LMFDB - Embedded newform 483.2.bb.a.26.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(26,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 55, 48]))

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

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

chi := DirichletCharacter("483.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.bb (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$1200$
Relative dimension:	$60$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			26.19
Character	$\chi$	$=$	483.26
Dual form			483.2.bb.a.353.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.397865 + 0.993819i) q^{2} +(-1.24011 - 1.20919i) q^{3} +(0.618088 + 0.589346i) q^{4} +(1.43145 + 4.13589i) q^{5} +(1.69511 - 0.751347i) q^{6} +(2.25080 + 1.39065i) q^{7} +(-2.77914 + 1.26919i) q^{8} +(0.0757244 + 2.99904i) q^{9} +O(q^{10})$	\(q+(-0.397865 + 0.993819i) q^{2} +(-1.24011 - 1.20919i) q^{3} +(0.618088 + 0.589346i) q^{4} +(1.43145 + 4.13589i) q^{5} +(1.69511 - 0.751347i) q^{6} +(2.25080 + 1.39065i) q^{7} +(-2.77914 + 1.26919i) q^{8} +(0.0757244 + 2.99904i) q^{9} +(-4.67985 - 0.222929i) q^{10} +(-0.917592 - 2.29203i) q^{11} +(-0.0538642 - 1.47824i) q^{12} +(-0.665313 + 1.03525i) q^{13} +(-2.27757 + 1.68359i) q^{14} +(3.22593 - 6.85984i) q^{15} +(-0.0743508 - 1.56082i) q^{16} +(-0.788328 - 3.24953i) q^{17} +(-3.01064 - 1.11796i) q^{18} +(0.490460 + 0.118984i) q^{19} +(-1.55271 + 3.39996i) q^{20} +(-1.10966 - 4.44619i) q^{21} +2.64295 q^{22} +(4.77187 - 0.478842i) q^{23} +(4.98113 + 1.78658i) q^{24} +(-11.1263 + 8.74983i) q^{25} +(-0.764144 - 1.07309i) q^{26} +(3.53250 - 3.81070i) q^{27} +(0.571614 + 2.18604i) q^{28} +(0.514705 - 1.75292i) q^{29} +(5.53395 + 5.93528i) q^{30} +(-3.19645 - 2.27619i) q^{31} +(-4.19366 - 1.45144i) q^{32} +(-1.63359 + 3.95191i) q^{33} +(3.54309 + 0.509420i) q^{34} +(-2.52970 + 11.2997i) q^{35} +(-1.72067 + 1.89830i) q^{36} +(5.78778 - 1.11550i) q^{37} +(-0.313386 + 0.440089i) q^{38} +(2.07687 - 0.479327i) q^{39} +(-9.22744 - 9.67746i) q^{40} +(-7.44760 + 8.59499i) q^{41} +(4.86021 + 0.666183i) q^{42} +(-2.14338 + 4.69335i) q^{43} +(0.783648 - 1.95746i) q^{44} +(-12.2953 + 4.60616i) q^{45} +(-1.42268 + 4.93289i) q^{46} +(-0.499932 + 0.865907i) q^{47} +(-1.79512 + 2.02548i) q^{48} +(3.13217 + 6.26015i) q^{49} +(-4.26898 - 14.5388i) q^{50} +(-2.95169 + 4.98300i) q^{51} +(-1.02134 + 0.247775i) q^{52} +(5.06572 - 9.82613i) q^{53} +(2.38168 + 5.02682i) q^{54} +(8.16613 - 7.07599i) q^{55} +(-8.02029 - 1.00813i) q^{56} +(-0.464347 - 0.740611i) q^{57} +(1.53731 + 1.20895i) q^{58} +(-0.311971 + 6.54907i) q^{59} +(6.03672 - 2.33879i) q^{60} +(-1.03816 + 10.8721i) q^{61} +(3.53388 - 2.27108i) q^{62} +(-4.00019 + 6.85554i) q^{63} +(5.15753 - 5.95211i) q^{64} +(-5.23404 - 1.26976i) q^{65} +(-3.27753 - 3.19582i) q^{66} +(7.04287 - 5.53858i) q^{67} +(1.42784 - 2.47309i) q^{68} +(-6.49663 - 5.17627i) q^{69} +(-10.2234 - 7.00982i) q^{70} +(14.2424 - 2.04775i) q^{71} +(-4.01681 - 8.23867i) q^{72} +(5.75962 - 6.04051i) q^{73} +(-1.19415 + 6.19583i) q^{74} +(24.3780 + 2.60310i) q^{75} +(0.233024 + 0.362593i) q^{76} +(1.12211 - 6.43495i) q^{77} +(-0.349949 + 2.25474i) q^{78} +(6.14242 - 3.16664i) q^{79} +(6.34894 - 2.54173i) q^{80} +(-8.98853 + 0.454202i) q^{81} +(-5.57873 - 10.8212i) q^{82} +(-1.44316 - 1.66549i) q^{83} +(1.93448 - 3.40211i) q^{84} +(12.3113 - 7.91197i) q^{85} +(-3.81157 - 3.99746i) q^{86} +(-2.75791 + 1.55144i) q^{87} +(5.45915 + 5.20529i) q^{88} +(-3.32381 - 4.66764i) q^{89} +(0.314195 - 14.0520i) q^{90} +(-2.93716 + 1.40491i) q^{91} +(3.23164 + 2.51631i) q^{92} +(1.21160 + 6.68783i) q^{93} +(-0.661650 - 0.841356i) q^{94} +(0.209961 + 2.19881i) q^{95} +(3.44551 + 6.87086i) q^{96} +(-9.31283 - 8.06961i) q^{97} +(-7.46764 + 0.622108i) q^{98} +(6.80443 - 2.92546i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1200 q - 27 q^{3} - 74 q^{4} - 36 q^{7} - 13 q^{9}+O(q^{10}) $ 1200 * q - 27 * q^3 - 74 * q^4 - 36 * q^7 - 13 * q^9	$ 1200 q - 27 q^{3} - 74 q^{4} - 36 q^{7} - 13 q^{9} - 54 q^{10} - 15 q^{12} - 64 q^{15} + 38 q^{16} + 43 q^{18} - 54 q^{19} - 70 q^{21} - 160 q^{22} - 66 q^{24} + 34 q^{25} - 76 q^{28} - 23 q^{30} - 54 q^{31} - 3 q^{33} - 28 q^{36} + 26 q^{37} + 5 q^{39} - 30 q^{40} - 68 q^{42} - 176 q^{43} - 96 q^{45} - 22 q^{46} - 128 q^{49} - 23 q^{51} - 102 q^{52} + 21 q^{54} - 36 q^{57} + 58 q^{58} - 43 q^{60} - 126 q^{61} + 41 q^{63} + 40 q^{64} - 132 q^{66} - 10 q^{67} + 20 q^{70} + 59 q^{72} - 30 q^{73} - 81 q^{75} + 164 q^{78} - 14 q^{79} - 97 q^{81} - 66 q^{82} + 24 q^{84} - 56 q^{85} - 399 q^{87} - 74 q^{88} - 156 q^{91} + 8 q^{93} - 126 q^{94} - 117 q^{96} + 196 q^{99}+O(q^{100}) $ 1200 * q - 27 * q^3 - 74 * q^4 - 36 * q^7 - 13 * q^9 - 54 * q^10 - 15 * q^12 - 64 * q^15 + 38 * q^16 + 43 * q^18 - 54 * q^19 - 70 * q^21 - 160 * q^22 - 66 * q^24 + 34 * q^25 - 76 * q^28 - 23 * q^30 - 54 * q^31 - 3 * q^33 - 28 * q^36 + 26 * q^37 + 5 * q^39 - 30 * q^40 - 68 * q^42 - 176 * q^43 - 96 * q^45 - 22 * q^46 - 128 * q^49 - 23 * q^51 - 102 * q^52 + 21 * q^54 - 36 * q^57 + 58 * q^58 - 43 * q^60 - 126 * q^61 + 41 * q^63 + 40 * q^64 - 132 * q^66 - 10 * q^67 + 20 * q^70 + 59 * q^72 - 30 * q^73 - 81 * q^75 + 164 * q^78 - 14 * q^79 - 97 * q^81 - 66 * q^82 + 24 * q^84 - 56 * q^85 - 399 * q^87 - 74 * q^88 - 156 * q^91 + 8 * q^93 - 126 * q^94 - 117 * q^96 + 196 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{11}\right)$

Coefficient data

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

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

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

$2$	−0.397865	+	0.993819i	−0.281333	+	0.702736i	0.718640	+	0.695383i	$0.244765\pi$
$2$	−0.397865	+	0.993819i	−0.281333	+	0.702736i	−0.999973	+	0.00735382i	$0.997659\pi$
$3$	−1.24011	−	1.20919i	−0.715975	−	0.698126i
$3$	−1.24011	−	1.20919i	−0.715975	−	0.698126i
$4$	0.618088	+	0.589346i	0.309044	+	0.294673i
$5$	1.43145	+	4.13589i	0.640162	+	1.84963i	0.514363	+	0.857572i	$0.328028\pi$
$5$	1.43145	+	4.13589i	0.640162	+	1.84963i	0.125799	+	0.992056i	$0.459851\pi$
$6$	1.69511	−	0.751347i	0.692026	−	0.306736i
$7$	2.25080	+	1.39065i	0.850721	+	0.525618i
$7$	2.25080	+	1.39065i	0.850721	+	0.525618i
$8$	−2.77914	+	1.26919i	−0.982576	+	0.448727i
$9$	0.0757244	+	2.99904i	0.0252415	+	0.999681i
$10$	−4.67985	−	0.222929i	−1.47990	−	0.0704963i
$11$	−0.917592	−	2.29203i	−0.276664	−	0.691074i	−1.00000		0.000577498i	$-0.999816\pi$
$11$	−0.917592	−	2.29203i	−0.276664	−	0.691074i	0.723335	−	0.690497i	$-0.242608\pi$
$12$	−0.0538642	−	1.47824i	−0.0155492	−	0.426730i
$13$	−0.665313	+	1.03525i	−0.184525	+	0.287126i	−0.921176	−	0.389147i	$-0.872770\pi$
$13$	−0.665313	+	1.03525i	−0.184525	+	0.287126i	0.736651	+	0.676273i	$0.236406\pi$
$14$	−2.27757	+	1.68359i	−0.608707	+	0.449959i
$15$	3.22593	−	6.85984i	0.832932	−	1.77120i
$16$	−0.0743508	−	1.56082i	−0.0185877	−	0.390204i
$17$	−0.788328	−	3.24953i	−0.191198	−	0.788127i	−0.983930	−	0.178557i	$-0.942857\pi$
$17$	−0.788328	−	3.24953i	−0.191198	−	0.788127i	0.792732	−	0.609570i	$-0.208658\pi$
$18$	−3.01064	−	1.11796i	−0.709614	−	0.263505i
$19$	0.490460	+	0.118984i	0.112519	+	0.0272969i	0.291623	−	0.956533i	$-0.405805\pi$
$19$	0.490460	+	0.118984i	0.112519	+	0.0272969i	−0.179104	+	0.983830i	$0.557320\pi$
$20$	−1.55271	+	3.39996i	−0.347197	+	0.760255i
$21$	−1.10966	−	4.44619i	−0.242148	−	0.970239i
$22$	2.64295			0.563478
$23$	4.77187	−	0.478842i	0.995003	−	0.0998454i
$23$	4.77187	−	0.478842i	0.995003	−	0.0998454i
$24$	4.98113	+	1.78658i	1.01677	+	0.364684i
$25$	−11.1263	+	8.74983i	−2.22526	+	1.74997i
$26$	−0.764144	−	1.07309i	−0.149861	−	0.210450i
$27$	3.53250	−	3.81070i	0.679831	−	0.733369i
$28$	0.571614	+	2.18604i	0.108025	+	0.413123i
$29$	0.514705	−	1.75292i	0.0955783	−	0.325510i	−0.897799	−	0.440405i	$-0.854835\pi$
$29$	0.514705	−	1.75292i	0.0955783	−	0.325510i	0.993378	+	0.114895i	$0.0366531\pi$
$30$	5.53395	+	5.93528i	1.01036	+	1.08363i
$31$	−3.19645	−	2.27619i	−0.574100	−	0.408815i	0.255798	−	0.966730i	$-0.417662\pi$
$31$	−3.19645	−	2.27619i	−0.574100	−	0.408815i	−0.829898	+	0.557915i	$0.811601\pi$
$32$	−4.19366	−	1.45144i	−0.741341	−	0.256581i
$33$	−1.63359	+	3.95191i	−0.284372	+	0.687939i
$34$	3.54309	+	0.509420i	0.607636	+	0.0873648i
$35$	−2.52970	+	11.2997i	−0.427597	+	1.91000i
$36$	−1.72067	+	1.89830i	−0.286778	+	0.316383i
$37$	5.78778	−	1.11550i	0.951505	−	0.183388i	0.310198	−	0.950672i	$-0.399605\pi$
$37$	5.78778	−	1.11550i	0.951505	−	0.183388i	0.641307	+	0.767284i	$0.278393\pi$
$38$	−0.313386	+	0.440089i	−0.0508379	+	0.0713918i
$39$	2.07687	−	0.479327i	0.332565	−	0.0767538i
$40$	−9.22744	−	9.67746i	−1.45899	−	1.53014i
$41$	−7.44760	+	8.59499i	−1.16312	+	1.34231i	−0.234131	+	0.972205i	$0.575224\pi$
$41$	−7.44760	+	8.59499i	−1.16312	+	1.34231i	−0.928989	+	0.370107i	$0.879321\pi$
$42$	4.86021	+	0.666183i	0.749947	+	0.102794i
$43$	−2.14338	+	4.69335i	−0.326863	+	0.715729i	−0.999711	−	0.0240513i	$-0.992343\pi$
$43$	−2.14338	+	4.69335i	−0.326863	+	0.715729i	0.672848	+	0.739781i	$0.265071\pi$
$44$	0.783648	−	1.95746i	0.118139	−	0.295098i
$45$	−12.2953	+	4.60616i	−1.83288	+	0.686646i
$46$	−1.42268	+	4.93289i	−0.209762	+	0.727315i
$47$	−0.499932	+	0.865907i	−0.0729226	+	0.126306i	−0.900181	−	0.435516i	$-0.856566\pi$
$47$	−0.499932	+	0.865907i	−0.0729226	+	0.126306i	0.827258	+	0.561822i	$0.189899\pi$
$48$	−1.79512	+	2.02548i	−0.259103	+	0.292353i
$49$	3.13217	+	6.26015i	0.447452	+	0.894308i
$50$	−4.26898	−	14.5388i	−0.603724	−	2.05610i
$51$	−2.95169	+	4.98300i	−0.413319	+	0.697759i
$52$	−1.02134	+	0.247775i	−0.141634	+	0.0343602i
$53$	5.06572	−	9.82613i	0.695830	−	1.34972i	−0.230523	−	0.973067i	$-0.574044\pi$
$53$	5.06572	−	9.82613i	0.695830	−	1.34972i	0.926353	−	0.376655i	$-0.122926\pi$
$54$	2.38168	+	5.02682i	0.324106	+	0.684063i
$55$	8.16613	−	7.07599i	1.10112	−	0.954126i
$56$	−8.02029	−	1.00813i	−1.07176	−	0.134717i
$57$	−0.464347	−	0.740611i	−0.0615043	−	0.0980964i
$58$	1.53731	+	1.20895i	0.201858	+	0.158743i
$59$	−0.311971	+	6.54907i	−0.0406151	+	0.852616i	0.883018	+	0.469339i	$0.155508\pi$
$59$	−0.311971	+	6.54907i	−0.0406151	+	0.852616i	−0.923633	+	0.383277i	$0.874795\pi$
$60$	6.03672	−	2.33879i	0.779338	−	0.301937i
$61$	−1.03816	+	10.8721i	−0.132923	+	1.39204i	0.645243	+	0.763977i	$0.276756\pi$
$61$	−1.03816	+	10.8721i	−0.132923	+	1.39204i	−0.778166	+	0.628058i	$0.783850\pi$
$62$	3.53388	−	2.27108i	0.448803	−	0.288428i
$63$	−4.00019	+	6.85554i	−0.503977	+	0.863717i
$64$	5.15753	−	5.95211i	0.644691	−	0.744014i
$65$	−5.23404	−	1.26976i	−0.649202	−	0.157495i
$66$	−3.27753	−	3.19582i	−0.403436	−	0.393378i
$67$	7.04287	−	5.53858i	0.860424	−	0.676645i	−0.0871454	−	0.996196i	$-0.527774\pi$
$67$	7.04287	−	5.53858i	0.860424	−	0.676645i	0.947569	+	0.319551i	$0.103532\pi$
$68$	1.42784	−	2.47309i	0.173151	−	0.299907i
$69$	−6.49663	−	5.17627i	−0.782102	−	0.623150i
$70$	−10.2234	−	7.00982i	−1.22193	−	0.837834i
$71$	14.2424	−	2.04775i	1.69027	−	0.243024i	0.771050	−	0.636775i	$-0.219732\pi$
$71$	14.2424	−	2.04775i	1.69027	−	0.243024i	0.919217	+	0.393751i	$0.128823\pi$
$72$	−4.01681	−	8.23867i	−0.473386	−	0.970936i
$73$	5.75962	−	6.04051i	0.674112	−	0.706989i	−0.294476	−	0.955659i	$-0.595145\pi$
$73$	5.75962	−	6.04051i	0.674112	−	0.706989i	0.968588	+	0.248670i	$0.0799936\pi$
$74$	−1.19415	+	6.19583i	−0.138817	+	0.720250i
$75$	24.3780	+	2.60310i	2.81493	+	0.300580i
$76$	0.233024	+	0.362593i	0.0267297	+	0.0415923i
$77$	1.12211	−	6.43495i	0.127877	−	0.733331i
$78$	−0.349949	+	2.25474i	−0.0396240	+	0.255299i
$79$	6.14242	−	3.16664i	0.691076	−	0.356275i	−0.0766450	−	0.997058i	$-0.524421\pi$
$79$	6.14242	−	3.16664i	0.691076	−	0.356275i	0.767721	+	0.640784i	$0.221390\pi$
$80$	6.34894	−	2.54173i	0.709833	−	0.284174i
$81$	−8.98853	+	0.454202i	−0.998726	+	0.0504668i
$82$	−5.57873	−	10.8212i	−0.616067	−	1.19500i
$83$	−1.44316	−	1.66549i	−0.158407	−	0.182812i	0.670998	−	0.741459i	$-0.265866\pi$
$83$	−1.44316	−	1.66549i	−0.158407	−	0.182812i	−0.829405	+	0.558647i	$0.811320\pi$
$84$	1.93448	−	3.40211i	0.211069	−	0.371201i
$85$	12.3113	−	7.91197i	1.33534	−	0.858174i
$86$	−3.81157	−	3.99746i	−0.411012	−	0.431057i
$87$	−2.75791	+	1.55144i	−0.295679	+	0.166331i
$88$	5.45915	+	5.20529i	0.581948	+	0.554886i
$89$	−3.32381	−	4.66764i	−0.352323	−	0.494769i	0.599941	−	0.800044i	$-0.295191\pi$
$89$	−3.32381	−	4.66764i	−0.352323	−	0.494769i	−0.952264	+	0.305276i	$0.901251\pi$
$90$	0.314195	−	14.0520i	0.0331190	−	1.48121i
$91$	−2.93716	+	1.40491i	−0.307898	+	0.147275i
$92$	3.23164	+	2.51631i	0.336921	+	0.262344i
$93$	1.21160	+	6.68783i	0.125637	+	0.693495i
$94$	−0.661650	−	0.841356i	−0.0682440	−	0.0867793i
$95$	0.209961	+	2.19881i	0.0215415	+	0.225593i
$96$	3.44551	+	6.87086i	0.351656	+	0.701254i
$97$	−9.31283	−	8.06961i	−0.945575	−	0.819345i	0.0381051	−	0.999274i	$-0.487868\pi$
$97$	−9.31283	−	8.06961i	−0.945575	−	0.819345i	−0.983680	+	0.179929i	$0.942413\pi$
$98$	−7.46764	+	0.622108i	−0.754346	+	0.0628424i
$99$	6.80443	−	2.92546i	0.683871	−	0.294020i
$100$	−12.0337	−	1.14908i	−1.20337	−	0.114908i
$101$	−0.527820	+	1.52504i	−0.0525201	+	0.151747i	−0.968210	−	0.250139i	$-0.919524\pi$
$101$	−0.527820	+	1.52504i	−0.0525201	+	0.151747i	0.915690	+	0.401885i	$0.131645\pi$
$102$	−3.77783	−	4.91601i	−0.374061	−	0.486757i
$103$	0.514716	−	0.654515i	0.0507165	−	0.0644912i	−0.760033	−	0.649884i	$-0.774817\pi$
$103$	0.514716	−	0.654515i	0.0507165	−	0.0644912i	0.810750	+	0.585393i	$0.199060\pi$
$104$	0.535073	−	3.72151i	0.0524682	−	0.364924i
$105$	16.8006	−	10.9539i	1.63957	−	1.06899i
$106$	7.74992	+	8.94388i	0.752739	+	0.868707i
$107$	−0.502651	+	5.26400i	−0.0485931	+	0.508890i	0.938108	+	0.346344i	$0.112577\pi$
$107$	−0.502651	+	5.26400i	−0.0485931	+	0.508890i	−0.986701	+	0.162547i	$0.948029\pi$
$108$	4.42922	−	0.273479i	0.426202	−	0.0263156i
$109$	3.25725	+	13.4266i	0.311988	+	1.28603i	0.884656	+	0.466244i	$0.154393\pi$
$109$	3.25725	+	13.4266i	0.311988	+	1.28603i	−0.572669	+	0.819787i	$0.694092\pi$
$110$	3.78324	+	10.9309i	0.360717	+	1.04222i
$111$	−8.52631	−	5.61518i	−0.809282	−	0.532969i
$112$	2.00321	−	3.61648i	0.189285	−	0.341725i
$113$	−2.37686	+	0.341742i	−0.223597	+	0.0321483i	−0.253202	−	0.967413i	$-0.581484\pi$
$113$	−2.37686	+	0.341742i	−0.223597	+	0.0321483i	0.0296058	+	0.999562i	$0.490575\pi$
$114$	0.920782	−	0.166814i	0.0862391	−	0.0156236i
$115$	8.81111	+	19.0505i	0.821640	+	1.77647i
$116$	1.35121	−	0.780122i	0.125457	−	0.0724325i
$117$	−3.15513	−	1.91691i	−0.291692	−	0.177218i
$118$	−6.38447	−	2.91569i	−0.587738	−	0.268411i
$119$	2.74461	−	8.41032i	0.251598	−	0.770973i
$120$	−0.258877	+	23.1588i	−0.0236321	+	2.11410i
$121$	3.54963	−	3.38456i	0.322693	−	0.307688i
$122$	−10.3919	−	5.35740i	−0.940838	−	0.485036i
$123$	19.6288	−	1.65314i	1.76987	−	0.149059i
$124$	−0.634230	−	3.29070i	−0.0569556	−	0.295514i
$125$	−33.7059	−	21.6615i	−3.01475	−	1.93746i
$126$	−5.22163	−	6.70305i	−0.465180	−	0.597155i
$127$	1.22317	−	8.50734i	0.108539	−	0.754904i	−0.860759	−	0.509013i	$-0.830010\pi$
$127$	1.22317	−	8.50734i	0.108539	−	0.754904i	0.969298	−	0.245891i	$-0.0790805\pi$
$128$	−0.203652	−	0.395030i	−0.0180005	−	0.0349161i
$129$	8.33317	−	3.22850i	0.733695	−	0.284253i
$130$	3.34436	−	4.69649i	0.293319	−	0.411909i
$131$	−0.0718542	−	1.50840i	−0.00627793	−	0.131790i	−0.999830	−	0.0184167i	$-0.994137\pi$
$131$	−0.0718542	−	1.50840i	−0.00627793	−	0.131790i	0.993552	−	0.113373i	$-0.0361656\pi$
$132$	−3.33874	+	1.47988i	−0.290600	+	0.128807i
$133$	0.938459	+	0.949869i	0.0813747	+	0.0823641i
$134$	2.70223	+	9.20295i	0.233437	+	0.795014i
$135$	20.8172	+	9.15525i	1.79166	+	0.787959i
$136$	6.31516	+	8.03037i	0.541520	+	0.688599i
$137$	5.54370	−	3.20066i	0.473631	−	0.273451i	−0.244128	−	0.969743i	$-0.578502\pi$
$137$	5.54370	−	3.20066i	0.473631	−	0.273451i	0.717758	+	0.696292i	$0.245168\pi$
$138$	7.72906	−	4.39702i	0.657942	−	0.374299i
$139$			15.9683i			1.35442i	0.735791	+	0.677208i	$0.236810\pi$
$139$			15.9683i			1.35442i	−0.735791	+	0.677208i	$0.763190\pi$
$140$	−8.22301	+	5.49334i	−0.694971	+	0.464272i
$141$	1.66701	−	0.469305i	0.140388	−	0.0395226i
$142$	−3.63147	+	14.9691i	−0.304747	+	1.25618i
$143$	2.98331	+	0.574986i	0.249477	+	0.0480827i
$144$	4.67533	−	0.341173i	0.389611	−	0.0284311i
$145$	7.98668	−	0.380453i	0.663258	−	0.0315949i
$146$	3.71163	+	8.12733i	0.307176	+	0.672623i
$147$	3.68549	−	11.5506i	0.303974	−	0.952680i
$148$	4.23477	+	2.72152i	0.348096	+	0.223708i
$149$	−1.48953	+	1.89409i	−0.122027	+	0.155170i	−0.843228	−	0.537556i	$-0.819348\pi$
$149$	−1.48953	+	1.89409i	−0.122027	+	0.155170i	0.721201	+	0.692725i	$0.243590\pi$
$150$	−12.2862	+	23.1916i	−1.00316	+	1.89359i
$151$	0.178096	−	3.73869i	0.0144932	−	0.304251i	−0.979969	−	0.199152i	$-0.936181\pi$
$151$	0.178096	−	3.73869i	0.0144932	−	0.304251i	0.994462	−	0.105098i	$-0.0335158\pi$
$152$	−1.51407	+	0.291813i	−0.122807	+	0.0236692i
$153$	9.68579	−	2.61030i	0.783050	−	0.211030i
$154$	5.94873	+	3.67542i	0.479363	+	0.296174i
$155$	4.83851	−	16.4784i	0.388638	−	1.32358i
$156$	1.56618	+	0.927727i	0.125395	+	0.0742776i
$157$	1.09958	−	1.15321i	0.0877559	−	0.0920358i	−0.678392	−	0.734701i	$-0.737323\pi$
$157$	1.09958	−	1.15321i	0.0877559	−	0.0920358i	0.766148	+	0.642665i	$0.222171\pi$
$158$	0.703210	+	7.36435i	0.0559444	+	0.585876i
$159$	−18.1637	+	6.06002i	−1.44047	+	0.480591i
$160$		−	19.4222i		−	1.53546i
$161$	11.4064	+	5.55824i	0.898950	+	0.438051i
$162$	3.12483	−	9.11369i	0.245510	−	0.716039i
$163$	−4.92358	−	1.97110i	−0.385644	−	0.154389i	0.170735	−	0.985317i	$-0.445386\pi$
$163$	−4.92358	−	1.97110i	−0.385644	−	0.154389i	−0.556380	+	0.830928i	$0.687810\pi$
$164$	−9.66869	+	0.923248i	−0.754998	+	0.0720936i
$165$	−18.6831	−	1.09942i	−1.45447	−	0.0855894i
$166$	2.22938	−	0.771597i	0.173034	−	0.0598876i
$167$	3.14653	+	0.923904i	0.243486	+	0.0714939i	0.401198	−	0.915991i	$-0.368594\pi$
$167$	3.14653	+	0.923904i	0.243486	+	0.0714939i	−0.157713	+	0.987485i	$0.550412\pi$
$168$	8.72699	+	10.9482i	0.673302	+	0.844675i
$169$	4.77130	+	10.4477i	0.367023	+	0.803668i
$170$	2.96484	+	15.3831i	0.227393	+	1.17983i
$171$	−0.319699	+	1.47992i	−0.0244480	+	0.113172i
$172$	−4.09080	+	1.63771i	−0.311921	+	0.124874i
$173$	17.9210	+	14.0932i	1.36251	+	1.07149i	0.989635	+	0.143607i	$0.0458701\pi$
$173$	17.9210	+	14.0932i	1.36251	+	1.07149i	0.372874	+	0.927882i	$0.378372\pi$
$174$	−0.444572	−	3.35812i	−0.0337029	−	0.254579i
$175$	−37.2110	+	4.22123i	−2.81289	+	0.319095i
$176$	−3.50922	+	1.60261i	−0.264517	+	0.120801i
$177$	8.30594	−	7.74431i	0.624313	−	0.582098i
$178$	5.96122	−	1.44618i	0.446812	−	0.108395i
$179$	−0.332248	+	1.72387i	−0.0248334	+	0.128848i	−0.992230	−	0.124420i	$-0.960293\pi$
$179$	−0.332248	+	1.72387i	−0.0248334	+	0.128848i	0.967396	+	0.253267i	$0.0815052\pi$
$180$	−10.3142	−	4.39919i	−0.768776	−	0.327896i
$181$	5.98419	+	2.73289i	0.444801	+	0.203134i	0.625208	−	0.780458i	$-0.285014\pi$
$181$	5.98419	+	2.73289i	0.444801	+	0.203134i	−0.180407	+	0.983592i	$0.557741\pi$
$182$	−0.227636	−	3.47797i	−0.0168735	−	0.257804i
$183$	14.4339	−	12.2273i	1.06699	−	0.903866i
$184$	−12.6540	+	7.38719i	−0.932862	+	0.544591i
$185$	12.8985	+	22.3409i	0.948317	+	1.64253i
$186$	−7.12855	−	1.45674i	−0.522690	−	0.106813i
$187$	−6.72467	+	4.78862i	−0.491757	+	0.350178i
$188$	−0.819321	+	0.240574i	−0.0597551	+	0.0175457i
$189$	13.2503	−	3.66461i	0.963818	−	0.266561i
$190$	−2.26875	−	0.666166i	−0.164593	−	0.0483288i
$191$	11.9215	−	0.567890i	0.862608	−	0.0410911i	0.388387	−	0.921497i	$-0.373033\pi$
$191$	11.9215	−	0.567890i	0.862608	−	0.0410911i	0.474222	+	0.880405i	$0.342730\pi$
$192$	−13.5931	+	1.14481i	−0.980998	+	0.0826198i
$193$	7.20442	−	20.8158i	0.518585	−	1.49835i	−0.316694	−	0.948528i	$-0.602573\pi$
$193$	7.20442	−	20.8158i	0.518585	−	1.49835i	0.835279	−	0.549826i	$-0.185306\pi$
$194$	11.7250	−	6.04465i	0.841805	−	0.433981i
$195$	4.95537	+	7.90358i	0.354862	+	0.565987i
$196$	−1.75344	+	5.71525i	−0.125246	+	0.408232i
$197$	−3.42562	+	5.33036i	−0.244065	+	0.379773i	−0.941576	−	0.336802i	$-0.890655\pi$
$197$	−3.42562	+	5.33036i	−0.244065	+	0.379773i	0.697510	+	0.716575i	$0.254291\pi$
$198$	0.200135	+	7.92631i	0.0142230	+	0.563298i
$199$	−4.11852	−	2.93278i	−0.291954	−	0.207899i	0.424690	−	0.905339i	$-0.360383\pi$
$199$	−4.11852	−	2.93278i	−0.291954	−	0.207899i	−0.716644	+	0.697439i	$0.754323\pi$
$200$	19.8164	−	38.4385i	1.40123	−	2.71801i
$201$	−15.4311	−	1.64774i	−1.08843	−	0.116223i
$202$	−1.30561	−	1.13132i	−0.0918624	−	0.0795992i
$203$	3.59621	−	3.22970i	0.252404	−	0.226680i
$204$	−4.76111	+	1.34037i	−0.333344	+	0.0938445i
$205$	−46.2088	−	18.4992i	−3.22736	−	1.29204i
$206$	0.445682	+	0.771943i	0.0310521	+	0.0537838i
$207$	1.79741	+	14.2748i	0.124929	+	0.992166i
$208$	1.66530	+	0.961460i	0.115468	+	0.0666653i
$209$	−0.177326	−	1.23333i	−0.0122659	−	0.0853112i
$210$	4.20187	+	21.0549i	0.289957	+	1.45293i
$211$	−3.74748	+	1.10036i	−0.257987	+	0.0757519i	−0.408169	−	0.912907i	$-0.633832\pi$
$211$	−3.74748	+	1.10036i	−0.257987	+	0.0757519i	0.150181	+	0.988658i	$0.452014\pi$
$212$	8.92205	−	3.08795i	0.612769	−	0.212081i
$213$	−20.1383	−	14.6824i	−1.37985	−	1.00602i
$214$	−5.03148	−	2.59391i	−0.343945	−	0.177316i
$215$	−22.4793	−	2.14652i	−1.53308	−	0.146391i
$216$	−4.98083	+	15.0739i	−0.338903	+	1.02565i
$217$	−4.02918	−	9.56839i	−0.273519	−	0.649545i
$218$	−14.6395	−	2.10484i	−0.991513	−	0.142558i
$219$	−14.4467	+	0.526409i	−0.976214	+	0.0355714i
$220$	9.21759	+	0.439088i	0.621450	+	0.0296033i
$221$	3.88855	+	1.34584i	0.261572	+	0.0905311i
$222$	8.97279	−	6.23953i	0.602215	−	0.418770i
$223$	−8.31422	−	12.9372i	−0.556762	−	0.866338i	0.442780	−	0.896631i	$-0.353992\pi$
$223$	−8.31422	−	12.9372i	−0.556762	−	0.866338i	−0.999541	+	0.0302926i	$0.990356\pi$
$224$	−7.42062	−	9.09882i	−0.495811	−	0.607940i
$225$	−27.0837	−	32.7057i	−1.80558	−	2.18038i
$226$	0.606042	−	2.49814i	0.0403133	−	0.166174i
$227$	16.6986	−	1.59453i	1.10833	−	0.105832i	0.475198	−	0.879879i	$-0.342376\pi$
$227$	16.6986	−	1.59453i	1.10833	−	0.105832i	0.633129	+	0.774046i	$0.281770\pi$
$228$	0.149469	−	0.731424i	0.00989880	−	0.0484397i
$229$	−13.8186	−	7.97815i	−0.913156	−	0.527211i	−0.0317106	−	0.999497i	$-0.510095\pi$
$229$	−13.8186	−	7.97815i	−0.913156	−	0.527211i	−0.881445	+	0.472286i	$0.843429\pi$
$230$	−22.4384	+	1.17712i	−1.47954	+	0.0776172i
$231$	−9.17261	+	6.62318i	−0.603514	+	0.435773i
$232$	0.794359	+	5.52489i	0.0521522	+	0.362727i
$233$	−8.90321	+	6.33995i	−0.583269	+	0.415344i	−0.833242	−	0.552909i	$-0.813518\pi$
$233$	−8.90321	+	6.33995i	−0.583269	+	0.415344i	0.249973	+	0.968253i	$0.419578\pi$
$234$	3.16038	−	2.37296i	0.206601	−	0.155125i
$235$	−4.29693	−	0.828165i	−0.280301	−	0.0540235i
$236$	−4.05249	+	3.86404i	−0.263795	+	0.251528i
$237$	−11.4463	−	3.50038i	−0.743518	−	0.227374i
$238$	7.26636	+	6.07382i	0.471008	+	0.393707i
$239$	7.95032	−	6.88899i	0.514264	−	0.445612i	−0.358660	−	0.933468i	$-0.616766\pi$
$239$	7.95032	−	6.88899i	0.514264	−	0.445612i	0.872924	+	0.487856i	$0.162221\pi$
$240$	−10.9468	−	4.52505i	−0.706612	−	0.292091i
$241$	−1.67130	−	4.17470i	−0.107658	−	0.268916i	0.864750	−	0.502202i	$-0.167477\pi$
$241$	−1.67130	−	4.17470i	−0.107658	−	0.268916i	−0.972408	+	0.233286i	$0.925052\pi$
$242$	1.95137	+	4.87429i	0.125439	+	0.313331i
$243$	11.6959	+	10.3056i	0.750295	+	0.661103i
$244$	−7.04913	+	6.10810i	−0.451274	+	0.391031i
$245$	−21.4078	+	21.9154i	−1.36769	+	1.40012i
$246$	−6.16669	+	20.1652i	−0.393174	+	1.28569i
$247$	−0.449487	+	0.428585i	−0.0286002	+	0.0272702i
$248$	11.7723	+	2.26893i	0.747543	+	0.144077i
$249$	−0.224228	+	3.81044i	−0.0142098	+	0.241477i
$250$	34.9380	−	24.8793i	2.20967	−	1.57350i
$251$	−0.833280	−	5.79559i	−0.0525962	−	0.365814i	−0.999073	−	0.0430432i	$-0.986295\pi$
$251$	−0.833280	−	5.79559i	−0.0525962	−	0.365814i	0.946477	−	0.322771i	$-0.104614\pi$
$252$	−6.51275	+	1.87983i	−0.410265	+	0.118418i
$253$	−5.47615	−	10.4979i	−0.344283	−	0.659997i
$254$	7.96810	+	4.60038i	0.499963	+	0.288654i
$255$	−24.8343	−	5.07497i	−1.55519	−	0.317807i
$256$	16.1538	−	1.54250i	1.00961	−	0.0964065i
$257$	4.82669	−	19.8959i	0.301081	−	1.24107i	−0.597359	−	0.801974i	$-0.703783\pi$
$257$	4.82669	−	19.8959i	0.301081	−	1.24107i	0.898439	−	0.439098i	$-0.144702\pi$
$258$	−0.106934	+	9.56617i	−0.00665741	+	0.595564i
$259$	14.5784	+	5.53803i	0.905857	+	0.344116i
$260$	−2.48676	−	3.86948i	−0.154223	−	0.239975i
$261$	5.29607	+	1.41088i	0.327819	+	0.0873315i
$262$	1.52767	+	0.528732i	0.0943798	+	0.0326652i
$263$	14.3716	+	0.684605i	0.886193	+	0.0422146i	0.485741	−	0.874103i	$-0.338550\pi$
$263$	14.3716	+	0.684605i	0.886193	+	0.0422146i	0.400452	+	0.916318i	$0.368853\pi$
$264$	−0.475746	−	13.0563i	−0.0292801	−	0.803557i
$265$	47.8911	+	6.88570i	2.94193	+	0.422985i
$266$	−1.31738	+	0.554739i	−0.0807736	+	0.0340132i
$267$	−1.52218	+	9.80748i	−0.0931559	+	0.600208i
$268$	7.61725	+	0.727359i	0.465298	+	0.0444305i
$269$	13.9345	+	7.18374i	0.849603	+	0.438001i	0.827307	−	0.561751i	$-0.189872\pi$
$269$	13.9345	+	7.18374i	0.849603	+	0.438001i	0.0222962	+	0.999751i	$0.492902\pi$
$270$	−17.3811	+	17.0460i	−1.05778	+	1.03739i
$271$	−14.1177	+	4.88619i	−0.857590	+	0.296815i	−0.720255	−	0.693710i	$-0.755975\pi$
$271$	−14.1177	+	4.88619i	−0.857590	+	0.296815i	−0.137336	+	0.990525i	$0.543854\pi$
$272$	−5.01331	+	1.47204i	−0.303976	+	0.0892555i
$273$	5.34119	+	1.80934i	0.323263	+	0.109506i
$274$	0.975230	+	6.78287i	0.0589158	+	0.409768i
$275$	30.2643	+	17.4731i	1.82501	+	1.05367i
$276$	−0.964874	−	7.02815i	−0.0580786	−	0.423045i
$277$	2.05187	+	3.55394i	0.123285	+	0.213536i	0.921061	−	0.389418i	$-0.127324\pi$
$277$	2.05187	+	3.55394i	0.123285	+	0.213536i	−0.797776	+	0.602953i	$0.793990\pi$
$278$	−15.8696	−	6.35325i	−0.951798	−	0.381042i
$279$	6.58433	−	9.75867i	0.394194	−	0.584236i
$280$	−7.31109	−	34.6142i	−0.436921	−	2.06859i
$281$	4.72206	+	4.09169i	0.281695	+	0.244090i	0.784235	−	0.620464i	$-0.213056\pi$
$281$	4.72206	+	4.09169i	0.281695	+	0.244090i	−0.502540	+	0.864554i	$0.667601\pi$
$282$	−0.196843	+	1.84343i	−0.0117218	+	0.109775i
$283$	−11.5405	+	22.3854i	−0.686010	+	1.33067i	0.246364	+	0.969177i	$0.420764\pi$
$283$	−11.5405	+	22.3854i	−0.686010	+	1.33067i	−0.932374	+	0.361496i	$0.882266\pi$
$284$	10.0099	+	7.12803i	0.593979	+	0.422971i
$285$	2.39840	−	2.98064i	0.142069	−	0.176558i
$286$	−1.75839	+	2.73610i	−0.103976	+	0.161789i
$287$	−28.7157	+	8.98854i	−1.69503	+	0.530577i
$288$	4.03537	−	12.6869i	0.237786	−	0.747581i
$289$	5.17221	−	2.66646i	0.304248	−	0.156851i
$290$	−2.79952	+	8.08869i	−0.164394	+	0.474984i
$291$	1.79121	+	21.2681i	0.105002	+	1.24676i
$292$	7.11990	−	0.339163i	0.416661	−	0.0198480i
$293$	25.6736	+	7.53846i	1.49987	+	0.440402i	0.925676	−	0.378317i	$-0.123497\pi$
$293$	25.6736	+	7.53846i	1.49987	+	0.440402i	0.574194	+	0.818719i	$0.305315\pi$
$294$	10.0129	+	8.25831i	0.583965	+	0.481634i
$295$	−27.5328	+	8.08437i	−1.60302	+	0.470690i
$296$	−14.6693	+	10.4459i	−0.852635	+	0.607158i
$297$	−11.9756	−	4.59996i	−0.694897	−	0.266917i
$298$	−1.28975	−	2.23391i	−0.0747132	−	0.129407i
$299$	−2.67907	+	5.25864i	−0.154934	+	0.304115i
$300$	13.5336	+	15.9760i	0.781364	+	0.922376i
$301$	−11.3511	+	7.58307i	−0.654269	+	0.437081i
$302$	3.64473	+	1.66449i	0.209731	+	0.0957808i
$303$	2.49861	−	1.25297i	0.143541	−	0.0719814i
$304$	0.149246	−	0.774364i	0.00855987	−	0.0444128i
$305$	−46.4521	+	11.2692i	−2.65984	+	0.645270i
$306$	−1.25947	+	10.6645i	−0.0719994	+	0.609647i
$307$	11.1240	−	5.08017i	0.634881	−	0.289940i	−0.0718580	−	0.997415i	$-0.522893\pi$
$307$	11.1240	−	5.08017i	0.634881	−	0.289940i	0.706739	+	0.707474i	$0.250166\pi$
$308$	4.48598	−	3.31606i	0.255612	−	0.188950i
$309$	−1.42973	+	0.189278i	−0.0813347	+	0.0107677i
$310$	14.4515	+	11.3648i	0.820791	+	0.645477i
$311$	26.1749	−	10.4789i	1.48424	−	0.594201i	0.518819	−	0.854884i	$-0.326372\pi$
$311$	26.1749	−	10.4789i	1.48424	−	0.594201i	0.965425	+	0.260683i	$0.0839477\pi$
$312$	−5.16356	+	3.96807i	−0.292329	+	0.224647i
$313$	−2.08508	−	10.8184i	−0.117855	−	0.611492i	−0.992043	−	0.125903i	$-0.959817\pi$
$313$	−2.08508	−	10.8184i	−0.117855	−	0.611492i	0.874187	−	0.485589i	$-0.161395\pi$
$314$	0.708593	+	1.55160i	0.0399882	+	0.0875620i
$315$	−34.0799	−	6.73102i	−1.92018	−	0.379250i
$316$	5.66280	+	1.66275i	0.318557	+	0.0935369i
$317$	−22.9589	+	7.94615i	−1.28950	+	0.446300i	−0.883868	−	0.467736i	$-0.845070\pi$
$317$	−22.9589	+	7.94615i	−1.28950	+	0.446300i	−0.405632	+	0.914037i	$0.632948\pi$
$318$	1.20413	−	20.4625i	0.0675240	−	1.14748i
$319$	−4.49005	+	0.428748i	−0.251395	+	0.0240053i
$320$	32.0000	+	12.8109i	1.78886	+	0.716150i
$321$	6.98851	−	5.92012i	0.390061	−	0.330429i
$322$	−10.0621	+	9.12447i	−0.560739	+	0.508487i
$323$		−	1.68756i		−	0.0938985i
$324$	−5.82339	−	5.01662i	−0.323521	−	0.278701i
$325$	−1.65576	−	17.3399i	−0.0918449	−	0.961843i
$326$	3.91784	−	4.10891i	0.216989	−	0.227572i
$327$	12.1959	−	20.5890i	0.674435	−	1.13857i
$328$	9.78926	−	33.3392i	0.540521	−	1.84085i
$329$	−2.32942	+	1.25375i	−0.128425	+	0.0691214i
$330$	8.52596	−	18.1302i	0.469339	−	0.998033i
$331$	−24.2911	+	4.68172i	−1.33516	+	0.257331i	−0.806364	−	0.591419i	$-0.798568\pi$
$331$	−24.2911	+	4.68172i	−1.33516	+	0.257331i	−0.528794	+	0.848750i	$0.677356\pi$
$332$	0.0895527	−	1.87994i	0.00491484	−	0.103175i
$333$	3.78372	+	17.2733i	0.207347	+	0.946573i
$334$	−2.17009	+	2.75949i	−0.118742	+	0.150993i
$335$	32.9885	+	21.2004i	1.80235	+	1.15830i
$336$	−6.85719	+	2.06256i	−0.374090	+	0.112522i
$337$	10.3201	+	22.5979i	0.562172	+	1.23098i	0.950862	+	0.309615i	$0.100200\pi$
$337$	10.3201	+	22.5979i	0.562172	+	1.23098i	−0.388690	+	0.921368i	$0.627072\pi$
$338$	−12.2814	+	0.585037i	−0.668023	+	0.0318218i
$339$	3.36079	+	2.45028i	0.182533	+	0.133081i
$340$	12.2723	+	2.36530i	0.665561	+	0.128276i
$341$	−2.28405	+	9.41499i	−0.123688	+	0.509850i
$342$	−1.34358	−	0.906532i	−0.0726523	−	0.0490196i
$343$	−1.65584	+	18.4461i	−0.0894070	+	0.995995i
$344$		−	15.7639i		−	0.849930i
$345$	12.1089	−	34.2789i	0.651923	−	1.84552i
$346$	−21.1363	+	12.2030i	−1.13629	+	0.656039i
$347$	−15.7078	−	19.9741i	−0.843239	−	1.07227i	−0.996460	−	0.0840732i	$-0.973207\pi$
$347$	−15.7078	−	19.9741i	−0.843239	−	1.07227i	0.153221	−	0.988192i	$-0.451035\pi$
$348$	−2.61896	−	0.666436i	−0.140391	−	0.0357247i
$349$	6.10642	+	20.7965i	0.326869	+	1.11321i	0.944981	+	0.327124i	$0.106079\pi$
$349$	6.10642	+	20.7965i	0.326869	+	1.11321i	−0.618112	+	0.786090i	$0.712102\pi$
$350$	10.6098	−	38.6605i	0.567120	−	2.06649i
$351$	1.59479	+	6.19232i	0.0851237	+	0.330522i
$352$	0.521319	+	10.9438i	0.0277864	+	0.583308i
$353$	0.0780581	−	0.109617i	0.00415461	−	0.00583434i	−0.812493	−	0.582970i	$-0.801890\pi$
$353$	0.0780581	−	0.109617i	0.00415461	−	0.00583434i	0.816648	+	0.577136i	$0.195830\pi$
$354$	4.39180	+	11.3358i	0.233421	+	0.602491i
$355$	28.8566	+	55.9740i	1.53155	+	2.97079i
$356$	0.696446	−	4.84389i	0.0369115	−	0.256725i
$357$	−13.5733	+	7.11094i	−0.718374	+	0.376351i
$358$	−1.58102	−	1.01606i	−0.0835596	−	0.0537005i
$359$	−0.831206	−	4.31270i	−0.0438694	−	0.227616i	0.953376	−	0.301784i	$-0.0975820\pi$
$359$	−0.831206	−	4.31270i	−0.0438694	−	0.227616i	−0.997246	+	0.0741679i	$0.976370\pi$
$360$	28.3244	−	28.4063i	1.49283	−	1.49714i
$361$	−16.6615	−	8.58959i	−0.876920	−	0.452084i
$362$	−5.09690	+	4.85988i	−0.267887	+	0.255430i
$363$	−8.49449	−	0.0949543i	−0.445845	−	0.00498381i
$364$	−2.64340	−	0.862641i	−0.138552	−	0.0452147i
$365$	33.2275	+	15.1745i	1.73921	+	0.794269i
$366$	6.40895	+	19.2095i	0.335001	+	1.00410i
$367$	17.0425	−	9.83949i	0.889611	−	0.513617i	0.0157960	−	0.999875i	$-0.494972\pi$
$367$	17.0425	−	9.83949i	0.889611	−	0.513617i	0.873815	+	0.486258i	$0.161638\pi$
$368$	−1.10218	−	7.41240i	−0.0574549	−	0.386398i
$369$	−26.3407	−	21.6848i	−1.37124	−	1.12887i
$370$	−27.3346	+	3.93013i	−1.42106	+	0.204318i
$371$	25.0666	−	15.0719i	1.30140	−	0.782496i
$372$	−3.19256	+	4.84772i	−0.165527	+	0.251343i
$373$	3.27511	+	9.46282i	0.169579	+	0.489966i	0.997483	−	0.0709032i	$-0.0225881\pi$
$373$	3.27511	+	9.46282i	0.169579	+	0.489966i	−0.827904	+	0.560870i	$0.810467\pi$
$374$	−2.08351	−	8.58834i	−0.107736	−	0.444092i
$375$	15.6061	+	67.6194i	0.805895	+	3.49185i
$376$	0.290379	−	3.04099i	0.0149752	−	0.156827i
$377$	1.47227	+	1.69909i	0.0758258	+	0.0875077i
$378$	−1.62988	+	14.6264i	−0.0838317	+	0.752302i
$379$	3.91744	−	27.2464i	0.201225	−	1.39955i	−0.599431	−	0.800427i	$-0.704606\pi$
$379$	3.91744	−	27.2464i	0.201225	−	1.39955i	0.800656	−	0.599125i	$-0.204485\pi$
$380$	−1.16608	+	1.48280i	−0.0598189	+	0.0760659i
$381$	−11.8038	+	9.07095i	−0.604729	+	0.464719i
$382$	−4.17876	+	12.0737i	−0.213804	+	0.617747i
$383$	−26.4955	−	2.53001i	−1.35386	−	0.129278i	−0.607233	−	0.794524i	$-0.707721\pi$
$383$	−26.4955	−	2.53001i	−1.35386	−	0.129278i	−0.746624	+	0.665246i	$0.768327\pi$
$384$	−0.225116	+	0.736133i	−0.0114879	+	0.0375656i
$385$	28.2205	−	4.57035i	1.43825	−	0.232927i
$386$	17.8208	+	15.4418i	0.907052	+	0.785965i
$387$	−14.2379	−	6.07270i	−0.723752	−	0.308692i
$388$	−1.00036	−	10.4762i	−0.0507854	−	0.531849i
$389$	−1.67389	−	2.12852i	−0.0848695	−	0.107920i	0.741764	−	0.670661i	$-0.233989\pi$
$389$	−1.67389	−	2.12852i	−0.0848695	−	0.107920i	−0.826634	+	0.562741i	$0.809747\pi$
$390$	−9.82630	+	1.78019i	−0.497574	+	0.0901433i
$391$	−5.31781	−	15.1288i	−0.268933	−	0.765099i
$392$	−16.6501	−	13.4226i	−0.840956	−	0.677941i
$393$	−1.73484	+	1.95747i	−0.0875111	+	0.0987411i
$394$	−3.93448	−	5.52521i	−0.198216	−	0.278356i
$395$	21.8894	+	20.8715i	1.10138	+	1.05016i
$396$	5.92984	+	2.20197i	0.297986	+	0.110653i
$397$	−21.1564	−	22.1882i	−1.06181	−	1.11359i	−0.993256	−	0.115944i	$-0.963011\pi$
$397$	−21.1564	−	22.1882i	−1.06181	−	1.11359i	−0.0685522	−	0.997648i	$-0.521838\pi$
$398$	4.55327	−	2.92621i	0.228235	−	0.146678i
$399$	−0.0152175	−	2.31271i	−0.000761826	−	0.115780i
$400$	14.4841	+	16.7156i	0.724206	+	0.835779i
$401$	−7.40143	−	14.3568i	−0.369610	−	0.716943i	0.628538	−	0.777779i	$-0.283654\pi$
$401$	−7.40143	−	14.3568i	−0.369610	−	0.716943i	−0.998148	+	0.0608356i	$0.980623\pi$
$402$	7.77705	−	14.6801i	0.387884	−	0.732179i
$403$	4.48306	−	1.79475i	0.223317	−	0.0894027i
$404$	−1.22501	+	0.631538i	−0.0609467	+	0.0314202i
$405$	−14.7451	−	36.5254i	−0.732692	−	1.81496i
$406$	1.77893	+	4.85897i	0.0882869	+	0.241146i
$407$	−7.86759	−	12.2422i	−0.389982	−	0.606824i
$408$	1.87878	−	17.5947i	0.0930134	−	0.871069i
$409$	0.513069	−	2.66205i	0.0253696	−	0.131630i	−0.967036	−	0.254641i	$-0.918043\pi$
$409$	0.513069	−	2.66205i	0.0253696	−	0.131630i	0.992405	+	0.123011i	$0.0392549\pi$
$410$	36.7698	−	38.5630i	1.81593	−	1.90449i
$411$	−10.7450	−	2.73423i	−0.530011	−	0.134870i
$412$	0.703875	−	0.101202i	0.0346774	−	0.00498586i
$413$	−9.80967	+	14.3068i	−0.482702	+	0.703991i
$414$	−14.9017	−	3.89313i	−0.732378	−	0.191337i
$415$	4.82250	−	8.35282i	0.236727	−	0.410024i
$416$	4.29269	−	3.37581i	0.210467	−	0.165513i
$417$	19.3087	−	19.8024i	0.945553	−	0.969729i
$418$	1.29626	+	0.314469i	0.0634021	+	0.0153812i
$419$	−1.45621	+	1.68056i	−0.0711406	+	0.0821006i	−0.790204	−	0.612844i	$-0.790026\pi$
$419$	−1.45621	+	1.68056i	−0.0711406	+	0.0821006i	0.719064	+	0.694944i	$0.244571\pi$
$420$	16.8399	+	3.13085i	0.821702	+	0.152770i
$421$	−18.0828	+	11.6211i	−0.881302	+	0.566378i	−0.901190	−	0.433424i	$-0.857305\pi$
$421$	−18.0828	+	11.6211i	−0.881302	+	0.566378i	0.0198881	+	0.999802i	$0.493669\pi$
$422$	0.397434	−	4.16211i	0.0193468	−	0.202609i
$423$	−2.63475	−	1.43375i	−0.128106	−	0.0697112i
$424$	−1.60712	+	33.7376i	−0.0780486	+	1.63844i
$425$	37.2040	+	29.2576i	1.80466	+	1.41920i
$426$	22.6039	−	14.1722i	1.09516	−	0.686644i
$427$	−17.4561	+	23.0273i	−0.844759	+	1.11437i
$428$	−3.41300	+	2.95738i	−0.164974	+	0.142950i
$429$	−3.00435	−	4.32043i	−0.145052	−	0.208592i
$430$	11.0770	−	21.4864i	0.534180	−	1.03617i
$431$	−15.7662	+	3.82485i	−0.759433	+	0.184236i	−0.596734	−	0.802439i	$-0.703535\pi$
$431$	−15.7662	+	3.82485i	−0.759433	+	0.184236i	−0.162699	+	0.986676i	$0.552020\pi$
$432$	−6.21044	−	5.23026i	−0.298800	−	0.251641i
$433$	−1.19062	−	4.05488i	−0.0572176	−	0.194865i	0.925924	−	0.377709i	$-0.123288\pi$
$433$	−1.19062	−	4.05488i	−0.0572176	−	0.194865i	−0.983142	+	0.182844i	$0.941470\pi$
$434$	11.1123	−	0.197350i	0.533409	−	0.00947310i
$435$	−10.3644	−	9.18561i	−0.496934	−	0.440416i
$436$	−5.89962	+	10.2184i	−0.282540	+	0.489374i
$437$	2.39738	+	0.332924i	0.114682	+	0.0159259i
$438$	5.22467	−	14.5668i	0.249644	−	0.696029i
$439$	11.1274	−	27.7949i	0.531082	−	1.32658i	−0.384009	−	0.923330i	$-0.625457\pi$
$439$	11.1274	−	27.7949i	0.531082	−	1.32658i	0.915090	−	0.403249i	$-0.132119\pi$
$440$	−13.7140	+	30.0296i	−0.653792	+	1.43160i
$441$	−18.5373	+	9.86755i	−0.882729	+	0.469883i
$442$	−2.88464	+	3.32906i	−0.137209	+	0.158347i
$443$	−3.56992	−	3.74402i	−0.169612	−	0.177884i	0.633442	−	0.773790i	$-0.281641\pi$
$443$	−3.56992	−	3.74402i	−0.169612	−	0.177884i	−0.803054	+	0.595906i	$0.796793\pi$
$444$	−1.96073	−	8.49562i	−0.0930522	−	0.403184i
$445$	14.5470	−	20.4284i	0.689594	−	0.968399i
$446$	16.1652	−	3.11558i	0.765443	−	0.147527i
$447$	4.13748	−	0.547749i	0.195696	−	0.0259077i
$448$	19.8859	−	6.22464i	0.939519	−	0.294087i
$449$	−29.6934	−	4.26927i	−1.40132	−	0.201479i	−0.600136	−	0.799898i	$-0.704887\pi$
$449$	−29.6934	−	4.26927i	−1.40132	−	0.201479i	−0.801184	+	0.598418i	$0.795796\pi$
$450$	43.2792	−	13.9038i	2.04020	−	0.655431i
$451$	26.5339	+	9.18346i	1.24943	+	0.432432i
$452$	−1.67052	−	1.18957i	−0.0785744	−	0.0559526i
$453$	−4.74165	+	4.42103i	−0.222782	+	0.207718i
$454$	−5.05913	+	17.2298i	−0.237437	+	0.808636i
$455$	−10.0149	−	10.1367i	−0.469508	−	0.475216i
$456$	2.23047	+	1.46892i	0.104451	+	0.0687884i
$457$	21.3438	+	29.9731i	0.998419	+	1.40208i	0.914028	+	0.405650i	$0.132955\pi$
$457$	21.3438	+	29.9731i	0.998419	+	1.40208i	0.0843904	+	0.996433i	$0.473106\pi$
$458$	13.4268	−	10.5589i	0.627391	−	0.493386i
$459$	−15.1677	−	8.47491i	−0.707970	−	0.395575i
$460$	−5.78129	+	16.9677i	−0.269554	+	0.791122i
$461$	−3.45975			−0.161137			−0.0805684	−	0.996749i	$-0.525674\pi$
$461$	−3.45975			−0.161137			−0.0805684	+	0.996749i	$0.525674\pi$
$462$	−2.93278	−	11.7511i	−0.136445	−	0.546708i
$463$	−0.486598	+	1.06550i	−0.0226141	+	0.0495180i	−0.920602	−	0.390502i	$-0.872301\pi$
$463$	−0.486598	+	1.06550i	−0.0226141	+	0.0495180i	0.897988	+	0.440020i	$0.145029\pi$
$464$	−2.77426	−	0.673029i	−0.128792	−	0.0312446i
$465$	−25.9258	+	14.5843i	−1.20228	+	0.676332i
$466$	−2.75848	−	11.3706i	−0.127784	−	0.526734i
$467$	−0.665468	−	13.9699i	−0.0307942	−	0.646450i	−0.960522	−	0.278203i	$-0.910261\pi$
$467$	−0.665468	−	13.9699i	−0.0307942	−	0.646450i	0.929728	−	0.368247i	$-0.120042\pi$
$468$	−0.820427	−	3.04428i	−0.0379243	−	0.140722i
$469$	23.5543	−	2.67201i	1.08764	−	0.123382i
$470$	2.53264	−	3.94087i	0.116822	−	0.181779i
$471$	−2.75804	+	0.100498i	−0.127084	+	0.00463069i
$472$	−7.44502	−	18.5968i	−0.342685	−	0.855985i
$473$	12.7241	+	0.606122i	0.585053	+	0.0278695i
$474$	8.03284	−	9.98289i	0.368960	−	0.458529i
$475$	−6.49810	+	2.96758i	−0.298153	+	0.136162i
$476$	6.65300	−	3.58080i	0.304940	−	0.164126i
$477$	29.8526	+	14.4482i	1.36686	+	0.661540i
$478$	3.68326	+	10.6421i	0.168468	+	0.486757i
$479$	−5.74793	−	5.48064i	−0.262630	−	0.250417i	0.547310	−	0.836930i	$-0.315652\pi$
$479$	−5.74793	−	5.48064i	−0.262630	−	0.250417i	−0.809940	+	0.586513i	$0.800500\pi$
$480$	−23.4851	+	24.0856i	−1.07194	+	1.09935i
$481$	−2.69586	+	6.73394i	−0.122921	+	0.307041i
$482$	4.81385			0.219265
$483$	−7.42418	−	20.6853i	−0.337812	−	0.941214i
$484$	4.18866			0.190394
$485$	20.0442	−	50.0681i	0.910162	−	2.27348i
$486$	−14.8953	+	7.52343i	−0.675664	+	0.341270i
$487$	−22.2595	−	21.2244i	−1.00867	−	0.961767i	−0.00940213	−	0.999956i	$-0.502993\pi$
$487$	−22.2595	−	21.2244i	−1.00867	−	0.961767i	−0.999271	+	0.0381883i	$0.987841\pi$
$488$	−10.9136	−	31.5329i	−0.494037	−	1.42743i
$489$	3.72232	+	8.39791i	0.168329	+	0.379767i
$490$	−13.2625	−	29.9949i	−0.599139	−	1.35503i
$491$	−2.76633	+	1.26334i	−0.124843	+	0.0570137i	−0.476857	−	0.878981i	$-0.658224\pi$
$491$	−2.76633	+	1.26334i	−0.124843	+	0.0570137i	0.352014	+	0.935995i	$0.385497\pi$
$492$	13.1066	+	10.5464i	0.590890	+	0.475466i
$493$	−6.10194	−	0.290671i	−0.274818	−	0.0130912i
$494$	−0.247101	−	0.617229i	−0.0111176	−	0.0277704i
$495$	21.8396	+	23.9547i	0.981616	+	1.07669i
$496$	−3.31505	+	5.15831i	−0.148850	+	0.231615i
$497$	34.9045	+	15.1972i	1.56568	+	0.681689i
$498$	−3.69768	−	1.73888i	−0.165697	−	0.0779213i
$499$	1.26324	+	26.5186i	0.0565503	+	1.18714i	0.831651	+	0.555299i	$0.187396\pi$
$499$	1.26324	+	26.5186i	0.0565503	+	1.18714i	−0.775100	+	0.631838i	$0.782301\pi$
$500$	−8.06713	−	33.2531i	−0.360773	−	1.48713i
$501$	−2.78485	−	4.95049i	−0.124418	−	0.221171i
$502$	6.09130	+	1.47773i	0.271868	+	0.0659545i
$503$	−13.9535	+	30.5539i	−0.622155	+	1.36233i	0.291786	+	0.956484i	$0.405750\pi$
$503$	−13.9535	+	30.5539i	−0.622155	+	1.36233i	−0.913941	+	0.405846i	$0.866977\pi$
$504$	2.41610	−	24.1296i	0.107622	−	1.07482i
$505$	−7.06294			−0.314297
$506$	12.6118	−	1.26555i	0.560662	−	0.0562607i
$507$	6.71631	−	18.7256i	0.298282	−	0.831635i
$508$	5.76979	−	4.53741i	0.255993	−	0.201315i
$509$	−22.0768	−	31.0025i	−0.978537	−	1.37416i	−0.926822	−	0.375501i	$-0.877471\pi$
$509$	−22.0768	−	31.0025i	−0.978537	−	1.37416i	−0.0517146	−	0.998662i	$-0.516469\pi$
$510$	14.9243	−	22.6617i	0.660860	−	1.00348i
$511$	21.3640	−	5.58633i	0.945087	−	0.247125i
$512$	−4.64365	+	15.8148i	−0.205222	+	0.698923i
$513$	2.18596	−	1.44868i	0.0965127	−	0.0639608i
$514$	17.8526	+	12.7127i	0.787442	+	0.560735i
$515$	3.44379	+	1.19191i	0.151752	+	0.0525217i
$516$	7.05333	+	2.91562i	0.310506	+	0.128353i
$517$	2.44342	+	0.351311i	0.107462	+	0.0154506i
$518$	−11.3040	+	12.2849i	−0.496671	+	0.539767i
$519$	−5.18256	−	39.1470i	−0.227489	−	1.71836i
$520$	16.1577	−	3.11414i	0.708562	−	0.136564i
$521$	7.13483	−	10.0195i	0.312582	−	0.438961i	−0.628159	−	0.778085i	$-0.716191\pi$
$521$	7.13483	−	10.0195i	0.312582	−	0.438961i	0.940742	+	0.339124i	$0.110131\pi$
$522$	−3.50929	+	4.70200i	−0.153597	+	0.205801i
$523$	2.91084	+	3.05280i	0.127282	+	0.133490i	0.784291	−	0.620393i	$-0.213027\pi$
$523$	2.91084	+	3.05280i	0.127282	+	0.133490i	−0.657009	+	0.753883i	$0.728179\pi$
$524$	0.844560	−	0.974674i	0.0368948	−	0.0425788i
$525$	51.2499	+	39.7604i	2.23673	+	1.73529i
$526$	−6.39835	+	14.0104i	−0.278981	+	0.610884i
$527$	−4.87668	+	12.1814i	−0.212432	+	0.530628i
$528$	6.28966	+	2.25591i	0.273722	+	0.0981758i
$529$	22.5414	−	4.56994i	0.980062	−	0.198693i
$530$	−25.8974	+	44.8555i	−1.12491	+	1.94840i
$531$	−19.6646	−	0.439690i	−0.853370	−	0.0190809i
$532$	0.0202491	+	1.14018i	0.000877909	+	0.0494330i
$533$	−3.94296	−	13.4285i	−0.170788	−	0.581652i
$534$	−9.14124	−	5.41483i	−0.395580	−	0.234323i
$535$	−22.4909	+	5.45622i	−0.972365	+	0.235893i
$536$	−12.5436	+	24.3313i	−0.541802	+	1.05095i
$537$	2.49650	−	1.73603i	0.107732	−	0.0749151i
$538$	−12.6834	+	10.9902i	−0.546820	+	0.473823i
$539$	11.4744	−	12.9233i	0.494239	−	0.556646i
$540$	7.47127	+	17.9273i	0.321512	+	0.771468i
$541$	23.7425	+	18.6713i	1.02077	+	0.802743i	0.980514	−	0.196447i	$-0.0629403\pi$
$541$	23.7425	+	18.6713i	1.02077	+	0.802743i	0.0402558	+	0.999189i	$0.487183\pi$
$542$	0.760960	−	15.9745i	0.0326860	−	0.686164i
$543$	−4.11645	−	10.6251i	−0.176654	−	0.455966i
$544$	−1.41052	+	14.7716i	−0.0604755	+	0.633328i
$545$	−50.8682	+	32.6910i	−2.17896	+	1.40033i
$546$	−3.92323	+	4.58830i	−0.167899	+	0.196361i
$547$	23.7450	−	27.4032i	1.01526	−	1.17168i	0.0301893	−	0.999544i	$-0.490389\pi$
$547$	23.7450	−	27.4032i	1.01526	−	1.17168i	0.985074	−	0.172132i	$-0.0550656\pi$
$548$	5.31279	+	1.28887i	0.226951	+	0.0550578i
$549$	−32.6847	−	2.29021i	−1.39495	−	0.0977439i
$550$	−29.4062	+	23.1253i	−1.25389	+	0.986067i
$551$	0.461012	−	0.798497i	0.0196398	−	0.0340171i
$552$	24.6248	+	6.14014i	1.04810	+	0.261342i
$553$	18.2290	+	1.41452i	0.775177	+	0.0601516i
$554$	−4.34834	+	0.625197i	−0.184743	+	0.0265621i
$555$	11.0188	−	43.3018i	0.467723	−	1.83806i
$556$	−9.41087	+	9.86984i	−0.399110	+	0.418574i
$557$	5.43791	−	28.2145i	0.230411	−	1.19549i	−0.663823	−	0.747890i	$-0.731067\pi$
$557$	5.43791	−	28.2145i	0.230411	−	1.19549i	0.894235	−	0.447599i	$-0.147721\pi$
$558$	7.07868	+	10.4263i	0.299664	+	0.441379i
$559$	−3.43276	−	5.34148i	−0.145190	−	0.225921i
$560$	17.8248	+	3.10826i	0.753237	+	0.131348i
$561$	14.1296	+	2.19301i	0.596554	+	0.0925889i
$562$	−5.94514	+	3.06493i	−0.250781	+	0.129286i
$563$	−23.6796	+	9.47990i	−0.997978	+	0.399530i	−0.812401	−	0.583100i	$-0.801840\pi$
$563$	−23.6796	+	9.47990i	−0.997978	+	0.399530i	−0.185577	+	0.982630i	$0.559415\pi$
$564$	1.30694	+	0.692376i	0.0550323	+	0.0291543i
$565$	−4.81576	−	9.34127i	−0.202601	−	0.392990i
$566$	−17.6555	−	20.3755i	−0.742115	−	0.856447i
$567$	−20.8630	−	11.4776i	−0.876163	−	0.482015i
$568$	−36.9828	+	23.7674i	−1.55176	+	0.997258i
$569$	−10.7880	−	11.3141i	−0.452257	−	0.474313i	0.457646	−	0.889134i	$-0.348693\pi$
$569$	−10.7880	−	11.3141i	−0.452257	−	0.474313i	−0.909903	+	0.414821i	$0.863844\pi$
$570$	2.00797	+	3.56947i	0.0841048	+	0.149509i
$571$	−22.7029	−	21.6472i	−0.950087	−	0.905906i	0.0455739	−	0.998961i	$-0.485488\pi$
$571$	−22.7029	−	21.6472i	−0.950087	−	0.905906i	−0.995661	+	0.0930548i	$0.970337\pi$
$572$	1.50508	+	2.11359i	0.0629307	+	0.0883737i
$573$	−15.4706	−	13.7111i	−0.646293	−	0.572789i
$574$	2.49199	−	32.1144i	0.104014	−	1.34043i
$575$	−48.9035	+	47.0808i	−2.03942	+	1.96340i
$576$	18.2412	+	15.0169i	0.760049	+	0.625706i
$577$	−8.32440	−	10.5853i	−0.346549	−	0.440673i	0.581266	−	0.813714i	$-0.302558\pi$
$577$	−8.32440	−	10.5853i	−0.346549	−	0.440673i	−0.927815	+	0.373041i	$0.878315\pi$
$578$	0.592137	+	6.20114i	0.0246296	+	0.257933i
$579$	−34.1045	+	17.1023i	−1.41733	+	0.710747i
$580$	5.16069	+	4.47176i	0.214286	+	0.185680i
$581$	−0.932131	−	5.75562i	−0.0386713	−	0.238784i
$582$	−21.8493	−	6.68172i	−0.905685	−	0.276966i
$583$	−27.1701	−	2.59443i	−1.12527	−	0.107450i
$584$	−8.34023	+	24.0975i	−0.345121	+	0.997162i
$585$	3.41173	−	15.7933i	0.141058	−	0.652971i
$586$	−17.7065	+	22.5157i	−0.731450	+	0.930114i
$587$	2.68991	−	18.7087i	0.111024	−	0.772192i	−0.855902	−	0.517138i	$-0.826998\pi$
$587$	2.68991	−	18.7087i	0.111024	−	0.772192i	0.966927	−	0.255054i	$-0.0820933\pi$
$588$	9.08528	−	4.96728i	0.374670	−	0.204847i
$589$	−1.29690	−	1.49670i	−0.0534379	−	0.0616706i
$590$	2.91995	−	30.5792i	0.120213	−	1.25892i
$591$	10.6935	−	2.46800i	0.439874	−	0.101520i
$592$	−2.17142	−	8.95072i	−0.0892449	−	0.367872i
$593$	0.768273	+	2.21978i	0.0315492	+	0.0911553i	0.959676	−	0.281110i	$-0.0907025\pi$
$593$	0.768273	+	2.21978i	0.0315492	+	0.0911553i	−0.928126	+	0.372265i	$0.878581\pi$
$594$	9.33622	−	10.0715i	0.383070	−	0.413237i
$595$	38.7130	−	0.687525i	1.58708	−	0.0281858i
$596$	−2.03693	+	0.292866i	−0.0834359	+	0.0119963i
$597$	1.56111	+	8.61703i	0.0638919	+	0.352671i
$598$	−4.16023	−	4.75474i	−0.170125	−	0.194436i
$599$	−4.92402	+	2.84288i	−0.201190	+	0.116157i	−0.597210	−	0.802085i	$-0.703724\pi$
$599$	−4.92402	+	2.84288i	−0.201190	+	0.116157i	0.396020	+	0.918242i	$0.370391\pi$
$600$	−71.0538	+	23.7060i	−2.90076	+	0.967793i
$601$	−31.5048	−	14.3878i	−1.28511	−	0.586890i	−0.348514	−	0.937303i	$-0.613314\pi$
$601$	−31.5048	−	14.3878i	−1.28511	−	0.586890i	−0.936595	+	0.350414i	$0.886041\pi$
$602$	−3.01998	−	14.2980i	−0.123085	−	0.582744i
$603$	17.1437	+	20.7025i	0.698147	+	0.843070i
$604$	2.31346	−	2.20588i	0.0941335	−	0.0897561i
$605$	19.0793	+	9.83606i	0.775684	+	0.399893i
$606$	0.251118	+	2.98168i	0.0102010	+	0.121123i
$607$	−1.24843	−	6.47749i	−0.0506724	−	0.262913i	0.947753	−	0.319004i	$-0.103348\pi$
$607$	−1.24843	−	6.47749i	−0.0506724	−	0.262913i	−0.998426	+	0.0560910i	$0.982136\pi$
$608$	−1.88412	−	1.21085i	−0.0764112	−	0.0491065i
$609$	−8.36499	−	0.343325i	−0.338967	−	0.0139122i
$610$	7.28217	−	50.6486i	0.294846	−	2.05070i
$611$	−0.563817	−	1.09365i	−0.0228096	−	0.0442445i
$612$	7.52504	+	4.09489i	0.304182	+	0.165526i
$613$	9.80824	−	13.7737i	0.396151	−	0.556316i	−0.567537	−	0.823348i	$-0.692104\pi$
$613$	9.80824	−	13.7737i	0.396151	−	0.556316i	0.963688	+	0.267032i	$0.0860429\pi$
$614$	0.622909	+	13.0765i	0.0251386	+	0.527724i
$615$	34.9348	+	78.8162i	1.40871	+	3.17817i
$616$	5.04868	+	19.3078i	0.203417	+	0.777935i
$617$	11.0678	+	37.6935i	0.445573	+	1.51748i	0.810101	+	0.586290i	$0.199412\pi$
$617$	11.0678	+	37.6935i	0.445573	+	1.51748i	−0.364529	+	0.931192i	$0.618770\pi$
$618$	0.380733	−	1.49620i	0.0153153	−	0.0601862i
$619$	15.0479	+	19.1349i	0.604826	+	0.769099i	0.987979	−	0.154586i	$-0.0494044\pi$
$619$	15.0479	+	19.1349i	0.604826	+	0.769099i	−0.383154	+	0.923685i	$0.625162\pi$
$620$	12.7021	−	7.33357i	0.510129	−	0.294523i
$621$	15.0319	−	19.8756i	0.603210	−	0.797582i
$622$			30.1823i			1.21020i
$623$	−0.990151	−	15.1282i	−0.0396696	−	0.606097i
$624$	−0.902558	−	3.20597i	−0.0361313	−	0.128342i
$625$	24.6559	−	101.633i	0.986237	−	4.06532i
$626$	11.5811	+	2.23208i	0.462875	+	0.0892118i
$627$	−1.27143	+	1.74388i	−0.0507758	+	0.0696438i
$628$	1.35927	−	0.0647502i	0.0542409	−	0.00258381i
$629$	−8.18753	−	17.9282i	−0.326458	−	0.714844i
$630$	20.2486	−	31.1912i	0.806724	−	1.24269i
$631$	−29.6036	−	19.0251i	−1.17850	−	0.757377i	−0.203391	−	0.979098i	$-0.565196\pi$
$631$	−29.6036	−	19.0251i	−1.17850	−	0.757377i	−0.975110	+	0.221721i	$0.928833\pi$
$632$	−13.0516	+	16.5965i	−0.519165	+	0.660172i
$633$	5.97781	+	3.16685i	0.237597	+	0.125871i
$634$	1.23751	−	25.9785i	0.0491477	−	1.03174i
$635$	36.9363	−	7.11890i	1.46577	−	0.282505i
$636$	−14.7982	−	6.95905i	−0.586787	−	0.275944i
$637$	−8.56468	−	0.922397i	−0.339345	−	0.0365467i
$638$	1.36034	−	4.63289i	0.0538563	−	0.183418i
$639$	7.21980	+	42.5586i	0.285611	+	1.68359i
$640$	1.34229	−	1.40775i	0.0530585	−	0.0556461i
$641$	1.87462	+	19.6319i	0.0740431	+	0.775414i	0.953890	+	0.300157i	$0.0970390\pi$
$641$	1.87462	+	19.6319i	0.0740431	+	0.775414i	−0.879847	+	0.475258i	$0.842355\pi$
$642$	3.10304	+	9.30073i	0.122467	+	0.367070i
$643$			4.49062i			0.177093i	0.996072	+	0.0885463i	$0.0282221\pi$
$643$			4.49062i			0.177093i	−0.996072	+	0.0885463i	$0.971778\pi$
$644$	3.77444	+	10.1578i	0.148734	+	0.400273i
$645$	25.2812	+	29.8437i	0.995447	+	1.17509i
$646$	1.67713	+	0.671422i	0.0659859	+	0.0264168i
$647$	−2.76958	+	0.264462i	−0.108883	+	0.0103971i	−0.149355	−	0.988784i	$-0.547720\pi$
$647$	−2.76958	+	0.264462i	−0.108883	+	0.0103971i	0.0404722	+	0.999181i	$0.487114\pi$
$648$	24.4040	−	12.6705i	0.958678	−	0.497743i
$649$	15.2970	−	5.29433i	0.600458	−	0.207821i
$650$	17.8915	+	5.25341i	0.701761	+	0.206056i
$651$	−6.57338	+	16.7379i	−0.257631	+	0.656008i
$652$	−1.88154	−	4.12000i	−0.0736869	−	0.161352i
$653$	−2.07212	−	10.7512i	−0.0810884	−	0.420727i	−0.999675	−	0.0255060i	$-0.991880\pi$
$653$	−2.07212	−	10.7512i	−0.0810884	−	0.420727i	0.918586	−	0.395221i	$-0.129332\pi$
$654$	15.6094	+	20.3122i	0.610375	+	0.794269i
$655$	6.13575	−	2.45638i	0.239743	−	0.0959788i
$656$	13.9689	+	10.9853i	0.545395	+	0.428904i
$657$	18.5519	+	16.8159i	0.723779	+	0.656052i
$658$	−0.319204	−	2.81385i	−0.0124439	−	0.109695i
$659$	4.22091	−	1.92763i	0.164423	−	0.0750897i	−0.331503	−	0.943454i	$-0.607556\pi$
$659$	4.22091	−	1.92763i	0.164423	−	0.0750897i	0.495927	+	0.868364i	$0.334828\pi$
$660$	−10.8998	−	11.6903i	−0.424276	−	0.455045i
$661$	−34.4716	+	8.36272i	−1.34079	+	0.325272i	−0.841075	−	0.540918i	$-0.818077\pi$
$661$	−34.4716	+	8.36272i	−1.34079	+	0.325272i	−0.499715	+	0.866190i	$0.666562\pi$
$662$	5.01179	−	26.0036i	0.194789	−	1.01066i
$663$	−3.19484	−	6.37098i	−0.124077	−	0.247428i
$664$	6.12458	+	2.79700i	0.237680	+	0.108545i
$665$	−2.58520	+	5.24105i	−0.100250	+	0.203239i
$666$	−18.6720	−	3.11213i	−0.723525	−	0.120592i
$667$	1.61673	−	8.61118i	0.0626001	−	0.333426i
$668$	1.40033	+	2.42545i	0.0541805	+	0.0938434i
$669$	−5.33298	+	26.0969i	−0.206185	+	1.00897i
$670$	−34.1943	+	24.3497i	−1.32104	+	0.940710i
$671$	25.8719	−	7.59669i	0.998775	−	0.293267i
$672$	−1.79984	+	20.2564i	−0.0694302	+	0.781409i
$673$	−32.2006	−	9.45494i	−1.24124	−	0.364461i	−0.405759	−	0.913980i	$-0.632993\pi$
$673$	−32.2006	−	9.45494i	−1.24124	−	0.364461i	−0.835481	+	0.549519i	$0.814811\pi$
$674$	−26.5642	+	1.26541i	−1.02321	+	0.0487417i
$675$	−5.96081	+	73.3078i	−0.229432	+	2.82162i
$676$	−3.20822	+	9.26953i	−0.123393	+	0.356521i
$677$	−12.2552	+	6.31801i	−0.471007	+	0.242821i	−0.677353	−	0.735658i	$-0.736873\pi$
$677$	−12.2552	+	6.31801i	−0.471007	+	0.242821i	0.206346	+	0.978479i	$0.433843\pi$
$678$	−3.77228	+	2.36514i	−0.144874	+	0.0908326i
$679$	−9.73924	−	31.1140i	−0.373758	−	1.19404i
$680$	−24.1730	+	37.6139i	−0.926991	+	1.44243i
$681$	−22.6362	−	18.2144i	−0.867419	−	0.697978i
$682$	−8.44806	−	6.01583i	−0.323493	−	0.230358i
$683$	−0.267361	+	0.518607i	−0.0102303	+	0.0198440i	−0.893895	−	0.448276i	$-0.852038\pi$
$683$	−0.267361	+	0.518607i	−0.0102303	+	0.0198440i	0.883665	+	0.468120i	$0.155068\pi$
$684$	−1.06979	+	0.726307i	−0.0409043	+	0.0277711i
$685$	21.1731	+	18.3466i	0.808983	+	0.700988i
$686$	−17.6733	−	8.98466i	−0.674769	−	0.343036i
$687$	7.48938	+	26.6030i	0.285738	+	1.01497i
$688$	7.48482	+	2.99647i	0.285356	+	0.114239i
$689$	6.80218	+	11.7817i	0.259143	+	0.448848i
$690$	29.2493	+	25.6725i	1.11350	+	0.977335i
$691$	17.8038	+	10.2790i	0.677287	+	0.391032i	0.798832	−	0.601554i	$-0.205452\pi$
$691$	17.8038	+	10.2790i	0.677287	+	0.391032i	−0.121545	+	0.992586i	$0.538785\pi$
$692$	2.77097	+	19.2725i	0.105337	+	0.732632i
$693$	19.3837	+	2.87798i	0.736325	+	0.109326i
$694$	26.1002	−	7.66372i	0.990751	−	0.290911i
$695$	−66.0433	+	22.8578i	−2.50517	+	0.867047i
$696$	5.69555	−	7.81198i	0.215889	−	0.296112i
$697$	33.8008	+	17.4255i	1.28030	+	0.660040i
$698$	−23.0975	−	2.20555i	−0.874255	−	0.0834812i
$699$	18.7071	+	2.90346i	0.707568	+	0.109819i
$700$	−25.4875	−	19.3211i	−0.963336	−	0.730268i
$701$	14.5838	+	2.09683i	0.550821	+	0.0791962i	0.412106	−	0.911136i	$-0.364793\pi$
$701$	14.5838	+	2.09683i	0.550821	+	0.0791962i	0.138716	+	0.990332i	$0.455703\pi$
$702$	−6.78856	−	0.878775i	−0.256218	−	0.0331672i
$703$	2.97140	+	0.141545i	0.112068	+	0.00533848i
$704$	−18.3749	−	6.35963i	−0.692532	−	0.239688i
$705$	4.32724	+	6.22281i	0.162973	+	0.234365i
$706$	0.0778832	+	0.121189i	0.00293117	+	0.00456099i
$707$	−3.30881	+	2.69853i	−0.124441	+	0.101489i
$708$	9.69788	+	0.108406i	0.364469	+	0.00407415i
$709$	5.00454	−	20.6290i	0.187950	−	0.774739i	−0.797296	−	0.603589i	$-0.793737\pi$
$709$	5.00454	−	20.6290i	0.187950	−	0.774739i	0.985245	−	0.171149i	$-0.0547481\pi$
$710$	−67.1091	+	6.40814i	−2.51856	+	0.240493i
$711$	9.96202	+	18.1816i	0.373605	+	0.681863i
$712$	15.1615	+	8.75348i	0.568201	+	0.328051i
$713$	−16.3430	−	9.33106i	−0.612050	−	0.349451i
$714$	−1.66666	−	16.3186i	−0.0623731	−	0.610707i
$715$	1.89237	+	13.1617i	0.0707706	+	0.492220i
$716$	−1.22131	+	0.869692i	−0.0456426	+	0.0325019i
$717$	−18.1893	−	1.07036i	−0.679293	−	0.0399734i
$718$	4.61676	+	0.889807i	0.172296	+	0.0332073i
$719$	31.4226	−	29.9614i	1.17186	−	1.11737i	0.180865	−	0.983508i	$-0.442110\pi$
$719$	31.4226	−	29.9614i	1.17186	−	1.11737i	0.991000	−	0.133863i	$-0.0427381\pi$
$720$	8.10354	+	18.8483i	0.302001	+	0.702434i
$721$	2.06872	−	0.757387i	0.0770433	−	0.0282066i
$722$	15.1655	−	13.1410i	0.564402	−	0.489057i
$723$	−2.97542	+	7.19799i	−0.110657	+	0.267696i
$724$	2.08814	+	5.21592i	0.0776051	+	0.193848i
$725$	9.61102	+	24.0072i	0.356944	+	0.891604i
$726$	3.47403	−	8.40421i	0.128933	−	0.311910i
$727$	14.6617	−	12.7045i	0.543773	−	0.471182i	−0.339129	−	0.940740i	$-0.610132\pi$
$727$	14.6617	−	12.7045i	0.543773	−	0.471182i	0.882902	+	0.469558i	$0.155587\pi$
$728$	6.37967	−	7.63227i	0.236446	−	0.282871i
$729$	−2.04282	−	26.9226i	−0.0756601	−	0.997134i
$730$	−28.3008	+	26.9847i	−1.04746	+	0.998750i
$731$	16.9409	+	3.26509i	0.626581	+	0.120764i
$732$	16.1275	+	0.949032i	0.596090	+	0.0350772i
$733$	0.175607	−	0.125049i	0.00648620	−	0.00461881i	−0.576809	−	0.816879i	$-0.695702\pi$
$733$	0.175607	−	0.125049i	0.00648620	−	0.00461881i	0.583295	+	0.812260i	$0.301763\pi$
$734$	2.99806	+	20.8520i	0.110660	+	0.769660i
$735$	53.0478	−	1.29131i	1.95670	−	0.0476306i
$736$	−20.7066	−	4.91797i	−0.763255	−	0.181279i
$737$	−19.1571	−	11.0603i	−0.705660	−	0.407413i
$738$	32.0309	−	17.5503i	1.17907	−	0.646035i
$739$	−19.6877	+	1.87995i	−0.724225	+	0.0691551i	−0.450656	−	0.892697i	$-0.648810\pi$
$739$	−19.6877	+	1.87995i	−0.724225	+	0.0691551i	−0.273568	+	0.961853i	$0.588204\pi$
$740$	−5.19408	+	21.4103i	−0.190938	+	0.787058i
$741$	1.07565	+	0.0120240i	0.0395151	+	0.000441713i
$742$	5.00564	+	30.9083i	0.183763	+	1.13468i
$743$	10.8810	+	16.9312i	0.399185	+	0.621144i	0.981419	−	0.191878i	$-0.0614576\pi$
$743$	10.8810	+	16.9312i	0.399185	+	0.621144i	−0.582234	+	0.813021i	$0.697821\pi$
$744$	−11.8554	−	17.0487i	−0.434639	−	0.625035i
$745$	−9.96592	−	3.44924i	−0.365123	−	0.126370i
$746$	−10.7074	−	0.510056i	−0.392025	−	0.0186745i
$747$	4.88561	−	4.45422i	0.178755	−	0.162971i
$748$	−6.97859	−	1.00337i	−0.255163	−	0.0366868i
$749$	−8.45177	+	11.1492i	−0.308821	+	0.407382i
$750$	−73.4106	−	11.3938i	−2.68057	−	0.416041i
$751$	7.70606	+	0.735840i	0.281198	+	0.0268512i	0.234702	−	0.972067i	$-0.424588\pi$
$751$	7.70606	+	0.735840i	0.281198	+	0.0268512i	0.0464960	+	0.998918i	$0.485195\pi$
$752$	1.38869	+	0.715921i	0.0506404	+	0.0261069i
$753$	−5.97461	+	8.19474i	−0.217727	+	0.298633i
$754$	−2.27436	+	0.787162i	−0.0828271	+	0.0286667i
$755$	15.7178	−	4.61516i	0.572029	−	0.167963i
$756$	10.3496	+	5.54396i	0.376411	+	0.201632i
$757$	−1.15190	−	8.01161i	−0.0418663	−	0.291187i	−0.999988	−	0.00482654i	$-0.998464\pi$
$757$	−1.15190	−	8.01161i	−0.0418663	−	0.291187i	0.958122	−	0.286360i	$-0.0924454\pi$
$758$	25.5193	+	14.7336i	0.926904	+	0.535149i
$759$	−5.90294	+	19.6402i	−0.214263	+	0.712894i
$760$	−3.37422	−	5.84432i	−0.122396	−	0.211996i
$761$	−19.5813	−	7.83916i	−0.709820	−	0.284169i	−0.0114791	−	0.999934i	$-0.503654\pi$
$761$	−19.5813	−	7.83916i	−0.709820	−	0.284169i	−0.698341	+	0.715765i	$0.746078\pi$
$762$	−4.31855	−	15.3399i	−0.156445	−	0.555706i
$763$	−11.3403	+	34.7501i	−0.410546	+	1.25804i
$764$	7.70321	+	6.67487i	0.278692	+	0.241488i
$765$	24.6606	+	36.3229i	0.891606	+	1.31326i
$766$	13.0560	−	25.3251i	0.471733	−	0.915035i
$767$	−6.57235	−	4.68015i	−0.237314	−	0.168990i
$768$	−21.8976	−	17.6202i	−0.790163	−	0.635813i
$769$	−14.3878	+	22.3878i	−0.518837	+	0.807326i	−0.997500	−	0.0706732i	$-0.977485\pi$
$769$	−14.3878	+	22.3878i	−0.518837	+	0.807326i	0.478663	+	0.877999i	$0.341122\pi$
$770$	−6.68586	+	29.8645i	−0.240942	+	1.07624i
$771$	−30.0435	+	18.8366i	−1.08199	+	0.678385i
$772$	16.7207	−	8.62010i	0.601790	−	0.310244i
$773$	−11.4786	+	33.1653i	−0.412858	+	1.19287i	0.526571	+	0.850131i	$0.323477\pi$
$773$	−11.4786	+	33.1653i	−0.412858	+	1.19287i	−0.939429	+	0.342744i	$0.888644\pi$
$774$	11.6999	−	11.7338i	0.420545	−	0.421761i
$775$	55.4810	−	2.64289i	1.99294	−	0.0949352i
$776$	36.1236	+	10.6068i	1.29676	+	0.380763i
$777$	−11.3822	−	24.4958i	−0.408335	−	0.878781i
$778$	2.78135	−	0.816677i	0.0997161	−	0.0292793i
$779$	−4.67542	+	3.32935i	−0.167514	+	0.119286i
$780$	−1.59508	+	7.80553i	−0.0571131	+	0.279483i
$781$	−17.7623	−	30.7652i	−0.635584	−	1.10086i
$782$	17.1511	+	0.734303i	0.613322	+	0.0262586i
$783$	−4.86167	−	8.15360i	−0.173742	−	0.291386i
$784$	9.53807	−	5.35418i	0.340645	−	0.191221i
$785$	6.34352	+	2.89699i	0.226410	+	0.103398i
$786$	−1.25514	−	2.50292i	−0.0447692	−	0.0892764i
$787$	7.97606	−	41.3837i	0.284316	−	1.47517i	−0.506034	−	0.862514i	$-0.668889\pi$
$787$	7.97606	−	41.3837i	0.284316	−	1.47517i	0.790349	−	0.612656i	$-0.209899\pi$
$788$	−5.25876	+	1.27576i	−0.187336	+	0.0454471i
$789$	−16.9945	−	18.2270i	−0.605021	−	0.648899i
$790$	−29.4516	+	13.4501i	−1.04784	+	0.478532i
$791$	−5.82508	−	2.53620i	−0.207116	−	0.0901771i
$792$	−15.1975	+	16.7664i	−0.540020	+	0.595768i
$793$	−10.5647	−	8.30814i	−0.375162	−	0.295031i
$794$	30.4684	−	12.1977i	1.08128	−	0.432881i
$795$	−51.0639	−	66.4484i	−1.81105	−	2.35668i
$796$	−0.817183	−	4.23995i	−0.0289643	−	0.150281i
$797$	10.4785	+	22.9447i	0.371168	+	0.812744i	0.999397	+	0.0347159i	$0.0110526\pi$
$797$	10.4785	+	22.9447i	0.371168	+	0.812744i	−0.628229	+	0.778028i	$0.716220\pi$
$798$	2.30447	+	0.905024i	0.0815774	+	0.0320375i
$799$	3.20790	+	0.941925i	0.113487	+	0.0333229i
$800$	59.3598	−	20.5446i	2.09869	−	0.726362i
$801$	13.7468	−	10.3217i	0.485718	−	0.364700i
$802$	17.2128	−	1.64363i	0.607806	−	0.0580384i
$803$	−19.1300	−	7.65851i	−0.675085	−	0.270263i
$804$	−8.56668	−	10.1127i	−0.302124	−	0.356647i
$805$	−6.66063	+	55.1320i	−0.234756	+	1.94315i
$806$			5.16942i			0.182085i
$807$	−8.59377	−	25.7581i	−0.302515	−	0.906727i
$808$	−0.468676	−	4.90820i	−0.0164880	−	0.172670i
$809$	−6.04709	+	6.34201i	−0.212604	+	0.222973i	−0.821398	−	0.570356i	$-0.806805\pi$
$809$	−6.04709	+	6.34201i	−0.212604	+	0.222973i	0.608793	+	0.793329i	$0.291654\pi$
$810$	42.1663	−	0.121793i	1.48157	−	0.00427937i
$811$	−2.74811	+	9.35920i	−0.0964992	+	0.328646i	−0.993567	−	0.113247i	$-0.963875\pi$
$811$	−2.74811	+	9.35920i	−0.0964992	+	0.328646i	0.897068	+	0.441893i	$0.145693\pi$
$812$	4.12618	+	0.123171i	0.144801	+	0.00432245i
$813$	23.4158	+	11.0116i	0.821228	+	0.386194i
$814$	15.2968	−	2.94821i	0.536152	−	0.103335i
$815$	1.10443	−	23.1849i	0.0386866	−	0.812132i
$816$	7.99701	+	4.23655i	0.279951	+	0.148309i
$817$	−1.60968	+	2.04687i	−0.0563155	+	0.0716109i
$818$	2.44147	+	1.56904i	0.0853639	+	0.0548601i
$819$	−4.43580	−	8.70227i	−0.155000	−	0.304082i
$820$	−17.6587	−	38.6671i	−0.616668	−	1.35031i
$821$	−52.2243	+	2.48775i	−1.82264	+	0.0868231i	−0.930800	−	0.365528i	$-0.880889\pi$
$821$	−52.2243	+	2.48775i	−1.82264	+	0.0868231i	−0.891840	+	0.452351i	$0.850586\pi$
$822$	6.99238	−	9.59071i	0.243887	−	0.334515i
$823$	−24.2674	−	4.67715i	−0.845908	−	0.163035i	−0.252159	−	0.967686i	$-0.581141\pi$
$823$	−24.2674	−	4.67715i	−0.845908	−	0.163035i	−0.593749	+	0.804651i	$0.702353\pi$
$824$	−0.599765	+	2.47226i	−0.0208938	+	0.0861254i
$825$	−16.4027	−	58.2638i	−0.571068	−	2.02849i
$826$	−10.3154	−	15.4412i	−0.358920	−	0.537268i
$827$		−	54.8718i		−	1.90808i	−0.299679	−	0.954040i	$-0.596880\pi$
$827$		−	54.8718i		−	1.90808i	0.299679	−	0.954040i	$-0.403120\pi$
$828$	−7.30182	+	9.88237i	−0.253756	+	0.343436i
$829$	−2.38067	+	1.37448i	−0.0826841	+	0.0477377i	−0.540772	−	0.841169i	$-0.681868\pi$
$829$	−2.38067	+	1.37448i	−0.0826841	+	0.0477377i	0.458088	+	0.888907i	$0.348534\pi$
$830$	6.38249	+	8.11599i	0.221539	+	0.281710i
$831$	1.75285	−	6.88836i	0.0608057	−	0.238955i
$832$	2.73053	+	9.29934i	0.0946642	+	0.322397i
$833$	17.8734	−	15.1131i	0.619276	−	0.523639i
$834$	11.9978	+	27.0681i	0.415448	+	0.937291i
$835$	0.682919	+	14.3362i	0.0236334	+	0.496126i
$836$	0.617254	−	0.866812i	0.0213482	−	0.0299793i
$837$	−19.9653	+	4.14009i	−0.690103	+	0.143102i
$838$	−1.09079	−	2.11585i	−0.0376809	−	0.0730907i
$839$	1.59913	−	11.1222i	0.0552080	−	0.383980i	−0.943419	−	0.331602i	$-0.892411\pi$
$839$	1.59913	−	11.1222i	0.0552080	−	0.383980i	0.998627	−	0.0523780i	$-0.0166801\pi$
$840$	−32.7885	+	51.7657i	−1.13131	+	1.78609i
$841$	21.5885	+	13.8741i	0.744432	+	0.478417i
$842$	−4.35477	−	22.5947i	−0.150075	−	0.778664i
$843$	−0.908230	−	10.7840i	−0.0312811	−	0.371420i
$844$	−2.96476	−	1.52844i	−0.102051	−	0.0526112i
$845$	−36.3807	+	34.6889i	−1.25153	+	1.19333i
$846$	2.47316	−	2.04803i	0.0850291	−	0.0704127i
$847$	12.6962	−	2.68166i	0.436248	−	0.0921429i
$848$	−15.7134	−	7.17608i	−0.539601	−	0.246428i
$849$	41.3796	−	13.8056i	1.42014	−	0.473809i
$850$	−43.8789	+	25.3335i	−1.50503	+	0.868932i
$851$	27.0844	−	8.09446i	0.928440	−	0.277475i
$852$	−3.79422	−	20.9434i	−0.129988	−	0.717509i
$853$	−15.2645	+	2.19470i	−0.522645	+	0.0751450i	−0.398588	−	0.917130i	$-0.630500\pi$
$853$	−15.2645	+	2.19470i	−0.522645	+	0.0751450i	−0.124057	+	0.992275i	$0.539591\pi$
$854$	−15.9398	−	26.5099i	−0.545447	−	0.907151i
$855$	−6.57842	+	0.796185i	−0.224977	+	0.0272290i
$856$	−5.28409	−	15.2674i	−0.180606	−	0.521828i
$857$	−0.0790489	−	0.325844i	−0.00270026	−	0.0111306i	0.970446	−	0.241320i	$-0.0775805\pi$
$857$	−0.0790489	−	0.325844i	−0.00270026	−	0.0111306i	−0.973146	+	0.230190i	$0.926065\pi$
$858$	5.48905	−	1.26684i	0.187393	−	0.0432491i
$859$	4.07115	−	42.6350i	0.138906	−	1.45469i	−0.610205	−	0.792244i	$-0.708913\pi$
$859$	4.07115	−	42.6350i	0.138906	−	1.45469i	0.749111	−	0.662445i	$-0.230481\pi$
$860$	−12.6292	−	14.5748i	−0.430651	−	0.496998i
$861$	46.4793	+	23.5760i	1.58401	+	0.803466i
$862$	2.47163	−	17.1906i	0.0841841	−	0.585513i
$863$	1.50326	−	1.91155i	0.0511715	−	0.0650699i	−0.759794	−	0.650164i	$-0.774700\pi$
$863$	1.50326	−	1.91155i	0.0511715	−	0.0650699i	0.810965	+	0.585094i	$0.198943\pi$
$864$	−20.3451	+	10.8535i	−0.692155	+	0.369245i
$865$	−32.6352	+	94.2931i	−1.10963	+	3.20606i
$866$	4.50353	+	0.430035i	0.153036	+	0.0146132i
$867$	−9.63834	−	2.94749i	−0.327335	−	0.100102i
$868$	3.14870	−	8.28869i	0.106874	−	0.281336i
$869$	−12.8943	−	11.1730i	−0.437409	−	0.379017i
$870$	13.2525	−	6.64568i	0.449300	−	0.225310i
$871$	1.04808	+	10.9760i	0.0355129	+	0.371908i
$872$	−26.0932	−	33.1802i	−0.883628	−	1.12363i
$873$	23.4959	−	28.5407i	0.795216	−	0.965955i
$874$	−1.28470	+	2.25011i	−0.0434557	+	0.0761110i
$875$	−45.7416	−	95.6289i	−1.54635	−	3.23285i
$876$	−9.23954	−	8.18871i	−0.312175	−	0.276671i
$877$	9.27635	+	13.0268i	0.313240	+	0.439884i	0.940941	−	0.338570i	$-0.109943\pi$
$877$	9.27635	+	13.0268i	0.313240	+	0.439884i	−0.627701	+	0.778455i	$0.716004\pi$
$878$	23.1959	+	22.1173i	0.782824	+	0.746421i
$879$	−22.7226	−	40.3928i	−0.766415	−	1.36241i
$880$	−11.6515	−	12.2197i	−0.392771	−	0.411927i
$881$	−23.7269	+	15.2484i	−0.799381	+	0.513731i	−0.875414	−	0.483374i	$-0.839411\pi$
$881$	−23.7269	+	15.2484i	−0.799381	+	0.513731i	0.0760329	+	0.997105i	$0.475775\pi$
$882$	−2.43121	−	22.3487i	−0.0818632	−	0.752519i
$883$	1.67043	+	1.92778i	0.0562146	+	0.0648751i	0.783160	−	0.621820i	$-0.213606\pi$
$883$	1.67043	+	1.92778i	0.0562146	+	0.0648751i	−0.726946	+	0.686695i	$0.759061\pi$
$884$	1.61030	+	3.12355i	0.0541603	+	0.105056i
$885$	43.9192	+	23.2669i	1.47633	+	0.782109i
$886$	5.14123	−	2.05824i	0.172723	−	0.0691478i
$887$	37.0287	−	19.0896i	1.24330	−	0.640967i	0.294143	−	0.955761i	$-0.404966\pi$
$887$	37.0287	−	19.0896i	1.24330	−	0.640967i	0.949160	+	0.314794i	$0.101936\pi$
$888$	30.8226	+	4.78385i	1.03434	+	0.160536i
$889$	14.5839	−	17.4473i	0.489127	−	0.585163i
$890$	14.5144	+	22.5848i	0.486524	+	0.757046i
$891$	9.28885	+	20.1853i	0.311188	+	0.676231i
$892$	2.48555	−	12.8963i	0.0832224	−	0.431799i
$893$	−0.348226	+	0.365209i	−0.0116529	+	0.0122212i
$894$	−1.10180	+	4.32984i	−0.0368496	+	0.144811i
$895$	−7.60532	+	1.09348i	−0.254218	+	0.0365510i
$896$	0.0909705	−	1.17234i	0.00303911	−	0.0391652i
$897$	9.68102	−	3.28178i	0.323240	−	0.109575i
$898$	16.0569	−	27.8113i	0.535825	−	0.928076i
$899$	−5.63521	+	4.43158i	−0.187945	+	0.147801i
$900$	2.53490	−	36.1767i	0.0844966	−	1.20589i
$901$	−35.9237	−	8.71501i	−1.19679	−	0.290339i
$902$	−19.6836	+	22.7161i	−0.655392	+	0.756363i
$903$	23.2460	+	4.32186i	0.773578	+	0.143822i
$904$	6.17191	−	3.96645i	0.205275	−	0.131922i
$905$	−2.73689	+	28.6620i	−0.0909771	+	0.952756i
$906$	−2.50716	−	6.47131i	−0.0832949	−	0.214995i
$907$	−1.11714	+	23.4516i	−0.0370939	+	0.778697i	0.901314	+	0.433167i	$0.142604\pi$
$907$	−1.11714	+	23.4516i	−0.0370939	+	0.778697i	−0.938408	+	0.345530i	$0.887699\pi$
$908$	11.2610	+	8.85571i	0.373708	+	0.293887i
$909$	−4.61362	−	1.46747i	−0.153024	−	0.0486730i
$910$	14.0587	−	5.92000i	0.466040	−	0.196246i
$911$	41.2642	−	35.7557i	1.36715	−	1.18464i	0.404286	−	0.914632i	$-0.367520\pi$
$911$	41.2642	−	35.7557i	1.36715	−	1.18464i	0.962859	−	0.270006i	$-0.0870256\pi$
$912$	−1.12143	+	0.779826i	−0.0371344	+	0.0258226i
$913$	−2.49314	+	4.83602i	−0.0825109	+	0.160049i
$914$	−38.2798	+	9.28658i	−1.26618	+	0.307173i
$915$	71.2321	+	42.1944i	2.35486	+	1.39490i
$916$	−3.83920	−	13.0751i	−0.126851	−	0.432014i
$917$	1.93594	−	3.49504i	0.0639303	−	0.115416i
$918$	14.4572	−	11.7021i	0.477160	−	0.386228i
$919$	−1.35508	+	2.34707i	−0.0447000	+	0.0774227i	−0.887510	−	0.460789i	$-0.847567\pi$
$919$	−1.35508	+	2.34707i	−0.0447000	+	0.0774227i	0.842810	+	0.538212i	$0.180900\pi$
$920$	−48.6661	−	41.7611i	−1.60447	−	1.37682i
$921$	−19.9378	−	7.15109i	−0.656974	−	0.235636i
$922$	1.37652	−	3.43837i	0.0453331	−	0.113237i
$923$	−7.35575	+	16.1069i	−0.242118	+	0.530163i
$924$	−9.57282	−	1.31213i	−0.314923	−	0.0431661i
$925$	−54.6362	+	63.0535i	−1.79643	+	2.07319i
$926$	−0.865315	−	0.907516i	−0.0284360	−	0.0298228i
$927$	2.00189	+	1.49409i	0.0657508	+	0.0490725i
$928$	−4.70276	+	6.60410i	−0.154376	+	0.216790i
$929$	−33.8514	+	6.52431i	−1.11063	+	0.214056i	−0.711394	−	0.702794i	$-0.751936\pi$
$929$	−33.8514	+	6.52431i	−1.11063	+	0.214056i	−0.399233	+	0.916849i	$0.630724\pi$
$930$	−4.17922	−	31.5682i	−0.137042	−	1.03516i
$931$	0.791341	+	3.44303i	0.0259352	+	0.112841i
$932$	−9.23939	−	1.32842i	−0.302646	−	0.0435140i
$933$	−45.1306	−	18.6555i	−1.47751	−	0.610755i
$934$	14.1483	+	4.89678i	0.462947	+	0.160228i
$935$	−29.4312	−	20.9579i	−0.962504	−	0.685396i
$936$	11.2015	+	1.32290i	0.366132	+	0.0432403i
$937$	6.13164	−	20.8824i	0.200312	−	0.682199i	−0.796659	−	0.604428i	$-0.793402\pi$
$937$	6.13164	−	20.8824i	0.200312	−	0.682199i	0.996971	−	0.0777710i	$-0.0247803\pi$
$938$	−6.71595	+	24.4718i	−0.219283	+	0.799033i
$939$	−10.4958	+	15.9372i	−0.342517	+	0.520091i
$940$	−2.16780	−	3.04425i	−0.0707060	−	0.0992926i
$941$	−15.1748	+	11.9336i	−0.494684	+	0.389024i	−0.834101	−	0.551612i	$-0.814013\pi$
$941$	−15.1748	+	11.9336i	−0.494684	+	0.389024i	0.339417	+	0.940636i	$0.389770\pi$
$942$	0.997450	−	2.78097i	0.0324987	−	0.0906091i
$943$	−31.4233	+	44.5804i	−1.02328	+	1.45174i
$944$	10.2451			0.333449
$945$	34.1236	+	49.5562i	1.11004	+	1.61206i
$946$	−5.66484	+	12.4043i	−0.184180	+	0.403298i
$947$	22.0305	+	5.34454i	0.715894	+	0.173674i	0.577131	−	0.816652i	$-0.304172\pi$
$947$	22.0305	+	5.34454i	0.715894	+	0.173674i	0.138763	+	0.990326i	$0.455687\pi$
$948$	−5.01190	−	8.90938i	−0.162779	−	0.289363i
$949$	2.42148	+	9.98146i	0.0786045	+	0.324012i
$950$	−0.363873	−	7.63863i	−0.0118056	−	0.247830i
$951$	38.0798	+	17.9076i	1.23482	+	0.580693i
$952$	3.04666	+	26.8569i	0.0987428	+	0.870438i
$953$	−23.4817	+	36.5382i	−0.760646	+	1.18359i	0.217580	+	0.976043i	$0.430184\pi$
$953$	−23.4817	+	36.5382i	−0.760646	+	1.18359i	−0.978225	+	0.207545i	$0.933453\pi$
$954$	−26.2362	+	23.9196i	−0.849430	+	0.774426i
$955$	19.4137	+	48.4931i	0.628213	+	1.56920i
$956$	8.97400	+	0.427484i	0.290240	+	0.0138258i
$957$	6.08658	+	4.89763i	0.196751	+	0.158318i
$958$	7.73367	−	3.53185i	0.249864	−	0.114109i
$959$	16.9288	+	0.505341i	0.546658	+	0.0163183i
$960$	−24.1926	−	54.5809i	−0.780814	−	1.76159i
$961$	−5.10280	−	14.7436i	−0.164607	−	0.475599i
$962$	−5.61973	−	5.35840i	−0.181187	−	0.172762i
$963$	−15.8250	−	1.10886i	−0.509955	−	0.0357325i
$964$	1.42733	−	3.56531i	0.0459713	−	0.114831i
$965$	96.4047			3.10338
$966$	23.5113	+	0.851663i	0.756463	+	0.0274018i
$967$	29.6986			0.955041			0.477521	−	0.878621i	$-0.341536\pi$
$967$	29.6986			0.955041			0.477521	+	0.878621i	$0.341536\pi$
$968$	−5.56926	+	13.9114i	−0.179003	+	0.447128i
$969$	−2.04058	+	2.09276i	−0.0655529	+	0.0672290i
$970$	41.7837	+	39.8407i	1.34159	+	1.27921i
$971$	17.4233	+	50.3412i	0.559139	+	1.61553i	0.770023	+	0.638016i	$0.220245\pi$
$971$	17.4233	+	50.3412i	0.559139	+	1.61553i	−0.210884	+	0.977511i	$0.567634\pi$
$972$	1.15558	+	13.2627i	0.0370651	+	0.425402i
$973$	−22.2064	+	35.9415i	−0.711905	+	1.15223i
$974$	29.9494	−	13.6775i	0.959642	−	0.438254i
$975$	−18.9139	+	23.5054i	−0.605728	+	0.752775i
$976$	17.0466	+	0.812030i	0.545649	+	0.0259924i
$977$	−1.19523	−	2.98555i	−0.0382389	−	0.0955161i	0.908019	−	0.418928i	$-0.137594\pi$
$977$	−1.19523	−	2.98555i	−0.0382389	−	0.0955161i	−0.946258	+	0.323412i	$0.895170\pi$
$978$	−9.82699	+	0.358077i	−0.314232	+	0.0114500i
$979$	−7.64849	+	11.9013i	−0.244447	+	0.380366i
$980$	−26.1476	+	0.929035i	−0.835256	+	0.0296769i
$981$	−40.0202	+	10.7853i	−1.27775	+	0.344350i
$982$	−0.154906	−	3.25187i	−0.00494324	−	0.103771i
$983$	2.57447	+	10.6121i	0.0821130	+	0.338474i	0.998019	−	0.0629194i	$-0.0200411\pi$
$983$	2.57447	+	10.6121i	0.0821130	+	0.338474i	−0.915906	+	0.401394i	$0.868526\pi$
$984$	−52.4531	+	29.5070i	−1.67214	+	0.940649i
$985$	−26.9494	−	6.53786i	−0.858679	−	0.208313i
$986$	2.71662	−	5.94858i	0.0865149	−	0.189441i
$987$	4.40475	+	1.26193i	0.140205	+	0.0401677i
$988$	−0.530408			−0.0168745
$989$	−7.98056	+	23.4224i	−0.253767	+	0.744789i
$990$	−32.4959	+	12.1738i	−1.03279	+	0.386910i
$991$	18.1260	−	14.2544i	0.575791	−	0.452807i	−0.287310	−	0.957838i	$-0.592761\pi$
$991$	18.1260	−	14.2544i	0.575791	−	0.452807i	0.863102	+	0.505030i	$0.168519\pi$
$992$	10.1011	+	14.1850i	0.320710	+	0.450374i
$993$	35.7846	+	23.5667i	1.13559	+	0.747866i
$994$	−28.9906	+	28.6424i	−0.919526	+	0.908481i
$995$	6.23424	−	21.2319i	0.197639	−	0.673096i
$996$	−2.38426	+	2.22304i	−0.0755482	+	0.0704397i
$997$	12.2491	+	8.72258i	0.387934	+	0.276247i	0.757339	−	0.653022i	$-0.226499\pi$
$997$	12.2491	+	8.72258i	0.387934	+	0.276247i	−0.369405	+	0.929269i	$0.620438\pi$
$998$	−26.8573	−	9.29541i	−0.850154	−	0.294241i
$999$	16.1945	−	25.9960i	0.512372	−	0.822477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.bb.a.26.19	✓	1200
3.2	odd	2	inner	483.2.bb.a.26.42	yes	1200
7.3	odd	6	inner	483.2.bb.a.164.19	yes	1200
21.17	even	6	inner	483.2.bb.a.164.42	yes	1200
23.8	even	11	inner	483.2.bb.a.215.42	yes	1200
69.8	odd	22	inner	483.2.bb.a.215.19	yes	1200
161.31	odd	66	inner	483.2.bb.a.353.42	yes	1200
483.353	even	66	inner	483.2.bb.a.353.19	yes	1200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.bb.a.26.19	✓	1200	1.1	even	1	trivial
483.2.bb.a.26.42	yes	1200	3.2	odd	2	inner
483.2.bb.a.164.19	yes	1200	7.3	odd	6	inner
483.2.bb.a.164.42	yes	1200	21.17	even	6	inner
483.2.bb.a.215.19	yes	1200	69.8	odd	22	inner
483.2.bb.a.215.42	yes	1200	23.8	even	11	inner
483.2.bb.a.353.19	yes	1200	483.353	even	66	inner
483.2.bb.a.353.42	yes	1200	161.31	odd	66	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.bb (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.397865 + 0.993819i) q^{2} +(-1.24011 - 1.20919i) q^{3} +(0.618088 + 0.589346i) q^{4} +(1.43145 + 4.13589i) q^{5} +(1.69511 - 0.751347i) q^{6} +(2.25080 + 1.39065i) q^{7} +(-2.77914 + 1.26919i) q^{8} +(0.0757244 + 2.99904i) q^{9} +O(q^{10})\)	\(q+(-0.397865 + 0.993819i) q^{2} +(-1.24011 - 1.20919i) q^{3} +(0.618088 + 0.589346i) q^{4} +(1.43145 + 4.13589i) q^{5} +(1.69511 - 0.751347i) q^{6} +(2.25080 + 1.39065i) q^{7} +(-2.77914 + 1.26919i) q^{8} +(0.0757244 + 2.99904i) q^{9} +(-4.67985 - 0.222929i) q^{10} +(-0.917592 - 2.29203i) q^{11} +(-0.0538642 - 1.47824i) q^{12} +(-0.665313 + 1.03525i) q^{13} +(-2.27757 + 1.68359i) q^{14} +(3.22593 - 6.85984i) q^{15} +(-0.0743508 - 1.56082i) q^{16} +(-0.788328 - 3.24953i) q^{17} +(-3.01064 - 1.11796i) q^{18} +(0.490460 + 0.118984i) q^{19} +(-1.55271 + 3.39996i) q^{20} +(-1.10966 - 4.44619i) q^{21} +2.64295 q^{22} +(4.77187 - 0.478842i) q^{23} +(4.98113 + 1.78658i) q^{24} +(-11.1263 + 8.74983i) q^{25} +(-0.764144 - 1.07309i) q^{26} +(3.53250 - 3.81070i) q^{27} +(0.571614 + 2.18604i) q^{28} +(0.514705 - 1.75292i) q^{29} +(5.53395 + 5.93528i) q^{30} +(-3.19645 - 2.27619i) q^{31} +(-4.19366 - 1.45144i) q^{32} +(-1.63359 + 3.95191i) q^{33} +(3.54309 + 0.509420i) q^{34} +(-2.52970 + 11.2997i) q^{35} +(-1.72067 + 1.89830i) q^{36} +(5.78778 - 1.11550i) q^{37} +(-0.313386 + 0.440089i) q^{38} +(2.07687 - 0.479327i) q^{39} +(-9.22744 - 9.67746i) q^{40} +(-7.44760 + 8.59499i) q^{41} +(4.86021 + 0.666183i) q^{42} +(-2.14338 + 4.69335i) q^{43} +(0.783648 - 1.95746i) q^{44} +(-12.2953 + 4.60616i) q^{45} +(-1.42268 + 4.93289i) q^{46} +(-0.499932 + 0.865907i) q^{47} +(-1.79512 + 2.02548i) q^{48} +(3.13217 + 6.26015i) q^{49} +(-4.26898 - 14.5388i) q^{50} +(-2.95169 + 4.98300i) q^{51} +(-1.02134 + 0.247775i) q^{52} +(5.06572 - 9.82613i) q^{53} +(2.38168 + 5.02682i) q^{54} +(8.16613 - 7.07599i) q^{55} +(-8.02029 - 1.00813i) q^{56} +(-0.464347 - 0.740611i) q^{57} +(1.53731 + 1.20895i) q^{58} +(-0.311971 + 6.54907i) q^{59} +(6.03672 - 2.33879i) q^{60} +(-1.03816 + 10.8721i) q^{61} +(3.53388 - 2.27108i) q^{62} +(-4.00019 + 6.85554i) q^{63} +(5.15753 - 5.95211i) q^{64} +(-5.23404 - 1.26976i) q^{65} +(-3.27753 - 3.19582i) q^{66} +(7.04287 - 5.53858i) q^{67} +(1.42784 - 2.47309i) q^{68} +(-6.49663 - 5.17627i) q^{69} +(-10.2234 - 7.00982i) q^{70} +(14.2424 - 2.04775i) q^{71} +(-4.01681 - 8.23867i) q^{72} +(5.75962 - 6.04051i) q^{73} +(-1.19415 + 6.19583i) q^{74} +(24.3780 + 2.60310i) q^{75} +(0.233024 + 0.362593i) q^{76} +(1.12211 - 6.43495i) q^{77} +(-0.349949 + 2.25474i) q^{78} +(6.14242 - 3.16664i) q^{79} +(6.34894 - 2.54173i) q^{80} +(-8.98853 + 0.454202i) q^{81} +(-5.57873 - 10.8212i) q^{82} +(-1.44316 - 1.66549i) q^{83} +(1.93448 - 3.40211i) q^{84} +(12.3113 - 7.91197i) q^{85} +(-3.81157 - 3.99746i) q^{86} +(-2.75791 + 1.55144i) q^{87} +(5.45915 + 5.20529i) q^{88} +(-3.32381 - 4.66764i) q^{89} +(0.314195 - 14.0520i) q^{90} +(-2.93716 + 1.40491i) q^{91} +(3.23164 + 2.51631i) q^{92} +(1.21160 + 6.68783i) q^{93} +(-0.661650 - 0.841356i) q^{94} +(0.209961 + 2.19881i) q^{95} +(3.44551 + 6.87086i) q^{96} +(-9.31283 - 8.06961i) q^{97} +(-7.46764 + 0.622108i) q^{98} +(6.80443 - 2.92546i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1200 q - 27 q^{3} - 74 q^{4} - 36 q^{7} - 13 q^{9}+O(q^{10}) \) 1200 * q - 27 * q^3 - 74 * q^4 - 36 * q^7 - 13 * q^9	\( 1200 q - 27 q^{3} - 74 q^{4} - 36 q^{7} - 13 q^{9} - 54 q^{10} - 15 q^{12} - 64 q^{15} + 38 q^{16} + 43 q^{18} - 54 q^{19} - 70 q^{21} - 160 q^{22} - 66 q^{24} + 34 q^{25} - 76 q^{28} - 23 q^{30} - 54 q^{31} - 3 q^{33} - 28 q^{36} + 26 q^{37} + 5 q^{39} - 30 q^{40} - 68 q^{42} - 176 q^{43} - 96 q^{45} - 22 q^{46} - 128 q^{49} - 23 q^{51} - 102 q^{52} + 21 q^{54} - 36 q^{57} + 58 q^{58} - 43 q^{60} - 126 q^{61} + 41 q^{63} + 40 q^{64} - 132 q^{66} - 10 q^{67} + 20 q^{70} + 59 q^{72} - 30 q^{73} - 81 q^{75} + 164 q^{78} - 14 q^{79} - 97 q^{81} - 66 q^{82} + 24 q^{84} - 56 q^{85} - 399 q^{87} - 74 q^{88} - 156 q^{91} + 8 q^{93} - 126 q^{94} - 117 q^{96} + 196 q^{99}+O(q^{100}) \) 1200 * q - 27 * q^3 - 74 * q^4 - 36 * q^7 - 13 * q^9 - 54 * q^10 - 15 * q^12 - 64 * q^15 + 38 * q^16 + 43 * q^18 - 54 * q^19 - 70 * q^21 - 160 * q^22 - 66 * q^24 + 34 * q^25 - 76 * q^28 - 23 * q^30 - 54 * q^31 - 3 * q^33 - 28 * q^36 + 26 * q^37 + 5 * q^39 - 30 * q^40 - 68 * q^42 - 176 * q^43 - 96 * q^45 - 22 * q^46 - 128 * q^49 - 23 * q^51 - 102 * q^52 + 21 * q^54 - 36 * q^57 + 58 * q^58 - 43 * q^60 - 126 * q^61 + 41 * q^63 + 40 * q^64 - 132 * q^66 - 10 * q^67 + 20 * q^70 + 59 * q^72 - 30 * q^73 - 81 * q^75 + 164 * q^78 - 14 * q^79 - 97 * q^81 - 66 * q^82 + 24 * q^84 - 56 * q^85 - 399 * q^87 - 74 * q^88 - 156 * q^91 + 8 * q^93 - 126 * q^94 - 117 * q^96 + 196 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more