Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(189.798744245\) |
Analytic rank: | \(1\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −32.6149 | −0.360347 | −0.180173 | − | 0.983635i | \(-0.557666\pi\) | ||||
−0.180173 | + | 0.983635i | \(0.557666\pi\) | |||||||
\(3\) | −729.000 | −0.577350 | ||||||||
\(4\) | −7128.27 | −0.870150 | ||||||||
\(5\) | −49381.7 | −1.41339 | −0.706694 | − | 0.707520i | \(-0.749814\pi\) | ||||
−0.706694 | + | 0.707520i | \(0.749814\pi\) | |||||||
\(6\) | 23776.2 | 0.208046 | ||||||||
\(7\) | −593230. | −1.90584 | −0.952919 | − | 0.303224i | \(-0.901937\pi\) | ||||
−0.952919 | + | 0.303224i | \(0.901937\pi\) | |||||||
\(8\) | 499669. | 0.673903 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | 1.61058e6 | 0.509310 | ||||||||
\(11\) | −7.46381e6 | −1.27031 | −0.635153 | − | 0.772386i | \(-0.719063\pi\) | ||||
−0.635153 | + | 0.772386i | \(0.719063\pi\) | |||||||
\(12\) | 5.19651e6 | 0.502381 | ||||||||
\(13\) | −3.21219e7 | −1.84573 | −0.922867 | − | 0.385119i | \(-0.874160\pi\) | ||||
−0.922867 | + | 0.385119i | \(0.874160\pi\) | |||||||
\(14\) | 1.93481e7 | 0.686763 | ||||||||
\(15\) | 3.59993e7 | 0.816020 | ||||||||
\(16\) | 4.20982e7 | 0.627311 | ||||||||
\(17\) | −1.18628e7 | −0.119198 | −0.0595990 | − | 0.998222i | \(-0.518982\pi\) | ||||
−0.0595990 | + | 0.998222i | \(0.518982\pi\) | |||||||
\(18\) | −1.73329e7 | −0.120116 | ||||||||
\(19\) | −3.23570e8 | −1.57787 | −0.788933 | − | 0.614479i | \(-0.789366\pi\) | ||||
−0.788933 | + | 0.614479i | \(0.789366\pi\) | |||||||
\(20\) | 3.52006e8 | 1.22986 | ||||||||
\(21\) | 4.32465e8 | 1.10034 | ||||||||
\(22\) | 2.43431e8 | 0.457751 | ||||||||
\(23\) | −7.23407e8 | −1.01895 | −0.509474 | − | 0.860486i | \(-0.670160\pi\) | ||||
−0.509474 | + | 0.860486i | \(0.670160\pi\) | |||||||
\(24\) | −3.64258e8 | −0.389078 | ||||||||
\(25\) | 1.21785e9 | 0.997664 | ||||||||
\(26\) | 1.04765e9 | 0.665104 | ||||||||
\(27\) | −3.87420e8 | −0.192450 | ||||||||
\(28\) | 4.22871e9 | 1.65837 | ||||||||
\(29\) | −1.75782e9 | −0.548766 | −0.274383 | − | 0.961620i | \(-0.588474\pi\) | ||||
−0.274383 | + | 0.961620i | \(0.588474\pi\) | |||||||
\(30\) | −1.17411e9 | −0.294050 | ||||||||
\(31\) | −3.99789e9 | −0.809058 | −0.404529 | − | 0.914525i | \(-0.632565\pi\) | ||||
−0.404529 | + | 0.914525i | \(0.632565\pi\) | |||||||
\(32\) | −5.46631e9 | −0.899952 | ||||||||
\(33\) | 5.44112e9 | 0.733411 | ||||||||
\(34\) | 3.86903e8 | 0.0429526 | ||||||||
\(35\) | 2.92947e10 | 2.69369 | ||||||||
\(36\) | −3.78825e9 | −0.290050 | ||||||||
\(37\) | 1.32018e7 | 0.000845903 0 | 0.000422951 | − | 1.00000i | \(-0.499865\pi\) | ||||
0.000422951 | 1.00000i | \(0.499865\pi\) | ||||||||
\(38\) | 1.05532e10 | 0.568579 | ||||||||
\(39\) | 2.34168e10 | 1.06563 | ||||||||
\(40\) | −2.46745e10 | −0.952486 | ||||||||
\(41\) | −2.57951e10 | −0.848089 | −0.424044 | − | 0.905641i | \(-0.639390\pi\) | ||||
−0.424044 | + | 0.905641i | \(0.639390\pi\) | |||||||
\(42\) | −1.41048e10 | −0.396503 | ||||||||
\(43\) | 5.80646e10 | 1.40077 | 0.700385 | − | 0.713765i | \(-0.253012\pi\) | ||||
0.700385 | + | 0.713765i | \(0.253012\pi\) | |||||||
\(44\) | 5.32041e10 | 1.10536 | ||||||||
\(45\) | −2.62435e10 | −0.471129 | ||||||||
\(46\) | 2.35938e10 | 0.367174 | ||||||||
\(47\) | −6.92329e10 | −0.936864 | −0.468432 | − | 0.883500i | \(-0.655181\pi\) | ||||
−0.468432 | + | 0.883500i | \(0.655181\pi\) | |||||||
\(48\) | −3.06896e10 | −0.362178 | ||||||||
\(49\) | 2.55033e11 | 2.63222 | ||||||||
\(50\) | −3.97201e10 | −0.359505 | ||||||||
\(51\) | 8.64797e9 | 0.0688190 | ||||||||
\(52\) | 2.28973e11 | 1.60607 | ||||||||
\(53\) | 3.07489e11 | 1.90562 | 0.952812 | − | 0.303562i | \(-0.0981759\pi\) | ||||
0.952812 | + | 0.303562i | \(0.0981759\pi\) | |||||||
\(54\) | 1.26357e10 | 0.0693488 | ||||||||
\(55\) | 3.68576e11 | 1.79543 | ||||||||
\(56\) | −2.96419e11 | −1.28435 | ||||||||
\(57\) | 2.35883e11 | 0.910982 | ||||||||
\(58\) | 5.73310e10 | 0.197746 | ||||||||
\(59\) | −4.21805e10 | −0.130189 | ||||||||
\(60\) | −2.56613e11 | −0.710060 | ||||||||
\(61\) | 1.31563e11 | 0.326957 | 0.163479 | − | 0.986547i | \(-0.447729\pi\) | ||||
0.163479 | + | 0.986547i | \(0.447729\pi\) | |||||||
\(62\) | 1.30391e11 | 0.291541 | ||||||||
\(63\) | −3.15267e11 | −0.635280 | ||||||||
\(64\) | −1.66585e11 | −0.303016 | ||||||||
\(65\) | 1.58623e12 | 2.60874 | ||||||||
\(66\) | −1.77461e11 | −0.264282 | ||||||||
\(67\) | −2.68168e11 | −0.362178 | −0.181089 | − | 0.983467i | \(-0.557962\pi\) | ||||
−0.181089 | + | 0.983467i | \(0.557962\pi\) | |||||||
\(68\) | 8.45612e10 | 0.103720 | ||||||||
\(69\) | 5.27364e11 | 0.588289 | ||||||||
\(70\) | −9.55444e11 | −0.970662 | ||||||||
\(71\) | −1.88084e12 | −1.74250 | −0.871252 | − | 0.490837i | \(-0.836691\pi\) | ||||
−0.871252 | + | 0.490837i | \(0.836691\pi\) | |||||||
\(72\) | 2.65544e11 | 0.224634 | ||||||||
\(73\) | −7.87484e11 | −0.609036 | −0.304518 | − | 0.952507i | \(-0.598495\pi\) | ||||
−0.304518 | + | 0.952507i | \(0.598495\pi\) | |||||||
\(74\) | −4.30574e8 | −0.000304818 0 | ||||||||
\(75\) | −8.87814e11 | −0.576002 | ||||||||
\(76\) | 2.30650e12 | 1.37298 | ||||||||
\(77\) | 4.42776e12 | 2.42100 | ||||||||
\(78\) | −7.63738e11 | −0.383998 | ||||||||
\(79\) | −1.97942e12 | −0.916140 | −0.458070 | − | 0.888916i | \(-0.651459\pi\) | ||||
−0.458070 | + | 0.888916i | \(0.651459\pi\) | |||||||
\(80\) | −2.07888e12 | −0.886634 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | 8.41303e11 | 0.305606 | ||||||||
\(83\) | −2.48510e11 | −0.0834327 | −0.0417164 | − | 0.999129i | \(-0.513283\pi\) | ||||
−0.0417164 | + | 0.999129i | \(0.513283\pi\) | |||||||
\(84\) | −3.08273e12 | −0.957458 | ||||||||
\(85\) | 5.85805e11 | 0.168473 | ||||||||
\(86\) | −1.89377e12 | −0.504763 | ||||||||
\(87\) | 1.28145e12 | 0.316830 | ||||||||
\(88\) | −3.72943e12 | −0.856062 | ||||||||
\(89\) | −5.76318e11 | −0.122921 | −0.0614607 | − | 0.998110i | \(-0.519576\pi\) | ||||
−0.0614607 | + | 0.998110i | \(0.519576\pi\) | |||||||
\(90\) | 8.55928e11 | 0.169770 | ||||||||
\(91\) | 1.90557e13 | 3.51767 | ||||||||
\(92\) | 5.15664e12 | 0.886637 | ||||||||
\(93\) | 2.91446e12 | 0.467110 | ||||||||
\(94\) | 2.25802e12 | 0.337596 | ||||||||
\(95\) | 1.59785e13 | 2.23014 | ||||||||
\(96\) | 3.98494e12 | 0.519588 | ||||||||
\(97\) | 6.37387e12 | 0.776939 | 0.388469 | − | 0.921462i | \(-0.373004\pi\) | ||||
0.388469 | + | 0.921462i | \(0.373004\pi\) | |||||||
\(98\) | −8.31788e12 | −0.948513 | ||||||||
\(99\) | −3.96658e12 | −0.423435 | ||||||||
\(100\) | −8.68117e12 | −0.868117 | ||||||||
\(101\) | −1.09909e13 | −1.03025 | −0.515126 | − | 0.857114i | \(-0.672255\pi\) | ||||
−0.515126 | + | 0.857114i | \(0.672255\pi\) | |||||||
\(102\) | −2.82053e11 | −0.0247987 | ||||||||
\(103\) | 1.84278e13 | 1.52066 | 0.760330 | − | 0.649537i | \(-0.225037\pi\) | ||||
0.760330 | + | 0.649537i | \(0.225037\pi\) | |||||||
\(104\) | −1.60503e13 | −1.24385 | ||||||||
\(105\) | −2.13559e13 | −1.55520 | ||||||||
\(106\) | −1.00287e13 | −0.686685 | ||||||||
\(107\) | −3.02082e12 | −0.194594 | −0.0972972 | − | 0.995255i | \(-0.531020\pi\) | ||||
−0.0972972 | + | 0.995255i | \(0.531020\pi\) | |||||||
\(108\) | 2.76164e12 | 0.167460 | ||||||||
\(109\) | −1.23735e13 | −0.706674 | −0.353337 | − | 0.935496i | \(-0.614953\pi\) | ||||
−0.353337 | + | 0.935496i | \(0.614953\pi\) | |||||||
\(110\) | −1.20211e13 | −0.646979 | ||||||||
\(111\) | −9.62408e9 | −0.000488382 0 | ||||||||
\(112\) | −2.49739e13 | −1.19555 | ||||||||
\(113\) | −1.12544e12 | −0.0508527 | −0.0254264 | − | 0.999677i | \(-0.508094\pi\) | ||||
−0.0254264 | + | 0.999677i | \(0.508094\pi\) | |||||||
\(114\) | −7.69329e12 | −0.328269 | ||||||||
\(115\) | 3.57231e13 | 1.44017 | ||||||||
\(116\) | 1.25302e13 | 0.477509 | ||||||||
\(117\) | −1.70709e13 | −0.615245 | ||||||||
\(118\) | 1.37571e12 | 0.0469132 | ||||||||
\(119\) | 7.03737e12 | 0.227172 | ||||||||
\(120\) | 1.79877e13 | 0.549918 | ||||||||
\(121\) | 2.11858e13 | 0.613677 | ||||||||
\(122\) | −4.29092e12 | −0.117818 | ||||||||
\(123\) | 1.88046e13 | 0.489644 | ||||||||
\(124\) | 2.84980e13 | 0.704002 | ||||||||
\(125\) | 1.40820e11 | 0.00330179 | ||||||||
\(126\) | 1.02824e13 | 0.228921 | ||||||||
\(127\) | −5.23070e13 | −1.10621 | −0.553103 | − | 0.833113i | \(-0.686556\pi\) | ||||
−0.553103 | + | 0.833113i | \(0.686556\pi\) | |||||||
\(128\) | 5.02132e13 | 1.00914 | ||||||||
\(129\) | −4.23291e13 | −0.808735 | ||||||||
\(130\) | −5.17348e13 | −0.940050 | ||||||||
\(131\) | −2.08064e13 | −0.359694 | −0.179847 | − | 0.983695i | \(-0.557560\pi\) | ||||
−0.179847 | + | 0.983695i | \(0.557560\pi\) | |||||||
\(132\) | −3.87858e13 | −0.638178 | ||||||||
\(133\) | 1.91952e14 | 3.00716 | ||||||||
\(134\) | 8.74628e12 | 0.130510 | ||||||||
\(135\) | 1.91315e13 | 0.272007 | ||||||||
\(136\) | −5.92746e12 | −0.0803278 | ||||||||
\(137\) | −1.29775e14 | −1.67690 | −0.838448 | − | 0.544982i | \(-0.816537\pi\) | ||||
−0.838448 | + | 0.544982i | \(0.816537\pi\) | |||||||
\(138\) | −1.71999e13 | −0.211988 | ||||||||
\(139\) | −1.29110e14 | −1.51832 | −0.759160 | − | 0.650904i | \(-0.774390\pi\) | ||||
−0.759160 | + | 0.650904i | \(0.774390\pi\) | |||||||
\(140\) | −2.08821e14 | −2.34391 | ||||||||
\(141\) | 5.04708e13 | 0.540898 | ||||||||
\(142\) | 6.13435e13 | 0.627906 | ||||||||
\(143\) | 2.39752e14 | 2.34465 | ||||||||
\(144\) | 2.23727e13 | 0.209104 | ||||||||
\(145\) | 8.68041e13 | 0.775619 | ||||||||
\(146\) | 2.56837e13 | 0.219464 | ||||||||
\(147\) | −1.85919e14 | −1.51971 | ||||||||
\(148\) | −9.41057e10 | −0.000736062 0 | ||||||||
\(149\) | 7.93459e13 | 0.594037 | 0.297019 | − | 0.954872i | \(-0.404008\pi\) | ||||
0.297019 | + | 0.954872i | \(0.404008\pi\) | |||||||
\(150\) | 2.89559e13 | 0.207560 | ||||||||
\(151\) | 1.38875e14 | 0.953401 | 0.476700 | − | 0.879066i | \(-0.341833\pi\) | ||||
0.476700 | + | 0.879066i | \(0.341833\pi\) | |||||||
\(152\) | −1.61678e14 | −1.06333 | ||||||||
\(153\) | −6.30437e12 | −0.0397326 | ||||||||
\(154\) | −1.44411e14 | −0.872399 | ||||||||
\(155\) | 1.97423e14 | 1.14351 | ||||||||
\(156\) | −1.66922e14 | −0.927262 | ||||||||
\(157\) | 2.73625e14 | 1.45817 | 0.729086 | − | 0.684422i | \(-0.239945\pi\) | ||||
0.729086 | + | 0.684422i | \(0.239945\pi\) | |||||||
\(158\) | 6.45585e13 | 0.330128 | ||||||||
\(159\) | −2.24160e14 | −1.10021 | ||||||||
\(160\) | 2.69936e14 | 1.27198 | ||||||||
\(161\) | 4.29147e14 | 1.94195 | ||||||||
\(162\) | −9.21140e12 | −0.0400385 | ||||||||
\(163\) | −3.32716e14 | −1.38949 | −0.694743 | − | 0.719258i | \(-0.744482\pi\) | ||||
−0.694743 | + | 0.719258i | \(0.744482\pi\) | |||||||
\(164\) | 1.83874e14 | 0.737965 | ||||||||
\(165\) | −2.68692e14 | −1.03659 | ||||||||
\(166\) | 8.10513e12 | 0.0300647 | ||||||||
\(167\) | 7.36631e13 | 0.262781 | 0.131390 | − | 0.991331i | \(-0.458056\pi\) | ||||
0.131390 | + | 0.991331i | \(0.458056\pi\) | |||||||
\(168\) | 2.16089e14 | 0.741520 | ||||||||
\(169\) | 7.28940e14 | 2.40673 | ||||||||
\(170\) | −1.91060e13 | −0.0607087 | ||||||||
\(171\) | −1.71959e14 | −0.525956 | ||||||||
\(172\) | −4.13900e14 | −1.21888 | ||||||||
\(173\) | −1.87114e14 | −0.530648 | −0.265324 | − | 0.964159i | \(-0.585479\pi\) | ||||
−0.265324 | + | 0.964159i | \(0.585479\pi\) | |||||||
\(174\) | −4.17943e13 | −0.114169 | ||||||||
\(175\) | −7.22467e14 | −1.90139 | ||||||||
\(176\) | −3.14213e14 | −0.796877 | ||||||||
\(177\) | 3.07496e13 | 0.0751646 | ||||||||
\(178\) | 1.87965e13 | 0.0442943 | ||||||||
\(179\) | −1.42845e14 | −0.324579 | −0.162289 | − | 0.986743i | \(-0.551888\pi\) | ||||
−0.162289 | + | 0.986743i | \(0.551888\pi\) | |||||||
\(180\) | 1.87071e14 | 0.409953 | ||||||||
\(181\) | −7.50258e14 | −1.58599 | −0.792994 | − | 0.609229i | \(-0.791479\pi\) | ||||
−0.792994 | + | 0.609229i | \(0.791479\pi\) | |||||||
\(182\) | −6.21498e14 | −1.26758 | ||||||||
\(183\) | −9.59097e13 | −0.188769 | ||||||||
\(184\) | −3.61464e14 | −0.686671 | ||||||||
\(185\) | −6.51925e11 | −0.00119559 | ||||||||
\(186\) | −9.50548e13 | −0.168322 | ||||||||
\(187\) | 8.85416e13 | 0.151418 | ||||||||
\(188\) | 4.93511e14 | 0.815212 | ||||||||
\(189\) | 2.29830e14 | 0.366779 | ||||||||
\(190\) | −5.21136e14 | −0.803623 | ||||||||
\(191\) | 9.67976e14 | 1.44261 | 0.721303 | − | 0.692619i | \(-0.243543\pi\) | ||||
0.721303 | + | 0.692619i | \(0.243543\pi\) | |||||||
\(192\) | 1.21440e14 | 0.174947 | ||||||||
\(193\) | −8.10463e14 | −1.12878 | −0.564392 | − | 0.825507i | \(-0.690889\pi\) | ||||
−0.564392 | + | 0.825507i | \(0.690889\pi\) | |||||||
\(194\) | −2.07883e14 | −0.279967 | ||||||||
\(195\) | −1.15636e15 | −1.50616 | ||||||||
\(196\) | −1.81795e15 | −2.29043 | ||||||||
\(197\) | −2.58693e14 | −0.315323 | −0.157661 | − | 0.987493i | \(-0.550395\pi\) | ||||
−0.157661 | + | 0.987493i | \(0.550395\pi\) | |||||||
\(198\) | 1.29369e14 | 0.152584 | ||||||||
\(199\) | −1.10138e15 | −1.25716 | −0.628582 | − | 0.777743i | \(-0.716364\pi\) | ||||
−0.628582 | + | 0.777743i | \(0.716364\pi\) | |||||||
\(200\) | 6.08522e14 | 0.672328 | ||||||||
\(201\) | 1.95495e14 | 0.209103 | ||||||||
\(202\) | 3.58466e14 | 0.371248 | ||||||||
\(203\) | 1.04279e15 | 1.04586 | ||||||||
\(204\) | −6.16451e13 | −0.0598828 | ||||||||
\(205\) | 1.27380e15 | 1.19868 | ||||||||
\(206\) | −6.01021e14 | −0.547965 | ||||||||
\(207\) | −3.84448e14 | −0.339649 | ||||||||
\(208\) | −1.35227e15 | −1.15785 | ||||||||
\(209\) | 2.41507e15 | 2.00437 | ||||||||
\(210\) | 6.96519e14 | 0.560412 | ||||||||
\(211\) | −9.00591e14 | −0.702574 | −0.351287 | − | 0.936268i | \(-0.614256\pi\) | ||||
−0.351287 | + | 0.936268i | \(0.614256\pi\) | |||||||
\(212\) | −2.19187e15 | −1.65818 | ||||||||
\(213\) | 1.37114e15 | 1.00603 | ||||||||
\(214\) | 9.85236e13 | 0.0701215 | ||||||||
\(215\) | −2.86733e15 | −1.97983 | ||||||||
\(216\) | −1.93582e14 | −0.129693 | ||||||||
\(217\) | 2.37167e15 | 1.54193 | ||||||||
\(218\) | 4.03559e14 | 0.254648 | ||||||||
\(219\) | 5.74076e14 | 0.351627 | ||||||||
\(220\) | −2.62731e15 | −1.56230 | ||||||||
\(221\) | 3.81055e14 | 0.220008 | ||||||||
\(222\) | 3.13888e11 | 0.000175987 0 | ||||||||
\(223\) | 6.59002e14 | 0.358844 | 0.179422 | − | 0.983772i | \(-0.442577\pi\) | ||||
0.179422 | + | 0.983772i | \(0.442577\pi\) | |||||||
\(224\) | 3.24278e15 | 1.71516 | ||||||||
\(225\) | 6.47216e14 | 0.332555 | ||||||||
\(226\) | 3.67062e13 | 0.0183246 | ||||||||
\(227\) | 1.47614e14 | 0.0716077 | 0.0358039 | − | 0.999359i | \(-0.488601\pi\) | ||||
0.0358039 | + | 0.999359i | \(0.488601\pi\) | |||||||
\(228\) | −1.68144e15 | −0.792691 | ||||||||
\(229\) | −1.52534e15 | −0.698935 | −0.349468 | − | 0.936948i | \(-0.613638\pi\) | ||||
−0.349468 | + | 0.936948i | \(0.613638\pi\) | |||||||
\(230\) | −1.16510e15 | −0.518960 | ||||||||
\(231\) | −3.22784e15 | −1.39776 | ||||||||
\(232\) | −8.78327e14 | −0.369815 | ||||||||
\(233\) | 4.99824e14 | 0.204646 | 0.102323 | − | 0.994751i | \(-0.467372\pi\) | ||||
0.102323 | + | 0.994751i | \(0.467372\pi\) | |||||||
\(234\) | 5.56765e14 | 0.221701 | ||||||||
\(235\) | 3.41884e15 | 1.32415 | ||||||||
\(236\) | 3.00674e14 | 0.113284 | ||||||||
\(237\) | 1.44300e15 | 0.528933 | ||||||||
\(238\) | −2.29523e14 | −0.0818607 | ||||||||
\(239\) | −3.20105e15 | −1.11098 | −0.555489 | − | 0.831524i | \(-0.687469\pi\) | ||||
−0.555489 | + | 0.831524i | \(0.687469\pi\) | |||||||
\(240\) | 1.51550e15 | 0.511898 | ||||||||
\(241\) | 3.80901e15 | 1.25228 | 0.626139 | − | 0.779711i | \(-0.284634\pi\) | ||||
0.626139 | + | 0.779711i | \(0.284634\pi\) | |||||||
\(242\) | −6.90971e14 | −0.221136 | ||||||||
\(243\) | −2.05891e14 | −0.0641500 | ||||||||
\(244\) | −9.37819e14 | −0.284502 | ||||||||
\(245\) | −1.25940e16 | −3.72035 | ||||||||
\(246\) | −6.13310e14 | −0.176442 | ||||||||
\(247\) | 1.03937e16 | 2.91232 | ||||||||
\(248\) | −1.99762e15 | −0.545226 | ||||||||
\(249\) | 1.81164e14 | 0.0481699 | ||||||||
\(250\) | −4.59283e12 | −0.00118979 | ||||||||
\(251\) | −1.73870e15 | −0.438879 | −0.219440 | − | 0.975626i | \(-0.570423\pi\) | ||||
−0.219440 | + | 0.975626i | \(0.570423\pi\) | |||||||
\(252\) | 2.24731e15 | 0.552789 | ||||||||
\(253\) | 5.39937e15 | 1.29437 | ||||||||
\(254\) | 1.70599e15 | 0.398618 | ||||||||
\(255\) | −4.27052e14 | −0.0972679 | ||||||||
\(256\) | −2.73032e14 | −0.0606253 | ||||||||
\(257\) | −8.48539e15 | −1.83699 | −0.918495 | − | 0.395433i | \(-0.870594\pi\) | ||||
−0.918495 | + | 0.395433i | \(0.870594\pi\) | |||||||
\(258\) | 1.38056e15 | 0.291425 | ||||||||
\(259\) | −7.83168e12 | −0.00161215 | ||||||||
\(260\) | −1.13071e16 | −2.26999 | ||||||||
\(261\) | −9.34177e14 | −0.182922 | ||||||||
\(262\) | 6.78597e14 | 0.129614 | ||||||||
\(263\) | −8.76144e15 | −1.63254 | −0.816269 | − | 0.577672i | \(-0.803961\pi\) | ||||
−0.816269 | + | 0.577672i | \(0.803961\pi\) | |||||||
\(264\) | 2.71876e15 | 0.494248 | ||||||||
\(265\) | −1.51844e16 | −2.69338 | ||||||||
\(266\) | −6.26048e15 | −1.08362 | ||||||||
\(267\) | 4.20136e14 | 0.0709686 | ||||||||
\(268\) | 1.91158e15 | 0.315149 | ||||||||
\(269\) | −3.68286e15 | −0.592646 | −0.296323 | − | 0.955088i | \(-0.595761\pi\) | ||||
−0.296323 | + | 0.955088i | \(0.595761\pi\) | |||||||
\(270\) | −6.23971e14 | −0.0980167 | ||||||||
\(271\) | −4.77488e15 | −0.732254 | −0.366127 | − | 0.930565i | \(-0.619316\pi\) | ||||
−0.366127 | + | 0.930565i | \(0.619316\pi\) | |||||||
\(272\) | −4.99401e14 | −0.0747742 | ||||||||
\(273\) | −1.38916e16 | −2.03093 | ||||||||
\(274\) | 4.23258e15 | 0.604264 | ||||||||
\(275\) | −9.08981e15 | −1.26734 | ||||||||
\(276\) | −3.75919e15 | −0.511900 | ||||||||
\(277\) | 2.27248e15 | 0.302260 | 0.151130 | − | 0.988514i | \(-0.451709\pi\) | ||||
0.151130 | + | 0.988514i | \(0.451709\pi\) | |||||||
\(278\) | 4.21090e15 | 0.547122 | ||||||||
\(279\) | −2.12464e15 | −0.269686 | ||||||||
\(280\) | 1.46377e16 | 1.81528 | ||||||||
\(281\) | 5.04454e15 | 0.611266 | 0.305633 | − | 0.952149i | \(-0.401132\pi\) | ||||
0.305633 | + | 0.952149i | \(0.401132\pi\) | |||||||
\(282\) | −1.64610e15 | −0.194911 | ||||||||
\(283\) | −6.57935e15 | −0.761327 | −0.380663 | − | 0.924714i | \(-0.624304\pi\) | ||||
−0.380663 | + | 0.924714i | \(0.624304\pi\) | |||||||
\(284\) | 1.34072e16 | 1.51624 | ||||||||
\(285\) | −1.16483e16 | −1.28757 | ||||||||
\(286\) | −7.81947e15 | −0.844886 | ||||||||
\(287\) | 1.53024e16 | 1.61632 | ||||||||
\(288\) | −2.90502e15 | −0.299984 | ||||||||
\(289\) | −9.76385e15 | −0.985792 | ||||||||
\(290\) | −2.83111e15 | −0.279492 | ||||||||
\(291\) | −4.64655e15 | −0.448566 | ||||||||
\(292\) | 5.61340e15 | 0.529953 | ||||||||
\(293\) | 6.70612e15 | 0.619201 | 0.309601 | − | 0.950867i | \(-0.399805\pi\) | ||||
0.309601 | + | 0.950867i | \(0.399805\pi\) | |||||||
\(294\) | 6.06374e15 | 0.547624 | ||||||||
\(295\) | 2.08295e15 | 0.184007 | ||||||||
\(296\) | 6.59650e12 | 0.000570056 0 | ||||||||
\(297\) | 2.89163e15 | 0.244470 | ||||||||
\(298\) | −2.58786e15 | −0.214059 | ||||||||
\(299\) | 2.32372e16 | 1.88071 | ||||||||
\(300\) | 6.32858e15 | 0.501208 | ||||||||
\(301\) | −3.44457e16 | −2.66964 | ||||||||
\(302\) | −4.52941e15 | −0.343555 | ||||||||
\(303\) | 8.01235e15 | 0.594817 | ||||||||
\(304\) | −1.36217e16 | −0.989814 | ||||||||
\(305\) | −6.49682e15 | −0.462117 | ||||||||
\(306\) | 2.05616e14 | 0.0143175 | ||||||||
\(307\) | −4.66913e15 | −0.318300 | −0.159150 | − | 0.987254i | \(-0.550875\pi\) | ||||
−0.159150 | + | 0.987254i | \(0.550875\pi\) | |||||||
\(308\) | −3.15623e16 | −2.10663 | ||||||||
\(309\) | −1.34339e16 | −0.877953 | ||||||||
\(310\) | −6.43891e15 | −0.412061 | ||||||||
\(311\) | −1.33184e16 | −0.834663 | −0.417331 | − | 0.908754i | \(-0.637035\pi\) | ||||
−0.417331 | + | 0.908754i | \(0.637035\pi\) | |||||||
\(312\) | 1.17007e16 | 0.718134 | ||||||||
\(313\) | −2.68156e15 | −0.161194 | −0.0805971 | − | 0.996747i | \(-0.525683\pi\) | ||||
−0.0805971 | + | 0.996747i | \(0.525683\pi\) | |||||||
\(314\) | −8.92426e15 | −0.525448 | ||||||||
\(315\) | 1.55684e16 | 0.897896 | ||||||||
\(316\) | 1.41098e16 | 0.797179 | ||||||||
\(317\) | 1.64263e16 | 0.909188 | 0.454594 | − | 0.890699i | \(-0.349784\pi\) | ||||
0.454594 | + | 0.890699i | \(0.349784\pi\) | |||||||
\(318\) | 7.31094e15 | 0.396458 | ||||||||
\(319\) | 1.31200e16 | 0.697100 | ||||||||
\(320\) | 8.22625e15 | 0.428279 | ||||||||
\(321\) | 2.20218e15 | 0.112349 | ||||||||
\(322\) | −1.39966e16 | −0.699775 | ||||||||
\(323\) | 3.83845e15 | 0.188078 | ||||||||
\(324\) | −2.01323e15 | −0.0966833 | ||||||||
\(325\) | −3.91197e16 | −1.84142 | ||||||||
\(326\) | 1.08515e16 | 0.500697 | ||||||||
\(327\) | 9.02026e15 | 0.407999 | ||||||||
\(328\) | −1.28890e16 | −0.571529 | ||||||||
\(329\) | 4.10711e16 | 1.78551 | ||||||||
\(330\) | 8.76335e15 | 0.373534 | ||||||||
\(331\) | 3.69112e16 | 1.54268 | 0.771340 | − | 0.636423i | \(-0.219587\pi\) | ||||
0.771340 | + | 0.636423i | \(0.219587\pi\) | |||||||
\(332\) | 1.77145e15 | 0.0725990 | ||||||||
\(333\) | 7.01595e12 | 0.000281968 0 | ||||||||
\(334\) | −2.40251e15 | −0.0946921 | ||||||||
\(335\) | 1.32426e16 | 0.511897 | ||||||||
\(336\) | 1.82060e16 | 0.690254 | ||||||||
\(337\) | 2.34882e16 | 0.873486 | 0.436743 | − | 0.899586i | \(-0.356132\pi\) | ||||
0.436743 | + | 0.899586i | \(0.356132\pi\) | |||||||
\(338\) | −2.37743e16 | −0.867259 | ||||||||
\(339\) | 8.20449e14 | 0.0293598 | ||||||||
\(340\) | −4.17578e15 | −0.146597 | ||||||||
\(341\) | 2.98395e16 | 1.02775 | ||||||||
\(342\) | 5.60841e15 | 0.189526 | ||||||||
\(343\) | −9.38160e16 | −3.11075 | ||||||||
\(344\) | 2.90131e16 | 0.943983 | ||||||||
\(345\) | −2.60421e16 | −0.831481 | ||||||||
\(346\) | 6.10270e15 | 0.191217 | ||||||||
\(347\) | −5.54474e16 | −1.70506 | −0.852530 | − | 0.522679i | \(-0.824933\pi\) | ||||
−0.852530 | + | 0.522679i | \(0.824933\pi\) | |||||||
\(348\) | −9.13452e15 | −0.275690 | ||||||||
\(349\) | 1.44672e16 | 0.428568 | 0.214284 | − | 0.976771i | \(-0.431258\pi\) | ||||
0.214284 | + | 0.976771i | \(0.431258\pi\) | |||||||
\(350\) | 2.35632e16 | 0.685159 | ||||||||
\(351\) | 1.24447e16 | 0.355212 | ||||||||
\(352\) | 4.07995e16 | 1.14321 | ||||||||
\(353\) | 1.03356e16 | 0.284314 | 0.142157 | − | 0.989844i | \(-0.454596\pi\) | ||||
0.142157 | + | 0.989844i | \(0.454596\pi\) | |||||||
\(354\) | −1.00289e15 | −0.0270853 | ||||||||
\(355\) | 9.28793e16 | 2.46283 | ||||||||
\(356\) | 4.10815e15 | 0.106960 | ||||||||
\(357\) | −5.13024e15 | −0.131158 | ||||||||
\(358\) | 4.65887e15 | 0.116961 | ||||||||
\(359\) | 4.31346e16 | 1.06344 | 0.531719 | − | 0.846921i | \(-0.321546\pi\) | ||||
0.531719 | + | 0.846921i | \(0.321546\pi\) | |||||||
\(360\) | −1.31130e16 | −0.317495 | ||||||||
\(361\) | 6.26448e16 | 1.48966 | ||||||||
\(362\) | 2.44696e16 | 0.571506 | ||||||||
\(363\) | −1.54444e16 | −0.354306 | ||||||||
\(364\) | −1.35834e17 | −3.06090 | ||||||||
\(365\) | 3.88873e16 | 0.860804 | ||||||||
\(366\) | 3.12808e15 | 0.0680223 | ||||||||
\(367\) | −6.09304e16 | −1.30168 | −0.650840 | − | 0.759215i | \(-0.725583\pi\) | ||||
−0.650840 | + | 0.759215i | \(0.725583\pi\) | |||||||
\(368\) | −3.04541e16 | −0.639197 | ||||||||
\(369\) | −1.37085e16 | −0.282696 | ||||||||
\(370\) | 2.12625e13 | 0.000430826 0 | ||||||||
\(371\) | −1.82412e17 | −3.63181 | ||||||||
\(372\) | −2.07751e16 | −0.406456 | ||||||||
\(373\) | −2.48061e16 | −0.476926 | −0.238463 | − | 0.971152i | \(-0.576644\pi\) | ||||
−0.238463 | + | 0.971152i | \(0.576644\pi\) | |||||||
\(374\) | −2.88777e15 | −0.0545629 | ||||||||
\(375\) | −1.02658e14 | −0.00190629 | ||||||||
\(376\) | −3.45935e16 | −0.631355 | ||||||||
\(377\) | 5.64644e16 | 1.01288 | ||||||||
\(378\) | −7.49586e15 | −0.132168 | ||||||||
\(379\) | 6.71368e16 | 1.16361 | 0.581803 | − | 0.813330i | \(-0.302347\pi\) | ||||
0.581803 | + | 0.813330i | \(0.302347\pi\) | |||||||
\(380\) | −1.13899e17 | −1.94055 | ||||||||
\(381\) | 3.81318e16 | 0.638668 | ||||||||
\(382\) | −3.15704e16 | −0.519839 | ||||||||
\(383\) | −4.37732e15 | −0.0708624 | −0.0354312 | − | 0.999372i | \(-0.511280\pi\) | ||||
−0.0354312 | + | 0.999372i | \(0.511280\pi\) | |||||||
\(384\) | −3.66054e16 | −0.582629 | ||||||||
\(385\) | −2.18650e17 | −3.42181 | ||||||||
\(386\) | 2.64331e16 | 0.406754 | ||||||||
\(387\) | 3.08579e16 | 0.466923 | ||||||||
\(388\) | −4.54346e16 | −0.676053 | ||||||||
\(389\) | 1.30948e15 | 0.0191614 | 0.00958069 | − | 0.999954i | \(-0.496950\pi\) | ||||
0.00958069 | + | 0.999954i | \(0.496950\pi\) | |||||||
\(390\) | 3.77147e16 | 0.542738 | ||||||||
\(391\) | 8.58162e15 | 0.121456 | ||||||||
\(392\) | 1.27432e17 | 1.77386 | ||||||||
\(393\) | 1.51678e16 | 0.207669 | ||||||||
\(394\) | 8.43726e15 | 0.113625 | ||||||||
\(395\) | 9.77471e16 | 1.29486 | ||||||||
\(396\) | 2.82748e16 | 0.368452 | ||||||||
\(397\) | −6.82367e16 | −0.874742 | −0.437371 | − | 0.899281i | \(-0.644090\pi\) | ||||
−0.437371 | + | 0.899281i | \(0.644090\pi\) | |||||||
\(398\) | 3.59214e16 | 0.453015 | ||||||||
\(399\) | −1.39933e17 | −1.73618 | ||||||||
\(400\) | 5.12693e16 | 0.625846 | ||||||||
\(401\) | 1.20322e17 | 1.44513 | 0.722563 | − | 0.691305i | \(-0.242964\pi\) | ||||
0.722563 | + | 0.691305i | \(0.242964\pi\) | |||||||
\(402\) | −6.37604e15 | −0.0753497 | ||||||||
\(403\) | 1.28420e17 | 1.49331 | ||||||||
\(404\) | 7.83460e16 | 0.896474 | ||||||||
\(405\) | −1.39469e16 | −0.157043 | ||||||||
\(406\) | −3.40105e16 | −0.376872 | ||||||||
\(407\) | −9.85354e13 | −0.00107455 | ||||||||
\(408\) | 4.32112e15 | 0.0463773 | ||||||||
\(409\) | 1.41649e17 | 1.49628 | 0.748140 | − | 0.663541i | \(-0.230947\pi\) | ||||
0.748140 | + | 0.663541i | \(0.230947\pi\) | |||||||
\(410\) | −4.15450e16 | −0.431940 | ||||||||
\(411\) | 9.46057e16 | 0.968156 | ||||||||
\(412\) | −1.31358e17 | −1.32320 | ||||||||
\(413\) | 2.50228e16 | 0.248119 | ||||||||
\(414\) | 1.25387e16 | 0.122391 | ||||||||
\(415\) | 1.22719e16 | 0.117923 | ||||||||
\(416\) | 1.75588e17 | 1.66107 | ||||||||
\(417\) | 9.41211e16 | 0.876603 | ||||||||
\(418\) | −7.87672e16 | −0.722270 | ||||||||
\(419\) | 9.73646e16 | 0.879043 | 0.439522 | − | 0.898232i | \(-0.355148\pi\) | ||||
0.439522 | + | 0.898232i | \(0.355148\pi\) | |||||||
\(420\) | 1.52230e17 | 1.35326 | ||||||||
\(421\) | −3.87678e16 | −0.339342 | −0.169671 | − | 0.985501i | \(-0.554271\pi\) | ||||
−0.169671 | + | 0.985501i | \(0.554271\pi\) | |||||||
\(422\) | 2.93727e16 | 0.253170 | ||||||||
\(423\) | −3.67932e16 | −0.312288 | ||||||||
\(424\) | 1.53643e17 | 1.28420 | ||||||||
\(425\) | −1.44471e16 | −0.118919 | ||||||||
\(426\) | −4.47194e16 | −0.362521 | ||||||||
\(427\) | −7.80474e16 | −0.623128 | ||||||||
\(428\) | 2.15332e16 | 0.169326 | ||||||||
\(429\) | −1.74779e17 | −1.35368 | ||||||||
\(430\) | 9.35177e16 | 0.713426 | ||||||||
\(431\) | 1.81275e17 | 1.36219 | 0.681093 | − | 0.732197i | \(-0.261505\pi\) | ||||
0.681093 | + | 0.732197i | \(0.261505\pi\) | |||||||
\(432\) | −1.63097e16 | −0.120726 | ||||||||
\(433\) | 1.53686e17 | 1.12063 | 0.560314 | − | 0.828280i | \(-0.310680\pi\) | ||||
0.560314 | + | 0.828280i | \(0.310680\pi\) | |||||||
\(434\) | −7.73517e16 | −0.555631 | ||||||||
\(435\) | −6.32802e16 | −0.447804 | ||||||||
\(436\) | 8.82014e16 | 0.614913 | ||||||||
\(437\) | 2.34073e17 | 1.60776 | ||||||||
\(438\) | −1.87234e16 | −0.126708 | ||||||||
\(439\) | 9.58773e16 | 0.639288 | 0.319644 | − | 0.947538i | \(-0.396437\pi\) | ||||
0.319644 | + | 0.947538i | \(0.396437\pi\) | |||||||
\(440\) | 1.84166e17 | 1.20995 | ||||||||
\(441\) | 1.35535e17 | 0.877407 | ||||||||
\(442\) | −1.24281e16 | −0.0792791 | ||||||||
\(443\) | 8.53921e16 | 0.536776 | 0.268388 | − | 0.963311i | \(-0.413509\pi\) | ||||
0.268388 | + | 0.963311i | \(0.413509\pi\) | |||||||
\(444\) | 6.86030e13 | 0.000424966 0 | ||||||||
\(445\) | 2.84596e16 | 0.173735 | ||||||||
\(446\) | −2.14933e16 | −0.129308 | ||||||||
\(447\) | −5.78431e16 | −0.342967 | ||||||||
\(448\) | 9.88233e16 | 0.577500 | ||||||||
\(449\) | 4.57049e16 | 0.263246 | 0.131623 | − | 0.991300i | \(-0.457981\pi\) | ||||
0.131623 | + | 0.991300i | \(0.457981\pi\) | |||||||
\(450\) | −2.11089e16 | −0.119835 | ||||||||
\(451\) | 1.92529e17 | 1.07733 | ||||||||
\(452\) | 8.02247e15 | 0.0442495 | ||||||||
\(453\) | −1.01240e17 | −0.550446 | ||||||||
\(454\) | −4.81442e15 | −0.0258036 | ||||||||
\(455\) | −9.41002e17 | −4.97183 | ||||||||
\(456\) | 1.17863e17 | 0.613913 | ||||||||
\(457\) | 8.21711e16 | 0.421952 | 0.210976 | − | 0.977491i | \(-0.432336\pi\) | ||||
0.210976 | + | 0.977491i | \(0.432336\pi\) | |||||||
\(458\) | 4.97489e16 | 0.251859 | ||||||||
\(459\) | 4.59589e15 | 0.0229397 | ||||||||
\(460\) | −2.54644e17 | −1.25316 | ||||||||
\(461\) | −4.06761e16 | −0.197371 | −0.0986855 | − | 0.995119i | \(-0.531464\pi\) | ||||
−0.0986855 | + | 0.995119i | \(0.531464\pi\) | |||||||
\(462\) | 1.05276e17 | 0.503680 | ||||||||
\(463\) | −1.51468e17 | −0.714569 | −0.357284 | − | 0.933996i | \(-0.616297\pi\) | ||||
−0.357284 | + | 0.933996i | \(0.616297\pi\) | |||||||
\(464\) | −7.40009e16 | −0.344247 | ||||||||
\(465\) | −1.43921e17 | −0.660207 | ||||||||
\(466\) | −1.63017e16 | −0.0737436 | ||||||||
\(467\) | 1.42903e17 | 0.637503 | 0.318751 | − | 0.947838i | \(-0.396737\pi\) | ||||
0.318751 | + | 0.947838i | \(0.396737\pi\) | |||||||
\(468\) | 1.21686e17 | 0.535355 | ||||||||
\(469\) | 1.59086e17 | 0.690252 | ||||||||
\(470\) | −1.11505e17 | −0.477154 | ||||||||
\(471\) | −1.99473e17 | −0.841876 | ||||||||
\(472\) | −2.10763e16 | −0.0877347 | ||||||||
\(473\) | −4.33384e17 | −1.77941 | ||||||||
\(474\) | −4.70631e16 | −0.190600 | ||||||||
\(475\) | −3.94061e17 | −1.57418 | ||||||||
\(476\) | −5.01643e16 | −0.197674 | ||||||||
\(477\) | 1.63413e17 | 0.635208 | ||||||||
\(478\) | 1.04402e17 | 0.400338 | ||||||||
\(479\) | 3.12586e17 | 1.18247 | 0.591233 | − | 0.806501i | \(-0.298641\pi\) | ||||
0.591233 | + | 0.806501i | \(0.298641\pi\) | |||||||
\(480\) | −1.96783e17 | −0.734379 | ||||||||
\(481\) | −4.24065e14 | −0.00156131 | ||||||||
\(482\) | −1.24230e17 | −0.451255 | ||||||||
\(483\) | −3.12848e17 | −1.12118 | ||||||||
\(484\) | −1.51018e17 | −0.533991 | ||||||||
\(485\) | −3.14753e17 | −1.09812 | ||||||||
\(486\) | 6.71511e15 | 0.0231163 | ||||||||
\(487\) | 1.02307e17 | 0.347511 | 0.173755 | − | 0.984789i | \(-0.444410\pi\) | ||||
0.173755 | + | 0.984789i | \(0.444410\pi\) | |||||||
\(488\) | 6.57381e16 | 0.220337 | ||||||||
\(489\) | 2.42550e17 | 0.802220 | ||||||||
\(490\) | 4.10751e17 | 1.34062 | ||||||||
\(491\) | 3.46345e17 | 1.11552 | 0.557762 | − | 0.830001i | \(-0.311660\pi\) | ||||
0.557762 | + | 0.830001i | \(0.311660\pi\) | |||||||
\(492\) | −1.34044e17 | −0.426064 | ||||||||
\(493\) | 2.08526e16 | 0.0654118 | ||||||||
\(494\) | −3.38989e17 | −1.04945 | ||||||||
\(495\) | 1.95876e17 | 0.598478 | ||||||||
\(496\) | −1.68304e17 | −0.507531 | ||||||||
\(497\) | 1.11577e18 | 3.32093 | ||||||||
\(498\) | −5.90864e15 | −0.0173579 | ||||||||
\(499\) | −4.97714e17 | −1.44320 | −0.721599 | − | 0.692311i | \(-0.756593\pi\) | ||||
−0.721599 | + | 0.692311i | \(0.756593\pi\) | |||||||
\(500\) | −1.00380e15 | −0.00287305 | ||||||||
\(501\) | −5.37004e16 | −0.151716 | ||||||||
\(502\) | 5.67074e16 | 0.158149 | ||||||||
\(503\) | 4.86081e17 | 1.33819 | 0.669093 | − | 0.743178i | \(-0.266683\pi\) | ||||
0.669093 | + | 0.743178i | \(0.266683\pi\) | |||||||
\(504\) | −1.57529e17 | −0.428117 | ||||||||
\(505\) | 5.42749e17 | 1.45615 | ||||||||
\(506\) | −1.76100e17 | −0.466424 | ||||||||
\(507\) | −5.31397e17 | −1.38953 | ||||||||
\(508\) | 3.72858e17 | 0.962565 | ||||||||
\(509\) | −1.14739e17 | −0.292446 | −0.146223 | − | 0.989252i | \(-0.546712\pi\) | ||||
−0.146223 | + | 0.989252i | \(0.546712\pi\) | |||||||
\(510\) | 1.39282e16 | 0.0350502 | ||||||||
\(511\) | 4.67159e17 | 1.16072 | ||||||||
\(512\) | −4.02441e17 | −0.987297 | ||||||||
\(513\) | 1.25358e17 | 0.303661 | ||||||||
\(514\) | 2.76750e17 | 0.661953 | ||||||||
\(515\) | −9.09997e17 | −2.14928 | ||||||||
\(516\) | 3.01733e17 | 0.703721 | ||||||||
\(517\) | 5.16741e17 | 1.19010 | ||||||||
\(518\) | 2.55429e14 | 0.000580935 0 | ||||||||
\(519\) | 1.36406e17 | 0.306370 | ||||||||
\(520\) | 7.92591e17 | 1.75804 | ||||||||
\(521\) | −7.05193e16 | −0.154477 | −0.0772383 | − | 0.997013i | \(-0.524610\pi\) | ||||
−0.0772383 | + | 0.997013i | \(0.524610\pi\) | |||||||
\(522\) | 3.04681e16 | 0.0659154 | ||||||||
\(523\) | −3.02176e17 | −0.645653 | −0.322826 | − | 0.946458i | \(-0.604633\pi\) | ||||
−0.322826 | + | 0.946458i | \(0.604633\pi\) | |||||||
\(524\) | 1.48313e17 | 0.312987 | ||||||||
\(525\) | 5.26678e17 | 1.09777 | ||||||||
\(526\) | 2.85753e17 | 0.588280 | ||||||||
\(527\) | 4.74261e16 | 0.0964380 | ||||||||
\(528\) | 2.29061e17 | 0.460077 | ||||||||
\(529\) | 1.92811e16 | 0.0382534 | ||||||||
\(530\) | 4.95236e17 | 0.970553 | ||||||||
\(531\) | −2.24165e16 | −0.0433963 | ||||||||
\(532\) | −1.36828e18 | −2.61668 | ||||||||
\(533\) | 8.28586e17 | 1.56535 | ||||||||
\(534\) | −1.37027e16 | −0.0255733 | ||||||||
\(535\) | 1.49173e17 | 0.275037 | ||||||||
\(536\) | −1.33995e17 | −0.244072 | ||||||||
\(537\) | 1.04134e17 | 0.187396 | ||||||||
\(538\) | 1.20116e17 | 0.213558 | ||||||||
\(539\) | −1.90352e18 | −3.34373 | ||||||||
\(540\) | −1.36374e17 | −0.236687 | ||||||||
\(541\) | −9.37497e17 | −1.60764 | −0.803818 | − | 0.594876i | \(-0.797201\pi\) | ||||
−0.803818 | + | 0.594876i | \(0.797201\pi\) | |||||||
\(542\) | 1.55732e17 | 0.263865 | ||||||||
\(543\) | 5.46938e17 | 0.915671 | ||||||||
\(544\) | 6.48457e16 | 0.107272 | ||||||||
\(545\) | 6.11023e17 | 0.998804 | ||||||||
\(546\) | 4.53072e17 | 0.731839 | ||||||||
\(547\) | 2.15393e17 | 0.343806 | 0.171903 | − | 0.985114i | \(-0.445008\pi\) | ||||
0.171903 | + | 0.985114i | \(0.445008\pi\) | |||||||
\(548\) | 9.25069e17 | 1.45915 | ||||||||
\(549\) | 6.99181e16 | 0.108986 | ||||||||
\(550\) | 2.96463e17 | 0.456681 | ||||||||
\(551\) | 5.68778e17 | 0.865880 | ||||||||
\(552\) | 2.63507e17 | 0.396450 | ||||||||
\(553\) | 1.17425e18 | 1.74601 | ||||||||
\(554\) | −7.41165e16 | −0.108918 | ||||||||
\(555\) | 4.75254e14 | 0.000690273 0 | ||||||||
\(556\) | 9.20330e17 | 1.32117 | ||||||||
\(557\) | −5.89344e17 | −0.836200 | −0.418100 | − | 0.908401i | \(-0.637304\pi\) | ||||
−0.418100 | + | 0.908401i | \(0.637304\pi\) | |||||||
\(558\) | 6.92949e16 | 0.0971805 | ||||||||
\(559\) | −1.86515e18 | −2.58545 | ||||||||
\(560\) | 1.23325e18 | 1.68978 | ||||||||
\(561\) | −6.45468e16 | −0.0874211 | ||||||||
\(562\) | −1.64527e17 | −0.220268 | ||||||||
\(563\) | −9.24963e17 | −1.22411 | −0.612054 | − | 0.790816i | \(-0.709656\pi\) | ||||
−0.612054 | + | 0.790816i | \(0.709656\pi\) | |||||||
\(564\) | −3.59769e17 | −0.470663 | ||||||||
\(565\) | 5.55764e16 | 0.0718746 | ||||||||
\(566\) | 2.14585e17 | 0.274342 | ||||||||
\(567\) | −1.67546e17 | −0.211760 | ||||||||
\(568\) | −9.39799e17 | −1.17428 | ||||||||
\(569\) | 1.17097e18 | 1.44650 | 0.723248 | − | 0.690588i | \(-0.242648\pi\) | ||||
0.723248 | + | 0.690588i | \(0.242648\pi\) | |||||||
\(570\) | 3.79908e17 | 0.463972 | ||||||||
\(571\) | 1.34858e18 | 1.62832 | 0.814162 | − | 0.580638i | \(-0.197197\pi\) | ||||
0.814162 | + | 0.580638i | \(0.197197\pi\) | |||||||
\(572\) | −1.70901e18 | −2.04019 | ||||||||
\(573\) | −7.05655e17 | −0.832889 | ||||||||
\(574\) | −4.99086e17 | −0.582436 | ||||||||
\(575\) | −8.81002e17 | −1.01657 | ||||||||
\(576\) | −8.85301e16 | −0.101005 | ||||||||
\(577\) | −5.35816e17 | −0.604467 | −0.302234 | − | 0.953234i | \(-0.597732\pi\) | ||||
−0.302234 | + | 0.953234i | \(0.597732\pi\) | |||||||
\(578\) | 3.18447e17 | 0.355227 | ||||||||
\(579\) | 5.90827e17 | 0.651703 | ||||||||
\(580\) | −6.18763e17 | −0.674905 | ||||||||
\(581\) | 1.47424e17 | 0.159009 | ||||||||
\(582\) | 1.51547e17 | 0.161639 | ||||||||
\(583\) | −2.29504e18 | −2.42072 | ||||||||
\(584\) | −3.93481e17 | −0.410431 | ||||||||
\(585\) | 8.42990e17 | 0.869579 | ||||||||
\(586\) | −2.18719e17 | −0.223127 | ||||||||
\(587\) | 3.42527e17 | 0.345579 | 0.172790 | − | 0.984959i | \(-0.444722\pi\) | ||||
0.172790 | + | 0.984959i | \(0.444722\pi\) | |||||||
\(588\) | 1.32528e18 | 1.32238 | ||||||||
\(589\) | 1.29360e18 | 1.27659 | ||||||||
\(590\) | −6.79351e16 | −0.0663065 | ||||||||
\(591\) | 1.88588e17 | 0.182052 | ||||||||
\(592\) | 5.55769e14 | 0.000530644 0 | ||||||||
\(593\) | 7.46915e17 | 0.705368 | 0.352684 | − | 0.935743i | \(-0.385269\pi\) | ||||
0.352684 | + | 0.935743i | \(0.385269\pi\) | |||||||
\(594\) | −9.43103e16 | −0.0880942 | ||||||||
\(595\) | −3.47517e17 | −0.321082 | ||||||||
\(596\) | −5.65599e17 | −0.516901 | ||||||||
\(597\) | 8.02906e17 | 0.725824 | ||||||||
\(598\) | −7.57878e17 | −0.677706 | ||||||||
\(599\) | 1.27547e18 | 1.12823 | 0.564114 | − | 0.825697i | \(-0.309218\pi\) | ||||
0.564114 | + | 0.825697i | \(0.309218\pi\) | |||||||
\(600\) | −4.43613e17 | −0.388169 | ||||||||
\(601\) | −1.90753e17 | −0.165115 | −0.0825577 | − | 0.996586i | \(-0.526309\pi\) | ||||
−0.0825577 | + | 0.996586i | \(0.526309\pi\) | |||||||
\(602\) | 1.12344e18 | 0.961997 | ||||||||
\(603\) | −1.42516e17 | −0.120726 | ||||||||
\(604\) | −9.89942e17 | −0.829602 | ||||||||
\(605\) | −1.04619e18 | −0.867363 | ||||||||
\(606\) | −2.61322e17 | −0.214340 | ||||||||
\(607\) | −1.14134e18 | −0.926163 | −0.463081 | − | 0.886316i | \(-0.653256\pi\) | ||||
−0.463081 | + | 0.886316i | \(0.653256\pi\) | |||||||
\(608\) | 1.76874e18 | 1.42001 | ||||||||
\(609\) | −7.60195e17 | −0.603827 | ||||||||
\(610\) | 2.11893e17 | 0.166522 | ||||||||
\(611\) | 2.22389e18 | 1.72920 | ||||||||
\(612\) | 4.49393e16 | 0.0345734 | ||||||||
\(613\) | −2.01905e18 | −1.53693 | −0.768466 | − | 0.639891i | \(-0.778980\pi\) | ||||
−0.768466 | + | 0.639891i | \(0.778980\pi\) | |||||||
\(614\) | 1.52283e17 | 0.114698 | ||||||||
\(615\) | −9.28603e17 | −0.692057 | ||||||||
\(616\) | 2.21241e18 | 1.63152 | ||||||||
\(617\) | 1.09685e17 | 0.0800372 | 0.0400186 | − | 0.999199i | \(-0.487258\pi\) | ||||
0.0400186 | + | 0.999199i | \(0.487258\pi\) | |||||||
\(618\) | 4.38144e17 | 0.316368 | ||||||||
\(619\) | 1.27610e18 | 0.911793 | 0.455896 | − | 0.890033i | \(-0.349319\pi\) | ||||
0.455896 | + | 0.890033i | \(0.349319\pi\) | |||||||
\(620\) | −1.40728e18 | −0.995027 | ||||||||
\(621\) | 2.80263e17 | 0.196096 | ||||||||
\(622\) | 4.34380e17 | 0.300768 | ||||||||
\(623\) | 3.41889e17 | 0.234268 | ||||||||
\(624\) | 9.85806e17 | 0.668485 | ||||||||
\(625\) | −1.49359e18 | −1.00233 | ||||||||
\(626\) | 8.74588e16 | 0.0580858 | ||||||||
\(627\) | −1.76058e18 | −1.15723 | ||||||||
\(628\) | −1.95048e18 | −1.26883 | ||||||||
\(629\) | −1.56610e14 | −0.000100830 0 | ||||||||
\(630\) | −5.07762e17 | −0.323554 | ||||||||
\(631\) | −1.14820e18 | −0.724144 | −0.362072 | − | 0.932150i | \(-0.617931\pi\) | ||||
−0.362072 | + | 0.932150i | \(0.617931\pi\) | |||||||
\(632\) | −9.89054e17 | −0.617389 | ||||||||
\(633\) | 6.56531e17 | 0.405631 | ||||||||
\(634\) | −5.35741e17 | −0.327623 | ||||||||
\(635\) | 2.58301e18 | 1.56350 | ||||||||
\(636\) | 1.59787e18 | 0.957350 | ||||||||
\(637\) | −8.19215e18 | −4.85838 | ||||||||
\(638\) | −4.27908e17 | −0.251198 | ||||||||
\(639\) | −9.99558e17 | −0.580834 | ||||||||
\(640\) | −2.47961e18 | −1.42631 | ||||||||
\(641\) | 8.40358e17 | 0.478506 | 0.239253 | − | 0.970957i | \(-0.423098\pi\) | ||||
0.239253 | + | 0.970957i | \(0.423098\pi\) | |||||||
\(642\) | −7.18237e16 | −0.0404846 | ||||||||
\(643\) | −4.24702e17 | −0.236981 | −0.118490 | − | 0.992955i | \(-0.537805\pi\) | ||||
−0.118490 | + | 0.992955i | \(0.537805\pi\) | |||||||
\(644\) | −3.05908e18 | −1.68979 | ||||||||
\(645\) | 2.09029e18 | 1.14306 | ||||||||
\(646\) | −1.25190e17 | −0.0677735 | ||||||||
\(647\) | −2.33545e18 | −1.25168 | −0.625839 | − | 0.779953i | \(-0.715243\pi\) | ||||
−0.625839 | + | 0.779953i | \(0.715243\pi\) | |||||||
\(648\) | 1.41121e17 | 0.0748781 | ||||||||
\(649\) | 3.14828e17 | 0.165380 | ||||||||
\(650\) | 1.27588e18 | 0.663551 | ||||||||
\(651\) | −1.72895e18 | −0.890236 | ||||||||
\(652\) | 2.37169e18 | 1.20906 | ||||||||
\(653\) | −1.42232e18 | −0.717898 | −0.358949 | − | 0.933357i | \(-0.616865\pi\) | ||||
−0.358949 | + | 0.933357i | \(0.616865\pi\) | |||||||
\(654\) | −2.94195e17 | −0.147021 | ||||||||
\(655\) | 1.02745e18 | 0.508386 | ||||||||
\(656\) | −1.08592e18 | −0.532016 | ||||||||
\(657\) | −4.18501e17 | −0.203012 | ||||||||
\(658\) | −1.33953e18 | −0.643403 | ||||||||
\(659\) | 3.43005e18 | 1.63134 | 0.815672 | − | 0.578515i | \(-0.196368\pi\) | ||||
0.815672 | + | 0.578515i | \(0.196368\pi\) | |||||||
\(660\) | 1.91531e18 | 0.901993 | ||||||||
\(661\) | −3.05212e18 | −1.42328 | −0.711642 | − | 0.702542i | \(-0.752048\pi\) | ||||
−0.711642 | + | 0.702542i | \(0.752048\pi\) | |||||||
\(662\) | −1.20385e18 | −0.555900 | ||||||||
\(663\) | −2.77789e17 | −0.127021 | ||||||||
\(664\) | −1.24173e17 | −0.0562255 | ||||||||
\(665\) | −9.47891e18 | −4.25028 | ||||||||
\(666\) | −2.28824e14 | −0.000101606 0 | ||||||||
\(667\) | 1.27162e18 | 0.559164 | ||||||||
\(668\) | −5.25091e17 | −0.228659 | ||||||||
\(669\) | −4.80413e17 | −0.207178 | ||||||||
\(670\) | −4.31906e17 | −0.184461 | ||||||||
\(671\) | −9.81964e17 | −0.415336 | ||||||||
\(672\) | −2.36399e18 | −0.990251 | ||||||||
\(673\) | 5.47273e17 | 0.227042 | 0.113521 | − | 0.993536i | \(-0.463787\pi\) | ||||
0.113521 | + | 0.993536i | \(0.463787\pi\) | |||||||
\(674\) | −7.66066e17 | −0.314758 | ||||||||
\(675\) | −4.71821e17 | −0.192001 | ||||||||
\(676\) | −5.19608e18 | −2.09422 | ||||||||
\(677\) | 1.76536e18 | 0.704702 | 0.352351 | − | 0.935868i | \(-0.385382\pi\) | ||||
0.352351 | + | 0.935868i | \(0.385382\pi\) | |||||||
\(678\) | −2.67588e16 | −0.0105797 | ||||||||
\(679\) | −3.78117e18 | −1.48072 | ||||||||
\(680\) | 2.92708e17 | 0.113534 | ||||||||
\(681\) | −1.07611e17 | −0.0413427 | ||||||||
\(682\) | −9.73211e17 | −0.370347 | ||||||||
\(683\) | 5.51479e17 | 0.207871 | 0.103936 | − | 0.994584i | \(-0.466856\pi\) | ||||
0.103936 | + | 0.994584i | \(0.466856\pi\) | |||||||
\(684\) | 1.22577e18 | 0.457660 | ||||||||
\(685\) | 6.40849e18 | 2.37010 | ||||||||
\(686\) | 3.05980e18 | 1.12095 | ||||||||
\(687\) | 1.11198e18 | 0.403530 | ||||||||
\(688\) | 2.44441e18 | 0.878719 | ||||||||
\(689\) | −9.87714e18 | −3.51727 | ||||||||
\(690\) | 8.49361e17 | 0.299622 | ||||||||
\(691\) | 3.12190e17 | 0.109097 | 0.0545484 | − | 0.998511i | \(-0.482628\pi\) | ||||
0.0545484 | + | 0.998511i | \(0.482628\pi\) | |||||||
\(692\) | 1.33380e18 | 0.461744 | ||||||||
\(693\) | 2.35309e18 | 0.806999 | ||||||||
\(694\) | 1.80841e18 | 0.614413 | ||||||||
\(695\) | 6.37567e18 | 2.14597 | ||||||||
\(696\) | 6.40300e17 | 0.213513 | ||||||||
\(697\) | 3.06001e17 | 0.101090 | ||||||||
\(698\) | −4.71846e17 | −0.154433 | ||||||||
\(699\) | −3.64372e17 | −0.118152 | ||||||||
\(700\) | 5.14994e18 | 1.65449 | ||||||||
\(701\) | 3.33857e18 | 1.06266 | 0.531329 | − | 0.847166i | \(-0.321693\pi\) | ||||
0.531329 | + | 0.847166i | \(0.321693\pi\) | |||||||
\(702\) | −4.05881e17 | −0.127999 | ||||||||
\(703\) | −4.27170e15 | −0.00133472 | ||||||||
\(704\) | 1.24336e18 | 0.384923 | ||||||||
\(705\) | −2.49233e18 | −0.764499 | ||||||||
\(706\) | −3.37093e17 | −0.102452 | ||||||||
\(707\) | 6.52013e18 | 1.96350 | ||||||||
\(708\) | −2.19192e17 | −0.0654045 | ||||||||
\(709\) | 4.09782e18 | 1.21158 | 0.605790 | − | 0.795625i | \(-0.292857\pi\) | ||||
0.605790 | + | 0.795625i | \(0.292857\pi\) | |||||||
\(710\) | −3.02925e18 | −0.887474 | ||||||||
\(711\) | −1.05194e18 | −0.305380 | ||||||||
\(712\) | −2.87968e17 | −0.0828370 | ||||||||
\(713\) | 2.89210e18 | 0.824387 | ||||||||
\(714\) | 1.67322e17 | 0.0472623 | ||||||||
\(715\) | −1.18393e19 | −3.31389 | ||||||||
\(716\) | 1.01824e18 | 0.282432 | ||||||||
\(717\) | 2.33356e18 | 0.641424 | ||||||||
\(718\) | −1.40683e18 | −0.383207 | ||||||||
\(719\) | −6.78179e18 | −1.83065 | −0.915327 | − | 0.402711i | \(-0.868068\pi\) | ||||
−0.915327 | + | 0.402711i | \(0.868068\pi\) | |||||||
\(720\) | −1.10480e18 | −0.295545 | ||||||||
\(721\) | −1.09319e19 | −2.89813 | ||||||||
\(722\) | −2.04315e18 | −0.536796 | ||||||||
\(723\) | −2.77677e18 | −0.723003 | ||||||||
\(724\) | 5.34804e18 | 1.38005 | ||||||||
\(725\) | −2.14076e18 | −0.547484 | ||||||||
\(726\) | 5.03718e17 | 0.127673 | ||||||||
\(727\) | −1.21628e18 | −0.305535 | −0.152767 | − | 0.988262i | \(-0.548819\pi\) | ||||
−0.152767 | + | 0.988262i | \(0.548819\pi\) | |||||||
\(728\) | 9.52152e18 | 2.37057 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | −1.26830e18 | −0.310188 | ||||||||
\(731\) | −6.88809e17 | −0.166969 | ||||||||
\(732\) | 6.83670e17 | 0.164257 | ||||||||
\(733\) | −6.38425e18 | −1.52032 | −0.760158 | − | 0.649738i | \(-0.774878\pi\) | ||||
−0.760158 | + | 0.649738i | \(0.774878\pi\) | |||||||
\(734\) | 1.98724e18 | 0.469056 | ||||||||
\(735\) | 9.18102e18 | 2.14794 | ||||||||
\(736\) | 3.95437e18 | 0.917004 | ||||||||
\(737\) | 2.00156e18 | 0.460076 | ||||||||
\(738\) | 4.47103e17 | 0.101869 | ||||||||
\(739\) | −4.65232e18 | −1.05070 | −0.525352 | − | 0.850885i | \(-0.676066\pi\) | ||||
−0.525352 | + | 0.850885i | \(0.676066\pi\) | |||||||
\(740\) | 4.64710e15 | 0.00104034 | ||||||||
\(741\) | −7.57700e18 | −1.68143 | ||||||||
\(742\) | 5.94935e18 | 1.30871 | ||||||||
\(743\) | −1.39759e18 | −0.304756 | −0.152378 | − | 0.988322i | \(-0.548693\pi\) | ||||
−0.152378 | + | 0.988322i | \(0.548693\pi\) | |||||||
\(744\) | 1.45626e18 | 0.314787 | ||||||||
\(745\) | −3.91824e18 | −0.839605 | ||||||||
\(746\) | 8.09048e17 | 0.171859 | ||||||||
\(747\) | −1.32068e17 | −0.0278109 | ||||||||
\(748\) | −6.31149e17 | −0.131756 | ||||||||
\(749\) | 1.79204e18 | 0.370865 | ||||||||
\(750\) | 3.34817e15 | 0.000686926 0 | ||||||||
\(751\) | 2.75161e18 | 0.559664 | 0.279832 | − | 0.960049i | \(-0.409721\pi\) | ||||
0.279832 | + | 0.960049i | \(0.409721\pi\) | |||||||
\(752\) | −2.91458e18 | −0.587705 | ||||||||
\(753\) | 1.26751e18 | 0.253387 | ||||||||
\(754\) | −1.84158e18 | −0.364987 | ||||||||
\(755\) | −6.85791e18 | −1.34752 | ||||||||
\(756\) | −1.63829e18 | −0.319153 | ||||||||
\(757\) | 1.44803e18 | 0.279676 | 0.139838 | − | 0.990174i | \(-0.455342\pi\) | ||||
0.139838 | + | 0.990174i | \(0.455342\pi\) | |||||||
\(758\) | −2.18966e18 | −0.419302 | ||||||||
\(759\) | −3.93614e18 | −0.747307 | ||||||||
\(760\) | 7.98394e18 | 1.50290 | ||||||||
\(761\) | 7.31139e17 | 0.136458 | 0.0682292 | − | 0.997670i | \(-0.478265\pi\) | ||||
0.0682292 | + | 0.997670i | \(0.478265\pi\) | |||||||
\(762\) | −1.24366e18 | −0.230142 | ||||||||
\(763\) | 7.34032e18 | 1.34681 | ||||||||
\(764\) | −6.90000e18 | −1.25528 | ||||||||
\(765\) | 3.11321e17 | 0.0561576 | ||||||||
\(766\) | 1.42766e17 | 0.0255351 | ||||||||
\(767\) | 1.35492e18 | 0.240294 | ||||||||
\(768\) | 1.99040e17 | 0.0350021 | ||||||||
\(769\) | −1.33513e18 | −0.232811 | −0.116405 | − | 0.993202i | \(-0.537137\pi\) | ||||
−0.116405 | + | 0.993202i | \(0.537137\pi\) | |||||||
\(770\) | 7.13126e18 | 1.23304 | ||||||||
\(771\) | 6.18585e18 | 1.06059 | ||||||||
\(772\) | 5.77720e18 | 0.982211 | ||||||||
\(773\) | 7.68371e18 | 1.29540 | 0.647700 | − | 0.761895i | \(-0.275731\pi\) | ||||
0.647700 | + | 0.761895i | \(0.275731\pi\) | |||||||
\(774\) | −1.00643e18 | −0.168254 | ||||||||
\(775\) | −4.86883e18 | −0.807168 | ||||||||
\(776\) | 3.18482e18 | 0.523581 | ||||||||
\(777\) | 5.70930e15 | 0.000930778 0 | ||||||||
\(778\) | −4.27086e16 | −0.00690474 | ||||||||
\(779\) | 8.34652e18 | 1.33817 | ||||||||
\(780\) | 8.24288e18 | 1.31058 | ||||||||
\(781\) | 1.40383e19 | 2.21351 | ||||||||
\(782\) | −2.79889e17 | −0.0437664 | ||||||||
\(783\) | 6.81015e17 | 0.105610 | ||||||||
\(784\) | 1.07364e19 | 1.65122 | ||||||||
\(785\) | −1.35121e19 | −2.06096 | ||||||||
\(786\) | −4.94697e17 | −0.0748329 | ||||||||
\(787\) | −1.22732e19 | −1.84129 | −0.920646 | − | 0.390399i | \(-0.872337\pi\) | ||||
−0.920646 | + | 0.390399i | \(0.872337\pi\) | |||||||
\(788\) | 1.84404e18 | 0.274378 | ||||||||
\(789\) | 6.38709e18 | 0.942546 | ||||||||
\(790\) | −3.18801e18 | −0.466599 | ||||||||
\(791\) | 6.67648e17 | 0.0969171 | ||||||||
\(792\) | −1.98197e18 | −0.285354 | ||||||||
\(793\) | −4.22606e18 | −0.603476 | ||||||||
\(794\) | 2.22553e18 | 0.315211 | ||||||||
\(795\) | 1.10694e19 | 1.55503 | ||||||||
\(796\) | 7.85093e18 | 1.09392 | ||||||||
\(797\) | 1.13007e19 | 1.56181 | 0.780904 | − | 0.624651i | \(-0.214759\pi\) | ||||
0.780904 | + | 0.624651i | \(0.214759\pi\) | |||||||
\(798\) | 4.56389e18 | 0.625629 | ||||||||
\(799\) | 8.21295e17 | 0.111672 | ||||||||
\(800\) | −6.65716e18 | −0.897850 | ||||||||
\(801\) | −3.06279e17 | −0.0409738 | ||||||||
\(802\) | −3.92428e18 | −0.520747 | ||||||||
\(803\) | 5.87763e18 | 0.773662 | ||||||||
\(804\) | −1.39354e18 | −0.181951 | ||||||||
\(805\) | −2.11920e19 | −2.74473 | ||||||||
\(806\) | −4.18839e18 | −0.538108 | ||||||||
\(807\) | 2.68481e18 | 0.342165 | ||||||||
\(808\) | −5.49180e18 | −0.694290 | ||||||||
\(809\) | 1.47159e19 | 1.84553 | 0.922765 | − | 0.385364i | \(-0.125924\pi\) | ||||
0.922765 | + | 0.385364i | \(0.125924\pi\) | |||||||
\(810\) | 4.54875e17 | 0.0565900 | ||||||||
\(811\) | 9.51436e17 | 0.117421 | 0.0587103 | − | 0.998275i | \(-0.481301\pi\) | ||||
0.0587103 | + | 0.998275i | \(0.481301\pi\) | |||||||
\(812\) | −7.43330e18 | −0.910055 | ||||||||
\(813\) | 3.48088e18 | 0.422767 | ||||||||
\(814\) | 3.21372e15 | 0.000387212 0 | ||||||||
\(815\) | 1.64301e19 | 1.96388 | ||||||||
\(816\) | 3.64064e17 | 0.0431709 | ||||||||
\(817\) | −1.87880e19 | −2.21023 | ||||||||
\(818\) | −4.61987e18 | −0.539180 | ||||||||
\(819\) | 1.01270e19 | 1.17256 | ||||||||
\(820\) | −9.08002e18 | −1.04303 | ||||||||
\(821\) | 7.29378e17 | 0.0831231 | 0.0415616 | − | 0.999136i | \(-0.486767\pi\) | ||||
0.0415616 | + | 0.999136i | \(0.486767\pi\) | |||||||
\(822\) | −3.08555e18 | −0.348872 | ||||||||
\(823\) | 1.50596e19 | 1.68933 | 0.844663 | − | 0.535299i | \(-0.179801\pi\) | ||||
0.844663 | + | 0.535299i | \(0.179801\pi\) | |||||||
\(824\) | 9.20780e18 | 1.02478 | ||||||||
\(825\) | 6.62647e18 | 0.731698 | ||||||||
\(826\) | −8.16115e17 | −0.0894089 | ||||||||
\(827\) | 1.03556e19 | 1.12562 | 0.562808 | − | 0.826588i | \(-0.309721\pi\) | ||||
0.562808 | + | 0.826588i | \(0.309721\pi\) | |||||||
\(828\) | 2.74045e18 | 0.295546 | ||||||||
\(829\) | 4.59391e18 | 0.491562 | 0.245781 | − | 0.969325i | \(-0.420956\pi\) | ||||
0.245781 | + | 0.969325i | \(0.420956\pi\) | |||||||
\(830\) | −4.00245e17 | −0.0424931 | ||||||||
\(831\) | −1.65663e18 | −0.174510 | ||||||||
\(832\) | 5.35102e18 | 0.559288 | ||||||||
\(833\) | −3.02541e18 | −0.313755 | ||||||||
\(834\) | −3.06975e18 | −0.315881 | ||||||||
\(835\) | −3.63761e18 | −0.371411 | ||||||||
\(836\) | −1.72153e19 | −1.74411 | ||||||||
\(837\) | 1.54886e18 | 0.155703 | ||||||||
\(838\) | −3.17554e18 | −0.316760 | ||||||||
\(839\) | −1.09522e19 | −1.08405 | −0.542025 | − | 0.840362i | \(-0.682342\pi\) | ||||
−0.542025 | + | 0.840362i | \(0.682342\pi\) | |||||||
\(840\) | −1.06709e19 | −1.04805 | ||||||||
\(841\) | −7.17070e18 | −0.698856 | ||||||||
\(842\) | 1.26441e18 | 0.122281 | ||||||||
\(843\) | −3.67747e18 | −0.352915 | ||||||||
\(844\) | 6.41966e18 | 0.611345 | ||||||||
\(845\) | −3.59963e19 | −3.40165 | ||||||||
\(846\) | 1.20001e18 | 0.112532 | ||||||||
\(847\) | −1.25680e19 | −1.16957 | ||||||||
\(848\) | 1.29447e19 | 1.19542 | ||||||||
\(849\) | 4.79635e18 | 0.439552 | ||||||||
\(850\) | 4.71191e17 | 0.0428523 | ||||||||
\(851\) | −9.55024e15 | −0.000861930 0 | ||||||||
\(852\) | −9.77382e18 | −0.875401 | ||||||||
\(853\) | 6.06853e18 | 0.539405 | 0.269703 | − | 0.962944i | \(-0.413075\pi\) | ||||
0.269703 | + | 0.962944i | \(0.413075\pi\) | |||||||
\(854\) | 2.54551e18 | 0.224542 | ||||||||
\(855\) | 8.49161e18 | 0.743379 | ||||||||
\(856\) | −1.50941e18 | −0.131138 | ||||||||
\(857\) | −1.77836e19 | −1.53336 | −0.766679 | − | 0.642030i | \(-0.778092\pi\) | ||||
−0.766679 | + | 0.642030i | \(0.778092\pi\) | |||||||
\(858\) | 5.70039e18 | 0.487795 | ||||||||
\(859\) | −3.69923e18 | −0.314163 | −0.157082 | − | 0.987586i | \(-0.550209\pi\) | ||||
−0.157082 | + | 0.987586i | \(0.550209\pi\) | |||||||
\(860\) | 2.04391e19 | 1.72275 | ||||||||
\(861\) | −1.11555e19 | −0.933183 | ||||||||
\(862\) | −5.91227e18 | −0.490859 | ||||||||
\(863\) | −2.31117e18 | −0.190441 | −0.0952206 | − | 0.995456i | \(-0.530356\pi\) | ||||
−0.0952206 | + | 0.995456i | \(0.530356\pi\) | |||||||
\(864\) | 2.11776e18 | 0.173196 | ||||||||
\(865\) | 9.24001e18 | 0.750012 | ||||||||
\(866\) | −5.01243e18 | −0.403815 | ||||||||
\(867\) | 7.11785e18 | 0.569147 | ||||||||
\(868\) | −1.69059e19 | −1.34171 | ||||||||
\(869\) | 1.47740e19 | 1.16378 | ||||||||
\(870\) | 2.06388e18 | 0.161365 | ||||||||
\(871\) | 8.61407e18 | 0.668483 | ||||||||
\(872\) | −6.18264e18 | −0.476230 | ||||||||
\(873\) | 3.38733e18 | 0.258980 | ||||||||
\(874\) | −7.63426e18 | −0.579352 | ||||||||
\(875\) | −8.35388e16 | −0.00629268 | ||||||||
\(876\) | −4.09217e18 | −0.305968 | ||||||||
\(877\) | −2.10598e19 | −1.56299 | −0.781495 | − | 0.623912i | \(-0.785542\pi\) | ||||
−0.781495 | + | 0.623912i | \(0.785542\pi\) | |||||||
\(878\) | −3.12703e18 | −0.230365 | ||||||||
\(879\) | −4.88876e18 | −0.357496 | ||||||||
\(880\) | 1.55164e19 | 1.12630 | ||||||||
\(881\) | −2.90922e18 | −0.209620 | −0.104810 | − | 0.994492i | \(-0.533424\pi\) | ||||
−0.104810 | + | 0.994492i | \(0.533424\pi\) | |||||||
\(882\) | −4.42046e18 | −0.316171 | ||||||||
\(883\) | 8.09516e18 | 0.574753 | 0.287376 | − | 0.957818i | \(-0.407217\pi\) | ||||
0.287376 | + | 0.957818i | \(0.407217\pi\) | |||||||
\(884\) | −2.71626e18 | −0.191440 | ||||||||
\(885\) | −1.51847e18 | −0.106237 | ||||||||
\(886\) | −2.78505e18 | −0.193426 | ||||||||
\(887\) | −2.60308e18 | −0.179467 | −0.0897334 | − | 0.995966i | \(-0.528602\pi\) | ||||
−0.0897334 | + | 0.995966i | \(0.528602\pi\) | |||||||
\(888\) | −4.80885e15 | −0.000329122 0 | ||||||||
\(889\) | 3.10301e19 | 2.10825 | ||||||||
\(890\) | −9.28206e17 | −0.0626050 | ||||||||
\(891\) | −2.10800e18 | −0.141145 | ||||||||
\(892\) | −4.69755e18 | −0.312248 | ||||||||
\(893\) | 2.24017e19 | 1.47825 | ||||||||
\(894\) | 1.88655e18 | 0.123587 | ||||||||
\(895\) | 7.05393e18 | 0.458756 | ||||||||
\(896\) | −2.97880e19 | −1.92326 | ||||||||
\(897\) | −1.69399e19 | −1.08583 | ||||||||
\(898\) | −1.49066e18 | −0.0948598 | ||||||||
\(899\) | 7.02756e18 | 0.443983 | ||||||||
\(900\) | −4.61353e18 | −0.289372 | ||||||||
\(901\) | −3.64768e18 | −0.227146 | ||||||||
\(902\) | −6.27932e18 | −0.388213 | ||||||||
\(903\) | 2.51109e19 | 1.54132 | ||||||||
\(904\) | −5.62349e17 | −0.0342698 | ||||||||
\(905\) | 3.70490e19 | 2.24162 | ||||||||
\(906\) | 3.30194e18 | 0.198352 | ||||||||
\(907\) | 1.56993e19 | 0.936338 | 0.468169 | − | 0.883639i | \(-0.344914\pi\) | ||||
0.468169 | + | 0.883639i | \(0.344914\pi\) | |||||||
\(908\) | −1.05223e18 | −0.0623095 | ||||||||
\(909\) | −5.84101e18 | −0.343417 | ||||||||
\(910\) | 3.06907e19 | 1.79158 | ||||||||
\(911\) | −2.52252e19 | −1.46206 | −0.731031 | − | 0.682344i | \(-0.760961\pi\) | ||||
−0.731031 | + | 0.682344i | \(0.760961\pi\) | |||||||
\(912\) | 9.93023e18 | 0.571469 | ||||||||
\(913\) | 1.85483e18 | 0.105985 | ||||||||
\(914\) | −2.68000e18 | −0.152049 | ||||||||
\(915\) | 4.73618e18 | 0.266803 | ||||||||
\(916\) | 1.08731e19 | 0.608179 | ||||||||
\(917\) | 1.23430e19 | 0.685518 | ||||||||
\(918\) | −1.49894e17 | −0.00826623 | ||||||||
\(919\) | 5.88065e18 | 0.322014 | 0.161007 | − | 0.986953i | \(-0.448526\pi\) | ||||
0.161007 | + | 0.986953i | \(0.448526\pi\) | |||||||
\(920\) | 1.78497e19 | 0.970533 | ||||||||
\(921\) | 3.40379e18 | 0.183770 | ||||||||
\(922\) | 1.32665e18 | 0.0711220 | ||||||||
\(923\) | 6.04162e19 | 3.21620 | ||||||||
\(924\) | 2.30089e19 | 1.21626 | ||||||||
\(925\) | 1.60778e16 | 0.000843927 0 | ||||||||
\(926\) | 4.94010e18 | 0.257493 | ||||||||
\(927\) | 9.79330e18 | 0.506886 | ||||||||
\(928\) | 9.60879e18 | 0.493863 | ||||||||
\(929\) | 2.49712e19 | 1.27449 | 0.637247 | − | 0.770660i | \(-0.280073\pi\) | ||||
0.637247 | + | 0.770660i | \(0.280073\pi\) | |||||||
\(930\) | 4.69397e18 | 0.237904 | ||||||||
\(931\) | −8.25212e19 | −4.15330 | ||||||||
\(932\) | −3.56288e18 | −0.178073 | ||||||||
\(933\) | 9.70915e18 | 0.481893 | ||||||||
\(934\) | −4.66077e18 | −0.229722 | ||||||||
\(935\) | −4.37234e18 | −0.214012 | ||||||||
\(936\) | −8.52978e18 | −0.414615 | ||||||||
\(937\) | −3.36764e18 | −0.162562 | −0.0812809 | − | 0.996691i | \(-0.525901\pi\) | ||||
−0.0812809 | + | 0.996691i | \(0.525901\pi\) | |||||||
\(938\) | −5.18856e18 | −0.248730 | ||||||||
\(939\) | 1.95486e18 | 0.0930655 | ||||||||
\(940\) | −2.43704e19 | −1.15221 | ||||||||
\(941\) | 2.58779e19 | 1.21506 | 0.607528 | − | 0.794298i | \(-0.292161\pi\) | ||||
0.607528 | + | 0.794298i | \(0.292161\pi\) | |||||||
\(942\) | 6.50578e18 | 0.303367 | ||||||||
\(943\) | 1.86603e19 | 0.864158 | ||||||||
\(944\) | −1.77572e18 | −0.0816690 | ||||||||
\(945\) | −1.13494e19 | −0.518401 | ||||||||
\(946\) | 1.41348e19 | 0.641203 | ||||||||
\(947\) | −2.93965e19 | −1.32440 | −0.662202 | − | 0.749326i | \(-0.730378\pi\) | ||||
−0.662202 | + | 0.749326i | \(0.730378\pi\) | |||||||
\(948\) | −1.02861e19 | −0.460251 | ||||||||
\(949\) | 2.52955e19 | 1.12412 | ||||||||
\(950\) | 1.28522e19 | 0.567251 | ||||||||
\(951\) | −1.19748e19 | −0.524920 | ||||||||
\(952\) | 3.51635e18 | 0.153092 | ||||||||
\(953\) | −2.37641e19 | −1.02758 | −0.513792 | − | 0.857915i | \(-0.671760\pi\) | ||||
−0.513792 | + | 0.857915i | \(0.671760\pi\) | |||||||
\(954\) | −5.32968e18 | −0.228895 | ||||||||
\(955\) | −4.78003e19 | −2.03896 | ||||||||
\(956\) | 2.28179e19 | 0.966718 | ||||||||
\(957\) | −9.56450e18 | −0.402471 | ||||||||
\(958\) | −1.01950e19 | −0.426098 | ||||||||
\(959\) | 7.69863e19 | 3.19589 | ||||||||
\(960\) | −5.99694e18 | −0.247267 | ||||||||
\(961\) | −8.43444e18 | −0.345425 | ||||||||
\(962\) | 1.38308e16 | 0.000562614 0 | ||||||||
\(963\) | −1.60539e18 | −0.0648648 | ||||||||
\(964\) | −2.71516e19 | −1.08967 | ||||||||
\(965\) | 4.00220e19 | 1.59541 | ||||||||
\(966\) | 1.02035e19 | 0.404015 | ||||||||
\(967\) | 4.21463e17 | 0.0165763 | 0.00828815 | − | 0.999966i | \(-0.497362\pi\) | ||||
0.00828815 | + | 0.999966i | \(0.497362\pi\) | |||||||
\(968\) | 1.05859e19 | 0.413558 | ||||||||
\(969\) | −2.79823e18 | −0.108587 | ||||||||
\(970\) | 1.02656e19 | 0.395702 | ||||||||
\(971\) | 3.40026e19 | 1.30193 | 0.650964 | − | 0.759109i | \(-0.274365\pi\) | ||||
0.650964 | + | 0.759109i | \(0.274365\pi\) | |||||||
\(972\) | 1.46765e18 | 0.0558202 | ||||||||
\(973\) | 7.65919e19 | 2.89367 | ||||||||
\(974\) | −3.33674e18 | −0.125224 | ||||||||
\(975\) | 2.85182e19 | 1.06315 | ||||||||
\(976\) | 5.53857e18 | 0.205104 | ||||||||
\(977\) | −2.63305e19 | −0.968600 | −0.484300 | − | 0.874902i | \(-0.660926\pi\) | ||||
−0.484300 | + | 0.874902i | \(0.660926\pi\) | |||||||
\(978\) | −7.91073e18 | −0.289077 | ||||||||
\(979\) | 4.30153e18 | 0.156148 | ||||||||
\(980\) | 8.97733e19 | 3.23726 | ||||||||
\(981\) | −6.57577e18 | −0.235558 | ||||||||
\(982\) | −1.12960e19 | −0.401976 | ||||||||
\(983\) | −2.63878e19 | −0.932836 | −0.466418 | − | 0.884564i | \(-0.654456\pi\) | ||||
−0.466418 | + | 0.884564i | \(0.654456\pi\) | |||||||
\(984\) | 9.39607e18 | 0.329973 | ||||||||
\(985\) | 1.27747e19 | 0.445673 | ||||||||
\(986\) | −6.80106e17 | −0.0235709 | ||||||||
\(987\) | −2.99408e19 | −1.03087 | ||||||||
\(988\) | −7.40890e19 | −2.53416 | ||||||||
\(989\) | −4.20044e19 | −1.42731 | ||||||||
\(990\) | −6.38848e18 | −0.215660 | ||||||||
\(991\) | 6.22964e18 | 0.208922 | 0.104461 | − | 0.994529i | \(-0.466688\pi\) | ||||
0.104461 | + | 0.994529i | \(0.466688\pi\) | |||||||
\(992\) | 2.18537e19 | 0.728114 | ||||||||
\(993\) | −2.69083e19 | −0.890667 | ||||||||
\(994\) | −3.63908e19 | −1.19669 | ||||||||
\(995\) | 5.43880e19 | 1.77686 | ||||||||
\(996\) | −1.29138e18 | −0.0419150 | ||||||||
\(997\) | −2.53077e19 | −0.816083 | −0.408042 | − | 0.912963i | \(-0.633788\pi\) | ||||
−0.408042 | + | 0.912963i | \(0.633788\pi\) | |||||||
\(998\) | 1.62329e19 | 0.520052 | ||||||||
\(999\) | −5.11463e15 | −0.000162794 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 | 177.14.a.b.1.15 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.b.1.15 | ✓ | 31 | 1.1 | even | 1 | trivial |