LMFDB - Embedded newform 45.5.h.a.14.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,5,Mod(14,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("45.14"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	45.h (of order $6$, degree $2$, 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:	$4.65164833877$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			14.3
Character	$\chi$	$=$	45.14
Dual form			45.5.h.a.29.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.12350 - 5.41005i) q^{2} +(-7.73715 - 4.59745i) q^{3} +(-11.5125 + 19.9402i) q^{4} +(-11.8313 - 22.0232i) q^{5} +(-0.705517 + 56.2185i) q^{6} +(-10.1314 + 5.84936i) q^{7} +43.8846 q^{8} +(38.7269 + 71.1423i) q^{9} +(-82.1915 + 132.797i) q^{10} +(141.466 - 81.6756i) q^{11} +(180.748 - 101.352i) q^{12} +(48.3682 + 27.9254i) q^{13} +(63.2907 + 36.5409i) q^{14} +(-9.70982 + 224.790i) q^{15} +(47.1259 + 81.6244i) q^{16} -256.666 q^{17} +(263.921 - 431.727i) q^{18} -618.990 q^{19} +(575.353 + 17.6224i) q^{20} +(105.280 + 1.32122i) q^{21} +(-883.739 - 510.227i) q^{22} +(-329.624 + 570.926i) q^{23} +(-339.542 - 201.758i) q^{24} +(-345.040 + 521.126i) q^{25} -348.899i q^{26} +(27.4379 - 728.483i) q^{27} -269.362i q^{28} +(122.649 - 70.8112i) q^{29} +(1246.46 - 649.601i) q^{30} +(300.023 - 519.656i) q^{31} +(645.472 - 1117.99i) q^{32} +(-1470.05 - 18.4484i) q^{33} +(801.696 + 1388.58i) q^{34} +(248.689 + 153.920i) q^{35} +(-1864.43 - 46.8029i) q^{36} +751.406i q^{37} +(1933.41 + 3348.77i) q^{38} +(-245.846 - 438.433i) q^{39} +(-519.213 - 966.479i) q^{40} +(-2039.87 - 1177.72i) q^{41} +(-321.695 - 573.699i) q^{42} +(1719.96 - 993.020i) q^{43} +3761.15i q^{44} +(1108.59 - 1694.60i) q^{45} +4118.32 q^{46} +(433.754 + 751.284i) q^{47} +(10.6445 - 848.199i) q^{48} +(-1132.07 + 1960.80i) q^{49} +(3897.05 + 238.949i) q^{50} +(1985.86 + 1180.01i) q^{51} +(-1113.67 + 642.980i) q^{52} -3196.69 q^{53} +(-4026.84 + 2126.97i) q^{54} +(-3472.49 - 2149.21i) q^{55} +(-444.612 + 256.697i) q^{56} +(4789.21 + 2845.78i) q^{57} +(-766.185 - 442.357i) q^{58} +(-2390.76 - 1380.31i) q^{59} +(-4370.57 - 2781.51i) q^{60} +(48.4383 + 83.8977i) q^{61} -3748.49 q^{62} +(-808.494 - 494.243i) q^{63} -6556.49 q^{64} +(42.7461 - 1395.62i) q^{65} +(4491.87 + 8010.65i) q^{66} +(3757.13 + 2169.18i) q^{67} +(2954.86 - 5117.96i) q^{68} +(5175.15 - 2901.91i) q^{69} +(55.9341 - 1826.19i) q^{70} -8119.50i q^{71} +(1699.51 + 3122.05i) q^{72} +2097.20i q^{73} +(4065.15 - 2347.01i) q^{74} +(5065.48 - 2445.73i) q^{75} +(7126.10 - 12342.8i) q^{76} +(-955.501 + 1654.98i) q^{77} +(-1604.05 + 2699.49i) q^{78} +(-929.960 - 1610.74i) q^{79} +(1240.07 - 2003.58i) q^{80} +(-3561.46 + 5510.24i) q^{81} +14714.4i q^{82} +(-6081.60 - 10533.6i) q^{83} +(-1238.38 + 2084.09i) q^{84} +(3036.70 + 5652.60i) q^{85} +(-10744.6 - 6203.39i) q^{86} +(-1274.50 - 15.9944i) q^{87} +(6208.20 - 3584.30i) q^{88} +10695.7i q^{89} +(-12630.5 - 704.465i) q^{90} -653.383 q^{91} +(-7589.57 - 13145.5i) q^{92} +(-4710.42 + 2641.31i) q^{93} +(2709.66 - 4693.26i) q^{94} +(7323.46 + 13632.1i) q^{95} +(-10134.0 + 5682.53i) q^{96} +(5624.85 - 3247.51i) q^{97} +14144.1 q^{98} +(11289.1 + 6901.20i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 162 q^{4} + 6 q^{5} - 36 q^{6} - 126 q^{9} + 28 q^{10} + 228 q^{11} + 282 q^{14} + 450 q^{15} - 1058 q^{16} - 8 q^{19} - 2196 q^{20} + 1056 q^{21} + 2970 q^{24} - 148 q^{25} + 2370 q^{29} + 1068 q^{30}+ \cdots + 44568 q^{99}+O(q^{100}) $ 44 * q - 162 * q^4 + 6 * q^5 - 36 * q^6 - 126 * q^9 + 28 * q^10 + 228 * q^11 + 282 * q^14 + 450 * q^15 - 1058 * q^16 - 8 * q^19 - 2196 * q^20 + 1056 * q^21 + 2970 * q^24 - 148 * q^25 + 2370 * q^29 + 1068 * q^30 - 1112 * q^31 - 436 * q^34 - 648 * q^36 - 6420 * q^39 - 850 * q^40 + 1830 * q^41 - 1944 * q^45 - 5668 * q^46 + 5396 * q^49 + 13524 * q^50 - 1500 * q^51 + 17766 * q^54 - 3072 * q^55 - 8250 * q^56 - 27348 * q^59 - 28722 * q^60 + 2782 * q^61 + 8348 * q^64 - 24906 * q^65 + 27240 * q^66 + 19662 * q^69 + 4782 * q^70 + 64728 * q^74 + 28446 * q^75 - 1776 * q^76 + 7900 * q^79 - 47754 * q^81 - 113166 * q^84 + 6766 * q^85 + 9192 * q^86 + 10674 * q^90 + 1560 * q^91 - 18826 * q^94 + 58746 * q^95 + 1902 * q^96 + 44568 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−3.12350	−	5.41005i	−0.780874	−	1.35251i	−0.931433	−	0.363913i	$-0.881441\pi$
$2$	−3.12350	−	5.41005i	−0.780874	−	1.35251i	0.150559	−	0.988601i	$-0.451893\pi$
$3$	−7.73715	−	4.59745i	−0.859683	−	0.510828i
$3$	−7.73715	−	4.59745i	−0.859683	−	0.510828i
$4$	−11.5125	+	19.9402i	−0.719529	+	1.24626i
$5$	−11.8313	−	22.0232i	−0.473253	−	0.880927i
$5$	−11.8313	−	22.0232i	−0.473253	−	0.880927i
$6$	−0.705517	+	56.2185i	−0.0195977	+	1.56163i
$7$	−10.1314	+	5.84936i	−0.206763	+	0.119375i	−0.599806	−	0.800145i	$-0.704756\pi$
$7$	−10.1314	+	5.84936i	−0.206763	+	0.119375i	0.393043	+	0.919520i	$0.371422\pi$
$8$	43.8846			0.685697
$9$	38.7269	+	71.1423i	0.478109	+	0.878300i
$10$	−82.1915	+	132.797i	−0.821915	+	1.32797i
$11$	141.466	−	81.6756i	1.16914	−	0.675005i	0.215665	−	0.976467i	$-0.430808\pi$
$11$	141.466	−	81.6756i	1.16914	−	0.675005i	0.953478	+	0.301462i	$0.0974748\pi$
$12$	180.748	−	101.352i	1.25519	−	0.703833i
$13$	48.3682	+	27.9254i	0.286202	+	0.165239i	0.636228	−	0.771501i	$-0.280494\pi$
$13$	48.3682	+	27.9254i	0.286202	+	0.165239i	−0.350026	+	0.936740i	$0.613827\pi$
$14$	63.2907	+	36.5409i	0.322912	+	0.186433i
$15$	−9.70982	+	224.790i	−0.0431548	+	0.999068i
$16$	47.1259	+	81.6244i	0.184085	+	0.318845i
$17$	−256.666			−0.888118			−0.444059	−	0.895998i	$-0.646462\pi$
$17$	−256.666			−0.888118			−0.444059	+	0.895998i	$0.646462\pi$
$18$	263.921	−	431.727i	0.814570	−	1.33249i
$19$	−618.990			−1.71465			−0.857327	−	0.514773i	$-0.827876\pi$
$19$	−618.990			−1.71465			−0.857327	+	0.514773i	$0.827876\pi$
$20$	575.353	+	17.6224i	1.43838	+	0.0440560i
$21$	105.280	+	1.32122i	0.238731	+	0.00299596i
$22$	−883.739	−	510.227i	−1.82591	−	1.05419i
$23$	−329.624	+	570.926i	−0.623108	+	1.07925i	0.365795	+	0.930695i	$0.380797\pi$
$23$	−329.624	+	570.926i	−0.623108	+	1.07925i	−0.988903	+	0.148560i	$0.952536\pi$
$24$	−339.542	−	201.758i	−0.589482	−	0.350273i
$25$	−345.040	+	521.126i	−0.552064	+	0.833802i
$26$		−	348.899i		−	0.516124i
$27$	27.4379	−	728.483i	0.0376378	−	0.999291i
$28$		−	269.362i		−	0.343574i
$29$	122.649	−	70.8112i	0.145837	−	0.0841988i	−0.425306	−	0.905050i	$-0.639834\pi$
$29$	122.649	−	70.8112i	0.145837	−	0.0841988i	0.571143	+	0.820851i	$0.306500\pi$
$30$	1246.46	−	649.601i	1.38495	−	0.721779i
$31$	300.023	−	519.656i	0.312199	−	0.540745i	−0.666639	−	0.745381i	$-0.732268\pi$
$31$	300.023	−	519.656i	0.312199	−	0.540745i	0.978838	+	0.204636i	$0.0656011\pi$
$32$	645.472	−	1117.99i	0.630344	−	1.09179i
$33$	−1470.05	−	18.4484i	−1.34990	−	0.0169407i
$34$	801.696	+	1388.58i	0.693508	+	1.20119i
$35$	248.689	+	153.920i	0.203012	+	0.125649i
$36$	−1864.43	−	46.8029i	−1.43860	−	0.0361134i
$37$			751.406i			0.548872i	0.961605	+	0.274436i	$0.0884912\pi$
$37$			751.406i			0.548872i	−0.961605	+	0.274436i	$0.911509\pi$
$38$	1933.41	+	3348.77i	1.33893	+	2.31909i
$39$	−245.846	−	438.433i	−0.161635	−	0.288253i
$40$	−519.213	−	966.479i	−0.324508	−	0.604049i
$41$	−2039.87	−	1177.72i	−1.21348	−	0.700606i	−0.249968	−	0.968254i	$-0.580420\pi$
$41$	−2039.87	−	1177.72i	−1.21348	−	0.700606i	−0.963517	+	0.267648i	$0.913754\pi$
$42$	−321.695	−	573.699i	−0.182367	−	0.325226i
$43$	1719.96	−	993.020i	0.930211	−	0.537058i	0.0433329	−	0.999061i	$-0.486202\pi$
$43$	1719.96	−	993.020i	0.930211	−	0.537058i	0.886878	+	0.462003i	$0.152869\pi$
$44$			3761.15i			1.94274i
$45$	1108.59	−	1694.60i	0.547452	−	0.836837i
$46$	4118.32			1.94628
$47$	433.754	+	751.284i	0.196358	+	0.340101i	0.947345	−	0.320216i	$-0.103755\pi$
$47$	433.754	+	751.284i	0.196358	+	0.340101i	−0.750987	+	0.660317i	$0.770422\pi$
$48$	10.6445	−	848.199i	0.00462001	−	0.368142i
$49$	−1132.07	+	1960.80i	−0.471499	+	0.816661i
$50$	3897.05	+	238.949i	1.55882	+	0.0955795i
$51$	1985.86	+	1180.01i	0.763500	+	0.453675i
$52$	−1113.67	+	642.980i	−0.411862	+	0.237788i
$53$	−3196.69			−1.13802			−0.569009	−	0.822332i	$-0.692673\pi$
$53$	−3196.69			−1.13802			−0.569009	+	0.822332i	$0.692673\pi$
$54$	−4026.84	+	2126.97i	−1.38095	+	0.729415i
$55$	−3472.49	−	2149.21i	−1.14793	−	0.710481i
$56$	−444.612	+	256.697i	−0.141777	+	0.0818550i
$57$	4789.21	+	2845.78i	1.47406	+	0.875893i
$58$	−766.185	−	442.357i	−0.227760	−	0.131497i
$59$	−2390.76	−	1380.31i	−0.686803	−	0.396526i	0.115610	−	0.993295i	$-0.463118\pi$
$59$	−2390.76	−	1380.31i	−0.686803	−	0.396526i	−0.802413	+	0.596769i	$0.796451\pi$
$60$	−4370.57	−	2781.51i	−1.21405	−	0.772641i
$61$	48.4383	+	83.8977i	0.0130176	+	0.0225471i	0.872461	−	0.488684i	$-0.162523\pi$
$61$	48.4383	+	83.8977i	0.0130176	+	0.0225471i	−0.859443	+	0.511231i	$0.829190\pi$
$62$	−3748.49			−0.975153
$63$	−808.494	−	494.243i	−0.203702	−	0.124526i
$64$	−6556.49			−1.60071
$65$	42.7461	−	1395.62i	0.0101174	−	0.330323i
$66$	4491.87	+	8010.65i	1.03119	+	1.83899i
$67$	3757.13	+	2169.18i	0.836963	+	0.483221i	0.856231	−	0.516594i	$-0.172800\pi$
$67$	3757.13	+	2169.18i	0.836963	+	0.483221i	−0.0192680	+	0.999814i	$0.506134\pi$
$68$	2954.86	−	5117.96i	0.639026	−	1.10683i
$69$	5175.15	−	2901.91i	1.08699	−	0.609516i
$70$	55.9341	−	1826.19i	0.0114151	−	0.372692i
$71$		−	8119.50i		−	1.61069i	−0.592805	−	0.805346i	$-0.701979\pi$
$71$		−	8119.50i		−	1.61069i	0.592805	−	0.805346i	$-0.298021\pi$
$72$	1699.51	+	3122.05i	0.327838	+	0.602248i
$73$			2097.20i			0.393545i	0.980449	+	0.196772i	$0.0630460\pi$
$73$			2097.20i			0.393545i	−0.980449	+	0.196772i	$0.936954\pi$
$74$	4065.15	−	2347.01i	0.742357	−	0.428600i
$75$	5065.48	−	2445.73i	0.900529	−	0.434796i
$76$	7126.10	−	12342.8i	1.23374	−	2.13690i
$77$	−955.501	+	1654.98i	−0.161157	+	0.279132i
$78$	−1604.05	+	2699.49i	−0.263650	+	0.443703i
$79$	−929.960	−	1610.74i	−0.149008	−	0.258090i	0.781853	−	0.623463i	$-0.214275\pi$
$79$	−929.960	−	1610.74i	−0.149008	−	0.258090i	−0.930861	+	0.365373i	$0.880941\pi$
$80$	1240.07	−	2003.58i	0.193760	−	0.313060i
$81$	−3561.46	+	5510.24i	−0.542823	+	0.839847i
$82$			14714.4i			2.18834i
$83$	−6081.60	−	10533.6i	−0.882799	−	1.52905i	−0.848216	−	0.529650i	$-0.822323\pi$
$83$	−6081.60	−	10533.6i	−0.882799	−	1.52905i	−0.0345824	−	0.999402i	$-0.511010\pi$
$84$	−1238.38	+	2084.09i	−0.175507	+	0.295365i
$85$	3036.70	+	5652.60i	0.420304	+	0.782367i
$86$	−10744.6	−	6203.39i	−1.45276	−	0.838749i
$87$	−1274.50	−	15.9944i	−0.168384	−	0.00211315i
$88$	6208.20	−	3584.30i	0.801678	−	0.462849i
$89$			10695.7i			1.35030i	0.737681	+	0.675150i	$0.235921\pi$
$89$			10695.7i			1.35030i	−0.737681	+	0.675150i	$0.764079\pi$
$90$	−12630.5	−	704.465i	−1.55932	−	0.0869710i
$91$	−653.383			−0.0789015
$92$	−7589.57	−	13145.5i	−0.896688	−	1.55311i
$93$	−4710.42	+	2641.31i	−0.544620	+	0.305389i
$94$	2709.66	−	4693.26i	0.306661	−	0.531153i
$95$	7323.46	+	13632.1i	0.811464	+	1.51048i
$96$	−10134.0	+	5682.53i	−1.09961	+	0.616594i
$97$	5624.85	−	3247.51i	0.597816	−	0.345149i	−0.170366	−	0.985381i	$-0.554495\pi$
$97$	5624.85	−	3247.51i	0.597816	−	0.345149i	0.768182	+	0.640232i	$0.221162\pi$
$98$	14144.1			1.47273
$99$	11289.1	+	6901.20i	1.15184	+	0.704132i
$100$	−6419.09	−	12879.6i	−0.641909	−	1.28796i
$101$	−12212.2	+	7050.72i	−1.19716	+	0.691179i	−0.959920	−	0.280273i	$-0.909575\pi$
$101$	−12212.2	+	7050.72i	−1.19716	+	0.691179i	−0.237237	+	0.971452i	$0.576242\pi$
$102$	181.082	−	14429.4i	0.0174051	−	1.38691i
$103$	−16916.7	−	9766.87i	−1.59456	−	0.920621i	−0.992510	−	0.122164i	$-0.961017\pi$
$103$	−16916.7	−	9766.87i	−1.59456	−	0.920621i	−0.602052	−	0.798457i	$-0.705650\pi$
$104$	2122.62	+	1225.50i	0.196248	+	0.113304i
$105$	−1216.51	−	2334.24i	−0.110341	−	0.211722i
$106$	9984.85	+	17294.3i	0.888648	+	1.53918i
$107$	−2000.10			−0.174697			−0.0873484	−	0.996178i	$-0.527839\pi$
$107$	−2000.10			−0.174697			−0.0873484	+	0.996178i	$0.527839\pi$
$108$	14210.2	+	8933.75i	1.21830	+	0.765925i
$109$	−612.947			−0.0515905			−0.0257952	−	0.999667i	$-0.508212\pi$
$109$	−612.947			−0.0515905			−0.0257952	+	0.999667i	$0.508212\pi$
$110$	−781.017	+	25499.4i	−0.0645469	+	2.10739i
$111$	3454.55	−	5813.74i	0.280379	−	0.471856i
$112$	−954.901	−	551.312i	−0.0761241	−	0.0439503i
$113$	−5114.57	+	8858.70i	−0.400546	+	0.693766i	−0.993792	−	0.111255i	$-0.964513\pi$
$113$	−5114.57	+	8858.70i	−0.400546	+	0.693766i	0.593246	+	0.805021i	$0.297846\pi$
$114$	436.708	−	34798.7i	0.0336032	−	2.67765i
$115$	16473.5	+	504.564i	1.24563	+	0.0381523i
$116$			3260.84i			0.242334i
$117$	−113.528	+	4522.49i	−0.00829340	+	0.330374i
$118$			17245.5i			1.23855i
$119$	2600.38	−	1501.33i	0.183630	−	0.106019i
$120$	−426.112	+	9864.84i	−0.0295911	+	0.685059i
$121$	6021.31	−	10429.2i	0.411264	−	0.712330i
$122$	302.594	−	524.108i	0.0203302	−	0.0352129i
$123$	10368.3	+	18490.4i	0.685323	+	1.22218i
$124$	6908.01	+	11965.0i	0.449272	+	0.778163i
$125$	15559.1	+	1433.26i	0.995784	+	0.0917287i
$126$	−148.554	+	5917.77i	−0.00935714	+	0.372749i
$127$		−	12148.6i		−	0.753217i	−0.926373	−	0.376608i	$-0.877090\pi$
$127$		−	12148.6i		−	0.753217i	0.926373	−	0.376608i	$-0.122910\pi$
$128$	10151.6	+	17583.1i	0.619606	+	1.07319i
$129$	−17872.9	−	224.297i	−1.07403	−	0.0134786i
$130$	−7683.87	+	4127.94i	−0.454667	+	0.244257i
$131$	18790.7	+	10848.8i	1.09497	+	0.632179i	0.934894	−	0.354926i	$-0.115494\pi$
$131$	18790.7	+	10848.8i	1.09497	+	0.632179i	0.160072	+	0.987105i	$0.448827\pi$
$132$	17291.7	−	29100.6i	0.992407	−	1.67014i
$133$	6271.23	−	3620.70i	0.354527	−	0.204686i
$134$		−	27101.7i		−	1.50934i
$135$	−16368.1	+	8014.65i	−0.898115	+	0.439761i
$136$	−11263.7			−0.608980
$137$	−12652.3	−	21914.5i	−0.674108	−	1.16759i	−0.976729	−	0.214478i	$-0.931195\pi$
$137$	−12652.3	−	21914.5i	−0.674108	−	1.16759i	0.302621	−	0.953111i	$-0.402138\pi$
$138$	−31864.0	−	18933.8i	−1.67318	−	0.994212i
$139$	9215.64	−	15962.0i	0.476975	−	0.826145i	−0.522677	−	0.852531i	$-0.675066\pi$
$139$	9215.64	−	15962.0i	0.476975	−	0.826145i	0.999652	+	0.0263857i	$0.00839980\pi$
$140$	−5932.21	+	3186.91i	−0.302664	+	0.162597i
$141$	97.9738	−	7806.95i	0.00492801	−	0.392684i
$142$	−43926.9	+	25361.2i	−2.17848	+	1.25775i
$143$	9123.29			0.446149
$144$	−3981.91	+	6513.70i	−0.192029	+	0.314125i
$145$	−3010.58	−	1863.32i	−0.143191	−	0.0886240i
$146$	11346.0	−	6550.60i	0.532275	−	0.307309i
$147$	17773.7	−	9966.38i	0.822513	−	0.461214i
$148$	−14983.2	−	8650.54i	−0.684038	−	0.394929i
$149$	−4718.18	−	2724.04i	−0.212521	−	0.122699i	0.389961	−	0.920831i	$-0.372488\pi$
$149$	−4718.18	−	2724.04i	−0.212521	−	0.122699i	−0.602483	+	0.798132i	$0.705822\pi$
$150$	−29053.5	−	19765.3i	−1.29127	−	0.878457i
$151$	−5918.21	−	10250.6i	−0.259559	−	0.449570i	0.706565	−	0.707649i	$-0.250244\pi$
$151$	−5918.21	−	10250.6i	−0.259559	−	0.449570i	−0.966124	+	0.258079i	$0.916911\pi$
$152$	−27164.1			−1.17573
$153$	−9939.87	−	18259.8i	−0.424618	−	0.780034i
$154$	11938.0			0.503374
$155$	−14994.1	−	459.253i	−0.624105	−	0.0191156i
$156$	11572.7	+	145.233i	0.475539	+	0.00596781i
$157$	11987.0	+	6920.68i	0.486307	+	0.280769i	0.723041	−	0.690805i	$-0.242744\pi$
$157$	11987.0	+	6920.68i	0.486307	+	0.280769i	−0.236734	+	0.971574i	$0.576077\pi$
$158$	−5809.46	+	10062.3i	−0.232713	+	0.403071i
$159$	24733.3	+	14696.6i	0.978334	+	0.581331i
$160$	−32258.5	−	988.040i	−1.26010	−	0.0385953i
$161$		−	7712.36i		−	0.297533i
$162$	40934.9	+	2056.48i	1.55978	+	0.0783599i
$163$		−	6615.52i		−	0.248994i	−0.992220	−	0.124497i	$-0.960268\pi$
$163$		−	6615.52i		−	0.248994i	0.992220	−	0.124497i	$-0.0397317\pi$
$164$	46967.8	−	27116.9i	1.74627	−	1.00821i
$165$	16986.3	+	32593.3i	0.623922	+	1.19718i
$166$	−37991.7	+	65803.6i	−1.37871	+	2.38799i
$167$	−5567.71	+	9643.56i	−0.199638	+	0.345784i	−0.948411	−	0.317043i	$-0.897310\pi$
$167$	−5567.71	+	9643.56i	−0.199638	+	0.345784i	0.748773	+	0.662827i	$0.230643\pi$
$168$	4620.18	+	57.9812i	0.163697	+	0.00205432i
$169$	−12720.8	−	22033.1i	−0.445392	−	0.771442i
$170$	21095.8	−	34084.6i	0.729957	−	1.17940i
$171$	−23971.5	−	44036.4i	−0.819792	−	1.50598i
$172$			45728.4i			1.54571i
$173$	8883.33	+	15386.4i	0.296813	+	0.514096i	0.975405	−	0.220420i	$-0.0707427\pi$
$173$	8883.33	+	15386.4i	0.296813	+	0.514096i	−0.678592	+	0.734516i	$0.737409\pi$
$174$	3894.37	+	6945.08i	0.128629	+	0.229392i
$175$	447.478	−	7298.00i	0.0146115	−	0.238302i
$176$	13333.4	+	7698.07i	0.430444	+	0.248517i
$177$	12151.8	+	21671.0i	0.387876	+	0.691725i
$178$	57864.4	−	33408.0i	1.82630	−	1.05441i
$179$			26305.1i			0.820983i	0.911864	+	0.410492i	$0.134643\pi$
$179$			26305.1i			0.820983i	−0.911864	+	0.410492i	$0.865357\pi$
$180$	21027.9	+	41614.4i	0.649010	+	1.28440i
$181$	−34338.0			−1.04814			−0.524069	−	0.851676i	$-0.675587\pi$
$181$	−34338.0			−1.04814			−0.524069	+	0.851676i	$0.675587\pi$
$182$	2040.84	+	3534.84i	0.0616121	+	0.106715i
$183$	10.9410	−	871.821i	0.000326703	−	0.0260331i
$184$	−14465.4	+	25054.9i	−0.427264	+	0.740042i
$185$	16548.3	−	8890.13i	0.483516	−	0.259755i
$186$	29002.6	+	17233.5i	0.838322	+	0.498135i
$187$	−36309.6	+	20963.4i	−1.03834	+	0.599484i
$188$	−19974.3			−0.565140
$189$	3983.18	+	7541.05i	0.111508	+	0.211110i
$190$	50875.7	−	82200.2i	1.40930	−	2.27701i
$191$	28521.7	−	16467.0i	0.781822	−	0.451385i	−0.0552534	−	0.998472i	$-0.517597\pi$
$191$	28521.7	−	16467.0i	0.781822	−	0.451385i	0.837076	+	0.547087i	$0.184263\pi$
$192$	50728.5	+	30143.2i	1.37610	+	0.817685i
$193$	−22892.6	−	13217.0i	−0.614582	−	0.354829i	0.160174	−	0.987089i	$-0.448794\pi$
$193$	−22892.6	−	13217.0i	−0.614582	−	0.354829i	−0.774757	+	0.632259i	$0.782128\pi$
$194$	−35138.4	−	20287.2i	−0.933638	−	0.539036i
$195$	−6747.01	+	10601.6i	−0.177436	+	0.278805i
$196$	−26065.8	−	45147.3i	−0.678515	−	1.17522i
$197$	−3784.70			−0.0975212			−0.0487606	−	0.998810i	$-0.515527\pi$
$197$	−3784.70			−0.0975212			−0.0487606	+	0.998810i	$0.515527\pi$
$198$	2074.28	−	82630.7i	0.0529100	−	2.10771i
$199$	26809.9			0.677002			0.338501	−	0.940966i	$-0.390080\pi$
$199$	26809.9			0.677002			0.338501	+	0.940966i	$0.390080\pi$
$200$	−15141.9	+	22869.4i	−0.378549	+	0.571736i
$201$	−19096.7	−	34056.4i	−0.472680	−	0.842960i
$202$	76289.5	+	44045.8i	1.86966	+	1.07945i
$203$	−828.401	+	1434.83i	−0.0201024	+	0.0348184i
$204$	−46391.8	+	26013.6i	−1.11476	+	0.625087i
$205$	−1802.76	+	58858.3i	−0.0428974	+	1.40055i
$206$			122027.i			2.87556i
$207$	−53382.3	−	1340.06i	−1.24582	−	0.0312740i
$208$			5264.03i			0.121672i
$209$	−87566.2	+	50556.4i	−2.00467	+	1.15740i
$210$	−8828.59	+	13872.3i	−0.200195	+	0.314566i
$211$	−6063.80	+	10502.8i	−0.136201	+	0.235907i	−0.926056	−	0.377387i	$-0.876823\pi$
$211$	−6063.80	+	10502.8i	−0.136201	+	0.235907i	0.789855	+	0.613294i	$0.210156\pi$
$212$	36801.8	−	63742.5i	0.818836	−	1.41827i
$213$	−37329.0	+	62821.8i	−0.822787	+	1.38468i
$214$	6247.31	+	10820.7i	0.136416	+	0.236280i
$215$	−42218.8	−	26130.3i	−0.913334	−	0.565284i
$216$	1204.10	−	31969.2i	0.0258081	−	0.685212i
$217$			7019.78i			0.149075i
$218$	1914.54	+	3316.07i	0.0402857	+	0.0697768i
$219$	9641.78	−	16226.3i	0.201034	−	0.338324i
$220$	82832.4	−	44499.4i	1.71141	−	0.919408i
$221$	−12414.5	−	7167.50i	−0.254181	−	0.146752i
$222$	−42242.9	−	530.130i	−0.857133	−	0.0107566i
$223$	72090.3	−	41621.4i	1.44966	−	0.836964i	0.451203	−	0.892421i	$-0.350995\pi$
$223$	72090.3	−	41621.4i	1.44966	−	0.836964i	0.998461	+	0.0554578i	$0.0176618\pi$
$224$			15102.4i			0.300988i
$225$	−50436.4	−	4365.35i	−0.996275	−	0.0862291i
$226$	63901.4			1.25110
$227$	−7195.28	−	12462.6i	−0.139636	−	0.241856i	0.787723	−	0.616029i	$-0.211260\pi$
$227$	−7195.28	−	12462.6i	−0.139636	−	0.241856i	−0.927359	+	0.374173i	$0.877926\pi$
$228$	−111881.	+	62735.9i	−2.15222	+	1.20683i
$229$	23945.3	−	41474.5i	0.456614	−	0.790879i	−0.542165	−	0.840272i	$-0.682395\pi$
$229$	23945.3	−	41474.5i	0.456614	−	0.790879i	0.998779	+	0.0493932i	$0.0157287\pi$
$230$	−48725.1	−	90698.5i	−0.921080	−	1.71453i
$231$	15001.5	−	8411.92i	0.281133	−	0.157642i
$232$	5382.39	−	3107.52i	0.0999998	−	0.0577349i
$233$	34930.9			0.643425			0.321713	−	0.946837i	$-0.395741\pi$
$233$	34930.9			0.643425			0.321713	+	0.946837i	$0.395741\pi$
$234$	24821.5	−	13511.8i	0.453311	−	0.246764i
$235$	11413.8	−	18441.3i	0.206678	−	0.333930i
$236$	55047.1	−	31781.4i	0.988349	−	0.570624i
$237$	−210.054	+	16738.0i	−0.00373968	+	0.297993i
$238$	−16244.6	−	9378.82i	−0.286784	−	0.165575i
$239$	2441.57	+	1409.64i	0.0427438	+	0.0246782i	0.521220	−	0.853423i	$-0.325477\pi$
$239$	2441.57	+	1409.64i	0.0427438	+	0.0246782i	−0.478476	+	0.878101i	$0.658811\pi$
$240$	−18806.0	+	9800.88i	−0.326492	+	0.170154i
$241$	4579.84	+	7932.51i	0.0788526	+	0.136577i	0.902755	−	0.430155i	$-0.141541\pi$
$241$	4579.84	+	7932.51i	0.0788526	+	0.136577i	−0.823903	+	0.566732i	$0.808208\pi$
$242$	−75230.2			−1.28458
$243$	52888.6	−	26259.9i	0.895673	−	0.444713i
$244$	−2230.58			−0.0374660
$245$	56577.0	+	1732.89i	0.942557	+	0.0288694i
$246$	67648.7	−	113847.i	1.11787	−	1.88128i
$247$	−29939.4	−	17285.5i	−0.490738	−	0.283328i
$248$	13166.4	−	22804.9i	0.214074	−	0.370787i
$249$	−1373.68	+	109460.i	−0.0221557	+	1.76546i
$250$	−40844.9	−	88652.5i	−0.653518	−	1.41844i
$251$			8151.50i			0.129387i	0.997905	+	0.0646934i	$0.0206069\pi$
$251$			8151.50i			0.129387i	−0.997905	+	0.0646934i	$0.979393\pi$
$252$	19163.1	−	10431.6i	0.301761	−	0.164266i
$253$			107689.i			1.68240i
$254$	−65724.8	+	37946.2i	−1.01874	+	0.588168i
$255$	2492.18	−	57696.1i	0.0383265	−	0.887291i
$256$	10965.2	−	18992.3i	0.167316	−	0.289799i
$257$	−7267.83	+	12588.3i	−0.110037	+	0.190590i	−0.915785	−	0.401669i	$-0.868430\pi$
$257$	−7267.83	+	12588.3i	−0.110037	+	0.190590i	0.805748	+	0.592259i	$0.201764\pi$
$258$	54612.6	+	97394.2i	0.820453	+	1.46317i
$259$	−4395.25	−	7612.79i	−0.0655215	−	0.113487i
$260$	27336.7	+	16919.3i	0.404389	+	0.250286i
$261$	9787.47	+	5983.21i	0.143678	+	0.0878321i
$262$		−	135545.i		−	1.97461i
$263$	−4565.64	−	7907.92i	−0.0660070	−	0.114328i	0.831133	−	0.556073i	$-0.187693\pi$
$263$	−4565.64	−	7907.92i	−0.0660070	−	0.114328i	−0.897140	+	0.441746i	$0.854359\pi$
$264$	−64512.4	−	809.602i	−0.925626	−	0.0116162i
$265$	37821.1	+	70401.2i	0.538570	+	1.00251i
$266$	−39176.3	−	22618.5i	−0.553682	−	0.319668i
$267$	49173.1	−	82754.3i	0.689771	−	1.16083i
$268$	−86507.5	+	49945.1i	−1.20444	+	0.695382i
$269$		−	121211.i		−	1.67508i	−0.546373	−	0.837542i	$-0.683992\pi$
$269$		−	121211.i		−	1.67508i	0.546373	−	0.837542i	$-0.316008\pi$
$270$	94485.5	+	63518.8i	1.29610	+	0.871314i
$271$	−77369.8			−1.05350			−0.526748	−	0.850021i	$-0.676589\pi$
$271$	−77369.8			−1.05350			−0.526748	+	0.850021i	$0.676589\pi$
$272$	−12095.6	−	20950.2i	−0.163490	−	0.283172i
$273$	5055.32	+	3003.90i	0.0678302	+	0.0403051i
$274$	−79039.0	+	136900.i	−1.05279	+	1.82348i
$275$	−6248.22	+	101903.i	−0.0826210	+	1.34748i
$276$	−1714.29	+	136602.i	−0.0225043	+	1.79324i
$277$	42196.8	−	24362.3i	0.549946	−	0.317512i	−0.199154	−	0.979968i	$-0.563819\pi$
$277$	42196.8	−	24362.3i	0.549946	−	0.317512i	0.749100	+	0.662457i	$0.230486\pi$
$278$	−115140.			−1.48983
$279$	48588.5	+	1219.72i	0.624201	+	0.0156694i
$280$	10913.6	+	6754.71i	0.139205	+	0.0861570i
$281$	73895.8	−	42663.8i	0.935852	−	0.540314i	0.0471945	−	0.998886i	$-0.484972\pi$
$281$	73895.8	−	42663.8i	0.935852	−	0.540314i	0.888658	+	0.458571i	$0.151639\pi$
$282$	−42542.1	+	23855.0i	−0.534959	+	0.299972i
$283$	−20687.9	−	11944.2i	−0.258311	−	0.149136i	0.365253	−	0.930908i	$-0.380983\pi$
$283$	−20687.9	−	11944.2i	−0.258311	−	0.149136i	−0.623564	+	0.781772i	$0.714316\pi$
$284$	161904.	+	93475.4i	2.00734	+	1.15894i
$285$	6010.28	−	139143.i	0.0739955	−	1.71306i
$286$	−28496.6	−	49357.5i	−0.348386	−	0.603422i
$287$	27555.6			0.334539
$288$	104534.	+	2624.11i	1.26029	+	0.0316371i
$289$	−17643.5			−0.211247
$290$	−677.127	+	22107.5i	−0.00805145	+	0.262871i
$291$	−58450.6	−	733.528i	−0.690244	−	0.00866225i
$292$	−41818.5	−	24143.9i	−0.490459	−	0.283167i
$293$	65662.9	−	113732.i	0.764865	−	1.32479i	−0.175452	−	0.984488i	$-0.556139\pi$
$293$	65662.9	−	113732.i	0.764865	−	1.32479i	0.940318	−	0.340298i	$-0.110528\pi$
$294$	−109435.	−	65026.7i	−1.26608	−	0.752310i
$295$	−2112.87	+	68983.0i	−0.0242789	+	0.792680i
$296$			32975.2i			0.376360i
$297$	−55617.8	−	105297.i	−0.630523	−	1.19372i
$298$			34034.2i			0.383251i
$299$	−31886.7	+	18409.8i	−0.356670	+	0.205924i
$300$	−9547.93	+	129163.i	−0.106088	+	1.43514i
$301$	−11617.1	+	20121.3i	−0.128222	+	0.222087i
$302$	−36971.0	+	64035.7i	−0.405366	+	0.702115i
$303$	126903.	+	1592.57i	1.38225	+	0.0173466i
$304$	−29170.4	−	50524.7i	−0.315643	−	0.546709i
$305$	1274.60	−	2059.39i	0.0137017	−	0.0221380i
$306$	−67739.5	+	110810.i	−0.723434	+	1.18341i
$307$			53610.8i			0.568821i	0.958703	+	0.284411i	$0.0917979\pi$
$307$			53610.8i			0.568821i	−0.958703	+	0.284411i	$0.908202\pi$
$308$	−22000.3	−	38105.7i	−0.231914	−	0.401687i
$309$	85984.3	+	153341.i	0.900539	+	1.60599i
$310$	44349.5	+	82553.6i	0.461494	+	0.859038i
$311$	−98969.6	−	57140.1i	−1.02325	−	0.590773i	−0.108205	−	0.994129i	$-0.534510\pi$
$311$	−98969.6	−	57140.1i	−1.02325	−	0.590773i	−0.915043	+	0.403356i	$0.867844\pi$
$312$	−10788.9	−	19240.5i	−0.110832	−	0.197655i
$313$	−56425.5	+	32577.3i	−0.575953	+	0.332526i	−0.759523	−	0.650480i	$-0.774568\pi$
$313$	−56425.5	+	32577.3i	−0.575953	+	0.332526i	0.183571	+	0.983007i	$0.441234\pi$
$314$		−	86466.9i		−	0.876982i
$315$	−1319.25	+	23653.2i	−0.0132955	+	0.238379i
$316$	42824.5			0.428863
$317$	25542.8	+	44241.5i	0.254186	+	0.440262i	0.964674	−	0.263447i	$-0.0848593\pi$
$317$	25542.8	+	44241.5i	0.254186	+	0.440262i	−0.710488	+	0.703709i	$0.751526\pi$
$318$	2255.32	−	179713.i	0.0223025	−	1.77716i
$319$	11567.1	−	20034.8i	0.113669	−	0.196881i
$320$	77571.9	+	144395.i	0.757538	+	1.41010i
$321$	15475.1	+	9195.38i	0.150184	+	0.0892400i
$322$	−41724.3	+	24089.5i	−0.402418	+	0.232336i
$323$	158874.			1.52281
$324$	−68873.9	−	134452.i	−0.656092	−	1.28079i
$325$	−31241.6	+	15570.6i	−0.295779	+	0.147414i
$326$	−35790.3	+	20663.5i	−0.336768	+	0.194433i
$327$	4742.46	+	2817.99i	0.0443515	+	0.0263539i
$328$	−89518.9	−	51683.7i	−0.832084	−	0.480404i
$329$	−8789.06	−	5074.37i	−0.0811990	−	0.0468803i
$330$	123275.	−	193702.i	1.13200	−	1.77871i
$331$	73770.8	+	127775.i	0.673331	+	1.16624i	0.976954	+	0.213451i	$0.0684703\pi$
$331$	73770.8	+	127775.i	0.673331	+	1.16624i	−0.303623	+	0.952792i	$0.598196\pi$
$332$	280057.			2.54080
$333$	−53456.8	+	29099.6i	−0.482075	+	0.262421i
$334$	69562.9			0.623570
$335$	3320.41	−	108408.i	0.0295871	−	0.965988i
$336$	4853.58	+	8655.70i	0.0429916	+	0.0766697i
$337$	102326.	+	59078.0i	0.901003	+	0.520194i	0.877526	−	0.479530i	$-0.159193\pi$
$337$	102326.	+	59078.0i	0.901003	+	0.520194i	0.0234776	+	0.999724i	$0.492526\pi$
$338$	−79467.0	+	137641.i	−0.695590	+	1.20480i
$339$	80299.7	−	45027.1i	0.698738	−	0.391809i
$340$	−147674.	−	4523.08i	−1.27745	−	0.0391270i
$341$		−	98018.3i		−	0.842944i
$342$	−163364.	+	267235.i	−1.39670	+	2.28476i
$343$		−	54576.2i		−	0.463890i
$344$	75479.9	−	43578.3i	0.637844	−	0.368259i
$345$	−125138.	−	79639.9i	−1.05136	−	0.669103i
$346$	55494.1	−	96118.6i	0.463548	−	0.802888i
$347$	−53312.9	+	92340.6i	−0.442765	+	0.766891i	−0.997894	−	0.0648732i	$-0.979336\pi$
$347$	−53312.9	+	92340.6i	−0.442765	+	0.766891i	0.555129	+	0.831765i	$0.312669\pi$
$348$	14991.6	−	25229.6i	0.123791	−	0.208330i
$349$	18479.4	+	32007.3i	0.151718	+	0.262784i	0.931859	−	0.362820i	$-0.118186\pi$
$349$	18479.4	+	32007.3i	0.151718	+	0.262784i	−0.780141	+	0.625604i	$0.784853\pi$
$350$	−40880.3	+	20374.4i	−0.333716	+	0.166322i
$351$	21670.3	−	34469.2i	0.175894	−	0.279780i
$352$		−	210877.i		−	1.70194i
$353$	−10960.5	−	18984.1i	−0.0879589	−	0.152349i	0.818689	−	0.574237i	$-0.194701\pi$
$353$	−10960.5	−	18984.1i	−0.0879589	−	0.152349i	−0.906648	+	0.421887i	$0.861368\pi$
$354$	79285.5	−	133431.i	0.632685	−	1.06476i
$355$	−178817.	+	96064.4i	−1.41890	+	0.762265i
$356$	−213274.	−	123134.i	−1.68282	−	0.971579i
$357$	−27021.9	−	339.112i	−0.212021	−	0.00266077i
$358$	142312.	−	82164.0i	1.11039	−	0.641085i
$359$			118640.i			0.920536i	0.887780	+	0.460268i	$0.152247\pi$
$359$			118640.i			0.920536i	−0.887780	+	0.460268i	$0.847753\pi$
$360$	48650.0	−	74366.7i	0.375386	−	0.573817i
$361$	252827.			1.94003
$362$	107255.	+	185771.i	0.818464	+	1.41762i
$363$	−94535.6	+	53009.7i	−0.717434	+	0.402293i
$364$	7522.05	−	13028.6i	0.0567719	−	0.0983318i
$365$	46187.0	−	24812.6i	0.346684	−	0.186246i
$366$	−4750.78	+	2663.94i	−0.0354652	+	0.0198867i
$367$	−51171.2	+	29543.7i	−0.379921	+	0.219347i	−0.677784	−	0.735261i	$-0.737059\pi$
$367$	−51171.2	+	29543.7i	−0.379921	+	0.219347i	0.297863	+	0.954609i	$0.403726\pi$
$368$	−62135.3			−0.458820
$369$	4787.91	−	190730.i	0.0351636	−	1.40077i
$370$	−99784.8	−	61759.2i	−0.728888	−	0.451126i
$371$	32386.9	−	18698.6i	0.235300	−	0.135851i
$372$	1560.34	−	124334.i	0.0112754	−	0.898474i
$373$	−151372.	−	87394.5i	−1.08800	−	0.628155i	−0.154954	−	0.987922i	$-0.549523\pi$
$373$	−151372.	−	87394.5i	−1.08800	−	0.628155i	−0.933042	+	0.359767i	$0.882856\pi$
$374$	226826.	+	130958.i	1.62162	+	0.936243i
$375$	−113794.	−	82621.7i	−0.809201	−	0.587532i
$376$	19035.1	+	32969.8i	0.134642	+	0.233207i
$377$	7909.72			0.0556517
$378$	28356.0	−	45103.6i	0.198455	−	0.315666i
$379$	−113098.			−0.787366			−0.393683	−	0.919246i	$-0.628799\pi$
$379$	−113098.			−0.787366			−0.393683	+	0.919246i	$0.628799\pi$
$380$	−356138.	−	10908.1i	−2.46633	−	0.0755408i
$381$	−55852.8	+	93995.8i	−0.384764	+	0.647528i
$382$	−178175.	−	102869.i	−1.22101	−	0.704950i
$383$	−88361.6	+	153047.i	−0.602374	+	1.04334i	0.390087	+	0.920778i	$0.372445\pi$
$383$	−88361.6	+	153047.i	−0.602374	+	1.04334i	−0.992461	+	0.122564i	$0.960888\pi$
$384$	2292.99	−	182715.i	0.0155503	−	1.23911i
$385$	47752.6	+	1462.61i	0.322163	+	0.00986749i
$386$			165133.i			1.10831i
$387$	137254.	+	83905.5i	0.916441	+	0.560232i
$388$			149547.i			0.993379i
$389$	−137462.	+	79363.5i	−0.908410	+	0.524471i	−0.879919	−	0.475123i	$-0.842404\pi$
$389$	−137462.	+	79363.5i	−0.908410	+	0.524471i	−0.0284910	+	0.999594i	$0.509070\pi$
$390$	78429.3	+	3387.75i	0.515643	+	0.0222732i
$391$	84603.3	−	146537.i	0.553393	−	0.958506i
$392$	−49680.5	+	86049.1i	−0.323306	+	0.559982i
$393$	−95509.6	−	170328.i	−0.618389	−	1.10281i
$394$	11821.5	+	20475.4i	0.0761518	+	0.131899i
$395$	−24470.9	+	39537.8i	−0.156840	+	0.253407i
$396$	−267577.	+	145658.i	−1.70631	+	0.928844i
$397$			17831.6i			0.113138i	0.998399	+	0.0565692i	$0.0180161\pi$
$397$			17831.6i			0.113138i	−0.998399	+	0.0565692i	$0.981984\pi$
$398$	−83740.7	−	145043.i	−0.528653	−	0.915654i
$399$	−65167.4	−	817.821i	−0.409340	−	0.00513704i
$400$	−58796.9	−	3605.15i	−0.367481	−	0.0225322i
$401$	−11529.4	−	6656.51i	−0.0716999	−	0.0413960i	0.463721	−	0.885981i	$-0.346514\pi$
$401$	−11529.4	−	6656.51i	−0.0716999	−	0.0413960i	−0.535421	+	0.844585i	$0.679847\pi$
$402$	−124599.	+	209690.i	−0.771012	+	1.29755i
$403$	29023.2	−	16756.5i	0.178704	−	0.103175i
$404$		−	324684.i		−	1.98929i
$405$	163490.	+	13241.2i	0.996736	+	0.0807269i
$406$	10350.0			0.0627898
$407$	61371.6	+	106299.i	0.370492	+	0.641710i
$408$	87148.9	+	51784.3i	0.523530	+	0.311084i
$409$	151977.	−	263232.i	0.908515	−	1.57359i	0.0923857	−	0.995723i	$-0.470551\pi$
$409$	151977.	−	263232.i	0.908515	−	1.57359i	0.816129	−	0.577870i	$-0.196116\pi$
$410$	324058.	−	174091.i	1.92777	−	1.03564i
$411$	−2857.83	+	227724.i	−0.0169182	+	1.34811i
$412$	389506.	−	224881.i	2.29467	−	1.32483i
$413$	32295.7			0.189341
$414$	159490.	+	292987.i	0.930533	+	1.70941i
$415$	−160031.	+	258563.i	−0.929196	+	1.50131i
$416$	62440.6	−	36050.1i	0.360812	−	0.208315i
$417$	−144687.	+	81131.5i	−0.832066	+	0.466571i
$418$	547025.	+	315825.i	3.13080	+	1.80757i
$419$	−59656.6	−	34442.8i	−0.339806	−	0.196187i	0.320380	−	0.947289i	$-0.396189\pi$
$419$	−59656.6	−	34442.8i	−0.339806	−	0.196187i	−0.660186	+	0.751102i	$0.729523\pi$
$420$	60550.0	+	2615.46i	0.343254	+	0.0148269i
$421$	32715.1	+	56664.2i	0.184580	+	0.319702i	0.943435	−	0.331558i	$-0.107574\pi$
$421$	32715.1	+	56664.2i	0.184580	+	0.319702i	−0.758855	+	0.651260i	$0.774241\pi$
$422$	75761.1			0.425423
$423$	−36650.1	+	59953.1i	−0.204831	+	0.335067i
$424$	−140286.			−0.780336
$425$	88560.0	−	133755.i	0.490298	−	0.740514i
$426$	456466.	+	5728.45i	2.51530	+	0.0315659i
$427$	−981.496	−	566.667i	−0.00538310	−	0.00310794i
$428$	23026.1	−	39882.4i	0.125699	−	0.217718i
$429$	−70588.3	−	41943.9i	−0.383546	−	0.227905i
$430$	−9495.68	+	310024.i	−0.0513558	+	1.67671i
$431$			95087.7i			0.511882i	0.966692	+	0.255941i	$0.0823852\pi$
$431$			95087.7i			0.511882i	−0.966692	+	0.255941i	$0.917615\pi$
$432$	60755.1	−	32090.8i	0.325548	−	0.171954i
$433$			71258.3i			0.380067i	0.981778	+	0.190033i	$0.0608596\pi$
$433$			71258.3i			0.380067i	−0.981778	+	0.190033i	$0.939140\pi$
$434$	37977.4	−	21926.3i	0.201626	−	0.116409i
$435$	14726.8	+	28257.8i	0.0778268	+	0.149334i
$436$	7056.52	−	12222.3i	0.0371208	−	0.0642952i
$437$	204034.	−	353397.i	1.06841	−	1.85055i
$438$	−117901.	−	1479.61i	−0.614569	−	0.00771257i
$439$	2158.46	+	3738.57i	0.0111999	+	0.0193989i	0.871571	−	0.490269i	$-0.163102\pi$
$439$	2158.46	+	3738.57i	0.0111999	+	0.0193989i	−0.860371	+	0.509668i	$0.829768\pi$
$440$	−152389.	−	94317.1i	−0.787133	−	0.487175i
$441$	−183338.	−	4602.33i	−0.942702	−	0.0236647i
$442$			89550.7i			0.458379i
$443$	103102.	+	178578.i	0.525364	+	0.909957i	0.999564	+	0.0295399i	$0.00940421\pi$
$443$	103102.	+	178578.i	0.525364	+	0.909957i	−0.474199	+	0.880417i	$0.657262\pi$
$444$	76156.5	+	135815.i	0.386315	+	0.688940i
$445$	235554.	−	126544.i	1.18951	−	0.639033i
$446$	−450348.	−	260008.i	−2.26401	−	1.30713i
$447$	23981.6	+	42768.0i	0.120023	+	0.214044i
$448$	66426.4	−	38351.3i	0.330967	−	0.191084i
$449$			65145.6i			0.323141i	0.986861	+	0.161571i	$0.0516560\pi$
$449$			65145.6i			0.323141i	−0.986861	+	0.161571i	$0.948344\pi$
$450$	133921.	+	286499.i	0.661340	+	1.41481i
$451$	−384763.			−1.89165
$452$	−117763.	−	203971.i	−0.576409	−	0.998370i
$453$	−1336.77	+	106519.i	−0.00651419	+	0.519078i
$454$	−44948.9	+	77853.8i	−0.218076	+	0.377718i
$455$	7730.38	+	14389.6i	0.0373403	+	0.0695064i
$456$	210173.	+	124886.i	1.01076	+	0.600597i
$457$	−106732.	+	61621.8i	−0.511049	+	0.295054i	−0.733265	−	0.679943i	$-0.762004\pi$
$457$	−106732.	+	61621.8i	−0.511049	+	0.295054i	0.222216	+	0.974998i	$0.428671\pi$
$458$	−299172.			−1.42623
$459$	−7042.39	+	186977.i	−0.0334268	+	0.887489i
$460$	−199711.	+	322675.i	−0.943816	+	1.52493i
$461$	−54232.6	+	31311.2i	−0.255187	+	0.147332i	−0.622137	−	0.782908i	$-0.713735\pi$
$461$	−54232.6	+	31311.2i	−0.255187	+	0.147332i	0.366950	+	0.930241i	$0.380402\pi$
$462$	−92366.1	−	54884.4i	−0.432742	−	0.257137i
$463$	−310023.	−	178992.i	−1.44621	−	0.834971i	−0.447959	−	0.894054i	$-0.647849\pi$
$463$	−310023.	−	178992.i	−1.44621	−	0.834971i	−0.998253	+	0.0590826i	$0.981182\pi$
$464$	11559.8	+	6674.08i	0.0536928	+	0.0309995i
$465$	113900.	+	72488.1i	0.526768	+	0.335244i
$466$	−109107.	−	188978.i	−0.502434	−	0.870242i
$467$	−246564.			−1.13057			−0.565283	−	0.824897i	$-0.691233\pi$
$467$	−246564.			−1.13057			−0.565283	+	0.824897i	$0.691233\pi$
$468$	−88872.2	−	54328.8i	−0.405765	−	0.248049i
$469$	−50753.2			−0.230737
$470$	−135419.	−	4147.74i	−0.613035	−	0.0187766i
$471$	−60927.5	−	108656.i	−0.274645	−	0.489792i
$472$	−104918.	−	60574.3i	−0.470939	−	0.271897i
$473$	162211.	−	280958.i	0.725033	−	1.25579i
$474$	91209.4	−	51144.6i	0.405960	−	0.227637i
$475$	213576.	−	322572.i	0.946598	−	1.42968i
$476$			69136.1i			0.305134i
$477$	−123798.	−	227420.i	−0.544097	−	0.999521i
$478$		−	17612.0i		−	0.0770822i
$479$	276821.	−	159823.i	1.20650	−	0.696575i	0.244509	−	0.969647i	$-0.421373\pi$
$479$	276821.	−	159823.i	1.20650	−	0.696575i	0.961993	+	0.273072i	$0.0880398\pi$
$480$	245046.	+	155951.i	1.06357	+	0.676872i
$481$	−20983.3	+	36344.2i	−0.0906951	+	0.157089i
$482$	28610.2	−	49554.3i	0.123148	−	0.213298i
$483$	−35457.2	+	59671.7i	−0.151988	+	0.255784i
$484$	138640.	+	240132.i	0.591832	+	1.02508i
$485$	−138070.	−	85454.7i	−0.586969	−	0.363289i
$486$	−307265.	−	204107.i	−1.30089	−	0.864145i
$487$		−	443400.i		−	1.86955i	−0.355235	−	0.934777i	$-0.615599\pi$
$487$		−	443400.i		−	1.86955i	0.355235	−	0.934777i	$-0.384401\pi$
$488$	2125.70	+	3681.82i	0.00892611	+	0.0154605i
$489$	−30414.5	+	51185.2i	−0.127193	+	0.214056i
$490$	−167343.	−	311497.i	−0.696972	−	1.29736i
$491$	277417.	+	160167.i	1.15072	+	0.664370i	0.949063	−	0.315086i	$-0.102033\pi$
$491$	277417.	+	160167.i	1.15072	+	0.664370i	0.201659	+	0.979456i	$0.435367\pi$
$492$	−488065.	−	6125.00i	−2.01627	−	0.0253032i
$493$	−31479.7	+	18174.8i	−0.129520	+	0.0747785i
$494$			215965.i			0.884973i
$495$	18420.9	−	330273.i	0.0751797	−	1.34792i
$496$	56555.4			0.229885
$497$	47493.9	+	82261.8i	0.192276	+	0.333032i
$498$	596476.	−	334467.i	2.40511	−	1.34863i
$499$	84138.0	−	145731.i	0.337902	−	0.585264i	−0.646136	−	0.763223i	$-0.723616\pi$
$499$	84138.0	−	145731.i	0.337902	−	0.585264i	0.984038	+	0.177958i	$0.0569493\pi$
$500$	−207703.	+	293751.i	−0.830813	+	1.17500i
$501$	87414.0	−	49016.4i	0.348262	−	0.195284i
$502$	44100.0	−	25461.2i	0.174997	−	0.101035i
$503$	−273094.			−1.07938			−0.539692	−	0.841863i	$-0.681459\pi$
$503$	−273094.			−1.07938			−0.539692	+	0.841863i	$0.681459\pi$
$504$	−35480.5	−	21689.7i	−0.139678	−	0.0853871i
$505$	299766.	+	185532.i	1.17544	+	0.727505i
$506$	582604.	−	336366.i	2.27548	−	1.31375i
$507$	−2873.31	+	228957.i	−0.0111781	+	0.890714i
$508$	242246.	+	139861.i	0.938704	+	0.541961i
$509$	−344899.	−	199128.i	−1.33124	−	0.768592i	−0.345751	−	0.938326i	$-0.612376\pi$
$509$	−344899.	−	199128.i	−1.33124	−	0.768592i	−0.985490	+	0.169734i	$0.945709\pi$
$510$	−319923.	+	166731.i	−1.23000	+	0.641025i
$511$	−12267.3	−	21247.6i	−0.0469793	−	0.0813705i
$512$	187853.			0.716602
$513$	−16983.8	+	450924.i	−0.0645357	+	1.71344i
$514$	90804.2			0.343700
$515$	−14950.4	+	488114.i	−0.0563687	+	1.84038i
$516$	210234.	−	353807.i	0.789594	−	1.32882i
$517$	122723.	+	70854.2i	0.459140	+	0.265085i
$518$	−27457.1	+	47557.1i	−0.102328	+	0.177237i
$519$	2006.51	−	159887.i	0.00744916	−	0.593580i
$520$	1875.90	−	61246.1i	0.00693749	−	0.226502i
$521$			384980.i			1.41828i	0.705067	+	0.709141i	$0.250917\pi$
$521$			384980.i			1.41828i	−0.705067	+	0.709141i	$0.749083\pi$
$522$	1798.36	−	71639.3i	0.00659989	−	0.262912i
$523$		−	279373.i		−	1.02137i	−0.859769	−	0.510683i	$-0.829392\pi$
$523$		−	279373.i		−	1.02137i	0.859769	−	0.510683i	$-0.170608\pi$
$524$	−432655.	+	249793.i	−1.57572	+	0.909742i
$525$	−37014.4	+	54408.4i	−0.134293	+	0.197400i
$526$	−28521.5	+	49400.7i	−0.103086	+	0.178551i
$527$	−77005.8	+	133378.i	−0.277270	+	0.480245i
$528$	−67771.3	−	120861.i	−0.243096	−	0.433529i
$529$	−77383.7	−	134032.i	−0.276527	−	0.478959i
$530$	262741.	−	424512.i	0.935353	−	1.51126i
$531$	5611.52	−	223539.i	0.0199018	−	0.792802i
$532$			166732.i			0.589111i
$533$	−65776.5	−	113928.i	−0.231535	−	0.401030i
$534$	−601297.	−	7546.01i	−2.10866	−	0.0264628i
$535$	23663.9	+	44048.6i	0.0826757	+	0.153895i
$536$	164880.	+	95193.6i	0.573903	+	0.331343i
$537$	120937.	−	203527.i	0.419381	−	0.705785i
$538$	−655757.	+	378601.i	−2.26557	+	1.30803i
$539$			369850.i			1.27306i
$540$	28624.1	−	418652.i	0.0981624	−	1.43571i
$541$	276109.			0.943377			0.471689	−	0.881765i	$-0.343645\pi$
$541$	276109.			0.943377			0.471689	+	0.881765i	$0.343645\pi$
$542$	241664.	+	418575.i	0.822648	+	1.42487i
$543$	265678.	+	157867.i	0.901066	+	0.535418i
$544$	−165671.	+	286950.i	−0.559820	+	0.969636i
$545$	7251.97	+	13499.0i	0.0244153	+	0.0454474i
$546$	460.973	−	36732.2i	0.00154629	−	0.123215i
$547$	271696.	−	156864.i	0.908046	−	0.524261i	0.0282443	−	0.999601i	$-0.491008\pi$
$547$	271696.	−	156864.i	0.908046	−	0.524261i	0.879802	+	0.475340i	$0.157675\pi$
$548$	582638.			1.94016
$549$	−4092.81	+	6695.11i	−0.0135793	+	0.0222133i
$550$	570818.	−	284491.i	1.88700	−	0.940466i
$551$	−75918.2	+	43831.4i	−0.250059	+	0.144372i
$552$	227110.	−	127349.i	0.745346	−	0.417944i
$553$	18843.6	+	10879.3i	0.0616188	+	0.0355756i
$554$	−263603.	−	152191.i	−0.858877	−	0.495873i
$555$	−168909.	−	7296.02i	−0.548361	−	0.0236865i
$556$	212189.	+	367523.i	0.686395	+	1.18887i
$557$	−37442.2			−0.120684			−0.0603422	−	0.998178i	$-0.519219\pi$
$557$	−37442.2			−0.120684			−0.0603422	+	0.998178i	$0.519219\pi$
$558$	−145167.	−	266676.i	−0.466230	−	0.856477i
$559$	110922.			0.354972
$560$	−843.908	+	27552.7i	−0.00269103	+	0.0878594i
$561$	377311.	+	4735.08i	1.19887	+	0.0150453i
$562$	−461627.	−	266520.i	−1.46157	−	0.843835i
$563$	229254.	−	397080.i	0.723270	−	1.25274i	−0.236412	−	0.971653i	$-0.575971\pi$
$563$	229254.	−	397080.i	0.723270	−	1.25274i	0.959682	−	0.281088i	$-0.0906953\pi$
$564$	154544.	+	91830.9i	0.485841	+	0.288689i
$565$	255609.	+	7829.01i	0.800717	+	0.0245250i
$566$			149230.i			0.465826i
$567$	3851.16	−	76658.7i	0.0119791	−	0.238449i
$568$		−	356321.i		−	1.10445i
$569$	85924.9	−	49608.7i	0.265396	−	0.153226i	−0.361398	−	0.932412i	$-0.617700\pi$
$569$	85924.9	−	49608.7i	0.265396	−	0.153226i	0.626794	+	0.779185i	$0.284367\pi$
$570$	−771544.	+	402097.i	−2.37471	+	1.23760i
$571$	−228171.	+	395203.i	−0.699823	+	1.21213i	0.268705	+	0.963222i	$0.413404\pi$
$571$	−228171.	+	395203.i	−0.699823	+	1.21213i	−0.968528	+	0.248906i	$0.919929\pi$
$572$	−105032.	+	181920.i	−0.321017	+	0.556017i
$573$	−296382.	−	3719.47i	−0.902700	−	0.0113285i
$574$	−86069.8	−	149077.i	−0.261233	−	0.452468i
$575$	−183791.	−	368768.i	−0.555889	−	1.11537i
$576$	−253912.	−	466444.i	−0.765313	−	1.40590i
$577$			319678.i			0.960198i	0.877214	+	0.480099i	$0.159399\pi$
$577$			319678.i			0.960198i	−0.877214	+	0.480099i	$0.840601\pi$
$578$	55109.5	+	95452.5i	0.164957	+	0.285714i
$579$	116359.	+	207510.i	0.347089	+	0.618986i
$580$	71814.1	−	38580.1i	0.213478	−	0.114685i
$581$	123230.	+	71147.0i	0.365060	+	0.210768i
$582$	178602.	+	318512.i	0.527278	+	0.940329i
$583$	−452224.	+	261092.i	−1.33050	+	0.768167i
$584$			92034.9i			0.269853i
$585$	100943.	−	51006.8i	0.294960	−	0.149044i
$586$	−820392.			−2.38905
$587$	−67386.2	−	116716.i	−0.195567	−	0.338731i	0.751520	−	0.659711i	$-0.229321\pi$
$587$	−67386.2	−	116716.i	−0.195567	−	0.338731i	−0.947086	+	0.320980i	$0.895988\pi$
$588$	−5887.59	+	469148.i	−0.0170288	+	1.35692i
$589$	−185711.	+	321661.i	−0.535313	+	0.927189i
$590$	379801.	−	204037.i	1.09107	−	0.586146i
$591$	29282.8	+	17400.0i	0.0838373	+	0.0498165i
$592$	−61333.1	+	35410.7i	−0.175005	+	0.101039i
$593$	135712.			0.385929			0.192965	−	0.981206i	$-0.438190\pi$
$593$	135712.			0.385929			0.192965	+	0.981206i	$0.438190\pi$
$594$	−395940.	+	629790.i	−1.12216	+	1.78494i
$595$	−63830.1	−	39506.0i	−0.180298	−	0.111591i
$596$	108636.	−	62720.9i	0.305830	−	0.176571i
$597$	−207432.	−	123257.i	−0.582007	−	0.345831i
$598$	199196.	+	115006.i	0.557029	+	0.321601i
$599$	99590.5	+	57498.6i	0.277565	+	0.160252i	0.632320	−	0.774707i	$-0.282103\pi$
$599$	99590.5	+	57498.6i	0.277565	+	0.160252i	−0.354756	+	0.934959i	$0.615436\pi$
$600$	222297.	−	107330.i	0.617491	−	0.298138i
$601$	−29970.1	−	51909.8i	−0.0829736	−	0.143714i	0.821552	−	0.570133i	$-0.193108\pi$
$601$	−29970.1	−	51909.8i	−0.0829736	−	0.143714i	−0.904526	+	0.426419i	$0.859775\pi$
$602$	145143.			0.400502
$603$	−8818.60	+	351296.i	−0.0242530	+	0.966137i
$604$	272533.			0.747042
$605$	−300924.	−	9216.97i	−0.822142	−	0.0251813i
$606$	−387765.	−	691526.i	−1.05590	−	1.88306i
$607$	130456.	+	75319.0i	0.354069	+	0.204422i	0.666476	−	0.745526i	$-0.267802\pi$
$607$	130456.	+	75319.0i	0.354069	+	0.204422i	−0.312407	+	0.949948i	$0.601135\pi$
$608$	−399541.	+	692025.i	−1.08082	+	1.87204i
$609$	13006.0	−	7292.97i	0.0350679	−	0.0196639i
$610$	−15122.6	−	463.188i	−0.0406412	−	0.00124479i
$611$			48451.0i			0.129784i
$612$	478536.	+	12012.7i	1.27765	+	0.0320729i
$613$		−	404962.i		−	1.07769i	−0.842405	−	0.538845i	$-0.818861\pi$
$613$		−	404962.i		−	1.07769i	0.842405	−	0.538845i	$-0.181139\pi$
$614$	290038.	−	167453.i	0.769338	−	0.444178i
$615$	284547.	−	447107.i	0.752321	−	1.18212i
$616$	−41931.8	+	72628.0i	−0.110505	+	0.191400i
$617$	−319373.	+	553170.i	−0.838934	+	1.45308i	0.0518531	+	0.998655i	$0.483487\pi$
$617$	−319373.	+	553170.i	−0.838934	+	1.45308i	−0.890787	+	0.454421i	$0.849846\pi$
$618$	561014.	−	944141.i	1.46891	−	2.47207i
$619$	233385.	+	404234.i	0.609104	+	1.05500i	0.991388	+	0.130954i	$0.0418041\pi$
$619$	233385.	+	404234.i	0.609104	+	1.05500i	−0.382284	+	0.924045i	$0.624863\pi$
$620$	181777.	−	293698.i	0.472885	−	0.764044i
$621$	406866.	+	255791.i	1.05504	+	0.663287i
$622$			713908.i			1.84528i
$623$	−62563.1	−	108363.i	−0.161192	−	0.279192i
$624$	24201.1	−	40728.6i	0.0621536	−	0.104600i
$625$	−152520.	−	359619.i	−0.390451	−	0.920624i
$626$	352490.	+	203510.i	0.899493	+	0.519322i
$627$	909943.	+	11419.4i	2.31462	+	0.0290474i
$628$	−275999.	+	159348.i	−0.699823	+	0.404043i
$629$		−	192861.i		−	0.487463i
$630$	132086.	−	66743.3i	0.332793	−	0.168162i
$631$	−392613.			−0.986066			−0.493033	−	0.870011i	$-0.664112\pi$
$631$	−392613.			−0.986066			−0.493033	+	0.870011i	$0.664112\pi$
$632$	−40811.0	−	70686.7i	−0.102175	−	0.176972i
$633$	95202.7	−	53383.8i	0.237598	−	0.133230i
$634$	159566.	−	276376.i	0.396974	−	0.687579i
$635$	−267551.	+	143734.i	−0.663529	+	0.356462i
$636$	−577794.	+	323991.i	−1.42843	+	0.800975i
$637$	−109512.	+	63227.0i	−0.269888	+	0.155820i
$638$	−144519.			−0.355045
$639$	577640.	−	314443.i	1.41467	−	0.770087i
$640$	267129.	−	431603.i	0.652171	−	1.05372i
$641$	300549.	−	173522.i	0.731476	−	0.422318i	−0.0874862	−	0.996166i	$-0.527883\pi$
$641$	300549.	−	173522.i	0.731476	−	0.422318i	0.818962	+	0.573848i	$0.194550\pi$
$642$	1411.11	−	112443.i	0.00342365	−	0.272811i
$643$	67732.2	+	39105.2i	0.163822	+	0.0945828i	0.579670	−	0.814852i	$-0.303182\pi$
$643$	67732.2	+	39105.2i	0.163822	+	0.0945828i	−0.415847	+	0.909434i	$0.636515\pi$
$644$	153786.	+	88788.3i	0.370804	+	0.214084i
$645$	206521.	+	396273.i	0.496414	+	0.952521i
$646$	−496241.	−	859515.i	−1.18913	−	2.05963i
$647$	−429610.			−1.02628			−0.513139	−	0.858305i	$-0.671518\pi$
$647$	−429610.			−1.02628			−0.513139	+	0.858305i	$0.671518\pi$
$648$	−156293.	+	241815.i	−0.372212	+	0.575881i
$649$	−450950.			−1.07063
$650$	181821.	+	120384.i	0.430345	+	0.284933i
$651$	32273.1	−	54313.1i	0.0761515	−	0.128157i
$652$	131915.	+	76160.9i	0.310311	+	0.179158i
$653$	−5255.41	+	9102.64i	−0.0123248	+	0.0213472i	−0.872122	−	0.489288i	$-0.837257\pi$
$653$	−5255.41	+	9102.64i	−0.0123248	+	0.0213472i	0.859797	+	0.510636i	$0.170590\pi$
$654$	432.444	−	34458.9i	0.00101105	−	0.0805650i
$655$	16606.6	−	542187.i	0.0387077	−	1.26377i
$656$		−	222004.i		−	0.515885i
$657$	−149200.	+	81218.0i	−0.345650	+	0.188157i
$658$			63399.1i			0.146430i
$659$	257603.	−	148727.i	0.593172	−	0.342468i	−0.173179	−	0.984890i	$-0.555404\pi$
$659$	257603.	−	148727.i	0.593172	−	0.342468i	0.766351	+	0.642423i	$0.222071\pi$
$660$	−845470.	−	36520.1i	−1.94093	−	0.0838386i
$661$	−24001.9	+	41572.4i	−0.0549341	+	0.0951486i	−0.892185	−	0.451671i	$-0.850828\pi$
$661$	−24001.9	+	41572.4i	−0.0549341	+	0.0951486i	0.837251	+	0.546819i	$0.184162\pi$
$662$	460846.	−	798208.i	1.05157	−	1.82138i
$663$	63100.4	+	112531.i	0.143551	+	0.256003i
$664$	−266889.	−	462265.i	−0.605333	−	1.04847i
$665$	−153936.	−	95274.7i	−0.348094	−	0.215444i
$666$	324403.	+	198312.i	0.731368	+	0.447095i
$667$			93364.3i			0.209860i
$668$	−128196.	−	222042.i	−0.287291	−	0.497603i
$669$	−749126.	−	9401.19i	−1.67380	−	0.0210054i
$670$	−596865.	+	320648.i	−1.32962	+	0.714298i
$671$	13704.8	+	7912.46i	0.0304388	+	0.0175738i
$672$	69432.6	−	116849.i	0.153753	−	0.258755i
$673$	462003.	−	266738.i	1.02003	−	0.588917i	0.105920	−	0.994375i	$-0.466221\pi$
$673$	462003.	−	266738.i	1.02003	−	0.588917i	0.914114	+	0.405458i	$0.132888\pi$
$674$		−	738119.i		−	1.62483i
$675$	370165.	+	265654.i	0.812433	+	0.583055i
$676$	585793.			1.28189
$677$	−285619.	−	494707.i	−0.623175	−	1.07937i	−0.988891	−	0.148645i	$-0.952509\pi$
$677$	−285619.	−	494707.i	−0.623175	−	1.07937i	0.365715	−	0.930727i	$-0.380824\pi$
$678$	−494415.	−	293784.i	−1.07555	−	0.639099i
$679$	−37991.7	+	65803.6i	−0.0824042	+	0.142728i
$680$	133264.	+	248062.i	0.288202	+	0.536467i
$681$	−1625.23	+	129505.i	−0.00350445	+	0.279249i
$682$	−530285.	+	306160.i	−1.14009	+	0.658233i
$683$	89045.3			0.190884			0.0954420	−	0.995435i	$-0.469574\pi$
$683$	89045.3			0.190884			0.0954420	+	0.995435i	$0.469574\pi$
$684$	1.15406e6	+	28970.5i	2.46671	+	0.0619219i
$685$	−332932.	+	537921.i	−0.709537	+	1.14640i
$686$	−295260.	+	170469.i	−0.627417	+	0.362240i
$687$	−375945.	+	210807.i	−0.796546	+	0.446654i
$688$	162109.	+	93593.8i	0.342477	+	0.197729i
$689$	−154618.	−	89268.8i	−0.325703	−	0.188045i
$690$	−39988.2	+	925759.i	−0.0839911	+	1.94446i
$691$	227407.	+	393880.i	0.476264	+	0.824913i	0.999630	−	0.0271946i	$-0.00865738\pi$
$691$	227407.	+	393880.i	0.476264	+	0.824913i	−0.523366	+	0.852108i	$0.675324\pi$
$692$	−409076.			−0.854263
$693$	−154742.	−	3884.51i	−0.322213	−	0.00808852i
$694$	666090.			1.38297
$695$	−460566.	−	14106.6i	−0.953503	−	0.0292047i
$696$	−55931.0	−	701.909i	−0.115461	−	0.00144898i
$697$	523565.	+	302280.i	1.07772	+	0.622221i
$698$	115441.	−	199949.i	0.236946	−	0.410402i
$699$	−270266.	−	160593.i	−0.553142	−	0.328680i
$700$	140372.	+	92940.7i	0.286473	+	0.189675i
$701$		−	77719.5i		−	0.158159i	−0.996868	−	0.0790795i	$-0.974802\pi$
$701$		−	77719.5i		−	0.158159i	0.996868	−	0.0790795i	$-0.0251981\pi$
$702$	−254168.	−	9573.08i	−0.515758	−	0.0194257i
$703$		−	465113.i		−	0.941126i
$704$	−927523.	+	535505.i	−1.87145	+	1.08048i
$705$	−173093.	+	90208.9i	−0.348258	+	0.181498i
$706$	−68470.0	+	118593.i	−0.137370	+	0.237931i
$707$	82484.4	−	142867.i	0.165019	−	0.285821i
$708$	−572021.	−	7178.61i	−1.14116	−	0.0143210i
$709$	−121338.	−	210163.i	−0.241381	−	0.418085i	0.719727	−	0.694258i	$-0.244267\pi$
$709$	−121338.	−	210163.i	−0.241381	−	0.418085i	−0.961108	+	0.276173i	$0.910934\pi$
$710$	1.07825e6	+	667354.i	2.13896	+	1.32385i
$711$	78577.2	−	128538.i	0.155438	−	0.254269i
$712$			469378.i			0.925897i
$713$	197790.	+	342582.i	0.389068	+	0.673885i
$714$	82568.1	+	147249.i	0.161963	+	0.288839i
$715$	−107941.	−	200924.i	−0.211141	−	0.393024i
$716$	−524529.	−	302837.i	−1.02316	−	0.590721i
$717$	−12410.0	−	22131.6i	−0.0241398	−	0.0430501i
$718$	641847.	−	370570.i	1.24504	−	0.718823i
$719$		−	513112.i		−	0.992555i	−0.868164	−	0.496278i	$-0.834700\pi$
$719$		−	513112.i		−	0.992555i	0.868164	−	0.496278i	$-0.165300\pi$
$720$	190564.	+	10628.6i	0.367599	+	0.0205028i
$721$	228520.			0.439595
$722$	−789705.	−	1.36781e6i	−1.51492	−	2.62392i
$723$	1034.47	−	82430.6i	0.00197897	−	0.157693i
$724$	395315.	−	684706.i	0.754165	−	1.30625i
$725$	−5417.08	+	88348.1i	−0.0103060	+	0.168082i
$726$	582067.	+	345867.i	1.10433	+	0.656200i
$727$	−112849.	+	65153.1i	−0.213514	+	0.123273i	−0.602944	−	0.797784i	$-0.706006\pi$
$727$	−112849.	+	65153.1i	−0.213514	+	0.123273i	0.389429	+	0.921056i	$0.372672\pi$
$728$	−28673.5			−0.0541025
$729$	−529935.	−	39976.2i	−0.997167	−	0.0752222i
$730$	−278503.	−	172372.i	−0.522617	−	0.323460i
$731$	−441456.	+	254874.i	−0.826137	+	0.476971i
$732$	17258.3	+	10255.0i	0.0322089	+	0.0191387i
$733$	720205.	+	415810.i	1.34044	+	0.773904i	0.986872	−	0.161504i	$-0.0516344\pi$
$733$	720205.	+	415810.i	1.34044	+	0.773904i	0.353570	+	0.935408i	$0.384968\pi$
$734$	319666.	+	184559.i	0.593341	+	0.342565i
$735$	−429777.	−	273517.i	−0.795553	−	0.506303i
$736$	425526.	+	737033.i	0.785545	+	1.36060i
$737$	708676.			1.30471
$738$	−1.04682e6	+	569843.i	−1.92202	+	1.04627i
$739$	304925.			0.558346			0.279173	−	0.960241i	$-0.409940\pi$
$739$	304925.			0.558346			0.279173	+	0.960241i	$0.409940\pi$
$740$	−13241.6	+	432324.i	−0.0241811	+	0.789489i
$741$	152176.	+	271386.i	0.277147	+	0.494254i
$742$	−202321.	−	116810.i	−0.367479	−	0.212164i
$743$	−297321.	+	514976.i	−0.538578	+	0.932844i	0.460403	+	0.887710i	$0.347705\pi$
$743$	−297321.	+	514976.i	−0.538578	+	0.932844i	−0.998981	+	0.0451342i	$0.985628\pi$
$744$	−206715.	+	115913.i	−0.373444	+	0.209404i
$745$	−4169.76	+	136138.i	−0.00751275	+	0.245283i
$746$			1.09191e6i			1.96204i
$747$	513866.	−	840594.i	0.920892	−	1.50642i
$748$		−	965359.i		−	1.72538i
$749$	20263.8	−	11699.3i	0.0361208	−	0.0208544i
$750$	−91553.1	+	873700.i	−0.162761	+	1.55324i
$751$	467888.	−	810405.i	0.829587	−	1.43689i	−0.0687758	−	0.997632i	$-0.521909\pi$
$751$	467888.	−	810405.i	0.829587	−	1.43689i	0.898363	−	0.439254i	$-0.144757\pi$
$752$	−40882.0	+	70809.8i	−0.0722931	+	0.125215i
$753$	37476.1	−	63069.3i	0.0660944	−	0.111232i
$754$	−24706.0	−	42792.0i	−0.0434570	−	0.0752697i
$755$	−155731.	+	251616.i	−0.273201	+	0.441413i
$756$	−196226.	−	7390.75i	−0.343331	−	0.0129314i
$757$		−	555428.i		−	0.969251i	−0.874722	−	0.484625i	$-0.838956\pi$
$757$		−	555428.i		−	0.969251i	0.874722	−	0.484625i	$-0.161044\pi$
$758$	353261.	+	611867.i	0.614834	+	1.06492i
$759$	495095.	−	833206.i	0.859419	−	1.44633i
$760$	321388.	+	598240.i	0.556419	+	1.03573i
$761$	−889745.	−	513694.i	−1.53637	−	0.887024i	−0.999047	−	0.0436482i	$-0.986102\pi$
$761$	−889745.	−	513694.i	−1.53637	−	0.887024i	−0.537324	−	0.843376i	$-0.680565\pi$
$762$	682978.	+	8571.07i	1.17624	+	0.0147613i
$763$	6210.00	−	3585.35i	0.0106670	−	0.00615860i
$764$			758302.i			1.29914i
$765$	−284537.	+	434945.i	−0.486201	+	0.743210i
$766$	1.10399e6			1.88151
$767$	−77091.2	−	133526.i	−0.131043	−	0.226973i
$768$	−172155.	+	96534.1i	−0.291876	+	0.163666i
$769$	−509460.	+	882411.i	−0.861504	+	1.49217i	0.00897253	+	0.999960i	$0.497144\pi$
$769$	−509460.	+	882411.i	−0.861504	+	1.49217i	−0.870477	+	0.492209i	$0.836189\pi$
$770$	−141242.	−	262913.i	−0.238223	−	0.443435i
$771$	114106.	−	63983.7i	0.191956	−	0.107637i
$772$	527100.	−	304321.i	0.884419	−	0.510620i
$773$	1.11045e6			1.85841			0.929203	−	0.369569i	$-0.120495\pi$
$773$	1.11045e6			1.85841			0.929203	+	0.369569i	$0.120495\pi$
$774$	25219.3	−	1.00463e6i	0.0420971	−	1.67697i
$775$	167286.	+	335652.i	0.278520	+	0.558838i
$776$	246845.	−	142516.i	0.409921	−	0.236668i
$777$	−992.773	+	79108.2i	−0.00164440	+	0.131033i
$778$	858721.	+	495783.i	1.41871	+	0.819092i
$779$	1.26266e6	+	728996.i	2.08071	+	1.20130i
$780$	−133722.	−	256586.i	−0.219793	−	0.421740i
$781$	−663165.	−	1.14864e6i	−1.08723	−	1.88313i
$782$	−1.05703e6			−1.72852
$783$	−48219.6	−	91290.4i	−0.0786502	−	0.148902i
$784$	−213399.			−0.347185
$785$	10593.7	−	345872.i	0.0171912	−	0.561276i
$786$	−623162.	+	1.04873e6i	−1.00869	+	1.69754i
$787$	−154665.	−	89296.0i	−0.249714	−	0.144172i	0.369919	−	0.929064i	$-0.379385\pi$
$787$	−154665.	−	89296.0i	−0.249714	−	0.144172i	−0.619633	+	0.784891i	$0.712719\pi$
$788$	43571.2	−	75467.5i	0.0701693	−	0.121537i
$789$	−1031.26	+	82175.0i	−0.00165659	+	0.132004i
$790$	290337.	+	8892.68i	0.465208	+	0.0142488i
$791$		−	119668.i		−	0.191260i
$792$	495420.	+	302857.i	0.789811	+	0.482822i
$793$			5410.64i			0.00860403i
$794$	96470.0	−	55697.0i	0.153021	−	0.0883468i
$795$	31039.3	−	718585.i	0.0491109	−	1.13696i
$796$	−308648.	+	534595.i	−0.487122	+	0.843720i
$797$	−136648.	+	236682.i	−0.215123	+	0.372604i	−0.953311	−	0.301991i	$-0.902349\pi$
$797$	−136648.	+	236682.i	−0.215123	+	0.372604i	0.738188	+	0.674596i	$0.235682\pi$
$798$	199126.	+	355114.i	0.312695	+	0.557650i
$799$	−111330.	−	192829.i	−0.174389	−	0.302050i
$800$	359900.	+	722124.i	0.562344	+	1.12832i
$801$	−760918.	+	414212.i	−1.18597	+	0.645591i
$802$			83166.4i			0.129300i
$803$	171290.	+	296683.i	0.265645	+	0.460110i
$804$	898942.	+	11281.3i	1.39066	+	0.0174521i
$805$	−169851.	+	91247.4i	−0.262105	+	0.140809i
$806$	−181308.	−	104678.i	−0.279091	−	0.161133i
$807$	−557261.	+	937825.i	−0.855680	+	1.44004i
$808$	−535928.	+	309418.i	−0.820888	+	0.473940i
$809$		−	92441.7i		−	0.141244i	−0.997503	−	0.0706222i	$-0.977502\pi$
$809$		−	92441.7i		−	0.141244i	0.997503	−	0.0706222i	$-0.0224985\pi$
$810$	−439024.	−	925847.i	−0.669141	−	1.41114i
$811$	496286.			0.754554			0.377277	−	0.926101i	$-0.376861\pi$
$811$	496286.			0.754554			0.377277	+	0.926101i	$0.376861\pi$
$812$	−19073.9	−	33036.9i	−0.0289285	−	0.0501057i
$813$	598622.	+	355704.i	0.905673	+	0.538156i
$814$	383388.	−	664047.i	0.578615	−	1.00219i
$815$	−145695.	+	78270.3i	−0.219345	+	0.117837i
$816$	−2732.09	+	217704.i	−0.00410312	+	0.326953i
$817$	−1.06464e6	+	614669.i	−1.59499	+	0.920868i
$818$	−1.89880e6			−2.83774
$819$	−25303.5	−	46483.2i	−0.0377235	−	0.0692992i
$820$	−1.15289e6	−	713552.i	−1.71459	−	1.06120i
$821$	−542621.	+	313282.i	−0.805026	+	0.464782i	−0.845226	−	0.534410i	$-0.820534\pi$
$821$	−542621.	+	313282.i	−0.805026	+	0.464782i	0.0401995	+	0.999192i	$0.487201\pi$
$822$	1.24093e6	−	695834.i	1.83655	−	1.02982i
$823$	−1.08322e6	−	625394.i	−1.59924	−	0.923325i	−0.991633	−	0.129091i	$-0.958794\pi$
$823$	−1.08322e6	−	625394.i	−1.59924	−	0.923325i	−0.607612	−	0.794234i	$-0.707872\pi$
$824$	−742384.	−	428615.i	−1.09339	−	0.631267i
$825$	516838.	−	759714.i	0.759358	−	1.11620i
$826$	−100875.	−	174721.i	−0.147851	−	0.256086i
$827$	−399216.			−0.583709			−0.291855	−	0.956463i	$-0.594272\pi$
$827$	−399216.			−0.583709			−0.291855	+	0.956463i	$0.594272\pi$
$828$	641283.	−	1.04902e6i	0.935382	−	1.53012i
$829$	537391.			0.781954			0.390977	−	0.920400i	$-0.372137\pi$
$829$	537391.			0.781954			0.390977	+	0.920400i	$0.372137\pi$
$830$	1.89870e6	+	58154.9i	2.75613	+	0.0844170i
$831$	−438488.	−	5502.82i	−0.634973	−	0.00796863i
$832$	−317126.	−	183093.i	−0.458126	−	0.264499i
$833$	290564.	−	503271.i	0.418747	−	0.725291i
$834$	890855.	+	529351.i	1.28078	+	0.761047i
$835$	278255.	+	8522.64i	0.399090	+	0.0122237i
$836$		−	2.32811e6i		−	3.33113i
$837$	−370328.	−	232820.i	−0.528611	−	0.332330i
$838$			430327.i			0.612789i
$839$	713313.	−	411831.i	1.01334	−	0.585053i	0.101174	−	0.994869i	$-0.467740\pi$
$839$	713313.	−	411831.i	1.01334	−	0.585053i	0.912168	+	0.409815i	$0.134407\pi$
$840$	−53385.9	−	102437.i	−0.0756603	−	0.145177i
$841$	−343612.	+	595154.i	−0.485821	+	0.841467i
$842$	204371.	−	353981.i	0.288267	−	0.499293i
$843$	−767887.	−	9636.64i	−1.08054	−	0.0135603i
$844$	−139619.	−	241827.i	−0.196001	−	0.339484i
$845$	−334735.	+	540834.i	−0.468801	+	0.757445i
$846$	438826.	+	11015.9i	0.613129	+	0.0153914i
$847$			140883.i			0.196378i
$848$	−150647.	−	260928.i	−0.209492	−	0.362851i
$849$	105153.	+	187525.i	0.145883	+	0.260162i
$850$	−1.00024e6	−	61330.0i	−1.38442	−	0.0848858i
$851$	−428997.	−	247682.i	−0.592373	−	0.342007i
$852$	−822928.	−	1.46758e6i	−1.13366	−	2.02173i
$853$	−838778.	+	484269.i	−1.15279	+	0.665562i	−0.949565	−	0.313571i	$-0.898475\pi$
$853$	−838778.	+	484269.i	−1.15279	+	0.665562i	−0.203222	+	0.979133i	$0.565141\pi$
$854$			7079.93i			0.00970763i
$855$	−686205.	+	1.04894e6i	−0.938689	+	1.43489i
$856$	−87773.8			−0.119789
$857$	230029.	+	398421.i	0.313199	+	0.542476i	0.979053	−	0.203606i	$-0.0652660\pi$
$857$	230029.	+	398421.i	0.313199	+	0.542476i	−0.665854	+	0.746082i	$0.731933\pi$
$858$	−6436.64	+	512898.i	−0.00874349	+	0.696717i
$859$	−389235.	+	674176.i	−0.527504	+	0.913664i	0.471982	+	0.881608i	$0.343539\pi$
$859$	−389235.	+	674176.i	−0.527504	+	0.913664i	−0.999486	+	0.0320561i	$0.989794\pi$
$860$	1.00708e6	−	541027.i	1.36166	−	0.731513i
$861$	−213202.	−	126686.i	−0.287597	−	0.170892i
$862$	514429.	−	297006.i	0.692327	−	0.399715i
$863$	665897.			0.894098			0.447049	−	0.894509i	$-0.352475\pi$
$863$	665897.			0.894098			0.447049	+	0.894509i	$0.352475\pi$
$864$	−796727.	−	500891.i	−1.06729	−	0.670990i
$865$	233755.	−	377680.i	0.312413	−	0.504768i
$866$	385511.	−	222575.i	0.514045	−	0.296784i
$867$	136511.	+	81115.3i	0.181605	+	0.107911i
$868$	−139976.	−	80814.9i	−0.185786	−	0.107264i
$869$	−263116.	−	151910.i	−0.348424	−	0.201163i
$870$	106877.	−	167936.i	0.141204	−	0.221873i
$871$	121150.	+	209838.i	0.159694	+	0.276598i
$872$	−26898.9			−0.0353755
$873$	448868.	+	274399.i	0.588966	+	0.360043i
$874$	−2.54920e6			−3.33719
$875$	−166019.	+	76490.0i	−0.216842	+	0.0999053i
$876$	212555.	+	379064.i	0.276990	+	0.493974i
$877$	1.13315e6	+	654227.i	1.47330	+	0.850608i	0.999548	−	0.0300525i	$-0.00956746\pi$
$877$	1.13315e6	+	654227.i	1.47330	+	0.850608i	0.473748	+	0.880661i	$0.342901\pi$
$878$	13483.9	−	23354.8i	0.0174915	−	0.0302962i
$879$	−1.03092e6	+	578075.i	−1.33428	+	0.748181i
$880$	11783.6	−	384723.i	0.0152165	−	0.496801i
$881$		−	521436.i		−	0.671814i	−0.941895	−	0.335907i	$-0.890957\pi$
$881$		−	521436.i		−	0.671814i	0.941895	−	0.335907i	$-0.109043\pi$
$882$	547755.	+	1.00624e6i	0.704125	+	1.29350i
$883$			1.26259e6i			1.61935i	0.586882	+	0.809673i	$0.300355\pi$
$883$			1.26259e6i			1.61935i	−0.586882	+	0.809673i	$0.699645\pi$
$884$	285842.	−	165031.i	0.365782	−	0.211184i
$885$	333494.	−	524018.i	0.425795	−	0.669051i
$886$	644079.	−	1.11558e6i	0.820486	−	1.42112i
$887$	334515.	−	579397.i	0.425176	−	0.736426i	−0.571261	−	0.820768i	$-0.693546\pi$
$887$	334515.	−	579397.i	0.425176	−	0.736426i	0.996437	+	0.0843427i	$0.0268790\pi$
$888$	151602.	−	255134.i	0.192255	−	0.323551i
$889$	71061.8	+	123083.i	0.0899151	+	0.155737i
$890$	−1.42036e6	−	879097.i	−1.79316	−	1.10983i
$891$	−53774.4	+	1.07040e6i	−0.0677361	+	1.34831i
$892$			1.91666e6i			2.40888i
$893$	−268489.	−	465037.i	−0.336685	−	0.583156i
$894$	156471.	−	263327.i	0.195775	−	0.329474i
$895$	579322.	−	311224.i	0.723226	−	0.388533i
$896$	−205700.	−	118761.i	−0.256223	−	0.147931i
$897$	331350.	+	4158.29i	0.411815	+	0.00516809i
$898$	352441.	−	203482.i	0.437053	−	0.252333i
$899$		−	84980.0i		−	0.105147i
$900$	667693.	−	955455.i	0.824313	−	1.17957i
$901$	820482.			1.01069
$902$	1.20181e6	+	2.08159e6i	1.47714	+	2.55848i
$903$	182390.	−	102273.i	0.223679	−	0.125425i
$904$	−224451.	+	388761.i	−0.274653	+	0.475714i
$905$	406264.	+	756232.i	0.496034	+	0.923332i
$906$	580451.	−	325481.i	0.707147	−	0.396524i
$907$	−928585.	+	536119.i	−1.12877	+	0.651698i	−0.943626	−	0.331013i	$-0.892610\pi$
$907$	−928585.	+	536119.i	−1.12877	+	0.651698i	−0.185148	+	0.982711i	$0.559276\pi$
$908$	331342.			0.401887
$909$	−974545.	−	595752.i	−1.17943	−	0.721004i
$910$	53702.5	−	86767.5i	0.0648503	−	0.104779i
$911$	408450.	−	235819.i	0.492155	−	0.284146i	−0.233313	−	0.972402i	$-0.574957\pi$
$911$	408450.	−	235819.i	0.492155	−	0.284146i	0.725468	+	0.688256i	$0.241623\pi$
$912$	−6588.84	+	525026.i	−0.00792172	+	0.631235i
$913$	−1.72068e6	−	993437.i	−2.06424	−	1.19179i
$914$	666755.	+	384951.i	0.798130	+	0.460801i
$915$	−19329.7	+	10073.8i	−0.0230878	+	0.0120324i
$916$	551338.	+	954946.i	0.657094	+	1.13812i
$917$	−253835.			−0.301865
$918$	1.03355e6	−	545922.i	1.22644	−	0.647807i
$919$	729318.			0.863547			0.431774	−	0.901982i	$-0.357888\pi$
$919$	729318.			0.863547			0.431774	+	0.901982i	$0.357888\pi$
$920$	722933.	+	22142.6i	0.854127	+	0.0261609i
$921$	246473.	−	414795.i	0.290570	−	0.489006i
$922$	338791.	+	195601.i	0.398538	+	0.230096i
$923$	226740.	−	392726.i	0.266149	−	0.460984i
$924$	−4969.30	+	395975.i	−0.00582038	+	0.463792i
$925$	−391577.	−	259265.i	−0.457651	−	0.303013i
$926$			2.23632e6i			2.60803i
$927$	39706.4	−	1.58173e6i	0.0462062	−	1.84066i
$928$		−	182827.i		−	0.212297i
$929$	−55251.5	+	31899.5i	−0.0640196	+	0.0369617i	−0.531668	−	0.846953i	$-0.678435\pi$
$929$	−55251.5	+	31899.5i	−0.0640196	+	0.0369617i	0.467649	+	0.883914i	$0.345101\pi$
$930$	36397.1	−	842624.i	0.0420825	−	0.974244i
$931$	700740.	−	1.21372e6i	0.808458	−	1.40029i
$932$	−402141.	+	696528.i	−0.462963	+	0.801876i
$933$	503043.	+	897110.i	0.577886	+	1.03058i
$934$	770142.	+	1.33392e6i	0.882830	+	1.52911i
$935$	891270.	+	551628.i	1.01950	+	0.630991i
$936$	−4982.15	+	198468.i	−0.00568676	+	0.226537i
$937$		−	1.06986e6i		−	1.21856i	−0.792953	−	0.609282i	$-0.791458\pi$
$937$		−	1.06986e6i		−	1.21856i	0.792953	−	0.609282i	$-0.208542\pi$
$938$	158527.	+	274578.i	0.180177	+	0.312075i
$939$	586345.	+	7358.36i	0.665000	+	0.00834546i
$940$	236322.	+	439897.i	0.267454	+	0.497847i
$941$	1.33153e6	+	768761.i	1.50374	+	0.868185i	0.999991	+	0.00433542i	$0.00138001\pi$
$941$	1.33153e6	+	768761.i	1.50374	+	0.868185i	0.503750	+	0.863850i	$0.331953\pi$
$942$	−397528.	+	669007.i	−0.447987	+	0.753927i
$943$	1.34478e6	−	776409.i	1.51226	−	0.873106i
$944$		−	260193.i		−	0.291978i
$945$	118951.	−	176943.i	0.133201	−	0.198139i
$946$	−2.02666e6			−2.26464
$947$	124371.	+	215417.i	0.138682	+	0.240203i	0.926998	−	0.375067i	$-0.122380\pi$
$947$	124371.	+	215417.i	0.138682	+	0.240203i	−0.788316	+	0.615270i	$0.789047\pi$
$948$	−331340.	−	196884.i	−0.368686	−	0.219075i
$949$	−58565.1	+	101438.i	−0.0650289	+	0.112633i
$950$	−2.41224e6	−	147907.i	−2.67284	−	0.163886i
$951$	5769.47	−	459735.i	0.00637933	−	0.508331i
$952$	114117.	−	65885.4i	0.125915	−	0.0726969i
$953$	399593.			0.439979			0.219990	−	0.975502i	$-0.429398\pi$
$953$	399593.			0.439979			0.219990	+	0.975502i	$0.429398\pi$
$954$	−843672.	+	1.38010e6i	−0.926994	+	1.51640i
$955$	−700104.	−	433311.i	−0.767637	−	0.475109i
$956$	−56217.0	+	32456.9i	−0.0615108	+	0.0355133i
$957$	−181605.	+	101833.i	−0.198292	+	0.111190i
$958$	−1.72930e6	−	998412.i	−1.88425	−	1.08787i
$959$	256371.	+	148016.i	0.278761	+	0.160943i
$960$	63662.4	−	1.47384e6i	0.0690781	−	1.59921i
$961$	281733.	+	487975.i	0.305063	+	0.528385i
$962$	262165.			0.283286
$963$	−77457.7	−	142292.i	−0.0835242	−	0.153436i
$964$	−210901.			−0.226947
$965$	−20231.6	+	660542.i	−0.0217258	+	0.709326i
$966$	433578.	+	5441.20i	0.464636	+	0.00583097i
$967$	54468.4	+	31447.3i	0.0582494	+	0.0336303i	0.528842	−	0.848720i	$-0.322626\pi$
$967$	54468.4	+	31447.3i	0.0582494	+	0.0336303i	−0.470592	+	0.882351i	$0.655960\pi$
$968$	264243.	−	457682.i	0.282002	−	0.488443i
$969$	−1.22923e6	−	730414.i	−1.30914	−	0.777896i
$970$	−31054.1	+	1.01388e6i	−0.0330047	+	1.07757i
$971$		−	625318.i		−	0.663227i	−0.943415	−	0.331613i	$-0.892407\pi$
$971$		−	625318.i		−	0.663227i	0.943415	−	0.331613i	$-0.107593\pi$
$972$	−85251.3	+	1.35692e6i	−0.0902337	+	1.43623i
$973$			215622.i			0.227755i
$974$	−2.39882e6	+	1.38496e6i	−2.52860	+	1.45989i
$975$	313306.	+	23160.1i	0.329579	+	0.0243630i
$976$	−4565.40	+	7907.50i	−0.00479269	+	0.00830117i
$977$	−503360.	+	871845.i	−0.527339	+	0.913377i	0.472154	+	0.881516i	$0.343477\pi$
$977$	−503360.	+	871845.i	−0.527339	+	0.913377i	−0.999492	+	0.0318610i	$0.989857\pi$
$978$	371915.	+	4667.36i	0.388835	+	0.00487971i
$979$	873579.	+	1.51308e6i	0.911459	+	1.57869i
$980$	−685894.	+	1.10820e6i	−0.714176	+	1.15390i
$981$	−23737.5	−	43606.4i	−0.0246659	−	0.0453119i
$982$		−	2.00112e6i		−	2.07516i
$983$	−243439.	−	421648.i	−0.251932	−	0.436358i	0.712126	−	0.702052i	$-0.247732\pi$
$983$	−243439.	−	421648.i	−0.251932	−	0.436358i	−0.964058	+	0.265693i	$0.914399\pi$
$984$	455007.	+	811443.i	0.469924	+	0.838046i
$985$	44778.0	+	83351.1i	0.0461522	+	0.0859090i
$986$	196654.	+	113538.i	0.202278	+	0.116785i
$987$	44673.1	+	79668.4i	0.0458576	+	0.0817809i
$988$	689353.	−	397998.i	0.706200	−	0.407725i
$989$			1.30929e6i			1.33858i
$990$	−1.84433e6	+	931948.i	−1.88178	+	0.950871i
$991$	−645585.			−0.657364			−0.328682	−	0.944441i	$-0.606604\pi$
$991$	−645585.			−0.657364			−0.328682	+	0.944441i	$0.606604\pi$
$992$	−387313.	−	670846.i	−0.393585	−	0.681710i
$993$	16662.9	−	1.32777e6i	0.0168987	−	1.34656i
$994$	296694.	−	513889.i	0.300287	−	0.520112i
$995$	−317197.	−	590440.i	−0.320393	−	0.596389i
$996$	−2.16684e6	−	1.28755e6i	−2.18428	−	1.29791i
$997$	985456.	−	568953.i	0.991395	−	0.572382i	0.0857043	−	0.996321i	$-0.472686\pi$
$997$	985456.	−	568953.i	0.991395	−	0.572382i	0.905691	+	0.423938i	$0.139353\pi$
$998$	−1.05122e6			−1.05544
$999$	547387.	+	20617.0i	0.548483	+	0.0206583i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.h.a.14.3	✓	44
3.2	odd	2		135.5.h.a.44.20		44
5.4	even	2	inner	45.5.h.a.14.20	yes	44
9.2	odd	6	inner	45.5.h.a.29.20	yes	44
9.4	even	3		405.5.d.a.404.39		44
9.5	odd	6		405.5.d.a.404.5		44
9.7	even	3		135.5.h.a.89.3		44
15.14	odd	2		135.5.h.a.44.3		44
45.4	even	6		405.5.d.a.404.6		44
45.14	odd	6		405.5.d.a.404.40		44
45.29	odd	6	inner	45.5.h.a.29.3	yes	44
45.34	even	6		135.5.h.a.89.20		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.h.a.14.3	✓	44	1.1	even	1	trivial
45.5.h.a.14.20	yes	44	5.4	even	2	inner
45.5.h.a.29.3	yes	44	45.29	odd	6	inner
45.5.h.a.29.20	yes	44	9.2	odd	6	inner
135.5.h.a.44.3		44	15.14	odd	2
135.5.h.a.44.20		44	3.2	odd	2
135.5.h.a.89.3		44	9.7	even	3
135.5.h.a.89.20		44	45.34	even	6
405.5.d.a.404.5		44	9.5	odd	6
405.5.d.a.404.6		44	45.4	even	6
405.5.d.a.404.39		44	9.4	even	3
405.5.d.a.404.40		44	45.14	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	45.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.12350 - 5.41005i) q^{2} +(-7.73715 - 4.59745i) q^{3} +(-11.5125 + 19.9402i) q^{4} +(-11.8313 - 22.0232i) q^{5} +(-0.705517 + 56.2185i) q^{6} +(-10.1314 + 5.84936i) q^{7} +43.8846 q^{8} +(38.7269 + 71.1423i) q^{9} +(-82.1915 + 132.797i) q^{10} +(141.466 - 81.6756i) q^{11} +(180.748 - 101.352i) q^{12} +(48.3682 + 27.9254i) q^{13} +(63.2907 + 36.5409i) q^{14} +(-9.70982 + 224.790i) q^{15} +(47.1259 + 81.6244i) q^{16} -256.666 q^{17} +(263.921 - 431.727i) q^{18} -618.990 q^{19} +(575.353 + 17.6224i) q^{20} +(105.280 + 1.32122i) q^{21} +(-883.739 - 510.227i) q^{22} +(-329.624 + 570.926i) q^{23} +(-339.542 - 201.758i) q^{24} +(-345.040 + 521.126i) q^{25} -348.899i q^{26} +(27.4379 - 728.483i) q^{27} -269.362i q^{28} +(122.649 - 70.8112i) q^{29} +(1246.46 - 649.601i) q^{30} +(300.023 - 519.656i) q^{31} +(645.472 - 1117.99i) q^{32} +(-1470.05 - 18.4484i) q^{33} +(801.696 + 1388.58i) q^{34} +(248.689 + 153.920i) q^{35} +(-1864.43 - 46.8029i) q^{36} +751.406i q^{37} +(1933.41 + 3348.77i) q^{38} +(-245.846 - 438.433i) q^{39} +(-519.213 - 966.479i) q^{40} +(-2039.87 - 1177.72i) q^{41} +(-321.695 - 573.699i) q^{42} +(1719.96 - 993.020i) q^{43} +3761.15i q^{44} +(1108.59 - 1694.60i) q^{45} +4118.32 q^{46} +(433.754 + 751.284i) q^{47} +(10.6445 - 848.199i) q^{48} +(-1132.07 + 1960.80i) q^{49} +(3897.05 + 238.949i) q^{50} +(1985.86 + 1180.01i) q^{51} +(-1113.67 + 642.980i) q^{52} -3196.69 q^{53} +(-4026.84 + 2126.97i) q^{54} +(-3472.49 - 2149.21i) q^{55} +(-444.612 + 256.697i) q^{56} +(4789.21 + 2845.78i) q^{57} +(-766.185 - 442.357i) q^{58} +(-2390.76 - 1380.31i) q^{59} +(-4370.57 - 2781.51i) q^{60} +(48.4383 + 83.8977i) q^{61} -3748.49 q^{62} +(-808.494 - 494.243i) q^{63} -6556.49 q^{64} +(42.7461 - 1395.62i) q^{65} +(4491.87 + 8010.65i) q^{66} +(3757.13 + 2169.18i) q^{67} +(2954.86 - 5117.96i) q^{68} +(5175.15 - 2901.91i) q^{69} +(55.9341 - 1826.19i) q^{70} -8119.50i q^{71} +(1699.51 + 3122.05i) q^{72} +2097.20i q^{73} +(4065.15 - 2347.01i) q^{74} +(5065.48 - 2445.73i) q^{75} +(7126.10 - 12342.8i) q^{76} +(-955.501 + 1654.98i) q^{77} +(-1604.05 + 2699.49i) q^{78} +(-929.960 - 1610.74i) q^{79} +(1240.07 - 2003.58i) q^{80} +(-3561.46 + 5510.24i) q^{81} +14714.4i q^{82} +(-6081.60 - 10533.6i) q^{83} +(-1238.38 + 2084.09i) q^{84} +(3036.70 + 5652.60i) q^{85} +(-10744.6 - 6203.39i) q^{86} +(-1274.50 - 15.9944i) q^{87} +(6208.20 - 3584.30i) q^{88} +10695.7i q^{89} +(-12630.5 - 704.465i) q^{90} -653.383 q^{91} +(-7589.57 - 13145.5i) q^{92} +(-4710.42 + 2641.31i) q^{93} +(2709.66 - 4693.26i) q^{94} +(7323.46 + 13632.1i) q^{95} +(-10134.0 + 5682.53i) q^{96} +(5624.85 - 3247.51i) q^{97} +14144.1 q^{98} +(11289.1 + 6901.20i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} + 6 q^{5} - 36 q^{6} - 126 q^{9} + 28 q^{10} + 228 q^{11} + 282 q^{14} + 450 q^{15} - 1058 q^{16} - 8 q^{19} - 2196 q^{20} + 1056 q^{21} + 2970 q^{24} - 148 q^{25} + 2370 q^{29} + 1068 q^{30}+ \cdots + 44568 q^{99}+O(q^{100}) \) 44 * q - 162 * q^4 + 6 * q^5 - 36 * q^6 - 126 * q^9 + 28 * q^10 + 228 * q^11 + 282 * q^14 + 450 * q^15 - 1058 * q^16 - 8 * q^19 - 2196 * q^20 + 1056 * q^21 + 2970 * q^24 - 148 * q^25 + 2370 * q^29 + 1068 * q^30 - 1112 * q^31 - 436 * q^34 - 648 * q^36 - 6420 * q^39 - 850 * q^40 + 1830 * q^41 - 1944 * q^45 - 5668 * q^46 + 5396 * q^49 + 13524 * q^50 - 1500 * q^51 + 17766 * q^54 - 3072 * q^55 - 8250 * q^56 - 27348 * q^59 - 28722 * q^60 + 2782 * q^61 + 8348 * q^64 - 24906 * q^65 + 27240 * q^66 + 19662 * q^69 + 4782 * q^70 + 64728 * q^74 + 28446 * q^75 - 1776 * q^76 + 7900 * q^79 - 47754 * q^81 - 113166 * q^84 + 6766 * q^85 + 9192 * q^86 + 10674 * q^90 + 1560 * q^91 - 18826 * q^94 + 58746 * q^95 + 1902 * q^96 + 44568 * q^99

Introduction

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