LMFDB - Embedded newform 31.5.f.a.15.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,5,Mod(15,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.15"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	31.f (of order $10$, degree $4$, 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:	$3.20446885560$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			15.8
Character	$\chi$	$=$	31.15
Dual form			31.5.f.a.29.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.11734 - 2.26488i) q^{2} +(-8.18387 + 11.2641i) q^{3} +(-0.356154 + 1.09613i) q^{4} +40.0060 q^{5} +53.6495i q^{6} +(-8.49904 + 26.1574i) q^{7} +(20.4238 + 62.8580i) q^{8} +(-34.8745 - 107.333i) q^{9} +(124.712 - 90.6087i) q^{10} +(-133.505 - 43.3784i) q^{11} +(-9.43223 - 12.9824i) q^{12} +(163.328 - 224.802i) q^{13} +(32.7489 + 100.791i) q^{14} +(-327.404 + 450.633i) q^{15} +(191.115 + 138.853i) q^{16} +(-114.667 + 37.2574i) q^{17} +(-351.811 - 255.605i) q^{18} +(207.405 - 150.689i) q^{19} +(-14.2483 + 43.8518i) q^{20} +(-225.085 - 309.803i) q^{21} +(-514.427 + 167.148i) q^{22} +(781.887 - 254.050i) q^{23} +(-875.187 - 284.365i) q^{24} +975.481 q^{25} -1070.70i q^{26} +(421.833 + 137.062i) q^{27} +(-25.6449 - 18.6321i) q^{28} +(23.1624 + 31.8803i) q^{29} +2146.30i q^{30} +(-838.947 + 468.710i) q^{31} -147.231 q^{32} +(1581.21 - 1148.82i) q^{33} +(-273.071 + 375.850i) q^{34} +(-340.013 + 1046.45i) q^{35} +130.071 q^{36} -289.826i q^{37} +(305.261 - 939.495i) q^{38} +(1195.54 + 3679.51i) q^{39} +(817.075 + 2514.70i) q^{40} +(543.737 - 395.048i) q^{41} +(-1403.33 - 455.970i) q^{42} +(-845.722 - 1164.04i) q^{43} +(95.0969 - 130.890i) q^{44} +(-1395.19 - 4293.95i) q^{45} +(1862.01 - 2562.84i) q^{46} +(-1606.66 - 1167.31i) q^{47} +(-3128.12 + 1016.39i) q^{48} +(1330.48 + 966.647i) q^{49} +(3040.90 - 2209.35i) q^{50} +(518.743 - 1596.53i) q^{51} +(188.243 + 259.094i) q^{52} +(-3255.73 + 1057.85i) q^{53} +(1625.42 - 528.132i) q^{54} +(-5341.01 - 1735.40i) q^{55} -1817.78 q^{56} +3569.46i q^{57} +(144.410 + 46.9217i) q^{58} +(2390.22 + 1736.60i) q^{59} +(-377.346 - 519.372i) q^{60} +3430.53i q^{61} +(-1553.71 + 3361.24i) q^{62} +3103.94 q^{63} +(-3516.81 + 2555.11i) q^{64} +(6534.12 - 8993.45i) q^{65} +(2327.23 - 7162.49i) q^{66} +2831.54 q^{67} -138.959i q^{68} +(-3537.20 + 10886.4i) q^{69} +(1310.15 + 4032.23i) q^{70} +(-1902.53 - 5855.37i) q^{71} +(6034.45 - 4384.28i) q^{72} +(-6561.51 - 2131.96i) q^{73} +(-656.420 - 903.484i) q^{74} +(-7983.21 + 10987.9i) q^{75} +(91.3063 + 281.012i) q^{76} +(2269.33 - 3123.47i) q^{77} +(12060.5 + 8762.50i) q^{78} +(-1916.37 + 622.665i) q^{79} +(7645.75 + 5554.96i) q^{80} +(2399.41 - 1743.27i) q^{81} +(800.277 - 2463.00i) q^{82} +(2633.41 + 3624.58i) q^{83} +(419.749 - 136.385i) q^{84} +(-4587.35 + 1490.52i) q^{85} +(-5272.80 - 1713.24i) q^{86} -548.662 q^{87} -9277.82i q^{88} +(-2910.29 - 945.612i) q^{89} +(-14074.5 - 10225.8i) q^{90} +(4492.10 + 6182.85i) q^{91} +947.531i q^{92} +(1586.23 - 13285.9i) q^{93} -7652.32 q^{94} +(8297.46 - 6028.46i) q^{95} +(1204.92 - 1658.43i) q^{96} +(-3657.46 + 11256.5i) q^{97} +6336.88 q^{98} +15842.3i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} - 5 q^{3} - 79 q^{4} - 2 q^{5} - 73 q^{7} + 173 q^{8} + 62 q^{9} + 84 q^{10} + 100 q^{11} + 150 q^{12} - 260 q^{13} + 488 q^{14} - 1075 q^{15} + 777 q^{16} - 725 q^{17} - 786 q^{18} - 1581 q^{19}+ \cdots + 74456 q^{98}+O(q^{100}) $ 36 * q - 3 * q^2 - 5 * q^3 - 79 * q^4 - 2 * q^5 - 73 * q^7 + 173 * q^8 + 62 * q^9 + 84 * q^10 + 100 * q^11 + 150 * q^12 - 260 * q^13 + 488 * q^14 - 1075 * q^15 + 777 * q^16 - 725 * q^17 - 786 * q^18 - 1581 * q^19 + 827 * q^20 + 2335 * q^21 - 1030 * q^22 + 1675 * q^23 - 165 * q^24 + 1294 * q^25 - 2855 * q^27 + 352 * q^28 - 575 * q^29 + 895 * q^31 - 5470 * q^32 + 4468 * q^33 + 1815 * q^34 - 3042 * q^35 + 7808 * q^36 - 6604 * q^38 + 595 * q^39 + 1482 * q^40 - 1740 * q^41 + 3840 * q^42 - 10055 * q^43 - 5780 * q^44 + 6774 * q^45 + 16515 * q^46 + 693 * q^47 + 4710 * q^48 - 944 * q^49 - 6240 * q^50 + 12641 * q^51 + 15885 * q^52 - 10835 * q^53 - 25960 * q^54 - 14010 * q^55 - 19976 * q^56 + 4755 * q^58 - 6021 * q^59 + 35 * q^60 - 11088 * q^62 - 15564 * q^63 + 6935 * q^64 + 26645 * q^65 + 23988 * q^66 + 28596 * q^67 - 4229 * q^69 + 8041 * q^70 + 31101 * q^71 + 20690 * q^72 + 6125 * q^73 - 47295 * q^74 - 27475 * q^75 + 12511 * q^76 + 35950 * q^77 + 29801 * q^78 - 29050 * q^79 - 47358 * q^80 - 1965 * q^81 + 9198 * q^82 + 21640 * q^83 - 35875 * q^84 - 55360 * q^85 - 27935 * q^86 - 2262 * q^87 - 11645 * q^89 - 14916 * q^90 + 670 * q^91 - 36224 * q^93 - 52442 * q^94 + 73983 * q^95 + 29810 * q^96 + 55059 * q^97 + 74456 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	3.11734	−	2.26488i	0.779334	−	0.566219i	−0.125445	−	0.992101i	$-0.540036\pi$
$2$	3.11734	−	2.26488i	0.779334	−	0.566219i	0.904779	+	0.425881i	$0.140036\pi$
$3$	−8.18387	+	11.2641i	−0.909318	+	1.25157i	0.0580804	+	0.998312i	$0.481502\pi$
$3$	−8.18387	+	11.2641i	−0.909318	+	1.25157i	−0.967399	+	0.253258i	$0.918498\pi$
$4$	−0.356154	+	1.09613i	−0.0222596	+	0.0685082i
$5$	40.0060			1.60024			0.800120	−	0.599840i	$-0.204769\pi$
$5$	40.0060			1.60024			0.800120	+	0.599840i	$0.204769\pi$
$6$			53.6495i			1.49026i
$7$	−8.49904	+	26.1574i	−0.173450	+	0.533824i	−0.999559	−	0.0296859i	$-0.990549\pi$
$7$	−8.49904	+	26.1574i	−0.173450	+	0.533824i	0.826109	+	0.563510i	$0.190549\pi$
$8$	20.4238	+	62.8580i	0.319122	+	0.982157i
$9$	−34.8745	−	107.333i	−0.430549	−	1.32509i
$10$	124.712	−	90.6087i	1.24712	−	0.906087i
$11$	−133.505	−	43.3784i	−1.10335	−	0.358500i	−0.299958	−	0.953952i	$-0.596973\pi$
$11$	−133.505	−	43.3784i	−1.10335	−	0.358500i	−0.803390	+	0.595453i	$0.796973\pi$
$12$	−9.43223	−	12.9824i	−0.0655016	−	0.0901552i
$13$	163.328	−	224.802i	0.966441	−	1.33019i	0.0226163	−	0.999744i	$-0.492800\pi$
$13$	163.328	−	224.802i	0.966441	−	1.33019i	0.943824	−	0.330447i	$-0.107200\pi$
$14$	32.7489	+	100.791i	0.167086	+	0.514238i
$15$	−327.404	+	450.633i	−1.45513	+	2.00281i
$16$	191.115	+	138.853i	0.746543	+	0.542395i
$17$	−114.667	+	37.2574i	−0.396770	+	0.128918i	−0.500604	−	0.865676i	$-0.666889\pi$
$17$	−114.667	+	37.2574i	−0.396770	+	0.128918i	0.103834	+	0.994595i	$0.466889\pi$
$18$	−351.811	−	255.605i	−1.08584	−	0.788906i
$19$	207.405	−	150.689i	0.574530	−	0.417420i	−0.262218	−	0.965009i	$-0.584454\pi$
$19$	207.405	−	150.689i	0.574530	−	0.417420i	0.836748	+	0.547588i	$0.184454\pi$
$20$	−14.2483	+	43.8518i	−0.0356208	+	0.109630i
$21$	−225.085	−	309.803i	−0.510397	−	0.702501i
$22$	−514.427	+	167.148i	−1.06287	+	0.345346i
$23$	781.887	−	254.050i	1.47805	−	0.480247i	0.544518	−	0.838749i	$-0.316713\pi$
$23$	781.887	−	254.050i	1.47805	−	0.480247i	0.933529	+	0.358503i	$0.116713\pi$
$24$	−875.187	−	284.365i	−1.51942	−	0.493690i
$25$	975.481			1.56077
$26$		−	1070.70i		−	1.58388i
$27$	421.833	+	137.062i	0.578645	+	0.188013i
$28$	−25.6449	−	18.6321i	−0.0327104	−	0.0237655i
$29$	23.1624	+	31.8803i	0.0275415	+	0.0379076i	0.822566	−	0.568670i	$-0.192542\pi$
$29$	23.1624	+	31.8803i	0.0275415	+	0.0379076i	−0.795024	+	0.606578i	$0.792542\pi$
$30$			2146.30i			2.38478i
$31$	−838.947	+	468.710i	−0.872994	+	0.487731i
$31$	−838.947	+	468.710i	−0.872994	+	0.487731i
$32$	−147.231			−0.143780
$33$	1581.21	−	1148.82i	1.45198	−	1.05493i
$34$	−273.071	+	375.850i	−0.236220	+	0.325129i
$35$	−340.013	+	1046.45i	−0.277562	+	0.854247i
$36$	130.071			0.100364
$37$		−	289.826i		−	0.211706i	−0.994382	−	0.105853i	$-0.966243\pi$
$37$		−	289.826i		−	0.211706i	0.994382	−	0.105853i	$-0.0337573\pi$
$38$	305.261	−	939.495i	0.211399	−	0.650620i
$39$	1195.54	+	3679.51i	0.786025	+	2.41914i
$40$	817.075	+	2514.70i	0.510672	+	1.57169i
$41$	543.737	−	395.048i	0.323461	−	0.235008i	−0.414190	−	0.910190i	$-0.635935\pi$
$41$	543.737	−	395.048i	0.323461	−	0.235008i	0.737651	+	0.675182i	$0.235935\pi$
$42$	−1403.33	−	455.970i	−0.795539	−	0.258486i
$43$	−845.722	−	1164.04i	−0.457394	−	0.629549i	0.516572	−	0.856244i	$-0.327208\pi$
$43$	−845.722	−	1164.04i	−0.457394	−	0.629549i	−0.973966	+	0.226695i	$0.927208\pi$
$44$	95.0969	−	130.890i	0.0491203	−	0.0676083i
$45$	−1395.19	−	4293.95i	−0.688982	−	2.12047i
$46$	1862.01	−	2562.84i	0.879968	−	1.21117i
$47$	−1606.66	−	1167.31i	−0.727325	−	0.528433i	0.161391	−	0.986891i	$-0.448402\pi$
$47$	−1606.66	−	1167.31i	−0.727325	−	0.528433i	−0.888716	+	0.458458i	$0.848402\pi$
$48$	−3128.12	+	1016.39i	−1.35769	+	0.441140i
$49$	1330.48	+	966.647i	0.554134	+	0.402602i
$50$	3040.90	−	2209.35i	1.21636	−	0.883738i
$51$	518.743	−	1596.53i	0.199440	−	0.613813i
$52$	188.243	+	259.094i	0.0696163	+	0.0958187i
$53$	−3255.73	+	1057.85i	−1.15903	+	0.376593i	−0.824539	−	0.565804i	$-0.808566\pi$
$53$	−3255.73	+	1057.85i	−1.15903	+	0.376593i	−0.334495	+	0.942398i	$0.608566\pi$
$54$	1625.42	−	528.132i	0.557415	−	0.181115i
$55$	−5341.01	−	1735.40i	−1.76562	−	0.573686i
$56$	−1817.78			−0.579651
$57$			3569.46i			1.09863i
$58$	144.410	+	46.9217i	0.0429281	+	0.0139482i
$59$	2390.22	+	1736.60i	0.686648	+	0.498879i	0.875557	−	0.483115i	$-0.160495\pi$
$59$	2390.22	+	1736.60i	0.686648	+	0.498879i	−0.188908	+	0.981995i	$0.560495\pi$
$60$	−377.346	−	519.372i	−0.104818	−	0.144270i
$61$			3430.53i			0.921937i	0.887416	+	0.460969i	$0.152498\pi$
$61$			3430.53i			0.921937i	−0.887416	+	0.460969i	$0.847502\pi$
$62$	−1553.71	+	3361.24i	−0.404191	+	0.874412i
$63$	3103.94			0.782046
$64$	−3516.81	+	2555.11i	−0.858595	+	0.623806i
$65$	6534.12	−	8993.45i	1.54654	−	2.12863i
$66$	2327.23	−	7162.49i	0.534259	−	1.64428i
$67$	2831.54			0.630773			0.315387	−	0.948963i	$-0.397866\pi$
$67$	2831.54			0.630773			0.315387	+	0.948963i	$0.397866\pi$
$68$		−	138.959i		−	0.0300517i
$69$	−3537.20	+	10886.4i	−0.742953	+	2.28658i
$70$	1310.15	+	4032.23i	0.267378	+	0.822904i
$71$	−1902.53	−	5855.37i	−0.377410	−	1.16155i	−0.941838	−	0.336067i	$-0.890903\pi$
$71$	−1902.53	−	5855.37i	−0.377410	−	1.16155i	0.564428	−	0.825482i	$-0.309097\pi$
$72$	6034.45	−	4384.28i	1.16405	−	0.845734i
$73$	−6561.51	−	2131.96i	−1.23128	−	0.400068i	−0.380105	−	0.924943i	$-0.624112\pi$
$73$	−6561.51	−	2131.96i	−1.23128	−	0.400068i	−0.851179	+	0.524875i	$0.824112\pi$
$74$	−656.420	−	903.484i	−0.119872	−	0.164990i
$75$	−7983.21	+	10987.9i	−1.41924	+	1.95341i
$76$	91.3063	+	281.012i	0.0158079	+	0.0486516i
$77$	2269.33	−	3123.47i	0.382751	−	0.526812i
$78$	12060.5	+	8762.50i	1.98234	+	1.44025i
$79$	−1916.37	+	622.665i	−0.307061	+	0.0997701i	−0.458494	−	0.888697i	$-0.651611\pi$
$79$	−1916.37	+	622.665i	−0.307061	+	0.0997701i	0.151433	+	0.988467i	$0.451611\pi$
$80$	7645.75	+	5554.96i	1.19465	+	0.867962i
$81$	2399.41	−	1743.27i	0.365708	−	0.265702i
$82$	800.277	−	2463.00i	0.119018	−	0.366299i
$83$	2633.41	+	3624.58i	0.382263	+	0.526140i	0.956182	−	0.292772i	$-0.0945776\pi$
$83$	2633.41	+	3624.58i	0.382263	+	0.526140i	−0.573919	+	0.818912i	$0.694578\pi$
$84$	419.749	−	136.385i	0.0594883	−	0.0193289i
$85$	−4587.35	+	1490.52i	−0.634927	+	0.206300i
$86$	−5272.80	−	1713.24i	−0.712926	−	0.231644i
$87$	−548.662			−0.0724881
$88$		−	9277.82i		−	1.19807i
$89$	−2910.29	−	945.612i	−0.367415	−	0.119380i	0.119490	−	0.992835i	$-0.461874\pi$
$89$	−2910.29	−	945.612i	−0.367415	−	0.119380i	−0.486905	+	0.873455i	$0.661874\pi$
$90$	−14074.5	−	10225.8i	−1.73760	−	1.26244i
$91$	4492.10	+	6182.85i	0.542459	+	0.746631i
$92$			947.531i			0.111948i
$93$	1586.23	−	13285.9i	0.183400	−	1.53612i
$94$	−7652.32			−0.866038
$95$	8297.46	−	6028.46i	0.919386	−	0.667973i
$96$	1204.92	−	1658.43i	0.130742	−	0.179951i
$97$	−3657.46	+	11256.5i	−0.388719	+	1.19636i	0.545026	+	0.838419i	$0.316520\pi$
$97$	−3657.46	+	11256.5i	−0.388719	+	1.19636i	−0.933746	+	0.357937i	$0.883480\pi$
$98$	6336.88			0.659817
$99$			15842.3i			1.61639i
$100$	−347.422	+	1069.25i	−0.0347422	+	0.106925i
$101$	−5253.04	−	16167.2i	−0.514954	−	1.58486i	−0.783366	−	0.621560i	$-0.786499\pi$
$101$	−5253.04	−	16167.2i	−0.514954	−	1.58486i	0.268413	−	0.963304i	$-0.413501\pi$
$102$	−1998.84	−	6151.81i	−0.192123	−	0.591292i
$103$	142.494	−	103.528i	0.0134314	−	0.00975849i	−0.581049	−	0.813868i	$-0.697358\pi$
$103$	142.494	−	103.528i	0.0134314	−	0.00975849i	0.594481	+	0.804110i	$0.297358\pi$
$104$	17466.4	+	5675.19i	1.61487	+	0.524703i
$105$	−9004.75	−	12394.0i	−0.816757	−	1.12417i
$106$	−7753.30	+	10671.5i	−0.690041	+	0.949760i
$107$	−1949.61	−	6000.27i	−0.170286	−	0.524087i	0.829101	−	0.559099i	$-0.188853\pi$
$107$	−1949.61	−	6000.27i	−0.170286	−	0.524087i	−0.999387	+	0.0350122i	$0.988853\pi$
$108$	−300.475	+	413.568i	−0.0257609	+	0.0354568i
$109$	5800.21	+	4214.10i	0.488192	+	0.354693i	0.804489	−	0.593968i	$-0.202439\pi$
$109$	5800.21	+	4214.10i	0.488192	+	0.354693i	−0.316296	+	0.948660i	$0.602439\pi$
$110$	−20580.2	+	6686.91i	−1.70084	+	0.552637i
$111$	3264.63	+	2371.90i	0.264965	+	0.192508i
$112$	−5256.33	+	3818.94i	−0.419031	+	0.304444i
$113$	−568.446	+	1749.50i	−0.0445177	+	0.137011i	−0.970845	−	0.239709i	$-0.922948\pi$
$113$	−568.446	+	1749.50i	−0.0445177	+	0.137011i	0.926327	+	0.376720i	$0.122948\pi$
$114$	8084.38	+	11127.2i	0.622067	+	0.856202i
$115$	31280.2	−	10163.5i	2.36523	−	0.768510i
$116$	−43.1944	+	14.0347i	−0.00321005	+	0.00104301i
$117$	−29824.6	−	9690.61i	−2.17873	−	0.707912i
$118$	11384.3			0.817604
$119$		−	3316.03i		−	0.234166i
$120$	−35012.7	−	11376.3i	−2.43144	−	0.790023i
$121$	4097.11	+	2976.73i	0.279838	+	0.203314i
$122$	7769.73	+	10694.1i	0.522019	+	0.718497i
$123$			9357.75i			0.618531i
$124$	−214.972	−	1086.53i	−0.0139810	−	0.0706639i
$125$	14021.3			0.897366
$126$	9676.02	−	7030.04i	0.609475	−	0.442809i
$127$	−706.088	+	971.847i	−0.0437775	+	0.0602546i	−0.830345	−	0.557250i	$-0.811856\pi$
$127$	−706.088	+	971.847i	−0.0437775	+	0.0602546i	0.786567	+	0.617505i	$0.211856\pi$
$128$	−4448.11	+	13689.9i	−0.271491	+	0.835564i
$129$	20033.1			1.20384
$130$		−	42834.6i		−	2.53459i
$131$	−6646.07	+	20454.5i	−0.387277	+	1.19192i	0.547537	+	0.836781i	$0.315565\pi$
$131$	−6646.07	+	20454.5i	−0.387277	+	1.19192i	−0.934815	+	0.355136i	$0.884435\pi$
$132$	696.097	+	2142.37i	0.0399505	+	0.122955i
$133$	2178.88	+	6705.89i	0.123177	+	0.379099i
$134$	8826.87	−	6413.09i	0.491583	−	0.357156i
$135$	16875.8	+	5483.29i	0.925972	+	0.300866i
$136$	−4683.86	−	6446.77i	−0.253236	−	0.348550i
$137$	5084.12	−	6997.69i	0.270879	−	0.372832i	−0.651807	−	0.758384i	$-0.725989\pi$
$137$	5084.12	−	6997.69i	0.270879	−	0.372832i	0.922686	+	0.385552i	$0.125989\pi$
$138$	13629.7	+	41947.9i	0.715694	+	2.20268i
$139$	6855.63	−	9435.97i	0.354828	−	0.488379i	−0.593871	−	0.804561i	$-0.702401\pi$
$139$	6855.63	−	9435.97i	0.354828	−	0.488379i	0.948699	+	0.316182i	$0.102401\pi$
$140$	−1025.95	−	745.397i	−0.0523444	−	0.0380305i
$141$	26297.4	−	8544.55i	1.32274	−	0.429785i
$142$	−19192.5	−	13944.2i	−0.951821	−	0.691538i
$143$	−31556.8	+	22927.3i	−1.54319	+	1.12120i
$144$	8238.43	−	25355.3i	0.397301	−	1.22277i
$145$	926.636	+	1275.40i	0.0440730	+	0.0606613i
$146$	−25283.1	+	8214.97i	−1.18611	+	0.385390i
$147$	−21776.9	+	7075.73i	−1.00777	+	0.327444i
$148$	317.687	+	103.223i	0.0145036	+	0.00471250i
$149$	−13393.2			−0.603272			−0.301636	−	0.953423i	$-0.597533\pi$
$149$	−13393.2			−0.603272			−0.301636	+	0.953423i	$0.597533\pi$
$150$			52334.1i			2.32596i
$151$	21963.3	+	7136.32i	0.963262	+	0.312983i	0.748093	−	0.663594i	$-0.230970\pi$
$151$	21963.3	+	7136.32i	0.963262	+	0.312983i	0.215169	+	0.976577i	$0.430970\pi$
$152$	13708.0	+	9959.45i	0.593318	+	0.431070i
$153$	7997.87	+	11008.1i	0.341658	+	0.470252i
$154$		−	14876.7i		−	0.627284i
$155$	−33562.9	+	18751.2i	−1.39700	+	0.780487i
$156$	−4459.02			−0.183227
$157$	−678.948	+	493.284i	−0.0275446	+	0.0200124i	−0.601472	−	0.798894i	$-0.705419\pi$
$157$	−678.948	+	493.284i	−0.0275446	+	0.0200124i	0.573928	+	0.818906i	$0.305419\pi$
$158$	−4563.70	+	6281.39i	−0.182811	+	0.251618i
$159$	14728.7	−	45330.2i	0.582599	−	1.79306i
$160$	−5890.12			−0.230083
$161$			22611.3i			0.872315i
$162$	3531.46	−	10868.7i	0.134563	−	0.414142i
$163$	−2628.27	−	8088.99i	−0.0989225	−	0.304452i	0.889334	−	0.457259i	$-0.151169\pi$
$163$	−2628.27	−	8088.99i	−0.0989225	−	0.304452i	−0.988256	+	0.152807i	$0.951169\pi$
$164$	239.370	+	736.705i	0.00889984	+	0.0273909i
$165$	63257.8	−	45959.5i	2.32352	−	1.68814i
$166$	16418.5	+	5334.68i	0.595822	+	0.193594i
$167$	−32673.7	−	44971.6i	−1.17156	−	1.61252i	−0.652519	−	0.757772i	$-0.726288\pi$
$167$	−32673.7	−	44971.6i	−1.17156	−	1.61252i	−0.519045	−	0.854747i	$-0.673712\pi$
$168$	14876.5	−	20475.7i	0.527087	−	0.725473i
$169$	−15034.1	−	46270.1i	−0.526385	−	1.62005i
$170$	−10924.5	+	15036.2i	−0.378009	+	0.520285i
$171$	−23407.0	−	17006.2i	−0.800485	−	0.581586i
$172$	1577.14	−	512.445i	0.0533107	−	0.0173217i
$173$	−44858.1	−	32591.3i	−1.49882	−	1.08895i	−0.970850	−	0.239689i	$-0.922954\pi$
$173$	−44858.1	−	32591.3i	−1.49882	−	1.08895i	−0.527967	−	0.849265i	$-0.677046\pi$
$174$	−1710.36	+	1242.65i	−0.0564924	+	0.0410441i
$175$	−8290.66	+	25516.0i	−0.270715	+	0.833176i
$176$	−19491.6	−	26827.9i	−0.629248	−	0.866086i
$177$	−39122.5	+	12711.7i	−1.24876	+	0.405748i
$178$	−11214.1	+	3643.67i	−0.353934	+	0.115000i
$179$	46037.1	+	14958.4i	1.43682	+	0.466851i	0.920904	−	0.389790i	$-0.127452\pi$
$179$	46037.1	+	14958.4i	1.43682	+	0.466851i	0.515914	+	0.856640i	$0.327452\pi$
$180$	5203.63			0.160606
$181$			47236.9i			1.44187i	0.693005	+	0.720933i	$0.256286\pi$
$181$			47236.9i			1.44187i	−0.693005	+	0.720933i	$0.743714\pi$
$182$	28006.8	+	9099.96i	0.845514	+	0.274724i
$183$	−38641.9	−	28075.0i	−1.15387	−	0.838334i
$184$	31938.2	+	43959.2i	0.943355	+	1.29842i
$185$		−	11594.8i		−	0.338781i
$186$	−25146.1	−	45009.1i	−0.726849	−	1.30099i
$187$	16924.7			0.483993
$188$	1851.74	−	1345.37i	0.0523920	−	0.0380650i
$189$	−7170.35	+	9869.14i	−0.200732	+	0.276284i
$190$	12212.3	−	37585.5i	0.338290	−	1.04115i
$191$	36061.2			0.988493			0.494247	−	0.869322i	$-0.335444\pi$
$191$	36061.2			0.988493			0.494247	+	0.869322i	$0.335444\pi$
$192$		−	60524.4i		−	1.64183i
$193$	−2058.13	+	6334.26i	−0.0552532	+	0.170052i	−0.974875	−	0.222754i	$-0.928495\pi$
$193$	−2058.13	+	6334.26i	−0.0552532	+	0.170052i	0.919622	+	0.392805i	$0.128495\pi$
$194$	14093.1	+	43374.0i	0.374457	+	1.15246i
$195$	47828.9	+	147202.i	1.25783	+	3.87120i
$196$	−1533.43	+	1114.10i	−0.0399163	+	0.0290009i
$197$	35169.2	+	11427.2i	0.906214	+	0.294447i	0.724799	−	0.688960i	$-0.241932\pi$
$197$	35169.2	+	11427.2i	0.906214	+	0.294447i	0.181414	+	0.983407i	$0.441932\pi$
$198$	35880.8	+	49385.7i	0.915233	+	1.25971i
$199$	−44624.6	+	61420.5i	−1.12686	+	1.55098i	−0.332949	+	0.942945i	$0.608044\pi$
$199$	−44624.6	+	61420.5i	−1.12686	+	1.55098i	−0.793907	+	0.608040i	$0.791956\pi$
$200$	19923.0	+	61316.8i	0.498076	+	1.53292i
$201$	−23173.0	+	31894.8i	−0.573574	+	0.789457i
$202$	−52992.2	−	38501.1i	−1.29870	−	0.943562i
$203$	−1030.76	+	334.916i	−0.0250131	+	0.00812724i
$204$	1565.25	+	1137.22i	0.0376117	+	0.0273265i
$205$	21752.8	−	15804.3i	0.517615	−	0.376069i
$206$	209.723	−	645.462i	0.00494211	−	0.0152103i
$207$	−54535.8	−	75062.1i	−1.27274	−	1.75178i
$208$	62429.0	−	20284.4i	1.44298	−	0.468852i
$209$	−34226.3	+	11120.8i	−0.783552	+	0.254591i
$210$	−56141.7	−	18241.5i	−1.27305	−	0.413640i
$211$	12394.6			0.278399			0.139200	−	0.990264i	$-0.455547\pi$
$211$	12394.6			0.278399			0.139200	+	0.990264i	$0.455547\pi$
$212$		−	3945.46i		−	0.0877861i
$213$	81525.6	+	26489.3i	1.79695	+	0.583863i
$214$	−19667.5	−	14289.3i	−0.429458	−	0.312020i
$215$	−33834.0	−	46568.4i	−0.731941	−	1.00743i
$216$			29314.9i			0.628320i
$217$	−5129.96	−	25928.2i	−0.108942	−	0.550622i
$218$	27625.6			0.581299
$219$	77713.3	−	56462.0i	1.62034	−	1.17725i
$220$	3804.45	−	5236.37i	0.0786043	−	0.108190i
$221$	−10352.8	+	31862.5i	−0.211969	+	0.652372i
$222$	15549.0			0.315498
$223$			14232.9i			0.286210i	0.989707	+	0.143105i	$0.0457087\pi$
$223$			14232.9i			0.286210i	−0.989707	+	0.143105i	$0.954291\pi$
$224$	1251.32	−	3851.17i	0.0249386	−	0.0767533i
$225$	−34019.4	−	104701.i	−0.671988	−	2.06817i
$226$	2190.36	+	6741.24i	0.0428843	+	0.131984i
$227$	−19952.1	+	14496.0i	−0.387201	+	0.281318i	−0.764308	−	0.644852i	$-0.776919\pi$
$227$	−19952.1	+	14496.0i	−0.387201	+	0.281318i	0.377106	+	0.926170i	$0.376919\pi$
$228$	−3912.59	−	1271.28i	−0.0752653	−	0.0244552i
$229$	42396.5	+	58353.8i	0.808461	+	1.11275i	0.991559	+	0.129656i	$0.0413874\pi$
$229$	42396.5	+	58353.8i	0.808461	+	1.11275i	−0.183098	+	0.983095i	$0.558613\pi$
$230$	74491.6	−	102529.i	1.40816	−	1.93817i
$231$	16611.2	+	51124.1i	0.311299	+	0.958080i
$232$	−1530.87	+	2107.06i	−0.0284421	+	0.0391473i
$233$	20683.3	+	15027.3i	0.380985	+	0.276802i	0.761751	−	0.647870i	$-0.224340\pi$
$233$	20683.3	+	15027.3i	0.380985	+	0.276802i	−0.380766	+	0.924671i	$0.624340\pi$
$234$	−114921.	+	37340.2i	−2.09879	+	0.681939i
$235$	−64276.1	−	46699.3i	−1.16390	−	0.845620i
$236$	−2754.83	+	2001.50i	−0.0494619	+	0.0359361i
$237$	8669.51	−	26682.0i	0.154347	−	0.475031i
$238$	−7510.40	−	10337.2i	−0.132589	−	0.182494i
$239$	−31819.9	+	10338.9i	−0.557061	+	0.181000i	−0.573999	−	0.818856i	$-0.694608\pi$
$239$	−31819.9	+	10338.9i	−0.557061	+	0.181000i	0.0169371	+	0.999857i	$0.494608\pi$
$240$	−125144.	+	40661.6i	−2.17263	+	0.705930i
$241$	35625.8	+	11575.5i	0.613381	+	0.199300i	0.599199	−	0.800600i	$-0.295486\pi$
$241$	35625.8	+	11575.5i	0.613381	+	0.199300i	0.0141816	+	0.999899i	$0.495486\pi$
$242$	19514.0			0.333208
$243$			77220.8i			1.30774i
$244$	−3760.31	−	1221.80i	−0.0631602	−	0.0205220i
$245$	53227.0	+	38671.7i	0.886748	+	0.644260i
$246$	21194.2	+	29171.3i	0.350224	+	0.482042i
$247$		−	71237.0i		−	1.16765i
$248$	−46596.7	−	43161.7i	−0.757620	−	0.701771i
$249$	−62379.2			−1.00610
$250$	43709.3	−	31756.6i	0.699348	−	0.508106i
$251$	−5718.05	+	7870.22i	−0.0907613	+	0.124922i	−0.851983	−	0.523570i	$-0.824600\pi$
$251$	−5718.05	+	7870.22i	−0.0907613	+	0.124922i	0.761222	+	0.648492i	$0.224600\pi$
$252$	−1105.48	+	3402.32i	−0.0174081	+	0.0535765i
$253$	−115406.			−1.80297
$254$			4628.78i			0.0717462i
$255$	20752.9	−	63870.7i	0.319152	−	0.982249i
$256$	−4353.17	−	13397.7i	−0.0664241	−	0.204432i
$257$	−18623.7	−	57317.8i	−0.281968	−	0.867807i	−0.987291	−	0.158922i	$-0.949198\pi$
$257$	−18623.7	−	57317.8i	−0.281968	−	0.867807i	0.705323	−	0.708886i	$-0.250802\pi$
$258$	62450.0	−	45372.6i	0.938195	−	0.681638i
$259$	7581.08	+	2463.24i	0.113014	+	0.0367204i
$260$	7530.83	+	10365.3i	0.111403	+	0.153333i
$261$	2614.02	−	3597.89i	0.0383732	−	0.0528162i
$262$	25608.9	+	78816.1i	0.373068	+	1.14819i
$263$	44691.3	−	61512.3i	0.646117	−	0.889304i	−0.352806	−	0.935696i	$-0.614772\pi$
$263$	44691.3	−	61512.3i	0.646117	−	0.889304i	0.998923	+	0.0463923i	$0.0147724\pi$
$264$	104507.	+	75928.5i	1.49946	+	1.08942i
$265$	−130249.	+	42320.4i	−1.85473	+	0.602640i
$266$	21980.3	+	15969.6i	0.310649	+	0.225700i
$267$	34468.9	−	25043.1i	0.483510	−	0.351291i
$268$	−1008.47	+	3103.74i	−0.0140408	+	0.0432131i
$269$	40988.9	+	56416.4i	0.566450	+	0.779652i	0.992129	−	0.125223i	$-0.0399645\pi$
$269$	40988.9	+	56416.4i	0.566450	+	0.779652i	−0.425678	+	0.904875i	$0.639965\pi$
$270$	65026.7	−	21128.4i	0.891998	−	0.289828i
$271$	33490.1	−	10881.6i	0.456014	−	0.148168i	−0.0719983	−	0.997405i	$-0.522938\pi$
$271$	33490.1	−	10881.6i	0.456014	−	0.148168i	0.528012	+	0.849237i	$0.322938\pi$
$272$	−27087.8	−	8801.36i	−0.366130	−	0.118963i
$273$	−106407.			−1.42773
$274$		−	33329.1i		−	0.443938i
$275$	−130232.	−	42314.9i	−1.72207	−	0.559535i
$276$	−10673.1	−	7754.47i	−0.140111	−	0.101797i
$277$	62265.3	+	85700.8i	0.811496	+	1.11693i	0.991091	+	0.133188i	$0.0425213\pi$
$277$	62265.3	+	85700.8i	0.811496	+	1.11693i	−0.179595	+	0.983741i	$0.557479\pi$
$278$		−	44942.3i		−	0.581521i
$279$	79565.7	+	73700.4i	1.02216	+	0.946807i
$280$	−72722.3			−0.927580
$281$	82225.3	−	59740.2i	1.04134	−	0.756578i	0.0707938	−	0.997491i	$-0.477447\pi$
$281$	82225.3	−	59740.2i	1.04134	−	0.756578i	0.970547	+	0.240913i	$0.0774468\pi$
$282$	62625.5	−	86196.6i	0.787505	−	1.08391i
$283$	23389.5	−	71985.6i	0.292044	−	0.898820i	−0.692154	−	0.721750i	$-0.743338\pi$
$283$	23389.5	−	71985.6i	0.292044	−	0.898820i	0.984198	−	0.177070i	$-0.0566620\pi$
$284$	7095.84			0.0879766
$285$			142800.i			1.75808i
$286$	−46445.5	+	142944.i	−0.567821	+	1.74757i
$287$	5712.18	+	17580.3i	0.0693486	+	0.213433i
$288$	5134.60	+	15802.7i	0.0619044	+	0.190522i
$289$	−55809.6	+	40548.1i	−0.668211	+	0.485483i
$290$	5777.27	+	1877.15i	0.0686953	+	0.0223204i
$291$	−96862.6	−	133320.i	−1.14385	−	1.57438i
$292$	4673.82	−	6432.96i	0.0548159	−	0.0754476i
$293$	−4740.90	−	14591.0i	−0.0552237	−	0.169961i	0.919640	−	0.392761i	$-0.128480\pi$
$293$	−4740.90	−	14591.0i	−0.0552237	−	0.169961i	−0.974864	+	0.222800i	$0.928480\pi$
$294$	−51860.2	+	71379.4i	−0.599983	+	0.825806i
$295$	95623.3	+	69474.4i	1.09880	+	0.798327i
$296$	18217.9	−	5919.35i	0.207929	−	0.0675601i
$297$	−50371.3	−	36596.9i	−0.571045	−	0.414888i
$298$	−41751.2	+	30334.0i	−0.470150	+	0.341584i
$299$	70593.2	−	217264.i	0.789625	−	2.43022i
$300$	−9200.96	−	12664.0i	−0.102233	−	0.140712i
$301$	37636.0	−	12228.7i	0.415403	−	0.134973i
$302$	84630.1	−	27498.0i	0.927920	−	0.301500i
$303$	225100.	+	73139.3i	2.45182	+	0.796646i
$304$	60561.9			0.655318
$305$			137242.i			1.47532i
$306$	49864.1	+	16201.8i	0.532531	+	0.173030i
$307$	−55068.3	−	40009.5i	−0.584285	−	0.424508i	0.255981	−	0.966682i	$-0.417601\pi$
$307$	−55068.3	−	40009.5i	−0.584285	−	0.424508i	−0.840266	+	0.542174i	$0.817601\pi$
$308$	2615.50	+	3599.92i	0.0275710	+	0.0379482i
$309$			2452.33i			0.0256839i
$310$	−62157.8	+	134470.i	−0.646803	+	1.39927i
$311$	−104736.			−1.08287			−0.541436	−	0.840742i	$-0.682119\pi$
$311$	−104736.			−1.08287			−0.541436	+	0.840742i	$0.682119\pi$
$312$	−206869.	+	150299.i	−2.12513	+	1.54400i
$313$	24669.5	−	33954.6i	0.251809	−	0.346585i	−0.664335	−	0.747435i	$-0.731285\pi$
$313$	24669.5	−	33954.6i	0.251809	−	0.346585i	0.916144	+	0.400850i	$0.131285\pi$
$314$	−999.280	+	3075.47i	−0.0101351	+	0.0311926i
$315$	124176.			1.25146
$316$		−	2322.35i		−	0.0232570i
$317$	−16693.9	+	51378.4i	−0.166126	+	0.511284i	−0.999118	−	0.0420021i	$-0.986626\pi$
$317$	−16693.9	+	51378.4i	−0.166126	+	0.511284i	0.832991	+	0.553286i	$0.186626\pi$
$318$	−56753.2	−	174668.i	−0.561223	−	1.72727i
$319$	−1709.38	−	5260.94i	−0.0167980	−	0.0516990i
$320$	−140693.	+	102220.i	−1.37396	+	0.998240i
$321$	83543.2	+	27144.8i	0.810776	+	0.263437i
$322$	51211.8	+	70487.0i	0.493922	+	0.679825i
$323$	−18168.2	+	25006.3i	−0.174143	+	0.239687i
$324$	1056.29	+	3250.94i	0.0100622	+	0.0309684i
$325$	159324.	−	219290.i	1.50839	−	2.07612i
$326$	−26513.8	−	19263.4i	−0.249480	−	0.181258i
$327$	−94936.4	+	30846.7i	−0.887845	+	0.288478i
$328$	35937.2	+	26109.9i	0.334038	+	0.242693i
$329$	44188.8	−	32105.0i	0.408245	−	0.296607i
$330$	93103.3	−	286543.i	0.854943	−	2.63124i
$331$	−12560.7	−	17288.4i	−0.114646	−	0.157797i	0.747838	−	0.663882i	$-0.231092\pi$
$331$	−12560.7	−	17288.4i	−0.114646	−	0.157797i	−0.862484	+	0.506085i	$0.831092\pi$
$332$	−4910.91	+	1595.65i	−0.0445539	+	0.0144765i
$333$	−31107.8	+	10107.5i	−0.280531	+	0.0911499i
$334$	−203710.	−	66189.4i	−1.82608	−	0.593329i
$335$	113279.			1.00939
$336$		−	90461.7i		−	0.801283i
$337$	79656.5	+	25882.0i	0.701393	+	0.227896i	0.637937	−	0.770088i	$-0.279788\pi$
$337$	79656.5	+	25882.0i	0.701393	+	0.227896i	0.0634556	+	0.997985i	$0.479788\pi$
$338$	−151662.	−	110189.i	−1.32753	−	0.964508i
$339$	−15054.5	−	20720.7i	−0.130998	−	0.180304i
$340$		−	5559.19i		−	0.0480899i
$341$	132336.	−	26182.9i	1.13807	−	0.225169i
$342$	−111484.			−0.953151
$343$	−90016.9	+	65401.1i	−0.765131	+	0.555900i
$344$	55896.2	−	76934.5i	0.472351	−	0.650136i
$345$	−141509.	+	435521.i	−1.18890	+	3.65907i
$346$	−213653.			−1.78467
$347$		−	22122.1i		−	0.183725i	−0.995772	−	0.0918625i	$-0.970718\pi$
$347$		−	22122.1i		−	0.183725i	0.995772	−	0.0918625i	$-0.0292820\pi$
$348$	195.408	−	601.405i	0.00161356	−	0.00496602i
$349$	54061.8	+	166385.i	0.443854	+	1.36604i	0.883736	+	0.467986i	$0.155020\pi$
$349$	54061.8	+	166385.i	0.443854	+	1.36604i	−0.439882	+	0.898055i	$0.644980\pi$
$350$	31945.9	+	98319.3i	0.260783	+	0.802607i
$351$	99709.1	−	72442.9i	0.809320	−	0.588006i
$352$	19656.1	+	6386.65i	0.158640	+	0.0515451i
$353$	−70154.3	−	96559.1i	−0.562996	−	0.774897i	0.428708	−	0.903443i	$-0.358969\pi$
$353$	−70154.3	−	96559.1i	−0.562996	−	0.774897i	−0.991704	+	0.128546i	$0.958969\pi$
$354$	−93167.7	+	128234.i	−0.743462	+	1.02329i
$355$	−76112.4	−	234250.i	−0.603947	−	1.85876i
$356$	2073.03	−	2853.28i	0.0163571	−	0.0225136i
$357$	37352.1	+	27137.9i	0.293075	+	0.212932i
$358$	177392.	−	57638.1i	1.38410	−	0.449722i
$359$	−11714.3	−	8510.91i	−0.0908920	−	0.0660369i	0.541411	−	0.840758i	$-0.317890\pi$
$359$	−11714.3	−	8510.91i	−0.0908920	−	0.0660369i	−0.632303	+	0.774721i	$0.717890\pi$
$360$	241414.	−	175398.i	1.86276	−	1.35338i
$361$	−19961.5	+	61435.3i	−0.153172	+	0.471415i
$362$	106986.	+	147253.i	0.816412	+	1.12369i
$363$	−67060.5	+	21789.3i	−0.508924	+	0.165360i
$364$	−8377.09	+	2721.88i	−0.0632252	+	0.0205431i
$365$	−262500.	−	85291.4i	−1.97035	−	0.640206i
$366$	−184046.			−1.37393
$367$		−	68377.8i		−	0.507672i	−0.967247	−	0.253836i	$-0.918308\pi$
$367$		−	68377.8i		−	0.507672i	0.967247	−	0.253836i	$-0.0816923\pi$
$368$	184706.	+	60014.6i	1.36391	+	0.443161i
$369$	−61364.1	−	44583.7i	−0.450673	−	0.327433i
$370$	−26260.7	−	36144.8i	−0.191824	−	0.264023i
$371$		−	94152.0i		−	0.684040i
$372$	13998.1	+	6470.53i	0.101154	+	0.0467578i
$373$	180440.			1.29693			0.648463	−	0.761246i	$-0.275412\pi$
$373$	180440.			1.29693			0.648463	+	0.761246i	$0.275412\pi$
$374$	52760.1	−	38332.5i	0.377192	−	0.274046i
$375$	−114749.	+	157938.i	−0.815992	+	1.12312i
$376$	40560.5	−	124832.i	0.286898	−	0.882982i
$377$	10949.9			0.0770417
$378$			47005.4i			0.328976i
$379$	23009.3	−	70815.2i	0.160186	−	0.493001i	−0.838463	−	0.544958i	$-0.816546\pi$
$379$	23009.3	−	70815.2i	0.160186	−	0.493001i	0.998649	+	0.0519564i	$0.0165457\pi$
$380$	3652.80	+	11242.2i	0.0252964	+	0.0778543i
$381$	−5168.47	−	15906.9i	−0.0356051	−	0.109581i
$382$	112415.	−	81674.3i	0.770367	−	0.559704i
$383$	−159635.	−	51868.5i	−1.08825	−	0.353595i	−0.290682	−	0.956820i	$-0.593882\pi$
$383$	−159635.	−	51868.5i	−1.08825	−	0.353595i	−0.797571	+	0.603224i	$0.793882\pi$
$384$	−117802.	−	162140.i	−0.798894	−	1.09958i
$385$	90786.9	−	124957.i	0.612494	−	0.843026i
$386$	7930.45	+	24407.4i	0.0532259	+	0.163813i
$387$	−95444.9	+	131369.i	−0.637281	+	0.877142i
$388$	−11036.0	−	8018.11i	−0.0733074	−	0.0532609i
$389$	16844.6	−	5473.14i	0.111317	−	0.0361691i	−0.252829	−	0.967511i	$-0.581361\pi$
$389$	16844.6	−	5473.14i	0.111317	−	0.0361691i	0.364146	+	0.931342i	$0.381361\pi$
$390$	482494.	+	350553.i	3.17222	+	2.30475i
$391$	−80191.0	+	58262.2i	−0.524532	+	0.381095i
$392$	−33588.2	+	103374.i	−0.218582	+	0.672726i
$393$	−176011.	−	242259.i	−1.13961	−	1.56854i
$394$	135516.	−	44031.7i	0.872965	−	0.283643i
$395$	−76666.2	+	24910.4i	−0.491371	+	0.159656i
$396$	−17365.2	−	5642.29i	−0.110736	−	0.0359803i
$397$	218129.			1.38399			0.691995	−	0.721902i	$-0.256732\pi$
$397$	218129.			1.38399			0.691995	+	0.721902i	$0.256732\pi$
$398$			292538.i			1.84678i
$399$	−93367.6	−	30337.0i	−0.586476	−	0.190558i
$400$	186429.	+	135449.i	1.16518	+	0.846554i
$401$	−26172.7	−	36023.6i	−0.162764	−	0.224026i	0.719843	−	0.694137i	$-0.244214\pi$
$401$	−26172.7	−	36023.6i	−0.162764	−	0.224026i	−0.882607	+	0.470111i	$0.844214\pi$
$402$			151911.i			0.940019i
$403$	−31656.9	+	265151.i	−0.194921	+	1.63261i
$404$	19592.3			0.120039
$405$	95990.7	−	69741.4i	0.585220	−	0.425187i
$406$	−2454.70	+	3378.60i	−0.0148917	+	0.0204967i
$407$	−12572.2	+	38693.2i	−0.0758966	+	0.233586i
$408$	110949.			0.666506
$409$			165285.i			0.988068i	0.869443	+	0.494034i	$0.164478\pi$
$409$			165285.i			0.988068i	−0.869443	+	0.494034i	$0.835522\pi$
$410$	32015.9	−	98534.7i	0.190457	−	0.586167i
$411$	37215.1	+	114536.i	0.220311	+	0.678047i
$412$	62.7302	+	193.064i	0.000369558	+	0.00113738i
$413$	−65739.5	+	47762.5i	−0.385413	+	0.280019i
$414$	−340013.	−	110477.i	−1.98379	−	0.644571i
$415$	105352.	+	145005.i	0.611713	+	0.841951i
$416$	−24047.0	+	33097.8i	−0.138955	+	0.191255i
$417$	50182.4	+	154445.i	0.288588	+	0.888184i
$418$	−81507.7	+	112186.i	−0.466494	+	0.642074i
$419$	225829.	+	164074.i	1.28633	+	0.934571i	0.999724	−	0.0234792i	$-0.00747434\pi$
$419$	225829.	+	164074.i	1.28633	+	0.934571i	0.286602	+	0.958050i	$0.407474\pi$
$420$	16792.5	−	5456.21i	0.0951955	−	0.0309309i
$421$	−246090.	−	178795.i	−1.38845	−	1.00877i	−0.996034	−	0.0889758i	$-0.971641\pi$
$421$	−246090.	−	178795.i	−1.38845	−	1.00877i	−0.392412	−	0.919789i	$-0.628359\pi$
$422$	38638.2	−	28072.3i	0.216966	−	0.157635i
$423$	−69258.7	+	213156.i	−0.387074	+	1.19129i
$424$	−132989.	−	183043.i	−0.739747	−	1.01817i
$425$	−111855.	+	36343.9i	−0.619267	+	0.201212i
$426$	314138.	−	102070.i	1.73102	−	0.562441i
$427$	−89733.6	−	29156.2i	−0.492152	−	0.159910i
$428$	7271.44			0.0396948
$429$		−	543094.i		−	2.95094i
$430$	−210944.	−	68539.7i	−1.14085	−	0.370686i
$431$	113324.	+	82335.1i	0.610055	+	0.443231i	0.849434	−	0.527695i	$-0.176944\pi$
$431$	113324.	+	82335.1i	0.610055	+	0.443231i	−0.239379	+	0.970926i	$0.576944\pi$
$432$	61587.0	+	84767.3i	0.330006	+	0.454214i
$433$			29239.6i			0.155954i	0.996955	+	0.0779770i	$0.0248461\pi$
$433$			29239.6i			0.155954i	−0.996955	+	0.0779770i	$0.975154\pi$
$434$	−74716.1	−	69208.3i	−0.396675	−	0.367433i
$435$	−21949.8			−0.115998
$436$	−6684.98	+	4856.92i	−0.0351663	+	0.0255498i
$437$	123885.	−	170513.i	0.648717	−	0.892883i
$438$	114379.	−	352022.i	0.596208	−	1.83494i
$439$	−75710.4			−0.392850			−0.196425	−	0.980519i	$-0.562933\pi$
$439$	−75710.4			−0.392850			−0.196425	+	0.980519i	$0.562933\pi$
$440$		−	371169.i		−	1.91719i
$441$	57353.1	−	176515.i	0.294903	−	0.907619i
$442$	39891.7	+	122774.i	0.204191	+	0.628437i
$443$	−1393.95	−	4290.15i	−0.00710298	−	0.0218607i	0.947442	−	0.319927i	$-0.103658\pi$
$443$	−1393.95	−	4290.15i	−0.00710298	−	0.0218607i	−0.954545	+	0.298066i	$0.903658\pi$
$444$	−3762.62	+	2733.70i	−0.0190864	+	0.0138671i
$445$	−116429.	−	37830.1i	−0.587952	−	0.191037i
$446$	32235.9	+	44368.9i	0.162058	+	0.223053i
$447$	109608.	−	150863.i	0.548566	−	0.755037i
$448$	−36945.5	−	113706.i	−0.184079	−	0.566538i
$449$	−47736.5	+	65703.7i	−0.236787	+	0.325909i	−0.910829	−	0.412783i	$-0.864557\pi$
$449$	−47736.5	+	65703.7i	−0.236787	+	0.325909i	0.674042	+	0.738693i	$0.264557\pi$
$450$	−343185.	−	249338.i	−1.69474	−	1.23130i
$451$	−89728.3	+	29154.5i	−0.441140	+	0.143335i
$452$	−1715.22	−	1246.18i	−0.00839545	−	0.00609965i
$453$	−260130.	+	188995.i	−1.26763	+	0.920989i
$454$	−29365.6	+	90378.1i	−0.142471	+	0.438482i
$455$	179711.	+	247351.i	0.868065	+	1.19479i
$456$	−224369.	+	72901.9i	−1.07903	+	0.350598i
$457$	62486.1	−	20303.0i	0.299193	−	0.0972136i	−0.155574	−	0.987824i	$-0.549723\pi$
$457$	62486.1	−	20303.0i	0.299193	−	0.0972136i	0.454767	+	0.890611i	$0.349723\pi$
$458$	264328.	+	85885.5i	1.26012	+	0.409439i
$459$	−53476.6			−0.253828
$460$			37906.9i			0.179144i
$461$	−21881.7	−	7109.79i	−0.102962	−	0.0334545i	0.257083	−	0.966389i	$-0.417239\pi$
$461$	−21881.7	−	7109.79i	−0.102962	−	0.0334545i	−0.360045	+	0.932935i	$0.617239\pi$
$462$	167573.	+	121749.i	0.785089	+	0.570401i
$463$	−88521.1	−	121839.i	−0.412938	−	0.568361i	0.550994	−	0.834509i	$-0.314249\pi$
$463$	−88521.1	−	121839.i	−0.412938	−	0.568361i	−0.963932	+	0.266149i	$0.914249\pi$
$464$			9308.98i			0.0432380i
$465$	63458.6	−	531514.i	0.293484	−	2.45815i
$466$	98511.7			0.453645
$467$	16761.9	−	12178.2i	0.0768581	−	0.0558407i	−0.548693	−	0.836024i	$-0.684874\pi$
$467$	16761.9	−	12178.2i	0.0768581	−	0.0558407i	0.625551	+	0.780183i	$0.284874\pi$
$468$	21244.3	−	29240.3i	0.0969955	−	0.133503i
$469$	−24065.4	+	74065.7i	−0.109408	+	0.336722i
$470$	−306139.			−1.38587
$471$		−	11684.7i		−	0.0526716i
$472$	−60341.7	+	185713.i	−0.270853	+	0.833600i
$473$	62414.1	+	192091.i	0.278972	+	0.858587i
$474$	−33405.7	−	102812.i	−0.148684	−	0.457602i
$475$	202320.	−	146994.i	0.896709	−	0.651497i
$476$	3634.80	+	1181.02i	0.0160423	+	0.00521246i
$477$	227084.	+	312554.i	0.998043	+	1.37369i
$478$	−75777.0	+	104298.i	−0.331651	+	0.456479i
$479$	−37962.9	−	116838.i	−0.165458	−	0.509228i	0.833612	−	0.552351i	$-0.186269\pi$
$479$	−37962.9	−	116838.i	−0.165458	−	0.509228i	−0.999070	+	0.0431231i	$0.986269\pi$
$480$	48203.9	−	66347.0i	0.209219	−	0.287965i
$481$	−65153.5	−	47336.8i	−0.281610	−	0.204601i
$482$	137275.	−	44603.2i	0.590876	−	0.191987i
$483$	−254696.	−	185048.i	−1.09176	−	0.793213i
$484$	−4722.09	+	3430.80i	−0.0201578	+	0.0146455i
$485$	−146320.	+	450328.i	−0.622045	+	1.91446i
$486$	174896.	+	240723.i	0.740468	+	1.01917i
$487$	−175232.	+	56936.3i	−0.738849	+	0.240066i	−0.654176	−	0.756342i	$-0.726984\pi$
$487$	−175232.	+	56936.3i	−0.738849	+	0.240066i	−0.0846726	+	0.996409i	$0.526984\pi$
$488$	−215636.	+	70064.5i	−0.905487	+	0.294211i
$489$	112625.	+	36594.0i	0.470995	+	0.153036i
$490$	253513.			1.05587
$491$		−	211906.i		−	0.878984i	−0.898247	−	0.439492i	$-0.855159\pi$
$491$		−	211906.i		−	0.878984i	0.898247	−	0.439492i	$-0.144841\pi$
$492$	−10257.3	−	3332.80i	−0.0423744	−	0.0137683i
$493$	−3843.73	−	2792.63i	−0.0158146	−	0.0114900i
$494$	−161343.	−	222070.i	−0.661144	−	0.909987i
$495$			633786.i			2.58662i
$496$	−225417.	−	26913.0i	−0.916270	−	0.109395i
$497$	169331.			0.685525
$498$	−194457.	+	141281.i	−0.784088	+	0.569673i
$499$	−119316.	+	164224.i	−0.479177	+	0.659531i	−0.978347	−	0.206973i	$-0.933639\pi$
$499$	−119316.	+	164224.i	−0.479177	+	0.659531i	0.499169	+	0.866505i	$0.333639\pi$
$500$	−4993.76	+	15369.2i	−0.0199751	+	0.0614769i
$501$	773963.			3.08350
$502$			37484.8i			0.148747i
$503$	−23459.0	+	72199.2i	−0.0927198	+	0.285362i	−0.986653	−	0.162839i	$-0.947935\pi$
$503$	−23459.0	+	72199.2i	−0.0927198	+	0.285362i	0.893933	+	0.448201i	$0.147935\pi$
$504$	63394.3	+	195108.i	0.249568	+	0.768091i
$505$	−210153.	−	646785.i	−0.824050	−	2.53616i
$506$	−359760.	+	261381.i	−1.40512	+	1.02088i
$507$	644230.	+	209323.i	2.50625	+	0.814331i
$508$	−813.794	−	1120.09i	−0.00315346	−	0.00434036i
$509$	−172252.	+	237084.i	−0.664857	+	0.915098i	−0.999630	−	0.0272013i	$-0.991340\pi$
$509$	−172252.	+	237084.i	−0.664857	+	0.915098i	0.334773	+	0.942299i	$0.391340\pi$
$510$	−79965.7	−	246109.i	−0.307442	−	0.946210i
$511$	111533.	−	153512.i	0.427132	−	0.587897i
$512$	−230239.	−	167279.i	−0.878293	−	0.638117i
$513$	108144.	−	35138.1i	0.410930	−	0.133519i
$514$	−187874.	−	136499.i	−0.711116	−	0.516656i
$515$	5700.61	−	4141.74i	0.0214935	−	0.0156159i
$516$	−7134.88	+	21958.9i	−0.0267971	+	0.0824729i
$517$	163862.	+	225536.i	0.613050	+	0.843791i
$518$	29211.7	−	9491.46i	0.108867	−	0.0353731i
$519$	734225.	−	238564.i	2.72580	−	0.885667i
$520$	698762.	+	227042.i	2.58418	+	0.839651i
$521$	−444713.			−1.63834			−0.819172	−	0.573549i	$-0.805566\pi$
$521$	−444713.			−1.63834			−0.819172	+	0.573549i	$0.805566\pi$
$522$		−	17136.3i		−	0.0628891i
$523$	−115228.	−	37439.7i	−0.421263	−	0.136877i	0.0907116	−	0.995877i	$-0.471086\pi$
$523$	−115228.	−	37439.7i	−0.421263	−	0.136877i	−0.511975	+	0.859001i	$0.671086\pi$
$524$	−20053.8	−	14569.9i	−0.0730354	−	0.0530633i
$525$	−219566.	−	302207.i	−0.796611	−	1.09644i
$526$		−	292975.i		−	1.05891i
$527$	78736.2	−	85002.3i	0.283500	−	0.306062i
$528$	461709.			1.65615
$529$	320409.	−	232791.i	1.14497	−	0.831868i
$530$	−310179.	+	426924.i	−1.10423	+	1.51984i
$531$	103036.	−	317112.i	0.365426	−	1.12467i
$532$	−8126.55			−0.0287133
$533$		−	186756.i		−	0.657386i
$534$	50731.6	−	156136.i	0.177908	−	0.547545i
$535$	−77996.0	−	240047.i	−0.272499	−	0.838666i
$536$	57830.9	+	177985.i	0.201294	+	0.619518i
$537$	−545254.	+	396150.i	−1.89082	+	1.37376i
$538$	255552.	+	83034.0i	0.882908	+	0.286874i
$539$	−135694.	−	186766.i	−0.467070	−	0.642867i
$540$	−12020.8	+	16545.2i	−0.0412236	+	0.0567394i
$541$	69894.4	+	215113.i	0.238807	+	0.734974i	0.996593	+	0.0824707i	$0.0262811\pi$
$541$	69894.4	+	215113.i	0.238807	+	0.734974i	−0.757786	+	0.652503i	$0.773719\pi$
$542$	79754.4	−	109773.i	0.271491	−	0.373676i
$543$	−532083.	−	386581.i	−1.80459	−	1.31111i
$544$	16882.5	−	5485.44i	0.0570476	−	0.0185359i
$545$	232043.	+	168589.i	0.781225	+	0.567593i
$546$	−331707.	+	240999.i	−1.11268	+	0.808408i
$547$	−177477.	+	546219.i	−0.593155	+	1.82554i	−0.0294492	+	0.999566i	$0.509375\pi$
$547$	−177477.	+	546219.i	−0.593155	+	1.82554i	−0.563705	+	0.825976i	$0.690625\pi$
$548$	5859.65	+	8065.12i	0.0195124	+	0.0268565i
$549$	368208.	−	119638.i	1.22165	−	0.396939i
$550$	−501814.	+	163049.i	−1.65889	+	0.539006i
$551$	9608.02	+	3121.83i	0.0316469	+	0.0102827i
$552$	−756540.			−2.48287
$553$		−	55419.2i		−	0.181222i
$554$	388204.	+	126135.i	1.26485	+	0.410976i
$555$	130605.	+	94890.1i	0.424008	+	0.308060i
$556$	7901.39	+	10875.3i	0.0255596	+	0.0351798i
$557$		−	13133.6i		−	0.0423323i	−0.999776	−	0.0211662i	$-0.993262\pi$
$557$		−	13133.6i		−	0.0423323i	0.999776	−	0.0211662i	$-0.00673790\pi$
$558$	414955.	+	49542.3i	1.33270	+	0.159114i
$559$	−399809.			−1.27947
$560$	−210285.	+	152781.i	−0.670551	+	0.487183i
$561$	−138510.	+	190642.i	−0.440103	+	0.605750i
$562$	121020.	−	372460.i	0.383163	−	1.17925i
$563$	41817.1			0.131928			0.0659640	−	0.997822i	$-0.478988\pi$
$563$	41817.1			0.131928			0.0659640	+	0.997822i	$0.478988\pi$
$564$			31868.6i			0.100185i
$565$	−22741.3	+	69990.4i	−0.0712390	+	0.219251i
$566$	−90125.5	−	277378.i	−0.281329	−	0.865843i
$567$	25206.7	+	77578.3i	0.0784062	+	0.241309i
$568$	329200.	−	239178.i	1.02038	−	0.741352i
$569$	−35063.3	−	11392.8i	−0.108300	−	0.0351888i	0.254366	−	0.967108i	$-0.418133\pi$
$569$	−35063.3	−	11392.8i	−0.108300	−	0.0351888i	−0.362666	+	0.931919i	$0.618133\pi$
$570$	323424.	+	445155.i	0.995457	+	1.37013i
$571$	74384.6	−	102382.i	0.228145	−	0.314014i	−0.679563	−	0.733617i	$-0.737831\pi$
$571$	74384.6	−	102382.i	0.228145	−	0.314014i	0.907708	+	0.419603i	$0.137831\pi$
$572$	−13892.3	−	42756.0i	−0.0424601	−	0.130679i
$573$	−295120.	+	406198.i	−0.898855	+	1.23717i
$574$	57624.0	+	41866.3i	0.174896	+	0.127069i
$575$	762716.	−	247821.i	2.30689	−	0.749554i
$576$	396893.	+	288360.i	1.19627	+	0.869140i
$577$	63844.2	−	46385.5i	0.191765	−	0.139326i	−0.487760	−	0.872978i	$-0.662186\pi$
$577$	63844.2	−	46385.5i	0.191765	−	0.139326i	0.679525	+	0.733652i	$0.262186\pi$
$578$	−82141.0	+	252804.i	−0.245869	+	0.756708i
$579$	−54506.5	−	75021.7i	−0.162589	−	0.223784i
$580$	−1728.04	+	561.473i	−0.00513685	+	0.00166906i
$581$	−117191.	+	38077.6i	−0.347170	+	0.112802i
$582$	−603906.	−	196221.i	−1.78289	−	0.579295i
$583$	480544.			1.41383
$584$		−	455987.i		−	1.33698i
$585$	−1.19316e6	−	387683.i	−3.48649	−	1.13283i
$586$	−47825.7	−	34747.4i	−0.139273	−	0.101188i
$587$	316705.	+	435907.i	0.919134	+	1.26508i	0.963950	+	0.266084i	$0.0857300\pi$
$587$	316705.	+	435907.i	0.919134	+	1.26508i	−0.0448156	+	0.998995i	$0.514270\pi$
$588$		−	26390.3i		−	0.0763291i
$589$	−103373.	+	223633.i	−0.297972	+	0.644622i
$590$	455441.			1.30836
$591$	−416538.	+	302632.i	−1.19256	+	0.866444i
$592$	40243.2	−	55390.0i	0.114828	−	0.158048i
$593$	94991.4	−	292353.i	0.270131	−	0.831378i	−0.720336	−	0.693626i	$-0.756012\pi$
$593$	94991.4	−	292353.i	0.270131	−	0.831378i	0.990467	−	0.137752i	$-0.0439878\pi$
$594$	−239912.			−0.679953
$595$		−	132661.i		−	0.374722i
$596$	4770.06	−	14680.7i	0.0134286	−	0.0413290i
$597$	−326647.	−	1.00531e6i	−0.916494	−	2.82068i
$598$	−272013.	−	837169.i	−0.760653	−	2.34105i
$599$	103234.	−	75003.8i	0.287719	−	0.209040i	−0.434558	−	0.900644i	$-0.643095\pi$
$599$	103234.	−	75003.8i	0.287719	−	0.209040i	0.722277	+	0.691604i	$0.243095\pi$
$600$	−853728.	−	277393.i	−2.37147	−	0.770536i
$601$	−80750.2	−	111143.i	−0.223560	−	0.307704i	0.682473	−	0.730911i	$-0.260904\pi$
$601$	−80750.2	−	111143.i	−0.223560	−	0.307704i	−0.906033	+	0.423207i	$0.860904\pi$
$602$	89627.5	−	123362.i	0.247314	−	0.340398i
$603$	−98748.5	−	303917.i	−0.271579	−	0.835834i
$604$	−15644.7	+	21533.1i	−0.0428838	+	0.0590244i
$605$	163909.	+	119087.i	0.447809	+	0.325352i
$606$	867363.	−	281823.i	2.36187	−	0.767417i
$607$	240364.	+	174635.i	0.652368	+	0.473973i	0.864077	−	0.503360i	$-0.167903\pi$
$607$	240364.	+	174635.i	0.652368	+	0.473973i	−0.211709	+	0.977333i	$0.567903\pi$
$608$	−30536.5	+	22186.0i	−0.0826060	+	0.0600168i
$609$	4663.10	−	14351.6i	0.0125730	−	0.0386959i
$610$	310836.	+	427829.i	0.835355	+	1.14977i
$611$	−524827.	+	170527.i	−1.40583	+	0.456783i
$612$	−14914.8	+	4846.12i	−0.0398213	+	0.0129387i
$613$	243272.	+	79043.8i	0.647398	+	0.210352i	0.614266	−	0.789099i	$-0.289452\pi$
$613$	243272.	+	79043.8i	0.647398	+	0.210352i	0.0331313	+	0.999451i	$0.489452\pi$
$614$	−262283.			−0.695718
$615$			374366.i			0.989798i
$616$	242684.	+	78852.7i	0.639556	+	0.207804i
$617$	167019.	+	121347.i	0.438729	+	0.318756i	0.785130	−	0.619331i	$-0.212596\pi$
$617$	167019.	+	121347.i	0.438729	+	0.318756i	−0.346400	+	0.938087i	$0.612596\pi$
$618$	5554.22	+	7644.73i	0.0145427	+	0.0200164i
$619$			354786.i			0.925945i	0.886373	+	0.462972i	$0.153217\pi$
$619$			354786.i			0.925945i	−0.886373	+	0.462972i	$0.846783\pi$
$620$	−8600.19	−	43467.7i	−0.0223730	−	0.113079i
$621$	364646.			0.945558
$622$	−326499.	+	237215.i	−0.843919	+	0.613143i
$623$	49469.4	−	68088.8i	0.127456	−	0.175428i
$624$	−282425.	+	869213.i	−0.725326	+	2.23232i
$625$	−48737.5			−0.124768
$626$		−	161721.i		−	0.412685i
$627$	154837.	−	476541.i	0.393859	−	1.21217i
$628$	−298.894	−	919.901i	−0.000757875	−	0.00233250i
$629$	10798.2	+	33233.3i	0.0272928	+	0.0839987i
$630$	387099.	−	281244.i	0.975306	−	0.708602i
$631$	169140.	+	54957.0i	0.424803	+	0.138027i	0.513614	−	0.858022i	$-0.328306\pi$
$631$	169140.	+	54957.0i	0.424803	+	0.138027i	−0.0888103	+	0.996049i	$0.528306\pi$
$632$	−78279.1	−	107742.i	−0.195980	−	0.269743i
$633$	−101436.	+	139614.i	−0.253153	+	0.348436i
$634$	64325.4	+	197973.i	0.160031	+	0.492525i
$635$	−28247.8	+	38879.7i	−0.0700546	+	0.0964219i
$636$	44442.2	+	32289.1i	0.109870	+	0.0798256i
$637$	434609.	−	141213.i	1.07108	−	0.348013i
$638$	−17244.1	−	12528.6i	−0.0423642	−	0.0307794i
$639$	−562123.	+	408406.i	−1.37667	+	1.00021i
$640$	−177951.	+	547677.i	−0.434451	+	1.33710i
$641$	−285751.	−	393303.i	−0.695460	−	0.957218i	−0.999989	−	0.00471512i	$-0.998499\pi$
$641$	−285751.	−	393303.i	−0.695460	−	0.957218i	0.304529	−	0.952503i	$-0.401501\pi$
$642$	321912.	−	104596.i	0.781029	−	0.253772i
$643$	−88343.4	+	28704.5i	−0.213674	+	0.0694270i	−0.413898	−	0.910323i	$-0.635833\pi$
$643$	−88343.4	+	28704.5i	−0.213674	+	0.0694270i	0.200224	+	0.979750i	$0.435833\pi$
$644$	−24784.9	−	8053.11i	−0.0597607	−	0.0194174i
$645$	801445.			1.92644
$646$			119102.i			0.285400i
$647$	110612.	+	35940.0i	0.264237	+	0.0858559i	0.438139	−	0.898907i	$-0.355638\pi$
$647$	110612.	+	35940.0i	0.264237	+	0.0858559i	−0.173902	+	0.984763i	$0.555638\pi$
$648$	158584.	+	115218.i	0.377667	+	0.274391i
$649$	−243776.	−	335529.i	−0.578764	−	0.796601i
$650$		−	1.04445e6i		−	2.47207i
$651$	334042.	+	154409.i	0.788204	+	0.364342i
$652$	9802.66			0.0230594
$653$	237292.	−	172402.i	0.556488	−	0.404312i	−0.273684	−	0.961820i	$-0.588242\pi$
$653$	237292.	−	172402.i	0.556488	−	0.404312i	0.830172	+	0.557507i	$0.188242\pi$
$654$	−226085.	+	311179.i	−0.528586	+	0.727536i
$655$	−265883.	+	818303.i	−0.619737	+	1.90735i
$656$	158770.			0.368944
$657$			778615.i			1.80382i
$658$	65037.4	−	200164.i	0.150214	−	0.462312i
$659$	236296.	+	727245.i	0.544109	+	1.67460i	0.723098	+	0.690745i	$0.242717\pi$
$659$	236296.	+	727245.i	0.544109	+	1.67460i	−0.178989	+	0.983851i	$0.557283\pi$
$660$	27848.1	+	85707.5i	0.0639304	+	0.196757i
$661$	−675028.	+	490436.i	−1.54497	+	1.12248i	−0.597842	+	0.801614i	$0.703975\pi$
$661$	−675028.	+	490436.i	−1.54497	+	1.12248i	−0.947124	+	0.320869i	$0.896025\pi$
$662$	−78312.1	−	25445.1i	−0.178695	−	0.0580616i
$663$	−274178.	−	377373.i	−0.623742	−	0.858507i
$664$	−174050.	+	239559.i	−0.394764	+	0.543345i
$665$	87168.1	+	268276.i	0.197113	+	0.606650i
$666$	−74081.0	+	101964.i	−0.167016	+	0.229878i
$667$	26209.6	+	19042.4i	0.0589127	+	0.0428026i
$668$	60931.6	−	19797.9i	0.136549	−	0.0443676i
$669$	−160322.	−	116481.i	−0.358212	−	0.260256i
$670$	353128.	−	256562.i	0.786651	−	0.571536i
$671$	148811.	−	457993.i	0.330514	−	1.01722i
$672$	33139.4	+	45612.5i	0.0733849	+	0.101006i
$673$	660735.	−	214686.i	1.45881	−	0.473995i	0.531100	−	0.847309i	$-0.321779\pi$
$673$	660735.	−	214686.i	1.45881	−	0.473995i	0.927705	+	0.373314i	$0.121779\pi$
$674$	306936.	−	99729.4i	0.675659	−	0.219535i
$675$	411490.	+	133701.i	0.903132	+	0.293445i
$676$	56072.6			0.122704
$677$		−	851594.i		−	1.85804i	−0.370029	−	0.929020i	$-0.620652\pi$
$677$		−	851594.i		−	1.85804i	0.370029	−	0.929020i	$-0.379348\pi$
$678$	−93859.8	−	30496.9i	−0.204183	−	0.0663431i
$679$	−263356.	−	191339.i	−0.571220	−	0.415015i
$680$	−187382.	−	257910.i	−0.405239	−	0.557763i
$681$		−	343377.i		−	0.740417i
$682$	353234.	−	381345.i	0.759440	−	0.819878i
$683$	−785143.			−1.68309			−0.841545	−	0.540187i	$-0.818354\pi$
$683$	−785143.			−1.68309			−0.841545	+	0.540187i	$0.818354\pi$
$684$	26977.5	−	19600.3i	0.0576619	−	0.0418938i
$685$	203395.	−	279950.i	0.433471	−	0.596622i
$686$	−132487.	+	407754.i	−0.281531	+	0.866464i
$687$	−1.00427e6			−2.12783
$688$		−	339896.i		−	0.718073i
$689$	−293946.	+	904672.i	−0.619197	+	1.90569i
$690$	545269.	+	1.67817e6i	1.14528	+	3.52482i
$691$	62040.1	+	190940.i	0.129932	+	0.399890i	0.994767	−	0.102166i	$-0.0325772\pi$
$691$	62040.1	+	190940.i	0.129932	+	0.399890i	−0.864835	+	0.502056i	$0.832577\pi$
$692$	51700.7	−	37562.8i	0.107965	−	0.0784414i
$693$	−414392.	−	134644.i	−0.862869	−	0.280363i
$694$	−50103.9	−	68962.2i	−0.104029	−	0.143183i
$695$	274267.	−	377495.i	0.567810	−	0.781524i
$696$	−11205.8	−	34487.8i	−0.0231325	−	0.0711946i
$697$	−47630.0	+	65557.1i	−0.0980427	+	0.134944i
$698$	545371.	+	396235.i	1.11939	+	0.813284i
$699$	−338538.	+	109998.i	−0.692873	+	0.225128i
$700$	−25016.1	−	18175.3i	−0.0510533	−	0.0370924i
$701$	188294.	−	136804.i	0.383178	−	0.278395i	−0.379476	−	0.925202i	$-0.623896\pi$
$701$	188294.	−	136804.i	0.383178	−	0.278395i	0.762654	+	0.646806i	$0.223896\pi$
$702$	146752.	−	451658.i	0.297791	−	0.916506i
$703$	−43673.5	−	60111.4i	−0.0883705	−	0.121632i
$704$	580348.	−	188567.i	1.17096	−	0.380469i
$705$	1.05205e6	−	341833.i	2.11670	−	0.687759i
$706$	−437389.	−	142116.i	−0.877524	−	0.285125i
$707$	467537.			0.935357
$708$		−	47410.7i		−	0.0945823i
$709$	419623.	+	136344.i	0.834770	+	0.271233i	0.695053	−	0.718958i	$-0.255381\pi$
$709$	419623.	+	136344.i	0.834770	+	0.271233i	0.139717	+	0.990192i	$0.455381\pi$
$710$	−767816.	−	557851.i	−1.52314	−	1.10663i
$711$	133665.	+	183974.i	0.264410	+	0.363929i
$712$		−	202248.i		−	0.398956i
$713$	−536886.	+	579613.i	−1.05609	+	1.14014i
$714$	177903.			0.348970
$715$	−1.26246e6	+	917231.i	−2.46948	+	1.79418i
$716$	−32792.6	+	45135.2i	−0.0639661	+	0.0880418i
$717$	143951.	−	443036.i	0.280012	−	0.861788i
$718$	−55793.4			−0.108227
$719$		−	922107.i		−	1.78371i	−0.452324	−	0.891854i	$-0.649405\pi$
$719$		−	922107.i		−	1.78371i	0.452324	−	0.891854i	$-0.350595\pi$
$720$	329587.	−	1.01436e6i	0.635777	−	1.95672i
$721$	1496.95	+	4607.15i	0.00287964	+	0.00886262i
$722$	76916.6	+	236725.i	0.147552	+	0.454119i
$723$	−421945.	+	306561.i	−0.807196	+	0.586462i
$724$	−51777.9	−	16823.6i	−0.0987795	−	0.0320954i
$725$	22594.5	+	31098.7i	0.0429860	+	0.0591651i
$726$	−159700.	+	219808.i	−0.302992	+	0.417033i
$727$	−307420.	−	946141.i	−0.581652	−	1.79014i	−0.612319	−	0.790611i	$-0.709763\pi$
$727$	−307420.	−	946141.i	−0.581652	−	1.79014i	0.0306667	−	0.999530i	$-0.490237\pi$
$728$	−296896.	+	408642.i	−0.560198	+	0.771046i
$729$	−675472.	−	490759.i	−1.27102	−	0.923450i
$730$	−1.01148e6	+	328648.i	−1.89806	+	0.616717i
$731$	140345.	+	101967.i	0.262641	+	0.190820i
$732$	44536.3	−	32357.5i	0.0831175	−	0.0603884i
$733$	138039.	−	424841.i	0.256918	−	0.790711i	−0.736528	−	0.676407i	$-0.763536\pi$
$733$	138039.	−	424841.i	0.256918	−	0.790711i	0.993446	−	0.114304i	$-0.0364639\pi$
$734$	−154867.	−	213157.i	−0.287454	−	0.395646i
$735$	−871206.	+	283072.i	−1.61267	+	0.523989i
$736$	−115118.	+	37404.1i	−0.212514	+	0.0690499i
$737$	−378025.	−	122828.i	−0.695963	−	0.226132i
$738$	−292269.			−0.536624
$739$			40825.0i			0.0747545i	0.999301	+	0.0373772i	$0.0119003\pi$
$739$			40825.0i			0.0747545i	−0.999301	+	0.0373772i	$0.988100\pi$
$740$	12709.4	+	4129.53i	0.0232092	+	0.00754114i
$741$	802422.	+	582994.i	1.46139	+	1.06176i
$742$	−213243.	−	293503.i	−0.387317	−	0.533096i
$743$			661826.i			1.19885i	0.800430	+	0.599427i	$0.204605\pi$
$743$			661826.i			1.19885i	−0.800430	+	0.599427i	$0.795395\pi$
$744$	867520.	−	171641.i	1.56723	−	0.310081i
$745$	−535810.			−0.965380
$746$	562492.	−	408674.i	1.01074	−	0.734345i
$747$	297197.	−	409056.i	0.532602	−	0.733064i
$748$	−6027.82	+	18551.7i	−0.0107735	+	0.0331574i
$749$	173521.			0.309306
$750$			752239.i			1.33731i
$751$	141607.	−	435820.i	0.251075	−	0.772730i	−0.743502	−	0.668733i	$-0.766837\pi$
$751$	141607.	−	435820.i	0.251075	−	0.772730i	0.994578	−	0.103997i	$-0.0331631\pi$
$752$	−144973.	−	446180.i	−0.256360	−	0.788995i
$753$	−41855.4	−	128818.i	−0.0738179	−	0.227188i
$754$	34134.4	−	24800.1i	0.0600412	−	0.0436225i
$755$	878666.	+	285496.i	1.54145	+	0.500848i
$756$	−8264.11	−	11374.6i	−0.0144595	−	0.0199018i
$757$	315447.	−	434175.i	0.550471	−	0.757658i	−0.439605	−	0.898191i	$-0.644882\pi$
$757$	315447.	−	434175.i	0.550471	−	0.757658i	0.990076	+	0.140533i	$0.0448817\pi$
$758$	−88660.2	−	272868.i	−0.154309	−	0.474913i
$759$	944469.	−	1.29995e6i	1.63947	−	2.25654i
$760$	548403.	+	398438.i	0.949451	+	0.689816i
$761$	−484951.	+	157570.i	−0.837391	+	0.272085i	−0.696155	−	0.717891i	$-0.745107\pi$
$761$	−484951.	+	157570.i	−0.837391	+	0.272085i	−0.141235	+	0.989976i	$0.545107\pi$
$762$	−52139.1	−	37881.3i	−0.0897953	−	0.0652401i
$763$	−159526.	+	115903.i	−0.274020	+	0.199087i
$764$	−12843.4	+	39527.8i	−0.0220035	+	0.0677198i
$765$	319963.	+	440391.i	0.546735	+	0.752516i
$766$	−615112.	+	199862.i	−1.04833	+	0.340622i
$767$	780783.	−	253692.i	1.32721	−	0.431237i
$768$	186539.	+	60610.2i	0.316262	+	0.102760i
$769$	219507.			0.371189			0.185594	−	0.982626i	$-0.440579\pi$
$769$	219507.			0.371189			0.185594	+	0.982626i	$0.440579\pi$
$770$		−	595156.i		−	1.00380i
$771$	798049.	+	259302.i	1.34252	+	0.436211i
$772$	−6210.16	−	4511.95i	−0.0104200	−	0.00757059i
$773$	184173.	+	253493.i	0.308225	+	0.424235i	0.934827	−	0.355105i	$-0.115555\pi$
$773$	184173.	+	253493.i	0.308225	+	0.424235i	−0.626602	+	0.779339i	$0.715555\pi$
$774$			625692.i			1.04443i
$775$	−818377.	+	457217.i	−1.36254	+	0.761236i
$776$	−782261.			−1.29906
$777$	−89788.8	+	65235.4i	−0.148724	+	0.108054i
$778$	40114.3	−	55212.6i	0.0662735	−	0.0912176i
$779$	53244.7	−	163870.i	0.0877407	−	0.270038i
$780$	−178387.			−0.293207
$781$			864251.i			1.41689i
$782$	−118026.	+	363246.i	−0.193002	+	0.594000i
$783$	5401.09	+	16622.8i	0.00880963	+	0.0271133i
$784$	120052.	+	369481.i	0.195315	+	0.601119i
$785$	−27162.0	+	19734.3i	−0.0440780	+	0.0320246i
$786$	−1.09737e6	−	356558.i	−1.77627	−	0.577146i
$787$	266965.	+	367446.i	0.431027	+	0.593258i	0.968189	−	0.250221i	$-0.0805033\pi$
$787$	266965.	+	367446.i	0.431027	+	0.593258i	−0.537161	+	0.843480i	$0.680503\pi$
$788$	−25051.4	+	34480.2i	−0.0403440	+	0.0555287i
$789$	327135.	+	1.00682e6i	0.525500	+	1.61732i
$790$	−182575.	+	251294.i	−0.292542	+	0.402649i
$791$	−40931.0	−	29738.1i	−0.0654184	−	0.0475292i
$792$	−995813.	+	323559.i	−1.58755	+	0.515826i
$793$	771191.	+	560303.i	1.22635	+	0.890998i
$794$	679983.	−	494036.i	1.07859	−	0.783642i
$795$	589236.	−	1.81348e6i	0.932298	−	2.86932i
$796$	−51431.7	−	70789.6i	−0.0811717	−	0.111723i
$797$	−1.07590e6	+	349582.i	−1.69378	+	0.550342i	−0.987504	−	0.157596i	$-0.949625\pi$
$797$	−1.07590e6	+	349582.i	−1.69378	+	0.550342i	−0.706274	+	0.707938i	$0.749625\pi$
$798$	−359768.	+	116896.i	−0.564958	+	0.183566i
$799$	227721.	+	73991.1i	0.356706	+	0.115901i
$800$	−143621.			−0.224408
$801$			345347.i			0.538258i
$802$	−163178.	−	53019.7i	−0.253696	−	0.0824307i
$803$	783514.	+	569256.i	1.21511	+	0.882829i
$804$	−26707.8	−	36760.1i	−0.0413167	−	0.0568675i
$805$			904587.i			1.39591i
$806$	501849.	+	898264.i	0.772508	+	1.38272i
$807$	−970929.			−1.49087
$808$	908951.	−	660392.i	1.39225	−	1.01153i
$809$	−323051.	+	444642.i	−0.493599	+	0.679381i	−0.981047	−	0.193772i	$-0.937928\pi$
$809$	−323051.	+	444642.i	−0.493599	+	0.679381i	0.487448	+	0.873152i	$0.337928\pi$
$810$	141280.	−	434815.i	0.215333	−	0.662726i
$811$	342459.			0.520675			0.260337	−	0.965518i	$-0.416166\pi$
$811$	342459.			0.520675			0.260337	+	0.965518i	$0.416166\pi$
$812$		−	1249.13i		−	0.00189451i
$813$	−151507.	+	466290.i	−0.229219	+	0.705464i
$814$	48443.7	+	149094.i	0.0731119	+	0.225015i
$815$	−105147.	−	323608.i	−0.158300	−	0.487197i
$816$	320822.	−	233091.i	0.481820	−	0.350062i
$817$	−350814.	−	113987.i	−0.525573	−	0.170769i
$818$	374350.	+	515249.i	0.559463	+	0.770035i
$819$	506962.	−	697773.i	0.755801	−	1.04027i
$820$	9576.24	+	29472.6i	0.0142419	+	0.0438320i
$821$	397152.	−	546633.i	0.589211	−	0.810979i	−0.405456	−	0.914114i	$-0.632887\pi$
$821$	397152.	−	546633.i	0.589211	−	0.810979i	0.994667	+	0.103135i	$0.0328874\pi$
$822$	375423.	+	272761.i	0.555619	+	0.403681i
$823$	360855.	−	117249.i	0.532762	−	0.173105i	−0.0302675	−	0.999542i	$-0.509636\pi$
$823$	360855.	−	117249.i	0.532762	−	0.173105i	0.563029	+	0.826437i	$0.309636\pi$
$824$	9417.83	+	6842.45i	0.0138706	+	0.0100776i
$825$	1.54244e6	−	1.12065e6i	2.26621	−	1.64650i
$826$	−96755.8	+	297784.i	−0.141813	+	0.436456i
$827$	−91211.9	−	125542.i	−0.133365	−	0.183561i	0.737112	−	0.675771i	$-0.236189\pi$
$827$	−91211.9	−	125542.i	−0.133365	−	0.183561i	−0.870476	+	0.492210i	$0.836189\pi$
$828$	101701.	−	33044.7i	0.148342	−	0.0481993i
$829$	−1.17381e6	+	381394.i	−1.70800	+	0.554964i	−0.989999	−	0.141074i	$-0.954945\pi$
$829$	−1.17381e6	+	381394.i	−1.70800	+	0.554964i	−0.718005	+	0.696038i	$0.754945\pi$
$830$	656837.	+	213419.i	0.953458	+	0.309797i
$831$	−1.47492e6			−2.13582
$832$			1.20791e6i			1.74497i
$833$	−188576.	−	61272.0i	−0.271766	−	0.0883023i
$834$	506235.	+	367801.i	0.727814	+	0.528788i
$835$	−1.30715e6	−	1.79913e6i	−1.87478	−	2.58042i
$836$		−	41477.2i		−	0.0593468i
$837$	−418137.	+	82729.5i	−0.596854	+	0.118089i
$838$	1.07559e6			1.53165
$839$	769745.	−	559253.i	1.09351	−	0.794482i	0.113522	−	0.993535i	$-0.463787\pi$
$839$	769745.	−	559253.i	1.09351	−	0.794482i	0.979989	+	0.199053i	$0.0637867\pi$
$840$	595149.	−	819153.i	0.843466	−	1.16093i
$841$	218082.	−	671187.i	0.308339	−	0.948968i
$842$	−1.17209e6			−1.65325
$843$			1.41510e6i			1.99128i
$844$	−4414.39	+	13586.1i	−0.00619707	+	0.0190726i
$845$	−601454.	−	1.85108e6i	−0.842342	−	2.59246i
$846$	266871.	+	821343.i	0.372872	+	1.14758i
$847$	−112685.	+	81870.4i	−0.157072	+	0.114120i
$848$	−769104.	−	249897.i	−1.06953	−	0.347512i
$849$	619438.	+	852584.i	0.859375	+	1.18283i
$850$	−266375.	+	366634.i	−0.368685	+	0.507452i
$851$	−73630.3	−	226611.i	−0.101671	−	0.312912i
$852$	−58071.4	+	79928.5i	−0.0799988	+	0.110109i
$853$	1.04291e6	+	757719.i	1.43334	+	1.04138i	0.989383	+	0.145334i	$0.0464256\pi$
$853$	1.04291e6	+	757719.i	1.43334	+	1.04138i	0.443957	+	0.896048i	$0.353574\pi$
$854$	−345765.	+	112346.i	−0.474095	+	0.154043i
$855$	−936420.	−	680349.i	−1.28097	−	0.930678i
$856$	337347.	−	245097.i	0.460394	−	0.334496i
$857$	−360882.	+	1.11068e6i	−0.491364	+	1.51226i	0.331184	+	0.943566i	$0.392552\pi$
$857$	−360882.	+	1.11068e6i	−0.491364	+	1.51226i	−0.822548	+	0.568696i	$0.807448\pi$
$858$	−1.23004e6	−	1.69301e6i	−1.67088	−	2.29977i
$859$	935417.	−	303935.i	1.26771	−	0.411903i	0.403472	−	0.914992i	$-0.367803\pi$
$859$	935417.	−	303935.i	1.26771	−	0.411903i	0.864235	+	0.503089i	$0.167803\pi$
$860$	63095.2	−	20500.9i	0.0853099	−	0.0277189i
$861$	−244774.	−	79531.9i	−0.330186	−	0.107284i
$862$	539749.			0.726403
$863$			997996.i			1.34001i	0.742357	+	0.670004i	$0.233708\pi$
$863$			997996.i			1.34001i	−0.742357	+	0.670004i	$0.766292\pi$
$864$	−62106.8	−	20179.7i	−0.0831977	−	0.0270326i
$865$	−1.79459e6	−	1.30385e6i	−2.39847	−	1.74259i
$866$	66224.2	+	91149.8i	0.0883041	+	0.121540i
$867$		−	960486.i		−	1.27777i
$868$	30247.8	+	3611.34i	0.0401471	+	0.00479324i
$869$	282855.			0.374563
$870$	−68424.9	+	49713.6i	−0.0904015	+	0.0656805i
$871$	462471.	−	636537.i	0.609605	−	0.839049i
$872$	−146428.	+	450658.i	−0.192571	+	0.592672i
$873$	1.33574e6			1.75265
$874$		−	812131.i		−	1.06317i
$875$	−119168.	+	366762.i	−0.155648	+	0.479035i
$876$	34211.8	+	105293.i	0.0445828	+	0.137212i
$877$	−138034.	−	424824.i	−0.179468	−	0.552344i	0.820342	−	0.571874i	$-0.193783\pi$
$877$	−138034.	−	424824.i	−0.179468	−	0.552344i	−0.999809	+	0.0195292i	$0.993783\pi$
$878$	−236015.	+	171475.i	−0.306161	+	0.222439i
$879$	203153.	+	66008.5i	0.262934	+	0.0854324i
$880$	−779781.	−	1.07328e6i	−1.00695	−	1.38595i
$881$	481534.	−	662775.i	0.620405	−	0.853915i	−0.376977	−	0.926223i	$-0.623036\pi$
$881$	481534.	−	662775.i	0.620405	−	0.853915i	0.997382	+	0.0723079i	$0.0230364\pi$
$882$	−220995.	−	680154.i	−0.284083	−	0.874319i
$883$	−269782.	+	371323.i	−0.346012	+	0.476245i	−0.946185	−	0.323625i	$-0.895098\pi$
$883$	−269782.	+	371323.i	−0.346012	+	0.476245i	0.600173	+	0.799870i	$0.295098\pi$
$884$	−31238.3	−	22695.9i	−0.0399745	−	0.0290431i
$885$	−1.56514e6	+	508544.i	−1.99832	+	0.649295i
$886$	−14062.1	−	10216.7i	−0.0179136	−	0.0130150i
$887$	531510.	−	386165.i	0.675560	−	0.490823i	−0.196322	−	0.980540i	$-0.562900\pi$
$887$	531510.	−	386165.i	0.675560	−	0.490823i	0.871882	+	0.489716i	$0.162900\pi$
$888$	−82416.4	+	253652.i	−0.104517	+	0.321671i
$889$	−19419.9	−	26729.2i	−0.0245721	−	0.0338206i
$890$	−448630.	+	145769.i	−0.566380	+	0.184028i
$891$	−395954.	+	128653.i	−0.498757	+	0.162056i
$892$	−15601.2	−	5069.13i	−0.0196077	−	0.00637094i
$893$	−509130.			−0.638449
$894$		−	718541.i		−	0.899035i
$895$	1.84176e6	+	598424.i	2.29925	+	0.747073i
$896$	−320286.	−	232702.i	−0.398954	−	0.289857i
$897$	1.86956e6	+	2.57323e6i	2.32356	+	3.19811i
$898$			312938.i			0.388066i
$899$	−34374.7	−	15889.5i	−0.0425323	−	0.0196603i
$900$	126882.			0.156644
$901$	333910.	−	242600.i	0.411320	−	0.298842i
$902$	−213682.	+	294108.i	−0.262636	+	0.361488i
$903$	−170262.	+	524014.i	−0.208806	+	0.642639i
$904$	−121580.			−0.148773
$905$			1.88976e6i			2.30733i
$906$	−382860.	+	1.17832e6i	−0.466427	+	1.43552i
$907$	38481.9	+	118435.i	0.0467781	+	0.143968i	0.971717	−	0.236147i	$-0.0758845\pi$
$907$	38481.9	+	118435.i	0.0467781	+	0.143968i	−0.924939	+	0.380115i	$0.875885\pi$
$908$	−8783.53	−	27032.9i	−0.0106536	−	0.0327885i
$909$	−1.55207e6	+	1.12765e6i	−1.87838	+	1.36472i
$910$	1.12044e6	+	364053.i	1.35303	+	0.439625i
$911$	375356.	+	516633.i	0.452279	+	0.622508i	0.972885	−	0.231288i	$-0.0742941\pi$
$911$	375356.	+	516633.i	0.452279	+	0.622508i	−0.520606	+	0.853797i	$0.674294\pi$
$912$	−495630.	+	682176.i	−0.595893	+	0.820176i
$913$	−194345.	−	598133.i	−0.233148	−	0.717557i
$914$	148806.	−	204815.i	0.178127	−	0.245171i
$915$	−1.54591e6	−	1.12317e6i	−1.84647	−	1.34154i
$916$	−79063.1	+	25689.1i	−0.0942286	+	0.0306167i
$917$	−478550.	−	347687.i	−0.569101	−	0.413476i
$918$	−166705.	+	121118.i	−0.197816	+	0.143722i
$919$	323975.	−	997094.i	0.383602	−	1.18061i	−0.553887	−	0.832592i	$-0.686856\pi$
$919$	323975.	−	997094.i	0.383602	−	1.18061i	0.937489	−	0.348014i	$-0.113144\pi$
$920$	1.27772e6	+	1.75863e6i	1.50959	+	2.07778i
$921$	901343.	−	292864.i	1.06260	−	0.345260i
$922$	−84315.3	+	27395.7i	−0.0991847	+	0.0322271i
$923$	−1.62704e6	−	528657.i	−1.90983	−	0.620541i
$924$	−61954.8			−0.0725657
$925$		−	282719.i		−	0.330425i
$926$	−551900.	−	179323.i	−0.643634	−	0.209129i
$927$	−16081.3	−	11683.8i	−0.0187138	−	0.0135964i
$928$	−3410.22	−	4693.77i	−0.00395992	−	0.00545037i
$929$			402455.i			0.466322i	0.972438	+	0.233161i	$0.0749069\pi$
$929$			402455.i			0.466322i	−0.972438	+	0.233161i	$0.925093\pi$
$930$	−1.00599e6	−	1.80064e6i	−1.16313	−	2.08190i
$931$	421611.			0.486421
$932$	−23838.3	+	17319.5i	−0.0274438	+	0.0199391i
$933$	857149.	−	1.17976e6i	0.984675	−	1.35529i
$934$	24670.3	−	75927.3i	0.0282801	−	0.0870371i
$935$	677091.			0.774505
$936$		−	2.07264e6i		−	2.36576i
$937$	439843.	−	1.35370e6i	0.500977	−	1.54185i	−0.306452	−	0.951886i	$-0.599142\pi$
$937$	439843.	−	1.35370e6i	0.500977	−	1.54185i	0.807429	−	0.589964i	$-0.200858\pi$
$938$	92729.8	+	285393.i	0.105393	+	0.324368i
$939$	180577.	+	555760.i	0.204801	+	0.630313i
$940$	74080.8	−	53822.8i	0.0838397	−	0.0609131i
$941$	616990.	+	200472.i	0.696785	+	0.226399i	0.635929	−	0.771747i	$-0.280617\pi$
$941$	616990.	+	200472.i	0.696785	+	0.226399i	0.0608558	+	0.998147i	$0.480617\pi$
$942$	−26464.5	−	36425.2i	−0.0298237	−	0.0410488i
$943$	324779.	−	447020.i	0.365228	−	0.502694i
$944$	215675.	+	663780.i	0.242023	+	0.744869i
$945$	−286857.	+	394825.i	−0.321219	+	0.442121i
$946$	629628.	+	457452.i	0.703561	+	0.511167i
$947$	567661.	−	184444.i	0.632979	−	0.205667i	0.0250845	−	0.999685i	$-0.492015\pi$
$947$	567661.	−	184444.i	0.632979	−	0.205667i	0.607894	+	0.794018i	$0.292015\pi$
$948$	26159.3	+	19005.8i	0.0291078	+	0.0211480i
$949$	−1.55095e6	+	1.12683e6i	−1.72213	+	1.25120i
$950$	297776.	−	916460.i	0.329946	−	1.01547i
$951$	−442113.	−	608516.i	−0.488846	−	0.672838i
$952$	208439.	−	67725.9i	0.229988	−	0.0747276i
$953$	−851882.	+	276793.i	−0.937980	+	0.304768i	−0.737822	−	0.674996i	$-0.764146\pi$
$953$	−851882.	+	276793.i	−0.937980	+	0.304768i	−0.200158	+	0.979764i	$0.564146\pi$
$954$	1.41579e6	+	460019.i	1.55562	+	0.505451i
$955$	1.44267e6			1.58183
$956$		−	38561.0i		−	0.0421923i
$957$	73249.2	+	23800.1i	0.0799796	+	0.0259869i
$958$	−382966.	−	278241.i	−0.417282	−	0.303173i
$959$	139831.	+	192461.i	0.152043	+	0.209269i
$960$		−	2.42134e6i		−	2.62732i
$961$	484143.	−	786445.i	0.524236	−	0.851573i
$962$	−310318.			−0.335317
$963$	−576034.	+	418513.i	−0.621148	+	0.451291i
$964$	−25376.6	+	34927.8i	−0.0273073	+	0.0375853i
$965$	−82337.4	+	253408.i	−0.0884184	+	0.272124i
$966$	−1.21308e6			−1.29998
$967$		−	1.62107e6i		−	1.73360i	−0.498653	−	0.866802i	$-0.666172\pi$
$967$		−	1.62107e6i		−	1.73360i	0.498653	−	0.866802i	$-0.333828\pi$
$968$	−103433.	+	318333.i	−0.110384	+	0.339727i
$969$	−132989.	−	409297.i	−0.141634	−	0.435904i
$970$	563808.	+	1.73522e6i	0.599222	+	1.84422i
$971$	892591.	−	648505.i	0.946703	−	0.687820i	−0.00332154	−	0.999994i	$-0.501057\pi$
$971$	892591.	−	648505.i	0.946703	−	0.687820i	0.950025	+	0.312174i	$0.101057\pi$
$972$	−84644.0	−	27502.5i	−0.0895909	−	0.0291098i
$973$	188554.	+	259522.i	0.199163	+	0.274125i
$974$	−417303.	+	574369.i	−0.439880	+	0.605443i
$975$	1.16623e6	+	3.58929e6i	1.22680	+	3.77571i
$976$	−476339.	+	655625.i	−0.500054	+	0.688265i
$977$	112479.	+	81720.9i	0.117837	+	0.0856138i	0.645143	−	0.764062i	$-0.276798\pi$
$977$	112479.	+	81720.9i	0.117837	+	0.0856138i	−0.527306	+	0.849676i	$0.676798\pi$
$978$	433971.	−	141006.i	0.453714	−	0.147421i
$979$	347520.	+	252488.i	0.362589	+	0.263436i
$980$	−61346.3	+	44570.7i	−0.0638757	+	0.0464084i
$981$	250031.	−	769517.i	0.259810	−	0.799613i
$982$	−479942.	−	660583.i	−0.497698	−	0.685022i
$983$	−186874.	+	60719.1i	−0.193394	+	0.0628374i	−0.404113	−	0.914709i	$-0.632420\pi$
$983$	−186874.	+	60719.1i	−0.193394	+	0.0628374i	0.210719	+	0.977547i	$0.432420\pi$
$984$	−588210.	+	191121.i	−0.607494	+	0.197387i
$985$	1.40698e6	+	457156.i	1.45016	+	0.471185i
$986$	−18307.2			−0.0188308
$987$			760492.i			0.780657i
$988$	78085.0	+	25371.4i	0.0799933	+	0.0259914i
$989$	−956982.	−	695288.i	−0.978389	−	0.710841i
$990$	1.43545e6	+	1.97572e6i	1.46459	+	2.01584i
$991$			82455.5i			0.0839600i	0.999118	+	0.0419800i	$0.0133666\pi$
$991$			82455.5i			0.0839600i	−0.999118	+	0.0419800i	$0.986633\pi$
$992$	123519.	−	69008.5i	0.125519	−	0.0701261i
$993$	297534.			0.301743
$994$	527861.	−	383513.i	0.534253	−	0.388157i
$995$	−1.78525e6	+	2.45719e6i	−1.80324	+	2.48195i
$996$	22216.6	−	68375.7i	0.0223954	−	0.0689261i
$997$	−984583.			−0.990517			−0.495259	−	0.868746i	$-0.664927\pi$
$997$	−984583.			−0.990517			−0.495259	+	0.868746i	$0.664927\pi$
$998$			782177.i			0.785315i
$999$	39724.0	−	122258.i	0.0398036	−	0.122503i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.5.f.a.15.8	✓	36
31.29	odd	10	inner	31.5.f.a.29.8	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.5.f.a.15.8	✓	36	1.1	even	1	trivial
31.5.f.a.29.8	yes	36	31.29	odd	10	inner

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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	31.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.11734 - 2.26488i) q^{2} +(-8.18387 + 11.2641i) q^{3} +(-0.356154 + 1.09613i) q^{4} +40.0060 q^{5} +53.6495i q^{6} +(-8.49904 + 26.1574i) q^{7} +(20.4238 + 62.8580i) q^{8} +(-34.8745 - 107.333i) q^{9} +(124.712 - 90.6087i) q^{10} +(-133.505 - 43.3784i) q^{11} +(-9.43223 - 12.9824i) q^{12} +(163.328 - 224.802i) q^{13} +(32.7489 + 100.791i) q^{14} +(-327.404 + 450.633i) q^{15} +(191.115 + 138.853i) q^{16} +(-114.667 + 37.2574i) q^{17} +(-351.811 - 255.605i) q^{18} +(207.405 - 150.689i) q^{19} +(-14.2483 + 43.8518i) q^{20} +(-225.085 - 309.803i) q^{21} +(-514.427 + 167.148i) q^{22} +(781.887 - 254.050i) q^{23} +(-875.187 - 284.365i) q^{24} +975.481 q^{25} -1070.70i q^{26} +(421.833 + 137.062i) q^{27} +(-25.6449 - 18.6321i) q^{28} +(23.1624 + 31.8803i) q^{29} +2146.30i q^{30} +(-838.947 + 468.710i) q^{31} -147.231 q^{32} +(1581.21 - 1148.82i) q^{33} +(-273.071 + 375.850i) q^{34} +(-340.013 + 1046.45i) q^{35} +130.071 q^{36} -289.826i q^{37} +(305.261 - 939.495i) q^{38} +(1195.54 + 3679.51i) q^{39} +(817.075 + 2514.70i) q^{40} +(543.737 - 395.048i) q^{41} +(-1403.33 - 455.970i) q^{42} +(-845.722 - 1164.04i) q^{43} +(95.0969 - 130.890i) q^{44} +(-1395.19 - 4293.95i) q^{45} +(1862.01 - 2562.84i) q^{46} +(-1606.66 - 1167.31i) q^{47} +(-3128.12 + 1016.39i) q^{48} +(1330.48 + 966.647i) q^{49} +(3040.90 - 2209.35i) q^{50} +(518.743 - 1596.53i) q^{51} +(188.243 + 259.094i) q^{52} +(-3255.73 + 1057.85i) q^{53} +(1625.42 - 528.132i) q^{54} +(-5341.01 - 1735.40i) q^{55} -1817.78 q^{56} +3569.46i q^{57} +(144.410 + 46.9217i) q^{58} +(2390.22 + 1736.60i) q^{59} +(-377.346 - 519.372i) q^{60} +3430.53i q^{61} +(-1553.71 + 3361.24i) q^{62} +3103.94 q^{63} +(-3516.81 + 2555.11i) q^{64} +(6534.12 - 8993.45i) q^{65} +(2327.23 - 7162.49i) q^{66} +2831.54 q^{67} -138.959i q^{68} +(-3537.20 + 10886.4i) q^{69} +(1310.15 + 4032.23i) q^{70} +(-1902.53 - 5855.37i) q^{71} +(6034.45 - 4384.28i) q^{72} +(-6561.51 - 2131.96i) q^{73} +(-656.420 - 903.484i) q^{74} +(-7983.21 + 10987.9i) q^{75} +(91.3063 + 281.012i) q^{76} +(2269.33 - 3123.47i) q^{77} +(12060.5 + 8762.50i) q^{78} +(-1916.37 + 622.665i) q^{79} +(7645.75 + 5554.96i) q^{80} +(2399.41 - 1743.27i) q^{81} +(800.277 - 2463.00i) q^{82} +(2633.41 + 3624.58i) q^{83} +(419.749 - 136.385i) q^{84} +(-4587.35 + 1490.52i) q^{85} +(-5272.80 - 1713.24i) q^{86} -548.662 q^{87} -9277.82i q^{88} +(-2910.29 - 945.612i) q^{89} +(-14074.5 - 10225.8i) q^{90} +(4492.10 + 6182.85i) q^{91} +947.531i q^{92} +(1586.23 - 13285.9i) q^{93} -7652.32 q^{94} +(8297.46 - 6028.46i) q^{95} +(1204.92 - 1658.43i) q^{96} +(-3657.46 + 11256.5i) q^{97} +6336.88 q^{98} +15842.3i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} - 5 q^{3} - 79 q^{4} - 2 q^{5} - 73 q^{7} + 173 q^{8} + 62 q^{9} + 84 q^{10} + 100 q^{11} + 150 q^{12} - 260 q^{13} + 488 q^{14} - 1075 q^{15} + 777 q^{16} - 725 q^{17} - 786 q^{18} - 1581 q^{19}+ \cdots + 74456 q^{98}+O(q^{100}) \) 36 * q - 3 * q^2 - 5 * q^3 - 79 * q^4 - 2 * q^5 - 73 * q^7 + 173 * q^8 + 62 * q^9 + 84 * q^10 + 100 * q^11 + 150 * q^12 - 260 * q^13 + 488 * q^14 - 1075 * q^15 + 777 * q^16 - 725 * q^17 - 786 * q^18 - 1581 * q^19 + 827 * q^20 + 2335 * q^21 - 1030 * q^22 + 1675 * q^23 - 165 * q^24 + 1294 * q^25 - 2855 * q^27 + 352 * q^28 - 575 * q^29 + 895 * q^31 - 5470 * q^32 + 4468 * q^33 + 1815 * q^34 - 3042 * q^35 + 7808 * q^36 - 6604 * q^38 + 595 * q^39 + 1482 * q^40 - 1740 * q^41 + 3840 * q^42 - 10055 * q^43 - 5780 * q^44 + 6774 * q^45 + 16515 * q^46 + 693 * q^47 + 4710 * q^48 - 944 * q^49 - 6240 * q^50 + 12641 * q^51 + 15885 * q^52 - 10835 * q^53 - 25960 * q^54 - 14010 * q^55 - 19976 * q^56 + 4755 * q^58 - 6021 * q^59 + 35 * q^60 - 11088 * q^62 - 15564 * q^63 + 6935 * q^64 + 26645 * q^65 + 23988 * q^66 + 28596 * q^67 - 4229 * q^69 + 8041 * q^70 + 31101 * q^71 + 20690 * q^72 + 6125 * q^73 - 47295 * q^74 - 27475 * q^75 + 12511 * q^76 + 35950 * q^77 + 29801 * q^78 - 29050 * q^79 - 47358 * q^80 - 1965 * q^81 + 9198 * q^82 + 21640 * q^83 - 35875 * q^84 - 55360 * q^85 - 27935 * q^86 - 2262 * q^87 - 11645 * q^89 - 14916 * q^90 + 670 * q^91 - 36224 * q^93 - 52442 * q^94 + 73983 * q^95 + 29810 * q^96 + 55059 * q^97 + 74456 * q^98

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