Properties

Label 4.12.a.a.1.1
Level 4
Weight 12
Character 4.1
Self dual Yes
Analytic conductor 3.073
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 4.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(3.07337272224\)
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 \(\chi\) = 4.1

$q$-expansion

\(f(q)\) \(=\) \(q-516.000 q^{3} -10530.0 q^{5} +49304.0 q^{7} +89109.0 q^{9} +O(q^{10})\) \(q-516.000 q^{3} -10530.0 q^{5} +49304.0 q^{7} +89109.0 q^{9} -309420. q^{11} -1.72359e6 q^{13} +5.43348e6 q^{15} -2.27950e6 q^{17} +4.55044e6 q^{19} -2.54409e7 q^{21} -7.28287e6 q^{23} +6.20528e7 q^{25} +4.54276e7 q^{27} -6.90400e7 q^{29} -1.41741e8 q^{31} +1.59661e8 q^{33} -5.19171e8 q^{35} +7.11367e8 q^{37} +8.89375e8 q^{39} -1.22526e9 q^{41} -3.36062e7 q^{43} -9.38318e8 q^{45} +1.23215e8 q^{47} +4.53558e8 q^{49} +1.17622e9 q^{51} +1.10612e9 q^{53} +3.25819e9 q^{55} -2.34803e9 q^{57} -9.06278e9 q^{59} -3.85415e9 q^{61} +4.39343e9 q^{63} +1.81494e10 q^{65} -1.53138e10 q^{67} +3.75796e9 q^{69} +2.06196e10 q^{71} -2.06372e9 q^{73} -3.20192e10 q^{75} -1.52556e10 q^{77} +1.36899e10 q^{79} -3.92260e10 q^{81} +6.55704e10 q^{83} +2.40032e10 q^{85} +3.56247e10 q^{87} -2.97155e10 q^{89} -8.49801e10 q^{91} +7.31382e10 q^{93} -4.79162e10 q^{95} -2.34396e10 q^{97} -2.75721e10 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −516.000 −1.22598 −0.612989 0.790091i \(-0.710033\pi\)
−0.612989 + 0.790091i \(0.710033\pi\)
\(4\) 0 0
\(5\) −10530.0 −1.50693 −0.753465 0.657487i \(-0.771619\pi\)
−0.753465 + 0.657487i \(0.771619\pi\)
\(6\) 0 0
\(7\) 49304.0 1.10877 0.554387 0.832259i \(-0.312953\pi\)
0.554387 + 0.832259i \(0.312953\pi\)
\(8\) 0 0
\(9\) 89109.0 0.503023
\(10\) 0 0
\(11\) −309420. −0.579280 −0.289640 0.957136i \(-0.593536\pi\)
−0.289640 + 0.957136i \(0.593536\pi\)
\(12\) 0 0
\(13\) −1.72359e6 −1.28750 −0.643749 0.765237i \(-0.722622\pi\)
−0.643749 + 0.765237i \(0.722622\pi\)
\(14\) 0 0
\(15\) 5.43348e6 1.84746
\(16\) 0 0
\(17\) −2.27950e6 −0.389378 −0.194689 0.980865i \(-0.562370\pi\)
−0.194689 + 0.980865i \(0.562370\pi\)
\(18\) 0 0
\(19\) 4.55044e6 0.421608 0.210804 0.977528i \(-0.432392\pi\)
0.210804 + 0.977528i \(0.432392\pi\)
\(20\) 0 0
\(21\) −2.54409e7 −1.35933
\(22\) 0 0
\(23\) −7.28287e6 −0.235939 −0.117969 0.993017i \(-0.537638\pi\)
−0.117969 + 0.993017i \(0.537638\pi\)
\(24\) 0 0
\(25\) 6.20528e7 1.27084
\(26\) 0 0
\(27\) 4.54276e7 0.609283
\(28\) 0 0
\(29\) −6.90400e7 −0.625046 −0.312523 0.949910i \(-0.601174\pi\)
−0.312523 + 0.949910i \(0.601174\pi\)
\(30\) 0 0
\(31\) −1.41741e8 −0.889212 −0.444606 0.895726i \(-0.646656\pi\)
−0.444606 + 0.895726i \(0.646656\pi\)
\(32\) 0 0
\(33\) 1.59661e8 0.710185
\(34\) 0 0
\(35\) −5.19171e8 −1.67085
\(36\) 0 0
\(37\) 7.11367e8 1.68649 0.843246 0.537528i \(-0.180642\pi\)
0.843246 + 0.537528i \(0.180642\pi\)
\(38\) 0 0
\(39\) 8.89375e8 1.57844
\(40\) 0 0
\(41\) −1.22526e9 −1.65165 −0.825825 0.563927i \(-0.809290\pi\)
−0.825825 + 0.563927i \(0.809290\pi\)
\(42\) 0 0
\(43\) −3.36062e7 −0.0348613 −0.0174306 0.999848i \(-0.505549\pi\)
−0.0174306 + 0.999848i \(0.505549\pi\)
\(44\) 0 0
\(45\) −9.38318e8 −0.758021
\(46\) 0 0
\(47\) 1.23215e8 0.0783653 0.0391827 0.999232i \(-0.487525\pi\)
0.0391827 + 0.999232i \(0.487525\pi\)
\(48\) 0 0
\(49\) 4.53558e8 0.229379
\(50\) 0 0
\(51\) 1.17622e9 0.477368
\(52\) 0 0
\(53\) 1.10612e9 0.363317 0.181658 0.983362i \(-0.441853\pi\)
0.181658 + 0.983362i \(0.441853\pi\)
\(54\) 0 0
\(55\) 3.25819e9 0.872935
\(56\) 0 0
\(57\) −2.34803e9 −0.516882
\(58\) 0 0
\(59\) −9.06278e9 −1.65035 −0.825174 0.564879i \(-0.808923\pi\)
−0.825174 + 0.564879i \(0.808923\pi\)
\(60\) 0 0
\(61\) −3.85415e9 −0.584271 −0.292136 0.956377i \(-0.594366\pi\)
−0.292136 + 0.956377i \(0.594366\pi\)
\(62\) 0 0
\(63\) 4.39343e9 0.557739
\(64\) 0 0
\(65\) 1.81494e10 1.94017
\(66\) 0 0
\(67\) −1.53138e10 −1.38570 −0.692852 0.721080i \(-0.743646\pi\)
−0.692852 + 0.721080i \(0.743646\pi\)
\(68\) 0 0
\(69\) 3.75796e9 0.289256
\(70\) 0 0
\(71\) 2.06196e10 1.35631 0.678156 0.734918i \(-0.262779\pi\)
0.678156 + 0.734918i \(0.262779\pi\)
\(72\) 0 0
\(73\) −2.06372e9 −0.116513 −0.0582566 0.998302i \(-0.518554\pi\)
−0.0582566 + 0.998302i \(0.518554\pi\)
\(74\) 0 0
\(75\) −3.20192e10 −1.55802
\(76\) 0 0
\(77\) −1.52556e10 −0.642291
\(78\) 0 0
\(79\) 1.36899e10 0.500553 0.250277 0.968174i \(-0.419478\pi\)
0.250277 + 0.968174i \(0.419478\pi\)
\(80\) 0 0
\(81\) −3.92260e10 −1.24999
\(82\) 0 0
\(83\) 6.55704e10 1.82717 0.913584 0.406650i \(-0.133303\pi\)
0.913584 + 0.406650i \(0.133303\pi\)
\(84\) 0 0
\(85\) 2.40032e10 0.586765
\(86\) 0 0
\(87\) 3.56247e10 0.766293
\(88\) 0 0
\(89\) −2.97155e10 −0.564077 −0.282038 0.959403i \(-0.591011\pi\)
−0.282038 + 0.959403i \(0.591011\pi\)
\(90\) 0 0
\(91\) −8.49801e10 −1.42754
\(92\) 0 0
\(93\) 7.31382e10 1.09015
\(94\) 0 0
\(95\) −4.79162e10 −0.635334
\(96\) 0 0
\(97\) −2.34396e10 −0.277144 −0.138572 0.990352i \(-0.544251\pi\)
−0.138572 + 0.990352i \(0.544251\pi\)
\(98\) 0 0
\(99\) −2.75721e10 −0.291391
\(100\) 0 0
\(101\) −1.52020e11 −1.43924 −0.719620 0.694368i \(-0.755684\pi\)
−0.719620 + 0.694368i \(0.755684\pi\)
\(102\) 0 0
\(103\) 1.69858e11 1.44371 0.721856 0.692043i \(-0.243289\pi\)
0.721856 + 0.692043i \(0.243289\pi\)
\(104\) 0 0
\(105\) 2.67892e11 2.04842
\(106\) 0 0
\(107\) −3.39932e10 −0.234305 −0.117153 0.993114i \(-0.537377\pi\)
−0.117153 + 0.993114i \(0.537377\pi\)
\(108\) 0 0
\(109\) 1.20016e11 0.747127 0.373563 0.927605i \(-0.378136\pi\)
0.373563 + 0.927605i \(0.378136\pi\)
\(110\) 0 0
\(111\) −3.67065e11 −2.06760
\(112\) 0 0
\(113\) −1.17612e10 −0.0600510 −0.0300255 0.999549i \(-0.509559\pi\)
−0.0300255 + 0.999549i \(0.509559\pi\)
\(114\) 0 0
\(115\) 7.66886e10 0.355544
\(116\) 0 0
\(117\) −1.53588e11 −0.647641
\(118\) 0 0
\(119\) −1.12389e11 −0.431732
\(120\) 0 0
\(121\) −1.89571e11 −0.664435
\(122\) 0 0
\(123\) 6.32235e11 2.02489
\(124\) 0 0
\(125\) −1.39256e11 −0.408138
\(126\) 0 0
\(127\) −7.54679e10 −0.202694 −0.101347 0.994851i \(-0.532315\pi\)
−0.101347 + 0.994851i \(0.532315\pi\)
\(128\) 0 0
\(129\) 1.73408e10 0.0427392
\(130\) 0 0
\(131\) 7.60244e11 1.72171 0.860857 0.508847i \(-0.169928\pi\)
0.860857 + 0.508847i \(0.169928\pi\)
\(132\) 0 0
\(133\) 2.24355e11 0.467468
\(134\) 0 0
\(135\) −4.78353e11 −0.918148
\(136\) 0 0
\(137\) −6.83847e11 −1.21059 −0.605293 0.796003i \(-0.706944\pi\)
−0.605293 + 0.796003i \(0.706944\pi\)
\(138\) 0 0
\(139\) −9.47422e11 −1.54868 −0.774341 0.632769i \(-0.781918\pi\)
−0.774341 + 0.632769i \(0.781918\pi\)
\(140\) 0 0
\(141\) −6.35787e10 −0.0960742
\(142\) 0 0
\(143\) 5.33314e11 0.745822
\(144\) 0 0
\(145\) 7.26991e11 0.941901
\(146\) 0 0
\(147\) −2.34036e11 −0.281214
\(148\) 0 0
\(149\) 1.07160e12 1.19539 0.597693 0.801725i \(-0.296084\pi\)
0.597693 + 0.801725i \(0.296084\pi\)
\(150\) 0 0
\(151\) −8.94017e11 −0.926771 −0.463386 0.886157i \(-0.653365\pi\)
−0.463386 + 0.886157i \(0.653365\pi\)
\(152\) 0 0
\(153\) −2.03124e11 −0.195866
\(154\) 0 0
\(155\) 1.49253e12 1.33998
\(156\) 0 0
\(157\) 4.55657e11 0.381233 0.190616 0.981665i \(-0.438951\pi\)
0.190616 + 0.981665i \(0.438951\pi\)
\(158\) 0 0
\(159\) −5.70759e11 −0.445419
\(160\) 0 0
\(161\) −3.59075e11 −0.261603
\(162\) 0 0
\(163\) −1.45519e12 −0.990575 −0.495287 0.868729i \(-0.664937\pi\)
−0.495287 + 0.868729i \(0.664937\pi\)
\(164\) 0 0
\(165\) −1.68123e12 −1.07020
\(166\) 0 0
\(167\) −3.63036e11 −0.216277 −0.108138 0.994136i \(-0.534489\pi\)
−0.108138 + 0.994136i \(0.534489\pi\)
\(168\) 0 0
\(169\) 1.17862e12 0.657651
\(170\) 0 0
\(171\) 4.05486e11 0.212079
\(172\) 0 0
\(173\) −1.79133e12 −0.878866 −0.439433 0.898275i \(-0.644821\pi\)
−0.439433 + 0.898275i \(0.644821\pi\)
\(174\) 0 0
\(175\) 3.05945e12 1.40907
\(176\) 0 0
\(177\) 4.67639e12 2.02329
\(178\) 0 0
\(179\) −7.17420e11 −0.291798 −0.145899 0.989300i \(-0.546607\pi\)
−0.145899 + 0.989300i \(0.546607\pi\)
\(180\) 0 0
\(181\) −1.81682e12 −0.695153 −0.347576 0.937652i \(-0.612995\pi\)
−0.347576 + 0.937652i \(0.612995\pi\)
\(182\) 0 0
\(183\) 1.98874e12 0.716304
\(184\) 0 0
\(185\) −7.49069e12 −2.54143
\(186\) 0 0
\(187\) 7.05324e11 0.225559
\(188\) 0 0
\(189\) 2.23976e12 0.675557
\(190\) 0 0
\(191\) 4.65644e12 1.32547 0.662736 0.748853i \(-0.269395\pi\)
0.662736 + 0.748853i \(0.269395\pi\)
\(192\) 0 0
\(193\) −3.54446e12 −0.952762 −0.476381 0.879239i \(-0.658052\pi\)
−0.476381 + 0.879239i \(0.658052\pi\)
\(194\) 0 0
\(195\) −9.36511e12 −2.37861
\(196\) 0 0
\(197\) 8.66061e11 0.207962 0.103981 0.994579i \(-0.466842\pi\)
0.103981 + 0.994579i \(0.466842\pi\)
\(198\) 0 0
\(199\) 5.22516e8 0.000118688 0 5.93441e−5 1.00000i \(-0.499981\pi\)
5.93441e−5 1.00000i \(0.499981\pi\)
\(200\) 0 0
\(201\) 7.90190e12 1.69884
\(202\) 0 0
\(203\) −3.40395e12 −0.693035
\(204\) 0 0
\(205\) 1.29020e13 2.48892
\(206\) 0 0
\(207\) −6.48969e11 −0.118683
\(208\) 0 0
\(209\) −1.40800e12 −0.244229
\(210\) 0 0
\(211\) 3.51292e12 0.578248 0.289124 0.957292i \(-0.406636\pi\)
0.289124 + 0.957292i \(0.406636\pi\)
\(212\) 0 0
\(213\) −1.06397e13 −1.66281
\(214\) 0 0
\(215\) 3.53873e11 0.0525335
\(216\) 0 0
\(217\) −6.98838e12 −0.985935
\(218\) 0 0
\(219\) 1.06488e12 0.142843
\(220\) 0 0
\(221\) 3.92894e12 0.501323
\(222\) 0 0
\(223\) −1.34171e13 −1.62923 −0.814616 0.580000i \(-0.803052\pi\)
−0.814616 + 0.580000i \(0.803052\pi\)
\(224\) 0 0
\(225\) 5.52946e12 0.639262
\(226\) 0 0
\(227\) 6.80436e12 0.749281 0.374641 0.927170i \(-0.377766\pi\)
0.374641 + 0.927170i \(0.377766\pi\)
\(228\) 0 0
\(229\) −6.91721e12 −0.725832 −0.362916 0.931822i \(-0.618219\pi\)
−0.362916 + 0.931822i \(0.618219\pi\)
\(230\) 0 0
\(231\) 7.87191e12 0.787434
\(232\) 0 0
\(233\) 7.43160e12 0.708965 0.354483 0.935063i \(-0.384657\pi\)
0.354483 + 0.935063i \(0.384657\pi\)
\(234\) 0 0
\(235\) −1.29745e12 −0.118091
\(236\) 0 0
\(237\) −7.06397e12 −0.613668
\(238\) 0 0
\(239\) 1.24747e13 1.03477 0.517383 0.855754i \(-0.326906\pi\)
0.517383 + 0.855754i \(0.326906\pi\)
\(240\) 0 0
\(241\) 6.40984e12 0.507871 0.253936 0.967221i \(-0.418275\pi\)
0.253936 + 0.967221i \(0.418275\pi\)
\(242\) 0 0
\(243\) 1.21933e13 0.923179
\(244\) 0 0
\(245\) −4.77596e12 −0.345659
\(246\) 0 0
\(247\) −7.84312e12 −0.542820
\(248\) 0 0
\(249\) −3.38343e13 −2.24007
\(250\) 0 0
\(251\) −1.80663e13 −1.14463 −0.572314 0.820035i \(-0.693954\pi\)
−0.572314 + 0.820035i \(0.693954\pi\)
\(252\) 0 0
\(253\) 2.25347e12 0.136675
\(254\) 0 0
\(255\) −1.23856e13 −0.719361
\(256\) 0 0
\(257\) 2.99754e13 1.66775 0.833877 0.551950i \(-0.186116\pi\)
0.833877 + 0.551950i \(0.186116\pi\)
\(258\) 0 0
\(259\) 3.50732e13 1.86994
\(260\) 0 0
\(261\) −6.15209e12 −0.314412
\(262\) 0 0
\(263\) −1.35042e13 −0.661777 −0.330888 0.943670i \(-0.607348\pi\)
−0.330888 + 0.943670i \(0.607348\pi\)
\(264\) 0 0
\(265\) −1.16475e13 −0.547493
\(266\) 0 0
\(267\) 1.53332e13 0.691546
\(268\) 0 0
\(269\) 2.82116e13 1.22121 0.610605 0.791935i \(-0.290926\pi\)
0.610605 + 0.791935i \(0.290926\pi\)
\(270\) 0 0
\(271\) −3.01156e13 −1.25158 −0.625792 0.779990i \(-0.715224\pi\)
−0.625792 + 0.779990i \(0.715224\pi\)
\(272\) 0 0
\(273\) 4.38497e13 1.75014
\(274\) 0 0
\(275\) −1.92004e13 −0.736173
\(276\) 0 0
\(277\) 8.74924e12 0.322353 0.161176 0.986926i \(-0.448471\pi\)
0.161176 + 0.986926i \(0.448471\pi\)
\(278\) 0 0
\(279\) −1.26304e13 −0.447294
\(280\) 0 0
\(281\) −5.09851e13 −1.73603 −0.868017 0.496534i \(-0.834606\pi\)
−0.868017 + 0.496534i \(0.834606\pi\)
\(282\) 0 0
\(283\) 1.57604e13 0.516109 0.258055 0.966130i \(-0.416919\pi\)
0.258055 + 0.966130i \(0.416919\pi\)
\(284\) 0 0
\(285\) 2.47247e13 0.778906
\(286\) 0 0
\(287\) −6.04103e13 −1.83131
\(288\) 0 0
\(289\) −2.90758e13 −0.848385
\(290\) 0 0
\(291\) 1.20948e13 0.339773
\(292\) 0 0
\(293\) −1.05220e13 −0.284659 −0.142329 0.989819i \(-0.545459\pi\)
−0.142329 + 0.989819i \(0.545459\pi\)
\(294\) 0 0
\(295\) 9.54311e13 2.48696
\(296\) 0 0
\(297\) −1.40562e13 −0.352946
\(298\) 0 0
\(299\) 1.25527e13 0.303771
\(300\) 0 0
\(301\) −1.65692e12 −0.0386533
\(302\) 0 0
\(303\) 7.84423e13 1.76448
\(304\) 0 0
\(305\) 4.05842e13 0.880457
\(306\) 0 0
\(307\) −5.62241e13 −1.17669 −0.588344 0.808611i \(-0.700220\pi\)
−0.588344 + 0.808611i \(0.700220\pi\)
\(308\) 0 0
\(309\) −8.76466e13 −1.76996
\(310\) 0 0
\(311\) −1.94567e13 −0.379216 −0.189608 0.981860i \(-0.560722\pi\)
−0.189608 + 0.981860i \(0.560722\pi\)
\(312\) 0 0
\(313\) 2.61189e13 0.491430 0.245715 0.969342i \(-0.420977\pi\)
0.245715 + 0.969342i \(0.420977\pi\)
\(314\) 0 0
\(315\) −4.62628e13 −0.840474
\(316\) 0 0
\(317\) 3.21160e13 0.563503 0.281751 0.959487i \(-0.409085\pi\)
0.281751 + 0.959487i \(0.409085\pi\)
\(318\) 0 0
\(319\) 2.13624e13 0.362077
\(320\) 0 0
\(321\) 1.75405e13 0.287253
\(322\) 0 0
\(323\) −1.03727e13 −0.164165
\(324\) 0 0
\(325\) −1.06954e14 −1.63620
\(326\) 0 0
\(327\) −6.19284e13 −0.915961
\(328\) 0 0
\(329\) 6.07497e12 0.0868894
\(330\) 0 0
\(331\) 2.69111e13 0.372287 0.186143 0.982523i \(-0.440401\pi\)
0.186143 + 0.982523i \(0.440401\pi\)
\(332\) 0 0
\(333\) 6.33892e13 0.848344
\(334\) 0 0
\(335\) 1.61254e14 2.08816
\(336\) 0 0
\(337\) 4.37528e13 0.548329 0.274164 0.961683i \(-0.411599\pi\)
0.274164 + 0.961683i \(0.411599\pi\)
\(338\) 0 0
\(339\) 6.06878e12 0.0736213
\(340\) 0 0
\(341\) 4.38574e13 0.515103
\(342\) 0 0
\(343\) −7.51279e13 −0.854444
\(344\) 0 0
\(345\) −3.95713e13 −0.435889
\(346\) 0 0
\(347\) −9.17892e13 −0.979443 −0.489722 0.871879i \(-0.662902\pi\)
−0.489722 + 0.871879i \(0.662902\pi\)
\(348\) 0 0
\(349\) 1.10757e14 1.14507 0.572534 0.819881i \(-0.305960\pi\)
0.572534 + 0.819881i \(0.305960\pi\)
\(350\) 0 0
\(351\) −7.82988e13 −0.784451
\(352\) 0 0
\(353\) −6.25419e12 −0.0607310 −0.0303655 0.999539i \(-0.509667\pi\)
−0.0303655 + 0.999539i \(0.509667\pi\)
\(354\) 0 0
\(355\) −2.17125e14 −2.04387
\(356\) 0 0
\(357\) 5.79925e13 0.529294
\(358\) 0 0
\(359\) 2.07090e13 0.183291 0.0916453 0.995792i \(-0.470787\pi\)
0.0916453 + 0.995792i \(0.470787\pi\)
\(360\) 0 0
\(361\) −9.57837e13 −0.822247
\(362\) 0 0
\(363\) 9.78186e13 0.814582
\(364\) 0 0
\(365\) 2.17310e13 0.175577
\(366\) 0 0
\(367\) 2.05329e14 1.60985 0.804926 0.593375i \(-0.202205\pi\)
0.804926 + 0.593375i \(0.202205\pi\)
\(368\) 0 0
\(369\) −1.09182e14 −0.830817
\(370\) 0 0
\(371\) 5.45362e13 0.402836
\(372\) 0 0
\(373\) −1.65041e14 −1.18357 −0.591783 0.806097i \(-0.701576\pi\)
−0.591783 + 0.806097i \(0.701576\pi\)
\(374\) 0 0
\(375\) 7.18559e13 0.500369
\(376\) 0 0
\(377\) 1.18997e14 0.804745
\(378\) 0 0
\(379\) 1.19092e14 0.782289 0.391144 0.920329i \(-0.372079\pi\)
0.391144 + 0.920329i \(0.372079\pi\)
\(380\) 0 0
\(381\) 3.89414e13 0.248499
\(382\) 0 0
\(383\) −4.97765e13 −0.308625 −0.154313 0.988022i \(-0.549316\pi\)
−0.154313 + 0.988022i \(0.549316\pi\)
\(384\) 0 0
\(385\) 1.60642e14 0.967888
\(386\) 0 0
\(387\) −2.99462e12 −0.0175360
\(388\) 0 0
\(389\) −1.93513e14 −1.10151 −0.550754 0.834667i \(-0.685660\pi\)
−0.550754 + 0.834667i \(0.685660\pi\)
\(390\) 0 0
\(391\) 1.66013e13 0.0918693
\(392\) 0 0
\(393\) −3.92286e14 −2.11078
\(394\) 0 0
\(395\) −1.44154e14 −0.754299
\(396\) 0 0
\(397\) −4.07502e13 −0.207387 −0.103694 0.994609i \(-0.533066\pi\)
−0.103694 + 0.994609i \(0.533066\pi\)
\(398\) 0 0
\(399\) −1.15767e14 −0.573106
\(400\) 0 0
\(401\) −1.55462e13 −0.0748740 −0.0374370 0.999299i \(-0.511919\pi\)
−0.0374370 + 0.999299i \(0.511919\pi\)
\(402\) 0 0
\(403\) 2.44303e14 1.14486
\(404\) 0 0
\(405\) 4.13050e14 1.88365
\(406\) 0 0
\(407\) −2.20111e14 −0.976951
\(408\) 0 0
\(409\) 3.61195e14 1.56050 0.780250 0.625468i \(-0.215092\pi\)
0.780250 + 0.625468i \(0.215092\pi\)
\(410\) 0 0
\(411\) 3.52865e14 1.48415
\(412\) 0 0
\(413\) −4.46831e14 −1.82986
\(414\) 0 0
\(415\) −6.90457e14 −2.75342
\(416\) 0 0
\(417\) 4.88870e14 1.89865
\(418\) 0 0
\(419\) 3.11674e14 1.17902 0.589512 0.807760i \(-0.299320\pi\)
0.589512 + 0.807760i \(0.299320\pi\)
\(420\) 0 0
\(421\) 2.62039e14 0.965636 0.482818 0.875721i \(-0.339613\pi\)
0.482818 + 0.875721i \(0.339613\pi\)
\(422\) 0 0
\(423\) 1.09795e13 0.0394196
\(424\) 0 0
\(425\) −1.41449e14 −0.494837
\(426\) 0 0
\(427\) −1.90025e14 −0.647825
\(428\) 0 0
\(429\) −2.75190e14 −0.914362
\(430\) 0 0
\(431\) 3.81245e14 1.23475 0.617376 0.786668i \(-0.288196\pi\)
0.617376 + 0.786668i \(0.288196\pi\)
\(432\) 0 0
\(433\) −2.90598e14 −0.917505 −0.458753 0.888564i \(-0.651704\pi\)
−0.458753 + 0.888564i \(0.651704\pi\)
\(434\) 0 0
\(435\) −3.75128e14 −1.15475
\(436\) 0 0
\(437\) −3.31403e13 −0.0994738
\(438\) 0 0
\(439\) −5.51507e13 −0.161434 −0.0807172 0.996737i \(-0.525721\pi\)
−0.0807172 + 0.996737i \(0.525721\pi\)
\(440\) 0 0
\(441\) 4.04161e13 0.115383
\(442\) 0 0
\(443\) −1.24887e14 −0.347774 −0.173887 0.984766i \(-0.555633\pi\)
−0.173887 + 0.984766i \(0.555633\pi\)
\(444\) 0 0
\(445\) 3.12904e14 0.850025
\(446\) 0 0
\(447\) −5.52946e14 −1.46552
\(448\) 0 0
\(449\) −1.82240e14 −0.471290 −0.235645 0.971839i \(-0.575720\pi\)
−0.235645 + 0.971839i \(0.575720\pi\)
\(450\) 0 0
\(451\) 3.79121e14 0.956768
\(452\) 0 0
\(453\) 4.61313e14 1.13620
\(454\) 0 0
\(455\) 8.94840e14 2.15121
\(456\) 0 0
\(457\) 2.77455e14 0.651110 0.325555 0.945523i \(-0.394449\pi\)
0.325555 + 0.945523i \(0.394449\pi\)
\(458\) 0 0
\(459\) −1.03552e14 −0.237241
\(460\) 0 0
\(461\) 5.08550e13 0.113757 0.0568785 0.998381i \(-0.481885\pi\)
0.0568785 + 0.998381i \(0.481885\pi\)
\(462\) 0 0
\(463\) −4.59886e12 −0.0100451 −0.00502255 0.999987i \(-0.501599\pi\)
−0.00502255 + 0.999987i \(0.501599\pi\)
\(464\) 0 0
\(465\) −7.70145e14 −1.64279
\(466\) 0 0
\(467\) 2.85607e14 0.595012 0.297506 0.954720i \(-0.403845\pi\)
0.297506 + 0.954720i \(0.403845\pi\)
\(468\) 0 0
\(469\) −7.55030e14 −1.53643
\(470\) 0 0
\(471\) −2.35119e14 −0.467383
\(472\) 0 0
\(473\) 1.03984e13 0.0201944
\(474\) 0 0
\(475\) 2.82368e14 0.535797
\(476\) 0 0
\(477\) 9.85654e13 0.182757
\(478\) 0 0
\(479\) 6.32901e14 1.14681 0.573403 0.819273i \(-0.305623\pi\)
0.573403 + 0.819273i \(0.305623\pi\)
\(480\) 0 0
\(481\) −1.22611e15 −2.17135
\(482\) 0 0
\(483\) 1.85283e14 0.320719
\(484\) 0 0
\(485\) 2.46819e14 0.417638
\(486\) 0 0
\(487\) −7.43316e14 −1.22960 −0.614800 0.788683i \(-0.710763\pi\)
−0.614800 + 0.788683i \(0.710763\pi\)
\(488\) 0 0
\(489\) 7.50877e14 1.21442
\(490\) 0 0
\(491\) −1.26044e15 −1.99330 −0.996652 0.0817625i \(-0.973945\pi\)
−0.996652 + 0.0817625i \(0.973945\pi\)
\(492\) 0 0
\(493\) 1.57377e14 0.243379
\(494\) 0 0
\(495\) 2.90334e14 0.439106
\(496\) 0 0
\(497\) 1.01663e15 1.50384
\(498\) 0 0
\(499\) 4.48550e14 0.649019 0.324510 0.945882i \(-0.394801\pi\)
0.324510 + 0.945882i \(0.394801\pi\)
\(500\) 0 0
\(501\) 1.87327e14 0.265150
\(502\) 0 0
\(503\) 4.23495e14 0.586441 0.293221 0.956045i \(-0.405273\pi\)
0.293221 + 0.956045i \(0.405273\pi\)
\(504\) 0 0
\(505\) 1.60077e15 2.16884
\(506\) 0 0
\(507\) −6.08166e14 −0.806266
\(508\) 0 0
\(509\) −9.69213e14 −1.25739 −0.628697 0.777650i \(-0.716412\pi\)
−0.628697 + 0.777650i \(0.716412\pi\)
\(510\) 0 0
\(511\) −1.01750e14 −0.129187
\(512\) 0 0
\(513\) 2.06716e14 0.256879
\(514\) 0 0
\(515\) −1.78860e15 −2.17558
\(516\) 0 0
\(517\) −3.81251e13 −0.0453955
\(518\) 0 0
\(519\) 9.24327e14 1.07747
\(520\) 0 0
\(521\) −6.74209e14 −0.769462 −0.384731 0.923029i \(-0.625706\pi\)
−0.384731 + 0.923029i \(0.625706\pi\)
\(522\) 0 0
\(523\) 4.55642e14 0.509172 0.254586 0.967050i \(-0.418061\pi\)
0.254586 + 0.967050i \(0.418061\pi\)
\(524\) 0 0
\(525\) −1.57868e15 −1.72750
\(526\) 0 0
\(527\) 3.23098e14 0.346239
\(528\) 0 0
\(529\) −8.99770e14 −0.944333
\(530\) 0 0
\(531\) −8.07575e14 −0.830163
\(532\) 0 0
\(533\) 2.11185e15 2.12649
\(534\) 0 0
\(535\) 3.57949e14 0.353081
\(536\) 0 0
\(537\) 3.70189e14 0.357738
\(538\) 0 0
\(539\) −1.40340e14 −0.132875
\(540\) 0 0
\(541\) 1.14966e15 1.06655 0.533277 0.845941i \(-0.320960\pi\)
0.533277 + 0.845941i \(0.320960\pi\)
\(542\) 0 0
\(543\) 9.37480e14 0.852242
\(544\) 0 0
\(545\) −1.26377e15 −1.12587
\(546\) 0 0
\(547\) −8.71517e14 −0.760931 −0.380466 0.924795i \(-0.624236\pi\)
−0.380466 + 0.924795i \(0.624236\pi\)
\(548\) 0 0
\(549\) −3.43439e14 −0.293902
\(550\) 0 0
\(551\) −3.14163e14 −0.263524
\(552\) 0 0
\(553\) 6.74965e14 0.555000
\(554\) 0 0
\(555\) 3.86520e15 3.11573
\(556\) 0 0
\(557\) −6.80516e14 −0.537818 −0.268909 0.963166i \(-0.586663\pi\)
−0.268909 + 0.963166i \(0.586663\pi\)
\(558\) 0 0
\(559\) 5.79235e13 0.0448838
\(560\) 0 0
\(561\) −3.63947e14 −0.276530
\(562\) 0 0
\(563\) −8.84626e14 −0.659119 −0.329559 0.944135i \(-0.606900\pi\)
−0.329559 + 0.944135i \(0.606900\pi\)
\(564\) 0 0
\(565\) 1.23846e14 0.0904927
\(566\) 0 0
\(567\) −1.93400e15 −1.38596
\(568\) 0 0
\(569\) −1.85892e15 −1.30660 −0.653300 0.757099i \(-0.726616\pi\)
−0.653300 + 0.757099i \(0.726616\pi\)
\(570\) 0 0
\(571\) 1.74453e14 0.120276 0.0601382 0.998190i \(-0.480846\pi\)
0.0601382 + 0.998190i \(0.480846\pi\)
\(572\) 0 0
\(573\) −2.40272e15 −1.62500
\(574\) 0 0
\(575\) −4.51922e14 −0.299841
\(576\) 0 0
\(577\) −6.79199e14 −0.442110 −0.221055 0.975261i \(-0.570950\pi\)
−0.221055 + 0.975261i \(0.570950\pi\)
\(578\) 0 0
\(579\) 1.82894e15 1.16807
\(580\) 0 0
\(581\) 3.23288e15 2.02592
\(582\) 0 0
\(583\) −3.42256e14 −0.210462
\(584\) 0 0
\(585\) 1.61728e15 0.975950
\(586\) 0 0
\(587\) −3.34702e14 −0.198221 −0.0991104 0.995076i \(-0.531600\pi\)
−0.0991104 + 0.995076i \(0.531600\pi\)
\(588\) 0 0
\(589\) −6.44983e14 −0.374899
\(590\) 0 0
\(591\) −4.46888e14 −0.254957
\(592\) 0 0
\(593\) 1.98542e15 1.11186 0.555931 0.831228i \(-0.312362\pi\)
0.555931 + 0.831228i \(0.312362\pi\)
\(594\) 0 0
\(595\) 1.18345e15 0.650590
\(596\) 0 0
\(597\) −2.69618e11 −0.000145509 0
\(598\) 0 0
\(599\) 4.19216e14 0.222121 0.111061 0.993814i \(-0.464575\pi\)
0.111061 + 0.993814i \(0.464575\pi\)
\(600\) 0 0
\(601\) −2.53284e15 −1.31764 −0.658822 0.752299i \(-0.728945\pi\)
−0.658822 + 0.752299i \(0.728945\pi\)
\(602\) 0 0
\(603\) −1.36459e15 −0.697041
\(604\) 0 0
\(605\) 1.99618e15 1.00126
\(606\) 0 0
\(607\) 9.43383e14 0.464676 0.232338 0.972635i \(-0.425362\pi\)
0.232338 + 0.972635i \(0.425362\pi\)
\(608\) 0 0
\(609\) 1.75644e15 0.849645
\(610\) 0 0
\(611\) −2.12372e14 −0.100895
\(612\) 0 0
\(613\) −1.26745e15 −0.591422 −0.295711 0.955277i \(-0.595557\pi\)
−0.295711 + 0.955277i \(0.595557\pi\)
\(614\) 0 0
\(615\) −6.65744e15 −3.05136
\(616\) 0 0
\(617\) 4.35186e15 1.95933 0.979663 0.200649i \(-0.0643051\pi\)
0.979663 + 0.200649i \(0.0643051\pi\)
\(618\) 0 0
\(619\) −1.26851e15 −0.561040 −0.280520 0.959848i \(-0.590507\pi\)
−0.280520 + 0.959848i \(0.590507\pi\)
\(620\) 0 0
\(621\) −3.30843e14 −0.143754
\(622\) 0 0
\(623\) −1.46509e15 −0.625433
\(624\) 0 0
\(625\) −1.56356e15 −0.655804
\(626\) 0 0
\(627\) 7.26527e14 0.299420
\(628\) 0 0
\(629\) −1.62156e15 −0.656682
\(630\) 0 0
\(631\) 3.34776e15 1.33227 0.666137 0.745830i \(-0.267947\pi\)
0.666137 + 0.745830i \(0.267947\pi\)
\(632\) 0 0
\(633\) −1.81266e15 −0.708920
\(634\) 0 0
\(635\) 7.94677e14 0.305447
\(636\) 0 0
\(637\) −7.81749e14 −0.295325
\(638\) 0 0
\(639\) 1.83739e15 0.682256
\(640\) 0 0
\(641\) −4.75533e14 −0.173565 −0.0867825 0.996227i \(-0.527659\pi\)
−0.0867825 + 0.996227i \(0.527659\pi\)
\(642\) 0 0
\(643\) 4.59955e15 1.65027 0.825135 0.564935i \(-0.191099\pi\)
0.825135 + 0.564935i \(0.191099\pi\)
\(644\) 0 0
\(645\) −1.82599e14 −0.0644050
\(646\) 0 0
\(647\) 4.98217e15 1.72761 0.863803 0.503830i \(-0.168076\pi\)
0.863803 + 0.503830i \(0.168076\pi\)
\(648\) 0 0
\(649\) 2.80421e15 0.956013
\(650\) 0 0
\(651\) 3.60601e15 1.20873
\(652\) 0 0
\(653\) −3.59598e15 −1.18521 −0.592605 0.805493i \(-0.701900\pi\)
−0.592605 + 0.805493i \(0.701900\pi\)
\(654\) 0 0
\(655\) −8.00537e15 −2.59450
\(656\) 0 0
\(657\) −1.83896e14 −0.0586088
\(658\) 0 0
\(659\) −3.26177e15 −1.02231 −0.511156 0.859488i \(-0.670783\pi\)
−0.511156 + 0.859488i \(0.670783\pi\)
\(660\) 0 0
\(661\) −2.94481e14 −0.0907714 −0.0453857 0.998970i \(-0.514452\pi\)
−0.0453857 + 0.998970i \(0.514452\pi\)
\(662\) 0 0
\(663\) −2.02733e15 −0.614611
\(664\) 0 0
\(665\) −2.36246e15 −0.704442
\(666\) 0 0
\(667\) 5.02810e14 0.147473
\(668\) 0 0
\(669\) 6.92324e15 1.99740
\(670\) 0 0
\(671\) 1.19255e15 0.338457
\(672\) 0 0
\(673\) −3.07023e15 −0.857211 −0.428606 0.903492i \(-0.640995\pi\)
−0.428606 + 0.903492i \(0.640995\pi\)
\(674\) 0 0
\(675\) 2.81891e15 0.774302
\(676\) 0 0
\(677\) −4.04157e15 −1.09223 −0.546113 0.837712i \(-0.683893\pi\)
−0.546113 + 0.837712i \(0.683893\pi\)
\(678\) 0 0
\(679\) −1.15567e15 −0.307290
\(680\) 0 0
\(681\) −3.51105e15 −0.918603
\(682\) 0 0
\(683\) −6.60126e15 −1.69947 −0.849734 0.527211i \(-0.823238\pi\)
−0.849734 + 0.527211i \(0.823238\pi\)
\(684\) 0 0
\(685\) 7.20091e15 1.82427
\(686\) 0 0
\(687\) 3.56928e15 0.889854
\(688\) 0 0
\(689\) −1.90650e15 −0.467770
\(690\) 0 0
\(691\) 9.73449e14 0.235063 0.117531 0.993069i \(-0.462502\pi\)
0.117531 + 0.993069i \(0.462502\pi\)
\(692\) 0 0
\(693\) −1.35942e15 −0.323087
\(694\) 0 0
\(695\) 9.97636e15 2.33376
\(696\) 0 0
\(697\) 2.79299e15 0.643115
\(698\) 0 0
\(699\) −3.83471e15 −0.869176
\(700\) 0 0
\(701\) 4.39327e15 0.980255 0.490127 0.871651i \(-0.336950\pi\)
0.490127 + 0.871651i \(0.336950\pi\)
\(702\) 0 0
\(703\) 3.23704e15 0.711039
\(704\) 0 0
\(705\) 6.69484e14 0.144777
\(706\) 0 0
\(707\) −7.49519e15 −1.59579
\(708\) 0 0
\(709\) 1.72732e15 0.362091 0.181046 0.983475i \(-0.442052\pi\)
0.181046 + 0.983475i \(0.442052\pi\)
\(710\) 0 0
\(711\) 1.21989e15 0.251790
\(712\) 0 0
\(713\) 1.03228e15 0.209800
\(714\) 0 0
\(715\) −5.61580e15 −1.12390
\(716\) 0 0
\(717\) −6.43696e15 −1.26860
\(718\) 0 0
\(719\) −6.55073e15 −1.27140 −0.635698 0.771938i \(-0.719288\pi\)
−0.635698 + 0.771938i \(0.719288\pi\)
\(720\) 0 0
\(721\) 8.37467e15 1.60075
\(722\) 0 0
\(723\) −3.30748e15 −0.622639
\(724\) 0 0
\(725\) −4.28413e15 −0.794334
\(726\) 0 0
\(727\) −2.68611e15 −0.490552 −0.245276 0.969453i \(-0.578879\pi\)
−0.245276 + 0.969453i \(0.578879\pi\)
\(728\) 0 0
\(729\) 6.57047e14 0.118194
\(730\) 0 0
\(731\) 7.66054e13 0.0135742
\(732\) 0 0
\(733\) −3.79856e14 −0.0663052 −0.0331526 0.999450i \(-0.510555\pi\)
−0.0331526 + 0.999450i \(0.510555\pi\)
\(734\) 0 0
\(735\) 2.46440e15 0.423770
\(736\) 0 0
\(737\) 4.73839e15 0.802711
\(738\) 0 0
\(739\) 1.97557e15 0.329722 0.164861 0.986317i \(-0.447282\pi\)
0.164861 + 0.986317i \(0.447282\pi\)
\(740\) 0 0
\(741\) 4.04705e15 0.665485
\(742\) 0 0
\(743\) 7.86579e15 1.27439 0.637197 0.770701i \(-0.280094\pi\)
0.637197 + 0.770701i \(0.280094\pi\)
\(744\) 0 0
\(745\) −1.12839e16 −1.80136
\(746\) 0 0
\(747\) 5.84292e15 0.919107
\(748\) 0 0
\(749\) −1.67600e15 −0.259791
\(750\) 0 0
\(751\) −5.45429e15 −0.833141 −0.416571 0.909103i \(-0.636768\pi\)
−0.416571 + 0.909103i \(0.636768\pi\)
\(752\) 0 0
\(753\) 9.32223e15 1.40329
\(754\) 0 0
\(755\) 9.41400e15 1.39658
\(756\) 0 0
\(757\) −1.14636e16 −1.67608 −0.838039 0.545611i \(-0.816298\pi\)
−0.838039 + 0.545611i \(0.816298\pi\)
\(758\) 0 0
\(759\) −1.16279e15 −0.167560
\(760\) 0 0
\(761\) −7.25092e15 −1.02986 −0.514929 0.857233i \(-0.672182\pi\)
−0.514929 + 0.857233i \(0.672182\pi\)
\(762\) 0 0
\(763\) 5.91728e15 0.828394
\(764\) 0 0
\(765\) 2.13890e15 0.295156
\(766\) 0 0
\(767\) 1.56206e16 2.12482
\(768\) 0 0
\(769\) 1.06294e16 1.42533 0.712664 0.701506i \(-0.247488\pi\)
0.712664 + 0.701506i \(0.247488\pi\)
\(770\) 0 0
\(771\) −1.54673e16 −2.04463
\(772\) 0 0
\(773\) −3.37768e14 −0.0440181 −0.0220090 0.999758i \(-0.507006\pi\)
−0.0220090 + 0.999758i \(0.507006\pi\)
\(774\) 0 0
\(775\) −8.79540e15 −1.13005
\(776\) 0 0
\(777\) −1.80978e16 −2.29250
\(778\) 0 0
\(779\) −5.57549e15 −0.696349
\(780\) 0 0
\(781\) −6.38012e15 −0.785685
\(782\) 0 0
\(783\) −3.13632e15 −0.380830
\(784\) 0 0
\(785\) −4.79807e15 −0.574491
\(786\) 0 0
\(787\) 1.05334e16 1.24368 0.621839 0.783145i \(-0.286386\pi\)
0.621839 + 0.783145i \(0.286386\pi\)
\(788\) 0 0
\(789\) 6.96816e15 0.811324
\(790\) 0 0
\(791\) −5.79875e14 −0.0665830
\(792\) 0 0
\(793\) 6.64299e15 0.752248
\(794\) 0 0
\(795\) 6.01009e15 0.671215
\(796\) 0 0
\(797\) 1.44072e16 1.58693 0.793467 0.608613i \(-0.208274\pi\)
0.793467 + 0.608613i \(0.208274\pi\)
\(798\) 0 0
\(799\) −2.80868e14 −0.0305137
\(800\) 0 0
\(801\) −2.64792e15 −0.283743
\(802\) 0 0
\(803\) 6.38556e14 0.0674937
\(804\) 0 0
\(805\) 3.78106e15 0.394217
\(806\) 0 0
\(807\) −1.45572e16 −1.49718
\(808\) 0 0
\(809\) 3.25295e15 0.330036 0.165018 0.986291i \(-0.447232\pi\)
0.165018 + 0.986291i \(0.447232\pi\)
\(810\) 0 0
\(811\) −3.71598e15 −0.371928 −0.185964 0.982557i \(-0.559541\pi\)
−0.185964 + 0.982557i \(0.559541\pi\)
\(812\) 0 0
\(813\) 1.55396e16 1.53442
\(814\) 0 0
\(815\) 1.53231e16 1.49273
\(816\) 0 0
\(817\) −1.52923e14 −0.0146978
\(818\) 0 0
\(819\) −7.57249e15 −0.718087
\(820\) 0 0
\(821\) −1.73451e16 −1.62289 −0.811444 0.584430i \(-0.801318\pi\)
−0.811444 + 0.584430i \(0.801318\pi\)
\(822\) 0 0
\(823\) −1.13360e16 −1.04655 −0.523274 0.852165i \(-0.675290\pi\)
−0.523274 + 0.852165i \(0.675290\pi\)
\(824\) 0 0
\(825\) 9.90739e15 0.902532
\(826\) 0 0
\(827\) 2.73855e14 0.0246173 0.0123086 0.999924i \(-0.496082\pi\)
0.0123086 + 0.999924i \(0.496082\pi\)
\(828\) 0 0
\(829\) −6.81354e14 −0.0604398 −0.0302199 0.999543i \(-0.509621\pi\)
−0.0302199 + 0.999543i \(0.509621\pi\)
\(830\) 0 0
\(831\) −4.51461e15 −0.395198
\(832\) 0 0
\(833\) −1.03389e15 −0.0893151
\(834\) 0 0
\(835\) 3.82277e15 0.325914
\(836\) 0 0
\(837\) −6.43894e15 −0.541782
\(838\) 0 0
\(839\) −1.25824e16 −1.04489 −0.522447 0.852672i \(-0.674981\pi\)
−0.522447 + 0.852672i \(0.674981\pi\)
\(840\) 0 0
\(841\) −7.43398e15 −0.609318
\(842\) 0 0
\(843\) 2.63083e16 2.12834
\(844\) 0 0
\(845\) −1.24108e16 −0.991034
\(846\) 0 0
\(847\) −9.34661e15 −0.736708
\(848\) 0 0
\(849\) −8.13237e15 −0.632739
\(850\) 0 0
\(851\) −5.18079e15 −0.397909
\(852\) 0 0
\(853\) 1.74651e16 1.32419 0.662097 0.749418i \(-0.269667\pi\)
0.662097 + 0.749418i \(0.269667\pi\)
\(854\) 0 0
\(855\) −4.26976e15 −0.319588
\(856\) 0 0
\(857\) 1.42451e14 0.0105262 0.00526310 0.999986i \(-0.498325\pi\)
0.00526310 + 0.999986i \(0.498325\pi\)
\(858\) 0 0
\(859\) 1.42828e16 1.04196 0.520981 0.853569i \(-0.325566\pi\)
0.520981 + 0.853569i \(0.325566\pi\)
\(860\) 0 0
\(861\) 3.11717e16 2.24514
\(862\) 0 0
\(863\) −2.56691e16 −1.82537 −0.912684 0.408666i \(-0.865994\pi\)
−0.912684 + 0.408666i \(0.865994\pi\)
\(864\) 0 0
\(865\) 1.88627e16 1.32439
\(866\) 0 0
\(867\) 1.50031e16 1.04010
\(868\) 0 0
\(869\) −4.23592e15 −0.289961
\(870\) 0 0
\(871\) 2.63947e16 1.78409
\(872\) 0 0
\(873\) −2.08868e15 −0.139410
\(874\) 0 0
\(875\) −6.86586e15 −0.452533
\(876\) 0 0
\(877\) −2.75472e16 −1.79300 −0.896500 0.443043i \(-0.853899\pi\)
−0.896500 + 0.443043i \(0.853899\pi\)
\(878\) 0 0
\(879\) 5.42933e15 0.348985
\(880\) 0 0
\(881\) −6.19012e14 −0.0392945 −0.0196472 0.999807i \(-0.506254\pi\)
−0.0196472 + 0.999807i \(0.506254\pi\)
\(882\) 0 0
\(883\) −1.45657e16 −0.913162 −0.456581 0.889682i \(-0.650926\pi\)
−0.456581 + 0.889682i \(0.650926\pi\)
\(884\) 0 0
\(885\) −4.92424e16 −3.04896
\(886\) 0 0
\(887\) 1.37845e16 0.842971 0.421485 0.906835i \(-0.361509\pi\)
0.421485 + 0.906835i \(0.361509\pi\)
\(888\) 0 0
\(889\) −3.72087e15 −0.224742
\(890\) 0 0
\(891\) 1.21373e16 0.724095
\(892\) 0 0
\(893\) 5.60681e14 0.0330395
\(894\) 0 0
\(895\) 7.55443e15 0.439719
\(896\) 0 0
\(897\) −6.47720e15 −0.372417
\(898\) 0 0
\(899\) 9.78578e15 0.555798
\(900\) 0 0
\(901\) −2.52141e15 −0.141467
\(902\) 0 0
\(903\) 8.54971e14 0.0473881
\(904\) 0 0
\(905\) 1.91311e16 1.04755
\(906\) 0 0
\(907\) −1.60515e16 −0.868312 −0.434156 0.900838i \(-0.642953\pi\)
−0.434156 + 0.900838i \(0.642953\pi\)
\(908\) 0 0
\(909\) −1.35464e16 −0.723971
\(910\) 0 0
\(911\) −5.36888e15 −0.283487 −0.141743 0.989903i \(-0.545271\pi\)
−0.141743 + 0.989903i \(0.545271\pi\)
\(912\) 0 0
\(913\) −2.02888e16 −1.05844
\(914\) 0 0
\(915\) −2.09414e16 −1.07942
\(916\) 0 0
\(917\) 3.74831e16 1.90899
\(918\) 0 0
\(919\) 1.82347e16 0.917621 0.458811 0.888534i \(-0.348276\pi\)
0.458811 + 0.888534i \(0.348276\pi\)
\(920\) 0 0
\(921\) 2.90116e16 1.44259
\(922\) 0 0
\(923\) −3.55399e16 −1.74625
\(924\) 0 0
\(925\) 4.41423e16 2.14326
\(926\) 0 0
\(927\) 1.51359e16 0.726221
\(928\) 0 0
\(929\) 1.38866e16 0.658429 0.329214 0.944255i \(-0.393216\pi\)
0.329214 + 0.944255i \(0.393216\pi\)
\(930\) 0 0
\(931\) 2.06389e15 0.0967081
\(932\) 0 0
\(933\) 1.00396e16 0.464911
\(934\) 0 0
\(935\) −7.42706e15 −0.339901
\(936\) 0 0
\(937\) −3.44922e16 −1.56010 −0.780051 0.625716i \(-0.784807\pi\)
−0.780051 + 0.625716i \(0.784807\pi\)
\(938\) 0 0
\(939\) −1.34774e16 −0.602483
\(940\) 0 0
\(941\) −3.72679e15 −0.164662 −0.0823308 0.996605i \(-0.526236\pi\)
−0.0823308 + 0.996605i \(0.526236\pi\)
\(942\) 0 0
\(943\) 8.92343e15 0.389688
\(944\) 0 0
\(945\) −2.35847e16 −1.01802
\(946\) 0 0
\(947\) 3.18404e16 1.35848 0.679240 0.733916i \(-0.262310\pi\)
0.679240 + 0.733916i \(0.262310\pi\)
\(948\) 0 0
\(949\) 3.55701e15 0.150010
\(950\) 0 0
\(951\) −1.65719e16 −0.690842
\(952\) 0 0
\(953\) −2.83117e15 −0.116669 −0.0583344 0.998297i \(-0.518579\pi\)
−0.0583344 + 0.998297i \(0.518579\pi\)
\(954\) 0 0
\(955\) −4.90323e16 −1.99739
\(956\) 0 0
\(957\) −1.10230e16 −0.443898
\(958\) 0 0
\(959\) −3.37164e16 −1.34227
\(960\) 0 0
\(961\) −5.31805e15 −0.209302
\(962\) 0 0
\(963\) −3.02910e15 −0.117861
\(964\) 0 0
\(965\) 3.73231e16 1.43575
\(966\) 0 0
\(967\) 2.32651e16 0.884827 0.442414 0.896811i \(-0.354122\pi\)
0.442414 + 0.896811i \(0.354122\pi\)
\(968\) 0 0
\(969\) 5.35234e15 0.201262
\(970\) 0 0
\(971\) 2.26973e16 0.843857 0.421928 0.906629i \(-0.361353\pi\)
0.421928 + 0.906629i \(0.361353\pi\)
\(972\) 0 0
\(973\) −4.67117e16 −1.71714
\(974\) 0 0
\(975\) 5.51882e16 2.00595
\(976\) 0 0
\(977\) 1.97456e16 0.709660 0.354830 0.934931i \(-0.384539\pi\)
0.354830 + 0.934931i \(0.384539\pi\)
\(978\) 0 0
\(979\) 9.19457e15 0.326758
\(980\) 0 0
\(981\) 1.06945e16 0.375822
\(982\) 0 0
\(983\) −8.32703e15 −0.289365 −0.144682 0.989478i \(-0.546216\pi\)
−0.144682 + 0.989478i \(0.546216\pi\)
\(984\) 0 0
\(985\) −9.11963e15 −0.313385
\(986\) 0 0
\(987\) −3.13469e15 −0.106525
\(988\) 0 0
\(989\) 2.44750e14 0.00822513
\(990\) 0 0
\(991\) −2.72947e16 −0.907138 −0.453569 0.891221i \(-0.649849\pi\)
−0.453569 + 0.891221i \(0.649849\pi\)
\(992\) 0 0
\(993\) −1.38861e16 −0.456416
\(994\) 0 0
\(995\) −5.50209e12 −0.000178855 0
\(996\) 0 0
\(997\) 3.85037e16 1.23788 0.618941 0.785437i \(-0.287562\pi\)
0.618941 + 0.785437i \(0.287562\pi\)
\(998\) 0 0
\(999\) 3.23157e16 1.02755
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 \(a_p\))