Properties

Label 16.12.a.a.1.1
Level 16
Weight 12
Character 16.1
Self dual Yes
Analytic conductor 12.293
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 16.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(12.293490889\)
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 \(\chi\) = 16.1

$q$-expansion

\(f(q)\) \(=\) \(q-252.000 q^{3} +4830.00 q^{5} +16744.0 q^{7} -113643. q^{9} +O(q^{10})\) \(q-252.000 q^{3} +4830.00 q^{5} +16744.0 q^{7} -113643. q^{9} -534612. q^{11} -577738. q^{13} -1.21716e6 q^{15} -6.90593e6 q^{17} -1.06614e7 q^{19} -4.21949e6 q^{21} -1.86433e7 q^{23} -2.54992e7 q^{25} +7.32791e7 q^{27} +1.28407e8 q^{29} +5.28432e7 q^{31} +1.34722e8 q^{33} +8.08735e7 q^{35} -1.82213e8 q^{37} +1.45590e8 q^{39} +3.08120e8 q^{41} +1.71257e7 q^{43} -5.48896e8 q^{45} -2.68735e9 q^{47} -1.69697e9 q^{49} +1.74030e9 q^{51} -1.59606e9 q^{53} -2.58218e9 q^{55} +2.68668e9 q^{57} +5.18920e9 q^{59} +6.95648e9 q^{61} -1.90284e9 q^{63} -2.79047e9 q^{65} +1.54818e10 q^{67} +4.69810e9 q^{69} -9.79149e9 q^{71} +1.46379e9 q^{73} +6.42580e9 q^{75} -8.95154e9 q^{77} -3.81168e10 q^{79} +1.66519e9 q^{81} +2.93351e10 q^{83} -3.33557e10 q^{85} -3.23585e10 q^{87} -2.49929e10 q^{89} -9.67365e9 q^{91} -1.33165e10 q^{93} -5.14947e10 q^{95} +7.50136e10 q^{97} +6.07549e10 q^{99} +O(q^{100})\)

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
\(3\) −252.000 −0.598734 −0.299367 0.954138i \(-0.596775\pi\)
−0.299367 + 0.954138i \(0.596775\pi\)
\(4\) 0 0
\(5\) 4830.00 0.691213 0.345607 0.938379i \(-0.387673\pi\)
0.345607 + 0.938379i \(0.387673\pi\)
\(6\) 0 0
\(7\) 16744.0 0.376548 0.188274 0.982117i \(-0.439711\pi\)
0.188274 + 0.982117i \(0.439711\pi\)
\(8\) 0 0
\(9\) −113643. −0.641518
\(10\) 0 0
\(11\) −534612. −1.00087 −0.500436 0.865773i \(-0.666827\pi\)
−0.500436 + 0.865773i \(0.666827\pi\)
\(12\) 0 0
\(13\) −577738. −0.431561 −0.215781 0.976442i \(-0.569230\pi\)
−0.215781 + 0.976442i \(0.569230\pi\)
\(14\) 0 0
\(15\) −1.21716e6 −0.413853
\(16\) 0 0
\(17\) −6.90593e6 −1.17965 −0.589825 0.807531i \(-0.700803\pi\)
−0.589825 + 0.807531i \(0.700803\pi\)
\(18\) 0 0
\(19\) −1.06614e7 −0.987803 −0.493901 0.869518i \(-0.664430\pi\)
−0.493901 + 0.869518i \(0.664430\pi\)
\(20\) 0 0
\(21\) −4.21949e6 −0.225452
\(22\) 0 0
\(23\) −1.86433e7 −0.603975 −0.301988 0.953312i \(-0.597650\pi\)
−0.301988 + 0.953312i \(0.597650\pi\)
\(24\) 0 0
\(25\) −2.54992e7 −0.522224
\(26\) 0 0
\(27\) 7.32791e7 0.982832
\(28\) 0 0
\(29\) 1.28407e8 1.16251 0.581257 0.813720i \(-0.302561\pi\)
0.581257 + 0.813720i \(0.302561\pi\)
\(30\) 0 0
\(31\) 5.28432e7 0.331512 0.165756 0.986167i \(-0.446994\pi\)
0.165756 + 0.986167i \(0.446994\pi\)
\(32\) 0 0
\(33\) 1.34722e8 0.599256
\(34\) 0 0
\(35\) 8.08735e7 0.260275
\(36\) 0 0
\(37\) −1.82213e8 −0.431987 −0.215993 0.976395i \(-0.569299\pi\)
−0.215993 + 0.976395i \(0.569299\pi\)
\(38\) 0 0
\(39\) 1.45590e8 0.258390
\(40\) 0 0
\(41\) 3.08120e8 0.415345 0.207673 0.978198i \(-0.433411\pi\)
0.207673 + 0.978198i \(0.433411\pi\)
\(42\) 0 0
\(43\) 1.71257e7 0.0177653 0.00888264 0.999961i \(-0.497173\pi\)
0.00888264 + 0.999961i \(0.497173\pi\)
\(44\) 0 0
\(45\) −5.48896e8 −0.443426
\(46\) 0 0
\(47\) −2.68735e9 −1.70917 −0.854586 0.519310i \(-0.826189\pi\)
−0.854586 + 0.519310i \(0.826189\pi\)
\(48\) 0 0
\(49\) −1.69697e9 −0.858212
\(50\) 0 0
\(51\) 1.74030e9 0.706296
\(52\) 0 0
\(53\) −1.59606e9 −0.524241 −0.262120 0.965035i \(-0.584422\pi\)
−0.262120 + 0.965035i \(0.584422\pi\)
\(54\) 0 0
\(55\) −2.58218e9 −0.691817
\(56\) 0 0
\(57\) 2.68668e9 0.591431
\(58\) 0 0
\(59\) 5.18920e9 0.944963 0.472481 0.881341i \(-0.343358\pi\)
0.472481 + 0.881341i \(0.343358\pi\)
\(60\) 0 0
\(61\) 6.95648e9 1.05457 0.527285 0.849689i \(-0.323210\pi\)
0.527285 + 0.849689i \(0.323210\pi\)
\(62\) 0 0
\(63\) −1.90284e9 −0.241562
\(64\) 0 0
\(65\) −2.79047e9 −0.298301
\(66\) 0 0
\(67\) 1.54818e10 1.40091 0.700456 0.713696i \(-0.252980\pi\)
0.700456 + 0.713696i \(0.252980\pi\)
\(68\) 0 0
\(69\) 4.69810e9 0.361620
\(70\) 0 0
\(71\) −9.79149e9 −0.644062 −0.322031 0.946729i \(-0.604366\pi\)
−0.322031 + 0.946729i \(0.604366\pi\)
\(72\) 0 0
\(73\) 1.46379e9 0.0826425 0.0413212 0.999146i \(-0.486843\pi\)
0.0413212 + 0.999146i \(0.486843\pi\)
\(74\) 0 0
\(75\) 6.42580e9 0.312673
\(76\) 0 0
\(77\) −8.95154e9 −0.376876
\(78\) 0 0
\(79\) −3.81168e10 −1.39370 −0.696848 0.717219i \(-0.745415\pi\)
−0.696848 + 0.717219i \(0.745415\pi\)
\(80\) 0 0
\(81\) 1.66519e9 0.0530635
\(82\) 0 0
\(83\) 2.93351e10 0.817444 0.408722 0.912659i \(-0.365975\pi\)
0.408722 + 0.912659i \(0.365975\pi\)
\(84\) 0 0
\(85\) −3.33557e10 −0.815390
\(86\) 0 0
\(87\) −3.23585e10 −0.696037
\(88\) 0 0
\(89\) −2.49929e10 −0.474430 −0.237215 0.971457i \(-0.576235\pi\)
−0.237215 + 0.971457i \(0.576235\pi\)
\(90\) 0 0
\(91\) −9.67365e9 −0.162503
\(92\) 0 0
\(93\) −1.33165e10 −0.198488
\(94\) 0 0
\(95\) −5.14947e10 −0.682782
\(96\) 0 0
\(97\) 7.50136e10 0.886942 0.443471 0.896289i \(-0.353747\pi\)
0.443471 + 0.896289i \(0.353747\pi\)
\(98\) 0 0
\(99\) 6.07549e10 0.642078
\(100\) 0 0
\(101\) 8.17430e10 0.773896 0.386948 0.922101i \(-0.373529\pi\)
0.386948 + 0.922101i \(0.373529\pi\)
\(102\) 0 0
\(103\) 2.25755e11 1.91881 0.959407 0.282025i \(-0.0910061\pi\)
0.959407 + 0.282025i \(0.0910061\pi\)
\(104\) 0 0
\(105\) −2.03801e10 −0.155835
\(106\) 0 0
\(107\) −9.02413e10 −0.622006 −0.311003 0.950409i \(-0.600665\pi\)
−0.311003 + 0.950409i \(0.600665\pi\)
\(108\) 0 0
\(109\) 7.34827e10 0.457445 0.228723 0.973492i \(-0.426545\pi\)
0.228723 + 0.973492i \(0.426545\pi\)
\(110\) 0 0
\(111\) 4.59178e10 0.258645
\(112\) 0 0
\(113\) −8.51469e10 −0.434748 −0.217374 0.976088i \(-0.569749\pi\)
−0.217374 + 0.976088i \(0.569749\pi\)
\(114\) 0 0
\(115\) −9.00470e10 −0.417476
\(116\) 0 0
\(117\) 6.56559e10 0.276854
\(118\) 0 0
\(119\) −1.15633e11 −0.444195
\(120\) 0 0
\(121\) 4.98320e8 0.00174658
\(122\) 0 0
\(123\) −7.76464e10 −0.248681
\(124\) 0 0
\(125\) −3.59001e11 −1.05218
\(126\) 0 0
\(127\) 2.62717e11 0.705615 0.352808 0.935696i \(-0.385227\pi\)
0.352808 + 0.935696i \(0.385227\pi\)
\(128\) 0 0
\(129\) −4.31568e9 −0.0106367
\(130\) 0 0
\(131\) −6.31529e11 −1.43021 −0.715107 0.699015i \(-0.753622\pi\)
−0.715107 + 0.699015i \(0.753622\pi\)
\(132\) 0 0
\(133\) −1.78515e11 −0.371955
\(134\) 0 0
\(135\) 3.53938e11 0.679347
\(136\) 0 0
\(137\) −2.97199e11 −0.526119 −0.263059 0.964780i \(-0.584732\pi\)
−0.263059 + 0.964780i \(0.584732\pi\)
\(138\) 0 0
\(139\) −5.96794e11 −0.975535 −0.487767 0.872974i \(-0.662189\pi\)
−0.487767 + 0.872974i \(0.662189\pi\)
\(140\) 0 0
\(141\) 6.77212e11 1.02334
\(142\) 0 0
\(143\) 3.08866e11 0.431938
\(144\) 0 0
\(145\) 6.20204e11 0.803546
\(146\) 0 0
\(147\) 4.27635e11 0.513840
\(148\) 0 0
\(149\) −1.11543e12 −1.24428 −0.622142 0.782905i \(-0.713737\pi\)
−0.622142 + 0.782905i \(0.713737\pi\)
\(150\) 0 0
\(151\) 8.24447e11 0.854653 0.427326 0.904097i \(-0.359456\pi\)
0.427326 + 0.904097i \(0.359456\pi\)
\(152\) 0 0
\(153\) 7.84811e11 0.756767
\(154\) 0 0
\(155\) 2.55233e11 0.229146
\(156\) 0 0
\(157\) 1.31512e12 1.10031 0.550156 0.835062i \(-0.314568\pi\)
0.550156 + 0.835062i \(0.314568\pi\)
\(158\) 0 0
\(159\) 4.02206e11 0.313881
\(160\) 0 0
\(161\) −3.12163e11 −0.227425
\(162\) 0 0
\(163\) 3.57833e11 0.243584 0.121792 0.992556i \(-0.461136\pi\)
0.121792 + 0.992556i \(0.461136\pi\)
\(164\) 0 0
\(165\) 6.50708e11 0.414214
\(166\) 0 0
\(167\) −2.75483e12 −1.64117 −0.820587 0.571521i \(-0.806354\pi\)
−0.820587 + 0.571521i \(0.806354\pi\)
\(168\) 0 0
\(169\) −1.45838e12 −0.813755
\(170\) 0 0
\(171\) 1.21160e12 0.633693
\(172\) 0 0
\(173\) −9.50387e11 −0.466280 −0.233140 0.972443i \(-0.574900\pi\)
−0.233140 + 0.972443i \(0.574900\pi\)
\(174\) 0 0
\(175\) −4.26959e11 −0.196642
\(176\) 0 0
\(177\) −1.30768e12 −0.565781
\(178\) 0 0
\(179\) −1.68138e12 −0.683873 −0.341936 0.939723i \(-0.611083\pi\)
−0.341936 + 0.939723i \(0.611083\pi\)
\(180\) 0 0
\(181\) −9.96774e11 −0.381386 −0.190693 0.981650i \(-0.561073\pi\)
−0.190693 + 0.981650i \(0.561073\pi\)
\(182\) 0 0
\(183\) −1.75303e12 −0.631406
\(184\) 0 0
\(185\) −8.80090e11 −0.298595
\(186\) 0 0
\(187\) 3.69200e12 1.18068
\(188\) 0 0
\(189\) 1.22698e12 0.370083
\(190\) 0 0
\(191\) −2.76240e12 −0.786328 −0.393164 0.919468i \(-0.628619\pi\)
−0.393164 + 0.919468i \(0.628619\pi\)
\(192\) 0 0
\(193\) 5.44239e12 1.46293 0.731466 0.681878i \(-0.238836\pi\)
0.731466 + 0.681878i \(0.238836\pi\)
\(194\) 0 0
\(195\) 7.03200e11 0.178603
\(196\) 0 0
\(197\) −2.87609e12 −0.690619 −0.345309 0.938489i \(-0.612226\pi\)
−0.345309 + 0.938489i \(0.612226\pi\)
\(198\) 0 0
\(199\) −7.28391e11 −0.165452 −0.0827262 0.996572i \(-0.526363\pi\)
−0.0827262 + 0.996572i \(0.526363\pi\)
\(200\) 0 0
\(201\) −3.90142e12 −0.838773
\(202\) 0 0
\(203\) 2.15004e12 0.437742
\(204\) 0 0
\(205\) 1.48822e12 0.287092
\(206\) 0 0
\(207\) 2.11868e12 0.387461
\(208\) 0 0
\(209\) 5.69972e12 0.988665
\(210\) 0 0
\(211\) 6.79317e12 1.11820 0.559099 0.829101i \(-0.311147\pi\)
0.559099 + 0.829101i \(0.311147\pi\)
\(212\) 0 0
\(213\) 2.46745e12 0.385622
\(214\) 0 0
\(215\) 8.27172e10 0.0122796
\(216\) 0 0
\(217\) 8.84806e11 0.124830
\(218\) 0 0
\(219\) −3.68875e11 −0.0494808
\(220\) 0 0
\(221\) 3.98982e12 0.509092
\(222\) 0 0
\(223\) −7.33486e12 −0.890667 −0.445333 0.895365i \(-0.646915\pi\)
−0.445333 + 0.895365i \(0.646915\pi\)
\(224\) 0 0
\(225\) 2.89781e12 0.335016
\(226\) 0 0
\(227\) 1.35984e12 0.149743 0.0748713 0.997193i \(-0.476145\pi\)
0.0748713 + 0.997193i \(0.476145\pi\)
\(228\) 0 0
\(229\) −1.18244e13 −1.24075 −0.620375 0.784305i \(-0.713020\pi\)
−0.620375 + 0.784305i \(0.713020\pi\)
\(230\) 0 0
\(231\) 2.25579e12 0.225649
\(232\) 0 0
\(233\) −1.75634e13 −1.67552 −0.837761 0.546038i \(-0.816135\pi\)
−0.837761 + 0.546038i \(0.816135\pi\)
\(234\) 0 0
\(235\) −1.29799e13 −1.18140
\(236\) 0 0
\(237\) 9.60545e12 0.834452
\(238\) 0 0
\(239\) 7.13958e12 0.592221 0.296111 0.955154i \(-0.404310\pi\)
0.296111 + 0.955154i \(0.404310\pi\)
\(240\) 0 0
\(241\) −2.31307e11 −0.0183271 −0.00916357 0.999958i \(-0.502917\pi\)
−0.00916357 + 0.999958i \(0.502917\pi\)
\(242\) 0 0
\(243\) −1.34008e13 −1.01460
\(244\) 0 0
\(245\) −8.19634e12 −0.593207
\(246\) 0 0
\(247\) 6.15951e12 0.426297
\(248\) 0 0
\(249\) −7.39245e12 −0.489431
\(250\) 0 0
\(251\) −1.29831e13 −0.822567 −0.411284 0.911507i \(-0.634919\pi\)
−0.411284 + 0.911507i \(0.634919\pi\)
\(252\) 0 0
\(253\) 9.96692e12 0.604502
\(254\) 0 0
\(255\) 8.40563e12 0.488201
\(256\) 0 0
\(257\) 2.39612e13 1.33314 0.666571 0.745442i \(-0.267761\pi\)
0.666571 + 0.745442i \(0.267761\pi\)
\(258\) 0 0
\(259\) −3.05098e12 −0.162664
\(260\) 0 0
\(261\) −1.45925e13 −0.745774
\(262\) 0 0
\(263\) 2.42737e13 1.18954 0.594771 0.803895i \(-0.297243\pi\)
0.594771 + 0.803895i \(0.297243\pi\)
\(264\) 0 0
\(265\) −7.70895e12 −0.362362
\(266\) 0 0
\(267\) 6.29822e12 0.284057
\(268\) 0 0
\(269\) 2.58377e13 1.11845 0.559225 0.829016i \(-0.311099\pi\)
0.559225 + 0.829016i \(0.311099\pi\)
\(270\) 0 0
\(271\) 3.76793e12 0.156593 0.0782964 0.996930i \(-0.475052\pi\)
0.0782964 + 0.996930i \(0.475052\pi\)
\(272\) 0 0
\(273\) 2.43776e12 0.0972963
\(274\) 0 0
\(275\) 1.36322e13 0.522680
\(276\) 0 0
\(277\) −1.64189e13 −0.604931 −0.302466 0.953160i \(-0.597810\pi\)
−0.302466 + 0.953160i \(0.597810\pi\)
\(278\) 0 0
\(279\) −6.00526e12 −0.212671
\(280\) 0 0
\(281\) 2.10357e13 0.716263 0.358132 0.933671i \(-0.383414\pi\)
0.358132 + 0.933671i \(0.383414\pi\)
\(282\) 0 0
\(283\) −1.67132e13 −0.547310 −0.273655 0.961828i \(-0.588233\pi\)
−0.273655 + 0.961828i \(0.588233\pi\)
\(284\) 0 0
\(285\) 1.29767e13 0.408805
\(286\) 0 0
\(287\) 5.15917e12 0.156397
\(288\) 0 0
\(289\) 1.34200e13 0.391575
\(290\) 0 0
\(291\) −1.89034e13 −0.531042
\(292\) 0 0
\(293\) −2.39269e13 −0.647312 −0.323656 0.946175i \(-0.604912\pi\)
−0.323656 + 0.946175i \(0.604912\pi\)
\(294\) 0 0
\(295\) 2.50639e13 0.653171
\(296\) 0 0
\(297\) −3.91759e13 −0.983690
\(298\) 0 0
\(299\) 1.07709e13 0.260652
\(300\) 0 0
\(301\) 2.86753e11 0.00668947
\(302\) 0 0
\(303\) −2.05992e13 −0.463358
\(304\) 0 0
\(305\) 3.35998e13 0.728933
\(306\) 0 0
\(307\) −1.53111e13 −0.320439 −0.160219 0.987081i \(-0.551220\pi\)
−0.160219 + 0.987081i \(0.551220\pi\)
\(308\) 0 0
\(309\) −5.68903e13 −1.14886
\(310\) 0 0
\(311\) −4.98752e13 −0.972080 −0.486040 0.873936i \(-0.661559\pi\)
−0.486040 + 0.873936i \(0.661559\pi\)
\(312\) 0 0
\(313\) −9.94808e13 −1.87174 −0.935870 0.352345i \(-0.885384\pi\)
−0.935870 + 0.352345i \(0.885384\pi\)
\(314\) 0 0
\(315\) −9.19071e12 −0.166971
\(316\) 0 0
\(317\) 8.33692e13 1.46278 0.731392 0.681958i \(-0.238871\pi\)
0.731392 + 0.681958i \(0.238871\pi\)
\(318\) 0 0
\(319\) −6.86477e13 −1.16353
\(320\) 0 0
\(321\) 2.27408e13 0.372416
\(322\) 0 0
\(323\) 7.36271e13 1.16526
\(324\) 0 0
\(325\) 1.47319e13 0.225372
\(326\) 0 0
\(327\) −1.85176e13 −0.273888
\(328\) 0 0
\(329\) −4.49970e13 −0.643585
\(330\) 0 0
\(331\) 6.35840e13 0.879618 0.439809 0.898091i \(-0.355046\pi\)
0.439809 + 0.898091i \(0.355046\pi\)
\(332\) 0 0
\(333\) 2.07073e13 0.277127
\(334\) 0 0
\(335\) 7.47772e13 0.968329
\(336\) 0 0
\(337\) 1.21001e14 1.51644 0.758221 0.651997i \(-0.226069\pi\)
0.758221 + 0.651997i \(0.226069\pi\)
\(338\) 0 0
\(339\) 2.14570e13 0.260298
\(340\) 0 0
\(341\) −2.82506e13 −0.331802
\(342\) 0 0
\(343\) −6.15223e13 −0.699705
\(344\) 0 0
\(345\) 2.26918e13 0.249957
\(346\) 0 0
\(347\) 1.55662e14 1.66100 0.830499 0.557020i \(-0.188055\pi\)
0.830499 + 0.557020i \(0.188055\pi\)
\(348\) 0 0
\(349\) −2.56430e13 −0.265112 −0.132556 0.991176i \(-0.542318\pi\)
−0.132556 + 0.991176i \(0.542318\pi\)
\(350\) 0 0
\(351\) −4.23361e13 −0.424152
\(352\) 0 0
\(353\) 2.49098e13 0.241885 0.120943 0.992659i \(-0.461408\pi\)
0.120943 + 0.992659i \(0.461408\pi\)
\(354\) 0 0
\(355\) −4.72929e13 −0.445184
\(356\) 0 0
\(357\) 2.91395e13 0.265954
\(358\) 0 0
\(359\) −1.57584e14 −1.39474 −0.697370 0.716712i \(-0.745646\pi\)
−0.697370 + 0.716712i \(0.745646\pi\)
\(360\) 0 0
\(361\) −2.82438e12 −0.0242457
\(362\) 0 0
\(363\) −1.25577e11 −0.00104574
\(364\) 0 0
\(365\) 7.07011e12 0.0571236
\(366\) 0 0
\(367\) 1.77901e14 1.39481 0.697406 0.716676i \(-0.254338\pi\)
0.697406 + 0.716676i \(0.254338\pi\)
\(368\) 0 0
\(369\) −3.50157e13 −0.266452
\(370\) 0 0
\(371\) −2.67244e13 −0.197402
\(372\) 0 0
\(373\) −5.51617e13 −0.395585 −0.197792 0.980244i \(-0.563377\pi\)
−0.197792 + 0.980244i \(0.563377\pi\)
\(374\) 0 0
\(375\) 9.04683e13 0.629976
\(376\) 0 0
\(377\) −7.41854e13 −0.501696
\(378\) 0 0
\(379\) −1.46463e14 −0.962083 −0.481042 0.876698i \(-0.659741\pi\)
−0.481042 + 0.876698i \(0.659741\pi\)
\(380\) 0 0
\(381\) −6.62047e13 −0.422476
\(382\) 0 0
\(383\) −2.31450e14 −1.43504 −0.717519 0.696539i \(-0.754722\pi\)
−0.717519 + 0.696539i \(0.754722\pi\)
\(384\) 0 0
\(385\) −4.32360e13 −0.260502
\(386\) 0 0
\(387\) −1.94622e12 −0.0113967
\(388\) 0 0
\(389\) −1.49872e14 −0.853093 −0.426547 0.904466i \(-0.640270\pi\)
−0.426547 + 0.904466i \(0.640270\pi\)
\(390\) 0 0
\(391\) 1.28749e14 0.712480
\(392\) 0 0
\(393\) 1.59145e14 0.856317
\(394\) 0 0
\(395\) −1.84104e14 −0.963341
\(396\) 0 0
\(397\) 2.08111e14 1.05912 0.529562 0.848271i \(-0.322356\pi\)
0.529562 + 0.848271i \(0.322356\pi\)
\(398\) 0 0
\(399\) 4.49857e13 0.222702
\(400\) 0 0
\(401\) −1.33408e14 −0.642521 −0.321261 0.946991i \(-0.604107\pi\)
−0.321261 + 0.946991i \(0.604107\pi\)
\(402\) 0 0
\(403\) −3.05295e13 −0.143068
\(404\) 0 0
\(405\) 8.04286e12 0.0366782
\(406\) 0 0
\(407\) 9.74134e13 0.432364
\(408\) 0 0
\(409\) −2.06168e14 −0.890722 −0.445361 0.895351i \(-0.646925\pi\)
−0.445361 + 0.895351i \(0.646925\pi\)
\(410\) 0 0
\(411\) 7.48941e13 0.315005
\(412\) 0 0
\(413\) 8.68880e13 0.355824
\(414\) 0 0
\(415\) 1.41689e14 0.565028
\(416\) 0 0
\(417\) 1.50392e14 0.584085
\(418\) 0 0
\(419\) −7.34035e13 −0.277677 −0.138838 0.990315i \(-0.544337\pi\)
−0.138838 + 0.990315i \(0.544337\pi\)
\(420\) 0 0
\(421\) 1.71112e14 0.630563 0.315282 0.948998i \(-0.397901\pi\)
0.315282 + 0.948998i \(0.397901\pi\)
\(422\) 0 0
\(423\) 3.05398e14 1.09646
\(424\) 0 0
\(425\) 1.76096e14 0.616042
\(426\) 0 0
\(427\) 1.16479e14 0.397096
\(428\) 0 0
\(429\) −7.78341e13 −0.258616
\(430\) 0 0
\(431\) 7.17758e13 0.232463 0.116231 0.993222i \(-0.462919\pi\)
0.116231 + 0.993222i \(0.462919\pi\)
\(432\) 0 0
\(433\) 9.98812e13 0.315356 0.157678 0.987491i \(-0.449599\pi\)
0.157678 + 0.987491i \(0.449599\pi\)
\(434\) 0 0
\(435\) −1.56291e14 −0.481110
\(436\) 0 0
\(437\) 1.98764e14 0.596608
\(438\) 0 0
\(439\) 2.90312e13 0.0849788 0.0424894 0.999097i \(-0.486471\pi\)
0.0424894 + 0.999097i \(0.486471\pi\)
\(440\) 0 0
\(441\) 1.92848e14 0.550558
\(442\) 0 0
\(443\) −3.28370e14 −0.914414 −0.457207 0.889360i \(-0.651150\pi\)
−0.457207 + 0.889360i \(0.651150\pi\)
\(444\) 0 0
\(445\) −1.20716e14 −0.327932
\(446\) 0 0
\(447\) 2.81089e14 0.744994
\(448\) 0 0
\(449\) −6.12368e14 −1.58364 −0.791822 0.610752i \(-0.790867\pi\)
−0.791822 + 0.610752i \(0.790867\pi\)
\(450\) 0 0
\(451\) −1.64725e14 −0.415708
\(452\) 0 0
\(453\) −2.07761e14 −0.511709
\(454\) 0 0
\(455\) −4.67237e13 −0.112325
\(456\) 0 0
\(457\) 3.03483e14 0.712189 0.356095 0.934450i \(-0.384108\pi\)
0.356095 + 0.934450i \(0.384108\pi\)
\(458\) 0 0
\(459\) −5.06060e14 −1.15940
\(460\) 0 0
\(461\) −7.29308e14 −1.63138 −0.815691 0.578487i \(-0.803643\pi\)
−0.815691 + 0.578487i \(0.803643\pi\)
\(462\) 0 0
\(463\) −1.22188e14 −0.266891 −0.133445 0.991056i \(-0.542604\pi\)
−0.133445 + 0.991056i \(0.542604\pi\)
\(464\) 0 0
\(465\) −6.43186e13 −0.137197
\(466\) 0 0
\(467\) 6.17381e14 1.28621 0.643103 0.765780i \(-0.277647\pi\)
0.643103 + 0.765780i \(0.277647\pi\)
\(468\) 0 0
\(469\) 2.59228e14 0.527510
\(470\) 0 0
\(471\) −3.31409e14 −0.658794
\(472\) 0 0
\(473\) −9.15561e12 −0.0177808
\(474\) 0 0
\(475\) 2.71858e14 0.515854
\(476\) 0 0
\(477\) 1.81381e14 0.336310
\(478\) 0 0
\(479\) −1.05084e15 −1.90410 −0.952052 0.305938i \(-0.901030\pi\)
−0.952052 + 0.305938i \(0.901030\pi\)
\(480\) 0 0
\(481\) 1.05272e14 0.186429
\(482\) 0 0
\(483\) 7.86651e13 0.136167
\(484\) 0 0
\(485\) 3.62316e14 0.613066
\(486\) 0 0
\(487\) 2.19910e14 0.363777 0.181889 0.983319i \(-0.441779\pi\)
0.181889 + 0.983319i \(0.441779\pi\)
\(488\) 0 0
\(489\) −9.01739e13 −0.145842
\(490\) 0 0
\(491\) 4.83863e14 0.765199 0.382599 0.923914i \(-0.375029\pi\)
0.382599 + 0.923914i \(0.375029\pi\)
\(492\) 0 0
\(493\) −8.86768e14 −1.37136
\(494\) 0 0
\(495\) 2.93446e14 0.443813
\(496\) 0 0
\(497\) −1.63949e14 −0.242520
\(498\) 0 0
\(499\) 1.08878e14 0.157538 0.0787691 0.996893i \(-0.474901\pi\)
0.0787691 + 0.996893i \(0.474901\pi\)
\(500\) 0 0
\(501\) 6.94218e14 0.982626
\(502\) 0 0
\(503\) −5.06588e14 −0.701506 −0.350753 0.936468i \(-0.614074\pi\)
−0.350753 + 0.936468i \(0.614074\pi\)
\(504\) 0 0
\(505\) 3.94818e14 0.534927
\(506\) 0 0
\(507\) 3.67512e14 0.487222
\(508\) 0 0
\(509\) 8.57534e13 0.111251 0.0556254 0.998452i \(-0.482285\pi\)
0.0556254 + 0.998452i \(0.482285\pi\)
\(510\) 0 0
\(511\) 2.45097e13 0.0311188
\(512\) 0 0
\(513\) −7.81259e14 −0.970844
\(514\) 0 0
\(515\) 1.09040e15 1.32631
\(516\) 0 0
\(517\) 1.43669e15 1.71066
\(518\) 0 0
\(519\) 2.39498e14 0.279178
\(520\) 0 0
\(521\) 9.27575e14 1.05862 0.529312 0.848428i \(-0.322450\pi\)
0.529312 + 0.848428i \(0.322450\pi\)
\(522\) 0 0
\(523\) 2.18187e13 0.0243820 0.0121910 0.999926i \(-0.496119\pi\)
0.0121910 + 0.999926i \(0.496119\pi\)
\(524\) 0 0
\(525\) 1.07594e14 0.117736
\(526\) 0 0
\(527\) −3.64931e14 −0.391069
\(528\) 0 0
\(529\) −6.05238e14 −0.635214
\(530\) 0 0
\(531\) −5.89717e14 −0.606211
\(532\) 0 0
\(533\) −1.78013e14 −0.179247
\(534\) 0 0
\(535\) −4.35865e14 −0.429939
\(536\) 0 0
\(537\) 4.23709e14 0.409458
\(538\) 0 0
\(539\) 9.07218e14 0.858961
\(540\) 0 0
\(541\) −1.69527e15 −1.57273 −0.786363 0.617765i \(-0.788038\pi\)
−0.786363 + 0.617765i \(0.788038\pi\)
\(542\) 0 0
\(543\) 2.51187e14 0.228349
\(544\) 0 0
\(545\) 3.54921e14 0.316192
\(546\) 0 0
\(547\) −7.52145e14 −0.656706 −0.328353 0.944555i \(-0.606494\pi\)
−0.328353 + 0.944555i \(0.606494\pi\)
\(548\) 0 0
\(549\) −7.90555e14 −0.676526
\(550\) 0 0
\(551\) −1.36900e15 −1.14834
\(552\) 0 0
\(553\) −6.38228e14 −0.524793
\(554\) 0 0
\(555\) 2.21783e14 0.178779
\(556\) 0 0
\(557\) 1.87489e14 0.148174 0.0740870 0.997252i \(-0.476396\pi\)
0.0740870 + 0.997252i \(0.476396\pi\)
\(558\) 0 0
\(559\) −9.89417e12 −0.00766681
\(560\) 0 0
\(561\) −9.30383e14 −0.706913
\(562\) 0 0
\(563\) −2.44971e14 −0.182524 −0.0912618 0.995827i \(-0.529090\pi\)
−0.0912618 + 0.995827i \(0.529090\pi\)
\(564\) 0 0
\(565\) −4.11259e14 −0.300503
\(566\) 0 0
\(567\) 2.78819e13 0.0199809
\(568\) 0 0
\(569\) 1.35243e15 0.950596 0.475298 0.879825i \(-0.342340\pi\)
0.475298 + 0.879825i \(0.342340\pi\)
\(570\) 0 0
\(571\) −1.43223e15 −0.987447 −0.493723 0.869619i \(-0.664364\pi\)
−0.493723 + 0.869619i \(0.664364\pi\)
\(572\) 0 0
\(573\) 6.96126e14 0.470801
\(574\) 0 0
\(575\) 4.75389e14 0.315410
\(576\) 0 0
\(577\) −8.77659e14 −0.571293 −0.285647 0.958335i \(-0.592208\pi\)
−0.285647 + 0.958335i \(0.592208\pi\)
\(578\) 0 0
\(579\) −1.37148e15 −0.875907
\(580\) 0 0
\(581\) 4.91187e14 0.307807
\(582\) 0 0
\(583\) 8.53271e14 0.524698
\(584\) 0 0
\(585\) 3.17118e14 0.191365
\(586\) 0 0
\(587\) 2.43425e15 1.44164 0.720818 0.693124i \(-0.243766\pi\)
0.720818 + 0.693124i \(0.243766\pi\)
\(588\) 0 0
\(589\) −5.63383e14 −0.327469
\(590\) 0 0
\(591\) 7.24775e14 0.413497
\(592\) 0 0
\(593\) −3.03318e14 −0.169863 −0.0849313 0.996387i \(-0.527067\pi\)
−0.0849313 + 0.996387i \(0.527067\pi\)
\(594\) 0 0
\(595\) −5.58507e14 −0.307033
\(596\) 0 0
\(597\) 1.83555e14 0.0990619
\(598\) 0 0
\(599\) 1.70198e15 0.901795 0.450898 0.892576i \(-0.351104\pi\)
0.450898 + 0.892576i \(0.351104\pi\)
\(600\) 0 0
\(601\) 2.33922e15 1.21692 0.608458 0.793586i \(-0.291788\pi\)
0.608458 + 0.793586i \(0.291788\pi\)
\(602\) 0 0
\(603\) −1.75940e15 −0.898710
\(604\) 0 0
\(605\) 2.40689e12 0.00120726
\(606\) 0 0
\(607\) 2.49607e15 1.22947 0.614737 0.788732i \(-0.289262\pi\)
0.614737 + 0.788732i \(0.289262\pi\)
\(608\) 0 0
\(609\) −5.41810e14 −0.262091
\(610\) 0 0
\(611\) 1.55258e15 0.737612
\(612\) 0 0
\(613\) 2.47301e15 1.15397 0.576983 0.816756i \(-0.304230\pi\)
0.576983 + 0.816756i \(0.304230\pi\)
\(614\) 0 0
\(615\) −3.75032e14 −0.171892
\(616\) 0 0
\(617\) 2.43368e13 0.0109571 0.00547854 0.999985i \(-0.498256\pi\)
0.00547854 + 0.999985i \(0.498256\pi\)
\(618\) 0 0
\(619\) −4.22545e15 −1.86885 −0.934425 0.356160i \(-0.884086\pi\)
−0.934425 + 0.356160i \(0.884086\pi\)
\(620\) 0 0
\(621\) −1.36616e15 −0.593606
\(622\) 0 0
\(623\) −4.18481e14 −0.178645
\(624\) 0 0
\(625\) −4.88896e14 −0.205058
\(626\) 0 0
\(627\) −1.43633e15 −0.591947
\(628\) 0 0
\(629\) 1.25835e15 0.509594
\(630\) 0 0
\(631\) 4.26326e15 1.69660 0.848302 0.529513i \(-0.177625\pi\)
0.848302 + 0.529513i \(0.177625\pi\)
\(632\) 0 0
\(633\) −1.71188e15 −0.669503
\(634\) 0 0
\(635\) 1.26892e15 0.487731
\(636\) 0 0
\(637\) 9.80401e14 0.370371
\(638\) 0 0
\(639\) 1.11273e15 0.413177
\(640\) 0 0
\(641\) 1.00830e15 0.368018 0.184009 0.982925i \(-0.441092\pi\)
0.184009 + 0.982925i \(0.441092\pi\)
\(642\) 0 0
\(643\) −3.03982e14 −0.109066 −0.0545328 0.998512i \(-0.517367\pi\)
−0.0545328 + 0.998512i \(0.517367\pi\)
\(644\) 0 0
\(645\) −2.08447e13 −0.00735221
\(646\) 0 0
\(647\) −3.43583e15 −1.19140 −0.595700 0.803207i \(-0.703125\pi\)
−0.595700 + 0.803207i \(0.703125\pi\)
\(648\) 0 0
\(649\) −2.77421e15 −0.945788
\(650\) 0 0
\(651\) −2.22971e14 −0.0747400
\(652\) 0 0
\(653\) −1.18539e15 −0.390695 −0.195347 0.980734i \(-0.562583\pi\)
−0.195347 + 0.980734i \(0.562583\pi\)
\(654\) 0 0
\(655\) −3.05028e15 −0.988583
\(656\) 0 0
\(657\) −1.66350e14 −0.0530167
\(658\) 0 0
\(659\) 2.26510e15 0.709934 0.354967 0.934879i \(-0.384492\pi\)
0.354967 + 0.934879i \(0.384492\pi\)
\(660\) 0 0
\(661\) −5.33012e15 −1.64297 −0.821484 0.570232i \(-0.806853\pi\)
−0.821484 + 0.570232i \(0.806853\pi\)
\(662\) 0 0
\(663\) −1.00543e15 −0.304810
\(664\) 0 0
\(665\) −8.62227e14 −0.257100
\(666\) 0 0
\(667\) −2.39392e15 −0.702130
\(668\) 0 0
\(669\) 1.84839e15 0.533272
\(670\) 0 0
\(671\) −3.71902e15 −1.05549
\(672\) 0 0
\(673\) 4.74120e15 1.32375 0.661874 0.749615i \(-0.269761\pi\)
0.661874 + 0.749615i \(0.269761\pi\)
\(674\) 0 0
\(675\) −1.86856e15 −0.513259
\(676\) 0 0
\(677\) −1.41307e15 −0.381880 −0.190940 0.981602i \(-0.561154\pi\)
−0.190940 + 0.981602i \(0.561154\pi\)
\(678\) 0 0
\(679\) 1.25603e15 0.333976
\(680\) 0 0
\(681\) −3.42680e14 −0.0896559
\(682\) 0 0
\(683\) 3.03116e15 0.780359 0.390180 0.920739i \(-0.372413\pi\)
0.390180 + 0.920739i \(0.372413\pi\)
\(684\) 0 0
\(685\) −1.43547e15 −0.363660
\(686\) 0 0
\(687\) 2.97975e15 0.742879
\(688\) 0 0
\(689\) 9.22102e14 0.226242
\(690\) 0 0
\(691\) 2.74731e15 0.663405 0.331703 0.943384i \(-0.392377\pi\)
0.331703 + 0.943384i \(0.392377\pi\)
\(692\) 0 0
\(693\) 1.01728e15 0.241773
\(694\) 0 0
\(695\) −2.88251e15 −0.674303
\(696\) 0 0
\(697\) −2.12786e15 −0.489962
\(698\) 0 0
\(699\) 4.42597e15 1.00319
\(700\) 0 0
\(701\) 5.72747e15 1.27795 0.638974 0.769228i \(-0.279359\pi\)
0.638974 + 0.769228i \(0.279359\pi\)
\(702\) 0 0
\(703\) 1.94265e15 0.426718
\(704\) 0 0
\(705\) 3.27093e15 0.707345
\(706\) 0 0
\(707\) 1.36870e15 0.291409
\(708\) 0 0
\(709\) 6.98326e14 0.146388 0.0731938 0.997318i \(-0.476681\pi\)
0.0731938 + 0.997318i \(0.476681\pi\)
\(710\) 0 0
\(711\) 4.33171e15 0.894081
\(712\) 0 0
\(713\) −9.85170e14 −0.200225
\(714\) 0 0
\(715\) 1.49182e15 0.298561
\(716\) 0 0
\(717\) −1.79917e15 −0.354583
\(718\) 0 0
\(719\) −9.70979e15 −1.88452 −0.942260 0.334882i \(-0.891304\pi\)
−0.942260 + 0.334882i \(0.891304\pi\)
\(720\) 0 0
\(721\) 3.78004e15 0.722525
\(722\) 0 0
\(723\) 5.82893e13 0.0109731
\(724\) 0 0
\(725\) −3.27427e15 −0.607093
\(726\) 0 0
\(727\) −2.46469e15 −0.450114 −0.225057 0.974346i \(-0.572257\pi\)
−0.225057 + 0.974346i \(0.572257\pi\)
\(728\) 0 0
\(729\) 3.08202e15 0.554413
\(730\) 0 0
\(731\) −1.18269e14 −0.0209568
\(732\) 0 0
\(733\) 7.91285e15 1.38121 0.690607 0.723230i \(-0.257343\pi\)
0.690607 + 0.723230i \(0.257343\pi\)
\(734\) 0 0
\(735\) 2.06548e15 0.355173
\(736\) 0 0
\(737\) −8.27677e15 −1.40213
\(738\) 0 0
\(739\) 8.40694e15 1.40312 0.701558 0.712613i \(-0.252488\pi\)
0.701558 + 0.712613i \(0.252488\pi\)
\(740\) 0 0
\(741\) −1.55220e15 −0.255239
\(742\) 0 0
\(743\) −1.36287e15 −0.220809 −0.110404 0.993887i \(-0.535215\pi\)
−0.110404 + 0.993887i \(0.535215\pi\)
\(744\) 0 0
\(745\) −5.38754e15 −0.860065
\(746\) 0 0
\(747\) −3.33373e15 −0.524405
\(748\) 0 0
\(749\) −1.51100e15 −0.234215
\(750\) 0 0
\(751\) −6.81722e15 −1.04133 −0.520664 0.853762i \(-0.674316\pi\)
−0.520664 + 0.853762i \(0.674316\pi\)
\(752\) 0 0
\(753\) 3.27173e15 0.492499
\(754\) 0 0
\(755\) 3.98208e15 0.590747
\(756\) 0 0
\(757\) −6.67049e14 −0.0975282 −0.0487641 0.998810i \(-0.515528\pi\)
−0.0487641 + 0.998810i \(0.515528\pi\)
\(758\) 0 0
\(759\) −2.51166e15 −0.361936
\(760\) 0 0
\(761\) −7.74408e15 −1.09990 −0.549951 0.835197i \(-0.685354\pi\)
−0.549951 + 0.835197i \(0.685354\pi\)
\(762\) 0 0
\(763\) 1.23039e15 0.172250
\(764\) 0 0
\(765\) 3.79064e15 0.523088
\(766\) 0 0
\(767\) −2.99800e15 −0.407809
\(768\) 0 0
\(769\) 2.52411e15 0.338465 0.169232 0.985576i \(-0.445871\pi\)
0.169232 + 0.985576i \(0.445871\pi\)
\(770\) 0 0
\(771\) −6.03822e15 −0.798197
\(772\) 0 0
\(773\) −1.11453e16 −1.45246 −0.726229 0.687453i \(-0.758729\pi\)
−0.726229 + 0.687453i \(0.758729\pi\)
\(774\) 0 0
\(775\) −1.34746e15 −0.173124
\(776\) 0 0
\(777\) 7.68847e14 0.0973922
\(778\) 0 0
\(779\) −3.28500e15 −0.410279
\(780\) 0 0
\(781\) 5.23465e15 0.644624
\(782\) 0 0
\(783\) 9.40952e15 1.14256
\(784\) 0 0
\(785\) 6.35201e15 0.760551
\(786\) 0 0
\(787\) −1.32271e16 −1.56172 −0.780861 0.624705i \(-0.785219\pi\)
−0.780861 + 0.624705i \(0.785219\pi\)
\(788\) 0 0
\(789\) −6.11698e15 −0.712219
\(790\) 0 0
\(791\) −1.42570e15 −0.163703
\(792\) 0 0
\(793\) −4.01902e15 −0.455112
\(794\) 0 0
\(795\) 1.94266e15 0.216958
\(796\) 0 0
\(797\) 2.30248e15 0.253615 0.126807 0.991927i \(-0.459527\pi\)
0.126807 + 0.991927i \(0.459527\pi\)
\(798\) 0 0
\(799\) 1.85587e16 2.01623
\(800\) 0 0
\(801\) 2.84027e15 0.304355
\(802\) 0 0
\(803\) −7.82560e14 −0.0827146
\(804\) 0 0
\(805\) −1.50775e15 −0.157199
\(806\) 0 0
\(807\) −6.51110e15 −0.669653
\(808\) 0 0
\(809\) 5.60472e15 0.568639 0.284320 0.958730i \(-0.408232\pi\)
0.284320 + 0.958730i \(0.408232\pi\)
\(810\) 0 0
\(811\) 5.08516e15 0.508968 0.254484 0.967077i \(-0.418094\pi\)
0.254484 + 0.967077i \(0.418094\pi\)
\(812\) 0 0
\(813\) −9.49519e14 −0.0937574
\(814\) 0 0
\(815\) 1.72833e15 0.168368
\(816\) 0 0
\(817\) −1.82584e14 −0.0175486
\(818\) 0 0
\(819\) 1.09934e15 0.104249
\(820\) 0 0
\(821\) 2.79111e14 0.0261150 0.0130575 0.999915i \(-0.495844\pi\)
0.0130575 + 0.999915i \(0.495844\pi\)
\(822\) 0 0
\(823\) 1.35265e16 1.24878 0.624391 0.781112i \(-0.285347\pi\)
0.624391 + 0.781112i \(0.285347\pi\)
\(824\) 0 0
\(825\) −3.43531e15 −0.312946
\(826\) 0 0
\(827\) −2.72544e14 −0.0244994 −0.0122497 0.999925i \(-0.503899\pi\)
−0.0122497 + 0.999925i \(0.503899\pi\)
\(828\) 0 0
\(829\) 1.80459e16 1.60077 0.800385 0.599486i \(-0.204628\pi\)
0.800385 + 0.599486i \(0.204628\pi\)
\(830\) 0 0
\(831\) 4.13757e15 0.362193
\(832\) 0 0
\(833\) 1.17191e16 1.01239
\(834\) 0 0
\(835\) −1.33058e16 −1.13440
\(836\) 0 0
\(837\) 3.87230e15 0.325821
\(838\) 0 0
\(839\) 7.96183e15 0.661184 0.330592 0.943774i \(-0.392752\pi\)
0.330592 + 0.943774i \(0.392752\pi\)
\(840\) 0 0
\(841\) 4.28775e15 0.351440
\(842\) 0 0
\(843\) −5.30100e15 −0.428851
\(844\) 0 0
\(845\) −7.04397e15 −0.562478
\(846\) 0 0
\(847\) 8.34387e12 0.000657671 0
\(848\) 0 0
\(849\) 4.21172e15 0.327693
\(850\) 0 0
\(851\) 3.39705e15 0.260909
\(852\) 0 0
\(853\) −1.49826e16 −1.13598 −0.567988 0.823037i \(-0.692278\pi\)
−0.567988 + 0.823037i \(0.692278\pi\)
\(854\) 0 0
\(855\) 5.85201e15 0.438017
\(856\) 0 0
\(857\) −2.22561e16 −1.64458 −0.822290 0.569068i \(-0.807304\pi\)
−0.822290 + 0.569068i \(0.807304\pi\)
\(858\) 0 0
\(859\) −5.44237e15 −0.397032 −0.198516 0.980098i \(-0.563612\pi\)
−0.198516 + 0.980098i \(0.563612\pi\)
\(860\) 0 0
\(861\) −1.30011e15 −0.0936403
\(862\) 0 0
\(863\) −1.08110e16 −0.768787 −0.384393 0.923169i \(-0.625589\pi\)
−0.384393 + 0.923169i \(0.625589\pi\)
\(864\) 0 0
\(865\) −4.59037e15 −0.322299
\(866\) 0 0
\(867\) −3.38185e15 −0.234449
\(868\) 0 0
\(869\) 2.03777e16 1.39491
\(870\) 0 0
\(871\) −8.94444e15 −0.604579
\(872\) 0 0
\(873\) −8.52477e15 −0.568989
\(874\) 0 0
\(875\) −6.01111e15 −0.396197
\(876\) 0 0
\(877\) −2.81024e16 −1.82914 −0.914568 0.404431i \(-0.867470\pi\)
−0.914568 + 0.404431i \(0.867470\pi\)
\(878\) 0 0
\(879\) 6.02957e15 0.387568
\(880\) 0 0
\(881\) 4.22209e15 0.268016 0.134008 0.990980i \(-0.457215\pi\)
0.134008 + 0.990980i \(0.457215\pi\)
\(882\) 0 0
\(883\) −5.16092e14 −0.0323551 −0.0161776 0.999869i \(-0.505150\pi\)
−0.0161776 + 0.999869i \(0.505150\pi\)
\(884\) 0 0
\(885\) −6.31609e15 −0.391075
\(886\) 0 0
\(887\) −5.71906e15 −0.349740 −0.174870 0.984592i \(-0.555950\pi\)
−0.174870 + 0.984592i \(0.555950\pi\)
\(888\) 0 0
\(889\) 4.39894e15 0.265698
\(890\) 0 0
\(891\) −8.90230e14 −0.0531098
\(892\) 0 0
\(893\) 2.86510e16 1.68832
\(894\) 0 0
\(895\) −8.12109e15 −0.472702
\(896\) 0 0
\(897\) −2.71427e15 −0.156061
\(898\) 0 0
\(899\) 6.78541e15 0.385388
\(900\) 0 0
\(901\) 1.10223e16 0.618421
\(902\) 0 0
\(903\) −7.22617e13 −0.00400521
\(904\) 0 0
\(905\) −4.81442e15 −0.263619
\(906\) 0 0
\(907\) 8.43778e13 0.00456445 0.00228222 0.999997i \(-0.499274\pi\)
0.00228222 + 0.999997i \(0.499274\pi\)
\(908\) 0 0
\(909\) −9.28952e15 −0.496468
\(910\) 0 0
\(911\) 1.10091e16 0.581298 0.290649 0.956830i \(-0.406129\pi\)
0.290649 + 0.956830i \(0.406129\pi\)
\(912\) 0 0
\(913\) −1.56829e16 −0.818158
\(914\) 0 0
\(915\) −8.46715e15 −0.436437
\(916\) 0 0
\(917\) −1.05743e16 −0.538544
\(918\) 0 0
\(919\) 4.86351e15 0.244746 0.122373 0.992484i \(-0.460950\pi\)
0.122373 + 0.992484i \(0.460950\pi\)
\(920\) 0 0
\(921\) 3.85840e15 0.191857
\(922\) 0 0
\(923\) 5.65691e15 0.277952
\(924\) 0 0
\(925\) 4.64630e15 0.225594
\(926\) 0 0
\(927\) −2.56555e16 −1.23095
\(928\) 0 0
\(929\) 3.57534e15 0.169524 0.0847620 0.996401i \(-0.472987\pi\)
0.0847620 + 0.996401i \(0.472987\pi\)
\(930\) 0 0
\(931\) 1.80921e16 0.847744
\(932\) 0 0
\(933\) 1.25685e16 0.582017
\(934\) 0 0
\(935\) 1.78323e16 0.816102
\(936\) 0 0
\(937\) 3.86373e16 1.74759 0.873795 0.486295i \(-0.161652\pi\)
0.873795 + 0.486295i \(0.161652\pi\)
\(938\) 0 0
\(939\) 2.50692e16 1.12067
\(940\) 0 0
\(941\) −3.48997e16 −1.54198 −0.770991 0.636846i \(-0.780239\pi\)
−0.770991 + 0.636846i \(0.780239\pi\)
\(942\) 0 0
\(943\) −5.74437e15 −0.250858
\(944\) 0 0
\(945\) 5.92634e15 0.255806
\(946\) 0 0
\(947\) 2.85123e16 1.21649 0.608243 0.793751i \(-0.291875\pi\)
0.608243 + 0.793751i \(0.291875\pi\)
\(948\) 0 0
\(949\) −8.45688e14 −0.0356653
\(950\) 0 0
\(951\) −2.10091e16 −0.875817
\(952\) 0 0
\(953\) 4.00334e16 1.64973 0.824863 0.565332i \(-0.191252\pi\)
0.824863 + 0.565332i \(0.191252\pi\)
\(954\) 0 0
\(955\) −1.33424e16 −0.543520
\(956\) 0 0
\(957\) 1.72992e16 0.696644
\(958\) 0 0
\(959\) −4.97630e15 −0.198109
\(960\) 0 0
\(961\) −2.26161e16 −0.890100
\(962\) 0 0
\(963\) 1.02553e16 0.399028
\(964\) 0 0
\(965\) 2.62867e16 1.01120
\(966\) 0 0
\(967\) −1.84953e16 −0.703422 −0.351711 0.936109i \(-0.614400\pi\)
−0.351711 + 0.936109i \(0.614400\pi\)
\(968\) 0 0
\(969\) −1.85540e16 −0.697682
\(970\) 0 0
\(971\) 2.14877e16 0.798884 0.399442 0.916759i \(-0.369204\pi\)
0.399442 + 0.916759i \(0.369204\pi\)
\(972\) 0 0
\(973\) −9.99271e15 −0.367335
\(974\) 0 0
\(975\) −3.71243e15 −0.134938
\(976\) 0 0
\(977\) −8.73880e15 −0.314074 −0.157037 0.987593i \(-0.550194\pi\)
−0.157037 + 0.987593i \(0.550194\pi\)
\(978\) 0 0
\(979\) 1.33615e16 0.474844
\(980\) 0 0
\(981\) −8.35079e15 −0.293459
\(982\) 0 0
\(983\) −1.18924e16 −0.413263 −0.206631 0.978419i \(-0.566250\pi\)
−0.206631 + 0.978419i \(0.566250\pi\)
\(984\) 0 0
\(985\) −1.38915e16 −0.477365
\(986\) 0 0
\(987\) 1.13392e16 0.385336
\(988\) 0 0
\(989\) −3.19279e14 −0.0107298
\(990\) 0 0
\(991\) −2.34409e16 −0.779056 −0.389528 0.921015i \(-0.627362\pi\)
−0.389528 + 0.921015i \(0.627362\pi\)
\(992\) 0 0
\(993\) −1.60232e16 −0.526657
\(994\) 0 0
\(995\) −3.51813e15 −0.114363
\(996\) 0 0
\(997\) −2.14004e16 −0.688016 −0.344008 0.938967i \(-0.611785\pi\)
−0.344008 + 0.938967i \(0.611785\pi\)
\(998\) 0 0
\(999\) −1.33524e16 −0.424571
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 \(a_p\))