LMFDB - Embedded newform 27.3.f.a.20.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,3,Mod(2,27)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("27.2"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	27.f (of order $18$, degree $6$, 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:	$0.735696713773$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			20.5
Character	$\chi$	$=$	27.20
Dual form			27.3.f.a.23.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.898786 + 2.46939i) q^{2} +(-2.94744 + 0.559079i) q^{3} +(-2.22591 + 1.86776i) q^{4} +(6.15614 - 1.08549i) q^{5} +(-4.02971 - 6.77591i) q^{6} +(-6.21846 - 5.21791i) q^{7} +(2.49037 + 1.43782i) q^{8} +(8.37486 - 3.29571i) q^{9} +(8.21356 + 14.2263i) q^{10} +(-7.99059 - 1.40896i) q^{11} +(5.51652 - 6.74957i) q^{12} +(-9.12402 - 3.32087i) q^{13} +(7.29600 - 20.0456i) q^{14} +(-17.5380 + 6.64120i) q^{15} +(-3.33052 + 18.8883i) q^{16} +(-13.0143 + 7.51380i) q^{17} +(15.6656 + 17.7187i) q^{18} +(8.93226 - 15.4711i) q^{19} +(-11.6756 + 13.9144i) q^{20} +(21.2458 + 11.9029i) q^{21} +(-3.70256 - 20.9983i) q^{22} +(16.9268 + 20.1726i) q^{23} +(-8.14409 - 2.84557i) q^{24} +(13.2275 - 4.81440i) q^{25} -25.5156i q^{26} +(-22.8419 + 14.3961i) q^{27} +23.5875 q^{28} +(5.18906 + 14.2568i) q^{29} +(-32.1626 - 37.3392i) q^{30} +(25.0755 - 21.0408i) q^{31} +(-38.3082 + 6.75478i) q^{32} +(24.3395 - 0.314547i) q^{33} +(-30.2516 - 25.3841i) q^{34} +(-43.9457 - 25.3721i) q^{35} +(-12.4861 + 22.9782i) q^{36} +(-15.8096 - 27.3831i) q^{37} +(46.2325 + 8.15204i) q^{38} +(28.7492 + 4.68704i) q^{39} +(16.8918 + 6.14813i) q^{40} +(5.65018 - 15.5238i) q^{41} +(-10.2975 + 63.1624i) q^{42} +(-14.5559 + 82.5505i) q^{43} +(20.4179 - 11.7883i) q^{44} +(47.9794 - 29.3797i) q^{45} +(-34.6005 + 59.9298i) q^{46} +(8.46562 - 10.0889i) q^{47} +(-0.743531 - 57.5342i) q^{48} +(2.93393 + 16.6391i) q^{49} +(23.7773 + 28.3367i) q^{50} +(34.1581 - 29.4225i) q^{51} +(26.5118 - 9.64952i) q^{52} +25.7140i q^{53} +(-56.0796 - 43.4666i) q^{54} -50.7206 q^{55} +(-7.98389 - 21.9356i) q^{56} +(-17.6778 + 50.5941i) q^{57} +(-30.5419 + 25.6277i) q^{58} +(-22.3660 + 3.94373i) q^{59} +(26.6338 - 47.5395i) q^{60} +(26.1131 + 21.9115i) q^{61} +(74.4955 + 43.0100i) q^{62} +(-69.2755 - 23.2050i) q^{63} +(-12.7517 - 22.0867i) q^{64} +(-59.7736 - 10.5397i) q^{65} +(22.6528 + 59.8212i) q^{66} +(-7.61567 - 2.77188i) q^{67} +(14.9346 - 41.0326i) q^{68} +(-61.1690 - 49.9942i) q^{69} +(23.1558 - 131.323i) q^{70} +(35.7557 - 20.6436i) q^{71} +(25.5952 + 3.83398i) q^{72} +(40.4046 - 69.9827i) q^{73} +(53.4101 - 63.6517i) q^{74} +(-36.2956 + 21.5854i) q^{75} +(9.01395 + 51.1206i) q^{76} +(42.3374 + 50.4557i) q^{77} +(14.2652 + 75.2057i) q^{78} +(25.9652 - 9.45057i) q^{79} +119.894i q^{80} +(59.2766 - 55.2022i) q^{81} +43.4126 q^{82} +(-6.01607 - 16.5290i) q^{83} +(-69.5229 + 13.1873i) q^{84} +(-71.9616 + 60.3830i) q^{85} +(-216.932 + 38.2510i) q^{86} +(-23.2652 - 39.1201i) q^{87} +(-17.8737 - 14.9978i) q^{88} +(24.4986 + 14.1443i) q^{89} +(115.673 + 92.0739i) q^{90} +(39.4094 + 68.2590i) q^{91} +(-75.3552 - 13.2871i) q^{92} +(-62.1451 + 76.0358i) q^{93} +(32.5223 + 11.8372i) q^{94} +(38.1945 - 104.938i) q^{95} +(109.135 - 41.3267i) q^{96} +(29.2825 - 166.069i) q^{97} +(-38.4516 + 22.2000i) q^{98} +(-71.5636 + 14.5348i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 15 q^{5} - 18 q^{6} - 6 q^{7} - 9 q^{8} - 3 q^{10} - 6 q^{11} - 15 q^{12} - 6 q^{13} - 15 q^{14} - 9 q^{15} - 18 q^{16} - 9 q^{17} + 63 q^{18} - 3 q^{19} + 213 q^{20}+ \cdots + 513 q^{99}+O(q^{100}) $ 30 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 15 * q^5 - 18 * q^6 - 6 * q^7 - 9 * q^8 - 3 * q^10 - 6 * q^11 - 15 * q^12 - 6 * q^13 - 15 * q^14 - 9 * q^15 - 18 * q^16 - 9 * q^17 + 63 * q^18 - 3 * q^19 + 213 * q^20 + 132 * q^21 - 42 * q^22 + 120 * q^23 + 144 * q^24 - 15 * q^25 - 90 * q^27 - 12 * q^28 - 168 * q^29 - 243 * q^30 + 39 * q^31 - 360 * q^32 - 207 * q^33 + 54 * q^34 - 252 * q^35 - 360 * q^36 - 3 * q^37 - 84 * q^38 + 15 * q^39 - 33 * q^40 + 228 * q^41 + 486 * q^42 - 96 * q^43 + 639 * q^44 + 477 * q^45 - 3 * q^46 + 399 * q^47 + 453 * q^48 - 78 * q^49 + 303 * q^50 + 36 * q^51 - 9 * q^52 - 54 * q^54 - 12 * q^55 - 393 * q^56 - 192 * q^57 + 129 * q^58 - 474 * q^59 - 846 * q^60 + 138 * q^61 - 900 * q^62 - 585 * q^63 - 51 * q^64 - 411 * q^65 - 423 * q^66 + 354 * q^67 + 99 * q^68 + 99 * q^69 + 489 * q^70 + 315 * q^71 + 720 * q^72 - 66 * q^73 + 321 * q^74 + 255 * q^75 + 258 * q^76 + 201 * q^77 + 180 * q^78 + 30 * q^79 + 36 * q^81 - 12 * q^82 - 33 * q^83 - 588 * q^84 - 261 * q^85 - 258 * q^86 - 279 * q^87 - 642 * q^88 + 72 * q^89 + 288 * q^90 + 96 * q^91 - 3 * q^92 + 591 * q^93 - 861 * q^94 + 681 * q^95 + 270 * q^96 - 582 * q^97 + 882 * q^98 + 513 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	0.898786	+	2.46939i	0.449393	+	1.23470i	0.933148	+	0.359493i	$0.117050\pi$
$2$	0.898786	+	2.46939i	0.449393	+	1.23470i	−0.483755	+	0.875203i	$0.660727\pi$
$3$	−2.94744	+	0.559079i	−0.982482	+	0.186360i
$3$	−2.94744	+	0.559079i	−0.982482	+	0.186360i
$4$	−2.22591	+	1.86776i	−0.556477	+	0.466940i
$5$	6.15614	−	1.08549i	1.23123	−	0.217099i	0.480076	−	0.877227i	$-0.340609\pi$
$5$	6.15614	−	1.08549i	1.23123	−	0.217099i	0.751153	+	0.660128i	$0.229498\pi$
$6$	−4.02971	−	6.77591i	−0.671618	−	1.12932i
$7$	−6.21846	−	5.21791i	−0.888352	−	0.745415i	0.0795272	−	0.996833i	$-0.474659\pi$
$7$	−6.21846	−	5.21791i	−0.888352	−	0.745415i	−0.967879	+	0.251417i	$0.919103\pi$
$8$	2.49037	+	1.43782i	0.311297	+	0.179727i
$9$	8.37486	−	3.29571i	0.930540	−	0.366190i
$10$	8.21356	+	14.2263i	0.821356	+	1.42263i
$11$	−7.99059	−	1.40896i	−0.726417	−	0.128087i	−0.201802	−	0.979426i	$-0.564680\pi$
$11$	−7.99059	−	1.40896i	−0.726417	−	0.128087i	−0.524615	+	0.851339i	$0.675791\pi$
$12$	5.51652	−	6.74957i	0.459710	−	0.562465i
$13$	−9.12402	−	3.32087i	−0.701848	−	0.255452i	−0.0336483	−	0.999434i	$-0.510713\pi$
$13$	−9.12402	−	3.32087i	−0.701848	−	0.255452i	−0.668200	+	0.743982i	$0.732935\pi$
$14$	7.29600	−	20.0456i	0.521143	−	1.43183i
$15$	−17.5380	+	6.64120i	−1.16920	+	0.442747i
$16$	−3.33052	+	18.8883i	−0.208157	+	1.18052i
$17$	−13.0143	+	7.51380i	−0.765546	+	0.441988i	−0.831284	−	0.555849i	$-0.812393\pi$
$17$	−13.0143	+	7.51380i	−0.765546	+	0.441988i	0.0657372	+	0.997837i	$0.479060\pi$
$18$	15.6656	+	17.7187i	0.870311	+	0.984372i
$19$	8.93226	−	15.4711i	0.470119	−	0.814270i	−0.529297	−	0.848437i	$-0.677544\pi$
$19$	8.93226	−	15.4711i	0.470119	−	0.814270i	0.999416	+	0.0341664i	$0.0108776\pi$
$20$	−11.6756	+	13.9144i	−0.583778	+	0.695720i
$21$	21.2458	+	11.9029i	1.01170	+	0.566804i
$22$	−3.70256	−	20.9983i	−0.168298	−	0.954466i
$23$	16.9268	+	20.1726i	0.735949	+	0.877070i	0.996076	−	0.0885045i	$-0.0282088\pi$
$23$	16.9268	+	20.1726i	0.735949	+	0.877070i	−0.260127	+	0.965575i	$0.583764\pi$
$24$	−8.14409	−	2.84557i	−0.339337	−	0.118566i
$25$	13.2275	−	4.81440i	0.529099	−	0.192576i
$26$		−	25.5156i		−	0.981367i
$27$	−22.8419	+	14.3961i	−0.845996	+	0.533190i
$28$	23.5875			0.842411
$29$	5.18906	+	14.2568i	0.178933	+	0.491615i	0.996440	−	0.0843038i	$-0.0268666\pi$
$29$	5.18906	+	14.2568i	0.178933	+	0.491615i	−0.817507	+	0.575919i	$0.804644\pi$
$30$	−32.1626	−	37.3392i	−1.07209	−	1.24464i
$31$	25.0755	−	21.0408i	0.808886	−	0.678736i	−0.141456	−	0.989945i	$-0.545178\pi$
$31$	25.0755	−	21.0408i	0.808886	−	0.678736i	0.950342	+	0.311209i	$0.100734\pi$
$32$	−38.3082	+	6.75478i	−1.19713	+	0.211087i
$33$	24.3395	−	0.314547i	0.737562	−	0.00953171i
$34$	−30.2516	−	25.3841i	−0.889752	−	0.746591i
$35$	−43.9457	−	25.3721i	−1.25559	−	0.724917i
$36$	−12.4861	+	22.9782i	−0.346836	+	0.638282i
$37$	−15.8096	−	27.3831i	−0.427287	−	0.740083i	0.569344	−	0.822100i	$-0.307197\pi$
$37$	−15.8096	−	27.3831i	−0.427287	−	0.740083i	−0.996631	+	0.0820163i	$0.973864\pi$
$38$	46.2325	+	8.15204i	1.21664	+	0.214527i
$39$	28.7492	+	4.68704i	0.737159	+	0.120181i
$40$	16.8918	+	6.14813i	0.422296	+	0.153703i
$41$	5.65018	−	15.5238i	0.137809	−	0.378628i	−0.851520	−	0.524321i	$-0.824319\pi$
$41$	5.65018	−	15.5238i	0.137809	−	0.378628i	0.989330	+	0.145693i	$0.0465413\pi$
$42$	−10.2975	+	63.1624i	−0.245179	+	1.50387i
$43$	−14.5559	+	82.5505i	−0.338509	+	1.91978i	0.0508761	+	0.998705i	$0.483799\pi$
$43$	−14.5559	+	82.5505i	−0.338509	+	1.91978i	−0.389385	+	0.921075i	$0.627312\pi$
$44$	20.4179	−	11.7883i	0.464044	−	0.267916i
$45$	47.9794	−	29.3797i	1.06621	−	0.652882i
$46$	−34.6005	+	59.9298i	−0.752185	+	1.30282i
$47$	8.46562	−	10.0889i	0.180120	−	0.214658i	−0.668429	−	0.743776i	$-0.733033\pi$
$47$	8.46562	−	10.0889i	0.180120	−	0.214658i	0.848548	+	0.529118i	$0.177477\pi$
$48$	−0.743531	−	57.5342i	−0.0154902	−	1.19863i
$49$	2.93393	+	16.6391i	0.0598761	+	0.339574i
$50$	23.7773	+	28.3367i	0.475546	+	0.566734i
$51$	34.1581	−	29.4225i	0.669766	−	0.576912i
$52$	26.5118	−	9.64952i	0.509843	−	0.185568i
$53$			25.7140i			0.485169i	0.970130	+	0.242585i	$0.0779952\pi$
$53$			25.7140i			0.485169i	−0.970130	+	0.242585i	$0.922005\pi$
$54$	−56.0796	−	43.4666i	−1.03851	−	0.804936i
$55$	−50.7206			−0.922193
$56$	−7.98389	−	21.9356i	−0.142569	−	0.391706i
$57$	−17.6778	+	50.5941i	−0.310136	+	0.887617i
$58$	−30.5419	+	25.6277i	−0.526584	+	0.441856i
$59$	−22.3660	+	3.94373i	−0.379085	+	0.0668428i	−0.359944	−	0.932974i	$-0.617204\pi$
$59$	−22.3660	+	3.94373i	−0.379085	+	0.0668428i	−0.0191407	+	0.999817i	$0.506093\pi$
$60$	26.6338	−	47.5395i	0.443897	−	0.792325i
$61$	26.1131	+	21.9115i	0.428084	+	0.359205i	0.831228	−	0.555931i	$-0.187638\pi$
$61$	26.1131	+	21.9115i	0.428084	+	0.359205i	−0.403144	+	0.915137i	$0.632083\pi$
$62$	74.4955	+	43.0100i	1.20154	+	0.693710i
$63$	−69.2755	−	23.2050i	−1.09961	−	0.368334i
$64$	−12.7517	−	22.0867i	−0.199246	−	0.345104i
$65$	−59.7736	−	10.5397i	−0.919593	−	0.162149i
$66$	22.6528	+	59.8212i	0.343224	+	0.906382i
$67$	−7.61567	−	2.77188i	−0.113667	−	0.0413713i	0.284561	−	0.958658i	$-0.408152\pi$
$67$	−7.61567	−	2.77188i	−0.113667	−	0.0413713i	−0.398227	+	0.917287i	$0.630375\pi$
$68$	14.9346	−	41.0326i	0.219627	−	0.603420i
$69$	−61.1690	−	49.9942i	−0.886507	−	0.724554i
$70$	23.1558	−	131.323i	0.330798	−	1.87605i
$71$	35.7557	−	20.6436i	0.503601	−	0.290754i	−0.226598	−	0.973988i	$-0.572760\pi$
$71$	35.7557	−	20.6436i	0.503601	−	0.290754i	0.730199	+	0.683234i	$0.239427\pi$
$72$	25.5952	+	3.83398i	0.355488	+	0.0532498i
$73$	40.4046	−	69.9827i	0.553487	−	0.958668i	−0.444532	−	0.895763i	$-0.646630\pi$
$73$	40.4046	−	69.9827i	0.553487	−	0.958668i	0.998020	−	0.0629050i	$-0.0200365\pi$
$74$	53.4101	−	63.6517i	0.721758	−	0.860158i
$75$	−36.2956	+	21.5854i	−0.483941	+	0.287805i
$76$	9.01395	+	51.1206i	0.118605	+	0.672640i
$77$	42.3374	+	50.4557i	0.549836	+	0.655269i
$78$	14.2652	+	75.2057i	0.182887	+	0.964175i
$79$	25.9652	−	9.45057i	0.328674	−	0.119627i	−0.172412	−	0.985025i	$-0.555156\pi$
$79$	25.9652	−	9.45057i	0.328674	−	0.119627i	0.501086	+	0.865397i	$0.332934\pi$
$80$			119.894i			1.49868i
$81$	59.2766	−	55.2022i	0.731810	−	0.681508i
$82$	43.4126			0.529421
$83$	−6.01607	−	16.5290i	−0.0724827	−	0.199145i	0.898161	−	0.439667i	$-0.144904\pi$
$83$	−6.01607	−	16.5290i	−0.0724827	−	0.199145i	−0.970644	+	0.240522i	$0.922681\pi$
$84$	−69.5229	+	13.1873i	−0.827654	+	0.156991i
$85$	−71.9616	+	60.3830i	−0.846607	+	0.710388i
$86$	−216.932	+	38.2510i	−2.52247	+	0.444779i
$87$	−23.2652	−	39.1201i	−0.267416	−	0.449657i
$88$	−17.8737	−	14.9978i	−0.203111	−	0.170430i
$89$	24.4986	+	14.1443i	0.275265	+	0.158924i	0.631278	−	0.775557i	$-0.282531\pi$
$89$	24.4986	+	14.1443i	0.275265	+	0.158924i	−0.356013	+	0.934481i	$0.615864\pi$
$90$	115.673	+	92.0739i	1.28526	+	1.02304i
$91$	39.4094	+	68.2590i	0.433070	+	0.750099i
$92$	−75.3552	−	13.2871i	−0.819078	−	0.144426i
$93$	−62.1451	+	76.0358i	−0.668227	+	0.817589i
$94$	32.5223	+	11.8372i	0.345982	+	0.125927i
$95$	38.1945	−	104.938i	0.402047	−	1.10461i
$96$	109.135	−	41.3267i	1.13682	−	0.430486i
$97$	29.2825	−	166.069i	0.301881	−	1.71205i	−0.335953	−	0.941879i	$-0.609058\pi$
$97$	29.2825	−	166.069i	0.301881	−	1.71205i	0.637834	−	0.770174i	$-0.279831\pi$
$98$	−38.4516	+	22.2000i	−0.392363	+	0.226531i
$99$	−71.5636	+	14.5348i	−0.722865	+	0.146816i
$100$	−20.4510	+	35.4221i	−0.204510	+	0.354221i
$101$	−44.8847	+	53.4915i	−0.444403	+	0.529619i	−0.941020	−	0.338351i	$-0.890131\pi$
$101$	−44.8847	+	53.4915i	−0.444403	+	0.529619i	0.496617	+	0.867970i	$0.334575\pi$
$102$	103.357	+	57.9052i	1.01330	+	0.567698i
$103$	12.1315	+	68.8014i	0.117782	+	0.667974i	0.985335	+	0.170630i	$0.0545803\pi$
$103$	12.1315	+	68.8014i	0.117782	+	0.667974i	−0.867553	+	0.497344i	$0.834309\pi$
$104$	−17.9474	−	21.3889i	−0.172571	−	0.205662i
$105$	143.713	+	50.2137i	1.36869	+	0.478226i
$106$	−63.4979	+	23.1113i	−0.599037	+	0.218031i
$107$		−	121.432i		−	1.13488i	−0.823416	−	0.567438i	$-0.807935\pi$
$107$		−	121.432i		−	1.13488i	0.823416	−	0.567438i	$-0.192065\pi$
$108$	23.9555	−	74.7076i	0.221810	−	0.691737i
$109$	−119.633			−1.09755			−0.548777	−	0.835969i	$-0.684907\pi$
$109$	−119.633			−1.09755			−0.548777	+	0.835969i	$0.684907\pi$
$110$	−45.5870	−	125.249i	−0.414427	−	1.13863i
$111$	61.9073	+	71.8713i	0.557723	+	0.647489i
$112$	119.268	−	100.078i	1.06489	−	0.893552i
$113$	122.474	−	21.5955i	1.08384	−	0.191111i	0.396929	−	0.917849i	$-0.370076\pi$
$113$	122.474	−	21.5955i	1.08384	−	0.191111i	0.686914	+	0.726738i	$0.258965\pi$
$114$	−140.825	+	1.81992i	−1.23531	+	0.0159643i
$115$	126.101	+	105.811i	1.09653	+	0.920100i
$116$	−38.1787	−	22.0425i	−0.329127	−	0.190021i
$117$	−87.3571	+	2.25826i	−0.746642	+	0.0193013i
$118$	−29.8408	−	51.6859i	−0.252889	−	0.438016i
$119$	120.135	+	21.1831i	1.00954	+	0.178009i
$120$	−53.2250	−	8.67740i	−0.443542	−	0.0723116i
$121$	−51.8384	−	18.8676i	−0.428417	−	0.155931i
$122$	−30.6381	+	84.1774i	−0.251132	+	0.689979i
$123$	−7.97461	+	48.9143i	−0.0648342	+	0.397677i
$124$	−16.5165	+	93.6699i	−0.133198	+	0.755402i
$125$	−59.1363	+	34.1424i	−0.473091	+	0.273139i
$126$	−4.96142	−	191.925i	−0.0393763	−	1.52321i
$127$	58.7300	−	101.723i	0.462441	−	0.800971i	−0.536641	−	0.843811i	$-0.680307\pi$
$127$	58.7300	−	101.723i	0.462441	−	0.800971i	0.999082	+	0.0428396i	$0.0136404\pi$
$128$	−56.9361	+	67.8538i	−0.444814	+	0.530108i
$129$	−3.24957	−	251.451i	−0.0251905	−	1.94923i
$130$	−27.6970	−	157.077i	−0.213054	−	1.20829i
$131$	3.02933	+	3.61022i	0.0231247	+	0.0275589i	0.777483	−	0.628904i	$-0.216496\pi$
$131$	3.02933	+	3.61022i	0.0231247	+	0.0275589i	−0.754358	+	0.656463i	$0.772052\pi$
$132$	−53.5901	+	46.1606i	−0.405986	+	0.349701i
$133$	−136.272	+	49.5989i	−1.02460	+	0.372924i
$134$		−	21.2974i		−	0.158936i
$135$	−124.991	+	113.419i	−0.925859	+	0.840143i
$136$	−43.2139			−0.317749
$137$	75.5147	+	207.475i	0.551202	+	1.51442i	0.832071	+	0.554669i	$0.187155\pi$
$137$	75.5147	+	207.475i	0.551202	+	1.51442i	−0.280869	+	0.959746i	$0.590623\pi$
$138$	68.4776	−	195.984i	0.496215	−	1.42018i
$139$	−27.3980	+	22.9896i	−0.197108	+	0.165393i	−0.736000	−	0.676982i	$-0.763288\pi$
$139$	−27.3980	+	22.9896i	−0.197108	+	0.165393i	0.538892	+	0.842375i	$0.318843\pi$
$140$	145.208	−	25.6041i	1.03720	−	0.182886i
$141$	−19.3114	+	34.4695i	−0.136961	+	0.244465i
$142$	83.1137	+	69.7407i	0.585308	+	0.491132i
$143$	68.2274	+	39.3911i	0.477114	+	0.275462i
$144$	34.3577	+	169.163i	0.238595	+	1.17474i
$145$	47.4203	+	82.1344i	0.327037	+	0.566444i
$146$	209.130	+	36.8753i	1.43240	+	0.252570i
$147$	−17.9502	−	47.4026i	−0.122110	−	0.322467i
$148$	86.3358	+	31.4237i	0.583350	+	0.212322i
$149$	−57.3691	+	157.620i	−0.385028	+	1.05786i	0.584183	+	0.811622i	$0.301415\pi$
$149$	−57.3691	+	157.620i	−0.385028	+	1.05786i	−0.969211	+	0.246233i	$0.920807\pi$
$150$	−85.9248	−	70.2275i	−0.572832	−	0.468183i
$151$	−14.5375	+	82.4463i	−0.0962748	+	0.546002i	0.898074	+	0.439844i	$0.144966\pi$
$151$	−14.5375	+	82.4463i	−0.0962748	+	0.546002i	−0.994349	+	0.106158i	$0.966145\pi$
$152$	44.4893	−	25.6859i	0.292693	−	0.168986i
$153$	−84.2296	+	105.818i	−0.550520	+	0.691623i
$154$	−86.5428	+	149.896i	−0.561966	+	0.973354i
$155$	131.528	−	156.750i	0.848571	−	1.01129i
$156$	−72.7473	+	43.2636i	−0.466329	+	0.277331i
$157$	−12.9271	−	73.3133i	−0.0823383	−	0.466963i	−0.997899	−	0.0647844i	$-0.979364\pi$
$157$	−12.9271	−	73.3133i	−0.0823383	−	0.466963i	0.915561	−	0.402179i	$-0.131747\pi$
$158$	46.6744	+	55.6243i	0.295407	+	0.352053i
$159$	−14.3761	−	75.7905i	−0.0904159	−	0.476670i
$160$	−228.499	+	83.1667i	−1.42812	+	0.519792i
$161$		−	213.765i		−	1.32773i
$162$	189.593	+	96.7624i	1.17033	+	0.597299i
$163$	254.830			1.56337			0.781687	−	0.623670i	$-0.214359\pi$
$163$	254.830			1.56337			0.781687	+	0.623670i	$0.214359\pi$
$164$	16.4178	+	45.1076i	0.100109	+	0.275047i
$165$	149.496	−	28.3568i	0.906038	−	0.171859i
$166$	35.4095	−	29.7121i	0.213310	−	0.178988i
$167$	−156.190	+	27.5405i	−0.935269	+	0.164913i	−0.620457	−	0.784241i	$-0.713053\pi$
$167$	−156.190	+	27.5405i	−0.935269	+	0.164913i	−0.314813	+	0.949154i	$0.601942\pi$
$168$	35.7958	+	60.1902i	0.213070	+	0.358275i
$169$	−57.2419	−	48.0317i	−0.338710	−	0.284211i
$170$	−213.787	−	123.430i	−1.25757	−	0.726060i
$171$	23.8181	−	159.007i	0.139287	−	0.929864i
$172$	−121.784	−	210.937i	−0.708049	−	1.22638i
$173$	−293.553	−	51.7613i	−1.69684	−	0.299198i	−0.760249	−	0.649632i	$-0.774923\pi$
$173$	−293.553	−	51.7613i	−1.69684	−	0.299198i	−0.936587	+	0.350434i	$0.886034\pi$
$174$	75.6926	−	92.6115i	0.435015	−	0.532250i
$175$	−107.376	−	39.0815i	−0.613575	−	0.223323i
$176$	53.2256	−	146.236i	0.302418	−	0.830887i
$177$	63.7177	−	24.1283i	0.359987	−	0.136318i
$178$	−12.9088	+	73.2093i	−0.0725212	+	0.411288i
$179$	25.3997	−	14.6645i	0.141898	−	0.0819248i	−0.427370	−	0.904077i	$-0.640560\pi$
$179$	25.3997	−	14.6645i	0.141898	−	0.0819248i	0.569268	+	0.822152i	$0.307227\pi$
$180$	−51.9235	+	155.010i	−0.288464	+	0.861169i
$181$	−41.7019	+	72.2299i	−0.230397	+	0.399060i	−0.957925	−	0.287018i	$-0.907336\pi$
$181$	−41.7019	+	72.2299i	−0.230397	+	0.399060i	0.727528	+	0.686078i	$0.240669\pi$
$182$	−133.138	+	158.667i	−0.731526	+	0.871799i
$183$	−89.2173	−	49.9837i	−0.487526	−	0.273135i
$184$	13.1496	+	74.5750i	0.0714652	+	0.405299i
$185$	−127.050	−	151.413i	−0.686759	−	0.818448i
$186$	−243.617	−	85.1208i	−1.30977	−	0.457638i
$187$	114.578	−	41.7031i	0.612719	−	0.223011i
$188$			38.2688i			0.203557i
$189$	217.159	+	29.6651i	1.14899	+	0.156958i
$190$	293.463			1.54454
$191$	53.6797	+	147.484i	0.281046	+	0.772166i	0.997239	+	0.0742641i	$0.0236608\pi$
$191$	53.6797	+	147.484i	0.281046	+	0.772166i	−0.716193	+	0.697902i	$0.754117\pi$
$192$	49.9333	+	57.9700i	0.260069	+	0.301927i
$193$	−31.7673	+	26.6559i	−0.164598	+	0.138114i	−0.721366	−	0.692554i	$-0.756485\pi$
$193$	−31.7673	+	26.6559i	−0.164598	+	0.138114i	0.556769	+	0.830668i	$0.312041\pi$
$194$	436.409	−	76.9506i	2.24953	−	0.396653i
$195$	182.072	−	2.35296i	0.933702	−	0.0120665i
$196$	−37.6086	−	31.5573i	−0.191880	−	0.161007i
$197$	−182.437	−	105.330i	−0.926074	−	0.534669i	−0.0405063	−	0.999179i	$-0.512897\pi$
$197$	−182.437	−	105.330i	−0.926074	−	0.534669i	−0.885568	+	0.464510i	$0.846230\pi$
$198$	−100.213	−	163.655i	−0.506124	−	0.826540i
$199$	87.7654	+	152.014i	0.441032	+	0.763890i	0.997766	−	0.0668004i	$-0.0212791\pi$
$199$	87.7654	+	152.014i	0.441032	+	0.763890i	−0.556734	+	0.830691i	$0.687946\pi$
$200$	39.8636	+	7.02902i	0.199318	+	0.0351451i
$201$	23.9965	+	3.91220i	0.119385	+	0.0194637i
$202$	−172.433	−	62.7606i	−0.853631	−	0.310696i
$203$	42.1229	−	115.732i	0.207502	−	0.570107i
$204$	−21.0786	+	129.291i	−0.103326	+	0.633779i
$205$	17.9324	−	101.700i	0.0874751	−	0.496096i
$206$	−158.994	+	91.7952i	−0.771815	+	0.445608i
$207$	208.243	+	113.157i	1.00600	+	0.546652i
$208$	93.1133	−	161.277i	0.447660	−	0.775370i
$209$	−93.1722	+	111.038i	−0.445800	+	0.531284i
$210$	5.16949	+	400.014i	0.0246166	+	1.90483i
$211$	−45.2968	−	256.891i	−0.214677	−	1.21749i	−0.881466	−	0.472247i	$-0.843443\pi$
$211$	−45.2968	−	256.891i	−0.214677	−	1.21749i	0.666789	−	0.745246i	$-0.267668\pi$
$212$	−48.0275	−	57.2369i	−0.226545	−	0.269985i
$213$	−93.8465	+	80.8360i	−0.440594	+	0.379512i
$214$	299.862	−	109.141i	1.40123	−	0.510005i
$215$			523.993i			2.43718i
$216$	−77.5838	+	3.00925i	−0.359184	+	0.0139317i
$217$	−265.720			−1.22452
$218$	−107.525	−	295.422i	−0.493233	−	1.35515i
$219$	−79.9643	+	228.860i	−0.365134	+	1.04502i
$220$	112.899	−	94.7339i	0.513179	−	0.430609i
$221$	143.695	−	25.3373i	0.650204	−	0.114648i
$222$	−121.837	+	217.470i	−0.548816	+	0.979596i
$223$	−298.157	−	250.184i	−1.33703	−	1.12190i	−0.982379	−	0.186901i	$-0.940156\pi$
$223$	−298.157	−	250.184i	−1.33703	−	1.12190i	−0.354650	−	0.934999i	$-0.615400\pi$
$224$	273.464	+	157.885i	1.22082	+	0.704842i
$225$	94.9113	−	83.9138i	0.421828	−	0.372950i
$226$	163.406	+	283.027i	0.723035	+	1.25233i
$227$	−343.139	−	60.5046i	−1.51162	−	0.266540i	−0.644489	−	0.764614i	$-0.722930\pi$
$227$	−343.139	−	60.5046i	−1.51162	−	0.266540i	−0.867135	+	0.498074i	$0.834041\pi$
$228$	−55.1486	−	145.636i	−0.241880	−	0.638753i
$229$	342.540	+	124.675i	1.49581	+	0.544430i	0.954972	−	0.296696i	$-0.0958849\pi$
$229$	342.540	+	124.675i	1.49581	+	0.544430i	0.540838	+	0.841127i	$0.318107\pi$
$230$	−147.952	+	406.495i	−0.643270	+	1.76737i
$231$	−152.996	−	125.045i	−0.662319	−	0.541323i
$232$	−7.57603	+	42.9658i	−0.0326553	+	0.185197i
$233$	164.260	−	94.8353i	0.704976	−	0.407018i	−0.104222	−	0.994554i	$-0.533235\pi$
$233$	164.260	−	94.8353i	0.704976	−	0.407018i	0.809198	+	0.587536i	$0.199902\pi$
$234$	−84.0918	−	213.689i	−0.359367	−	0.913202i
$235$	41.1641	−	71.2983i	0.175166	−	0.303397i
$236$	42.4187	−	50.5527i	0.179740	−	0.214206i
$237$	−71.2475	+	42.3716i	−0.300622	+	0.178783i
$238$	55.6664	+	315.700i	0.233893	+	1.32647i
$239$	−196.756	−	234.485i	−0.823249	−	0.981110i	0.176746	−	0.984256i	$-0.443443\pi$
$239$	−196.756	−	234.485i	−0.823249	−	0.981110i	−0.999995	+	0.00314661i	$0.998998\pi$
$240$	−67.0303	−	353.382i	−0.279293	−	1.47242i
$241$	277.120	−	100.864i	1.14988	−	0.418521i	0.304406	−	0.952542i	$-0.401542\pi$
$241$	277.120	−	100.864i	1.14988	−	0.418521i	0.845471	+	0.534021i	$0.179320\pi$
$242$		−	144.967i		−	0.599039i
$243$	−143.852	+	195.846i	−0.591984	+	0.805949i
$244$	−99.0509			−0.405946
$245$	36.1234	+	99.2481i	0.147442	+	0.405094i
$246$	−127.956	+	24.2710i	−0.520147	+	0.0986627i
$247$	−132.876	+	111.496i	−0.537959	+	0.451401i
$248$	92.7002	−	16.3455i	0.373791	−	0.0659094i
$249$	26.9730	+	45.3549i	0.108325	+	0.182148i
$250$	−137.462	−	115.344i	−0.549847	−	0.461377i
$251$	158.404	+	91.4547i	0.631092	+	0.364361i	0.781175	−	0.624312i	$-0.214621\pi$
$251$	158.404	+	91.4547i	0.631092	+	0.364361i	−0.150083	+	0.988673i	$0.547954\pi$
$252$	197.542	−	77.7376i	0.783898	−	0.308482i
$253$	−106.833	−	185.040i	−0.422265	−	0.731384i
$254$	303.980	+	53.6000i	1.19677	+	0.211023i
$255$	178.344	−	218.208i	0.699388	−	0.855716i
$256$	−314.593	−	114.502i	−1.22888	−	0.447275i
$257$	−91.7859	+	252.180i	−0.357144	+	0.981244i	0.622872	+	0.782324i	$0.285966\pi$
$257$	−91.7859	+	252.180i	−0.357144	+	0.981244i	−0.980016	+	0.198920i	$0.936256\pi$
$258$	618.011	−	234.025i	2.39539	−	0.907074i
$259$	−44.5708	+	252.774i	−0.172088	+	0.975961i
$260$	152.736	−	88.1822i	0.587447	−	0.339162i
$261$	90.4440	+	102.297i	0.346529	+	0.391944i
$262$	−6.19233	+	10.7254i	−0.0236348	+	0.0409368i
$263$	226.246	−	269.629i	0.860250	−	1.02521i	−0.139139	−	0.990273i	$-0.544434\pi$
$263$	226.246	−	269.629i	0.860250	−	1.02521i	0.999390	−	0.0349337i	$-0.0111220\pi$
$264$	61.0668	+	34.2125i	0.231314	+	0.129593i
$265$	27.9123	+	158.299i	0.105330	+	0.597354i
$266$	−244.958	−	291.930i	−0.920896	−	1.09748i
$267$	−80.1160	−	27.9928i	−0.300060	−	0.104842i
$268$	22.1290	−	8.05429i	0.0825708	−	0.0300533i
$269$		−	164.243i		−	0.610570i	−0.952261	−	0.305285i	$-0.901248\pi$
$269$		−	164.243i		−	0.610570i	0.952261	−	0.305285i	$-0.0987518\pi$
$270$	−392.417	−	206.712i	−1.45340	−	0.765601i
$271$	−128.850			−0.475462			−0.237731	−	0.971331i	$-0.576404\pi$
$271$	−128.850			−0.475462			−0.237731	+	0.971331i	$0.576404\pi$
$272$	−98.5786	−	270.843i	−0.362421	−	0.995745i
$273$	−154.319	−	179.157i	−0.565272	−	0.656252i
$274$	−444.466	+	372.951i	−1.62214	+	1.36113i
$275$	−112.479	+	19.8330i	−0.409013	+	0.0721200i
$276$	229.534	−	2.96633i	0.831644	−	0.0107476i
$277$	115.074	+	96.5583i	0.415428	+	0.348586i	0.826421	−	0.563053i	$-0.190373\pi$
$277$	115.074	+	96.5583i	0.415428	+	0.348586i	−0.410992	+	0.911639i	$0.634818\pi$
$278$	−81.3953	−	46.9936i	−0.292789	−	0.169042i
$279$	140.659	−	258.855i	0.504155	−	0.927797i
$280$	−72.9609	−	126.372i	−0.260575	−	0.451328i
$281$	453.995	+	80.0516i	1.61564	+	0.284881i	0.907140	−	0.420828i	$-0.138261\pi$
$281$	453.995	+	80.0516i	1.61564	+	0.284881i	0.708501	+	0.705710i	$0.249372\pi$
$282$	−102.476	−	16.7068i	−0.363389	−	0.0592441i
$283$	64.7049	+	23.5506i	0.228639	+	0.0832178i	0.453799	−	0.891104i	$-0.350068\pi$
$283$	64.7049	+	23.5506i	0.228639	+	0.0832178i	−0.225160	+	0.974322i	$0.572291\pi$
$284$	−41.0317	+	112.734i	−0.144478	+	0.396949i
$285$	−53.9072	+	330.654i	−0.189148	+	1.16019i
$286$	−35.9503	+	203.884i	−0.125700	+	0.712882i
$287$	−116.137	+	67.0517i	−0.404658	+	0.233630i
$288$	−298.565	+	182.823i	−1.03668	+	0.634802i
$289$	−31.5856	+	54.7078i	−0.109293	+	0.189300i
$290$	−160.201	+	190.921i	−0.552419	+	0.658347i
$291$	6.53725	+	505.851i	0.0224648	+	1.73832i
$292$	40.7741	+	231.241i	0.139637	+	0.791922i
$293$	328.314	+	391.270i	1.12053	+	1.33539i	0.935772	+	0.352607i	$0.114705\pi$
$293$	328.314	+	391.270i	1.12053	+	1.33539i	0.184755	+	0.982785i	$0.440851\pi$
$294$	100.922	−	86.9309i	0.343273	−	0.295683i
$295$	−133.407	+	48.5563i	−0.452228	+	0.164598i
$296$		−	90.9255i		−	0.307181i
$297$	202.804	−	82.8503i	0.682841	−	0.278957i
$298$	−440.789			−1.47916
$299$	−87.4501	−	240.267i	−0.292475	−	0.803569i
$300$	40.4744	−	115.839i	0.134915	−	0.386128i
$301$	521.256	−	437.386i	1.73175	−	1.45311i
$302$	−216.658	+	38.2027i	−0.717412	+	0.126499i
$303$	102.389	−	182.757i	0.337919	−	0.603160i
$304$	262.474	+	220.242i	0.863402	+	0.724480i
$305$	184.541	+	106.545i	0.605053	+	0.349327i
$306$	−337.011	−	112.888i	−1.10134	−	0.368915i
$307$	−26.3017	−	45.5559i	−0.0856734	−	0.148391i	0.820005	−	0.572357i	$-0.193971\pi$
$307$	−26.3017	−	45.5559i	−0.0856734	−	0.148391i	−0.905678	+	0.423966i	$0.860637\pi$
$308$	−188.478	−	33.2338i	−0.611942	−	0.107902i
$309$	−74.2224	−	196.006i	−0.240202	−	0.634323i
$310$	505.292	+	183.911i	1.62997	+	0.593262i
$311$	−121.357	+	333.427i	−0.390217	+	1.07211i	0.576686	+	0.816966i	$0.304346\pi$
$311$	−121.357	+	333.427i	−0.390217	+	1.07211i	−0.966903	+	0.255146i	$0.917877\pi$
$312$	64.8571	+	53.0086i	0.207875	+	0.169899i
$313$	29.2161	−	165.693i	0.0933421	−	0.529369i	−0.901901	−	0.431943i	$-0.857828\pi$
$313$	29.2161	−	165.693i	0.0933421	−	0.529369i	0.995243	−	0.0974258i	$-0.0310609\pi$
$314$	169.421	−	97.8150i	0.539556	−	0.311513i
$315$	−451.658	−	67.6554i	−1.43384	−	0.214779i
$316$	−40.1448	+	69.5329i	−0.127041	+	0.220041i
$317$	327.814	−	390.674i	1.03411	−	1.23241i	0.0619572	−	0.998079i	$-0.480266\pi$
$317$	327.814	−	390.674i	1.03411	−	1.23241i	0.972157	−	0.234330i	$-0.0752898\pi$
$318$	174.235	−	103.620i	0.547910	−	0.325848i
$319$	−21.3764	−	121.232i	−0.0670107	−	0.380037i
$320$	−102.476	−	122.127i	−0.320239	−	0.381646i
$321$	67.8898	+	357.913i	0.211495	+	1.11499i
$322$	527.870	−	192.129i	1.63935	−	0.596674i
$323$			268.461i			0.831149i
$324$	−28.8400	+	233.589i	−0.0890123	+	0.720955i
$325$	−136.676			−0.420541
$326$	229.038	+	629.276i	0.702569	+	1.93029i
$327$	352.613	−	66.8845i	1.07833	−	0.204540i
$328$	36.3914	−	30.5360i	0.110949	−	0.0930976i
$329$	−105.286	+	18.5648i	−0.320019	+	0.0564280i
$330$	204.389	+	343.678i	0.619361	+	1.04145i
$331$	−259.951	−	218.125i	−0.785350	−	0.658987i	0.159240	−	0.987240i	$-0.449096\pi$
$331$	−259.951	−	218.125i	−0.785350	−	0.658987i	−0.944590	+	0.328253i	$0.893540\pi$
$332$	44.2634	+	25.5555i	0.133324	+	0.0769744i
$333$	−222.650	−	177.226i	−0.668619	−	0.532209i
$334$	−208.390	−	360.941i	−0.623921	−	1.08066i
$335$	−49.8920	−	8.79731i	−0.148931	−	0.0262606i
$336$	−295.585	+	361.654i	−0.879716	+	1.07635i
$337$	64.1227	+	23.3388i	0.190275	+	0.0692545i	0.435400	−	0.900237i	$-0.356607\pi$
$337$	64.1227	+	23.3388i	0.190275	+	0.0692545i	−0.245125	+	0.969491i	$0.578829\pi$
$338$	67.1609	−	184.523i	0.198701	−	0.545926i
$339$	−348.913	+	132.124i	−1.02924	+	0.389748i
$340$	47.3991	−	268.814i	0.139409	−	0.790629i
$341$	−230.013	+	132.798i	−0.674526	+	0.389438i
$342$	414.057	−	84.0966i	1.21069	−	0.245896i
$343$	−130.305	+	225.695i	−0.379897	+	0.658002i
$344$	−154.942	+	184.653i	−0.450414	+	0.536782i
$345$	−430.833	−	241.373i	−1.24879	−	0.699632i
$346$	−136.022	−	771.419i	−0.393127	−	2.22954i
$347$	−111.265	−	132.600i	−0.320648	−	0.382134i	0.581510	−	0.813539i	$-0.302462\pi$
$347$	−111.265	−	132.600i	−0.320648	−	0.382134i	−0.902158	+	0.431406i	$0.858018\pi$
$348$	124.853	+	43.6241i	0.358773	+	0.125357i
$349$	−431.866	+	157.186i	−1.23744	+	0.450390i	−0.876138	−	0.482060i	$-0.839889\pi$
$349$	−431.866	+	157.186i	−1.23744	+	0.450390i	−0.361299	+	0.932450i	$0.617667\pi$
$350$		−	300.278i		−	0.857939i
$351$	256.218	−	55.4956i	0.729965	−	0.158107i
$352$	315.623			0.896655
$353$	−137.578	−	377.991i	−0.389738	−	1.07080i	−0.967119	−	0.254322i	$-0.918148\pi$
$353$	−137.578	−	377.991i	−0.389738	−	1.07080i	0.577381	−	0.816475i	$-0.304075\pi$
$354$	116.851	+	135.658i	0.330087	+	0.383214i
$355$	197.709	−	165.897i	0.556926	−	0.467316i
$356$	−80.9497	+	14.2736i	−0.227387	+	0.0400944i
$357$	−365.935	+	4.72908i	−1.02503	+	0.0132467i
$358$	59.0414	+	49.5416i	0.164920	+	0.138384i
$359$	−197.249	−	113.882i	−0.549439	−	0.317219i	0.199457	−	0.979907i	$-0.436082\pi$
$359$	−197.249	−	113.882i	−0.549439	−	0.317219i	−0.748896	+	0.662688i	$0.769416\pi$
$360$	161.729	−	4.18084i	0.449248	−	0.0116134i
$361$	20.9294	+	36.2507i	0.0579761	+	0.100418i
$362$	−215.845	−	38.0593i	−0.596257	−	0.105136i
$363$	163.339	+	26.6296i	0.449971	+	0.0733597i
$364$	−215.213	−	78.3312i	−0.591245	−	0.215195i
$365$	172.770	−	474.683i	0.473343	−	1.30050i
$366$	43.2422	−	265.237i	0.118148	−	0.724692i
$367$	−40.8884	+	231.890i	−0.111413	+	0.631852i	0.877052	+	0.480396i	$0.159507\pi$
$367$	−40.8884	+	231.890i	−0.111413	+	0.631852i	−0.988464	+	0.151456i	$0.951604\pi$
$368$	−437.401	+	252.534i	−1.18859	+	0.686233i
$369$	−3.84223	−	148.631i	−0.0104126	−	0.402793i
$370$	259.707	−	449.825i	0.701910	−	1.21574i
$371$	134.173	−	159.901i	0.361653	−	0.431001i
$372$	−3.68728	−	285.321i	−0.00991204	−	0.766991i
$373$	113.349	+	642.835i	0.303885	+	1.72342i	0.628707	+	0.777642i	$0.283585\pi$
$373$	113.349	+	642.835i	0.303885	+	1.72342i	−0.324822	+	0.945775i	$0.605304\pi$
$374$	205.963	+	245.457i	0.550703	+	0.656302i
$375$	155.213	−	133.695i	0.413901	−	0.356519i
$376$	35.5886	−	12.9532i	0.0946506	−	0.0344500i
$377$		−	147.312i		−	0.390748i
$378$	121.924	+	562.914i	0.322552	+	1.48919i
$379$	625.053			1.64922			0.824608	−	0.565705i	$-0.191396\pi$
$379$	625.053			1.64922			0.824608	+	0.565705i	$0.191396\pi$
$380$	110.982	+	304.921i	0.292059	+	0.802425i
$381$	−116.232	+	332.659i	−0.305071	+	0.873119i
$382$	−315.949	+	265.113i	−0.827091	+	0.694012i
$383$	104.921	−	18.5004i	0.273945	−	0.0483039i	−0.0349879	−	0.999388i	$-0.511139\pi$
$383$	104.921	−	18.5004i	0.273945	−	0.0483039i	0.308933	+	0.951084i	$0.400028\pi$
$384$	129.880	−	231.827i	0.338230	−	0.603717i
$385$	315.404	+	264.656i	0.819232	+	0.687417i
$386$	−94.3760	−	54.4880i	−0.244497	−	0.141161i
$387$	150.159	+	739.321i	0.388007	+	1.91039i
$388$	244.997	+	424.347i	0.631436	+	1.09368i
$389$	−584.613	−	103.083i	−1.50286	−	0.264995i	−0.639190	−	0.769049i	$-0.720730\pi$
$389$	−584.613	−	103.083i	−1.50286	−	0.264995i	−0.863672	+	0.504054i	$0.831841\pi$
$390$	169.454	+	447.492i	0.434497	+	1.14742i
$391$	−371.864	−	135.347i	−0.951058	−	0.346157i
$392$	−16.6175	+	45.6561i	−0.0423915	+	0.116470i
$393$	−10.9472	−	8.94729i	−0.0278555	−	0.0227666i
$394$	96.1293	−	545.177i	0.243983	−	1.38370i
$395$	149.587	−	86.3642i	0.378702	−	0.218643i
$396$	132.146	−	166.017i	0.333703	−	0.419234i
$397$	−187.410	+	324.603i	−0.472064	+	0.817640i	−0.999489	−	0.0319623i	$-0.989824\pi$
$397$	−187.410	+	324.603i	−0.472064	+	0.817640i	0.527425	+	0.849602i	$0.323158\pi$
$398$	−296.500	+	353.355i	−0.744976	+	0.887828i
$399$	373.924	−	222.377i	0.937153	−	0.557335i
$400$	46.8816	+	265.879i	0.117204	+	0.664697i
$401$	−176.385	−	210.207i	−0.439862	−	0.524207i	0.499879	−	0.866095i	$-0.333378\pi$
$401$	−176.385	−	210.207i	−0.439862	−	0.524207i	−0.939741	+	0.341889i	$0.888933\pi$
$402$	11.9069	+	62.7729i	0.0296192	+	0.156152i
$403$	−298.663	+	108.704i	−0.741099	+	0.269738i
$404$		−	202.901i		−	0.502231i
$405$	304.994	−	404.177i	0.753071	−	0.997968i
$406$	323.646			0.797158
$407$	87.7467	+	241.082i	0.215594	+	0.592339i
$408$	127.371	−	24.1600i	0.312183	−	0.0592156i
$409$	−422.454	+	354.481i	−1.03289	+	0.866701i	−0.991193	−	0.132429i	$-0.957722\pi$
$409$	−422.454	+	354.481i	−1.03289	+	0.866701i	−0.0417017	+	0.999130i	$0.513278\pi$
$410$	267.254	−	47.1241i	0.651839	−	0.114937i
$411$	−338.570	−	569.302i	−0.823772	−	1.38516i
$412$	−155.508	−	130.487i	−0.377447	−	0.316715i
$413$	159.660	+	92.1798i	0.386586	+	0.223196i
$414$	−92.2633	+	615.937i	−0.222858	+	1.48777i
$415$	−54.9779	−	95.2245i	−0.132477	−	0.229457i
$416$	371.957	+	65.5861i	0.894128	+	0.157659i
$417$	67.9010	−	83.0783i	0.162832	−	0.199228i
$418$	−357.939	−	130.279i	−0.856314	−	0.311673i
$419$	−29.9567	+	82.3055i	−0.0714958	+	0.196433i	−0.970294	−	0.241930i	$-0.922219\pi$
$419$	−29.9567	+	82.3055i	−0.0714958	+	0.196433i	0.898798	+	0.438363i	$0.144442\pi$
$420$	−413.678	+	156.649i	−0.984948	+	0.372975i
$421$	51.4449	−	291.759i	0.122197	−	0.693013i	−0.860736	−	0.509051i	$-0.829996\pi$
$421$	51.4449	−	291.759i	0.122197	−	0.693013i	0.982933	−	0.183962i	$-0.0588924\pi$
$422$	593.653	−	342.746i	1.40676	−	0.812194i
$423$	37.6482	−	112.394i	0.0890029	−	0.265706i
$424$	−36.9720	+	64.0374i	−0.0871981	+	0.151032i
$425$	−135.972	+	162.045i	−0.319933	+	0.381281i
$426$	−283.964	−	159.090i	−0.666581	−	0.373450i
$427$	−48.0512	−	272.512i	−0.112532	−	0.638201i
$428$	226.805	+	270.296i	0.529918	+	0.631532i
$429$	−223.119	−	77.9586i	−0.520091	−	0.181722i
$430$	−1293.95	+	470.957i	−3.00917	+	1.09525i
$431$			586.175i			1.36003i	0.733196	+	0.680017i	$0.238028\pi$
$431$			586.175i			1.36003i	−0.733196	+	0.680017i	$0.761972\pi$
$432$	−195.843	−	479.391i	−0.453340	−	1.10970i
$433$	415.367			0.959277			0.479639	−	0.877466i	$-0.340768\pi$
$433$	415.367			0.959277			0.479639	+	0.877466i	$0.340768\pi$
$434$	−238.825	−	656.167i	−0.550288	−	1.51190i
$435$	−185.688	−	215.575i	−0.426870	−	0.495575i
$436$	266.293	−	223.446i	0.610764	−	0.512492i
$437$	463.288	−	81.6902i	1.06016	−	0.186934i
$438$	−637.015	+	8.23232i	−1.45437	+	0.0187953i
$439$	256.133	+	214.921i	0.583447	+	0.489570i	0.886077	−	0.463538i	$-0.153420\pi$
$439$	256.133	+	214.921i	0.583447	+	0.489570i	−0.302630	+	0.953108i	$0.597865\pi$
$440$	−126.313	−	72.9270i	−0.287076	−	0.165743i
$441$	79.4090	+	129.681i	0.180066	+	0.294062i
$442$	191.719	+	332.067i	0.433753	+	0.751282i
$443$	444.780	+	78.4268i	1.00402	+	0.177036i	0.651402	−	0.758732i	$-0.274181\pi$
$443$	444.780	+	78.4268i	1.00402	+	0.177036i	0.352616	+	0.935768i	$0.385292\pi$
$444$	−272.038	−	44.3510i	−0.612699	−	0.0998896i
$445$	166.170	+	60.4810i	0.373416	+	0.135912i
$446$	349.823	−	961.129i	0.784355	−	2.15500i
$447$	80.9702	−	496.651i	0.181141	−	1.11108i
$448$	−35.9500	+	203.883i	−0.0802455	+	0.455095i
$449$	−165.422	+	95.5067i	−0.368424	+	0.212710i	−0.672770	−	0.739852i	$-0.734896\pi$
$449$	−165.422	+	95.5067i	−0.368424	+	0.212710i	0.304346	+	0.952562i	$0.401562\pi$
$450$	292.521	+	158.953i	0.650047	+	0.353229i
$451$	−67.0206	+	116.083i	−0.148604	+	0.257390i
$452$	−232.281	+	276.822i	−0.513897	+	0.612438i
$453$	−3.24547	−	251.133i	−0.00716438	−	0.554378i
$454$	−158.998	−	901.725i	−0.350217	−	1.98618i
$455$	316.704	+	377.434i	0.696054	+	0.829525i
$456$	−116.769	+	100.581i	−0.256073	+	0.220572i
$457$	362.489	−	131.935i	0.793192	−	0.288698i	0.0865297	−	0.996249i	$-0.472422\pi$
$457$	362.489	−	131.935i	0.793192	−	0.288698i	0.706662	+	0.707551i	$0.250200\pi$
$458$			957.923i			2.09153i
$459$	189.101	−	358.985i	0.411985	−	0.782102i
$460$	−478.320			−1.03983
$461$	148.113	+	406.937i	0.321286	+	0.882727i	0.990234	+	0.139417i	$0.0445229\pi$
$461$	148.113	+	406.937i	0.321286	+	0.882727i	−0.668947	+	0.743310i	$0.733255\pi$
$462$	171.276	−	490.196i	0.370727	−	1.06103i
$463$	423.513	−	355.369i	0.914714	−	0.767536i	−0.0582960	−	0.998299i	$-0.518567\pi$
$463$	423.513	−	355.369i	0.914714	−	0.767536i	0.973010	+	0.230763i	$0.0741223\pi$
$464$	−286.570	+	50.5299i	−0.617607	+	0.108901i
$465$	−300.038	+	535.545i	−0.645242	+	1.15171i
$466$	381.820	+	320.385i	0.819355	+	0.687521i
$467$	−186.467	−	107.657i	−0.399286	−	0.230528i	0.286890	−	0.957964i	$-0.407379\pi$
$467$	−186.467	−	107.657i	−0.399286	−	0.230528i	−0.686176	+	0.727436i	$0.740712\pi$
$468$	190.231	−	168.189i	0.406476	−	0.359377i
$469$	32.8943	+	56.9747i	0.0701372	+	0.121481i
$470$	213.061	+	37.5684i	0.453322	+	0.0799329i
$471$	79.0898	+	208.860i	0.167919	+	0.443439i
$472$	−61.3700	−	22.3369i	−0.130021	−	0.0473239i
$473$	232.620	−	639.119i	0.491798	−	1.35120i
$474$	−168.668	−	137.855i	−0.355841	−	0.290833i
$475$	43.6669	−	247.647i	0.0919304	−	0.521363i
$476$	−306.975	+	177.232i	−0.644905	+	0.372336i
$477$	84.7457	+	215.351i	0.177664	+	0.451469i
$478$	402.194	−	696.621i	0.841411	−	1.45737i
$479$	−145.585	+	173.501i	−0.303935	+	0.362216i	−0.896295	−	0.443457i	$-0.853752\pi$
$479$	−145.585	+	173.501i	−0.303935	+	0.362216i	0.592360	+	0.805673i	$0.298196\pi$
$480$	626.991	−	372.878i	1.30623	−	0.776829i
$481$	53.3117	+	302.346i	0.110835	+	0.628577i
$482$	498.144	+	593.664i	1.03349	+	1.23167i
$483$	119.512	+	630.061i	0.247436	+	1.30447i
$484$	150.628	−	54.8241i	0.311215	−	0.113273i
$485$		−	1054.13i		−	2.17347i
$486$	−612.912	−	179.204i	−1.26114	−	0.368733i
$487$	−443.130			−0.909919			−0.454959	−	0.890512i	$-0.650346\pi$
$487$	−443.130			−0.909919			−0.454959	+	0.890512i	$0.650346\pi$
$488$	33.5267	+	92.1138i	0.0687023	+	0.188758i
$489$	−751.098	+	142.470i	−1.53599	+	0.291350i
$490$	−212.615	+	178.406i	−0.433909	+	0.364093i
$491$	−657.316	+	115.902i	−1.33873	+	0.236054i	−0.796735	−	0.604329i	$-0.793441\pi$
$491$	−657.316	+	115.902i	−1.33873	+	0.236054i	−0.541993	+	0.840383i	$0.682330\pi$
$492$	−73.6094	−	123.773i	−0.149613	−	0.251572i
$493$	−174.655	−	146.553i	−0.354270	−	0.297268i
$494$	−394.754	−	227.912i	−0.799098	−	0.461360i
$495$	−424.778	+	167.160i	−0.858138	+	0.337698i
$496$	313.911	+	543.710i	0.632885	+	1.09619i
$497$	−330.061	−	58.1987i	−0.664108	−	0.117100i
$498$	−87.7560	+	107.371i	−0.176217	+	0.215605i
$499$	54.0177	+	19.6608i	0.108252	+	0.0394005i	0.395578	−	0.918432i	$-0.370544\pi$
$499$	54.0177	+	19.6608i	0.108252	+	0.0394005i	−0.287326	+	0.957833i	$0.592766\pi$
$500$	67.8624	−	186.450i	0.135725	−	0.372901i
$501$	444.964	−	168.497i	0.888152	−	0.336321i
$502$	−83.4662	+	473.360i	−0.166267	+	0.942949i
$503$	423.202	−	244.336i	0.841356	−	0.485757i	−0.0163686	−	0.999866i	$-0.505211\pi$
$503$	423.202	−	244.336i	0.841356	−	0.485757i	0.857725	+	0.514109i	$0.171877\pi$
$504$	−139.157	−	157.395i	−0.276105	−	0.312291i
$505$	−218.252	+	378.024i	−0.432182	+	0.748562i
$506$	360.917	−	430.124i	0.713275	−	0.850048i
$507$	195.571	+	109.568i	0.385741	+	0.216110i
$508$	59.2671	+	336.120i	0.116667	+	0.661654i
$509$	182.714	+	217.750i	0.358966	+	0.427799i	0.915058	−	0.403322i	$-0.132144\pi$
$509$	182.714	+	217.750i	0.358966	+	0.427799i	−0.556093	+	0.831120i	$0.687700\pi$
$510$	699.133	+	244.280i	1.37085	+	0.478980i
$511$	−616.418	+	224.358i	−1.20630	+	0.439056i
$512$		−	525.459i		−	1.02629i
$513$	18.6946	+	481.980i	0.0364417	+	0.939532i
$514$	−705.227			−1.37204
$515$	149.367	+	410.382i	0.290033	+	0.796859i
$516$	476.883	+	553.638i	0.924192	+	1.07294i
$517$	−81.8602	+	68.6889i	−0.158337	+	0.132860i
$518$	−664.258	+	117.127i	−1.28235	+	0.226113i
$519$	894.169	−	11.5556i	1.72287	−	0.0222651i
$520$	−133.704	−	112.191i	−0.257124	−	0.215752i
$521$	35.1966	+	20.3207i	0.0675558	+	0.0390033i	0.533397	−	0.845865i	$-0.320915\pi$
$521$	35.1966	+	20.3207i	0.0675558	+	0.0390033i	−0.465842	+	0.884868i	$0.654248\pi$
$522$	−171.323	+	315.285i	−0.328204	+	0.603995i
$523$	−174.951	−	303.024i	−0.334514	−	0.579395i	0.648877	−	0.760893i	$-0.275239\pi$
$523$	−174.951	−	303.024i	−0.334514	−	0.579395i	−0.983391	+	0.181498i	$0.941905\pi$
$524$	−13.4860	−	2.37795i	−0.0257367	−	0.00453808i
$525$	338.333	+	55.1592i	0.644444	+	0.105065i
$526$	869.167	+	316.351i	1.65241	+	0.601428i
$527$	−168.243	+	462.243i	−0.319246	+	0.877122i
$528$	−75.1220	+	460.780i	−0.142276	+	0.872689i
$529$	−28.5567	+	161.953i	−0.0539825	+	0.306150i
$530$	−365.815	+	211.203i	−0.690216	+	0.398497i
$531$	−174.315	+	106.740i	−0.328276	+	0.201017i
$532$	210.690	−	364.926i	0.396034	−	0.685951i
$533$	−103.105	+	122.876i	−0.193442	+	0.230536i
$534$	−2.88186	−	222.997i	−0.00539673	−	0.417598i
$535$	−131.813	−	747.550i	−0.246380	−	1.39729i
$536$	−14.9804	−	17.8530i	−0.0279485	−	0.0333078i
$537$	−66.6656	+	57.4233i	−0.124145	+	0.106934i
$538$	405.582	−	147.620i	0.753869	−	0.274386i
$539$		−	137.090i		−	0.254342i
$540$	66.3786	−	485.914i	0.122923	−	0.899841i
$541$	145.531			0.269003			0.134501	−	0.990913i	$-0.457057\pi$
$541$	145.531			0.269003			0.134501	+	0.990913i	$0.457057\pi$
$542$	−115.809	−	318.182i	−0.213669	−	0.587051i
$543$	82.5320	−	236.208i	0.151993	−	0.435006i
$544$	447.800	−	375.749i	0.823163	−	0.690715i
$545$	−736.481	+	129.861i	−1.35134	+	0.238278i
$546$	303.709	−	542.098i	0.556243	−	0.992854i
$547$	372.320	+	312.413i	0.680657	+	0.571139i	0.916198	−	0.400725i	$-0.131242\pi$
$547$	372.320	+	312.413i	0.680657	+	0.571139i	−0.235541	+	0.971864i	$0.575686\pi$
$548$	−555.602	−	320.777i	−1.01387	−	0.585359i
$549$	290.908	+	97.4448i	0.529887	+	0.177495i
$550$	−150.070	−	259.928i	−0.272854	−	0.472597i
$551$	266.919	+	47.0651i	0.484427	+	0.0854176i
$552$	−80.4510	−	212.454i	−0.145745	−	0.384881i
$553$	−210.776	−	76.7162i	−0.381150	−	0.138727i
$554$	−135.014	+	370.947i	−0.243707	+	0.669580i
$555$	459.126	+	375.250i	0.827254	+	0.676126i
$556$	18.0463	−	102.346i	0.0324574	−	0.184075i
$557$	2.82805	−	1.63278i	0.00507730	−	0.00293138i	−0.497459	−	0.867487i	$-0.665734\pi$
$557$	2.82805	−	1.63278i	0.00507730	−	0.00293138i	0.502537	+	0.864556i	$0.332400\pi$
$558$	765.638	+	114.687i	1.37211	+	0.205533i
$559$	406.948	−	704.855i	0.727993	−	1.26092i
$560$	625.597	−	745.558i	1.11714	−	1.33135i
$561$	−314.398	+	186.976i	−0.560425	+	0.333291i
$562$	210.365	+	1193.04i	0.374316	+	2.12285i
$563$	−427.292	−	509.227i	−0.758956	−	0.904489i	0.238825	−	0.971063i	$-0.423238\pi$
$563$	−427.292	−	509.227i	−0.758956	−	0.904489i	−0.997781	+	0.0665739i	$0.978793\pi$
$564$	−21.3953	−	112.795i	−0.0379349	−	0.199991i
$565$	730.527	−	265.890i	1.29297	−	0.470602i
$566$			180.949i			0.319697i
$567$	−656.649	+	33.9726i	−1.15811	+	0.0599164i
$568$	118.727			0.209026
$569$	25.9713	+	71.3556i	0.0456438	+	0.125405i	0.960420	−	0.278555i	$-0.0898555\pi$
$569$	25.9713	+	71.3556i	0.0456438	+	0.125405i	−0.914776	+	0.403960i	$0.867633\pi$
$570$	−864.965	+	164.069i	−1.51748	+	0.287840i
$571$	−225.287	+	189.038i	−0.394548	+	0.331065i	−0.818382	−	0.574675i	$-0.805129\pi$
$571$	−225.287	+	189.038i	−0.394548	+	0.331065i	0.423834	+	0.905740i	$0.360684\pi$
$572$	−225.441	+	39.7513i	−0.394128	+	0.0694953i
$573$	−240.673	−	404.689i	−0.420023	−	0.706264i
$574$	−269.959	−	226.523i	−0.470312	−	0.394639i
$575$	321.018	+	185.340i	0.558292	+	0.322330i
$576$	−179.585	−	142.947i	−0.311780	−	0.248172i
$577$	−529.296	−	916.768i	−0.917325	−	1.58885i	−0.803461	−	0.595357i	$-0.797011\pi$
$577$	−529.296	−	916.768i	−0.917325	−	1.58885i	−0.113864	−	0.993496i	$-0.536323\pi$
$578$	−163.484	−	28.8266i	−0.282844	−	0.0498730i
$579$	78.7297	−	96.3274i	0.135975	−	0.166369i
$580$	−258.961	−	94.2539i	−0.446484	−	0.162507i
$581$	−48.8362	+	134.176i	−0.0840554	+	0.230940i
$582$	−1243.27	+	470.794i	−2.13620	+	0.808925i
$583$	36.2299	−	205.470i	0.0621438	−	0.352435i
$584$	201.245	−	116.189i	0.344597	−	0.198953i
$585$	−535.331	+	108.728i	−0.915096	+	0.185859i
$586$	−671.115	+	1162.40i	−1.14525	+	1.98363i
$587$	89.2844	−	106.405i	0.152103	−	0.181269i	−0.684612	−	0.728907i	$-0.740029\pi$
$587$	89.2844	−	106.405i	0.152103	−	0.181269i	0.836715	+	0.547638i	$0.184473\pi$
$588$	128.492	+	71.9873i	0.218524	+	0.122427i
$589$	−101.545	−	575.888i	−0.172402	−	0.977738i
$590$	−239.809	−	285.793i	−0.406456	−	0.484396i
$591$	596.609	+	208.457i	1.00949	+	0.352720i
$592$	569.874	−	207.417i	0.962625	−	0.350367i
$593$			145.309i			0.245040i	0.992466	+	0.122520i	$0.0390975\pi$
$593$			145.309i			0.245040i	−0.992466	+	0.122520i	$0.960902\pi$
$594$	386.867	+	426.337i	0.651291	+	0.717740i
$595$	762.563			1.28162
$596$	−166.698	−	458.000i	−0.279695	−	0.768457i
$597$	−343.672	−	398.986i	−0.575664	−	0.668318i
$598$	514.715	−	431.897i	0.860728	−	0.722236i
$599$	−22.6235	+	3.98914i	−0.0377688	+	0.00665966i	−0.192501	−	0.981297i	$-0.561660\pi$
$599$	−22.6235	+	3.98914i	−0.0377688	+	0.00665966i	0.154732	+	0.987957i	$0.450549\pi$
$600$	−121.425	+	1.56921i	−0.202376	+	0.00261536i
$601$	−710.406	−	596.102i	−1.18204	−	0.991849i	−0.999963	−	0.00856516i	$-0.997274\pi$
$601$	−710.406	−	596.102i	−1.18204	−	0.991849i	−0.182077	−	0.983284i	$-0.558282\pi$
$602$	1548.58	+	894.071i	2.57238	+	1.48517i
$603$	−72.9155	+	1.88493i	−0.120921	+	0.00312592i
$604$	−121.631	−	210.670i	−0.201375	−	0.348792i
$605$	−339.605	−	59.8816i	−0.561331	−	0.0989779i
$606$	543.326	+	88.5797i	0.896578	+	0.146171i
$607$	−492.373	−	179.209i	−0.811158	−	0.295237i	−0.0970557	−	0.995279i	$-0.530943\pi$
$607$	−492.373	−	179.209i	−0.811158	−	0.295237i	−0.714102	+	0.700042i	$0.753165\pi$
$608$	−237.675	+	653.007i	−0.390913	+	1.07403i
$609$	−59.4517	+	364.663i	−0.0976219	+	0.598789i
$610$	−97.2382	+	551.465i	−0.159407	+	0.904041i
$611$	−110.745	+	63.9384i	−0.181251	+	0.104646i
$612$	−10.1558	−	392.862i	−0.0165945	−	0.641932i
$613$	−35.0848	+	60.7687i	−0.0572346	+	0.0991333i	−0.893223	−	0.449614i	$-0.851562\pi$
$613$	−35.0848	+	60.7687i	−0.0572346	+	0.0991333i	0.835988	+	0.548747i	$0.184895\pi$
$614$	88.8559	−	105.894i	0.144716	−	0.172466i
$615$	4.00337	+	309.780i	0.00650954	+	0.503707i
$616$	32.8897	+	186.527i	0.0533924	+	0.302804i
$617$	427.172	+	509.083i	0.692337	+	0.825095i	0.991636	−	0.129064i	$-0.0411974\pi$
$617$	427.172	+	509.083i	0.692337	+	0.825095i	−0.299299	+	0.954159i	$0.596753\pi$
$618$	417.305	−	359.451i	0.675251	−	0.581637i
$619$	912.210	−	332.017i	1.47368	−	0.536377i	0.524585	−	0.851358i	$-0.324220\pi$
$619$	912.210	−	332.017i	1.47368	−	0.536377i	0.949098	+	0.314981i	$0.101998\pi$
$620$			594.574i			0.958990i
$621$	−677.048	−	217.100i	−1.09025	−	0.349597i
$622$	−932.436			−1.49909
$623$	−78.5400	−	215.787i	−0.126067	−	0.346367i
$624$	−184.280	+	527.413i	−0.295320	+	0.845213i
$625$	−596.569	+	500.581i	−0.954510	+	0.800929i
$626$	435.419	−	76.7761i	0.695558	−	0.122646i
$627$	212.541	−	379.370i	0.338981	−	0.605056i
$628$	165.706	+	139.044i	0.263863	+	0.221408i
$629$	411.502	+	237.581i	0.654216	+	0.377712i
$630$	−238.876	−	1176.13i	−0.379169	−	1.86687i
$631$	94.6588	+	163.954i	0.150014	+	0.259832i	0.931232	−	0.364426i	$-0.118735\pi$
$631$	94.6588	+	163.954i	0.150014	+	0.259832i	−0.781218	+	0.624258i	$0.785401\pi$
$632$	78.2513	+	13.7978i	0.123815	+	0.0218320i
$633$	277.132	+	731.848i	0.437808	+	1.15616i
$634$	1259.36	+	458.370i	1.98637	+	0.722981i
$635$	251.130	−	689.974i	0.395480	−	1.08657i
$636$	173.558	+	141.852i	0.272890	+	0.223037i
$637$	28.4872	−	161.559i	0.0447209	−	0.253625i
$638$	280.156	−	161.748i	0.439116	−	0.253524i
$639$	231.414	−	290.727i	0.362150	−	0.454972i
$640$	−276.852	+	479.522i	−0.432581	+	0.749253i
$641$	−445.262	+	530.643i	−0.694637	+	0.827836i	−0.991908	−	0.126957i	$-0.959479\pi$
$641$	−445.262	+	530.643i	−0.694637	+	0.827836i	0.297271	+	0.954793i	$0.403923\pi$
$642$	−822.810	+	489.334i	−1.28163	+	0.762202i
$643$	184.867	+	1048.43i	0.287506	+	1.63053i	0.696193	+	0.717854i	$0.254876\pi$
$643$	184.867	+	1048.43i	0.287506	+	1.63053i	−0.408687	+	0.912675i	$0.634013\pi$
$644$	399.262	+	475.822i	0.619972	+	0.738854i
$645$	−292.953	−	1544.44i	−0.454191	−	2.39448i
$646$	−662.936	+	241.289i	−1.02622	+	0.373512i
$647$			352.755i			0.545217i	0.962125	+	0.272608i	$0.0878863\pi$
$647$			352.755i			0.545217i	−0.962125	+	0.272608i	$0.912114\pi$
$648$	226.992	−	52.2451i	0.350296	−	0.0806251i
$649$	184.274			0.283935
$650$	−122.842	−	337.506i	−0.188988	−	0.519240i
$651$	783.195	−	148.558i	1.20306	−	0.228200i
$652$	−567.229	+	475.961i	−0.869982	+	0.730002i
$653$	461.316	−	81.3425i	0.706457	−	0.124567i	0.191135	−	0.981564i	$-0.438783\pi$
$653$	461.316	−	81.3425i	0.706457	−	0.124567i	0.515322	+	0.856996i	$0.327672\pi$
$654$	482.088	+	810.625i	0.737137	+	1.23949i
$655$	22.5679	+	18.9367i	0.0344548	+	0.0289110i
$656$	274.399	+	158.424i	0.418291	+	0.241501i
$657$	107.740	−	719.257i	0.163988	−	1.09476i
$658$	−140.474	−	243.307i	−0.213486	−	0.369768i
$659$	−84.6349	−	14.9234i	−0.128429	−	0.0226455i	0.109064	−	0.994035i	$-0.465215\pi$
$659$	−84.6349	−	14.9234i	−0.128429	−	0.0226455i	−0.237493	+	0.971389i	$0.576326\pi$
$660$	−279.801	+	342.343i	−0.423941	+	0.518701i
$661$	−115.687	−	42.1068i	−0.175019	−	0.0637016i	0.253024	−	0.967460i	$-0.418575\pi$
$661$	−115.687	−	42.1068i	−0.175019	−	0.0637016i	−0.428043	+	0.903758i	$0.640797\pi$
$662$	304.996	−	837.968i	0.460718	−	1.26581i
$663$	−409.368	+	155.017i	−0.617447	+	0.233812i
$664$	8.78345	−	49.8134i	0.0132281	−	0.0750202i
$665$	−785.070	+	453.260i	−1.18056	+	0.681594i
$666$	237.525	−	709.098i	0.356644	−	1.06471i
$667$	−199.763	+	346.000i	−0.299495	+	0.518741i
$668$	296.226	−	353.028i	0.443452	−	0.528485i
$669$	1018.67	+	570.709i	1.52268	+	0.853078i
$670$	−23.1182	−	131.110i	−0.0345048	−	0.195686i
$671$	−177.787	−	211.878i	−0.264958	−	0.315765i
$672$	−894.290	−	312.468i	−1.33079	−	0.464982i
$673$	598.221	−	217.735i	0.888887	−	0.323528i	0.143096	−	0.989709i	$-0.454294\pi$
$673$	598.221	−	217.735i	0.888887	−	0.323528i	0.745791	+	0.666180i	$0.232072\pi$
$674$			179.321i			0.266054i
$675$	−232.832	+	300.394i	−0.344936	+	0.445029i
$676$	217.127			0.321194
$677$	56.5391	+	155.340i	0.0835141	+	0.229453i	0.974420	−	0.224735i	$-0.0721516\pi$
$677$	56.5391	+	155.340i	0.0835141	+	0.229453i	−0.890906	+	0.454188i	$0.849929\pi$
$678$	−639.865	−	742.851i	−0.943753	−	1.09565i
$679$	−1048.63	+	879.901i	−1.54437	+	1.29588i
$680$	−266.031	+	46.9084i	−0.391222	+	0.0689830i
$681$	1045.21	−	13.5075i	1.53481	−	0.0198348i
$682$	−534.664	−	448.636i	−0.783965	−	0.657824i
$683$	−1129.58	−	652.163i	−1.65385	−	0.954851i	−0.975468	−	0.220142i	$-0.929348\pi$
$683$	−1129.58	−	652.163i	−1.65385	−	0.954851i	−0.678383	−	0.734709i	$-0.737319\pi$
$684$	243.969	+	398.421i	0.356680	+	0.582487i
$685$	690.092	+	1195.27i	1.00743	+	1.74493i
$686$	−674.445	−	118.923i	−0.983155	−	0.173357i
$687$	−1079.32	−	175.964i	−1.57107	−	0.256134i
$688$	−1510.76	−	549.872i	−2.19587	−	0.799232i
$689$	85.3928	−	234.615i	0.123937	−	0.340515i
$690$	208.818	−	1280.84i	0.302635	−	1.85629i
$691$	−62.8288	+	356.320i	−0.0909245	+	0.515658i	0.904996	+	0.425421i	$0.139874\pi$
$691$	−62.8288	+	356.320i	−0.0909245	+	0.515658i	−0.995920	+	0.0902378i	$0.971237\pi$
$692$	750.099	−	433.070i	1.08396	−	0.625824i
$693$	520.857	+	283.028i	0.751597	+	0.408410i
$694$	227.439	−	393.936i	0.327722	−	0.567632i
$695$	−143.711	+	171.268i	−0.206778	+	0.246428i
$696$	−1.69133	−	130.875i	−0.00243007	−	0.188039i
$697$	43.1093	+	244.485i	0.0618498	+	0.350767i
$698$	−776.309	−	925.169i	−1.11219	−	1.32546i
$699$	−431.125	+	371.356i	−0.616775	+	0.531267i
$700$	312.003	−	113.560i	0.445719	−	0.162228i
$701$		−	893.344i		−	1.27438i	−0.770705	−	0.637192i	$-0.780096\pi$
$701$		−	893.344i		−	1.27438i	0.770705	−	0.637192i	$-0.219904\pi$
$702$	367.325	+	582.823i	0.523255	+	0.830233i
$703$	−564.863			−0.803504
$704$	70.7748	+	194.452i	0.100532	+	0.276210i
$705$	−81.4675	+	233.162i	−0.115557	+	0.330726i
$706$	809.756	−	679.466i	1.14696	−	0.962417i
$707$	558.228	−	98.4307i	0.789573	−	0.139223i
$708$	−96.7639	+	172.717i	−0.136672	+	0.243950i
$709$	−529.040	−	443.917i	−0.746178	−	0.626118i	0.188311	−	0.982109i	$-0.439699\pi$
$709$	−529.040	−	443.917i	−0.746178	−	0.626118i	−0.934489	+	0.355992i	$0.884143\pi$
$710$	587.363	+	339.114i	0.827272	+	0.477626i
$711$	186.309	−	164.721i	0.262038	−	0.231675i
$712$	40.6737	+	70.4490i	0.0571260	+	0.0989452i
$713$	848.896	+	149.683i	1.19060	+	0.209935i
$714$	−340.575	−	899.386i	−0.476996	−	1.25964i
$715$	462.776	+	168.437i	0.647239	+	0.235576i
$716$	−29.1476	+	80.0825i	−0.0407090	+	0.111847i
$717$	711.025	+	581.130i	0.991666	+	0.810502i
$718$	103.934	−	589.439i	0.144755	−	0.820946i
$719$	417.508	−	241.049i	0.580679	−	0.335255i	−0.180724	−	0.983534i	$-0.557844\pi$
$719$	417.508	−	241.049i	0.580679	−	0.335255i	0.761403	+	0.648279i	$0.224511\pi$
$720$	395.136	+	1004.10i	0.548801	+	1.39458i
$721$	283.560	−	491.140i	0.393287	−	0.681192i
$722$	−70.7063	+	84.2645i	−0.0979312	+	0.116710i
$723$	−760.406	+	452.222i	−1.05174	+	0.625480i
$724$	−42.0833	−	238.666i	−0.0581261	−	0.329650i
$725$	137.276	+	163.600i	0.189347	+	0.225655i
$726$	81.0482	+	427.284i	0.111637	+	0.588545i
$727$	−324.225	+	118.008i	−0.445977	+	0.162322i	−0.555239	−	0.831691i	$-0.687373\pi$
$727$	−324.225	+	118.008i	−0.445977	+	0.162322i	0.109263	+	0.994013i	$0.465151\pi$
$728$			226.654i			0.311338i
$729$	314.503	−	657.669i	0.431418	−	0.902152i
$730$	1327.46			1.81844
$731$	−430.834	−	1183.71i	−0.589376	−	1.61930i
$732$	291.947	−	55.3773i	0.398835	−	0.0756520i
$733$	413.108	−	346.639i	0.563585	−	0.472904i	−0.315925	−	0.948784i	$-0.602315\pi$
$733$	413.108	−	346.639i	0.563585	−	0.472904i	0.879510	+	0.475880i	$0.157870\pi$
$734$	−609.376	+	107.450i	−0.830213	+	0.146389i
$735$	−161.959	−	272.333i	−0.220353	−	0.370521i
$736$	−784.699	−	658.440i	−1.06617	−	0.894620i
$737$	56.9482	+	32.8791i	0.0772704	+	0.0446121i
$738$	363.574	−	143.075i	0.492648	−	0.193869i
$739$	−368.737	−	638.671i	−0.498968	−	0.864237i	0.501032	−	0.865429i	$-0.332954\pi$
$739$	−368.737	−	638.671i	−0.498968	−	0.864237i	−0.999999	+	0.00119161i	$0.999621\pi$
$740$	565.606	+	99.7315i	0.764332	+	0.134772i
$741$	329.309	−	402.917i	0.444412	−	0.543747i
$742$	515.452	+	187.609i	0.694679	+	0.252842i
$743$	−356.128	+	978.454i	−0.479311	+	1.31690i	0.430768	+	0.902463i	$0.358243\pi$
$743$	−356.128	+	978.454i	−0.479311	+	1.31690i	−0.910079	+	0.414434i	$0.863980\pi$
$744$	−264.090	+	100.004i	−0.354960	+	0.134414i
$745$	−182.077	+	1032.61i	−0.244398	+	1.38605i
$746$	−1485.54	+	857.674i	−1.99133	+	1.14970i
$747$	−104.858	−	118.601i	−0.140373	−	0.158770i
$748$	−177.150	+	306.832i	−0.236831	+	0.410204i
$749$	−633.619	+	755.118i	−0.845953	+	1.00817i
$750$	469.648	+	263.119i	0.626197	+	0.350825i
$751$	41.8554	+	237.374i	0.0557329	+	0.316077i	0.999911	−	0.0133592i	$-0.00425248\pi$
$751$	41.8554	+	237.374i	0.0557329	+	0.316077i	−0.944178	+	0.329436i	$0.893141\pi$
$752$	162.368	+	193.503i	0.215915	+	0.257317i
$753$	−518.018	−	180.997i	−0.687939	−	0.240368i
$754$	363.771	−	132.402i	0.482455	−	0.175599i
$755$			523.331i			0.693154i
$756$	−538.783	+	339.569i	−0.712677	+	0.449165i
$757$	32.7615			0.0432781			0.0216391	−	0.999766i	$-0.493112\pi$
$757$	32.7615			0.0432781			0.0216391	+	0.999766i	$0.493112\pi$
$758$	561.788	+	1543.50i	0.741145	+	2.03628i
$759$	418.336	+	485.668i	0.551168	+	0.639879i
$760$	246.001	−	206.419i	0.323685	−	0.271604i
$761$	314.502	−	55.4551i	0.413274	−	0.0728714i	0.0368545	−	0.999321i	$-0.488266\pi$
$761$	314.502	−	55.4551i	0.413274	−	0.0728714i	0.376420	+	0.926449i	$0.377155\pi$
$762$	−925.932	+	11.9661i	−1.21513	+	0.0157035i
$763$	743.936	+	624.236i	0.975014	+	0.818134i
$764$	−394.950	−	228.025i	−0.516951	−	0.298462i
$765$	−403.664	+	742.863i	−0.527665	+	0.971063i
$766$	139.986	+	242.463i	0.182750	+	0.316531i
$767$	217.164	+	38.2920i	0.283135	+	0.0499243i
$768$	991.261	+	161.608i	1.29070	+	0.210426i
$769$	447.488	+	162.872i	0.581910	+	0.211798i	0.616167	−	0.787615i	$-0.288685\pi$
$769$	447.488	+	162.872i	0.581910	+	0.211798i	−0.0342578	+	0.999413i	$0.510907\pi$
$770$	−370.058	+	1016.73i	−0.480595	+	1.32042i
$771$	129.546	−	794.601i	0.168023	−	1.03061i
$772$	20.9243	−	118.667i	0.0271040	−	0.153714i
$773$	1122.62	−	648.147i	1.45229	−	0.838482i	0.453682	−	0.891164i	$-0.350110\pi$
$773$	1122.62	−	648.147i	1.45229	−	0.838482i	0.998611	+	0.0526817i	$0.0167769\pi$
$774$	−1690.71	+	1035.29i	−2.18439	+	1.33759i
$775$	230.386	−	399.040i	0.297272	−	0.514890i
$776$	311.701	−	371.471i	0.401677	−	0.478700i
$777$	−9.95035	−	769.955i	−0.0128061	−	0.990934i
$778$	−270.889	−	1536.29i	−0.348187	−	1.97467i
$779$	−189.701	−	226.077i	−0.243519	−	0.290214i
$780$	−400.880	+	345.304i	−0.513949	+	0.442697i
$781$	−314.795	+	114.576i	−0.403066	+	0.146704i
$782$		−	1039.93i		−	1.32983i
$783$	−323.771	−	250.951i	−0.413501	−	0.320499i
$784$	−324.056			−0.413337
$785$	−159.162	−	437.295i	−0.202754	−	0.557063i
$786$	12.2552	−	35.0746i	0.0155918	−	0.0446242i
$787$	659.528	−	553.410i	0.838028	−	0.703189i	−0.119091	−	0.992883i	$-0.537998\pi$
$787$	659.528	−	553.410i	0.838028	−	0.703189i	0.957119	+	0.289694i	$0.0935535\pi$
$788$	602.818	−	106.293i	0.764997	−	0.134890i
$789$	−516.103	+	921.207i	−0.654123	+	1.16756i
$790$	347.714	+	291.766i	0.440144	+	0.369325i
$791$	−874.285	−	504.769i	−1.10529	−	0.638140i
$792$	−199.119	−	66.6983i	−0.251412	−	0.0842150i
$793$	−165.492	−	286.640i	−0.208690	−	0.361462i
$794$	−970.013	−	171.039i	−1.22168	−	0.215415i
$795$	−170.772	−	450.972i	−0.214807	−	0.567260i
$796$	−479.284	−	174.445i	−0.602115	−	0.219152i
$797$	−198.415	+	545.140i	−0.248952	+	0.683990i	0.750774	+	0.660560i	$0.229681\pi$
$797$	−198.415	+	545.140i	−0.248952	+	0.683990i	−0.999725	+	0.0234300i	$0.992541\pi$
$798$	885.213	+	723.497i	1.10929	+	0.906637i
$799$	−34.3678	+	194.909i	−0.0430135	+	0.243942i
$800$	−474.201	+	273.780i	−0.592751	+	0.342225i
$801$	251.788	+	37.7161i	0.314342	+	0.0470863i
$802$	360.552	−	624.494i	0.449566	−	0.778671i
$803$	−421.459	+	502.275i	−0.524855	+	0.625498i
$804$	−60.7210	+	36.1114i	−0.0755236	+	0.0449147i
$805$	−232.041	−	1315.97i	−0.288249	−	1.63474i
$806$	−536.868	−	639.814i	−0.666089	−	0.793814i
$807$	91.8250	+	484.098i	0.113786	+	0.599874i
$808$	−188.691	+	68.6779i	−0.233528	+	0.0849974i
$809$			661.323i			0.817457i	0.912656	+	0.408729i	$0.134028\pi$
$809$			661.323i			0.817457i	−0.912656	+	0.408729i	$0.865972\pi$
$810$	1272.20	+	389.881i	1.57061	+	0.481335i
$811$	−168.725			−0.208045			−0.104023	−	0.994575i	$-0.533171\pi$
$811$	−168.725			−0.208045			−0.104023	+	0.994575i	$0.533171\pi$
$812$	122.397	+	336.283i	0.150735	+	0.414142i
$813$	379.779	−	72.0374i	0.467133	−	0.0886069i
$814$	−516.461	+	433.362i	−0.634473	+	0.532386i
$815$	1568.77	−	276.617i	1.92487	−	0.339407i
$816$	441.977	+	743.180i	0.541639	+	0.910760i
$817$	1147.13	+	962.559i	1.40408	+	1.17816i
$818$	−1255.05	−	724.602i	−1.53429	−	0.885822i
$819$	555.010	+	441.778i	0.677668	+	0.539412i
$820$	150.035	+	259.868i	0.182969	+	0.316912i
$821$	149.275	+	26.3213i	0.181822	+	0.0320600i	0.263817	−	0.964573i	$-0.415018\pi$
$821$	149.275	+	26.3213i	0.181822	+	0.0320600i	−0.0819959	+	0.996633i	$0.526129\pi$
$822$	1101.53	−	1347.74i	1.34006	−	1.63959i
$823$	−211.263	−	76.8935i	−0.256699	−	0.0934307i	0.210465	−	0.977601i	$-0.432502\pi$
$823$	−211.263	−	76.8935i	−0.256699	−	0.0934307i	−0.467164	+	0.884171i	$0.654724\pi$
$824$	−68.7118	+	188.784i	−0.0833881	+	0.229107i
$825$	320.436	−	121.341i	0.388407	−	0.147080i
$826$	−84.1280	+	477.113i	−0.101850	+	0.577619i
$827$	292.855	−	169.080i	0.354117	−	0.204449i	−0.312380	−	0.949957i	$-0.601126\pi$
$827$	292.855	−	169.080i	0.354117	−	0.204449i	0.666497	+	0.745508i	$0.267793\pi$
$828$	−674.880	+	137.070i	−0.815072	+	0.165544i
$829$	401.806	−	695.949i	0.484688	−	0.839504i	−0.515157	−	0.857096i	$-0.672267\pi$
$829$	401.806	−	695.949i	0.484688	−	0.839504i	0.999845	+	0.0175917i	$0.00559990\pi$
$830$	185.733	−	221.348i	0.223775	−	0.266685i
$831$	−393.157	−	220.265i	−0.473113	−	0.265060i
$832$	43.0002	+	243.866i	0.0516829	+	0.293108i
$833$	−163.206	−	194.502i	−0.195926	−	0.233495i
$834$	266.181	+	93.0047i	0.319162	+	0.111516i
$835$	−931.633	+	339.087i	−1.11573	+	0.406092i
$836$		−	421.184i		−	0.503809i
$837$	−269.865	+	841.601i	−0.322419	+	1.00550i
$838$	−230.169			−0.274665
$839$	292.066	+	802.443i	0.348111	+	0.956428i	0.982965	+	0.183795i	$0.0588384\pi$
$839$	292.066	+	802.443i	0.348111	+	0.956428i	−0.634853	+	0.772633i	$0.718939\pi$
$840$	285.700	+	331.683i	0.340119	+	0.394861i
$841$	467.912	−	392.625i	0.556376	−	0.466855i
$842$	766.705	−	135.191i	0.910576	−	0.160559i
$843$	−1382.88	+	17.8714i	−1.64043	+	0.0211997i
$844$	580.637	+	487.213i	0.687959	+	0.577266i
$845$	−404.527	−	233.554i	−0.478731	−	0.276395i
$846$	311.382	−	8.04949i	0.368064	−	0.00951476i
$847$	223.906	+	387.816i	0.264351	+	0.457870i
$848$	−485.693	−	85.6407i	−0.572751	−	0.100991i
$849$	−203.881	−	33.2391i	−0.240142	−	0.0391509i
$850$	−522.361	−	190.124i	−0.614542	−	0.223675i
$851$	284.781	−	782.430i	0.334643	−	0.919424i
$852$	57.9117	−	355.216i	0.0679714	−	0.416920i
$853$	−138.765	+	786.975i	−0.162679	+	0.922596i	0.788747	+	0.614718i	$0.210730\pi$
$853$	−138.765	+	786.975i	−0.162679	+	0.922596i	−0.951426	+	0.307878i	$0.900381\pi$
$854$	629.751	−	363.587i	0.737414	−	0.425746i
$855$	−25.9729	−	1004.72i	−0.0303777	−	1.17511i
$856$	174.597	−	302.410i	0.203968	−	0.353283i
$857$	998.416	−	1189.87i	1.16501	−	1.38841i	0.258616	−	0.965980i	$-0.416734\pi$
$857$	998.416	−	1189.87i	1.16501	−	1.38841i	0.906397	−	0.422427i	$-0.138822\pi$
$858$	−8.02583	−	621.037i	−0.00935411	−	0.723819i
$859$	−4.90592	−	27.8228i	−0.00571119	−	0.0323898i	0.981819	−	0.189820i	$-0.0607903\pi$
$859$	−4.90592	−	27.8228i	−0.00571119	−	0.0323898i	−0.987530	+	0.157430i	$0.949679\pi$
$860$	−978.693	−	1166.36i	−1.13802	−	1.35623i
$861$	304.820	−	262.561i	0.354030	−	0.304949i
$862$	−1447.50	+	526.846i	−1.67923	+	0.611190i
$863$		−	951.550i		−	1.10261i	−0.834305	−	0.551304i	$-0.814131\pi$
$863$		−	951.550i		−	1.10261i	0.834305	−	0.551304i	$-0.185869\pi$
$864$	777.790	−	705.782i	0.900220	−	0.816877i
$865$	−1863.34			−2.15415
$866$	373.326	+	1025.70i	0.431092	+	1.18442i
$867$	62.5107	−	178.907i	0.0721000	−	0.206352i
$868$	591.468	−	496.301i	0.681415	−	0.571775i
$869$	−220.793	+	38.9318i	−0.254077	+	0.0448006i
$870$	365.445	−	652.293i	0.420052	−	0.749762i
$871$	60.2805	+	50.5813i	0.0692084	+	0.0580727i
$872$	−297.932	−	172.011i	−0.341665	−	0.197260i
$873$	−302.079	−	1487.31i	−0.346024	−	1.70368i
$874$	618.122	+	1070.62i	0.707233	+	1.22496i
$875$	545.889	+	96.2549i	0.623873	+	0.110006i
$876$	−249.461	−	658.775i	−0.284773	−	0.752026i
$877$	214.431	+	78.0465i	0.244505	+	0.0889926i	0.461366	−	0.887210i	$-0.347360\pi$
$877$	214.431	+	78.0465i	0.244505	+	0.0889926i	−0.216861	+	0.976203i	$0.569582\pi$
$878$	−300.516	+	825.662i	−0.342274	+	0.940390i
$879$	−1186.44	−	969.692i	−1.34976	−	1.10318i
$880$	168.926	−	958.026i	0.191961	−	1.08867i
$881$	−1343.36	+	775.592i	−1.52482	+	0.880354i	−0.525250	+	0.850948i	$0.676028\pi$
$881$	−1343.36	+	775.592i	−1.52482	+	0.880354i	−0.999568	+	0.0294054i	$0.990639\pi$
$882$	−248.862	+	312.648i	−0.282156	+	0.354476i
$883$	−781.794	+	1354.11i	−0.885384	+	1.53353i	−0.0401121	+	0.999195i	$0.512772\pi$
$883$	−781.794	+	1354.11i	−0.885384	+	1.53353i	−0.845272	+	0.534336i	$0.820562\pi$
$884$	−272.528	+	324.786i	−0.308290	+	0.367405i
$885$	366.064	−	217.702i	0.413632	−	0.245991i
$886$	206.096	+	1168.83i	0.232614	+	1.31922i
$887$	451.340	+	537.886i	0.508839	+	0.606411i	0.957904	−	0.287088i	$-0.0926873\pi$
$887$	451.340	+	537.886i	0.508839	+	0.606411i	−0.449065	+	0.893499i	$0.648243\pi$
$888$	50.8345	+	267.998i	0.0572461	+	0.301799i
$889$	−895.993	+	326.115i	−1.00787	+	0.366833i
$890$			464.699i			0.522134i
$891$	−551.433	+	357.580i	−0.618892	+	0.401324i
$892$	1130.95			1.26789
$893$	−80.4701	−	221.090i	−0.0901121	−	0.247581i
$894$	1299.20	−	246.436i	1.45325	−	0.275655i
$895$	140.446	−	117.848i	0.156923	−	0.131674i
$896$	708.110	−	124.859i	0.790302	−	0.139352i
$897$	392.083	+	659.283i	0.437104	+	0.734986i
$898$	−384.523	−	322.653i	−0.428199	−	0.359302i
$899$	430.094	+	248.315i	0.478413	+	0.276212i
$900$	−54.5332	+	364.056i	−0.0605924	+	0.404507i
$901$	−193.210	−	334.649i	−0.214439	−	0.371419i
$902$	−346.892	−	61.1664i	−0.384581	−	0.0678120i
$903$	−1291.84	+	1580.59i	−1.43061	+	1.75038i
$904$	336.057	+	122.315i	0.371745	+	0.135304i
$905$	−178.318	+	489.924i	−0.197036	+	0.541353i
$906$	617.230	−	233.729i	0.681269	−	0.257979i
$907$	280.357	−	1589.99i	0.309104	−	1.75302i	−0.294424	−	0.955675i	$-0.595128\pi$
$907$	280.357	−	1589.99i	0.309104	−	1.75302i	0.603528	−	0.797341i	$-0.293761\pi$
$908$	876.803	−	506.222i	0.965642	−	0.557514i
$909$	−199.611	+	595.911i	−0.219594	+	0.655568i
$910$	−647.383	+	1121.30i	−0.711410	+	1.23220i
$911$	−394.005	+	469.556i	−0.432497	+	0.515430i	−0.937641	−	0.347605i	$-0.886995\pi$
$911$	−394.005	+	469.556i	−0.432497	+	0.515430i	0.505144	+	0.863035i	$0.331439\pi$
$912$	−896.761	−	502.408i	−0.983291	−	0.550885i
$913$	24.7833	+	140.553i	0.0271449	+	0.153946i
$914$	651.599	+	776.546i	0.712910	+	0.849613i
$915$	−603.491	−	210.862i	−0.659554	−	0.230450i
$916$	−995.326	+	362.269i	−1.08660	+	0.395490i
$917$		−	38.2568i		−	0.0417195i
$918$	1056.44	+	144.315i	1.15080	+	0.157206i
$919$	628.091			0.683451			0.341725	−	0.939800i	$-0.388989\pi$
$919$	628.091			0.683451			0.341725	+	0.939800i	$0.388989\pi$
$920$	161.901	+	444.821i	0.175980	+	0.483501i
$921$	102.992	+	119.569i	0.111827	+	0.129825i
$922$	−871.766	+	731.499i	−0.945516	+	0.793382i
$923$	−394.790	+	69.6122i	−0.427725	+	0.0754195i
$924$	574.109	−	7.41937i	0.621331	−	0.00802963i
$925$	−340.955	−	286.095i	−0.368600	−	0.309292i
$926$	1258.19	+	726.418i	1.35874	+	0.784469i
$927$	328.349	+	536.220i	0.354206	+	0.578446i
$928$	−295.086	−	511.103i	−0.317980	−	0.550758i
$929$	1234.51	+	217.678i	1.32886	+	0.234314i	0.792603	−	0.609738i	$-0.208726\pi$
$929$	1234.51	+	217.678i	1.32886	+	0.234314i	0.536260	+	0.844053i	$0.319837\pi$
$930$	−1592.14	−	259.570i	−1.71198	−	0.279108i
$931$	283.633	+	103.234i	0.304654	+	0.110885i
$932$	−188.497	+	517.892i	−0.202250	+	0.555678i
$933$	171.282	−	1050.61i	0.183583	−	1.12605i
$934$	98.2529	−	557.220i	0.105196	−	0.596595i
$935$	660.093	−	381.105i	0.705981	−	0.407599i
$936$	−220.799	−	119.980i	−0.235896	−	0.128183i
$937$	460.132	−	796.972i	0.491070	−	0.850557i	−0.508878	−	0.860839i	$-0.669939\pi$
$937$	460.132	−	796.972i	0.491070	−	0.850557i	0.999947	+	0.0102815i	$0.00327275\pi$
$938$	−111.128	+	132.437i	−0.118473	+	0.141191i
$939$	6.52243	+	504.704i	0.00694614	+	0.537491i
$940$	41.5405	+	235.588i	0.0441921	+	0.250626i
$941$	−439.314	−	523.554i	−0.466859	−	0.556381i	0.480317	−	0.877095i	$-0.340522\pi$
$941$	−439.314	−	523.554i	−0.466859	−	0.556381i	−0.947176	+	0.320714i	$0.896077\pi$
$942$	−444.672	+	383.024i	−0.472050	+	0.406607i
$943$	408.794	−	148.789i	0.433504	−	0.157783i
$944$		−	435.590i		−	0.461430i
$945$	1369.06	−	53.1020i	1.44874	−	0.0561926i
$946$	1787.31			1.88934
$947$	−287.907	−	791.018i	−0.304020	−	0.835288i	−0.993791	−	0.111261i	$-0.964511\pi$
$947$	−287.907	−	791.018i	−0.304020	−	0.835288i	0.689771	−	0.724027i	$-0.257711\pi$
$948$	79.4503	−	227.389i	0.0838084	−	0.239861i
$949$	−601.056	+	504.346i	−0.633357	+	0.531450i
$950$	650.786	−	114.751i	0.685038	−	0.120791i
$951$	−747.797	+	1334.76i	−0.786327	+	1.40354i
$952$	268.724	+	225.486i	0.282273	+	0.236855i
$953$	1277.52	+	737.576i	1.34052	+	0.773952i	0.986884	−	0.161430i	$-0.0516105\pi$
$953$	1277.52	+	737.576i	1.34052	+	0.773952i	0.353640	+	0.935382i	$0.384944\pi$
$954$	−455.618	+	402.825i	−0.477587	+	0.422248i
$955$	490.553	+	849.662i	0.513668	+	0.889698i
$956$	875.924	+	154.449i	0.916238	+	0.161558i
$957$	130.784	+	345.373i	0.136660	+	0.360891i
$958$	−559.293	−	203.566i	−0.583813	−	0.212490i
$959$	613.000	−	1684.20i	0.639207	−	1.75621i
$960$	370.322	+	302.669i	0.385752	+	0.315281i
$961$	19.1872	−	108.816i	0.0199659	−	0.113232i
$962$	−698.694	+	403.391i	−0.726294	+	0.419326i
$963$	−400.203	−	1016.97i	−0.415580	−	1.05605i
$964$	−428.456	+	742.107i	−0.444456	+	0.769821i
$965$	−166.629	+	198.581i	−0.172673	+	0.205783i
$966$	−1448.45	+	861.411i	−1.49943	+	0.891730i
$967$	56.3919	+	319.814i	0.0583163	+	0.330728i	0.999983	−	0.00581841i	$-0.00185207\pi$
$967$	56.3919	+	319.814i	0.0583163	+	0.330728i	−0.941667	+	0.336547i	$0.890741\pi$
$968$	−101.969	−	121.522i	−0.105340	−	0.125539i
$969$	−150.091	−	791.274i	−0.154892	−	0.816588i
$970$	2603.06	−	947.438i	2.68357	−	0.976740i
$971$			1203.37i			1.23931i	0.784873	+	0.619657i	$0.212728\pi$
$971$			1203.37i			1.23931i	−0.784873	+	0.619657i	$0.787272\pi$
$972$	−45.5907	−	704.616i	−0.0469040	−	0.724914i
$973$	290.331			0.298387
$974$	−398.279	−	1094.26i	−0.408911	−	1.12347i
$975$	402.844	−	76.4125i	0.413174	−	0.0783718i
$976$	−500.842	+	420.256i	−0.513157	+	0.430590i
$977$	186.452	−	32.8765i	0.190841	−	0.0336505i	−0.0774104	−	0.996999i	$-0.524665\pi$
$977$	186.452	−	32.8765i	0.190841	−	0.0336505i	0.268252	+	0.963349i	$0.413554\pi$
$978$	−1026.89	−	1726.71i	−1.04999	−	1.76555i
$979$	−175.829	−	147.538i	−0.179601	−	0.150703i
$980$	−265.779	−	153.448i	−0.271203	−	0.156579i
$981$	−1001.91	+	394.277i	−1.02132	+	0.401913i
$982$	−876.994	−	1519.00i	−0.893070	−	1.54684i
$983$	−1245.48	−	219.613i	−1.26702	−	0.223411i	−0.500562	−	0.865701i	$-0.666873\pi$
$983$	−1245.48	−	219.613i	−1.26702	−	0.223411i	−0.766462	+	0.642290i	$0.777984\pi$
$984$	−90.1896	+	110.349i	−0.0916561	+	0.112143i
$985$	−1237.44	−	450.391i	−1.25628	−	0.457250i
$986$	204.919	−	563.012i	0.207829	−	0.571006i
$987$	299.946	−	113.582i	0.303897	−	0.115078i
$988$	87.5217	−	496.360i	0.0885847	−	0.502389i
$989$	−1911.64	+	1103.69i	−1.93291	+	1.11596i
$990$	−794.569	−	898.703i	−0.802595	−	0.907781i
$991$	697.271	−	1207.71i	0.703604	−	1.21868i	−0.263589	−	0.964635i	$-0.584906\pi$
$991$	697.271	−	1207.71i	0.703604	−	1.21868i	0.967193	−	0.254043i	$-0.0817603\pi$
$992$	−818.471	+	975.416i	−0.825072	+	0.983282i
$993$	888.140	+	497.578i	0.894401	+	0.501085i
$994$	−152.939	−	867.360i	−0.153862	−	0.872595i
$995$	705.307	+	840.552i	0.708851	+	0.844776i
$996$	−144.751	−	50.5767i	−0.145333	−	0.0507798i
$997$	−947.882	+	345.001i	−0.950734	+	0.346039i	−0.770396	−	0.637566i	$-0.779941\pi$
$997$	−947.882	+	345.001i	−0.950734	+	0.346039i	−0.180338	+	0.983605i	$0.557719\pi$
$998$			151.062i			0.151365i
$999$	755.332	+	397.884i	0.756088	+	0.398282i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.3.f.a.20.5	✓	30
3.2	odd	2		81.3.f.a.62.1		30
4.3	odd	2		432.3.bc.a.209.5		30
9.2	odd	6		243.3.f.b.107.1		30
9.4	even	3		243.3.f.d.26.1		30
9.5	odd	6		243.3.f.a.26.5		30
9.7	even	3		243.3.f.c.107.5		30
27.2	odd	18		729.3.b.a.728.26		30
27.4	even	9		81.3.f.a.17.1		30
27.5	odd	18		243.3.f.d.215.1		30
27.13	even	9		243.3.f.b.134.1		30
27.14	odd	18		243.3.f.c.134.5		30
27.22	even	9		243.3.f.a.215.5		30
27.23	odd	18	inner	27.3.f.a.23.5	yes	30
27.25	even	9		729.3.b.a.728.5		30
108.23	even	18		432.3.bc.a.401.5		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.20.5	✓	30	1.1	even	1	trivial
27.3.f.a.23.5	yes	30	27.23	odd	18	inner
81.3.f.a.17.1		30	27.4	even	9
81.3.f.a.62.1		30	3.2	odd	2
243.3.f.a.26.5		30	9.5	odd	6
243.3.f.a.215.5		30	27.22	even	9
243.3.f.b.107.1		30	9.2	odd	6
243.3.f.b.134.1		30	27.13	even	9
243.3.f.c.107.5		30	9.7	even	3
243.3.f.c.134.5		30	27.14	odd	18
243.3.f.d.26.1		30	9.4	even	3
243.3.f.d.215.1		30	27.5	odd	18
432.3.bc.a.209.5		30	4.3	odd	2
432.3.bc.a.401.5		30	108.23	even	18
729.3.b.a.728.5		30	27.25	even	9
729.3.b.a.728.26		30	27.2	odd	18

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.898786 + 2.46939i) q^{2} +(-2.94744 + 0.559079i) q^{3} +(-2.22591 + 1.86776i) q^{4} +(6.15614 - 1.08549i) q^{5} +(-4.02971 - 6.77591i) q^{6} +(-6.21846 - 5.21791i) q^{7} +(2.49037 + 1.43782i) q^{8} +(8.37486 - 3.29571i) q^{9} +(8.21356 + 14.2263i) q^{10} +(-7.99059 - 1.40896i) q^{11} +(5.51652 - 6.74957i) q^{12} +(-9.12402 - 3.32087i) q^{13} +(7.29600 - 20.0456i) q^{14} +(-17.5380 + 6.64120i) q^{15} +(-3.33052 + 18.8883i) q^{16} +(-13.0143 + 7.51380i) q^{17} +(15.6656 + 17.7187i) q^{18} +(8.93226 - 15.4711i) q^{19} +(-11.6756 + 13.9144i) q^{20} +(21.2458 + 11.9029i) q^{21} +(-3.70256 - 20.9983i) q^{22} +(16.9268 + 20.1726i) q^{23} +(-8.14409 - 2.84557i) q^{24} +(13.2275 - 4.81440i) q^{25} -25.5156i q^{26} +(-22.8419 + 14.3961i) q^{27} +23.5875 q^{28} +(5.18906 + 14.2568i) q^{29} +(-32.1626 - 37.3392i) q^{30} +(25.0755 - 21.0408i) q^{31} +(-38.3082 + 6.75478i) q^{32} +(24.3395 - 0.314547i) q^{33} +(-30.2516 - 25.3841i) q^{34} +(-43.9457 - 25.3721i) q^{35} +(-12.4861 + 22.9782i) q^{36} +(-15.8096 - 27.3831i) q^{37} +(46.2325 + 8.15204i) q^{38} +(28.7492 + 4.68704i) q^{39} +(16.8918 + 6.14813i) q^{40} +(5.65018 - 15.5238i) q^{41} +(-10.2975 + 63.1624i) q^{42} +(-14.5559 + 82.5505i) q^{43} +(20.4179 - 11.7883i) q^{44} +(47.9794 - 29.3797i) q^{45} +(-34.6005 + 59.9298i) q^{46} +(8.46562 - 10.0889i) q^{47} +(-0.743531 - 57.5342i) q^{48} +(2.93393 + 16.6391i) q^{49} +(23.7773 + 28.3367i) q^{50} +(34.1581 - 29.4225i) q^{51} +(26.5118 - 9.64952i) q^{52} +25.7140i q^{53} +(-56.0796 - 43.4666i) q^{54} -50.7206 q^{55} +(-7.98389 - 21.9356i) q^{56} +(-17.6778 + 50.5941i) q^{57} +(-30.5419 + 25.6277i) q^{58} +(-22.3660 + 3.94373i) q^{59} +(26.6338 - 47.5395i) q^{60} +(26.1131 + 21.9115i) q^{61} +(74.4955 + 43.0100i) q^{62} +(-69.2755 - 23.2050i) q^{63} +(-12.7517 - 22.0867i) q^{64} +(-59.7736 - 10.5397i) q^{65} +(22.6528 + 59.8212i) q^{66} +(-7.61567 - 2.77188i) q^{67} +(14.9346 - 41.0326i) q^{68} +(-61.1690 - 49.9942i) q^{69} +(23.1558 - 131.323i) q^{70} +(35.7557 - 20.6436i) q^{71} +(25.5952 + 3.83398i) q^{72} +(40.4046 - 69.9827i) q^{73} +(53.4101 - 63.6517i) q^{74} +(-36.2956 + 21.5854i) q^{75} +(9.01395 + 51.1206i) q^{76} +(42.3374 + 50.4557i) q^{77} +(14.2652 + 75.2057i) q^{78} +(25.9652 - 9.45057i) q^{79} +119.894i q^{80} +(59.2766 - 55.2022i) q^{81} +43.4126 q^{82} +(-6.01607 - 16.5290i) q^{83} +(-69.5229 + 13.1873i) q^{84} +(-71.9616 + 60.3830i) q^{85} +(-216.932 + 38.2510i) q^{86} +(-23.2652 - 39.1201i) q^{87} +(-17.8737 - 14.9978i) q^{88} +(24.4986 + 14.1443i) q^{89} +(115.673 + 92.0739i) q^{90} +(39.4094 + 68.2590i) q^{91} +(-75.3552 - 13.2871i) q^{92} +(-62.1451 + 76.0358i) q^{93} +(32.5223 + 11.8372i) q^{94} +(38.1945 - 104.938i) q^{95} +(109.135 - 41.3267i) q^{96} +(29.2825 - 166.069i) q^{97} +(-38.4516 + 22.2000i) q^{98} +(-71.5636 + 14.5348i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 15 q^{5} - 18 q^{6} - 6 q^{7} - 9 q^{8} - 3 q^{10} - 6 q^{11} - 15 q^{12} - 6 q^{13} - 15 q^{14} - 9 q^{15} - 18 q^{16} - 9 q^{17} + 63 q^{18} - 3 q^{19} + 213 q^{20}+ \cdots + 513 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 15 * q^5 - 18 * q^6 - 6 * q^7 - 9 * q^8 - 3 * q^10 - 6 * q^11 - 15 * q^12 - 6 * q^13 - 15 * q^14 - 9 * q^15 - 18 * q^16 - 9 * q^17 + 63 * q^18 - 3 * q^19 + 213 * q^20 + 132 * q^21 - 42 * q^22 + 120 * q^23 + 144 * q^24 - 15 * q^25 - 90 * q^27 - 12 * q^28 - 168 * q^29 - 243 * q^30 + 39 * q^31 - 360 * q^32 - 207 * q^33 + 54 * q^34 - 252 * q^35 - 360 * q^36 - 3 * q^37 - 84 * q^38 + 15 * q^39 - 33 * q^40 + 228 * q^41 + 486 * q^42 - 96 * q^43 + 639 * q^44 + 477 * q^45 - 3 * q^46 + 399 * q^47 + 453 * q^48 - 78 * q^49 + 303 * q^50 + 36 * q^51 - 9 * q^52 - 54 * q^54 - 12 * q^55 - 393 * q^56 - 192 * q^57 + 129 * q^58 - 474 * q^59 - 846 * q^60 + 138 * q^61 - 900 * q^62 - 585 * q^63 - 51 * q^64 - 411 * q^65 - 423 * q^66 + 354 * q^67 + 99 * q^68 + 99 * q^69 + 489 * q^70 + 315 * q^71 + 720 * q^72 - 66 * q^73 + 321 * q^74 + 255 * q^75 + 258 * q^76 + 201 * q^77 + 180 * q^78 + 30 * q^79 + 36 * q^81 - 12 * q^82 - 33 * q^83 - 588 * q^84 - 261 * q^85 - 258 * q^86 - 279 * q^87 - 642 * q^88 + 72 * q^89 + 288 * q^90 + 96 * q^91 - 3 * q^92 + 591 * q^93 - 861 * q^94 + 681 * q^95 + 270 * q^96 - 582 * q^97 + 882 * q^98 + 513 * q^99

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