LMFDB - Embedded newform 45.5.h.a.14.1

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			14.1
Character	$\chi$	$=$	45.14
Dual form			45.5.h.a.29.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.75365 - 6.50151i) q^{2} +(3.49115 - 8.29529i) q^{3} +(-20.1797 + 34.9523i) q^{4} +(2.78274 + 24.8446i) q^{5} +(-67.0364 + 8.43986i) q^{6} +(-60.4872 + 34.9223i) q^{7} +182.874 q^{8} +(-56.6237 - 57.9202i) q^{9} +(151.082 - 111.350i) q^{10} +(-45.1408 + 26.0621i) q^{11} +(219.489 + 289.421i) q^{12} +(-104.287 - 60.2100i) q^{13} +(454.095 + 262.172i) q^{14} +(215.809 + 63.6528i) q^{15} +(-363.567 - 629.717i) q^{16} -80.3611 q^{17} +(-164.023 + 585.552i) q^{18} -254.262 q^{19} +(-924.533 - 404.095i) q^{20} +(78.5207 + 623.678i) q^{21} +(338.885 + 195.656i) q^{22} +(125.271 - 216.975i) q^{23} +(638.439 - 1516.99i) q^{24} +(-609.513 + 138.272i) q^{25} +904.028i q^{26} +(-678.147 + 267.502i) q^{27} -2818.89i q^{28} +(250.329 - 144.527i) q^{29} +(-396.230 - 1642.01i) q^{30} +(-11.0660 + 19.1668i) q^{31} +(-1266.42 + 2193.50i) q^{32} +(58.5990 + 465.443i) q^{33} +(301.647 + 522.468i) q^{34} +(-1035.95 - 1405.60i) q^{35} +(3167.10 - 810.316i) q^{36} +2475.27i q^{37} +(954.410 + 1653.09i) q^{38} +(-863.541 + 654.887i) q^{39} +(508.889 + 4543.43i) q^{40} +(421.197 + 243.178i) q^{41} +(3760.11 - 2851.57i) q^{42} +(-86.4441 + 49.9085i) q^{43} -2103.70i q^{44} +(1281.44 - 1567.97i) q^{45} -1880.89 q^{46} +(-1739.31 - 3012.56i) q^{47} +(-6492.95 + 817.460i) q^{48} +(1238.63 - 2145.37i) q^{49} +(3186.87 + 3443.73i) q^{50} +(-280.553 + 666.619i) q^{51} +(4208.96 - 2430.04i) q^{52} +2919.00 q^{53} +(4284.69 + 3404.87i) q^{54} +(-773.118 - 1048.98i) q^{55} +(-11061.5 + 6386.36i) q^{56} +(-887.667 + 2109.18i) q^{57} +(-1879.29 - 1085.01i) q^{58} +(-1516.90 - 875.781i) q^{59} +(-6579.77 + 6258.51i) q^{60} +(-2791.13 - 4834.38i) q^{61} +166.151 q^{62} +(5447.72 + 1526.00i) q^{63} +7380.58 q^{64} +(1205.69 - 2758.52i) q^{65} +(2806.12 - 2128.09i) q^{66} +(-3328.98 - 1921.99i) q^{67} +(1621.67 - 2808.81i) q^{68} +(-1362.53 - 1796.65i) q^{69} +(-5249.94 + 12011.4i) q^{70} -988.642i q^{71} +(-10355.0 - 10592.1i) q^{72} +6017.38i q^{73} +(16093.0 - 9291.29i) q^{74} +(-980.893 + 5538.82i) q^{75} +(5130.94 - 8887.05i) q^{76} +(1820.29 - 3152.84i) q^{77} +(7499.18 + 3156.10i) q^{78} +(-31.6455 - 54.8116i) q^{79} +(14633.4 - 10785.0i) q^{80} +(-148.505 + 6559.32i) q^{81} -3651.22i q^{82} +(-727.823 - 1260.63i) q^{83} +(-23383.5 - 9841.16i) q^{84} +(-223.624 - 1996.54i) q^{85} +(648.961 + 374.678i) q^{86} +(-324.961 - 2581.12i) q^{87} +(-8255.07 + 4766.06i) q^{88} +12837.4i q^{89} +(-15004.3 - 2445.66i) q^{90} +8410.68 q^{91} +(5055.85 + 8756.99i) q^{92} +(120.361 + 158.710i) q^{93} +(-13057.5 + 22616.2i) q^{94} +(-707.544 - 6317.05i) q^{95} +(13774.5 + 18163.1i) q^{96} +(-6340.40 + 3660.63i) q^{97} -18597.5 q^{98} +(4065.56 + 1138.84i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 162 q^{4} + 6 q^{5} - 36 q^{6} - 126 q^{9} + 28 q^{10} + 228 q^{11} + 282 q^{14} + 450 q^{15} - 1058 q^{16} - 8 q^{19} - 2196 q^{20} + 1056 q^{21} + 2970 q^{24} - 148 q^{25} + 2370 q^{29} + 1068 q^{30}+ \cdots + 44568 q^{99}+O(q^{100}) $ 44 * q - 162 * q^4 + 6 * q^5 - 36 * q^6 - 126 * q^9 + 28 * q^10 + 228 * q^11 + 282 * q^14 + 450 * q^15 - 1058 * q^16 - 8 * q^19 - 2196 * q^20 + 1056 * q^21 + 2970 * q^24 - 148 * q^25 + 2370 * q^29 + 1068 * q^30 - 1112 * q^31 - 436 * q^34 - 648 * q^36 - 6420 * q^39 - 850 * q^40 + 1830 * q^41 - 1944 * q^45 - 5668 * q^46 + 5396 * q^49 + 13524 * q^50 - 1500 * q^51 + 17766 * q^54 - 3072 * q^55 - 8250 * q^56 - 27348 * q^59 - 28722 * q^60 + 2782 * q^61 + 8348 * q^64 - 24906 * q^65 + 27240 * q^66 + 19662 * q^69 + 4782 * q^70 + 64728 * q^74 + 28446 * q^75 - 1776 * q^76 + 7900 * q^79 - 47754 * q^81 - 113166 * q^84 + 6766 * q^85 + 9192 * q^86 + 10674 * q^90 + 1560 * q^91 - 18826 * q^94 + 58746 * q^95 + 1902 * q^96 + 44568 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−3.75365	−	6.50151i	−0.938412	−	1.62538i	−0.768434	−	0.639929i	$-0.778964\pi$
$2$	−3.75365	−	6.50151i	−0.938412	−	1.62538i	−0.169977	−	0.985448i	$-0.554369\pi$
$3$	3.49115	−	8.29529i	0.387906	−	0.921699i
$3$	3.49115	−	8.29529i	0.387906	−	0.921699i
$4$	−20.1797	+	34.9523i	−1.26123	+	2.18452i
$5$	2.78274	+	24.8446i	0.111309	+	0.993786i
$5$	2.78274	+	24.8446i	0.111309	+	0.993786i
$6$	−67.0364	+	8.43986i	−1.86212	+	0.234440i
$7$	−60.4872	+	34.9223i	−1.23443	+	0.712700i	−0.967951	−	0.251140i	$-0.919194\pi$
$7$	−60.4872	+	34.9223i	−1.23443	+	0.712700i	−0.266481	+	0.963840i	$0.585861\pi$
$8$	182.874			2.85740
$9$	−56.6237	−	57.9202i	−0.699058	−	0.715065i
$10$	151.082	−	111.350i	1.51082	−	1.11350i
$11$	−45.1408	+	26.0621i	−0.373065	+	0.215389i	−0.674797	−	0.738004i	$-0.735769\pi$
$11$	−45.1408	+	26.0621i	−0.373065	+	0.215389i	0.301732	+	0.953393i	$0.402435\pi$
$12$	219.489	+	289.421i	1.52423	+	2.00986i
$13$	−104.287	−	60.2100i	−0.617082	−	0.356272i	0.158650	−	0.987335i	$-0.449286\pi$
$13$	−104.287	−	60.2100i	−0.617082	−	0.356272i	−0.775732	+	0.631063i	$0.782619\pi$
$14$	454.095	+	262.172i	2.31681	+	1.33761i
$15$	215.809	+	63.6528i	0.959149	+	0.282901i
$16$	−363.567	−	629.717i	−1.42018	−	2.45983i
$17$	−80.3611			−0.278066			−0.139033	−	0.990288i	$-0.544399\pi$
$17$	−80.3611			−0.278066			−0.139033	+	0.990288i	$0.544399\pi$
$18$	−164.023	+	585.552i	−0.506245	+	1.80726i
$19$	−254.262			−0.704327			−0.352163	−	0.935939i	$-0.614554\pi$
$19$	−254.262			−0.704327			−0.352163	+	0.935939i	$0.614554\pi$
$20$	−924.533	−	404.095i	−2.31133	−	1.01024i
$21$	78.5207	+	623.678i	0.178051	+	1.41423i
$22$	338.885	+	195.656i	0.700177	+	0.404247i
$23$	125.271	−	216.975i	0.236806	−	0.410161i	−0.722990	−	0.690859i	$-0.757233\pi$
$23$	125.271	−	216.975i	0.236806	−	0.410161i	0.959796	+	0.280698i	$0.0905659\pi$
$24$	638.439	−	1516.99i	1.10840	−	2.63366i
$25$	−609.513	+	138.272i	−0.975220	+	0.221235i
$26$			904.028i			1.33732i
$27$	−678.147	+	267.502i	−0.930243	+	0.366944i
$28$		−	2818.89i		−	3.59552i
$29$	250.329	−	144.527i	0.297656	−	0.171852i	−0.343733	−	0.939067i	$-0.611692\pi$
$29$	250.329	−	144.527i	0.297656	−	0.171852i	0.641389	+	0.767216i	$0.278358\pi$
$30$	−396.230	−	1642.01i	−0.440255	−	1.82446i
$31$	−11.0660	+	19.1668i	−0.0115151	+	0.0199447i	−0.871726	−	0.489995i	$-0.836999\pi$
$31$	−11.0660	+	19.1668i	−0.0115151	+	0.0199447i	0.860210	+	0.509939i	$0.170332\pi$
$32$	−1266.42	+	2193.50i	−1.23674	+	2.14209i
$33$	58.5990	+	465.443i	0.0538100	+	0.427404i
$34$	301.647	+	522.468i	0.260941	+	0.451962i
$35$	−1035.95	−	1405.60i	−0.845675	−	1.14743i
$36$	3167.10	−	810.316i	2.44375	−	0.625244i
$37$			2475.27i			1.80809i	0.427440	+	0.904044i	$0.359415\pi$
$37$			2475.27i			1.80809i	−0.427440	+	0.904044i	$0.640585\pi$
$38$	954.410	+	1653.09i	0.660949	+	1.14480i
$39$	−863.541	+	654.887i	−0.567745	+	0.430564i
$40$	508.889	+	4543.43i	0.318055	+	2.83964i
$41$	421.197	+	243.178i	0.250563	+	0.144663i	0.620022	−	0.784584i	$-0.287124\pi$
$41$	421.197	+	243.178i	0.250563	+	0.144663i	−0.369459	+	0.929247i	$0.620457\pi$
$42$	3760.11	−	2851.57i	2.13158	−	1.61654i
$43$	−86.4441	+	49.9085i	−0.0467518	+	0.0269922i	−0.523194	−	0.852214i	$-0.675260\pi$
$43$	−86.4441	+	49.9085i	−0.0467518	+	0.0269922i	0.476442	+	0.879206i	$0.341926\pi$
$44$		−	2103.70i		−	1.08662i
$45$	1281.44	−	1567.97i	0.632809	−	0.774308i
$46$	−1880.89			−0.888888
$47$	−1739.31	−	3012.56i	−0.787372	−	1.36377i	−0.927572	−	0.373645i	$-0.878108\pi$
$47$	−1739.31	−	3012.56i	−0.787372	−	1.36377i	0.140199	−	0.990123i	$-0.455226\pi$
$48$	−6492.95	+	817.460i	−2.81812	+	0.354800i
$49$	1238.63	−	2145.37i	0.515881	−	0.893533i
$50$	3186.87	+	3443.73i	1.27475	+	1.37749i
$51$	−280.553	+	666.619i	−0.107863	+	0.256293i
$52$	4208.96	−	2430.04i	1.55657	−	0.898685i
$53$	2919.00			1.03916			0.519581	−	0.854421i	$-0.326088\pi$
$53$	2919.00			1.03916			0.519581	+	0.854421i	$0.326088\pi$
$54$	4284.69	+	3404.87i	1.46937	+	1.16765i
$55$	−773.118	−	1048.98i	−0.255576	−	0.346772i
$56$	−11061.5	+	6386.36i	−3.52727	+	2.03647i
$57$	−887.667	+	2109.18i	−0.273212	+	0.649177i
$58$	−1879.29	−	1085.01i	−0.558648	−	0.322535i
$59$	−1516.90	−	875.781i	−0.435765	−	0.251589i	0.266035	−	0.963963i	$-0.414286\pi$
$59$	−1516.90	−	875.781i	−0.435765	−	0.251589i	−0.701800	+	0.712374i	$0.747620\pi$
$60$	−6579.77	+	6258.51i	−1.82771	+	1.73848i
$61$	−2791.13	−	4834.38i	−0.750103	−	1.29922i	−0.947772	−	0.318947i	$-0.896671\pi$
$61$	−2791.13	−	4834.38i	−0.750103	−	1.29922i	0.197670	−	0.980269i	$-0.436663\pi$
$62$	166.151			0.0432235
$63$	5447.72	+	1526.00i	1.37257	+	0.384480i
$64$	7380.58			1.80190
$65$	1205.69	−	2758.52i	0.285371	−	0.652903i
$66$	2806.12	−	2128.09i	0.644197	−	0.488542i
$67$	−3328.98	−	1921.99i	−0.741586	−	0.428155i	0.0810595	−	0.996709i	$-0.474170\pi$
$67$	−3328.98	−	1921.99i	−0.741586	−	0.428155i	−0.822646	+	0.568554i	$0.807503\pi$
$68$	1621.67	−	2808.81i	0.350706	−	0.607441i
$69$	−1362.53	−	1796.65i	−0.286186	−	0.377368i
$70$	−5249.94	+	12011.4i	−1.07142	+	2.45130i
$71$		−	988.642i		−	0.196120i	−0.995180	−	0.0980601i	$-0.968736\pi$
$71$		−	988.642i		−	0.196120i	0.995180	−	0.0980601i	$-0.0312637\pi$
$72$	−10355.0	−	10592.1i	−1.99749	−	2.04323i
$73$			6017.38i			1.12918i	0.825373	+	0.564588i	$0.190965\pi$
$73$			6017.38i			1.12918i	−0.825373	+	0.564588i	$0.809035\pi$
$74$	16093.0	−	9291.29i	2.93882	−	1.69673i
$75$	−980.893	+	5538.82i	−0.174381	+	0.984678i
$76$	5130.94	−	8887.05i	0.888320	−	1.53862i
$77$	1820.29	−	3152.84i	0.307015	−	0.531766i
$78$	7499.18	+	3156.10i	1.23261	+	0.518754i
$79$	−31.6455	−	54.8116i	−0.00507058	−	0.00878250i	0.863479	−	0.504385i	$-0.168281\pi$
$79$	−31.6455	−	54.8116i	−0.00507058	−	0.00878250i	−0.868550	+	0.495602i	$0.834947\pi$
$80$	14633.4	−	10785.0i	2.28647	−	1.68516i
$81$	−148.505	+	6559.32i	−0.0226346	+	0.999744i
$82$		−	3651.22i		−	0.543013i
$83$	−727.823	−	1260.63i	−0.105650	−	0.182991i	0.808354	−	0.588697i	$-0.200359\pi$
$83$	−727.823	−	1260.63i	−0.105650	−	0.182991i	−0.914004	+	0.405706i	$0.867026\pi$
$84$	−23383.5	−	9841.16i	−3.31399	−	1.39472i
$85$	−223.624	−	1996.54i	−0.0309514	−	0.276338i
$86$	648.961	+	374.678i	0.0877449	+	0.0506595i
$87$	−324.961	−	2581.12i	−0.0429332	−	0.341012i
$88$	−8255.07	+	4766.06i	−1.06600	+	0.615453i
$89$			12837.4i			1.62068i	0.585963	+	0.810338i	$0.300717\pi$
$89$			12837.4i			1.62068i	−0.585963	+	0.810338i	$0.699283\pi$
$90$	−15004.3	−	2445.66i	−1.85238	−	0.301934i
$91$	8410.68			1.01566
$92$	5055.85	+	8756.99i	0.597336	+	1.03462i
$93$	120.361	+	158.710i	0.0139162	+	0.0183501i
$94$	−13057.5	+	22616.2i	−1.47776	+	2.55955i
$95$	−707.544	−	6317.05i	−0.0783982	−	0.699950i
$96$	13774.5	+	18163.1i	1.49462	+	1.97083i
$97$	−6340.40	+	3660.63i	−0.673865	+	0.389056i	−0.797540	−	0.603267i	$-0.793866\pi$
$97$	−6340.40	+	3660.63i	−0.673865	+	0.389056i	0.123674	+	0.992323i	$0.460532\pi$
$98$	−18597.5			−1.93644
$99$	4065.56	+	1138.84i	0.414811	+	0.116196i
$100$	7466.87	−	24094.2i	0.746687	−	2.40942i
$101$	−3312.92	+	1912.71i	−0.324764	+	0.187502i	−0.653514	−	0.756914i	$-0.726706\pi$
$101$	−3312.92	+	1912.71i	−0.324764	+	0.187502i	0.328750	+	0.944417i	$0.393373\pi$
$102$	5387.12	−	678.236i	0.517793	−	0.0651899i
$103$	15821.3	+	9134.42i	1.49131	+	0.861007i	0.999950	−	0.00995073i	$-0.00316747\pi$
$103$	15821.3	+	9134.42i	1.49131	+	0.861007i	0.491358	+	0.870958i	$0.336501\pi$
$104$	−19071.3	−	11010.8i	−1.76325	−	1.01801i
$105$	−15276.5	+	3686.35i	−1.38563	+	0.334363i
$106$	−10956.9	−	18977.9i	−0.975161	−	1.68903i
$107$	−7204.92			−0.629306			−0.314653	−	0.949207i	$-0.601888\pi$
$107$	−7204.92			−0.629306			−0.314653	+	0.949207i	$0.601888\pi$
$108$	4335.01	−	29100.9i	0.371657	−	2.49494i
$109$	405.823			0.0341573			0.0170786	−	0.999854i	$-0.494563\pi$
$109$	405.823			0.0341573			0.0170786	+	0.999854i	$0.494563\pi$
$110$	−3917.97	+	8963.95i	−0.323799	+	0.740822i
$111$	20533.1	+	8641.55i	1.66651	+	0.701367i
$112$	43982.3	+	25393.2i	3.50624	+	2.02433i
$113$	4457.95	−	7721.40i	0.349123	−	0.604699i	−0.636971	−	0.770888i	$-0.719813\pi$
$113$	4457.95	−	7721.40i	0.349123	−	0.604699i	0.986094	+	0.166189i	$0.0531461\pi$
$114$	17044.8	−	2145.93i	1.31154	−	0.165123i
$115$	5739.26	+	2508.52i	0.433971	+	0.189680i
$116$			11666.1i			0.866980i
$117$	2417.73	+	9449.63i	0.176618	+	0.690308i
$118$			13149.5i			0.944376i
$119$	4860.82	−	2806.39i	0.343254	−	0.198178i
$120$	39465.7	+	11640.4i	2.74067	+	0.808362i
$121$	−5962.04	+	10326.6i	−0.407215	+	0.705317i
$122$	−20953.8	+	36293.1i	−1.40781	+	2.43840i
$123$	3487.69	−	2644.98i	0.230530	−	0.174828i
$124$	−446.617	−	773.563i	−0.0290464	−	0.0503098i
$125$	−5131.43	−	14758.4i	−0.328412	−	0.944535i
$126$	−10527.5	−	41146.4i	−0.663108	−	2.59174i
$127$		−	20437.2i		−	1.26711i	−0.773698	−	0.633554i	$-0.781595\pi$
$127$		−	20437.2i		−	1.26711i	0.773698	−	0.633554i	$-0.218405\pi$
$128$	−7441.41	−	12888.9i	−0.454188	−	0.786676i
$129$	112.216	+	891.317i	0.00674337	+	0.0535615i
$130$	−22460.3	+	2515.67i	−1.32901	+	0.148856i
$131$	−14858.5	−	8578.54i	−0.865828	−	0.499886i	0.000131898	−	1.00000i	$-0.499958\pi$
$131$	−14858.5	−	8578.54i	−0.865828	−	0.499886i	−0.865959	+	0.500114i	$0.833291\pi$
$132$	−17450.8	−	7344.34i	−1.00154	−	0.421507i
$133$	15379.6	−	8879.41i	0.869444	−	0.501973i
$134$			28857.9i			1.60714i
$135$	−8533.10	−	16103.9i	−0.468209	−	0.883618i
$136$	−14695.9			−0.794546
$137$	13150.5	+	22777.4i	0.700652	+	1.21356i	0.968238	+	0.250031i	$0.0804408\pi$
$137$	13150.5	+	22777.4i	0.700652	+	1.21356i	−0.267586	+	0.963534i	$0.586226\pi$
$138$	−6566.46	+	15602.5i	−0.344805	+	0.819287i
$139$	11478.7	−	19881.6i	0.594103	−	1.02902i	−0.399570	−	0.916703i	$-0.630841\pi$
$139$	11478.7	−	19881.6i	0.594103	−	1.02902i	0.993673	−	0.112313i	$-0.0358260\pi$
$140$	70034.3	−	7844.22i	3.57318	−	0.400215i
$141$	−31062.3	+	3910.73i	−1.56241	+	0.196707i
$142$	−6427.66	+	3711.01i	−0.318769	+	0.184041i
$143$	6276.79			0.306949
$144$	−15886.8	+	56714.8i	−0.766146	+	2.73509i
$145$	4287.33	+	5817.15i	0.203916	+	0.276678i
$146$	39122.0	−	22587.1i	1.83534	−	1.05963i
$147$	−13472.2	−	17764.6i	−0.623455	−	0.822094i
$148$	−86516.5	−	49950.3i	−3.94980	−	2.28042i
$149$	−26156.1	−	15101.2i	−1.17815	−	0.680205i	−0.222564	−	0.974918i	$-0.571443\pi$
$149$	−26156.1	−	15101.2i	−1.17815	−	0.680205i	−0.955586	+	0.294713i	$0.904776\pi$
$150$	39692.6	−	14413.5i	1.76411	−	0.640599i
$151$	11178.6	+	19361.9i	0.490269	+	0.849170i	0.999937	−	0.0112007i	$-0.00356537\pi$
$151$	11178.6	+	19361.9i	0.490269	+	0.849170i	−0.509669	+	0.860371i	$0.670232\pi$
$152$	−46497.8			−2.01254
$153$	4550.35	+	4654.53i	0.194384	+	0.198835i
$154$	−27331.0			−1.15243
$155$	−506.987	−	221.594i	−0.0211025	−	0.00922348i
$156$	−5463.81	−	43398.2i	−0.224516	−	1.78329i
$157$	23926.5	+	13814.0i	0.970690	+	0.560428i	0.899446	−	0.437031i	$-0.143970\pi$
$157$	23926.5	+	13814.0i	0.970690	+	0.560428i	0.0712432	+	0.997459i	$0.477303\pi$
$158$	−237.572	+	411.487i	−0.00951658	+	0.0164832i
$159$	10190.7	−	24214.0i	0.403097	−	0.957794i
$160$	−58020.8	−	25359.8i	−2.26644	−	0.990615i
$161$			17498.9i			0.675087i
$162$	43202.9	−	23655.9i	1.64620	−	0.901382i
$163$			674.702i			0.0253943i	0.999919	+	0.0126972i	$0.00404174\pi$
$163$			674.702i			0.0253943i	−0.999919	+	0.0126972i	$0.995958\pi$
$164$	−16999.3	+	9814.53i	−0.632037	+	0.364907i
$165$	−11400.7	+	2751.08i	−0.418759	+	0.101050i
$166$	−5463.98	+	9463.89i	−0.198286	+	0.343442i
$167$	20258.6	−	35088.9i	0.726401	−	1.25816i	−0.231994	−	0.972717i	$-0.574525\pi$
$167$	20258.6	−	35088.9i	0.726401	−	1.25816i	0.958395	−	0.285446i	$-0.0921418\pi$
$168$	14359.4	+	114054.i	0.508764	+	4.04103i
$169$	−7030.01	−	12176.3i	−0.246140	−	0.426327i
$170$	−12141.1	+	8948.21i	−0.420109	+	0.309627i
$171$	14397.3	+	14726.9i	0.492366	+	0.503639i
$172$		−	4028.56i		−	0.136174i
$173$	13276.1	+	22994.9i	0.443588	+	0.768317i	0.997953	−	0.0639571i	$-0.0203721\pi$
$173$	13276.1	+	22994.9i	0.443588	+	0.768317i	−0.554365	+	0.832274i	$0.687039\pi$
$174$	−15561.4	+	11801.3i	−0.513983	+	0.389792i
$175$	32038.9	−	29649.3i	1.04617	−	0.968139i
$176$	32823.5	+	18950.6i	1.05964	+	0.611784i
$177$	−12560.6	+	9525.62i	−0.400925	+	0.304051i
$178$	83462.3	−	48187.0i	2.63421	−	1.52086i
$179$			42490.3i			1.32612i	0.748565	+	0.663062i	$0.230743\pi$
$179$			42490.3i			1.32612i	−0.748565	+	0.663062i	$0.769257\pi$
$180$	28945.2	+	76430.5i	0.893371	+	2.35897i
$181$	46294.0			1.41308			0.706542	−	0.707671i	$-0.250254\pi$
$181$	46294.0			1.41308			0.706542	+	0.707671i	$0.250254\pi$
$182$	−31570.7	−	54682.1i	−0.953108	−	1.65083i
$183$	−49846.9	+	6275.70i	−1.48846	+	0.187396i
$184$	22908.7	−	39679.0i	0.676651	−	1.17199i
$185$	−61497.2	+	6888.02i	−1.79685	+	0.201257i
$186$	580.058	−	1378.27i	0.0167666	−	0.0398390i
$187$	3627.57	−	2094.38i	0.103737	−	0.0598924i
$188$	140395.			3.97224
$189$	31677.4	−	39862.9i	0.886801	−	1.11595i
$190$	−38414.5	+	28312.1i	−1.06411	+	0.784268i
$191$	−4296.95	+	2480.85i	−0.117786	+	0.0680038i	−0.557736	−	0.830019i	$-0.688330\pi$
$191$	−4296.95	+	2480.85i	−0.117786	+	0.0680038i	0.439949	+	0.898023i	$0.354996\pi$
$192$	25766.7	−	61224.0i	0.698967	−	1.66081i
$193$	−38203.3	−	22056.7i	−1.02562	−	0.592142i	−0.109893	−	0.993943i	$-0.535051\pi$
$193$	−38203.3	−	22056.7i	−1.02562	−	0.592142i	−0.915727	+	0.401802i	$0.868384\pi$
$194$	47599.2	+	27481.4i	1.26473	+	0.730190i
$195$	−18673.4	−	19632.0i	−0.491083	−	0.516291i
$196$	49990.5	+	86586.1i	1.30129	+	2.25391i
$197$	−16721.9			−0.430876			−0.215438	−	0.976518i	$-0.569118\pi$
$197$	−16721.9			−0.430876			−0.215438	+	0.976518i	$0.569118\pi$
$198$	−7856.54	−	30707.1i	−0.200402	−	0.783264i
$199$	−56999.6			−1.43935			−0.719673	−	0.694313i	$-0.755708\pi$
$199$	−56999.6			−1.43935			−0.719673	+	0.694313i	$0.755708\pi$
$200$	−111464.	+	25286.3i	−2.78659	+	0.632158i
$201$	−27565.4	+	20904.9i	−0.682296	+	0.517436i
$202$	24871.0	+	14359.3i	0.609524	+	0.351909i
$203$	−10094.4	+	17484.1i	−0.244957	+	0.424279i
$204$	−17638.4	−	23258.2i	−0.423837	−	0.558875i
$205$	−4869.59	+	11141.2i	−0.115874	+	0.265108i
$206$		−	137150.i		−	3.23192i
$207$	−19660.5	+	5030.24i	−0.458833	+	0.117394i
$208$			87561.5i			2.02389i
$209$	11477.6	−	6626.59i	0.262760	−	0.151704i
$210$	81309.6	+	85483.3i	1.84375	+	1.93840i
$211$	−15675.9	+	27151.4i	−0.352101	+	0.609856i	−0.986617	−	0.163053i	$-0.947866\pi$
$211$	−15675.9	+	27151.4i	−0.352101	+	0.609856i	0.634517	+	0.772909i	$0.281199\pi$
$212$	−58904.7	+	102026.i	−1.31062	+	2.27007i
$213$	−8201.07	−	3451.50i	−0.180764	−	0.0760761i
$214$	27044.7	+	46842.8i	0.590548	+	1.02286i
$215$	−1480.51	−	2008.79i	−0.0320284	−	0.0434568i
$216$	−124015.	+	48919.1i	−2.65808	+	1.04851i
$217$		−	1545.80i		−	0.0328271i
$218$	−1523.31	−	2638.46i	−0.0320536	−	0.0555184i
$219$	49915.9	+	21007.6i	1.04076	+	0.438014i
$220$	52265.7	−	5854.05i	1.07987	−	0.120951i
$221$	8380.60	+	4838.54i	0.171590	+	0.0990673i
$222$	−20890.9	−	165933.i	−0.423889	−	3.36688i
$223$	−41371.8	+	23886.0i	−0.831944	+	0.480323i	−0.854518	−	0.519422i	$-0.826147\pi$
$223$	−41371.8	+	23886.0i	−0.831944	+	0.480323i	0.0225737	+	0.999745i	$0.492814\pi$
$224$		−	176905.i		−	3.52568i
$225$	42521.6	+	27473.6i	0.839934	+	0.542689i
$226$	−66934.3			−1.31049
$227$	9312.24	+	16129.3i	0.180718	+	0.313014i	0.942125	−	0.335261i	$-0.108824\pi$
$227$	9312.24	+	16129.3i	0.180718	+	0.313014i	−0.761407	+	0.648274i	$0.775491\pi$
$228$	−55807.8	−	73588.6i	−1.07356	−	1.41560i
$229$	−47002.0	+	81409.9i	−0.896284	+	1.55241i	−0.0640772	+	0.997945i	$0.520410\pi$
$229$	−47002.0	+	81409.9i	−0.896284	+	1.55241i	−0.832207	+	0.554465i	$0.812923\pi$
$230$	−5234.01	−	46730.0i	−0.0989416	−	0.883364i
$231$	−19798.8	−	26106.9i	−0.371035	−	0.489251i
$232$	45778.5	−	26430.2i	0.850522	−	0.491049i
$233$	−72051.8			−1.32719			−0.663595	−	0.748092i	$-0.730970\pi$
$233$	−72051.8			−1.32719			−0.663595	+	0.748092i	$0.730970\pi$
$234$	52361.5	−	51189.5i	0.956270	−	0.934865i
$235$	70006.1	−	51595.6i	1.26765	−	0.934280i
$236$	61221.2	−	35346.1i	1.09920	−	0.634625i
$237$	−565.157	+	71.1530i	−0.0100617	+	0.00126677i
$238$	−36491.6	−	21068.4i	−0.644227	−	0.371944i
$239$	46442.6	+	26813.6i	0.813056	+	0.469418i	0.848016	−	0.529970i	$-0.177797\pi$
$239$	46442.6	+	26813.6i	0.813056	+	0.469418i	−0.0349597	+	0.999389i	$0.511130\pi$
$240$	−38377.7	−	159040.i	−0.666279	−	2.76112i
$241$	3162.61	+	5477.81i	0.0544518	+	0.0943132i	0.891966	−	0.452102i	$-0.149326\pi$
$241$	3162.61	+	5477.81i	0.0544518	+	0.0943132i	−0.837515	+	0.546415i	$0.815992\pi$
$242$	89517.5			1.52854
$243$	53893.0	+	24131.5i	0.912683	+	0.408669i
$244$	225297.			3.78422
$245$	56747.8	+	24803.4i	0.945403	+	0.413217i
$246$	−30287.9	−	12747.0i	−0.500494	−	0.210638i
$247$	26516.2	+	15309.1i	0.434627	+	0.250932i
$248$	−2023.67	+	3505.11i	−0.0329031	+	0.0569899i
$249$	−12998.2	+	1636.47i	−0.209645	+	0.0263942i
$250$	−76689.9	+	88759.7i	−1.22704	+	1.42016i
$251$			11578.9i			0.183790i	0.995769	+	0.0918948i	$0.0292924\pi$
$251$			11578.9i			0.183790i	−0.995769	+	0.0918948i	$0.970708\pi$
$252$	−163271.	+	159616.i	−2.57103	+	2.51348i
$253$			13059.2i			0.204022i
$254$	−132873.	+	76714.0i	−2.05953	+	1.18907i
$255$	−17342.6	−	5115.21i	−0.266707	−	0.0786653i
$256$	3179.78	−	5507.53i	0.0485195	−	0.0840383i
$257$	19148.3	−	33165.9i	0.289911	−	0.502140i	−0.683877	−	0.729597i	$-0.739708\pi$
$257$	19148.3	−	33165.9i	0.289911	−	0.502140i	0.973788	+	0.227457i	$0.0730411\pi$
$258$	5373.68	−	4075.27i	0.0807296	−	0.0612233i
$259$	−86442.1	−	149722.i	−1.28862	−	2.23196i
$260$	72086.0	+	97807.9i	1.06636	+	1.44686i
$261$	−22545.6	−	6315.42i	−0.330964	−	0.0927088i
$262$			128803.i			1.87639i
$263$	−62926.2	−	108991.i	−0.909745	−	1.57572i	−0.814418	−	0.580279i	$-0.802944\pi$
$263$	−62926.2	−	108991.i	−0.909745	−	1.57572i	−0.0953275	−	0.995446i	$-0.530390\pi$
$264$	10716.2	+	85117.2i	0.153757	+	1.22126i
$265$	8122.81	+	72521.6i	0.115668	+	1.03270i
$266$	−115459.	−	66660.3i	−1.63179	−	0.942116i
$267$	106490.	+	44817.2i	1.49378	+	0.628669i
$268$	134356.	−	77570.4i	1.87063	−	1.08001i
$269$			5288.09i			0.0730792i	0.999332	+	0.0365396i	$0.0116335\pi$
$269$			5288.09i			0.0730792i	−0.999332	+	0.0365396i	$0.988366\pi$
$270$	−72669.6	+	115927.i	−0.996840	+	1.59021i
$271$	4773.83			0.0650022			0.0325011	−	0.999472i	$-0.489653\pi$
$271$	4773.83			0.0650022			0.0325011	+	0.999472i	$0.489653\pi$
$272$	29216.7	+	50604.7i	0.394905	+	0.683996i
$273$	29363.0	−	69769.1i	0.393980	−	0.936133i
$274$	98725.0	−	170997.i	1.31500	−	2.27765i
$275$	23910.3	−	22126.9i	0.316169	−	0.292587i
$276$	90292.6	−	11367.8i	1.18532	−	0.149231i
$277$	−53317.8	+	30783.0i	−0.694884	+	0.401192i	−0.805439	−	0.592678i	$-0.798071\pi$
$277$	−53317.8	+	30783.0i	−0.694884	+	0.401192i	0.110555	+	0.993870i	$0.464737\pi$
$278$	−172347.			−2.23005
$279$	1736.74	−	444.354i	0.0223114	−	0.00570848i
$280$	−189448.	−	257048.i	−2.41643	−	3.27867i
$281$	108628.	−	62716.7i	1.37572	−	0.794274i	0.384082	−	0.923299i	$-0.374518\pi$
$281$	108628.	−	62716.7i	1.37572	−	0.794274i	0.991641	+	0.129025i	$0.0411847\pi$
$282$	142022.	+	187272.i	1.78591	+	2.35491i
$283$	−13802.0	−	7968.60i	−0.172333	−	0.0994967i	0.411352	−	0.911476i	$-0.365057\pi$
$283$	−13802.0	−	7968.60i	−0.172333	−	0.0994967i	−0.583686	+	0.811980i	$0.698390\pi$
$284$	34555.3	+	19950.5i	0.428428	+	0.247353i
$285$	−54871.9	−	16184.5i	−0.675554	−	0.199255i
$286$	−23560.9	−	40808.6i	−0.288044	−	0.498907i
$287$	−33969.3			−0.412404
$288$	198757.	−	50852.9i	2.39628	−	0.613099i
$289$	−77063.1			−0.922679
$290$	21727.1	−	49709.6i	0.258348	−	0.591077i
$291$	8230.71	+	65375.3i	0.0971967	+	0.772018i
$292$	−210321.	−	121429.i	−2.46671	−	1.42415i
$293$	53650.1	−	92924.7i	0.624936	−	1.08242i	−0.363617	−	0.931548i	$-0.618458\pi$
$293$	53650.1	−	92924.7i	0.624936	−	1.08242i	0.988553	−	0.150872i	$-0.0482082\pi$
$294$	−64926.8	+	154272.i	−0.751155	+	1.78481i
$295$	17537.3	−	40123.8i	0.201521	−	0.461061i
$296$			452662.i			5.16643i
$297$	23640.5	−	29749.2i	0.268005	−	0.337258i
$298$			226739.i			2.55325i
$299$	−26128.1	+	15085.1i	−0.292258	+	0.168735i
$300$	−173800.	−	146056.i	−1.93111	−	1.62285i
$301$	3485.84	−	6037.65i	0.0384746	−	0.0666400i
$302$	83921.1	−	145356.i	0.920147	−	1.59374i
$303$	4300.62	+	34159.2i	0.0468431	+	0.372068i
$304$	92441.3	+	160113.i	1.00027	+	1.73253i
$305$	112342.	−	82797.5i	1.20765	−	0.890056i
$306$	13181.1	−	47055.6i	0.140769	−	0.502537i
$307$		−	72255.8i		−	0.766647i	−0.923614	−	0.383324i	$-0.874779\pi$
$307$		−	72255.8i		−	0.766647i	0.923614	−	0.383324i	$-0.125221\pi$
$308$	73466.1	+	127247.i	0.774436	+	1.34136i
$309$	131007.	−	99352.5i	1.37208	−	1.04055i
$310$	462.354	+	4127.96i	0.00481118	+	0.0429549i
$311$	−14917.6	−	8612.67i	−0.154233	−	0.0890465i	0.420897	−	0.907108i	$-0.361715\pi$
$311$	−14917.6	−	8612.67i	−0.154233	−	0.0890465i	−0.575130	+	0.818062i	$0.695049\pi$
$312$	−157919.	+	119762.i	−1.62228	+	1.23029i
$313$	−114069.	+	65857.5i	−1.16433	+	0.672228i	−0.952339	−	0.305043i	$-0.901329\pi$
$313$	−114069.	+	65857.5i	−1.16433	+	0.672228i	−0.211994	+	0.977271i	$0.567996\pi$
$314$		−	207411.i		−	2.10365i
$315$	−22753.4	+	139593.i	−0.229311	+	1.40683i
$316$	2554.39			0.0255807
$317$	60158.8	+	104198.i	0.598661	+	1.03691i	0.993019	+	0.117954i	$0.0376335\pi$
$317$	60158.8	+	104198.i	0.598661	+	1.03691i	−0.394358	+	0.918957i	$0.629033\pi$
$318$	−195680.	+	24636.0i	−1.93505	+	0.243621i
$319$	−7533.36	+	13048.2i	−0.0740300	+	0.128224i
$320$	20538.2	+	183368.i	0.200568	+	1.79070i
$321$	−25153.5	+	59766.9i	−0.244111	+	0.580031i
$322$	113769.	−	65684.8i	1.09727	−	0.633510i
$323$	20432.8			0.195849
$324$	−226267.	−	137556.i	−2.15541	−	1.31036i
$325$	71889.5	+	22278.8i	0.680611	+	0.210924i
$326$	4386.58	−	2532.59i	0.0412753	−	0.0238303i
$327$	1416.79	−	3366.42i	0.0132498	−	0.0314827i
$328$	77025.7	+	44470.8i	0.715959	+	0.413359i
$329$	210411.	+	121481.i	1.94391	+	1.12232i
$330$	60680.3	+	63795.2i	0.557212	+	0.585814i
$331$	25048.8	+	43385.8i	0.228629	+	0.395997i	0.957402	−	0.288758i	$-0.0932424\pi$
$331$	25048.8	+	43385.8i	0.228629	+	0.395997i	−0.728773	+	0.684755i	$0.759909\pi$
$332$	58749.0			0.532997
$333$	143368.	−	140159.i	1.29290	−	1.26396i
$334$	−304174.			−2.72665
$335$	38487.4	−	88055.7i	0.342949	−	0.784636i
$336$	364193.	−	276195.i	3.22591	−	2.44645i
$337$	−43062.0	−	24861.8i	−0.379170	−	0.218914i	0.298287	−	0.954476i	$-0.403585\pi$
$337$	−43062.0	−	24861.8i	−0.379170	−	0.218914i	−0.677457	+	0.735562i	$0.736918\pi$
$338$	−52776.3	+	91411.3i	−0.461962	+	0.800141i
$339$	−48487.9	−	63936.6i	−0.421924	−	0.556353i
$340$	74296.5	+	32473.5i	0.642703	+	0.280913i
$341$		−	1153.61i		−	0.00992087i
$342$	41704.9	−	148884.i	0.356562	−	1.27290i
$343$			5326.54i			0.0452749i
$344$	−15808.3	+	9126.95i	−0.133589	+	0.0771274i
$345$	40845.5	−	38851.2i	0.343168	−	0.326412i
$346$	99667.9	−	172630.i	0.832536	−	1.44199i
$347$	−87328.8	+	151258.i	−0.725268	+	1.25620i	0.233596	+	0.972334i	$0.424951\pi$
$347$	−87328.8	+	151258.i	−0.725268	+	1.25620i	−0.958864	+	0.283867i	$0.908383\pi$
$348$	96773.6	+	40728.1i	0.799095	+	0.336307i
$349$	35802.9	+	62012.4i	0.293946	+	0.509129i	0.974739	−	0.223347i	$-0.0716982\pi$
$349$	35802.9	+	62012.4i	0.293946	+	0.509129i	−0.680793	+	0.732476i	$0.738365\pi$
$350$	−313028.	−	97008.4i	−2.55533	−	0.791905i
$351$	86828.1	+	12934.3i	0.704768	+	0.104985i
$352$		−	132022.i		−	1.06552i
$353$	−36940.0	−	63982.0i	−0.296447	−	0.513462i	0.678873	−	0.734256i	$-0.262469\pi$
$353$	−36940.0	−	63982.0i	−0.296447	−	0.513462i	−0.975321	+	0.220794i	$0.929135\pi$
$354$	109079.	+	45906.9i	0.870431	+	0.366329i
$355$	24562.4	−	2751.13i	0.194901	−	0.0218300i
$356$	−448696.	−	259055.i	−3.54040	−	2.04405i
$357$	−6310.01	−	50119.4i	−0.0495101	−	0.393251i
$358$	276251.	−	159494.i	2.15545	−	1.24445i
$359$			192955.i			1.49715i	0.663048	+	0.748577i	$0.269263\pi$
$359$			192955.i			1.49715i	−0.663048	+	0.748577i	$0.730737\pi$
$360$	234341.	−	286741.i	1.80819	−	2.21251i
$361$	−65671.8			−0.503924
$362$	−173771.	−	300981.i	−1.32605	−	2.29679i
$363$	64847.4	+	85508.4i	0.492129	+	0.648926i
$364$	−169725.	+	293973.i	−1.28098	+	2.21873i
$365$	−149500.	+	16744.8i	−1.12216	+	0.125688i
$366$	227909.	+	300523.i	1.70137	+	2.24345i
$367$	−43992.7	+	25399.2i	−0.326624	+	0.188577i	−0.654341	−	0.756199i	$-0.727054\pi$
$367$	−43992.7	+	25399.2i	−0.326624	+	0.188577i	0.327717	+	0.944776i	$0.393721\pi$
$368$	−182177.			−1.34524
$369$	−9764.80	−	38165.5i	−0.0717151	−	0.280297i
$370$	275621.	+	373970.i	2.01330	+	2.73170i
$371$	−176562.	+	101938.i	−1.28277	+	0.740610i
$372$	−7976.14	+	1004.19i	−0.0576377	+	0.00725656i
$373$	−60191.5	−	34751.6i	−0.432631	−	0.249780i	0.267836	−	0.963465i	$-0.413691\pi$
$373$	−60191.5	−	34751.6i	−0.432631	−	0.249780i	−0.700467	+	0.713685i	$0.747025\pi$
$374$	−27233.2	−	15723.1i	−0.194695	−	0.112407i
$375$	−140339.	−	8956.89i	−0.997970	−	0.0636934i
$376$	−318073.	−	550919.i	−2.24984	−	3.89683i
$377$	−34808.0			−0.244904
$378$	−378075.	−	56319.7i	−2.64603	−	0.394164i
$379$	−81228.0			−0.565493			−0.282747	−	0.959195i	$-0.591246\pi$
$379$	−81228.0			−0.565493			−0.282747	+	0.959195i	$0.591246\pi$
$380$	235074.	+	102746.i	1.62793	+	0.711538i
$381$	−169533.	−	71349.3i	−1.16789	−	0.491519i
$382$	32258.5	+	18624.5i	0.221064	+	0.127631i
$383$	−47993.4	+	83127.0i	−0.327178	+	0.566689i	−0.981951	−	0.189137i	$-0.939431\pi$
$383$	−47993.4	+	83127.0i	−0.327178	+	0.566689i	0.654773	+	0.755826i	$0.272764\pi$
$384$	−132896.	+	16731.6i	−0.901260	+	0.113468i
$385$	83396.6	+	36451.0i	0.562635	+	0.245917i
$386$			331172.i			2.22269i
$387$	7785.50	+	2180.85i	0.0519834	+	0.0145615i
$388$		−	295482.i		−	1.96276i
$389$	28758.0	−	16603.5i	0.190047	−	0.109723i	−0.401958	−	0.915658i	$-0.631670\pi$
$389$	28758.0	−	16603.5i	0.190047	−	0.109723i	0.592004	+	0.805935i	$0.298337\pi$
$390$	−57543.9	+	195097.i	−0.378330	+	1.28269i
$391$	−10066.9	+	17436.4i	−0.0658479	+	0.114052i
$392$	226513.	−	392332.i	1.47408	−	2.55318i
$393$	−123035.	+	93306.3i	−0.796604	+	0.604124i
$394$	62768.0	+	108717.i	0.404339	+	0.700336i
$395$	1273.71	−	938.747i	0.00816352	−	0.00601664i
$396$	−121847.	+	119119.i	−0.777006	+	0.759613i
$397$		−	180216.i		−	1.14344i	−0.820449	−	0.571720i	$-0.806276\pi$
$397$		−	180216.i		−	1.14344i	0.820449	−	0.571720i	$-0.193724\pi$
$398$	213956.	+	370583.i	1.35070	+	2.33948i
$399$	−19964.8	−	158578.i	−0.125406	−	0.996084i
$400$	308671.	+	333549.i	1.92919	+	2.08468i
$401$	119290.	+	68872.3i	0.741850	+	0.428307i	0.822742	−	0.568415i	$-0.192443\pi$
$401$	119290.	+	68872.3i	0.741850	+	0.428307i	−0.0808914	+	0.996723i	$0.525777\pi$
$402$	239384.	+	100747.i	1.48130	+	0.623420i
$403$	2308.07	−	1332.57i	0.0142115	−	0.00820500i
$404$		−	154392.i		−	0.945937i
$405$	−163377.	+	14563.3i	−0.996051	+	0.0887870i
$406$	151564.			0.919483
$407$	−64510.7	−	111736.i	−0.389442	−	0.674534i
$408$	−51305.7	+	121907.i	−0.308209	+	0.732332i
$409$	−17209.2	+	29807.2i	−0.102876	+	0.178187i	−0.912868	−	0.408254i	$-0.866138\pi$
$409$	−17209.2	+	29807.2i	−0.102876	+	0.178187i	0.809992	+	0.586440i	$0.199471\pi$
$410$	90713.2	−	10160.4i	0.539638	−	0.0604424i
$411$	234856.	−	29568.2i	1.39033	−	0.175042i
$412$	−638539.	+	368660.i	−3.76177	+	2.17186i
$413$	122337.			0.717229
$414$	106503.	+	108941.i	0.621384	+	0.635612i
$415$	29294.5	−	21590.5i	0.170094	−	0.125362i
$416$	264141.	−	152502.i	1.52633	−	0.881229i
$417$	−124850.	−	164629.i	−0.717987	−	0.946745i
$418$	−86165.7	−	49747.8i	−0.493153	−	0.284722i
$419$	−130348.	−	75256.4i	−0.742465	−	0.428662i	0.0804998	−	0.996755i	$-0.474348\pi$
$419$	−130348.	−	75256.4i	−0.742465	−	0.428662i	−0.822965	+	0.568092i	$0.807682\pi$
$420$	179430.	−	608340.i	1.01718	−	3.44864i
$421$	54563.0	+	94505.9i	0.307847	+	0.533206i	0.977891	−	0.209115i	$-0.0670583\pi$
$421$	54563.0	+	94505.9i	0.307847	+	0.533206i	−0.670045	+	0.742321i	$0.733725\pi$
$422$	235367.			1.32166
$423$	−76002.5	+	271324.i	−0.424763	+	1.51638i
$424$	533809.			2.96930
$425$	48981.1	−	11111.7i	0.271176	−	0.0615181i
$426$	8343.99	+	66275.0i	0.0459785	+	0.365200i
$427$	337655.	+	194945.i	1.85190	+	1.06920i
$428$	145393.	−	251829.i	0.793701	−	1.37473i
$429$	21913.2	−	52067.8i	0.119067	−	0.282914i
$430$	−7502.85	+	17165.8i	−0.0405779	+	0.0928385i
$431$		−	344386.i		−	1.85392i	−0.375159	−	0.926960i	$-0.622412\pi$
$431$		−	344386.i		−	1.85392i	0.375159	−	0.926960i	$-0.377588\pi$
$432$	415003.	+	329786.i	2.22374	+	1.76711i
$433$		−	42720.4i		−	0.227855i	−0.993489	−	0.113928i	$-0.963657\pi$
$433$		−	42720.4i		−	0.227855i	0.993489	−	0.113928i	$-0.0363432\pi$
$434$	−10050.0	+	5802.37i	−0.0533564	+	0.0308054i
$435$	63222.6	−	15256.1i	0.334114	−	0.0806242i
$436$	−8189.39	+	14184.4i	−0.0430803	+	0.0746172i
$437$	−31851.6	+	55168.5i	−0.166789	+	0.288887i
$438$	−50785.8	−	403384.i	−0.264724	−	2.10266i
$439$	−99941.2	−	173103.i	−0.518579	−	0.898206i	−0.999767	−	0.0215883i	$-0.993128\pi$
$439$	−99941.2	−	173103.i	−0.518579	−	0.898206i	0.481187	−	0.876618i	$-0.340206\pi$
$440$	−141383.	−	191831.i	−0.730283	−	0.990865i
$441$	−194396.	+	49737.2i	−0.999565	+	0.255743i
$442$		−	72648.7i		−	0.371863i
$443$	50100.2	+	86776.2i	0.255289	+	0.442174i	0.964974	−	0.262345i	$-0.0844960\pi$
$443$	50100.2	+	86776.2i	0.255289	+	0.442174i	−0.709685	+	0.704519i	$0.751163\pi$
$444$	−716394.	+	543295.i	−3.63401	+	2.75594i
$445$	−318940.	+	35723.0i	−1.61060	+	0.180396i
$446$	310590.	+	179319.i	1.56141	+	0.901482i
$447$	−216584.	+	164252.i	−1.08396	+	0.822044i
$448$	−446430.	+	257747.i	−2.22432	+	1.28421i
$449$			26310.5i			0.130508i	0.997869	+	0.0652539i	$0.0207857\pi$
$449$			26310.5i			0.130508i	−0.997869	+	0.0652539i	$0.979214\pi$
$450$	19008.8	−	379581.i	0.0938706	−	1.87447i
$451$	−25350.9			−0.124635
$452$	179921.	+	311632.i	0.880651	+	1.52533i
$453$	199639.	−	25134.5i	0.972857	−	0.122482i
$454$	69909.7	−	121087.i	0.339177	−	0.587471i
$455$	23404.7	+	208960.i	0.113053	+	1.00935i
$456$	−162331.	+	385713.i	−0.780677	+	1.85496i
$457$	−57206.0	+	33027.9i	−0.273911	+	0.158143i	−0.630664	−	0.776056i	$-0.717217\pi$
$457$	−57206.0	+	33027.9i	−0.273911	+	0.158143i	0.356753	+	0.934199i	$0.383884\pi$
$458$	705716.			3.36433
$459$	54496.7	−	21496.8i	0.258669	−	0.102035i
$460$	−203495.	+	149979.i	−0.961698	+	0.708787i
$461$	−66871.8	+	38608.5i	−0.314660	+	0.181669i	−0.649010	−	0.760780i	$-0.724817\pi$
$461$	−66871.8	+	38608.5i	−0.314660	+	0.181669i	0.334350	+	0.942449i	$0.391483\pi$
$462$	−95416.5	+	226718.i	−0.447033	+	1.06219i
$463$	141018.	+	81416.6i	0.657827	+	0.379797i	0.791449	−	0.611236i	$-0.209327\pi$
$463$	141018.	+	81416.6i	0.657827	+	0.379797i	−0.133621	+	0.991032i	$0.542661\pi$
$464$	−182023.	−	105091.i	−0.845453	−	0.488122i
$465$	−3608.15	+	3431.99i	−0.0166870	+	0.0158723i
$466$	270457.	+	468446.i	1.24545	+	2.15718i
$467$	115736.			0.530681			0.265340	−	0.964155i	$-0.414516\pi$
$467$	115736.			0.530681			0.265340	+	0.964155i	$0.414516\pi$
$468$	−379076.	−	106186.i	−1.73075	−	0.484813i
$469$	268481.			1.22058
$470$	−598227.	−	261473.i	−2.70814	−	1.18367i
$471$	198122.	−	150251.i	0.893082	−	0.677291i
$472$	−277401.	−	160157.i	−1.24515	−	0.718890i
$473$	2601.44	−	4505.82i	0.0116276	−	0.0201397i
$474$	2584.00	+	3407.29i	0.0115010	+	0.0151654i
$475$	154976.	−	35157.3i	0.686874	−	0.155822i
$476$			226529.i			0.999793i
$477$	−165285.	−	169069.i	−0.726434	−	0.743067i
$478$		−	402596.i		−	1.76203i
$479$	−372227.	+	214906.i	−1.62232	+	0.936648i	−0.636026	+	0.771668i	$0.719423\pi$
$479$	−372227.	+	214906.i	−1.62232	+	0.936648i	−0.986297	+	0.164980i	$0.947244\pi$
$480$	−412926.	+	392765.i	−1.79221	+	1.70471i
$481$	149036.	−	258138.i	0.644171	−	1.11574i
$482$	23742.7	−	41123.5i	0.102196	−	0.177009i
$483$	145159.	+	61091.4i	0.622227	+	0.261870i
$484$	−240625.	−	416774.i	−1.02719	−	1.77914i
$485$	−108591.	−	147338.i	−0.461646	−	0.626372i
$486$	−45404.4	−	440967.i	−0.192232	−	1.86695i
$487$		−	116726.i		−	0.492166i	−0.969249	−	0.246083i	$-0.920856\pi$
$487$		−	116726.i		−	0.492166i	0.969249	−	0.246083i	$-0.0791435\pi$
$488$	−510424.	−	884081.i	−2.14334	−	3.71238i
$489$	5596.85	+	2355.48i	0.0234059	+	0.00985060i
$490$	−51752.0	−	462049.i	−0.215544	−	1.92440i
$491$	−91898.2	−	53057.5i	−0.381192	−	0.220081i	0.297145	−	0.954832i	$-0.403966\pi$
$491$	−91898.2	−	53057.5i	−0.381192	−	0.220081i	−0.678337	+	0.734751i	$0.737299\pi$
$492$	22067.4	+	175278.i	0.0911635	+	0.724097i
$493$	−20116.7	+	11614.4i	−0.0827681	+	0.0477862i
$494$		−	229860.i		−	0.941911i
$495$	−16980.6	+	104177.i	−0.0693014	+	0.425167i
$496$	16092.9			0.0654140
$497$	34525.6	+	59800.1i	0.139775	+	0.242097i
$498$	59430.1	+	78365.1i	0.239634	+	0.315983i
$499$	−55602.4	+	96306.1i	−0.223302	+	0.386770i	−0.955809	−	0.293990i	$-0.905017\pi$
$499$	−55602.4	+	96306.1i	−0.223302	+	0.386770i	0.732507	+	0.680760i	$0.238350\pi$
$500$	619390.	+	118464.i	2.47756	+	0.473856i
$501$	−220347.	−	290552.i	−0.877873	−	1.15757i
$502$	75280.5	−	43463.2i	0.298727	−	0.172470i
$503$	−48033.5			−0.189849			−0.0949246	−	0.995484i	$-0.530261\pi$
$503$	−48033.5			−0.189849			−0.0949246	+	0.995484i	$0.530261\pi$
$504$	996243.	+	279065.i	3.92197	+	1.09861i
$505$	−56739.6	−	76985.6i	−0.222487	−	0.301875i
$506$	84904.8	−	49019.8i	0.331613	−	0.191457i
$507$	−125549.	+	15806.6i	−0.488425	+	0.0614924i
$508$	714327.	+	412417.i	2.76802	+	1.59812i
$509$	130713.	+	75467.0i	0.504525	+	0.291287i	0.730580	−	0.682827i	$-0.239250\pi$
$509$	130713.	+	75467.0i	0.504525	+	0.291287i	−0.226055	+	0.974114i	$0.572583\pi$
$510$	31841.5	+	131954.i	0.122420	+	0.507320i
$511$	−210141.	−	363974.i	−0.804763	−	1.39389i
$512$	−285868.			−1.09050
$513$	172427.	−	68015.6i	0.655195	−	0.258449i
$514$	−287504.			−1.08822
$515$	−182915.	+	418493.i	−0.689660	+	1.57788i
$516$	−33418.1	−	14064.3i	−0.125511	−	0.0528225i
$517$	157027.	+	90659.8i	0.587482	+	0.339183i
$518$	−648946.	+	1.12401e6i	−2.41852	+	4.18900i
$519$	237099.	−	29850.6i	0.880227	−	0.110820i
$520$	220490.	−	504460.i	0.815420	−	1.86561i
$521$		−	398056.i		−	1.46645i	−0.679984	−	0.733227i	$-0.738013\pi$
$521$		−	398056.i		−	1.46645i	0.679984	−	0.733227i	$-0.261987\pi$
$522$	43568.5	+	170286.i	0.159894	+	0.624940i
$523$			303039.i			1.10789i	0.832554	+	0.553943i	$0.186878\pi$
$523$			303039.i			1.10789i	−0.832554	+	0.553943i	$0.813122\pi$
$524$	599680.	−	346225.i	2.18402	−	1.26094i
$525$	−134097.	−	369282.i	−0.486518	−	1.33980i
$526$	−472405.	+	818230.i	−1.70743	+	2.95736i
$527$	889.274	−	1540.27i	0.00320195	−	0.00554594i
$528$	271793.	−	206121.i	0.974922	−	0.739356i
$529$	108535.	+	187988.i	0.387845	+	0.671768i
$530$	441010.	−	325031.i	1.56999	−	1.15711i
$531$	35167.0	+	137449.i	0.124723	+	0.487475i
$532$			716736.i			2.53242i
$533$	−29283.5	−	50720.5i	−0.103079	−	0.178537i
$534$	−108346.	−	860572.i	−0.379952	−	3.01790i
$535$	−20049.4	−	179004.i	−0.0700476	−	0.625395i
$536$	−608783.	−	351481.i	−2.11901	−	1.22341i
$537$	352470.	+	148340.i	1.22229	+	0.514411i
$538$	34380.5	−	19849.6i	0.118781	−	0.0685784i
$539$			129125.i			0.444461i
$540$	735066.	+	26721.5i	2.52080	+	0.0916375i
$541$	298904.			1.02126			0.510632	−	0.859800i	$-0.329412\pi$
$541$	298904.			1.02126			0.510632	+	0.859800i	$0.329412\pi$
$542$	−17919.3	−	31037.1i	−0.0609988	−	0.105653i
$543$	161619.	−	384023.i	0.548143	−	1.30244i
$544$	101771.	−	176272.i	0.343894	−	0.595642i
$545$	1129.30	+	10082.5i	0.00380203	+	0.0339450i
$546$	−563822.	+	70985.0i	−1.89129	+	0.238112i
$547$	114500.	−	66106.6i	0.382675	−	0.220938i	−0.296306	−	0.955093i	$-0.595755\pi$
$547$	114500.	−	66106.6i	0.382675	−	0.220938i	0.678982	+	0.734155i	$0.262422\pi$
$548$	−1.06150e6			−3.53474
$549$	−121964.	+	435404.i	−0.404658	+	1.44460i
$550$	−233609.	−	72396.2i	−0.772260	−	0.239326i
$551$	−63649.1	+	36747.8i	−0.209647	+	0.121040i
$552$	−249171.	−	328560.i	−0.817749	−	1.07829i
$553$	3828.29	+	2210.27i	0.0125186	+	0.00722760i
$554$	400272.	+	231097.i	1.30418	+	0.752966i
$555$	−157558.	+	534185.i	−0.511510	+	1.73423i
$556$	463272.	+	802411.i	1.49860	+	2.59566i
$557$	347933.			1.12146			0.560731	−	0.827998i	$-0.310520\pi$
$557$	347933.			1.12146			0.560731	+	0.827998i	$0.310520\pi$
$558$	−9408.09	−	9623.51i	−0.0302157	−	0.0309076i
$559$	12020.0			0.0384662
$560$	−508494.	+	1.16339e6i	−1.62147	+	3.70978i
$561$	−4709.08	−	37403.5i	−0.0149627	−	0.118847i
$562$	−815506.	−	470833.i	−2.58199	−	1.49071i
$563$	257060.	−	445240.i	0.810993	−	1.40468i	−0.101176	−	0.994869i	$-0.532261\pi$
$563$	257060.	−	445240.i	0.810993	−	1.40468i	0.912170	−	0.409813i	$-0.134406\pi$
$564$	490139.	−	1.16462e6i	1.54085	−	3.66121i
$565$	204241.	+	89269.7i	0.639802	+	0.279645i
$566$			119645.i			0.373476i
$567$	−220084.	−	401941.i	−0.684576	−	1.25025i
$568$		−	180796.i		−	0.560394i
$569$	395004.	−	228056.i	1.22005	−	0.704396i	0.255121	−	0.966909i	$-0.417885\pi$
$569$	395004.	−	228056.i	1.22005	−	0.704396i	0.964928	+	0.262513i	$0.0845513\pi$
$570$	100746.	+	417501.i	0.310084	+	1.28501i
$571$	−131436.	+	227654.i	−0.403128	+	0.698238i	−0.994102	−	0.108453i	$-0.965410\pi$
$571$	−131436.	+	227654.i	−0.403128	+	0.698238i	0.590974	+	0.806691i	$0.298744\pi$
$572$	−126664.	+	219388.i	−0.387134	+	0.670535i
$573$	5578.04	+	44305.5i	0.0169892	+	0.134942i
$574$	127509.	+	220852.i	0.387005	+	0.670312i
$575$	−46352.4	+	149570.i	−0.140196	+	0.452387i
$576$	−417916.	−	427485.i	−1.25963	−	1.28847i
$577$		−	297110.i		−	0.892414i	−0.894930	−	0.446207i	$-0.852775\pi$
$577$		−	297110.i		−	0.892414i	0.894930	−	0.446207i	$-0.147225\pi$
$578$	289268.	+	501026.i	0.865853	+	1.49970i
$579$	−316340.	+	239904.i	−0.943620	+	0.715617i
$580$	−289840.	+	32463.6i	−0.861593	+	0.0965031i
$581$	88047.8	+	50834.4i	0.260835	+	0.150593i
$582$	394143.	−	298908.i	1.16361	−	0.882452i
$583$	−131766.	+	76075.3i	−0.387674	+	0.223824i
$584$			1.10042e6i			3.22651i
$585$	−228045.	+	86363.5i	−0.666359	+	0.252359i
$586$	−805534.			−2.34579
$587$	−153333.	−	265581.i	−0.444999	−	0.770762i	0.553053	−	0.833146i	$-0.313463\pi$
$587$	−153333.	−	265581.i	−0.444999	−	0.770762i	−0.998052	+	0.0623847i	$0.980129\pi$
$588$	892781.	−	112401.i	2.58220	−	0.325098i
$589$	2813.66	−	4873.40i	0.00811037	−	0.0140476i
$590$	−326694.	+	36591.6i	−0.938508	+	0.105118i
$591$	−58378.6	+	138713.i	−0.167139	+	0.397138i
$592$	1.55872e6	−	899927.i	4.44759	−	2.56782i
$593$	84728.9			0.240947			0.120474	−	0.992717i	$-0.461559\pi$
$593$	84728.9			0.240947			0.120474	+	0.992717i	$0.461559\pi$
$594$	−282153.	−	42030.7i	−0.799670	−	0.119123i
$595$	83250.2	+	112956.i	0.235153	+	0.319062i
$596$	1.05565e6	−	609477.i	2.97184	−	1.71579i
$597$	−198994.	+	472828.i	−0.558331	+	1.32664i
$598$	196152.	+	113248.i	0.548516	+	0.316686i
$599$	−480015.	−	277137.i	−1.33783	−	0.772397i	−0.351345	−	0.936246i	$-0.614276\pi$
$599$	−480015.	−	277137.i	−1.33783	−	0.772397i	−0.986485	+	0.163849i	$0.947609\pi$
$600$	−179379.	+	1.01290e6i	−0.498276	+	2.81362i
$601$	−2710.09	−	4694.01i	−0.00750299	−	0.0129956i	0.862250	−	0.506484i	$-0.169055\pi$
$601$	−2710.09	−	4694.01i	−0.00750299	−	0.0129956i	−0.869753	+	0.493488i	$0.835722\pi$
$602$	−52338.4			−0.144420
$603$	77177.3	+	301645.i	0.212254	+	0.829587i
$604$	−902325.			−2.47337
$605$	−273150.	−	119389.i	−0.746261	−	0.326176i
$606$	205943.	−	156182.i	0.560792	−	0.425290i
$607$	−96836.6	−	55908.6i	−0.262822	−	0.151740i	0.362799	−	0.931867i	$-0.381821\pi$
$607$	−96836.6	−	55908.6i	−0.262822	−	0.151740i	−0.625621	+	0.780127i	$0.715154\pi$
$608$	322002.	−	557723.i	0.871066	−	1.50873i
$609$	109794.	+	144776.i	0.296037	+	0.390357i
$610$	−959999.	−	419597.i	−2.57995	−	1.12765i
$611$			418894.i			1.12208i
$612$	−254511.	+	65117.9i	−0.679524	+	0.173859i
$613$			631873.i			1.68155i	0.541387	+	0.840774i	$0.317900\pi$
$613$			631873.i			1.68155i	−0.541387	+	0.840774i	$0.682100\pi$
$614$	−469771.	+	271223.i	−1.24609	+	0.719431i
$615$	75418.9	+	79290.2i	0.199402	+	0.209638i
$616$	332884.	−	576571.i	0.877266	−	1.51947i
$617$	−84321.4	+	146049.i	−0.221497	+	0.383644i	−0.955263	−	0.295759i	$-0.904428\pi$
$617$	−84321.4	+	146049.i	−0.221497	+	0.383644i	0.733766	+	0.679402i	$0.237761\pi$
$618$	−1.13770e6	−	478810.i	−2.97885	−	1.25368i
$619$	−101411.	−	175648.i	−0.264668	−	0.458419i	0.702808	−	0.711379i	$-0.251929\pi$
$619$	−101411.	−	175648.i	−0.264668	−	0.458419i	−0.967477	+	0.252960i	$0.918596\pi$
$620$	17976.1	−	13248.7i	0.0467640	−	0.0344658i
$621$	−26910.6	+	180651.i	−0.0697815	+	0.468444i
$622$			129316.i			0.334249i
$623$	−448310.	−	776496.i	−1.15506	−	2.00061i
$624$	726349.	+	305691.i	1.86542	+	0.785078i
$625$	352387.	−	168557.i	0.902110	−	0.431507i
$626$	856346.	+	494412.i	2.18525	+	1.26165i
$627$	−14899.5	−	118344.i	−0.0378998	−	0.301032i
$628$	−965662.	+	557525.i	−2.44853	+	1.41366i
$629$		−	198916.i		−	0.502768i
$630$	992973.	−	376052.i	2.50182	−	0.947472i
$631$	539826.			1.35580			0.677900	−	0.735154i	$-0.262890\pi$
$631$	539826.			1.35580			0.677900	+	0.735154i	$0.262890\pi$
$632$	−5787.12	−	10023.6i	−0.0144887	−	0.0250951i
$633$	170502.	+	224826.i	0.425522	+	0.561097i
$634$	451630.	−	782246.i	1.12358	−	1.94610i
$635$	507755.	−	56871.3i	1.25923	−	0.141041i
$636$	640690.	+	844820.i	1.58392	+	2.08857i
$637$	−258346.	+	149156.i	−0.636682	+	0.367589i
$638$	113110.			0.277882
$639$	−57262.3	+	55980.6i	−0.140239	+	0.137099i
$640$	299513.	−	220746.i	0.731232	−	0.538930i
$641$	20172.9	−	11646.8i	0.0490967	−	0.0283460i	−0.475251	−	0.879850i	$-0.657643\pi$
$641$	20172.9	−	11646.8i	0.0490967	−	0.0283460i	0.524347	+	0.851504i	$0.324309\pi$
$642$	482992.	−	60808.5i	1.17184	−	0.147535i
$643$	86672.6	+	50040.4i	0.209633	+	0.121032i	0.601141	−	0.799143i	$-0.294713\pi$
$643$	86672.6	+	50040.4i	0.209633	+	0.121032i	−0.391508	+	0.920175i	$0.628046\pi$
$644$	−611628.	−	353124.i	−1.47474	−	0.851442i
$645$	−21832.2	+	5268.28i	−0.0524781	+	0.0126634i
$646$	−76697.4	−	132844.i	−0.183787	−	0.318329i
$647$	−315310.			−0.753232			−0.376616	−	0.926370i	$-0.622912\pi$
$647$	−315310.			−0.753232			−0.376616	+	0.926370i	$0.622912\pi$
$648$	−27157.7	+	1.19953e6i	−0.0646760	+	2.85667i
$649$	91298.7			0.216758
$650$	−125002.	−	551017.i	−0.295863	−	1.30418i
$651$	−12822.8	−	5396.61i	−0.0302567	−	0.0127338i
$652$	−23582.4	−	13615.3i	−0.0554744	−	0.0320282i
$653$	78070.8	−	135223.i	0.183089	−	0.317120i	−0.759842	−	0.650108i	$-0.774724\pi$
$653$	78070.8	−	135223.i	0.183089	−	0.317120i	0.942931	+	0.332988i	$0.108057\pi$
$654$	−27204.9	+	3425.08i	−0.0636051	+	0.00800785i
$655$	171784.	−	393025.i	0.400405	−	0.916089i
$656$		−	353646.i		−	0.821791i
$657$	348528.	−	340726.i	0.807433	−	0.789360i
$658$		−	1.82399e6i		−	4.21279i
$659$	223765.	−	129191.i	0.515253	−	0.297482i	−0.219737	−	0.975559i	$-0.570520\pi$
$659$	223765.	−	129191.i	0.515253	−	0.297482i	0.734990	+	0.678077i	$0.237187\pi$
$660$	133907.	−	453997.i	0.307407	−	1.04223i
$661$	−155879.	+	269991.i	−0.356768	+	0.617940i	−0.987419	−	0.158127i	$-0.949455\pi$
$661$	−155879.	+	269991.i	−0.356768	+	0.617940i	0.630651	+	0.776066i	$0.282788\pi$
$662$	188049.	−	325710.i	0.429096	−	0.743216i
$663$	69395.1	−	52627.5i	0.157871	−	0.119725i
$664$	−133100.	−	230535.i	−0.301884	−	0.522879i
$665$	263403.	+	357391.i	0.595631	+	0.808166i
$666$	−1.44940e6	−	406002.i	−3.26768	−	0.915334i
$667$		−	72420.1i		−	0.162782i
$668$	817626.	+	1.41617e6i	1.83232	+	3.17367i
$669$	53706.3	+	426580.i	0.119998	+	0.953122i
$670$	−716963.	+	80303.8i	−1.59716	+	0.178890i
$671$	251988.	+	145485.i	0.559674	+	0.323128i
$672$	−1.46748e6	−	617601.i	−3.24962	−	1.36763i
$673$	−561672.	+	324282.i	−1.24009	+	0.715965i	−0.969112	−	0.246621i	$-0.920680\pi$
$673$	−561672.	+	324282.i	−1.24009	+	0.715965i	−0.270976	+	0.962586i	$0.587347\pi$
$674$			373290.i			0.821726i
$675$	376351.	−	256815.i	0.826011	−	0.563654i
$676$	567455.			1.24176
$677$	124983.	+	216477.i	0.272693	+	0.472318i	0.969551	−	0.244891i	$-0.0787523\pi$
$677$	124983.	+	216477.i	0.272693	+	0.472318i	−0.696857	+	0.717210i	$0.745419\pi$
$678$	−233678.	+	555240.i	−0.508345	+	1.20787i
$679$	255675.	−	442842.i	0.554561	−	0.960527i
$680$	−40894.9	−	365115.i	−0.0884405	−	0.789609i
$681$	166308.	−	20938.0i	0.358606	−	0.0451483i
$682$	−7500.20	+	4330.24i	−0.0161252	+	0.00930986i
$683$	−100280.			−0.214968			−0.107484	−	0.994207i	$-0.534279\pi$
$683$	−100280.			−0.214968			−0.107484	+	0.994207i	$0.534279\pi$
$684$	−805273.	+	206033.i	−1.72120	+	0.440376i
$685$	−529302.	+	390104.i	−1.12803	+	0.831379i
$686$	34630.5	−	19994.0i	0.0735887	−	0.0424865i
$687$	511228.	+	674110.i	1.08318	+	1.42829i
$688$	62856.5	+	36290.2i	0.132792	+	0.0766677i
$689$	−304414.	−	175753.i	−0.641247	−	0.370224i
$690$	−405911.	−	119724.i	−0.852576	−	0.251468i
$691$	−252295.	−	436987.i	−0.528387	−	0.915193i	−0.999452	−	0.0330947i	$-0.989464\pi$
$691$	−252295.	−	436987.i	−0.528387	−	0.915193i	0.471065	−	0.882098i	$-0.343870\pi$
$692$	−1.07164e6			−2.23787
$693$	−285685.	+	73093.8i	−0.594869	+	0.152200i
$694$	1.31121e6			2.72240
$695$	525894.	+	229858.i	1.08875	+	0.475872i
$696$	−59426.8	−	472018.i	−0.122677	−	0.974406i
$697$	−33847.8	−	19542.1i	−0.0696731	−	0.0402258i
$698$	268783.	−	465545.i	0.551684	−	0.955545i
$699$	−251544.	+	597691.i	−0.514825	+	1.22327i
$700$	389774.	+	1.71815e6i	0.795457	+	3.50643i
$701$		−	309177.i		−	0.629175i	−0.949228	−	0.314588i	$-0.898134\pi$
$701$		−	309177.i		−	0.629175i	0.949228	−	0.314588i	$-0.101866\pi$
$702$	−241830.	−	613064.i	−0.490722	−	1.24403i
$703$		−	629367.i		−	1.27348i
$704$	−333165.	+	192353.i	−0.672225	+	0.388109i
$705$	−183599.	−	760849.i	−0.369395	−	1.53081i
$706$	−277320.	+	480332.i	−0.556379	+	0.963678i
$707$	133593.	−	231389.i	0.267266	−	0.462918i
$708$	−79473.5	−	631246.i	−0.158546	−	1.25931i
$709$	345777.	+	598903.i	0.687866	+	1.19142i	0.972527	+	0.232790i	$0.0747855\pi$
$709$	345777.	+	598903.i	0.687866	+	1.19142i	−0.284661	+	0.958628i	$0.591881\pi$
$710$	−110085.	−	149366.i	−0.218380	−	0.296303i
$711$	−1382.81	+	4936.55i	−0.00273542	+	0.00976527i
$712$			2.34762e6i			4.63092i
$713$	2772.48	+	4802.08i	0.00545368	+	0.00944605i
$714$	−302166.	+	229155.i	−0.592720	+	0.449504i
$715$	17466.6	+	155945.i	0.0341663	+	0.305041i
$716$	−1.48513e6	−	857443.i	−2.89694	−	1.67255i
$717$	384565.	−	291644.i	0.748052	−	0.567303i
$718$	1.25450e6	−	724284.i	2.43344	−	1.40495i
$719$		−	903805.i		−	1.74830i	−0.485652	−	0.874152i	$-0.661418\pi$
$719$		−	903805.i		−	1.74830i	0.485652	−	0.874152i	$-0.338582\pi$
$720$	−1.45327e6	−	236880.i	−2.80337	−	0.456944i
$721$	−1.27598e6			−2.45456
$722$	246509.	+	426966.i	0.472888	+	0.819066i
$723$	56481.2	−	7110.95i	0.108051	−	0.0136035i
$724$	−934201.	+	1.61808e6i	−1.78223	+	3.08691i
$725$	−132594.	+	122705.i	−0.252260	+	0.233445i
$726$	312519.	−	742574.i	0.592930	−	1.40886i
$727$	−491618.	+	283836.i	−0.930163	+	0.537030i	−0.886863	−	0.462032i	$-0.847120\pi$
$727$	−491618.	+	283836.i	−0.930163	+	0.537030i	−0.0432999	+	0.999062i	$0.513787\pi$
$728$	1.53809e6			2.90215
$729$	388326.	−	362812.i	0.730704	−	0.682694i
$730$	670035.	+	909119.i	1.25734	+	1.70598i
$731$	6946.74	−	4010.70i	0.0130001	−	0.00750561i
$732$	786546.	−	1.86891e6i	1.46792	−	3.48791i
$733$	−502558.	−	290152.i	−0.935359	−	0.540030i	−0.0468567	−	0.998902i	$-0.514920\pi$
$733$	−502558.	−	290152.i	−0.935359	−	0.540030i	−0.888503	+	0.458872i	$0.848254\pi$
$734$	330266.	+	190679.i	0.613016	+	0.353925i
$735$	403866.	−	384147.i	0.747589	−	0.711088i
$736$	317290.	+	549562.i	0.585734	+	1.01452i
$737$	200364.			0.368880
$738$	−211479.	+	206746.i	−0.388289	+	0.379598i
$739$	−257218.			−0.470991			−0.235495	−	0.971875i	$-0.575671\pi$
$739$	−257218.			−0.470991			−0.235495	+	0.971875i	$0.575671\pi$
$740$	1.00025e6	−	2.28847e6i	1.82660	−	4.17909i
$741$	219566.	−	166513.i	0.399878	−	0.303258i
$742$	1.32550e6	+	765281.i	2.40754	+	1.38999i
$743$	12250.1	−	21217.8i	0.0221902	−	0.0384346i	−0.854717	−	0.519094i	$-0.826269\pi$
$743$	12250.1	−	21217.8i	0.0221902	−	0.0384346i	0.876907	+	0.480660i	$0.159603\pi$
$744$	22010.9	+	29023.8i	0.0397642	+	0.0524335i
$745$	302399.	−	691862.i	0.544839	−	1.24654i
$746$			521781.i			0.937584i
$747$	−31803.7	+	113537.i	−0.0569949	+	0.203468i
$748$			169056.i			0.302153i
$749$	435805.	−	251612.i	0.776835	−	0.448506i
$750$	468551.	+	946039.i	0.832980	+	1.68185i
$751$	415860.	−	720290.i	0.737339	−	1.27711i	−0.216351	−	0.976316i	$-0.569416\pi$
$751$	415860.	−	720290.i	0.737339	−	1.27711i	0.953690	−	0.300792i	$-0.0972511\pi$
$752$	−1.26471e6	+	2.19054e6i	−2.23643	+	3.87361i
$753$	96050.6	+	40423.8i	0.169399	+	0.0712930i
$754$	130657.	+	226304.i	0.229821	+	0.398061i
$755$	−449933.	+	331608.i	−0.789322	+	0.581743i
$756$	754059.	+	1.91162e6i	1.31935	+	3.34471i
$757$			181974.i			0.317553i	0.987315	+	0.158777i	$0.0507550\pi$
$757$			181974.i			0.317553i	−0.987315	+	0.158777i	$0.949245\pi$
$758$	304901.	+	528105.i	0.530666	+	0.919140i
$759$	108330.	+	45591.8i	0.188047	+	0.0791413i
$760$	−129391.	−	1.15522e6i	−0.224015	−	2.00004i
$761$	−483422.	−	279104.i	−0.834752	−	0.481944i	0.0207248	−	0.999785i	$-0.493403\pi$
$761$	−483422.	−	279104.i	−0.834752	−	0.481944i	−0.855477	+	0.517841i	$0.826736\pi$
$762$	172487.	+	1.37004e6i	0.297062	+	2.35951i
$763$	−24547.1	+	14172.2i	−0.0421648	+	0.0243439i
$764$		−	200251.i		−	0.343075i
$765$	−102978.	+	126004.i	−0.175963	+	0.215309i
$766$	720601.			1.22811
$767$	105462.	+	182665.i	0.179268	+	0.310502i
$768$	−34585.5	−	45604.8i	−0.0586370	−	0.0773193i
$769$	72166.2	−	124996.i	0.122034	−	0.211369i	−0.798536	−	0.601948i	$-0.794392\pi$
$769$	72166.2	−	124996.i	0.122034	−	0.211369i	0.920570	+	0.390578i	$0.127725\pi$
$770$	−76054.8	−	679028.i	−0.128276	−	1.14527i
$771$	−208271.	−	274628.i	−0.350364	−	0.461993i
$772$	1.54186e6	−	890196.i	2.58709	−	1.49366i
$773$	−629040.			−1.05274			−0.526368	−	0.850257i	$-0.676447\pi$
$773$	−629040.			−1.05274			−0.526368	+	0.850257i	$0.676447\pi$
$774$	−15045.2	−	58803.6i	−0.0251140	−	0.0981572i
$775$	4094.61	−	13212.5i	0.00681726	−	0.0219980i
$776$	−1.15949e6	+	669433.i	−1.92550	+	1.11169i
$777$	−1.54377e6	+	194360.i	−2.55706	+	0.321933i
$778$	−215895.	−	124647.i	−0.356684	−	0.205931i
$779$	−107094.	−	61830.9i	−0.176478	−	0.101890i
$780$	1.06301e6	−	256512.i	1.74722	−	0.421617i
$781$	25766.0	+	44628.1i	0.0422421	+	0.0731655i
$782$	151150.			0.247170
$783$	−131098.	+	164974.i	−0.213832	+	0.269087i
$784$	−1.80130e6			−2.93059
$785$	−276622.	+	632887.i	−0.448898	+	1.02704i
$786$	1.06846e6	+	449671.i	1.72947	+	0.727864i
$787$	975783.	+	563368.i	1.57545	+	0.909585i	0.995483	+	0.0949424i	$0.0302667\pi$
$787$	975783.	+	563368.i	1.57545	+	0.909585i	0.579964	+	0.814642i	$0.303067\pi$
$788$	337443.	−	584468.i	0.543435	−	0.941257i
$789$	−1.12380e6	+	141486.i	−1.80524	+	0.227279i
$790$	−10884.3	−	4757.33i	−0.0174401	−	0.00762271i
$791$			622728.i			0.995280i
$792$	743484.	+	208263.i	1.18528	+	0.332018i
$793$			672216.i			1.06896i
$794$	−1.17168e6	+	676469.i	−1.85852	+	1.07302i
$795$	629946.	+	185803.i	0.996711	+	0.293980i
$796$	1.15024e6	−	1.99227e6i	1.81535	−	3.14428i
$797$	−130038.	+	225232.i	−0.204717	+	0.354580i	−0.950042	−	0.312121i	$-0.898961\pi$
$797$	−130038.	+	225232.i	−0.204717	+	0.354580i	0.745326	+	0.666700i	$0.232294\pi$
$798$	−956052.	+	725046.i	−1.50133	+	1.13857i
$799$	139773.	+	242093.i	0.218942	+	0.379218i
$800$	468598.	−	1.51208e6i	0.732184	−	2.36262i
$801$	743544.	−	726900.i	1.15889	−	1.13295i
$802$		−	1.03409e6i		−	1.60771i
$803$	−156825.	−	271629.i	−0.243212	−	0.421256i
$804$	−174412.	−	1.38533e6i	−0.269815	−	2.14309i
$805$	−434755.	+	48694.9i	−0.670892	+	0.0751436i
$806$	−17327.4	−	10004.0i	−0.0266724	−	0.0153993i
$807$	43866.2	+	18461.5i	0.0673571	+	0.0283478i
$808$	−605845.	+	349785.i	−0.927980	+	0.535769i
$809$			278756.i			0.425920i	0.977061	+	0.212960i	$0.0683103\pi$
$809$			278756.i			0.425920i	−0.977061	+	0.212960i	$0.931690\pi$
$810$	707944.	+	1.00753e6i	1.07902	+	1.53564i
$811$	384901.			0.585204			0.292602	−	0.956234i	$-0.405479\pi$
$811$	384901.			0.585204			0.292602	+	0.956234i	$0.405479\pi$
$812$	−407406.	−	705649.i	−0.617897	−	1.07023i
$813$	16666.1	−	39600.3i	0.0252147	−	0.0599125i
$814$	−484301.	+	838834.i	−0.730914	+	1.26598i
$815$	−16762.7	+	1877.52i	−0.0252365	+	0.00282663i
$816$	521781.	−	65692.0i	0.783624	−	0.0986579i
$817$	21979.5	−	12689.8i	0.0329286	−	0.0190113i
$818$	258389.			0.386161
$819$	−476244.	−	487149.i	−0.710006	−	0.726263i
$820$	−291143.	−	395030.i	−0.432991	−	0.587492i
$821$	−299051.	+	172657.i	−0.443668	+	0.256152i	−0.705152	−	0.709056i	$-0.749121\pi$
$821$	−299051.	+	172657.i	−0.443668	+	0.256152i	0.261484	+	0.965208i	$0.415788\pi$
$822$	−1.07380e6	−	1.41593e6i	−1.58921	−	2.09555i
$823$	−991676.	−	572545.i	−1.46410	−	0.845298i	−0.464901	−	0.885362i	$-0.653910\pi$
$823$	−991676.	−	572545.i	−1.46410	−	0.845298i	−0.999197	+	0.0400648i	$0.987244\pi$
$824$	2.89330e6	+	1.67045e6i	4.26126	+	2.46024i
$825$	−100075.	−	275591.i	−0.147033	−	0.404908i
$826$	−459210.	−	795376.i	−0.673057	−	1.16577i
$827$	−62165.6			−0.0908948			−0.0454474	−	0.998967i	$-0.514471\pi$
$827$	−62165.6			−0.0908948			−0.0454474	+	0.998967i	$0.514471\pi$
$828$	220926.	−	788690.i	0.322245	−	1.15039i
$829$	710786.			1.03426			0.517130	−	0.855907i	$-0.327000\pi$
$829$	710786.			1.03426			0.517130	+	0.855907i	$0.327000\pi$
$830$	−250332.	−	109415.i	−0.363379	−	0.158826i
$831$	69213.9	+	549755.i	0.100228	+	0.796099i
$832$	−769697.	−	444385.i	−1.11192	−	0.641967i
$833$	−99537.8	+	172405.i	−0.143449	+	0.248461i
$834$	−601690.	+	1.42967e6i	−0.865050	+	2.05544i
$835$	928146.	+	405675.i	1.33120	+	0.581842i
$836$			534892.i			0.765338i
$837$	2377.19	−	15958.1i	0.00339323	−	0.0227788i
$838$			1.12994e6i			1.60905i
$839$	3896.65	−	2249.73i	0.00553563	−	0.00319600i	−0.497230	−	0.867619i	$-0.665649\pi$
$839$	3896.65	−	2249.73i	0.00553563	−	0.00319600i	0.502765	+	0.864423i	$0.332316\pi$
$840$	−2.79368e6	+	674136.i	−3.95929	+	0.955408i
$841$	−311864.	+	540165.i	−0.440934	+	0.763720i
$842$	409621.	−	709484.i	0.577774	−	1.00073i
$843$	−141015.	−	1.12006e6i	−0.198431	−	1.57611i
$844$	−632670.	−	1.09582e6i	−0.888162	−	1.53834i
$845$	282954.	−	208542.i	0.396280	−	0.292065i
$846$	2.04930e6	−	524322.i	2.86328	−	0.732584i
$847$		−	832832.i		−	1.16089i
$848$	−1.06125e6	−	1.83815e6i	−1.47580	−	2.55616i
$849$	−114287.	+	86672.1i	−0.158555	+	0.120244i
$850$	−256101.	−	276742.i	−0.354465	−	0.383034i
$851$	537072.	+	310079.i	0.741606	+	0.428167i
$852$	286133.	−	216996.i	0.394175	−	0.298932i
$853$	556320.	−	321192.i	0.764587	−	0.441434i	−0.0663534	−	0.997796i	$-0.521136\pi$
$853$	556320.	−	321192.i	0.764587	−	0.441434i	0.830940	+	0.556362i	$0.187803\pi$
$854$		−	2.92702e6i		−	4.01338i
$855$	−325821.	+	398676.i	−0.445705	+	0.545366i
$856$	−1.31759e6			−1.79818
$857$	−229205.	−	396994.i	−0.312077	−	0.540533i	0.666735	−	0.745295i	$-0.267691\pi$
$857$	−229205.	−	396994.i	−0.312077	−	0.540533i	−0.978812	+	0.204762i	$0.934358\pi$
$858$	−420774.	+	52975.2i	−0.571576	+	0.0719611i
$859$	−125873.	+	218018.i	−0.170587	+	0.295465i	−0.938625	−	0.344939i	$-0.887900\pi$
$859$	−125873.	+	218018.i	−0.170587	+	0.295465i	0.768038	+	0.640404i	$0.221233\pi$
$860$	100088.	−	11210.4i	0.135327	−	0.0151574i
$861$	−118592.	+	281785.i	−0.159974	+	0.380113i
$862$	−2.23903e6	+	1.29270e6i	−3.01332	+	1.73974i
$863$	−167993.			−0.225564			−0.112782	−	0.993620i	$-0.535976\pi$
$863$	−167993.			−0.225564			−0.112782	+	0.993620i	$0.535976\pi$
$864$	272051.	−	1.82628e6i	0.364438	−	2.44648i
$865$	−534357.	+	393830.i	−0.714167	+	0.526352i
$866$	−277747.	+	160357.i	−0.370351	+	0.213822i
$867$	−269039.	+	639261.i	−0.357912	+	0.850433i
$868$	54029.2	+	31193.8i	0.0717115	+	0.0414027i
$869$	2857.01	+	1649.49i	0.00378331	+	0.00218429i
$870$	−336503.	−	353776.i	−0.444581	−	0.467402i
$871$	231446.	+	400876.i	0.305080	+	0.528413i
$872$	74214.2			0.0976010
$873$	571042.	+	159959.i	0.749272	+	0.209884i
$874$	478238.			0.626067
$875$	825781.	+	713490.i	1.07857	+	0.931905i
$876$	−1.74155e6	+	1.32075e6i	−2.26949	+	1.72112i
$877$	−105904.	−	61143.7i	−0.137693	−	0.0794973i	0.429571	−	0.903033i	$-0.358665\pi$
$877$	−105904.	−	61143.7i	−0.137693	−	0.0794973i	−0.567264	+	0.823536i	$0.691998\pi$
$878$	−750288.	+	1.29954e6i	−0.973282	+	1.68577i
$879$	−583537.	−	769458.i	−0.755250	−	0.995880i
$880$	−379483.	+	868222.i	−0.490034	+	1.12115i
$881$			1.16563e6i			1.50179i	0.660420	+	0.750897i	$0.270378\pi$
$881$			1.16563e6i			1.50179i	−0.660420	+	0.750897i	$0.729622\pi$
$882$	1.05306e6	+	1.07717e6i	1.35368	+	1.38468i
$883$		−	417334.i		−	0.535257i	−0.963522	−	0.267629i	$-0.913760\pi$
$883$		−	417334.i		−	0.535257i	0.963522	−	0.267629i	$-0.0862400\pi$
$884$	−338237.	+	195281.i	−0.432829	+	0.249894i
$885$	−271614.	−	285556.i	−0.346789	−	0.364590i
$886$	376117.	−	651454.i	0.479133	−	0.829882i
$887$	−162099.	+	280764.i	−0.206031	+	0.356856i	−0.950461	−	0.310844i	$-0.899388\pi$
$887$	−162099.	+	280764.i	−0.206031	+	0.356856i	0.744430	+	0.667701i	$0.232722\pi$
$888$	3.75496e6	+	1.58031e6i	4.76189	+	2.00409i
$889$	713714.	+	1.23619e6i	0.903068	+	1.56416i
$890$	1.42944e6	+	1.93950e6i	1.80462	+	2.44855i
$891$	−164246.	−	299963.i	−0.206890	−	0.377844i
$892$		−	1.92805e6i		−	2.42320i
$893$	442239.	+	765981.i	0.554567	+	0.960539i
$894$	1.88086e6	+	791579.i	2.35333	+	0.990420i
$895$	−1.05566e6	+	118239.i	−1.31788	+	0.147610i
$896$	900220.	+	519742.i	1.12133	+	0.647399i
$897$	33917.9	+	269405.i	0.0421546	+	0.334827i
$898$	171058.	−	98760.3i	0.212124	−	0.122470i
$899$			6397.34i			0.00791554i
$900$	−1.81834e6	+	931819.i	−2.24487	+	1.15039i
$901$	−234574.			−0.288956
$902$	95158.3	+	164819.i	0.116959	+	0.202579i
$903$	−37914.5	−	49994.4i	−0.0464975	−	0.0613121i
$904$	815242.	−	1.41204e6i	0.997585	−	1.72787i
$905$	128824.	+	1.15016e6i	0.157290	+	1.40430i
$906$	−912786.	−	1.20361e6i	−1.11202	−	1.46632i
$907$	−269459.	+	155572.i	−0.327550	+	0.189111i	−0.654753	−	0.755843i	$-0.727227\pi$
$907$	−269459.	+	155572.i	−0.327550	+	0.189111i	0.327203	+	0.944954i	$0.393894\pi$
$908$	−751674.			−0.911712
$909$	298374.	+	83579.9i	0.361105	+	0.101152i
$910$	1.27070e6	−	936530.i	1.53448	−	1.13094i
$911$	844172.	−	487383.i	1.01717	−	0.587264i	0.103888	−	0.994589i	$-0.466872\pi$
$911$	844172.	−	487383.i	1.01717	−	0.587264i	0.913284	+	0.407324i	$0.133538\pi$
$912$	1.65091e6	−	207849.i	1.98488	−	0.249895i
$913$	65709.0	+	37937.1i	0.0788286	+	0.0455117i
$914$	429462.	+	247950.i	0.514082	+	0.296806i
$915$	−294628.	−	1.22096e6i	−0.351910	−	1.45835i
$916$	−1.89698e6	−	3.28566e6i	−2.26085	−	3.91590i
$917$	1.19833e6			1.42507
$918$	−344323.	−	273619.i	−0.408583	−	0.324684i
$919$	917855.			1.08678			0.543392	−	0.839479i	$-0.317140\pi$
$919$	917855.			1.08678			0.543392	+	0.839479i	$0.317140\pi$
$920$	1.04956e6	+	458742.i	1.24003	+	0.541992i
$921$	−599383.	−	252256.i	−0.706618	−	0.297387i
$922$	502026.	+	289845.i	0.590561	+	0.340961i
$923$	−59526.1	+	103102.i	−0.0698722	+	0.121022i
$924$	1.31203e6	−	165184.i	1.53674	−	0.193475i
$925$	−342261.	−	1.50871e6i	−0.400013	−	1.76328i
$926$		−	1.22244e6i		−	1.42562i
$927$	−366792.	−	1.43360e6i	−0.426836	−	1.66828i
$928$			732127.i			0.850141i
$929$	−239512.	+	138282.i	−0.277521	+	0.160227i	−0.632301	−	0.774723i	$-0.717889\pi$
$929$	−239512.	+	138282.i	−0.277521	+	0.160227i	0.354780	+	0.934950i	$0.384556\pi$
$930$	35856.8	+	10576.0i	0.0414578	+	0.0122280i
$931$	−314937.	+	545487.i	−0.363349	+	0.629339i
$932$	1.45399e6	−	2.51838e6i	1.67390	−	2.89927i
$933$	−123524.	+	93677.5i	−0.141902	+	0.107615i
$934$	−434431.	−	752456.i	−0.497997	−	0.862556i
$935$	62128.6	+	84297.5i	0.0710671	+	0.0964254i
$936$	442139.	+	1.72809e6i	0.504670	+	1.97249i
$937$		−	1.51274e6i		−	1.72300i	−0.507755	−	0.861502i	$-0.669524\pi$
$937$		−	1.51274e6i		−	1.72300i	0.507755	−	0.861502i	$-0.330476\pi$
$938$	−1.00778e6	−	1.74553e6i	−1.14541	−	1.98391i
$939$	148077.	+	1.17615e6i	0.167941	+	1.33393i
$940$	390682.	+	3.48806e6i	0.442148	+	3.94755i
$941$	−467746.	−	270053.i	−0.528239	−	0.304979i	0.212060	−	0.977257i	$-0.431983\pi$
$941$	−467746.	−	270053.i	−0.528239	−	0.304979i	−0.740299	+	0.672278i	$0.765316\pi$
$942$	−1.72054e6	−	724104.i	−1.93893	−	0.816017i
$943$	105527.	−	60926.1i	0.118670	−	0.0685141i
$944$			1.27362e6i			1.42921i
$945$	1.07853e6	+	676086.i	1.20773	+	0.757074i
$946$	−39059.5			−0.0436460
$947$	554287.	+	960054.i	0.618066	+	1.07052i	0.989838	+	0.142198i	$0.0454169\pi$
$947$	554287.	+	960054.i	0.618066	+	1.07052i	−0.371772	+	0.928324i	$0.621250\pi$
$948$	8917.76	−	21189.4i	0.00992291	−	0.0235777i
$949$	362306.	−	627533.i	0.402294	−	0.696794i
$950$	−810301.	−	875609.i	−0.897840	−	0.970204i
$951$	1.07438e6	−	135264.i	1.18794	−	0.149561i
$952$	888915.	−	513215.i	0.980813	−	0.566273i
$953$	−1.08856e6			−1.19857			−0.599287	−	0.800534i	$-0.704549\pi$
$953$	−1.08856e6			−1.19857			−0.599287	+	0.800534i	$0.704549\pi$
$954$	−478785.	+	1.70923e6i	−0.526070	+	1.87803i
$955$	−73593.1	−	99852.8i	−0.0806920	−	0.109485i
$956$	−1.87440e6	+	1.08218e6i	−2.05091	+	1.18409i
$957$	81938.3	+	108045.i	0.0894670	+	0.117972i
$958$	2.79442e6	+	1.61336e6i	3.04481	+	1.75792i
$959$	−1.59088e6	−	918494.i	−1.72981	−	0.998709i
$960$	1.59279e6	+	469794.i	1.72829	+	0.509760i
$961$	461516.	+	799368.i	0.499735	+	0.865566i
$962$	−2.23772e6			−2.41799
$963$	407970.	+	417311.i	0.439921	+	0.449994i
$964$	−255283.			−0.274706
$965$	441681.	−	1.01053e6i	0.474301	−	1.08516i
$966$	−147689.	−	1.17307e6i	−0.158268	−	1.25710i
$967$	709046.	+	409368.i	0.758266	+	0.437785i	0.828673	−	0.559733i	$-0.189096\pi$
$967$	709046.	+	409368.i	0.758266	+	0.437785i	−0.0704069	+	0.997518i	$0.522430\pi$
$968$	−1.09030e6	+	1.88845e6i	−1.16358	+	2.01537i
$969$	71333.9	−	169496.i	0.0759711	−	0.180514i
$970$	−550310.	+	1.25906e6i	−0.584877	+	1.33814i
$971$			914500.i			0.969941i	0.874530	+	0.484971i	$0.161170\pi$
$971$			914500.i			0.969941i	−0.874530	+	0.484971i	$0.838830\pi$
$972$	−1.93100e6	+	1.39672e6i	−2.04385	+	1.47835i
$973$			1.60344e6i			1.69367i
$974$	−758898.	+	438150.i	−0.799955	+	0.461854i
$975$	435786.	−	518566.i	0.458421	−	0.545500i
$976$	−2.02953e6	+	3.51525e6i	−2.13057	+	3.69025i
$977$	−166613.	+	288582.i	−0.174550	+	0.302329i	−0.940005	−	0.341159i	$-0.889180\pi$
$977$	−166613.	+	288582.i	−0.174550	+	0.302329i	0.765455	+	0.643489i	$0.222514\pi$
$978$	−5694.38	−	45229.6i	−0.00595345	−	0.0472874i
$979$	−334569.	−	579490.i	−0.349076	−	0.604617i
$980$	−2.01209e6	+	1.48294e6i	−2.09505	+	1.54409i
$981$	−22979.2	−	23505.3i	−0.0238779	−	0.0244247i
$982$			796636.i			0.826108i
$983$	54972.2	+	95214.7i	0.0568900	+	0.0985364i	0.893068	−	0.449922i	$-0.148548\pi$
$983$	54972.2	+	95214.7i	0.0568900	+	0.0985364i	−0.836178	+	0.548458i	$0.815215\pi$
$984$	637807.	−	483697.i	0.658717	−	0.499555i
$985$	−46532.5	−	415449.i	−0.0479606	−	0.428199i
$986$	151022.	+	87192.5i	0.155341	+	0.0896862i
$987$	1.74230e6	−	1.32131e6i	1.78850	−	1.35635i
$988$	−1.07018e6	+	617868.i	−1.09633	+	0.632968i
$989$			25008.3i			0.0255677i
$990$	741044.	−	280643.i	0.756090	−	0.286341i
$991$	−1.49460e6			−1.52187			−0.760933	−	0.648830i	$-0.775259\pi$
$991$	−1.49460e6			−1.52187			−0.760933	+	0.648830i	$0.775259\pi$
$992$	−28028.3	−	48546.4i	−0.0284822	−	0.0493326i
$993$	447347.	−	56320.8i	0.453676	−	0.0571176i
$994$	259194.	−	448937.i	0.262332	−	0.454373i
$995$	−158615.	−	1.41613e6i	−0.160213	−	1.43040i
$996$	205102.	−	487340.i	0.206752	−	0.491263i
$997$	1.11051e6	−	641153.i	1.11720	−	0.645018i	0.176518	−	0.984297i	$-0.443517\pi$
$997$	1.11051e6	−	641153.i	1.11720	−	0.645018i	0.940686	+	0.339280i	$0.110183\pi$
$998$	834846.			0.838196
$999$	−662140.	−	1.67860e6i	−0.663467	−	1.68196i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.h.a.14.1	✓	44
3.2	odd	2		135.5.h.a.44.22		44
5.4	even	2	inner	45.5.h.a.14.22	yes	44
9.2	odd	6	inner	45.5.h.a.29.22	yes	44
9.4	even	3		405.5.d.a.404.43		44
9.5	odd	6		405.5.d.a.404.1		44
9.7	even	3		135.5.h.a.89.1		44
15.14	odd	2		135.5.h.a.44.1		44
45.4	even	6		405.5.d.a.404.2		44
45.14	odd	6		405.5.d.a.404.44		44
45.29	odd	6	inner	45.5.h.a.29.1	yes	44
45.34	even	6		135.5.h.a.89.22		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.h.a.14.1	✓	44	1.1	even	1	trivial
45.5.h.a.14.22	yes	44	5.4	even	2	inner
45.5.h.a.29.1	yes	44	45.29	odd	6	inner
45.5.h.a.29.22	yes	44	9.2	odd	6	inner
135.5.h.a.44.1		44	15.14	odd	2
135.5.h.a.44.22		44	3.2	odd	2
135.5.h.a.89.1		44	9.7	even	3
135.5.h.a.89.22		44	45.34	even	6
405.5.d.a.404.1		44	9.5	odd	6
405.5.d.a.404.2		44	45.4	even	6
405.5.d.a.404.43		44	9.4	even	3
405.5.d.a.404.44		44	45.14	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-3.75365 - 6.50151i) q^{2} +(3.49115 - 8.29529i) q^{3} +(-20.1797 + 34.9523i) q^{4} +(2.78274 + 24.8446i) q^{5} +(-67.0364 + 8.43986i) q^{6} +(-60.4872 + 34.9223i) q^{7} +182.874 q^{8} +(-56.6237 - 57.9202i) q^{9} +(151.082 - 111.350i) q^{10} +(-45.1408 + 26.0621i) q^{11} +(219.489 + 289.421i) q^{12} +(-104.287 - 60.2100i) q^{13} +(454.095 + 262.172i) q^{14} +(215.809 + 63.6528i) q^{15} +(-363.567 - 629.717i) q^{16} -80.3611 q^{17} +(-164.023 + 585.552i) q^{18} -254.262 q^{19} +(-924.533 - 404.095i) q^{20} +(78.5207 + 623.678i) q^{21} +(338.885 + 195.656i) q^{22} +(125.271 - 216.975i) q^{23} +(638.439 - 1516.99i) q^{24} +(-609.513 + 138.272i) q^{25} +904.028i q^{26} +(-678.147 + 267.502i) q^{27} -2818.89i q^{28} +(250.329 - 144.527i) q^{29} +(-396.230 - 1642.01i) q^{30} +(-11.0660 + 19.1668i) q^{31} +(-1266.42 + 2193.50i) q^{32} +(58.5990 + 465.443i) q^{33} +(301.647 + 522.468i) q^{34} +(-1035.95 - 1405.60i) q^{35} +(3167.10 - 810.316i) q^{36} +2475.27i q^{37} +(954.410 + 1653.09i) q^{38} +(-863.541 + 654.887i) q^{39} +(508.889 + 4543.43i) q^{40} +(421.197 + 243.178i) q^{41} +(3760.11 - 2851.57i) q^{42} +(-86.4441 + 49.9085i) q^{43} -2103.70i q^{44} +(1281.44 - 1567.97i) q^{45} -1880.89 q^{46} +(-1739.31 - 3012.56i) q^{47} +(-6492.95 + 817.460i) q^{48} +(1238.63 - 2145.37i) q^{49} +(3186.87 + 3443.73i) q^{50} +(-280.553 + 666.619i) q^{51} +(4208.96 - 2430.04i) q^{52} +2919.00 q^{53} +(4284.69 + 3404.87i) q^{54} +(-773.118 - 1048.98i) q^{55} +(-11061.5 + 6386.36i) q^{56} +(-887.667 + 2109.18i) q^{57} +(-1879.29 - 1085.01i) q^{58} +(-1516.90 - 875.781i) q^{59} +(-6579.77 + 6258.51i) q^{60} +(-2791.13 - 4834.38i) q^{61} +166.151 q^{62} +(5447.72 + 1526.00i) q^{63} +7380.58 q^{64} +(1205.69 - 2758.52i) q^{65} +(2806.12 - 2128.09i) q^{66} +(-3328.98 - 1921.99i) q^{67} +(1621.67 - 2808.81i) q^{68} +(-1362.53 - 1796.65i) q^{69} +(-5249.94 + 12011.4i) q^{70} -988.642i q^{71} +(-10355.0 - 10592.1i) q^{72} +6017.38i q^{73} +(16093.0 - 9291.29i) q^{74} +(-980.893 + 5538.82i) q^{75} +(5130.94 - 8887.05i) q^{76} +(1820.29 - 3152.84i) q^{77} +(7499.18 + 3156.10i) q^{78} +(-31.6455 - 54.8116i) q^{79} +(14633.4 - 10785.0i) q^{80} +(-148.505 + 6559.32i) q^{81} -3651.22i q^{82} +(-727.823 - 1260.63i) q^{83} +(-23383.5 - 9841.16i) q^{84} +(-223.624 - 1996.54i) q^{85} +(648.961 + 374.678i) q^{86} +(-324.961 - 2581.12i) q^{87} +(-8255.07 + 4766.06i) q^{88} +12837.4i q^{89} +(-15004.3 - 2445.66i) q^{90} +8410.68 q^{91} +(5055.85 + 8756.99i) q^{92} +(120.361 + 158.710i) q^{93} +(-13057.5 + 22616.2i) q^{94} +(-707.544 - 6317.05i) q^{95} +(13774.5 + 18163.1i) q^{96} +(-6340.40 + 3660.63i) q^{97} -18597.5 q^{98} +(4065.56 + 1138.84i) 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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