Properties

Label 5.34.a.a.1.2
Level 5
Weight 34
Character 5.1
Self dual Yes
Analytic conductor 34.491
Analytic rank 1
Dimension 5
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 34 \)
Character orbit: \([\chi]\) = 5.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(34.4914144405\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{21}\cdot 3^{5}\cdot 5^{4}\cdot 11 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(15553.7\)
Character \(\chi\) = 5.1

$q$-expansion

\(f(q)\) \(=\) \(q-56118.7 q^{2} +5.48591e7 q^{3} -5.44063e9 q^{4} -1.52588e11 q^{5} -3.07862e12 q^{6} +7.38557e13 q^{7} +7.87377e14 q^{8} -2.54954e15 q^{9} +O(q^{10})\) \(q-56118.7 q^{2} +5.48591e7 q^{3} -5.44063e9 q^{4} -1.52588e11 q^{5} -3.07862e12 q^{6} +7.38557e13 q^{7} +7.87377e14 q^{8} -2.54954e15 q^{9} +8.56303e15 q^{10} +3.54535e16 q^{11} -2.98468e17 q^{12} -1.27272e18 q^{13} -4.14468e18 q^{14} -8.37083e18 q^{15} +2.54805e18 q^{16} +1.95420e20 q^{17} +1.43077e20 q^{18} +9.67568e20 q^{19} +8.30174e20 q^{20} +4.05165e21 q^{21} -1.98961e21 q^{22} -3.06053e22 q^{23} +4.31948e22 q^{24} +2.32831e22 q^{25} +7.14231e22 q^{26} -4.44830e23 q^{27} -4.01821e23 q^{28} -1.16201e23 q^{29} +4.69760e23 q^{30} -3.89265e23 q^{31} -6.90651e24 q^{32} +1.94495e24 q^{33} -1.09667e25 q^{34} -1.12695e25 q^{35} +1.38711e25 q^{36} -2.73400e25 q^{37} -5.42987e25 q^{38} -6.98200e25 q^{39} -1.20144e26 q^{40} -7.27564e26 q^{41} -2.27373e26 q^{42} -1.74161e27 q^{43} -1.92889e26 q^{44} +3.89029e26 q^{45} +1.71753e27 q^{46} +2.14063e26 q^{47} +1.39784e26 q^{48} -2.27634e27 q^{49} -1.30662e27 q^{50} +1.07206e28 q^{51} +6.92437e27 q^{52} -1.96400e28 q^{53} +2.49633e28 q^{54} -5.40978e27 q^{55} +5.81522e28 q^{56} +5.30799e28 q^{57} +6.52106e27 q^{58} +2.54315e29 q^{59} +4.55425e28 q^{60} -2.81524e29 q^{61} +2.18451e28 q^{62} -1.88298e29 q^{63} +3.65697e29 q^{64} +1.94201e29 q^{65} -1.09148e29 q^{66} -8.18392e29 q^{67} -1.06321e30 q^{68} -1.67898e30 q^{69} +6.32429e29 q^{70} -3.59524e30 q^{71} -2.00745e30 q^{72} -2.19852e30 q^{73} +1.53429e30 q^{74} +1.27729e30 q^{75} -5.26418e30 q^{76} +2.61844e30 q^{77} +3.91821e30 q^{78} +3.90404e31 q^{79} -3.88802e29 q^{80} -1.02299e31 q^{81} +4.08299e31 q^{82} +4.98882e30 q^{83} -2.20435e31 q^{84} -2.98187e31 q^{85} +9.77368e31 q^{86} -6.37469e30 q^{87} +2.79153e31 q^{88} -1.23819e32 q^{89} -2.18318e31 q^{90} -9.39972e31 q^{91} +1.66512e32 q^{92} -2.13547e31 q^{93} -1.20129e31 q^{94} -1.47639e32 q^{95} -3.78885e32 q^{96} +1.97176e32 q^{97} +1.27745e32 q^{98} -9.03903e31 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + 30472q^{2} - 14988714q^{3} + 1141311360q^{4} - 762939453125q^{5} + 12925063115760q^{6} - 65452561787158q^{7} + 155610638035200q^{8} + 14541250990408965q^{9} + O(q^{10}) \) \( 5q + 30472q^{2} - 14988714q^{3} + 1141311360q^{4} - 762939453125q^{5} + 12925063115760q^{6} - 65452561787158q^{7} + 155610638035200q^{8} + 14541250990408965q^{9} - 4649658203125000q^{10} - 287801801877976640q^{11} - 405379955363513088q^{12} + 2397201150889907466q^{13} + 11676449916272482320q^{14} + 2287096252441406250q^{15} - 89180089543245957120q^{16} - \)\(30\!\cdots\!18\)\(q^{17} + \)\(53\!\cdots\!56\)\(q^{18} + \)\(91\!\cdots\!00\)\(q^{19} - \)\(17\!\cdots\!00\)\(q^{20} - \)\(10\!\cdots\!40\)\(q^{21} - \)\(13\!\cdots\!96\)\(q^{22} + \)\(55\!\cdots\!46\)\(q^{23} - \)\(71\!\cdots\!00\)\(q^{24} + \)\(11\!\cdots\!25\)\(q^{25} - \)\(42\!\cdots\!40\)\(q^{26} + \)\(67\!\cdots\!00\)\(q^{27} - \)\(13\!\cdots\!36\)\(q^{28} - \)\(92\!\cdots\!50\)\(q^{29} - \)\(19\!\cdots\!00\)\(q^{30} - \)\(13\!\cdots\!40\)\(q^{31} - \)\(81\!\cdots\!08\)\(q^{32} - \)\(33\!\cdots\!48\)\(q^{33} - \)\(68\!\cdots\!80\)\(q^{34} + \)\(99\!\cdots\!50\)\(q^{35} - \)\(18\!\cdots\!20\)\(q^{36} - \)\(14\!\cdots\!38\)\(q^{37} - \)\(33\!\cdots\!00\)\(q^{38} - \)\(78\!\cdots\!20\)\(q^{39} - \)\(23\!\cdots\!00\)\(q^{40} - \)\(13\!\cdots\!90\)\(q^{41} - \)\(26\!\cdots\!36\)\(q^{42} - \)\(23\!\cdots\!94\)\(q^{43} - \)\(18\!\cdots\!80\)\(q^{44} - \)\(22\!\cdots\!25\)\(q^{45} - \)\(28\!\cdots\!40\)\(q^{46} - \)\(77\!\cdots\!98\)\(q^{47} - \)\(73\!\cdots\!04\)\(q^{48} + \)\(41\!\cdots\!85\)\(q^{49} + \)\(70\!\cdots\!00\)\(q^{50} + \)\(73\!\cdots\!60\)\(q^{51} + \)\(48\!\cdots\!72\)\(q^{52} + \)\(10\!\cdots\!86\)\(q^{53} + \)\(64\!\cdots\!00\)\(q^{54} + \)\(43\!\cdots\!00\)\(q^{55} + \)\(14\!\cdots\!00\)\(q^{56} + \)\(20\!\cdots\!00\)\(q^{57} + \)\(21\!\cdots\!00\)\(q^{58} + \)\(25\!\cdots\!00\)\(q^{59} + \)\(61\!\cdots\!00\)\(q^{60} + \)\(74\!\cdots\!10\)\(q^{61} + \)\(53\!\cdots\!24\)\(q^{62} - \)\(10\!\cdots\!34\)\(q^{63} - \)\(10\!\cdots\!40\)\(q^{64} - \)\(36\!\cdots\!50\)\(q^{65} - \)\(33\!\cdots\!80\)\(q^{66} - \)\(37\!\cdots\!18\)\(q^{67} + \)\(11\!\cdots\!44\)\(q^{68} - \)\(27\!\cdots\!20\)\(q^{69} - \)\(17\!\cdots\!00\)\(q^{70} - \)\(55\!\cdots\!40\)\(q^{71} - \)\(15\!\cdots\!00\)\(q^{72} - \)\(13\!\cdots\!54\)\(q^{73} - \)\(36\!\cdots\!80\)\(q^{74} - \)\(34\!\cdots\!50\)\(q^{75} + \)\(71\!\cdots\!00\)\(q^{76} + \)\(47\!\cdots\!44\)\(q^{77} + \)\(12\!\cdots\!72\)\(q^{78} - \)\(10\!\cdots\!00\)\(q^{79} + \)\(13\!\cdots\!00\)\(q^{80} + \)\(78\!\cdots\!05\)\(q^{81} + \)\(27\!\cdots\!84\)\(q^{82} + \)\(92\!\cdots\!26\)\(q^{83} + \)\(17\!\cdots\!20\)\(q^{84} + \)\(47\!\cdots\!50\)\(q^{85} + \)\(65\!\cdots\!60\)\(q^{86} + \)\(13\!\cdots\!00\)\(q^{87} + \)\(19\!\cdots\!00\)\(q^{88} - \)\(60\!\cdots\!50\)\(q^{89} - \)\(82\!\cdots\!00\)\(q^{90} - \)\(26\!\cdots\!40\)\(q^{91} - \)\(69\!\cdots\!68\)\(q^{92} - \)\(69\!\cdots\!88\)\(q^{93} - \)\(36\!\cdots\!80\)\(q^{94} - \)\(14\!\cdots\!00\)\(q^{95} - \)\(34\!\cdots\!40\)\(q^{96} - \)\(86\!\cdots\!98\)\(q^{97} - \)\(19\!\cdots\!96\)\(q^{98} - \)\(17\!\cdots\!20\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −56118.7 −0.605498 −0.302749 0.953070i \(-0.597904\pi\)
−0.302749 + 0.953070i \(0.597904\pi\)
\(3\) 5.48591e7 0.735780 0.367890 0.929869i \(-0.380080\pi\)
0.367890 + 0.929869i \(0.380080\pi\)
\(4\) −5.44063e9 −0.633372
\(5\) −1.52588e11 −0.447214
\(6\) −3.07862e12 −0.445513
\(7\) 7.38557e13 0.839975 0.419987 0.907530i \(-0.362035\pi\)
0.419987 + 0.907530i \(0.362035\pi\)
\(8\) 7.87377e14 0.989004
\(9\) −2.54954e15 −0.458628
\(10\) 8.56303e15 0.270787
\(11\) 3.54535e16 0.232638 0.116319 0.993212i \(-0.462891\pi\)
0.116319 + 0.993212i \(0.462891\pi\)
\(12\) −2.98468e17 −0.466022
\(13\) −1.27272e18 −0.530476 −0.265238 0.964183i \(-0.585451\pi\)
−0.265238 + 0.964183i \(0.585451\pi\)
\(14\) −4.14468e18 −0.508603
\(15\) −8.37083e18 −0.329051
\(16\) 2.54805e18 0.0345325
\(17\) 1.95420e20 0.974006 0.487003 0.873400i \(-0.338090\pi\)
0.487003 + 0.873400i \(0.338090\pi\)
\(18\) 1.43077e20 0.277699
\(19\) 9.67568e20 0.769568 0.384784 0.923007i \(-0.374276\pi\)
0.384784 + 0.923007i \(0.374276\pi\)
\(20\) 8.30174e20 0.283253
\(21\) 4.05165e21 0.618036
\(22\) −1.98961e21 −0.140862
\(23\) −3.06053e22 −1.04061 −0.520305 0.853981i \(-0.674182\pi\)
−0.520305 + 0.853981i \(0.674182\pi\)
\(24\) 4.31948e22 0.727689
\(25\) 2.32831e22 0.200000
\(26\) 7.14231e22 0.321202
\(27\) −4.44830e23 −1.07323
\(28\) −4.01821e23 −0.532017
\(29\) −1.16201e23 −0.0862271 −0.0431135 0.999070i \(-0.513728\pi\)
−0.0431135 + 0.999070i \(0.513728\pi\)
\(30\) 4.69760e23 0.199239
\(31\) −3.89265e23 −0.0961121 −0.0480560 0.998845i \(-0.515303\pi\)
−0.0480560 + 0.998845i \(0.515303\pi\)
\(32\) −6.90651e24 −1.00991
\(33\) 1.94495e24 0.171170
\(34\) −1.09667e25 −0.589759
\(35\) −1.12695e25 −0.375648
\(36\) 1.38711e25 0.290482
\(37\) −2.73400e25 −0.364310 −0.182155 0.983270i \(-0.558307\pi\)
−0.182155 + 0.983270i \(0.558307\pi\)
\(38\) −5.42987e25 −0.465972
\(39\) −6.98200e25 −0.390314
\(40\) −1.20144e26 −0.442296
\(41\) −7.27564e26 −1.78212 −0.891061 0.453883i \(-0.850038\pi\)
−0.891061 + 0.453883i \(0.850038\pi\)
\(42\) −2.27373e26 −0.374220
\(43\) −1.74161e27 −1.94411 −0.972055 0.234754i \(-0.924572\pi\)
−0.972055 + 0.234754i \(0.924572\pi\)
\(44\) −1.92889e26 −0.147346
\(45\) 3.89029e26 0.205105
\(46\) 1.71753e27 0.630087
\(47\) 2.14063e26 0.0550714 0.0275357 0.999621i \(-0.491234\pi\)
0.0275357 + 0.999621i \(0.491234\pi\)
\(48\) 1.39784e26 0.0254083
\(49\) −2.27634e27 −0.294443
\(50\) −1.30662e27 −0.121100
\(51\) 1.07206e28 0.716654
\(52\) 6.92437e27 0.335989
\(53\) −1.96400e28 −0.695970 −0.347985 0.937500i \(-0.613134\pi\)
−0.347985 + 0.937500i \(0.613134\pi\)
\(54\) 2.49633e28 0.649838
\(55\) −5.40978e27 −0.104039
\(56\) 5.81522e28 0.830738
\(57\) 5.30799e28 0.566233
\(58\) 6.52106e27 0.0522103
\(59\) 2.54315e29 1.53573 0.767864 0.640612i \(-0.221319\pi\)
0.767864 + 0.640612i \(0.221319\pi\)
\(60\) 4.55425e28 0.208412
\(61\) −2.81524e29 −0.980785 −0.490392 0.871502i \(-0.663147\pi\)
−0.490392 + 0.871502i \(0.663147\pi\)
\(62\) 2.18451e28 0.0581957
\(63\) −1.88298e29 −0.385236
\(64\) 3.65697e29 0.576968
\(65\) 1.94201e29 0.237236
\(66\) −1.09148e29 −0.103643
\(67\) −8.18392e29 −0.606355 −0.303178 0.952934i \(-0.598048\pi\)
−0.303178 + 0.952934i \(0.598048\pi\)
\(68\) −1.06321e30 −0.616908
\(69\) −1.67898e30 −0.765660
\(70\) 6.32429e29 0.227454
\(71\) −3.59524e30 −1.02321 −0.511606 0.859220i \(-0.670949\pi\)
−0.511606 + 0.859220i \(0.670949\pi\)
\(72\) −2.00745e30 −0.453585
\(73\) −2.19852e30 −0.395642 −0.197821 0.980238i \(-0.563387\pi\)
−0.197821 + 0.980238i \(0.563387\pi\)
\(74\) 1.53429e30 0.220589
\(75\) 1.27729e30 0.147156
\(76\) −5.26418e30 −0.487423
\(77\) 2.61844e30 0.195410
\(78\) 3.91821e30 0.236334
\(79\) 3.90404e31 1.90839 0.954194 0.299188i \(-0.0967156\pi\)
0.954194 + 0.299188i \(0.0967156\pi\)
\(80\) −3.88802e29 −0.0154434
\(81\) −1.02299e31 −0.331032
\(82\) 4.08299e31 1.07907
\(83\) 4.98882e30 0.107947 0.0539734 0.998542i \(-0.482811\pi\)
0.0539734 + 0.998542i \(0.482811\pi\)
\(84\) −2.20435e31 −0.391447
\(85\) −2.98187e31 −0.435589
\(86\) 9.77368e31 1.17715
\(87\) −6.37469e30 −0.0634441
\(88\) 2.79153e31 0.230080
\(89\) −1.23819e32 −0.846937 −0.423469 0.905911i \(-0.639188\pi\)
−0.423469 + 0.905911i \(0.639188\pi\)
\(90\) −2.18318e31 −0.124191
\(91\) −9.39972e31 −0.445587
\(92\) 1.66512e32 0.659093
\(93\) −2.13547e31 −0.0707173
\(94\) −1.20129e31 −0.0333456
\(95\) −1.47639e32 −0.344161
\(96\) −3.78885e32 −0.743073
\(97\) 1.97176e32 0.325926 0.162963 0.986632i \(-0.447895\pi\)
0.162963 + 0.986632i \(0.447895\pi\)
\(98\) 1.27745e32 0.178285
\(99\) −9.03903e31 −0.106694
\(100\) −1.26674e32 −0.126674
\(101\) −1.97472e33 −1.67573 −0.837865 0.545878i \(-0.816196\pi\)
−0.837865 + 0.545878i \(0.816196\pi\)
\(102\) −6.01624e32 −0.433932
\(103\) 5.57056e32 0.342046 0.171023 0.985267i \(-0.445293\pi\)
0.171023 + 0.985267i \(0.445293\pi\)
\(104\) −1.00211e33 −0.524643
\(105\) −6.18233e32 −0.276394
\(106\) 1.10217e33 0.421409
\(107\) 3.76704e33 1.23358 0.616791 0.787127i \(-0.288432\pi\)
0.616791 + 0.787127i \(0.288432\pi\)
\(108\) 2.42016e33 0.679753
\(109\) 7.25238e33 1.74962 0.874810 0.484467i \(-0.160986\pi\)
0.874810 + 0.484467i \(0.160986\pi\)
\(110\) 3.03590e32 0.0629953
\(111\) −1.49985e33 −0.268051
\(112\) 1.88188e32 0.0290064
\(113\) −3.76366e32 −0.0500976 −0.0250488 0.999686i \(-0.507974\pi\)
−0.0250488 + 0.999686i \(0.507974\pi\)
\(114\) −2.97878e33 −0.342853
\(115\) 4.67000e33 0.465375
\(116\) 6.32207e32 0.0546138
\(117\) 3.24484e33 0.243291
\(118\) −1.42719e34 −0.929881
\(119\) 1.44329e34 0.818140
\(120\) −6.59100e33 −0.325432
\(121\) −2.19682e34 −0.945880
\(122\) 1.57988e34 0.593863
\(123\) −3.99135e34 −1.31125
\(124\) 2.11785e33 0.0608747
\(125\) −3.55271e33 −0.0894427
\(126\) 1.05671e34 0.233260
\(127\) −4.97180e34 −0.963279 −0.481640 0.876369i \(-0.659959\pi\)
−0.481640 + 0.876369i \(0.659959\pi\)
\(128\) 3.88040e34 0.660560
\(129\) −9.55430e34 −1.43044
\(130\) −1.08983e34 −0.143646
\(131\) 3.26112e34 0.378782 0.189391 0.981902i \(-0.439349\pi\)
0.189391 + 0.981902i \(0.439349\pi\)
\(132\) −1.05817e34 −0.108414
\(133\) 7.14604e34 0.646418
\(134\) 4.59271e34 0.367147
\(135\) 6.78757e34 0.479963
\(136\) 1.53869e35 0.963296
\(137\) −4.83496e34 −0.268228 −0.134114 0.990966i \(-0.542819\pi\)
−0.134114 + 0.990966i \(0.542819\pi\)
\(138\) 9.42222e34 0.463605
\(139\) −1.61945e35 −0.707334 −0.353667 0.935371i \(-0.615065\pi\)
−0.353667 + 0.935371i \(0.615065\pi\)
\(140\) 6.13130e34 0.237925
\(141\) 1.17433e34 0.0405204
\(142\) 2.01760e35 0.619552
\(143\) −4.51223e34 −0.123409
\(144\) −6.49637e33 −0.0158376
\(145\) 1.77309e34 0.0385619
\(146\) 1.23378e35 0.239561
\(147\) −1.24878e35 −0.216645
\(148\) 1.48747e35 0.230744
\(149\) −4.97369e35 −0.690407 −0.345204 0.938528i \(-0.612190\pi\)
−0.345204 + 0.938528i \(0.612190\pi\)
\(150\) −7.16797e34 −0.0891026
\(151\) 1.20125e35 0.133818 0.0669090 0.997759i \(-0.478686\pi\)
0.0669090 + 0.997759i \(0.478686\pi\)
\(152\) 7.61841e35 0.761106
\(153\) −4.98232e35 −0.446707
\(154\) −1.46944e35 −0.118320
\(155\) 5.93972e34 0.0429826
\(156\) 3.79864e35 0.247214
\(157\) −1.58453e36 −0.928018 −0.464009 0.885830i \(-0.653590\pi\)
−0.464009 + 0.885830i \(0.653590\pi\)
\(158\) −2.19089e36 −1.15553
\(159\) −1.07743e36 −0.512081
\(160\) 1.05385e36 0.451647
\(161\) −2.26038e36 −0.874086
\(162\) 5.74090e35 0.200439
\(163\) −3.31440e36 −1.04546 −0.522732 0.852497i \(-0.675087\pi\)
−0.522732 + 0.852497i \(0.675087\pi\)
\(164\) 3.95840e36 1.12875
\(165\) −2.96776e35 −0.0765496
\(166\) −2.79966e35 −0.0653615
\(167\) 7.73877e36 1.63625 0.818126 0.575039i \(-0.195013\pi\)
0.818126 + 0.575039i \(0.195013\pi\)
\(168\) 3.19018e36 0.611240
\(169\) −4.13633e36 −0.718595
\(170\) 1.67339e36 0.263748
\(171\) −2.46686e36 −0.352946
\(172\) 9.47543e36 1.23135
\(173\) 4.62098e36 0.545725 0.272862 0.962053i \(-0.412030\pi\)
0.272862 + 0.962053i \(0.412030\pi\)
\(174\) 3.57739e35 0.0384153
\(175\) 1.71959e36 0.167995
\(176\) 9.03374e34 0.00803357
\(177\) 1.39515e37 1.12996
\(178\) 6.94855e36 0.512819
\(179\) −1.73851e37 −1.16977 −0.584886 0.811115i \(-0.698861\pi\)
−0.584886 + 0.811115i \(0.698861\pi\)
\(180\) −2.11656e36 −0.129908
\(181\) −2.20579e37 −1.23557 −0.617785 0.786347i \(-0.711970\pi\)
−0.617785 + 0.786347i \(0.711970\pi\)
\(182\) 5.27500e36 0.269802
\(183\) −1.54442e37 −0.721641
\(184\) −2.40979e37 −1.02917
\(185\) 4.17176e36 0.162924
\(186\) 1.19840e36 0.0428192
\(187\) 6.92833e36 0.226591
\(188\) −1.16463e36 −0.0348807
\(189\) −3.28532e37 −0.901485
\(190\) 8.28532e36 0.208389
\(191\) 3.27319e37 0.754954 0.377477 0.926019i \(-0.376792\pi\)
0.377477 + 0.926019i \(0.376792\pi\)
\(192\) 2.00618e37 0.424521
\(193\) −8.15189e37 −1.58330 −0.791649 0.610976i \(-0.790777\pi\)
−0.791649 + 0.610976i \(0.790777\pi\)
\(194\) −1.10652e37 −0.197348
\(195\) 1.06537e37 0.174554
\(196\) 1.23847e37 0.186492
\(197\) 1.16510e38 1.61313 0.806565 0.591145i \(-0.201324\pi\)
0.806565 + 0.591145i \(0.201324\pi\)
\(198\) 5.07259e36 0.0646032
\(199\) −1.05328e38 −1.23443 −0.617216 0.786794i \(-0.711739\pi\)
−0.617216 + 0.786794i \(0.711739\pi\)
\(200\) 1.83325e37 0.197801
\(201\) −4.48962e37 −0.446144
\(202\) 1.10819e38 1.01465
\(203\) −8.58211e36 −0.0724285
\(204\) −5.83265e37 −0.453909
\(205\) 1.11017e38 0.796989
\(206\) −3.12613e37 −0.207108
\(207\) 7.80296e37 0.477253
\(208\) −3.24294e36 −0.0183187
\(209\) 3.43037e37 0.179031
\(210\) 3.46944e37 0.167356
\(211\) 3.80288e38 1.69610 0.848051 0.529915i \(-0.177776\pi\)
0.848051 + 0.529915i \(0.177776\pi\)
\(212\) 1.06854e38 0.440808
\(213\) −1.97232e38 −0.752858
\(214\) −2.11401e38 −0.746931
\(215\) 2.65748e38 0.869432
\(216\) −3.50249e38 −1.06143
\(217\) −2.87495e37 −0.0807317
\(218\) −4.06994e38 −1.05939
\(219\) −1.20609e38 −0.291106
\(220\) 2.94326e37 0.0658953
\(221\) −2.48714e38 −0.516687
\(222\) 8.41696e37 0.162305
\(223\) 4.60089e38 0.823780 0.411890 0.911234i \(-0.364869\pi\)
0.411890 + 0.911234i \(0.364869\pi\)
\(224\) −5.10085e38 −0.848301
\(225\) −5.93612e37 −0.0917257
\(226\) 2.11212e37 0.0303340
\(227\) 1.13977e39 1.52192 0.760958 0.648801i \(-0.224729\pi\)
0.760958 + 0.648801i \(0.224729\pi\)
\(228\) −2.88788e38 −0.358636
\(229\) −1.46028e39 −1.68713 −0.843566 0.537025i \(-0.819548\pi\)
−0.843566 + 0.537025i \(0.819548\pi\)
\(230\) −2.62075e38 −0.281784
\(231\) 1.43645e38 0.143779
\(232\) −9.14941e37 −0.0852789
\(233\) −2.05161e37 −0.0178124 −0.00890620 0.999960i \(-0.502835\pi\)
−0.00890620 + 0.999960i \(0.502835\pi\)
\(234\) −1.82096e38 −0.147313
\(235\) −3.26634e37 −0.0246287
\(236\) −1.38364e39 −0.972688
\(237\) 2.14172e39 1.40415
\(238\) −8.09954e38 −0.495382
\(239\) 9.20750e38 0.525505 0.262752 0.964863i \(-0.415370\pi\)
0.262752 + 0.964863i \(0.415370\pi\)
\(240\) −2.13293e37 −0.0113629
\(241\) 1.79093e39 0.890834 0.445417 0.895323i \(-0.353056\pi\)
0.445417 + 0.895323i \(0.353056\pi\)
\(242\) 1.23283e39 0.572728
\(243\) 1.91164e39 0.829663
\(244\) 1.53167e39 0.621202
\(245\) 3.47341e38 0.131679
\(246\) 2.23989e39 0.793959
\(247\) −1.23144e39 −0.408238
\(248\) −3.06499e38 −0.0950552
\(249\) 2.73682e38 0.0794250
\(250\) 1.99374e38 0.0541574
\(251\) −4.16615e39 −1.05954 −0.529772 0.848140i \(-0.677723\pi\)
−0.529772 + 0.848140i \(0.677723\pi\)
\(252\) 1.02446e39 0.243998
\(253\) −1.08507e39 −0.242085
\(254\) 2.79011e39 0.583264
\(255\) −1.63583e39 −0.320497
\(256\) −5.31894e39 −0.976936
\(257\) −1.03274e40 −1.77867 −0.889336 0.457254i \(-0.848833\pi\)
−0.889336 + 0.457254i \(0.848833\pi\)
\(258\) 5.36175e39 0.866126
\(259\) −2.01922e39 −0.306011
\(260\) −1.05657e39 −0.150259
\(261\) 2.96260e38 0.0395462
\(262\) −1.83010e39 −0.229352
\(263\) −7.85107e39 −0.923972 −0.461986 0.886887i \(-0.652863\pi\)
−0.461986 + 0.886887i \(0.652863\pi\)
\(264\) 1.53141e39 0.169288
\(265\) 2.99683e39 0.311247
\(266\) −4.01027e39 −0.391405
\(267\) −6.79258e39 −0.623159
\(268\) 4.45257e39 0.384049
\(269\) 1.76099e40 1.42838 0.714189 0.699953i \(-0.246796\pi\)
0.714189 + 0.699953i \(0.246796\pi\)
\(270\) −3.80910e39 −0.290616
\(271\) 1.63883e40 1.17636 0.588179 0.808730i \(-0.299845\pi\)
0.588179 + 0.808730i \(0.299845\pi\)
\(272\) 4.97940e38 0.0336349
\(273\) −5.15660e39 −0.327853
\(274\) 2.71332e39 0.162411
\(275\) 8.25467e38 0.0465276
\(276\) 9.13470e39 0.484947
\(277\) −3.39112e40 −1.69601 −0.848003 0.529991i \(-0.822195\pi\)
−0.848003 + 0.529991i \(0.822195\pi\)
\(278\) 9.08817e39 0.428289
\(279\) 9.92449e38 0.0440797
\(280\) −8.87333e39 −0.371517
\(281\) 3.38855e40 1.33770 0.668851 0.743396i \(-0.266786\pi\)
0.668851 + 0.743396i \(0.266786\pi\)
\(282\) −6.59017e38 −0.0245350
\(283\) 2.32437e40 0.816263 0.408131 0.912923i \(-0.366181\pi\)
0.408131 + 0.912923i \(0.366181\pi\)
\(284\) 1.95604e40 0.648074
\(285\) −8.09935e39 −0.253227
\(286\) 2.53220e39 0.0747238
\(287\) −5.37347e40 −1.49694
\(288\) 1.76084e40 0.463175
\(289\) −2.06553e39 −0.0513118
\(290\) −9.95035e38 −0.0233492
\(291\) 1.08169e40 0.239810
\(292\) 1.19613e40 0.250589
\(293\) 3.19376e40 0.632393 0.316197 0.948694i \(-0.397594\pi\)
0.316197 + 0.948694i \(0.397594\pi\)
\(294\) 7.00797e39 0.131178
\(295\) −3.88055e40 −0.686799
\(296\) −2.15269e40 −0.360303
\(297\) −1.57708e40 −0.249674
\(298\) 2.79117e40 0.418040
\(299\) 3.89519e40 0.552019
\(300\) −6.94924e39 −0.0932045
\(301\) −1.28628e41 −1.63300
\(302\) −6.74127e39 −0.0810265
\(303\) −1.08332e41 −1.23297
\(304\) 2.46541e39 0.0265751
\(305\) 4.29572e40 0.438620
\(306\) 2.79601e40 0.270480
\(307\) −9.23782e40 −0.846810 −0.423405 0.905940i \(-0.639165\pi\)
−0.423405 + 0.905940i \(0.639165\pi\)
\(308\) −1.42460e40 −0.123767
\(309\) 3.05596e40 0.251670
\(310\) −3.33329e39 −0.0260259
\(311\) 2.21387e40 0.163910 0.0819550 0.996636i \(-0.473884\pi\)
0.0819550 + 0.996636i \(0.473884\pi\)
\(312\) −5.49746e40 −0.386022
\(313\) 2.73315e40 0.182046 0.0910231 0.995849i \(-0.470986\pi\)
0.0910231 + 0.995849i \(0.470986\pi\)
\(314\) 8.89219e40 0.561913
\(315\) 2.87320e40 0.172283
\(316\) −2.12404e41 −1.20872
\(317\) 2.26706e41 1.22457 0.612286 0.790636i \(-0.290250\pi\)
0.612286 + 0.790636i \(0.290250\pi\)
\(318\) 6.04642e40 0.310064
\(319\) −4.11974e39 −0.0200597
\(320\) −5.58009e40 −0.258028
\(321\) 2.06656e41 0.907644
\(322\) 1.26849e41 0.529257
\(323\) 1.89082e41 0.749565
\(324\) 5.56572e40 0.209666
\(325\) −2.96327e40 −0.106095
\(326\) 1.86000e41 0.633027
\(327\) 3.97859e41 1.28733
\(328\) −5.72867e41 −1.76253
\(329\) 1.58097e40 0.0462586
\(330\) 1.66547e40 0.0463506
\(331\) −2.06805e41 −0.547520 −0.273760 0.961798i \(-0.588267\pi\)
−0.273760 + 0.961798i \(0.588267\pi\)
\(332\) −2.71423e40 −0.0683705
\(333\) 6.97046e40 0.167083
\(334\) −4.34290e41 −0.990747
\(335\) 1.24877e41 0.271170
\(336\) 1.03238e40 0.0213423
\(337\) 5.63835e40 0.110984 0.0554918 0.998459i \(-0.482327\pi\)
0.0554918 + 0.998459i \(0.482327\pi\)
\(338\) 2.32125e41 0.435108
\(339\) −2.06471e40 −0.0368608
\(340\) 1.62233e41 0.275890
\(341\) −1.38008e40 −0.0223593
\(342\) 1.38437e41 0.213708
\(343\) −7.39098e41 −1.08730
\(344\) −1.37130e42 −1.92273
\(345\) 2.56192e41 0.342413
\(346\) −2.59323e41 −0.330435
\(347\) 2.54567e41 0.309289 0.154645 0.987970i \(-0.450577\pi\)
0.154645 + 0.987970i \(0.450577\pi\)
\(348\) 3.46823e40 0.0401837
\(349\) −1.42434e42 −1.57397 −0.786983 0.616974i \(-0.788358\pi\)
−0.786983 + 0.616974i \(0.788358\pi\)
\(350\) −9.65009e40 −0.101721
\(351\) 5.66143e41 0.569323
\(352\) −2.44860e41 −0.234944
\(353\) 4.58433e41 0.419752 0.209876 0.977728i \(-0.432694\pi\)
0.209876 + 0.977728i \(0.432694\pi\)
\(354\) −7.82941e41 −0.684187
\(355\) 5.48590e41 0.457594
\(356\) 6.73651e41 0.536427
\(357\) 7.91774e41 0.601971
\(358\) 9.75628e41 0.708295
\(359\) 1.13078e42 0.784004 0.392002 0.919964i \(-0.371783\pi\)
0.392002 + 0.919964i \(0.371783\pi\)
\(360\) 3.06313e41 0.202849
\(361\) −6.44582e41 −0.407764
\(362\) 1.23786e42 0.748135
\(363\) −1.20516e42 −0.695959
\(364\) 5.11404e41 0.282222
\(365\) 3.35467e41 0.176937
\(366\) 8.66707e41 0.436952
\(367\) 1.40753e42 0.678369 0.339185 0.940720i \(-0.389849\pi\)
0.339185 + 0.940720i \(0.389849\pi\)
\(368\) −7.79840e40 −0.0359349
\(369\) 1.85496e42 0.817332
\(370\) −2.34114e41 −0.0986503
\(371\) −1.45053e42 −0.584597
\(372\) 1.16183e41 0.0447904
\(373\) −4.43848e42 −1.63696 −0.818480 0.574535i \(-0.805183\pi\)
−0.818480 + 0.574535i \(0.805183\pi\)
\(374\) −3.88809e41 −0.137200
\(375\) −1.94899e41 −0.0658101
\(376\) 1.68548e41 0.0544658
\(377\) 1.47891e41 0.0457414
\(378\) 1.84368e42 0.545847
\(379\) −1.41996e42 −0.402466 −0.201233 0.979543i \(-0.564495\pi\)
−0.201233 + 0.979543i \(0.564495\pi\)
\(380\) 8.03250e41 0.217982
\(381\) −2.72748e42 −0.708761
\(382\) −1.83687e42 −0.457123
\(383\) 1.04448e40 0.00248955 0.00124478 0.999999i \(-0.499604\pi\)
0.00124478 + 0.999999i \(0.499604\pi\)
\(384\) 2.12875e42 0.486027
\(385\) −3.99543e41 −0.0873899
\(386\) 4.57473e42 0.958684
\(387\) 4.44030e42 0.891624
\(388\) −1.07276e42 −0.206433
\(389\) 3.78074e41 0.0697282 0.0348641 0.999392i \(-0.488900\pi\)
0.0348641 + 0.999392i \(0.488900\pi\)
\(390\) −5.97871e41 −0.105692
\(391\) −5.98090e42 −1.01356
\(392\) −1.79233e42 −0.291205
\(393\) 1.78902e42 0.278700
\(394\) −6.53838e42 −0.976747
\(395\) −5.95709e42 −0.853457
\(396\) 4.91780e41 0.0675772
\(397\) −1.40626e43 −1.85363 −0.926815 0.375519i \(-0.877464\pi\)
−0.926815 + 0.375519i \(0.877464\pi\)
\(398\) 5.91086e42 0.747446
\(399\) 3.92025e42 0.475621
\(400\) 5.93264e40 0.00690651
\(401\) −3.90184e42 −0.435900 −0.217950 0.975960i \(-0.569937\pi\)
−0.217950 + 0.975960i \(0.569937\pi\)
\(402\) 2.51952e42 0.270139
\(403\) 4.95424e41 0.0509852
\(404\) 1.07437e43 1.06136
\(405\) 1.56096e42 0.148042
\(406\) 4.81617e41 0.0438553
\(407\) −9.69301e41 −0.0847522
\(408\) 8.44112e42 0.708773
\(409\) 1.05489e43 0.850694 0.425347 0.905030i \(-0.360152\pi\)
0.425347 + 0.905030i \(0.360152\pi\)
\(410\) −6.23015e42 −0.482575
\(411\) −2.65242e42 −0.197357
\(412\) −3.03073e42 −0.216642
\(413\) 1.87826e43 1.28997
\(414\) −4.37892e42 −0.288976
\(415\) −7.61234e41 −0.0482753
\(416\) 8.79002e42 0.535735
\(417\) −8.88418e42 −0.520442
\(418\) −1.92508e42 −0.108403
\(419\) 2.64714e43 1.43300 0.716498 0.697589i \(-0.245744\pi\)
0.716498 + 0.697589i \(0.245744\pi\)
\(420\) 3.36358e42 0.175060
\(421\) 2.92799e43 1.46526 0.732630 0.680627i \(-0.238293\pi\)
0.732630 + 0.680627i \(0.238293\pi\)
\(422\) −2.13413e43 −1.02699
\(423\) −5.45762e41 −0.0252573
\(424\) −1.54641e43 −0.688317
\(425\) 4.54998e42 0.194801
\(426\) 1.10684e43 0.455854
\(427\) −2.07922e43 −0.823834
\(428\) −2.04951e43 −0.781316
\(429\) −2.47537e42 −0.0908017
\(430\) −1.49134e43 −0.526440
\(431\) 7.41005e42 0.251736 0.125868 0.992047i \(-0.459828\pi\)
0.125868 + 0.992047i \(0.459828\pi\)
\(432\) −1.13345e42 −0.0370613
\(433\) −2.63001e43 −0.827766 −0.413883 0.910330i \(-0.635828\pi\)
−0.413883 + 0.910330i \(0.635828\pi\)
\(434\) 1.61338e42 0.0488829
\(435\) 9.72700e41 0.0283731
\(436\) −3.94575e43 −1.10816
\(437\) −2.96128e43 −0.800821
\(438\) 6.76840e42 0.176264
\(439\) 1.79135e43 0.449278 0.224639 0.974442i \(-0.427880\pi\)
0.224639 + 0.974442i \(0.427880\pi\)
\(440\) −4.25954e42 −0.102895
\(441\) 5.80362e42 0.135040
\(442\) 1.39575e43 0.312853
\(443\) −3.40634e43 −0.735575 −0.367788 0.929910i \(-0.619885\pi\)
−0.367788 + 0.929910i \(0.619885\pi\)
\(444\) 8.16011e42 0.169776
\(445\) 1.88932e43 0.378762
\(446\) −2.58196e43 −0.498797
\(447\) −2.72852e43 −0.507988
\(448\) 2.70088e43 0.484638
\(449\) 8.25218e43 1.42726 0.713632 0.700521i \(-0.247049\pi\)
0.713632 + 0.700521i \(0.247049\pi\)
\(450\) 3.33127e42 0.0555397
\(451\) −2.57947e43 −0.414589
\(452\) 2.04767e42 0.0317304
\(453\) 6.58996e42 0.0984605
\(454\) −6.39625e43 −0.921517
\(455\) 1.43428e43 0.199272
\(456\) 4.17939e43 0.560006
\(457\) 1.09927e44 1.42065 0.710323 0.703876i \(-0.248549\pi\)
0.710323 + 0.703876i \(0.248549\pi\)
\(458\) 8.19488e43 1.02156
\(459\) −8.69288e43 −1.04533
\(460\) −2.54077e43 −0.294756
\(461\) 5.08918e43 0.569616 0.284808 0.958585i \(-0.408070\pi\)
0.284808 + 0.958585i \(0.408070\pi\)
\(462\) −8.06120e42 −0.0870576
\(463\) 5.67339e43 0.591229 0.295615 0.955307i \(-0.404476\pi\)
0.295615 + 0.955307i \(0.404476\pi\)
\(464\) −2.96086e41 −0.00297764
\(465\) 3.25847e42 0.0316257
\(466\) 1.15134e42 0.0107854
\(467\) 8.56548e43 0.774503 0.387251 0.921974i \(-0.373425\pi\)
0.387251 + 0.921974i \(0.373425\pi\)
\(468\) −1.76540e43 −0.154094
\(469\) −6.04429e43 −0.509323
\(470\) 1.83303e42 0.0149126
\(471\) −8.69259e43 −0.682817
\(472\) 2.00242e44 1.51884
\(473\) −6.17462e43 −0.452273
\(474\) −1.20190e44 −0.850212
\(475\) 2.25280e43 0.153914
\(476\) −7.85239e43 −0.518187
\(477\) 5.00732e43 0.319192
\(478\) −5.16713e43 −0.318192
\(479\) −1.29441e44 −0.770079 −0.385040 0.922900i \(-0.625812\pi\)
−0.385040 + 0.922900i \(0.625812\pi\)
\(480\) 5.78132e43 0.332312
\(481\) 3.47961e43 0.193258
\(482\) −1.00504e44 −0.539398
\(483\) −1.24002e44 −0.643134
\(484\) 1.19521e44 0.599094
\(485\) −3.00866e43 −0.145759
\(486\) −1.07279e44 −0.502359
\(487\) 2.61068e44 1.18175 0.590876 0.806762i \(-0.298782\pi\)
0.590876 + 0.806762i \(0.298782\pi\)
\(488\) −2.21666e44 −0.970000
\(489\) −1.81825e44 −0.769231
\(490\) −1.94923e43 −0.0797313
\(491\) −1.66397e44 −0.658114 −0.329057 0.944310i \(-0.606731\pi\)
−0.329057 + 0.944310i \(0.606731\pi\)
\(492\) 2.17154e44 0.830509
\(493\) −2.27080e43 −0.0839857
\(494\) 6.91068e43 0.247187
\(495\) 1.37925e43 0.0477152
\(496\) −9.91868e41 −0.00331899
\(497\) −2.65529e44 −0.859472
\(498\) −1.53587e43 −0.0480917
\(499\) 6.52589e43 0.197688 0.0988441 0.995103i \(-0.468485\pi\)
0.0988441 + 0.995103i \(0.468485\pi\)
\(500\) 1.93290e43 0.0566505
\(501\) 4.24542e44 1.20392
\(502\) 2.33799e44 0.641552
\(503\) −1.10537e43 −0.0293519 −0.0146759 0.999892i \(-0.504672\pi\)
−0.0146759 + 0.999892i \(0.504672\pi\)
\(504\) −1.48262e44 −0.381000
\(505\) 3.01319e44 0.749409
\(506\) 6.08926e43 0.146582
\(507\) −2.26915e44 −0.528727
\(508\) 2.70497e44 0.610114
\(509\) −4.80472e44 −1.04912 −0.524559 0.851374i \(-0.675770\pi\)
−0.524559 + 0.851374i \(0.675770\pi\)
\(510\) 9.18005e43 0.194061
\(511\) −1.62373e44 −0.332329
\(512\) −3.48319e43 −0.0690276
\(513\) −4.30404e44 −0.825923
\(514\) 5.79562e44 1.07698
\(515\) −8.50000e43 −0.152968
\(516\) 5.19814e44 0.905999
\(517\) 7.58928e42 0.0128117
\(518\) 1.13316e44 0.185289
\(519\) 2.53503e44 0.401533
\(520\) 1.52909e44 0.234627
\(521\) −2.39684e44 −0.356301 −0.178150 0.984003i \(-0.557011\pi\)
−0.178150 + 0.984003i \(0.557011\pi\)
\(522\) −1.66257e43 −0.0239451
\(523\) 7.19573e44 1.00415 0.502073 0.864825i \(-0.332571\pi\)
0.502073 + 0.864825i \(0.332571\pi\)
\(524\) −1.77425e44 −0.239910
\(525\) 9.43349e43 0.123607
\(526\) 4.40592e44 0.559463
\(527\) −7.60702e43 −0.0936138
\(528\) 4.95583e42 0.00591094
\(529\) 7.16821e43 0.0828690
\(530\) −1.68178e44 −0.188460
\(531\) −6.48388e44 −0.704329
\(532\) −3.88789e44 −0.409423
\(533\) 9.25982e44 0.945374
\(534\) 3.81191e44 0.377322
\(535\) −5.74805e44 −0.551674
\(536\) −6.44383e44 −0.599688
\(537\) −9.53729e44 −0.860695
\(538\) −9.88243e44 −0.864880
\(539\) −8.07041e43 −0.0684985
\(540\) −3.69286e44 −0.303995
\(541\) 8.82482e44 0.704613 0.352307 0.935885i \(-0.385397\pi\)
0.352307 + 0.935885i \(0.385397\pi\)
\(542\) −9.19689e44 −0.712283
\(543\) −1.21007e45 −0.909107
\(544\) −1.34967e45 −0.983662
\(545\) −1.10663e45 −0.782454
\(546\) 2.89382e44 0.198515
\(547\) −5.81429e44 −0.386996 −0.193498 0.981101i \(-0.561983\pi\)
−0.193498 + 0.981101i \(0.561983\pi\)
\(548\) 2.63052e44 0.169888
\(549\) 7.17759e44 0.449816
\(550\) −4.63241e43 −0.0281723
\(551\) −1.12433e44 −0.0663576
\(552\) −1.32199e45 −0.757240
\(553\) 2.88335e45 1.60300
\(554\) 1.90306e45 1.02693
\(555\) 2.28859e44 0.119876
\(556\) 8.81085e44 0.448006
\(557\) 2.61541e45 1.29101 0.645504 0.763757i \(-0.276647\pi\)
0.645504 + 0.763757i \(0.276647\pi\)
\(558\) −5.56950e43 −0.0266902
\(559\) 2.21657e45 1.03130
\(560\) −2.87152e43 −0.0129721
\(561\) 3.80082e44 0.166721
\(562\) −1.90161e45 −0.809976
\(563\) 1.43034e45 0.591632 0.295816 0.955245i \(-0.404408\pi\)
0.295816 + 0.955245i \(0.404408\pi\)
\(564\) −6.38908e43 −0.0256645
\(565\) 5.74290e43 0.0224043
\(566\) −1.30441e45 −0.494245
\(567\) −7.55537e44 −0.278058
\(568\) −2.83081e45 −1.01196
\(569\) 5.30235e45 1.84127 0.920633 0.390430i \(-0.127674\pi\)
0.920633 + 0.390430i \(0.127674\pi\)
\(570\) 4.54525e44 0.153328
\(571\) −3.41063e45 −1.11774 −0.558868 0.829257i \(-0.688764\pi\)
−0.558868 + 0.829257i \(0.688764\pi\)
\(572\) 2.45493e44 0.0781637
\(573\) 1.79564e45 0.555480
\(574\) 3.01552e45 0.906393
\(575\) −7.12586e44 −0.208122
\(576\) −9.32360e44 −0.264614
\(577\) 2.80984e45 0.774962 0.387481 0.921878i \(-0.373345\pi\)
0.387481 + 0.921878i \(0.373345\pi\)
\(578\) 1.15915e44 0.0310692
\(579\) −4.47205e45 −1.16496
\(580\) −9.64672e43 −0.0244240
\(581\) 3.68453e44 0.0906725
\(582\) −6.07028e44 −0.145204
\(583\) −6.96309e44 −0.161909
\(584\) −1.73106e45 −0.391292
\(585\) −4.95124e44 −0.108803
\(586\) −1.79230e45 −0.382913
\(587\) −5.96514e45 −1.23906 −0.619529 0.784973i \(-0.712677\pi\)
−0.619529 + 0.784973i \(0.712677\pi\)
\(588\) 6.79412e44 0.137217
\(589\) −3.76641e44 −0.0739648
\(590\) 2.17771e45 0.415855
\(591\) 6.39162e45 1.18691
\(592\) −6.96638e43 −0.0125805
\(593\) −1.29305e45 −0.227099 −0.113549 0.993532i \(-0.536222\pi\)
−0.113549 + 0.993532i \(0.536222\pi\)
\(594\) 8.85038e44 0.151177
\(595\) −2.20228e45 −0.365884
\(596\) 2.70600e45 0.437285
\(597\) −5.77818e45 −0.908270
\(598\) −2.18593e45 −0.334246
\(599\) −1.23551e46 −1.83782 −0.918910 0.394467i \(-0.870929\pi\)
−0.918910 + 0.394467i \(0.870929\pi\)
\(600\) 1.00571e45 0.145538
\(601\) −4.92073e45 −0.692788 −0.346394 0.938089i \(-0.612594\pi\)
−0.346394 + 0.938089i \(0.612594\pi\)
\(602\) 7.21841e45 0.988780
\(603\) 2.08653e45 0.278092
\(604\) −6.53556e44 −0.0847566
\(605\) 3.35208e45 0.423010
\(606\) 6.07943e45 0.746559
\(607\) 2.23242e45 0.266786 0.133393 0.991063i \(-0.457413\pi\)
0.133393 + 0.991063i \(0.457413\pi\)
\(608\) −6.68252e45 −0.777197
\(609\) −4.70807e44 −0.0532914
\(610\) −2.41070e45 −0.265584
\(611\) −2.72441e44 −0.0292141
\(612\) 2.71069e45 0.282932
\(613\) 1.28306e45 0.130362 0.0651808 0.997873i \(-0.479238\pi\)
0.0651808 + 0.997873i \(0.479238\pi\)
\(614\) 5.18414e45 0.512742
\(615\) 6.09031e45 0.586408
\(616\) 2.06170e45 0.193261
\(617\) 1.81527e46 1.65667 0.828333 0.560235i \(-0.189289\pi\)
0.828333 + 0.560235i \(0.189289\pi\)
\(618\) −1.71496e45 −0.152386
\(619\) −1.88787e46 −1.63334 −0.816670 0.577104i \(-0.804183\pi\)
−0.816670 + 0.577104i \(0.804183\pi\)
\(620\) −3.23158e44 −0.0272240
\(621\) 1.36142e46 1.11681
\(622\) −1.24239e45 −0.0992472
\(623\) −9.14471e45 −0.711406
\(624\) −1.77905e44 −0.0134785
\(625\) 5.42101e44 0.0400000
\(626\) −1.53381e45 −0.110229
\(627\) 1.88187e45 0.131727
\(628\) 8.62084e45 0.587781
\(629\) −5.34279e45 −0.354840
\(630\) −1.61240e45 −0.104317
\(631\) −1.84920e46 −1.16547 −0.582733 0.812664i \(-0.698017\pi\)
−0.582733 + 0.812664i \(0.698017\pi\)
\(632\) 3.07395e46 1.88740
\(633\) 2.08622e46 1.24796
\(634\) −1.27224e46 −0.741476
\(635\) 7.58636e45 0.430792
\(636\) 5.86192e45 0.324338
\(637\) 2.89713e45 0.156195
\(638\) 2.31195e44 0.0121461
\(639\) 9.16623e45 0.469274
\(640\) −5.92103e45 −0.295411
\(641\) −2.03686e46 −0.990382 −0.495191 0.868784i \(-0.664902\pi\)
−0.495191 + 0.868784i \(0.664902\pi\)
\(642\) −1.15973e46 −0.549577
\(643\) −3.33285e46 −1.53934 −0.769671 0.638440i \(-0.779580\pi\)
−0.769671 + 0.638440i \(0.779580\pi\)
\(644\) 1.22979e46 0.553622
\(645\) 1.45787e46 0.639711
\(646\) −1.06110e46 −0.453860
\(647\) −2.86276e46 −1.19361 −0.596807 0.802385i \(-0.703564\pi\)
−0.596807 + 0.802385i \(0.703564\pi\)
\(648\) −8.05480e45 −0.327391
\(649\) 9.01638e45 0.357269
\(650\) 1.66295e45 0.0642405
\(651\) −1.57717e45 −0.0594007
\(652\) 1.80324e46 0.662168
\(653\) −4.94384e43 −0.00177010 −0.000885048 1.00000i \(-0.500282\pi\)
−0.000885048 1.00000i \(0.500282\pi\)
\(654\) −2.23273e46 −0.779478
\(655\) −4.97607e45 −0.169397
\(656\) −1.85387e45 −0.0615412
\(657\) 5.60522e45 0.181453
\(658\) −8.87222e44 −0.0280095
\(659\) 3.69093e45 0.113639 0.0568194 0.998384i \(-0.481904\pi\)
0.0568194 + 0.998384i \(0.481904\pi\)
\(660\) 1.61464e45 0.0484844
\(661\) −1.92860e46 −0.564830 −0.282415 0.959292i \(-0.591136\pi\)
−0.282415 + 0.959292i \(0.591136\pi\)
\(662\) 1.16056e46 0.331522
\(663\) −1.36442e46 −0.380168
\(664\) 3.92808e45 0.106760
\(665\) −1.09040e46 −0.289087
\(666\) −3.91173e45 −0.101168
\(667\) 3.55638e45 0.0897287
\(668\) −4.21037e46 −1.03636
\(669\) 2.52400e46 0.606120
\(670\) −7.00792e45 −0.164193
\(671\) −9.98104e45 −0.228168
\(672\) −2.79828e46 −0.624163
\(673\) 6.71207e46 1.46086 0.730428 0.682989i \(-0.239320\pi\)
0.730428 + 0.682989i \(0.239320\pi\)
\(674\) −3.16417e45 −0.0672003
\(675\) −1.03570e46 −0.214646
\(676\) 2.25042e46 0.455138
\(677\) 6.40029e46 1.26324 0.631621 0.775278i \(-0.282390\pi\)
0.631621 + 0.775278i \(0.282390\pi\)
\(678\) 1.15869e45 0.0223191
\(679\) 1.45625e46 0.273770
\(680\) −2.34786e46 −0.430799
\(681\) 6.25268e46 1.11980
\(682\) 7.74485e44 0.0135385
\(683\) 8.73990e46 1.49130 0.745650 0.666338i \(-0.232139\pi\)
0.745650 + 0.666338i \(0.232139\pi\)
\(684\) 1.34212e46 0.223546
\(685\) 7.37757e45 0.119955
\(686\) 4.14772e46 0.658357
\(687\) −8.01093e46 −1.24136
\(688\) −4.43770e45 −0.0671350
\(689\) 2.49962e46 0.369196
\(690\) −1.43772e46 −0.207331
\(691\) 4.89363e46 0.689039 0.344519 0.938779i \(-0.388042\pi\)
0.344519 + 0.938779i \(0.388042\pi\)
\(692\) −2.51410e46 −0.345647
\(693\) −6.67584e45 −0.0896205
\(694\) −1.42859e46 −0.187274
\(695\) 2.47109e46 0.316329
\(696\) −5.01928e45 −0.0627464
\(697\) −1.42181e47 −1.73580
\(698\) 7.99324e46 0.953034
\(699\) −1.12550e45 −0.0131060
\(700\) −9.35562e45 −0.106403
\(701\) −3.51093e46 −0.390009 −0.195004 0.980802i \(-0.562472\pi\)
−0.195004 + 0.980802i \(0.562472\pi\)
\(702\) −3.17712e46 −0.344724
\(703\) −2.64533e46 −0.280361
\(704\) 1.29652e46 0.134225
\(705\) −1.79188e45 −0.0181213
\(706\) −2.57267e46 −0.254159
\(707\) −1.45845e47 −1.40757
\(708\) −7.59049e46 −0.715684
\(709\) 9.47916e46 0.873187 0.436593 0.899659i \(-0.356185\pi\)
0.436593 + 0.899659i \(0.356185\pi\)
\(710\) −3.07862e46 −0.277072
\(711\) −9.95351e46 −0.875241
\(712\) −9.74920e46 −0.837624
\(713\) 1.19136e46 0.100015
\(714\) −4.44333e46 −0.364492
\(715\) 6.88511e45 0.0551901
\(716\) 9.45857e46 0.740901
\(717\) 5.05115e46 0.386656
\(718\) −6.34577e46 −0.474713
\(719\) −1.57057e46 −0.114823 −0.0574116 0.998351i \(-0.518285\pi\)
−0.0574116 + 0.998351i \(0.518285\pi\)
\(720\) 9.91267e44 0.00708279
\(721\) 4.11417e46 0.287310
\(722\) 3.61731e46 0.246900
\(723\) 9.82486e46 0.655457
\(724\) 1.20009e47 0.782576
\(725\) −2.70552e45 −0.0172454
\(726\) 6.76317e46 0.421402
\(727\) 5.94494e46 0.362101 0.181051 0.983474i \(-0.442050\pi\)
0.181051 + 0.983474i \(0.442050\pi\)
\(728\) −7.40112e46 −0.440687
\(729\) 1.61739e47 0.941480
\(730\) −1.88260e46 −0.107135
\(731\) −3.40345e47 −1.89358
\(732\) 8.40259e46 0.457068
\(733\) 2.58199e47 1.37322 0.686608 0.727028i \(-0.259099\pi\)
0.686608 + 0.727028i \(0.259099\pi\)
\(734\) −7.89885e46 −0.410751
\(735\) 1.90548e46 0.0968866
\(736\) 2.11376e47 1.05093
\(737\) −2.90149e46 −0.141061
\(738\) −1.04098e47 −0.494893
\(739\) −1.03631e47 −0.481790 −0.240895 0.970551i \(-0.577441\pi\)
−0.240895 + 0.970551i \(0.577441\pi\)
\(740\) −2.26970e46 −0.103192
\(741\) −6.75556e46 −0.300373
\(742\) 8.14018e46 0.353973
\(743\) −2.33354e47 −0.992428 −0.496214 0.868200i \(-0.665277\pi\)
−0.496214 + 0.868200i \(0.665277\pi\)
\(744\) −1.68142e46 −0.0699397
\(745\) 7.58925e46 0.308760
\(746\) 2.49081e47 0.991176
\(747\) −1.27192e46 −0.0495075
\(748\) −3.76945e46 −0.143516
\(749\) 2.78217e47 1.03618
\(750\) 1.09375e46 0.0398479
\(751\) −1.20809e47 −0.430568 −0.215284 0.976552i \(-0.569068\pi\)
−0.215284 + 0.976552i \(0.569068\pi\)
\(752\) 5.45442e44 0.00190175
\(753\) −2.28551e47 −0.779591
\(754\) −8.29945e45 −0.0276963
\(755\) −1.83297e46 −0.0598452
\(756\) 1.78742e47 0.570976
\(757\) 5.96569e47 1.86457 0.932285 0.361724i \(-0.117812\pi\)
0.932285 + 0.361724i \(0.117812\pi\)
\(758\) 7.96864e46 0.243693
\(759\) −5.95258e46 −0.178121
\(760\) −1.16248e47 −0.340377
\(761\) −3.41953e47 −0.979760 −0.489880 0.871790i \(-0.662959\pi\)
−0.489880 + 0.871790i \(0.662959\pi\)
\(762\) 1.53063e47 0.429153
\(763\) 5.35630e47 1.46964
\(764\) −1.78082e47 −0.478167
\(765\) 7.60241e46 0.199773
\(766\) −5.86149e44 −0.00150742
\(767\) −3.23671e47 −0.814668
\(768\) −2.91792e47 −0.718809
\(769\) −7.47483e47 −1.80226 −0.901129 0.433551i \(-0.857260\pi\)
−0.901129 + 0.433551i \(0.857260\pi\)
\(770\) 2.24218e46 0.0529144
\(771\) −5.66554e47 −1.30871
\(772\) 4.43514e47 1.00282
\(773\) 1.39866e47 0.309565 0.154782 0.987949i \(-0.450532\pi\)
0.154782 + 0.987949i \(0.450532\pi\)
\(774\) −2.49184e47 −0.539877
\(775\) −9.06329e45 −0.0192224
\(776\) 1.55251e47 0.322342
\(777\) −1.10772e47 −0.225156
\(778\) −2.12170e46 −0.0422203
\(779\) −7.03968e47 −1.37147
\(780\) −5.79627e46 −0.110557
\(781\) −1.27464e47 −0.238038
\(782\) 3.35640e47 0.613709
\(783\) 5.16898e46 0.0925414
\(784\) −5.80022e45 −0.0101679
\(785\) 2.41780e47 0.415022
\(786\) −1.00397e47 −0.168753
\(787\) 6.12282e47 1.00779 0.503893 0.863766i \(-0.331901\pi\)
0.503893 + 0.863766i \(0.331901\pi\)
\(788\) −6.33886e47 −1.02171
\(789\) −4.30702e47 −0.679840
\(790\) 3.34304e47 0.516767
\(791\) −2.77968e46 −0.0420807
\(792\) −7.11713e46 −0.105521
\(793\) 3.58300e47 0.520283
\(794\) 7.89176e47 1.12237
\(795\) 1.64404e47 0.229009
\(796\) 5.73049e47 0.781855
\(797\) −7.29365e47 −0.974726 −0.487363 0.873199i \(-0.662041\pi\)
−0.487363 + 0.873199i \(0.662041\pi\)
\(798\) −2.19999e47 −0.287988
\(799\) 4.18321e46 0.0536399
\(800\) −1.60805e47 −0.201983
\(801\) 3.15681e47 0.388430
\(802\) 2.18966e47 0.263937
\(803\) −7.79452e46 −0.0920414
\(804\) 2.44264e47 0.282575
\(805\) 3.44906e47 0.390903
\(806\) −2.78026e46 −0.0308714
\(807\) 9.66061e47 1.05097
\(808\) −1.55485e48 −1.65730
\(809\) 4.30397e47 0.449489 0.224744 0.974418i \(-0.427845\pi\)
0.224744 + 0.974418i \(0.427845\pi\)
\(810\) −8.75991e46 −0.0896390
\(811\) 1.20340e48 1.20660 0.603302 0.797513i \(-0.293851\pi\)
0.603302 + 0.797513i \(0.293851\pi\)
\(812\) 4.66921e46 0.0458742
\(813\) 8.99045e47 0.865541
\(814\) 5.43959e46 0.0513173
\(815\) 5.05737e47 0.467546
\(816\) 2.73165e46 0.0247479
\(817\) −1.68512e48 −1.49613
\(818\) −5.91992e47 −0.515094
\(819\) 2.39650e47 0.204359
\(820\) −6.04004e47 −0.504791
\(821\) 1.31428e48 1.07653 0.538264 0.842776i \(-0.319080\pi\)
0.538264 + 0.842776i \(0.319080\pi\)
\(822\) 1.48850e47 0.119499
\(823\) 1.85531e48 1.45989 0.729945 0.683506i \(-0.239546\pi\)
0.729945 + 0.683506i \(0.239546\pi\)
\(824\) 4.38613e47 0.338285
\(825\) 4.52844e46 0.0342340
\(826\) −1.05406e48 −0.781076
\(827\) 3.05619e47 0.221993 0.110997 0.993821i \(-0.464596\pi\)
0.110997 + 0.993821i \(0.464596\pi\)
\(828\) −4.24530e47 −0.302279
\(829\) −1.49161e48 −1.04113 −0.520567 0.853821i \(-0.674279\pi\)
−0.520567 + 0.853821i \(0.674279\pi\)
\(830\) 4.27195e46 0.0292306
\(831\) −1.86034e48 −1.24789
\(832\) −4.65428e47 −0.306068
\(833\) −4.44841e47 −0.286789
\(834\) 4.98569e47 0.315127
\(835\) −1.18084e48 −0.731754
\(836\) −1.86634e47 −0.113393
\(837\) 1.73157e47 0.103150
\(838\) −1.48554e48 −0.867676
\(839\) 1.58547e48 0.907999 0.454000 0.891002i \(-0.349997\pi\)
0.454000 + 0.891002i \(0.349997\pi\)
\(840\) −4.86782e47 −0.273355
\(841\) −1.80257e48 −0.992565
\(842\) −1.64315e48 −0.887212
\(843\) 1.85893e48 0.984254
\(844\) −2.06900e48 −1.07426
\(845\) 6.31153e47 0.321365
\(846\) 3.06274e46 0.0152933
\(847\) −1.62248e48 −0.794515
\(848\) −5.00438e46 −0.0240336
\(849\) 1.27513e48 0.600589
\(850\) −2.55339e47 −0.117952
\(851\) 8.36751e47 0.379104
\(852\) 1.07306e48 0.476839
\(853\) 1.56569e48 0.682414 0.341207 0.939988i \(-0.389164\pi\)
0.341207 + 0.939988i \(0.389164\pi\)
\(854\) 1.16683e48 0.498830
\(855\) 3.76413e47 0.157842
\(856\) 2.96608e48 1.22002
\(857\) −3.16984e48 −1.27895 −0.639476 0.768811i \(-0.720849\pi\)
−0.639476 + 0.768811i \(0.720849\pi\)
\(858\) 1.38914e47 0.0549802
\(859\) −8.88897e47 −0.345115 −0.172558 0.984999i \(-0.555203\pi\)
−0.172558 + 0.984999i \(0.555203\pi\)
\(860\) −1.44584e48 −0.550674
\(861\) −2.94784e48 −1.10142
\(862\) −4.15842e47 −0.152426
\(863\) 4.50727e48 1.62082 0.810411 0.585862i \(-0.199244\pi\)
0.810411 + 0.585862i \(0.199244\pi\)
\(864\) 3.07223e48 1.08387
\(865\) −7.05106e47 −0.244055
\(866\) 1.47593e48 0.501211
\(867\) −1.13313e47 −0.0377542
\(868\) 1.56415e47 0.0511332
\(869\) 1.38412e48 0.443963
\(870\) −5.45867e46 −0.0171798
\(871\) 1.04158e48 0.321657
\(872\) 5.71036e48 1.73038
\(873\) −5.02708e47 −0.149479
\(874\) 1.66183e48 0.484895
\(875\) −2.62388e47 −0.0751296
\(876\) 6.56186e47 0.184378
\(877\) −3.88746e48 −1.07195 −0.535973 0.844235i \(-0.680055\pi\)
−0.535973 + 0.844235i \(0.680055\pi\)
\(878\) −1.00528e48 −0.272037
\(879\) 1.75207e48 0.465302
\(880\) −1.37844e46 −0.00359272
\(881\) −4.23545e48 −1.08342 −0.541711 0.840565i \(-0.682223\pi\)
−0.541711 + 0.840565i \(0.682223\pi\)
\(882\) −3.25691e47 −0.0817663
\(883\) 2.06647e48 0.509188 0.254594 0.967048i \(-0.418058\pi\)
0.254594 + 0.967048i \(0.418058\pi\)
\(884\) 1.35316e48 0.327255
\(885\) −2.12883e48 −0.505333
\(886\) 1.91160e48 0.445389
\(887\) −1.92447e48 −0.440121 −0.220060 0.975486i \(-0.570625\pi\)
−0.220060 + 0.975486i \(0.570625\pi\)
\(888\) −1.18095e48 −0.265104
\(889\) −3.67195e48 −0.809130
\(890\) −1.06026e48 −0.229340
\(891\) −3.62687e47 −0.0770105
\(892\) −2.50317e48 −0.521759
\(893\) 2.07120e47 0.0423812
\(894\) 1.53121e48 0.307585
\(895\) 2.65275e48 0.523138
\(896\) 2.86590e48 0.554854
\(897\) 2.13686e48 0.406164
\(898\) −4.63102e48 −0.864205
\(899\) 4.52331e46 0.00828746
\(900\) 3.22962e47 0.0580965
\(901\) −3.83806e48 −0.677879
\(902\) 1.44757e48 0.251033
\(903\) −7.05639e48 −1.20153
\(904\) −2.96342e47 −0.0495467
\(905\) 3.36577e48 0.552564
\(906\) −3.69820e47 −0.0596177
\(907\) −2.02864e48 −0.321133 −0.160567 0.987025i \(-0.551332\pi\)
−0.160567 + 0.987025i \(0.551332\pi\)
\(908\) −6.20107e48 −0.963940
\(909\) 5.03465e48 0.768537
\(910\) −8.04902e47 −0.120659
\(911\) 3.08415e48 0.454028 0.227014 0.973891i \(-0.427104\pi\)
0.227014 + 0.973891i \(0.427104\pi\)
\(912\) 1.35250e47 0.0195534
\(913\) 1.76871e47 0.0251125
\(914\) −6.16894e48 −0.860198
\(915\) 2.35659e48 0.322728
\(916\) 7.94481e48 1.06858
\(917\) 2.40852e48 0.318168
\(918\) 4.87833e48 0.632946
\(919\) −7.76805e48 −0.989933 −0.494967 0.868912i \(-0.664820\pi\)
−0.494967 + 0.868912i \(0.664820\pi\)
\(920\) 3.67705e48 0.460257
\(921\) −5.06778e48 −0.623066
\(922\) −2.85598e48 −0.344902
\(923\) 4.57572e48 0.542789
\(924\) −7.81521e47 −0.0910653
\(925\) −6.36560e47 −0.0728619
\(926\) −3.18383e48 −0.357988
\(927\) −1.42024e48 −0.156872
\(928\) 8.02544e47 0.0870818
\(929\) −1.29507e49 −1.38049 −0.690244 0.723576i \(-0.742497\pi\)
−0.690244 + 0.723576i \(0.742497\pi\)
\(930\) −1.82861e47 −0.0191493
\(931\) −2.20251e48 −0.226594
\(932\) 1.11621e47 0.0112819
\(933\) 1.21451e48 0.120602
\(934\) −4.80683e48 −0.468960
\(935\) −1.05718e48 −0.101334
\(936\) 2.55491e48 0.240616
\(937\) 1.36587e49 1.26388 0.631940 0.775017i \(-0.282259\pi\)
0.631940 + 0.775017i \(0.282259\pi\)
\(938\) 3.39198e48 0.308394
\(939\) 1.49938e48 0.133946
\(940\) 1.77709e47 0.0155991
\(941\) −1.17124e45 −0.000101022 0 −5.05109e−5 1.00000i \(-0.500016\pi\)
−5.05109e−5 1.00000i \(0.500016\pi\)
\(942\) 4.87817e48 0.413444
\(943\) 2.22673e49 1.85449
\(944\) 6.48009e47 0.0530326
\(945\) 5.01301e48 0.403156
\(946\) 3.46511e48 0.273851
\(947\) 1.87235e49 1.45416 0.727081 0.686551i \(-0.240876\pi\)
0.727081 + 0.686551i \(0.240876\pi\)
\(948\) −1.16523e49 −0.889352
\(949\) 2.79809e48 0.209879
\(950\) −1.26424e48 −0.0931944
\(951\) 1.24369e49 0.901015
\(952\) 1.13641e49 0.809144
\(953\) −2.01399e49 −1.40937 −0.704685 0.709521i \(-0.748912\pi\)
−0.704685 + 0.709521i \(0.748912\pi\)
\(954\) −2.81004e48 −0.193270
\(955\) −4.99449e48 −0.337626
\(956\) −5.00946e48 −0.332840
\(957\) −2.26005e47 −0.0147595
\(958\) 7.26405e48 0.466282
\(959\) −3.57089e48 −0.225305
\(960\) −3.06119e48 −0.189852
\(961\) −1.62519e49 −0.990762
\(962\) −1.95271e48 −0.117017
\(963\) −9.60423e48 −0.565756
\(964\) −9.74376e48 −0.564229
\(965\) 1.24388e49 0.708072
\(966\) 6.95884e48 0.389417
\(967\) 1.68504e49 0.926985 0.463493 0.886101i \(-0.346596\pi\)
0.463493 + 0.886101i \(0.346596\pi\)
\(968\) −1.72973e49 −0.935478
\(969\) 1.03729e49 0.551514
\(970\) 1.68842e48 0.0882566
\(971\) −1.57857e49 −0.811234 −0.405617 0.914043i \(-0.632943\pi\)
−0.405617 + 0.914043i \(0.632943\pi\)
\(972\) −1.04005e49 −0.525485
\(973\) −1.19606e49 −0.594143
\(974\) −1.46508e49 −0.715549
\(975\) −1.62562e48 −0.0780627
\(976\) −7.17338e47 −0.0338690
\(977\) −1.78305e49 −0.827759 −0.413880 0.910332i \(-0.635827\pi\)
−0.413880 + 0.910332i \(0.635827\pi\)
\(978\) 1.02038e49 0.465768
\(979\) −4.38981e48 −0.197030
\(980\) −1.88975e48 −0.0834017
\(981\) −1.84903e49 −0.802425
\(982\) 9.33798e48 0.398486
\(983\) 1.52674e48 0.0640667 0.0320333 0.999487i \(-0.489802\pi\)
0.0320333 + 0.999487i \(0.489802\pi\)
\(984\) −3.14269e49 −1.29683
\(985\) −1.77780e49 −0.721414
\(986\) 1.27435e48 0.0508532
\(987\) 8.67307e47 0.0340361
\(988\) 6.69980e48 0.258566
\(989\) 5.33025e49 2.02306
\(990\) −7.74016e47 −0.0288914
\(991\) 1.40402e49 0.515416 0.257708 0.966223i \(-0.417033\pi\)
0.257708 + 0.966223i \(0.417033\pi\)
\(992\) 2.68847e48 0.0970648
\(993\) −1.13451e49 −0.402854
\(994\) 1.49011e49 0.520408
\(995\) 1.60717e49 0.552055
\(996\) −1.48900e48 −0.0503056
\(997\) −7.92661e48 −0.263401 −0.131701 0.991290i \(-0.542044\pi\)
−0.131701 + 0.991290i \(0.542044\pi\)
\(998\) −3.66225e48 −0.119700
\(999\) 1.21617e49 0.390988
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 \(a_p\))