LMFDB - Embedded newform 273.2.cc.a.50.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(50,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 7]))

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

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

chi := DirichletCharacter("273.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cc (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			50.12
Character	$\chi$	$=$	273.50
Dual form			273.2.cc.a.71.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.609155 - 0.163223i) q^{2} +(-1.67612 - 0.436610i) q^{3} +(-1.38762 - 0.801144i) q^{4} +(-1.27442 + 1.27442i) q^{5} +(0.949752 + 0.539544i) q^{6} +(0.258819 + 0.965926i) q^{7} +(1.60638 + 1.60638i) q^{8} +(2.61874 + 1.46362i) q^{9} +O(q^{10})$	\(q+(-0.609155 - 0.163223i) q^{2} +(-1.67612 - 0.436610i) q^{3} +(-1.38762 - 0.801144i) q^{4} +(-1.27442 + 1.27442i) q^{5} +(0.949752 + 0.539544i) q^{6} +(0.258819 + 0.965926i) q^{7} +(1.60638 + 1.60638i) q^{8} +(2.61874 + 1.46362i) q^{9} +(0.984333 - 0.568305i) q^{10} +(0.0816216 - 0.304616i) q^{11} +(1.97603 + 1.94866i) q^{12} +(0.401999 - 3.58307i) q^{13} -0.630644i q^{14} +(2.69250 - 1.57965i) q^{15} +(0.885952 + 1.53451i) q^{16} +(2.52815 - 4.37889i) q^{17} +(-1.35633 - 1.31901i) q^{18} +(6.67945 - 1.78975i) q^{19} +(2.78940 - 0.747418i) q^{20} +(-0.0120785 - 1.73201i) q^{21} +(-0.0994404 + 0.172236i) q^{22} +(3.83795 + 6.64753i) q^{23} +(-1.99112 - 3.39384i) q^{24} +1.75172i q^{25} +(-0.829718 + 2.11703i) q^{26} +(-3.75029 - 3.59657i) q^{27} +(0.414703 - 1.54769i) q^{28} +(-7.11966 + 4.11054i) q^{29} +(-1.89799 + 0.522776i) q^{30} +(4.10833 + 4.10833i) q^{31} +(-1.46517 - 5.46807i) q^{32} +(-0.269806 + 0.474935i) q^{33} +(-2.25477 + 2.25477i) q^{34} +(-1.56084 - 0.901150i) q^{35} +(-2.46126 - 4.12894i) q^{36} +(1.94323 + 0.520686i) q^{37} -4.36095 q^{38} +(-2.23820 + 5.83013i) q^{39} -4.09440 q^{40} +(1.90379 + 0.510120i) q^{41} +(-0.275345 + 1.05703i) q^{42} +(10.0161 + 5.78280i) q^{43} +(-0.357301 + 0.357301i) q^{44} +(-5.20264 + 1.47211i) q^{45} +(-1.25288 - 4.67582i) q^{46} +(-2.22295 - 2.22295i) q^{47} +(-0.814976 - 2.95884i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(0.285920 - 1.06707i) q^{50} +(-6.14935 + 6.23572i) q^{51} +(-3.42838 + 4.64989i) q^{52} -10.8218i q^{53} +(1.69747 + 2.80300i) q^{54} +(0.284188 + 0.492228i) q^{55} +(-1.13588 + 1.96740i) q^{56} +(-11.9770 + 0.0835236i) q^{57} +(5.00791 - 1.34187i) q^{58} +(7.70478 - 2.06449i) q^{59} +(-5.00170 + 0.0348803i) q^{60} +(-1.19322 + 2.06671i) q^{61} +(-1.83204 - 3.17318i) q^{62} +(-0.735967 + 2.90832i) q^{63} +0.0262467i q^{64} +(4.05402 + 5.07865i) q^{65} +(0.241874 - 0.245271i) q^{66} +(3.16749 - 11.8212i) q^{67} +(-7.01625 + 4.05083i) q^{68} +(-3.53049 - 12.8177i) q^{69} +(0.803704 + 0.803704i) q^{70} +(2.77760 + 10.3661i) q^{71} +(1.85557 + 6.55782i) q^{72} +(-2.96677 + 2.96677i) q^{73} +(-1.09874 - 0.634357i) q^{74} +(0.764817 - 2.93608i) q^{75} +(-10.7024 - 2.86770i) q^{76} +0.315362 q^{77} +(2.31502 - 3.18613i) q^{78} -3.53094 q^{79} +(-3.08468 - 0.826539i) q^{80} +(4.71564 + 7.66569i) q^{81} +(-1.07644 - 0.621485i) q^{82} +(1.60068 - 1.60068i) q^{83} +(-1.37083 + 2.41305i) q^{84} +(2.35861 + 8.80247i) q^{85} +(-5.15748 - 5.15748i) q^{86} +(13.7281 - 3.78123i) q^{87} +(0.620443 - 0.358213i) q^{88} +(2.95402 - 11.0245i) q^{89} +(3.40950 - 0.0475559i) q^{90} +(3.56503 - 0.539066i) q^{91} -12.2990i q^{92} +(-5.09231 - 8.67978i) q^{93} +(0.991286 + 1.71696i) q^{94} +(-6.23151 + 10.7933i) q^{95} +(0.0683759 + 9.80484i) q^{96} +(-8.11684 + 2.17490i) q^{97} +(0.609155 - 0.163223i) q^{98} +(0.659588 - 0.678248i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{6}+O(q^{10}) $ 112 * q - 12 * q^6	$ 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) $ 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$1$

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 $

$2$	−0.609155	−	0.163223i	−0.430738	−	0.115416i	0.0369346	−	0.999318i	$-0.488241\pi$
$2$	−0.609155	−	0.163223i	−0.430738	−	0.115416i	−0.467673	+	0.883902i	$0.654907\pi$
$3$	−1.67612	−	0.436610i	−0.967707	−	0.252077i
$3$	−1.67612	−	0.436610i	−0.967707	−	0.252077i
$4$	−1.38762	−	0.801144i	−0.693811	−	0.400572i
$5$	−1.27442	+	1.27442i	−0.569937	+	0.569937i	−0.932111	−	0.362174i	$-0.882035\pi$
$5$	−1.27442	+	1.27442i	−0.569937	+	0.569937i	0.362174	+	0.932111i	$0.382035\pi$
$6$	0.949752	+	0.539544i	0.387735	+	0.220268i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$8$	1.60638	+	1.60638i	0.567940	+	0.567940i
$9$	2.61874	+	1.46362i	0.872915	+	0.487873i
$10$	0.984333	−	0.568305i	0.311273	−	0.179714i
$11$	0.0816216	−	0.304616i	0.0246098	−	0.0918451i	−0.952529	−	0.304449i	$-0.901528\pi$
$11$	0.0816216	−	0.304616i	0.0246098	−	0.0918451i	0.977138	+	0.212604i	$0.0681944\pi$
$12$	1.97603	+	1.94866i	0.570431	+	0.562530i
$13$	0.401999	−	3.58307i	0.111494	−	0.993765i
$13$	0.401999	−	3.58307i	0.111494	−	0.993765i
$14$		−	0.630644i		−	0.168547i
$15$	2.69250	−	1.57965i	0.695200	−	0.407864i
$16$	0.885952	+	1.53451i	0.221488	+	0.383628i
$17$	2.52815	−	4.37889i	0.613168	−	1.06204i	−0.377535	−	0.925995i	$-0.623228\pi$
$17$	2.52815	−	4.37889i	0.613168	−	1.06204i	0.990703	−	0.136042i	$-0.0434383\pi$
$18$	−1.35633	−	1.31901i	−0.319689	−	0.310894i
$19$	6.67945	−	1.78975i	1.53237	−	0.410597i	0.608579	−	0.793494i	$-0.291740\pi$
$19$	6.67945	−	1.78975i	1.53237	−	0.410597i	0.923791	+	0.382896i	$0.125073\pi$
$20$	2.78940	−	0.747418i	0.623730	−	0.167128i
$21$	−0.0120785	−	1.73201i	−0.00263574	−	0.377955i
$22$	−0.0994404	+	0.172236i	−0.0212008	+	0.0367208i
$23$	3.83795	+	6.64753i	0.800269	+	1.38611i	0.919439	+	0.393232i	$0.128643\pi$
$23$	3.83795	+	6.64753i	0.800269	+	1.38611i	−0.119170	+	0.992874i	$0.538023\pi$
$24$	−1.99112	−	3.39384i	−0.406435	−	0.692765i
$25$			1.75172i			0.350343i
$26$	−0.829718	+	2.11703i	−0.162721	+	0.415184i
$27$	−3.75029	−	3.59657i	−0.721744	−	0.692160i
$28$	0.414703	−	1.54769i	0.0783714	−	0.292486i
$29$	−7.11966	+	4.11054i	−1.32209	+	0.763308i	−0.984061	−	0.177829i	$-0.943093\pi$
$29$	−7.11966	+	4.11054i	−1.32209	+	0.763308i	−0.338026	+	0.941137i	$0.609759\pi$
$30$	−1.89799	+	0.522776i	−0.346523	+	0.0954455i
$31$	4.10833	+	4.10833i	0.737878	+	0.737878i	0.972167	−	0.234289i	$-0.0752763\pi$
$31$	4.10833	+	4.10833i	0.737878	+	0.737878i	−0.234289	+	0.972167i	$0.575276\pi$
$32$	−1.46517	−	5.46807i	−0.259007	−	0.966627i
$33$	−0.269806	+	0.474935i	−0.0469671	+	0.0826756i
$34$	−2.25477	+	2.25477i	−0.386690	+	0.386690i
$35$	−1.56084	−	0.901150i	−0.263830	−	0.152322i
$36$	−2.46126	−	4.12894i	−0.410209	−	0.688157i
$37$	1.94323	+	0.520686i	0.319464	+	0.0856002i	0.414988	−	0.909827i	$-0.363786\pi$
$37$	1.94323	+	0.520686i	0.319464	+	0.0856002i	−0.0955235	+	0.995427i	$0.530452\pi$
$38$	−4.36095			−0.707439
$39$	−2.23820	+	5.83013i	−0.358399	+	0.933568i
$40$	−4.09440			−0.647381
$41$	1.90379	+	0.510120i	0.297323	+	0.0796674i	0.404397	−	0.914584i	$-0.367481\pi$
$41$	1.90379	+	0.510120i	0.297323	+	0.0796674i	−0.107074	+	0.994251i	$0.534148\pi$
$42$	−0.275345	+	1.05703i	−0.0424867	+	0.163104i
$43$	10.0161	+	5.78280i	1.52744	+	0.881869i	0.999468	+	0.0326090i	$0.0103816\pi$
$43$	10.0161	+	5.78280i	1.52744	+	0.881869i	0.527974	+	0.849260i	$0.322952\pi$
$44$	−0.357301	+	0.357301i	−0.0538652	+	0.0538652i
$45$	−5.20264	+	1.47211i	−0.775564	+	0.219449i
$46$	−1.25288	−	4.67582i	−0.184727	−	0.689412i
$47$	−2.22295	−	2.22295i	−0.324250	−	0.324250i	0.526145	−	0.850395i	$-0.323637\pi$
$47$	−2.22295	−	2.22295i	−0.324250	−	0.324250i	−0.850395	+	0.526145i	$0.823637\pi$
$48$	−0.814976	−	2.95884i	−0.117632	−	0.427072i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	0.285920	−	1.06707i	0.0404352	−	0.150906i
$51$	−6.14935	+	6.23572i	−0.861082	+	0.873176i
$52$	−3.42838	+	4.64989i	−0.475431	+	0.644824i
$53$		−	10.8218i		−	1.48648i	−0.669023	−	0.743242i	$-0.733287\pi$
$53$		−	10.8218i		−	1.48648i	0.669023	−	0.743242i	$-0.266713\pi$
$54$	1.69747	+	2.80300i	0.230996	+	0.381440i
$55$	0.284188	+	0.492228i	0.0383199	+	0.0663720i
$56$	−1.13588	+	1.96740i	−0.151788	+	0.262905i
$57$	−11.9770	+	0.0835236i	−1.58639	+	0.0110630i
$58$	5.00791	−	1.34187i	0.657571	−	0.176196i
$59$	7.70478	−	2.06449i	1.00308	−	0.268774i	0.280343	−	0.959900i	$-0.409552\pi$
$59$	7.70478	−	2.06449i	1.00308	−	0.268774i	0.722734	+	0.691126i	$0.242885\pi$
$60$	−5.00170	+	0.0348803i	−0.645717	+	0.00450303i
$61$	−1.19322	+	2.06671i	−0.152776	+	0.264615i	−0.932247	−	0.361823i	$-0.882155\pi$
$61$	−1.19322	+	2.06671i	−0.152776	+	0.264615i	0.779471	+	0.626438i	$0.215488\pi$
$62$	−1.83204	−	3.17318i	−0.232669	−	0.402995i
$63$	−0.735967	+	2.90832i	−0.0927232	+	0.366414i
$64$			0.0262467i			0.00328083i
$65$	4.05402	+	5.07865i	0.502839	+	0.629928i
$66$	0.241874	−	0.245271i	0.0297726	−	0.0301908i
$67$	3.16749	−	11.8212i	0.386971	−	1.44420i	−0.448066	−	0.894001i	$-0.647887\pi$
$67$	3.16749	−	11.8212i	0.386971	−	1.44420i	0.835036	−	0.550195i	$-0.185446\pi$
$68$	−7.01625	+	4.05083i	−0.850845	+	0.491236i
$69$	−3.53049	−	12.8177i	−0.425021	−	1.54307i
$70$	0.803704	+	0.803704i	0.0960610	+	0.0960610i
$71$	2.77760	+	10.3661i	0.329641	+	1.23024i	0.909564	+	0.415564i	$0.136416\pi$
$71$	2.77760	+	10.3661i	0.329641	+	1.23024i	−0.579923	+	0.814671i	$0.696917\pi$
$72$	1.85557	+	6.55782i	0.218681	+	0.772846i
$73$	−2.96677	+	2.96677i	−0.347234	+	0.347234i	−0.859078	−	0.511844i	$-0.828963\pi$
$73$	−2.96677	+	2.96677i	−0.347234	+	0.347234i	0.511844	+	0.859078i	$0.328963\pi$
$74$	−1.09874	−	0.634357i	−0.127726	−	0.0737425i
$75$	0.764817	−	2.93608i	0.0883134	−	0.339030i
$76$	−10.7024	−	2.86770i	−1.22765	−	0.328948i
$77$	0.315362			0.0359388
$78$	2.31502	−	3.18613i	0.262125	−	0.360758i
$79$	−3.53094			−0.397262			−0.198631	−	0.980074i	$-0.563649\pi$
$79$	−3.53094			−0.397262			−0.198631	+	0.980074i	$0.563649\pi$
$80$	−3.08468	−	0.826539i	−0.344878	−	0.0924098i
$81$	4.71564	+	7.66569i	0.523960	+	0.851743i
$82$	−1.07644	−	0.621485i	−0.118873	−	0.0686315i
$83$	1.60068	−	1.60068i	0.175698	−	0.175698i	−0.613780	−	0.789477i	$-0.710352\pi$
$83$	1.60068	−	1.60068i	0.175698	−	0.175698i	0.789477	+	0.613780i	$0.210352\pi$
$84$	−1.37083	+	2.41305i	−0.149570	+	0.263285i
$85$	2.35861	+	8.80247i	0.255828	+	0.954762i
$86$	−5.15748	−	5.15748i	−0.556146	−	0.556146i
$87$	13.7281	−	3.78123i	1.47181	−	0.405391i
$88$	0.620443	−	0.358213i	0.0661395	−	0.0381856i
$89$	2.95402	−	11.0245i	0.313125	−	1.16860i	−0.612597	−	0.790395i	$-0.709875\pi$
$89$	2.95402	−	11.0245i	0.313125	−	1.16860i	0.925722	−	0.378204i	$-0.123458\pi$
$90$	3.40950	−	0.0475559i	0.359393	−	0.00501283i
$91$	3.56503	−	0.539066i	0.373716	−	0.0565095i
$92$		−	12.2990i		−	1.28226i
$93$	−5.09231	−	8.67978i	−0.528048	−	0.900052i
$94$	0.991286	+	1.71696i	0.102243	+	0.177091i
$95$	−6.23151	+	10.7933i	−0.639340	+	1.10737i
$96$	0.0683759	+	9.80484i	0.00697858	+	1.00070i
$97$	−8.11684	+	2.17490i	−0.824141	+	0.220828i	−0.646156	−	0.763205i	$-0.723624\pi$
$97$	−8.11684	+	2.17490i	−0.824141	+	0.220828i	−0.177985	+	0.984033i	$0.556958\pi$
$98$	0.609155	−	0.163223i	0.0615340	−	0.0164880i
$99$	0.659588	−	0.678248i	0.0662911	−	0.0681665i
$100$	1.40338	−	2.43072i	0.140338	−	0.243072i
$101$	3.12439	+	5.41160i	0.310888	+	0.538474i	0.978555	−	0.205986i	$-0.0660402\pi$
$101$	3.12439	+	5.41160i	0.310888	+	0.538474i	−0.667667	+	0.744460i	$0.732707\pi$
$102$	4.76372	−	2.79481i	0.471679	−	0.276727i
$103$			1.91019i			0.188216i	0.995562	+	0.0941081i	$0.0299999\pi$
$103$			1.91019i			0.188216i	−0.995562	+	0.0941081i	$0.970000\pi$
$104$	6.40153	−	5.11000i	0.627722	−	0.501077i
$105$	2.22270	+	2.19191i	0.216913	+	0.213909i
$106$	−1.76636	+	6.59214i	−0.171564	+	0.640285i
$107$	−2.63741	+	1.52271i	−0.254968	+	0.147206i	−0.622037	−	0.782988i	$-0.713695\pi$
$107$	−2.63741	+	1.52271i	−0.254968	+	0.147206i	0.367069	+	0.930194i	$0.380361\pi$
$108$	2.32262	+	7.99520i	0.223494	+	0.769339i
$109$	0.562125	+	0.562125i	0.0538418	+	0.0538418i	0.733515	−	0.679673i	$-0.237878\pi$
$109$	0.562125	+	0.562125i	0.0538418	+	0.0538418i	−0.679673	+	0.733515i	$0.737878\pi$
$110$	−0.0927719	−	0.346229i	−0.00884545	−	0.0330117i
$111$	−3.02974	−	1.72116i	−0.287570	−	0.163366i
$112$	−1.25292	+	1.25292i	−0.118390	+	0.118390i
$113$	3.31932	+	1.91641i	0.312255	+	0.180280i	0.647935	−	0.761696i	$-0.275633\pi$
$113$	3.31932	+	1.91641i	0.312255	+	0.180280i	−0.335680	+	0.941976i	$0.608966\pi$
$114$	7.30946	+	1.90403i	0.684594	+	0.178329i
$115$	−13.3629	−	3.58058i	−1.24610	−	0.333891i
$116$	13.1725			1.22304
$117$	6.29698	−	8.79477i	0.582156	−	0.813077i
$118$	−5.03038			−0.463084
$119$	4.88402	+	1.30867i	0.447717	+	0.119966i
$120$	6.86269	+	1.78765i	0.626475	+	0.163190i
$121$	9.44015	+	5.45027i	0.858196	+	0.495479i
$122$	1.06419	−	1.06419i	0.0963471	−	0.0963471i
$123$	−2.96826	−	1.68624i	−0.267639	−	0.152043i
$124$	−2.40945	−	8.99217i	−0.216375	−	0.807521i
$125$	−8.60451	−	8.60451i	−0.769611	−	0.769611i
$126$	0.923023	−	1.65150i	0.0822294	−	0.147127i
$127$	6.03384	−	3.48364i	0.535416	−	0.309123i	−0.207803	−	0.978171i	$-0.566631\pi$
$127$	6.03384	−	3.48364i	0.535416	−	0.309123i	0.743219	+	0.669048i	$0.233298\pi$
$128$	−2.92605	+	10.9202i	−0.258628	+	0.965214i
$129$	−14.2634	−	14.0658i	−1.25582	−	1.23842i
$130$	−1.64058	−	3.75539i	−0.143888	−	0.329370i
$131$			19.8147i			1.73122i	0.500717	+	0.865611i	$0.333070\pi$
$131$			19.8147i			1.73122i	−0.500717	+	0.865611i	$0.666930\pi$
$132$	0.754880	−	0.442878i	0.0657039	−	0.0385475i
$133$	3.45754	+	5.98863i	0.299806	+	0.519280i
$134$	−3.85899	+	6.68397i	−0.333366	+	0.577407i
$135$	9.36297	−	0.195909i	0.805837	−	0.0168611i
$136$	11.0953	−	2.97298i	0.951417	−	0.254931i
$137$	9.79349	−	2.62416i	0.836714	−	0.224197i	0.185073	−	0.982725i	$-0.440748\pi$
$137$	9.79349	−	2.62416i	0.836714	−	0.224197i	0.651641	+	0.758528i	$0.274081\pi$
$138$	0.0584691	+	8.38425i	0.00497722	+	0.713715i
$139$	1.41297	−	2.44734i	0.119847	−	0.207581i	−0.799860	−	0.600187i	$-0.795093\pi$
$139$	1.41297	−	2.44734i	0.119847	−	0.207581i	0.919707	+	0.392606i	$0.128426\pi$
$140$	1.44390	+	2.50091i	0.122032	+	0.211366i
$141$	2.75536	+	4.69649i	0.232043	+	0.395516i
$142$		−	6.76796i		−	0.567955i
$143$	−1.05865	−	0.414911i	−0.0885286	−	0.0346966i
$144$	0.0741366	+	5.31519i	0.00617805	+	0.442933i
$145$	3.83488	−	14.3120i	0.318470	−	1.18854i
$146$	2.29147	−	1.32298i	0.189643	−	0.109491i
$147$	1.66987	−	0.459944i	0.137728	−	0.0379355i
$148$	−2.27932	−	2.27932i	−0.187359	−	0.187359i
$149$	−1.33154	−	4.96939i	−0.109084	−	0.407108i	0.889692	−	0.456561i	$-0.150919\pi$
$149$	−1.33154	−	4.96939i	−0.109084	−	0.407108i	−0.998776	+	0.0494528i	$0.984252\pi$
$150$	−0.945128	+	1.66370i	−0.0771693	+	0.135840i
$151$	−1.87948	+	1.87948i	−0.152950	+	0.152950i	−0.779434	−	0.626484i	$-0.784493\pi$
$151$	−1.87948	+	1.87948i	−0.152950	+	0.152950i	0.626484	+	0.779434i	$0.284493\pi$
$152$	13.6047	+	7.85470i	1.10349	+	0.637100i
$153$	13.0296	−	7.76694i	1.05338	−	0.627920i
$154$	−0.192104	−	0.0514742i	−0.0154802	−	0.00414791i
$155$	−10.4715			−0.841088
$156$	7.77655	−	6.29690i	0.622623	−	0.504155i
$157$	−3.25190			−0.259530			−0.129765	−	0.991545i	$-0.541422\pi$
$157$	−3.25190			−0.259530			−0.129765	+	0.991545i	$0.541422\pi$
$158$	2.15089	+	0.576330i	0.171116	+	0.0458503i
$159$	−4.72489	+	18.1386i	−0.374708	+	1.43848i
$160$	8.83584	+	5.10138i	0.698535	+	0.403299i
$161$	−5.42769	+	5.42769i	−0.427762	+	0.427762i
$162$	−1.62134	−	5.43929i	−0.127385	−	0.427351i
$163$	−3.67133	−	13.7016i	−0.287561	−	1.07319i	−0.946948	−	0.321387i	$-0.895851\pi$
$163$	−3.67133	−	13.7016i	−0.287561	−	1.07319i	0.659387	−	0.751804i	$-0.270816\pi$
$164$	−2.23307	−	2.23307i	−0.174373	−	0.174373i
$165$	−0.261421	−	0.949112i	−0.0203516	−	0.0738882i
$166$	−1.23633	+	0.713796i	−0.0959579	+	0.0554013i
$167$	1.41528	−	5.28188i	0.109517	−	0.408724i	−0.889301	−	0.457322i	$-0.848809\pi$
$167$	1.41528	−	5.28188i	0.109517	−	0.408724i	0.998818	+	0.0485980i	$0.0154753\pi$
$168$	2.76286	−	2.80166i	0.213159	−	0.216153i
$169$	−12.6768	−	2.88078i	−0.975138	−	0.221599i
$170$		−	5.74705i		−	0.440779i
$171$	20.1113	+	5.08927i	1.53795	+	0.389186i
$172$	−9.26572	−	16.0487i	−0.706504	−	1.22370i
$173$	9.81362	−	16.9977i	0.746115	−	1.29231i	−0.203557	−	0.979063i	$-0.565250\pi$
$173$	9.81362	−	16.9977i	0.746115	−	1.29231i	0.949672	−	0.313246i	$-0.101417\pi$
$174$	−8.97972	+	0.0626218i	−0.680751	+	0.00474735i
$175$	−1.69203	+	0.453377i	−0.127905	+	0.0342721i
$176$	0.539750	−	0.144626i	0.0406852	−	0.0109016i
$177$	−13.8155	+	0.0963450i	−1.03844	+	0.00724174i
$178$	−3.59891	+	6.23350i	−0.269750	+	0.467220i
$179$	8.89183	+	15.4011i	0.664607	+	1.15113i	0.979392	+	0.201970i	$0.0647343\pi$
$179$	8.89183	+	15.4011i	0.664607	+	1.15113i	−0.314785	+	0.949163i	$0.601932\pi$
$180$	8.39867	+	2.12533i	0.626000	+	0.158413i
$181$			3.11482i			0.231522i	0.993277	+	0.115761i	$0.0369307\pi$
$181$			3.11482i			0.231522i	−0.993277	+	0.115761i	$0.963069\pi$
$182$	−2.25964	−	0.253518i	−0.167496	−	0.0187920i
$183$	2.90232	−	2.94308i	0.214545	−	0.217559i
$184$	−4.51324	+	16.8437i	−0.332721	+	1.24173i
$185$	−3.14005	+	1.81291i	−0.230861	+	0.133288i
$186$	1.68527	+	6.11852i	0.123570	+	0.448631i
$187$	−1.12753	−	1.12753i	−0.0824530	−	0.0824530i
$188$	1.30371	+	4.86552i	0.0950829	+	0.354854i
$189$	2.50337	−	4.55336i	0.182093	−	0.331209i
$190$	5.55767	−	5.55767i	0.403196	−	0.403196i
$191$	−5.69718	−	3.28927i	−0.412233	−	0.238003i	0.279515	−	0.960141i	$-0.409826\pi$
$191$	−5.69718	−	3.28927i	−0.412233	−	0.238003i	−0.691749	+	0.722138i	$0.743160\pi$
$192$	0.0114596	−	0.0439925i	0.000827022	−	0.00317489i
$193$	−18.4159	−	4.93452i	−1.32560	−	0.355195i	−0.474530	−	0.880239i	$-0.657382\pi$
$193$	−18.4159	−	4.93452i	−1.32560	−	0.355195i	−0.851075	+	0.525045i	$0.824049\pi$
$194$	5.29941			0.380476
$195$	−4.57762	−	10.2824i	−0.327810	−	0.736340i
$196$	1.60229			0.114449
$197$	5.96842	+	1.59923i	0.425232	+	0.113941i	0.465087	−	0.885265i	$-0.346023\pi$
$197$	5.96842	+	1.59923i	0.425232	+	0.113941i	−0.0398551	+	0.999205i	$0.512690\pi$
$198$	−0.512497	+	0.305499i	−0.0364216	+	0.0217108i
$199$	12.1913	+	7.03867i	0.864220	+	0.498958i	0.865423	−	0.501042i	$-0.167050\pi$
$199$	12.1913	+	7.03867i	0.864220	+	0.498958i	−0.00120308	+	0.999999i	$0.500383\pi$
$200$	−2.81392	+	2.81392i	−0.198974	+	0.198974i
$201$	−10.4704	+	18.4308i	−0.738523	+	1.30001i
$202$	−1.01994	−	3.80648i	−0.0717629	−	0.267823i
$203$	−5.81318	−	5.81318i	−0.408005	−	0.408005i
$204$	13.5287	−	3.72631i	0.947198	−	0.260894i
$205$	−3.07634	+	1.77612i	−0.214861	+	0.124050i
$206$	0.311786	−	1.16360i	0.0217231	−	0.0810718i
$207$	0.321161	+	23.0255i	0.0223222	+	1.60038i
$208$	5.85442	−	2.55755i	0.405931	−	0.177335i
$209$		−	2.18075i		−	0.150845i
$210$	−0.996198	−	1.69801i	−0.0687442	−	0.117174i
$211$	6.07452	+	10.5214i	0.418187	+	0.724322i	0.995757	−	0.0920194i	$-0.0293322\pi$
$211$	6.07452	+	10.5214i	0.418187	+	0.724322i	−0.577570	+	0.816341i	$0.695999\pi$
$212$	−8.66979	+	15.0165i	−0.595444	+	1.03134i
$213$	−0.129624	−	18.5876i	−0.00888171	−	1.27360i
$214$	1.85514	−	0.497082i	0.126814	−	0.0339798i
$215$	−20.1344	+	5.39500i	−1.37316	+	0.367936i
$216$	−0.246939	−	11.8018i	−0.0168021	−	0.803013i
$217$	−2.90503	+	5.03166i	−0.197206	+	0.341571i
$218$	−0.250670	−	0.434173i	−0.0169775	−	0.0294059i
$219$	6.26798	−	3.67734i	0.423551	−	0.248492i
$220$		−	0.910702i		−	0.0613995i
$221$	−14.6736	−	10.8189i	−0.987051	−	0.727756i
$222$	1.56465	+	1.54298i	0.105012	+	0.103558i
$223$	−6.76870	+	25.2611i	−0.453266	+	1.69161i	0.239871	+	0.970805i	$0.422895\pi$
$223$	−6.76870	+	25.2611i	−0.453266	+	1.69161i	−0.693137	+	0.720806i	$0.743772\pi$
$224$	4.90254	−	2.83048i	0.327565	−	0.189120i
$225$	−2.56385	+	4.58730i	−0.170923	+	0.305820i
$226$	−1.70918	−	1.70918i	−0.113693	−	0.113693i
$227$	−4.97849	−	18.5800i	−0.330434	−	1.23320i	−0.908735	−	0.417373i	$-0.862951\pi$
$227$	−4.97849	−	18.5800i	−0.330434	−	1.23320i	0.578302	−	0.815823i	$-0.303716\pi$
$228$	16.6864	+	9.47937i	1.10508	+	0.627787i
$229$	−7.88965	+	7.88965i	−0.521363	+	0.521363i	−0.917983	−	0.396620i	$-0.870183\pi$
$229$	−7.88965	+	7.88965i	−0.521363	+	0.521363i	0.396620	+	0.917983i	$0.370183\pi$
$230$	7.55565	+	4.36226i	0.498205	+	0.287639i
$231$	−0.528583	−	0.137690i	−0.0347782	−	0.00905933i
$232$	−18.0399	−	4.83379i	−1.18438	−	0.317354i
$233$	11.1531			0.730664			0.365332	−	0.930877i	$-0.380955\pi$
$233$	11.1531			0.730664			0.365332	+	0.930877i	$0.380955\pi$
$234$	−5.27135	+	4.32957i	−0.344599	+	0.283033i
$235$	5.66593			0.369605
$236$	−12.3453	−	3.30791i	−0.803610	−	0.215327i
$237$	5.91827	+	1.54164i	0.384433	+	0.100140i
$238$	−2.76152	−	1.59437i	−0.179003	−	0.103347i
$239$	4.34364	−	4.34364i	0.280966	−	0.280966i	−0.552528	−	0.833494i	$-0.686337\pi$
$239$	4.34364	−	4.34364i	0.280966	−	0.280966i	0.833494	+	0.552528i	$0.186337\pi$
$240$	4.80942	+	2.73218i	0.310447	+	0.176361i
$241$	−1.11886	−	4.17564i	−0.0720721	−	0.268977i	0.920481	−	0.390786i	$-0.127797\pi$
$241$	−1.11886	−	4.17564i	−0.0720721	−	0.268977i	−0.992553	+	0.121810i	$0.961130\pi$
$242$	−4.86091	−	4.86091i	−0.312471	−	0.312471i
$243$	−4.55705	−	14.9075i	−0.292335	−	0.956316i
$244$	3.31147	−	1.91188i	0.211995	−	0.122395i
$245$	0.466469	−	1.74089i	0.0298016	−	0.111221i
$246$	1.53290	+	1.51167i	0.0977341	+	0.0963805i
$247$	−3.72768	−	24.6524i	−0.237186	−	1.56859i
$248$			13.1991i			0.838141i
$249$	−3.38181	+	1.98406i	−0.214313	+	0.125735i
$250$	3.83703	+	6.64594i	0.242675	+	0.420326i
$251$	−3.33231	+	5.77174i	−0.210334	+	0.364309i	−0.951819	−	0.306660i	$-0.900788\pi$
$251$	−3.33231	+	5.77174i	−0.210334	+	0.364309i	0.741485	+	0.670969i	$0.234122\pi$
$252$	3.35123	−	3.44604i	0.211108	−	0.217080i
$253$	2.33820	−	0.626520i	0.147002	−	0.0393890i
$254$	−4.24415	+	1.13722i	−0.266302	+	0.0713553i
$255$	−0.110071	−	15.7838i	−0.00689292	−	0.988418i
$256$	3.59108	−	6.21993i	0.224443	−	0.388746i
$257$	−7.30409	−	12.6511i	−0.455617	−	0.789151i	0.543107	−	0.839664i	$-0.317248\pi$
$257$	−7.30409	−	12.6511i	−0.455617	−	0.789151i	−0.998723	+	0.0505124i	$0.983915\pi$
$258$	6.39274	+	10.8964i	0.397995	+	0.678378i
$259$			2.01178i			0.125006i
$260$	−1.55672	−	10.2951i	−0.0965434	−	0.638475i
$261$	−24.6608	+	0.343971i	−1.52647	+	0.0212912i
$262$	3.23421	−	12.0703i	0.199810	−	0.745703i
$263$	−16.1283	+	9.31168i	−0.994514	+	0.574183i	−0.906620	−	0.421947i	$-0.861347\pi$
$263$	−16.1283	+	9.31168i	−0.994514	+	0.574183i	−0.0878933	+	0.996130i	$0.528013\pi$
$264$	−1.19634	+	0.329516i	−0.0736294	+	0.0202803i
$265$	13.7915	+	13.7915i	0.847202	+	0.847202i
$266$	−1.12870	−	4.21235i	−0.0692048	−	0.258276i
$267$	−9.76470	+	17.1887i	−0.597590	+	1.05193i
$268$	−13.8658	+	13.8658i	−0.846989	+	0.846989i
$269$	−17.4833	−	10.0940i	−1.06597	−	0.615440i	−0.138895	−	0.990307i	$-0.544355\pi$
$269$	−17.4833	−	10.0940i	−1.06597	−	0.615440i	−0.927078	+	0.374867i	$0.877688\pi$
$270$	−5.73548	−	1.40891i	−0.349050	−	0.0857436i
$271$	−8.59660	−	2.30345i	−0.522206	−	0.139925i	−0.0119194	−	0.999929i	$-0.503794\pi$
$271$	−8.59660	−	2.30345i	−0.522206	−	0.139925i	−0.510287	+	0.860004i	$0.670461\pi$
$272$	8.95929			0.543237
$273$	−6.21077	−	0.652988i	−0.375893	−	0.0395206i
$274$	−6.39408			−0.386280
$275$	0.533600	+	0.142978i	0.0321773	+	0.00862189i
$276$	−5.36987	+	20.6146i	−0.323228	+	1.24085i
$277$	−8.54400	−	4.93288i	−0.513359	−	0.296388i	0.220854	−	0.975307i	$-0.429115\pi$
$277$	−8.54400	−	4.93288i	−0.513359	−	0.296388i	−0.734213	+	0.678919i	$0.762449\pi$
$278$	−1.26018	+	1.26018i	−0.0755807	+	0.0755807i
$279$	4.74563	+	16.7717i	0.284113	+	1.00410i
$280$	−1.05971	−	3.95488i	−0.0633296	−	0.236349i
$281$	10.1561	+	10.1561i	0.605862	+	0.605862i	0.941862	−	0.336000i	$-0.109074\pi$
$281$	10.1561	+	10.1561i	0.605862	+	0.605862i	−0.336000	+	0.941862i	$0.609074\pi$
$282$	−0.911871	−	3.31063i	−0.0543011	−	0.197145i
$283$	−16.0853	+	9.28686i	−0.956173	+	0.552047i	−0.894993	−	0.446080i	$-0.852820\pi$
$283$	−16.0853	+	9.28686i	−0.956173	+	0.552047i	−0.0611797	+	0.998127i	$0.519486\pi$
$284$	4.45052	−	16.6096i	0.264090	−	0.985596i
$285$	15.1572	−	15.3701i	0.897836	−	0.910446i
$286$	0.577158	+	0.425541i	0.0341281	+	0.0251628i
$287$			1.97095i			0.116342i
$288$	4.16628	−	16.4639i	0.245501	−	0.970146i
$289$	−4.28313	−	7.41860i	−0.251949	−	0.436388i
$290$	−4.67208	+	8.09227i	−0.274354	+	0.475195i
$291$	14.5544	−	0.101498i	0.853192	−	0.00594990i
$292$	6.49357	−	1.73995i	0.380008	−	0.101823i
$293$	−25.7930	+	6.91120i	−1.50684	+	0.403757i	−0.915385	−	0.402581i	$-0.868113\pi$
$293$	−25.7930	+	6.91120i	−1.50684	+	0.403757i	−0.591456	+	0.806337i	$0.701447\pi$
$294$	−1.09228	+	0.00761723i	−0.0637031	+	0.000444246i
$295$	−7.18809	+	12.4501i	−0.418507	+	0.724875i
$296$	2.28514	+	3.95797i	0.132821	+	0.230053i
$297$	−1.40168	+	0.848841i	−0.0813335	+	0.0492547i
$298$			3.24447i			0.187947i
$299$	25.3614	−	11.0794i	1.46669	−	0.640736i
$300$	−3.41350	+	3.46145i	−0.197079	+	0.199847i
$301$	−2.99340	+	11.1715i	−0.172537	+	0.643916i
$302$	1.45167	−	0.838123i	0.0835344	−	0.0482286i
$303$	−2.87409	−	10.4346i	−0.165112	−	0.599453i
$304$	8.66406	+	8.66406i	0.496918	+	0.496918i
$305$	−1.11320	−	4.15451i	−0.0637415	−	0.237887i
$306$	−9.20480	+	2.60454i	−0.526204	+	0.148892i
$307$	−5.35964	+	5.35964i	−0.305891	+	0.305891i	−0.843313	−	0.537423i	$-0.819398\pi$
$307$	−5.35964	+	5.35964i	−0.305891	+	0.305891i	0.537423	+	0.843313i	$0.319398\pi$
$308$	−0.437603	−	0.252650i	−0.0249347	−	0.0143961i
$309$	0.834006	−	3.20170i	0.0474449	−	0.182138i
$310$	6.37875	+	1.70918i	0.362288	+	0.0970749i
$311$	−6.89236			−0.390830			−0.195415	−	0.980721i	$-0.562605\pi$
$311$	−6.89236			−0.390830			−0.195415	+	0.980721i	$0.562605\pi$
$312$	−12.9608	+	5.77000i	−0.733761	+	0.326662i
$313$	16.4655			0.930687			0.465344	−	0.885130i	$-0.345931\pi$
$313$	16.4655			0.930687			0.465344	+	0.885130i	$0.345931\pi$
$314$	1.98091	+	0.530784i	0.111789	+	0.0299539i
$315$	−2.76849	−	4.64435i	−0.155987	−	0.261680i
$316$	4.89961	+	2.82879i	0.275625	+	0.159132i
$317$	16.1569	−	16.1569i	0.907460	−	0.907460i	−0.0886063	−	0.996067i	$-0.528241\pi$
$317$	16.1569	−	16.1569i	0.907460	−	0.907460i	0.996067	+	0.0886063i	$0.0282413\pi$
$318$	5.83882	−	10.2780i	0.327425	−	0.576361i
$319$	0.671017	+	2.50427i	0.0375697	+	0.140212i
$320$	−0.0334492	−	0.0334492i	−0.00186987	−	0.00186987i
$321$	5.08545	−	1.40072i	0.283842	−	0.0781808i
$322$	4.19223	−	2.42038i	0.233624	−	0.134883i
$323$	9.04954	−	33.7733i	0.503530	−	1.87920i
$324$	−0.402200	−	14.4150i	−0.0223445	−	0.800832i
$325$	6.27652	+	0.704188i	0.348159	+	0.0390613i
$326$			8.94564i			0.495453i
$327$	−0.696758	−	1.18762i	−0.0385308	−	0.0656754i
$328$	2.23877	+	3.87766i	0.123615	+	0.214108i
$329$	1.57186	−	2.72255i	0.0866596	−	0.150099i
$330$	0.00432945	+	0.620826i	0.000238328	+	0.0341754i
$331$	18.4789	−	4.95141i	1.01569	−	0.272154i	0.287687	−	0.957725i	$-0.407114\pi$
$331$	18.4789	−	4.95141i	1.01569	−	0.272154i	0.728006	+	0.685570i	$0.240447\pi$
$332$	−3.50352	+	0.938765i	−0.192281	+	0.0515214i
$333$	4.32672	+	4.20769i	0.237103	+	0.230580i
$334$	−1.72424	+	2.98648i	−0.0943465	+	0.163413i
$335$	11.0285	+	19.1019i	0.602551	+	1.04365i
$336$	2.64709	−	1.55301i	0.144411	−	0.0847237i
$337$			19.4165i			1.05768i	0.848721	+	0.528841i	$0.177373\pi$
$337$			19.4165i			1.05768i	−0.848721	+	0.528841i	$0.822627\pi$
$338$	7.25193	+	3.82398i	0.394453	+	0.207997i
$339$	−4.72684	−	4.66137i	−0.256727	−	0.253171i
$340$	3.77918	−	14.1041i	0.204955	−	0.764902i
$341$	1.58679	−	0.916134i	0.0859295	−	0.0496114i
$342$	−11.4202	−	6.38277i	−0.617534	−	0.345141i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	6.80029	+	25.3790i	0.366647	+	1.36835i
$345$	20.8345	+	11.8358i	1.12169	+	0.637220i
$346$	−8.75242	+	8.75242i	−0.470533	+	0.470533i
$347$	6.71799	+	3.87863i	0.360640	+	0.208216i	0.669362	−	0.742937i	$-0.266568\pi$
$347$	6.71799	+	3.87863i	0.360640	+	0.208216i	−0.308721	+	0.951153i	$0.599901\pi$
$348$	−22.0787	−	5.75126i	−1.18354	−	0.308300i
$349$	16.5432	+	4.43274i	0.885538	+	0.237279i	0.672795	−	0.739829i	$-0.265094\pi$
$349$	16.5432	+	4.43274i	0.885538	+	0.237279i	0.212743	+	0.977108i	$0.431760\pi$
$350$	1.10471			0.0590492
$351$	−14.3944	+	11.9917i	−0.768315	+	0.640072i
$352$	−1.78525			−0.0951541
$353$	24.6284	+	6.59915i	1.31084	+	0.351237i	0.845537	−	0.533916i	$-0.179280\pi$
$353$	24.6284	+	6.59915i	1.31084	+	0.351237i	0.465299	+	0.885154i	$0.345947\pi$
$354$	8.43152	+	2.19632i	0.448130	+	0.116733i
$355$	−16.7506	−	9.67098i	−0.889031	−	0.513282i
$356$	−12.9313	+	12.9313i	−0.685358	+	0.685358i
$357$	−7.61482	−	4.32590i	−0.403019	−	0.228951i
$358$	−2.90270	−	10.8330i	−0.153412	−	0.572543i
$359$	−3.28169	−	3.28169i	−0.173201	−	0.173201i	0.615183	−	0.788384i	$-0.289082\pi$
$359$	−3.28169	−	3.28169i	−0.173201	−	0.173201i	−0.788384	+	0.615183i	$0.789082\pi$
$360$	−10.7222	−	5.99264i	−0.565108	−	0.315840i
$361$	24.9573	−	14.4091i	1.31354	−	0.758374i
$362$	0.508409	−	1.89741i	0.0267214	−	0.0997255i
$363$	−13.4432	−	13.2570i	−0.705583	−	0.695810i
$364$	−5.37878	−	2.10808i	−0.281925	−	0.110493i
$365$		−	7.56182i		−	0.395804i
$366$	−2.24834	+	1.31907i	−0.117523	+	0.0689489i
$367$	−6.52188	−	11.2962i	−0.340440	−	0.589659i	0.644075	−	0.764963i	$-0.277243\pi$
$367$	−6.52188	−	11.2962i	−0.340440	−	0.589659i	−0.984514	+	0.175304i	$0.943909\pi$
$368$	−6.80048	+	11.7788i	−0.354500	+	0.614011i
$369$	4.23893	+	4.12231i	0.220670	+	0.214599i
$370$	2.20869	−	0.591816i	0.114824	−	0.0307671i
$371$	10.4530	−	2.80088i	0.542694	−	0.145414i
$372$	0.112443	+	16.1239i	0.00582991	+	0.835987i
$373$	−3.41630	+	5.91720i	−0.176889	+	0.306381i	−0.940813	−	0.338925i	$-0.889937\pi$
$373$	−3.41630	+	5.91720i	−0.176889	+	0.306381i	0.763924	+	0.645306i	$0.223270\pi$
$374$	0.502802	+	0.870878i	0.0259993	+	0.0450320i
$375$	10.6654	+	18.1790i	0.550757	+	0.938759i
$376$		−	7.14179i		−	0.368310i
$377$	11.8663	+	27.1627i	0.611143	+	1.39895i
$378$	−2.26815	+	2.36510i	−0.116661	+	0.121648i
$379$	4.78838	−	17.8705i	0.245962	−	0.917944i	−0.726935	−	0.686706i	$-0.759056\pi$
$379$	4.78838	−	17.8705i	0.245962	−	0.917944i	0.972897	−	0.231238i	$-0.0742775\pi$
$380$	17.2940	−	9.98468i	0.887162	−	0.512203i
$381$	−11.6344	+	3.20455i	−0.596049	+	0.164174i
$382$	2.93358	+	2.93358i	0.150095	+	0.150095i
$383$	−2.05533	−	7.67059i	−0.105022	−	0.391949i	0.893325	−	0.449411i	$-0.148366\pi$
$383$	−2.05533	−	7.67059i	−0.105022	−	0.391949i	−0.998348	+	0.0574617i	$0.981699\pi$
$384$	9.67225	−	17.0259i	0.493585	−	0.868851i
$385$	−0.401902	+	0.401902i	−0.0204828	+	0.0204828i
$386$	10.4127	+	6.01178i	0.529993	+	0.305992i
$387$	17.7658	+	29.8035i	0.903086	+	1.51499i
$388$	13.0055	+	3.48482i	0.660255	+	0.176915i
$389$	−10.5589			−0.535358			−0.267679	−	0.963508i	$-0.586257\pi$
$389$	−10.5589			−0.535358			−0.267679	+	0.963508i	$0.586257\pi$
$390$	1.11016	+	7.01077i	0.0562150	+	0.355004i
$391$	38.8118			1.96280
$392$	−2.19435	−	0.587975i	−0.110832	−	0.0296972i
$393$	8.65131	−	33.2118i	0.436401	−	1.67532i
$394$	−3.37466	−	1.94836i	−0.170013	−	0.0981571i
$395$	4.49989	−	4.49989i	0.226414	−	0.226414i
$396$	−1.45863	+	0.412727i	−0.0732990	+	0.0207403i
$397$	−3.87604	−	14.4656i	−0.194533	−	0.726006i	−0.992387	−	0.123156i	$-0.960698\pi$
$397$	−3.87604	−	14.4656i	−0.194533	−	0.726006i	0.797855	−	0.602850i	$-0.205968\pi$
$398$	−6.27754	−	6.27754i	−0.314665	−	0.314665i
$399$	−3.18054	−	11.5472i	−0.159226	−	0.578085i
$400$	−2.68803	+	1.55194i	−0.134402	+	0.0775968i
$401$	−5.52699	+	20.6270i	−0.276005	+	1.03006i	0.679160	+	0.733990i	$0.262344\pi$
$401$	−5.52699	+	20.6270i	−0.276005	+	1.03006i	−0.955165	+	0.296074i	$0.904323\pi$
$402$	9.38641	−	9.51825i	0.468152	−	0.474727i
$403$	16.3720	−	13.0689i	0.815546	−	0.651008i
$404$		−	10.0123i		−	0.498133i
$405$	−15.7790	−	3.75960i	−0.784064	−	0.186816i
$406$	2.59229	+	4.48997i	0.128653	+	0.222834i
$407$	0.317218	−	0.549438i	0.0157239	−	0.0272346i
$408$	−19.8951	+	0.138742i	−0.984955	+	0.00686877i
$409$	−7.99993	+	2.14358i	−0.395571	+	0.105993i	−0.451121	−	0.892463i	$-0.648976\pi$
$409$	−7.99993	+	2.14358i	−0.395571	+	0.105993i	0.0555495	+	0.998456i	$0.482309\pi$
$410$	2.16387	−	0.579808i	0.106866	−	0.0286347i
$411$	−17.5608	+	0.122463i	−0.866209	+	0.00604067i
$412$	1.53033	−	2.65062i	0.0753941	−	0.130586i
$413$	3.98829	+	6.90792i	0.196251	+	0.339917i
$414$	3.56265	−	14.0785i	0.175094	−	0.691921i
$415$			4.07988i			0.200273i
$416$	−20.1815	+	3.05163i	−0.989478	+	0.149619i
$417$	−3.43685	+	3.48512i	−0.168303	+	0.170667i
$418$	−0.355947	+	1.32841i	−0.0174100	+	0.0649748i
$419$	−8.86700	+	5.11937i	−0.433181	+	0.250097i	−0.700701	−	0.713455i	$-0.747129\pi$
$419$	−8.86700	+	5.11937i	−0.433181	+	0.250097i	0.267520	+	0.963552i	$0.413796\pi$
$420$	−1.32823	−	4.82224i	−0.0648108	−	0.235301i
$421$	−19.7924	−	19.7924i	−0.964624	−	0.964624i	0.0347716	−	0.999395i	$-0.488930\pi$
$421$	−19.7924	−	19.7924i	−0.964624	−	0.964624i	−0.999395	+	0.0347716i	$0.988930\pi$
$422$	−1.98300	−	7.40066i	−0.0965310	−	0.360258i
$423$	−2.56778	−	9.07489i	−0.124850	−	0.441236i
$424$	17.3838	−	17.3838i	0.844234	−	0.844234i
$425$	7.67058	+	4.42861i	0.372078	+	0.214819i
$426$	−2.95496	+	11.3439i	−0.143168	+	0.549614i
$427$	−2.30512	−	0.617654i	−0.111552	−	0.0298904i
$428$	4.87965			0.235867
$429$	1.59327	+	1.15766i	0.0769236	+	0.0558922i
$430$	13.1456			0.633936
$431$	−5.58772	−	1.49723i	−0.269151	−	0.0721188i	0.121719	−	0.992565i	$-0.461159\pi$
$431$	−5.58772	−	1.49723i	−0.269151	−	0.0721188i	−0.390870	+	0.920446i	$0.627826\pi$
$432$	2.19640	−	8.94126i	0.105675	−	0.430187i
$433$	8.01191	+	4.62568i	0.385028	+	0.222296i	0.680004	−	0.733209i	$-0.261978\pi$
$433$	8.01191	+	4.62568i	0.385028	+	0.222296i	−0.294976	+	0.955505i	$0.595312\pi$
$434$	2.59089	−	2.59089i	0.124367	−	0.124367i
$435$	−12.6765	+	22.3142i	−0.607790	+	1.06988i
$436$	−0.329674	−	1.23036i	−0.0157885	−	0.0589236i
$437$	37.5328	+	37.5328i	1.79544	+	1.79544i
$438$	−4.41840	+	1.21699i	−0.211119	+	0.0581502i
$439$	−4.20489	+	2.42770i	−0.200689	+	0.115868i	−0.596977	−	0.802259i	$-0.703632\pi$
$439$	−4.20489	+	2.42770i	−0.200689	+	0.115868i	0.396288	+	0.918126i	$0.370298\pi$
$440$	−0.334191	+	1.24722i	−0.0159319	+	0.0594588i
$441$	−2.99971	+	0.0418401i	−0.142843	+	0.00199239i
$442$	7.17260	+	8.98543i	0.341166	+	0.427393i
$443$		−	4.36895i		−	0.207575i	−0.994599	−	0.103788i	$-0.966904\pi$
$443$		−	4.36895i		−	0.207575i	0.994599	−	0.103788i	$-0.0330962\pi$
$444$	2.82523	+	4.81558i	0.134080	+	0.228537i
$445$	10.2852	+	17.8145i	0.487566	+	0.844490i
$446$	8.24638	−	14.2832i	0.390477	−	0.676327i
$447$	0.0621401	+	8.91064i	0.00293912	+	0.421459i
$448$	−0.0253523	+	0.00679314i	−0.00119778	+	0.000320945i
$449$	−32.9659	+	8.83320i	−1.55576	+	0.416864i	−0.931318	−	0.364207i	$-0.881340\pi$
$449$	−32.9659	+	8.83320i	−1.55576	+	0.416864i	−0.624441	+	0.781072i	$0.714673\pi$
$450$	2.31053	−	2.37590i	0.108919	−	0.112001i
$451$	0.310781	−	0.538289i	0.0146341	−	0.0253471i
$452$	−3.07064	−	5.31850i	−0.144431	−	0.250161i
$453$	3.97084	−	2.32964i	0.186566	−	0.109456i
$454$			12.1307i			0.569321i
$455$	−3.85634	+	5.23033i	−0.180788	+	0.245202i
$456$	−19.3737	−	19.1054i	−0.907257	−	0.894690i
$457$	0.461237	−	1.72136i	0.0215758	−	0.0805218i	−0.954299	−	0.298855i	$-0.903395\pi$
$457$	0.461237	−	1.72136i	0.0215758	−	0.0805218i	0.975874	+	0.218333i	$0.0700620\pi$
$458$	6.09379	−	3.51825i	0.284744	−	0.164397i
$459$	−25.2303	+	7.32945i	−1.17765	+	0.342109i
$460$	15.6741	+	15.6741i	0.730808	+	0.730808i
$461$	3.47367	+	12.9639i	0.161785	+	0.603790i	0.998428	+	0.0560419i	$0.0178481\pi$
$461$	3.47367	+	12.9639i	0.161785	+	0.603790i	−0.836643	+	0.547748i	$0.815485\pi$
$462$	0.299515	+	0.170151i	0.0139347	+	0.00791616i
$463$	24.4616	−	24.4616i	1.13683	−	1.13683i	0.147809	−	0.989016i	$-0.452778\pi$
$463$	24.4616	−	24.4616i	1.13683	−	1.13683i	0.989016	−	0.147809i	$-0.0472221\pi$
$464$	−12.6153	−	7.28347i	−0.585653	−	0.338127i
$465$	17.5514	+	4.57194i	0.813927	+	0.212019i
$466$	−6.79397	−	1.82044i	−0.314725	−	0.0843302i
$467$	−2.11536			−0.0978873			−0.0489436	−	0.998802i	$-0.515585\pi$
$467$	−2.11536			−0.0978873			−0.0489436	+	0.998802i	$0.515585\pi$
$468$	−15.7837	+	7.15903i	−0.729602	+	0.330926i
$469$	12.2383			0.565110
$470$	−3.45143	−	0.924809i	−0.159203	−	0.0426583i
$471$	5.45057	+	1.41981i	0.251149	+	0.0654214i
$472$	15.6931	+	9.06044i	0.722336	+	0.417041i
$473$	2.57906	−	2.57906i	0.118586	−	0.118586i
$474$	−3.35352	−	1.90510i	−0.154032	−	0.0875040i
$475$	3.13514	+	11.7005i	0.143850	+	0.536855i
$476$	−5.72874	−	5.72874i	−0.262576	−	0.262576i
$477$	15.8389	−	28.3394i	0.725216	−	1.29757i
$478$	−3.35493	+	1.93697i	−0.153451	+	0.0885949i
$479$	2.62409	−	9.79324i	0.119898	−	0.447465i	−0.879709	−	0.475513i	$-0.842263\pi$
$479$	2.62409	−	9.79324i	0.119898	−	0.447465i	0.999607	+	0.0280482i	$0.00892919\pi$
$480$	−12.5826	−	12.4083i	−0.574315	−	0.566360i
$481$	2.64683	−	6.75340i	0.120685	−	0.307929i
$482$			2.72624i			0.124177i
$483$	11.4672	−	6.72766i	0.521777	−	0.306119i
$484$	−8.73291	−	15.1258i	−0.396950	−	0.687538i
$485$	7.57252	−	13.1160i	0.343850	−	0.595566i
$486$	0.342709	+	9.82479i	0.0155456	+	0.445662i
$487$	10.1101	−	2.70899i	0.458132	−	0.122756i	−0.0223699	−	0.999750i	$-0.507121\pi$
$487$	10.1101	−	2.70899i	0.458132	−	0.122756i	0.480502	+	0.876994i	$0.340454\pi$
$488$	−5.23668	+	1.40316i	−0.237053	+	0.0635182i
$489$	0.171332	+	24.5684i	0.00774792	+	1.11102i
$490$	−0.568305	+	0.984333i	−0.0256734	+	0.0444676i
$491$	−12.5057	−	21.6606i	−0.564376	−	0.977528i	−0.997107	−	0.0760051i	$-0.975783\pi$
$491$	−12.5057	−	21.6606i	−0.564376	−	0.977528i	0.432731	−	0.901523i	$-0.357550\pi$
$492$	2.76791	+	4.71787i	0.124787	+	0.212698i
$493$			41.5683i			1.87214i
$494$	−1.75310	+	15.6256i	−0.0788755	+	0.703028i
$495$	0.0237809	+	1.70496i	0.00106887	+	0.0766323i
$496$	−2.66450	+	9.94407i	−0.119640	+	0.446502i
$497$	−9.29403	+	5.36591i	−0.416894	+	0.240694i
$498$	2.38389	−	0.656612i	0.106825	−	0.0294235i
$499$	−9.11595	−	9.11595i	−0.408086	−	0.408086i	0.472985	−	0.881071i	$-0.343177\pi$
$499$	−9.11595	−	9.11595i	−0.408086	−	0.408086i	−0.881071	+	0.472985i	$0.843177\pi$
$500$	5.04636	+	18.8333i	0.225680	+	0.842249i
$501$	−4.67829	+	8.23513i	−0.209011	+	0.367918i
$502$	2.97198	−	2.97198i	0.132646	−	0.132646i
$503$	−16.4105	−	9.47462i	−0.731709	−	0.422452i	0.0873380	−	0.996179i	$-0.472164\pi$
$503$	−16.4105	−	9.47462i	−0.731709	−	0.422452i	−0.819047	+	0.573726i	$0.805497\pi$
$504$	−5.85411	+	3.48963i	−0.260763	+	0.155440i
$505$	−10.8784	−	2.91486i	−0.484083	−	0.129710i
$506$	−1.52659			−0.0678653
$507$	19.9900	+	10.3633i	0.887788	+	0.460252i
$508$	−11.1636			−0.495304
$509$	2.60485	+	0.697967i	0.115458	+	0.0309368i	0.316085	−	0.948731i	$-0.397631\pi$
$509$	2.60485	+	0.697967i	0.115458	+	0.0309368i	−0.200627	+	0.979668i	$0.564298\pi$
$510$	−2.50922	+	9.63273i	−0.111110	+	0.426545i
$511$	−3.63354	−	2.09782i	−0.160738	−	0.0928023i
$512$	12.7855	−	12.7855i	0.565043	−	0.565043i
$513$	−31.4868	−	17.3110i	−1.39018	−	0.764299i
$514$	2.38439	+	8.89865i	0.105171	+	0.392503i
$515$	−2.43438	−	2.43438i	−0.107271	−	0.107271i
$516$	8.52342	+	30.9450i	0.375223	+	1.36228i
$517$	−0.858586	+	0.495705i	−0.0377606	+	0.0218011i
$518$	0.328367	−	1.22548i	0.0144276	−	0.0538447i
$519$	−23.8701	+	24.2054i	−1.04778	+	1.06250i
$520$	−1.64594	+	14.6705i	−0.0721794	+	0.643344i
$521$		−	28.6317i		−	1.25438i	−0.778867	−	0.627189i	$-0.784205\pi$
$521$		−	28.6317i		−	1.25438i	0.778867	−	0.627189i	$-0.215795\pi$
$522$	15.0784	+	3.81568i	0.659965	+	0.167008i
$523$	−5.09573	−	8.82606i	−0.222821	−	0.385937i	0.732843	−	0.680398i	$-0.238193\pi$
$523$	−5.09573	−	8.82606i	−0.222821	−	0.385937i	−0.955663	+	0.294461i	$0.904860\pi$
$524$	15.8745	−	27.4954i	0.693479	−	1.20114i
$525$	3.03399	−	0.0211581i	0.132414	−	0.000923414i
$526$	11.3445	−	3.03976i	0.494645	−	0.132540i
$527$	28.3764	−	7.60344i	1.23610	−	0.331211i
$528$	−0.967829	+	0.00674934i	−0.0421194	+	0.000293727i
$529$	−17.9598	+	31.1073i	−0.780860	+	1.35249i
$530$	−6.15006	−	10.6522i	−0.267142	−	0.462703i
$531$	23.1985	+	5.87050i	1.00673	+	0.254758i
$532$		−	11.0799i		−	0.480376i
$533$	2.59312	−	6.61636i	0.112321	−	0.286587i
$534$	8.75380	−	8.87675i	0.378814	−	0.384135i
$535$	1.42060	−	5.30174i	0.0614178	−	0.229214i
$536$	24.0776	−	13.9012i	1.03999	−	0.600440i
$537$	−8.17949	−	29.6963i	−0.352971	−	1.28149i
$538$	9.00246	+	9.00246i	0.388123	+	0.388123i
$539$	0.0816216	+	0.304616i	0.00351569	+	0.0131207i
$540$	−13.1492	−	7.22924i	−0.565852	−	0.311097i
$541$	9.65873	−	9.65873i	0.415261	−	0.415261i	−0.468305	−	0.883567i	$-0.655135\pi$
$541$	9.65873	−	9.65873i	0.415261	−	0.415261i	0.883567	+	0.468305i	$0.155135\pi$
$542$	4.86069	+	2.80632i	0.208785	+	0.120542i
$543$	1.35996	−	5.22080i	0.0583614	−	0.224046i
$544$	−27.6483	−	7.40833i	−1.18541	−	0.317629i
$545$	−1.43276			−0.0613729
$546$	3.67674	+	1.41151i	0.157350	+	0.0604070i
$547$	−23.5740			−1.00795			−0.503976	−	0.863718i	$-0.668130\pi$
$547$	−23.5740			−1.00795			−0.503976	+	0.863718i	$0.668130\pi$
$548$	−15.6920	−	4.20466i	−0.670329	−	0.179614i
$549$	−6.14961	+	3.66577i	−0.262459	+	0.156451i
$550$	−0.301708	−	0.174191i	−0.0128649	−	0.00742755i
$551$	−40.1985	+	40.1985i	−1.71252	+	1.71252i
$552$	14.9188	−	26.2614i	0.634988	−	1.11776i
$553$	−0.913874	−	3.41063i	−0.0388619	−	0.145035i
$554$	4.39946	+	4.39946i	0.186915	+	0.186915i
$555$	6.05464	−	1.66767i	0.257005	−	0.0707888i
$556$	−3.92135	+	2.26399i	−0.166302	+	0.0960146i
$557$	−7.67187	+	28.6318i	−0.325068	+	1.21317i	0.589176	+	0.808005i	$0.299452\pi$
$557$	−7.67187	+	28.6318i	−0.325068	+	1.21317i	−0.914244	+	0.405165i	$0.867214\pi$
$558$	−0.153305	−	10.9912i	−0.00648993	−	0.465293i
$559$	24.7467	−	33.5638i	1.04667	−	1.41960i
$560$		−	3.19350i		−	0.134950i
$561$	1.39758	+	2.38216i	0.0590059	+	0.100575i
$562$	−4.52894	−	7.84435i	−0.191042	−	0.330894i
$563$	2.35749	−	4.08330i	0.0993564	−	0.172090i	−0.812062	−	0.583571i	$-0.801655\pi$
$563$	2.35749	−	4.08330i	0.0993564	−	0.172090i	0.911418	+	0.411481i	$0.134988\pi$
$564$	−0.0608412	−	8.72439i	−0.00256188	−	0.367363i
$565$	−6.67250	+	1.78789i	−0.280714	+	0.0752172i
$566$	11.3143	−	3.03165i	0.475575	−	0.127430i
$567$	−6.18399	+	6.53898i	−0.259703	+	0.274611i
$568$	−12.1901	+	21.1138i	−0.511484	+	0.885917i
$569$	−20.2729	−	35.1137i	−0.849884	−	1.47204i	−0.881311	−	0.472536i	$-0.843339\pi$
$569$	−20.2729	−	35.1137i	−0.849884	−	1.47204i	0.0314272	−	0.999506i	$-0.489995\pi$
$570$	−11.7418	+	6.88878i	−0.491812	+	0.288539i
$571$		−	6.05830i		−	0.253532i	−0.991933	−	0.126766i	$-0.959540\pi$
$571$		−	6.05830i		−	0.253532i	0.991933	−	0.126766i	$-0.0404597\pi$
$572$	1.13660	+	1.42387i	0.0475236	+	0.0595350i
$573$	8.11302	+	8.00065i	0.338926	+	0.334232i
$574$	0.321704	−	1.20062i	0.0134277	−	0.0501128i
$575$	−11.6446	+	6.72301i	−0.485613	+	0.280369i
$576$	−0.0384151	+	0.0687333i	−0.00160063	+	0.00286389i
$577$	−6.59498	−	6.59498i	−0.274552	−	0.274552i	0.556377	−	0.830930i	$-0.312191\pi$
$577$	−6.59498	−	6.59498i	−0.274552	−	0.274552i	−0.830930	+	0.556377i	$0.812191\pi$
$578$	1.39821	+	5.21819i	0.0581578	+	0.217048i
$579$	28.7127	+	16.3114i	1.19326	+	0.677879i
$580$	−16.7873	+	16.7873i	−0.697055	+	0.697055i
$581$	1.96043	+	1.13185i	0.0813322	+	0.0469572i
$582$	−8.88244	−	2.31378i	−0.368189	−	0.0959091i
$583$	−3.29648	−	0.883289i	−0.136526	−	0.0365821i
$584$	−9.53152			−0.394417
$585$	3.18322	+	19.2332i	0.131610	+	0.795195i
$586$	16.8400			0.695653
$587$	−22.4749	−	6.02213i	−0.927638	−	0.248560i	−0.236791	−	0.971561i	$-0.576096\pi$
$587$	−22.4749	−	6.02213i	−0.927638	−	0.248560i	−0.690847	+	0.723001i	$0.742762\pi$
$588$	−2.68562	−	0.699575i	−0.110753	−	0.0288500i
$589$	34.7943	+	20.0885i	1.43367	+	0.827731i
$590$	6.41081	−	6.41081i	0.263929	−	0.263929i
$591$	−9.30553	−	5.28637i	−0.382778	−	0.217452i
$592$	0.922605	+	3.44321i	0.0379188	+	0.141515i
$593$	32.1694	+	32.1694i	1.32104	+	1.32104i	0.912935	+	0.408104i	$0.133810\pi$
$593$	32.1694	+	32.1694i	1.32104	+	1.32104i	0.408104	+	0.912935i	$0.366190\pi$
$594$	0.992389	−	0.288291i	0.0407182	−	0.0118287i
$595$	−7.89208	+	4.55649i	−0.323544	+	0.186798i
$596$	−2.13352	+	7.96239i	−0.0873922	+	0.326152i
$597$	−17.3610	−	17.1205i	−0.710536	−	0.700695i
$598$	−17.2575	+	2.60949i	−0.705710	+	0.106710i
$599$			8.93813i			0.365202i	0.983187	+	0.182601i	$0.0584516\pi$
$599$			8.93813i			0.365202i	−0.983187	+	0.182601i	$0.941548\pi$
$600$	5.94504	−	3.48787i	0.242705	−	0.142392i
$601$	−15.1969	−	26.3218i	−0.619895	−	1.07369i	−0.989504	−	0.144502i	$-0.953842\pi$
$601$	−15.1969	−	26.3218i	−0.619895	−	1.07369i	0.369610	−	0.929187i	$-0.379491\pi$
$602$	3.64689	−	6.31660i	0.148636	−	0.257445i
$603$	25.5967	−	26.3208i	1.04238	−	1.07187i
$604$	4.11375	−	1.10228i	0.167386	−	0.0448510i
$605$	−18.9766	+	5.08477i	−0.771510	+	0.206725i
$606$	0.0475984	+	6.82542i	0.00193355	+	0.277264i
$607$	−12.8174	+	22.2003i	−0.520241	+	0.901084i	0.479482	+	0.877552i	$0.340825\pi$
$607$	−12.8174	+	22.2003i	−0.520241	+	0.901084i	−0.999723	+	0.0235326i	$0.992509\pi$
$608$	−19.5730	−	33.9014i	−0.793789	−	1.37488i
$609$	7.20548	+	12.2817i	0.291981	+	0.497678i
$610$			2.71244i			0.109824i
$611$	−8.85861	+	7.07136i	−0.358381	+	0.286077i
$612$	−24.3026	+	0.338974i	−0.982376	+	0.0137022i
$613$	−3.15766	+	11.7846i	−0.127537	+	0.475974i	−0.999917	−	0.0128535i	$-0.995908\pi$
$613$	−3.15766	+	11.7846i	−0.127537	+	0.475974i	0.872381	+	0.488827i	$0.162575\pi$
$614$	4.13967	−	2.39004i	0.167063	−	0.0964540i
$615$	5.93178	−	1.63383i	0.239192	−	0.0658826i
$616$	0.506590	+	0.506590i	0.0204111	+	0.0204111i
$617$	−9.64811	−	36.0072i	−0.388418	−	1.44960i	−0.832708	−	0.553713i	$-0.813211\pi$
$617$	−9.64811	−	36.0072i	−0.388418	−	1.44960i	0.444290	−	0.895883i	$-0.353456\pi$
$618$	−1.03063	+	1.81420i	−0.0414580	+	0.0729779i
$619$	21.6072	−	21.6072i	0.868467	−	0.868467i	−0.123836	−	0.992303i	$-0.539520\pi$
$619$	21.6072	−	21.6072i	0.868467	−	0.868467i	0.992303	+	0.123836i	$0.0395197\pi$
$620$	14.5304	+	8.38915i	0.583556	+	0.336916i
$621$	9.51485	−	38.7337i	0.381818	−	1.55433i
$622$	4.19852	+	1.12499i	0.168345	+	0.0451080i
$623$	11.4134			0.457270
$624$	−10.9294	+	1.73067i	−0.437524	+	0.0692821i
$625$	13.1729			0.526916
$626$	−10.0301	−	2.68755i	−0.400882	−	0.107416i
$627$	−0.952136	+	3.65519i	−0.0380246	+	0.145974i
$628$	4.51241	+	2.60524i	0.180065	+	0.103960i
$629$	7.19280	−	7.19280i	0.286796	−	0.286796i
$630$	0.928378	+	3.28101i	0.0369875	+	0.130719i
$631$	3.33810	+	12.4580i	0.132888	+	0.495944i	0.999998	−	0.00217292i	$-0.000691663\pi$
$631$	3.33810	+	12.4580i	0.132888	+	0.495944i	−0.867110	+	0.498117i	$0.834025\pi$
$632$	−5.67202	−	5.67202i	−0.225621	−	0.225621i
$633$	−5.58788	−	20.2873i	−0.222098	−	0.806347i
$634$	−12.4792	+	7.20488i	−0.495613	+	0.286142i
$635$	−3.25002	+	12.1292i	−0.128973	+	0.481334i
$636$	21.0880	−	21.3841i	0.836192	−	0.847936i
$637$	1.44339	+	3.30403i	0.0571894	+	0.130910i
$638$		−	1.63501i		−	0.0647308i
$639$	−7.89827	+	31.2116i	−0.312451	+	1.23471i
$640$	−10.1878	−	17.6458i	−0.402710	−	0.697513i
$641$	−5.71446	+	9.89773i	−0.225707	+	0.390937i	−0.956531	−	0.291629i	$-0.905803\pi$
$641$	−5.71446	+	9.89773i	−0.225707	+	0.390937i	0.730824	+	0.682566i	$0.239136\pi$
$642$	−3.32646	+	0.0231977i	−0.131285	+	0.000915539i
$643$	−35.3484	+	9.47157i	−1.39400	+	0.373522i	−0.876188	−	0.481970i	$-0.839921\pi$
$643$	−35.3484	+	9.47157i	−1.39400	+	0.373522i	−0.517816	+	0.855492i	$0.673255\pi$
$644$	11.8799	−	3.18322i	0.468135	−	0.125436i
$645$	36.1032	−	0.251772i	1.42156	−	0.00991353i
$646$	−11.0252	+	19.0961i	−0.433779	+	0.751327i
$647$	12.9626	+	22.4519i	0.509614	+	0.882677i	0.999938	+	0.0111367i	$0.00354499\pi$
$647$	12.9626	+	22.4519i	0.509614	+	0.882677i	−0.490324	+	0.871540i	$0.663122\pi$
$648$	−4.73890	+	19.8891i	−0.186162	+	0.781317i
$649$		−	2.51551i		−	0.0987423i
$650$	−3.70844	−	1.45343i	−0.145457	−	0.0570083i
$651$	7.06604	−	7.16529i	0.276940	−	0.280830i
$652$	−5.88253	+	21.9539i	−0.230378	+	0.859781i
$653$	−10.8995	+	6.29284i	−0.426531	+	0.246258i	−0.697868	−	0.716227i	$-0.745868\pi$
$653$	−10.8995	+	6.29284i	−0.426531	+	0.246258i	0.271336	+	0.962485i	$0.412534\pi$
$654$	0.230588	+	0.837170i	0.00901671	+	0.0327359i
$655$	−25.2523	−	25.2523i	−0.986688	−	0.986688i
$656$	0.903884	+	3.37334i	0.0352907	+	0.131707i
$657$	−12.1114	+	3.42699i	−0.472512	+	0.133700i
$658$	−1.40189	+	1.40189i	−0.0546513	+	0.0546513i
$659$	0.796513	+	0.459867i	0.0310277	+	0.0179139i	0.515434	−	0.856929i	$-0.327631\pi$
$659$	0.796513	+	0.459867i	0.0310277	+	0.0179139i	−0.484406	+	0.874843i	$0.660964\pi$
$660$	−0.397622	+	1.52644i	−0.0154774	+	0.0594168i
$661$	8.51519	+	2.28164i	0.331202	+	0.0887454i	0.420588	−	0.907252i	$-0.361824\pi$
$661$	8.51519	+	2.28164i	0.331202	+	0.0887454i	−0.0893858	+	0.995997i	$0.528490\pi$
$662$	−12.0647			−0.468908
$663$	19.8710	+	24.5403i	0.771726	+	0.953067i
$664$	5.14260			0.199572
$665$	−12.0384	−	3.22567i	−0.466828	−	0.125086i
$666$	−1.94886	−	3.26935i	−0.0755167	−	0.126685i
$667$	−54.6499	−	31.5521i	−2.11605	−	1.22170i
$668$	−6.19541	+	6.19541i	−0.239708	+	0.239708i
$669$	22.3744	−	39.3854i	0.865044	−	1.52273i
$670$	−3.60020	−	13.4361i	−0.139088	−	0.519083i
$671$	0.532161	+	0.532161i	0.0205438	+	0.0205438i
$672$	−9.45305	+	2.60372i	−0.364659	+	0.100441i
$673$	−22.3101	+	12.8808i	−0.859993	+	0.496517i	−0.864010	−	0.503475i	$-0.832055\pi$
$673$	−22.3101	+	12.8808i	−0.859993	+	0.496517i	0.00401719	+	0.999992i	$0.498721\pi$
$674$	3.16921	−	11.8276i	0.122073	−	0.455584i
$675$	6.30017	−	6.56945i	0.242494	−	0.252858i
$676$	15.2827	+	14.1534i	0.587795	+	0.544361i
$677$			44.2529i			1.70078i	0.526156	+	0.850388i	$0.323633\pi$
$677$			44.2529i			1.70078i	−0.526156	+	0.850388i	$0.676367\pi$
$678$	2.11854	+	3.61103i	0.0813620	+	0.138681i
$679$	−4.20159	−	7.27736i	−0.161242	−	0.279280i
$680$	−10.3513	+	17.9289i	−0.396953	+	0.687542i
$681$	0.232335	+	33.3159i	0.00890308	+	1.27667i
$682$	−1.11614	+	0.299068i	−0.0427391	+	0.0114519i
$683$	39.2468	−	10.5162i	1.50174	−	0.402389i	0.588056	−	0.808820i	$-0.299893\pi$
$683$	39.2468	−	10.5162i	1.50174	−	0.402389i	0.913682	+	0.406431i	$0.133227\pi$
$684$	−23.8296	−	23.1740i	−0.911148	−	0.886080i
$685$	−9.13673	+	15.8253i	−0.349096	+	0.604653i
$686$	0.315322	+	0.546154i	0.0120391	+	0.0208522i
$687$	16.6687	−	9.77929i	0.635950	−	0.373103i
$688$			20.4931i			0.781294i
$689$	−38.7751	−	4.35034i	−1.47722	−	0.165735i
$690$	−10.7596	−	10.6105i	−0.409609	−	0.403936i
$691$	−11.8998	+	44.4108i	−0.452691	+	1.68947i	0.242097	+	0.970252i	$0.422165\pi$
$691$	−11.8998	+	44.4108i	−0.452691	+	1.68947i	−0.694788	+	0.719214i	$0.744502\pi$
$692$	−27.2352	+	15.7242i	−1.03533	+	0.597746i
$693$	0.825851	+	0.461569i	0.0313715	+	0.0175336i
$694$	−3.45922	−	3.45922i	−0.131310	−	0.131310i
$695$	1.31822	+	4.91966i	0.0500029	+	0.186613i
$696$	28.1266	+	15.9784i	1.06614	+	0.605660i
$697$	7.04685	−	7.04685i	0.266918	−	0.266918i
$698$	−9.35387	−	5.40046i	−0.354049	−	0.204410i
$699$	−18.6939	−	4.86955i	−0.707069	−	0.184183i
$700$	2.71112	+	0.726441i	0.102471	+	0.0274569i
$701$	−18.9716			−0.716546			−0.358273	−	0.933617i	$-0.616634\pi$
$701$	−18.9716			−0.716546			−0.358273	+	0.933617i	$0.616634\pi$
$702$	10.7257	−	4.95535i	0.404817	−	0.187028i
$703$	13.9116			0.524685
$704$	0.00799515	+	0.00214229i	0.000301328	+	8.07407e-5i
$705$	−9.49677	−	2.47380i	−0.357669	−	0.0931688i
$706$	−13.9254	−	8.03982i	−0.524088	−	0.302583i
$707$	−4.41855	+	4.41855i	−0.166177	+	0.166177i
$708$	19.2479	+	10.9345i	0.723380	+	0.410944i
$709$	−4.94048	−	18.4381i	−0.185544	−	0.692458i	−0.994514	−	0.104608i	$-0.966641\pi$
$709$	−4.94048	−	18.4381i	−0.185544	−	0.692458i	0.808970	−	0.587850i	$-0.200026\pi$
$710$	8.62521	+	8.62521i	0.323699	+	0.323699i
$711$	−9.24663	−	5.16795i	−0.346776	−	0.193813i
$712$	22.4548	−	12.9643i	0.841531	−	0.485858i
$713$	−11.5427	+	43.0778i	−0.432276	+	1.61328i
$714$	3.93252	+	3.87805i	0.147171	+	0.145132i
$715$	1.87793	−	0.820390i	0.0702306	−	0.0306809i
$716$		−	28.4946i		−	1.06489i
$717$	−9.17692	+	5.38397i	−0.342718	+	0.201068i
$718$	1.46341	+	2.53471i	0.0546141	+	0.0945944i
$719$	8.75094	−	15.1571i	0.326355	−	0.565263i	−0.655431	−	0.755255i	$-0.727513\pi$
$719$	8.75094	−	15.1571i	0.326355	−	0.565263i	0.981786	+	0.189992i	$0.0608462\pi$
$720$	−6.86826	−	6.67930i	−0.255965	−	0.248923i
$721$	−1.84510	+	0.494392i	−0.0687150	+	0.0184121i
$722$	−17.5548	+	4.70378i	−0.653321	+	0.175057i
$723$	0.0522146	+	7.48737i	0.00194188	+	0.278458i
$724$	2.49542	−	4.32219i	0.0927414	−	0.160633i
$725$	−7.20050	−	12.4716i	−0.267420	−	0.463184i
$726$	6.02514	+	10.2698i	0.223614	+	0.381147i
$727$		−	21.0745i		−	0.781610i	−0.920474	−	0.390805i	$-0.872197\pi$
$727$		−	21.0745i		−	0.781610i	0.920474	−	0.390805i	$-0.127803\pi$
$728$	6.59272	+	4.86084i	0.244343	+	0.180155i
$729$	1.12939	+	26.9764i	0.0418292	+	0.999125i
$730$	−1.23426	+	4.60632i	−0.0456820	+	0.170488i
$731$	50.6446	−	29.2396i	1.87316	−	1.08147i
$732$	−6.38515	+	1.75871i	−0.236002	+	0.0650038i
$733$	−14.8333	−	14.8333i	−0.547880	−	0.547880i	0.377947	−	0.925827i	$-0.376630\pi$
$733$	−14.8333	−	14.8333i	−0.547880	−	0.547880i	−0.925827	+	0.377947i	$0.876630\pi$
$734$	2.12904	+	7.94568i	0.0785843	+	0.293280i
$735$	−1.54195	+	2.71427i	−0.0568756	+	0.100117i
$736$	30.7259	−	30.7259i	1.13257	−	1.13257i
$737$	−3.34240	−	1.92974i	−0.123119	−	0.0710828i
$738$	−1.90931	−	3.20301i	−0.0702828	−	0.117905i
$739$	−31.4520	−	8.42753i	−1.15698	−	0.310012i	−0.371221	−	0.928545i	$-0.621061\pi$
$739$	−31.4520	−	8.42753i	−1.15698	−	0.310012i	−0.785759	+	0.618533i	$0.787727\pi$
$740$	5.80961			0.213566
$741$	−4.51546	+	42.9479i	−0.165879	+	1.57773i
$742$	−6.82468			−0.250542
$743$	44.5817	+	11.9456i	1.63554	+	0.438242i	0.955515	−	0.294944i	$-0.0953009\pi$
$743$	44.5817	+	11.9456i	1.63554	+	0.438242i	0.680028	+	0.733186i	$0.261968\pi$
$744$	5.76284	−	22.1232i	0.211276	−	0.811075i
$745$	8.03002	+	4.63613i	0.294197	+	0.169855i
$746$	3.04688	−	3.04688i	0.111554	−	0.111554i
$747$	6.53456	−	1.84899i	0.239087	−	0.0676509i
$748$	0.661270	+	2.46790i	0.0241784	+	0.0902352i
$749$	−2.15344	−	2.15344i	−0.0786850	−	0.0786850i
$750$	−3.52964	−	12.8147i	−0.128884	−	0.467925i
$751$	36.9022	−	21.3055i	1.34658	−	0.777448i	0.358816	−	0.933408i	$-0.383180\pi$
$751$	36.9022	−	21.3055i	1.34658	−	0.777448i	0.987763	+	0.155960i	$0.0498471\pi$
$752$	1.44172	−	5.38057i	0.0525741	−	0.196209i
$753$	8.10535	−	8.21919i	0.295375	−	0.299524i
$754$	−2.79483	−	18.4831i	−0.101782	−	0.673116i
$755$		−	4.79050i		−	0.174344i
$756$	−7.12163	+	4.31279i	−0.259011	+	0.156855i
$757$	9.21758	+	15.9653i	0.335019	+	0.580270i	0.983488	−	0.180971i	$-0.0579240\pi$
$757$	9.21758	+	15.9653i	0.335019	+	0.580270i	−0.648470	+	0.761241i	$0.724591\pi$
$758$	−5.83373	+	10.1043i	−0.211891	+	0.367005i
$759$	−4.19265	+	0.0292382i	−0.152184	+	0.00106128i
$760$	−27.3483	+	7.32795i	−0.992027	+	0.265813i
$761$	33.3602	−	8.93885i	1.20931	−	0.324033i	0.402817	−	0.915280i	$-0.368031\pi$
$761$	33.3602	−	8.93885i	1.20931	−	0.324033i	0.806490	+	0.591247i	$0.201364\pi$
$762$	7.61022	−	0.0530713i	0.275689	−	0.00192257i
$763$	−0.397482	+	0.688460i	−0.0143898	+	0.0249239i
$764$	5.27036	+	9.12852i	0.190675	+	0.330258i
$765$	−6.70686	+	26.5035i	−0.242487	+	0.958237i
$766$			5.00806i			0.180948i
$767$	−4.29990	−	28.4367i	−0.155260	−	1.02679i
$768$	−8.73476	+	8.85744i	−0.315188	+	0.319615i
$769$	9.02680	−	33.6885i	0.325515	−	1.21484i	−0.588278	−	0.808658i	$-0.700194\pi$
$769$	9.02680	−	33.6885i	0.325515	−	1.21484i	0.913793	−	0.406180i	$-0.133139\pi$
$770$	0.310421	−	0.179221i	0.0111868	−	0.00645869i
$771$	6.71894	+	24.3937i	0.241977	+	0.878518i
$772$	21.6010	+	21.6010i	0.777438	+	0.777438i
$773$	0.986478	+	3.68159i	0.0354811	+	0.132417i	0.981395	−	0.192002i	$-0.0614979\pi$
$773$	0.986478	+	3.68159i	0.0354811	+	0.132417i	−0.945913	+	0.324419i	$0.894831\pi$
$774$	−5.95753	−	21.0547i	−0.214139	−	0.756796i
$775$	−7.19663	+	7.19663i	−0.258510	+	0.258510i
$776$	−16.5324	−	9.54501i	−0.593480	−	0.342646i
$777$	0.878361	−	3.37197i	0.0315110	−	0.120969i
$778$	6.43202	+	1.72345i	0.230599	+	0.0617889i
$779$	13.6293			0.488320
$780$	−1.88570	+	17.9355i	−0.0675189	+	0.642193i
$781$	3.38440			0.121104
$782$	−23.6424	−	6.33496i	−0.845450	−	0.226538i
$783$	41.4846	+	10.1906i	1.48254	+	0.364183i
$784$	−1.53451	−	0.885952i	−0.0548040	−	0.0316411i
$785$	4.14428	−	4.14428i	0.147916	−	0.147916i
$786$	−10.6909	+	18.8191i	−0.381332	+	0.671254i
$787$	−10.8951	−	40.6612i	−0.388369	−	1.44941i	−0.832787	−	0.553594i	$-0.813256\pi$
$787$	−10.8951	−	40.6612i	−0.388369	−	1.44941i	0.444417	−	0.895820i	$-0.353411\pi$
$788$	−7.00069	−	7.00069i	−0.249389	−	0.249389i
$789$	31.0985	−	8.56570i	1.10714	−	0.304947i
$790$	−3.47562	+	2.00665i	−0.123657	+	0.0713934i
$791$	−0.992006	+	3.70222i	−0.0352717	+	0.131636i
$792$	2.14907	−	0.0299753i	0.0763639	−	0.00106513i
$793$	6.92550	+	5.10619i	0.245932	+	0.181326i
$794$			9.44443i			0.335170i
$795$	−17.0946	−	29.1376i	−0.606284	−	1.03340i
$796$	−11.2780	−	19.5340i	−0.399737	−	0.692365i
$797$	23.5774	−	40.8372i	0.835153	−	1.44653i	−0.0587526	−	0.998273i	$-0.518712\pi$
$797$	23.5774	−	40.8372i	0.835153	−	1.44653i	0.893906	−	0.448255i	$-0.147954\pi$
$798$	0.0526737	+	7.55320i	0.00186463	+	0.267380i
$799$	−15.3540	+	4.11410i	−0.543186	+	0.145546i
$800$	9.57851	−	2.56655i	0.338651	−	0.0907414i
$801$	23.8715	−	24.5469i	0.843460	−	0.867322i
$802$	6.73359	−	11.6629i	0.237771	−	0.411832i
$803$	0.661573	+	1.14588i	0.0233464	+	0.0404372i
$804$	29.2947	−	17.1868i	1.03314	−	0.606131i
$805$		−	13.8343i		−	0.487595i
$806$	−12.1062	+	5.28871i	−0.426423	+	0.186287i
$807$	24.8969	+	24.5520i	0.876412	+	0.864273i
$808$	−3.67413	+	13.7120i	−0.129255	+	0.482387i
$809$	20.4385	−	11.8002i	0.718579	−	0.414872i	−0.0956507	−	0.995415i	$-0.530493\pi$
$809$	20.4385	−	11.8002i	0.718579	−	0.414872i	0.814229	+	0.580543i	$0.197160\pi$
$810$	8.99820	+	4.86567i	0.316165	+	0.170962i
$811$	−22.6050	−	22.6050i	−0.793769	−	0.793769i	0.188336	−	0.982105i	$-0.439691\pi$
$811$	−22.6050	−	22.6050i	−0.793769	−	0.793769i	−0.982105	+	0.188336i	$0.939691\pi$
$812$	3.40930	+	12.7237i	0.119643	+	0.446514i
$813$	13.4032	+	7.61422i	0.470071	+	0.267042i
$814$	−0.282916	+	0.282916i	−0.00991620	+	0.00991620i
$815$	22.1404	+	12.7827i	0.775543	+	0.447760i
$816$	−15.0168	−	3.91171i	−0.525694	−	0.136937i
$817$	77.2518	+	20.6996i	2.70270	+	0.724186i
$818$	5.22308			0.182621
$819$	10.1249	+	3.80617i	0.353792	+	0.132998i
$820$	5.69173			0.198764
$821$	−14.0330	−	3.76014i	−0.489756	−	0.131230i	0.00548586	−	0.999985i	$-0.498254\pi$
$821$	−14.0330	−	3.76014i	−0.489756	−	0.131230i	−0.495242	+	0.868755i	$0.664920\pi$
$822$	10.7172	+	2.79172i	0.373806	+	0.0973723i
$823$	46.6180	+	26.9149i	1.62500	+	0.938195i	0.985554	+	0.169359i	$0.0541698\pi$
$823$	46.6180	+	26.9149i	1.62500	+	0.938195i	0.639447	+	0.768836i	$0.279164\pi$
$824$	−3.06848	+	3.06848i	−0.106896	+	0.106896i
$825$	−0.831952	−	0.472623i	−0.0289648	−	0.0164546i
$826$	−1.30196	−	4.85898i	−0.0453009	−	0.169065i
$827$	35.3752	+	35.3752i	1.23011	+	1.23011i	0.963919	+	0.266196i	$0.0857667\pi$
$827$	35.3752	+	35.3752i	1.23011	+	1.23011i	0.266196	+	0.963919i	$0.414233\pi$
$828$	18.0011	−	32.2080i	0.625581	−	1.11930i
$829$	−48.5976	+	28.0578i	−1.68786	+	0.974488i	−0.731712	+	0.681614i	$0.761278\pi$
$829$	−48.5976	+	28.0578i	−1.68786	+	0.974488i	−0.956151	+	0.292874i	$0.905388\pi$
$830$	0.665928	−	2.48528i	0.0231147	−	0.0862653i
$831$	12.1670	+	11.9985i	0.422069	+	0.416223i
$832$	0.0940436	+	0.0105511i	0.00326038	+	0.000365795i
$833$			5.05631i			0.175191i
$834$	2.66242	−	1.56201i	0.0921922	−	0.0540879i
$835$	4.92767	+	8.53497i	0.170529	+	0.295365i
$836$	−1.74709	+	3.02605i	−0.0604245	+	0.104658i
$837$	−0.631549	−	30.1833i	−0.0218295	−	1.04329i
$838$	6.23698	−	1.67119i	0.215453	−	0.0577304i
$839$	21.2201	−	5.68592i	0.732601	−	0.196300i	0.126814	−	0.991927i	$-0.459525\pi$
$839$	21.2201	−	5.68592i	0.732601	−	0.196300i	0.605787	+	0.795627i	$0.292858\pi$
$840$	0.0494541	+	7.09153i	0.00170633	+	0.244681i
$841$	19.2930	−	33.4165i	0.665277	−	1.15229i
$842$	8.82609	+	15.2872i	0.304167	+	0.526833i
$843$	−12.5886	−	21.4571i	−0.433574	−	0.739021i
$844$		−	19.4663i		−	0.670057i
$845$	19.8269	−	12.4842i	0.682065	−	0.429470i
$846$	0.0829510	+	5.94714i	0.00285191	+	0.204467i
$847$	−2.82127	+	10.5291i	−0.0969400	+	0.361785i
$848$	16.6061	−	9.58756i	0.570257	−	0.329238i
$849$	31.0156	−	8.54287i	1.06445	−	0.293190i
$850$	−3.94972	−	3.94972i	−0.135474	−	0.135474i
$851$	3.99674	+	14.9160i	0.137006	+	0.511315i
$852$	−14.7115	+	25.8964i	−0.504007	+	0.887197i
$853$	0.488804	−	0.488804i	0.0167363	−	0.0167363i	−0.698689	−	0.715425i	$-0.746233\pi$
$853$	0.488804	−	0.488804i	0.0167363	−	0.0167363i	0.715425	+	0.698689i	$0.246233\pi$
$854$	1.30336	+	0.752495i	0.0446000	+	0.0257498i
$855$	−32.1160	+	19.1443i	−1.09834	+	0.654722i
$856$	−6.68273	−	1.79063i	−0.228411	−	0.0612026i
$857$	5.40279			0.184556			0.0922778	−	0.995733i	$-0.470585\pi$
$857$	5.40279			0.184556			0.0922778	+	0.995733i	$0.470585\pi$
$858$	−0.781590	−	0.965250i	−0.0266831	−	0.0329531i
$859$	5.60038			0.191083			0.0955413	−	0.995425i	$-0.469542\pi$
$859$	5.60038			0.191083			0.0955413	+	0.995425i	$0.469542\pi$
$860$	32.2611	+	8.64435i	1.10010	+	0.294770i
$861$	0.860538	−	3.30355i	0.0293271	−	0.112585i
$862$	3.15941	+	1.82409i	0.107610	+	0.0621286i
$863$	−1.63216	+	1.63216i	−0.0555593	+	0.0555593i	−0.734341	−	0.678781i	$-0.762508\pi$
$863$	−1.63216	+	1.63216i	−0.0555593	+	0.0555593i	0.678781	+	0.734341i	$0.262508\pi$
$864$	−14.1715	+	25.7764i	−0.482124	+	0.876932i
$865$	9.15550	+	34.1688i	0.311296	+	1.16177i
$866$	−4.12548	−	4.12548i	−0.140190	−	0.140190i
$867$	3.94000	+	14.3045i	0.133809	+	0.485807i
$868$	8.06216	−	4.65469i	0.273648	−	0.157991i
$869$	−0.288201	+	1.07558i	−0.00977654	+	0.0364866i
$870$	11.3641	−	11.5237i	0.385280	−	0.390691i
$871$	−41.0830	−	16.1015i	−1.39205	−	0.545578i
$872$			1.80597i			0.0611579i
$873$	−24.4392	−	6.18446i	−0.827140	−	0.209312i
$874$	−16.7371	−	28.9895i	−0.566142	−	0.980586i
$875$	6.08431	−	10.5383i	0.205687	−	0.356261i
$876$	−11.6437	+	0.0811993i	−0.393403	+	0.00274347i
$877$	10.9892	−	2.94455i	0.371079	−	0.0994304i	−0.0684597	−	0.997654i	$-0.521808\pi$
$877$	10.9892	−	2.94455i	0.371079	−	0.0994304i	0.439539	+	0.898223i	$0.355142\pi$
$878$	2.95769	−	0.792510i	0.0998172	−	0.0267459i
$879$	46.2495	−	0.322530i	1.55996	−	0.0108787i
$880$	−0.503554	+	0.872180i	−0.0169748	+	0.0294012i
$881$	3.83832	+	6.64817i	0.129316	+	0.223983i	0.923412	−	0.383810i	$-0.125388\pi$
$881$	3.83832	+	6.64817i	0.129316	+	0.223983i	−0.794096	+	0.607793i	$0.792055\pi$
$882$	1.83412	+	0.464133i	0.0617580	+	0.0156282i
$883$		−	0.491631i		−	0.0165447i	−0.999966	−	0.00827235i	$-0.997367\pi$
$883$		−	0.491631i		−	0.0165447i	0.999966	−	0.00827235i	$-0.00263320\pi$
$884$	11.6939	+	26.7681i	0.393308	+	0.900310i
$885$	17.4839	−	17.7295i	0.587717	−	0.595971i
$886$	−0.713112	+	2.66137i	−0.0239575	+	0.0894105i
$887$	−22.7820	+	13.1532i	−0.764945	+	0.441641i	−0.831068	−	0.556170i	$-0.812270\pi$
$887$	−22.7820	+	13.1532i	−0.764945	+	0.441641i	0.0661237	+	0.997811i	$0.478937\pi$
$888$	−2.10207	−	7.63174i	−0.0705408	−	0.256105i
$889$	4.92661	+	4.92661i	0.165233	+	0.165233i
$890$	−3.35756	−	12.5306i	−0.112546	−	0.420027i
$891$	2.71999	−	0.810772i	0.0911230	−	0.0271619i
$892$	29.6302	−	29.6302i	0.992093	−	0.992093i
$893$	−18.8266	−	10.8695i	−0.630008	−	0.363735i
$894$	1.41657	−	5.43811i	0.0473771	−	0.181878i
$895$	−30.9594	−	8.29554i	−1.03486	−	0.277289i
$896$	−11.3054			−0.377686
$897$	−47.3461	+	7.49727i	−1.58084	+	0.250326i
$898$	21.5232			0.718237
$899$	−46.1374	−	12.3625i	−1.53877	−	0.412311i
$900$	7.23273	−	4.31142i	0.241091	−	0.143714i
$901$	−47.3873	−	27.3591i	−1.57870	−	0.911464i
$902$	−0.277175	+	0.277175i	−0.00922893	+	0.00922893i
$903$	9.89489	−	17.4178i	0.329281	−	0.579629i
$904$	2.25360	+	8.41055i	0.0749536	+	0.279731i
$905$	−3.96958	−	3.96958i	−0.131953	−	0.131953i
$906$	−2.79911	+	0.770979i	−0.0929941	+	0.0256141i
$907$	−32.8532	+	18.9678i	−1.09087	+	0.629816i	−0.933809	−	0.357773i	$-0.883536\pi$
$907$	−32.8532	+	18.9678i	−1.09087	+	0.629816i	−0.157064	+	0.987588i	$0.550203\pi$
$908$	−7.97697	+	29.7705i	−0.264725	+	0.987967i
$909$	0.261449	+	18.7445i	0.00867173	+	0.621716i
$910$	3.20282	−	2.55664i	0.106172	−	0.0847518i
$911$			3.04911i			0.101021i	0.998724	+	0.0505107i	$0.0160849\pi$
$911$			3.04911i			0.101021i	−0.998724	+	0.0505107i	$0.983915\pi$
$912$	−10.7392	−	18.3048i	−0.355610	−	0.606133i
$913$	−0.356943	−	0.618243i	−0.0118131	−	0.0204609i
$914$	−0.561930	+	0.973291i	−0.0185870	+	0.0321936i
$915$	0.0519504	+	7.44948i	0.00171743	+	0.246272i
$916$	17.2686	−	4.62711i	0.570571	−	0.152884i
$917$	−19.1396	+	5.12843i	−0.632044	+	0.169356i
$918$	16.5655	−	0.346613i	0.546743	−	0.0114399i
$919$	−24.7387	+	42.8486i	−0.816053	+	1.41345i	0.0925155	+	0.995711i	$0.470509\pi$
$919$	−24.7387	+	42.8486i	−0.816053	+	1.41345i	−0.908569	+	0.417735i	$0.862824\pi$
$920$	−15.7141	−	27.2176i	−0.518079	−	0.897338i
$921$	11.3235	−	6.64331i	0.373120	−	0.218905i
$922$		−	8.46402i		−	0.278748i
$923$	38.2592	−	5.78516i	1.25932	−	0.190421i
$924$	0.623164	+	0.614533i	0.0205006	+	0.0202166i
$925$	−0.912094	+	3.40398i	−0.0299895	+	0.111922i
$926$	−18.8936	+	10.9082i	−0.620881	+	0.358466i
$927$	−2.79579	+	5.00229i	−0.0918256	+	0.164297i
$928$	32.9082	+	32.9082i	1.08026	+	1.08026i
$929$	−7.55117	−	28.1813i	−0.247746	−	0.924600i	−0.971983	−	0.235049i	$-0.924475\pi$
$929$	−7.55117	−	28.1813i	−0.247746	−	0.924600i	0.724238	−	0.689550i	$-0.242192\pi$
$930$	−9.94529	−	5.64981i	−0.326119	−	0.185265i
$931$	−4.88969	+	4.88969i	−0.160253	+	0.160253i
$932$	−15.4763	−	8.93524i	−0.506943	−	0.292683i
$933$	11.5524	+	3.00927i	0.378209	+	0.0985192i
$934$	1.28858	+	0.345275i	0.0421638	+	0.0112977i
$935$	2.87388			0.0939861
$936$	24.2431	−	4.01239i	0.792409	−	0.131149i
$937$	−27.8598			−0.910139			−0.455070	−	0.890456i	$-0.650386\pi$
$937$	−27.8598			−0.910139			−0.455070	+	0.890456i	$0.650386\pi$
$938$	−7.45500	−	1.99756i	−0.243414	−	0.0652227i
$939$	−27.5982	−	7.18902i	−0.900633	−	0.234605i
$940$	−7.86218	−	4.53923i	−0.256436	−	0.148053i
$941$	10.6348	−	10.6348i	0.346685	−	0.346685i	−0.512188	−	0.858873i	$-0.671165\pi$
$941$	10.6348	−	10.6348i	0.346685	−	0.346685i	0.858873	+	0.512188i	$0.171165\pi$
$942$	−3.08850	−	1.75454i	−0.100629	−	0.0571661i
$943$	3.91564	+	14.6134i	0.127511	+	0.475876i
$944$	9.99405	+	9.99405i	0.325279	+	0.325279i
$945$	2.61255	+	8.99323i	0.0849862	+	0.292550i
$946$	−1.99201	+	1.15009i	−0.0647659	+	0.0373926i
$947$	−8.61168	+	32.1392i	−0.279842	+	1.04438i	0.672685	+	0.739929i	$0.265141\pi$
$947$	−8.61168	+	32.1392i	−0.279842	+	1.04438i	−0.952527	+	0.304455i	$0.901526\pi$
$948$	−6.97725	−	6.88061i	−0.226610	−	0.223472i
$949$	9.43752	+	11.8228i	0.306355	+	0.383784i
$950$		−	7.63914i		−	0.247847i
$951$	−34.1351	+	20.0266i	−1.10691	+	0.649406i
$952$	5.74336	+	9.94780i	0.186144	+	0.322410i
$953$	−23.8115	+	41.2427i	−0.771330	+	1.33598i	0.165505	+	0.986209i	$0.447075\pi$
$953$	−23.8115	+	41.2427i	−0.771330	+	1.33598i	−0.936834	+	0.349773i	$0.886259\pi$
$954$	−14.2740	+	14.6778i	−0.462138	+	0.475213i
$955$	11.4525	−	3.06869i	0.370594	−	0.0993004i
$956$	−9.50721	+	2.54745i	−0.307485	+	0.0823904i
$957$	−0.0313148	−	4.49042i	−0.00101226	−	0.145155i
$958$	−3.19696	+	5.53729i	−0.103289	+	0.178902i
$959$	5.06948	+	8.78060i	0.163702	+	0.283540i
$960$	0.0414606	+	0.0706691i	0.00133813	+	0.00228084i
$961$			2.75674i			0.0889272i
$962$	−2.71464	+	3.68185i	−0.0875235	+	0.118708i
$963$	−9.13538	+	0.127421i	−0.294384	+	0.00410608i
$964$	−1.79274	+	6.69058i	−0.0577401	+	0.215489i
$965$	29.7582	−	17.1809i	0.957950	−	0.553073i
$966$	−8.08343	+	2.22648i	−0.260080	+	0.0716358i
$967$	9.84247	+	9.84247i	0.316513	+	0.316513i	0.847426	−	0.530913i	$-0.178151\pi$
$967$	9.84247	+	9.84247i	0.316513	+	0.316513i	−0.530913	+	0.847426i	$0.678151\pi$
$968$	6.40925	+	23.9197i	0.206001	+	0.768807i
$969$	−29.9139	+	52.6570i	−0.960972	+	1.69159i
$970$	−6.75367	+	6.75367i	−0.216847	+	0.216847i
$971$	−42.9034	−	24.7703i	−1.37684	−	0.794916i	−0.385058	−	0.922892i	$-0.625819\pi$
$971$	−42.9034	−	24.7703i	−1.37684	−	0.794916i	−0.991777	+	0.127976i	$0.959152\pi$
$972$	−5.61959	+	24.3368i	−0.180248	+	0.780604i
$973$	2.72966	+	0.731409i	0.0875088	+	0.0234479i
$974$	−6.60079			−0.211503
$975$	−10.2127	−	3.92069i	−0.327069	−	0.125563i
$976$	−4.22853			−0.135352
$977$	−22.3621	−	5.99192i	−0.715428	−	0.191698i	−0.117297	−	0.993097i	$-0.537423\pi$
$977$	−22.3621	−	5.99192i	−0.715428	−	0.191698i	−0.598131	+	0.801398i	$0.704090\pi$
$978$	3.90575	−	14.9939i	0.124892	−	0.479454i
$979$	−3.11714	−	1.79968i	−0.0996242	−	0.0575180i
$980$	−2.04199	+	2.04199i	−0.0652288	+	0.0652288i
$981$	0.649324	+	2.29480i	0.0207313	+	0.0732673i
$982$	4.08244	+	15.2359i	0.130276	+	0.486196i
$983$	−38.9070	−	38.9070i	−1.24094	−	1.24094i	−0.959611	−	0.281330i	$-0.909225\pi$
$983$	−38.9070	−	38.9070i	−1.24094	−	1.24094i	−0.281330	−	0.959611i	$-0.590775\pi$
$984$	−2.05941	−	7.47689i	−0.0656518	−	0.238354i
$985$	−9.64435	+	5.56817i	−0.307295	+	0.177417i
$986$	6.78489	−	25.3216i	0.216075	−	0.806403i
$987$	−3.82332	+	3.87702i	−0.121698	+	0.123407i
$988$	−14.5775	+	37.1946i	−0.463773	+	1.18332i
$989$			88.7766i			2.82293i
$990$	0.263802	−	1.04247i	0.00838418	−	0.0331318i
$991$	−28.7147	−	49.7353i	−0.912152	−	1.57989i	−0.811019	−	0.585020i	$-0.801087\pi$
$991$	−28.7147	−	49.7353i	−0.912152	−	1.57989i	−0.101133	−	0.994873i	$-0.532247\pi$
$992$	16.4453	−	28.4840i	0.522137	−	0.904368i
$993$	−33.1347	+	0.231071i	−1.05150	+	0.00733282i
$994$	6.53735	−	1.75168i	0.207352	−	0.0555598i
$995$	−24.5071	+	6.56664i	−0.776926	+	0.208177i
$996$	6.28218	−	0.0438100i	0.199059	−	0.00138817i
$997$	12.1462	−	21.0379i	0.384675	−	0.666277i	−0.607049	−	0.794665i	$-0.707647\pi$
$997$	12.1462	−	21.0379i	0.384675	−	0.666277i	0.991724	+	0.128387i	$0.0409800\pi$
$998$	4.06510	+	7.04096i	0.128679	+	0.222878i
$999$	−5.41498	−	8.94167i	−0.171322	−	0.282902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cc.a.50.12	✓	112
3.2	odd	2	inner	273.2.cc.a.50.17	yes	112
13.6	odd	12	inner	273.2.cc.a.71.17	yes	112
39.32	even	12	inner	273.2.cc.a.71.12	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cc.a.50.12	✓	112	1.1	even	1	trivial
273.2.cc.a.50.17	yes	112	3.2	odd	2	inner
273.2.cc.a.71.12	yes	112	39.32	even	12	inner
273.2.cc.a.71.17	yes	112	13.6	odd	12	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.609155 - 0.163223i) q^{2} +(-1.67612 - 0.436610i) q^{3} +(-1.38762 - 0.801144i) q^{4} +(-1.27442 + 1.27442i) q^{5} +(0.949752 + 0.539544i) q^{6} +(0.258819 + 0.965926i) q^{7} +(1.60638 + 1.60638i) q^{8} +(2.61874 + 1.46362i) q^{9} +O(q^{10})\)	\(q+(-0.609155 - 0.163223i) q^{2} +(-1.67612 - 0.436610i) q^{3} +(-1.38762 - 0.801144i) q^{4} +(-1.27442 + 1.27442i) q^{5} +(0.949752 + 0.539544i) q^{6} +(0.258819 + 0.965926i) q^{7} +(1.60638 + 1.60638i) q^{8} +(2.61874 + 1.46362i) q^{9} +(0.984333 - 0.568305i) q^{10} +(0.0816216 - 0.304616i) q^{11} +(1.97603 + 1.94866i) q^{12} +(0.401999 - 3.58307i) q^{13} -0.630644i q^{14} +(2.69250 - 1.57965i) q^{15} +(0.885952 + 1.53451i) q^{16} +(2.52815 - 4.37889i) q^{17} +(-1.35633 - 1.31901i) q^{18} +(6.67945 - 1.78975i) q^{19} +(2.78940 - 0.747418i) q^{20} +(-0.0120785 - 1.73201i) q^{21} +(-0.0994404 + 0.172236i) q^{22} +(3.83795 + 6.64753i) q^{23} +(-1.99112 - 3.39384i) q^{24} +1.75172i q^{25} +(-0.829718 + 2.11703i) q^{26} +(-3.75029 - 3.59657i) q^{27} +(0.414703 - 1.54769i) q^{28} +(-7.11966 + 4.11054i) q^{29} +(-1.89799 + 0.522776i) q^{30} +(4.10833 + 4.10833i) q^{31} +(-1.46517 - 5.46807i) q^{32} +(-0.269806 + 0.474935i) q^{33} +(-2.25477 + 2.25477i) q^{34} +(-1.56084 - 0.901150i) q^{35} +(-2.46126 - 4.12894i) q^{36} +(1.94323 + 0.520686i) q^{37} -4.36095 q^{38} +(-2.23820 + 5.83013i) q^{39} -4.09440 q^{40} +(1.90379 + 0.510120i) q^{41} +(-0.275345 + 1.05703i) q^{42} +(10.0161 + 5.78280i) q^{43} +(-0.357301 + 0.357301i) q^{44} +(-5.20264 + 1.47211i) q^{45} +(-1.25288 - 4.67582i) q^{46} +(-2.22295 - 2.22295i) q^{47} +(-0.814976 - 2.95884i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(0.285920 - 1.06707i) q^{50} +(-6.14935 + 6.23572i) q^{51} +(-3.42838 + 4.64989i) q^{52} -10.8218i q^{53} +(1.69747 + 2.80300i) q^{54} +(0.284188 + 0.492228i) q^{55} +(-1.13588 + 1.96740i) q^{56} +(-11.9770 + 0.0835236i) q^{57} +(5.00791 - 1.34187i) q^{58} +(7.70478 - 2.06449i) q^{59} +(-5.00170 + 0.0348803i) q^{60} +(-1.19322 + 2.06671i) q^{61} +(-1.83204 - 3.17318i) q^{62} +(-0.735967 + 2.90832i) q^{63} +0.0262467i q^{64} +(4.05402 + 5.07865i) q^{65} +(0.241874 - 0.245271i) q^{66} +(3.16749 - 11.8212i) q^{67} +(-7.01625 + 4.05083i) q^{68} +(-3.53049 - 12.8177i) q^{69} +(0.803704 + 0.803704i) q^{70} +(2.77760 + 10.3661i) q^{71} +(1.85557 + 6.55782i) q^{72} +(-2.96677 + 2.96677i) q^{73} +(-1.09874 - 0.634357i) q^{74} +(0.764817 - 2.93608i) q^{75} +(-10.7024 - 2.86770i) q^{76} +0.315362 q^{77} +(2.31502 - 3.18613i) q^{78} -3.53094 q^{79} +(-3.08468 - 0.826539i) q^{80} +(4.71564 + 7.66569i) q^{81} +(-1.07644 - 0.621485i) q^{82} +(1.60068 - 1.60068i) q^{83} +(-1.37083 + 2.41305i) q^{84} +(2.35861 + 8.80247i) q^{85} +(-5.15748 - 5.15748i) q^{86} +(13.7281 - 3.78123i) q^{87} +(0.620443 - 0.358213i) q^{88} +(2.95402 - 11.0245i) q^{89} +(3.40950 - 0.0475559i) q^{90} +(3.56503 - 0.539066i) q^{91} -12.2990i q^{92} +(-5.09231 - 8.67978i) q^{93} +(0.991286 + 1.71696i) q^{94} +(-6.23151 + 10.7933i) q^{95} +(0.0683759 + 9.80484i) q^{96} +(-8.11684 + 2.17490i) q^{97} +(0.609155 - 0.163223i) q^{98} +(0.659588 - 0.678248i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{6}+O(q^{10}) \) 112 * q - 12 * q^6	\( 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) \) 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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