Properties

Label 2.48.a.a.1.1
Level 2
Weight 48
Character 2.1
Self dual Yes
Analytic conductor 27.982
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 48 \)
Character orbit: \([\chi]\) = 2.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(27.981532531\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 2.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+8.38861e6 q^{2}\) \(-1.96635e11 q^{3}\) \(+7.03687e13 q^{4}\) \(+2.06700e16 q^{5}\) \(-1.64949e18 q^{6}\) \(-5.11729e19 q^{7}\) \(+5.90296e20 q^{8}\) \(+1.20763e22 q^{9}\) \(+O(q^{10})\) \(q\)\(+8.38861e6 q^{2}\) \(-1.96635e11 q^{3}\) \(+7.03687e13 q^{4}\) \(+2.06700e16 q^{5}\) \(-1.64949e18 q^{6}\) \(-5.11729e19 q^{7}\) \(+5.90296e20 q^{8}\) \(+1.20763e22 q^{9}\) \(+1.73392e23 q^{10}\) \(+5.29743e24 q^{11}\) \(-1.38369e25 q^{12}\) \(-1.25094e26 q^{13}\) \(-4.29269e26 q^{14}\) \(-4.06443e27 q^{15}\) \(+4.95176e27 q^{16}\) \(-4.48300e28 q^{17}\) \(+1.01304e29 q^{18}\) \(-1.11132e30 q^{19}\) \(+1.45452e30 q^{20}\) \(+1.00624e31 q^{21}\) \(+4.44381e31 q^{22}\) \(-1.78238e32 q^{23}\) \(-1.16073e32 q^{24}\) \(-2.83295e32 q^{25}\) \(-1.04937e33 q^{26}\) \(+2.85365e33 q^{27}\) \(-3.60097e33 q^{28}\) \(-3.05341e34 q^{29}\) \(-3.40949e34 q^{30}\) \(-1.10802e35 q^{31}\) \(+4.15384e34 q^{32}\) \(-1.04166e36 q^{33}\) \(-3.76062e35 q^{34}\) \(-1.05774e36 q^{35}\) \(+8.49797e35 q^{36}\) \(+6.20377e36 q^{37}\) \(-9.32243e36 q^{38}\) \(+2.45978e37 q^{39}\) \(+1.22014e37 q^{40}\) \(-3.56698e37 q^{41}\) \(+8.44092e37 q^{42}\) \(+3.38085e38 q^{43}\) \(+3.72774e38 q^{44}\) \(+2.49618e38 q^{45}\) \(-1.49517e39 q^{46}\) \(-2.29839e39 q^{47}\) \(-9.73687e38 q^{48}\) \(-2.62467e39 q^{49}\) \(-2.37645e39 q^{50}\) \(+8.81513e39 q^{51}\) \(-8.80272e39 q^{52}\) \(-2.95957e40 q^{53}\) \(+2.39382e40 q^{54}\) \(+1.09498e41 q^{55}\) \(-3.02071e40 q^{56}\) \(+2.18524e41 q^{57}\) \(-2.56139e41 q^{58}\) \(+4.02898e41 q^{59}\) \(-2.86009e41 q^{60}\) \(+5.75153e41 q^{61}\) \(-9.29472e41 q^{62}\) \(-6.17981e41 q^{63}\) \(+3.48449e41 q^{64}\) \(-2.58569e42 q^{65}\) \(-8.73806e42 q^{66}\) \(-1.86803e42 q^{67}\) \(-3.15463e42 q^{68}\) \(+3.50478e43 q^{69}\) \(-8.87298e42 q^{70}\) \(+5.52020e43 q^{71}\) \(+7.12862e42 q^{72}\) \(-7.91827e43 q^{73}\) \(+5.20410e43 q^{74}\) \(+5.57057e43 q^{75}\) \(-7.82022e43 q^{76}\) \(-2.71085e44 q^{77}\) \(+2.06342e44 q^{78}\) \(+8.82751e43 q^{79}\) \(+1.02353e44 q^{80}\) \(-8.82223e44 q^{81}\) \(-2.99220e44 q^{82}\) \(-7.37731e44 q^{83}\) \(+7.08076e44 q^{84}\) \(-9.26635e44 q^{85}\) \(+2.83607e45 q^{86}\) \(+6.00406e45 q^{87}\) \(+3.12705e45 q^{88}\) \(-8.27703e45 q^{89}\) \(+2.09394e45 q^{90}\) \(+6.40143e45 q^{91}\) \(-1.25424e46 q^{92}\) \(+2.17874e46 q^{93}\) \(-1.92803e46 q^{94}\) \(-2.29709e46 q^{95}\) \(-8.16788e45 q^{96}\) \(-6.19542e46 q^{97}\) \(-2.20174e46 q^{98}\) \(+6.39736e46 q^{99}\) \(+O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.38861e6 0.707107
\(3\) −1.96635e11 −1.20590 −0.602949 0.797780i \(-0.706008\pi\)
−0.602949 + 0.797780i \(0.706008\pi\)
\(4\) 7.03687e13 0.500000
\(5\) 2.06700e16 0.775434 0.387717 0.921779i \(-0.373264\pi\)
0.387717 + 0.921779i \(0.373264\pi\)
\(6\) −1.64949e18 −0.852698
\(7\) −5.11729e19 −0.706701 −0.353351 0.935491i \(-0.614958\pi\)
−0.353351 + 0.935491i \(0.614958\pi\)
\(8\) 5.90296e20 0.353553
\(9\) 1.20763e22 0.454189
\(10\) 1.73392e23 0.548314
\(11\) 5.29743e24 1.78376 0.891882 0.452269i \(-0.149385\pi\)
0.891882 + 0.452269i \(0.149385\pi\)
\(12\) −1.38369e25 −0.602949
\(13\) −1.25094e26 −0.830937 −0.415469 0.909608i \(-0.636382\pi\)
−0.415469 + 0.909608i \(0.636382\pi\)
\(14\) −4.29269e26 −0.499713
\(15\) −4.06443e27 −0.935093
\(16\) 4.95176e27 0.250000
\(17\) −4.48300e28 −0.544527 −0.272263 0.962223i \(-0.587772\pi\)
−0.272263 + 0.962223i \(0.587772\pi\)
\(18\) 1.01304e29 0.321160
\(19\) −1.11132e30 −0.988848 −0.494424 0.869221i \(-0.664621\pi\)
−0.494424 + 0.869221i \(0.664621\pi\)
\(20\) 1.45452e30 0.387717
\(21\) 1.00624e31 0.852209
\(22\) 4.44381e31 1.26131
\(23\) −1.78238e32 −1.77990 −0.889952 0.456055i \(-0.849262\pi\)
−0.889952 + 0.456055i \(0.849262\pi\)
\(24\) −1.16073e32 −0.426349
\(25\) −2.83295e32 −0.398703
\(26\) −1.04937e33 −0.587561
\(27\) 2.85365e33 0.658192
\(28\) −3.60097e33 −0.353351
\(29\) −3.05341e34 −1.31351 −0.656753 0.754105i \(-0.728071\pi\)
−0.656753 + 0.754105i \(0.728071\pi\)
\(30\) −3.40949e34 −0.661211
\(31\) −1.10802e35 −0.994367 −0.497183 0.867645i \(-0.665632\pi\)
−0.497183 + 0.867645i \(0.665632\pi\)
\(32\) 4.15384e34 0.176777
\(33\) −1.04166e36 −2.15104
\(34\) −3.76062e35 −0.385039
\(35\) −1.05774e36 −0.548000
\(36\) 8.49797e35 0.227094
\(37\) 6.20377e36 0.870793 0.435397 0.900239i \(-0.356608\pi\)
0.435397 + 0.900239i \(0.356608\pi\)
\(38\) −9.32243e36 −0.699221
\(39\) 2.45978e37 1.00203
\(40\) 1.22014e37 0.274157
\(41\) −3.56698e37 −0.448621 −0.224311 0.974518i \(-0.572013\pi\)
−0.224311 + 0.974518i \(0.572013\pi\)
\(42\) 8.44092e37 0.602603
\(43\) 3.38085e38 1.38841 0.694205 0.719777i \(-0.255756\pi\)
0.694205 + 0.719777i \(0.255756\pi\)
\(44\) 3.72774e38 0.891882
\(45\) 2.49618e38 0.352193
\(46\) −1.49517e39 −1.25858
\(47\) −2.29839e39 −1.16714 −0.583571 0.812062i \(-0.698345\pi\)
−0.583571 + 0.812062i \(0.698345\pi\)
\(48\) −9.73687e38 −0.301474
\(49\) −2.62467e39 −0.500573
\(50\) −2.37645e39 −0.281925
\(51\) 8.81513e39 0.656644
\(52\) −8.80272e39 −0.415469
\(53\) −2.95957e40 −0.892781 −0.446391 0.894838i \(-0.647291\pi\)
−0.446391 + 0.894838i \(0.647291\pi\)
\(54\) 2.39382e40 0.465412
\(55\) 1.09498e41 1.38319
\(56\) −3.02071e40 −0.249857
\(57\) 2.18524e41 1.19245
\(58\) −2.56139e41 −0.928790
\(59\) 4.02898e41 0.977626 0.488813 0.872389i \(-0.337430\pi\)
0.488813 + 0.872389i \(0.337430\pi\)
\(60\) −2.86009e41 −0.467547
\(61\) 5.75153e41 0.637577 0.318788 0.947826i \(-0.396724\pi\)
0.318788 + 0.947826i \(0.396724\pi\)
\(62\) −9.29472e41 −0.703124
\(63\) −6.17981e41 −0.320976
\(64\) 3.48449e41 0.125000
\(65\) −2.58569e42 −0.644337
\(66\) −8.73806e42 −1.52101
\(67\) −1.86803e42 −0.228364 −0.114182 0.993460i \(-0.536425\pi\)
−0.114182 + 0.993460i \(0.536425\pi\)
\(68\) −3.15463e42 −0.272263
\(69\) 3.50478e43 2.14638
\(70\) −8.87298e42 −0.387494
\(71\) 5.52020e43 1.72736 0.863681 0.504038i \(-0.168153\pi\)
0.863681 + 0.504038i \(0.168153\pi\)
\(72\) 7.12862e42 0.160580
\(73\) −7.91827e43 −1.28986 −0.644931 0.764241i \(-0.723114\pi\)
−0.644931 + 0.764241i \(0.723114\pi\)
\(74\) 5.20410e43 0.615744
\(75\) 5.57057e43 0.480795
\(76\) −7.82022e43 −0.494424
\(77\) −2.71085e44 −1.26059
\(78\) 2.06342e44 0.708539
\(79\) 8.82751e43 0.224699 0.112350 0.993669i \(-0.464162\pi\)
0.112350 + 0.993669i \(0.464162\pi\)
\(80\) 1.02353e44 0.193858
\(81\) −8.82223e44 −1.24790
\(82\) −2.99220e44 −0.317223
\(83\) −7.37731e44 −0.588251 −0.294125 0.955767i \(-0.595028\pi\)
−0.294125 + 0.955767i \(0.595028\pi\)
\(84\) 7.08076e44 0.426105
\(85\) −9.26635e44 −0.422244
\(86\) 2.83607e45 0.981754
\(87\) 6.00406e45 1.58395
\(88\) 3.12705e45 0.630655
\(89\) −8.27703e45 −1.28000 −0.639999 0.768375i \(-0.721065\pi\)
−0.639999 + 0.768375i \(0.721065\pi\)
\(90\) 2.09394e45 0.249038
\(91\) 6.40143e45 0.587224
\(92\) −1.25424e46 −0.889952
\(93\) 2.17874e46 1.19910
\(94\) −1.92803e46 −0.825293
\(95\) −2.29709e46 −0.766786
\(96\) −8.16788e45 −0.213175
\(97\) −6.19542e46 −1.26746 −0.633731 0.773554i \(-0.718477\pi\)
−0.633731 + 0.773554i \(0.718477\pi\)
\(98\) −2.20174e46 −0.353959
\(99\) 6.39736e46 0.810165
\(100\) −1.99351e46 −0.199351
\(101\) 1.21967e47 0.965363 0.482682 0.875796i \(-0.339663\pi\)
0.482682 + 0.875796i \(0.339663\pi\)
\(102\) 7.39467e46 0.464317
\(103\) 1.65592e47 0.826732 0.413366 0.910565i \(-0.364353\pi\)
0.413366 + 0.910565i \(0.364353\pi\)
\(104\) −7.38425e46 −0.293781
\(105\) 2.07989e47 0.660832
\(106\) −2.48266e47 −0.631292
\(107\) −4.61678e47 −0.941500 −0.470750 0.882267i \(-0.656017\pi\)
−0.470750 + 0.882267i \(0.656017\pi\)
\(108\) 2.00808e47 0.329096
\(109\) 2.51311e47 0.331657 0.165829 0.986155i \(-0.446970\pi\)
0.165829 + 0.986155i \(0.446970\pi\)
\(110\) 9.18533e47 0.978063
\(111\) −1.21988e48 −1.05009
\(112\) −2.53396e47 −0.176675
\(113\) −8.86375e47 −0.501504 −0.250752 0.968051i \(-0.580678\pi\)
−0.250752 + 0.968051i \(0.580678\pi\)
\(114\) 1.83311e48 0.843189
\(115\) −3.68417e48 −1.38020
\(116\) −2.14865e48 −0.656753
\(117\) −1.51068e48 −0.377402
\(118\) 3.37975e48 0.691286
\(119\) 2.29408e48 0.384818
\(120\) −2.39922e48 −0.330605
\(121\) 1.92430e49 2.18181
\(122\) 4.82474e48 0.450835
\(123\) 7.01391e48 0.540991
\(124\) −7.79698e48 −0.497183
\(125\) −2.05426e49 −1.08460
\(126\) −5.18400e48 −0.226964
\(127\) 2.35947e49 0.857883 0.428941 0.903332i \(-0.358887\pi\)
0.428941 + 0.903332i \(0.358887\pi\)
\(128\) 2.92300e48 0.0883883
\(129\) −6.64793e49 −1.67428
\(130\) −2.16903e49 −0.455615
\(131\) 3.57925e49 0.627938 0.313969 0.949433i \(-0.398341\pi\)
0.313969 + 0.949433i \(0.398341\pi\)
\(132\) −7.33002e49 −1.07552
\(133\) 5.68694e49 0.698820
\(134\) −1.56702e49 −0.161477
\(135\) 5.89849e49 0.510384
\(136\) −2.64630e49 −0.192519
\(137\) −1.00526e50 −0.615665 −0.307832 0.951441i \(-0.599604\pi\)
−0.307832 + 0.951441i \(0.599604\pi\)
\(138\) 2.94002e50 1.51772
\(139\) −5.50254e49 −0.239726 −0.119863 0.992790i \(-0.538246\pi\)
−0.119863 + 0.992790i \(0.538246\pi\)
\(140\) −7.44319e49 −0.274000
\(141\) 4.51942e50 1.40745
\(142\) 4.63068e50 1.22143
\(143\) −6.62677e50 −1.48219
\(144\) 5.97992e49 0.113547
\(145\) −6.31139e50 −1.01854
\(146\) −6.64233e50 −0.912070
\(147\) 5.16102e50 0.603640
\(148\) 4.36551e50 0.435397
\(149\) 3.78314e48 0.00322089 0.00161044 0.999999i \(-0.499487\pi\)
0.00161044 + 0.999999i \(0.499487\pi\)
\(150\) 4.67293e50 0.339973
\(151\) −8.86913e50 −0.551979 −0.275990 0.961161i \(-0.589006\pi\)
−0.275990 + 0.961161i \(0.589006\pi\)
\(152\) −6.56007e50 −0.349610
\(153\) −5.41383e50 −0.247318
\(154\) −2.27402e51 −0.891370
\(155\) −2.29027e51 −0.771065
\(156\) 1.73092e51 0.501013
\(157\) 5.52046e51 1.37510 0.687548 0.726139i \(-0.258687\pi\)
0.687548 + 0.726139i \(0.258687\pi\)
\(158\) 7.40505e50 0.158886
\(159\) 5.81953e51 1.07660
\(160\) 8.58597e50 0.137079
\(161\) 9.12096e51 1.25786
\(162\) −7.40062e51 −0.882400
\(163\) 7.64913e51 0.789229 0.394615 0.918847i \(-0.370878\pi\)
0.394615 + 0.918847i \(0.370878\pi\)
\(164\) −2.51004e51 −0.224311
\(165\) −2.15310e52 −1.66799
\(166\) −6.18853e51 −0.415956
\(167\) −1.01020e52 −0.589615 −0.294807 0.955557i \(-0.595255\pi\)
−0.294807 + 0.955557i \(0.595255\pi\)
\(168\) 5.93977e51 0.301302
\(169\) −7.01551e51 −0.309543
\(170\) −7.77318e51 −0.298572
\(171\) −1.34207e52 −0.449124
\(172\) 2.37906e52 0.694205
\(173\) −1.26608e52 −0.322387 −0.161193 0.986923i \(-0.551534\pi\)
−0.161193 + 0.986923i \(0.551534\pi\)
\(174\) 5.03657e52 1.12003
\(175\) 1.44970e52 0.281764
\(176\) 2.62316e52 0.445941
\(177\) −7.92236e52 −1.17892
\(178\) −6.94328e52 −0.905096
\(179\) 1.53886e53 1.75854 0.879269 0.476325i \(-0.158031\pi\)
0.879269 + 0.476325i \(0.158031\pi\)
\(180\) 1.75653e52 0.176097
\(181\) 6.25255e52 0.550314 0.275157 0.961399i \(-0.411270\pi\)
0.275157 + 0.961399i \(0.411270\pi\)
\(182\) 5.36991e52 0.415230
\(183\) −1.13095e53 −0.768852
\(184\) −1.05213e53 −0.629291
\(185\) 1.28232e53 0.675242
\(186\) 1.82766e53 0.847895
\(187\) −2.37484e53 −0.971307
\(188\) −1.61735e53 −0.583571
\(189\) −1.46030e53 −0.465145
\(190\) −1.92694e53 −0.542199
\(191\) −1.11993e52 −0.0278553 −0.0139276 0.999903i \(-0.504433\pi\)
−0.0139276 + 0.999903i \(0.504433\pi\)
\(192\) −6.85172e52 −0.150737
\(193\) 3.30249e53 0.643050 0.321525 0.946901i \(-0.395805\pi\)
0.321525 + 0.946901i \(0.395805\pi\)
\(194\) −5.19709e53 −0.896231
\(195\) 5.08436e53 0.777004
\(196\) −1.84695e53 −0.250287
\(197\) 3.35582e53 0.403499 0.201749 0.979437i \(-0.435337\pi\)
0.201749 + 0.979437i \(0.435337\pi\)
\(198\) 5.36649e53 0.572873
\(199\) −4.53521e53 −0.430081 −0.215041 0.976605i \(-0.568988\pi\)
−0.215041 + 0.976605i \(0.568988\pi\)
\(200\) −1.67228e53 −0.140963
\(201\) 3.67320e53 0.275383
\(202\) 1.02313e54 0.682615
\(203\) 1.56252e54 0.928257
\(204\) 6.20310e53 0.328322
\(205\) −7.37293e53 −0.347876
\(206\) 1.38909e54 0.584588
\(207\) −2.15246e54 −0.808412
\(208\) −6.19436e53 −0.207734
\(209\) −5.88714e54 −1.76387
\(210\) 1.74473e54 0.467279
\(211\) 2.34865e54 0.562574 0.281287 0.959624i \(-0.409239\pi\)
0.281287 + 0.959624i \(0.409239\pi\)
\(212\) −2.08261e54 −0.446391
\(213\) −1.08546e55 −2.08302
\(214\) −3.87284e54 −0.665741
\(215\) 6.98821e54 1.07662
\(216\) 1.68450e54 0.232706
\(217\) 5.67004e54 0.702720
\(218\) 2.10815e54 0.234517
\(219\) 1.55701e55 1.55544
\(220\) 7.70521e54 0.691595
\(221\) 5.60797e54 0.452468
\(222\) −1.02331e55 −0.742524
\(223\) −1.63862e55 −1.06983 −0.534913 0.844907i \(-0.679656\pi\)
−0.534913 + 0.844907i \(0.679656\pi\)
\(224\) −2.12564e54 −0.124928
\(225\) −3.42117e54 −0.181086
\(226\) −7.43546e54 −0.354617
\(227\) 6.42416e54 0.276190 0.138095 0.990419i \(-0.455902\pi\)
0.138095 + 0.990419i \(0.455902\pi\)
\(228\) 1.53773e55 0.596225
\(229\) 2.68073e55 0.937819 0.468910 0.883246i \(-0.344647\pi\)
0.468910 + 0.883246i \(0.344647\pi\)
\(230\) −3.09051e55 −0.975946
\(231\) 5.33046e55 1.52014
\(232\) −1.80242e55 −0.464395
\(233\) −6.96307e55 −1.62157 −0.810787 0.585341i \(-0.800961\pi\)
−0.810787 + 0.585341i \(0.800961\pi\)
\(234\) −1.26725e55 −0.266864
\(235\) −4.75076e55 −0.905040
\(236\) 2.83514e55 0.488813
\(237\) −1.73579e55 −0.270964
\(238\) 1.92442e55 0.272107
\(239\) −1.13696e54 −0.0145678 −0.00728390 0.999973i \(-0.502319\pi\)
−0.00728390 + 0.999973i \(0.502319\pi\)
\(240\) −2.01261e55 −0.233773
\(241\) −1.08595e56 −1.14396 −0.571979 0.820268i \(-0.693824\pi\)
−0.571979 + 0.820268i \(0.693824\pi\)
\(242\) 1.61422e56 1.54277
\(243\) 9.76002e55 0.846649
\(244\) 4.04728e55 0.318788
\(245\) −5.42519e55 −0.388161
\(246\) 5.88369e55 0.382538
\(247\) 1.39020e56 0.821670
\(248\) −6.54058e55 −0.351562
\(249\) 1.45063e56 0.709370
\(250\) −1.72324e56 −0.766929
\(251\) 3.63653e56 1.47352 0.736758 0.676156i \(-0.236356\pi\)
0.736758 + 0.676156i \(0.236356\pi\)
\(252\) −4.34866e55 −0.160488
\(253\) −9.44204e56 −3.17493
\(254\) 1.97927e56 0.606615
\(255\) 1.82208e56 0.509184
\(256\) 2.45199e55 0.0625000
\(257\) 2.18320e56 0.507769 0.253884 0.967235i \(-0.418292\pi\)
0.253884 + 0.967235i \(0.418292\pi\)
\(258\) −5.57669e56 −1.18389
\(259\) −3.17465e56 −0.615391
\(260\) −1.81952e56 −0.322168
\(261\) −3.68740e56 −0.596580
\(262\) 3.00249e56 0.444019
\(263\) 1.02288e57 1.38314 0.691570 0.722309i \(-0.256919\pi\)
0.691570 + 0.722309i \(0.256919\pi\)
\(264\) −6.14886e56 −0.760506
\(265\) −6.11741e56 −0.692292
\(266\) 4.77055e56 0.494140
\(267\) 1.62755e57 1.54355
\(268\) −1.31451e56 −0.114182
\(269\) 5.80374e56 0.461880 0.230940 0.972968i \(-0.425820\pi\)
0.230940 + 0.972968i \(0.425820\pi\)
\(270\) 4.94801e56 0.360896
\(271\) 1.66765e57 1.11513 0.557565 0.830133i \(-0.311736\pi\)
0.557565 + 0.830133i \(0.311736\pi\)
\(272\) −2.21988e56 −0.136132
\(273\) −1.25874e57 −0.708132
\(274\) −8.43272e56 −0.435341
\(275\) −1.50074e57 −0.711191
\(276\) 2.46627e57 1.07319
\(277\) −3.42098e57 −1.36734 −0.683669 0.729792i \(-0.739617\pi\)
−0.683669 + 0.729792i \(0.739617\pi\)
\(278\) −4.61586e56 −0.169512
\(279\) −1.33808e57 −0.451630
\(280\) −6.24380e56 −0.193747
\(281\) 1.12913e57 0.322214 0.161107 0.986937i \(-0.448494\pi\)
0.161107 + 0.986937i \(0.448494\pi\)
\(282\) 3.79117e57 0.995219
\(283\) −7.01471e57 −1.69445 −0.847225 0.531234i \(-0.821728\pi\)
−0.847225 + 0.531234i \(0.821728\pi\)
\(284\) 3.88449e57 0.863681
\(285\) 4.51688e57 0.924665
\(286\) −5.55894e57 −1.04807
\(287\) 1.82532e57 0.317041
\(288\) 5.01632e56 0.0802900
\(289\) −4.76823e57 −0.703490
\(290\) −5.29438e57 −0.720215
\(291\) 1.21823e58 1.52843
\(292\) −5.57199e57 −0.644931
\(293\) −7.39186e57 −0.789523 −0.394761 0.918784i \(-0.629173\pi\)
−0.394761 + 0.918784i \(0.629173\pi\)
\(294\) 4.32938e57 0.426838
\(295\) 8.32788e57 0.758084
\(296\) 3.66206e57 0.307872
\(297\) 1.51170e58 1.17406
\(298\) 3.17353e55 0.00227751
\(299\) 2.22965e58 1.47899
\(300\) 3.91994e57 0.240397
\(301\) −1.73008e58 −0.981191
\(302\) −7.43997e57 −0.390308
\(303\) −2.39830e58 −1.16413
\(304\) −5.50299e57 −0.247212
\(305\) 1.18884e58 0.494398
\(306\) −4.54145e57 −0.174880
\(307\) −2.91735e58 −1.04049 −0.520243 0.854018i \(-0.674159\pi\)
−0.520243 + 0.854018i \(0.674159\pi\)
\(308\) −1.90759e58 −0.630294
\(309\) −3.25611e58 −0.996954
\(310\) −1.92122e58 −0.545226
\(311\) 1.96485e58 0.516964 0.258482 0.966016i \(-0.416778\pi\)
0.258482 + 0.966016i \(0.416778\pi\)
\(312\) 1.45200e58 0.354269
\(313\) 5.30059e58 1.19959 0.599794 0.800155i \(-0.295249\pi\)
0.599794 + 0.800155i \(0.295249\pi\)
\(314\) 4.63089e58 0.972340
\(315\) −1.27737e58 −0.248895
\(316\) 6.21181e57 0.112350
\(317\) 1.71533e58 0.288041 0.144020 0.989575i \(-0.453997\pi\)
0.144020 + 0.989575i \(0.453997\pi\)
\(318\) 4.88177e58 0.761273
\(319\) −1.61752e59 −2.34298
\(320\) 7.20243e57 0.0969292
\(321\) 9.07819e58 1.13535
\(322\) 7.65121e58 0.889441
\(323\) 4.98205e58 0.538454
\(324\) −6.20809e58 −0.623951
\(325\) 3.54386e58 0.331297
\(326\) 6.41655e58 0.558069
\(327\) −4.94165e58 −0.399944
\(328\) −2.10557e58 −0.158612
\(329\) 1.17615e59 0.824820
\(330\) −1.80615e59 −1.17944
\(331\) −3.07803e59 −1.87204 −0.936020 0.351947i \(-0.885520\pi\)
−0.936020 + 0.351947i \(0.885520\pi\)
\(332\) −5.19132e58 −0.294125
\(333\) 7.49188e58 0.395505
\(334\) −8.47413e58 −0.416921
\(335\) −3.86122e58 −0.177081
\(336\) 4.98264e58 0.213052
\(337\) 2.88763e59 1.15143 0.575716 0.817650i \(-0.304723\pi\)
0.575716 + 0.817650i \(0.304723\pi\)
\(338\) −5.88504e58 −0.218880
\(339\) 1.74292e59 0.604762
\(340\) −6.52061e58 −0.211122
\(341\) −5.86964e59 −1.77371
\(342\) −1.12581e59 −0.317578
\(343\) 4.02629e59 1.06046
\(344\) 1.99570e59 0.490877
\(345\) 7.24436e59 1.66438
\(346\) −1.06206e59 −0.227962
\(347\) −3.66533e59 −0.735141 −0.367570 0.929996i \(-0.619810\pi\)
−0.367570 + 0.929996i \(0.619810\pi\)
\(348\) 4.22498e59 0.791977
\(349\) −3.54128e59 −0.620530 −0.310265 0.950650i \(-0.600418\pi\)
−0.310265 + 0.950650i \(0.600418\pi\)
\(350\) 1.21610e59 0.199237
\(351\) −3.56975e59 −0.546916
\(352\) 2.20047e59 0.315328
\(353\) 4.56710e59 0.612259 0.306129 0.951990i \(-0.400966\pi\)
0.306129 + 0.951990i \(0.400966\pi\)
\(354\) −6.64576e59 −0.833620
\(355\) 1.14102e60 1.33945
\(356\) −5.82444e59 −0.639999
\(357\) −4.51096e59 −0.464051
\(358\) 1.29089e60 1.24347
\(359\) −9.09804e59 −0.820783 −0.410391 0.911910i \(-0.634608\pi\)
−0.410391 + 0.911910i \(0.634608\pi\)
\(360\) 1.47348e59 0.124519
\(361\) −2.80144e58 −0.0221800
\(362\) 5.24502e59 0.389131
\(363\) −3.78384e60 −2.63104
\(364\) 4.50460e59 0.293612
\(365\) −1.63670e60 −1.00020
\(366\) −9.48710e59 −0.543661
\(367\) 1.74699e60 0.938939 0.469470 0.882949i \(-0.344445\pi\)
0.469470 + 0.882949i \(0.344445\pi\)
\(368\) −8.82592e59 −0.444976
\(369\) −4.30760e59 −0.203759
\(370\) 1.07569e60 0.477468
\(371\) 1.51449e60 0.630930
\(372\) 1.53316e60 0.599552
\(373\) 4.07052e60 1.49449 0.747243 0.664551i \(-0.231377\pi\)
0.747243 + 0.664551i \(0.231377\pi\)
\(374\) −1.99216e60 −0.686818
\(375\) 4.03938e60 1.30792
\(376\) −1.35673e60 −0.412647
\(377\) 3.81964e60 1.09144
\(378\) −1.22499e60 −0.328907
\(379\) 2.62308e60 0.661896 0.330948 0.943649i \(-0.392632\pi\)
0.330948 + 0.943649i \(0.392632\pi\)
\(380\) −1.61644e60 −0.383393
\(381\) −4.63954e60 −1.03452
\(382\) −9.39467e58 −0.0196967
\(383\) −4.33638e60 −0.854981 −0.427491 0.904020i \(-0.640602\pi\)
−0.427491 + 0.904020i \(0.640602\pi\)
\(384\) −5.74764e59 −0.106587
\(385\) −5.60331e60 −0.977502
\(386\) 2.77033e60 0.454705
\(387\) 4.08284e60 0.630600
\(388\) −4.35964e60 −0.633731
\(389\) −8.25352e60 −1.12934 −0.564668 0.825318i \(-0.690996\pi\)
−0.564668 + 0.825318i \(0.690996\pi\)
\(390\) 4.26507e60 0.549425
\(391\) 7.99042e60 0.969205
\(392\) −1.54933e60 −0.176979
\(393\) −7.03804e60 −0.757228
\(394\) 2.81506e60 0.285317
\(395\) 1.82464e60 0.174239
\(396\) 4.50174e60 0.405083
\(397\) −2.22502e60 −0.188693 −0.0943467 0.995539i \(-0.530076\pi\)
−0.0943467 + 0.995539i \(0.530076\pi\)
\(398\) −3.80441e60 −0.304113
\(399\) −1.11825e61 −0.842705
\(400\) −1.40281e60 −0.0996757
\(401\) 1.02772e61 0.688626 0.344313 0.938855i \(-0.388112\pi\)
0.344313 + 0.938855i \(0.388112\pi\)
\(402\) 3.08130e60 0.194725
\(403\) 1.38606e61 0.826256
\(404\) 8.58268e60 0.482682
\(405\) −1.82355e61 −0.967665
\(406\) 1.31074e61 0.656377
\(407\) 3.28640e61 1.55329
\(408\) 5.20354e60 0.232159
\(409\) −2.81920e61 −1.18749 −0.593743 0.804655i \(-0.702350\pi\)
−0.593743 + 0.804655i \(0.702350\pi\)
\(410\) −6.18486e60 −0.245985
\(411\) 1.97668e61 0.742428
\(412\) 1.16525e61 0.413366
\(413\) −2.06174e61 −0.690889
\(414\) −1.80562e61 −0.571634
\(415\) −1.52489e61 −0.456149
\(416\) −5.19621e60 −0.146890
\(417\) 1.08199e61 0.289085
\(418\) −4.93849e61 −1.24724
\(419\) −3.13668e61 −0.748928 −0.374464 0.927241i \(-0.622173\pi\)
−0.374464 + 0.927241i \(0.622173\pi\)
\(420\) 1.46359e61 0.330416
\(421\) 6.99827e61 1.49404 0.747018 0.664803i \(-0.231485\pi\)
0.747018 + 0.664803i \(0.231485\pi\)
\(422\) 1.97019e61 0.397800
\(423\) −2.77561e61 −0.530103
\(424\) −1.74702e61 −0.315646
\(425\) 1.27001e61 0.217104
\(426\) −9.10551e61 −1.47292
\(427\) −2.94323e61 −0.450576
\(428\) −3.24877e61 −0.470750
\(429\) 1.30305e62 1.78738
\(430\) 5.86214e61 0.761285
\(431\) −2.82940e61 −0.347920 −0.173960 0.984753i \(-0.555656\pi\)
−0.173960 + 0.984753i \(0.555656\pi\)
\(432\) 1.41306e61 0.164548
\(433\) −1.51590e62 −1.67188 −0.835938 0.548823i \(-0.815076\pi\)
−0.835938 + 0.548823i \(0.815076\pi\)
\(434\) 4.75638e61 0.496898
\(435\) 1.24104e62 1.22825
\(436\) 1.76845e61 0.165829
\(437\) 1.98080e62 1.76005
\(438\) 1.30611e62 1.09986
\(439\) −1.10003e62 −0.877986 −0.438993 0.898490i \(-0.644665\pi\)
−0.438993 + 0.898490i \(0.644665\pi\)
\(440\) 6.46360e61 0.489031
\(441\) −3.16965e61 −0.227355
\(442\) 4.70431e61 0.319943
\(443\) −1.34508e62 −0.867481 −0.433741 0.901038i \(-0.642807\pi\)
−0.433741 + 0.901038i \(0.642807\pi\)
\(444\) −8.58411e61 −0.525044
\(445\) −1.71086e62 −0.992554
\(446\) −1.37457e62 −0.756482
\(447\) −7.43896e59 −0.00388406
\(448\) −1.78311e61 −0.0883377
\(449\) −7.92587e61 −0.372613 −0.186306 0.982492i \(-0.559652\pi\)
−0.186306 + 0.982492i \(0.559652\pi\)
\(450\) −2.86989e61 −0.128047
\(451\) −1.88958e62 −0.800234
\(452\) −6.23731e61 −0.250752
\(453\) 1.74398e62 0.665631
\(454\) 5.38898e61 0.195296
\(455\) 1.32317e62 0.455354
\(456\) 1.28994e62 0.421594
\(457\) −3.26630e62 −1.01397 −0.506985 0.861955i \(-0.669240\pi\)
−0.506985 + 0.861955i \(0.669240\pi\)
\(458\) 2.24876e62 0.663138
\(459\) −1.27929e62 −0.358403
\(460\) −2.59251e62 −0.690098
\(461\) 5.58029e62 1.41151 0.705757 0.708454i \(-0.250607\pi\)
0.705757 + 0.708454i \(0.250607\pi\)
\(462\) 4.47152e62 1.07490
\(463\) 5.76010e62 1.31606 0.658031 0.752991i \(-0.271390\pi\)
0.658031 + 0.752991i \(0.271390\pi\)
\(464\) −1.51198e62 −0.328377
\(465\) 4.50346e62 0.929826
\(466\) −5.84105e62 −1.14663
\(467\) −4.90192e62 −0.914997 −0.457499 0.889210i \(-0.651255\pi\)
−0.457499 + 0.889210i \(0.651255\pi\)
\(468\) −1.06305e62 −0.188701
\(469\) 9.55926e61 0.161385
\(470\) −3.98522e62 −0.639960
\(471\) −1.08551e63 −1.65823
\(472\) 2.37829e62 0.345643
\(473\) 1.79098e63 2.47659
\(474\) −1.45609e62 −0.191601
\(475\) 3.14832e62 0.394256
\(476\) 1.61432e62 0.192409
\(477\) −3.57407e62 −0.405491
\(478\) −9.53750e60 −0.0103010
\(479\) 4.76619e62 0.490103 0.245051 0.969510i \(-0.421195\pi\)
0.245051 + 0.969510i \(0.421195\pi\)
\(480\) −1.68830e62 −0.165303
\(481\) −7.76055e62 −0.723574
\(482\) −9.10962e62 −0.808900
\(483\) −1.79350e63 −1.51685
\(484\) 1.35411e63 1.09091
\(485\) −1.28059e63 −0.982832
\(486\) 8.18730e62 0.598671
\(487\) −9.40089e62 −0.654996 −0.327498 0.944852i \(-0.606205\pi\)
−0.327498 + 0.944852i \(0.606205\pi\)
\(488\) 3.39511e62 0.225417
\(489\) −1.50408e63 −0.951730
\(490\) −4.55098e62 −0.274471
\(491\) 2.46181e63 1.41527 0.707634 0.706579i \(-0.249763\pi\)
0.707634 + 0.706579i \(0.249763\pi\)
\(492\) 4.93560e62 0.270496
\(493\) 1.36885e63 0.715240
\(494\) 1.16618e63 0.581009
\(495\) 1.32233e63 0.628229
\(496\) −5.48664e62 −0.248592
\(497\) −2.82484e63 −1.22073
\(498\) 1.21688e63 0.501601
\(499\) 3.13630e63 1.23326 0.616630 0.787253i \(-0.288498\pi\)
0.616630 + 0.787253i \(0.288498\pi\)
\(500\) −1.44556e63 −0.542301
\(501\) 1.98639e63 0.711015
\(502\) 3.05054e63 1.04193
\(503\) −2.01256e63 −0.655997 −0.327998 0.944678i \(-0.606374\pi\)
−0.327998 + 0.944678i \(0.606374\pi\)
\(504\) −3.64792e62 −0.113482
\(505\) 2.52106e63 0.748575
\(506\) −7.92056e63 −2.24501
\(507\) 1.37949e63 0.373278
\(508\) 1.66033e63 0.428941
\(509\) −7.12023e63 −1.75641 −0.878206 0.478283i \(-0.841259\pi\)
−0.878206 + 0.478283i \(0.841259\pi\)
\(510\) 1.52848e63 0.360047
\(511\) 4.05201e63 0.911547
\(512\) 2.05688e62 0.0441942
\(513\) −3.17132e63 −0.650852
\(514\) 1.83140e63 0.359047
\(515\) 3.42278e63 0.641076
\(516\) −4.67806e63 −0.837140
\(517\) −1.21755e64 −2.08190
\(518\) −2.66309e63 −0.435147
\(519\) 2.48955e63 0.388765
\(520\) −1.52632e63 −0.227807
\(521\) 1.00318e64 1.43117 0.715585 0.698526i \(-0.246160\pi\)
0.715585 + 0.698526i \(0.246160\pi\)
\(522\) −3.09322e63 −0.421846
\(523\) −2.57269e63 −0.335427 −0.167714 0.985836i \(-0.553638\pi\)
−0.167714 + 0.985836i \(0.553638\pi\)
\(524\) 2.51867e63 0.313969
\(525\) −2.85062e63 −0.339778
\(526\) 8.58057e63 0.978028
\(527\) 4.96724e63 0.541460
\(528\) −5.15804e63 −0.537759
\(529\) 2.17410e64 2.16806
\(530\) −5.13166e63 −0.489525
\(531\) 4.86553e63 0.444027
\(532\) 4.00183e63 0.349410
\(533\) 4.46208e63 0.372776
\(534\) 1.36529e64 1.09145
\(535\) −9.54287e63 −0.730071
\(536\) −1.10269e63 −0.0807387
\(537\) −3.02592e64 −2.12062
\(538\) 4.86853e63 0.326599
\(539\) −1.39040e64 −0.892904
\(540\) 4.15069e63 0.255192
\(541\) −1.17177e64 −0.689774 −0.344887 0.938644i \(-0.612083\pi\)
−0.344887 + 0.938644i \(0.612083\pi\)
\(542\) 1.39892e64 0.788516
\(543\) −1.22947e64 −0.663622
\(544\) −1.86217e63 −0.0962597
\(545\) 5.19459e63 0.257178
\(546\) −1.05591e64 −0.500725
\(547\) 7.70176e63 0.349855 0.174927 0.984581i \(-0.444031\pi\)
0.174927 + 0.984581i \(0.444031\pi\)
\(548\) −7.07387e63 −0.307832
\(549\) 6.94575e63 0.289580
\(550\) −1.25891e64 −0.502888
\(551\) 3.39332e64 1.29886
\(552\) 2.06886e64 0.758860
\(553\) −4.51729e63 −0.158795
\(554\) −2.86973e64 −0.966854
\(555\) −2.52148e64 −0.814273
\(556\) −3.87207e63 −0.119863
\(557\) 1.83973e64 0.545957 0.272978 0.962020i \(-0.411991\pi\)
0.272978 + 0.962020i \(0.411991\pi\)
\(558\) −1.12246e64 −0.319351
\(559\) −4.22925e64 −1.15368
\(560\) −5.23768e63 −0.137000
\(561\) 4.66976e64 1.17130
\(562\) 9.47181e63 0.227840
\(563\) 3.16333e64 0.729790 0.364895 0.931049i \(-0.381105\pi\)
0.364895 + 0.931049i \(0.381105\pi\)
\(564\) 3.18026e64 0.703726
\(565\) −1.83213e64 −0.388883
\(566\) −5.88437e64 −1.19816
\(567\) 4.51459e64 0.881894
\(568\) 3.25855e64 0.610715
\(569\) 8.24261e64 1.48227 0.741133 0.671358i \(-0.234289\pi\)
0.741133 + 0.671358i \(0.234289\pi\)
\(570\) 3.78903e64 0.653837
\(571\) −4.09282e64 −0.677756 −0.338878 0.940830i \(-0.610047\pi\)
−0.338878 + 0.940830i \(0.610047\pi\)
\(572\) −4.66318e64 −0.741097
\(573\) 2.20217e63 0.0335906
\(574\) 1.53119e64 0.224182
\(575\) 5.04940e64 0.709652
\(576\) 4.20799e63 0.0567736
\(577\) −1.08012e65 −1.39907 −0.699534 0.714599i \(-0.746609\pi\)
−0.699534 + 0.714599i \(0.746609\pi\)
\(578\) −3.99988e64 −0.497443
\(579\) −6.49384e64 −0.775453
\(580\) −4.44125e64 −0.509269
\(581\) 3.77518e64 0.415718
\(582\) 1.02193e65 1.08076
\(583\) −1.56781e65 −1.59251
\(584\) −4.67412e64 −0.456035
\(585\) −3.12257e64 −0.292650
\(586\) −6.20074e64 −0.558277
\(587\) −8.27524e64 −0.715789 −0.357895 0.933762i \(-0.616505\pi\)
−0.357895 + 0.933762i \(0.616505\pi\)
\(588\) 3.63174e64 0.301820
\(589\) 1.23136e65 0.983278
\(590\) 6.98593e64 0.536046
\(591\) −6.59870e64 −0.486578
\(592\) 3.07196e64 0.217698
\(593\) 9.13374e64 0.622104 0.311052 0.950393i \(-0.399319\pi\)
0.311052 + 0.950393i \(0.399319\pi\)
\(594\) 1.26811e65 0.830185
\(595\) 4.74186e64 0.298401
\(596\) 2.66215e62 0.00161044
\(597\) 8.91780e64 0.518634
\(598\) 1.87037e65 1.04580
\(599\) −9.38897e64 −0.504763 −0.252382 0.967628i \(-0.581214\pi\)
−0.252382 + 0.967628i \(0.581214\pi\)
\(600\) 3.28828e64 0.169987
\(601\) −8.67884e64 −0.431431 −0.215716 0.976456i \(-0.569208\pi\)
−0.215716 + 0.976456i \(0.569208\pi\)
\(602\) −1.45130e65 −0.693807
\(603\) −2.25590e64 −0.103720
\(604\) −6.24110e64 −0.275990
\(605\) 3.97752e65 1.69185
\(606\) −2.01184e65 −0.823163
\(607\) 5.32801e64 0.209716 0.104858 0.994487i \(-0.466561\pi\)
0.104858 + 0.994487i \(0.466561\pi\)
\(608\) −4.61624e64 −0.174805
\(609\) −3.07245e65 −1.11938
\(610\) 9.97271e64 0.349593
\(611\) 2.87515e65 0.969821
\(612\) −3.80964e64 −0.123659
\(613\) 1.74087e65 0.543807 0.271903 0.962325i \(-0.412347\pi\)
0.271903 + 0.962325i \(0.412347\pi\)
\(614\) −2.44725e65 −0.735735
\(615\) 1.44977e65 0.419503
\(616\) −1.60020e65 −0.445685
\(617\) −4.55160e65 −1.22029 −0.610144 0.792290i \(-0.708888\pi\)
−0.610144 + 0.792290i \(0.708888\pi\)
\(618\) −2.73143e65 −0.704953
\(619\) −2.56378e65 −0.637017 −0.318509 0.947920i \(-0.603182\pi\)
−0.318509 + 0.947920i \(0.603182\pi\)
\(620\) −1.61163e65 −0.385533
\(621\) −5.08630e65 −1.17152
\(622\) 1.64824e65 0.365549
\(623\) 4.23560e65 0.904577
\(624\) 1.21803e65 0.250506
\(625\) −2.23321e65 −0.442333
\(626\) 4.44645e65 0.848237
\(627\) 1.15762e66 2.12705
\(628\) 3.88468e65 0.687548
\(629\) −2.78115e65 −0.474170
\(630\) −1.07153e65 −0.175996
\(631\) −4.23671e65 −0.670407 −0.335203 0.942146i \(-0.608805\pi\)
−0.335203 + 0.942146i \(0.608805\pi\)
\(632\) 5.21084e64 0.0794432
\(633\) −4.61825e65 −0.678407
\(634\) 1.43892e65 0.203676
\(635\) 4.87703e65 0.665231
\(636\) 4.09513e65 0.538301
\(637\) 3.28331e65 0.415945
\(638\) −1.35688e66 −1.65674
\(639\) 6.66638e65 0.784549
\(640\) 6.04184e64 0.0685393
\(641\) 2.49269e65 0.272587 0.136293 0.990669i \(-0.456481\pi\)
0.136293 + 0.990669i \(0.456481\pi\)
\(642\) 7.61534e65 0.802816
\(643\) −9.57846e65 −0.973505 −0.486752 0.873540i \(-0.661819\pi\)
−0.486752 + 0.873540i \(0.661819\pi\)
\(644\) 6.41830e65 0.628930
\(645\) −1.37412e66 −1.29829
\(646\) 4.17925e65 0.380745
\(647\) −3.65746e65 −0.321313 −0.160657 0.987010i \(-0.551361\pi\)
−0.160657 + 0.987010i \(0.551361\pi\)
\(648\) −5.20772e65 −0.441200
\(649\) 2.13432e66 1.74385
\(650\) 2.97280e65 0.234262
\(651\) −1.11493e66 −0.847409
\(652\) 5.38259e65 0.394615
\(653\) −1.29709e66 −0.917301 −0.458650 0.888617i \(-0.651667\pi\)
−0.458650 + 0.888617i \(0.651667\pi\)
\(654\) −4.14535e65 −0.282803
\(655\) 7.39830e65 0.486924
\(656\) −1.76628e65 −0.112155
\(657\) −9.56237e65 −0.585841
\(658\) 9.86627e65 0.583236
\(659\) −1.65954e66 −0.946628 −0.473314 0.880894i \(-0.656942\pi\)
−0.473314 + 0.880894i \(0.656942\pi\)
\(660\) −1.51511e66 −0.833993
\(661\) −3.53637e65 −0.187855 −0.0939275 0.995579i \(-0.529942\pi\)
−0.0939275 + 0.995579i \(0.529942\pi\)
\(662\) −2.58204e66 −1.32373
\(663\) −1.10272e66 −0.545630
\(664\) −4.35479e65 −0.207978
\(665\) 1.17549e66 0.541889
\(666\) 6.28465e65 0.279664
\(667\) 5.44234e66 2.33792
\(668\) −7.10862e65 −0.294807
\(669\) 3.22209e66 1.29010
\(670\) −3.23902e65 −0.125215
\(671\) 3.04684e66 1.13729
\(672\) 4.17974e65 0.150651
\(673\) −7.59962e65 −0.264507 −0.132254 0.991216i \(-0.542221\pi\)
−0.132254 + 0.991216i \(0.542221\pi\)
\(674\) 2.42232e66 0.814186
\(675\) −8.08427e65 −0.262423
\(676\) −4.93673e65 −0.154772
\(677\) 1.68304e65 0.0509637 0.0254818 0.999675i \(-0.491888\pi\)
0.0254818 + 0.999675i \(0.491888\pi\)
\(678\) 1.46207e66 0.427632
\(679\) 3.17037e66 0.895717
\(680\) −5.46989e65 −0.149286
\(681\) −1.26321e66 −0.333057
\(682\) −4.92381e66 −1.25421
\(683\) −6.47982e66 −1.59469 −0.797345 0.603524i \(-0.793763\pi\)
−0.797345 + 0.603524i \(0.793763\pi\)
\(684\) −9.44396e65 −0.224562
\(685\) −2.07786e66 −0.477407
\(686\) 3.37750e66 0.749856
\(687\) −5.27124e66 −1.13091
\(688\) 1.67412e66 0.347102
\(689\) 3.70224e66 0.741845
\(690\) 6.07701e66 1.17689
\(691\) −8.13920e66 −1.52352 −0.761759 0.647861i \(-0.775664\pi\)
−0.761759 + 0.647861i \(0.775664\pi\)
\(692\) −8.90923e65 −0.161193
\(693\) −3.27371e66 −0.572545
\(694\) −3.07470e66 −0.519823
\(695\) −1.13737e66 −0.185892
\(696\) 3.54417e66 0.560013
\(697\) 1.59908e66 0.244286
\(698\) −2.97064e66 −0.438781
\(699\) 1.36918e67 1.95545
\(700\) 1.02014e66 0.140882
\(701\) −4.13550e66 −0.552274 −0.276137 0.961118i \(-0.589054\pi\)
−0.276137 + 0.961118i \(0.589054\pi\)
\(702\) −2.99453e66 −0.386728
\(703\) −6.89437e66 −0.861082
\(704\) 1.84589e66 0.222970
\(705\) 9.34163e66 1.09139
\(706\) 3.83116e66 0.432932
\(707\) −6.24141e66 −0.682223
\(708\) −5.57487e66 −0.589458
\(709\) 5.79936e66 0.593190 0.296595 0.955003i \(-0.404149\pi\)
0.296595 + 0.955003i \(0.404149\pi\)
\(710\) 9.57159e66 0.947138
\(711\) 1.06604e66 0.102056
\(712\) −4.88590e66 −0.452548
\(713\) 1.97491e67 1.76988
\(714\) −3.78407e66 −0.328134
\(715\) −1.36975e67 −1.14934
\(716\) 1.08287e67 0.879269
\(717\) 2.23565e65 0.0175673
\(718\) −7.63199e66 −0.580381
\(719\) −3.81716e66 −0.280939 −0.140469 0.990085i \(-0.544861\pi\)
−0.140469 + 0.990085i \(0.544861\pi\)
\(720\) 1.23605e66 0.0880483
\(721\) −8.47383e66 −0.584253
\(722\) −2.35002e65 −0.0156836
\(723\) 2.13536e67 1.37950
\(724\) 4.39984e66 0.275157
\(725\) 8.65017e66 0.523699
\(726\) −3.17412e67 −1.86043
\(727\) −1.41840e67 −0.804898 −0.402449 0.915442i \(-0.631841\pi\)
−0.402449 + 0.915442i \(0.631841\pi\)
\(728\) 3.77874e66 0.207615
\(729\) 4.26568e66 0.226930
\(730\) −1.37297e67 −0.707250
\(731\) −1.51564e67 −0.756027
\(732\) −7.95836e66 −0.384426
\(733\) −3.13854e66 −0.146820 −0.0734098 0.997302i \(-0.523388\pi\)
−0.0734098 + 0.997302i \(0.523388\pi\)
\(734\) 1.46548e67 0.663930
\(735\) 1.06678e67 0.468083
\(736\) −7.40372e66 −0.314645
\(737\) −9.89578e66 −0.407346
\(738\) −3.61348e66 −0.144079
\(739\) 3.40636e67 1.31567 0.657835 0.753162i \(-0.271473\pi\)
0.657835 + 0.753162i \(0.271473\pi\)
\(740\) 9.02350e66 0.337621
\(741\) −2.73361e67 −0.990850
\(742\) 1.27045e67 0.446135
\(743\) −1.68868e67 −0.574526 −0.287263 0.957852i \(-0.592745\pi\)
−0.287263 + 0.957852i \(0.592745\pi\)
\(744\) 1.28610e67 0.423948
\(745\) 7.81974e64 0.00249758
\(746\) 3.41460e67 1.05676
\(747\) −8.90909e66 −0.267177
\(748\) −1.67114e67 −0.485653
\(749\) 2.36254e67 0.665360
\(750\) 3.38848e67 0.924838
\(751\) 5.49068e66 0.145240 0.0726202 0.997360i \(-0.476864\pi\)
0.0726202 + 0.997360i \(0.476864\pi\)
\(752\) −1.13811e67 −0.291785
\(753\) −7.15068e67 −1.77691
\(754\) 3.20414e67 0.771766
\(755\) −1.83325e67 −0.428023
\(756\) −1.02759e67 −0.232573
\(757\) 4.95348e67 1.08682 0.543410 0.839468i \(-0.317133\pi\)
0.543410 + 0.839468i \(0.317133\pi\)
\(758\) 2.20040e67 0.468031
\(759\) 1.85663e68 3.82863
\(760\) −1.35596e67 −0.271100
\(761\) −9.42386e67 −1.82679 −0.913397 0.407070i \(-0.866550\pi\)
−0.913397 + 0.407070i \(0.866550\pi\)
\(762\) −3.89193e67 −0.731515
\(763\) −1.28603e67 −0.234382
\(764\) −7.88082e65 −0.0139276
\(765\) −1.11904e67 −0.191779
\(766\) −3.63762e67 −0.604563
\(767\) −5.04001e67 −0.812345
\(768\) −4.82147e66 −0.0753686
\(769\) −7.17781e67 −1.08824 −0.544118 0.839009i \(-0.683136\pi\)
−0.544118 + 0.839009i \(0.683136\pi\)
\(770\) −4.70040e67 −0.691198
\(771\) −4.29293e67 −0.612317
\(772\) 2.32392e67 0.321525
\(773\) −9.60953e67 −1.28969 −0.644843 0.764315i \(-0.723077\pi\)
−0.644843 + 0.764315i \(0.723077\pi\)
\(774\) 3.42493e67 0.445902
\(775\) 3.13896e67 0.396457
\(776\) −3.65713e67 −0.448115
\(777\) 6.24245e67 0.742098
\(778\) −6.92355e67 −0.798562
\(779\) 3.96405e67 0.443618
\(780\) 3.57780e67 0.388502
\(781\) 2.92429e68 3.08121
\(782\) 6.70285e67 0.685332
\(783\) −8.71338e67 −0.864540
\(784\) −1.29968e67 −0.125143
\(785\) 1.14108e68 1.06630
\(786\) −5.90394e67 −0.535441
\(787\) 8.61160e67 0.758015 0.379008 0.925394i \(-0.376265\pi\)
0.379008 + 0.925394i \(0.376265\pi\)
\(788\) 2.36145e67 0.201749
\(789\) −2.01134e68 −1.66793
\(790\) 1.53062e67 0.123206
\(791\) 4.53584e67 0.354413
\(792\) 3.77633e67 0.286437
\(793\) −7.19483e67 −0.529786
\(794\) −1.86648e67 −0.133426
\(795\) 1.20289e68 0.834834
\(796\) −3.19137e67 −0.215041
\(797\) −1.65301e67 −0.108144 −0.0540722 0.998537i \(-0.517220\pi\)
−0.0540722 + 0.998537i \(0.517220\pi\)
\(798\) −9.38056e67 −0.595883
\(799\) 1.03037e68 0.635540
\(800\) −1.17676e67 −0.0704814
\(801\) −9.99563e67 −0.581361
\(802\) 8.62116e67 0.486932
\(803\) −4.19465e68 −2.30081
\(804\) 2.58478e67 0.137691
\(805\) 1.88530e68 0.975387
\(806\) 1.16272e68 0.584252
\(807\) −1.14122e68 −0.556980
\(808\) 7.19967e67 0.341307
\(809\) 2.92290e68 1.34593 0.672966 0.739673i \(-0.265020\pi\)
0.672966 + 0.739673i \(0.265020\pi\)
\(810\) −1.52971e68 −0.684242
\(811\) −2.83385e68 −1.23137 −0.615683 0.787994i \(-0.711120\pi\)
−0.615683 + 0.787994i \(0.711120\pi\)
\(812\) 1.09952e68 0.464129
\(813\) −3.27917e68 −1.34473
\(814\) 2.75683e68 1.09834
\(815\) 1.58107e68 0.611995
\(816\) 4.36504e67 0.164161
\(817\) −3.75721e68 −1.37293
\(818\) −2.36492e68 −0.839679
\(819\) 7.73058e67 0.266711
\(820\) −5.18824e67 −0.173938
\(821\) −1.55031e68 −0.505072 −0.252536 0.967588i \(-0.581265\pi\)
−0.252536 + 0.967588i \(0.581265\pi\)
\(822\) 1.65816e68 0.524976
\(823\) −2.72599e68 −0.838740 −0.419370 0.907815i \(-0.637749\pi\)
−0.419370 + 0.907815i \(0.637749\pi\)
\(824\) 9.77483e67 0.292294
\(825\) 2.95097e68 0.857624
\(826\) −1.72952e68 −0.488533
\(827\) 4.52263e68 1.24169 0.620843 0.783935i \(-0.286790\pi\)
0.620843 + 0.783935i \(0.286790\pi\)
\(828\) −1.51466e68 −0.404206
\(829\) 7.53936e68 1.95570 0.977852 0.209296i \(-0.0671171\pi\)
0.977852 + 0.209296i \(0.0671171\pi\)
\(830\) −1.27917e68 −0.322546
\(831\) 6.72683e68 1.64887
\(832\) −4.35889e67 −0.103867
\(833\) 1.17664e68 0.272576
\(834\) 9.07638e67 0.204414
\(835\) −2.08807e68 −0.457207
\(836\) −4.14271e68 −0.881935
\(837\) −3.16190e68 −0.654485
\(838\) −2.63123e68 −0.529572
\(839\) −1.96939e68 −0.385413 −0.192706 0.981256i \(-0.561726\pi\)
−0.192706 + 0.981256i \(0.561726\pi\)
\(840\) 1.22775e68 0.233639
\(841\) 3.91944e68 0.725300
\(842\) 5.87057e68 1.05644
\(843\) −2.22026e68 −0.388557
\(844\) 1.65271e68 0.281287
\(845\) −1.45010e68 −0.240030
\(846\) −2.32835e68 −0.374839
\(847\) −9.84721e68 −1.54189
\(848\) −1.46551e68 −0.223195
\(849\) 1.37934e69 2.04333
\(850\) 1.06536e68 0.153516
\(851\) −1.10575e69 −1.54993
\(852\) −7.63826e68 −1.04151
\(853\) −3.49668e68 −0.463824 −0.231912 0.972737i \(-0.574498\pi\)
−0.231912 + 0.972737i \(0.574498\pi\)
\(854\) −2.46896e68 −0.318606
\(855\) −2.77405e68 −0.348266
\(856\) −2.72527e68 −0.332871
\(857\) 5.38103e68 0.639464 0.319732 0.947508i \(-0.396407\pi\)
0.319732 + 0.947508i \(0.396407\pi\)
\(858\) 1.09308e69 1.26387
\(859\) −8.79126e68 −0.989036 −0.494518 0.869167i \(-0.664655\pi\)
−0.494518 + 0.869167i \(0.664655\pi\)
\(860\) 4.91752e68 0.538310
\(861\) −3.58922e68 −0.382319
\(862\) −2.37348e68 −0.246016
\(863\) 9.57146e68 0.965438 0.482719 0.875775i \(-0.339649\pi\)
0.482719 + 0.875775i \(0.339649\pi\)
\(864\) 1.18536e68 0.116353
\(865\) −2.61698e68 −0.249989
\(866\) −1.27163e69 −1.18220
\(867\) 9.37600e68 0.848337
\(868\) 3.98994e68 0.351360
\(869\) 4.67631e68 0.400810
\(870\) 1.04106e69 0.868505
\(871\) 2.33680e68 0.189756
\(872\) 1.48348e68 0.117258
\(873\) −7.48180e68 −0.575667
\(874\) 1.66161e69 1.24455
\(875\) 1.05122e69 0.766489
\(876\) 1.09565e69 0.777720
\(877\) −1.79736e69 −1.24207 −0.621033 0.783784i \(-0.713287\pi\)
−0.621033 + 0.783784i \(0.713287\pi\)
\(878\) −9.22771e68 −0.620830
\(879\) 1.45350e69 0.952084
\(880\) 5.42206e68 0.345797
\(881\) −7.63566e67 −0.0474146 −0.0237073 0.999719i \(-0.507547\pi\)
−0.0237073 + 0.999719i \(0.507547\pi\)
\(882\) −2.65889e68 −0.160764
\(883\) −1.09005e69 −0.641757 −0.320879 0.947120i \(-0.603978\pi\)
−0.320879 + 0.947120i \(0.603978\pi\)
\(884\) 3.94626e68 0.226234
\(885\) −1.63755e69 −0.914171
\(886\) −1.12833e69 −0.613402
\(887\) 2.23120e69 1.18123 0.590613 0.806955i \(-0.298886\pi\)
0.590613 + 0.806955i \(0.298886\pi\)
\(888\) −7.20087e68 −0.371262
\(889\) −1.20741e69 −0.606267
\(890\) −1.43517e69 −0.701842
\(891\) −4.67351e69 −2.22596
\(892\) −1.15307e69 −0.534913
\(893\) 2.55424e69 1.15412
\(894\) −6.24026e66 −0.00274644
\(895\) 3.18081e69 1.36363
\(896\) −1.49579e68 −0.0624642
\(897\) −4.38427e69 −1.78351
\(898\) −6.64870e68 −0.263477
\(899\) 3.38323e69 1.30611
\(900\) −2.40744e68 −0.0905432
\(901\) 1.32677e69 0.486143
\(902\) −1.58510e69 −0.565851
\(903\) 3.40194e69 1.18322
\(904\) −5.23224e68 −0.177308
\(905\) 1.29240e69 0.426732
\(906\) 1.46295e69 0.470672
\(907\) 3.40839e68 0.106851 0.0534255 0.998572i \(-0.482986\pi\)
0.0534255 + 0.998572i \(0.482986\pi\)
\(908\) 4.52060e68 0.138095
\(909\) 1.47292e69 0.438457
\(910\) 1.10996e69 0.321984
\(911\) −1.74063e69 −0.492068 −0.246034 0.969261i \(-0.579127\pi\)
−0.246034 + 0.969261i \(0.579127\pi\)
\(912\) 1.08208e69 0.298112
\(913\) −3.90808e69 −1.04930
\(914\) −2.73997e69 −0.716984
\(915\) −2.33767e69 −0.596194
\(916\) 1.88640e69 0.468910
\(917\) −1.83161e69 −0.443764
\(918\) −1.07315e69 −0.253429
\(919\) 5.31109e69 1.22256 0.611279 0.791415i \(-0.290655\pi\)
0.611279 + 0.791415i \(0.290655\pi\)
\(920\) −2.17475e69 −0.487973
\(921\) 5.73652e69 1.25472
\(922\) 4.68109e69 0.998091
\(923\) −6.90544e69 −1.43533
\(924\) 3.75098e69 0.760070
\(925\) −1.75750e69 −0.347188
\(926\) 4.83192e69 0.930596
\(927\) 1.99975e69 0.375493
\(928\) −1.26834e69 −0.232197
\(929\) 2.19849e69 0.392424 0.196212 0.980562i \(-0.437136\pi\)
0.196212 + 0.980562i \(0.437136\pi\)
\(930\) 3.77777e69 0.657486
\(931\) 2.91685e69 0.494991
\(932\) −4.89983e69 −0.810787
\(933\) −3.86357e69 −0.623406
\(934\) −4.11203e69 −0.647001
\(935\) −4.90878e69 −0.753184
\(936\) −8.91748e68 −0.133432
\(937\) −3.73566e69 −0.545113 −0.272557 0.962140i \(-0.587869\pi\)
−0.272557 + 0.962140i \(0.587869\pi\)
\(938\) 8.01889e68 0.114116
\(939\) −1.04228e70 −1.44658
\(940\) −3.34305e69 −0.452520
\(941\) −3.51161e69 −0.463607 −0.231804 0.972763i \(-0.574463\pi\)
−0.231804 + 0.972763i \(0.574463\pi\)
\(942\) −9.10594e69 −1.17254
\(943\) 6.35771e69 0.798502
\(944\) 1.99505e69 0.244406
\(945\) −3.01843e69 −0.360689
\(946\) 1.50239e70 1.75122
\(947\) −1.80829e69 −0.205610 −0.102805 0.994702i \(-0.532782\pi\)
−0.102805 + 0.994702i \(0.532782\pi\)
\(948\) −1.22146e69 −0.135482
\(949\) 9.90529e69 1.07179
\(950\) 2.64100e69 0.278781
\(951\) −3.37293e69 −0.347348
\(952\) 1.35419e69 0.136054
\(953\) −5.47380e69 −0.536544 −0.268272 0.963343i \(-0.586453\pi\)
−0.268272 + 0.963343i \(0.586453\pi\)
\(954\) −2.99815e69 −0.286726
\(955\) −2.31490e68 −0.0215999
\(956\) −8.00063e67 −0.00728390
\(957\) 3.18061e70 2.82540
\(958\) 3.99817e69 0.346555
\(959\) 5.14419e69 0.435091
\(960\) −1.41625e69 −0.116887
\(961\) −1.39491e68 −0.0112343
\(962\) −6.51002e69 −0.511644
\(963\) −5.57538e69 −0.427619
\(964\) −7.64171e69 −0.571979
\(965\) 6.82624e69 0.498643
\(966\) −1.50449e70 −1.07258
\(967\) 2.03692e70 1.41727 0.708633 0.705577i \(-0.249312\pi\)
0.708633 + 0.705577i \(0.249312\pi\)
\(968\) 1.13591e70 0.771386
\(969\) −9.79643e69 −0.649321
\(970\) −1.07424e70 −0.694967
\(971\) 6.08262e69 0.384095 0.192047 0.981386i \(-0.438487\pi\)
0.192047 + 0.981386i \(0.438487\pi\)
\(972\) 6.86800e69 0.423324
\(973\) 2.81581e69 0.169415
\(974\) −7.88604e69 −0.463152
\(975\) −6.96845e69 −0.399510
\(976\) 2.84802e69 0.159394
\(977\) −1.09440e70 −0.597935 −0.298968 0.954263i \(-0.596642\pi\)
−0.298968 + 0.954263i \(0.596642\pi\)
\(978\) −1.26172e70 −0.672974
\(979\) −4.38470e70 −2.28321
\(980\) −3.81764e69 −0.194081
\(981\) 3.03492e69 0.150635
\(982\) 2.06511e70 1.00075
\(983\) 2.00353e70 0.947958 0.473979 0.880536i \(-0.342817\pi\)
0.473979 + 0.880536i \(0.342817\pi\)
\(984\) 4.14028e69 0.191269
\(985\) 6.93646e69 0.312886
\(986\) 1.14827e70 0.505751
\(987\) −2.31272e70 −0.994649
\(988\) 9.78263e69 0.410835
\(989\) −6.02597e70 −2.47124
\(990\) 1.10925e70 0.444225
\(991\) −1.91105e70 −0.747379 −0.373690 0.927554i \(-0.621908\pi\)
−0.373690 + 0.927554i \(0.621908\pi\)
\(992\) −4.60252e69 −0.175781
\(993\) 6.05247e70 2.25749
\(994\) −2.36965e70 −0.863186
\(995\) −9.37427e69 −0.333499
\(996\) 1.02079e70 0.354685
\(997\) 1.24124e70 0.421229 0.210614 0.977569i \(-0.432454\pi\)
0.210614 + 0.977569i \(0.432454\pi\)
\(998\) 2.63092e70 0.872046
\(999\) 1.77034e70 0.573149
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 \(a_p\))