LMFDB - Embedded newform 45.5.h.a.14.7

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			14.7
Character	$\chi$	$=$	45.14
Dual form			45.5.h.a.29.7

$q$-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} +(15.0736 - 19.9446i) 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} +(65.6368 + 215.213i) q^{15} +(73.7366 + 127.716i) q^{16} +321.724 q^{17} +(-178.362 + 198.677i) q^{18} -422.726 q^{19} +(-49.9921 - 118.239i) 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} +(-170.570 - 601.274i) q^{25} +697.974i q^{26} +(693.815 + 223.745i) q^{27} +383.909i q^{28} +(599.538 - 346.144i) q^{29} +(506.174 - 542.063i) 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} +(-1050.11 + 1389.44i) q^{40} +(132.735 + 76.6349i) q^{41} +(-2025.53 + 903.607i) q^{42} +(1831.30 - 1057.30i) q^{43} +533.931i q^{44} +(-1914.71 - 659.176i) q^{45} -1454.85 q^{46} +(-1057.05 - 1830.86i) q^{47} +(-1320.09 - 137.767i) q^{48} +(1594.32 - 2761.45i) q^{49} +(-1435.28 + 1477.88i) 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} +(1125.57 + 260.668i) q^{60} +(2044.93 + 3541.93i) q^{61} +2515.26 q^{62} +(4506.34 + 4045.56i) q^{63} +4431.38 q^{64} +(-4875.84 + 2061.52i) 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} +(5674.60 - 2399.24i) q^{70} -4657.74i q^{71} +(1751.63 + 5364.15i) q^{72} +5910.56i q^{73} +(452.501 - 261.251i) q^{74} +(5281.72 + 1934.96i) 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} +(4849.56 - 6416.64i) q^{85} +(-6036.38 - 3485.11i) q^{86} +(-646.723 + 6196.93i) q^{87} +(6273.31 - 3621.90i) q^{88} -9281.82i q^{89} +(1273.96 + 6552.14i) q^{90} +15831.3 q^{91} +(-1133.20 - 1962.77i) q^{92} +(-2797.94 - 6271.88i) q^{93} +(-3484.26 + 6034.91i) q^{94} +(-6372.02 + 8431.07i) 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	0.583084	−	0.812412i	$-0.301846\pi$
$2$	−1.64811	−	2.85461i	−0.412027	−	0.713652i	−0.995111	+	0.0987596i	$0.968513\pi$
$3$	−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
$5$	15.0736	−	19.9446i	0.602946	−	0.797782i
$5$	15.0736	−	19.9446i	0.602946	−	0.797782i
$6$	29.5057	+	3.07927i	0.819603	+	0.0855353i
$7$	−64.7475	+	37.3820i	−1.32138	+	0.762897i	−0.983948	−	0.178454i	$-0.942891\pi$
$7$	−64.7475	+	37.3820i	−1.32138	+	0.762897i	−0.337429	+	0.941351i	$0.609557\pi$
$8$	−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	−0.152827	−	0.988253i	$-0.548838\pi$
$13$	−183.381	−	105.875i	−1.08509	−	0.626479i	−0.932266	+	0.361774i	$0.882171\pi$
$14$	213.422	+	123.219i	1.08889	+	0.628669i
$15$	65.6368	+	215.213i	0.291719	+	0.956504i
$16$	73.7366	+	127.716i	0.288034	+	0.498889i
$17$	321.724			1.11323			0.556616	−	0.830770i	$-0.312099\pi$
$17$	321.724			1.11323			0.556616	+	0.830770i	$0.312099\pi$
$18$	−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	$0.699099\pi$
$20$	−49.9921	−	118.239i	−0.124980	−	0.295599i
$21$	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	−0.578480	−	0.815696i	$-0.696354\pi$
$23$	220.685	−	382.237i	0.417173	−	0.722566i	0.995654	+	0.0931306i	$0.0296874\pi$
$24$	368.162	−	507.515i	0.639170	−	0.881102i
$25$	−170.570	−	601.274i	−0.272912	−	0.962039i
$26$			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	$0.198308\pi$
$30$	506.174	−	542.063i	0.562415	−	0.602292i
$31$	−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	$0.0184388\pi$
$37$			158.516i			0.115790i	−0.998323	+	0.0578948i	$0.981561\pi$
$38$	696.698	+	1206.72i	0.482478	+	0.835676i
$39$	1740.42	−	776.416i	1.14426	−	0.510464i
$40$	−1050.11	+	1389.44i	−0.656320	+	0.868403i
$41$	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	0.0850269	−	0.996379i	$-0.472902\pi$
$43$	1831.30	−	1057.30i	0.990430	−	0.571825i	0.905403	+	0.424554i	$0.139569\pi$
$44$			533.931i			0.275791i
$45$	−1914.71	−	659.176i	−0.945535	−	0.325519i
$46$	−1454.85			−0.687547
$47$	−1057.05	−	1830.86i	−0.478518	−	0.828818i	0.521178	−	0.853448i	$-0.325493\pi$
$47$	−1057.05	−	1830.86i	−0.478518	−	0.828818i	−0.999697	+	0.0246296i	$0.992159\pi$
$48$	−1320.09	−	137.767i	−0.572956	−	0.0597947i
$49$	1594.32	−	2761.45i	0.664025	−	1.15013i
$50$	−1435.28	+	1477.88i	−0.574114	+	0.591151i
$51$	−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	$-0.595084\pi$
$53$	−1653.34			−0.588585			−0.294292	+	0.955715i	$0.595084\pi$
$54$	−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	$0.826197\pi$
$60$	1125.57	+	260.668i	0.312659	+	0.0724078i
$61$	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
$65$	−4875.84	+	2061.52i	−1.15405	+	0.487935i
$66$	−2817.06	+	1256.71i	−0.646708	+	0.288502i
$67$	−6150.36	−	3550.91i	−1.37010	−	0.791025i	−0.379156	−	0.925333i	$-0.623786\pi$
$67$	−6150.36	−	3550.91i	−1.37010	−	0.791025i	−0.990940	+	0.134307i	$0.957119\pi$
$68$	826.018	−	1430.70i	0.178637	−	0.309408i
$69$	1618.35	+	3627.71i	0.339919	+	0.761964i
$70$	5674.60	−	2399.24i	1.15808	−	0.489641i
$71$		−	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	$0.187116\pi$
$73$			5910.56i			1.10913i	−0.832140	+	0.554566i	$0.812884\pi$
$74$	452.501	−	261.251i	0.0826335	−	0.0477085i
$75$	5281.72	+	1934.96i	0.938973	+	0.343992i
$76$	−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	0.975159	−	0.221506i	$-0.0710972\pi$
$83$	2037.42	+	3528.92i	0.295750	+	0.512254i	−0.679409	+	0.733760i	$0.737764\pi$
$84$	−2796.79	−	2028.85i	−0.396370	−	0.287535i
$85$	4849.56	−	6416.64i	0.671219	−	0.888117i
$86$	−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	$-0.199259\pi$
$90$	1273.96	+	6552.14i	0.157279	+	0.808906i
$91$	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
$95$	−6372.02	+	8431.07i	−0.706041	+	0.934191i
$96$	−2304.65	−	5166.13i	−0.250071	−	0.560561i
$97$	−3065.38	+	1769.80i	−0.325793	+	0.188097i	−0.653972	−	0.756519i	$-0.726898\pi$
$97$	−3065.38	+	1769.80i	−0.325793	+	0.188097i	0.328179	+	0.944616i	$0.393565\pi$
$98$	−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	0.321832	−	0.946797i	$-0.395701\pi$
$103$	−3577.38	−	2065.40i	−0.337202	−	0.194684i	−0.659034	+	0.752113i	$0.729035\pi$
$104$	12775.3	+	7375.82i	1.18115	+	0.681936i
$105$	−12294.9	−	11480.9i	−1.11519	−	1.04135i
$106$	2724.88	+	4719.63i	0.242513	+	0.420045i
$107$	2304.93			0.201322			0.100661	−	0.994921i	$-0.467904\pi$
$107$	2304.93			0.201322			0.100661	+	0.994921i	$0.467904\pi$
$108$	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	$0.578848\pi$
$110$	7892.09	−	3336.80i	0.652239	−	0.275769i
$111$	−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	−0.996500	−	0.0835967i	$-0.973359\pi$
$113$	−5437.72	+	9418.40i	−0.425853	+	0.737599i	0.570647	+	0.821196i	$0.306693\pi$
$114$	−12472.8	−	1301.69i	−0.959743	−	0.100161i
$115$	−4297.02	−	10163.2i	−0.324917	−	0.768482i
$116$		−	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
$120$	−4572.61	−	14992.9i	−0.317542	−	1.04118i
$121$	−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	$0.144200\pi$
$127$			14118.7i			0.875362i	−0.899130	+	0.437681i	$0.855800\pi$
$128$	−2275.07	−	3940.53i	−0.138859	−	0.240511i
$129$	−1975.43	+	18928.7i	−0.118709	+	1.13747i
$130$	13920.8	+	10521.0i	0.823714	+	0.622545i
$131$	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
$135$	14920.8	−	10465.2i	0.818701	−	0.574220i
$136$	−22413.0			−1.21178
$137$	1484.21	+	2570.73i	0.0790780	+	0.136967i	0.902852	−	0.429951i	$-0.141469\pi$
$137$	1484.21	+	2570.73i	0.0790780	+	0.136967i	−0.823774	+	0.566918i	$0.808136\pi$
$138$	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	$0.155942\pi$
$140$	7656.89	+	5786.91i	0.390657	+	0.295250i
$141$	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	$0.693850\pi$
$150$	−3181.31	−	18266.3i	−0.141392	−	0.811834i
$151$	−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
$155$	7429.04	+	17570.9i	0.309221	+	0.731359i
$156$	1015.76	−	9733.05i	0.0417389	−	0.399945i
$157$	−36703.3	−	21190.6i	−1.48904	−	0.859696i	−0.489115	−	0.872219i	$-0.662680\pi$
$157$	−36703.3	−	21190.6i	−1.48904	−	0.859696i	−0.999922	+	0.0125237i	$0.996013\pi$
$158$	−4491.63	+	7779.73i	−0.179924	+	0.311638i
$159$	8737.41	−	12044.6i	0.345612	−	0.476429i
$160$	6119.27	+	14473.1i	0.239034	+	0.565355i
$161$			32998.5i			1.27304i
$162$	19782.5	+	8738.21i	0.753793	+	0.332960i
$163$			11554.3i			0.434881i	0.976074	+	0.217440i	$0.0697708\pi$
$163$			11554.3i			0.434881i	−0.976074	+	0.217440i	$0.930229\pi$
$164$	681.589	−	393.516i	0.0253417	−	0.0146310i
$165$	−17099.5	−	15967.3i	−0.628080	−	0.586496i
$166$	6715.79	−	11632.1i	0.243714	−	0.422125i
$167$	21457.0	−	37164.6i	0.769371	−	1.33259i	−0.168533	−	0.985696i	$-0.553903\pi$
$167$	21457.0	−	37164.6i	0.769371	−	1.33259i	0.937904	−	0.346894i	$-0.112764\pi$
$168$	−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	0.764888	−	0.644163i	$-0.222794\pi$
$173$	−5250.07	−	9093.39i	−0.175418	−	0.303832i	−0.940306	+	0.340331i	$0.889461\pi$
$174$	18755.7	−	8367.08i	0.619490	−	0.276360i
$175$	33520.8	+	32554.7i	1.09456	+	1.06301i
$176$	−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	$-0.0863842\pi$
$180$	−7847.31	+	6822.28i	−0.242201	+	0.210564i
$181$	−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
$185$	3161.53	+	2389.41i	0.0923748	+	0.0698148i
$186$	−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	0.333640	−	0.942701i	$-0.391723\pi$
$193$	−11768.6	−	6794.59i	−0.315943	−	0.182410i	−0.649583	+	0.760291i	$0.725056\pi$
$194$	10104.2	+	5833.65i	0.268471	+	0.155002i
$195$	10749.2	−	46415.3i	0.282687	−	1.22065i
$196$	−8186.77	−	14179.9i	−0.213108	−	0.369114i
$197$	−17552.2			−0.452272			−0.226136	−	0.974096i	$-0.572609\pi$
$197$	−17552.2			−0.452272			−0.226136	+	0.974096i	$0.572609\pi$
$198$	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	$0.286438\pi$
$200$	11882.8	+	41888.0i	0.297071	+	1.04720i
$201$	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
$205$	3529.26	−	1492.18i	0.0839799	−	0.0355070i
$206$			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
$210$	−12510.1	+	54019.0i	−0.283676	+	1.22492i
$211$	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
$220$	10649.0	+	8048.29i	0.220021	+	0.166287i
$221$	−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	0.187649	−	0.982236i	$-0.439913\pi$
$223$	56299.0	−	32504.2i	1.13212	−	0.653627i	0.944466	+	0.328609i	$0.106580\pi$
$224$		−	46992.3i		−	0.936549i
$225$	−42008.6	+	28251.8i	−0.829800	+	0.558061i
$226$	35847.8			0.701852
$227$	18101.8	+	31353.3i	0.351294	+	0.608459i	0.986476	−	0.163903i	$-0.0524085\pi$
$227$	18101.8	+	31353.3i	0.351294	+	0.608459i	−0.635183	+	0.772362i	$0.719075\pi$
$228$	−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	$-0.0817198\pi$
$230$	−21929.9	+	29016.3i	−0.414554	+	0.548513i
$231$	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	$-0.471967\pi$
$233$	9549.91			0.175909			0.0879544	+	0.996125i	$0.471967\pi$
$234$	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	$0.754295\pi$
$240$	−22646.3	+	24251.9i	−0.393164	+	0.421041i
$241$	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
$245$	−31043.6	−	73423.2i	−0.517178	−	1.22321i
$246$	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
$250$	7840.61	+	50903.1i	0.125450	+	0.814450i
$251$			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
$255$	21116.9	+	69239.4i	0.324751	+	1.06481i
$256$	27952.0	−	48414.2i	0.426513	−	0.738742i
$257$	19063.1	−	33018.3i	0.288621	−	0.499906i	−0.684860	−	0.728675i	$-0.740137\pi$
$257$	19063.1	−	33018.3i	0.288621	−	0.499906i	0.973481	+	0.228769i	$0.0734699\pi$
$258$	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	0.831404	−	0.555668i	$-0.187537\pi$
$263$	−4531.99	−	7849.64i	−0.0655206	−	0.113485i	−0.896925	+	0.442183i	$0.854204\pi$
$264$	−6767.03	+	64842.0i	−0.0970936	+	0.930355i
$265$	−24921.8	+	32975.0i	−0.354885	+	0.469563i
$266$	−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	$-0.163730\pi$
$270$	−54465.1	−	25345.4i	−0.747121	−	0.347673i
$271$	−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
$275$	46619.9	+	45276.4i	0.616462	+	0.598696i
$276$	20287.5	+	2117.24i	0.266324	+	0.0277940i
$277$	−79016.2	+	45620.0i	−1.02981	+	0.594560i	−0.916930	−	0.399048i	$-0.869341\pi$
$277$	−79016.2	+	45620.0i	−1.02981	+	0.594560i	−0.112879	+	0.993609i	$0.536007\pi$
$278$	−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	$-0.925904\pi$
$283$	−132893.	−	76726.0i	−1.65932	−	0.958009i	−0.686291	−	0.727327i	$-0.740763\pi$
$284$	−20712.9	−	11958.6i	−0.256806	−	0.148267i
$285$	−27746.3	−	90976.2i	−0.341599	−	1.12005i
$286$	−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
$290$	−52544.7	+	22216.1i	−0.624789	+	0.264163i
$291$	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	−0.774303	−	0.632815i	$-0.781899\pi$
$293$	13811.6	−	23922.4i	0.160883	−	0.278657i	0.935186	+	0.354158i	$0.115233\pi$
$294$	55544.9	−	76569.2i	0.642614	−	0.885849i
$295$	−77022.5	+	32565.4i	−0.885062	+	0.374208i
$296$		−	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
$300$	22165.4	−	18519.8i	0.246282	−	0.205776i
$301$	−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	$0.0546530\pi$
$307$			32205.8i			0.341710i	−0.985296	+	0.170855i	$0.945347\pi$
$308$	−19959.4	−	34570.7i	−0.210400	−	0.364424i
$309$	33951.9	−	15146.3i	0.355589	−	0.158631i
$310$	37914.2	−	50165.7i	0.394528	−	0.522016i
$311$	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	−0.381865	−	0.924218i	$-0.624718\pi$
$313$	22297.7	−	12873.6i	0.227599	−	0.131405i	0.609464	+	0.792814i	$0.291385\pi$
$314$			139698.i			1.41687i
$315$	148614.	−	28895.6i	1.49775	−	0.291213i
$316$	−13994.4			−0.140146
$317$	−27356.9	−	47383.6i	−0.272238	−	0.471530i	0.697196	−	0.716880i	$-0.254431\pi$
$317$	−27356.9	−	47383.6i	−0.272238	−	0.471530i	−0.969435	+	0.245350i	$0.921097\pi$
$318$	−48782.9	−	5091.07i	−0.482406	−	0.0503448i
$319$	−35992.0	+	62339.9i	−0.353691	+	0.612611i
$320$	66797.1	−	88382.0i	0.652316	−	0.863105i
$321$	−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
$330$	−17398.7	+	75128.2i	−0.159768	+	0.689883i
$331$	−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
$335$	−163530.	+	69141.0i	−1.45716	+	0.616092i
$336$	90622.5	−	40427.5i	0.802708	−	0.358095i
$337$	93020.1	+	53705.2i	0.819063	+	0.472886i	0.850093	−	0.526632i	$-0.176546\pi$
$337$	93020.1	+	53705.2i	0.819063	+	0.472886i	−0.0310304	+	0.999518i	$0.509879\pi$
$338$	26826.2	−	46464.4i	0.234815	−	0.406712i
$339$	−39876.6	−	89387.6i	−0.346991	−	0.777818i
$340$	−16083.7	−	38040.5i	−0.139132	−	0.329070i
$341$		−	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
$345$	96747.6	+	22405.5i	0.812834	+	0.188242i
$346$	−17305.4	+	29973.8i	−0.144554	+	0.250374i
$347$	−25914.5	+	44885.2i	−0.215220	+	0.372773i	−0.953341	−	0.301896i	$-0.902380\pi$
$347$	−25914.5	+	44885.2i	−0.215220	+	0.372773i	0.738120	+	0.674669i	$0.235714\pi$
$348$	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	$0.181330\pi$
$353$	110669.	+	191685.i	0.888132	+	1.53829i	0.0460508	+	0.998939i	$0.485336\pi$
$354$	−80322.8	−	58267.8i	−0.640962	−	0.464967i
$355$	−92896.6	−	70209.2i	−0.737128	−	0.557105i
$356$	−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	$0.989952\pi$
$360$	133389.	+	45921.8i	1.02924	+	0.354335i
$361$	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
$365$	117884.	+	89093.8i	0.884846	+	0.668747i
$366$	49430.7	+	110804.i	0.369007	+	0.827168i
$367$	219142.	−	126522.i	1.62702	−	0.939362i	0.642047	−	0.766665i	$-0.278085\pi$
$367$	219142.	−	126522.i	1.62702	−	0.939362i	0.984975	−	0.172696i	$-0.0552479\pi$
$368$	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	0.634081	−	0.773267i	$-0.281379\pi$
$373$	39158.2	+	22608.0i	0.281452	+	0.162497i	−0.352628	+	0.935763i	$0.614712\pi$
$374$	95494.8	+	55133.9i	0.682710	+	0.394163i
$375$	118207.	−	76174.7i	0.840580	−	0.541687i
$376$	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	$0.678219\pi$
$380$	21132.9	+	49982.9i	0.146350	+	0.346142i
$381$	−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	−0.554288	−	0.832325i	$-0.687009\pi$
$383$	65081.6	−	112725.i	0.443671	−	0.768460i	0.997959	+	0.0638650i	$0.0203427\pi$
$384$	40730.0	+	4250.66i	0.276218	+	0.0288266i
$385$	−75684.5	−	179006.i	−0.510606	−	1.20767i
$386$			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	$0.273038\pi$
$390$	−150213.	+	45812.7i	−0.987596	+	0.301201i
$391$	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	$0.186285\pi$
$397$			174124.i			1.10478i	−0.833585	+	0.552392i	$0.813715\pi$
$398$	−81154.0	−	140563.i	−0.512323	−	0.887369i
$399$	−29524.5	+	282905.i	−0.185454	+	1.77703i
$400$	64214.8	−	66120.4i	0.401343	−	0.413253i
$401$	−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
$405$	−2613.25	+	164004.i	−0.0159320	+	0.999873i
$406$	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	$0.916314\pi$
$410$	−10076.2	−	7615.36i	−0.0599417	−	0.0453026i
$411$	−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	$0.910598\pi$
$420$	−82622.3	+	25198.5i	−0.468380	+	0.142849i
$421$	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
$425$	−54876.5	−	193444.i	−0.303815	−	1.07097i
$426$	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
$430$	−160499.	+	67859.6i	−0.868032	+	0.367007i
$431$			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	$-0.863452\pi$
$433$		−	155969.i		−	0.831884i	0.909391	−	0.415942i	$-0.136548\pi$
$434$	−162857.	+	94025.4i	−0.864622	+	0.499190i
$435$	113847.	+	106309.i	0.601646	+	0.561812i
$436$	−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	0.815211	−	0.579164i	$-0.196621\pi$
$443$	−18440.7	−	31940.2i	−0.0939657	−	0.162753i	−0.909176	+	0.416411i	$0.863288\pi$
$444$	−6690.20	+	2984.56i	−0.0339370	+	0.0151396i
$445$	−185122.	−	139911.i	−0.934840	−	0.706531i
$446$	−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	$-0.155778\pi$
$450$	149883.	+	73356.1i	0.740162	+	0.362252i
$451$	−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
$455$	238635.	−	315747.i	1.15269	−	1.52516i
$456$	−155632.	+	214540.i	−0.748459	+	1.03176i
$457$	324761.	−	187501.i	1.55500	−	0.897781i	0.557281	−	0.830324i	$-0.311845\pi$
$457$	324761.	−	187501.i	1.55500	−	0.897781i	0.997722	−	0.0674575i	$-0.0214887\pi$
$458$	−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	0.153643	−	0.988126i	$-0.450899\pi$
$463$	−134040.	−	77388.2i	−0.625278	−	0.361005i	−0.778921	+	0.627122i	$0.784233\pi$
$464$	88415.9	+	51046.9i	0.410671	+	0.237101i
$465$	−167265.	−	38736.4i	−0.773569	−	0.179149i
$466$	−15739.3	−	27261.3i	−0.0724792	−	0.125538i
$467$	55941.6			0.256508			0.128254	−	0.991741i	$-0.459063\pi$
$467$	55941.6			0.256508			0.128254	+	0.991741i	$0.459063\pi$
$468$	65537.6	+	58836.3i	0.299226	+	0.268629i
$469$	530960.			2.41388
$470$	67843.1	+	160460.i	0.307121	+	0.726393i
$471$	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
$475$	72104.4	+	254174.i	0.319576	+	1.12653i
$476$			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	$0.336999\pi$
$480$	−137776.	−	31907.1i	−0.597984	−	0.138486i
$481$	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	$0.0654514\pi$
$487$			96848.3i			0.408352i	−0.978934	+	0.204176i	$0.934549\pi$
$488$	−142461.	−	246750.i	−0.598214	−	1.03614i
$489$	−84173.8	−	61061.5i	−0.352014	−	0.255358i
$490$	−158431.	+	209627.i	−0.659856	+	0.873081i
$491$	−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
$495$	206689.	−	40187.3i	0.843541	−	0.164013i
$496$	−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	$0.0668409\pi$
$500$	−62567.2	+	50227.1i	−0.250269	+	0.200908i
$501$	157351.	+	352719.i	0.626895	+	1.40525i
$502$	311467.	−	179826.i	1.23596	−	0.713582i
$503$	450974.			1.78244			0.891222	−	0.453567i	$-0.149849\pi$
$503$	450974.			1.78244			0.891222	+	0.453567i	$0.149849\pi$
$504$	−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	$0.665735\pi$
$510$	162848.	−	174395.i	0.626099	−	0.670491i
$511$	−220949.	−	382694.i	−0.846154	−	1.46558i
$512$	−257074.			−0.980658
$513$	−293293.	−	94582.9i	−1.11447	−	0.359400i
$514$	−125672.			−0.475679
$515$	−95117.6	+	40216.1i	−0.358630	+	0.151630i
$516$	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
$520$	339678.	−	143617.i	1.25620	−	0.531128i
$521$			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	$-0.947116\pi$
$523$		−	90470.5i		−	0.330753i	0.986231	−	0.165376i	$-0.0528839\pi$
$524$	69142.6	−	39919.5i	0.251816	−	0.145386i
$525$	−414311.	+	72157.6i	−1.50317	+	0.261796i
$526$	−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
$535$	34743.8	−	45970.9i	0.121386	−	0.160611i
$536$	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
$540$	−8229.71	−	93221.8i	−0.0282226	−	0.319691i
$541$	−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
$545$	−87820.0	+	116198.i	−0.295665	+	0.391207i
$546$	467113.	+	48748.7i	1.56688	+	0.163523i
$547$	−476095.	+	274874.i	−1.59118	+	0.918667i	−0.598073	+	0.801441i	$0.704067\pi$
$547$	−476095.	+	274874.i	−1.59118	+	0.918667i	−0.993105	+	0.117226i	$0.962600\pi$
$548$	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
$555$	−34114.7	+	10404.5i	−0.110753	+	0.0337780i
$556$	−3342.12	−	5788.72i	−0.0108112	−	0.0187255i
$557$	−173508.			−0.559254			−0.279627	−	0.960109i	$-0.590211\pi$
$557$	−173508.			−0.559254			−0.279627	+	0.960109i	$0.590211\pi$
$558$	−63242.4	−	193672.i	−0.203114	−	0.622011i
$559$	−447768.			−1.43294
$560$	−253882.	+	107342.i	−0.809573	+	0.342291i
$561$	31251.1	−	299449.i	0.0992977	−	0.951475i
$562$	−348752.	−	201352.i	−1.10419	−	0.637505i
$563$	−115344.	+	199782.i	−0.363898	+	0.630289i	−0.988599	−	0.150575i	$-0.951888\pi$
$563$	−115344.	+	199782.i	−0.363898	+	0.630289i	0.624701	+	0.780864i	$0.285221\pi$
$564$	57369.6	−	79084.6i	0.180353	−	0.248619i
$565$	105880.	+	250423.i	0.331677	+	0.784470i
$566$			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	$0.122777\pi$
$570$	−213973.	+	229144.i	−0.658580	+	0.705275i
$571$	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	$0.0740423\pi$
$577$			153493.i			0.461038i	−0.973068	+	0.230519i	$0.925958\pi$
$578$	−32938.2	−	57050.6i	−0.0985925	−	0.170767i
$579$	111692.	−	49827.0i	0.333170	−	0.148630i
$580$	−70900.0	−	53584.7i	−0.210761	−	0.159289i
$581$	−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
$585$	281331.	+	323600.i	0.822063	+	0.945576i
$586$	−91052.2			−0.265152
$587$	−310244.	−	537358.i	−0.900382	−	1.55951i	−0.827000	−	0.562203i	$-0.809954\pi$
$587$	−310244.	−	537358.i	−0.900382	−	1.55951i	−0.0733820	−	0.997304i	$-0.523379\pi$
$588$	146566.	+	15295.9i	0.423914	+	0.0442405i
$589$	161286.	−	279355.i	0.464906	−	0.805241i
$590$	219903.	+	166198.i	0.631724	+	0.477443i
$591$	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	$-0.796892\pi$
$593$	−564917.			−1.60648			−0.803240	+	0.595655i	$0.796892\pi$
$594$	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	$0.663244\pi$
$600$	−367953.	−	134799.i	−1.02209	−	0.374443i
$601$	−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
$605$	37279.6	+	88172.5i	0.101850	+	0.240892i
$606$	−104385.	+	46566.9i	−0.284244	+	0.126804i
$607$	−85786.9	−	49529.1i	−0.232833	−	0.134426i	0.379046	−	0.925378i	$-0.376252\pi$
$607$	−85786.9	−	49529.1i	−0.232833	−	0.134426i	−0.611878	+	0.790952i	$0.709586\pi$
$608$	132850.	−	230104.i	0.359382	−	0.622467i
$609$	−189780.	−	425411.i	−0.511700	−	1.14703i
$610$	−131247.	−	310422.i	−0.352721	−	0.834242i
$611$			447659.i			1.19913i
$612$	−130931.	−	27629.4i	−0.349576	−	0.0737681i
$613$		−	599020.i		−	1.59412i	−0.603902	−	0.797059i	$-0.706388\pi$
$613$		−	599020.i		−	1.59412i	0.603902	−	0.797059i	$-0.293612\pi$
$614$	91935.0	−	53078.7i	0.243862	−	0.140794i
$615$	−7780.52	+	33596.5i	−0.0205711	+	0.0888268i
$616$	−270788.	+	469018.i	−0.713620	+	1.23603i
$617$	318998.	−	552521.i	0.837950	−	1.45137i	−0.0536564	−	0.998559i	$-0.517088\pi$
$617$	318998.	−	552521.i	0.837950	−	1.45137i	0.891606	−	0.452812i	$-0.149579\pi$
$618$	−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
$625$	−332437.	+	205119.i	−0.851038	+	0.525104i
$626$	−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
$630$	−327418.	−	376611.i	−0.824937	−	0.948883i
$631$	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
$635$	281591.	+	212821.i	0.698348	+	0.527796i
$636$	−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	0.879484	−	0.475928i	$-0.157888\pi$
$643$	375023.	+	216520.i	0.907060	+	0.523691i	0.0275761	+	0.999620i	$0.491221\pi$
$644$	146744.	+	84722.8i	0.353826	+	0.204281i
$645$	347747.	+	324723.i	0.835880	+	0.780538i
$646$	224145.	+	388230.i	0.537110	+	0.930302i
$647$	295249.			0.705311			0.352655	−	0.935753i	$-0.385279\pi$
$647$	295249.			0.705311			0.352655	+	0.935753i	$0.385279\pi$
$648$	368990.	−	269747.i	0.878749	−	0.642401i
$649$	347809.			0.825755
$650$	419674.	−	119053.i	0.993310	−	0.281783i
$651$	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	−0.748211	−	0.663461i	$-0.769087\pi$
$653$	85481.8	−	148059.i	0.200469	−	0.347222i	0.948680	+	0.316239i	$0.102420\pi$
$654$	−171902.	−	17940.0i	−0.401907	−	0.0419438i
$655$	358019.	−	151372.i	0.834495	−	0.352827i
$656$			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	$0.988301\pi$
$660$	−114909.	+	35045.5i	−0.263795	+	0.0804534i
$661$	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
$670$	466885.	+	352862.i	1.04007	+	0.786058i
$671$	−368289.	−	212632.i	−0.817983	−	0.472262i
$672$	342341.	+	248341.i	0.758088	+	0.549933i
$673$	−649893.	+	375216.i	−1.43487	+	0.828421i	−0.997487	−	0.0708548i	$-0.977427\pi$
$673$	−649893.	+	375216.i	−1.43487	+	0.828421i	−0.437381	+	0.899276i	$0.644094\pi$
$674$		−	354048.i		−	0.779368i
$675$	16188.3	−	455337.i	0.0355298	−	0.999369i
$676$	83581.4			0.182901
$677$	−393173.	−	680996.i	−0.857841	−	1.48582i	−0.873984	−	0.485955i	$-0.838472\pi$
$677$	−393173.	−	680996.i	−0.857841	−	1.48582i	0.0161427	−	0.999870i	$-0.494861\pi$
$678$	−189446.	+	261153.i	−0.412121	+	0.568113i
$679$	132317.	−	229180.i	0.286997	−	0.497093i
$680$	−337846.	+	447018.i	−0.730637	+	0.966734i
$681$	−324073.	−	33820.8i	−0.698793	−	0.0729273i
$682$	−226497.	+	130768.i	−0.486961	+	0.281147i
$683$	80351.5			0.172247			0.0861237	−	0.996284i	$-0.472552\pi$
$683$	80351.5			0.172247			0.0861237	+	0.996284i	$0.472552\pi$
$684$	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
$690$	−95491.7	−	313103.i	−0.200571	−	0.657642i
$691$	−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
$695$	−12673.1	−	29973.9i	−0.0262369	−	0.0620545i
$696$	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
$700$	230834.	−	65483.4i	0.471091	−	0.133640i
$701$		−	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
$705$	324644.	−	347662.i	0.653175	−	0.699487i
$706$	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
$715$	331887.	−	439133.i	0.649200	−	0.858983i
$716$	−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	$0.955376\pi$
$720$	−56997.1	−	293144.i	−0.109948	−	0.565478i
$721$	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
$725$	−310391.	−	301445.i	−0.590517	−	0.573499i
$726$	−66702.8	+	91950.5i	−0.126553	+	0.174454i
$727$	4108.19	−	2371.86i	0.00777288	−	0.00448767i	−0.496109	−	0.868261i	$-0.665238\pi$
$727$	4108.19	−	2371.86i	0.00777288	−	0.00448767i	0.503881	+	0.863773i	$0.331905\pi$
$728$	−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	0.596201	−	0.802835i	$-0.296676\pi$
$733$	106934.	+	61738.6i	0.199026	+	0.114908i	−0.397175	+	0.917743i	$0.630009\pi$
$734$	−722340.	−	417043.i	−1.34076	−	0.774085i
$735$	698947.	+	161867.i	1.29381	+	0.299629i
$736$	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	$0.614374\pi$
$740$	18742.8	−	7924.54i	0.0342272	−	0.0144714i
$741$	−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	$0.490023\pi$
$743$	−469203.	+	812684.i	−0.849930	+	1.47212i	−0.881270	+	0.472614i	$0.843311\pi$
$744$	194920.	+	436933.i	0.352135	+	0.789349i
$745$	−87206.0	+	36871.0i	−0.157121	+	0.0664313i
$746$		−	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
$750$	−412266.	−	211889.i	−0.732918	−	0.376692i
$751$	−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	$-0.806327\pi$
$757$		−	655098.i		−	1.14318i	0.820539	−	0.571590i	$-0.193673\pi$
$758$	251458.	+	435538.i	0.437650	+	0.758031i
$759$	−334336.	−	242535.i	−0.580363	−	0.421008i
$760$	443909.	−	587354.i	0.768541	−	1.01689i
$761$	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
$765$	−616008.	−	212073.i	−1.05260	−	0.362378i
$766$	−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	$0.945174\pi$
$770$	−386257.	+	511072.i	−0.651470	+	0.861986i
$771$	139796.	+	313368.i	0.235173	+	0.527164i
$772$	−60430.9	+	34889.8i	−0.101397	+	0.0585415i
$773$	−160727.			−0.268987			−0.134493	−	0.990914i	$-0.542941\pi$
$773$	−160727.			−0.268987			−0.134493	+	0.990914i	$0.542941\pi$
$774$	−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
$780$	−178810.	−	166971.i	−0.293902	−	0.274444i
$781$	242156.	+	419426.i	0.397002	+	0.687627i
$782$	−468061.			−0.765400
$783$	493417.	−	106016.i	0.804804	−	0.172920i
$784$	470240.			0.765046
$785$	−975890.	+	412610.i	−1.58366	+	0.669576i
$786$	373359.	+	270843.i	0.604341	+	0.438402i
$787$	−37127.1	−	21435.3i	−0.0599434	−	0.0346083i	0.469729	−	0.882811i	$-0.344352\pi$
$787$	−37127.1	−	21435.3i	−0.0599434	−	0.0346083i	−0.529672	+	0.848202i	$0.677685\pi$
$788$	−45064.8	+	78054.6i	−0.0725747	+	0.125703i
$789$	81135.2	+	8467.42i	0.130333	+	0.0136018i
$790$	87457.9	+	206852.i	0.140134	+	0.331441i
$791$		−	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
$795$	−108520.	−	355820.i	−0.171701	−	0.562984i
$796$	126424.	−	218973.i	0.199528	−	0.345592i
$797$	−12555.0	+	21745.9i	−0.0197652	+	0.0342343i	−0.875739	−	0.482785i	$-0.839625\pi$
$797$	−12555.0	+	21745.9i	−0.0197652	+	0.0342343i	0.855974	+	0.517019i	$0.172959\pi$
$798$	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
$805$	658141.	+	497408.i	1.01561	+	0.767576i
$806$	−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	$0.876824\pi$
$810$	472475.	−	262837.i	0.720126	−	0.400605i
$811$	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
$815$	230446.	+	174166.i	0.346940	+	0.262210i
$816$	−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	0.775242	−	0.631664i	$-0.217628\pi$
$823$	417117.	+	240822.i	0.615826	+	0.355547i	−0.159416	+	0.987211i	$0.550961\pi$
$824$	249219.	+	143887.i	0.367052	+	0.211917i
$825$	−576213.	+	100355.i	−0.846594	+	0.147445i
$826$	−412163.	−	713888.i	−0.604101	−	1.04633i
$827$	178175.			0.260517			0.130259	−	0.991480i	$-0.458419\pi$
$827$	178175.			0.260517			0.130259	+	0.991480i	$0.458419\pi$
$828$	−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	$0.610444\pi$
$830$	−130765.	−	309281.i	−0.189817	−	0.448949i
$831$	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
$835$	−417796.	−	988156.i	−0.599227	−	1.41727i
$836$		−	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	$0.280399\pi$
$840$	856530.	+	799821.i	1.21390	+	1.13353i
$841$	−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
$850$	−461766.	+	475469.i	−0.639122	+	0.658088i
$851$	60590.7	+	34982.0i	0.0836655	+	0.0483043i
$852$	196581.	−	87696.5i	0.270809	−	0.120810i
$853$	471332.	−	272124.i	0.647782	−	0.373997i	−0.139824	−	0.990176i	$-0.544654\pi$
$853$	471332.	−	272124.i	0.647782	−	0.373997i	0.787606	+	0.616179i	$0.211320\pi$
$854$			1.00790e6i			1.38198i
$855$	809397.	+	278651.i	1.10721	+	0.381178i
$856$	−160574.			−0.219143
$857$	−542845.	−	940236.i	−0.739119	−	1.28019i	−0.952892	−	0.303309i	$-0.901909\pi$
$857$	−542845.	−	940236.i	−0.739119	−	1.28019i	0.213773	−	0.976883i	$-0.431425\pi$
$858$	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	$0.256855\pi$
$860$	−216566.	−	163676.i	−0.292815	−	0.221303i
$861$	60557.8	−	83479.6i	0.0816891	−	0.112609i
$862$	544144.	−	314162.i	0.732317	−	0.422804i
$863$	472099.			0.633887			0.316943	−	0.948444i	$-0.397344\pi$
$863$	472099.			0.633887			0.316943	+	0.948444i	$0.397344\pi$
$864$	−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
$870$	115839.	−	500196.i	0.153044	−	0.660848i
$871$	751905.	+	1.30234e6i	0.991121	+	1.71667i
$872$	405875.			0.533776
$873$	213347.	+	191532.i	0.279935	+	0.251311i
$874$	615003.			0.805108
$875$	1.15457e6	−	177839.i	1.50801	−	0.232279i
$876$	−249457.	+	111285.i	−0.325078	+	0.145020i
$877$	93901.6	+	54214.1i	0.122088	+	0.0704877i	0.559800	−	0.828627i	$-0.310878\pi$
$877$	93901.6	+	54214.1i	0.122088	+	0.0704877i	−0.437712	+	0.899115i	$0.644211\pi$
$878$	−382917.	+	663231.i	−0.496724	+	0.860351i
$879$	101285.	+	227041.i	0.131090	+	0.293851i
$880$	−353093.	+	149289.i	−0.455957	+	0.192780i
$881$			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	$0.153910\pi$
$883$			724958.i			0.929804i	−0.885362	+	0.464902i	$0.846090\pi$
$884$	−302951.	+	174909.i	−0.387676	+	0.223825i
$885$	169802.	−	733211.i	0.216799	−	0.936143i
$886$	−60784.5	+	105282.i	−0.0774329	+	0.134118i
$887$	236222.	−	409149.i	0.300244	−	0.520037i	−0.675947	−	0.736950i	$-0.736265\pi$
$887$	236222.	−	409149.i	0.300244	−	0.520037i	0.976191	+	0.216913i	$0.0695987\pi$
$888$	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
$895$	−342610.	−	258937.i	−0.427715	−	0.323257i
$896$	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
$900$	17779.6	+	259348.i	0.0219502	+	0.320182i
$901$	−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
$905$	−206740.	+	273546.i	−0.252422	+	0.333989i
$906$	−395055.	−	885557.i	−0.481284	−	1.07885i
$907$	−48764.6	+	28154.2i	−0.0592775	+	0.0342239i	−0.529346	−	0.848406i	$-0.677563\pi$
$907$	−48764.6	+	28154.2i	−0.0592775	+	0.0342239i	0.470068	+	0.882630i	$0.344229\pi$
$908$	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
$915$	−628048.	+	672578.i	−0.750154	+	0.803342i
$916$	−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	$0.779762\pi$
$920$	299354.	+	708021.i	0.353679	+	0.836509i
$921$	−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
$925$	95311.5	−	27038.1i	0.111394	−	0.0316004i
$926$			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	$-0.0375539\pi$
$930$	165094.	+	541318.i	0.190882	+	0.625873i
$931$	−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	$0.0123967\pi$
$937$			68368.4i			0.0778711i	−0.999242	+	0.0389355i	$0.987603\pi$
$938$	−875081.	−	1.51568e6i	−0.994586	−	1.72267i
$939$	−24052.5	+	230473.i	−0.0272791	+	0.261389i
$940$	−163636.	+	216513.i	−0.185192	+	0.245035i
$941$	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
$945$	−574877.	+	1.23536e6i	−0.643741	+	1.38335i
$946$	724762.			0.809866
$947$	357191.	+	618674.i	0.398292	+	0.689861i	0.993515	−	0.113699i	$-0.0362699\pi$
$947$	357191.	+	618674.i	0.398292	+	0.689861i	−0.595224	+	0.803560i	$0.702937\pi$
$948$	73956.3	−	101949.i	0.0822922	−	0.113441i
$949$	625780.	−	1.08388e6i	0.694848	−	1.20351i
$950$	606732.	−	624736.i	0.672279	−	0.692229i
$951$	489765.	+	51112.8i	0.541535	+	0.0565156i
$952$	1.45119e6	−	837844.i	1.60122	−	0.924462i
$953$	−143104.			−0.157567			−0.0787836	−	0.996892i	$-0.525104\pi$
$953$	−143104.			−0.157567			−0.0787836	+	0.996892i	$0.525104\pi$
$954$	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
$960$	290862.	+	953693.i	0.315605	+	1.03482i
$961$	170619.	+	295521.i	0.184748	+	0.319994i
$962$	−110640.			−0.119553
$963$	−57954.1	−	177477.i	−0.0624930	−	0.191377i
$964$	515895.			0.555146
$965$	−312910.	+	132300.i	−0.336020	+	0.142070i
$966$	−101611.	+	973645.i	−0.108890	+	1.04339i
$967$	363441.	+	209833.i	0.388670	+	0.224399i	0.681584	−	0.731740i	$-0.261292\pi$
$967$	363441.	+	209833.i	0.388670	+	0.224399i	−0.292914	+	0.956139i	$0.594625\pi$
$968$	133381.	−	231022.i	0.142345	−	0.246549i
$969$	718727.	−	990773.i	0.765450	−	1.05518i
$970$	268656.	−	113589.i	0.285531	−	0.120724i
$971$		−	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
$975$	−763702.	−	914035.i	−0.803369	−	0.961510i
$976$	−301573.	+	522340.i	−0.316587	+	0.548344i
$977$	−685507.	+	1.18733e6i	−0.718163	+	1.24389i	0.243564	+	0.969885i	$0.421683\pi$
$977$	−685507.	+	1.18733e6i	−0.718163	+	1.24389i	−0.961727	+	0.274009i	$0.911650\pi$
$978$	−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	0.877239	−	0.480054i	$-0.159383\pi$
$983$	22108.8	+	38293.6i	0.0228801	+	0.0396295i	−0.854359	+	0.519684i	$0.826050\pi$
$984$	87761.5	−	39151.2i	0.0906387	−	0.0404347i
$985$	−264576.	+	350071.i	−0.272695	+	0.360814i
$986$	−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
$990$	−455364.	−	523782.i	−0.464610	−	0.534417i
$991$	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
$995$	742236.	−	982083.i	0.749715	−	0.991978i
$996$	−110578.	+	152433.i	−0.111468	+	0.153660i
$997$	−306196.	+	176782.i	−0.308041	+	0.177848i	−0.646050	−	0.763295i	$-0.723580\pi$
$997$	−306196.	+	176782.i	−0.308041	+	0.177848i	0.338008	+	0.941143i	$0.390247\pi$
$998$	−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.14.7	✓	44
3.2	odd	2		135.5.h.a.44.16		44
5.4	even	2	inner	45.5.h.a.14.16	yes	44
9.2	odd	6	inner	45.5.h.a.29.16	yes	44
9.4	even	3		405.5.d.a.404.31		44
9.5	odd	6		405.5.d.a.404.13		44
9.7	even	3		135.5.h.a.89.7		44
15.14	odd	2		135.5.h.a.44.7		44
45.4	even	6		405.5.d.a.404.14		44
45.14	odd	6		405.5.d.a.404.32		44
45.29	odd	6	inner	45.5.h.a.29.7	yes	44
45.34	even	6		135.5.h.a.89.16		44

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.64811 - 2.85461i) q^{2} +(-5.28472 + 7.28504i) q^{3} +(2.56747 - 4.44699i) q^{4} +(15.0736 - 19.9446i) 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} +(65.6368 + 215.213i) q^{15} +(73.7366 + 127.716i) q^{16} +321.724 q^{17} +(-178.362 + 198.677i) q^{18} -422.726 q^{19} +(-49.9921 - 118.239i) 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} +(-170.570 - 601.274i) q^{25} +697.974i q^{26} +(693.815 + 223.745i) q^{27} +383.909i q^{28} +(599.538 - 346.144i) q^{29} +(506.174 - 542.063i) 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} +(-1050.11 + 1389.44i) q^{40} +(132.735 + 76.6349i) q^{41} +(-2025.53 + 903.607i) q^{42} +(1831.30 - 1057.30i) q^{43} +533.931i q^{44} +(-1914.71 - 659.176i) q^{45} -1454.85 q^{46} +(-1057.05 - 1830.86i) q^{47} +(-1320.09 - 137.767i) q^{48} +(1594.32 - 2761.45i) q^{49} +(-1435.28 + 1477.88i) 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} +(1125.57 + 260.668i) q^{60} +(2044.93 + 3541.93i) q^{61} +2515.26 q^{62} +(4506.34 + 4045.56i) q^{63} +4431.38 q^{64} +(-4875.84 + 2061.52i) 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} +(5674.60 - 2399.24i) q^{70} -4657.74i q^{71} +(1751.63 + 5364.15i) q^{72} +5910.56i q^{73} +(452.501 - 261.251i) q^{74} +(5281.72 + 1934.96i) 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} +(4849.56 - 6416.64i) q^{85} +(-6036.38 - 3485.11i) q^{86} +(-646.723 + 6196.93i) q^{87} +(6273.31 - 3621.90i) q^{88} -9281.82i q^{89} +(1273.96 + 6552.14i) q^{90} +15831.3 q^{91} +(-1133.20 - 1962.77i) q^{92} +(-2797.94 - 6271.88i) q^{93} +(-3484.26 + 6034.91i) q^{94} +(-6372.02 + 8431.07i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more