Properties

Label 3.39.b.a.2.9
Level 3
Weight 39
Character 3.2
Analytic conductor 27.439
Analytic rank 0
Dimension 12
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 39 \)
Character orbit: \([\chi]\) \(=\) 3.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(27.4390407101\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 17353504902 x^{10} + 111006258614054318328 x^{8} + 323765701965839203118204176384 x^{6} + 420150309279704216298413492838082805760 x^{4} + 190068212511425710374530430459662273636990976000 x^{2} + 27342285412416035125187079526375866471795145886924800000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{75}\cdot 3^{91}\cdot 5^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2.9
Root \(53338.0i\) of defining polynomial
Character \(\chi\) \(=\) 3.2
Dual form 3.39.b.a.2.4

$q$-expansion

\(f(q)\) \(=\) \(q+640056. i q^{2} +(2.88152e8 - 1.12598e9i) q^{3} -1.34793e11 q^{4} -3.15820e13i q^{5} +(7.20687e14 + 1.84433e14i) q^{6} +9.50531e15 q^{7} +8.96619e16i q^{8} +(-1.18479e18 - 6.48904e17i) q^{9} +O(q^{10})\) \(q+640056. i q^{2} +(2.88152e8 - 1.12598e9i) q^{3} -1.34793e11 q^{4} -3.15820e13i q^{5} +(7.20687e14 + 1.84433e14i) q^{6} +9.50531e15 q^{7} +8.96619e16i q^{8} +(-1.18479e18 - 6.48904e17i) q^{9} +2.02142e19 q^{10} -6.59450e19i q^{11} +(-3.88410e19 + 1.51774e20i) q^{12} -1.55676e21 q^{13} +6.08393e21i q^{14} +(-3.55605e22 - 9.10042e21i) q^{15} -9.44403e22 q^{16} +2.67217e23i q^{17} +(4.15335e23 - 7.58331e23i) q^{18} -1.27892e24 q^{19} +4.25704e24i q^{20} +(2.73898e24 - 1.07027e25i) q^{21} +4.22085e25 q^{22} -4.27683e25i q^{23} +(1.00957e26 + 2.58363e25i) q^{24} -6.33625e26 q^{25} -9.96411e26i q^{26} +(-1.07205e27 + 1.14706e27i) q^{27} -1.28125e27 q^{28} -6.33374e27i q^{29} +(5.82478e27 - 2.27607e28i) q^{30} +2.54059e28 q^{31} -3.58010e28i q^{32} +(-7.42524e28 - 1.90022e28i) q^{33} -1.71034e29 q^{34} -3.00197e29i q^{35} +(1.59702e29 + 8.74680e28i) q^{36} -9.87322e28 q^{37} -8.18580e29i q^{38} +(-4.48583e29 + 1.75287e30i) q^{39} +2.83170e30 q^{40} +3.57778e30i q^{41} +(6.85035e30 + 1.75310e30i) q^{42} -8.11666e30 q^{43} +8.88895e30i q^{44} +(-2.04937e31 + 3.74180e31i) q^{45} +2.73741e31 q^{46} -7.20582e31i q^{47} +(-2.72132e31 + 1.06337e32i) q^{48} -3.95839e31 q^{49} -4.05555e32i q^{50} +(3.00880e32 + 7.69993e31i) q^{51} +2.09841e32 q^{52} -4.09843e32i q^{53} +(-7.34182e32 - 6.86171e32i) q^{54} -2.08268e33 q^{55} +8.52264e32i q^{56} +(-3.68524e32 + 1.44003e33i) q^{57} +4.05394e33 q^{58} -1.03957e33i q^{59} +(4.79333e33 + 1.22668e33i) q^{60} +5.64098e33 q^{61} +1.62612e34i q^{62} +(-1.12618e34 - 6.16804e33i) q^{63} -3.04493e33 q^{64} +4.91655e34i q^{65} +(1.21625e34 - 4.75257e34i) q^{66} -6.14474e34 q^{67} -3.60191e34i q^{68} +(-4.81561e34 - 1.23238e34i) q^{69} +1.92143e35 q^{70} -1.97414e35i q^{71} +(5.81820e34 - 1.06230e35i) q^{72} -1.80385e35 q^{73} -6.31941e34i q^{74} +(-1.82580e35 + 7.13446e35i) q^{75} +1.72390e35 q^{76} -6.26828e35i q^{77} +(-1.12193e36 - 2.87118e35i) q^{78} +1.59780e36 q^{79} +2.98261e36i q^{80} +(9.82647e35 + 1.53763e36i) q^{81} -2.28998e36 q^{82} -2.62427e36i q^{83} +(-3.69196e35 + 1.44266e36i) q^{84} +8.43926e36 q^{85} -5.19512e36i q^{86} +(-7.13163e36 - 1.82508e36i) q^{87} +5.91276e36 q^{88} +3.89397e36i q^{89} +(-2.39496e37 - 1.31171e37i) q^{90} -1.47975e37 q^{91} +5.76489e36i q^{92} +(7.32076e36 - 2.86064e37i) q^{93} +4.61213e37 q^{94} +4.03909e37i q^{95} +(-4.03110e37 - 1.03161e37i) q^{96} +8.00800e37 q^{97} -2.53359e37i q^{98} +(-4.27920e37 + 7.81309e37i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 114742404q^{3} - 1699274528448q^{4} - 483611204680128q^{6} + 8107872236538648q^{7} - 424319151461513940q^{9} + O(q^{10}) \) \( 12q - 114742404q^{3} - 1699274528448q^{4} - 483611204680128q^{6} + 8107872236538648q^{7} - 424319151461513940q^{9} + 8521437485093339520q^{10} - 2862564534392665536q^{12} + \)\(10\!\cdots\!52\)\(q^{13} + \)\(63\!\cdots\!80\)\(q^{15} + \)\(67\!\cdots\!56\)\(q^{16} + \)\(14\!\cdots\!20\)\(q^{18} - \)\(46\!\cdots\!60\)\(q^{19} + \)\(33\!\cdots\!52\)\(q^{21} - \)\(13\!\cdots\!60\)\(q^{22} + \)\(78\!\cdots\!84\)\(q^{24} - \)\(12\!\cdots\!20\)\(q^{25} + \)\(35\!\cdots\!04\)\(q^{27} - \)\(77\!\cdots\!68\)\(q^{28} - \)\(31\!\cdots\!40\)\(q^{30} + \)\(62\!\cdots\!84\)\(q^{31} - \)\(20\!\cdots\!40\)\(q^{33} + \)\(27\!\cdots\!04\)\(q^{34} + \)\(52\!\cdots\!44\)\(q^{36} - \)\(10\!\cdots\!52\)\(q^{37} + \)\(37\!\cdots\!68\)\(q^{39} - \)\(86\!\cdots\!40\)\(q^{40} + \)\(37\!\cdots\!80\)\(q^{42} + \)\(10\!\cdots\!92\)\(q^{43} - \)\(61\!\cdots\!20\)\(q^{45} + \)\(13\!\cdots\!64\)\(q^{46} - \)\(16\!\cdots\!64\)\(q^{48} - \)\(74\!\cdots\!52\)\(q^{49} + \)\(71\!\cdots\!72\)\(q^{51} - \)\(99\!\cdots\!32\)\(q^{52} + \)\(12\!\cdots\!12\)\(q^{54} - \)\(14\!\cdots\!40\)\(q^{55} - \)\(19\!\cdots\!12\)\(q^{57} + \)\(54\!\cdots\!20\)\(q^{58} - \)\(21\!\cdots\!80\)\(q^{60} + \)\(19\!\cdots\!24\)\(q^{61} - \)\(68\!\cdots\!88\)\(q^{63} - \)\(33\!\cdots\!44\)\(q^{64} + \)\(29\!\cdots\!20\)\(q^{66} - \)\(12\!\cdots\!52\)\(q^{67} + \)\(14\!\cdots\!32\)\(q^{69} + \)\(13\!\cdots\!80\)\(q^{70} - \)\(84\!\cdots\!40\)\(q^{72} + \)\(90\!\cdots\!72\)\(q^{73} - \)\(19\!\cdots\!60\)\(q^{75} + \)\(37\!\cdots\!48\)\(q^{76} - \)\(47\!\cdots\!80\)\(q^{78} + \)\(33\!\cdots\!20\)\(q^{79} - \)\(38\!\cdots\!88\)\(q^{81} + \)\(97\!\cdots\!60\)\(q^{82} - \)\(23\!\cdots\!52\)\(q^{84} + \)\(16\!\cdots\!60\)\(q^{85} - \)\(46\!\cdots\!20\)\(q^{87} + \)\(11\!\cdots\!20\)\(q^{88} - \)\(16\!\cdots\!20\)\(q^{90} + \)\(12\!\cdots\!24\)\(q^{91} - \)\(17\!\cdots\!28\)\(q^{93} + \)\(32\!\cdots\!64\)\(q^{94} - \)\(45\!\cdots\!24\)\(q^{96} + \)\(24\!\cdots\!28\)\(q^{97} - \)\(34\!\cdots\!40\)\(q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 640056.i 1.22081i 0.792090 + 0.610405i \(0.208993\pi\)
−0.792090 + 0.610405i \(0.791007\pi\)
\(3\) 2.88152e8 1.12598e9i 0.247924 0.968780i
\(4\) −1.34793e11 −0.490375
\(5\) 3.15820e13i 1.65581i −0.560871 0.827903i \(-0.689534\pi\)
0.560871 0.827903i \(-0.310466\pi\)
\(6\) 7.20687e14 + 1.84433e14i 1.18270 + 0.302668i
\(7\) 9.50531e15 0.833880 0.416940 0.908934i \(-0.363103\pi\)
0.416940 + 0.908934i \(0.363103\pi\)
\(8\) 8.96619e16i 0.622154i
\(9\) −1.18479e18 6.48904e17i −0.877068 0.480367i
\(10\) 2.02142e19 2.02142
\(11\) 6.59450e19i 1.07825i −0.842225 0.539127i \(-0.818754\pi\)
0.842225 0.539127i \(-0.181246\pi\)
\(12\) −3.88410e19 + 1.51774e20i −0.121576 + 0.475066i
\(13\) −1.55676e21 −1.06487 −0.532436 0.846470i \(-0.678723\pi\)
−0.532436 + 0.846470i \(0.678723\pi\)
\(14\) 6.08393e21i 1.01801i
\(15\) −3.55605e22 9.10042e21i −1.60411 0.410514i
\(16\) −9.44403e22 −1.24991
\(17\) 2.67217e23i 1.11773i 0.829260 + 0.558863i \(0.188762\pi\)
−0.829260 + 0.558863i \(0.811238\pi\)
\(18\) 4.15335e23 7.58331e23i 0.586436 1.07073i
\(19\) −1.27892e24 −0.646436 −0.323218 0.946325i \(-0.604765\pi\)
−0.323218 + 0.946325i \(0.604765\pi\)
\(20\) 4.25704e24i 0.811967i
\(21\) 2.73898e24 1.07027e25i 0.206739 0.807846i
\(22\) 4.22085e25 1.31634
\(23\) 4.27683e25i 0.573183i −0.958053 0.286592i \(-0.907478\pi\)
0.958053 0.286592i \(-0.0925223\pi\)
\(24\) 1.00957e26 + 2.58363e25i 0.602731 + 0.154247i
\(25\) −6.33625e26 −1.74170
\(26\) 9.96411e26i 1.30001i
\(27\) −1.07205e27 + 1.14706e27i −0.682815 + 0.730591i
\(28\) −1.28125e27 −0.408914
\(29\) 6.33374e27i 1.03776i −0.854846 0.518881i \(-0.826349\pi\)
0.854846 0.518881i \(-0.173651\pi\)
\(30\) 5.82478e27 2.27607e28i 0.501159 1.95831i
\(31\) 2.54059e28 1.17236 0.586182 0.810179i \(-0.300630\pi\)
0.586182 + 0.810179i \(0.300630\pi\)
\(32\) 3.58010e28i 0.903744i
\(33\) −7.42524e28 1.90022e28i −1.04459 0.267325i
\(34\) −1.71034e29 −1.36453
\(35\) 3.00197e29i 1.38074i
\(36\) 1.59702e29 + 8.74680e28i 0.430092 + 0.235560i
\(37\) −9.87322e28 −0.157989 −0.0789944 0.996875i \(-0.525171\pi\)
−0.0789944 + 0.996875i \(0.525171\pi\)
\(38\) 8.18580e29i 0.789175i
\(39\) −4.48583e29 + 1.75287e30i −0.264007 + 1.03163i
\(40\) 2.83170e30 1.03017
\(41\) 3.57778e30i 0.814180i 0.913388 + 0.407090i \(0.133457\pi\)
−0.913388 + 0.407090i \(0.866543\pi\)
\(42\) 6.85035e30 + 1.75310e30i 0.986226 + 0.252388i
\(43\) −8.11666e30 −0.747269 −0.373634 0.927576i \(-0.621889\pi\)
−0.373634 + 0.927576i \(0.621889\pi\)
\(44\) 8.88895e30i 0.528749i
\(45\) −2.04937e31 + 3.74180e31i −0.795394 + 1.45225i
\(46\) 2.73741e31 0.699747
\(47\) 7.20582e31i 1.22412i −0.790811 0.612060i \(-0.790341\pi\)
0.790811 0.612060i \(-0.209659\pi\)
\(48\) −2.72132e31 + 1.06337e32i −0.309882 + 1.21088i
\(49\) −3.95839e31 −0.304644
\(50\) 4.05555e32i 2.12628i
\(51\) 3.00880e32 + 7.69993e31i 1.08283 + 0.277111i
\(52\) 2.09841e32 0.522187
\(53\) 4.09843e32i 0.710192i −0.934830 0.355096i \(-0.884448\pi\)
0.934830 0.355096i \(-0.115552\pi\)
\(54\) −7.34182e32 6.86171e32i −0.891912 0.833587i
\(55\) −2.08268e33 −1.78538
\(56\) 8.52264e32i 0.518802i
\(57\) −3.68524e32 + 1.44003e33i −0.160267 + 0.626254i
\(58\) 4.05394e33 1.26691
\(59\) 1.03957e33i 0.234783i −0.993086 0.117392i \(-0.962547\pi\)
0.993086 0.117392i \(-0.0374532\pi\)
\(60\) 4.79333e33 + 1.22668e33i 0.786617 + 0.201306i
\(61\) 5.64098e33 0.676220 0.338110 0.941107i \(-0.390212\pi\)
0.338110 + 0.941107i \(0.390212\pi\)
\(62\) 1.62612e34i 1.43123i
\(63\) −1.12618e34 6.16804e33i −0.731369 0.400568i
\(64\) −3.04493e33 −0.146608
\(65\) 4.91655e34i 1.76322i
\(66\) 1.21625e34 4.75257e34i 0.326352 1.27525i
\(67\) −6.14474e34 −1.23903 −0.619515 0.784984i \(-0.712671\pi\)
−0.619515 + 0.784984i \(0.712671\pi\)
\(68\) 3.60191e34i 0.548105i
\(69\) −4.81561e34 1.23238e34i −0.555288 0.142106i
\(70\) 1.92143e35 1.68562
\(71\) 1.97414e35i 1.32272i −0.750068 0.661361i \(-0.769979\pi\)
0.750068 0.661361i \(-0.230021\pi\)
\(72\) 5.81820e34 1.06230e35i 0.298862 0.545672i
\(73\) −1.80385e35 −0.712962 −0.356481 0.934303i \(-0.616023\pi\)
−0.356481 + 0.934303i \(0.616023\pi\)
\(74\) 6.31941e34i 0.192874i
\(75\) −1.82580e35 + 7.13446e35i −0.431807 + 1.68732i
\(76\) 1.72390e35 0.316996
\(77\) 6.26828e35i 0.899134i
\(78\) −1.12193e36 2.87118e35i −1.25942 0.322302i
\(79\) 1.59780e36 1.40802 0.704009 0.710191i \(-0.251392\pi\)
0.704009 + 0.710191i \(0.251392\pi\)
\(80\) 2.98261e36i 2.06960i
\(81\) 9.82647e35 + 1.53763e36i 0.538495 + 0.842628i
\(82\) −2.28998e36 −0.993959
\(83\) 2.62427e36i 0.904744i −0.891829 0.452372i \(-0.850578\pi\)
0.891829 0.452372i \(-0.149422\pi\)
\(84\) −3.69196e35 + 1.44266e36i −0.101379 + 0.396148i
\(85\) 8.43926e36 1.85074
\(86\) 5.19512e36i 0.912273i
\(87\) −7.13163e36 1.82508e36i −1.00536 0.257286i
\(88\) 5.91276e36 0.670840
\(89\) 3.89397e36i 0.356437i 0.983991 + 0.178218i \(0.0570333\pi\)
−0.983991 + 0.178218i \(0.942967\pi\)
\(90\) −2.39496e37 1.31171e37i −1.77293 0.971025i
\(91\) −1.47975e37 −0.887975
\(92\) 5.76489e36i 0.281075i
\(93\) 7.32076e36 2.86064e37i 0.290657 1.13576i
\(94\) 4.61213e37 1.49442
\(95\) 4.03909e37i 1.07037i
\(96\) −4.03110e37 1.03161e37i −0.875529 0.224060i
\(97\) 8.00800e37 1.42844 0.714219 0.699923i \(-0.246782\pi\)
0.714219 + 0.699923i \(0.246782\pi\)
\(98\) 2.53359e37i 0.371913i
\(99\) −4.27920e37 + 7.81309e37i −0.517957 + 0.945701i
\(100\) 8.54084e37 0.854084
\(101\) 5.86969e37i 0.485858i 0.970044 + 0.242929i \(0.0781082\pi\)
−0.970044 + 0.242929i \(0.921892\pi\)
\(102\) −4.92838e37 + 1.92580e38i −0.338299 + 1.32193i
\(103\) −1.79233e38 −1.02214 −0.511071 0.859539i \(-0.670751\pi\)
−0.511071 + 0.859539i \(0.670751\pi\)
\(104\) 1.39582e38i 0.662515i
\(105\) −3.38014e38 8.65023e37i −1.33764 0.342319i
\(106\) 2.62322e38 0.867009
\(107\) 1.11640e38i 0.308694i 0.988017 + 0.154347i \(0.0493274\pi\)
−0.988017 + 0.154347i \(0.950673\pi\)
\(108\) 1.44505e38 1.54616e38i 0.334836 0.358264i
\(109\) 9.48509e38 1.84475 0.922376 0.386294i \(-0.126245\pi\)
0.922376 + 0.386294i \(0.126245\pi\)
\(110\) 1.33303e39i 2.17961i
\(111\) −2.84499e37 + 1.11170e38i −0.0391691 + 0.153056i
\(112\) −8.97684e38 −1.04227
\(113\) 2.89986e38i 0.284372i 0.989840 + 0.142186i \(0.0454131\pi\)
−0.989840 + 0.142186i \(0.954587\pi\)
\(114\) −9.21701e38 2.35876e38i −0.764536 0.195655i
\(115\) −1.35071e39 −0.949080
\(116\) 8.53746e38i 0.508893i
\(117\) 1.84443e39 + 1.01019e39i 0.933964 + 0.511529i
\(118\) 6.65385e38 0.286625
\(119\) 2.53998e39i 0.932049i
\(120\) 8.15961e38 3.18843e39i 0.255403 0.998005i
\(121\) −6.08310e38 −0.162631
\(122\) 3.61054e39i 0.825536i
\(123\) 4.02849e39 + 1.03095e39i 0.788761 + 0.201855i
\(124\) −3.42455e39 −0.574898
\(125\) 8.52168e39i 1.22810i
\(126\) 3.94789e39 7.20817e39i 0.489017 0.892862i
\(127\) 6.95430e39 0.741280 0.370640 0.928777i \(-0.379138\pi\)
0.370640 + 0.928777i \(0.379138\pi\)
\(128\) 1.17898e40i 1.08272i
\(129\) −2.33883e39 + 9.13916e39i −0.185266 + 0.723939i
\(130\) −3.14687e40 −2.15256
\(131\) 2.23746e40i 1.32313i −0.749889 0.661563i \(-0.769893\pi\)
0.749889 0.661563i \(-0.230107\pi\)
\(132\) 1.00087e40 + 2.56137e39i 0.512241 + 0.131089i
\(133\) −1.21565e40 −0.539050
\(134\) 3.93297e40i 1.51262i
\(135\) 3.62264e40 + 3.38575e40i 1.20972 + 1.13061i
\(136\) −2.39592e40 −0.695398
\(137\) 1.97371e40i 0.498416i 0.968450 + 0.249208i \(0.0801703\pi\)
−0.968450 + 0.249208i \(0.919830\pi\)
\(138\) 7.88791e39 3.08226e40i 0.173484 0.677901i
\(139\) 3.39057e40 0.650117 0.325059 0.945694i \(-0.394616\pi\)
0.325059 + 0.945694i \(0.394616\pi\)
\(140\) 4.04645e40i 0.677083i
\(141\) −8.11358e40 2.07637e40i −1.18590 0.303488i
\(142\) 1.26356e41 1.61479
\(143\) 1.02660e41i 1.14820i
\(144\) 1.11892e41 + 6.12827e40i 1.09625 + 0.600414i
\(145\) −2.00032e41 −1.71833
\(146\) 1.15456e41i 0.870390i
\(147\) −1.14062e40 + 4.45705e40i −0.0755286 + 0.295133i
\(148\) 1.33084e40 0.0774738
\(149\) 3.13683e41i 1.60676i 0.595463 + 0.803382i \(0.296968\pi\)
−0.595463 + 0.803382i \(0.703032\pi\)
\(150\) −4.56645e41 1.16862e41i −2.05989 0.527155i
\(151\) 2.49290e41 0.991157 0.495578 0.868563i \(-0.334956\pi\)
0.495578 + 0.868563i \(0.334956\pi\)
\(152\) 1.14670e41i 0.402183i
\(153\) 1.73399e41 3.16596e41i 0.536918 0.980321i
\(154\) 4.01205e41 1.09767
\(155\) 8.02369e41i 1.94121i
\(156\) 6.04660e40 2.36275e41i 0.129462 0.505884i
\(157\) 3.35685e41 0.636559 0.318280 0.947997i \(-0.396895\pi\)
0.318280 + 0.947997i \(0.396895\pi\)
\(158\) 1.02268e42i 1.71892i
\(159\) −4.61473e41 1.18097e41i −0.688020 0.176073i
\(160\) −1.13067e42 −1.49643
\(161\) 4.06526e41i 0.477966i
\(162\) −9.84168e41 + 6.28949e41i −1.02869 + 0.657400i
\(163\) 8.93945e41 0.831278 0.415639 0.909530i \(-0.363558\pi\)
0.415639 + 0.909530i \(0.363558\pi\)
\(164\) 4.82261e41i 0.399254i
\(165\) −6.00127e41 + 2.34504e42i −0.442638 + 1.72964i
\(166\) 1.67968e42 1.10452
\(167\) 1.94932e42i 1.14359i −0.820396 0.571795i \(-0.806247\pi\)
0.820396 0.571795i \(-0.193753\pi\)
\(168\) 9.59628e41 + 2.45582e41i 0.502605 + 0.128623i
\(169\) 2.86282e41 0.133951
\(170\) 5.40160e42i 2.25940i
\(171\) 1.51525e42 + 8.29897e41i 0.566968 + 0.310526i
\(172\) 1.09407e42 0.366442
\(173\) 6.41502e42i 1.92452i −0.272136 0.962259i \(-0.587730\pi\)
0.272136 0.962259i \(-0.412270\pi\)
\(174\) 1.16815e42 4.56464e42i 0.314097 1.22736i
\(175\) −6.02280e42 −1.45236
\(176\) 6.22787e42i 1.34772i
\(177\) −1.17053e42 2.99555e41i −0.227453 0.0582083i
\(178\) −2.49236e42 −0.435141
\(179\) 1.15790e42i 0.181745i 0.995863 + 0.0908726i \(0.0289656\pi\)
−0.995863 + 0.0908726i \(0.971034\pi\)
\(180\) 2.76241e42 5.04370e42i 0.390042 0.712150i
\(181\) −1.08797e43 −1.38269 −0.691344 0.722526i \(-0.742981\pi\)
−0.691344 + 0.722526i \(0.742981\pi\)
\(182\) 9.47120e42i 1.08405i
\(183\) 1.62546e42 6.35161e42i 0.167651 0.655108i
\(184\) 3.83469e42 0.356609
\(185\) 3.11816e42i 0.261599i
\(186\) 1.83097e43 + 4.68570e42i 1.38655 + 0.354836i
\(187\) 1.76217e43 1.20519
\(188\) 9.71297e42i 0.600279i
\(189\) −1.01902e43 + 1.09032e43i −0.569386 + 0.609225i
\(190\) −2.58524e43 −1.30672
\(191\) 1.16526e43i 0.533075i −0.963825 0.266537i \(-0.914120\pi\)
0.963825 0.266537i \(-0.0858796\pi\)
\(192\) −8.77404e41 + 3.42852e42i −0.0363476 + 0.142031i
\(193\) −1.38553e43 −0.520029 −0.260014 0.965605i \(-0.583727\pi\)
−0.260014 + 0.965605i \(0.583727\pi\)
\(194\) 5.12557e43i 1.74385i
\(195\) 5.53591e43 + 1.41671e43i 1.70817 + 0.437144i
\(196\) 5.33565e42 0.149390
\(197\) 1.34295e43i 0.341351i −0.985327 0.170676i \(-0.945405\pi\)
0.985327 0.170676i \(-0.0545950\pi\)
\(198\) −5.00081e43 2.73893e43i −1.15452 0.632327i
\(199\) 8.89031e42 0.186513 0.0932563 0.995642i \(-0.470272\pi\)
0.0932563 + 0.995642i \(0.470272\pi\)
\(200\) 5.68120e43i 1.08360i
\(201\) −1.77062e43 + 6.91882e43i −0.307185 + 1.20035i
\(202\) −3.75693e43 −0.593140
\(203\) 6.02041e43i 0.865369i
\(204\) −4.05566e43 1.03790e43i −0.530993 0.135888i
\(205\) 1.12994e44 1.34813
\(206\) 1.14719e44i 1.24784i
\(207\) −2.77526e43 + 5.06714e43i −0.275338 + 0.502720i
\(208\) 1.47021e44 1.33099
\(209\) 8.43384e43i 0.697021i
\(210\) 5.53663e43 2.16348e44i 0.417906 1.63300i
\(211\) −1.25172e44 −0.863259 −0.431629 0.902051i \(-0.642061\pi\)
−0.431629 + 0.902051i \(0.642061\pi\)
\(212\) 5.52441e43i 0.348261i
\(213\) −2.22283e44 5.68852e43i −1.28143 0.327934i
\(214\) −7.14559e43 −0.376857
\(215\) 2.56340e44i 1.23733i
\(216\) −1.02848e44 9.61220e43i −0.454540 0.424817i
\(217\) 2.41491e44 0.977611
\(218\) 6.07098e44i 2.25209i
\(219\) −5.19783e43 + 2.03109e44i −0.176760 + 0.690703i
\(220\) 2.80731e44 0.875506
\(221\) 4.15993e44i 1.19023i
\(222\) −7.11550e43 1.82095e43i −0.186852 0.0478181i
\(223\) −6.66529e43 −0.160704 −0.0803520 0.996767i \(-0.525604\pi\)
−0.0803520 + 0.996767i \(0.525604\pi\)
\(224\) 3.40299e44i 0.753614i
\(225\) 7.50712e44 + 4.11162e44i 1.52758 + 0.836652i
\(226\) −1.85607e44 −0.347164
\(227\) 7.05437e43i 0.121330i 0.998158 + 0.0606648i \(0.0193221\pi\)
−0.998158 + 0.0606648i \(0.980678\pi\)
\(228\) 4.96746e43 1.94107e44i 0.0785908 0.307099i
\(229\) −9.62962e43 −0.140196 −0.0700979 0.997540i \(-0.522331\pi\)
−0.0700979 + 0.997540i \(0.522331\pi\)
\(230\) 8.64529e44i 1.15865i
\(231\) −7.05792e44 1.80622e44i −0.871063 0.222917i
\(232\) 5.67895e44 0.645649
\(233\) 4.41342e44i 0.462395i −0.972907 0.231197i \(-0.925736\pi\)
0.972907 0.231197i \(-0.0742643\pi\)
\(234\) −6.46576e44 + 1.18054e45i −0.624479 + 1.14019i
\(235\) −2.27574e45 −2.02691
\(236\) 1.40128e44i 0.115132i
\(237\) 4.60410e44 1.79908e45i 0.349081 1.36406i
\(238\) −1.62573e45 −1.13785
\(239\) 1.33189e44i 0.0860813i −0.999073 0.0430407i \(-0.986295\pi\)
0.999073 0.0430407i \(-0.0137045\pi\)
\(240\) 3.35835e45 + 8.59447e44i 2.00499 + 0.513104i
\(241\) 2.28762e45 1.26200 0.631000 0.775783i \(-0.282645\pi\)
0.631000 + 0.775783i \(0.282645\pi\)
\(242\) 3.89352e44i 0.198541i
\(243\) 2.01448e45 6.63365e44i 0.949827 0.312776i
\(244\) −7.60367e44 −0.331602
\(245\) 1.25014e45i 0.504432i
\(246\) −6.59863e44 + 2.57846e45i −0.246426 + 0.962927i
\(247\) 1.99097e45 0.688371
\(248\) 2.27794e45i 0.729391i
\(249\) −2.95487e45 7.56190e44i −0.876497 0.224307i
\(250\) −5.45435e45 −1.49928
\(251\) 3.22130e45i 0.820787i 0.911908 + 0.410394i \(0.134609\pi\)
−0.911908 + 0.410394i \(0.865391\pi\)
\(252\) 1.51801e45 + 8.31410e44i 0.358645 + 0.196429i
\(253\) −2.82036e45 −0.618037
\(254\) 4.45114e45i 0.904962i
\(255\) 2.43179e45 9.50240e45i 0.458842 1.79296i
\(256\) 6.70916e45 1.17519
\(257\) 3.34070e45i 0.543386i −0.962384 0.271693i \(-0.912416\pi\)
0.962384 0.271693i \(-0.0875835\pi\)
\(258\) −5.84957e45 1.49698e45i −0.883791 0.226174i
\(259\) −9.38480e44 −0.131744
\(260\) 6.62718e45i 0.864640i
\(261\) −4.10999e45 + 7.50414e45i −0.498507 + 0.910188i
\(262\) 1.43210e46 1.61529
\(263\) 4.17907e45i 0.438450i −0.975674 0.219225i \(-0.929647\pi\)
0.975674 0.219225i \(-0.0703529\pi\)
\(264\) 1.70377e45 6.65762e45i 0.166317 0.649896i
\(265\) −1.29437e46 −1.17594
\(266\) 7.78086e45i 0.658077i
\(267\) 4.38451e45 + 1.12206e45i 0.345309 + 0.0883691i
\(268\) 8.28270e45 0.607590
\(269\) 4.32268e45i 0.295433i −0.989030 0.147717i \(-0.952808\pi\)
0.989030 0.147717i \(-0.0471924\pi\)
\(270\) −2.16707e46 + 2.31869e46i −1.38026 + 1.47683i
\(271\) 1.17659e46 0.698571 0.349285 0.937016i \(-0.386424\pi\)
0.349285 + 0.937016i \(0.386424\pi\)
\(272\) 2.52361e46i 1.39705i
\(273\) −4.26392e45 + 1.66616e46i −0.220150 + 0.860252i
\(274\) −1.26328e46 −0.608471
\(275\) 4.17844e46i 1.87799i
\(276\) 6.49112e45 + 1.66116e45i 0.272300 + 0.0696851i
\(277\) 1.48250e46 0.580602 0.290301 0.956935i \(-0.406245\pi\)
0.290301 + 0.956935i \(0.406245\pi\)
\(278\) 2.17016e46i 0.793669i
\(279\) −3.01006e46 1.64860e46i −1.02824 0.563165i
\(280\) 2.69162e46 0.859036
\(281\) 1.30765e45i 0.0390005i 0.999810 + 0.0195003i \(0.00620752\pi\)
−0.999810 + 0.0195003i \(0.993792\pi\)
\(282\) 1.32899e46 5.19314e46i 0.370502 1.44776i
\(283\) 2.61530e46 0.681679 0.340839 0.940122i \(-0.389289\pi\)
0.340839 + 0.940122i \(0.389289\pi\)
\(284\) 2.66100e46i 0.648630i
\(285\) 4.54791e46 + 1.16387e46i 1.03695 + 0.265371i
\(286\) −6.57084e46 −1.40174
\(287\) 3.40079e46i 0.678929i
\(288\) −2.32314e46 + 4.24166e46i −0.434129 + 0.792645i
\(289\) −1.42495e46 −0.249311
\(290\) 1.28032e47i 2.09776i
\(291\) 2.30752e46 9.01681e46i 0.354143 1.38384i
\(292\) 2.43147e46 0.349619
\(293\) 1.80643e46i 0.243408i −0.992566 0.121704i \(-0.961164\pi\)
0.992566 0.121704i \(-0.0388359\pi\)
\(294\) −2.85276e46 7.30060e45i −0.360302 0.0922060i
\(295\) −3.28318e46 −0.388755
\(296\) 8.85252e45i 0.0982934i
\(297\) 7.56428e46 + 7.06963e46i 0.787762 + 0.736248i
\(298\) −2.00775e47 −1.96155
\(299\) 6.65799e46i 0.610366i
\(300\) 2.46106e46 9.61678e46i 0.211748 0.827419i
\(301\) −7.71514e46 −0.623132
\(302\) 1.59559e47i 1.21001i
\(303\) 6.60913e46 + 1.69136e46i 0.470689 + 0.120456i
\(304\) 1.20782e47 0.807985
\(305\) 1.78154e47i 1.11969i
\(306\) 2.02639e47 + 1.10985e47i 1.19679 + 0.655475i
\(307\) 2.11365e46 0.117329 0.0586643 0.998278i \(-0.481316\pi\)
0.0586643 + 0.998278i \(0.481316\pi\)
\(308\) 8.44922e46i 0.440913i
\(309\) −5.16464e46 + 2.01812e47i −0.253413 + 0.990230i
\(310\) 5.13561e47 2.36984
\(311\) 1.90047e47i 0.824926i −0.910974 0.412463i \(-0.864669\pi\)
0.910974 0.412463i \(-0.135331\pi\)
\(312\) −1.57166e47 4.02208e46i −0.641831 0.164253i
\(313\) −4.36802e47 −1.67858 −0.839290 0.543684i \(-0.817029\pi\)
−0.839290 + 0.543684i \(0.817029\pi\)
\(314\) 2.14857e47i 0.777118i
\(315\) −1.94799e47 + 3.55670e47i −0.663263 + 1.21101i
\(316\) −2.15373e47 −0.690457
\(317\) 2.82613e47i 0.853229i −0.904434 0.426614i \(-0.859706\pi\)
0.904434 0.426614i \(-0.140294\pi\)
\(318\) 7.55887e46 2.95368e47i 0.214952 0.839941i
\(319\) −4.17678e47 −1.11897
\(320\) 9.61651e46i 0.242755i
\(321\) 1.25704e47 + 3.21694e46i 0.299057 + 0.0765327i
\(322\) 2.60199e47 0.583505
\(323\) 3.41750e47i 0.722538i
\(324\) −1.32454e47 2.07262e47i −0.264065 0.413204i
\(325\) 9.86400e47 1.85468
\(326\) 5.72175e47i 1.01483i
\(327\) 2.73315e47 1.06800e48i 0.457358 1.78716i
\(328\) −3.20791e47 −0.506546
\(329\) 6.84936e47i 1.02077i
\(330\) −1.50096e48 3.84115e47i −2.11156 0.540376i
\(331\) 8.26572e47 1.09787 0.548933 0.835867i \(-0.315034\pi\)
0.548933 + 0.835867i \(0.315034\pi\)
\(332\) 3.53735e47i 0.443664i
\(333\) 1.16977e47 + 6.40678e46i 0.138567 + 0.0758925i
\(334\) 1.24767e48 1.39611
\(335\) 1.94063e48i 2.05160i
\(336\) −2.58670e47 + 1.01077e48i −0.258404 + 1.00973i
\(337\) −1.06999e48 −1.01021 −0.505105 0.863058i \(-0.668546\pi\)
−0.505105 + 0.863058i \(0.668546\pi\)
\(338\) 1.83237e47i 0.163529i
\(339\) 3.26517e47 + 8.35601e46i 0.275494 + 0.0705025i
\(340\) −1.13756e48 −0.907556
\(341\) 1.67539e48i 1.26411i
\(342\) −5.31180e47 + 9.69845e47i −0.379093 + 0.692159i
\(343\) −1.61133e48 −1.08792
\(344\) 7.27756e47i 0.464917i
\(345\) −3.89210e47 + 1.52087e48i −0.235300 + 0.919450i
\(346\) 4.10597e48 2.34947
\(347\) 2.30805e48i 1.25022i 0.780539 + 0.625108i \(0.214945\pi\)
−0.780539 + 0.625108i \(0.785055\pi\)
\(348\) 9.61297e47 + 2.46009e47i 0.493005 + 0.126167i
\(349\) 2.58261e48 1.25423 0.627114 0.778928i \(-0.284236\pi\)
0.627114 + 0.778928i \(0.284236\pi\)
\(350\) 3.85493e48i 1.77306i
\(351\) 1.66892e48 1.78569e48i 0.727111 0.777985i
\(352\) −2.36090e48 −0.974465
\(353\) 7.29378e47i 0.285255i 0.989776 + 0.142627i \(0.0455551\pi\)
−0.989776 + 0.142627i \(0.954445\pi\)
\(354\) 1.91732e47 7.49207e47i 0.0710612 0.277677i
\(355\) −6.23472e48 −2.19017
\(356\) 5.24881e47i 0.174788i
\(357\) 2.85996e48 + 7.31902e47i 0.902950 + 0.231077i
\(358\) −7.41120e47 −0.221876
\(359\) 2.35585e47i 0.0668888i 0.999441 + 0.0334444i \(0.0106477\pi\)
−0.999441 + 0.0334444i \(0.989352\pi\)
\(360\) −3.35497e48 1.83750e48i −0.903527 0.494858i
\(361\) −2.27851e48 −0.582121
\(362\) 6.96361e48i 1.68800i
\(363\) −1.75286e47 + 6.84942e47i −0.0403200 + 0.157553i
\(364\) 1.99460e48 0.435441
\(365\) 5.69692e48i 1.18053i
\(366\) 4.06538e48 + 1.04039e48i 0.799762 + 0.204670i
\(367\) 1.34691e48 0.251585 0.125793 0.992057i \(-0.459853\pi\)
0.125793 + 0.992057i \(0.459853\pi\)
\(368\) 4.03906e48i 0.716426i
\(369\) 2.32164e48 4.23891e48i 0.391105 0.714091i
\(370\) −1.99580e48 −0.319362
\(371\) 3.89568e48i 0.592215i
\(372\) −9.86790e47 + 3.85595e48i −0.142531 + 0.556950i
\(373\) −9.41851e48 −1.29275 −0.646375 0.763020i \(-0.723716\pi\)
−0.646375 + 0.763020i \(0.723716\pi\)
\(374\) 1.12788e49i 1.47131i
\(375\) 9.59520e48 + 2.45554e48i 1.18976 + 0.304476i
\(376\) 6.46088e48 0.761592
\(377\) 9.86009e48i 1.10508i
\(378\) −6.97862e48 6.52227e48i −0.743748 0.695112i
\(379\) 1.30347e49 1.32116 0.660580 0.750756i \(-0.270310\pi\)
0.660580 + 0.750756i \(0.270310\pi\)
\(380\) 5.44442e48i 0.524884i
\(381\) 2.00390e48 7.83037e48i 0.183781 0.718137i
\(382\) 7.45830e48 0.650782
\(383\) 1.34719e49i 1.11854i 0.828984 + 0.559272i \(0.188919\pi\)
−0.828984 + 0.559272i \(0.811081\pi\)
\(384\) −1.32751e49 3.39726e48i −1.04892 0.268433i
\(385\) −1.97965e49 −1.48879
\(386\) 8.86817e48i 0.634856i
\(387\) 9.61653e48 + 5.26694e48i 0.655405 + 0.358963i
\(388\) −1.07943e49 −0.700470
\(389\) 3.22298e49i 1.99166i −0.0912415 0.995829i \(-0.529084\pi\)
0.0912415 0.995829i \(-0.470916\pi\)
\(390\) −9.06776e48 + 3.54329e49i −0.533670 + 2.08535i
\(391\) 1.14284e49 0.640662
\(392\) 3.54917e48i 0.189536i
\(393\) −2.51933e49 6.44730e48i −1.28182 0.328034i
\(394\) 8.59563e48 0.416725
\(395\) 5.04618e49i 2.33140i
\(396\) 5.76808e48 1.05315e49i 0.253993 0.463749i
\(397\) 1.66907e49 0.700574 0.350287 0.936642i \(-0.386084\pi\)
0.350287 + 0.936642i \(0.386084\pi\)
\(398\) 5.69029e48i 0.227696i
\(399\) −3.50293e48 + 1.36880e49i −0.133643 + 0.522220i
\(400\) 5.98398e49 2.17696
\(401\) 5.22212e49i 1.81177i 0.423522 + 0.905886i \(0.360794\pi\)
−0.423522 + 0.905886i \(0.639206\pi\)
\(402\) −4.42843e49 1.13330e49i −1.46540 0.375014i
\(403\) −3.95508e49 −1.24842
\(404\) 7.91195e48i 0.238253i
\(405\) 4.85614e49 3.10340e49i 1.39523 0.891644i
\(406\) 3.85340e49 1.05645
\(407\) 6.51090e48i 0.170352i
\(408\) −6.90390e48 + 2.69775e49i −0.172406 + 0.673687i
\(409\) −5.82974e49 −1.38965 −0.694826 0.719178i \(-0.744519\pi\)
−0.694826 + 0.719178i \(0.744519\pi\)
\(410\) 7.23221e49i 1.64580i
\(411\) 2.22234e49 + 5.68728e48i 0.482855 + 0.123569i
\(412\) 2.41594e49 0.501233
\(413\) 9.88146e48i 0.195781i
\(414\) −3.24325e49 1.77632e49i −0.613726 0.336135i
\(415\) −8.28799e49 −1.49808
\(416\) 5.57335e49i 0.962371i
\(417\) 9.77001e48 3.81770e49i 0.161180 0.629820i
\(418\) −5.39813e49 −0.850930
\(419\) 6.06466e49i 0.913567i 0.889578 + 0.456783i \(0.150999\pi\)
−0.889578 + 0.456783i \(0.849001\pi\)
\(420\) 4.55620e49 + 1.16599e49i 0.655944 + 0.167865i
\(421\) 1.33651e50 1.83913 0.919564 0.392941i \(-0.128542\pi\)
0.919564 + 0.392941i \(0.128542\pi\)
\(422\) 8.01172e49i 1.05387i
\(423\) −4.67589e49 + 8.53737e49i −0.588027 + 1.07364i
\(424\) 3.67473e49 0.441849
\(425\) 1.69316e50i 1.94674i
\(426\) 3.64097e49 1.42273e50i 0.400345 1.56438i
\(427\) 5.36193e49 0.563886
\(428\) 1.50484e49i 0.151376i
\(429\) 1.15593e50 + 2.95818e49i 1.11235 + 0.284666i
\(430\) −1.64072e50 −1.51055
\(431\) 8.75519e49i 0.771254i −0.922655 0.385627i \(-0.873985\pi\)
0.922655 0.385627i \(-0.126015\pi\)
\(432\) 1.01245e50 1.08329e50i 0.853456 0.913171i
\(433\) −2.17140e50 −1.75174 −0.875871 0.482545i \(-0.839713\pi\)
−0.875871 + 0.482545i \(0.839713\pi\)
\(434\) 1.54568e50i 1.19348i
\(435\) −5.76397e49 + 2.25231e50i −0.426016 + 1.66469i
\(436\) −1.27853e50 −0.904621
\(437\) 5.46973e49i 0.370526i
\(438\) −1.30001e50 3.32690e49i −0.843216 0.215790i
\(439\) −6.53351e49 −0.405808 −0.202904 0.979199i \(-0.565038\pi\)
−0.202904 + 0.979199i \(0.565038\pi\)
\(440\) 1.86737e50i 1.11078i
\(441\) 4.68986e49 + 2.56862e49i 0.267194 + 0.146341i
\(442\) 2.66258e50 1.45305
\(443\) 1.65500e50i 0.865223i 0.901580 + 0.432612i \(0.142408\pi\)
−0.901580 + 0.432612i \(0.857592\pi\)
\(444\) 3.83486e48 1.49850e49i 0.0192076 0.0750550i
\(445\) 1.22979e50 0.590190
\(446\) 4.26616e49i 0.196189i
\(447\) 3.53200e50 + 9.03885e49i 1.55660 + 0.398355i
\(448\) −2.89430e49 −0.122254
\(449\) 1.27526e50i 0.516321i −0.966102 0.258160i \(-0.916884\pi\)
0.966102 0.258160i \(-0.0831163\pi\)
\(450\) −2.63167e50 + 4.80497e50i −1.02139 + 1.86489i
\(451\) 2.35937e50 0.877893
\(452\) 3.90882e49i 0.139449i
\(453\) 7.18334e49 2.80694e50i 0.245731 0.960213i
\(454\) −4.51519e49 −0.148120
\(455\) 4.67333e50i 1.47031i
\(456\) −1.29116e50 3.30425e49i −0.389626 0.0997106i
\(457\) −1.64482e50 −0.476112 −0.238056 0.971251i \(-0.576510\pi\)
−0.238056 + 0.971251i \(0.576510\pi\)
\(458\) 6.16349e49i 0.171152i
\(459\) −3.06514e50 2.86470e50i −0.816600 0.763200i
\(460\) 1.82067e50 0.465406
\(461\) 1.38516e50i 0.339767i −0.985464 0.169884i \(-0.945661\pi\)
0.985464 0.169884i \(-0.0543392\pi\)
\(462\) 1.15608e50 4.51746e50i 0.272139 1.06340i
\(463\) 2.37863e50 0.537387 0.268694 0.963226i \(-0.413408\pi\)
0.268694 + 0.963226i \(0.413408\pi\)
\(464\) 5.98160e50i 1.29711i
\(465\) −9.03448e50 2.31204e50i −1.88060 0.481271i
\(466\) 2.82484e50 0.564496
\(467\) 2.32560e50i 0.446184i 0.974797 + 0.223092i \(0.0716151\pi\)
−0.974797 + 0.223092i \(0.928385\pi\)
\(468\) −2.48617e50 1.36166e50i −0.457993 0.250841i
\(469\) −5.84076e50 −1.03320
\(470\) 1.45660e51i 2.47447i
\(471\) 9.67284e49 3.77973e50i 0.157818 0.616686i
\(472\) 9.32101e49 0.146071
\(473\) 5.35253e50i 0.805745i
\(474\) 1.15151e51 + 2.94688e50i 1.66526 + 0.426161i
\(475\) 8.10356e50 1.12589
\(476\) 3.42373e50i 0.457054i
\(477\) −2.65949e50 + 4.85577e50i −0.341153 + 0.622887i
\(478\) 8.52485e49 0.105089
\(479\) 2.65576e50i 0.314640i −0.987548 0.157320i \(-0.949715\pi\)
0.987548 0.157320i \(-0.0502854\pi\)
\(480\) −3.25804e50 + 1.27310e51i −0.370999 + 1.44971i
\(481\) 1.53702e50 0.168238
\(482\) 1.46420e51i 1.54066i
\(483\) −4.57738e50 1.17141e50i −0.463044 0.118499i
\(484\) 8.19961e49 0.0797501
\(485\) 2.52909e51i 2.36522i
\(486\) 4.24590e50 + 1.28938e51i 0.381840 + 1.15956i
\(487\) −1.00479e51 −0.869014 −0.434507 0.900669i \(-0.643077\pi\)
−0.434507 + 0.900669i \(0.643077\pi\)
\(488\) 5.05781e50i 0.420713i
\(489\) 2.57592e50 1.00656e51i 0.206094 0.805325i
\(490\) −8.00159e50 −0.615816
\(491\) 2.22260e51i 1.64556i 0.568362 + 0.822779i \(0.307577\pi\)
−0.568362 + 0.822779i \(0.692423\pi\)
\(492\) −5.43014e50 1.38965e50i −0.386789 0.0989845i
\(493\) 1.69248e51 1.15993
\(494\) 1.27433e51i 0.840369i
\(495\) 2.46753e51 + 1.35146e51i 1.56590 + 0.857637i
\(496\) −2.39934e51 −1.46535
\(497\) 1.87648e51i 1.10299i
\(498\) 4.84004e50 1.89128e51i 0.273837 1.07004i
\(499\) 2.09860e50 0.114293 0.0571465 0.998366i \(-0.481800\pi\)
0.0571465 + 0.998366i \(0.481800\pi\)
\(500\) 1.14867e51i 0.602232i
\(501\) −2.19489e51 5.61701e50i −1.10789 0.283523i
\(502\) −2.06181e51 −1.00202
\(503\) 1.59022e51i 0.744157i 0.928201 + 0.372078i \(0.121355\pi\)
−0.928201 + 0.372078i \(0.878645\pi\)
\(504\) 5.53038e50 1.00975e51i 0.249215 0.455025i
\(505\) 1.85377e51 0.804486
\(506\) 1.80519e51i 0.754505i
\(507\) 8.24928e49 3.22347e50i 0.0332097 0.129769i
\(508\) −9.37393e50 −0.363506
\(509\) 4.63601e51i 1.73183i −0.500188 0.865917i \(-0.666736\pi\)
0.500188 0.865917i \(-0.333264\pi\)
\(510\) 6.08206e51 + 1.55648e51i 2.18886 + 0.560158i
\(511\) −1.71462e51 −0.594524
\(512\) 1.05347e51i 0.351961i
\(513\) 1.37107e51 1.46700e51i 0.441396 0.472280i
\(514\) 2.13824e51 0.663371
\(515\) 5.66054e51i 1.69247i
\(516\) 3.15259e50 1.23190e51i 0.0908497 0.355002i
\(517\) −4.75188e51 −1.31991
\(518\) 6.00680e50i 0.160834i
\(519\) −7.22315e51 1.84850e51i −1.86443 0.477133i
\(520\) −4.40827e51 −1.09700
\(521\) 3.58692e51i 0.860606i 0.902684 + 0.430303i \(0.141593\pi\)
−0.902684 + 0.430303i \(0.858407\pi\)
\(522\) −4.80307e51 2.63062e51i −1.11117 0.608582i
\(523\) 8.65118e51 1.92994 0.964969 0.262365i \(-0.0845024\pi\)
0.964969 + 0.262365i \(0.0845024\pi\)
\(524\) 3.01595e51i 0.648829i
\(525\) −1.73548e51 + 6.78152e51i −0.360076 + 1.40702i
\(526\) 2.67484e51 0.535264
\(527\) 6.78890e51i 1.31038i
\(528\) 7.01243e51 + 1.79457e51i 1.30564 + 0.334131i
\(529\) 3.73834e51 0.671461
\(530\) 8.28466e51i 1.43560i
\(531\) −6.74583e50 + 1.23167e51i −0.112782 + 0.205921i
\(532\) 1.63862e51 0.264337
\(533\) 5.56974e51i 0.866997i
\(534\) −7.18178e50 + 2.80633e51i −0.107882 + 0.421556i
\(535\) 3.52582e51 0.511138
\(536\) 5.50949e51i 0.770869i
\(537\) 1.30377e51 + 3.33651e50i 0.176071 + 0.0450589i
\(538\) 2.76675e51 0.360668
\(539\) 2.61036e51i 0.328484i
\(540\) −4.88308e51 4.56376e51i −0.593216 0.554423i
\(541\) −8.93589e51 −1.04807 −0.524034 0.851697i \(-0.675574\pi\)
−0.524034 + 0.851697i \(0.675574\pi\)
\(542\) 7.53086e51i 0.852821i
\(543\) −3.13501e51 + 1.22503e52i −0.342801 + 1.33952i
\(544\) 9.56665e51 1.01014
\(545\) 2.99558e52i 3.05455i
\(546\) −1.06643e52 2.72915e51i −1.05020 0.268761i
\(547\) 4.41976e51 0.420378 0.210189 0.977661i \(-0.432592\pi\)
0.210189 + 0.977661i \(0.432592\pi\)
\(548\) 2.66043e51i 0.244411i
\(549\) −6.68337e51 3.66046e51i −0.593091 0.324834i
\(550\) −2.67443e52 −2.29267
\(551\) 8.10035e51i 0.670847i
\(552\) 1.10497e51 4.31777e51i 0.0884117 0.345475i
\(553\) 1.51876e52 1.17412
\(554\) 9.48882e51i 0.708805i
\(555\) 3.51097e51 + 8.98505e50i 0.253432 + 0.0648565i
\(556\) −4.57027e51 −0.318802
\(557\) 1.02056e52i 0.688005i 0.938969 + 0.344003i \(0.111783\pi\)
−0.938969 + 0.344003i \(0.888217\pi\)
\(558\) 1.05520e52 1.92661e52i 0.687517 1.25529i
\(559\) 1.26357e52 0.795745
\(560\) 2.83507e52i 1.72580i
\(561\) 5.07772e51 1.98415e52i 0.298796 1.16757i
\(562\) −8.36967e50 −0.0476122
\(563\) 2.11318e52i 1.16219i −0.813837 0.581094i \(-0.802625\pi\)
0.813837 0.581094i \(-0.197375\pi\)
\(564\) 1.09366e52 + 2.79881e51i 0.581538 + 0.148823i
\(565\) 9.15834e51 0.470865
\(566\) 1.67394e52i 0.832200i
\(567\) 9.34036e51 + 1.46156e52i 0.449040 + 0.702651i
\(568\) 1.77005e52 0.822937
\(569\) 9.67361e51i 0.434966i 0.976064 + 0.217483i \(0.0697847\pi\)
−0.976064 + 0.217483i \(0.930215\pi\)
\(570\) −7.44943e51 + 2.91092e52i −0.323967 + 1.26592i
\(571\) −3.71935e52 −1.56452 −0.782260 0.622952i \(-0.785933\pi\)
−0.782260 + 0.622952i \(0.785933\pi\)
\(572\) 1.38379e52i 0.563050i
\(573\) −1.31205e52 3.35772e51i −0.516432 0.132162i
\(574\) −2.17670e52 −0.828842
\(575\) 2.70991e52i 0.998310i
\(576\) 3.60760e51 + 1.97587e51i 0.128585 + 0.0704257i
\(577\) −4.10688e52 −1.41635 −0.708177 0.706035i \(-0.750482\pi\)
−0.708177 + 0.706035i \(0.750482\pi\)
\(578\) 9.12048e51i 0.304361i
\(579\) −3.99244e51 + 1.56007e52i −0.128927 + 0.503793i
\(580\) 2.69630e52 0.842629
\(581\) 2.49445e52i 0.754448i
\(582\) 5.77126e52 + 1.47694e52i 1.68941 + 0.432342i
\(583\) −2.70271e52 −0.765767
\(584\) 1.61737e52i 0.443572i
\(585\) 3.19037e52 5.82507e52i 0.846993 1.54646i
\(586\) 1.15621e52 0.297155
\(587\) 6.81962e52i 1.69682i −0.529338 0.848411i \(-0.677560\pi\)
0.529338 0.848411i \(-0.322440\pi\)
\(588\) 1.53748e51 6.00781e51i 0.0370374 0.144726i
\(589\) −3.24921e52 −0.757858
\(590\) 2.10142e52i 0.474596i
\(591\) −1.51213e52 3.86974e51i −0.330694 0.0846291i
\(592\) 9.32430e51 0.197471
\(593\) 8.57574e52i 1.75886i 0.476025 + 0.879432i \(0.342077\pi\)
−0.476025 + 0.879432i \(0.657923\pi\)
\(594\) −4.52496e52 + 4.84156e52i −0.898819 + 0.961708i
\(595\) 8.02178e52 1.54329
\(596\) 4.22824e52i 0.787918i
\(597\) 2.56176e51 1.00103e52i 0.0462409 0.180690i
\(598\) −4.26149e52 −0.745141
\(599\) 8.74442e51i 0.148123i −0.997254 0.0740613i \(-0.976404\pi\)
0.997254 0.0740613i \(-0.0235960\pi\)
\(600\) −6.39689e52 1.63705e52i −1.04977 0.268651i
\(601\) 4.20628e52 0.668780 0.334390 0.942435i \(-0.391470\pi\)
0.334390 + 0.942435i \(0.391470\pi\)
\(602\) 4.93812e52i 0.760726i
\(603\) 7.28022e52 + 3.98735e52i 1.08671 + 0.595189i
\(604\) −3.36026e52 −0.486039
\(605\) 1.92116e52i 0.269285i
\(606\) −1.08257e52 + 4.23021e52i −0.147053 + 0.574622i
\(607\) −1.96991e52 −0.259335 −0.129667 0.991558i \(-0.541391\pi\)
−0.129667 + 0.991558i \(0.541391\pi\)
\(608\) 4.57866e52i 0.584212i
\(609\) −6.77884e52 1.73479e52i −0.838352 0.214546i
\(610\) 1.14028e53 1.36693
\(611\) 1.12177e53i 1.30353i
\(612\) −2.33730e52 + 4.26750e52i −0.263292 + 0.480725i
\(613\) −8.00587e52 −0.874298 −0.437149 0.899389i \(-0.644012\pi\)
−0.437149 + 0.899389i \(0.644012\pi\)
\(614\) 1.35285e52i 0.143236i
\(615\) 3.25593e52 1.27228e53i 0.334232 1.30604i
\(616\) 5.62026e52 0.559400
\(617\) 9.48033e52i 0.914966i 0.889218 + 0.457483i \(0.151249\pi\)
−0.889218 + 0.457483i \(0.848751\pi\)
\(618\) −1.29171e53 3.30566e52i −1.20888 0.309369i
\(619\) 6.24570e52 0.566838 0.283419 0.958996i \(-0.408531\pi\)
0.283419 + 0.958996i \(0.408531\pi\)
\(620\) 1.08154e53i 0.951920i
\(621\) 4.90578e52 + 4.58498e52i 0.418762 + 0.391378i
\(622\) 1.21641e53 1.00708
\(623\) 3.70134e52i 0.297225i
\(624\) 4.23643e52 1.65542e53i 0.329984 1.28944i
\(625\) 3.86203e52 0.291807
\(626\) 2.79577e53i 2.04923i
\(627\) 9.49630e52 + 2.43023e52i 0.675260 + 0.172808i
\(628\) −4.52481e52 −0.312153
\(629\) 2.63830e52i 0.176588i
\(630\) −2.27648e53 1.24682e53i −1.47841 0.809718i
\(631\) −1.78963e53 −1.12773 −0.563866 0.825867i \(-0.690686\pi\)
−0.563866 + 0.825867i \(0.690686\pi\)
\(632\) 1.43262e53i 0.876005i
\(633\) −3.60686e52 + 1.40941e53i −0.214022 + 0.836308i
\(634\) 1.80888e53 1.04163
\(635\) 2.19631e53i 1.22742i
\(636\) 6.22035e52 + 1.59187e52i 0.337388 + 0.0863421i
\(637\) 6.16226e52 0.324407
\(638\) 2.67337e53i 1.36605i
\(639\) −1.28103e53 + 2.33893e53i −0.635392 + 1.16012i
\(640\) −3.72346e53 −1.79278
\(641\) 2.19558e53i 1.02624i −0.858318 0.513118i \(-0.828490\pi\)
0.858318 0.513118i \(-0.171510\pi\)
\(642\) −2.05902e52 + 8.04576e52i −0.0934318 + 0.365091i
\(643\) −3.76988e52 −0.166081 −0.0830403 0.996546i \(-0.526463\pi\)
−0.0830403 + 0.996546i \(0.526463\pi\)
\(644\) 5.47970e52i 0.234383i
\(645\) 2.88633e53 + 7.38651e52i 1.19870 + 0.306764i
\(646\) 2.18739e53 0.882081
\(647\) 2.71575e52i 0.106343i 0.998585 + 0.0531715i \(0.0169330\pi\)
−0.998585 + 0.0531715i \(0.983067\pi\)
\(648\) −1.37867e53 + 8.81060e52i −0.524245 + 0.335027i
\(649\) −6.85547e52 −0.253156
\(650\) 6.31351e53i 2.26421i
\(651\) 6.95861e52 2.71913e53i 0.242373 0.947089i
\(652\) −1.20498e53 −0.407638
\(653\) 1.97468e52i 0.0648852i −0.999474 0.0324426i \(-0.989671\pi\)
0.999474 0.0324426i \(-0.0103286\pi\)
\(654\) 6.83578e53 + 1.74937e53i 2.18178 + 0.558346i
\(655\) −7.06636e53 −2.19084
\(656\) 3.37887e53i 1.01765i
\(657\) 2.13718e53 + 1.17053e53i 0.625316 + 0.342483i
\(658\) 4.38397e53 1.24616
\(659\) 6.36429e51i 0.0175763i −0.999961 0.00878814i \(-0.997203\pi\)
0.999961 0.00878814i \(-0.00279739\pi\)
\(660\) 8.08932e52 3.16096e53i 0.217059 0.848172i
\(661\) 6.25141e53 1.62986 0.814930 0.579560i \(-0.196775\pi\)
0.814930 + 0.579560i \(0.196775\pi\)
\(662\) 5.29052e53i 1.34028i
\(663\) −4.68397e53 1.19869e53i −1.15307 0.295087i
\(664\) 2.35297e53 0.562890
\(665\) 3.83928e53i 0.892562i
\(666\) −4.10069e52 + 7.48717e52i −0.0926503 + 0.169164i
\(667\) −2.70883e53 −0.594828
\(668\) 2.62756e53i 0.560789i
\(669\) −1.92062e52 + 7.50495e52i −0.0398423 + 0.155687i
\(670\) −1.24211e54 −2.50461
\(671\) 3.71995e53i 0.729137i
\(672\) −3.83169e53 9.80580e52i −0.730086 0.186839i
\(673\) −8.96991e53 −1.66151 −0.830753 0.556641i \(-0.812090\pi\)
−0.830753 + 0.556641i \(0.812090\pi\)
\(674\) 6.84854e53i 1.23327i
\(675\) 6.79277e53 7.26805e53i 1.18926 1.27247i
\(676\) −3.85889e52 −0.0656864
\(677\) 2.57942e53i 0.426911i −0.976953 0.213455i \(-0.931528\pi\)
0.976953 0.213455i \(-0.0684718\pi\)
\(678\) −5.34831e52 + 2.08989e53i −0.0860701 + 0.336325i
\(679\) 7.61185e53 1.19114
\(680\) 7.56680e53i 1.15144i
\(681\) 7.94305e52 + 2.03273e52i 0.117542 + 0.0300805i
\(682\) 1.07234e54 1.54323
\(683\) 7.21883e53i 1.01035i −0.863016 0.505177i \(-0.831427\pi\)
0.863016 0.505177i \(-0.168573\pi\)
\(684\) −2.04246e53 1.11865e53i −0.278027 0.152274i
\(685\) 6.23336e53 0.825280
\(686\) 1.03134e54i 1.32814i
\(687\) −2.77480e52 + 1.08427e53i −0.0347579 + 0.135819i
\(688\) 7.66540e53 0.934017
\(689\) 6.38026e53i 0.756263i
\(690\) −9.73439e53 2.49116e53i −1.12247 0.287256i
\(691\) 6.84772e53 0.768181 0.384090 0.923296i \(-0.374515\pi\)
0.384090 + 0.923296i \(0.374515\pi\)
\(692\) 8.64702e53i 0.943736i
\(693\) −4.06751e53 + 7.42658e53i −0.431914 + 0.788601i
\(694\) −1.47728e54 −1.52627
\(695\) 1.07081e54i 1.07647i
\(696\) 1.63640e53 6.39436e53i 0.160072 0.625491i
\(697\) −9.56046e53 −0.910030
\(698\) 1.65302e54i 1.53117i
\(699\) −4.96940e53 1.27174e53i −0.447959 0.114639i
\(700\) 8.11834e53 0.712204
\(701\) 6.20423e53i 0.529719i 0.964287 + 0.264860i \(0.0853256\pi\)
−0.964287 + 0.264860i \(0.914674\pi\)
\(702\) 1.14294e54 + 1.06820e54i 0.949772 + 0.887663i
\(703\) 1.26271e53 0.102130
\(704\) 2.00798e53i 0.158081i
\(705\) −6.55760e53 + 2.56243e54i −0.502518 + 1.96363i
\(706\) −4.66842e53 −0.348242
\(707\) 5.57932e53i 0.405147i
\(708\) 1.57780e53 + 4.03781e52i 0.111537 + 0.0285439i
\(709\) 1.50676e54 1.03697 0.518485 0.855087i \(-0.326496\pi\)
0.518485 + 0.855087i \(0.326496\pi\)
\(710\) 3.99057e54i 2.67378i
\(711\) −1.89306e54 1.03682e54i −1.23493 0.676365i
\(712\) −3.49141e53 −0.221759
\(713\) 1.08657e54i 0.671979i
\(714\) −4.68458e53 + 1.83053e54i −0.282101 + 1.10233i
\(715\) 3.24222e54 1.90120
\(716\) 1.56077e53i 0.0891234i
\(717\) −1.49968e53 3.83788e52i −0.0833939 0.0213416i
\(718\) −1.50788e53 −0.0816584
\(719\) 2.78504e54i 1.46887i 0.678681 + 0.734434i \(0.262552\pi\)
−0.678681 + 0.734434i \(0.737448\pi\)
\(720\) 1.93543e54 3.53377e54i 0.994169 1.81518i
\(721\) −1.70367e54 −0.852343
\(722\) 1.45837e54i 0.710659i
\(723\) 6.59181e53 2.57580e54i 0.312880 1.22260i
\(724\) 1.46651e54 0.678036
\(725\) 4.01321e54i 1.80747i
\(726\) −4.38401e53 1.12193e53i −0.192343 0.0492231i
\(727\) −1.29791e54 −0.554743 −0.277371 0.960763i \(-0.589463\pi\)
−0.277371 + 0.960763i \(0.589463\pi\)
\(728\) 1.32677e54i 0.552458i
\(729\) −1.66455e53 2.45941e54i −0.0675263 0.997717i
\(730\) −3.64635e54 −1.44120
\(731\) 2.16891e54i 0.835242i
\(732\) −2.19101e53 + 8.56155e53i −0.0822119 + 0.321249i
\(733\) −3.00923e54 −1.10022 −0.550111 0.835092i \(-0.685415\pi\)
−0.550111 + 0.835092i \(0.685415\pi\)
\(734\) 8.62100e53i 0.307137i
\(735\) 1.40763e54 + 3.60230e53i 0.488684 + 0.125061i
\(736\) −1.53115e54 −0.518011
\(737\) 4.05215e54i 1.33599i
\(738\) 2.71314e54 + 1.48598e54i 0.871769 + 0.477465i
\(739\) −3.54901e54 −1.11138 −0.555690 0.831389i \(-0.687546\pi\)
−0.555690 + 0.831389i \(0.687546\pi\)
\(740\) 4.20307e53i 0.128282i
\(741\) 5.73702e53 2.24178e54i 0.170663 0.666880i
\(742\) 2.49345e54 0.722982
\(743\) 7.43135e53i 0.210030i 0.994471 + 0.105015i \(0.0334890\pi\)
−0.994471 + 0.105015i \(0.966511\pi\)
\(744\) 2.56491e54 + 6.56394e53i 0.706620 + 0.180833i
\(745\) 9.90675e54 2.66049
\(746\) 6.02837e54i 1.57820i
\(747\) −1.70290e54 + 3.10921e54i −0.434609 + 0.793521i
\(748\) −2.37528e54 −0.590996
\(749\) 1.06117e54i 0.257414i
\(750\) −1.57168e54 + 6.14146e54i −0.371707 + 1.45247i
\(751\) −5.13765e54 −1.18469 −0.592346 0.805684i \(-0.701798\pi\)
−0.592346 + 0.805684i \(0.701798\pi\)
\(752\) 6.80520e54i 1.53004i
\(753\) 3.62711e54 + 9.28225e53i 0.795162 + 0.203493i
\(754\) −6.31101e54 −1.34910
\(755\) 7.87307e54i 1.64116i
\(756\) 1.37357e54 1.46967e54i 0.279213 0.298749i
\(757\) 8.88483e54 1.76128 0.880638 0.473789i \(-0.157114\pi\)
0.880638 + 0.473789i \(0.157114\pi\)
\(758\)