Properties

Label 2.84.a.a.1.2
Level 2
Weight 84
Character 2.1
Self dual Yes
Analytic conductor 87.254
Analytic rank 0
Dimension 3
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 84 \)
Character orbit: \([\chi]\) = 2.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(87.2544256533\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{24}\cdot 3^{7}\cdot 5^{3}\cdot 7\cdot 11\cdot 17 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.56747e14\)
Character \(\chi\) = 2.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.19902e12 q^{2} -7.32556e17 q^{3} +4.83570e24 q^{4} -1.23719e29 q^{5} +1.61091e30 q^{6} +6.61589e34 q^{7} -1.06338e37 q^{8} -3.99030e39 q^{9} +O(q^{10})\) \(q-2.19902e12 q^{2} -7.32556e17 q^{3} +4.83570e24 q^{4} -1.23719e29 q^{5} +1.61091e30 q^{6} +6.61589e34 q^{7} -1.06338e37 q^{8} -3.99030e39 q^{9} +2.72062e41 q^{10} -2.35451e43 q^{11} -3.54242e42 q^{12} +2.17555e46 q^{13} -1.45485e47 q^{14} +9.06313e46 q^{15} +2.33840e49 q^{16} -2.06003e51 q^{17} +8.77477e51 q^{18} -1.54338e53 q^{19} -5.98270e53 q^{20} -4.84651e52 q^{21} +5.17762e55 q^{22} +3.09757e56 q^{23} +7.78987e54 q^{24} +4.96671e57 q^{25} -4.78409e58 q^{26} +5.84663e57 q^{27} +3.19925e59 q^{28} -4.67177e59 q^{29} -1.99300e59 q^{30} -1.70498e61 q^{31} -5.14220e61 q^{32} +1.72481e61 q^{33} +4.53006e63 q^{34} -8.18513e63 q^{35} -1.92959e64 q^{36} -9.03184e64 q^{37} +3.39393e65 q^{38} -1.59371e64 q^{39} +1.31561e66 q^{40} -8.21191e66 q^{41} +1.06576e65 q^{42} -5.19673e67 q^{43} -1.13857e68 q^{44} +4.93677e68 q^{45} -6.81164e68 q^{46} -3.72927e69 q^{47} -1.71301e67 q^{48} -9.52692e69 q^{49} -1.09219e70 q^{50} +1.50909e69 q^{51} +1.05203e71 q^{52} -4.87207e71 q^{53} -1.28569e70 q^{54} +2.91298e72 q^{55} -7.03522e71 q^{56} +1.13061e71 q^{57} +1.02733e72 q^{58} +2.59897e73 q^{59} +4.38266e71 q^{60} -2.95096e73 q^{61} +3.74928e73 q^{62} -2.63994e74 q^{63} +1.13078e74 q^{64} -2.69158e75 q^{65} -3.79289e73 q^{66} +9.82765e75 q^{67} -9.96170e75 q^{68} -2.26915e74 q^{69} +1.79993e76 q^{70} -2.74633e76 q^{71} +4.24322e76 q^{72} +1.97027e77 q^{73} +1.98612e77 q^{74} -3.63839e75 q^{75} -7.46332e77 q^{76} -1.55772e78 q^{77} +3.50461e76 q^{78} +2.44890e78 q^{79} -2.89306e78 q^{80} +1.59204e79 q^{81} +1.80582e79 q^{82} -4.50780e79 q^{83} -2.34363e77 q^{84} +2.54866e80 q^{85} +1.14277e80 q^{86} +3.42233e77 q^{87} +2.50374e80 q^{88} +1.00507e81 q^{89} -1.08561e81 q^{90} +1.43932e81 q^{91} +1.49790e81 q^{92} +1.24899e79 q^{93} +8.20075e81 q^{94} +1.90946e82 q^{95} +3.76695e79 q^{96} +2.37614e82 q^{97} +2.09499e82 q^{98} +9.39519e82 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 6597069766656q^{2} - \)\(10\!\cdots\!76\)\(q^{3} + \)\(14\!\cdots\!12\)\(q^{4} - \)\(30\!\cdots\!50\)\(q^{5} + \)\(22\!\cdots\!52\)\(q^{6} - \)\(56\!\cdots\!88\)\(q^{7} - \)\(31\!\cdots\!24\)\(q^{8} - \)\(12\!\cdots\!89\)\(q^{9} + O(q^{10}) \) \( 3q - 6597069766656q^{2} - \)\(10\!\cdots\!76\)\(q^{3} + \)\(14\!\cdots\!12\)\(q^{4} - \)\(30\!\cdots\!50\)\(q^{5} + \)\(22\!\cdots\!52\)\(q^{6} - \)\(56\!\cdots\!88\)\(q^{7} - \)\(31\!\cdots\!24\)\(q^{8} - \)\(12\!\cdots\!89\)\(q^{9} + \)\(66\!\cdots\!00\)\(q^{10} - \)\(14\!\cdots\!64\)\(q^{11} - \)\(49\!\cdots\!04\)\(q^{12} - \)\(12\!\cdots\!26\)\(q^{13} + \)\(12\!\cdots\!76\)\(q^{14} + \)\(49\!\cdots\!00\)\(q^{15} + \)\(70\!\cdots\!48\)\(q^{16} + \)\(30\!\cdots\!02\)\(q^{17} + \)\(28\!\cdots\!28\)\(q^{18} - \)\(11\!\cdots\!00\)\(q^{19} - \)\(14\!\cdots\!00\)\(q^{20} + \)\(11\!\cdots\!96\)\(q^{21} + \)\(32\!\cdots\!28\)\(q^{22} + \)\(19\!\cdots\!04\)\(q^{23} + \)\(10\!\cdots\!08\)\(q^{24} + \)\(12\!\cdots\!25\)\(q^{25} + \)\(27\!\cdots\!52\)\(q^{26} - \)\(29\!\cdots\!60\)\(q^{27} - \)\(27\!\cdots\!52\)\(q^{28} - \)\(13\!\cdots\!70\)\(q^{29} - \)\(10\!\cdots\!00\)\(q^{30} - \)\(15\!\cdots\!44\)\(q^{31} - \)\(15\!\cdots\!96\)\(q^{32} - \)\(13\!\cdots\!12\)\(q^{33} - \)\(67\!\cdots\!04\)\(q^{34} - \)\(47\!\cdots\!00\)\(q^{35} - \)\(62\!\cdots\!56\)\(q^{36} - \)\(14\!\cdots\!98\)\(q^{37} + \)\(25\!\cdots\!00\)\(q^{38} + \)\(22\!\cdots\!92\)\(q^{39} + \)\(32\!\cdots\!00\)\(q^{40} - \)\(14\!\cdots\!14\)\(q^{41} - \)\(25\!\cdots\!92\)\(q^{42} - \)\(18\!\cdots\!96\)\(q^{43} - \)\(72\!\cdots\!56\)\(q^{44} - \)\(44\!\cdots\!50\)\(q^{45} - \)\(42\!\cdots\!08\)\(q^{46} - \)\(34\!\cdots\!88\)\(q^{47} - \)\(23\!\cdots\!16\)\(q^{48} - \)\(24\!\cdots\!81\)\(q^{49} - \)\(28\!\cdots\!00\)\(q^{50} - \)\(15\!\cdots\!84\)\(q^{51} - \)\(60\!\cdots\!04\)\(q^{52} - \)\(38\!\cdots\!66\)\(q^{53} + \)\(63\!\cdots\!20\)\(q^{54} + \)\(16\!\cdots\!00\)\(q^{55} + \)\(60\!\cdots\!04\)\(q^{56} + \)\(13\!\cdots\!00\)\(q^{57} + \)\(29\!\cdots\!40\)\(q^{58} + \)\(31\!\cdots\!60\)\(q^{59} + \)\(23\!\cdots\!00\)\(q^{60} - \)\(30\!\cdots\!94\)\(q^{61} + \)\(33\!\cdots\!88\)\(q^{62} - \)\(99\!\cdots\!56\)\(q^{63} + \)\(33\!\cdots\!92\)\(q^{64} - \)\(19\!\cdots\!00\)\(q^{65} + \)\(29\!\cdots\!24\)\(q^{66} - \)\(98\!\cdots\!28\)\(q^{67} + \)\(14\!\cdots\!08\)\(q^{68} - \)\(21\!\cdots\!68\)\(q^{69} + \)\(10\!\cdots\!00\)\(q^{70} + \)\(81\!\cdots\!96\)\(q^{71} + \)\(13\!\cdots\!12\)\(q^{72} + \)\(54\!\cdots\!14\)\(q^{73} + \)\(31\!\cdots\!96\)\(q^{74} + \)\(91\!\cdots\!00\)\(q^{75} - \)\(55\!\cdots\!00\)\(q^{76} - \)\(30\!\cdots\!56\)\(q^{77} - \)\(49\!\cdots\!84\)\(q^{78} - \)\(40\!\cdots\!80\)\(q^{79} - \)\(70\!\cdots\!00\)\(q^{80} + \)\(33\!\cdots\!23\)\(q^{81} + \)\(32\!\cdots\!28\)\(q^{82} + \)\(52\!\cdots\!84\)\(q^{83} + \)\(56\!\cdots\!84\)\(q^{84} + \)\(31\!\cdots\!00\)\(q^{85} + \)\(40\!\cdots\!92\)\(q^{86} + \)\(57\!\cdots\!40\)\(q^{87} + \)\(15\!\cdots\!12\)\(q^{88} + \)\(73\!\cdots\!30\)\(q^{89} + \)\(97\!\cdots\!00\)\(q^{90} + \)\(39\!\cdots\!96\)\(q^{91} + \)\(94\!\cdots\!16\)\(q^{92} + \)\(13\!\cdots\!48\)\(q^{93} + \)\(75\!\cdots\!76\)\(q^{94} + \)\(51\!\cdots\!00\)\(q^{95} + \)\(52\!\cdots\!32\)\(q^{96} + \)\(11\!\cdots\!82\)\(q^{97} + \)\(53\!\cdots\!12\)\(q^{98} + \)\(19\!\cdots\!32\)\(q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.19902e12 −0.707107
\(3\) −7.32556e17 −0.0115960 −0.00579801 0.999983i \(-0.501846\pi\)
−0.00579801 + 0.999983i \(0.501846\pi\)
\(4\) 4.83570e24 0.500000
\(5\) −1.23719e29 −1.21670 −0.608348 0.793670i \(-0.708168\pi\)
−0.608348 + 0.793670i \(0.708168\pi\)
\(6\) 1.61091e30 0.00819962
\(7\) 6.61589e34 0.561073 0.280537 0.959843i \(-0.409488\pi\)
0.280537 + 0.959843i \(0.409488\pi\)
\(8\) −1.06338e37 −0.353553
\(9\) −3.99030e39 −0.999866
\(10\) 2.72062e41 0.860334
\(11\) −2.35451e43 −1.42595 −0.712974 0.701191i \(-0.752652\pi\)
−0.712974 + 0.701191i \(0.752652\pi\)
\(12\) −3.54242e42 −0.00579801
\(13\) 2.17555e46 1.28505 0.642525 0.766265i \(-0.277887\pi\)
0.642525 + 0.766265i \(0.277887\pi\)
\(14\) −1.45485e47 −0.396739
\(15\) 9.06313e46 0.0141088
\(16\) 2.33840e49 0.250000
\(17\) −2.06003e51 −1.77928 −0.889638 0.456666i \(-0.849043\pi\)
−0.889638 + 0.456666i \(0.849043\pi\)
\(18\) 8.77477e51 0.707012
\(19\) −1.54338e53 −1.31886 −0.659429 0.751767i \(-0.729202\pi\)
−0.659429 + 0.751767i \(0.729202\pi\)
\(20\) −5.98270e53 −0.608348
\(21\) −4.84651e52 −0.00650621
\(22\) 5.17762e55 1.00830
\(23\) 3.09757e56 0.953491 0.476745 0.879041i \(-0.341816\pi\)
0.476745 + 0.879041i \(0.341816\pi\)
\(24\) 7.78987e54 0.00409981
\(25\) 4.96671e57 0.480350
\(26\) −4.78409e58 −0.908668
\(27\) 5.84663e57 0.0231905
\(28\) 3.19925e59 0.280537
\(29\) −4.67177e59 −0.0954914 −0.0477457 0.998860i \(-0.515204\pi\)
−0.0477457 + 0.998860i \(0.515204\pi\)
\(30\) −1.99300e59 −0.00997645
\(31\) −1.70498e61 −0.218881 −0.109441 0.993993i \(-0.534906\pi\)
−0.109441 + 0.993993i \(0.534906\pi\)
\(32\) −5.14220e61 −0.176777
\(33\) 1.72481e61 0.0165353
\(34\) 4.53006e63 1.25814
\(35\) −8.18513e63 −0.682656
\(36\) −1.92959e64 −0.499933
\(37\) −9.03184e64 −0.750593 −0.375297 0.926905i \(-0.622459\pi\)
−0.375297 + 0.926905i \(0.622459\pi\)
\(38\) 3.39393e65 0.932574
\(39\) −1.59371e64 −0.0149015
\(40\) 1.31561e66 0.430167
\(41\) −8.21191e66 −0.963638 −0.481819 0.876271i \(-0.660024\pi\)
−0.481819 + 0.876271i \(0.660024\pi\)
\(42\) 1.06576e65 0.00460059
\(43\) −5.19673e67 −0.844869 −0.422435 0.906393i \(-0.638824\pi\)
−0.422435 + 0.906393i \(0.638824\pi\)
\(44\) −1.13857e68 −0.712974
\(45\) 4.93677e68 1.21653
\(46\) −6.81164e68 −0.674220
\(47\) −3.72927e69 −1.51204 −0.756019 0.654550i \(-0.772858\pi\)
−0.756019 + 0.654550i \(0.772858\pi\)
\(48\) −1.71301e67 −0.00289900
\(49\) −9.52692e69 −0.685197
\(50\) −1.09219e70 −0.339659
\(51\) 1.50909e69 0.0206325
\(52\) 1.05203e71 0.642525
\(53\) −4.87207e71 −1.34979 −0.674893 0.737916i \(-0.735810\pi\)
−0.674893 + 0.737916i \(0.735810\pi\)
\(54\) −1.28569e70 −0.0163981
\(55\) 2.91298e72 1.73495
\(56\) −7.03522e71 −0.198369
\(57\) 1.13061e71 0.0152935
\(58\) 1.02733e72 0.0675226
\(59\) 2.59897e73 0.840316 0.420158 0.907451i \(-0.361975\pi\)
0.420158 + 0.907451i \(0.361975\pi\)
\(60\) 4.38266e71 0.00705441
\(61\) −2.95096e73 −0.239208 −0.119604 0.992822i \(-0.538162\pi\)
−0.119604 + 0.992822i \(0.538162\pi\)
\(62\) 3.74928e73 0.154772
\(63\) −2.63994e74 −0.560998
\(64\) 1.13078e74 0.125000
\(65\) −2.69158e75 −1.56352
\(66\) −3.79289e73 −0.0116922
\(67\) 9.82765e75 1.62310 0.811550 0.584283i \(-0.198624\pi\)
0.811550 + 0.584283i \(0.198624\pi\)
\(68\) −9.96170e75 −0.889638
\(69\) −2.26915e74 −0.0110567
\(70\) 1.79993e76 0.482711
\(71\) −2.74633e76 −0.408819 −0.204410 0.978885i \(-0.565527\pi\)
−0.204410 + 0.978885i \(0.565527\pi\)
\(72\) 4.24322e76 0.353506
\(73\) 1.97027e77 0.926035 0.463017 0.886349i \(-0.346767\pi\)
0.463017 + 0.886349i \(0.346767\pi\)
\(74\) 1.98612e77 0.530750
\(75\) −3.63839e75 −0.00557015
\(76\) −7.46332e77 −0.659429
\(77\) −1.55772e78 −0.800061
\(78\) 3.50461e76 0.0105369
\(79\) 2.44890e78 0.433957 0.216978 0.976176i \(-0.430380\pi\)
0.216978 + 0.976176i \(0.430380\pi\)
\(80\) −2.89306e78 −0.304174
\(81\) 1.59204e79 0.999597
\(82\) 1.80582e79 0.681395
\(83\) −4.50780e79 −1.02855 −0.514273 0.857627i \(-0.671938\pi\)
−0.514273 + 0.857627i \(0.671938\pi\)
\(84\) −2.34363e77 −0.00325311
\(85\) 2.54866e80 2.16484
\(86\) 1.14277e80 0.597413
\(87\) 3.42233e77 0.00110732
\(88\) 2.50374e80 0.504149
\(89\) 1.00507e81 1.26623 0.633115 0.774058i \(-0.281776\pi\)
0.633115 + 0.774058i \(0.281776\pi\)
\(90\) −1.08561e81 −0.860219
\(91\) 1.43932e81 0.721007
\(92\) 1.49790e81 0.476745
\(93\) 1.24899e79 0.00253815
\(94\) 8.20075e81 1.06917
\(95\) 1.90946e82 1.60465
\(96\) 3.76695e79 0.00204990
\(97\) 2.37614e82 0.841096 0.420548 0.907270i \(-0.361838\pi\)
0.420548 + 0.907270i \(0.361838\pi\)
\(98\) 2.09499e82 0.484507
\(99\) 9.39519e82 1.42576
\(100\) 2.40175e82 0.240175
\(101\) 1.86756e83 1.23577 0.617884 0.786269i \(-0.287990\pi\)
0.617884 + 0.786269i \(0.287990\pi\)
\(102\) −3.31852e81 −0.0145894
\(103\) −1.33705e83 −0.392105 −0.196052 0.980593i \(-0.562812\pi\)
−0.196052 + 0.980593i \(0.562812\pi\)
\(104\) −2.31344e83 −0.454334
\(105\) 5.99607e81 0.00791609
\(106\) 1.07138e84 0.954443
\(107\) −1.76716e84 −1.06623 −0.533114 0.846044i \(-0.678978\pi\)
−0.533114 + 0.846044i \(0.678978\pi\)
\(108\) 2.82726e82 0.0115952
\(109\) 1.72699e83 0.0483159 0.0241579 0.999708i \(-0.492310\pi\)
0.0241579 + 0.999708i \(0.492310\pi\)
\(110\) −6.40571e84 −1.22679
\(111\) 6.61633e82 0.00870389
\(112\) 1.54706e84 0.140268
\(113\) −4.40696e84 −0.276302 −0.138151 0.990411i \(-0.544116\pi\)
−0.138151 + 0.990411i \(0.544116\pi\)
\(114\) −2.48624e83 −0.0108141
\(115\) −3.83230e85 −1.16011
\(116\) −2.25913e84 −0.0477457
\(117\) −8.68110e85 −1.28488
\(118\) −5.71520e85 −0.594193
\(119\) −1.36289e86 −0.998305
\(120\) −9.63757e83 −0.00498822
\(121\) 2.81728e86 1.03333
\(122\) 6.48923e85 0.169145
\(123\) 6.01568e84 0.0111744
\(124\) −8.24476e85 −0.109441
\(125\) 6.64750e86 0.632256
\(126\) 5.80529e86 0.396685
\(127\) 2.59885e87 1.27916 0.639582 0.768722i \(-0.279107\pi\)
0.639582 + 0.768722i \(0.279107\pi\)
\(128\) −2.48662e86 −0.0883883
\(129\) 3.80690e85 0.00979711
\(130\) 5.91884e87 1.10557
\(131\) 7.20837e87 0.979667 0.489833 0.871816i \(-0.337058\pi\)
0.489833 + 0.871816i \(0.337058\pi\)
\(132\) 8.34066e85 0.00826765
\(133\) −1.02108e88 −0.739976
\(134\) −2.16112e88 −1.14770
\(135\) −7.23341e86 −0.0282158
\(136\) 2.19060e88 0.629069
\(137\) 7.82178e88 1.65730 0.828651 0.559765i \(-0.189109\pi\)
0.828651 + 0.559765i \(0.189109\pi\)
\(138\) 4.98991e86 0.00781826
\(139\) −1.30461e89 −1.51484 −0.757419 0.652929i \(-0.773540\pi\)
−0.757419 + 0.652929i \(0.773540\pi\)
\(140\) −3.95809e88 −0.341328
\(141\) 2.73190e87 0.0175336
\(142\) 6.03925e88 0.289079
\(143\) −5.12235e89 −1.83241
\(144\) −9.33093e88 −0.249966
\(145\) 5.77988e88 0.116184
\(146\) −4.33267e89 −0.654806
\(147\) 6.97900e87 0.00794555
\(148\) −4.36753e89 −0.375297
\(149\) −3.63174e89 −0.235985 −0.117993 0.993014i \(-0.537646\pi\)
−0.117993 + 0.993014i \(0.537646\pi\)
\(150\) 8.00090e87 0.00393869
\(151\) −1.21094e90 −0.452458 −0.226229 0.974074i \(-0.572640\pi\)
−0.226229 + 0.974074i \(0.572640\pi\)
\(152\) 1.64120e90 0.466287
\(153\) 8.22014e90 1.77904
\(154\) 3.42545e90 0.565729
\(155\) 2.10938e90 0.266312
\(156\) −7.70672e88 −0.00745073
\(157\) 1.43682e91 1.06554 0.532768 0.846262i \(-0.321152\pi\)
0.532768 + 0.846262i \(0.321152\pi\)
\(158\) −5.38518e90 −0.306854
\(159\) 3.56906e89 0.0156521
\(160\) 6.36190e90 0.215084
\(161\) 2.04932e91 0.534978
\(162\) −3.50093e91 −0.706822
\(163\) −6.52333e90 −0.102020 −0.0510098 0.998698i \(-0.516244\pi\)
−0.0510098 + 0.998698i \(0.516244\pi\)
\(164\) −3.97104e91 −0.481819
\(165\) −2.13392e90 −0.0201184
\(166\) 9.91275e91 0.727292
\(167\) −2.55968e92 −1.46370 −0.731849 0.681467i \(-0.761342\pi\)
−0.731849 + 0.681467i \(0.761342\pi\)
\(168\) 5.15369e89 0.00230029
\(169\) 1.86687e92 0.651354
\(170\) −5.60455e92 −1.53077
\(171\) 6.15855e92 1.31868
\(172\) −2.51299e92 −0.422435
\(173\) −1.23154e93 −1.62755 −0.813777 0.581177i \(-0.802592\pi\)
−0.813777 + 0.581177i \(0.802592\pi\)
\(174\) −7.52579e89 −0.000782993 0
\(175\) 3.28592e92 0.269512
\(176\) −5.50579e92 −0.356487
\(177\) −1.90389e91 −0.00974432
\(178\) −2.21018e93 −0.895360
\(179\) 4.00341e93 1.28537 0.642687 0.766129i \(-0.277820\pi\)
0.642687 + 0.766129i \(0.277820\pi\)
\(180\) 2.38728e93 0.608266
\(181\) 7.45433e93 1.50920 0.754602 0.656183i \(-0.227830\pi\)
0.754602 + 0.656183i \(0.227830\pi\)
\(182\) −3.16510e93 −0.509829
\(183\) 2.16174e91 0.00277386
\(184\) −3.29391e93 −0.337110
\(185\) 1.11741e94 0.913244
\(186\) −2.74656e91 −0.00179474
\(187\) 4.85036e94 2.53716
\(188\) −1.80336e94 −0.756019
\(189\) 3.86807e92 0.0130116
\(190\) −4.19894e94 −1.13466
\(191\) −2.24626e94 −0.488176 −0.244088 0.969753i \(-0.578488\pi\)
−0.244088 + 0.969753i \(0.578488\pi\)
\(192\) −8.28361e91 −0.00144950
\(193\) −8.03970e94 −1.13400 −0.566998 0.823719i \(-0.691895\pi\)
−0.566998 + 0.823719i \(0.691895\pi\)
\(194\) −5.22519e94 −0.594744
\(195\) 1.97173e93 0.0181305
\(196\) −4.60694e94 −0.342598
\(197\) 1.17845e95 0.709516 0.354758 0.934958i \(-0.384563\pi\)
0.354758 + 0.934958i \(0.384563\pi\)
\(198\) −2.06603e95 −1.00816
\(199\) 2.16660e95 0.857781 0.428891 0.903356i \(-0.358905\pi\)
0.428891 + 0.903356i \(0.358905\pi\)
\(200\) −5.28151e94 −0.169829
\(201\) −7.19930e93 −0.0188215
\(202\) −4.10680e95 −0.873820
\(203\) −3.09079e94 −0.0535777
\(204\) 7.29750e93 0.0103163
\(205\) 1.01597e96 1.17246
\(206\) 2.94020e95 0.277260
\(207\) −1.23603e96 −0.953363
\(208\) 5.08731e95 0.321263
\(209\) 3.63390e96 1.88062
\(210\) −1.31855e94 −0.00559752
\(211\) −1.07711e96 −0.375439 −0.187719 0.982223i \(-0.560110\pi\)
−0.187719 + 0.982223i \(0.560110\pi\)
\(212\) −2.35599e96 −0.674893
\(213\) 2.01184e94 0.00474067
\(214\) 3.88603e96 0.753936
\(215\) 6.42936e96 1.02795
\(216\) −6.21720e94 −0.00819907
\(217\) −1.12799e96 −0.122808
\(218\) −3.79769e95 −0.0341645
\(219\) −1.44333e95 −0.0107383
\(220\) 1.40863e97 0.867473
\(221\) −4.48170e97 −2.28646
\(222\) −1.45495e95 −0.00615458
\(223\) −4.04527e97 −1.42002 −0.710011 0.704190i \(-0.751310\pi\)
−0.710011 + 0.704190i \(0.751310\pi\)
\(224\) −3.40202e96 −0.0991847
\(225\) −1.98187e97 −0.480286
\(226\) 9.69100e96 0.195375
\(227\) −8.85082e96 −0.148563 −0.0742815 0.997237i \(-0.523666\pi\)
−0.0742815 + 0.997237i \(0.523666\pi\)
\(228\) 5.46730e95 0.00764675
\(229\) −2.54255e96 −0.0296549 −0.0148274 0.999890i \(-0.504720\pi\)
−0.0148274 + 0.999890i \(0.504720\pi\)
\(230\) 8.42731e97 0.820321
\(231\) 1.14111e96 0.00927752
\(232\) 4.96788e96 0.0337613
\(233\) −1.71386e98 −0.974324 −0.487162 0.873312i \(-0.661968\pi\)
−0.487162 + 0.873312i \(0.661968\pi\)
\(234\) 1.90899e98 0.908545
\(235\) 4.61382e98 1.83969
\(236\) 1.25679e98 0.420158
\(237\) −1.79395e96 −0.00503217
\(238\) 2.99704e98 0.705908
\(239\) −6.03124e98 −1.19370 −0.596848 0.802354i \(-0.703580\pi\)
−0.596848 + 0.802354i \(0.703580\pi\)
\(240\) 2.11932e96 0.00352721
\(241\) 5.02162e98 0.703293 0.351646 0.936133i \(-0.385622\pi\)
0.351646 + 0.936133i \(0.385622\pi\)
\(242\) −6.19527e98 −0.730673
\(243\) −3.49955e97 −0.0347818
\(244\) −1.42700e98 −0.119604
\(245\) 1.17866e99 0.833676
\(246\) −1.32286e97 −0.00790147
\(247\) −3.35770e99 −1.69480
\(248\) 1.81304e98 0.0773861
\(249\) 3.30221e97 0.0119270
\(250\) −1.46180e99 −0.447072
\(251\) 5.27365e99 1.36663 0.683317 0.730122i \(-0.260537\pi\)
0.683317 + 0.730122i \(0.260537\pi\)
\(252\) −1.27660e99 −0.280499
\(253\) −7.29326e99 −1.35963
\(254\) −5.71493e99 −0.904506
\(255\) −1.86703e98 −0.0251035
\(256\) 5.46813e98 0.0625000
\(257\) 1.47183e100 1.43098 0.715488 0.698625i \(-0.246204\pi\)
0.715488 + 0.698625i \(0.246204\pi\)
\(258\) −8.37145e97 −0.00692760
\(259\) −5.97537e99 −0.421138
\(260\) −1.30157e100 −0.781758
\(261\) 1.86418e99 0.0954786
\(262\) −1.58514e100 −0.692729
\(263\) 3.80826e100 1.42090 0.710449 0.703749i \(-0.248492\pi\)
0.710449 + 0.703749i \(0.248492\pi\)
\(264\) −1.83413e98 −0.00584611
\(265\) 6.02769e100 1.64228
\(266\) 2.24538e100 0.523242
\(267\) −7.36273e98 −0.0146832
\(268\) 4.75236e100 0.811550
\(269\) −5.22540e100 −0.764539 −0.382269 0.924051i \(-0.624857\pi\)
−0.382269 + 0.924051i \(0.624857\pi\)
\(270\) 1.59064e99 0.0199516
\(271\) 7.94839e100 0.855172 0.427586 0.903975i \(-0.359364\pi\)
0.427586 + 0.903975i \(0.359364\pi\)
\(272\) −4.81718e100 −0.444819
\(273\) −1.05438e99 −0.00836081
\(274\) −1.72003e101 −1.17189
\(275\) −1.16941e101 −0.684954
\(276\) −1.09729e99 −0.00552835
\(277\) −3.58227e101 −1.55327 −0.776637 0.629948i \(-0.783076\pi\)
−0.776637 + 0.629948i \(0.783076\pi\)
\(278\) 2.86887e101 1.07115
\(279\) 6.80337e100 0.218852
\(280\) 8.70393e100 0.241355
\(281\) −5.10359e101 −1.22057 −0.610286 0.792181i \(-0.708946\pi\)
−0.610286 + 0.792181i \(0.708946\pi\)
\(282\) −6.00751e99 −0.0123981
\(283\) −4.70816e101 −0.838907 −0.419454 0.907777i \(-0.637778\pi\)
−0.419454 + 0.907777i \(0.637778\pi\)
\(284\) −1.32804e101 −0.204410
\(285\) −1.39878e100 −0.0186075
\(286\) 1.12642e102 1.29571
\(287\) −5.43291e101 −0.540672
\(288\) 2.05189e101 0.176753
\(289\) 2.90325e102 2.16582
\(290\) −1.27101e101 −0.0821546
\(291\) −1.74066e100 −0.00975335
\(292\) 9.52765e101 0.463017
\(293\) −7.77907e101 −0.328036 −0.164018 0.986457i \(-0.552446\pi\)
−0.164018 + 0.986457i \(0.552446\pi\)
\(294\) −1.53470e100 −0.00561835
\(295\) −3.21543e102 −1.02241
\(296\) 9.60430e101 0.265375
\(297\) −1.37659e101 −0.0330684
\(298\) 7.98629e101 0.166867
\(299\) 6.73893e102 1.22528
\(300\) −1.75942e100 −0.00278507
\(301\) −3.43810e102 −0.474034
\(302\) 2.66288e102 0.319936
\(303\) −1.36809e101 −0.0143300
\(304\) −3.60904e102 −0.329715
\(305\) 3.65091e102 0.291043
\(306\) −1.80763e103 −1.25797
\(307\) −2.89674e102 −0.176062 −0.0880312 0.996118i \(-0.528058\pi\)
−0.0880312 + 0.996118i \(0.528058\pi\)
\(308\) −7.53265e102 −0.400031
\(309\) 9.79462e100 0.00454685
\(310\) −4.63859e102 −0.188311
\(311\) −1.09171e103 −0.387749 −0.193875 0.981026i \(-0.562105\pi\)
−0.193875 + 0.981026i \(0.562105\pi\)
\(312\) 1.69473e101 0.00526846
\(313\) −9.43698e102 −0.256888 −0.128444 0.991717i \(-0.540998\pi\)
−0.128444 + 0.991717i \(0.540998\pi\)
\(314\) −3.15961e103 −0.753447
\(315\) 3.26612e103 0.682564
\(316\) 1.18421e103 0.216978
\(317\) 2.18142e103 0.350574 0.175287 0.984517i \(-0.443915\pi\)
0.175287 + 0.984517i \(0.443915\pi\)
\(318\) −7.84845e101 −0.0110677
\(319\) 1.09997e103 0.136166
\(320\) −1.39900e103 −0.152087
\(321\) 1.29455e102 0.0123640
\(322\) −4.50651e103 −0.378287
\(323\) 3.17941e104 2.34661
\(324\) 7.69862e103 0.499798
\(325\) 1.08053e104 0.617274
\(326\) 1.43450e103 0.0721388
\(327\) −1.26512e101 −0.000560271 0
\(328\) 8.73240e103 0.340698
\(329\) −2.46724e104 −0.848364
\(330\) 4.69254e102 0.0142259
\(331\) −5.37346e104 −1.43679 −0.718394 0.695637i \(-0.755122\pi\)
−0.718394 + 0.695637i \(0.755122\pi\)
\(332\) −2.17984e104 −0.514273
\(333\) 3.60398e104 0.750492
\(334\) 5.62879e104 1.03499
\(335\) −1.21587e105 −1.97482
\(336\) −1.13331e102 −0.00162655
\(337\) −6.28692e104 −0.797622 −0.398811 0.917033i \(-0.630577\pi\)
−0.398811 + 0.917033i \(0.630577\pi\)
\(338\) −4.10530e104 −0.460577
\(339\) 3.22834e102 0.00320400
\(340\) 1.23245e105 1.08242
\(341\) 4.01438e104 0.312113
\(342\) −1.35428e105 −0.932448
\(343\) −1.55016e105 −0.945519
\(344\) 5.52611e104 0.298706
\(345\) 2.80737e103 0.0134526
\(346\) 2.70819e105 1.15085
\(347\) 3.23846e105 1.22086 0.610429 0.792071i \(-0.290997\pi\)
0.610429 + 0.792071i \(0.290997\pi\)
\(348\) 1.65494e102 0.000553660 0
\(349\) −1.45038e105 −0.430752 −0.215376 0.976531i \(-0.569098\pi\)
−0.215376 + 0.976531i \(0.569098\pi\)
\(350\) −7.22581e104 −0.190574
\(351\) 1.27196e104 0.0298009
\(352\) 1.21074e105 0.252074
\(353\) −1.83016e105 −0.338718 −0.169359 0.985554i \(-0.554170\pi\)
−0.169359 + 0.985554i \(0.554170\pi\)
\(354\) 4.18670e103 0.00689027
\(355\) 3.39774e105 0.497409
\(356\) 4.86024e105 0.633115
\(357\) 9.98396e103 0.0115764
\(358\) −8.80360e105 −0.908897
\(359\) 1.83689e106 1.68913 0.844566 0.535452i \(-0.179859\pi\)
0.844566 + 0.535452i \(0.179859\pi\)
\(360\) −5.24968e105 −0.430109
\(361\) 1.01256e106 0.739387
\(362\) −1.63923e106 −1.06717
\(363\) −2.06382e104 −0.0119825
\(364\) 6.96013e105 0.360504
\(365\) −2.43761e106 −1.12670
\(366\) −4.75372e103 −0.00196141
\(367\) −2.93248e106 −1.08042 −0.540212 0.841529i \(-0.681656\pi\)
−0.540212 + 0.841529i \(0.681656\pi\)
\(368\) 7.24338e105 0.238373
\(369\) 3.27680e106 0.963509
\(370\) −2.45722e106 −0.645761
\(371\) −3.22331e106 −0.757329
\(372\) 6.03975e103 0.00126907
\(373\) 3.30772e106 0.621745 0.310873 0.950452i \(-0.399379\pi\)
0.310873 + 0.950452i \(0.399379\pi\)
\(374\) −1.06660e107 −1.79404
\(375\) −4.86967e104 −0.00733165
\(376\) 3.96564e106 0.534586
\(377\) −1.01637e106 −0.122711
\(378\) −8.50597e104 −0.00920056
\(379\) 2.50774e106 0.243084 0.121542 0.992586i \(-0.461216\pi\)
0.121542 + 0.992586i \(0.461216\pi\)
\(380\) 9.23357e106 0.802325
\(381\) −1.90380e105 −0.0148332
\(382\) 4.93959e106 0.345192
\(383\) 1.15247e107 0.722571 0.361286 0.932455i \(-0.382338\pi\)
0.361286 + 0.932455i \(0.382338\pi\)
\(384\) 1.82159e104 0.00102495
\(385\) 1.92720e107 0.973432
\(386\) 1.76795e107 0.801856
\(387\) 2.07365e107 0.844756
\(388\) 1.14903e107 0.420548
\(389\) −3.97495e107 −1.30744 −0.653722 0.756735i \(-0.726793\pi\)
−0.653722 + 0.756735i \(0.726793\pi\)
\(390\) −4.33588e105 −0.0128202
\(391\) −6.38110e107 −1.69652
\(392\) 1.01308e107 0.242254
\(393\) −5.28053e105 −0.0113602
\(394\) −2.59143e107 −0.501703
\(395\) −3.02976e107 −0.527994
\(396\) 4.54324e107 0.712878
\(397\) 1.94436e107 0.274770 0.137385 0.990518i \(-0.456130\pi\)
0.137385 + 0.990518i \(0.456130\pi\)
\(398\) −4.76441e107 −0.606543
\(399\) 7.48000e105 0.00858077
\(400\) 1.16142e107 0.120088
\(401\) −1.42569e108 −1.32903 −0.664513 0.747277i \(-0.731361\pi\)
−0.664513 + 0.747277i \(0.731361\pi\)
\(402\) 1.58314e106 0.0133088
\(403\) −3.70926e107 −0.281273
\(404\) 9.03095e107 0.617884
\(405\) −1.96966e108 −1.21621
\(406\) 6.79672e106 0.0378852
\(407\) 2.12655e108 1.07031
\(408\) −1.60474e106 −0.00729469
\(409\) 3.38003e108 1.38804 0.694021 0.719955i \(-0.255837\pi\)
0.694021 + 0.719955i \(0.255837\pi\)
\(410\) −2.23414e108 −0.829051
\(411\) −5.72989e106 −0.0192181
\(412\) −6.46557e107 −0.196052
\(413\) 1.71945e108 0.471479
\(414\) 2.71805e108 0.674129
\(415\) 5.57701e108 1.25143
\(416\) −1.11871e108 −0.227167
\(417\) 9.55699e106 0.0175661
\(418\) −7.99102e108 −1.32980
\(419\) −1.08958e109 −1.64202 −0.821008 0.570917i \(-0.806588\pi\)
−0.821008 + 0.570917i \(0.806588\pi\)
\(420\) 2.89952e106 0.00395804
\(421\) 1.48564e109 1.83741 0.918705 0.394945i \(-0.129236\pi\)
0.918705 + 0.394945i \(0.129236\pi\)
\(422\) 2.36859e108 0.265475
\(423\) 1.48809e109 1.51183
\(424\) 5.18087e108 0.477221
\(425\) −1.02316e109 −0.854676
\(426\) −4.42408e106 −0.00335216
\(427\) −1.95232e108 −0.134213
\(428\) −8.54547e108 −0.533114
\(429\) 3.75241e107 0.0212487
\(430\) −1.41383e109 −0.726870
\(431\) −2.63902e109 −1.23207 −0.616035 0.787719i \(-0.711262\pi\)
−0.616035 + 0.787719i \(0.711262\pi\)
\(432\) 1.36718e107 0.00579762
\(433\) 7.65361e108 0.294862 0.147431 0.989072i \(-0.452900\pi\)
0.147431 + 0.989072i \(0.452900\pi\)
\(434\) 2.48048e108 0.0868386
\(435\) −4.23408e106 −0.00134727
\(436\) 8.35120e107 0.0241579
\(437\) −4.78073e109 −1.25752
\(438\) 3.17392e107 0.00759313
\(439\) −3.61884e109 −0.787574 −0.393787 0.919202i \(-0.628835\pi\)
−0.393787 + 0.919202i \(0.628835\pi\)
\(440\) −3.09761e109 −0.613396
\(441\) 3.80153e109 0.685105
\(442\) 9.85536e109 1.61677
\(443\) 5.85530e109 0.874570 0.437285 0.899323i \(-0.355940\pi\)
0.437285 + 0.899323i \(0.355940\pi\)
\(444\) 3.19946e107 0.00435194
\(445\) −1.24347e110 −1.54062
\(446\) 8.89564e109 1.00411
\(447\) 2.66045e107 0.00273649
\(448\) 7.48113e108 0.0701342
\(449\) 1.16917e110 0.999206 0.499603 0.866255i \(-0.333479\pi\)
0.499603 + 0.866255i \(0.333479\pi\)
\(450\) 4.35817e109 0.339613
\(451\) 1.93350e110 1.37410
\(452\) −2.13107e109 −0.138151
\(453\) 8.87078e107 0.00524670
\(454\) 1.94632e109 0.105050
\(455\) −1.78072e110 −0.877247
\(456\) −1.20227e108 −0.00540707
\(457\) 4.93283e108 0.0202570 0.0101285 0.999949i \(-0.496776\pi\)
0.0101285 + 0.999949i \(0.496776\pi\)
\(458\) 5.59112e108 0.0209692
\(459\) −1.20442e109 −0.0412622
\(460\) −1.85319e110 −0.580055
\(461\) −4.52351e110 −1.29386 −0.646930 0.762550i \(-0.723947\pi\)
−0.646930 + 0.762550i \(0.723947\pi\)
\(462\) −2.50934e108 −0.00656020
\(463\) −2.00646e110 −0.479533 −0.239766 0.970831i \(-0.577071\pi\)
−0.239766 + 0.970831i \(0.577071\pi\)
\(464\) −1.09245e109 −0.0238729
\(465\) −1.54524e108 −0.00308815
\(466\) 3.76881e110 0.688951
\(467\) −1.74428e110 −0.291720 −0.145860 0.989305i \(-0.546595\pi\)
−0.145860 + 0.989305i \(0.546595\pi\)
\(468\) −4.19792e110 −0.642439
\(469\) 6.50186e110 0.910678
\(470\) −1.01459e111 −1.30086
\(471\) −1.05255e109 −0.0123560
\(472\) −2.76370e110 −0.297097
\(473\) 1.22357e111 1.20474
\(474\) 3.94495e108 0.00355828
\(475\) −7.66551e110 −0.633514
\(476\) −6.59055e110 −0.499152
\(477\) 1.94410e111 1.34960
\(478\) 1.32628e111 0.844070
\(479\) 1.70754e111 0.996431 0.498216 0.867053i \(-0.333989\pi\)
0.498216 + 0.867053i \(0.333989\pi\)
\(480\) −4.66044e108 −0.00249411
\(481\) −1.96492e111 −0.964550
\(482\) −1.10426e111 −0.497303
\(483\) −1.50124e109 −0.00620362
\(484\) 1.36236e111 0.516664
\(485\) −2.93975e111 −1.02336
\(486\) 7.69559e109 0.0245944
\(487\) 5.73073e111 1.68174 0.840869 0.541239i \(-0.182045\pi\)
0.840869 + 0.541239i \(0.182045\pi\)
\(488\) 3.13800e110 0.0845727
\(489\) 4.77870e108 0.00118302
\(490\) −2.59191e111 −0.589498
\(491\) 3.97537e111 0.830799 0.415400 0.909639i \(-0.363642\pi\)
0.415400 + 0.909639i \(0.363642\pi\)
\(492\) 2.90900e109 0.00558718
\(493\) 9.62399e110 0.169906
\(494\) 7.38366e111 1.19840
\(495\) −1.16237e112 −1.73471
\(496\) −3.98692e110 −0.0547203
\(497\) −1.81694e111 −0.229378
\(498\) −7.26164e109 −0.00843368
\(499\) −1.46410e112 −1.56458 −0.782288 0.622916i \(-0.785948\pi\)
−0.782288 + 0.622916i \(0.785948\pi\)
\(500\) 3.21453e111 0.316128
\(501\) 1.87511e110 0.0169731
\(502\) −1.15969e112 −0.966356
\(503\) 2.83844e111 0.217775 0.108888 0.994054i \(-0.465271\pi\)
0.108888 + 0.994054i \(0.465271\pi\)
\(504\) 2.80727e111 0.198343
\(505\) −2.31053e112 −1.50355
\(506\) 1.60381e112 0.961402
\(507\) −1.36759e110 −0.00755310
\(508\) 1.25673e112 0.639582
\(509\) −7.25643e111 −0.340357 −0.170179 0.985413i \(-0.554434\pi\)
−0.170179 + 0.985413i \(0.554434\pi\)
\(510\) 4.10565e110 0.0177509
\(511\) 1.30351e112 0.519574
\(512\) −1.20245e111 −0.0441942
\(513\) −9.02357e110 −0.0305849
\(514\) −3.23658e112 −1.01185
\(515\) 1.65419e112 0.477072
\(516\) 1.84090e110 0.00489856
\(517\) 8.78059e112 2.15609
\(518\) 1.31400e112 0.297789
\(519\) 9.02172e110 0.0188731
\(520\) 2.86217e112 0.552786
\(521\) 5.90803e112 1.05360 0.526802 0.849988i \(-0.323391\pi\)
0.526802 + 0.849988i \(0.323391\pi\)
\(522\) −4.09937e111 −0.0675136
\(523\) −6.09468e112 −0.927110 −0.463555 0.886068i \(-0.653426\pi\)
−0.463555 + 0.886068i \(0.653426\pi\)
\(524\) 3.48575e112 0.489833
\(525\) −2.40712e110 −0.00312526
\(526\) −8.37445e112 −1.00473
\(527\) 3.51230e112 0.389450
\(528\) 4.03330e110 0.00413383
\(529\) −9.58868e111 −0.0908550
\(530\) −1.32550e113 −1.16127
\(531\) −1.03707e113 −0.840203
\(532\) −4.93765e112 −0.369988
\(533\) −1.78654e113 −1.23832
\(534\) 1.61908e111 0.0103826
\(535\) 2.18632e113 1.29727
\(536\) −1.04505e113 −0.573852
\(537\) −2.93272e111 −0.0149052
\(538\) 1.14908e113 0.540611
\(539\) 2.24312e113 0.977055
\(540\) −3.49786e111 −0.0141079
\(541\) −2.22947e113 −0.832750 −0.416375 0.909193i \(-0.636700\pi\)
−0.416375 + 0.909193i \(0.636700\pi\)
\(542\) −1.74787e113 −0.604698
\(543\) −5.46071e111 −0.0175007
\(544\) 1.05931e113 0.314535
\(545\) −2.13662e112 −0.0587857
\(546\) 2.31861e111 0.00591199
\(547\) −2.02028e113 −0.477460 −0.238730 0.971086i \(-0.576731\pi\)
−0.238730 + 0.971086i \(0.576731\pi\)
\(548\) 3.78238e113 0.828651
\(549\) 1.17752e113 0.239176
\(550\) 2.57157e113 0.484336
\(551\) 7.21031e112 0.125940
\(552\) 2.41297e111 0.00390913
\(553\) 1.62016e113 0.243482
\(554\) 7.87750e113 1.09833
\(555\) −8.18567e111 −0.0105900
\(556\) −6.30870e113 −0.757419
\(557\) 7.81160e113 0.870462 0.435231 0.900319i \(-0.356667\pi\)
0.435231 + 0.900319i \(0.356667\pi\)
\(558\) −1.49608e113 −0.154751
\(559\) −1.13058e114 −1.08570
\(560\) −1.91401e113 −0.170664
\(561\) −3.55316e112 −0.0294209
\(562\) 1.12229e114 0.863075
\(563\) −8.55541e113 −0.611143 −0.305571 0.952169i \(-0.598847\pi\)
−0.305571 + 0.952169i \(0.598847\pi\)
\(564\) 1.32106e112 0.00876680
\(565\) 5.45225e113 0.336175
\(566\) 1.03534e114 0.593197
\(567\) 1.05327e114 0.560847
\(568\) 2.92040e113 0.144539
\(569\) −3.03861e114 −1.39803 −0.699014 0.715108i \(-0.746377\pi\)
−0.699014 + 0.715108i \(0.746377\pi\)
\(570\) 3.07596e112 0.0131575
\(571\) −2.02235e114 −0.804372 −0.402186 0.915558i \(-0.631749\pi\)
−0.402186 + 0.915558i \(0.631749\pi\)
\(572\) −2.47702e114 −0.916207
\(573\) 1.64551e112 0.00566089
\(574\) 1.19471e114 0.382313
\(575\) 1.53847e114 0.458010
\(576\) −4.51216e113 −0.124983
\(577\) −1.99169e114 −0.513363 −0.256682 0.966496i \(-0.582629\pi\)
−0.256682 + 0.966496i \(0.582629\pi\)
\(578\) −6.38431e114 −1.53147
\(579\) 5.88953e112 0.0131498
\(580\) 2.79498e113 0.0580920
\(581\) −2.98231e114 −0.577090
\(582\) 3.82774e112 0.00689666
\(583\) 1.14713e115 1.92472
\(584\) −2.09515e114 −0.327403
\(585\) 1.07402e115 1.56331
\(586\) 1.71064e114 0.231956
\(587\) −7.37323e114 −0.931487 −0.465743 0.884920i \(-0.654213\pi\)
−0.465743 + 0.884920i \(0.654213\pi\)
\(588\) 3.37484e112 0.00397277
\(589\) 2.63143e114 0.288673
\(590\) 7.07080e114 0.722953
\(591\) −8.63279e112 −0.00822755
\(592\) −2.11201e114 −0.187648
\(593\) 1.20108e115 0.994954 0.497477 0.867477i \(-0.334260\pi\)
0.497477 + 0.867477i \(0.334260\pi\)
\(594\) 3.02716e113 0.0233829
\(595\) 1.68616e115 1.21463
\(596\) −1.75620e114 −0.117993
\(597\) −1.58716e113 −0.00994684
\(598\) −1.48191e115 −0.866406
\(599\) 1.21792e115 0.664361 0.332181 0.943216i \(-0.392216\pi\)
0.332181 + 0.943216i \(0.392216\pi\)
\(600\) 3.86900e112 0.00196934
\(601\) −2.21766e115 −1.05343 −0.526715 0.850042i \(-0.676576\pi\)
−0.526715 + 0.850042i \(0.676576\pi\)
\(602\) 7.56047e114 0.335192
\(603\) −3.92153e115 −1.62288
\(604\) −5.85573e114 −0.226229
\(605\) −3.48552e115 −1.25725
\(606\) 3.00846e113 0.0101328
\(607\) 3.73785e115 1.17569 0.587844 0.808975i \(-0.299977\pi\)
0.587844 + 0.808975i \(0.299977\pi\)
\(608\) 7.93637e114 0.233143
\(609\) 2.26418e112 0.000621288 0
\(610\) −8.02843e114 −0.205799
\(611\) −8.11321e115 −1.94304
\(612\) 3.97502e115 0.889519
\(613\) −3.47576e115 −0.726842 −0.363421 0.931625i \(-0.618391\pi\)
−0.363421 + 0.931625i \(0.618391\pi\)
\(614\) 6.37000e114 0.124495
\(615\) −7.44256e113 −0.0135958
\(616\) 1.65645e115 0.282864
\(617\) 9.31989e115 1.48791 0.743955 0.668230i \(-0.232948\pi\)
0.743955 + 0.668230i \(0.232948\pi\)
\(618\) −2.15386e113 −0.00321511
\(619\) −3.57176e115 −0.498563 −0.249282 0.968431i \(-0.580195\pi\)
−0.249282 + 0.968431i \(0.580195\pi\)
\(620\) 1.02004e115 0.133156
\(621\) 1.81104e114 0.0221119
\(622\) 2.40069e115 0.274180
\(623\) 6.64946e115 0.710448
\(624\) −3.72674e113 −0.00372536
\(625\) −1.33597e116 −1.24961
\(626\) 2.07521e115 0.181647
\(627\) −2.66203e114 −0.0218077
\(628\) 6.94805e115 0.532768
\(629\) 1.86059e116 1.33551
\(630\) −7.18226e115 −0.482646
\(631\) 2.74127e116 1.72478 0.862388 0.506247i \(-0.168968\pi\)
0.862388 + 0.506247i \(0.168968\pi\)
\(632\) −2.60411e115 −0.153427
\(633\) 7.89044e113 0.00435359
\(634\) −4.79699e115 −0.247893
\(635\) −3.21528e116 −1.55636
\(636\) 1.72589e114 0.00782607
\(637\) −2.07263e116 −0.880512
\(638\) −2.41886e115 −0.0962838
\(639\) 1.09587e116 0.408764
\(640\) 3.07642e115 0.107542
\(641\) 1.15285e114 0.00377714 0.00188857 0.999998i \(-0.499399\pi\)
0.00188857 + 0.999998i \(0.499399\pi\)
\(642\) −2.84673e114 −0.00874266
\(643\) 5.51605e116 1.58808 0.794041 0.607865i \(-0.207974\pi\)
0.794041 + 0.607865i \(0.207974\pi\)
\(644\) 9.90991e115 0.267489
\(645\) −4.70987e114 −0.0119201
\(646\) −6.99159e116 −1.65931
\(647\) 2.69348e116 0.599495 0.299748 0.954019i \(-0.403098\pi\)
0.299748 + 0.954019i \(0.403098\pi\)
\(648\) −1.69294e116 −0.353411
\(649\) −6.11930e116 −1.19825
\(650\) −2.37611e116 −0.436479
\(651\) 8.26318e113 0.00142409
\(652\) −3.15449e115 −0.0510098
\(653\) 1.50164e116 0.227860 0.113930 0.993489i \(-0.463656\pi\)
0.113930 + 0.993489i \(0.463656\pi\)
\(654\) 2.78202e113 0.000396172 0
\(655\) −8.91815e116 −1.19196
\(656\) −1.92027e116 −0.240910
\(657\) −7.86198e116 −0.925910
\(658\) 5.42553e116 0.599884
\(659\) 6.97853e116 0.724468 0.362234 0.932087i \(-0.382014\pi\)
0.362234 + 0.932087i \(0.382014\pi\)
\(660\) −1.03190e115 −0.0100592
\(661\) 1.28721e117 1.17839 0.589196 0.807990i \(-0.299445\pi\)
0.589196 + 0.807990i \(0.299445\pi\)
\(662\) 1.18164e117 1.01596
\(663\) 3.28310e115 0.0265138
\(664\) 4.79351e116 0.363646
\(665\) 1.26328e117 0.900327
\(666\) −7.92523e116 −0.530678
\(667\) −1.44712e116 −0.0910502
\(668\) −1.23778e117 −0.731849
\(669\) 2.96338e115 0.0164666
\(670\) 2.67373e117 1.39641
\(671\) 6.94806e116 0.341098
\(672\) 2.49217e114 0.00115015
\(673\) −1.41274e117 −0.612966 −0.306483 0.951876i \(-0.599152\pi\)
−0.306483 + 0.951876i \(0.599152\pi\)
\(674\) 1.38251e117 0.564004
\(675\) 2.90385e115 0.0111395
\(676\) 9.02765e116 0.325677
\(677\) −2.45656e117 −0.833484 −0.416742 0.909025i \(-0.636828\pi\)
−0.416742 + 0.909025i \(0.636828\pi\)
\(678\) −7.09920e114 −0.00226557
\(679\) 1.57203e117 0.471916
\(680\) −2.71020e117 −0.765386
\(681\) 6.48372e114 0.00172274
\(682\) −8.82771e116 −0.220697
\(683\) −3.59496e117 −0.845737 −0.422869 0.906191i \(-0.638977\pi\)
−0.422869 + 0.906191i \(0.638977\pi\)
\(684\) 2.97809e117 0.659341
\(685\) −9.67705e117 −2.01643
\(686\) 3.40884e117 0.668583
\(687\) 1.86256e114 0.000343878 0
\(688\) −1.21521e117 −0.211217
\(689\) −1.05994e118 −1.73454
\(690\) −6.17348e115 −0.00951245
\(691\) 3.64308e117 0.528603 0.264302 0.964440i \(-0.414859\pi\)
0.264302 + 0.964440i \(0.414859\pi\)
\(692\) −5.95536e117 −0.813777
\(693\) 6.21576e117 0.799954
\(694\) −7.12144e117 −0.863276
\(695\) 1.61405e118 1.84310
\(696\) −3.63925e114 −0.000391497 0
\(697\) 1.69168e118 1.71458
\(698\) 3.18942e117 0.304588
\(699\) 1.25549e116 0.0112983
\(700\) 1.58897e117 0.134756
\(701\) −1.93265e118 −1.54474 −0.772371 0.635172i \(-0.780929\pi\)
−0.772371 + 0.635172i \(0.780929\pi\)
\(702\) −2.79708e116 −0.0210724
\(703\) 1.39396e118 0.989926
\(704\) −2.66243e117 −0.178243
\(705\) −3.37988e116 −0.0213331
\(706\) 4.02456e117 0.239510
\(707\) 1.23556e118 0.693356
\(708\) −9.20665e115 −0.00487216
\(709\) 2.50803e117 0.125174 0.0625870 0.998040i \(-0.480065\pi\)
0.0625870 + 0.998040i \(0.480065\pi\)
\(710\) −7.47171e117 −0.351721
\(711\) −9.77184e117 −0.433898
\(712\) −1.06878e118 −0.447680
\(713\) −5.28129e117 −0.208701
\(714\) −2.19550e116 −0.00818572
\(715\) 6.33733e118 2.22949
\(716\) 1.93593e118 0.642687
\(717\) 4.41822e116 0.0138421
\(718\) −4.03936e118 −1.19440
\(719\) −4.74549e118 −1.32444 −0.662220 0.749309i \(-0.730386\pi\)
−0.662220 + 0.749309i \(0.730386\pi\)
\(720\) 1.15442e118 0.304133
\(721\) −8.84576e117 −0.220000
\(722\) −2.22664e118 −0.522826
\(723\) −3.67861e116 −0.00815539
\(724\) 3.60469e118 0.754602
\(725\) −2.32033e117 −0.0458693
\(726\) 4.53838e116 0.00847289
\(727\) −7.22350e118 −1.27371 −0.636854 0.770985i \(-0.719764\pi\)
−0.636854 + 0.770985i \(0.719764\pi\)
\(728\) −1.53055e118 −0.254915
\(729\) −6.35100e118 −0.999193
\(730\) 5.36035e118 0.796700
\(731\) 1.07054e119 1.50326
\(732\) 1.04536e116 0.00138693
\(733\) −9.11017e118 −1.14212 −0.571060 0.820908i \(-0.693468\pi\)
−0.571060 + 0.820908i \(0.693468\pi\)
\(734\) 6.44860e118 0.763975
\(735\) −8.63437e116 −0.00966732
\(736\) −1.59284e118 −0.168555
\(737\) −2.31393e119 −2.31446
\(738\) −7.20576e118 −0.681304
\(739\) 1.20282e119 1.07512 0.537558 0.843227i \(-0.319347\pi\)
0.537558 + 0.843227i \(0.319347\pi\)
\(740\) 5.40348e118 0.456622
\(741\) 2.45970e117 0.0196529
\(742\) 7.08813e118 0.535512
\(743\) 1.32005e119 0.943096 0.471548 0.881840i \(-0.343695\pi\)
0.471548 + 0.881840i \(0.343695\pi\)
\(744\) −1.32815e116 −0.000897370 0
\(745\) 4.49317e118 0.287122
\(746\) −7.27376e118 −0.439640
\(747\) 1.79875e119 1.02841
\(748\) 2.34549e119 1.26858
\(749\) −1.16914e119 −0.598232
\(750\) 1.07085e117 0.00518426
\(751\) 1.21121e119 0.554833 0.277416 0.960750i \(-0.410522\pi\)
0.277416 + 0.960750i \(0.410522\pi\)
\(752\) −8.72053e118 −0.378009
\(753\) −3.86324e117 −0.0158475
\(754\) 2.23501e118 0.0867700
\(755\) 1.49816e119 0.550503
\(756\) 1.87048e117 0.00650578
\(757\) −1.68795e118 −0.0555750 −0.0277875 0.999614i \(-0.508846\pi\)
−0.0277875 + 0.999614i \(0.508846\pi\)
\(758\) −5.51459e118 −0.171886
\(759\) 5.34272e117 0.0157663
\(760\) −2.03048e119 −0.567330
\(761\) −2.63589e118 −0.0697371 −0.0348686 0.999392i \(-0.511101\pi\)
−0.0348686 + 0.999392i \(0.511101\pi\)
\(762\) 4.18650e117 0.0104887
\(763\) 1.14256e118 0.0271087
\(764\) −1.08623e119 −0.244088
\(765\) −1.01699e120 −2.16455
\(766\) −2.53431e119 −0.510935
\(767\) 5.65419e119 1.07985
\(768\) −4.00571e116 −0.000724751 0
\(769\) −1.12559e119 −0.192947 −0.0964736 0.995336i \(-0.530756\pi\)
−0.0964736 + 0.995336i \(0.530756\pi\)
\(770\) −4.23795e119 −0.688320
\(771\) −1.07820e118 −0.0165936
\(772\) −3.88776e119 −0.566998
\(773\) 1.59287e119 0.220157 0.110078 0.993923i \(-0.464890\pi\)
0.110078 + 0.993923i \(0.464890\pi\)
\(774\) −4.56001e119 −0.597332
\(775\) −8.46812e118 −0.105140
\(776\) −2.52675e119 −0.297372
\(777\) 4.37729e117 0.00488352
\(778\) 8.74100e119 0.924502
\(779\) 1.26741e120 1.27090
\(780\) 9.53470e117 0.00906527
\(781\) 6.46626e119 0.582955
\(782\) 1.40322e120 1.19962
\(783\) −2.73141e117 −0.00221449
\(784\) −2.22778e119 −0.171299
\(785\) −1.77763e120 −1.29643
\(786\) 1.16120e118 0.00803289
\(787\) 1.91554e120 1.25701 0.628506 0.777805i \(-0.283667\pi\)
0.628506 + 0.777805i \(0.283667\pi\)
\(788\) 5.69862e119 0.354758
\(789\) −2.78976e118 −0.0164767
\(790\) 6.66251e119 0.373348
\(791\) −2.91559e119 −0.155025
\(792\) −9.99068e119 −0.504081
\(793\) −6.41997e119 −0.307394
\(794\) −4.27569e119 −0.194292
\(795\) −4.41562e118 −0.0190439
\(796\) 1.04770e120 0.428891
\(797\) −3.07246e120 −1.19390 −0.596948 0.802280i \(-0.703620\pi\)
−0.596948 + 0.802280i \(0.703620\pi\)
\(798\) −1.64487e118 −0.00606752
\(799\) 7.68241e120 2.69033
\(800\) −2.55398e119 −0.0849147
\(801\) −4.01055e120 −1.26606
\(802\) 3.13512e120 0.939763
\(803\) −4.63902e120 −1.32048
\(804\) −3.48137e118 −0.00941074
\(805\) −2.53541e120 −0.650906
\(806\) 8.15675e119 0.198890
\(807\) 3.82789e118 0.00886560
\(808\) −1.98593e120 −0.436910
\(809\) −7.09944e120 −1.48375 −0.741874 0.670539i \(-0.766063\pi\)
−0.741874 + 0.670539i \(0.766063\pi\)
\(810\) 4.33132e120 0.859987
\(811\) 1.43742e120 0.271156 0.135578 0.990767i \(-0.456711\pi\)
0.135578 + 0.990767i \(0.456711\pi\)
\(812\) −1.49461e119 −0.0267888
\(813\) −5.82264e118 −0.00991658
\(814\) −4.67634e120 −0.756821
\(815\) 8.07062e119 0.124127
\(816\) 3.52885e118 0.00515813
\(817\) 8.02053e120 1.11426
\(818\) −7.43275e120 −0.981494
\(819\) −5.74332e120 −0.720910
\(820\) 4.91294e120 0.586228
\(821\) −7.78548e119 −0.0883170 −0.0441585 0.999025i \(-0.514061\pi\)
−0.0441585 + 0.999025i \(0.514061\pi\)
\(822\) 1.26002e119 0.0135892
\(823\) 1.65033e121 1.69230 0.846151 0.532943i \(-0.178914\pi\)
0.846151 + 0.532943i \(0.178914\pi\)
\(824\) 1.42179e120 0.138630
\(825\) 8.56661e118 0.00794274
\(826\) −3.78111e120 −0.333386
\(827\) −1.35079e121 −1.13269 −0.566343 0.824170i \(-0.691642\pi\)
−0.566343 + 0.824170i \(0.691642\pi\)
\(828\) −5.97705e120 −0.476681
\(829\) 6.10580e120 0.463158 0.231579 0.972816i \(-0.425611\pi\)
0.231579 + 0.972816i \(0.425611\pi\)
\(830\) −1.22640e121 −0.884893
\(831\) 2.62421e119 0.0180118
\(832\) 2.46007e120 0.160631
\(833\) 1.96257e121 1.21915
\(834\) −2.10160e119 −0.0124211
\(835\) 3.16681e121 1.78088
\(836\) 1.75724e121 0.940312
\(837\) −9.96837e118 −0.00507595
\(838\) 2.39601e121 1.16108
\(839\) 1.35734e121 0.625991 0.312996 0.949755i \(-0.398667\pi\)
0.312996 + 0.949755i \(0.398667\pi\)
\(840\) −6.37611e118 −0.00279876
\(841\) −2.37168e121 −0.990881
\(842\) −3.26695e121 −1.29924
\(843\) 3.73867e119 0.0141538
\(844\) −5.20859e120 −0.187719
\(845\) −2.30968e121 −0.792500
\(846\) −3.27235e121 −1.06903
\(847\) 1.86388e121 0.579772
\(848\) −1.13929e121 −0.337446
\(849\) 3.44899e119 0.00972798
\(850\) 2.24995e121 0.604347
\(851\) −2.79768e121 −0.715684
\(852\) 9.72866e118 0.00237034
\(853\) −1.76135e121 −0.408752 −0.204376 0.978892i \(-0.565517\pi\)
−0.204376 + 0.978892i \(0.565517\pi\)
\(854\) 4.29321e120 0.0949030
\(855\) −7.61931e121 −1.60443
\(856\) 1.87917e121 0.376968
\(857\) −1.71907e121 −0.328541 −0.164270 0.986415i \(-0.552527\pi\)
−0.164270 + 0.986415i \(0.552527\pi\)
\(858\) −8.25163e119 −0.0150251
\(859\) −1.24485e121 −0.215974 −0.107987 0.994152i \(-0.534440\pi\)
−0.107987 + 0.994152i \(0.534440\pi\)
\(860\) 3.10905e121 0.513975
\(861\) 3.97991e119 0.00626964
\(862\) 5.80326e121 0.871205
\(863\) −1.09444e122 −1.56583 −0.782914 0.622130i \(-0.786267\pi\)
−0.782914 + 0.622130i \(0.786267\pi\)
\(864\) −3.00646e119 −0.00409953
\(865\) 1.52365e122 1.98024
\(866\) −1.68305e121 −0.208499
\(867\) −2.12679e120 −0.0251149
\(868\) −5.45464e120 −0.0614042
\(869\) −5.76595e121 −0.618800
\(870\) 9.31085e118 0.000952665 0
\(871\) 2.13805e122 2.08576
\(872\) −1.83645e120 −0.0170822
\(873\) −9.48152e121 −0.840983
\(874\) 1.05129e122 0.889201
\(875\) 4.39791e121 0.354742
\(876\) −6.97953e119 −0.00536916
\(877\) 8.92250e121 0.654642 0.327321 0.944913i \(-0.393854\pi\)
0.327321 + 0.944913i \(0.393854\pi\)
\(878\) 7.95791e121 0.556899
\(879\) 5.69860e119 0.00380391
\(880\) 6.81172e121 0.433736
\(881\) 4.39476e121 0.266953 0.133476 0.991052i \(-0.457386\pi\)
0.133476 + 0.991052i \(0.457386\pi\)
\(882\) −8.35965e121 −0.484442
\(883\) −1.29544e122 −0.716223 −0.358112 0.933679i \(-0.616579\pi\)
−0.358112 + 0.933679i \(0.616579\pi\)
\(884\) −2.16722e122 −1.14323
\(885\) 2.35548e120 0.0118559
\(886\) −1.28759e122 −0.618414
\(887\) −1.63443e122 −0.749092 −0.374546 0.927208i \(-0.622201\pi\)
−0.374546 + 0.927208i \(0.622201\pi\)
\(888\) −7.03568e119 −0.00307729
\(889\) 1.71937e122 0.717705
\(890\) 2.73442e122 1.08938
\(891\) −3.74846e122 −1.42537
\(892\) −1.95617e122 −0.710011
\(893\) 5.75567e122 1.99416
\(894\) −5.85040e119 −0.00193499
\(895\) −4.95299e122 −1.56391
\(896\) −1.64512e121 −0.0495923
\(897\) −4.93664e120 −0.0142084
\(898\) −2.57103e122 −0.706545
\(899\) 7.96526e120 0.0209013
\(900\) −9.58371e121 −0.240143
\(901\) 1.00366e123 2.40164
\(902\) −4.25181e122 −0.971634
\(903\) 2.51860e120 0.00549690
\(904\) 4.68628e121 0.0976873
\(905\) −9.22245e122 −1.83624
\(906\) −1.95071e120 −0.00370998
\(907\) 5.78479e122 1.05096 0.525479 0.850807i \(-0.323886\pi\)
0.525479 + 0.850807i \(0.323886\pi\)
\(908\) −4.28000e121 −0.0742815
\(909\) −7.45212e122 −1.23560
\(910\) 3.91584e122 0.620307
\(911\) 4.10656e120 0.00621534 0.00310767 0.999995i \(-0.499011\pi\)
0.00310767 + 0.999995i \(0.499011\pi\)
\(912\) 2.64382e120 0.00382337
\(913\) 1.06136e123 1.46665
\(914\) −1.08474e121 −0.0143238
\(915\) −2.67449e120 −0.00337494
\(916\) −1.22950e121 −0.0148274
\(917\) 4.76898e122 0.549665
\(918\) 2.64856e121 0.0291768
\(919\) −8.16430e122 −0.859657 −0.429828 0.902911i \(-0.641426\pi\)
−0.429828 + 0.902911i \(0.641426\pi\)
\(920\) 4.07520e122 0.410161
\(921\) 2.12202e120 0.00204162
\(922\) 9.94730e122 0.914897
\(923\) −5.97478e122 −0.525353
\(924\) 5.51809e120 0.00463876
\(925\) −4.48585e122 −0.360548
\(926\) 4.41224e122 0.339081
\(927\) 5.33522e122 0.392052
\(928\) 2.40232e121 0.0168807
\(929\) 2.25330e123 1.51415 0.757073 0.653330i \(-0.226629\pi\)
0.757073 + 0.653330i \(0.226629\pi\)
\(930\) 3.39802e120 0.00218365
\(931\) 1.47037e123 0.903677
\(932\) −8.28770e122 −0.487162
\(933\) 7.99738e120 0.00449634
\(934\) 3.83572e122 0.206277
\(935\) −6.00083e123 −3.08695
\(936\) 9.23133e122 0.454273
\(937\) 8.41190e122 0.396006 0.198003 0.980201i \(-0.436555\pi\)
0.198003 + 0.980201i \(0.436555\pi\)
\(938\) −1.42977e123 −0.643947
\(939\) 6.91311e120 0.00297887
\(940\) 2.23111e123 0.919845
\(941\) −3.05113e123 −1.20362 −0.601812 0.798638i \(-0.705554\pi\)
−0.601812 + 0.798638i \(0.705554\pi\)
\(942\) 2.31459e121 0.00873698
\(943\) −2.54370e123 −0.918820
\(944\) 6.07744e122 0.210079
\(945\) −4.78554e121 −0.0158311
\(946\) −2.69067e123 −0.851879
\(947\) −5.94796e123 −1.80237 −0.901185 0.433436i \(-0.857301\pi\)
−0.901185 + 0.433436i \(0.857301\pi\)
\(948\) −8.67503e120 −0.00251608
\(949\) 4.28643e123 1.19000
\(950\) 1.68566e123 0.447962
\(951\) −1.59801e121 −0.00406526
\(952\) 1.44928e123 0.352954
\(953\) 6.37411e123 1.48615 0.743077 0.669206i \(-0.233365\pi\)
0.743077 + 0.669206i \(0.233365\pi\)
\(954\) −4.27513e123 −0.954314
\(955\) 2.77906e123 0.593961
\(956\) −2.91653e123 −0.596848
\(957\) −8.05790e120 −0.00157898
\(958\) −3.75492e123 −0.704583
\(959\) 5.17480e123 0.929868
\(960\) 1.02484e121 0.00176360
\(961\) −5.77696e123 −0.952091
\(962\) 4.32091e123 0.682040
\(963\) 7.05151e123 1.06608
\(964\) 2.42830e123 0.351646
\(965\) 9.94666e123 1.37973
\(966\) 3.30127e121 0.00438662
\(967\) 3.24393e123 0.412927 0.206463 0.978454i \(-0.433805\pi\)
0.206463 + 0.978454i \(0.433805\pi\)
\(968\) −2.99585e123 −0.365336
\(969\) −2.32909e122 −0.0272114
\(970\) 6.46457e123 0.723623
\(971\) 8.24664e123 0.884462 0.442231 0.896901i \(-0.354187\pi\)
0.442231 + 0.896901i \(0.354187\pi\)
\(972\) −1.69228e122 −0.0173909
\(973\) −8.63115e123 −0.849936
\(974\) −1.26020e124 −1.18917
\(975\) −7.91550e121 −0.00715792
\(976\) −6.90054e122 −0.0598020
\(977\) 4.25843e123 0.353692 0.176846 0.984239i \(-0.443411\pi\)
0.176846 + 0.984239i \(0.443411\pi\)
\(978\) −1.05085e121 −0.000836522 0
\(979\) −2.36645e124 −1.80558
\(980\) 5.69967e123 0.416838
\(981\) −6.89120e122 −0.0483094
\(982\) −8.74194e123 −0.587464
\(983\) 4.08523e123 0.263175 0.131588 0.991305i \(-0.457993\pi\)
0.131588 + 0.991305i \(0.457993\pi\)
\(984\) −6.39697e121 −0.00395073
\(985\) −1.45797e124 −0.863265
\(986\) −2.11634e123 −0.120141
\(987\) 1.80739e122 0.00983764
\(988\) −1.62368e124 −0.847400
\(989\) −1.60973e124 −0.805575
\(990\) 2.55607e124 1.22663
\(991\) 3.01427e124 1.38716 0.693578 0.720382i \(-0.256033\pi\)
0.693578 + 0.720382i \(0.256033\pi\)
\(992\) 8.76733e122 0.0386931
\(993\) 3.93636e122 0.0166610
\(994\) 3.99550e123 0.162194
\(995\) −2.68050e124 −1.04366
\(996\) 1.59685e122 0.00596351
\(997\) 4.45172e123 0.159470 0.0797350 0.996816i \(-0.474593\pi\)
0.0797350 + 0.996816i \(0.474593\pi\)
\(998\) 3.21958e124 1.10632
\(999\) −5.28058e122 −0.0174066
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 \(a_p\))