LMFDB - Embedded newform 483.2.j.a.229.20

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			229.20
Character	$\chi$	$=$	483.229
Dual form			483.2.j.a.367.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.287128 - 0.497320i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.835115 + 1.44646i) q^{4} +(0.504635 - 0.874053i) q^{5} -0.574256i q^{6} +(1.18416 - 2.36596i) q^{7} +2.10765 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.289790 - 0.501930i) q^{10} +(-0.838252 + 0.483965i) q^{11} +(1.44646 + 0.835115i) q^{12} +1.03692i q^{13} +(-0.836635 - 1.26824i) q^{14} -1.00927i q^{15} +(-1.06506 + 1.84475i) q^{16} +(-0.530685 - 0.919173i) q^{17} +(-0.287128 - 0.497320i) q^{18} +(-0.0986713 + 0.170904i) q^{19} +1.68571 q^{20} +(-0.157470 - 2.64106i) q^{21} +0.555840i q^{22} +(-2.02588 - 4.34693i) q^{23} +(1.82528 - 1.05383i) q^{24} +(1.99069 + 3.44797i) q^{25} +(0.515682 + 0.297729i) q^{26} -1.00000i q^{27} +(4.41118 - 0.263011i) q^{28} +1.16434 q^{29} +(-0.501930 - 0.289790i) q^{30} +(-2.03191 + 1.17312i) q^{31} +(2.71927 + 4.70991i) q^{32} +(-0.483965 + 0.838252i) q^{33} -0.609497 q^{34} +(-1.47041 - 2.22896i) q^{35} +1.67023 q^{36} +(5.62442 + 3.24726i) q^{37} +(0.0566626 + 0.0981424i) q^{38} +(0.518461 + 0.898000i) q^{39} +(1.06359 - 1.84220i) q^{40} -8.07293i q^{41} +(-1.35867 - 0.680009i) q^{42} +8.57509i q^{43} +(-1.40007 - 0.808333i) q^{44} +(-0.504635 - 0.874053i) q^{45} +(-2.74350 - 0.240617i) q^{46} +(-3.46026 - 1.99778i) q^{47} +2.13013i q^{48} +(-4.19554 - 5.60334i) q^{49} +2.28633 q^{50} +(-0.919173 - 0.530685i) q^{51} +(-1.49987 + 0.865949i) q^{52} +(-8.28588 + 4.78385i) q^{53} +(-0.497320 - 0.287128i) q^{54} +0.976903i q^{55} +(2.49579 - 4.98662i) q^{56} +0.197343i q^{57} +(0.334314 - 0.579049i) q^{58} +(3.57952 - 2.06664i) q^{59} +(1.45987 - 0.842857i) q^{60} +(1.73860 - 3.01135i) q^{61} +1.34734i q^{62} +(-1.45690 - 2.20849i) q^{63} -1.13715 q^{64} +(0.906324 + 0.523267i) q^{65} +(0.277920 + 0.481371i) q^{66} +(-8.02600 + 4.63381i) q^{67} +(0.886365 - 1.53523i) q^{68} +(-3.92793 - 2.75162i) q^{69} +(-1.53070 + 0.0912662i) q^{70} -4.70241 q^{71} +(1.05383 - 1.82528i) q^{72} +(-8.64734 + 4.99255i) q^{73} +(3.22985 - 1.86476i) q^{74} +(3.44797 + 1.99069i) q^{75} -0.329608 q^{76} +(0.152420 + 2.55636i) q^{77} +0.595458 q^{78} +(-4.23226 - 2.44349i) q^{79} +(1.07494 + 1.86185i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.01483 - 2.31796i) q^{82} +7.71346 q^{83} +(3.68869 - 2.43336i) q^{84} -1.07121 q^{85} +(4.26456 + 2.46215i) q^{86} +(1.00835 - 0.582169i) q^{87} +(-1.76674 + 1.02003i) q^{88} +(-5.52710 + 9.57321i) q^{89} -0.579579 q^{90} +(2.45331 + 1.22788i) q^{91} +(4.59583 - 6.56054i) q^{92} +(-1.17312 + 2.03191i) q^{93} +(-1.98708 + 1.14724i) q^{94} +(0.0995860 + 0.172488i) q^{95} +(4.70991 + 2.71927i) q^{96} +8.08305 q^{97} +(-3.99131 + 0.477652i) q^{98} +0.967930i 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 $

$2$	0.287128	−	0.497320i	0.203030	−	0.351658i	−0.746473	−	0.665415i	$-0.768254\pi$
$2$	0.287128	−	0.497320i	0.203030	−	0.351658i	0.949503	+	0.313757i	$0.101588\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.835115	+	1.44646i	0.417558	+	0.723231i
$5$	0.504635	−	0.874053i	0.225680	−	0.390889i	−0.730844	−	0.682545i	$-0.760873\pi$
$5$	0.504635	−	0.874053i	0.225680	−	0.390889i	0.956523	+	0.291657i	$0.0942064\pi$
$6$		−	0.574256i		−	0.234439i
$7$	1.18416	−	2.36596i	0.447570	−	0.894249i
$7$	1.18416	−	2.36596i	0.447570	−	0.894249i
$8$	2.10765			0.745167
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.289790	−	0.501930i	−0.0916395	−	0.158724i
$11$	−0.838252	+	0.483965i	−0.252743	+	0.145921i	−0.621019	−	0.783795i	$-0.713281\pi$
$11$	−0.838252	+	0.483965i	−0.252743	+	0.145921i	0.368277	+	0.929716i	$0.379948\pi$
$12$	1.44646	+	0.835115i	0.417558	+	0.241077i
$13$			1.03692i			0.287590i	0.989607	+	0.143795i	$0.0459306\pi$
$13$			1.03692i			0.287590i	−0.989607	+	0.143795i	$0.954069\pi$
$14$	−0.836635	−	1.26824i	−0.223600	−	0.338951i
$15$		−	1.00927i		−	0.260592i
$16$	−1.06506	+	1.84475i	−0.266266	+	0.461187i
$17$	−0.530685	−	0.919173i	−0.128710	−	0.222932i	0.794467	−	0.607307i	$-0.207750\pi$
$17$	−0.530685	−	0.919173i	−0.128710	−	0.222932i	−0.923177	+	0.384375i	$0.874417\pi$
$18$	−0.287128	−	0.497320i	−0.0676767	−	0.117219i
$19$	−0.0986713	+	0.170904i	−0.0226367	+	0.0392080i	−0.877122	−	0.480268i	$-0.840539\pi$
$19$	−0.0986713	+	0.170904i	−0.0226367	+	0.0392080i	0.854485	+	0.519476i	$0.173873\pi$
$20$	1.68571			0.376937
$21$	−0.157470	−	2.64106i	−0.0343627	−	0.576327i
$22$			0.555840i			0.118505i
$23$	−2.02588	−	4.34693i	−0.422424	−	0.906398i
$23$	−2.02588	−	4.34693i	−0.422424	−	0.906398i
$24$	1.82528	−	1.05383i	0.372584	−	0.215111i
$25$	1.99069	+	3.44797i	0.398137	+	0.689594i
$26$	0.515682	+	0.297729i	0.101133	+	0.0583895i
$27$		−	1.00000i		−	0.192450i
$28$	4.41118	−	0.263011i	0.833635	−	0.0497044i
$29$	1.16434			0.216212			0.108106	−	0.994139i	$-0.465521\pi$
$29$	1.16434			0.216212			0.108106	+	0.994139i	$0.465521\pi$
$30$	−0.501930	−	0.289790i	−0.0916395	−	0.0529081i
$31$	−2.03191	+	1.17312i	−0.364941	+	0.210699i	−0.671246	−	0.741234i	$-0.734241\pi$
$31$	−2.03191	+	1.17312i	−0.364941	+	0.210699i	0.306305	+	0.951933i	$0.400907\pi$
$32$	2.71927	+	4.70991i	0.480704	+	0.832603i
$33$	−0.483965	+	0.838252i	−0.0842475	+	0.145921i
$34$	−0.609497			−0.104528
$35$	−1.47041	−	2.22896i	−0.248544	−	0.376764i
$36$	1.67023			0.278372
$37$	5.62442	+	3.24726i	0.924648	+	0.533846i	0.885115	−	0.465372i	$-0.154080\pi$
$37$	5.62442	+	3.24726i	0.924648	+	0.533846i	0.0395333	+	0.999218i	$0.487413\pi$
$38$	0.0566626	+	0.0981424i	0.00919188	+	0.0159208i
$39$	0.518461	+	0.898000i	0.0830201	+	0.143795i
$40$	1.06359	−	1.84220i	0.168169	−	0.291277i
$41$		−	8.07293i		−	1.26078i	−0.776279	−	0.630390i	$-0.782895\pi$
$41$		−	8.07293i		−	1.26078i	0.776279	−	0.630390i	$-0.217105\pi$
$42$	−1.35867	−	0.680009i	−0.209647	−	0.104928i
$43$			8.57509i			1.30769i	0.756629	+	0.653844i	$0.226845\pi$
$43$			8.57509i			1.30769i	−0.756629	+	0.653844i	$0.773155\pi$
$44$	−1.40007	−	0.808333i	−0.211069	−	0.121861i
$45$	−0.504635	−	0.874053i	−0.0752265	−	0.130296i
$46$	−2.74350	−	0.240617i	−0.404507	−	0.0354771i
$47$	−3.46026	−	1.99778i	−0.504731	−	0.291407i	0.225934	−	0.974143i	$-0.427457\pi$
$47$	−3.46026	−	1.99778i	−0.504731	−	0.291407i	−0.730665	+	0.682736i	$0.760790\pi$
$48$			2.13013i			0.307458i
$49$	−4.19554	−	5.60334i	−0.599363	−	0.800477i
$50$	2.28633			0.323335
$51$	−0.919173	−	0.530685i	−0.128710	−	0.0743107i
$52$	−1.49987	+	0.865949i	−0.207994	+	0.120085i
$53$	−8.28588	+	4.78385i	−1.13815	+	0.657113i	−0.945973	−	0.324247i	$-0.894889\pi$
$53$	−8.28588	+	4.78385i	−1.13815	+	0.657113i	−0.192180	+	0.981360i	$0.561556\pi$
$54$	−0.497320	−	0.287128i	−0.0676767	−	0.0390732i
$55$			0.976903i			0.131726i
$56$	2.49579	−	4.98662i	0.333514	−	0.666365i
$57$			0.197343i			0.0261387i
$58$	0.334314	−	0.579049i	0.0438976	−	0.0760328i
$59$	3.57952	−	2.06664i	0.466014	−	0.269053i	−0.248556	−	0.968618i	$-0.579956\pi$
$59$	3.57952	−	2.06664i	0.466014	−	0.269053i	0.714570	+	0.699564i	$0.246623\pi$
$60$	1.45987	−	0.842857i	0.188468	−	0.108812i
$61$	1.73860	−	3.01135i	0.222605	−	0.385564i	−0.732993	−	0.680236i	$-0.761877\pi$
$61$	1.73860	−	3.01135i	0.222605	−	0.385564i	0.955598	+	0.294672i	$0.0952105\pi$
$62$			1.34734i			0.171113i
$63$	−1.45690	−	2.20849i	−0.183553	−	0.278244i
$64$	−1.13715			−0.142143
$65$	0.906324	+	0.523267i	0.112416	+	0.0649032i
$66$	0.277920	+	0.481371i	0.0342096	+	0.0592527i
$67$	−8.02600	+	4.63381i	−0.980532	+	0.566110i	−0.902431	−	0.430835i	$-0.858219\pi$
$67$	−8.02600	+	4.63381i	−0.980532	+	0.566110i	−0.0781010	+	0.996945i	$0.524886\pi$
$68$	0.886365	−	1.53523i	0.107488	−	0.186174i
$69$	−3.92793	−	2.75162i	−0.472867	−	0.331256i
$70$	−1.53070	+	0.0912662i	−0.182954	+	0.0109084i
$71$	−4.70241			−0.558073			−0.279037	−	0.960280i	$-0.590015\pi$
$71$	−4.70241			−0.558073			−0.279037	+	0.960280i	$0.590015\pi$
$72$	1.05383	−	1.82528i	0.124195	−	0.215111i
$73$	−8.64734	+	4.99255i	−1.01209	+	0.584333i	−0.911804	−	0.410625i	$-0.865311\pi$
$73$	−8.64734	+	4.99255i	−1.01209	+	0.584333i	−0.100291	+	0.994958i	$0.531977\pi$
$74$	3.22985	−	1.86476i	0.375463	−	0.216774i
$75$	3.44797	+	1.99069i	0.398137	+	0.229865i
$76$	−0.329608			−0.0378086
$77$	0.152420	+	2.55636i	0.0173699	+	0.291325i
$78$	0.595458			0.0674223
$79$	−4.23226	−	2.44349i	−0.476166	−	0.274915i	0.242651	−	0.970114i	$-0.421983\pi$
$79$	−4.23226	−	2.44349i	−0.476166	−	0.274915i	−0.718817	+	0.695199i	$0.755316\pi$
$80$	1.07494	+	1.86185i	0.120182	+	0.208161i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.01483	−	2.31796i	−0.443364	−	0.255976i
$83$	7.71346			0.846662			0.423331	−	0.905975i	$-0.360861\pi$
$83$	7.71346			0.846662			0.423331	+	0.905975i	$0.360861\pi$
$84$	3.68869	−	2.43336i	0.402469	−	0.265502i
$85$	−1.07121			−0.116189
$86$	4.26456	+	2.46215i	0.459860	+	0.265500i
$87$	1.00835	−	0.582169i	0.108106	−	0.0624151i
$88$	−1.76674	+	1.02003i	−0.188335	+	0.108736i
$89$	−5.52710	+	9.57321i	−0.585871	+	1.01476i	0.408895	+	0.912581i	$0.365914\pi$
$89$	−5.52710	+	9.57321i	−0.585871	+	1.01476i	−0.994766	+	0.102177i	$0.967419\pi$
$90$	−0.579579			−0.0610930
$91$	2.45331	+	1.22788i	0.257177	+	0.128717i
$92$	4.59583	−	6.56054i	0.479149	−	0.683984i
$93$	−1.17312	+	2.03191i	−0.121647	+	0.210699i
$94$	−1.98708	+	1.14724i	−0.204951	+	0.118329i
$95$	0.0995860	+	0.172488i	0.0102173	+	0.0176969i
$96$	4.70991	+	2.71927i	0.480704	+	0.277534i
$97$	8.08305			0.820709			0.410355	−	0.911926i	$-0.365405\pi$
$97$	8.08305			0.820709			0.410355	+	0.911926i	$0.365405\pi$
$98$	−3.99131	+	0.477652i	−0.403183	+	0.0482501i
$99$			0.967930i			0.0972807i
$100$	−3.32491	+	5.75891i	−0.332491	+	0.575891i
$101$	−2.38568	+	1.37737i	−0.237384	+	0.137054i	−0.613974	−	0.789326i	$-0.710430\pi$
$101$	−2.38568	+	1.37737i	−0.237384	+	0.137054i	0.376590	+	0.926380i	$0.377097\pi$
$102$	−0.527840	+	0.304749i	−0.0522640	+	0.0301746i
$103$	−4.18158	+	7.24271i	−0.412023	+	0.713646i	−0.995111	−	0.0987639i	$-0.968511\pi$
$103$	−4.18158	+	7.24271i	−0.412023	+	0.713646i	0.583087	+	0.812409i	$0.301844\pi$
$104$			2.18547i			0.214303i
$105$	−2.38789	−	1.19513i	−0.233035	−	0.116633i
$106$			5.49431i			0.533655i
$107$	−2.72445	−	1.57296i	−0.263383	−	0.152064i	0.362494	−	0.931986i	$-0.381925\pi$
$107$	−2.72445	−	1.57296i	−0.263383	−	0.152064i	−0.625877	+	0.779922i	$0.715259\pi$
$108$	1.44646	−	0.835115i	0.139186	−	0.0803590i
$109$	1.87840	−	1.08450i	0.179918	−	0.103876i	−0.407336	−	0.913278i	$-0.633542\pi$
$109$	1.87840	−	1.08450i	0.179918	−	0.103876i	0.587254	+	0.809402i	$0.300209\pi$
$110$	0.485834	+	0.280496i	0.0463224	+	0.0267443i
$111$	6.49452			0.616432
$112$	3.10339	+	4.70437i	0.293243	+	0.444521i
$113$			10.1131i			0.951364i	0.879617	+	0.475682i	$0.157799\pi$
$113$			10.1131i			0.951364i	−0.879617	+	0.475682i	$0.842201\pi$
$114$	0.0981424	+	0.0566626i	0.00919188	+	0.00530694i
$115$	−4.82178	−	0.422891i	−0.449633	−	0.0394348i
$116$	0.972356	+	1.68417i	0.0902810	+	0.156371i
$117$	0.898000	+	0.518461i	0.0830201	+	0.0479317i
$118$		−	2.37356i		−	0.218504i
$119$	−2.80314	+	0.167134i	−0.256963	+	0.0153211i
$120$		−	2.12719i		−	0.194185i
$121$	−5.03156	+	8.71491i	−0.457414	+	0.792264i
$122$	−0.998404	−	1.72929i	−0.0903912	−	0.156562i
$123$	−4.03647	−	6.99136i	−0.363956	−	0.630390i
$124$	−3.39375	−	1.95938i	−0.304768	−	0.175958i
$125$	9.06463			0.810765
$126$	−1.51664	+	0.0904280i	−0.135113	+	0.00805596i
$127$	−7.49833			−0.665369			−0.332685	−	0.943038i	$-0.607954\pi$
$127$	−7.49833			−0.665369			−0.332685	+	0.943038i	$0.607954\pi$
$128$	−5.76505	+	9.98536i	−0.509563	+	0.882589i
$129$	4.28754	+	7.42624i	0.377497	+	0.653844i
$130$	0.520462	−	0.300489i	0.0456475	−	0.0263546i
$131$	−0.130892	−	0.0755707i	−0.0114361	−	0.00660265i	0.494271	−	0.869308i	$-0.335435\pi$
$131$	−0.130892	−	0.0755707i	−0.0114361	−	0.00660265i	−0.505707	+	0.862705i	$0.668768\pi$
$132$	−1.61667			−0.140713
$133$	0.287509	+	0.435829i	0.0249302	+	0.0377912i
$134$			5.32199i			0.459750i
$135$	−0.874053	−	0.504635i	−0.0752265	−	0.0434321i
$136$	−1.11850	−	1.93729i	−0.0959104	−	0.166122i
$137$	6.92584	−	3.99864i	0.591714	−	0.341626i	−0.174061	−	0.984735i	$-0.555689\pi$
$137$	6.92584	−	3.99864i	0.591714	−	0.341626i	0.765775	+	0.643108i	$0.222356\pi$
$138$	−2.49625	+	1.16337i	−0.212495	+	0.0990327i
$139$		−	7.09728i		−	0.601984i	−0.953627	−	0.300992i	$-0.902682\pi$
$139$		−	7.09728i		−	0.601984i	0.953627	−	0.300992i	$-0.0973177\pi$
$140$	1.99615	−	3.98833i	0.168705	−	0.337076i
$141$	−3.99557			−0.336488
$142$	−1.35019	+	2.33860i	−0.113306	+	0.196251i
$143$	−0.501834	−	0.869202i	−0.0419654	−	0.0726863i
$144$	1.06506	+	1.84475i	0.0887554	+	0.153729i
$145$	0.587566	−	1.01769i	0.0487947	−	0.0845148i
$146$			5.73400i			0.474549i
$147$	−6.43512	−	2.75486i	−0.530759	−	0.227217i
$148$			10.8473i			0.891646i
$149$	−17.3405	−	10.0115i	−1.42059	−	0.820178i	−0.424241	−	0.905549i	$-0.639459\pi$
$149$	−17.3405	−	10.0115i	−1.42059	−	0.820178i	−0.996349	+	0.0853716i	$0.972792\pi$
$150$	1.98002	−	1.14316i	0.161668	−	0.0933389i
$151$	2.61606	+	4.53115i	0.212892	+	0.368740i	0.952618	−	0.304168i	$-0.0983784\pi$
$151$	2.61606	+	4.53115i	0.212892	+	0.368740i	−0.739726	+	0.672908i	$0.765045\pi$
$152$	−0.207965	+	0.360205i	−0.0168682	+	0.0292165i
$153$	−1.06137			−0.0858066
$154$	1.31509	+	0.658202i	0.105973	+	0.0530394i
$155$			2.36799i			0.190202i
$156$	−0.865949	+	1.49987i	−0.0693314	+	0.120085i
$157$	−1.74979	−	3.03073i	−0.139649	−	0.241879i	0.787715	−	0.616040i	$-0.211264\pi$
$157$	−1.74979	−	3.03073i	−0.139649	−	0.241879i	−0.927364	+	0.374161i	$0.877931\pi$
$158$	−2.43040	+	1.40319i	−0.193352	+	0.111632i
$159$	−4.78385	+	8.28588i	−0.379384	+	0.657113i
$160$	5.48896			0.433940
$161$	−12.6836	−	0.354312i	−0.999610	−	0.0279237i
$162$	−0.574256			−0.0451178
$163$	−0.390384	+	0.676165i	−0.0305773	+	0.0529614i	−0.880909	−	0.473286i	$-0.843068\pi$
$163$	−0.390384	+	0.676165i	−0.0305773	+	0.0529614i	0.850332	+	0.526247i	$0.176401\pi$
$164$	11.6772	−	6.74183i	0.911835	−	0.526448i
$165$	0.488452	+	0.846023i	0.0380259	+	0.0658628i
$166$	2.21475	−	3.83606i	0.171898	−	0.297736i
$167$		−	13.5043i		−	1.04499i	−0.852642	−	0.522496i	$-0.825001\pi$
$167$		−	13.5043i		−	1.04499i	0.852642	−	0.522496i	$-0.174999\pi$
$168$	−0.331892	−	5.56643i	−0.0256060	−	0.429460i
$169$	11.9248			0.917292
$170$	−0.307574	+	0.532733i	−0.0235898	+	0.0408588i
$171$	0.0986713	+	0.170904i	0.00754558	+	0.0130693i
$172$	−12.4035	+	7.16118i	−0.945761	+	0.546035i
$173$	5.80194	+	3.34975i	0.441113	+	0.254677i	0.704070	−	0.710131i	$-0.251364\pi$
$173$	5.80194	+	3.34975i	0.441113	+	0.254677i	−0.262956	+	0.964808i	$0.584698\pi$
$174$		−	0.668628i		−	0.0506885i
$175$	10.5151	−	0.626946i	0.794863	−	0.0473927i
$176$		−	2.06182i		−	0.155415i
$177$	2.06664	−	3.57952i	0.155338	−	0.269053i
$178$	3.17397	+	5.49747i	0.237899	+	0.412053i
$179$	−7.63602	−	13.2260i	−0.570743	−	0.988555i	−0.996490	−	0.0837132i	$-0.973322\pi$
$179$	−7.63602	−	13.2260i	−0.570743	−	0.988555i	0.425747	−	0.904842i	$-0.360011\pi$
$180$	0.842857	−	1.45987i	0.0628228	−	0.108812i
$181$	20.6442			1.53447			0.767234	−	0.641367i	$-0.221633\pi$
$181$	20.6442			1.53447			0.767234	+	0.641367i	$0.221633\pi$
$182$	1.31506	−	0.867525i	0.0974790	−	0.0643052i
$183$		−	3.47721i		−	0.257043i
$184$	−4.26984	−	9.16182i	−0.314777	−	0.675418i
$185$	5.67655	−	3.27736i	0.417349	−	0.240956i
$186$	0.673672	+	1.16683i	0.0493961	+	0.0855565i
$187$	0.889695	+	0.513666i	0.0650610	+	0.0375630i
$188$		−	6.67352i		−	0.486717i
$189$	−2.36596	−	1.18416i	−0.172098	−	0.0861348i
$190$	0.114376			0.00829768
$191$	−11.4420	−	6.60607i	−0.827917	−	0.477998i	0.0252218	−	0.999682i	$-0.491971\pi$
$191$	−11.4420	−	6.60607i	−0.827917	−	0.477998i	−0.853139	+	0.521684i	$0.825304\pi$
$192$	−0.984797	+	0.568573i	−0.0710716	+	0.0410332i
$193$	1.48712	+	2.57576i	0.107045	+	0.185407i	0.914572	−	0.404424i	$-0.132528\pi$
$193$	1.48712	+	2.57576i	0.107045	+	0.185407i	−0.807527	+	0.589831i	$0.799194\pi$
$194$	2.32087	−	4.01986i	0.166629	−	0.288609i
$195$	1.04653			0.0749438
$196$	4.60126	−	10.7481i	0.328661	−	0.767723i
$197$	6.99929			0.498679			0.249340	−	0.968416i	$-0.419786\pi$
$197$	6.99929			0.498679			0.249340	+	0.968416i	$0.419786\pi$
$198$	0.481371	+	0.277920i	0.0342096	+	0.0197509i
$199$	−11.1823	−	19.3683i	−0.792693	−	1.37298i	−0.924294	−	0.381682i	$-0.875345\pi$
$199$	−11.1823	−	19.3683i	−0.792693	−	1.37298i	0.131601	−	0.991303i	$-0.457988\pi$
$200$	4.19567	+	7.26712i	0.296679	+	0.513863i
$201$	−4.63381	+	8.02600i	−0.326844	+	0.566110i
$202$			1.58193i			0.111304i
$203$	1.37876	−	2.75478i	0.0967699	−	0.193347i
$204$		−	1.77273i		−	0.124116i
$205$	−7.05617	−	4.07388i	−0.492825	−	0.284532i
$206$	2.40130	+	4.15917i	0.167306	+	0.289783i
$207$	−4.77749	−	0.419007i	−0.332059	−	0.0291230i
$208$	−1.91286	−	1.10439i	−0.132633	−	0.0765755i
$209$		−	0.191014i		−	0.0132127i
$210$	−1.28000	+	0.844391i	−0.0883281	+	0.0582685i
$211$	21.7460			1.49706			0.748528	−	0.663104i	$-0.230761\pi$
$211$	21.7460			1.49706			0.748528	+	0.663104i	$0.230761\pi$
$212$	−13.8393	−	7.99014i	−0.950489	−	0.548765i
$213$	−4.07240	+	2.35120i	−0.279037	+	0.161102i
$214$	−1.56453	+	0.903283i	−0.106949	+	0.0617471i
$215$	7.49508	+	4.32729i	0.511160	+	0.295119i
$216$		−	2.10765i		−	0.143407i
$217$	0.369463	+	6.19658i	0.0250808	+	0.420651i
$218$		−	1.24556i		−	0.0843597i
$219$	−4.99255	+	8.64734i	−0.337365	+	0.584333i
$220$	−1.41305	+	0.815827i	−0.0952680	+	0.0550030i
$221$	0.953109	−	0.550278i	0.0641131	−	0.0370157i
$222$	1.86476	−	3.22985i	0.125154	−	0.216774i
$223$		−	19.2308i		−	1.28779i	−0.765113	−	0.643896i	$-0.777317\pi$
$223$		−	19.2308i		−	1.28779i	0.765113	−	0.643896i	$-0.222683\pi$
$224$	14.3635	−	0.856406i	0.959703	−	0.0572211i
$225$	3.98137			0.265425
$226$	5.02947	+	2.90376i	0.334555	+	0.193156i
$227$	13.0462	+	22.5967i	0.865908	+	1.49980i	0.866142	+	0.499797i	$0.166592\pi$
$227$	13.0462	+	22.5967i	0.865908	+	1.49980i	−0.000234228		1.00000i	$0.500075\pi$
$228$	−0.285449	+	0.164804i	−0.0189043	+	0.0109144i
$229$	6.39404	−	11.0748i	0.422530	−	0.731843i	−0.573656	−	0.819096i	$-0.694475\pi$
$229$	6.39404	−	11.0748i	0.422530	−	0.731843i	0.996186	+	0.0872529i	$0.0278088\pi$
$230$	−1.59478	+	2.27654i	−0.105157	+	0.150111i
$231$	1.41018	+	2.13767i	0.0927831	+	0.140648i
$232$	2.45402			0.161114
$233$	−8.26346	+	14.3127i	−0.541357	+	0.937658i	0.457469	+	0.889225i	$0.348756\pi$
$233$	−8.26346	+	14.3127i	−0.541357	+	0.937658i	−0.998826	+	0.0484326i	$0.984577\pi$
$234$	0.515682	−	0.297729i	0.0337112	−	0.0194632i
$235$	−3.49234	+	2.01630i	−0.227815	+	0.131529i
$236$	5.97862	+	3.45176i	0.389175	+	0.224690i
$237$	−4.88699			−0.317444
$238$	−0.721741	+	1.44205i	−0.0467835	+	0.0934740i
$239$	8.63893			0.558806			0.279403	−	0.960174i	$-0.409863\pi$
$239$	8.63893			0.558806			0.279403	+	0.960174i	$0.409863\pi$
$240$	1.86185	+	1.07494i	0.120182	+	0.0693870i
$241$	−10.9696	−	18.9998i	−0.706611	−	1.22389i	−0.966107	−	0.258142i	$-0.916890\pi$
$241$	−10.9696	−	18.9998i	−0.706611	−	1.22389i	0.259496	−	0.965744i	$-0.416444\pi$
$242$	2.88940	+	5.00459i	0.185738	+	0.321707i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	5.80774			0.371802
$245$	−7.01484	+	0.839486i	−0.448161	+	0.0536328i
$246$	−4.63593			−0.295576
$247$	−0.177214	−	0.102314i	−0.0112758	−	0.00651011i
$248$	−4.28255	+	2.47253i	−0.271942	+	0.157006i
$249$	6.68005	−	3.85673i	0.423331	−	0.244410i
$250$	2.60271	−	4.50802i	0.164610	−	0.285112i
$251$	−1.53663			−0.0969910			−0.0484955	−	0.998823i	$-0.515443\pi$
$251$	−1.53663			−0.0969910			−0.0484955	+	0.998823i	$0.515443\pi$
$252$	1.97782	−	3.95170i	0.124591	−	0.248934i
$253$	3.80196	+	2.66337i	0.239027	+	0.167445i
$254$	−2.15298	+	3.72907i	−0.135090	+	0.233983i
$255$	−0.927693	+	0.535604i	−0.0580944	+	0.0335408i
$256$	2.17347	+	3.76455i	0.135842	+	0.235285i
$257$	−11.5449	−	6.66547i	−0.720153	−	0.415781i	0.0946559	−	0.995510i	$-0.469825\pi$
$257$	−11.5449	−	6.66547i	−0.720153	−	0.415781i	−0.814809	+	0.579729i	$0.803158\pi$
$258$	4.92429			0.306573
$259$	14.3431	−	9.46188i	0.891236	−	0.587933i
$260$			1.74795i			0.108403i
$261$	0.582169	−	1.00835i	0.0360354	−	0.0624151i
$262$	−0.0751657	+	0.0433969i	−0.00464375	+	0.00268107i
$263$	21.3445	−	12.3233i	1.31616	−	0.759885i	0.333051	−	0.942909i	$-0.391922\pi$
$263$	21.3445	−	12.3233i	1.31616	−	0.759885i	0.983108	+	0.183024i	$0.0585885\pi$
$264$	−1.02003	+	1.76674i	−0.0627785	+	0.108736i
$265$			9.65640i			0.593188i
$266$	0.299299	−	0.0178453i	0.0183512	−	0.00109417i
$267$			11.0542i			0.676506i
$268$	−13.4053	−	7.73953i	−0.818857	−	0.472767i
$269$	1.80941	−	1.04466i	0.110322	−	0.0636943i	−0.443824	−	0.896114i	$-0.646378\pi$
$269$	1.80941	−	1.04466i	0.110322	−	0.0636943i	0.554146	+	0.832420i	$0.313045\pi$
$270$	−0.501930	+	0.289790i	−0.0305465	+	0.0176360i
$271$	28.0542	+	16.1971i	1.70417	+	0.983905i	0.941433	+	0.337199i	$0.109479\pi$
$271$	28.0542	+	16.1971i	1.70417	+	0.983905i	0.762739	+	0.646706i	$0.223854\pi$
$272$	2.26085			0.137084
$273$	2.73857	−	0.163284i	0.165746	−	0.00988239i
$274$		−	4.59248i		−	0.277442i
$275$	−3.33740	−	1.92685i	−0.201253	−	0.116193i
$276$	0.699838	−	7.97951i	0.0421253	−	0.480310i
$277$	6.26270	+	10.8473i	0.376289	+	0.651752i	0.990519	−	0.137375i	$-0.0438665\pi$
$277$	6.26270	+	10.8473i	0.376289	+	0.651752i	−0.614230	+	0.789127i	$0.710533\pi$
$278$	−3.52962	−	2.03783i	−0.211693	−	0.122221i
$279$			2.34624i			0.140466i
$280$	−3.09911	−	4.69788i	−0.185207	−	0.280752i
$281$			14.2056i			0.847433i	0.905795	+	0.423717i	$0.139275\pi$
$281$			14.2056i			0.847433i	−0.905795	+	0.423717i	$0.860725\pi$
$282$	−1.14724	+	1.98708i	−0.0683171	+	0.118329i
$283$	−13.3953	−	23.2013i	−0.796268	−	1.37918i	−0.922031	−	0.387116i	$-0.873471\pi$
$283$	−13.3953	−	23.2013i	−0.796268	−	1.37918i	0.125763	−	0.992060i	$-0.459862\pi$
$284$	−3.92705	−	6.80185i	−0.233028	−	0.403616i
$285$	0.172488	+	0.0995860i	0.0102173	+	0.00589896i
$286$	−0.576362			−0.0340810
$287$	−19.1002	−	9.55962i	−1.12745	−	0.564287i
$288$	5.43854			0.320469
$289$	7.93675	−	13.7469i	0.466868	−	0.808638i
$290$	−0.337413	−	0.584416i	−0.0198136	−	0.0343181i
$291$	7.00012	−	4.04152i	0.410355	−	0.236918i
$292$	−14.4431	−	8.33870i	−0.845216	−	0.487986i
$293$	21.8475			1.27635			0.638173	−	0.769893i	$-0.279690\pi$
$293$	21.8475			1.27635			0.638173	+	0.769893i	$0.279690\pi$
$294$	−3.21775	+	2.40931i	−0.187663	+	0.140514i
$295$		−	4.17159i		−	0.242879i
$296$	11.8543	+	6.84409i	0.689018	+	0.397804i
$297$	0.483965	+	0.838252i	0.0280825	+	0.0486403i
$298$	−9.95789	+	5.74919i	−0.576845	+	0.333042i
$299$	4.50743	−	2.10067i	0.260671	−	0.121485i
$300$			6.64981i			0.383927i
$301$	20.2883	+	10.1543i	1.16940	+	0.585281i
$302$	3.00458			0.172894
$303$	−1.37737	+	2.38568i	−0.0791280	+	0.137054i
$304$	−0.210183	−	0.364047i	−0.0120548	−	0.0208795i
$305$	−1.75472	−	3.03927i	−0.100475	−	0.174028i
$306$	−0.304749	+	0.527840i	−0.0174213	+	0.0301746i
$307$		−	18.3047i		−	1.04470i	−0.852730	−	0.522352i	$-0.825055\pi$
$307$		−	18.3047i		−	1.04470i	0.852730	−	0.522352i	$-0.174945\pi$
$308$	−3.57039	+	2.35533i	−0.203442	+	0.134207i
$309$			8.36316i			0.475764i
$310$	1.17765	+	0.679917i	0.0668861	+	0.0386167i
$311$	6.06433	−	3.50124i	0.343877	−	0.198537i	−0.318108	−	0.948054i	$-0.603048\pi$
$311$	6.06433	−	3.50124i	0.343877	−	0.198537i	0.661985	+	0.749517i	$0.269714\pi$
$312$	1.09273	+	1.89267i	0.0618639	+	0.107151i
$313$	0.910888	−	1.57770i	0.0514864	−	0.0891771i	−0.839134	−	0.543925i	$-0.816937\pi$
$313$	0.910888	−	1.57770i	0.0514864	−	0.0891771i	0.890620	+	0.454748i	$0.150271\pi$
$314$	−2.00966			−0.113412
$315$	−2.66554	+	0.158930i	−0.150186	+	0.00895467i
$316$		−	8.16239i		−	0.459171i
$317$	−7.16145	+	12.4040i	−0.402227	+	0.696678i	−0.993994	−	0.109431i	$-0.965097\pi$
$317$	−7.16145	+	12.4040i	−0.402227	+	0.696678i	0.591767	+	0.806109i	$0.298430\pi$
$318$	2.74716	+	4.75821i	0.154053	+	0.266827i
$319$	−0.976009	+	0.563499i	−0.0546460	+	0.0315499i
$320$	−0.573844	+	0.993926i	−0.0320788	+	0.0555622i
$321$	−3.14592			−0.175588
$322$	−3.81803	+	6.20609i	−0.212771	+	0.345852i
$323$	0.209453			0.0116543
$324$	0.835115	−	1.44646i	0.0463953	−	0.0803590i
$325$	−3.57527	+	2.06419i	−0.198321	+	0.114500i
$326$	0.224180	+	0.388292i	0.0124162	+	0.0215055i
$327$	1.08450	−	1.87840i	0.0599728	−	0.103876i
$328$		−	17.0149i		−	0.939492i
$329$	−8.82418	+	5.82116i	−0.486493	+	0.320931i
$330$	0.560992			0.0308816
$331$	14.5351	−	25.1755i	0.798922	−	1.38377i	−0.121397	−	0.992604i	$-0.538737\pi$
$331$	14.5351	−	25.1755i	0.798922	−	1.38377i	0.920319	−	0.391169i	$-0.127929\pi$
$332$	6.44163	+	11.1572i	0.353530	+	0.612332i
$333$	5.62442	−	3.24726i	0.308216	−	0.177949i
$334$	−6.71594	−	3.87745i	−0.367480	−	0.212165i
$335$			9.35353i			0.511038i
$336$	5.03980	+	2.52241i	0.274944	+	0.137609i
$337$			2.66665i			0.145262i	0.997359	+	0.0726309i	$0.0231395\pi$
$337$			2.66665i			0.145262i	−0.997359	+	0.0726309i	$0.976860\pi$
$338$	3.42394	−	5.93044i	0.186238	−	0.322573i
$339$	5.05657	+	8.75824i	0.274635	+	0.475682i
$340$	−0.894582	−	1.54946i	−0.0485155	−	0.0840313i
$341$	1.13550	−	1.96675i	0.0614908	−	0.106505i
$342$	0.113325			0.00612792
$343$	−18.2255	+	3.29125i	−0.984083	+	0.177711i
$344$			18.0733i			0.974446i
$345$	−4.38723	+	2.04466i	−0.236200	+	0.110081i
$346$	3.33180	−	1.92361i	0.179119	−	0.103414i
$347$	−15.7011	−	27.1951i	−0.842879	−	1.45991i	−0.887450	−	0.460904i	$-0.847525\pi$
$347$	−15.7011	−	27.1951i	−0.842879	−	1.45991i	0.0445710	−	0.999006i	$-0.485808\pi$
$348$	1.68417	+	0.972356i	0.0902810	+	0.0521238i
$349$		−	3.17937i		−	0.170188i	−0.996373	−	0.0850939i	$-0.972881\pi$
$349$		−	3.17937i		−	0.170188i	0.996373	−	0.0850939i	$-0.0271190\pi$
$350$	2.70737	−	5.40936i	0.144715	−	0.289142i
$351$	1.03692			0.0553468
$352$	−4.55887	−	2.63206i	−0.242989	−	0.140290i
$353$	−13.0700	+	7.54598i	−0.695647	+	0.401632i	−0.805724	−	0.592291i	$-0.798224\pi$
$353$	−13.0700	+	7.54598i	−0.695647	+	0.401632i	0.110077	+	0.993923i	$0.464890\pi$
$354$	−1.18678	−	2.05556i	−0.0630765	−	0.109252i
$355$	−2.37300	+	4.11016i	−0.125946	+	0.218144i
$356$	−18.4630			−0.978539
$357$	−2.34402	+	1.54631i	−0.124059	+	0.0818395i
$358$	−8.77005			−0.463512
$359$	3.32793	+	1.92138i	0.175641	+	0.101407i	0.585243	−	0.810858i	$-0.300999\pi$
$359$	3.32793	+	1.92138i	0.175641	+	0.101407i	−0.409602	+	0.912264i	$0.634332\pi$
$360$	−1.06359	−	1.84220i	−0.0560563	−	0.0970924i
$361$	9.48053	+	16.4208i	0.498975	+	0.864250i
$362$	5.92751	−	10.2668i	0.311543	−	0.539609i
$363$			10.0631i			0.528176i
$364$	0.272722	+	4.57405i	0.0142945	+	0.239745i
$365$			10.0777i			0.527488i
$366$	−1.72929	−	0.998404i	−0.0903912	−	0.0521874i
$367$	−8.15537	−	14.1255i	−0.425707	−	0.737346i	0.570779	−	0.821104i	$-0.306641\pi$
$367$	−8.15537	−	14.1255i	−0.425707	−	0.737346i	−0.996486	+	0.0837575i	$0.973308\pi$
$368$	10.1767	+	0.892539i	0.530496	+	0.0465268i
$369$	−6.99136	−	4.03647i	−0.363956	−	0.210130i
$370$		−	3.76409i		−	0.195686i
$371$	1.50663	+	25.2689i	0.0782201	+	1.31190i
$372$	−3.91877			−0.203179
$373$	18.7011	+	10.7971i	0.968308	+	0.559053i	0.898720	−	0.438523i	$-0.144498\pi$
$373$	18.7011	+	10.7971i	0.968308	+	0.559053i	0.0695879	+	0.997576i	$0.477832\pi$
$374$	0.510913	−	0.294976i	0.0264187	−	0.0152528i
$375$	7.85020	−	4.53232i	0.405383	−	0.234048i
$376$	−7.29303	−	4.21063i	−0.376109	−	0.217147i
$377$			1.20733i			0.0621805i
$378$	−1.26824	+	0.836635i	−0.0652312	+	0.0430319i
$379$		−	12.1139i		−	0.622248i	−0.950369	−	0.311124i	$-0.899294\pi$
$379$		−	12.1139i		−	0.622248i	0.950369	−	0.311124i	$-0.100706\pi$
$380$	−0.166332	+	0.288095i	−0.00853263	+	0.0147789i
$381$	−6.49375	+	3.74917i	−0.332685	+	0.192076i
$382$	−6.57066	+	3.79357i	−0.336184	+	0.194096i
$383$	−7.25738	+	12.5701i	−0.370835	+	0.642305i	−0.989694	−	0.143197i	$-0.954262\pi$
$383$	−7.25738	+	12.5701i	−0.370835	+	0.642305i	0.618859	+	0.785502i	$0.287595\pi$
$384$			11.5301i			0.588393i
$385$	2.31131	+	1.15681i	0.117796	+	0.0589564i
$386$	1.70797			0.0869333
$387$	7.42624	+	4.28754i	0.377497	+	0.217948i
$388$	6.75028	+	11.6918i	0.342693	+	0.593562i
$389$	2.41099	−	1.39199i	0.122242	−	0.0705766i	−0.437632	−	0.899154i	$-0.644183\pi$
$389$	2.41099	−	1.39199i	0.122242	−	0.0705766i	0.559874	+	0.828578i	$0.310849\pi$
$390$	0.300489	−	0.520462i	0.0152158	−	0.0263546i
$391$	−2.92048	+	4.16898i	−0.147695	+	0.210834i
$392$	−8.84274	−	11.8099i	−0.446626	−	0.596489i
$393$	−0.151141			−0.00762408
$394$	2.00969	−	3.48089i	0.101247	−	0.175365i
$395$	−4.27149	+	2.46614i	−0.214922	+	0.124085i
$396$	−1.40007	+	0.808333i	−0.0703564	+	0.0406203i
$397$	−1.18975	−	0.686901i	−0.0597117	−	0.0344746i	0.469847	−	0.882748i	$-0.344309\pi$
$397$	−1.18975	−	0.686901i	−0.0597117	−	0.0344746i	−0.529559	+	0.848273i	$0.677642\pi$
$398$	−12.8430			−0.643762
$399$	0.466905	+	0.233685i	0.0233745	+	0.0116989i
$400$	−8.48084			−0.424042
$401$	21.7078	+	12.5330i	1.08404	+	0.625870i	0.931983	−	0.362502i	$-0.118077\pi$
$401$	21.7078	+	12.5330i	1.08404	+	0.625870i	0.152055	+	0.988372i	$0.451411\pi$
$402$	2.66099	+	4.60898i	0.132718	+	0.229875i
$403$	−1.21644	−	2.10693i	−0.0605950	−	0.104954i
$404$	−3.98463	−	2.30053i	−0.198243	−	0.114456i
$405$	−1.00927			−0.0501510
$406$	−0.974126	−	1.47666i	−0.0483451	−	0.0732853i
$407$	−6.28624			−0.311597
$408$	−1.93729	−	1.11850i	−0.0959104	−	0.0553739i
$409$	−16.3468	+	9.43785i	−0.808299	+	0.466672i	−0.846365	−	0.532604i	$-0.821214\pi$
$409$	−16.3468	+	9.43785i	−0.808299	+	0.466672i	0.0380659	+	0.999275i	$0.487880\pi$
$410$	−4.05205	+	2.33945i	−0.200116	+	0.115537i
$411$	3.99864	−	6.92584i	0.197238	−	0.341626i
$412$	−13.9684			−0.688174
$413$	−0.650866	−	10.9162i	−0.0320270	−	0.537152i
$414$	−1.58013	+	2.25563i	−0.0776592	+	0.110858i
$415$	3.89248	−	6.74197i	0.191074	−	0.330951i
$416$	−4.88381	+	2.81967i	−0.239448	+	0.138246i
$417$	−3.54864	−	6.14643i	−0.173778	−	0.300992i
$418$	−0.0949951	−	0.0548454i	−0.00464636	−	0.00268258i
$419$	−38.9926			−1.90491			−0.952456	−	0.304677i	$-0.901452\pi$
$419$	−38.9926			−1.90491			−0.952456	+	0.304677i	$0.901452\pi$
$420$	−0.265449	−	4.45207i	−0.0129526	−	0.217239i
$421$		−	21.9797i		−	1.07122i	−0.844464	−	0.535612i	$-0.820081\pi$
$421$		−	21.9797i		−	1.07122i	0.844464	−	0.535612i	$-0.179919\pi$
$422$	6.24388	−	10.8147i	0.303947	−	0.526452i
$423$	−3.46026	+	1.99778i	−0.168244	+	0.0971356i
$424$	−17.4637	+	10.0827i	−0.848114	+	0.489659i
$425$	2.11285	−	3.65957i	0.102488	−	0.177515i
$426$			2.70038i			0.130834i
$427$	−5.06596	−	7.67938i	−0.245159	−	0.371631i
$428$		−	5.25442i		−	0.253982i
$429$	−0.869202	−	0.501834i	−0.0419654	−	0.0242288i
$430$	4.30409	−	2.48497i	0.207562	−	0.119836i
$431$	27.0968	−	15.6444i	1.30521	−	0.753563i	0.323916	−	0.946086i	$-0.395000\pi$
$431$	27.0968	−	15.6444i	1.30521	−	0.753563i	0.981292	+	0.192523i	$0.0616671\pi$
$432$	1.84475	+	1.06506i	0.0887554	+	0.0512430i
$433$	33.4890			1.60938			0.804688	−	0.593698i	$-0.202332\pi$
$433$	33.4890			1.60938			0.804688	+	0.593698i	$0.202332\pi$
$434$	3.18776	+	1.59547i	0.153018	+	0.0765849i
$435$		−	1.17513i		−	0.0563432i
$436$	3.13736	+	1.81136i	0.150253	+	0.0867483i
$437$	0.942803	+	0.0826879i	0.0451004	+	0.00395550i
$438$	2.86700	+	4.96579i	0.136990	+	0.237274i
$439$	1.80175	+	1.04024i	0.0859927	+	0.0496479i	0.542380	−	0.840133i	$-0.317523\pi$
$439$	1.80175	+	1.04024i	0.0859927	+	0.0496479i	−0.456387	+	0.889781i	$0.650857\pi$
$440$			2.05897i			0.0981576i
$441$	−6.95041	+	0.831775i	−0.330972	+	0.0396083i
$442$		−	0.632001i		−	0.0300612i
$443$	−8.86653	+	15.3573i	−0.421262	+	0.729646i	−0.996063	−	0.0886464i	$-0.971746\pi$
$443$	−8.86653	+	15.3573i	−0.421262	+	0.729646i	0.574802	+	0.818293i	$0.305079\pi$
$444$	5.42367	+	9.39407i	0.257396	+	0.445823i
$445$	5.57833	+	9.66195i	0.264438	+	0.458021i
$446$	−9.56388	−	5.52171i	−0.452863	−	0.261460i
$447$	−20.0231			−0.947060
$448$	−1.34656	+	2.69044i	−0.0636190	+	0.127111i
$449$	−22.6881			−1.07072			−0.535360	−	0.844624i	$-0.679824\pi$
$449$	−22.6881			−1.07072			−0.535360	+	0.844624i	$0.679824\pi$
$450$	1.14316	−	1.98002i	0.0538892	−	0.0933389i
$451$	3.90702	+	6.76715i	0.183974	+	0.318653i
$452$	−14.6283	+	8.44564i	−0.688056	+	0.397249i
$453$	4.53115	+	2.61606i	0.212892	+	0.122913i
$454$	14.9837			0.703222
$455$	2.31126	−	1.52470i	0.108354	−	0.0714789i
$456$			0.415929i			0.0194777i
$457$	35.3986	+	20.4374i	1.65588	+	0.956020i	0.974588	+	0.224003i	$0.0719126\pi$
$457$	35.3986	+	20.4374i	1.65588	+	0.956020i	0.681287	+	0.732017i	$0.261421\pi$
$458$	−3.67181	−	6.35977i	−0.171573	−	0.297172i
$459$	−0.919173	+	0.530685i	−0.0429033	+	0.0247702i
$460$	−3.41505	−	7.32768i	−0.159227	−	0.341655i
$461$			36.0866i			1.68072i	0.542030	+	0.840359i	$0.317656\pi$
$461$			36.0866i			1.68072i	−0.542030	+	0.840359i	$0.682344\pi$
$462$	1.46801	−	0.0875280i	0.0682978	−	0.00407217i
$463$	5.75908			0.267647			0.133824	−	0.991005i	$-0.457274\pi$
$463$	5.75908			0.267647			0.133824	+	0.991005i	$0.457274\pi$
$464$	−1.24010	+	2.14791i	−0.0575700	+	0.0997141i
$465$	1.18400	+	2.05074i	0.0549066	+	0.0951009i
$466$	4.74534	+	8.21917i	0.219824	+	0.380746i
$467$	−7.99198	+	13.8425i	−0.369825	+	0.640555i	−0.989538	−	0.144273i	$-0.953916\pi$
$467$	−7.99198	+	13.8425i	−0.369825	+	0.640555i	0.619713	+	0.784828i	$0.287249\pi$
$468$			1.73190i			0.0800570i
$469$	1.45937	+	24.4764i	0.0673875	+	1.13021i
$470$			2.31575i			0.106818i
$471$	−3.03073	−	1.74979i	−0.139649	−	0.0806262i
$472$	7.54438	−	4.35575i	0.347258	−	0.200490i
$473$	−4.15004	−	7.18809i	−0.190819	−	0.330509i
$474$	−1.40319	+	2.43040i	−0.0644507	+	0.111632i
$475$	−0.785695			−0.0360501
$476$	−2.58270	−	3.91506i	−0.118378	−	0.179446i
$477$			9.56771i			0.438075i
$478$	2.48048	−	4.29632i	0.113454	−	0.196509i
$479$	9.17615	+	15.8936i	0.419269	+	0.726195i	0.995866	−	0.0908336i	$-0.0289531\pi$
$479$	9.17615	+	15.8936i	0.419269	+	0.726195i	−0.576597	+	0.817029i	$0.695620\pi$
$480$	4.75358	−	2.74448i	0.216970	−	0.125268i
$481$	−3.36715	+	5.83208i	−0.153529	+	0.265920i
$482$	−12.5987			−0.573853
$483$	−11.1615	+	6.03497i	−0.507866	+	0.274601i
$484$	−16.8077			−0.763987
$485$	4.07899	−	7.06502i	0.185217	−	0.320806i
$486$	−0.497320	+	0.287128i	−0.0225589	+	0.0130244i
$487$	−2.09258	−	3.62445i	−0.0948238	−	0.164240i	0.814711	−	0.579867i	$-0.196895\pi$
$487$	−2.09258	−	3.62445i	−0.0948238	−	0.164240i	−0.909535	+	0.415627i	$0.863562\pi$
$488$	3.66437	−	6.34688i	0.165878	−	0.287310i
$489$			0.780768i			0.0353076i
$490$	−1.59666	+	3.72966i	−0.0721298	+	0.168489i
$491$	1.39590			0.0629962			0.0314981	−	0.999504i	$-0.489972\pi$
$491$	1.39590			0.0629962			0.0314981	+	0.999504i	$0.489972\pi$
$492$	6.74183	−	11.6772i	0.303945	−	0.526448i
$493$	−0.617896	−	1.07023i	−0.0278286	−	0.0482006i
$494$	−0.101766	+	0.0587546i	−0.00457867	+	0.00264349i
$495$	0.846023	+	0.488452i	0.0380259	+	0.0219543i
$496$		−	4.99781i		−	0.224408i
$497$	−5.56839	+	11.1257i	−0.249776	+	0.499056i
$498$		−	4.42950i		−	0.198491i
$499$	0.874357	−	1.51443i	0.0391416	−	0.0677952i	−0.845791	−	0.533514i	$-0.820871\pi$
$499$	0.874357	−	1.51443i	0.0391416	−	0.0677952i	0.884933	+	0.465719i	$0.154204\pi$
$500$	7.57001	+	13.1116i	0.338541	+	0.586371i
$501$	−6.75213	−	11.6950i	−0.301663	−	0.522496i
$502$	−0.441208	+	0.764195i	−0.0196921	+	0.0341077i
$503$	19.3471			0.862645			0.431322	−	0.902198i	$-0.358047\pi$
$503$	19.3471			0.862645			0.431322	+	0.902198i	$0.358047\pi$
$504$	−3.07064	−	4.65473i	−0.136777	−	0.207338i
$505$			2.78028i			0.123721i
$506$	2.41620	−	1.12606i	0.107413	−	0.0500596i
$507$	10.3272	−	5.96240i	0.458646	−	0.264799i
$508$	−6.26197	−	10.8461i	−0.277830	−	0.481216i
$509$	−22.1060	−	12.7629i	−0.979830	−	0.565705i	−0.0776110	−	0.996984i	$-0.524729\pi$
$509$	−22.1060	−	12.7629i	−0.979830	−	0.565705i	−0.902219	+	0.431279i	$0.858063\pi$
$510$			0.615147i			0.0272392i
$511$	1.57235	+	26.3712i	0.0695567	+	1.16659i
$512$	−20.5639			−0.908806
$513$	0.170904	+	0.0986713i	0.00754558	+	0.00435644i
$514$	−6.62974	+	3.82768i	−0.292426	+	0.168832i
$515$	4.22034	+	7.30985i	0.185971	+	0.322111i
$516$	−7.16118	+	12.4035i	−0.315254	+	0.546035i
$517$	3.86743			0.170090
$518$	−0.587286	−	9.84987i	−0.0258039	−	0.432779i
$519$	6.69950			0.294076
$520$	1.91022	+	1.10286i	0.0837685	+	0.0483638i
$521$	0.361463	+	0.626072i	0.0158360	+	0.0274287i	0.873835	−	0.486223i	$-0.161626\pi$
$521$	0.361463	+	0.626072i	0.0158360	+	0.0274287i	−0.857999	+	0.513652i	$0.828292\pi$
$522$	−0.334314	−	0.579049i	−0.0146325	−	0.0253443i
$523$	−4.14122	+	7.17279i	−0.181083	+	0.313644i	−0.942250	−	0.334912i	$-0.891293\pi$
$523$	−4.14122	+	7.17279i	−0.181083	+	0.313644i	0.761167	+	0.648556i	$0.224627\pi$
$524$		−	0.252441i		−	0.0110279i
$525$	8.79283	−	5.80048i	0.383751	−	0.253154i
$526$		−	14.1534i		−	0.617118i
$527$	2.15660	+	1.24512i	0.0939431	+	0.0542381i
$528$	−1.03091	−	1.78559i	−0.0448645	−	0.0777077i
$529$	−14.7917	+	17.6127i	−0.643116	+	0.765769i
$530$	4.80232	+	2.77262i	0.208600	+	0.120435i
$531$		−	4.13327i		−	0.179369i
$532$	−0.390307	+	0.779839i	−0.0169220	+	0.0338103i
$533$	8.37099			0.362588
$534$	5.49747	+	3.17397i	0.237899	+	0.137351i
$535$	−2.74971	+	1.58754i	−0.118880	+	0.0686355i
$536$	−16.9160	+	9.76646i	−0.730660	+	0.421847i
$537$	−13.2260	−	7.63602i	−0.570743	−	0.329518i
$538$		−	1.19981i		−	0.0517274i
$539$	6.22875	+	2.66652i	0.268291	+	0.114855i
$540$		−	1.68571i		−	0.0725415i
$541$	−4.79408	+	8.30359i	−0.206114	+	0.356999i	−0.950487	−	0.310764i	$-0.899415\pi$
$541$	−4.79408	+	8.30359i	−0.206114	+	0.356999i	0.744373	+	0.667764i	$0.232748\pi$
$542$	16.1103	−	9.30129i	0.691997	−	0.399524i
$543$	17.8784	−	10.3221i	0.767234	−	0.442963i
$544$	2.88615	−	4.99896i	0.123743	−	0.214329i
$545$		−	2.18910i		−	0.0937707i
$546$	0.705116	−	1.40883i	0.0301762	−	0.0602924i
$547$	−14.2844			−0.610758			−0.305379	−	0.952231i	$-0.598783\pi$
$547$	−14.2844			−0.610758			−0.305379	+	0.952231i	$0.598783\pi$
$548$	11.5677	+	6.67864i	0.494150	+	0.285297i
$549$	−1.73860	−	3.01135i	−0.0742018	−	0.128521i
$550$	−1.91652	+	1.10650i	−0.0817207	+	0.0471814i
$551$	−0.114887	+	0.198990i	−0.00489434	+	0.00847724i
$552$	−8.27870	−	5.79945i	−0.352365	−	0.246841i
$553$	−10.7929	+	7.11987i	−0.458959	+	0.302768i
$554$	7.19279			0.305592
$555$	3.27736	−	5.67655i	0.139116	−	0.240956i
$556$	10.2659	−	5.92705i	0.435373	−	0.251363i
$557$	−11.8963	+	6.86831i	−0.504061	+	0.291020i	−0.730389	−	0.683031i	$-0.760661\pi$
$557$	−11.8963	+	6.86831i	−0.504061	+	0.291020i	0.226328	+	0.974051i	$0.427328\pi$
$558$	1.16683	+	0.673672i	0.0493961	+	0.0285188i
$559$	−8.89169			−0.376078
$560$	5.67795	−	0.338541i	0.239937	−	0.0143060i
$561$	1.02733			0.0433740
$562$	7.06471	+	4.07881i	0.298007	+	0.172054i
$563$	−22.3223	−	38.6634i	−0.940775	−	1.62947i	−0.763998	−	0.645218i	$-0.776766\pi$
$563$	−22.3223	−	38.6634i	−0.940775	−	1.62947i	−0.176776	−	0.984251i	$-0.556567\pi$
$564$	−3.33676	−	5.77944i	−0.140503	−	0.243358i
$565$	8.83943	+	5.10344i	0.371877	+	0.214704i
$566$	−15.3847			−0.646665
$567$	−2.64106	+	0.157470i	−0.110914	+	0.00661311i
$568$	−9.91103			−0.415858
$569$	16.6620	+	9.61981i	0.698507	+	0.403283i	0.806791	−	0.590837i	$-0.201202\pi$
$569$	16.6620	+	9.61981i	0.698507	+	0.403283i	−0.108284	+	0.994120i	$0.534536\pi$
$570$	0.0990522	−	0.0571878i	0.00414884	−	0.00239533i
$571$	25.9690	−	14.9932i	1.08677	−	0.627446i	0.154055	−	0.988062i	$-0.450767\pi$
$571$	25.9690	−	14.9932i	1.08677	−	0.627446i	0.932714	+	0.360616i	$0.117434\pi$
$572$	0.838178	−	1.45177i	0.0350460	−	0.0607014i
$573$	−13.2121			−0.551945
$574$	−10.2384	+	6.75410i	−0.427343	+	0.281911i
$575$	10.9552	−	15.6385i	0.456864	−	0.652172i
$576$	−0.568573	+	0.984797i	−0.0236905	+	0.0410332i
$577$	−32.1362	+	18.5538i	−1.33785	+	0.772407i	−0.986488	−	0.163834i	$-0.947614\pi$
$577$	−32.1362	+	18.5538i	−1.33785	+	0.772407i	−0.351360	+	0.936241i	$0.614281\pi$
$578$	−4.55772	−	7.89421i	−0.189576	−	0.328356i
$579$	2.57576	+	1.48712i	0.107045	+	0.0618024i
$580$	1.96274			0.0814983
$581$	9.13395	−	18.2497i	0.378940	−	0.757127i
$582$		−	4.64174i		−	0.192406i
$583$	4.63044	−	8.02016i	0.191773	−	0.332161i
$584$	−18.2256	+	10.5225i	−0.754180	+	0.435426i
$585$	0.906324	−	0.523267i	0.0374719	−	0.0216344i
$586$	6.27303	−	10.8652i	0.259137	−	0.448838i
$587$			0.557336i			0.0230037i	0.999934	+	0.0115019i	$0.00366124\pi$
$587$			0.557336i			0.0230037i	−0.999934	+	0.0115019i	$0.996339\pi$
$588$	−1.38926	−	11.6088i	−0.0572919	−	0.478738i
$589$		−	0.463014i		−	0.0190782i
$590$	−2.07461	−	1.19778i	−0.0854105	−	0.0493118i
$591$	6.06157	−	3.49965i	0.249340	−	0.143956i
$592$	−11.9807	+	6.91708i	−0.492405	+	0.284290i
$593$	24.4436	+	14.1125i	1.00378	+	0.579531i	0.909364	−	0.416002i	$-0.136569\pi$
$593$	24.4436	+	14.1125i	1.00378	+	0.579531i	0.0944138	+	0.995533i	$0.469902\pi$
$594$	0.555840			0.0228064
$595$	−1.26848	+	2.53444i	−0.0520026	+	0.103902i
$596$		−	33.4432i		−	1.36989i
$597$	−19.3683	−	11.1823i	−0.792693	−	0.457662i
$598$	0.249501	−	2.84480i	0.0102029	−	0.116332i
$599$	−9.87881	−	17.1106i	−0.403637	−	0.699120i	0.590525	−	0.807020i	$-0.298921\pi$
$599$	−9.87881	−	17.1106i	−0.403637	−	0.699120i	−0.994162	+	0.107900i	$0.965588\pi$
$600$	7.26712	+	4.19567i	0.296679	+	0.171288i
$601$			27.1216i			1.10631i	0.833077	+	0.553157i	$0.186577\pi$
$601$			27.1216i			1.10631i	−0.833077	+	0.553157i	$0.813423\pi$
$602$	10.8753	−	7.17422i	0.443242	−	0.292399i
$603$			9.26762i			0.377407i
$604$	−4.36942	+	7.56806i	−0.177789	+	0.307940i
$605$	5.07820	+	8.79570i	0.206458	+	0.357596i
$606$	0.790964	+	1.36999i	0.0321307	+	0.0556520i
$607$	−7.32578	−	4.22954i	−0.297344	−	0.171672i	0.343905	−	0.939004i	$-0.388250\pi$
$607$	−7.32578	−	4.22954i	−0.297344	−	0.171672i	−0.641249	+	0.767333i	$0.721584\pi$
$608$	−1.07326			−0.0435263
$609$	−0.183348	−	3.07509i	−0.00742964	−	0.124609i
$610$	−2.01532			−0.0815978
$611$	2.07155	−	3.58802i	0.0838057	−	0.145156i
$612$	−0.886365	−	1.53523i	−0.0358292	−	0.0620580i
$613$	−5.03989	+	2.90978i	−0.203559	+	0.117525i	−0.598315	−	0.801261i	$-0.704163\pi$
$613$	−5.03989	+	2.90978i	−0.203559	+	0.117525i	0.394755	+	0.918786i	$0.370829\pi$
$614$	−9.10330	−	5.25579i	−0.367379	−	0.212106i
$615$	−8.14777			−0.328550
$616$	0.321248	+	5.38792i	0.0129434	+	0.217086i
$617$			8.53053i			0.343426i	0.985147	+	0.171713i	$0.0549302\pi$
$617$			8.53053i			0.343426i	−0.985147	+	0.171713i	$0.945070\pi$
$618$	4.15917	+	2.40130i	0.167306	+	0.0965943i
$619$	−14.4812	−	25.0822i	−0.582048	−	1.00814i	−0.995236	−	0.0974915i	$-0.968918\pi$
$619$	−14.4812	−	25.0822i	−0.582048	−	1.00814i	0.413188	−	0.910646i	$-0.364415\pi$
$620$	−3.42521	+	1.97755i	−0.137560	+	0.0794202i
$621$	−4.34693	+	2.02588i	−0.174436	+	0.0812956i
$622$		−	4.02122i		−	0.161236i
$623$	16.1049	+	24.4131i	0.645229	+	0.978089i
$624$	−2.20878			−0.0884218
$625$	−5.37911	+	9.31688i	−0.215164	+	0.372675i
$626$	−0.523083	−	0.906005i	−0.0209066	−	0.0362113i
$627$	−0.0955070	−	0.165423i	−0.00381418	−	0.00660635i
$628$	2.92256	−	5.06202i	0.116623	−	0.201997i
$629$		−	6.89308i		−	0.274845i
$630$	−0.686313	+	1.37126i	−0.0273434	+	0.0546324i
$631$		−	8.04844i		−	0.320403i	−0.987084	−	0.160202i	$-0.948786\pi$
$631$		−	8.04844i		−	0.320403i	0.987084	−	0.160202i	$-0.0512144\pi$
$632$	−8.92012	−	5.15003i	−0.354823	−	0.204857i
$633$	18.8326	−	10.8730i	0.748528	−	0.432163i
$634$	4.11250	+	7.12306i	0.163328	+	0.282893i
$635$	−3.78392	+	6.55394i	−0.150160	+	0.260085i
$636$	−15.9803			−0.633659
$637$	5.81022	−	4.35045i	0.230209	−	0.172371i
$638$			0.647185i			0.0256223i
$639$	−2.35120	+	4.07240i	−0.0930122	+	0.161102i
$640$	5.81849	+	10.0779i	0.229996	+	0.398365i
$641$	29.9162	−	17.2721i	1.18162	−	0.682209i	0.225231	−	0.974305i	$-0.427686\pi$
$641$	29.9162	−	17.2721i	1.18162	−	0.682209i	0.956389	+	0.292097i	$0.0943530\pi$
$642$	−0.903283	+	1.56453i	−0.0356497	+	0.0617471i
$643$	−24.5429			−0.967877			−0.483939	−	0.875102i	$-0.660794\pi$
$643$	−24.5429			−0.967877			−0.483939	+	0.875102i	$0.660794\pi$
$644$	−10.0798	−	18.6423i	−0.397199	−	0.734609i
$645$	8.65458			0.340774
$646$	0.0601399	−	0.104165i	0.00236617	−	0.00409833i
$647$	20.7726	−	11.9930i	0.816654	−	0.471495i	−0.0326073	−	0.999468i	$-0.510381\pi$
$647$	20.7726	−	11.9930i	0.816654	−	0.471495i	0.849261	+	0.527973i	$0.177048\pi$
$648$	−1.05383	−	1.82528i	−0.0413982	−	0.0717037i
$649$	−2.00036	+	3.46473i	−0.0785210	+	0.136002i
$650$			2.37074i			0.0929881i
$651$	3.41825	+	5.18166i	0.133972	+	0.203085i
$652$	−1.30406			−0.0510711
$653$	22.4130	−	38.8204i	0.877088	−	1.51916i	0.0225653	−	0.999745i	$-0.492817\pi$
$653$	22.4130	−	38.8204i	0.877088	−	1.51916i	0.854522	−	0.519415i	$-0.173850\pi$
$654$	−0.622778	−	1.07868i	−0.0243526	−	0.0421799i
$655$	−0.132106	+	0.0762713i	−0.00516180	+	0.00298016i
$656$	14.8925	+	8.59820i	0.581455	+	0.335703i
$657$			9.98509i			0.389556i
$658$	0.361311	+	6.05986i	0.0140854	+	0.236238i
$659$			17.0640i			0.664717i	0.943153	+	0.332359i	$0.107844\pi$
$659$			17.0640i			0.664717i	−0.943153	+	0.332359i	$0.892156\pi$
$660$	−0.815827	+	1.41305i	−0.0317560	+	0.0550030i
$661$	−6.54377	−	11.3341i	−0.254523	−	0.440847i	0.710243	−	0.703957i	$-0.248585\pi$
$661$	−6.54377	−	11.3341i	−0.254523	−	0.440847i	−0.964766	+	0.263110i	$0.915252\pi$
$662$	−8.34687	−	14.4572i	−0.324410	−	0.561895i
$663$	0.550278	−	0.953109i	0.0213710	−	0.0370157i
$664$	16.2573			0.630905
$665$	0.526025	−	0.0313636i	0.0203984	−	0.00121623i
$666$		−	3.72951i		−	0.144516i
$667$	−2.35880	−	5.06130i	−0.0913332	−	0.195974i
$668$	19.5334	−	11.2776i	0.755770	−	0.436344i
$669$	−9.61541	−	16.6544i	−0.371753	−	0.643896i
$670$	4.65170	+	2.68566i	0.179711	+	0.103756i
$671$			3.36570i			0.129931i
$672$	12.0110	−	7.92343i	0.463333	−	0.305653i
$673$	−22.7511			−0.876992			−0.438496	−	0.898733i	$-0.644489\pi$
$673$	−22.7511			−0.876992			−0.438496	+	0.898733i	$0.644489\pi$
$674$	1.32618	+	0.765670i	0.0510825	+	0.0294925i
$675$	3.44797	−	1.99069i	0.132712	−	0.0766216i
$676$	9.95858	+	17.2488i	0.383022	+	0.663414i
$677$	16.3633	−	28.3421i	0.628893	−	1.08927i	−0.358882	−	0.933383i	$-0.616842\pi$
$677$	16.3633	−	28.3421i	0.628893	−	1.08927i	0.987774	−	0.155891i	$-0.0498249\pi$
$678$	5.80753			0.223037
$679$	9.57160	−	19.1242i	0.367324	−	0.733918i
$680$	−2.25773			−0.0865801
$681$	22.5967	+	13.0462i	0.865908	+	0.499932i
$682$	−0.652068	−	1.12941i	−0.0249690	−	0.0432475i
$683$	19.3274	+	33.4760i	0.739541	+	1.28092i	0.952702	+	0.303905i	$0.0982906\pi$
$683$	19.3274	+	33.4760i	0.739541	+	1.28092i	−0.213162	+	0.977017i	$0.568376\pi$
$684$	−0.164804	+	0.285449i	−0.00630143	+	0.0109144i
$685$		−	8.07141i		−	0.308393i
$686$	−3.59624	+	10.0089i	−0.137305	+	0.382142i
$687$		−	12.7881i		−	0.487896i
$688$	−15.8189	−	9.13302i	−0.603088	−	0.348193i
$689$	−4.96048	−	8.59180i	−0.188979	−	0.327322i
$690$	−0.242848	+	2.76893i	−0.00924506	+	0.105412i
$691$	−0.569882	−	0.329022i	−0.0216794	−	0.0125166i	0.489121	−	0.872216i	$-0.337318\pi$
$691$	−0.569882	−	0.329022i	−0.0216794	−	0.0125166i	−0.510801	+	0.859699i	$0.670651\pi$
$692$			11.1897i			0.425369i
$693$	2.29009	+	1.14618i	0.0869932	+	0.0435399i
$694$	−18.0329			−0.684519
$695$	−6.20340	−	3.58154i	−0.235309	−	0.135855i
$696$	2.12524	−	1.22701i	0.0805571	−	0.0465097i
$697$	−7.42042	+	4.28418i	−0.281068	+	0.162275i
$698$	−1.58116	−	0.912886i	−0.0598480	−	0.0345532i
$699$			16.5269i			0.625105i
$700$	9.68813	+	14.6860i	0.366177	+	0.555080i
$701$		−	35.3032i		−	1.33338i	−0.745334	−	0.666691i	$-0.767710\pi$
$701$		−	35.3032i		−	1.33338i	0.745334	−	0.666691i	$-0.232290\pi$
$702$	0.297729	−	0.515682i	0.0112371	−	0.0194632i
$703$	−1.10994	+	0.640822i	−0.0418621	+	0.0241691i
$704$	0.953215	−	0.550339i	0.0359257	−	0.0207417i
$705$	−2.01630	+	3.49234i	−0.0759384	+	0.131529i
$706$			8.66665i			0.326174i
$707$	0.433789	+	7.27545i	0.0163143	+	0.273621i
$708$	6.90352			0.259450
$709$	44.0060	+	25.4069i	1.65268	+	0.954175i	0.975965	+	0.217929i	$0.0699301\pi$
$709$	44.0060	+	25.4069i	1.65268	+	0.954175i	0.676714	+	0.736246i	$0.263403\pi$
$710$	1.36271	+	2.36028i	0.0511415	+	0.0885797i
$711$	−4.23226	+	2.44349i	−0.158722	+	0.0916382i
$712$	−11.6492	+	20.1770i	−0.436572	+	0.756165i
$713$	9.21588	+	6.45597i	0.345137	+	0.241778i
$714$	0.0959775	+	1.60972i	0.00359187	+	0.0602422i
$715$	−1.01297			−0.0378830
$716$	12.7539	−	22.0904i	0.476636	−	0.825558i
$717$	7.48154	−	4.31947i	0.279403	−	0.161313i
$718$	1.91108	−	1.10336i	0.0713209	−	0.0411772i
$719$	38.1170	+	22.0069i	1.42153	+	0.820718i	0.996429	−	0.0844300i	$-0.0269069\pi$
$719$	38.1170	+	22.0069i	1.42153	+	0.820718i	0.425096	+	0.905148i	$0.360240\pi$
$720$	2.14988			0.0801212
$721$	12.1843	+	18.4700i	0.453768	+	0.687858i
$722$	10.8885			0.405228
$723$	−18.9998	−	10.9696i	−0.706611	−	0.407962i
$724$	17.2402	+	29.8610i	0.640729	+	1.10977i
$725$	2.31783	+	4.01460i	0.0860821	+	0.149099i
$726$	5.00459	+	2.88940i	0.185738	+	0.107236i
$727$	22.4700			0.833366			0.416683	−	0.909052i	$-0.363193\pi$
$727$	22.4700			0.833366			0.416683	+	0.909052i	$0.363193\pi$
$728$	5.17073	+	2.58794i	0.191640	+	0.0959154i
$729$	−1.00000			−0.0370370
$730$	5.01182	+	2.89358i	0.185496	+	0.107096i
$731$	7.88198	−	4.55067i	0.291526	−	0.168312i
$732$	5.02965	−	2.90387i	0.185901	−	0.107330i
$733$	−7.44618	+	12.8972i	−0.275031	+	0.476367i	−0.970143	−	0.242534i	$-0.922021\pi$
$733$	−7.44618	+	12.8972i	−0.275031	+	0.476367i	0.695112	+	0.718901i	$0.255355\pi$
$734$	−9.36654			−0.345725
$735$	−5.65528	+	4.23443i	−0.208598	+	0.156189i
$736$	14.9648	−	21.3622i	0.551609	−	0.787421i
$737$	4.48521	−	7.76861i	0.165215	−	0.286160i
$738$	−4.01483	+	2.31796i	−0.147788	+	0.0853254i
$739$	−10.2912	−	17.8249i	−0.378568	−	0.655699i	0.612286	−	0.790636i	$-0.290250\pi$
$739$	−10.2912	−	17.8249i	−0.378568	−	0.655699i	−0.990854	+	0.134937i	$0.956917\pi$
$740$	9.48115	+	5.47395i	0.348534	+	0.201226i
$741$	−0.204629			−0.00751722
$742$	12.9993	+	6.50613i	0.477220	+	0.238848i
$743$		−	2.29867i		−	0.0843302i	−0.999111	−	0.0421651i	$-0.986574\pi$
$743$		−	2.29867i		−	0.0843302i	0.999111	−	0.0421651i	$-0.0134255\pi$
$744$	−2.47253	+	4.28255i	−0.0906474	+	0.157006i
$745$	−17.5013	+	10.1044i	−0.641196	+	0.370195i
$746$	10.7392	−	6.20030i	0.393191	−	0.227009i
$747$	3.85673	−	6.68005i	0.141110	−	0.244410i
$748$			1.71588i			0.0627388i
$749$	−6.94775	+	4.58331i	−0.253865	+	0.167470i
$750$		−	5.20542i		−	0.190075i
$751$	4.88492	+	2.82031i	0.178253	+	0.102915i	0.586472	−	0.809970i	$-0.300517\pi$
$751$	4.88492	+	2.82031i	0.178253	+	0.102915i	−0.408219	+	0.912884i	$0.633850\pi$
$752$	7.37081	−	4.25554i	0.268786	−	0.155184i
$753$	−1.33076	+	0.768313i	−0.0484955	+	0.0279989i
$754$	0.600428	+	0.346657i	0.0218663	+	0.0126245i
$755$	5.28062			0.192182
$756$	−0.263011	−	4.41118i	−0.00956562	−	0.160433i
$757$		−	27.7039i		−	1.00692i	−0.864020	−	0.503458i	$-0.832061\pi$
$757$		−	27.7039i		−	1.00692i	0.864020	−	0.503458i	$-0.167939\pi$
$758$	−6.02448	−	3.47823i	−0.218819	−	0.126335i
$759$	4.62428	+	0.405570i	0.167851	+	0.0147212i
$760$	0.209892	+	0.363544i	0.00761360	+	0.0131871i
$761$	22.6799	+	13.0943i	0.822146	+	0.474666i	0.851156	−	0.524913i	$-0.175902\pi$
$761$	22.6799	+	13.0943i	0.822146	+	0.474666i	−0.0290098	+	0.999579i	$0.509235\pi$
$762$			4.30596i			0.155988i
$763$	−0.341551	−	5.72844i	−0.0123650	−	0.207383i
$764$		−	22.0673i		−	0.798367i
$765$	−0.535604	+	0.927693i	−0.0193648	+	0.0335408i
$766$	4.16759	+	7.21848i	0.150581	+	0.260814i
$767$	2.14294	+	3.71168i	0.0773771	+	0.134021i
$768$	3.76455	+	2.17347i	0.135842	+	0.0784282i
$769$	−13.9861			−0.504350			−0.252175	−	0.967682i	$-0.581146\pi$
$769$	−13.9861			−0.504350			−0.252175	+	0.967682i	$0.581146\pi$
$770$	1.23895	−	0.817312i	0.0446485	−	0.0294539i
$771$	−13.3309			−0.480102
$772$	−2.48382	+	4.30211i	−0.0893948	+	0.154836i
$773$	−5.21752	−	9.03701i	−0.187661	−	0.325039i	0.756809	−

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+(0.287128 - 0.497320i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.835115 + 1.44646i) q^{4} +(0.504635 - 0.874053i) q^{5} -0.574256i q^{6} +(1.18416 - 2.36596i) q^{7} +2.10765 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.289790 - 0.501930i) q^{10} +(-0.838252 + 0.483965i) q^{11} +(1.44646 + 0.835115i) q^{12} +1.03692i q^{13} +(-0.836635 - 1.26824i) q^{14} -1.00927i q^{15} +(-1.06506 + 1.84475i) q^{16} +(-0.530685 - 0.919173i) q^{17} +(-0.287128 - 0.497320i) q^{18} +(-0.0986713 + 0.170904i) q^{19} +1.68571 q^{20} +(-0.157470 - 2.64106i) q^{21} +0.555840i q^{22} +(-2.02588 - 4.34693i) q^{23} +(1.82528 - 1.05383i) q^{24} +(1.99069 + 3.44797i) q^{25} +(0.515682 + 0.297729i) q^{26} -1.00000i q^{27} +(4.41118 - 0.263011i) q^{28} +1.16434 q^{29} +(-0.501930 - 0.289790i) q^{30} +(-2.03191 + 1.17312i) q^{31} +(2.71927 + 4.70991i) q^{32} +(-0.483965 + 0.838252i) q^{33} -0.609497 q^{34} +(-1.47041 - 2.22896i) q^{35} +1.67023 q^{36} +(5.62442 + 3.24726i) q^{37} +(0.0566626 + 0.0981424i) q^{38} +(0.518461 + 0.898000i) q^{39} +(1.06359 - 1.84220i) q^{40} -8.07293i q^{41} +(-1.35867 - 0.680009i) q^{42} +8.57509i q^{43} +(-1.40007 - 0.808333i) q^{44} +(-0.504635 - 0.874053i) q^{45} +(-2.74350 - 0.240617i) q^{46} +(-3.46026 - 1.99778i) q^{47} +2.13013i q^{48} +(-4.19554 - 5.60334i) q^{49} +2.28633 q^{50} +(-0.919173 - 0.530685i) q^{51} +(-1.49987 + 0.865949i) q^{52} +(-8.28588 + 4.78385i) q^{53} +(-0.497320 - 0.287128i) q^{54} +0.976903i q^{55} +(2.49579 - 4.98662i) q^{56} +0.197343i q^{57} +(0.334314 - 0.579049i) q^{58} +(3.57952 - 2.06664i) q^{59} +(1.45987 - 0.842857i) q^{60} +(1.73860 - 3.01135i) q^{61} +1.34734i q^{62} +(-1.45690 - 2.20849i) q^{63} -1.13715 q^{64} +(0.906324 + 0.523267i) q^{65} +(0.277920 + 0.481371i) q^{66} +(-8.02600 + 4.63381i) q^{67} +(0.886365 - 1.53523i) q^{68} +(-3.92793 - 2.75162i) q^{69} +(-1.53070 + 0.0912662i) q^{70} -4.70241 q^{71} +(1.05383 - 1.82528i) q^{72} +(-8.64734 + 4.99255i) q^{73} +(3.22985 - 1.86476i) q^{74} +(3.44797 + 1.99069i) q^{75} -0.329608 q^{76} +(0.152420 + 2.55636i) q^{77} +0.595458 q^{78} +(-4.23226 - 2.44349i) q^{79} +(1.07494 + 1.86185i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.01483 - 2.31796i) q^{82} +7.71346 q^{83} +(3.68869 - 2.43336i) q^{84} -1.07121 q^{85} +(4.26456 + 2.46215i) q^{86} +(1.00835 - 0.582169i) q^{87} +(-1.76674 + 1.02003i) q^{88} +(-5.52710 + 9.57321i) q^{89} -0.579579 q^{90} +(2.45331 + 1.22788i) q^{91} +(4.59583 - 6.56054i) q^{92} +(-1.17312 + 2.03191i) q^{93} +(-1.98708 + 1.14724i) q^{94} +(0.0995860 + 0.172488i) q^{95} +(4.70991 + 2.71927i) q^{96} +8.08305 q^{97} +(-3.99131 + 0.477652i) q^{98} +0.967930i 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

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Representations

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Database

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