Properties

Label 8.14.a.a.1.1
Level 8
Weight 14
Character 8.1
Self dual Yes
Analytic conductor 8.578
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 14 \)
Character orbit: \([\chi]\) = 8.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(8.57847431615\)
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 \(\chi\) = 8.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-12.0000 q^{3}\) \(-4330.00 q^{5}\) \(-139992. q^{7}\) \(-1.59418e6 q^{9}\) \(+O(q^{10})\) \(q\)\(-12.0000 q^{3}\) \(-4330.00 q^{5}\) \(-139992. q^{7}\) \(-1.59418e6 q^{9}\) \(-6.48432e6 q^{11}\) \(-2.25880e7 q^{13}\) \(+51960.0 q^{15}\) \(-2.37323e7 q^{17}\) \(+3.25345e8 q^{19}\) \(+1.67990e6 q^{21}\) \(+9.21601e8 q^{23}\) \(-1.20195e9 q^{25}\) \(+3.82620e7 q^{27}\) \(-3.86588e9 q^{29}\) \(-2.25340e9 q^{31}\) \(+7.78119e7 q^{33}\) \(+6.06165e8 q^{35}\) \(+1.82504e10 q^{37}\) \(+2.71056e8 q^{39}\) \(+3.44228e10 q^{41}\) \(-1.71925e10 q^{43}\) \(+6.90280e9 q^{45}\) \(-6.73717e10 q^{47}\) \(-7.72913e10 q^{49}\) \(+2.84787e8 q^{51}\) \(-8.72812e10 q^{53}\) \(+2.80771e10 q^{55}\) \(-3.90414e9 q^{57}\) \(+5.40215e11 q^{59}\) \(-5.12766e10 q^{61}\) \(+2.23172e11 q^{63}\) \(+9.78062e10 q^{65}\) \(+2.55199e10 q^{67}\) \(-1.10592e10 q^{69}\) \(-1.38750e12 q^{71}\) \(-8.19049e11 q^{73}\) \(+1.44235e10 q^{75}\) \(+9.07753e11 q^{77}\) \(-4.03094e12 q^{79}\) \(+2.54118e12 q^{81}\) \(+4.18082e12 q^{83}\) \(+1.02761e11 q^{85}\) \(+4.63906e10 q^{87}\) \(+2.67703e12 q^{89}\) \(+3.16214e12 q^{91}\) \(+2.70408e10 q^{93}\) \(-1.40874e12 q^{95}\) \(-1.40395e13 q^{97}\) \(+1.03372e13 q^{99}\) \(+O(q^{100})\)

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
\(3\) −12.0000 −0.00950371 −0.00475185 0.999989i \(-0.501513\pi\)
−0.00475185 + 0.999989i \(0.501513\pi\)
\(4\) 0 0
\(5\) −4330.00 −0.123932 −0.0619659 0.998078i \(-0.519737\pi\)
−0.0619659 + 0.998078i \(0.519737\pi\)
\(6\) 0 0
\(7\) −139992. −0.449745 −0.224872 0.974388i \(-0.572196\pi\)
−0.224872 + 0.974388i \(0.572196\pi\)
\(8\) 0 0
\(9\) −1.59418e6 −0.999910
\(10\) 0 0
\(11\) −6.48432e6 −1.10360 −0.551801 0.833976i \(-0.686059\pi\)
−0.551801 + 0.833976i \(0.686059\pi\)
\(12\) 0 0
\(13\) −2.25880e7 −1.29792 −0.648958 0.760824i \(-0.724795\pi\)
−0.648958 + 0.760824i \(0.724795\pi\)
\(14\) 0 0
\(15\) 51960.0 0.00117781
\(16\) 0 0
\(17\) −2.37323e7 −0.238463 −0.119232 0.992866i \(-0.538043\pi\)
−0.119232 + 0.992866i \(0.538043\pi\)
\(18\) 0 0
\(19\) 3.25345e8 1.58652 0.793260 0.608883i \(-0.208382\pi\)
0.793260 + 0.608883i \(0.208382\pi\)
\(20\) 0 0
\(21\) 1.67990e6 0.00427424
\(22\) 0 0
\(23\) 9.21601e8 1.29811 0.649055 0.760741i \(-0.275164\pi\)
0.649055 + 0.760741i \(0.275164\pi\)
\(24\) 0 0
\(25\) −1.20195e9 −0.984641
\(26\) 0 0
\(27\) 3.82620e7 0.0190066
\(28\) 0 0
\(29\) −3.86588e9 −1.20687 −0.603436 0.797411i \(-0.706202\pi\)
−0.603436 + 0.797411i \(0.706202\pi\)
\(30\) 0 0
\(31\) −2.25340e9 −0.456024 −0.228012 0.973658i \(-0.573223\pi\)
−0.228012 + 0.973658i \(0.573223\pi\)
\(32\) 0 0
\(33\) 7.78119e7 0.0104883
\(34\) 0 0
\(35\) 6.06165e8 0.0557377
\(36\) 0 0
\(37\) 1.82504e10 1.16939 0.584697 0.811252i \(-0.301213\pi\)
0.584697 + 0.811252i \(0.301213\pi\)
\(38\) 0 0
\(39\) 2.71056e8 0.0123350
\(40\) 0 0
\(41\) 3.44228e10 1.13175 0.565877 0.824490i \(-0.308538\pi\)
0.565877 + 0.824490i \(0.308538\pi\)
\(42\) 0 0
\(43\) −1.71925e10 −0.414757 −0.207379 0.978261i \(-0.566493\pi\)
−0.207379 + 0.978261i \(0.566493\pi\)
\(44\) 0 0
\(45\) 6.90280e9 0.123921
\(46\) 0 0
\(47\) −6.73717e10 −0.911679 −0.455839 0.890062i \(-0.650661\pi\)
−0.455839 + 0.890062i \(0.650661\pi\)
\(48\) 0 0
\(49\) −7.72913e10 −0.797730
\(50\) 0 0
\(51\) 2.84787e8 0.00226628
\(52\) 0 0
\(53\) −8.72812e10 −0.540913 −0.270457 0.962732i \(-0.587175\pi\)
−0.270457 + 0.962732i \(0.587175\pi\)
\(54\) 0 0
\(55\) 2.80771e10 0.136771
\(56\) 0 0
\(57\) −3.90414e9 −0.0150778
\(58\) 0 0
\(59\) 5.40215e11 1.66736 0.833678 0.552251i \(-0.186231\pi\)
0.833678 + 0.552251i \(0.186231\pi\)
\(60\) 0 0
\(61\) −5.12766e10 −0.127431 −0.0637155 0.997968i \(-0.520295\pi\)
−0.0637155 + 0.997968i \(0.520295\pi\)
\(62\) 0 0
\(63\) 2.23172e11 0.449704
\(64\) 0 0
\(65\) 9.78062e10 0.160853
\(66\) 0 0
\(67\) 2.55199e10 0.0344662 0.0172331 0.999851i \(-0.494514\pi\)
0.0172331 + 0.999851i \(0.494514\pi\)
\(68\) 0 0
\(69\) −1.10592e10 −0.0123369
\(70\) 0 0
\(71\) −1.38750e12 −1.28545 −0.642723 0.766099i \(-0.722195\pi\)
−0.642723 + 0.766099i \(0.722195\pi\)
\(72\) 0 0
\(73\) −8.19049e11 −0.633449 −0.316724 0.948518i \(-0.602583\pi\)
−0.316724 + 0.948518i \(0.602583\pi\)
\(74\) 0 0
\(75\) 1.44235e10 0.00935774
\(76\) 0 0
\(77\) 9.07753e11 0.496339
\(78\) 0 0
\(79\) −4.03094e12 −1.86565 −0.932824 0.360332i \(-0.882663\pi\)
−0.932824 + 0.360332i \(0.882663\pi\)
\(80\) 0 0
\(81\) 2.54118e12 0.999729
\(82\) 0 0
\(83\) 4.18082e12 1.40364 0.701818 0.712357i \(-0.252372\pi\)
0.701818 + 0.712357i \(0.252372\pi\)
\(84\) 0 0
\(85\) 1.02761e11 0.0295532
\(86\) 0 0
\(87\) 4.63906e10 0.0114698
\(88\) 0 0
\(89\) 2.67703e12 0.570976 0.285488 0.958382i \(-0.407844\pi\)
0.285488 + 0.958382i \(0.407844\pi\)
\(90\) 0 0
\(91\) 3.16214e12 0.583731
\(92\) 0 0
\(93\) 2.70408e10 0.00433392
\(94\) 0 0
\(95\) −1.40874e12 −0.196620
\(96\) 0 0
\(97\) −1.40395e13 −1.71133 −0.855666 0.517528i \(-0.826852\pi\)
−0.855666 + 0.517528i \(0.826852\pi\)
\(98\) 0 0
\(99\) 1.03372e13 1.10350
\(100\) 0 0
\(101\) −6.22392e12 −0.583411 −0.291706 0.956508i \(-0.594223\pi\)
−0.291706 + 0.956508i \(0.594223\pi\)
\(102\) 0 0
\(103\) −2.11756e13 −1.74740 −0.873702 0.486461i \(-0.838288\pi\)
−0.873702 + 0.486461i \(0.838288\pi\)
\(104\) 0 0
\(105\) −7.27398e9 −0.000529715 0
\(106\) 0 0
\(107\) 1.87895e13 1.21038 0.605188 0.796083i \(-0.293098\pi\)
0.605188 + 0.796083i \(0.293098\pi\)
\(108\) 0 0
\(109\) −9.95159e12 −0.568356 −0.284178 0.958772i \(-0.591721\pi\)
−0.284178 + 0.958772i \(0.591721\pi\)
\(110\) 0 0
\(111\) −2.19005e11 −0.0111136
\(112\) 0 0
\(113\) 2.08879e13 0.943812 0.471906 0.881649i \(-0.343566\pi\)
0.471906 + 0.881649i \(0.343566\pi\)
\(114\) 0 0
\(115\) −3.99053e12 −0.160877
\(116\) 0 0
\(117\) 3.60094e13 1.29780
\(118\) 0 0
\(119\) 3.32233e12 0.107248
\(120\) 0 0
\(121\) 7.52375e12 0.217936
\(122\) 0 0
\(123\) −4.13074e11 −0.0107559
\(124\) 0 0
\(125\) 1.04901e13 0.245960
\(126\) 0 0
\(127\) −6.26814e13 −1.32561 −0.662803 0.748794i \(-0.730633\pi\)
−0.662803 + 0.748794i \(0.730633\pi\)
\(128\) 0 0
\(129\) 2.06310e11 0.00394173
\(130\) 0 0
\(131\) −6.97773e12 −0.120629 −0.0603144 0.998179i \(-0.519210\pi\)
−0.0603144 + 0.998179i \(0.519210\pi\)
\(132\) 0 0
\(133\) −4.55457e13 −0.713529
\(134\) 0 0
\(135\) −1.65675e11 −0.00235552
\(136\) 0 0
\(137\) −5.78591e13 −0.747632 −0.373816 0.927503i \(-0.621951\pi\)
−0.373816 + 0.927503i \(0.621951\pi\)
\(138\) 0 0
\(139\) −3.93498e13 −0.462750 −0.231375 0.972865i \(-0.574322\pi\)
−0.231375 + 0.972865i \(0.574322\pi\)
\(140\) 0 0
\(141\) 8.08461e11 0.00866433
\(142\) 0 0
\(143\) 1.46468e14 1.43238
\(144\) 0 0
\(145\) 1.67393e13 0.149570
\(146\) 0 0
\(147\) 9.27495e11 0.00758139
\(148\) 0 0
\(149\) −4.31370e13 −0.322953 −0.161476 0.986877i \(-0.551626\pi\)
−0.161476 + 0.986877i \(0.551626\pi\)
\(150\) 0 0
\(151\) 2.19599e14 1.50758 0.753788 0.657117i \(-0.228224\pi\)
0.753788 + 0.657117i \(0.228224\pi\)
\(152\) 0 0
\(153\) 3.78335e13 0.238442
\(154\) 0 0
\(155\) 9.75723e12 0.0565159
\(156\) 0 0
\(157\) 6.61866e13 0.352714 0.176357 0.984326i \(-0.443569\pi\)
0.176357 + 0.984326i \(0.443569\pi\)
\(158\) 0 0
\(159\) 1.04737e12 0.00514068
\(160\) 0 0
\(161\) −1.29017e14 −0.583818
\(162\) 0 0
\(163\) −2.47622e14 −1.03412 −0.517058 0.855950i \(-0.672973\pi\)
−0.517058 + 0.855950i \(0.672973\pi\)
\(164\) 0 0
\(165\) −3.36925e11 −0.00129983
\(166\) 0 0
\(167\) −6.05226e13 −0.215904 −0.107952 0.994156i \(-0.534429\pi\)
−0.107952 + 0.994156i \(0.534429\pi\)
\(168\) 0 0
\(169\) 2.07344e14 0.684586
\(170\) 0 0
\(171\) −5.18658e14 −1.58638
\(172\) 0 0
\(173\) −2.82357e14 −0.800752 −0.400376 0.916351i \(-0.631121\pi\)
−0.400376 + 0.916351i \(0.631121\pi\)
\(174\) 0 0
\(175\) 1.68264e14 0.442837
\(176\) 0 0
\(177\) −6.48257e12 −0.0158461
\(178\) 0 0
\(179\) −1.65618e14 −0.376324 −0.188162 0.982138i \(-0.560253\pi\)
−0.188162 + 0.982138i \(0.560253\pi\)
\(180\) 0 0
\(181\) 8.52134e14 1.80135 0.900673 0.434497i \(-0.143074\pi\)
0.900673 + 0.434497i \(0.143074\pi\)
\(182\) 0 0
\(183\) 6.15319e11 0.00121107
\(184\) 0 0
\(185\) −7.90242e13 −0.144925
\(186\) 0 0
\(187\) 1.53888e14 0.263168
\(188\) 0 0
\(189\) −5.35638e12 −0.00854810
\(190\) 0 0
\(191\) 9.30990e14 1.38748 0.693742 0.720223i \(-0.255961\pi\)
0.693742 + 0.720223i \(0.255961\pi\)
\(192\) 0 0
\(193\) 4.17870e14 0.581994 0.290997 0.956724i \(-0.406013\pi\)
0.290997 + 0.956724i \(0.406013\pi\)
\(194\) 0 0
\(195\) −1.17367e12 −0.00152870
\(196\) 0 0
\(197\) −1.17420e15 −1.43124 −0.715621 0.698489i \(-0.753856\pi\)
−0.715621 + 0.698489i \(0.753856\pi\)
\(198\) 0 0
\(199\) 9.52478e13 0.108720 0.0543601 0.998521i \(-0.482688\pi\)
0.0543601 + 0.998521i \(0.482688\pi\)
\(200\) 0 0
\(201\) −3.06239e11 −0.000327557 0
\(202\) 0 0
\(203\) 5.41192e14 0.542784
\(204\) 0 0
\(205\) −1.49051e14 −0.140260
\(206\) 0 0
\(207\) −1.46920e15 −1.29799
\(208\) 0 0
\(209\) −2.10964e15 −1.75089
\(210\) 0 0
\(211\) 7.61637e14 0.594172 0.297086 0.954851i \(-0.403985\pi\)
0.297086 + 0.954851i \(0.403985\pi\)
\(212\) 0 0
\(213\) 1.66500e13 0.0122165
\(214\) 0 0
\(215\) 7.44435e13 0.0514016
\(216\) 0 0
\(217\) 3.15458e14 0.205094
\(218\) 0 0
\(219\) 9.82859e12 0.00602011
\(220\) 0 0
\(221\) 5.36065e14 0.309505
\(222\) 0 0
\(223\) −1.62673e15 −0.885796 −0.442898 0.896572i \(-0.646050\pi\)
−0.442898 + 0.896572i \(0.646050\pi\)
\(224\) 0 0
\(225\) 1.91613e15 0.984552
\(226\) 0 0
\(227\) 1.50895e15 0.731991 0.365996 0.930617i \(-0.380729\pi\)
0.365996 + 0.930617i \(0.380729\pi\)
\(228\) 0 0
\(229\) 1.69644e15 0.777334 0.388667 0.921378i \(-0.372936\pi\)
0.388667 + 0.921378i \(0.372936\pi\)
\(230\) 0 0
\(231\) −1.08930e13 −0.00471706
\(232\) 0 0
\(233\) 1.27819e15 0.523339 0.261670 0.965158i \(-0.415727\pi\)
0.261670 + 0.965158i \(0.415727\pi\)
\(234\) 0 0
\(235\) 2.91720e14 0.112986
\(236\) 0 0
\(237\) 4.83712e13 0.0177306
\(238\) 0 0
\(239\) −1.10138e15 −0.382252 −0.191126 0.981566i \(-0.561214\pi\)
−0.191126 + 0.981566i \(0.561214\pi\)
\(240\) 0 0
\(241\) 9.15325e14 0.300929 0.150465 0.988615i \(-0.451923\pi\)
0.150465 + 0.988615i \(0.451923\pi\)
\(242\) 0 0
\(243\) −9.14962e13 −0.0285077
\(244\) 0 0
\(245\) 3.34671e14 0.0988641
\(246\) 0 0
\(247\) −7.34890e15 −2.05917
\(248\) 0 0
\(249\) −5.01699e13 −0.0133397
\(250\) 0 0
\(251\) 5.68301e15 1.43450 0.717248 0.696818i \(-0.245402\pi\)
0.717248 + 0.696818i \(0.245402\pi\)
\(252\) 0 0
\(253\) −5.97596e15 −1.43260
\(254\) 0 0
\(255\) −1.23313e12 −0.000280865 0
\(256\) 0 0
\(257\) −7.40938e15 −1.60404 −0.802022 0.597294i \(-0.796242\pi\)
−0.802022 + 0.597294i \(0.796242\pi\)
\(258\) 0 0
\(259\) −2.55491e15 −0.525929
\(260\) 0 0
\(261\) 6.16290e15 1.20676
\(262\) 0 0
\(263\) 4.44830e15 0.828861 0.414431 0.910081i \(-0.363981\pi\)
0.414431 + 0.910081i \(0.363981\pi\)
\(264\) 0 0
\(265\) 3.77928e14 0.0670364
\(266\) 0 0
\(267\) −3.21243e13 −0.00542639
\(268\) 0 0
\(269\) −3.99525e15 −0.642916 −0.321458 0.946924i \(-0.604173\pi\)
−0.321458 + 0.946924i \(0.604173\pi\)
\(270\) 0 0
\(271\) 5.58778e15 0.856917 0.428458 0.903562i \(-0.359057\pi\)
0.428458 + 0.903562i \(0.359057\pi\)
\(272\) 0 0
\(273\) −3.79457e13 −0.00554761
\(274\) 0 0
\(275\) 7.79386e15 1.08665
\(276\) 0 0
\(277\) −9.01343e14 −0.119887 −0.0599435 0.998202i \(-0.519092\pi\)
−0.0599435 + 0.998202i \(0.519092\pi\)
\(278\) 0 0
\(279\) 3.59233e15 0.455983
\(280\) 0 0
\(281\) 1.24836e16 1.51268 0.756342 0.654176i \(-0.226985\pi\)
0.756342 + 0.654176i \(0.226985\pi\)
\(282\) 0 0
\(283\) −5.47980e15 −0.634093 −0.317046 0.948410i \(-0.602691\pi\)
−0.317046 + 0.948410i \(0.602691\pi\)
\(284\) 0 0
\(285\) 1.69049e13 0.00186862
\(286\) 0 0
\(287\) −4.81892e15 −0.509000
\(288\) 0 0
\(289\) −9.34136e15 −0.943135
\(290\) 0 0
\(291\) 1.68474e14 0.0162640
\(292\) 0 0
\(293\) 4.61630e15 0.426240 0.213120 0.977026i \(-0.431637\pi\)
0.213120 + 0.977026i \(0.431637\pi\)
\(294\) 0 0
\(295\) −2.33913e15 −0.206638
\(296\) 0 0
\(297\) −2.48103e14 −0.0209757
\(298\) 0 0
\(299\) −2.08171e16 −1.68484
\(300\) 0 0
\(301\) 2.40681e15 0.186535
\(302\) 0 0
\(303\) 7.46870e13 0.00554457
\(304\) 0 0
\(305\) 2.22028e14 0.0157928
\(306\) 0 0
\(307\) −2.22392e16 −1.51607 −0.758037 0.652211i \(-0.773842\pi\)
−0.758037 + 0.652211i \(0.773842\pi\)
\(308\) 0 0
\(309\) 2.54107e14 0.0166068
\(310\) 0 0
\(311\) 1.51173e16 0.947393 0.473697 0.880688i \(-0.342919\pi\)
0.473697 + 0.880688i \(0.342919\pi\)
\(312\) 0 0
\(313\) 8.36531e15 0.502856 0.251428 0.967876i \(-0.419100\pi\)
0.251428 + 0.967876i \(0.419100\pi\)
\(314\) 0 0
\(315\) −9.66336e14 −0.0557326
\(316\) 0 0
\(317\) −9.34425e15 −0.517201 −0.258600 0.965984i \(-0.583261\pi\)
−0.258600 + 0.965984i \(0.583261\pi\)
\(318\) 0 0
\(319\) 2.50676e16 1.33191
\(320\) 0 0
\(321\) −2.25474e14 −0.0115031
\(322\) 0 0
\(323\) −7.72117e15 −0.378327
\(324\) 0 0
\(325\) 2.71498e16 1.27798
\(326\) 0 0
\(327\) 1.19419e14 0.00540149
\(328\) 0 0
\(329\) 9.43151e15 0.410023
\(330\) 0 0
\(331\) 3.92466e16 1.64029 0.820144 0.572157i \(-0.193893\pi\)
0.820144 + 0.572157i \(0.193893\pi\)
\(332\) 0 0
\(333\) −2.90944e16 −1.16929
\(334\) 0 0
\(335\) −1.10501e14 −0.00427146
\(336\) 0 0
\(337\) −3.01727e16 −1.12207 −0.561036 0.827792i \(-0.689597\pi\)
−0.561036 + 0.827792i \(0.689597\pi\)
\(338\) 0 0
\(339\) −2.50655e14 −0.00896972
\(340\) 0 0
\(341\) 1.46118e16 0.503269
\(342\) 0 0
\(343\) 2.43838e16 0.808519
\(344\) 0 0
\(345\) 4.78864e13 0.00152893
\(346\) 0 0
\(347\) −4.02701e16 −1.23834 −0.619172 0.785255i \(-0.712532\pi\)
−0.619172 + 0.785255i \(0.712532\pi\)
\(348\) 0 0
\(349\) −4.36418e16 −1.29282 −0.646409 0.762991i \(-0.723730\pi\)
−0.646409 + 0.762991i \(0.723730\pi\)
\(350\) 0 0
\(351\) −8.64264e14 −0.0246689
\(352\) 0 0
\(353\) −3.08122e16 −0.847593 −0.423796 0.905758i \(-0.639303\pi\)
−0.423796 + 0.905758i \(0.639303\pi\)
\(354\) 0 0
\(355\) 6.00788e15 0.159308
\(356\) 0 0
\(357\) −3.98679e13 −0.00101925
\(358\) 0 0
\(359\) −4.06926e16 −1.00323 −0.501616 0.865090i \(-0.667261\pi\)
−0.501616 + 0.865090i \(0.667261\pi\)
\(360\) 0 0
\(361\) 6.37963e16 1.51705
\(362\) 0 0
\(363\) −9.02849e13 −0.00207120
\(364\) 0 0
\(365\) 3.54648e15 0.0785045
\(366\) 0 0
\(367\) −1.06190e16 −0.226857 −0.113429 0.993546i \(-0.536183\pi\)
−0.113429 + 0.993546i \(0.536183\pi\)
\(368\) 0 0
\(369\) −5.48762e16 −1.13165
\(370\) 0 0
\(371\) 1.22187e16 0.243273
\(372\) 0 0
\(373\) 7.41221e16 1.42508 0.712542 0.701630i \(-0.247544\pi\)
0.712542 + 0.701630i \(0.247544\pi\)
\(374\) 0 0
\(375\) −1.25881e14 −0.00233753
\(376\) 0 0
\(377\) 8.73226e16 1.56642
\(378\) 0 0
\(379\) 4.60131e16 0.797493 0.398746 0.917061i \(-0.369445\pi\)
0.398746 + 0.917061i \(0.369445\pi\)
\(380\) 0 0
\(381\) 7.52177e14 0.0125982
\(382\) 0 0
\(383\) −7.36970e16 −1.19305 −0.596524 0.802595i \(-0.703452\pi\)
−0.596524 + 0.802595i \(0.703452\pi\)
\(384\) 0 0
\(385\) −3.93057e15 −0.0615122
\(386\) 0 0
\(387\) 2.74079e16 0.414720
\(388\) 0 0
\(389\) 7.03726e16 1.02975 0.514874 0.857266i \(-0.327839\pi\)
0.514874 + 0.857266i \(0.327839\pi\)
\(390\) 0 0
\(391\) −2.18717e16 −0.309552
\(392\) 0 0
\(393\) 8.37328e13 0.00114642
\(394\) 0 0
\(395\) 1.74540e16 0.231213
\(396\) 0 0
\(397\) −1.07601e17 −1.37936 −0.689680 0.724115i \(-0.742249\pi\)
−0.689680 + 0.724115i \(0.742249\pi\)
\(398\) 0 0
\(399\) 5.46548e14 0.00678117
\(400\) 0 0
\(401\) −3.85722e16 −0.463272 −0.231636 0.972802i \(-0.574408\pi\)
−0.231636 + 0.972802i \(0.574408\pi\)
\(402\) 0 0
\(403\) 5.08999e16 0.591881
\(404\) 0 0
\(405\) −1.10033e16 −0.123898
\(406\) 0 0
\(407\) −1.18341e17 −1.29054
\(408\) 0 0
\(409\) −5.34639e16 −0.564753 −0.282377 0.959304i \(-0.591123\pi\)
−0.282377 + 0.959304i \(0.591123\pi\)
\(410\) 0 0
\(411\) 6.94309e14 0.00710527
\(412\) 0 0
\(413\) −7.56257e16 −0.749884
\(414\) 0 0
\(415\) −1.81030e16 −0.173955
\(416\) 0 0
\(417\) 4.72197e14 0.00439784
\(418\) 0 0
\(419\) 1.04340e17 0.942016 0.471008 0.882129i \(-0.343890\pi\)
0.471008 + 0.882129i \(0.343890\pi\)
\(420\) 0 0
\(421\) −7.03173e16 −0.615500 −0.307750 0.951467i \(-0.599576\pi\)
−0.307750 + 0.951467i \(0.599576\pi\)
\(422\) 0 0
\(423\) 1.07403e17 0.911596
\(424\) 0 0
\(425\) 2.85251e16 0.234801
\(426\) 0 0
\(427\) 7.17831e15 0.0573114
\(428\) 0 0
\(429\) −1.75762e15 −0.0136129
\(430\) 0 0
\(431\) 6.40437e16 0.481254 0.240627 0.970618i \(-0.422647\pi\)
0.240627 + 0.970618i \(0.422647\pi\)
\(432\) 0 0
\(433\) −1.12484e17 −0.820201 −0.410101 0.912040i \(-0.634506\pi\)
−0.410101 + 0.912040i \(0.634506\pi\)
\(434\) 0 0
\(435\) −2.00871e14 −0.00142147
\(436\) 0 0
\(437\) 2.99838e17 2.05948
\(438\) 0 0
\(439\) −3.14978e16 −0.210020 −0.105010 0.994471i \(-0.533487\pi\)
−0.105010 + 0.994471i \(0.533487\pi\)
\(440\) 0 0
\(441\) 1.23216e17 0.797658
\(442\) 0 0
\(443\) 1.14104e17 0.717261 0.358631 0.933480i \(-0.383244\pi\)
0.358631 + 0.933480i \(0.383244\pi\)
\(444\) 0 0
\(445\) −1.15915e16 −0.0707621
\(446\) 0 0
\(447\) 5.17644e14 0.00306925
\(448\) 0 0
\(449\) −7.86758e16 −0.453148 −0.226574 0.973994i \(-0.572753\pi\)
−0.226574 + 0.973994i \(0.572753\pi\)
\(450\) 0 0
\(451\) −2.23209e17 −1.24900
\(452\) 0 0
\(453\) −2.63518e15 −0.0143276
\(454\) 0 0
\(455\) −1.36921e16 −0.0723428
\(456\) 0 0
\(457\) 2.35679e17 1.21022 0.605112 0.796140i \(-0.293128\pi\)
0.605112 + 0.796140i \(0.293128\pi\)
\(458\) 0 0
\(459\) −9.08045e14 −0.00453236
\(460\) 0 0
\(461\) −2.33465e17 −1.13283 −0.566415 0.824120i \(-0.691670\pi\)
−0.566415 + 0.824120i \(0.691670\pi\)
\(462\) 0 0
\(463\) −1.43911e17 −0.678920 −0.339460 0.940620i \(-0.610244\pi\)
−0.339460 + 0.940620i \(0.610244\pi\)
\(464\) 0 0
\(465\) −1.17087e14 −0.000537110 0
\(466\) 0 0
\(467\) −2.72838e17 −1.21715 −0.608576 0.793496i \(-0.708259\pi\)
−0.608576 + 0.793496i \(0.708259\pi\)
\(468\) 0 0
\(469\) −3.57259e15 −0.0155010
\(470\) 0 0
\(471\) −7.94239e14 −0.00335209
\(472\) 0 0
\(473\) 1.11482e17 0.457727
\(474\) 0 0
\(475\) −3.91050e17 −1.56215
\(476\) 0 0
\(477\) 1.39142e17 0.540864
\(478\) 0 0
\(479\) 3.61844e17 1.36880 0.684401 0.729106i \(-0.260064\pi\)
0.684401 + 0.729106i \(0.260064\pi\)
\(480\) 0 0
\(481\) −4.12240e17 −1.51778
\(482\) 0 0
\(483\) 1.54820e15 0.00554844
\(484\) 0 0
\(485\) 6.07909e16 0.212089
\(486\) 0 0
\(487\) 3.33934e17 1.13429 0.567143 0.823619i \(-0.308049\pi\)
0.567143 + 0.823619i \(0.308049\pi\)
\(488\) 0 0
\(489\) 2.97146e15 0.00982793
\(490\) 0 0
\(491\) −1.79534e16 −0.0578251 −0.0289125 0.999582i \(-0.509204\pi\)
−0.0289125 + 0.999582i \(0.509204\pi\)
\(492\) 0 0
\(493\) 9.17461e16 0.287795
\(494\) 0 0
\(495\) −4.47600e16 −0.136759
\(496\) 0 0
\(497\) 1.94239e17 0.578123
\(498\) 0 0
\(499\) 4.21623e17 1.22256 0.611281 0.791414i \(-0.290655\pi\)
0.611281 + 0.791414i \(0.290655\pi\)
\(500\) 0 0
\(501\) 7.26271e14 0.00205189
\(502\) 0 0
\(503\) 3.53513e17 0.973225 0.486612 0.873618i \(-0.338232\pi\)
0.486612 + 0.873618i \(0.338232\pi\)
\(504\) 0 0
\(505\) 2.69496e16 0.0723032
\(506\) 0 0
\(507\) −2.48813e15 −0.00650611
\(508\) 0 0
\(509\) −5.95547e17 −1.51792 −0.758962 0.651135i \(-0.774293\pi\)
−0.758962 + 0.651135i \(0.774293\pi\)
\(510\) 0 0
\(511\) 1.14660e17 0.284890
\(512\) 0 0
\(513\) 1.24484e16 0.0301543
\(514\) 0 0
\(515\) 9.16903e16 0.216559
\(516\) 0 0
\(517\) 4.36860e17 1.00613
\(518\) 0 0
\(519\) 3.38828e15 0.00761012
\(520\) 0 0
\(521\) −6.18807e17 −1.35553 −0.677767 0.735277i \(-0.737052\pi\)
−0.677767 + 0.735277i \(0.737052\pi\)
\(522\) 0 0
\(523\) −3.97661e17 −0.849674 −0.424837 0.905270i \(-0.639669\pi\)
−0.424837 + 0.905270i \(0.639669\pi\)
\(524\) 0 0
\(525\) −2.01917e15 −0.00420859
\(526\) 0 0
\(527\) 5.34783e16 0.108745
\(528\) 0 0
\(529\) 3.45311e17 0.685092
\(530\) 0 0
\(531\) −8.61199e17 −1.66720
\(532\) 0 0
\(533\) −7.77544e17 −1.46892
\(534\) 0 0
\(535\) −8.13584e16 −0.150004
\(536\) 0 0
\(537\) 1.98741e15 0.00357647
\(538\) 0 0
\(539\) 5.01182e17 0.880376
\(540\) 0 0
\(541\) 4.06842e17 0.697660 0.348830 0.937186i \(-0.386579\pi\)
0.348830 + 0.937186i \(0.386579\pi\)
\(542\) 0 0
\(543\) −1.02256e16 −0.0171195
\(544\) 0 0
\(545\) 4.30904e16 0.0704374
\(546\) 0 0
\(547\) −2.81721e17 −0.449678 −0.224839 0.974396i \(-0.572186\pi\)
−0.224839 + 0.974396i \(0.572186\pi\)
\(548\) 0 0
\(549\) 8.17440e16 0.127419
\(550\) 0 0
\(551\) −1.25774e18 −1.91473
\(552\) 0 0
\(553\) 5.64299e17 0.839065
\(554\) 0 0
\(555\) 9.48290e14 0.00137733
\(556\) 0 0
\(557\) 1.23400e18 1.75088 0.875442 0.483324i \(-0.160571\pi\)
0.875442 + 0.483324i \(0.160571\pi\)
\(558\) 0 0
\(559\) 3.88345e17 0.538320
\(560\) 0 0
\(561\) −1.84665e15 −0.00250107
\(562\) 0 0
\(563\) 1.42261e18 1.88270 0.941348 0.337437i \(-0.109560\pi\)
0.941348 + 0.337437i \(0.109560\pi\)
\(564\) 0 0
\(565\) −9.04448e16 −0.116968
\(566\) 0 0
\(567\) −3.55744e17 −0.449623
\(568\) 0 0
\(569\) −4.50797e17 −0.556866 −0.278433 0.960456i \(-0.589815\pi\)
−0.278433 + 0.960456i \(0.589815\pi\)
\(570\) 0 0
\(571\) 7.13748e17 0.861807 0.430904 0.902398i \(-0.358195\pi\)
0.430904 + 0.902398i \(0.358195\pi\)
\(572\) 0 0
\(573\) −1.11719e16 −0.0131863
\(574\) 0 0
\(575\) −1.10772e18 −1.27817
\(576\) 0 0
\(577\) 1.28447e18 1.44905 0.724524 0.689250i \(-0.242060\pi\)
0.724524 + 0.689250i \(0.242060\pi\)
\(578\) 0 0
\(579\) −5.01444e15 −0.00553110
\(580\) 0 0
\(581\) −5.85282e17 −0.631277
\(582\) 0 0
\(583\) 5.65960e17 0.596953
\(584\) 0 0
\(585\) −1.55921e17 −0.160839
\(586\) 0 0
\(587\) −5.80690e16 −0.0585864 −0.0292932 0.999571i \(-0.509326\pi\)
−0.0292932 + 0.999571i \(0.509326\pi\)
\(588\) 0 0
\(589\) −7.33133e17 −0.723491
\(590\) 0 0
\(591\) 1.40904e16 0.0136021
\(592\) 0 0
\(593\) −1.39716e18 −1.31944 −0.659722 0.751509i \(-0.729326\pi\)
−0.659722 + 0.751509i \(0.729326\pi\)
\(594\) 0 0
\(595\) −1.43857e16 −0.0132914
\(596\) 0 0
\(597\) −1.14297e15 −0.00103324
\(598\) 0 0
\(599\) 5.23231e17 0.462827 0.231414 0.972855i \(-0.425665\pi\)
0.231414 + 0.972855i \(0.425665\pi\)
\(600\) 0 0
\(601\) −1.51221e18 −1.30897 −0.654484 0.756076i \(-0.727114\pi\)
−0.654484 + 0.756076i \(0.727114\pi\)
\(602\) 0 0
\(603\) −4.06833e16 −0.0344631
\(604\) 0 0
\(605\) −3.25778e16 −0.0270092
\(606\) 0 0
\(607\) −1.70314e18 −1.38205 −0.691024 0.722832i \(-0.742840\pi\)
−0.691024 + 0.722832i \(0.742840\pi\)
\(608\) 0 0
\(609\) −6.49431e15 −0.00515846
\(610\) 0 0
\(611\) 1.52180e18 1.18328
\(612\) 0 0
\(613\) −6.08885e17 −0.463492 −0.231746 0.972776i \(-0.574444\pi\)
−0.231746 + 0.972776i \(0.574444\pi\)
\(614\) 0 0
\(615\) 1.78861e15 0.00133299
\(616\) 0 0
\(617\) 5.93917e17 0.433383 0.216692 0.976240i \(-0.430473\pi\)
0.216692 + 0.976240i \(0.430473\pi\)
\(618\) 0 0
\(619\) 1.00496e18 0.718055 0.359028 0.933327i \(-0.383108\pi\)
0.359028 + 0.933327i \(0.383108\pi\)
\(620\) 0 0
\(621\) 3.52623e16 0.0246726
\(622\) 0 0
\(623\) −3.74762e17 −0.256793
\(624\) 0 0
\(625\) 1.42181e18 0.954159
\(626\) 0 0
\(627\) 2.53157e16 0.0166399
\(628\) 0 0
\(629\) −4.33123e17 −0.278857
\(630\) 0 0
\(631\) −7.35349e16 −0.0463770 −0.0231885 0.999731i \(-0.507382\pi\)
−0.0231885 + 0.999731i \(0.507382\pi\)
\(632\) 0 0
\(633\) −9.13964e15 −0.00564683
\(634\) 0 0
\(635\) 2.71410e17 0.164285
\(636\) 0 0
\(637\) 1.74586e18 1.03539
\(638\) 0 0
\(639\) 2.21192e18 1.28533
\(640\) 0 0
\(641\) 2.82655e18 1.60946 0.804728 0.593644i \(-0.202311\pi\)
0.804728 + 0.593644i \(0.202311\pi\)
\(642\) 0 0
\(643\) −1.57731e18 −0.880126 −0.440063 0.897967i \(-0.645044\pi\)
−0.440063 + 0.897967i \(0.645044\pi\)
\(644\) 0 0
\(645\) −8.93322e14 −0.000488506 0
\(646\) 0 0
\(647\) −1.78710e18 −0.957789 −0.478895 0.877872i \(-0.658962\pi\)
−0.478895 + 0.877872i \(0.658962\pi\)
\(648\) 0 0
\(649\) −3.50293e18 −1.84010
\(650\) 0 0
\(651\) −3.78550e15 −0.00194916
\(652\) 0 0
\(653\) 3.34506e18 1.68837 0.844185 0.536051i \(-0.180085\pi\)
0.844185 + 0.536051i \(0.180085\pi\)
\(654\) 0 0
\(655\) 3.02136e16 0.0149497
\(656\) 0 0
\(657\) 1.30571e18 0.633392
\(658\) 0 0
\(659\) −1.69802e18 −0.807584 −0.403792 0.914851i \(-0.632308\pi\)
−0.403792 + 0.914851i \(0.632308\pi\)
\(660\) 0 0
\(661\) −1.72815e18 −0.805883 −0.402942 0.915226i \(-0.632012\pi\)
−0.402942 + 0.915226i \(0.632012\pi\)
\(662\) 0 0
\(663\) −6.43278e15 −0.00294145
\(664\) 0 0
\(665\) 1.97213e17 0.0884289
\(666\) 0 0
\(667\) −3.56280e18 −1.56665
\(668\) 0 0
\(669\) 1.95208e16 0.00841835
\(670\) 0 0
\(671\) 3.32494e17 0.140633
\(672\) 0 0
\(673\) −1.82377e18 −0.756608 −0.378304 0.925681i \(-0.623493\pi\)
−0.378304 + 0.925681i \(0.623493\pi\)
\(674\) 0 0
\(675\) −4.59892e16 −0.0187146
\(676\) 0 0
\(677\) −3.09138e18 −1.23403 −0.617014 0.786952i \(-0.711658\pi\)
−0.617014 + 0.786952i \(0.711658\pi\)
\(678\) 0 0
\(679\) 1.96541e18 0.769662
\(680\) 0 0
\(681\) −1.81074e16 −0.00695663
\(682\) 0 0
\(683\) 3.14496e17 0.118544 0.0592722 0.998242i \(-0.481122\pi\)
0.0592722 + 0.998242i \(0.481122\pi\)
\(684\) 0 0
\(685\) 2.50530e17 0.0926554
\(686\) 0 0
\(687\) −2.03573e16 −0.00738756
\(688\) 0 0
\(689\) 1.97151e18 0.702060
\(690\) 0 0
\(691\) −4.48311e17 −0.156665 −0.0783325 0.996927i \(-0.524960\pi\)
−0.0783325 + 0.996927i \(0.524960\pi\)
\(692\) 0 0
\(693\) −1.44712e18 −0.496294
\(694\) 0 0
\(695\) 1.70385e17 0.0573494
\(696\) 0 0
\(697\) −8.16932e17 −0.269881
\(698\) 0 0
\(699\) −1.53383e16 −0.00497366
\(700\) 0 0
\(701\) 3.21704e18 1.02398 0.511988 0.858992i \(-0.328909\pi\)
0.511988 + 0.858992i \(0.328909\pi\)
\(702\) 0 0
\(703\) 5.93767e18 1.85527
\(704\) 0 0
\(705\) −3.50064e15 −0.00107379
\(706\) 0 0
\(707\) 8.71299e17 0.262386
\(708\) 0 0
\(709\) −3.21328e18 −0.950053 −0.475026 0.879971i \(-0.657562\pi\)
−0.475026 + 0.879971i \(0.657562\pi\)
\(710\) 0 0
\(711\) 6.42603e18 1.86548
\(712\) 0 0
\(713\) −2.07674e18 −0.591970
\(714\) 0 0
\(715\) −6.34207e17 −0.177518
\(716\) 0 0
\(717\) 1.32165e16 0.00363281
\(718\) 0 0
\(719\) −2.51628e18 −0.679237 −0.339619 0.940563i \(-0.610298\pi\)
−0.339619 + 0.940563i \(0.610298\pi\)
\(720\) 0 0
\(721\) 2.96441e18 0.785886
\(722\) 0 0
\(723\) −1.09839e16 −0.00285994
\(724\) 0 0
\(725\) 4.64661e18 1.18834
\(726\) 0 0
\(727\) −1.20284e18 −0.302157 −0.151078 0.988522i \(-0.548275\pi\)
−0.151078 + 0.988522i \(0.548275\pi\)
\(728\) 0 0
\(729\) −4.05036e18 −0.999458
\(730\) 0 0
\(731\) 4.08017e17 0.0989044
\(732\) 0 0
\(733\) −1.79874e18 −0.428345 −0.214173 0.976796i \(-0.568705\pi\)
−0.214173 + 0.976796i \(0.568705\pi\)
\(734\) 0 0
\(735\) −4.01605e15 −0.000939576 0
\(736\) 0 0
\(737\) −1.65479e17 −0.0380369
\(738\) 0 0
\(739\) −2.14261e18 −0.483898 −0.241949 0.970289i \(-0.577787\pi\)
−0.241949 + 0.970289i \(0.577787\pi\)
\(740\) 0 0
\(741\) 8.81868e16 0.0195697
\(742\) 0 0
\(743\) −5.34550e18 −1.16563 −0.582816 0.812604i \(-0.698049\pi\)
−0.582816 + 0.812604i \(0.698049\pi\)
\(744\) 0 0
\(745\) 1.86783e17 0.0400241
\(746\) 0 0
\(747\) −6.66498e18 −1.40351
\(748\) 0 0
\(749\) −2.63038e18 −0.544360
\(750\) 0 0
\(751\) 3.42693e18 0.697021 0.348511 0.937305i \(-0.386688\pi\)
0.348511 + 0.937305i \(0.386688\pi\)
\(752\) 0 0
\(753\) −6.81961e16 −0.0136330
\(754\) 0 0
\(755\) −9.50862e17 −0.186837
\(756\) 0 0
\(757\) 1.77769e18 0.343347 0.171674 0.985154i \(-0.445083\pi\)
0.171674 + 0.985154i \(0.445083\pi\)
\(758\) 0 0
\(759\) 7.17115e16 0.0136150
\(760\) 0 0
\(761\) 4.61017e18 0.860432 0.430216 0.902726i \(-0.358437\pi\)
0.430216 + 0.902726i \(0.358437\pi\)
\(762\) 0 0
\(763\) 1.39314e18 0.255615
\(764\) 0 0
\(765\) −1.63819e17 −0.0295505
\(766\) 0 0
\(767\) −1.22024e19 −2.16409
\(768\) 0 0
\(769\) 4.06261e18 0.708409 0.354204 0.935168i \(-0.384752\pi\)
0.354204 + 0.935168i \(0.384752\pi\)
\(770\) 0 0
\(771\) 8.89125e16 0.0152444
\(772\) 0 0
\(773\) −2.77091e18 −0.467149 −0.233574 0.972339i \(-0.575042\pi\)
−0.233574 + 0.972339i \(0.575042\pi\)
\(774\) 0 0
\(775\) 2.70849e18 0.449020
\(776\) 0 0
\(777\) 3.06589e16 0.00499827
\(778\) 0 0
\(779\) 1.11993e19 1.79555
\(780\) 0 0
\(781\) 8.99700e18 1.41862
\(782\) 0 0
\(783\) −1.47916e17 −0.0229385
\(784\) 0 0
\(785\) −2.86588e17 −0.0437125
\(786\) 0 0
\(787\) 4.81906e18 0.722980 0.361490 0.932376i \(-0.382268\pi\)
0.361490 + 0.932376i \(0.382268\pi\)
\(788\) 0 0
\(789\) −5.33796e16 −0.00787726
\(790\) 0 0
\(791\) −2.92414e18 −0.424475
\(792\) 0 0
\(793\) 1.15824e18 0.165395
\(794\) 0 0
\(795\) −4.53513e15 −0.000637094 0
\(796\) 0 0
\(797\) −8.13421e17 −0.112418 −0.0562090 0.998419i \(-0.517901\pi\)
−0.0562090 + 0.998419i \(0.517901\pi\)
\(798\) 0 0
\(799\) 1.59888e18 0.217402
\(800\) 0 0
\(801\) −4.26766e18 −0.570924
\(802\) 0 0
\(803\) 5.31098e18 0.699075
\(804\) 0 0
\(805\) 5.58642e17 0.0723537
\(806\) 0 0
\(807\) 4.79430e16 0.00611009
\(808\) 0 0
\(809\) −6.03069e18 −0.756313 −0.378156 0.925742i \(-0.623442\pi\)
−0.378156 + 0.925742i \(0.623442\pi\)
\(810\) 0 0
\(811\) 3.20788e18 0.395897 0.197948 0.980212i \(-0.436572\pi\)
0.197948 + 0.980212i \(0.436572\pi\)
\(812\) 0 0
\(813\) −6.70533e16 −0.00814389
\(814\) 0 0
\(815\) 1.07220e18 0.128160
\(816\) 0 0
\(817\) −5.59349e18 −0.658021
\(818\) 0 0
\(819\) −5.04102e18 −0.583678
\(820\) 0 0
\(821\) −1.08418e19 −1.23558 −0.617789 0.786344i \(-0.711971\pi\)
−0.617789 + 0.786344i \(0.711971\pi\)
\(822\) 0 0
\(823\) −3.62368e18 −0.406491 −0.203246 0.979128i \(-0.565149\pi\)
−0.203246 + 0.979128i \(0.565149\pi\)
\(824\) 0 0
\(825\) −9.35263e16 −0.0103272
\(826\) 0 0
\(827\) 5.78670e18 0.628992 0.314496 0.949259i \(-0.398164\pi\)
0.314496 + 0.949259i \(0.398164\pi\)
\(828\) 0 0
\(829\) −8.10871e18 −0.867655 −0.433828 0.900996i \(-0.642837\pi\)
−0.433828 + 0.900996i \(0.642837\pi\)
\(830\) 0 0
\(831\) 1.08161e16 0.00113937
\(832\) 0 0
\(833\) 1.83430e18 0.190229
\(834\) 0 0
\(835\) 2.62063e17 0.0267573
\(836\) 0 0
\(837\) −8.62197e16 −0.00866744
\(838\) 0 0
\(839\) −1.53236e19 −1.51673 −0.758365 0.651830i \(-0.774002\pi\)
−0.758365 + 0.651830i \(0.774002\pi\)
\(840\) 0 0
\(841\) 4.68439e18 0.456541
\(842\) 0 0
\(843\) −1.49803e17 −0.0143761
\(844\) 0 0
\(845\) −8.97800e17 −0.0848420
\(846\) 0 0
\(847\) −1.05326e18 −0.0980156
\(848\) 0 0
\(849\) 6.57576e16 0.00602623
\(850\) 0 0
\(851\) 1.68196e19 1.51800
\(852\) 0 0
\(853\) 9.91139e18 0.880979 0.440490 0.897758i \(-0.354805\pi\)
0.440490 + 0.897758i \(0.354805\pi\)
\(854\) 0 0
\(855\) 2.24579e18 0.196603
\(856\) 0 0
\(857\) −3.72370e18 −0.321069 −0.160535 0.987030i \(-0.551322\pi\)
−0.160535 + 0.987030i \(0.551322\pi\)
\(858\) 0 0
\(859\) −3.07811e18 −0.261414 −0.130707 0.991421i \(-0.541725\pi\)
−0.130707 + 0.991421i \(0.541725\pi\)
\(860\) 0 0
\(861\) 5.78271e16 0.00483739
\(862\) 0 0
\(863\) −4.68138e18 −0.385748 −0.192874 0.981224i \(-0.561781\pi\)
−0.192874 + 0.981224i \(0.561781\pi\)
\(864\) 0 0
\(865\) 1.22260e18 0.0992387
\(866\) 0 0
\(867\) 1.12096e17 0.00896328
\(868\) 0 0
\(869\) 2.61379e19 2.05893
\(870\) 0 0
\(871\) −5.76445e17 −0.0447342
\(872\) 0 0
\(873\) 2.23814e19 1.71118
\(874\) 0 0
\(875\) −1.46853e18 −0.110619
\(876\) 0 0
\(877\) −3.27869e18 −0.243334 −0.121667 0.992571i \(-0.538824\pi\)
−0.121667 + 0.992571i \(0.538824\pi\)
\(878\) 0 0
\(879\) −5.53956e16 −0.00405086
\(880\) 0 0
\(881\) −8.02437e18 −0.578186 −0.289093 0.957301i \(-0.593354\pi\)
−0.289093 + 0.957301i \(0.593354\pi\)
\(882\) 0 0
\(883\) −2.07925e19 −1.47626 −0.738128 0.674661i \(-0.764290\pi\)
−0.738128 + 0.674661i \(0.764290\pi\)
\(884\) 0 0
\(885\) 2.80695e16 0.00196383
\(886\) 0 0
\(887\) 2.61191e19 1.80075 0.900376 0.435112i \(-0.143291\pi\)
0.900376 + 0.435112i \(0.143291\pi\)
\(888\) 0 0
\(889\) 8.77489e18 0.596184
\(890\) 0 0
\(891\) −1.64778e19 −1.10330
\(892\) 0 0
\(893\) −2.19191e19 −1.44640
\(894\) 0 0
\(895\) 7.17124e17 0.0466385
\(896\) 0 0
\(897\) 2.49806e17 0.0160122
\(898\) 0 0
\(899\) 8.71138e18 0.550363
\(900\) 0 0
\(901\) 2.07138e18 0.128988
\(902\) 0 0
\(903\) −2.88818e16 −0.00177277
\(904\) 0 0
\(905\) −3.68974e18 −0.223244
\(906\) 0 0
\(907\) −2.55190e19 −1.52201 −0.761004 0.648747i \(-0.775293\pi\)
−0.761004 + 0.648747i \(0.775293\pi\)
\(908\) 0 0
\(909\) 9.92204e18 0.583359
\(910\) 0 0
\(911\) −1.62951e19 −0.944466 −0.472233 0.881474i \(-0.656552\pi\)
−0.472233 + 0.881474i \(0.656552\pi\)
\(912\) 0 0
\(913\) −2.71098e19 −1.54905
\(914\) 0 0
\(915\) −2.66433e15 −0.000150090 0
\(916\) 0 0
\(917\) 9.76826e17 0.0542521
\(918\) 0 0
\(919\) −2.25963e18 −0.123733 −0.0618667 0.998084i \(-0.519705\pi\)
−0.0618667 + 0.998084i \(0.519705\pi\)
\(920\) 0 0
\(921\) 2.66871e17 0.0144083
\(922\) 0 0
\(923\) 3.13409e19 1.66840
\(924\) 0 0
\(925\) −2.19361e19 −1.15143
\(926\) 0 0
\(927\) 3.37577e19 1.74725
\(928\) 0 0
\(929\) −1.38768e19 −0.708250 −0.354125 0.935198i \(-0.615221\pi\)
−0.354125 + 0.935198i \(0.615221\pi\)
\(930\) 0 0
\(931\) −2.51463e19 −1.26561
\(932\) 0 0
\(933\) −1.81407e17 −0.00900375
\(934\) 0 0
\(935\) −6.66334e17 −0.0326149
\(936\) 0 0
\(937\) 1.27938e19 0.617578 0.308789 0.951131i \(-0.400076\pi\)
0.308789 + 0.951131i \(0.400076\pi\)
\(938\) 0 0
\(939\) −1.00384e17 −0.00477900
\(940\) 0 0
\(941\) −1.00758e19 −0.473093 −0.236547 0.971620i \(-0.576016\pi\)
−0.236547 + 0.971620i \(0.576016\pi\)
\(942\) 0 0
\(943\) 3.17241e19 1.46914
\(944\) 0 0
\(945\) 2.31931e16 0.00105938
\(946\) 0 0
\(947\) 1.66672e19 0.750912 0.375456 0.926840i \(-0.377486\pi\)
0.375456 + 0.926840i \(0.377486\pi\)
\(948\) 0 0
\(949\) 1.85007e19 0.822163
\(950\) 0 0
\(951\) 1.12131e17 0.00491532
\(952\) 0 0
\(953\) 2.79060e19 1.20668 0.603341 0.797483i \(-0.293836\pi\)
0.603341 + 0.797483i \(0.293836\pi\)
\(954\) 0 0
\(955\) −4.03119e18 −0.171954
\(956\) 0 0
\(957\) −3.00811e17 −0.0126580
\(958\) 0 0
\(959\) 8.09981e18 0.336243
\(960\) 0 0
\(961\) −1.93397e19 −0.792042
\(962\) 0 0
\(963\) −2.99538e19 −1.21027
\(964\) 0 0
\(965\) −1.80938e18 −0.0721276
\(966\) 0 0
\(967\) 4.06377e19 1.59829 0.799147 0.601136i \(-0.205285\pi\)
0.799147 + 0.601136i \(0.205285\pi\)
\(968\) 0 0
\(969\) 9.26541e16 0.00359550
\(970\) 0 0
\(971\) 3.91648e18 0.149958 0.0749792 0.997185i \(-0.476111\pi\)
0.0749792 + 0.997185i \(0.476111\pi\)
\(972\) 0 0
\(973\) 5.50865e18 0.208119
\(974\) 0 0
\(975\) −3.25797e17 −0.0121456
\(976\) 0 0
\(977\) 8.91758e18 0.328044 0.164022 0.986457i \(-0.447553\pi\)
0.164022 + 0.986457i \(0.447553\pi\)
\(978\) 0 0
\(979\) −1.73587e19 −0.630130
\(980\) 0 0
\(981\) 1.58646e19 0.568304
\(982\) 0 0
\(983\) −3.03354e19 −1.07239 −0.536194 0.844095i \(-0.680138\pi\)
−0.536194 + 0.844095i \(0.680138\pi\)
\(984\) 0 0
\(985\) 5.08430e18 0.177376
\(986\) 0 0
\(987\) −1.13178e17 −0.00389673
\(988\) 0 0
\(989\) −1.58446e19 −0.538401
\(990\) 0 0
\(991\) −4.90085e19 −1.64359 −0.821794 0.569785i \(-0.807027\pi\)
−0.821794 + 0.569785i \(0.807027\pi\)
\(992\) 0 0
\(993\) −4.70959e17 −0.0155888
\(994\) 0 0
\(995\) −4.12423e17 −0.0134739
\(996\) 0 0
\(997\) −1.57448e19 −0.507715 −0.253857 0.967242i \(-0.581699\pi\)
−0.253857 + 0.967242i \(0.581699\pi\)
\(998\) 0 0
\(999\) 6.98297e17 0.0222262
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 \(a_p\))