LMFDB - Embedded newform 273.2.cc.a.50.17

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			50.17
Character	$\chi$	$=$	273.50
Dual form			273.2.cc.a.71.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.609155 + 0.163223i) q^{2} +(0.459944 - 1.66987i) q^{3} +(-1.38762 - 0.801144i) q^{4} +(1.27442 - 1.27442i) q^{5} +(0.552737 - 0.942134i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-1.60638 - 1.60638i) q^{8} +(-2.57690 - 1.53609i) q^{9} +O(q^{10})$	\(q+(0.609155 + 0.163223i) q^{2} +(0.459944 - 1.66987i) q^{3} +(-1.38762 - 0.801144i) q^{4} +(1.27442 - 1.27442i) q^{5} +(0.552737 - 0.942134i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-1.60638 - 1.60638i) q^{8} +(-2.57690 - 1.53609i) 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} +(-1.54195 - 2.71427i) q^{15} +(0.885952 + 1.53451i) q^{16} +(-2.52815 + 4.37889i) q^{17} +(-1.31901 - 1.35633i) q^{18} +(6.67945 - 1.78975i) q^{19} +(-2.78940 + 0.747418i) q^{20} +(1.73201 + 0.0120785i) q^{21} +(-0.0994404 + 0.172236i) q^{22} +(-3.83795 - 6.64753i) q^{23} +(-3.42128 + 1.94359i) 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} +(-0.496255 - 1.90509i) q^{30} +(4.10833 + 4.10833i) q^{31} +(1.46517 + 5.46807i) q^{32} +(0.471126 + 0.276403i) q^{33} +(-2.25477 + 2.25477i) q^{34} +(1.56084 + 0.901150i) q^{35} +(2.34514 + 4.19598i) q^{36} +(1.94323 + 0.520686i) q^{37} +4.36095 q^{38} +(-5.79835 - 2.31930i) q^{39} -4.09440 q^{40} +(-1.90379 - 0.510120i) q^{41} +(1.05309 + 0.290061i) q^{42} +(10.0161 + 5.78280i) q^{43} +(0.357301 - 0.357301i) q^{44} +(-5.24167 + 1.32643i) q^{45} +(-1.25288 - 4.67582i) q^{46} +(2.22295 + 2.22295i) q^{47} +(2.96992 - 0.773630i) 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} +(-2.87155 + 1.57874i) q^{54} +(0.284188 + 0.492228i) q^{55} +(1.13588 - 1.96740i) q^{56} +(0.0835236 - 11.9770i) q^{57} +(5.00791 - 1.34187i) q^{58} +(-7.70478 + 2.06449i) q^{59} +(-0.0348803 + 5.00170i) q^{60} +(-1.19322 + 2.06671i) q^{61} +(1.83204 + 3.17318i) q^{62} +(0.816796 - 2.88667i) 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} +(-12.8657 + 3.35138i) q^{69} +(0.803704 + 0.803704i) q^{70} +(-2.77760 - 10.3661i) q^{71} +(1.67194 + 6.60702i) q^{72} +(-2.96677 + 2.96677i) q^{73} +(1.09874 + 0.634357i) q^{74} +(2.92513 + 0.805691i) q^{75} +(-10.7024 - 2.86770i) q^{76} -0.315362 q^{77} +(-3.15353 - 2.35923i) q^{78} -3.53094 q^{79} +(3.08468 + 0.826539i) q^{80} +(4.28086 + 7.91670i) q^{81} +(-1.07644 - 0.621485i) q^{82} +(-1.60068 + 1.60068i) q^{83} +(-2.39370 - 1.40435i) q^{84} +(2.35861 + 8.80247i) q^{85} +(5.15748 + 5.15748i) q^{86} +(-3.58940 - 13.7795i) 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} +(8.74996 - 4.97076i) q^{93} +(0.991286 + 1.71696i) q^{94} +(6.23151 - 10.7933i) q^{95} +(9.80484 + 0.0683759i) q^{96} +(-8.11684 + 2.17490i) q^{97} +(-0.609155 + 0.163223i) q^{98} +(0.678248 - 0.659588i) 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	0.467673	−	0.883902i	$-0.345093\pi$
$2$	0.609155	+	0.163223i	0.430738	+	0.115416i	−0.0369346	+	0.999318i	$0.511759\pi$
$3$	0.459944	−	1.66987i	0.265549	−	0.964097i
$3$	0.459944	−	1.66987i	0.265549	−	0.964097i
$4$	−1.38762	−	0.801144i	−0.693811	−	0.400572i
$5$	1.27442	−	1.27442i	0.569937	−	0.569937i	−0.362174	−	0.932111i	$-0.617965\pi$
$5$	1.27442	−	1.27442i	0.569937	−	0.569937i	0.932111	+	0.362174i	$0.117965\pi$
$6$	0.552737	−	0.942134i	0.225654	−	0.384625i
$7$	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
$9$	−2.57690	−	1.53609i	−0.858968	−	0.512030i
$10$	0.984333	−	0.568305i	0.311273	−	0.179714i
$11$	−0.0816216	+	0.304616i	−0.0246098	+	0.0918451i	−0.977138	−	0.212604i	$-0.931806\pi$
$11$	−0.0816216	+	0.304616i	−0.0246098	+	0.0918451i	0.952529	+	0.304449i	$0.0984723\pi$
$12$	−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
$15$	−1.54195	−	2.71427i	−0.398129	−	0.700821i
$16$	0.885952	+	1.53451i	0.221488	+	0.383628i
$17$	−2.52815	+	4.37889i	−0.613168	+	1.06204i	0.377535	+	0.925995i	$0.376772\pi$
$17$	−2.52815	+	4.37889i	−0.613168	+	1.06204i	−0.990703	+	0.136042i	$0.956562\pi$
$18$	−1.31901	−	1.35633i	−0.310894	−	0.319689i
$19$	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
$21$	1.73201	+	0.0120785i	0.377955	+	0.00263574i
$22$	−0.0994404	+	0.172236i	−0.0212008	+	0.0367208i
$23$	−3.83795	−	6.64753i	−0.800269	−	1.38611i	−0.919439	−	0.393232i	$-0.871357\pi$
$23$	−3.83795	−	6.64753i	−0.800269	−	1.38611i	0.119170	−	0.992874i	$-0.461977\pi$
$24$	−3.42128	+	1.94359i	−0.698366	+	0.396734i
$25$			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	0.338026	−	0.941137i	$-0.390241\pi$
$29$	7.11966	−	4.11054i	1.32209	−	0.763308i	0.984061	+	0.177829i	$0.0569074\pi$
$30$	−0.496255	−	1.90509i	−0.0906034	−	0.347821i
$31$	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
$33$	0.471126	+	0.276403i	0.0820125	+	0.0481156i
$34$	−2.25477	+	2.25477i	−0.386690	+	0.386690i
$35$	1.56084	+	0.901150i	0.263830	+	0.152322i
$36$	2.34514	+	4.19598i	0.390857	+	0.699330i
$37$	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
$39$	−5.79835	−	2.31930i	−0.928479	−	0.371384i
$40$	−4.09440			−0.647381
$41$	−1.90379	−	0.510120i	−0.297323	−	0.0796674i	0.107074	−	0.994251i	$-0.465852\pi$
$41$	−1.90379	−	0.510120i	−0.297323	−	0.0796674i	−0.404397	+	0.914584i	$0.632519\pi$
$42$	1.05309	+	0.290061i	0.162495	+	0.0447574i
$43$	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
$45$	−5.24167	+	1.32643i	−0.781382	+	0.197733i
$46$	−1.25288	−	4.67582i	−0.184727	−	0.689412i
$47$	2.22295	+	2.22295i	0.324250	+	0.324250i	0.850395	−	0.526145i	$-0.176363\pi$
$47$	2.22295	+	2.22295i	0.324250	+	0.324250i	−0.526145	+	0.850395i	$0.676363\pi$
$48$	2.96992	−	0.773630i	0.428671	−	0.111664i
$49$	−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	$0.266713\pi$
$53$			10.8218i			1.48648i	−0.669023	+	0.743242i	$0.733287\pi$
$54$	−2.87155	+	1.57874i	−0.390769	+	0.214839i
$55$	0.284188	+	0.492228i	0.0383199	+	0.0663720i
$56$	1.13588	−	1.96740i	0.151788	−	0.262905i
$57$	0.0835236	−	11.9770i	0.0110630	−	1.58639i
$58$	5.00791	−	1.34187i	0.657571	−	0.176196i
$59$	−7.70478	+	2.06449i	−1.00308	+	0.268774i	−0.722734	−	0.691126i	$-0.757115\pi$
$59$	−7.70478	+	2.06449i	−1.00308	+	0.268774i	−0.280343	+	0.959900i	$0.590448\pi$
$60$	−0.0348803	+	5.00170i	−0.00450303	+	0.645717i
$61$	−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
$63$	0.816796	−	2.88667i	0.102907	−	0.363686i
$64$			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
$69$	−12.8657	+	3.35138i	−1.54885	+	0.403458i
$70$	0.803704	+	0.803704i	0.0960610	+	0.0960610i
$71$	−2.77760	−	10.3661i	−0.329641	−	1.23024i	−0.909564	−	0.415564i	$-0.863584\pi$
$71$	−2.77760	−	10.3661i	−0.329641	−	1.23024i	0.579923	−	0.814671i	$-0.303083\pi$
$72$	1.67194	+	6.60702i	0.197040	+	0.778645i
$73$	−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
$75$	2.92513	+	0.805691i	0.337765	+	0.0930332i
$76$	−10.7024	−	2.86770i	−1.22765	−	0.328948i
$77$	−0.315362			−0.0359388
$78$	−3.15353	−	2.35923i	−0.357068	−	0.267131i
$79$	−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
$81$	4.28086	+	7.91670i	0.475651	+	0.879634i
$82$	−1.07644	−	0.621485i	−0.118873	−	0.0686315i
$83$	−1.60068	+	1.60068i	−0.175698	+	0.175698i	−0.789477	−	0.613780i	$-0.789648\pi$
$83$	−1.60068	+	1.60068i	−0.175698	+	0.175698i	0.613780	+	0.789477i	$0.289648\pi$
$84$	−2.39370	−	1.40435i	−0.261174	−	0.153227i
$85$	2.35861	+	8.80247i	0.255828	+	0.954762i
$86$	5.15748	+	5.15748i	0.556146	+	0.556146i
$87$	−3.58940	−	13.7795i	−0.384824	−	1.47732i
$88$	0.620443	−	0.358213i	0.0661395	−	0.0381856i
$89$	−2.95402	+	11.0245i	−0.313125	+	1.16860i	0.612597	+	0.790395i	$0.290125\pi$
$89$	−2.95402	+	11.0245i	−0.313125	+	1.16860i	−0.925722	+	0.378204i	$0.876542\pi$
$90$	−3.40950	−	0.0475559i	−0.359393	−	0.00501283i
$91$	3.56503	−	0.539066i	0.373716	−	0.0565095i
$92$			12.2990i			1.28226i
$93$	8.74996	−	4.97076i	0.907329	−	0.515444i
$94$	0.991286	+	1.71696i	0.102243	+	0.177091i
$95$	6.23151	−	10.7933i	0.639340	−	1.10737i
$96$	9.80484	+	0.0683759i	1.00070	+	0.00697858i
$97$	−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
$99$	0.678248	−	0.659588i	0.0681665	−	0.0662911i
$100$	1.40338	−	2.43072i	0.140338	−	0.243072i
$101$	−3.12439	−	5.41160i	−0.310888	−	0.538474i	0.667667	−	0.744460i	$-0.267293\pi$
$101$	−3.12439	−	5.41160i	−0.310888	−	0.538474i	−0.978555	+	0.205986i	$0.933960\pi$
$102$	2.72810	+	4.80224i	0.270122	+	0.475492i
$103$			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	−0.367069	−	0.930194i	$-0.619639\pi$
$107$	2.63741	−	1.52271i	0.254968	−	0.147206i	0.622037	+	0.782988i	$0.286305\pi$
$108$	8.08536	−	1.98615i	0.778014	−	0.191118i
$109$	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
$111$	1.76325	−	3.00544i	0.167360	−	0.285264i
$112$	−1.25292	+	1.25292i	−0.118390	+	0.118390i
$113$	−3.31932	−	1.91641i	−0.312255	−	0.180280i	0.335680	−	0.941976i	$-0.391034\pi$
$113$	−3.31932	−	1.91641i	−0.312255	−	0.180280i	−0.647935	+	0.761696i	$0.724367\pi$
$114$	2.00579	−	7.28220i	0.187860	−	0.682040i
$115$	−13.3629	−	3.58058i	−1.24610	−	0.333891i
$116$	−13.1725			−1.22304
$117$	−6.53983	+	8.61572i	−0.604607	+	0.796524i
$118$	−5.03038			−0.463084
$119$	−4.88402	−	1.30867i	−0.447717	−	0.119966i
$120$	−1.88319	+	6.83709i	−0.171911	+	0.624138i
$121$	9.44015	+	5.45027i	0.858196	+	0.495479i
$122$	−1.06419	+	1.06419i	−0.0963471	+	0.0963471i
$123$	−1.72747	+	2.94446i	−0.155761	+	0.265493i
$124$	−2.40945	−	8.99217i	−0.216375	−	0.807521i
$125$	8.60451	+	8.60451i	0.769611	+	0.769611i
$126$	0.968725	−	1.62511i	0.0863009	−	0.144776i
$127$	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	$-0.666930\pi$
$131$		−	19.8147i		−	1.73122i	0.500717	−	0.865611i	$-0.333070\pi$
$132$	−0.432306	−	0.760983i	−0.0376274	−	0.0662351i
$133$	3.45754	+	5.98863i	0.299806	+	0.519280i
$134$	3.85899	−	6.68397i	0.333366	−	0.577407i
$135$	−0.195909	+	9.36297i	−0.0168611	+	0.805837i
$136$	11.0953	−	2.97298i	0.951417	−	0.254931i
$137$	−9.79349	+	2.62416i	−0.836714	+	0.224197i	−0.651641	−	0.758528i	$-0.725919\pi$
$137$	−9.79349	+	2.62416i	−0.836714	+	0.224197i	−0.185073	+	0.982725i	$0.559252\pi$
$138$	−8.38425	−	0.0584691i	−0.713715	−	0.00497722i
$139$	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
$141$	4.73446	−	2.68960i	0.398713	−	0.226505i
$142$		−	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
$147$	0.436610	+	1.67612i	0.0360110	+	0.138244i
$148$	−2.27932	−	2.27932i	−0.187359	−	0.187359i
$149$	1.33154	+	4.96939i	0.109084	+	0.407108i	0.998776	−	0.0494528i	$-0.0157477\pi$
$149$	1.33154	+	4.96939i	0.109084	+	0.407108i	−0.889692	+	0.456561i	$0.849081\pi$
$150$	1.65035	+	0.968239i	0.134751	+	0.0790564i
$151$	−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
$153$	13.2412	−	7.40051i	1.07049	−	0.598296i
$154$	−0.192104	−	0.0514742i	−0.0154802	−	0.00414791i
$155$	10.4715			0.841088
$156$	6.18783	+	7.86362i	0.495423	+	0.629593i
$157$	−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
$159$	18.0709	+	4.97740i	1.43312	+	0.394734i
$160$	8.83584	+	5.10138i	0.698535	+	0.403299i
$161$	5.42769	−	5.42769i	0.427762	−	0.427762i
$162$	1.31552	+	5.52124i	0.103357	+	0.433789i
$163$	−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
$165$	0.952665	−	0.248159i	0.0741649	−	0.0193191i
$166$	−1.23633	+	0.713796i	−0.0959579	+	0.0554013i
$167$	−1.41528	+	5.28188i	−0.109517	+	0.408724i	−0.998818	−	0.0485980i	$-0.984525\pi$
$167$	−1.41528	+	5.28188i	−0.109517	+	0.408724i	0.889301	+	0.457322i	$0.151191\pi$
$168$	−2.76286	−	2.80166i	−0.213159	−	0.216153i
$169$	−12.6768	−	2.88078i	−0.975138	−	0.221599i
$170$			5.74705i			0.440779i
$171$	−19.9615	−	5.64820i	−1.52649	−	0.431929i
$172$	−9.26572	−	16.0487i	−0.706504	−	1.22370i
$173$	−9.81362	+	16.9977i	−0.746115	+	1.29231i	0.203557	+	0.979063i	$0.434750\pi$
$173$	−9.81362	+	16.9977i	−0.746115	+	1.29231i	−0.949672	+	0.313246i	$0.898583\pi$
$174$	0.0626218	−	8.97972i	0.00474735	−	0.680751i
$175$	−1.69203	+	0.453377i	−0.127905	+	0.0342721i
$176$	−0.539750	+	0.144626i	−0.0406852	+	0.0109016i
$177$	−0.0963450	+	13.8155i	−0.00724174	+	1.03844i
$178$	−3.59891	+	6.23350i	−0.269750	+	0.467220i
$179$	−8.89183	−	15.4011i	−0.664607	−	1.15113i	−0.979392	−	0.201970i	$-0.935266\pi$
$179$	−8.89183	−	15.4011i	−0.664607	−	1.15113i	0.314785	−	0.949163i	$-0.398068\pi$
$180$	8.33612	+	2.35875i	0.621338	+	0.175811i
$181$			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
$186$	6.14143	−	1.59977i	0.450311	−	0.117301i
$187$	−1.12753	−	1.12753i	−0.0824530	−	0.0824530i
$188$	−1.30371	−	4.86552i	−0.0950829	−	0.354854i
$189$	−4.44467	−	2.69164i	−0.323302	−	0.195788i
$190$	5.55767	−	5.55767i	0.403196	−	0.403196i
$191$	5.69718	+	3.28927i	0.412233	+	0.238003i	0.691749	−	0.722138i	$-0.256840\pi$
$191$	5.69718	+	3.28927i	0.412233	+	0.238003i	−0.279515	+	0.960141i	$0.590174\pi$
$192$	0.0438284	+	0.0120720i	0.00316304	+	0.000871221i
$193$	−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
$195$	−10.3453	+	4.43377i	−0.740841	+	0.317509i
$196$	1.60229			0.114449
$197$	−5.96842	−	1.59923i	−0.425232	−	0.113941i	0.0398551	−	0.999205i	$-0.487310\pi$
$197$	−5.96842	−	1.59923i	−0.425232	−	0.113941i	−0.465087	+	0.885265i	$0.653977\pi$
$198$	0.520818	−	0.291086i	0.0370129	−	0.0206866i
$199$	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
$201$	−18.2830	−	10.7264i	−1.28959	−	0.756582i
$202$	−1.01994	−	3.80648i	−0.0717629	−	0.267823i
$203$	5.81318	+	5.81318i	0.408005	+	0.408005i
$204$	−3.53727	−	13.5793i	−0.247658	−	0.950744i
$205$	−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
$210$	1.71174	−	0.972420i	0.118121	−	0.0671033i
$211$	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
$213$	−18.5876	−	0.129624i	−1.27360	−	0.00888171i
$214$	1.85514	−	0.497082i	0.126814	−	0.0339798i
$215$	20.1344	−	5.39500i	1.37316	−	0.367936i
$216$	11.8018	+	0.246939i	0.803013	+	0.0168021i
$217$	−2.90503	+	5.03166i	−0.197206	+	0.341571i
$218$	0.250670	+	0.434173i	0.0169775	+	0.0294059i
$219$	3.58956	+	6.31866i	0.242560	+	0.426975i
$220$		−	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
$225$	2.69079	−	4.51400i	0.179386	−	0.300934i
$226$	−1.70918	−	1.70918i	−0.113693	−	0.113693i
$227$	4.97849	+	18.5800i	0.330434	+	1.23320i	0.908735	+	0.417373i	$0.137049\pi$
$227$	4.97849	+	18.5800i	0.330434	+	1.23320i	−0.578302	+	0.815823i	$0.696284\pi$
$228$	−9.71117	+	16.5526i	−0.643138	+	1.09622i
$229$	−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
$231$	−0.145049	+	0.526611i	−0.00954349	+	0.0346485i
$232$	−18.0399	−	4.83379i	−1.18438	−	0.317354i
$233$	−11.1531			−0.730664			−0.365332	−	0.930877i	$-0.619045\pi$
$233$	−11.1531			−0.730664			−0.365332	+	0.930877i	$0.619045\pi$
$234$	−5.39005	+	4.18087i	−0.352359	+	0.273312i
$235$	5.66593			0.369605
$236$	12.3453	+	3.30791i	0.803610	+	0.215327i
$237$	−1.62403	+	5.89620i	−0.105492	+	0.382999i
$238$	−2.76152	−	1.59437i	−0.179003	−	0.103347i
$239$	−4.34364	+	4.34364i	−0.280966	+	0.280966i	−0.833494	−	0.552528i	$-0.813663\pi$
$239$	−4.34364	+	4.34364i	−0.280966	+	0.280966i	0.552528	+	0.833494i	$0.313663\pi$
$240$	2.79899	−	4.77085i	0.180674	−	0.307957i
$241$	−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
$243$	15.1888	−	3.50723i	0.974361	−	0.224989i
$244$	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
$249$	1.93670	+	3.40915i	0.122733	+	0.216046i
$250$	3.83703	+	6.64594i	0.242675	+	0.420326i
$251$	3.33231	−	5.77174i	0.210334	−	0.364309i	−0.741485	−	0.670969i	$-0.765878\pi$
$251$	3.33231	−	5.77174i	0.210334	−	0.364309i	0.951819	+	0.306660i	$0.0992116\pi$
$252$	−3.44604	+	3.35123i	−0.217080	+	0.211108i
$253$	2.33820	−	0.626520i	0.147002	−	0.0393890i
$254$	4.24415	−	1.13722i	0.266302	−	0.0713553i
$255$	15.7838	+	0.110071i	0.988418	+	0.00689292i
$256$	3.59108	−	6.21993i	0.224443	−	0.388746i
$257$	7.30409	+	12.6511i	0.455617	+	0.789151i	0.998723	−	0.0505124i	$-0.0160854\pi$
$257$	7.30409	+	12.6511i	0.455617	+	0.789151i	−0.543107	+	0.839664i	$0.682752\pi$
$258$	10.9845	−	6.24015i	0.683862	−	0.388495i
$259$			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	0.0878933	−	0.996130i	$-0.471987\pi$
$263$	16.1283	−	9.31168i	0.994514	−	0.574183i	0.906620	+	0.421947i	$0.138653\pi$
$264$	−0.312799	−	1.20081i	−0.0192514	−	0.0739050i
$265$	13.7915	+	13.7915i	0.847202	+	0.847202i
$266$	1.12870	+	4.21235i	0.0692048	+	0.258276i
$267$	17.0508	+	10.0035i	1.04349	+	0.612203i
$268$	−13.8658	+	13.8658i	−0.846989	+	0.846989i
$269$	17.4833	+	10.0940i	1.06597	+	0.615440i	0.927078	−	0.374867i	$-0.122312\pi$
$269$	17.4833	+	10.0940i	1.06597	+	0.615440i	0.138895	+	0.990307i	$0.455645\pi$
$270$	−1.64759	+	5.67153i	−0.100269	+	0.345158i
$271$	−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
$273$	0.739544	−	6.20105i	0.0447592	−	0.375305i
$274$	−6.39408			−0.386280
$275$	−0.533600	−	0.142978i	−0.0321773	−	0.00862189i
$276$	20.5377	+	5.65686i	1.23622	+	0.340503i
$277$	−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
$279$	−4.27601	−	16.8975i	−0.255998	−	1.01163i
$280$	−1.05971	−	3.95488i	−0.0633296	−	0.236349i
$281$	−10.1561	−	10.1561i	−0.605862	−	0.605862i	0.336000	−	0.941862i	$-0.390926\pi$
$281$	−10.1561	−	10.1561i	−0.605862	−	0.605862i	−0.941862	+	0.336000i	$0.890926\pi$
$282$	3.32302	−	0.865610i	0.197883	−	0.0515463i
$283$	−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
$288$	4.62385	−	16.3413i	0.272463	−	0.962921i
$289$	−4.28313	−	7.41860i	−0.251949	−	0.436388i
$290$	4.67208	−	8.09227i	0.274354	−	0.475195i
$291$	−0.101498	+	14.5544i	−0.00594990	+	0.853192i
$292$	6.49357	−	1.73995i	0.380008	−	0.101823i
$293$	25.7930	−	6.91120i	1.50684	−	0.403757i	0.591456	−	0.806337i	$-0.298553\pi$
$293$	25.7930	−	6.91120i	1.50684	−	0.403757i	0.915385	+	0.402581i	$0.131887\pi$
$294$	−0.00761723	+	1.09228i	−0.000444246	+	0.0637031i
$295$	−7.18809	+	12.4501i	−0.418507	+	0.724875i
$296$	−2.28514	−	3.95797i	−0.132821	−	0.230053i
$297$	−0.789467	−	1.43596i	−0.0458095	−	0.0833226i
$298$			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
$303$	−10.4737	+	2.72828i	−0.601698	+	0.156735i
$304$	8.66406	+	8.66406i	0.496918	+	0.496918i
$305$	1.11320	+	4.15451i	0.0637415	+	0.237887i
$306$	9.27387	−	2.34680i	0.530152	−	0.134158i
$307$	−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
$309$	3.18975	+	0.878578i	0.181459	+	0.0499806i
$310$	6.37875	+	1.70918i	0.362288	+	0.0970749i
$311$	6.89236			0.390830			0.195415	−	0.980721i	$-0.437395\pi$
$311$	6.89236			0.390830			0.195415	+	0.980721i	$0.437395\pi$
$312$	5.58868	+	13.0400i	0.316397	+	0.738245i
$313$	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
$315$	−2.63788	−	4.71976i	−0.148628	−	0.265928i
$316$	4.89961	+	2.82879i	0.275625	+	0.159132i
$317$	−16.1569	+	16.1569i	−0.907460	+	0.907460i	−0.996067	−	0.0886063i	$-0.971759\pi$
$317$	−16.1569	+	16.1569i	−0.907460	+	0.907460i	0.0886063	+	0.996067i	$0.471759\pi$
$318$	10.1956	+	5.98159i	0.571738	+	0.335431i
$319$	0.671017	+	2.50427i	0.0375697	+	0.140212i
$320$	0.0334492	+	0.0334492i	0.00186987	+	0.00186987i
$321$	−1.32966	−	5.10449i	−0.0742145	−	0.284905i
$322$	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
$327$	1.19722	−	0.680127i	0.0662064	−	0.0376111i
$328$	2.23877	+	3.87766i	0.123615	+	0.214108i
$329$	−1.57186	+	2.72255i	−0.0866596	+	0.150099i
$330$	0.620826	+	0.00432945i	0.0341754	+	0.000238328i
$331$	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
$333$	−4.20769	−	4.32672i	−0.230580	−	0.237103i
$334$	−1.72424	+	2.98648i	−0.0943465	+	0.163413i
$335$	−11.0285	−	19.1019i	−0.602551	−	1.04365i
$336$	1.51594	+	2.66849i	0.0827014	+	0.145578i
$337$			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
$342$	−11.2377	−	6.69880i	−0.607668	−	0.362230i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−6.80029	−	25.3790i	−0.366647	−	1.36835i
$345$	−12.1253	+	20.6674i	−0.652802	+	1.11269i
$346$	−8.75242	+	8.75242i	−0.470533	+	0.470533i
$347$	−6.71799	−	3.87863i	−0.360640	−	0.208216i	0.308721	−	0.951153i	$-0.400099\pi$
$347$	−6.71799	−	3.87863i	−0.360640	−	0.208216i	−0.669362	+	0.742937i	$0.733432\pi$
$348$	−6.05862	+	21.9964i	−0.324776	+	1.17913i
$349$	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
$351$	11.3791	+	14.8834i	0.607374	+	0.794416i
$352$	−1.78525			−0.0951541
$353$	−24.6284	−	6.59915i	−1.31084	−	0.351237i	−0.465299	−	0.885154i	$-0.654053\pi$
$353$	−24.6284	−	6.59915i	−1.31084	−	0.351237i	−0.845537	+	0.533916i	$0.820720\pi$
$354$	−2.31369	+	8.40006i	−0.122971	+	0.446458i
$355$	−16.7506	−	9.67098i	−0.889031	−	0.513282i
$356$	12.9313	−	12.9313i	0.685358	−	0.685358i
$357$	−4.43168	+	7.55374i	−0.234549	+	0.399786i
$358$	−2.90270	−	10.8330i	−0.153412	−	0.572543i
$359$	3.28169	+	3.28169i	0.173201	+	0.173201i	0.788384	−	0.615183i	$-0.210918\pi$
$359$	3.28169	+	3.28169i	0.173201	+	0.173201i	−0.615183	+	0.788384i	$0.710918\pi$
$360$	10.5509	+	6.28935i	0.556079	+	0.331478i
$361$	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
$366$	1.28758	+	2.26652i	0.0673031	+	0.118473i
$367$	−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
$369$	4.12231	+	4.23893i	0.214599	+	0.220670i
$370$	2.20869	−	0.591816i	0.114824	−	0.0307671i
$371$	−10.4530	+	2.80088i	−0.542694	+	0.145414i
$372$	−16.1239	−	0.112443i	−0.835987	−	0.00582991i
$373$	−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
$375$	18.3260	−	10.4108i	0.946349	−	0.537611i
$376$		−	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
$381$	−3.04198	−	11.6780i	−0.155845	−	0.598281i
$382$	2.93358	+	2.93358i	0.150095	+	0.150095i
$383$	2.05533	+	7.67059i	0.105022	+	0.391949i	0.998348	−	0.0574617i	$-0.0183007\pi$
$383$	2.05533	+	7.67059i	0.105022	+	0.391949i	−0.893325	+	0.449411i	$0.851634\pi$
$384$	−16.8894	−	9.90876i	−0.861882	−	0.505654i
$385$	−0.401902	+	0.401902i	−0.0204828	+	0.0204828i
$386$	−10.4127	−	6.01178i	−0.529993	−	0.305992i
$387$	−16.9276	−	30.2874i	−0.860481	−	1.53959i
$388$	13.0055	+	3.48482i	0.660255	+	0.176915i
$389$	10.5589			0.535358			0.267679	−	0.963508i	$-0.413743\pi$
$389$	10.5589			0.535358			0.267679	+	0.963508i	$0.413743\pi$
$390$	−7.02557	+	1.01227i	−0.355754	+	0.0512584i
$391$	38.8118			1.96280
$392$	2.19435	+	0.587975i	0.110832	+	0.0296972i
$393$	−33.0880	−	9.11366i	−1.66907	−	0.459724i
$394$	−3.37466	−	1.94836i	−0.170013	−	0.0981571i
$395$	−4.49989	+	4.49989i	−0.226414	+	0.226414i
$396$	−1.46958	+	0.371884i	−0.0738490	+	0.0186879i
$397$	−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
$399$	11.5905	−	3.01919i	0.580250	−	0.151148i
$400$	−2.68803	+	1.55194i	−0.134402	+	0.0775968i
$401$	5.52699	−	20.6270i	0.276005	−	1.03006i	−0.679160	−	0.733990i	$-0.737656\pi$
$401$	5.52699	−	20.6270i	0.276005	−	1.03006i	0.955165	−	0.296074i	$-0.0956774\pi$
$402$	−9.38641	−	9.51825i	−0.468152	−	0.474727i
$403$	16.3720	−	13.0689i	0.815546	−	0.651008i
$404$			10.0123i			0.498133i
$405$	15.5448	+	4.63358i	0.772427	+	0.230245i
$406$	2.59229	+	4.48997i	0.128653	+	0.222834i
$407$	−0.317218	+	0.549438i	−0.0157239	+	0.0272346i
$408$	0.138742	−	19.8951i	0.00686877	−	0.984955i
$409$	−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
$411$	−0.122463	+	17.5608i	−0.00604067	+	0.866209i
$412$	1.53033	−	2.65062i	0.0753941	−	0.130586i
$413$	−3.98829	−	6.90792i	−0.196251	−	0.339917i
$414$	−3.95392	+	13.9737i	−0.194325	+	0.686769i
$415$			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	−0.267520	−	0.963552i	$-0.586204\pi$
$419$	8.86700	−	5.11937i	0.433181	−	0.250097i	0.700701	+	0.713455i	$0.252871\pi$
$420$	−4.84030	+	1.26084i	−0.236182	+	0.0615229i
$421$	−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
$423$	−2.31368	−	9.14297i	−0.112495	−	0.444547i
$424$	17.3838	−	17.3838i	0.844234	−	0.844234i
$425$	−7.67058	−	4.42861i	−0.372078	−	0.214819i
$426$	−11.3016	−	3.11288i	−0.547564	−	0.150820i
$427$	−2.30512	−	0.617654i	−0.111552	−	0.0298904i
$428$	−4.87965			−0.235867
$429$	1.17976	−	1.57696i	0.0569596	−	0.0761366i
$430$	13.1456			0.633936
$431$	5.58772	+	1.49723i	0.269151	+	0.0721188i	0.390870	−	0.920446i	$-0.372174\pi$
$431$	5.58772	+	1.49723i	0.269151	+	0.0721188i	−0.121719	+	0.992565i	$0.538841\pi$
$432$	−8.84156	−	2.56849i	−0.425390	−	0.123576i
$433$	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
$435$	−22.1352	−	12.9864i	−1.06130	−	0.622652i
$436$	−0.329674	−	1.23036i	−0.0157885	−	0.0589236i
$437$	−37.5328	−	37.5328i	−1.79544	−	1.79544i
$438$	1.15525	+	4.43494i	0.0552001	+	0.211910i
$439$	−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	$0.0330962\pi$
$443$			4.36895i			0.207575i	−0.994599	+	0.103788i	$0.966904\pi$
$444$	−4.85452	+	2.75780i	−0.230385	+	0.130879i
$445$	10.2852	+	17.8145i	0.487566	+	0.844490i
$446$	−8.24638	+	14.2832i	−0.390477	+	0.676327i
$447$	8.91064	+	0.0621401i	0.421459	+	0.00293912i
$448$	−0.0253523	+	0.00679314i	−0.00119778	+	0.000320945i
$449$	32.9659	−	8.83320i	1.55576	−	0.416864i	0.624441	−	0.781072i	$-0.285327\pi$
$449$	32.9659	−	8.83320i	1.55576	−	0.416864i	0.931318	+	0.364207i	$0.118660\pi$
$450$	2.37590	−	2.31053i	0.112001	−	0.108919i
$451$	0.310781	−	0.538289i	0.0146341	−	0.0253471i
$452$	3.07064	+	5.31850i	0.144431	+	0.250161i
$453$	2.27403	+	4.00294i	0.106843	+	0.188075i
$454$			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
$459$	−6.26767	−	25.5148i	−0.292550	−	1.19093i
$460$	15.6741	+	15.6741i	0.730808	+	0.730808i
$461$	−3.47367	−	12.9639i	−0.161785	−	0.603790i	−0.998428	−	0.0560419i	$-0.982152\pi$
$461$	−3.47367	−	12.9639i	−0.161785	−	0.603790i	0.836643	−	0.547748i	$-0.184515\pi$
$462$	−0.174312	+	0.297113i	−0.00810973	+	0.0138229i
$463$	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
$465$	4.81628	−	17.4859i	0.223350	−	0.810891i
$466$	−6.79397	−	1.82044i	−0.314725	−	0.0843302i
$467$	2.11536			0.0978873			0.0489436	−	0.998802i	$-0.484415\pi$
$467$	2.11536			0.0978873			0.0489436	+	0.998802i	$0.484415\pi$
$468$	15.9772	−	6.71602i	0.738548	−	0.310448i
$469$	12.2383			0.565110
$470$	3.45143	+	0.924809i	0.159203	+	0.0426583i
$471$	−1.49569	+	5.43023i	−0.0689178	+	0.250212i
$472$	15.6931	+	9.06044i	0.722336	+	0.417041i
$473$	−2.57906	+	2.57906i	−0.118586	+	0.118586i
$474$	−1.95168	+	3.32662i	−0.0896437	+	0.152797i
$475$	3.13514	+	11.7005i	0.143850	+	0.536855i
$476$	5.72874	+	5.72874i	0.262576	+	0.262576i
$477$	16.6232	−	27.8866i	0.761124	−	1.27684i
$478$	−3.35493	+	1.93697i	−0.153451	+	0.0885949i
$479$	−2.62409	+	9.79324i	−0.119898	+	0.447465i	−0.999607	−	0.0280482i	$-0.991071\pi$
$479$	−2.62409	+	9.79324i	−0.119898	+	0.447465i	0.879709	+	0.475513i	$0.157737\pi$
$480$	12.5826	−	12.4083i	0.574315	−	0.566360i
$481$	2.64683	−	6.75340i	0.120685	−	0.307929i
$482$		−	2.72624i		−	0.124177i
$483$	−6.56708	−	11.5599i	−0.298812	−	0.525995i
$484$	−8.73291	−	15.1258i	−0.396950	−	0.687538i
$485$	−7.57252	+	13.1160i	−0.343850	+	0.595566i
$486$	9.82479	+	0.342709i	0.445662	+	0.0155456i
$487$	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
$489$	−24.5684	−	0.171332i	−1.11102	−	0.00774792i
$490$	−0.568305	+	0.984333i	−0.0256734	+	0.0444676i
$491$	12.5057	+	21.6606i	0.564376	+	0.977528i	0.997107	+	0.0760051i	$0.0242165\pi$
$491$	12.5057	+	21.6606i	0.564376	+	0.977528i	−0.432731	+	0.901523i	$0.642450\pi$
$492$	4.75601	−	2.70184i	0.214417	−	0.121808i
$493$			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
$498$	0.623301	+	2.39281i	0.0279308	+	0.107225i
$499$	−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
$501$	8.16908	+	4.79269i	0.364968	+	0.214121i
$502$	2.97198	−	2.97198i	0.132646	−	0.132646i
$503$	16.4105	+	9.47462i	0.731709	+	0.422452i	0.819047	−	0.573726i	$-0.194503\pi$
$503$	16.4105	+	9.47462i	0.731709	+	0.422452i	−0.0873380	+	0.996179i	$0.527836\pi$
$504$	−5.94916	+	3.32499i	−0.264997	+	0.148107i
$505$	−10.8784	−	2.91486i	−0.484083	−	0.129710i
$506$	1.52659			0.0678653
$507$	−10.6411	+	19.8435i	−0.472589	+	0.881283i
$508$	−11.1636			−0.495304
$509$	−2.60485	−	0.697967i	−0.115458	−	0.0309368i	0.200627	−	0.979668i	$-0.435702\pi$
$509$	−2.60485	−	0.697967i	−0.115458	−	0.0309368i	−0.316085	+	0.948731i	$0.602369\pi$
$510$	9.59680	+	2.64332i	0.424953	+	0.117048i
$511$	−3.63354	−	2.09782i	−0.160738	−	0.0928023i
$512$	−12.7855	+	12.7855i	−0.565043	+	0.565043i
$513$	−18.6129	+	30.7352i	−0.821780	+	1.35699i
$514$	2.38439	+	8.89865i	0.105171	+	0.392503i
$515$	2.43438	+	2.43438i	0.107271	+	0.107271i
$516$	−31.0609	+	8.09101i	−1.36738	+	0.356187i
$517$	−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	$0.215795\pi$
$521$			28.6317i			1.25438i	−0.778867	+	0.627189i	$0.784205\pi$
$522$	−14.9661	−	4.23474i	−0.655050	−	0.185349i
$523$	−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
$525$	−0.0211581	+	3.03399i	−0.000923414	+	0.132414i
$526$	11.3445	−	3.03976i	0.494645	−	0.132540i
$527$	−28.3764	+	7.60344i	−1.23610	+	0.331211i
$528$	−0.00674934	+	0.967829i	−0.000293727	+	0.0421194i
$529$	−17.9598	+	31.1073i	−0.780860	+	1.35249i
$530$	6.15006	+	10.6522i	0.267142	+	0.462703i
$531$	23.0257	+	6.51524i	0.999231	+	0.282737i
$532$		−	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
$537$	−29.8075	+	7.76453i	−1.28629	+	0.335064i
$538$	9.00246	+	9.00246i	0.388123	+	0.388123i
$539$	−0.0816216	−	0.304616i	−0.00351569	−	0.0131207i
$540$	7.77294	−	12.8353i	0.334494	−	0.552344i
$541$	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
$543$	5.20132	+	1.43264i	0.223210	+	0.0614805i
$544$	−27.6483	−	7.40833i	−1.18541	−	0.317629i
$545$	1.43276			0.0613729
$546$	1.46265	−	3.65670i	0.0625956	−	0.156492i
$547$	−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
$549$	6.24945	−	3.49283i	0.266720	−	0.149070i
$550$	−0.301708	−	0.174191i	−0.0128649	−	0.00742755i
$551$	40.1985	−	40.1985i	1.71252	−	1.71252i
$552$	26.0508	+	15.2836i	1.10880	+	0.650515i
$553$	−0.913874	−	3.41063i	−0.0388619	−	0.145035i
$554$	−4.39946	−	4.39946i	−0.186915	−	0.186915i
$555$	−1.58307	−	6.07731i	−0.0671976	−	0.257967i
$556$	−3.92135	+	2.26399i	−0.166302	+	0.0960146i
$557$	7.67187	−	28.6318i	0.325068	−	1.21317i	−0.589176	−	0.808005i	$-0.700548\pi$
$557$	7.67187	−	28.6318i	0.325068	−	1.21317i	0.914244	−	0.405165i	$-0.132786\pi$
$558$	0.153305	−	10.9912i	0.00648993	−	0.465293i
$559$	24.7467	−	33.5638i	1.04667	−	1.41960i
$560$			3.19350i			0.134950i
$561$	−2.40142	+	1.36422i	−0.101388	+	0.0575975i
$562$	−4.52894	−	7.84435i	−0.191042	−	0.330894i
$563$	−2.35749	+	4.08330i	−0.0993564	+	0.172090i	−0.911418	−	0.411481i	$-0.865012\pi$
$563$	−2.35749	+	4.08330i	−0.0993564	+	0.172090i	0.812062	+	0.583571i	$0.198345\pi$
$564$	−8.72439	−	0.0608412i	−0.367363	−	0.00256188i
$565$	−6.67250	+	1.78789i	−0.280714	+	0.0752172i
$566$	−11.3143	+	3.03165i	−0.475575	+	0.127430i
$567$	−6.53898	+	6.18399i	−0.274611	+	0.259703i
$568$	−12.1901	+	21.1138i	−0.511484	+	0.885917i
$569$	20.2729	+	35.1137i	0.849884	+	1.47204i	0.881311	+	0.472536i	$0.156661\pi$
$569$	20.2729	+	35.1137i	0.849884	+	1.47204i	−0.0314272	+	0.999506i	$0.510005\pi$
$570$	−6.72435	−	11.8368i	−0.281652	−	0.495788i
$571$		−	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
$576$	0.0403172	−	0.0676351i	0.00167988	−	0.00281813i
$577$	−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
$579$	−16.7103	+	28.4825i	−0.694455	+	1.18369i
$580$	−16.7873	+	16.7873i	−0.697055	+	0.697055i
$581$	−1.96043	−	1.13185i	−0.0813322	−	0.0469572i
$582$	−2.43743	+	8.84931i	−0.101035	+	0.366816i
$583$	−3.29648	−	0.883289i	−0.136526	−	0.0365821i
$584$	9.53152			0.394417
$585$	2.64556	+	19.3145i	0.109380	+	0.798557i
$586$	16.8400			0.695653
$587$	22.4749	+	6.02213i	0.927638	+	0.248560i	0.690847	−	0.723001i	$-0.257238\pi$
$587$	22.4749	+	6.02213i	0.927638	+	0.248560i	0.236791	+	0.971561i	$0.423904\pi$
$588$	0.736962	−	2.67561i	0.0303918	−	0.110340i
$589$	34.7943	+	20.0885i	1.43367	+	0.827731i
$590$	−6.41081	+	6.41081i	−0.263929	+	0.263929i
$591$	−5.41564	+	9.23090i	−0.222770	+	0.379708i
$592$	0.922605	+	3.44321i	0.0379188	+	0.141515i
$593$	−32.1694	−	32.1694i	−1.32104	−	1.32104i	−0.912935	−	0.408104i	$-0.866190\pi$
$593$	−32.1694	−	32.1694i	−1.32104	−	1.32104i	−0.408104	−	0.912935i	$-0.633810\pi$
$594$	−0.246527	−	1.00358i	−0.0101151	−	0.0411774i
$595$	−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	$-0.941548\pi$
$599$		−	8.93813i		−	0.365202i	0.983187	−	0.182601i	$-0.0584516\pi$
$600$	−3.40462	−	5.99311i	−0.138993	−	0.244668i
$601$	−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
$603$	−26.3208	+	25.5967i	−1.07187	+	1.04238i
$604$	4.11375	−	1.10228i	0.167386	−	0.0448510i
$605$	18.9766	−	5.08477i	0.771510	−	0.206725i
$606$	−6.82542	−	0.0475984i	−0.277264	−	0.00193355i
$607$	−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
$609$	12.3810	−	7.03349i	0.501702	−	0.285011i
$610$			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
$615$	1.55095	+	5.95399i	0.0625402	+	0.240088i
$616$	0.506590	+	0.506590i	0.0204111	+	0.0204111i
$617$	9.64811	+	36.0072i	0.388418	+	1.44960i	0.832708	+	0.553713i	$0.186789\pi$
$617$	9.64811	+	36.0072i	0.388418	+	1.44960i	−0.444290	+	0.895883i	$0.646544\pi$
$618$	1.79965	+	1.05583i	0.0723926	+	0.0424717i
$619$	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
$621$	38.3018	+	11.1267i	1.53700	+	0.446500i
$622$	4.19852	+	1.12499i	0.168345	+	0.0451080i
$623$	−11.4134			−0.457270
$624$	−1.57807	−	10.9524i	−0.0631733	−	0.438448i
$625$	13.1729			0.526916
$626$	10.0301	+	2.68755i	0.400882	+	0.107416i
$627$	3.64156	+	1.00302i	0.145430	+	0.0400568i
$628$	4.51241	+	2.60524i	0.180065	+	0.103960i
$629$	−7.19280	+	7.19280i	−0.286796	+	0.286796i
$630$	−0.836507	−	3.30563i	−0.0333273	−	0.131699i
$631$	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
$633$	20.3632	−	5.30440i	0.809366	−	0.210831i
$634$	−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
$639$	−8.76571	+	30.9792i	−0.346766	+	1.22552i
$640$	−10.1878	−	17.6458i	−0.402710	−	0.697513i
$641$	5.71446	−	9.89773i	0.225707	−	0.390937i	−0.730824	−	0.682566i	$-0.760864\pi$
$641$	5.71446	−	9.89773i	0.225707	−	0.390937i	0.956531	+	0.291629i	$0.0941973\pi$
$642$	0.0231977	−	3.32646i	0.000915539	−	0.131285i
$643$	−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
$645$	0.251772	−	36.1032i	0.00991353	−	1.42156i
$646$	−11.0252	+	19.0961i	−0.433779	+	0.751327i
$647$	−12.9626	−	22.4519i	−0.509614	−	0.882677i	−0.999938	−	0.0111367i	$-0.996455\pi$
$647$	−12.9626	−	22.4519i	−0.509614	−	0.882677i	0.490324	−	0.871540i	$-0.336878\pi$
$648$	5.84054	−	19.5939i	0.229438	−	0.769721i
$649$		−	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	−0.271336	−	0.962485i	$-0.587466\pi$
$653$	10.8995	−	6.29284i	0.426531	−	0.246258i	0.697868	+	0.716227i	$0.254132\pi$
$654$	0.840305	−	0.218890i	0.0328585	−	0.00855927i
$655$	−25.2523	−	25.2523i	−0.986688	−	0.986688i
$656$	−0.903884	−	3.37334i	−0.0352907	−	0.131707i
$657$	12.2023	−	3.08786i	0.476058	−	0.120469i
$658$	−1.40189	+	1.40189i	−0.0546513	+	0.0546513i
$659$	−0.796513	−	0.459867i	−0.0310277	−	0.0179139i	0.484406	−	0.874843i	$-0.339036\pi$
$659$	−0.796513	−	0.459867i	−0.0310277	−	0.0179139i	−0.515434	+	0.856929i	$0.672369\pi$
$660$	−1.52075	−	0.418872i	−0.0591951	−	0.0163046i
$661$	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
$663$	24.8151	−	19.5268i	0.963738	−	0.758359i
$664$	5.14260			0.199572
$665$	12.0384	+	3.22567i	0.466828	+	0.125086i
$666$	−1.85691	−	3.32244i	−0.0719540	−	0.128742i
$667$	−54.6499	−	31.5521i	−2.11605	−	1.22170i
$668$	6.19541	−	6.19541i	0.239708	−	0.239708i
$669$	39.0695	+	22.9215i	1.51051	+	0.886197i
$670$	−3.60020	−	13.4361i	−0.139088	−	0.519083i
$671$	−0.532161	−	0.532161i	−0.0205438	−	0.0205438i
$672$	2.47163	+	9.48844i	0.0953453	+	0.366025i
$673$	−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	$-0.676367\pi$
$677$		−	44.2529i		−	1.70078i	0.526156	−	0.850388i	$-0.323633\pi$
$678$	−3.64022	+	2.06797i	−0.139802	+	0.0794200i
$679$	−4.20159	−	7.27736i	−0.161242	−	0.279280i
$680$	10.3513	−	17.9289i	0.396953	−	0.687542i
$681$	33.3159	+	0.232335i	1.27667	+	0.00890308i
$682$	−1.11614	+	0.299068i	−0.0427391	+	0.0114519i
$683$	−39.2468	+	10.5162i	−1.50174	+	0.402389i	−0.913682	−	0.406431i	$-0.866773\pi$
$683$	−39.2468	+	10.5162i	−1.50174	+	0.402389i	−0.588056	+	0.808820i	$0.700107\pi$
$684$	23.1740	+	23.8296i	0.886080	+	0.911148i
$685$	−9.13673	+	15.8253i	−0.349096	+	0.604653i
$686$	−0.315322	−	0.546154i	−0.0120391	−	0.0208522i
$687$	9.54586	+	16.8035i	0.364197	+	0.641092i
$688$			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
$693$	0.812656	+	0.484423i	0.0308703	+	0.0184017i
$694$	−3.45922	−	3.45922i	−0.131310	−	0.131310i
$695$	−1.31822	−	4.91966i	−0.0500029	−	0.186613i
$696$	−16.3691	+	27.9010i	−0.620471	+	1.05759i
$697$	7.04685	−	7.04685i	0.266918	−	0.266918i
$698$	9.35387	+	5.40046i	0.354049	+	0.204410i
$699$	−5.12980	+	18.6242i	−0.194027	+	0.704431i
$700$	2.71112	+	0.726441i	0.102471	+	0.0274569i
$701$	18.9716			0.716546			0.358273	−	0.933617i	$-0.383366\pi$
$701$	18.9716			0.716546			0.358273	+	0.933617i	$0.383366\pi$
$702$	4.50236	+	10.9236i	0.169931	+	0.412286i
$703$	13.9116			0.524685
$704$	−0.00799515	−	0.00214229i	−0.000301328	−	8.07407e-5i
$705$	2.60601	−	9.46135i	0.0981481	−	0.356335i
$706$	−13.9254	−	8.03982i	−0.524088	−	0.302583i
$707$	4.41855	−	4.41855i	0.166177	−	0.166177i
$708$	11.2019	−	19.0935i	0.420993	−	0.717578i
$709$	−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
$711$	9.09889	+	5.42384i	0.341235	+	0.203410i
$712$	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
$717$	5.25546	+	9.25112i	0.196269	+	0.345489i
$718$	1.46341	+	2.53471i	0.0546141	+	0.0945944i
$719$	−8.75094	+	15.1571i	−0.326355	+	0.565263i	−0.981786	−	0.189992i	$-0.939154\pi$
$719$	−8.75094	+	15.1571i	−0.326355	+	0.565263i	0.655431	+	0.755255i	$0.272487\pi$
$720$	−6.67930	−	6.86826i	−0.248923	−	0.255965i
$721$	−1.84510	+	0.494392i	−0.0687150	+	0.0184121i
$722$	17.5548	−	4.70378i	0.653321	−	0.175057i
$723$	−7.48737	−	0.0522146i	−0.278458	−	0.00194188i
$724$	2.49542	−	4.32219i	0.0927414	−	0.160633i
$725$	7.20050	+	12.4716i	0.267420	+	0.463184i
$726$	10.3528	−	5.88132i	0.384229	−	0.218276i
$727$		−	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
$732$	−1.66949	−	6.40906i	−0.0617061	−	0.236886i
$733$	−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
$735$	2.69250	+	1.57965i	0.0993143	+	0.0582663i
$736$	30.7259	−	30.7259i	1.13257	−	1.13257i
$737$	3.34240	+	1.92974i	0.123119	+	0.0710828i
$738$	1.81924	+	3.25502i	0.0669670	+	0.119819i
$739$	−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
$741$	−42.8807	−	5.11400i	−1.57526	−	0.187867i
$742$	−6.82468			−0.250542
$743$	−44.5817	−	11.9456i	−1.63554	−	0.438242i	−0.680028	−	0.733186i	$-0.738032\pi$
$743$	−44.5817	−	11.9456i	−1.63554	−	0.438242i	−0.955515	+	0.294944i	$0.904699\pi$
$744$	−22.0407	−	6.07083i	−0.808050	−	0.222567i
$745$	8.03002	+	4.63613i	0.294197	+	0.169855i
$746$	−3.04688	+	3.04688i	−0.111554	+	0.111554i
$747$	6.58359	−	1.66601i	0.240881	−	0.0609562i
$748$	0.661270	+	2.46790i	0.0241784	+	0.0902352i
$749$	2.15344	+	2.15344i	0.0786850	+	0.0786850i
$750$	12.8626	−	3.35057i	0.469677	−	0.122346i
$751$	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
$756$	4.01112	+	7.29580i	0.145883	+	0.265346i
$757$	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
$759$	0.0292382	−	4.19265i	0.00106128	−	0.152184i
$760$	−27.3483	+	7.32795i	−0.992027	+	0.265813i
$761$	−33.3602	+	8.93885i	−1.20931	+	0.324033i	−0.806490	−	0.591247i	$-0.798636\pi$
$761$	−33.3602	+	8.93885i	−1.20931	+	0.324033i	−0.402817	+	0.915280i	$0.631969\pi$
$762$	0.0530713	−	7.61022i	0.00192257	−	0.275689i
$763$	−0.397482	+	0.688460i	−0.0143898	+	0.0249239i
$764$	−5.27036	−	9.12852i	−0.190675	−	0.330258i
$765$	7.44345	−	26.3061i	0.269118	−	0.951101i
$766$			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
$771$	24.4850	−	6.37808i	0.881807	−	0.229701i
$772$	21.6010	+	21.6010i	0.777438	+	0.777438i
$773$	−0.986478	−	3.68159i	−0.0354811	−	0.132417i	0.945913	−	0.324419i	$-0.105169\pi$
$773$	−0.986478	−	3.68159i	−0.0354811	−	0.132417i	−0.981395	+	0.192002i	$0.938502\pi$
$774$	−5.36798	−	21.2127i	−0.192948	−	0.762474i
$775$	−7.19663	+	7.19663i	−0.258510	+	0.258510i
$776$	16.5324	+	9.54501i	0.593480	+	0.342646i
$777$	3.35939	+	0.925304i	0.120518	+	0.0331951i
$778$	6.43202	+	1.72345i	0.230599	+	0.0617889i
$779$	−13.6293			−0.488320
$780$	17.9074	+	2.13566i	0.641189	+	0.0764688i
$781$	3.38440			0.121104
$782$	23.6424	+	6.33496i	0.845450	+	0.226538i
$783$	−11.9170	+	41.0221i	−0.425878	+	1.46601i
$784$	−1.53451	−	0.885952i	−0.0548040	−	0.0316411i
$785$	−4.14428	+	4.14428i	−0.147916	+	0.147916i
$786$	−18.6681	−	10.9523i	−0.665871	−	0.390657i
$787$	−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
$789$	−8.13114	−	31.2150i	−0.289476	−	1.11128i
$790$	−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
$795$	29.3732	−	16.6866i	1.04176	−	0.591812i
$796$	−11.2780	−	19.5340i	−0.399737	−	0.692365i
$797$	−23.5774	+	40.8372i	−0.835153	+	1.44653i	0.0587526	+	0.998273i	$0.481288\pi$
$797$	−23.5774	+	40.8372i	−0.835153	+	1.44653i	−0.893906	+	0.448255i	$0.852046\pi$
$798$	7.55320	+	0.0526737i	0.267380	+	0.00186463i
$799$	−15.3540	+	4.11410i	−0.543186	+	0.145546i
$800$	−9.57851	+	2.56655i	−0.338651	+	0.0907414i
$801$	24.5469	−	23.8715i	0.867322	−	0.843460i
$802$	6.73359	−	11.6629i	0.237771	−	0.411832i
$803$	−0.661573	−	1.14588i	−0.0233464	−	0.0404372i
$804$	16.7765	+	29.5315i	0.591663	+	1.04150i
$805$		−	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	−0.814229	−	0.580543i	$-0.802840\pi$
$809$	−20.4385	+	11.8002i	−0.718579	+	0.414872i	0.0956507	+	0.995415i	$0.469507\pi$
$810$	8.71289	+	5.35984i	0.306140	+	0.188325i
$811$	−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
$813$	−7.80041	+	13.2957i	−0.273572	+	0.466301i
$814$	−0.282916	+	0.282916i	−0.00991620	+	0.00991620i
$815$	−22.1404	−	12.7827i	−0.775543	−	0.447760i
$816$	−4.12077	+	14.9608i	−0.144256	+	0.523733i
$817$	77.2518	+	20.6996i	2.70270	+	0.724186i
$818$	−5.22308			−0.182621
$819$	−10.0148	−	4.08708i	−0.349945	−	0.142814i
$820$	5.69173			0.198764
$821$	14.0330	+	3.76014i	0.489756	+	0.131230i	0.495242	−	0.868755i	$-0.335080\pi$
$821$	14.0330	+	3.76014i	0.489756	+	0.131230i	−0.00548586	+	0.999985i	$0.501746\pi$
$822$	−2.94092	+	10.6773i	−0.102576	+	0.372412i
$823$	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
$825$	−0.484180	+	0.825279i	−0.0168570	+	0.0287325i
$826$	−1.30196	−	4.85898i	−0.0453009	−	0.169065i
$827$	−35.3752	−	35.3752i	−1.23011	−	1.23011i	−0.963919	−	0.266196i	$-0.914233\pi$
$827$	−35.3752	−	35.3752i	−1.23011	−	1.23011i	−0.266196	−	0.963919i	$-0.585767\pi$
$828$	18.8924	−	31.6934i	0.656556	−	1.10142i
$829$	−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
$834$	−1.52472	−	2.68395i	−0.0527968	−	0.0929376i
$835$	4.92767	+	8.53497i	0.170529	+	0.295365i
$836$	1.74709	−	3.02605i	0.0604245	−	0.104658i
$837$	−30.1833	−	0.631549i	−1.04329	−	0.0218295i
$838$	6.23698	−	1.67119i	0.215453	−	0.0577304i
$839$	−21.2201	+	5.68592i	−0.732601	+	0.196300i	−0.605787	−	0.795627i	$-0.707142\pi$
$839$	−21.2201	+	5.68592i	−0.732601	+	0.196300i	−0.126814	+	0.991927i	$0.540475\pi$
$840$	−7.09153	−	0.0494541i	−0.244681	−	0.00170633i
$841$	19.2930	−	33.4165i	0.665277	−	1.15229i
$842$	−8.82609	−	15.2872i	−0.304167	−	0.526833i
$843$	−21.6306	+	12.2881i	−0.744996	+	0.423224i
$844$		−	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
$849$	8.10947	+	31.1318i	0.278316	+	1.06844i
$850$	−3.94972	−	3.94972i	−0.135474	−	0.135474i
$851$	−3.99674	−	14.9160i	−0.137006	−	0.511315i
$852$	25.6887	+	15.0712i	0.880082	+	0.516332i
$853$	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
$855$	−32.6375	+	18.2411i	−1.11618	+	0.623834i
$856$	−6.68273	−	1.79063i	−0.228411	−	0.0612026i
$857$	−5.40279			−0.184556			−0.0922778	−	0.995733i	$-0.529415\pi$
$857$	−5.40279			−0.184556			−0.0922778	+	0.995733i	$0.529415\pi$
$858$	0.976056	−	0.768052i	0.0333220	−	0.0262209i
$859$	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
$861$	−3.29123	−	0.906528i	−0.112165	−	0.0308944i
$862$	3.15941	+	1.82409i	0.107610	+	0.0621286i
$863$	1.63216	−	1.63216i	0.0555593	−	0.0555593i	−0.678781	−	0.734341i	$-0.737492\pi$
$863$	1.63216	−	1.63216i	0.0555593	−	0.0555593i	0.734341	+	0.678781i	$0.237492\pi$
$864$	−25.1611	−	15.2373i	−0.855998	−	0.518383i
$865$	9.15550	+	34.1688i	0.311296	+	1.16177i
$866$	4.12548	+	4.12548i	0.140190	+	0.140190i
$867$	−14.3581	+	3.74012i	−0.487626	+	0.127021i
$868$	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
$873$	24.2572	+	6.86368i	0.820981	+	0.232300i
$874$	−16.7371	−	28.9895i	−0.566142	−	0.980586i
$875$	−6.08431	+	10.5383i	−0.205687	+	0.356261i
$876$	0.0811993	−	11.6437i	0.00274347	−	0.393403i
$877$	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
$879$	0.322530	−	46.2495i	0.0108787	−	1.55996i
$880$	−0.503554	+	0.872180i	−0.0169748	+	0.0294012i
$881$	−3.83832	−	6.64817i	−0.129316	−	0.223983i	0.794096	−	0.607793i	$-0.207945\pi$
$881$	−3.83832	−	6.64817i	−0.129316	−	0.223983i	−0.923412	+	0.383810i	$0.874612\pi$
$882$	1.82046	+	0.515108i	0.0612980	+	0.0173446i
$883$		−	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	−0.0661237	−	0.997811i	$-0.521063\pi$
$887$	22.7820	−	13.1532i	0.764945	−	0.441641i	0.831068	+	0.556170i	$0.187730\pi$
$888$	−7.66032	+	1.99543i	−0.257063	+	0.0669621i
$889$	4.92661	+	4.92661i	0.165233	+	0.165233i
$890$	3.35756	+	12.5306i	0.112546	+	0.420027i
$891$	−2.76096	+	0.657845i	−0.0924958	+	0.0220386i
$892$	29.6302	−	29.6302i	0.992093	−	0.992093i
$893$	18.8266	+	10.8695i	0.630008	+	0.363735i
$894$	5.41782	+	1.49227i	0.181199	+	0.0499090i
$895$	−30.9594	−	8.29554i	−1.03486	−	0.277289i
$896$	11.3054			0.377686
$897$	6.83621	+	47.4461i	0.228255	+	1.58418i
$898$	21.5232			0.718237
$899$	46.1374	+	12.3625i	1.53877	+	0.412311i
$900$	−7.35017	+	4.10802i	−0.245006	+	0.136934i
$901$	−47.3873	−	27.3591i	−1.57870	−	0.911464i
$902$	0.277175	−	0.277175i	0.00922893	−	0.00922893i
$903$	17.2781	+	10.1368i	0.574981	+	0.337333i
$904$	2.25360	+	8.41055i	0.0749536	+	0.279731i
$905$	3.96958	+	3.96958i	0.131953	+	0.131953i
$906$	0.731866	+	2.80959i	0.0243146	+	0.0933423i
$907$	−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	$-0.983915\pi$
$911$		−	3.04911i		−	0.101021i	0.998724	−	0.0505107i	$-0.0160849\pi$
$912$	18.4528	−	10.4828i	0.611033	−	0.347122i
$913$	−0.356943	−	0.618243i	−0.0118131	−	0.0204609i
$914$	0.561930	−	0.973291i	0.0185870	−	0.0321936i
$915$	7.44948	+	0.0519504i	0.246272	+	0.00171743i
$916$	17.2686	−	4.62711i	0.570571	−	0.152884i
$917$	19.1396	−	5.12843i	0.632044	−	0.169356i
$918$	0.346613	−	16.5655i	0.0114399	−	0.546743i
$919$	−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
$921$	6.48474	+	11.4150i	0.213679	+	0.376137i
$922$		−	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
$927$	2.93421	−	4.92236i	0.0963723	−	0.161672i
$928$	32.9082	+	32.9082i	1.08026	+	1.08026i
$929$	7.55117	+	28.1813i	0.247746	+	0.924600i	0.971983	+	0.235049i	$0.0755252\pi$
$929$	7.55117	+	28.1813i	0.247746	+	0.924600i	−0.724238	+	0.689550i	$0.757808\pi$
$930$	5.78797	−	9.86552i	0.189795	−	0.323503i
$931$	−4.88969	+	4.88969i	−0.160253	+	0.160253i
$932$	15.4763	+	8.93524i	0.506943	+	0.292683i
$933$	3.17010	−	11.5093i	0.103784	−	0.376798i
$934$	1.28858	+	0.345275i	0.0421638	+	0.0112977i
$935$	−2.87388			−0.0939861
$936$	24.3455	−	3.33467i	0.795759	−	0.108997i
$937$	−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
$939$	7.57322	−	27.4952i	0.247143	−	0.897273i
$940$	−7.86218	−	4.53923i	−0.256436	−	0.148053i
$941$	−10.6348	+	10.6348i	−0.346685	+	0.346685i	−0.858873	−	0.512188i	$-0.828835\pi$
$941$	−10.6348	+	10.6348i	−0.346685	+	0.346685i	0.512188	+	0.858873i	$0.328835\pi$
$942$	−1.79745	+	3.06373i	−0.0585639	+	0.0998216i
$943$	3.91564	+	14.6134i	0.127511	+	0.475876i
$944$	−9.99405	−	9.99405i	−0.325279	−	0.325279i
$945$	−9.09464	+	2.23408i	−0.295849	+	0.0726747i
$946$	−1.99201	+	1.15009i	−0.0647659	+	0.0373926i
$947$	8.61168	−	32.1392i	0.279842	−	1.04438i	−0.672685	−	0.739929i	$-0.734859\pi$
$947$	8.61168	−	32.1392i	0.279842	−	1.04438i	0.952527	−	0.304455i	$-0.0984744\pi$
$948$	6.97725	−	6.88061i	0.226610	−	0.223472i
$949$	9.43752	+	11.8228i	0.306355	+	0.383784i
$950$			7.63914i			0.247847i
$951$	19.5486	+	34.4111i	0.633905	+	1.11586i
$952$	5.74336	+	9.94780i	0.186144	+	0.322410i
$953$	23.8115	−	41.2427i	0.771330	−	1.33598i	−0.165505	−	0.986209i	$-0.552925\pi$
$953$	23.8115	−	41.2427i	0.771330	−	1.33598i	0.936834	−	0.349773i	$-0.113741\pi$
$954$	14.6778	−	14.2740i	0.475213	−	0.462138i
$955$	11.4525	−	3.06869i	0.370594	−	0.0993004i
$956$	9.50721	−	2.54745i	0.307485	−	0.0823904i
$957$	4.49042	+	0.0313148i	0.145155	+	0.00101226i
$958$	−3.19696	+	5.53729i	−0.103289	+	0.178902i
$959$	−5.06948	−	8.78060i	−0.163702	−	0.283540i
$960$	0.0712405	−	0.0404710i	0.00229928	−	0.00130619i
$961$			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
$966$	−2.11353	−	8.11370i	−0.0680016	−	0.261054i
$967$	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
$969$	52.2347	+	30.6454i	1.67802	+	0.984471i
$970$	−6.75367	+	6.75367i	−0.216847	+	0.216847i
$971$	42.9034	+	24.7703i	1.37684	+	0.794916i	0.991777	−	0.127976i	$-0.0408480\pi$
$971$	42.9034	+	24.7703i	1.37684	+	0.794916i	0.385058	+	0.922892i	$0.374181\pi$
$972$	−23.8861	−	7.30170i	−0.766147	−	0.234202i
$973$	2.72966	+	0.731409i	0.0875088	+	0.0234479i
$974$	6.60079			0.211503
$975$	4.06275	−	10.1571i	0.130112	−	0.325286i
$976$	−4.22853			−0.135352
$977$	22.3621	+	5.99192i	0.715428	+	0.191698i	0.598131	−	0.801398i	$-0.295910\pi$
$977$	22.3621	+	5.99192i	0.715428	+	0.191698i	0.117297	+	0.993097i	$0.462577\pi$
$978$	−14.9380	−	4.11449i	−0.477665	−	0.131567i
$979$	−3.11714	−	1.79968i	−0.0996242	−	0.0575180i
$980$	2.04199	−	2.04199i	0.0652288	−	0.0652288i
$981$	−0.585068	−	2.31202i	−0.0186798	−	0.0738170i
$982$	4.08244	+	15.2359i	0.130276	+	0.486196i
$983$	38.9070	+	38.9070i	1.24094	+	1.24094i	0.959611	+	0.281330i	$0.0907754\pi$
$983$	38.9070	+	38.9070i	1.24094	+	1.24094i	0.281330	+	0.959611i	$0.409225\pi$
$984$	7.50488	−	1.95494i	0.239247	−	0.0623211i
$985$	−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
$990$	0.292775	−	1.03471i	0.00930499	−	0.0328851i
$991$	−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
$993$	0.231071	−	33.1347i	0.00733282	−	1.05150i
$994$	6.53735	−	1.75168i	0.207352	−	0.0555598i
$995$	24.5071	−	6.56664i	0.776926	−	0.208177i
$996$	0.0438100	−	6.28218i	0.00138817	−	0.199059i
$997$	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
$999$	−9.16035	+	5.03622i	−0.289821	+	0.159339i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.609155 + 0.163223i) q^{2} +(0.459944 - 1.66987i) q^{3} +(-1.38762 - 0.801144i) q^{4} +(1.27442 - 1.27442i) q^{5} +(0.552737 - 0.942134i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-1.60638 - 1.60638i) q^{8} +(-2.57690 - 1.53609i) q^{9} +O(q^{10})\)	\(q+(0.609155 + 0.163223i) q^{2} +(0.459944 - 1.66987i) q^{3} +(-1.38762 - 0.801144i) q^{4} +(1.27442 - 1.27442i) q^{5} +(0.552737 - 0.942134i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-1.60638 - 1.60638i) q^{8} +(-2.57690 - 1.53609i) 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} +(-1.54195 - 2.71427i) q^{15} +(0.885952 + 1.53451i) q^{16} +(-2.52815 + 4.37889i) q^{17} +(-1.31901 - 1.35633i) q^{18} +(6.67945 - 1.78975i) q^{19} +(-2.78940 + 0.747418i) q^{20} +(1.73201 + 0.0120785i) q^{21} +(-0.0994404 + 0.172236i) q^{22} +(-3.83795 - 6.64753i) q^{23} +(-3.42128 + 1.94359i) 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} +(-0.496255 - 1.90509i) q^{30} +(4.10833 + 4.10833i) q^{31} +(1.46517 + 5.46807i) q^{32} +(0.471126 + 0.276403i) q^{33} +(-2.25477 + 2.25477i) q^{34} +(1.56084 + 0.901150i) q^{35} +(2.34514 + 4.19598i) q^{36} +(1.94323 + 0.520686i) q^{37} +4.36095 q^{38} +(-5.79835 - 2.31930i) q^{39} -4.09440 q^{40} +(-1.90379 - 0.510120i) q^{41} +(1.05309 + 0.290061i) q^{42} +(10.0161 + 5.78280i) q^{43} +(0.357301 - 0.357301i) q^{44} +(-5.24167 + 1.32643i) q^{45} +(-1.25288 - 4.67582i) q^{46} +(2.22295 + 2.22295i) q^{47} +(2.96992 - 0.773630i) 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} +(-2.87155 + 1.57874i) q^{54} +(0.284188 + 0.492228i) q^{55} +(1.13588 - 1.96740i) q^{56} +(0.0835236 - 11.9770i) q^{57} +(5.00791 - 1.34187i) q^{58} +(-7.70478 + 2.06449i) q^{59} +(-0.0348803 + 5.00170i) q^{60} +(-1.19322 + 2.06671i) q^{61} +(1.83204 + 3.17318i) q^{62} +(0.816796 - 2.88667i) 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} +(-12.8657 + 3.35138i) q^{69} +(0.803704 + 0.803704i) q^{70} +(-2.77760 - 10.3661i) q^{71} +(1.67194 + 6.60702i) q^{72} +(-2.96677 + 2.96677i) q^{73} +(1.09874 + 0.634357i) q^{74} +(2.92513 + 0.805691i) q^{75} +(-10.7024 - 2.86770i) q^{76} -0.315362 q^{77} +(-3.15353 - 2.35923i) q^{78} -3.53094 q^{79} +(3.08468 + 0.826539i) q^{80} +(4.28086 + 7.91670i) q^{81} +(-1.07644 - 0.621485i) q^{82} +(-1.60068 + 1.60068i) q^{83} +(-2.39370 - 1.40435i) q^{84} +(2.35861 + 8.80247i) q^{85} +(5.15748 + 5.15748i) q^{86} +(-3.58940 - 13.7795i) 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} +(8.74996 - 4.97076i) q^{93} +(0.991286 + 1.71696i) q^{94} +(6.23151 - 10.7933i) q^{95} +(9.80484 + 0.0683759i) q^{96} +(-8.11684 + 2.17490i) q^{97} +(-0.609155 + 0.163223i) q^{98} +(0.678248 - 0.659588i) 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

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Database

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