Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,16,Mod(1,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.1");
S:= CuspForms(chi, 16);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.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: | \(102.739323672\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{22}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 22 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3\cdot 5 \) |
Twist minimal: | no (minimal twist has level 24) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(4.69042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 72.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 180276. | 1.03196 | 0.515981 | − | 0.856600i | \(-0.327427\pi\) | ||||
0.515981 | + | 0.856600i | \(0.327427\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.48794e6 | 0.682887 | 0.341444 | − | 0.939902i | \(-0.389084\pi\) | ||||
0.341444 | + | 0.939902i | \(0.389084\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.90021e7 | −0.603452 | −0.301726 | − | 0.953395i | \(-0.597563\pi\) | ||||
−0.301726 | + | 0.953395i | \(0.597563\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.07919e8 | −0.919009 | −0.459504 | − | 0.888175i | \(-0.651973\pi\) | ||||
−0.459504 | + | 0.888175i | \(0.651973\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.64604e9 | 1.56398 | 0.781988 | − | 0.623293i | \(-0.214206\pi\) | ||||
0.781988 | + | 0.623293i | \(0.214206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.76142e9 | 1.22204 | 0.611019 | − | 0.791616i | \(-0.290760\pi\) | ||||
0.611019 | + | 0.791616i | \(0.290760\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.16387e9 | 0.316240 | 0.158120 | − | 0.987420i | \(-0.449457\pi\) | ||||
0.158120 | + | 0.987420i | \(0.449457\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.98199e9 | 0.0649459 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.10143e11 | 1.18569 | 0.592845 | − | 0.805316i | \(-0.298005\pi\) | ||||
0.592845 | + | 0.805316i | \(0.298005\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.05870e10 | −0.199675 | −0.0998375 | − | 0.995004i | \(-0.531832\pi\) | ||||
−0.0998375 | + | 0.995004i | \(0.531832\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.68240e11 | 0.704714 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.68194e11 | −1.33033 | −0.665163 | − | 0.746698i | \(-0.731638\pi\) | ||||
−0.665163 | + | 0.746698i | \(0.731638\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.15551e11 | 0.734181 | 0.367091 | − | 0.930185i | \(-0.380354\pi\) | ||||
0.367091 | + | 0.930185i | \(0.380354\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.32094e12 | −0.741091 | −0.370545 | − | 0.928814i | \(-0.620829\pi\) | ||||
−0.370545 | + | 0.928814i | \(0.620829\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.60974e11 | 0.247888 | 0.123944 | − | 0.992289i | \(-0.460446\pi\) | ||||
0.123944 | + | 0.992289i | \(0.460446\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.53361e12 | −0.533665 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.28543e11 | −0.108576 | −0.0542879 | − | 0.998525i | \(-0.517289\pi\) | ||||
−0.0542879 | + | 0.998525i | \(0.517289\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.03115e12 | −0.622740 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.80695e13 | 1.99153 | 0.995766 | − | 0.0919215i | \(-0.0293009\pi\) | ||||
0.995766 | + | 0.0919215i | \(0.0293009\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.83644e13 | −0.748175 | −0.374087 | − | 0.927393i | \(-0.622044\pi\) | ||||
−0.374087 | + | 0.927393i | \(0.622044\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.74829e13 | −0.948382 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.19085e13 | 1.65108 | 0.825540 | − | 0.564344i | \(-0.190871\pi\) | ||||
0.825540 | + | 0.564344i | \(0.190871\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.15622e13 | −0.542327 | −0.271163 | − | 0.962533i | \(-0.587408\pi\) | ||||
−0.271163 | + | 0.962533i | \(0.587408\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.55562e14 | 1.64810 | 0.824048 | − | 0.566521i | \(-0.191711\pi\) | ||||
0.824048 | + | 0.566521i | \(0.191711\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.80326e13 | −0.412090 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.78006e14 | −1.04287 | −0.521437 | − | 0.853290i | \(-0.674604\pi\) | ||||
−0.521437 | + | 0.853290i | \(0.674604\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.25716e13 | −0.0913010 | −0.0456505 | − | 0.998957i | \(-0.514536\pi\) | ||||
−0.0456505 | + | 0.998957i | \(0.514536\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.77019e14 | 1.61396 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.76725e14 | −1.38211 | −0.691057 | − | 0.722800i | \(-0.742855\pi\) | ||||
−0.691057 | + | 0.722800i | \(0.742855\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.09371e14 | −0.627580 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.58371e14 | 1.26110 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.91989e14 | 0.618255 | 0.309128 | − | 0.951021i | \(-0.399963\pi\) | ||||
0.309128 | + | 0.951021i | \(0.399963\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.44221e15 | 1.33850 | 0.669251 | − | 0.743036i | \(-0.266615\pi\) | ||||
0.669251 | + | 0.743036i | \(0.266615\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.69202e14 | −0.375907 | −0.187954 | − | 0.982178i | \(-0.560185\pi\) | ||||
−0.187954 | + | 0.982178i | \(0.560185\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.01230e15 | 1.21147 | 0.605737 | − | 0.795665i | \(-0.292878\pi\) | ||||
0.605737 | + | 0.795665i | \(0.292878\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.49631e15 | 1.30798 | 0.653988 | − | 0.756505i | \(-0.273095\pi\) | ||||
0.653988 | + | 0.756505i | \(0.273095\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.14810e15 | 0.459085 | 0.229542 | − | 0.973299i | \(-0.426277\pi\) | ||||
0.229542 | + | 0.973299i | \(0.426277\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.30924e14 | 0.326348 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.93714e15 | 1.06802 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.65609e15 | −0.635846 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.14429e15 | −0.964940 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00922e16 | 1.68057 | 0.840285 | − | 0.542145i | \(-0.182388\pi\) | ||||
0.840285 | + | 0.542145i | \(0.182388\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.72987e15 | −1.02009 | −0.510044 | − | 0.860148i | \(-0.670371\pi\) | ||||
−0.510044 | + | 0.860148i | \(0.670371\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.08469e15 | 0.834514 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.09348e15 | 0.197454 | 0.0987268 | − | 0.995115i | \(-0.468523\pi\) | ||||
0.0987268 | + | 0.995115i | \(0.468523\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.30677e16 | 1.95161 | 0.975806 | − | 0.218640i | \(-0.0701619\pi\) | ||||
0.975806 | + | 0.218640i | \(0.0701619\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.10929e15 | 0.554578 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.98562e16 | 1.22359 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.00896e16 | 1.51189 | 0.755943 | − | 0.654638i | \(-0.227179\pi\) | ||||
0.755943 | + | 0.654638i | \(0.227179\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.01711e16 | 0.917072 | 0.458536 | − | 0.888676i | \(-0.348374\pi\) | ||||
0.458536 | + | 0.888676i | \(0.348374\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.51411e15 | −0.206057 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.86362e15 | −0.0632572 | −0.0316286 | − | 0.999500i | \(-0.510069\pi\) | ||||
−0.0316286 | + | 0.999500i | \(0.510069\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.68351e15 | 0.215956 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.03185e15 | 0.180162 | 0.0900808 | − | 0.995934i | \(-0.471287\pi\) | ||||
0.0900808 | + | 0.995934i | \(0.471287\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.76392e15 | −0.0804020 | −0.0402010 | − | 0.999192i | \(-0.512800\pi\) | ||||
−0.0402010 | + | 0.999192i | \(0.512800\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.95546e15 | −0.155423 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.10801e16 | 1.32913 | 0.664567 | − | 0.747229i | \(-0.268616\pi\) | ||||
0.664567 | + | 0.747229i | \(0.268616\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.94908e15 | 0.0443507 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.36381e16 | 0.427005 | 0.213503 | − | 0.976942i | \(-0.431513\pi\) | ||||
0.213503 | + | 0.976942i | \(0.431513\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.25177e16 | −0.846944 | −0.423472 | − | 0.905909i | \(-0.639189\pi\) | ||||
−0.423472 | + | 0.905909i | \(0.639189\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.38487e17 | −1.37285 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.03201e17 | −0.943784 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.46831e17 | 1.14569 | 0.572845 | − | 0.819664i | \(-0.305840\pi\) | ||||
0.572845 | + | 0.819664i | \(0.305840\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.95671e16 | −0.141204 | −0.0706019 | − | 0.997505i | \(-0.522492\pi\) | ||||
−0.0706019 | + | 0.997505i | \(0.522492\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.99325e17 | −1.23329 | −0.616645 | − | 0.787241i | \(-0.711509\pi\) | ||||
−0.616645 | + | 0.787241i | \(0.711509\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.09007e17 | 1.77244 | 0.886219 | − | 0.463267i | \(-0.153323\pi\) | ||||
0.886219 | + | 0.463267i | \(0.153323\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.63886e17 | 0.809693 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.65052e17 | 0.757647 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.85705e17 | −0.737441 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.17876e17 | −1.91473 | −0.957364 | − | 0.288885i | \(-0.906715\pi\) | ||||
−0.957364 | + | 0.288885i | \(0.906715\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.38135e17 | −0.764777 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.55115e16 | −0.136356 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.50164e17 | −1.43731 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.24384e16 | −0.0303722 | −0.0151861 | − | 0.999885i | \(-0.504834\pi\) | ||||
−0.0151861 | + | 0.999885i | \(0.504834\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.95457e16 | −0.127250 | −0.0636248 | − | 0.997974i | \(-0.520266\pi\) | ||||
−0.0636248 | + | 0.997974i | \(0.520266\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.30572e17 | −1.66192 | −0.830962 | − | 0.556330i | \(-0.812209\pi\) | ||||
−0.830962 | + | 0.556330i | \(0.812209\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.86376e17 | −0.854678 | −0.427339 | − | 0.904091i | \(-0.640549\pi\) | ||||
−0.427339 | + | 0.904091i | \(0.640549\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.55213e17 | 0.255811 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.15538e18 | 1.67780 | 0.838901 | − | 0.544284i | \(-0.183198\pi\) | ||||
0.838901 | + | 0.544284i | \(0.183198\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.02560e17 | −0.958420 | −0.479210 | − | 0.877700i | \(-0.659077\pi\) | ||||
−0.479210 | + | 0.877700i | \(0.659077\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.56749e17 | −0.550722 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.89991e17 | −1.12306 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.63469e16 | 0.0566653 | 0.0283327 | − | 0.999599i | \(-0.490980\pi\) | ||||
0.0283327 | + | 0.999599i | \(0.490980\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.01402e17 | −0.190836 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.50968e17 | −0.379881 | −0.189940 | − | 0.981796i | \(-0.560829\pi\) | ||||
−0.189940 | + | 0.981796i | \(0.560829\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.14302e18 | −0.908463 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.13174e17 | 0.505275 | 0.252637 | − | 0.967561i | \(-0.418702\pi\) | ||||
0.252637 | + | 0.967561i | \(0.418702\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.67394e17 | −0.112046 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.32811e18 | 1.39271 | 0.696357 | − | 0.717695i | \(-0.254803\pi\) | ||||
0.696357 | + | 0.717695i | \(0.254803\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.29160e18 | 1.29679 | 0.648394 | − | 0.761305i | \(-0.275441\pi\) | ||||
0.648394 | + | 0.761305i | \(0.275441\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.73018e16 | −0.0391917 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.15077e18 | −1.99311 | −0.996554 | − | 0.0829450i | \(-0.973567\pi\) | ||||
−0.996554 | + | 0.0829450i | \(0.973567\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.67332e18 | −1.15280 | −0.576400 | − | 0.817168i | \(-0.695543\pi\) | ||||
−0.576400 | + | 0.817168i | \(0.695543\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.19921e18 | 1.30811 | 0.654055 | − | 0.756447i | \(-0.273066\pi\) | ||||
0.654055 | + | 0.756447i | \(0.273066\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.36228e18 | 0.501363 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.13912e18 | 1.44602 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.61525e18 | −0.824149 | −0.412075 | − | 0.911150i | \(-0.635196\pi\) | ||||
−0.412075 | + | 0.911150i | \(0.635196\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.86304e18 | 2.05519 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.07367e18 | −0.290627 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.96548e18 | −0.506081 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.31067e18 | −0.772088 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.27984e18 | 0.728308 | 0.364154 | − | 0.931339i | \(-0.381358\pi\) | ||||
0.364154 | + | 0.931339i | \(0.381358\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.63232e17 | −0.0328929 | −0.0164465 | − | 0.999865i | \(-0.505235\pi\) | ||||
−0.0164465 | + | 0.999865i | \(0.505235\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.41673e18 | 0.464136 | 0.232068 | − | 0.972700i | \(-0.425451\pi\) | ||||
0.232068 | + | 0.972700i | \(0.425451\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.53593e18 | 0.268180 | 0.134090 | − | 0.990969i | \(-0.457189\pi\) | ||||
0.134090 | + | 0.990969i | \(0.457189\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.29580e18 | −0.715507 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.25989e19 | 1.91124 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.12094e17 | −0.0596858 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.28107e18 | 0.169280 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.02981e19 | 1.30032 | 0.650158 | − | 0.759799i | \(-0.274703\pi\) | ||||
0.650158 | + | 0.759799i | \(0.274703\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.47662e19 | 1.70385 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.20546e18 | 1.01583 | 0.507915 | − | 0.861407i | \(-0.330416\pi\) | ||||
0.507915 | + | 0.861407i | \(0.330416\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.19296e18 | 0.120494 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.08339e19 | −1.04732 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.40238e19 | 1.24279 | 0.621393 | − | 0.783499i | \(-0.286567\pi\) | ||||
0.621393 | + | 0.783499i | \(0.286567\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.91289e18 | 0.162367 | 0.0811837 | − | 0.996699i | \(-0.474130\pi\) | ||||
0.0811837 | + | 0.996699i | \(0.474130\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.19204e19 | −1.70820 | −0.854100 | − | 0.520108i | \(-0.825892\pi\) | ||||
−0.854100 | + | 0.520108i | \(0.825892\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.49268e18 | −0.559660 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.18890e19 | −0.816465 | −0.408232 | − | 0.912878i | \(-0.633855\pi\) | ||||
−0.408232 | + | 0.912878i | \(0.633855\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.48998e18 | 0.493375 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.80442e19 | 1.70077 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.04460e18 | −0.468284 | −0.234142 | − | 0.972202i | \(-0.575228\pi\) | ||||
−0.234142 | + | 0.972202i | \(0.575228\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.38161e18 | −0.0741450 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.28069e18 | 0.323736 | 0.161868 | − | 0.986812i | \(-0.448248\pi\) | ||||
0.161868 | + | 0.986812i | \(0.448248\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.29008e19 | −1.08966 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.77049e18 | −0.0809652 | −0.0404826 | − | 0.999180i | \(-0.512890\pi\) | ||||
−0.0404826 | + | 0.999180i | \(0.512890\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.93577e19 | −1.66356 | −0.831781 | − | 0.555104i | \(-0.812679\pi\) | ||||
−0.831781 | + | 0.555104i | \(0.812679\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.04619e19 | −0.425261 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.94320e18 | 0.336412 | 0.168206 | − | 0.985752i | \(-0.446203\pi\) | ||||
0.168206 | + | 0.985752i | \(0.446203\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.36638e19 | 0.494592 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.20903e19 | −1.07621 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.03814e19 | −1.94973 | −0.974864 | − | 0.222801i | \(-0.928480\pi\) | ||||
−0.974864 | + | 0.222801i | \(0.928480\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.38522e19 | −1.01392 | −0.506961 | − | 0.861969i | \(-0.669231\pi\) | ||||
−0.506961 | + | 0.861969i | \(0.669231\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.35962e18 | 0.183503 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.99612e19 | 0.802788 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.86132e19 | 1.77208 | 0.886039 | − | 0.463610i | \(-0.153446\pi\) | ||||
0.886039 | + | 0.463610i | \(0.153446\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.66450e19 | 1.35999 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.06912e18 | −0.0942192 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.41796e19 | −0.521007 | −0.260504 | − | 0.965473i | \(-0.583889\pi\) | ||||
−0.260504 | + | 0.965473i | \(0.583889\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.62042e19 | −0.960651 | −0.480325 | − | 0.877090i | \(-0.659481\pi\) | ||||
−0.480325 | + | 0.877090i | \(0.659481\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.24443e18 | 0.101574 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.73251e19 | −0.510919 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.20343e19 | −1.08156 | −0.540782 | − | 0.841163i | \(-0.681872\pi\) | ||||
−0.540782 | + | 0.841163i | \(0.681872\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.88817e19 | −1.49676 | −0.748382 | − | 0.663268i | \(-0.769169\pi\) | ||||
−0.748382 | + | 0.663268i | \(0.769169\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.45874e19 | 0.386457 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.31215e19 | −1.26249 | −0.631247 | − | 0.775581i | \(-0.717457\pi\) | ||||
−0.631247 | + | 0.775581i | \(0.717457\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.77868e18 | −0.138756 | −0.0693781 | − | 0.997590i | \(-0.522101\pi\) | ||||
−0.0693781 | + | 0.997590i | \(0.522101\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.03970e20 | −1.42629 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.32320e20 | 1.69737 | 0.848686 | − | 0.528896i | \(-0.177394\pi\) | ||||
0.848686 | + | 0.528896i | \(0.177394\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.57084e19 | −0.443043 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.57722e19 | −0.647638 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.82187e19 | 0.654170 | 0.327085 | − | 0.944995i | \(-0.393934\pi\) | ||||
0.327085 | + | 0.944995i | \(0.393934\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.69152e19 | −0.283296 | −0.141648 | − | 0.989917i | \(-0.545240\pi\) | ||||
−0.141648 | + | 0.989917i | \(0.545240\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.40379e18 | −0.0856283 | −0.0428142 | − | 0.999083i | \(-0.513632\pi\) | ||||
−0.0428142 | + | 0.999083i | \(0.513632\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.70165e20 | −1.62553 | −0.812763 | − | 0.582594i | \(-0.802038\pi\) | ||||
−0.812763 | + | 0.582594i | \(0.802038\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.21875e20 | 1.12750 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.15196e19 | 0.447213 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.43709e18 | 0.0793662 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.27871e19 | 0.179958 | 0.0899792 | − | 0.995944i | \(-0.471320\pi\) | ||||
0.0899792 | + | 0.995944i | \(0.471320\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.59722e20 | 1.22258 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.86941e19 | 0.638016 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.00043e20 | −0.697785 | −0.348892 | − | 0.937163i | \(-0.613442\pi\) | ||||
−0.348892 | + | 0.937163i | \(0.613442\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.86698e20 | 1.22469 | 0.612347 | − | 0.790589i | \(-0.290226\pi\) | ||||
0.612347 | + | 0.790589i | \(0.290226\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.91443e20 | 1.85439 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.18419e19 | −0.370348 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.19986e19 | −0.0697229 | −0.0348615 | − | 0.999392i | \(-0.511099\pi\) | ||||
−0.0348615 | + | 0.999392i | \(0.511099\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.88293e19 | 0.267252 | 0.133626 | − | 0.991032i | \(-0.457338\pi\) | ||||
0.133626 | + | 0.991032i | \(0.457338\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.59997e20 | 1.38128 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.07524e19 | −0.204066 | −0.102033 | − | 0.994781i | \(-0.532535\pi\) | ||||
−0.102033 | + | 0.994781i | \(0.532535\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.31466e20 | 1.12546 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.45861e19 | −0.387922 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.35798e19 | −0.149589 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.05648e19 | −0.338737 | −0.169368 | − | 0.985553i | \(-0.554173\pi\) | ||||
−0.169368 | + | 0.985553i | \(0.554173\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.97463e19 | 0.244089 | 0.122045 | − | 0.992525i | \(-0.461055\pi\) | ||||
0.122045 | + | 0.992525i | \(0.461055\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.09345e19 | −0.312287 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.39970e20 | −0.899992 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.90361e20 | −0.674719 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.62770e20 | 1.25020 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.88159e19 | 0.322041 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.73325e19 | 0.118334 | 0.0591668 | − | 0.998248i | \(-0.481156\pi\) | ||||
0.0591668 | + | 0.998248i | \(0.481156\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.50026e20 | 1.34978 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.54198e20 | −1.03357 | −0.516787 | − | 0.856114i | \(-0.672872\pi\) | ||||
−0.516787 | + | 0.856114i | \(0.672872\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.24436e20 | 1.44896 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.64862e20 | −0.712165 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.54417e20 | 0.648084 | 0.324042 | − | 0.946043i | \(-0.394958\pi\) | ||||
0.324042 | + | 0.946043i | \(0.394958\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.74650e20 | 0.681069 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.20356e19 | 0.0517979 | 0.0258989 | − | 0.999665i | \(-0.491755\pi\) | ||||
0.0258989 | + | 0.999665i | \(0.491755\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.06976e20 | 0.473758 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.27873e19 | −0.136311 | −0.0681553 | − | 0.997675i | \(-0.521711\pi\) | ||||
−0.0681553 | + | 0.997675i | \(0.521711\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.68918e20 | −0.568656 | −0.284328 | − | 0.958727i | \(-0.591770\pi\) | ||||
−0.284328 | + | 0.958727i | \(0.591770\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.02347e19 | 0.0205385 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.77749e19 | −0.171614 | −0.0858068 | − | 0.996312i | \(-0.527347\pi\) | ||||
−0.0858068 | + | 0.996312i | \(0.527347\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.35850e19 | −0.0623483 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.62151e19 | 0.0655203 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.86642e19 | −0.135205 | −0.0676023 | − | 0.997712i | \(-0.521535\pi\) | ||||
−0.0676023 | + | 0.997712i | \(0.521535\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.45637e20 | −0.244010 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.19336e20 | 0.827062 | 0.413531 | − | 0.910490i | \(-0.364295\pi\) | ||||
0.413531 | + | 0.910490i | \(0.364295\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.09774e20 | 1.10216 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.64161e20 | −1.27613 | −0.638063 | − | 0.769984i | \(-0.720264\pi\) | ||||
−0.638063 | + | 0.769984i | \(0.720264\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.03488e21 | −1.49049 | −0.745246 | − | 0.666789i | \(-0.767668\pi\) | ||||
−0.745246 | + | 0.666789i | \(0.767668\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.78829e20 | −0.656169 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.83953e20 | −1.04803 | −0.524016 | − | 0.851708i | \(-0.675567\pi\) | ||||
−0.524016 | + | 0.851708i | \(0.675567\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.79013e20 | −0.227812 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.35634e20 | 0.789321 | 0.394660 | − | 0.918827i | \(-0.370862\pi\) | ||||
0.394660 | + | 0.918827i | \(0.370862\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.35838e20 | −0.751982 | −0.375991 | − | 0.926623i | \(-0.622698\pi\) | ||||
−0.375991 | + | 0.926623i | \(0.622698\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.93312e20 | 0.800293 | 0.400146 | − | 0.916451i | \(-0.368959\pi\) | ||||
0.400146 | + | 0.916451i | \(0.368959\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.58131e20 | −0.943829 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.87880e20 | −1.06073 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.03267e21 | −2.08060 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.31697e20 | −0.531428 | −0.265714 | − | 0.964052i | \(-0.585608\pi\) | ||||
−0.265714 | + | 0.964052i | \(0.585608\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.81938e21 | 1.73428 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.26786e20 | 0.490443 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.53876e20 | −0.847338 | −0.423669 | − | 0.905817i | \(-0.639258\pi\) | ||||
−0.423669 | + | 0.905817i | \(0.639258\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.77350e20 | 0.414242 | 0.207121 | − | 0.978315i | \(-0.433591\pi\) | ||||
0.207121 | + | 0.978315i | \(0.433591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.56151e19 | 0.0543528 | 0.0271764 | − | 0.999631i | \(-0.491348\pi\) | ||||
0.0271764 | + | 0.999631i | \(0.491348\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.48479e21 | −1.20179 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.02258e21 | −0.790405 | −0.395202 | − | 0.918594i | \(-0.629326\pi\) | ||||
−0.395202 | + | 0.918594i | \(0.629326\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.39351e21 | −1.05269 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.53156e21 | 1.10533 | 0.552666 | − | 0.833403i | \(-0.313610\pi\) | ||||
0.552666 | + | 0.833403i | \(0.313610\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.86754e21 | −1.31752 | −0.658762 | − | 0.752352i | \(-0.728919\pi\) | ||||
−0.658762 | + | 0.752352i | \(0.728919\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.27720e21 | 0.861187 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.68764e20 | 0.374963 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.16250e20 | 0.451487 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.69039e20 | −0.165845 | −0.0829225 | − | 0.996556i | \(-0.526425\pi\) | ||||
−0.0829225 | + | 0.996556i | \(0.526425\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.96920e20 | −0.410930 | −0.205465 | − | 0.978664i | \(-0.565871\pi\) | ||||
−0.205465 | + | 0.978664i | \(0.565871\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.32049e20 | 0.422199 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.53069e20 | −0.360416 | −0.180208 | − | 0.983629i | \(-0.557677\pi\) | ||||
−0.180208 | + | 0.983629i | \(0.557677\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.77405e20 | 0.203765 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.93062e20 | 0.0997821 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.57344e21 | −0.795728 | −0.397864 | − | 0.917444i | \(-0.630248\pi\) | ||||
−0.397864 | + | 0.917444i | \(0.630248\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.15856e21 | 2.01399 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.42259e21 | 1.14824 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.61982e20 | −0.391393 | −0.195696 | − | 0.980665i | \(-0.562697\pi\) | ||||
−0.195696 | + | 0.980665i | \(0.562697\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.65769e21 | −1.62571 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.14592e21 | 0.914047 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.35234e20 | −0.139798 | −0.0698990 | − | 0.997554i | \(-0.522268\pi\) | ||||
−0.0698990 | + | 0.997554i | \(0.522268\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.57947e20 | −0.0631452 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.46191e21 | 0.572303 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.77763e20 | −0.329542 | −0.164771 | − | 0.986332i | \(-0.552689\pi\) | ||||
−0.164771 | + | 0.986332i | \(0.552689\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.98143e20 | −0.256702 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.18302e20 | 0.0770057 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.41420e21 | 0.834189 | 0.417094 | − | 0.908863i | \(-0.363048\pi\) | ||||
0.417094 | + | 0.908863i | \(0.363048\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.49528e21 | −1.15905 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.91963e21 | 1.59828 | 0.799140 | − | 0.601145i | \(-0.205289\pi\) | ||||
0.799140 | + | 0.601145i | \(0.205289\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.19460e21 | −0.996347 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.65946e21 | 0.812755 | 0.406377 | − | 0.913705i | \(-0.366792\pi\) | ||||
0.406377 | + | 0.913705i | \(0.366792\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.83744e21 | −1.41971 | −0.709854 | − | 0.704349i | \(-0.751239\pi\) | ||||
−0.709854 | + | 0.704349i | \(0.751239\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.42444e21 | 1.56021 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.99417e21 | 0.827301 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.22604e21 | 1.14455 | 0.572274 | − | 0.820063i | \(-0.306061\pi\) | ||||
0.572274 | + | 0.820063i | \(0.306061\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.63638e21 | 0.946383 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.96399e21 | −0.756235 | −0.378118 | − | 0.925758i | \(-0.623429\pi\) | ||||
−0.378118 | + | 0.925758i | \(0.623429\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.04604e21 | 1.72807 | 0.864033 | − | 0.503435i | \(-0.167931\pi\) | ||||
0.864033 | + | 0.503435i | \(0.167931\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.71435e21 | 0.893201 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.91539e21 | −1.83024 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.87704e21 | −0.425623 | −0.212811 | − | 0.977093i | \(-0.568262\pi\) | ||||
−0.212811 | + | 0.977093i | \(0.568262\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.89238e21 | 0.412726 | 0.206363 | − | 0.978476i | \(-0.433837\pi\) | ||||
0.206363 | + | 0.978476i | \(0.433837\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.06231e19 | −0.0129681 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.35932e21 | 0.897197 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.62101e21 | 0.327268 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.35967e20 | −0.0652791 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.32042e21 | −0.632968 | −0.316484 | − | 0.948598i | \(-0.602502\pi\) | ||||
−0.316484 | + | 0.948598i | \(0.602502\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.70830e21 | 0.313503 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.81831e21 | 0.687579 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.76651e21 | 1.17335 | 0.586675 | − | 0.809823i | \(-0.300437\pi\) | ||||
0.586675 | + | 0.809823i | \(0.300437\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.27818e21 | 0.387691 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.06725e21 | −0.994546 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.38516e21 | 0.222859 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.69947e21 | 0.418471 | 0.209236 | − | 0.977865i | \(-0.432902\pi\) | ||||
0.209236 | + | 0.977865i | \(0.432902\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.26290e20 | 0.0496532 | 0.0248266 | − | 0.999692i | \(-0.492097\pi\) | ||||
0.0248266 | + | 0.999692i | \(0.492097\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.26768e21 | 0.185920 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.28957e21 | −0.905640 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.38301e21 | 1.16366 | 0.581830 | − | 0.813310i | \(-0.302337\pi\) | ||||
0.581830 | + | 0.813310i | \(0.302337\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.89689e21 | −0.394851 | −0.197426 | − | 0.980318i | \(-0.563258\pi\) | ||||
−0.197426 | + | 0.980318i | \(0.563258\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.61354e21 | 1.26355 | 0.631774 | − | 0.775152i | \(-0.282327\pi\) | ||||
0.631774 | + | 0.775152i | \(0.282327\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.25187e21 | −1.06511 | −0.532554 | − | 0.846396i | \(-0.678768\pi\) | ||||
−0.532554 | + | 0.846396i | \(0.678768\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.70403e21 | −0.834639 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.78546e20 | −0.0829718 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.55522e22 | −1.83475 | −0.917376 | − | 0.398023i | \(-0.869696\pi\) | ||||
−0.917376 | + | 0.398023i | \(0.869696\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.50226e21 | 0.405862 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.43418e21 | −0.160390 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.95209e21 | −0.434211 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.96686e21 | −0.420702 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.58685e22 | −1.65355 | −0.826775 | − | 0.562533i | \(-0.809827\pi\) | ||||
−0.826775 | + | 0.562533i | \(0.809827\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.84075e21 | −0.285810 | −0.142905 | − | 0.989736i | \(-0.545644\pi\) | ||||
−0.142905 | + | 0.989736i | \(0.545644\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.71405e22 | −1.69463 | −0.847314 | − | 0.531092i | \(-0.821782\pi\) | ||||
−0.847314 | + | 0.531092i | \(0.821782\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.14547e22 | −1.09371 | −0.546855 | − | 0.837227i | \(-0.684175\pi\) | ||||
−0.546855 | + | 0.837227i | \(0.684175\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.46168e22 | 1.37162 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.94261e21 | 0.629324 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.70304e22 | −1.51736 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.65438e21 | −0.658946 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.03589e22 | 0.876628 | 0.438314 | − | 0.898822i | \(-0.355576\pi\) | ||||
0.438314 | + | 0.898822i | \(0.355576\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.85579e21 | −0.560710 | −0.280355 | − | 0.959896i | \(-0.590452\pi\) | ||||
−0.280355 | + | 0.959896i | \(0.590452\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.80330e21 | 0.144998 | 0.0724990 | − | 0.997368i | \(-0.476903\pi\) | ||||
0.0724990 | + | 0.997368i | \(0.476903\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.74255e22 | 1.35444 | 0.677218 | − | 0.735783i | \(-0.263186\pi\) | ||||
0.677218 | + | 0.735783i | \(0.263186\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.50165e22 | 1.14764 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.09946e21 | 0.302929 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.06415e21 | 0.440653 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.36894e21 | −0.236753 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.45697e21 | −0.169810 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.30732e22 | −0.874014 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.57258e21 | 0.169167 | 0.0845833 | − | 0.996416i | \(-0.473044\pi\) | ||||
0.0845833 | + | 0.996416i | \(0.473044\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.51786e21 | −0.605552 | −0.302776 | − | 0.953062i | \(-0.597913\pi\) | ||||
−0.302776 | + | 0.953062i | \(0.597913\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.80338e20 | 0.0550958 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.15016e22 | −0.696605 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.52473e22 | −0.908505 | −0.454252 | − | 0.890873i | \(-0.650094\pi\) | ||||
−0.454252 | + | 0.890873i | \(0.650094\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.64158e21 | 0.498403 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.52255e21 | −0.0863992 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.69216e22 | −1.47905 | −0.739525 | − | 0.673130i | \(-0.764950\pi\) | ||||
−0.739525 | + | 0.673130i | \(0.764950\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.20636e22 | −0.652158 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.86047e22 | −0.973950 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.04500e21 | −0.208387 | −0.104194 | − | 0.994557i | \(-0.533226\pi\) | ||||
−0.104194 | + | 0.994557i | \(0.533226\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.59999e22 | 1.29733 | 0.648663 | − | 0.761076i | \(-0.275328\pi\) | ||||
0.648663 | + | 0.761076i | \(0.275328\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.72779e21 | 0.232178 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.85830e22 | 1.35982 | 0.679912 | − | 0.733294i | \(-0.262018\pi\) | ||||
0.679912 | + | 0.733294i | \(0.262018\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.23444e22 | −1.51461 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.29856e21 | 0.331162 | 0.165581 | − | 0.986196i | \(-0.447050\pi\) | ||||
0.165581 | + | 0.986196i | \(0.447050\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.64701e22 | 1.18231 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.11497e21 | 0.134839 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.25297e22 | −0.960130 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.52749e21 | −0.145717 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.15063e22 | −1.68817 | −0.844084 | − | 0.536211i | \(-0.819855\pi\) | ||||
−0.844084 | + | 0.536211i | \(0.819855\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.94891e21 | 0.234581 | 0.117291 | − | 0.993098i | \(-0.462579\pi\) | ||||
0.117291 | + | 0.993098i | \(0.462579\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.43233e22 | 1.33273 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.79538e22 | 1.80557 | 0.902783 | − | 0.430096i | \(-0.141520\pi\) | ||||
0.902783 | + | 0.430096i | \(0.141520\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.24935e22 | 0.834040 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.87969e22 | −1.75485 | −0.877426 | − | 0.479712i | \(-0.840741\pi\) | ||||
−0.877426 | + | 0.479712i | \(0.840741\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.59336e22 | −1.27271 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.82119e21 | −0.234362 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.75510e21 | 0.0932362 | 0.0466181 | − | 0.998913i | \(-0.485156\pi\) | ||||
0.0466181 | + | 0.998913i | \(0.485156\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.57067e22 | 1.82909 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.10140e22 | 0.356232 | 0.178116 | − | 0.984009i | \(-0.443000\pi\) | ||||
0.178116 | + | 0.984009i | \(0.443000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 72.16.a.f.1.2 | 2 | ||
3.2 | odd | 2 | 24.16.a.c.1.1 | ✓ | 2 | ||
4.3 | odd | 2 | 144.16.a.u.1.2 | 2 | |||
12.11 | even | 2 | 48.16.a.h.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.16.a.c.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
48.16.a.h.1.1 | 2 | 12.11 | even | 2 | |||
72.16.a.f.1.2 | 2 | 1.1 | even | 1 | trivial | ||
144.16.a.u.1.2 | 2 | 4.3 | odd | 2 |