LMFDB - Embedded newform 45.5.h.a.14.20

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			14.20
Character	$\chi$	$=$	45.14
Dual form			45.5.h.a.29.20

$q$-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} +(-24.9883 + 0.765363i) 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} +(-196.857 - 108.961i) q^{15} +(47.1259 + 81.6244i) q^{16} +256.666 q^{17} +(-263.921 + 431.727i) q^{18} -618.990 q^{19} +(272.415 - 507.082i) 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} +(623.828 - 38.2502i) q^{25} -348.899i q^{26} +(-27.4379 + 728.483i) q^{27} +269.362i q^{28} +(122.649 - 70.8112i) q^{29} +(-25.3979 - 1405.34i) 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} +(1096.60 - 33.5877i) q^{40} +(-2039.87 - 1177.72i) q^{41} +(321.695 + 573.699i) q^{42} +(-1719.96 + 993.020i) q^{43} +3761.15i q^{44} +(-1022.17 - 1748.08i) q^{45} +4118.32 q^{46} +(-433.754 - 751.284i) q^{47} +(-10.6445 + 848.199i) q^{48} +(-1132.07 + 1960.80i) q^{49} +(2155.46 + 3255.47i) 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} +(4439.00 - 2670.95i) q^{60} +(48.4383 + 83.8977i) q^{61} +3748.49 q^{62} +(808.494 + 494.243i) q^{63} -6556.49 q^{64} +(1230.01 + 660.788i) 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} +(-1609.49 - 864.655i) q^{70} -8119.50i q^{71} +(-1699.51 - 3122.05i) q^{72} -2097.20i q^{73} +(4065.15 - 2347.01i) q^{74} +(5002.51 + 2572.07i) 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} +(-6413.64 + 196.443i) q^{85} +(-10744.6 - 6203.39i) q^{86} +(1274.50 + 15.9944i) q^{87} +(-6208.20 + 3584.30i) q^{88} +10695.7i q^{89} +(6264.49 - 10990.1i) q^{90} -653.383 q^{91} +(7589.57 + 13145.5i) q^{92} +(4710.42 - 2641.31i) q^{93} +(2709.66 - 4693.26i) q^{94} +(15467.5 - 473.752i) 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	$0.118559\pi$
$2$	3.12350	+	5.41005i	0.780874	+	1.35251i	−0.150559	+	0.988601i	$0.548107\pi$
$3$	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
$5$	−24.9883	+	0.765363i	−0.999531	+	0.0306145i
$5$	−24.9883	+	0.765363i	−0.999531	+	0.0306145i
$6$	−0.705517	+	56.2185i	−0.0195977	+	1.56163i
$7$	10.1314	−	5.84936i	0.206763	−	0.119375i	−0.393043	−	0.919520i	$-0.628578\pi$
$7$	10.1314	−	5.84936i	0.206763	−	0.119375i	0.599806	+	0.800145i	$0.295244\pi$
$8$	−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	0.350026	−	0.936740i	$-0.386173\pi$
$13$	−48.3682	−	27.9254i	−0.286202	−	0.165239i	−0.636228	+	0.771501i	$0.719506\pi$
$14$	63.2907	+	36.5409i	0.322912	+	0.186433i
$15$	−196.857	−	108.961i	−0.874919	−	0.484270i
$16$	47.1259	+	81.6244i	0.184085	+	0.318845i
$17$	256.666			0.888118			0.444059	−	0.895998i	$-0.353538\pi$
$17$	256.666			0.888118			0.444059	+	0.895998i	$0.353538\pi$
$18$	−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	$0.827876\pi$
$20$	272.415	−	507.082i	0.681038	−	1.26770i
$21$	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	$-0.619203\pi$
$23$	329.624	−	570.926i	0.623108	−	1.07925i	0.988903	−	0.148560i	$-0.0474637\pi$
$24$	−339.542	−	201.758i	−0.589482	−	0.350273i
$25$	623.828	−	38.2502i	0.998126	−	0.0612003i
$26$		−	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	$0.306500\pi$
$30$	−25.3979	−	1405.34i	−0.0282199	−	1.56149i
$31$	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	$-0.911509\pi$
$37$		−	751.406i		−	0.548872i	0.961605	−	0.274436i	$-0.0884912\pi$
$38$	−1933.41	−	3348.77i	−1.33893	−	2.31909i
$39$	−245.846	−	438.433i	−0.161635	−	0.288253i
$40$	1096.60	−	33.5877i	0.685376	−	0.0209923i
$41$	−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	−0.886878	−	0.462003i	$-0.847131\pi$
$43$	−1719.96	+	993.020i	−0.930211	+	0.537058i	−0.0433329	+	0.999061i	$0.513798\pi$
$44$			3761.15i			1.94274i
$45$	−1022.17	−	1748.08i	−0.504774	−	0.863251i
$46$	4118.32			1.94628
$47$	−433.754	−	751.284i	−0.196358	−	0.340101i	0.750987	−	0.660317i	$-0.229578\pi$
$47$	−433.754	−	751.284i	−0.196358	−	0.340101i	−0.947345	+	0.320216i	$0.896245\pi$
$48$	−10.6445	+	848.199i	−0.00462001	+	0.368142i
$49$	−1132.07	+	1960.80i	−0.471499	+	0.816661i
$50$	2155.46	+	3255.47i	0.862185	+	1.30219i
$51$	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	$-0.307327\pi$
$53$	3196.69			1.13802			0.569009	+	0.822332i	$0.307327\pi$
$54$	−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	$0.796451\pi$
$60$	4439.00	−	2670.95i	1.23306	−	0.741931i
$61$	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
$65$	1230.01	+	660.788i	0.291127	+	0.156400i
$66$	4491.87	+	8010.65i	1.03119	+	1.83899i
$67$	−3757.13	−	2169.18i	−0.836963	−	0.483221i	0.0192680	−	0.999814i	$-0.493866\pi$
$67$	−3757.13	−	2169.18i	−0.836963	−	0.483221i	−0.856231	+	0.516594i	$0.827200\pi$
$68$	−2954.86	+	5117.96i	−0.639026	+	1.10683i
$69$	5175.15	−	2901.91i	1.08699	−	0.609516i
$70$	−1609.49	−	864.655i	−0.328468	−	0.176460i
$71$		−	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	$-0.936954\pi$
$73$		−	2097.20i		−	0.393545i	0.980449	−	0.196772i	$-0.0630460\pi$
$74$	4065.15	−	2347.01i	0.742357	−	0.428600i
$75$	5002.51	+	2572.07i	0.889334	+	0.457258i
$76$	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	$0.177677\pi$
$83$	6081.60	+	10533.6i	0.882799	+	1.52905i	0.0345824	+	0.999402i	$0.488990\pi$
$84$	−1238.38	+	2084.09i	−0.175507	+	0.295365i
$85$	−6413.64	+	196.443i	−0.887702	+	0.0271893i
$86$	−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	$0.764079\pi$
$90$	6264.49	−	10990.1i	0.773394	−	1.35680i
$91$	−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
$95$	15467.5	−	473.752i	1.71385	−	0.0524932i
$96$	−10134.0	+	5682.53i	−1.09961	+	0.616594i
$97$	−5624.85	+	3247.51i	−0.597816	+	0.345149i	−0.768182	−	0.640232i	$-0.778838\pi$
$97$	−5624.85	+	3247.51i	−0.597816	+	0.345149i	0.170366	+	0.985381i	$0.445505\pi$
$98$	−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	$0.0389833\pi$
$103$	16916.7	+	9766.87i	1.59456	+	0.920621i	0.602052	+	0.798457i	$0.294350\pi$
$104$	2122.62	+	1225.50i	0.196248	+	0.113304i
$105$	−2631.78	+	47.5625i	−0.238711	+	0.00431406i
$106$	9984.85	+	17294.3i	0.888648	+	1.53918i
$107$	2000.10			0.174697			0.0873484	−	0.996178i	$-0.472161\pi$
$107$	2000.10			0.174697			0.0873484	+	0.996178i	$0.472161\pi$
$108$	−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	$0.508212\pi$
$110$	−22473.6	−	12073.3i	−1.85732	−	0.997795i
$111$	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	−0.593246	−	0.805021i	$-0.702154\pi$
$113$	5114.57	−	8858.70i	0.400546	−	0.693766i	0.993792	+	0.111255i	$0.0354871\pi$
$114$	436.708	−	34798.7i	0.0336032	−	2.67765i
$115$	−7799.78	+	14518.7i	−0.589775	+	1.09783i
$116$			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
$120$	8638.99	+	4781.70i	0.599930	+	0.332063i
$121$	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	$0.122910\pi$
$127$			12148.6i			0.753217i	−0.926373	+	0.376608i	$0.877090\pi$
$128$	−10151.6	−	17583.1i	−0.619606	−	1.07319i
$129$	−17872.9	−	224.297i	−1.07403	−	0.0134786i
$130$	267.035	+	8718.40i	0.0158009	+	0.515882i
$131$	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
$135$	128.073	−	18224.5i	0.00702733	−	0.999975i
$136$	−11263.7			−0.608980
$137$	12652.3	+	21914.5i	0.674108	+	1.16759i	0.976729	+	0.214478i	$0.0688049\pi$
$137$	12652.3	+	21914.5i	0.674108	+	1.16759i	−0.302621	+	0.953111i	$0.597862\pi$
$138$	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	$0.00839980\pi$
$140$	−206.160	−	6730.90i	−0.0105184	−	0.343413i
$141$	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	$0.705822\pi$
$150$	1710.25	+	35097.7i	0.0760110	+	1.55990i
$151$	−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
$155$	−7099.34	+	13214.9i	−0.295498	+	0.550049i
$156$	11572.7	+	145.233i	0.475539	+	0.00596781i
$157$	−11987.0	−	6920.68i	−0.486307	−	0.280769i	0.236734	−	0.971574i	$-0.423923\pi$
$157$	−11987.0	−	6920.68i	−0.486307	−	0.280769i	−0.723041	+	0.690805i	$0.757256\pi$
$158$	5809.46	−	10062.3i	0.232713	−	0.403071i
$159$	24733.3	+	14696.6i	0.978334	+	0.581331i
$160$	15273.6	−	28430.7i	0.596624	−	1.11057i
$161$		−	7712.36i		−	0.297533i
$162$	−40934.9	−	2056.48i	−1.55978	−	0.0783599i
$163$			6615.52i			0.248994i	0.992220	+	0.124497i	$0.0397317\pi$
$163$			6615.52i			0.248994i	−0.992220	+	0.124497i	$0.960268\pi$
$164$	46967.8	−	27116.9i	1.74627	−	1.00821i
$165$	−36748.0	+	664.124i	−1.34979	+	0.0243939i
$166$	−37991.7	+	65803.6i	−1.37871	+	2.38799i
$167$	5567.71	−	9643.56i	0.199638	−	0.345784i	−0.748773	−	0.662827i	$-0.769357\pi$
$167$	5567.71	−	9643.56i	0.199638	−	0.345784i	0.948411	+	0.317043i	$0.102690\pi$
$168$	−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	0.678592	−	0.734516i	$-0.262591\pi$
$173$	−8883.33	−	15386.4i	−0.296813	−	0.514096i	−0.975405	+	0.220420i	$0.929257\pi$
$174$	3894.37	+	6945.08i	0.128629	+	0.229392i
$175$	6096.51	−	4036.53i	0.199070	−	0.131805i
$176$	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	$0.865357\pi$
$180$	46624.8	−	257.441i	1.43904	−	0.00794572i
$181$	−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
$185$	575.098	+	18776.4i	0.0168035	+	0.548615i
$186$	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	0.774757	−	0.632259i	$-0.217872\pi$
$193$	22892.6	+	13217.0i	0.614582	+	0.354829i	−0.160174	+	0.987089i	$0.551206\pi$
$194$	−35138.4	−	20287.2i	−0.933638	−	0.539036i
$195$	6478.83	+	10767.5i	0.170384	+	0.283170i
$196$	−26065.8	−	45147.3i	−0.678515	−	1.17522i
$197$	3784.70			0.0975212			0.0487606	−	0.998810i	$-0.484473\pi$
$197$	3784.70			0.0975212			0.0487606	+	0.998810i	$0.484473\pi$
$198$	−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	$0.390080\pi$
$200$	−27376.5	+	1678.60i	−0.684412	+	0.0419649i
$201$	−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
$205$	51874.2	+	27867.9i	1.23436	+	0.663127i
$206$			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
$210$	−8477.68	−	14089.5i	−0.192238	−	0.319490i
$211$	−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
$220$	−2878.64	−	93984.7i	−0.0594761	−	1.94183i
$221$	−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	−0.998461	−	0.0554578i	$-0.982338\pi$
$223$	−72090.3	+	41621.4i	−1.44966	+	0.836964i	−0.451203	+	0.892421i	$0.649005\pi$
$224$			15102.4i			0.300988i
$225$	26880.1	+	42899.3i	0.530966	+	0.847393i
$226$	63901.4			1.25110
$227$	7195.28	+	12462.6i	0.139636	+	0.241856i	0.927359	−	0.374173i	$-0.122074\pi$
$227$	7195.28	+	12462.6i	0.139636	+	0.241856i	−0.787723	+	0.616029i	$0.788740\pi$
$228$	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	$0.0157287\pi$
$230$	−102910.	+	3152.01i	−1.94536	+	0.0595843i
$231$	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	$-0.604259\pi$
$233$	−34930.9			−0.643425			−0.321713	+	0.946837i	$0.604259\pi$
$234$	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	$0.658811\pi$
$240$	−383.191	−	21203.2i	−0.00665263	−	0.368111i
$241$	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
$245$	26787.8	−	49863.5i	0.446277	−	0.830713i
$246$	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
$250$	−56352.9	−	79698.9i	−0.901646	−	1.27518i
$251$			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
$255$	−50526.4	−	27966.5i	−0.777031	−	0.430089i
$256$	10965.2	−	18992.3i	0.167316	−	0.289799i
$257$	7267.83	−	12588.3i	0.110037	−	0.190590i	−0.805748	−	0.592259i	$-0.798236\pi$
$257$	7267.83	−	12588.3i	0.110037	−	0.190590i	0.915785	+	0.401669i	$0.131570\pi$
$258$	−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	0.897140	−	0.441746i	$-0.145641\pi$
$263$	4565.64	+	7907.92i	0.0660070	+	0.114328i	−0.831133	+	0.556073i	$0.812307\pi$
$264$	−64512.4	−	809.602i	−0.925626	−	0.0116162i
$265$	−79879.8	+	2446.63i	−1.13748	+	0.0348398i
$266$	−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	$-0.316008\pi$
$270$	98995.8	−	56231.4i	1.35797	−	0.771350i
$271$	−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
$275$	85126.6	−	56362.7i	1.12564	−	0.745292i
$276$	−1714.29	+	136602.i	−0.0225043	+	1.79324i
$277$	−42196.8	+	24362.3i	−0.549946	+	0.317512i	−0.749100	−	0.662457i	$-0.769514\pi$
$277$	−42196.8	+	24362.3i	−0.549946	+	0.317512i	0.199154	+	0.979968i	$0.436181\pi$
$278$	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	0.623564	−	0.781772i	$-0.285684\pi$
$283$	20687.9	+	11944.2i	0.258311	+	0.149136i	−0.365253	+	0.930908i	$0.619017\pi$
$284$	161904.	+	93475.4i	2.00734	+	1.15894i
$285$	121852.	+	67445.6i	1.50018	+	0.830355i
$286$	−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
$290$	−19484.2	−	10467.3i	−0.231679	−	0.124463i
$291$	−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	$0.443861\pi$
$293$	−65662.9	+	113732.i	−0.764865	+	1.32479i	−0.940318	+	0.340298i	$0.889472\pi$
$294$	−109435.	−	65026.7i	−1.26608	−	0.752310i
$295$	60797.4	+	32661.7i	0.698620	+	0.375314i
$296$			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
$300$	−108879.	+	70139.9i	−1.20976	+	0.779332i
$301$	−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	$-0.908202\pi$
$307$		−	53610.8i		−	0.568821i	0.958703	−	0.284411i	$-0.0917979\pi$
$308$	22000.3	+	38105.7i	0.231914	+	0.401687i
$309$	85984.3	+	153341.i	0.900539	+	1.60599i
$310$	−93668.2	+	2868.95i	−0.974696	+	0.0298538i
$311$	−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	−0.183571	−	0.983007i	$-0.558766\pi$
$313$	56425.5	−	32577.3i	0.575953	−	0.332526i	0.759523	+	0.650480i	$0.225432\pi$
$314$		−	86466.9i		−	0.876982i
$315$	−20581.2	−	11731.5i	−0.207419	−	0.118231i
$316$	42824.5			0.428863
$317$	−25542.8	−	44241.5i	−0.254186	−	0.440262i	0.710488	−	0.703709i	$-0.248474\pi$
$317$	−25542.8	−	44241.5i	−0.254186	−	0.440262i	−0.964674	+	0.263447i	$0.915141\pi$
$318$	−2255.32	+	179713.i	−0.0223025	+	1.77716i
$319$	11567.1	−	20034.8i	0.113669	−	0.196881i
$320$	163835.	−	5018.09i	1.59996	−	0.0490048i
$321$	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
$330$	−118375.	−	196734.i	−1.08701	−	1.80656i
$331$	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
$335$	95544.3	+	51328.4i	0.851364	+	0.457371i
$336$	4853.58	+	8655.70i	0.0429916	+	0.0766697i
$337$	−102326.	−	59078.0i	−0.901003	−	0.520194i	−0.0234776	−	0.999724i	$-0.507474\pi$
$337$	−102326.	−	59078.0i	−0.901003	−	0.520194i	−0.877526	+	0.479530i	$0.840807\pi$
$338$	79467.0	−	137641.i	0.695590	−	1.20480i
$339$	80299.7	−	45027.1i	0.698738	−	0.391809i
$340$	69919.7	−	130151.i	0.604842	−	1.12587i
$341$		−	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
$345$	−127097.	+	76474.5i	−1.06782	+	0.642508i
$346$	55494.1	−	96118.6i	0.463548	−	0.802888i
$347$	53312.9	−	92340.6i	0.442765	−	0.766891i	−0.555129	−	0.831765i	$-0.687331\pi$
$347$	53312.9	−	92340.6i	0.442765	−	0.766891i	0.997894	+	0.0648732i	$0.0206643\pi$
$348$	−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	0.906648	−	0.421887i	$-0.138632\pi$
$353$	10960.5	+	18984.1i	0.0879589	+	0.152349i	−0.818689	+	0.574237i	$0.805299\pi$
$354$	79285.5	−	133431.i	0.632685	−	1.06476i
$355$	6214.36	+	202892.i	0.0493105	+	1.60994i
$356$	−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	$0.847753\pi$
$360$	44857.5	+	76714.0i	0.346122	+	0.591929i
$361$	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
$365$	1605.12	+	52405.4i	0.0120482	+	0.393360i
$366$	−4750.78	+	2663.94i	−0.0354652	+	0.0198867i
$367$	51171.2	−	29543.7i	0.379921	−	0.219347i	−0.297863	−	0.954609i	$-0.596274\pi$
$367$	51171.2	−	29543.7i	0.379921	−	0.219347i	0.677784	+	0.735261i	$0.262941\pi$
$368$	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	0.933042	−	0.359767i	$-0.117144\pi$
$373$	151372.	+	87394.5i	1.08800	+	0.628155i	0.154954	+	0.987922i	$0.450477\pi$
$374$	226826.	+	130958.i	1.62162	+	0.936243i
$375$	−126973.	−	60443.0i	−0.902916	−	0.429817i
$376$	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	$0.628799\pi$
$380$	−168622.	+	313878.i	−1.16774	+	2.17367i
$381$	−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	$-0.627555\pi$
$383$	88361.6	−	153047.i	0.602374	−	1.04334i	0.992461	−	0.122564i	$-0.0391117\pi$
$384$	2292.99	−	182715.i	0.0155503	−	1.23911i
$385$	−22609.7	+	42086.3i	−0.152536	+	0.283935i
$386$			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	$0.509070\pi$
$390$	−38016.3	+	68683.2i	−0.249943	+	0.451566i
$391$	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	$-0.981984\pi$
$397$		−	17831.6i		−	0.113138i	0.998399	−	0.0565692i	$-0.0180161\pi$
$398$	83740.7	+	145043.i	0.528653	+	0.915654i
$399$	−65167.4	−	817.821i	−0.409340	−	0.00513704i
$400$	32520.6	+	49117.0i	0.203254	+	0.306981i
$401$	−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
$405$	84777.4	−	140417.i	0.516857	−	0.856072i
$406$	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	$-0.196116\pi$
$410$	11261.8	+	367688.i	0.0669949	+	2.18731i
$411$	−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	$0.729523\pi$
$420$	29349.9	−	53025.8i	0.166383	−	0.300600i
$421$	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
$425$	160116.	−	9817.53i	0.886453	−	0.0543531i
$426$	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
$430$	273237.	+	146789.i	1.47775	+	0.793880i
$431$			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	$-0.939140\pi$
$433$		−	71258.3i		−	0.380067i	0.981778	−	0.190033i	$-0.0608596\pi$
$434$	37977.4	−	21926.3i	0.201626	−	0.116409i
$435$	−31859.8	+	575.782i	−0.168370	+	0.00304285i
$436$	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	$-0.990596\pi$
$443$	−103102.	−	178578.i	−0.525364	−	0.909957i	0.474199	−	0.880417i	$-0.342738\pi$
$444$	76156.5	+	135815.i	0.386315	+	0.688940i
$445$	−8186.10	−	267268.i	−0.0413387	−	1.34967i
$446$	−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	$0.948344\pi$
$450$	−148128.	+	279419.i	−0.731494	+	1.37985i
$451$	−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
$455$	16326.9	−	500.075i	0.0788645	−	0.00241553i
$456$	210173.	+	124886.i	1.01076	+	0.600597i
$457$	106732.	−	61621.8i	0.511049	−	0.295054i	−0.222216	−	0.974998i	$-0.571329\pi$
$457$	106732.	−	61621.8i	0.511049	−	0.295054i	0.733265	+	0.679943i	$0.237996\pi$
$458$	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	0.998253	−	0.0590826i	$-0.0188175\pi$
$463$	310023.	+	178992.i	1.44621	+	0.834971i	0.447959	+	0.894054i	$0.352151\pi$
$464$	11559.8	+	6674.08i	0.0536928	+	0.0309995i
$465$	−115684.	+	69606.9i	−0.535015	+	0.321919i
$466$	−109107.	−	188978.i	−0.502434	−	0.870242i
$467$	246564.			1.13057			0.565283	−	0.824897i	$-0.308767\pi$
$467$	246564.			1.13057			0.565283	+	0.824897i	$0.308767\pi$
$468$	88872.2	+	54328.8i	0.405765	+	0.248049i
$469$	−50753.2			−0.230737
$470$	−64117.6	+	119350.i	−0.290256	+	0.540292i
$471$	−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
$475$	−386143.	+	23676.5i	−1.71144	+	0.104937i
$476$			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	$0.0880398\pi$
$480$	248883.	−	149753.i	1.08022	−	0.649969i
$481$	−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	$0.384401\pi$
$487$			443400.i			1.86955i	−0.355235	+	0.934777i	$0.615599\pi$
$488$	−2125.70	−	3681.82i	−0.00892611	−	0.0154605i
$489$	−30414.5	+	51185.2i	−0.127193	+	0.214056i
$490$	353436.	−	10825.3i	1.47204	−	0.0450868i
$491$	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
$495$	−287378.	−	163809.i	−1.17285	−	0.668539i
$496$	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	$0.0569493\pi$
$500$	150544.	−	326752.i	0.602177	−	1.30701i
$501$	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	$-0.318541\pi$
$503$	273094.			1.07938			0.539692	+	0.841863i	$0.318541\pi$
$504$	−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	$0.945709\pi$
$510$	−6518.78	−	360704.i	−0.0250626	−	1.38679i
$511$	−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
$515$	−430195.	−	231110.i	−1.62200	−	0.871372i
$516$	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
$520$	−53978.6	−	28998.5i	−0.199625	−	0.107243i
$521$			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	$0.170608\pi$
$523$			279373.i			1.02137i	−0.859769	+	0.510683i	$0.829392\pi$
$524$	−432655.	+	249793.i	−1.57572	+	0.909742i
$525$	65727.3	−	3202.77i	0.238467	−	0.0116200i
$526$	−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
$535$	−49979.1	+	1530.80i	−0.174615	+	0.00534825i
$536$	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
$540$	361926.	+	212363.i	1.24117	+	0.728269i
$541$	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
$545$	15316.5	−	469.126i	0.0515663	−	0.00157942i
$546$	460.973	−	36732.2i	0.00154629	−	0.123215i
$547$	−271696.	+	156864.i	−0.908046	+	0.524261i	−0.879802	−	0.475340i	$-0.842325\pi$
$547$	−271696.	+	156864.i	−0.908046	+	0.524261i	−0.0282443	+	0.999601i	$0.508992\pi$
$548$	−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
$555$	−81873.8	+	147919.i	−0.265802	+	0.480219i
$556$	212189.	+	367523.i	0.686395	+	1.18887i
$557$	37442.2			0.120684			0.0603422	−	0.998178i	$-0.480781\pi$
$557$	37442.2			0.120684			0.0603422	+	0.998178i	$0.480781\pi$
$558$	145167.	+	266676.i	0.466230	+	0.856477i
$559$	110922.			0.354972
$560$	−24283.3	−	13045.5i	−0.0774340	−	0.0415992i
$561$	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	$0.424029\pi$
$563$	−229254.	+	397080.i	−0.723270	+	1.25274i	−0.959682	+	0.281088i	$0.909305\pi$
$564$	154544.	+	91830.9i	0.485841	+	0.288689i
$565$	−121024.	+	225278.i	−0.379119	+	0.705704i
$566$			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	$0.284367\pi$
$570$	15721.0	+	869893.i	0.0483873	+	2.67742i
$571$	−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	$-0.840601\pi$
$577$		−	319678.i		−	0.960198i	0.877214	−	0.480099i	$-0.159399\pi$
$578$	−55109.5	−	95452.5i	−0.164957	−	0.285714i
$579$	116359.	+	207510.i	0.347089	+	0.618986i
$580$	−2495.73	−	81482.9i	−0.00741893	−	0.242220i
$581$	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
$585$	624.467	+	113096.i	0.00182473	+	0.330473i
$586$	−820392.			−2.38905
$587$	67386.2	+	116716.i	0.195567	+	0.338731i	0.947086	−	0.320980i	$-0.104012\pi$
$587$	67386.2	+	116716.i	0.195567	+	0.338731i	−0.751520	+	0.659711i	$0.770679\pi$
$588$	5887.59	−	469148.i	0.0170288	−	1.35692i
$589$	−185711.	+	321661.i	−0.535313	+	0.927189i
$590$	13199.1	+	430936.i	0.0379175	+	1.23797i
$591$	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	$-0.561810\pi$
$593$	−135712.			−0.385929			−0.192965	+	0.981206i	$0.561810\pi$
$594$	−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	$0.615436\pi$
$600$	−219533.	−	112875.i	−0.609814	−	0.313540i
$601$	−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
$605$	−142480.	+	265217.i	−0.389263	+	0.724586i
$606$	−387765.	−	691526.i	−1.05590	−	1.88306i
$607$	−130456.	−	75319.0i	−0.354069	−	0.204422i	0.312407	−	0.949948i	$-0.398865\pi$
$607$	−130456.	−	75319.0i	−0.354069	−	0.204422i	−0.666476	+	0.745526i	$0.732198\pi$
$608$	399541.	−	692025.i	1.08082	−	1.87204i
$609$	13006.0	−	7292.97i	0.0350679	−	0.0196639i
$610$	7160.17	−	13328.2i	0.0192426	−	0.0358187i
$611$			48451.0i			0.129784i
$612$	−478536.	−	12012.7i	−1.27765	−	0.0320729i
$613$			404962.i			1.07769i	0.842405	+	0.538845i	$0.181139\pi$
$613$			404962.i			1.07769i	−0.842405	+	0.538845i	$0.818861\pi$
$614$	290038.	−	167453.i	0.769338	−	0.444178i
$615$	273237.	+	454107.i	0.722418	+	1.20063i
$616$	−41931.8	+	72628.0i	−0.110505	+	0.191400i
$617$	319373.	−	553170.i	0.838934	−	1.45308i	−0.0518531	−	0.998655i	$-0.516513\pi$
$617$	319373.	−	553170.i	0.838934	−	1.45308i	0.890787	−	0.454421i	$-0.150154\pi$
$618$	−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
$625$	387699.	−	47723.1i	0.992509	−	0.122171i
$626$	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
$630$	−817.127	−	147988.i	−0.00205877	−	0.372861i
$631$	−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
$635$	−9298.11	−	303573.i	−0.0230594	−	0.752864i
$636$	−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	0.415847	−	0.909434i	$-0.363485\pi$
$643$	−67732.2	−	39105.2i	−0.163822	−	0.0945828i	−0.579670	+	0.814852i	$0.696818\pi$
$644$	153786.	+	88788.3i	0.370804	+	0.214084i
$645$	446786.	−	8074.48i	1.07394	−	0.0194086i
$646$	−496241.	−	859515.i	−1.18913	−	2.05963i
$647$	429610.			1.02628			0.513139	−	0.858305i	$-0.328482\pi$
$647$	429610.			1.02628			0.513139	+	0.858305i	$0.328482\pi$
$648$	156293.	−	241815.i	0.372212	−	0.575881i
$649$	−450950.			−1.07063
$650$	−13345.5	−	217653.i	−0.0315869	−	0.515156i
$651$	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	−0.859797	−	0.510636i	$-0.829410\pi$
$653$	5255.41	−	9102.64i	0.0123248	−	0.0213472i	0.872122	+	0.489288i	$0.162743\pi$
$654$	432.444	−	34458.9i	0.00101105	−	0.0805650i
$655$	−477851.	−	256712.i	−1.11381	−	0.598361i
$656$		−	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	$0.222071\pi$
$660$	409817.	−	740407.i	0.940811	−	1.69974i
$661$	−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
$670$	20742.6	+	677224.i	0.0462076	+	1.50863i
$671$	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	−0.914114	−	0.405458i	$-0.867112\pi$
$673$	−462003.	+	266738.i	−1.02003	+	0.588917i	−0.105920	+	0.994375i	$0.533779\pi$
$674$		−	738119.i		−	1.62483i
$675$	10748.1	+	455498.i	0.0235897	+	0.999722i
$676$	585793.			1.28189
$677$	285619.	+	494707.i	0.623175	+	1.07937i	0.988891	+	0.148645i	$0.0474911\pi$
$677$	285619.	+	494707.i	0.623175	+	1.07937i	−0.365715	+	0.930727i	$0.619176\pi$
$678$	494415.	+	293784.i	1.07555	+	0.639099i
$679$	−37991.7	+	65803.6i	−0.0824042	+	0.142728i
$680$	281460.	−	8620.81i	0.608695	−	0.0186436i
$681$	−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	$-0.530426\pi$
$683$	−89045.3			−0.190884			−0.0954420	+	0.995435i	$0.530426\pi$
$684$	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
$690$	−810719.	−	448735.i	−1.70283	−	0.942523i
$691$	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
$695$	−218066.	+	405915.i	−0.451460	+	0.840360i
$696$	−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
$700$	10303.2	+	168036.i	0.0210268	+	0.342930i
$701$		−	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
$705$	3526.95	+	195157.i	0.00709613	+	0.392651i
$706$	−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
$715$	227975.	−	6982.63i	0.445940	−	0.0136586i
$716$	−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	$-0.165300\pi$
$720$	94515.8	−	165814.i	0.182322	−	0.319857i
$721$	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
$725$	73803.1	−	48865.4i	0.140410	−	0.0929662i
$726$	582067.	+	345867.i	1.10433	+	0.656200i
$727$	112849.	−	65153.1i	0.213514	−	0.123273i	−0.389429	−	0.921056i	$-0.627328\pi$
$727$	112849.	−	65153.1i	0.213514	−	0.123273i	0.602944	+	0.797784i	$0.293994\pi$
$728$	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	−0.353570	−	0.935408i	$-0.615032\pi$
$733$	−720205.	−	415810.i	−1.34044	−	0.773904i	−0.986872	+	0.161504i	$0.948366\pi$
$734$	319666.	+	184559.i	0.593341	+	0.342565i
$735$	436506.	−	262646.i	0.808008	−	0.486179i
$736$	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	$0.409940\pi$
$740$	−381024.	−	204694.i	−0.695808	−	0.373803i
$741$	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	$-0.652295\pi$
$743$	297321.	−	514976.i	0.538578	−	0.932844i	0.998981	−	0.0451342i	$-0.0143715\pi$
$744$	−206715.	+	115913.i	−0.373444	+	0.209404i
$745$	119984.	+	64458.1i	0.216178	+	0.116135i
$746$			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
$750$	−69598.6	−	875722.i	−0.123731	−	1.55684i
$751$	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	$0.161044\pi$
$757$			555428.i			0.969251i	−0.874722	+	0.484625i	$0.838956\pi$
$758$	−353261.	−	611867.i	−0.614834	−	1.06492i
$759$	495095.	−	833206.i	0.859419	−	1.44633i
$760$	−678785.	+	20790.4i	−1.17518	+	0.0359945i
$761$	−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
$765$	−262356.	−	448674.i	−0.448299	−	0.766669i
$766$	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	$0.836189\pi$
$770$	−298310.	+	9136.91i	−0.503138	+	0.0154105i
$771$	114106.	−	63983.7i	0.191956	−	0.107637i
$772$	−527100.	+	304321.i	−0.884419	+	0.510620i
$773$	−1.11045e6			−1.85841			−0.929203	−	0.369569i	$-0.879505\pi$
$773$	−1.11045e6			−1.85841			−0.929203	+	0.369569i	$0.879505\pi$
$774$	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
$780$	−289294.	+	5228.22i	−0.475499	+	0.00859340i
$781$	−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
$785$	304831.	+	163762.i	0.494674	+	0.265750i
$786$	−623162.	+	1.04873e6i	−1.00869	+	1.69754i
$787$	154665.	+	89296.0i	0.249714	+	0.144172i	0.619633	−	0.784891i	$-0.287281\pi$
$787$	154665.	+	89296.0i	0.249714	+	0.144172i	−0.369919	+	0.929064i	$0.620615\pi$
$788$	−43571.2	+	75467.5i	−0.0701693	+	0.121537i
$789$	−1031.26	+	82175.0i	−0.00165659	+	0.132004i
$790$	−137467.	+	255885.i	−0.220264	+	0.410007i
$791$		−	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
$795$	−629290.	−	348314.i	−0.995673	−	0.551107i
$796$	−308648.	+	534595.i	−0.487122	+	0.843720i
$797$	136648.	−	236682.i	0.215123	−	0.372604i	−0.738188	−	0.674596i	$-0.764318\pi$
$797$	136648.	−	236682.i	0.215123	−	0.372604i	0.953311	+	0.301991i	$0.0976514\pi$
$798$	−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
$805$	5902.76	+	192719.i	0.00910884	+	0.297394i
$806$	−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	$-0.0224985\pi$
$810$	1.02447e6	+	20057.8i	1.56145	+	0.0305713i
$811$	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
$815$	−5063.27	−	165310.i	−0.00762282	−	0.248877i
$816$	−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	$0.0412058\pi$
$823$	1.08322e6	+	625394.i	1.59924	+	0.923325i	0.607612	+	0.794234i	$0.292128\pi$
$824$	−742384.	−	428615.i	−1.09339	−	0.631267i
$825$	917762.	−	44720.9i	1.34841	−	0.0657056i
$826$	−100875.	−	174721.i	−0.147851	−	0.256086i
$827$	399216.			0.583709			0.291855	−	0.956463i	$-0.405728\pi$
$827$	399216.			0.583709			0.291855	+	0.956463i	$0.405728\pi$
$828$	−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	$0.372137\pi$
$830$	898984.	−	1.67340e6i	1.30496	−	2.42908i
$831$	−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
$835$	−131747.	+	245237.i	−0.188959	+	0.351733i
$836$		−	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	$0.134407\pi$
$840$	115495.	−	2087.26i	0.163683	−	0.00295814i
$841$	−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
$850$	553234.	+	835569.i	0.765722	+	1.15650i
$851$	−428997.	−	247682.i	−0.592373	−	0.342007i
$852$	822928.	+	1.46758e6i	1.13366	+	2.02173i
$853$	838778.	−	484269.i	1.15279	−	0.665562i	0.203222	−	0.979133i	$-0.434859\pi$
$853$	838778.	−	484269.i	1.15279	−	0.665562i	0.949565	+	0.313571i	$0.101525\pi$
$854$			7079.93i			0.00970763i
$855$	632711.	+	1.08205e6i	0.865512	+	1.48018i
$856$	−87773.8			−0.119789
$857$	−230029.	−	398421.i	−0.313199	−	0.542476i	0.665854	−	0.746082i	$-0.268067\pi$
$857$	−230029.	−	398421.i	−0.313199	−	0.542476i	−0.979053	+	0.203606i	$0.934734\pi$
$858$	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	$0.989794\pi$
$860$	34998.8	+	1.14267e6i	0.0473213	+	1.54499i
$861$	−213202.	−	126686.i	−0.287597	−	0.170892i
$862$	−514429.	+	297006.i	−0.692327	+	0.399715i
$863$	−665897.			−0.894098			−0.447049	−	0.894509i	$-0.647525\pi$
$863$	−665897.			−0.894098			−0.447049	+	0.894509i	$0.647525\pi$
$864$	−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
$870$	−102629.	−	170565.i	−0.135591	−	0.225347i
$871$	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
$875$	−149252.	+	105532.i	−0.194941	+	0.137838i
$876$	212555.	+	379064.i	0.276990	+	0.493974i
$877$	−1.13315e6	−	654227.i	−1.47330	−	0.850608i	−0.473748	−	0.880661i	$-0.657099\pi$
$877$	−1.13315e6	−	654227.i	−1.47330	−	0.850608i	−0.999548	+	0.0300525i	$0.990433\pi$
$878$	−13483.9	+	23354.8i	−0.0174915	+	0.0302962i
$879$	−1.03092e6	+	578075.i	−1.33428	+	0.748181i
$880$	−339072.	−	182157.i	−0.437851	−	0.235223i
$881$		−	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	$-0.699645\pi$
$883$		−	1.26259e6i		−	1.61935i	0.586882	−	0.809673i	$-0.300355\pi$
$884$	285842.	−	165031.i	0.365782	−	0.211184i
$885$	320238.	+	532222.i	0.408871	+	0.679526i
$886$	644079.	−	1.11558e6i	0.820486	−	1.42112i
$887$	−334515.	+	579397.i	−0.425176	+	0.736426i	−0.996437	−	0.0843427i	$-0.973121\pi$
$887$	−334515.	+	579397.i	−0.425176	+	0.736426i	0.571261	+	0.820768i	$0.306454\pi$
$888$	−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
$895$	−20133.0	−	657320.i	−0.0251340	−	0.820599i
$896$	−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
$900$	−1.16488e6	+	42117.9i	−1.43812	+	0.0519974i
$901$	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
$905$	858049.	−	26281.0i	1.04765	−	0.0320882i
$906$	580451.	−	325481.i	0.707147	−	0.396524i
$907$	928585.	−	536119.i	1.12877	−	0.651698i	0.185148	−	0.982711i	$-0.440724\pi$
$907$	928585.	−	536119.i	1.12877	−	0.651698i	0.943626	+	0.331013i	$0.107390\pi$
$908$	−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
$915$	−393.864	−	21793.7i	−0.000470439	−	0.0260309i
$916$	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	$0.357888\pi$
$920$	342290.	−	637150.i	0.404407	−	0.752776i
$921$	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
$925$	−28741.4	−	468749.i	−0.0335912	−	0.547844i
$926$			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	$0.345101\pi$
$930$	−737915.	−	408438.i	−0.853179	−	0.472237i
$931$	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	$0.208542\pi$
$937$			1.06986e6i			1.21856i	−0.792953	+	0.609282i	$0.791458\pi$
$938$	−158527.	−	274578.i	−0.180177	−	0.312075i
$939$	586345.	+	7358.36i	0.665000	+	0.00834546i
$940$	−499123.	+	15287.6i	−0.564875	+	0.0173015i
$941$	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
$945$	−105304.	−	185389.i	−0.117919	−	0.207597i
$946$	−2.02666e6			−2.26464
$947$	−124371.	−	215417.i	−0.138682	−	0.240203i	0.788316	−	0.615270i	$-0.210953\pi$
$947$	−124371.	−	215417.i	−0.138682	−	0.240203i	−0.926998	+	0.375067i	$0.877620\pi$
$948$	331340.	+	196884.i	0.368686	+	0.219075i
$949$	−58565.1	+	101438.i	−0.0650289	+	0.112633i
$950$	−1.33421e6	−	2.01510e6i	−1.47835	−	2.23280i
$951$	5769.47	−	459735.i	0.00637933	−	0.508331i
$952$	−114117.	+	65885.4i	−0.125915	+	0.0726969i
$953$	−399593.			−0.439979			−0.219990	−	0.975502i	$-0.570602\pi$
$953$	−399593.			−0.439979			−0.219990	+	0.975502i	$0.570602\pi$
$954$	−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
$960$	1.29069e6	+	714400.i	1.40049	+	0.775173i
$961$	281733.	+	487975.i	0.305063	+	0.528385i
$962$	−262165.			−0.283286
$963$	77457.7	+	142292.i	0.0835242	+	0.153436i
$964$	−210901.			−0.226947
$965$	−582162.	−	312750.i	−0.625157	−	0.335848i
$966$	433578.	+	5441.20i	0.464636	+	0.00583097i
$967$	−54468.4	−	31447.3i	−0.0582494	−	0.0336303i	0.470592	−	0.882351i	$-0.344040\pi$
$967$	−54468.4	−	31447.3i	−0.0582494	−	0.0336303i	−0.528842	+	0.848720i	$0.677374\pi$
$968$	−264243.	+	457682.i	−0.282002	+	0.488443i
$969$	−1.22923e6	−	730414.i	−1.30914	−	0.777896i
$970$	893575.	+	480048.i	0.949703	+	0.510201i
$971$		−	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
$975$	−170136.	−	264104.i	−0.178973	−	0.277821i
$976$	−4565.40	+	7907.50i	−0.00479269	+	0.00830117i
$977$	503360.	−	871845.i	0.527339	−	0.913377i	−0.472154	−	0.881516i	$-0.656523\pi$
$977$	503360.	−	871845.i	0.527339	−	0.913377i	0.999492	−	0.0318610i	$-0.0101434\pi$
$978$	−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	0.964058	−	0.265693i	$-0.0856009\pi$
$983$	243439.	+	421648.i	0.251932	+	0.436358i	−0.712126	+	0.702052i	$0.752268\pi$
$984$	455007.	+	811443.i	0.469924	+	0.838046i
$985$	−94573.1	+	2896.67i	−0.0974755	+	0.00298556i
$986$	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
$990$	−11409.7	−	2.06639e6i	−0.0116413	−	2.10834i
$991$	−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
$995$	−669934.	+	20519.3i	−0.676684	+	0.0207261i
$996$	−2.16684e6	−	1.28755e6i	−2.18428	−	1.29791i
$997$	−985456.	+	568953.i	−0.991395	+	0.572382i	−0.905691	−	0.423938i	$-0.860647\pi$
$997$	−985456.	+	568953.i	−0.991395	+	0.572382i	−0.0857043	+	0.996321i	$0.527314\pi$
$998$	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.14.20	yes	44
3.2	odd	2		135.5.h.a.44.3		44
5.4	even	2	inner	45.5.h.a.14.3	✓	44
9.2	odd	6	inner	45.5.h.a.29.3	yes	44
9.4	even	3		405.5.d.a.404.6		44
9.5	odd	6		405.5.d.a.404.40		44
9.7	even	3		135.5.h.a.89.20		44
15.14	odd	2		135.5.h.a.44.20		44
45.4	even	6		405.5.d.a.404.39		44
45.14	odd	6		405.5.d.a.404.5		44
45.29	odd	6	inner	45.5.h.a.29.20	yes	44
45.34	even	6		135.5.h.a.89.3		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.h.a.14.3	✓	44	5.4	even	2	inner
45.5.h.a.14.20	yes	44	1.1	even	1	trivial
45.5.h.a.29.3	yes	44	9.2	odd	6	inner
45.5.h.a.29.20	yes	44	45.29	odd	6	inner
135.5.h.a.44.3		44	3.2	odd	2
135.5.h.a.44.20		44	15.14	odd	2
135.5.h.a.89.3		44	45.34	even	6
135.5.h.a.89.20		44	9.7	even	3
405.5.d.a.404.5		44	45.14	odd	6
405.5.d.a.404.6		44	9.4	even	3
405.5.d.a.404.39		44	45.4	even	6
405.5.d.a.404.40		44	9.5	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} +(-24.9883 + 0.765363i) 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} +(-196.857 - 108.961i) q^{15} +(47.1259 + 81.6244i) q^{16} +256.666 q^{17} +(-263.921 + 431.727i) q^{18} -618.990 q^{19} +(272.415 - 507.082i) 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} +(623.828 - 38.2502i) q^{25} -348.899i q^{26} +(-27.4379 + 728.483i) q^{27} +269.362i q^{28} +(122.649 - 70.8112i) q^{29} +(-25.3979 - 1405.34i) 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} +(1096.60 - 33.5877i) q^{40} +(-2039.87 - 1177.72i) q^{41} +(321.695 + 573.699i) q^{42} +(-1719.96 + 993.020i) q^{43} +3761.15i q^{44} +(-1022.17 - 1748.08i) q^{45} +4118.32 q^{46} +(-433.754 - 751.284i) q^{47} +(-10.6445 + 848.199i) q^{48} +(-1132.07 + 1960.80i) q^{49} +(2155.46 + 3255.47i) 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} +(4439.00 - 2670.95i) q^{60} +(48.4383 + 83.8977i) q^{61} +3748.49 q^{62} +(808.494 + 494.243i) q^{63} -6556.49 q^{64} +(1230.01 + 660.788i) 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} +(-1609.49 - 864.655i) q^{70} -8119.50i q^{71} +(-1699.51 - 3122.05i) q^{72} -2097.20i q^{73} +(4065.15 - 2347.01i) q^{74} +(5002.51 + 2572.07i) 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} +(-6413.64 + 196.443i) q^{85} +(-10744.6 - 6203.39i) q^{86} +(1274.50 + 15.9944i) q^{87} +(-6208.20 + 3584.30i) q^{88} +10695.7i q^{89} +(6264.49 - 10990.1i) q^{90} -653.383 q^{91} +(7589.57 + 13145.5i) q^{92} +(4710.42 - 2641.31i) q^{93} +(2709.66 - 4693.26i) q^{94} +(15467.5 - 473.752i) 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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