LMFDB - Embedded newform 45.5.h.a.14.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,5,Mod(14,45)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			14.17
Character	$\chi$	$=$	45.14
Dual form			45.5.h.a.29.17

$q$-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} +(1.07184 - 24.9770i) 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} +(-202.683 + 97.6956i) q^{15} +(156.435 + 270.954i) q^{16} +487.118 q^{17} +(-373.347 - 23.5961i) q^{18} +8.08421 q^{19} +(112.432 + 71.5090i) 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} +(-622.702 - 53.5429i) q^{25} -1210.54i q^{26} +(725.735 + 68.9159i) q^{27} +280.741i q^{28} +(25.7123 - 14.8450i) q^{29} +(-858.789 - 585.067i) 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} +(52.8198 - 1230.85i) q^{40} +(2234.51 + 1290.10i) q^{41} +(69.0838 - 2188.33i) q^{42} +(597.707 - 345.086i) q^{43} -11.7099i q^{44} +(1636.73 + 1192.37i) q^{45} -1651.88 q^{46} +(-817.918 - 1416.68i) q^{47} +(1484.16 - 2392.94i) q^{48} +(186.752 - 323.464i) q^{49} +(-1223.80 - 2614.25i) 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} +(89.1936 - 1195.89i) q^{60} +(-256.779 - 444.755i) q^{61} -4934.37 q^{62} +(-269.116 + 4258.06i) q^{63} +1973.94 q^{64} +(-3516.69 + 5529.20i) 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} +(3263.88 - 5131.71i) q^{70} +4437.85i q^{71} +(-2209.88 + 3324.08i) q^{72} -4046.87i q^{73} +(-6887.47 + 3976.48i) q^{74} +(2222.90 + 5167.14i) 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} +(522.115 - 12166.8i) q^{85} +(2760.46 + 1593.75i) q^{86} +(-227.080 - 140.840i) q^{87} +(-93.7642 + 54.1348i) q^{88} +7631.84i q^{89} +(-989.529 + 9299.81i) q^{90} -13806.4 q^{91} +(-953.164 - 1650.93i) q^{92} +(9610.91 + 303.409i) q^{93} +(3777.49 - 6542.81i) q^{94} +(8.66501 - 201.919i) 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	$0.0292281\pi$
$2$	2.30921	+	3.99967i	0.577303	+	0.999918i	−0.418484	+	0.908224i	$0.637439\pi$
$3$	−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
$5$	1.07184	−	24.9770i	0.0428738	−	0.999080i
$5$	1.07184	−	24.9770i	0.0428738	−	0.999080i
$6$	21.9084	−	35.3233i	0.608566	−	0.981204i
$7$	45.6166	−	26.3368i	0.930952	−	0.537485i	0.0438393	−	0.999039i	$-0.486041\pi$
$7$	45.6166	−	26.3368i	0.930952	−	0.537485i	0.887112	+	0.461553i	$0.152708\pi$
$8$	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	−0.355898	−	0.934525i	$-0.615825\pi$
$13$	−226.996	−	131.056i	−1.34317	−	0.775479i	−0.987271	+	0.159045i	$0.949158\pi$
$14$	210.677	+	121.634i	1.07488	+	0.620584i
$15$	−202.683	+	97.6956i	−0.900815	+	0.434203i
$16$	156.435	+	270.954i	0.611075	+	1.05841i
$17$	487.118			1.68553			0.842765	−	0.538281i	$-0.180926\pi$
$17$	487.118			1.68553			0.842765	+	0.538281i	$0.180926\pi$
$18$	−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	$0.496436\pi$
$20$	112.432	+	71.5090i	0.281079	+	0.178772i
$21$	−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	−0.984069	−	0.177789i	$-0.943105\pi$
$23$	−178.836	+	309.753i	−0.338064	+	0.585544i	0.646004	+	0.763334i	$0.276439\pi$
$24$	−209.527	−	390.901i	−0.363762	−	0.678647i
$25$	−622.702	−	53.5429i	−0.996324	−	0.0856687i
$26$		−	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	$0.327714\pi$
$30$	−858.789	−	585.067i	−0.954210	−	0.650075i
$31$	−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	$0.216506\pi$
$37$			1722.01i			1.25786i	−0.777463	+	0.628929i	$0.783494\pi$
$38$	18.6682	+	32.3342i	0.0129281	+	0.0223921i
$39$	−74.4349	+	2357.83i	−0.0489382	+	1.55019i
$40$	52.8198	−	1230.85i	0.0330124	−	0.769282i
$41$	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	−0.329585	−	0.944126i	$-0.606909\pi$
$43$	597.707	−	345.086i	0.323260	−	0.186634i	0.652845	+	0.757492i	$0.273575\pi$
$44$		−	11.7099i		−	0.00604852i
$45$	1636.73	+	1192.37i	0.808261	+	0.588824i
$46$	−1651.88			−0.780661
$47$	−817.918	−	1416.68i	−0.370266	−	0.641320i	0.619340	−	0.785123i	$-0.287400\pi$
$47$	−817.918	−	1416.68i	−0.370266	−	0.641320i	−0.989606	+	0.143803i	$0.954067\pi$
$48$	1484.16	−	2392.94i	0.644167	−	1.03860i
$49$	186.752	−	323.464i	0.0777809	−	0.134720i
$50$	−1223.80	−	2614.25i	−0.489519	−	1.04570i
$51$	−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	$-0.296327\pi$
$53$	3354.40			1.19416			0.597081	+	0.802181i	$0.296327\pi$
$54$	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	$0.600429\pi$
$60$	89.1936	−	1195.89i	0.0247760	−	0.332192i
$61$	−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
$65$	−3516.69	+	5529.20i	−0.832353	+	1.30869i
$66$	−2.88154	+	91.2770i	−0.000661511	+	0.0209543i
$67$	−3800.99	−	2194.50i	−0.846735	−	0.488863i	0.0128128	−	0.999918i	$-0.495921\pi$
$67$	−3800.99	−	2194.50i	−0.846735	−	0.488863i	−0.859548	+	0.511055i	$0.829255\pi$
$68$	−1298.13	+	2248.42i	−0.280737	+	0.486251i
$69$	3217.44	+	101.572i	0.675791	+	0.0213342i
$70$	3263.88	−	5131.71i	0.666097	−	1.04729i
$71$			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	$-0.876026\pi$
$73$		−	4046.87i		−	0.759406i	0.925108	−	0.379703i	$-0.123974\pi$
$74$	−6887.47	+	3976.48i	−1.25775	+	0.726165i
$75$	2222.90	+	5167.14i	0.395182	+	0.918603i
$76$	−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	0.526356	−	0.850264i	$-0.323558\pi$
$83$	−3259.68	−	5645.94i	−0.473172	−	0.819559i	−0.999528	+	0.0307056i	$0.990225\pi$
$84$	2226.93	−	1193.66i	0.315608	−	0.169170i
$85$	522.115	−	12166.8i	0.0722650	−	1.68398i
$86$	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	$0.840002\pi$
$90$	−989.529	+	9299.81i	−0.122164	+	1.14812i
$91$	−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
$95$	8.66501	−	201.919i	0.000960112	−	0.0223733i
$96$	5905.53	+	186.433i	0.640791	+	0.0202293i
$97$	11001.1	−	6351.50i	1.16921	−	0.675045i	0.215718	−	0.976456i	$-0.430791\pi$
$97$	11001.1	−	6351.50i	1.16921	−	0.675045i	0.953494	+	0.301411i	$0.0974575\pi$
$98$	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	0.269364	−	0.963038i	$-0.413187\pi$
$103$	−4561.55	−	2633.61i	−0.429970	−	0.248243i	−0.699334	+	0.714795i	$0.746520\pi$
$104$	−11186.2	−	6458.36i	−1.03423	−	0.597111i
$105$	−6672.75	+	9794.57i	−0.605238	+	0.888397i
$106$	7746.02	+	13416.5i	0.689393	+	1.19406i
$107$	−19673.1			−1.71833			−0.859164	−	0.511700i	$-0.829016\pi$
$107$	−19673.1			−1.71833			−0.859164	+	0.511700i	$0.829016\pi$
$108$	−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	$0.602712\pi$
$110$	−136.139	+	214.048i	−0.0112511	+	0.0176899i
$111$	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	−0.710571	−	0.703625i	$-0.751563\pi$
$113$	3244.24	−	5619.19i	0.254072	−	0.440065i	0.964643	+	0.263560i	$0.0848967\pi$
$114$	177.112	−	285.561i	0.0136282	−	0.0219730i
$115$	7545.02	+	4798.79i	0.570512	+	0.362858i
$116$			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
$120$	−9988.11	+	4814.38i	−0.693619	+	0.334332i
$121$	−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	$0.280993\pi$
$127$			24919.2i			1.54500i	−0.635017	+	0.772498i	$0.719007\pi$
$128$	9810.23	+	16991.8i	0.598769	+	1.03710i
$129$	−5278.69	−	3273.97i	−0.317210	−	0.196741i
$130$	−30235.8	−	1297.51i	−1.78910	−	0.0767760i
$131$	−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
$135$	2499.19	−	18052.8i	0.137130	−	0.990553i
$136$	24004.9			1.29784
$137$	−930.725	−	1612.06i	−0.0495884	−	0.0858897i	0.840166	−	0.542330i	$-0.182458\pi$
$137$	−930.725	−	1612.06i	−0.0495884	−	0.0858897i	−0.889754	+	0.456440i	$0.849124\pi$
$138$	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	$0.125877\pi$
$140$	7012.07	+	300.910i	0.357759	+	0.0153526i
$141$	−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	$0.782355\pi$
$150$	−15533.7	+	20822.9i	−0.690387	+	0.925462i
$151$	−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
$155$	22537.9	+	14334.6i	0.938103	+	0.596654i
$156$	−10684.8	−	6627.00i	−0.439055	−	0.272313i
$157$	7659.23	+	4422.06i	0.310732	+	0.179401i	0.647254	−	0.762274i	$-0.275917\pi$
$157$	7659.23	+	4422.06i	0.310732	+	0.179401i	−0.336522	+	0.941676i	$0.609251\pi$
$158$	9260.58	−	16039.8i	0.370957	−	0.642517i
$159$	−14262.3	−	26608.3i	−0.564152	−	1.05250i
$160$	13848.7	+	8808.05i	0.540964	+	0.344065i
$161$			18839.8i			0.726818i
$162$	18334.0	−	24125.6i	0.698599	−	0.919279i
$163$		−	45394.1i		−	1.70854i	−0.519833	−	0.854268i	$-0.674006\pi$
$163$		−	45394.1i		−	1.70854i	0.519833	−	0.854268i	$-0.325994\pi$
$164$	−11909.6	+	6875.99i	−0.442801	+	0.255651i
$165$	278.326	−	408.540i	0.0102232	−	0.0150060i
$166$	15054.6	−	26075.3i	0.546328	−	0.946267i
$167$	−19920.0	+	34502.5i	−0.714261	+	1.23714i	0.248983	+	0.968508i	$0.419904\pi$
$167$	−19920.0	+	34502.5i	−0.714261	+	1.23714i	−0.963244	+	0.268629i	$0.913430\pi$
$168$	−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	$0.0179005\pi$
$173$	16397.7	+	28401.6i	0.547886	+	0.948966i	−0.450533	+	0.892760i	$0.648766\pi$
$174$	38.9398	−	1233.48i	0.00128616	−	0.0407410i
$175$	−29815.7	+	13957.5i	−0.973575	+	0.455756i
$176$	−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	$-0.0161088\pi$
$180$	−9865.44	+	4377.20i	−0.304489	+	0.135099i
$181$	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
$185$	43010.6	+	1845.72i	1.25670	+	0.0539291i
$186$	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	0.976286	−	0.216484i	$-0.0694590\pi$
$193$	47565.0	+	27461.7i	1.27695	+	0.737246i	0.300662	+	0.953731i	$0.402792\pi$
$194$	50807.8	+	29333.9i	1.34998	+	0.779411i
$195$	58811.9	+	4386.39i	1.54666	+	0.115355i
$196$	995.355	+	1724.01i	0.0259099	+	0.0448773i
$197$	−27187.3			−0.700540			−0.350270	−	0.936649i	$-0.613910\pi$
$197$	−27187.3			−0.700540			−0.350270	+	0.936649i	$0.613910\pi$
$198$	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	$0.522776\pi$
$200$	−30686.4	−	2638.56i	−0.767159	−	0.0659640i
$201$	−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
$205$	34617.8	−	54428.7i	0.823743	−	1.29515i
$206$		−	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
$210$	−54583.9	−	4071.05i	−1.23773	−	0.0923141i
$211$	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
$220$	−292.479	−	12.5512i	−0.00604296	−	0.000259323i
$221$	−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	−0.960037	−	0.279872i	$-0.909708\pi$
$223$	−59559.4	+	34386.7i	−1.19768	+	0.691481i	−0.237643	+	0.971353i	$0.576375\pi$
$224$			34580.0i			0.689175i
$225$	31536.1	−	39602.6i	0.622936	−	0.782273i
$226$	29966.6			0.586706
$227$	−13649.9	−	23642.3i	−0.264897	−	0.458816i	0.702639	−	0.711546i	$-0.252005\pi$
$227$	−13649.9	−	23642.3i	−0.264897	−	0.458816i	−0.967537	+	0.252731i	$0.918671\pi$
$228$	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	$0.996639\pi$
$230$	−1770.56	+	41259.0i	−0.0334699	+	0.779944i
$231$	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	$-0.497825\pi$
$233$	741.777			0.0136635			0.00683174	+	0.999977i	$0.497825\pi$
$234$	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	$0.417395\pi$
$240$	−58177.8	−	39634.8i	−1.01003	−	0.688103i
$241$	−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
$245$	−7878.99	−	5011.21i	−0.131262	−	0.0834853i
$246$	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
$250$	−66607.8	+	27764.7i	−1.06572	+	0.444236i
$251$			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
$255$	−98730.8	+	47589.3i	−1.51835	+	0.731862i
$256$	−29516.2	+	51123.6i	−0.450382	+	0.780084i
$257$	28514.6	−	49388.7i	0.431719	−	0.747759i	−0.565302	−	0.824884i	$-0.691241\pi$
$257$	28514.6	−	49388.7i	0.431719	−	0.747759i	0.997021	+	0.0771245i	$0.0245739\pi$
$258$	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	0.702735	−	0.711452i	$-0.251962\pi$
$263$	−18313.7	−	31720.3i	−0.264768	−	0.458591i	−0.967503	+	0.252861i	$0.918629\pi$
$264$	828.084	+	513.598i	0.0118814	+	0.00736911i
$265$	3595.40	−	83783.0i	0.0511982	−	1.19306i
$266$	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	$-0.115382\pi$
$270$	77976.5	−	31691.9i	1.06964	−	0.434731i
$271$	−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
$275$	1243.64	−	582.180i	0.0164448	−	0.00769824i
$276$	−9043.04	+	14580.3i	−0.118712	+	0.191403i
$277$	65710.4	−	37937.9i	0.856396	−	0.494440i	−0.00640796	−	0.999979i	$-0.502040\pi$
$277$	65710.4	−	37937.9i	0.856396	−	0.494440i	0.862804	+	0.505539i	$0.168706\pi$
$278$	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	−0.224170	−	0.974550i	$-0.571967\pi$
$283$	−94524.2	−	54573.6i	−1.18024	−	0.681412i	−0.956070	+	0.293138i	$0.905300\pi$
$284$	−20484.1	−	11826.5i	−0.253968	−	0.146629i
$285$	−1638.54	+	789.792i	−0.0201728	+	0.00972351i
$286$	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
$290$	1839.72	−	2892.54i	0.0218754	−	0.0343941i
$291$	−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	−0.525507	−	0.850790i	$-0.676124\pi$
$293$	40696.9	−	70489.1i	0.474052	−	0.821082i	0.999559	+	0.0297072i	$0.00945748\pi$
$294$	−7334.39	−	13683.3i	−0.0848534	−	0.158305i
$295$	19297.4	−	30340.8i	0.221745	−	0.348644i
$296$			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
$300$	−29774.1	−	3509.60i	−0.330824	−	0.0389955i
$301$	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	$-0.841864\pi$
$307$		−	89841.0i		−	0.953230i	0.879112	−	0.476615i	$-0.158136\pi$
$308$	−308.402	−	534.168i	−0.00325099	−	0.00563088i
$309$	−1495.79	+	47381.4i	−0.0156659	+	0.496239i
$310$	−5288.88	+	123246.i	−0.0550352	+	1.28248i
$311$	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	$0.704359\pi$
$313$	−155948.	+	90036.4i	−1.59181	+	0.919029i	−0.992997	+	0.118136i	$0.962308\pi$
$314$			40845.9i			0.414275i
$315$	106065.	+	11285.7i	1.06894	+	0.113738i
$316$	21374.1			0.214049
$317$	5275.71	+	9137.79i	0.0525004	+	0.0909333i	0.891081	−	0.453844i	$-0.149948\pi$
$317$	5275.71	+	9137.79i	0.0525004	+	0.0909333i	−0.838581	+	0.544777i	$0.816614\pi$
$318$	73489.5	−	118489.i	0.726727	−	1.17172i
$319$	−32.6153	+	56.4914i	−0.000320509	+	0.000555138i
$320$	2115.76	−	49303.2i	0.0206617	−	0.481477i
$321$	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
$330$	2276.74	+	169.807i	0.0209067	+	0.00155929i
$331$	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
$335$	−58886.2	+	92585.3i	−0.524716	+	0.824997i
$336$	4680.01	−	148246.i	0.0414542	−	1.31312i
$337$	−139338.	−	80447.0i	−1.22690	−	0.708353i	−0.260523	−	0.965468i	$-0.583895\pi$
$337$	−139338.	−	80447.0i	−1.22690	−	0.708353i	−0.966381	+	0.257114i	$0.917228\pi$
$338$	−92695.7	+	160554.i	−0.811384	+	1.40536i
$339$	−58367.3	−	1842.61i	−0.507891	−	0.0160337i
$340$	54767.5	+	34833.3i	0.473768	+	0.301326i
$341$		−	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
$345$	5985.56	−	80253.2i	0.0502883	−	0.674255i
$346$	−75731.4	+	131171.i	−0.632592	+	1.09568i
$347$	−30149.8	+	52221.1i	−0.250395	+	0.433697i	−0.963635	−	0.267223i	$-0.913894\pi$
$347$	−30149.8	+	52221.1i	−0.250395	+	0.433697i	0.713239	+	0.700921i	$0.247227\pi$
$348$	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	0.816466	−	0.577394i	$-0.195930\pi$
$353$	−11439.7	−	19814.2i	−0.0918050	−	0.159011i	−0.908271	+	0.418383i	$0.862597\pi$
$354$	52692.2	−	28243.6i	0.420474	−	0.225379i
$355$	110844.	+	4756.68i	0.879542	+	0.0377440i
$356$	−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	$-0.359142\pi$
$360$	80657.0	+	58759.2i	0.622353	+	0.453389i
$361$	−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
$365$	−101079.	−	4337.62i	−0.758708	−	0.0325586i
$366$	−21335.8	−	673.556i	−0.159275	−	0.00502819i
$367$	43801.9	−	25289.1i	0.325208	−	0.187759i	−0.328504	−	0.944503i	$-0.606544\pi$
$367$	43801.9	−	25289.1i	0.325208	−	0.187759i	0.653712	+	0.756744i	$0.273211\pi$
$368$	−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	0.688876	−	0.724880i	$-0.258105\pi$
$373$	56423.6	+	32576.2i	0.405549	+	0.234144i	−0.283326	+	0.959024i	$0.591438\pi$
$374$	−4280.56	−	2471.38i	−0.0306025	−	0.0176684i
$375$	131442.	−	49983.0i	0.934701	−	0.355435i
$376$	−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	$0.564569\pi$
$380$	908.922	+	578.094i	0.00629447	+	0.00400342i
$381$	197668.	−	105952.i	1.36171	−	0.729894i
$382$	−191875.	−	110779.i	−1.31489	−	0.759154i
$383$	47179.9	−	81718.0i	0.321632	−	0.557084i	−0.659193	−	0.751974i	$-0.729102\pi$
$383$	47179.9	−	81718.0i	0.321632	−	0.557084i	0.980825	+	0.194891i	$0.0624352\pi$
$384$	93073.4	−	150064.i	0.631195	−	1.01769i
$385$	2441.23	+	1552.68i	0.0164698	+	0.0104751i
$386$			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	$0.482265\pi$
$390$	118265.	+	245357.i	0.777547	+	1.61313i
$391$	−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	$0.100932\pi$
$397$			98285.2i			0.623602i	−0.950148	+	0.311801i	$0.899068\pi$
$398$	−13075.3	−	22647.0i	−0.0825437	−	0.142970i
$399$	−3256.86	−	2019.98i	−0.0204575	−	0.0126882i
$400$	−82904.9	−	177099.i	−0.518155	−	1.10687i
$401$	−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
$405$	−153827.	+	56933.1i	−0.937828	+	0.347100i
$406$	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	$-0.0571467\pi$
$410$	297637.	+	12772.5i	1.77059	+	0.0759818i
$411$	−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	$0.650527\pi$
$420$	−27427.2	−	56901.5i	−0.155483	−	0.322571i
$421$	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
$425$	−303330.	−	26081.7i	−1.67933	−	0.144397i
$426$	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
$430$	42766.0	−	67239.9i	0.231293	−	0.363655i
$431$			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	$-0.991628\pi$
$433$		−	9861.68i		−	0.0525987i	0.999654	−	0.0262994i	$-0.00837231\pi$
$434$	−225090.	+	129956.i	−1.19502	+	0.689946i
$435$	−3761.17	+	5520.82i	−0.0198767	+	0.0291760i
$436$	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	0.994414	−	0.105553i	$-0.0336611\pi$
$443$	79637.0	+	137935.i	0.405796	+	0.702859i	−0.588618	+	0.808411i	$0.700328\pi$
$444$	−2606.38	+	82560.9i	−0.0132212	+	0.418802i
$445$	190621.	+	8180.14i	0.962609	+	0.0413086i
$446$	−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	$0.992641\pi$
$450$	231221.	+	34683.4i	1.14183	+	0.171276i
$451$	−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
$455$	−14798.3	+	344842.i	−0.0714806	+	1.66570i
$456$	−1693.86	−	3160.12i	−0.00814608	−	0.0151976i
$457$	208802.	−	120552.i	0.999775	−	0.577220i	0.0915931	−	0.995797i	$-0.470804\pi$
$457$	208802.	−	120552.i	0.999775	−	0.577220i	0.908182	+	0.418576i	$0.137471\pi$
$458$	−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	−0.467088	−	0.884211i	$-0.654697\pi$
$463$	−314347.	−	181488.i	−1.46638	−	0.846616i	−0.999293	+	0.0375951i	$0.988030\pi$
$464$	8044.62	+	4644.56i	0.0373654	+	0.0215729i
$465$	17879.6	−	239727.i	0.0826900	−	1.10869i
$466$	1712.92	+	2966.86i	0.00788797	+	0.0136624i
$467$	225929.			1.03595			0.517974	−	0.855396i	$-0.326686\pi$
$467$	225929.			1.03595			0.517974	+	0.855396i	$0.326686\pi$
$468$	−7137.50	+	112933.i	−0.0325878	+	0.515618i
$469$	−231185.			−1.05103
$470$	−159371.	−	101363.i	−0.721462	−	0.458865i
$471$	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
$475$	−5034.06	−	432.852i	−0.0223116	−	0.00191846i
$476$			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	$0.251357\pi$
$480$	10986.3	−	147303.i	0.0476838	−	0.639334i
$481$	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	$0.215772\pi$
$487$			297474.i			1.25427i	−0.778911	+	0.627134i	$0.784228\pi$
$488$	−12653.9	−	21917.2i	−0.0531356	−	0.0920335i
$489$	−360081.	+	193008.i	−1.50585	+	0.807155i
$490$	1848.93	−	43085.3i	0.00770066	−	0.179447i
$491$	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
$495$	−4424.07	−	470.735i	−0.0180556	−	0.00192117i
$496$	−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	$0.887172\pi$
$500$	−66182.7	−	50548.7i	−0.264731	−	0.202195i
$501$	358382.	+	11313.8i	1.42781	+	0.0450749i
$502$	−193090.	+	111480.i	−0.766217	+	0.442376i
$503$	−76671.8			−0.303040			−0.151520	−	0.988454i	$-0.548417\pi$
$503$	−76671.8			−0.303040			−0.151520	+	0.988454i	$0.548417\pi$
$504$	−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	$0.508737\pi$
$510$	−418332.	−	284997.i	−1.60835	−	1.09572i
$511$	−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
$515$	−70669.1	+	111111.i	−0.266450	+	0.418932i
$516$	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
$520$	−173300.	+	272476.i	−0.640904	+	1.00768i
$521$		−	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	$0.127681\pi$
$523$			213600.i			0.780905i	−0.920623	+	0.390452i	$0.872319\pi$
$524$	39294.5	−	22686.7i	0.143110	−	0.0826244i
$525$	237487.	+	177164.i	0.861631	+	0.642770i
$526$	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
$535$	−21086.5	+	491376.i	−0.0736712	+	1.71675i
$536$	−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
$540$	76667.5	+	59644.9i	0.262920	+	0.204544i
$541$	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
$545$	−8076.49	+	188205.i	−0.0271913	+	0.633634i
$546$	−302475.	+	487687.i	−1.01462	+	1.63590i
$547$	150902.	−	87123.4i	0.504337	−	0.291179i	−0.226166	−	0.974089i	$-0.572619\pi$
$547$	150902.	−	87123.4i	0.504337	−	0.291179i	0.730503	+	0.682910i	$0.239286\pi$
$548$	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
$555$	−168233.	−	349022.i	−0.546166	−	1.13310i
$556$	13160.1	+	22793.9i	0.0425704	+	0.0737342i
$557$	−376126.			−1.21234			−0.606168	−	0.795337i	$-0.707294\pi$
$557$	−376126.			−1.21234			−0.606168	+	0.795337i	$0.707294\pi$
$558$	221277.	−	332842.i	0.710670	−	1.06898i
$559$	−180903.			−0.578924
$560$	221108.	−	347642.i	0.705063	−	1.10855i
$561$	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	$-0.535554\pi$
$563$	255128.	−	441894.i	0.804897	−	1.39412i	0.916360	−	0.400355i	$-0.131113\pi$
$564$	−37070.5	−	69159.9i	−0.116539	−	0.217418i
$565$	−136873.	−	87054.4i	−0.428768	−	0.272705i
$566$		−	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	$0.410175\pi$
$570$	−6942.63	−	4729.81i	−0.0213685	−	0.0145577i
$571$	−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	$-0.943619\pi$
$577$		−	117325.i		−	0.352403i	0.984354	−	0.176201i	$-0.0563810\pi$
$578$	355072.	+	615003.i	1.06282	+	1.84086i
$579$	15597.2	−	494064.i	0.0465254	−	1.47376i
$580$	3952.43	+	169.612i	0.0117492	+	0.000504196i
$581$	−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
$585$	−215263.	−	485166.i	−0.629011	−	1.41768i
$586$	375911.			1.09469
$587$	−92049.2	−	159434.i	−0.267143	−	0.462705i	0.700980	−	0.713181i	$-0.252746\pi$
$587$	−92049.2	−	159434.i	−0.267143	−	0.462705i	−0.968123	+	0.250476i	$0.919413\pi$
$588$	9443.32	−	15225.7i	0.0273130	−	0.0440374i
$589$	−4318.63	+	7480.09i	−0.0124485	+	0.0215614i
$590$	165915.	+	7119.94i	0.476630	+	0.0204537i
$591$	115596.	+	215659.i	0.330953	+	0.617436i
$592$	−466584.	+	269382.i	−1.33133	+	0.768645i
$593$	459312.			1.30617			0.653083	−	0.757286i	$-0.273475\pi$
$593$	459312.			1.30617			0.653083	+	0.757286i	$0.273475\pi$
$594$	−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	$0.615792\pi$
$600$	109543.	+	254633.i	0.304286	+	0.707315i
$601$	−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
$605$	308747.	+	196370.i	0.843514	+	0.536493i
$606$	6120.87	−	193887.i	0.0166674	−	0.527963i
$607$	−516300.	−	298086.i	−1.40128	−	0.809029i	−0.406755	−	0.913537i	$-0.633340\pi$
$607$	−516300.	−	298086.i	−1.40128	−	0.809029i	−0.994524	+	0.104509i	$0.966673\pi$
$608$	−2653.63	+	4596.22i	−0.00717849	+	0.0124335i
$609$	−14067.9	−	444.113i	−0.0379311	−	0.00119745i
$610$	−50033.3	−	31822.3i	−0.134462	−	0.0855207i
$611$			428773.i			1.14854i
$612$	−93451.6	−	188392.i	−0.249508	−	0.502990i
$613$		−	338475.i		−	0.900753i	−0.892839	−	0.450377i	$-0.851290\pi$
$613$		−	338475.i		−	0.900753i	0.892839	−	0.450377i	$-0.148710\pi$
$614$	359334.	−	207462.i	0.953152	−	0.550302i
$615$	−578936.	−	43179.0i	−1.53066	−	0.114162i
$616$	−2851.47	+	4938.89i	−0.00751463	+	0.0130157i
$617$	252706.	−	437700.i	0.663813	−	1.14976i	−0.315792	−	0.948828i	$-0.602270\pi$
$617$	252706.	−	437700.i	0.663813	−	1.14976i	0.979606	−	0.200930i	$-0.0643965\pi$
$618$	−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
$625$	384891.	+	66682.6i	0.985322	+	0.170707i
$626$	−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
$630$	199788.	+	450287.i	0.503371	+	1.13451i
$631$	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
$635$	622408.	+	26709.5i	1.54358	+	0.0662398i
$636$	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	−0.188616	−	0.982051i	$-0.560400\pi$
$643$	−468605.	−	270549.i	−1.13340	−	0.654372i	−0.944789	+	0.327679i	$0.893733\pi$
$644$	−86960.3	−	50206.6i	−0.209676	−	0.121057i
$645$	−87431.9	+	128337.i	−0.210160	+	0.308483i
$646$	9093.60	+	15750.6i	0.0217907	+	0.0377426i
$647$	−692153.			−1.65346			−0.826730	−	0.562599i	$-0.809802\pi$
$647$	−692153.			−1.65346			−0.826730	+	0.562599i	$0.809802\pi$
$648$	−125122.	−	298130.i	−0.297978	−	0.709996i
$649$	−3160.04			−0.00750245
$650$	−64816.1	+	753809.i	−0.153411	+	1.78416i
$651$	446408.	−	239280.i	1.05334	−	0.564605i
$652$	209529.	+	120971.i	0.492888	+	0.284569i
$653$	−3155.89	+	5466.17i	−0.00740109	+	0.0128191i	−0.869702	−	0.493577i	$-0.835689\pi$
$653$	−3155.89	+	5466.17i	−0.00740109	+	0.0128191i	0.862301	+	0.506396i	$0.169023\pi$
$654$	−165083.	+	266166.i	−0.385963	+	0.622297i
$655$	−114218.	+	179582.i	−0.266227	+	0.418582i
$656$			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	$0.243400\pi$
$660$	1144.01	+	2373.41i	0.00262628	+	0.00544860i
$661$	−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
$670$	−506292.	−	21726.6i	−1.12785	−	0.0483996i
$671$	977.151	+	564.159i	0.00217029	+	0.00125301i
$672$	274300.	−	147028.i	0.607418	−	0.325583i
$673$	−413218.	+	238572.i	−0.912324	+	0.526731i	−0.881178	−	0.472784i	$-0.843249\pi$
$673$	−413218.	+	238572.i	−0.912324	+	0.526731i	−0.0311462	+	0.999515i	$0.509916\pi$
$674$		−	743076.i		−	1.63574i
$675$	−448227.	−	81772.0i	−0.983763	−	0.179472i
$676$	−213948.			−0.468183
$677$	104291.	+	180637.i	0.227546	+	0.394122i	0.957080	−	0.289823i	$-0.0935964\pi$
$677$	104291.	+	180637.i	0.227546	+	0.394122i	−0.729534	+	0.683944i	$0.760263\pi$
$678$	−127413.	−	237705.i	−0.277174	−	0.517105i
$679$	334556.	−	579468.i	0.725654	−	1.25687i
$680$	25729.5	−	599570.i	0.0556434	−	1.29665i
$681$	−129502.	+	208798.i	−0.279243	+	0.450229i
$682$	9388.67	−	5420.55i	0.0201853	−	0.0116540i
$683$	166389.			0.356683			0.178342	−	0.983969i	$-0.442927\pi$
$683$	166389.			0.356683			0.178342	+	0.983969i	$0.442927\pi$
$684$	−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
$690$	334809.	−	161381.i	0.703232	−	0.338965i
$691$	−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
$695$	−104172.	−	66255.5i	−0.215665	−	0.137168i
$696$	−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
$700$	15031.7	−	174818.i	0.0306769	−	0.356772i
$701$		−	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
$705$	304182.	+	207230.i	0.612005	+	0.416940i
$706$	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
$715$	617.248	−	14383.6i	0.00120739	−	0.0281356i
$716$	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	$0.969709\pi$
$720$	−67034.6	+	630006.i	−0.129311	+	1.21529i
$721$	−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
$725$	−16806.0	+	7867.31i	−0.0319733	+	0.0149675i
$726$	287406.	+	536195.i	0.545285	+	1.01730i
$727$	40935.0	−	23633.8i	0.0774508	−	0.0447163i	−0.460774	−	0.887517i	$-0.652428\pi$
$727$	40935.0	−	23633.8i	0.0774508	−	0.0447163i	0.538225	+	0.842801i	$0.319095\pi$
$728$	−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	0.420423	−	0.907328i	$-0.361882\pi$
$733$	−83352.7	−	48123.7i	−0.155136	−	0.0895676i	−0.575558	+	0.817761i	$0.695215\pi$
$734$	202296.	+	116796.i	0.375487	+	0.216788i
$735$	−6250.51	+	83805.6i	−0.0115702	+	0.155131i
$736$	−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	$0.359663\pi$
$740$	−123139.	+	193608.i	−0.224870	+	0.353558i
$741$	−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	$0.370472\pi$
$743$	−329802.	+	571234.i	−0.597415	+	1.03475i	−0.993201	+	0.116410i	$0.962861\pi$
$744$	473620.	+	14951.8i	0.855626	+	0.0270114i
$745$	−211780.	+	332977.i	−0.381569	+	0.599931i
$746$			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
$750$	503444.	+	410305.i	0.895011	+	0.729431i
$751$	−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	$-0.998869\pi$
$757$		−	4073.41i		−	0.00710831i	0.999994	−	0.00355415i	$-0.00113132\pi$
$758$	−133648.	−	231485.i	−0.232608	−	0.402889i
$759$	−6233.43	+	3341.19i	−0.0108204	+	0.00579986i
$760$	427.006	−	9950.46i	0.000739277	−	0.0172273i
$761$	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
$765$	797281.	+	580825.i	1.36235	+	0.992481i
$766$	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	$0.976806\pi$
$770$	−572.874	+	13349.6i	−0.000966224	+	0.0225158i
$771$	−513007.	−	16195.2i	−0.863008	−	0.0272445i
$772$	−253513.	+	146366.i	−0.425370	+	0.245587i
$773$	617606.			1.03360			0.516800	−	0.856106i	$-0.327123\pi$
$773$	617606.			1.03360			0.516800	+	0.856106i	$0.327123\pi$
$774$	−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
$780$	−176975.	+	259772.i	−0.290886	+	0.426976i
$781$	−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
$785$	118659.	−	186565.i	0.192559	−	0.302755i
$786$	−311877.	+	167169.i	−0.504821	+	0.270590i
$787$	359252.	+	207414.i	0.580029	+	0.334880i	0.761145	−	0.648582i	$-0.224638\pi$
$787$	359252.	+	207414.i	0.580029	+	0.334880i	−0.181116	+	0.983462i	$0.557971\pi$
$788$	72451.7	−	125490.i	0.116680	−	0.202096i
$789$	−173749.	+	280140.i	−0.279106	+	0.450008i
$790$	−390700.	−	248494.i	−0.626022	−	0.398163i
$791$		−	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
$795$	−679882.	+	327711.i	−1.07572	+	0.518509i
$796$	15089.3	−	26135.5i	0.0238146	−	0.0412481i
$797$	−235403.	+	407730.i	−0.370592	+	0.641884i	−0.989657	−	0.143456i	$-0.954178\pi$
$797$	−235403.	+	407730.i	−0.370592	+	0.641884i	0.619065	+	0.785340i	$0.287512\pi$
$798$	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
$805$	470563.	+	20193.4i	0.726150	+	0.0311614i
$806$	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	$-0.0716430\pi$
$810$	−582933.	−	483788.i	−0.888482	−	0.737369i
$811$	−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
$815$	−1.13381e6	−	48655.4i	−1.70697	−	0.0732514i
$816$	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	0.713714	−	0.700437i	$-0.247012\pi$
$823$	314264.	+	181440.i	0.463975	+	0.267876i	−0.249739	+	0.968313i	$0.580345\pi$
$824$	−224790.	−	129783.i	−0.331073	−	0.191145i
$825$	−9905.78	−	7389.63i	−0.0145539	−	0.0108571i
$826$	174947.	+	303018.i	0.256417	+	0.444128i
$827$	109531.			0.160149			0.0800747	−	0.996789i	$-0.474484\pi$
$827$	109531.			0.160149			0.0800747	+	0.996789i	$0.474484\pi$
$828$	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	$0.545244\pi$
$830$	−635148.	−	403968.i	−0.921974	−	0.586395i
$831$	−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
$835$	840418.	+	534524.i	1.20538	+	0.766645i
$836$		−	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	$0.215404\pi$
$840$	−328829.	+	482670.i	−0.466027	+	0.684057i
$841$	−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
$850$	−596134.	−	1.27345e6i	−0.825099	−	1.76256i
$851$	−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	−0.521787	−	0.853076i	$-0.674735\pi$
$853$	−31939.1	+	18440.1i	−0.0438960	+	0.0253434i	0.477891	+	0.878419i	$0.341401\pi$
$854$		−	124933.i		−	0.171301i
$855$	13231.7	+	9639.36i	0.0181002	+	0.0131861i
$856$	−969480.			−1.32310
$857$	340133.	+	589127.i	0.463113	+	0.802135i	0.999114	−	0.0420823i	$-0.0133992\pi$
$857$	340133.	+	589127.i	0.463113	+	0.802135i	−0.536001	+	0.844217i	$0.680066\pi$
$858$	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	$-0.100371\pi$
$860$	91878.0	+	3942.78i	0.124227	+	0.00533096i
$861$	−577857.	−	1.07807e6i	−0.779496	−	1.45425i
$862$	−659733.	+	380897.i	−0.887879	+	0.512617i
$863$	−296486.			−0.398092			−0.199046	−	0.979990i	$-0.563784\pi$
$863$	−296486.			−0.398092			−0.199046	+	0.979990i	$0.563784\pi$
$864$	−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
$870$	−30766.8	−	2294.69i	−0.0406484	−	0.00303170i
$871$	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
$875$	316659.	+	759668.i	0.413596	+	0.992220i
$876$	6125.24	−	194026.i	0.00798205	−	0.252843i
$877$	−270519.	−	156184.i	−0.351722	−	0.203067i	0.313722	−	0.949515i	$-0.398424\pi$
$877$	−270519.	−	156184.i	−0.351722	−	0.203067i	−0.665443	+	0.746448i	$0.731757\pi$
$878$	−88427.0	+	153160.i	−0.114709	+	0.198681i
$879$	−732179.	−	23114.3i	−0.947632	−	0.0299160i
$880$	−9222.59	+	14500.4i	−0.0119093	+	0.0187247i
$881$		−	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	$-0.931712\pi$
$883$		−	331976.i		−	0.425780i	0.977076	−	0.212890i	$-0.0682876\pi$
$884$	589339.	−	340255.i	0.754155	−	0.435412i
$885$	−322722.	−	24069.8i	−0.412043	−	0.0307316i
$886$	−367797.	+	637044.i	−0.468534	+	0.811525i
$887$	306317.	−	530557.i	0.389335	−	0.674349i	−0.603025	−	0.797722i	$-0.706038\pi$
$887$	306317.	−	530557.i	0.389335	−	0.674349i	0.992360	+	0.123374i	$0.0393714\pi$
$888$	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
$895$	−80966.5	−	3474.53i	−0.101079	−	0.00433761i
$896$	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
$900$	98755.1	+	251101.i	0.121920	+	0.310001i
$901$	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
$905$	3188.81	−	74308.3i	0.00389342	−	0.0907278i
$906$	−645039.	−	20363.4i	−0.785832	−	0.0248081i
$907$	96590.6	−	55766.6i	0.117414	−	0.0677891i	−0.440143	−	0.897928i	$-0.645072\pi$
$907$	96590.6	−	55766.6i	0.117414	−	0.0677891i	0.557557	+	0.830139i	$0.311739\pi$
$908$	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
$915$	95495.5	+	65058.2i	0.114062	+	0.0777069i
$916$	−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	$0.468501\pi$
$920$	371814.	+	236481.i	0.439288	+	0.279397i
$921$	−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
$925$	92201.3	−	1.07230e6i	0.107759	−	1.25323i
$926$		−	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	$0.311345\pi$
$930$	1.00012e6	−	482067.i	1.15634	−	0.557367i
$931$	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	$-0.986362\pi$
$937$		−	75209.2i		−	0.0856627i	0.999082	−	0.0428314i	$-0.0136378\pi$
$938$	−533854.	−	924663.i	−0.606760	−	1.05094i
$939$	1.37726e6	+	854210.i	1.56201	+	0.968799i
$940$	9345.12	−	217768.i	0.0105762	−	0.246455i
$941$	−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
$945$	−361449.	−	889330.i	−0.404747	−	0.995862i
$946$	−7003.14			−0.00782547
$947$	−105097.	−	182033.i	−0.117190	−	0.202978i	0.801463	−	0.598044i	$-0.204055\pi$
$947$	−105097.	−	182033.i	−0.117190	−	0.202978i	−0.918653	+	0.395066i	$0.870722\pi$
$948$	−90878.9	−	169547.i	−0.101122	−	0.188657i
$949$	−530367.	+	918623.i	−0.588904	+	1.02001i
$950$	−9893.44	−	21134.1i	−0.0109623	−	0.0234173i
$951$	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	$-0.564355\pi$
$953$	−364743.			−0.401607			−0.200803	+	0.979632i	$0.564355\pi$
$954$	−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
$960$	−400085.	+	192846.i	−0.434120	+	0.209251i
$961$	−108991.	−	188778.i	−0.118017	−	0.204411i
$962$	2.08457e6			2.25250
$963$	882222.	−	1.32703e6i	0.951317	−	1.43096i
$964$	471154.			0.507000
$965$	736893.	−	1.15860e6i	0.791316	−	1.24417i
$966$	665486.	+	412751.i	0.713157	+	0.442317i
$967$	−702148.	−	405385.i	−0.750889	−	0.433526i	0.0751260	−	0.997174i	$-0.476064\pi$
$967$	−702148.	−	405385.i	−0.750889	−	0.433526i	−0.826015	+	0.563648i	$0.809397\pi$
$968$	−360631.	+	624631.i	−0.384868	+	0.666611i
$969$	−16743.6	−	31237.3i	−0.0178320	−	0.0332679i
$970$	787131.	−	1.23759e6i	0.836573	−	1.31532i
$971$		−	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
$975$	172596.	−	1.46424e6i	0.181561	−	1.54030i
$976$	80338.6	−	139151.i	0.0843382	−	0.146078i
$977$	−659593.	+	1.14245e6i	−0.691014	+	1.19687i	0.280492	+	0.959856i	$0.409502\pi$
$977$	−659593.	+	1.14245e6i	−0.691014	+	1.19687i	−0.971506	+	0.237015i	$0.923831\pi$
$978$	−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	0.993206	−	0.116373i	$-0.0371267\pi$
$983$	382478.	+	662471.i	0.395821	+	0.685582i	−0.597384	+	0.801955i	$0.703793\pi$
$984$	36108.3	−	1.14378e6i	0.0372921	−	1.18128i
$985$	−29140.5	+	679057.i	−0.0300348	+	0.699896i
$986$	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
$990$	−8333.32	−	18781.8i	−0.00850252	−	0.0191632i
$991$	−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
$995$	−6069.01	+	141425.i	−0.00613016	+	0.142850i
$996$	−147739.	−	275626.i	−0.148928	−	0.277844i
$997$	550617.	−	317899.i	0.553936	−	0.319815i	−0.196772	−	0.980449i	$-0.563046\pi$
$997$	550617.	−	317899.i	0.553936	−	0.319815i	0.750708	+	0.660634i	$0.229713\pi$
$998$	−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.14.17	yes	44
3.2	odd	2		135.5.h.a.44.6		44
5.4	even	2	inner	45.5.h.a.14.6	✓	44
9.2	odd	6	inner	45.5.h.a.29.6	yes	44
9.4	even	3		405.5.d.a.404.11		44
9.5	odd	6		405.5.d.a.404.33		44
9.7	even	3		135.5.h.a.89.17		44
15.14	odd	2		135.5.h.a.44.17		44
45.4	even	6		405.5.d.a.404.34		44
45.14	odd	6		405.5.d.a.404.12		44
45.29	odd	6	inner	45.5.h.a.29.17	yes	44
45.34	even	6		135.5.h.a.89.6		44

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

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} +(1.07184 - 24.9770i) 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} +(-202.683 + 97.6956i) q^{15} +(156.435 + 270.954i) q^{16} +487.118 q^{17} +(-373.347 - 23.5961i) q^{18} +8.08421 q^{19} +(112.432 + 71.5090i) 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} +(-622.702 - 53.5429i) q^{25} -1210.54i q^{26} +(725.735 + 68.9159i) q^{27} +280.741i q^{28} +(25.7123 - 14.8450i) q^{29} +(-858.789 - 585.067i) 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} +(52.8198 - 1230.85i) q^{40} +(2234.51 + 1290.10i) q^{41} +(69.0838 - 2188.33i) q^{42} +(597.707 - 345.086i) q^{43} -11.7099i q^{44} +(1636.73 + 1192.37i) q^{45} -1651.88 q^{46} +(-817.918 - 1416.68i) q^{47} +(1484.16 - 2392.94i) q^{48} +(186.752 - 323.464i) q^{49} +(-1223.80 - 2614.25i) 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} +(89.1936 - 1195.89i) q^{60} +(-256.779 - 444.755i) q^{61} -4934.37 q^{62} +(-269.116 + 4258.06i) q^{63} +1973.94 q^{64} +(-3516.69 + 5529.20i) 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} +(3263.88 - 5131.71i) q^{70} +4437.85i q^{71} +(-2209.88 + 3324.08i) q^{72} -4046.87i q^{73} +(-6887.47 + 3976.48i) q^{74} +(2222.90 + 5167.14i) 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} +(522.115 - 12166.8i) q^{85} +(2760.46 + 1593.75i) q^{86} +(-227.080 - 140.840i) q^{87} +(-93.7642 + 54.1348i) q^{88} +7631.84i q^{89} +(-989.529 + 9299.81i) q^{90} -13806.4 q^{91} +(-953.164 - 1650.93i) q^{92} +(9610.91 + 303.409i) q^{93} +(3777.49 - 6542.81i) q^{94} +(8.66501 - 201.919i) 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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