LMFDB - Embedded newform 45.5.h.a.14.6

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			14.6
Character	$\chi$	$=$	45.14
Dual form			45.5.h.a.29.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.30921 - 3.99967i) q^{2} +(4.25182 + 7.93234i) q^{3} +(-2.66491 + 4.61577i) q^{4} +(-21.0948 + 13.4168i) q^{5} +(21.9084 - 35.3233i) q^{6} +(-45.6166 + 26.3368i) q^{7} -49.2794 q^{8} +(-44.8440 + 67.4538i) q^{9} +(102.375 + 53.3902i) q^{10} +(-1.90271 + 1.09853i) q^{11} +(-47.9446 - 1.51357i) q^{12} +(226.996 + 131.056i) q^{13} +(210.677 + 121.634i) q^{14} +(-196.118 - 110.285i) q^{15} +(156.435 + 270.954i) q^{16} -487.118 q^{17} +(373.347 + 23.5961i) q^{18} +8.08421 q^{19} +(-5.71274 - 133.123i) q^{20} +(-402.866 - 249.867i) q^{21} +(8.78750 + 5.07347i) q^{22} +(178.836 - 309.753i) q^{23} +(-209.527 - 390.901i) q^{24} +(264.982 - 566.047i) q^{25} -1210.54i q^{26} +(-725.735 - 68.9159i) q^{27} -280.741i q^{28} +(25.7123 - 14.8450i) q^{29} +(11.7714 + 1039.08i) q^{30} +(-534.206 + 925.271i) q^{31} +(328.248 - 568.543i) q^{32} +(-16.8039 - 10.4222i) q^{33} +(1124.86 + 1948.31i) q^{34} +(608.920 - 1167.60i) q^{35} +(-191.846 - 386.748i) q^{36} -1722.01i q^{37} +(-18.6682 - 32.3342i) q^{38} +(-74.4349 + 2357.83i) q^{39} +(1039.54 - 661.169i) q^{40} +(2234.51 + 1290.10i) q^{41} +(-69.0838 + 2188.33i) q^{42} +(-597.707 + 345.086i) q^{43} -11.7099i q^{44} +(40.9641 - 2024.59i) q^{45} -1651.88 q^{46} +(817.918 + 1416.68i) q^{47} +(-1484.16 + 2392.94i) q^{48} +(186.752 - 323.464i) q^{49} +(-2875.90 + 247.284i) q^{50} +(-2071.14 - 3863.99i) q^{51} +(-1209.85 + 698.506i) q^{52} -3354.40 q^{53} +(1400.24 + 3061.84i) q^{54} +(25.3986 - 48.7014i) q^{55} +(2247.96 - 1297.86i) q^{56} +(34.3726 + 64.1267i) q^{57} +(-118.750 - 68.5606i) q^{58} +(1245.61 + 719.153i) q^{59} +(1031.69 - 611.332i) q^{60} +(-256.779 - 444.755i) q^{61} +4934.37 q^{62} +(269.116 - 4258.06i) q^{63} +1973.94 q^{64} +(-6546.78 + 280.943i) q^{65} +(-2.88154 + 91.2770i) q^{66} +(3800.99 + 2194.50i) q^{67} +(1298.13 - 2248.42i) q^{68} +(3217.44 + 101.572i) q^{69} +(-6076.13 + 260.746i) q^{70} +4437.85i q^{71} +(2209.88 - 3324.08i) q^{72} +4046.87i q^{73} +(-6887.47 + 3976.48i) q^{74} +(5616.74 - 304.810i) q^{75} +(-21.5437 + 37.3148i) q^{76} +(57.8634 - 100.222i) q^{77} +(9602.45 - 5147.02i) q^{78} +(-2005.14 - 3473.00i) q^{79} +(-6935.28 - 3616.86i) q^{80} +(-2539.03 - 6049.80i) q^{81} -11916.4i q^{82} +(3259.68 + 5645.94i) q^{83} +(2226.93 - 1193.66i) q^{84} +(10275.7 - 6535.55i) q^{85} +(2760.46 + 1593.75i) q^{86} +(227.080 + 140.840i) q^{87} +(93.7642 - 54.1348i) q^{88} +7631.84i q^{89} +(-8192.27 + 4511.35i) q^{90} -13806.4 q^{91} +(953.164 + 1650.93i) q^{92} +(-9610.91 - 303.409i) q^{93} +(3777.49 - 6542.81i) q^{94} +(-170.535 + 108.464i) q^{95} +(5905.53 + 186.433i) q^{96} +(-11001.1 + 6351.50i) q^{97} -1725.00 q^{98} +(11.2250 - 177.607i) 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 $

$2$	−2.30921	−	3.99967i	−0.577303	−	0.999918i	−0.995787	−	0.0916939i	$-0.970772\pi$
$2$	−2.30921	−	3.99967i	−0.577303	−	0.999918i	0.418484	−	0.908224i	$-0.362561\pi$
$3$	4.25182	+	7.93234i	0.472425	+	0.881371i
$3$	4.25182	+	7.93234i	0.472425	+	0.881371i
$4$	−2.66491	+	4.61577i	−0.166557	+	0.288485i
$5$	−21.0948	+	13.4168i	−0.843792	+	0.536670i
$5$	−21.0948	+	13.4168i	−0.843792	+	0.536670i
$6$	21.9084	−	35.3233i	0.608566	−	0.981204i
$7$	−45.6166	+	26.3368i	−0.930952	+	0.537485i	−0.887112	−	0.461553i	$-0.847292\pi$
$7$	−45.6166	+	26.3368i	−0.930952	+	0.537485i	−0.0438393	+	0.999039i	$0.513959\pi$
$8$	−49.2794			−0.769990
$9$	−44.8440	+	67.4538i	−0.553629	+	0.832763i
$10$	102.375	+	53.3902i	1.02375	+	0.533902i
$11$	−1.90271	+	1.09853i	−0.0157249	+	0.00907875i	−0.507842	−	0.861450i	$-0.669557\pi$
$11$	−1.90271	+	1.09853i	−0.0157249	+	0.00907875i	0.492117	+	0.870529i	$0.336223\pi$
$12$	−47.9446	−	1.51357i	−0.332948	−	0.0105109i
$13$	226.996	+	131.056i	1.34317	+	0.775479i	0.987271	−	0.159045i	$-0.0508416\pi$
$13$	226.996	+	131.056i	1.34317	+	0.775479i	0.355898	+	0.934525i	$0.384175\pi$
$14$	210.677	+	121.634i	1.07488	+	0.620584i
$15$	−196.118	−	110.285i	−0.871634	−	0.490158i
$16$	156.435	+	270.954i	0.611075	+	1.05841i
$17$	−487.118			−1.68553			−0.842765	−	0.538281i	$-0.819074\pi$
$17$	−487.118			−1.68553			−0.842765	+	0.538281i	$0.819074\pi$
$18$	373.347	+	23.5961i	1.15231	+	0.0728274i
$19$	8.08421			0.0223939			0.0111970	−	0.999937i	$-0.496436\pi$
$19$	8.08421			0.0223939			0.0111970	+	0.999937i	$0.496436\pi$
$20$	−5.71274	−	133.123i	−0.0142819	−	0.332808i
$21$	−402.866	−	249.867i	−0.913529	−	0.566592i
$22$	8.78750	+	5.07347i	0.0181560	+	0.0104824i
$23$	178.836	−	309.753i	0.338064	−	0.585544i	−0.646004	−	0.763334i	$-0.723561\pi$
$23$	178.836	−	309.753i	0.338064	−	0.585544i	0.984069	+	0.177789i	$0.0568946\pi$
$24$	−209.527	−	390.901i	−0.363762	−	0.678647i
$25$	264.982	−	566.047i	0.423971	−	0.905676i
$26$		−	1210.54i		−	1.79075i
$27$	−725.735	−	68.9159i	−0.995522	−	0.0945348i
$28$		−	280.741i		−	0.358088i
$29$	25.7123	−	14.8450i	0.0305735	−	0.0176516i	−0.484635	−	0.874716i	$-0.661048\pi$
$29$	25.7123	−	14.8450i	0.0305735	−	0.0176516i	0.515209	+	0.857065i	$0.327714\pi$
$30$	11.7714	+	1039.08i	0.0130793	+	1.15453i
$31$	−534.206	+	925.271i	−0.555885	+	0.962821i	0.441949	+	0.897040i	$0.354287\pi$
$31$	−534.206	+	925.271i	−0.555885	+	0.962821i	−0.997834	+	0.0657811i	$0.979046\pi$
$32$	328.248	−	568.543i	0.320555	−	0.555218i
$33$	−16.8039	−	10.4222i	−0.0154306	−	0.00957040i
$34$	1124.86	+	1948.31i	0.973062	+	1.68539i
$35$	608.920	−	1167.60i	0.497078	−	0.953140i
$36$	−191.846	−	386.748i	−0.148029	−	0.298417i
$37$		−	1722.01i		−	1.25786i	−0.777463	−	0.628929i	$-0.783494\pi$
$37$		−	1722.01i		−	1.25786i	0.777463	−	0.628929i	$-0.216506\pi$
$38$	−18.6682	−	32.3342i	−0.0129281	−	0.0223921i
$39$	−74.4349	+	2357.83i	−0.0489382	+	1.55019i
$40$	1039.54	−	661.169i	0.649712	−	0.413231i
$41$	2234.51	+	1290.10i	1.32928	+	0.767458i	0.985188	−	0.171479i	$-0.0548547\pi$
$41$	2234.51	+	1290.10i	1.32928	+	0.767458i	0.344088	+	0.938937i	$0.388188\pi$
$42$	−69.0838	+	2188.33i	−0.0391632	+	1.24055i
$43$	−597.707	+	345.086i	−0.323260	+	0.186634i	−0.652845	−	0.757492i	$-0.726425\pi$
$43$	−597.707	+	345.086i	−0.323260	+	0.186634i	0.329585	+	0.944126i	$0.393091\pi$
$44$		−	11.7099i		−	0.00604852i
$45$	40.9641	−	2024.59i	0.0202292	−	0.999795i
$46$	−1651.88			−0.780661
$47$	817.918	+	1416.68i	0.370266	+	0.641320i	0.989606	−	0.143803i	$-0.0459331\pi$
$47$	817.918	+	1416.68i	0.370266	+	0.641320i	−0.619340	+	0.785123i	$0.712600\pi$
$48$	−1484.16	+	2392.94i	−0.644167	+	1.03860i
$49$	186.752	−	323.464i	0.0777809	−	0.134720i
$50$	−2875.90	+	247.284i	−1.15036	+	0.0989135i
$51$	−2071.14	−	3863.99i	−0.796287	−	1.48558i
$52$	−1209.85	+	698.506i	−0.447429	+	0.258323i
$53$	−3354.40			−1.19416			−0.597081	−	0.802181i	$-0.703673\pi$
$53$	−3354.40			−1.19416			−0.597081	+	0.802181i	$0.703673\pi$
$54$	1400.24	+	3061.84i	0.480190	+	1.05001i
$55$	25.3986	−	48.7014i	0.00839622	−	0.0160996i
$56$	2247.96	−	1297.86i	0.716824	−	0.413858i
$57$	34.3726	+	64.1267i	0.0105795	+	0.0197374i
$58$	−118.750	−	68.5606i	−0.0353003	−	0.0203807i
$59$	1245.61	+	719.153i	0.357831	+	0.206594i	0.668129	−	0.744046i	$-0.267095\pi$
$59$	1245.61	+	719.153i	0.357831	+	0.206594i	−0.310298	+	0.950639i	$0.600429\pi$
$60$	1031.69	−	611.332i	0.286580	−	0.169814i
$61$	−256.779	−	444.755i	−0.0690081	−	0.119526i	0.829457	−	0.558571i	$-0.188650\pi$
$61$	−256.779	−	444.755i	−0.0690081	−	0.119526i	−0.898465	+	0.439045i	$0.855317\pi$
$62$	4934.37			1.28366
$63$	269.116	−	4258.06i	0.0678044	−	1.07283i
$64$	1973.94			0.481920
$65$	−6546.78	+	280.943i	−1.54953	+	0.0664954i
$66$	−2.88154	+	91.2770i	−0.000661511	+	0.0209543i
$67$	3800.99	+	2194.50i	0.846735	+	0.488863i	0.859548	−	0.511055i	$-0.170745\pi$
$67$	3800.99	+	2194.50i	0.846735	+	0.488863i	−0.0128128	+	0.999918i	$0.504079\pi$
$68$	1298.13	−	2248.42i	0.280737	−	0.486251i
$69$	3217.44	+	101.572i	0.675791	+	0.0213342i
$70$	−6076.13	+	260.746i	−1.24003	+	0.0532135i
$71$			4437.85i			0.880351i	0.897912	+	0.440176i	$0.145084\pi$
$71$			4437.85i			0.880351i	−0.897912	+	0.440176i	$0.854916\pi$
$72$	2209.88	−	3324.08i	0.426289	−	0.641219i
$73$			4046.87i			0.759406i	0.925108	+	0.379703i	$0.123974\pi$
$73$			4046.87i			0.759406i	−0.925108	+	0.379703i	$0.876026\pi$
$74$	−6887.47	+	3976.48i	−1.25775	+	0.726165i
$75$	5616.74	−	304.810i	0.998531	−	0.0541885i
$76$	−21.5437	+	37.3148i	−0.00372987	+	0.00646032i
$77$	57.8634	−	100.222i	0.00975939	−	0.0169038i
$78$	9602.45	−	5147.02i	1.57831	−	0.845993i
$79$	−2005.14	−	3473.00i	−0.321285	−	0.556482i	0.659469	−	0.751732i	$-0.270781\pi$
$79$	−2005.14	−	3473.00i	−0.321285	−	0.556482i	−0.980753	+	0.195250i	$0.937448\pi$
$80$	−6935.28	−	3616.86i	−1.08364	−	0.565135i
$81$	−2539.03	−	6049.80i	−0.386989	−	0.922084i
$82$		−	11916.4i		−	1.77222i
$83$	3259.68	+	5645.94i	0.473172	+	0.819559i	0.999528	−	0.0307056i	$-0.00977544\pi$
$83$	3259.68	+	5645.94i	0.473172	+	0.819559i	−0.526356	+	0.850264i	$0.676442\pi$
$84$	2226.93	−	1193.66i	0.315608	−	0.169170i
$85$	10275.7	−	6535.55i	1.42224	−	0.904574i
$86$	2760.46	+	1593.75i	0.373237	+	0.215489i
$87$	227.080	+	140.840i	0.0300013	+	0.0186075i
$88$	93.7642	−	54.1348i	0.0121080	−	0.00699054i
$89$			7631.84i			0.963495i	0.876310	+	0.481747i	$0.159998\pi$
$89$			7631.84i			0.963495i	−0.876310	+	0.481747i	$0.840002\pi$
$90$	−8192.27	+	4511.35i	−1.01139	+	0.556957i
$91$	−13806.4			−1.66724
$92$	953.164	+	1650.93i	0.112614	+	0.195053i
$93$	−9610.91	−	303.409i	−1.11122	−	0.0350802i
$94$	3777.49	−	6542.81i	0.427512	−	0.740472i
$95$	−170.535	+	108.464i	−0.0188958	+	0.0120182i
$96$	5905.53	+	186.433i	0.640791	+	0.0202293i
$97$	−11001.1	+	6351.50i	−1.16921	+	0.675045i	−0.953494	−	0.301411i	$-0.902542\pi$
$97$	−11001.1	+	6351.50i	−1.16921	+	0.675045i	−0.215718	+	0.976456i	$0.569209\pi$
$98$	−1725.00			−0.179612
$99$	11.2250	−	177.607i	0.00114529	−	0.0181213i
$100$	1906.59	+	2731.56i	0.190659	+	0.273156i
$101$	4041.66	−	2333.45i	0.396202	−	0.228748i	−0.288642	−	0.957437i	$-0.593204\pi$
$101$	4041.66	−	2333.45i	0.396202	−	0.228748i	0.684844	+	0.728690i	$0.259870\pi$
$102$	−10672.0	+	17206.7i	−1.02576	+	1.65385i
$103$	4561.55	+	2633.61i	0.429970	+	0.248243i	0.699334	−	0.714795i	$-0.253480\pi$
$103$	4561.55	+	2633.61i	0.429970	+	0.248243i	−0.269364	+	0.963038i	$0.586813\pi$
$104$	−11186.2	−	6458.36i	−1.03423	−	0.597111i
$105$	11850.8	−	134.253i	1.07490	−	0.0121772i
$106$	7746.02	+	13416.5i	0.689393	+	1.19406i
$107$	19673.1			1.71833			0.859164	−	0.511700i	$-0.170984\pi$
$107$	19673.1			1.71833			0.859164	+	0.511700i	$0.170984\pi$
$108$	2252.12	−	3166.17i	0.193083	−	0.271448i
$109$	−7535.14			−0.634218			−0.317109	−	0.948389i	$-0.602712\pi$
$109$	−7535.14			−0.634218			−0.317109	+	0.948389i	$0.602712\pi$
$110$	−253.440	+	10.8759i	−0.0209455	+	0.000898837i
$111$	13659.5	−	7321.68i	1.10864	−	0.594244i
$112$	−14272.1	−	8239.99i	−1.13776	−	0.656887i
$113$	−3244.24	+	5619.19i	−0.254072	+	0.440065i	−0.964643	−	0.263560i	$-0.915103\pi$
$113$	−3244.24	+	5619.19i	−0.254072	+	0.440065i	0.710571	+	0.703625i	$0.248437\pi$
$114$	177.112	−	285.561i	0.0136282	−	0.0219730i
$115$	383.368	+	8933.57i	0.0289881	+	0.675506i
$116$			158.243i			0.0117600i
$117$	−19019.6	+	9434.65i	−1.38941	+	0.689214i
$118$		−	6642.70i		−	0.477069i
$119$	22220.7	−	12829.1i	1.56915	−	0.905948i
$120$	9664.55	+	5434.80i	0.671149	+	0.377417i
$121$	−7318.09	+	12675.3i	−0.499835	+	0.865740i
$122$	−1185.92	+	2054.07i	−0.0796772	+	0.138005i
$123$	−732.727	+	23210.2i	−0.0484320	+	1.53415i
$124$	−2847.22	−	4931.54i	−0.185173	−	0.320729i
$125$	2004.78	+	15495.9i	0.128306	+	0.991735i
$126$	−17652.3	+	8756.39i	−1.11189	+	0.551549i
$127$		−	24919.2i		−	1.54500i	−0.635017	−	0.772498i	$-0.719007\pi$
$127$		−	24919.2i		−	1.54500i	0.635017	−	0.772498i	$-0.280993\pi$
$128$	−9810.23	−	16991.8i	−0.598769	−	1.03710i
$129$	−5278.69	−	3273.97i	−0.317210	−	0.196741i
$130$	16241.6	+	25536.2i	0.961040	+	1.51102i
$131$	−7372.56	−	4256.55i	−0.429611	−	0.248036i	0.269570	−	0.962981i	$-0.413119\pi$
$131$	−7372.56	−	4256.55i	−0.429611	−	0.248036i	−0.699181	+	0.714945i	$0.746452\pi$
$132$	92.8872	−	49.7886i	0.00533099	−	0.00285747i
$133$	−368.775	+	212.912i	−0.0208477	+	0.0120364i
$134$		−	20270.3i		−	1.12889i
$135$	16233.9	−	8283.24i	0.890747	−	0.454499i
$136$	24004.9			1.29784
$137$	930.725	+	1612.06i	0.0495884	+	0.0858897i	0.889754	−	0.456440i	$-0.150876\pi$
$137$	930.725	+	1612.06i	0.0495884	+	0.0858897i	−0.840166	+	0.542330i	$0.817542\pi$
$138$	−7023.50	−	13103.3i	−0.368804	−	0.688052i
$139$	2469.13	−	4276.67i	0.127795	−	0.221348i	−0.795027	−	0.606574i	$-0.792543\pi$
$139$	2469.13	−	4276.67i	0.127795	−	0.221348i	0.922822	+	0.385226i	$0.125877\pi$
$140$	3766.63	+	5922.18i	0.192175	+	0.302152i
$141$	−7759.91	+	12511.5i	−0.390318	+	0.629318i
$142$	17749.9	−	10247.9i	0.880279	−	0.508229i
$143$	−575.875			−0.0281615
$144$	−25292.0	−	1598.49i	−1.21972	−	0.0770877i
$145$	−343.225	+	658.129i	−0.0163246	+	0.0313022i
$146$	16186.2	−	9345.09i	0.759344	−	0.438407i
$147$	3359.86	+	106.068i	0.155484	+	0.00490852i
$148$	7948.39	+	4589.00i	0.362874	+	0.209505i
$149$	−13670.0	−	7892.39i	−0.615739	−	0.355497i	0.159469	−	0.987203i	$-0.449022\pi$
$149$	−13670.0	−	7892.39i	−0.615739	−	0.355497i	−0.775208	+	0.631706i	$0.782355\pi$
$150$	−14189.4	−	21761.2i	−0.630639	−	0.967165i
$151$	−7763.12	−	13446.1i	−0.340473	−	0.589716i	0.644048	−	0.764985i	$-0.277254\pi$
$151$	−7763.12	−	13446.1i	−0.340473	−	0.589716i	−0.984521	+	0.175269i	$0.943920\pi$
$152$	−398.385			−0.0172431
$153$	21844.3	−	32858.0i	0.933160	−	1.40365i
$154$	−534.475			−0.0225365
$155$	−1145.17	−	26685.7i	−0.0476658	−	1.11075i
$156$	−10684.8	−	6627.00i	−0.439055	−	0.272313i
$157$	−7659.23	−	4422.06i	−0.310732	−	0.179401i	0.336522	−	0.941676i	$-0.390749\pi$
$157$	−7659.23	−	4422.06i	−0.310732	−	0.179401i	−0.647254	+	0.762274i	$0.724083\pi$
$158$	−9260.58	+	16039.8i	−0.370957	+	0.642517i
$159$	−14262.3	−	26608.3i	−0.564152	−	1.05250i
$160$	703.662	+	16397.3i	0.0274868	+	0.640521i
$161$			18839.8i			0.726818i
$162$	−18334.0	+	24125.6i	−0.698599	+	0.919279i
$163$			45394.1i			1.70854i	0.519833	+	0.854268i	$0.325994\pi$
$163$			45394.1i			1.70854i	−0.519833	+	0.854268i	$0.674006\pi$
$164$	−11909.6	+	6875.99i	−0.442801	+	0.255651i
$165$	494.306	−	5.59982i	0.0181563	−	0.000205687i
$166$	15054.6	−	26075.3i	0.546328	−	0.946267i
$167$	19920.0	−	34502.5i	0.714261	−	1.23714i	−0.248983	−	0.968508i	$-0.580096\pi$
$167$	19920.0	−	34502.5i	0.714261	−	1.23714i	0.963244	−	0.268629i	$-0.0865704\pi$
$168$	19853.0	+	12313.3i	0.703408	+	0.436271i
$169$	20070.9	+	34763.8i	0.702737	+	1.21718i
$170$	−49868.7	−	26007.3i	−1.72556	−	0.899908i
$171$	−362.528	+	545.311i	−0.0123979	+	0.0186488i
$172$		−	3678.50i		−	0.124341i
$173$	−16397.7	−	28401.6i	−0.547886	−	0.948966i	−0.998419	−	0.0562065i	$-0.982099\pi$
$173$	−16397.7	−	28401.6i	−0.547886	−	0.948966i	0.450533	−	0.892760i	$-0.351234\pi$
$174$	38.9398	−	1233.48i	0.00128616	−	0.0407410i
$175$	2820.30	+	32799.9i	0.0920913	+	1.07102i
$176$	−595.300	−	343.697i	−0.0192181	−	0.0110956i
$177$	−408.452	+	12938.3i	−0.0130375	+	0.412982i
$178$	30524.9	−	17623.5i	0.963415	−	0.556228i
$179$		−	3241.64i		−	0.101172i	−0.998720	−	0.0505858i	$-0.983891\pi$
$179$		−	3241.64i		−	0.101172i	0.998720	−	0.0505858i	$-0.0161088\pi$
$180$	9235.85	+	5584.43i	0.285057	+	0.172359i
$181$	2975.07			0.0908113			0.0454057	−	0.998969i	$-0.485542\pi$
$181$	2975.07			0.0908113			0.0454057	+	0.998969i	$0.485542\pi$
$182$	31881.8	+	55221.0i	0.962500	+	1.66710i
$183$	2436.16	−	3927.88i	0.0727452	−	0.117289i
$184$	−8812.92	+	15264.4i	−0.260306	+	0.450863i
$185$	23103.8	+	36325.4i	0.675055	+	1.06137i
$186$	20980.1	+	39141.1i	0.606431	+	1.13138i
$187$	926.844	−	535.113i	0.0265047	−	0.0153025i
$188$	−8718.73			−0.246682
$189$	34920.6	−	15969.8i	0.977594	−	0.447071i
$190$	827.621	+	431.618i	0.0229258	+	0.0119562i
$191$	−41545.5	+	23986.3i	−1.13882	+	0.657501i	−0.946139	−	0.323760i	$-0.895053\pi$
$191$	−41545.5	+	23986.3i	−1.13882	+	0.657501i	−0.192685	+	0.981261i	$0.561720\pi$
$192$	8392.86	+	15658.0i	0.227671	+	0.424750i
$193$	−47565.0	−	27461.7i	−1.27695	−	0.737246i	−0.300662	−	0.953731i	$-0.597208\pi$
$193$	−47565.0	−	27461.7i	−1.27695	−	0.737246i	−0.976286	+	0.216484i	$0.930541\pi$
$194$	50807.8	+	29333.9i	1.34998	+	0.779411i
$195$	−30064.3	−	50736.7i	−0.790645	−	1.33430i
$196$	995.355	+	1724.01i	0.0259099	+	0.0448773i
$197$	27187.3			0.700540			0.350270	−	0.936649i	$-0.386090\pi$
$197$	27187.3			0.700540			0.350270	+	0.936649i	$0.386090\pi$
$198$	−736.291	+	365.236i	−0.0187810	+	0.00931630i
$199$	−5662.22			−0.142982			−0.0714909	−	0.997441i	$-0.522776\pi$
$199$	−5662.22			−0.142982			−0.0714909	+	0.997441i	$0.522776\pi$
$200$	−13058.1	+	27894.5i	−0.326453	+	0.697361i
$201$	−1246.40	+	39481.4i	−0.0308506	+	0.977239i
$202$	−18666.1	−	10776.9i	−0.457458	−	0.264113i
$203$	−781.940	+	1354.36i	−0.0189750	+	0.0328656i
$204$	23354.7	+	737.289i	0.561195	+	0.0177165i
$205$	−64445.5	+	2765.56i	−1.53350	+	0.0658076i
$206$		−	24326.3i		−	0.573246i
$207$	12874.3	+	25953.7i	0.300457	+	0.605702i
$208$			82007.0i			1.89550i
$209$	−15.3819	+	8.88074i	−0.000352141	+	0.000203309i
$210$	−27902.9	−	47089.2i	−0.632720	−	1.06778i
$211$	25552.1	−	44257.5i	0.573933	−	0.994081i	−0.422224	−	0.906492i	$-0.638750\pi$
$211$	25552.1	−	44257.5i	0.573933	−	0.994081i	0.996157	−	0.0875895i	$-0.0279164\pi$
$212$	8939.19	−	15483.1i	0.198896	−	0.344498i
$213$	−35202.5	+	18869.0i	−0.775916	+	0.415900i
$214$	−45429.4	−	78686.1i	−0.991996	−	1.71819i
$215$	7978.58	−	15298.8i	0.172603	−	0.330964i
$216$	35763.8	+	3396.13i	0.766542	+	0.0727909i
$217$		−	56277.0i		−	1.19512i
$218$	17400.2	+	30138.1i	0.366136	+	0.634166i
$219$	−32101.2	+	17206.6i	−0.669318	+	0.358762i
$220$	157.109	+	247.019i	0.00324606	+	0.00510369i
$221$	−110574.	−	63839.8i	−2.26395	−	1.30709i
$222$	−60827.1	−	37726.4i	−1.23422	−	0.765490i
$223$	59559.4	−	34386.7i	1.19768	−	0.691481i	0.237643	−	0.971353i	$-0.423625\pi$
$223$	59559.4	−	34386.7i	1.19768	−	0.691481i	0.960037	+	0.279872i	$0.0902919\pi$
$224$			34580.0i			0.689175i
$225$	26299.2	+	43257.8i	0.519491	+	0.854476i
$226$	29966.6			0.586706
$227$	13649.9	+	23642.3i	0.264897	+	0.458816i	0.967537	−	0.252731i	$-0.0813286\pi$
$227$	13649.9	+	23642.3i	0.264897	+	0.458816i	−0.702639	+	0.711546i	$0.747995\pi$
$228$	−387.594	−	12.2360i	−0.00745603	−	0.000235381i
$229$	−26698.6	+	46243.3i	−0.509117	+	0.881816i	0.490827	+	0.871257i	$0.336695\pi$
$229$	−26698.6	+	46243.3i	−0.509117	+	0.881816i	−0.999944	+	0.0105593i	$0.996639\pi$
$230$	34846.1	−	22162.9i	0.658716	−	0.418958i
$231$	1041.02	+	32.8643i	0.0195091	+	0.000615885i
$232$	−1267.09	+	731.553i	−0.0235413	+	0.0135916i
$233$	−741.777			−0.0136635			−0.00683174	−	0.999977i	$-0.502175\pi$
$233$	−741.777			−0.0136635			−0.00683174	+	0.999977i	$0.502175\pi$
$234$	81655.8	+	54285.6i	1.49127	+	0.991410i
$235$	−36261.0	−	18910.7i	−0.656605	−	0.342430i
$236$	−6638.88	+	3832.96i	−0.119199	+	0.0688193i
$237$	19023.5	−	30672.0i	0.338684	−	0.546067i
$238$	−102625.	−	59250.3i	−1.81175	−	1.04601i
$239$	69798.3	+	40298.1i	1.22194	+	0.705486i	0.965331	−	0.261029i	$-0.0840619\pi$
$239$	69798.3	+	40298.1i	1.22194	+	0.705486i	0.256607	+	0.966516i	$0.417395\pi$
$240$	−797.438	−	70391.3i	−0.0138444	−	1.22207i
$241$	−44199.7	−	76556.1i	−0.761001	−	1.31809i	−0.942335	−	0.334671i	$-0.891375\pi$
$241$	−44199.7	−	76556.1i	−0.761001	−	1.31809i	0.181334	−	0.983422i	$-0.441958\pi$
$242$	67596.0			1.15422
$243$	37193.5	−	45863.1i	0.629875	−	0.776696i
$244$	2737.18			0.0459752
$245$	400.338	+	9329.01i	0.00666951	+	0.155419i
$246$	94525.1	−	50666.5i	1.56199	−	0.837242i
$247$	1835.08	+	1059.48i	0.0300789	+	0.0173660i
$248$	26325.3	−	45596.8i	0.428026	−	0.741363i
$249$	−30925.9	+	49862.5i	−0.498797	+	0.804220i
$250$	57348.9	−	43801.7i	0.917582	−	0.700827i
$251$			48276.4i			0.766280i	0.923690	+	0.383140i	$0.125157\pi$
$251$			48276.4i			0.766280i	−0.923690	+	0.383140i	$0.874843\pi$
$252$	18937.1	+	12589.5i	0.298202	+	0.198248i
$253$			785.825i			0.0122768i
$254$	−99668.8	+	57543.8i	−1.54487	+	0.891930i
$255$	95532.5	+	53722.1i	1.46917	+	0.826176i
$256$	−29516.2	+	51123.6i	−0.450382	+	0.780084i
$257$	−28514.6	+	49388.7i	−0.431719	+	0.747759i	−0.997021	−	0.0771245i	$-0.975426\pi$
$257$	−28514.6	+	49388.7i	−0.431719	+	0.747759i	0.565302	+	0.824884i	$0.308759\pi$
$258$	−905.193	+	28673.3i	−0.0135988	+	0.430763i
$259$	45352.1	+	78552.2i	0.676080	+	1.17101i
$260$	16149.8	−	30967.1i	0.238903	−	0.458093i
$261$	−151.690	+	2400.10i	−0.00222677	+	0.0352330i
$262$			39317.1i			0.572768i
$263$	18313.7	+	31720.3i	0.264768	+	0.458591i	0.967503	−	0.252861i	$-0.0813714\pi$
$263$	18313.7	+	31720.3i	0.264768	+	0.458591i	−0.702735	+	0.711452i	$0.748038\pi$
$264$	828.084	+	513.598i	0.0118814	+	0.00736911i
$265$	70760.5	−	45005.2i	1.00763	−	0.640871i
$266$	1703.16	+	983.318i	0.0240708	+	0.0138973i
$267$	−60538.3	+	32449.2i	−0.849196	+	0.455179i
$268$	−20258.6	+	11696.3i	−0.282059	+	0.162847i
$269$		−	51318.1i		−	0.709196i	−0.935019	−	0.354598i	$-0.884618\pi$
$269$		−	51318.1i		−	0.709196i	0.935019	−	0.354598i	$-0.115382\pi$
$270$	−70617.7	−	45802.4i	−0.968692	−	0.628291i
$271$	−17528.9			−0.238679			−0.119340	−	0.992853i	$-0.538078\pi$
$271$	−17528.9			−0.238679			−0.119340	+	0.992853i	$0.538078\pi$
$272$	−76202.4	−	131986.i	−1.02999	−	1.78399i
$273$	−58702.3	−	109517.i	−0.787643	−	1.46945i
$274$	4298.48	−	7445.19i	0.0572551	−	0.0991687i
$275$	117.637	+	1368.11i	0.00155553	+	0.0180907i
$276$	−9043.04	+	14580.3i	−0.118712	+	0.191403i
$277$	−65710.4	+	37937.9i	−0.856396	+	0.494440i	−0.862804	−	0.505539i	$-0.831294\pi$
$277$	−65710.4	+	37937.9i	−0.856396	+	0.494440i	0.00640796	+	0.999979i	$0.497960\pi$
$278$	−22807.0			−0.295106
$279$	−38457.2	−	77527.1i	−0.494048	−	0.995967i
$280$	−30007.2	+	57538.4i	−0.382745	+	0.733908i
$281$	67750.7	−	39115.9i	0.858027	−	0.495382i	−0.00532421	−	0.999986i	$-0.501695\pi$
$281$	67750.7	−	39115.9i	0.858027	−	0.495382i	0.863351	+	0.504604i	$0.168361\pi$
$282$	67961.0	+	2145.48i	0.854598	+	0.0269790i
$283$	94524.2	+	54573.6i	1.18024	+	0.681412i	0.956070	−	0.293138i	$-0.0946997\pi$
$283$	94524.2	+	54573.6i	1.18024	+	0.681412i	0.224170	+	0.974550i	$0.428033\pi$
$284$	−20484.1	−	11826.5i	−0.253968	−	0.146629i
$285$	−1585.46	−	891.571i	−0.0195193	−	0.0109766i
$286$	1329.82	+	2303.31i	0.0162577	+	0.0281592i
$287$	−135908.			−1.64999
$288$	23630.4	+	47637.3i	0.284896	+	0.574331i
$289$	153763.			1.84101
$290$	3424.88	−	146.972i	0.0407239	−	0.00174759i
$291$	−97157.1	−	60259.1i	−1.14733	−	0.711602i
$292$	−18679.4	−	10784.6i	−0.219078	−	0.126484i
$293$	−40696.9	+	70489.1i	−0.474052	+	0.821082i	−0.999559	−	0.0297072i	$-0.990543\pi$
$293$	−40696.9	+	70489.1i	−0.474052	+	0.821082i	0.525507	+	0.850790i	$0.323876\pi$
$294$	−7334.39	−	13683.3i	−0.0848534	−	0.158305i
$295$	−35924.6	+	1541.64i	−0.412808	+	0.0177149i
$296$			84859.5i			0.968538i
$297$	1456.57	−	666.114i	0.0165127	−	0.00755154i
$298$			72900.8i			0.820918i
$299$	81189.9	−	46875.0i	0.908155	−	0.524323i
$300$	−13561.2	+	26737.8i	−0.150680	+	0.297087i
$301$	18176.9	−	31483.4i	0.200626	−	0.347495i
$302$	−35853.4	+	62099.9i	−0.393112	+	0.680890i
$303$	35694.2	+	22138.4i	0.388787	+	0.241135i
$304$	1264.65	+	2190.45i	0.0136844	+	0.0237020i
$305$	11383.9	+	5936.87i	0.122374	+	0.0638202i
$306$	−181864.	−	11494.1i	−1.94225	−	0.122753i
$307$			89841.0i			0.953230i	0.879112	+	0.476615i	$0.158136\pi$
$307$			89841.0i			0.953230i	−0.879112	+	0.476615i	$0.841864\pi$
$308$	308.402	+	534.168i	0.00325099	+	0.00563088i
$309$	−1495.79	+	47381.4i	−0.0156659	+	0.496239i
$310$	−104090.	+	66203.3i	−1.08314	+	0.688900i
$311$	41303.4	+	23846.5i	0.427036	+	0.246550i	0.698083	−	0.716017i	$-0.254036\pi$
$311$	41303.4	+	23846.5i	0.427036	+	0.246550i	−0.271047	+	0.962566i	$0.587370\pi$
$312$	3668.11	−	116193.i	0.0376819	−	1.19363i
$313$	155948.	−	90036.4i	1.59181	−	0.919029i	0.598808	−	0.800893i	$-0.295641\pi$
$313$	155948.	−	90036.4i	1.59181	−	0.919029i	0.992997	−	0.118136i	$-0.0376920\pi$
$314$			40845.9i			0.414275i
$315$	51452.4	+	93433.7i	0.518543	+	0.941634i
$316$	21374.1			0.214049
$317$	−5275.71	−	9137.79i	−0.0525004	−	0.0909333i	0.838581	−	0.544777i	$-0.183386\pi$
$317$	−5275.71	−	9137.79i	−0.0525004	−	0.0909333i	−0.891081	+	0.453844i	$0.850052\pi$
$318$	−73489.5	+	118489.i	−0.726727	+	1.17172i
$319$	−32.6153	+	56.4914i	−0.000320509	+	0.000555138i
$320$	−41639.9	+	26483.9i	−0.406640	+	0.258632i
$321$	83646.7	+	156054.i	0.811781	+	1.51448i
$322$	75353.2	−	43505.2i	0.726758	−	0.419594i
$323$	−3937.97			−0.0377457
$324$	34690.7	+	4402.59i	0.330464	+	0.0419391i
$325$	134334.	−	93762.9i	1.27180	−	0.887696i
$326$	181561.	−	104825.i	1.70840	−	0.986343i
$327$	−32038.1	−	59771.3i	−0.299620	−	0.558981i
$328$	−110115.	−	63575.2i	−1.02353	−	0.590935i
$329$	−74621.4	−	43082.7i	−0.689400	−	0.398025i
$330$	−1163.85	−	1964.13i	−0.0106874	−	0.0180361i
$331$	102147.	+	176924.i	0.932329	+	1.61484i	0.779329	+	0.626615i	$0.215560\pi$
$331$	102147.	+	176924.i	0.932329	+	1.61484i	0.153001	+	0.988226i	$0.451106\pi$
$332$	−34747.1			−0.315241
$333$	116156.	+	77221.7i	1.04750	+	0.696387i
$334$	−183998.			−1.64938
$335$	−109624.	+	4704.33i	−0.976826	+	0.0419188i
$336$	4680.01	−	148246.i	0.0414542	−	1.31312i
$337$	139338.	+	80447.0i	1.22690	+	0.708353i	0.966381	−	0.257114i	$-0.0827717\pi$
$337$	139338.	+	80447.0i	1.22690	+	0.708353i	0.260523	+	0.965468i	$0.416105\pi$
$338$	92695.7	−	160554.i	0.811384	−	1.40536i
$339$	−58367.3	−	1842.61i	−0.507891	−	0.0160337i
$340$	2782.78	+	64846.8i	0.0240725	+	0.560958i
$341$		−	2347.36i		−	0.0201870i
$342$	3018.22	+	190.756i	0.0258047	+	0.00163089i
$343$		−	106795.i		−	0.907746i
$344$	29454.6	−	17005.6i	0.248907	−	0.143706i
$345$	−69234.1	+	41025.0i	−0.581677	+	0.344675i
$346$	−75731.4	+	131171.i	−0.632592	+	1.09568i
$347$	30149.8	−	52221.1i	0.250395	−	0.433697i	−0.713239	−	0.700921i	$-0.752773\pi$
$347$	30149.8	−	52221.1i	0.250395	−	0.433697i	0.963635	+	0.267223i	$0.0861061\pi$
$348$	−1255.24	+	672.820i	−0.0103649	+	0.00555572i
$349$	−11957.3	−	20710.7i	−0.0981711	−	0.170037i	0.812757	−	0.582603i	$-0.197966\pi$
$349$	−11957.3	−	20710.7i	−0.0981711	−	0.170037i	−0.910928	+	0.412566i	$0.864633\pi$
$350$	124676.	−	87022.3i	1.01777	−	0.710386i
$351$	−155707.	−	110756.i	−1.26384	−	0.898983i
$352$			1442.36i			0.0116410i
$353$	11439.7	+	19814.2i	0.0918050	+	0.159011i	0.908271	−	0.418383i	$-0.137403\pi$
$353$	11439.7	+	19814.2i	0.0918050	+	0.159011i	−0.816466	+	0.577394i	$0.804070\pi$
$354$	52692.2	−	28243.6i	0.420474	−	0.225379i
$355$	−59541.5	−	93615.6i	−0.472458	−	0.742833i
$356$	−35226.8	−	20338.2i	−0.277954	−	0.160477i
$357$	196244.	+	121715.i	1.53978	+	0.955009i
$358$	−12965.5	+	7485.63i	−0.101163	+	0.0584067i
$359$		−	232933.i		−	1.80735i	−0.428216	−	0.903677i	$-0.640858\pi$
$359$		−	232933.i		−	1.80735i	0.428216	−	0.903677i	$-0.359142\pi$
$360$	−2018.68	+	99770.3i	−0.0155763	+	0.769833i
$361$	−130256.			−0.999499
$362$	−6870.06	−	11899.3i	−0.0524256	−	0.0908038i
$363$	−131660.	−	4156.40i	−0.999173	−	0.0315431i
$364$	36792.8	−	63727.0i	0.277690	−	0.480973i
$365$	−54295.9	−	85368.0i	−0.407550	−	0.640781i
$366$	−21335.8	−	673.556i	−0.159275	−	0.00502819i
$367$	−43801.9	+	25289.1i	−0.325208	+	0.187759i	−0.653712	−	0.756744i	$-0.726789\pi$
$367$	−43801.9	+	25289.1i	−0.325208	+	0.187759i	0.328504	+	0.944503i	$0.393456\pi$
$368$	111905.			0.826329
$369$	−187226.	+	92873.4i	−1.37504	+	0.682085i
$370$	91938.3	−	176290.i	0.671573	−	1.28773i
$371$	153017.	−	88344.2i	1.11171	−	0.641845i
$372$	27012.7	−	43553.2i	0.195201	−	0.314727i
$373$	−56423.6	−	32576.2i	−0.405549	−	0.234144i	0.283326	−	0.959024i	$-0.408562\pi$
$373$	−56423.6	−	32576.2i	−0.405549	−	0.234144i	−0.688876	+	0.724880i	$0.741895\pi$
$374$	−4280.56	−	2471.38i	−0.0306025	−	0.0176684i
$375$	−114394.	+	81788.2i	−0.813471	+	0.581605i
$376$	−40306.5	−	69812.9i	−0.285101	−	0.493810i
$377$	7782.12			0.0547539
$378$	−144513.	−	102793.i	−1.01140	−	0.719418i
$379$	−57876.1			−0.402922			−0.201461	−	0.979497i	$-0.564569\pi$
$379$	−57876.1			−0.402922			−0.201461	+	0.979497i	$0.564569\pi$
$380$	−46.1830	−	1076.20i	−0.000319827	−	0.00745288i
$381$	197668.	−	105952.i	1.36171	−	0.729894i
$382$	191875.	+	110779.i	1.31489	+	0.759154i
$383$	−47179.9	+	81718.0i	−0.321632	+	0.557084i	−0.980825	−	0.194891i	$-0.937565\pi$
$383$	−47179.9	+	81718.0i	−0.321632	+	0.557084i	0.659193	+	0.751974i	$0.270898\pi$
$384$	93073.4	−	150064.i	0.631195	−	1.01769i
$385$	124.041	+	2890.51i	0.000836843	+	0.0195008i
$386$			253659.i			1.70246i
$387$	3526.18	−	55792.7i	0.0235441	−	0.372525i
$388$		−	67704.8i		−	0.449734i
$389$	−118204.	+	68245.3i	−0.781150	+	0.450997i	−0.836838	−	0.547451i	$-0.815598\pi$
$389$	−118204.	+	68245.3i	−0.781150	+	0.450997i	0.0556879	+	0.998448i	$0.482265\pi$
$390$	−133505.	+	237409.i	−0.877748	+	1.56087i
$391$	−87114.3	+	150886.i	−0.569817	+	0.986953i
$392$	−9203.01	+	15940.1i	−0.0598905	+	0.103733i
$393$	2417.56	−	76579.8i	0.0156528	−	0.495826i
$394$	−62781.2	−	108740.i	−0.404424	−	0.700483i
$395$	88894.4	+	46359.9i	0.569745	+	0.297131i
$396$	789.880	+	525.120i	0.00503698	+	0.00334864i
$397$		−	98285.2i		−	0.623602i	−0.950148	−	0.311801i	$-0.899068\pi$
$397$		−	98285.2i		−	0.623602i	0.950148	−	0.311801i	$-0.100932\pi$
$398$	13075.3	+	22647.0i	0.0825437	+	0.142970i
$399$	−3256.86	−	2019.98i	−0.0204575	−	0.0126882i
$400$	194825.	−	16752.0i	1.21766	−	0.104700i
$401$	−39459.3	−	22781.9i	−0.245392	−	0.141677i	0.372260	−	0.928128i	$-0.378583\pi$
$401$	−39459.3	−	22781.9i	−0.245392	−	0.141677i	−0.617653	+	0.786451i	$0.711916\pi$
$402$	160791.	−	86185.8i	0.994968	−	0.533314i
$403$	−242525.	+	140022.i	−1.49330	+	0.862155i
$404$			24873.8i			0.152398i
$405$	134729.	+	93553.7i	0.821393	+	0.570362i
$406$	7222.66			0.0438172
$407$	1891.67	+	3276.48i	0.0114198	+	0.0197796i
$408$	102065.	+	190415.i	0.613133	+	1.14388i
$409$	108165.	−	187348.i	0.646609	−	1.11996i	−0.337319	−	0.941391i	$-0.609520\pi$
$409$	108165.	−	187348.i	0.646609	−	1.11996i	0.983927	−	0.178569i	$-0.0571467\pi$
$410$	159880.	+	251375.i	0.951099	+	1.49539i
$411$	−8830.15	+	14237.0i	−0.0522739	+	0.0842822i
$412$	−24312.3	+	14036.7i	−0.143229	+	0.0826934i
$413$	−75760.7			−0.444164
$414$	74076.9	−	111426.i	0.432197	−	0.650106i
$415$	−144513.	−	75365.6i	−0.839092	−	0.437600i
$416$	149022.	−	86037.9i	0.861120	−	0.497168i
$417$	44422.3	+	1402.38i	0.255463	+	0.00806478i
$418$	71.0401	+	41.0150i	0.000406584	+	0.000234742i
$419$	15411.4	+	8897.78i	0.0877838	+	0.0506820i	0.543249	−	0.839571i	$-0.317194\pi$
$419$	15411.4	+	8897.78i	0.0877838	+	0.0506820i	−0.455466	+	0.890253i	$0.650527\pi$
$420$	−30961.7	+	55058.3i	−0.175520	+	0.312122i
$421$	50184.0	+	86921.3i	0.283140	+	0.490413i	0.972156	−	0.234333i	$-0.0752905\pi$
$421$	50184.0	+	86921.3i	0.283140	+	0.490413i	−0.689016	+	0.724746i	$0.741957\pi$
$422$	−236021.			−1.32533
$423$	−132239.	−	8357.69i	−0.739058	−	0.0467095i
$424$	165303.			0.919493
$425$	−129077.	+	275732.i	−0.714616	+	1.52654i
$426$	156760.	+	97226.1i	0.863804	+	0.535752i
$427$	23426.8	+	13525.5i	0.128487	+	0.0741817i
$428$	−52427.2	+	90806.6i	−0.286200	+	0.495713i
$429$	−2448.52	−	4568.04i	−0.0133042	−	0.0248207i
$430$	−79614.5	+	3416.51i	−0.430581	+	0.0184776i
$431$			164947.i			0.887952i	0.896039	+	0.443976i	$0.146432\pi$
$431$			164947.i			0.887952i	−0.896039	+	0.443976i	$0.853568\pi$
$432$	−94857.5	−	207421.i	−0.508281	−	1.11144i
$433$			9861.68i			0.0525987i	0.999654	+	0.0262994i	$0.00837231\pi$
$433$			9861.68i			0.0525987i	−0.999654	+	0.0262994i	$0.991628\pi$
$434$	−225090.	+	129956.i	−1.19502	+	0.689946i
$435$	−6679.83	+	75.6735i	−0.0353010	+	0.000399913i
$436$	20080.5	−	34780.4i	0.105633	−	0.182963i
$437$	1445.75	−	2504.11i	0.00757059	−	0.0131126i
$438$	142949.	+	88660.5i	0.745132	+	0.462149i
$439$	19146.6	+	33162.9i	0.0993487	+	0.172077i	0.911415	−	0.411488i	$-0.134991\pi$
$439$	19146.6	+	33162.9i	0.0993487	+	0.172077i	−0.812067	+	0.583565i	$0.801657\pi$
$440$	−1251.62	+	2399.97i	−0.00646500	+	0.0123966i
$441$	13444.2	+	27102.5i	0.0691284	+	0.139358i
$442$			589678.i			3.01836i
$443$	−79637.0	−	137935.i	−0.405796	−	0.702859i	0.588618	−	0.808411i	$-0.299672\pi$
$443$	−79637.0	−	137935.i	−0.405796	−	0.702859i	−0.994414	+	0.105553i	$0.966339\pi$
$444$	−2606.38	+	82560.9i	−0.0132212	+	0.418802i
$445$	−102395.	−	160992.i	−0.517079	−	0.812989i
$446$	−275071.	−	158812.i	−1.38285	−	0.798388i
$447$	4482.58	−	141992.i	0.0224343	−	0.710640i
$448$	−90044.6	+	51987.3i	−0.448644	+	0.259025i
$449$			9321.06i			0.0462352i	0.999733	+	0.0231176i	$0.00735922\pi$
$449$			9321.06i			0.0462352i	−0.999733	+	0.0231176i	$0.992641\pi$
$450$	112287.	−	205080.i	0.554502	−	1.01274i
$451$	−5668.83			−0.0278702
$452$	−17291.3	−	29949.3i	−0.0846349	−	0.146592i
$453$	73651.7	−	118750.i	0.358911	−	0.578679i
$454$	63041.0	−	109190.i	0.305852	−	0.529751i
$455$	291243.	−	185237.i	1.40680	−	0.894755i
$456$	−1693.86	−	3160.12i	−0.00814608	−	0.0151976i
$457$	−208802.	+	120552.i	−0.999775	+	0.577220i	−0.908182	−	0.418576i	$-0.862529\pi$
$457$	−208802.	+	120552.i	−0.999775	+	0.577220i	−0.0915931	+	0.995797i	$0.529196\pi$
$458$	246611.			1.17566
$459$	353519.	+	33570.2i	1.67798	+	0.159341i
$460$	−42256.9	−	22037.7i	−0.199702	−	0.104148i
$461$	−183415.	+	105895.i	−0.863043	+	0.498278i	−0.865030	−	0.501720i	$-0.832701\pi$
$461$	−183415.	+	105895.i	−0.863043	+	0.498278i	0.00198694	+	0.999998i	$0.499368\pi$
$462$	−2272.49	−	4239.64i	−0.0106468	−	0.0198630i
$463$	314347.	+	181488.i	1.46638	+	0.846616i	0.999293	−	0.0375951i	$-0.0119697\pi$
$463$	314347.	+	181488.i	1.46638	+	0.846616i	0.467088	+	0.884211i	$0.345303\pi$
$464$	8044.62	+	4644.56i	0.0373654	+	0.0215729i
$465$	206811.	−	122547.i	0.956462	−	0.566756i
$466$	1712.92	+	2966.86i	0.00788797	+	0.0136624i
$467$	−225929.			−1.03595			−0.517974	−	0.855396i	$-0.673314\pi$
$467$	−225929.			−1.03595			−0.517974	+	0.855396i	$0.673314\pi$
$468$	7137.50	−	112933.i	0.0325878	−	0.515618i
$469$	−231185.			−1.05103
$470$	8097.76	+	188701.i	0.0366581	+	0.854237i
$471$	2511.57	−	79557.5i	0.0113215	−	0.358624i
$472$	−61382.8	−	35439.4i	−0.275526	−	0.159075i
$473$	758.174	−	1313.20i	0.00338881	−	0.00586959i
$474$	−166607.	−	5259.66i	−0.741545	−	0.0234100i
$475$	2142.17	−	4576.05i	0.00949437	−	0.0202817i
$476$			136754.i			0.603568i
$477$	150425.	−	226267.i	0.661124	−	0.994455i
$478$		−	372227.i		−	1.62912i
$479$	101218.	−	58438.2i	0.441150	−	0.254698i	−0.262935	−	0.964813i	$-0.584691\pi$
$479$	101218.	−	58438.2i	0.441150	−	0.254698i	0.704085	+	0.710115i	$0.251357\pi$
$480$	−127077.	+	75300.3i	−0.551551	+	0.326824i
$481$	225680.	−	390888.i	0.975443	−	1.68952i
$482$	−204133.	+	353568.i	−0.878656	+	1.52188i
$483$	−149444.	+	80103.7i	−0.640596	+	0.343367i
$484$	−39004.1	−	67557.2i	−0.166502	−	0.288390i
$485$	146850.	−	281583.i	0.624296	−	1.19708i
$486$	−269325.	−	42854.1i	−1.14026	−	0.181434i
$487$		−	297474.i		−	1.25427i	−0.778911	−	0.627134i	$-0.784228\pi$
$487$		−	297474.i		−	1.25427i	0.778911	−	0.627134i	$-0.215772\pi$
$488$	12653.9	+	21917.2i	0.0531356	+	0.0920335i
$489$	−360081.	+	193008.i	−1.50585	+	0.807155i
$490$	36388.5	−	23143.9i	0.151556	−	0.0963926i
$491$	176709.	+	102023.i	0.732984	+	0.423189i	0.819513	−	0.573061i	$-0.194244\pi$
$491$	176709.	+	102023.i	0.732984	+	0.423189i	−0.0865286	+	0.996249i	$0.527577\pi$
$492$	−105180.	−	65235.2i	−0.434514	−	0.269496i
$493$	−12524.9	+	7231.28i	−0.0515326	+	0.0297524i
$494$		−	9786.30i		−	0.0401019i
$495$	2146.12	+	3897.19i	0.00875879	+	0.0159053i
$496$	−334274.			−1.35875
$497$	−116879.	−	202440.i	−0.473176	−	0.819564i
$498$	270848.	+	8550.45i	1.09211	+	0.0344771i
$499$	−191606.	+	331872.i	−0.769501	+	1.33281i	0.168333	+	0.985730i	$0.446162\pi$
$499$	−191606.	+	331872.i	−0.769501	+	1.33281i	−0.937834	+	0.347084i	$0.887172\pi$
$500$	−76867.8	−	32041.5i	−0.307471	−	0.128166i
$501$	358382.	+	11313.8i	1.42781	+	0.0450749i
$502$	193090.	−	111480.i	0.766217	−	0.442376i
$503$	76671.8			0.303040			0.151520	−	0.988454i	$-0.451583\pi$
$503$	76671.8			0.303040			0.151520	+	0.988454i	$0.451583\pi$
$504$	−13261.8	+	209835.i	−0.0522087	+	0.826068i
$505$	−53950.7	+	103450.i	−0.211551	+	0.405645i
$506$	3143.04	−	1814.64i	0.0122758	−	0.00708743i
$507$	−190420.	+	307018.i	−0.740793	+	1.19440i
$508$	115021.	+	66407.6i	0.445709	+	0.257330i
$509$	213621.	+	123334.i	0.824534	+	0.476045i	0.851977	−	0.523579i	$-0.175403\pi$
$509$	213621.	+	123334.i	0.824534	+	0.476045i	−0.0274438	+	0.999623i	$0.508737\pi$
$510$	−5734.05	−	506154.i	−0.0220455	−	1.94600i
$511$	−106582.	−	184605.i	−0.408170	−	0.706970i
$512$	−41290.4			−0.157510
$513$	−5867.00	−	557.131i	−0.0222936	−	0.00211701i
$514$	263385.			0.996930
$515$	−131560.	+	5645.64i	−0.496030	+	0.0212862i
$516$	29179.1	−	15640.3i	0.109590	−	0.0587418i
$517$	−3112.52	−	1797.01i	−0.0116448	−	0.00672311i
$518$	209455.	−	362787.i	0.780606	−	1.35205i
$519$	155571.	−	250831.i	0.577556	−	0.931206i
$520$	322621.	−	13844.7i	1.19312	−	0.0512008i
$521$		−	170783.i		−	0.629171i	−0.949229	−	0.314586i	$-0.898134\pi$
$521$		−	170783.i		−	0.629171i	0.949229	−	0.314586i	$-0.101866\pi$
$522$	9949.91	−	4935.64i	0.0365156	−	0.0181135i
$523$		−	213600.i		−	0.780905i	−0.920623	−	0.390452i	$-0.872319\pi$
$523$		−	213600.i		−	0.780905i	0.920623	−	0.390452i	$-0.127681\pi$
$524$	39294.5	−	22686.7i	0.143110	−	0.0826244i
$525$	−248189.	+	161831.i	−0.900458	+	0.587142i
$526$	84580.5	−	146498.i	0.305702	−	0.529492i
$527$	260221.	−	450717.i	0.936962	−	1.62287i
$528$	195.207	−	6183.46i	0.000700209	−	0.0221801i
$529$	75956.0	+	131560.i	0.271425	+	0.470123i
$530$	−343407.	−	179092.i	−1.22252	−	0.637565i
$531$	−104368.	+	51771.4i	−0.370149	+	0.183612i
$532$		−	2269.57i		−	0.00801900i
$533$	338150.	+	585693.i	1.19030	+	2.06165i
$534$	269582.	+	167201.i	0.945385	+	0.586350i
$535$	−415001.	+	263950.i	−1.44991	+	0.922175i
$536$	−187311.	−	108144.i	−0.651978	−	0.376419i
$537$	25713.8	−	13782.9i	0.0891697	−	0.0477960i
$538$	−205256.	+	118504.i	−0.709137	+	0.409421i
$539$			820.609i			0.00282461i
$540$	−5028.36	+	97005.9i	−0.0172440	+	0.332668i
$541$	445341.			1.52159			0.760795	−	0.648992i	$-0.224809\pi$
$541$	445341.			1.52159			0.760795	+	0.648992i	$0.224809\pi$
$542$	40477.8	+	70109.7i	0.137790	+	0.238660i
$543$	12649.5	+	23599.3i	0.0429015	+	0.0800384i
$544$	−159896.	+	276948.i	−0.540306	+	0.935837i
$545$	158952.	−	101097.i	0.535148	−	0.340366i
$546$	−302475.	+	487687.i	−1.01462	+	1.63590i
$547$	−150902.	+	87123.4i	−0.504337	+	0.291179i	−0.730503	−	0.682910i	$-0.760714\pi$
$547$	−150902.	+	87123.4i	−0.504337	+	0.291179i	0.226166	+	0.974089i	$0.427381\pi$
$548$	−9921.21			−0.0330372
$549$	41515.4	+	2623.83i	0.137741	+	0.00870545i
$550$	5200.35	−	3629.77i	0.0171912	−	0.0119992i
$551$	207.864	−	120.010i	0.000684661	−	0.000395289i
$552$	−158554.	−	5005.41i	−0.520353	−	0.0164271i
$553$	182935.	+	105618.i	0.598201	+	0.345372i
$554$	303478.	+	175213.i	0.988799	+	0.570884i
$555$	−189912.	+	337716.i	−0.616549	+	1.09639i
$556$	13160.1	+	22793.9i	0.0425704	+	0.0737342i
$557$	376126.			1.21234			0.606168	−	0.795337i	$-0.292706\pi$
$557$	376126.			1.21234			0.606168	+	0.795337i	$0.292706\pi$
$558$	−221277.	+	332842.i	−0.710670	+	1.06898i
$559$	−180903.			−0.578924
$560$	411621.	−	17664.0i	1.31257	−	0.0563264i
$561$	8185.48	+	5076.83i	0.0260087	+	0.0161312i
$562$	−312901.	−	180654.i	−0.990683	−	0.571971i
$563$	−255128.	+	441894.i	−0.804897	+	1.39412i	0.111463	+	0.993769i	$0.464446\pi$
$563$	−255128.	+	441894.i	−0.804897	+	1.39412i	−0.916360	+	0.400355i	$0.868887\pi$
$564$	−37070.5	−	69159.9i	−0.116539	−	0.217418i
$565$	−6954.64	−	162063.i	−0.0217860	−	0.507676i
$566$		−	504088.i		−	1.57352i
$567$	275154.	+	209101.i	0.855875	+	0.650415i
$568$		−	218694.i		−	0.677862i
$569$	−134061.	+	77400.4i	−0.414075	+	0.239067i	−0.692539	−	0.721380i	$-0.743508\pi$
$569$	−134061.	+	77400.4i	−0.414075	+	0.239067i	0.278464	+	0.960447i	$0.410175\pi$
$570$	95.1622	+	8400.13i	0.000292897	+	0.0258545i
$571$	−45551.8	+	78898.0i	−0.139712	+	0.241988i	−0.927388	−	0.374102i	$-0.877951\pi$
$571$	−45551.8	+	78898.0i	−0.139712	+	0.241988i	0.787676	+	0.616090i	$0.211284\pi$
$572$	1534.66	−	2658.10i	0.00469050	−	0.00812419i
$573$	−366911.	−	227567.i	−1.11751	−	0.693107i
$574$	313840.	+	543587.i	0.952544	+	1.64985i
$575$	−127947.	−	183308.i	−0.386984	−	0.554430i
$576$	−88519.5	+	133150.i	−0.266805	+	0.401325i
$577$			117325.i			0.352403i	0.984354	+	0.176201i	$0.0563810\pi$
$577$			117325.i			0.352403i	−0.984354	+	0.176201i	$0.943619\pi$
$578$	−355072.	−	615003.i	−1.06282	−	1.84086i
$579$	15597.2	−	494064.i	0.0465254	−	1.47376i
$580$	−2123.10	−	3338.10i	−0.00631125	−	0.00992301i
$581$	−297392.	−	171699.i	−0.881001	−	0.508646i
$582$	−16660.6	+	527747.i	−0.0491863	+	1.55805i
$583$	6382.44	−	3684.91i	0.0187780	−	0.0108415i
$584$		−	199427.i		−	0.584735i
$585$	274633.	−	454204.i	0.802492	−	1.32721i
$586$	375911.			1.09469
$587$	92049.2	+	159434.i	0.267143	+	0.462705i	0.968123	−	0.250476i	$-0.0805870\pi$
$587$	92049.2	+	159434.i	0.267143	+	0.462705i	−0.700980	+	0.713181i	$0.747254\pi$
$588$	−9443.32	+	15225.7i	−0.0273130	+	0.0440374i
$589$	−4318.63	+	7480.09i	−0.0124485	+	0.0215614i
$590$	89123.5	+	140127.i	0.256028	+	0.402547i
$591$	115596.	+	215659.i	0.330953	+	0.617436i
$592$	466584.	−	269382.i	1.33133	−	0.768645i
$593$	−459312.			−1.30617			−0.653083	−	0.757286i	$-0.726525\pi$
$593$	−459312.			−1.30617			−0.653083	+	0.757286i	$0.726525\pi$
$594$	−6027.76	−	4287.59i	−0.0170837	−	0.0121518i
$595$	−296616.	+	568758.i	−0.837840	+	1.60655i
$596$	72858.9	−	42065.1i	0.205111	−	0.118421i
$597$	−24074.8	−	44914.6i	−0.0675481	−	0.126020i
$598$	−374970.	−	216489.i	−1.04856	−	0.605387i
$599$	98904.0	+	57102.3i	0.275652	+	0.159147i	0.631453	−	0.775414i	$-0.282459\pi$
$599$	98904.0	+	57102.3i	0.275652	+	0.159147i	−0.355802	+	0.934561i	$0.615792\pi$
$600$	−276789.	+	15020.9i	−0.768859	+	0.0417246i
$601$	−45927.0	−	79547.9i	−0.127151	−	0.220232i	0.795421	−	0.606058i	$-0.207250\pi$
$601$	−45927.0	−	79547.9i	−0.127151	−	0.220232i	−0.922572	+	0.385826i	$0.873917\pi$
$602$	−167897.			−0.463288
$603$	−318479.	+	157981.i	−0.875884	+	0.434481i
$604$	82752.2			0.226833
$605$	−15687.7	−	365568.i	−0.0428596	−	0.998751i
$606$	6120.87	−	193887.i	0.0166674	−	0.527963i
$607$	516300.	+	298086.i	1.40128	+	0.809029i	0.994524	−	0.104509i	$-0.0333270\pi$
$607$	516300.	+	298086.i	1.40128	+	0.809029i	0.406755	+	0.913537i	$0.366660\pi$
$608$	2653.63	−	4596.22i	0.00717849	−	0.0124335i
$609$	−14067.9	−	444.113i	−0.0379311	−	0.00119745i
$610$	−2542.23	−	59241.2i	−0.00683212	−	0.159208i
$611$			428773.i			1.14854i
$612$	93451.6	+	188392.i	0.249508	+	0.502990i
$613$			338475.i			0.900753i	0.892839	+	0.450377i	$0.148710\pi$
$613$			338475.i			0.900753i	−0.892839	+	0.450377i	$0.851290\pi$
$614$	359334.	−	207462.i	0.953152	−	0.550302i
$615$	−295948.	−	499445.i	−0.782467	−	1.32050i
$616$	−2851.47	+	4938.89i	−0.00751463	+	0.0130157i
$617$	−252706.	+	437700.i	−0.663813	+	1.14976i	0.315792	+	0.948828i	$0.397730\pi$
$617$	−252706.	+	437700.i	−0.663813	+	1.14976i	−0.979606	+	0.200930i	$0.935604\pi$
$618$	192964.	−	103431.i	0.505243	−	0.270816i
$619$	−1186.23	−	2054.61i	−0.00309590	−	0.00536226i	0.864473	−	0.502679i	$-0.167652\pi$
$619$	−1186.23	−	2054.61i	−0.00309590	−	0.00536226i	−0.867569	+	0.497316i	$0.834319\pi$
$620$	126227.	+	65829.3i	0.328374	+	0.171252i
$621$	−151134.	+	212474.i	−0.391904	+	0.550963i
$622$		−	220267.i		−	0.569335i
$623$	−200998.	−	348139.i	−0.517864	−	0.896967i
$624$	−650508.	+	348680.i	−1.67064	+	0.895483i
$625$	−250194.	−	299984.i	−0.640498	−	0.767960i
$626$	−720232.	−	415826.i	−1.83791	−	1.06112i
$627$	−135.846	−	84.2550i	−0.000345551	−	0.000214319i
$628$	40822.4	−	23568.8i	0.103509	−	0.0597611i
$629$			838822.i			2.12016i
$630$	254889.	−	421551.i	0.642201	−	1.06211i
$631$	92165.6			0.231478			0.115739	−	0.993280i	$-0.463076\pi$
$631$	92165.6			0.231478			0.115739	+	0.993280i	$0.463076\pi$
$632$	98812.0	+	171147.i	0.247386	+	0.428485i
$633$	459708.	+	14512.6i	1.14729	+	0.0362192i
$634$	−24365.4	+	42202.2i	−0.0606172	+	0.104992i
$635$	334335.	+	525666.i	0.829153	+	1.30366i
$636$	160825.	+	5077.13i	0.397594	+	0.0125517i
$637$	84783.7	−	48949.9i	0.208946	−	0.120635i
$638$	301.263			0.000740124
$639$	−299350.	−	199011.i	−0.733124	−	0.487388i
$640$	434920.	+	226818.i	1.06182	+	0.553754i
$641$	449455.	−	259493.i	1.09388	−	0.631552i	0.159274	−	0.987234i	$-0.449085\pi$
$641$	449455.	−	259493.i	1.09388	−	0.631552i	0.934607	+	0.355682i	$0.115751\pi$
$642$	431007.	−	694921.i	1.04572	−	1.68603i
$643$	468605.	+	270549.i	1.13340	+	0.654372i	0.944789	−	0.327679i	$-0.106267\pi$
$643$	468605.	+	270549.i	1.13340	+	0.654372i	0.188616	+	0.982051i	$0.439600\pi$
$644$	−86960.3	−	50206.6i	−0.209676	−	0.121057i
$645$	155279.	−	1759.10i	0.373244	−	0.00422835i
$646$	9093.60	+	15750.6i	0.0217907	+	0.0377426i
$647$	692153.			1.65346			0.826730	−	0.562599i	$-0.190198\pi$
$647$	692153.			1.65346			0.826730	+	0.562599i	$0.190198\pi$
$648$	125122.	+	298130.i	0.297978	+	0.709996i
$649$	−3160.04			−0.00750245
$650$	−685225.	−	320772.i	−1.62184	−	0.759224i
$651$	446408.	−	239280.i	1.05334	−	0.564605i
$652$	−209529.	−	120971.i	−0.492888	−	0.284569i
$653$	3155.89	−	5466.17i	0.00740109	−	0.0128191i	−0.862301	−	0.506396i	$-0.830977\pi$
$653$	3155.89	−	5466.17i	0.00740109	−	0.0128191i	0.869702	+	0.493577i	$0.164311\pi$
$654$	−165083.	+	266166.i	−0.385963	+	0.622297i
$655$	212632.	−	9124.72i	0.495616	−	0.0212685i
$656$			807266.i			1.87590i
$657$	−272977.	−	181478.i	−0.632405	−	0.420430i
$658$			397948.i			0.919125i
$659$	209705.	−	121073.i	0.482879	−	0.278790i	−0.238737	−	0.971084i	$-0.576733\pi$
$659$	209705.	−	121073.i	0.482879	−	0.278790i	0.721615	+	0.692294i	$0.243400\pi$
$660$	−1291.44	+	2296.52i	−0.00296473	+	0.00527209i
$661$	−95483.2	+	165382.i	−0.218536	+	0.378516i	−0.954361	−	0.298656i	$-0.903462\pi$
$661$	−95483.2	+	165382.i	−0.218536	+	0.378516i	0.735824	+	0.677172i	$0.236795\pi$
$662$	471758.	−	817108.i	1.07647	−	1.86451i
$663$	36258.6	−	1.14854e6i	0.0824868	−	2.61289i
$664$	−160635.	−	278228.i	−0.364338	−	0.631052i
$665$	4922.64	−	9439.10i	0.0111315	−	0.0213446i
$666$	40632.6	−	642907.i	0.0916065	−	1.44944i
$667$		−	10619.3i		−	0.0238695i
$668$	106170.	+	183892.i	0.237931	+	0.412108i
$669$	526003.	+	326240.i	1.17527	+	0.728928i
$670$	271962.	+	427598.i	0.605840	+	0.952546i
$671$	977.151	+	564.159i	0.00217029	+	0.00125301i
$672$	−274300.	+	147028.i	−0.607418	+	0.325583i
$673$	413218.	−	238572.i	0.912324	−	0.526731i	0.0311462	−	0.999515i	$-0.490084\pi$
$673$	413218.	−	238572.i	0.912324	−	0.526731i	0.881178	+	0.472784i	$0.156751\pi$
$674$		−	743076.i		−	1.63574i
$675$	−231316.	+	392539.i	−0.507690	+	0.861540i
$676$	−213948.			−0.468183
$677$	−104291.	−	180637.i	−0.227546	−	0.394122i	0.729534	−	0.683944i	$-0.239737\pi$
$677$	−104291.	−	180637.i	−0.227546	−	0.394122i	−0.957080	+	0.289823i	$0.906404\pi$
$678$	127413.	+	237705.i	0.277174	+	0.517105i
$679$	334556.	−	579468.i	0.725654	−	1.25687i
$680$	−506378.	+	322068.i	−1.09511	+	0.696513i
$681$	−129502.	+	208798.i	−0.279243	+	0.450229i
$682$	−9388.67	+	5420.55i	−0.0201853	+	0.0116540i
$683$	−166389.			−0.356683			−0.178342	−	0.983969i	$-0.557073\pi$
$683$	−166389.			−0.356683			−0.178342	+	0.983969i	$0.557073\pi$
$684$	−1550.92	−	3126.55i	−0.00331495	−	0.00668272i
$685$	−41262.1	−	21518.9i	−0.0879367	−	0.0458604i
$686$	−427147.	+	246613.i	−0.907672	+	0.524045i
$687$	−480335.	−	15163.8i	−1.01773	−	0.0321288i
$688$	−187005.	−	107967.i	−0.395072	−	0.228095i
$689$	−761435.	−	439615.i	−1.60396	−	0.926048i
$690$	323963.	+	182178.i	0.680451	+	0.382647i
$691$	−25681.9	−	44482.3i	−0.0537862	−	0.0931604i	0.837879	−	0.545856i	$-0.183796\pi$
$691$	−25681.9	−	44482.3i	−0.0537862	−	0.0931604i	−0.891665	+	0.452696i	$0.850462\pi$
$692$	174794.			0.365017
$693$	4165.55	+	8397.48i	0.00867374	+	0.0174857i
$694$	−278489.			−0.578216
$695$	5293.05	+	123343.i	0.0109581	+	0.255356i
$696$	−11190.4	−	6940.53i	−0.0231007	−	0.0143276i
$697$	−1.08847e6	−	628430.i	−2.24054	−	1.29357i
$698$	−55224.1	+	95650.9i	−0.113349	+	0.196326i
$699$	−3153.90	−	5884.02i	−0.00645497	−	0.0120426i
$700$	−158913.	−	74391.2i	−0.324312	−	0.151819i
$701$		−	30751.1i		−	0.0625783i	−0.999510	−	0.0312892i	$-0.990039\pi$
$701$		−	30751.1i		−	0.0625783i	0.999510	−	0.0312892i	$-0.00996128\pi$
$702$	−83425.7	+	878535.i	−0.169288	+	1.78273i
$703$		−	13921.1i		−	0.0281684i
$704$	−3755.83	+	2168.43i	−0.00757811	+	0.00437523i
$705$	−4169.39	−	368040.i	−0.00838870	−	0.740485i
$706$	52833.5	−	91510.3i	0.105999	−	0.183595i
$707$	−122911.	+	212889.i	−0.245897	+	0.425906i
$708$	−58631.7	−	36364.8i	−0.116968	−	0.0725462i
$709$	−452291.	−	783391.i	−0.899758	−	1.55843i	−0.827803	−	0.561019i	$-0.810410\pi$
$709$	−452291.	−	783391.i	−0.899758	−	1.55843i	−0.0719549	−	0.997408i	$-0.522924\pi$
$710$	−236938.	+	454325.i	−0.470021	+	0.901259i
$711$	324186.	+	20489.0i	0.641290	+	0.0405304i
$712$		−	376092.i		−	0.741881i
$713$	191070.	+	330943.i	0.375850	+	0.650991i
$714$	33652.0	−	1.06598e6i	0.0660107	−	2.09098i
$715$	12148.0	−	7726.37i	0.0237625	−	0.0151134i
$716$	14962.7	+	8638.69i	0.0291865	+	0.0168509i
$717$	−22887.8	+	725004.i	−0.0445211	+	1.41027i
$718$	−931657.	+	537893.i	−1.80720	+	1.04339i
$719$			98242.0i			0.190038i	0.995475	+	0.0950188i	$0.0302911\pi$
$719$			98242.0i			0.190038i	−0.995475	+	0.0950188i	$0.969709\pi$
$720$	554977.	−	305617.i	1.07056	−	0.589539i
$721$	−277444.			−0.533709
$722$	300788.	+	520980.i	0.577013	+	0.999416i
$723$	419340.	−	676110.i	0.802212	−	1.29342i
$724$	−7928.30	+	13732.2i	−0.0151253	+	0.0261977i
$725$	−1589.69	−	18488.1i	−0.00302438	−	0.0351735i
$726$	287406.	+	536195.i	0.545285	+	1.01730i
$727$	−40935.0	+	23633.8i	−0.0774508	+	0.0447163i	−0.538225	−	0.842801i	$-0.680905\pi$
$727$	−40935.0	+	23633.8i	−0.0774508	+	0.0447163i	0.460774	+	0.887517i	$0.347572\pi$
$728$	680369.			1.28375
$729$	521942.	+	100029.i	0.982126	+	0.188223i
$730$	−216063.	+	414299.i	−0.405448	+	0.777442i
$731$	291154.	−	168098.i	0.544864	−	0.314578i
$732$	11638.0	+	21712.2i	0.0217198	+	0.0405212i
$733$	83352.7	+	48123.7i	0.155136	+	0.0895676i	0.575558	−	0.817761i	$-0.304785\pi$
$733$	83352.7	+	48123.7i	0.155136	+	0.0895676i	−0.420423	+	0.907328i	$0.638118\pi$
$734$	202296.	+	116796.i	0.375487	+	0.216788i
$735$	−72298.7	+	42840.9i	−0.133831	+	0.0793020i
$736$	−117405.	−	203352.i	−0.216736	−	0.375398i
$737$	−9642.90			−0.0177530
$738$	803808.	+	534380.i	1.47584	+	0.981155i
$739$	466099.			0.853473			0.426736	−	0.904376i	$-0.359663\pi$
$739$	466099.			0.853473			0.426736	+	0.904376i	$0.359663\pi$
$740$	−229239.	+	9837.39i	−0.418625	+	0.0179646i
$741$	−601.748	+	19061.2i	−0.00109592	+	0.0347148i
$742$	−706695.	−	408011.i	−1.28358	−	0.741078i
$743$	329802.	−	571234.i	0.597415	−	1.03475i	−0.395786	−	0.918343i	$-0.629528\pi$
$743$	329802.	−	571234.i	0.597415	−	1.03475i	0.993201	−	0.116410i	$-0.0371388\pi$
$744$	473620.	+	14951.8i	0.855626	+	0.0270114i
$745$	394257.	−	16918.8i	0.710340	−	0.0304830i
$746$			300901.i			0.540688i
$747$	−527017.	−	33308.2i	−0.944460	−	0.0596912i
$748$			5704.12i			0.0101950i
$749$	−897423.	+	518127.i	−1.59968	+	0.923576i
$750$	591287.	+	268674.i	1.05118	+	0.477642i
$751$	−141713.	+	245454.i	−0.251263	+	0.435201i	−0.963874	−	0.266359i	$-0.914179\pi$
$751$	−141713.	+	245454.i	−0.251263	+	0.435201i	0.712611	+	0.701560i	$0.247513\pi$
$752$	−255902.	+	443236.i	−0.452521	+	0.783789i
$753$	−382945.	+	205263.i	−0.675377	+	0.362010i
$754$	−17970.5	−	31125.9i	−0.0316096	−	0.0547494i
$755$	344165.	+	179487.i	0.603771	+	0.314876i
$756$	−19347.5	+	203744.i	−0.0338518	+	0.356484i
$757$			4073.41i			0.00710831i	0.999994	+	0.00355415i	$0.00113132\pi$
$757$			4073.41i			0.00710831i	−0.999994	+	0.00355415i	$0.998869\pi$
$758$	133648.	+	231485.i	0.232608	+	0.402889i
$759$	−6233.43	+	3341.19i	−0.0108204	+	0.00579986i
$760$	8403.85	−	5345.03i	0.0145496	−	0.00925386i
$761$	782690.	+	451886.i	1.35151	+	0.780297i	0.988462	−	0.151471i	$-0.0484012\pi$
$761$	782690.	+	451886.i	1.35151	+	0.780297i	0.363053	+	0.931769i	$0.381735\pi$
$762$	−880231.	−	545940.i	−1.51596	−	0.940232i
$763$	343728.	−	198451.i	0.590426	−	0.340883i
$764$		−	255686.i		−	0.438046i
$765$	−19954.4	+	986213.i	−0.0340969	+	1.68519i
$766$	435794.			0.742717
$767$	188499.	+	326489.i	0.320418	+	0.554981i
$768$	−531028.	−	16764.1i	−0.900315	−	0.0284222i
$769$	−332180.	+	575352.i	−0.561721	+	0.972929i	0.435626	+	0.900128i	$0.356527\pi$
$769$	−332180.	+	575352.i	−0.561721	+	0.972929i	−0.997346	+	0.0728012i	$0.976806\pi$
$770$	11274.7	−	7170.92i	0.0190161	−	0.0120947i
$771$	−513007.	−	16195.2i	−0.863008	−	0.0272445i
$772$	253513.	−	146366.i	0.425370	−	0.245587i
$773$	−617606.			−1.03360			−0.516800	−	0.856106i	$-0.672877\pi$
$773$	−617606.			−1.03360			−0.516800	+	0.856106i	$0.672877\pi$
$774$	−231295.	+	114734.i	−0.386086	+	0.191518i
$775$	382193.	+	547566.i	0.636325	+	0.911660i
$776$	542128.	−	312998.i	0.900282	−	0.519778i
$777$	−430273.	+	693739.i	−0.712693	+	1.14909i
$778$	545918.	+	315186.i	0.901920	+	0.520724i
$779$	18064.3	+	10429.4i	0.0297677	+	0.0171864i
$780$	314308.	−	3560.68i	0.516613	−	0.00585253i
$781$	−4875.10	−	8443.93i	−0.00799248	−	0.0138434i
$782$	804661.			1.31583
$783$	−19683.4	+	9001.56i	−0.0321053	+	0.0146823i
$784$	116858.			0.190120
$785$	220900.	−	9479.52i	0.358473	−	0.0153832i
$786$	−311877.	+	167169.i	−0.504821	+	0.270590i
$787$	−359252.	−	207414.i	−0.580029	−	0.334880i	0.181116	−	0.983462i	$-0.442029\pi$
$787$	−359252.	−	207414.i	−0.580029	−	0.334880i	−0.761145	+	0.648582i	$0.775362\pi$
$788$	−72451.7	+	125490.i	−0.116680	+	0.202096i
$789$	−173749.	+	280140.i	−0.279106	+	0.450008i
$790$	−19851.8	−	462603.i	−0.0318087	−	0.741232i
$791$		−	341772.i		−	0.546240i
$792$	−553.162	+	8752.37i	−0.000881865	+	0.0139533i
$793$		−	134610.i		−	0.214058i
$794$	−393109.	+	226961.i	−0.623550	+	0.360007i
$795$	657857.	+	369942.i	1.04087	+	0.585328i
$796$	15089.3	−	26135.5i	0.0238146	−	0.0412481i
$797$	235403.	−	407730.i	0.370592	−	0.641884i	−0.619065	−	0.785340i	$-0.712488\pi$
$797$	235403.	−	407730.i	0.370592	−	0.641884i	0.989657	+	0.143456i	$0.0458216\pi$
$798$	−558.488	+	17690.9i	−0.000877017	+	0.0277808i
$799$	−398423.	−	690089.i	−0.624095	−	1.08097i
$800$	−234843.	−	336458.i	−0.366941	−	0.525715i
$801$	−514797.	−	342242.i	−0.802363	−	0.533419i
$802$			210433.i			0.327163i
$803$	−4445.61	−	7700.02i	−0.00689446	−	0.0119415i
$804$	−178915.	−	110968.i	−0.276781	−	0.171666i
$805$	−252769.	−	397423.i	−0.390061	−	0.613283i
$806$	1.12008e6	+	646679.i	1.72417	+	0.995449i
$807$	407073.	−	218196.i	0.625064	−	0.335042i
$808$	−199170.	+	114991.i	−0.305072	+	0.176133i
$809$		−	292131.i		−	0.446355i	−0.974778	−	0.223178i	$-0.928357\pi$
$809$		−	292131.i		−	0.446355i	0.974778	−	0.223178i	$-0.0716430\pi$
$810$	63066.1	−	754907.i	0.0961227	−	1.15060i
$811$	−730678.			−1.11092			−0.555462	−	0.831542i	$-0.687459\pi$
$811$	−730678.			−1.11092			−0.555462	+	0.831542i	$0.687459\pi$
$812$	−4167.60	−	7218.50i	−0.00632084	−	0.0109480i
$813$	−74529.6	−	139045.i	−0.112758	−	0.210365i
$814$	8736.55	−	15132.2i	0.0131853	−	0.0228377i
$815$	−609041.	−	957580.i	−0.916920	−	1.44165i
$816$	722962.	−	1.16565e6i	1.08576	−	1.75060i
$817$	−4831.99	+	2789.75i	−0.00723906	+	0.00417947i
$818$	−999107.			−1.49316
$819$	619133.	−	931293.i	0.923030	−	1.38841i
$820$	158977.	−	304835.i	0.236432	−	0.453354i
$821$	−490256.	+	283049.i	−0.727338	+	0.419929i	−0.817448	−	0.576003i	$-0.804612\pi$
$821$	−490256.	+	283049.i	−0.727338	+	0.419929i	0.0901094	+	0.995932i	$0.471278\pi$
$822$	77334.1	+	2441.38i	0.114453	+	0.00361319i
$823$	−314264.	−	181440.i	−0.463975	−	0.267876i	0.249739	−	0.968313i	$-0.419655\pi$
$823$	−314264.	−	181440.i	−0.463975	−	0.267876i	−0.713714	+	0.700437i	$0.752988\pi$
$824$	−224790.	−	129783.i	−0.331073	−	0.191145i
$825$	−10352.2	+	6750.11i	−0.0152098	+	0.00991751i
$826$	174947.	+	303018.i	0.256417	+	0.444128i
$827$	−109531.			−0.160149			−0.0800747	−	0.996789i	$-0.525516\pi$
$827$	−109531.			−0.160149			−0.0800747	+	0.996789i	$0.525516\pi$
$828$	−154105.	−	9739.66i	−0.224779	−	0.0142064i
$829$	−194710.			−0.283321			−0.141661	−	0.989915i	$-0.545244\pi$
$829$	−194710.			−0.283321			−0.141661	+	0.989915i	$0.545244\pi$
$830$	32272.4	+	752038.i	0.0468462	+	1.09165i
$831$	−580325.	−	359932.i	−0.840368	−	0.521216i
$832$	448077.	+	258697.i	0.647300	+	0.373719i
$833$	−90970.3	+	157565.i	−0.131102	+	0.227075i
$834$	−96971.4	−	180913.i	−0.139416	−	0.260098i
$835$	42702.3	+	995086.i	0.0612461	+	1.42721i
$836$		−	94.6656i		−	0.000135450i
$837$	451458.	−	634687.i	0.644416	−	0.905959i
$838$		−	82187.4i		−	0.117035i
$839$	441445.	−	254868.i	0.627122	−	0.362069i	−0.152514	−	0.988301i	$-0.548737\pi$
$839$	441445.	−	254868.i	0.627122	−	0.362069i	0.779637	+	0.626232i	$0.215404\pi$
$840$	−583999.	+	6615.93i	−0.827664	+	0.00937631i
$841$	−353200.	+	611760.i	−0.499377	+	0.864946i
$842$	231771.	−	401439.i	0.326915	−	0.566234i
$843$	598344.	+	371107.i	0.841969	+	0.522209i
$844$	136188.	+	235885.i	0.191185	+	0.331143i
$845$	−889807.	−	464049.i	−1.24619	−	0.649906i
$846$	271940.	+	548212.i	0.379955	+	0.765963i
$847$		−	770939.i		−	1.07462i
$848$	−524746.	−	908887.i	−0.729722	−	1.26392i
$849$	−30995.8	+	981835.i	−0.0430018	+	1.36214i
$850$	1.40091e6	−	120456.i	1.93897	−	0.166722i
$851$	−533397.	−	307957.i	−0.736532	−	0.425237i
$852$	6717.00	−	212771.i	0.00925330	−	0.293111i
$853$	31939.1	−	18440.1i	0.0438960	−	0.0253434i	−0.477891	−	0.878419i	$-0.658599\pi$
$853$	31939.1	−	18440.1i	0.0438960	−	0.0253434i	0.521787	+	0.853076i	$0.325265\pi$
$854$		−	124933.i		−	0.171301i
$855$	331.162	−	16367.2i	0.000453011	−	0.0223894i
$856$	−969480.			−1.32310
$857$	−340133.	−	589127.i	−0.463113	−	0.802135i	0.536001	−	0.844217i	$-0.319934\pi$
$857$	−340133.	−	589127.i	−0.463113	−	0.802135i	−0.999114	+	0.0420823i	$0.986601\pi$
$858$	−12616.5	+	20341.8i	−0.0171382	+	0.0276322i
$859$	548928.	−	950771.i	0.743925	−	1.28852i	−0.206770	−	0.978390i	$-0.566295\pi$
$859$	548928.	−	950771.i	0.743925	−	1.28852i	0.950695	−	0.310126i	$-0.100371\pi$
$860$	49353.5	+	77597.3i	0.0667300	+	0.104918i
$861$	−577857.	−	1.07807e6i	−0.779496	−	1.45425i
$862$	659733.	−	380897.i	0.887879	−	0.512617i
$863$	296486.			0.398092			0.199046	−	0.979990i	$-0.436216\pi$
$863$	296486.			0.398092			0.199046	+	0.979990i	$0.436216\pi$
$864$	−277403.	+	389990.i	−0.371607	+	0.522428i
$865$	726963.	+	379123.i	0.971583	+	0.506696i
$866$	39443.5	−	22772.7i	0.0525944	−	0.0303654i
$867$	653775.	+	1.21970e6i	0.869741	+	1.62262i
$868$	259762.	+	149973.i	0.344775	+	0.199056i
$869$	7630.38	+	4405.40i	0.0101043	+	0.00583373i
$870$	15727.8	+	26542.4i	0.0207792	+	0.0350672i
$871$	575206.	+	996286.i	0.758206	+	1.31325i
$872$	371327.			0.488341
$873$	64901.1	−	1.02689e6i	0.0851577	−	1.34740i
$874$	−13354.1			−0.0174821
$875$	−499562.	−	654069.i	−0.652489	−	0.854295i
$876$	6125.24	−	194026.i	0.00798205	−	0.252843i
$877$	270519.	+	156184.i	0.351722	+	0.203067i	0.665443	−	0.746448i	$-0.268243\pi$
$877$	270519.	+	156184.i	0.351722	+	0.203067i	−0.313722	+	0.949515i	$0.601576\pi$
$878$	88427.0	−	153160.i	0.114709	−	0.198681i
$879$	−732179.	−	23114.3i	−0.947632	−	0.0299160i
$880$	17169.0	−	736.778i	0.0221708	−	0.000951418i
$881$		−	468939.i		−	0.604178i	−0.953280	−	0.302089i	$-0.902316\pi$
$881$		−	468939.i		−	0.604178i	0.953280	−	0.302089i	$-0.0976840\pi$
$882$	77355.8	−	116358.i	0.0994387	−	0.149575i
$883$			331976.i			0.425780i	0.977076	+	0.212890i	$0.0682876\pi$
$883$			331976.i			0.425780i	−0.977076	+	0.212890i	$0.931712\pi$
$884$	589339.	−	340255.i	0.754155	−	0.435412i
$885$	−164974.	−	278411.i	−0.210634	−	0.355468i
$886$	−367797.	+	637044.i	−0.468534	+	0.811525i
$887$	−306317.	+	530557.i	−0.389335	+	0.674349i	−0.992360	−	0.123374i	$-0.960629\pi$
$887$	−306317.	+	530557.i	−0.389335	+	0.674349i	0.603025	+	0.797722i	$0.293962\pi$
$888$	−673134.	+	360807.i	−0.853642	+	0.457562i
$889$	656292.	+	1.13673e6i	0.830412	+	1.43832i
$890$	−407465.	+	781309.i	−0.514411	+	0.986377i
$891$	11476.9	+	8721.79i	0.0144567	+	0.0109863i
$892$			366550.i			0.460684i
$893$	6612.23	+	11452.7i	0.00829172	+	0.0143617i
$894$	−578274.	+	309961.i	−0.723533	+	0.387822i
$895$	43492.3	+	68381.8i	0.0542958	+	0.0853678i
$896$	895019.	+	516740.i	1.11485	+	0.643659i
$897$	717034.	+	444722.i	0.891158	+	0.552718i
$898$	37281.2	−	21524.3i	0.0462314	−	0.0266917i
$899$			31721.2i			0.0392491i
$900$	−269753.	+	6112.67i	−0.333029	+	0.00754650i
$901$	1.63399e6			2.01280
$902$	13090.5	+	22673.5i	0.0160896	+	0.0278679i
$903$	327022.	+	10323.8i	0.401052	+	0.0126609i
$904$	159874.	−	276910.i	0.195633	−	0.338846i
$905$	−62758.5	+	39915.8i	−0.0766259	+	0.0487357i
$906$	−645039.	−	20363.4i	−0.785832	−	0.0248081i
$907$	−96590.6	+	55766.6i	−0.117414	+	0.0677891i	−0.557557	−	0.830139i	$-0.688261\pi$
$907$	−96590.6	+	55766.6i	−0.117414	+	0.0677891i	0.440143	+	0.897928i	$0.354928\pi$
$908$	−145503.			−0.176482
$909$	−23843.8	+	377267.i	−0.0288568	+	0.456584i
$910$	−1.41343e6	−	737125.i	−1.70683	−	0.890140i
$911$	106056.	−	61231.6i	0.127791	−	0.0737801i	−0.434742	−	0.900555i	$-0.643160\pi$
$911$	106056.	−	61231.6i	0.127791	−	0.0737801i	0.562533	+	0.826775i	$0.309827\pi$
$912$	−11998.3	+	19345.1i	−0.0144254	+	0.0232584i
$913$	−12404.4	−	7161.71i	−0.0148811	−	0.00859162i
$914$	964336.	+	556759.i	1.15435	+	0.666462i
$915$	1308.95	+	115543.i	0.00156344	+	0.138007i
$916$	−142299.	−	246469.i	−0.169594	−	0.293746i
$917$	448415.			0.533263
$918$	−682080.	−	1.49148e6i	−0.809376	−	1.76983i
$919$	166880.			0.197594			0.0987971	−	0.995108i	$-0.468501\pi$
$919$	166880.			0.197594			0.0987971	+	0.995108i	$0.468501\pi$
$920$	−18892.1	−	440241.i	−0.0223206	−	0.520133i
$921$	−712649.	+	381988.i	−0.840149	+	0.450330i
$922$	847087.	+	489066.i	0.996475	+	0.575315i
$923$	−581607.	+	1.00737e6i	−0.682694	+	1.18246i
$924$	−2925.93	+	4717.54i	−0.00342705	+	0.00552550i
$925$	−974738.	−	456300.i	−1.13921	−	0.533295i
$926$		−	1.67638e6i		−	1.95501i
$927$	−382205.	+	189592.i	−0.444772	+	0.220628i
$928$		−	19491.4i		−	0.0226333i
$929$	103179.	−	59570.5i	0.119553	−	0.0690239i	−0.439031	−	0.898472i	$-0.644678\pi$
$929$	103179.	−	59570.5i	0.119553	−	0.0690239i	0.558584	+	0.829448i	$0.311345\pi$
$930$	−967718.	−	544190.i	−1.11888	−	0.629194i
$931$	1509.74	−	2614.95i	0.00174182	−	0.00301692i
$932$	1976.77	−	3423.87i	0.00227575	−	0.00394171i
$933$	−13543.9	+	429024.i	−0.0155590	+	0.492854i
$934$	521718.	+	903641.i	0.598056	+	1.03586i
$935$	−12372.1	+	23723.3i	−0.0141521	+	0.0271364i
$936$	937275.	−	464934.i	1.06983	−	0.530688i
$937$			75209.2i			0.0856627i	0.999082	+	0.0428314i	$0.0136378\pi$
$937$			75209.2i			0.0856627i	−0.999082	+	0.0428314i	$0.986362\pi$
$938$	533854.	+	924663.i	0.606760	+	1.05094i
$939$	1.37726e6	+	854210.i	1.56201	+	0.968799i
$940$	183920.	−	116977.i	0.208148	−	0.132387i
$941$	−117440.	−	67804.2i	−0.132629	−	0.0765733i	0.432218	−	0.901769i	$-0.357731\pi$
$941$	−117440.	−	67804.2i	−0.132629	−	0.0765733i	−0.564846	+	0.825196i	$0.691065\pi$
$942$	−324003.	+	173670.i	−0.365130	+	0.195714i
$943$	799222.	−	461431.i	0.898761	−	0.518900i
$944$			450003.i			0.504977i
$945$	−522381.	+	805401.i	−0.584956	+	0.901880i
$946$	−7003.14			−0.00782547
$947$	105097.	+	182033.i	0.117190	+	0.202978i	0.918653	−	0.395066i	$-0.129278\pi$
$947$	105097.	+	182033.i	0.117190	+	0.202978i	−0.801463	+	0.598044i	$0.795945\pi$
$948$	90878.9	+	169547.i	0.101122	+	0.188657i
$949$	−530367.	+	918623.i	−0.588904	+	1.02001i
$950$	−23249.4	+	1999.09i	−0.0257611	+	0.00221506i
$951$	50052.7	−	80701.0i	0.0553435	−	0.0892314i
$952$	−1.09502e6	+	632211.i	−1.20823	+	0.697571i
$953$	364743.			0.401607			0.200803	−	0.979632i	$-0.435645\pi$
$953$	364743.			0.401607			0.200803	+	0.979632i	$0.435645\pi$
$954$	−1.25236e6	−	79150.7i	−1.37604	−	0.0869677i
$955$	554576.	−	1.06339e6i	0.608071	−	1.16597i
$956$	−372013.	+	214782.i	−0.407045	+	0.235008i
$957$	−586.784	−	18.5243i	−0.000640699	−	2.02264e-5i
$958$	−467467.	−	269892.i	−0.509355	−	0.294076i
$959$	−84913.1	−	49024.6i	−0.0923289	−	0.0533061i
$960$	−387125.	−	217697.i	−0.420057	−	0.236217i
$961$	−108991.	−	188778.i	−0.118017	−	0.204411i
$962$	−2.08457e6			−2.25250
$963$	−882222.	+	1.32703e6i	−0.951317	+	1.43096i
$964$	471154.			0.507000
$965$	1.37182e6	−	58869.3i	1.47314	−	0.0632170i
$966$	665486.	+	412751.i	0.713157	+	0.442317i
$967$	702148.	+	405385.i	0.750889	+	0.433526i	0.826015	−	0.563648i	$-0.190603\pi$
$967$	702148.	+	405385.i	0.750889	+	0.433526i	−0.0751260	+	0.997174i	$0.523936\pi$
$968$	360631.	−	624631.i	0.384868	−	0.666611i
$969$	−16743.6	−	31237.3i	−0.0178320	−	0.0332679i
$970$	−1.46535e6	+	62882.7i	−1.55739	+	0.0668325i
$971$		−	822586.i		−	0.872454i	−0.899837	−	0.436227i	$-0.856314\pi$
$971$		−	822586.i		−	0.872454i	0.899837	−	0.436227i	$-0.143686\pi$
$972$	112576.	+	293898.i	0.119155	+	0.311074i
$973$			260116.i			0.274752i
$974$	−1.18980e6	+	686929.i	−1.25417	+	0.724093i
$975$	1.31492e6	+	666916.i	1.38322	+	0.701556i
$976$	80338.6	−	139151.i	0.0843382	−	0.146078i
$977$	659593.	−	1.14245e6i	0.691014	−	1.19687i	−0.280492	−	0.959856i	$-0.590498\pi$
$977$	659593.	−	1.14245e6i	0.691014	−	1.19687i	0.971506	−	0.237015i	$-0.0761689\pi$
$978$	1.60347e6	+	994511.i	1.67642	+	1.03976i
$979$	−8383.79	−	14521.2i	−0.00874732	−	0.0151508i
$980$	−44127.4	−	23013.1i	−0.0459469	−	0.0239620i
$981$	337906.	−	508274.i	0.351122	−	0.528153i
$982$		−	942368.i		−	0.977232i
$983$	−382478.	−	662471.i	−0.395821	−	0.685582i	0.597384	−	0.801955i	$-0.296207\pi$
$983$	−382478.	−	662471.i	−0.395821	−	0.685582i	−0.993206	+	0.116373i	$0.962873\pi$
$984$	36108.3	−	1.14378e6i	0.0372921	−	1.18128i
$985$	−573510.	+	364765.i	−0.591111	+	0.375959i
$986$	57845.5	+	33397.1i	0.0594998	+	0.0343522i
$987$	24469.4	−	775102.i	0.0251182	−	0.795655i
$988$	−9780.67	+	5646.87i	−0.0100197	+	0.00578487i
$989$			246855.i			0.252377i
$990$	10631.6	−	17583.2i	0.0108475	−	0.0179402i
$991$	−1.52049e6			−1.54823			−0.774116	−	0.633043i	$-0.781806\pi$
$991$	−1.52049e6			−1.54823			−0.774116	+	0.633043i	$0.781806\pi$
$992$	350704.	+	607438.i	0.356384	+	0.617275i
$993$	−969108.	+	1.56251e6i	−0.982819	+	1.58462i
$994$	−539795.	+	934952.i	−0.546331	+	0.946274i
$995$	119443.	−	75968.6i	0.120647	−	0.0767340i
$996$	−147739.	−	275626.i	−0.148928	−	0.277844i
$997$	−550617.	+	317899.i	−0.553936	+	0.319815i	−0.750708	−	0.660634i	$-0.770287\pi$
$997$	−550617.	+	317899.i	−0.553936	+	0.319815i	0.196772	+	0.980449i	$0.436954\pi$
$998$	1.76984e6			1.77694
$999$	−118674.	+	1.24972e6i	−0.118911	+	1.25223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.h.a.14.6	✓	44
3.2	odd	2		135.5.h.a.44.17		44
5.4	even	2	inner	45.5.h.a.14.17	yes	44
9.2	odd	6	inner	45.5.h.a.29.17	yes	44
9.4	even	3		405.5.d.a.404.34		44
9.5	odd	6		405.5.d.a.404.12		44
9.7	even	3		135.5.h.a.89.6		44
15.14	odd	2		135.5.h.a.44.6		44
45.4	even	6		405.5.d.a.404.11		44
45.14	odd	6		405.5.d.a.404.33		44
45.29	odd	6	inner	45.5.h.a.29.6	yes	44
45.34	even	6		135.5.h.a.89.17		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.h.a.14.6	✓	44	1.1	even	1	trivial
45.5.h.a.14.17	yes	44	5.4	even	2	inner
45.5.h.a.29.6	yes	44	45.29	odd	6	inner
45.5.h.a.29.17	yes	44	9.2	odd	6	inner
135.5.h.a.44.6		44	15.14	odd	2
135.5.h.a.44.17		44	3.2	odd	2
135.5.h.a.89.6		44	9.7	even	3
135.5.h.a.89.17		44	45.34	even	6
405.5.d.a.404.11		44	45.4	even	6
405.5.d.a.404.12		44	9.5	odd	6
405.5.d.a.404.33		44	45.14	odd	6
405.5.d.a.404.34		44	9.4	even	3

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+(-2.30921 - 3.99967i) q^{2} +(4.25182 + 7.93234i) q^{3} +(-2.66491 + 4.61577i) q^{4} +(-21.0948 + 13.4168i) q^{5} +(21.9084 - 35.3233i) q^{6} +(-45.6166 + 26.3368i) q^{7} -49.2794 q^{8} +(-44.8440 + 67.4538i) q^{9} +(102.375 + 53.3902i) q^{10} +(-1.90271 + 1.09853i) q^{11} +(-47.9446 - 1.51357i) q^{12} +(226.996 + 131.056i) q^{13} +(210.677 + 121.634i) q^{14} +(-196.118 - 110.285i) q^{15} +(156.435 + 270.954i) q^{16} -487.118 q^{17} +(373.347 + 23.5961i) q^{18} +8.08421 q^{19} +(-5.71274 - 133.123i) q^{20} +(-402.866 - 249.867i) q^{21} +(8.78750 + 5.07347i) q^{22} +(178.836 - 309.753i) q^{23} +(-209.527 - 390.901i) q^{24} +(264.982 - 566.047i) q^{25} -1210.54i q^{26} +(-725.735 - 68.9159i) q^{27} -280.741i q^{28} +(25.7123 - 14.8450i) q^{29} +(11.7714 + 1039.08i) q^{30} +(-534.206 + 925.271i) q^{31} +(328.248 - 568.543i) q^{32} +(-16.8039 - 10.4222i) q^{33} +(1124.86 + 1948.31i) q^{34} +(608.920 - 1167.60i) q^{35} +(-191.846 - 386.748i) q^{36} -1722.01i q^{37} +(-18.6682 - 32.3342i) q^{38} +(-74.4349 + 2357.83i) q^{39} +(1039.54 - 661.169i) q^{40} +(2234.51 + 1290.10i) q^{41} +(-69.0838 + 2188.33i) q^{42} +(-597.707 + 345.086i) q^{43} -11.7099i q^{44} +(40.9641 - 2024.59i) q^{45} -1651.88 q^{46} +(817.918 + 1416.68i) q^{47} +(-1484.16 + 2392.94i) q^{48} +(186.752 - 323.464i) q^{49} +(-2875.90 + 247.284i) q^{50} +(-2071.14 - 3863.99i) q^{51} +(-1209.85 + 698.506i) q^{52} -3354.40 q^{53} +(1400.24 + 3061.84i) q^{54} +(25.3986 - 48.7014i) q^{55} +(2247.96 - 1297.86i) q^{56} +(34.3726 + 64.1267i) q^{57} +(-118.750 - 68.5606i) q^{58} +(1245.61 + 719.153i) q^{59} +(1031.69 - 611.332i) q^{60} +(-256.779 - 444.755i) q^{61} +4934.37 q^{62} +(269.116 - 4258.06i) q^{63} +1973.94 q^{64} +(-6546.78 + 280.943i) q^{65} +(-2.88154 + 91.2770i) q^{66} +(3800.99 + 2194.50i) q^{67} +(1298.13 - 2248.42i) q^{68} +(3217.44 + 101.572i) q^{69} +(-6076.13 + 260.746i) q^{70} +4437.85i q^{71} +(2209.88 - 3324.08i) q^{72} +4046.87i q^{73} +(-6887.47 + 3976.48i) q^{74} +(5616.74 - 304.810i) q^{75} +(-21.5437 + 37.3148i) q^{76} +(57.8634 - 100.222i) q^{77} +(9602.45 - 5147.02i) q^{78} +(-2005.14 - 3473.00i) q^{79} +(-6935.28 - 3616.86i) q^{80} +(-2539.03 - 6049.80i) q^{81} -11916.4i q^{82} +(3259.68 + 5645.94i) q^{83} +(2226.93 - 1193.66i) q^{84} +(10275.7 - 6535.55i) q^{85} +(2760.46 + 1593.75i) q^{86} +(227.080 + 140.840i) q^{87} +(93.7642 - 54.1348i) q^{88} +7631.84i q^{89} +(-8192.27 + 4511.35i) q^{90} -13806.4 q^{91} +(953.164 + 1650.93i) q^{92} +(-9610.91 - 303.409i) q^{93} +(3777.49 - 6542.81i) q^{94} +(-170.535 + 108.464i) q^{95} +(5905.53 + 186.433i) q^{96} +(-11001.1 + 6351.50i) q^{97} -1725.00 q^{98} +(11.2250 - 177.607i) 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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