Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,10,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, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
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: | \(37.0825802038\) |
Analytic rank: | \(1\) |
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 | \(\chi\) | \(=\) | 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 | ||||||||
\(5\) | 2074.00 | 1.48403 | 0.742017 | − | 0.670381i | \(-0.233869\pi\) | ||||
0.742017 | + | 0.670381i | \(0.233869\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4344.00 | −0.683831 | −0.341915 | − | 0.939731i | \(-0.611076\pi\) | ||||
−0.341915 | + | 0.939731i | \(0.611076\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −93644.0 | −1.92847 | −0.964235 | − | 0.265049i | \(-0.914612\pi\) | ||||
−0.964235 | + | 0.265049i | \(0.914612\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12242.0 | −0.118880 | −0.0594398 | − | 0.998232i | \(-0.518931\pi\) | ||||
−0.0594398 | + | 0.998232i | \(0.518931\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 319598. | 0.928077 | 0.464038 | − | 0.885815i | \(-0.346400\pi\) | ||||
0.464038 | + | 0.885815i | \(0.346400\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −553516. | −0.974404 | −0.487202 | − | 0.873289i | \(-0.661982\pi\) | ||||
−0.487202 | + | 0.873289i | \(0.661982\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 712936. | 0.531221 | 0.265611 | − | 0.964080i | \(-0.414426\pi\) | ||||
0.265611 | + | 0.964080i | \(0.414426\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.34835e6 | 1.20236 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.07584e6 | −0.545007 | −0.272504 | − | 0.962155i | \(-0.587852\pi\) | ||||
−0.272504 | + | 0.962155i | \(0.587852\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.42045e6 | −1.24864 | −0.624321 | − | 0.781168i | \(-0.714624\pi\) | ||||
−0.624321 | + | 0.781168i | \(0.714624\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.00946e6 | −1.01483 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.81978e7 | −1.59628 | −0.798142 | − | 0.602470i | \(-0.794183\pi\) | ||||
−0.798142 | + | 0.602470i | \(0.794183\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.03383e6 | −0.499281 | −0.249640 | − | 0.968339i | \(-0.580312\pi\) | ||||
−0.249640 | + | 0.968339i | \(0.580312\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.95947e7 | 0.874040 | 0.437020 | − | 0.899452i | \(-0.356034\pi\) | ||||
0.437020 | + | 0.899452i | \(0.356034\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.84842e7 | 0.552535 | 0.276267 | − | 0.961081i | \(-0.410902\pi\) | ||||
0.276267 | + | 0.961081i | \(0.410902\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.14833e7 | −0.532375 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.02558e7 | −0.178536 | −0.0892682 | − | 0.996008i | \(-0.528453\pi\) | ||||
−0.0892682 | + | 0.996008i | \(0.528453\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.94218e8 | −2.86191 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.21667e8 | −1.30719 | −0.653593 | − | 0.756847i | \(-0.726739\pi\) | ||||
−0.653593 | + | 0.756847i | \(0.726739\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.59490e7 | −0.424905 | −0.212452 | − | 0.977171i | \(-0.568145\pi\) | ||||
−0.212452 | + | 0.977171i | \(0.568145\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.53899e7 | −0.176421 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.05354e7 | 0.306379 | 0.153190 | − | 0.988197i | \(-0.451045\pi\) | ||||
0.153190 | + | 0.988197i | \(0.451045\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.67045e8 | −1.24716 | −0.623579 | − | 0.781760i | \(-0.714322\pi\) | ||||
−0.623579 | + | 0.781760i | \(0.714322\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.76213e8 | −0.726250 | −0.363125 | − | 0.931740i | \(-0.618290\pi\) | ||||
−0.363125 | + | 0.931740i | \(0.618290\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.06790e8 | 1.31875 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.69686e8 | −0.778997 | −0.389499 | − | 0.921027i | \(-0.627352\pi\) | ||||
−0.389499 | + | 0.921027i | \(0.627352\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.27033e8 | 0.525094 | 0.262547 | − | 0.964919i | \(-0.415438\pi\) | ||||
0.262547 | + | 0.964919i | \(0.415438\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.62846e8 | 1.37730 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.21416e7 | −0.121880 | −0.0609398 | − | 0.998141i | \(-0.519410\pi\) | ||||
−0.0609398 | + | 0.998141i | \(0.519410\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.31792e7 | 0.0812935 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.14799e9 | −1.44605 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.28777e8 | 0.262385 | 0.131192 | − | 0.991357i | \(-0.458119\pi\) | ||||
0.131192 | + | 0.991357i | \(0.458119\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.03256e8 | 0.768082 | 0.384041 | − | 0.923316i | \(-0.374532\pi\) | ||||
0.384041 | + | 0.923316i | \(0.374532\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.81726e8 | 0.684363 | 0.342182 | − | 0.939634i | \(-0.388834\pi\) | ||||
0.342182 | + | 0.939634i | \(0.388834\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.00756e9 | 0.743093 | 0.371546 | − | 0.928414i | \(-0.378828\pi\) | ||||
0.371546 | + | 0.928414i | \(0.378828\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.80692e8 | −0.326173 | −0.163086 | − | 0.986612i | \(-0.552145\pi\) | ||||
−0.163086 | + | 0.986612i | \(0.552145\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.89781e9 | 1.67193 | 0.835963 | − | 0.548786i | \(-0.184910\pi\) | ||||
0.835963 | + | 0.548786i | \(0.184910\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.47863e9 | 0.788350 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.38833e9 | −0.634647 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.41125e9 | 2.71900 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.19699e8 | 0.300303 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.24330e9 | −1.44740 | −0.723698 | − | 0.690117i | \(-0.757559\pi\) | ||||
−0.723698 | + | 0.690117i | \(0.757559\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.89728e9 | −0.859546 | −0.429773 | − | 0.902937i | \(-0.641406\pi\) | ||||
−0.429773 | + | 0.902937i | \(0.641406\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.40447e9 | 0.666327 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.35617e9 | 0.571432 | 0.285716 | − | 0.958314i | \(-0.407769\pi\) | ||||
0.285716 | + | 0.958314i | \(0.407769\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.71527e9 | −0.616946 | −0.308473 | − | 0.951233i | \(-0.599818\pi\) | ||||
−0.308473 | + | 0.951233i | \(0.599818\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.14639e9 | 0.229256 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.30529e9 | −0.808809 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.67402e9 | −0.278242 | −0.139121 | − | 0.990275i | \(-0.544428\pi\) | ||||
−0.139121 | + | 0.990275i | \(0.544428\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.32709e9 | 0.833860 | 0.416930 | − | 0.908938i | \(-0.363106\pi\) | ||||
0.416930 | + | 0.908938i | \(0.363106\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.33160e10 | −1.85303 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.15835e10 | −1.52156 | −0.760782 | − | 0.649008i | \(-0.775184\pi\) | ||||
−0.760782 | + | 0.649008i | \(0.775184\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.09699e9 | −0.363265 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.48418e8 | 0.105234 | 0.0526169 | − | 0.998615i | \(-0.483244\pi\) | ||||
0.0526169 | + | 0.998615i | \(0.483244\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.44718e10 | 1.43978 | 0.719891 | − | 0.694087i | \(-0.244192\pi\) | ||||
0.719891 | + | 0.694087i | \(0.244192\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.04546e10 | −0.985868 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.39886e10 | 1.18732 | 0.593658 | − | 0.804717i | \(-0.297683\pi\) | ||||
0.593658 | + | 0.804717i | \(0.297683\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.02012e10 | −0.822208 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.54924e9 | 0.331207 | 0.165604 | − | 0.986192i | \(-0.447043\pi\) | ||||
0.165604 | + | 0.986192i | \(0.447043\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.56484e10 | 1.08372 | 0.541859 | − | 0.840469i | \(-0.317721\pi\) | ||||
0.541859 | + | 0.840469i | \(0.317721\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.77421e10 | −2.36894 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.99284e10 | −1.78977 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.02052e10 | −1.09853 | −0.549267 | − | 0.835647i | \(-0.685093\pi\) | ||||
−0.549267 | + | 0.835647i | \(0.685093\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.10827e9 | −0.368770 | −0.184385 | − | 0.982854i | \(-0.559029\pi\) | ||||
−0.184385 | + | 0.982854i | \(0.559029\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.25924e10 | −1.06872 | −0.534359 | − | 0.845257i | \(-0.679447\pi\) | ||||
−0.534359 | + | 0.845257i | \(0.679447\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.55506e10 | 1.60697 | 0.803485 | − | 0.595325i | \(-0.202977\pi\) | ||||
0.803485 | + | 0.595325i | \(0.202977\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.01744e9 | 0.372693 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.87362e10 | −0.740949 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.18335e10 | 1.87911 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.58480e9 | −0.193971 | −0.0969854 | − | 0.995286i | \(-0.530920\pi\) | ||||
−0.0969854 | + | 0.995286i | \(0.530920\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.06395e10 | 1.29710 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.78904e10 | 0.853859 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.91252e9 | −0.110329 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.74713e10 | 1.28546 | 0.642731 | − | 0.766092i | \(-0.277801\pi\) | ||||
0.642731 | + | 0.766092i | \(0.277801\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.37702e10 | 0.844146 | 0.422073 | − | 0.906562i | \(-0.361303\pi\) | ||||
0.422073 | + | 0.906562i | \(0.361303\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.28989e9 | 0.175171 | 0.0875854 | − | 0.996157i | \(-0.472085\pi\) | ||||
0.0875854 | + | 0.996157i | \(0.472085\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.79739e10 | −1.51092 | −0.755458 | − | 0.655197i | \(-0.772586\pi\) | ||||
−0.755458 | + | 0.655197i | \(0.772586\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.83362e10 | 0.819980 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.11283e10 | 0.617114 | 0.308557 | − | 0.951206i | \(-0.400154\pi\) | ||||
0.308557 | + | 0.951206i | \(0.400154\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.42372e10 | 0.271861 | 0.135931 | − | 0.990718i | \(-0.456598\pi\) | ||||
0.135931 | + | 0.990718i | \(0.456598\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.45563e10 | −0.790063 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.77614e9 | 0.115837 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.78389e10 | 0.919789 | 0.459894 | − | 0.887974i | \(-0.347887\pi\) | ||||
0.459894 | + | 0.887974i | \(0.347887\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.67622e10 | −1.02444 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.87176e10 | 0.267641 | 0.133820 | − | 0.991006i | \(-0.457276\pi\) | ||||
0.133820 | + | 0.991006i | \(0.457276\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.90510e10 | 1.09159 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.80437e10 | 0.361439 | 0.180719 | − | 0.983535i | \(-0.442157\pi\) | ||||
0.180719 | + | 0.983535i | \(0.442157\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.12705e10 | −0.264954 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.46600e10 | 0.520036 | 0.260018 | − | 0.965604i | \(-0.416271\pi\) | ||||
0.260018 | + | 0.965604i | \(0.416271\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.03375e11 | −1.16427 | −0.582137 | − | 0.813090i | \(-0.697783\pi\) | ||||
−0.582137 | + | 0.813090i | \(0.697783\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.19909e11 | −2.31871 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.81403e11 | 1.85133 | 0.925666 | − | 0.378341i | \(-0.123505\pi\) | ||||
0.925666 | + | 0.378341i | \(0.123505\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.25487e11 | 1.20066 | 0.600332 | − | 0.799751i | \(-0.295035\pi\) | ||||
0.600332 | + | 0.799751i | \(0.295035\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.33561e11 | 1.23777 | 0.618886 | − | 0.785481i | \(-0.287584\pi\) | ||||
0.618886 | + | 0.785481i | \(0.287584\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.92430e10 | 0.341423 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.64450e10 | −0.138673 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.50635e9 | 0.0277940 | 0.0138970 | − | 0.999903i | \(-0.495576\pi\) | ||||
0.0138970 | + | 0.999903i | \(0.495576\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.52336e11 | −1.93991 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.72776e9 | −0.0631513 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.51195e10 | −0.597695 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.52981e10 | −0.630573 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.94357e11 | −1.89126 | −0.945629 | − | 0.325246i | \(-0.894553\pi\) | ||||
−0.945629 | + | 0.325246i | \(0.894553\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.40305e10 | −0.145660 | −0.0728301 | − | 0.997344i | \(-0.523203\pi\) | ||||
−0.0728301 | + | 0.997344i | \(0.523203\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.55229e11 | −1.50308 | −0.751539 | − | 0.659689i | \(-0.770688\pi\) | ||||
−0.751539 | + | 0.659689i | \(0.770688\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.30255e11 | −1.28069 | −0.640343 | − | 0.768089i | \(-0.721208\pi\) | ||||
−0.640343 | + | 0.768089i | \(0.721208\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.94390e11 | 1.05103 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.76903e11 | −0.904322 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.87485e10 | −0.142936 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.02953e10 | −0.377840 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.21212e11 | −0.555035 | −0.277518 | − | 0.960721i | \(-0.589512\pi\) | ||||
−0.277518 | + | 0.960721i | \(0.589512\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.04810e11 | 0.454677 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.52249e11 | 1.06536 | 0.532678 | − | 0.846318i | \(-0.321186\pi\) | ||||
0.532678 | + | 0.846318i | \(0.321186\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.01236e11 | 2.40797 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.68619e11 | 1.04789 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.99996e11 | −1.11079 | −0.555397 | − | 0.831585i | \(-0.687434\pi\) | ||||
−0.555397 | + | 0.831585i | \(0.687434\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.25625e11 | −0.453275 | −0.226638 | − | 0.973979i | \(-0.572773\pi\) | ||||
−0.226638 | + | 0.973979i | \(0.572773\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.31672e11 | 1.47968 | 0.739841 | − | 0.672782i | \(-0.234901\pi\) | ||||
0.739841 | + | 0.672782i | \(0.234901\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.53851e11 | −1.85082 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.83615e11 | −0.583421 | −0.291711 | − | 0.956507i | \(-0.594224\pi\) | ||||
−0.291711 | + | 0.956507i | \(0.594224\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.63077e10 | −0.0505372 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.65467e11 | −1.07778 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.77185e11 | 1.08532 | 0.542659 | − | 0.839953i | \(-0.317418\pi\) | ||||
0.542659 | + | 0.839953i | \(0.317418\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.45510e10 | 0.122089 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.69400e11 | 0.720623 | 0.360312 | − | 0.932832i | \(-0.382670\pi\) | ||||
0.360312 | + | 0.932832i | \(0.382670\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.54124e10 | 0.0647903 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.04102e11 | −0.508124 | −0.254062 | − | 0.967188i | \(-0.581767\pi\) | ||||
−0.254062 | + | 0.967188i | \(0.581767\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.10631e10 | 0.0975117 | 0.0487559 | − | 0.998811i | \(-0.484474\pi\) | ||||
0.0487559 | + | 0.998811i | \(0.484474\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.43681e11 | 1.95706 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.86342e11 | 0.634032 | 0.317016 | − | 0.948420i | \(-0.397319\pi\) | ||||
0.317016 | + | 0.948420i | \(0.397319\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.27853e11 | 0.493014 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.59328e11 | −1.15606 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.73016e11 | 0.753651 | 0.376826 | − | 0.926284i | \(-0.377016\pi\) | ||||
0.376826 | + | 0.926284i | \(0.377016\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.70676e11 | −0.909018 | −0.454509 | − | 0.890742i | \(-0.650185\pi\) | ||||
−0.454509 | + | 0.890742i | \(0.650185\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.85991e10 | 0.148438 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.70411e12 | 3.07838 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.60520e11 | −1.52057 | −0.760284 | − | 0.649590i | \(-0.774940\pi\) | ||||
−0.760284 | + | 0.649590i | \(0.774940\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.28520e11 | 0.893894 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.70866e11 | 0.779257 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.46565e11 | −1.34183 | −0.670914 | − | 0.741535i | \(-0.734098\pi\) | ||||
−0.670914 | + | 0.741535i | \(0.734098\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.27835e11 | −0.353468 | −0.176734 | − | 0.984259i | \(-0.556553\pi\) | ||||
−0.176734 | + | 0.984259i | \(0.556553\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.50528e11 | 1.11588 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.99602e11 | 0.290563 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.47351e11 | 0.903633 | 0.451817 | − | 0.892111i | \(-0.350776\pi\) | ||||
0.451817 | + | 0.892111i | \(0.350776\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.69898e11 | 0.779114 | 0.389557 | − | 0.921002i | \(-0.372628\pi\) | ||||
0.389557 | + | 0.921002i | \(0.372628\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.94621e11 | −0.517624 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.98042e11 | 0.768496 | 0.384248 | − | 0.923230i | \(-0.374461\pi\) | ||||
0.384248 | + | 0.923230i | \(0.374461\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.10867e11 | −0.383494 | −0.191747 | − | 0.981444i | \(-0.561415\pi\) | ||||
−0.191747 | + | 0.981444i | \(0.561415\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.49622e11 | −0.180873 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.47114e11 | −0.867517 | −0.433759 | − | 0.901029i | \(-0.642813\pi\) | ||||
−0.433759 | + | 0.901029i | \(0.642813\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.45964e11 | 0.962848 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.10294e11 | 0.120642 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.54275e12 | −1.65452 | −0.827260 | − | 0.561819i | \(-0.810102\pi\) | ||||
−0.827260 | + | 0.561819i | \(0.810102\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.62766e12 | −1.67846 | −0.839230 | − | 0.543777i | \(-0.816994\pi\) | ||||
−0.839230 | + | 0.543777i | \(0.816994\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.11591e12 | −1.12854 | −0.564268 | − | 0.825592i | \(-0.690842\pi\) | ||||
−0.564268 | + | 0.825592i | \(0.690842\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.30194e11 | 0.515832 | 0.257916 | − | 0.966167i | \(-0.416964\pi\) | ||||
0.257916 | + | 0.966167i | \(0.416964\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.19526e11 | −0.209512 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.83493e12 | −1.68556 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.29985e12 | −1.17158 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.10019e12 | 1.82284 | 0.911422 | − | 0.411473i | \(-0.134986\pi\) | ||||
0.911422 | + | 0.411473i | \(0.134986\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.22777e11 | 0.189766 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.74483e11 | 0.389388 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.05307e12 | −0.848351 | −0.424176 | − | 0.905580i | \(-0.639436\pi\) | ||||
−0.424176 | + | 0.905580i | \(0.639436\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.10556e12 | −1.63494 | −0.817470 | − | 0.575971i | \(-0.804624\pi\) | ||||
−0.817470 | + | 0.575971i | \(0.804624\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.63434e11 | −0.505809 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.16004e12 | 0.852845 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.88807e11 | 0.208523 | 0.104262 | − | 0.994550i | \(-0.466752\pi\) | ||||
0.104262 | + | 0.994550i | \(0.466752\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.17681e11 | −0.360584 | −0.180292 | − | 0.983613i | \(-0.557704\pi\) | ||||
−0.180292 | + | 0.983613i | \(0.557704\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.66595e12 | 1.13986 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.01747e11 | −0.397360 | −0.198680 | − | 0.980064i | \(-0.563665\pi\) | ||||
−0.198680 | + | 0.980064i | \(0.563665\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.65471e11 | 0.496632 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.62130e12 | 1.01562 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.73093e12 | −1.06555 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.67285e11 | 0.0994691 | 0.0497345 | − | 0.998762i | \(-0.484162\pi\) | ||||
0.0497345 | + | 0.998762i | \(0.484162\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.57966e12 | −0.923222 | −0.461611 | − | 0.887083i | \(-0.652728\pi\) | ||||
−0.461611 | + | 0.887083i | \(0.652728\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.05196e12 | −1.15884 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.29287e12 | −0.717804 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.10592e11 | 0.0593543 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.08968e12 | 1.10277 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.01178e12 | 1.02667 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.08736e12 | −1.54953 | −0.774765 | − | 0.632250i | \(-0.782132\pi\) | ||||
−0.774765 | + | 0.632250i | \(0.782132\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.96955e11 | −0.484051 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.62136e11 | 0.125194 | 0.0625969 | − | 0.998039i | \(-0.480062\pi\) | ||||
0.0625969 | + | 0.998039i | \(0.480062\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.14901e12 | 0.531057 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.17151e12 | 0.532702 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.64238e11 | −0.160338 | −0.0801691 | − | 0.996781i | \(-0.525546\pi\) | ||||
−0.0801691 | + | 0.996781i | \(0.525546\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.39879e11 | −0.103906 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.04052e12 | −1.27544 | −0.637721 | − | 0.770267i | \(-0.720123\pi\) | ||||
−0.637721 | + | 0.770267i | \(0.720123\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.01006e12 | 2.48119 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.35845e11 | 0.294294 | 0.147147 | − | 0.989115i | \(-0.452991\pi\) | ||||
0.147147 | + | 0.989115i | \(0.452991\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.44618e12 | 0.569324 | 0.284662 | − | 0.958628i | \(-0.408119\pi\) | ||||
0.284662 | + | 0.958628i | \(0.408119\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.67422e12 | 0.638717 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.26945e12 | −0.852371 | −0.426186 | − | 0.904636i | \(-0.640143\pi\) | ||||
−0.426186 | + | 0.904636i | \(0.640143\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.86229e11 | −0.359075 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.60391e11 | 0.344302 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.41977e12 | −1.18885 | −0.594423 | − | 0.804153i | \(-0.702619\pi\) | ||||
−0.594423 | + | 0.804153i | \(0.702619\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.55382e12 | 1.21668 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.32482e12 | 0.439959 | 0.219979 | − | 0.975505i | \(-0.429401\pi\) | ||||
0.219979 | + | 0.975505i | \(0.429401\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.87940e12 | −0.941838 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.19936e12 | 1.33279 | 0.666395 | − | 0.745599i | \(-0.267836\pi\) | ||||
0.666395 | + | 0.745599i | \(0.267836\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.05682e12 | 0.330418 | 0.165209 | − | 0.986259i | \(-0.447170\pi\) | ||||
0.165209 | + | 0.986259i | \(0.447170\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.32969e13 | 4.03508 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.97096e12 | 1.78523 | 0.892617 | − | 0.450816i | \(-0.148867\pi\) | ||||
0.892617 | + | 0.450816i | \(0.148867\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.26283e11 | −0.0656851 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.80650e12 | 0.802774 | 0.401387 | − | 0.915909i | \(-0.368528\pi\) | ||||
0.401387 | + | 0.915909i | \(0.368528\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.48302e12 | −0.411968 | −0.205984 | − | 0.978555i | \(-0.566039\pi\) | ||||
−0.205984 | + | 0.978555i | \(0.566039\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.53469e12 | 0.420158 | 0.210079 | − | 0.977684i | \(-0.432628\pi\) | ||||
0.210079 | + | 0.977684i | \(0.432628\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.13383e11 | 0.0833450 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.88657e12 | −0.756696 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.81597e12 | −1.48147 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.43498e12 | −1.11368 | −0.556839 | − | 0.830620i | \(-0.687986\pi\) | ||||
−0.556839 | + | 0.830620i | \(0.687986\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.80061e12 | −2.14798 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.62998e11 | 0.0632886 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.56257e12 | 1.06745 | 0.533725 | − | 0.845658i | \(-0.320792\pi\) | ||||
0.533725 | + | 0.845658i | \(0.320792\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.32818e12 | −0.767818 | −0.383909 | − | 0.923371i | \(-0.625422\pi\) | ||||
−0.383909 | + | 0.923371i | \(0.625422\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.31374e12 | −0.519093 | −0.259547 | − | 0.965731i | \(-0.583573\pi\) | ||||
−0.259547 | + | 0.965731i | \(0.583573\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.13933e13 | 2.52087 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.03697e12 | −1.51453 | −0.757263 | − | 0.653110i | \(-0.773464\pi\) | ||||
−0.757263 | + | 0.653110i | \(0.773464\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.00895e12 | −1.27559 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.20320e12 | −0.455060 | −0.227530 | − | 0.973771i | \(-0.573065\pi\) | ||||
−0.227530 | + | 0.973771i | \(0.573065\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.29570e12 | −1.48648 | −0.743242 | − | 0.669022i | \(-0.766713\pi\) | ||||
−0.743242 | + | 0.669022i | \(0.766713\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.98688e12 | 0.988852 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.47994e12 | −0.289519 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.30284e12 | 0.819416 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.47079e12 | −0.840073 | −0.420036 | − | 0.907507i | \(-0.637983\pi\) | ||||
−0.420036 | + | 0.907507i | \(0.637983\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.42095e12 | 0.625890 | 0.312945 | − | 0.949771i | \(-0.398684\pi\) | ||||
0.312945 | + | 0.949771i | \(0.398684\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.93805e11 | −0.179427 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.18730e12 | 1.61546 | 0.807728 | − | 0.589556i | \(-0.200697\pi\) | ||||
0.807728 | + | 0.589556i | \(0.200697\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.88670e12 | 0.848024 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.25551e11 | 0.0212243 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.88811e12 | −0.315047 | −0.157524 | − | 0.987515i | \(-0.550351\pi\) | ||||
−0.157524 | + | 0.987515i | \(0.550351\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.63148e12 | −0.915568 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.88720e12 | −0.463371 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.61907e12 | −0.253242 | −0.126621 | − | 0.991951i | \(-0.540413\pi\) | ||||
−0.126621 | + | 0.991951i | \(0.540413\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.00727e13 | 1.55542 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.48934e12 | −0.525238 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.06375e13 | −1.58099 | −0.790497 | − | 0.612466i | \(-0.790178\pi\) | ||||
−0.790497 | + | 0.612466i | \(0.790178\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.57737e12 | −0.663305 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.37761e12 | 0.340223 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.32770e13 | −1.85276 | −0.926380 | − | 0.376589i | \(-0.877097\pi\) | ||||
−0.926380 | + | 0.376589i | \(0.877097\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.39582e12 | −0.467989 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.87480e12 | −0.655293 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.60017e12 | 0.345221 | 0.172611 | − | 0.984990i | \(-0.444780\pi\) | ||||
0.172611 | + | 0.984990i | \(0.444780\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.26244e12 | 0.811176 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.14818e13 | −1.46906 | −0.734532 | − | 0.678574i | \(-0.762598\pi\) | ||||
−0.734532 | + | 0.678574i | \(0.762598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.73234e12 | −0.590843 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.75984e12 | −0.957090 | −0.478545 | − | 0.878063i | \(-0.658836\pi\) | ||||
−0.478545 | + | 0.878063i | \(0.658836\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.58115e12 | 0.310717 | 0.155358 | − | 0.987858i | \(-0.450347\pi\) | ||||
0.155358 | + | 0.987858i | \(0.450347\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.47191e12 | −0.412920 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.37683e12 | −0.508150 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.39208e12 | −0.962697 | −0.481349 | − | 0.876529i | \(-0.659853\pi\) | ||||
−0.481349 | + | 0.876529i | \(0.659853\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.10484e13 | 1.23748 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.15875e12 | 0.903009 | 0.451505 | − | 0.892269i | \(-0.350887\pi\) | ||||
0.451505 | + | 0.892269i | \(0.350887\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.27433e12 | 0.678167 | 0.339083 | − | 0.940756i | \(-0.389883\pi\) | ||||
0.339083 | + | 0.940756i | \(0.389883\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.08813e12 | 0.223047 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.48944e12 | 0.155398 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.12027e12 | 0.631106 | 0.315553 | − | 0.948908i | \(-0.397810\pi\) | ||||
0.315553 | + | 0.948908i | \(0.397810\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.62875e12 | 0.667765 | 0.333883 | − | 0.942615i | \(-0.391641\pi\) | ||||
0.333883 | + | 0.942615i | \(0.391641\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.50775e13 | −1.50131 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.00037e12 | 0.486501 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.50071e13 | 2.40511 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.40241e13 | −2.25805 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.19503e13 | 1.11043 | 0.555216 | − | 0.831706i | \(-0.312636\pi\) | ||||
0.555216 | + | 0.831706i | \(0.312636\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.25881e13 | −1.14331 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.62507e11 | 0.0505125 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.18887e13 | 1.04369 | 0.521844 | − | 0.853041i | \(-0.325244\pi\) | ||||
0.521844 | + | 0.853041i | \(0.325244\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.90751e12 | 0.512795 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.65013e13 | 1.40055 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.42317e12 | −0.539098 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.68063e13 | 1.37944 | 0.689722 | − | 0.724074i | \(-0.257733\pi\) | ||||
0.689722 | + | 0.724074i | \(0.257733\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.98473e13 | 1.61104 | 0.805521 | − | 0.592567i | \(-0.201886\pi\) | ||||
0.805521 | + | 0.592567i | \(0.201886\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.96702e12 | 0.156171 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.08460e13 | −0.851668 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.83992e12 | −0.371787 | −0.185893 | − | 0.982570i | \(-0.559518\pi\) | ||||
−0.185893 | + | 0.982570i | \(0.559518\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.41664e12 | 0.639499 | 0.319749 | − | 0.947502i | \(-0.396401\pi\) | ||||
0.319749 | + | 0.947502i | \(0.396401\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.16658e13 | 1.61064 | 0.805321 | − | 0.592839i | \(-0.201993\pi\) | ||||
0.805321 | + | 0.592839i | \(0.201993\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.67734e12 | −0.270420 | −0.135210 | − | 0.990817i | \(-0.543171\pi\) | ||||
−0.135210 | + | 0.990817i | \(0.543171\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.86601e12 | −0.494085 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.00144e13 | 2.13669 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.46942e13 | 1.02381 | 0.511903 | − | 0.859043i | \(-0.328941\pi\) | ||||
0.511903 | + | 0.859043i | \(0.328941\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.01980e13 | −0.702967 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.16829e13 | −1.46306 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.78505e13 | −1.85933 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.29738e13 | −0.847979 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.99845e13 | −1.29248 | −0.646238 | − | 0.763136i | \(-0.723659\pi\) | ||||
−0.646238 | + | 0.763136i | \(0.723659\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.11989e13 | −1.34245 | −0.671226 | − | 0.741252i | \(-0.734232\pi\) | ||||
−0.671226 | + | 0.741252i | \(0.734232\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.51809e13 | 1.57798 | 0.788992 | − | 0.614404i | \(-0.210603\pi\) | ||||
0.788992 | + | 0.614404i | \(0.210603\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.15905e13 | −1.32500 | −0.662498 | − | 0.749064i | \(-0.730504\pi\) | ||||
−0.662498 | + | 0.749064i | \(0.730504\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.90123e13 | 1.76202 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.52544e13 | 1.50227 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.18655e11 | −0.0364222 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.56077e12 | −0.205356 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.63182e13 | 1.50230 | 0.751152 | − | 0.660129i | \(-0.229498\pi\) | ||||
0.751152 | + | 0.660129i | \(0.229498\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.23513e12 | −0.236851 | −0.118425 | − | 0.992963i | \(-0.537785\pi\) | ||||
−0.118425 | + | 0.992963i | \(0.537785\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.56557e13 | −1.42024 | −0.710119 | − | 0.704081i | \(-0.751359\pi\) | ||||
−0.710119 | + | 0.704081i | \(0.751359\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.14044e13 | 1.70347 | 0.851735 | − | 0.523973i | \(-0.175551\pi\) | ||||
0.851735 | + | 0.523973i | \(0.175551\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.84329e13 | 0.989774 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.02313e13 | −0.538392 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.43512e12 | 0.491523 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.33278e13 | 0.680519 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.27772e12 | −0.165695 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.24548e13 | 1.60827 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.87001e13 | −1.89880 | −0.949400 | − | 0.314070i | \(-0.898307\pi\) | ||||
−0.949400 | + | 0.314070i | \(0.898307\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.73436e13 | −0.834269 | −0.417135 | − | 0.908845i | \(-0.636966\pi\) | ||||
−0.417135 | + | 0.908845i | \(0.636966\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.12602e13 | −1.01263 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.25858e13 | 0.587784 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.75232e12 | −0.0810387 | −0.0405194 | − | 0.999179i | \(-0.512901\pi\) | ||||
−0.0405194 | + | 0.999179i | \(0.512901\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.26916e12 | 0.148262 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.27347e13 | −1.91930 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.99977e13 | 0.880865 | 0.440432 | − | 0.897786i | \(-0.354825\pi\) | ||||
0.440432 | + | 0.897786i | \(0.354825\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.18913e13 | 0.518749 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.20716e13 | −2.65608 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.62137e12 | 0.195859 | 0.0979293 | − | 0.995193i | \(-0.468778\pi\) | ||||
0.0979293 | + | 0.995193i | \(0.468778\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.64959e13 | −0.685838 | −0.342919 | − | 0.939365i | \(-0.611416\pi\) | ||||
−0.342919 | + | 0.939365i | \(0.611416\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.44055e12 | −0.265228 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.99606e13 | −0.806490 | −0.403245 | − | 0.915092i | \(-0.632118\pi\) | ||||
−0.403245 | + | 0.915092i | \(0.632118\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.15720e12 | 0.0863363 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.83087e12 | 0.346805 | 0.173402 | − | 0.984851i | \(-0.444524\pi\) | ||||
0.173402 | + | 0.984851i | \(0.444524\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.19056e13 | −1.63026 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.02352e13 | −0.390763 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.47825e13 | 0.559105 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.47426e13 | −0.547268 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.03562e13 | 0.748647 | 0.374323 | − | 0.927298i | \(-0.377875\pi\) | ||||
0.374323 | + | 0.927298i | \(0.377875\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.66888e12 | −0.276851 | −0.138425 | − | 0.990373i | \(-0.544204\pi\) | ||||
−0.138425 | + | 0.990373i | \(0.544204\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.17951e13 | 0.421886 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.23017e12 | −0.218763 | −0.109382 | − | 0.994000i | \(-0.534887\pi\) | ||||
−0.109382 | + | 0.994000i | \(0.534887\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.75563e12 | 0.235041 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.22800e13 | −1.78585 | −0.892924 | − | 0.450207i | \(-0.851350\pi\) | ||||
−0.892924 | + | 0.450207i | \(0.851350\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.68565e13 | −1.58601 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.39698e13 | 0.464308 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.73672e13 | −1.23072 | −0.615359 | − | 0.788247i | \(-0.710989\pi\) | ||||
−0.615359 | + | 0.788247i | \(0.710989\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.37319e13 | 2.38480 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.66230e13 | 1.17389 | 0.586943 | − | 0.809628i | \(-0.300331\pi\) | ||||
0.586943 | + | 0.809628i | \(0.300331\pi\) | |||||||
\(998\) | 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 | 72.10.a.e.1.1 | 1 | ||
3.2 | odd | 2 | 8.10.a.a.1.1 | ✓ | 1 | ||
4.3 | odd | 2 | 144.10.a.n.1.1 | 1 | |||
12.11 | even | 2 | 16.10.a.c.1.1 | 1 | |||
15.2 | even | 4 | 200.10.c.b.49.2 | 2 | |||
15.8 | even | 4 | 200.10.c.b.49.1 | 2 | |||
15.14 | odd | 2 | 200.10.a.b.1.1 | 1 | |||
21.20 | even | 2 | 392.10.a.b.1.1 | 1 | |||
24.5 | odd | 2 | 64.10.a.f.1.1 | 1 | |||
24.11 | even | 2 | 64.10.a.d.1.1 | 1 | |||
48.5 | odd | 4 | 256.10.b.i.129.2 | 2 | |||
48.11 | even | 4 | 256.10.b.c.129.1 | 2 | |||
48.29 | odd | 4 | 256.10.b.i.129.1 | 2 | |||
48.35 | even | 4 | 256.10.b.c.129.2 | 2 | |||
60.23 | odd | 4 | 400.10.c.g.49.2 | 2 | |||
60.47 | odd | 4 | 400.10.c.g.49.1 | 2 | |||
60.59 | even | 2 | 400.10.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.10.a.a.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
16.10.a.c.1.1 | 1 | 12.11 | even | 2 | |||
64.10.a.d.1.1 | 1 | 24.11 | even | 2 | |||
64.10.a.f.1.1 | 1 | 24.5 | odd | 2 | |||
72.10.a.e.1.1 | 1 | 1.1 | even | 1 | trivial | ||
144.10.a.n.1.1 | 1 | 4.3 | odd | 2 | |||
200.10.a.b.1.1 | 1 | 15.14 | odd | 2 | |||
200.10.c.b.49.1 | 2 | 15.8 | even | 4 | |||
200.10.c.b.49.2 | 2 | 15.2 | even | 4 | |||
256.10.b.c.129.1 | 2 | 48.11 | even | 4 | |||
256.10.b.c.129.2 | 2 | 48.35 | even | 4 | |||
256.10.b.i.129.1 | 2 | 48.29 | odd | 4 | |||
256.10.b.i.129.2 | 2 | 48.5 | odd | 4 | |||
392.10.a.b.1.1 | 1 | 21.20 | even | 2 | |||
400.10.a.d.1.1 | 1 | 60.59 | even | 2 | |||
400.10.c.g.49.1 | 2 | 60.47 | odd | 4 | |||
400.10.c.g.49.2 | 2 | 60.23 | odd | 4 |