0.227443i
$403$	0.595894	−	2.02943i	0.0296836	−	0.101093i
$404$	−12.6391	−	12.6800i	−0.628819	−	0.630853i
$405$	0.994303	+	0.142959i	0.0494073	+	0.00710370i
$406$	−19.9594	+	5.07716i	−0.990566	+	0.251975i
$407$	9.76488	−	21.3821i	0.484027	−	1.05987i
$408$	−13.0150	+	12.0586i	−0.644338	+	0.596992i
$409$	−2.96817	−	20.6440i	−0.146766	−	1.02078i	−0.921468	−	0.388455i	$-0.873009\pi$
$409$	−2.96817	−	20.6440i	−0.146766	−	1.02078i	0.774701	−	0.632327i	$-0.217900\pi$
$410$	−0.345517	−	0.0126196i	−0.0170639	−	0.000623236i
$411$	11.7037	−	10.1413i	0.577299	−	0.500233i
$412$	−24.0576	−	32.2456i	−1.18523	−	1.58863i
$413$		−	25.6999i		−	1.26461i
$414$	2.23588	−	6.40319i	0.109887	−	0.314700i
$415$	−17.8105			−0.874281
$416$	−2.42264	+	0.992048i	−0.118780	+	0.0486392i
$417$	1.73538	+	2.00273i	0.0849817	+	0.0980741i
$418$	1.32332	−	36.2319i	0.0647259	−	1.77216i
$419$	−7.90159	+	1.13608i	−0.386018	+	0.0555010i	−0.332592	−	0.943071i	$-0.607923\pi$
$419$	−7.90159	+	1.13608i	−0.386018	+	0.0555010i	−0.0534258	+	0.998572i	$0.517014\pi$
$420$	−1.92663	+	8.78821i	−0.0940099	+	0.428821i
$421$	31.9134	+	14.5744i	1.55537	+	0.710312i	0.993168	−	0.116692i	$-0.0372290\pi$
$421$	31.9134	+	14.5744i	1.55537	+	0.710312i	0.562197	+	0.827003i	$0.309956\pi$
$422$	1.34090	−	0.341091i	0.0652740	−	0.0166041i
$423$	0.117655	−	0.818306i	0.00572056	−	0.0397874i
$424$	9.24622	−	1.64508i	0.449036	−	0.0798922i
$425$	24.0208	+	7.05316i	1.16518	+	0.342128i
$426$	3.61417	+	4.49234i	0.175107	+	0.217654i
$427$	−28.2517	+	12.9021i	−1.36719	+	0.624376i
$428$	3.37676	+	15.6443i	0.163222	+	0.756197i
$429$	1.07829	+	0.934347i	0.0520605	+	0.0451107i
$430$	5.04108	+	8.51195i	0.243103	+	0.410482i
$431$	−17.2206	−	11.0670i	−0.829489	−	0.533080i	0.0556268	−	0.998452i	$-0.482284\pi$
$431$	−17.2206	−	11.0670i	−0.829489	−	0.533080i	−0.885115	+	0.465372i	$0.845921\pi$
$432$	−2.62919	+	3.01452i	−0.126497	+	0.145036i
$433$	7.90417	−	5.07970i	0.379850	−	0.244115i	−0.336758	−	0.941591i	$-0.609330\pi$
$433$	7.90417	−	5.07970i	0.379850	−	0.244115i	0.716608	+	0.697477i	$0.245694\pi$
$434$	28.7816	−	3.07083i	1.38156	−	0.147405i
$435$	−0.920330	−	3.13436i	−0.0441265	−	0.150281i
$436$	−11.6827	+	4.33594i	−0.559500	+	0.207654i
$437$	30.4972	−	25.6957i	1.45888	−	1.22919i
$438$	14.4642	+	10.0600i	0.691127	+	0.480686i
$439$	19.5887	−	5.75175i	0.934916	−	0.274516i	0.221423	−	0.975178i	$-0.428930\pi$
$439$	19.5887	−	5.75175i	0.934916	−	0.274516i	0.713494	+	0.700662i	$0.247112\pi$
$440$	3.90201	+	7.84264i	0.186021	+	0.373883i
$441$	−10.9818	+	7.05759i	−0.522944	+	0.336076i
$442$	1.84065	−	3.66974i	0.0875507	−	0.174552i
$443$	−10.6141	+	16.5159i	−0.504293	+	0.784696i	−0.996304	−	0.0858932i	$-0.972626\pi$
$443$	−10.6141	+	16.5159i	−0.504293	+	0.784696i	0.492011	+	0.870589i	$0.336262\pi$
$444$	−15.2080	−	1.11239i	−0.721741	−	0.0527918i
$445$	11.2819	+	9.77583i	0.534814	+	0.463419i
$446$	−4.38552	−	4.08968i	−0.207660	−	0.193652i
$447$	−3.75974	−	8.23269i	−0.177830	−	0.389393i
$448$	−25.2094	−	25.4549i	−1.19103	−	1.20263i
$449$	−16.8292	−	4.94151i	−0.794220	−	0.233204i	−0.140640	−	0.990061i	$-0.544916\pi$
$449$	−16.8292	−	4.94151i	−0.794220	−	0.233204i	−0.653581	+	0.756857i	$0.726734\pi$
$450$	5.55353	+	1.00660i	0.261796	+	0.0474515i
$451$	−0.742715	−	0.106786i	−0.0349731	−	0.00502837i
$452$	8.33468	+	3.12402i	0.392030	+	0.146942i
$453$	20.5766	+	9.39703i	0.966774	+	0.441511i
$454$	10.9583	+	26.5162i	0.514298	+	1.24447i
$455$	−0.296272	−	2.06061i	−0.0138894	−	0.0966031i
$456$	−22.3338	+	7.37335i	−1.04588	+	0.345289i
$457$	12.1219	+	13.9894i	0.567037	+	0.654395i	0.964767	−	0.263107i	$-0.0847474\pi$
$457$	12.1219	+	13.9894i	0.567037	+	0.654395i	−0.397730	+	0.917503i	$0.630202\pi$
$458$	−21.2171	−	7.08075i	−0.991408	−	0.330862i
$459$		−	6.27297i		−	0.292797i
$460$	−3.50623	+	8.97448i	−0.163479	+	0.418437i
$461$			6.11650i			0.284874i	0.989804	+	0.142437i	$0.0454938\pi$
$461$			6.11650i			0.284874i	−0.989804	+	0.142437i	$0.954506\pi$
$462$	−6.18107	+	18.5212i	−0.287570	+	0.861685i
$463$	−15.0092	−	17.3215i	−0.697535	−	0.804998i	0.290883	−	0.956759i	$-0.406051\pi$
$463$	−15.0092	−	17.3215i	−0.697535	−	0.804998i	−0.988417	+	0.151761i	$0.951506\pi$
$464$	12.4690	+	3.70503i	0.578860	+	0.172002i
$465$	0.653383	+	4.54438i	0.0302999	+	0.210741i
$466$	−26.9124	+	11.1220i	−1.24669	+	0.515218i
$467$	−25.1299	−	11.4765i	−1.16288	−	0.531067i	−0.261967	−	0.965077i	$-0.584371\pi$
$467$	−25.1299	−	11.4765i	−1.16288	−	0.531067i	−0.900908	+	0.434010i	$0.857098\pi$
$468$	0.324852	−	0.866683i	0.0150163	−	0.0400624i
$469$	22.8020	+	3.27843i	1.05290	+	0.151384i
$470$	−0.209461	+	1.15562i	−0.00966172	+	0.0533049i
$471$	−11.9445	−	3.50721i	−0.550371	−	0.161604i
$472$	−8.31656	+	13.9397i	−0.382801	+	0.641629i
$473$	8.91875	+	19.5293i	0.410084	+	0.897959i
$474$	−2.42919	+	2.60491i	−0.111576	+	0.119648i
$475$	25.0804	+	21.7323i	1.15077	+	0.997145i
$476$	56.0333	+	4.09856i	2.56828	+	0.187857i
$477$	−1.79513	+	2.79327i	−0.0821933	+	0.127895i
$478$	25.7499	+	12.9155i	1.17777	+	0.590741i
$479$	24.2972	−	15.6149i	1.11017	−	0.713462i	0.148838	−	0.988862i	$-0.452447\pi$
$479$	24.2972	−	15.6149i	1.11017	−	0.713462i	0.961330	+	0.275400i	$0.0888102\pi$
$480$	3.88890	−	4.14330i	0.177503	−	0.189115i
$481$	3.38548	−	0.994065i	0.154364	−	0.0453255i
$482$	7.08061	−	10.1805i	0.322513	−	0.463707i
$483$	−19.6574	+	8.65050i	−0.894443	+	0.393611i
$484$	−1.04015	−	2.80257i	−0.0472797	−	0.127390i
$485$	3.08062	+	10.4916i	0.139884	+	0.476400i
$486$	−0.150037	−	1.40623i	−0.00680581	−	0.0637880i
$487$	−14.6987	+	9.44629i	−0.666062	+	0.428052i	−0.829504	−	0.558501i	$-0.811377\pi$
$487$	−14.6987	+	9.44629i	−0.666062	+	0.428052i	0.163442	+	0.986553i	$0.447740\pi$
$488$	19.4990	+	2.14416i	0.882676	+	0.0970613i
$489$	−1.41703	−	0.910670i	−0.0640803	−	0.0411819i
$490$	15.9565	−	9.45003i	0.720842	−	0.426909i
$491$	21.1518	+	18.3281i	0.954568	+	0.827138i	0.985027	−	0.172398i	$-0.0551516\pi$
$491$	21.1518	+	18.3281i	0.954568	+	0.827138i	−0.0304596	+	0.999536i	$0.509697\pi$
$492$	0.102699	+	0.475799i	0.00463004	+	0.0214507i
$493$	−18.5560	+	8.47422i	−0.835718	+	0.381660i
$494$	4.24027	−	3.41138i	0.190779	−	0.153485i
$495$	−2.97158	−	0.872534i	−0.133562	−	0.0392175i
$496$	−16.6050	−	7.64816i	−0.745585	−	0.343413i
$497$	2.59830	−	18.0716i	0.116550	−	0.810621i
$498$	6.18141	+	24.3004i	0.276995	+	1.08893i
$499$	26.0498	+	11.8966i	1.16615	+	0.532563i	0.901923	−	0.431897i	$-0.142156\pi$
$499$	26.0498	+	11.8966i	1.16615	+	0.532563i	0.264228	+	0.964460i	$0.414883\pi$
$500$	−17.6442	−	3.86813i	−0.789074	−	0.172988i
$501$	−0.404218	+	0.0581177i	−0.0180591	+	0.00259651i
$502$	−43.5168	−	1.58939i	−1.94225	−	0.0709382i
$503$	21.5887	+	24.9147i	0.962592	+	1.11089i	0.993778	+	0.111376i	$0.0355259\pi$
$503$	21.5887	+	24.9147i	0.962592	+	1.11089i	−0.0311868	+	0.999514i	$0.509929\pi$
$504$	12.6592	−	0.421418i	0.563886	−	0.0187714i
$505$	−8.99219			−0.400147
$506$	−9.63271	+	18.5595i	−0.428226	+	0.825071i
$507$		−	12.7858i		−	0.567839i
$508$	−2.96599	−	3.97546i	−0.131594	−	0.176383i
$509$	4.25715	−	3.68884i	0.188695	−	0.163505i	−0.555390	−	0.831590i	$-0.687431\pi$
$509$	4.25715	−	3.68884i	0.188695	−	0.163505i	0.744085	+	0.668085i	$0.232886\pi$
$510$	−0.325264	+	8.90554i	−0.0144029	+	0.394344i
$511$	−7.93980	−	55.2225i	−0.351236	−	2.44290i
$512$	5.43641	+	21.9646i	0.240257	+	0.970709i
$513$	3.45434	−	7.56394i	0.152513	−	0.333956i
$514$	−0.691836	−	2.71975i	−0.0305156	−	0.119963i
$515$	−20.0010	−	2.87571i	−0.881349	−	0.126719i
$516$	9.86401	−	9.83220i	0.434239	−	0.432838i
$517$	−0.718090	+	2.44559i	−0.0315816	+	0.107557i
$518$	30.2674	+	37.6217i	1.32987	+	1.65300i
$519$	−5.14584	−	11.2678i	−0.225877	−	0.494602i
$520$	−0.506121	+	1.21356i	−0.0221949	+	0.0532181i
$521$	4.60562	−	5.31517i	0.201776	−	0.232862i	−0.645839	−	0.763474i	$-0.723492\pi$
$521$	4.60562	−	5.31517i	0.201776	−	0.232862i	0.847615	+	0.530612i	$0.178038\pi$
$522$	−3.95707	+	2.34352i	−0.173196	+	0.102573i
$523$	13.4154	−	20.8747i	0.586614	−	0.912789i	−0.413384	−	0.910557i	$-0.635653\pi$
$523$	13.4154	−	20.8747i	0.586614	−	0.912789i	0.999998	−	0.00223199i	$-0.000710466\pi$
$524$	13.7935	+	25.3581i	0.602571	+	1.10778i
$525$	−9.66238	−	15.0350i	−0.421701	−	0.656179i
$526$	38.2378	−	4.07976i	1.66725	−	0.177886i
$527$	27.5087	−	8.07729i	1.19830	−	0.351852i
$528$	9.34615	−	8.04577i	0.406739	−	0.350147i
$529$	−22.2392	+	5.86663i	−0.966922	+	0.255071i
$530$	2.69333	−	3.87245i	0.116991	−	0.168208i
$531$	−1.61684	−	5.50645i	−0.0701649	−	0.238960i
$532$	65.3080	+	35.7979i	2.83146	+	1.55204i
$533$	−0.0608929	−	0.0947513i	−0.00263757	−	0.00410413i
$534$	9.42246	−	18.7858i	0.407750	−	0.812939i
$535$	6.76244	+	4.34596i	0.292366	+	0.187892i
$536$	−11.3070	−	9.15701i	−0.488387	−	0.395523i
$537$	2.29530	−	2.64891i	0.0990494	−	0.114309i
$538$	21.4443	−	22.9956i	0.924530	−	0.991409i
$539$	36.6097	−	16.7191i	1.57689	−	0.720143i
$540$	0.140087	+	2.00417i	0.00602841	+	0.0862456i
$541$	−8.86803	+	30.2017i	−0.381266	+	1.29847i	0.515850	+	0.856679i	$0.327476\pi$
$541$	−8.86803	+	30.2017i	−0.381266	+	1.29847i	−0.897116	+	0.441795i	$0.854342\pi$
$542$	16.8666	+	3.05713i	0.724482	+	0.131315i
$543$	0.378369	−	2.63162i	0.0162374	−	0.112933i
$544$	−29.0664	−	20.3556i	−1.24621	−	0.872738i
$545$	−2.60004	+	5.69329i	−0.111373	+	0.243874i
$546$	−2.70865	+	1.11940i	−0.115920	+	0.0479059i
$547$	16.5648	−	2.38166i	0.708259	−	0.101832i	0.221235	−	0.975221i	$-0.428991\pi$
$547$	16.5648	−	2.38166i	0.708259	−	0.101832i	0.487025	+	0.873388i	$0.338082\pi$
$548$	24.7646	+	18.6011i	1.05789	+	0.794598i
$549$	−5.24148	+	4.54177i	−0.223701	+	0.193838i
$550$	−16.5060	−	5.50853i	−0.703817	−	0.234884i
$551$	−27.0413			−1.15200
$552$	13.4616	+	1.66912i	0.572963	+	0.0710424i
$553$	11.2787			0.479618
$554$	6.42609	+	2.14458i	0.273019	+	0.0911143i
$555$	−5.78817	+	5.01548i	−0.245694	+	0.212895i
$556$	−3.18301	+	4.23772i	−0.134990	+	0.179719i
$557$	9.65953	−	1.38883i	0.409287	−	0.0588467i	0.0654037	−	0.997859i	$-0.479166\pi$
$557$	9.65953	−	1.38883i	0.409287	−	0.0588467i	0.343884	+	0.939012i	$0.388257\pi$
$558$	5.97353	−	2.46867i	0.252880	−	0.104507i
$559$	−1.33874	+	2.93143i	−0.0566227	+	0.123986i
$560$	−17.9937	−	0.0581264i	−0.760374	−	0.00245629i
$561$	−2.75237	+	19.1431i	−0.116205	+	0.808224i
$562$	12.4275	+	2.25253i	0.524221	+	0.0950171i
$563$	−5.85912	+	19.9543i	−0.246933	+	0.840975i	0.738982	+	0.673725i	$0.235307\pi$
$563$	−5.85912	+	19.9543i	−0.246933	+	0.840975i	−0.985915	+	0.167250i	$0.946511\pi$
$564$	1.64942	−	0.115291i	0.0694530	−	0.00485463i
$565$	4.06661	−	1.85716i	0.171084	−	0.0781313i
$566$	−18.4271	+	19.7600i	−0.774547	+	0.830576i
$567$	−2.93259	+	3.38438i	−0.123157	+	0.142131i
$568$	−7.25733	+	8.96127i	−0.304511	+	0.376007i
$569$	−15.6032	−	10.0276i	−0.654121	−	0.420378i	0.171049	−	0.985263i	$-0.445284\pi$
$569$	−15.6032	−	10.0276i	−0.654121	−	0.420378i	−0.825170	+	0.564884i	$0.808921\pi$
$570$	−5.29622	+	10.5592i	−0.221834	+	0.442276i
$571$	−15.9073	−	24.7522i	−0.665698	−	1.03585i	−0.995769	−	0.0918904i	$-0.970709\pi$
$571$	−15.9073	−	24.7522i	−0.665698	−	1.03585i	0.330071	−	0.943956i	$-0.392927\pi$
$572$	−1.37162	+	2.50231i	−0.0573502	+	0.104627i
$573$	0.0708742	+	0.241376i	0.00296081	+	0.0100836i
$574$	0.880084	−	1.26538i	0.0367340	−	0.0528159i
$575$	−7.70926	−	17.5185i	−0.321498	−	0.730574i
$576$	−7.00277	−	3.86797i	−0.291782	−	0.161165i
$577$	−19.1617	+	5.62639i	−0.797713	+	0.234230i	−0.655094	−	0.755548i	$-0.727371\pi$
$577$	−19.1617	+	5.62639i	−0.797713	+	0.234230i	−0.142620	+	0.989778i	$0.545553\pi$
$578$	31.4294	−	3.35334i	1.30729	−	0.139481i
$579$	3.76146	+	5.85294i	0.156321	+	0.243240i
$580$	5.73924	−	3.12184i	0.238309	−	0.129627i
$581$	42.9263	−	66.7947i	1.78088	−	2.77111i
$582$	13.2455	−	7.84445i	0.549043	−	0.325163i
$583$	6.70377	−	7.73656i	0.277642	−	0.320415i
$584$	−13.5636	+	32.5223i	−0.561264	+	1.34578i
$585$	−0.193117	−	0.422867i	−0.00798440	−	0.0174834i
$586$	5.80225	+	7.21206i	0.239689	+	0.297928i
$587$	−0.0536258	+	0.182633i	−0.00221337	+	0.00753806i	−0.960592	−	0.277961i	$-0.910341\pi$
$587$	−0.0536258	+	0.182633i	−0.00221337	+	0.00753806i	0.958379	+	0.285499i	$0.0921595\pi$
$588$	−18.4315	−	18.4911i	−0.760101	−	0.762560i
$589$	37.6180	+	5.40865i	1.55002	+	0.222859i
$590$	2.00986	+	7.90118i	0.0827447	+	0.325287i
$591$	1.00465	−	2.19988i	0.0413258	−	0.0904909i
$592$	−4.24268	−	30.2008i	−0.174373	−	1.24124i
$593$	2.08131	+	14.4758i	0.0854691	+	0.594451i	0.986876	+	0.161478i	$0.0516262\pi$
$593$	2.08131	+	14.4758i	0.0854691	+	0.594451i	−0.901407	+	0.432973i	$0.857465\pi$
$594$	−0.159142	+	4.35721i	−0.00652966	+	0.178779i
$595$	21.3263	−	18.4793i	0.874291	−	0.757578i
$596$	14.5082	−	10.8242i	0.594280	−	0.443376i
$597$			22.6542i			0.927174i
$598$	−3.05228	+	0.731604i	−0.124817	+	0.0299175i
$599$	−24.4734			−0.999957			−0.499979	−	0.866038i	$-0.666659\pi$
$599$	−24.4734			−0.999957			−0.499979	+	0.866038i	$0.666659\pi$
$600$	0.375564	+	11.2818i	0.0153324	+	0.460577i
$601$	−0.896747	−	1.03490i	−0.0365791	−	0.0422145i	0.737165	−	0.675713i	$-0.236164\pi$
$601$	−0.896747	−	1.03490i	−0.0365791	−	0.0422145i	−0.773744	+	0.633498i	$0.781618\pi$
$602$	−44.0723	−	1.60968i	−1.79625	−	0.0656059i
$603$	5.09179	−	0.732089i	0.207354	−	0.0298130i
$604$	−9.68819	+	44.1921i	−0.394207	+	1.79815i
$605$	−1.36577	−	0.623726i	−0.0555264	−	0.0253581i
$606$	3.12088	+	12.2688i	0.126777	+	0.498388i
$607$	−6.23344	+	43.3545i	−0.253007	+	1.75970i	0.326934	+	0.945047i	$0.393984\pi$
$607$	−6.23344	+	43.3545i	−0.253007	+	1.75970i	−0.579942	+	0.814658i	$0.696925\pi$
$608$	−23.8390	−	40.5508i	−0.966800	−	1.64455i
$609$	13.9730	+	4.10283i	0.566213	+	0.166255i
$610$	7.67668	−	6.17604i	0.310820	−	0.250061i
$611$	−0.348017	+	0.158934i	−0.0140793	+	0.00642978i
$612$	12.2635	−	2.64703i	0.495723	−	0.107000i
$613$	−19.8530	−	17.2027i	−0.801855	−	0.694811i	0.154187	−	0.988042i	$-0.450724\pi$
$613$	−19.8530	−	17.2027i	−0.801855	−	0.694811i	−0.956042	+	0.293230i	$0.905270\pi$
$614$	19.3308	−	11.4484i	0.780128	−	0.462020i
$615$	0.205670	+	0.132176i	0.00829341	+	0.00532985i
$616$	−38.8168	−	4.26840i	−1.56397	−	0.171979i
$617$	6.01869	−	3.86798i	0.242303	−	0.155719i	−0.413853	−	0.910344i	$-0.635817\pi$
$617$	6.01869	−	3.86798i	0.242303	−	0.155719i	0.656157	+	0.754625i	$0.272181\pi$
$618$	3.01808	+	28.2872i	0.121405	+	1.13788i
$619$	4.27665	+	14.5649i	0.171893	+	0.585414i	0.999702	+	0.0244043i	$0.00776890\pi$
$619$	4.27665	+	14.5649i	0.171893	+	0.585414i	−0.827809	+	0.561010i	$0.810413\pi$
$620$	−8.60845	+	3.19496i	−0.345724	+	0.128313i
$621$	−3.66756	+	3.09014i	−0.147174	+	0.124003i
$622$	4.68887	−	6.74163i	0.188007	−	0.270315i
$623$	−63.8537	+	18.7491i	−2.55824	+	0.751168i
$624$	1.83142	+	0.269360i	0.0733157	+	0.0107830i
$625$	9.15460	−	5.88330i	0.366184	−	0.235332i
$626$	−13.1352	−	6.58830i	−0.524990	−	0.263322i
$627$	−13.8604	+	21.5671i	−0.553530	+	0.861309i
$628$	1.81627	−	24.8311i	0.0724771	−	0.990868i
$629$	36.1454	+	31.3201i	1.44121	+	1.24882i
$630$	4.33879	−	4.65265i	0.172862	−	0.185366i
$631$	−3.60830	−	7.90107i	−0.143644	−	0.314537i	0.824112	−	0.566427i	$-0.191675\pi$
$631$	−3.60830	−	7.90107i	−0.143644	−	0.314537i	−0.967756	+	0.251891i	$0.918948\pi$
$632$	−6.11760	−	3.64981i	−0.243345	−	0.145182i
$633$	−0.938725	−	0.275635i	−0.0373110	−	0.0109555i
$634$	1.50632	−	8.31057i	0.0598237	−	0.330055i
$635$	−2.46586	−	0.354537i	−0.0978547	−	0.0140694i
$636$	−6.21828	−	2.33075i	−0.246571	−	0.0924202i
$637$	5.49528	+	2.50961i	0.217731	+	0.0994343i
$638$	13.1040	−	5.41546i	0.518792	−	0.214400i
$639$	−0.580213	−	4.03547i	−0.0229529	−	0.159641i
$640$	9.74107	+	5.85435i	0.385049	+	0.231413i
$641$	−13.9539	−	16.1037i	−0.551146	−	0.636057i	0.410003	−	0.912084i	$-0.365528\pi$
$641$	−13.9539	−	16.1037i	−0.551146	−	0.636057i	−0.961150	+	0.276027i	$0.910982\pi$
$642$	3.58256	−	10.7349i	0.141392	−	0.423674i
$643$			33.6298i			1.32623i	0.748518	+	0.663114i	$0.230766\pi$
$643$			33.6298i			1.32623i	−0.748518	+	0.663114i	$0.769234\pi$
$644$	−25.2064	−	34.7795i	−0.993273	−	1.37050i
$645$		−	6.99520i		−	0.275436i
$646$	69.9746	+	23.3526i	2.75311	+	0.918794i
$647$	−15.9042	−	18.3545i	−0.625260	−	0.721588i	0.351437	−	0.936211i	$-0.385693\pi$
$647$	−15.9042	−	18.3545i	−0.625260	−	0.721588i	−0.976697	+	0.214623i	$0.931148\pi$
$648$	2.68584	−	0.886712i	0.105510	−	0.0348333i
$649$	2.51805	+	17.5134i	0.0988419	+	0.687461i
$650$	−0.997600	−	2.41393i	−0.0391291	−	0.0946822i
$651$	−18.6176	−	8.50237i	−0.729681	−	0.333234i
$652$	1.18239	−	3.15454i	0.0463060	−	0.123541i
$653$	−26.3681	−	3.79116i	−1.03186	−	0.148359i	−0.394478	−	0.918905i	$-0.629075\pi$
$653$	−26.3681	−	3.79116i	−1.03186	−	0.148359i	−0.637384	+	0.770546i	$0.719984\pi$
$654$	8.67025	+	1.57152i	0.339034	+	0.0614511i
$655$	13.9115	+	4.08478i	0.543566	+	0.159605i
$656$	−0.886841	+	0.401549i	−0.0346253	+	0.0156779i
$657$	−5.17535	−	11.3324i	−0.201910	−	0.442121i
$658$	−3.82910	−	3.57080i	−0.149274	−	0.139204i
$659$	−12.0209	−	10.4162i	−0.468269	−	0.405757i	0.388508	−	0.921446i	$-0.372991\pi$
$659$	−12.0209	−	10.4162i	−0.468269	−	0.405757i	−0.856776	+	0.515688i	$0.827536\pi$
$660$	0.451857	−	6.17755i	0.0175885	−	0.240461i
$661$	15.4285	−	24.0072i	0.600099	−	0.933772i	−0.399754	−	0.916622i	$-0.630905\pi$
$661$	15.4285	−	24.0072i	0.600099	−	0.933772i	0.999853	−	0.0171492i	$-0.00545904\pi$
$662$	−0.268041	+	0.534400i	−0.0104177	+	0.0207700i
$663$	−2.44217	+	1.56949i	−0.0948461	+	0.0609539i
$664$	−44.8983	+	22.3386i	−1.74239	+	0.866907i
$665$	35.8912	−	10.5386i	1.39180	−	0.408670i
$666$	8.85194	+	6.15662i	0.343006	+	0.238564i
$667$	14.0955	+	6.67445i	0.545778	+	0.258436i
$668$	−0.284188	−	0.765712i	−0.0109956	−	0.0296263i
$669$	1.19460	+	4.06842i	0.0461857	+	0.157294i
$670$	−7.26663	+	0.775308i	−0.280734	+	0.0299527i
$671$	17.9882	−	11.5603i	0.694425	−	0.446280i
$672$	6.16571	+	24.5706i	0.237847	+	0.947833i
$673$	14.9932	+	9.63555i	0.577945	+	0.371423i	0.796716	−	0.604353i	$-0.206568\pi$
$673$	14.9932	+	9.63555i	0.577945	+	0.371423i	−0.218771	+	0.975776i	$0.570205\pi$
$674$	2.30693	+	3.89529i	0.0888597	+	0.150041i
$675$	−3.01614	−	2.61350i	−0.116091	−	0.100594i
$676$	24.9960	−	5.39528i	0.961385	−	0.207511i
$677$	−36.0415	+	16.4596i	−1.38519	+	0.632594i	−0.961900	−	0.273402i	$-0.911851\pi$
$677$	−36.0415	+	16.4596i	−1.38519	+	0.632594i	−0.423287	+	0.905996i	$0.639124\pi$
$678$	−3.94527	−	4.90388i	−0.151517	−	0.188332i
$679$	−46.7717	−	13.7334i	−1.79493	−	0.527039i
$680$	−17.5474	+	3.12202i	−0.672912	+	0.119724i
$681$	2.88726	−	20.0813i	0.110640	−	0.769518i
$682$	−19.3125	+	4.91262i	−0.739515	+	0.188114i
$683$	−15.0735	−	6.88383i	−0.576771	−	0.263403i	0.105600	−	0.994409i	$-0.466324\pi$
$683$	−15.0735	−	6.88383i	−0.576771	−	0.263403i	−0.682371	+	0.731006i	$0.739051\pi$
$684$	16.2450	+	3.56137i	0.621142	+	0.136172i
$685$	15.3979	−	2.21389i	0.588325	−	0.0845884i
$686$	−1.39944	+	38.3158i	−0.0534308	+	1.46291i
$687$	10.3574	+	11.9530i	0.395158	+	0.456037i
$688$	23.3841	+	15.1350i	0.891510	+	0.577016i
$689$	1.53661			0.0585401
$690$	5.36696	−	4.19681i	0.204317	−	0.159770i
$691$			27.7608i			1.05607i	0.849222	+	0.528035i	$0.177071\pi$
$691$			27.7608i			1.05607i	−0.849222	+	0.528035i	$0.822929\pi$
$692$	19.8569	−	14.8147i	0.754847	−	0.563171i
$693$	10.4343	−	9.04137i	0.396366	−	0.343453i
$694$	−18.4443	−	0.673656i	−0.700137	−	0.0255716i
$695$	0.378841	+	2.63490i	0.0143702	+	0.0999473i
$696$	−6.25130	−	6.74707i	−0.236955	−	0.255747i
$697$	0.634216	−	1.38874i	0.0240226	−	0.0526022i
$698$	−38.5111	+	9.79625i	−1.45767	+	0.370794i
$699$	20.3814	+	2.93040i	0.770895	+	0.110838i
$700$	25.3157	−	25.2341i	0.956845	−	0.953759i
$701$	−6.48583	+	22.0887i	−0.244966	+	0.834279i	0.741589	+	0.670854i	$0.234072\pi$
$701$	−6.48583	+	22.0887i	−0.244966	+	0.834279i	−0.986556	+	0.163425i	$0.947746\pi$
$702$	−0.509931	+	0.410249i	−0.0192461	+	0.0154839i
$703$	26.3370	+	57.6700i	0.993319	+	2.17507i
$704$	19.6731	+	14.8764i	0.741459	+	0.560676i
$705$	0.543838	−	0.627622i	0.0204821	−	0.0236376i
$706$	−6.37747	−	10.7685i	−0.240019	−	0.405276i
$707$	21.6728	−	33.7235i	0.815088	−	1.26830i
$708$	10.0827	−	5.48446i	0.378932	−	0.206119i
$709$	−5.10367	−	7.94146i	−0.191672	−	0.298248i	0.732095	−	0.681203i	$-0.238543\pi$
$709$	−5.10367	−	7.94146i	−0.191672	−	0.298248i	−0.923767	+	0.382955i	$0.874906\pi$
$710$	0.614465	+	5.75912i	0.0230605	+	0.216136i
$711$	2.41656	−	0.709567i	0.0906283	−	0.0266109i
$712$	40.7018	+	10.4936i	1.52536	+	0.393265i
$713$	−18.2736	−	12.1043i	−0.684353	−	0.453311i
$714$	−32.6146	−	22.6838i	−1.22057	−	0.848918i
$715$	0.403793	+	1.37519i	0.0151010	+	0.0514292i
$716$	6.14712	+	3.36948i	0.229729	+	0.125924i
$717$	−11.0128	−	17.1363i	−0.411281	−	0.639966i
$718$	−37.0718	−	18.5943i	−1.38351	−	0.693932i
$719$	−26.0705	−	16.7545i	−0.972267	−	0.624838i	−0.0449002	−	0.998991i	$-0.514297\pi$
$719$	−26.0705	−	16.7545i	−0.972267	−	0.624838i	−0.927367	+	0.374153i	$0.877933\pi$
$720$	−3.85899	+	1.11957i	−0.143816	+	0.0417240i
$721$	58.9907	−	68.0789i	2.19693	−	2.53539i
$722$	51.8645	+	48.3658i	1.93020	+	1.79999i
$723$	−7.97620	+	3.64261i	−0.296638	+	0.135470i
$724$	5.30441	−	0.370769i	0.197137	−	0.0137795i
$725$	−3.65641	+	12.4526i	−0.135796	+	0.462478i
$726$	−0.376993	+	2.07991i	−0.0139915	+	0.0771929i
$727$	−0.350742	+	2.43947i	−0.0130083	+	0.0904748i	−0.995291	−	0.0969287i	$-0.969098\pi$
$727$	−0.350742	+	2.43947i	−0.0130083	+	0.0904748i	0.982283	+	0.187404i	$0.0600072\pi$
$728$	−3.33138	−	4.82300i	−0.123469	−	0.178752i
$729$	−0.415415	+	0.909632i	−0.0153857	+	0.0336901i
$730$	6.75969	+	16.3567i	0.250187	+	0.605388i
$731$	−43.2383	+	6.21672i	−1.59922	+	0.229934i
$732$	−11.0908	−	8.33048i	−0.409929	−	0.307903i
$733$	−11.4008	+	9.87883i	−0.421097	+	0.364883i	−0.839482	−	0.543387i	$-0.817142\pi$
$733$	−11.4008	+	9.87883i	−0.421097	+	0.364883i	0.418385	+	0.908270i	$0.362596\pi$
$734$	−11.8713	+	35.5715i	−0.438176	+	1.31297i
$735$	−13.1132			−0.483689
$736$	2.41734	+	27.0214i	0.0891042	+	0.996022i
$737$	−15.8598			−0.584203
$738$	0.108958	−	0.326488i	0.00401082	−	0.0120182i
$739$	19.9437	−	17.2813i	0.733640	−	0.635702i	−0.205730	−	0.978609i	$-0.565957\pi$
$739$	19.9437	−	17.2813i	0.733640	−	0.635702i	0.939370	+	0.342906i	$0.111411\pi$
$740$	−12.2476	−	9.19935i	−0.450231	−	0.338175i
$741$	−3.80904	+	0.547657i	−0.139929	+	0.0201187i
$742$	8.03148	+	19.4341i	0.294845	+	0.713447i
$743$	−0.449366	+	0.983975i	−0.0164857	+	0.0360985i	−0.917696	−	0.397284i	$-0.869953\pi$
$743$	−0.449366	+	0.983975i	−0.0164857	+	0.0360985i	0.901210	+	0.433383i	$0.142680\pi$
$744$	7.34687	+	10.6364i	0.269349	+	0.389950i
$745$	1.29386	−	8.99901i	0.0474035	−	0.329698i
$746$	5.90698	−	32.5896i	0.216270	−	1.19319i
$747$	4.99517	−	17.0120i	0.182764	−	0.622436i
$748$	−38.5858	+	2.69708i	−1.41084	+	0.0986150i
$749$	−32.5974	+	14.8867i	−1.19108	+	0.543949i
$750$	9.34121	+	8.71106i	0.341093	+	0.318083i
$751$	33.5686	−	38.7402i	1.22493	−	1.41365i	0.344969	−	0.938614i	$-0.387890\pi$
$751$	33.5686	−	38.7402i	1.22493	−	1.41365i	0.879966	−	0.475036i	$-0.157565\pi$
$752$	0.921402	+	3.17592i	0.0336001	+	0.115814i
$753$	25.9035	+	16.6471i	0.943975	+	0.606656i
$754$	1.90242	+	0.954207i	0.0692822	+	0.0347502i
$755$	12.2851	+	19.1160i	0.447101	+	0.695703i
$756$	−7.85387	−	4.30502i	−0.285643	−	0.156572i
$757$	12.0445	+	41.0198i	0.437765	+	1.49089i	0.822983	+	0.568065i	$0.192308\pi$
$757$	12.0445	+	41.0198i	0.437765	+	1.49089i	−0.385218	+	0.922825i	$0.625874\pi$
$758$	−17.2443	−	11.9936i	−0.626341	−	0.435626i
$759$	12.5481	−	7.82095i	0.455467	−	0.283882i
$760$	−22.8779	−	5.89830i	−0.829867	−	0.213954i
$761$	−5.19063	+	1.52411i	−0.188160	+	0.0552488i	−0.374455	−	0.927245i	$-0.622170\pi$
$761$	−5.19063	+	1.52411i	−0.188160	+	0.0552488i	0.186295	+	0.982494i	$0.440352\pi$
$762$	0.372090	+	3.48744i	0.0134794	+	0.126337i
$763$	−15.0850	−	23.4728i	−0.546115	−	0.849772i
$764$	−0.441977	+	0.240412i	−0.0159902	+	0.00869779i
$765$	3.40678	−	5.30105i	0.123172	−	0.191660i
$766$	−6.72528	−	11.3557i	−0.242994	−	0.410300i
$767$	−1.73922	+	2.00717i	−0.0627997	+	0.0724747i
$768$	4.60681	−	15.3224i	0.166234	−	0.552901i
$769$	5.27922	+	11.5599i	0.190374	+	0.416860i	0.980617	−	0.195933i	$-0.0627734\pi$
$769$	5.27922	+	11.5599i	0.190374	+	0.416860i	−0.790244	+	0.612793i	$0.790046\pi$
$770$	−15.2821	+	12.2947i	−0.550727	+	0.443071i
$771$	−0.559070	+	1.90402i	−0.0201344	+	0.0685715i
$772$	−9.85514	+	9.82335i	−0.354694	+	0.353550i
$773$	−15.7304	−	2.26170i	−0.565785	−	0.0813475i	−0.146514	−	0.989209i	$-0.546805\pi$
$773$	−15.7304	−	2.26170i	−0.565785	−	0.0813475i	−0.419271	+	0.907861i	$0.637714\pi$
$774$	−9.54417	+	2.42780i	−0.343058	+	0.0872654i
$775$	7.57725	−	16.5919i	0.272183	−	0.595997i
$776$	20.9250	+	22.5845i	0.751162	+	0.810735i
$777$	−4.85908	−	33.7956i	−0.174318	−	1.21241i
$778$	−19.4926	−	0.711944i	−0.698845	−	0.0255244i
$779$	1.52948	−	1.32530i	0.0547991	−	0.0474837i
$780$	0.745206	−	0.555978i	0.0266826	−	0.0199072i
$781$			12.5696i			0.449775i
$782$	−30.7107	−	29.4441i	−1.09821	−	1.05292i
$783$	3.25196			0.116215
$784$	28.3721	−	43.8359i	1.01329	−	1.56557i
$785$	−8.18908	−	9.45071i	−0.292281	−	0.337310i
$786$	0.745024	−	20.3983i	0.0265741	−	0.727585i
$787$	−10.6017	+	1.52430i	−0.377911	+	0.0543354i	−0.328653	−	0.944451i	$-0.606595\pi$
$787$	−10.6017	+	1.52430i	−0.377911	+	0.0543354i	−0.0492578	+	0.998786i	$0.515686\pi$
$788$	4.72465	+	1.03578i	0.168309	+	0.0368981i
$789$	−24.7344	−	11.2958i	−0.880569	−	0.402143i
$790$	−3.46752	+	0.882049i	−0.123369	+	0.0313819i
$791$	−2.83633	+	19.7271i	−0.100848	+	0.701416i
$792$	−8.58541	+	1.52751i	−0.305069	+	0.0542777i
$793$	3.07960	+	0.904252i	0.109360	+	0.0321109i
$794$	13.6548	+	16.9726i	0.484590	+	0.602335i
$795$	−3.03399	+	1.38558i	−0.107605	+	0.0491414i
$796$	−44.2884	+	9.55946i	−1.56976	+	0.338826i
$797$	−3.03684	−	2.63144i	−0.107571	−	0.0932104i	0.599415	−	0.800438i	$-0.295400\pi$
$797$	−3.03684	−	2.63144i	−0.107571	−	0.0932104i	−0.706985	+	0.707228i	$0.749945\pi$
$798$	−26.8354	−	45.3120i	−0.949962	−	1.60403i
$799$	−4.36273	−	2.80376i	−0.154342	−	0.0991898i
$800$	−21.8972	+	5.49484i	−0.774182	+	0.194272i
$801$	−12.5017	+	8.03436i	−0.441726	+	0.283880i
$802$	−19.8224	+	2.11493i	−0.699952	+	0.0746809i
$803$	10.8213	+	36.8538i	0.381874	+	1.30054i
$804$	3.57982	+	9.64542i	0.126251	+	0.340168i
$805$	−21.3097	−	3.36550i	−0.751069	−	0.118618i
$806$	−2.45566	−	1.70794i	−0.0864971	−	0.0601596i
$807$	−21.3329	+	6.26389i	−0.750952	+	0.220499i
$808$	−22.6684	+	11.2784i	−0.797471	+	0.396772i
$809$	−4.59597	+	2.95365i	−0.161586	+	0.103845i	−0.618935	−	0.785443i	$-0.712435\pi$
$809$	−4.59597	+	2.95365i	−0.161586	+	0.103845i	0.457349	+	0.889287i	$0.348799\pi$
$810$	0.636918	−	1.26984i	0.0223790	−	0.0446175i
$811$	18.9434	−	29.4765i	0.665193	−	1.03506i	−0.330631	−	0.943760i	$-0.607261\pi$
$811$	18.9434	−	29.4765i	0.665193	−	1.03506i	0.995823	−	0.0913000i	$-0.0291022\pi$
$812$	−2.12473	+	29.0481i	−0.0745632	+	1.01939i
$813$	−9.16030	−	7.93744i	−0.321266	−	0.278378i
$814$	−24.3121	−	22.6720i	−0.852137	−	0.794653i
$815$	−0.702905	−	1.53915i	−0.0246217	−	0.0539140i
$816$	10.3498	+	22.8579i	0.362314	+	0.800187i
$817$	−55.5601	−	16.3139i	−1.94380	−	0.570751i
$818$	−29.0224	−	5.26043i	−1.01475	−	0.183927i
$819$	2.05133	+	0.294936i	0.0716792	+	0.0103059i
$820$	−0.171614	+	0.457855i	−0.00599302	+	0.0159890i
$821$	−9.58237	−	4.37612i	−0.334427	−	0.152728i	0.241122	−	0.970495i	$-0.422484\pi$
$821$	−9.58237	−	4.37612i	−0.334427	−	0.152728i	−0.575549	+	0.817767i	$0.695212\pi$
$822$	−8.36471	−	20.2404i	−0.291753	−	0.705966i
$823$	4.78353	+	33.2702i	0.166743	+	1.15973i	0.885560	+	0.464526i	$0.153775\pi$
$823$	4.78353	+	33.2702i	0.166743	+	1.15973i	−0.718816	+	0.695200i	$0.755316\pi$
$824$	−54.0273	+	17.8367i	−1.88213	+	0.621372i
$825$	8.05760	+	9.29896i	0.280530	+	0.323748i
$826$	−34.4760	−	11.5056i	−1.19957	−	0.400332i
$827$		−	56.9260i		−	1.97951i	−0.142775	−	0.989755i	$-0.545603\pi$
$827$		−	56.9260i		−	1.97951i	0.142775	−	0.989755i	$-0.454397\pi$
$828$	−7.58878	−	5.86605i	−0.263728	−	0.203859i
$829$		−	12.8171i		−	0.445155i	−0.974915	−	0.222578i	$-0.928553\pi$
$829$		−	12.8171i		−	0.445155i	0.974915	−	0.222578i	$-0.0714471\pi$
$830$	−7.97360	+	23.8924i	−0.276768	+	0.829318i
$831$	−3.13698	−	3.62026i	−0.108821	−	0.125586i
$832$	0.246219	+	3.69406i	0.00853611	+	0.128068i
$833$	11.6539	+	81.0546i	0.403783	+	2.80837i
$834$	3.46354	−	1.43137i	0.119933	−	0.0495642i
$835$	−0.373152	−	0.170413i	−0.0129135	−	0.00589738i
$836$	−48.0120	−	17.9959i	−1.66053	−	0.622403i
$837$	−4.52390	−	0.650438i	−0.156369	−	0.0224824i
$838$	−2.01345	+	11.1084i	−0.0695534	+	0.383735i
$839$	24.5244	+	7.20103i	0.846678	+	0.248607i	0.676167	−	0.736749i	$-0.263640\pi$
$839$	24.5244	+	7.20103i	0.846678	+	0.248607i	0.170511	+	0.985356i	$0.445458\pi$
$840$	10.9267	+	6.51895i	0.377006	+	0.224925i
$841$	7.65393	+	16.7598i	0.263929	+	0.577923i
$842$	33.8386	−	36.2864i	1.16616	−	1.25051i
$843$	−6.74939	−	5.84838i	−0.232461	−	0.201429i
$844$	0.142742	−	1.95150i	0.00491339	−	0.0671733i
$845$	6.94384	−	10.8048i	0.238875	−	0.371697i
$846$	−1.04507	−	0.524180i	−0.0359302	−	0.0180217i
$847$	5.63091	−	3.61877i	0.193480	−	0.124342i
$848$	1.93261	−	13.1401i	0.0663661	−	0.451234i
$849$	18.3313	−	5.38255i	0.629128	−	0.184729i
$850$	20.2156	−	29.0659i	0.693390	−	0.996951i
$851$	0.506015	−	36.5615i	0.0173460	−	1.25331i
$852$	7.64442	−	2.83716i	0.261893	−	0.0971997i
$853$	−2.94500	−	10.0297i	−0.100835	−	0.343412i	0.893587	−	0.448891i	$-0.148181\pi$
$853$	−2.94500	−	10.0297i	−0.100835	−	0.343412i	−0.994422	+	0.105479i	$0.966363\pi$
$854$	4.65990	+	43.6752i	0.159458	+	1.49454i
$855$	7.02702	−	4.51599i	0.240319	−	0.154444i
$856$	22.4983	+	2.47397i	0.768976	+	0.0845586i
$857$	−6.33759	−	4.07292i	−0.216488	−	0.139128i	0.427903	−	0.903825i	$-0.359253\pi$
$857$	−6.33759	−	4.07292i	−0.216488	−	0.139128i	−0.644391	+	0.764696i	$0.722889\pi$
$858$	1.73615	−	1.02821i	0.0592713	−	0.0351026i
$859$	−4.67299	−	4.04916i	−0.159440	−	0.138156i	0.571487	−	0.820611i	$-0.306367\pi$
$859$	−4.67299	−	4.04916i	−0.159440	−	0.138156i	−0.730927	+	0.682455i	$0.760912\pi$
$860$	13.6755	−	2.95179i	0.466330	−	0.100655i
$861$	−0.991401	+	0.452758i	−0.0337869	+	0.0154299i
$862$	−22.5557	+	18.1465i	−0.768252	+	0.618074i
$863$	41.8480	+	12.2877i	1.42452	+	0.418277i	0.901031	−	0.433755i	$-0.142812\pi$
$863$	41.8480	+	12.2877i	1.42452	+	0.418277i	0.523490	+	0.852032i	$0.324630\pi$
$864$	2.86686	+	4.87659i	0.0975324	+	0.165905i
$865$	1.77087	−	12.3167i	0.0602113	−	0.418779i
$866$	−3.27569	−	12.8774i	−0.111313	−	0.437593i
$867$	−20.3304	−	9.28457i	−0.690456	−	0.315321i
$868$	8.76581	−	39.9847i	0.297531	−	1.35717i
$869$	−7.68594	+	1.10507i	−0.260727	+	0.0374870i
$870$	−4.61671	−	0.168619i	−0.156521	−	0.00571673i
$871$	−1.55897	−	1.79915i	−0.0528238	−	0.0609620i
$872$	0.586336	+	17.6133i	0.0198559	+	0.596461i
$873$	−10.8853			−0.368410
$874$	−20.8170	−	52.4152i	−0.704146	−	1.77297i
$875$		−	40.4453i		−	1.36730i
$876$	19.9708	−	14.8997i	0.674751	−	0.503414i
$877$	8.48912	−	7.35587i	0.286657	−	0.248390i	−0.499647	−	0.866229i	$-0.666537\pi$
$877$	8.48912	−	7.35587i	0.286657	−	0.248390i	0.786305	+	0.617839i	$0.211992\pi$
$878$	1.05381	−	28.8528i	0.0355645	−	0.973736i
$879$	−0.931482	−	6.47860i	−0.0314181	−	0.218518i
$880$	12.2677	−	1.72339i	0.413542	−	0.0580956i
$881$	−15.1138	+	33.0945i	−0.509196	+	1.11498i	0.464174	+	0.885744i	$0.346351\pi$
$881$	−15.1138	+	33.0945i	−0.509196	+	1.11498i	−0.973370	+	0.229239i	$0.926376\pi$
$882$	4.55116	+	17.8915i	0.153245	+	0.602439i
$883$	−33.0750	−	4.75547i	−1.11306	−	0.160034i	−0.438842	−	0.898564i	$-0.644611\pi$
$883$	−33.0750	−	4.75547i	−1.11306	−	0.160034i	−0.674221	+	0.738530i	$0.735520\pi$
$884$	−4.09885	−	4.11211i	−0.137859	−	0.138305i
$885$	1.62416	−	5.53139i	0.0545956	−	0.185935i
$886$	17.4040	+	21.6327i	0.584697	+	0.726766i
$887$	5.95857	+	13.0474i	0.200069	+	0.438090i	0.982899	−	0.184146i	$-0.0589518\pi$
$887$	5.95857	+	13.0474i	0.200069	+	0.438090i	−0.782830	+	0.622236i	$0.786225\pi$
$888$	−8.30076	+	19.9033i	−0.278555	+	0.667910i
$889$	7.27278	−	8.39324i	0.243921	−	0.281500i
$890$	18.1649	−	10.7579i	0.608889	−	0.360606i
$891$	1.66683	−	2.59364i	0.0558410	−	0.0868903i
$892$	−7.44958	+	4.05217i	−0.249430	+	0.135677i
$893$	−3.71664	−	5.78320i	−0.124372	−	0.193527i
$894$	−12.7272	+	1.35792i	−0.425662	+	0.0454156i
$895$	3.37827	−	0.991948i	0.112923	−	0.0331572i
$896$	−45.4333	+	22.4220i	−1.51782	+	0.749066i
$897$	2.12066	+	0.654694i	0.0708069	+	0.0218596i
$898$	−14.1632	+	20.3638i	−0.472634	+	0.679550i
$899$	4.18733	+	14.2608i	0.139655	+	0.475623i
$900$	3.83660	−	6.99931i	0.127887	−	0.233310i
$901$	11.2608	+	17.5221i	0.375151	+	0.583746i
$902$	−0.475759	+	0.948531i	−0.0158410	+	0.0315826i
$903$	26.2342	+	16.8597i	0.873018	+	0.561055i
$904$	7.92218	−	9.78222i	0.263488	−	0.325352i
$905$	1.74895	−	2.01839i	0.0581369	−	0.0670936i
$906$	21.8179	−	23.3962i	0.724852	−	0.777286i
$907$	−4.49190	+	2.05138i	−0.149151	+	0.0681150i	−0.488592	−	0.872512i	$-0.662489\pi$
$907$	−4.49190	+	2.05138i	−0.149151	+	0.0681150i	0.339441	+	0.940627i	$0.389762\pi$
$908$	40.4769	−	2.82926i	1.34327	−	0.0938923i
$909$	2.52197	−	8.58906i	0.0836486	−	0.284881i
$910$	−2.89691	−	0.525077i	−0.0960318	−	0.0174061i
$911$	3.25099	−	22.6111i	0.107710	−	0.749139i	−0.862357	−	0.506301i	$-0.831012\pi$
$911$	3.25099	−	22.6111i	0.107710	−	0.749139i	0.970067	−	0.242838i	$-0.0780785\pi$
$912$	−0.107447	+	33.2614i	−0.00355791	+	1.10139i
$913$	−22.7080	+	49.7236i	−0.751525	+	1.64561i
$914$	24.1933	−	9.99832i	0.800244	−	0.330715i
$915$	−6.89597	+	0.991490i	−0.227974	+	0.0327777i
$916$	−18.9974	+	25.2923i	−0.627692	+	0.835681i
$917$	−48.8483	+	42.3273i	−1.61311	+	1.39777i
$918$	−8.41507	−	2.80835i	−0.277739	−	0.0926895i
$919$	53.5957			1.76796			0.883980	−	0.467525i	$-0.154854\pi$
$919$	53.5957			1.76796			0.883980	+	0.467525i	$0.154854\pi$
$920$	10.4694	+	8.72134i	0.345166	+	0.287534i
$921$	−15.8863			−0.523470
$922$	8.20517	+	2.73831i	0.270223	+	0.0901813i
$923$	−1.42591	+	1.23556i	−0.0469343	+	0.0406688i
$924$	22.0787	+	16.5836i	0.726335	+	0.545560i
$925$	30.1184	−	4.33037i	0.990287	−	0.142382i
$926$	−29.9559	+	12.3798i	−0.984413	+	0.406826i
$927$	8.35632	−	18.2978i	0.274458	−	0.600978i
$928$	10.5525	−	15.0682i	0.346403	−	0.494639i
$929$	0.0287966	−	0.200285i	0.000944785	−	0.00657113i	−0.989344	−	0.145600i	$-0.953489\pi$
$929$	0.0287966	−	0.200285i	0.000944785	−	0.00657113i	0.990288	+	0.139028i	$0.0443980\pi$
$930$	6.38872	+	1.15798i	0.209494	+	0.0379716i
$931$	−30.5821	+	104.153i	−1.00229	+	3.41348i
$932$	2.87154	+	41.0817i	0.0940603	+	1.34568i
$933$	−5.28195	+	2.41218i	−0.172923	+	0.0789714i
$934$	−26.6459	+	28.5734i	−0.871881	+	0.934951i
$935$	−12.7223	+	14.6824i	−0.416065	+	0.480165i
$936$	−1.01721	−	0.823789i	−0.0332484	−	0.0269264i
$937$	24.5049	+	15.7483i	0.800540	+	0.514476i	0.875792	−	0.482689i	$-0.160340\pi$
$937$	24.5049	+	15.7483i	0.800540	+	0.514476i	−0.0752519	+	0.997165i	$0.523976\pi$
$938$	14.6062	−	29.1207i	0.476910	−	0.950825i
$939$	5.61773	+	8.74136i	0.183328	+	0.285263i
$940$	1.45647	+	0.798351i	0.0475049	+	0.0260393i
$941$	−5.70436	−	19.4273i	−0.185957	−	0.633311i	−0.998714	−	0.0507075i	$-0.983852\pi$
$941$	−5.70436	−	19.4273i	−0.185957	−	0.633311i	0.812757	−	0.582603i	$-0.197966\pi$
$942$	−10.0523	+	14.4531i	−0.327521	+	0.470908i
$943$	−1.12437	+	0.313309i	−0.0366144	+	0.0102027i
$944$	14.9767	+	17.3972i	0.487448	+	0.566231i
$945$	−4.31624	+	1.26736i	−0.140407	+	0.0412273i
$946$	30.1911	−	3.22122i	0.981597	−	0.104731i
$947$	17.2186	+	26.7926i	0.559528	+	0.870642i	0.999627	−	0.0273067i	$-0.00869308\pi$
$947$	17.2186	+	26.7926i	0.559528	+	0.870642i	−0.440099	+	0.897949i	$0.645057\pi$
$948$	2.40691	+	4.42491i	0.0781730	+	0.143714i
$949$	−3.11704	+	4.85021i	−0.101183	+	0.157445i
$950$	40.3817	−	23.9155i	1.31016	−	0.775921i
$951$	−3.91097	+	4.51349i	−0.126822	+	0.146360i
$952$	30.5838	−	73.3327i	0.991226	−	2.37673i
$953$	12.9627	+	28.3843i	0.419903	+	0.919459i	0.994859	+	0.101274i	$0.0322920\pi$
$953$	12.9627	+	28.3843i	0.419903	+	0.919459i	−0.574956	+	0.818184i	$0.694981\pi$
$954$	2.94346	+	3.65866i	0.0952981	+	0.118453i
$955$	−0.0711952	+	0.242468i	−0.00230382	+	0.00784609i
$956$	28.8539	−	28.7609i	0.933202	−	0.930192i
$957$	−9.92396	−	1.42685i	−0.320796	−	0.0461235i
$958$	−10.0694	−	39.5849i	−0.325328	−	1.27893i
$959$	−28.8090	+	63.0829i	−0.930291	+	2.03705i
$960$	−3.81713	−	7.07180i	−0.123197	−	0.228241i
$961$	1.43899	+	10.0084i	0.0464189	+	0.322850i
$962$	0.182129	−	4.98659i	0.00587207	−	0.160774i
$963$	−6.04773	+	5.24039i	−0.194886	+	0.168869i
$964$	−10.4870	−	14.0562i	−0.337762	−	0.452720i
$965$			6.98891i			0.224981i
$966$	2.80403	+	30.2428i	0.0902182	+	0.973046i
$967$	2.03888			0.0655658			0.0327829	−	0.999462i	$-0.489563\pi$
$967$	2.03888			0.0655658			0.0327829	+	0.999462i	$0.489563\pi$
$968$	−4.22527	+	0.140657i	−0.135805	+	0.00452088i
$969$	−34.1589	−	39.4215i	−1.09734	−	1.26640i
$970$	15.4535	+	0.564419i	0.496182	+	0.0181224i
$971$	−10.8021	+	1.55311i	−0.346657	+	0.0498418i	−0.313444	−	0.949607i	$-0.601483\pi$
$971$	−10.8021	+	1.55311i	−0.346657	+	0.0498418i	−0.0332127	+	0.999448i	$0.510574\pi$
$972$	−1.95360	−	0.428287i	−0.0626619	−	0.0137373i
$973$	−10.7947	−	4.92979i	−0.346063	−	0.158042i
$974$	6.09153	+	23.9471i	0.195185	+	0.767313i
$975$	−0.262845	+	1.82813i	−0.00841778	+	0.0585469i
$976$	11.6059	−	25.1976i	0.371495	−	0.806555i
$977$	20.8446	+	6.12053i	0.666878	+	0.195813i	0.597613	−	0.801785i	$-0.296116\pi$
$977$	20.8446	+	6.12053i	0.666878	+	0.195813i	0.0692659	+	0.997598i	$0.477934\pi$
$978$	−1.85604	+	1.49322i	−0.0593496	+	0.0477479i
$979$	41.6765	−	19.0330i	1.33199	−	0.608298i
$980$	−5.53343	−	25.6361i	−0.176759	−	0.818914i
$981$	−4.70884	−	4.08023i	−0.150342	−	0.130272i
$982$	34.0564	−	20.1694i	1.08678	−	0.643631i
$983$	2.51591	+	1.61688i	0.0802452	+	0.0515705i	0.580148	−	0.814511i	$-0.302995\pi$
$983$	2.51591	+	1.61688i	0.0802452	+	0.0515705i	−0.499903	+	0.866081i	$0.666631\pi$
$984$	0.684254	+	0.0752423i	0.0218132	+	0.00239864i
$985$	2.04372	−	1.31342i	0.0651184	−	0.0418491i
$986$	3.06067	+	28.6863i	0.0974714	+	0.913558i
$987$	1.04303	+	3.55224i	0.0332001	+	0.113069i
$988$	−2.67797	−	7.21549i	−0.0851976	−	0.229555i
$989$	24.9344	+	22.2173i	0.792868	+	0.706469i
$990$	−2.50084	+	3.59569i	−0.0794818	+	0.114279i
$991$	−27.9269	+	8.20008i	−0.887127	+	0.260484i	−0.693384	−	0.720568i	$-0.743881\pi$
$991$	−27.9269	+	8.20008i	−0.887127	+	0.260484i	−0.193743	+	0.981052i	$0.562063\pi$
$992$	−17.6938	+	18.8512i	−0.561778	+	0.598528i
$993$	0.355637	−	0.228554i	0.0112858	−	0.00725295i
$994$	−23.0794	−	11.5761i	−0.732035	−	0.367170i
$995$	−12.3032	+	19.1442i	−0.390039	+	0.606912i
$996$	35.3659	+	2.58684i	1.12061	+	0.0819671i
$997$	10.8370	+	9.39032i	0.343212	+	0.297395i	0.809361	−	0.587311i	$-0.199814\pi$
$997$	10.8370	+	9.39032i	0.343212	+	0.297395i	−0.466149	+	0.884706i	$0.654359\pi$
$998$	27.6213	−	29.6194i	0.874337	−	0.937585i
$999$	−3.16726	−	6.93533i	−0.100208	−	0.219424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.469.29	yes	480
8.5	even	2	inner	552.2.bb.a.469.36	yes	480
23.18	even	11	inner	552.2.bb.a.133.36	yes	480
184.133	even	22	inner	552.2.bb.a.133.29	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.133.29	✓	480	184.133	even	22	inner
552.2.bb.a.133.36	yes	480	23.18	even	11	inner
552.2.bb.a.469.29	yes	480	1.1	even	1	trivial
552.2.bb.a.469.36	yes	480	8.5	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.447692 - 1.34148i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(-1.59914 - 1.20114i) q^{4} +(-0.994303 + 0.142959i) q^{5} +(0.540141 + 1.30700i) q^{6} +(1.86030 - 4.07350i) q^{7} +(-2.32723 + 1.60748i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.447692 - 1.34148i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(-1.59914 - 1.20114i) q^{4} +(-0.994303 + 0.142959i) q^{5} +(0.540141 + 1.30700i) q^{6} +(1.86030 - 4.07350i) q^{7} +(-2.32723 + 1.60748i) q^{8} +(0.142315 - 0.989821i) q^{9} +(-0.253364 + 1.39784i) q^{10} +(-0.868601 + 2.95818i) q^{11} +(1.99513 - 0.139456i) q^{12} +(-0.420961 + 0.192246i) q^{13} +(-4.63168 - 4.31923i) q^{14} +(0.657826 - 0.759171i) q^{15} +(1.11453 + 3.84159i) q^{16} +(-5.27716 - 3.39142i) q^{17} +(-1.26411 - 0.634047i) q^{18} +(-4.49564 - 6.99535i) q^{19} +(1.76175 + 0.965685i) q^{20} +(1.26165 + 4.29678i) q^{21} +(3.57948 + 2.48957i) q^{22} +(0.616760 + 4.75601i) q^{23} +(0.706126 - 2.73887i) q^{24} +(-3.82926 + 1.12437i) q^{25} +(0.0694343 + 0.650778i) q^{26} +(0.540641 + 0.841254i) q^{27} +(-7.86774 + 4.27963i) q^{28} +(1.75814 - 2.73572i) q^{29} +(-0.723911 - 1.22234i) q^{30} +(-2.99299 + 3.45409i) q^{31} +(5.65239 + 0.224732i) q^{32} +(-1.28075 - 2.80446i) q^{33} +(-6.91207 + 5.56089i) q^{34} +(-1.26736 + 4.31624i) q^{35} +(-1.41650 + 1.41193i) q^{36} +(-7.54673 - 1.08506i) q^{37} +(-11.3968 + 2.89906i) q^{38} +(0.192246 - 0.420961i) q^{39} +(2.08417 - 1.93102i) q^{40} +(0.0346364 + 0.240901i) q^{41} +(6.32889 + 0.231155i) q^{42} +(5.26279 - 4.56024i) q^{43} +(4.94221 - 3.68725i) q^{44} +1.00453i q^{45} +(6.65621 + 1.30185i) q^{46} +0.826720 q^{47} +(-3.35801 - 2.17342i) q^{48} +(-8.54863 - 9.86565i) q^{49} +(-0.206003 + 5.64026i) q^{50} +(6.20912 - 0.892736i) q^{51} +(0.904092 + 0.198203i) q^{52} +(-3.02032 - 1.37933i) q^{53} +(1.37057 - 0.348637i) q^{54} +(0.440753 - 3.06551i) q^{55} +(2.21872 + 12.4704i) q^{56} +(7.97856 + 2.34272i) q^{57} +(-2.88281 - 3.58327i) q^{58} +(5.22030 - 2.38403i) q^{59} +(-1.96383 + 0.423884i) q^{60} +(-5.24148 - 4.54177i) q^{61} +(3.29366 + 5.56140i) q^{62} +(-3.76729 - 2.42109i) q^{63} +(2.83200 - 7.48196i) q^{64} +(0.391079 - 0.251332i) q^{65} +(-4.33551 + 0.462574i) q^{66} +(1.44928 + 4.93578i) q^{67} +(4.36536 + 11.7620i) q^{68} +(-3.58064 - 3.19046i) q^{69} +(5.22277 + 3.63249i) q^{70} +(3.91182 - 1.14861i) q^{71} +(1.25992 + 2.53231i) q^{72} +(10.4806 - 6.73545i) q^{73} +(-4.83419 + 9.63802i) q^{74} +(2.15766 - 3.35738i) q^{75} +(-1.21322 + 16.5865i) q^{76} +(10.4343 + 9.04137i) q^{77} +(-0.478644 - 0.446356i) q^{78} +(1.04626 + 2.29099i) q^{79} +(-1.65737 - 3.66038i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(0.338671 + 0.0613854i) q^{82} +(17.5497 + 2.52327i) q^{83} +(3.14348 - 8.38660i) q^{84} +(5.73193 + 2.61768i) q^{85} +(-3.76136 - 9.10152i) q^{86} +(0.462802 + 3.21886i) q^{87} +(-2.73379 - 8.28063i) q^{88} +(-9.73176 - 11.2311i) q^{89} +(1.34756 + 0.449719i) q^{90} +2.07242i q^{91} +(4.72634 - 8.34636i) q^{92} -4.57042i q^{93} +(0.370116 - 1.10903i) q^{94} +(5.47008 + 6.31281i) q^{95} +(-4.41896 + 3.53169i) q^{96} +(-1.54914 - 10.7745i) q^{97} +(-17.0617 + 7.05106i) q^{98} +(2.80446 + 1.28075i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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