LMFDB - Embedded newform 483.2.j.a.229.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(229,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("483.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.j (of order $6$, degree $2$, 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:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.15
Character	$\chi$	$=$	483.229
Dual form			483.2.j.a.367.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0934478 + 0.161856i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.982535 + 1.70180i) q^{4} +(-0.724626 + 1.25509i) q^{5} -0.186896i q^{6} +(2.60010 - 0.489382i) q^{7} -0.741054 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.135429 - 0.234571i) q^{10} +(4.61819 - 2.66631i) q^{11} +(-1.70180 - 0.982535i) q^{12} +3.91841i q^{13} +(-0.163764 + 0.466574i) q^{14} -1.44925i q^{15} +(-1.89582 + 3.28366i) q^{16} +(1.03831 + 1.79840i) q^{17} +(0.0934478 + 0.161856i) q^{18} +(-1.06710 + 1.84827i) q^{19} -2.84788 q^{20} +(-2.00706 + 1.72387i) q^{21} +0.996644i q^{22} +(-2.51606 - 4.08282i) q^{23} +(0.641772 - 0.370527i) q^{24} +(1.44983 + 2.51119i) q^{25} +(-0.634219 - 0.366167i) q^{26} +1.00000i q^{27} +(3.38752 + 3.94401i) q^{28} -8.65961 q^{29} +(0.234571 + 0.135429i) q^{30} +(-7.14716 + 4.12641i) q^{31} +(-1.09537 - 1.89724i) q^{32} +(-2.66631 + 4.61819i) q^{33} -0.388110 q^{34} +(-1.26988 + 3.61797i) q^{35} +1.96507 q^{36} +(5.53132 + 3.19351i) q^{37} +(-0.199436 - 0.345434i) q^{38} +(-1.95920 - 3.39344i) q^{39} +(0.536987 - 0.930089i) q^{40} -4.11260i q^{41} +(-0.0914633 - 0.485947i) q^{42} -10.1862i q^{43} +(9.07507 + 5.23949i) q^{44} +(0.724626 + 1.25509i) q^{45} +(0.895951 - 0.0257105i) q^{46} +(11.0034 + 6.35281i) q^{47} -3.79164i q^{48} +(6.52101 - 2.54488i) q^{49} -0.541935 q^{50} +(-1.79840 - 1.03831i) q^{51} +(-6.66835 + 3.84997i) q^{52} +(-4.43763 + 2.56207i) q^{53} +(-0.161856 - 0.0934478i) q^{54} +7.72832i q^{55} +(-1.92681 + 0.362658i) q^{56} -2.13420i q^{57} +(0.809222 - 1.40161i) q^{58} +(2.91345 - 1.68208i) q^{59} +(2.46634 - 1.42394i) q^{60} +(0.0910049 - 0.157625i) q^{61} -1.54242i q^{62} +(0.876232 - 2.49644i) q^{63} -7.17384 q^{64} +(-4.91795 - 2.83938i) q^{65} +(-0.498322 - 0.863119i) q^{66} +(8.60060 - 4.96556i) q^{67} +(-2.04035 + 3.53399i) q^{68} +(4.22039 + 2.27779i) q^{69} +(-0.466924 - 0.543630i) q^{70} -2.34739 q^{71} +(-0.370527 + 0.641772i) q^{72} +(10.6249 - 6.13431i) q^{73} +(-1.03378 + 0.596853i) q^{74} +(-2.51119 - 1.44983i) q^{75} -4.19385 q^{76} +(10.7029 - 9.19273i) q^{77} +0.732333 q^{78} +(2.40707 + 1.38972i) q^{79} +(-2.74752 - 4.75885i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.665651 + 0.384314i) q^{82} -12.3156 q^{83} +(-4.90568 - 1.72186i) q^{84} -3.00954 q^{85} +(1.64869 + 0.951873i) q^{86} +(7.49944 - 4.32981i) q^{87} +(-3.42233 + 1.97588i) q^{88} +(0.209480 - 0.362830i) q^{89} -0.270859 q^{90} +(1.91760 + 10.1882i) q^{91} +(4.47602 - 8.29335i) q^{92} +(4.12641 - 7.14716i) q^{93} +(-2.05649 + 1.18731i) q^{94} +(-1.54650 - 2.67861i) q^{95} +(1.89724 + 1.09537i) q^{96} -7.35396 q^{97} +(-0.197469 + 1.29328i) q^{98} -5.33263i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50}+ \cdots + 112 q^{98}+O(q^{100}) $ 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9 - 44 * q^16 - 4 * q^18 - 16 * q^23 - 12 * q^25 + 84 * q^26 + 24 * q^29 - 12 * q^31 + 8 * q^32 + 32 * q^35 - 72 * q^36 - 8 * q^46 - 12 * q^47 + 8 * q^49 - 96 * q^50 - 108 * q^52 - 24 * q^58 + 36 * q^59 + 168 * q^64 - 40 * q^70 - 16 * q^71 - 12 * q^72 + 48 * q^73 - 48 * q^75 - 32 * q^78 - 32 * q^81 - 24 * q^82 + 88 * q^85 + 36 * q^87 + 152 * q^92 + 24 * q^93 - 108 * q^94 - 44 * q^95 + 60 * q^96 + 112 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	−0.0934478	+	0.161856i	−0.0660776	+	0.114450i	−0.897171	−	0.441682i	$-0.854382\pi$
$2$	−0.0934478	+	0.161856i	−0.0660776	+	0.114450i	0.831094	+	0.556132i	$0.187715\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.982535	+	1.70180i	0.491268	+	0.850900i
$5$	−0.724626	+	1.25509i	−0.324063	+	0.561293i	−0.981322	−	0.192371i	$-0.938382\pi$
$5$	−0.724626	+	1.25509i	−0.324063	+	0.561293i	0.657260	+	0.753664i	$0.271715\pi$
$6$		−	0.186896i		−	0.0762998i
$7$	2.60010	−	0.489382i	0.982744	−	0.184969i
$7$	2.60010	−	0.489382i	0.982744	−	0.184969i
$8$	−0.741054			−0.262002
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.135429	−	0.234571i	−0.0428265	−	0.0741777i
$11$	4.61819	−	2.66631i	1.39244	−	0.803924i	0.398852	−	0.917015i	$-0.369409\pi$
$11$	4.61819	−	2.66631i	1.39244	−	0.803924i	0.993585	+	0.113092i	$0.0360753\pi$
$12$	−1.70180	−	0.982535i	−0.491268	−	0.283633i
$13$			3.91841i			1.08677i	0.839483	+	0.543385i	$0.182858\pi$
$13$			3.91841i			1.08677i	−0.839483	+	0.543385i	$0.817142\pi$
$14$	−0.163764	+	0.466574i	−0.0437677	+	0.124697i
$15$		−	1.44925i		−	0.374195i
$16$	−1.89582	+	3.28366i	−0.473955	+	0.820914i
$17$	1.03831	+	1.79840i	0.251827	+	0.436177i	0.964029	−	0.265798i	$-0.0856354\pi$
$17$	1.03831	+	1.79840i	0.251827	+	0.436177i	−0.712202	+	0.701975i	$0.752302\pi$
$18$	0.0934478	+	0.161856i	0.0220259	+	0.0381499i
$19$	−1.06710	+	1.84827i	−0.244810	+	0.424023i	−0.962078	−	0.272774i	$-0.912059\pi$
$19$	−1.06710	+	1.84827i	−0.244810	+	0.424023i	0.717268	+	0.696797i	$0.245392\pi$
$20$	−2.84788			−0.636806
$21$	−2.00706	+	1.72387i	−0.437976	+	0.376178i
$22$			0.996644i			0.212485i
$23$	−2.51606	−	4.08282i	−0.524636	−	0.851327i
$23$	−2.51606	−	4.08282i	−0.524636	−	0.851327i
$24$	0.641772	−	0.370527i	0.131001	−	0.0756335i
$25$	1.44983	+	2.51119i	0.289967	+	0.502237i
$26$	−0.634219	−	0.366167i	−0.124381	−	0.0718112i
$27$			1.00000i			0.192450i
$28$	3.38752	+	3.94401i	0.640180	+	0.745348i
$29$	−8.65961			−1.60805			−0.804025	−	0.594596i	$-0.797312\pi$
$29$	−8.65961			−1.60805			−0.804025	+	0.594596i	$0.797312\pi$
$30$	0.234571	+	0.135429i	0.0428265	+	0.0247259i
$31$	−7.14716	+	4.12641i	−1.28367	+	0.741126i	−0.977517	−	0.210857i	$-0.932374\pi$
$31$	−7.14716	+	4.12641i	−1.28367	+	0.741126i	−0.306151	+	0.951983i	$0.599041\pi$
$32$	−1.09537	−	1.89724i	−0.193637	−	0.335389i
$33$	−2.66631	+	4.61819i	−0.464146	+	0.803924i
$34$	−0.388110			−0.0665604
$35$	−1.26988	+	3.61797i	−0.214649	+	0.611549i
$36$	1.96507			0.327512
$37$	5.53132	+	3.19351i	0.909344	+	0.525010i	0.880220	−	0.474566i	$-0.157395\pi$
$37$	5.53132	+	3.19351i	0.909344	+	0.525010i	0.0291240	+	0.999576i	$0.490728\pi$
$38$	−0.199436	−	0.345434i	−0.0323528	−	0.0560368i
$39$	−1.95920	−	3.39344i	−0.313724	−	0.543385i
$40$	0.536987	−	0.930089i	0.0849051	−	0.147060i
$41$		−	4.11260i		−	0.642281i	−0.947032	−	0.321140i	$-0.895934\pi$
$41$		−	4.11260i		−	0.642281i	0.947032	−	0.321140i	$-0.104066\pi$
$42$	−0.0914633	−	0.485947i	−0.0141131	−	0.0749832i
$43$		−	10.1862i		−	1.55337i	−0.629887	−	0.776687i	$-0.716899\pi$
$43$		−	10.1862i		−	1.55337i	0.629887	−	0.776687i	$-0.283101\pi$
$44$	9.07507	+	5.23949i	1.36812	+	0.789883i
$45$	0.724626	+	1.25509i	0.108021	+	0.187098i
$46$	0.895951	−	0.0257105i	0.132101	−	0.00379081i
$47$	11.0034	+	6.35281i	1.60501	+	0.926653i	0.990464	+	0.137772i	$0.0439942\pi$
$47$	11.0034	+	6.35281i	1.60501	+	0.926653i	0.614546	+	0.788881i	$0.289339\pi$
$48$		−	3.79164i		−	0.547276i
$49$	6.52101	−	2.54488i	0.931573	−	0.363554i
$50$	−0.541935			−0.0766412
$51$	−1.79840	−	1.03831i	−0.251827	−	0.145392i
$52$	−6.66835	+	3.84997i	−0.924734	+	0.533895i
$53$	−4.43763	+	2.56207i	−0.609556	+	0.351927i	−0.772792	−	0.634660i	$-0.781140\pi$
$53$	−4.43763	+	2.56207i	−0.609556	+	0.351927i	0.163236	+	0.986587i	$0.447807\pi$
$54$	−0.161856	−	0.0934478i	−0.0220259	−	0.0127166i
$55$			7.72832i			1.04209i
$56$	−1.92681	+	0.362658i	−0.257481	+	0.0484622i
$57$		−	2.13420i		−	0.282682i
$58$	0.809222	−	1.40161i	0.106256	−	0.184041i
$59$	2.91345	−	1.68208i	0.379299	−	0.218988i	−0.298214	−	0.954499i	$-0.596391\pi$
$59$	2.91345	−	1.68208i	0.379299	−	0.218988i	0.677513	+	0.735511i	$0.263058\pi$
$60$	2.46634	−	1.42394i	0.318403	−	0.183830i
$61$	0.0910049	−	0.157625i	0.0116520	−	0.0201818i	−0.860141	−	0.510057i	$-0.829624\pi$
$61$	0.0910049	−	0.157625i	0.0116520	−	0.0201818i	0.871793	+	0.489875i	$0.162958\pi$
$62$		−	1.54242i		−	0.195887i
$63$	0.876232	−	2.49644i	0.110395	−	0.314522i
$64$	−7.17384			−0.896730
$65$	−4.91795	−	2.83938i	−0.609997	−	0.352182i
$66$	−0.498322	−	0.863119i	−0.0613392	−	0.106243i
$67$	8.60060	−	4.96556i	1.05073	−	0.606640i	0.127877	−	0.991790i	$-0.459184\pi$
$67$	8.60060	−	4.96556i	1.05073	−	0.606640i	0.922854	+	0.385150i	$0.125850\pi$
$68$	−2.04035	+	3.53399i	−0.247429	+	0.428559i
$69$	4.22039	+	2.27779i	0.508075	+	0.274214i
$70$	−0.466924	−	0.543630i	−0.0558081	−	0.0649762i
$71$	−2.34739			−0.278584			−0.139292	−	0.990251i	$-0.544483\pi$
$71$	−2.34739			−0.278584			−0.139292	+	0.990251i	$0.544483\pi$
$72$	−0.370527	+	0.641772i	−0.0436670	+	0.0756335i
$73$	10.6249	−	6.13431i	1.24355	−	0.717966i	0.273738	−	0.961804i	$-0.411740\pi$
$73$	10.6249	−	6.13431i	1.24355	−	0.717966i	0.969816	+	0.243838i	$0.0784066\pi$
$74$	−1.03378	+	0.596853i	−0.120174	+	0.0693828i
$75$	−2.51119	−	1.44983i	−0.289967	−	0.167412i
$76$	−4.19385			−0.481068
$77$	10.7029	−	9.19273i	1.21971	−	1.04761i
$78$	0.732333			0.0829204
$79$	2.40707	+	1.38972i	0.270817	+	0.156356i	0.629259	−	0.777196i	$-0.283359\pi$
$79$	2.40707	+	1.38972i	0.270817	+	0.156356i	−0.358442	+	0.933552i	$0.616692\pi$
$80$	−2.74752	−	4.75885i	−0.307182	−	0.532055i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.665651	+	0.384314i	0.0735088	+	0.0424404i
$83$	−12.3156			−1.35182			−0.675909	−	0.736985i	$-0.736249\pi$
$83$	−12.3156			−1.35182			−0.675909	+	0.736985i	$0.736249\pi$
$84$	−4.90568	−	1.72186i	−0.535254	−	0.187870i
$85$	−3.00954			−0.326430
$86$	1.64869	+	0.951873i	0.177783	+	0.102643i
$87$	7.49944	−	4.32981i	0.804025	−	0.464204i
$88$	−3.42233	+	1.97588i	−0.364821	+	0.210630i
$89$	0.209480	−	0.362830i	0.0222048	−	0.0384599i	−0.854709	−	0.519107i	$-0.826265\pi$
$89$	0.209480	−	0.362830i	0.0222048	−	0.0384599i	0.876914	+	0.480647i	$0.159598\pi$
$90$	−0.270859			−0.0285510
$91$	1.91760	+	10.1882i	0.201019	+	1.06802i
$92$	4.47602	−	8.29335i	0.466658	−	0.864642i
$93$	4.12641	−	7.14716i	0.427889	−	0.741126i
$94$	−2.05649	+	1.18731i	−0.212110	+	0.122462i
$95$	−1.54650	−	2.67861i	−0.158667	−	0.274820i
$96$	1.89724	+	1.09537i	0.193637	+	0.111796i
$97$	−7.35396			−0.746681			−0.373341	−	0.927694i	$-0.621788\pi$
$97$	−7.35396			−0.746681			−0.373341	+	0.927694i	$0.621788\pi$
$98$	−0.197469	+	1.29328i	−0.0199474	+	0.130641i
$99$		−	5.33263i		−	0.535949i
$100$	−2.84903	+	4.93466i	−0.284903	+	0.493466i
$101$	5.26761	−	3.04126i	0.524147	−	0.302616i	−0.214483	−	0.976728i	$-0.568807\pi$
$101$	5.26761	−	3.04126i	0.524147	−	0.302616i	0.738630	+	0.674112i	$0.235473\pi$
$102$	0.336113	−	0.194055i	0.0332802	−	0.0192143i
$103$	6.30610	−	10.9225i	0.621358	−	1.07622i	−0.367875	−	0.929875i	$-0.619915\pi$
$103$	6.30610	−	10.9225i	0.621358	−	1.07622i	0.989233	−	0.146349i	$-0.0467521\pi$
$104$		−	2.90375i		−	0.284736i
$105$	−0.709237	−	3.76820i	−0.0692145	−	0.367738i
$106$		−	0.957678i		−	0.0930179i
$107$	7.42553	+	4.28713i	0.717853	+	0.414453i	0.813962	−	0.580918i	$-0.197306\pi$
$107$	7.42553	+	4.28713i	0.717853	+	0.414453i	−0.0961088	+	0.995371i	$0.530640\pi$
$108$	−1.70180	+	0.982535i	−0.163756	+	0.0945445i
$109$	−14.5330	+	8.39061i	−1.39201	+	0.803675i	−0.993537	−	0.113507i	$-0.963792\pi$
$109$	−14.5330	+	8.39061i	−1.39201	+	0.803675i	−0.398469	+	0.917182i	$0.630458\pi$
$110$	−1.25088	−	0.722194i	−0.119266	−	0.0688585i
$111$	−6.38702			−0.606229
$112$	−3.32236	+	9.46561i	−0.313933	+	0.894416i
$113$		−	18.5060i		−	1.74090i	−0.492259	−	0.870449i	$-0.663829\pi$
$113$		−	18.5060i		−	1.74090i	0.492259	−	0.870449i	$-0.336171\pi$
$114$	0.345434	+	0.199436i	0.0323528	+	0.0186789i
$115$	6.94751	−	0.199368i	0.647858	−	0.0185912i
$116$	−8.50837	−	14.7369i	−0.789982	−	1.36829i
$117$	3.39344	+	1.95920i	0.313724	+	0.181128i
$118$			0.628747i			0.0578809i
$119$	3.57981	+	4.16789i	0.328160	+	0.382070i
$120$			1.07397i			0.0980399i
$121$	8.71845	−	15.1008i	0.792587	−	1.37280i
$122$	0.0170084	+	0.0294594i	0.00153987	+	0.00266713i
$123$	2.05630	+	3.56162i	0.185411	+	0.321140i
$124$	−14.0447	−	8.10869i	−1.26125	−	0.728182i
$125$	−11.4486			−1.02399
$126$	0.322183	+	0.375111i	0.0287023	+	0.0334175i
$127$	18.3991			1.63266			0.816328	−	0.577588i	$-0.196006\pi$
$127$	18.3991			1.63266			0.816328	+	0.577588i	$0.196006\pi$
$128$	2.86113	−	4.95562i	0.252890	−	0.438019i
$129$	5.09308	+	8.82147i	0.448420	+	0.776687i
$130$	0.919143	−	0.530667i	0.0806142	−	0.0465426i
$131$	−5.27311	−	3.04443i	−0.460713	−	0.265993i	0.251631	−	0.967823i	$-0.419033\pi$
$131$	−5.27311	−	3.04443i	−0.460713	−	0.265993i	−0.712344	+	0.701830i	$0.752366\pi$
$132$	−10.4790			−0.912079
$133$	−1.87005	+	5.32791i	−0.162154	+	0.461988i
$134$			1.85608i			0.160341i
$135$	−1.25509	−	0.724626i	−0.108021	−	0.0623659i
$136$	−0.769443	−	1.33271i	−0.0659792	−	0.114279i
$137$	8.28401	−	4.78277i	0.707750	−	0.408620i	−0.102477	−	0.994735i	$-0.532677\pi$
$137$	8.28401	−	4.78277i	0.707750	−	0.408620i	0.810228	+	0.586115i	$0.199344\pi$
$138$	−0.763061	+	0.470241i	−0.0649561	+	0.0400296i
$139$			9.96244i			0.845003i	0.906362	+	0.422501i	$0.138848\pi$
$139$			9.96244i			0.845003i	−0.906362	+	0.422501i	$0.861152\pi$
$140$	−7.40477	+	1.39370i	−0.625817	+	0.117789i
$141$	−12.7056			−1.07001
$142$	0.219358	−	0.379940i	0.0184081	−	0.0318838i
$143$	10.4477	+	18.0960i	0.873681	+	1.51326i
$144$	1.89582	+	3.28366i	0.157985	+	0.273638i
$145$	6.27498	−	10.8686i	0.521109	−	0.902587i
$146$			2.29295i			0.189766i
$147$	−4.37492	+	5.46444i	−0.360837	+	0.450699i
$148$			12.5509i			1.03168i
$149$	8.13457	+	4.69649i	0.666410	+	0.384752i	0.794715	−	0.606983i	$-0.207620\pi$
$149$	8.13457	+	4.69649i	0.666410	+	0.384752i	−0.128305	+	0.991735i	$0.540954\pi$
$150$	0.469330	−	0.270968i	0.0383206	−	0.0221244i
$151$	2.51092	+	4.34905i	0.204336	+	0.353920i	0.949921	−	0.312490i	$-0.101163\pi$
$151$	2.51092	+	4.34905i	0.204336	+	0.353920i	−0.745585	+	0.666411i	$0.767830\pi$
$152$	0.790779	−	1.36967i	0.0641406	−	0.111095i
$153$	2.07662			0.167884
$154$	0.487739	+	2.59137i	0.0393032	+	0.208819i
$155$		−	11.9604i		−	0.960684i
$156$	3.84997	−	6.66835i	0.308245	−	0.533895i
$157$	−12.1654	−	21.0711i	−0.970904	−	1.68165i	−0.692839	−	0.721092i	$-0.743640\pi$
$157$	−12.1654	−	21.0711i	−0.970904	−	1.68165i	−0.278064	−	0.960562i	$-0.589693\pi$
$158$	−0.449871	+	0.259733i	−0.0357898	+	0.0206633i
$159$	2.56207	−	4.43763i	0.203185	−	0.351927i
$160$	3.17495			0.251002
$161$	−8.54007	−	9.38441i	−0.673052	−	0.739595i
$162$	0.186896			0.0146839
$163$	1.58146	−	2.73917i	0.123869	−	0.214548i	−0.797421	−	0.603423i	$-0.793803\pi$
$163$	1.58146	−	2.73917i	0.123869	−	0.214548i	0.921290	+	0.388875i	$0.127136\pi$
$164$	6.99883	−	4.04078i	0.546517	−	0.315532i
$165$	−3.86416	−	6.69292i	−0.300824	−	0.521043i
$166$	1.15087	−	1.99337i	0.0893248	−	0.154715i
$167$			3.69594i			0.286001i	0.989723	+	0.143000i	$0.0456750\pi$
$167$			3.69594i			0.286001i	−0.989723	+	0.143000i	$0.954325\pi$
$168$	1.48734	−	1.27748i	0.114751	−	0.0985595i
$169$	−2.35392			−0.181071
$170$	0.281235	−	0.487113i	0.0215697	−	0.0373599i
$171$	1.06710	+	1.84827i	0.0816032	+	0.141341i
$172$	17.3348	−	10.0083i	1.32177	−	0.763122i
$173$	−6.41803	−	3.70545i	−0.487954	−	0.281720i	0.235771	−	0.971809i	$-0.424238\pi$
$173$	−6.41803	−	3.70545i	−0.487954	−	0.281720i	−0.723725	+	0.690088i	$0.757572\pi$
$174$			1.61844i			0.122694i
$175$	4.99864	+	5.81981i	0.377862	+	0.439936i
$176$			20.2194i			1.52409i
$177$	−1.68208	+	2.91345i	−0.126433	+	0.218988i
$178$	0.0391509	+	0.0678113i	0.00293448	+	0.00508267i
$179$	5.23012	+	9.05884i	0.390918	+	0.677090i	0.992571	−	0.121668i	$-0.0388243\pi$
$179$	5.23012	+	9.05884i	0.390918	+	0.677090i	−0.601653	+	0.798758i	$0.705491\pi$
$180$	−1.42394	+	2.46634i	−0.106134	+	0.183830i
$181$	−0.964418			−0.0716846			−0.0358423	−	0.999357i	$-0.511411\pi$
$181$	−0.964418			−0.0716846			−0.0358423	+	0.999357i	$0.511411\pi$
$182$	−1.82823	−	0.641693i	−0.135517	−	0.0475655i
$183$			0.182010i			0.0134546i
$184$	1.86454	+	3.02559i	0.137456	+	0.223049i
$185$	−8.01628	+	4.62820i	−0.589369	+	0.340272i
$186$	0.771208	+	1.33577i	0.0565477	+	0.0979436i
$187$	9.59021	+	5.53691i	0.701306	+	0.404899i
$188$			24.9674i			1.82094i
$189$	0.489382	+	2.60010i	0.0355973	+	0.189129i
$190$	0.578067			0.0419374
$191$	7.75783	+	4.47899i	0.561337	+	0.324088i	0.753682	−	0.657239i	$-0.228276\pi$
$191$	7.75783	+	4.47899i	0.561337	+	0.324088i	−0.192345	+	0.981327i	$0.561609\pi$
$192$	6.21273	−	3.58692i	0.448365	−	0.258864i
$193$	1.79919	+	3.11629i	0.129508	+	0.224315i	0.923486	−	0.383632i	$-0.125327\pi$
$193$	1.79919	+	3.11629i	0.129508	+	0.224315i	−0.793978	+	0.607947i	$0.791993\pi$
$194$	0.687211	−	1.19028i	0.0493389	−	0.0854575i
$195$	5.67876			0.406664
$196$	10.7380	+	8.59703i	0.767000	+	0.614073i
$197$	2.75200			0.196072			0.0980359	−	0.995183i	$-0.468744\pi$
$197$	2.75200			0.196072			0.0980359	+	0.995183i	$0.468744\pi$
$198$	0.863119	+	0.498322i	0.0613392	+	0.0354142i
$199$	−6.97707	−	12.0846i	−0.494591	−	0.856657i	0.505389	−	0.862891i	$-0.331349\pi$
$199$	−6.97707	−	12.0846i	−0.494591	−	0.856657i	−0.999981	+	0.00623445i	$0.998016\pi$
$200$	−1.07441	−	1.86093i	−0.0759720	−	0.131587i
$201$	−4.96556	+	8.60060i	−0.350244	+	0.606640i
$202$			1.13679i			0.0799846i
$203$	−22.5158	+	4.23785i	−1.58030	+	0.297439i
$204$		−	4.08070i		−	0.285706i
$205$	5.16168	+	2.98010i	0.360508	+	0.208139i
$206$	1.17858	+	2.04136i	0.0821157	+	0.142228i
$207$	−4.79386	+	0.137566i	−0.333196	+	0.00956152i
$208$	−12.8667	−	7.42860i	−0.892146	−	0.515081i
$209$			11.3809i			0.787233i
$210$	0.676183	+	0.237335i	0.0466610	+	0.0163777i
$211$	−9.73927			−0.670479			−0.335240	−	0.942133i	$-0.608817\pi$
$211$	−9.73927			−0.670479			−0.335240	+	0.942133i	$0.608817\pi$
$212$	−8.72026	−	5.03464i	−0.598910	−	0.345781i
$213$	2.03290	−	1.17369i	0.139292	−	0.0804203i
$214$	−1.38780	+	0.801246i	−0.0948680	+	0.0547721i
$215$	12.7845	+	7.38115i	0.871897	+	0.503390i
$216$		−	0.741054i		−	0.0504223i
$217$	−16.5639	+	14.2268i	−1.12443	+	0.965776i
$218$		−	3.13634i		−	0.212420i
$219$	−6.13431	+	10.6249i	−0.414518	+	0.717966i
$220$	−13.1521	+	7.59334i	−0.886711	+	0.511943i
$221$	−7.04688	+	4.06852i	−0.474024	+	0.273678i
$222$	0.596853	−	1.03378i	0.0400582	−	0.0693828i
$223$		−	21.7488i		−	1.45641i	−0.685361	−	0.728203i	$-0.740356\pi$
$223$		−	21.7488i		−	1.45641i	0.685361	−	0.728203i	$-0.259644\pi$
$224$	−3.77656	−	4.39696i	−0.252332	−	0.293784i
$225$	2.89967			0.193311
$226$	2.99531	+	1.72934i	0.199245	+	0.115034i
$227$	11.0671	+	19.1688i	0.734550	+	1.27228i	0.954920	+	0.296862i	$0.0959402\pi$
$227$	11.0671	+	19.1688i	0.734550	+	1.27228i	−0.220370	+	0.975416i	$0.570726\pi$
$228$	3.63198	−	2.09693i	0.240534	−	0.138872i
$229$	9.06872	−	15.7075i	0.599278	−	1.03798i	−0.393650	−	0.919260i	$-0.628788\pi$
$229$	9.06872	−	15.7075i	0.599278	−	1.03798i	0.992928	−	0.118719i	$-0.0378789\pi$
$230$	−0.616960	+	1.14313i	−0.0406811	+	0.0753757i
$231$	−4.67262	+	13.3126i	−0.307436	+	0.875904i
$232$	6.41724			0.421312
$233$	−0.468161	+	0.810879i	−0.0306702	+	0.0531224i	−0.880953	−	0.473204i	$-0.843098\pi$
$233$	−0.468161	+	0.810879i	−0.0306702	+	0.0531224i	0.850283	+	0.526326i	$0.176431\pi$
$234$	−0.634219	+	0.366167i	−0.0414602	+	0.0239371i
$235$	−15.9467	+	9.20683i	−1.04025	+	0.600587i
$236$	5.72513	+	3.30541i	0.372674	+	0.215164i
$237$	−2.77945			−0.180544
$238$	−1.00912	+	0.189934i	−0.0654118	+	0.0123116i
$239$	−6.45167			−0.417324			−0.208662	−	0.977988i	$-0.566911\pi$
$239$	−6.45167			−0.417324			−0.208662	+	0.977988i	$0.566911\pi$
$240$	4.75885	+	2.74752i	0.307182	+	0.177352i
$241$	2.33037	+	4.03632i	0.150112	+	0.260002i	0.931269	−	0.364333i	$-0.118703\pi$
$241$	2.33037	+	4.03632i	0.150112	+	0.260002i	−0.781156	+	0.624335i	$0.785370\pi$
$242$	1.62944	+	2.82227i	0.104744	+	0.181423i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	0.357662			0.0228970
$245$	−1.53124	+	10.0285i	−0.0978276	+	0.640700i
$246$	−0.768627			−0.0490059
$247$	−7.24228	−	4.18133i	−0.460815	−	0.266052i
$248$	5.29643	−	3.05790i	0.336324	−	0.194177i
$249$	10.6657	−	6.15782i	0.675909	−	0.390236i
$250$	1.06985	−	1.85303i	0.0676631	−	0.117196i
$251$	26.0444			1.64391			0.821953	−	0.569555i	$-0.192885\pi$
$251$	26.0444			1.64391			0.821953	+	0.569555i	$0.192885\pi$
$252$	5.10937	−	0.961669i	0.321860	−	0.0605795i
$253$	−22.5057	−	12.1466i	−1.41492	−	0.763651i
$254$	−1.71936	+	2.97801i	−0.107882	+	0.186857i
$255$	2.60634	−	1.50477i	0.163215	−	0.0942324i
$256$	−6.63911	−	11.4993i	−0.414944	−	0.718704i
$257$	−26.5881	−	15.3506i	−1.65852	−	0.957546i	−0.973400	−	0.229113i	$-0.926417\pi$
$257$	−26.5881	−	15.3506i	−1.65852	−	0.957546i	−0.685118	−	0.728432i	$-0.740249\pi$
$258$	−1.90375			−0.118522
$259$	15.9448	+	5.59651i	0.990763	+	0.347750i
$260$		−	11.1592i		−	0.692062i
$261$	−4.32981	+	7.49944i	−0.268008	+	0.464204i
$262$	0.985520	−	0.568990i	0.0608856	−	0.0351523i
$263$	14.7869	−	8.53721i	0.911798	−	0.526427i	0.0307889	−	0.999526i	$-0.490198\pi$
$263$	14.7869	−	8.53721i	0.911798	−	0.526427i	0.881009	+	0.473099i	$0.156865\pi$
$264$	1.97588	−	3.42233i	0.121607	−	0.210630i
$265$		−	7.42616i		−	0.456186i
$266$	−0.687603	−	0.800561i	−0.0421596	−	0.0490855i
$267$			0.418960i			0.0256399i
$268$	16.9008	+	9.75768i	1.03238	+	0.596045i
$269$	−10.0488	+	5.80169i	−0.612687	+	0.353735i	−0.774016	−	0.633165i	$-0.781755\pi$
$269$	−10.0488	+	5.80169i	−0.612687	+	0.353735i	0.161329	+	0.986901i	$0.448422\pi$
$270$	0.234571	−	0.135429i	0.0142755	−	0.00824197i
$271$	−13.5116	−	7.80093i	−0.820772	−	0.473873i	0.0299105	−	0.999553i	$-0.490478\pi$
$271$	−13.5116	−	7.80093i	−0.820772	−	0.473873i	−0.850683	+	0.525680i	$0.823811\pi$
$272$	−7.87378			−0.477418
$273$	−6.75481	−	7.86448i	−0.408820	−	0.475980i
$274$			1.78776i			0.108002i
$275$	13.3912	+	7.73143i	0.807521	+	0.466223i
$276$	0.270327	+	9.42027i	0.0162718	+	0.567033i
$277$	2.85589	+	4.94655i	0.171594	+	0.297209i	0.938977	−	0.343979i	$-0.111775\pi$
$277$	2.85589	+	4.94655i	0.171594	+	0.297209i	−0.767383	+	0.641189i	$0.778442\pi$
$278$	−1.61248	−	0.930968i	−0.0967103	−	0.0558357i
$279$			8.25283i			0.494084i
$280$	0.941050	−	2.68111i	0.0562385	−	0.160227i
$281$		−	4.03042i		−	0.240435i	−0.992748	−	0.120217i	$-0.961641\pi$
$281$		−	4.03042i		−	0.240435i	0.992748	−	0.120217i	$-0.0383592\pi$
$282$	1.18731	−	2.05649i	0.0707034	−	0.122462i
$283$	9.82335	+	17.0145i	0.583937	+	1.01141i	0.995007	+	0.0998053i	$0.0318220\pi$
$283$	9.82335	+	17.0145i	0.583937	+	1.01141i	−0.411070	+	0.911604i	$0.634845\pi$
$284$	−2.30639	−	3.99479i	−0.136859	−	0.237047i
$285$	2.67861	+	1.54650i	0.158667	+	0.0916066i
$286$	−3.90526			−0.230923
$287$	−2.01263	−	10.6932i	−0.118802	−	0.631198i
$288$	−2.19075			−0.129091
$289$	6.34383	−	10.9878i	0.373167	−	0.646343i
$290$	1.17277	+	2.03129i	0.0688672	+	0.119281i
$291$	6.36871	−	3.67698i	0.373341	−	0.215548i
$292$	20.8787	+	12.0543i	1.22184	+	0.705427i
$293$	−13.5839			−0.793579			−0.396790	−	0.917910i	$-0.629876\pi$
$293$	−13.5839			−0.793579			−0.396790	+	0.917910i	$0.629876\pi$
$294$	−0.475627	−	1.21875i	−0.0277391	−	0.0710788i
$295$			4.87552i			0.283864i
$296$	−4.09901	−	2.36656i	−0.238250	−	0.137554i
$297$	2.66631	+	4.61819i	0.154715	+	0.267975i
$298$	−1.52031	+	0.877754i	−0.0880694	+	0.0508469i
$299$	15.9982	−	9.85897i	0.925197	−	0.570159i
$300$		−	5.69805i		−	0.328977i
$301$	−4.98492	−	26.4850i	−0.287326	−	1.52657i
$302$	−0.938561			−0.0540081
$303$	−3.04126	+	5.26761i	−0.174716	+	0.302616i
$304$	−4.04606	−	7.00798i	−0.232057	−	0.401935i
$305$	0.131889	+	0.228438i	0.00755194	+	0.0130803i
$306$	−0.194055	+	0.336113i	−0.0110934	+	0.0192143i
$307$		−	10.1146i		−	0.577269i	−0.957439	−	0.288635i	$-0.906799\pi$
$307$		−	10.1146i		−	0.577269i	0.957439	−	0.288635i	$-0.0932013\pi$
$308$	26.1602	+	9.18202i	1.49061	+	0.523194i
$309$			12.6122i			0.717483i
$310$	1.93587	+	1.11768i	0.109950	+	0.0634797i
$311$	−11.0548	+	6.38247i	−0.626858	+	0.361917i	−0.779534	−	0.626359i	$-0.784544\pi$
$311$	−11.0548	+	6.38247i	−0.626858	+	0.361917i	0.152676	+	0.988276i	$0.451211\pi$
$312$	1.45188	+	2.51472i	0.0821963	+	0.142368i
$313$	−10.3943	+	18.0035i	−0.587520	+	1.01762i	0.407036	+	0.913412i	$0.366562\pi$
$313$	−10.3943	+	18.0035i	−0.587520	+	1.01762i	−0.994556	+	0.104203i	$0.966771\pi$
$314$	4.54731			0.256620
$315$	2.49832	+	2.90873i	0.140764	+	0.163889i
$316$			5.46181i			0.307251i
$317$	−13.8649	+	24.0147i	−0.778730	+	1.34880i	0.153945	+	0.988079i	$0.450802\pi$
$317$	−13.8649	+	24.0147i	−0.778730	+	1.34880i	−0.932674	+	0.360720i	$0.882531\pi$
$318$	0.478839	+	0.829374i	0.0268520	+	0.0465090i
$319$	−39.9917	+	23.0892i	−2.23911	+	1.29275i
$320$	5.19835	−	9.00381i	0.290597	−	0.503328i
$321$	−8.57427			−0.478569
$322$	2.31698	−	0.505312i	0.129120	−	0.0281599i
$323$	−4.43192			−0.246598
$324$	0.982535	−	1.70180i	0.0545853	−	0.0945445i
$325$	−9.83986	+	5.68104i	−0.545817	+	0.315128i
$326$	0.295568	+	0.511938i	0.0163700	+	0.0283536i
$327$	8.39061	−	14.5330i	0.464002	−	0.803675i
$328$			3.04766i			0.168279i
$329$	31.7188	+	11.1331i	1.74872	+	0.613786i
$330$	1.44439			0.0795110
$331$	−4.21629	+	7.30282i	−0.231748	+	0.401399i	−0.958323	−	0.285688i	$-0.907778\pi$
$331$	−4.21629	+	7.30282i	−0.231748	+	0.401399i	0.726575	+	0.687088i	$0.241111\pi$
$332$	−12.1006	−	20.9588i	−0.664104	−	1.15026i
$333$	5.53132	−	3.19351i	0.303115	−	0.175003i
$334$	−0.598212	−	0.345378i	−0.0327327	−	0.0188982i
$335$			14.3927i			0.786357i
$336$	−1.85556	−	9.85863i	−0.101229	−	0.537833i
$337$		−	24.2495i		−	1.32095i	−0.750847	−	0.660477i	$-0.770354\pi$
$337$		−	24.2495i		−	1.32095i	0.750847	−	0.660477i	$-0.229646\pi$
$338$	0.219969	−	0.380997i	0.0119647	−	0.0207235i
$339$	9.25300	+	16.0267i	0.502554	+	0.870449i
$340$	−2.95698	−	5.12164i	−0.160365	−	0.277760i
$341$	−22.0046	+	38.1131i	−1.19162	+	2.06394i
$342$	−0.398873			−0.0215686
$343$	15.7098	−	9.80820i	0.848252	−	0.529593i
$344$			7.54849i			0.406987i
$345$	−5.91703	+	3.64641i	−0.318562	+	0.196316i
$346$	1.19950	−	0.692533i	0.0644856	−	0.0372308i
$347$	10.1286	+	17.5432i	0.543730	+	0.941768i	0.998686	+	0.0512539i	$0.0163218\pi$
$347$	10.1286	+	17.5432i	0.543730	+	0.941768i	−0.454956	+	0.890514i	$0.650345\pi$
$348$	14.7369	+	8.50837i	0.789982	+	0.456097i
$349$		−	13.3859i		−	0.716532i	−0.933620	−	0.358266i	$-0.883368\pi$
$349$		−	13.3859i		−	0.716532i	0.933620	−	0.358266i	$-0.116632\pi$
$350$	−1.40908	+	0.265213i	−0.0753187	+	0.0141762i
$351$	−3.91841			−0.209149
$352$	−10.1173	−	5.84122i	−0.539254	−	0.311338i
$353$	16.5588	−	9.56026i	0.881339	−	0.508841i	0.0102390	−	0.999948i	$-0.496741\pi$
$353$	16.5588	−	9.56026i	0.881339	−	0.508841i	0.871100	+	0.491107i	$0.163407\pi$
$354$	−0.314374	−	0.544511i	−0.0167088	−	0.0289404i
$355$	1.70098	−	2.94618i	0.0902786	−	0.156367i
$356$	0.823286			0.0436341
$357$	−5.18415	−	1.81960i	−0.274374	−	0.0963033i
$358$	−1.95497			−0.103324
$359$	−24.2700	−	14.0123i	−1.28092	−	0.739539i	−0.303903	−	0.952703i	$-0.598290\pi$
$359$	−24.2700	−	14.0123i	−1.28092	−	0.739539i	−0.977016	+	0.213164i	$0.931623\pi$
$360$	−0.536987	−	0.930089i	−0.0283017	−	0.0490200i
$361$	7.22259	+	12.5099i	0.380137	+	0.658416i
$362$	0.0901227	−	0.156097i	0.00473675	−	0.00820429i
$363$			17.4369i			0.915200i
$364$	−15.4542	+	13.2737i	−0.810023	+	0.695729i
$365$			17.7803i			0.930664i
$366$	−0.0294594	−	0.0170084i	−0.00153987	−	0.000889044i
$367$	−1.27482	−	2.20805i	−0.0665450	−	0.115259i	0.830833	−	0.556521i	$-0.187864\pi$
$367$	−1.27482	−	2.20805i	−0.0665450	−	0.115259i	−0.897378	+	0.441262i	$0.854531\pi$
$368$	18.1766	−	0.521602i	0.947520	−	0.0271904i
$369$	−3.56162	−	2.05630i	−0.185411	−	0.107047i
$370$		−	1.72998i		−	0.0899374i
$371$	−10.2844	+	8.83332i	−0.533942	+	0.458603i
$372$	16.2174			0.840832
$373$	9.30258	+	5.37085i	0.481669	+	0.278092i	0.721112	−	0.692819i	$-0.243631\pi$
$373$	9.30258	+	5.37085i	0.481669	+	0.278092i	−0.239443	+	0.970911i	$0.576965\pi$
$374$	−1.79237	+	1.03482i	−0.0926811	+	0.0535095i
$375$	9.91479	−	5.72430i	0.511997	−	0.295602i
$376$	−8.15411	−	4.70778i	−0.420516	−	0.242785i
$377$		−	33.9319i		−	1.74758i
$378$	−0.466574	−	0.163764i	−0.0239980	−	0.00842310i
$379$		−	5.96074i		−	0.306183i	−0.988212	−	0.153091i	$-0.951077\pi$
$379$		−	5.96074i		−	0.306183i	0.988212	−	0.153091i	$-0.0489229\pi$
$380$	3.03897	−	5.26366i	0.155896	−	0.270020i
$381$	−15.9341	+	9.19955i	−0.816328	+	0.471307i
$382$	−1.44990	+	0.837102i	−0.0741835	+	0.0428299i
$383$	6.39922	−	11.0838i	0.326985	−	0.566355i	−0.654927	−	0.755692i	$-0.727301\pi$
$383$	6.39922	−	11.0838i	0.326985	−	0.566355i	0.981912	+	0.189337i	$0.0606340\pi$
$384$			5.72226i			0.292013i
$385$	3.78210	+	20.0944i	0.192754	+	1.02410i
$386$	−0.672521			−0.0342304
$387$	−8.82147	−	5.09308i	−0.448420	−	0.258896i
$388$	−7.22552	−	12.5150i	−0.366820	−	0.635351i
$389$	19.3223	−	11.1558i	0.979682	−	0.565619i	0.0775077	−	0.996992i	$-0.475304\pi$
$389$	19.3223	−	11.1558i	0.979682	−	0.565619i	0.902174	+	0.431372i	$0.141970\pi$
$390$	−0.530667	+	0.919143i	−0.0268714	+	0.0465426i
$391$	4.73010	−	8.76412i	0.239212	−	0.443221i
$392$	−4.83242	+	1.88589i	−0.244074	+	0.0952520i
$393$	6.08886			0.307142
$394$	−0.257168	+	0.445428i	−0.0129559	+	0.0224404i
$395$	−3.48845	+	2.01406i	−0.175523	+	0.101338i
$396$	9.07507	−	5.23949i	0.456039	−	0.263294i
$397$	4.46097	+	2.57554i	0.223890	+	0.129263i	0.607750	−	0.794128i	$-0.292072\pi$
$397$	4.46097	+	2.57554i	0.223890	+	0.129263i	−0.383860	+	0.923391i	$0.625406\pi$
$398$	2.60797			0.130725
$399$	−1.04444	−	5.54913i	−0.0522873	−	0.277804i
$400$	−10.9945			−0.549725
$401$	−7.05763	−	4.07473i	−0.352441	−	0.203482i	0.313319	−	0.949648i	$-0.398559\pi$
$401$	−7.05763	−	4.07473i	−0.352441	−	0.203482i	−0.665760	+	0.746166i	$0.731893\pi$
$402$	−0.928041	−	1.60741i	−0.0462865	−	0.0801706i
$403$	−16.1690	−	28.0055i	−0.805434	−	1.39505i
$404$	10.3512	+	5.97628i	0.514993	+	0.297331i
$405$	1.44925			0.0720139
$406$	1.41813	−	4.04035i	0.0703807	−	0.200519i
$407$	34.0596			1.68827
$408$	1.33271	+	0.769443i	0.0659792	+	0.0380931i
$409$	17.7447	−	10.2449i	0.877417	−	0.506577i	0.00761097	−	0.999971i	$-0.497577\pi$
$409$	17.7447	−	10.2449i	0.877417	−	0.506577i	0.869806	+	0.493394i	$0.164244\pi$
$410$	−0.964696	+	0.556967i	−0.0476429	+	0.0275067i
$411$	−4.78277	+	8.28401i	−0.235917	+	0.408620i
$412$	24.7838			1.22101
$413$	6.75207	−	5.79936i	0.332248	−	0.285368i
$414$	0.425709	−	0.788771i	0.0209225	−	0.0387660i
$415$	8.92424	−	15.4572i	0.438074	−	0.758766i
$416$	7.43418	−	4.29212i	0.364490	−	0.210439i
$417$	−4.98122	−	8.62772i	−0.243931	−	0.422501i
$418$	−1.84207	−	1.06352i	−0.0900986	−	0.0520184i
$419$	−29.6118			−1.44663			−0.723316	−	0.690517i	$-0.757383\pi$
$419$	−29.6118			−1.44663			−0.723316	+	0.690517i	$0.757383\pi$
$420$	5.71587	−	4.90936i	0.278906	−	0.239552i
$421$		−	24.5725i		−	1.19759i	−0.800903	−	0.598794i	$-0.795647\pi$
$421$		−	24.5725i		−	1.19759i	0.800903	−	0.598794i	$-0.204353\pi$
$422$	0.910113	−	1.57636i	0.0443036	−	0.0767361i
$423$	11.0034	−	6.35281i	0.535003	−	0.308884i
$424$	3.28853	−	1.89863i	0.159705	−	0.0922057i
$425$	−3.01075	+	5.21477i	−0.146043	+	0.252954i
$426$			0.438717i			0.0212559i
$427$	0.159483	−	0.454377i	0.00771791	−	0.0219888i
$428$			16.8490i			0.814429i
$429$	−18.0960	−	10.4477i	−0.873681	−	0.504420i
$430$	−2.38937	+	1.37950i	−0.115226	+	0.0665256i
$431$	−7.74940	+	4.47412i	−0.373275	+	0.215511i	−0.674888	−	0.737920i	$-0.735808\pi$
$431$	−7.74940	+	4.47412i	−0.373275	+	0.215511i	0.301613	+	0.953430i	$0.402475\pi$
$432$	−3.28366	−	1.89582i	−0.157985	−	0.0912127i
$433$	−1.82679			−0.0877898			−0.0438949	−	0.999036i	$-0.513977\pi$
$433$	−1.82679			−0.0877898			−0.0438949	+	0.999036i	$0.513977\pi$
$434$	−0.754830	−	4.01043i	−0.0362330	−	0.192507i
$435$			12.5500i			0.601724i
$436$	−28.5583	−	16.4881i	−1.36769	−	0.789639i
$437$	10.2311	−	0.293594i	0.489418	−	0.0140445i
$438$	−1.14647	−	1.98575i	−0.0547807	−	0.0948829i
$439$	−24.6397	−	14.2257i	−1.17599	−	0.678958i	−0.220906	−	0.975295i	$-0.570901\pi$
$439$	−24.6397	−	14.2257i	−1.17599	−	0.678958i	−0.955083	+	0.296337i	$0.904235\pi$
$440$		−	5.72710i		−	0.273029i
$441$	1.05658	−	6.91980i	0.0503131	−	0.329514i
$442$		−	1.52077i		−	0.0723359i
$443$	7.75212	−	13.4271i	0.368314	−	0.637939i	−0.620988	−	0.783820i	$-0.713268\pi$
$443$	7.75212	−	13.4271i	0.368314	−	0.637939i	0.989302	+	0.145881i	$0.0466018\pi$
$444$	−6.27547	−	10.8694i	−0.297821	−	0.515841i
$445$	0.303589	+	0.525832i	0.0143915	+	0.0249268i
$446$	3.52018	+	2.03238i	0.166685	+	0.0962358i
$447$	−9.39299			−0.444273
$448$	−18.6527	+	3.51075i	−0.881256	+	0.165867i
$449$	−0.171119			−0.00807562			−0.00403781	−	0.999992i	$-0.501285\pi$
$449$	−0.171119			−0.00807562			−0.00403781	+	0.999992i	$0.501285\pi$
$450$	−0.270968	+	0.469330i	−0.0127735	+	0.0221244i
$451$	−10.9655	−	18.9928i	−0.516345	−	0.894335i
$452$	31.4935	−	18.1828i	1.48133	−	0.855246i
$453$	−4.34905	−	2.51092i	−0.204336	−	0.117973i
$454$	−4.13679			−0.194149
$455$	−14.1767	−	4.97591i	−0.664613	−	0.233274i
$456$			1.58156i			0.0740632i
$457$	−9.55649	−	5.51744i	−0.447034	−	0.258095i	0.259543	−	0.965732i	$-0.416428\pi$
$457$	−9.55649	−	5.51744i	−0.447034	−	0.258095i	−0.706577	+	0.707637i	$0.749761\pi$
$458$	1.69490	+	2.93566i	0.0791976	+	0.137174i
$459$	−1.79840	+	1.03831i	−0.0839422	+	0.0484641i
$460$	7.16545	+	11.6274i	0.334091	+	0.542130i
$461$			18.3704i			0.855594i	0.903875	+	0.427797i	$0.140710\pi$
$461$			18.3704i			0.855594i	−0.903875	+	0.427797i	$0.859290\pi$
$462$	−1.71808	−	2.00032i	−0.0799323	−	0.0930635i
$463$	−7.81860			−0.363361			−0.181681	−	0.983358i	$-0.558154\pi$
$463$	−7.81860			−0.363361			−0.181681	+	0.983358i	$0.558154\pi$
$464$	16.4171	−	28.4352i	0.762143	−	1.32007i
$465$	5.98021	+	10.3580i	0.277326	+	0.480342i
$466$	−0.0874972	−	0.151550i	−0.00405323	−	0.00702040i
$467$	−6.08093	+	10.5325i	−0.281392	+	0.487385i	−0.971728	−	0.236104i	$-0.924129\pi$
$467$	−6.08093	+	10.5325i	−0.281392	+	0.487385i	0.690336	+	0.723489i	$0.257463\pi$
$468$			7.69995i			0.355930i
$469$	19.9324	−	17.1199i	0.920391	−	0.790524i
$470$		−	3.44143i		−	0.158741i
$471$	21.0711	+	12.1654i	0.970904	+	0.560552i
$472$	−2.15902	+	1.24651i	−0.0993771	+	0.0573754i
$473$	−27.1595	−	47.0416i	−1.24879	−	2.16297i
$474$	0.259733	−	0.449871i	0.0119299	−	0.0206633i
$475$	−6.18848			−0.283947
$476$	−3.57564	+	10.1872i	−0.163889	+	0.466930i
$477$			5.12414i			0.234618i
$478$	0.602894	−	1.04424i	0.0275757	−	0.0477626i
$479$	5.11621	+	8.86153i	0.233766	+	0.404894i	0.958913	−	0.283700i	$-0.0915619\pi$
$479$	5.11621	+	8.86153i	0.233766	+	0.404894i	−0.725148	+	0.688593i	$0.758229\pi$
$480$	−2.74958	+	1.58747i	−0.125501	+	0.0724579i
$481$	−12.5135	+	21.6740i	−0.570566	+	0.988249i
$482$	−0.871071			−0.0396762
$483$	12.0881	+	3.85710i	0.550029	+	0.175504i
$484$	34.2647			1.55749
$485$	5.32887	−	9.22987i	0.241971	−	0.419107i
$486$	−0.161856	+	0.0934478i	−0.00734195	+	0.00423888i
$487$	12.5834	+	21.7951i	0.570208	+	0.987629i	0.996544	+	0.0830642i	$0.0264707\pi$
$487$	12.5834	+	21.7951i	0.570208	+	0.987629i	−0.426336	+	0.904565i	$0.640196\pi$
$488$	−0.0674396	+	0.116809i	−0.00305285	+	0.00528768i
$489$			3.16292i			0.143032i
$490$	−1.48009	−	1.18499i	−0.0668637	−	0.0535322i
$491$	−43.5097			−1.96356			−0.981782	−	0.190009i	$-0.939148\pi$
$491$	−43.5097			−1.96356			−0.981782	+	0.190009i	$0.939148\pi$
$492$	−4.04078	+	6.99883i	−0.182172	+	0.315532i
$493$	−8.99135	−	15.5735i	−0.404950	−	0.701394i
$494$	1.35355	−	0.781473i	0.0608991	−	0.0351601i
$495$	6.69292	+	3.86416i	0.300824	+	0.173681i
$496$		−	31.2918i		−	1.40504i
$497$	−6.10344	+	1.14877i	−0.273777	+	0.0515294i
$498$			2.30174i			0.103143i
$499$	14.2830	−	24.7389i	0.639394	−	1.10746i	−0.346172	−	0.938171i	$-0.612519\pi$
$499$	14.2830	−	24.7389i	0.639394	−	1.10746i	0.985566	−	0.169292i	$-0.0541481\pi$
$500$	−11.2487	−	19.4833i	−0.503055	−	0.871317i
$501$	−1.84797	−	3.20078i	−0.0825613	−	0.143000i
$502$	−2.43379	+	4.21545i	−0.108625	+	0.188145i
$503$	−9.05716			−0.403839			−0.201919	−	0.979402i	$-0.564718\pi$
$503$	−9.05716			−0.403839			−0.201919	+	0.979402i	$0.564718\pi$
$504$	−0.649335	+	1.85000i	−0.0289237	+	0.0824054i
$505$			8.81509i			0.392266i
$506$	4.06912	−	2.50762i	0.180894	−	0.111477i
$507$	2.03856	−	1.17696i	0.0905354	−	0.0522706i
$508$	18.0778	+	31.3116i	0.802071	+	1.38923i
$509$	−0.839421	−	0.484640i	−0.0372067	−	0.0214813i	0.481281	−	0.876566i	$-0.340172\pi$
$509$	−0.839421	−	0.484640i	−0.0372067	−	0.0214813i	−0.518488	+	0.855085i	$0.673505\pi$
$510$			0.562470i			0.0249066i
$511$	24.6238	−	21.1494i	1.08929	−	0.935596i
$512$	13.9262			0.615455
$513$	−1.84827	−	1.06710i	−0.0816032	−	0.0471136i
$514$	4.96919	−	2.86896i	0.219182	−	0.126545i
$515$	9.13912	+	15.8294i	0.402718	+	0.697528i
$516$	−10.0083	+	17.3348i	−0.440589	+	0.763122i
$517$	67.7544			2.97983
$518$	−2.39584	+	2.05779i	−0.105267	+	0.0904141i
$519$	7.41091			0.325303
$520$	3.64447	+	2.10413i	0.159820	+	0.0922724i
$521$	−8.32779	−	14.4242i	−0.364847	−	0.631934i	0.623905	−	0.781501i	$-0.285545\pi$
$521$	−8.32779	−	14.4242i	−0.364847	−	0.631934i	−0.988752	+	0.149567i	$0.952212\pi$
$522$	−0.809222	−	1.40161i	−0.0354187	−	0.0613469i
$523$	−6.74538	+	11.6833i	−0.294955	+	0.510877i	−0.974974	−	0.222317i	$-0.928638\pi$
$523$	−6.74538	+	11.6833i	−0.294955	+	0.510877i	0.680019	+	0.733194i	$0.261971\pi$
$524$		−	11.9650i		−	0.522695i
$525$	−7.23885	−	2.54078i	−0.315929	−	0.110889i
$526$			3.19113i			0.139140i
$527$	−14.8419	−	8.56898i	−0.646524	−	0.373271i
$528$	−10.1097	−	17.5105i	−0.439968	−	0.762047i
$529$	−10.3388	+	20.5453i	−0.449515	+	0.893273i
$530$	1.20197	+	0.693959i	0.0522103	+	0.0301436i
$531$		−	3.36416i		−	0.145992i
$532$	−10.9044	+	2.05239i	−0.472767	+	0.0889826i
$533$	16.1149			0.698012
$534$	−0.0678113	−	0.0391509i	−0.00293448	−	0.00169422i
$535$	−10.7615	+	6.21313i	−0.465259	+	0.268617i
$536$	−6.37351	+	3.67975i	−0.275294	+	0.158941i
$537$	−9.05884	−	5.23012i	−0.390918	−	0.225697i
$538$		−	2.16862i		−	0.0934958i
$539$	23.3298	−	29.1398i	1.00489	−	1.25514i
$540$		−	2.84788i		−	0.122553i
$541$	−15.0312	+	26.0347i	−0.646240	+	1.11932i	0.337774	+	0.941227i	$0.390326\pi$
$541$	−15.0312	+	26.0347i	−0.646240	+	1.11932i	−0.984014	+	0.178093i	$0.943007\pi$
$542$	2.52526	−	1.45796i	0.108469	−	0.0626247i
$543$	0.835211	−	0.482209i	0.0358423	−	0.0206936i
$544$	2.27467	−	3.93985i	0.0975258	−	0.168920i
$545$		−	24.3202i		−	1.04176i
$546$	1.90414	−	0.358390i	0.0814896	−	0.0153377i
$547$	10.4846			0.448289			0.224145	−	0.974556i	$-0.428041\pi$
$547$	10.4846			0.448289			0.224145	+	0.974556i	$0.428041\pi$
$548$	16.2787	+	9.39848i	0.695390	+	0.401483i
$549$	−0.0910049	−	0.157625i	−0.00388399	−	0.00672728i
$550$	−2.50276	+	1.44497i	−0.106718	+	0.0616137i
$551$	9.24067	−	16.0053i	0.393666	−	0.681849i
$552$	−3.12753	−	1.68797i	−0.133117	−	0.0718447i
$553$	6.93872	+	2.43544i	0.295065	+	0.103565i
$554$	−1.06751			−0.0453540
$555$	4.62820	−	8.01628i	0.196456	−	0.340272i
$556$	−16.9541	+	9.78844i	−0.719013	+	0.415122i
$557$	−13.7349	+	7.92988i	−0.581968	+	0.336000i	−0.761915	−	0.647677i	$-0.775741\pi$
$557$	−13.7349	+	7.92988i	−0.581968	+	0.336000i	0.179947	+	0.983676i	$0.442407\pi$
$558$	−1.33577	−	0.771208i	−0.0565477	−	0.0326479i
$559$	39.9135			1.68816
$560$	−9.47271	−	11.0289i	−0.400295	−	0.466055i
$561$	−11.0738			−0.467537
$562$	0.652349	+	0.376634i	0.0275177	+	0.0158873i
$563$	5.83500	+	10.1065i	0.245916	+	0.425939i	0.962389	−	0.271676i	$-0.0875780\pi$
$563$	5.83500	+	10.1065i	0.245916	+	0.425939i	−0.716473	+	0.697615i	$0.754245\pi$
$564$	−12.4837	−	21.6224i	−0.525660	−	0.910469i
$565$	23.2267	+	13.4099i	0.977153	+	0.564160i
$566$	−3.67188			−0.154341
$567$	−1.72387	−	2.00706i	−0.0723955	−	0.0842886i
$568$	1.73954			0.0729896
$569$	−24.6789	−	14.2484i	−1.03459	−	0.597324i	−0.116297	−	0.993214i	$-0.537103\pi$
$569$	−24.6789	−	14.2484i	−1.03459	−	0.597324i	−0.918298	+	0.395891i	$0.870436\pi$
$570$	−0.500621	+	0.289033i	−0.0209687	+	0.0121063i
$571$	−28.0520	+	16.1958i	−1.17394	+	0.677774i	−0.954604	−	0.297876i	$-0.903722\pi$
$571$	−28.0520	+	16.1958i	−1.17394	+	0.677774i	−0.219334	+	0.975650i	$0.570388\pi$
$572$	−20.5305	+	35.5598i	−0.858422	+	1.48683i
$573$	−8.95797			−0.374225
$574$	1.91883	+	0.673496i	0.0800905	+	0.0281112i
$575$	6.60485	−	12.2377i	0.275441	−	0.510348i
$576$	−3.58692	+	6.21273i	−0.149455	+	0.258864i
$577$	−9.57907	+	5.53048i	−0.398782	+	0.230237i	−0.685958	−	0.727641i	$-0.740617\pi$
$577$	−9.57907	+	5.53048i	−0.398782	+	0.230237i	0.287176	+	0.957878i	$0.407283\pi$
$578$	1.18563	+	2.05358i	0.0493159	+	0.0854176i
$579$	−3.11629	−	1.79919i	−0.129508	−	0.0747717i
$580$	24.6615			1.02401
$581$	−32.0219	+	6.02705i	−1.32849	+	0.250044i
$582$			1.37442i			0.0569716i
$583$	−13.6626	+	23.6642i	−0.565845	+	0.980072i
$584$	−7.87365	+	4.54585i	−0.325814	+	0.188109i
$585$	−4.91795	+	2.83938i	−0.203332	+	0.117394i
$586$	1.26938	−	2.19864i	0.0524378	−	0.0908249i
$587$			6.98429i			0.288272i	0.989558	+	0.144136i	$0.0460403\pi$
$587$			6.98429i			0.288272i	−0.989558	+	0.144136i	$0.953960\pi$
$588$	−13.5979	−	2.07624i	−0.560768	−	0.0856229i
$589$		−	17.6132i		−	0.725739i
$590$	−0.789133	−	0.455606i	−0.0324881	−	0.0187570i
$591$	−2.38330	+	1.37600i	−0.0980359	+	0.0566010i
$592$	−20.9728	+	12.1086i	−0.861976	+	0.497662i
$593$	7.45682	+	4.30519i	0.306215	+	0.176793i	0.645231	−	0.763987i	$-0.276761\pi$
$593$	7.45682	+	4.30519i	0.306215	+	0.176793i	−0.339017	+	0.940780i	$0.610094\pi$
$594$	−0.996644			−0.0408928
$595$	−7.82510	+	1.47281i	−0.320798	+	0.0603795i
$596$			18.4579i			0.756064i
$597$	12.0846	+	6.97707i	0.494591	+	0.285552i
$598$	0.100744	+	3.51070i	0.00411974	+	0.143563i
$599$	−0.0408697	−	0.0707884i	−0.00166989	−	0.00289233i	0.865189	−	0.501445i	$-0.167198\pi$
$599$	−0.0408697	−	0.0707884i	−0.00166989	−	0.00289233i	−0.866859	+	0.498553i	$0.833865\pi$
$600$	1.86093	+	1.07441i	0.0759720	+	0.0438624i
$601$			14.6099i			0.595951i	0.954573	+	0.297976i	$0.0963114\pi$
$601$			14.6099i			0.595951i	−0.954573	+	0.297976i	$0.903689\pi$
$602$	4.75259	+	1.66812i	0.193701	+	0.0679876i
$603$		−	9.93112i		−	0.404427i
$604$	−4.93414	+	8.54618i	−0.200767	+	0.347739i
$605$	12.6352	+	21.8849i	0.513695	+	0.889746i
$606$	−0.568397	−	0.984493i	−0.0230896	−	0.0399923i
$607$	22.2778	+	12.8621i	0.904228	+	0.522057i	0.878570	−	0.477614i	$-0.158498\pi$
$607$	22.2778	+	12.8621i	0.904228	+	0.522057i	0.0256588	+	0.999671i	$0.491832\pi$
$608$	4.67550			0.189616
$609$	17.3804	−	14.9280i	0.704288	−	0.604913i
$610$	−0.0492989			−0.00199606
$611$	−24.8929	+	43.1158i	−1.00706	+	1.74428i
$612$	2.04035	+	3.53399i	0.0824762	+	0.142853i
$613$	0.217488	−	0.125567i	0.00878426	−	0.00507160i	−0.495601	−	0.868550i	$-0.665052\pi$
$613$	0.217488	−	0.125567i	0.00878426	−	0.00507160i	0.504386	+	0.863478i	$0.331719\pi$
$614$	1.63711	+	0.945184i	0.0660683	+	0.0381445i
$615$	−5.96020			−0.240338
$616$	−7.93143	+	6.81231i	−0.319566	+	0.274476i
$617$			23.2287i			0.935152i	0.883953	+	0.467576i	$0.154873\pi$
$617$			23.2287i			0.935152i	−0.883953	+	0.467576i	$0.845127\pi$
$618$	−2.04136	−	1.17858i	−0.0821157	−	0.0474095i
$619$	−17.7998	−	30.8302i	−0.715435	−	1.23917i	−0.962792	−	0.270245i	$-0.912895\pi$
$619$	−17.7998	−	30.8302i	−0.715435	−	1.23917i	0.247357	−	0.968924i	$-0.420438\pi$
$620$	20.3543	−	11.7515i	0.817447	−	0.471953i
$621$	4.08282	−	2.51606i	0.163838	−	0.100966i
$622$		−	2.38571i		−	0.0956583i
$623$	0.367106	−	1.04591i	0.0147078	−	0.0419035i
$624$	14.8572			0.594764
$625$	1.04678	−	1.81308i	0.0418714	−	0.0725234i
$626$	−1.94265	−	3.36477i	−0.0776438	−	0.134483i
$627$	−5.69045	−	9.85614i	−0.227255	−	0.393616i
$628$	23.9058	−	41.4061i	0.953947	−	1.65228i
$629$			13.2634i			0.528846i
$630$	−0.704259	+	0.132553i	−0.0280584	+	0.00528105i
$631$			37.3477i			1.48679i	0.668853	+	0.743395i	$0.266786\pi$
$631$			37.3477i			1.48679i	−0.668853	+	0.743395i	$0.733214\pi$
$632$	−1.78377	−	1.02986i	−0.0709545	−	0.0409656i
$633$	8.43446	−	4.86964i	0.335240	−	0.193551i
$634$	−2.59129	−	4.48824i	−0.102913	−	0.178251i
$635$	−13.3325	+	23.0925i	−0.529083	+	0.916398i
$636$	10.0693			0.399273
$637$	9.97188	+	25.5520i	0.395100	+	1.01241i
$638$		−	8.63055i		−	0.341687i
$639$	−1.17369	+	2.03290i	−0.0464307	+	0.0804203i
$640$	4.14650	+	7.18194i	0.163905	+	0.283891i
$641$	−23.8482	+	13.7688i	−0.941949	+	0.543835i	−0.890571	−	0.454845i	$-0.849695\pi$
$641$	−23.8482	+	13.7688i	−0.941949	+	0.543835i	−0.0513784	+	0.998679i	$0.516361\pi$
$642$	0.801246	−	1.38780i	0.0316227	−	0.0547721i
$643$	1.93708			0.0763911			0.0381956	−	0.999270i	$-0.487839\pi$
$643$	1.93708			0.0763911			0.0381956	+	0.999270i	$0.487839\pi$
$644$	7.57948	−	23.7540i	0.298673	−	0.936039i
$645$	−14.7623			−0.581265
$646$	0.414153	−	0.717334i	0.0162946	−	0.0282231i
$647$	22.4410	−	12.9563i	0.882248	−	0.509366i	0.0108488	−	0.999941i	$-0.496547\pi$
$647$	22.4410	−	12.9563i	0.882248	−	0.509366i	0.871399	+	0.490575i	$0.163213\pi$
$648$	0.370527	+	0.641772i	0.0145557	+	0.0252112i
$649$	8.96991	−	15.5363i	0.352100	−	0.609855i
$650$		−	2.12352i		−	0.0832915i
$651$	7.23139	−	20.6027i	0.283420	−	0.807483i
$652$	6.21535			0.243412
$653$	−21.6709	+	37.5351i	−0.848048	+	1.46886i	0.0348991	+	0.999391i	$0.488889\pi$
$653$	−21.6709	+	37.5351i	−0.848048	+	1.46886i	−0.882947	+	0.469472i	$0.844444\pi$
$654$	1.56817	+	2.71615i	0.0613202	+	0.106210i
$655$	7.64206	−	4.41214i	0.298600	−	0.172397i
$656$	13.5044	+	7.79676i	0.527257	+	0.304412i
$657$		−	12.2686i		−	0.478644i
$658$	−4.76601	+	4.09353i	−0.185799	+	0.159583i
$659$			19.0358i			0.741528i	0.928727	+	0.370764i	$0.120904\pi$
$659$			19.0358i			0.741528i	−0.928727	+	0.370764i	$0.879096\pi$
$660$	7.59334	−	13.1521i	0.295570	−	0.511943i
$661$	11.6478	+	20.1745i	0.453045	+	0.784697i	0.998573	−	0.0533951i	$-0.0170043\pi$
$661$	11.6478	+	20.1745i	0.453045	+	0.784697i	−0.545528	+	0.838092i	$0.683671\pi$
$662$	−0.788005	−	1.36487i	−0.0306267	−	0.0530470i
$663$	4.06852	−	7.04688i	0.158008	−	0.273678i
$664$	9.12656			0.354179
$665$	−5.33191	−	6.20782i	−0.206762	−	0.240729i
$666$			1.19371i			0.0462552i
$667$	21.7881	+	35.3556i	0.843640	+	1.36898i
$668$	−6.28976	+	3.63139i	−0.243358	+	0.140503i
$669$	10.8744	+	18.8350i	0.420428	+	0.728203i
$670$	−2.32955	−	1.34497i	−0.0899983	−	0.0519606i
$671$		−	0.970590i		−	0.0374692i
$672$	5.46908	+	1.91960i	0.210974	+	0.0740503i
$673$	−15.2244			−0.586858			−0.293429	−	0.955981i	$-0.594796\pi$
$673$	−15.2244			−0.586858			−0.293429	+	0.955981i	$0.594796\pi$
$674$	3.92493	+	2.26606i	0.151183	+	0.0872854i
$675$	−2.51119	+	1.44983i	−0.0966556	+	0.0558042i
$676$	−2.31281	−	4.00590i	−0.0889542	−	0.154073i
$677$	17.7941	−	30.8203i	0.683883	−	1.18452i	−0.289904	−	0.957056i	$-0.593623\pi$
$677$	17.7941	−	30.8203i	0.683883	−	1.18452i	0.973787	−	0.227464i	$-0.0730433\pi$
$678$	−3.45869			−0.132830
$679$	−19.1210	+	3.59889i	−0.733797	+	0.138113i
$680$	2.23023			0.0855255
$681$	−19.1688	−	11.0671i	−0.734550	−	0.424093i
$682$	−4.11257	−	7.12317i	−0.157478	−	0.272760i
$683$	3.98393	+	6.90037i	0.152441	+	0.264035i	0.932124	−	0.362139i	$-0.117953\pi$
$683$	3.98393	+	6.90037i	0.152441	+	0.264035i	−0.779683	+	0.626174i	$0.784620\pi$
$684$	−2.09693	+	3.63198i	−0.0801780	+	0.138872i
$685$			13.8629i			0.529674i
$686$	0.119468	+	3.45929i	0.00456132	+	0.132076i
$687$			18.1374i			0.691986i
$688$	33.4478	+	19.3111i	1.27519	+	0.736229i
$689$	−10.0392	−	17.3885i	−0.382464	−	0.662447i
$690$	−0.0372610	−	1.29846i	−0.00141850	−	0.0494315i
$691$	−0.438063	−	0.252916i	−0.0166647	−	0.00962137i	0.491645	−	0.870796i	$-0.336396\pi$
$691$	−0.438063	−	0.252916i	−0.0166647	−	0.00962137i	−0.508309	+	0.861175i	$0.669729\pi$
$692$		−	14.5629i		−	0.553600i
$693$	−2.60969	−	13.8653i	−0.0991339	−	0.526701i
$694$	−3.78597			−0.143713
$695$	−12.5037	−	7.21904i	−0.474294	−	0.273834i
$696$	−5.55749	+	3.20862i	−0.210656	+	0.121622i
$697$	7.39612	−	4.27015i	0.280148	−	0.161743i
$698$	2.16660	+	1.25088i	0.0820068	+	0.0473467i
$699$		−	0.936322i		−	0.0354149i
$700$	−4.99282	+	14.2249i	−0.188711	+	0.537649i
$701$			6.24425i			0.235842i	0.993023	+	0.117921i	$0.0376230\pi$
$701$			6.24425i			0.235842i	−0.993023	+	0.117921i	$0.962377\pi$
$702$	0.366167	−	0.634219i	0.0138201	−	0.0239371i
$703$	−11.8050	+	6.81559i	−0.445232	+	0.257055i
$704$	−33.1302	+	19.1277i	−1.24864	+	0.720902i
$705$	9.20683	−	15.9467i	0.346749	−	0.600587i
$706$			3.57354i			0.134492i
$707$	12.2080	−	10.4854i	0.459128	−	0.394345i
$708$	−6.61081			−0.248450
$709$	−5.60789	−	3.23772i	−0.210609	−	0.121595i	0.390986	−	0.920397i	$-0.372134\pi$
$709$	−5.60789	−	3.23772i	−0.210609	−	0.121595i	−0.601594	+	0.798802i	$0.705468\pi$
$710$	0.317906	+	0.550629i	0.0119308	+	0.0206647i
$711$	2.40707	−	1.38972i	0.0902722	−	0.0521187i
$712$	−0.155236	+	0.268877i	−0.00581772	+	0.0100766i
$713$	34.8301	+	18.7982i	1.30440	+	0.703999i
$714$	0.778961	−	0.669050i	0.0291519	−	0.0250386i
$715$	−30.2827			−1.13251
$716$	−10.2776	+	17.8013i	−0.384090	+	0.665264i
$717$	5.58731	−	3.22583i	0.208662	−	0.120471i
$718$	4.53595	−	2.61883i	0.169280	−	0.0977339i
$719$	10.8578	+	6.26873i	0.404926	+	0.233784i	0.688607	−	0.725134i	$-0.258222\pi$
$719$	10.8578	+	6.26873i	0.404926	+	0.233784i	−0.283681	+	0.958919i	$0.591556\pi$
$720$	−5.49504			−0.204788
$721$	11.0512	−	31.4856i	0.411568	−	1.17258i
$722$	−2.69974			−0.100474
$723$	−4.03632	−	2.33037i	−0.150112	−	0.0866673i
$724$	−0.947575	−	1.64125i	−0.0352163	−	0.0609965i
$725$	−12.5550	−	21.7459i	−0.466281	−	0.807623i
$726$	−2.82227	−	1.62944i	−0.104744	−	0.0604742i
$727$	−7.28081			−0.270030			−0.135015	−	0.990844i	$-0.543108\pi$
$727$	−7.28081			−0.270030			−0.135015	+	0.990844i	$0.543108\pi$
$728$	−1.42104	−	7.55004i	−0.0526674	−	0.279823i
$729$	−1.00000			−0.0370370
$730$	−2.87785	−	1.66153i	−0.106514	−	0.0614960i
$731$	18.3188	−	10.5764i	0.677545	−	0.391181i
$732$	−0.309744	+	0.178831i	−0.0114485	+	0.00660978i
$733$	−24.3282	+	42.1377i	−0.898582	+	1.55639i	−0.0692752	+	0.997598i	$0.522069\pi$
$733$	−24.3282	+	42.1377i	−0.898582	+	1.55639i	−0.829307	+	0.558793i	$0.811265\pi$
$734$	0.476516			0.0175885
$735$	−3.68817	−	9.45059i	−0.136040	−	0.348590i
$736$	−4.99007	+	9.24581i	−0.183937	+	0.340805i
$737$	26.4795	−	45.8638i	0.975384	−	1.68942i
$738$	0.665651	−	0.384314i	0.0245029	−	0.0141468i
$739$	3.49653	+	6.05617i	0.128622	+	0.222780i	0.923143	−	0.384457i	$-0.125611\pi$
$739$	3.49653	+	6.05617i	0.128622	+	0.222780i	−0.794521	+	0.607237i	$0.792278\pi$
$740$	−15.7526	−	9.09474i	−0.579075	−	0.334329i
$741$	8.36267			0.307210
$742$	−0.468670	−	2.49006i	−0.0172054	−	0.0914129i
$743$			26.3785i			0.967734i	0.875141	+	0.483867i	$0.160768\pi$
$743$			26.3785i			0.967734i	−0.875141	+	0.483867i	$0.839232\pi$
$744$	−3.05790	+	5.29643i	−0.112108	+	0.194177i
$745$	−11.7890	+	6.80640i	−0.431917	+	0.249367i
$746$	−1.73861	+	1.00379i	−0.0636551	+	0.0367513i
$747$	−6.15782	+	10.6657i	−0.225303	+	0.390236i
$748$			21.7608i			0.795655i
$749$	21.4051	+	7.51304i	0.782127	+	0.274521i
$750$			2.13969i			0.0781306i
$751$	9.06606	+	5.23429i	0.330825	+	0.191002i	0.656207	−	0.754581i	$-0.272160\pi$
$751$	9.06606	+	5.23429i	0.330825	+	0.191002i	−0.325382	+	0.945583i	$0.605493\pi$
$752$	−41.7209	+	24.0876i	−1.52141	+	0.878384i
$753$	−22.5551	+	13.0222i	−0.821953	+	0.474555i
$754$	5.49209	+	3.17086i	0.200010	+	0.115476i
$755$	−7.27792			−0.264871
$756$	−3.94401	+	3.38752i	−0.143442	+	0.123203i
$757$		−	12.7206i		−	0.462339i	−0.972914	−	0.231169i	$-0.925745\pi$
$757$		−	12.7206i		−	0.462339i	0.972914	−	0.231169i	$-0.0742551\pi$
$758$	0.964784	+	0.557018i	0.0350425	+	0.0202318i
$759$	25.5639	−	0.733590i	0.927909	−	0.0266276i
$760$	1.14604	+	1.98500i	0.0415712	+	0.0720034i
$761$	−38.6002	−	22.2858i	−1.39926	−	0.807860i	−0.404941	−	0.914343i	$-0.632708\pi$
$761$	−38.6002	−	22.2858i	−1.39926	−	0.807860i	−0.994315	+	0.106482i	$0.966041\pi$
$762$		−	3.43871i		−	0.124571i
$763$	−33.6809	+	28.9286i	−1.21933	+	1.04728i
$764$			17.6030i			0.636856i
$765$	−1.50477	+	2.60634i	−0.0544051	+	0.0942324i
$766$	1.19599	+	2.07151i	0.0432128	+	0.0748467i
$767$	6.59108	+	11.4161i	0.237990	+	0.412211i
$768$	11.4993	+	6.63911i	0.414944	+	0.239568i
$769$	16.9933			0.612795			0.306398	−	0.951904i	$-0.400876\pi$
$769$	16.9933			0.612795			0.306398	+	0.951904i	$0.400876\pi$
$770$	−3.60583	−	1.26562i	−0.129945	−	0.0456097i
$771$	30.7012			1.10568
$772$	−3.53553	+	6.12372i	−0.127247	+	0.220397i
$773$	4.87690	+	8.44703i	0.175410	+	0.303819i	0.940303

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.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0934478 + 0.161856i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.982535 + 1.70180i) q^{4} +(-0.724626 + 1.25509i) q^{5} -0.186896i q^{6} +(2.60010 - 0.489382i) q^{7} -0.741054 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.135429 - 0.234571i) q^{10} +(4.61819 - 2.66631i) q^{11} +(-1.70180 - 0.982535i) q^{12} +3.91841i q^{13} +(-0.163764 + 0.466574i) q^{14} -1.44925i q^{15} +(-1.89582 + 3.28366i) q^{16} +(1.03831 + 1.79840i) q^{17} +(0.0934478 + 0.161856i) q^{18} +(-1.06710 + 1.84827i) q^{19} -2.84788 q^{20} +(-2.00706 + 1.72387i) q^{21} +0.996644i q^{22} +(-2.51606 - 4.08282i) q^{23} +(0.641772 - 0.370527i) q^{24} +(1.44983 + 2.51119i) q^{25} +(-0.634219 - 0.366167i) q^{26} +1.00000i q^{27} +(3.38752 + 3.94401i) q^{28} -8.65961 q^{29} +(0.234571 + 0.135429i) q^{30} +(-7.14716 + 4.12641i) q^{31} +(-1.09537 - 1.89724i) q^{32} +(-2.66631 + 4.61819i) q^{33} -0.388110 q^{34} +(-1.26988 + 3.61797i) q^{35} +1.96507 q^{36} +(5.53132 + 3.19351i) q^{37} +(-0.199436 - 0.345434i) q^{38} +(-1.95920 - 3.39344i) q^{39} +(0.536987 - 0.930089i) q^{40} -4.11260i q^{41} +(-0.0914633 - 0.485947i) q^{42} -10.1862i q^{43} +(9.07507 + 5.23949i) q^{44} +(0.724626 + 1.25509i) q^{45} +(0.895951 - 0.0257105i) q^{46} +(11.0034 + 6.35281i) q^{47} -3.79164i q^{48} +(6.52101 - 2.54488i) q^{49} -0.541935 q^{50} +(-1.79840 - 1.03831i) q^{51} +(-6.66835 + 3.84997i) q^{52} +(-4.43763 + 2.56207i) q^{53} +(-0.161856 - 0.0934478i) q^{54} +7.72832i q^{55} +(-1.92681 + 0.362658i) q^{56} -2.13420i q^{57} +(0.809222 - 1.40161i) q^{58} +(2.91345 - 1.68208i) q^{59} +(2.46634 - 1.42394i) q^{60} +(0.0910049 - 0.157625i) q^{61} -1.54242i q^{62} +(0.876232 - 2.49644i) q^{63} -7.17384 q^{64} +(-4.91795 - 2.83938i) q^{65} +(-0.498322 - 0.863119i) q^{66} +(8.60060 - 4.96556i) q^{67} +(-2.04035 + 3.53399i) q^{68} +(4.22039 + 2.27779i) q^{69} +(-0.466924 - 0.543630i) q^{70} -2.34739 q^{71} +(-0.370527 + 0.641772i) q^{72} +(10.6249 - 6.13431i) q^{73} +(-1.03378 + 0.596853i) q^{74} +(-2.51119 - 1.44983i) q^{75} -4.19385 q^{76} +(10.7029 - 9.19273i) q^{77} +0.732333 q^{78} +(2.40707 + 1.38972i) q^{79} +(-2.74752 - 4.75885i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.665651 + 0.384314i) q^{82} -12.3156 q^{83} +(-4.90568 - 1.72186i) q^{84} -3.00954 q^{85} +(1.64869 + 0.951873i) q^{86} +(7.49944 - 4.32981i) q^{87} +(-3.42233 + 1.97588i) q^{88} +(0.209480 - 0.362830i) q^{89} -0.270859 q^{90} +(1.91760 + 10.1882i) q^{91} +(4.47602 - 8.29335i) q^{92} +(4.12641 - 7.14716i) q^{93} +(-2.05649 + 1.18731i) q^{94} +(-1.54650 - 2.67861i) q^{95} +(1.89724 + 1.09537i) q^{96} -7.35396 q^{97} +(-0.197469 + 1.29328i) q^{98} -5.33263i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50}+ \cdots + 112 q^{98}+O(q^{100}) \) 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9 - 44 * q^16 - 4 * q^18 - 16 * q^23 - 12 * q^25 + 84 * q^26 + 24 * q^29 - 12 * q^31 + 8 * q^32 + 32 * q^35 - 72 * q^36 - 8 * q^46 - 12 * q^47 + 8 * q^49 - 96 * q^50 - 108 * q^52 - 24 * q^58 + 36 * q^59 + 168 * q^64 - 40 * q^70 - 16 * q^71 - 12 * q^72 + 48 * q^73 - 48 * q^75 - 32 * q^78 - 32 * q^81 - 24 * q^82 + 88 * q^85 + 36 * q^87 + 152 * q^92 + 24 * q^93 - 108 * q^94 - 44 * q^95 + 60 * q^96 + 112 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more