Properties

Label 5.34.a.a.1.1
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 1.1
Root \(33794.2\)
Character \(\chi\) = 5.1

$q$-expansion

\(f(q)\) \(=\) \(q-129081. q^{2} -6.82881e7 q^{3} +8.07187e9 q^{4} -1.52588e11 q^{5} +8.81467e12 q^{6} -1.39338e14 q^{7} +6.68716e13 q^{8} -8.95800e14 q^{9} +O(q^{10})\) \(q-129081. q^{2} -6.82881e7 q^{3} +8.07187e9 q^{4} -1.52588e11 q^{5} +8.81467e12 q^{6} -1.39338e14 q^{7} +6.68716e13 q^{8} -8.95800e14 q^{9} +1.96961e16 q^{10} -1.11807e17 q^{11} -5.51213e17 q^{12} +3.82676e18 q^{13} +1.79859e19 q^{14} +1.04199e19 q^{15} -7.79687e19 q^{16} +1.35670e20 q^{17} +1.15630e20 q^{18} +1.50898e21 q^{19} -1.23167e21 q^{20} +9.51513e21 q^{21} +1.44321e22 q^{22} +2.26444e22 q^{23} -4.56653e21 q^{24} +2.32831e22 q^{25} -4.93961e23 q^{26} +4.40790e23 q^{27} -1.12472e24 q^{28} -6.82827e23 q^{29} -1.34501e24 q^{30} -5.41504e24 q^{31} +9.48983e24 q^{32} +7.63507e24 q^{33} -1.75124e25 q^{34} +2.12613e25 q^{35} -7.23078e24 q^{36} -7.55931e24 q^{37} -1.94780e26 q^{38} -2.61322e26 q^{39} -1.02038e25 q^{40} -1.95728e26 q^{41} -1.22822e27 q^{42} +5.44732e26 q^{43} -9.02490e26 q^{44} +1.36688e26 q^{45} -2.92295e27 q^{46} -3.58134e27 q^{47} +5.32433e27 q^{48} +1.16841e28 q^{49} -3.00539e27 q^{50} -9.26465e27 q^{51} +3.08891e28 q^{52} +4.28944e28 q^{53} -5.68974e28 q^{54} +1.70604e28 q^{55} -9.31777e27 q^{56} -1.03045e29 q^{57} +8.81397e28 q^{58} -2.15590e28 q^{59} +8.41084e28 q^{60} +5.24247e29 q^{61} +6.98976e29 q^{62} +1.24819e29 q^{63} -5.55207e29 q^{64} -5.83917e29 q^{65} -9.85539e29 q^{66} -1.47500e30 q^{67} +1.09511e30 q^{68} -1.54634e30 q^{69} -2.74442e30 q^{70} -1.24706e30 q^{71} -5.99036e28 q^{72} -9.14380e30 q^{73} +9.75760e29 q^{74} -1.58996e30 q^{75} +1.21803e31 q^{76} +1.55789e31 q^{77} +3.37316e31 q^{78} -2.52252e31 q^{79} +1.18971e31 q^{80} -2.51209e31 q^{81} +2.52647e31 q^{82} -1.28605e31 q^{83} +7.68050e31 q^{84} -2.07016e31 q^{85} -7.03143e31 q^{86} +4.66289e31 q^{87} -7.47670e30 q^{88} +1.22503e32 q^{89} -1.76438e31 q^{90} -5.33214e32 q^{91} +1.82783e32 q^{92} +3.69782e32 q^{93} +4.62282e32 q^{94} -2.30252e32 q^{95} -6.48042e32 q^{96} +2.05513e31 q^{97} -1.50819e33 q^{98} +1.00156e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + 30472q^{2} - 14988714q^{3} + 1141311360q^{4} - 762939453125q^{5} + 12925063115760q^{6} - 65452561787158q^{7} + 155610638035200q^{8} + 14541250990408965q^{9} + O(q^{10}) \) \( 5q + 30472q^{2} - 14988714q^{3} + 1141311360q^{4} - 762939453125q^{5} + 12925063115760q^{6} - 65452561787158q^{7} + 155610638035200q^{8} + 14541250990408965q^{9} - 4649658203125000q^{10} - 287801801877976640q^{11} - 405379955363513088q^{12} + 2397201150889907466q^{13} + 11676449916272482320q^{14} + 2287096252441406250q^{15} - 89180089543245957120q^{16} - \)\(30\!\cdots\!18\)\(q^{17} + \)\(53\!\cdots\!56\)\(q^{18} + \)\(91\!\cdots\!00\)\(q^{19} - \)\(17\!\cdots\!00\)\(q^{20} - \)\(10\!\cdots\!40\)\(q^{21} - \)\(13\!\cdots\!96\)\(q^{22} + \)\(55\!\cdots\!46\)\(q^{23} - \)\(71\!\cdots\!00\)\(q^{24} + \)\(11\!\cdots\!25\)\(q^{25} - \)\(42\!\cdots\!40\)\(q^{26} + \)\(67\!\cdots\!00\)\(q^{27} - \)\(13\!\cdots\!36\)\(q^{28} - \)\(92\!\cdots\!50\)\(q^{29} - \)\(19\!\cdots\!00\)\(q^{30} - \)\(13\!\cdots\!40\)\(q^{31} - \)\(81\!\cdots\!08\)\(q^{32} - \)\(33\!\cdots\!48\)\(q^{33} - \)\(68\!\cdots\!80\)\(q^{34} + \)\(99\!\cdots\!50\)\(q^{35} - \)\(18\!\cdots\!20\)\(q^{36} - \)\(14\!\cdots\!38\)\(q^{37} - \)\(33\!\cdots\!00\)\(q^{38} - \)\(78\!\cdots\!20\)\(q^{39} - \)\(23\!\cdots\!00\)\(q^{40} - \)\(13\!\cdots\!90\)\(q^{41} - \)\(26\!\cdots\!36\)\(q^{42} - \)\(23\!\cdots\!94\)\(q^{43} - \)\(18\!\cdots\!80\)\(q^{44} - \)\(22\!\cdots\!25\)\(q^{45} - \)\(28\!\cdots\!40\)\(q^{46} - \)\(77\!\cdots\!98\)\(q^{47} - \)\(73\!\cdots\!04\)\(q^{48} + \)\(41\!\cdots\!85\)\(q^{49} + \)\(70\!\cdots\!00\)\(q^{50} + \)\(73\!\cdots\!60\)\(q^{51} + \)\(48\!\cdots\!72\)\(q^{52} + \)\(10\!\cdots\!86\)\(q^{53} + \)\(64\!\cdots\!00\)\(q^{54} + \)\(43\!\cdots\!00\)\(q^{55} + \)\(14\!\cdots\!00\)\(q^{56} + \)\(20\!\cdots\!00\)\(q^{57} + \)\(21\!\cdots\!00\)\(q^{58} + \)\(25\!\cdots\!00\)\(q^{59} + \)\(61\!\cdots\!00\)\(q^{60} + \)\(74\!\cdots\!10\)\(q^{61} + \)\(53\!\cdots\!24\)\(q^{62} - \)\(10\!\cdots\!34\)\(q^{63} - \)\(10\!\cdots\!40\)\(q^{64} - \)\(36\!\cdots\!50\)\(q^{65} - \)\(33\!\cdots\!80\)\(q^{66} - \)\(37\!\cdots\!18\)\(q^{67} + \)\(11\!\cdots\!44\)\(q^{68} - \)\(27\!\cdots\!20\)\(q^{69} - \)\(17\!\cdots\!00\)\(q^{70} - \)\(55\!\cdots\!40\)\(q^{71} - \)\(15\!\cdots\!00\)\(q^{72} - \)\(13\!\cdots\!54\)\(q^{73} - \)\(36\!\cdots\!80\)\(q^{74} - \)\(34\!\cdots\!50\)\(q^{75} + \)\(71\!\cdots\!00\)\(q^{76} + \)\(47\!\cdots\!44\)\(q^{77} + \)\(12\!\cdots\!72\)\(q^{78} - \)\(10\!\cdots\!00\)\(q^{79} + \)\(13\!\cdots\!00\)\(q^{80} + \)\(78\!\cdots\!05\)\(q^{81} + \)\(27\!\cdots\!84\)\(q^{82} + \)\(92\!\cdots\!26\)\(q^{83} + \)\(17\!\cdots\!20\)\(q^{84} + \)\(47\!\cdots\!50\)\(q^{85} + \)\(65\!\cdots\!60\)\(q^{86} + \)\(13\!\cdots\!00\)\(q^{87} + \)\(19\!\cdots\!00\)\(q^{88} - \)\(60\!\cdots\!50\)\(q^{89} - \)\(82\!\cdots\!00\)\(q^{90} - \)\(26\!\cdots\!40\)\(q^{91} - \)\(69\!\cdots\!68\)\(q^{92} - \)\(69\!\cdots\!88\)\(q^{93} - \)\(36\!\cdots\!80\)\(q^{94} - \)\(14\!\cdots\!00\)\(q^{95} - \)\(34\!\cdots\!40\)\(q^{96} - \)\(86\!\cdots\!98\)\(q^{97} - \)\(19\!\cdots\!96\)\(q^{98} - \)\(17\!\cdots\!20\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −129081. −1.39273 −0.696364 0.717689i \(-0.745200\pi\)
−0.696364 + 0.717689i \(0.745200\pi\)
\(3\) −6.82881e7 −0.915892 −0.457946 0.888980i \(-0.651415\pi\)
−0.457946 + 0.888980i \(0.651415\pi\)
\(4\) 8.07187e9 0.939690
\(5\) −1.52588e11 −0.447214
\(6\) 8.81467e12 1.27559
\(7\) −1.39338e14 −1.58472 −0.792360 0.610054i \(-0.791148\pi\)
−0.792360 + 0.610054i \(0.791148\pi\)
\(8\) 6.68716e13 0.0839957
\(9\) −8.95800e14 −0.161142
\(10\) 1.96961e16 0.622847
\(11\) −1.11807e17 −0.733650 −0.366825 0.930290i \(-0.619555\pi\)
−0.366825 + 0.930290i \(0.619555\pi\)
\(12\) −5.51213e17 −0.860654
\(13\) 3.82676e18 1.59502 0.797510 0.603306i \(-0.206150\pi\)
0.797510 + 0.603306i \(0.206150\pi\)
\(14\) 1.79859e19 2.20708
\(15\) 1.04199e19 0.409599
\(16\) −7.79687e19 −1.05667
\(17\) 1.35670e20 0.676203 0.338101 0.941110i \(-0.390215\pi\)
0.338101 + 0.941110i \(0.390215\pi\)
\(18\) 1.15630e20 0.224427
\(19\) 1.50898e21 1.20019 0.600093 0.799930i \(-0.295130\pi\)
0.600093 + 0.799930i \(0.295130\pi\)
\(20\) −1.23167e21 −0.420242
\(21\) 9.51513e21 1.45143
\(22\) 1.44321e22 1.02177
\(23\) 2.26444e22 0.769931 0.384965 0.922931i \(-0.374213\pi\)
0.384965 + 0.922931i \(0.374213\pi\)
\(24\) −4.56653e21 −0.0769310
\(25\) 2.32831e22 0.200000
\(26\) −4.93961e23 −2.22143
\(27\) 4.40790e23 1.06348
\(28\) −1.12472e24 −1.48914
\(29\) −6.82827e23 −0.506691 −0.253346 0.967376i \(-0.581531\pi\)
−0.253346 + 0.967376i \(0.581531\pi\)
\(30\) −1.34501e24 −0.570460
\(31\) −5.41504e24 −1.33701 −0.668503 0.743709i \(-0.733065\pi\)
−0.668503 + 0.743709i \(0.733065\pi\)
\(32\) 9.48983e24 1.38766
\(33\) 7.63507e24 0.671944
\(34\) −1.75124e25 −0.941766
\(35\) 2.12613e25 0.708708
\(36\) −7.23078e24 −0.151424
\(37\) −7.55931e24 −0.100729 −0.0503644 0.998731i \(-0.516038\pi\)
−0.0503644 + 0.998731i \(0.516038\pi\)
\(38\) −1.94780e26 −1.67153
\(39\) −2.61322e26 −1.46087
\(40\) −1.02038e25 −0.0375640
\(41\) −1.95728e26 −0.479423 −0.239711 0.970844i \(-0.577053\pi\)
−0.239711 + 0.970844i \(0.577053\pi\)
\(42\) −1.22822e27 −2.02145
\(43\) 5.44732e26 0.608069 0.304035 0.952661i \(-0.401666\pi\)
0.304035 + 0.952661i \(0.401666\pi\)
\(44\) −9.02490e26 −0.689403
\(45\) 1.36688e26 0.0720650
\(46\) −2.92295e27 −1.07230
\(47\) −3.58134e27 −0.921363 −0.460682 0.887565i \(-0.652395\pi\)
−0.460682 + 0.887565i \(0.652395\pi\)
\(48\) 5.32433e27 0.967798
\(49\) 1.16841e28 1.51134
\(50\) −3.00539e27 −0.278545
\(51\) −9.26465e27 −0.619329
\(52\) 3.08891e28 1.49882
\(53\) 4.28944e28 1.52002 0.760010 0.649912i \(-0.225194\pi\)
0.760010 + 0.649912i \(0.225194\pi\)
\(54\) −5.68974e28 −1.48114
\(55\) 1.70604e28 0.328098
\(56\) −9.31777e27 −0.133110
\(57\) −1.03045e29 −1.09924
\(58\) 8.81397e28 0.705683
\(59\) −2.15590e28 −0.130188 −0.0650940 0.997879i \(-0.520735\pi\)
−0.0650940 + 0.997879i \(0.520735\pi\)
\(60\) 8.41084e28 0.384896
\(61\) 5.24247e29 1.82639 0.913196 0.407521i \(-0.133607\pi\)
0.913196 + 0.407521i \(0.133607\pi\)
\(62\) 6.98976e29 1.86209
\(63\) 1.24819e29 0.255365
\(64\) −5.55207e29 −0.875962
\(65\) −5.83917e29 −0.713314
\(66\) −9.85539e29 −0.935834
\(67\) −1.47500e30 −1.09284 −0.546422 0.837510i \(-0.684011\pi\)
−0.546422 + 0.837510i \(0.684011\pi\)
\(68\) 1.09511e30 0.635421
\(69\) −1.54634e30 −0.705173
\(70\) −2.74442e30 −0.987037
\(71\) −1.24706e30 −0.354914 −0.177457 0.984129i \(-0.556787\pi\)
−0.177457 + 0.984129i \(0.556787\pi\)
\(72\) −5.99036e28 −0.0135353
\(73\) −9.14380e30 −1.64551 −0.822753 0.568398i \(-0.807563\pi\)
−0.822753 + 0.568398i \(0.807563\pi\)
\(74\) 9.75760e29 0.140288
\(75\) −1.58996e30 −0.183178
\(76\) 1.21803e31 1.12780
\(77\) 1.55789e31 1.16263
\(78\) 3.37316e31 2.03459
\(79\) −2.52252e31 −1.23307 −0.616536 0.787327i \(-0.711464\pi\)
−0.616536 + 0.787327i \(0.711464\pi\)
\(80\) 1.18971e31 0.472558
\(81\) −2.51209e31 −0.812891
\(82\) 2.52647e31 0.667706
\(83\) −1.28605e31 −0.278273 −0.139136 0.990273i \(-0.544433\pi\)
−0.139136 + 0.990273i \(0.544433\pi\)
\(84\) 7.68050e31 1.36390
\(85\) −2.07016e31 −0.302407
\(86\) −7.03143e31 −0.846875
\(87\) 4.66289e31 0.464074
\(88\) −7.47670e30 −0.0616234
\(89\) 1.22503e32 0.837935 0.418967 0.908001i \(-0.362392\pi\)
0.418967 + 0.908001i \(0.362392\pi\)
\(90\) −1.76438e31 −0.100367
\(91\) −5.33214e32 −2.52766
\(92\) 1.82783e32 0.723496
\(93\) 3.69782e32 1.22455
\(94\) 4.62282e32 1.28321
\(95\) −2.30252e32 −0.536739
\(96\) −6.48042e32 −1.27095
\(97\) 2.05513e31 0.0339707 0.0169854 0.999856i \(-0.494593\pi\)
0.0169854 + 0.999856i \(0.494593\pi\)
\(98\) −1.50819e33 −2.10488
\(99\) 1.00156e32 0.118222
\(100\) 1.87938e32 0.187938
\(101\) 4.29097e32 0.364127 0.182064 0.983287i \(-0.441722\pi\)
0.182064 + 0.983287i \(0.441722\pi\)
\(102\) 1.19589e33 0.862556
\(103\) −1.12430e33 −0.690346 −0.345173 0.938539i \(-0.612180\pi\)
−0.345173 + 0.938539i \(0.612180\pi\)
\(104\) 2.55902e32 0.133975
\(105\) −1.45189e33 −0.649100
\(106\) −5.53684e33 −2.11697
\(107\) 6.03479e33 1.97619 0.988097 0.153831i \(-0.0491611\pi\)
0.988097 + 0.153831i \(0.0491611\pi\)
\(108\) 3.55800e33 0.999342
\(109\) −1.99935e32 −0.0482337 −0.0241169 0.999709i \(-0.507677\pi\)
−0.0241169 + 0.999709i \(0.507677\pi\)
\(110\) −2.20216e33 −0.456951
\(111\) 5.16211e32 0.0922567
\(112\) 1.08640e34 1.67453
\(113\) 9.03195e33 1.20223 0.601114 0.799163i \(-0.294724\pi\)
0.601114 + 0.799163i \(0.294724\pi\)
\(114\) 1.33011e34 1.53094
\(115\) −3.45526e33 −0.344323
\(116\) −5.51169e33 −0.476133
\(117\) −3.42801e33 −0.257025
\(118\) 2.78285e33 0.181316
\(119\) −1.89040e34 −1.07159
\(120\) 6.96798e32 0.0344046
\(121\) −1.07244e34 −0.461758
\(122\) −6.76702e34 −2.54367
\(123\) 1.33659e34 0.439100
\(124\) −4.37095e34 −1.25637
\(125\) −3.55271e33 −0.0894427
\(126\) −1.61117e34 −0.355654
\(127\) 7.84484e34 1.51993 0.759963 0.649966i \(-0.225217\pi\)
0.759963 + 0.649966i \(0.225217\pi\)
\(128\) −9.85056e33 −0.167686
\(129\) −3.71987e34 −0.556926
\(130\) 7.53724e34 0.993453
\(131\) 1.29629e35 1.50566 0.752829 0.658216i \(-0.228689\pi\)
0.752829 + 0.658216i \(0.228689\pi\)
\(132\) 6.16293e34 0.631419
\(133\) −2.10258e35 −1.90196
\(134\) 1.90394e35 1.52203
\(135\) −6.72592e34 −0.475603
\(136\) 9.07248e33 0.0567981
\(137\) −3.35566e35 −1.86161 −0.930804 0.365518i \(-0.880892\pi\)
−0.930804 + 0.365518i \(0.880892\pi\)
\(138\) 1.99603e35 0.982114
\(139\) −1.22685e35 −0.535855 −0.267927 0.963439i \(-0.586339\pi\)
−0.267927 + 0.963439i \(0.586339\pi\)
\(140\) 1.71619e35 0.665966
\(141\) 2.44563e35 0.843869
\(142\) 1.60971e35 0.494299
\(143\) −4.27858e35 −1.17019
\(144\) 6.98443e34 0.170275
\(145\) 1.04191e35 0.226599
\(146\) 1.18029e36 2.29174
\(147\) −7.97887e35 −1.38422
\(148\) −6.10178e34 −0.0946538
\(149\) 6.68791e34 0.0928361 0.0464181 0.998922i \(-0.485219\pi\)
0.0464181 + 0.998922i \(0.485219\pi\)
\(150\) 2.05232e35 0.255118
\(151\) −6.76462e34 −0.0753570 −0.0376785 0.999290i \(-0.511996\pi\)
−0.0376785 + 0.999290i \(0.511996\pi\)
\(152\) 1.00908e35 0.100810
\(153\) −1.21533e35 −0.108965
\(154\) −2.01094e36 −1.61923
\(155\) 8.26269e35 0.597927
\(156\) −2.10936e36 −1.37276
\(157\) 7.84957e35 0.459729 0.229864 0.973223i \(-0.426172\pi\)
0.229864 + 0.973223i \(0.426172\pi\)
\(158\) 3.25609e36 1.71733
\(159\) −2.92918e36 −1.39217
\(160\) −1.44803e36 −0.620581
\(161\) −3.15523e36 −1.22012
\(162\) 3.24262e36 1.13214
\(163\) −4.51268e36 −1.42344 −0.711720 0.702464i \(-0.752083\pi\)
−0.711720 + 0.702464i \(0.752083\pi\)
\(164\) −1.57989e36 −0.450509
\(165\) −1.16502e36 −0.300502
\(166\) 1.66005e36 0.387558
\(167\) 7.01398e36 1.48300 0.741502 0.670950i \(-0.234114\pi\)
0.741502 + 0.670950i \(0.234114\pi\)
\(168\) 6.36293e35 0.121914
\(169\) 8.88797e36 1.54409
\(170\) 2.67218e36 0.421171
\(171\) −1.35174e36 −0.193401
\(172\) 4.39701e36 0.571397
\(173\) 1.06789e37 1.26115 0.630574 0.776129i \(-0.282819\pi\)
0.630574 + 0.776129i \(0.282819\pi\)
\(174\) −6.01889e36 −0.646329
\(175\) −3.24422e36 −0.316944
\(176\) 8.71743e36 0.775228
\(177\) 1.47222e36 0.119238
\(178\) −1.58127e37 −1.16702
\(179\) 1.01966e36 0.0686086 0.0343043 0.999411i \(-0.489078\pi\)
0.0343043 + 0.999411i \(0.489078\pi\)
\(180\) 1.10333e36 0.0677188
\(181\) −3.22152e37 −1.80453 −0.902266 0.431180i \(-0.858097\pi\)
−0.902266 + 0.431180i \(0.858097\pi\)
\(182\) 6.88276e37 3.52034
\(183\) −3.57998e37 −1.67278
\(184\) 1.51427e36 0.0646709
\(185\) 1.15346e36 0.0450473
\(186\) −4.77318e37 −1.70547
\(187\) −1.51688e37 −0.496096
\(188\) −2.89081e37 −0.865796
\(189\) −6.14189e37 −1.68532
\(190\) 2.97210e37 0.747532
\(191\) −2.89210e37 −0.667057 −0.333529 0.942740i \(-0.608239\pi\)
−0.333529 + 0.942740i \(0.608239\pi\)
\(192\) 3.79140e37 0.802286
\(193\) 4.75455e37 0.923451 0.461726 0.887023i \(-0.347230\pi\)
0.461726 + 0.887023i \(0.347230\pi\)
\(194\) −2.65277e36 −0.0473120
\(195\) 3.98746e37 0.653319
\(196\) 9.43128e37 1.42019
\(197\) 2.87965e37 0.398701 0.199350 0.979928i \(-0.436117\pi\)
0.199350 + 0.979928i \(0.436117\pi\)
\(198\) −1.29283e37 −0.164651
\(199\) −1.09912e38 −1.28815 −0.644076 0.764961i \(-0.722758\pi\)
−0.644076 + 0.764961i \(0.722758\pi\)
\(200\) 1.55698e36 0.0167991
\(201\) 1.00725e38 1.00093
\(202\) −5.53881e37 −0.507130
\(203\) 9.51438e37 0.802964
\(204\) −7.47831e37 −0.581977
\(205\) 2.98657e37 0.214404
\(206\) 1.45125e38 0.961464
\(207\) −2.02848e37 −0.124068
\(208\) −2.98368e38 −1.68541
\(209\) −1.68714e38 −0.880516
\(210\) 1.87411e38 0.904019
\(211\) 9.20360e37 0.410485 0.205242 0.978711i \(-0.434202\pi\)
0.205242 + 0.978711i \(0.434202\pi\)
\(212\) 3.46238e38 1.42835
\(213\) 8.51591e37 0.325063
\(214\) −7.78974e38 −2.75230
\(215\) −8.31195e37 −0.271937
\(216\) 2.94763e37 0.0893278
\(217\) 7.54521e38 2.11878
\(218\) 2.58077e37 0.0671765
\(219\) 6.24413e38 1.50711
\(220\) 1.37709e38 0.308310
\(221\) 5.19177e38 1.07856
\(222\) −6.66328e37 −0.128488
\(223\) −8.19419e38 −1.46715 −0.733577 0.679606i \(-0.762151\pi\)
−0.733577 + 0.679606i \(0.762151\pi\)
\(224\) −1.32229e39 −2.19905
\(225\) −2.08570e37 −0.0322285
\(226\) −1.16585e39 −1.67438
\(227\) −3.68201e38 −0.491652 −0.245826 0.969314i \(-0.579059\pi\)
−0.245826 + 0.969314i \(0.579059\pi\)
\(228\) −8.31768e38 −1.03294
\(229\) 5.37397e38 0.620883 0.310442 0.950592i \(-0.399523\pi\)
0.310442 + 0.950592i \(0.399523\pi\)
\(230\) 4.46007e38 0.479549
\(231\) −1.06386e39 −1.06484
\(232\) −4.56617e37 −0.0425599
\(233\) 5.60193e38 0.486368 0.243184 0.969980i \(-0.421808\pi\)
0.243184 + 0.969980i \(0.421808\pi\)
\(234\) 4.42490e38 0.357966
\(235\) 5.46469e38 0.412046
\(236\) −1.74022e38 −0.122336
\(237\) 1.72258e39 1.12936
\(238\) 2.44014e39 1.49244
\(239\) 4.65466e38 0.265658 0.132829 0.991139i \(-0.457594\pi\)
0.132829 + 0.991139i \(0.457594\pi\)
\(240\) −8.12429e38 −0.432812
\(241\) −8.56759e38 −0.426165 −0.213082 0.977034i \(-0.568350\pi\)
−0.213082 + 0.977034i \(0.568350\pi\)
\(242\) 1.38431e39 0.643103
\(243\) −7.34921e38 −0.318961
\(244\) 4.23166e39 1.71624
\(245\) −1.78286e39 −0.675890
\(246\) −1.72528e39 −0.611546
\(247\) 5.77450e39 1.91432
\(248\) −3.62112e38 −0.112303
\(249\) 8.78222e38 0.254868
\(250\) 4.58587e38 0.124569
\(251\) −5.15351e39 −1.31065 −0.655325 0.755347i \(-0.727468\pi\)
−0.655325 + 0.755347i \(0.727468\pi\)
\(252\) 1.00752e39 0.239964
\(253\) −2.53180e39 −0.564859
\(254\) −1.01262e40 −2.11684
\(255\) 1.41367e39 0.276972
\(256\) 6.04071e39 1.10950
\(257\) −5.66916e39 −0.976388 −0.488194 0.872735i \(-0.662344\pi\)
−0.488194 + 0.872735i \(0.662344\pi\)
\(258\) 4.80163e39 0.775646
\(259\) 1.05330e39 0.159627
\(260\) −4.71331e39 −0.670294
\(261\) 6.11676e38 0.0816494
\(262\) −1.67326e40 −2.09697
\(263\) −1.47291e39 −0.173343 −0.0866715 0.996237i \(-0.527623\pi\)
−0.0866715 + 0.996237i \(0.527623\pi\)
\(264\) 5.10569e38 0.0564404
\(265\) −6.54517e39 −0.679773
\(266\) 2.71403e40 2.64891
\(267\) −8.36547e39 −0.767458
\(268\) −1.19060e40 −1.02693
\(269\) −2.15538e39 −0.174828 −0.0874139 0.996172i \(-0.527860\pi\)
−0.0874139 + 0.996172i \(0.527860\pi\)
\(270\) 8.68186e39 0.662385
\(271\) −6.55007e39 −0.470168 −0.235084 0.971975i \(-0.575536\pi\)
−0.235084 + 0.971975i \(0.575536\pi\)
\(272\) −1.05780e40 −0.714525
\(273\) 3.64121e40 2.31506
\(274\) 4.33150e40 2.59271
\(275\) −2.60320e39 −0.146730
\(276\) −1.24819e40 −0.662644
\(277\) −2.17785e40 −1.08921 −0.544604 0.838693i \(-0.683320\pi\)
−0.544604 + 0.838693i \(0.683320\pi\)
\(278\) 1.58362e40 0.746299
\(279\) 4.85079e39 0.215448
\(280\) 1.42178e39 0.0595284
\(281\) 4.97063e38 0.0196226 0.00981131 0.999952i \(-0.496877\pi\)
0.00981131 + 0.999952i \(0.496877\pi\)
\(282\) −3.15683e40 −1.17528
\(283\) −2.67595e40 −0.939728 −0.469864 0.882739i \(-0.655697\pi\)
−0.469864 + 0.882739i \(0.655697\pi\)
\(284\) −1.00661e40 −0.333509
\(285\) 1.57234e40 0.491595
\(286\) 5.52281e40 1.62975
\(287\) 2.72724e40 0.759751
\(288\) −8.50098e39 −0.223611
\(289\) −2.18481e40 −0.542750
\(290\) −1.34490e40 −0.315591
\(291\) −1.40341e39 −0.0311135
\(292\) −7.38076e40 −1.54627
\(293\) 1.28487e40 0.254415 0.127207 0.991876i \(-0.459399\pi\)
0.127207 + 0.991876i \(0.459399\pi\)
\(294\) 1.02992e41 1.92784
\(295\) 3.28965e39 0.0582218
\(296\) −5.05503e38 −0.00846079
\(297\) −4.92833e40 −0.780222
\(298\) −8.63280e39 −0.129295
\(299\) 8.66547e40 1.22805
\(300\) −1.28339e40 −0.172131
\(301\) −7.59019e40 −0.963619
\(302\) 8.73181e39 0.104952
\(303\) −2.93022e40 −0.333501
\(304\) −1.17653e41 −1.26820
\(305\) −7.99938e40 −0.816787
\(306\) 1.56876e40 0.151758
\(307\) 5.95612e40 0.545984 0.272992 0.962016i \(-0.411987\pi\)
0.272992 + 0.962016i \(0.411987\pi\)
\(308\) 1.25751e41 1.09251
\(309\) 7.67761e40 0.632283
\(310\) −1.06655e41 −0.832750
\(311\) −3.80156e40 −0.281459 −0.140730 0.990048i \(-0.544945\pi\)
−0.140730 + 0.990048i \(0.544945\pi\)
\(312\) −1.74750e40 −0.122706
\(313\) −2.52982e41 −1.68503 −0.842515 0.538673i \(-0.818926\pi\)
−0.842515 + 0.538673i \(0.818926\pi\)
\(314\) −1.01323e41 −0.640277
\(315\) −1.90459e40 −0.114203
\(316\) −2.03615e41 −1.15870
\(317\) 2.56047e41 1.38306 0.691530 0.722348i \(-0.256937\pi\)
0.691530 + 0.722348i \(0.256937\pi\)
\(318\) 3.78100e41 1.93892
\(319\) 7.63446e40 0.371734
\(320\) 8.47178e40 0.391742
\(321\) −4.12104e41 −1.80998
\(322\) 4.07279e41 1.69930
\(323\) 2.04723e41 0.811569
\(324\) −2.02773e41 −0.763865
\(325\) 8.90987e40 0.319004
\(326\) 5.82499e41 1.98246
\(327\) 1.36532e40 0.0441769
\(328\) −1.30886e40 −0.0402695
\(329\) 4.99017e41 1.46010
\(330\) 1.50381e41 0.418518
\(331\) 3.97632e41 1.05274 0.526368 0.850257i \(-0.323553\pi\)
0.526368 + 0.850257i \(0.323553\pi\)
\(332\) −1.03809e41 −0.261490
\(333\) 6.77163e39 0.0162317
\(334\) −9.05368e41 −2.06542
\(335\) 2.25067e41 0.488735
\(336\) −7.41883e41 −1.53369
\(337\) −3.16941e41 −0.623857 −0.311928 0.950106i \(-0.600975\pi\)
−0.311928 + 0.950106i \(0.600975\pi\)
\(338\) −1.14726e42 −2.15049
\(339\) −6.16774e41 −1.10111
\(340\) −1.67101e41 −0.284169
\(341\) 6.05438e41 0.980894
\(342\) 1.74484e41 0.269354
\(343\) −5.50823e41 −0.810324
\(344\) 3.64271e40 0.0510752
\(345\) 2.35953e41 0.315363
\(346\) −1.37844e42 −1.75644
\(347\) 3.65901e41 0.444557 0.222279 0.974983i \(-0.428651\pi\)
0.222279 + 0.974983i \(0.428651\pi\)
\(348\) 3.76383e41 0.436086
\(349\) 1.01851e42 1.12550 0.562752 0.826626i \(-0.309743\pi\)
0.562752 + 0.826626i \(0.309743\pi\)
\(350\) 4.18766e41 0.441416
\(351\) 1.68680e42 1.69627
\(352\) −1.06103e42 −1.01806
\(353\) −1.09904e42 −1.00631 −0.503153 0.864197i \(-0.667827\pi\)
−0.503153 + 0.864197i \(0.667827\pi\)
\(354\) −1.90036e41 −0.166066
\(355\) 1.90286e41 0.158722
\(356\) 9.88826e41 0.787399
\(357\) 1.29092e42 0.981462
\(358\) −1.31618e41 −0.0955531
\(359\) −1.88943e42 −1.31000 −0.655002 0.755627i \(-0.727332\pi\)
−0.655002 + 0.755627i \(0.727332\pi\)
\(360\) 9.14056e39 0.00605315
\(361\) 6.96243e41 0.440445
\(362\) 4.15836e42 2.51322
\(363\) 7.32349e41 0.422921
\(364\) −4.30403e42 −2.37522
\(365\) 1.39523e42 0.735893
\(366\) 4.62106e42 2.32972
\(367\) −3.72944e42 −1.79744 −0.898718 0.438527i \(-0.855500\pi\)
−0.898718 + 0.438527i \(0.855500\pi\)
\(368\) −1.76555e42 −0.813565
\(369\) 1.75333e41 0.0772553
\(370\) −1.48889e41 −0.0627386
\(371\) −5.97683e42 −2.40880
\(372\) 2.98484e42 1.15070
\(373\) 2.08286e42 0.768181 0.384091 0.923295i \(-0.374515\pi\)
0.384091 + 0.923295i \(0.374515\pi\)
\(374\) 1.95800e42 0.690926
\(375\) 2.42608e41 0.0819198
\(376\) −2.39490e41 −0.0773906
\(377\) −2.61301e42 −0.808183
\(378\) 7.92799e42 2.34719
\(379\) 1.44890e42 0.410668 0.205334 0.978692i \(-0.434172\pi\)
0.205334 + 0.978692i \(0.434172\pi\)
\(380\) −1.85856e42 −0.504368
\(381\) −5.35709e42 −1.39209
\(382\) 3.73314e42 0.929029
\(383\) −3.31373e42 −0.789837 −0.394919 0.918716i \(-0.629227\pi\)
−0.394919 + 0.918716i \(0.629227\pi\)
\(384\) 6.72676e41 0.153582
\(385\) −2.37716e42 −0.519943
\(386\) −6.13721e42 −1.28612
\(387\) −4.87970e41 −0.0979857
\(388\) 1.65887e41 0.0319219
\(389\) 3.52845e42 0.650752 0.325376 0.945585i \(-0.394509\pi\)
0.325376 + 0.945585i \(0.394509\pi\)
\(390\) −5.14704e42 −0.909895
\(391\) 3.07217e42 0.520629
\(392\) 7.81337e41 0.126946
\(393\) −8.85213e42 −1.37902
\(394\) −3.71707e42 −0.555282
\(395\) 3.84907e42 0.551446
\(396\) 8.08450e41 0.111092
\(397\) 2.11298e42 0.278517 0.139258 0.990256i \(-0.455528\pi\)
0.139258 + 0.990256i \(0.455528\pi\)
\(398\) 1.41874e43 1.79405
\(399\) 1.43581e43 1.74199
\(400\) −1.81535e42 −0.211335
\(401\) −3.95709e42 −0.442073 −0.221037 0.975266i \(-0.570944\pi\)
−0.221037 + 0.975266i \(0.570944\pi\)
\(402\) −1.30016e43 −1.39402
\(403\) −2.07221e43 −2.13255
\(404\) 3.46362e42 0.342167
\(405\) 3.83314e42 0.363536
\(406\) −1.22812e43 −1.11831
\(407\) 8.45182e41 0.0738996
\(408\) −6.19542e41 −0.0520209
\(409\) 4.44989e42 0.358851 0.179426 0.983772i \(-0.442576\pi\)
0.179426 + 0.983772i \(0.442576\pi\)
\(410\) −3.85508e42 −0.298607
\(411\) 2.29151e43 1.70503
\(412\) −9.07519e42 −0.648711
\(413\) 3.00399e42 0.206311
\(414\) 2.61838e42 0.172793
\(415\) 1.96236e42 0.124447
\(416\) 3.63153e43 2.21335
\(417\) 8.37792e42 0.490785
\(418\) 2.17777e43 1.22632
\(419\) 2.01206e43 1.08920 0.544601 0.838695i \(-0.316681\pi\)
0.544601 + 0.838695i \(0.316681\pi\)
\(420\) −1.17195e43 −0.609953
\(421\) −1.46744e43 −0.734354 −0.367177 0.930151i \(-0.619676\pi\)
−0.367177 + 0.930151i \(0.619676\pi\)
\(422\) −1.18801e43 −0.571694
\(423\) 3.20816e42 0.148471
\(424\) 2.86842e42 0.127675
\(425\) 3.15882e42 0.135241
\(426\) −1.09924e43 −0.452724
\(427\) −7.30476e43 −2.89432
\(428\) 4.87120e43 1.85701
\(429\) 2.92176e43 1.07176
\(430\) 1.07291e43 0.378734
\(431\) 9.38421e42 0.318803 0.159402 0.987214i \(-0.449044\pi\)
0.159402 + 0.987214i \(0.449044\pi\)
\(432\) −3.43678e43 −1.12375
\(433\) 3.99047e42 0.125595 0.0627976 0.998026i \(-0.479998\pi\)
0.0627976 + 0.998026i \(0.479998\pi\)
\(434\) −9.73941e43 −2.95088
\(435\) −7.11501e42 −0.207540
\(436\) −1.61385e42 −0.0453248
\(437\) 3.41699e43 0.924060
\(438\) −8.05996e43 −2.09899
\(439\) 9.80249e42 0.245851 0.122925 0.992416i \(-0.460772\pi\)
0.122925 + 0.992416i \(0.460772\pi\)
\(440\) 1.14085e42 0.0275588
\(441\) −1.04666e43 −0.243540
\(442\) −6.70157e43 −1.50214
\(443\) −2.57496e42 −0.0556044 −0.0278022 0.999613i \(-0.508851\pi\)
−0.0278022 + 0.999613i \(0.508851\pi\)
\(444\) 4.16679e42 0.0866926
\(445\) −1.86924e43 −0.374736
\(446\) 1.05771e44 2.04335
\(447\) −4.56704e42 −0.0850278
\(448\) 7.73615e43 1.38815
\(449\) −7.29533e43 −1.26177 −0.630885 0.775876i \(-0.717308\pi\)
−0.630885 + 0.775876i \(0.717308\pi\)
\(450\) 2.69223e42 0.0448855
\(451\) 2.18837e43 0.351728
\(452\) 7.29048e43 1.12972
\(453\) 4.61943e42 0.0690188
\(454\) 4.75276e43 0.684737
\(455\) 8.13620e43 1.13040
\(456\) −6.89080e42 −0.0923315
\(457\) 1.18400e44 1.53015 0.765077 0.643939i \(-0.222701\pi\)
0.765077 + 0.643939i \(0.222701\pi\)
\(458\) −6.93676e43 −0.864721
\(459\) 5.98020e43 0.719129
\(460\) −2.78904e43 −0.323557
\(461\) −1.64770e44 −1.84423 −0.922113 0.386921i \(-0.873539\pi\)
−0.922113 + 0.386921i \(0.873539\pi\)
\(462\) 1.37323e44 1.48303
\(463\) −5.84287e43 −0.608892 −0.304446 0.952530i \(-0.598471\pi\)
−0.304446 + 0.952530i \(0.598471\pi\)
\(464\) 5.32391e43 0.535407
\(465\) −5.64243e43 −0.547637
\(466\) −7.23100e43 −0.677378
\(467\) 9.91255e43 0.896307 0.448154 0.893957i \(-0.352082\pi\)
0.448154 + 0.893957i \(0.352082\pi\)
\(468\) −2.76705e43 −0.241524
\(469\) 2.05524e44 1.73185
\(470\) −7.05386e43 −0.573868
\(471\) −5.36032e43 −0.421062
\(472\) −1.44169e42 −0.0109352
\(473\) −6.09047e43 −0.446110
\(474\) −2.22352e44 −1.57289
\(475\) 3.51336e43 0.240037
\(476\) −1.52591e44 −1.00696
\(477\) −3.84248e43 −0.244939
\(478\) −6.00826e43 −0.369989
\(479\) −1.45337e44 −0.864647 −0.432324 0.901719i \(-0.642306\pi\)
−0.432324 + 0.901719i \(0.642306\pi\)
\(480\) 9.88833e43 0.568385
\(481\) −2.89277e43 −0.160664
\(482\) 1.10591e44 0.593531
\(483\) 2.15465e44 1.11750
\(484\) −8.65661e43 −0.433910
\(485\) −3.13587e42 −0.0151922
\(486\) 9.48640e43 0.444225
\(487\) 3.00271e43 0.135921 0.0679604 0.997688i \(-0.478351\pi\)
0.0679604 + 0.997688i \(0.478351\pi\)
\(488\) 3.50573e43 0.153409
\(489\) 3.08162e44 1.30372
\(490\) 2.30132e44 0.941331
\(491\) −2.65183e44 −1.04882 −0.524410 0.851466i \(-0.675714\pi\)
−0.524410 + 0.851466i \(0.675714\pi\)
\(492\) 1.07888e44 0.412617
\(493\) −9.26391e43 −0.342626
\(494\) −7.45376e44 −2.66613
\(495\) −1.52827e43 −0.0528705
\(496\) 4.22203e44 1.41278
\(497\) 1.73763e44 0.562439
\(498\) −1.13361e44 −0.354961
\(499\) −5.34386e44 −1.61881 −0.809405 0.587251i \(-0.800210\pi\)
−0.809405 + 0.587251i \(0.800210\pi\)
\(500\) −2.86771e43 −0.0840484
\(501\) −4.78971e44 −1.35827
\(502\) 6.65218e44 1.82538
\(503\) −6.08597e44 −1.61606 −0.808031 0.589140i \(-0.799466\pi\)
−0.808031 + 0.589140i \(0.799466\pi\)
\(504\) 8.34686e42 0.0214496
\(505\) −6.54750e43 −0.162843
\(506\) 3.26806e44 0.786695
\(507\) −6.06942e44 −1.41422
\(508\) 6.33225e44 1.42826
\(509\) 1.32394e44 0.289084 0.144542 0.989499i \(-0.453829\pi\)
0.144542 + 0.989499i \(0.453829\pi\)
\(510\) −1.82478e44 −0.385747
\(511\) 1.27408e45 2.60767
\(512\) −6.95122e44 −1.37755
\(513\) 6.65142e44 1.27637
\(514\) 7.31779e44 1.35984
\(515\) 1.71554e44 0.308732
\(516\) −3.00263e44 −0.523337
\(517\) 4.00418e44 0.675958
\(518\) −1.35961e44 −0.222317
\(519\) −7.29242e44 −1.15508
\(520\) −3.90475e43 −0.0599154
\(521\) 7.67376e44 1.14074 0.570369 0.821389i \(-0.306800\pi\)
0.570369 + 0.821389i \(0.306800\pi\)
\(522\) −7.89555e43 −0.113715
\(523\) −4.46260e44 −0.622745 −0.311373 0.950288i \(-0.600789\pi\)
−0.311373 + 0.950288i \(0.600789\pi\)
\(524\) 1.04635e45 1.41485
\(525\) 2.21541e44 0.290286
\(526\) 1.90124e44 0.241420
\(527\) −7.34659e44 −0.904087
\(528\) −5.95296e44 −0.710025
\(529\) −3.52236e44 −0.407207
\(530\) 8.44855e44 0.946739
\(531\) 1.93126e43 0.0209788
\(532\) −1.69718e45 −1.78725
\(533\) −7.49003e44 −0.764689
\(534\) 1.07982e45 1.06886
\(535\) −9.20835e44 −0.883781
\(536\) −9.86358e43 −0.0917942
\(537\) −6.96303e43 −0.0628381
\(538\) 2.78217e44 0.243487
\(539\) −1.30636e45 −1.10879
\(540\) −5.42908e44 −0.446919
\(541\) 2.76410e44 0.220698 0.110349 0.993893i \(-0.464803\pi\)
0.110349 + 0.993893i \(0.464803\pi\)
\(542\) 8.45487e44 0.654815
\(543\) 2.19991e45 1.65276
\(544\) 1.28749e45 0.938341
\(545\) 3.05076e43 0.0215708
\(546\) −4.70010e45 −3.22425
\(547\) −1.10195e45 −0.733453 −0.366726 0.930329i \(-0.619521\pi\)
−0.366726 + 0.930329i \(0.619521\pi\)
\(548\) −2.70864e45 −1.74933
\(549\) −4.69620e44 −0.294309
\(550\) 3.36023e44 0.204355
\(551\) −1.03037e45 −0.608124
\(552\) −1.03406e44 −0.0592315
\(553\) 3.51484e45 1.95407
\(554\) 2.81118e45 1.51697
\(555\) −7.87675e43 −0.0412584
\(556\) −9.90297e44 −0.503537
\(557\) 9.98180e44 0.492718 0.246359 0.969179i \(-0.420766\pi\)
0.246359 + 0.969179i \(0.420766\pi\)
\(558\) −6.26143e44 −0.300061
\(559\) 2.08456e45 0.969882
\(560\) −1.65772e45 −0.748873
\(561\) 1.03585e45 0.454370
\(562\) −6.41612e43 −0.0273290
\(563\) 2.41489e45 0.998870 0.499435 0.866351i \(-0.333541\pi\)
0.499435 + 0.866351i \(0.333541\pi\)
\(564\) 1.97408e45 0.792975
\(565\) −1.37817e45 −0.537653
\(566\) 3.45414e45 1.30878
\(567\) 3.50030e45 1.28820
\(568\) −8.33927e43 −0.0298113
\(569\) 3.12759e45 1.08607 0.543035 0.839710i \(-0.317275\pi\)
0.543035 + 0.839710i \(0.317275\pi\)
\(570\) −2.02959e45 −0.684658
\(571\) 4.44750e44 0.145754 0.0728770 0.997341i \(-0.476782\pi\)
0.0728770 + 0.997341i \(0.476782\pi\)
\(572\) −3.45361e45 −1.09961
\(573\) 1.97496e45 0.610952
\(574\) −3.52033e45 −1.05813
\(575\) 5.27231e44 0.153986
\(576\) 4.97354e44 0.141154
\(577\) −2.41991e45 −0.667420 −0.333710 0.942676i \(-0.608301\pi\)
−0.333710 + 0.942676i \(0.608301\pi\)
\(578\) 2.82017e45 0.755903
\(579\) −3.24679e45 −0.845781
\(580\) 8.41017e44 0.212933
\(581\) 1.79197e45 0.440985
\(582\) 1.81153e44 0.0433326
\(583\) −4.79589e45 −1.11516
\(584\) −6.11461e44 −0.138216
\(585\) 5.23073e44 0.114945
\(586\) −1.65851e45 −0.354330
\(587\) −5.33169e45 −1.10748 −0.553741 0.832689i \(-0.686800\pi\)
−0.553741 + 0.832689i \(0.686800\pi\)
\(588\) −6.44044e45 −1.30074
\(589\) −8.17117e45 −1.60466
\(590\) −4.24629e44 −0.0810871
\(591\) −1.96646e45 −0.365167
\(592\) 5.89389e44 0.106437
\(593\) 4.45568e45 0.782549 0.391274 0.920274i \(-0.372034\pi\)
0.391274 + 0.920274i \(0.372034\pi\)
\(594\) 6.36152e45 1.08664
\(595\) 2.88452e45 0.479230
\(596\) 5.39840e44 0.0872372
\(597\) 7.50565e45 1.17981
\(598\) −1.11854e46 −1.71035
\(599\) −6.35076e44 −0.0944676 −0.0472338 0.998884i \(-0.515041\pi\)
−0.0472338 + 0.998884i \(0.515041\pi\)
\(600\) −1.06323e44 −0.0153862
\(601\) 5.17167e45 0.728119 0.364059 0.931376i \(-0.381390\pi\)
0.364059 + 0.931376i \(0.381390\pi\)
\(602\) 9.79747e45 1.34206
\(603\) 1.32131e45 0.176103
\(604\) −5.46031e44 −0.0708122
\(605\) 1.63641e45 0.206505
\(606\) 3.78235e45 0.464476
\(607\) −8.40877e45 −1.00489 −0.502446 0.864609i \(-0.667566\pi\)
−0.502446 + 0.864609i \(0.667566\pi\)
\(608\) 1.43199e46 1.66545
\(609\) −6.49719e45 −0.735428
\(610\) 1.03256e46 1.13756
\(611\) −1.37049e46 −1.46959
\(612\) −9.81001e44 −0.102393
\(613\) 2.24884e45 0.228486 0.114243 0.993453i \(-0.463556\pi\)
0.114243 + 0.993453i \(0.463556\pi\)
\(614\) −7.68820e45 −0.760408
\(615\) −2.03947e45 −0.196371
\(616\) 1.04179e45 0.0976558
\(617\) −2.01918e46 −1.84277 −0.921384 0.388654i \(-0.872940\pi\)
−0.921384 + 0.388654i \(0.872940\pi\)
\(618\) −9.91031e45 −0.880597
\(619\) −6.12733e44 −0.0530122 −0.0265061 0.999649i \(-0.508438\pi\)
−0.0265061 + 0.999649i \(0.508438\pi\)
\(620\) 6.66954e45 0.561866
\(621\) 9.98143e45 0.818806
\(622\) 4.90708e45 0.391996
\(623\) −1.70693e46 −1.32789
\(624\) 2.03749e46 1.54366
\(625\) 5.42101e44 0.0400000
\(626\) 3.26550e46 2.34679
\(627\) 1.15211e46 0.806457
\(628\) 6.33607e45 0.432002
\(629\) −1.02557e45 −0.0681131
\(630\) 2.45845e45 0.159053
\(631\) −3.45501e45 −0.217753 −0.108877 0.994055i \(-0.534725\pi\)
−0.108877 + 0.994055i \(0.534725\pi\)
\(632\) −1.68685e45 −0.103573
\(633\) −6.28496e45 −0.375960
\(634\) −3.30507e46 −1.92623
\(635\) −1.19703e46 −0.679732
\(636\) −2.36440e46 −1.30821
\(637\) 4.47124e46 2.41061
\(638\) −9.85461e45 −0.517724
\(639\) 1.11711e45 0.0571917
\(640\) 1.50308e45 0.0749914
\(641\) −1.11074e44 −0.00540077 −0.00270039 0.999996i \(-0.500860\pi\)
−0.00270039 + 0.999996i \(0.500860\pi\)
\(642\) 5.31946e46 2.52081
\(643\) 2.41519e46 1.11550 0.557751 0.830009i \(-0.311665\pi\)
0.557751 + 0.830009i \(0.311665\pi\)
\(644\) −2.54686e46 −1.14654
\(645\) 5.67607e45 0.249065
\(646\) −2.64258e46 −1.13029
\(647\) 2.20068e46 0.917563 0.458781 0.888549i \(-0.348286\pi\)
0.458781 + 0.888549i \(0.348286\pi\)
\(648\) −1.67988e45 −0.0682794
\(649\) 2.41044e45 0.0955123
\(650\) −1.15009e46 −0.444286
\(651\) −5.15248e46 −1.94057
\(652\) −3.64258e46 −1.33759
\(653\) 2.59836e46 0.930319 0.465159 0.885227i \(-0.345997\pi\)
0.465159 + 0.885227i \(0.345997\pi\)
\(654\) −1.76236e45 −0.0615264
\(655\) −1.97799e46 −0.673351
\(656\) 1.52606e46 0.506593
\(657\) 8.19102e45 0.265161
\(658\) −6.44135e46 −2.03352
\(659\) −8.95518e45 −0.275718 −0.137859 0.990452i \(-0.544022\pi\)
−0.137859 + 0.990452i \(0.544022\pi\)
\(660\) −9.40388e45 −0.282379
\(661\) 5.29479e45 0.155069 0.0775345 0.996990i \(-0.475295\pi\)
0.0775345 + 0.996990i \(0.475295\pi\)
\(662\) −5.13266e46 −1.46617
\(663\) −3.54536e46 −0.987841
\(664\) −8.60006e44 −0.0233737
\(665\) 3.20829e46 0.850581
\(666\) −8.74086e44 −0.0226063
\(667\) −1.54622e46 −0.390117
\(668\) 5.66159e46 1.39356
\(669\) 5.59565e46 1.34375
\(670\) −2.90518e46 −0.680674
\(671\) −5.86144e46 −1.33993
\(672\) 9.02970e46 2.01410
\(673\) 5.71426e46 1.24369 0.621844 0.783141i \(-0.286384\pi\)
0.621844 + 0.783141i \(0.286384\pi\)
\(674\) 4.09109e46 0.868862
\(675\) 1.02629e46 0.212696
\(676\) 7.17426e46 1.45096
\(677\) −8.00955e46 −1.58087 −0.790433 0.612548i \(-0.790145\pi\)
−0.790433 + 0.612548i \(0.790145\pi\)
\(678\) 7.96136e46 1.53355
\(679\) −2.86357e45 −0.0538341
\(680\) −1.38435e45 −0.0254009
\(681\) 2.51437e46 0.450300
\(682\) −7.81503e46 −1.36612
\(683\) −1.21546e45 −0.0207395 −0.0103697 0.999946i \(-0.503301\pi\)
−0.0103697 + 0.999946i \(0.503301\pi\)
\(684\) −1.09111e46 −0.181737
\(685\) 5.12033e46 0.832537
\(686\) 7.11005e46 1.12856
\(687\) −3.66978e46 −0.568662
\(688\) −4.24720e46 −0.642530
\(689\) 1.64147e47 2.42446
\(690\) −3.04570e46 −0.439215
\(691\) −8.60411e46 −1.21149 −0.605743 0.795661i \(-0.707124\pi\)
−0.605743 + 0.795661i \(0.707124\pi\)
\(692\) 8.61988e46 1.18509
\(693\) −1.39556e46 −0.187349
\(694\) −4.72308e46 −0.619147
\(695\) 1.87202e46 0.239641
\(696\) 3.11815e45 0.0389803
\(697\) −2.65544e46 −0.324187
\(698\) −1.31470e47 −1.56752
\(699\) −3.82545e46 −0.445460
\(700\) −2.61869e46 −0.297829
\(701\) 2.40906e46 0.267609 0.133804 0.991008i \(-0.457281\pi\)
0.133804 + 0.991008i \(0.457281\pi\)
\(702\) −2.17733e47 −2.36245
\(703\) −1.14068e46 −0.120893
\(704\) 6.20758e46 0.642649
\(705\) −3.73173e46 −0.377390
\(706\) 1.41864e47 1.40151
\(707\) −5.97896e46 −0.577039
\(708\) 1.18836e46 0.112047
\(709\) 1.49721e46 0.137917 0.0689586 0.997620i \(-0.478032\pi\)
0.0689586 + 0.997620i \(0.478032\pi\)
\(710\) −2.45622e46 −0.221057
\(711\) 2.25968e46 0.198700
\(712\) 8.19195e45 0.0703829
\(713\) −1.22620e47 −1.02940
\(714\) −1.66633e47 −1.36691
\(715\) 6.52859e46 0.523323
\(716\) 8.23053e45 0.0644708
\(717\) −3.17858e46 −0.243314
\(718\) 2.43889e47 1.82448
\(719\) 4.37252e46 0.319673 0.159836 0.987144i \(-0.448903\pi\)
0.159836 + 0.987144i \(0.448903\pi\)
\(720\) −1.06574e46 −0.0761492
\(721\) 1.56658e47 1.09401
\(722\) −8.98715e46 −0.613420
\(723\) 5.85064e46 0.390321
\(724\) −2.60037e47 −1.69570
\(725\) −1.58983e46 −0.101338
\(726\) −9.45321e46 −0.589013
\(727\) −1.19298e47 −0.726634 −0.363317 0.931666i \(-0.618356\pi\)
−0.363317 + 0.931666i \(0.618356\pi\)
\(728\) −3.56569e46 −0.212313
\(729\) 1.89835e47 1.10502
\(730\) −1.80098e47 −1.02490
\(731\) 7.39038e46 0.411178
\(732\) −2.88972e47 −1.57189
\(733\) 3.02145e47 1.60694 0.803471 0.595343i \(-0.202984\pi\)
0.803471 + 0.595343i \(0.202984\pi\)
\(734\) 4.81398e47 2.50334
\(735\) 1.21748e47 0.619042
\(736\) 2.14891e47 1.06840
\(737\) 1.64915e47 0.801765
\(738\) −2.26321e46 −0.107596
\(739\) −4.95875e46 −0.230536 −0.115268 0.993334i \(-0.536773\pi\)
−0.115268 + 0.993334i \(0.536773\pi\)
\(740\) 9.31057e45 0.0423305
\(741\) −3.94329e47 −1.75331
\(742\) 7.71493e47 3.35481
\(743\) −7.50450e46 −0.319158 −0.159579 0.987185i \(-0.551014\pi\)
−0.159579 + 0.987185i \(0.551014\pi\)
\(744\) 2.47280e46 0.102857
\(745\) −1.02049e46 −0.0415176
\(746\) −2.68856e47 −1.06987
\(747\) 1.15205e46 0.0448415
\(748\) −1.22441e47 −0.466176
\(749\) −8.40876e47 −3.13171
\(750\) −3.13160e46 −0.114092
\(751\) −2.61189e47 −0.930884 −0.465442 0.885078i \(-0.654105\pi\)
−0.465442 + 0.885078i \(0.654105\pi\)
\(752\) 2.79232e47 0.973580
\(753\) 3.51923e47 1.20041
\(754\) 3.37289e47 1.12558
\(755\) 1.03220e46 0.0337007
\(756\) −4.95765e47 −1.58368
\(757\) −7.29946e46 −0.228144 −0.114072 0.993472i \(-0.536389\pi\)
−0.114072 + 0.993472i \(0.536389\pi\)
\(758\) −1.87025e47 −0.571948
\(759\) 1.72892e47 0.517350
\(760\) −1.53973e46 −0.0450838
\(761\) −3.25049e47 −0.931327 −0.465663 0.884962i \(-0.654184\pi\)
−0.465663 + 0.884962i \(0.654184\pi\)
\(762\) 6.91496e47 1.93880
\(763\) 2.78585e46 0.0764370
\(764\) −2.33447e47 −0.626827
\(765\) 1.85445e46 0.0487306
\(766\) 4.27739e47 1.10003
\(767\) −8.25012e46 −0.207652
\(768\) −4.12508e47 −1.01618
\(769\) 4.28447e47 1.03303 0.516514 0.856279i \(-0.327229\pi\)
0.516514 + 0.856279i \(0.327229\pi\)
\(770\) 3.06845e47 0.724139
\(771\) 3.87136e47 0.894266
\(772\) 3.83781e47 0.867758
\(773\) −8.22105e47 −1.81956 −0.909779 0.415094i \(-0.863749\pi\)
−0.909779 + 0.415094i \(0.863749\pi\)
\(774\) 6.29875e46 0.136467
\(775\) −1.26079e47 −0.267401
\(776\) 1.37430e45 0.00285340
\(777\) −7.19278e46 −0.146201
\(778\) −4.55454e47 −0.906320
\(779\) −2.95349e47 −0.575397
\(780\) 3.21863e47 0.613917
\(781\) 1.39429e47 0.260383
\(782\) −3.96557e47 −0.725095
\(783\) −3.00983e47 −0.538856
\(784\) −9.10996e47 −1.59699
\(785\) −1.19775e47 −0.205597
\(786\) 1.14264e48 1.92060
\(787\) −9.92861e47 −1.63420 −0.817100 0.576496i \(-0.804420\pi\)
−0.817100 + 0.576496i \(0.804420\pi\)
\(788\) 2.32442e47 0.374655
\(789\) 1.00582e47 0.158763
\(790\) −4.96840e47 −0.768014
\(791\) −1.25850e48 −1.90520
\(792\) 6.69762e45 0.00993014
\(793\) 2.00617e48 2.91313
\(794\) −2.72744e47 −0.387898
\(795\) 4.46957e47 0.622599
\(796\) −8.87192e47 −1.21046
\(797\) 1.14954e48 1.53625 0.768124 0.640301i \(-0.221190\pi\)
0.768124 + 0.640301i \(0.221190\pi\)
\(798\) −1.85336e48 −2.42611
\(799\) −4.85881e47 −0.623028
\(800\) 2.20952e47 0.277532
\(801\) −1.09738e47 −0.135027
\(802\) 5.10784e47 0.615687
\(803\) 1.02234e48 1.20723
\(804\) 8.13040e47 0.940561
\(805\) 4.81450e47 0.545656
\(806\) 2.67482e48 2.97006
\(807\) 1.47187e47 0.160123
\(808\) 2.86944e46 0.0305851
\(809\) −1.50525e48 −1.57202 −0.786009 0.618215i \(-0.787856\pi\)
−0.786009 + 0.618215i \(0.787856\pi\)
\(810\) −4.94785e47 −0.506306
\(811\) 1.19205e48 1.19522 0.597612 0.801786i \(-0.296116\pi\)
0.597612 + 0.801786i \(0.296116\pi\)
\(812\) 7.67989e47 0.754537
\(813\) 4.47292e47 0.430623
\(814\) −1.09097e47 −0.102922
\(815\) 6.88580e47 0.636581
\(816\) 7.22353e47 0.654428
\(817\) 8.21988e47 0.729796
\(818\) −5.74394e47 −0.499782
\(819\) 4.77653e47 0.407313
\(820\) 2.41072e47 0.201474
\(821\) −1.82470e48 −1.49461 −0.747306 0.664480i \(-0.768653\pi\)
−0.747306 + 0.664480i \(0.768653\pi\)
\(822\) −2.95790e48 −2.37464
\(823\) 1.63942e48 1.29001 0.645004 0.764180i \(-0.276856\pi\)
0.645004 + 0.764180i \(0.276856\pi\)
\(824\) −7.51836e46 −0.0579861
\(825\) 1.77768e47 0.134389
\(826\) −3.87757e47 −0.287336
\(827\) −1.07814e48 −0.783129 −0.391565 0.920151i \(-0.628066\pi\)
−0.391565 + 0.920151i \(0.628066\pi\)
\(828\) −1.63737e47 −0.116586
\(829\) −1.12436e48 −0.784795 −0.392397 0.919796i \(-0.628354\pi\)
−0.392397 + 0.919796i \(0.628354\pi\)
\(830\) −2.53303e47 −0.173321
\(831\) 1.48721e48 0.997597
\(832\) −2.12464e48 −1.39718
\(833\) 1.58519e48 1.02197
\(834\) −1.08143e48 −0.683530
\(835\) −1.07025e48 −0.663220
\(836\) −1.36184e48 −0.827412
\(837\) −2.38689e48 −1.42188
\(838\) −2.59717e48 −1.51696
\(839\) 2.27412e48 1.30239 0.651195 0.758911i \(-0.274268\pi\)
0.651195 + 0.758911i \(0.274268\pi\)
\(840\) −9.70905e46 −0.0545216
\(841\) −1.34982e48 −0.743264
\(842\) 1.89418e48 1.02275
\(843\) −3.39435e46 −0.0179722
\(844\) 7.42903e47 0.385729
\(845\) −1.35620e48 −0.690537
\(846\) −4.14112e47 −0.206779
\(847\) 1.49432e48 0.731757
\(848\) −3.34442e48 −1.60616
\(849\) 1.82736e48 0.860689
\(850\) −4.07742e47 −0.188353
\(851\) −1.71176e47 −0.0775542
\(852\) 6.87393e47 0.305458
\(853\) 1.39001e48 0.605840 0.302920 0.953016i \(-0.402038\pi\)
0.302920 + 0.953016i \(0.402038\pi\)
\(854\) 9.42904e48 4.03100
\(855\) 2.06259e47 0.0864914
\(856\) 4.03556e47 0.165992
\(857\) 7.18028e47 0.289706 0.144853 0.989453i \(-0.453729\pi\)
0.144853 + 0.989453i \(0.453729\pi\)
\(858\) −3.77142e48 −1.49267
\(859\) −4.63630e48 −1.80005 −0.900025 0.435838i \(-0.856452\pi\)
−0.900025 + 0.435838i \(0.856452\pi\)
\(860\) −6.70930e47 −0.255536
\(861\) −1.86238e48 −0.695850
\(862\) −1.21132e48 −0.444006
\(863\) 4.88949e48 1.75827 0.879135 0.476572i \(-0.158121\pi\)
0.879135 + 0.476572i \(0.158121\pi\)
\(864\) 4.18302e48 1.47575
\(865\) −1.62947e48 −0.564003
\(866\) −5.15092e47 −0.174920
\(867\) 1.49197e48 0.497100
\(868\) 6.09040e48 1.99100
\(869\) 2.82035e48 0.904642
\(870\) 9.18410e47 0.289047
\(871\) −5.64448e48 −1.74311
\(872\) −1.33700e46 −0.00405143
\(873\) −1.84098e46 −0.00547412
\(874\) −4.41067e48 −1.28696
\(875\) 4.95029e47 0.141742
\(876\) 5.04018e48 1.41621
\(877\) −7.15117e46 −0.0197189 −0.00985947 0.999951i \(-0.503138\pi\)
−0.00985947 + 0.999951i \(0.503138\pi\)
\(878\) −1.26531e48 −0.342403
\(879\) −8.77410e47 −0.233016
\(880\) −1.33017e48 −0.346692
\(881\) −1.25763e48 −0.321698 −0.160849 0.986979i \(-0.551423\pi\)
−0.160849 + 0.986979i \(0.551423\pi\)
\(882\) 1.35104e48 0.339185
\(883\) −6.34796e47 −0.156417 −0.0782083 0.996937i \(-0.524920\pi\)
−0.0782083 + 0.996937i \(0.524920\pi\)
\(884\) 4.19073e48 1.01351
\(885\) −2.24644e47 −0.0533249
\(886\) 3.32378e47 0.0774418
\(887\) −5.08980e47 −0.116402 −0.0582011 0.998305i \(-0.518536\pi\)
−0.0582011 + 0.998305i \(0.518536\pi\)
\(888\) 3.45198e46 0.00774916
\(889\) −1.09309e49 −2.40866
\(890\) 2.41283e48 0.521905
\(891\) 2.80869e48 0.596377
\(892\) −6.61425e48 −1.37867
\(893\) −5.40416e48 −1.10581
\(894\) 5.89517e47 0.118421
\(895\) −1.55587e47 −0.0306827
\(896\) 1.37256e48 0.265735
\(897\) −5.91748e48 −1.12476
\(898\) 9.41686e48 1.75730
\(899\) 3.69753e48 0.677450
\(900\) −1.68355e47 −0.0302847
\(901\) 5.81949e48 1.02784
\(902\) −2.82476e48 −0.489862
\(903\) 5.18319e48 0.882571
\(904\) 6.03981e47 0.100982
\(905\) 4.91565e48 0.807011
\(906\) −5.96278e47 −0.0961244
\(907\) 4.07509e47 0.0645085 0.0322543 0.999480i \(-0.489731\pi\)
0.0322543 + 0.999480i \(0.489731\pi\)
\(908\) −2.97207e48 −0.462001
\(909\) −3.84385e47 −0.0586763
\(910\) −1.05023e49 −1.57434
\(911\) −5.53521e48 −0.814855 −0.407428 0.913237i \(-0.633574\pi\)
−0.407428 + 0.913237i \(0.633574\pi\)
\(912\) 8.03430e48 1.16154
\(913\) 1.43790e48 0.204155
\(914\) −1.52832e49 −2.13109
\(915\) 5.46262e48 0.748089
\(916\) 4.33780e48 0.583438
\(917\) −1.80623e49 −2.38605
\(918\) −7.71928e48 −1.00155
\(919\) 5.10117e48 0.650075 0.325038 0.945701i \(-0.394623\pi\)
0.325038 + 0.945701i \(0.394623\pi\)
\(920\) −2.31059e47 −0.0289217
\(921\) −4.06732e48 −0.500063
\(922\) 2.12687e49 2.56850
\(923\) −4.77219e48 −0.566095
\(924\) −8.58731e48 −1.00062
\(925\) −1.76004e47 −0.0201458
\(926\) 7.54202e48 0.848021
\(927\) 1.00715e48 0.111244
\(928\) −6.47990e48 −0.703116
\(929\) 4.04144e48 0.430801 0.215401 0.976526i \(-0.430894\pi\)
0.215401 + 0.976526i \(0.430894\pi\)
\(930\) 7.28329e48 0.762709
\(931\) 1.76311e49 1.81388
\(932\) 4.52180e48 0.457035
\(933\) 2.59601e48 0.257786
\(934\) −1.27952e49 −1.24831
\(935\) 2.31458e48 0.221861
\(936\) −2.29237e47 −0.0215890
\(937\) 4.94756e48 0.457812 0.228906 0.973448i \(-0.426485\pi\)
0.228906 + 0.973448i \(0.426485\pi\)
\(938\) −2.65292e49 −2.41200
\(939\) 1.72756e49 1.54331
\(940\) 4.41103e48 0.387196
\(941\) −1.04427e49 −0.900712 −0.450356 0.892849i \(-0.648703\pi\)
−0.450356 + 0.892849i \(0.648703\pi\)
\(942\) 6.91913e48 0.586424
\(943\) −4.43214e48 −0.369122
\(944\) 1.68093e48 0.137566
\(945\) 9.37177e48 0.753697
\(946\) 7.86161e48 0.621309
\(947\) 1.15016e49 0.893271 0.446636 0.894716i \(-0.352622\pi\)
0.446636 + 0.894716i \(0.352622\pi\)
\(948\) 1.39045e49 1.06125
\(949\) −3.49912e49 −2.62462
\(950\) −4.53507e48 −0.334306
\(951\) −1.74849e49 −1.26673
\(952\) −1.26414e48 −0.0900091
\(953\) 8.00029e48 0.559852 0.279926 0.960022i \(-0.409690\pi\)
0.279926 + 0.960022i \(0.409690\pi\)
\(954\) 4.95990e48 0.341134
\(955\) 4.41300e48 0.298317
\(956\) 3.75718e48 0.249636
\(957\) −5.21343e48 −0.340468
\(958\) 1.87601e49 1.20422
\(959\) 4.67571e49 2.95013
\(960\) −5.78522e48 −0.358793
\(961\) 1.29192e49 0.787586
\(962\) 3.73400e48 0.223762
\(963\) −5.40596e48 −0.318448
\(964\) −6.91565e48 −0.400463
\(965\) −7.25487e48 −0.412980
\(966\) −2.78123e49 −1.55638
\(967\) 2.45742e49 1.35190 0.675948 0.736949i \(-0.263734\pi\)
0.675948 + 0.736949i \(0.263734\pi\)
\(968\) −7.17159e47 −0.0387857
\(969\) −1.39801e49 −0.743309
\(970\) 4.04781e47 0.0211586
\(971\) −3.60689e49 −1.85360 −0.926800 0.375556i \(-0.877452\pi\)
−0.926800 + 0.375556i \(0.877452\pi\)
\(972\) −5.93219e48 −0.299724
\(973\) 1.70947e49 0.849179
\(974\) −3.87592e48 −0.189301
\(975\) −6.08438e48 −0.292173
\(976\) −4.08749e49 −1.92990
\(977\) 1.33484e49 0.619683 0.309841 0.950788i \(-0.399724\pi\)
0.309841 + 0.950788i \(0.399724\pi\)
\(978\) −3.97778e49 −1.81572
\(979\) −1.36966e49 −0.614751
\(980\) −1.43910e49 −0.635127
\(981\) 1.79101e47 0.00777250
\(982\) 3.42300e49 1.46072
\(983\) −1.85345e49 −0.777765 −0.388882 0.921287i \(-0.627139\pi\)
−0.388882 + 0.921287i \(0.627139\pi\)
\(984\) 8.93798e47 0.0368825
\(985\) −4.39400e48 −0.178304
\(986\) 1.19579e49 0.477185
\(987\) −3.40769e49 −1.33730
\(988\) 4.66110e49 1.79887
\(989\) 1.23351e49 0.468171
\(990\) 1.97270e48 0.0736342
\(991\) −1.48569e49 −0.545398 −0.272699 0.962099i \(-0.587916\pi\)
−0.272699 + 0.962099i \(0.587916\pi\)
\(992\) −5.13878e49 −1.85531
\(993\) −2.71535e49 −0.964192
\(994\) −2.24294e49 −0.783325
\(995\) 1.67712e49 0.576079
\(996\) 7.08890e48 0.239497
\(997\) −2.13570e49 −0.709694 −0.354847 0.934924i \(-0.615467\pi\)
−0.354847 + 0.934924i \(0.615467\pi\)
\(998\) 6.89789e49 2.25456
\(999\) −3.33207e48 −0.107123
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 \(a_p\))