Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,26,Mod(1,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.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: | \(35.6397101957\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 9.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 48.0000 | 0.00828641 | 0.00414320 | − | 0.999991i | \(-0.498681\pi\) | ||||
0.00414320 | + | 0.999991i | \(0.498681\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.35521e7 | −0.999931 | ||||||||
\(5\) | 7.41990e8 | 1.35917 | 0.679584 | − | 0.733598i | \(-0.262160\pi\) | ||||
0.679584 | + | 0.733598i | \(0.262160\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.90806e10 | 1.06718 | 0.533588 | − | 0.845745i | \(-0.320843\pi\) | ||||
0.533588 | + | 0.845745i | \(0.320843\pi\) | |||||||
\(8\) | −3.22111e9 | −0.0165722 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.56155e10 | 0.0112626 | ||||||||
\(11\) | −8.41952e12 | −0.808870 | −0.404435 | − | 0.914567i | \(-0.632532\pi\) | ||||
−0.404435 | + | 0.914567i | \(0.632532\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.16510e13 | −0.972008 | −0.486004 | − | 0.873957i | \(-0.661546\pi\) | ||||
−0.486004 | + | 0.873957i | \(0.661546\pi\) | |||||||
\(14\) | 1.87587e12 | 0.00884305 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.12567e15 | 0.999794 | ||||||||
\(17\) | 2.51990e15 | 1.04899 | 0.524496 | − | 0.851413i | \(-0.324254\pi\) | ||||
0.524496 | + | 0.851413i | \(0.324254\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.08206e15 | −0.630421 | −0.315210 | − | 0.949022i | \(-0.602075\pi\) | ||||
−0.315210 | + | 0.949022i | \(0.602075\pi\) | |||||||
\(20\) | −2.48953e16 | −1.35907 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.04137e14 | −0.00670262 | ||||||||
\(23\) | 9.49953e16 | 0.903866 | 0.451933 | − | 0.892052i | \(-0.350735\pi\) | ||||
0.451933 | + | 0.892052i | \(0.350735\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.52526e17 | 0.847336 | ||||||||
\(26\) | −3.91925e15 | −0.00805445 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.31124e18 | −1.06710 | ||||||||
\(29\) | 2.71247e17 | 0.142361 | 0.0711803 | − | 0.997463i | \(-0.477323\pi\) | ||||
0.0711803 | + | 0.997463i | \(0.477323\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.29167e18 | 0.978599 | 0.489299 | − | 0.872116i | \(-0.337253\pi\) | ||||
0.489299 | + | 0.872116i | \(0.337253\pi\) | |||||||
\(32\) | 1.62115e17 | 0.0248569 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.20955e17 | 0.00869237 | ||||||||
\(35\) | 2.89974e19 | 1.45047 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.03015e19 | 0.506998 | 0.253499 | − | 0.967336i | \(-0.418419\pi\) | ||||
0.253499 | + | 0.967336i | \(0.418419\pi\) | |||||||
\(38\) | −2.91939e17 | −0.00522392 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.39003e18 | −0.0225245 | ||||||||
\(41\) | 1.83744e20 | 1.27179 | 0.635895 | − | 0.771775i | \(-0.280631\pi\) | ||||
0.635895 | + | 0.771775i | \(0.280631\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.00902e20 | 1.14834 | 0.574168 | − | 0.818737i | \(-0.305326\pi\) | ||||
0.574168 | + | 0.818737i | \(0.305326\pi\) | |||||||
\(44\) | 2.82493e20 | 0.808814 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.55977e18 | 0.00748980 | ||||||||
\(47\) | 9.24361e20 | 1.16043 | 0.580214 | − | 0.814464i | \(-0.302969\pi\) | ||||
0.580214 | + | 0.814464i | \(0.302969\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.86224e20 | 0.138863 | ||||||||
\(50\) | 1.21212e19 | 0.00702137 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.73957e21 | 0.971941 | ||||||||
\(53\) | 9.90292e20 | 0.276895 | 0.138447 | − | 0.990370i | \(-0.455789\pi\) | ||||
0.138447 | + | 0.990370i | \(0.455789\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.24719e21 | −1.09939 | ||||||||
\(56\) | −1.25883e20 | −0.0176855 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.30199e19 | 0.00117966 | ||||||||
\(59\) | −1.30526e22 | −0.955093 | −0.477547 | − | 0.878606i | \(-0.658474\pi\) | ||||
−0.477547 | + | 0.878606i | \(0.658474\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.01545e21 | 0.434875 | 0.217438 | − | 0.976074i | \(-0.430230\pi\) | ||||
0.217438 | + | 0.976074i | \(0.430230\pi\) | |||||||
\(62\) | 2.06000e20 | 0.00810907 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.77634e22 | −0.999588 | ||||||||
\(65\) | −6.05842e22 | −1.32112 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.66891e22 | −0.398473 | −0.199236 | − | 0.979951i | \(-0.563846\pi\) | ||||
−0.199236 | + | 0.979951i | \(0.563846\pi\) | |||||||
\(68\) | −8.45480e22 | −1.04892 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.39188e21 | 0.0120192 | ||||||||
\(71\) | 1.92391e23 | 1.39141 | 0.695704 | − | 0.718329i | \(-0.255093\pi\) | ||||
0.695704 | + | 0.718329i | \(0.255093\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.24046e22 | 0.216709 | 0.108355 | − | 0.994112i | \(-0.465442\pi\) | ||||
0.108355 | + | 0.994112i | \(0.465442\pi\) | |||||||
\(74\) | 9.74471e20 | 0.00420119 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.04066e23 | 0.630377 | ||||||||
\(77\) | −3.29040e23 | −0.863206 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.71681e23 | −0.517274 | −0.258637 | − | 0.965975i | \(-0.583273\pi\) | ||||
−0.258637 | + | 0.965975i | \(0.583273\pi\) | |||||||
\(80\) | 8.35234e23 | 1.35889 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.81972e21 | 0.0105386 | ||||||||
\(83\) | 9.31454e23 | 0.956501 | 0.478251 | − | 0.878223i | \(-0.341271\pi\) | ||||
0.478251 | + | 0.878223i | \(0.341271\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.86974e24 | 1.42575 | ||||||||
\(86\) | 1.44433e22 | 0.00951558 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.71202e22 | 0.0134048 | ||||||||
\(89\) | 1.76364e24 | 0.756892 | 0.378446 | − | 0.925623i | \(-0.376459\pi\) | ||||
0.378446 | + | 0.925623i | \(0.376459\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.19097e24 | −1.03730 | ||||||||
\(92\) | −3.18729e24 | −0.903804 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.43693e22 | 0.00961578 | ||||||||
\(95\) | −4.51282e24 | −0.856847 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.82924e24 | 0.414022 | 0.207011 | − | 0.978339i | \(-0.433626\pi\) | ||||
0.207011 | + | 0.978339i | \(0.433626\pi\) | |||||||
\(98\) | 8.93877e21 | 0.00115067 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.47278e24 | −0.847278 | ||||||||
\(101\) | −1.86342e24 | −0.164549 | −0.0822744 | − | 0.996610i | \(-0.526218\pi\) | ||||
−0.0822744 | + | 0.996610i | \(0.526218\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.85812e24 | 0.335740 | 0.167870 | − | 0.985809i | \(-0.446311\pi\) | ||||
0.167870 | + | 0.985809i | \(0.446311\pi\) | |||||||
\(104\) | 2.63007e23 | 0.0161084 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.75340e22 | 0.00229446 | ||||||||
\(107\) | −3.58304e25 | −1.53799 | −0.768997 | − | 0.639252i | \(-0.779244\pi\) | ||||
−0.768997 | + | 0.639252i | \(0.779244\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.77795e25 | −1.62709 | −0.813543 | − | 0.581505i | \(-0.802464\pi\) | ||||
−0.813543 | + | 0.581505i | \(0.802464\pi\) | |||||||
\(110\) | −2.99865e23 | −0.00910999 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.39918e25 | 1.06696 | ||||||||
\(113\) | 7.46476e25 | 1.62008 | 0.810038 | − | 0.586378i | \(-0.199447\pi\) | ||||
0.810038 | + | 0.586378i | \(0.199447\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.04855e25 | 1.22851 | ||||||||
\(116\) | −9.10091e24 | −0.142351 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.26523e23 | −0.00791429 | ||||||||
\(119\) | 9.84792e25 | 1.11946 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.74588e25 | −0.345730 | ||||||||
\(122\) | 4.32742e23 | 0.00360355 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.43995e26 | −0.978532 | ||||||||
\(125\) | −3.37587e25 | −0.207496 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.35905e26 | 1.69305 | 0.846524 | − | 0.532350i | \(-0.178691\pi\) | ||||
0.846524 | + | 0.532350i | \(0.178691\pi\) | |||||||
\(128\) | −7.25231e24 | −0.0331399 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.90804e24 | −0.0109474 | ||||||||
\(131\) | 1.74971e26 | 0.598513 | 0.299257 | − | 0.954173i | \(-0.403261\pi\) | ||||
0.299257 | + | 0.954173i | \(0.403261\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.37690e26 | −0.672769 | ||||||||
\(134\) | −1.28108e24 | −0.00330191 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.11689e24 | −0.0173841 | ||||||||
\(137\) | −6.18313e26 | −1.20837 | −0.604187 | − | 0.796843i | \(-0.706502\pi\) | ||||
−0.604187 | + | 0.796843i | \(0.706502\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.84462e26 | −0.789905 | −0.394952 | − | 0.918702i | \(-0.629239\pi\) | ||||
−0.394952 | + | 0.918702i | \(0.629239\pi\) | |||||||
\(140\) | −9.72925e26 | −1.45037 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.23474e24 | 0.0115298 | ||||||||
\(143\) | 6.87462e26 | 0.786228 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.01262e26 | 0.193492 | ||||||||
\(146\) | 2.03542e24 | 0.00179574 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.81158e26 | −0.506963 | ||||||||
\(149\) | −9.05569e26 | −0.619574 | −0.309787 | − | 0.950806i | \(-0.600258\pi\) | ||||
−0.309787 | + | 0.950806i | \(0.600258\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.16190e27 | 0.672907 | 0.336454 | − | 0.941700i | \(-0.390772\pi\) | ||||
0.336454 | + | 0.941700i | \(0.390772\pi\) | |||||||
\(152\) | 1.95910e25 | 0.0104475 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.57939e25 | −0.00715287 | ||||||||
\(155\) | 3.18437e27 | 1.33008 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.41505e26 | −0.121521 | −0.0607605 | − | 0.998152i | \(-0.519353\pi\) | ||||
−0.0607605 | + | 0.998152i | \(0.519353\pi\) | |||||||
\(158\) | −1.30407e25 | −0.00428634 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.20287e26 | 0.0337847 | ||||||||
\(161\) | 3.71247e27 | 0.964583 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.63202e27 | 1.03140 | 0.515698 | − | 0.856771i | \(-0.327533\pi\) | ||||
0.515698 | + | 0.856771i | \(0.327533\pi\) | |||||||
\(164\) | −6.16501e27 | −1.27170 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.47098e25 | 0.00792596 | ||||||||
\(167\) | 8.26470e27 | 1.35916 | 0.679581 | − | 0.733600i | \(-0.262162\pi\) | ||||
0.679581 | + | 0.733600i | \(0.262162\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.89517e26 | −0.0552004 | ||||||||
\(170\) | 8.97475e25 | 0.0118144 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.00959e28 | −1.14826 | ||||||||
\(173\) | 6.02602e27 | 0.637462 | 0.318731 | − | 0.947845i | \(-0.396743\pi\) | ||||
0.318731 | + | 0.947845i | \(0.396743\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.86886e27 | 0.904256 | ||||||||
\(176\) | −9.47758e27 | −0.808703 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.46545e25 | 0.00627191 | ||||||||
\(179\) | −2.41023e28 | −1.66493 | −0.832463 | − | 0.554081i | \(-0.813070\pi\) | ||||
−0.832463 | + | 0.554081i | \(0.813070\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.19193e27 | −0.492498 | −0.246249 | − | 0.969207i | \(-0.579198\pi\) | ||||
−0.246249 | + | 0.969207i | \(0.579198\pi\) | |||||||
\(182\) | −1.53167e26 | −0.00859551 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.05991e26 | −0.0149791 | ||||||||
\(185\) | 1.50635e28 | 0.689095 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.12163e28 | −0.848497 | ||||||||
\(188\) | −3.10143e28 | −1.16035 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.16616e26 | −0.00710018 | ||||||||
\(191\) | −5.50602e27 | −0.169013 | −0.0845066 | − | 0.996423i | \(-0.526931\pi\) | ||||
−0.0845066 | + | 0.996423i | \(0.526931\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.08716e28 | 0.562457 | 0.281228 | − | 0.959641i | \(-0.409258\pi\) | ||||
0.281228 | + | 0.959641i | \(0.409258\pi\) | |||||||
\(194\) | 1.35804e26 | 0.00343075 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.24823e27 | −0.138853 | ||||||||
\(197\) | 5.99370e28 | 1.24988 | 0.624938 | − | 0.780674i | \(-0.285124\pi\) | ||||
0.624938 | + | 0.780674i | \(0.285124\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.24042e27 | 0.0411782 | 0.0205891 | − | 0.999788i | \(-0.493446\pi\) | ||||
0.0205891 | + | 0.999788i | \(0.493446\pi\) | |||||||
\(200\) | −8.13414e26 | −0.0140423 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.94444e25 | −0.00136352 | ||||||||
\(203\) | 1.06005e28 | 0.151924 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.36336e29 | 1.72858 | ||||||||
\(206\) | 2.33190e26 | 0.00278208 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −9.19120e28 | −0.971808 | ||||||||
\(209\) | 5.12080e28 | 0.509928 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.52475e28 | −0.665214 | −0.332607 | − | 0.943066i | \(-0.607928\pi\) | ||||
−0.332607 | + | 0.943066i | \(0.607928\pi\) | |||||||
\(212\) | −3.32264e28 | −0.276876 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.71986e27 | −0.0127444 | ||||||||
\(215\) | 2.23266e29 | 1.56078 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.67721e29 | 1.04434 | ||||||||
\(218\) | −2.29342e27 | −0.0134827 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.09607e29 | 1.09931 | ||||||||
\(221\) | −2.05752e29 | −1.01963 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.16696e29 | −1.40227 | −0.701135 | − | 0.713029i | \(-0.747323\pi\) | ||||
−0.701135 | + | 0.713029i | \(0.747323\pi\) | |||||||
\(224\) | 6.33554e27 | 0.0265267 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.58308e27 | 0.0134246 | ||||||||
\(227\) | −3.85094e29 | −1.36535 | −0.682674 | − | 0.730723i | \(-0.739183\pi\) | ||||
−0.682674 | + | 0.730723i | \(0.739183\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.68261e29 | −1.80553 | −0.902765 | − | 0.430134i | \(-0.858466\pi\) | ||||
−0.902765 | + | 0.430134i | \(0.858466\pi\) | |||||||
\(230\) | 3.38331e27 | 0.0101799 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.73718e26 | −0.00235924 | ||||||||
\(233\) | −4.95586e29 | −1.26815 | −0.634075 | − | 0.773272i | \(-0.718619\pi\) | ||||
−0.634075 | + | 0.773272i | \(0.718619\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.85867e29 | 1.57722 | ||||||||
\(236\) | 4.37941e29 | 0.955028 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.72700e27 | 0.00927628 | ||||||||
\(239\) | 1.44023e29 | 0.268200 | 0.134100 | − | 0.990968i | \(-0.457186\pi\) | ||||
0.134100 | + | 0.990968i | \(0.457186\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.19456e29 | −0.536041 | −0.268020 | − | 0.963413i | \(-0.586369\pi\) | ||||
−0.268020 | + | 0.963413i | \(0.586369\pi\) | |||||||
\(242\) | −1.79802e27 | −0.00286486 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.02488e29 | −0.434845 | ||||||||
\(245\) | 1.38177e29 | 0.188738 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.96606e29 | 0.612774 | ||||||||
\(248\) | −1.38239e28 | −0.0162176 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.62042e27 | −0.00171940 | ||||||||
\(251\) | −6.21677e29 | −0.627543 | −0.313771 | − | 0.949499i | \(-0.601593\pi\) | ||||
−0.313771 | + | 0.949499i | \(0.601593\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.99814e29 | −0.731110 | ||||||||
\(254\) | 1.61234e28 | 0.0140293 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.26678e30 | 0.999313 | ||||||||
\(257\) | 2.29446e30 | 1.72392 | 0.861960 | − | 0.506977i | \(-0.169237\pi\) | ||||
0.861960 | + | 0.506977i | \(0.169237\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.93394e29 | 0.541056 | ||||||||
\(260\) | 2.03273e30 | 1.32103 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.39859e27 | 0.00495952 | ||||||||
\(263\) | −7.73316e29 | −0.435422 | −0.217711 | − | 0.976013i | \(-0.569859\pi\) | ||||
−0.217711 | + | 0.976013i | \(0.569859\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.34787e29 | 0.376347 | ||||||||
\(266\) | −1.14091e28 | −0.00557484 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.95475e29 | 0.398445 | ||||||||
\(269\) | −3.62259e30 | −1.53856 | −0.769282 | − | 0.638910i | \(-0.779386\pi\) | ||||
−0.769282 | + | 0.638910i | \(0.779386\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.62767e30 | −1.40447 | −0.702234 | − | 0.711946i | \(-0.747814\pi\) | ||||
−0.702234 | + | 0.711946i | \(0.747814\pi\) | |||||||
\(272\) | 2.83657e30 | 1.04877 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.96790e28 | −0.0100131 | ||||||||
\(275\) | −2.12614e30 | −0.685384 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.54808e30 | −0.750266 | −0.375133 | − | 0.926971i | \(-0.622403\pi\) | ||||
−0.375133 | + | 0.926971i | \(0.622403\pi\) | |||||||
\(278\) | −2.32542e28 | −0.00654547 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −9.34040e28 | −0.0240375 | ||||||||
\(281\) | −3.59817e30 | −0.885631 | −0.442816 | − | 0.896613i | \(-0.646020\pi\) | ||||
−0.442816 | + | 0.896613i | \(0.646020\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.82265e30 | 0.861061 | 0.430530 | − | 0.902576i | \(-0.358327\pi\) | ||||
0.430530 | + | 0.902576i | \(0.358327\pi\) | |||||||
\(284\) | −6.45511e30 | −1.39131 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.29982e28 | 0.00651500 | ||||||||
\(287\) | 7.18084e30 | 1.35722 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.79269e29 | 0.100382 | ||||||||
\(290\) | 9.66060e27 | 0.00160335 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.42276e30 | −0.216694 | ||||||||
\(293\) | −1.30007e29 | −0.0189723 | −0.00948615 | − | 0.999955i | \(-0.503020\pi\) | ||||
−0.00948615 | + | 0.999955i | \(0.503020\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.68487e30 | −1.29813 | ||||||||
\(296\) | −6.53934e28 | −0.00840210 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.34673e28 | −0.00513404 | ||||||||
\(299\) | −7.75646e30 | −0.878565 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.17594e31 | 1.22548 | ||||||||
\(302\) | 5.57710e28 | 0.00557599 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.84638e30 | −0.630291 | ||||||||
\(305\) | 6.68937e30 | 0.591068 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.43602e31 | 1.16931 | 0.584657 | − | 0.811281i | \(-0.301229\pi\) | ||||
0.584657 | + | 0.811281i | \(0.301229\pi\) | |||||||
\(308\) | 1.10400e31 | 0.863146 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.52850e29 | 0.0110216 | ||||||||
\(311\) | 2.24630e31 | 1.55584 | 0.777918 | − | 0.628366i | \(-0.216276\pi\) | ||||
0.777918 | + | 0.628366i | \(0.216276\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.37956e30 | −0.0881934 | −0.0440967 | − | 0.999027i | \(-0.514041\pi\) | ||||
−0.0440967 | + | 0.999027i | \(0.514041\pi\) | |||||||
\(314\) | −1.63922e28 | −0.00100697 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.11548e30 | 0.517239 | ||||||||
\(317\) | 1.02787e31 | 0.560655 | 0.280327 | − | 0.959904i | \(-0.409557\pi\) | ||||
0.280327 | + | 0.959904i | \(0.409557\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.28377e30 | −0.115151 | ||||||||
\(320\) | −2.80200e31 | −1.35861 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.78199e29 | 0.00799293 | ||||||||
\(323\) | −1.53262e31 | −0.661306 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.06190e31 | −0.823617 | ||||||||
\(326\) | 2.22337e29 | 0.00854656 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.91861e29 | −0.0210764 | ||||||||
\(329\) | 3.61246e31 | 1.23838 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.75356e30 | −0.182847 | −0.0914233 | − | 0.995812i | \(-0.529142\pi\) | ||||
−0.0914233 | + | 0.995812i | \(0.529142\pi\) | |||||||
\(332\) | −3.12523e31 | −0.956435 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.96706e29 | 0.0112626 | ||||||||
\(335\) | −1.98030e31 | −0.541591 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.69268e31 | 1.69913 | 0.849564 | − | 0.527485i | \(-0.176865\pi\) | ||||
0.849564 | + | 0.527485i | \(0.176865\pi\) | |||||||
\(338\) | −1.86968e28 | −0.000457413 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.27338e31 | −1.42566 | ||||||||
\(341\) | −3.61337e31 | −0.791559 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.51320e31 | −0.918984 | ||||||||
\(344\) | −9.69239e29 | −0.0190305 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.89249e29 | 0.00528227 | ||||||||
\(347\) | −9.41781e29 | −0.0165894 | −0.00829472 | − | 0.999966i | \(-0.502640\pi\) | ||||
−0.00829472 | + | 0.999966i | \(0.502640\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.39081e31 | −0.555886 | −0.277943 | − | 0.960598i | \(-0.589653\pi\) | ||||
−0.277943 | + | 0.960598i | \(0.589653\pi\) | |||||||
\(350\) | 4.73705e29 | 0.00749303 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.36493e30 | −0.0201060 | ||||||||
\(353\) | −1.30313e31 | −0.185269 | −0.0926346 | − | 0.995700i | \(-0.529529\pi\) | ||||
−0.0926346 | + | 0.995700i | \(0.529529\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.42752e32 | 1.89116 | ||||||||
\(356\) | −5.91737e31 | −0.756840 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.15691e30 | −0.0137963 | ||||||||
\(359\) | 1.30336e32 | 1.50101 | 0.750506 | − | 0.660864i | \(-0.229810\pi\) | ||||
0.750506 | + | 0.660864i | \(0.229810\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.60851e31 | −0.602570 | ||||||||
\(362\) | −3.93213e29 | −0.00408104 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.07064e32 | 1.03723 | ||||||||
\(365\) | 3.14638e31 | 0.294544 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.06294e32 | −1.80369 | −0.901844 | − | 0.432061i | \(-0.857786\pi\) | ||||
−0.901844 | + | 0.432061i | \(0.857786\pi\) | |||||||
\(368\) | 1.06933e32 | 0.903680 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.23048e29 | 0.00571012 | ||||||||
\(371\) | 3.87012e31 | 0.295495 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.46051e32 | 1.75657 | 0.878283 | − | 0.478142i | \(-0.158689\pi\) | ||||
0.878283 | + | 0.478142i | \(0.158689\pi\) | |||||||
\(374\) | −1.01838e30 | −0.00703099 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.97747e30 | −0.0192309 | ||||||||
\(377\) | −2.21476e31 | −0.138376 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.12743e31 | 0.416815 | 0.208407 | − | 0.978042i | \(-0.433172\pi\) | ||||
0.208407 | + | 0.978042i | \(0.433172\pi\) | |||||||
\(380\) | 1.51415e32 | 0.856788 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.64289e29 | −0.00140051 | ||||||||
\(383\) | −1.33051e32 | −0.682393 | −0.341196 | − | 0.939992i | \(-0.610832\pi\) | ||||
−0.341196 | + | 0.939992i | \(0.610832\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.44144e32 | −1.17324 | ||||||||
\(386\) | 1.00184e30 | 0.00466075 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.49271e31 | −0.413993 | ||||||||
\(389\) | −2.40509e32 | −1.01569 | −0.507844 | − | 0.861449i | \(-0.669557\pi\) | ||||
−0.507844 | + | 0.861449i | \(0.669557\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.39379e32 | 0.948147 | ||||||||
\(392\) | −5.99850e29 | −0.00230127 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.87698e30 | 0.0103570 | ||||||||
\(395\) | −2.01585e32 | −0.703062 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.12137e32 | −1.34946 | −0.674730 | − | 0.738065i | \(-0.735740\pi\) | ||||
−0.674730 | + | 0.738065i | \(0.735740\pi\) | |||||||
\(398\) | 1.07540e29 | 0.000341219 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.84260e32 | 0.847161 | ||||||||
\(401\) | 7.16647e31 | 0.207014 | 0.103507 | − | 0.994629i | \(-0.466994\pi\) | ||||
0.103507 | + | 0.994629i | \(0.466994\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.50419e32 | −0.951206 | ||||||||
\(404\) | 6.25219e31 | 0.164537 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.08824e29 | 0.00125890 | ||||||||
\(407\) | −1.70929e32 | −0.410095 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.34430e32 | 0.303358 | 0.151679 | − | 0.988430i | \(-0.451532\pi\) | ||||
0.151679 | + | 0.988430i | \(0.451532\pi\) | |||||||
\(410\) | 6.54415e30 | 0.0143237 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.63000e32 | −0.335717 | ||||||||
\(413\) | −5.10102e32 | −1.01925 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.91130e32 | 1.30004 | ||||||||
\(416\) | −1.32368e31 | −0.0241612 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.45798e30 | 0.00422547 | ||||||||
\(419\) | 1.71876e32 | 0.286774 | 0.143387 | − | 0.989667i | \(-0.454201\pi\) | ||||
0.143387 | + | 0.989667i | \(0.454201\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.27664e32 | −1.30115 | −0.650576 | − | 0.759441i | \(-0.725472\pi\) | ||||
−0.650576 | + | 0.759441i | \(0.725472\pi\) | |||||||
\(422\) | −3.61188e30 | −0.00551223 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.18984e30 | −0.00458877 | ||||||||
\(425\) | 6.36340e32 | 0.888848 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.52329e32 | 0.464088 | ||||||||
\(428\) | 1.20219e33 | 1.53789 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.07168e31 | 0.0129333 | ||||||||
\(431\) | 7.83836e31 | 0.0918881 | 0.0459441 | − | 0.998944i | \(-0.485370\pi\) | ||||
0.0459441 | + | 0.998944i | \(0.485370\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.33273e32 | 0.700635 | 0.350318 | − | 0.936631i | \(-0.386074\pi\) | ||||
0.350318 | + | 0.936631i | \(0.386074\pi\) | |||||||
\(434\) | 8.05060e30 | 0.00865380 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.60310e33 | 1.62697 | ||||||||
\(437\) | −5.77767e32 | −0.569816 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.48299e33 | −1.38144 | −0.690718 | − | 0.723124i | \(-0.742705\pi\) | ||||
−0.690718 | + | 0.723124i | \(0.742705\pi\) | |||||||
\(440\) | 2.01229e31 | 0.0182193 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.87612e30 | −0.00844905 | ||||||||
\(443\) | 1.20901e33 | 1.00551 | 0.502753 | − | 0.864430i | \(-0.332321\pi\) | ||||
0.502753 | + | 0.864430i | \(0.332321\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.30860e33 | 1.02874 | ||||||||
\(446\) | −1.52014e31 | −0.0116198 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.47581e33 | −1.06674 | ||||||||
\(449\) | 9.48861e32 | 0.666996 | 0.333498 | − | 0.942751i | \(-0.391771\pi\) | ||||
0.333498 | + | 0.942751i | \(0.391771\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.54704e33 | −1.02871 | ||||||||
\(452\) | −2.50459e33 | −1.61996 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.84845e31 | −0.0113138 | ||||||||
\(455\) | −2.36767e33 | −1.40987 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.90644e33 | 1.07466 | 0.537329 | − | 0.843373i | \(-0.319433\pi\) | ||||
0.537329 | + | 0.843373i | \(0.319433\pi\) | |||||||
\(458\) | −2.72765e31 | −0.0149614 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.36494e33 | −1.22842 | ||||||||
\(461\) | 4.56270e31 | 0.0230653 | 0.0115327 | − | 0.999933i | \(-0.496329\pi\) | ||||
0.0115327 | + | 0.999933i | \(0.496329\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.13521e33 | 1.02254 | 0.511269 | − | 0.859421i | \(-0.329176\pi\) | ||||
0.511269 | + | 0.859421i | \(0.329176\pi\) | |||||||
\(464\) | 3.05334e32 | 0.142331 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.37882e31 | −0.0105084 | ||||||||
\(467\) | 2.67225e33 | 1.14926 | 0.574628 | − | 0.818415i | \(-0.305147\pi\) | ||||
0.574628 | + | 0.818415i | \(0.305147\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.04302e33 | −0.425240 | ||||||||
\(470\) | 3.29216e31 | 0.0130695 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.20438e31 | 0.0158280 | ||||||||
\(473\) | −2.53345e33 | −0.928854 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.53588e33 | −0.534178 | ||||||||
\(476\) | −3.30419e33 | −1.11938 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.91313e30 | 0.00222242 | ||||||||
\(479\) | −1.97240e33 | −0.617733 | −0.308867 | − | 0.951105i | \(-0.599950\pi\) | ||||
−0.308867 | + | 0.951105i | \(0.599950\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.65764e33 | −0.492806 | ||||||||
\(482\) | −1.53339e31 | −0.00444185 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.25682e33 | 0.345706 | ||||||||
\(485\) | 2.09927e33 | 0.562725 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.96366e32 | −0.100922 | −0.0504608 | − | 0.998726i | \(-0.516069\pi\) | ||||
−0.0504608 | + | 0.998726i | \(0.516069\pi\) | |||||||
\(488\) | −2.90398e31 | −0.00720686 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.63248e30 | 0.00156396 | ||||||||
\(491\) | 7.22626e33 | 1.66110 | 0.830548 | − | 0.556947i | \(-0.188027\pi\) | ||||
0.830548 | + | 0.556947i | \(0.188027\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.83515e32 | 0.149335 | ||||||||
\(494\) | 2.38371e31 | 0.00507769 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.83099e33 | 0.978397 | ||||||||
\(497\) | 7.51874e33 | 1.48488 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.19830e33 | 1.53981 | 0.769905 | − | 0.638159i | \(-0.220304\pi\) | ||||
0.769905 | + | 0.638159i | \(0.220304\pi\) | |||||||
\(500\) | 1.13268e33 | 0.207482 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.98405e31 | −0.00520008 | ||||||||
\(503\) | −4.72562e33 | −0.803265 | −0.401633 | − | 0.915801i | \(-0.631557\pi\) | ||||
−0.401633 | + | 0.915801i | \(0.631557\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.38264e33 | −0.223649 | ||||||||
\(506\) | −3.83911e31 | −0.00605827 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.12703e34 | −1.69293 | ||||||||
\(509\) | −1.96955e33 | −0.288665 | −0.144332 | − | 0.989529i | \(-0.546103\pi\) | ||||
−0.144332 | + | 0.989529i | \(0.546103\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.65720e33 | 0.231267 | ||||||||
\(512\) | 3.04153e32 | 0.0414207 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.10134e32 | 0.0142851 | ||||||||
\(515\) | 3.60468e33 | 0.456327 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.78267e33 | −0.938635 | ||||||||
\(518\) | 3.80829e31 | 0.00448341 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.95149e32 | 0.0218940 | ||||||||
\(521\) | −7.39782e33 | −0.810274 | −0.405137 | − | 0.914256i | \(-0.632776\pi\) | ||||
−0.405137 | + | 0.914256i | \(0.632776\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.70332e34 | 1.77838 | 0.889191 | − | 0.457535i | \(-0.151268\pi\) | ||||
0.889191 | + | 0.457535i | \(0.151268\pi\) | |||||||
\(524\) | −5.87063e33 | −0.598472 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.71192e31 | −0.00360808 | ||||||||
\(527\) | 1.08146e34 | 1.02654 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.02166e33 | −0.183026 | ||||||||
\(530\) | 3.52698e31 | 0.00311856 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.97502e33 | 0.672723 | ||||||||
\(533\) | −1.50029e34 | −1.23619 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.65858e34 | −2.09039 | ||||||||
\(536\) | 8.59686e31 | 0.00660358 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.73884e32 | −0.0127492 | ||||||||
\(539\) | −1.56792e33 | −0.112322 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.28681e34 | −0.880134 | −0.440067 | − | 0.897965i | \(-0.645045\pi\) | ||||
−0.440067 | + | 0.897965i | \(0.645045\pi\) | |||||||
\(542\) | −1.74128e32 | −0.0116380 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.08513e32 | 0.0260747 | ||||||||
\(545\) | −3.54519e34 | −2.21148 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.06624e34 | 1.23123 | 0.615616 | − | 0.788046i | \(-0.288907\pi\) | ||||
0.615616 | + | 0.788046i | \(0.288907\pi\) | |||||||
\(548\) | 2.07457e34 | 1.20829 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.02055e32 | −0.00567937 | ||||||||
\(551\) | −1.64974e33 | −0.0897471 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.06175e34 | −0.552022 | ||||||||
\(554\) | −1.22308e32 | −0.00621701 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.62547e34 | 0.789851 | ||||||||
\(557\) | 3.28751e33 | 0.156198 | 0.0780992 | − | 0.996946i | \(-0.475115\pi\) | ||||
0.0780992 | + | 0.996946i | \(0.475115\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.45689e34 | −1.11619 | ||||||||
\(560\) | 3.26415e34 | 1.45017 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.72712e32 | −0.00733870 | ||||||||
\(563\) | 1.80804e34 | 0.751371 | 0.375685 | − | 0.926747i | \(-0.377407\pi\) | ||||
0.375685 | + | 0.926747i | \(0.377407\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.53878e34 | 2.20195 | ||||||||
\(566\) | 1.83487e32 | 0.00713510 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.19712e32 | −0.0230587 | ||||||||
\(569\) | 3.05967e33 | 0.111371 | 0.0556854 | − | 0.998448i | \(-0.482266\pi\) | ||||
0.0556854 | + | 0.998448i | \(0.482266\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.29884e34 | −0.452486 | −0.226243 | − | 0.974071i | \(-0.572644\pi\) | ||||
−0.226243 | + | 0.974071i | \(0.572644\pi\) | |||||||
\(572\) | −2.30658e34 | −0.786174 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.44680e32 | 0.0112465 | ||||||||
\(575\) | 2.39888e34 | 0.765878 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.31490e31 | −0.00223620 | −0.00111810 | − | 0.999999i | \(-0.500356\pi\) | ||||
−0.00111810 | + | 0.999999i | \(0.500356\pi\) | |||||||
\(578\) | 2.78049e31 | 0.000831808 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.75278e33 | −0.193479 | ||||||||
\(581\) | 3.64018e34 | 1.02075 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.33778e33 | −0.223972 | ||||||||
\(584\) | −1.36590e32 | −0.00359136 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.24031e30 | −0.000157212 0 | ||||||||
\(587\) | −5.16226e34 | −1.27310 | −0.636551 | − | 0.771234i | \(-0.719640\pi\) | ||||
−0.636551 | + | 0.771234i | \(0.719640\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.61022e34 | −0.616929 | ||||||||
\(590\) | −4.64874e32 | −0.0107568 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.28527e34 | 0.506894 | ||||||||
\(593\) | −2.40705e34 | −0.522758 | −0.261379 | − | 0.965236i | \(-0.584177\pi\) | ||||
−0.261379 | + | 0.965236i | \(0.584177\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.30706e34 | 1.52153 | ||||||||
\(596\) | 3.03838e34 | 0.619531 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.72310e32 | −0.00728015 | ||||||||
\(599\) | 8.30672e33 | 0.159072 | 0.0795361 | − | 0.996832i | \(-0.474656\pi\) | ||||
0.0795361 | + | 0.996832i | \(0.474656\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.00405e34 | −0.551792 | −0.275896 | − | 0.961187i | \(-0.588975\pi\) | ||||
−0.275896 | + | 0.961187i | \(0.588975\pi\) | |||||||
\(602\) | 5.64452e32 | 0.0101548 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.89841e34 | −0.672861 | ||||||||
\(605\) | −2.77941e34 | −0.469905 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.00963e35 | −1.63796 | −0.818978 | − | 0.573825i | \(-0.805459\pi\) | ||||
−0.818978 | + | 0.573825i | \(0.805459\pi\) | |||||||
\(608\) | −9.85991e32 | −0.0156703 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.21090e32 | 0.00489783 | ||||||||
\(611\) | −7.54750e34 | −1.12795 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.02453e33 | −0.0146983 | −0.00734915 | − | 0.999973i | \(-0.502339\pi\) | ||||
−0.00734915 | + | 0.999973i | \(0.502339\pi\) | |||||||
\(614\) | 6.89290e32 | 0.00968941 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.05987e33 | 0.0143053 | ||||||||
\(617\) | −4.53271e34 | −0.599505 | −0.299753 | − | 0.954017i | \(-0.596904\pi\) | ||||
−0.299753 | + | 0.954017i | \(0.596904\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.24784e35 | 1.58499 | 0.792496 | − | 0.609878i | \(-0.208781\pi\) | ||||
0.792496 | + | 0.609878i | \(0.208781\pi\) | |||||||
\(620\) | −1.06842e35 | −1.32999 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.07823e33 | 0.0128923 | ||||||||
\(623\) | 6.89239e34 | 0.807736 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00307e35 | −1.12936 | ||||||||
\(626\) | −6.62189e31 | −0.000730807 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.14582e34 | 0.121513 | ||||||||
\(629\) | 5.11577e34 | 0.531836 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.83338e34 | 0.482930 | 0.241465 | − | 0.970410i | \(-0.422372\pi\) | ||||
0.241465 | + | 0.970410i | \(0.422372\pi\) | |||||||
\(632\) | 8.75116e32 | 0.00857239 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.93375e32 | 0.00464581 | ||||||||
\(635\) | 2.49238e35 | 2.30114 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.52054e34 | −0.134976 | ||||||||
\(638\) | −1.09621e32 | −0.000954190 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.38114e33 | −0.0450427 | ||||||||
\(641\) | −8.30494e34 | −0.681728 | −0.340864 | − | 0.940113i | \(-0.610720\pi\) | ||||
−0.340864 | + | 0.940113i | \(0.610720\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.25724e34 | 0.415069 | 0.207535 | − | 0.978228i | \(-0.433456\pi\) | ||||
0.207535 | + | 0.978228i | \(0.433456\pi\) | |||||||
\(644\) | −1.24561e35 | −0.964517 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.35656e32 | −0.00547985 | ||||||||
\(647\) | 2.03021e35 | 1.48333 | 0.741665 | − | 0.670770i | \(-0.234036\pi\) | ||||
0.741665 | + | 0.670770i | \(0.234036\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.09896e35 | 0.772546 | ||||||||
\(650\) | −9.89711e32 | −0.00682483 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.55414e35 | −1.03132 | ||||||||
\(653\) | −1.67657e35 | −1.09146 | −0.545728 | − | 0.837962i | \(-0.683747\pi\) | ||||
−0.545728 | + | 0.837962i | \(0.683747\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.29826e35 | 0.813479 | ||||||||
\(656\) | 2.06835e35 | 1.27153 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.73398e33 | 0.0102617 | ||||||||
\(659\) | 2.92521e35 | 1.69859 | 0.849296 | − | 0.527917i | \(-0.177027\pi\) | ||||
0.849296 | + | 0.527917i | \(0.177027\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.30227e34 | 0.464172 | 0.232086 | − | 0.972695i | \(-0.425445\pi\) | ||||
0.232086 | + | 0.972695i | \(0.425445\pi\) | |||||||
\(662\) | −2.76171e32 | −0.00151514 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.00032e33 | −0.0158514 | ||||||||
\(665\) | −1.76364e35 | −0.914406 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.57672e34 | 0.128675 | ||||||||
\(668\) | −2.77298e35 | −1.35907 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −9.50545e32 | −0.00448784 | ||||||||
\(671\) | −7.59057e34 | −0.351757 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.23598e35 | −1.44483 | −0.722417 | − | 0.691458i | \(-0.756969\pi\) | ||||
−0.722417 | + | 0.691458i | \(0.756969\pi\) | |||||||
\(674\) | 3.21249e33 | 0.0140797 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.30691e34 | 0.0551966 | ||||||||
\(677\) | −7.76333e34 | −0.321877 | −0.160938 | − | 0.986964i | \(-0.551452\pi\) | ||||
−0.160938 | + | 0.986964i | \(0.551452\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.10568e35 | 0.441834 | ||||||||
\(680\) | −6.02265e33 | −0.0236280 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.73442e33 | −0.00655918 | ||||||||
\(683\) | 2.49909e35 | 0.927945 | 0.463973 | − | 0.885850i | \(-0.346424\pi\) | ||||
0.463973 | + | 0.885850i | \(0.346424\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.58782e35 | −1.64238 | ||||||||
\(686\) | −2.16634e33 | −0.00761508 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.38716e35 | 1.14810 | ||||||||
\(689\) | −8.08584e34 | −0.269144 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.56964e34 | −0.275098 | −0.137549 | − | 0.990495i | \(-0.543922\pi\) | ||||
−0.137549 | + | 0.990495i | \(0.543922\pi\) | |||||||
\(692\) | −2.02186e35 | −0.637419 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.52055e31 | −0.000137467 0 | ||||||||
\(695\) | −3.59466e35 | −1.07361 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.63017e35 | 1.33410 | ||||||||
\(698\) | −1.62759e33 | −0.00460630 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.31121e35 | −0.904193 | ||||||||
\(701\) | −4.53464e35 | −1.21637 | −0.608187 | − | 0.793793i | \(-0.708103\pi\) | ||||
−0.608187 | + | 0.793793i | \(0.708103\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.23475e35 | −0.319622 | ||||||||
\(704\) | 3.17949e35 | 0.808536 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.25502e32 | −0.00153522 | ||||||||
\(707\) | −7.28238e34 | −0.175602 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.93254e35 | −1.14813 | −0.574067 | − | 0.818808i | \(-0.694635\pi\) | ||||
−0.574067 | + | 0.818808i | \(0.694635\pi\) | |||||||
\(710\) | 6.85209e33 | 0.0156709 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.68087e33 | −0.0125434 | ||||||||
\(713\) | 4.07688e35 | 0.884522 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.10090e35 | 1.06862 | ||||||||
\(716\) | 8.08682e35 | 1.66481 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.25613e33 | 0.0124380 | ||||||||
\(719\) | −2.13499e35 | −0.417142 | −0.208571 | − | 0.978007i | \(-0.566881\pi\) | ||||
−0.208571 | + | 0.978007i | \(0.566881\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.89858e35 | 0.358293 | ||||||||
\(722\) | −2.69208e33 | −0.00499314 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.74857e35 | 0.492464 | ||||||||
\(725\) | 6.84968e34 | 0.120627 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.12190e35 | 0.871467 | 0.435734 | − | 0.900076i | \(-0.356489\pi\) | ||||
0.435734 | + | 0.900076i | \(0.356489\pi\) | |||||||
\(728\) | 1.02785e34 | 0.0171904 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.51026e33 | 0.00244071 | ||||||||
\(731\) | 7.58243e35 | 1.20459 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.77366e35 | 0.272315 | 0.136157 | − | 0.990687i | \(-0.456525\pi\) | ||||
0.136157 | + | 0.990687i | \(0.456525\pi\) | |||||||
\(734\) | −9.90213e33 | −0.0149461 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.54001e34 | 0.0224674 | ||||||||
\(737\) | 2.24709e35 | 0.322312 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.13535e36 | −1.57425 | −0.787124 | − | 0.616794i | \(-0.788431\pi\) | ||||
−0.787124 | + | 0.616794i | \(0.788431\pi\) | |||||||
\(740\) | −5.05412e35 | −0.689048 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.85766e33 | 0.00244860 | ||||||||
\(743\) | −4.03749e34 | −0.0523301 | −0.0261651 | − | 0.999658i | \(-0.508330\pi\) | ||||
−0.0261651 | + | 0.999658i | \(0.508330\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.71923e35 | −0.842104 | ||||||||
\(746\) | 1.18104e34 | 0.0145556 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.11853e35 | 0.848439 | ||||||||
\(749\) | −1.40027e36 | −1.64131 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.72405e35 | 0.875681 | 0.437840 | − | 0.899053i | \(-0.355744\pi\) | ||||
0.437840 | + | 0.899053i | \(0.355744\pi\) | |||||||
\(752\) | 1.04052e36 | 1.16019 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.06308e33 | −0.00114664 | ||||||||
\(755\) | 8.62115e35 | 0.914594 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.31585e35 | 0.340327 | 0.170163 | − | 0.985416i | \(-0.445570\pi\) | ||||
0.170163 | + | 0.985416i | \(0.445570\pi\) | |||||||
\(758\) | 3.42117e33 | 0.00345390 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.45363e34 | 0.0141999 | ||||||||
\(761\) | −2.02230e36 | −1.94329 | −0.971646 | − | 0.236440i | \(-0.924019\pi\) | ||||
−0.971646 | + | 0.236440i | \(0.924019\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.86725e36 | −1.73639 | ||||||||
\(764\) | 1.84739e35 | 0.169002 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.38646e33 | −0.00565458 | ||||||||
\(767\) | 1.06576e36 | 0.928358 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.71193e35 | 0.650255 | 0.325128 | − | 0.945670i | \(-0.394593\pi\) | ||||
0.325128 | + | 0.945670i | \(0.394593\pi\) | |||||||
\(770\) | −1.17189e34 | −0.00972195 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.00286e35 | −0.562418 | ||||||||
\(773\) | −1.96060e36 | −1.54934 | −0.774668 | − | 0.632368i | \(-0.782083\pi\) | ||||
−0.774668 | + | 0.632368i | \(0.782083\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.08376e36 | 0.829202 | ||||||||
\(776\) | −9.11331e33 | −0.00686127 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.15444e34 | −0.00841641 | ||||||||
\(779\) | −1.11754e36 | −0.801763 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.61983e36 | −1.12547 | ||||||||
\(782\) | 1.14902e34 | 0.00785674 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.09627e35 | 0.138834 | ||||||||
\(785\) | −2.53393e35 | −0.165167 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.92654e35 | −0.563637 | −0.281818 | − | 0.959468i | \(-0.590938\pi\) | ||||
−0.281818 | + | 0.959468i | \(0.590938\pi\) | |||||||
\(788\) | −2.01101e36 | −1.24979 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.67606e33 | −0.00582586 | ||||||||
\(791\) | 2.91727e36 | 1.72890 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.36121e35 | −0.422702 | ||||||||
\(794\) | −1.97826e34 | −0.0111822 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.51710e34 | −0.0411753 | ||||||||
\(797\) | 2.35494e36 | 1.26984 | 0.634921 | − | 0.772577i | \(-0.281032\pi\) | ||||
0.634921 | + | 0.772577i | \(0.281032\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.32930e36 | 1.21728 | ||||||||
\(800\) | 4.09381e34 | 0.0210622 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.43990e33 | 0.00171541 | ||||||||
\(803\) | −3.57026e35 | −0.175289 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.75462e36 | 1.31103 | ||||||||
\(806\) | −1.68201e34 | −0.00788208 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.00231e33 | 0.00272694 | ||||||||
\(809\) | 1.29617e36 | 0.579834 | 0.289917 | − | 0.957052i | \(-0.406372\pi\) | ||||
0.289917 | + | 0.957052i | \(0.406372\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.63606e36 | 1.14339 | 0.571695 | − | 0.820467i | \(-0.306286\pi\) | ||||
0.571695 | + | 0.820467i | \(0.306286\pi\) | |||||||
\(812\) | −3.55669e35 | −0.151913 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.20458e33 | −0.00339822 | ||||||||
\(815\) | 3.43691e36 | 1.40184 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.83010e36 | −0.723935 | ||||||||
\(818\) | 6.45265e33 | 0.00251375 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.57438e36 | −1.72846 | ||||||||
\(821\) | 5.92271e35 | 0.220410 | 0.110205 | − | 0.993909i | \(-0.464849\pi\) | ||||
0.110205 | + | 0.993909i | \(0.464849\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.76928e35 | 0.172169 | 0.0860845 | − | 0.996288i | \(-0.472564\pi\) | ||||
0.0860845 | + | 0.996288i | \(0.472564\pi\) | |||||||
\(824\) | −1.56486e34 | −0.00556396 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.44849e34 | −0.00844594 | ||||||||
\(827\) | −4.17794e36 | −1.41953 | −0.709763 | − | 0.704440i | \(-0.751198\pi\) | ||||
−0.709763 | + | 0.704440i | \(0.751198\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.18023e36 | −1.04840 | −0.524199 | − | 0.851596i | \(-0.675635\pi\) | ||||
−0.524199 | + | 0.851596i | \(0.675635\pi\) | |||||||
\(830\) | 3.31742e34 | 0.0107727 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.08342e36 | 0.971608 | ||||||||
\(833\) | 4.69267e35 | 0.145666 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.13232e36 | 1.84733 | ||||||||
\(836\) | −1.71814e36 | −0.509893 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.25006e33 | 0.00237633 | ||||||||
\(839\) | 3.57270e36 | 1.01384 | 0.506922 | − | 0.861992i | \(-0.330783\pi\) | ||||
0.506922 | + | 0.861992i | \(0.330783\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.55679e36 | −0.979733 | ||||||||
\(842\) | −3.97279e34 | −0.0107819 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.52471e36 | 0.665168 | ||||||||
\(845\) | −2.89018e35 | −0.0750266 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.46391e36 | −0.368954 | ||||||||
\(848\) | 1.11474e36 | 0.276838 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.05443e34 | 0.00736535 | ||||||||
\(851\) | 1.92855e36 | 0.458258 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.75466e36 | −0.404884 | −0.202442 | − | 0.979294i | \(-0.564888\pi\) | ||||
−0.202442 | + | 0.979294i | \(0.564888\pi\) | |||||||
\(854\) | 1.69118e34 | 0.00384562 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.15414e35 | 0.0254880 | ||||||||
\(857\) | −7.10324e36 | −1.54595 | −0.772976 | − | 0.634435i | \(-0.781233\pi\) | ||||
−0.772976 | + | 0.634435i | \(0.781233\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.56695e36 | −1.59958 | −0.799791 | − | 0.600279i | \(-0.795056\pi\) | ||||
−0.799791 | + | 0.600279i | \(0.795056\pi\) | |||||||
\(860\) | −7.49105e36 | −1.56067 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.76241e33 | 0.000761423 0 | ||||||||
\(863\) | −5.72195e36 | −1.14132 | −0.570662 | − | 0.821185i | \(-0.693313\pi\) | ||||
−0.570662 | + | 0.821185i | \(0.693313\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.47125e36 | 0.866418 | ||||||||
\(866\) | 3.03971e34 | 0.00580575 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.62739e36 | −1.04426 | ||||||||
\(869\) | 2.28742e36 | 0.418407 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.17919e36 | 0.387318 | ||||||||
\(872\) | 1.53903e35 | 0.0269645 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.77328e34 | −0.00472173 | ||||||||
\(875\) | −1.31931e36 | −0.221435 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.21926e36 | 0.525123 | 0.262561 | − | 0.964915i | \(-0.415433\pi\) | ||||
0.262561 | + | 0.964915i | \(0.415433\pi\) | |||||||
\(878\) | −7.11834e34 | −0.0114471 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −7.03227e36 | −1.09916 | ||||||||
\(881\) | 1.04633e37 | 1.61238 | 0.806191 | − | 0.591655i | \(-0.201525\pi\) | ||||
0.806191 | + | 0.591655i | \(0.201525\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.11745e36 | 0.616765 | 0.308382 | − | 0.951263i | \(-0.400212\pi\) | ||||
0.308382 | + | 0.951263i | \(0.400212\pi\) | |||||||
\(884\) | 6.90343e36 | 1.01956 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.80326e34 | 0.00833202 | ||||||||
\(887\) | 2.52904e36 | 0.358022 | 0.179011 | − | 0.983847i | \(-0.442710\pi\) | ||||
0.179011 | + | 0.983847i | \(0.442710\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.31273e37 | 1.80678 | ||||||||
\(890\) | 6.28128e34 | 0.00852458 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.06258e37 | 1.40217 | ||||||||
\(893\) | −5.62202e36 | −0.731558 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.78836e37 | −2.26291 | ||||||||
\(896\) | −2.83425e35 | −0.0353661 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.55453e34 | 0.00552700 | ||||||||
\(899\) | 1.16410e36 | 0.139314 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.49544e36 | 0.290460 | ||||||||
\(902\) | −7.42578e34 | −0.00852433 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.40448e35 | −0.0268483 | ||||||||
\(905\) | −6.07833e36 | −0.669387 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.93129e36 | −0.528286 | −0.264143 | − | 0.964484i | \(-0.585089\pi\) | ||||
−0.264143 | + | 0.964484i | \(0.585089\pi\) | |||||||
\(908\) | 1.29207e37 | 1.36525 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.13648e35 | −0.0116827 | ||||||||
\(911\) | 7.10548e36 | 0.720466 | 0.360233 | − | 0.932862i | \(-0.382697\pi\) | ||||
0.360233 | + | 0.932862i | \(0.382697\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.84240e36 | −0.773685 | ||||||||
\(914\) | 9.15090e34 | 0.00890505 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.90664e37 | 1.80541 | ||||||||
\(917\) | 6.83795e36 | 0.638718 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.64155e36 | 0.240112 | 0.120056 | − | 0.992767i | \(-0.461693\pi\) | ||||
0.120056 | + | 0.992767i | \(0.461693\pi\) | |||||||
\(920\) | −2.27042e35 | −0.0203591 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.19009e33 | 0.000191129 0 | ||||||||
\(923\) | −1.57089e37 | −1.35246 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.12665e36 | 0.429597 | ||||||||
\(926\) | 1.02490e35 | 0.00847316 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.39731e34 | 0.00353865 | ||||||||
\(929\) | −5.01934e36 | −0.398520 | −0.199260 | − | 0.979947i | \(-0.563854\pi\) | ||||
−0.199260 | + | 0.979947i | \(0.563854\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.13263e36 | −0.0875419 | ||||||||
\(932\) | 1.66280e37 | 1.26806 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.28268e35 | 0.00952320 | ||||||||
\(935\) | −1.57423e37 | −1.15325 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.70189e37 | −1.21391 | −0.606956 | − | 0.794735i | \(-0.707610\pi\) | ||||
−0.606956 | + | 0.794735i | \(0.707610\pi\) | |||||||
\(938\) | −5.00652e34 | −0.00352371 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.30123e37 | −1.57711 | ||||||||
\(941\) | 1.51254e37 | 1.02291 | 0.511455 | − | 0.859310i | \(-0.329107\pi\) | ||||
0.511455 | + | 0.859310i | \(0.329107\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.74548e37 | 1.14953 | ||||||||
\(944\) | −1.46929e37 | −0.954897 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.21605e35 | −0.00769687 | ||||||||
\(947\) | −1.65329e36 | −0.103270 | −0.0516351 | − | 0.998666i | \(-0.516443\pi\) | ||||
−0.0516351 | + | 0.998666i | \(0.516443\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.46238e36 | −0.210643 | ||||||||
\(950\) | −7.37220e34 | −0.00442642 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.17213e35 | −0.0185519 | ||||||||
\(953\) | −2.77784e37 | −1.60341 | −0.801706 | − | 0.597718i | \(-0.796074\pi\) | ||||
−0.801706 | + | 0.597718i | \(0.796074\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.08541e36 | −0.229717 | ||||||||
\(956\) | −4.83229e36 | −0.268182 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.46752e34 | −0.00511879 | ||||||||
\(959\) | −2.41640e37 | −1.28955 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.14395e35 | −0.0423441 | ||||||||
\(962\) | −7.95666e34 | −0.00408359 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.07184e37 | 0.536004 | ||||||||
\(965\) | 1.54865e37 | 0.764473 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.82441e36 | 0.183965 | 0.0919823 | − | 0.995761i | \(-0.470680\pi\) | ||||
0.0919823 | + | 0.995761i | \(0.470680\pi\) | |||||||
\(968\) | 1.20659e35 | 0.00572952 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.00765e35 | 0.00466297 | ||||||||
\(971\) | 1.67087e37 | 0.763311 | 0.381655 | − | 0.924305i | \(-0.375354\pi\) | ||||
0.381655 | + | 0.924305i | \(0.375354\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.89331e37 | −0.842967 | ||||||||
\(974\) | −1.90256e34 | −0.000836277 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.01484e37 | 0.434786 | ||||||||
\(977\) | 3.54376e37 | 1.49893 | 0.749466 | − | 0.662043i | \(-0.230310\pi\) | ||||
0.749466 | + | 0.662043i | \(0.230310\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.48490e37 | −0.612227 | ||||||||
\(980\) | −4.63612e36 | −0.188725 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.46860e35 | 0.0137645 | ||||||||
\(983\) | −2.26759e37 | −0.888476 | −0.444238 | − | 0.895909i | \(-0.646525\pi\) | ||||
−0.444238 | + | 0.895909i | \(0.646525\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.44726e37 | 1.69879 | ||||||||
\(986\) | 3.28087e34 | 0.00123745 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.66622e37 | −0.612732 | ||||||||
\(989\) | 2.85843e37 | 1.03794 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.82706e36 | −0.0646891 | −0.0323445 | − | 0.999477i | \(-0.510297\pi\) | ||||
−0.0323445 | + | 0.999477i | \(0.510297\pi\) | |||||||
\(992\) | 6.95742e35 | 0.0243250 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.60899e35 | 0.0123043 | ||||||||
\(995\) | 1.66237e36 | 0.0559680 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.34599e37 | 0.770260 | 0.385130 | − | 0.922862i | \(-0.374157\pi\) | ||||
0.385130 | + | 0.922862i | \(0.374157\pi\) | |||||||
\(998\) | 3.93518e35 | 0.0127595 | ||||||||
\(999\) | 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 | 9.26.a.a.1.1 | 1 | ||
3.2 | odd | 2 | 1.26.a.a.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 16.26.a.b.1.1 | 1 | |||
15.2 | even | 4 | 25.26.b.a.24.1 | 2 | |||
15.8 | even | 4 | 25.26.b.a.24.2 | 2 | |||
15.14 | odd | 2 | 25.26.a.a.1.1 | 1 | |||
21.20 | even | 2 | 49.26.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.26.a.a.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
9.26.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
16.26.a.b.1.1 | 1 | 12.11 | even | 2 | |||
25.26.a.a.1.1 | 1 | 15.14 | odd | 2 | |||
25.26.b.a.24.1 | 2 | 15.2 | even | 4 | |||
25.26.b.a.24.2 | 2 | 15.8 | even | 4 | |||
49.26.a.a.1.1 | 1 | 21.20 | even | 2 |