Properties

Label 2.50.a.b.1.3
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 1.3
Root \(4.17763e7\)
Character \(\chi\) = 2.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.67772e7 q^{2}\) \(+7.94355e11 q^{3}\) \(+2.81475e14 q^{4}\) \(-5.65262e16 q^{5}\) \(+1.33271e19 q^{6}\) \(-4.38546e20 q^{7}\) \(+4.72237e21 q^{8}\) \(+3.91700e23 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.67772e7 q^{2}\) \(+7.94355e11 q^{3}\) \(+2.81475e14 q^{4}\) \(-5.65262e16 q^{5}\) \(+1.33271e19 q^{6}\) \(-4.38546e20 q^{7}\) \(+4.72237e21 q^{8}\) \(+3.91700e23 q^{9}\) \(-9.48353e23 q^{10}\) \(+5.68225e25 q^{11}\) \(+2.23591e26 q^{12}\) \(+1.61873e27 q^{13}\) \(-7.35759e27 q^{14}\) \(-4.49019e28 q^{15}\) \(+7.92282e28 q^{16}\) \(+2.39583e30 q^{17}\) \(+6.57164e30 q^{18}\) \(-9.22680e30 q^{19}\) \(-1.59107e31 q^{20}\) \(-3.48361e32 q^{21}\) \(+9.53324e32 q^{22}\) \(-1.45988e33 q^{23}\) \(+3.75123e33 q^{24}\) \(-1.45684e34 q^{25}\) \(+2.71577e34 q^{26}\) \(+1.21060e35 q^{27}\) \(-1.23440e35 q^{28}\) \(+1.26757e36 q^{29}\) \(-7.53328e35 q^{30}\) \(-2.70852e36 q^{31}\) \(+1.32923e36 q^{32}\) \(+4.51372e37 q^{33}\) \(+4.01954e37 q^{34}\) \(+2.47894e37 q^{35}\) \(+1.10254e38 q^{36}\) \(-7.30159e37 q^{37}\) \(-1.54800e38 q^{38}\) \(+1.28584e39 q^{39}\) \(-2.66938e38 q^{40}\) \(+1.21786e39 q^{41}\) \(-5.84453e39 q^{42}\) \(-1.71091e40 q^{43}\) \(+1.59941e40 q^{44}\) \(-2.21413e40 q^{45}\) \(-2.44928e40 q^{46}\) \(-1.04023e41 q^{47}\) \(+6.29353e40 q^{48}\) \(-6.46007e40 q^{49}\) \(-2.44416e41 q^{50}\) \(+1.90314e42 q^{51}\) \(+4.55631e41 q^{52}\) \(-1.17198e41 q^{53}\) \(+2.03105e42 q^{54}\) \(-3.21196e42 q^{55}\) \(-2.07098e42 q^{56}\) \(-7.32935e42 q^{57}\) \(+2.12663e43 q^{58}\) \(-8.71601e42 q^{59}\) \(-1.26388e43 q^{60}\) \(-2.61290e43 q^{61}\) \(-4.54414e43 q^{62}\) \(-1.71779e44 q^{63}\) \(+2.23007e43 q^{64}\) \(-9.15004e43 q^{65}\) \(+7.57277e44 q^{66}\) \(+3.87604e44 q^{67}\) \(+6.74368e44 q^{68}\) \(-1.15966e45 q^{69}\) \(+4.15897e44 q^{70}\) \(+2.06352e44 q^{71}\) \(+1.84975e45 q^{72}\) \(+4.21892e44 q^{73}\) \(-1.22500e45 q^{74}\) \(-1.15724e46 q^{75}\) \(-2.59711e45 q^{76}\) \(-2.49193e46 q^{77}\) \(+2.15728e46 q^{78}\) \(+8.65650e45 q^{79}\) \(-4.47847e45 q^{80}\) \(+2.43119e45 q^{81}\) \(+2.04322e46 q^{82}\) \(+1.57334e47 q^{83}\) \(-9.80550e46 q^{84}\) \(-1.35427e47 q^{85}\) \(-2.87044e47 q^{86}\) \(+1.00690e48 q^{87}\) \(+2.68337e47 q^{88}\) \(-2.35938e47 q^{89}\) \(-3.71470e47 q^{90}\) \(-7.09886e47 q^{91}\) \(-4.10921e47 q^{92}\) \(-2.15153e48 q^{93}\) \(-1.74522e48 q^{94}\) \(+5.21556e47 q^{95}\) \(+1.05588e48 q^{96}\) \(+1.57542e48 q^{97}\) \(-1.08382e48 q^{98}\) \(+2.22574e49 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(3q \) \(\mathstrut +\mathstrut 50331648q^{2} \) \(\mathstrut -\mathstrut 16203614388q^{3} \) \(\mathstrut +\mathstrut 844424930131968q^{4} \) \(\mathstrut -\mathstrut 101813016401840430q^{5} \) \(\mathstrut -\mathstrut 271851538568183808q^{6} \) \(\mathstrut -\mathstrut 125479179230203797096q^{7} \) \(\mathstrut +\mathstrut 14167099448608935641088q^{8} \) \(\mathstrut +\mathstrut 389432931519696922052199q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut 50331648q^{2} \) \(\mathstrut -\mathstrut 16203614388q^{3} \) \(\mathstrut +\mathstrut 844424930131968q^{4} \) \(\mathstrut -\mathstrut 101813016401840430q^{5} \) \(\mathstrut -\mathstrut 271851538568183808q^{6} \) \(\mathstrut -\mathstrut \)\(12\!\cdots\!96\)\(q^{7} \) \(\mathstrut +\mathstrut \)\(14\!\cdots\!88\)\(q^{8} \) \(\mathstrut +\mathstrut \)\(38\!\cdots\!99\)\(q^{9} \) \(\mathstrut -\mathstrut \)\(17\!\cdots\!80\)\(q^{10} \) \(\mathstrut -\mathstrut \)\(25\!\cdots\!04\)\(q^{11} \) \(\mathstrut -\mathstrut \)\(45\!\cdots\!28\)\(q^{12} \) \(\mathstrut +\mathstrut \)\(29\!\cdots\!42\)\(q^{13} \) \(\mathstrut -\mathstrut \)\(21\!\cdots\!36\)\(q^{14} \) \(\mathstrut +\mathstrut \)\(87\!\cdots\!80\)\(q^{15} \) \(\mathstrut +\mathstrut \)\(23\!\cdots\!08\)\(q^{16} \) \(\mathstrut +\mathstrut \)\(39\!\cdots\!54\)\(q^{17} \) \(\mathstrut +\mathstrut \)\(65\!\cdots\!84\)\(q^{18} \) \(\mathstrut +\mathstrut \)\(14\!\cdots\!80\)\(q^{19} \) \(\mathstrut -\mathstrut \)\(28\!\cdots\!80\)\(q^{20} \) \(\mathstrut -\mathstrut \)\(10\!\cdots\!84\)\(q^{21} \) \(\mathstrut -\mathstrut \)\(43\!\cdots\!64\)\(q^{22} \) \(\mathstrut -\mathstrut \)\(49\!\cdots\!08\)\(q^{23} \) \(\mathstrut -\mathstrut \)\(76\!\cdots\!48\)\(q^{24} \) \(\mathstrut +\mathstrut \)\(39\!\cdots\!25\)\(q^{25} \) \(\mathstrut +\mathstrut \)\(49\!\cdots\!72\)\(q^{26} \) \(\mathstrut +\mathstrut \)\(19\!\cdots\!00\)\(q^{27} \) \(\mathstrut -\mathstrut \)\(35\!\cdots\!76\)\(q^{28} \) \(\mathstrut +\mathstrut \)\(93\!\cdots\!30\)\(q^{29} \) \(\mathstrut +\mathstrut \)\(14\!\cdots\!80\)\(q^{30} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!56\)\(q^{31} \) \(\mathstrut +\mathstrut \)\(39\!\cdots\!28\)\(q^{32} \) \(\mathstrut +\mathstrut \)\(84\!\cdots\!84\)\(q^{33} \) \(\mathstrut +\mathstrut \)\(65\!\cdots\!64\)\(q^{34} \) \(\mathstrut +\mathstrut \)\(30\!\cdots\!60\)\(q^{35} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!44\)\(q^{36} \) \(\mathstrut +\mathstrut \)\(30\!\cdots\!74\)\(q^{37} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!80\)\(q^{38} \) \(\mathstrut +\mathstrut \)\(36\!\cdots\!68\)\(q^{39} \) \(\mathstrut -\mathstrut \)\(48\!\cdots\!80\)\(q^{40} \) \(\mathstrut -\mathstrut \)\(11\!\cdots\!54\)\(q^{41} \) \(\mathstrut -\mathstrut \)\(18\!\cdots\!44\)\(q^{42} \) \(\mathstrut -\mathstrut \)\(17\!\cdots\!48\)\(q^{43} \) \(\mathstrut -\mathstrut \)\(72\!\cdots\!24\)\(q^{44} \) \(\mathstrut -\mathstrut \)\(11\!\cdots\!90\)\(q^{45} \) \(\mathstrut -\mathstrut \)\(83\!\cdots\!28\)\(q^{46} \) \(\mathstrut -\mathstrut \)\(21\!\cdots\!56\)\(q^{47} \) \(\mathstrut -\mathstrut \)\(12\!\cdots\!68\)\(q^{48} \) \(\mathstrut +\mathstrut \)\(37\!\cdots\!51\)\(q^{49} \) \(\mathstrut +\mathstrut \)\(66\!\cdots\!00\)\(q^{50} \) \(\mathstrut +\mathstrut \)\(22\!\cdots\!16\)\(q^{51} \) \(\mathstrut +\mathstrut \)\(82\!\cdots\!52\)\(q^{52} \) \(\mathstrut +\mathstrut \)\(74\!\cdots\!02\)\(q^{53} \) \(\mathstrut +\mathstrut \)\(32\!\cdots\!00\)\(q^{54} \) \(\mathstrut +\mathstrut \)\(32\!\cdots\!40\)\(q^{55} \) \(\mathstrut -\mathstrut \)\(59\!\cdots\!16\)\(q^{56} \) \(\mathstrut -\mathstrut \)\(20\!\cdots\!80\)\(q^{57} \) \(\mathstrut +\mathstrut \)\(15\!\cdots\!80\)\(q^{58} \) \(\mathstrut -\mathstrut \)\(53\!\cdots\!40\)\(q^{59} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!80\)\(q^{60} \) \(\mathstrut -\mathstrut \)\(12\!\cdots\!94\)\(q^{61} \) \(\mathstrut +\mathstrut \)\(40\!\cdots\!96\)\(q^{62} \) \(\mathstrut -\mathstrut \)\(46\!\cdots\!68\)\(q^{63} \) \(\mathstrut +\mathstrut \)\(66\!\cdots\!48\)\(q^{64} \) \(\mathstrut -\mathstrut \)\(42\!\cdots\!20\)\(q^{65} \) \(\mathstrut +\mathstrut \)\(14\!\cdots\!44\)\(q^{66} \) \(\mathstrut +\mathstrut \)\(11\!\cdots\!24\)\(q^{67} \) \(\mathstrut +\mathstrut \)\(11\!\cdots\!24\)\(q^{68} \) \(\mathstrut +\mathstrut \)\(77\!\cdots\!68\)\(q^{69} \) \(\mathstrut +\mathstrut \)\(50\!\cdots\!60\)\(q^{70} \) \(\mathstrut -\mathstrut \)\(40\!\cdots\!24\)\(q^{71} \) \(\mathstrut +\mathstrut \)\(18\!\cdots\!04\)\(q^{72} \) \(\mathstrut -\mathstrut \)\(10\!\cdots\!18\)\(q^{73} \) \(\mathstrut +\mathstrut \)\(51\!\cdots\!84\)\(q^{74} \) \(\mathstrut -\mathstrut \)\(38\!\cdots\!00\)\(q^{75} \) \(\mathstrut +\mathstrut \)\(41\!\cdots\!80\)\(q^{76} \) \(\mathstrut -\mathstrut \)\(23\!\cdots\!72\)\(q^{77} \) \(\mathstrut +\mathstrut \)\(60\!\cdots\!88\)\(q^{78} \) \(\mathstrut +\mathstrut \)\(36\!\cdots\!60\)\(q^{79} \) \(\mathstrut -\mathstrut \)\(80\!\cdots\!80\)\(q^{80} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!17\)\(q^{81} \) \(\mathstrut -\mathstrut \)\(19\!\cdots\!64\)\(q^{82} \) \(\mathstrut +\mathstrut \)\(15\!\cdots\!92\)\(q^{83} \) \(\mathstrut -\mathstrut \)\(30\!\cdots\!04\)\(q^{84} \) \(\mathstrut +\mathstrut \)\(56\!\cdots\!60\)\(q^{85} \) \(\mathstrut -\mathstrut \)\(29\!\cdots\!68\)\(q^{86} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!20\)\(q^{87} \) \(\mathstrut -\mathstrut \)\(12\!\cdots\!84\)\(q^{88} \) \(\mathstrut +\mathstrut \)\(54\!\cdots\!70\)\(q^{89} \) \(\mathstrut -\mathstrut \)\(19\!\cdots\!40\)\(q^{90} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!44\)\(q^{91} \) \(\mathstrut -\mathstrut \)\(13\!\cdots\!48\)\(q^{92} \) \(\mathstrut -\mathstrut \)\(23\!\cdots\!76\)\(q^{93} \) \(\mathstrut -\mathstrut \)\(36\!\cdots\!96\)\(q^{94} \) \(\mathstrut -\mathstrut \)\(28\!\cdots\!00\)\(q^{95} \) \(\mathstrut -\mathstrut \)\(21\!\cdots\!88\)\(q^{96} \) \(\mathstrut +\mathstrut \)\(43\!\cdots\!14\)\(q^{97} \) \(\mathstrut +\mathstrut \)\(62\!\cdots\!16\)\(q^{98} \) \(\mathstrut +\mathstrut \)\(17\!\cdots\!68\)\(q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 7.94355e11 1.62384 0.811921 0.583767i \(-0.198422\pi\)
0.811921 + 0.583767i \(0.198422\pi\)
\(4\) 2.81475e14 0.500000
\(5\) −5.65262e16 −0.424116 −0.212058 0.977257i \(-0.568017\pi\)
−0.212058 + 0.977257i \(0.568017\pi\)
\(6\) 1.33271e19 1.14823
\(7\) −4.38546e20 −0.865194 −0.432597 0.901587i \(-0.642403\pi\)
−0.432597 + 0.901587i \(0.642403\pi\)
\(8\) 4.72237e21 0.353553
\(9\) 3.91700e23 1.63686
\(10\) −9.48353e23 −0.299895
\(11\) 5.68225e25 1.73940 0.869700 0.493580i \(-0.164312\pi\)
0.869700 + 0.493580i \(0.164312\pi\)
\(12\) 2.23591e26 0.811921
\(13\) 1.61873e27 0.827106 0.413553 0.910480i \(-0.364288\pi\)
0.413553 + 0.910480i \(0.364288\pi\)
\(14\) −7.35759e27 −0.611785
\(15\) −4.49019e28 −0.688698
\(16\) 7.92282e28 0.250000
\(17\) 2.39583e30 1.71182 0.855910 0.517124i \(-0.172997\pi\)
0.855910 + 0.517124i \(0.172997\pi\)
\(18\) 6.57164e30 1.15744
\(19\) −9.22680e30 −0.432104 −0.216052 0.976382i \(-0.569318\pi\)
−0.216052 + 0.976382i \(0.569318\pi\)
\(20\) −1.59107e31 −0.212058
\(21\) −3.48361e32 −1.40494
\(22\) 9.53324e32 1.22994
\(23\) −1.45988e33 −0.633849 −0.316925 0.948451i \(-0.602650\pi\)
−0.316925 + 0.948451i \(0.602650\pi\)
\(24\) 3.75123e33 0.574115
\(25\) −1.45684e34 −0.820125
\(26\) 2.71577e34 0.584852
\(27\) 1.21060e35 1.03416
\(28\) −1.23440e35 −0.432597
\(29\) 1.26757e36 1.88027 0.940135 0.340802i \(-0.110699\pi\)
0.940135 + 0.340802i \(0.110699\pi\)
\(30\) −7.53328e35 −0.486983
\(31\) −2.70852e36 −0.784099 −0.392049 0.919944i \(-0.628234\pi\)
−0.392049 + 0.919944i \(0.628234\pi\)
\(32\) 1.32923e36 0.176777
\(33\) 4.51372e37 2.82451
\(34\) 4.01954e37 1.21044
\(35\) 2.47894e37 0.366943
\(36\) 1.10254e38 0.818431
\(37\) −7.30159e37 −0.276997 −0.138499 0.990363i \(-0.544228\pi\)
−0.138499 + 0.990363i \(0.544228\pi\)
\(38\) −1.54800e38 −0.305544
\(39\) 1.28584e39 1.34309
\(40\) −2.66938e38 −0.149948
\(41\) 1.21786e39 0.373587 0.186793 0.982399i \(-0.440191\pi\)
0.186793 + 0.982399i \(0.440191\pi\)
\(42\) −5.84453e39 −0.993441
\(43\) −1.71091e40 −1.63400 −0.816998 0.576640i \(-0.804363\pi\)
−0.816998 + 0.576640i \(0.804363\pi\)
\(44\) 1.59941e40 0.869700
\(45\) −2.21413e40 −0.694220
\(46\) −2.44928e40 −0.448199
\(47\) −1.04023e41 −1.12392 −0.561958 0.827166i \(-0.689952\pi\)
−0.561958 + 0.827166i \(0.689952\pi\)
\(48\) 6.29353e40 0.405960
\(49\) −6.46007e40 −0.251439
\(50\) −2.44416e41 −0.579916
\(51\) 1.90314e42 2.77973
\(52\) 4.55631e41 0.413553
\(53\) −1.17198e41 −0.0667057 −0.0333528 0.999444i \(-0.510619\pi\)
−0.0333528 + 0.999444i \(0.510619\pi\)
\(54\) 2.03105e42 0.731264
\(55\) −3.21196e42 −0.737708
\(56\) −2.07098e42 −0.305892
\(57\) −7.32935e42 −0.701668
\(58\) 2.12663e43 1.32955
\(59\) −8.71601e42 −0.358462 −0.179231 0.983807i \(-0.557361\pi\)
−0.179231 + 0.983807i \(0.557361\pi\)
\(60\) −1.26388e43 −0.344349
\(61\) −2.61290e43 −0.474834 −0.237417 0.971408i \(-0.576301\pi\)
−0.237417 + 0.971408i \(0.576301\pi\)
\(62\) −4.54414e43 −0.554441
\(63\) −1.71779e44 −1.41620
\(64\) 2.23007e43 0.125000
\(65\) −9.15004e43 −0.350789
\(66\) 7.57277e44 1.99723
\(67\) 3.87604e44 0.707222 0.353611 0.935393i \(-0.384954\pi\)
0.353611 + 0.935393i \(0.384954\pi\)
\(68\) 6.74368e44 0.855910
\(69\) −1.15966e45 −1.02927
\(70\) 4.15897e44 0.259468
\(71\) 2.06352e44 0.0909449 0.0454724 0.998966i \(-0.485521\pi\)
0.0454724 + 0.998966i \(0.485521\pi\)
\(72\) 1.84975e45 0.578718
\(73\) 4.21892e44 0.0941438 0.0470719 0.998892i \(-0.485011\pi\)
0.0470719 + 0.998892i \(0.485011\pi\)
\(74\) −1.22500e45 −0.195867
\(75\) −1.15724e46 −1.33175
\(76\) −2.59711e45 −0.216052
\(77\) −2.49193e46 −1.50492
\(78\) 2.15728e46 0.949707
\(79\) 8.65650e45 0.278919 0.139460 0.990228i \(-0.455463\pi\)
0.139460 + 0.990228i \(0.455463\pi\)
\(80\) −4.47847e45 −0.106029
\(81\) 2.43119e45 0.0424557
\(82\) 2.04322e46 0.264166
\(83\) 1.57334e47 1.51150 0.755750 0.654860i \(-0.227272\pi\)
0.755750 + 0.654860i \(0.227272\pi\)
\(84\) −9.80550e46 −0.702469
\(85\) −1.35427e47 −0.726011
\(86\) −2.87044e47 −1.15541
\(87\) 1.00690e48 3.05326
\(88\) 2.68337e47 0.614971
\(89\) −2.35938e47 −0.409962 −0.204981 0.978766i \(-0.565713\pi\)
−0.204981 + 0.978766i \(0.565713\pi\)
\(90\) −3.71470e47 −0.490887
\(91\) −7.09886e47 −0.715607
\(92\) −4.10921e47 −0.316925
\(93\) −2.15153e48 −1.27325
\(94\) −1.74522e48 −0.794729
\(95\) 5.21556e47 0.183262
\(96\) 1.05588e48 0.287057
\(97\) 1.57542e48 0.332269 0.166135 0.986103i \(-0.446871\pi\)
0.166135 + 0.986103i \(0.446871\pi\)
\(98\) −1.08382e48 −0.177794
\(99\) 2.22574e49 2.84716
\(100\) −4.10063e48 −0.410063
\(101\) −2.10004e49 −1.64571 −0.822857 0.568248i \(-0.807621\pi\)
−0.822857 + 0.568248i \(0.807621\pi\)
\(102\) 3.19294e49 1.96556
\(103\) −3.08538e49 −1.49554 −0.747769 0.663960i \(-0.768875\pi\)
−0.747769 + 0.663960i \(0.768875\pi\)
\(104\) 7.64421e48 0.292426
\(105\) 1.96915e49 0.595857
\(106\) −1.96626e48 −0.0471680
\(107\) −1.65194e49 −0.314842 −0.157421 0.987532i \(-0.550318\pi\)
−0.157421 + 0.987532i \(0.550318\pi\)
\(108\) 3.40754e49 0.517082
\(109\) −9.19427e49 −1.11319 −0.556593 0.830785i \(-0.687892\pi\)
−0.556593 + 0.830785i \(0.687892\pi\)
\(110\) −5.38878e49 −0.521638
\(111\) −5.80005e49 −0.449800
\(112\) −3.47452e49 −0.216298
\(113\) 6.93766e49 0.347369 0.173685 0.984801i \(-0.444433\pi\)
0.173685 + 0.984801i \(0.444433\pi\)
\(114\) −1.22966e50 −0.496154
\(115\) 8.25217e49 0.268826
\(116\) 3.56789e50 0.940135
\(117\) 6.34055e50 1.35386
\(118\) −1.46230e50 −0.253471
\(119\) −1.05068e51 −1.48106
\(120\) −2.12043e50 −0.243491
\(121\) 2.16161e51 2.02552
\(122\) −4.38372e50 −0.335758
\(123\) 9.67409e50 0.606646
\(124\) −7.62381e50 −0.392049
\(125\) 1.82760e51 0.771945
\(126\) −2.88197e51 −1.00141
\(127\) −3.58918e51 −1.02755 −0.513776 0.857924i \(-0.671754\pi\)
−0.513776 + 0.857924i \(0.671754\pi\)
\(128\) 3.74144e50 0.0883883
\(129\) −1.35907e52 −2.65335
\(130\) −1.53512e51 −0.248045
\(131\) 8.30864e51 1.11271 0.556357 0.830944i \(-0.312199\pi\)
0.556357 + 0.830944i \(0.312199\pi\)
\(132\) 1.27050e52 1.41226
\(133\) 4.04638e51 0.373854
\(134\) 6.50292e51 0.500081
\(135\) −6.84308e51 −0.438605
\(136\) 1.13140e52 0.605220
\(137\) 1.87006e52 0.835989 0.417995 0.908449i \(-0.362733\pi\)
0.417995 + 0.908449i \(0.362733\pi\)
\(138\) −1.94559e52 −0.727805
\(139\) 7.10289e51 0.222624 0.111312 0.993785i \(-0.464495\pi\)
0.111312 + 0.993785i \(0.464495\pi\)
\(140\) 6.97759e51 0.183471
\(141\) −8.26315e52 −1.82506
\(142\) 3.46200e51 0.0643077
\(143\) 9.19800e52 1.43867
\(144\) 3.10337e52 0.409216
\(145\) −7.16508e52 −0.797453
\(146\) 7.07818e51 0.0665697
\(147\) −5.13159e52 −0.408298
\(148\) −2.05522e52 −0.138499
\(149\) −1.54238e53 −0.881308 −0.440654 0.897677i \(-0.645253\pi\)
−0.440654 + 0.897677i \(0.645253\pi\)
\(150\) −1.94153e53 −0.941692
\(151\) −2.11963e52 −0.0873626 −0.0436813 0.999046i \(-0.513909\pi\)
−0.0436813 + 0.999046i \(0.513909\pi\)
\(152\) −4.35723e52 −0.152772
\(153\) 9.38449e53 2.80201
\(154\) −4.18077e53 −1.06414
\(155\) 1.53102e53 0.332549
\(156\) 3.61932e53 0.671544
\(157\) 2.10086e53 0.333316 0.166658 0.986015i \(-0.446702\pi\)
0.166658 + 0.986015i \(0.446702\pi\)
\(158\) 1.45232e53 0.197226
\(159\) −9.30971e52 −0.108319
\(160\) −7.51362e52 −0.0749739
\(161\) 6.40226e53 0.548403
\(162\) 4.07886e52 0.0300207
\(163\) −2.57326e54 −1.62887 −0.814436 0.580253i \(-0.802954\pi\)
−0.814436 + 0.580253i \(0.802954\pi\)
\(164\) 3.42796e53 0.186793
\(165\) −2.55144e54 −1.19792
\(166\) 2.63962e54 1.06879
\(167\) 3.95831e53 0.138343 0.0691713 0.997605i \(-0.477964\pi\)
0.0691713 + 0.997605i \(0.477964\pi\)
\(168\) −1.64509e54 −0.496721
\(169\) −1.20995e54 −0.315896
\(170\) −2.27210e54 −0.513367
\(171\) −3.61414e54 −0.707294
\(172\) −4.81580e54 −0.816998
\(173\) 8.07344e54 1.18831 0.594154 0.804351i \(-0.297487\pi\)
0.594154 + 0.804351i \(0.297487\pi\)
\(174\) 1.68930e55 2.15898
\(175\) 6.38890e54 0.709568
\(176\) 4.50194e54 0.434850
\(177\) −6.92361e54 −0.582086
\(178\) −3.95839e54 −0.289887
\(179\) 1.08682e55 0.693841 0.346921 0.937894i \(-0.387227\pi\)
0.346921 + 0.937894i \(0.387227\pi\)
\(180\) −6.23223e54 −0.347110
\(181\) −9.05176e54 −0.440158 −0.220079 0.975482i \(-0.570631\pi\)
−0.220079 + 0.975482i \(0.570631\pi\)
\(182\) −1.19099e55 −0.506010
\(183\) −2.07557e55 −0.771055
\(184\) −6.89410e54 −0.224100
\(185\) 4.12731e54 0.117479
\(186\) −3.60966e55 −0.900325
\(187\) 1.36137e56 2.97754
\(188\) −2.92800e55 −0.561958
\(189\) −5.30905e55 −0.894752
\(190\) 8.75026e54 0.129586
\(191\) −9.68165e55 −1.26076 −0.630379 0.776287i \(-0.717101\pi\)
−0.630379 + 0.776287i \(0.717101\pi\)
\(192\) 1.77147e55 0.202980
\(193\) −5.34429e55 −0.539183 −0.269591 0.962975i \(-0.586889\pi\)
−0.269591 + 0.962975i \(0.586889\pi\)
\(194\) 2.64312e55 0.234950
\(195\) −7.26838e55 −0.569626
\(196\) −1.81835e55 −0.125720
\(197\) 2.48206e56 1.51492 0.757461 0.652880i \(-0.226439\pi\)
0.757461 + 0.652880i \(0.226439\pi\)
\(198\) 3.73417e56 2.01325
\(199\) 5.78065e55 0.275471 0.137736 0.990469i \(-0.456018\pi\)
0.137736 + 0.990469i \(0.456018\pi\)
\(200\) −6.87971e55 −0.289958
\(201\) 3.07895e56 1.14842
\(202\) −3.52329e56 −1.16370
\(203\) −5.55887e56 −1.62680
\(204\) 5.35687e56 1.38986
\(205\) −6.88408e55 −0.158444
\(206\) −5.17641e56 −1.05750
\(207\) −5.71836e56 −1.03752
\(208\) 1.28249e56 0.206776
\(209\) −5.24290e56 −0.751602
\(210\) 3.30369e56 0.421335
\(211\) 5.32965e54 0.00605032 0.00302516 0.999995i \(-0.499037\pi\)
0.00302516 + 0.999995i \(0.499037\pi\)
\(212\) −3.29884e55 −0.0333528
\(213\) 1.63916e56 0.147680
\(214\) −2.77150e56 −0.222627
\(215\) 9.67115e56 0.693004
\(216\) 5.71691e56 0.365632
\(217\) 1.18781e57 0.678397
\(218\) −1.54254e57 −0.787142
\(219\) 3.35132e56 0.152875
\(220\) −9.04087e56 −0.368854
\(221\) 3.87820e57 1.41586
\(222\) −9.73088e56 −0.318056
\(223\) 4.37480e57 1.28082 0.640412 0.768032i \(-0.278764\pi\)
0.640412 + 0.768032i \(0.278764\pi\)
\(224\) −5.82928e56 −0.152946
\(225\) −5.70642e57 −1.34243
\(226\) 1.16395e57 0.245627
\(227\) 2.82668e57 0.535357 0.267679 0.963508i \(-0.413743\pi\)
0.267679 + 0.963508i \(0.413743\pi\)
\(228\) −2.06303e57 −0.350834
\(229\) −7.37233e57 −1.12625 −0.563126 0.826371i \(-0.690401\pi\)
−0.563126 + 0.826371i \(0.690401\pi\)
\(230\) 1.38448e57 0.190089
\(231\) −1.97948e58 −2.44375
\(232\) 5.98592e57 0.664776
\(233\) 5.28015e57 0.527747 0.263874 0.964557i \(-0.415000\pi\)
0.263874 + 0.964557i \(0.415000\pi\)
\(234\) 1.06377e58 0.957322
\(235\) 5.88005e57 0.476671
\(236\) −2.45334e57 −0.179231
\(237\) 6.87633e57 0.452921
\(238\) −1.76276e58 −1.04727
\(239\) −1.17485e58 −0.629845 −0.314923 0.949117i \(-0.601979\pi\)
−0.314923 + 0.949117i \(0.601979\pi\)
\(240\) −3.55749e57 −0.172174
\(241\) 2.71621e58 1.18726 0.593631 0.804738i \(-0.297694\pi\)
0.593631 + 0.804738i \(0.297694\pi\)
\(242\) 3.62658e58 1.43226
\(243\) −2.70384e58 −0.965222
\(244\) −7.35466e57 −0.237417
\(245\) 3.65163e57 0.106639
\(246\) 1.62304e58 0.428963
\(247\) −1.49357e58 −0.357395
\(248\) −1.27906e58 −0.277221
\(249\) 1.24979e59 2.45444
\(250\) 3.06621e58 0.545847
\(251\) −3.65004e58 −0.589239 −0.294620 0.955615i \(-0.595193\pi\)
−0.294620 + 0.955615i \(0.595193\pi\)
\(252\) −4.83514e58 −0.708102
\(253\) −8.29542e58 −1.10252
\(254\) −6.02165e58 −0.726590
\(255\) −1.07577e59 −1.17893
\(256\) 6.27710e57 0.0625000
\(257\) −9.35018e57 −0.0846172 −0.0423086 0.999105i \(-0.513471\pi\)
−0.0423086 + 0.999105i \(0.513471\pi\)
\(258\) −2.28015e59 −1.87620
\(259\) 3.20209e58 0.239656
\(260\) −2.57551e58 −0.175394
\(261\) 4.96506e59 3.07774
\(262\) 1.39396e59 0.786807
\(263\) −8.31210e58 −0.427361 −0.213681 0.976904i \(-0.568545\pi\)
−0.213681 + 0.976904i \(0.568545\pi\)
\(264\) 2.13155e59 0.998616
\(265\) 6.62478e57 0.0282910
\(266\) 6.78870e58 0.264354
\(267\) −1.87419e59 −0.665713
\(268\) 1.09101e59 0.353611
\(269\) −4.44312e59 −1.31449 −0.657244 0.753678i \(-0.728278\pi\)
−0.657244 + 0.753678i \(0.728278\pi\)
\(270\) −1.14808e59 −0.310141
\(271\) 6.43014e59 1.58662 0.793309 0.608819i \(-0.208356\pi\)
0.793309 + 0.608819i \(0.208356\pi\)
\(272\) 1.89818e59 0.427955
\(273\) −5.63901e59 −1.16203
\(274\) 3.13743e59 0.591134
\(275\) −8.27811e59 −1.42653
\(276\) −3.26417e59 −0.514636
\(277\) 1.24422e60 1.79533 0.897663 0.440682i \(-0.145263\pi\)
0.897663 + 0.440682i \(0.145263\pi\)
\(278\) 1.19167e59 0.157419
\(279\) −1.06093e60 −1.28346
\(280\) 1.17064e59 0.129734
\(281\) 8.54992e59 0.868275 0.434137 0.900847i \(-0.357053\pi\)
0.434137 + 0.900847i \(0.357053\pi\)
\(282\) −1.38633e60 −1.29051
\(283\) −1.94873e60 −1.66335 −0.831677 0.555260i \(-0.812619\pi\)
−0.831677 + 0.555260i \(0.812619\pi\)
\(284\) 5.80828e58 0.0454724
\(285\) 4.14301e59 0.297589
\(286\) 1.54317e60 1.01729
\(287\) −5.34086e59 −0.323225
\(288\) 5.20659e59 0.289359
\(289\) 3.78119e60 1.93033
\(290\) −1.20210e60 −0.563884
\(291\) 1.25145e60 0.539553
\(292\) 1.18752e59 0.0470719
\(293\) −1.71967e60 −0.626887 −0.313443 0.949607i \(-0.601483\pi\)
−0.313443 + 0.949607i \(0.601483\pi\)
\(294\) −8.60937e59 −0.288710
\(295\) 4.92683e59 0.152030
\(296\) −3.44808e59 −0.0979333
\(297\) 6.87895e60 1.79882
\(298\) −2.58768e60 −0.623179
\(299\) −2.36315e60 −0.524260
\(300\) −3.25735e60 −0.665877
\(301\) 7.50315e60 1.41372
\(302\) −3.55615e59 −0.0617747
\(303\) −1.66818e61 −2.67238
\(304\) −7.31023e59 −0.108026
\(305\) 1.47697e60 0.201385
\(306\) 1.57446e61 1.98132
\(307\) −4.30346e59 −0.0499951 −0.0249976 0.999688i \(-0.507958\pi\)
−0.0249976 + 0.999688i \(0.507958\pi\)
\(308\) −7.01416e60 −0.752460
\(309\) −2.45089e61 −2.42852
\(310\) 2.56863e60 0.235148
\(311\) −4.46188e59 −0.0377475 −0.0188737 0.999822i \(-0.506008\pi\)
−0.0188737 + 0.999822i \(0.506008\pi\)
\(312\) 6.07222e60 0.474854
\(313\) 3.50202e60 0.253211 0.126605 0.991953i \(-0.459592\pi\)
0.126605 + 0.991953i \(0.459592\pi\)
\(314\) 3.52466e60 0.235690
\(315\) 9.71000e60 0.600635
\(316\) 2.43659e60 0.139460
\(317\) 8.94498e59 0.0473836 0.0236918 0.999719i \(-0.492458\pi\)
0.0236918 + 0.999719i \(0.492458\pi\)
\(318\) −1.56191e60 −0.0765934
\(319\) 7.20264e61 3.27054
\(320\) −1.26058e60 −0.0530145
\(321\) −1.31223e61 −0.511253
\(322\) 1.07412e61 0.387779
\(323\) −2.21059e61 −0.739684
\(324\) 6.84319e59 0.0212278
\(325\) −2.35822e61 −0.678330
\(326\) −4.31721e61 −1.15179
\(327\) −7.30351e61 −1.80764
\(328\) 5.75116e60 0.132083
\(329\) 4.56191e61 0.972405
\(330\) −4.28060e61 −0.847058
\(331\) 2.61998e61 0.481407 0.240704 0.970599i \(-0.422622\pi\)
0.240704 + 0.970599i \(0.422622\pi\)
\(332\) 4.42855e61 0.755750
\(333\) −2.86003e61 −0.453406
\(334\) 6.64094e60 0.0978230
\(335\) −2.19098e61 −0.299944
\(336\) −2.76000e61 −0.351235
\(337\) 1.36805e62 1.61872 0.809358 0.587316i \(-0.199815\pi\)
0.809358 + 0.587316i \(0.199815\pi\)
\(338\) −2.02997e61 −0.223372
\(339\) 5.51096e61 0.564073
\(340\) −3.81195e61 −0.363005
\(341\) −1.53905e62 −1.36386
\(342\) −6.06352e61 −0.500133
\(343\) 1.41003e62 1.08274
\(344\) −8.07956e61 −0.577705
\(345\) 6.55515e61 0.436531
\(346\) 1.35450e62 0.840261
\(347\) −7.99219e61 −0.461949 −0.230974 0.972960i \(-0.574191\pi\)
−0.230974 + 0.972960i \(0.574191\pi\)
\(348\) 2.83417e62 1.52663
\(349\) −1.83544e62 −0.921548 −0.460774 0.887517i \(-0.652428\pi\)
−0.460774 + 0.887517i \(0.652428\pi\)
\(350\) 1.07188e62 0.501740
\(351\) 1.95963e62 0.855362
\(352\) 7.55301e61 0.307486
\(353\) 1.40284e61 0.0532756 0.0266378 0.999645i \(-0.491520\pi\)
0.0266378 + 0.999645i \(0.491520\pi\)
\(354\) −1.16159e62 −0.411597
\(355\) −1.16643e61 −0.0385712
\(356\) −6.64108e61 −0.204981
\(357\) −8.34616e62 −2.40500
\(358\) 1.82339e62 0.490620
\(359\) −5.18325e62 −1.30253 −0.651265 0.758850i \(-0.725761\pi\)
−0.651265 + 0.758850i \(0.725761\pi\)
\(360\) −1.04559e62 −0.245444
\(361\) −3.70826e62 −0.813286
\(362\) −1.51863e62 −0.311238
\(363\) 1.71708e63 3.28912
\(364\) −1.99815e62 −0.357803
\(365\) −2.38480e61 −0.0399279
\(366\) −3.48223e62 −0.545218
\(367\) 1.17851e62 0.172590 0.0862948 0.996270i \(-0.472497\pi\)
0.0862948 + 0.996270i \(0.472497\pi\)
\(368\) −1.15664e62 −0.158462
\(369\) 4.77034e62 0.611510
\(370\) 6.92448e61 0.0830702
\(371\) 5.13969e61 0.0577134
\(372\) −6.05601e62 −0.636626
\(373\) −1.26964e63 −1.24972 −0.624860 0.780737i \(-0.714844\pi\)
−0.624860 + 0.780737i \(0.714844\pi\)
\(374\) 2.28401e63 2.10544
\(375\) 1.45176e63 1.25352
\(376\) −4.91237e62 −0.397364
\(377\) 2.05184e63 1.55518
\(378\) −8.90711e62 −0.632685
\(379\) −8.52756e61 −0.0567759 −0.0283880 0.999597i \(-0.509037\pi\)
−0.0283880 + 0.999597i \(0.509037\pi\)
\(380\) 1.46805e62 0.0916311
\(381\) −2.85108e63 −1.66858
\(382\) −1.62431e63 −0.891491
\(383\) 2.26804e63 1.16756 0.583781 0.811911i \(-0.301573\pi\)
0.583781 + 0.811911i \(0.301573\pi\)
\(384\) 2.97203e62 0.143529
\(385\) 1.40859e63 0.638261
\(386\) −8.96623e62 −0.381260
\(387\) −6.70165e63 −2.67463
\(388\) 4.43443e62 0.166135
\(389\) −3.69467e62 −0.129960 −0.0649802 0.997887i \(-0.520698\pi\)
−0.0649802 + 0.997887i \(0.520698\pi\)
\(390\) −1.21943e63 −0.402786
\(391\) −3.49764e63 −1.08504
\(392\) −3.05068e62 −0.0888972
\(393\) 6.60001e63 1.80687
\(394\) 4.16421e63 1.07121
\(395\) −4.89319e62 −0.118294
\(396\) 6.26490e63 1.42358
\(397\) −6.48767e63 −1.38587 −0.692933 0.721002i \(-0.743682\pi\)
−0.692933 + 0.721002i \(0.743682\pi\)
\(398\) 9.69832e62 0.194787
\(399\) 3.21426e63 0.607079
\(400\) −1.15422e63 −0.205031
\(401\) 6.26348e63 1.04659 0.523297 0.852150i \(-0.324702\pi\)
0.523297 + 0.852150i \(0.324702\pi\)
\(402\) 5.16562e63 0.812053
\(403\) −4.38435e63 −0.648532
\(404\) −5.91110e63 −0.822857
\(405\) −1.37426e62 −0.0180061
\(406\) −9.32624e63 −1.15032
\(407\) −4.14895e63 −0.481809
\(408\) 8.98734e63 0.982782
\(409\) 4.09059e63 0.421274 0.210637 0.977564i \(-0.432446\pi\)
0.210637 + 0.977564i \(0.432446\pi\)
\(410\) −1.15496e63 −0.112037
\(411\) 1.48549e64 1.35751
\(412\) −8.68458e63 −0.747769
\(413\) 3.82238e63 0.310139
\(414\) −9.59382e63 −0.733640
\(415\) −8.89347e63 −0.641052
\(416\) 2.15165e63 0.146213
\(417\) 5.64221e63 0.361507
\(418\) −8.79613e63 −0.531463
\(419\) 4.65451e63 0.265235 0.132617 0.991167i \(-0.457662\pi\)
0.132617 + 0.991167i \(0.457662\pi\)
\(420\) 5.54268e63 0.297929
\(421\) −6.78354e63 −0.343990 −0.171995 0.985098i \(-0.555021\pi\)
−0.171995 + 0.985098i \(0.555021\pi\)
\(422\) 8.94167e61 0.00427822
\(423\) −4.07460e64 −1.83970
\(424\) −5.53454e62 −0.0235840
\(425\) −3.49034e64 −1.40391
\(426\) 2.75006e63 0.104426
\(427\) 1.14588e64 0.410824
\(428\) −4.64981e63 −0.157421
\(429\) 7.30648e64 2.33617
\(430\) 1.62255e64 0.490028
\(431\) 5.56035e64 1.58639 0.793193 0.608971i \(-0.208417\pi\)
0.793193 + 0.608971i \(0.208417\pi\)
\(432\) 9.59138e63 0.258541
\(433\) 3.47009e64 0.883869 0.441934 0.897047i \(-0.354292\pi\)
0.441934 + 0.897047i \(0.354292\pi\)
\(434\) 1.99282e64 0.479699
\(435\) −5.69162e64 −1.29494
\(436\) −2.58796e64 −0.556593
\(437\) 1.34701e64 0.273889
\(438\) 5.62258e63 0.108099
\(439\) −4.09271e64 −0.744099 −0.372049 0.928213i \(-0.621345\pi\)
−0.372049 + 0.928213i \(0.621345\pi\)
\(440\) −1.51681e64 −0.260819
\(441\) −2.53041e64 −0.411572
\(442\) 6.50654e64 1.00116
\(443\) −1.21785e65 −1.77298 −0.886488 0.462751i \(-0.846862\pi\)
−0.886488 + 0.462751i \(0.846862\pi\)
\(444\) −1.63257e64 −0.224900
\(445\) 1.33367e64 0.173871
\(446\) 7.33970e64 0.905679
\(447\) −1.22520e65 −1.43110
\(448\) −9.77991e63 −0.108149
\(449\) 5.54542e64 0.580629 0.290315 0.956931i \(-0.406240\pi\)
0.290315 + 0.956931i \(0.406240\pi\)
\(450\) −9.57379e64 −0.949243
\(451\) 6.92016e64 0.649817
\(452\) 1.95278e64 0.173685
\(453\) −1.68374e64 −0.141863
\(454\) 4.74239e64 0.378555
\(455\) 4.01272e64 0.303500
\(456\) −3.46119e64 −0.248077
\(457\) −1.52223e65 −1.03403 −0.517014 0.855977i \(-0.672956\pi\)
−0.517014 + 0.855977i \(0.672956\pi\)
\(458\) −1.23687e65 −0.796380
\(459\) 2.90040e65 1.77030
\(460\) 2.32278e64 0.134413
\(461\) 1.88013e65 1.03161 0.515806 0.856706i \(-0.327493\pi\)
0.515806 + 0.856706i \(0.327493\pi\)
\(462\) −3.32101e65 −1.72799
\(463\) 3.45913e65 1.70699 0.853497 0.521098i \(-0.174477\pi\)
0.853497 + 0.521098i \(0.174477\pi\)
\(464\) 1.00427e65 0.470067
\(465\) 1.21618e65 0.540007
\(466\) 8.85861e64 0.373174
\(467\) −1.96639e65 −0.785970 −0.392985 0.919545i \(-0.628558\pi\)
−0.392985 + 0.919545i \(0.628558\pi\)
\(468\) 1.78471e65 0.676929
\(469\) −1.69982e65 −0.611884
\(470\) 9.86509e64 0.337057
\(471\) 1.66883e65 0.541252
\(472\) −4.11602e64 −0.126736
\(473\) −9.72185e65 −2.84217
\(474\) 1.15366e65 0.320263
\(475\) 1.34419e65 0.354379
\(476\) −2.95741e65 −0.740529
\(477\) −4.59066e64 −0.109188
\(478\) −1.97107e65 −0.445368
\(479\) 5.20394e64 0.111715 0.0558576 0.998439i \(-0.482211\pi\)
0.0558576 + 0.998439i \(0.482211\pi\)
\(480\) −5.96848e64 −0.121746
\(481\) −1.18193e65 −0.229106
\(482\) 4.55705e65 0.839521
\(483\) 5.08567e65 0.890519
\(484\) 6.08439e65 1.01276
\(485\) −8.90528e64 −0.140921
\(486\) −4.53629e65 −0.682515
\(487\) 1.99942e65 0.286051 0.143026 0.989719i \(-0.454317\pi\)
0.143026 + 0.989719i \(0.454317\pi\)
\(488\) −1.23391e65 −0.167879
\(489\) −2.04408e66 −2.64503
\(490\) 6.12642e64 0.0754055
\(491\) −3.18295e65 −0.372677 −0.186339 0.982486i \(-0.559662\pi\)
−0.186339 + 0.982486i \(0.559662\pi\)
\(492\) 2.72302e65 0.303323
\(493\) 3.03688e66 3.21869
\(494\) −2.50579e65 −0.252717
\(495\) −1.25813e66 −1.20753
\(496\) −2.14591e65 −0.196025
\(497\) −9.04947e64 −0.0786849
\(498\) 2.09679e66 1.73555
\(499\) 6.39909e65 0.504260 0.252130 0.967693i \(-0.418869\pi\)
0.252130 + 0.967693i \(0.418869\pi\)
\(500\) 5.14424e65 0.385972
\(501\) 3.14430e65 0.224647
\(502\) −6.12375e65 −0.416655
\(503\) 1.03311e66 0.669471 0.334735 0.942312i \(-0.391353\pi\)
0.334735 + 0.942312i \(0.391353\pi\)
\(504\) −8.11202e65 −0.500703
\(505\) 1.18708e66 0.697974
\(506\) −1.39174e66 −0.779598
\(507\) −9.61133e65 −0.512966
\(508\) −1.01026e66 −0.513776
\(509\) −1.63284e66 −0.791333 −0.395666 0.918394i \(-0.629486\pi\)
−0.395666 + 0.918394i \(0.629486\pi\)
\(510\) −1.80485e66 −0.833627
\(511\) −1.85019e65 −0.0814526
\(512\) 1.05312e65 0.0441942
\(513\) −1.11700e66 −0.446866
\(514\) −1.56870e65 −0.0598334
\(515\) 1.74405e66 0.634281
\(516\) −3.82545e66 −1.32668
\(517\) −5.91088e66 −1.95494
\(518\) 5.37221e65 0.169463
\(519\) 6.41318e66 1.92963
\(520\) −4.32098e65 −0.124023
\(521\) 3.93193e66 1.07667 0.538334 0.842732i \(-0.319054\pi\)
0.538334 + 0.842732i \(0.319054\pi\)
\(522\) 8.32999e66 2.17629
\(523\) −2.10835e66 −0.525596 −0.262798 0.964851i \(-0.584645\pi\)
−0.262798 + 0.964851i \(0.584645\pi\)
\(524\) 2.33867e66 0.556357
\(525\) 5.07505e66 1.15223
\(526\) −1.39454e66 −0.302190
\(527\) −6.48917e66 −1.34224
\(528\) 3.57614e66 0.706128
\(529\) −3.17348e66 −0.598235
\(530\) 1.11145e65 0.0200047
\(531\) −3.41406e66 −0.586753
\(532\) 1.13895e66 0.186927
\(533\) 1.97137e66 0.308996
\(534\) −3.14437e66 −0.470730
\(535\) 9.33781e65 0.133530
\(536\) 1.83041e66 0.250041
\(537\) 8.63324e66 1.12669
\(538\) −7.45431e66 −0.929484
\(539\) −3.67077e66 −0.437354
\(540\) −1.92615e66 −0.219303
\(541\) −8.41780e66 −0.915937 −0.457968 0.888968i \(-0.651423\pi\)
−0.457968 + 0.888968i \(0.651423\pi\)
\(542\) 1.07880e67 1.12191
\(543\) −7.19031e66 −0.714746
\(544\) 3.18461e66 0.302610
\(545\) 5.19717e66 0.472120
\(546\) −9.46069e66 −0.821681
\(547\) 5.67745e66 0.471481 0.235740 0.971816i \(-0.424248\pi\)
0.235740 + 0.971816i \(0.424248\pi\)
\(548\) 5.26374e66 0.417995
\(549\) −1.02347e67 −0.777238
\(550\) −1.38884e67 −1.00871
\(551\) −1.16956e67 −0.812472
\(552\) −5.47636e66 −0.363902
\(553\) −3.79628e66 −0.241319
\(554\) 2.08746e67 1.26949
\(555\) 3.27855e66 0.190767
\(556\) 1.99929e66 0.111312
\(557\) 2.68265e67 1.42926 0.714631 0.699502i \(-0.246595\pi\)
0.714631 + 0.699502i \(0.246595\pi\)
\(558\) −1.77994e67 −0.907544
\(559\) −2.76950e67 −1.35149
\(560\) 1.96402e66 0.0917357
\(561\) 1.08141e68 4.83506
\(562\) 1.43444e67 0.613963
\(563\) −2.46352e67 −1.00949 −0.504744 0.863269i \(-0.668413\pi\)
−0.504744 + 0.863269i \(0.668413\pi\)
\(564\) −2.32587e67 −0.912531
\(565\) −3.92160e66 −0.147325
\(566\) −3.26943e67 −1.17617
\(567\) −1.06619e66 −0.0367324
\(568\) 9.74467e65 0.0321539
\(569\) −2.62664e67 −0.830137 −0.415069 0.909790i \(-0.636242\pi\)
−0.415069 + 0.909790i \(0.636242\pi\)
\(570\) 6.95081e66 0.210427
\(571\) 5.51879e67 1.60051 0.800257 0.599658i \(-0.204697\pi\)
0.800257 + 0.599658i \(0.204697\pi\)
\(572\) 2.58901e67 0.719334
\(573\) −7.69066e67 −2.04727
\(574\) −8.96048e66 −0.228555
\(575\) 2.12681e67 0.519836
\(576\) 8.73520e66 0.204608
\(577\) −4.65003e66 −0.104387 −0.0521937 0.998637i \(-0.516621\pi\)
−0.0521937 + 0.998637i \(0.516621\pi\)
\(578\) 6.34379e67 1.36495
\(579\) −4.24526e67 −0.875548
\(580\) −2.01679e67 −0.398726
\(581\) −6.89981e67 −1.30774
\(582\) 2.09958e67 0.381521
\(583\) −6.65951e66 −0.116028
\(584\) 1.99233e66 0.0332848
\(585\) −3.58407e67 −0.574193
\(586\) −2.88513e67 −0.443276
\(587\) −9.45616e67 −1.39342 −0.696709 0.717354i \(-0.745353\pi\)
−0.696709 + 0.717354i \(0.745353\pi\)
\(588\) −1.44441e67 −0.204149
\(589\) 2.49910e67 0.338812
\(590\) 8.26585e66 0.107501
\(591\) 1.97164e68 2.45999
\(592\) −5.78492e66 −0.0692493
\(593\) −9.11419e67 −1.04684 −0.523418 0.852076i \(-0.675343\pi\)
−0.523418 + 0.852076i \(0.675343\pi\)
\(594\) 1.15410e68 1.27196
\(595\) 5.93912e67 0.628140
\(596\) −4.34141e67 −0.440654
\(597\) 4.59188e67 0.447321
\(598\) −3.96471e67 −0.370708
\(599\) 1.33989e68 1.20258 0.601289 0.799032i \(-0.294654\pi\)
0.601289 + 0.799032i \(0.294654\pi\)
\(600\) −5.46493e67 −0.470846
\(601\) 1.90045e68 1.57193 0.785963 0.618274i \(-0.212168\pi\)
0.785963 + 0.618274i \(0.212168\pi\)
\(602\) 1.25882e68 0.999654
\(603\) 1.51825e68 1.15762
\(604\) −5.96624e66 −0.0436813
\(605\) −1.22188e68 −0.859054
\(606\) −2.79874e68 −1.88966
\(607\) −2.65855e68 −1.72394 −0.861968 0.506962i \(-0.830768\pi\)
−0.861968 + 0.506962i \(0.830768\pi\)
\(608\) −1.22645e67 −0.0763859
\(609\) −4.41572e68 −2.64166
\(610\) 2.47795e67 0.142401
\(611\) −1.68385e68 −0.929597
\(612\) 2.64150e68 1.40101
\(613\) 3.75059e68 1.91125 0.955627 0.294580i \(-0.0951798\pi\)
0.955627 + 0.294580i \(0.0951798\pi\)
\(614\) −7.22001e66 −0.0353519
\(615\) −5.46840e67 −0.257288
\(616\) −1.17678e68 −0.532069
\(617\) 1.14520e68 0.497617 0.248809 0.968553i \(-0.419961\pi\)
0.248809 + 0.968553i \(0.419961\pi\)
\(618\) −4.11191e68 −1.71722
\(619\) 4.65278e68 1.86763 0.933817 0.357750i \(-0.116456\pi\)
0.933817 + 0.357750i \(0.116456\pi\)
\(620\) 4.30945e67 0.166274
\(621\) −1.76734e68 −0.655504
\(622\) −7.48579e66 −0.0266915
\(623\) 1.03470e68 0.354697
\(624\) 1.01875e68 0.335772
\(625\) 1.55479e68 0.492731
\(626\) 5.87541e67 0.179047
\(627\) −4.16472e68 −1.22048
\(628\) 5.91340e67 0.166658
\(629\) −1.74934e68 −0.474170
\(630\) 1.62907e68 0.424713
\(631\) 4.71150e67 0.118152 0.0590758 0.998253i \(-0.481185\pi\)
0.0590758 + 0.998253i \(0.481185\pi\)
\(632\) 4.08792e67 0.0986129
\(633\) 4.23363e66 0.00982476
\(634\) 1.50072e67 0.0335052
\(635\) 2.02883e68 0.435802
\(636\) −2.62045e67 −0.0541597
\(637\) −1.04571e68 −0.207967
\(638\) 1.20840e69 2.31262
\(639\) 8.08279e67 0.148864
\(640\) −2.11490e67 −0.0374869
\(641\) −1.14710e69 −1.95694 −0.978471 0.206383i \(-0.933831\pi\)
−0.978471 + 0.206383i \(0.933831\pi\)
\(642\) −2.20155e68 −0.361511
\(643\) 5.88590e68 0.930345 0.465173 0.885220i \(-0.345992\pi\)
0.465173 + 0.885220i \(0.345992\pi\)
\(644\) 1.80208e68 0.274201
\(645\) 7.68233e68 1.12533
\(646\) −3.70875e68 −0.523036
\(647\) −8.23336e68 −1.11795 −0.558975 0.829185i \(-0.688805\pi\)
−0.558975 + 0.829185i \(0.688805\pi\)
\(648\) 1.14810e67 0.0150103
\(649\) −4.95266e68 −0.623510
\(650\) −3.95643e68 −0.479652
\(651\) 9.43544e68 1.10161
\(652\) −7.24308e68 −0.814436
\(653\) −4.04310e68 −0.437866 −0.218933 0.975740i \(-0.570258\pi\)
−0.218933 + 0.975740i \(0.570258\pi\)
\(654\) −1.22533e69 −1.27819
\(655\) −4.69656e68 −0.471920
\(656\) 9.64885e67 0.0933967
\(657\) 1.65255e68 0.154100
\(658\) 7.65362e68 0.687594
\(659\) −1.59048e69 −1.37669 −0.688343 0.725385i \(-0.741662\pi\)
−0.688343 + 0.725385i \(0.741662\pi\)
\(660\) −7.18166e68 −0.598961
\(661\) 1.64318e69 1.32053 0.660266 0.751032i \(-0.270444\pi\)
0.660266 + 0.751032i \(0.270444\pi\)
\(662\) 4.39560e68 0.340406
\(663\) 3.08066e69 2.29913
\(664\) 7.42987e68 0.534396
\(665\) −2.28727e68 −0.158557
\(666\) −4.79834e68 −0.320607
\(667\) −1.85050e69 −1.19181
\(668\) 1.11416e68 0.0691713
\(669\) 3.47515e69 2.07986
\(670\) −3.67585e68 −0.212093
\(671\) −1.48472e69 −0.825927
\(672\) −4.63052e68 −0.248360
\(673\) −1.44435e69 −0.746968 −0.373484 0.927637i \(-0.621837\pi\)
−0.373484 + 0.927637i \(0.621837\pi\)
\(674\) 2.29521e69 1.14460
\(675\) −1.76365e69 −0.848144
\(676\) −3.40572e68 −0.157948
\(677\) 4.42761e69 1.98037 0.990186 0.139755i \(-0.0446314\pi\)
0.990186 + 0.139755i \(0.0446314\pi\)
\(678\) 9.24586e68 0.398860
\(679\) −6.90897e68 −0.287477
\(680\) −6.39538e68 −0.256684
\(681\) 2.24539e69 0.869336
\(682\) −2.58210e69 −0.964396
\(683\) −6.24013e68 −0.224847 −0.112423 0.993660i \(-0.535861\pi\)
−0.112423 + 0.993660i \(0.535861\pi\)
\(684\) −1.01729e69 −0.353647
\(685\) −1.05707e69 −0.354557
\(686\) 2.36564e69 0.765611
\(687\) −5.85624e69 −1.82885
\(688\) −1.35553e69 −0.408499
\(689\) −1.89712e68 −0.0551726
\(690\) 1.09977e69 0.308674
\(691\) −1.65576e69 −0.448524 −0.224262 0.974529i \(-0.571997\pi\)
−0.224262 + 0.974529i \(0.571997\pi\)
\(692\) 2.27247e69 0.594154
\(693\) −9.76089e69 −2.46335
\(694\) −1.34087e69 −0.326647
\(695\) −4.01499e68 −0.0944185
\(696\) 4.75494e69 1.07949
\(697\) 2.91778e69 0.639513
\(698\) −3.07936e69 −0.651633
\(699\) 4.19431e69 0.856978
\(700\) 1.79832e69 0.354784
\(701\) 3.50945e69 0.668572 0.334286 0.942472i \(-0.391505\pi\)
0.334286 + 0.942472i \(0.391505\pi\)
\(702\) 3.28772e69 0.604833
\(703\) 6.73704e68 0.119692
\(704\) 1.26718e69 0.217425
\(705\) 4.67085e69 0.774038
\(706\) 2.35358e68 0.0376716
\(707\) 9.20966e69 1.42386
\(708\) −1.94882e69 −0.291043
\(709\) −7.32363e69 −1.05656 −0.528280 0.849070i \(-0.677163\pi\)
−0.528280 + 0.849070i \(0.677163\pi\)
\(710\) −1.95694e68 −0.0272739
\(711\) 3.39075e69 0.456552
\(712\) −1.11419e69 −0.144943
\(713\) 3.95412e69 0.497000
\(714\) −1.40025e70 −1.70059
\(715\) −5.19928e69 −0.610162
\(716\) 3.05914e69 0.346921
\(717\) −9.33248e69 −1.02277
\(718\) −8.69604e69 −0.921028
\(719\) 5.39270e69 0.552012 0.276006 0.961156i \(-0.410989\pi\)
0.276006 + 0.961156i \(0.410989\pi\)
\(720\) −1.75422e69 −0.173555
\(721\) 1.35308e70 1.29393
\(722\) −6.22142e69 −0.575080
\(723\) 2.15764e70 1.92792
\(724\) −2.54784e69 −0.220079
\(725\) −1.84664e70 −1.54206
\(726\) 2.88079e70 2.32576
\(727\) 1.12907e70 0.881309 0.440655 0.897677i \(-0.354746\pi\)
0.440655 + 0.897677i \(0.354746\pi\)
\(728\) −3.35234e69 −0.253005
\(729\) −2.20599e70 −1.60982
\(730\) −4.00103e68 −0.0282333
\(731\) −4.09907e70 −2.79711
\(732\) −5.84221e69 −0.385528
\(733\) 4.27091e69 0.272567 0.136283 0.990670i \(-0.456484\pi\)
0.136283 + 0.990670i \(0.456484\pi\)
\(734\) 1.97721e69 0.122039
\(735\) 2.90069e69 0.173166
\(736\) −1.94052e69 −0.112050
\(737\) 2.20246e70 1.23014
\(738\) 8.00330e69 0.432403
\(739\) −2.03599e70 −1.06411 −0.532055 0.846710i \(-0.678580\pi\)
−0.532055 + 0.846710i \(0.678580\pi\)
\(740\) 1.16174e69 0.0587395
\(741\) −1.18642e70 −0.580354
\(742\) 8.62297e68 0.0408095
\(743\) 1.12304e70 0.514243 0.257122 0.966379i \(-0.417226\pi\)
0.257122 + 0.966379i \(0.417226\pi\)
\(744\) −1.01603e70 −0.450163
\(745\) 8.71849e69 0.373777
\(746\) −2.13010e70 −0.883686
\(747\) 6.16276e70 2.47412
\(748\) 3.83193e70 1.48877
\(749\) 7.24453e69 0.272399
\(750\) 2.43566e70 0.886370
\(751\) −1.72919e69 −0.0609066 −0.0304533 0.999536i \(-0.509695\pi\)
−0.0304533 + 0.999536i \(0.509695\pi\)
\(752\) −8.24159e69 −0.280979
\(753\) −2.89943e70 −0.956831
\(754\) 3.44242e70 1.09968
\(755\) 1.19815e69 0.0370519
\(756\) −1.49436e70 −0.447376
\(757\) −1.67080e69 −0.0484256 −0.0242128 0.999707i \(-0.507708\pi\)
−0.0242128 + 0.999707i \(0.507708\pi\)
\(758\) −1.43069e69 −0.0401466
\(759\) −6.58951e70 −1.79031
\(760\) 2.46298e69 0.0647930
\(761\) −1.82952e70 −0.466030 −0.233015 0.972473i \(-0.574859\pi\)
−0.233015 + 0.972473i \(0.574859\pi\)
\(762\) −4.78332e70 −1.17987
\(763\) 4.03211e70 0.963122
\(764\) −2.72514e70 −0.630379
\(765\) −5.30470e70 −1.18838
\(766\) 3.80513e70 0.825591
\(767\) −1.41088e70 −0.296486
\(768\) 4.98625e69 0.101490
\(769\) 1.74967e70 0.344954 0.172477 0.985014i \(-0.444823\pi\)
0.172477 + 0.985014i \(0.444823\pi\)
\(770\) 2.36323e70 0.451318
\(771\) −7.42736e69 −0.137405
\(772\) −1.50428e70 −0.269591
\(773\) 5.68036e70 0.986229 0.493115 0.869964i \(-0.335858\pi\)
0.493115 + 0.869964i \(0.335858\pi\)
\(774\) −1.12435e71 −1.89125
\(775\) 3.94587e70 0.643059
\(776\) 7.43973e69 0.117475
\(777\) 2.54359e70 0.389164
\(778\) −6.19863e69 −0.0918958
\(779\) −1.12369e70 −0.161428
\(780\) −2.04587e70 −0.284813
\(781\) 1.17254e70 0.158190
\(782\) −5.86806e70 −0.767237
\(783\) 1.53452e71 1.94451
\(784\) −5.11819e69 −0.0628598
\(785\) −1.18754e70 −0.141365
\(786\) 1.10730e71 1.27765
\(787\) 2.11456e70 0.236505 0.118252 0.992984i \(-0.462271\pi\)
0.118252 + 0.992984i \(0.462271\pi\)
\(788\) 6.98639e70 0.757461
\(789\) −6.60276e70 −0.693967
\(790\) −8.20941e69 −0.0836466
\(791\) −3.04249e70 −0.300542
\(792\) 1.05108e71 1.00662
\(793\) −4.22957e70 −0.392738
\(794\) −1.08845e71 −0.979956
\(795\) 5.26243e69 0.0459400
\(796\) 1.62711e70 0.137736
\(797\) 1.36404e71 1.11969 0.559844 0.828598i \(-0.310861\pi\)
0.559844 + 0.828598i \(0.310861\pi\)
\(798\) 5.39264e70 0.429270
\(799\) −2.49223e71 −1.92394
\(800\) −1.93647e70 −0.144979
\(801\) −9.24171e70 −0.671051
\(802\) 1.05084e71 0.740054
\(803\) 2.39730e70 0.163754
\(804\) 8.66648e70 0.574208
\(805\) −3.61896e70 −0.232586
\(806\) −7.35572e70 −0.458582
\(807\) −3.52941e71 −2.13452
\(808\) −9.91717e70 −0.581848
\(809\) 1.21224e71 0.690002 0.345001 0.938602i \(-0.387879\pi\)
0.345001 + 0.938602i \(0.387879\pi\)
\(810\) −2.30562e69 −0.0127323
\(811\) −2.96765e71 −1.59001 −0.795007 0.606600i \(-0.792533\pi\)
−0.795007 + 0.606600i \(0.792533\pi\)
\(812\) −1.56468e71 −0.813399
\(813\) 5.10781e71 2.57642
\(814\) −6.96078e70 −0.340690
\(815\) 1.45457e71 0.690831
\(816\) 1.50782e71 0.694932
\(817\) 1.57863e71 0.706056
\(818\) 6.86287e70 0.297886
\(819\) −2.78062e71 −1.17135
\(820\) −1.93770e70 −0.0792221
\(821\) 4.81615e71 1.91114 0.955570 0.294766i \(-0.0952416\pi\)
0.955570 + 0.294766i \(0.0952416\pi\)
\(822\) 2.49223e71 0.959908
\(823\) −1.34527e71 −0.502935 −0.251468 0.967866i \(-0.580913\pi\)
−0.251468 + 0.967866i \(0.580913\pi\)
\(824\) −1.45703e71 −0.528752
\(825\) −6.57575e71 −2.31645
\(826\) 6.41288e70 0.219302
\(827\) 7.76898e70 0.257916 0.128958 0.991650i \(-0.458837\pi\)
0.128958 + 0.991650i \(0.458837\pi\)
\(828\) −1.60958e71 −0.518762
\(829\) −5.87735e70 −0.183906 −0.0919529 0.995763i \(-0.529311\pi\)
−0.0919529 + 0.995763i \(0.529311\pi\)
\(830\) −1.49208e71 −0.453292
\(831\) 9.88353e71 2.91533
\(832\) 3.60988e70 0.103388
\(833\) −1.54773e71 −0.430419
\(834\) 9.46606e70 0.255624
\(835\) −2.23748e70 −0.0586733
\(836\) −1.47575e71 −0.375801
\(837\) −3.27894e71 −0.810886
\(838\) 7.80898e70 0.187549
\(839\) −2.93145e70 −0.0683777 −0.0341888 0.999415i \(-0.510885\pi\)
−0.0341888 + 0.999415i \(0.510885\pi\)
\(840\) 9.29907e70 0.210667
\(841\) 1.15226e72 2.53542
\(842\) −1.13809e71 −0.243237
\(843\) 6.79167e71 1.40994
\(844\) 1.50016e69 0.00302516
\(845\) 6.83941e70 0.133977
\(846\) −6.83604e71 −1.30086
\(847\) −9.47966e71 −1.75246
\(848\) −9.28541e69 −0.0166764
\(849\) −1.54799e72 −2.70102
\(850\) −5.85581e71 −0.992713
\(851\) 1.06595e71 0.175574
\(852\) 4.61383e70 0.0738400
\(853\) −5.36884e71 −0.834889 −0.417445 0.908702i \(-0.637074\pi\)
−0.417445 + 0.908702i \(0.637074\pi\)
\(854\) 1.92246e71 0.290496
\(855\) 2.04294e71 0.299975
\(856\) −7.80108e70 −0.111313
\(857\) 2.07429e71 0.287634 0.143817 0.989604i \(-0.454062\pi\)
0.143817 + 0.989604i \(0.454062\pi\)
\(858\) 1.22582e72 1.65192
\(859\) −7.03695e71 −0.921620 −0.460810 0.887499i \(-0.652441\pi\)
−0.460810 + 0.887499i \(0.652441\pi\)
\(860\) 2.72219e71 0.346502
\(861\) −4.24254e71 −0.524866
\(862\) 9.32871e71 1.12174
\(863\) −3.68596e71 −0.430810 −0.215405 0.976525i \(-0.569107\pi\)
−0.215405 + 0.976525i \(0.569107\pi\)
\(864\) 1.60917e71 0.182816
\(865\) −4.56361e71 −0.503981
\(866\) 5.82185e71 0.624990
\(867\) 3.00361e72 3.13455
\(868\) 3.34339e71 0.339199
\(869\) 4.91884e71 0.485152
\(870\) −9.54895e71 −0.915659
\(871\) 6.27425e71 0.584947
\(872\) −4.34187e71 −0.393571
\(873\) 6.17094e71 0.543879
\(874\) 2.25990e71 0.193669
\(875\) −8.01488e71 −0.667882
\(876\) 9.43313e70 0.0764373
\(877\) −1.93572e72 −1.52529 −0.762645 0.646817i \(-0.776100\pi\)
−0.762645 + 0.646817i \(0.776100\pi\)
\(878\) −6.86643e71 −0.526157
\(879\) −1.36603e72 −1.01796
\(880\) −2.54478e71 −0.184427
\(881\) 5.95854e71 0.419982 0.209991 0.977703i \(-0.432657\pi\)
0.209991 + 0.977703i \(0.432657\pi\)
\(882\) −4.24532e71 −0.291025
\(883\) 1.87124e72 1.24765 0.623826 0.781564i \(-0.285578\pi\)
0.623826 + 0.781564i \(0.285578\pi\)
\(884\) 1.09162e72 0.707928
\(885\) 3.91365e71 0.246872
\(886\) −2.04322e72 −1.25368
\(887\) −2.12365e72 −1.26752 −0.633758 0.773531i \(-0.718489\pi\)
−0.633758 + 0.773531i \(0.718489\pi\)
\(888\) −2.73900e71 −0.159028
\(889\) 1.57402e72 0.889033
\(890\) 2.23753e71 0.122946
\(891\) 1.38146e71 0.0738474
\(892\) 1.23140e72 0.640412
\(893\) 9.59804e71 0.485648
\(894\) −2.05554e72 −1.01194
\(895\) −6.14341e71 −0.294269
\(896\) −1.64080e71 −0.0764731
\(897\) −1.87718e72 −0.851316
\(898\) 9.30367e71 0.410567
\(899\) −3.43323e72 −1.47432
\(900\) −1.60622e72 −0.671216
\(901\) −2.80788e71 −0.114188
\(902\) 1.16101e72 0.459490
\(903\) 5.96016e72 2.29566
\(904\) 3.27622e71 0.122814
\(905\) 5.11662e71 0.186678
\(906\) −2.82485e71 −0.100312
\(907\) 2.10319e72 0.726943 0.363471 0.931605i \(-0.381591\pi\)
0.363471 + 0.931605i \(0.381591\pi\)
\(908\) 7.95641e71 0.267679
\(909\) −8.22587e72 −2.69381
\(910\) 6.73222e71 0.214607
\(911\) 4.91507e72 1.52521 0.762604 0.646866i \(-0.223921\pi\)
0.762604 + 0.646866i \(0.223921\pi\)
\(912\) −5.80691e71 −0.175417
\(913\) 8.94009e72 2.62910
\(914\) −2.55387e72 −0.731168
\(915\) 1.17324e72 0.327017
\(916\) −2.07513e72 −0.563126
\(917\) −3.64372e72 −0.962713
\(918\) 4.86607e72 1.25179
\(919\) −1.76130e72 −0.441166 −0.220583 0.975368i \(-0.570796\pi\)
−0.220583 + 0.975368i \(0.570796\pi\)
\(920\) 3.89698e71 0.0950443
\(921\) −3.41847e71 −0.0811842
\(922\) 3.15434e72 0.729459
\(923\) 3.34026e71 0.0752210
\(924\) −5.57173e72 −1.22188
\(925\) 1.06372e72 0.227172
\(926\) 5.80345e72 1.20703
\(927\) −1.20854e73 −2.44799
\(928\) 1.68489e72 0.332388
\(929\) −4.47943e72 −0.860671 −0.430336 0.902669i \(-0.641605\pi\)
−0.430336 + 0.902669i \(0.641605\pi\)
\(930\) 2.04041e72 0.381842
\(931\) 5.96058e71 0.108648
\(932\) 1.48623e72 0.263874
\(933\) −3.54431e71 −0.0612959
\(934\) −3.29906e72 −0.555765
\(935\) −7.69533e72 −1.26282
\(936\) 2.99424e72 0.478661
\(937\) 6.98453e72 1.08772 0.543860 0.839176i \(-0.316962\pi\)
0.543860 + 0.839176i \(0.316962\pi\)
\(938\) −2.85183e72 −0.432667
\(939\) 2.78185e72 0.411174
\(940\) 1.65509e72 0.238335
\(941\) −1.60971e72 −0.225840 −0.112920 0.993604i \(-0.536020\pi\)
−0.112920 + 0.993604i \(0.536020\pi\)
\(942\) 2.79983e72 0.382723
\(943\) −1.77793e72 −0.236798
\(944\) −6.90554e71 −0.0896156
\(945\) 3.00101e72 0.379479
\(946\) −1.63106e73 −2.00972
\(947\) −1.31016e72 −0.157307 −0.0786537 0.996902i \(-0.525062\pi\)
−0.0786537 + 0.996902i \(0.525062\pi\)
\(948\) 1.93552e72 0.226460
\(949\) 6.82928e71 0.0778668
\(950\) 2.25518e72 0.250584
\(951\) 7.10549e71 0.0769434
\(952\) −4.96172e72 −0.523633
\(953\) −4.69763e72 −0.483173 −0.241587 0.970379i \(-0.577668\pi\)
−0.241587 + 0.970379i \(0.577668\pi\)
\(954\) −7.70185e71 −0.0772076
\(955\) 5.47267e72 0.534708
\(956\) −3.30691e72 −0.314923
\(957\) 5.72145e73 5.31084
\(958\) 8.73076e71 0.0789945
\(959\) −8.20106e72 −0.723293
\(960\) −1.00135e72 −0.0860872
\(961\) −4.59618e72 −0.385189
\(962\) −1.98294e72 −0.162002
\(963\) −6.47066e72 −0.515353
\(964\) 7.64546e72 0.593631
\(965\) 3.02093e72 0.228676
\(966\) 8.53233e72 0.629692
\(967\) −1.35157e73 −0.972503 −0.486252 0.873819i \(-0.661636\pi\)
−0.486252 + 0.873819i \(0.661636\pi\)
\(968\) 1.02079e73 0.716128
\(969\) −1.75599e73 −1.20113
\(970\) −1.49406e72 −0.0996460
\(971\) 1.73168e73 1.12615 0.563074 0.826406i \(-0.309619\pi\)
0.563074 + 0.826406i \(0.309619\pi\)
\(972\) −7.61063e72 −0.482611
\(973\) −3.11495e72 −0.192613
\(974\) 3.35447e72 0.202269
\(975\) −1.87326e73 −1.10150
\(976\) −2.07015e72 −0.118709
\(977\) −1.61768e72 −0.0904639 −0.0452320 0.998977i \(-0.514403\pi\)
−0.0452320 + 0.998977i \(0.514403\pi\)
\(978\) −3.42940e73 −1.87032
\(979\) −1.34066e73 −0.713088
\(980\) 1.02784e72 0.0533197
\(981\) −3.60139e73 −1.82213
\(982\) −5.34010e72 −0.263523
\(983\) −1.86672e72 −0.0898499 −0.0449249 0.998990i \(-0.514305\pi\)
−0.0449249 + 0.998990i \(0.514305\pi\)
\(984\) 4.56846e72 0.214482
\(985\) −1.40302e73 −0.642503
\(986\) 5.09504e73 2.27595
\(987\) 3.62378e73 1.57903
\(988\) −4.20401e72 −0.178698
\(989\) 2.49773e73 1.03571
\(990\) −2.11078e73 −0.853850
\(991\) 2.80003e73 1.10499 0.552494 0.833517i \(-0.313676\pi\)
0.552494 + 0.833517i \(0.313676\pi\)
\(992\) −3.60024e72 −0.138610
\(993\) 2.08120e73 0.781729
\(994\) −1.51825e72 −0.0556387
\(995\) −3.26758e72 −0.116832
\(996\) 3.51784e73 1.22722
\(997\) −1.83032e73 −0.623011 −0.311505 0.950244i \(-0.600833\pi\)
−0.311505 + 0.950244i \(0.600833\pi\)
\(998\) 1.07359e73 0.356566
\(999\) −8.83932e72 −0.286460
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 \(a_p\))