LMFDB - Embedded newform 504.2.y.a.173.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(173,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1, 5]))

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

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

chi := DirichletCharacter("504.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.y (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			173.15
Character	$\chi$	$=$	504.173
Dual form			504.2.y.a.437.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26678 - 0.628698i) q^{2} +(1.22962 + 1.21985i) q^{3} +(1.20948 + 1.59285i) q^{4} -1.38607i q^{5} +(-0.790746 - 2.31834i) q^{6} +(1.97507 - 1.76042i) q^{7} +(-0.530723 - 2.77819i) q^{8} +(0.0239358 + 2.99990i) q^{9} +O(q^{10})$	\(q+(-1.26678 - 0.628698i) q^{2} +(1.22962 + 1.21985i) q^{3} +(1.20948 + 1.59285i) q^{4} -1.38607i q^{5} +(-0.790746 - 2.31834i) q^{6} +(1.97507 - 1.76042i) q^{7} +(-0.530723 - 2.77819i) q^{8} +(0.0239358 + 2.99990i) q^{9} +(-0.871418 + 1.75585i) q^{10} +5.20313 q^{11} +(-0.455837 + 3.43398i) q^{12} +(-0.870678 - 1.50806i) q^{13} +(-3.60876 + 0.988348i) q^{14} +(1.69079 - 1.70434i) q^{15} +(-1.07433 + 3.85303i) q^{16} +(-3.22355 - 5.58335i) q^{17} +(1.85571 - 3.81528i) q^{18} +(-2.71587 + 4.70403i) q^{19} +(2.20780 - 1.67642i) q^{20} +(4.57604 + 0.244638i) q^{21} +(-6.59123 - 3.27120i) q^{22} -7.99985i q^{23} +(2.73638 - 4.06352i) q^{24} +3.07882 q^{25} +(0.154846 + 2.45778i) q^{26} +(-3.63000 + 3.71794i) q^{27} +(5.19289 + 1.01680i) q^{28} +(-1.60874 + 2.78642i) q^{29} +(-3.21338 + 1.09603i) q^{30} +(4.05580 + 2.34162i) q^{31} +(3.78334 - 4.20552i) q^{32} +(6.39787 + 6.34703i) q^{33} +(0.573292 + 9.09952i) q^{34} +(-2.44006 - 2.73758i) q^{35} +(-4.74944 + 3.66644i) q^{36} +(3.76378 + 2.17302i) q^{37} +(6.39783 - 4.25152i) q^{38} +(0.769000 - 2.91644i) q^{39} +(-3.85076 + 0.735618i) q^{40} +(3.48168 + 6.03045i) q^{41} +(-5.64305 - 3.18685i) q^{42} +(3.34096 + 1.92891i) q^{43} +(6.29306 + 8.28779i) q^{44} +(4.15807 - 0.0331766i) q^{45} +(-5.02949 + 10.1341i) q^{46} +(-2.56361 - 4.44031i) q^{47} +(-6.02113 + 3.42724i) q^{48} +(0.801824 - 6.95393i) q^{49} +(-3.90019 - 1.93565i) q^{50} +(2.84710 - 10.7976i) q^{51} +(1.34904 - 3.21082i) q^{52} +(4.69481 + 8.13166i) q^{53} +(6.93589 - 2.42765i) q^{54} -7.21188i q^{55} +(-5.93900 - 4.55283i) q^{56} +(-9.07769 + 2.47122i) q^{57} +(3.78974 - 2.51838i) q^{58} +(-0.218244 - 0.126003i) q^{59} +(4.75973 + 0.631820i) q^{60} +(1.37228 + 2.37687i) q^{61} +(-3.66565 - 5.51620i) q^{62} +(5.32838 + 5.88289i) q^{63} +(-7.43667 + 2.94890i) q^{64} +(-2.09027 + 1.20682i) q^{65} +(-4.11435 - 12.0626i) q^{66} +(-2.68973 - 1.55292i) q^{67} +(4.99462 - 11.8875i) q^{68} +(9.75861 - 9.83679i) q^{69} +(1.36992 + 5.00199i) q^{70} +4.12297i q^{71} +(8.32160 - 1.65862i) q^{72} +(0.167502 - 0.0967074i) q^{73} +(-3.40172 - 5.11902i) q^{74} +(3.78578 + 3.75569i) q^{75} +(-10.7776 + 1.36344i) q^{76} +(10.2766 - 9.15970i) q^{77} +(-2.80772 + 3.21102i) q^{78} +(-7.77890 - 13.4735i) q^{79} +(5.34055 + 1.48910i) q^{80} +(-8.99885 + 0.143610i) q^{81} +(-0.619201 - 9.82820i) q^{82} +(-9.02192 - 5.20881i) q^{83} +(5.14494 + 7.58482i) q^{84} +(-7.73889 + 4.46805i) q^{85} +(-3.01957 - 4.54396i) q^{86} +(-5.37716 + 1.46382i) q^{87} +(-2.76142 - 14.4553i) q^{88} +(-6.20023 + 10.7391i) q^{89} +(-5.28823 - 2.57214i) q^{90} +(-4.37447 - 1.44576i) q^{91} +(12.7426 - 9.67564i) q^{92} +(2.13068 + 7.82677i) q^{93} +(0.455926 + 7.23664i) q^{94} +(6.52010 + 3.76438i) q^{95} +(9.78217 - 0.556093i) q^{96} +(-3.76021 - 2.17096i) q^{97} +(-5.38766 + 8.30501i) q^{98} +(0.124541 + 15.6089i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) $ 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9	$ 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9} - 6 q^{10} - 3 q^{12} - 3 q^{14} - 2 q^{15} + q^{16} - 15 q^{18} - 6 q^{22} - 12 q^{24} - 156 q^{25} + 6 q^{26} - 8 q^{28} - 14 q^{30} - 6 q^{31} - 33 q^{32} - 6 q^{33} - 6 q^{34} + 22 q^{36} - 66 q^{38} + 10 q^{39} - 15 q^{42} + 9 q^{44} + 2 q^{46} - 6 q^{47} - 9 q^{48} - 2 q^{49} + 9 q^{50} + 24 q^{54} + 60 q^{56} + 4 q^{57} + 6 q^{58} + 34 q^{60} - 12 q^{62} - 30 q^{63} - 8 q^{64} - 6 q^{65} - 21 q^{66} - 36 q^{68} + 30 q^{70} + 9 q^{72} - 12 q^{73} - 12 q^{76} + 19 q^{78} + 2 q^{79} + 57 q^{80} + 6 q^{81} + 9 q^{84} + 12 q^{87} - 18 q^{88} + 24 q^{89} + 75 q^{90} - 36 q^{92} - 3 q^{94} + 54 q^{95} - 54 q^{96} + 45 q^{98}+O(q^{100}) $ 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9 - 6 * q^10 - 3 * q^12 - 3 * q^14 - 2 * q^15 + q^16 - 15 * q^18 - 6 * q^22 - 12 * q^24 - 156 * q^25 + 6 * q^26 - 8 * q^28 - 14 * q^30 - 6 * q^31 - 33 * q^32 - 6 * q^33 - 6 * q^34 + 22 * q^36 - 66 * q^38 + 10 * q^39 - 15 * q^42 + 9 * q^44 + 2 * q^46 - 6 * q^47 - 9 * q^48 - 2 * q^49 + 9 * q^50 + 24 * q^54 + 60 * q^56 + 4 * q^57 + 6 * q^58 + 34 * q^60 - 12 * q^62 - 30 * q^63 - 8 * q^64 - 6 * q^65 - 21 * q^66 - 36 * q^68 + 30 * q^70 + 9 * q^72 - 12 * q^73 - 12 * q^76 + 19 * q^78 + 2 * q^79 + 57 * q^80 + 6 * q^81 + 9 * q^84 + 12 * q^87 - 18 * q^88 + 24 * q^89 + 75 * q^90 - 36 * q^92 - 3 * q^94 + 54 * q^95 - 54 * q^96 + 45 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.26678	−	0.628698i	−0.895751	−	0.444557i
$2$	−1.26678	−	0.628698i	−0.895751	−	0.444557i
$3$	1.22962	+	1.21985i	0.709922	+	0.704280i
$3$	1.22962	+	1.21985i	0.709922	+	0.704280i
$4$	1.20948	+	1.59285i	0.604738	+	0.796424i
$5$		−	1.38607i		−	0.619868i	−0.950758	−	0.309934i	$-0.899693\pi$
$5$		−	1.38607i		−	0.619868i	0.950758	−	0.309934i	$-0.100307\pi$
$6$	−0.790746	−	2.31834i	−0.322821	−	0.946460i
$7$	1.97507	−	1.76042i	0.746507	−	0.665377i
$7$	1.97507	−	1.76042i	0.746507	−	0.665377i
$8$	−0.530723	−	2.77819i	−0.187639	−	0.982238i
$9$	0.0239358	+	2.99990i	0.00797860	+	0.999968i
$10$	−0.871418	+	1.75585i	−0.275567	+	0.555247i
$11$	5.20313			1.56880			0.784401	−	0.620254i	$-0.212971\pi$
$11$	5.20313			1.56880			0.784401	+	0.620254i	$0.212971\pi$
$12$	−0.455837	+	3.43398i	−0.131589	+	0.991304i
$13$	−0.870678	−	1.50806i	−0.241483	−	0.418260i	0.719654	−	0.694333i	$-0.244300\pi$
$13$	−0.870678	−	1.50806i	−0.241483	−	0.418260i	−0.961137	+	0.276072i	$0.910967\pi$
$14$	−3.60876	+	0.988348i	−0.964482	+	0.264147i
$15$	1.69079	−	1.70434i	0.436561	−	0.440058i
$16$	−1.07433	+	3.85303i	−0.268583	+	0.963257i
$17$	−3.22355	−	5.58335i	−0.781825	−	1.35416i	−0.930878	−	0.365331i	$-0.880956\pi$
$17$	−3.22355	−	5.58335i	−0.781825	−	1.35416i	0.149053	−	0.988829i	$-0.452378\pi$
$18$	1.85571	−	3.81528i	0.437396	−	0.899269i
$19$	−2.71587	+	4.70403i	−0.623064	+	1.07918i	0.365848	+	0.930674i	$0.380779\pi$
$19$	−2.71587	+	4.70403i	−0.623064	+	1.07918i	−0.988912	+	0.148503i	$0.952554\pi$
$20$	2.20780	−	1.67642i	0.493678	−	0.374858i
$21$	4.57604	+	0.244638i	0.998574	+	0.0533844i
$22$	−6.59123	−	3.27120i	−1.40526	−	0.697422i
$23$		−	7.99985i		−	1.66808i	−0.551701	−	0.834042i	$-0.686021\pi$
$23$		−	7.99985i		−	1.66808i	0.551701	−	0.834042i	$-0.313979\pi$
$24$	2.73638	−	4.06352i	0.558562	−	0.829463i
$25$	3.07882			0.615763
$26$	0.154846	+	2.45778i	0.0303678	+	0.482010i
$27$	−3.63000	+	3.71794i	−0.698594	+	0.715519i
$28$	5.19289	+	1.01680i	0.981364	+	0.192157i
$29$	−1.60874	+	2.78642i	−0.298736	+	0.517425i	−0.975847	−	0.218455i	$-0.929898\pi$
$29$	−1.60874	+	2.78642i	−0.298736	+	0.517425i	0.677111	+	0.735881i	$0.263232\pi$
$30$	−3.21338	+	1.09603i	−0.586681	+	0.200106i
$31$	4.05580	+	2.34162i	0.728444	+	0.420567i	0.817853	−	0.575428i	$-0.195164\pi$
$31$	4.05580	+	2.34162i	0.728444	+	0.420567i	−0.0894089	+	0.995995i	$0.528498\pi$
$32$	3.78334	−	4.20552i	0.668806	−	0.743437i
$33$	6.39787	+	6.34703i	1.11373	+	1.10488i
$34$	0.573292	+	9.09952i	0.0983188	+	1.56056i
$35$	−2.44006	−	2.73758i	−0.412446	−	0.462736i
$36$	−4.74944	+	3.66644i	−0.791574	+	0.611074i
$37$	3.76378	+	2.17302i	0.618761	+	0.357242i	0.776387	−	0.630257i	$-0.217050\pi$
$37$	3.76378	+	2.17302i	0.618761	+	0.357242i	−0.157625	+	0.987499i	$0.550384\pi$
$38$	6.39783	−	4.25152i	1.03787	−	0.689687i
$39$	0.769000	−	2.91644i	0.123139	−	0.467004i
$40$	−3.85076	+	0.735618i	−0.608858	+	0.116311i
$41$	3.48168	+	6.03045i	0.543748	+	0.941798i	0.998685	+	0.0512748i	$0.0163284\pi$
$41$	3.48168	+	6.03045i	0.543748	+	0.941798i	−0.454937	+	0.890524i	$0.650338\pi$
$42$	−5.64305	−	3.18685i	−0.870741	−	0.491742i
$43$	3.34096	+	1.92891i	0.509492	+	0.294155i	0.732625	−	0.680633i	$-0.238295\pi$
$43$	3.34096	+	1.92891i	0.509492	+	0.294155i	−0.223133	+	0.974788i	$0.571628\pi$
$44$	6.29306	+	8.28779i	0.948715	+	1.24943i
$45$	4.15807	−	0.0331766i	0.619848	−	0.00494568i
$46$	−5.02949	+	10.1341i	−0.741558	+	1.49419i
$47$	−2.56361	−	4.44031i	−0.373941	−	0.647685i	0.616227	−	0.787569i	$-0.288660\pi$
$47$	−2.56361	−	4.44031i	−0.373941	−	0.647685i	−0.990168	+	0.139884i	$0.955327\pi$
$48$	−6.02113	+	3.42724i	−0.869076	+	0.494679i
$49$	0.801824	−	6.95393i	0.114546	−	0.993418i
$50$	−3.90019	−	1.93565i	−0.551570	−	0.273742i
$51$	2.84710	−	10.7976i	0.398674	−	1.51197i
$52$	1.34904	−	3.21082i	0.187079	−	0.445261i
$53$	4.69481	+	8.13166i	0.644882	+	1.11697i	0.984329	+	0.176344i	$0.0564270\pi$
$53$	4.69481	+	8.13166i	0.644882	+	1.11697i	−0.339446	+	0.940625i	$0.610240\pi$
$54$	6.93589	−	2.42765i	0.943854	−	0.330362i
$55$		−	7.21188i		−	0.972450i
$56$	−5.93900	−	4.55283i	−0.793633	−	0.608397i
$57$	−9.07769	+	2.47122i	−1.20237	+	0.327321i
$58$	3.78974	−	2.51838i	0.497618	−	0.330679i
$59$	−0.218244	−	0.126003i	−0.0284129	−	0.0164042i	0.485726	−	0.874111i	$-0.338555\pi$
$59$	−0.218244	−	0.126003i	−0.0284129	−	0.0164042i	−0.514139	+	0.857707i	$0.671889\pi$
$60$	4.75973	+	0.631820i	0.614478	+	0.0815676i
$61$	1.37228	+	2.37687i	0.175703	+	0.304326i	0.940404	−	0.340058i	$-0.110447\pi$
$61$	1.37228	+	2.37687i	0.175703	+	0.304326i	−0.764701	+	0.644385i	$0.777114\pi$
$62$	−3.66565	−	5.51620i	−0.465538	−	0.700558i
$63$	5.32838	+	5.88289i	0.671312	+	0.741175i
$64$	−7.43667	+	2.94890i	−0.929583	+	0.368612i
$65$	−2.09027	+	1.20682i	−0.259266	+	0.149687i
$66$	−4.11435	−	12.0626i	−0.506441	−	1.48481i
$67$	−2.68973	−	1.55292i	−0.328603	−	0.189719i	0.326618	−	0.945157i	$-0.394091\pi$
$67$	−2.68973	−	1.55292i	−0.328603	−	0.189719i	−0.655221	+	0.755437i	$0.727424\pi$
$68$	4.99462	−	11.8875i	0.605686	−	1.44158i
$69$	9.75861	−	9.83679i	1.17480	−	1.18421i
$70$	1.36992	+	5.00199i	0.163736	+	0.597852i
$71$			4.12297i			0.489306i	0.969611	+	0.244653i	$0.0786741\pi$
$71$			4.12297i			0.489306i	−0.969611	+	0.244653i	$0.921326\pi$
$72$	8.32160	−	1.65862i	0.980710	−	0.195470i
$73$	0.167502	−	0.0967074i	0.0196046	−	0.0113187i	−0.490166	−	0.871629i	$-0.663064\pi$
$73$	0.167502	−	0.0967074i	0.0196046	−	0.0113187i	0.509770	+	0.860311i	$0.329730\pi$
$74$	−3.40172	−	5.11902i	−0.395441	−	0.595074i
$75$	3.78578	+	3.75569i	0.437144	+	0.433670i
$76$	−10.7776	+	1.36344i	−1.23627	+	0.156397i
$77$	10.2766	−	9.15970i	1.17112	−	1.04384i
$78$	−2.80772	+	3.21102i	−0.317911	+	0.363577i
$79$	−7.77890	−	13.4735i	−0.875195	−	1.51588i	−0.856555	−	0.516056i	$-0.827400\pi$
$79$	−7.77890	−	13.4735i	−0.875195	−	1.51588i	−0.0186403	−	0.999826i	$-0.505934\pi$
$80$	5.34055	+	1.48910i	0.597092	+	0.166486i
$81$	−8.99885	+	0.143610i	−0.999873	+	0.0159567i
$82$	−0.619201	−	9.82820i	−0.0683793	−	1.08534i
$83$	−9.02192	−	5.20881i	−0.990285	−	0.571741i	−0.0849254	−	0.996387i	$-0.527065\pi$
$83$	−9.02192	−	5.20881i	−0.990285	−	0.571741i	−0.905359	+	0.424646i	$0.860399\pi$
$84$	5.14494	+	7.58482i	0.561359	+	0.827572i
$85$	−7.73889	+	4.46805i	−0.839401	+	0.484628i
$86$	−3.01957	−	4.54396i	−0.325609	−	0.489988i
$87$	−5.37716	+	1.46382i	−0.576492	+	0.156938i
$88$	−2.76142	−	14.4553i	−0.294368	−	1.54094i
$89$	−6.20023	+	10.7391i	−0.657224	+	1.13834i	0.324108	+	0.946020i	$0.394936\pi$
$89$	−6.20023	+	10.7391i	−0.657224	+	1.13834i	−0.981331	+	0.192324i	$0.938397\pi$
$90$	−5.28823	−	2.57214i	−0.557428	−	0.271128i
$91$	−4.37447	−	1.44576i	−0.458569	−	0.151557i
$92$	12.7426	−	9.67564i	1.32850	−	1.00875i
$93$	2.13068	+	7.82677i	0.220941	+	0.811598i
$94$	0.455926	+	7.23664i	0.0470252	+	0.746402i
$95$	6.52010	+	3.76438i	0.668948	+	0.386217i
$96$	9.78217	−	0.556093i	0.998388	−	0.0567560i
$97$	−3.76021	−	2.17096i	−0.381791	−	0.220427i	0.296806	−	0.954938i	$-0.404078\pi$
$97$	−3.76021	−	2.17096i	−0.381791	−	0.220427i	−0.678597	+	0.734511i	$0.737412\pi$
$98$	−5.38766	+	8.30501i	−0.544236	+	0.838932i
$99$	0.124541	+	15.6089i	0.0125168	+	1.56875i
$100$	3.72376	+	4.90409i	0.372376	+	0.490409i
$101$		−	0.644801i		−	0.0641601i	−0.999485	−	0.0320800i	$-0.989787\pi$
$101$		−	0.644801i		−	0.0641601i	0.999485	−	0.0320800i	$-0.0102131\pi$
$102$	−10.3951	+	11.8883i	−1.02927	+	1.17712i
$103$			16.5592i			1.63162i	0.578318	+	0.815811i	$0.303709\pi$
$103$			16.5592i			1.63162i	−0.578318	+	0.815811i	$0.696291\pi$
$104$	−3.72758	+	3.21927i	−0.365520	+	0.315675i
$105$	0.339085	−	6.34270i	0.0330913	−	0.618984i
$106$	−0.834951	−	13.2527i	−0.0810976	−	1.28721i
$107$	−8.15654	+	14.1275i	−0.788523	+	1.36576i	0.138349	+	0.990383i	$0.455820\pi$
$107$	−8.15654	+	14.1275i	−0.788523	+	1.36576i	−0.926872	+	0.375378i	$0.877513\pi$
$108$	−10.3125	−	1.28527i	−0.992323	−	0.123675i
$109$	6.27766	−	3.62441i	0.601291	−	0.347155i	−0.168258	−	0.985743i	$-0.553814\pi$
$109$	6.27766	−	3.62441i	0.601291	−	0.347155i	0.769549	+	0.638588i	$0.220481\pi$
$110$	−4.53410	+	9.13589i	−0.432309	+	0.871073i
$111$	1.97727	+	7.26323i	0.187674	+	0.689395i
$112$	4.66107	+	9.50128i	0.440430	+	0.897787i
$113$	−1.93433	+	1.11679i	−0.181966	+	0.105058i	−0.588216	−	0.808704i	$-0.700170\pi$
$113$	−1.93433	+	1.11679i	−0.181966	+	0.105058i	0.406250	+	0.913762i	$0.366836\pi$
$114$	13.0531	+	2.57664i	1.22254	+	0.241324i
$115$	−11.0883			−1.03399
$116$	−6.38408	+	0.807631i	−0.592747	+	0.0749867i
$117$	4.50319	−	2.64805i	0.416320	−	0.244812i
$118$	0.197250	+	0.296828i	0.0181583	+	0.0273253i
$119$	−16.1958	−	5.35271i	−1.48467	−	0.490682i
$120$	−5.63232	−	3.79281i	−0.514158	−	0.346235i
$121$	16.0725			1.46114
$122$	−0.244054	−	3.87372i	−0.0220956	−	0.350711i
$123$	−3.07509	+	11.6623i	−0.277272	+	1.05155i
$124$	1.17556	+	9.29241i	0.105568	+	0.834483i
$125$		−	11.1978i		−	1.00156i
$126$	−3.05133	−	10.8023i	−0.271834	−	0.962344i
$127$	−8.94093			−0.793379			−0.396690	−	0.917953i	$-0.629841\pi$
$127$	−8.94093			−0.793379			−0.396690	+	0.917953i	$0.629841\pi$
$128$	11.2746	+	0.939805i	0.996544	+	0.0830678i
$129$	1.75514	+	6.44729i	0.154532	+	0.567652i
$130$	3.40664	−	0.214627i	0.298782	−	0.0188240i
$131$		−	11.9865i		−	1.04727i	−0.851944	−	0.523633i	$-0.824576\pi$
$131$		−	11.9865i		−	1.04727i	0.851944	−	0.523633i	$-0.175424\pi$
$132$	−2.37178	+	17.8674i	−0.206437	+	1.55516i
$133$	2.91703	+	14.0719i	0.252939	+	1.22019i
$134$	2.43099	+	3.65824i	0.210006	+	0.316024i
$135$	5.15332	+	5.03142i	0.443527	+	0.433036i
$136$	−13.8008	+	11.9188i	−1.18341	+	1.02203i
$137$			18.6348i			1.59208i	0.605242	+	0.796041i	$0.293076\pi$
$137$			18.6348i			1.59208i	−0.605242	+	0.796041i	$0.706924\pi$
$138$	−18.5464	+	6.32585i	−1.57878	+	0.538492i
$139$	−4.09328	−	7.08978i	−0.347188	−	0.601347i	0.638561	−	0.769571i	$-0.279530\pi$
$139$	−4.09328	−	7.08978i	−0.347188	−	0.601347i	−0.985749	+	0.168224i	$0.946197\pi$
$140$	1.40935	−	7.19770i	0.119112	−	0.608316i
$141$	2.26423	−	8.58711i	0.190683	−	0.723165i
$142$	2.59210	−	5.22290i	0.217524	−	0.438296i
$143$	−4.53025	−	7.84662i	−0.378838	−	0.656167i
$144$	−11.5844	−	3.13067i	−0.965369	−	0.260889i
$145$	3.86217	+	2.22982i	0.320736	+	0.185177i
$146$	−0.272989	+	0.0171990i	−0.0225927	+	0.00142340i
$147$	9.46868	−	7.57259i	0.780964	−	0.624577i
$148$	1.09091	+	8.62334i	0.0896726	+	0.708834i
$149$	−12.6877			−1.03942			−0.519710	−	0.854343i	$-0.673960\pi$
$149$	−12.6877			−1.03942			−0.519710	+	0.854343i	$0.673960\pi$
$150$	−2.43456	−	7.13776i	−0.198781	−	0.582796i
$151$	−14.1866			−1.15449			−0.577246	−	0.816570i	$-0.695873\pi$
$151$	−14.1866			−1.15449			−0.577246	+	0.816570i	$0.695873\pi$
$152$	14.5100	+	5.04867i	1.17692	+	0.409501i
$153$	16.6723	−	9.80397i	1.34788	−	0.792604i
$154$	−18.7768	+	5.14250i	−1.51308	+	0.414395i
$155$	3.24564	−	5.62162i	0.260696	−	0.451539i
$156$	5.57553	−	2.30246i	0.446400	−	0.184345i
$157$	−3.88033	+	6.72093i	−0.309684	+	0.536389i	−0.978293	−	0.207225i	$-0.933557\pi$
$157$	−3.88033	+	6.72093i	−0.309684	+	0.536389i	0.668609	+	0.743614i	$0.266890\pi$
$158$	1.38344	+	21.9585i	0.110061	+	1.74693i
$159$	−4.14655	+	15.7258i	−0.328843	+	1.24714i
$160$	−5.82913	−	5.24396i	−0.460833	−	0.414571i
$161$	−14.0831	−	15.8003i	−1.10991	−	1.24524i
$162$	11.4899	+	5.47564i	0.902730	+	0.430207i
$163$	−4.22665	−	2.44026i	−0.331057	−	0.191136i	0.325254	−	0.945627i	$-0.394550\pi$
$163$	−4.22665	−	2.44026i	−0.331057	−	0.191136i	−0.656310	+	0.754491i	$0.727884\pi$
$164$	−5.39458	+	12.8395i	−0.421246	+	1.00260i
$165$	8.79741	−	8.86788i	0.684878	−	0.690364i
$166$	8.15405	+	12.2705i	0.632877	+	0.952376i
$167$	−6.03358	−	10.4505i	−0.466893	−	0.808682i	0.532392	−	0.846498i	$-0.321293\pi$
$167$	−6.03358	−	10.4505i	−0.466893	−	0.808682i	−0.999285	+	0.0378160i	$0.987960\pi$
$168$	−1.74896	−	12.8429i	−0.134935	−	0.990854i
$169$	4.98384	−	8.63226i	0.383372	−	0.664020i
$170$	12.6126	−	0.794622i	0.967339	−	0.0609447i
$171$	−14.1766	−	8.03476i	−1.08411	−	0.614433i
$172$	0.968362	+	7.65461i	0.0738369	+	0.583659i
$173$	−12.2413	+	7.06753i	−0.930691	+	0.537335i	−0.887030	−	0.461712i	$-0.847235\pi$
$173$	−12.2413	+	7.06753i	−0.930691	+	0.537335i	−0.0436609	+	0.999046i	$0.513902\pi$
$174$	7.73199	+	1.52627i	0.586161	+	0.115706i
$175$	6.08089	−	5.42002i	0.459672	−	0.409715i
$176$	−5.58988	+	20.0478i	−0.421353	+	1.51116i
$177$	−0.114652	−	0.421161i	−0.00861781	−	0.0316564i
$178$	14.6060	−	9.70606i	1.09477	−	0.727500i
$179$	7.76339	+	13.4466i	0.580263	+	1.00504i	0.995448	+	0.0953076i	$0.0303835\pi$
$179$	7.76339	+	13.4466i	0.580263	+	1.00504i	−0.415185	+	0.909737i	$0.636283\pi$
$180$	5.08193	+	6.58305i	0.378785	+	0.490671i
$181$	−8.47380			−0.629853			−0.314926	−	0.949116i	$-0.601980\pi$
$181$	−8.47380			−0.629853			−0.314926	+	0.949116i	$0.601980\pi$
$182$	4.63256	+	4.58169i	0.343388	+	0.339618i
$183$	−1.21203	+	4.59662i	−0.0895957	+	0.339792i
$184$	−22.2251	+	4.24571i	−1.63846	+	0.312998i
$185$	3.01195	−	5.21685i	0.221443	−	0.383550i
$186$	2.22157	−	11.2544i	0.162894	−	0.825211i
$187$	−16.7725	−	29.0509i	−1.22653	−	2.12441i
$188$	3.97210	−	9.45389i	0.289695	−	0.689496i
$189$	−0.624359	+	13.7335i	−0.0454154	+	0.998968i
$190$	−5.89289	−	8.86783i	−0.427515	−	0.643340i
$191$	4.20800	−	2.42949i	0.304481	−	0.175792i	−0.339973	−	0.940435i	$-0.610418\pi$
$191$	4.20800	−	2.42949i	0.304481	−	0.175792i	0.644454	+	0.764643i	$0.277085\pi$
$192$	−12.7415	−	5.44558i	−0.919538	−	0.393001i
$193$	3.53742	−	6.12699i	0.254629	−	0.441030i	−0.710166	−	0.704034i	$-0.751380\pi$
$193$	3.53742	−	6.12699i	0.254629	−	0.441030i	0.964795	+	0.263004i	$0.0847134\pi$
$194$	3.39849	+	5.11417i	0.243997	+	0.367176i
$195$	−4.04238	−	1.06589i	−0.289481	−	0.0763297i
$196$	12.0463	−	7.13343i	0.860453	−	0.509531i
$197$	−8.25539			−0.588172			−0.294086	−	0.955779i	$-0.595015\pi$
$197$	−8.25539			−0.588172			−0.294086	+	0.955779i	$0.595015\pi$
$198$	9.65551	−	19.8514i	0.686187	−	1.41077i
$199$	4.84893	−	2.79953i	0.343732	−	0.198454i	−0.318189	−	0.948027i	$-0.603075\pi$
$199$	4.84893	−	2.79953i	0.343732	−	0.198454i	0.661921	+	0.749574i	$0.269741\pi$
$200$	−1.63400	−	8.55354i	−0.115541	−	0.604826i
$201$	−1.41303	−	5.19057i	−0.0996672	−	0.366114i
$202$	−0.405385	+	0.816822i	−0.0285228	+	0.0574714i
$203$	1.72790	+	8.33545i	0.121275	+	0.585034i
$204$	20.6425	−	8.52450i	1.44526	−	0.596834i
$205$	8.35861	−	4.82585i	0.583791	−	0.337052i
$206$	10.4107	−	20.9769i	0.725349	−	1.46153i
$207$	23.9988	−	0.191483i	1.66803	−	0.0133090i
$208$	6.74599	−	1.73459i	0.467750	−	0.120272i
$209$	−14.1310	+	24.4756i	−0.977463	+	1.69302i
$210$	−4.41719	+	7.82164i	−0.304815	+	0.539745i
$211$	19.7205	−	11.3856i	1.35761	−	0.783818i	0.368311	−	0.929703i	$-0.379936\pi$
$211$	19.7205	−	11.3856i	1.35761	−	0.783818i	0.989302	+	0.145885i	$0.0466029\pi$
$212$	−7.27423	+	17.3132i	−0.499596	+	1.18907i
$213$	−5.02940	+	5.06969i	−0.344609	+	0.347369i
$214$	19.2145	−	12.7685i	1.31348	−	0.872838i
$215$	2.67359	−	4.63080i	0.182337	−	0.315818i
$216$	12.2557	+	8.11162i	0.833893	+	0.551926i
$217$	12.1327	−	2.51506i	0.823624	−	0.170733i
$218$	−10.2311	+	0.644584i	−0.692937	+	0.0436567i
$219$	0.323933	+	0.0854139i	0.0218893	+	0.00577174i
$220$	11.4874	−	8.72261i	0.774483	−	0.588078i
$221$	−5.61334	+	9.72259i	−0.377594	+	0.654012i
$222$	2.06161	−	10.4440i	0.138366	−	0.700958i
$223$	0.613094	+	0.353970i	0.0410558	+	0.0237036i	0.520387	−	0.853930i	$-0.325788\pi$
$223$	0.613094	+	0.353970i	0.0410558	+	0.0237036i	−0.479332	+	0.877634i	$0.659121\pi$
$224$	0.0688757	−	14.9665i	0.00460195	−	0.999989i
$225$	0.0736940	+	9.23616i	0.00491293	+	0.615744i
$226$	3.15250	−	0.198615i	0.209701	−	0.0132117i
$227$			2.04953i			0.136032i	0.997684	+	0.0680159i	$0.0216669\pi$
$227$			2.04953i			0.136032i	−0.997684	+	0.0680159i	$0.978333\pi$
$228$	−14.9155	−	11.4705i	−0.987805	−	0.759653i
$229$	7.59899			0.502155			0.251078	−	0.967967i	$-0.419215\pi$
$229$	7.59899			0.502155			0.251078	+	0.967967i	$0.419215\pi$
$230$	14.0465	+	6.97122i	0.926199	+	0.459668i
$231$	23.8097	+	1.27288i	1.56656	+	0.0837495i
$232$	8.59500	+	2.99057i	0.564289	+	0.196340i
$233$	13.3108	+	7.68498i	0.872018	+	0.503460i	0.868018	−	0.496532i	$-0.165394\pi$
$233$	13.3108	+	7.68498i	0.872018	+	0.503460i	0.00399972	+	0.999992i	$0.498727\pi$
$234$	−7.36939	+	0.523352i	−0.481752	+	0.0342126i
$235$	−6.15456	+	3.55334i	−0.401479	+	0.231794i
$236$	−0.0632570	−	0.500028i	−0.00411768	−	0.0325490i
$237$	6.87048	−	26.0563i	0.446286	−	1.69254i
$238$	17.1513	+	16.9630i	1.11175	+	1.09955i
$239$	1.33351	−	0.769903i	0.0862576	−	0.0498009i	−0.456251	−	0.889851i	$-0.650808\pi$
$239$	1.33351	−	0.769903i	0.0862576	−	0.0498009i	0.542508	+	0.840050i	$0.317475\pi$
$240$	4.75039	+	8.34569i	0.306636	+	0.538712i
$241$			10.6532i			0.686235i	0.939293	+	0.343117i	$0.111483\pi$
$241$			10.6532i			0.686235i	−0.939293	+	0.343117i	$0.888517\pi$
$242$	−20.3604	−	10.1048i	−1.30882	−	0.649559i
$243$	−11.2404	−	10.8007i	−0.721070	−	0.692863i
$244$	−2.12624	+	5.06060i	−0.136119	+	0.323972i
$245$	−9.63861	−	1.11138i	−0.615788	−	0.0710036i
$246$	11.2275	−	12.8403i	0.715842	−	0.818667i
$247$	9.45860			0.601836
$248$	4.35295	−	12.5105i	0.276413	−	0.794420i
$249$	−4.73958	−	17.4103i	−0.300359	−	1.10333i
$250$	−7.04003	+	14.1852i	−0.445251	+	0.897148i
$251$			12.8373i			0.810282i	0.914254	+	0.405141i	$0.132778\pi$
$251$			12.8373i			0.810282i	−0.914254	+	0.405141i	$0.867222\pi$
$252$	−2.92601	+	15.6025i	−0.184321	+	0.982866i
$253$		−	41.6242i		−	2.61689i
$254$	11.3262	+	5.62115i	0.710670	+	0.352702i
$255$	−14.9663	−	3.94627i	−0.937223	−	0.247125i
$256$	−13.6916	−	8.27886i	−0.855726	−	0.517428i
$257$	0.661572			0.0412677			0.0206339	−	0.999787i	$-0.493432\pi$
$257$	0.661572			0.0412677			0.0206339	+	0.999787i	$0.493432\pi$
$258$	1.83002	−	9.27077i	0.113932	−	0.577173i
$259$	11.2592	−	2.33397i	0.699610	−	0.145026i
$260$	−4.45041	−	1.86987i	−0.276003	−	0.115964i
$261$	−8.39750	−	4.75937i	−0.519792	−	0.294598i
$262$	−7.53590	+	15.1843i	−0.465570	+	0.938090i
$263$		−	17.1566i		−	1.05792i	−0.848647	−	0.528960i	$-0.822582\pi$
$263$		−	17.1566i		−	1.05792i	0.848647	−	0.528960i	$-0.177418\pi$
$264$	14.2377	−	21.1430i	0.876273	−	1.30126i
$265$	11.2710	−	6.50733i	0.692374	−	0.399742i
$266$	5.15172	−	19.6599i	0.315872	−	1.20543i
$267$	−20.7240	+	5.64170i	−1.26829	+	0.345266i
$268$	−0.779607	−	6.16255i	−0.0476221	−	0.376438i
$269$	−21.4399	+	12.3783i	−1.30721	+	0.754720i	−0.981630	−	0.190793i	$-0.938894\pi$
$269$	−21.4399	+	12.3783i	−1.30721	+	0.754720i	−0.325584	+	0.945513i	$0.605561\pi$
$270$	−3.36489	−	9.61360i	−0.204781	−	0.585065i
$271$	−6.84775	−	3.95355i	−0.415971	−	0.240161i	0.277381	−	0.960760i	$-0.410534\pi$
$271$	−6.84775	−	3.95355i	−0.415971	−	0.240161i	−0.693352	+	0.720599i	$0.743867\pi$
$272$	24.9759	−	6.42204i	1.51439	−	0.389394i
$273$	−3.61533	−	7.11394i	−0.218810	−	0.430555i
$274$	11.7157	−	23.6063i	0.707771	−	1.42611i
$275$	16.0195			0.966011
$276$	27.4713	+	3.64663i	1.65358	+	0.219501i
$277$			16.1423i			0.969895i	0.874543	+	0.484948i	$0.161161\pi$
$277$			16.1423i			0.969895i	−0.874543	+	0.484948i	$0.838839\pi$
$278$	0.727971	+	11.5546i	0.0436608	+	0.693002i
$279$	−6.92755	+	12.2231i	−0.414742	+	0.731776i
$280$	−6.31053	+	8.23186i	−0.377126	+	0.491948i
$281$	−2.93071	−	1.69205i	−0.174831	−	0.100939i	0.410031	−	0.912072i	$-0.365518\pi$
$281$	−2.93071	−	1.69205i	−0.174831	−	0.100939i	−0.584862	+	0.811133i	$0.698851\pi$
$282$	−8.26699	+	9.45449i	−0.492292	+	0.563006i
$283$	−11.4833	+	19.8897i	−0.682613	+	1.18232i	0.291567	+	0.956550i	$0.405823\pi$
$283$	−11.4833	+	19.8897i	−0.682613	+	1.18232i	−0.974180	+	0.225771i	$0.927510\pi$
$284$	−6.56726	+	4.98663i	−0.389695	+	0.295902i
$285$	3.42527	+	12.5823i	0.202896	+	0.745311i
$286$	0.805683	+	12.7881i	0.0476410	+	0.756178i
$287$	17.4927	+	5.78135i	1.03256	+	0.341262i
$288$	12.7067	+	11.2490i	0.748750	+	0.662853i
$289$	−12.2825	+	21.2739i	−0.722500	+	1.25141i
$290$	−3.49064	−	5.25284i	−0.204977	−	0.308457i
$291$	−1.97539	−	7.25634i	−0.115799	−	0.425374i
$292$	0.356630	+	0.149840i	0.0208702	+	0.00876873i
$293$	16.3803	−	9.45715i	0.956945	−	0.552492i	0.0617134	−	0.998094i	$-0.480344\pi$
$293$	16.3803	−	9.45715i	0.956945	−	0.552492i	0.895231	+	0.445602i	$0.147010\pi$
$294$	−16.7556	+	3.63988i	−0.977208	+	0.212282i
$295$	−0.174649	+	0.302501i	−0.0101685	+	0.0176123i
$296$	4.03953	−	11.6098i	0.234793	−	0.674803i
$297$	−18.8873	+	19.3449i	−1.09595	+	1.12251i
$298$	16.0726	+	7.97677i	0.931062	+	0.462082i
$299$	−12.0642	+	6.96530i	−0.697693	+	0.402814i
$300$	−1.40344	+	10.5726i	−0.0810275	+	0.610409i
$301$	9.99433	−	2.07178i	0.576064	−	0.119415i
$302$	17.9714	+	8.91911i	1.03414	+	0.513237i
$303$	0.786560	−	0.792861i	0.0451867	−	0.0455487i
$304$	−15.2070	−	15.5180i	−0.872181	−	0.890019i
$305$	3.29450	−	1.90208i	0.188642	−	0.108913i
$306$	−27.2840	+	1.93763i	−1.55972	+	0.110767i
$307$	−4.12945			−0.235680			−0.117840	−	0.993033i	$-0.537597\pi$
$307$	−4.12945			−0.235680			−0.117840	+	0.993033i	$0.537597\pi$
$308$	27.0193	+	5.29054i	1.53957	+	0.301457i
$309$	−20.1997	+	20.3615i	−1.14912	+	1.15832i
$310$	−7.64582	+	5.08084i	−0.434254	+	0.288572i
$311$	−5.49870	+	9.52403i	−0.311803	+	0.540058i	−0.978753	−	0.205044i	$-0.934266\pi$
$311$	−5.49870	+	9.52403i	−0.311803	+	0.540058i	0.666950	+	0.745102i	$0.267599\pi$
$312$	−8.51054	−	0.588607i	−0.481814	−	0.0333233i
$313$	22.7308	−	13.1236i	1.28482	−	0.741792i	0.307096	−	0.951678i	$-0.400643\pi$
$313$	22.7308	−	13.1236i	1.28482	−	0.741792i	0.977726	+	0.209886i	$0.0673093\pi$
$314$	9.14098	−	6.07440i	0.515855	−	0.342798i
$315$	8.15408	−	7.38549i	0.459431	−	0.416125i
$316$	12.0528	−	28.6864i	0.678021	−	1.61374i
$317$	−9.66558	−	16.7413i	−0.542873	−	0.940284i	−0.998737	−	0.0502346i	$-0.984003\pi$
$317$	−9.66558	−	16.7413i	−0.542873	−	0.940284i	0.455864	−	0.890049i	$-0.349330\pi$
$318$	15.1396	−	17.3143i	0.848986	−	0.970936i
$319$	−8.37048	+	14.4981i	−0.468657	+	0.811738i
$320$	4.08737	+	10.3077i	0.228491	+	0.576219i
$321$	−27.2629	+	7.42177i	−1.52167	+	0.414243i
$322$	7.90664	+	28.8696i	0.440620	+	1.60884i
$323$	35.0189			1.94851
$324$	−11.1127	−	14.1601i	−0.617370	−	0.786673i
$325$	−2.68066	−	4.64304i	−0.148696	−	0.257549i
$326$	3.82006	+	5.74856i	0.211573	+	0.318383i
$327$	12.1404	+	3.20115i	0.671364	+	0.177024i
$328$	14.9059	−	12.8733i	0.823042	−	0.710808i
$329$	−12.8801	−	4.25689i	−0.710105	−	0.234690i
$330$	−16.7196	+	5.70276i	−0.920385	+	0.313927i
$331$	21.9216	−	12.6565i	1.20492	−	0.695662i	0.243276	−	0.969957i	$-0.421778\pi$
$331$	21.9216	−	12.6565i	1.20492	−	0.695662i	0.961645	+	0.274295i	$0.0884446\pi$
$332$	−2.61496	−	20.6705i	−0.143515	−	1.13444i
$333$	−6.42876	+	11.3430i	−0.352294	+	0.621592i
$334$	1.07304	+	17.0318i	0.0587144	+	0.931938i
$335$	−2.15245	+	3.72815i	−0.117601	+	0.203691i
$336$	−5.85878	+	17.3688i	−0.319623	+	0.947545i
$337$	0.991156	+	1.71673i	0.0539917	+	0.0935164i	0.891758	−	0.452513i	$-0.149472\pi$
$337$	0.991156	+	1.71673i	0.0539917	+	0.0935164i	−0.837766	+	0.546029i	$0.816139\pi$
$338$	−11.7405	+	7.80187i	−0.638601	+	0.424366i
$339$	−3.74080	−	0.986367i	−0.203172	−	0.0535721i
$340$	−16.4769	−	6.92288i	−0.893588	−	0.375446i
$341$	21.1029	+	12.1837i	1.14278	+	0.659786i
$342$	12.9073	+	19.0911i	0.697946	+	1.03233i
$343$	−10.6582	−	15.1461i	−0.575488	−	0.817810i
$344$	3.58574	−	10.3055i	0.193330	−	0.555637i
$345$	−13.6344	−	13.5261i	−0.734054	−	0.728221i
$346$	19.9504	−	1.25693i	1.07254	−	0.0675728i
$347$	4.00441	−	6.93584i	0.214968	−	0.372335i	−0.738295	−	0.674478i	$-0.764369\pi$
$347$	4.00441	−	6.93584i	0.214968	−	0.372335i	0.953263	+	0.302143i	$0.0977020\pi$
$348$	−8.83519	−	6.79454i	−0.473616	−	0.364225i
$349$	−11.3440	+	19.6483i	−0.607229	+	1.05175i	0.384466	+	0.923139i	$0.374386\pi$
$349$	−11.3440	+	19.6483i	−0.607229	+	1.05175i	−0.991695	+	0.128612i	$0.958948\pi$
$350$	−11.1107	+	3.04294i	−0.593893	+	0.162652i
$351$	8.76744	+	2.23712i	0.467971	+	0.119409i
$352$	19.6852	−	21.8818i	1.04922	−	1.16631i
$353$	8.10532			0.431403			0.215701	−	0.976459i	$-0.430796\pi$
$353$	8.10532			0.431403			0.215701	+	0.976459i	$0.430796\pi$
$354$	−0.119543	+	0.605601i	−0.00635366	+	0.0321873i
$355$	5.71471			0.303305
$356$	−24.6048	+	3.11269i	−1.30405	+	0.164972i
$357$	−13.3852	−	26.3382i	−0.708419	−	1.39397i
$358$	−1.38068	−	21.9147i	−0.0729713	−	1.15823i
$359$	−2.25907	−	1.30428i	−0.119229	−	0.0688370i	0.439199	−	0.898390i	$-0.355262\pi$
$359$	−2.25907	−	1.30428i	−0.119229	−	0.0688370i	−0.558429	+	0.829553i	$0.688596\pi$
$360$	−2.29896	−	11.5343i	−0.121166	−	0.607911i
$361$	−5.25191	−	9.09657i	−0.276416	−	0.478767i
$362$	10.7345	+	5.32747i	0.564191	+	0.280005i
$363$	19.7631	+	19.6061i	1.03729	+	1.02905i
$364$	−2.98794	−	8.71649i	−0.156611	−	0.456868i
$365$	−0.134043	−	0.232169i	−0.00701613	−	0.0121523i
$366$	4.42527	−	5.06092i	0.231312	−	0.264539i
$367$		−	4.27671i		−	0.223243i	−0.993751	−	0.111621i	$-0.964396\pi$
$367$		−	4.27671i		−	0.223243i	0.993751	−	0.111621i	$-0.0356044\pi$
$368$	30.8236	+	8.59449i	1.60679	+	0.448019i
$369$	−18.0074	+	10.5891i	−0.937430	+	0.551245i
$370$	−7.09531	+	4.71501i	−0.368868	+	0.245122i
$371$	23.5878	+	7.79576i	1.22462	+	0.404735i
$372$	−9.88985	+	12.8601i	−0.512765	+	0.666768i
$373$		−	4.40257i		−	0.227956i	−0.993483	−	0.113978i	$-0.963641\pi$
$373$		−	4.40257i		−	0.227956i	0.993483	−	0.113978i	$-0.0363594\pi$
$374$	2.98291	+	47.3460i	0.154243	+	2.44820i
$375$	13.6596	−	13.7690i	0.705379	−	0.711030i
$376$	−10.9754	+	9.47877i	−0.566015	+	0.488830i
$377$	5.60278			0.288558
$378$	9.42518	−	17.0049i	0.484779	−	0.874637i
$379$		−	4.49987i		−	0.231143i	−0.993299	−	0.115572i	$-0.963130\pi$
$379$		−	4.49987i		−	0.231143i	0.993299	−	0.115572i	$-0.0368699\pi$
$380$	1.88982	+	14.9385i	0.0969457	+	0.766327i
$381$	−10.9940	−	10.9066i	−0.563238	−	0.558761i
$382$	−6.85805	+	0.432074i	−0.350888	+	0.0221068i
$383$	−27.4489			−1.40258			−0.701288	−	0.712878i	$-0.747391\pi$
$383$	−27.4489			−1.40258			−0.701288	+	0.712878i	$0.747391\pi$
$384$	12.7171	+	14.9089i	0.648965	+	0.760818i
$385$	−12.6960	−	14.2440i	−0.647046	−	0.725941i
$386$	−8.33316	+	5.53759i	−0.424147	+	0.281856i
$387$	−5.70656	+	10.0687i	−0.290081	+	0.511823i
$388$	−1.08988	−	8.61516i	−0.0553302	−	0.437369i
$389$	−6.95851			−0.352810			−0.176405	−	0.984318i	$-0.556447\pi$
$389$	−6.95851			−0.352810			−0.176405	+	0.984318i	$0.556447\pi$
$390$	4.45069	+	3.89168i	0.225370	+	0.197063i
$391$	−44.6659	+	25.7879i	−2.25885	+	1.30415i
$392$	−19.7449	+	1.46299i	−0.997266	+	0.0738923i
$393$	14.6217	−	14.7389i	0.737569	−	0.743478i
$394$	10.4578	+	5.19015i	0.526855	+	0.261476i
$395$	−18.6751	+	10.7821i	−0.939647	+	0.542506i
$396$	−24.7120	+	19.0770i	−1.24182	+	0.958653i
$397$	−12.2029	+	21.1360i	−0.612445	+	1.06079i	0.378382	+	0.925650i	$0.376481\pi$
$397$	−12.2029	+	21.1360i	−0.612445	+	1.06079i	−0.990827	+	0.135137i	$0.956853\pi$
$398$	−7.90261	+	0.497884i	−0.396122	+	0.0249567i
$399$	−13.5787	+	20.8614i	−0.679786	+	1.04438i
$400$	−3.30767	+	11.8628i	−0.165384	+	0.593138i
$401$		−	11.2309i		−	0.560845i	−0.959877	−	0.280422i	$-0.909526\pi$
$401$		−	11.2309i		−	0.560845i	0.959877	−	0.280422i	$-0.0904745\pi$
$402$	−1.47330	+	7.46369i	−0.0734817	+	0.372255i
$403$		−	8.15519i		−	0.406239i
$404$	1.02707	−	0.779872i	0.0510986	−	0.0388001i
$405$	0.199054	+	12.4730i	0.00989105	+	0.619789i
$406$	3.05161	−	11.6455i	0.151449	−	0.577958i
$407$	19.5834	+	11.3065i	0.970714	+	0.560442i
$408$	−31.5089	−	2.17922i	−1.55992	−	0.107888i
$409$	5.82799	+	3.36479i	0.288176	+	0.166378i	0.637119	−	0.770766i	$-0.280126\pi$
$409$	5.82799	+	3.36479i	0.288176	+	0.166378i	−0.348943	+	0.937144i	$0.613459\pi$
$410$	−13.6225	+	0.858254i	−0.672770	+	0.0423862i
$411$	−22.7317	+	22.9138i	−1.12127	+	1.13025i
$412$	−26.3762	+	20.0279i	−1.29946	+	0.986705i
$413$	−0.652867	+	0.135336i	−0.0321255	+	0.00665946i
$414$	−30.5216	−	14.8454i	−1.50006	−	0.729613i
$415$	−7.21976	+	12.5050i	−0.354404	+	0.613846i
$416$	−9.63623	−	2.04384i	−0.472455	−	0.100208i
$417$	3.61527	−	13.7109i	0.177040	−	0.671427i
$418$	33.2887	−	22.1212i	1.62820	−	1.08198i
$419$	30.0574	−	17.3537i	1.46840	−	0.847782i	0.469028	−	0.883183i	$-0.344604\pi$
$419$	30.0574	−	17.3537i	1.46840	−	0.847782i	0.999373	+	0.0354015i	$0.0112710\pi$
$420$	10.5131	−	7.13124i	0.512986	−	0.347969i
$421$	−5.77919	−	3.33661i	−0.281660	−	0.162617i	0.352515	−	0.935806i	$-0.385327\pi$
$421$	−5.77919	−	3.33661i	−0.281660	−	0.162617i	−0.634175	+	0.773190i	$0.718660\pi$
$422$	−32.1397	+	2.02488i	−1.56453	+	0.0985695i
$423$	13.2591	−	7.79687i	0.644681	−	0.379097i
$424$	20.0996	−	17.3587i	0.976124	−	0.843015i
$425$	−9.92471	−	17.1901i	−0.481419	−	0.833842i
$426$	9.55846	−	3.26022i	0.463109	−	0.157958i
$427$	6.89465	+	2.27868i	0.333655	+	0.110273i
$428$	−32.3682	+	4.09480i	−1.56458	+	0.197930i
$429$	4.00120	−	15.1746i	0.193180	−	0.732636i
$430$	−6.29824	+	4.18533i	−0.303728	+	0.201835i
$431$	6.38913	−	3.68876i	0.307753	−	0.177682i	−0.338167	−	0.941086i	$-0.609807\pi$
$431$	6.38913	−	3.68876i	0.307753	−	0.177682i	0.645921	+	0.763404i	$0.276474\pi$
$432$	−10.4255	−	17.9808i	−0.501598	−	0.865101i
$433$		−	13.3585i		−	0.641969i	−0.947084	−	0.320984i	$-0.895986\pi$
$433$		−	13.3585i		−	0.641969i	0.947084	−	0.320984i	$-0.104014\pi$
$434$	−16.9508	−	4.44180i	−0.813663	−	0.213213i
$435$	2.02895	+	7.45310i	0.0972809	+	0.357349i
$436$	13.3658	+	5.61572i	0.640107	+	0.268944i
$437$	37.6315	+	21.7266i	1.80016	+	1.03932i
$438$	−0.356653	−	0.311857i	−0.0170415	−	0.0149011i
$439$	30.3635	−	17.5304i	1.44917	−	0.836679i	0.450739	−	0.892656i	$-0.351161\pi$
$439$	30.3635	−	17.5304i	1.44917	−	0.836679i	0.998432	+	0.0559765i	$0.0178272\pi$
$440$	−20.0360	+	3.82751i	−0.955178	+	0.182470i
$441$	20.8803	+	2.23895i	0.994300	+	0.106616i
$442$	13.2235	−	8.78732i	0.628976	−	0.417970i
$443$	−0.808024	−	1.39954i	−0.0383904	−	0.0664941i	0.846192	−	0.532878i	$-0.178890\pi$
$443$	−0.808024	−	1.39954i	−0.0383904	−	0.0664941i	−0.884582	+	0.466384i	$0.845556\pi$
$444$	−9.17777	+	11.9342i	−0.435558	+	0.566372i
$445$	14.8851	+	8.59394i	0.705624	+	0.407392i
$446$	−0.554117	−	0.833855i	−0.0262382	−	0.0394842i
$447$	−15.6011	−	15.4771i	−0.737908	−	0.732043i
$448$	−9.49665	+	18.9160i	−0.448674	+	0.893695i
$449$			11.9158i			0.562340i	0.959658	+	0.281170i	$0.0907225\pi$
$449$			11.9158i			0.562340i	−0.959658	+	0.281170i	$0.909278\pi$
$450$	5.71340	−	11.7465i	0.269332	−	0.553737i
$451$	18.1156	+	31.3772i	0.853032	+	1.47749i
$452$	−4.11840	−	1.73037i	−0.193713	−	0.0813896i
$453$	−17.4442	−	17.3056i	−0.819599	−	0.813086i
$454$	1.28853	−	2.59630i	0.0604739	−	0.121851i
$455$	−2.00393	+	6.06332i	−0.0939455	+	0.284253i
$456$	11.6833	+	23.9080i	0.547118	+	1.11960i
$457$	16.6473	+	28.8340i	0.778727	+	1.34880i	0.932675	+	0.360717i	$0.117468\pi$
$457$	16.6473	+	28.8340i	0.778727	+	1.34880i	−0.153948	+	0.988079i	$0.549199\pi$
$458$	−9.62626	−	4.77747i	−0.449806	−	0.223236i
$459$	32.4600	+	8.28258i	1.51510	+	0.386598i
$460$	−13.4111	−	17.6620i	−0.625295	−	0.823497i
$461$	−29.9194	−	17.2740i	−1.39349	−	0.804530i	−0.399787	−	0.916608i	$-0.630916\pi$
$461$	−29.9194	−	17.2740i	−1.39349	−	0.804530i	−0.993699	+	0.112078i	$0.964249\pi$
$462$	−29.3615	−	16.5816i	−1.36602	−	0.771446i
$463$	9.17910	+	15.8987i	0.426589	+	0.738874i	0.996567	−	0.0827859i	$-0.0263818\pi$
$463$	9.17910	+	15.8987i	0.426589	+	0.738874i	−0.569978	+	0.821660i	$0.693048\pi$
$464$	−9.00783	−	9.19206i	−0.418178	−	0.426731i
$465$	10.8484	−	2.95326i	0.503084	−	0.136954i
$466$	−12.0303	−	18.1037i	−0.557294	−	0.838636i
$467$	−19.0319	−	10.9881i	−0.880690	−	0.508467i	−0.00980427	−	0.999952i	$-0.503121\pi$
$467$	−19.0319	−	10.9881i	−0.880690	−	0.508467i	−0.870886	+	0.491485i	$0.836454\pi$
$468$	9.66445	+	3.97015i	0.446739	+	0.183520i
$469$	−8.04621	+	1.66794i	−0.371539	+	0.0770183i
$470$	10.0305	−	0.631944i	0.462671	−	0.0291494i
$471$	−12.9699	+	3.53078i	−0.597620	+	0.162690i
$472$	−0.234234	+	0.673196i	−0.0107815	+	0.0309863i
$473$	17.3834	+	10.0363i	0.799292	+	0.461471i
$474$	−25.0850	+	28.6883i	−1.15219	+	1.31770i
$475$	−8.36167	+	14.4828i	−0.383660	+	0.664518i
$476$	−11.0624	−	32.2714i	−0.507043	−	1.47916i
$477$	−24.2818	+	14.2786i	−1.11179	+	0.653774i
$478$	−2.17330	+	0.136924i	−0.0994047	+	0.00626274i
$479$	9.76198			0.446036			0.223018	−	0.974814i	$-0.428409\pi$
$479$	9.76198			0.446036			0.223018	+	0.974814i	$0.428409\pi$
$480$	−0.770782	−	13.5587i	−0.0351812	−	0.618869i
$481$		−	7.56800i		−	0.345071i
$482$	6.69767	−	13.4953i	0.305070	−	0.614695i
$483$	1.95707	−	36.6077i	0.0890496	−	1.66571i
$484$	19.4393	+	25.6011i	0.883607	+	1.16369i
$485$	−3.00909	+	5.21190i	−0.136636	+	0.236660i
$486$	7.44874	+	20.7489i	0.337882	+	0.941189i
$487$	17.7009	+	30.6588i	0.802102	+	1.38928i	0.918230	+	0.396048i	$0.129619\pi$
$487$	17.7009	+	30.6588i	0.802102	+	1.38928i	−0.116128	+	0.993234i	$0.537048\pi$
$488$	5.87508	−	5.07392i	0.265952	−	0.229686i
$489$	−2.22043	−	8.15646i	−0.100411	−	0.368848i
$490$	11.5113	+	7.46766i	0.520028	+	0.337354i
$491$	11.9769	+	20.7447i	0.540511	+	0.936193i	0.998875	+	0.0474283i	$0.0151025\pi$
$491$	11.9769	+	20.7447i	0.540511	+	0.936193i	−0.458363	+	0.888765i	$0.651564\pi$
$492$	−22.2955	+	9.20713i	−1.00516	+	0.415089i
$493$	20.7434			0.934236
$494$	−11.9820	−	5.94660i	−0.539095	−	0.267550i
$495$	21.6350	−	0.172622i	0.972419	−	0.00775879i
$496$	−13.3796	+	13.1114i	−0.600762	+	0.588721i
$497$	7.25816	+	8.14316i	0.325573	+	0.365271i
$498$	−4.94177	+	25.0348i	−0.221446	+	1.12184i
$499$		−	20.2887i		−	0.908248i	−0.890939	−	0.454124i	$-0.849952\pi$
$499$		−	20.2887i		−	0.908248i	0.890939	−	0.454124i	$-0.150048\pi$
$500$	17.8364	−	13.5435i	0.797667	−	0.605682i
$501$	5.32898	−	20.2102i	0.238081	−	0.902924i
$502$	8.07078	−	16.2620i	0.360216	−	0.725811i
$503$	14.6466			0.653058			0.326529	−	0.945187i	$-0.394121\pi$
$503$	14.6466			0.653058			0.326529	+	0.945187i	$0.394121\pi$
$504$	13.5159	−	17.9254i	0.602046	−	0.798462i
$505$	−0.893737			−0.0397708
$506$	−26.1691	+	52.7289i	−1.16336	+	2.34408i
$507$	16.6583	−	4.53488i	0.739821	−	0.201401i
$508$	−10.8139	−	14.2415i	−0.479787	−	0.631867i
$509$			10.1980i			0.452020i	0.974125	+	0.226010i	$0.0725683\pi$
$509$			10.1980i			0.452020i	−0.974125	+	0.226010i	$0.927432\pi$
$510$	16.4780	+	14.4083i	0.729657	+	0.638012i
$511$	0.160583	−	0.485879i	0.00710377	−	0.0214940i
$512$	12.1394	+	19.0954i	0.536491	+	0.843906i
$513$	−7.63070	−	27.1731i	−0.336903	−	1.19972i
$514$	−0.838068	−	0.415929i	−0.0369656	−	0.0183459i
$515$	22.9521			1.01139
$516$	−8.14675	+	10.5935i	−0.358641	+	0.466354i
$517$	−13.3388	−	23.1035i	−0.586639	−	1.01609i
$518$	−15.7303	−	4.12198i	−0.691149	−	0.181110i
$519$	−23.6735	−	6.24219i	−1.03915	−	0.274002i
$520$	4.46213	+	5.16668i	0.195677	+	0.226574i
$521$	5.15787	+	8.93369i	0.225970	+	0.391392i	0.956610	−	0.291371i	$-0.0941114\pi$
$521$	5.15787	+	8.93369i	0.225970	+	0.391392i	−0.730640	+	0.682763i	$0.760778\pi$
$522$	7.64560	+	11.3086i	0.334639	+	0.494964i
$523$	18.3254	−	31.7405i	0.801314	−	1.38792i	−0.117438	−	0.993080i	$-0.537468\pi$
$523$	18.3254	−	31.7405i	0.801314	−	1.38792i	0.918752	−	0.394836i	$-0.129199\pi$
$524$	19.0927	−	14.4974i	0.834069	−	0.633323i
$525$	14.0888	+	0.753195i	0.614885	+	0.0328721i
$526$	−10.7863	+	21.7337i	−0.470306	+	0.947633i
$527$		−	30.1933i		−	1.31524i
$528$	−31.3287	+	17.8324i	−1.36341	+	0.776054i
$529$	−40.9976			−1.78251
$530$	−18.3691	+	1.15730i	−0.797902	+	0.0502698i
$531$	0.372774	−	0.657727i	0.0161770	−	0.0285429i
$532$	−18.8863	+	21.6660i	−0.818824	+	0.939340i
$533$	6.06285	−	10.5012i	0.262611	−	0.454856i
$534$	29.7998	+	5.88237i	1.28956	+	0.254555i
$535$	19.5817	+	11.3055i	0.846592	+	0.488780i
$536$	−2.88679	+	8.29675i	−0.124691	+	0.358365i
$537$	−6.85678	+	26.0044i	−0.295892	+	1.12217i
$538$	34.9419	−	2.20143i	1.50645	−	0.0949103i
$539$	4.17199	−	36.1822i	0.179700	−	1.55848i
$540$	−1.78147	+	14.2938i	−0.0766624	+	0.615109i
$541$	34.4796	+	19.9068i	1.48240	+	0.855862i	0.999800	−	0.0199818i	$-0.00636084\pi$
$541$	34.4796	+	19.9068i	1.48240	+	0.855862i	0.482595	+	0.875843i	$0.339694\pi$
$542$	6.18902	+	9.31346i	0.265841	+	0.400047i
$543$	−10.4196	−	10.3368i	−0.447146	−	0.443593i
$544$	−35.6766	−	7.56699i	−1.52962	−	0.324432i
$545$	−5.02368	−	8.70126i	−0.215191	−	0.372721i
$546$	0.107316	+	11.2848i	0.00459271	+	0.482944i
$547$	−15.3036	−	8.83557i	−0.654337	−	0.377781i	0.135779	−	0.990739i	$-0.456646\pi$
$547$	−15.3036	−	8.83557i	−0.654337	−	0.377781i	−0.790116	+	0.612958i	$0.789980\pi$
$548$	−29.6825	+	22.5384i	−1.26797	+	0.962794i
$549$	−7.09752	+	4.17361i	−0.302915	+	0.178125i
$550$	−20.2932	−	10.0714i	−0.865305	−	0.429447i
$551$	−8.73827	−	15.1351i	−0.372263	−	0.644778i
$552$	−32.5076	−	21.8907i	−1.38361	−	0.931728i
$553$	−39.0829	−	12.9169i	−1.66197	−	0.549282i
$554$	10.1486	−	20.4488i	0.431174	−	0.868784i
$555$	10.0673	−	2.74062i	0.427334	−	0.116333i
$556$	6.34221	−	15.0949i	0.268969	−	0.640166i
$557$	7.40013	+	12.8174i	0.313554	+	0.543091i	0.979129	−	0.203240i	$-0.0651471\pi$
$557$	7.40013	+	12.8174i	0.313554	+	0.543091i	−0.665575	+	0.746331i	$0.731814\pi$
$558$	16.4603	−	11.1286i	0.696821	−	0.471113i
$559$		−	6.71782i		−	0.284134i
$560$	13.1694	−	6.46056i	0.556510	−	0.273009i
$561$	14.8138	−	56.1815i	0.625440	−	2.37198i
$562$	2.64878	+	3.98598i	0.111732	+	0.168139i
$563$	−18.9746	−	10.9550i	−0.799685	−	0.461698i	0.0436760	−	0.999046i	$-0.486093\pi$
$563$	−18.9746	−	10.9550i	−0.799685	−	0.461698i	−0.843361	+	0.537347i	$0.819426\pi$
$564$	16.4165	−	6.77933i	0.691259	−	0.285461i
$565$	1.54794	+	2.68111i	0.0651223	+	0.112795i
$566$	27.0515	−	17.9764i	1.13706	−	0.755604i
$567$	−17.5206	+	16.1254i	−0.735795	+	0.677204i
$568$	11.4544	−	2.18815i	0.480615	−	0.0918129i
$569$	16.7409	−	9.66538i	0.701816	−	0.405194i	−0.106207	−	0.994344i	$-0.533871\pi$
$569$	16.7409	−	9.66538i	0.701816	−	0.405194i	0.808023	+	0.589150i	$0.200537\pi$
$570$	3.57139	−	18.0925i	0.149589	−	0.757811i
$571$	15.7691	+	9.10430i	0.659917	+	0.381003i	0.792245	−	0.610203i	$-0.208912\pi$
$571$	15.7691	+	9.10430i	0.659917	+	0.381003i	−0.132329	+	0.991206i	$0.542245\pi$
$572$	7.01925	−	16.7063i	0.293489	−	0.698526i
$573$	8.13787	+	2.14578i	0.339964	+	0.0896411i
$574$	−18.5248	−	18.3214i	−0.773208	−	0.764719i
$575$		−	24.6301i		−	1.02715i
$576$	−9.02442	−	22.2387i	−0.376017	−	0.926613i
$577$	−6.86249	+	3.96206i	−0.285689	+	0.164943i	−0.635996	−	0.771692i	$-0.719411\pi$
$577$	−6.86249	+	3.96206i	−0.285689	+	0.164943i	0.350307	+	0.936635i	$0.386077\pi$
$578$	28.9341	−	19.2274i	1.20350	−	0.799756i
$579$	11.8237	−	3.21876i	0.491375	−	0.133767i
$580$	1.11943	+	8.84877i	0.0464819	+	0.367425i
$581$	−26.9887	+	5.59462i	−1.11968	+	0.232104i
$582$	−2.05966	+	10.4341i	−0.0853756	+	0.432509i
$583$	24.4277	+	42.3100i	1.01169	+	1.75230i
$584$	−0.357569	−	0.414028i	−0.0147963	−	0.0171326i
$585$	−3.67037	−	6.24173i	−0.151751	−	0.258064i
$586$	−26.6959	+	1.68191i	−1.10280	+	0.0694790i
$587$	−27.1868	−	15.6963i	−1.12212	−	0.647856i	−0.180178	−	0.983634i	$-0.557667\pi$
$587$	−27.1868	−	15.6963i	−1.12212	−	0.647856i	−0.941941	+	0.335778i	$0.891001\pi$
$588$	23.5141	+	5.92330i	0.969707	+	0.244273i
$589$	−22.0301	+	12.7191i	−0.907733	+	0.524080i
$590$	0.411424	−	0.273401i	0.0169381	−	0.0112558i
$591$	−10.1510	−	10.0703i	−0.417556	−	0.414238i
$592$	−12.4162	+	12.1674i	−0.510304	+	0.500077i
$593$	−11.0681	+	19.1706i	−0.454514	+	0.787241i	−0.998660	−	0.0517493i	$-0.983520\pi$
$593$	−11.0681	+	19.1706i	−0.454514	+	0.787241i	0.544146	+	0.838990i	$0.316854\pi$
$594$	36.0883	−	12.6314i	1.48072	−	0.518272i
$595$	−7.41922	+	22.4485i	−0.304158	+	0.920297i
$596$	−15.3455	−	20.2097i	−0.628578	−	0.827820i
$597$	9.37736	+	2.47260i	0.383790	+	0.101197i
$598$	19.6619	−	1.23875i	0.804033	−	0.0506561i
$599$	9.82771	+	5.67403i	0.401549	+	0.231835i	0.687152	−	0.726513i	$-0.258861\pi$
$599$	9.82771	+	5.67403i	0.401549	+	0.231835i	−0.285603	+	0.958348i	$0.592194\pi$
$600$	8.42482	−	12.5108i	0.343942	−	0.510753i
$601$	20.6626	+	11.9296i	0.842845	+	0.486617i	0.858230	−	0.513265i	$-0.171564\pi$
$601$	20.6626	+	11.9296i	0.842845	+	0.486617i	−0.0153855	+	0.999882i	$0.504898\pi$
$602$	−13.9632	−	3.65893i	−0.569096	−	0.149127i
$603$	4.59422	−	8.10611i	0.187091	−	0.330106i
$604$	−17.1584	−	22.5972i	−0.698166	−	0.919465i
$605$		−	22.2776i		−	0.905713i
$606$	−1.49487	+	0.509873i	−0.0607250	+	0.0207122i
$607$		−	34.6622i		−	1.40689i	−0.710748	−	0.703447i	$-0.751643\pi$
$607$		−	34.6622i		−	1.40689i	0.710748	−	0.703447i	$-0.248357\pi$
$608$	9.50781	+	29.2186i	0.385593	+	1.18497i
$609$	−8.04333	+	12.3572i	−0.325932	+	0.500740i
$610$	−5.36924	+	0.338276i	−0.217394	+	0.0136964i
$611$	−4.46416	+	7.73215i	−0.180601	+	0.312809i
$612$	35.7811	+	14.6988i	1.44636	+	0.594165i
$613$	4.24565	−	2.45123i	0.171480	−	0.0990042i	−0.411803	−	0.911273i	$-0.635101\pi$
$613$	4.24565	−	2.45123i	0.171480	−	0.0990042i	0.583284	+	0.812269i	$0.301768\pi$
$614$	5.23111	+	2.59618i	0.211110	+	0.104773i
$615$	16.1647	+	4.26228i	0.651825	+	0.171872i
$616$	−30.9014	−	23.6889i	−1.24505	−	0.954454i
$617$	8.08176	−	4.66601i	0.325359	−	0.187846i	−0.328420	−	0.944532i	$-0.606516\pi$
$617$	8.08176	−	4.66601i	0.325359	−	0.187846i	0.653779	+	0.756686i	$0.273183\pi$
$618$	38.3898	−	13.0941i	1.54427	−	0.526721i
$619$	19.5284			0.784914			0.392457	−	0.919770i	$-0.371625\pi$
$619$	19.5284			0.784914			0.392457	+	0.919770i	$0.371625\pi$
$620$	12.8799	−	1.62940i	0.517270	−	0.0654383i
$621$	29.7430	+	29.0395i	1.19355	+	1.16531i
$622$	12.9534	−	8.60785i	0.519384	−	0.345143i
$623$	6.65948	+	32.1256i	0.266806	+	1.28708i
$624$	10.4109	+	6.09620i	0.416771	+	0.244043i
$625$	−0.126799			−0.00507198
$626$	−37.0458	+	2.33398i	−1.48065	+	0.0932845i
$627$	−47.2324	+	12.8581i	−1.88628	+	0.513501i
$628$	−15.3986	+	1.94803i	−0.614471	+	0.0777349i
$629$		−	28.0193i		−	1.11720i
$630$	−14.9727	+	4.22935i	−0.596527	+	0.168501i
$631$	−34.2088			−1.36183			−0.680916	−	0.732362i	$-0.738418\pi$
$631$	−34.2088			−1.36183			−0.680916	+	0.732362i	$0.738418\pi$
$632$	−33.3034	+	28.7619i	−1.32474	+	1.14409i
$633$	38.1374	+	10.0560i	1.51583	+	0.399690i
$634$	1.71898	+	27.2843i	0.0682693	+	1.08360i
$635$			12.3927i			0.491791i
$636$	−30.0640	+	12.4152i	−1.19212	+	0.492294i
$637$	−11.1851	+	4.84543i	−0.443168	+	0.191983i
$638$	19.7185	−	13.1034i	0.780663	−	0.518770i
$639$	−12.3685	+	0.0986865i	−0.489291	+	0.00390398i
$640$	1.30263	−	15.6274i	0.0514911	−	0.617726i
$641$			31.5273i			1.24525i	0.782519	+	0.622627i	$0.213935\pi$
$641$			31.5273i			1.24525i	−0.782519	+	0.622627i	$0.786065\pi$
$642$	39.2023	+	7.73838i	1.54719	+	0.305410i
$643$	5.85239	+	10.1366i	0.230796	+	0.399750i	0.958043	−	0.286626i	$-0.0925338\pi$
$643$	5.85239	+	10.1366i	0.230796	+	0.399750i	−0.727247	+	0.686376i	$0.759200\pi$
$644$	8.13425	−	41.5424i	0.320535	−	1.63700i
$645$	8.93638	−	2.43275i	0.351870	−	0.0957893i
$646$	−44.3614	−	22.0163i	−1.74538	−	0.866222i
$647$	15.3103	+	26.5183i	0.601912	+	1.04254i	0.992531	+	0.121990i	$0.0389275\pi$
$647$	15.3103	+	26.5183i	0.601912	+	1.04254i	−0.390619	+	0.920552i	$0.627739\pi$
$648$	5.17488	+	24.9243i	0.203288	+	0.979119i
$649$	−1.13555	−	0.655611i	−0.0445743	−	0.0257350i
$650$	0.476742	+	7.56704i	0.0186994	+	0.296804i
$651$	17.9867	+	11.7075i	0.704953	+	0.458855i
$652$	−1.22507	−	9.68384i	−0.0479776	−	0.379248i
$653$	−10.0839			−0.394613			−0.197307	−	0.980342i	$-0.563219\pi$
$653$	−10.0839			−0.394613			−0.197307	+	0.980342i	$0.563219\pi$
$654$	−13.3667	−	11.6878i	−0.522678	−	0.457029i
$655$	−16.6141			−0.649167
$656$	−26.9760	+	6.93631i	−1.05323	+	0.270817i
$657$	0.294122	+	0.500176i	0.0114748	+	0.0195137i
$658$	13.6400	+	13.4903i	0.531744	+	0.525905i
$659$	−2.53394	+	4.38892i	−0.0987085	+	0.170968i	−0.911150	−	0.412074i	$-0.864804\pi$
$659$	−2.53394	+	4.38892i	−0.0987085	+	0.170968i	0.812442	+	0.583042i	$0.198138\pi$
$660$	24.7655	+	3.28744i	0.963994	+	0.127963i
$661$	1.21790	−	2.10946i	0.0473708	−	0.0820486i	−0.841368	−	0.540463i	$-0.818249\pi$
$661$	1.21790	−	2.10946i	0.0473708	−	0.0820486i	0.888739	+	0.458414i	$0.151582\pi$
$662$	−35.7270	+	2.25089i	−1.38857	+	0.0874834i
$663$	−18.7624	+	5.10768i	−0.728671	+	0.198366i
$664$	−9.68291	+	27.8290i	−0.375770	+	1.07998i
$665$	19.5046	−	4.04320i	0.756355	−	0.156789i
$666$	15.2752	−	10.3273i	0.591900	−	0.400177i
$667$	22.2910	+	12.8697i	0.863109	+	0.498316i
$668$	9.34854	−	22.2502i	0.361706	−	0.860886i
$669$	0.322083	+	1.18313i	0.0124525	+	0.0457425i
$670$	5.07057	−	3.36952i	0.195893	−	0.130176i
$671$	7.14017	+	12.3671i	0.275643	+	0.477428i
$672$	18.3415	−	18.3191i	0.707540	−	0.706673i
$673$	6.65719	−	11.5306i	0.256616	−	0.444472i	−0.708717	−	0.705493i	$-0.750726\pi$
$673$	6.65719	−	11.5306i	0.256616	−	0.444472i	0.965333	+	0.261021i	$0.0840592\pi$
$674$	−0.176272	−	2.79786i	−0.00678976	−	0.107770i
$675$	−11.1761	+	11.4469i	−0.430168	+	0.440590i
$676$	19.7777	−	2.50202i	0.760682	−	0.0962316i
$677$	13.0897	−	7.55735i	0.503079	−	0.290453i	−0.226905	−	0.973917i	$-0.572861\pi$
$677$	13.0897	−	7.55735i	0.503079	−	0.290453i	0.729984	+	0.683464i	$0.239527\pi$
$678$	4.11866	+	3.60135i	0.158176	+	0.138309i
$679$	−11.2485	+	2.33176i	−0.431677	+	0.0894846i
$680$	16.5203	+	19.1288i	0.633525	+	0.733556i
$681$	−2.50011	+	2.52014i	−0.0958045	+	0.0965720i
$682$	−19.0728	−	28.7015i	−0.730337	−	1.09904i
$683$	−3.03394	−	5.25494i	−0.116091	−	0.201075i	0.802125	−	0.597157i	$-0.203703\pi$
$683$	−3.03394	−	5.25494i	−0.116091	−	0.201075i	−0.918215	+	0.396082i	$0.870370\pi$
$684$	−4.34816	−	32.2991i	−0.166256	−	1.23499i
$685$	25.8292			0.986881
$686$	3.97931	+	25.8875i	0.151931	+	0.988391i
$687$	9.34387	+	9.26962i	0.356491	+	0.353658i
$688$	−11.0214	+	10.8005i	−0.420188	+	0.411766i
$689$	8.17534	−	14.1601i	0.311456	−	0.539457i
$690$	8.76805	+	25.7066i	0.333794	+	0.978633i
$691$	1.38091	+	2.39180i	0.0525322	+	0.0909885i	0.891096	−	0.453815i	$-0.149937\pi$
$691$	1.38091	+	2.39180i	0.0525322	+	0.0909885i	−0.838564	+	0.544804i	$0.816604\pi$
$692$	−26.0631	−	10.9506i	−0.990771	−	0.416278i
$693$	27.7242	+	30.6094i	1.05316	+	1.16276i
$694$	−9.43327	+	6.26864i	−0.358082	+	0.237954i
$695$	−9.82691	+	5.67357i	−0.372756	+	0.215211i
$696$	6.92055	+	14.1619i	0.262323	+	0.536804i
$697$	22.4467	−	38.8789i	0.850231	−	1.47264i
$698$	26.7232	−	17.7582i	1.01149	−	0.672159i
$699$	6.99269	+	25.6868i	0.264488	+	0.971562i
$700$	15.9880	+	3.13054i	0.604288	+	0.118323i
$701$	2.81981			0.106503			0.0532513	−	0.998581i	$-0.483042\pi$
$701$	2.81981			0.106503			0.0532513	+	0.998581i	$0.483042\pi$
$702$	−9.69997	−	8.34602i	−0.366102	−	0.315000i
$703$	−20.4439	+	11.8033i	−0.771055	+	0.445169i
$704$	−38.6939	+	15.3435i	−1.45833	+	0.578280i
$705$	−11.9023	−	3.13838i	−0.448267	−	0.118198i
$706$	−10.2677	−	5.09580i	−0.386429	−	0.191783i
$707$	−1.13512	−	1.27353i	−0.0426907	−	0.0478960i
$708$	0.532176	−	0.692008i	0.0200004	−	0.0260073i
$709$	−5.82924	+	3.36551i	−0.218922	+	0.126394i	−0.605451	−	0.795883i	$-0.707007\pi$
$709$	−5.82924	+	3.36551i	−0.218922	+	0.126394i	0.386529	+	0.922277i	$0.373674\pi$
$710$	−7.23929	−	3.59283i	−0.271686	−	0.134836i
$711$	40.2329	−	23.6585i	1.50885	−	0.887262i
$712$	33.1259	+	11.5259i	1.24145	+	0.431952i
$713$	18.7326	−	32.4458i	0.701542	−	1.21511i
$714$	0.397321	+	41.7800i	0.0148694	+	1.56358i
$715$	−10.8759	+	6.27923i	−0.406737	+	0.234830i
$716$	−12.0287	+	28.6292i	−0.449535	+	1.06992i
$717$	2.57888	+	0.679993i	0.0963100	+	0.0253948i
$718$	2.04176	+	3.07251i	0.0761977	+	0.114665i
$719$	11.8537	−	20.5311i	0.442067	−	0.765683i	−0.555776	−	0.831332i	$-0.687579\pi$
$719$	11.8537	−	20.5311i	0.442067	−	0.765683i	0.997843	+	0.0656497i	$0.0209120\pi$
$720$	−4.33932	+	16.0568i	−0.161717	+	0.598401i
$721$	29.1511	+	32.7055i	1.08564	+	1.21802i
$722$	0.934027	+	14.8252i	0.0347609	+	0.551739i
$723$	−12.9953	+	13.0994i	−0.483302	+	0.487173i
$724$	−10.2489	−	13.4975i	−0.380896	−	0.501630i
$725$	−4.95302	+	8.57888i	−0.183951	+	0.318612i
$726$	−12.7093	−	37.2616i	−0.471685	−	1.38291i
$727$	−33.8289	−	19.5311i	−1.25464	−	0.724369i	−0.282616	−	0.959233i	$-0.591202\pi$
$727$	−33.8289	−	19.5311i	−1.25464	−	0.724369i	−0.972028	+	0.234864i	$0.924535\pi$
$728$	−1.69497	+	12.9204i	−0.0628198	+	0.478862i
$729$	−0.646212	−	26.9923i	−0.0239338	−	0.999714i
$730$	0.0238389	+	0.378381i	0.000882318	+	0.0140045i
$731$		−	24.8717i		−	0.919912i
$732$	−8.78764	+	3.62893i	−0.324801	+	0.134129i
$733$	−42.5629			−1.57210			−0.786049	−	0.618164i	$-0.787877\pi$
$733$	−42.5629			−1.57210			−0.786049	+	0.618164i	$0.787877\pi$
$734$	−2.68876	+	5.41767i	−0.0992440	+	0.199970i
$735$	−10.4961	−	13.1242i	−0.387155	−	0.484094i
$736$	−33.6435	−	30.2661i	−1.24012	−	1.11562i
$737$	−13.9950	−	8.08003i	−0.515513	−	0.297632i
$738$	29.4688	−	2.09279i	1.08476	−	0.0770366i
$739$	−18.9808	+	10.9585i	−0.698218	+	0.403117i	−0.806684	−	0.590984i	$-0.798740\pi$
$739$	−18.9808	+	10.9585i	−0.698218	+	0.403117i	0.108465	+	0.994100i	$0.465406\pi$
$740$	11.9525	−	1.51208i	0.439384	−	0.0555852i
$741$	11.6305	+	11.5381i	0.427257	+	0.423861i
$742$	−24.9794	−	24.7051i	−0.917022	−	0.906953i
$743$	−14.8490	+	8.57308i	−0.544758	+	0.314516i	−0.747005	−	0.664819i	$-0.768509\pi$
$743$	−14.8490	+	8.57308i	−0.544758	+	0.314516i	0.202247	+	0.979334i	$0.435176\pi$
$744$	20.6134	−	10.0733i	0.755726	−	0.369304i
$745$			17.5861i			0.644304i
$746$	−2.76789	+	5.57710i	−0.101340	+	0.204192i
$747$	15.4100	−	27.1896i	0.563822	−	0.994815i
$748$	25.9876	−	61.8524i	0.950202	−	2.26155i
$749$	8.76069	+	42.2619i	0.320109	+	1.54422i
$750$	−25.9603	+	8.85460i	−0.947937	+	0.323324i
$751$	−48.3706			−1.76507			−0.882533	−	0.470250i	$-0.844164\pi$
$751$	−48.3706			−1.76507			−0.882533	+	0.470250i	$0.844164\pi$
$752$	19.8628	−	5.10730i	0.724321	−	0.186244i
$753$	−15.6596	+	15.7850i	−0.570666	+	0.575237i
$754$	−7.09751	−	3.52246i	−0.258476	−	0.128280i
$755$			19.6636i			0.715633i
$756$	−22.6306	+	15.6159i	−0.823067	+	0.567944i
$757$			39.5129i			1.43612i	0.695980	+	0.718061i	$0.254970\pi$
$757$			39.5129i			1.43612i	−0.695980	+	0.718061i	$0.745030\pi$
$758$	−2.82906	+	5.70036i	−0.102756	+	0.207047i
$759$	50.7753	−	51.1820i	1.84303	−	1.85779i
$760$	6.99779	−	20.1119i	0.253837	−	0.729536i
$761$	−12.2459			−0.443913			−0.221956	−	0.975057i	$-0.571244\pi$
$761$	−12.2459			−0.443913			−0.221956	+	0.975057i	$0.571244\pi$
$762$	7.07000	+	20.7282i	0.256119	+	0.750902i
$763$	6.01834	−	18.2098i	0.217879	−	0.659239i
$764$	8.95930	+	3.76430i	0.324136	+	0.136188i
$765$	−13.5890	−	23.1090i	−0.491310	−	0.835507i
$766$	34.7719	+	17.2571i	1.25636	+	0.623525i
$767$			0.438833i			0.0158453i
$768$	−6.73655	−	26.8816i	−0.243084	−	0.970005i
$769$	−19.6851	+	11.3652i	−0.709862	+	0.409839i	−0.811010	−	0.585032i	$-0.801082\pi$
$769$	−19.6851	+	11.3652i	−0.709862	+	0.409839i	0.101148	+	0.994871i	$0.467749\pi$
$770$	7.12785	+	26.0260i	0.256870	+	0.937911i
$771$	0.813483	+	0.807018i	0.0292969	+	0.0290640i
$772$	14.0378	−	1.77588i	0.505231	−	0.0639153i
$773$	−7.30819	+	4.21939i	−0.262857	+	0.151761i	−0.625637	−	0.780114i	$-0.715161\pi$
$773$	−7.30819	+	4.21939i	−0.262857	+	0.151761i	0.362780	+	0.931875i	$0.381828\pi$
$774$	13.5592	−	9.16719i	0.487374	−	0.329508i
$775$	12.4871	+	7.20942i	0.448549	+	0.258970i
$776$	−4.03570	+	11.5987i	−0.144873	+	0.416371i
$777$	16.6916	+	10.8646i	0.598808	+	0.389765i
$778$	8.81491	+	4.37480i	0.316030	+	0.156844i
$779$	−37.8232			−1.35516
$780$	−3.19137	−	7.72806i	−0.114269	−	0.276709i
$781$			21.4523i			0.767624i
$782$	72.7948	−	4.58625i	2.60314	−	0.164004i
$783$	−4.52003	−	16.0959i	−0.161533	−	0.575221i
$784$	25.9322	+	10.5603i	0.926151	+	0.377152i
$785$	9.31566	+	5.37840i	0.332490	+	0.191963i
$786$	−27.7889	+	9.47829i	−0.991196	+	0.338079i
$787$	0.806833	−	1.39748i	0.0287605	−	0.0498146i	−0.851287	−	0.524700i	$-0.824177\pi$
$787$	0.806833	−	1.39748i	0.0287605	−	0.0498146i	0.880047	+	0.474886i	$0.157511\pi$
$788$	−9.98470	−	13.1496i	−0.355690	−	0.468434i
$789$	20.9285	−	21.0961i	0.745073	−	0.751041i
$790$	30.4360	−	1.91754i	1.08286	−	0.0682231i
$791$	−1.85443	+	5.61097i	−0.0659358	+	0.199503i
$792$	43.2983	−	8.63000i	1.53854	−	0.306654i
$793$	2.38963	−	4.13897i	0.0848584	−	0.146979i
$794$	28.7466	−	19.1028i	1.02018	−	0.677933i
$795$	21.7971	+	5.74740i	0.773062	+	0.203839i
$796$	10.3239	+	4.33765i	0.365921	+	0.153744i
$797$	33.9341	−	19.5918i	1.20201	−	0.693979i	0.241005	−	0.970524i	$-0.422523\pi$
$797$	33.9341	−	19.5918i	1.20201	−	0.693979i	0.961001	+	0.276545i	$0.0891895\pi$
$798$	30.3168	−	17.8900i	1.07320	−	0.633298i
$799$	−16.5278	+	28.6271i	−0.584713	+	1.01275i
$800$	11.6482	−	12.9480i	0.411826	−	0.457782i
$801$	−32.3647	−	18.3431i	−1.14355	−	0.648120i
$802$	−7.06085	+	14.2271i	−0.249327	+	0.502377i
$803$	0.871535	−	0.503181i	0.0307558	−	0.0177569i
$804$	6.55877	−	8.52861i	0.231310	−	0.300781i
$805$	−21.9003	+	19.5202i	−0.771883	+	0.687995i
$806$	−5.12715	+	10.3308i	−0.180596	+	0.363889i
$807$	−41.4627	−	10.9328i	−1.45955	−	0.384852i
$808$	−1.79138	+	0.342211i	−0.0630205	+	0.0120389i
$809$	26.9604	−	15.5656i	0.947878	−	0.547258i	0.0554570	−	0.998461i	$-0.482338\pi$
$809$	26.9604	−	15.5656i	0.947878	−	0.547258i	0.892421	+	0.451203i	$0.149005\pi$
$810$	7.58961	−	15.9257i	0.266672	−	0.559574i
$811$	−36.2595			−1.27324			−0.636621	−	0.771177i	$-0.719669\pi$
$811$	−36.2595			−1.27324			−0.636621	+	0.771177i	$0.719669\pi$
$812$	−11.1873	+	12.8338i	−0.392596	+	0.450379i
$813$	−3.59740	−	13.2146i	−0.126166	−	0.463456i
$814$	−17.6996	−	26.6349i	−0.620369	−	0.933553i
$815$	−3.38236	+	5.85842i	−0.118479	+	0.205211i
$816$	38.5449	+	22.5702i	1.34934	+	0.790115i
$817$	−18.1472	+	10.4773i	−0.634892	+	0.366555i
$818$	−5.26736	−	7.92651i	−0.184169	−	0.277144i
$819$	4.23245	−	13.1576i	0.147894	−	0.459764i
$820$	17.7964	+	7.47725i	0.621477	+	0.261117i
$821$	7.72528	+	13.3806i	0.269614	+	0.466986i	0.968762	−	0.247991i	$-0.0797705\pi$
$821$	7.72528	+	13.3806i	0.269614	+	0.466986i	−0.699148	+	0.714977i	$0.746437\pi$
$822$	43.2020	−	14.7354i	1.50684	−	0.513957i
$823$	11.6298	−	20.1434i	0.405389	−	0.702154i	−0.588978	−	0.808149i	$-0.700470\pi$
$823$	11.6298	−	20.1434i	0.405389	−	0.702154i	0.994367	+	0.105995i	$0.0338029\pi$
$824$	46.0045	−	8.78833i	1.60264	−	0.306156i
$825$	19.6979	+	19.5413i	0.685792	+	0.680342i
$826$	0.912126	+	0.239015i	0.0317369	+	0.00831638i
$827$	19.1746			0.666764			0.333382	−	0.942792i	$-0.391810\pi$
$827$	19.1746			0.666764			0.333382	+	0.942792i	$0.391810\pi$
$828$	29.3310	+	37.9948i	1.01932	+	1.32041i
$829$	−23.2242	−	40.2255i	−0.806610	−	1.39709i	−0.915199	−	0.403003i	$-0.867966\pi$
$829$	−23.2242	−	40.2255i	−0.806610	−	1.39709i	0.108589	−	0.994087i	$-0.465367\pi$
$830$	17.0077	−	11.3021i	0.590347	−	0.392300i
$831$	−19.6911	+	19.8489i	−0.683078	+	0.688550i
$832$	10.9221	+	8.64739i	0.378654	+	0.299794i
$833$	−41.4109	+	17.9394i	−1.43480	+	0.621565i
$834$	−13.1998	+	15.0959i	−0.457072	+	0.522727i
$835$	−14.4851	+	8.36295i	−0.501276	+	0.289412i
$836$	−56.0771	+	7.09415i	−1.93947	+	0.245356i
$837$	−23.4286	+	6.57917i	−0.809810	+	0.227409i
$838$	−48.9864	+	3.08627i	−1.69221	+	0.106613i
$839$	13.1026	−	22.6945i	0.452354	−	0.783499i	−0.546178	−	0.837669i	$-0.683918\pi$
$839$	13.1026	−	22.6945i	0.452354	−	0.783499i	0.998532	+	0.0541696i	$0.0172512\pi$
$840$	−17.8012	+	2.42418i	−0.614199	+	0.0836421i
$841$	9.32390	+	16.1495i	0.321514	+	0.556878i
$842$	5.22325	+	7.86013i	0.180005	+	0.270878i
$843$	−1.53962	−	5.65560i	−0.0530273	−	0.194789i
$844$	41.9870	+	17.6411i	1.44525	+	0.607231i
$845$	−11.9649	−	6.90794i	−0.411605	−	0.237640i
$846$	−21.6983	+	1.54095i	−0.746003	+	0.0529789i
$847$	31.7444	−	28.2944i	1.09075	−	0.972208i
$848$	−36.3753	+	9.35315i	−1.24913	+	0.321188i
$849$	−38.3826	+	10.4489i	−1.31729	+	0.358605i
$850$	1.76506	+	28.0158i	0.0605411	+	0.960933i
$851$	17.3838	−	30.1097i	0.595910	−	1.03215i
$852$	−14.1582	−	1.87940i	−0.485051	−	0.0643871i
$853$	20.6174	−	35.7104i	0.705926	−	1.22270i	−0.260430	−	0.965493i	$-0.583864\pi$
$853$	20.6174	−	35.7104i	0.705926	−	1.22270i	0.966356	−	0.257207i	$-0.0828022\pi$
$854$	−7.30142	−	7.22125i	−0.249849	−	0.247106i
$855$	−11.1367	+	19.6498i	−0.380868	+	0.672008i
$856$	43.5778	+	15.1626i	1.48946	+	0.518247i
$857$	10.3816			0.354630			0.177315	−	0.984154i	$-0.443259\pi$
$857$	10.3816			0.354630			0.177315	+	0.984154i	$0.443259\pi$
$858$	−14.6089	+	16.7074i	−0.498739	+	0.570380i
$859$	−21.7106			−0.740756			−0.370378	−	0.928881i	$-0.620772\pi$
$859$	−21.7106			−0.740756			−0.370378	+	0.928881i	$0.620772\pi$
$860$	10.6098	−	1.34222i	0.361791	−	0.0457692i
$861$	14.4570	+	28.4474i	0.492695	+	0.969483i
$862$	−10.4128	+	0.656029i	−0.354660	+	0.0223444i
$863$	41.4300	+	23.9196i	1.41029	+	0.814234i	0.995416	−	0.0956426i	$-0.0304906\pi$
$863$	41.4300	+	23.9196i	1.41029	+	0.814234i	0.414879	+	0.909877i	$0.363824\pi$
$864$	1.90237	+	29.3323i	0.0647199	+	0.997903i
$865$	9.79608	+	16.9673i	0.333077	+	0.576906i
$866$	−8.39847	+	16.9223i	−0.285392	+	0.575044i
$867$	−41.0538	+	11.1761i	−1.39426	+	0.379559i
$868$	18.6804	+	16.2837i	0.634054	+	0.552705i
$869$	−40.4746	−	70.1041i	−1.37301	−	2.37812i
$870$	2.11551	−	10.7171i	0.0717224	−	0.363342i
$871$			5.40837i			0.183255i
$872$	−13.4010	−	15.5170i	−0.453815	−	0.525471i
$873$	6.42266	−	11.3322i	0.217374	−	0.383538i
$874$	−34.0115	−	51.1817i	−1.15046	−	1.73125i
$875$	−19.7128	−	22.1164i	−0.666415	−	0.747672i
$876$	0.255738	+	0.619282i	0.00864057	+	0.0209236i
$877$		−	15.2628i		−	0.515387i	−0.966227	−	0.257693i	$-0.917038\pi$
$877$		−	15.2628i		−	0.515387i	0.966227	−	0.257693i	$-0.0829624\pi$
$878$	−49.4853	+	3.11769i	−1.67005	+	0.105217i
$879$	31.6778	+	8.35274i	1.06847	+	0.281731i
$880$	27.7876	+	7.74795i	0.936719	+	0.261183i
$881$	17.9939			0.606231			0.303115	−	0.952954i	$-0.401973\pi$
$881$	17.9939			0.606231			0.303115	+	0.952954i	$0.401973\pi$
$882$	−25.0432	−	15.9637i	−0.843248	−	0.537525i
$883$			15.1963i			0.511395i	0.966757	+	0.255697i	$0.0823051\pi$
$883$			15.1963i			0.511395i	−0.966757	+	0.255697i	$0.917695\pi$
$884$	−22.2758	+	2.81805i	−0.749217	+	0.0947813i
$885$	−0.583757	+	0.158916i	−0.0196228	+	0.00534190i
$886$	0.143703	+	2.28092i	0.00482781	+	0.0766289i
$887$	44.8745			1.50674			0.753369	−	0.657598i	$-0.228428\pi$
$887$	44.8745			1.50674			0.753369	+	0.657598i	$0.228428\pi$
$888$	19.1292	−	9.34798i	0.641935	−	0.313698i
$889$	−17.6590	+	15.7398i	−0.592264	+	0.527897i
$890$	−13.4532	−	20.2449i	−0.450954	−	0.678611i
$891$	−46.8222	+	0.747222i	−1.56860	+	0.0250329i
$892$	0.177703	+	1.40469i	0.00594992	+	0.0470323i
$893$	27.8497			0.931956
$894$	10.0328	+	29.4146i	0.335546	+	0.983770i
$895$	18.6379	−	10.7606i	0.622995	−	0.359686i
$896$	23.9226	−	17.9919i	0.799199	−	0.601067i
$897$	−23.3311	−	6.15189i	−0.779002	−	0.205406i
$898$	7.49143	−	15.0947i	0.249992	−	0.503716i
$899$	−13.0495	+	7.53412i	−0.435224	+	0.251277i
$900$	−14.6227	+	11.2883i	−0.487422	+	0.376277i
$901$	30.2679	−	52.4255i	1.00837	−	1.74655i
$902$	−3.22178	−	51.1374i	−0.107274	−	1.70269i
$903$	14.8165	+	9.64407i	0.493062	+	0.320935i
$904$	4.12923	+	4.78123i	0.137336	+	0.159021i
$905$			11.7453i			0.390426i
$906$	11.2180	+	32.8895i	0.372694	+	1.09268i
$907$		−	57.0745i		−	1.89513i	−0.319567	−	0.947564i	$-0.603538\pi$
$907$		−	57.0745i		−	1.89513i	0.319567	−	0.947564i	$-0.396462\pi$
$908$	−3.26458	+	2.47885i	−0.108339	+	0.0822637i
$909$	1.93434	−	0.0154338i	0.0641580	−	0.000511908i
$910$	6.35054	−	6.42104i	0.210518	−	0.212855i
$911$	38.3006	+	22.1129i	1.26896	+	0.732632i	0.974791	−	0.223122i	$-0.0716249\pi$
$911$	38.3006	+	22.1129i	1.26896	+	0.732632i	0.294166	+	0.955754i	$0.404958\pi$
$912$	0.230790	−	37.6315i	0.00764223	−	1.24610i
$913$	−46.9422	−	27.1021i	−1.55356	−	0.896949i
$914$	−2.96064	−	46.9925i	−0.0979293	−	1.55437i
$915$	6.37123	+	1.67995i	0.210626	+	0.0555375i
$916$	9.19080	+	12.1040i	0.303672	+	0.399928i
$917$	−21.1013	−	23.6742i	−0.696828	−	0.781792i
$918$	−35.9126	−	30.8998i	−1.18529	−	1.01985i
$919$	−4.64681	+	8.04851i	−0.153284	+	0.265496i	−0.932433	−	0.361343i	$-0.882318\pi$
$919$	−4.64681	+	8.04851i	−0.153284	+	0.265496i	0.779149	+	0.626839i	$0.215652\pi$
$920$	5.88484	+	30.8055i	0.194017	+	1.01563i
$921$	−5.07765	−	5.03730i	−0.167314	−	0.165985i
$922$	27.0413	+	40.6927i	0.890557	+	1.34014i
$923$	6.21768	−	3.58978i	0.204657	−	0.118159i
$924$	26.7698	+	39.4648i	0.880662	+	1.29830i
$925$	11.5880	+	6.69033i	0.381011	+	0.219977i
$926$	−1.63246	−	25.9110i	−0.0536460	−	0.851490i
$927$	−49.6759	+	0.396357i	−1.63157	+	0.0130181i
$928$	5.63193	+	17.3076i	0.184877	+	0.568148i
$929$	−16.0965	−	27.8799i	−0.528108	−	0.914710i	−0.999463	−	0.0327664i	$-0.989568\pi$
$929$	−16.0965	−	27.8799i	−0.528108	−	0.914710i	0.471355	−	0.881944i	$-0.343765\pi$
$930$	−15.5993	−	3.07925i	−0.511522	−	0.100973i
$931$	30.5338	+	22.6578i	1.00070	+	0.742578i
$932$	3.85807	+	30.4969i	0.126375	+	0.998958i
$933$	−18.3792	+	5.00336i	−0.601708	+	0.163803i
$934$	17.2011	+	25.8848i	0.562836	+	0.846976i
$935$	−40.2664	+	23.2478i	−1.31685	+	0.760286i
$936$	−9.74673	−	11.1053i	−0.318582	−	0.362989i
$937$			15.0349i			0.491170i	0.969375	+	0.245585i	$0.0789800\pi$
$937$			15.0349i			0.491170i	−0.969375	+	0.245585i	$0.921020\pi$
$938$	11.2414	+	2.94572i	0.367046	+	0.0961811i
$939$	43.9592	+	11.5911i	1.43455	+	0.378260i
$940$	−13.1037	−	5.50560i	−0.427397	−	0.179573i
$941$	5.11708	+	2.95435i	0.166812	+	0.0963090i	0.581082	−	0.813845i	$-0.302630\pi$
$941$	5.11708	+	2.95435i	0.166812	+	0.0963090i	−0.414270	+	0.910154i	$0.635963\pi$
$942$	18.6498	+	3.68140i	0.607643	+	0.119946i
$943$	48.2427	−	27.8530i	1.57100	−	0.907017i
$944$	0.719960	−	0.705531i	0.0234327	−	0.0229631i
$945$	19.0356	+	0.865404i	0.619229	+	0.0281516i
$946$	−15.7112	−	23.6428i	−0.510816	−	0.768694i
$947$	−9.73326	−	16.8585i	−0.316289	−	0.547828i	0.663422	−	0.748245i	$-0.269103\pi$
$947$	−9.73326	−	16.8585i	−0.316289	−	0.547828i	−0.979711	+	0.200418i	$0.935770\pi$
$948$	49.8135	−	20.5709i	1.61787	−	0.668112i
$949$	−0.291681	−	0.168402i	−0.00946836	−	0.00546656i
$950$	19.6978	−	13.0896i	0.639080	−	0.424684i
$951$	8.53683	−	32.3760i	0.276826	−	1.04986i
$952$	−6.27536	+	47.8358i	−0.203385	+	1.55037i
$953$		−	9.07704i		−	0.294034i	−0.989134	−	0.147017i	$-0.953033\pi$
$953$		−	9.07704i		−	0.294034i	0.989134	−	0.147017i	$-0.0469672\pi$
$954$	39.7367	−	2.82199i	1.28652	−	0.0913651i
$955$	−3.36744	−	5.83258i	−0.108968	−	0.188738i
$956$	2.83919	+	1.19290i	0.0918259	+	0.0385812i
$957$	−27.9780	+	7.61644i	−0.904401	+	0.246205i
$958$	−12.3663	−	6.13734i	−0.399537	−	0.198289i
$959$	32.8052	+	36.8052i	1.05934	+	1.18850i
$960$	−7.54794	+	17.6606i	−0.243609	+	0.569992i
$961$	−4.53364	−	7.85250i	−0.146247	−	0.253306i
$962$	−4.75799	+	9.58701i	−0.153404	+	0.309098i
$963$	−42.5765	−	24.1307i	−1.37201	−	0.777601i
$964$	−16.9690	+	12.8848i	−0.546534	+	0.414993i
$965$	−8.49241	−	4.90310i	−0.273380	−	0.157836i
$966$	−25.4943	+	45.1435i	−0.820267	+	1.45247i
$967$	−13.9378	−	24.1409i	−0.448208	−	0.776319i	0.550061	−	0.835124i	$-0.314604\pi$
$967$	−13.9378	−	24.1409i	−0.448208	−	0.776319i	−0.998269	+	0.0588052i	$0.981271\pi$
$968$	−8.53006	−	44.6525i	−0.274167	−	1.43519i
$969$	43.0600	+	42.7178i	1.38329	+	1.37229i
$970$	7.08858	−	4.71053i	0.227601	−	0.151246i
$971$	24.0862	+	13.9062i	0.772964	+	0.446271i	0.833931	−	0.551869i	$-0.186085\pi$
$971$	24.0862	+	13.9062i	0.772964	+	0.446271i	−0.0609669	+	0.998140i	$0.519418\pi$
$972$	3.60885	−	30.9673i	0.115754	−	0.993278i
$973$	−20.5655	−	6.79691i	−0.659301	−	0.217899i
$974$	−3.14801	−	49.9665i	−0.100869	−	1.60103i
$975$	2.36761	−	8.97918i	0.0758242	−	0.287564i
$976$	−10.6324	+	2.73390i	−0.340335	+	0.0875101i
$977$	13.3158	+	7.68790i	0.426011	+	0.245958i	0.697646	−	0.716443i	$-0.254231\pi$
$977$	13.3158	+	7.68790i	0.426011	+	0.245958i	−0.271635	+	0.962400i	$0.587564\pi$
$978$	−2.31515	+	11.7284i	−0.0740304	+	0.375034i
$979$	−32.2606	+	55.8770i	−1.03105	+	1.78584i
$980$	−9.88741	−	16.6970i	−0.315842	−	0.533367i
$981$	11.0231	+	18.7456i	0.351942	+	0.598502i
$982$	−2.13004	−	33.8088i	−0.0679723	−	1.07888i
$983$	−4.46865			−0.142528			−0.0712638	−	0.997457i	$-0.522703\pi$
$983$	−4.46865			−0.142528			−0.0712638	+	0.997457i	$0.522703\pi$
$984$	34.0321	+	2.35373i	1.08490	+	0.0750342i
$985$			11.4425i			0.364589i
$986$	−26.2774	−	13.0413i	−0.836842	−	0.415321i
$987$	−10.6449	−	20.9462i	−0.338832	−	0.666724i
$988$	11.4400	+	15.0661i	0.363953	+	0.479317i
$989$	15.4310	−	26.7272i	0.490676	−	0.849876i
$990$	−27.5153	−	13.3832i	−0.874494	−	0.425346i
$991$	−8.93541	−	15.4766i	−0.283843	−	0.491630i	0.688485	−	0.725250i	$-0.258276\pi$
$991$	−8.93541	−	15.4766i	−0.283843	−	0.491630i	−0.972328	+	0.233620i	$0.924943\pi$
$992$	25.1922	−	8.19762i	0.799853	−	0.260275i
$993$	42.3943	+	11.1784i	1.34534	+	0.354737i
$994$	−4.07493	−	14.8788i	−0.129249	−	0.471927i
$995$	−3.88034	−	6.72095i	−0.123015	−	0.213068i
$996$	21.9995	−	28.6067i	0.697080	−	0.906439i
$997$	2.76970			0.0877172			0.0438586	−	0.999038i	$-0.486035\pi$
$997$	2.76970			0.0877172			0.0438586	+	0.999038i	$0.486035\pi$
$998$	−12.7555	+	25.7014i	−0.403768	+	0.813564i
$999$	−21.7417	+	6.10546i	−0.687876	+	0.193168i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.y.a.173.15	✓	184
7.3	odd	6		504.2.ca.a.101.75	yes	184
8.5	even	2	inner	504.2.y.a.173.44	yes	184
9.5	odd	6		504.2.ca.a.5.18	yes	184
56.45	odd	6		504.2.ca.a.101.18	yes	184
63.59	even	6	inner	504.2.y.a.437.44	yes	184
72.5	odd	6		504.2.ca.a.5.75	yes	184
504.437	even	6	inner	504.2.y.a.437.15	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.y.a.173.15	✓	184	1.1	even	1	trivial
504.2.y.a.173.44	yes	184	8.5	even	2	inner
504.2.y.a.437.15	yes	184	504.437	even	6	inner
504.2.y.a.437.44	yes	184	63.59	even	6	inner
504.2.ca.a.5.18	yes	184	9.5	odd	6
504.2.ca.a.5.75	yes	184	72.5	odd	6
504.2.ca.a.101.18	yes	184	56.45	odd	6
504.2.ca.a.101.75	yes	184	7.3	odd	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.y (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26678 - 0.628698i) q^{2} +(1.22962 + 1.21985i) q^{3} +(1.20948 + 1.59285i) q^{4} -1.38607i q^{5} +(-0.790746 - 2.31834i) q^{6} +(1.97507 - 1.76042i) q^{7} +(-0.530723 - 2.77819i) q^{8} +(0.0239358 + 2.99990i) q^{9} +O(q^{10})\)	\(q+(-1.26678 - 0.628698i) q^{2} +(1.22962 + 1.21985i) q^{3} +(1.20948 + 1.59285i) q^{4} -1.38607i q^{5} +(-0.790746 - 2.31834i) q^{6} +(1.97507 - 1.76042i) q^{7} +(-0.530723 - 2.77819i) q^{8} +(0.0239358 + 2.99990i) q^{9} +(-0.871418 + 1.75585i) q^{10} +5.20313 q^{11} +(-0.455837 + 3.43398i) q^{12} +(-0.870678 - 1.50806i) q^{13} +(-3.60876 + 0.988348i) q^{14} +(1.69079 - 1.70434i) q^{15} +(-1.07433 + 3.85303i) q^{16} +(-3.22355 - 5.58335i) q^{17} +(1.85571 - 3.81528i) q^{18} +(-2.71587 + 4.70403i) q^{19} +(2.20780 - 1.67642i) q^{20} +(4.57604 + 0.244638i) q^{21} +(-6.59123 - 3.27120i) q^{22} -7.99985i q^{23} +(2.73638 - 4.06352i) q^{24} +3.07882 q^{25} +(0.154846 + 2.45778i) q^{26} +(-3.63000 + 3.71794i) q^{27} +(5.19289 + 1.01680i) q^{28} +(-1.60874 + 2.78642i) q^{29} +(-3.21338 + 1.09603i) q^{30} +(4.05580 + 2.34162i) q^{31} +(3.78334 - 4.20552i) q^{32} +(6.39787 + 6.34703i) q^{33} +(0.573292 + 9.09952i) q^{34} +(-2.44006 - 2.73758i) q^{35} +(-4.74944 + 3.66644i) q^{36} +(3.76378 + 2.17302i) q^{37} +(6.39783 - 4.25152i) q^{38} +(0.769000 - 2.91644i) q^{39} +(-3.85076 + 0.735618i) q^{40} +(3.48168 + 6.03045i) q^{41} +(-5.64305 - 3.18685i) q^{42} +(3.34096 + 1.92891i) q^{43} +(6.29306 + 8.28779i) q^{44} +(4.15807 - 0.0331766i) q^{45} +(-5.02949 + 10.1341i) q^{46} +(-2.56361 - 4.44031i) q^{47} +(-6.02113 + 3.42724i) q^{48} +(0.801824 - 6.95393i) q^{49} +(-3.90019 - 1.93565i) q^{50} +(2.84710 - 10.7976i) q^{51} +(1.34904 - 3.21082i) q^{52} +(4.69481 + 8.13166i) q^{53} +(6.93589 - 2.42765i) q^{54} -7.21188i q^{55} +(-5.93900 - 4.55283i) q^{56} +(-9.07769 + 2.47122i) q^{57} +(3.78974 - 2.51838i) q^{58} +(-0.218244 - 0.126003i) q^{59} +(4.75973 + 0.631820i) q^{60} +(1.37228 + 2.37687i) q^{61} +(-3.66565 - 5.51620i) q^{62} +(5.32838 + 5.88289i) q^{63} +(-7.43667 + 2.94890i) q^{64} +(-2.09027 + 1.20682i) q^{65} +(-4.11435 - 12.0626i) q^{66} +(-2.68973 - 1.55292i) q^{67} +(4.99462 - 11.8875i) q^{68} +(9.75861 - 9.83679i) q^{69} +(1.36992 + 5.00199i) q^{70} +4.12297i q^{71} +(8.32160 - 1.65862i) q^{72} +(0.167502 - 0.0967074i) q^{73} +(-3.40172 - 5.11902i) q^{74} +(3.78578 + 3.75569i) q^{75} +(-10.7776 + 1.36344i) q^{76} +(10.2766 - 9.15970i) q^{77} +(-2.80772 + 3.21102i) q^{78} +(-7.77890 - 13.4735i) q^{79} +(5.34055 + 1.48910i) q^{80} +(-8.99885 + 0.143610i) q^{81} +(-0.619201 - 9.82820i) q^{82} +(-9.02192 - 5.20881i) q^{83} +(5.14494 + 7.58482i) q^{84} +(-7.73889 + 4.46805i) q^{85} +(-3.01957 - 4.54396i) q^{86} +(-5.37716 + 1.46382i) q^{87} +(-2.76142 - 14.4553i) q^{88} +(-6.20023 + 10.7391i) q^{89} +(-5.28823 - 2.57214i) q^{90} +(-4.37447 - 1.44576i) q^{91} +(12.7426 - 9.67564i) q^{92} +(2.13068 + 7.82677i) q^{93} +(0.455926 + 7.23664i) q^{94} +(6.52010 + 3.76438i) q^{95} +(9.78217 - 0.556093i) q^{96} +(-3.76021 - 2.17096i) q^{97} +(-5.38766 + 8.30501i) q^{98} +(0.124541 + 15.6089i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9	\( 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9} - 6 q^{10} - 3 q^{12} - 3 q^{14} - 2 q^{15} + q^{16} - 15 q^{18} - 6 q^{22} - 12 q^{24} - 156 q^{25} + 6 q^{26} - 8 q^{28} - 14 q^{30} - 6 q^{31} - 33 q^{32} - 6 q^{33} - 6 q^{34} + 22 q^{36} - 66 q^{38} + 10 q^{39} - 15 q^{42} + 9 q^{44} + 2 q^{46} - 6 q^{47} - 9 q^{48} - 2 q^{49} + 9 q^{50} + 24 q^{54} + 60 q^{56} + 4 q^{57} + 6 q^{58} + 34 q^{60} - 12 q^{62} - 30 q^{63} - 8 q^{64} - 6 q^{65} - 21 q^{66} - 36 q^{68} + 30 q^{70} + 9 q^{72} - 12 q^{73} - 12 q^{76} + 19 q^{78} + 2 q^{79} + 57 q^{80} + 6 q^{81} + 9 q^{84} + 12 q^{87} - 18 q^{88} + 24 q^{89} + 75 q^{90} - 36 q^{92} - 3 q^{94} + 54 q^{95} - 54 q^{96} + 45 q^{98}+O(q^{100}) \) 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9 - 6 * q^10 - 3 * q^12 - 3 * q^14 - 2 * q^15 + q^16 - 15 * q^18 - 6 * q^22 - 12 * q^24 - 156 * q^25 + 6 * q^26 - 8 * q^28 - 14 * q^30 - 6 * q^31 - 33 * q^32 - 6 * q^33 - 6 * q^34 + 22 * q^36 - 66 * q^38 + 10 * q^39 - 15 * q^42 + 9 * q^44 + 2 * q^46 - 6 * q^47 - 9 * q^48 - 2 * q^49 + 9 * q^50 + 24 * q^54 + 60 * q^56 + 4 * q^57 + 6 * q^58 + 34 * q^60 - 12 * q^62 - 30 * q^63 - 8 * q^64 - 6 * q^65 - 21 * q^66 - 36 * q^68 + 30 * q^70 + 9 * q^72 - 12 * q^73 - 12 * q^76 + 19 * q^78 + 2 * q^79 + 57 * q^80 + 6 * q^81 + 9 * q^84 + 12 * q^87 - 18 * q^88 + 24 * q^89 + 75 * q^90 - 36 * q^92 - 3 * q^94 + 54 * q^95 - 54 * q^96 + 45 * q^98

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