Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [64,14,Mod(1,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(68.6277945292\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 8) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 64.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 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 | \(-0.480263\pi\) | ||||
0.0619659 | + | 0.998078i | \(0.480263\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 139992. | 0.449745 | 0.224872 | − | 0.974388i | \(-0.427804\pi\) | ||||
0.224872 | + | 0.974388i | \(0.427804\pi\) | |||||||
\(8\) | 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 | \(-0.275205\pi\) | ||||
0.648958 | + | 0.760824i | \(0.275205\pi\) | |||||||
\(14\) | 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 | \(-0.724836\pi\) | ||||
−0.649055 | + | 0.760741i | \(0.724836\pi\) | |||||||
\(24\) | 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 | \(-0.293798\pi\) | ||||
0.603436 | + | 0.797411i | \(0.293798\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.25340e9 | 0.456024 | 0.228012 | − | 0.973658i | \(-0.426777\pi\) | ||||
0.228012 | + | 0.973658i | \(0.426777\pi\) | |||||||
\(32\) | 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 | \(-0.698787\pi\) | ||||
−0.584697 | + | 0.811252i | \(0.698787\pi\) | |||||||
\(38\) | 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 | \(-0.349339\pi\) | ||||
0.455839 | + | 0.890062i | \(0.349339\pi\) | |||||||
\(48\) | 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 | \(-0.412825\pi\) | ||||
0.270457 | + | 0.962732i | \(0.412825\pi\) | |||||||
\(54\) | 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 | \(-0.479705\pi\) | ||||
0.0637155 | + | 0.997968i | \(0.479705\pi\) | |||||||
\(62\) | 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 | \(-0.277805\pi\) | ||||
0.642723 | + | 0.766099i | \(0.277805\pi\) | |||||||
\(72\) | 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 | \(-0.117337\pi\) | ||||
0.932824 | + | 0.360332i | \(0.117337\pi\) | |||||||
\(80\) | 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 | \(-0.405777\pi\) | ||||
0.291706 | + | 0.956508i | \(0.405777\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.11756e13 | 1.74740 | 0.873702 | − | 0.486461i | \(-0.161712\pi\) | ||||
0.873702 | + | 0.486461i | \(0.161712\pi\) | |||||||
\(104\) | 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 | \(-0.408279\pi\) | ||||
0.284178 | + | 0.958772i | \(0.408279\pi\) | |||||||
\(110\) | 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 | \(-0.269367\pi\) | ||||
0.662803 | + | 0.748794i | \(0.269367\pi\) | |||||||
\(128\) | 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 | \(-0.448374\pi\) | ||||
0.161476 | + | 0.986877i | \(0.448374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.19599e14 | −1.50758 | −0.753788 | − | 0.657117i | \(-0.771776\pi\) | ||||
−0.753788 | + | 0.657117i | \(0.771776\pi\) | |||||||
\(152\) | 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 | \(-0.556431\pi\) | ||||
−0.176357 | + | 0.984326i | \(0.556431\pi\) | |||||||
\(158\) | 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 | \(-0.465571\pi\) | ||||
0.107952 | + | 0.994156i | \(0.465571\pi\) | |||||||
\(168\) | 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 | \(-0.368879\pi\) | ||||
0.400376 | + | 0.916351i | \(0.368879\pi\) | |||||||
\(174\) | 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 | \(-0.856926\pi\) | ||||
−0.900673 | + | 0.434497i | \(0.856926\pi\) | |||||||
\(182\) | 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 | \(-0.744039\pi\) | ||||
−0.693742 | + | 0.720223i | \(0.744039\pi\) | |||||||
\(192\) | 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 | \(-0.246144\pi\) | ||||
0.715621 | + | 0.698489i | \(0.246144\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.52478e13 | −0.108720 | −0.0543601 | − | 0.998521i | \(-0.517312\pi\) | ||||
−0.0543601 | + | 0.998521i | \(0.517312\pi\) | |||||||
\(200\) | 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 | \(-0.353950\pi\) | ||||
0.442898 | + | 0.896572i | \(0.353950\pi\) | |||||||
\(224\) | 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 | \(-0.627064\pi\) | ||||
−0.388667 | + | 0.921378i | \(0.627064\pi\) | |||||||
\(230\) | 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 | \(-0.438786\pi\) | ||||
0.191126 | + | 0.981566i | \(0.438786\pi\) | |||||||
\(240\) | 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 | \(-0.636019\pi\) | ||||
−0.414431 | + | 0.910081i | \(0.636019\pi\) | |||||||
\(264\) | 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 | \(-0.395827\pi\) | ||||
0.321458 | + | 0.946924i | \(0.395827\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.58778e15 | −0.856917 | −0.428458 | − | 0.903562i | \(-0.640943\pi\) | ||||
−0.428458 | + | 0.903562i | \(0.640943\pi\) | |||||||
\(272\) | 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 | \(-0.480908\pi\) | ||||
0.0599435 | + | 0.998202i | \(0.480908\pi\) | |||||||
\(278\) | 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 | \(-0.568363\pi\) | ||||
−0.213120 | + | 0.977026i | \(0.568363\pi\) | |||||||
\(294\) | 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 | \(-0.657081\pi\) | ||||
−0.473697 | + | 0.880688i | \(0.657081\pi\) | |||||||
\(312\) | 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 | \(-0.416739\pi\) | ||||
0.258600 | + | 0.965984i | \(0.416739\pi\) | |||||||
\(318\) | 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 | \(-0.276270\pi\) | ||||
0.646409 | + | 0.762991i | \(0.276270\pi\) | |||||||
\(350\) | 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 | \(-0.332739\pi\) | ||||
0.501616 | + | 0.865090i | \(0.332739\pi\) | |||||||
\(360\) | 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 | \(-0.463817\pi\) | ||||
0.113429 | + | 0.993546i | \(0.463817\pi\) | |||||||
\(368\) | 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 | \(-0.752456\pi\) | ||||
−0.712542 | + | 0.701630i | \(0.752456\pi\) | |||||||
\(374\) | 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 | \(-0.296548\pi\) | ||||
0.596524 | + | 0.802595i | \(0.296548\pi\) | |||||||
\(384\) | 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 | \(-0.672161\pi\) | ||||
−0.514874 | + | 0.857266i | \(0.672161\pi\) | |||||||
\(390\) | 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 | \(-0.257751\pi\) | ||||
0.689680 | + | 0.724115i | \(0.257751\pi\) | |||||||
\(398\) | 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 | \(-0.400424\pi\) | ||||
0.307750 | + | 0.951467i | \(0.400424\pi\) | |||||||
\(422\) | 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 | \(-0.577353\pi\) | ||||
−0.240627 | + | 0.970618i | \(0.577353\pi\) | |||||||
\(432\) | 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 | \(-0.466513\pi\) | ||||
0.105010 | + | 0.994471i | \(0.466513\pi\) | |||||||
\(440\) | 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 | \(-0.308330\pi\) | ||||
0.566415 | + | 0.824120i | \(0.308330\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.43911e17 | 0.678920 | 0.339460 | − | 0.940620i | \(-0.389756\pi\) | ||||
0.339460 | + | 0.940620i | \(0.389756\pi\) | |||||||
\(464\) | 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 | \(-0.739936\pi\) | ||||
−0.684401 | + | 0.729106i | \(0.739936\pi\) | |||||||
\(480\) | 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 | \(-0.691951\pi\) | ||||
−0.567143 | + | 0.823619i | \(0.691951\pi\) | |||||||
\(488\) | 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 | \(-0.661768\pi\) | ||||
−0.486612 | + | 0.873618i | \(0.661768\pi\) | |||||||
\(504\) | 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 | \(-0.225707\pi\) | ||||
0.758962 | + | 0.651135i | \(0.225707\pi\) | |||||||
\(510\) | 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 | \(-0.613421\pi\) | ||||
−0.348830 | + | 0.937186i | \(0.613421\pi\) | |||||||
\(542\) | 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 | \(-0.839429\pi\) | ||||
−0.875442 | + | 0.483324i | \(0.839429\pi\) | |||||||
\(558\) | 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 | \(-0.574335\pi\) | ||||
−0.231414 | + | 0.972855i | \(0.574335\pi\) | |||||||
\(600\) | 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 | \(-0.257160\pi\) | ||||
0.691024 | + | 0.722832i | \(0.257160\pi\) | |||||||
\(608\) | 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 | \(-0.425556\pi\) | ||||
0.231746 | + | 0.972776i | \(0.425556\pi\) | |||||||
\(614\) | 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 | \(-0.492618\pi\) | ||||
0.0231885 | + | 0.999731i | \(0.492618\pi\) | |||||||
\(632\) | 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 | \(-0.341038\pi\) | ||||
0.478895 | + | 0.877872i | \(0.341038\pi\) | |||||||
\(648\) | 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 | \(-0.819915\pi\) | ||||
−0.844185 | + | 0.536051i | \(0.819915\pi\) | |||||||
\(654\) | 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 | \(-0.367988\pi\) | ||||
0.402942 | + | 0.915226i | \(0.367988\pi\) | |||||||
\(662\) | 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 | \(-0.288342\pi\) | ||||
0.617014 | + | 0.786952i | \(0.288342\pi\) | |||||||
\(678\) | 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 | \(-0.671091\pi\) | ||||
−0.511988 | + | 0.858992i | \(0.671091\pi\) | |||||||
\(702\) | 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 | \(-0.342438\pi\) | ||||
0.475026 | + | 0.879971i | \(0.342438\pi\) | |||||||
\(710\) | 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 | \(-0.389702\pi\) | ||||
0.339619 | + | 0.940563i | \(0.389702\pi\) | |||||||
\(720\) | 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 | \(-0.451725\pi\) | ||||
0.151078 | + | 0.988522i | \(0.451725\pi\) | |||||||
\(728\) | 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 | \(-0.431295\pi\) | ||||
0.214173 | + | 0.976796i | \(0.431295\pi\) | |||||||
\(734\) | 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 | \(-0.301951\pi\) | ||||
0.582816 | + | 0.812604i | \(0.301951\pi\) | |||||||
\(744\) | 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 | \(-0.613312\pi\) | ||||
−0.348511 | + | 0.937305i | \(0.613312\pi\) | |||||||
\(752\) | 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 | \(-0.554917\pi\) | ||||
−0.171674 | + | 0.985154i | \(0.554917\pi\) | |||||||
\(758\) | 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 | \(-0.424958\pi\) | ||||
0.233574 | + | 0.972339i | \(0.424958\pi\) | |||||||
\(774\) | 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 | \(-0.482099\pi\) | ||||
0.0562090 | + | 0.998419i | \(0.482099\pi\) | |||||||
\(798\) | 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 | \(-0.288029\pi\) | ||||
0.617789 | + | 0.786344i | \(0.288029\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.62368e18 | 0.406491 | 0.203246 | − | 0.979128i | \(-0.434851\pi\) | ||||
0.203246 | + | 0.979128i | \(0.434851\pi\) | |||||||
\(824\) | 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 | \(-0.357163\pi\) | ||||
0.433828 | + | 0.900996i | \(0.357163\pi\) | |||||||
\(830\) | 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 | \(-0.225998\pi\) | ||||
0.758365 | + | 0.651830i | \(0.225998\pi\) | |||||||
\(840\) | 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 | \(-0.645195\pi\) | ||||
−0.440490 | + | 0.897758i | \(0.645195\pi\) | |||||||
\(854\) | 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 | \(-0.438219\pi\) | ||||
0.192874 | + | 0.981224i | \(0.438219\pi\) | |||||||
\(864\) | 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 | \(-0.461176\pi\) | ||||
0.121667 | + | 0.992571i | \(0.461176\pi\) | |||||||
\(878\) | 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 | \(-0.856709\pi\) | ||||
−0.900376 | + | 0.435112i | \(0.856709\pi\) | |||||||
\(888\) | 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 | \(-0.343448\pi\) | ||||
0.472233 | + | 0.881474i | \(0.343448\pi\) | |||||||
\(912\) | 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 | \(-0.480295\pi\) | ||||
0.0618667 | + | 0.998084i | \(0.480295\pi\) | |||||||
\(920\) | 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 | \(-0.423984\pi\) | ||||
0.236547 | + | 0.971620i | \(0.423984\pi\) | |||||||
\(942\) | 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 | \(-0.794715\pi\) | ||||
−0.799147 | + | 0.601136i | \(0.794715\pi\) | |||||||
\(968\) | 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 | \(-0.319862\pi\) | ||||
0.536194 | + | 0.844095i | \(0.319862\pi\) | |||||||
\(984\) | 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 | \(-0.192973\pi\) | ||||
0.821794 | + | 0.569785i | \(0.192973\pi\) | |||||||
\(992\) | 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 | \(-0.418301\pi\) | ||||
0.253857 | + | 0.967242i | \(0.418301\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.98297e17 | −0.0222262 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 64.14.a.d.1.1 | 1 | ||
4.3 | odd | 2 | 64.14.a.f.1.1 | 1 | |||
8.3 | odd | 2 | 8.14.a.a.1.1 | ✓ | 1 | ||
8.5 | even | 2 | 16.14.a.c.1.1 | 1 | |||
24.5 | odd | 2 | 144.14.a.f.1.1 | 1 | |||
24.11 | even | 2 | 72.14.a.a.1.1 | 1 | |||
40.3 | even | 4 | 200.14.c.a.49.1 | 2 | |||
40.19 | odd | 2 | 200.14.a.a.1.1 | 1 | |||
40.27 | even | 4 | 200.14.c.a.49.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.14.a.a.1.1 | ✓ | 1 | 8.3 | odd | 2 | ||
16.14.a.c.1.1 | 1 | 8.5 | even | 2 | |||
64.14.a.d.1.1 | 1 | 1.1 | even | 1 | trivial | ||
64.14.a.f.1.1 | 1 | 4.3 | odd | 2 | |||
72.14.a.a.1.1 | 1 | 24.11 | even | 2 | |||
144.14.a.f.1.1 | 1 | 24.5 | odd | 2 | |||
200.14.a.a.1.1 | 1 | 40.19 | odd | 2 | |||
200.14.c.a.49.1 | 2 | 40.3 | even | 4 | |||
200.14.c.a.49.2 | 2 | 40.27 | even | 4 |