LMFDB - Embedded newform 45.5.h.a.14.16

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			14.16
Character	$\chi$	$=$	45.14
Dual form			45.5.h.a.29.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.64811 + 2.85461i) q^{2} +(5.28472 - 7.28504i) q^{3} +(2.56747 - 4.44699i) q^{4} +(-9.73566 + 23.0264i) q^{5} +(29.5057 + 3.07927i) q^{6} +(64.7475 - 37.3820i) q^{7} +69.6654 q^{8} +(-25.1435 - 76.9987i) q^{9} +(-81.7769 + 10.1586i) q^{10} +(-90.0492 + 51.9899i) q^{11} +(-18.8281 - 42.2052i) q^{12} +(183.381 + 105.875i) q^{13} +(213.422 + 123.219i) q^{14} +(116.298 + 192.613i) q^{15} +(73.7366 + 127.716i) q^{16} -321.724 q^{17} +(178.362 - 198.677i) q^{18} -422.726 q^{19} +(77.4023 + 102.414i) q^{20} +(69.8432 - 669.241i) q^{21} +(-296.822 - 171.370i) q^{22} +(-220.685 + 382.237i) q^{23} +(368.162 - 507.515i) q^{24} +(-435.434 - 448.355i) q^{25} +697.974i q^{26} +(-693.815 - 223.745i) q^{27} -383.909i q^{28} +(599.538 - 346.144i) q^{29} +(-358.162 + 649.433i) q^{30} +(-381.537 + 660.842i) q^{31} +(314.271 - 544.334i) q^{32} +(-97.1362 + 930.764i) q^{33} +(-530.237 - 918.397i) q^{34} +(230.414 + 1854.84i) q^{35} +(-406.968 - 85.8792i) q^{36} -158.516i q^{37} +(-696.698 - 1206.72i) q^{38} +(1740.42 - 776.416i) q^{39} +(-678.239 + 1604.15i) q^{40} +(132.735 + 76.6349i) q^{41} +(2025.53 - 903.607i) q^{42} +(-1831.30 + 1057.30i) q^{43} +533.931i q^{44} +(2017.80 + 170.669i) q^{45} -1454.85 q^{46} +(1057.05 + 1830.86i) q^{47} +(1320.09 + 137.767i) q^{48} +(1594.32 - 2761.45i) q^{49} +(562.237 - 1981.93i) q^{50} +(-1700.22 + 2343.77i) q^{51} +(941.650 - 543.662i) q^{52} +1653.34 q^{53} +(-504.777 - 2349.33i) q^{54} +(-320.454 - 2579.67i) q^{55} +(4510.66 - 2604.23i) q^{56} +(-2233.99 + 3079.57i) q^{57} +(1976.21 + 1140.96i) q^{58} +(-2896.82 - 1672.48i) q^{59} +(1155.14 - 22.6489i) q^{60} +(2044.93 + 3541.93i) q^{61} -2515.26 q^{62} +(-4506.34 - 4045.56i) q^{63} +4431.38 q^{64} +(-4223.25 + 3191.84i) q^{65} +(-2817.06 + 1256.71i) q^{66} +(6150.36 + 3550.91i) q^{67} +(-826.018 + 1430.70i) q^{68} +(1618.35 + 3627.71i) q^{69} +(-4915.10 + 3714.72i) q^{70} -4657.74i q^{71} +(-1751.63 - 5364.15i) q^{72} -5910.56i q^{73} +(452.501 - 261.251i) q^{74} +(-5567.43 + 802.719i) q^{75} +(-1085.34 + 1879.86i) q^{76} +(-3886.97 + 6732.44i) q^{77} +(5084.76 + 3688.59i) q^{78} +(-1362.66 - 2360.20i) q^{79} +(-3658.71 + 454.496i) q^{80} +(-5296.61 + 3872.03i) q^{81} +505.210i q^{82} +(-2037.42 - 3528.92i) q^{83} +(-2796.79 - 2028.85i) q^{84} +(3132.20 - 7408.16i) q^{85} +(-6036.38 - 3485.11i) q^{86} +(646.723 - 6196.93i) q^{87} +(-6273.31 + 3621.90i) q^{88} -9281.82i q^{89} +(2838.35 + 6041.30i) q^{90} +15831.3 q^{91} +(1133.20 + 1962.77i) q^{92} +(2797.94 + 6271.88i) q^{93} +(-3484.26 + 6034.91i) q^{94} +(4115.51 - 9733.87i) q^{95} +(-2304.65 - 5166.13i) q^{96} +(3065.38 - 1769.80i) q^{97} +10510.5 q^{98} +(6267.31 + 5626.47i) 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 $

$2$	1.64811	+	2.85461i	0.412027	+	0.713652i	0.995111	−	0.0987596i	$-0.0314875\pi$
$2$	1.64811	+	2.85461i	0.412027	+	0.713652i	−0.583084	+	0.812412i	$0.698154\pi$
$3$	5.28472	−	7.28504i	0.587191	−	0.809448i
$3$	5.28472	−	7.28504i	0.587191	−	0.809448i
$4$	2.56747	−	4.44699i	0.160467	−	0.277937i
$5$	−9.73566	+	23.0264i	−0.389426	+	0.921058i
$5$	−9.73566	+	23.0264i	−0.389426	+	0.921058i
$6$	29.5057	+	3.07927i	0.819603	+	0.0855353i
$7$	64.7475	−	37.3820i	1.32138	−	0.762897i	0.337429	−	0.941351i	$-0.390443\pi$
$7$	64.7475	−	37.3820i	1.32138	−	0.762897i	0.983948	+	0.178454i	$0.0571094\pi$
$8$	69.6654			1.08852
$9$	−25.1435	−	76.9987i	−0.310414	−	0.950602i
$10$	−81.7769	+	10.1586i	−0.817769	+	0.101586i
$11$	−90.0492	+	51.9899i	−0.744208	+	0.429669i	−0.823597	−	0.567175i	$-0.808036\pi$
$11$	−90.0492	+	51.9899i	−0.744208	+	0.429669i	0.0793890	+	0.996844i	$0.474703\pi$
$12$	−18.8281	−	42.2052i	−0.130751	−	0.293092i
$13$	183.381	+	105.875i	1.08509	+	0.626479i	0.932266	−	0.361774i	$-0.117829\pi$
$13$	183.381	+	105.875i	1.08509	+	0.626479i	0.152827	+	0.988253i	$0.451162\pi$
$14$	213.422	+	123.219i	1.08889	+	0.628669i
$15$	116.298	+	192.613i	0.516881	+	0.856057i
$16$	73.7366	+	127.716i	0.288034	+	0.498889i
$17$	−321.724			−1.11323			−0.556616	−	0.830770i	$-0.687901\pi$
$17$	−321.724			−1.11323			−0.556616	+	0.830770i	$0.687901\pi$
$18$	178.362	−	198.677i	0.550500	−	0.613201i
$19$	−422.726			−1.17099			−0.585493	−	0.810678i	$-0.699099\pi$
$19$	−422.726			−1.17099			−0.585493	+	0.810678i	$0.699099\pi$
$20$	77.4023	+	102.414i	0.193506	+	0.256035i
$21$	69.8432	−	669.241i	0.158375	−	1.51755i
$22$	−296.822	−	171.370i	−0.613268	−	0.354071i
$23$	−220.685	+	382.237i	−0.417173	+	0.722566i	−0.995654	−	0.0931306i	$-0.970313\pi$
$23$	−220.685	+	382.237i	−0.417173	+	0.722566i	0.578480	+	0.815696i	$0.303646\pi$
$24$	368.162	−	507.515i	0.639170	−	0.881102i
$25$	−435.434	−	448.355i	−0.696694	−	0.717368i
$26$			697.974i			1.03251i
$27$	−693.815	−	223.745i	−0.951735	−	0.306921i
$28$		−	383.909i		−	0.489679i
$29$	599.538	−	346.144i	0.712887	−	0.411586i	−0.0992418	−	0.995063i	$-0.531642\pi$
$29$	599.538	−	346.144i	0.712887	−	0.411586i	0.812129	+	0.583478i	$0.198308\pi$
$30$	−358.162	+	649.433i	−0.397958	+	0.721592i
$31$	−381.537	+	660.842i	−0.397021	+	0.687661i	−0.993357	−	0.115074i	$-0.963289\pi$
$31$	−381.537	+	660.842i	−0.397021	+	0.687661i	0.596336	+	0.802735i	$0.296623\pi$
$32$	314.271	−	544.334i	0.306905	−	0.531576i
$33$	−97.1362	+	930.764i	−0.0891976	+	0.854696i
$34$	−530.237	−	918.397i	−0.458682	−	0.794461i
$35$	230.414	+	1854.84i	0.188093	+	1.51416i
$36$	−406.968	−	85.8792i	−0.314018	−	0.0662648i
$37$		−	158.516i		−	0.115790i	−0.998323	−	0.0578948i	$-0.981561\pi$
$37$		−	158.516i		−	0.115790i	0.998323	−	0.0578948i	$-0.0184388\pi$
$38$	−696.698	−	1206.72i	−0.482478	−	0.835676i
$39$	1740.42	−	776.416i	1.14426	−	0.510464i
$40$	−678.239	+	1604.15i	−0.423899	+	1.00259i
$41$	132.735	+	76.6349i	0.0789622	+	0.0455888i	0.538961	−	0.842331i	$-0.318817\pi$
$41$	132.735	+	76.6349i	0.0789622	+	0.0455888i	−0.459999	+	0.887919i	$0.652150\pi$
$42$	2025.53	−	903.607i	1.14826	−	0.512249i
$43$	−1831.30	+	1057.30i	−0.990430	+	0.571825i	−0.905403	−	0.424554i	$-0.860431\pi$
$43$	−1831.30	+	1057.30i	−0.990430	+	0.571825i	−0.0850269	+	0.996379i	$0.527098\pi$
$44$			533.931i			0.275791i
$45$	2017.80	+	170.669i	0.996442	+	0.0842808i
$46$	−1454.85			−0.687547
$47$	1057.05	+	1830.86i	0.478518	+	0.828818i	0.999697	−	0.0246296i	$-0.00784064\pi$
$47$	1057.05	+	1830.86i	0.478518	+	0.828818i	−0.521178	+	0.853448i	$0.674507\pi$
$48$	1320.09	+	137.767i	0.572956	+	0.0597947i
$49$	1594.32	−	2761.45i	0.664025	−	1.15013i
$50$	562.237	−	1981.93i	0.224895	−	0.792773i
$51$	−1700.22	+	2343.77i	−0.653680	+	0.901104i
$52$	941.650	−	543.662i	0.348243	−	0.201058i
$53$	1653.34			0.588585			0.294292	−	0.955715i	$-0.404916\pi$
$53$	1653.34			0.588585			0.294292	+	0.955715i	$0.404916\pi$
$54$	−504.777	−	2349.33i	−0.173106	−	0.805668i
$55$	−320.454	−	2579.67i	−0.105935	−	0.852783i
$56$	4510.66	−	2604.23i	1.43835	−	0.830430i
$57$	−2233.99	+	3079.57i	−0.687592	+	0.947852i
$58$	1976.21	+	1140.96i	0.587458	+	0.339169i
$59$	−2896.82	−	1672.48i	−0.832181	−	0.480460i	0.0224180	−	0.999749i	$-0.492864\pi$
$59$	−2896.82	−	1672.48i	−0.832181	−	0.480460i	−0.854599	+	0.519289i	$0.826197\pi$
$60$	1155.14	−	22.6489i	0.320872	−	0.00629136i
$61$	2044.93	+	3541.93i	0.549566	+	0.951875i	0.998304	+	0.0582124i	$0.0185401\pi$
$61$	2044.93	+	3541.93i	0.549566	+	0.951875i	−0.448739	+	0.893663i	$0.648127\pi$
$62$	−2515.26			−0.654334
$63$	−4506.34	−	4045.56i	−1.13538	−	1.01929i
$64$	4431.38			1.08188
$65$	−4223.25	+	3191.84i	−0.999587	+	0.755466i
$66$	−2817.06	+	1256.71i	−0.646708	+	0.288502i
$67$	6150.36	+	3550.91i	1.37010	+	0.791025i	0.990940	−	0.134307i	$-0.0428810\pi$
$67$	6150.36	+	3550.91i	1.37010	+	0.791025i	0.379156	+	0.925333i	$0.376214\pi$
$68$	−826.018	+	1430.70i	−0.178637	+	0.309408i
$69$	1618.35	+	3627.71i	0.339919	+	0.761964i
$70$	−4915.10	+	3714.72i	−1.00308	+	0.758107i
$71$		−	4657.74i		−	0.923972i	−0.886887	−	0.461986i	$-0.847137\pi$
$71$		−	4657.74i		−	0.923972i	0.886887	−	0.461986i	$-0.152863\pi$
$72$	−1751.63	−	5364.15i	−0.337892	−	1.03475i
$73$		−	5910.56i		−	1.10913i	−0.832140	−	0.554566i	$-0.812884\pi$
$73$		−	5910.56i		−	1.10913i	0.832140	−	0.554566i	$-0.187116\pi$
$74$	452.501	−	261.251i	0.0826335	−	0.0477085i
$75$	−5567.43	+	802.719i	−0.989765	+	0.142706i
$76$	−1085.34	+	1879.86i	−0.187904	+	0.325460i
$77$	−3886.97	+	6732.44i	−0.655587	+	1.13551i
$78$	5084.76	+	3688.59i	0.835760	+	0.606278i
$79$	−1362.66	−	2360.20i	−0.218340	−	0.378176i	0.735961	−	0.677024i	$-0.236731\pi$
$79$	−1362.66	−	2360.20i	−0.218340	−	0.378176i	−0.954301	+	0.298848i	$0.903398\pi$
$80$	−3658.71	+	454.496i	−0.571673	+	0.0710150i
$81$	−5296.61	+	3872.03i	−0.807287	+	0.590159i
$82$			505.210i			0.0751354i
$83$	−2037.42	−	3528.92i	−0.295750	−	0.512254i	0.679409	−	0.733760i	$-0.262236\pi$
$83$	−2037.42	−	3528.92i	−0.295750	−	0.512254i	−0.975159	+	0.221506i	$0.928903\pi$
$84$	−2796.79	−	2028.85i	−0.396370	−	0.287535i
$85$	3132.20	−	7408.16i	0.433522	−	1.02535i
$86$	−6036.38	−	3485.11i	−0.816168	−	0.471215i
$87$	646.723	−	6196.93i	0.0854436	−	0.818725i
$88$	−6273.31	+	3621.90i	−0.810087	+	0.467704i
$89$		−	9281.82i		−	1.17180i	−0.810384	−	0.585899i	$-0.800741\pi$
$89$		−	9281.82i		−	1.17180i	0.810384	−	0.585899i	$-0.199259\pi$
$90$	2838.35	+	6041.30i	0.350414	+	0.745839i
$91$	15831.3			1.91176
$92$	1133.20	+	1962.77i	0.133885	+	0.231896i
$93$	2797.94	+	6271.88i	0.323499	+	0.725156i
$94$	−3484.26	+	6034.91i	−0.394325	+	0.682992i
$95$	4115.51	−	9733.87i	0.456013	−	1.07854i
$96$	−2304.65	−	5166.13i	−0.250071	−	0.560561i
$97$	3065.38	−	1769.80i	0.325793	−	0.188097i	−0.328179	−	0.944616i	$-0.606435\pi$
$97$	3065.38	−	1769.80i	0.325793	−	0.188097i	0.653972	+	0.756519i	$0.273102\pi$
$98$	10510.5			1.09439
$99$	6267.31	+	5626.47i	0.639456	+	0.574071i
$100$	−3111.80	+	785.231i	−0.311180	+	0.0785231i
$101$	−3336.73	+	1926.46i	−0.327098	+	0.188850i	−0.654552	−	0.756017i	$-0.727143\pi$
$101$	−3336.73	+	1926.46i	−0.327098	+	0.188850i	0.327454	+	0.944867i	$0.393809\pi$
$102$	−9492.70	−	990.676i	−0.912409	−	0.0952207i
$103$	3577.38	+	2065.40i	0.337202	+	0.194684i	0.659034	−	0.752113i	$-0.270965\pi$
$103$	3577.38	+	2065.40i	0.337202	+	0.194684i	−0.321832	+	0.946797i	$0.604299\pi$
$104$	12775.3	+	7375.82i	1.18115	+	0.681936i
$105$	14730.3	+	8123.74i	1.33608	+	0.736848i
$106$	2724.88	+	4719.63i	0.242513	+	0.420045i
$107$	−2304.93			−0.201322			−0.100661	−	0.994921i	$-0.532096\pi$
$107$	−2304.93			−0.201322			−0.100661	+	0.994921i	$0.532096\pi$
$108$	−2776.34	+	2510.93i	−0.238027	+	0.215272i
$109$	−5826.06			−0.490368			−0.245184	−	0.969477i	$-0.578848\pi$
$109$	−5826.06			−0.490368			−0.245184	+	0.969477i	$0.578848\pi$
$110$	6835.80	−	5166.35i	0.564942	−	0.426971i
$111$	−1154.79	−	837.712i	−0.0937257	−	0.0679906i
$112$	9548.52	+	5512.84i	0.761202	+	0.439480i
$113$	5437.72	−	9418.40i	0.425853	−	0.737599i	−0.570647	−	0.821196i	$-0.693307\pi$
$113$	5437.72	−	9418.40i	0.425853	−	0.737599i	0.996500	+	0.0835967i	$0.0266407\pi$
$114$	−12472.8	−	1301.69i	−0.959743	−	0.100161i
$115$	−6653.05	−	8802.92i	−0.503066	−	0.665627i
$116$		−	3554.86i		−	0.264184i
$117$	3541.40	−	16782.1i	0.258704	−	1.22596i
$118$		−	11025.7i		−	0.791850i
$119$	−20830.8	+	12026.7i	−1.47100	+	0.849282i
$120$	8101.96	+	13418.5i	0.562636	+	0.931837i
$121$	−1914.59	+	3316.17i	−0.130769	+	0.226499i
$122$	−6740.55	+	11675.0i	−0.452872	+	0.784397i
$123$	1259.76	−	561.989i	0.0832677	−	0.0371465i
$124$	1959.17	+	3393.39i	0.127418	+	0.220694i
$125$	14563.3	−	5661.45i	0.932049	−	0.362333i
$126$	4121.55	−	19531.4i	0.259609	−	1.23025i
$127$		−	14118.7i		−	0.875362i	−0.899130	−	0.437681i	$-0.855800\pi$
$127$		−	14118.7i		−	0.875362i	0.899130	−	0.437681i	$-0.144200\pi$
$128$	2275.07	+	3940.53i	0.138859	+	0.240511i
$129$	−1975.43	+	18928.7i	−0.118709	+	1.13747i
$130$	−16071.8	−	6795.24i	−0.950997	−	0.402085i
$131$	13465.1	+	7774.09i	0.784634	+	0.453009i	0.838070	−	0.545562i	$-0.183684\pi$
$131$	13465.1	+	7774.09i	0.784634	+	0.453009i	−0.0534358	+	0.998571i	$0.517017\pi$
$132$	3889.71	+	2821.67i	0.223238	+	0.161942i
$133$	−27370.4	+	15802.3i	−1.54731	+	0.893342i
$134$			23409.2i			1.30370i
$135$	11906.8	−	13797.8i	0.653323	−	0.757080i
$136$	−22413.0			−1.21178
$137$	−1484.21	−	2570.73i	−0.0790780	−	0.136967i	0.823774	−	0.566918i	$-0.191864\pi$
$137$	−1484.21	−	2570.73i	−0.0790780	−	0.136967i	−0.902852	+	0.429951i	$0.858531\pi$
$138$	−7688.47	+	10598.6i	−0.403722	+	0.556534i
$139$	650.858	−	1127.32i	0.0336865	−	0.0583468i	−0.848691	−	0.528890i	$-0.822609\pi$
$139$	650.858	−	1127.32i	0.0336865	−	0.0583468i	0.882377	+	0.470543i	$0.155942\pi$
$140$	8840.05	+	3737.61i	0.451023	+	0.190694i
$141$	18924.1	+	1974.95i	0.951867	+	0.0993386i
$142$	13296.0	−	7676.47i	0.659394	−	0.380702i
$143$	−22017.7			−1.07671
$144$	7979.94	−	8888.84i	0.384835	−	0.428667i
$145$	2133.55	+	17175.2i	0.101477	+	0.816893i
$146$	16872.3	−	9741.26i	0.791534	−	0.456993i
$147$	−11691.7	−	26208.2i	−0.541057	−	1.21284i
$148$	−704.919	−	406.985i	−0.0321822	−	0.0185804i
$149$	−3279.82	−	1893.61i	−0.147733	−	0.0852938i	0.424311	−	0.905516i	$-0.360516\pi$
$149$	−3279.82	−	1893.61i	−0.147733	−	0.0852938i	−0.572044	+	0.820223i	$0.693850\pi$
$150$	−11467.2	−	14569.9i	−0.509652	−	0.647550i
$151$	−16343.3	−	28307.5i	−0.716781	−	1.24150i	−0.962269	−	0.272101i	$-0.912282\pi$
$151$	−16343.3	−	28307.5i	−0.716781	−	1.24150i	0.245488	−	0.969400i	$-0.421052\pi$
$152$	−29449.3			−1.27464
$153$	8089.27	+	24772.4i	0.345562	+	1.05824i
$154$	−25624.6			−1.08048
$155$	−11502.3	−	15219.2i	−0.478765	−	0.633473i
$156$	1015.76	−	9733.05i	0.0417389	−	0.399945i
$157$	36703.3	+	21190.6i	1.48904	+	0.859696i	0.999922	−	0.0125237i	$-0.00398653\pi$
$157$	36703.3	+	21190.6i	1.48904	+	0.859696i	0.489115	+	0.872219i	$0.337320\pi$
$158$	4491.63	−	7779.73i	0.179924	−	0.311638i
$159$	8737.41	−	12044.6i	0.345612	−	0.476429i
$160$	9474.43	+	12536.0i	0.370095	+	0.489687i
$161$			32998.5i			1.27304i
$162$	−19782.5	−	8738.21i	−0.753793	−	0.332960i
$163$		−	11554.3i		−	0.434881i	−0.976074	−	0.217440i	$-0.930229\pi$
$163$		−	11554.3i		−	0.434881i	0.976074	−	0.217440i	$-0.0697708\pi$
$164$	681.589	−	393.516i	0.0253417	−	0.0146310i
$165$	−20486.5	−	11298.3i	−0.752488	−	0.414997i
$166$	6715.79	−	11632.1i	0.243714	−	0.422125i
$167$	−21457.0	+	37164.6i	−0.769371	+	1.33259i	0.168533	+	0.985696i	$0.446097\pi$
$167$	−21457.0	+	37164.6i	−0.769371	+	1.33259i	−0.937904	+	0.346894i	$0.887236\pi$
$168$	4865.65	−	46622.9i	0.172394	−	1.65189i
$169$	8138.49	+	14096.3i	0.284951	+	0.493550i
$170$	26309.6	−	3268.26i	0.910367	−	0.113089i
$171$	10628.8	+	32549.3i	0.363490	+	1.11314i
$172$			10858.4i			0.367036i
$173$	5250.07	+	9093.39i	0.175418	+	0.303832i	0.940306	−	0.340331i	$-0.110539\pi$
$173$	5250.07	+	9093.39i	0.175418	+	0.303832i	−0.764888	+	0.644163i	$0.777206\pi$
$174$	18755.7	−	8367.08i	0.619490	−	0.276360i
$175$	−44953.6	−	12752.5i	−1.46787	−	0.416408i
$176$	−13279.9	−	7667.13i	−0.428714	−	0.247518i
$177$	−27493.0	+	12264.9i	−0.877556	+	0.391486i
$178$	26496.0	−	15297.5i	0.836257	−	0.482813i
$179$		−	17178.1i		−	0.536130i	−0.963401	−	0.268065i	$-0.913616\pi$
$179$		−	17178.1i		−	0.536130i	0.963401	−	0.268065i	$-0.0863842\pi$
$180$	5939.59	−	8534.93i	0.183321	−	0.263424i
$181$	−13715.3			−0.418647			−0.209324	−	0.977846i	$-0.567126\pi$
$181$	−13715.3			−0.418647			−0.209324	+	0.977846i	$0.567126\pi$
$182$	26091.6	+	45192.0i	0.787696	+	1.36433i
$183$	36610.0	+	3820.68i	1.09319	+	0.114088i
$184$	−15374.1	+	26628.7i	−0.454102	+	0.786528i
$185$	3650.06	+	1543.26i	0.106649	+	0.0450915i
$186$	−13292.4	+	18323.8i	−0.384219	+	0.529650i
$187$	28971.0	−	16726.4i	0.828477	−	0.478321i
$188$	10855.8			0.307146
$189$	−53286.8	+	11449.2i	−1.49175	+	0.320518i
$190$	34569.2	−	4294.29i	0.957595	−	0.118955i
$191$	−14234.1	+	8218.06i	−0.390178	+	0.225270i	−0.682237	−	0.731131i	$-0.738993\pi$
$191$	−14234.1	+	8218.06i	−0.390178	+	0.225270i	0.292059	+	0.956400i	$0.405660\pi$
$192$	23418.6	−	32282.8i	0.635271	−	0.875727i
$193$	11768.6	+	6794.59i	0.315943	+	0.182410i	0.649583	−	0.760291i	$-0.274944\pi$
$193$	11768.6	+	6794.59i	0.315943	+	0.182410i	−0.333640	+	0.942701i	$0.608277\pi$
$194$	10104.2	+	5833.65i	0.268471	+	0.155002i
$195$	933.973	+	47634.5i	0.0245621	+	1.25272i
$196$	−8186.77	−	14179.9i	−0.213108	−	0.369114i
$197$	17552.2			0.452272			0.226136	−	0.974096i	$-0.427391\pi$
$197$	17552.2			0.452272			0.226136	+	0.974096i	$0.427391\pi$
$198$	−5732.15	+	27163.8i	−0.146213	+	0.692882i
$199$	49240.7			1.24342			0.621710	−	0.783248i	$-0.286438\pi$
$199$	49240.7			1.24342			0.621710	+	0.783248i	$0.286438\pi$
$200$	−30334.7	−	31234.8i	−0.758367	−	0.780871i
$201$	58371.4	−	26040.0i	1.44480	−	0.644539i
$202$	−10998.6	−	6350.04i	−0.269547	−	0.155623i
$203$	25879.1	−	44823.9i	0.627995	−	1.08772i
$204$	6057.46	+	13578.4i	0.145556	+	0.326279i
$205$	−3056.90	+	2310.33i	−0.0727399	+	0.0549752i
$206$			13616.0i			0.320860i
$207$	34980.6	+	7381.67i	0.816368	+	0.172272i
$208$			31227.4i			0.721788i
$209$	38066.1	−	21977.5i	0.871457	−	0.503136i
$210$	1086.97	+	55438.0i	0.0246480	+	1.25710i
$211$	8187.40	−	14181.0i	0.183900	−	0.318524i	−0.759306	−	0.650734i	$-0.774461\pi$
$211$	8187.40	−	14181.0i	0.183900	−	0.318524i	0.943205	+	0.332211i	$0.107795\pi$
$212$	4244.89	−	7352.37i	0.0944485	−	0.163590i
$213$	−33931.8	−	24614.9i	−0.747907	−	0.542548i
$214$	−3798.78	−	6579.69i	−0.0829501	−	0.143674i
$215$	−6516.99	−	52462.0i	−0.140984	−	1.13493i
$216$	−48334.9	−	15587.3i	−1.03598	−	0.334090i
$217$			57050.5i			1.21155i
$218$	−9601.99	−	16631.1i	−0.202045	−	0.349952i
$219$	−43058.7	−	31235.7i	−0.897785	−	0.651272i
$220$	−12294.5	−	5198.17i	−0.254019	−	0.107400i
$221$	−58998.0	−	34062.5i	−1.20796	−	0.697416i
$222$	488.113	−	4677.13i	0.00990409	−	0.0949015i
$223$	−56299.0	+	32504.2i	−1.13212	+	0.653627i	−0.944466	−	0.328609i	$-0.893420\pi$
$223$	−56299.0	+	32504.2i	−1.13212	+	0.653627i	−0.187649	+	0.982236i	$0.560087\pi$
$224$		−	46992.3i		−	0.936549i
$225$	−23574.5	+	44801.1i	−0.465668	+	0.884959i
$226$	35847.8			0.701852
$227$	−18101.8	−	31353.3i	−0.351294	−	0.608459i	0.635183	−	0.772362i	$-0.280925\pi$
$227$	−18101.8	−	31353.3i	−0.351294	−	0.608459i	−0.986476	+	0.163903i	$0.947592\pi$
$228$	7959.13	+	17841.2i	0.153107	+	0.343206i
$229$	36892.9	−	63900.5i	0.703513	−	1.21852i	−0.263712	−	0.964601i	$-0.584947\pi$
$229$	36892.9	−	63900.5i	0.703513	−	1.21852i	0.967225	−	0.253919i	$-0.0817198\pi$
$230$	14163.9	−	33500.0i	0.267749	−	0.633271i
$231$	28504.5	+	63895.8i	0.534182	+	1.19742i
$232$	41767.1	−	24114.2i	0.775993	−	0.448020i
$233$	−9549.91			−0.175909			−0.0879544	−	0.996125i	$-0.528033\pi$
$233$	−9549.91			−0.175909			−0.0879544	+	0.996125i	$0.528033\pi$
$234$	53743.1	−	17549.5i	0.981501	−	0.320504i
$235$	−52449.2	+	6515.40i	−0.949737	+	0.117979i
$236$	−14875.0	+	8588.09i	−0.267075	+	0.154196i
$237$	−24395.4	−	2545.95i	−0.434321	−	0.0453266i
$238$	−68663.0	−	39642.6i	−1.21218	−	0.699855i
$239$	−26893.8	−	15527.1i	−0.470821	−	0.271829i	0.245762	−	0.969330i	$-0.420962\pi$
$239$	−26893.8	−	15527.1i	−0.470821	−	0.271829i	−0.716583	+	0.697502i	$0.754295\pi$
$240$	−16024.2	+	29055.7i	−0.278198	+	0.504440i
$241$	50233.7	+	87007.4i	0.864891	+	1.49803i	0.867156	+	0.498037i	$0.165946\pi$
$241$	50233.7	+	87007.4i	0.864891	+	1.49803i	−0.00226486	+	0.999997i	$0.500721\pi$
$242$	−12621.8			−0.215522
$243$	216.817	+	59048.6i	0.00367181	+	0.999993i
$244$	21001.2			0.352749
$245$	48064.6	+	63596.2i	0.800743	+	1.05949i
$246$	3680.48	+	2669.90i	0.0608182	+	0.0441188i
$247$	−77519.7	−	44756.0i	−1.27063	−	0.733597i
$248$	−26579.9	+	46037.8i	−0.432166	+	0.748534i
$249$	−36475.5	−	3806.65i	−0.588305	−	0.0613966i
$250$	40163.1	+	32241.7i	0.642609	+	0.515868i
$251$			109110.i			1.73188i	0.500147	+	0.865940i	$0.333279\pi$
$251$			109110.i			1.73188i	−0.500147	+	0.865940i	$0.666721\pi$
$252$	−29560.5	+	9652.81i	−0.465490	+	0.152003i
$253$		−	45893.5i		−	0.716986i
$254$	40303.4	−	23269.2i	0.624704	−	0.360673i
$255$	−37415.9	−	61968.2i	−0.575409	−	0.952991i
$256$	27952.0	−	48414.2i	0.426513	−	0.738742i
$257$	−19063.1	+	33018.3i	−0.288621	+	0.499906i	−0.973481	−	0.228769i	$-0.926530\pi$
$257$	−19063.1	+	33018.3i	−0.288621	+	0.499906i	0.684860	+	0.728675i	$0.259863\pi$
$258$	−57289.7	+	25557.4i	−0.860671	+	0.383953i
$259$	−5925.64	−	10263.5i	−0.0883355	−	0.153002i
$260$	3351.01	+	26975.7i	0.0495711	+	0.399049i
$261$	−41727.1	−	37460.4i	−0.612544	−	0.549910i
$262$			51250.2i			0.746608i
$263$	4531.99	+	7849.64i	0.0655206	+	0.113485i	0.896925	−	0.442183i	$-0.145796\pi$
$263$	4531.99	+	7849.64i	0.0655206	+	0.113485i	−0.831404	+	0.555668i	$0.812463\pi$
$264$	−6767.03	+	64842.0i	−0.0970936	+	0.930355i
$265$	−16096.3	+	38070.4i	−0.229211	+	0.542121i
$266$	−90218.9	−	52087.9i	−1.27507	−	0.736162i
$267$	−67618.4	−	49051.8i	−0.948511	−	0.688070i
$268$	31581.8	−	18233.7i	0.439710	−	0.253867i
$269$		−	71201.8i		−	0.983980i	−0.870601	−	0.491990i	$-0.836270\pi$
$269$		−	71201.8i		−	0.983980i	0.870601	−	0.491990i	$-0.163730\pi$
$270$	59011.0	+	11249.0i	0.809478	+	0.154308i
$271$	−43394.0			−0.590869			−0.295434	−	0.955363i	$-0.595464\pi$
$271$	−43394.0			−0.590869			−0.295434	+	0.955363i	$0.595464\pi$
$272$	−23722.9	−	41089.2i	−0.320648	−	0.555379i
$273$	83663.7	−	115331.i	1.12257	−	1.54747i
$274$	4892.30	−	8473.70i	0.0651646	−	0.112868i
$275$	62520.4	+	17735.9i	0.826716	+	0.234524i
$276$	20287.5	+	2117.24i	0.266324	+	0.0277940i
$277$	79016.2	−	45620.0i	1.02981	−	0.594560i	0.112879	−	0.993609i	$-0.463993\pi$
$277$	79016.2	−	45620.0i	1.02981	−	0.594560i	0.916930	+	0.399048i	$0.130659\pi$
$278$	4290.74			0.0555191
$279$	60477.2	+	12762.0i	0.776932	+	0.163950i
$280$	16051.9	+	129218.i	0.204744	+	1.64819i
$281$	105804.	−	61085.8i	1.33995	−	0.773620i	0.353150	−	0.935567i	$-0.385110\pi$
$281$	105804.	−	61085.8i	1.33995	−	0.773620i	0.986800	+	0.161946i	$0.0517771\pi$
$282$	25551.2	+	57275.8i	0.321302	+	0.720232i
$283$	132893.	+	76726.0i	1.65932	+	0.958009i	0.973029	+	0.230682i	$0.0740958\pi$
$283$	132893.	+	76726.0i	1.65932	+	0.958009i	0.686291	+	0.727327i	$0.259237\pi$
$284$	−20712.9	−	11958.6i	−0.256806	−	0.148267i
$285$	−49162.2	−	81422.4i	−0.605260	−	1.00243i
$286$	−36287.6	−	62852.0i	−0.443635	−	0.768399i
$287$	11459.0			0.139118
$288$	−49814.9	−	10512.0i	−0.600584	−	0.126736i
$289$	19985.4			0.239286
$290$	−45512.1	+	34397.0i	−0.541166	+	0.409001i
$291$	3306.63	−	31684.3i	0.0390481	−	0.374161i
$292$	−26284.2	−	15175.2i	−0.308269	−	0.177979i
$293$	−13811.6	+	23922.4i	−0.160883	+	0.278657i	−0.935186	−	0.354158i	$-0.884767\pi$
$293$	−13811.6	+	23922.4i	−0.160883	+	0.278657i	0.774303	+	0.632815i	$0.218101\pi$
$294$	55544.9	−	76569.2i	0.642614	−	0.885849i
$295$	66713.7	−	50420.8i	0.766604	−	0.579383i
$296$		−	11043.1i		−	0.126039i
$297$	74110.0	−	15923.3i	0.840164	−	0.180518i
$298$		−	12483.5i		−	0.140573i
$299$	−80938.7	+	46730.0i	−0.905344	+	0.522701i
$300$	−10724.5	+	26819.3i	−0.119161	+	0.297992i
$301$	−79048.2	+	136916.i	−0.872487	+	1.51119i
$302$	53871.1	−	93307.5i	0.590666	−	1.02306i
$303$	−3599.33	+	34489.0i	−0.0392046	+	0.375660i
$304$	−31170.4	−	53988.7i	−0.337283	−	0.584192i
$305$	−101467.	+	12604.5i	−1.09075	+	0.135496i
$306$	−57383.4	+	63919.2i	−0.612835	+	0.682635i
$307$		−	32205.8i		−	0.341710i	−0.985296	−	0.170855i	$-0.945347\pi$
$307$		−	32205.8i		−	0.341710i	0.985296	−	0.170855i	$-0.0546530\pi$
$308$	19959.4	+	34570.7i	0.210400	+	0.364424i
$309$	33951.9	−	15146.3i	0.355589	−	0.158631i
$310$	24487.7	−	57917.5i	0.254815	−	0.602680i
$311$	158888.	+	91734.2i	1.64275	+	0.948441i	0.979851	+	0.199731i	$0.0640067\pi$
$311$	158888.	+	91734.2i	1.64275	+	0.948441i	0.662897	+	0.748710i	$0.269327\pi$
$312$	121247.	−	54089.3i	1.24555	−	0.555651i
$313$	−22297.7	+	12873.6i	−0.227599	+	0.131405i	−0.609464	−	0.792814i	$-0.708615\pi$
$313$	−22297.7	+	12873.6i	−0.227599	+	0.131405i	0.381865	+	0.924218i	$0.375282\pi$
$314$			139698.i			1.41687i
$315$	137027.	−	64378.8i	1.38097	−	0.648816i
$316$	−13994.4			−0.140146
$317$	27356.9	+	47383.6i	0.272238	+	0.471530i	0.969435	−	0.245350i	$-0.0789028\pi$
$317$	27356.9	+	47383.6i	0.272238	+	0.471530i	−0.697196	+	0.716880i	$0.745569\pi$
$318$	48782.9	+	5091.07i	0.482406	+	0.0503448i
$319$	−35992.0	+	62339.9i	−0.353691	+	0.612611i
$320$	−43142.5	+	102039.i	−0.421313	+	0.996475i
$321$	−12180.9	+	16791.5i	−0.118214	+	0.162960i
$322$	−94197.9	+	54385.2i	−0.908509	+	0.524528i
$323$	136001.			1.30358
$324$	3620.01	+	33495.3i	0.0344842	+	0.319076i
$325$	−32380.6	−	128321.i	−0.306562	−	1.21488i
$326$	32983.1	−	19042.8i	0.310354	−	0.179183i
$327$	−30789.1	+	42443.1i	−0.287940	+	0.396928i
$328$	9247.07	+	5338.80i	0.0859521	+	0.0496245i
$329$	136882.	+	79029.0i	1.26461	+	0.730121i
$330$	−1511.74	−	77101.8i	−0.0138819	−	0.708005i
$331$	−55872.0	−	96773.2i	−0.509963	−	0.883281i	−0.999933	−	0.0115425i	$-0.996326\pi$
$331$	−55872.0	−	96773.2i	−0.509963	−	0.883281i	0.489971	−	0.871739i	$-0.337007\pi$
$332$	−20924.1			−0.189832
$333$	−12205.5	+	3985.64i	−0.110070	+	0.0359426i
$334$	−141454.			−1.26801
$335$	−141643.	+	107050.i	−1.26213	+	0.953891i
$336$	90622.5	−	40427.5i	0.802708	−	0.358095i
$337$	−93020.1	−	53705.2i	−0.819063	−	0.472886i	0.0310304	−	0.999518i	$-0.490121\pi$
$337$	−93020.1	−	53705.2i	−0.819063	−	0.472886i	−0.850093	+	0.526632i	$0.823454\pi$
$338$	−26826.2	+	46464.4i	−0.234815	+	0.406712i
$339$	−39876.6	−	89387.6i	−0.346991	−	0.777818i
$340$	−24902.2	−	32949.1i	−0.215417	−	0.285027i
$341$		−	79344.4i		−	0.682351i
$342$	−75398.2	+	83985.9i	−0.644627	+	0.718049i
$343$		−	58887.7i		−	0.500537i
$344$	−127579.	+	73657.5i	−1.07810	+	0.622444i
$345$	−99289.1	+	1946.77i	−0.834187	+	0.0163559i
$346$	−17305.4	+	29973.8i	−0.144554	+	0.250374i
$347$	25914.5	−	44885.2i	0.215220	−	0.372773i	−0.738120	−	0.674669i	$-0.764286\pi$
$347$	25914.5	−	44885.2i	0.215220	−	0.372773i	0.953341	+	0.301896i	$0.0976197\pi$
$348$	−25897.3	−	18786.4i	−0.213843	−	0.155126i
$349$	57810.9	+	100131.i	0.474634	+	0.822090i	0.999578	−	0.0290468i	$-0.00924718\pi$
$349$	57810.9	+	100131.i	0.474634	+	0.822090i	−0.524944	+	0.851137i	$0.675914\pi$
$350$	−37685.1	−	149343.i	−0.307634	−	1.21912i
$351$	−103543.	−	114488.i	−0.840441	−	0.929279i
$352$			65355.7i			0.527471i
$353$	−110669.	−	191685.i	−0.888132	−	1.53829i	−0.842081	−	0.539351i	$-0.818670\pi$
$353$	−110669.	−	191685.i	−0.888132	−	1.53829i	−0.0460508	−	0.998939i	$-0.514664\pi$
$354$	−80322.8	−	58267.8i	−0.640962	−	0.464967i
$355$	107251.	+	45346.2i	0.851031	+	0.359819i
$356$	−41276.2	−	23830.8i	−0.325686	−	0.188035i
$357$	−22470.2	+	215311.i	−0.176308	+	1.68939i
$358$	49036.9	−	28311.4i	0.382610	−	0.220900i
$359$			8135.18i			0.0631216i	0.999502	+	0.0315608i	$0.0100478\pi$
$359$			8135.18i			0.0631216i	−0.999502	+	0.0315608i	$0.989952\pi$
$360$	140570.	+	11889.7i	1.08465	+	0.0917414i
$361$	48376.0			0.371206
$362$	−22604.3	−	39151.8i	−0.172494	−	0.298769i
$363$	14040.3	+	31472.9i	0.106553	+	0.238849i
$364$	40646.3	−	70401.4i	0.306774	−	0.531348i
$365$	136099.	+	57543.3i	1.02157	+	0.431925i
$366$	49430.7	+	110804.i	0.369007	+	0.827168i
$367$	−219142.	+	126522.i	−1.62702	+	0.939362i	−0.642047	+	0.766665i	$0.721915\pi$
$367$	−219142.	+	126522.i	−1.62702	+	0.939362i	−0.984975	+	0.172696i	$0.944752\pi$
$368$	−65090.2			−0.480640
$369$	2563.35	−	12147.3i	0.0188259	−	0.0892130i
$370$	1610.30	+	12962.9i	0.0117626	+	0.0946891i
$371$	107049.	−	61804.9i	0.777743	−	0.449030i
$372$	35074.6	+	3660.45i	0.253459	+	0.0264514i
$373$	−39158.2	−	22608.0i	−0.281452	−	0.162497i	0.352628	−	0.935763i	$-0.385288\pi$
$373$	−39158.2	−	22608.0i	−0.281452	−	0.162497i	−0.634081	+	0.773267i	$0.718621\pi$
$374$	95494.8	+	55133.9i	0.682710	+	0.394163i
$375$	35718.8	−	136013.i	0.254001	−	0.967204i
$376$	73639.6	+	127548.i	0.520878	+	0.902187i
$377$	146592.			1.03140
$378$	−120506.	−	133243.i	−0.843380	−	0.932529i
$379$	−152573.			−1.06219			−0.531093	−	0.847314i	$-0.678219\pi$
$379$	−152573.			−1.06219			−0.531093	+	0.847314i	$0.678219\pi$
$380$	−32720.0	−	43293.1i	−0.226592	−	0.299814i
$381$	−102855.	−	74613.4i	−0.708561	−	0.514005i
$382$	−46918.7	−	27088.5i	−0.321528	−	0.185634i
$383$	−65081.6	+	112725.i	−0.443671	+	0.768460i	−0.997959	−	0.0638650i	$-0.979657\pi$
$383$	−65081.6	+	112725.i	−0.443671	+	0.768460i	0.554288	+	0.832325i	$0.312991\pi$
$384$	40730.0	+	4250.66i	0.276218	+	0.0288266i
$385$	−117182.	−	155048.i	−0.790567	−	1.04603i
$386$			44792.9i			0.300631i
$387$	127456.	+	114424.i	0.851020	+	0.764002i
$388$		−	18175.6i		−	0.120733i
$389$	49350.3	−	28492.4i	0.326130	−	0.188291i	−0.327992	−	0.944681i	$-0.606372\pi$
$389$	49350.3	−	28492.4i	0.326130	−	0.188291i	0.654122	+	0.756389i	$0.273038\pi$
$390$	−134439.	+	81173.1i	−0.883884	+	0.533682i
$391$	70999.6	−	122975.i	0.464411	−	0.804383i
$392$	111069.	−	192378.i	0.722806	−	1.25194i
$393$	127794.	−	57010.0i	0.827418	−	0.369118i
$394$	28928.0	+	50104.7i	0.186348	+	0.322765i
$395$	67613.3	−	8399.13i	0.433349	−	0.0538320i
$396$	41112.0	−	13424.9i	0.262167	−	0.0856092i
$397$		−	174124.i		−	1.10478i	−0.833585	−	0.552392i	$-0.813715\pi$
$397$		−	174124.i		−	1.10478i	0.833585	−	0.552392i	$-0.186285\pi$
$398$	81154.0	+	140563.i	0.512323	+	0.887369i
$399$	−29524.5	+	282905.i	−0.185454	+	1.77703i
$400$	25154.5	−	88671.9i	0.157216	−	0.554199i
$401$	−255149.	−	147310.i	−1.58674	−	0.916104i	−0.993840	−	0.110826i	$-0.964650\pi$
$401$	−255149.	−	147310.i	−1.58674	−	0.916104i	−0.592898	−	0.805277i	$-0.702016\pi$
$402$	170537.	+	123711.i	1.05527	+	0.765519i
$403$	−139933.	+	80790.5i	−0.861610	+	0.497451i
$404$			19784.5i			0.121217i
$405$	−37593.2	−	159659.i	−0.229192	−	0.973381i
$406$	170606.			1.03501
$407$	8241.23	+	14274.2i	0.0497512	+	0.0861715i
$408$	−118447.	+	163280.i	−0.711545	+	0.980872i
$409$	−118417.	+	205104.i	−0.707891	+	1.22610i	0.257747	+	0.966212i	$0.417020\pi$
$409$	−118417.	+	205104.i	−0.707891	+	1.22610i	−0.965638	+	0.259890i	$0.916314\pi$
$410$	−11633.2	−	4918.56i	−0.0692040	−	0.0292597i
$411$	−26571.6	−	2773.06i	−0.157302	−	0.0164163i
$412$	18369.6	−	10605.7i	0.108220	−	0.0624806i
$413$	−250082.			−1.46617
$414$	36580.0	+	112022.i	0.213424	+	0.653584i
$415$	101094.	−	12558.2i	0.586988	−	0.0729175i
$416$	115263.	−	66546.8i	0.666042	−	0.384539i
$417$	−4772.96	−	10699.1i	−0.0274483	−	0.0615282i
$418$	125474.	+	72442.6i	0.718128	+	0.414611i
$419$	−210879.	−	121751.i	−1.20117	−	0.693498i	−0.240358	−	0.970684i	$-0.577265\pi$
$419$	−210879.	−	121751.i	−1.20117	−	0.693498i	−0.960816	+	0.277186i	$0.910598\pi$
$420$	73945.8	−	44647.9i	0.419194	−	0.253106i
$421$	143741.	+	248966.i	0.810990	+	1.40468i	0.912172	+	0.409808i	$0.134404\pi$
$421$	143741.	+	248966.i	0.810990	+	1.40468i	−0.101181	+	0.994868i	$0.532262\pi$
$422$	53974.9			0.303087
$423$	114396.	−	127426.i	0.639337	−	0.712157i
$424$	115180.			0.640688
$425$	140090.	+	144247.i	0.775582	+	0.798598i
$426$	14342.4	−	137430.i	0.0790322	−	0.757290i
$427$	264809.	+	152887.i	1.45237	+	0.838524i
$428$	−5917.85	+	10250.0i	−0.0323055	+	0.0559548i
$429$	−116357.	+	160400.i	−0.632237	+	0.871544i
$430$	139018.	−	105067.i	0.751853	−	0.568234i
$431$			190619.i			1.02615i	0.858343	+	0.513077i	$0.171495\pi$
$431$			190619.i			1.02615i	−0.858343	+	0.513077i	$0.828505\pi$
$432$	−22583.8	−	105109.i	−0.121012	−	0.563214i
$433$			155969.i			0.831884i	0.909391	+	0.415942i	$0.136548\pi$
$433$			155969.i			0.831884i	−0.909391	+	0.415942i	$0.863452\pi$
$434$	−162857.	+	94025.4i	−0.864622	+	0.499190i
$435$	136397.	+	75222.9i	0.720819	+	0.397532i
$436$	−14958.2	+	25908.4i	−0.0786879	+	0.136291i
$437$	93289.1	−	161581.i	0.488504	−	0.846114i
$438$	18200.2	−	174395.i	0.0948699	−	0.909048i
$439$	−116168.	−	201210.i	−0.602780	−	1.04405i	−0.992398	−	0.123069i	$-0.960726\pi$
$439$	−116168.	−	201210.i	−0.602780	−	1.04405i	0.389618	−	0.920977i	$-0.372607\pi$
$440$	−22324.6	−	179714.i	−0.115313	−	0.928273i
$441$	−252715.	−	53328.4i	−1.29943	−	0.274209i
$442$		−	224555.i		−	1.14942i
$443$	18440.7	+	31940.2i	0.0939657	+	0.162753i	0.909176	−	0.416411i	$-0.136712\pi$
$443$	18440.7	+	31940.2i	0.0939657	+	0.162753i	−0.815211	+	0.579164i	$0.803379\pi$
$444$	−6690.20	+	2984.56i	−0.0339370	+	0.0151396i
$445$	213727.	+	90364.7i	1.07929	+	0.456330i
$446$	−185574.	−	107141.i	−0.932925	−	0.538625i
$447$	−31127.9	+	13886.5i	−0.155788	+	0.0694986i
$448$	286921.	−	165654.i	1.42957	−	0.825364i
$449$		−	189541.i		−	0.940179i	−0.882619	−	0.470090i	$-0.844222\pi$
$449$		−	189541.i		−	0.940179i	0.882619	−	0.470090i	$-0.155778\pi$
$450$	−166743.	+	6541.18i	−0.823421	+	0.0323021i
$451$	−15937.0			−0.0783524
$452$	−27922.4	−	48363.0i	−0.136671	−	0.236721i
$453$	−292591.	−	30535.3i	−1.42582	−	0.148801i
$454$	59667.6	−	103347.i	0.289485	−	0.501403i
$455$	−154128.	+	364537.i	−0.744488	+	1.76084i
$456$	−155632.	+	214540.i	−0.748459	+	1.03176i
$457$	−324761.	+	187501.i	−1.55500	+	0.897781i	−0.557281	+	0.830324i	$0.688155\pi$
$457$	−324761.	+	187501.i	−1.55500	+	0.897781i	−0.997722	+	0.0674575i	$0.978511\pi$
$458$	243214.			1.15947
$459$	223217.	+	71984.3i	1.05950	+	0.341674i
$460$	−56228.0	+	6984.82i	−0.265728	+	0.0330095i
$461$	225319.	−	130088.i	1.06022	−	0.612119i	0.134728	−	0.990883i	$-0.456984\pi$
$461$	225319.	−	130088.i	1.06022	−	0.612119i	0.925493	+	0.378764i	$0.123651\pi$
$462$	−135419.	+	186676.i	−0.634447	+	0.874592i
$463$	134040.	+	77388.2i	0.625278	+	0.361005i	0.778921	−	0.627122i	$-0.215767\pi$
$463$	134040.	+	77388.2i	0.625278	+	0.361005i	−0.153643	+	0.988126i	$0.549101\pi$
$464$	88415.9	+	51046.9i	0.410671	+	0.237101i
$465$	−171659.	+	3365.72i	−0.793890	+	0.0155658i
$466$	−15739.3	−	27261.3i	−0.0724792	−	0.125538i
$467$	−55941.6			−0.256508			−0.128254	−	0.991741i	$-0.540937\pi$
$467$	−55941.6			−0.256508			−0.128254	+	0.991741i	$0.540937\pi$
$468$	−65537.6	−	58836.3i	−0.299226	−	0.268629i
$469$	530960.			2.41388
$470$	−105041.	−	138984.i	−0.475514	−	0.629171i
$471$	348341.	−	155398.i	1.57023	−	0.700493i
$472$	−201808.	−	116514.i	−0.905847	−	0.522991i
$473$	109938.	−	190419.i	0.491391	−	0.851114i
$474$	−32938.6	−	73835.3i	−0.146605	−	0.328630i
$475$	184069.	+	189531.i	0.815818	+	0.840028i
$476$			123513.i			0.545127i
$477$	−41570.6	−	127305.i	−0.182705	−	0.559510i
$478$		−	102362.i		−	0.448003i
$479$	−4576.67	+	2642.34i	−0.0199470	+	0.0115164i	−0.509940	−	0.860210i	$-0.670333\pi$
$479$	−4576.67	+	2642.34i	−0.0199470	+	0.0115164i	0.489993	+	0.871726i	$0.336999\pi$
$480$	141395.	−	2772.33i	0.613693	−	0.0120327i
$481$	16782.9	−	29068.8i	0.0725397	−	0.125642i
$482$	−165581.	+	286795.i	−0.712717	+	1.23446i
$483$	240395.	+	174388.i	1.03046	+	0.747519i
$484$	9831.32	+	17028.4i	0.0419683	+	0.0726912i
$485$	10908.7	+	87815.0i	0.0463754	+	0.373324i
$486$	−168203.	+	97937.5i	−0.712135	+	0.414645i
$487$		−	96848.3i		−	0.408352i	−0.978934	−	0.204176i	$-0.934549\pi$
$487$		−	96848.3i		−	0.408352i	0.978934	−	0.204176i	$-0.0654514\pi$
$488$	142461.	+	246750.i	0.598214	+	1.03614i
$489$	−84173.8	−	61061.5i	−0.352014	−	0.255358i
$490$	−102327.	+	242019.i	−0.426183	+	1.00799i
$491$	−278122.	−	160574.i	−1.15365	−	0.666058i	−0.203873	−	0.978997i	$-0.565353\pi$
$491$	−278122.	−	160574.i	−1.15365	−	0.666058i	−0.949773	+	0.312939i	$0.898686\pi$
$492$	735.231	−	7045.02i	0.00303734	−	0.0291040i
$493$	−192886.	+	111363.i	−0.793609	+	0.458191i
$494$		−	295051.i		−	1.20905i
$495$	−190574.	+	89536.5i	−0.777773	+	0.365418i
$496$	−112533.			−0.457422
$497$	−174116.	−	301577.i	−0.704896	−	1.22092i
$498$	−49249.1	−	110397.i	−0.198582	−	0.445142i
$499$	76815.9	−	133049.i	0.308496	−	0.534332i	−0.669537	−	0.742779i	$-0.733508\pi$
$499$	76815.9	−	133049.i	0.308496	−	0.534332i	0.978034	+	0.208447i	$0.0668409\pi$
$500$	12214.3	−	79298.3i	0.0488573	−	0.317193i
$501$	157351.	+	352719.i	0.626895	+	1.40525i
$502$	−311467.	+	179826.i	−1.23596	+	0.713582i
$503$	−450974.			−1.78244			−0.891222	−	0.453567i	$-0.850151\pi$
$503$	−450974.			−1.78244			−0.891222	+	0.453567i	$0.850151\pi$
$504$	−313936.	−	281836.i	−1.23589	−	1.10952i
$505$	−11874.3	−	95588.4i	−0.0465612	−	0.374820i
$506$	131008.	−	75637.6i	0.511679	−	0.295418i
$507$	145701.	+	15205.7i	0.566824	+	0.0591548i
$508$	−62785.8	−	36249.4i	−0.243296	−	0.140467i
$509$	1312.83	+	757.965i	0.00506727	+	0.00292559i	0.502531	−	0.864559i	$-0.332402\pi$
$509$	1312.83	+	757.965i	0.00506727	+	0.00292559i	−0.497464	+	0.867484i	$0.665735\pi$
$510$	115229.	−	208938.i	0.443020	−	0.803300i
$511$	−220949.	−	382694.i	−0.846154	−	1.46558i
$512$	257074.			0.980658
$513$	293293.	+	94582.9i	1.11447	+	0.359400i
$514$	−125672.			−0.475679
$515$	−82386.9	+	62266.2i	−0.310630	+	0.234768i
$516$	79103.8	+	57383.6i	0.297097	+	0.215520i
$517$	−190373.	−	109912.i	−0.712235	−	0.411209i
$518$	19532.2	−	33830.8i	0.0727933	−	0.126082i
$519$	93990.9	+	9809.06i	0.348940	+	0.0364160i
$520$	−294215.	+	222361.i	−1.08807	+	0.822341i
$521$			150269.i			0.553597i	0.960928	+	0.276798i	$0.0892734\pi$
$521$			150269.i			0.553597i	−0.960928	+	0.276798i	$0.910727\pi$
$522$	38164.1	−	180853.i	0.140060	−	0.663721i
$523$			90470.5i			0.330753i	0.986231	+	0.165376i	$0.0528839\pi$
$523$			90470.5i			0.330753i	−0.986231	+	0.165376i	$0.947116\pi$
$524$	69142.6	−	39919.5i	0.251816	−	0.145386i
$525$	−330470.	+	260096.i	−1.19898	+	0.943657i
$526$	−14938.4	+	25874.1i	−0.0539925	+	0.0935178i
$527$	122750.	−	212609.i	0.441977	−	0.765526i
$528$	−126036.	+	56225.6i	−0.452090	+	0.201682i
$529$	42517.0	+	73641.6i	0.151933	+	0.263155i
$530$	−135205.	+	16795.5i	−0.481327	+	0.0597919i
$531$	−55942.7	+	265104.i	−0.198406	+	0.940214i
$532$			162288.i			0.573407i
$533$	16227.4	+	28106.7i	0.0571209	+	0.0989363i
$534$	28581.2	−	273867.i	0.100230	−	0.960410i
$535$	22440.1	−	53074.4i	0.0784001	−	0.185429i
$536$	428467.	+	247376.i	1.49138	+	0.861048i
$537$	−125143.	−	90781.6i	−0.433970	−	0.314811i
$538$	203253.	−	117348.i	0.702219	−	0.405427i
$539$			331555.i			1.14124i
$540$	−30788.2	−	88374.9i	−0.105584	−	0.303069i
$541$	−323617.			−1.10570			−0.552849	−	0.833281i	$-0.686459\pi$
$541$	−323617.			−1.10570			−0.552849	+	0.833281i	$0.686459\pi$
$542$	−71518.0	−	123873.i	−0.243454	−	0.421675i
$543$	−72481.5	+	99916.5i	−0.245826	+	0.338873i
$544$	−101109.	+	175125.i	−0.341657	+	0.591767i
$545$	56720.6	−	134153.i	0.190962	−	0.451657i
$546$	467113.	+	48748.7i	1.56688	+	0.163523i
$547$	476095.	−	274874.i	1.59118	−	0.918667i	0.598073	−	0.801441i	$-0.295933\pi$
$547$	476095.	−	274874.i	1.59118	−	0.918667i	0.993105	−	0.117226i	$-0.0374002\pi$
$548$	−15242.7			−0.0507576
$549$	221307.	−	246514.i	0.734262	−	0.817893i
$550$	52411.5	+	207702.i	0.173261	+	0.686618i
$551$	−253440.	+	146324.i	−0.834781	+	0.481961i
$552$	112743.	+	252726.i	0.370009	+	0.829415i
$553$	−176458.	−	101878.i	−0.577019	−	0.333142i
$554$	260455.	+	150374.i	0.848619	+	0.489950i
$555$	30532.2	−	18435.1i	0.0991225	−	0.0598494i
$556$	−3342.12	−	5788.72i	−0.0108112	−	0.0187255i
$557$	173508.			0.559254			0.279627	−	0.960109i	$-0.409789\pi$
$557$	173508.			0.559254			0.279627	+	0.960109i	$0.409789\pi$
$558$	63242.4	+	193672.i	0.203114	+	0.622011i
$559$	−447768.			−1.43294
$560$	−219902.	+	166197.i	−0.701219	+	0.529966i
$561$	31251.1	−	299449.i	0.0992977	−	0.951475i
$562$	348752.	+	201352.i	1.10419	+	0.637505i
$563$	115344.	−	199782.i	0.363898	−	0.630289i	−0.624701	−	0.780864i	$-0.714779\pi$
$563$	115344.	−	199782.i	0.363898	−	0.630289i	0.988599	+	0.150575i	$0.0481125\pi$
$564$	57369.6	−	79084.6i	0.180353	−	0.248619i
$565$	163932.	+	216906.i	0.513533	+	0.679476i
$566$			505811.i			1.57890i
$567$	−198198.	+	448702.i	−0.616500	+	1.39570i
$568$		−	324483.i		−	1.00576i
$569$	344474.	−	198882.i	1.06398	−	0.614286i	0.137446	−	0.990509i	$-0.456111\pi$
$569$	344474.	−	198882.i	1.06398	−	0.614286i	0.926529	+	0.376223i	$0.122777\pi$
$570$	151404.	−	274532.i	0.466003	−	0.844974i
$571$	103103.	−	178580.i	0.316227	−	0.547721i	−0.663471	−	0.748202i	$-0.730917\pi$
$571$	103103.	−	178580.i	0.316227	−	0.547721i	0.979698	+	0.200481i	$0.0642505\pi$
$572$	−56529.9	+	97912.6i	−0.172777	+	0.299259i
$573$	−15354.3	+	147126.i	−0.0467651	+	0.448106i
$574$	18885.8	+	32711.1i	0.0573206	+	0.0992822i
$575$	267472.	−	67493.8i	0.808988	−	0.204140i
$576$	−111420.	−	341211.i	−0.335830	−	1.02844i
$577$		−	153493.i		−	0.461038i	−0.973068	−	0.230519i	$-0.925958\pi$
$577$		−	153493.i		−	0.461038i	0.973068	−	0.230519i	$-0.0740423\pi$
$578$	32938.2	+	57050.6i	0.0985925	+	0.170767i
$579$	111692.	−	49827.0i	0.333170	−	0.148630i
$580$	81855.7	+	34608.9i	0.243328	+	0.102880i
$581$	−263836.	−	152326.i	−0.781594	−	0.451254i
$582$	95896.0	−	42780.1i	0.283110	−	0.126298i
$583$	−148882.	+	85956.8i	−0.438030	+	0.252897i
$584$		−	411762.i		−	1.20731i
$585$	351955.	+	244931.i	1.02843	+	0.715702i
$586$	−91052.2			−0.265152
$587$	310244.	+	537358.i	0.900382	+	1.55951i	0.827000	+	0.562203i	$0.190046\pi$
$587$	310244.	+	537358.i	0.900382	+	1.55951i	0.0733820	+	0.997304i	$0.476621\pi$
$588$	−146566.	−	15295.9i	−0.423914	−	0.0442405i
$589$	161286.	−	279355.i	0.464906	−	0.805241i
$590$	253883.	+	107343.i	0.729340	+	0.308367i
$591$	92758.5	−	127869.i	0.265570	−	0.366091i
$592$	20244.9	−	11688.4i	0.0577661	−	0.0333513i
$593$	564917.			1.60648			0.803240	−	0.595655i	$-0.203108\pi$
$593$	564917.			1.60648			0.803240	+	0.595655i	$0.203108\pi$
$594$	167596.	+	185312.i	0.474997	+	0.525206i
$595$	−74129.8	−	596748.i	−0.209391	−	1.68561i
$596$	−16841.7	+	9723.56i	−0.0474126	+	0.0273737i
$597$	260223.	−	358720.i	0.730125	−	1.00648i
$598$	−266791.	−	154032.i	−0.746053	−	0.430734i
$599$	6681.40	+	3857.51i	0.0186215	+	0.0107511i	0.509282	−	0.860600i	$-0.329911\pi$
$599$	6681.40	+	3857.51i	0.0186215	+	0.0107511i	−0.490660	+	0.871351i	$0.663244\pi$
$600$	−387857.	+	55921.7i	−1.07738	+	0.155338i
$601$	−237001.	−	410498.i	−0.656147	−	1.13648i	−0.981605	−	0.190923i	$-0.938852\pi$
$601$	−237001.	−	410498.i	−0.656147	−	1.13648i	0.325458	−	0.945556i	$-0.394481\pi$
$602$	−521120.			−1.43795
$603$	118774.	−	562852.i	0.326654	−	1.54796i
$604$	−167844.			−0.460079
$605$	−57719.8	−	76371.4i	−0.157694	−	0.208651i
$606$	−104385.	+	46566.9i	−0.284244	+	0.126804i
$607$	85786.9	+	49529.1i	0.232833	+	0.134426i	0.611878	−	0.790952i	$-0.290414\pi$
$607$	85786.9	+	49529.1i	0.232833	+	0.134426i	−0.379046	+	0.925378i	$0.623748\pi$
$608$	−132850.	+	230104.i	−0.359382	+	0.622467i
$609$	−189780.	−	425411.i	−0.511700	−	1.14703i
$610$	−203209.	−	268874.i	−0.546115	−	0.722586i
$611$			447659.i			1.19913i
$612$	130931.	+	27629.4i	0.349576	+	0.0737681i
$613$			599020.i			1.59412i	0.603902	+	0.797059i	$0.293612\pi$
$613$			599020.i			1.59412i	−0.603902	+	0.797059i	$0.706388\pi$
$614$	91935.0	−	53078.7i	0.243862	−	0.140794i
$615$	676.032	+	34479.1i	0.00178738	+	0.0911602i
$616$	−270788.	+	469018.i	−0.713620	+	1.23603i
$617$	−318998.	+	552521.i	−0.837950	+	1.45137i	0.0536564	+	0.998559i	$0.482912\pi$
$617$	−318998.	+	552521.i	−0.837950	+	1.45137i	−0.891606	+	0.452812i	$0.850421\pi$
$618$	99193.2	+	71956.8i	0.259720	+	0.188406i
$619$	20452.5	+	35424.7i	0.0533783	+	0.0924539i	0.891480	−	0.453060i	$-0.149668\pi$
$619$	20452.5	+	35424.7i	0.0533783	+	0.0924539i	−0.838102	+	0.545514i	$0.816334\pi$
$620$	−97211.5	+	12075.9i	−0.252891	+	0.0314149i
$621$	238638.	−	215825.i	0.618809	−	0.559652i
$622$			604752.i			1.56313i
$623$	−346973.	−	600974.i	−0.893962	−	1.54839i
$624$	227493.	+	165028.i	0.584250	+	0.423827i
$625$	−11419.9	+	390458.i	−0.0292349	+	0.999573i
$626$	−73498.0	−	42434.1i	−0.187554	−	0.108284i
$627$	41062.0	−	393458.i	0.104449	−	1.00084i
$628$	188469.	−	108813.i	0.477882	−	0.275906i
$629$			50998.4i			0.128901i
$630$	409612.	+	285055.i	1.03203	+	0.718205i
$631$	330379.			0.829763			0.414881	−	0.909876i	$-0.363823\pi$
$631$	330379.			0.829763			0.414881	+	0.909876i	$0.363823\pi$
$632$	−94930.3	−	164424.i	−0.237668	−	0.411653i
$633$	−60040.9	−	134588.i	−0.149844	−	0.335892i
$634$	−90174.5	+	156187.i	−0.224339	+	0.388567i
$635$	325104.	+	137455.i	0.806259	+	0.340889i
$636$	−31129.2	−	69779.4i	−0.0769580	−	0.172509i
$637$	584737.	−	337598.i	1.44106	−	0.831995i
$638$	−237275.			−0.582922
$639$	−358640.	+	117112.i	−0.878329	+	0.286813i
$640$	−112886.	+	14023.0i	−0.275600	+	0.0342359i
$641$	−204552.	+	118098.i	−0.497838	+	0.287427i	−0.727820	−	0.685768i	$-0.759467\pi$
$641$	−204552.	+	118098.i	−0.497838	+	0.287427i	0.229982	+	0.973195i	$0.426133\pi$
$642$	−68008.7	−	7097.52i	−0.165004	−	0.0172201i
$643$	−375023.	−	216520.i	−0.907060	−	0.523691i	−0.0275761	−	0.999620i	$-0.508779\pi$
$643$	−375023.	−	216520.i	−0.907060	−	0.523691i	−0.879484	+	0.475928i	$0.842112\pi$
$644$	146744.	+	84722.8i	0.353826	+	0.204281i
$645$	−416628.	−	229770.i	−1.00145	−	0.552299i
$646$	224145.	+	388230.i	0.537110	+	0.930302i
$647$	−295249.			−0.705311			−0.352655	−	0.935753i	$-0.614721\pi$
$647$	−295249.			−0.705311			−0.352655	+	0.935753i	$0.614721\pi$
$648$	−368990.	+	269747.i	−0.878749	+	0.642401i
$649$	347809.			0.825755
$650$	312940.	−	303921.i	0.740687	−	0.719340i
$651$	415615.	+	301496.i	0.980684	+	0.711409i
$652$	−51382.1	−	29665.5i	−0.120869	−	0.0697840i
$653$	−85481.8	+	148059.i	−0.200469	+	0.347222i	−0.948680	−	0.316239i	$-0.897580\pi$
$653$	−85481.8	+	148059.i	−0.200469	+	0.347222i	0.748211	+	0.663461i	$0.230913\pi$
$654$	−171902.	−	17940.0i	−0.401907	−	0.0419438i
$655$	−310101.	+	234368.i	−0.722805	+	0.546280i
$656$			22603.2i			0.0525245i
$657$	−455106.	+	148612.i	−1.05434	+	0.344290i
$658$			520994.i			1.20332i
$659$	−664801.	+	383823.i	−1.53081	+	0.883812i	−0.531483	+	0.847069i	$0.678365\pi$
$659$	−664801.	+	383823.i	−1.53081	+	0.883812i	−0.999325	+	0.0367438i	$0.988301\pi$
$660$	−102842.	+	62095.2i	−0.236093	+	0.142551i
$661$	52552.0	−	91022.7i	0.120278	−	0.208328i	−0.799599	−	0.600534i	$-0.794955\pi$
$661$	52552.0	−	91022.7i	0.120278	−	0.208328i	0.919877	+	0.392206i	$0.128288\pi$
$662$	184166.	−	318986.i	0.420237	−	0.727872i
$663$	−559935.	+	249792.i	−1.27383	+	0.568265i
$664$	−141938.	−	245843.i	−0.321930	−	0.557599i
$665$	−97402.0	−	784089.i	−0.220254	−	1.77306i
$666$	−31493.5	−	28273.2i	−0.0710023	−	0.0637422i
$667$			305554.i			0.686811i
$668$	110180.	+	190838.i	0.246917	+	0.427673i
$669$	−60729.8	+	581916.i	−0.135691	+	1.30019i
$670$	−539030.	−	227904.i	−1.20078	−	0.507694i
$671$	−368289.	−	212632.i	−0.817983	−	0.472262i
$672$	−342341.	−	248341.i	−0.758088	−	0.549933i
$673$	649893.	−	375216.i	1.43487	−	0.828421i	0.437381	−	0.899276i	$-0.355906\pi$
$673$	649893.	−	375216.i	1.43487	−	0.828421i	0.997487	+	0.0708548i	$0.0225727\pi$
$674$		−	354048.i		−	0.779368i
$675$	201793.	+	408502.i	0.442893	+	0.896575i
$676$	83581.4			0.182901
$677$	393173.	+	680996.i	0.857841	+	1.48582i	0.873984	+	0.485955i	$0.161528\pi$
$677$	393173.	+	680996.i	0.857841	+	1.48582i	−0.0161427	+	0.999870i	$0.505139\pi$
$678$	189446.	−	261153.i	0.412121	−	0.568113i
$679$	132317.	−	229180.i	0.286997	−	0.497093i
$680$	218206.	−	516093.i	0.471898	−	1.11612i
$681$	−324073.	−	33820.8i	−0.698793	−	0.0729273i
$682$	226497.	−	130768.i	0.486961	−	0.281147i
$683$	−80351.5			−0.172247			−0.0861237	−	0.996284i	$-0.527448\pi$
$683$	−80351.5			−0.172247			−0.0861237	+	0.996284i	$0.527448\pi$
$684$	172036.	+	36303.3i	0.367711	+	0.0775951i
$685$	73644.7	−	9148.37i	0.156950	−	0.0194968i
$686$	168101.	−	97053.4i	0.357210	−	0.206235i
$687$	−270548.	−	606462.i	−0.573233	−	1.28496i
$688$	−270068.	−	155924.i	−0.570554	−	0.329410i
$689$	303190.	+	175047.i	0.638669	+	0.368736i
$690$	−169196.	−	280223.i	−0.355380	−	0.588580i
$691$	−6794.63	−	11768.7i	−0.0142302	−	0.0246474i	0.858823	−	0.512273i	$-0.171196\pi$
$691$	−6794.63	−	11768.7i	−0.0142302	−	0.0246474i	−0.873053	+	0.487626i	$0.837863\pi$
$692$	53917.7			0.112595
$693$	616121.	+	130015.i	1.28292	+	0.270724i
$694$	170840.			0.354707
$695$	19621.6	+	25962.1i	0.0406223	+	0.0537490i
$696$	45054.2	−	431712.i	0.0930073	−	0.891200i
$697$	−42704.2	−	24655.3i	−0.0879033	−	0.0507510i
$698$	−190557.	+	330055.i	−0.391124	+	0.677447i
$699$	−50468.6	+	69571.5i	−0.103292	+	0.142389i
$700$	−172127.	+	167167.i	−0.351281	+	0.341157i
$701$		−	758841.i		−	1.54424i	−0.635476	−	0.772120i	$-0.719196\pi$
$701$		−	758841.i		−	1.54424i	0.635476	−	0.772120i	$-0.280804\pi$
$702$	156168.	−	484264.i	0.316898	−	0.982671i
$703$			67008.7i			0.135588i
$704$	−399043.	+	230387.i	−0.805145	+	0.464851i
$705$	−229714.	+	416527.i	−0.462179	+	0.838040i
$706$	364790.	−	631835.i	0.731869	−	1.26763i
$707$	−144030.	+	249467.i	−0.288147	+	0.499085i
$708$	−16045.7	+	153751.i	−0.0320105	+	0.306726i
$709$	275281.	+	476800.i	0.547625	+	0.948514i	0.998437	+	0.0558948i	$0.0178011\pi$
$709$	275281.	+	476800.i	0.547625	+	0.948514i	−0.450812	+	0.892619i	$0.648866\pi$
$710$	47316.0	+	380896.i	0.0938624	+	0.755595i
$711$	−147470.	+	164267.i	−0.291719	+	0.324945i
$712$		−	646622.i		−	1.27553i
$713$	−168399.	−	291676.i	−0.331253	−	0.573748i
$714$	−651662.	+	290712.i	−1.27828	+	0.570252i
$715$	214357.	−	506990.i	0.419301	−	0.991715i
$716$	−76391.0	−	44104.4i	−0.149010	−	0.0860312i
$717$	−255242.	+	113866.i	−0.496493	+	0.221490i
$718$	−23222.7	+	13407.7i	−0.0450469	+	0.0260078i
$719$			144471.i			0.279463i	0.990189	+	0.139731i	$0.0446239\pi$
$719$			144471.i			0.279463i	−0.990189	+	0.139731i	$0.955376\pi$
$720$	126988.	+	270288.i	0.244962	+	0.521390i
$721$	308835.			0.594095
$722$	79728.9	+	138094.i	0.152947	+	0.264912i
$723$	899323.	+	93855.0i	1.72044	+	0.179548i
$724$	−35213.7	+	60991.9i	−0.0671791	+	0.116358i
$725$	−416255.	−	118084.i	−0.791923	−	0.224654i
$726$	−66702.8	+	91950.5i	−0.126553	+	0.174454i
$727$	−4108.19	+	2371.86i	−0.00777288	+	0.00448767i	−0.503881	−	0.863773i	$-0.668095\pi$
$727$	−4108.19	+	2371.86i	−0.00777288	+	0.00448767i	0.496109	+	0.868261i	$0.334762\pi$
$728$	1.10289e6			2.08099
$729$	431317.	+	310476.i	0.811599	+	0.584215i
$730$	60042.9	+	483348.i	0.112672	+	0.907014i
$731$	589175.	−	340160.i	1.10258	−	0.636574i
$732$	110986.	−	152995.i	0.207131	−	0.285532i
$733$	−106934.	−	61738.6i	−0.199026	−	0.114908i	0.397175	−	0.917743i	$-0.369991\pi$
$733$	−106934.	−	61738.6i	−0.199026	−	0.114908i	−0.596201	+	0.802835i	$0.703324\pi$
$734$	−722340.	−	417043.i	−1.34076	−	0.774085i
$735$	717308.	−	14064.3i	1.32779	−	0.0260341i
$736$	138710.	+	240252.i	0.256066	+	0.443519i
$737$	−738447.			−1.35952
$738$	38900.6	−	12702.8i	0.0714238	−	0.0233230i
$739$	−384069.			−0.703267			−0.351633	−	0.936138i	$-0.614374\pi$
$739$	−384069.			−0.703267			−0.351633	+	0.936138i	$0.614374\pi$
$740$	16234.3	−	12269.5i	0.0296462	−	0.0224060i
$741$	−735719.	+	328211.i	−1.33991	+	0.597746i
$742$	352858.	+	203723.i	0.640903	+	0.370025i
$743$	469203.	−	812684.i	0.849930	−	1.47212i	−0.0313395	−	0.999509i	$-0.509977\pi$
$743$	469203.	−	812684.i	0.849930	−	1.47212i	0.881270	−	0.472614i	$-0.156689\pi$
$744$	194920.	+	436933.i	0.352135	+	0.789349i
$745$	75534.3	−	57087.1i	0.136092	−	0.102855i
$746$		−	149042.i		−	0.267812i
$747$	−220494.	+	245608.i	−0.395145	+	0.440151i
$748$		−	171778.i		−	0.307019i
$749$	−149239.	+	86163.0i	−0.266022	+	0.153588i
$750$	447133.	−	122201.i	0.794903	−	0.217246i
$751$	−140131.	+	242714.i	−0.248459	+	0.430344i	−0.963098	−	0.269149i	$-0.913257\pi$
$751$	−140131.	+	242714.i	−0.248459	+	0.430344i	0.714639	+	0.699493i	$0.246591\pi$
$752$	−155886.	+	270003.i	−0.275659	+	0.477455i
$753$	794872.	+	576617.i	1.40187	+	1.01694i
$754$	241599.	+	418462.i	0.424964	+	0.736060i
$755$	810933.	−	100737.i	1.42263	−	0.176723i
$756$	−85897.8	+	266362.i	−0.150293	+	0.466045i
$757$			655098.i			1.14318i	0.820539	+	0.571590i	$0.193673\pi$
$757$			655098.i			1.14318i	−0.820539	+	0.571590i	$0.806327\pi$
$758$	−251458.	−	435538.i	−0.437650	−	0.758031i
$759$	−334336.	−	242535.i	−0.580363	−	0.421008i
$760$	286709.	−	678114.i	0.496380	−	1.17402i
$761$	760975.	+	439349.i	1.31402	+	0.758649i	0.982759	−	0.184891i	$-0.0591933\pi$
$761$	760975.	+	439349.i	1.31402	+	0.758649i	0.331259	+	0.943540i	$0.392527\pi$
$762$	43475.3	−	416583.i	0.0748744	−	0.717450i
$763$	−377223.	+	217790.i	−0.647961	+	0.374100i
$764$			84398.6i			0.144593i
$765$	−649173.	−	54908.2i	−1.10927	−	0.0938241i
$766$	−429046.			−0.731218
$767$	−354147.	−	613401.i	−0.601996	−	1.04269i
$768$	−204981.	−	459486.i	−0.347529	−	0.779023i
$769$	−379080.	+	656586.i	−0.641030	+	1.11030i	0.344173	+	0.938906i	$0.388159\pi$
$769$	−379080.	+	656586.i	−0.641030	+	1.11030i	−0.985203	+	0.171391i	$0.945174\pi$
$770$	249473.	−	590044.i	0.420767	−	0.995183i
$771$	139796.	+	313368.i	0.235173	+	0.527164i
$772$	60430.9	−	34889.8i	0.101397	−	0.0585415i
$773$	160727.			0.268987			0.134493	−	0.990914i	$-0.457059\pi$
$773$	160727.			0.268987			0.134493	+	0.990914i	$0.457059\pi$
$774$	−116573.	+	552421.i	−0.194588	+	0.922122i
$775$	462426.	−	116689.i	0.769908	−	0.194279i
$776$	213551.	−	123294.i	0.354632	−	0.204747i
$777$	−106085.	−	11071.3i	−0.175717	−	0.0183381i
$778$	162669.	+	93917.3i	0.268749	+	0.155162i
$779$	−56110.7	−	32395.5i	−0.0924636	−	0.0533839i
$780$	214228.	+	118147.i	0.352118	+	0.194193i
$781$	242156.	+	419426.i	0.397002	+	0.687627i
$782$	468061.			0.765400
$783$	−493417.	+	106016.i	−0.804804	+	0.172920i
$784$	470240.			0.765046
$785$	−845275.	+	638840.i	−1.37170	+	1.03670i
$786$	373359.	+	270843.i	0.604341	+	0.438402i
$787$	37127.1	+	21435.3i	0.0599434	+	0.0346083i	0.529672	−	0.848202i	$-0.322315\pi$
$787$	37127.1	+	21435.3i	0.0599434	+	0.0346083i	−0.469729	+	0.882811i	$0.655648\pi$
$788$	45064.8	−	78054.6i	0.0725747	−	0.125703i
$789$	81135.2	+	8467.42i	0.130333	+	0.0136018i
$790$	135410.	+	179167.i	0.216969	+	0.287081i
$791$		−	813090.i		−	1.29953i
$792$	436615.	+	391970.i	0.696062	+	0.624888i
$793$			866028.i			1.37716i
$794$	497055.	−	286975.i	0.788431	−	0.455201i
$795$	192280.	+	318454.i	0.304228	+	0.503863i
$796$	126424.	−	218973.i	0.199528	−	0.345592i
$797$	12555.0	−	21745.9i	0.0197652	−	0.0342343i	−0.855974	−	0.517019i	$-0.827041\pi$
$797$	12555.0	−	21745.9i	0.0197652	−	0.0342343i	0.875739	+	0.482785i	$0.160375\pi$
$798$	−856244.	+	381978.i	−1.34460	+	0.599836i
$799$	−340078.	−	589032.i	−0.532702	−	0.922667i
$800$	−380899.	+	96116.1i	−0.595155	+	0.150181i
$801$	−714688.	+	233377.i	−1.11391	+	0.363742i
$802$		−	971134.i		−	1.50984i
$803$	307290.	+	532242.i	0.476560	+	0.825425i
$804$	34067.3	−	326434.i	0.0527018	−	0.504991i
$805$	−759839.	−	321263.i	−1.17255	−	0.495756i
$806$	−461250.	−	266303.i	−0.710014	−	0.409926i
$807$	−518707.	−	376281.i	−0.796481	−	0.577784i
$808$	−232455.	+	134208.i	−0.356054	+	0.205568i
$809$			493979.i			0.754764i	0.926058	+	0.377382i	$0.123176\pi$
$809$			493979.i			0.754764i	−0.926058	+	0.377382i	$0.876824\pi$
$810$	393806.	−	370449.i	0.600223	−	0.564623i
$811$	223063.			0.339145			0.169572	−	0.985518i	$-0.445761\pi$
$811$	223063.			0.339145			0.169572	+	0.985518i	$0.445761\pi$
$812$	−132888.	−	230168.i	−0.201545	−	0.349086i
$813$	−229325.	+	316127.i	−0.346953	+	0.478278i
$814$	−27164.9	+	47051.0i	−0.0409977	+	0.0710101i
$815$	266055.	+	112489.i	0.400550	+	0.169354i
$816$	−424705.	−	44323.0i	−0.637833	−	0.0665654i
$817$	774139.	−	446950.i	1.15978	−	0.669598i
$818$	−780654.			−1.16668
$819$	−398053.	−	1.21899e6i	−0.593435	−	1.81732i
$820$	2425.54	+	19525.7i	0.00360729	+	0.0290388i
$821$	125277.	−	72328.7i	0.185860	−	0.107306i	−0.404183	−	0.914678i	$-0.632444\pi$
$821$	125277.	−	72328.7i	0.185860	−	0.107306i	0.590043	+	0.807372i	$0.299111\pi$
$822$	−35876.8	−	80421.7i	−0.0530971	−	0.119023i
$823$	−417117.	−	240822.i	−0.615826	−	0.355547i	0.159416	−	0.987211i	$-0.449039\pi$
$823$	−417117.	−	240822.i	−0.615826	−	0.355547i	−0.775242	+	0.631664i	$0.782372\pi$
$824$	249219.	+	143887.i	0.367052	+	0.211917i
$825$	459609.	−	361735.i	0.675275	−	0.531474i
$826$	−412163.	−	713888.i	−0.604101	−	1.04633i
$827$	−178175.			−0.260517			−0.130259	−	0.991480i	$-0.541581\pi$
$827$	−178175.			−0.260517			−0.130259	+	0.991480i	$0.541581\pi$
$828$	122638.	−	136606.i	0.178881	−	0.199255i
$829$	−467392.			−0.680099			−0.340049	−	0.940408i	$-0.610444\pi$
$829$	−467392.			−0.680099			−0.340049	+	0.940408i	$0.610444\pi$
$830$	202463.	+	267887.i	0.293893	+	0.388861i
$831$	85234.9	−	816725.i	0.123428	−	1.18270i
$832$	812630.	+	469172.i	1.17394	+	0.677775i
$833$	−512933.	+	888425.i	−0.739214	+	1.28036i
$834$	22675.3	−	31258.2i	0.0326003	−	0.0449398i
$835$	−646870.	−	855900.i	−0.927779	−	1.22758i
$836$		−	225706.i		−	0.322947i
$837$	412577.	−	373135.i	0.588917	−	0.532617i
$838$		−	802637.i		−	1.14296i
$839$	201821.	−	116521.i	0.286710	−	0.165532i	−0.349747	−	0.936844i	$-0.613733\pi$
$839$	201821.	−	116521.i	0.286710	−	0.165532i	0.636457	+	0.771312i	$0.280399\pi$
$840$	1.02619e6	+	565944.i	1.45435	+	0.802075i
$841$	−114010.	+	197471.i	−0.161194	+	0.279197i
$842$	−473801.	+	820647.i	−0.668300	+	1.15753i
$843$	114131.	−	1.09361e6i	0.160601	−	1.53888i
$844$	−42041.8	−	72818.6i	−0.0590197	−	0.102225i
$845$	−403821.	+	50163.8i	−0.565555	+	0.0702550i
$846$	552287.	+	116545.i	0.771657	+	0.162837i
$847$			286285.i			0.399054i
$848$	121911.	+	211157.i	0.169532	+	0.293639i
$849$	1.26126e6	−	562657.i	1.74980	−	0.780600i
$850$	−180885.	+	637635.i	−0.250360	+	0.882540i
$851$	60590.7	+	34982.0i	0.0836655	+	0.0483043i
$852$	−196581.	+	87696.5i	−0.270809	+	0.120810i
$853$	−471332.	+	272124.i	−0.647782	+	0.373997i	−0.787606	−	0.616179i	$-0.788680\pi$
$853$	−471332.	+	272124.i	−0.647782	+	0.373997i	0.139824	+	0.990176i	$0.455346\pi$
$854$			1.00790e6i			1.38198i
$855$	−852974.	−	72146.0i	−1.16682	−	0.0986915i
$856$	−160574.			−0.219143
$857$	542845.	+	940236.i	0.739119	+	1.28019i	0.952892	+	0.303309i	$0.0980913\pi$
$857$	542845.	+	940236.i	0.739119	+	1.28019i	−0.213773	+	0.976883i	$0.568575\pi$
$858$	−649649.	−	67798.5i	−0.882478	−	0.0920970i
$859$	−206281.	+	357289.i	−0.279558	+	0.484209i	−0.971275	−	0.237960i	$-0.923521\pi$
$859$	−206281.	+	357289.i	−0.279558	+	0.484209i	0.691717	+	0.722169i	$0.256855\pi$
$860$	−250030.	−	105714.i	−0.338061	−	0.142934i
$861$	60557.8	−	83479.6i	0.0816891	−	0.112609i
$862$	−544144.	+	314162.i	−0.732317	+	0.422804i
$863$	−472099.			−0.633887			−0.316943	−	0.948444i	$-0.602656\pi$
$863$	−472099.			−0.633887			−0.316943	+	0.948444i	$0.602656\pi$
$864$	−339838.	+	307350.i	−0.455244	+	0.411724i
$865$	−260501.	+	32360.3i	−0.348159	+	0.0432494i
$866$	−445231.	+	257054.i	−0.593676	+	0.342759i
$867$	105617.	−	145595.i	0.140507	−	0.193690i
$868$	253703.	+	146476.i	0.336733	+	0.194413i
$869$	245413.	+	141689.i	0.324981	+	0.187628i
$870$	10065.0	+	513336.i	0.0132977	+	0.678208i
$871$	751905.	+	1.30234e6i	0.991121	+	1.71667i
$872$	−405875.			−0.533776
$873$	−213347.	−	191532.i	−0.279935	−	0.251311i
$874$	615003.			0.805108
$875$	731298.	−	910968.i	0.955165	−	1.18984i
$876$	−249457.	+	111285.i	−0.325078	+	0.145020i
$877$	−93901.6	−	54214.1i	−0.122088	−	0.0704877i	0.437712	−	0.899115i	$-0.355789\pi$
$877$	−93901.6	−	54214.1i	−0.122088	−	0.0704877i	−0.559800	+	0.828627i	$0.689122\pi$
$878$	382917.	−	663231.i	0.496724	−	0.860351i
$879$	101285.	+	227041.i	0.131090	+	0.293851i
$880$	305835.	−	231143.i	0.394931	−	0.298480i
$881$			864610.i			1.11396i	0.830527	+	0.556978i	$0.188039\pi$
$881$			864610.i			1.11396i	−0.830527	+	0.556978i	$0.811961\pi$
$882$	−264270.	−	809294.i	−0.339712	−	1.04032i
$883$		−	724958.i		−	0.929804i	−0.885362	−	0.464902i	$-0.846090\pi$
$883$		−	724958.i		−	0.929804i	0.885362	−	0.464902i	$-0.153910\pi$
$884$	−302951.	+	174909.i	−0.387676	+	0.223825i
$885$	−14753.7	−	752472.i	−0.0188372	−	0.960735i
$886$	−60784.5	+	105282.i	−0.0774329	+	0.134118i
$887$	−236222.	+	409149.i	−0.300244	+	0.520037i	−0.976191	−	0.216913i	$-0.930401\pi$
$887$	−236222.	+	409149.i	−0.300244	+	0.520037i	0.675947	+	0.736950i	$0.263735\pi$
$888$	−80449.2	−	58359.5i	−0.102022	−	0.0740092i
$889$	−527785.	−	914151.i	−0.667812	−	1.15668i
$890$	94290.1	+	759038.i	0.119038	+	0.958261i
$891$	275649.	−	624044.i	0.347217	−	0.786068i
$892$			333815.i			0.419542i
$893$	−446841.	−	773951.i	−0.560338	−	0.970534i
$894$	−90942.6	−	65971.7i	−0.113787	−	0.0825435i
$895$	395551.	+	167241.i	0.493806	+	0.208783i
$896$	294610.	+	170093.i	0.366971	+	0.211871i
$897$	−87308.6	+	836596.i	−0.108511	+	1.03975i
$898$	541066.	−	312384.i	0.670961	−	0.387379i
$899$			528267.i			0.653633i
$900$	138703.	+	219861.i	0.171239	+	0.271433i
$901$	−531918.			−0.655232
$902$	−26265.9	−	45493.8i	−0.0322833	−	0.0559164i
$903$	579687.	+	1.29943e6i	0.710916	+	1.59359i
$904$	378821.	−	656137.i	0.463550	−	0.802893i
$905$	133528.	−	315815.i	0.163032	−	0.385598i
$906$	−395055.	−	885557.i	−0.481284	−	1.07885i
$907$	48764.6	−	28154.2i	0.0592775	−	0.0342239i	−0.470068	−	0.882630i	$-0.655771\pi$
$907$	48764.6	−	28154.2i	0.0592775	−	0.0342239i	0.529346	+	0.848406i	$0.322437\pi$
$908$	−185904.			−0.225484
$909$	232232.	+	208486.i	0.281057	+	0.252318i
$910$	−1.29463e6	+	160823.i	−1.56338	+	0.194207i
$911$	−22261.4	+	12852.6i	−0.0268235	+	0.0154865i	−0.513352	−	0.858178i	$-0.671596\pi$
$911$	−22261.4	+	12852.6i	−0.0268235	+	0.0154865i	0.486528	+	0.873665i	$0.338263\pi$
$912$	−558036.	−	58237.6i	−0.670923	−	0.0700187i
$913$	366936.	+	211851.i	0.440199	+	0.254149i
$914$	−1.07048e6	−	618043.i	−1.28141	−	0.739821i
$915$	−444399.	+	805800.i	−0.530800	+	0.962466i
$916$	−189443.	−	328125.i	−0.225781	−	0.391065i
$917$	1.16244e6			1.38240
$918$	162399.	+	755835.i	0.192707	+	0.896895i
$919$	−1.30069e6			−1.54007			−0.770036	−	0.638000i	$-0.779762\pi$
$919$	−1.30069e6			−1.54007			−0.770036	+	0.638000i	$0.779762\pi$
$920$	−463487.	−	613259.i	−0.547598	−	0.724549i
$921$	−234621.	−	170199.i	−0.276597	−	0.200649i
$922$	742702.	+	428799.i	0.873680	+	0.504420i
$923$	493138.	−	854140.i	0.578849	−	1.00260i
$924$	357328.	+	37291.4i	0.418527	+	0.0436782i
$925$	−71071.4	+	69023.2i	−0.0830638	+	0.0806699i
$926$			510177.i			0.594975i
$927$	69085.4	−	327385.i	0.0803946	−	0.380977i
$928$		−	435132.i		−	0.505272i
$929$	1.37354e6	−	793012.i	1.59151	−	0.918858i	0.598460	−	0.801152i	$-0.295779\pi$
$929$	1.37354e6	−	793012.i	1.59151	−	0.918858i	0.993049	−	0.117706i	$-0.0375539\pi$
$930$	−292520.	−	484472.i	−0.338213	−	0.560148i
$931$	−673962.	+	1.16734e6i	−0.777563	+	1.34678i
$932$	−24519.1	+	42468.4i	−0.0282276	+	0.0488916i
$933$	1.50797e6	−	672717.i	1.73232	−	0.772804i
$934$	−92197.9	−	159691.i	−0.105688	−	0.183058i
$935$	103098.	+	829942.i	0.117931	+	0.949346i
$936$	246713.	−	1.16913e6i	0.281605	−	1.33448i
$937$		−	68368.4i		−	0.0778711i	−0.999242	−	0.0389355i	$-0.987603\pi$
$937$		−	68368.4i		−	0.0778711i	0.999242	−	0.0389355i	$-0.0123967\pi$
$938$	875081.	+	1.51568e6i	0.994586	+	1.72267i
$939$	−24052.5	+	230473.i	−0.0272791	+	0.261389i
$940$	−105688.	+	249969.i	−0.119611	+	0.282899i
$941$	880194.	+	508180.i	0.994030	+	0.573903i	0.906476	−	0.422257i	$-0.138762\pi$
$941$	880194.	+	508180.i	0.994030	+	0.573903i	0.0875532	+	0.996160i	$0.472095\pi$
$942$	1.01770e6	+	738264.i	1.14689	+	0.831975i
$943$	−58585.4	+	33824.3i	−0.0658819	+	0.0380369i
$944$		−	493292.i		−	0.553554i
$945$	255148.	−	1.33847e6i	0.285712	−	1.49881i
$946$	724762.			0.809866
$947$	−357191.	−	618674.i	−0.398292	−	0.689861i	0.595224	−	0.803560i	$-0.297063\pi$
$947$	−357191.	−	618674.i	−0.398292	−	0.689861i	−0.993515	+	0.113699i	$0.963730\pi$
$948$	−73956.3	+	101949.i	−0.0822922	+	0.113441i
$949$	625780.	−	1.08388e6i	0.694848	−	1.20351i
$950$	−237672.	+	837813.i	−0.263348	+	0.928325i
$951$	489765.	+	51112.8i	0.541535	+	0.0565156i
$952$	−1.45119e6	+	837844.i	−1.60122	+	0.924462i
$953$	143104.			0.157567			0.0787836	−	0.996892i	$-0.474896\pi$
$953$	143104.			0.157567			0.0787836	+	0.996892i	$0.474896\pi$
$954$	294892.	−	328480.i	0.324016	−	0.360921i
$955$	−50654.3	−	407769.i	−0.0555405	−	0.447103i
$956$	−138098.	+	79730.9i	−0.151102	+	0.0872390i
$957$	263941.	+	591652.i	0.288193	+	0.646015i
$958$	−15085.7	−	8709.73i	−0.0164375	−	0.00949017i
$959$	−192198.	−	110966.i	−0.208984	−	0.120657i
$960$	515362.	+	853542.i	0.559204	+	0.926152i
$961$	170619.	+	295521.i	0.184748	+	0.319994i
$962$	110640.			0.119553
$963$	57954.1	+	177477.i	0.0624930	+	0.191377i
$964$	515895.			0.555146
$965$	−271030.	+	204838.i	−0.291047	+	0.219967i
$966$	−101611.	+	973645.i	−0.108890	+	1.04339i
$967$	−363441.	−	209833.i	−0.388670	−	0.224399i	0.292914	−	0.956139i	$-0.405375\pi$
$967$	−363441.	−	209833.i	−0.388670	−	0.224399i	−0.681584	+	0.731740i	$0.738708\pi$
$968$	−133381.	+	231022.i	−0.142345	+	0.246549i
$969$	718727.	−	990773.i	0.765450	−	1.05518i
$970$	−232699.	+	175869.i	−0.247315	+	0.186915i
$971$		−	180994.i		−	0.191967i	−0.995383	−	0.0959833i	$-0.969400\pi$
$971$		−	180994.i		−	0.191967i	0.995383	−	0.0959833i	$-0.0305995\pi$
$972$	263145.	+	150641.i	0.278524	+	0.159445i
$973$		−	97321.4i		−	0.102797i
$974$	276464.	−	159617.i	0.291421	−	0.168252i
$975$	−1.10595e6	−	442248.i	−1.16339	−	0.465218i
$976$	−301573.	+	522340.i	−0.316587	+	0.548344i
$977$	685507.	−	1.18733e6i	0.718163	−	1.24389i	−0.243564	−	0.969885i	$-0.578317\pi$
$977$	685507.	−	1.18733e6i	0.718163	−	1.24389i	0.961727	−	0.274009i	$-0.0883500\pi$
$978$	35579.0	−	340919.i	0.0371977	−	0.356430i
$979$	482561.	+	835821.i	0.503486	+	0.872063i
$980$	406216.	−	50461.4i	0.422965	−	0.0525421i
$981$	146488.	+	448599.i	0.152217	+	0.466145i
$982$		−	1.05857e6i		−	1.09774i
$983$	−22108.8	−	38293.6i	−0.0228801	−	0.0396295i	0.854359	−	0.519684i	$-0.173950\pi$
$983$	−22108.8	−	38293.6i	−0.0228801	−	0.0396295i	−0.877239	+	0.480054i	$0.840617\pi$
$984$	87761.5	−	39151.2i	0.0906387	−	0.0404347i
$985$	−170882.	+	404165.i	−0.176127	+	0.416568i
$986$	−635794.	−	367076.i	−0.653978	−	0.377574i
$987$	1.29911e6	−	579546.i	1.33356	−	0.594913i
$988$	−398059.	+	229820.i	−0.407788	+	0.235436i
$989$		−	933324.i		−	0.954200i
$990$	−569678.	−	396448.i	−0.581245	−	0.404498i
$991$	514486.			0.523873			0.261937	−	0.965085i	$-0.415639\pi$
$991$	514486.			0.523873			0.261937	+	0.965085i	$0.415639\pi$
$992$	239812.	+	415367.i	0.243696	+	0.422094i
$993$	−1.00026e6	−	104389.i	−1.01442	−	0.105866i
$994$	573923.	−	994064.i	0.580872	−	1.00610i
$995$	−479390.	+	1.13384e6i	−0.484221	+	1.14526i
$996$	−110578.	+	152433.i	−0.111468	+	0.153660i
$997$	306196.	−	176782.i	0.308041	−	0.177848i	−0.338008	−	0.941143i	$-0.609753\pi$
$997$	306196.	−	176782.i	0.308041	−	0.177848i	0.646050	+	0.763295i	$0.276420\pi$
$998$	506404.			0.508436
$999$	−35467.2	+	109981.i	−0.0355382	+	0.110201i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.h.a.14.16	yes	44
3.2	odd	2		135.5.h.a.44.7		44
5.4	even	2	inner	45.5.h.a.14.7	✓	44
9.2	odd	6	inner	45.5.h.a.29.7	yes	44
9.4	even	3		405.5.d.a.404.14		44
9.5	odd	6		405.5.d.a.404.32		44
9.7	even	3		135.5.h.a.89.16		44
15.14	odd	2		135.5.h.a.44.16		44
45.4	even	6		405.5.d.a.404.31		44
45.14	odd	6		405.5.d.a.404.13		44
45.29	odd	6	inner	45.5.h.a.29.16	yes	44
45.34	even	6		135.5.h.a.89.7		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.h.a.14.7	✓	44	5.4	even	2	inner
45.5.h.a.14.16	yes	44	1.1	even	1	trivial
45.5.h.a.29.7	yes	44	9.2	odd	6	inner
45.5.h.a.29.16	yes	44	45.29	odd	6	inner
135.5.h.a.44.7		44	3.2	odd	2
135.5.h.a.44.16		44	15.14	odd	2
135.5.h.a.89.7		44	45.34	even	6
135.5.h.a.89.16		44	9.7	even	3
405.5.d.a.404.13		44	45.14	odd	6
405.5.d.a.404.14		44	9.4	even	3
405.5.d.a.404.31		44	45.4	even	6
405.5.d.a.404.32		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+(1.64811 + 2.85461i) q^{2} +(5.28472 - 7.28504i) q^{3} +(2.56747 - 4.44699i) q^{4} +(-9.73566 + 23.0264i) q^{5} +(29.5057 + 3.07927i) q^{6} +(64.7475 - 37.3820i) q^{7} +69.6654 q^{8} +(-25.1435 - 76.9987i) q^{9} +(-81.7769 + 10.1586i) q^{10} +(-90.0492 + 51.9899i) q^{11} +(-18.8281 - 42.2052i) q^{12} +(183.381 + 105.875i) q^{13} +(213.422 + 123.219i) q^{14} +(116.298 + 192.613i) q^{15} +(73.7366 + 127.716i) q^{16} -321.724 q^{17} +(178.362 - 198.677i) q^{18} -422.726 q^{19} +(77.4023 + 102.414i) q^{20} +(69.8432 - 669.241i) q^{21} +(-296.822 - 171.370i) q^{22} +(-220.685 + 382.237i) q^{23} +(368.162 - 507.515i) q^{24} +(-435.434 - 448.355i) q^{25} +697.974i q^{26} +(-693.815 - 223.745i) q^{27} -383.909i q^{28} +(599.538 - 346.144i) q^{29} +(-358.162 + 649.433i) q^{30} +(-381.537 + 660.842i) q^{31} +(314.271 - 544.334i) q^{32} +(-97.1362 + 930.764i) q^{33} +(-530.237 - 918.397i) q^{34} +(230.414 + 1854.84i) q^{35} +(-406.968 - 85.8792i) q^{36} -158.516i q^{37} +(-696.698 - 1206.72i) q^{38} +(1740.42 - 776.416i) q^{39} +(-678.239 + 1604.15i) q^{40} +(132.735 + 76.6349i) q^{41} +(2025.53 - 903.607i) q^{42} +(-1831.30 + 1057.30i) q^{43} +533.931i q^{44} +(2017.80 + 170.669i) q^{45} -1454.85 q^{46} +(1057.05 + 1830.86i) q^{47} +(1320.09 + 137.767i) q^{48} +(1594.32 - 2761.45i) q^{49} +(562.237 - 1981.93i) q^{50} +(-1700.22 + 2343.77i) q^{51} +(941.650 - 543.662i) q^{52} +1653.34 q^{53} +(-504.777 - 2349.33i) q^{54} +(-320.454 - 2579.67i) q^{55} +(4510.66 - 2604.23i) q^{56} +(-2233.99 + 3079.57i) q^{57} +(1976.21 + 1140.96i) q^{58} +(-2896.82 - 1672.48i) q^{59} +(1155.14 - 22.6489i) q^{60} +(2044.93 + 3541.93i) q^{61} -2515.26 q^{62} +(-4506.34 - 4045.56i) q^{63} +4431.38 q^{64} +(-4223.25 + 3191.84i) q^{65} +(-2817.06 + 1256.71i) q^{66} +(6150.36 + 3550.91i) q^{67} +(-826.018 + 1430.70i) q^{68} +(1618.35 + 3627.71i) q^{69} +(-4915.10 + 3714.72i) q^{70} -4657.74i q^{71} +(-1751.63 - 5364.15i) q^{72} -5910.56i q^{73} +(452.501 - 261.251i) q^{74} +(-5567.43 + 802.719i) q^{75} +(-1085.34 + 1879.86i) q^{76} +(-3886.97 + 6732.44i) q^{77} +(5084.76 + 3688.59i) q^{78} +(-1362.66 - 2360.20i) q^{79} +(-3658.71 + 454.496i) q^{80} +(-5296.61 + 3872.03i) q^{81} +505.210i q^{82} +(-2037.42 - 3528.92i) q^{83} +(-2796.79 - 2028.85i) q^{84} +(3132.20 - 7408.16i) q^{85} +(-6036.38 - 3485.11i) q^{86} +(646.723 - 6196.93i) q^{87} +(-6273.31 + 3621.90i) q^{88} -9281.82i q^{89} +(2838.35 + 6041.30i) q^{90} +15831.3 q^{91} +(1133.20 + 1962.77i) q^{92} +(2797.94 + 6271.88i) q^{93} +(-3484.26 + 6034.91i) q^{94} +(4115.51 - 9733.87i) q^{95} +(-2304.65 - 5166.13i) q^{96} +(3065.38 - 1769.80i) q^{97} +10510.5 q^{98} +(6267.31 + 5626.47i) 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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