LMFDB - Embedded newform 483.2.j.a.229.19

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			229.19
Character	$\chi$	$=$	483.229
Dual form			483.2.j.a.367.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.287128 - 0.497320i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.835115 + 1.44646i) q^{4} +(-0.504635 + 0.874053i) q^{5} -0.574256i q^{6} +(-1.18416 + 2.36596i) q^{7} +2.10765 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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} +(4.77749 - 0.419007i) 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} +(1.16337 - 2.49625i) 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}+O(q^{10}) $ 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.956523	−	0.291657i	$-0.905794\pi$
$5$	−0.504635	+	0.874053i	−0.225680	+	0.390889i	0.730844	+	0.682545i	$0.239127\pi$
$6$		−	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	−0.368277	−	0.929716i	$-0.620052\pi$
$11$	0.838252	−	0.483965i	0.252743	−	0.145921i	0.621019	+	0.783795i	$0.286719\pi$
$12$	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	0.923177	−	0.384375i	$-0.125583\pi$
$17$	0.530685	+	0.919173i	0.128710	+	0.222932i	−0.794467	+	0.607307i	$0.792250\pi$
$18$	−0.287128	−	0.497320i	−0.0676767	−	0.117219i
$19$	0.0986713	−	0.170904i	0.0226367	−	0.0392080i	−0.854485	−	0.519476i	$-0.826127\pi$
$19$	0.0986713	−	0.170904i	0.0226367	−	0.0392080i	0.877122	+	0.480268i	$0.159461\pi$
$20$	−1.68571			−0.376937
$21$	0.157470	+	2.64106i	0.0343627	+	0.576327i
$22$		−	0.555840i		−	0.118505i
$23$	4.77749	−	0.419007i	0.996176	−	0.0873690i
$23$	4.77749	−	0.419007i	0.996176	−	0.0873690i
$24$	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	−0.0395333	−	0.999218i	$-0.512587\pi$
$37$	−5.62442	−	3.24726i	−0.924648	−	0.533846i	−0.885115	+	0.465372i	$0.845920\pi$
$38$	−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	$-0.773155\pi$
$43$		−	8.57509i		−	1.30769i	0.756629	−	0.653844i	$-0.226845\pi$
$44$	1.40007	+	0.808333i	0.211069	+	0.121861i
$45$	0.504635	+	0.874053i	0.0752265	+	0.130296i
$46$	1.16337	−	2.49625i	0.171530	−	0.368052i
$47$	−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	0.192180	−	0.981360i	$-0.438444\pi$
$53$	8.28588	−	4.78385i	1.13815	−	0.657113i	0.945973	+	0.324247i	$0.105111\pi$
$54$	−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	−0.955598	−	0.294672i	$-0.904790\pi$
$61$	−1.73860	+	3.01135i	−0.222605	+	0.385564i	0.732993	+	0.680236i	$0.238123\pi$
$62$			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	0.0781010	−	0.996945i	$-0.475114\pi$
$67$	8.02600	−	4.63381i	0.980532	−	0.566110i	0.902431	+	0.430835i	$0.141781\pi$
$68$	−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	0.718817	−	0.695199i	$-0.244684\pi$
$79$	4.23226	+	2.44349i	0.476166	+	0.274915i	−0.242651	+	0.970114i	$0.578017\pi$
$80$	−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	$-0.639139\pi$
$83$	−7.71346			−0.846662			−0.423331	+	0.905975i	$0.639139\pi$
$84$	−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	$-0.634086\pi$
$89$	5.52710	−	9.57321i	0.585871	−	1.01476i	0.994766	−	0.102177i	$-0.0325808\pi$
$90$	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	$-0.634595\pi$
$97$	−8.08305			−0.820709			−0.410355	+	0.911926i	$0.634595\pi$
$98$	−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	−0.583087	−	0.812409i	$-0.698156\pi$
$103$	4.18158	−	7.24271i	0.412023	−	0.713646i	0.995111	+	0.0987639i	$0.0314888\pi$
$104$			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	0.625877	−	0.779922i	$-0.284741\pi$
$107$	2.72445	+	1.57296i	0.263383	+	0.152064i	−0.362494	+	0.931986i	$0.618075\pi$
$108$	1.44646	−	0.835115i	0.139186	−	0.0803590i
$109$	−1.87840	+	1.08450i	−0.179918	+	0.103876i	−0.587254	−	0.809402i	$-0.699791\pi$
$109$	−1.87840	+	1.08450i	−0.179918	+	0.103876i	0.407336	+	0.913278i	$0.366458\pi$
$110$	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	$-0.842201\pi$
$113$		−	10.1131i		−	0.951364i	0.879617	−	0.475682i	$-0.157799\pi$
$114$	−0.0981424	−	0.0566626i	−0.00919188	−	0.00530694i
$115$	−2.04466	+	4.38723i	−0.190665	+	0.409111i
$116$	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	−0.765775	−	0.643108i	$-0.777644\pi$
$137$	−6.92584	+	3.99864i	−0.591714	+	0.341626i	0.174061	+	0.984735i	$0.444311\pi$
$138$	−0.240617	−	2.74350i	−0.0204827	−	0.233542i
$139$		−	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	0.996349	−	0.0853716i	$-0.0272077\pi$
$149$	17.3405	+	10.0115i	1.42059	+	0.820178i	0.424241	+	0.905549i	$0.360541\pi$
$150$	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	0.927364	−	0.374161i	$-0.122069\pi$
$157$	1.74979	+	3.03073i	0.139649	+	0.241879i	−0.787715	+	0.616040i	$0.788736\pi$
$158$	2.43040	−	1.40319i	0.193352	−	0.111632i
$159$	4.78385	−	8.28588i	0.379384	−	0.657113i
$160$	−5.48896			−0.433940
$161$	−4.66595	+	11.7995i	−0.367728	+	0.929933i
$162$	−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	$-0.778367\pi$
$181$	−20.6442			−1.53447			−0.767234	+	0.641367i	$0.778367\pi$
$182$	−1.31506	+	0.867525i	−0.0974790	+	0.0643052i
$183$			3.47721i			0.257043i
$184$	10.0693	−	0.883121i	0.742318	−	0.0651045i
$185$	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	0.853139	−	0.521684i	$-0.174696\pi$
$191$	11.4420	+	6.60607i	0.827917	+	0.477998i	−0.0252218	+	0.999682i	$0.508029\pi$
$192$	−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	$0.124655\pi$
$199$	11.1823	+	19.3683i	0.792693	+	1.37298i	−0.131601	+	0.991303i	$0.542012\pi$
$200$	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
$207$	2.02588	−	4.34693i	0.140808	−	0.302133i
$208$	−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	$-0.833408\pi$
$227$	−13.0462	−	22.5967i	−0.865908	−	1.49980i	0.000234228	−	1.00000i	$-0.499925\pi$
$228$	0.285449	−	0.164804i	0.0189043	−	0.0109144i
$229$	−6.39404	+	11.0748i	−0.422530	+	0.731843i	−0.996186	−	0.0872529i	$-0.972191\pi$
$229$	−6.39404	+	11.0748i	−0.422530	+	0.731843i	0.573656	+	0.819096i	$0.305525\pi$
$230$	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	$0.0831104\pi$
$241$	10.9696	+	18.9998i	0.706611	+	1.22389i	−0.259496	+	0.965744i	$0.583556\pi$
$242$	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	$-0.484557\pi$
$251$	1.53663			0.0969910			0.0484955	+	0.998823i	$0.484557\pi$
$252$	−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	−0.983108	−	0.183024i	$-0.941411\pi$
$263$	−21.3445	+	12.3233i	−1.31616	+	0.759885i	−0.333051	+	0.942909i	$0.608078\pi$
$264$	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
$276$	7.26038	+	3.38368i	0.437024	+	0.203674i
$277$	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	$-0.860725\pi$
$281$		−	14.2056i		−	0.847433i	0.905795	−	0.423717i	$-0.139275\pi$
$282$	−1.14724	+	1.98708i	−0.0683171	+	0.118329i
$283$	13.3953	+	23.2013i	0.796268	+	1.37918i	0.922031	+	0.387116i	$0.126529\pi$
$283$	13.3953	+	23.2013i	0.796268	+	1.37918i	−0.125763	+	0.992060i	$0.540138\pi$
$284$	−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	$-0.720310\pi$
$293$	−21.8475			−1.27635			−0.638173	+	0.769893i	$0.720310\pi$
$294$	−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
$299$	0.434477	+	4.95388i	0.0251265	+	0.286490i
$300$			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	−0.890620	−	0.454748i	$-0.849729\pi$
$313$	−0.910888	+	1.57770i	−0.0514864	+	0.0891771i	0.839134	+	0.543925i	$0.183063\pi$
$314$	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
$322$	4.52842	+	5.70844i	0.252359	+	0.318119i
$323$	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	$-0.976860\pi$
$337$		−	2.66665i		−	0.145262i	0.997359	−	0.0726309i	$-0.0231395\pi$
$338$	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
$345$	0.422891	+	4.82178i	0.0227677	+	0.259596i
$346$	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	0.409602	−	0.912264i	$-0.365668\pi$
$359$	−3.32793	−	1.92138i	−0.175641	−	0.101407i	−0.585243	+	0.810858i	$0.699001\pi$
$360$	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	0.996486	−	0.0837575i	$-0.0266921\pi$
$367$	8.15537	+	14.1255i	0.425707	+	0.737346i	−0.570779	+	0.821104i	$0.693359\pi$
$368$	−4.31538	+	9.25953i	−0.224955	+	0.482686i
$369$	−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	−0.0695879	−	0.997576i	$-0.522168\pi$
$373$	−18.7011	−	10.7971i	−0.968308	−	0.559053i	−0.898720	+	0.438523i	$0.855502\pi$
$374$	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	$0.100706\pi$
$379$			12.1139i			0.622248i	−0.950369	+	0.311124i	$0.899294\pi$
$380$	−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	−0.618859	−	0.785502i	$-0.712405\pi$
$383$	7.25738	−	12.5701i	0.370835	−	0.642305i	0.989694	+	0.143197i	$0.0457383\pi$
$384$			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	−0.559874	−	0.828578i	$-0.689151\pi$
$389$	−2.41099	+	1.39199i	−0.122242	+	0.0705766i	0.437632	+	0.899154i	$0.355817\pi$
$390$	−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	−0.152055	−	0.988372i	$-0.548589\pi$
$401$	−21.7078	−	12.5330i	−1.08404	−	0.625870i	−0.931983	+	0.362502i	$0.881923\pi$
$402$	−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	$-0.0985484\pi$
$419$	38.9926			1.90491			0.952456	+	0.304677i	$0.0985484\pi$
$420$	−0.265449	−	4.45207i	−0.0129526	−	0.217239i
$421$			21.9797i			1.07122i	0.844464	+	0.535612i	$0.179919\pi$
$421$			21.9797i			1.07122i	−0.844464	+	0.535612i	$0.820081\pi$
$422$	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	−0.981292	−	0.192523i	$-0.938333\pi$
$431$	−27.0968	+	15.6444i	−1.30521	+	0.753563i	−0.323916	+	0.946086i	$0.605000\pi$
$432$	1.84475	+	1.06506i	0.0887554	+	0.0512430i
$433$	−33.4890			−1.60938			−0.804688	−	0.593698i	$-0.797668\pi$
$433$	−33.4890			−1.60938			−0.804688	+	0.593698i	$0.797668\pi$
$434$	−3.18776	−	1.59547i	−0.153018	−	0.0765849i
$435$			1.17513i			0.0563432i
$436$	−3.13736	−	1.81136i	−0.150253	−	0.0867483i
$437$	0.399792	−	0.857835i	0.0191246	−	0.0410358i
$438$	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	$-0.928087\pi$
$457$	−35.3986	−	20.4374i	−1.65588	−	0.956020i	−0.681287	−	0.732017i	$-0.738579\pi$
$458$	3.67181	+	6.35977i	0.171573	+	0.297172i
$459$	0.919173	−	0.530685i	0.0429033	−	0.0247702i
$460$	−8.05348	+	0.706326i	−0.375496	+	0.0329326i
$461$			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	−0.619713	−	0.784828i	$-0.712751\pi$
$467$	7.99198	−	13.8425i	0.369825	−	0.640555i	0.989538	+	0.144273i	$0.0460844\pi$
$468$			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	0.576597	−	0.817029i	$-0.304380\pi$
$479$	−9.17615	−	15.8936i	−0.419269	−	0.726195i	−0.995866	+	0.0908336i	$0.971047\pi$
$480$	−4.75358	+	2.74448i	−0.216970	+	0.125268i
$481$	3.36715	−	5.83208i	0.153529	−	0.265920i
$482$	12.5987			0.573853
$483$	1.85893	+	12.5517i	0.0845844	+	0.571121i
$484$	−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	$-0.641953\pi$
$503$	−19.3471			−0.862645			−0.431322	+	0.902198i	$0.641953\pi$
$504$	3.07064	+	4.65473i	0.136777	+	0.207338i
$505$		−	2.78028i		−	0.123721i
$506$	−0.232901	−	2.65552i	−0.0103537	−	0.118052i
$507$	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	0.857999	−	0.513652i	$-0.171708\pi$
$521$	−0.361463	−	0.626072i	−0.0158360	−	0.0274287i	−0.873835	+	0.486223i	$0.838374\pi$
$522$	−0.334314	−	0.579049i	−0.0146325	−	0.0253443i
$523$	4.14122	−	7.17279i	0.181083	−	0.313644i	−0.761167	−	0.648556i	$-0.775373\pi$
$523$	4.14122	−	7.17279i	0.181083	−	0.313644i	0.942250	+	0.334912i	$0.108707\pi$
$524$		−	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
$529$	22.6489	−	4.00361i	0.984733	−	0.174070i
$530$	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	−0.226328	−	0.974051i	$-0.572672\pi$
$557$	11.8963	−	6.86831i	0.504061	−	0.291020i	0.730389	+	0.683031i	$0.239339\pi$
$558$	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	$0.223234\pi$
$563$	22.3223	+	38.6634i	0.940775	+	1.62947i	0.176776	+	0.984251i	$0.443433\pi$
$564$	−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	0.108284	−	0.994120i	$-0.465464\pi$
$569$	−16.6620	−	9.61981i	−0.698507	−	0.403283i	−0.806791	+	0.590837i	$0.798798\pi$
$570$	0.0990522	−	0.0571878i	0.00414884	−	0.00239533i
$571$	−25.9690	+	14.9932i	−1.08677	+	0.627446i	−0.932714	−	0.360616i	$-0.882566\pi$
$571$	−25.9690	+	14.9932i	−1.08677	+	0.627446i	−0.154055	+	0.988062i	$0.549233\pi$
$572$	−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
$598$	2.58842	+	1.20632i	0.105848	+	0.0493302i
$599$	−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	−0.394755	−	0.918786i	$-0.629171\pi$
$613$	5.03989	−	2.90978i	0.203559	−	0.117525i	0.598315	+	0.801261i	$0.295837\pi$
$614$	−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	$-0.945070\pi$
$617$		−	8.53053i		−	0.343426i	0.985147	−	0.171713i	$-0.0549302\pi$
$618$	−4.15917	−	2.40130i	−0.167306	−	0.0965943i
$619$	14.4812	+	25.0822i	0.582048	+	1.00814i	0.995236	+	0.0974915i	$0.0310819\pi$
$619$	14.4812	+	25.0822i	0.582048	+	1.00814i	−0.413188	+	0.910646i	$0.635585\pi$
$620$	3.42521	−	1.97755i	0.137560	−	0.0794202i
$621$	−0.419007	−	4.77749i	−0.0168142	−	0.191714i
$622$		−	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	$0.0512144\pi$
$631$			8.04844i			0.320403i	−0.987084	+	0.160202i	$0.948786\pi$
$632$	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	−0.956389	−	0.292097i	$-0.905647\pi$
$641$	−29.9162	+	17.2721i	−1.18162	+	0.682209i	−0.225231	+	0.974305i	$0.572314\pi$
$642$	0.903283	−	1.56453i	0.0356497	−	0.0617471i
$643$	24.5429			0.967877			0.483939	−	0.875102i	$-0.339206\pi$
$643$	24.5429			0.967877			0.483939	+	0.875102i	$0.339206\pi$
$644$	−20.9642	+	3.10485i	−0.826104	+	0.122348i
$645$	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	$-0.892156\pi$
$659$		−	17.0640i		−	0.664717i	0.943153	−	0.332359i	$-0.107844\pi$
$660$	−0.815827	+	1.41305i	−0.0317560	+	0.0550030i
$661$	6.54377	+	11.3341i	0.254523	+	0.440847i	0.964766	−	0.263110i	$-0.0847481\pi$
$661$	6.54377	+	11.3341i	0.254523	+	0.440847i	−0.710243	+	0.703957i	$0.751415\pi$
$662$	−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
$667$	5.56262	−	0.487866i	0.215385	−	0.0188902i
$668$	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	$0.383158\pi$
$677$	−16.3633	+	28.3421i	−0.628893	+	1.08927i	−0.987774	+	0.155891i	$0.950175\pi$
$678$	−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
$690$	2.51939	+	1.17416i	0.0959116	+	0.0446993i
$691$	−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	$0.232290\pi$
$701$			35.3032i			1.33338i	−0.745334	+	0.666691i	$0.767710\pi$
$702$	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	$-0.930070\pi$
$709$	−44.0060	−	25.4069i	−1.65268	−	0.954175i	−0.676714	−	0.736246i	$-0.736597\pi$
$710$	−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	$-0.636807\pi$
$727$	−22.4700			−0.833366			−0.416683	+	0.909052i	$0.636807\pi$
$728$	−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	−0.695112	−	0.718901i	$-0.744645\pi$
$733$	7.44618	−	12.8972i	0.275031	−	0.476367i	0.970143	+	0.242534i	$0.0779786\pi$
$734$	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	$0.0134255\pi$
$743$			2.29867i			0.0843302i	−0.999111	+	0.0421651i	$0.986574\pi$
$744$	−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	0.408219	−	0.912884i	$-0.366150\pi$
$751$	−4.88492	−	2.82031i	−0.178253	−	0.102915i	−0.586472	+	0.809970i	$0.699483\pi$
$752$	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	$0.167939\pi$
$757$			27.7039i			1.00692i	−0.864020	+	0.503458i	$0.832061\pi$
$758$	6.02448	+	3.47823i	0.218819	+	0.126335i
$759$	1.96091	−	4.20753i	0.0711764	−	0.152724i
$760$	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	$-0.418854\pi$
$769$	13.9861			0.504350			0.252175	+	0.967682i	$0.418854\pi$
$770$	−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	0.944470	−	0.328598i	$-0.106576\pi$
$773$	5.21752	+	9.03701i	0.187661	+	0.325039i	−0.756809	+	0.653636i	$0.773243\pi$
$774$	−4.26456	+	2.46215i	−0.153287	+	0.0885000i
$775$	−8.08978	−	4.67064i	−0.290594	−	0.167774i
$776$	−17.0362			−0.611565
$777$	7.69053	−	15.3658i	0.275896	−	0.551244i
$778$			1.59871i			0.0573167i
$779$	−1.37969	−	0.796567i	−0.0494327	−	0.0285400i
$780$	−0.873976	−	1.51377i	−0.0312934	−	0.0542017i
$781$	−3.94180	+	2.27580i	−0.141049	+	0.0814346i
$782$	2.91187	−	0.255384i	0.104128	−	0.00913250i
$783$		−	1.16434i		−	0.0416100i
$784$	14.8053	−	1.77179i	0.528760	−	0.0632782i
$785$	−3.53203			−0.126063
$786$	−0.0433969	+	0.0751657i	−0.00154792	+	0.00268107i
$787$	−7.87542	−	13.6406i	−0.280728	−	0.486236i	0.690836	−	0.723012i	$-0.257243\pi$
$787$	−7.87542	−	13.6406i	−0.280728	−	0.486236i	−0.971564	+	0.236776i	$0.923909\pi$
$788$	5.84522	+	10.1242i	0.208227	+	0.360660i
$789$	−12.3233	+	21.3445i	−0.438720	+	0.759885i
$790$			2.83240i			0.100772i
$791$	23.9273	+	11.9756i	0.850757	+	0.425802i
$792$		−	2.04006i		−	0.0724904i
$793$	−3.12253	−	1.80280i	−0.110884	−	0.0640191i
$794$	−0.683219	+	0.394457i	−0.0242465	+	0.0139988i
$795$	4.82820	+	8.36269i	0.171239	+	0.296594i
$796$	−18.6770	+	32.3496i	−0.661990	+	1.14660i
$797$	50.9046			1.80313			0.901566	−	0.432642i	$-0.142418\pi$
$797$	50.9046			1.80313			0.901566	+	0.432642i	$0.142418\pi$
$798$	0.250278	−	0.165104i	0.00885973	−	0.00584461i
$799$		−	4.24077i		−	0.150028i
$800$	−10.8264	+	18.7519i	−0.382772	+	0.662981i
$801$	−5.52710	−	9.57321i	−0.195290	−	0.338253i
$802$	−12.4659	+	7.19717i	−0.440185	+	0.254141i
$803$	−4.83244	+	8.37003i	−0.170533	+	0.295372i
$804$	15.4791			0.545905
$805$	−7.95882	−	10.0327i	−0.280511	−	0.353608i
$806$	−1.39709			−0.0492104
$807$	1.04466	−	1.80941i	0.0367739	−	0.0636943i
$808$	−5.02818	+	2.90302i	−0.176891	+	0.102128i
$809$	−3.33818	−	5.78190i	−0.117364	−	0.203281i	0.801358	−	0.598185i	$-0.204111\pi$
$809$	−3.33818	−	5.78190i	−0.117364	−	0.203281i	−0.918722	+	0.394904i	$0.870778\pi$
$810$	0.289790	−	0.501930i	0.0101822	−	0.0176360i
$811$			14.6739i			0.515269i	0.966242	+	0.257634i	$0.0829430\pi$
$811$			14.6739i			0.515269i	−0.966242	+	0.257634i	$0.917057\pi$
$812$	−5.13610	+	0.306234i	−0.180242	+	0.0107467i
$813$	32.3942			1.13612
$814$	−1.80495	+	3.12627i	−0.0632636	+	0.109576i
$815$	−0.394003	−	0.682433i	−0.0138013	−	0.0239046i
$816$	−1.95796	+	1.13043i	−0.0685422	+	0.0395729i
$817$	−1.46551	−	0.846115i	−0.0512718	−	0.0296018i
$818$			10.8395i			0.378993i
$819$	−2.29003	+	1.51069i	−0.0800202	+	0.0527879i
$820$			13.6086i			0.475235i
$821$	−14.7222	+	25.4995i	−0.513807	+	0.889940i	0.486064	+	0.873923i	$0.338432\pi$
$821$	−14.7222	+	25.4995i	−0.513807	+	0.889940i	−0.999872	+	0.0160174i	$0.994901\pi$
$822$	2.29624	+	3.97720i	0.0800905	+	0.138721i
$823$	−25.6944	−	44.5040i	−0.895651	−	1.55131i	−0.832997	−	0.553277i	$-0.813377\pi$
$823$	−25.6944	−	44.5040i	−0.895651	−	1.55131i	−0.0626537	−	0.998035i	$-0.519956\pi$
$824$	8.81331	−	15.2651i	0.307026	−	0.531785i
$825$	3.85369			0.134168
$826$	5.61574	+	2.81066i	0.195397	+	0.0977955i
$827$			31.8354i			1.10702i	0.832841	+	0.553512i	$0.186713\pi$
$827$			31.8354i			1.10702i	−0.832841	+	0.553512i	$0.813287\pi$
$828$	7.97951	−	0.699838i	0.277307	−	0.0243211i
$829$	29.5342	−	17.0516i	1.02577	−	0.592226i	0.109997	−	0.993932i	$-0.464916\pi$
$829$	29.5342	−	17.0516i	1.02577	−	0.592226i	0.915769	+	0.401706i	$0.131583\pi$
$830$	−2.23528	−	3.87162i	−0.0775877	−	0.134386i
$831$	10.8473	+	6.26270i	0.376289	+	0.217251i
$832$		−	1.17913i		−	0.0408790i
$833$	2.92393	−	6.83003i	0.101308	−	0.236647i
$834$	−4.07566			−0.141128
$835$	11.8035	+	6.81473i	0.408475	+	0.235833i
$836$	0.276294	−	0.159519i	0.00955584	−	0.00551707i
$837$	1.17312	+	2.03191i	0.0405490	+	0.0702330i
$838$	11.1959	−	19.3918i	0.386754	−	0.669878i
$839$	37.0755			1.27999			0.639995	−	0.768379i	$-0.278936\pi$
$839$	37.0755			1.27999			0.639995	+	0.768379i	$0.278936\pi$
$840$	−5.03285	−	2.51893i	−0.173650	−	0.0869112i
$841$	−27.6443			−0.953252
$842$	10.9309	+	6.31098i	0.376705	+	0.217491i
$843$	−7.10278	−	12.3024i	−0.244633	−	0.423717i
$844$	18.1604	+	31.4547i	0.625107	+	1.08272i
$845$	−6.01767	+	10.4229i	−0.207014	+	0.358559i
$846$			2.29448i			0.0788858i
$847$	−14.6610	−	22.2243i	−0.503757	−	0.763636i
$848$			20.3805i			0.699868i
$849$	23.2013	+	13.3953i	0.796268	+	0.459725i
$850$	1.21332	+	2.10153i	0.0416165	+	0.0720819i
$851$	−28.2312	−	13.1571i	−0.967754	−	0.451019i
$852$	−6.80185	−	3.92705i	−0.233028	−	0.134539i
$853$		−	0.427521i		−	0.0146380i	−0.999973	−	0.00731901i	$-0.997670\pi$
$853$		−	0.427521i		−	0.0146380i	0.999973	−	0.00731901i	$-0.00232973\pi$
$854$	−5.27369	+	0.314437i	−0.180462	+	0.0107598i
$855$	0.199172			0.00681154
$856$	5.74219	+	3.31525i	0.196264	+	0.113313i
$857$	−10.0545	+	5.80497i	−0.343455	+	0.198294i	−0.661799	−	0.749681i	$-0.730207\pi$
$857$	−10.0545	+	5.80497i	−0.343455	+	0.198294i	0.318344	+	0.947975i	$0.396873\pi$
$858$	0.499144	−	0.288181i	0.0170405	−	0.00983833i
$859$	−20.9479	−	12.0943i	−0.714734	−	0.412652i	0.0980774	−	0.995179i	$-0.468731\pi$
$859$	−20.9479	−	12.0943i	−0.714734	−	0.412652i	−0.812811	+	0.582527i	$0.802064\pi$
$860$			14.4551i			0.492916i
$861$	21.3211	−	1.27124i	0.726621	−	0.0433239i
$862$			17.9677i			0.611983i
$863$	7.21344	−	12.4941i	0.245548	−	0.425302i	−0.716737	−	0.697343i	$-0.754365\pi$
$863$	7.21344	−	12.4941i	0.245548	−	0.425302i	0.962286	+	0.272041i	$0.0876986\pi$
$864$	4.70991	−	2.71927i	0.160235	−	0.0925115i
$865$	−5.85572	+	3.38080i	−0.199101	+	0.114951i
$866$	−9.61561	+	16.6547i	−0.326752	+	0.565951i
$867$		−	15.8735i		−	0.539092i
$868$	8.65457	−	5.70927i	0.293755	−	0.193785i
$869$	4.73026			0.160463
$870$	0.584416	+	0.337413i	0.0198136	+	0.0114394i
$871$	4.80490	+	8.32233i	0.162808	+	0.281991i
$872$	−3.95902	+	2.28574i	−0.134069	+	0.0774049i
$873$	−4.04152	+	7.00012i	−0.136785	+	0.236918i
$874$	−0.311827	−	0.445133i	−0.0105477	−	0.0150568i
$875$	10.7340	−	21.4466i	0.362874	−	0.725026i
$876$	−16.6774			−0.563477
$877$	15.4374	−	26.7384i	0.521285	−	0.902892i	−0.478409	−	0.878137i	$-0.658786\pi$
$877$	15.4374	−	26.7384i	0.521285	−	0.902892i	0.999694	−	0.0247547i	$-0.00788047\pi$
$878$	1.03466	−	0.597363i	0.0349182	−	0.0201600i
$879$	−18.9205	+	10.9238i	−0.638173	+	0.368449i
$880$	−1.80214	−	1.04047i	−0.0607501	−	0.0350741i
$881$	23.1596			0.780266			0.390133	−	0.920759i	$-0.372429\pi$
$881$	23.1596			0.780266			0.390133	+	0.920759i	$0.372429\pi$
$882$	−1.58200	+	3.69540i	−0.0532686	+	0.124431i
$883$	−3.16635			−0.106556			−0.0532780	−	0.998580i	$-0.516967\pi$
$883$	−3.16635			−0.106556			−0.0532780	+	0.998580i	$0.516967\pi$
$884$	−1.59191	−	0.919091i	−0.0535418	−	0.0309124i
$885$	2.08579	+	3.61270i	0.0701132	+	0.121440i
$886$	5.09166	+	8.81901i	0.171058	+	0.296280i
$887$	−38.4548	−	22.2019i	−1.29118	−	0.745466i	−0.312320	−	0.949977i	$-0.601106\pi$
$887$	−38.4548	−	22.2019i	−1.29118	−	0.745466i	−0.978864	+	0.204511i	$0.934439\pi$
$888$	−13.6882			−0.459345
$889$	8.87921	−	17.7408i	0.297799	−	0.595006i
$890$	6.40678			0.214756
$891$	−0.838252	−	0.483965i	−0.0280825	−	0.0162134i
$892$	27.8167	−	16.0600i	0.931371	−	0.537727i
$893$	−0.682858	+	0.394248i	−0.0228510	+	0.0131930i
$894$	5.74919	−	9.95789i	0.192282	−	0.333042i
$895$	15.4136			0.515220
$896$	−16.7982	−	25.4641i	−0.561190	−	0.850696i
$897$	2.85321	+	4.07295i	0.0952659	+	0.135992i
$898$	−6.51440	+	11.2833i	−0.217388	+	0.376528i
$899$	−2.36583	+	1.36591i	−0.0789047	+	0.0455557i
$900$	3.32491	+	5.75891i	0.110830	+	0.191964i
$901$	8.79438	+	5.07744i	0.292983	+	0.169154i
$902$	−4.48726			−0.149409
$903$	22.6473	−	1.35032i	0.753656	−	0.0449358i
$904$		−	21.3150i		−	0.708925i
$905$	10.4178	−	18.0441i	0.346298	−	0.599806i
$906$	2.60204	−	1.50229i	0.0864470	−	0.0499102i
$907$	−2.43514	+	1.40593i	−0.0808576	+	0.0466831i	−0.539884	−	0.841740i	$-0.681532\pi$
$907$	−2.43514	+	1.40593i	−0.0808576	+	0.0466831i	0.459026	+	0.888423i	$0.348198\pi$
$908$	21.7902	−	37.7417i	0.723133	−	1.25250i
$909$			2.75474i			0.0913691i
$910$	−0.0946359	−	1.58722i	−0.00313715	−	0.0526158i
$911$		−	13.8815i		−	0.459916i	−0.973201	−	0.229958i	$-0.926141\pi$
$911$		−	13.8815i		−	0.459916i	0.973201	−	0.229958i	$-0.0738588\pi$
$912$	0.364047	+	0.210183i	0.0120548	+	0.00695984i
$913$	−6.46582	+	3.73305i	−0.213988	+	0.123546i
$914$	−20.3278	+	11.7363i	−0.672385	+	0.388202i
$915$	−3.03927	−	1.75472i	−0.100475	−	0.0580093i
$916$	−21.3590			−0.705722
$917$	0.333795	−	0.220199i	0.0110229	−	0.00727160i
$918$		−	0.609497i		−	0.0201164i
$919$	−15.5458	−	8.97538i	−0.512809	−	0.296070i	0.221179	−	0.975233i	$-0.429010\pi$
$919$	−15.5458	−	8.97538i	−0.512809	−	0.296070i	−0.733988	+	0.679163i	$0.762343\pi$
$920$	−4.30942	+	9.24675i	−0.142077	+	0.304856i
$921$	−9.15235	−	15.8523i	−0.301580	−	0.522352i
$922$	17.9466	+	10.3615i	0.591039	+	0.341236i
$923$		−	4.87603i		−	0.160496i
$924$	−1.91439	+	3.82497i	−0.0629788	+	0.125832i
$925$		−	25.8571i		−	0.850176i
$926$	1.65359	−	2.86411i	0.0543404	−	0.0941204i
$927$	−4.18158	−	7.24271i	−0.137341	−	0.237882i
$928$	3.16615	+	5.48393i	0.103934	+	0.180019i
$929$	−46.3567	−	26.7640i	−1.52091	−	0.878100i	−0.999695	−	0.0246766i	$-0.992144\pi$
$929$	−46.3567	−	26.7640i	−1.52091	−	0.878100i	−0.521218	−	0.853423i	$-0.674522\pi$
$930$	−1.35983			−0.0445907
$931$	−1.37161	+	0.164145i	−0.0449527	+	0.00537962i
$932$	−27.6038			−0.904191
$933$	3.50124	−	6.06433i	0.114626	−	0.198537i
$934$	−4.58944	−	7.94915i	−0.150171	−	0.260104i
$935$	−0.897943	+	0.518427i	−0.0293659	+	0.0169544i
$936$	1.89267	+	1.09273i	0.0618639	+	0.0357171i
$937$	43.7774			1.43015			0.715073	−	0.699050i	$-0.246393\pi$
$937$	43.7774			1.43015			0.715073	+	0.699050i	$0.246393\pi$
$938$	12.5916	+	6.30207i	0.411131	+	0.205770i
$939$			1.82178i			0.0594514i
$940$	5.83301	+	3.36769i	0.190252	+	0.109842i
$941$	−10.2743	−	17.7956i	−0.334933	−	0.580121i	0.648539	−	0.761181i	$-0.275380\pi$
$941$	−10.2743	−	17.7956i	−0.334933	−	0.580121i	−0.983472	+	0.181061i	$0.942047\pi$
$942$	1.74041	−	1.00483i	0.0567058	−	0.0327391i
$943$	−3.38262	−	38.5684i	−0.110153	−	1.25596i
$944$			8.80441i			0.286559i
$945$	−2.22896	+	1.47041i	−0.0725082	+	0.0478324i
$946$	−4.76637			−0.154968
$947$	−6.54054	+	11.3286i	−0.212539	+	0.368128i	−0.952508	−	0.304512i	$-0.901507\pi$
$947$	−6.54054	+	11.3286i	−0.212539	+	0.368128i	0.739969	+	0.672641i	$0.234840\pi$
$948$	4.08120	+	7.06884i	0.132551	+	0.229585i
$949$	−5.17688	−	8.96661i	−0.168049	−	0.291069i
$950$	0.225595	−	0.390742i	0.00731926	−	0.0126773i
$951$			14.3229i			0.464452i
$952$	−5.90804	+	0.352259i	−0.191481	+	0.0114168i
$953$		−	9.01734i		−	0.292100i	−0.989277	−	0.146050i	$-0.953344\pi$
$953$		−	9.01734i		−	0.292100i	0.989277	−	0.146050i	$-0.0466561\pi$
$954$	−4.75821	−	2.74716i	−0.154053	−	0.0889425i
$955$	−11.5481	+	6.66731i	−0.373688	+	0.215749i
$956$	7.21450	+	12.4959i	0.233334	+	0.404146i
$957$	0.563499	−	0.976009i	0.0182153	−	0.0315499i
$958$	−10.5389			−0.340497
$959$	−1.25933	−	21.1213i	−0.0406659	−	0.682042i
$960$		−	1.14769i		−	0.0370414i
$961$	−12.7476	+	22.0794i	−0.411212	+	0.712240i
$962$	−1.93361	−	3.34910i	−0.0623419	−	0.107979i
$963$	2.72445	−	1.57296i	0.0877942	−	0.0506880i
$964$	−18.3217	+	31.7341i	−0.590102	+	1.02209i
$965$	−3.00180			−0.0966314
$966$	6.77595	+	2.67945i	0.218013	+	0.0862098i
$967$	−52.0787			−1.67474			−0.837370	−	0.546637i	$-0.815908\pi$
$967$	−52.0787			−1.67474			−0.837370	+	0.546637i	$0.815908\pi$
$968$	−10.6048	+	18.3680i	−0.340850	+	0.590369i
$969$	0.181392	−	0.104727i	0.00582715	−	0.00336431i
$970$	−2.34238	−	4.05713i	−0.0752094	−	0.130266i
$971$	26.1328	−	45.2634i	0.838642	−	1.45257i	−0.0523877	−	0.998627i	$-0.516683\pi$
$971$	26.1328	−	45.2634i	0.838642	−	1.45257i	0.891030	−	0.453944i	$-0.149984\pi$
$972$		−	1.67023i		−	0.0535727i
$973$	16.7919	+	8.40430i	0.538323	+	0.269430i
$974$	−2.40335			−0.0770083
$975$	−2.06419	+	3.57527i	−0.0661068	+	0.114500i
$976$	−3.70345	−	6.41457i	−0.118545	−	0.205325i
$977$	48.0854	−	27.7621i	1.53839	−	0.888189i	0.539455	−	0.842015i	$-0.318630\pi$
$977$	48.0854	−	27.7621i	1.53839	−	0.888189i	0.998933	−	0.0461741i	$-0.0147029\pi$
$978$	0.388292	+	0.224180i	0.0124162	+	0.00716850i
$979$		−	10.6997i		−	0.341964i
$980$	7.07248	+	9.44563i	0.225922	+	0.301729i
$981$			2.16899i			0.0692506i
$982$	0.400802	−	0.694210i	0.0127901	−	0.0221531i
$983$	−21.9880	−	38.0844i	−0.701309	−	1.21470i	−0.968007	−	0.250923i	$-0.919266\pi$
$983$	−21.9880	−	38.0844i	−0.701309	−	1.21470i	0.266698	−	0.963780i	$-0.414067\pi$
$984$	−8.50746	−	14.7354i	−0.271208	−	0.469746i
$985$	−3.53209	+	6.11776i	−0.112542	+	0.194928i
$986$	0.709661			0.0226002
$987$	4.73138	−	9.45336i	0.150602	−	0.300904i
$988$			0.341777i			0.0108734i
$989$	−3.59302	−	40.9674i	−0.114251	−	1.30269i
$990$	0.485834	−	0.280496i	0.0154408	−	0.00891475i
$991$	−13.8449	−	23.9801i	−0.439798	−	0.761752i	0.557876	−	0.829925i	$-0.311617\pi$
$991$	−13.8449	−	23.9801i	−0.439798	−	0.761752i	−0.997674	+	0.0681722i	$0.978283\pi$
$992$	−11.0506	−	6.38007i	−0.350857	−	0.202568i
$993$		−	29.0702i		−	0.922515i
$994$	−3.93420	−	5.96377i	−0.124785	−	0.189159i
$995$	−22.5719			−0.715579
$996$	−11.1572	−	6.44163i	−0.353530	−	0.204111i
$997$	−14.6806	+	8.47583i	−0.464938	+	0.268432i	−0.714118	−	0.700025i	$-0.753172\pi$
$997$	−14.6806	+	8.47583i	−0.464938	+	0.268432i	0.249180	+	0.968457i	$0.419839\pi$
$998$	−0.502104	−	0.869670i	−0.0158938	−	0.0275289i
$999$	−3.24726	+	5.62442i	−0.102739	+	0.177949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.j.a.229.19	✓	64
7.3	odd	6	inner	483.2.j.a.367.20	yes	64
23.22	odd	2	inner	483.2.j.a.229.20	yes	64
161.45	even	6	inner	483.2.j.a.367.19	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.j.a.229.19	✓	64	1.1	even	1	trivial
483.2.j.a.229.20	yes	64	23.22	odd	2	inner
483.2.j.a.367.19	yes	64	161.45	even	6	inner
483.2.j.a.367.20	yes	64	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.287128 - 0.497320i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.835115 + 1.44646i) q^{4} +(-0.504635 + 0.874053i) q^{5} -0.574256i q^{6} +(-1.18416 + 2.36596i) q^{7} +2.10765 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(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} +(4.77749 - 0.419007i) 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} +(1.16337 - 2.49625i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9}+O(q^{10}) \) 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9	\( 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50} - 108 q^{52} - 24 q^{58} + 36 q^{59} + 168 q^{64} - 40 q^{70} - 16 q^{71} - 12 q^{72} + 48 q^{73} - 48 q^{75} - 32 q^{78} - 32 q^{81} - 24 q^{82} + 88 q^{85} + 36 q^{87} + 152 q^{92} + 24 q^{93} - 108 q^{94} - 44 q^{95} + 60 q^{96} + 112 q^{98}+O(q^{100}) \) 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

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