Properties

Label 2.50.a.b.1.1
Level 2
Weight 50
Character 2.1
Self dual Yes
Analytic conductor 30.413
Analytic rank 0
Dimension 3
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 50 \)
Character orbit: \([\chi]\) = 2.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(30.4132410198\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{22}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.00244e8\)
Character \(\chi\) = 2.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.67772e7 q^{2}\) \(-6.77152e11 q^{3}\) \(+2.81475e14 q^{4}\) \(-2.33026e17 q^{5}\) \(-1.13607e19 q^{6}\) \(-5.15430e20 q^{7}\) \(+4.72237e21 q^{8}\) \(+2.19235e23 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.67772e7 q^{2}\) \(-6.77152e11 q^{3}\) \(+2.81475e14 q^{4}\) \(-2.33026e17 q^{5}\) \(-1.13607e19 q^{6}\) \(-5.15430e20 q^{7}\) \(+4.72237e21 q^{8}\) \(+2.19235e23 q^{9}\) \(-3.90952e24 q^{10}\) \(-5.21317e25 q^{11}\) \(-1.90601e26 q^{12}\) \(+1.37568e27 q^{13}\) \(-8.64748e27 q^{14}\) \(+1.57794e29 q^{15}\) \(+7.92282e28 q^{16}\) \(-9.93263e29 q^{17}\) \(+3.67815e30 q^{18}\) \(+1.85532e31 q^{19}\) \(-6.55909e31 q^{20}\) \(+3.49024e32 q^{21}\) \(-8.74625e32 q^{22}\) \(-2.69345e33 q^{23}\) \(-3.19776e33 q^{24}\) \(+3.65374e34 q^{25}\) \(+2.30801e34 q^{26}\) \(+1.35867e34 q^{27}\) \(-1.45081e35 q^{28}\) \(-3.88028e34 q^{29}\) \(+2.64734e36 q^{30}\) \(-8.58347e35 q^{31}\) \(+1.32923e36 q^{32}\) \(+3.53011e37 q^{33}\) \(-1.66642e37 q^{34}\) \(+1.20108e38 q^{35}\) \(+6.17091e37 q^{36}\) \(+2.50854e38 q^{37}\) \(+3.11271e38 q^{38}\) \(-9.31545e38 q^{39}\) \(-1.10043e39 q^{40}\) \(+2.12382e38 q^{41}\) \(+5.85566e39 q^{42}\) \(-3.48149e39 q^{43}\) \(-1.46738e40 q^{44}\) \(-5.10874e40 q^{45}\) \(-4.51886e40 q^{46}\) \(+2.11562e40 q^{47}\) \(-5.36495e40 q^{48}\) \(+8.74461e39 q^{49}\) \(+6.12996e41 q^{50}\) \(+6.72589e41 q^{51}\) \(+3.87220e41 q^{52}\) \(-2.52544e42 q^{53}\) \(+2.27947e41 q^{54}\) \(+1.21480e43 q^{55}\) \(-2.43405e42 q^{56}\) \(-1.25633e43 q^{57}\) \(-6.51003e41 q^{58}\) \(-4.29058e43 q^{59}\) \(+4.44150e43 q^{60}\) \(-1.42312e43 q^{61}\) \(-1.44007e43 q^{62}\) \(-1.13000e44 q^{63}\) \(+2.23007e43 q^{64}\) \(-3.20569e44 q^{65}\) \(+5.92254e44 q^{66}\) \(+2.95546e44 q^{67}\) \(-2.79579e44 q^{68}\) \(+1.82387e45 q^{69}\) \(+2.01509e45 q^{70}\) \(-2.56483e45 q^{71}\) \(+1.03531e45 q^{72}\) \(-5.17938e45 q^{73}\) \(+4.20863e45 q^{74}\) \(-2.47414e46 q^{75}\) \(+5.22226e45 q^{76}\) \(+2.68703e46 q^{77}\) \(-1.56287e46 q^{78}\) \(+1.28546e46 q^{79}\) \(-1.84622e46 q^{80}\) \(-6.16630e46 q^{81}\) \(+3.56318e45 q^{82}\) \(+8.58374e46 q^{83}\) \(+9.82416e46 q^{84}\) \(+2.31456e47 q^{85}\) \(-5.84097e46 q^{86}\) \(+2.62754e46 q^{87}\) \(-2.46185e47 q^{88}\) \(+6.95931e47 q^{89}\) \(-8.57104e47 q^{90}\) \(-7.09067e47 q^{91}\) \(-7.58138e47 q^{92}\) \(+5.81231e47 q^{93}\) \(+3.54942e47 q^{94}\) \(-4.32337e48 q^{95}\) \(-9.00089e47 q^{96}\) \(+7.53593e48 q^{97}\) \(+1.46710e47 q^{98}\) \(-1.14291e49 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(3q \) \(\mathstrut +\mathstrut 50331648q^{2} \) \(\mathstrut -\mathstrut 16203614388q^{3} \) \(\mathstrut +\mathstrut 844424930131968q^{4} \) \(\mathstrut -\mathstrut 101813016401840430q^{5} \) \(\mathstrut -\mathstrut 271851538568183808q^{6} \) \(\mathstrut -\mathstrut 125479179230203797096q^{7} \) \(\mathstrut +\mathstrut 14167099448608935641088q^{8} \) \(\mathstrut +\mathstrut 389432931519696922052199q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut 50331648q^{2} \) \(\mathstrut -\mathstrut 16203614388q^{3} \) \(\mathstrut +\mathstrut 844424930131968q^{4} \) \(\mathstrut -\mathstrut 101813016401840430q^{5} \) \(\mathstrut -\mathstrut 271851538568183808q^{6} \) \(\mathstrut -\mathstrut \)\(12\!\cdots\!96\)\(q^{7} \) \(\mathstrut +\mathstrut \)\(14\!\cdots\!88\)\(q^{8} \) \(\mathstrut +\mathstrut \)\(38\!\cdots\!99\)\(q^{9} \) \(\mathstrut -\mathstrut \)\(17\!\cdots\!80\)\(q^{10} \) \(\mathstrut -\mathstrut \)\(25\!\cdots\!04\)\(q^{11} \) \(\mathstrut -\mathstrut \)\(45\!\cdots\!28\)\(q^{12} \) \(\mathstrut +\mathstrut \)\(29\!\cdots\!42\)\(q^{13} \) \(\mathstrut -\mathstrut \)\(21\!\cdots\!36\)\(q^{14} \) \(\mathstrut +\mathstrut \)\(87\!\cdots\!80\)\(q^{15} \) \(\mathstrut +\mathstrut \)\(23\!\cdots\!08\)\(q^{16} \) \(\mathstrut +\mathstrut \)\(39\!\cdots\!54\)\(q^{17} \) \(\mathstrut +\mathstrut \)\(65\!\cdots\!84\)\(q^{18} \) \(\mathstrut +\mathstrut \)\(14\!\cdots\!80\)\(q^{19} \) \(\mathstrut -\mathstrut \)\(28\!\cdots\!80\)\(q^{20} \) \(\mathstrut -\mathstrut \)\(10\!\cdots\!84\)\(q^{21} \) \(\mathstrut -\mathstrut \)\(43\!\cdots\!64\)\(q^{22} \) \(\mathstrut -\mathstrut \)\(49\!\cdots\!08\)\(q^{23} \) \(\mathstrut -\mathstrut \)\(76\!\cdots\!48\)\(q^{24} \) \(\mathstrut +\mathstrut \)\(39\!\cdots\!25\)\(q^{25} \) \(\mathstrut +\mathstrut \)\(49\!\cdots\!72\)\(q^{26} \) \(\mathstrut +\mathstrut \)\(19\!\cdots\!00\)\(q^{27} \) \(\mathstrut -\mathstrut \)\(35\!\cdots\!76\)\(q^{28} \) \(\mathstrut +\mathstrut \)\(93\!\cdots\!30\)\(q^{29} \) \(\mathstrut +\mathstrut \)\(14\!\cdots\!80\)\(q^{30} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!56\)\(q^{31} \) \(\mathstrut +\mathstrut \)\(39\!\cdots\!28\)\(q^{32} \) \(\mathstrut +\mathstrut \)\(84\!\cdots\!84\)\(q^{33} \) \(\mathstrut +\mathstrut \)\(65\!\cdots\!64\)\(q^{34} \) \(\mathstrut +\mathstrut \)\(30\!\cdots\!60\)\(q^{35} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!44\)\(q^{36} \) \(\mathstrut +\mathstrut \)\(30\!\cdots\!74\)\(q^{37} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!80\)\(q^{38} \) \(\mathstrut +\mathstrut \)\(36\!\cdots\!68\)\(q^{39} \) \(\mathstrut -\mathstrut \)\(48\!\cdots\!80\)\(q^{40} \) \(\mathstrut -\mathstrut \)\(11\!\cdots\!54\)\(q^{41} \) \(\mathstrut -\mathstrut \)\(18\!\cdots\!44\)\(q^{42} \) \(\mathstrut -\mathstrut \)\(17\!\cdots\!48\)\(q^{43} \) \(\mathstrut -\mathstrut \)\(72\!\cdots\!24\)\(q^{44} \) \(\mathstrut -\mathstrut \)\(11\!\cdots\!90\)\(q^{45} \) \(\mathstrut -\mathstrut \)\(83\!\cdots\!28\)\(q^{46} \) \(\mathstrut -\mathstrut \)\(21\!\cdots\!56\)\(q^{47} \) \(\mathstrut -\mathstrut \)\(12\!\cdots\!68\)\(q^{48} \) \(\mathstrut +\mathstrut \)\(37\!\cdots\!51\)\(q^{49} \) \(\mathstrut +\mathstrut \)\(66\!\cdots\!00\)\(q^{50} \) \(\mathstrut +\mathstrut \)\(22\!\cdots\!16\)\(q^{51} \) \(\mathstrut +\mathstrut \)\(82\!\cdots\!52\)\(q^{52} \) \(\mathstrut +\mathstrut \)\(74\!\cdots\!02\)\(q^{53} \) \(\mathstrut +\mathstrut \)\(32\!\cdots\!00\)\(q^{54} \) \(\mathstrut +\mathstrut \)\(32\!\cdots\!40\)\(q^{55} \) \(\mathstrut -\mathstrut \)\(59\!\cdots\!16\)\(q^{56} \) \(\mathstrut -\mathstrut \)\(20\!\cdots\!80\)\(q^{57} \) \(\mathstrut +\mathstrut \)\(15\!\cdots\!80\)\(q^{58} \) \(\mathstrut -\mathstrut \)\(53\!\cdots\!40\)\(q^{59} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!80\)\(q^{60} \) \(\mathstrut -\mathstrut \)\(12\!\cdots\!94\)\(q^{61} \) \(\mathstrut +\mathstrut \)\(40\!\cdots\!96\)\(q^{62} \) \(\mathstrut -\mathstrut \)\(46\!\cdots\!68\)\(q^{63} \) \(\mathstrut +\mathstrut \)\(66\!\cdots\!48\)\(q^{64} \) \(\mathstrut -\mathstrut \)\(42\!\cdots\!20\)\(q^{65} \) \(\mathstrut +\mathstrut \)\(14\!\cdots\!44\)\(q^{66} \) \(\mathstrut +\mathstrut \)\(11\!\cdots\!24\)\(q^{67} \) \(\mathstrut +\mathstrut \)\(11\!\cdots\!24\)\(q^{68} \) \(\mathstrut +\mathstrut \)\(77\!\cdots\!68\)\(q^{69} \) \(\mathstrut +\mathstrut \)\(50\!\cdots\!60\)\(q^{70} \) \(\mathstrut -\mathstrut \)\(40\!\cdots\!24\)\(q^{71} \) \(\mathstrut +\mathstrut \)\(18\!\cdots\!04\)\(q^{72} \) \(\mathstrut -\mathstrut \)\(10\!\cdots\!18\)\(q^{73} \) \(\mathstrut +\mathstrut \)\(51\!\cdots\!84\)\(q^{74} \) \(\mathstrut -\mathstrut \)\(38\!\cdots\!00\)\(q^{75} \) \(\mathstrut +\mathstrut \)\(41\!\cdots\!80\)\(q^{76} \) \(\mathstrut -\mathstrut \)\(23\!\cdots\!72\)\(q^{77} \) \(\mathstrut +\mathstrut \)\(60\!\cdots\!88\)\(q^{78} \) \(\mathstrut +\mathstrut \)\(36\!\cdots\!60\)\(q^{79} \) \(\mathstrut -\mathstrut \)\(80\!\cdots\!80\)\(q^{80} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!17\)\(q^{81} \) \(\mathstrut -\mathstrut \)\(19\!\cdots\!64\)\(q^{82} \) \(\mathstrut +\mathstrut \)\(15\!\cdots\!92\)\(q^{83} \) \(\mathstrut -\mathstrut \)\(30\!\cdots\!04\)\(q^{84} \) \(\mathstrut +\mathstrut \)\(56\!\cdots\!60\)\(q^{85} \) \(\mathstrut -\mathstrut \)\(29\!\cdots\!68\)\(q^{86} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!20\)\(q^{87} \) \(\mathstrut -\mathstrut \)\(12\!\cdots\!84\)\(q^{88} \) \(\mathstrut +\mathstrut \)\(54\!\cdots\!70\)\(q^{89} \) \(\mathstrut -\mathstrut \)\(19\!\cdots\!40\)\(q^{90} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!44\)\(q^{91} \) \(\mathstrut -\mathstrut \)\(13\!\cdots\!48\)\(q^{92} \) \(\mathstrut -\mathstrut \)\(23\!\cdots\!76\)\(q^{93} \) \(\mathstrut -\mathstrut \)\(36\!\cdots\!96\)\(q^{94} \) \(\mathstrut -\mathstrut \)\(28\!\cdots\!00\)\(q^{95} \) \(\mathstrut -\mathstrut \)\(21\!\cdots\!88\)\(q^{96} \) \(\mathstrut +\mathstrut \)\(43\!\cdots\!14\)\(q^{97} \) \(\mathstrut +\mathstrut \)\(62\!\cdots\!16\)\(q^{98} \) \(\mathstrut +\mathstrut \)\(17\!\cdots\!68\)\(q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.67772e7 0.707107
\(3\) −6.77152e11 −1.38425 −0.692126 0.721777i \(-0.743326\pi\)
−0.692126 + 0.721777i \(0.743326\pi\)
\(4\) 2.81475e14 0.500000
\(5\) −2.33026e17 −1.74839 −0.874196 0.485573i \(-0.838611\pi\)
−0.874196 + 0.485573i \(0.838611\pi\)
\(6\) −1.13607e19 −0.978814
\(7\) −5.15430e20 −1.01688 −0.508438 0.861099i \(-0.669777\pi\)
−0.508438 + 0.861099i \(0.669777\pi\)
\(8\) 4.72237e21 0.353553
\(9\) 2.19235e23 0.916153
\(10\) −3.90952e24 −1.23630
\(11\) −5.21317e25 −1.59581 −0.797905 0.602783i \(-0.794058\pi\)
−0.797905 + 0.602783i \(0.794058\pi\)
\(12\) −1.90601e26 −0.692126
\(13\) 1.37568e27 0.702920 0.351460 0.936203i \(-0.385685\pi\)
0.351460 + 0.936203i \(0.385685\pi\)
\(14\) −8.64748e27 −0.719040
\(15\) 1.57794e29 2.42021
\(16\) 7.92282e28 0.250000
\(17\) −9.93263e29 −0.709685 −0.354843 0.934926i \(-0.615466\pi\)
−0.354843 + 0.934926i \(0.615466\pi\)
\(18\) 3.67815e30 0.647818
\(19\) 1.85532e31 0.868871 0.434436 0.900703i \(-0.356948\pi\)
0.434436 + 0.900703i \(0.356948\pi\)
\(20\) −6.55909e31 −0.874196
\(21\) 3.49024e32 1.40761
\(22\) −8.74625e32 −1.12841
\(23\) −2.69345e33 −1.16944 −0.584718 0.811236i \(-0.698795\pi\)
−0.584718 + 0.811236i \(0.698795\pi\)
\(24\) −3.19776e33 −0.489407
\(25\) 3.65374e34 2.05687
\(26\) 2.30801e34 0.497039
\(27\) 1.35867e34 0.116065
\(28\) −1.45081e35 −0.508438
\(29\) −3.88028e34 −0.0575588 −0.0287794 0.999586i \(-0.509162\pi\)
−0.0287794 + 0.999586i \(0.509162\pi\)
\(30\) 2.64734e36 1.71135
\(31\) −8.58347e35 −0.248486 −0.124243 0.992252i \(-0.539650\pi\)
−0.124243 + 0.992252i \(0.539650\pi\)
\(32\) 1.32923e36 0.176777
\(33\) 3.53011e37 2.20900
\(34\) −1.66642e37 −0.501823
\(35\) 1.20108e38 1.77790
\(36\) 6.17091e37 0.458077
\(37\) 2.50854e38 0.951652 0.475826 0.879539i \(-0.342149\pi\)
0.475826 + 0.879539i \(0.342149\pi\)
\(38\) 3.11271e38 0.614385
\(39\) −9.31545e38 −0.973018
\(40\) −1.10043e39 −0.618150
\(41\) 2.12382e38 0.0651498 0.0325749 0.999469i \(-0.489629\pi\)
0.0325749 + 0.999469i \(0.489629\pi\)
\(42\) 5.85566e39 0.995332
\(43\) −3.48149e39 −0.332497 −0.166249 0.986084i \(-0.553165\pi\)
−0.166249 + 0.986084i \(0.553165\pi\)
\(44\) −1.46738e40 −0.797905
\(45\) −5.10874e40 −1.60179
\(46\) −4.51886e40 −0.826916
\(47\) 2.11562e40 0.228581 0.114290 0.993447i \(-0.463541\pi\)
0.114290 + 0.993447i \(0.463541\pi\)
\(48\) −5.36495e40 −0.346063
\(49\) 8.74461e39 0.0340358
\(50\) 6.12996e41 1.45443
\(51\) 6.72589e41 0.982383
\(52\) 3.87220e41 0.351460
\(53\) −2.52544e42 −1.43740 −0.718701 0.695319i \(-0.755263\pi\)
−0.718701 + 0.695319i \(0.755263\pi\)
\(54\) 2.27947e41 0.0820703
\(55\) 1.21480e43 2.79010
\(56\) −2.43405e42 −0.359520
\(57\) −1.25633e43 −1.20274
\(58\) −6.51003e41 −0.0407002
\(59\) −4.29058e43 −1.76458 −0.882290 0.470707i \(-0.843999\pi\)
−0.882290 + 0.470707i \(0.843999\pi\)
\(60\) 4.44150e43 1.21011
\(61\) −1.42312e43 −0.258619 −0.129309 0.991604i \(-0.541276\pi\)
−0.129309 + 0.991604i \(0.541276\pi\)
\(62\) −1.44007e43 −0.175706
\(63\) −1.13000e44 −0.931614
\(64\) 2.23007e43 0.125000
\(65\) −3.20569e44 −1.22898
\(66\) 5.92254e44 1.56200
\(67\) 2.95546e44 0.539254 0.269627 0.962965i \(-0.413100\pi\)
0.269627 + 0.962965i \(0.413100\pi\)
\(68\) −2.79579e44 −0.354843
\(69\) 1.82387e45 1.61879
\(70\) 2.01509e45 1.25716
\(71\) −2.56483e45 −1.13039 −0.565197 0.824956i \(-0.691200\pi\)
−0.565197 + 0.824956i \(0.691200\pi\)
\(72\) 1.03531e45 0.323909
\(73\) −5.17938e45 −1.15576 −0.577880 0.816122i \(-0.696120\pi\)
−0.577880 + 0.816122i \(0.696120\pi\)
\(74\) 4.20863e45 0.672920
\(75\) −2.47414e46 −2.84723
\(76\) 5.22226e45 0.434436
\(77\) 2.68703e46 1.62274
\(78\) −1.56287e46 −0.688027
\(79\) 1.28546e46 0.414185 0.207092 0.978321i \(-0.433600\pi\)
0.207092 + 0.978321i \(0.433600\pi\)
\(80\) −1.84622e46 −0.437098
\(81\) −6.16630e46 −1.07682
\(82\) 3.56318e45 0.0460679
\(83\) 8.58374e46 0.824638 0.412319 0.911040i \(-0.364719\pi\)
0.412319 + 0.911040i \(0.364719\pi\)
\(84\) 9.82416e46 0.703806
\(85\) 2.31456e47 1.24081
\(86\) −5.84097e46 −0.235111
\(87\) 2.62754e46 0.0796759
\(88\) −2.46185e47 −0.564204
\(89\) 6.95931e47 1.20924 0.604618 0.796516i \(-0.293326\pi\)
0.604618 + 0.796516i \(0.293326\pi\)
\(90\) −8.57104e47 −1.13264
\(91\) −7.09067e47 −0.714782
\(92\) −7.58138e47 −0.584718
\(93\) 5.81231e47 0.343967
\(94\) 3.54942e47 0.161631
\(95\) −4.32337e48 −1.51913
\(96\) −9.00089e47 −0.244703
\(97\) 7.53593e48 1.58939 0.794693 0.607011i \(-0.207632\pi\)
0.794693 + 0.607011i \(0.207632\pi\)
\(98\) 1.46710e47 0.0240670
\(99\) −1.14291e49 −1.46201
\(100\) 1.02844e49 1.02844
\(101\) 2.43523e49 1.90839 0.954195 0.299185i \(-0.0967147\pi\)
0.954195 + 0.299185i \(0.0967147\pi\)
\(102\) 1.12842e49 0.694650
\(103\) 4.35062e48 0.210882 0.105441 0.994426i \(-0.466375\pi\)
0.105441 + 0.994426i \(0.466375\pi\)
\(104\) 6.49647e48 0.248520
\(105\) −8.13316e49 −2.46106
\(106\) −4.23699e49 −1.01640
\(107\) 4.63551e49 0.883477 0.441739 0.897144i \(-0.354362\pi\)
0.441739 + 0.897144i \(0.354362\pi\)
\(108\) 3.82431e48 0.0580325
\(109\) −3.16577e49 −0.383293 −0.191646 0.981464i \(-0.561383\pi\)
−0.191646 + 0.981464i \(0.561383\pi\)
\(110\) 2.03810e50 1.97290
\(111\) −1.69866e50 −1.31733
\(112\) −4.08366e49 −0.254219
\(113\) −2.77559e50 −1.38974 −0.694869 0.719136i \(-0.744538\pi\)
−0.694869 + 0.719136i \(0.744538\pi\)
\(114\) −2.10778e50 −0.850463
\(115\) 6.27643e50 2.04463
\(116\) −1.09220e49 −0.0287794
\(117\) 3.01597e50 0.643982
\(118\) −7.19839e50 −1.24775
\(119\) 5.11958e50 0.721661
\(120\) 7.45160e50 0.855675
\(121\) 1.65053e51 1.54661
\(122\) −2.38760e50 −0.182871
\(123\) −1.43815e50 −0.0901837
\(124\) −2.41603e50 −0.124243
\(125\) −4.37479e51 −1.84783
\(126\) −1.89583e51 −0.658750
\(127\) −1.11605e51 −0.319516 −0.159758 0.987156i \(-0.551071\pi\)
−0.159758 + 0.987156i \(0.551071\pi\)
\(128\) 3.74144e50 0.0883883
\(129\) 2.35750e51 0.460260
\(130\) −5.37826e51 −0.869019
\(131\) 3.32081e51 0.444730 0.222365 0.974963i \(-0.428622\pi\)
0.222365 + 0.974963i \(0.428622\pi\)
\(132\) 9.93637e51 1.10450
\(133\) −9.56287e51 −0.883534
\(134\) 4.95845e51 0.381310
\(135\) −3.16605e51 −0.202927
\(136\) −4.69055e51 −0.250912
\(137\) 2.87128e52 1.28358 0.641788 0.766882i \(-0.278193\pi\)
0.641788 + 0.766882i \(0.278193\pi\)
\(138\) 3.05995e52 1.14466
\(139\) −2.07847e52 −0.651450 −0.325725 0.945465i \(-0.605608\pi\)
−0.325725 + 0.945465i \(0.605608\pi\)
\(140\) 3.38075e52 0.888948
\(141\) −1.43260e52 −0.316414
\(142\) −4.30308e52 −0.799309
\(143\) −7.17166e52 −1.12173
\(144\) 1.73696e52 0.229038
\(145\) 9.04205e51 0.100635
\(146\) −8.68956e52 −0.817246
\(147\) −5.92142e51 −0.0471142
\(148\) 7.06090e52 0.475826
\(149\) 2.65487e53 1.51698 0.758489 0.651686i \(-0.225938\pi\)
0.758489 + 0.651686i \(0.225938\pi\)
\(150\) −4.15091e53 −2.01330
\(151\) −2.97824e52 −0.122751 −0.0613754 0.998115i \(-0.519549\pi\)
−0.0613754 + 0.998115i \(0.519549\pi\)
\(152\) 8.76150e52 0.307192
\(153\) −2.17758e53 −0.650180
\(154\) 4.50808e53 1.14745
\(155\) 2.00017e53 0.434450
\(156\) −2.62206e53 −0.486509
\(157\) −7.16451e52 −0.113670 −0.0568349 0.998384i \(-0.518101\pi\)
−0.0568349 + 0.998384i \(0.518101\pi\)
\(158\) 2.15664e53 0.292873
\(159\) 1.71011e54 1.98973
\(160\) −3.09744e53 −0.309075
\(161\) 1.38828e54 1.18917
\(162\) −1.03453e54 −0.761424
\(163\) −8.62792e53 −0.546147 −0.273074 0.961993i \(-0.588040\pi\)
−0.273074 + 0.961993i \(0.588040\pi\)
\(164\) 5.97802e52 0.0325749
\(165\) −8.22606e54 −3.86220
\(166\) 1.44011e54 0.583107
\(167\) 1.80874e53 0.0632154 0.0316077 0.999500i \(-0.489937\pi\)
0.0316077 + 0.999500i \(0.489937\pi\)
\(168\) 1.64822e54 0.497666
\(169\) −1.93773e54 −0.505904
\(170\) 3.88318e54 0.877383
\(171\) 4.06751e54 0.796019
\(172\) −9.79953e53 −0.166249
\(173\) 8.09453e54 1.19141 0.595706 0.803202i \(-0.296872\pi\)
0.595706 + 0.803202i \(0.296872\pi\)
\(174\) 4.40827e53 0.0563394
\(175\) −1.88325e55 −2.09158
\(176\) −4.13030e54 −0.398953
\(177\) 2.90537e55 2.44262
\(178\) 1.16758e55 0.855058
\(179\) −9.52961e54 −0.608381 −0.304191 0.952611i \(-0.598386\pi\)
−0.304191 + 0.952611i \(0.598386\pi\)
\(180\) −1.43798e55 −0.800897
\(181\) 1.57599e55 0.766354 0.383177 0.923675i \(-0.374830\pi\)
0.383177 + 0.923675i \(0.374830\pi\)
\(182\) −1.18962e55 −0.505427
\(183\) 9.63667e54 0.357993
\(184\) −1.27194e55 −0.413458
\(185\) −5.84553e55 −1.66386
\(186\) 9.75143e54 0.243221
\(187\) 5.17805e55 1.13252
\(188\) 5.95494e54 0.114290
\(189\) −7.00298e54 −0.118024
\(190\) −7.25341e55 −1.07419
\(191\) −1.13259e56 −1.47487 −0.737435 0.675419i \(-0.763963\pi\)
−0.737435 + 0.675419i \(0.763963\pi\)
\(192\) −1.51010e55 −0.173031
\(193\) 5.85668e55 0.590878 0.295439 0.955362i \(-0.404534\pi\)
0.295439 + 0.955362i \(0.404534\pi\)
\(194\) 1.26432e56 1.12387
\(195\) 2.17074e56 1.70122
\(196\) 2.46139e54 0.0170179
\(197\) 6.36238e55 0.388327 0.194163 0.980969i \(-0.437801\pi\)
0.194163 + 0.980969i \(0.437801\pi\)
\(198\) −1.91748e56 −1.03379
\(199\) −1.38808e56 −0.661475 −0.330738 0.943723i \(-0.607298\pi\)
−0.330738 + 0.943723i \(0.607298\pi\)
\(200\) 1.72543e56 0.727215
\(201\) −2.00130e56 −0.746463
\(202\) 4.08565e56 1.34944
\(203\) 2.00001e55 0.0585302
\(204\) 1.89317e56 0.491191
\(205\) −4.94905e55 −0.113907
\(206\) 7.29914e55 0.149116
\(207\) −5.90498e56 −1.07138
\(208\) 1.08993e56 0.175730
\(209\) −9.67210e56 −1.38655
\(210\) −1.36452e57 −1.74023
\(211\) 5.64284e55 0.0640586 0.0320293 0.999487i \(-0.489803\pi\)
0.0320293 + 0.999487i \(0.489803\pi\)
\(212\) −7.10849e56 −0.718701
\(213\) 1.73678e57 1.56475
\(214\) 7.77710e56 0.624713
\(215\) 8.11277e56 0.581336
\(216\) 6.41613e55 0.0410352
\(217\) 4.42418e56 0.252679
\(218\) −5.31129e56 −0.271029
\(219\) 3.50722e57 1.59986
\(220\) 3.41937e57 1.39505
\(221\) −1.36641e57 −0.498852
\(222\) −2.84988e57 −0.931490
\(223\) −6.70689e57 −1.96360 −0.981798 0.189928i \(-0.939174\pi\)
−0.981798 + 0.189928i \(0.939174\pi\)
\(224\) −6.85124e56 −0.179760
\(225\) 8.01028e57 1.88441
\(226\) −4.65666e57 −0.982694
\(227\) 1.77430e57 0.336042 0.168021 0.985783i \(-0.446262\pi\)
0.168021 + 0.985783i \(0.446262\pi\)
\(228\) −3.53626e57 −0.601368
\(229\) 1.42321e57 0.217420 0.108710 0.994074i \(-0.465328\pi\)
0.108710 + 0.994074i \(0.465328\pi\)
\(230\) 1.05301e58 1.44577
\(231\) −1.81952e58 −2.24628
\(232\) −1.83241e56 −0.0203501
\(233\) 6.14657e57 0.614346 0.307173 0.951654i \(-0.400617\pi\)
0.307173 + 0.951654i \(0.400617\pi\)
\(234\) 5.05996e57 0.455364
\(235\) −4.92994e57 −0.399649
\(236\) −1.20769e58 −0.882290
\(237\) −8.70449e57 −0.573336
\(238\) 8.58922e57 0.510292
\(239\) −1.87389e58 −1.00460 −0.502301 0.864693i \(-0.667513\pi\)
−0.502301 + 0.864693i \(0.667513\pi\)
\(240\) 1.25017e58 0.605054
\(241\) 1.41041e58 0.616491 0.308245 0.951307i \(-0.400258\pi\)
0.308245 + 0.951307i \(0.400258\pi\)
\(242\) 2.76912e58 1.09362
\(243\) 3.85039e58 1.37452
\(244\) −4.00572e57 −0.129309
\(245\) −2.03772e57 −0.0595080
\(246\) −2.41281e57 −0.0637695
\(247\) 2.55233e58 0.610747
\(248\) −4.05343e57 −0.0878529
\(249\) −5.81249e58 −1.14151
\(250\) −7.33968e58 −1.30661
\(251\) 2.19883e58 0.354965 0.177482 0.984124i \(-0.443205\pi\)
0.177482 + 0.984124i \(0.443205\pi\)
\(252\) −3.18067e58 −0.465807
\(253\) 1.40414e59 1.86620
\(254\) −1.87242e58 −0.225932
\(255\) −1.56731e59 −1.71759
\(256\) 6.27710e57 0.0625000
\(257\) −1.39270e58 −0.126036 −0.0630180 0.998012i \(-0.520073\pi\)
−0.0630180 + 0.998012i \(0.520073\pi\)
\(258\) 3.95522e58 0.325453
\(259\) −1.29298e59 −0.967712
\(260\) −9.02322e58 −0.614489
\(261\) −8.50692e57 −0.0527327
\(262\) 5.57139e58 0.314472
\(263\) 1.50291e59 0.772710 0.386355 0.922350i \(-0.373734\pi\)
0.386355 + 0.922350i \(0.373734\pi\)
\(264\) 1.66705e59 0.781001
\(265\) 5.88493e59 2.51314
\(266\) −1.60438e59 −0.624753
\(267\) −4.71250e59 −1.67389
\(268\) 8.31889e58 0.269627
\(269\) 4.46165e59 1.31997 0.659986 0.751278i \(-0.270562\pi\)
0.659986 + 0.751278i \(0.270562\pi\)
\(270\) −5.31174e58 −0.143491
\(271\) −1.87553e59 −0.462782 −0.231391 0.972861i \(-0.574328\pi\)
−0.231391 + 0.972861i \(0.574328\pi\)
\(272\) −7.86944e58 −0.177421
\(273\) 4.80146e59 0.989438
\(274\) 4.81721e59 0.907626
\(275\) −1.90476e60 −3.28238
\(276\) 5.13374e59 0.809397
\(277\) −5.17979e59 −0.747408 −0.373704 0.927548i \(-0.621912\pi\)
−0.373704 + 0.927548i \(0.621912\pi\)
\(278\) −3.48709e59 −0.460645
\(279\) −1.88180e59 −0.227651
\(280\) 5.67196e59 0.628581
\(281\) −1.19166e60 −1.21017 −0.605085 0.796161i \(-0.706861\pi\)
−0.605085 + 0.796161i \(0.706861\pi\)
\(282\) −2.40350e59 −0.223738
\(283\) 2.07435e60 1.77058 0.885288 0.465044i \(-0.153961\pi\)
0.885288 + 0.465044i \(0.153961\pi\)
\(284\) −7.21936e59 −0.565197
\(285\) 2.92758e60 2.10285
\(286\) −1.20321e60 −0.793180
\(287\) −1.09468e59 −0.0662492
\(288\) 2.91413e59 0.161955
\(289\) −9.72261e59 −0.496347
\(290\) 1.51700e59 0.0711599
\(291\) −5.10297e60 −2.20011
\(292\) −1.45787e60 −0.577880
\(293\) 4.37111e60 1.59344 0.796719 0.604350i \(-0.206567\pi\)
0.796719 + 0.604350i \(0.206567\pi\)
\(294\) −9.93450e58 −0.0333147
\(295\) 9.99814e60 3.08518
\(296\) 1.18462e60 0.336460
\(297\) −7.08297e59 −0.185218
\(298\) 4.45413e60 1.07267
\(299\) −3.70533e60 −0.822020
\(300\) −6.96408e60 −1.42362
\(301\) 1.79447e60 0.338108
\(302\) −4.99666e59 −0.0867979
\(303\) −1.64902e61 −2.64169
\(304\) 1.46994e60 0.217218
\(305\) 3.31623e60 0.452167
\(306\) −3.65337e60 −0.459747
\(307\) −4.69486e60 −0.545421 −0.272711 0.962096i \(-0.587920\pi\)
−0.272711 + 0.962096i \(0.587920\pi\)
\(308\) 7.56330e60 0.811370
\(309\) −2.94603e60 −0.291914
\(310\) 3.35573e60 0.307203
\(311\) −1.13490e61 −0.960127 −0.480063 0.877234i \(-0.659386\pi\)
−0.480063 + 0.877234i \(0.659386\pi\)
\(312\) −4.39910e60 −0.344014
\(313\) 2.24105e61 1.62037 0.810186 0.586173i \(-0.199366\pi\)
0.810186 + 0.586173i \(0.199366\pi\)
\(314\) −1.20201e60 −0.0803767
\(315\) 2.63320e61 1.62883
\(316\) 3.61824e60 0.207092
\(317\) −1.97282e61 −1.04505 −0.522523 0.852625i \(-0.675009\pi\)
−0.522523 + 0.852625i \(0.675009\pi\)
\(318\) 2.86908e61 1.40695
\(319\) 2.02286e60 0.0918530
\(320\) −5.19665e60 −0.218549
\(321\) −3.13895e61 −1.22296
\(322\) 2.32915e61 0.840871
\(323\) −1.84282e61 −0.616625
\(324\) −1.73566e61 −0.538408
\(325\) 5.02638e61 1.44582
\(326\) −1.44752e61 −0.386184
\(327\) 2.14371e61 0.530574
\(328\) 1.00295e60 0.0230339
\(329\) −1.09045e61 −0.232438
\(330\) −1.38010e62 −2.73099
\(331\) −8.48788e60 −0.155960 −0.0779801 0.996955i \(-0.524847\pi\)
−0.0779801 + 0.996955i \(0.524847\pi\)
\(332\) 2.41611e61 0.412319
\(333\) 5.49959e61 0.871859
\(334\) 3.03456e60 0.0447000
\(335\) −6.88699e61 −0.942826
\(336\) 2.76526e61 0.351903
\(337\) −1.13716e62 −1.34552 −0.672760 0.739861i \(-0.734891\pi\)
−0.672760 + 0.739861i \(0.734891\pi\)
\(338\) −3.25097e61 −0.357728
\(339\) 1.87949e62 1.92375
\(340\) 6.51490e61 0.620404
\(341\) 4.47471e61 0.396536
\(342\) 6.82414e61 0.562871
\(343\) 1.27919e62 0.982265
\(344\) −1.64409e61 −0.117556
\(345\) −4.25009e62 −2.83029
\(346\) 1.35804e62 0.842456
\(347\) 1.85460e62 1.07196 0.535979 0.844231i \(-0.319943\pi\)
0.535979 + 0.844231i \(0.319943\pi\)
\(348\) 7.39586e60 0.0398380
\(349\) 1.74990e62 0.878598 0.439299 0.898341i \(-0.355227\pi\)
0.439299 + 0.898341i \(0.355227\pi\)
\(350\) −3.15957e62 −1.47897
\(351\) 1.86909e61 0.0815843
\(352\) −6.92949e61 −0.282102
\(353\) −4.46780e62 −1.69673 −0.848367 0.529409i \(-0.822414\pi\)
−0.848367 + 0.529409i \(0.822414\pi\)
\(354\) 4.87440e62 1.72720
\(355\) 5.97672e62 1.97637
\(356\) 1.95887e62 0.604618
\(357\) −3.46673e62 −0.998961
\(358\) −1.59880e62 −0.430190
\(359\) −6.15371e62 −1.54640 −0.773202 0.634160i \(-0.781346\pi\)
−0.773202 + 0.634160i \(0.781346\pi\)
\(360\) −2.41253e62 −0.566320
\(361\) −1.11739e62 −0.245063
\(362\) 2.64408e62 0.541894
\(363\) −1.11766e63 −2.14090
\(364\) −1.99585e62 −0.357391
\(365\) 1.20693e63 2.02072
\(366\) 1.61676e62 0.253140
\(367\) 1.78399e62 0.261261 0.130631 0.991431i \(-0.458300\pi\)
0.130631 + 0.991431i \(0.458300\pi\)
\(368\) −2.13397e62 −0.292359
\(369\) 4.65615e61 0.0596872
\(370\) −9.80718e62 −1.17653
\(371\) 1.30169e63 1.46166
\(372\) 1.63602e62 0.171983
\(373\) −6.15312e61 −0.0605661 −0.0302830 0.999541i \(-0.509641\pi\)
−0.0302830 + 0.999541i \(0.509641\pi\)
\(374\) 8.68733e62 0.800814
\(375\) 2.96240e63 2.55786
\(376\) 9.99073e61 0.0808156
\(377\) −5.33802e61 −0.0404592
\(378\) −1.17491e62 −0.0834553
\(379\) −1.93924e63 −1.29113 −0.645567 0.763704i \(-0.723379\pi\)
−0.645567 + 0.763704i \(0.723379\pi\)
\(380\) −1.21692e63 −0.759564
\(381\) 7.55736e62 0.442291
\(382\) −1.90016e63 −1.04289
\(383\) 4.92299e61 0.0253430 0.0126715 0.999920i \(-0.495966\pi\)
0.0126715 + 0.999920i \(0.495966\pi\)
\(384\) −2.53352e62 −0.122352
\(385\) −6.26146e63 −2.83719
\(386\) 9.82589e62 0.417814
\(387\) −7.63264e62 −0.304619
\(388\) 2.12118e63 0.794693
\(389\) 1.52402e63 0.536075 0.268038 0.963408i \(-0.413625\pi\)
0.268038 + 0.963408i \(0.413625\pi\)
\(390\) 3.64189e63 1.20294
\(391\) 2.67530e63 0.829931
\(392\) 4.12952e61 0.0120335
\(393\) −2.24869e63 −0.615619
\(394\) 1.06743e63 0.274588
\(395\) −2.99545e63 −0.724157
\(396\) −3.21700e63 −0.731003
\(397\) −4.22139e63 −0.901753 −0.450877 0.892586i \(-0.648889\pi\)
−0.450877 + 0.892586i \(0.648889\pi\)
\(398\) −2.32881e63 −0.467734
\(399\) 6.47551e63 1.22303
\(400\) 2.89479e63 0.514218
\(401\) 7.10002e63 1.18638 0.593188 0.805064i \(-0.297869\pi\)
0.593188 + 0.805064i \(0.297869\pi\)
\(402\) −3.35762e63 −0.527829
\(403\) −1.18081e63 −0.174665
\(404\) 6.85458e63 0.954195
\(405\) 1.43691e64 1.88270
\(406\) 3.35546e62 0.0413871
\(407\) −1.30774e64 −1.51866
\(408\) 3.17621e63 0.347325
\(409\) −4.19928e63 −0.432468 −0.216234 0.976342i \(-0.569377\pi\)
−0.216234 + 0.976342i \(0.569377\pi\)
\(410\) −8.30312e62 −0.0805447
\(411\) −1.94429e64 −1.77679
\(412\) 1.22459e63 0.105441
\(413\) 2.21149e64 1.79436
\(414\) −9.90691e63 −0.757582
\(415\) −2.00023e64 −1.44179
\(416\) 1.82859e63 0.124260
\(417\) 1.40744e64 0.901771
\(418\) −1.62271e64 −0.980442
\(419\) 2.50397e64 1.42687 0.713436 0.700720i \(-0.247138\pi\)
0.713436 + 0.700720i \(0.247138\pi\)
\(420\) −2.28928e64 −1.23053
\(421\) −2.02007e63 −0.102437 −0.0512184 0.998687i \(-0.516310\pi\)
−0.0512184 + 0.998687i \(0.516310\pi\)
\(422\) 9.46712e62 0.0452963
\(423\) 4.63818e63 0.209415
\(424\) −1.19261e64 −0.508199
\(425\) −3.62913e64 −1.45973
\(426\) 2.91383e64 1.10644
\(427\) 7.33518e63 0.262983
\(428\) 1.30478e64 0.441739
\(429\) 4.85630e64 1.55275
\(430\) 1.36110e64 0.411066
\(431\) −6.45676e64 −1.84213 −0.921067 0.389403i \(-0.872681\pi\)
−0.921067 + 0.389403i \(0.872681\pi\)
\(432\) 1.07645e63 0.0290162
\(433\) 5.64458e64 1.43773 0.718867 0.695148i \(-0.244661\pi\)
0.718867 + 0.695148i \(0.244661\pi\)
\(434\) 7.42254e63 0.178671
\(435\) −6.12283e63 −0.139305
\(436\) −8.91086e63 −0.191646
\(437\) −4.99721e64 −1.01609
\(438\) 5.88415e64 1.13127
\(439\) 4.39799e64 0.799602 0.399801 0.916602i \(-0.369079\pi\)
0.399801 + 0.916602i \(0.369079\pi\)
\(440\) 5.73675e64 0.986450
\(441\) 1.91712e63 0.0311820
\(442\) −2.29246e64 −0.352741
\(443\) 5.44392e64 0.792538 0.396269 0.918134i \(-0.370305\pi\)
0.396269 + 0.918134i \(0.370305\pi\)
\(444\) −4.78130e64 −0.658663
\(445\) −1.62170e65 −2.11422
\(446\) −1.12523e65 −1.38847
\(447\) −1.79775e65 −2.09988
\(448\) −1.14945e64 −0.127109
\(449\) 6.51981e64 0.682652 0.341326 0.939945i \(-0.389124\pi\)
0.341326 + 0.939945i \(0.389124\pi\)
\(450\) 1.34390e65 1.33248
\(451\) −1.10718e64 −0.103967
\(452\) −7.81258e64 −0.694869
\(453\) 2.01672e64 0.169918
\(454\) 2.97678e64 0.237617
\(455\) 1.65231e65 1.24972
\(456\) −5.93286e64 −0.425232
\(457\) 1.64423e65 1.11691 0.558453 0.829536i \(-0.311395\pi\)
0.558453 + 0.829536i \(0.311395\pi\)
\(458\) 2.38775e64 0.153739
\(459\) −1.34951e64 −0.0823696
\(460\) 1.76666e65 1.02232
\(461\) 7.21325e64 0.395784 0.197892 0.980224i \(-0.436590\pi\)
0.197892 + 0.980224i \(0.436590\pi\)
\(462\) −3.05265e65 −1.58836
\(463\) 1.94522e65 0.959916 0.479958 0.877291i \(-0.340652\pi\)
0.479958 + 0.877291i \(0.340652\pi\)
\(464\) −3.07427e63 −0.0143897
\(465\) −1.35442e65 −0.601388
\(466\) 1.03122e65 0.434408
\(467\) −7.84448e64 −0.313545 −0.156773 0.987635i \(-0.550109\pi\)
−0.156773 + 0.987635i \(0.550109\pi\)
\(468\) 8.48921e64 0.321991
\(469\) −1.52334e65 −0.548354
\(470\) −8.27106e64 −0.282595
\(471\) 4.85146e64 0.157348
\(472\) −2.02617e65 −0.623873
\(473\) 1.81496e65 0.530603
\(474\) −1.46037e65 −0.405410
\(475\) 6.77886e65 1.78716
\(476\) 1.44103e65 0.360831
\(477\) −5.53665e65 −1.31688
\(478\) −3.14386e65 −0.710362
\(479\) −3.87609e65 −0.832097 −0.416048 0.909342i \(-0.636585\pi\)
−0.416048 + 0.909342i \(0.636585\pi\)
\(480\) 2.09744e65 0.427838
\(481\) 3.45095e65 0.668935
\(482\) 2.36627e65 0.435925
\(483\) −9.40079e65 −1.64611
\(484\) 4.64582e65 0.773305
\(485\) −1.75607e66 −2.77887
\(486\) 6.45988e65 0.971933
\(487\) 8.09553e65 1.15821 0.579103 0.815255i \(-0.303403\pi\)
0.579103 + 0.815255i \(0.303403\pi\)
\(488\) −6.72049e64 −0.0914355
\(489\) 5.84241e65 0.756005
\(490\) −3.41872e64 −0.0420785
\(491\) −1.15921e66 −1.35727 −0.678634 0.734477i \(-0.737428\pi\)
−0.678634 + 0.734477i \(0.737428\pi\)
\(492\) −4.04803e64 −0.0450919
\(493\) 3.85414e64 0.0408486
\(494\) 4.28210e65 0.431863
\(495\) 2.66327e66 2.55616
\(496\) −6.80052e64 −0.0621214
\(497\) 1.32199e66 1.14947
\(498\) −9.75175e65 −0.807167
\(499\) 1.98775e66 1.56638 0.783191 0.621781i \(-0.213591\pi\)
0.783191 + 0.621781i \(0.213591\pi\)
\(500\) −1.23139e66 −0.923915
\(501\) −1.22479e65 −0.0875061
\(502\) 3.68902e65 0.250998
\(503\) −1.31100e66 −0.849548 −0.424774 0.905300i \(-0.639646\pi\)
−0.424774 + 0.905300i \(0.639646\pi\)
\(504\) −5.33629e65 −0.329375
\(505\) −5.67472e66 −3.33661
\(506\) 2.35576e66 1.31960
\(507\) 1.31213e66 0.700299
\(508\) −3.14141e65 −0.159758
\(509\) 7.52616e65 0.364744 0.182372 0.983230i \(-0.441623\pi\)
0.182372 + 0.983230i \(0.441623\pi\)
\(510\) −2.62950e66 −1.21452
\(511\) 2.66961e66 1.17526
\(512\) 1.05312e65 0.0441942
\(513\) 2.52076e65 0.100846
\(514\) −2.33656e65 −0.0891210
\(515\) −1.01381e66 −0.368704
\(516\) 6.63576e65 0.230130
\(517\) −1.10291e66 −0.364772
\(518\) −2.16925e66 −0.684275
\(519\) −5.48123e66 −1.64922
\(520\) −1.51384e66 −0.434510
\(521\) 2.28801e66 0.626519 0.313260 0.949667i \(-0.398579\pi\)
0.313260 + 0.949667i \(0.398579\pi\)
\(522\) −1.42722e65 −0.0372877
\(523\) 3.63925e65 0.0907237 0.0453618 0.998971i \(-0.485556\pi\)
0.0453618 + 0.998971i \(0.485556\pi\)
\(524\) 9.34724e65 0.222365
\(525\) 1.27524e67 2.89528
\(526\) 2.52146e66 0.546389
\(527\) 8.52564e65 0.176347
\(528\) 2.79684e66 0.552251
\(529\) 1.94992e66 0.367581
\(530\) 9.87327e66 1.77706
\(531\) −9.40644e66 −1.61663
\(532\) −2.69171e66 −0.441767
\(533\) 2.92170e65 0.0457951
\(534\) −7.90627e66 −1.18362
\(535\) −1.08019e67 −1.54466
\(536\) 1.39568e66 0.190655
\(537\) 6.45299e66 0.842153
\(538\) 7.48541e66 0.933362
\(539\) −4.55871e65 −0.0543147
\(540\) −8.91163e65 −0.101464
\(541\) −1.63939e67 −1.78382 −0.891908 0.452218i \(-0.850633\pi\)
−0.891908 + 0.452218i \(0.850633\pi\)
\(542\) −3.14662e66 −0.327236
\(543\) −1.06719e67 −1.06083
\(544\) −1.32027e66 −0.125456
\(545\) 7.37707e66 0.670146
\(546\) 8.05552e66 0.699638
\(547\) 1.43390e67 1.19078 0.595388 0.803439i \(-0.296999\pi\)
0.595388 + 0.803439i \(0.296999\pi\)
\(548\) 8.08194e66 0.641788
\(549\) −3.11997e66 −0.236934
\(550\) −3.19565e67 −2.32099
\(551\) −7.19915e65 −0.0500112
\(552\) 8.61299e66 0.572330
\(553\) −6.62563e66 −0.421174
\(554\) −8.69024e66 −0.528497
\(555\) 3.95831e67 2.30320
\(556\) −5.85037e66 −0.325725
\(557\) 1.82851e67 0.974193 0.487097 0.873348i \(-0.338056\pi\)
0.487097 + 0.873348i \(0.338056\pi\)
\(558\) −3.15713e66 −0.160973
\(559\) −4.78942e66 −0.233719
\(560\) 9.51597e66 0.444474
\(561\) −3.50632e67 −1.56770
\(562\) −1.99927e67 −0.855720
\(563\) −2.90085e67 −1.18869 −0.594346 0.804209i \(-0.702589\pi\)
−0.594346 + 0.804209i \(0.702589\pi\)
\(564\) −4.03240e66 −0.158207
\(565\) 6.46783e67 2.42981
\(566\) 3.48018e67 1.25199
\(567\) 3.17830e67 1.09499
\(568\) −1.21121e67 −0.399654
\(569\) −4.00130e66 −0.126459 −0.0632296 0.997999i \(-0.520140\pi\)
−0.0632296 + 0.997999i \(0.520140\pi\)
\(570\) 4.91166e67 1.48694
\(571\) −4.01640e67 −1.16480 −0.582401 0.812902i \(-0.697887\pi\)
−0.582401 + 0.812902i \(0.697887\pi\)
\(572\) −2.01864e67 −0.560863
\(573\) 7.66932e67 2.04159
\(574\) −1.83657e66 −0.0468453
\(575\) −9.84116e67 −2.40538
\(576\) 4.88910e66 0.114519
\(577\) −4.66796e67 −1.04790 −0.523950 0.851749i \(-0.675542\pi\)
−0.523950 + 0.851749i \(0.675542\pi\)
\(578\) −1.63118e67 −0.350970
\(579\) −3.96586e67 −0.817924
\(580\) 2.54511e66 0.0503177
\(581\) −4.42432e67 −0.838554
\(582\) −8.56136e67 −1.55571
\(583\) 1.31656e68 2.29382
\(584\) −2.44589e67 −0.408623
\(585\) −7.02799e67 −1.12593
\(586\) 7.33351e67 1.12673
\(587\) 2.48745e67 0.366539 0.183270 0.983063i \(-0.441332\pi\)
0.183270 + 0.983063i \(0.441332\pi\)
\(588\) −1.66673e66 −0.0235571
\(589\) −1.59251e67 −0.215902
\(590\) 1.67741e68 2.18155
\(591\) −4.30830e67 −0.537542
\(592\) 1.98747e67 0.237913
\(593\) 4.14071e66 0.0475592 0.0237796 0.999717i \(-0.492430\pi\)
0.0237796 + 0.999717i \(0.492430\pi\)
\(594\) −1.18833e67 −0.130969
\(595\) −1.19299e68 −1.26175
\(596\) 7.47279e67 0.758489
\(597\) 9.39940e67 0.915649
\(598\) −6.21650e67 −0.581256
\(599\) 2.10487e68 1.88915 0.944577 0.328291i \(-0.106473\pi\)
0.944577 + 0.328291i \(0.106473\pi\)
\(600\) −1.16838e68 −1.00665
\(601\) 1.59794e68 1.32171 0.660854 0.750514i \(-0.270194\pi\)
0.660854 + 0.750514i \(0.270194\pi\)
\(602\) 3.01061e67 0.239079
\(603\) 6.47941e67 0.494039
\(604\) −8.38300e66 −0.0613754
\(605\) −3.84615e68 −2.70408
\(606\) −2.76660e68 −1.86796
\(607\) 2.59164e68 1.68055 0.840275 0.542160i \(-0.182393\pi\)
0.840275 + 0.542160i \(0.182393\pi\)
\(608\) 2.46614e67 0.153596
\(609\) −1.35431e67 −0.0810205
\(610\) 5.56371e67 0.319730
\(611\) 2.91042e67 0.160674
\(612\) −6.12934e67 −0.325090
\(613\) −5.81382e67 −0.296265 −0.148132 0.988968i \(-0.547326\pi\)
−0.148132 + 0.988968i \(0.547326\pi\)
\(614\) −7.87666e67 −0.385671
\(615\) 3.35125e67 0.157676
\(616\) 1.26891e68 0.573725
\(617\) −3.39743e68 −1.47626 −0.738131 0.674657i \(-0.764291\pi\)
−0.738131 + 0.674657i \(0.764291\pi\)
\(618\) −4.94262e67 −0.206414
\(619\) 3.60992e67 0.144903 0.0724514 0.997372i \(-0.476918\pi\)
0.0724514 + 0.997372i \(0.476918\pi\)
\(620\) 5.62997e67 0.217225
\(621\) −3.65950e67 −0.135731
\(622\) −1.90405e68 −0.678912
\(623\) −3.58704e68 −1.22964
\(624\) −7.38046e67 −0.243254
\(625\) 3.70404e68 1.17386
\(626\) 3.75985e68 1.14578
\(627\) 6.54948e68 1.91934
\(628\) −2.01663e67 −0.0568349
\(629\) −2.49164e68 −0.675373
\(630\) 4.41777e68 1.15175
\(631\) −1.97407e68 −0.495044 −0.247522 0.968882i \(-0.579616\pi\)
−0.247522 + 0.968882i \(0.579616\pi\)
\(632\) 6.07040e67 0.146436
\(633\) −3.82106e67 −0.0886733
\(634\) −3.30984e68 −0.738959
\(635\) 2.60069e68 0.558640
\(636\) 4.81352e68 0.994864
\(637\) 1.20298e67 0.0239245
\(638\) 3.39379e67 0.0649498
\(639\) −5.62301e68 −1.03561
\(640\) −8.71853e67 −0.154537
\(641\) −8.01714e67 −0.136772 −0.0683861 0.997659i \(-0.521785\pi\)
−0.0683861 + 0.997659i \(0.521785\pi\)
\(642\) −5.26628e68 −0.864760
\(643\) 1.38094e67 0.0218276 0.0109138 0.999940i \(-0.496526\pi\)
0.0109138 + 0.999940i \(0.496526\pi\)
\(644\) 3.90767e68 0.594586
\(645\) −5.49357e68 −0.804715
\(646\) −3.09174e68 −0.436020
\(647\) −3.29500e67 −0.0447405 −0.0223702 0.999750i \(-0.507121\pi\)
−0.0223702 + 0.999750i \(0.507121\pi\)
\(648\) −2.91195e68 −0.380712
\(649\) 2.23675e69 2.81593
\(650\) 8.43287e68 1.02235
\(651\) −2.99584e68 −0.349771
\(652\) −2.42854e68 −0.273074
\(653\) −1.29443e69 −1.40186 −0.700929 0.713231i \(-0.747231\pi\)
−0.700929 + 0.713231i \(0.747231\pi\)
\(654\) 3.59655e68 0.375172
\(655\) −7.73833e68 −0.777563
\(656\) 1.68266e67 0.0162874
\(657\) −1.13550e69 −1.05885
\(658\) −1.82948e68 −0.164359
\(659\) −1.29161e69 −1.11799 −0.558995 0.829171i \(-0.688813\pi\)
−0.558995 + 0.829171i \(0.688813\pi\)
\(660\) −2.31543e69 −1.93110
\(661\) 9.63417e68 0.774245 0.387123 0.922028i \(-0.373469\pi\)
0.387123 + 0.922028i \(0.373469\pi\)
\(662\) −1.42403e68 −0.110280
\(663\) 9.25269e68 0.690536
\(664\) 4.05356e68 0.291554
\(665\) 2.22840e69 1.54476
\(666\) 9.22677e68 0.616497
\(667\) 1.04513e68 0.0673114
\(668\) 5.09116e67 0.0316077
\(669\) 4.54158e69 2.71811
\(670\) −1.15545e69 −0.666679
\(671\) 7.41896e68 0.412706
\(672\) 4.63933e68 0.248833
\(673\) 8.62520e68 0.446067 0.223034 0.974811i \(-0.428404\pi\)
0.223034 + 0.974811i \(0.428404\pi\)
\(674\) −1.90784e69 −0.951426
\(675\) 4.96422e68 0.238731
\(676\) −5.45421e68 −0.252952
\(677\) −2.63131e69 −1.17693 −0.588464 0.808524i \(-0.700267\pi\)
−0.588464 + 0.808524i \(0.700267\pi\)
\(678\) 3.15327e69 1.36030
\(679\) −3.88425e69 −1.61621
\(680\) 1.09302e69 0.438692
\(681\) −1.20147e69 −0.465167
\(682\) 7.50732e68 0.280393
\(683\) 1.91092e69 0.688551 0.344275 0.938869i \(-0.388125\pi\)
0.344275 + 0.938869i \(0.388125\pi\)
\(684\) 1.14490e69 0.398010
\(685\) −6.69082e69 −2.24420
\(686\) 2.14612e69 0.694566
\(687\) −9.63727e68 −0.300964
\(688\) −2.75832e68 −0.0831243
\(689\) −3.47420e69 −1.01038
\(690\) −7.13047e69 −2.00132
\(691\) −3.63593e69 −0.984926 −0.492463 0.870333i \(-0.663903\pi\)
−0.492463 + 0.870333i \(0.663903\pi\)
\(692\) 2.27841e69 0.595706
\(693\) 5.89090e69 1.48668
\(694\) 3.11150e69 0.757989
\(695\) 4.84337e69 1.13899
\(696\) 1.24082e68 0.0281697
\(697\) −2.10951e68 −0.0462358
\(698\) 2.93585e69 0.621263
\(699\) −4.16216e69 −0.850409
\(700\) −5.30087e69 −1.04579
\(701\) 8.99753e69 1.71408 0.857041 0.515248i \(-0.172300\pi\)
0.857041 + 0.515248i \(0.172300\pi\)
\(702\) 3.13582e68 0.0576888
\(703\) 4.65414e69 0.826863
\(704\) −1.16258e69 −0.199476
\(705\) 3.33832e69 0.553215
\(706\) −7.49573e69 −1.19977
\(707\) −1.25519e70 −1.94060
\(708\) 8.17789e69 1.22131
\(709\) −7.36602e69 −1.06267 −0.531337 0.847160i \(-0.678310\pi\)
−0.531337 + 0.847160i \(0.678310\pi\)
\(710\) 1.00273e70 1.39751
\(711\) 2.81817e69 0.379457
\(712\) 3.28644e69 0.427529
\(713\) 2.31191e69 0.290588
\(714\) −5.81621e69 −0.706372
\(715\) 1.67118e70 1.96122
\(716\) −2.68235e69 −0.304191
\(717\) 1.26890e70 1.39062
\(718\) −1.03242e70 −1.09347
\(719\) −7.15587e69 −0.732495 −0.366247 0.930518i \(-0.619358\pi\)
−0.366247 + 0.930518i \(0.619358\pi\)
\(720\) −4.04756e69 −0.400449
\(721\) −2.24244e69 −0.214441
\(722\) −1.87466e69 −0.173285
\(723\) −9.55058e69 −0.853378
\(724\) 4.43603e69 0.383177
\(725\) −1.41775e69 −0.118391
\(726\) −1.87512e70 −1.51384
\(727\) −1.60013e69 −0.124900 −0.0624501 0.998048i \(-0.519891\pi\)
−0.0624501 + 0.998048i \(0.519891\pi\)
\(728\) −3.34848e69 −0.252714
\(729\) −1.13171e70 −0.825866
\(730\) 2.02489e70 1.42887
\(731\) 3.45804e69 0.235968
\(732\) 2.71248e69 0.178997
\(733\) 2.09305e69 0.133577 0.0667887 0.997767i \(-0.478725\pi\)
0.0667887 + 0.997767i \(0.478725\pi\)
\(734\) 2.99304e69 0.184739
\(735\) 1.37984e69 0.0823740
\(736\) −3.58021e69 −0.206729
\(737\) −1.54073e70 −0.860546
\(738\) 7.81173e68 0.0422052
\(739\) 2.82972e70 1.47895 0.739477 0.673182i \(-0.235073\pi\)
0.739477 + 0.673182i \(0.235073\pi\)
\(740\) −1.64537e70 −0.831930
\(741\) −1.72831e70 −0.845427
\(742\) 2.18387e70 1.03355
\(743\) 3.69750e70 1.69310 0.846550 0.532310i \(-0.178676\pi\)
0.846550 + 0.532310i \(0.178676\pi\)
\(744\) 2.74478e69 0.121611
\(745\) −6.18653e70 −2.65227
\(746\) −1.03232e69 −0.0428267
\(747\) 1.88186e70 0.755495
\(748\) 1.45749e70 0.566261
\(749\) −2.38928e70 −0.898386
\(750\) 4.97007e70 1.80868
\(751\) 3.61337e70 1.27272 0.636361 0.771391i \(-0.280439\pi\)
0.636361 + 0.771391i \(0.280439\pi\)
\(752\) 1.67617e69 0.0571452
\(753\) −1.48894e70 −0.491361
\(754\) −8.95572e68 −0.0286090
\(755\) 6.94006e69 0.214616
\(756\) −1.97116e69 −0.0590118
\(757\) 3.99376e70 1.15753 0.578766 0.815493i \(-0.303534\pi\)
0.578766 + 0.815493i \(0.303534\pi\)
\(758\) −3.25351e70 −0.912969
\(759\) −9.50816e70 −2.58329
\(760\) −2.04165e70 −0.537093
\(761\) 6.65810e70 1.69600 0.848000 0.529996i \(-0.177807\pi\)
0.848000 + 0.529996i \(0.177807\pi\)
\(762\) 1.26791e70 0.312747
\(763\) 1.63173e70 0.389761
\(764\) −3.18794e70 −0.737435
\(765\) 5.07432e70 1.13677
\(766\) 8.25940e68 0.0179202
\(767\) −5.90246e70 −1.24036
\(768\) −4.25055e69 −0.0865157
\(769\) −5.73078e70 −1.12984 −0.564922 0.825144i \(-0.691094\pi\)
−0.564922 + 0.825144i \(0.691094\pi\)
\(770\) −1.05050e71 −2.00619
\(771\) 9.43066e69 0.174466
\(772\) 1.64851e70 0.295439
\(773\) −6.58392e70 −1.14311 −0.571553 0.820565i \(-0.693659\pi\)
−0.571553 + 0.820565i \(0.693659\pi\)
\(774\) −1.28055e70 −0.215398
\(775\) −3.13618e70 −0.511104
\(776\) 3.55874e70 0.561933
\(777\) 8.75540e70 1.33956
\(778\) 2.55688e70 0.379062
\(779\) 3.94036e69 0.0566068
\(780\) 6.11009e70 0.850608
\(781\) 1.33709e71 1.80389
\(782\) 4.48841e70 0.586850
\(783\) −5.27201e68 −0.00668056
\(784\) 6.92819e68 0.00850896
\(785\) 1.66952e70 0.198739
\(786\) −3.77267e70 −0.435308
\(787\) 1.47428e71 1.64892 0.824460 0.565920i \(-0.191479\pi\)
0.824460 + 0.565920i \(0.191479\pi\)
\(788\) 1.79085e70 0.194163
\(789\) −1.01770e71 −1.06963
\(790\) −5.02552e70 −0.512056
\(791\) 1.43062e71 1.41319
\(792\) −5.39724e70 −0.516897
\(793\) −1.95776e70 −0.181788
\(794\) −7.08231e70 −0.637636
\(795\) −3.98499e71 −3.47882
\(796\) −3.90709e70 −0.330738
\(797\) 3.58327e70 0.294138 0.147069 0.989126i \(-0.453016\pi\)
0.147069 + 0.989126i \(0.453016\pi\)
\(798\) 1.08641e71 0.864815
\(799\) −2.10137e70 −0.162220
\(800\) 4.85666e70 0.363607
\(801\) 1.52572e71 1.10784
\(802\) 1.19119e71 0.838895
\(803\) 2.70010e71 1.84437
\(804\) −5.63315e70 −0.373231
\(805\) −3.23506e71 −2.07914
\(806\) −1.98107e70 −0.123507
\(807\) −3.02122e71 −1.82717
\(808\) 1.15001e71 0.674718
\(809\) 4.95238e70 0.281887 0.140943 0.990018i \(-0.454986\pi\)
0.140943 + 0.990018i \(0.454986\pi\)
\(810\) 2.41073e71 1.33127
\(811\) −3.54799e71 −1.90095 −0.950477 0.310796i \(-0.899404\pi\)
−0.950477 + 0.310796i \(0.899404\pi\)
\(812\) 5.62953e69 0.0292651
\(813\) 1.27002e71 0.640607
\(814\) −2.19403e71 −1.07385
\(815\) 2.01053e71 0.954880
\(816\) 5.32880e70 0.245596
\(817\) −6.45928e70 −0.288897
\(818\) −7.04522e70 −0.305801
\(819\) −1.55452e71 −0.654850
\(820\) −1.39303e70 −0.0569537
\(821\) −1.95327e71 −0.775095 −0.387547 0.921850i \(-0.626678\pi\)
−0.387547 + 0.921850i \(0.626678\pi\)
\(822\) −3.26198e71 −1.25638
\(823\) 2.05807e71 0.769421 0.384710 0.923037i \(-0.374301\pi\)
0.384710 + 0.923037i \(0.374301\pi\)
\(824\) 2.05452e70 0.0745581
\(825\) 1.28981e72 4.54364
\(826\) 3.71027e71 1.26880
\(827\) −8.99522e70 −0.298625 −0.149313 0.988790i \(-0.547706\pi\)
−0.149313 + 0.988790i \(0.547706\pi\)
\(828\) −1.66210e71 −0.535691
\(829\) −4.10043e71 −1.28305 −0.641526 0.767102i \(-0.721698\pi\)
−0.641526 + 0.767102i \(0.721698\pi\)
\(830\) −3.35583e71 −1.01950
\(831\) 3.50750e71 1.03460
\(832\) 3.06787e70 0.0878650
\(833\) −8.68569e69 −0.0241547
\(834\) 2.36129e71 0.637648
\(835\) −4.21483e70 −0.110525
\(836\) −2.72245e71 −0.693277
\(837\) −1.16621e70 −0.0288405
\(838\) 4.20096e71 1.00895
\(839\) −6.23847e69 −0.0145516 −0.00727579 0.999974i \(-0.502316\pi\)
−0.00727579 + 0.999974i \(0.502316\pi\)
\(840\) −3.84078e71 −0.870115
\(841\) −4.52961e71 −0.996687
\(842\) −3.38912e70 −0.0724337
\(843\) 8.06932e71 1.67518
\(844\) 1.58832e70 0.0320293
\(845\) 4.51540e71 0.884518
\(846\) 7.78157e70 0.148079
\(847\) −8.50731e71 −1.57271
\(848\) −2.00086e71 −0.359351
\(849\) −1.40465e72 −2.45092
\(850\) −6.08866e71 −1.03219
\(851\) −6.75661e71 −1.11290
\(852\) 4.88860e71 0.782375
\(853\) 1.20122e72 1.86798 0.933989 0.357301i \(-0.116303\pi\)
0.933989 + 0.357301i \(0.116303\pi\)
\(854\) 1.23064e71 0.185957
\(855\) −9.47834e71 −1.39175
\(856\) 2.18906e71 0.312356
\(857\) 3.84535e71 0.533219 0.266610 0.963805i \(-0.414097\pi\)
0.266610 + 0.963805i \(0.414097\pi\)
\(858\) 8.14752e71 1.09796
\(859\) 4.56460e71 0.597820 0.298910 0.954281i \(-0.403377\pi\)
0.298910 + 0.954281i \(0.403377\pi\)
\(860\) 2.28354e71 0.290668
\(861\) 7.41264e70 0.0917056
\(862\) −1.08326e72 −1.30259
\(863\) 9.22876e71 1.07865 0.539323 0.842099i \(-0.318680\pi\)
0.539323 + 0.842099i \(0.318680\pi\)
\(864\) 1.80598e70 0.0205176
\(865\) −1.88623e72 −2.08306
\(866\) 9.47004e71 1.01663
\(867\) 6.58368e71 0.687070
\(868\) 1.24530e71 0.126339
\(869\) −6.70131e71 −0.660960
\(870\) −1.02724e71 −0.0985033
\(871\) 4.06578e71 0.379052
\(872\) −1.49499e71 −0.135514
\(873\) 1.65214e72 1.45612
\(874\) −8.38392e71 −0.718484
\(875\) 2.25490e72 1.87901
\(876\) 9.87196e71 0.799931
\(877\) 1.86935e72 1.47299 0.736496 0.676442i \(-0.236479\pi\)
0.736496 + 0.676442i \(0.236479\pi\)
\(878\) 7.37861e71 0.565404
\(879\) −2.95991e72 −2.20572
\(880\) 9.62466e71 0.697525
\(881\) −2.06246e72 −1.45370 −0.726850 0.686796i \(-0.759017\pi\)
−0.726850 + 0.686796i \(0.759017\pi\)
\(882\) 3.21640e70 0.0220490
\(883\) 1.01095e72 0.674051 0.337026 0.941495i \(-0.390579\pi\)
0.337026 + 0.941495i \(0.390579\pi\)
\(884\) −3.84611e71 −0.249426
\(885\) −6.77026e72 −4.27066
\(886\) 9.13338e71 0.560409
\(887\) 3.84733e71 0.229631 0.114815 0.993387i \(-0.463372\pi\)
0.114815 + 0.993387i \(0.463372\pi\)
\(888\) −8.02169e71 −0.465745
\(889\) 5.75247e71 0.324908
\(890\) −2.72076e72 −1.49498
\(891\) 3.21460e72 1.71839
\(892\) −1.88782e72 −0.981798
\(893\) 3.92515e71 0.198607
\(894\) −3.01612e72 −1.48484
\(895\) 2.22064e72 1.06369
\(896\) −1.92845e71 −0.0898799
\(897\) 2.50907e72 1.13788
\(898\) 1.09384e72 0.482708
\(899\) 3.33062e70 0.0143025
\(900\) 2.25469e72 0.942206
\(901\) 2.50843e72 1.02010
\(902\) −1.85755e71 −0.0735156
\(903\) −1.21513e72 −0.468027
\(904\) −1.31073e72 −0.491347
\(905\) −3.67247e72 −1.33989
\(906\) 3.38349e71 0.120150
\(907\) −1.65047e72 −0.570465 −0.285232 0.958458i \(-0.592071\pi\)
−0.285232 + 0.958458i \(0.592071\pi\)
\(908\) 4.99421e71 0.168021
\(909\) 5.33888e72 1.74838
\(910\) 2.77212e72 0.883684
\(911\) 1.74723e72 0.542188 0.271094 0.962553i \(-0.412614\pi\)
0.271094 + 0.962553i \(0.412614\pi\)
\(912\) −9.95369e71 −0.300684
\(913\) −4.47485e72 −1.31597
\(914\) 2.75856e72 0.789771
\(915\) −2.24559e72 −0.625913
\(916\) 4.00597e71 0.108710
\(917\) −1.71164e72 −0.452235
\(918\) −2.26411e71 −0.0582441
\(919\) −2.26784e72 −0.568044 −0.284022 0.958818i \(-0.591669\pi\)
−0.284022 + 0.958818i \(0.591669\pi\)
\(920\) 2.96396e72 0.722887
\(921\) 3.17913e72 0.755000
\(922\) 1.21018e72 0.279861
\(923\) −3.52839e72 −0.794576
\(924\) −5.12150e72 −1.12314
\(925\) 9.16554e72 1.95743
\(926\) 3.26353e72 0.678763
\(927\) 9.53809e71 0.193200
\(928\) −5.15777e70 −0.0101751
\(929\) −5.22436e72 −1.00380 −0.501901 0.864925i \(-0.667366\pi\)
−0.501901 + 0.864925i \(0.667366\pi\)
\(930\) −2.27233e72 −0.425246
\(931\) 1.62240e71 0.0295728
\(932\) 1.73011e72 0.307173
\(933\) 7.68500e72 1.32906
\(934\) −1.31608e72 −0.221710
\(935\) −1.20662e73 −1.98009
\(936\) 1.42425e72 0.227682
\(937\) 2.17978e72 0.339464 0.169732 0.985490i \(-0.445710\pi\)
0.169732 + 0.985490i \(0.445710\pi\)
\(938\) −2.55573e72 −0.387745
\(939\) −1.51753e73 −2.24300
\(940\) −1.38765e72 −0.199825
\(941\) −6.39953e72 −0.897847 −0.448924 0.893570i \(-0.648192\pi\)
−0.448924 + 0.893570i \(0.648192\pi\)
\(942\) 8.13940e71 0.111262
\(943\) −5.72040e71 −0.0761885
\(944\) −3.39934e72 −0.441145
\(945\) 1.63188e72 0.206352
\(946\) 3.04500e72 0.375193
\(947\) 8.32607e72 0.999691 0.499845 0.866115i \(-0.333390\pi\)
0.499845 + 0.866115i \(0.333390\pi\)
\(948\) −2.45010e72 −0.286668
\(949\) −7.12517e72 −0.812406
\(950\) 1.13730e73 1.26371
\(951\) 1.33590e73 1.44661
\(952\) 2.41765e72 0.255146
\(953\) 1.86907e73 1.92243 0.961214 0.275804i \(-0.0889441\pi\)
0.961214 + 0.275804i \(0.0889441\pi\)
\(954\) −9.28896e72 −0.931176
\(955\) 2.63922e73 2.57865
\(956\) −5.27452e72 −0.502301
\(957\) −1.36978e72 −0.127148
\(958\) −6.50300e72 −0.588381
\(959\) −1.47994e73 −1.30524
\(960\) 3.51892e72 0.302527
\(961\) −1.11955e73 −0.938255
\(962\) 5.78973e72 0.473008
\(963\) 1.01627e73 0.809401
\(964\) 3.96994e72 0.308245
\(965\) −1.36476e73 −1.03309
\(966\) −1.57719e73 −1.16398
\(967\) 7.70074e72 0.554095 0.277047 0.960856i \(-0.410644\pi\)
0.277047 + 0.960856i \(0.410644\pi\)
\(968\) 7.79439e72 0.546809
\(969\) 1.24787e73 0.853564
\(970\) −2.94619e73 −1.96496
\(971\) 2.89962e72 0.188569 0.0942845 0.995545i \(-0.469944\pi\)
0.0942845 + 0.995545i \(0.469944\pi\)
\(972\) 1.08379e73 0.687260
\(973\) 1.07131e73 0.662444
\(974\) 1.35820e73 0.818975
\(975\) −3.40362e73 −2.00137
\(976\) −1.12751e72 −0.0646547
\(977\) 1.83564e73 1.02653 0.513263 0.858231i \(-0.328437\pi\)
0.513263 + 0.858231i \(0.328437\pi\)
\(978\) 9.80194e72 0.534577
\(979\) −3.62801e73 −1.92971
\(980\) −5.73567e71 −0.0297540
\(981\) −6.94048e72 −0.351155
\(982\) −1.94483e73 −0.959733
\(983\) −1.42481e73 −0.685799 −0.342900 0.939372i \(-0.611409\pi\)
−0.342900 + 0.939372i \(0.611409\pi\)
\(984\) −6.79146e71 −0.0318848
\(985\) −1.48260e73 −0.678947
\(986\) 6.46617e71 0.0288843
\(987\) 7.38403e72 0.321753
\(988\) 7.18416e72 0.305373
\(989\) 9.37722e72 0.388834
\(990\) 4.46823e73 1.80748
\(991\) −1.87344e73 −0.739323 −0.369662 0.929166i \(-0.620526\pi\)
−0.369662 + 0.929166i \(0.620526\pi\)
\(992\) −1.14094e72 −0.0439265
\(993\) 5.74758e72 0.215888
\(994\) 2.21794e73 0.812798
\(995\) 3.23458e73 1.15652
\(996\) −1.63607e73 −0.570753
\(997\) −4.87977e73 −1.66099 −0.830497 0.557023i \(-0.811943\pi\)
−0.830497 + 0.557023i \(0.811943\pi\)
\(998\) 3.33489e73 1.10760
\(999\) 3.40827e72 0.110453
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 \(a_p\))