LMFDB - Embedded newform 462.2.y.d.25.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(25,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 24]))

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

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

chi := DirichletCharacter("462.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.y (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			25.4
Character	$\chi$	$=$	462.25
Dual form			462.2.y.d.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.913545 + 0.406737i) q^{2} +(0.978148 + 0.207912i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.111151 - 1.05753i) q^{5} +(0.809017 + 0.587785i) q^{6} +(2.10806 + 1.59878i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})$	\(q+(0.913545 + 0.406737i) q^{2} +(0.978148 + 0.207912i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.111151 - 1.05753i) q^{5} +(0.809017 + 0.587785i) q^{6} +(2.10806 + 1.59878i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.913545 + 0.406737i) q^{9} +(0.531680 - 0.920896i) q^{10} +(-1.81320 - 2.77710i) q^{11} +(0.500000 + 0.866025i) q^{12} +(4.60080 - 3.34268i) q^{13} +(1.27552 + 2.31798i) q^{14} +(0.328596 - 1.01131i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(-3.40738 + 1.51706i) q^{17} +(0.669131 + 0.743145i) q^{18} +(-5.61910 + 6.24064i) q^{19} +(0.860276 - 0.625027i) q^{20} +(1.72959 + 2.00213i) q^{21} +(-0.526893 - 3.27451i) q^{22} +(1.15986 + 2.00893i) q^{23} +(0.104528 + 0.994522i) q^{24} +(3.78471 + 0.804466i) q^{25} +(5.56263 - 1.18237i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.222440 + 2.63638i) q^{28} +(-0.545991 + 1.68039i) q^{29} +(0.711526 - 0.790230i) q^{30} +(-0.766870 - 7.29628i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.19619 - 3.09340i) q^{33} -3.72984 q^{34} +(1.92508 - 2.05164i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-2.65873 + 0.565131i) q^{37} +(-7.67160 + 3.41562i) q^{38} +(5.19524 - 2.31307i) q^{39} +(1.04012 - 0.221085i) q^{40} +(-3.16343 - 9.73605i) q^{41} +(0.765714 + 2.53252i) q^{42} -2.74467 q^{43} +(0.850520 - 3.20572i) q^{44} +(0.531680 - 0.920896i) q^{45} +(0.242476 + 2.30701i) q^{46} +(1.00254 - 1.11344i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(1.88780 + 6.74064i) q^{49} +(3.13030 + 2.27430i) q^{50} +(-3.64834 + 0.775478i) q^{51} +(5.56263 + 1.18237i) q^{52} +(0.900059 + 8.56349i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-3.13842 + 1.60884i) q^{55} +(-0.869105 + 2.49893i) q^{56} +(-6.79381 + 4.93599i) q^{57} +(-1.18226 + 1.31304i) q^{58} +(-7.19895 - 7.99524i) q^{59} +(0.971427 - 0.432507i) q^{60} +(-0.0678238 + 0.645300i) q^{61} +(2.26709 - 6.97740i) q^{62} +(1.27552 + 2.31798i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-3.02361 - 5.23705i) q^{65} +(0.165429 - 3.31250i) q^{66} +(-3.72640 + 6.45431i) q^{67} +(-3.40738 - 1.51706i) q^{68} +(0.716831 + 2.20618i) q^{69} +(2.59312 - 1.09126i) q^{70} +(-9.44303 - 6.86076i) q^{71} +(-0.104528 + 0.994522i) q^{72} +(-2.44030 - 2.71023i) q^{73} +(-2.65873 - 0.565131i) q^{74} +(3.53475 + 1.57377i) q^{75} -8.39761 q^{76} +(0.617644 - 8.75320i) q^{77} +5.68690 q^{78} +(-6.87252 - 3.05984i) q^{79} +(1.04012 + 0.221085i) q^{80} +(0.669131 + 0.743145i) q^{81} +(1.07007 - 10.1810i) q^{82} +(8.70619 + 6.32542i) q^{83} +(-0.330556 + 2.62502i) q^{84} +(1.22561 + 3.77204i) q^{85} +(-2.50738 - 1.11636i) q^{86} +(-0.883432 + 1.53015i) q^{87} +(2.08087 - 2.58263i) q^{88} +(-7.26014 - 12.5749i) q^{89} +(0.860276 - 0.625027i) q^{90} +(15.0430 + 0.309117i) q^{91} +(-0.716831 + 2.20618i) q^{92} +(0.766870 - 7.29628i) q^{93} +(1.36875 - 0.609405i) q^{94} +(5.97512 + 6.63605i) q^{95} +(-0.669131 + 0.743145i) q^{96} +(13.1370 - 9.54458i) q^{97} +(-1.01707 + 6.92572i) q^{98} +(-0.526893 - 3.27451i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9}+O(q^{10}) $ 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 20 q^{12} + 10 q^{13} + 5 q^{14} - 6 q^{15} + 5 q^{16} + 5 q^{18} - 13 q^{19} + 6 q^{20} - 2 q^{21} - 4 q^{22} - 20 q^{23} - 5 q^{24} + 12 q^{25} + 10 q^{27} - 3 q^{28} + 12 q^{29} + 3 q^{30} - 10 q^{31} - 20 q^{32} + 8 q^{33} - 13 q^{35} - 10 q^{36} + 3 q^{37} + 2 q^{38} + 5 q^{39} - 3 q^{40} - 44 q^{41} - 3 q^{42} + 36 q^{43} - 3 q^{44} + 12 q^{45} + 11 q^{47} + 10 q^{48} + 33 q^{49} - 4 q^{50} + 26 q^{53} + 20 q^{54} - 20 q^{55} + 8 q^{56} + 4 q^{57} - 6 q^{58} + 4 q^{59} + 3 q^{60} - 23 q^{61} + 5 q^{63} - 10 q^{64} - 50 q^{65} - 7 q^{66} - 108 q^{67} + 20 q^{69} - 86 q^{71} + 5 q^{72} - 35 q^{73} + 3 q^{74} - 2 q^{75} - 44 q^{76} - 37 q^{77} + 20 q^{78} + 3 q^{79} - 3 q^{80} + 5 q^{81} - 28 q^{82} - 88 q^{83} - 5 q^{84} + 96 q^{85} - 13 q^{86} + 6 q^{87} - 8 q^{88} + 6 q^{89} + 6 q^{90} + 40 q^{91} - 20 q^{92} + 10 q^{93} - 24 q^{94} + 36 q^{95} - 5 q^{96} + 60 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 20 * q^12 + 10 * q^13 + 5 * q^14 - 6 * q^15 + 5 * q^16 + 5 * q^18 - 13 * q^19 + 6 * q^20 - 2 * q^21 - 4 * q^22 - 20 * q^23 - 5 * q^24 + 12 * q^25 + 10 * q^27 - 3 * q^28 + 12 * q^29 + 3 * q^30 - 10 * q^31 - 20 * q^32 + 8 * q^33 - 13 * q^35 - 10 * q^36 + 3 * q^37 + 2 * q^38 + 5 * q^39 - 3 * q^40 - 44 * q^41 - 3 * q^42 + 36 * q^43 - 3 * q^44 + 12 * q^45 + 11 * q^47 + 10 * q^48 + 33 * q^49 - 4 * q^50 + 26 * q^53 + 20 * q^54 - 20 * q^55 + 8 * q^56 + 4 * q^57 - 6 * q^58 + 4 * q^59 + 3 * q^60 - 23 * q^61 + 5 * q^63 - 10 * q^64 - 50 * q^65 - 7 * q^66 - 108 * q^67 + 20 * q^69 - 86 * q^71 + 5 * q^72 - 35 * q^73 + 3 * q^74 - 2 * q^75 - 44 * q^76 - 37 * q^77 + 20 * q^78 + 3 * q^79 - 3 * q^80 + 5 * q^81 - 28 * q^82 - 88 * q^83 - 5 * q^84 + 96 * q^85 - 13 * q^86 + 6 * q^87 - 8 * q^88 + 6 * q^89 + 6 * q^90 + 40 * q^91 - 20 * q^92 + 10 * q^93 - 24 * q^94 + 36 * q^95 - 5 * q^96 + 60 * q^97 + 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.913545	+	0.406737i	0.645974	+	0.287606i
$2$	0.913545	+	0.406737i	0.645974	+	0.287606i
$3$	0.978148	+	0.207912i	0.564734	+	0.120038i
$3$	0.978148	+	0.207912i	0.564734	+	0.120038i
$4$	0.669131	+	0.743145i	0.334565	+	0.371572i
$5$	0.111151	−	1.05753i	0.0497084	−	0.472944i	−0.941145	−	0.338002i	$-0.890249\pi$
$5$	0.111151	−	1.05753i	0.0497084	−	0.472944i	0.990854	−	0.134941i	$-0.0430846\pi$
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$	2.10806	+	1.59878i	0.796770	+	0.604282i
$7$	2.10806	+	1.59878i	0.796770	+	0.604282i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	0.913545	+	0.406737i	0.304515	+	0.135579i
$10$	0.531680	−	0.920896i	0.168132	−	0.291213i
$11$	−1.81320	−	2.77710i	−0.546701	−	0.837328i
$11$	−1.81320	−	2.77710i	−0.546701	−	0.837328i
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	4.60080	−	3.34268i	1.27603	−	0.927092i	0.276607	−	0.960983i	$-0.410790\pi$
$13$	4.60080	−	3.34268i	1.27603	−	0.927092i	0.999426	+	0.0338911i	$0.0107900\pi$
$14$	1.27552	+	2.31798i	0.340898	+	0.619507i
$15$	0.328596	−	1.01131i	0.0848432	−	0.261120i
$16$	−0.104528	+	0.994522i	−0.0261321	+	0.248630i
$17$	−3.40738	+	1.51706i	−0.826411	+	0.367942i	−0.775958	−	0.630785i	$-0.782733\pi$
$17$	−3.40738	+	1.51706i	−0.826411	+	0.367942i	−0.0504529	+	0.998726i	$0.516066\pi$
$18$	0.669131	+	0.743145i	0.157716	+	0.175161i
$19$	−5.61910	+	6.24064i	−1.28911	+	1.43170i	−0.445001	+	0.895530i	$0.646797\pi$
$19$	−5.61910	+	6.24064i	−1.28911	+	1.43170i	−0.844109	+	0.536171i	$0.819870\pi$
$20$	0.860276	−	0.625027i	0.192364	−	0.139760i
$21$	1.72959	+	2.00213i	0.377426	+	0.436901i
$22$	−0.526893	−	3.27451i	−0.112334	−	0.698127i
$23$	1.15986	+	2.00893i	0.241847	+	0.418891i	0.961240	−	0.275712i	$-0.0889135\pi$
$23$	1.15986	+	2.00893i	0.241847	+	0.418891i	−0.719393	+	0.694603i	$0.755580\pi$
$24$	0.104528	+	0.994522i	0.0213368	+	0.203006i
$25$	3.78471	+	0.804466i	0.756943	+	0.160893i
$26$	5.56263	−	1.18237i	1.09092	−	0.231883i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	0.222440	+	2.63638i	0.0420372	+	0.498230i
$29$	−0.545991	+	1.68039i	−0.101388	+	0.312040i	−0.988866	−	0.148810i	$-0.952456\pi$
$29$	−0.545991	+	1.68039i	−0.101388	+	0.312040i	0.887478	+	0.460850i	$0.152456\pi$
$30$	0.711526	−	0.790230i	0.129906	−	0.144276i
$31$	−0.766870	−	7.29628i	−0.137734	−	1.31045i	−0.817034	−	0.576590i	$-0.804383\pi$
$31$	−0.766870	−	7.29628i	−0.137734	−	1.31045i	0.679300	−	0.733861i	$-0.262284\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.19619	−	3.09340i	−0.208229	−	0.538492i
$34$	−3.72984			−0.639663
$35$	1.92508	−	2.05164i	0.325398	−	0.346790i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	−2.65873	+	0.565131i	−0.437093	+	0.0929070i	−0.421202	−	0.906967i	$-0.638392\pi$
$37$	−2.65873	+	0.565131i	−0.437093	+	0.0929070i	−0.0158909	+	0.999874i	$0.505058\pi$
$38$	−7.67160	+	3.41562i	−1.24450	+	0.554086i
$39$	5.19524	−	2.31307i	0.831905	−	0.370388i
$40$	1.04012	−	0.221085i	0.164458	−	0.0349566i
$41$	−3.16343	−	9.73605i	−0.494045	−	1.52052i	−0.818439	−	0.574593i	$-0.805160\pi$
$41$	−3.16343	−	9.73605i	−0.494045	−	1.52052i	0.324394	−	0.945922i	$-0.394840\pi$
$42$	0.765714	+	2.53252i	0.118152	+	0.390777i
$43$	−2.74467			−0.418558			−0.209279	−	0.977856i	$-0.567112\pi$
$43$	−2.74467			−0.418558			−0.209279	+	0.977856i	$0.567112\pi$
$44$	0.850520	−	3.20572i	0.128221	−	0.483280i
$45$	0.531680	−	0.920896i	0.0792581	−	0.137279i
$46$	0.242476	+	2.30701i	0.0357512	+	0.340150i
$47$	1.00254	−	1.11344i	0.146236	−	0.162412i	−0.665577	−	0.746330i	$-0.731814\pi$
$47$	1.00254	−	1.11344i	0.146236	−	0.162412i	0.811813	+	0.583918i	$0.198481\pi$
$48$	−0.309017	+	0.951057i	−0.0446028	+	0.137273i
$49$	1.88780	+	6.74064i	0.269686	+	0.962948i
$50$	3.13030	+	2.27430i	0.442692	+	0.321634i
$51$	−3.64834	+	0.775478i	−0.510869	+	0.108589i
$52$	5.56263	+	1.18237i	0.771398	+	0.163966i
$53$	0.900059	+	8.56349i	0.123633	+	1.17629i	0.863790	+	0.503852i	$0.168084\pi$
$53$	0.900059	+	8.56349i	0.123633	+	1.17629i	−0.740157	+	0.672434i	$0.765249\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−3.13842	+	1.60884i	−0.423185	+	0.216937i
$56$	−0.869105	+	2.49893i	−0.116139	+	0.333934i
$57$	−6.79381	+	4.93599i	−0.899862	+	0.653788i
$58$	−1.18226	+	1.31304i	−0.155239	+	0.172410i
$59$	−7.19895	−	7.99524i	−0.937223	−	1.04089i	−0.999083	−	0.0428071i	$-0.986370\pi$
$59$	−7.19895	−	7.99524i	−0.937223	−	1.04089i	0.0618600	−	0.998085i	$-0.480297\pi$
$60$	0.971427	−	0.432507i	0.125411	−	0.0558364i
$61$	−0.0678238	+	0.645300i	−0.00868394	+	0.0826222i	−0.998005	−	0.0631271i	$-0.979893\pi$
$61$	−0.0678238	+	0.645300i	−0.00868394	+	0.0826222i	0.989322	+	0.145749i	$0.0465593\pi$
$62$	2.26709	−	6.97740i	0.287921	−	0.886131i
$63$	1.27552	+	2.31798i	0.160701	+	0.292038i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−3.02361	−	5.23705i	−0.375033	−	0.649576i
$66$	0.165429	−	3.31250i	0.0203629	−	0.407740i
$67$	−3.72640	+	6.45431i	−0.455252	+	0.788519i	−0.998703	−	0.0509217i	$-0.983784\pi$
$67$	−3.72640	+	6.45431i	−0.455252	+	0.788519i	0.543451	+	0.839441i	$0.317117\pi$
$68$	−3.40738	−	1.51706i	−0.413205	−	0.183971i
$69$	0.716831	+	2.20618i	0.0862963	+	0.265593i
$70$	2.59312	−	1.09126i	0.309937	−	0.130431i
$71$	−9.44303	−	6.86076i	−1.12068	−	0.814223i	−0.136369	−	0.990658i	$-0.543543\pi$
$71$	−9.44303	−	6.86076i	−1.12068	−	0.814223i	−0.984312	+	0.176435i	$0.943543\pi$
$72$	−0.104528	+	0.994522i	−0.0123188	+	0.117206i
$73$	−2.44030	−	2.71023i	−0.285616	−	0.317209i	0.583215	−	0.812318i	$-0.301795\pi$
$73$	−2.44030	−	2.71023i	−0.285616	−	0.317209i	−0.868831	+	0.495109i	$0.835128\pi$
$74$	−2.65873	−	0.565131i	−0.309072	−	0.0656952i
$75$	3.53475	+	1.57377i	0.408158	+	0.181724i
$76$	−8.39761			−0.963272
$77$	0.617644	−	8.75320i	0.0703871	−	0.997520i
$78$	5.68690			0.643915
$79$	−6.87252	−	3.05984i	−0.773219	−	0.344259i	−0.0180907	−	0.999836i	$-0.505759\pi$
$79$	−6.87252	−	3.05984i	−0.773219	−	0.344259i	−0.755128	+	0.655577i	$0.772425\pi$
$80$	1.04012	+	0.221085i	0.116289	+	0.0247180i
$81$	0.669131	+	0.743145i	0.0743478	+	0.0825716i
$82$	1.07007	−	10.1810i	0.118169	−	1.12430i
$83$	8.70619	+	6.32542i	0.955629	+	0.694305i	0.952131	−	0.305689i	$-0.0988868\pi$
$83$	8.70619	+	6.32542i	0.955629	+	0.694305i	0.00349736	+	0.999994i	$0.498887\pi$
$84$	−0.330556	+	2.62502i	−0.0360666	+	0.286413i
$85$	1.22561	+	3.77204i	0.132936	+	0.409136i
$86$	−2.50738	−	1.11636i	−0.270378	−	0.120380i
$87$	−0.883432	+	1.53015i	−0.0947138	+	0.164049i
$88$	2.08087	−	2.58263i	0.221822	−	0.275309i
$89$	−7.26014	−	12.5749i	−0.769573	−	1.33294i	−0.937795	−	0.347191i	$-0.887136\pi$
$89$	−7.26014	−	12.5749i	−0.769573	−	1.33294i	0.168221	−	0.985749i	$-0.446198\pi$
$90$	0.860276	−	0.625027i	0.0906810	−	0.0658836i
$91$	15.0430	+	0.309117i	1.57693	+	0.0324043i
$92$	−0.716831	+	2.20618i	−0.0747348	+	0.230010i
$93$	0.766870	−	7.29628i	0.0795207	−	0.756589i
$94$	1.36875	−	0.609405i	0.141175	−	0.0628553i
$95$	5.97512	+	6.63605i	0.613035	+	0.680844i
$96$	−0.669131	+	0.743145i	−0.0682929	+	0.0758469i
$97$	13.1370	−	9.54458i	1.33386	−	0.969105i	0.334213	−	0.942498i	$-0.391529\pi$
$97$	13.1370	−	9.54458i	1.33386	−	0.969105i	0.999646	−	0.0266077i	$-0.00847051\pi$
$98$	−1.01707	+	6.92572i	−0.102740	+	0.699603i
$99$	−0.526893	−	3.27451i	−0.0529548	−	0.329100i
$100$	1.93463	+	3.35088i	0.193463	+	0.335088i
$101$	0.368125	+	3.50248i	0.0366298	+	0.348510i	0.997452	+	0.0713433i	$0.0227286\pi$
$101$	0.368125	+	3.50248i	0.0366298	+	0.348510i	−0.960822	+	0.277166i	$0.910605\pi$
$102$	−3.64834	−	0.775478i	−0.361239	−	0.0767837i
$103$	−4.24569	+	0.902448i	−0.418340	+	0.0889209i	−0.412272	−	0.911061i	$-0.635265\pi$
$103$	−4.24569	+	0.902448i	−0.418340	+	0.0889209i	−0.00606766	+	0.999982i	$0.501931\pi$
$104$	4.60080	+	3.34268i	0.451146	+	0.327777i
$105$	2.30957	−	1.60656i	0.225391	−	0.156784i
$106$	−2.66084	+	8.18922i	−0.258444	+	0.795408i
$107$	−9.61882	+	10.6828i	−0.929886	+	1.03274i	0.0694957	+	0.997582i	$0.477861\pi$
$107$	−9.61882	+	10.6828i	−0.929886	+	1.03274i	−0.999382	+	0.0351608i	$0.988806\pi$
$108$	0.104528	+	0.994522i	0.0100583	+	0.0956979i
$109$	0.780713	−	1.35223i	0.0747787	−	0.129521i	−0.826211	−	0.563360i	$-0.809508\pi$
$109$	0.780713	−	1.35223i	0.0747787	−	0.129521i	0.900990	+	0.433840i	$0.142842\pi$
$110$	−3.52147	+	0.193242i	−0.335759	+	0.0184249i
$111$	−2.71813			−0.257994
$112$	−1.81037	+	1.92939i	−0.171064	+	0.182310i
$113$	−3.26158	−	10.0381i	−0.306824	−	0.944306i	−0.978990	−	0.203906i	$-0.934636\pi$
$113$	−3.26158	−	10.0381i	−0.306824	−	0.944306i	0.672167	−	0.740400i	$-0.265364\pi$
$114$	−8.21410	+	1.74596i	−0.769321	+	0.163524i
$115$	2.25343	−	1.00329i	0.210134	−	0.0935576i
$116$	−1.61411	+	0.718648i	−0.149866	+	0.0667248i
$117$	5.56263	−	1.18237i	0.514265	−	0.109310i
$118$	−3.32461	−	10.2321i	−0.306055	−	0.941941i
$119$	−9.60840	−	2.24960i	−0.880800	−	0.206220i
$120$	1.06336			0.0970710
$121$	−4.42460	+	10.0709i	−0.402236	+	0.915536i
$122$	−0.324427	+	0.561924i	−0.0293723	+	0.0508742i
$123$	−1.07007	−	10.1810i	−0.0964847	−	0.917990i
$124$	4.90906	−	5.45206i	0.440846	−	0.489610i
$125$	2.91441	−	8.96962i	0.260672	−	0.802267i
$126$	0.222440	+	2.63638i	0.0198165	+	0.234868i
$127$	9.40998	+	6.83675i	0.835000	+	0.606663i	0.920970	−	0.389634i	$-0.127399\pi$
$127$	9.40998	+	6.83675i	0.835000	+	0.606663i	−0.0859691	+	0.996298i	$0.527399\pi$
$128$	−0.978148	+	0.207912i	−0.0864569	+	0.0183770i
$129$	−2.68469	−	0.570649i	−0.236374	−	0.0502428i
$130$	−0.632107	−	6.01409i	−0.0554394	−	0.527471i
$131$	2.37580	+	4.11500i	0.207574	+	0.359529i	0.950950	−	0.309345i	$-0.100110\pi$
$131$	2.37580	+	4.11500i	0.207574	+	0.359529i	−0.743375	+	0.668874i	$0.766776\pi$
$132$	1.49844	−	2.95883i	0.130422	−	0.257533i
$133$	−21.8228	+	4.17192i	−1.89228	+	0.361751i
$134$	−6.02944	+	4.38064i	−0.520864	+	0.378430i
$135$	0.711526	−	0.790230i	0.0612384	−	0.0680122i
$136$	−2.49575	−	2.77181i	−0.214009	−	0.237681i
$137$	9.49085	−	4.22560i	0.810858	−	0.361017i	0.0409413	−	0.999162i	$-0.486964\pi$
$137$	9.49085	−	4.22560i	0.810858	−	0.361017i	0.769917	+	0.638144i	$0.220298\pi$
$138$	−0.242476	+	2.30701i	−0.0206409	+	0.196385i
$139$	−5.70880	+	17.5699i	−0.484214	+	1.49026i	0.348902	+	0.937159i	$0.386555\pi$
$139$	−5.70880	+	17.5699i	−0.484214	+	1.49026i	−0.833116	+	0.553098i	$0.813445\pi$
$140$	2.81279	+	0.0577999i	0.237724	+	0.00488498i
$141$	1.21213	−	0.880666i	0.102080	−	0.0741655i
$142$	−5.83611	−	10.1084i	−0.489756	−	0.848282i
$143$	−17.6251	−	6.71595i	−1.47389	−	0.561616i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	1.71638	+	0.764181i	0.142538	+	0.0634618i
$146$	−1.12698	−	3.46848i	−0.0932694	−	0.287054i
$147$	0.445093	+	6.98584i	0.0367106	+	0.576182i
$148$	−2.19901	−	1.59768i	−0.180758	−	0.131328i
$149$	−1.31560	+	12.5171i	−0.107778	+	1.02544i	0.798279	+	0.602288i	$0.205744\pi$
$149$	−1.31560	+	12.5171i	−0.107778	+	1.02544i	−0.906057	+	0.423155i	$0.860923\pi$
$150$	2.58904	+	2.87543i	0.211395	+	0.234778i
$151$	14.3796	+	3.05648i	1.17019	+	0.248733i	0.751712	−	0.659492i	$-0.229229\pi$
$151$	14.3796	+	3.05648i	1.17019	+	0.248733i	0.418483	+	0.908225i	$0.362562\pi$
$152$	−7.67160	−	3.41562i	−0.622249	−	0.277043i
$153$	−3.72984			−0.301540
$154$	4.12449	−	7.74523i	0.332361	−	0.624128i
$155$	−7.80131			−0.626616
$156$	5.19524	+	2.31307i	0.415952	+	0.185194i
$157$	9.17680	+	1.95059i	0.732389	+	0.155674i	0.558986	−	0.829177i	$-0.311190\pi$
$157$	9.17680	+	1.95059i	0.732389	+	0.155674i	0.173403	+	0.984851i	$0.444524\pi$
$158$	−5.03381	−	5.59061i	−0.400468	−	0.444765i
$159$	−0.900059	+	8.56349i	−0.0713793	+	0.679129i
$160$	0.860276	+	0.625027i	0.0680108	+	0.0494127i
$161$	−0.766796	+	6.08930i	−0.0604320	+	0.479904i
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	15.7395	+	7.00769i	1.23281	+	0.548884i	0.916601	−	0.399804i	$-0.130922\pi$
$163$	15.7395	+	7.00769i	1.23281	+	0.548884i	0.316214	+	0.948688i	$0.397588\pi$
$164$	5.11854	−	8.86558i	0.399691	−	0.692285i
$165$	−3.40434	+	0.921173i	−0.265027	+	0.0717132i
$166$	5.38072	+	9.31969i	0.417625	+	0.723348i
$167$	6.42366	−	4.66706i	0.497078	−	0.361148i	−0.310822	−	0.950468i	$-0.600604\pi$
$167$	6.42366	−	4.66706i	0.497078	−	0.361148i	0.807900	+	0.589320i	$0.200604\pi$
$168$	−1.36967	+	2.26363i	−0.105672	+	0.174643i
$169$	5.97666	−	18.3943i	0.459743	−	1.41494i
$170$	−0.414577	+	3.94443i	−0.0317966	+	0.302524i
$171$	−7.67160	+	3.41562i	−0.586662	+	0.261199i
$172$	−1.83654	−	2.03969i	−0.140035	−	0.155525i
$173$	7.01881	−	7.79518i	0.533631	−	0.592657i	−0.414693	−	0.909961i	$-0.636111\pi$
$173$	7.01881	−	7.79518i	0.533631	−	0.592657i	0.948324	+	0.317305i	$0.102778\pi$
$174$	−1.42942	+	1.03854i	−0.108364	+	0.0787312i
$175$	6.69223	+	7.74679i	0.505885	+	0.585602i
$176$	2.95142	−	1.51298i	0.222472	−	0.114045i
$177$	−5.37933	−	9.31727i	−0.404335	−	0.700329i
$178$	−1.51778	−	14.4407i	−0.113763	−	1.08238i
$179$	14.5811	+	3.09930i	1.08984	+	0.231652i	0.717580	−	0.696476i	$-0.245250\pi$
$179$	14.5811	+	3.09930i	1.08984	+	0.231652i	0.372259	+	0.928129i	$0.378583\pi$
$180$	1.04012	−	0.221085i	0.0775262	−	0.0164787i
$181$	−20.6633	−	15.0128i	−1.53589	−	1.11589i	−0.952847	−	0.303451i	$-0.901861\pi$
$181$	−20.6633	−	15.0128i	−1.53589	−	1.11589i	−0.583045	−	0.812440i	$-0.698139\pi$
$182$	13.6167	+	6.40091i	1.00934	+	0.474467i
$183$	−0.200507	+	0.617097i	−0.0148219	+	0.0456171i
$184$	−1.55219	+	1.72388i	−0.114429	+	0.127086i
$185$	0.302124	+	2.87452i	0.0222126	+	0.211339i
$186$	3.66824	−	6.35357i	0.268968	−	0.465866i
$187$	10.3913	+	6.71190i	0.759888	+	0.490823i
$188$	1.49828			0.109273
$189$	0.765714	+	2.53252i	0.0556975	+	0.184214i
$190$	2.75942	+	8.49263i	0.200190	+	0.616120i
$191$	−2.92175	+	0.621036i	−0.211410	+	0.0449366i	−0.312399	−	0.949951i	$-0.601133\pi$
$191$	−2.92175	+	0.621036i	−0.211410	+	0.0449366i	0.100989	+	0.994888i	$0.467799\pi$
$192$	−0.913545	+	0.406737i	−0.0659295	+	0.0293537i
$193$	12.5556	−	5.59011i	0.903771	−	0.402385i	0.0983937	−	0.995148i	$-0.468630\pi$
$193$	12.5556	−	5.59011i	0.903771	−	0.402385i	0.805377	+	0.592763i	$0.201963\pi$
$194$	15.8834	−	3.37611i	1.14036	−	0.242391i
$195$	−1.86869	−	5.75125i	−0.133820	−	0.411856i
$196$	−3.74608	+	5.91328i	−0.267577	+	0.422377i
$197$	−17.3632			−1.23708			−0.618540	−	0.785753i	$-0.712276\pi$
$197$	−17.3632			−1.23708			−0.618540	+	0.785753i	$0.712276\pi$
$198$	0.850520	−	3.20572i	0.0604438	−	0.227820i
$199$	−4.81751	+	8.34417i	−0.341504	+	0.591502i	−0.984712	−	0.174189i	$-0.944270\pi$
$199$	−4.81751	+	8.34417i	−0.341504	+	0.591502i	0.643208	+	0.765691i	$0.277603\pi$
$200$	0.404449	+	3.84807i	0.0285988	+	0.272100i
$201$	−4.98689	+	5.53851i	−0.351748	+	0.390656i
$202$	−1.08829	+	3.34940i	−0.0765716	+	0.235663i
$203$	−3.83755	+	2.66943i	−0.269343	+	0.187357i
$204$	−3.01751	−	2.19235i	−0.211268	−	0.153495i
$205$	−10.6478	+	2.26326i	−0.743676	+	0.158073i
$206$	−4.24569	−	0.902448i	−0.295811	−	0.0628766i
$207$	0.242476	+	2.30701i	0.0168533	+	0.160348i
$208$	2.84345	+	4.92500i	0.197158	+	0.341487i
$209$	27.5195	+	4.28927i	1.90356	+	0.296695i
$210$	2.76334	−	0.528275i	0.190689	−	0.0364545i
$211$	9.51510	−	6.91313i	0.655047	−	0.475919i	−0.209940	−	0.977714i	$-0.567327\pi$
$211$	9.51510	−	6.91313i	0.655047	−	0.475919i	0.864987	+	0.501795i	$0.167327\pi$
$212$	−5.76166	+	6.39897i	−0.395712	+	0.439483i
$213$	−7.81024	−	8.67416i	−0.535149	−	0.594343i
$214$	−13.1323	+	5.84688i	−0.897706	+	0.399684i
$215$	−0.305074	+	2.90258i	−0.0208058	+	0.197954i
$216$	−0.309017	+	0.951057i	−0.0210259	+	0.0647112i
$217$	10.0485	−	16.6070i	0.682140	−	1.12736i
$218$	1.26322	−	0.917783i	0.0855560	−	0.0621601i
$219$	−1.82349	−	3.15838i	−0.123220	−	0.213423i
$220$	−3.29562	−	1.25577i	−0.222191	−	0.0846643i
$221$	−10.6056	+	18.3695i	−0.713411	+	1.23566i
$222$	−2.48314	−	1.10556i	−0.166657	−	0.0742006i
$223$	−1.97128	−	6.06698i	−0.132007	−	0.406275i	0.863106	−	0.505023i	$-0.168516\pi$
$223$	−1.97128	−	6.06698i	−0.132007	−	0.406275i	−0.995112	+	0.0987482i	$0.968516\pi$
$224$	−2.43861	+	1.02624i	−0.162937	+	0.0685686i
$225$	3.13030	+	2.27430i	0.208687	+	0.151620i
$226$	1.10327	−	10.4969i	0.0733882	−	0.698242i
$227$	15.7433	+	17.4847i	1.04492	+	1.16050i	0.986759	+	0.162193i	$0.0518568\pi$
$227$	15.7433	+	17.4847i	1.04492	+	1.16050i	0.0581602	+	0.998307i	$0.481477\pi$
$228$	−8.21410	−	1.74596i	−0.543992	−	0.115629i
$229$	13.4249	+	5.97716i	0.887143	+	0.394982i	0.799144	−	0.601139i	$-0.205286\pi$
$229$	13.4249	+	5.97716i	0.887143	+	0.394982i	0.0879986	+	0.996121i	$0.471953\pi$
$230$	2.46669			0.162649
$231$	2.42404	−	8.43351i	0.159490	−	0.554884i
$232$	−1.76686			−0.116000
$233$	8.46358	+	3.76823i	0.554467	+	0.246865i	0.664789	−	0.747031i	$-0.268521\pi$
$233$	8.46358	+	3.76823i	0.554467	+	0.246865i	−0.110322	+	0.993896i	$0.535188\pi$
$234$	5.56263	+	1.18237i	0.363641	+	0.0772942i
$235$	−1.06606	−	1.18398i	−0.0695424	−	0.0772347i
$236$	1.12459	−	10.6997i	0.0732043	−	0.696493i
$237$	−6.08616	−	4.42186i	−0.395339	−	0.287230i
$238$	−7.86272	−	5.96320i	−0.509664	−	0.386537i
$239$	7.56232	+	23.2744i	0.489166	+	1.50550i	0.825856	+	0.563882i	$0.190693\pi$
$239$	7.56232	+	23.2744i	0.489166	+	1.50550i	−0.336690	+	0.941616i	$0.609307\pi$
$240$	0.971427	+	0.432507i	0.0627054	+	0.0279182i
$241$	1.08530	−	1.87980i	0.0699106	−	0.121089i	−0.828951	−	0.559321i	$-0.811062\pi$
$241$	1.08530	−	1.87980i	0.0699106	−	0.121089i	0.898862	+	0.438232i	$0.144395\pi$
$242$	−8.13827	+	7.40058i	−0.523148	+	0.475727i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−0.524934	+	0.381387i	−0.0336055	+	0.0244158i
$245$	7.33829	−	1.24719i	0.468826	−	0.0796798i
$246$	3.16343	−	9.73605i	0.201693	−	0.620748i
$247$	−4.99190	+	47.4948i	−0.317627	+	3.02202i
$248$	6.70220	−	2.98401i	0.425590	−	0.189485i
$249$	7.20081	+	7.99731i	0.456333	+	0.506809i
$250$	6.31072	−	7.00876i	0.399125	−	0.443273i
$251$	11.7759	−	8.55572i	0.743291	−	0.540032i	−0.150449	−	0.988618i	$-0.548072\pi$
$251$	11.7759	−	8.55572i	0.743291	−	0.540032i	0.893740	+	0.448585i	$0.148072\pi$
$252$	−0.869105	+	2.49893i	−0.0547485	+	0.157418i
$253$	3.47595	−	6.86364i	0.218531	−	0.431513i
$254$	5.81569	+	10.0731i	0.364909	+	0.632040i
$255$	0.414577	+	3.94443i	0.0259618	+	0.247010i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	5.09756	−	1.08352i	0.317977	−	0.0675882i	−0.0461582	−	0.998934i	$-0.514698\pi$
$257$	5.09756	−	1.08352i	0.317977	−	0.0675882i	0.364135	+	0.931346i	$0.381365\pi$
$258$	−2.22048	−	1.61328i	−0.138241	−	0.100438i
$259$	−6.50828	−	3.05940i	−0.404405	−	0.190102i
$260$	1.86869	−	5.75125i	0.115891	−	0.356677i
$261$	−1.18226	+	1.31304i	−0.0731802	+	0.0812748i
$262$	0.496677	+	4.72557i	0.0306848	+	0.291946i
$263$	−7.31780	+	12.6748i	−0.451235	+	0.781561i	−0.998463	−	0.0554220i	$-0.982350\pi$
$263$	−7.31780	+	12.6748i	−0.451235	+	0.781561i	0.547228	+	0.836983i	$0.315683\pi$
$264$	2.57236	−	2.09356i	0.158318	−	0.128849i
$265$	9.15623			0.562463
$266$	−21.6330	−	5.06489i	−1.32640	−	0.310548i
$267$	−4.48701	−	13.8096i	−0.274601	−	0.845134i
$268$	−7.28993	+	1.54952i	−0.445304	+	0.0946522i
$269$	11.7277	−	5.22153i	0.715053	−	0.318362i	−0.0167674	−	0.999859i	$-0.505337\pi$
$269$	11.7277	−	5.22153i	0.715053	−	0.318362i	0.731821	+	0.681497i	$0.238671\pi$
$270$	0.971427	−	0.432507i	0.0591192	−	0.0263216i
$271$	−20.0108	+	4.25342i	−1.21557	+	0.258377i	−0.770687	−	0.637214i	$-0.780087\pi$
$271$	−20.0108	+	4.25342i	−1.21557	+	0.258377i	−0.444880	+	0.895590i	$0.646754\pi$
$272$	−1.15258	−	3.54729i	−0.0698857	−	0.215086i
$273$	14.6500	+	3.42997i	0.886656	+	0.207591i
$274$	10.3890			0.627624
$275$	−4.62837	−	11.9692i	−0.279101	−	0.721770i
$276$	−1.15986	+	2.00893i	−0.0698152	+	0.120923i
$277$	1.87083	+	17.7998i	0.112408	+	1.06949i	0.894728	+	0.446611i	$0.147369\pi$
$277$	1.87083	+	17.7998i	0.112408	+	1.06949i	−0.782321	+	0.622876i	$0.785964\pi$
$278$	−12.3616	+	13.7289i	−0.741397	+	0.823405i
$279$	2.26709	−	6.97740i	0.135727	−	0.417726i
$280$	2.54610	+	1.19687i	0.152159	+	0.0715265i
$281$	16.7291	+	12.1544i	0.997977	+	0.725073i	0.961653	−	0.274267i	$-0.0884354\pi$
$281$	16.7291	+	12.1544i	0.997977	+	0.725073i	0.0363234	+	0.999340i	$0.488435\pi$
$282$	1.46554	−	0.311510i	0.0872715	−	0.0185501i
$283$	−7.42687	−	1.57863i	−0.441482	−	0.0938398i	−0.0181925	−	0.999835i	$-0.505791\pi$
$283$	−7.42687	−	1.57863i	−0.441482	−	0.0938398i	−0.423289	+	0.905995i	$0.639125\pi$
$284$	−1.22008	−	11.6083i	−0.0723984	−	0.688825i
$285$	4.46484	+	7.73333i	0.264474	+	0.458083i
$286$	−13.3697	−	13.3041i	−0.790570	−	0.786689i
$287$	8.89710	−	25.5818i	0.525179	−	1.51004i
$288$	−0.809017	+	0.587785i	−0.0476718	+	0.0346356i
$289$	−2.06647	+	2.29504i	−0.121557	+	0.135002i
$290$	1.25717	+	1.39623i	0.0738236	+	0.0819894i
$291$	14.8343	−	6.60467i	0.869605	−	0.387173i
$292$	0.381213	−	3.62700i	0.0223088	−	0.212254i
$293$	−4.16923	+	12.8316i	−0.243569	+	0.749628i	0.752300	+	0.658821i	$0.228945\pi$
$293$	−4.16923	+	12.8316i	−0.243569	+	0.749628i	−0.995869	+	0.0908068i	$0.971055\pi$
$294$	−2.43478	+	6.56291i	−0.141999	+	0.382757i
$295$	−9.25542	+	6.72445i	−0.538871	+	0.391513i
$296$	−1.35907	−	2.35397i	−0.0789941	−	0.136822i
$297$	0.165429	−	3.31250i	0.00959914	−	0.192211i
$298$	−6.29304	+	10.8999i	−0.364546	+	0.631412i
$299$	12.0515	+	5.36567i	0.696955	+	0.310304i
$300$	1.19567	+	3.67989i	0.0690320	+	0.212459i
$301$	−5.78592	−	4.38812i	−0.333495	−	0.252927i
$302$	11.8932	+	8.64094i	0.684379	+	0.497230i
$303$	−0.368125	+	3.50248i	−0.0211482	+	0.201212i
$304$	−5.61910	−	6.24064i	−0.322277	−	0.357925i
$305$	0.674888	+	0.143452i	0.0386440	+	0.00821403i
$306$	−3.40738	−	1.51706i	−0.194787	−	0.0867247i
$307$	−22.3237			−1.27408			−0.637041	−	0.770830i	$-0.719842\pi$
$307$	−22.3237			−1.27408			−0.637041	+	0.770830i	$0.719842\pi$
$308$	6.91818	−	5.39803i	0.394200	−	0.307582i
$309$	−4.34054			−0.246925
$310$	−7.12685	−	3.17308i	−0.404778	−	0.180219i
$311$	7.55131	+	1.60508i	0.428195	+	0.0910157i	0.416968	−	0.908921i	$-0.363093\pi$
$311$	7.55131	+	1.60508i	0.428195	+	0.0910157i	0.0112274	+	0.999937i	$0.496426\pi$
$312$	3.80528	+	4.22619i	0.215432	+	0.239261i
$313$	−0.270982	+	2.57822i	−0.0153168	+	0.145730i	−0.999507	−	0.0313826i	$-0.990009\pi$
$313$	−0.270982	+	2.57822i	−0.0153168	+	0.145730i	0.984191	+	0.177112i	$0.0566756\pi$
$314$	7.59005	+	5.51450i	0.428331	+	0.311201i
$315$	2.59312	−	1.09126i	0.146106	−	0.0614857i
$316$	−2.32471	−	7.15471i	−0.130775	−	0.402484i
$317$	−12.6612	−	5.63714i	−0.711125	−	0.316613i	0.0191023	−	0.999818i	$-0.493919\pi$
$317$	−12.6612	−	5.63714i	−0.711125	−	0.316613i	−0.730227	+	0.683204i	$0.760586\pi$
$318$	−4.30533	+	7.45705i	−0.241431	+	0.418171i
$319$	5.65660	−	1.53061i	0.316709	−	0.0856976i
$320$	0.531680	+	0.920896i	0.0297218	+	0.0514797i
$321$	−11.6297	+	8.44947i	−0.649106	+	0.471603i
$322$	−3.17724	+	5.25097i	−0.177061	+	0.292625i
$323$	9.67896	−	29.7888i	0.538552	−	1.65749i
$324$	−0.104528	+	0.994522i	−0.00580714	+	0.0552512i
$325$	20.1018	−	8.94989i	1.11505	−	0.496451i
$326$	11.5285	+	12.8037i	0.638504	+	0.709130i
$327$	1.04480	−	1.16037i	0.0577774	−	0.0641683i
$328$	8.28198	−	6.01721i	0.457296	−	0.332245i
$329$	3.89356	−	0.744342i	0.214659	−	0.0410369i
$330$	−3.48469	−	0.543135i	−0.191826	−	0.0298986i
$331$	−6.80794	−	11.7917i	−0.374198	−	0.648131i	0.616008	−	0.787740i	$-0.288749\pi$
$331$	−6.80794	−	11.7917i	−0.374198	−	0.648131i	−0.990207	+	0.139609i	$0.955415\pi$
$332$	1.12488	+	10.7025i	0.0617357	+	0.587376i
$333$	−2.65873	−	0.565131i	−0.145698	−	0.0309690i
$334$	7.76657	−	1.65084i	0.424968	−	0.0903297i
$335$	6.41146	+	4.65820i	0.350295	+	0.254505i
$336$	−2.17196	+	1.51083i	−0.118490	+	0.0824226i
$337$	6.85340	−	21.0926i	0.373328	−	1.14899i	−0.571271	−	0.820762i	$-0.693549\pi$
$337$	6.85340	−	21.0926i	0.373328	−	1.14899i	0.944599	−	0.328225i	$-0.106451\pi$
$338$	12.9416	−	14.3731i	0.703928	−	0.781792i
$339$	−1.10327	−	10.4969i	−0.0599212	−	0.570112i
$340$	−1.98308	+	3.43480i	−0.107548	+	0.186278i
$341$	−18.8720	+	15.3593i	−1.02198	+	0.831753i
$342$	−8.39761			−0.454091
$343$	−6.79720	+	17.2278i	−0.367014	+	0.930215i
$344$	−0.848149	−	2.61034i	−0.0457292	−	0.140740i
$345$	2.41279	−	0.512854i	0.129900	−	0.0276111i
$346$	9.58259	−	4.26644i	0.515163	−	0.229365i
$347$	10.4376	−	4.64713i	0.560321	−	0.249471i	−0.106978	−	0.994261i	$-0.534117\pi$
$347$	10.4376	−	4.64713i	0.560321	−	0.249471i	0.667298	+	0.744791i	$0.267451\pi$
$348$	−1.72825	+	0.367352i	−0.0926441	+	0.0196921i
$349$	0.273192	+	0.840798i	0.0146236	+	0.0450069i	0.958102	−	0.286427i	$-0.0924676\pi$
$349$	0.273192	+	0.840798i	0.0146236	+	0.0450069i	−0.943478	+	0.331434i	$0.892468\pi$
$350$	2.96275	+	9.79901i	0.158366	+	0.523779i
$351$	5.68690			0.303544
$352$	3.31164	−	0.181728i	0.176511	−	0.00968612i
$353$	−5.94944	+	10.3047i	−0.316657	+	0.548465i	−0.979788	−	0.200037i	$-0.935894\pi$
$353$	−5.94944	+	10.3047i	−0.316657	+	0.548465i	0.663132	+	0.748503i	$0.269227\pi$
$354$	−1.12459	−	10.6997i	−0.0597711	−	0.568684i
$355$	−8.30510	+	9.22374i	−0.440789	+	0.489546i
$356$	4.48701	−	13.8096i	0.237811	−	0.731908i
$357$	−8.93071	−	4.19814i	−0.472664	−	0.222189i
$358$	12.0599	+	8.76200i	0.637383	+	0.463086i
$359$	13.9046	−	2.95550i	0.733854	−	0.155986i	0.174198	−	0.984711i	$-0.444267\pi$
$359$	13.9046	−	2.95550i	0.733854	−	0.155986i	0.559656	+	0.828725i	$0.310933\pi$
$360$	1.04012	+	0.221085i	0.0548193	+	0.0116522i
$361$	−5.38530	−	51.2377i	−0.283437	−	2.69672i
$362$	−12.7706	−	22.1194i	−0.671210	−	1.16257i
$363$	−6.42177	+	8.93090i	−0.337055	+	0.468751i
$364$	9.83598	+	11.3859i	0.515546	+	0.596785i
$365$	−3.13741	+	2.27946i	−0.164219	+	0.119312i
$366$	−0.434168	+	0.482193i	−0.0226943	+	0.0252046i
$367$	0.281142	+	0.312240i	0.0146755	+	0.0162988i	0.750438	−	0.660941i	$-0.229843\pi$
$367$	0.281142	+	0.312240i	0.0146755	+	0.0162988i	−0.735762	+	0.677240i	$0.763176\pi$
$368$	−2.11916	+	0.943513i	−0.110469	+	0.0491840i
$369$	1.07007	−	10.1810i	0.0557055	−	0.530002i
$370$	−0.893168	+	2.74889i	−0.0464336	+	0.142908i
$371$	−11.7938	+	19.4913i	−0.612302	+	1.01194i
$372$	5.93533	−	4.31227i	0.307733	−	0.223581i
$373$	−10.3228	−	17.8796i	−0.534492	−	0.925768i	−0.999188	−	0.0402974i	$-0.987169\pi$
$373$	−10.3228	−	17.8796i	−0.534492	−	0.925768i	0.464695	−	0.885471i	$-0.346164\pi$
$374$	6.76296	+	10.3582i	0.349704	+	0.535607i
$375$	4.71561	−	8.16767i	0.243513	−	0.421777i
$376$	1.36875	+	0.609405i	0.0705877	+	0.0314277i
$377$	3.10500	+	9.55620i	0.159915	+	0.492169i
$378$	−0.330556	+	2.62502i	−0.0170020	+	0.135016i
$379$	12.1705	+	8.84240i	0.625158	+	0.454204i	0.854719	−	0.519090i	$-0.173729\pi$
$379$	12.1705	+	8.84240i	0.625158	+	0.454204i	−0.229562	+	0.973294i	$0.573729\pi$
$380$	−0.933406	+	8.88076i	−0.0478827	+	0.455574i
$381$	7.78291	+	8.64379i	0.398730	+	0.442835i
$382$	−2.92175	−	0.621036i	−0.149490	−	0.0317750i
$383$	−13.5390	−	6.02795i	−0.691811	−	0.308014i	0.0305472	−	0.999533i	$-0.490275\pi$
$383$	−13.5390	−	6.02795i	−0.691811	−	0.308014i	−0.722358	+	0.691519i	$0.756942\pi$
$384$	−1.00000			−0.0510310
$385$	−9.18816	−	1.62611i	−0.468272	−	0.0828742i
$386$	13.7438			0.699541
$387$	−2.50738	−	1.11636i	−0.127457	−	0.0567476i
$388$	15.8834	+	3.37611i	0.806356	+	0.171396i
$389$	24.7346	+	27.4706i	1.25410	+	1.39281i	0.886434	+	0.462855i	$0.153175\pi$
$389$	24.7346	+	27.4706i	1.25410	+	1.39281i	0.367662	+	0.929960i	$0.380158\pi$
$390$	0.632107	−	6.01409i	0.0320080	−	0.304536i
$391$	−6.99975	−	5.08562i	−0.353993	−	0.257191i
$392$	−5.82736	+	3.87838i	−0.294326	+	0.195888i
$393$	1.46832	+	4.51904i	0.0740671	+	0.227955i
$394$	−15.8621	−	7.06227i	−0.799122	−	0.355792i
$395$	−3.99978	+	6.92782i	−0.201251	+	0.348576i
$396$	2.08087	−	2.58263i	0.104568	−	0.129782i
$397$	3.50121	+	6.06427i	0.175721	+	0.304357i	0.940410	−	0.340041i	$-0.110441\pi$
$397$	3.50121	+	6.06427i	0.175721	+	0.304357i	−0.764690	+	0.644399i	$0.777108\pi$
$398$	−7.79489	+	5.66332i	−0.390723	+	0.283877i
$399$	−22.2133	−	0.456460i	−1.11206	−	0.0228516i
$400$	−1.19567	+	3.67989i	−0.0597835	+	0.183995i
$401$	0.466738	−	4.44072i	0.0233078	−	0.221759i	−0.976668	−	0.214756i	$-0.931104\pi$
$401$	0.466738	−	4.44072i	0.0233078	−	0.221759i	0.999975	−	0.00700260i	$-0.00222901\pi$
$402$	−6.80847	+	3.03132i	−0.339575	+	0.151189i
$403$	−27.9173	−	31.0053i	−1.39066	−	1.54449i
$404$	−2.35652	+	2.61719i	−0.117241	+	0.130210i
$405$	0.860276	−	0.625027i	0.0427475	−	0.0310578i
$406$	−4.59153	+	0.877775i	−0.227874	+	0.0435632i
$407$	6.39025	+	6.35888i	0.316753	+	0.315198i
$408$	−1.86492	−	3.23014i	−0.0923273	−	0.159916i
$409$	−0.519659	−	4.94422i	−0.0256955	−	0.244476i	−0.999829	−	0.0185022i	$-0.994110\pi$
$409$	−0.519659	−	4.94422i	−0.0256955	−	0.244476i	0.974133	−	0.225974i	$-0.0725564\pi$
$410$	−10.6478	−	2.26326i	−0.525859	−	0.111775i
$411$	10.1620	−	2.16000i	0.501255	−	0.106545i
$412$	−3.51157	−	2.55130i	−0.173003	−	0.125694i
$413$	−2.39315	−	28.3640i	−0.117759	−	1.39570i
$414$	−0.716831	+	2.20618i	−0.0352303	+	0.108428i
$415$	7.65705	−	8.50402i	0.375870	−	0.417446i
$416$	0.594443	+	5.65575i	0.0291450	+	0.277296i
$417$	−9.23703	+	15.9990i	−0.452339	+	0.783475i
$418$	23.3957	+	15.1116i	1.14432	+	0.739133i
$419$	−18.6110			−0.909209			−0.454604	−	0.890694i	$-0.650219\pi$
$419$	−18.6110			−0.909209			−0.454604	+	0.890694i	$0.650219\pi$
$420$	2.73931	+	0.641349i	0.133665	+	0.0312946i
$421$	−7.33815	−	22.5845i	−0.357639	−	1.10070i	−0.954463	−	0.298329i	$-0.903571\pi$
$421$	−7.33815	−	22.5845i	−0.357639	−	1.10070i	0.596824	−	0.802372i	$-0.296429\pi$
$422$	11.5043	−	2.44531i	0.560020	−	0.119036i
$423$	1.36875	−	0.609405i	0.0665507	−	0.0296303i
$424$	−7.86623	+	3.50227i	−0.382018	+	0.170085i
$425$	−14.1164	+	3.00053i	−0.684745	+	0.145547i
$426$	−3.60692	−	11.1009i	−0.174756	−	0.537843i
$427$	−1.17467	+	1.25189i	−0.0568462	+	0.0605834i
$428$	−14.3751			−0.694846
$429$	−15.8437	−	10.2337i	−0.764939	−	0.494086i
$430$	−1.45929	+	2.52756i	−0.0703730	+	0.121890i
$431$	−0.227785	−	2.16723i	−0.0109720	−	0.104392i	0.987665	−	0.156580i	$-0.0500470\pi$
$431$	−0.227785	−	2.16723i	−0.0109720	−	0.104392i	−0.998637	+	0.0521885i	$0.983380\pi$
$432$	−0.669131	+	0.743145i	−0.0321936	+	0.0357546i
$433$	−1.58562	+	4.88002i	−0.0761998	+	0.234519i	−0.981900	−	0.189400i	$-0.939346\pi$
$433$	−1.58562	+	4.88002i	−0.0761998	+	0.234519i	0.905700	+	0.423919i	$0.139346\pi$
$434$	15.9345	−	11.0842i	0.764880	−	0.532057i
$435$	1.51999	+	1.10434i	0.0728779	+	0.0529489i
$436$	1.52730	−	0.324639i	0.0731446	−	0.0155474i
$437$	−19.0544	−	4.05013i	−0.911494	−	0.193744i
$438$	−0.381213	−	3.62700i	−0.0182151	−	0.173305i
$439$	−18.2008	−	31.5248i	−0.868679	−	1.50460i	−0.863347	−	0.504610i	$-0.831636\pi$
$439$	−18.2008	−	31.5248i	−0.868679	−	1.50460i	−0.00533155	−	0.999986i	$-0.501697\pi$
$440$	−2.49993	−	2.48766i	−0.119179	−	0.118594i
$441$	−1.01707	+	6.92572i	−0.0484319	+	0.329796i
$442$	−17.1603	+	12.4677i	−0.816230	+	0.593026i
$443$	0.584835	−	0.649525i	0.0277864	−	0.0308599i	−0.729091	−	0.684416i	$-0.760057\pi$
$443$	0.584835	−	0.649525i	0.0277864	−	0.0308599i	0.756878	+	0.653556i	$0.226724\pi$
$444$	−1.81879	−	2.01997i	−0.0863157	−	0.0958633i
$445$	−14.1054	+	6.28013i	−0.668660	+	0.297707i
$446$	0.666808	−	6.34426i	0.0315743	−	0.300409i
$447$	−3.88931	+	11.9701i	−0.183958	+	0.566165i
$448$	−2.64519	−	0.0543560i	−0.124974	−	0.00256808i
$449$	−10.4851	+	7.61791i	−0.494825	+	0.359511i	−0.807037	−	0.590501i	$-0.798930\pi$
$449$	−10.4851	+	7.61791i	−0.494825	+	0.359511i	0.312212	+	0.950012i	$0.398930\pi$
$450$	1.93463	+	3.35088i	0.0911995	+	0.157962i
$451$	−21.3021	+	26.4386i	−1.00307	+	1.24495i
$452$	5.27735	−	9.14063i	0.248226	−	0.429939i
$453$	13.4299	+	5.97937i	0.630991	+	0.280935i
$454$	7.27055	+	22.3764i	0.341224	+	1.05018i
$455$	1.99895	−	15.8741i	0.0937120	−	0.744188i
$456$	−6.79381	−	4.93599i	−0.318149	−	0.231149i
$457$	3.51727	−	33.4646i	0.164531	−	1.56541i	−0.531289	−	0.847191i	$-0.678292\pi$
$457$	3.51727	−	33.4646i	0.164531	−	1.56541i	0.695820	−	0.718217i	$-0.255041\pi$
$458$	9.83314	+	10.9208i	0.459472	+	0.510296i
$459$	−3.64834	−	0.775478i	−0.170290	−	0.0361962i
$460$	2.25343	+	1.00329i	0.105067	+	0.0467788i
$461$	33.2372			1.54801			0.774006	−	0.633179i	$-0.218250\pi$
$461$	33.2372			1.54801			0.774006	+	0.633179i	$0.218250\pi$
$462$	5.64469	−	6.71845i	0.262615	−	0.312570i
$463$	−23.9755			−1.11424			−0.557119	−	0.830433i	$-0.688093\pi$
$463$	−23.9755			−1.11424			−0.557119	+	0.830433i	$0.688093\pi$
$464$	−1.61411	−	0.718648i	−0.0749332	−	0.0333624i
$465$	−7.63083	−	1.62198i	−0.353871	−	0.0752177i
$466$	6.19919	+	6.88489i	0.287172	+	0.318937i
$467$	2.53288	−	24.0988i	0.117208	−	1.11516i	−0.764912	−	0.644135i	$-0.777218\pi$
$467$	2.53288	−	24.0988i	0.117208	−	1.11516i	0.882120	−	0.471024i	$-0.156116\pi$
$468$	4.60080	+	3.34268i	0.212672	+	0.154515i
$469$	−18.1745	+	7.64836i	−0.839219	+	0.353168i
$470$	−0.492329	−	1.51523i	−0.0227094	−	0.0698924i
$471$	8.57072	+	3.81593i	0.394918	+	0.175829i
$472$	5.37933	−	9.31727i	0.247604	−	0.428862i
$473$	4.97664	+	7.62223i	0.228826	+	0.350470i
$474$	−3.76146	−	6.51503i	−0.172769	−	0.299245i
$475$	−26.2871	+	19.0987i	−1.20613	+	0.876307i
$476$	−4.75750	−	8.64571i	−0.218060	−	0.396275i
$477$	−2.66084	+	8.18922i	−0.121832	+	0.374959i
$478$	−2.55804	+	24.3381i	−0.117002	+	1.11320i
$479$	−19.7505	+	8.79348i	−0.902422	+	0.401784i	−0.804873	−	0.593446i	$-0.797767\pi$
$479$	−19.7505	+	8.79348i	−0.902422	+	0.401784i	−0.0975488	+	0.995231i	$0.531100\pi$
$480$	0.711526	+	0.790230i	0.0324766	+	0.0360689i
$481$	−10.3433	+	11.4873i	−0.471612	+	0.523778i
$482$	1.75606	−	1.27585i	0.0799863	−	0.0581134i
$483$	−2.01608	+	5.79681i	−0.0917346	+	0.263764i
$484$	−10.4448	+	3.45063i	−0.474762	+	0.156847i
$485$	−8.63353	−	14.9537i	−0.392028	−	0.679013i
$486$	0.104528	+	0.994522i	0.00474151	+	0.0451124i
$487$	31.5082	+	6.69726i	1.42777	+	0.303482i	0.856019	−	0.516945i	$-0.172931\pi$
$487$	31.5082	+	6.69726i	1.42777	+	0.303482i	0.571752	+	0.820427i	$0.306264\pi$
$488$	−0.634675	+	0.134904i	−0.0287304	+	0.00610684i
$489$	13.9386	+	10.1270i	0.630325	+	0.457958i
$490$	7.21113	+	1.84539i	0.325766	+	0.0833662i
$491$	2.90193	−	8.93122i	0.130962	−	0.403060i	−0.863978	−	0.503530i	$-0.832034\pi$
$491$	2.90193	−	8.93122i	0.130962	−	0.403060i	0.994940	+	0.100470i	$0.0320345\pi$
$492$	6.84995	−	7.60764i	0.308820	−	0.342979i
$493$	−0.688855	−	6.55402i	−0.0310245	−	0.295178i
$494$	−23.8782	+	41.3583i	−1.07433	+	1.86080i
$495$	−3.52147	+	0.193242i	−0.158278	+	0.00868558i
$496$	7.33647			0.329417
$497$	−8.93759	−	29.5602i	−0.400906	−	1.32596i
$498$	3.32547	+	10.2347i	0.149018	+	0.458630i
$499$	14.1765	−	3.01330i	0.634625	−	0.134894i	0.120645	−	0.992696i	$-0.461504\pi$
$499$	14.1765	−	3.01330i	0.634625	−	0.134894i	0.513980	+	0.857802i	$0.328170\pi$
$500$	8.61585	−	3.83602i	0.385312	−	0.171552i
$501$	7.25363	−	3.22952i	0.324068	−	0.144284i
$502$	14.2378	−	3.02633i	0.635463	−	0.135072i
$503$	8.16272	+	25.1223i	0.363958	+	1.12015i	0.950631	+	0.310323i	$0.100437\pi$
$503$	8.16272	+	25.1223i	0.363958	+	1.12015i	−0.586674	+	0.809823i	$0.699563\pi$
$504$	−1.81037	+	1.92939i	−0.0806405	+	0.0859419i
$505$	3.74491			0.166646
$506$	5.96713	−	4.85645i	0.265272	−	0.215896i
$507$	9.67043	−	16.7497i	0.429479	−	0.743879i
$508$	1.21581	+	11.5677i	0.0539428	+	0.513232i
$509$	−15.2988	+	16.9911i	−0.678108	+	0.753115i	−0.979732	−	0.200311i	$-0.935805\pi$
$509$	−15.2988	+	16.9911i	−0.678108	+	0.753115i	0.301624	+	0.953427i	$0.402471\pi$
$510$	−1.22561	+	3.77204i	−0.0542710	+	0.167029i
$511$	−0.811233	−	9.61483i	−0.0358868	−	0.425335i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−8.21410	+	1.74596i	−0.362662	+	0.0770861i
$514$	5.09756	+	1.08352i	0.224844	+	0.0477920i
$515$	0.482456	+	4.59027i	0.0212596	+	0.202271i
$516$	−1.37233	−	2.37695i	−0.0604137	−	0.104640i
$517$	−4.90995	−	0.765280i	−0.215939	−	0.0336570i
$518$	−4.70124	−	5.44206i	−0.206561	−	0.239110i
$519$	8.48615	−	6.16555i	0.372500	−	0.270637i
$520$	4.04638	−	4.49396i	0.177446	−	0.197073i
$521$	−6.57506	−	7.30235i	−0.288059	−	0.319922i	0.581696	−	0.813407i	$-0.302389\pi$
$521$	−6.57506	−	7.30235i	−0.288059	−	0.319922i	−0.869754	+	0.493485i	$0.835723\pi$
$522$	−1.61411	+	0.718648i	−0.0706477	+	0.0314544i
$523$	2.06777	−	19.6735i	0.0904173	−	0.860263i	−0.851486	−	0.524378i	$-0.824298\pi$
$523$	2.06777	−	19.6735i	0.0904173	−	0.860263i	0.941903	−	0.335885i	$-0.109035\pi$
$524$	−1.46832	+	4.51904i	−0.0641440	+	0.197415i
$525$	4.93534	+	8.96889i	0.215396	+	0.391435i
$526$	−11.8404	+	8.60259i	−0.516268	+	0.375091i
$527$	13.6819	+	23.6978i	0.595995	+	1.03229i
$528$	3.20149	−	0.866286i	0.139327	−	0.0377002i
$529$	8.80946	−	15.2584i	0.383020	−	0.663410i
$530$	8.36463	+	3.72417i	0.363336	+	0.161768i
$531$	−3.32461	−	10.2321i	−0.144276	−	0.444035i
$532$	−17.7026	−	13.4259i	−0.767507	−	0.582088i
$533$	−47.0988	−	34.2193i	−2.04008	−	1.48220i
$534$	1.51778	−	14.4407i	0.0656809	−	0.624912i
$535$	10.2283	+	11.3596i	0.442206	+	0.491120i
$536$	−7.28993	−	1.54952i	−0.314877	−	0.0669292i
$537$	13.6180	+	6.06314i	0.587662	+	0.261644i
$538$	12.8376			0.553469
$539$	15.2965	−	17.4648i	0.658866	−	0.752261i
$540$	1.06336			0.0457597
$541$	14.9597	+	6.66050i	0.643169	+	0.286357i	0.702287	−	0.711894i	$-0.252162\pi$
$541$	14.9597	+	6.66050i	0.643169	+	0.286357i	−0.0591180	+	0.998251i	$0.518829\pi$
$542$	−20.0108	−	4.25342i	−0.859535	−	0.182700i
$543$	−17.0904	−	18.9809i	−0.733421	−	0.814547i
$544$	0.389875	−	3.70941i	0.0167157	−	0.159040i
$545$	−1.34326	−	0.975933i	−0.0575388	−	0.0418044i
$546$	11.9883	+	9.09211i	0.513052	+	0.389106i
$547$	−3.96712	−	12.2095i	−0.169622	−	0.522042i	0.829725	−	0.558172i	$-0.188497\pi$
$547$	−3.96712	−	12.2095i	−0.169622	−	0.522042i	−0.999347	+	0.0361299i	$0.988497\pi$
$548$	9.49085	+	4.22560i	0.405429	+	0.180509i
$549$	−0.324427	+	0.561924i	−0.0138462	+	0.0239824i
$550$	0.640087	−	12.8169i	0.0272934	−	0.546516i
$551$	−7.41872	−	12.8496i	−0.316048	−	0.547411i
$552$	−1.87669	+	1.36349i	−0.0798771	+	0.0580341i
$553$	−9.59564	−	17.4380i	−0.408048	−	0.741538i
$554$	−5.53074	+	17.0219i	−0.234979	+	0.723190i
$555$	−0.302124	+	2.87452i	−0.0128244	+	0.122016i
$556$	−16.8769	+	7.51408i	−0.715740	+	0.318668i
$557$	−19.6577	−	21.8321i	−0.832925	−	0.925057i	0.165200	−	0.986260i	$-0.447173\pi$
$557$	−19.6577	−	21.8321i	−0.832925	−	0.925057i	−0.998125	+	0.0612031i	$0.980506\pi$
$558$	4.90906	−	5.45206i	0.207817	−	0.230804i
$559$	−12.6277	+	9.17455i	−0.534094	+	0.388042i
$560$	1.83917	+	2.12899i	0.0777191	+	0.0899661i
$561$	8.76875	+	8.72570i	0.370217	+	0.368399i
$562$	10.3392	+	17.9080i	0.436132	+	0.755403i
$563$	−2.16649	−	20.6127i	−0.0913065	−	0.868723i	−0.940306	−	0.340330i	$-0.889461\pi$
$563$	−2.16649	−	20.6127i	−0.0913065	−	0.868723i	0.849000	−	0.528393i	$-0.177205\pi$
$564$	1.46554	+	0.311510i	0.0617103	+	0.0131169i
$565$	−10.9782	+	2.33348i	−0.461855	+	0.0981704i
$566$	−6.14270	−	4.46293i	−0.258197	−	0.187591i
$567$	0.222440	+	2.63638i	0.00934159	+	0.110718i
$568$	3.60692	−	11.1009i	0.151343	−	0.465785i
$569$	−8.29213	+	9.20934i	−0.347624	+	0.386076i	−0.891447	−	0.453124i	$-0.850309\pi$
$569$	−8.29213	+	9.20934i	−0.347624	+	0.386076i	0.543823	+	0.839200i	$0.316976\pi$
$570$	0.933406	+	8.88076i	0.0390961	+	0.371974i
$571$	0.643690	−	1.11490i	0.0269376	−	0.0466573i	−0.852242	−	0.523147i	$-0.824758\pi$
$571$	0.643690	−	1.11490i	0.0269376	−	0.0466573i	0.879180	+	0.476490i	$0.158091\pi$
$572$	−6.80260	−	17.5919i	−0.284431	−	0.735553i
$573$	−2.98702			−0.124785
$574$	18.5330	−	19.7513i	0.773551	−	0.824405i
$575$	2.77361	+	8.53630i	0.115668	+	0.355988i
$576$	−0.978148	+	0.207912i	−0.0407562	+	0.00866299i
$577$	−0.597141	+	0.265864i	−0.0248593	+	0.0110681i	−0.419129	−	0.907927i	$-0.637664\pi$
$577$	−0.597141	+	0.265864i	−0.0248593	+	0.0110681i	0.394269	+	0.918995i	$0.370998\pi$
$578$	−2.82129	+	1.25612i	−0.117350	+	0.0522476i
$579$	13.4435	−	2.85750i	0.558691	−	0.118753i
$580$	0.580584	+	1.78686i	0.0241075	+	0.0741951i
$581$	8.24019	+	27.2536i	0.341861	+	1.13067i
$582$	16.2382			0.673095
$583$	22.1497	−	18.0269i	0.917347	−	0.746598i
$584$	1.82349	−	3.15838i	0.0754565	−	0.130695i
$585$	−0.632107	−	6.01409i	−0.0261344	−	0.248652i
$586$	−9.02785	+	10.0264i	−0.372937	+	0.414188i
$587$	−4.60855	+	14.1837i	−0.190215	+	0.585422i	−0.999999	−	0.00130586i	$-0.999584\pi$
$587$	−4.60855	+	14.1837i	−0.190215	+	0.585422i	0.809784	+	0.586728i	$0.199584\pi$
$588$	−4.89366	+	5.00520i	−0.201811	+	0.206411i
$589$	49.8426	+	36.2128i	2.05373	+	1.49212i
$590$	−11.1903	+	2.37858i	−0.460698	+	0.0979245i
$591$	−16.9838	−	3.61002i	−0.698621	−	0.148496i
$592$	−0.284122	−	2.70324i	−0.0116773	−	0.111103i
$593$	1.27241	+	2.20388i	0.0522516	+	0.0905024i	0.890968	−	0.454066i	$-0.150027\pi$
$593$	1.27241	+	2.20388i	0.0522516	+	0.0905024i	−0.838717	+	0.544568i	$0.816694\pi$
$594$	1.49844	−	2.95883i	0.0614817	−	0.121402i
$595$	−3.44701	+	9.91116i	−0.141314	+	0.406318i
$596$	−10.1824	+	7.39791i	−0.417085	+	0.303030i
$597$	−6.44708	+	7.16021i	−0.263862	+	0.293048i
$598$	8.82716	+	9.80356i	0.360970	+	0.400897i
$599$	−17.0794	+	7.60425i	−0.697846	+	0.310701i	−0.724823	−	0.688935i	$-0.758079\pi$
$599$	−17.0794	+	7.60425i	−0.697846	+	0.310701i	0.0269769	+	0.999636i	$0.491412\pi$
$600$	−0.404449	+	3.84807i	−0.0165115	+	0.157097i
$601$	−2.13954	+	6.58482i	−0.0872736	+	0.268600i	−0.985163	−	0.171620i	$-0.945100\pi$
$601$	−2.13954	+	6.58482i	−0.0872736	+	0.268600i	0.897890	+	0.440221i	$0.145100\pi$
$602$	−3.50089	−	6.36209i	−0.142686	−	0.259300i
$603$	−6.02944	+	4.38064i	−0.245538	+	0.178394i
$604$	7.35042	+	12.7313i	0.299084	+	0.518029i
$605$	10.1585	+	5.79856i	0.413002	+	0.235745i
$606$	−1.76088	+	3.04994i	−0.0715311	+	0.123895i
$607$	30.0158	+	13.3639i	1.21831	+	0.542424i	0.912267	−	0.409595i	$-0.134330\pi$
$607$	30.0158	+	13.3639i	1.21831	+	0.542424i	0.306038	+	0.952019i	$0.400997\pi$
$608$	−2.59501	−	7.98660i	−0.105241	−	0.323900i
$609$	−4.30870	+	1.81323i	−0.174597	+	0.0734756i
$610$	0.558194	+	0.405552i	0.0226006	+	0.0164203i
$611$	0.890642	−	8.47389i	0.0360315	−	0.342817i
$612$	−2.49575	−	2.77181i	−0.100885	−	0.112044i
$613$	−16.6040	−	3.52930i	−0.670631	−	0.142547i	−0.140002	−	0.990151i	$-0.544711\pi$
$613$	−16.6040	−	3.52930i	−0.670631	−	0.142547i	−0.530629	+	0.847604i	$0.678044\pi$
$614$	−20.3937	−	9.07988i	−0.823025	−	0.366434i
$615$	−10.8857			−0.438954
$616$	8.51565	−	2.11747i	0.343105	−	0.0853154i
$617$	7.83423			0.315394			0.157697	−	0.987488i	$-0.449593\pi$
$617$	7.83423			0.315394			0.157697	+	0.987488i	$0.449593\pi$
$618$	−3.96528	−	1.76546i	−0.159507	−	0.0710170i
$619$	25.7815	+	5.48002i	1.03624	+	0.220261i	0.694470	−	0.719521i	$-0.255639\pi$
$619$	25.7815	+	5.48002i	1.03624	+	0.220261i	0.341774	+	0.939782i	$0.388972\pi$
$620$	−5.22009	−	5.79750i	−0.209644	−	0.232833i
$621$	−0.242476	+	2.30701i	−0.00973023	+	0.0925770i
$622$	6.24562	+	4.53771i	0.250426	+	0.181945i
$623$	4.79977	−	38.1160i	0.192299	−	1.52709i
$624$	1.75735	+	5.40857i	0.0703503	+	0.216516i
$625$	8.51201	+	3.78979i	0.340481	+	0.151592i
$626$	−1.29621	+	2.24511i	−0.0518071	+	0.0897325i
$627$	26.0263	+	9.91716i	1.03939	+	0.396053i
$628$	4.69091	+	8.12489i	0.187188	+	0.324219i
$629$	8.20198	−	5.95908i	0.327034	−	0.237604i
$630$	2.81279	+	0.0577999i	0.112064	+	0.00230280i
$631$	5.08436	−	15.6480i	0.202405	−	0.622939i	−0.797405	−	0.603445i	$-0.793794\pi$
$631$	5.08436	−	15.6480i	0.202405	−	0.622939i	0.999810	−	0.0194941i	$-0.00620556\pi$
$632$	0.786358	−	7.48170i	0.0312797	−	0.297606i
$633$	10.7445	−	4.78376i	0.427055	−	0.190137i
$634$	−9.27377	−	10.2996i	−0.368308	−	0.409048i
$635$	8.27603	−	9.19146i	0.328424	−	0.364752i
$636$	−6.96617	+	5.06122i	−0.276227	+	0.200690i
$637$	31.2172	+	24.7020i	1.23687	+	0.978729i
$638$	5.79011	+	0.902465i	0.229233	+	0.0357289i
$639$	−5.83611	−	10.1084i	−0.230873	−	0.399884i
$640$	0.111151	+	1.05753i	0.00439364	+	0.0418027i
$641$	−23.4445	−	4.98327i	−0.926000	−	0.196827i	−0.279855	−	0.960042i	$-0.590287\pi$
$641$	−23.4445	−	4.98327i	−0.926000	−	0.196827i	−0.646145	+	0.763215i	$0.723620\pi$
$642$	−14.0610	+	2.98875i	−0.554942	+	0.117957i
$643$	13.2388	+	9.61857i	0.522088	+	0.379319i	0.817390	−	0.576085i	$-0.195420\pi$
$643$	13.2388	+	9.61857i	0.522088	+	0.379319i	−0.295302	+	0.955404i	$0.595420\pi$
$644$	−5.03832	+	3.50469i	−0.198537	+	0.138104i
$645$	−0.901888	+	2.77573i	−0.0355118	+	0.109294i
$646$	20.9583	−	23.2766i	0.824595	−	0.915806i
$647$	−1.83613	−	17.4696i	−0.0721858	−	0.686802i	−0.969447	−	0.245302i	$-0.921113\pi$
$647$	−1.83613	−	17.4696i	−0.0721858	−	0.686802i	0.897261	−	0.441501i	$-0.145554\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−9.15046	+	34.4892i	−0.359187	+	1.35382i
$650$	22.0041			0.863074
$651$	13.2818	−	14.1549i	0.520553	−	0.554775i
$652$	5.32407	+	16.3858i	0.208507	+	0.641718i
$653$	−12.2165	+	2.59669i	−0.478067	+	0.101616i	−0.440641	−	0.897683i	$-0.645249\pi$
$653$	−12.2165	+	2.59669i	−0.478067	+	0.101616i	−0.0374254	+	0.999299i	$0.511916\pi$
$654$	1.42643	−	0.635089i	0.0557779	−	0.0248339i
$655$	4.61583	−	2.05510i	0.180355	−	0.0802994i
$656$	10.0134	−	2.12841i	0.390957	−	0.0831004i
$657$	−1.12698	−	3.46848i	−0.0439676	−	0.135318i
$658$	3.85970	+	0.903664i	0.150467	+	0.0352285i
$659$	−6.99667			−0.272552			−0.136276	−	0.990671i	$-0.543513\pi$
$659$	−6.99667			−0.272552			−0.136276	+	0.990671i	$0.543513\pi$
$660$	−2.96251	−	1.91353i	−0.115316	−	0.0744840i
$661$	−9.58966	+	16.6098i	−0.372995	+	0.646046i	−0.990025	−	0.140894i	$-0.955002\pi$
$661$	−9.58966	+	16.6098i	−0.372995	+	0.646046i	0.617030	+	0.786940i	$0.288336\pi$
$662$	−1.42325	−	13.5413i	−0.0553161	−	0.526298i
$663$	−14.1931	+	15.7630i	−0.551214	+	0.612185i
$664$	−3.32547	+	10.2347i	−0.129053	+	0.397185i
$665$	1.98632	+	23.5421i	0.0770260	+	0.912922i
$666$	−2.19901	−	1.59768i	−0.0852101	−	0.0619088i
$667$	−4.00905	+	0.852151i	−0.155231	+	0.0329954i
$668$	7.76657	+	1.65084i	0.300498	+	0.0638728i
$669$	−0.666808	−	6.34426i	−0.0257803	−	0.245283i
$670$	3.96250	+	6.86325i	0.153085	+	0.265150i
$671$	1.91504	−	0.981706i	0.0739294	−	0.0378983i
$672$	−2.59869	+	0.496798i	−0.100247	+	0.0191644i
$673$	−8.31614	+	6.04203i	−0.320563	+	0.232903i	−0.736416	−	0.676529i	$-0.763483\pi$
$673$	−8.31614	+	6.04203i	−0.320563	+	0.232903i	0.415852	+	0.909432i	$0.363483\pi$
$674$	14.8400	−	16.4815i	0.571616	−	0.634844i
$675$	2.58904	+	2.87543i	0.0996524	+	0.110675i
$676$	17.6688	−	7.86664i	0.679568	−	0.302563i
$677$	−3.04557	+	28.9767i	−0.117051	+	1.11366i	0.765496	+	0.643441i	$0.222494\pi$
$677$	−3.04557	+	28.9767i	−0.117051	+	1.11366i	−0.882547	+	0.470224i	$0.844173\pi$
$678$	3.26158	−	10.0381i	0.125260	−	0.385511i
$679$	42.9532	+	0.882643i	1.64839	+	0.0338727i
$680$	−3.20869	+	2.33125i	−0.123048	+	0.0893994i
$681$	11.7640	+	20.3758i	0.450797	+	0.780804i
$682$	−23.4877	+	6.35548i	−0.899389	+	0.243364i
$683$	4.36730	−	7.56438i	0.167110	−	0.289443i	−0.770293	−	0.637691i	$-0.779890\pi$
$683$	4.36730	−	7.56438i	0.167110	−	0.289443i	0.937403	+	0.348248i	$0.113223\pi$
$684$	−7.67160	−	3.41562i	−0.293331	−	0.130599i
$685$	−3.41379	−	10.5066i	−0.130434	−	0.401436i
$686$	−13.2167	+	12.9737i	−0.504618	+	0.495339i
$687$	11.8888	+	8.63774i	0.453587	+	0.329550i
$688$	0.286896	−	2.72963i	0.0109378	−	0.104066i
$689$	32.7660	+	36.3903i	1.24828	+	1.38636i
$690$	2.41279	+	0.512854i	0.0918532	+	0.0195240i
$691$	−22.0174	−	9.80276i	−0.837580	−	0.372915i	−0.0573092	−	0.998356i	$-0.518252\pi$
$691$	−22.0174	−	9.80276i	−0.837580	−	0.372915i	−0.780271	+	0.625442i	$0.784919\pi$
$692$	10.4895			0.398749
$693$	4.12449	−	7.74523i	0.156677	−	0.294217i
$694$	11.4254			0.433702
$695$	17.9462	+	7.99017i	0.680738	+	0.303084i
$696$	−1.72825	−	0.367352i	−0.0655093	−	0.0139244i
$697$	25.5492	+	28.3753i	0.967746	+	1.07479i
$698$	−0.0924102	+	0.879224i	−0.00349778	+	0.0332791i
$699$	7.49517	+	5.44556i	0.283493	+	0.205970i
$700$	−1.27901	+	10.1569i	−0.0483420	+	0.383895i
$701$	6.36868	+	19.6008i	0.240542	+	0.740311i	0.996338	+	0.0855044i	$0.0272502\pi$
$701$	6.36868	+	19.6008i	0.240542	+	0.740311i	−0.755796	+	0.654807i	$0.772750\pi$
$702$	5.19524	+	2.31307i	0.196082	+	0.0873013i
$703$	11.4129	−	19.7677i	0.430446	−	0.745554i
$704$	3.09925	+	1.18095i	0.116807	+	0.0445087i
$705$	−0.796604	−	1.37976i	−0.0300019	−	0.0519647i
$706$	−9.62639	+	6.99398i	−0.362294	+	0.263222i
$707$	−4.82366	+	7.97197i	−0.181413	+	0.299817i
$708$	3.32461	−	10.2321i	0.124946	−	0.384546i
$709$	4.18039	−	39.7738i	0.156998	−	1.49374i	−0.578207	−	0.815890i	$-0.696247\pi$
$709$	4.18039	−	39.7738i	0.156998	−	1.49374i	0.735205	−	0.677845i	$-0.237086\pi$
$710$	−11.3387	+	5.04832i	−0.425535	+	0.189460i
$711$	−5.03381	−	5.59061i	−0.188783	−	0.209664i
$712$	9.71596	−	10.7907i	0.364121	−	0.404397i
$713$	13.7683	−	10.0032i	0.515626	−	0.374624i
$714$	−6.45108	−	7.46764i	−0.241426	−	0.279469i
$715$	−9.06140	+	17.8927i	−0.338877	+	0.669149i
$716$	7.45340	+	12.9097i	0.278547	+	0.482457i
$717$	2.55804	+	24.3381i	0.0955317	+	0.908924i
$718$	13.9046	+	2.95550i	0.518913	+	0.110298i
$719$	−1.62464	+	0.345329i	−0.0605890	+	0.0128786i	−0.238106	−	0.971239i	$-0.576527\pi$
$719$	−1.62464	+	0.345329i	−0.0605890	+	0.0128786i	0.177517	+	0.984118i	$0.443193\pi$
$720$	0.860276	+	0.625027i	0.0320606	+	0.0232934i
$721$	−10.3930	−	4.88551i	−0.387054	−	0.181946i
$722$	15.9205	−	48.9983i	0.592501	−	1.82353i
$723$	1.45242	−	1.61308i	0.0540161	−	0.0599909i
$724$	−2.66979	−	25.4013i	−0.0992219	−	0.944034i
$725$	−3.41823	+	5.92055i	−0.126950	+	0.219884i
$726$	−9.49910	+	5.54681i	−0.352545	+	0.205862i
$727$	23.1130			0.857215			0.428608	−	0.903491i	$-0.359004\pi$
$727$	23.1130			0.857215			0.428608	+	0.903491i	$0.359004\pi$
$728$	4.35454	+	14.4022i	0.161390	+	0.533782i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−3.79330	+	0.806292i	−0.140396	+	0.0298422i
$731$	9.35213	−	4.16384i	0.345901	−	0.154005i
$732$	−0.592758	+	0.263913i	−0.0219090	+	0.00975450i
$733$	−20.4610	+	4.34912i	−0.755745	+	0.160639i	−0.569643	−	0.821892i	$-0.692919\pi$
$733$	−20.4610	+	4.34912i	−0.755745	+	0.160639i	−0.186102	+	0.982530i	$0.559585\pi$
$734$	0.129837	+	0.399596i	0.00479236	+	0.0147494i
$735$	7.43723	+	0.305784i	0.274326	+	0.0112790i
$736$	−2.31971			−0.0855058
$737$	24.6810	−	1.35438i	0.909136	−	0.0498892i
$738$	5.11854	−	8.86558i	0.188416	−	0.326346i
$739$	−4.83130	−	45.9667i	−0.177722	−	1.69091i	−0.612575	−	0.790412i	$-0.709866\pi$
$739$	−4.83130	−	45.9667i	−0.177722	−	1.69091i	0.434853	−	0.900501i	$-0.356800\pi$
$740$	−1.93402	+	2.14795i	−0.0710961	+	0.0789602i
$741$	−14.7575	+	45.4190i	−0.542132	+	1.66851i
$742$	−18.7020	+	13.0092i	−0.686571	+	0.477584i
$743$	−33.0848	−	24.0375i	−1.21376	−	0.881851i	−0.218197	−	0.975905i	$-0.570018\pi$
$743$	−33.0848	−	24.0375i	−1.21376	−	0.881851i	−0.995567	+	0.0940534i	$0.970018\pi$
$744$	7.17615	−	1.52534i	0.263091	−	0.0559216i
$745$	13.0911	+	2.78259i	0.479619	+	0.101946i
$746$	−2.15805	−	20.5324i	−0.0790117	−	0.751746i
$747$	5.38072	+	9.31969i	0.196870	+	0.340989i
$748$	1.96523	+	12.2134i	0.0718558	+	0.446566i
$749$	−37.3564	+	7.14152i	−1.36497	+	0.260946i
$750$	7.63002	−	5.54353i	0.278609	−	0.202421i
$751$	4.40436	−	4.89154i	0.160717	−	0.178495i	−0.657408	−	0.753535i	$-0.728347\pi$
$751$	4.40436	−	4.89154i	0.160717	−	0.178495i	0.818125	+	0.575040i	$0.195014\pi$
$752$	1.00254	+	1.11344i	0.0365590	+	0.0406029i
$753$	13.2974	−	5.92040i	0.484586	−	0.215751i
$754$	−1.05030	+	9.99294i	−0.0382497	+	0.363921i
$755$	4.83064	−	14.8672i	0.175805	−	0.541072i
$756$	−1.36967	+	2.26363i	−0.0498144	+	0.0823273i
$757$	−3.44139	+	2.50032i	−0.125079	+	0.0908756i	−0.648566	−	0.761158i	$-0.724631\pi$
$757$	−3.44139	+	2.50032i	−0.125079	+	0.0908756i	0.523487	+	0.852034i	$0.324631\pi$
$758$	7.52180	+	13.0281i	0.273204	+	0.473203i
$759$	4.82703	−	5.99096i	0.175210	−	0.217458i
$760$	−4.46484	+	7.73333i	−0.161957	+	0.280517i
$761$	32.4708	+	14.4569i	1.17706	+	0.524063i	0.899618	−	0.436678i	$-0.143845\pi$
$761$	32.4708	+	14.4569i	1.17706	+	0.524063i	0.277447	+	0.960741i	$0.410512\pi$
$762$	3.59429	+	11.0621i	0.130207	+	0.400737i
$763$	3.80771	−	1.60240i	0.137848	−	0.0580107i
$764$	−2.41655	−	1.75573i	−0.0874277	−	0.0635199i
$765$	−0.414577	+	3.94443i	−0.0149891	+	0.142611i
$766$	−9.91671	−	11.0136i	−0.358305	−	0.397938i
$767$	−59.8464	−	12.7208i	−2.16093	−	0.459320i
$768$	−0.913545	−	0.406737i	−0.0329647	−	0.0146768i
$769$	38.6760			1.39469			0.697346	−	0.716735i	$-0.254364\pi$
$769$	38.6760			1.39469			0.697346	+	0.716735i	$0.254364\pi$
$770$	−7.73240	−	5.22269i	−0.278656	−	0.188213i
$771$	5.21145			0.187686
$772$	12.5556	+	5.59011i	0.451885	+	0.201192i
$773$	−19.1717	−	4.07507i	−0.689558	−	0.146570i	−0.150211	−	0.988654i	$-0.547995\pi$
$773$	−19.1717	−	4.07507i	−0.689558	−	0.146570i	−0.539347	+	0.842084i	$0.681329\pi$
$774$	−1.83654	−	2.03969i	−0.0660132	−	0.0733150i
$775$	2.96723	−	28.2313i	0.106586	−	1.01410i
$776$	13.1370	+	9.54458i	0.471590	+	0.342630i
$777$	−5.72998	−	4.34570i	−0.205562	−	0.155901i
$778$	11.4229	+	35.1561i	0.409531	+	1.26041i
$779$	78.5348	+	34.9660i	2.81380	+	1.25279i
$780$	3.02361	−	5.23705i	0.108263	−	0.187516i
$781$	−1.93092	+	38.6642i	−0.0690938	+	1.38351i
$782$	−4.32608	−	7.49299i	−0.154700	−	0.267949i
$783$	−1.42942	+	1.03854i	−0.0510834	+	0.0371143i
$784$	−6.90104	+	1.17287i	−0.246466	+	0.0418883i
$785$	3.08283	−	9.48797i	0.110031	−	0.338640i
$786$	−0.496677	+	4.72557i	−0.0177159	+	0.168555i
$787$	−40.8754	+	18.1989i	−1.45705	+	0.648721i	−0.973933	−	0.226834i	$-0.927162\pi$
$787$	−40.8754	+	18.1989i	−1.45705	+	0.648721i	−0.483118	+	0.875555i	$0.660496\pi$
$788$	−11.6183	−	12.9034i	−0.413884	−	0.459665i
$789$	−9.79312	+	10.8764i	−0.348644	+	0.387209i
$790$	−6.47178	+	4.70202i	−0.230256	+	0.167290i
$791$	9.17314	−	26.3755i	0.326159	−	0.937803i
$792$	2.95142	−	1.51298i	0.104874	−	0.0537615i
$793$	1.84499	+	3.19561i	0.0655174	+	0.113479i
$794$	0.731952	+	6.96406i	0.0259760	+	0.247145i
$795$	8.95614	+	1.90369i	0.317642	+	0.0675168i
$796$	−9.42447	+	2.00323i	−0.334041	+	0.0710027i
$797$	22.2291	+	16.1504i	0.787395	+	0.572076i	0.907189	−	0.420723i	$-0.138223\pi$
$797$	22.2291	+	16.1504i	0.787395	+	0.572076i	−0.119794	+	0.992799i	$0.538223\pi$
$798$	−20.1072	−	9.45196i	−0.711787	−	0.334596i
$799$	−1.72689	+	5.31483i	−0.0610931	+	0.188025i
$800$	−2.58904	+	2.87543i	−0.0915366	+	0.101662i
$801$	−1.51778	−	14.4407i	−0.0536282	−	0.510238i
$802$	2.23259	−	3.86696i	0.0788354	−	0.136547i
$803$	−3.10183	+	11.6912i	−0.109461	+	0.412573i
$804$	−7.45279			−0.262840
$805$	6.35441	+	1.48775i	0.223964	+	0.0524362i
$806$	−12.8927	−	39.6798i	−0.454128	−	1.39766i
$807$	12.5571	−	2.66909i	0.442030	−	0.0939564i
$808$	−3.21730	+	1.43243i	−0.113184	+	0.0503928i
$809$	−26.5651	+	11.8276i	−0.933981	+	0.415835i	−0.816569	−	0.577248i	$-0.804127\pi$
$809$	−26.5651	+	11.8276i	−0.933981	+	0.415835i	−0.117412	+	0.993083i	$0.537460\pi$
$810$	1.04012	−	0.221085i	0.0365462	−	0.00776813i
$811$	10.6557	+	32.7949i	0.374173	+	1.15159i	0.944035	+	0.329845i	$0.106997\pi$
$811$	10.6557	+	32.7949i	0.374173	+	1.15159i	−0.569862	+	0.821740i	$0.693003\pi$
$812$	−4.55160	−	1.06566i	−0.159730	−	0.0373972i
$813$	−20.4578			−0.717487
$814$	3.25139	+	8.40828i	0.113961	+	0.294710i
$815$	9.16034	−	15.8662i	0.320873	−	0.555768i
$816$	−0.389875	−	3.70941i	−0.0136483	−	0.129855i
$817$	15.4226	−	17.1285i	0.539567	−	0.599250i
$818$	1.53626	−	4.72814i	0.0537142	−	0.165315i
$819$	13.6167	+	6.40091i	0.475806	+	0.223666i
$820$	−8.80672	−	6.39846i	−0.307544	−	0.223444i
$821$	33.3080	−	7.07983i	1.16246	−	0.247088i	0.414004	−	0.910275i	$-0.364130\pi$
$821$	33.3080	−	7.07983i	1.16246	−	0.247088i	0.748454	+	0.663187i	$0.230797\pi$
$822$	10.1620	+	2.16000i	0.354441	+	0.0753387i
$823$	−2.38756	−	22.7162i	−0.0832252	−	0.791835i	−0.953930	−	0.300029i	$-0.903004\pi$
$823$	−2.38756	−	22.7162i	−0.0832252	−	0.791835i	0.870705	−	0.491806i	$-0.163663\pi$
$824$	−2.17027	−	3.75902i	−0.0756049	−	0.130952i
$825$	−2.03869	−	12.6699i	−0.0709781	−	0.441110i
$826$	9.35041	−	26.8851i	0.325342	−	0.935454i
$827$	−24.6151	+	17.8839i	−0.855952	+	0.621885i	−0.926781	−	0.375603i	$-0.877436\pi$
$827$	−24.6151	+	17.8839i	−0.855952	+	0.621885i	0.0708288	+	0.997488i	$0.477436\pi$
$828$	−1.55219	+	1.72388i	−0.0539424	+	0.0599091i
$829$	28.1812	+	31.2984i	0.978773	+	1.08704i	0.996192	+	0.0871888i	$0.0277883\pi$
$829$	28.1812	+	31.2984i	0.978773	+	1.08704i	−0.0174192	+	0.999848i	$0.505545\pi$
$830$	10.4540	−	4.65440i	0.362862	−	0.161557i
$831$	−1.87083	+	17.7998i	−0.0648985	+	0.617468i
$832$	−1.75735	+	5.40857i	−0.0609251	+	0.187508i
$833$	−16.6584	−	20.1040i	−0.577181	−	0.696562i
$834$	−14.9458	+	10.8588i	−0.517532	+	0.376009i
$835$	−4.22158	−	7.31199i	−0.146094	−	0.253042i
$836$	15.2266	+	23.3210i	0.526622	+	0.806575i
$837$	3.66824	−	6.35357i	0.126793	−	0.219612i
$838$	−17.0020	−	7.56979i	−0.587325	−	0.261494i
$839$	−8.78824	−	27.0474i	−0.303404	−	0.933781i	−0.980268	−	0.197673i	$-0.936662\pi$
$839$	−8.78824	−	27.0474i	−0.303404	−	0.933781i	0.676864	−	0.736108i	$-0.263338\pi$
$840$	2.24162	+	1.70008i	0.0773433	+	0.0586583i
$841$	20.9359	+	15.2108i	0.721928	+	0.524511i
$842$	2.48221	−	23.6167i	0.0855426	−	0.813884i
$843$	13.8365	+	15.3670i	0.476555	+	0.529268i
$844$	11.5043	+	2.44531i	0.395994	+	0.0841712i
$845$	−18.7882	−	8.36506i	−0.646335	−	0.287767i
$846$	1.49828			0.0515119
$847$	−25.4284	+	14.1561i	−0.873732	+	0.486408i
$848$	−8.61066			−0.295691
$849$	−6.93636	−	3.08827i	−0.238055	−	0.105989i
$850$	−14.1164	−	3.00053i	−0.484188	−	0.102917i
$851$	−4.21906	−	4.68574i	−0.144628	−	0.160625i
$852$	1.22008	−	11.6083i	0.0417993	−	0.397693i
$853$	−20.7207	−	15.0545i	−0.709463	−	0.515455i	0.173537	−	0.984827i	$-0.444480\pi$
$853$	−20.7207	−	15.0545i	−0.709463	−	0.515455i	−0.883000	+	0.469372i	$0.844480\pi$
$854$	−1.58230	+	0.665881i	−0.0541453	+	0.0227860i
$855$	2.75942	+	8.49263i	0.0943703	+	0.290442i
$856$	−13.1323	−	5.84688i	−0.448853	−	0.199842i
$857$	14.6857	−	25.4364i	0.501654	−	0.868890i	−0.498345	−	0.866979i	$-0.666059\pi$
$857$	14.6857	−	25.4364i	0.501654	−	0.868890i	0.999998	−	0.00191053i	$-0.000608142\pi$
$858$	−10.3115	−	15.7931i	−0.352029	−	0.539168i
$859$	6.51394	+	11.2825i	0.222253	+	0.384953i	0.955492	−	0.295018i	$-0.0953257\pi$
$859$	6.51394	+	11.2825i	0.222253	+	0.384953i	−0.733239	+	0.679971i	$0.761992\pi$
$860$	−2.36117	+	1.71549i	−0.0805153	+	0.0584978i
$861$	14.0214	−	23.1729i	0.477849	−	0.789732i
$862$	0.673400	−	2.07251i	0.0229361	−	0.0705901i
$863$	0.961305	−	9.14621i	0.0327232	−	0.311340i	−0.965901	−	0.258910i	$-0.916637\pi$
$863$	0.961305	−	9.14621i	0.0327232	−	0.311340i	0.998625	−	0.0524302i	$-0.0166967\pi$
$864$	−0.913545	+	0.406737i	−0.0310794	+	0.0138375i
$865$	−7.46352	−	8.28908i	−0.253767	−	0.281837i
$866$	−3.43342	+	3.81320i	−0.116672	+	0.129578i
$867$	−2.49847	+	1.81525i	−0.0848526	+	0.0616490i
$868$	19.0652	−	3.64475i	0.647116	−	0.123711i
$869$	3.96377	+	24.6338i	0.134462	+	0.835645i
$870$	0.939405	+	1.62710i	0.0318488	+	0.0551638i
$871$	4.43026	+	42.1511i	0.150114	+	1.42824i
$872$	1.52730	+	0.324639i	0.0517211	+	0.0109937i
$873$	15.8834	−	3.37611i	0.537570	−	0.114264i
$874$	−15.7597	−	11.4501i	−0.533080	−	0.387305i
$875$	20.4842	−	14.2490i	0.692492	−	0.481703i
$876$	1.12698	−	3.46848i	0.0380771	−	0.117189i
$877$	−11.1571	+	12.3913i	−0.376750	+	0.418423i	−0.901463	−	0.432856i	$-0.857506\pi$
$877$	−11.1571	+	12.3913i	−0.376750	+	0.418423i	0.524713	+	0.851279i	$0.324173\pi$
$878$	−3.80501	−	36.2023i	−0.128413	−	1.22177i
$879$	−6.74595	+	11.6843i	−0.227535	+	0.394103i
$880$	−1.27198	−	3.28940i	−0.0428783	−	0.110886i
$881$	13.2306			0.445750			0.222875	−	0.974847i	$-0.428456\pi$
$881$	13.2306			0.445750			0.222875	+	0.974847i	$0.428456\pi$
$882$	−3.74608	+	5.91328i	−0.126137	+	0.199110i
$883$	−17.6315	−	54.2641i	−0.593346	−	1.82613i	−0.562791	−	0.826599i	$-0.690272\pi$
$883$	−17.6315	−	54.2641i	−0.593346	−	1.82613i	−0.0305556	−	0.999533i	$-0.509728\pi$
$884$	−20.7477	+	4.41007i	−0.697822	+	0.148327i
$885$	−10.4513	+	4.65320i	−0.351315	+	0.156416i
$886$	0.798459	−	0.355497i	0.0268248	−	0.0119432i
$887$	−2.72825	+	0.579907i	−0.0916057	+	0.0194714i	−0.253486	−	0.967339i	$-0.581577\pi$
$887$	−2.72825	+	0.579907i	−0.0916057	+	0.0194714i	0.161881	+	0.986810i	$0.448244\pi$
$888$	−0.839949	−	2.58510i	−0.0281868	−	0.0867502i
$889$	8.90630	+	29.4567i	0.298708	+	0.987947i
$890$	−15.4403			−0.517559
$891$	0.850520	−	3.20572i	0.0284935	−	0.107396i
$892$	3.18960	−	5.52455i	0.106796	−	0.184976i
$893$	1.31517	+	12.5130i	0.0440106	+	0.418733i
$894$	−8.42173	+	9.35328i	−0.281665	+	0.312820i
$895$	4.89832	−	15.0755i	0.163733	−	0.503917i
$896$	−2.39440	−	1.12555i	−0.0799911	−	0.0376021i
$897$	10.6725	+	7.75406i	0.356346	+	0.258900i
$898$	−12.6771	+	2.69461i	−0.423042	+	0.0899203i
$899$	12.6793	+	2.69506i	0.422878	+	0.0898854i
$900$	0.404449	+	3.84807i	0.0134816	+	0.128269i
$901$	−16.0582	−	27.8136i	−0.534976	−	0.926606i
$902$	−30.2139	+	15.4885i	−1.00601	+	0.515712i
$903$	−4.74714	−	5.49519i	−0.157975	−	0.182869i
$904$	8.53893	−	6.20389i	0.284000	−	0.206338i
$905$	−18.1733	+	20.1835i	−0.604100	+	0.670921i
$906$	9.83678	+	10.9249i	0.326805	+	0.362954i
$907$	−5.82967	+	2.59554i	−0.193571	+	0.0861834i	−0.501233	−	0.865312i	$-0.667120\pi$
$907$	−5.82967	+	2.59554i	−0.193571	+	0.0861834i	0.307662	+	0.951496i	$0.400453\pi$
$908$	−2.45934	+	23.3991i	−0.0816162	+	0.776526i
$909$	−1.08829	+	3.34940i	−0.0360962	+	0.111093i
$910$	8.28270	−	13.6886i	0.274569	−	0.453774i
$911$	−39.9060	+	28.9934i	−1.32215	+	0.960595i	−0.322243	+	0.946657i	$0.604437\pi$
$911$	−39.9060	+	28.9934i	−1.32215	+	0.960595i	−0.999903	+	0.0139386i	$0.995563\pi$
$912$	−4.19881	−	7.27255i	−0.139036	−	0.240818i
$913$	1.78025	−	35.6473i	0.0589177	−	1.17975i
$914$	16.8245	−	29.1408i	0.556504	−	0.963893i
$915$	0.630315	+	0.280634i	0.0208376	+	0.00927748i
$916$	4.54113	+	13.9761i	0.150043	+	0.461785i
$917$	−1.57067	+	12.4730i	−0.0518681	+	0.411896i
$918$	−3.01751	−	2.19235i	−0.0995925	−	0.0723582i
$919$	2.97622	−	28.3168i	0.0981763	−	0.934085i	−0.828947	−	0.559328i	$-0.811059\pi$
$919$	2.97622	−	28.3168i	0.0981763	−	0.934085i	0.927123	−	0.374758i	$-0.122274\pi$
$920$	1.65054	+	1.83311i	0.0544166	+	0.0604358i
$921$	−21.8359	−	4.64137i	−0.719518	−	0.152938i
$922$	30.3637	+	13.5188i	0.999975	+	0.445218i
$923$	−66.3788			−2.18489
$924$	7.88932	−	3.84170i	0.259539	−	0.126383i
$925$	−10.5172			−0.345803
$926$	−21.9027	−	9.75173i	−0.719769	−	0.320462i
$927$	−4.24569	−	0.902448i	−0.139447	−	0.0296403i
$928$	−1.18226	−	1.31304i	−0.0388097	−	0.0431025i
$929$	2.82482	−	26.8764i	0.0926793	−	0.881785i	−0.845113	−	0.534588i	$-0.820467\pi$
$929$	2.82482	−	26.8764i	0.0926793	−	0.881785i	0.937792	−	0.347197i	$-0.112866\pi$
$930$	−6.31139	−	4.58549i	−0.206959	−	0.150364i
$931$	−52.6737	−	26.0952i	−1.72631	−	0.855236i
$932$	2.86290	+	8.81110i	0.0937774	+	0.288617i
$933$	7.05258	+	3.14001i	0.230891	+	0.102799i
$934$	12.1158	−	20.9851i	0.396440	−	0.686654i
$935$	8.25307	−	10.2431i	0.269904	−	0.334986i
$936$	2.84345	+	4.92500i	0.0929411	+	0.160979i
$937$	21.1569	−	15.3714i	0.691166	−	0.502162i	−0.185877	−	0.982573i	$-0.559513\pi$
$937$	21.1569	−	15.3714i	0.691166	−	0.502162i	0.877043	+	0.480411i	$0.159513\pi$
$938$	−19.7141	−	0.405104i	−0.643687	−	0.0132271i
$939$	−0.801104	+	2.46554i	−0.0261430	+	0.0804600i
$940$	0.166536	−	1.58448i	0.00543179	−	0.0516801i
$941$	−10.2839	+	4.57868i	−0.335245	+	0.149261i	−0.567454	−	0.823405i	$-0.692071\pi$
$941$	−10.2839	+	4.57868i	−0.335245	+	0.149261i	0.232209	+	0.972666i	$0.425405\pi$
$942$	6.27766	+	6.97205i	0.204537	+	0.227162i
$943$	15.8899	−	17.6475i	0.517447	−	0.574683i
$944$	8.70394	−	6.32378i	0.283289	−	0.205822i
$945$	2.76334	−	0.528275i	0.0898915	−	0.0171848i
$946$	1.44615	+	8.98743i	0.0470183	+	0.292207i
$947$	0.757864	+	1.31266i	0.0246273	+	0.0426557i	0.878076	−	0.478521i	$-0.158827\pi$
$947$	0.757864	+	1.31266i	0.0246273	+	0.0426557i	−0.853449	+	0.521176i	$0.825493\pi$
$948$	−0.786358	−	7.48170i	−0.0255397	−	0.242994i
$949$	−20.2868	−	4.31209i	−0.658537	−	0.139976i
$950$	−31.7826	+	6.75559i	−1.03116	+	0.219180i
$951$	−11.2125	−	8.14637i	−0.363591	−	0.264164i
$952$	−0.829665	−	9.83329i	−0.0268896	−	0.318699i
$953$	−17.0365	+	52.4330i	−0.551867	+	1.69847i	0.152209	+	0.988348i	$0.451361\pi$
$953$	−17.0365	+	52.4330i	−0.551867	+	1.69847i	−0.704076	+	0.710125i	$0.748639\pi$
$954$	−5.76166	+	6.39897i	−0.186541	+	0.207174i
$955$	0.332011	+	3.15887i	0.0107436	+	0.102219i
$956$	−12.2361	+	21.1935i	−0.395743	+	0.685448i
$957$	5.85122	−	0.321088i	0.189143	−	0.0103793i
$958$	−21.6196			−0.698497
$959$	26.7631	+	6.26598i	0.864224	+	0.202339i
$960$	0.328596	+	1.01131i	0.0106054	+	0.0326400i
$961$	−22.3251	+	4.74534i	−0.720164	+	0.153075i
$962$	−14.1214	+	6.28723i	−0.455291	+	0.202709i
$963$	−13.1323	+	5.84688i	−0.423183	+	0.188413i
$964$	2.12317	−	0.451295i	0.0683828	−	0.0145352i
$965$	−4.51616	−	13.8993i	−0.145380	−	0.447435i
$966$	−4.19955	+	4.47563i	−0.135118	+	0.144001i
$967$	−8.45189			−0.271795			−0.135897	−	0.990723i	$-0.543392\pi$
$967$	−8.45189			−0.271795			−0.135897	+	0.990723i	$0.543392\pi$
$968$	−10.9453	−	1.09596i	−0.351794	−	0.0352256i
$969$	15.6609	−	27.1254i	0.503100	−	0.871395i
$970$	−1.80490	−	17.1725i	−0.0579518	−	0.551375i
$971$	−8.41706	+	9.34809i	−0.270116	+	0.299995i	−0.862908	−	0.505361i	$-0.831359\pi$
$971$	−8.41706	+	9.34809i	−0.270116	+	0.299995i	0.592791	+	0.805356i	$0.298026\pi$
$972$	−0.309017	+	0.951057i	−0.00991172	+	0.0305052i
$973$	−40.1248	+	27.9112i	−1.28634	+	0.894791i
$974$	26.0601	+	18.9338i	0.835020	+	0.606677i
$975$	21.5233	−	4.57492i	0.689297	−	0.146515i
$976$	−0.634675	−	0.134904i	−0.0203155	−	0.00431819i
$977$	1.69582	+	16.1346i	0.0542540	+	0.516192i	0.987575	+	0.157149i	$0.0502303\pi$
$977$	1.69582	+	16.1346i	0.0542540	+	0.516192i	−0.933321	+	0.359043i	$0.883103\pi$
$978$	8.61453	+	14.9208i	0.275462	+	0.477115i
$979$	−21.7578	+	42.9630i	−0.695381	+	1.37310i
$980$	5.83711	+	4.61888i	0.186460	+	0.147545i
$981$	1.26322	−	0.917783i	0.0403315	−	0.0293026i
$982$	6.28370	−	6.97875i	0.200521	−	0.222701i
$983$	15.6868	+	17.4219i	0.500331	+	0.555674i	0.939419	−	0.342770i	$-0.111365\pi$
$983$	15.6868	+	17.4219i	0.500331	+	0.555674i	−0.439089	+	0.898444i	$0.644699\pi$
$984$	9.35204	−	4.16380i	0.298132	−	0.132737i
$985$	−1.92995	+	18.3622i	−0.0614933	+	0.585069i
$986$	2.03646	−	6.26758i	0.0648541	−	0.199600i
$987$	3.96324	+	0.0814404i	0.126151	+	0.00259228i
$988$	−38.6357	+	28.0705i	−1.22917	+	0.893042i
$989$	−3.18342	−	5.51385i	−0.101227	−	0.175330i
$990$	−3.29562	−	1.25577i	−0.104742	−	0.0399111i
$991$	−8.16524	+	14.1426i	−0.259378	+	0.449255i	−0.966075	−	0.258260i	$-0.916851\pi$
$991$	−8.16524	+	14.1426i	−0.259378	+	0.449255i	0.706698	+	0.707516i	$0.250184\pi$
$992$	6.70220	+	2.98401i	0.212795	+	0.0947425i
$993$	−4.20754	−	12.9495i	−0.133522	−	0.410939i
$994$	3.85833	−	30.6398i	0.122379	−	0.971837i
$995$	8.28877	+	6.02214i	0.262772	+	0.190915i
$996$	−1.12488	+	10.7025i	−0.0356431	+	0.339121i
$997$	−38.2543	−	42.4857i	−1.21153	−	1.34554i	−0.921432	−	0.388539i	$-0.872980\pi$
$997$	−38.2543	−	42.4857i	−1.21153	−	1.34554i	−0.290095	−	0.956998i	$-0.593687\pi$
$998$	14.1765	+	3.01330i	0.448748	+	0.0953843i
$999$	−2.48314	−	1.10556i	−0.0785630	−	0.0349785i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.d.25.4	✓	40
7.2	even	3	inner	462.2.y.d.289.2	yes	40
11.4	even	5	inner	462.2.y.d.235.2	yes	40
77.37	even	15	inner	462.2.y.d.37.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.d.25.4	✓	40	1.1	even	1	trivial
462.2.y.d.37.4	yes	40	77.37	even	15	inner
462.2.y.d.235.2	yes	40	11.4	even	5	inner
462.2.y.d.289.2	yes	40	7.2	even	3	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.913545 + 0.406737i) q^{2} +(0.978148 + 0.207912i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.111151 - 1.05753i) q^{5} +(0.809017 + 0.587785i) q^{6} +(2.10806 + 1.59878i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\)	\(q+(0.913545 + 0.406737i) q^{2} +(0.978148 + 0.207912i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.111151 - 1.05753i) q^{5} +(0.809017 + 0.587785i) q^{6} +(2.10806 + 1.59878i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.913545 + 0.406737i) q^{9} +(0.531680 - 0.920896i) q^{10} +(-1.81320 - 2.77710i) q^{11} +(0.500000 + 0.866025i) q^{12} +(4.60080 - 3.34268i) q^{13} +(1.27552 + 2.31798i) q^{14} +(0.328596 - 1.01131i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(-3.40738 + 1.51706i) q^{17} +(0.669131 + 0.743145i) q^{18} +(-5.61910 + 6.24064i) q^{19} +(0.860276 - 0.625027i) q^{20} +(1.72959 + 2.00213i) q^{21} +(-0.526893 - 3.27451i) q^{22} +(1.15986 + 2.00893i) q^{23} +(0.104528 + 0.994522i) q^{24} +(3.78471 + 0.804466i) q^{25} +(5.56263 - 1.18237i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.222440 + 2.63638i) q^{28} +(-0.545991 + 1.68039i) q^{29} +(0.711526 - 0.790230i) q^{30} +(-0.766870 - 7.29628i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.19619 - 3.09340i) q^{33} -3.72984 q^{34} +(1.92508 - 2.05164i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-2.65873 + 0.565131i) q^{37} +(-7.67160 + 3.41562i) q^{38} +(5.19524 - 2.31307i) q^{39} +(1.04012 - 0.221085i) q^{40} +(-3.16343 - 9.73605i) q^{41} +(0.765714 + 2.53252i) q^{42} -2.74467 q^{43} +(0.850520 - 3.20572i) q^{44} +(0.531680 - 0.920896i) q^{45} +(0.242476 + 2.30701i) q^{46} +(1.00254 - 1.11344i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(1.88780 + 6.74064i) q^{49} +(3.13030 + 2.27430i) q^{50} +(-3.64834 + 0.775478i) q^{51} +(5.56263 + 1.18237i) q^{52} +(0.900059 + 8.56349i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-3.13842 + 1.60884i) q^{55} +(-0.869105 + 2.49893i) q^{56} +(-6.79381 + 4.93599i) q^{57} +(-1.18226 + 1.31304i) q^{58} +(-7.19895 - 7.99524i) q^{59} +(0.971427 - 0.432507i) q^{60} +(-0.0678238 + 0.645300i) q^{61} +(2.26709 - 6.97740i) q^{62} +(1.27552 + 2.31798i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-3.02361 - 5.23705i) q^{65} +(0.165429 - 3.31250i) q^{66} +(-3.72640 + 6.45431i) q^{67} +(-3.40738 - 1.51706i) q^{68} +(0.716831 + 2.20618i) q^{69} +(2.59312 - 1.09126i) q^{70} +(-9.44303 - 6.86076i) q^{71} +(-0.104528 + 0.994522i) q^{72} +(-2.44030 - 2.71023i) q^{73} +(-2.65873 - 0.565131i) q^{74} +(3.53475 + 1.57377i) q^{75} -8.39761 q^{76} +(0.617644 - 8.75320i) q^{77} +5.68690 q^{78} +(-6.87252 - 3.05984i) q^{79} +(1.04012 + 0.221085i) q^{80} +(0.669131 + 0.743145i) q^{81} +(1.07007 - 10.1810i) q^{82} +(8.70619 + 6.32542i) q^{83} +(-0.330556 + 2.62502i) q^{84} +(1.22561 + 3.77204i) q^{85} +(-2.50738 - 1.11636i) q^{86} +(-0.883432 + 1.53015i) q^{87} +(2.08087 - 2.58263i) q^{88} +(-7.26014 - 12.5749i) q^{89} +(0.860276 - 0.625027i) q^{90} +(15.0430 + 0.309117i) q^{91} +(-0.716831 + 2.20618i) q^{92} +(0.766870 - 7.29628i) q^{93} +(1.36875 - 0.609405i) q^{94} +(5.97512 + 6.63605i) q^{95} +(-0.669131 + 0.743145i) q^{96} +(13.1370 - 9.54458i) q^{97} +(-1.01707 + 6.92572i) q^{98} +(-0.526893 - 3.27451i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9}+O(q^{10}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 20 q^{12} + 10 q^{13} + 5 q^{14} - 6 q^{15} + 5 q^{16} + 5 q^{18} - 13 q^{19} + 6 q^{20} - 2 q^{21} - 4 q^{22} - 20 q^{23} - 5 q^{24} + 12 q^{25} + 10 q^{27} - 3 q^{28} + 12 q^{29} + 3 q^{30} - 10 q^{31} - 20 q^{32} + 8 q^{33} - 13 q^{35} - 10 q^{36} + 3 q^{37} + 2 q^{38} + 5 q^{39} - 3 q^{40} - 44 q^{41} - 3 q^{42} + 36 q^{43} - 3 q^{44} + 12 q^{45} + 11 q^{47} + 10 q^{48} + 33 q^{49} - 4 q^{50} + 26 q^{53} + 20 q^{54} - 20 q^{55} + 8 q^{56} + 4 q^{57} - 6 q^{58} + 4 q^{59} + 3 q^{60} - 23 q^{61} + 5 q^{63} - 10 q^{64} - 50 q^{65} - 7 q^{66} - 108 q^{67} + 20 q^{69} - 86 q^{71} + 5 q^{72} - 35 q^{73} + 3 q^{74} - 2 q^{75} - 44 q^{76} - 37 q^{77} + 20 q^{78} + 3 q^{79} - 3 q^{80} + 5 q^{81} - 28 q^{82} - 88 q^{83} - 5 q^{84} + 96 q^{85} - 13 q^{86} + 6 q^{87} - 8 q^{88} + 6 q^{89} + 6 q^{90} + 40 q^{91} - 20 q^{92} + 10 q^{93} - 24 q^{94} + 36 q^{95} - 5 q^{96} + 60 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 20 * q^12 + 10 * q^13 + 5 * q^14 - 6 * q^15 + 5 * q^16 + 5 * q^18 - 13 * q^19 + 6 * q^20 - 2 * q^21 - 4 * q^22 - 20 * q^23 - 5 * q^24 + 12 * q^25 + 10 * q^27 - 3 * q^28 + 12 * q^29 + 3 * q^30 - 10 * q^31 - 20 * q^32 + 8 * q^33 - 13 * q^35 - 10 * q^36 + 3 * q^37 + 2 * q^38 + 5 * q^39 - 3 * q^40 - 44 * q^41 - 3 * q^42 + 36 * q^43 - 3 * q^44 + 12 * q^45 + 11 * q^47 + 10 * q^48 + 33 * q^49 - 4 * q^50 + 26 * q^53 + 20 * q^54 - 20 * q^55 + 8 * q^56 + 4 * q^57 - 6 * q^58 + 4 * q^59 + 3 * q^60 - 23 * q^61 + 5 * q^63 - 10 * q^64 - 50 * q^65 - 7 * q^66 - 108 * q^67 + 20 * q^69 - 86 * q^71 + 5 * q^72 - 35 * q^73 + 3 * q^74 - 2 * q^75 - 44 * q^76 - 37 * q^77 + 20 * q^78 + 3 * q^79 - 3 * q^80 + 5 * q^81 - 28 * q^82 - 88 * q^83 - 5 * q^84 + 96 * q^85 - 13 * q^86 + 6 * q^87 - 8 * q^88 + 6 * q^89 + 6 * q^90 + 40 * q^91 - 20 * q^92 + 10 * q^93 - 24 * q^94 + 36 * q^95 - 5 * q^96 + 60 * q^97 + 2 * q^98 - 4 * q^99

Introduction

L-functions

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