Properties

Label 1.104.a.a.1.5
Level 1
Weight 104
Character 1.1
Self dual Yes
Analytic conductor 67.184
Analytic rank 0
Dimension 8
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 104 \)
Character orbit: \([\chi]\) = 1.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(67.1843880807\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: multiple of \( 2^{104}\cdot 3^{40}\cdot 5^{12}\cdot 7^{8}\cdot 11\cdot 13^{3}\cdot 17^{2} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-6.19123e13\)
Character \(\chi\) = 1.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.03451e15 q^{2}\) \(+2.78778e24 q^{3}\) \(-6.00197e30 q^{4}\) \(+1.50905e36 q^{5}\) \(+5.67177e39 q^{6}\) \(+3.17629e43 q^{7}\) \(-3.28435e46 q^{8}\) \(-6.14348e48 q^{9}\) \(+O(q^{10})\) \(q\)\(+2.03451e15 q^{2}\) \(+2.78778e24 q^{3}\) \(-6.00197e30 q^{4}\) \(+1.50905e36 q^{5}\) \(+5.67177e39 q^{6}\) \(+3.17629e43 q^{7}\) \(-3.28435e46 q^{8}\) \(-6.14348e48 q^{9}\) \(+3.07017e51 q^{10}\) \(+4.12444e53 q^{11}\) \(-1.67322e55 q^{12}\) \(+3.42350e57 q^{13}\) \(+6.46220e58 q^{14}\) \(+4.20689e60 q^{15}\) \(-5.95320e60 q^{16}\) \(-4.21437e63 q^{17}\) \(-1.24990e64 q^{18}\) \(+6.28958e65 q^{19}\) \(-9.05726e66 q^{20}\) \(+8.85480e67 q^{21}\) \(+8.39123e68 q^{22}\) \(+1.29915e70 q^{23}\) \(-9.15603e70 q^{24}\) \(+1.29115e72 q^{25}\) \(+6.96516e72 q^{26}\) \(-5.59192e73 q^{27}\) \(-1.90640e74 q^{28}\) \(-2.77281e74 q^{29}\) \(+8.55897e75 q^{30}\) \(-2.34128e76 q^{31}\) \(+3.20960e77 q^{32}\) \(+1.14980e78 q^{33}\) \(-8.57417e78 q^{34}\) \(+4.79318e79 q^{35}\) \(+3.68730e79 q^{36}\) \(+3.44427e80 q^{37}\) \(+1.27962e81 q^{38}\) \(+9.54397e81 q^{39}\) \(-4.95623e82 q^{40}\) \(-6.63673e82 q^{41}\) \(+1.80152e83 q^{42}\) \(+1.02778e83 q^{43}\) \(-2.47548e84 q^{44}\) \(-9.27080e84 q^{45}\) \(+2.64313e85 q^{46}\) \(+1.11862e86 q^{47}\) \(-1.65962e85 q^{48}\) \(-1.00542e86 q^{49}\) \(+2.62685e87 q^{50}\) \(-1.17487e88 q^{51}\) \(-2.05478e88 q^{52}\) \(+7.07897e88 q^{53}\) \(-1.13768e89 q^{54}\) \(+6.22398e89 q^{55}\) \(-1.04320e90 q^{56}\) \(+1.75340e90 q^{57}\) \(-5.64131e89 q^{58}\) \(+2.61973e90 q^{59}\) \(-2.52496e91 q^{60}\) \(+7.62186e91 q^{61}\) \(-4.76335e91 q^{62}\) \(-1.95135e92 q^{63}\) \(+7.13370e92 q^{64}\) \(+5.16623e93 q^{65}\) \(+2.33929e93 q^{66}\) \(-1.52821e94 q^{67}\) \(+2.52945e94 q^{68}\) \(+3.62174e94 q^{69}\) \(+9.75177e94 q^{70}\) \(+2.72549e95 q^{71}\) \(+2.01773e95 q^{72}\) \(+1.73850e96 q^{73}\) \(+7.00741e95 q^{74}\) \(+3.59943e96 q^{75}\) \(-3.77499e96 q^{76}\) \(+1.31004e97 q^{77}\) \(+1.94173e97 q^{78}\) \(-1.50166e97 q^{79}\) \(-8.98366e96 q^{80}\) \(-7.04026e97 q^{81}\) \(-1.35025e98 q^{82}\) \(+6.73470e97 q^{83}\) \(-5.31463e98 q^{84}\) \(-6.35968e99 q^{85}\) \(+2.09104e98 q^{86}\) \(-7.72998e98 q^{87}\) \(-1.35461e100 q^{88}\) \(+2.96941e100 q^{89}\) \(-1.88615e100 q^{90}\) \(+1.08740e101 q^{91}\) \(-7.79745e100 q^{92}\) \(-6.52696e100 q^{93}\) \(+2.27584e101 q^{94}\) \(+9.49127e101 q^{95}\) \(+8.94767e101 q^{96}\) \(+1.14220e102 q^{97}\) \(-2.04554e101 q^{98}\) \(-2.53384e102 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(8q \) \(\mathstrut +\mathstrut 4388929556680440q^{2} \) \(\mathstrut +\mathstrut \)\(50\!\cdots\!40\)\(q^{3} \) \(\mathstrut +\mathstrut \)\(48\!\cdots\!64\)\(q^{4} \) \(\mathstrut +\mathstrut \)\(55\!\cdots\!20\)\(q^{5} \) \(\mathstrut +\mathstrut \)\(26\!\cdots\!36\)\(q^{6} \) \(\mathstrut +\mathstrut \)\(41\!\cdots\!00\)\(q^{7} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!80\)\(q^{8} \) \(\mathstrut +\mathstrut \)\(35\!\cdots\!16\)\(q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 4388929556680440q^{2} \) \(\mathstrut +\mathstrut \)\(50\!\cdots\!40\)\(q^{3} \) \(\mathstrut +\mathstrut \)\(48\!\cdots\!64\)\(q^{4} \) \(\mathstrut +\mathstrut \)\(55\!\cdots\!20\)\(q^{5} \) \(\mathstrut +\mathstrut \)\(26\!\cdots\!36\)\(q^{6} \) \(\mathstrut +\mathstrut \)\(41\!\cdots\!00\)\(q^{7} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!80\)\(q^{8} \) \(\mathstrut +\mathstrut \)\(35\!\cdots\!16\)\(q^{9} \) \(\mathstrut +\mathstrut \)\(20\!\cdots\!20\)\(q^{10} \) \(\mathstrut -\mathstrut \)\(53\!\cdots\!44\)\(q^{11} \) \(\mathstrut +\mathstrut \)\(25\!\cdots\!80\)\(q^{12} \) \(\mathstrut -\mathstrut \)\(15\!\cdots\!20\)\(q^{13} \) \(\mathstrut +\mathstrut \)\(20\!\cdots\!08\)\(q^{14} \) \(\mathstrut -\mathstrut \)\(30\!\cdots\!60\)\(q^{15} \) \(\mathstrut +\mathstrut \)\(36\!\cdots\!88\)\(q^{16} \) \(\mathstrut +\mathstrut \)\(20\!\cdots\!20\)\(q^{17} \) \(\mathstrut +\mathstrut \)\(26\!\cdots\!40\)\(q^{18} \) \(\mathstrut +\mathstrut \)\(14\!\cdots\!00\)\(q^{19} \) \(\mathstrut +\mathstrut \)\(25\!\cdots\!60\)\(q^{20} \) \(\mathstrut -\mathstrut \)\(46\!\cdots\!04\)\(q^{21} \) \(\mathstrut -\mathstrut \)\(13\!\cdots\!20\)\(q^{22} \) \(\mathstrut +\mathstrut \)\(40\!\cdots\!20\)\(q^{23} \) \(\mathstrut +\mathstrut \)\(41\!\cdots\!00\)\(q^{24} \) \(\mathstrut -\mathstrut \)\(36\!\cdots\!00\)\(q^{25} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!84\)\(q^{26} \) \(\mathstrut +\mathstrut \)\(63\!\cdots\!20\)\(q^{27} \) \(\mathstrut +\mathstrut \)\(51\!\cdots\!80\)\(q^{28} \) \(\mathstrut -\mathstrut \)\(11\!\cdots\!00\)\(q^{29} \) \(\mathstrut -\mathstrut \)\(31\!\cdots\!60\)\(q^{30} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!36\)\(q^{31} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!40\)\(q^{32} \) \(\mathstrut +\mathstrut \)\(16\!\cdots\!80\)\(q^{33} \) \(\mathstrut -\mathstrut \)\(16\!\cdots\!32\)\(q^{34} \) \(\mathstrut -\mathstrut \)\(15\!\cdots\!80\)\(q^{35} \) \(\mathstrut +\mathstrut \)\(80\!\cdots\!28\)\(q^{36} \) \(\mathstrut -\mathstrut \)\(92\!\cdots\!40\)\(q^{37} \) \(\mathstrut +\mathstrut \)\(19\!\cdots\!20\)\(q^{38} \) \(\mathstrut -\mathstrut \)\(78\!\cdots\!08\)\(q^{39} \) \(\mathstrut +\mathstrut \)\(19\!\cdots\!00\)\(q^{40} \) \(\mathstrut +\mathstrut \)\(22\!\cdots\!76\)\(q^{41} \) \(\mathstrut -\mathstrut \)\(18\!\cdots\!80\)\(q^{42} \) \(\mathstrut +\mathstrut \)\(96\!\cdots\!00\)\(q^{43} \) \(\mathstrut +\mathstrut \)\(26\!\cdots\!48\)\(q^{44} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!60\)\(q^{45} \) \(\mathstrut +\mathstrut \)\(27\!\cdots\!96\)\(q^{46} \) \(\mathstrut -\mathstrut \)\(29\!\cdots\!20\)\(q^{47} \) \(\mathstrut +\mathstrut \)\(12\!\cdots\!20\)\(q^{48} \) \(\mathstrut +\mathstrut \)\(26\!\cdots\!44\)\(q^{49} \) \(\mathstrut -\mathstrut \)\(65\!\cdots\!00\)\(q^{50} \) \(\mathstrut -\mathstrut \)\(20\!\cdots\!84\)\(q^{51} \) \(\mathstrut -\mathstrut \)\(36\!\cdots\!00\)\(q^{52} \) \(\mathstrut +\mathstrut \)\(16\!\cdots\!40\)\(q^{53} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!00\)\(q^{54} \) \(\mathstrut -\mathstrut \)\(60\!\cdots\!60\)\(q^{55} \) \(\mathstrut -\mathstrut \)\(50\!\cdots\!00\)\(q^{56} \) \(\mathstrut +\mathstrut \)\(55\!\cdots\!40\)\(q^{57} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!80\)\(q^{58} \) \(\mathstrut -\mathstrut \)\(37\!\cdots\!00\)\(q^{59} \) \(\mathstrut -\mathstrut \)\(44\!\cdots\!80\)\(q^{60} \) \(\mathstrut +\mathstrut \)\(56\!\cdots\!56\)\(q^{61} \) \(\mathstrut +\mathstrut \)\(70\!\cdots\!80\)\(q^{62} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!60\)\(q^{63} \) \(\mathstrut +\mathstrut \)\(26\!\cdots\!04\)\(q^{64} \) \(\mathstrut +\mathstrut \)\(51\!\cdots\!40\)\(q^{65} \) \(\mathstrut +\mathstrut \)\(36\!\cdots\!52\)\(q^{66} \) \(\mathstrut +\mathstrut \)\(36\!\cdots\!20\)\(q^{67} \) \(\mathstrut +\mathstrut \)\(12\!\cdots\!40\)\(q^{68} \) \(\mathstrut +\mathstrut \)\(14\!\cdots\!52\)\(q^{69} \) \(\mathstrut +\mathstrut \)\(85\!\cdots\!20\)\(q^{70} \) \(\mathstrut +\mathstrut \)\(13\!\cdots\!96\)\(q^{71} \) \(\mathstrut +\mathstrut \)\(56\!\cdots\!60\)\(q^{72} \) \(\mathstrut +\mathstrut \)\(44\!\cdots\!20\)\(q^{73} \) \(\mathstrut +\mathstrut \)\(94\!\cdots\!88\)\(q^{74} \) \(\mathstrut +\mathstrut \)\(15\!\cdots\!00\)\(q^{75} \) \(\mathstrut +\mathstrut \)\(62\!\cdots\!00\)\(q^{76} \) \(\mathstrut +\mathstrut \)\(37\!\cdots\!00\)\(q^{77} \) \(\mathstrut +\mathstrut \)\(44\!\cdots\!00\)\(q^{78} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!00\)\(q^{79} \) \(\mathstrut -\mathstrut \)\(25\!\cdots\!80\)\(q^{80} \) \(\mathstrut -\mathstrut \)\(31\!\cdots\!32\)\(q^{81} \) \(\mathstrut -\mathstrut \)\(34\!\cdots\!20\)\(q^{82} \) \(\mathstrut -\mathstrut \)\(25\!\cdots\!40\)\(q^{83} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!32\)\(q^{84} \) \(\mathstrut -\mathstrut \)\(77\!\cdots\!80\)\(q^{85} \) \(\mathstrut -\mathstrut \)\(22\!\cdots\!44\)\(q^{86} \) \(\mathstrut -\mathstrut \)\(19\!\cdots\!40\)\(q^{87} \) \(\mathstrut -\mathstrut \)\(40\!\cdots\!40\)\(q^{88} \) \(\mathstrut -\mathstrut \)\(24\!\cdots\!00\)\(q^{89} \) \(\mathstrut +\mathstrut \)\(19\!\cdots\!40\)\(q^{90} \) \(\mathstrut +\mathstrut \)\(15\!\cdots\!76\)\(q^{91} \) \(\mathstrut +\mathstrut \)\(77\!\cdots\!20\)\(q^{92} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!80\)\(q^{93} \) \(\mathstrut +\mathstrut \)\(72\!\cdots\!48\)\(q^{94} \) \(\mathstrut +\mathstrut \)\(27\!\cdots\!00\)\(q^{95} \) \(\mathstrut +\mathstrut \)\(88\!\cdots\!96\)\(q^{96} \) \(\mathstrut +\mathstrut \)\(50\!\cdots\!80\)\(q^{97} \) \(\mathstrut +\mathstrut \)\(88\!\cdots\!20\)\(q^{98} \) \(\mathstrut -\mathstrut \)\(72\!\cdots\!88\)\(q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.03451e15 0.638874 0.319437 0.947607i \(-0.396506\pi\)
0.319437 + 0.947607i \(0.396506\pi\)
\(3\) 2.78778e24 0.747332 0.373666 0.927563i \(-0.378101\pi\)
0.373666 + 0.927563i \(0.378101\pi\)
\(4\) −6.00197e30 −0.591840
\(5\) 1.50905e36 1.51966 0.759832 0.650119i \(-0.225281\pi\)
0.759832 + 0.650119i \(0.225281\pi\)
\(6\) 5.67177e39 0.477451
\(7\) 3.17629e43 0.953611 0.476806 0.879009i \(-0.341795\pi\)
0.476806 + 0.879009i \(0.341795\pi\)
\(8\) −3.28435e46 −1.01699
\(9\) −6.14348e48 −0.441494
\(10\) 3.07017e51 0.970874
\(11\) 4.12444e53 0.963035 0.481518 0.876436i \(-0.340086\pi\)
0.481518 + 0.876436i \(0.340086\pi\)
\(12\) −1.67322e55 −0.442301
\(13\) 3.42350e57 1.46686 0.733429 0.679766i \(-0.237919\pi\)
0.733429 + 0.679766i \(0.237919\pi\)
\(14\) 6.46220e58 0.609238
\(15\) 4.20689e60 1.13569
\(16\) −5.95320e60 −0.0578857
\(17\) −4.21437e63 −1.80556 −0.902782 0.430099i \(-0.858479\pi\)
−0.902782 + 0.430099i \(0.858479\pi\)
\(18\) −1.24990e64 −0.282059
\(19\) 6.28958e65 0.876620 0.438310 0.898824i \(-0.355577\pi\)
0.438310 + 0.898824i \(0.355577\pi\)
\(20\) −9.05726e66 −0.899398
\(21\) 8.85480e67 0.712665
\(22\) 8.39123e68 0.615258
\(23\) 1.29915e70 0.965329 0.482665 0.875805i \(-0.339669\pi\)
0.482665 + 0.875805i \(0.339669\pi\)
\(24\) −9.15603e70 −0.760026
\(25\) 1.29115e72 1.30938
\(26\) 6.96516e72 0.937138
\(27\) −5.59192e73 −1.07728
\(28\) −1.90640e74 −0.564385
\(29\) −2.77281e74 −0.134717 −0.0673586 0.997729i \(-0.521457\pi\)
−0.0673586 + 0.997729i \(0.521457\pi\)
\(30\) 8.55897e75 0.725566
\(31\) −2.34128e76 −0.366712 −0.183356 0.983047i \(-0.558696\pi\)
−0.183356 + 0.983047i \(0.558696\pi\)
\(32\) 3.20960e77 0.980004
\(33\) 1.14980e78 0.719707
\(34\) −8.57417e78 −1.15353
\(35\) 4.79318e79 1.44917
\(36\) 3.68730e79 0.261294
\(37\) 3.44427e80 0.595263 0.297632 0.954681i \(-0.403803\pi\)
0.297632 + 0.954681i \(0.403803\pi\)
\(38\) 1.27962e81 0.560050
\(39\) 9.54397e81 1.09623
\(40\) −4.95623e82 −1.54548
\(41\) −6.63673e82 −0.580211 −0.290105 0.956995i \(-0.593690\pi\)
−0.290105 + 0.956995i \(0.593690\pi\)
\(42\) 1.80152e83 0.455303
\(43\) 1.02778e83 0.0773171 0.0386586 0.999252i \(-0.487692\pi\)
0.0386586 + 0.999252i \(0.487692\pi\)
\(44\) −2.47548e84 −0.569963
\(45\) −9.27080e84 −0.670923
\(46\) 2.64313e85 0.616724
\(47\) 1.11862e86 0.862268 0.431134 0.902288i \(-0.358114\pi\)
0.431134 + 0.902288i \(0.358114\pi\)
\(48\) −1.65962e85 −0.0432599
\(49\) −1.00542e86 −0.0906253
\(50\) 2.62685e87 0.836529
\(51\) −1.17487e88 −1.34936
\(52\) −2.05478e88 −0.868145
\(53\) 7.07897e88 1.12141 0.560703 0.828017i \(-0.310531\pi\)
0.560703 + 0.828017i \(0.310531\pi\)
\(54\) −1.13768e89 −0.688243
\(55\) 6.22398e89 1.46349
\(56\) −1.04320e90 −0.969809
\(57\) 1.75340e90 0.655126
\(58\) −5.64131e89 −0.0860674
\(59\) 2.61973e90 0.165721 0.0828605 0.996561i \(-0.473594\pi\)
0.0828605 + 0.996561i \(0.473594\pi\)
\(60\) −2.52496e91 −0.672149
\(61\) 7.62186e91 0.866113 0.433056 0.901367i \(-0.357435\pi\)
0.433056 + 0.901367i \(0.357435\pi\)
\(62\) −4.76335e91 −0.234283
\(63\) −1.95135e92 −0.421014
\(64\) 7.13370e92 0.683985
\(65\) 5.16623e93 2.22913
\(66\) 2.33929e93 0.459802
\(67\) −1.52821e94 −1.38462 −0.692308 0.721602i \(-0.743406\pi\)
−0.692308 + 0.721602i \(0.743406\pi\)
\(68\) 2.52945e94 1.06860
\(69\) 3.62174e94 0.721422
\(70\) 9.75177e94 0.925837
\(71\) 2.72549e95 1.24635 0.623174 0.782083i \(-0.285843\pi\)
0.623174 + 0.782083i \(0.285843\pi\)
\(72\) 2.01773e95 0.448993
\(73\) 1.73850e96 1.90129 0.950643 0.310288i \(-0.100426\pi\)
0.950643 + 0.310288i \(0.100426\pi\)
\(74\) 7.00741e95 0.380298
\(75\) 3.59943e96 0.978541
\(76\) −3.77499e96 −0.518818
\(77\) 1.31004e97 0.918361
\(78\) 1.94173e97 0.700353
\(79\) −1.50166e97 −0.281046 −0.140523 0.990077i \(-0.544878\pi\)
−0.140523 + 0.990077i \(0.544878\pi\)
\(80\) −8.98366e96 −0.0879668
\(81\) −7.04026e97 −0.363588
\(82\) −1.35025e98 −0.370682
\(83\) 6.73470e97 0.0990368 0.0495184 0.998773i \(-0.484231\pi\)
0.0495184 + 0.998773i \(0.484231\pi\)
\(84\) −5.31463e98 −0.421783
\(85\) −6.35968e99 −2.74385
\(86\) 2.09104e98 0.0493959
\(87\) −7.72998e98 −0.100679
\(88\) −1.35461e100 −0.979393
\(89\) 2.96941e100 1.19974 0.599868 0.800099i \(-0.295220\pi\)
0.599868 + 0.800099i \(0.295220\pi\)
\(90\) −1.88615e100 −0.428635
\(91\) 1.08740e101 1.39881
\(92\) −7.79745e100 −0.571320
\(93\) −6.52696e100 −0.274056
\(94\) 2.27584e101 0.550881
\(95\) 9.49127e101 1.33217
\(96\) 8.94767e101 0.732388
\(97\) 1.14220e102 0.548276 0.274138 0.961690i \(-0.411607\pi\)
0.274138 + 0.961690i \(0.411607\pi\)
\(98\) −2.04554e101 −0.0578982
\(99\) −2.53384e102 −0.425175
\(100\) −7.74943e102 −0.774943
\(101\) 1.55388e103 0.930823 0.465412 0.885094i \(-0.345906\pi\)
0.465412 + 0.885094i \(0.345906\pi\)
\(102\) −2.39029e103 −0.862069
\(103\) −6.75321e103 −1.47365 −0.736823 0.676085i \(-0.763675\pi\)
−0.736823 + 0.676085i \(0.763675\pi\)
\(104\) −1.12440e104 −1.49177
\(105\) 1.33623e104 1.08301
\(106\) 1.44022e104 0.716437
\(107\) −4.76008e104 −1.45999 −0.729994 0.683453i \(-0.760477\pi\)
−0.729994 + 0.683453i \(0.760477\pi\)
\(108\) 3.35625e104 0.637575
\(109\) 1.58870e104 0.187749 0.0938745 0.995584i \(-0.470075\pi\)
0.0938745 + 0.995584i \(0.470075\pi\)
\(110\) 1.26628e105 0.934986
\(111\) 9.60188e104 0.444859
\(112\) −1.89091e104 −0.0552005
\(113\) −1.18642e105 −0.219128 −0.109564 0.993980i \(-0.534946\pi\)
−0.109564 + 0.993980i \(0.534946\pi\)
\(114\) 3.56730e105 0.418543
\(115\) 1.96048e106 1.46698
\(116\) 1.66423e105 0.0797311
\(117\) −2.10322e106 −0.647610
\(118\) 5.32987e105 0.105875
\(119\) −1.33861e107 −1.72181
\(120\) −1.38169e107 −1.15498
\(121\) −1.33096e106 −0.0725634
\(122\) 1.55068e107 0.553337
\(123\) −1.85017e107 −0.433610
\(124\) 1.40523e107 0.217035
\(125\) 4.60367e107 0.470153
\(126\) −3.97004e107 −0.268975
\(127\) 3.08889e108 1.39287 0.696436 0.717619i \(-0.254768\pi\)
0.696436 + 0.717619i \(0.254768\pi\)
\(128\) −1.80357e108 −0.543024
\(129\) 2.86523e107 0.0577816
\(130\) 1.05107e109 1.42413
\(131\) −1.75827e108 −0.160552 −0.0802759 0.996773i \(-0.525580\pi\)
−0.0802759 + 0.996773i \(0.525580\pi\)
\(132\) −6.90109e108 −0.425951
\(133\) 1.99775e109 0.835954
\(134\) −3.10915e109 −0.884595
\(135\) −8.43846e109 −1.63710
\(136\) 1.38414e110 1.83623
\(137\) −1.62149e110 −1.47504 −0.737521 0.675324i \(-0.764004\pi\)
−0.737521 + 0.675324i \(0.764004\pi\)
\(138\) 7.36847e109 0.460898
\(139\) −3.53740e110 −1.52554 −0.762768 0.646672i \(-0.776160\pi\)
−0.762768 + 0.646672i \(0.776160\pi\)
\(140\) −2.87685e110 −0.857676
\(141\) 3.11846e110 0.644401
\(142\) 5.54504e110 0.796260
\(143\) 1.41200e111 1.41264
\(144\) 3.65734e109 0.0255562
\(145\) −4.18430e110 −0.204725
\(146\) 3.53700e111 1.21468
\(147\) −2.80289e110 −0.0677272
\(148\) −2.06724e111 −0.352300
\(149\) −4.34460e111 −0.523428 −0.261714 0.965145i \(-0.584288\pi\)
−0.261714 + 0.965145i \(0.584288\pi\)
\(150\) 7.32309e111 0.625165
\(151\) −2.04570e112 −1.24031 −0.620155 0.784479i \(-0.712930\pi\)
−0.620155 + 0.784479i \(0.712930\pi\)
\(152\) −2.06572e112 −0.891509
\(153\) 2.58909e112 0.797146
\(154\) 2.66530e112 0.586717
\(155\) −3.53310e112 −0.557280
\(156\) −5.72826e112 −0.648793
\(157\) −1.35940e113 −1.10794 −0.553969 0.832537i \(-0.686887\pi\)
−0.553969 + 0.832537i \(0.686887\pi\)
\(158\) −3.05515e112 −0.179553
\(159\) 1.97346e113 0.838063
\(160\) 4.84345e113 1.48928
\(161\) 4.12648e113 0.920549
\(162\) −1.43235e113 −0.232287
\(163\) −4.93014e113 −0.582369 −0.291184 0.956667i \(-0.594049\pi\)
−0.291184 + 0.956667i \(0.594049\pi\)
\(164\) 3.98335e113 0.343392
\(165\) 1.73511e114 1.09371
\(166\) 1.37018e113 0.0632720
\(167\) −4.41492e114 −1.49632 −0.748160 0.663519i \(-0.769062\pi\)
−0.748160 + 0.663519i \(0.769062\pi\)
\(168\) −2.90822e114 −0.724769
\(169\) 6.27328e114 1.15167
\(170\) −1.29388e115 −1.75297
\(171\) −3.86399e114 −0.387023
\(172\) −6.16872e113 −0.0457594
\(173\) 3.12303e114 0.171871 0.0859353 0.996301i \(-0.472612\pi\)
0.0859353 + 0.996301i \(0.472612\pi\)
\(174\) −1.57267e114 −0.0643209
\(175\) 4.10106e115 1.24864
\(176\) −2.45536e114 −0.0557460
\(177\) 7.30322e114 0.123849
\(178\) 6.04131e115 0.766480
\(179\) −2.00781e115 −0.190893 −0.0954467 0.995435i \(-0.530428\pi\)
−0.0954467 + 0.995435i \(0.530428\pi\)
\(180\) 5.56431e115 0.397079
\(181\) −2.21886e116 −1.19037 −0.595186 0.803588i \(-0.702922\pi\)
−0.595186 + 0.803588i \(0.702922\pi\)
\(182\) 2.21234e116 0.893665
\(183\) 2.12481e116 0.647274
\(184\) −4.26686e116 −0.981726
\(185\) 5.19757e116 0.904600
\(186\) −1.32792e116 −0.175087
\(187\) −1.73819e117 −1.73882
\(188\) −6.71391e116 −0.510325
\(189\) −1.77616e117 −1.02730
\(190\) 1.93101e117 0.851087
\(191\) 9.40797e116 0.316430 0.158215 0.987405i \(-0.449426\pi\)
0.158215 + 0.987405i \(0.449426\pi\)
\(192\) 1.98872e117 0.511164
\(193\) −2.28210e117 −0.448883 −0.224442 0.974488i \(-0.572056\pi\)
−0.224442 + 0.974488i \(0.572056\pi\)
\(194\) 2.32383e117 0.350280
\(195\) 1.44023e118 1.66590
\(196\) 6.03450e116 0.0536357
\(197\) 4.84668e117 0.331462 0.165731 0.986171i \(-0.447002\pi\)
0.165731 + 0.986171i \(0.447002\pi\)
\(198\) −5.15513e117 −0.271633
\(199\) 1.43170e118 0.581992 0.290996 0.956724i \(-0.406013\pi\)
0.290996 + 0.956724i \(0.406013\pi\)
\(200\) −4.24058e118 −1.33162
\(201\) −4.26030e118 −1.03477
\(202\) 3.16139e118 0.594679
\(203\) −8.80726e117 −0.128468
\(204\) 7.05155e118 0.798603
\(205\) −1.00151e119 −0.881726
\(206\) −1.37395e119 −0.941475
\(207\) −7.98130e118 −0.426187
\(208\) −2.03808e118 −0.0849101
\(209\) 2.59410e119 0.844215
\(210\) 2.71858e119 0.691908
\(211\) 3.76260e119 0.749793 0.374897 0.927067i \(-0.377678\pi\)
0.374897 + 0.927067i \(0.377678\pi\)
\(212\) −4.24878e119 −0.663693
\(213\) 7.59806e119 0.931437
\(214\) −9.68443e119 −0.932749
\(215\) 1.55097e119 0.117496
\(216\) 1.83658e120 1.09557
\(217\) −7.43658e119 −0.349701
\(218\) 3.23223e119 0.119948
\(219\) 4.84655e120 1.42089
\(220\) −3.73561e120 −0.866152
\(221\) −1.44279e121 −2.64851
\(222\) 1.95351e120 0.284209
\(223\) −7.58239e120 −0.875196 −0.437598 0.899171i \(-0.644171\pi\)
−0.437598 + 0.899171i \(0.644171\pi\)
\(224\) 1.01946e121 0.934543
\(225\) −7.93214e120 −0.578084
\(226\) −2.41378e120 −0.139995
\(227\) 1.78241e121 0.823522 0.411761 0.911292i \(-0.364914\pi\)
0.411761 + 0.911292i \(0.364914\pi\)
\(228\) −1.05238e121 −0.387730
\(229\) 4.16736e121 1.22556 0.612778 0.790255i \(-0.290052\pi\)
0.612778 + 0.790255i \(0.290052\pi\)
\(230\) 3.98861e121 0.937213
\(231\) 3.65211e121 0.686321
\(232\) 9.10687e120 0.137006
\(233\) −1.50418e122 −1.81330 −0.906649 0.421887i \(-0.861368\pi\)
−0.906649 + 0.421887i \(0.861368\pi\)
\(234\) −4.27903e121 −0.413741
\(235\) 1.68805e122 1.31036
\(236\) −1.57235e121 −0.0980803
\(237\) −4.18630e121 −0.210035
\(238\) −2.72341e122 −1.10002
\(239\) 2.53592e122 0.825360 0.412680 0.910876i \(-0.364593\pi\)
0.412680 + 0.910876i \(0.364593\pi\)
\(240\) −2.50445e121 −0.0657405
\(241\) −7.15415e122 −1.51593 −0.757967 0.652293i \(-0.773807\pi\)
−0.757967 + 0.652293i \(0.773807\pi\)
\(242\) −2.70785e121 −0.0463589
\(243\) 5.81859e122 0.805554
\(244\) −4.57462e122 −0.512600
\(245\) −1.51723e122 −0.137720
\(246\) −3.76420e122 −0.277022
\(247\) 2.15324e123 1.28588
\(248\) 7.68956e122 0.372941
\(249\) 1.87749e122 0.0740134
\(250\) 9.36623e122 0.300368
\(251\) −5.02868e122 −0.131298 −0.0656489 0.997843i \(-0.520912\pi\)
−0.0656489 + 0.997843i \(0.520912\pi\)
\(252\) 1.17119e123 0.249173
\(253\) 5.35827e123 0.929646
\(254\) 6.28438e123 0.889869
\(255\) −1.77294e124 −2.05057
\(256\) −1.09038e124 −1.03091
\(257\) −7.82418e121 −0.00605178 −0.00302589 0.999995i \(-0.500963\pi\)
−0.00302589 + 0.999995i \(0.500963\pi\)
\(258\) 5.82934e122 0.0369152
\(259\) 1.09400e124 0.567650
\(260\) −3.10075e124 −1.31929
\(261\) 1.70347e123 0.0594769
\(262\) −3.57723e123 −0.102572
\(263\) −3.89288e123 −0.0917382 −0.0458691 0.998947i \(-0.514606\pi\)
−0.0458691 + 0.998947i \(0.514606\pi\)
\(264\) −3.77635e124 −0.731932
\(265\) 1.06825e125 1.70416
\(266\) 4.06445e124 0.534070
\(267\) 8.27807e124 0.896601
\(268\) 9.17224e124 0.819471
\(269\) 3.60596e124 0.265937 0.132969 0.991120i \(-0.457549\pi\)
0.132969 + 0.991120i \(0.457549\pi\)
\(270\) −1.71682e125 −1.04590
\(271\) −3.22184e125 −1.62250 −0.811251 0.584698i \(-0.801213\pi\)
−0.811251 + 0.584698i \(0.801213\pi\)
\(272\) 2.50890e124 0.104516
\(273\) 3.03144e125 1.04538
\(274\) −3.29894e125 −0.942366
\(275\) 5.32527e125 1.26098
\(276\) −2.17376e125 −0.426966
\(277\) 3.98168e124 0.0649170 0.0324585 0.999473i \(-0.489666\pi\)
0.0324585 + 0.999473i \(0.489666\pi\)
\(278\) −7.19689e125 −0.974625
\(279\) 1.43836e125 0.161901
\(280\) −1.57425e126 −1.47378
\(281\) 1.40414e125 0.109404 0.0547021 0.998503i \(-0.482579\pi\)
0.0547021 + 0.998503i \(0.482579\pi\)
\(282\) 6.34455e125 0.411691
\(283\) 1.21866e126 0.658994 0.329497 0.944157i \(-0.393121\pi\)
0.329497 + 0.944157i \(0.393121\pi\)
\(284\) −1.63583e126 −0.737639
\(285\) 2.64596e126 0.995572
\(286\) 2.87274e126 0.902497
\(287\) −2.10802e126 −0.553296
\(288\) −1.97181e126 −0.432666
\(289\) 1.23129e127 2.26006
\(290\) −8.51301e125 −0.130794
\(291\) 3.18421e126 0.409745
\(292\) −1.04344e127 −1.12526
\(293\) −1.07235e127 −0.969739 −0.484869 0.874587i \(-0.661133\pi\)
−0.484869 + 0.874587i \(0.661133\pi\)
\(294\) −5.70251e125 −0.0432692
\(295\) 3.95329e126 0.251840
\(296\) −1.13122e127 −0.605374
\(297\) −2.30635e127 −1.03745
\(298\) −8.83914e126 −0.334405
\(299\) 4.44764e127 1.41600
\(300\) −2.16037e127 −0.579140
\(301\) 3.26454e126 0.0737305
\(302\) −4.16201e127 −0.792402
\(303\) 4.33188e127 0.695634
\(304\) −3.74431e126 −0.0507437
\(305\) 1.15017e128 1.31620
\(306\) 5.26753e127 0.509276
\(307\) 1.28086e128 1.04683 0.523413 0.852079i \(-0.324659\pi\)
0.523413 + 0.852079i \(0.324659\pi\)
\(308\) −7.86284e127 −0.543523
\(309\) −1.88265e128 −1.10130
\(310\) −7.18813e127 −0.356032
\(311\) 2.66295e128 1.11738 0.558692 0.829375i \(-0.311303\pi\)
0.558692 + 0.829375i \(0.311303\pi\)
\(312\) −3.13457e128 −1.11485
\(313\) 4.07201e128 1.22822 0.614109 0.789221i \(-0.289516\pi\)
0.614109 + 0.789221i \(0.289516\pi\)
\(314\) −2.76572e128 −0.707833
\(315\) −2.94468e128 −0.639800
\(316\) 9.01293e127 0.166334
\(317\) −8.01048e128 −1.25634 −0.628169 0.778077i \(-0.716195\pi\)
−0.628169 + 0.778077i \(0.716195\pi\)
\(318\) 4.01503e128 0.535417
\(319\) −1.14363e128 −0.129737
\(320\) 1.07651e129 1.03943
\(321\) −1.32700e129 −1.09110
\(322\) 8.39536e128 0.588115
\(323\) −2.65066e129 −1.58279
\(324\) 4.22554e128 0.215186
\(325\) 4.42025e129 1.92067
\(326\) −1.00304e129 −0.372060
\(327\) 4.42895e128 0.140311
\(328\) 2.17973e129 0.590066
\(329\) 3.55306e129 0.822269
\(330\) 3.53010e129 0.698745
\(331\) −1.30045e129 −0.220268 −0.110134 0.993917i \(-0.535128\pi\)
−0.110134 + 0.993917i \(0.535128\pi\)
\(332\) −4.04215e128 −0.0586139
\(333\) −2.11598e129 −0.262805
\(334\) −8.98220e129 −0.955960
\(335\) −2.30613e130 −2.10415
\(336\) −5.27144e128 −0.0412531
\(337\) −5.22808e129 −0.351077 −0.175539 0.984473i \(-0.556167\pi\)
−0.175539 + 0.984473i \(0.556167\pi\)
\(338\) 1.27631e130 0.735774
\(339\) −3.30748e129 −0.163762
\(340\) 3.81706e130 1.62392
\(341\) −9.65646e129 −0.353157
\(342\) −7.86133e129 −0.247259
\(343\) −3.84321e130 −1.04003
\(344\) −3.37559e129 −0.0786304
\(345\) 5.46538e130 1.09632
\(346\) 6.35384e129 0.109804
\(347\) 9.07713e130 1.35201 0.676006 0.736896i \(-0.263709\pi\)
0.676006 + 0.736896i \(0.263709\pi\)
\(348\) 4.63951e129 0.0595856
\(349\) −1.79477e130 −0.198838 −0.0994192 0.995046i \(-0.531698\pi\)
−0.0994192 + 0.995046i \(0.531698\pi\)
\(350\) 8.34366e130 0.797723
\(351\) −1.91439e131 −1.58021
\(352\) 1.32378e131 0.943778
\(353\) −2.75396e131 −1.69653 −0.848263 0.529576i \(-0.822351\pi\)
−0.848263 + 0.529576i \(0.822351\pi\)
\(354\) 1.48585e130 0.0791237
\(355\) 4.11289e131 1.89403
\(356\) −1.78223e131 −0.710051
\(357\) −3.73174e131 −1.28676
\(358\) −4.08490e130 −0.121957
\(359\) −1.53432e131 −0.396781 −0.198390 0.980123i \(-0.563571\pi\)
−0.198390 + 0.980123i \(0.563571\pi\)
\(360\) 3.04485e131 0.682319
\(361\) −1.19191e131 −0.231538
\(362\) −4.51429e131 −0.760498
\(363\) −3.71042e130 −0.0542290
\(364\) −6.52657e131 −0.827873
\(365\) 2.62348e132 2.88931
\(366\) 4.32294e131 0.413527
\(367\) −1.72891e132 −1.43705 −0.718524 0.695502i \(-0.755182\pi\)
−0.718524 + 0.695502i \(0.755182\pi\)
\(368\) −7.73409e130 −0.0558788
\(369\) 4.07726e131 0.256160
\(370\) 1.05745e132 0.577925
\(371\) 2.24849e132 1.06939
\(372\) 3.91746e131 0.162197
\(373\) 1.52861e132 0.551178 0.275589 0.961276i \(-0.411127\pi\)
0.275589 + 0.961276i \(0.411127\pi\)
\(374\) −3.53637e132 −1.11089
\(375\) 1.28340e132 0.351360
\(376\) −3.67393e132 −0.876914
\(377\) −9.49273e131 −0.197611
\(378\) −3.61361e132 −0.656317
\(379\) −8.66564e132 −1.37367 −0.686833 0.726815i \(-0.741000\pi\)
−0.686833 + 0.726815i \(0.741000\pi\)
\(380\) −5.69663e132 −0.788430
\(381\) 8.61115e132 1.04094
\(382\) 1.91406e132 0.202159
\(383\) 4.11876e132 0.380215 0.190108 0.981763i \(-0.439116\pi\)
0.190108 + 0.981763i \(0.439116\pi\)
\(384\) −5.02794e132 −0.405819
\(385\) 1.97692e133 1.39560
\(386\) −4.64296e132 −0.286780
\(387\) −6.31416e131 −0.0341351
\(388\) −6.85547e132 −0.324492
\(389\) 3.94211e133 1.63427 0.817137 0.576444i \(-0.195560\pi\)
0.817137 + 0.576444i \(0.195560\pi\)
\(390\) 2.93017e133 1.06430
\(391\) −5.47509e133 −1.74296
\(392\) 3.30215e132 0.0921646
\(393\) −4.90168e132 −0.119985
\(394\) 9.86063e132 0.211762
\(395\) −2.26608e133 −0.427095
\(396\) 1.52081e133 0.251635
\(397\) −3.99698e133 −0.580792 −0.290396 0.956907i \(-0.593787\pi\)
−0.290396 + 0.956907i \(0.593787\pi\)
\(398\) 2.91280e133 0.371820
\(399\) 5.56930e133 0.624736
\(400\) −7.68646e132 −0.0757943
\(401\) −7.00698e133 −0.607569 −0.303785 0.952741i \(-0.598250\pi\)
−0.303785 + 0.952741i \(0.598250\pi\)
\(402\) −8.66762e133 −0.661087
\(403\) −8.01537e133 −0.537915
\(404\) −9.32635e133 −0.550898
\(405\) −1.06241e134 −0.552532
\(406\) −1.79185e133 −0.0820748
\(407\) 1.42057e134 0.573259
\(408\) 3.85869e134 1.37228
\(409\) 5.02399e134 1.57506 0.787532 0.616274i \(-0.211358\pi\)
0.787532 + 0.616274i \(0.211358\pi\)
\(410\) −2.03759e134 −0.563312
\(411\) −4.52035e134 −1.10235
\(412\) 4.05326e134 0.872163
\(413\) 8.32102e133 0.158033
\(414\) −1.62380e134 −0.272280
\(415\) 1.01630e134 0.150503
\(416\) 1.09881e135 1.43753
\(417\) −9.86150e134 −1.14008
\(418\) 5.27773e134 0.539347
\(419\) −6.61572e134 −0.597799 −0.298899 0.954285i \(-0.596620\pi\)
−0.298899 + 0.954285i \(0.596620\pi\)
\(420\) −8.02002e134 −0.640969
\(421\) −6.60189e133 −0.0466810 −0.0233405 0.999728i \(-0.507430\pi\)
−0.0233405 + 0.999728i \(0.507430\pi\)
\(422\) 7.65505e134 0.479023
\(423\) −6.87221e134 −0.380687
\(424\) −2.32498e135 −1.14045
\(425\) −5.44137e135 −2.36417
\(426\) 1.54583e135 0.595071
\(427\) 2.42093e135 0.825935
\(428\) 2.85698e135 0.864080
\(429\) 3.93636e135 1.05571
\(430\) 3.15547e134 0.0750652
\(431\) 7.77350e134 0.164073 0.0820365 0.996629i \(-0.473858\pi\)
0.0820365 + 0.996629i \(0.473858\pi\)
\(432\) 3.32898e134 0.0623588
\(433\) 2.15753e135 0.358782 0.179391 0.983778i \(-0.442587\pi\)
0.179391 + 0.983778i \(0.442587\pi\)
\(434\) −1.51298e135 −0.223415
\(435\) −1.16649e135 −0.152998
\(436\) −9.53533e134 −0.111117
\(437\) 8.17110e135 0.846226
\(438\) 9.86037e135 0.907771
\(439\) −3.01576e134 −0.0246873 −0.0123437 0.999924i \(-0.503929\pi\)
−0.0123437 + 0.999924i \(0.503929\pi\)
\(440\) −2.04417e136 −1.48835
\(441\) 6.17678e134 0.0400106
\(442\) −2.93537e136 −1.69206
\(443\) 5.43533e135 0.278890 0.139445 0.990230i \(-0.455468\pi\)
0.139445 + 0.990230i \(0.455468\pi\)
\(444\) −5.76302e135 −0.263285
\(445\) 4.48099e136 1.82319
\(446\) −1.54265e136 −0.559140
\(447\) −1.21118e136 −0.391175
\(448\) 2.26587e136 0.652256
\(449\) −3.00219e136 −0.770464 −0.385232 0.922820i \(-0.625879\pi\)
−0.385232 + 0.922820i \(0.625879\pi\)
\(450\) −1.61380e136 −0.369323
\(451\) −2.73728e136 −0.558763
\(452\) 7.12086e135 0.129689
\(453\) −5.70297e136 −0.926924
\(454\) 3.62633e136 0.526127
\(455\) 1.64095e137 2.12573
\(456\) −5.75876e136 −0.666254
\(457\) −1.80604e135 −0.0186656 −0.00933281 0.999956i \(-0.502971\pi\)
−0.00933281 + 0.999956i \(0.502971\pi\)
\(458\) 8.47854e136 0.782976
\(459\) 2.35664e137 1.94509
\(460\) −1.17667e137 −0.868215
\(461\) −1.19302e137 −0.787136 −0.393568 0.919295i \(-0.628759\pi\)
−0.393568 + 0.919295i \(0.628759\pi\)
\(462\) 7.43027e136 0.438473
\(463\) −1.54852e136 −0.0817517 −0.0408759 0.999164i \(-0.513015\pi\)
−0.0408759 + 0.999164i \(0.513015\pi\)
\(464\) 1.65071e135 0.00779821
\(465\) −9.84950e136 −0.416473
\(466\) −3.06026e137 −1.15847
\(467\) −6.39769e136 −0.216872 −0.108436 0.994103i \(-0.534584\pi\)
−0.108436 + 0.994103i \(0.534584\pi\)
\(468\) 1.26235e137 0.383281
\(469\) −4.85403e137 −1.32039
\(470\) 3.43435e137 0.837154
\(471\) −3.78971e137 −0.827998
\(472\) −8.60409e136 −0.168536
\(473\) 4.23903e136 0.0744591
\(474\) −8.51708e136 −0.134186
\(475\) 8.12078e137 1.14783
\(476\) 8.03427e137 1.01903
\(477\) −4.34895e137 −0.495095
\(478\) 5.15936e137 0.527301
\(479\) −1.42606e138 −1.30876 −0.654378 0.756168i \(-0.727069\pi\)
−0.654378 + 0.756168i \(0.727069\pi\)
\(480\) 1.35025e138 1.11298
\(481\) 1.17915e138 0.873166
\(482\) −1.45552e138 −0.968491
\(483\) 1.15037e138 0.687956
\(484\) 7.98837e136 0.0429459
\(485\) 1.72364e138 0.833196
\(486\) 1.18380e138 0.514648
\(487\) −3.06250e138 −1.19766 −0.598832 0.800875i \(-0.704368\pi\)
−0.598832 + 0.800875i \(0.704368\pi\)
\(488\) −2.50328e138 −0.880824
\(489\) −1.37442e138 −0.435223
\(490\) −3.08681e137 −0.0879858
\(491\) −4.93375e138 −1.26614 −0.633068 0.774096i \(-0.718205\pi\)
−0.633068 + 0.774096i \(0.718205\pi\)
\(492\) 1.11047e138 0.256628
\(493\) 1.16856e138 0.243241
\(494\) 4.38079e138 0.821513
\(495\) −3.82369e138 −0.646123
\(496\) 1.39381e137 0.0212274
\(497\) 8.65695e138 1.18853
\(498\) 3.81977e137 0.0472852
\(499\) −4.24913e138 −0.474375 −0.237188 0.971464i \(-0.576226\pi\)
−0.237188 + 0.971464i \(0.576226\pi\)
\(500\) −2.76311e138 −0.278255
\(501\) −1.23078e139 −1.11825
\(502\) −1.02309e138 −0.0838828
\(503\) 6.08452e138 0.450272 0.225136 0.974327i \(-0.427717\pi\)
0.225136 + 0.974327i \(0.427717\pi\)
\(504\) 6.40891e138 0.428165
\(505\) 2.34488e139 1.41454
\(506\) 1.09015e139 0.593927
\(507\) 1.74885e139 0.860682
\(508\) −1.85394e139 −0.824357
\(509\) 1.53528e138 0.0616909 0.0308454 0.999524i \(-0.490180\pi\)
0.0308454 + 0.999524i \(0.490180\pi\)
\(510\) −3.60706e139 −1.31005
\(511\) 5.52198e139 1.81309
\(512\) −3.89359e138 −0.115597
\(513\) −3.51708e139 −0.944361
\(514\) −1.59184e137 −0.00386632
\(515\) −1.01909e140 −2.23945
\(516\) −1.71970e138 −0.0341975
\(517\) 4.61368e139 0.830394
\(518\) 2.22576e139 0.362657
\(519\) 8.70631e138 0.128444
\(520\) −1.69677e140 −2.26699
\(521\) −1.73081e139 −0.209463 −0.104731 0.994501i \(-0.533398\pi\)
−0.104731 + 0.994501i \(0.533398\pi\)
\(522\) 3.46573e138 0.0379983
\(523\) 1.79396e140 1.78228 0.891140 0.453728i \(-0.149906\pi\)
0.891140 + 0.453728i \(0.149906\pi\)
\(524\) 1.05531e139 0.0950209
\(525\) 1.14329e140 0.933148
\(526\) −7.92011e138 −0.0586091
\(527\) 9.86700e139 0.662122
\(528\) −6.84501e138 −0.0416608
\(529\) −1.23415e139 −0.0681396
\(530\) 2.17337e140 1.08874
\(531\) −1.60942e139 −0.0731649
\(532\) −1.19905e140 −0.494751
\(533\) −2.27209e140 −0.851087
\(534\) 1.68418e140 0.572815
\(535\) −7.18318e140 −2.21869
\(536\) 5.01916e140 1.40813
\(537\) −5.59732e139 −0.142661
\(538\) 7.33638e139 0.169900
\(539\) −4.14680e139 −0.0872753
\(540\) 5.06474e140 0.968899
\(541\) −9.78427e139 −0.170165 −0.0850823 0.996374i \(-0.527115\pi\)
−0.0850823 + 0.996374i \(0.527115\pi\)
\(542\) −6.55487e140 −1.03657
\(543\) −6.18568e140 −0.889603
\(544\) −1.35264e141 −1.76946
\(545\) 2.39742e140 0.285315
\(546\) 6.16751e140 0.667865
\(547\) 1.16487e141 1.14797 0.573985 0.818866i \(-0.305397\pi\)
0.573985 + 0.818866i \(0.305397\pi\)
\(548\) 9.73212e140 0.872989
\(549\) −4.68247e140 −0.382384
\(550\) 1.08343e141 0.805606
\(551\) −1.74398e140 −0.118096
\(552\) −1.18951e141 −0.733675
\(553\) −4.76972e140 −0.268009
\(554\) 8.10078e139 0.0414738
\(555\) 1.44897e141 0.676037
\(556\) 2.12314e141 0.902873
\(557\) 4.79771e140 0.185991 0.0929954 0.995667i \(-0.470356\pi\)
0.0929954 + 0.995667i \(0.470356\pi\)
\(558\) 2.92636e140 0.103435
\(559\) 3.51862e140 0.113413
\(560\) −2.85347e140 −0.0838862
\(561\) −4.84569e141 −1.29948
\(562\) 2.85673e140 0.0698955
\(563\) 1.83903e141 0.410587 0.205294 0.978700i \(-0.434185\pi\)
0.205294 + 0.978700i \(0.434185\pi\)
\(564\) −1.87169e141 −0.381382
\(565\) −1.79036e141 −0.333002
\(566\) 2.47938e141 0.421014
\(567\) −2.23619e141 −0.346722
\(568\) −8.95145e141 −1.26752
\(569\) −1.41857e141 −0.183472 −0.0917361 0.995783i \(-0.529242\pi\)
−0.0917361 + 0.995783i \(0.529242\pi\)
\(570\) 5.38323e141 0.636045
\(571\) −3.61746e141 −0.390521 −0.195260 0.980751i \(-0.562555\pi\)
−0.195260 + 0.980751i \(0.562555\pi\)
\(572\) −8.47481e141 −0.836054
\(573\) 2.62274e141 0.236478
\(574\) −4.28879e141 −0.353486
\(575\) 1.67739e142 1.26398
\(576\) −4.38258e141 −0.301975
\(577\) 2.49111e142 1.56978 0.784891 0.619634i \(-0.212719\pi\)
0.784891 + 0.619634i \(0.212719\pi\)
\(578\) 2.50506e142 1.44389
\(579\) −6.36199e141 −0.335465
\(580\) 2.51141e141 0.121164
\(581\) 2.13914e141 0.0944426
\(582\) 6.47832e141 0.261775
\(583\) 2.91968e142 1.07995
\(584\) −5.70983e142 −1.93358
\(585\) −3.17386e142 −0.984149
\(586\) −2.18171e142 −0.619541
\(587\) 2.90860e140 0.00756523 0.00378261 0.999993i \(-0.498796\pi\)
0.00378261 + 0.999993i \(0.498796\pi\)
\(588\) 1.68229e141 0.0400837
\(589\) −1.47256e142 −0.321467
\(590\) 8.04302e141 0.160894
\(591\) 1.35115e142 0.247712
\(592\) −2.05045e141 −0.0344572
\(593\) 1.02020e143 1.57169 0.785846 0.618423i \(-0.212228\pi\)
0.785846 + 0.618423i \(0.212228\pi\)
\(594\) −4.69230e142 −0.662802
\(595\) −2.02002e143 −2.61657
\(596\) 2.60762e142 0.309786
\(597\) 3.99125e142 0.434942
\(598\) 9.04878e142 0.904646
\(599\) 2.07797e142 0.190616 0.0953079 0.995448i \(-0.469616\pi\)
0.0953079 + 0.995448i \(0.469616\pi\)
\(600\) −1.18218e143 −0.995162
\(601\) 1.09738e143 0.847857 0.423928 0.905696i \(-0.360651\pi\)
0.423928 + 0.905696i \(0.360651\pi\)
\(602\) 6.64174e141 0.0471045
\(603\) 9.38850e142 0.611300
\(604\) 1.22783e143 0.734065
\(605\) −2.00848e142 −0.110272
\(606\) 8.81326e142 0.444423
\(607\) −4.25344e143 −1.97025 −0.985127 0.171827i \(-0.945033\pi\)
−0.985127 + 0.171827i \(0.945033\pi\)
\(608\) 2.01871e143 0.859090
\(609\) −2.45527e142 −0.0960083
\(610\) 2.34004e143 0.840886
\(611\) 3.82959e143 1.26483
\(612\) −1.55396e143 −0.471783
\(613\) −3.81484e143 −1.06479 −0.532393 0.846497i \(-0.678707\pi\)
−0.532393 + 0.846497i \(0.678707\pi\)
\(614\) 2.60592e143 0.668790
\(615\) −2.79200e143 −0.658942
\(616\) −4.30264e143 −0.933960
\(617\) 4.27330e143 0.853253 0.426626 0.904428i \(-0.359702\pi\)
0.426626 + 0.904428i \(0.359702\pi\)
\(618\) −3.83027e143 −0.703594
\(619\) −1.02473e144 −1.73198 −0.865988 0.500066i \(-0.833309\pi\)
−0.865988 + 0.500066i \(0.833309\pi\)
\(620\) 2.12055e143 0.329820
\(621\) −7.26473e143 −1.03993
\(622\) 5.41780e143 0.713868
\(623\) 9.43173e143 1.14408
\(624\) −5.68172e142 −0.0634561
\(625\) −5.78454e143 −0.594905
\(626\) 8.28455e143 0.784677
\(627\) 7.23178e143 0.630909
\(628\) 8.15908e143 0.655722
\(629\) −1.45154e144 −1.07479
\(630\) −5.99098e143 −0.408752
\(631\) 1.58932e144 0.999306 0.499653 0.866226i \(-0.333461\pi\)
0.499653 + 0.866226i \(0.333461\pi\)
\(632\) 4.93198e143 0.285820
\(633\) 1.04893e144 0.560345
\(634\) −1.62974e144 −0.802642
\(635\) 4.66128e144 2.11670
\(636\) −1.18447e144 −0.495999
\(637\) −3.44206e143 −0.132934
\(638\) −2.32673e143 −0.0828859
\(639\) −1.67440e144 −0.550256
\(640\) −2.72167e144 −0.825213
\(641\) 2.24200e144 0.627259 0.313630 0.949545i \(-0.398455\pi\)
0.313630 + 0.949545i \(0.398455\pi\)
\(642\) −2.69981e144 −0.697074
\(643\) −5.62121e144 −1.33957 −0.669784 0.742556i \(-0.733613\pi\)
−0.669784 + 0.742556i \(0.733613\pi\)
\(644\) −2.47670e144 −0.544818
\(645\) 4.32377e143 0.0878086
\(646\) −5.39279e144 −1.01121
\(647\) 5.01297e144 0.868009 0.434005 0.900911i \(-0.357100\pi\)
0.434005 + 0.900911i \(0.357100\pi\)
\(648\) 2.31226e144 0.369764
\(649\) 1.08049e144 0.159595
\(650\) 8.99304e144 1.22707
\(651\) −2.07315e144 −0.261343
\(652\) 2.95906e144 0.344669
\(653\) 7.84346e143 0.0844265 0.0422132 0.999109i \(-0.486559\pi\)
0.0422132 + 0.999109i \(0.486559\pi\)
\(654\) 9.01074e143 0.0896410
\(655\) −2.65332e144 −0.243985
\(656\) 3.95098e143 0.0335859
\(657\) −1.06804e145 −0.839407
\(658\) 7.22874e144 0.525326
\(659\) 1.80063e145 1.21011 0.605055 0.796184i \(-0.293151\pi\)
0.605055 + 0.796184i \(0.293151\pi\)
\(660\) −1.04141e145 −0.647303
\(661\) 2.55974e145 1.47170 0.735851 0.677143i \(-0.236782\pi\)
0.735851 + 0.677143i \(0.236782\pi\)
\(662\) −2.64578e144 −0.140724
\(663\) −4.02218e145 −1.97931
\(664\) −2.21191e144 −0.100719
\(665\) 3.01471e145 1.27037
\(666\) −4.30499e144 −0.167899
\(667\) −3.60229e144 −0.130047
\(668\) 2.64982e145 0.885581
\(669\) −2.11380e145 −0.654063
\(670\) −4.69185e145 −1.34429
\(671\) 3.14359e145 0.834097
\(672\) 2.84204e145 0.698414
\(673\) −3.83411e145 −0.872747 −0.436374 0.899765i \(-0.643737\pi\)
−0.436374 + 0.899765i \(0.643737\pi\)
\(674\) −1.06366e145 −0.224294
\(675\) −7.21999e145 −1.41056
\(676\) −3.76520e145 −0.681606
\(677\) −6.89480e145 −1.15666 −0.578330 0.815803i \(-0.696295\pi\)
−0.578330 + 0.815803i \(0.696295\pi\)
\(678\) −6.72910e144 −0.104623
\(679\) 3.62797e145 0.522842
\(680\) 2.08874e146 2.79046
\(681\) 4.96896e145 0.615444
\(682\) −1.96462e145 −0.225623
\(683\) 1.61149e146 1.71617 0.858087 0.513505i \(-0.171653\pi\)
0.858087 + 0.513505i \(0.171653\pi\)
\(684\) 2.31916e145 0.229055
\(685\) −2.44690e146 −2.24157
\(686\) −7.81905e145 −0.664450
\(687\) 1.16177e146 0.915898
\(688\) −6.11860e143 −0.00447556
\(689\) 2.42349e146 1.64494
\(690\) 1.11194e146 0.700410
\(691\) −2.00519e146 −1.17229 −0.586146 0.810206i \(-0.699355\pi\)
−0.586146 + 0.810206i \(0.699355\pi\)
\(692\) −1.87443e145 −0.101720
\(693\) −8.04823e145 −0.405451
\(694\) 1.84675e146 0.863765
\(695\) −5.33811e146 −2.31830
\(696\) 2.53880e145 0.102389
\(697\) 2.79696e146 1.04761
\(698\) −3.65149e145 −0.127033
\(699\) −4.19331e146 −1.35514
\(700\) −2.46145e146 −0.738994
\(701\) 1.00291e146 0.279758 0.139879 0.990169i \(-0.455329\pi\)
0.139879 + 0.990169i \(0.455329\pi\)
\(702\) −3.89486e146 −1.00956
\(703\) 2.16630e146 0.521819
\(704\) 2.94226e146 0.658701
\(705\) 4.70591e146 0.979273
\(706\) −5.60296e146 −1.08387
\(707\) 4.93558e146 0.887644
\(708\) −4.38337e145 −0.0732986
\(709\) 2.89709e146 0.450486 0.225243 0.974303i \(-0.427682\pi\)
0.225243 + 0.974303i \(0.427682\pi\)
\(710\) 8.36773e146 1.21005
\(711\) 9.22543e145 0.124080
\(712\) −9.75258e146 −1.22011
\(713\) −3.04167e146 −0.353998
\(714\) −7.59226e146 −0.822078
\(715\) 2.13078e147 2.14673
\(716\) 1.20508e146 0.112978
\(717\) 7.06958e146 0.616818
\(718\) −3.12158e146 −0.253493
\(719\) 3.28991e146 0.248683 0.124342 0.992239i \(-0.460318\pi\)
0.124342 + 0.992239i \(0.460318\pi\)
\(720\) 5.51909e145 0.0388369
\(721\) −2.14502e147 −1.40529
\(722\) −2.42495e146 −0.147924
\(723\) −1.99442e147 −1.13291
\(724\) 1.33175e147 0.704509
\(725\) −3.58011e146 −0.176396
\(726\) −7.54888e145 −0.0346455
\(727\) −3.04275e146 −0.130090 −0.0650451 0.997882i \(-0.520719\pi\)
−0.0650451 + 0.997882i \(0.520719\pi\)
\(728\) −3.57141e147 −1.42257
\(729\) 2.60176e147 0.965605
\(730\) 5.33749e147 1.84591
\(731\) −4.33145e146 −0.139601
\(732\) −1.27530e147 −0.383083
\(733\) −3.31020e147 −0.926830 −0.463415 0.886141i \(-0.653376\pi\)
−0.463415 + 0.886141i \(0.653376\pi\)
\(734\) −3.51750e147 −0.918093
\(735\) −4.22969e146 −0.102923
\(736\) 4.16976e147 0.946026
\(737\) −6.30300e147 −1.33343
\(738\) 8.29524e146 0.163654
\(739\) 6.00062e147 1.10410 0.552049 0.833812i \(-0.313846\pi\)
0.552049 + 0.833812i \(0.313846\pi\)
\(740\) −3.11957e147 −0.535378
\(741\) 6.00276e147 0.960977
\(742\) 4.57458e147 0.683203
\(743\) 1.19318e148 1.66258 0.831292 0.555837i \(-0.187602\pi\)
0.831292 + 0.555837i \(0.187602\pi\)
\(744\) 2.14368e147 0.278711
\(745\) −6.55621e147 −0.795435
\(746\) 3.10997e147 0.352133
\(747\) −4.13745e146 −0.0437242
\(748\) 1.04326e148 1.02910
\(749\) −1.51194e148 −1.39226
\(750\) 2.61110e147 0.224475
\(751\) −2.25826e148 −1.81266 −0.906332 0.422567i \(-0.861129\pi\)
−0.906332 + 0.422567i \(0.861129\pi\)
\(752\) −6.65936e146 −0.0499130
\(753\) −1.40189e147 −0.0981231
\(754\) −1.93131e147 −0.126249
\(755\) −3.08707e148 −1.88485
\(756\) 1.06604e148 0.607998
\(757\) 2.36357e148 1.25931 0.629653 0.776876i \(-0.283197\pi\)
0.629653 + 0.776876i \(0.283197\pi\)
\(758\) −1.76303e148 −0.877600
\(759\) 1.49377e148 0.694754
\(760\) −3.11726e148 −1.35479
\(761\) 5.04058e147 0.204725 0.102363 0.994747i \(-0.467360\pi\)
0.102363 + 0.994747i \(0.467360\pi\)
\(762\) 1.75195e148 0.665028
\(763\) 5.04618e147 0.179040
\(764\) −5.64664e147 −0.187276
\(765\) 3.90705e148 1.21139
\(766\) 8.37966e147 0.242910
\(767\) 8.96865e147 0.243089
\(768\) −3.03974e148 −0.770431
\(769\) 1.01321e148 0.240156 0.120078 0.992764i \(-0.461686\pi\)
0.120078 + 0.992764i \(0.461686\pi\)
\(770\) 4.02206e148 0.891613
\(771\) −2.18121e146 −0.00452269
\(772\) 1.36971e148 0.265667
\(773\) −7.88187e147 −0.143016 −0.0715081 0.997440i \(-0.522781\pi\)
−0.0715081 + 0.997440i \(0.522781\pi\)
\(774\) −1.28462e147 −0.0218080
\(775\) −3.02293e148 −0.480166
\(776\) −3.75139e148 −0.557589
\(777\) 3.04984e148 0.424223
\(778\) 8.02028e148 1.04410
\(779\) −4.17423e148 −0.508624
\(780\) −8.64422e148 −0.985947
\(781\) 1.12411e149 1.20028
\(782\) −1.11391e149 −1.11353
\(783\) 1.55053e148 0.145128
\(784\) 5.98547e146 0.00524591
\(785\) −2.05140e149 −1.68369
\(786\) −9.97253e147 −0.0766556
\(787\) 8.34738e148 0.600968 0.300484 0.953787i \(-0.402852\pi\)
0.300484 + 0.953787i \(0.402852\pi\)
\(788\) −2.90896e148 −0.196172
\(789\) −1.08525e148 −0.0685589
\(790\) −4.61037e148 −0.272860
\(791\) −3.76842e148 −0.208963
\(792\) 8.32202e148 0.432396
\(793\) 2.60935e149 1.27046
\(794\) −8.13189e148 −0.371053
\(795\) 2.97805e149 1.27357
\(796\) −8.59299e148 −0.344446
\(797\) −2.07516e149 −0.779739 −0.389869 0.920870i \(-0.627480\pi\)
−0.389869 + 0.920870i \(0.627480\pi\)
\(798\) 1.13308e149 0.399128
\(799\) −4.71427e149 −1.55688
\(800\) 4.14407e149 1.28320
\(801\) −1.82425e149 −0.529676
\(802\) −1.42558e149 −0.388160
\(803\) 7.17034e149 1.83100
\(804\) 2.55702e149 0.612417
\(805\) 6.22705e149 1.39893
\(806\) −1.63074e149 −0.343660
\(807\) 1.00526e149 0.198743
\(808\) −5.10349e149 −0.946634
\(809\) −7.41910e149 −1.29123 −0.645613 0.763664i \(-0.723398\pi\)
−0.645613 + 0.763664i \(0.723398\pi\)
\(810\) −2.16148e149 −0.352999
\(811\) 4.24437e148 0.0650488 0.0325244 0.999471i \(-0.489645\pi\)
0.0325244 + 0.999471i \(0.489645\pi\)
\(812\) 5.28609e148 0.0760325
\(813\) −8.98178e149 −1.21255
\(814\) 2.89017e149 0.366240
\(815\) −7.43982e149 −0.885005
\(816\) 6.99425e148 0.0781084
\(817\) 6.46432e148 0.0677777
\(818\) 1.02214e150 1.00627
\(819\) −6.68045e149 −0.617568
\(820\) 6.01106e149 0.521840
\(821\) −1.75672e150 −1.43229 −0.716143 0.697954i \(-0.754094\pi\)
−0.716143 + 0.697954i \(0.754094\pi\)
\(822\) −9.19670e149 −0.704261
\(823\) −5.49390e149 −0.395175 −0.197587 0.980285i \(-0.563311\pi\)
−0.197587 + 0.980285i \(0.563311\pi\)
\(824\) 2.21799e150 1.49868
\(825\) 1.48457e150 0.942370
\(826\) 1.69292e149 0.100963
\(827\) 1.95843e150 1.09743 0.548713 0.836011i \(-0.315118\pi\)
0.548713 + 0.836011i \(0.315118\pi\)
\(828\) 4.79035e149 0.252235
\(829\) 1.30771e150 0.647072 0.323536 0.946216i \(-0.395128\pi\)
0.323536 + 0.946216i \(0.395128\pi\)
\(830\) 2.06767e149 0.0961523
\(831\) 1.11001e149 0.0485146
\(832\) 2.44223e150 1.00331
\(833\) 4.23721e149 0.163630
\(834\) −2.00633e150 −0.728369
\(835\) −6.66232e150 −2.27390
\(836\) −1.55697e150 −0.499640
\(837\) 1.30922e150 0.395050
\(838\) −1.34598e150 −0.381918
\(839\) 6.39010e150 1.70517 0.852583 0.522592i \(-0.175035\pi\)
0.852583 + 0.522592i \(0.175035\pi\)
\(840\) −4.38865e150 −1.10141
\(841\) −4.15948e150 −0.981851
\(842\) −1.34316e149 −0.0298233
\(843\) 3.91442e149 0.0817613
\(844\) −2.25830e150 −0.443758
\(845\) 9.46667e150 1.75016
\(846\) −1.39816e150 −0.243211
\(847\) −4.22751e149 −0.0691973
\(848\) −4.21425e149 −0.0649134
\(849\) 3.39736e150 0.492487
\(850\) −1.10705e151 −1.51041
\(851\) 4.47463e150 0.574625
\(852\) −4.56033e150 −0.551261
\(853\) −1.44958e151 −1.64955 −0.824777 0.565458i \(-0.808699\pi\)
−0.824777 + 0.565458i \(0.808699\pi\)
\(854\) 4.92540e150 0.527668
\(855\) −5.83094e150 −0.588144
\(856\) 1.56337e151 1.48479
\(857\) 1.26941e151 1.13524 0.567622 0.823289i \(-0.307863\pi\)
0.567622 + 0.823289i \(0.307863\pi\)
\(858\) 8.00856e150 0.674465
\(859\) 1.66179e151 1.31804 0.659020 0.752125i \(-0.270971\pi\)
0.659020 + 0.752125i \(0.270971\pi\)
\(860\) −9.30889e149 −0.0695389
\(861\) −5.87670e150 −0.413496
\(862\) 1.58153e150 0.104822
\(863\) −1.29085e151 −0.805972 −0.402986 0.915206i \(-0.632028\pi\)
−0.402986 + 0.915206i \(0.632028\pi\)
\(864\) −1.79478e151 −1.05573
\(865\) 4.71280e150 0.261186
\(866\) 4.38953e150 0.229217
\(867\) 3.43255e151 1.68902
\(868\) 4.46341e150 0.206967
\(869\) −6.19352e150 −0.270657
\(870\) −2.37324e150 −0.0977462
\(871\) −5.23182e151 −2.03104
\(872\) −5.21784e150 −0.190938
\(873\) −7.01711e150 −0.242061
\(874\) 1.66242e151 0.540632
\(875\) 1.46226e151 0.448343
\(876\) −2.90889e151 −0.840940
\(877\) −7.04040e150 −0.191919 −0.0959595 0.995385i \(-0.530592\pi\)
−0.0959595 + 0.995385i \(0.530592\pi\)
\(878\) −6.13560e149 −0.0157721
\(879\) −2.98948e151 −0.724717
\(880\) −3.70526e150 −0.0847152
\(881\) −2.47678e151 −0.534106 −0.267053 0.963682i \(-0.586050\pi\)
−0.267053 + 0.963682i \(0.586050\pi\)
\(882\) 1.25667e150 0.0255617
\(883\) 1.69334e151 0.324914 0.162457 0.986716i \(-0.448058\pi\)
0.162457 + 0.986716i \(0.448058\pi\)
\(884\) 8.65958e151 1.56749
\(885\) 1.10209e151 0.188208
\(886\) 1.10582e151 0.178176
\(887\) −7.00163e151 −1.06447 −0.532235 0.846597i \(-0.678648\pi\)
−0.532235 + 0.846597i \(0.678648\pi\)
\(888\) −3.15359e151 −0.452415
\(889\) 9.81122e151 1.32826
\(890\) 9.11662e151 1.16479
\(891\) −2.90371e151 −0.350148
\(892\) 4.55093e151 0.517976
\(893\) 7.03564e151 0.755881
\(894\) −2.46416e151 −0.249911
\(895\) −3.02987e151 −0.290094
\(896\) −5.72865e151 −0.517833
\(897\) 1.23990e152 1.05822
\(898\) −6.10800e151 −0.492229
\(899\) 6.49192e150 0.0494025
\(900\) 4.76085e151 0.342133
\(901\) −2.98334e152 −2.02477
\(902\) −5.56903e151 −0.356979
\(903\) 9.10081e150 0.0551012
\(904\) 3.89661e151 0.222850
\(905\) −3.34836e152 −1.80896
\(906\) −1.16028e152 −0.592187
\(907\) 3.02626e152 1.45925 0.729626 0.683846i \(-0.239694\pi\)
0.729626 + 0.683846i \(0.239694\pi\)
\(908\) −1.06979e152 −0.487393
\(909\) −9.54624e151 −0.410953
\(910\) 3.33852e152 1.35807
\(911\) 3.99594e151 0.153611 0.0768056 0.997046i \(-0.475528\pi\)
0.0768056 + 0.997046i \(0.475528\pi\)
\(912\) −1.04383e151 −0.0379224
\(913\) 2.77769e151 0.0953759
\(914\) −3.67440e150 −0.0119250
\(915\) 3.20643e152 0.983639
\(916\) −2.50124e152 −0.725333
\(917\) −5.58479e151 −0.153104
\(918\) 4.79461e152 1.24267
\(919\) −2.39448e152 −0.586763 −0.293382 0.955995i \(-0.594781\pi\)
−0.293382 + 0.955995i \(0.594781\pi\)
\(920\) −6.43889e152 −1.49189
\(921\) 3.57075e152 0.782327
\(922\) −2.42721e152 −0.502881
\(923\) 9.33072e152 1.82822
\(924\) −2.19199e152 −0.406192
\(925\) 4.44707e152 0.779425
\(926\) −3.15049e151 −0.0522291
\(927\) 4.14882e152 0.650607
\(928\) −8.89963e151 −0.132023
\(929\) −1.11712e153 −1.56780 −0.783900 0.620887i \(-0.786773\pi\)
−0.783900 + 0.620887i \(0.786773\pi\)
\(930\) −2.00389e152 −0.266074
\(931\) −6.32367e151 −0.0794439
\(932\) 9.02802e152 1.07318
\(933\) 7.42371e152 0.835058
\(934\) −1.30162e152 −0.138554
\(935\) −2.62301e153 −2.64242
\(936\) 6.90771e152 0.658609
\(937\) 8.66820e152 0.782240 0.391120 0.920340i \(-0.372088\pi\)
0.391120 + 0.920340i \(0.372088\pi\)
\(938\) −9.87557e152 −0.843560
\(939\) 1.13519e153 0.917887
\(940\) −1.01316e153 −0.775522
\(941\) −2.89204e152 −0.209575 −0.104787 0.994495i \(-0.533416\pi\)
−0.104787 + 0.994495i \(0.533416\pi\)
\(942\) −7.71020e152 −0.528986
\(943\) −8.62211e152 −0.560094
\(944\) −1.55958e151 −0.00959288
\(945\) −2.68030e153 −1.56115
\(946\) 8.62436e151 0.0475700
\(947\) 4.18335e152 0.218525 0.109262 0.994013i \(-0.465151\pi\)
0.109262 + 0.994013i \(0.465151\pi\)
\(948\) 2.51261e152 0.124307
\(949\) 5.95176e153 2.78892
\(950\) 1.65218e153 0.733317
\(951\) −2.23315e153 −0.938902
\(952\) 4.39645e153 1.75105
\(953\) 1.86919e153 0.705291 0.352645 0.935757i \(-0.385282\pi\)
0.352645 + 0.935757i \(0.385282\pi\)
\(954\) −8.84799e152 −0.316303
\(955\) 1.41971e153 0.480867
\(956\) −1.52205e153 −0.488481
\(957\) −3.18819e152 −0.0969570
\(958\) −2.90133e153 −0.836130
\(959\) −5.15032e153 −1.40662
\(960\) 3.00107e153 0.776797
\(961\) −3.52803e153 −0.865522
\(962\) 2.39899e153 0.557843
\(963\) 2.92434e153 0.644577
\(964\) 4.29390e153 0.897190
\(965\) −3.44380e153 −0.682152
\(966\) 2.34044e153 0.439517
\(967\) −6.73306e153 −1.19881 −0.599403 0.800447i \(-0.704595\pi\)
−0.599403 + 0.800447i \(0.704595\pi\)
\(968\) 4.37133e152 0.0737959
\(969\) −7.38945e153 −1.18287
\(970\) 3.50677e153 0.532307
\(971\) −1.32780e153 −0.191136 −0.0955679 0.995423i \(-0.530467\pi\)
−0.0955679 + 0.995423i \(0.530467\pi\)
\(972\) −3.49230e153 −0.476759
\(973\) −1.12358e154 −1.45477
\(974\) −6.23069e153 −0.765156
\(975\) 1.23227e154 1.43538
\(976\) −4.53744e152 −0.0501355
\(977\) 9.23515e153 0.967997 0.483998 0.875069i \(-0.339184\pi\)
0.483998 + 0.875069i \(0.339184\pi\)
\(978\) −2.79626e153 −0.278053
\(979\) 1.22472e154 1.15539
\(980\) 9.10635e152 0.0815082
\(981\) −9.76015e152 −0.0828901
\(982\) −1.00378e154 −0.808902
\(983\) 1.61819e154 1.23744 0.618720 0.785611i \(-0.287651\pi\)
0.618720 + 0.785611i \(0.287651\pi\)
\(984\) 6.07662e153 0.440975
\(985\) 7.31387e153 0.503711
\(986\) 2.37746e153 0.155400
\(987\) 9.90515e153 0.614508
\(988\) −1.29237e154 −0.761033
\(989\) 1.33524e153 0.0746365
\(990\) −7.77934e153 −0.412791
\(991\) −1.93430e154 −0.974383 −0.487191 0.873295i \(-0.661979\pi\)
−0.487191 + 0.873295i \(0.661979\pi\)
\(992\) −7.51457e153 −0.359379
\(993\) −3.62536e153 −0.164613
\(994\) 1.76127e154 0.759323
\(995\) 2.16050e154 0.884433
\(996\) −1.12686e153 −0.0438041
\(997\) −8.32043e153 −0.307146 −0.153573 0.988137i \(-0.549078\pi\)
−0.153573 + 0.988137i \(0.549078\pi\)
\(998\) −8.64490e153 −0.303066
\(999\) −1.92601e154 −0.641262
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 \(a_p\))