LMFDB - Embedded newform 153.3.t.a.7.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(7,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([32, 33])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.t (of order $48$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$544$
Relative dimension:	$34$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			7.15
Character	$\chi$	$=$	153.7
Dual form			153.3.t.a.22.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.434047 - 0.565661i) q^{2} +(1.99588 - 2.23974i) q^{3} +(0.903701 - 3.37266i) q^{4} +(-4.79864 + 4.20829i) q^{5} +(-2.13324 - 0.156838i) q^{6} +(-7.75304 - 6.79923i) q^{7} +(-4.93493 + 2.04412i) q^{8} +(-1.03291 - 8.94053i) q^{9} +(4.46330 + 0.887806i) q^{10} +(0.196496 + 2.99795i) q^{11} +(-5.75021 - 8.75548i) q^{12} +(2.50444 + 0.671062i) q^{13} +(-0.480878 + 7.33678i) q^{14} +(-0.152016 + 19.1470i) q^{15} +(-8.79709 - 5.07900i) q^{16} +(15.4025 - 7.19455i) q^{17} +(-4.60898 + 4.46489i) q^{18} +(-1.04095 + 2.51307i) q^{19} +(9.85659 + 19.9872i) q^{20} +(-30.7027 + 3.79436i) q^{21} +(1.61054 - 1.41240i) q^{22} +(5.65973 - 11.4768i) q^{23} +(-5.27125 + 15.1328i) q^{24} +(2.05404 - 15.6020i) q^{25} +(-0.707449 - 1.70793i) q^{26} +(-22.0861 - 15.5308i) q^{27} +(-29.9379 + 20.0039i) q^{28} +(10.1927 - 30.0267i) q^{29} +(10.8967 - 8.22470i) q^{30} +(3.41201 - 52.0572i) q^{31} +(3.73420 + 28.3640i) q^{32} +(7.10683 + 5.54346i) q^{33} +(-10.7551 - 5.58984i) q^{34} +65.8172 q^{35} +(-31.0868 - 4.59591i) q^{36} +(-13.1701 + 19.7104i) q^{37} +(1.87337 - 0.501968i) q^{38} +(6.50156 - 4.26994i) q^{39} +(15.0787 - 30.5766i) q^{40} +(-21.8897 + 7.43056i) q^{41} +(15.4727 + 15.7204i) q^{42} +(75.9054 + 9.99314i) q^{43} +(10.2886 + 2.04654i) q^{44} +(42.5809 + 38.5556i) q^{45} +(-8.94857 + 1.77998i) q^{46} +(-7.83018 - 29.2226i) q^{47} +(-28.9336 + 9.56615i) q^{48} +(7.48427 + 56.8486i) q^{49} +(-9.71699 + 5.61011i) q^{50} +(14.6277 - 48.8572i) q^{51} +(4.52652 - 7.84016i) q^{52} +(-29.0266 + 70.0763i) q^{53} +(0.801228 + 19.2343i) q^{54} +(-13.5592 - 13.5592i) q^{55} +(52.1592 + 17.7056i) q^{56} +(3.55103 + 7.34726i) q^{57} +(-21.4091 + 7.26740i) q^{58} +(65.2058 + 50.0342i) q^{59} +(64.4388 + 17.8158i) q^{60} +(43.9581 - 50.1246i) q^{61} +(-30.9277 + 20.6652i) q^{62} +(-52.7806 + 76.3393i) q^{63} +(-14.3076 + 14.3076i) q^{64} +(-14.8419 + 7.31922i) q^{65} +(0.0510201 - 6.42618i) q^{66} +(101.618 - 58.6692i) q^{67} +(-10.3455 - 58.4492i) q^{68} +(-14.4089 - 35.5827i) q^{69} +(-28.5677 - 37.2302i) q^{70} +(8.17495 - 12.2347i) q^{71} +(23.3728 + 42.0095i) q^{72} +(-11.5734 - 58.1835i) q^{73} +(16.8659 - 1.10545i) q^{74} +(-30.8449 - 35.7403i) q^{75} +(7.53503 + 5.78183i) q^{76} +(18.8603 - 24.5793i) q^{77} +(-5.23732 - 1.82433i) q^{78} +(-7.05647 - 107.661i) q^{79} +(63.5880 - 12.6484i) q^{80} +(-78.8662 + 18.4695i) q^{81} +(13.7043 + 9.15695i) q^{82} +(-117.420 + 90.0997i) q^{83} +(-14.9490 + 106.979i) q^{84} +(-43.6344 + 99.3424i) q^{85} +(-27.2938 - 47.2742i) q^{86} +(-46.9088 - 82.7589i) q^{87} +(-7.09786 - 14.3930i) q^{88} +(2.00069 + 2.00069i) q^{89} +(3.32727 - 40.8213i) q^{90} +(-14.8543 - 22.2310i) q^{91} +(-33.5926 - 29.4599i) q^{92} +(-109.785 - 111.542i) q^{93} +(-13.1314 + 17.1132i) q^{94} +(-5.58061 - 16.4399i) q^{95} +(70.9812 + 48.2476i) q^{96} +(-44.6102 + 131.417i) q^{97} +(28.9085 - 28.9085i) q^{98} +(26.6003 - 4.85339i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} + 176 q^{12} - 8 q^{13} - 8 q^{14} - 40 q^{15} - 32 q^{17} + 32 q^{18} - 32 q^{19} - 8 q^{20}+ \cdots + 448 q^{99}+O(q^{100}) $ 544 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 + 176 * q^12 - 8 * q^13 - 8 * q^14 - 40 * q^15 - 32 * q^17 + 32 * q^18 - 32 * q^19 - 8 * q^20 - 256 * q^21 - 8 * q^22 - 8 * q^23 + 176 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 72 * q^32 + 40 * q^34 - 64 * q^35 + 16 * q^36 - 32 * q^37 + 88 * q^38 - 192 * q^39 - 8 * q^40 - 440 * q^41 - 400 * q^42 - 248 * q^43 - 800 * q^44 - 176 * q^45 - 32 * q^46 + 112 * q^47 - 248 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 + 160 * q^53 - 312 * q^54 - 32 * q^55 - 488 * q^56 - 296 * q^57 - 8 * q^58 + 568 * q^59 + 2080 * q^60 - 8 * q^61 + 1120 * q^62 - 88 * q^63 - 288 * q^64 - 248 * q^65 - 24 * q^66 - 8 * q^68 - 416 * q^69 - 40 * q^70 - 32 * q^71 + 632 * q^72 - 32 * q^73 - 8 * q^74 + 752 * q^75 - 8 * q^76 - 8 * q^77 - 2304 * q^78 - 8 * q^79 - 432 * q^80 + 768 * q^81 + 352 * q^82 - 296 * q^83 - 8 * q^85 + 1184 * q^86 - 688 * q^87 - 8 * q^88 - 1184 * q^89 - 1136 * q^90 + 640 * q^91 - 2024 * q^92 - 528 * q^93 - 8 * q^94 + 472 * q^95 - 1064 * q^96 - 8 * q^97 - 848 * q^98 + 448 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.434047	−	0.565661i	−0.217023	−	0.282830i	0.672136	−	0.740428i	$-0.265377\pi$
$2$	−0.434047	−	0.565661i	−0.217023	−	0.282830i	−0.889160	+	0.457597i	$0.848710\pi$
$3$	1.99588	−	2.23974i	0.665294	−	0.746581i
$3$	1.99588	−	2.23974i	0.665294	−	0.746581i
$4$	0.903701	−	3.37266i	0.225925	−	0.843164i
$5$	−4.79864	+	4.20829i	−0.959727	+	0.841658i	−0.987446	−	0.157957i	$-0.949509\pi$
$5$	−4.79864	+	4.20829i	−0.959727	+	0.841658i	0.0277186	+	0.999616i	$0.491176\pi$
$6$	−2.13324	−	0.156838i	−0.355540	−	0.0261397i
$7$	−7.75304	−	6.79923i	−1.10758	−	0.971319i	−0.107838	−	0.994168i	$-0.534393\pi$
$7$	−7.75304	−	6.79923i	−1.10758	−	0.971319i	−0.999739	+	0.0228495i	$0.992726\pi$
$8$	−4.93493	+	2.04412i	−0.616867	+	0.255515i
$9$	−1.03291	−	8.94053i	−0.114768	−	0.993392i
$10$	4.46330	+	0.887806i	0.446330	+	0.0887806i
$11$	0.196496	+	2.99795i	0.0178633	+	0.272541i	0.997442	+	0.0714801i	$0.0227722\pi$
$11$	0.196496	+	2.99795i	0.0178633	+	0.272541i	−0.979579	+	0.201061i	$0.935561\pi$
$12$	−5.75021	−	8.75548i	−0.479184	−	0.729624i
$13$	2.50444	+	0.671062i	0.192649	+	0.0516201i	0.353853	−	0.935301i	$-0.384871\pi$
$13$	2.50444	+	0.671062i	0.192649	+	0.0516201i	−0.161204	+	0.986921i	$0.551538\pi$
$14$	−0.480878	+	7.33678i	−0.0343484	+	0.524056i
$15$	−0.152016	+	19.1470i	−0.0101344	+	1.27646i
$16$	−8.79709	−	5.07900i	−0.549818	−	0.317438i
$17$	15.4025	−	7.19455i	0.906032	−	0.423209i
$17$	15.4025	−	7.19455i	0.906032	−	0.423209i
$18$	−4.60898	+	4.46489i	−0.256054	+	0.248049i
$19$	−1.04095	+	2.51307i	−0.0547868	+	0.132267i	−0.948903	−	0.315568i	$-0.897805\pi$
$19$	−1.04095	+	2.51307i	−0.0547868	+	0.132267i	0.894116	+	0.447835i	$0.147805\pi$
$20$	9.85659	+	19.9872i	0.492830	+	0.999359i
$21$	−30.7027	+	3.79436i	−1.46203	+	0.180684i
$22$	1.61054	−	1.41240i	0.0732062	−	0.0642001i
$23$	5.65973	−	11.4768i	0.246075	−	0.498991i	−0.738434	−	0.674326i	$-0.764434\pi$
$23$	5.65973	−	11.4768i	0.246075	−	0.498991i	0.984509	+	0.175335i	$0.0561008\pi$
$24$	−5.27125	+	15.1328i	−0.219635	+	0.630534i
$25$	2.05404	−	15.6020i	0.0821617	−	0.624080i
$26$	−0.707449	−	1.70793i	−0.0272096	−	0.0656898i
$27$	−22.0861	−	15.5308i	−0.818003	−	0.575215i
$28$	−29.9379	+	20.0039i	−1.06921	+	0.714424i
$29$	10.1927	−	30.0267i	0.351473	−	1.03540i	−0.617145	−	0.786849i	$-0.711711\pi$
$29$	10.1927	−	30.0267i	0.351473	−	1.03540i	0.968618	−	0.248555i	$-0.0799558\pi$
$30$	10.8967	−	8.22470i	0.363223	−	0.274157i
$31$	3.41201	−	52.0572i	0.110065	−	1.67927i	−0.484170	−	0.874974i	$-0.660878\pi$
$31$	3.41201	−	52.0572i	0.110065	−	1.67927i	0.594235	−	0.804291i	$-0.297455\pi$
$32$	3.73420	+	28.3640i	0.116694	+	0.886376i
$33$	7.10683	+	5.54346i	0.215358	+	0.167984i
$34$	−10.7551	−	5.58984i	−0.316327	−	0.164407i
$35$	65.8172			1.88049
$36$	−31.0868	−	4.59591i	−0.863522	−	0.127664i
$37$	−13.1701	+	19.7104i	−0.355949	+	0.532715i	−0.965626	−	0.259935i	$-0.916299\pi$
$37$	−13.1701	+	19.7104i	−0.355949	+	0.532715i	0.609678	+	0.792650i	$0.291299\pi$
$38$	1.87337	−	0.501968i	0.0492992	−	0.0132097i
$39$	6.50156	−	4.26994i	0.166707	−	0.109486i
$40$	15.0787	−	30.5766i	0.376968	−	0.764415i
$41$	−21.8897	+	7.43056i	−0.533895	+	0.181233i	−0.575350	−	0.817907i	$-0.695134\pi$
$41$	−21.8897	+	7.43056i	−0.533895	+	0.181233i	0.0414546	+	0.999140i	$0.486801\pi$
$42$	15.4727	+	15.7204i	0.368398	+	0.374295i
$43$	75.9054	+	9.99314i	1.76524	+	0.232398i	0.942075	−	0.335401i	$-0.108872\pi$
$43$	75.9054	+	9.99314i	1.76524	+	0.232398i	0.823167	+	0.567800i	$0.192205\pi$
$44$	10.2886	+	2.04654i	0.233833	+	0.0465122i
$45$	42.5809	+	38.5556i	0.946243	+	0.856791i
$46$	−8.94857	+	1.77998i	−0.194534	+	0.0386952i
$47$	−7.83018	−	29.2226i	−0.166600	−	0.621758i	−0.997831	−	0.0658311i	$-0.979030\pi$
$47$	−7.83018	−	29.2226i	−0.166600	−	0.621758i	0.831231	−	0.555927i	$-0.187637\pi$
$48$	−28.9336	+	9.56615i	−0.602784	+	0.199295i
$49$	7.48427	+	56.8486i	0.152740	+	1.16018i
$50$	−9.71699	+	5.61011i	−0.194340	+	0.112202i
$51$	14.6277	−	48.8572i	0.286818	−	0.957985i
$52$	4.52652	−	7.84016i	0.0870485	−	0.150772i
$53$	−29.0266	+	70.0763i	−0.547671	+	1.32220i	0.371535	+	0.928419i	$0.378831\pi$
$53$	−29.0266	+	70.0763i	−0.547671	+	1.32220i	−0.919206	+	0.393776i	$0.871169\pi$
$54$	0.801228	+	19.2343i	0.0148376	+	0.356191i
$55$	−13.5592	−	13.5592i	−0.246530	−	0.246530i
$56$	52.1592	+	17.7056i	0.931413	+	0.316172i
$57$	3.55103	+	7.34726i	0.0622988	+	0.128899i
$58$	−21.4091	+	7.26740i	−0.369122	+	0.125300i
$59$	65.2058	+	50.0342i	1.10518	+	0.848037i	0.989397	−	0.145237i	$-0.0463944\pi$
$59$	65.2058	+	50.0342i	1.10518	+	0.848037i	0.115787	+	0.993274i	$0.463061\pi$
$60$	64.4388	+	17.8158i	1.07398	+	0.296930i
$61$	43.9581	−	50.1246i	0.720625	−	0.821715i	−0.269338	−	0.963046i	$-0.586805\pi$
$61$	43.9581	−	50.1246i	0.720625	−	0.821715i	0.989962	+	0.141331i	$0.0451381\pi$
$62$	−30.9277	+	20.6652i	−0.498834	+	0.333310i
$63$	−52.7806	+	76.3393i	−0.837787	+	1.21173i
$64$	−14.3076	+	14.3076i	−0.223556	+	0.223556i
$65$	−14.8419	+	7.31922i	−0.228337	+	0.112603i
$66$	0.0510201	−	6.42618i	0.000773032	−	0.0973663i
$67$	101.618	−	58.6692i	1.51669	−	0.875660i	0.516879	−	0.856058i	$-0.327094\pi$
$67$	101.618	−	58.6692i	1.51669	−	0.875660i	0.999808	−	0.0196017i	$-0.00623980\pi$
$68$	−10.3455	−	58.4492i	−0.152139	−	0.859547i
$69$	−14.4089	−	35.5827i	−0.208825	−	0.515691i
$70$	−28.5677	−	37.2302i	−0.408111	−	0.531860i
$71$	8.17495	−	12.2347i	0.115140	−	0.172319i	−0.769423	−	0.638739i	$-0.779456\pi$
$71$	8.17495	−	12.2347i	0.115140	−	0.172319i	0.884564	+	0.466420i	$0.154456\pi$
$72$	23.3728	+	42.0095i	0.324623	+	0.583466i
$73$	−11.5734	−	58.1835i	−0.158540	−	0.797034i	−0.975442	−	0.220257i	$-0.929310\pi$
$73$	−11.5734	−	58.1835i	−0.158540	−	0.797034i	0.816902	−	0.576777i	$-0.195690\pi$
$74$	16.8659	−	1.10545i	0.227917	−	0.0149385i
$75$	−30.8449	−	35.7403i	−0.411265	−	0.476537i
$76$	7.53503	+	5.78183i	0.0991451	+	0.0760767i
$77$	18.8603	−	24.5793i	0.244939	−	0.319211i
$78$	−5.23732	−	1.82433i	−0.0671451	−	0.0233888i
$79$	−7.05647	−	107.661i	−0.0893224	−	1.36280i	−0.773646	−	0.633618i	$-0.781569\pi$
$79$	−7.05647	−	107.661i	−0.0893224	−	1.36280i	0.684324	−	0.729178i	$-0.260097\pi$
$80$	63.5880	−	12.6484i	0.794850	−	0.158105i
$81$	−78.8662	+	18.4695i	−0.973657	+	0.228019i
$82$	13.7043	+	9.15695i	0.167126	+	0.111670i
$83$	−117.420	+	90.0997i	−1.41470	+	1.08554i	−0.431685	+	0.902025i	$0.642081\pi$
$83$	−117.420	+	90.0997i	−1.41470	+	1.08554i	−0.983017	+	0.183514i	$0.941253\pi$
$84$	−14.9490	+	106.979i	−0.177964	+	1.27355i
$85$	−43.6344	+	99.3424i	−0.513346	+	1.16873i
$86$	−27.2938	−	47.2742i	−0.317370	−	0.549700i
$87$	−46.9088	−	82.7589i	−0.539181	−	0.951251i
$88$	−7.09786	−	14.3930i	−0.0806575	−	0.163557i
$89$	2.00069	+	2.00069i	0.0224796	+	0.0224796i	0.718257	−	0.695778i	$-0.244940\pi$
$89$	2.00069	+	2.00069i	0.0224796	+	0.0224796i	−0.695778	+	0.718257i	$0.744940\pi$
$90$	3.32727	−	40.8213i	0.0369696	−	0.453570i
$91$	−14.8543	−	22.2310i	−0.163234	−	0.244297i
$92$	−33.5926	−	29.4599i	−0.365137	−	0.320216i
$93$	−109.785	−	111.542i	−1.18048	−	1.19938i
$94$	−13.1314	+	17.1132i	−0.139696	+	0.182055i
$95$	−5.58061	−	16.4399i	−0.0587433	−	0.173052i
$96$	70.9812	+	48.2476i	0.739388	+	0.502580i
$97$	−44.6102	+	131.417i	−0.459899	+	1.35482i	0.431710	+	0.902013i	$0.357911\pi$
$97$	−44.6102	+	131.417i	−0.459899	+	1.35482i	−0.891609	+	0.452807i	$0.850423\pi$
$98$	28.9085	−	28.9085i	0.294985	−	0.294985i
$99$	26.6003	−	4.85339i	0.268690	−	0.0490242i
$100$	−50.7639	−	21.0271i	−0.507639	−	0.210271i
$101$	−90.4534	−	52.2233i	−0.895578	−	0.517062i	−0.0198154	−	0.999804i	$-0.506308\pi$
$101$	−90.4534	−	52.2233i	−0.895578	−	0.517062i	−0.875763	+	0.482741i	$0.839641\pi$
$102$	−33.9857	+	12.9320i	−0.333194	+	0.126784i
$103$	13.5167	+	23.4117i	0.131231	+	0.227298i	0.924151	−	0.382027i	$-0.124774\pi$
$103$	13.5167	+	23.4117i	0.131231	+	0.227298i	−0.792921	+	0.609325i	$0.791441\pi$
$104$	−13.7310	+	1.80771i	−0.132028	+	0.0173819i
$105$	131.363	−	147.414i	1.25108	−	1.40394i
$106$	52.2383	−	13.9972i	0.492815	−	0.132049i
$107$	10.3778	+	52.1726i	0.0969885	+	0.487594i	0.998496	+	0.0548300i	$0.0174617\pi$
$107$	10.3778	+	52.1726i	0.0969885	+	0.487594i	−0.901507	+	0.432764i	$0.857538\pi$
$108$	−72.3392	+	60.4535i	−0.669808	+	0.559755i
$109$	−24.5004	+	123.172i	−0.224774	+	1.13002i	0.689302	+	0.724474i	$0.257917\pi$
$109$	−24.5004	+	123.172i	−0.224774	+	1.13002i	−0.914076	+	0.405543i	$0.867083\pi$
$110$	−1.78458	+	13.5552i	−0.0162234	+	0.123229i
$111$	17.8604	+	68.8374i	0.160904	+	0.620157i
$112$	33.6709	+	99.1912i	0.300633	+	0.885636i
$113$	57.1802	+	28.1982i	0.506020	+	0.249541i	0.677335	−	0.735675i	$-0.263135\pi$
$113$	57.1802	+	28.1982i	0.506020	+	0.249541i	−0.171315	+	0.985216i	$0.554802\pi$
$114$	2.61474	−	5.19774i	0.0229364	−	0.0455942i
$115$	21.1387	+	78.8908i	0.183815	+	0.686007i
$116$	−92.0587	−	61.5117i	−0.793610	−	0.530273i
$117$	3.41279	−	23.0841i	0.0291692	−	0.197300i
$118$		−	58.6016i		−	0.496624i
$119$	−168.334	−	48.9458i	−1.41457	−	0.411309i
$120$	−38.3885	−	94.7998i	−0.319904	−	0.789998i
$121$	111.016	−	14.6155i	0.917485	−	0.120789i
$122$	−47.4334	−	3.10895i	−0.388799	−	0.0254832i
$123$	−27.0467	+	63.8579i	−0.219892	+	0.519170i
$124$	−172.488	−	58.5517i	−1.39103	−	0.472191i
$125$	−32.8474	−	49.1596i	−0.262779	−	0.393276i
$126$	66.0914	−	3.27893i	0.524535	−	0.0260232i
$127$	−43.6842	+	18.0946i	−0.343970	+	0.142477i	−0.547979	−	0.836492i	$-0.684603\pi$
$127$	−43.6842	+	18.0946i	−0.343970	+	0.142477i	0.204009	+	0.978969i	$0.434603\pi$
$128$	127.760	+	16.8199i	0.998122	+	0.131405i
$129$	173.880	−	150.064i	1.34791	−	1.16328i
$130$	10.5823	+	5.21860i	0.0814021	+	0.0401431i
$131$	1.66132	+	1.89437i	0.0126818	+	0.0144608i	0.758146	−	0.652085i	$-0.226105\pi$
$131$	1.66132	+	1.89437i	0.0126818	+	0.0144608i	−0.745464	+	0.666546i	$0.767772\pi$
$132$	25.1186	−	18.9593i	0.190293	−	0.143631i
$133$	25.1575	−	12.4063i	0.189154	−	0.0932805i
$134$	−77.2939	−	32.0162i	−0.576820	−	0.238927i
$135$	171.341	−	18.4180i	1.26919	−	0.136430i
$136$	−61.3040	+	66.9892i	−0.450765	+	0.492568i
$137$	100.463	−	174.007i	0.733307	−	1.27012i	−0.222155	−	0.975011i	$-0.571309\pi$
$137$	100.463	−	174.007i	0.733307	−	1.27012i	0.955462	−	0.295114i	$-0.0953575\pi$
$138$	−13.8736	+	23.5951i	−0.100533	+	0.170979i
$139$	−104.968	−	6.87996i	−0.755165	−	0.0494961i	−0.317042	−	0.948411i	$-0.602690\pi$
$139$	−104.968	−	6.87996i	−0.755165	−	0.0494961i	−0.438122	+	0.898915i	$0.644356\pi$
$140$	59.4790	−	221.979i	0.424850	−	1.58556i
$141$	−81.0793	−	40.7873i	−0.575031	−	0.289272i
$142$	−10.4690	+	0.686174i	−0.0737253	+	0.00483221i
$143$	−1.51970	+	7.64004i	−0.0106273	+	0.0534268i
$144$	−36.3224	+	83.8969i	−0.252239	+	0.582617i
$145$	77.4502	+	186.981i	0.534139	+	1.28953i
$146$	−27.8887	+	31.8010i	−0.191019	+	0.217815i
$147$	142.264	+	96.7003i	0.967783	+	0.657825i
$148$	54.5747	+	62.2306i	0.368748	+	0.420477i
$149$	−74.7486	−	20.0288i	−0.501669	−	0.134422i	−0.000894259	−	1.00000i	$-0.500285\pi$
$149$	−74.7486	−	20.0288i	−0.501669	−	0.134422i	−0.500774	+	0.865578i	$0.666951\pi$
$150$	−6.82876	+	32.9607i	−0.0455251	+	0.219738i
$151$	−18.2189	+	13.9798i	−0.120655	+	0.0925816i	−0.667326	−	0.744766i	$-0.732561\pi$
$151$	−18.2189	+	13.9798i	−0.120655	+	0.0925816i	0.546672	+	0.837347i	$0.315895\pi$
$152$		−	14.5297i		−	0.0955900i
$153$	−80.2326	−	130.276i	−0.524396	−	0.851475i
$154$	−22.0898			−0.143440
$155$	202.699	+	264.162i	1.30774	+	1.70427i
$156$	−8.52556	−	25.7863i	−0.0546510	−	0.165297i
$157$	−13.0061	+	48.5392i	−0.0828411	+	0.309167i	−0.994897	−	0.100900i	$-0.967828\pi$
$157$	−13.0061	+	48.5392i	−0.0828411	+	0.309167i	0.912056	+	0.410067i	$0.134495\pi$
$158$	−57.8367	+	50.7214i	−0.366055	+	0.321022i
$159$	99.0195	+	204.876i	0.622764	+	1.28853i
$160$	−137.283	−	120.394i	−0.858020	−	0.752463i
$161$	−121.914	+	50.4982i	−0.757227	+	0.313654i
$162$	44.6791	+	36.5949i	0.275797	+	0.225894i
$163$	142.385	+	28.3222i	0.873530	+	0.173756i	0.611443	−	0.791288i	$-0.290589\pi$
$163$	142.385	+	28.3222i	0.873530	+	0.173756i	0.262087	+	0.965044i	$0.415589\pi$
$164$	5.27897	+	80.5415i	0.0321888	+	0.491107i
$165$	−57.4316	+	3.30657i	−0.348070	+	0.0200398i
$166$	101.932	+	27.3125i	0.614047	+	0.164533i
$167$	−8.55585	+	130.537i	−0.0512326	+	0.781659i	0.892520	+	0.451007i	$0.148935\pi$
$167$	−8.55585	+	130.537i	−0.0512326	+	0.781659i	−0.943753	+	0.330651i	$0.892732\pi$
$168$	143.760	−	81.4848i	0.855712	−	0.485029i
$169$	−140.536	−	81.1387i	−0.831576	−	0.480111i
$170$	75.1335	−	18.4370i	0.441962	−	0.108453i
$171$	23.5434	+	6.71086i	0.137681	+	0.0392448i
$172$	102.299	−	246.972i	0.594763	−	1.43588i
$173$	−3.13895	−	6.36517i	−0.0181442	−	0.0367929i	0.887612	−	0.460592i	$-0.152363\pi$
$173$	−3.13895	−	6.36517i	−0.0181442	−	0.0367929i	−0.905756	+	0.423799i	$0.860696\pi$
$174$	−26.4529	+	62.4557i	−0.152028	+	0.358941i
$175$	−122.007	+	106.997i	−0.697181	+	0.611411i
$176$	13.4980	−	27.3713i	0.0766933	−	0.155519i
$177$	242.207	−	46.1820i	1.36840	−	0.260916i
$178$	0.263319	−	2.00010i	0.00147932	−	0.0112365i
$179$	−26.5428	−	64.0800i	−0.148284	−	0.357989i	0.832232	−	0.554427i	$-0.187063\pi$
$179$	−26.5428	−	64.0800i	−0.148284	−	0.357989i	−0.980516	+	0.196438i	$0.937063\pi$
$180$	168.515	−	108.768i	0.936195	−	0.604267i
$181$	−80.0057	+	53.4581i	−0.442020	+	0.295349i	−0.756595	−	0.653884i	$-0.773138\pi$
$181$	−80.0057	+	53.4581i	−0.442020	+	0.295349i	0.314574	+	0.949233i	$0.398138\pi$
$182$	−6.12776	+	18.0518i	−0.0336690	+	0.0991857i
$183$	−24.5311	−	198.498i	−0.134050	−	1.08469i
$184$	−4.47048	+	68.2064i	−0.0242961	+	0.370687i
$185$	−19.7488	−	150.007i	−0.106750	−	0.810848i
$186$	−15.4432	+	110.516i	−0.0830281	+	0.594170i
$187$	24.5955	+	44.7624i	0.131527	+	0.239371i
$188$	−105.634			−0.561883
$189$	65.6367	+	270.579i	0.347284	+	1.43164i
$190$	−6.87719	+	10.2924i	−0.0361957	+	0.0541708i
$191$	187.622	−	50.2732i	0.982315	−	0.263211i	0.268296	−	0.963337i	$-0.413540\pi$
$191$	187.622	−	50.2732i	0.982315	−	0.263211i	0.714019	+	0.700126i	$0.246873\pi$
$192$	3.48908	+	60.6015i	0.0181723	+	0.315633i
$193$	55.6452	−	112.837i	0.288317	−	0.584649i	−0.703737	−	0.710460i	$-0.748487\pi$
$193$	55.6452	−	112.837i	0.288317	−	0.584649i	0.992054	+	0.125811i	$0.0401534\pi$
$194$	93.7007	−	31.8071i	0.482993	−	0.163954i
$195$	−13.2295	+	47.8504i	−0.0678436	+	0.245386i
$196$	198.494	+	26.1323i	1.01273	+	0.133328i
$197$	−131.953	−	26.2471i	−0.669812	−	0.133234i	−0.151542	−	0.988451i	$-0.548424\pi$
$197$	−131.953	−	26.2471i	−0.669812	−	0.133234i	−0.518270	+	0.855217i	$0.673424\pi$
$198$	−14.2912	−	12.9402i	−0.0721776	−	0.0653543i
$199$	3.83330	−	0.762491i	0.0192628	−	0.00383161i	−0.185450	−	0.982654i	$-0.559374\pi$
$199$	3.83330	−	0.762491i	0.0192628	−	0.00383161i	0.204712	+	0.978822i	$0.434374\pi$
$200$	21.7557	+	81.1935i	0.108779	+	0.405968i
$201$	71.4136	−	344.695i	0.355292	−	1.71490i
$202$	9.72034	+	73.8333i	0.0481205	+	0.365512i
$203$	−283.183	+	163.496i	−1.39499	+	0.805399i
$204$	−151.560	−	93.4865i	−0.742939	−	0.458267i
$205$	73.7708	−	127.775i	0.359858	−	0.623292i
$206$	7.37618	−	17.8077i	0.0358067	−	0.0864450i
$207$	−108.455	−	38.7465i	−0.523936	−	0.187181i
$208$	−18.6234	−	18.6234i	−0.0895357	−	0.0895357i
$209$	−7.73862	−	2.62691i	−0.0370269	−	0.0125689i
$210$	−140.404	−	10.3227i	−0.668590	−	0.0491555i
$211$	267.410	−	90.7734i	1.26735	−	0.430206i	0.394813	−	0.918762i	$-0.370809\pi$
$211$	267.410	−	90.7734i	1.26735	−	0.430206i	0.872533	+	0.488556i	$0.162476\pi$
$212$	210.112	+	161.225i	0.991095	+	0.760494i
$213$	−11.0863	−	42.7288i	−0.0520484	−	0.200605i
$214$	25.0076	−	28.5156i	0.116858	−	0.133251i
$215$	−406.296	+	271.479i	−1.88975	+	1.26269i
$216$	140.740	+	31.4969i	0.651574	+	0.145819i
$217$	−380.403	+	380.403i	−1.75301	+	1.75301i
$218$	80.3079	−	39.6035i	0.368385	−	0.181667i
$219$	−153.415	−	90.2059i	−0.700526	−	0.411899i
$220$	−57.9838	+	33.4770i	−0.263563	+	0.152168i
$221$	43.4027	−	7.68224i	0.196392	−	0.0347613i
$222$	31.1864	−	39.9816i	0.140479	−	0.180097i
$223$	193.641	+	252.358i	0.868346	+	1.13165i	0.990277	+	0.139112i	$0.0444247\pi$
$223$	193.641	+	252.358i	0.868346	+	1.13165i	−0.121931	+	0.992539i	$0.538909\pi$
$224$	163.902	−	245.297i	0.731707	−	1.09508i
$225$	−141.612	−	2.24877i	−0.629386	−	0.00999455i
$226$	−8.86830	−	44.5840i	−0.0392403	−	0.197274i
$227$	−213.672	+	14.0048i	−0.941288	+	0.0616952i	−0.528315	−	0.849048i	$-0.677176\pi$
$227$	−213.672	+	14.0048i	−0.941288	+	0.0616952i	−0.412972	+	0.910744i	$0.635509\pi$
$228$	27.9889	−	5.33669i	0.122758	−	0.0234065i
$229$	231.330	+	177.506i	1.01017	+	0.775133i	0.974536	−	0.224232i	$-0.0719872\pi$
$229$	231.330	+	177.506i	1.01017	+	0.775133i	0.0356375	+	0.999365i	$0.488654\pi$
$230$	35.4502	−	46.1996i	0.154131	−	0.200868i
$231$	−17.4083	−	91.2996i	−0.0753604	−	0.395236i
$232$	11.0778	+	169.015i	0.0477493	+	0.728513i
$233$	210.023	−	41.7762i	0.901387	−	0.179297i	0.277421	−	0.960749i	$-0.410520\pi$
$233$	210.023	−	41.7762i	0.901387	−	0.179297i	0.623966	+	0.781452i	$0.285520\pi$
$234$	−14.5391	+	8.08911i	−0.0621329	+	0.0345689i
$235$	160.551	+	107.277i	0.683198	+	0.456498i
$236$	227.675	−	174.701i	0.964723	−	0.740258i
$237$	−255.217	−	199.074i	−1.07686	−	0.839974i
$238$	45.3781	+	116.465i	0.190664	+	0.489348i
$239$	58.7381	+	101.737i	0.245766	+	0.425679i	0.962347	−	0.271825i	$-0.0876272\pi$
$239$	58.7381	+	101.737i	0.245766	+	0.425679i	−0.716581	+	0.697504i	$0.754294\pi$
$240$	98.5849	−	167.666i	0.410770	−	0.698607i
$241$	−136.124	−	276.031i	−0.564828	−	1.14536i	−0.972645	−	0.232295i	$-0.925377\pi$
$241$	−136.124	−	276.031i	−0.564828	−	1.14536i	0.407817	−	0.913064i	$-0.366290\pi$
$242$	−56.4535	−	56.4535i	−0.233279	−	0.233279i
$243$	−116.041	+	213.503i	−0.477533	+	0.878614i
$244$	−129.328	−	193.553i	−0.530034	−	0.793251i
$245$	−275.150	−	241.300i	−1.12306	−	0.984898i
$246$	47.8615	−	12.4180i	0.194559	−	0.0504798i
$247$	−4.29342	+	5.59529i	−0.0173823	+	0.0226530i
$248$	89.5730	+	263.873i	0.361181	+	1.06401i
$249$	−32.5566	+	442.820i	−0.130749	+	1.77839i
$250$	−13.5503	+	39.9180i	−0.0542014	+	0.159672i
$251$	301.086	−	301.086i	1.19955	−	1.19955i	0.225244	−	0.974302i	$-0.427682\pi$
$251$	301.086	−	301.086i	1.19955	−	1.19955i	0.974302	−	0.225244i	$-0.0723180\pi$
$252$	209.768	+	246.999i	0.832414	+	0.980153i
$253$	35.5190	+	14.7124i	0.140391	+	0.0581520i
$254$	29.1964	+	16.8566i	0.114947	+	0.0663644i
$255$	135.413	+	296.006i	0.531029	+	1.16081i
$256$	−5.47137	−	9.47670i	−0.0213726	−	0.0370184i
$257$	−274.560	+	36.1465i	−1.06833	+	0.140648i	−0.644126	−	0.764920i	$-0.722779\pi$
$257$	−274.560	+	36.1465i	−1.06833	+	0.140648i	−0.424202	+	0.905568i	$0.639445\pi$
$258$	−160.357	−	33.2227i	−0.621540	−	0.128770i
$259$	236.124	−	63.2693i	0.911677	−	0.244283i
$260$	11.2726	+	56.6710i	0.0433560	+	0.217965i
$261$	−278.983	−	60.1133i	−1.06890	−	0.230319i
$262$	0.350481	−	1.76199i	0.00133771	−	0.00672513i
$263$	−15.3772	+	116.801i	−0.0584683	+	0.444111i	0.937024	+	0.349266i	$0.113569\pi$
$263$	−15.3772	+	116.801i	−0.0584683	+	0.444111i	−0.995492	+	0.0948452i	$0.969764\pi$
$264$	−46.4032	−	12.8294i	−0.175770	−	0.0485962i
$265$	−155.614	−	458.423i	−0.587221	−	1.72990i
$266$	−17.9373	−	8.84570i	−0.0674335	−	0.0332545i
$267$	8.47417	−	0.487893i	0.0317385	−	0.00182731i
$268$	−106.039	−	395.742i	−0.395667	−	1.47665i
$269$	49.4329	+	33.0300i	0.183765	+	0.122788i	0.644050	−	0.764983i	$-0.277253\pi$
$269$	49.4329	+	33.0300i	0.183765	+	0.122788i	−0.460285	+	0.887771i	$0.652253\pi$
$270$	−84.7884	−	88.9267i	−0.314031	−	0.329358i
$271$		−	328.085i		−	1.21065i	−0.795980	−	0.605323i	$-0.793044\pi$
$271$		−	328.085i		−	1.21065i	0.795980	−	0.605323i	$-0.206956\pi$
$272$	−172.039	−	14.9384i	−0.632496	−	0.0549207i
$273$	−79.4392	−	11.1007i	−0.290986	−	0.0406618i
$274$	−142.035	+	18.6992i	−0.518375	+	0.0682453i
$275$	47.1776	+	3.09219i	0.171555	+	0.0112443i
$276$	−133.030	+	16.4403i	−0.481991	+	0.0595663i
$277$	−107.103	−	36.3567i	−0.386655	−	0.131252i	0.121341	−	0.992611i	$-0.461280\pi$
$277$	−107.103	−	36.3567i	−0.386655	−	0.131252i	−0.507997	+	0.861359i	$0.669614\pi$
$278$	41.6693	+	62.3625i	0.149889	+	0.224325i
$279$	−468.943	+	23.2652i	−1.68080	+	0.0833879i
$280$	−324.803	+	134.538i	−1.16001	+	0.480493i
$281$	44.8024	+	5.89834i	0.159439	+	0.0209905i	0.209823	−	0.977739i	$-0.432711\pi$
$281$	44.8024	+	5.89834i	0.159439	+	0.0209905i	−0.0503841	+	0.998730i	$0.516045\pi$
$282$	12.1204	+	63.5670i	0.0429803	+	0.225415i
$283$	188.350	+	92.8842i	0.665549	+	0.328213i	0.743492	−	0.668745i	$-0.233168\pi$
$283$	188.350	+	92.8842i	0.665549	+	0.328213i	−0.0779422	+	0.996958i	$0.524835\pi$
$284$	−33.8757	−	38.6278i	−0.119281	−	0.136013i
$285$	−47.9595	−	20.3131i	−0.168279	−	0.0712739i
$286$	4.98129	−	2.45650i	0.0174171	−	0.00858916i
$287$	220.234	+	91.2239i	0.767365	+	0.317853i
$288$	249.733	−	62.6832i	0.867127	−	0.217650i
$289$	185.477	−	221.629i	0.641788	−	0.766882i
$290$	72.1510	−	124.969i	0.248797	−	0.430928i
$291$	205.305	+	362.209i	0.705515	+	1.24471i
$292$	−206.692	−	13.5473i	−0.707848	−	0.0463948i
$293$	46.0843	−	171.989i	0.157284	−	0.586993i	−0.841615	−	0.540079i	$-0.818395\pi$
$293$	46.0843	−	171.989i	0.157284	−	0.586993i	0.998899	−	0.0469145i	$-0.0149388\pi$
$294$	−7.04970	−	122.446i	−0.0239786	−	0.416482i
$295$	−523.458	+	34.3092i	−1.77443	+	0.116302i
$296$	24.7031	−	124.191i	0.0834565	−	0.419564i
$297$	42.2207	−	69.2647i	0.142157	−	0.233214i
$298$	21.1149	+	50.9758i	0.0708553	+	0.171060i
$299$	21.8761	−	24.9449i	0.0731641	−	0.0834277i
$300$	−148.414	+	71.7306i	−0.494714	+	0.239102i
$301$	−520.552	−	593.576i	−1.72941	−	1.97201i
$302$	15.8157	+	4.23780i	0.0523698	+	0.0140325i
$303$	−297.501	+	98.3610i	−0.981852	+	0.324624i
$304$	21.9212	−	16.8208i	0.0721094	−	0.0553315i
$305$			425.518i			1.39514i
$306$	−38.8671	+	101.930i	−0.127017	+	0.333105i
$307$	511.829			1.66720			0.833598	−	0.552372i	$-0.186277\pi$
$307$	511.829			1.66720			0.833598	+	0.552372i	$0.186277\pi$
$308$	−65.8533	−	85.8217i	−0.213809	−	0.278642i
$309$	79.4140	+	16.4529i	0.257003	+	0.0532457i
$310$	61.4455	−	229.318i	0.198211	−	0.739735i
$311$	223.527	−	196.028i	0.718736	−	0.630315i	−0.219780	−	0.975549i	$-0.570534\pi$
$311$	223.527	−	196.028i	0.718736	−	0.630315i	0.938516	+	0.345235i	$0.112201\pi$
$312$	−23.3565	+	34.3618i	−0.0748607	+	0.110134i
$313$	72.5058	+	63.5859i	0.231648	+	0.203150i	0.767299	−	0.641290i	$-0.221600\pi$
$313$	72.5058	+	63.5859i	0.231648	+	0.203150i	−0.535651	+	0.844440i	$0.679934\pi$
$314$	33.1020	−	13.7113i	0.105420	−	0.0436665i
$315$	−67.9832	−	588.440i	−0.215820	−	1.86806i
$316$	−369.480	−	73.4942i	−1.16924	−	0.232576i
$317$	−30.3126	−	462.480i	−0.0956232	−	1.45893i	−0.728697	−	0.684837i	$-0.759874\pi$
$317$	−30.3126	−	462.480i	−0.0956232	−	1.45893i	0.633073	−	0.774092i	$-0.281793\pi$
$318$	72.9114	−	144.937i	0.229281	−	0.455778i
$319$	92.0215	+	24.6571i	0.288469	+	0.0772950i
$320$	8.44641	−	128.867i	0.0263950	−	0.402710i
$321$	137.566	+	80.8868i	0.428555	+	0.251984i
$322$	81.4811	+	47.0431i	0.253047	+	0.146097i
$323$	2.04718	+	46.1969i	0.00633802	+	0.143024i
$324$	−8.98008	+	282.680i	−0.0277163	+	0.872468i
$325$	15.6141	−	37.6958i	0.0480434	−	0.115987i
$326$	−45.7812	−	92.8350i	−0.140433	−	0.284770i
$327$	226.974	+	300.711i	0.694109	+	0.919606i
$328$	92.8354	−	81.4144i	0.283035	−	0.248215i
$329$	−137.984	+	279.803i	−0.419403	+	0.850466i
$330$	26.7984	+	31.0516i	0.0812072	+	0.0940957i
$331$	−8.16117	+	61.9903i	−0.0246561	+	0.187282i	−0.999341	−	0.0363018i	$-0.988442\pi$
$331$	−8.16117	+	61.9903i	−0.0246561	+	0.187282i	0.974685	+	0.223584i	$0.0717756\pi$
$332$	197.763	+	477.441i	0.595671	+	1.43808i
$333$	189.825	+	97.3886i	0.570046	+	0.292458i
$334$	77.5533	−	51.8195i	0.232196	−	0.155148i
$335$	−240.731	+	709.171i	−0.718600	+	2.11693i
$336$	289.366	+	122.560i	0.861209	+	0.364761i
$337$	17.9598	−	274.014i	0.0532932	−	0.813097i	−0.884639	−	0.466277i	$-0.845595\pi$
$337$	17.9598	−	274.014i	0.0532932	−	0.813097i	0.937932	−	0.346820i	$-0.112738\pi$
$338$	15.1024	+	114.714i	0.0446816	+	0.339391i
$339$	177.282	−	71.7889i	0.522955	−	0.211767i
$340$	295.615	+	236.940i	0.869457	+	0.696882i
$341$	156.735			0.459635
$342$	−6.42288	−	16.2304i	−0.0187803	−	0.0474574i
$343$	47.7759	−	71.5017i	0.139288	−	0.208460i
$344$	−395.015	+	105.844i	−1.14830	+	0.307686i
$345$	218.886	+	110.111i	0.634451	+	0.319163i
$346$	−2.23807	+	4.53836i	−0.00646842	+	0.0131167i
$347$	−537.296	+	182.388i	−1.54840	+	0.525613i	−0.959287	−	0.282434i	$-0.908858\pi$
$347$	−537.296	+	182.388i	−1.54840	+	0.525613i	−0.589118	+	0.808047i	$0.700525\pi$
$348$	−321.509	+	83.4180i	−0.923876	+	0.239707i
$349$	540.778	+	71.1948i	1.54951	+	0.203997i	0.856200	−	0.516645i	$-0.172819\pi$
$349$	540.778	+	71.1948i	1.54951	+	0.203997i	0.693308	+	0.720641i	$0.256152\pi$
$350$	113.481	+	22.5727i	0.324230	+	0.0644935i
$351$	−44.8910	−	53.7170i	−0.127895	−	0.153040i
$352$	−84.3003	+	16.7684i	−0.239489	+	0.0476374i
$353$	155.378	+	579.879i	0.440164	+	1.64272i	0.728397	+	0.685155i	$0.240266\pi$
$353$	155.378	+	579.879i	0.440164	+	1.64272i	−0.288233	+	0.957560i	$0.593068\pi$
$354$	−131.253	−	116.962i	−0.370770	−	0.330401i
$355$	12.2585	+	93.1124i	0.0345309	+	0.262288i
$356$	8.55566	−	4.93961i	0.0240327	−	0.0138753i
$357$	−445.601	+	279.335i	−1.24818	+	0.782451i
$358$	−24.7267	+	42.8279i	−0.0690691	+	0.119631i
$359$	68.6601	−	165.760i	0.191254	−	0.461728i	−0.798943	−	0.601407i	$-0.794607\pi$
$359$	68.6601	−	165.760i	0.191254	−	0.461728i	0.990197	+	0.139679i	$0.0446071\pi$
$360$	−288.946	−	103.229i	−0.802628	−	0.286747i
$361$	250.034	+	250.034i	0.692614	+	0.692614i
$362$	64.9654	+	22.0528i	0.179462	+	0.0609193i
$363$	188.839	−	277.818i	0.520219	−	0.765338i
$364$	−88.4014	+	30.0082i	−0.242861	+	0.0824402i
$365$	300.390	+	230.497i	0.822985	+	0.631499i
$366$	−101.635	+	100.034i	−0.277691	+	0.273316i
$367$	−170.536	+	194.459i	−0.464677	+	0.529862i	−0.935954	−	0.352123i	$-0.885460\pi$
$367$	−170.536	+	194.459i	−0.464677	+	0.529862i	0.471277	+	0.881985i	$0.343793\pi$
$368$	−108.080	+	72.2167i	−0.293695	+	0.196241i
$369$	89.0432	+	188.031i	0.241310	+	0.509568i
$370$	−76.2811	+	76.2811i	−0.206165	+	0.206165i
$371$	701.509	−	345.946i	1.89086	−	0.932469i
$372$	−475.406	+	269.466i	−1.27797	+	0.724371i
$373$	−103.410	+	59.7041i	−0.277240	+	0.160065i	−0.632173	−	0.774827i	$-0.717837\pi$
$373$	−103.410	+	59.7041i	−0.277240	+	0.160065i	0.354933	+	0.934892i	$0.384504\pi$
$374$	14.6447	−	33.3417i	0.0391571	−	0.0891488i
$375$	−175.664	−	24.5470i	−0.468438	−	0.0654586i
$376$	98.3758	+	128.206i	0.261638	+	0.340973i
$377$	45.6768	−	68.3601i	0.121159	−	0.181327i
$378$	124.567	−	154.572i	0.329541	−	0.408921i
$379$	−34.4037	−	172.959i	−0.0907750	−	0.456357i	−0.999261	−	0.0384411i	$-0.987761\pi$
$379$	−34.4037	−	172.959i	−0.0907750	−	0.456357i	0.908486	−	0.417915i	$-0.137239\pi$
$380$	−60.4895	+	3.96469i	−0.159183	+	0.0104334i
$381$	−46.6613	+	133.956i	−0.122471	+	0.351591i
$382$	−109.874	−	84.3096i	−0.287629	−	0.220706i
$383$	406.234	−	529.414i	1.06066	−	1.38228i	0.140802	−	0.990038i	$-0.455032\pi$
$383$	406.234	−	529.414i	1.06066	−	1.38228i	0.919861	−	0.392245i	$-0.128301\pi$
$384$	292.665	−	252.578i	0.762149	−	0.657756i
$385$	12.9328	+	197.317i	0.0335917	+	0.512511i
$386$	−87.9803	+	17.5004i	−0.227928	+	0.0453377i
$387$	10.9405	−	688.957i	0.0282701	−	1.78025i
$388$	402.912	+	269.217i	1.03843	+	0.693858i
$389$	269.187	−	206.554i	0.691997	−	0.530988i	−0.201819	−	0.979423i	$-0.564685\pi$
$389$	269.187	−	206.554i	0.691997	−	0.530988i	0.893815	+	0.448435i	$0.148019\pi$
$390$	32.8093	−	13.2859i	0.0841264	−	0.0340664i
$391$	4.60380	−	217.491i	0.0117744	−	0.556243i
$392$	−153.140	−	265.246i	−0.390662	−	0.676647i
$393$	7.55869	+	0.0600116i	0.0192333	+	0.000152701i
$394$	42.4268	+	86.0331i	0.107682	+	0.218358i
$395$	486.930	+	486.930i	1.23273	+	1.23273i
$396$	7.66989	−	94.0997i	0.0193684	−	0.237626i
$397$	291.692	+	436.547i	0.734739	+	1.09962i	0.991111	+	0.133037i	$0.0424729\pi$
$397$	291.692	+	436.547i	0.734739	+	1.09962i	−0.256372	+	0.966578i	$0.582527\pi$
$398$	−2.09514	−	1.83739i	−0.00526418	−	0.00461656i
$399$	22.4244	−	81.1079i	0.0562016	−	0.203278i
$400$	−97.3122	+	126.820i	−0.243281	+	0.317049i
$401$	52.7410	+	155.370i	0.131524	+	0.387456i	0.992663	−	0.120913i	$-0.0385821\pi$
$401$	52.7410	+	155.370i	0.131524	+	0.387456i	−0.861140	+	0.508369i	$0.830249\pi$
$402$	−225.978	+	109.218i	−0.562133	+	0.271687i
$403$	43.4788	−	128.084i	0.107888	−	0.317827i
$404$	−257.874	+	257.874i	−0.638302	+	0.638302i
$405$	300.725	−	420.520i	0.742531	−	1.03832i
$406$	215.398	+	89.2208i	0.530537	+	0.219756i
$407$	−61.6788	−	35.6103i	−0.151545	−	0.0874946i
$408$	27.6832	+	271.008i	0.0678509	+	0.664235i
$409$	−199.945	−	346.315i	−0.488863	−	0.846736i	0.511055	−	0.859548i	$-0.329255\pi$
$409$	−199.945	−	346.315i	−0.488863	−	0.846736i	−0.999918	+	0.0128125i	$0.995922\pi$
$410$	−104.297	+	13.7310i	−0.254384	+	0.0334902i
$411$	−189.219	−	572.309i	−0.460387	−	1.39248i
$412$	91.1747	−	24.4302i	0.221298	−	0.0592965i
$413$	−165.349	−	831.267i	−0.400361	−	2.01275i
$414$	25.1570	+	78.1664i	0.0607658	+	0.188808i
$415$	184.291	−	926.494i	0.444075	−	2.23252i
$416$	−9.68196	+	73.5418i	−0.0232739	+	0.176783i
$417$	−224.913	+	221.370i	−0.539359	+	0.530863i
$418$	1.87298	+	5.51763i	0.00448082	+	0.0132001i
$419$	502.506	+	247.809i	1.19930	+	0.591429i	0.928545	−	0.371220i	$-0.121060\pi$
$419$	502.506	+	247.809i	1.19930	+	0.591429i	0.270754	+	0.962649i	$0.412727\pi$
$420$	−378.462	−	576.261i	−0.901101	−	1.37205i
$421$	77.6392	+	289.753i	0.184416	+	0.688251i	0.994755	+	0.102289i	$0.0326165\pi$
$421$	77.6392	+	289.753i	0.184416	+	0.688251i	−0.810339	+	0.585962i	$0.800717\pi$
$422$	−167.415	−	111.863i	−0.396719	−	0.265079i
$423$	−253.178	+	100.190i	−0.598529	+	0.236856i
$424$		−	405.156i		−	0.955556i
$425$	−80.6120	−	255.088i	−0.189675	−	0.600208i
$426$	−19.3580	+	24.8174i	−0.0454414	+	0.0582568i
$427$	−681.618	+	89.7367i	−1.59630	+	0.210156i
$428$	185.339	+	12.1477i	0.433034	+	0.0283825i
$429$	14.0786	+	18.6523i	0.0328172	+	0.0434787i
$430$	329.917	+	111.992i	0.767248	+	0.260446i
$431$	−91.2238	−	136.526i	−0.211656	−	0.316766i	0.710417	−	0.703781i	$-0.248506\pi$
$431$	−91.2238	−	136.526i	−0.211656	−	0.316766i	−0.922073	+	0.387015i	$0.873506\pi$
$432$	115.412	+	248.801i	0.267158	+	0.575928i
$433$	89.4834	−	37.0652i	0.206659	−	0.0856010i	−0.276953	−	0.960883i	$-0.589325\pi$
$433$	89.4834	−	37.0652i	0.206659	−	0.0856010i	0.483612	+	0.875283i	$0.339325\pi$
$434$	380.292	+	50.0663i	0.876248	+	0.115360i
$435$	573.372	+	199.724i	1.31810	+	0.459136i
$436$	393.275	+	193.942i	0.902008	+	0.444821i
$437$	22.9506	+	26.1701i	0.0525184	+	0.0598858i
$438$	15.5635	+	125.935i	0.0355331	+	0.287522i
$439$	−451.343	+	222.578i	−1.02812	+	0.507010i	−0.876486	−	0.481427i	$-0.840119\pi$
$439$	−451.343	+	222.578i	−1.02812	+	0.507010i	−0.151629	+	0.988437i	$0.548452\pi$
$440$	94.6301	+	39.1971i	0.215068	+	0.0890842i
$441$	500.526	−	125.633i	1.13498	−	0.284882i
$442$	−23.1843	−	21.2167i	−0.0524533	−	0.0480017i
$443$	−250.891	+	434.556i	−0.566345	+	0.980938i	0.430578	+	0.902553i	$0.358310\pi$
$443$	−250.891	+	434.556i	−0.566345	+	0.980938i	−0.996923	+	0.0783850i	$0.975024\pi$
$444$	248.305	+	1.97140i	0.559246	+	0.00444009i
$445$	−18.0201	−	1.18110i	−0.0404945	−	0.00265415i
$446$	58.6997	−	219.070i	0.131614	−	0.491189i
$447$	−194.049	+	127.443i	−0.434114	+	0.285106i
$448$	208.208	−	13.6467i	0.464749	−	0.0304613i
$449$	−52.2049	+	262.452i	−0.116269	+	0.584525i	0.878093	+	0.478490i	$0.158816\pi$
$449$	−52.2049	+	262.452i	−0.116269	+	0.584525i	−0.994362	+	0.106035i	$0.966184\pi$
$450$	60.1941	+	81.0804i	0.133765	+	0.180179i
$451$	−26.5777	−	64.1642i	−0.0589306	−	0.142271i
$452$	146.777	−	167.367i	0.324727	−	0.370280i
$453$	−5.05147	+	68.7077i	−0.0111511	+	0.151673i
$454$	100.666	+	114.787i	0.221731	+	0.252836i
$455$	164.835	+	44.1674i	0.362274	+	0.0970712i
$456$	−32.5428	−	28.9995i	−0.0713657	−	0.0635954i
$457$	−480.291	+	368.540i	−1.05097	+	0.806434i	−0.981560	−	0.191155i	$-0.938777\pi$
$457$	−480.291	+	368.540i	−1.05097	+	0.806434i	−0.0694052	+	0.997589i	$0.522110\pi$
$458$		−	207.900i		−	0.453930i
$459$	−451.919	−	80.3143i	−0.984573	−	0.174977i
$460$	285.175			0.619945
$461$	−297.966	−	388.317i	−0.646347	−	0.842335i	0.349156	−	0.937064i	$-0.386468\pi$
$461$	−297.966	−	388.317i	−0.646347	−	0.842335i	−0.995503	+	0.0947291i	$0.969802\pi$
$462$	−44.0886	+	49.4755i	−0.0954299	+	0.107090i
$463$	−219.160	+	817.918i	−0.473349	+	1.76656i	0.154258	+	0.988031i	$0.450701\pi$
$463$	−219.160	+	817.918i	−0.473349	+	1.76656i	−0.627606	+	0.778531i	$0.715965\pi$
$464$	−242.172	+	212.379i	−0.521923	+	0.457714i
$465$	996.219	+	73.2432i	2.14241	+	0.157512i
$466$	−114.791	−	100.669i	−0.246333	−	0.216028i
$467$	−459.643	+	190.390i	−0.984246	+	0.407688i	−0.815997	−	0.578057i	$-0.803811\pi$
$467$	−459.643	+	190.390i	−0.984246	+	0.407688i	−0.168249	+	0.985745i	$0.553811\pi$
$468$	−74.7707	−	32.3713i	−0.159766	−	0.0691695i
$469$	−1186.75	−	236.060i	−2.53039	−	0.503326i
$470$	−9.00443	−	137.381i	−0.0191584	−	0.292300i
$471$	82.7570	+	126.009i	0.175705	+	0.267535i
$472$	−424.062	−	113.627i	−0.898437	−	0.240735i
$473$	−15.0438	+	229.524i	−0.0318051	+	0.485252i
$474$	−1.83221	+	230.773i	−0.00386542	+	0.486864i
$475$	37.0708	+	21.4029i	0.0780439	+	0.0450586i
$476$	−317.201	+	523.500i	−0.666389	+	1.09979i
$477$	656.501	+	187.130i	1.37631	+	0.392307i
$478$	32.0538	−	77.3846i	0.0670581	−	0.161893i
$479$	161.554	+	327.600i	0.337274	+	0.683924i	0.997759	−	0.0669154i	$-0.0213158\pi$
$479$	161.554	+	327.600i	0.337274	+	0.683924i	−0.660485	+	0.750840i	$0.729649\pi$
$480$	−543.653	+	67.1868i	−1.13261	+	0.139972i
$481$	−46.2106	+	40.5256i	−0.0960719	+	0.0842528i
$482$	−97.0562	+	196.810i	−0.201361	+	0.408320i
$483$	−130.222	+	373.844i	−0.269611	+	0.774003i
$484$	51.0319	−	387.626i	0.105438	−	0.800880i
$485$	−338.975	−	818.358i	−0.698917	−	1.68734i
$486$	171.137	−	27.0307i	0.352135	−	0.0556188i
$487$	274.557	−	183.453i	0.563773	−	0.376701i	−0.240782	−	0.970579i	$-0.577404\pi$
$487$	274.557	−	183.453i	0.563773	−	0.376701i	0.804555	+	0.593878i	$0.202404\pi$
$488$	−114.470	+	337.217i	−0.234569	+	0.691019i
$489$	347.619	−	262.379i	0.710877	−	0.536562i
$490$	−17.0660	+	260.377i	−0.0348286	+	0.531382i
$491$	−122.570	−	931.012i	−0.249633	−	1.89615i	−0.414839	−	0.909895i	$-0.636162\pi$
$491$	−122.570	−	931.012i	−0.249633	−	1.89615i	0.165205	−	0.986259i	$-0.447171\pi$
$492$	190.929	+	148.928i	0.388066	+	0.302699i
$493$	−59.0354	−	535.820i	−0.119747	−	1.08686i
$494$	5.02858			0.0101793
$495$	−107.221	+	135.232i	−0.216608	+	0.273195i
$496$	−294.415	+	440.623i	−0.593578	+	0.888352i
$497$	−146.567	+	39.2726i	−0.294904	+	0.0790192i
$498$	264.617	−	173.789i	0.531359	−	0.348973i
$499$	94.5083	−	191.644i	0.189395	−	0.384056i	−0.781376	−	0.624060i	$-0.785482\pi$
$499$	94.5083	−	191.644i	0.189395	−	0.384056i	0.970772	+	0.240004i	$0.0771488\pi$
$500$	−195.482	+	66.3574i	−0.390965	+	0.132715i
$501$	275.293	+	279.699i	0.549487	+	0.558282i
$502$	−300.998	−	39.6272i	−0.599598	−	0.0789386i
$503$	403.394	+	80.2401i	0.801977	+	0.159523i	0.579029	−	0.815307i	$-0.303432\pi$
$503$	403.394	+	80.2401i	0.801977	+	0.159523i	0.222948	+	0.974830i	$0.428432\pi$
$504$	104.422	−	484.619i	0.207187	−	0.961545i
$505$	653.824	−	130.054i	1.29470	−	0.257532i
$506$	−7.09465	−	26.4776i	−0.0140211	−	0.0523273i
$507$	−462.224	+	152.822i	−0.911685	+	0.301425i
$508$	21.5494	+	163.684i	0.0424201	+	0.322213i
$509$	−741.719	+	428.232i	−1.45721	+	0.841320i	−0.998873	−	0.0474594i	$-0.984888\pi$
$509$	−741.719	+	428.232i	−1.45721	+	0.841320i	−0.458336	+	0.888779i	$0.651554\pi$
$510$	108.664	−	205.078i	0.213066	−	0.402114i
$511$	−305.874	+	529.789i	−0.598579	+	1.03677i
$512$	194.268	−	469.004i	0.379429	−	0.916023i
$513$	62.0205	−	39.3372i	0.120898	−	0.0766806i
$514$	139.619	+	139.619i	0.271632	+	0.271632i
$515$	−163.385	−	55.4618i	−0.317253	−	0.107693i
$516$	−348.977	−	722.051i	−0.676312	−	1.39932i
$517$	86.0694	−	29.2166i	0.166479	−	0.0565118i
$518$	−138.278	−	106.104i	−0.266946	−	0.204835i
$519$	−20.5213	−	5.67367i	−0.0395401	−	0.0109319i
$520$	58.2825	−	66.4584i	0.112082	−	0.127805i
$521$	28.5734	−	19.0921i	0.0548434	−	0.0366452i	−0.527846	−	0.849340i	$-0.677000\pi$
$521$	28.5734	−	19.0921i	0.0548434	−	0.0366452i	0.582690	+	0.812695i	$0.302000\pi$
$522$	87.0880	+	183.902i	0.166835	+	0.352302i
$523$	−26.0414	+	26.0414i	−0.0497924	+	0.0497924i	−0.731565	−	0.681772i	$-0.761210\pi$
$523$	−26.0414	+	26.0414i	−0.0497924	+	0.0497924i	0.681772	+	0.731565i	$0.261210\pi$
$524$	7.89038	−	3.89110i	0.0150580	−	0.00742577i
$525$	−3.86505	+	486.817i	−0.00736199	+	0.927271i
$526$	72.7443	−	41.9989i	0.138297	−	0.0798459i
$527$	−321.975	−	826.362i	−0.610958	−	1.56805i
$528$	−34.3642	−	84.8619i	−0.0650837	−	0.160723i
$529$	222.350	+	289.773i	0.420322	+	0.547775i
$530$	−191.768	+	287.002i	−0.361827	+	0.541513i
$531$	379.981	−	634.656i	0.715594	−	1.19521i
$532$	−19.1074	−	96.0592i	−0.0359161	−	0.180562i
$533$	−59.8077	+	3.92001i	−0.112210	+	0.00735461i
$534$	−3.95417	−	4.58174i	−0.00740481	−	0.00858004i
$535$	−269.357	−	206.685i	−0.503470	−	0.386326i
$536$	−381.552	+	497.248i	−0.711850	+	0.927701i
$537$	−196.499	−	68.4470i	−0.365920	−	0.127462i
$538$	−2.77241	−	42.2988i	−0.00515318	−	0.0786224i
$539$	−168.959	+	33.6080i	−0.313467	+	0.0623525i
$540$	92.7235	−	594.519i	0.171710	−	1.10096i
$541$	−308.587	−	206.191i	−0.570402	−	0.381130i	0.236664	−	0.971591i	$-0.423946\pi$
$541$	−308.587	−	206.191i	−0.570402	−	0.381130i	−0.807066	+	0.590461i	$0.798946\pi$
$542$	−185.585	+	142.404i	−0.342407	+	0.262739i
$543$	−39.9495	+	285.888i	−0.0735718	+	0.526498i
$544$	261.583	+	410.013i	0.480851	+	0.753700i
$545$	−400.775	−	694.162i	−0.735366	−	1.27369i
$546$	28.2011	+	49.7539i	0.0516504	+	0.0911243i
$547$	322.199	+	653.356i	0.589030	+	1.19443i	0.963628	+	0.267248i	$0.0861141\pi$
$547$	322.199	+	653.356i	0.589030	+	1.19443i	−0.374598	+	0.927187i	$0.622219\pi$
$548$	−496.078	−	496.078i	−0.905251	−	0.905251i
$549$	−493.546	−	341.235i	−0.898990	−	0.621557i
$550$	−18.7282	−	28.0287i	−0.0340512	−	0.0509613i
$551$	64.8493	+	56.8713i	0.117694	+	0.103215i
$552$	143.842	+	146.145i	0.260584	+	0.264755i
$553$	−677.302	+	882.678i	−1.22478	+	1.59616i
$554$	25.9224	+	76.3648i	0.0467912	+	0.137843i
$555$	−375.393	−	255.164i	−0.676384	−	0.459755i
$556$	−118.063	+	347.803i	−0.212344	+	0.625545i
$557$	506.656	−	506.656i	0.909616	−	0.909616i	−0.0866251	−	0.996241i	$-0.527608\pi$
$557$	506.656	−	506.656i	0.909616	−	0.909616i	0.996241	+	0.0866251i	$0.0276082\pi$
$558$	216.704	+	255.165i	0.388358	+	0.457285i
$559$	183.394	+	75.9644i	0.328075	+	0.135893i
$560$	−579.000	−	334.286i	−1.03393	−	0.596939i
$561$	149.346	+	34.2529i	0.266214	+	0.0610568i
$562$	−16.1099	−	27.9031i	−0.0286652	−	0.0496497i
$563$	−469.472	+	61.8072i	−0.833876	+	0.109782i	−0.535361	−	0.844623i	$-0.679825\pi$
$563$	−469.472	+	61.8072i	−0.833876	+	0.109782i	−0.298515	+	0.954405i	$0.596491\pi$
$564$	−210.833	+	236.593i	−0.373817	+	0.419491i
$565$	−393.053	+	105.318i	−0.695669	+	0.186404i
$566$	−29.2120	−	146.859i	−0.0516113	−	0.259468i
$567$	737.031	+	393.035i	1.29988	+	0.693183i
$568$	−15.3337	+	77.0879i	−0.0269960	+	0.135718i
$569$	51.2431	−	389.230i	0.0900582	−	0.684060i	−0.885551	−	0.464543i	$-0.846219\pi$
$569$	51.2431	−	389.230i	0.0900582	−	0.684060i	0.975609	−	0.219517i	$-0.0704481\pi$
$570$	9.32638	+	35.9457i	0.0163621	+	0.0630625i
$571$	−272.977	−	804.164i	−0.478068	−	1.40834i	−0.872136	−	0.489263i	$-0.837266\pi$
$571$	−272.977	−	804.164i	−0.478068	−	1.40834i	0.394068	−	0.919081i	$-0.371067\pi$
$572$	24.3939	+	12.0297i	0.0426466	+	0.0210310i
$573$	261.873	−	520.565i	0.457020	−	0.908491i
$574$	−43.9901	−	164.173i	−0.0766377	−	0.286016i
$575$	−167.436	−	111.877i	−0.291192	−	0.194569i
$576$	142.696	+	113.139i	0.247736	+	0.196422i
$577$			150.131i			0.260192i	0.991501	+	0.130096i	$0.0415285\pi$
$577$			150.131i			0.260192i	−0.991501	+	0.130096i	$0.958472\pi$
$578$	−205.872	−	8.71962i	−0.356181	−	0.0150859i
$579$	−141.665	−	349.841i	−0.244673	−	0.604216i
$580$	700.615	−	92.2378i	1.20796	−	0.159031i
$581$	1522.97	+	99.8209i	2.62130	+	0.171809i
$582$	115.776	−	273.349i	0.198927	−	0.469671i
$583$	−215.789	−	73.2505i	−0.370136	−	0.125644i
$584$	176.048	+	263.474i	0.301452	+	0.451154i
$585$	80.7680	+	125.134i	0.138065	+	0.213905i
$586$	−117.290	+	48.5832i	−0.200154	+	0.0829065i
$587$	822.290	+	108.257i	1.40083	+	0.184423i	0.792797	−	0.609485i	$-0.208624\pi$
$587$	822.290	+	108.257i	1.40083	+	0.184423i	0.608037	+	0.793909i	$0.291957\pi$
$588$	454.701	−	392.420i	0.773301	−	0.667381i
$589$	127.272	+	62.7636i	0.216081	+	0.106560i
$590$	246.613	+	281.208i	0.417987	+	0.476623i
$591$	−322.149	+	243.155i	−0.545092	+	0.411429i
$592$	215.968	−	106.504i	0.364811	−	0.179905i
$593$	−1038.68	−	430.235i	−1.75156	−	0.725522i	−0.997647	−	0.0685527i	$-0.978162\pi$
$593$	−1038.68	−	430.235i	−1.75156	−	0.725522i	−0.753917	−	0.656969i	$-0.771838\pi$
$594$	−57.5061	+	6.18151i	−0.0968116	+	0.0104066i
$595$	1013.75	−	473.525i	1.70378	−	0.795841i
$596$	−135.101	+	234.001i	−0.226679	+	0.392620i
$597$	5.94303	−	10.1075i	0.00995483	−	0.0169304i
$598$	−23.6056	−	1.54719i	−0.0394742	−	0.00258728i
$599$	97.1423	−	362.540i	0.162174	−	0.605242i	−0.836210	−	0.548410i	$-0.815233\pi$
$599$	97.1423	−	362.540i	0.162174	−	0.605242i	0.998384	−	0.0568323i	$-0.0181000\pi$
$600$	225.275	+	113.325i	0.375458	+	0.188876i
$601$	−738.286	+	48.3898i	−1.22843	+	0.0805155i	−0.665760	−	0.746166i	$-0.731892\pi$
$601$	−738.286	+	48.3898i	−1.22843	+	0.0805155i	−0.562670	+	0.826682i	$0.690226\pi$
$602$	−109.819	+	552.096i	−0.182423	+	0.917102i
$603$	−629.496	−	847.919i	−1.04394	−	1.40617i
$604$	30.6848	+	74.0796i	0.0508026	+	0.122648i
$605$	−471.218	+	537.321i	−0.778872	+	0.888134i
$606$	184.768	+	125.592i	0.304898	+	0.207247i
$607$	249.738	+	284.772i	0.411430	+	0.469146i	0.920025	−	0.391860i	$-0.128168\pi$
$607$	249.738	+	284.772i	0.411430	+	0.469146i	−0.508595	+	0.861006i	$0.669835\pi$
$608$	−75.1681	−	20.1412i	−0.123632	−	0.0331270i
$609$	−199.011	+	960.577i	−0.326784	+	1.57730i
$610$	240.699	−	184.695i	0.394589	−	0.302779i
$611$		−	78.4407i		−	0.128381i
$612$	−511.881	+	152.867i	−0.836407	+	0.249782i
$613$	1013.47			1.65329			0.826645	−	0.562724i	$-0.190246\pi$
$613$	1013.47			1.65329			0.826645	+	0.562724i	$0.190246\pi$
$614$	−222.158	−	289.522i	−0.361821	−	0.471534i
$615$	−138.945	−	420.251i	−0.225927	−	0.683335i
$616$	−42.8316	+	159.850i	−0.0695318	+	0.259496i
$617$	283.585	−	248.698i	0.459620	−	0.403076i	−0.397979	−	0.917394i	$-0.630288\pi$
$617$	283.585	−	248.698i	0.459620	−	0.403076i	0.857599	+	0.514319i	$0.171955\pi$
$618$	−25.1626	−	52.0627i	−0.0407162	−	0.0842439i
$619$	172.550	+	151.322i	0.278756	+	0.244462i	0.787295	−	0.616577i	$-0.211481\pi$
$619$	172.550	+	151.322i	0.278756	+	0.244462i	−0.508539	+	0.861039i	$0.669814\pi$
$620$	1074.11	−	444.910i	1.73243	−	0.717597i
$621$	−303.245	+	165.577i	−0.488317	+	0.266630i
$622$	−207.906	−	41.3552i	−0.334255	−	0.0664874i
$623$	−1.90827	−	29.1146i	−0.00306303	−	0.0467328i
$624$	−78.8819	+	4.54155i	−0.126413	+	0.00727813i
$625$	744.511	+	199.491i	1.19122	+	0.319186i
$626$	4.49713	−	68.6129i	0.00718391	−	0.109605i
$627$	−21.3290	+	12.0895i	−0.0340175	+	0.0192815i
$628$	151.953	+	87.7299i	0.241963	+	0.139697i
$629$	−61.0452	+	398.344i	−0.0970511	+	0.633297i
$630$	−303.350	+	293.866i	−0.481508	+	0.466454i
$631$	−78.8191	+	190.286i	−0.124911	+	0.301563i	−0.973948	−	0.226771i	$-0.927183\pi$
$631$	−78.8191	+	190.286i	−0.124911	+	0.301563i	0.849037	+	0.528334i	$0.177183\pi$
$632$	254.895	+	516.875i	0.403314	+	0.817840i
$633$	330.409	−	780.103i	0.521974	−	1.23239i
$634$	−248.450	+	217.885i	−0.391877	+	0.343667i
$635$	133.477	−	270.665i	0.210201	−	0.426245i
$636$	780.461	−	148.812i	1.22714	−	0.233981i
$637$	−19.4051	+	147.396i	−0.0304632	+	0.231391i
$638$	−25.9941	−	62.7553i	−0.0407431	−	0.0983626i
$639$	−117.829	−	60.4511i	−0.184395	−	0.0946027i
$640$	−683.855	+	456.937i	−1.06852	+	0.713964i
$641$	76.3791	−	225.006i	0.119156	−	0.351023i	−0.870945	−	0.491381i	$-0.836492\pi$
$641$	76.3791	−	225.006i	0.119156	−	0.351023i	0.990101	+	0.140359i	$0.0448255\pi$
$642$	−13.9556	−	112.924i	−0.0217378	−	0.175895i
$643$	8.24823	−	125.844i	0.0128277	−	0.195713i	−0.986635	−	0.162945i	$-0.947901\pi$
$643$	8.24823	−	125.844i	0.0128277	−	0.195713i	0.999463	−	0.0327688i	$-0.0104325\pi$
$644$	60.1399	+	456.808i	0.0933849	+	0.709329i
$645$	−202.877	+	1451.84i	−0.314538	+	2.25091i
$646$	25.2432	−	21.2096i	0.0390762	−	0.0328323i
$647$	82.5974			0.127662			0.0638311	−	0.997961i	$-0.479668\pi$
$647$	82.5974			0.127662			0.0638311	+	0.997961i	$0.479668\pi$
$648$	351.446	−	252.358i	0.542354	−	0.389441i
$649$	−137.187	+	205.315i	−0.211383	+	0.316357i
$650$	−28.1003	+	7.52946i	−0.0432313	+	0.0115838i
$651$	92.7659	+	1611.24i	0.142497	+	2.47503i
$652$	224.195	−	454.622i	0.343857	−	0.697273i
$653$	550.898	−	187.005i	0.843641	−	0.286378i	0.134035	−	0.990977i	$-0.457206\pi$
$653$	550.898	−	187.005i	0.843641	−	0.286378i	0.709606	+	0.704599i	$0.248873\pi$
$654$	71.5834	−	258.913i	0.109455	−	0.395891i
$655$	−15.9441	−	2.09908i	−0.0243421	−	0.00320470i
$656$	230.306	+	45.8107i	0.351076	+	0.0698333i
$657$	−508.237	+	163.571i	−0.773572	+	0.248966i
$658$	218.165	−	43.3958i	0.331558	−	0.0659510i
$659$	97.6272	+	364.350i	0.148144	+	0.552883i	0.999595	+	0.0284482i	$0.00905656\pi$
$659$	97.6272	+	364.350i	0.148144	+	0.552883i	−0.851451	+	0.524434i	$0.824277\pi$
$660$	−40.7490	+	196.685i	−0.0617409	+	0.298008i
$661$	−39.8163	−	302.435i	−0.0602365	−	0.457542i	−0.994808	−	0.101767i	$-0.967550\pi$
$661$	−39.8163	−	302.435i	−0.0602365	−	0.457542i	0.934572	−	0.355775i	$-0.115783\pi$
$662$	38.6078	−	22.2902i	0.0583199	−	0.0336710i
$663$	69.4204	−	112.544i	0.104706	−	0.169749i
$664$	395.287	−	684.657i	0.595311	−	1.03111i
$665$	−68.5123	+	165.403i	−0.103026	+	0.248727i
$666$	−27.3042	−	149.648i	−0.0409973	−	0.224697i
$667$	−286.923	−	286.923i	−0.430169	−	0.430169i
$668$	432.525	+	146.822i	0.647492	+	0.219794i
$669$	951.702	+	69.9702i	1.42257	+	0.104589i
$670$	505.639	−	171.641i	0.754685	−	0.256181i
$671$	158.909	+	121.935i	0.236824	+	0.181721i
$672$	−222.273	−	856.684i	−0.330764	−	1.27483i
$673$	−796.960	+	908.759i	−1.18419	+	1.35031i	−0.261295	+	0.965259i	$0.584150\pi$
$673$	−796.960	+	908.759i	−1.18419	+	1.35031i	−0.922895	+	0.385052i	$0.874184\pi$
$674$	−162.794	+	108.776i	−0.241535	+	0.161388i
$675$	−287.677	+	312.686i	−0.426188	+	0.463238i
$676$	−400.656	+	400.656i	−0.592686	+	0.592686i
$677$	−647.111	+	319.120i	−0.955850	+	0.471373i	−0.852186	−	0.523239i	$-0.824723\pi$
$677$	−647.111	+	319.120i	−0.955850	+	0.471373i	−0.103665	+	0.994612i	$0.533057\pi$
$678$	−117.557	−	69.1216i	−0.173388	−	0.101949i
$679$	1239.40	−	715.570i	1.82534	−	1.05386i
$680$	12.2655	−	579.442i	0.0180375	−	0.852121i
$681$	−395.097	+	506.523i	−0.580172	+	0.743793i
$682$	−68.0305	−	88.6591i	−0.0997515	−	0.129999i
$683$	−507.848	+	760.048i	−0.743555	+	1.11281i	0.246086	+	0.969248i	$0.420855\pi$
$683$	−507.848	+	760.048i	−0.743555	+	1.11281i	−0.989641	+	0.143561i	$0.954145\pi$
$684$	43.9096	−	73.3393i	0.0641954	−	0.107221i
$685$	250.187	+	1257.77i	0.365236	+	1.83617i
$686$	−61.1827	+	4.01013i	−0.0891877	+	0.00584567i
$687$	859.274	−	163.839i	1.25076	−	0.238485i
$688$	−616.992	−	473.434i	−0.896790	−	0.688131i
$689$	−119.721	+	156.023i	−0.173760	+	0.226449i
$690$	−32.7209	−	171.609i	−0.0474216	−	0.248708i
$691$	−60.0509	−	916.200i	−0.0869043	−	1.32590i	−0.789252	−	0.614070i	$-0.789531\pi$
$691$	−60.0509	−	916.200i	−0.0869043	−	1.32590i	0.702347	−	0.711834i	$-0.252135\pi$
$692$	−24.3042	+	4.83441i	−0.0351217	+	0.00698613i
$693$	−239.233	−	143.233i	−0.345213	−	0.206686i
$694$	336.381	+	224.763i	0.484699	+	0.323866i
$695$	532.656	−	408.721i	0.766411	−	0.588088i
$696$	400.660	+	312.523i	0.575662	+	0.449027i
$697$	−283.698	+	271.936i	−0.407027	+	0.390152i
$698$	−194.451	−	336.799i	−0.278583	−	0.482520i
$699$	325.613	−	553.778i	0.465827	−	0.792244i
$700$	250.607	+	508.180i	0.358009	+	0.725971i
$701$	428.703	+	428.703i	0.611559	+	0.611559i	0.943352	−	0.331793i	$-0.107654\pi$
$701$	428.703	+	428.703i	0.611559	+	0.611559i	−0.331793	+	0.943352i	$0.607654\pi$
$702$	−10.9008	+	48.7088i	−0.0155282	+	0.0693858i
$703$	−35.8244	−	53.6150i	−0.0509593	−	0.0762660i
$704$	−45.7048	−	40.0820i	−0.0649216	−	0.0569347i
$705$	560.715	−	145.482i	0.795341	−	0.206357i
$706$	260.573	−	339.586i	0.369084	−	0.481000i
$707$	346.210	+	1019.90i	0.489690	+	1.44258i
$708$	63.1264	−	858.616i	0.0891616	−	1.21273i
$709$	−31.0748	+	91.5434i	−0.0438291	+	0.129116i	−0.966641	−	0.256133i	$-0.917551\pi$
$709$	−31.0748	+	91.5434i	−0.0438291	+	0.129116i	0.922812	+	0.385250i	$0.125885\pi$
$710$	47.3493	−	47.3493i	0.0666891	−	0.0666891i
$711$	−955.257	+	174.293i	−1.34354	+	0.245137i
$712$	−13.9629	−	5.78362i	−0.0196108	−	0.00812307i
$713$	−578.139	−	333.789i	−0.810854	−	0.468147i
$714$	351.421	+	130.815i	0.492186	+	0.183214i
$715$	−24.8590	−	43.0571i	−0.0347679	−	0.0602197i
$716$	−240.107	+	31.6106i	−0.335344	+	0.0441489i
$717$	345.100	+	71.4974i	0.481311	+	0.0997175i
$718$	−123.566	+	33.1094i	−0.172097	+	0.0461133i
$719$	228.511	+	1148.80i	0.317817	+	1.59778i	0.727871	+	0.685715i	$0.240510\pi$
$719$	228.511	+	1148.80i	0.317817	+	1.59778i	−0.410053	+	0.912062i	$0.634490\pi$
$720$	−178.764	−	555.446i	−0.248284	−	0.771452i
$721$	54.3857	−	273.415i	0.0754309	−	0.379217i
$722$	32.9079	−	249.961i	0.0455789	−	0.346206i
$723$	−889.927	−	246.044i	−1.23088	−	0.340310i
$724$	107.995	+	318.142i	0.149164	+	0.439422i
$725$	−447.541	−	220.703i	−0.617298	−	0.304418i
$726$	−239.116	+	13.7669i	−0.329361	+	0.0189626i
$727$	−172.380	−	643.333i	−0.237112	−	0.884914i	−0.977185	−	0.212388i	$-0.931876\pi$
$727$	−172.380	−	643.333i	−0.237112	−	0.884914i	0.740073	−	0.672526i	$-0.234791\pi$
$728$	118.748	+	79.3447i	0.163115	+	0.108990i
$729$	246.589	+	686.028i	0.338256	+	0.941054i
$730$		−	269.965i		−	0.369815i
$731$	1241.03	−	392.186i	1.69772	−	0.536506i
$732$	−691.634	−	96.6475i	−0.944855	−	0.132032i
$733$	−376.351	+	49.5476i	−0.513440	+	0.0675956i	−0.382794	−	0.923834i	$-0.625038\pi$
$733$	−376.351	+	49.5476i	−0.513440	+	0.0675956i	−0.130645	+	0.991429i	$0.541705\pi$
$734$	184.019	+	12.0612i	0.250707	+	0.0164322i
$735$	−1089.62	+	134.659i	−1.48247	+	0.183210i
$736$	346.663	+	117.676i	0.471009	+	0.159886i
$737$	195.855	+	293.118i	0.265746	+	0.397717i
$738$	67.7126	−	131.982i	0.0917515	−	0.178838i
$739$	−328.394	+	136.025i	−0.444376	+	0.184067i	−0.593640	−	0.804731i	$-0.702310\pi$
$739$	−328.394	+	136.025i	−0.444376	+	0.184067i	0.149264	+	0.988797i	$0.452310\pi$
$740$	−523.769	−	68.9555i	−0.707796	−	0.0931830i
$741$	3.96287	+	20.7837i	0.00534800	+	0.0280482i
$742$	−500.176	−	246.660i	−0.674092	−	0.332425i
$743$	166.595	+	189.966i	0.224220	+	0.255674i	0.853002	−	0.521908i	$-0.174780\pi$
$743$	166.595	+	189.966i	0.224220	+	0.255674i	−0.628782	+	0.777582i	$0.716446\pi$
$744$	769.786	+	326.040i	1.03466	+	0.438225i
$745$	442.979	−	218.453i	0.594602	−	0.293225i
$746$	78.6573	+	32.5809i	0.105439	+	0.0436741i
$747$	926.824	+	956.734i	1.24073	+	1.28077i
$748$	173.195	−	42.5003i	0.231544	−	0.0568185i
$749$	274.274	−	475.057i	0.366187	−	0.634255i
$750$	62.3613	+	110.021i	0.0831484	+	0.146695i
$751$	−771.642	−	50.5761i	−1.02749	−	0.0673450i	−0.457674	−	0.889120i	$-0.651317\pi$
$751$	−771.642	−	50.5761i	−1.02749	−	0.0673450i	−0.569812	+	0.821775i	$0.692984\pi$
$752$	−79.5390	+	296.844i	−0.105770	+	0.394739i
$753$	−73.4236	−	1275.29i	−0.0975081	−	1.69361i
$754$	−58.4945	+	3.83393i	−0.0775789	+	0.00508479i
$755$	28.5945	−	143.754i	0.0378736	−	0.190403i
$756$	971.887	+	23.1525i	1.28556	+	0.0306251i
$757$	37.4547	+	90.4237i	0.0494778	+	0.119450i	0.946686	−	0.322158i	$-0.104408\pi$
$757$	37.4547	+	90.4237i	0.0494778	+	0.119450i	−0.897208	+	0.441608i	$0.854408\pi$
$758$	−82.9034	+	94.5332i	−0.109371	+	0.124714i
$759$	103.844	−	50.1892i	0.136817	−	0.0661254i
$760$	61.1451	+	69.7226i	0.0804541	+	0.0917403i
$761$	−627.618	−	168.170i	−0.824728	−	0.220985i	−0.178316	−	0.983973i	$-0.557065\pi$
$761$	−627.618	−	168.170i	−0.824728	−	0.220985i	−0.646413	+	0.762988i	$0.723731\pi$
$762$	96.0270	−	31.7488i	0.126020	−	0.0416651i
$763$	1027.43	−	788.372i	1.34656	−	1.03325i
$764$		−	678.217i		−	0.887719i
$765$	933.245	+	287.503i	1.21993	+	0.375821i
$766$	−475.794			−0.621140
$767$	129.728	+	169.065i	0.169137	+	0.220423i
$768$	−32.1456	−	6.65989i	−0.0418562	−	0.00867173i
$769$	−137.685	+	513.849i	−0.179045	+	0.668204i	0.816782	+	0.576946i	$0.195756\pi$
$769$	−137.685	+	513.849i	−0.179045	+	0.668204i	−0.995827	+	0.0912585i	$0.970911\pi$
$770$	106.001	−	92.9603i	0.137663	−	0.120728i
$771$	−467.031	+	687.089i	−0.605747	+	0.891166i
$772$	−330.275	−	289.643i	−0.427817	−	0.375186i
$773$	−653.627	+	270.741i	−0.845572	+	0.350247i	−0.763048	−	0.646342i	$-0.776298\pi$
$773$	−653.627	+	270.741i	−0.845572	+	0.350247i	−0.0825237	+	0.996589i	$0.526298\pi$
$774$	−394.465	+	292.851i	−0.509644	+	0.378360i
$775$	−805.188	−	160.162i	−1.03895	−	0.206661i
$776$	−48.4841	−	739.725i	−0.0624796	−	0.953254i
$777$	329.569	−	655.136i	0.424156	−	0.843161i
$778$	−233.679	−	62.6142i	−0.300359	−	0.0804810i
$779$	4.11254	−	62.7453i	0.00527926	−	0.0805460i
$780$	149.427	+	87.8610i	0.191573	+	0.112642i
$781$	38.2853	+	22.1040i	0.0490209	+	0.0283022i
$782$	−125.025	+	91.7972i	−0.159878	+	0.117388i
$783$	−691.456	+	504.872i	−0.883085	+	0.644792i
$784$	222.895	−	538.115i	0.284305	−	0.686372i
$785$	−141.856	−	287.655i	−0.180708	−	0.366440i
$786$	−3.24688	−	4.30170i	−0.00413089	−	0.00547290i
$787$	38.0305	−	33.3519i	0.0483234	−	0.0423785i	−0.634844	−	0.772641i	$-0.718935\pi$
$787$	38.0305	−	33.3519i	0.0483234	−	0.0423785i	0.683167	+	0.730262i	$0.260602\pi$
$788$	−207.768	+	421.312i	−0.263665	+	0.534661i
$789$	230.914	+	267.562i	0.292666	+	0.339116i
$790$	64.0868	−	486.788i	0.0811225	−	0.616187i
$791$	−251.595	−	607.403i	−0.318072	−	0.767893i
$792$	−121.350	+	78.3253i	−0.153220	+	0.0988956i
$793$	143.727	−	96.0353i	0.181245	−	0.121104i
$794$	120.330	−	354.481i	0.151549	−	0.446449i
$795$	−1337.34	−	566.424i	−1.68219	−	0.712483i
$796$	0.892536	−	13.6175i	0.00112128	−	0.0171074i
$797$	11.8059	+	89.6745i	0.0148129	+	0.112515i	0.997254	−	0.0740584i	$-0.0235951\pi$
$797$	11.8059	+	89.6745i	0.0148129	+	0.112515i	−0.982441	+	0.186573i	$0.940262\pi$
$798$	−55.6128	+	22.5200i	−0.0696903	+	0.0282205i
$799$	−330.848	−	393.768i	−0.414078	−	0.492826i
$800$	450.206			0.562758
$801$	15.8207	−	19.9537i	0.0197512	−	0.0249110i
$802$	64.9946	−	97.2714i	0.0810407	−	0.121286i
$803$	172.157	−	46.1293i	0.214392	−	0.0574463i
$804$	−1098.00	−	552.355i	−1.36567	−	0.687009i
$805$	372.507	−	755.370i	0.462742	−	0.938348i
$806$	−91.3241	+	31.0004i	−0.113305	+	0.0384620i
$807$	172.641	−	44.7931i	0.213929	−	0.0555057i
$808$	553.132	+	72.8212i	0.684569	+	0.0901253i
$809$	46.3639	+	9.22236i	0.0573102	+	0.0113997i	0.223662	−	0.974667i	$-0.428199\pi$
$809$	46.3639	+	9.22236i	0.0573102	+	0.0113997i	−0.166352	+	0.986066i	$0.553199\pi$
$810$	−368.401	+	12.4172i	−0.454816	+	0.0153298i
$811$	−691.751	+	137.598i	−0.852960	+	0.169664i	−0.602161	−	0.798375i	$-0.705693\pi$
$811$	−691.751	+	137.598i	−0.852960	+	0.169664i	−0.250799	+	0.968039i	$0.580693\pi$
$812$	295.503	+	1102.83i	0.363920	+	1.35817i
$813$	−734.826	−	654.819i	−0.903846	−	0.805435i
$814$	6.62816	+	50.3458i	0.00814270	+	0.0618499i
$815$	−802.444	+	463.291i	−0.984594	+	0.568455i
$816$	−376.827	+	355.508i	−0.461798	+	0.435671i
$817$	−104.127	+	180.354i	−0.127451	+	0.220751i
$818$	−109.111	+	263.418i	−0.133388	+	0.322027i
$819$	−183.414	+	155.768i	−0.223949	+	0.190193i
$820$	−364.274	−	364.274i	−0.444236	−	0.444236i
$821$	561.965	+	190.761i	0.684489	+	0.232353i	0.641955	−	0.766742i	$-0.278124\pi$
$821$	561.965	+	190.761i	0.684489	+	0.232353i	0.0425338	+	0.999095i	$0.486457\pi$
$822$	−241.603	+	355.443i	−0.293921	+	0.432412i
$823$	183.352	−	62.2398i	0.222786	−	0.0756255i	−0.207815	−	0.978168i	$-0.566635\pi$
$823$	183.352	−	62.2398i	0.222786	−	0.0756255i	0.430600	+	0.902543i	$0.358302\pi$
$824$	−114.560	−	87.9053i	−0.139030	−	0.106681i
$825$	101.087	−	99.4942i	0.122529	−	0.120599i
$826$	−398.446	+	454.340i	−0.482380	+	0.550049i
$827$	1331.64	−	889.773i	1.61021	−	1.07590i	0.666302	−	0.745682i	$-0.267876\pi$
$827$	1331.64	−	889.773i	1.61021	−	1.07590i	0.943903	−	0.330223i	$-0.107124\pi$
$828$	−228.689	+	330.765i	−0.276195	+	0.399475i
$829$	−906.341	+	906.341i	−1.09329	+	1.09329i	−0.0981193	+	0.995175i	$0.531283\pi$
$829$	−906.341	+	906.341i	−1.09329	+	1.09329i	−0.995175	+	0.0981193i	$0.968717\pi$
$830$	−604.073	+	297.896i	−0.727799	+	0.358911i
$831$	−295.196	+	167.321i	−0.355229	+	0.201349i
$832$	−45.4337	+	26.2311i	−0.0546078	+	0.0315278i
$833$	524.277	+	821.768i	0.629385	+	0.986516i
$834$	222.843	+	31.1396i	0.267198	+	0.0373377i
$835$	−508.281	−	662.405i	−0.608720	−	0.793300i
$836$	−15.8530	+	23.7258i	−0.0189630	+	0.0283801i
$837$	−883.848	+	1096.75i	−1.05597	+	1.31033i
$838$	−77.9356	−	391.809i	−0.0930019	−	0.467552i
$839$	−608.453	+	39.8801i	−0.725212	+	0.0475329i	−0.423538	−	0.905878i	$-0.639212\pi$
$839$	−608.453	+	39.8801i	−0.725212	+	0.0475329i	−0.301674	+	0.953411i	$0.597545\pi$
$840$	−346.939	+	995.998i	−0.413022	+	1.18571i
$841$	−130.504	−	100.139i	−0.155177	−	0.119071i
$842$	130.203	−	169.684i	0.154636	−	0.201525i
$843$	102.631	−	88.5734i	0.121745	−	0.105069i
$844$	−64.4891	−	983.914i	−0.0764089	−	1.16577i
$845$	1015.84	−	202.063i	1.20218	−	0.239128i
$846$	166.565	+	99.7256i	0.196885	+	0.117879i
$847$	−960.083	−	641.507i	−1.13351	−	0.757388i
$848$	611.268	−	469.042i	0.720834	−	0.553116i
$849$	583.962	−	236.471i	0.687824	−	0.278529i
$850$	−109.304	+	156.319i	−0.128593	+	0.183905i
$851$	151.674	+	262.706i	0.178230	+	0.308703i
$852$	−154.128	−	1.22369i	−0.180902	−	0.00143625i
$853$	77.0710	+	156.285i	0.0903529	+	0.183218i	0.937358	−	0.348367i	$-0.113264\pi$
$853$	77.0710	+	156.285i	0.0903529	+	0.183218i	−0.847005	+	0.531584i	$0.821597\pi$
$854$	346.615	+	346.615i	0.405872	+	0.405872i
$855$	−141.218	+	66.8746i	−0.165167	+	0.0782159i
$856$	−157.860	−	236.255i	−0.184416	−	0.275999i
$857$	233.093	+	204.417i	0.271987	+	0.238526i	0.784463	−	0.620175i	$-0.212939\pi$
$857$	233.093	+	204.417i	0.271987	+	0.238526i	−0.512477	+	0.858701i	$0.671272\pi$
$858$	4.44014	−	16.0597i	0.00517498	−	0.0187176i
$859$	−327.777	+	427.167i	−0.381580	+	0.497285i	−0.944173	−	0.329449i	$-0.893137\pi$
$859$	−327.777	+	427.167i	−0.381580	+	0.497285i	0.562593	+	0.826734i	$0.309804\pi$
$860$	548.434	+	1615.63i	0.637714	+	1.87864i
$861$	643.879	−	311.196i	0.747827	−	0.361435i
$862$	−37.6320	+	110.860i	−0.0436567	+	0.128608i
$863$	375.435	−	375.435i	0.435035	−	0.435035i	−0.455302	−	0.890337i	$-0.650469\pi$
$863$	375.435	−	375.435i	0.435035	−	0.435035i	0.890337	+	0.455302i	$0.150469\pi$
$864$	358.042	−	684.445i	0.414401	−	0.792182i
$865$	41.8492	+	17.3345i	0.0483805	+	0.0200399i
$866$	−59.8063	−	34.5292i	−0.0690604	−	0.0398721i
$867$	−126.202	−	857.766i	−0.145562	−	0.989349i
$868$	939.197	+	1626.74i	1.08202	+	1.87412i
$869$	321.375	−	42.3099i	0.369822	−	0.0486880i
$870$	−135.894	−	411.024i	−0.156200	−	0.472441i
$871$	293.867	−	78.7413i	0.337390	−	0.0904033i
$872$	−130.870	−	657.927i	−0.150080	−	0.754503i
$873$	1221.02	+	263.097i	1.39865	+	0.301371i
$874$	4.84178	−	24.3413i	0.00553980	−	0.0278504i
$875$	−79.5804	+	604.473i	−0.0909490	+	0.690826i
$876$	−442.875	+	435.898i	−0.505565	+	0.497600i
$877$	−225.365	−	663.905i	−0.256973	−	0.757019i	−0.996477	−	0.0838663i	$-0.973273\pi$
$877$	−225.365	−	663.905i	−0.256973	−	0.757019i	0.739504	−	0.673152i	$-0.235060\pi$
$878$	321.807	+	158.698i	0.366523	+	0.180749i
$879$	−293.232	−	446.487i	−0.333598	−	0.507948i
$880$	50.4142	+	188.148i	0.0572889	+	0.213805i
$881$	819.250	+	547.406i	0.929910	+	0.621346i	0.925542	−	0.378645i	$-0.123610\pi$
$881$	819.250	+	547.406i	0.929910	+	0.621346i	0.00436748	+	0.999990i	$0.498610\pi$
$882$	−288.318	−	228.598i	−0.326891	−	0.259181i
$883$		−	1380.20i		−	1.56308i	−0.623858	−	0.781538i	$-0.714436\pi$
$883$		−	1380.20i		−	1.56308i	0.623858	−	0.781538i	$-0.285564\pi$
$884$	13.3134	−	153.325i	0.0150605	−	0.173444i
$885$	−967.916	+	1240.89i	−1.09369	+	1.40213i
$886$	354.710	−	46.6984i	0.400349	−	0.0527070i
$887$	1151.82	+	75.4946i	1.29856	+	0.0851122i	0.698945	−	0.715175i	$-0.253653\pi$
$887$	1151.82	+	75.4946i	1.29856	+	0.0851122i	0.599617	+	0.800287i	$0.295320\pi$
$888$	−228.851	−	303.199i	−0.257716	−	0.341441i
$889$	461.715	+	156.731i	0.519364	+	0.176300i
$890$	7.15345	+	10.7059i	0.00803758	+	0.0120291i
$891$	−70.8676	−	232.808i	−0.0795372	−	0.261288i
$892$	1026.11	−	425.029i	1.15035	−	0.476490i
$893$	81.5894	+	10.7415i	0.0913656	+	0.0120285i
$894$	156.316	+	54.4498i	0.174850	+	0.0609058i
$895$	397.037	+	195.797i	0.443616	+	0.218767i
$896$	−876.163	−	999.072i	−0.977860	−	1.11504i
$897$	−12.2081	−	98.7838i	−0.0136099	−	0.110127i
$898$	171.118	−	84.3861i	0.190555	−	0.0939712i
$899$	−1528.33	−	633.055i	−1.70003	−	0.704177i
$900$	−135.559	+	475.576i	−0.150621	+	0.528418i
$901$	57.0850	+	1288.19i	0.0633574	+	1.42973i
$902$	−24.7592	+	42.8842i	−0.0274493	+	0.0475435i
$903$	−2368.42	−	18.8039i	−2.62283	−	0.0208238i
$904$	−339.821	−	22.2730i	−0.375908	−	0.0246383i
$905$	158.951	−	593.213i	0.175636	−	0.655484i
$906$	41.0578	−	26.9649i	0.0453177	−	0.0297626i
$907$	979.696	−	64.2127i	1.08015	−	0.0707968i	0.485080	−	0.874470i	$-0.338791\pi$
$907$	979.696	−	64.2127i	1.08015	−	0.0707968i	0.595071	+	0.803673i	$0.297124\pi$
$908$	−145.862	+	733.299i	−0.160641	+	0.807598i
$909$	−373.474	+	862.644i	−0.410862	+	0.949003i
$910$	−46.5623	−	112.411i	−0.0511674	−	0.123529i
$911$	−447.384	+	510.144i	−0.491091	+	0.559982i	−0.943305	−	0.331927i	$-0.892301\pi$
$911$	−447.384	+	510.144i	−0.491091	+	0.559982i	0.452214	+	0.891910i	$0.350634\pi$
$912$	6.07801	−	82.6703i	0.00666449	−	0.0906472i
$913$	−293.187	−	334.316i	−0.321125	−	0.366173i
$914$	416.938	+	111.718i	0.456168	+	0.122230i
$915$	953.053	+	849.285i	1.04159	+	0.928180i
$916$	807.718	−	619.784i	0.881788	−	0.676620i
$917$		−	25.9828i		−	0.0283345i
$918$	150.723	+	290.493i	0.164187	+	0.316441i
$919$	−848.504			−0.923291			−0.461645	−	0.887065i	$-0.652741\pi$
$919$	−848.504			−0.923291			−0.461645	+	0.887065i	$0.652741\pi$
$920$	−265.580	−	346.111i	−0.288674	−	0.376207i
$921$	1021.55	−	1146.37i	1.10918	−	1.24470i
$922$	−90.3244	+	337.095i	−0.0979657	+	0.365613i
$923$	28.6839	−	25.1551i	0.0310768	−	0.0272536i
$924$	−323.654	−	23.7954i	−0.350275	−	0.0257526i
$925$	280.470	+	245.966i	0.303211	+	0.265909i
$926$	557.790	−	231.044i	0.602365	−	0.249508i
$927$	195.351	−	145.029i	0.210735	−	0.156450i
$928$	889.741	+	176.981i	0.958773	+	0.190712i
$929$	−69.6657	−	1062.89i	−0.0749900	−	1.14413i	−0.855093	−	0.518475i	$-0.826500\pi$
$929$	−69.6657	−	1062.89i	−0.0749900	−	1.14413i	0.780103	−	0.625652i	$-0.215167\pi$
$930$	−390.975	−	595.313i	−0.420403	−	0.640122i
$931$	−150.656	−	40.3680i	−0.161821	−	0.0433599i
$932$	48.9013	−	746.089i	0.0524692	−	0.800525i
$933$	7.08110	−	891.892i	0.00758961	−	0.955940i
$934$	307.203	+	177.364i	0.328911	+	0.189897i
$935$	−306.398	−	111.293i	−0.327698	−	0.119030i
$936$	30.3448	+	120.895i	0.0324196	+	0.129161i
$937$	455.284	−	1099.15i	0.485896	−	1.17306i	−0.470872	−	0.882202i	$-0.656061\pi$
$937$	455.284	−	1099.15i	0.485896	−	1.17306i	0.956767	−	0.290854i	$-0.0939395\pi$
$938$	381.577	+	773.762i	0.406799	+	0.824906i
$939$	287.129	−	35.4845i	0.305782	−	0.0377897i
$940$	506.899	−	444.539i	0.539254	−	0.472913i
$941$	−499.233	+	1012.34i	−0.530534	+	1.07582i	0.452392	+	0.891819i	$0.350571\pi$
$941$	−499.233	+	1012.34i	−0.530534	+	1.07582i	−0.982927	+	0.183998i	$0.941096\pi$
$942$	35.3579	−	101.506i	0.0375349	−	0.107756i
$943$	−38.6109	+	293.279i	−0.0409447	+	0.311006i
$944$	−319.498	−	771.336i	−0.338451	−	0.817094i
$945$	−1453.64	−	1022.19i	−1.53825	−	1.08169i
$946$	136.363	−	91.1146i	0.144147	−	0.0963157i
$947$	550.022	−	1620.31i	0.580804	−	1.71099i	−0.115555	−	0.993301i	$-0.536865\pi$
$947$	550.022	−	1620.31i	0.580804	−	1.71099i	0.696359	−	0.717693i	$-0.254802\pi$
$948$	−902.047	+	680.855i	−0.951526	+	0.718202i
$949$	10.0598	−	153.483i	0.0106004	−	0.161732i
$950$	−3.98372	−	30.2594i	−0.00419339	−	0.0318520i
$951$	−1096.34	−	855.164i	−1.15283	−	0.899226i
$952$	930.768	−	102.550i	0.977697	−	0.107720i
$953$	−877.769			−0.921059			−0.460530	−	0.887644i	$-0.652340\pi$
$953$	−877.769			−0.921059			−0.460530	+	0.887644i	$0.652340\pi$
$954$	−179.100	−	452.581i	−0.187736	−	0.474403i
$955$	−688.766	+	1030.81i	−0.721221	+	1.07938i
$956$	396.207	−	106.163i	0.414442	−	0.111049i
$957$	238.890	−	156.892i	0.249624	−	0.163942i
$958$	115.188	−	233.579i	0.120238	−	0.243819i
$959$	−1962.01	+	666.012i	−2.04589	+	0.694486i
$960$	−271.772	−	276.122i	−0.283096	−	0.287627i
$961$	−1745.53	−	229.804i	−1.81637	−	0.239130i
$962$	42.9813	+	8.54952i	0.0446791	+	0.00888723i
$963$	455.731	−	146.672i	0.473241	−	0.152308i
$964$	−1053.97	+	209.648i	−1.09333	+	0.217478i
$965$	207.831	+	775.636i	0.215369	+	0.803768i
$966$	267.991	−	88.6043i	0.277424	−	0.0917228i
$967$	20.8752	+	158.563i	0.0215876	+	0.163974i	0.998843	−	0.0480920i	$-0.0153141\pi$
$967$	20.8752	+	158.563i	0.0215876	+	0.163974i	−0.977255	+	0.212066i	$0.931981\pi$
$968$	−517.979	+	299.056i	−0.535103	+	0.308942i
$969$	107.555	+	87.6184i	0.110996	+	0.0904215i
$970$	−315.782	+	546.950i	−0.325548	+	0.563866i
$971$	−348.466	+	841.272i	−0.358874	+	0.866398i	0.636585	+	0.771206i	$0.280346\pi$
$971$	−348.466	+	841.272i	−0.358874	+	0.866398i	−0.995459	+	0.0951916i	$0.969654\pi$
$972$	615.207	+	584.308i	0.632929	+	0.601140i
$973$	767.042	+	767.042i	0.788327	+	0.788327i
$974$	−222.943	−	75.6790i	−0.228894	−	0.0776992i
$975$	−53.2651	−	110.208i	−0.0546308	−	0.113034i
$976$	−641.287	+	217.688i	−0.657056	+	0.223041i
$977$	−60.3979	−	46.3449i	−0.0618198	−	0.0474360i	0.577389	−	0.816469i	$-0.304071\pi$
$977$	−60.3979	−	46.3449i	−0.0618198	−	0.0474360i	−0.639209	+	0.769033i	$0.720738\pi$
$978$	−299.301	−	82.7496i	−0.306033	−	0.0846111i
$979$	−5.60484	+	6.39109i	−0.00572507	+	0.00652819i
$980$	−1062.48	+	709.923i	−1.08416	+	0.724411i
$981$	1126.53	+	91.8213i	1.14835	+	0.0935997i
$982$	−473.436	+	473.436i	−0.482114	+	0.482114i
$983$	−1480.46	+	730.081i	−1.50606	+	0.742707i	−0.993272	−	0.115808i	$-0.963054\pi$
$983$	−1480.46	+	730.081i	−1.50606	+	0.742707i	−0.512789	+	0.858515i	$0.671388\pi$
$984$	2.94093	−	370.421i	0.00298875	−	0.376444i
$985$	743.650	−	429.346i	0.754974	−	0.435885i
$986$	−277.468	+	265.965i	−0.281408	+	0.269742i
$987$	351.289	+	867.503i	0.355916	+	0.878929i
$988$	14.9910	+	19.5367i	0.0151731	+	0.0197740i
$989$	544.293	−	814.592i	0.550347	−	0.823653i
$990$	123.034	+	1.95376i	0.124277	+	0.00197350i
$991$	145.409	+	731.019i	0.146729	+	0.737658i	0.982158	+	0.188059i	$0.0602196\pi$
$991$	145.409	+	731.019i	0.146729	+	0.737658i	−0.835428	+	0.549599i	$0.814780\pi$
$992$	1489.29	−	97.6135i	1.50130	−	0.0984007i
$993$	122.554	+	142.004i	0.123418	+	0.143005i
$994$	85.8320	+	65.8612i	0.0863501	+	0.0662588i
$995$	−15.1858	+	19.7906i	−0.0152621	+	0.0198900i
$996$	1464.06	+	509.979i	1.46994	+	0.512027i
$997$	−21.1931	−	323.345i	−0.0212569	−	0.324318i	−0.995223	−	0.0976252i	$-0.968875\pi$
$997$	−21.1931	−	323.345i	−0.0212569	−	0.324318i	0.973966	−	0.226693i	$-0.0727913\pi$
$998$	−149.427	+	29.7228i	−0.149726	+	0.0297823i
$999$	596.995	−	230.784i	0.597592	−	0.231015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.t.a.7.15	✓	544
9.4	even	3	inner	153.3.t.a.58.20	yes	544
17.5	odd	16	inner	153.3.t.a.124.20	yes	544
153.22	odd	48	inner	153.3.t.a.22.15	yes	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.t.a.7.15	✓	544	1.1	even	1	trivial
153.3.t.a.22.15	yes	544	153.22	odd	48	inner
153.3.t.a.58.20	yes	544	9.4	even	3	inner
153.3.t.a.124.20	yes	544	17.5	odd	16	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.t (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.434047 - 0.565661i) q^{2} +(1.99588 - 2.23974i) q^{3} +(0.903701 - 3.37266i) q^{4} +(-4.79864 + 4.20829i) q^{5} +(-2.13324 - 0.156838i) q^{6} +(-7.75304 - 6.79923i) q^{7} +(-4.93493 + 2.04412i) q^{8} +(-1.03291 - 8.94053i) q^{9} +(4.46330 + 0.887806i) q^{10} +(0.196496 + 2.99795i) q^{11} +(-5.75021 - 8.75548i) q^{12} +(2.50444 + 0.671062i) q^{13} +(-0.480878 + 7.33678i) q^{14} +(-0.152016 + 19.1470i) q^{15} +(-8.79709 - 5.07900i) q^{16} +(15.4025 - 7.19455i) q^{17} +(-4.60898 + 4.46489i) q^{18} +(-1.04095 + 2.51307i) q^{19} +(9.85659 + 19.9872i) q^{20} +(-30.7027 + 3.79436i) q^{21} +(1.61054 - 1.41240i) q^{22} +(5.65973 - 11.4768i) q^{23} +(-5.27125 + 15.1328i) q^{24} +(2.05404 - 15.6020i) q^{25} +(-0.707449 - 1.70793i) q^{26} +(-22.0861 - 15.5308i) q^{27} +(-29.9379 + 20.0039i) q^{28} +(10.1927 - 30.0267i) q^{29} +(10.8967 - 8.22470i) q^{30} +(3.41201 - 52.0572i) q^{31} +(3.73420 + 28.3640i) q^{32} +(7.10683 + 5.54346i) q^{33} +(-10.7551 - 5.58984i) q^{34} +65.8172 q^{35} +(-31.0868 - 4.59591i) q^{36} +(-13.1701 + 19.7104i) q^{37} +(1.87337 - 0.501968i) q^{38} +(6.50156 - 4.26994i) q^{39} +(15.0787 - 30.5766i) q^{40} +(-21.8897 + 7.43056i) q^{41} +(15.4727 + 15.7204i) q^{42} +(75.9054 + 9.99314i) q^{43} +(10.2886 + 2.04654i) q^{44} +(42.5809 + 38.5556i) q^{45} +(-8.94857 + 1.77998i) q^{46} +(-7.83018 - 29.2226i) q^{47} +(-28.9336 + 9.56615i) q^{48} +(7.48427 + 56.8486i) q^{49} +(-9.71699 + 5.61011i) q^{50} +(14.6277 - 48.8572i) q^{51} +(4.52652 - 7.84016i) q^{52} +(-29.0266 + 70.0763i) q^{53} +(0.801228 + 19.2343i) q^{54} +(-13.5592 - 13.5592i) q^{55} +(52.1592 + 17.7056i) q^{56} +(3.55103 + 7.34726i) q^{57} +(-21.4091 + 7.26740i) q^{58} +(65.2058 + 50.0342i) q^{59} +(64.4388 + 17.8158i) q^{60} +(43.9581 - 50.1246i) q^{61} +(-30.9277 + 20.6652i) q^{62} +(-52.7806 + 76.3393i) q^{63} +(-14.3076 + 14.3076i) q^{64} +(-14.8419 + 7.31922i) q^{65} +(0.0510201 - 6.42618i) q^{66} +(101.618 - 58.6692i) q^{67} +(-10.3455 - 58.4492i) q^{68} +(-14.4089 - 35.5827i) q^{69} +(-28.5677 - 37.2302i) q^{70} +(8.17495 - 12.2347i) q^{71} +(23.3728 + 42.0095i) q^{72} +(-11.5734 - 58.1835i) q^{73} +(16.8659 - 1.10545i) q^{74} +(-30.8449 - 35.7403i) q^{75} +(7.53503 + 5.78183i) q^{76} +(18.8603 - 24.5793i) q^{77} +(-5.23732 - 1.82433i) q^{78} +(-7.05647 - 107.661i) q^{79} +(63.5880 - 12.6484i) q^{80} +(-78.8662 + 18.4695i) q^{81} +(13.7043 + 9.15695i) q^{82} +(-117.420 + 90.0997i) q^{83} +(-14.9490 + 106.979i) q^{84} +(-43.6344 + 99.3424i) q^{85} +(-27.2938 - 47.2742i) q^{86} +(-46.9088 - 82.7589i) q^{87} +(-7.09786 - 14.3930i) q^{88} +(2.00069 + 2.00069i) q^{89} +(3.32727 - 40.8213i) q^{90} +(-14.8543 - 22.2310i) q^{91} +(-33.5926 - 29.4599i) q^{92} +(-109.785 - 111.542i) q^{93} +(-13.1314 + 17.1132i) q^{94} +(-5.58061 - 16.4399i) q^{95} +(70.9812 + 48.2476i) q^{96} +(-44.6102 + 131.417i) q^{97} +(28.9085 - 28.9085i) q^{98} +(26.6003 - 4.85339i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} + 176 q^{12} - 8 q^{13} - 8 q^{14} - 40 q^{15} - 32 q^{17} + 32 q^{18} - 32 q^{19} - 8 q^{20}+ \cdots + 448 q^{99}+O(q^{100}) \) 544 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 + 176 * q^12 - 8 * q^13 - 8 * q^14 - 40 * q^15 - 32 * q^17 + 32 * q^18 - 32 * q^19 - 8 * q^20 - 256 * q^21 - 8 * q^22 - 8 * q^23 + 176 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 72 * q^32 + 40 * q^34 - 64 * q^35 + 16 * q^36 - 32 * q^37 + 88 * q^38 - 192 * q^39 - 8 * q^40 - 440 * q^41 - 400 * q^42 - 248 * q^43 - 800 * q^44 - 176 * q^45 - 32 * q^46 + 112 * q^47 - 248 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 + 160 * q^53 - 312 * q^54 - 32 * q^55 - 488 * q^56 - 296 * q^57 - 8 * q^58 + 568 * q^59 + 2080 * q^60 - 8 * q^61 + 1120 * q^62 - 88 * q^63 - 288 * q^64 - 248 * q^65 - 24 * q^66 - 8 * q^68 - 416 * q^69 - 40 * q^70 - 32 * q^71 + 632 * q^72 - 32 * q^73 - 8 * q^74 + 752 * q^75 - 8 * q^76 - 8 * q^77 - 2304 * q^78 - 8 * q^79 - 432 * q^80 + 768 * q^81 + 352 * q^82 - 296 * q^83 - 8 * q^85 + 1184 * q^86 - 688 * q^87 - 8 * q^88 - 1184 * q^89 - 1136 * q^90 + 640 * q^91 - 2024 * q^92 - 528 * q^93 - 8 * q^94 + 472 * q^95 - 1064 * q^96 - 8 * q^97 - 848 * q^98 + 448 * q^99

Introduction

L-functions

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