Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,20,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 20);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(22.8816696556\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 2925852 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1710.01\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 512.000 | 0.707107 | ||||||||
\(3\) | 51072.2 | 1.49807 | 0.749037 | − | 0.662529i | \(-0.230517\pi\) | ||||
0.749037 | + | 0.662529i | \(0.230517\pi\) | |||||||
\(4\) | 262144. | 0.500000 | ||||||||
\(5\) | 1.95312e6 | 0.447214 | ||||||||
\(6\) | 2.61490e7 | 1.05930 | ||||||||
\(7\) | 2.72650e7 | 0.255372 | 0.127686 | − | 0.991815i | \(-0.459245\pi\) | ||||
0.127686 | + | 0.991815i | \(0.459245\pi\) | |||||||
\(8\) | 1.34218e8 | 0.353553 | ||||||||
\(9\) | 1.44611e9 | 1.24422 | ||||||||
\(10\) | 1.00000e9 | 0.316228 | ||||||||
\(11\) | 8.90778e9 | 1.13904 | 0.569520 | − | 0.821977i | \(-0.307129\pi\) | ||||
0.569520 | + | 0.821977i | \(0.307129\pi\) | |||||||
\(12\) | 1.33883e10 | 0.749037 | ||||||||
\(13\) | −3.88993e10 | −1.01737 | −0.508686 | − | 0.860952i | \(-0.669869\pi\) | ||||
−0.508686 | + | 0.860952i | \(0.669869\pi\) | |||||||
\(14\) | 1.39597e10 | 0.180575 | ||||||||
\(15\) | 9.97505e10 | 0.669959 | ||||||||
\(16\) | 6.87195e10 | 0.250000 | ||||||||
\(17\) | −4.92493e11 | −1.00725 | −0.503623 | − | 0.863924i | \(-0.668000\pi\) | ||||
−0.503623 | + | 0.863924i | \(0.668000\pi\) | |||||||
\(18\) | 7.40410e11 | 0.879799 | ||||||||
\(19\) | 7.02926e11 | 0.499747 | 0.249873 | − | 0.968278i | \(-0.419611\pi\) | ||||
0.249873 | + | 0.968278i | \(0.419611\pi\) | |||||||
\(20\) | 5.12000e11 | 0.223607 | ||||||||
\(21\) | 1.39248e12 | 0.382566 | ||||||||
\(22\) | 4.56078e12 | 0.805423 | ||||||||
\(23\) | −5.93310e12 | −0.686858 | −0.343429 | − | 0.939179i | \(-0.611588\pi\) | ||||
−0.343429 | + | 0.939179i | \(0.611588\pi\) | |||||||
\(24\) | 6.85480e12 | 0.529649 | ||||||||
\(25\) | 3.81470e12 | 0.200000 | ||||||||
\(26\) | −1.99164e13 | −0.719391 | ||||||||
\(27\) | 1.44969e13 | 0.365864 | ||||||||
\(28\) | 7.14735e12 | 0.127686 | ||||||||
\(29\) | 1.42477e14 | 1.82374 | 0.911869 | − | 0.410481i | \(-0.134639\pi\) | ||||
0.911869 | + | 0.410481i | \(0.134639\pi\) | |||||||
\(30\) | 5.10722e13 | 0.473732 | ||||||||
\(31\) | 2.10392e14 | 1.42920 | 0.714600 | − | 0.699533i | \(-0.246609\pi\) | ||||
0.714600 | + | 0.699533i | \(0.246609\pi\) | |||||||
\(32\) | 3.51844e13 | 0.176777 | ||||||||
\(33\) | 4.54940e14 | 1.70637 | ||||||||
\(34\) | −2.52156e14 | −0.712230 | ||||||||
\(35\) | 5.32519e13 | 0.114206 | ||||||||
\(36\) | 3.79090e14 | 0.622112 | ||||||||
\(37\) | −1.00145e15 | −1.26681 | −0.633404 | − | 0.773821i | \(-0.718343\pi\) | ||||
−0.633404 | + | 0.773821i | \(0.718343\pi\) | |||||||
\(38\) | 3.59898e14 | 0.353374 | ||||||||
\(39\) | −1.98667e15 | −1.52410 | ||||||||
\(40\) | 2.62144e14 | 0.158114 | ||||||||
\(41\) | −4.08507e15 | −1.94874 | −0.974368 | − | 0.224961i | \(-0.927775\pi\) | ||||
−0.974368 | + | 0.224961i | \(0.927775\pi\) | |||||||
\(42\) | 7.12952e14 | 0.270515 | ||||||||
\(43\) | 3.21023e15 | 0.974060 | 0.487030 | − | 0.873385i | \(-0.338080\pi\) | ||||
0.487030 | + | 0.873385i | \(0.338080\pi\) | |||||||
\(44\) | 2.33512e15 | 0.569520 | ||||||||
\(45\) | 2.82444e15 | 0.556434 | ||||||||
\(46\) | −3.03774e15 | −0.485682 | ||||||||
\(47\) | −6.44781e15 | −0.840393 | −0.420196 | − | 0.907433i | \(-0.638039\pi\) | ||||
−0.420196 | + | 0.907433i | \(0.638039\pi\) | |||||||
\(48\) | 3.50966e15 | 0.374518 | ||||||||
\(49\) | −1.06555e16 | −0.934785 | ||||||||
\(50\) | 1.95312e15 | 0.141421 | ||||||||
\(51\) | −2.51527e16 | −1.50893 | ||||||||
\(52\) | −1.01972e16 | −0.508686 | ||||||||
\(53\) | 1.88410e15 | 0.0784300 | 0.0392150 | − | 0.999231i | \(-0.487514\pi\) | ||||
0.0392150 | + | 0.999231i | \(0.487514\pi\) | |||||||
\(54\) | 7.42243e15 | 0.258705 | ||||||||
\(55\) | 1.73980e16 | 0.509394 | ||||||||
\(56\) | 3.65944e15 | 0.0902877 | ||||||||
\(57\) | 3.59000e16 | 0.748658 | ||||||||
\(58\) | 7.29480e16 | 1.28958 | ||||||||
\(59\) | −4.28479e15 | −0.0643924 | −0.0321962 | − | 0.999482i | \(-0.510250\pi\) | ||||
−0.0321962 | + | 0.999482i | \(0.510250\pi\) | |||||||
\(60\) | 2.61490e16 | 0.334979 | ||||||||
\(61\) | −1.19883e17 | −1.31257 | −0.656287 | − | 0.754511i | \(-0.727874\pi\) | ||||
−0.656287 | + | 0.754511i | \(0.727874\pi\) | |||||||
\(62\) | 1.07721e17 | 1.01060 | ||||||||
\(63\) | 3.94282e16 | 0.317740 | ||||||||
\(64\) | 1.80144e16 | 0.125000 | ||||||||
\(65\) | −7.59752e16 | −0.454983 | ||||||||
\(66\) | 2.32929e17 | 1.20658 | ||||||||
\(67\) | 1.93776e17 | 0.870141 | 0.435071 | − | 0.900396i | \(-0.356723\pi\) | ||||
0.435071 | + | 0.900396i | \(0.356723\pi\) | |||||||
\(68\) | −1.29104e17 | −0.503623 | ||||||||
\(69\) | −3.03017e17 | −1.02896 | ||||||||
\(70\) | 2.72650e16 | 0.0807558 | ||||||||
\(71\) | 3.68964e17 | 0.955058 | 0.477529 | − | 0.878616i | \(-0.341532\pi\) | ||||
0.477529 | + | 0.878616i | \(0.341532\pi\) | |||||||
\(72\) | 1.94094e17 | 0.439899 | ||||||||
\(73\) | −9.09825e17 | −1.80880 | −0.904400 | − | 0.426685i | \(-0.859681\pi\) | ||||
−0.904400 | + | 0.426685i | \(0.859681\pi\) | |||||||
\(74\) | −5.12740e17 | −0.895769 | ||||||||
\(75\) | 1.94825e17 | 0.299615 | ||||||||
\(76\) | 1.84268e17 | 0.249873 | ||||||||
\(77\) | 2.42870e17 | 0.290879 | ||||||||
\(78\) | −1.01718e18 | −1.07770 | ||||||||
\(79\) | 5.25508e17 | 0.493313 | 0.246656 | − | 0.969103i | \(-0.420668\pi\) | ||||
0.246656 | + | 0.969103i | \(0.420668\pi\) | |||||||
\(80\) | 1.34218e17 | 0.111803 | ||||||||
\(81\) | −9.40371e17 | −0.696132 | ||||||||
\(82\) | −2.09156e18 | −1.37796 | ||||||||
\(83\) | −2.77280e18 | −1.62808 | −0.814042 | − | 0.580807i | \(-0.802737\pi\) | ||||
−0.814042 | + | 0.580807i | \(0.802737\pi\) | |||||||
\(84\) | 3.65031e17 | 0.191283 | ||||||||
\(85\) | −9.61900e17 | −0.450454 | ||||||||
\(86\) | 1.64364e18 | 0.688764 | ||||||||
\(87\) | 7.27660e18 | 2.73209 | ||||||||
\(88\) | 1.19558e18 | 0.402712 | ||||||||
\(89\) | −3.88866e17 | −0.117651 | −0.0588254 | − | 0.998268i | \(-0.518736\pi\) | ||||
−0.0588254 | + | 0.998268i | \(0.518736\pi\) | |||||||
\(90\) | 1.44611e18 | 0.393458 | ||||||||
\(91\) | −1.06059e18 | −0.259809 | ||||||||
\(92\) | −1.55533e18 | −0.343429 | ||||||||
\(93\) | 1.07452e19 | 2.14105 | ||||||||
\(94\) | −3.30128e18 | −0.594247 | ||||||||
\(95\) | 1.37290e18 | 0.223494 | ||||||||
\(96\) | 1.79694e18 | 0.264824 | ||||||||
\(97\) | −9.73741e17 | −0.130050 | −0.0650252 | − | 0.997884i | \(-0.520713\pi\) | ||||
−0.0650252 | + | 0.997884i | \(0.520713\pi\) | |||||||
\(98\) | −5.45562e18 | −0.660993 | ||||||||
\(99\) | 1.28817e19 | 1.41722 | ||||||||
\(100\) | 1.00000e18 | 0.100000 | ||||||||
\(101\) | −1.67461e19 | −1.52356 | −0.761781 | − | 0.647834i | \(-0.775675\pi\) | ||||
−0.761781 | + | 0.647834i | \(0.775675\pi\) | |||||||
\(102\) | −1.28782e19 | −1.06697 | ||||||||
\(103\) | 4.40800e18 | 0.332880 | 0.166440 | − | 0.986052i | \(-0.446773\pi\) | ||||
0.166440 | + | 0.986052i | \(0.446773\pi\) | |||||||
\(104\) | −5.22098e18 | −0.359695 | ||||||||
\(105\) | 2.71969e18 | 0.171089 | ||||||||
\(106\) | 9.64657e17 | 0.0554584 | ||||||||
\(107\) | −8.71914e18 | −0.458488 | −0.229244 | − | 0.973369i | \(-0.573625\pi\) | ||||
−0.229244 | + | 0.973369i | \(0.573625\pi\) | |||||||
\(108\) | 3.80028e18 | 0.182932 | ||||||||
\(109\) | 4.17114e19 | 1.83951 | 0.919757 | − | 0.392487i | \(-0.128385\pi\) | ||||
0.919757 | + | 0.392487i | \(0.128385\pi\) | |||||||
\(110\) | 8.90778e18 | 0.360196 | ||||||||
\(111\) | −5.11461e19 | −1.89777 | ||||||||
\(112\) | 1.87363e18 | 0.0638431 | ||||||||
\(113\) | −8.70592e18 | −0.272627 | −0.136314 | − | 0.990666i | \(-0.543525\pi\) | ||||
−0.136314 | + | 0.990666i | \(0.543525\pi\) | |||||||
\(114\) | 1.83808e19 | 0.529381 | ||||||||
\(115\) | −1.15881e19 | −0.307172 | ||||||||
\(116\) | 3.73494e19 | 0.911869 | ||||||||
\(117\) | −5.62528e19 | −1.26584 | ||||||||
\(118\) | −2.19381e18 | −0.0455323 | ||||||||
\(119\) | −1.34278e19 | −0.257222 | ||||||||
\(120\) | 1.33883e19 | 0.236866 | ||||||||
\(121\) | 1.81895e19 | 0.297413 | ||||||||
\(122\) | −6.13801e19 | −0.928130 | ||||||||
\(123\) | −2.08634e20 | −2.91935 | ||||||||
\(124\) | 5.51530e19 | 0.714600 | ||||||||
\(125\) | 7.45058e18 | 0.0894427 | ||||||||
\(126\) | 2.01873e19 | 0.224676 | ||||||||
\(127\) | 6.07257e19 | 0.626956 | 0.313478 | − | 0.949595i | \(-0.398506\pi\) | ||||
0.313478 | + | 0.949595i | \(0.398506\pi\) | |||||||
\(128\) | 9.22337e18 | 0.0883883 | ||||||||
\(129\) | 1.63954e20 | 1.45921 | ||||||||
\(130\) | −3.88993e19 | −0.321721 | ||||||||
\(131\) | 1.94831e20 | 1.49824 | 0.749120 | − | 0.662434i | \(-0.230477\pi\) | ||||
0.749120 | + | 0.662434i | \(0.230477\pi\) | |||||||
\(132\) | 1.19260e20 | 0.853183 | ||||||||
\(133\) | 1.91652e19 | 0.127622 | ||||||||
\(134\) | 9.92134e19 | 0.615283 | ||||||||
\(135\) | 2.83143e19 | 0.163620 | ||||||||
\(136\) | −6.61013e19 | −0.356115 | ||||||||
\(137\) | 1.21216e20 | 0.609135 | 0.304567 | − | 0.952491i | \(-0.401488\pi\) | ||||
0.304567 | + | 0.952491i | \(0.401488\pi\) | |||||||
\(138\) | −1.55144e20 | −0.727587 | ||||||||
\(139\) | 2.22493e20 | 0.974263 | 0.487131 | − | 0.873329i | \(-0.338043\pi\) | ||||
0.487131 | + | 0.873329i | \(0.338043\pi\) | |||||||
\(140\) | 1.39597e19 | 0.0571030 | ||||||||
\(141\) | −3.29304e20 | −1.25897 | ||||||||
\(142\) | 1.88910e20 | 0.675328 | ||||||||
\(143\) | −3.46506e20 | −1.15883 | ||||||||
\(144\) | 9.93761e19 | 0.311056 | ||||||||
\(145\) | 2.78275e20 | 0.815600 | ||||||||
\(146\) | −4.65830e20 | −1.27902 | ||||||||
\(147\) | −5.44201e20 | −1.40038 | ||||||||
\(148\) | −2.62523e20 | −0.633404 | ||||||||
\(149\) | 3.46894e20 | 0.785104 | 0.392552 | − | 0.919730i | \(-0.371592\pi\) | ||||
0.392552 | + | 0.919730i | \(0.371592\pi\) | |||||||
\(150\) | 9.97505e19 | 0.211860 | ||||||||
\(151\) | −1.05205e19 | −0.0209776 | −0.0104888 | − | 0.999945i | \(-0.503339\pi\) | ||||
−0.0104888 | + | 0.999945i | \(0.503339\pi\) | |||||||
\(152\) | 9.43451e19 | 0.176687 | ||||||||
\(153\) | −7.12200e20 | −1.25324 | ||||||||
\(154\) | 1.24350e20 | 0.205683 | ||||||||
\(155\) | 4.10922e20 | 0.639158 | ||||||||
\(156\) | −5.20795e20 | −0.762049 | ||||||||
\(157\) | −3.07714e19 | −0.0423741 | −0.0211871 | − | 0.999776i | \(-0.506745\pi\) | ||||
−0.0211871 | + | 0.999776i | \(0.506745\pi\) | |||||||
\(158\) | 2.69060e20 | 0.348825 | ||||||||
\(159\) | 9.62250e19 | 0.117494 | ||||||||
\(160\) | 6.87195e19 | 0.0790569 | ||||||||
\(161\) | −1.61766e20 | −0.175404 | ||||||||
\(162\) | −4.81470e20 | −0.492239 | ||||||||
\(163\) | 5.76318e20 | 0.555751 | 0.277875 | − | 0.960617i | \(-0.410370\pi\) | ||||
0.277875 | + | 0.960617i | \(0.410370\pi\) | |||||||
\(164\) | −1.07088e21 | −0.974368 | ||||||||
\(165\) | 8.88555e20 | 0.763110 | ||||||||
\(166\) | −1.41967e21 | −1.15123 | ||||||||
\(167\) | 6.89550e20 | 0.528153 | 0.264076 | − | 0.964502i | \(-0.414933\pi\) | ||||
0.264076 | + | 0.964502i | \(0.414933\pi\) | |||||||
\(168\) | 1.86896e20 | 0.135258 | ||||||||
\(169\) | 5.12350e19 | 0.0350464 | ||||||||
\(170\) | −4.92493e20 | −0.318519 | ||||||||
\(171\) | 1.01651e21 | 0.621797 | ||||||||
\(172\) | 8.41542e20 | 0.487030 | ||||||||
\(173\) | −4.14244e19 | −0.0226892 | −0.0113446 | − | 0.999936i | \(-0.503611\pi\) | ||||
−0.0113446 | + | 0.999936i | \(0.503611\pi\) | |||||||
\(174\) | 3.72562e21 | 1.93188 | ||||||||
\(175\) | 1.04008e20 | 0.0510744 | ||||||||
\(176\) | 6.12138e20 | 0.284760 | ||||||||
\(177\) | −2.18834e20 | −0.0964646 | ||||||||
\(178\) | −1.99099e20 | −0.0831917 | ||||||||
\(179\) | 3.65179e21 | 1.44678 | 0.723388 | − | 0.690441i | \(-0.242584\pi\) | ||||
0.723388 | + | 0.690441i | \(0.242584\pi\) | |||||||
\(180\) | 7.40410e20 | 0.278217 | ||||||||
\(181\) | 1.05232e21 | 0.375145 | 0.187573 | − | 0.982251i | \(-0.439938\pi\) | ||||
0.187573 | + | 0.982251i | \(0.439938\pi\) | |||||||
\(182\) | −5.43021e20 | −0.183712 | ||||||||
\(183\) | −6.12269e21 | −1.96633 | ||||||||
\(184\) | −7.96327e20 | −0.242841 | ||||||||
\(185\) | −1.95595e21 | −0.566534 | ||||||||
\(186\) | 5.50154e21 | 1.51395 | ||||||||
\(187\) | −4.38702e21 | −1.14729 | ||||||||
\(188\) | −1.69025e21 | −0.420196 | ||||||||
\(189\) | 3.95258e20 | 0.0934316 | ||||||||
\(190\) | 7.02926e20 | 0.158034 | ||||||||
\(191\) | −6.63681e21 | −1.41952 | −0.709761 | − | 0.704442i | \(-0.751197\pi\) | ||||
−0.709761 | + | 0.704442i | \(0.751197\pi\) | |||||||
\(192\) | 9.20036e20 | 0.187259 | ||||||||
\(193\) | −2.65526e21 | −0.514414 | −0.257207 | − | 0.966356i | \(-0.582802\pi\) | ||||
−0.257207 | + | 0.966356i | \(0.582802\pi\) | |||||||
\(194\) | −4.98555e20 | −0.0919596 | ||||||||
\(195\) | −3.88022e21 | −0.681597 | ||||||||
\(196\) | −2.79328e21 | −0.467393 | ||||||||
\(197\) | 1.02356e22 | 1.63186 | 0.815929 | − | 0.578153i | \(-0.196226\pi\) | ||||
0.815929 | + | 0.578153i | \(0.196226\pi\) | |||||||
\(198\) | 6.59541e21 | 1.00213 | ||||||||
\(199\) | −2.53082e21 | −0.366570 | −0.183285 | − | 0.983060i | \(-0.558673\pi\) | ||||
−0.183285 | + | 0.983060i | \(0.558673\pi\) | |||||||
\(200\) | 5.12000e20 | 0.0707107 | ||||||||
\(201\) | 9.89659e21 | 1.30354 | ||||||||
\(202\) | −8.57400e21 | −1.07732 | ||||||||
\(203\) | 3.88462e21 | 0.465732 | ||||||||
\(204\) | −6.59363e21 | −0.754463 | ||||||||
\(205\) | −7.97865e21 | −0.871501 | ||||||||
\(206\) | 2.25689e21 | 0.235382 | ||||||||
\(207\) | −8.57993e21 | −0.854605 | ||||||||
\(208\) | −2.67314e21 | −0.254343 | ||||||||
\(209\) | 6.26151e21 | 0.569232 | ||||||||
\(210\) | 1.39248e21 | 0.120978 | ||||||||
\(211\) | −1.43232e22 | −1.18948 | −0.594740 | − | 0.803918i | \(-0.702745\pi\) | ||||
−0.594740 | + | 0.803918i | \(0.702745\pi\) | |||||||
\(212\) | 4.93904e20 | 0.0392150 | ||||||||
\(213\) | 1.88438e22 | 1.43075 | ||||||||
\(214\) | −4.46420e21 | −0.324200 | ||||||||
\(215\) | 6.26998e21 | 0.435613 | ||||||||
\(216\) | 1.94574e21 | 0.129353 | ||||||||
\(217\) | 5.73633e21 | 0.364978 | ||||||||
\(218\) | 2.13562e22 | 1.30073 | ||||||||
\(219\) | −4.64668e22 | −2.70972 | ||||||||
\(220\) | 4.56078e21 | 0.254697 | ||||||||
\(221\) | 1.91576e22 | 1.02474 | ||||||||
\(222\) | −2.61868e22 | −1.34193 | ||||||||
\(223\) | 1.40599e22 | 0.690375 | 0.345187 | − | 0.938534i | \(-0.387815\pi\) | ||||
0.345187 | + | 0.938534i | \(0.387815\pi\) | |||||||
\(224\) | 9.59301e20 | 0.0451439 | ||||||||
\(225\) | 5.51648e21 | 0.248845 | ||||||||
\(226\) | −4.45743e21 | −0.192777 | ||||||||
\(227\) | 3.41441e22 | 1.41602 | 0.708011 | − | 0.706201i | \(-0.249592\pi\) | ||||
0.708011 | + | 0.706201i | \(0.249592\pi\) | |||||||
\(228\) | 9.41097e21 | 0.374329 | ||||||||
\(229\) | 2.26978e22 | 0.866057 | 0.433028 | − | 0.901380i | \(-0.357445\pi\) | ||||
0.433028 | + | 0.901380i | \(0.357445\pi\) | |||||||
\(230\) | −5.93310e21 | −0.217204 | ||||||||
\(231\) | 1.24039e22 | 0.435758 | ||||||||
\(232\) | 1.91229e22 | 0.644789 | ||||||||
\(233\) | 3.14636e22 | 1.01842 | 0.509211 | − | 0.860642i | \(-0.329937\pi\) | ||||
0.509211 | + | 0.860642i | \(0.329937\pi\) | |||||||
\(234\) | −2.88014e22 | −0.895083 | ||||||||
\(235\) | −1.25934e22 | −0.375835 | ||||||||
\(236\) | −1.12323e21 | −0.0321962 | ||||||||
\(237\) | 2.68389e22 | 0.739018 | ||||||||
\(238\) | −6.87504e21 | −0.181884 | ||||||||
\(239\) | −1.24777e22 | −0.317216 | −0.158608 | − | 0.987342i | \(-0.550701\pi\) | ||||
−0.158608 | + | 0.987342i | \(0.550701\pi\) | |||||||
\(240\) | 6.85480e21 | 0.167490 | ||||||||
\(241\) | −1.16264e21 | −0.0273076 | −0.0136538 | − | 0.999907i | \(-0.504346\pi\) | ||||
−0.0136538 | + | 0.999907i | \(0.504346\pi\) | |||||||
\(242\) | 9.31301e21 | 0.210302 | ||||||||
\(243\) | −6.48761e22 | −1.40872 | ||||||||
\(244\) | −3.14266e22 | −0.656287 | ||||||||
\(245\) | −2.08116e22 | −0.418049 | ||||||||
\(246\) | −1.06820e23 | −2.06429 | ||||||||
\(247\) | −2.73433e22 | −0.508429 | ||||||||
\(248\) | 2.82383e22 | 0.505299 | ||||||||
\(249\) | −1.41613e23 | −2.43899 | ||||||||
\(250\) | 3.81470e21 | 0.0632456 | ||||||||
\(251\) | 1.09655e23 | 1.75036 | 0.875182 | − | 0.483793i | \(-0.160741\pi\) | ||||
0.875182 | + | 0.483793i | \(0.160741\pi\) | |||||||
\(252\) | 1.03359e22 | 0.158870 | ||||||||
\(253\) | −5.28507e22 | −0.782359 | ||||||||
\(254\) | 3.10916e22 | 0.443325 | ||||||||
\(255\) | −4.91264e22 | −0.674813 | ||||||||
\(256\) | 4.72237e21 | 0.0625000 | ||||||||
\(257\) | −2.11998e22 | −0.270375 | −0.135187 | − | 0.990820i | \(-0.543164\pi\) | ||||
−0.135187 | + | 0.990820i | \(0.543164\pi\) | |||||||
\(258\) | 8.39442e22 | 1.03182 | ||||||||
\(259\) | −2.73044e22 | −0.323508 | ||||||||
\(260\) | −1.99164e22 | −0.227491 | ||||||||
\(261\) | 2.06037e23 | 2.26914 | ||||||||
\(262\) | 9.97536e22 | 1.05942 | ||||||||
\(263\) | −1.06654e23 | −1.09244 | −0.546222 | − | 0.837641i | \(-0.683934\pi\) | ||||
−0.546222 | + | 0.837641i | \(0.683934\pi\) | |||||||
\(264\) | 6.10611e22 | 0.603291 | ||||||||
\(265\) | 3.67987e21 | 0.0350750 | ||||||||
\(266\) | 9.81261e21 | 0.0902420 | ||||||||
\(267\) | −1.98603e22 | −0.176250 | ||||||||
\(268\) | 5.07973e22 | 0.435071 | ||||||||
\(269\) | 9.27742e22 | 0.766974 | 0.383487 | − | 0.923546i | \(-0.374723\pi\) | ||||
0.383487 | + | 0.923546i | \(0.374723\pi\) | |||||||
\(270\) | 1.44969e22 | 0.115696 | ||||||||
\(271\) | −9.46299e22 | −0.729156 | −0.364578 | − | 0.931173i | \(-0.618787\pi\) | ||||
−0.364578 | + | 0.931173i | \(0.618787\pi\) | |||||||
\(272\) | −3.38438e22 | −0.251811 | ||||||||
\(273\) | −5.41666e22 | −0.389212 | ||||||||
\(274\) | 6.20624e22 | 0.430723 | ||||||||
\(275\) | 3.39805e22 | 0.227808 | ||||||||
\(276\) | −7.94340e22 | −0.514482 | ||||||||
\(277\) | −7.04507e21 | −0.0440887 | −0.0220444 | − | 0.999757i | \(-0.507018\pi\) | ||||
−0.0220444 | + | 0.999757i | \(0.507018\pi\) | |||||||
\(278\) | 1.13916e23 | 0.688908 | ||||||||
\(279\) | 3.04251e23 | 1.77824 | ||||||||
\(280\) | 7.14735e21 | 0.0403779 | ||||||||
\(281\) | −1.00259e22 | −0.0547539 | −0.0273770 | − | 0.999625i | \(-0.508715\pi\) | ||||
−0.0273770 | + | 0.999625i | \(0.508715\pi\) | |||||||
\(282\) | −1.68604e23 | −0.890226 | ||||||||
\(283\) | −2.12867e23 | −1.08677 | −0.543383 | − | 0.839485i | \(-0.682857\pi\) | ||||
−0.543383 | + | 0.839485i | \(0.682857\pi\) | |||||||
\(284\) | 9.67218e22 | 0.477529 | ||||||||
\(285\) | 7.01172e22 | 0.334810 | ||||||||
\(286\) | −1.77411e23 | −0.819415 | ||||||||
\(287\) | −1.11379e23 | −0.497653 | ||||||||
\(288\) | 5.08806e22 | 0.219950 | ||||||||
\(289\) | 3.47675e21 | 0.0145427 | ||||||||
\(290\) | 1.42477e23 | 0.576717 | ||||||||
\(291\) | −4.97311e22 | −0.194825 | ||||||||
\(292\) | −2.38505e23 | −0.904400 | ||||||||
\(293\) | 5.10289e23 | 1.87315 | 0.936577 | − | 0.350462i | \(-0.113975\pi\) | ||||
0.936577 | + | 0.350462i | \(0.113975\pi\) | |||||||
\(294\) | −2.78631e23 | −0.990216 | ||||||||
\(295\) | −8.36872e21 | −0.0287972 | ||||||||
\(296\) | −1.34412e23 | −0.447885 | ||||||||
\(297\) | 1.29135e23 | 0.416734 | ||||||||
\(298\) | 1.77610e23 | 0.555152 | ||||||||
\(299\) | 2.30793e23 | 0.698790 | ||||||||
\(300\) | 5.10722e22 | 0.149807 | ||||||||
\(301\) | 8.75268e22 | 0.248748 | ||||||||
\(302\) | −5.38650e21 | −0.0148334 | ||||||||
\(303\) | −8.55260e23 | −2.28241 | ||||||||
\(304\) | 4.83047e22 | 0.124937 | ||||||||
\(305\) | −2.34146e23 | −0.587001 | ||||||||
\(306\) | −3.64646e23 | −0.886173 | ||||||||
\(307\) | −4.42100e23 | −1.04161 | −0.520806 | − | 0.853675i | \(-0.674369\pi\) | ||||
−0.520806 | + | 0.853675i | \(0.674369\pi\) | |||||||
\(308\) | 6.36670e22 | 0.145440 | ||||||||
\(309\) | 2.25126e23 | 0.498678 | ||||||||
\(310\) | 2.10392e23 | 0.451953 | ||||||||
\(311\) | −3.04953e23 | −0.635344 | −0.317672 | − | 0.948201i | \(-0.602901\pi\) | ||||
−0.317672 | + | 0.948201i | \(0.602901\pi\) | |||||||
\(312\) | −2.66647e23 | −0.538850 | ||||||||
\(313\) | −6.44559e23 | −1.26355 | −0.631774 | − | 0.775153i | \(-0.717673\pi\) | ||||
−0.631774 | + | 0.775153i | \(0.717673\pi\) | |||||||
\(314\) | −1.57550e22 | −0.0299630 | ||||||||
\(315\) | 7.70083e22 | 0.142098 | ||||||||
\(316\) | 1.37759e23 | 0.246656 | ||||||||
\(317\) | 1.02667e24 | 1.78389 | 0.891947 | − | 0.452140i | \(-0.149339\pi\) | ||||
0.891947 | + | 0.452140i | \(0.149339\pi\) | |||||||
\(318\) | 4.92672e22 | 0.0830807 | ||||||||
\(319\) | 1.26915e24 | 2.07731 | ||||||||
\(320\) | 3.51844e22 | 0.0559017 | ||||||||
\(321\) | −4.45306e23 | −0.686849 | ||||||||
\(322\) | −8.28240e22 | −0.124030 | ||||||||
\(323\) | −3.46186e23 | −0.503368 | ||||||||
\(324\) | −2.46513e23 | −0.348066 | ||||||||
\(325\) | −1.48389e23 | −0.203474 | ||||||||
\(326\) | 2.95075e23 | 0.392975 | ||||||||
\(327\) | 2.13030e24 | 2.75573 | ||||||||
\(328\) | −5.48289e23 | −0.688982 | ||||||||
\(329\) | −1.75799e23 | −0.214613 | ||||||||
\(330\) | 4.54940e23 | 0.539600 | ||||||||
\(331\) | 8.39874e23 | 0.967939 | 0.483970 | − | 0.875085i | \(-0.339194\pi\) | ||||
0.483970 | + | 0.875085i | \(0.339194\pi\) | |||||||
\(332\) | −7.26873e23 | −0.814042 | ||||||||
\(333\) | −1.44820e24 | −1.57619 | ||||||||
\(334\) | 3.53050e23 | 0.373460 | ||||||||
\(335\) | 3.78469e23 | 0.389139 | ||||||||
\(336\) | 9.56907e22 | 0.0956416 | ||||||||
\(337\) | −7.88161e23 | −0.765827 | −0.382913 | − | 0.923784i | \(-0.625079\pi\) | ||||
−0.382913 | + | 0.923784i | \(0.625079\pi\) | |||||||
\(338\) | 2.62323e22 | 0.0247815 | ||||||||
\(339\) | −4.44631e23 | −0.408416 | ||||||||
\(340\) | −2.52156e23 | −0.225227 | ||||||||
\(341\) | 1.87413e24 | 1.62792 | ||||||||
\(342\) | 5.20453e23 | 0.439677 | ||||||||
\(343\) | −6.01313e23 | −0.494090 | ||||||||
\(344\) | 4.30870e23 | 0.344382 | ||||||||
\(345\) | −5.91829e23 | −0.460166 | ||||||||
\(346\) | −2.12093e22 | −0.0160437 | ||||||||
\(347\) | −3.27984e23 | −0.241392 | −0.120696 | − | 0.992690i | \(-0.538513\pi\) | ||||
−0.120696 | + | 0.992690i | \(0.538513\pi\) | |||||||
\(348\) | 1.90752e24 | 1.36605 | ||||||||
\(349\) | −1.57618e24 | −1.09841 | −0.549204 | − | 0.835689i | \(-0.685069\pi\) | ||||
−0.549204 | + | 0.835689i | \(0.685069\pi\) | |||||||
\(350\) | 5.32519e22 | 0.0361151 | ||||||||
\(351\) | −5.63920e23 | −0.372220 | ||||||||
\(352\) | 3.13415e23 | 0.201356 | ||||||||
\(353\) | −1.44980e23 | −0.0906667 | −0.0453333 | − | 0.998972i | \(-0.514435\pi\) | ||||
−0.0453333 | + | 0.998972i | \(0.514435\pi\) | |||||||
\(354\) | −1.12043e23 | −0.0682108 | ||||||||
\(355\) | 7.20633e23 | 0.427115 | ||||||||
\(356\) | −1.01939e23 | −0.0588254 | ||||||||
\(357\) | −6.85788e23 | −0.385338 | ||||||||
\(358\) | 1.86971e24 | 1.02303 | ||||||||
\(359\) | 7.64624e23 | 0.407428 | 0.203714 | − | 0.979030i | \(-0.434699\pi\) | ||||
0.203714 | + | 0.979030i | \(0.434699\pi\) | |||||||
\(360\) | 3.79090e23 | 0.196729 | ||||||||
\(361\) | −1.48432e24 | −0.750253 | ||||||||
\(362\) | 5.38786e23 | 0.265268 | ||||||||
\(363\) | 9.28978e23 | 0.445546 | ||||||||
\(364\) | −2.78027e23 | −0.129904 | ||||||||
\(365\) | −1.77700e24 | −0.808920 | ||||||||
\(366\) | −3.13482e24 | −1.39041 | ||||||||
\(367\) | −2.08854e24 | −0.902639 | −0.451320 | − | 0.892362i | \(-0.649047\pi\) | ||||
−0.451320 | + | 0.892362i | \(0.649047\pi\) | |||||||
\(368\) | −4.07719e23 | −0.171714 | ||||||||
\(369\) | −5.90747e24 | −2.42466 | ||||||||
\(370\) | −1.00145e24 | −0.400600 | ||||||||
\(371\) | 5.13698e22 | 0.0200288 | ||||||||
\(372\) | 2.81679e24 | 1.07052 | ||||||||
\(373\) | 2.90964e24 | 1.07797 | 0.538984 | − | 0.842316i | \(-0.318808\pi\) | ||||
0.538984 | + | 0.842316i | \(0.318808\pi\) | |||||||
\(374\) | −2.24615e24 | −0.811258 | ||||||||
\(375\) | 3.80518e23 | 0.133992 | ||||||||
\(376\) | −8.65410e23 | −0.297124 | ||||||||
\(377\) | −5.54224e24 | −1.85542 | ||||||||
\(378\) | 2.02372e23 | 0.0660661 | ||||||||
\(379\) | 4.57048e24 | 1.45509 | 0.727544 | − | 0.686061i | \(-0.240662\pi\) | ||||
0.727544 | + | 0.686061i | \(0.240662\pi\) | |||||||
\(380\) | 3.59898e23 | 0.111747 | ||||||||
\(381\) | 3.10140e24 | 0.939226 | ||||||||
\(382\) | −3.39805e24 | −1.00375 | ||||||||
\(383\) | 4.74338e24 | 1.36678 | 0.683392 | − | 0.730052i | \(-0.260504\pi\) | ||||
0.683392 | + | 0.730052i | \(0.260504\pi\) | |||||||
\(384\) | 4.71058e23 | 0.132412 | ||||||||
\(385\) | 4.74356e23 | 0.130085 | ||||||||
\(386\) | −1.35949e24 | −0.363745 | ||||||||
\(387\) | 4.64235e24 | 1.21195 | ||||||||
\(388\) | −2.55260e23 | −0.0650252 | ||||||||
\(389\) | −1.60295e24 | −0.398472 | −0.199236 | − | 0.979952i | \(-0.563846\pi\) | ||||
−0.199236 | + | 0.979952i | \(0.563846\pi\) | |||||||
\(390\) | −1.98667e24 | −0.481962 | ||||||||
\(391\) | 2.92201e24 | 0.691834 | ||||||||
\(392\) | −1.43016e24 | −0.330496 | ||||||||
\(393\) | 9.95047e24 | 2.24447 | ||||||||
\(394\) | 5.24060e24 | 1.15390 | ||||||||
\(395\) | 1.02638e24 | 0.220616 | ||||||||
\(396\) | 3.37685e24 | 0.708610 | ||||||||
\(397\) | 5.17477e24 | 1.06018 | 0.530092 | − | 0.847940i | \(-0.322157\pi\) | ||||
0.530092 | + | 0.847940i | \(0.322157\pi\) | |||||||
\(398\) | −1.29578e24 | −0.259204 | ||||||||
\(399\) | 9.78812e23 | 0.191186 | ||||||||
\(400\) | 2.62144e23 | 0.0500000 | ||||||||
\(401\) | 1.04892e24 | 0.195377 | 0.0976883 | − | 0.995217i | \(-0.468855\pi\) | ||||
0.0976883 | + | 0.995217i | \(0.468855\pi\) | |||||||
\(402\) | 5.06705e24 | 0.921739 | ||||||||
\(403\) | −8.18410e24 | −1.45403 | ||||||||
\(404\) | −4.38989e24 | −0.761781 | ||||||||
\(405\) | −1.83666e24 | −0.311320 | ||||||||
\(406\) | 1.98893e24 | 0.329322 | ||||||||
\(407\) | −8.92066e24 | −1.44295 | ||||||||
\(408\) | −3.37594e24 | −0.533486 | ||||||||
\(409\) | −9.84304e24 | −1.51970 | −0.759850 | − | 0.650098i | \(-0.774728\pi\) | ||||
−0.759850 | + | 0.650098i | \(0.774728\pi\) | |||||||
\(410\) | −4.08507e24 | −0.616244 | ||||||||
\(411\) | 6.19076e24 | 0.912529 | ||||||||
\(412\) | 1.15553e24 | 0.166440 | ||||||||
\(413\) | −1.16825e23 | −0.0164440 | ||||||||
\(414\) | −4.39292e24 | −0.604297 | ||||||||
\(415\) | −5.41562e24 | −0.728101 | ||||||||
\(416\) | −1.36865e24 | −0.179848 | ||||||||
\(417\) | 1.13632e25 | 1.45952 | ||||||||
\(418\) | 3.20589e24 | 0.402508 | ||||||||
\(419\) | 1.39759e24 | 0.171533 | 0.0857664 | − | 0.996315i | \(-0.472666\pi\) | ||||
0.0857664 | + | 0.996315i | \(0.472666\pi\) | |||||||
\(420\) | 7.12952e23 | 0.0855444 | ||||||||
\(421\) | 2.96558e24 | 0.347880 | 0.173940 | − | 0.984756i | \(-0.444350\pi\) | ||||
0.173940 | + | 0.984756i | \(0.444350\pi\) | |||||||
\(422\) | −7.33348e24 | −0.841089 | ||||||||
\(423\) | −9.32425e24 | −1.04564 | ||||||||
\(424\) | 2.52879e23 | 0.0277292 | ||||||||
\(425\) | −1.87871e24 | −0.201449 | ||||||||
\(426\) | 9.64804e24 | 1.01169 | ||||||||
\(427\) | −3.26861e24 | −0.335195 | ||||||||
\(428\) | −2.28567e24 | −0.229244 | ||||||||
\(429\) | −1.76969e25 | −1.73601 | ||||||||
\(430\) | 3.21023e24 | 0.308025 | ||||||||
\(431\) | −1.73742e25 | −1.63069 | −0.815343 | − | 0.578978i | \(-0.803452\pi\) | ||||
−0.815343 | + | 0.578978i | \(0.803452\pi\) | |||||||
\(432\) | 9.96221e23 | 0.0914661 | ||||||||
\(433\) | 1.97317e25 | 1.77227 | 0.886133 | − | 0.463432i | \(-0.153382\pi\) | ||||
0.886133 | + | 0.463432i | \(0.153382\pi\) | |||||||
\(434\) | 2.93700e24 | 0.258078 | ||||||||
\(435\) | 1.42121e25 | 1.22183 | ||||||||
\(436\) | 1.09344e25 | 0.919757 | ||||||||
\(437\) | −4.17052e24 | −0.343255 | ||||||||
\(438\) | −2.37910e25 | −1.91606 | ||||||||
\(439\) | 2.37490e25 | 1.87168 | 0.935840 | − | 0.352425i | \(-0.114643\pi\) | ||||
0.935840 | + | 0.352425i | \(0.114643\pi\) | |||||||
\(440\) | 2.33512e24 | 0.180098 | ||||||||
\(441\) | −1.54091e25 | −1.16308 | ||||||||
\(442\) | 9.80870e24 | 0.724603 | ||||||||
\(443\) | −1.08663e25 | −0.785679 | −0.392840 | − | 0.919607i | \(-0.628507\pi\) | ||||
−0.392840 | + | 0.919607i | \(0.628507\pi\) | |||||||
\(444\) | −1.34076e25 | −0.948886 | ||||||||
\(445\) | −7.59504e23 | −0.0526150 | ||||||||
\(446\) | 7.19865e24 | 0.488169 | ||||||||
\(447\) | 1.77166e25 | 1.17614 | ||||||||
\(448\) | 4.91162e23 | 0.0319215 | ||||||||
\(449\) | 1.64022e25 | 1.04367 | 0.521834 | − | 0.853047i | \(-0.325248\pi\) | ||||
0.521834 | + | 0.853047i | \(0.325248\pi\) | |||||||
\(450\) | 2.82444e24 | 0.175960 | ||||||||
\(451\) | −3.63889e25 | −2.21969 | ||||||||
\(452\) | −2.28220e24 | −0.136314 | ||||||||
\(453\) | −5.37306e23 | −0.0314260 | ||||||||
\(454\) | 1.74818e25 | 1.00128 | ||||||||
\(455\) | −2.07146e24 | −0.116190 | ||||||||
\(456\) | 4.81841e24 | 0.264690 | ||||||||
\(457\) | −1.90127e25 | −1.02291 | −0.511457 | − | 0.859309i | \(-0.670894\pi\) | ||||
−0.511457 | + | 0.859309i | \(0.670894\pi\) | |||||||
\(458\) | 1.16213e25 | 0.612395 | ||||||||
\(459\) | −7.13963e24 | −0.368515 | ||||||||
\(460\) | −3.03774e24 | −0.153586 | ||||||||
\(461\) | −2.73913e25 | −1.35660 | −0.678302 | − | 0.734783i | \(-0.737284\pi\) | ||||
−0.678302 | + | 0.734783i | \(0.737284\pi\) | |||||||
\(462\) | 6.35082e24 | 0.308128 | ||||||||
\(463\) | 2.15999e25 | 1.02667 | 0.513337 | − | 0.858187i | \(-0.328409\pi\) | ||||
0.513337 | + | 0.858187i | \(0.328409\pi\) | |||||||
\(464\) | 9.79092e24 | 0.455935 | ||||||||
\(465\) | 2.09867e25 | 0.957505 | ||||||||
\(466\) | 1.61094e25 | 0.720133 | ||||||||
\(467\) | 6.57907e24 | 0.288174 | 0.144087 | − | 0.989565i | \(-0.453976\pi\) | ||||
0.144087 | + | 0.989565i | \(0.453976\pi\) | |||||||
\(468\) | −1.47463e25 | −0.632919 | ||||||||
\(469\) | 5.28330e24 | 0.222210 | ||||||||
\(470\) | −6.44781e24 | −0.265756 | ||||||||
\(471\) | −1.57157e24 | −0.0634796 | ||||||||
\(472\) | −5.75094e23 | −0.0227662 | ||||||||
\(473\) | 2.85960e25 | 1.10949 | ||||||||
\(474\) | 1.37415e25 | 0.522565 | ||||||||
\(475\) | 2.68145e24 | 0.0999494 | ||||||||
\(476\) | −3.52002e24 | −0.128611 | ||||||||
\(477\) | 2.72461e24 | 0.0975844 | ||||||||
\(478\) | −6.38858e24 | −0.224305 | ||||||||
\(479\) | 1.84209e25 | 0.634049 | 0.317024 | − | 0.948417i | \(-0.397316\pi\) | ||||
0.317024 | + | 0.948417i | \(0.397316\pi\) | |||||||
\(480\) | 3.50966e24 | 0.118433 | ||||||||
\(481\) | 3.89555e25 | 1.28882 | ||||||||
\(482\) | −5.95271e23 | −0.0193094 | ||||||||
\(483\) | −8.26174e24 | −0.262769 | ||||||||
\(484\) | 4.76826e24 | 0.148706 | ||||||||
\(485\) | −1.90184e24 | −0.0581603 | ||||||||
\(486\) | −3.32165e25 | −0.996116 | ||||||||
\(487\) | −5.85949e25 | −1.72320 | −0.861598 | − | 0.507591i | \(-0.830536\pi\) | ||||
−0.861598 | + | 0.507591i | \(0.830536\pi\) | |||||||
\(488\) | −1.60904e25 | −0.464065 | ||||||||
\(489\) | 2.94339e25 | 0.832555 | ||||||||
\(490\) | −1.06555e25 | −0.295605 | ||||||||
\(491\) | 1.17567e24 | 0.0319896 | 0.0159948 | − | 0.999872i | \(-0.494908\pi\) | ||||
0.0159948 | + | 0.999872i | \(0.494908\pi\) | |||||||
\(492\) | −5.46921e25 | −1.45967 | ||||||||
\(493\) | −7.01687e25 | −1.83695 | ||||||||
\(494\) | −1.39998e25 | −0.359513 | ||||||||
\(495\) | 2.51595e25 | 0.633800 | ||||||||
\(496\) | 1.44580e25 | 0.357300 | ||||||||
\(497\) | 1.00598e25 | 0.243895 | ||||||||
\(498\) | −7.25059e25 | −1.72462 | ||||||||
\(499\) | −1.57255e25 | −0.366985 | −0.183492 | − | 0.983021i | \(-0.558740\pi\) | ||||
−0.183492 | + | 0.983021i | \(0.558740\pi\) | |||||||
\(500\) | 1.95313e24 | 0.0447214 | ||||||||
\(501\) | 3.52169e25 | 0.791211 | ||||||||
\(502\) | 5.61434e25 | 1.23769 | ||||||||
\(503\) | −2.64249e24 | −0.0571632 | −0.0285816 | − | 0.999591i | \(-0.509099\pi\) | ||||
−0.0285816 | + | 0.999591i | \(0.509099\pi\) | |||||||
\(504\) | 5.29197e24 | 0.112338 | ||||||||
\(505\) | −3.27072e25 | −0.681358 | ||||||||
\(506\) | −2.70596e25 | −0.553211 | ||||||||
\(507\) | 2.61669e24 | 0.0525020 | ||||||||
\(508\) | 1.59189e25 | 0.313478 | ||||||||
\(509\) | 7.94197e25 | 1.53500 | 0.767501 | − | 0.641048i | \(-0.221500\pi\) | ||||
0.767501 | + | 0.641048i | \(0.221500\pi\) | |||||||
\(510\) | −2.51527e25 | −0.477165 | ||||||||
\(511\) | −2.48064e25 | −0.461918 | ||||||||
\(512\) | 2.41785e24 | 0.0441942 | ||||||||
\(513\) | 1.01903e25 | 0.182840 | ||||||||
\(514\) | −1.08543e25 | −0.191184 | ||||||||
\(515\) | 8.60937e24 | 0.148868 | ||||||||
\(516\) | 4.29794e25 | 0.729606 | ||||||||
\(517\) | −5.74356e25 | −0.957241 | ||||||||
\(518\) | −1.39798e25 | −0.228755 | ||||||||
\(519\) | −2.11564e24 | −0.0339900 | ||||||||
\(520\) | −1.01972e25 | −0.160861 | ||||||||
\(521\) | 4.66972e25 | 0.723324 | 0.361662 | − | 0.932309i | \(-0.382209\pi\) | ||||
0.361662 | + | 0.932309i | \(0.382209\pi\) | |||||||
\(522\) | 1.05491e26 | 1.60452 | ||||||||
\(523\) | −6.46849e25 | −0.966132 | −0.483066 | − | 0.875584i | \(-0.660477\pi\) | ||||
−0.483066 | + | 0.875584i | \(0.660477\pi\) | |||||||
\(524\) | 5.10739e25 | 0.749120 | ||||||||
\(525\) | 5.31190e24 | 0.0765133 | ||||||||
\(526\) | −5.46070e25 | −0.772474 | ||||||||
\(527\) | −1.03617e26 | −1.43955 | ||||||||
\(528\) | 3.12633e25 | 0.426591 | ||||||||
\(529\) | −3.94138e25 | −0.528226 | ||||||||
\(530\) | 1.88410e24 | 0.0248017 | ||||||||
\(531\) | −6.19628e24 | −0.0801186 | ||||||||
\(532\) | 5.02405e24 | 0.0638108 | ||||||||
\(533\) | 1.58906e26 | 1.98259 | ||||||||
\(534\) | −1.01685e25 | −0.124627 | ||||||||
\(535\) | −1.70296e25 | −0.205042 | ||||||||
\(536\) | 2.60082e25 | 0.307641 | ||||||||
\(537\) | 1.86505e26 | 2.16738 | ||||||||
\(538\) | 4.75004e25 | 0.542333 | ||||||||
\(539\) | −9.49170e25 | −1.06476 | ||||||||
\(540\) | 7.42243e24 | 0.0818098 | ||||||||
\(541\) | 1.28312e25 | 0.138961 | 0.0694805 | − | 0.997583i | \(-0.477866\pi\) | ||||
0.0694805 | + | 0.997583i | \(0.477866\pi\) | |||||||
\(542\) | −4.84505e25 | −0.515591 | ||||||||
\(543\) | 5.37441e25 | 0.561995 | ||||||||
\(544\) | −1.73281e25 | −0.178057 | ||||||||
\(545\) | 8.14676e25 | 0.822656 | ||||||||
\(546\) | −2.77333e25 | −0.275215 | ||||||||
\(547\) | 5.22682e25 | 0.509750 | 0.254875 | − | 0.966974i | \(-0.417966\pi\) | ||||
0.254875 | + | 0.966974i | \(0.417966\pi\) | |||||||
\(548\) | 3.17760e25 | 0.304567 | ||||||||
\(549\) | −1.73364e26 | −1.63314 | ||||||||
\(550\) | 1.73980e25 | 0.161085 | ||||||||
\(551\) | 1.00150e26 | 0.911408 | ||||||||
\(552\) | −4.06702e25 | −0.363793 | ||||||||
\(553\) | 1.43280e25 | 0.125978 | ||||||||
\(554\) | −3.60708e24 | −0.0311754 | ||||||||
\(555\) | −9.98947e25 | −0.848710 | ||||||||
\(556\) | 5.83252e25 | 0.487131 | ||||||||
\(557\) | 5.10671e25 | 0.419292 | 0.209646 | − | 0.977777i | \(-0.432769\pi\) | ||||
0.209646 | + | 0.977777i | \(0.432769\pi\) | |||||||
\(558\) | 1.55776e26 | 1.25741 | ||||||||
\(559\) | −1.24876e26 | −0.990981 | ||||||||
\(560\) | 3.65944e24 | 0.0285515 | ||||||||
\(561\) | −2.24055e26 | −1.71873 | ||||||||
\(562\) | −5.13328e24 | −0.0387169 | ||||||||
\(563\) | 1.95962e26 | 1.45325 | 0.726627 | − | 0.687032i | \(-0.241087\pi\) | ||||
0.726627 | + | 0.687032i | \(0.241087\pi\) | |||||||
\(564\) | −8.63250e25 | −0.629485 | ||||||||
\(565\) | −1.70037e25 | −0.121923 | ||||||||
\(566\) | −1.08988e26 | −0.768460 | ||||||||
\(567\) | −2.56392e25 | −0.177773 | ||||||||
\(568\) | 4.95215e25 | 0.337664 | ||||||||
\(569\) | −2.04702e25 | −0.137264 | −0.0686320 | − | 0.997642i | \(-0.521863\pi\) | ||||
−0.0686320 | + | 0.997642i | \(0.521863\pi\) | |||||||
\(570\) | 3.59000e25 | 0.236746 | ||||||||
\(571\) | −1.26019e26 | −0.817322 | −0.408661 | − | 0.912686i | \(-0.634004\pi\) | ||||
−0.408661 | + | 0.912686i | \(0.634004\pi\) | |||||||
\(572\) | −9.08346e25 | −0.579414 | ||||||||
\(573\) | −3.38957e26 | −2.12655 | ||||||||
\(574\) | −5.70262e25 | −0.351894 | ||||||||
\(575\) | −2.26330e25 | −0.137372 | ||||||||
\(576\) | 2.60509e25 | 0.155528 | ||||||||
\(577\) | −1.24271e26 | −0.729792 | −0.364896 | − | 0.931048i | \(-0.618895\pi\) | ||||
−0.364896 | + | 0.931048i | \(0.618895\pi\) | |||||||
\(578\) | 1.78010e24 | 0.0102832 | ||||||||
\(579\) | −1.35610e26 | −0.770629 | ||||||||
\(580\) | 7.29480e25 | 0.407800 | ||||||||
\(581\) | −7.56003e25 | −0.415767 | ||||||||
\(582\) | −2.54623e25 | −0.137762 | ||||||||
\(583\) | 1.67831e25 | 0.0893349 | ||||||||
\(584\) | −1.22115e26 | −0.639508 | ||||||||
\(585\) | −1.09869e26 | −0.566100 | ||||||||
\(586\) | 2.61268e26 | 1.32452 | ||||||||
\(587\) | 3.67268e26 | 1.83198 | 0.915991 | − | 0.401199i | \(-0.131407\pi\) | ||||
0.915991 | + | 0.401199i | \(0.131407\pi\) | |||||||
\(588\) | −1.42659e26 | −0.700188 | ||||||||
\(589\) | 1.47890e26 | 0.714238 | ||||||||
\(590\) | −4.28479e24 | −0.0203627 | ||||||||
\(591\) | 5.22753e26 | 2.44464 | ||||||||
\(592\) | −6.88188e25 | −0.316702 | ||||||||
\(593\) | −1.40519e26 | −0.636378 | −0.318189 | − | 0.948027i | \(-0.603075\pi\) | ||||
−0.318189 | + | 0.948027i | \(0.603075\pi\) | |||||||
\(594\) | 6.61173e25 | 0.294676 | ||||||||
\(595\) | −2.62262e25 | −0.115033 | ||||||||
\(596\) | 9.09361e25 | 0.392552 | ||||||||
\(597\) | −1.29255e26 | −0.549149 | ||||||||
\(598\) | 1.18166e26 | 0.494119 | ||||||||
\(599\) | 2.05613e26 | 0.846244 | 0.423122 | − | 0.906073i | \(-0.360934\pi\) | ||||
0.423122 | + | 0.906073i | \(0.360934\pi\) | |||||||
\(600\) | 2.61490e25 | 0.105930 | ||||||||
\(601\) | 2.32345e26 | 0.926457 | 0.463228 | − | 0.886239i | \(-0.346691\pi\) | ||||
0.463228 | + | 0.886239i | \(0.346691\pi\) | |||||||
\(602\) | 4.48137e25 | 0.175891 | ||||||||
\(603\) | 2.80222e26 | 1.08265 | ||||||||
\(604\) | −2.75789e24 | −0.0104888 | ||||||||
\(605\) | 3.55263e25 | 0.133007 | ||||||||
\(606\) | −4.37893e26 | −1.61391 | ||||||||
\(607\) | 2.30237e26 | 0.835376 | 0.417688 | − | 0.908591i | \(-0.362841\pi\) | ||||
0.417688 | + | 0.908591i | \(0.362841\pi\) | |||||||
\(608\) | 2.47320e25 | 0.0883436 | ||||||||
\(609\) | 1.98396e26 | 0.697701 | ||||||||
\(610\) | −1.19883e26 | −0.415073 | ||||||||
\(611\) | 2.50815e26 | 0.854992 | ||||||||
\(612\) | −1.86699e26 | −0.626619 | ||||||||
\(613\) | −7.21990e25 | −0.238592 | −0.119296 | − | 0.992859i | \(-0.538064\pi\) | ||||
−0.119296 | + | 0.992859i | \(0.538064\pi\) | |||||||
\(614\) | −2.26355e26 | −0.736531 | ||||||||
\(615\) | −4.07488e26 | −1.30557 | ||||||||
\(616\) | 3.25975e25 | 0.102841 | ||||||||
\(617\) | −1.44998e26 | −0.450458 | −0.225229 | − | 0.974306i | \(-0.572313\pi\) | ||||
−0.225229 | + | 0.974306i | \(0.572313\pi\) | |||||||
\(618\) | 1.15265e26 | 0.352619 | ||||||||
\(619\) | −2.13817e26 | −0.644141 | −0.322071 | − | 0.946716i | \(-0.604379\pi\) | ||||
−0.322071 | + | 0.946716i | \(0.604379\pi\) | |||||||
\(620\) | 1.07721e26 | 0.319579 | ||||||||
\(621\) | −8.60116e25 | −0.251297 | ||||||||
\(622\) | −1.56136e26 | −0.449256 | ||||||||
\(623\) | −1.06024e25 | −0.0300448 | ||||||||
\(624\) | −1.36523e26 | −0.381025 | ||||||||
\(625\) | 1.45519e25 | 0.0400000 | ||||||||
\(626\) | −3.30014e26 | −0.893463 | ||||||||
\(627\) | 3.19789e26 | 0.852751 | ||||||||
\(628\) | −8.06654e24 | −0.0211871 | ||||||||
\(629\) | 4.93205e26 | 1.27599 | ||||||||
\(630\) | 3.94282e25 | 0.100478 | ||||||||
\(631\) | 1.60890e26 | 0.403877 | 0.201939 | − | 0.979398i | \(-0.435276\pi\) | ||||
0.201939 | + | 0.979398i | \(0.435276\pi\) | |||||||
\(632\) | 7.05325e25 | 0.174412 | ||||||||
\(633\) | −7.31519e26 | −1.78193 | ||||||||
\(634\) | 5.25656e26 | 1.26140 | ||||||||
\(635\) | 1.18605e26 | 0.280383 | ||||||||
\(636\) | 2.52248e25 | 0.0587469 | ||||||||
\(637\) | 4.14492e26 | 0.951024 | ||||||||
\(638\) | 6.49805e26 | 1.46888 | ||||||||
\(639\) | 5.33564e26 | 1.18831 | ||||||||
\(640\) | 1.80144e25 | 0.0395285 | ||||||||
\(641\) | −5.97417e26 | −1.29160 | −0.645798 | − | 0.763509i | \(-0.723475\pi\) | ||||
−0.645798 | + | 0.763509i | \(0.723475\pi\) | |||||||
\(642\) | −2.27997e26 | −0.485675 | ||||||||
\(643\) | −8.08712e26 | −1.69742 | −0.848710 | − | 0.528858i | \(-0.822620\pi\) | ||||
−0.848710 | + | 0.528858i | \(0.822620\pi\) | |||||||
\(644\) | −4.24059e25 | −0.0877022 | ||||||||
\(645\) | 3.20222e26 | 0.652580 | ||||||||
\(646\) | −1.77247e26 | −0.355935 | ||||||||
\(647\) | −7.53176e26 | −1.49041 | −0.745205 | − | 0.666835i | \(-0.767649\pi\) | ||||
−0.745205 | + | 0.666835i | \(0.767649\pi\) | |||||||
\(648\) | −1.26214e26 | −0.246120 | ||||||||
\(649\) | −3.81679e25 | −0.0733456 | ||||||||
\(650\) | −7.59752e25 | −0.143878 | ||||||||
\(651\) | 2.92967e26 | 0.546764 | ||||||||
\(652\) | 1.51078e26 | 0.277875 | ||||||||
\(653\) | 1.75162e25 | 0.0317515 | 0.0158758 | − | 0.999874i | \(-0.494946\pi\) | ||||
0.0158758 | + | 0.999874i | \(0.494946\pi\) | |||||||
\(654\) | 1.09071e27 | 1.94859 | ||||||||
\(655\) | 3.80530e26 | 0.670033 | ||||||||
\(656\) | −2.80724e26 | −0.487184 | ||||||||
\(657\) | −1.31571e27 | −2.25055 | ||||||||
\(658\) | −9.00092e25 | −0.151754 | ||||||||
\(659\) | −1.10678e27 | −1.83929 | −0.919644 | − | 0.392754i | \(-0.871523\pi\) | ||||
−0.919644 | + | 0.392754i | \(0.871523\pi\) | |||||||
\(660\) | 2.32929e26 | 0.381555 | ||||||||
\(661\) | −1.90870e26 | −0.308194 | −0.154097 | − | 0.988056i | \(-0.549247\pi\) | ||||
−0.154097 | + | 0.988056i | \(0.549247\pi\) | |||||||
\(662\) | 4.30015e26 | 0.684437 | ||||||||
\(663\) | 9.78423e26 | 1.53514 | ||||||||
\(664\) | −3.72159e26 | −0.575614 | ||||||||
\(665\) | 3.74321e25 | 0.0570741 | ||||||||
\(666\) | −7.41480e26 | −1.11454 | ||||||||
\(667\) | −8.45327e26 | −1.25265 | ||||||||
\(668\) | 1.80761e26 | 0.264076 | ||||||||
\(669\) | 7.18069e26 | 1.03423 | ||||||||
\(670\) | 1.93776e26 | 0.275163 | ||||||||
\(671\) | −1.06789e27 | −1.49508 | ||||||||
\(672\) | 4.89937e25 | 0.0676288 | ||||||||
\(673\) | −1.19576e27 | −1.62742 | −0.813710 | − | 0.581270i | \(-0.802556\pi\) | ||||
−0.813710 | + | 0.581270i | \(0.802556\pi\) | |||||||
\(674\) | −4.03538e26 | −0.541521 | ||||||||
\(675\) | 5.53014e25 | 0.0731729 | ||||||||
\(676\) | 1.34309e25 | 0.0175232 | ||||||||
\(677\) | 4.22916e26 | 0.544079 | 0.272040 | − | 0.962286i | \(-0.412302\pi\) | ||||
0.272040 | + | 0.962286i | \(0.412302\pi\) | |||||||
\(678\) | −2.27651e26 | −0.288793 | ||||||||
\(679\) | −2.65490e25 | −0.0332113 | ||||||||
\(680\) | −1.29104e26 | −0.159259 | ||||||||
\(681\) | 1.74382e27 | 2.12131 | ||||||||
\(682\) | 9.59552e26 | 1.15111 | ||||||||
\(683\) | 7.22585e24 | 0.00854854 | 0.00427427 | − | 0.999991i | \(-0.498639\pi\) | ||||
0.00427427 | + | 0.999991i | \(0.498639\pi\) | |||||||
\(684\) | 2.66472e26 | 0.310898 | ||||||||
\(685\) | 2.36749e26 | 0.272413 | ||||||||
\(686\) | −3.07872e26 | −0.349375 | ||||||||
\(687\) | 1.15923e27 | 1.29742 | ||||||||
\(688\) | 2.20605e26 | 0.243515 | ||||||||
\(689\) | −7.32900e25 | −0.0797925 | ||||||||
\(690\) | −3.03017e26 | −0.325387 | ||||||||
\(691\) | −1.59913e26 | −0.169372 | −0.0846861 | − | 0.996408i | \(-0.526989\pi\) | ||||
−0.0846861 | + | 0.996408i | \(0.526989\pi\) | |||||||
\(692\) | −1.08592e25 | −0.0113446 | ||||||||
\(693\) | 3.51218e26 | 0.361919 | ||||||||
\(694\) | −1.67928e26 | −0.170690 | ||||||||
\(695\) | 4.34557e26 | 0.435703 | ||||||||
\(696\) | 9.76648e26 | 0.965941 | ||||||||
\(697\) | 2.01187e27 | 1.96285 | ||||||||
\(698\) | −8.07003e26 | −0.776691 | ||||||||
\(699\) | 1.60692e27 | 1.52567 | ||||||||
\(700\) | 2.72650e25 | 0.0255372 | ||||||||
\(701\) | −3.07030e26 | −0.283700 | −0.141850 | − | 0.989888i | \(-0.545305\pi\) | ||||
−0.141850 | + | 0.989888i | \(0.545305\pi\) | |||||||
\(702\) | −2.88727e26 | −0.263199 | ||||||||
\(703\) | −7.03942e26 | −0.633084 | ||||||||
\(704\) | 1.60468e26 | 0.142380 | ||||||||
\(705\) | −6.43172e26 | −0.563028 | ||||||||
\(706\) | −7.42296e25 | −0.0641110 | ||||||||
\(707\) | −4.56582e26 | −0.389076 | ||||||||
\(708\) | −5.73659e25 | −0.0482323 | ||||||||
\(709\) | −2.50359e26 | −0.207694 | −0.103847 | − | 0.994593i | \(-0.533115\pi\) | ||||
−0.103847 | + | 0.994593i | \(0.533115\pi\) | |||||||
\(710\) | 3.68964e26 | 0.302016 | ||||||||
\(711\) | 7.59944e26 | 0.613791 | ||||||||
\(712\) | −5.21927e25 | −0.0415958 | ||||||||
\(713\) | −1.24828e27 | −0.981657 | ||||||||
\(714\) | −3.51124e26 | −0.272475 | ||||||||
\(715\) | −6.76770e26 | −0.518244 | ||||||||
\(716\) | 9.57294e26 | 0.723388 | ||||||||
\(717\) | −6.37264e26 | −0.475212 | ||||||||
\(718\) | 3.91488e26 | 0.288095 | ||||||||
\(719\) | −4.99484e26 | −0.362741 | −0.181371 | − | 0.983415i | \(-0.558053\pi\) | ||||
−0.181371 | + | 0.983415i | \(0.558053\pi\) | |||||||
\(720\) | 1.94094e26 | 0.139108 | ||||||||
\(721\) | 1.20184e26 | 0.0850083 | ||||||||
\(722\) | −7.59969e26 | −0.530509 | ||||||||
\(723\) | −5.93786e25 | −0.0409087 | ||||||||
\(724\) | 2.75858e26 | 0.187573 | ||||||||
\(725\) | 5.43505e26 | 0.364748 | ||||||||
\(726\) | 4.75637e26 | 0.315048 | ||||||||
\(727\) | 1.17305e27 | 0.766900 | 0.383450 | − | 0.923562i | \(-0.374736\pi\) | ||||
0.383450 | + | 0.923562i | \(0.374736\pi\) | |||||||
\(728\) | −1.42350e26 | −0.0918562 | ||||||||
\(729\) | −2.22041e27 | −1.41423 | ||||||||
\(730\) | −9.09825e26 | −0.571993 | ||||||||
\(731\) | −1.58101e27 | −0.981117 | ||||||||
\(732\) | −1.60503e27 | −0.983166 | ||||||||
\(733\) | 7.29500e26 | 0.441101 | 0.220550 | − | 0.975376i | \(-0.429215\pi\) | ||||
0.220550 | + | 0.975376i | \(0.429215\pi\) | |||||||
\(734\) | −1.06933e27 | −0.638262 | ||||||||
\(735\) | −1.06289e27 | −0.626267 | ||||||||
\(736\) | −2.08752e26 | −0.121420 | ||||||||
\(737\) | 1.72612e27 | 0.991126 | ||||||||
\(738\) | −3.02463e27 | −1.71450 | ||||||||
\(739\) | 2.41117e27 | 1.34929 | 0.674647 | − | 0.738141i | \(-0.264296\pi\) | ||||
0.674647 | + | 0.738141i | \(0.264296\pi\) | |||||||
\(740\) | −5.12740e26 | −0.283267 | ||||||||
\(741\) | −1.39648e27 | −0.761663 | ||||||||
\(742\) | 2.63013e25 | 0.0141625 | ||||||||
\(743\) | 1.98675e27 | 1.05621 | 0.528105 | − | 0.849179i | \(-0.322903\pi\) | ||||
0.528105 | + | 0.849179i | \(0.322903\pi\) | |||||||
\(744\) | 1.44220e27 | 0.756974 | ||||||||
\(745\) | 6.77527e26 | 0.351109 | ||||||||
\(746\) | 1.48974e27 | 0.762238 | ||||||||
\(747\) | −4.00978e27 | −2.02570 | ||||||||
\(748\) | −1.15003e27 | −0.573646 | ||||||||
\(749\) | −2.37727e26 | −0.117085 | ||||||||
\(750\) | 1.94825e26 | 0.0947465 | ||||||||
\(751\) | 4.77748e26 | 0.229414 | 0.114707 | − | 0.993399i | \(-0.463407\pi\) | ||||
0.114707 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(752\) | −4.43090e26 | −0.210098 | ||||||||
\(753\) | 5.60033e27 | 2.62217 | ||||||||
\(754\) | −2.83763e27 | −1.31198 | ||||||||
\(755\) | −2.05479e25 | −0.00938147 | ||||||||
\(756\) | 1.03615e26 | 0.0467158 | ||||||||
\(757\) | 8.34040e25 | 0.0371344 | 0.0185672 | − | 0.999828i | \(-0.494090\pi\) | ||||
0.0185672 | + | 0.999828i | \(0.494090\pi\) | |||||||
\(758\) | 2.34009e27 | 1.02890 | ||||||||
\(759\) | −2.69920e27 | −1.17203 | ||||||||
\(760\) | 1.84268e26 | 0.0790169 | ||||||||
\(761\) | −2.96552e27 | −1.25587 | −0.627937 | − | 0.778264i | \(-0.716100\pi\) | ||||
−0.627937 | + | 0.778264i | \(0.716100\pi\) | |||||||
\(762\) | 1.58792e27 | 0.664133 | ||||||||
\(763\) | 1.13726e27 | 0.469761 | ||||||||
\(764\) | −1.73980e27 | −0.709761 | ||||||||
\(765\) | −1.39102e27 | −0.560465 | ||||||||
\(766\) | 2.42861e27 | 0.966462 | ||||||||
\(767\) | 1.66675e26 | 0.0655111 | ||||||||
\(768\) | 2.41182e26 | 0.0936296 | ||||||||
\(769\) | 9.68856e26 | 0.371500 | 0.185750 | − | 0.982597i | \(-0.440528\pi\) | ||||
0.185750 | + | 0.982597i | \(0.440528\pi\) | |||||||
\(770\) | 2.42870e26 | 0.0919841 | ||||||||
\(771\) | −1.08272e27 | −0.405041 | ||||||||
\(772\) | −6.96060e26 | −0.257207 | ||||||||
\(773\) | 5.16072e27 | 1.88367 | 0.941836 | − | 0.336074i | \(-0.109099\pi\) | ||||
0.941836 | + | 0.336074i | \(0.109099\pi\) | |||||||
\(774\) | 2.37688e27 | 0.856976 | ||||||||
\(775\) | 8.02582e26 | 0.285840 | ||||||||
\(776\) | −1.30693e26 | −0.0459798 | ||||||||
\(777\) | −1.39450e27 | −0.484638 | ||||||||
\(778\) | −8.20709e26 | −0.281762 | ||||||||
\(779\) | −2.87150e27 | −0.973875 | ||||||||
\(780\) | −1.01718e27 | −0.340799 | ||||||||
\(781\) | 3.28665e27 | 1.08785 | ||||||||
\(782\) | 1.49607e27 | 0.489201 | ||||||||
\(783\) | 2.06547e27 | 0.667241 | ||||||||
\(784\) | −7.32242e26 | −0.233696 | ||||||||
\(785\) | −6.01004e25 | −0.0189503 | ||||||||
\(786\) | 5.09464e27 | 1.58708 | ||||||||
\(787\) | −4.95523e27 | −1.52512 | −0.762559 | − | 0.646919i | \(-0.776057\pi\) | ||||
−0.762559 | + | 0.646919i | \(0.776057\pi\) | |||||||
\(788\) | 2.68319e27 | 0.815929 | ||||||||
\(789\) | −5.44708e27 | −1.63656 | ||||||||
\(790\) | 5.25508e26 | 0.155999 | ||||||||
\(791\) | −2.37367e26 | −0.0696214 | ||||||||
\(792\) | 1.72895e27 | 0.501063 | ||||||||
\(793\) | 4.66336e27 | 1.33538 | ||||||||
\(794\) | 2.64948e27 | 0.749663 | ||||||||
\(795\) | 1.87939e26 | 0.0525449 | ||||||||
\(796\) | −6.63439e26 | −0.183285 | ||||||||
\(797\) | 9.51644e26 | 0.259789 | 0.129894 | − | 0.991528i | \(-0.458536\pi\) | ||||
0.129894 | + | 0.991528i | \(0.458536\pi\) | |||||||
\(798\) | 5.01152e26 | 0.135189 | ||||||||
\(799\) | 3.17550e27 | 0.846481 | ||||||||
\(800\) | 1.34218e26 | 0.0353553 | ||||||||
\(801\) | −5.62344e26 | −0.146384 | ||||||||
\(802\) | 5.37049e26 | 0.138152 | ||||||||
\(803\) | −8.10452e27 | −2.06030 | ||||||||
\(804\) | 2.59433e27 | 0.651768 | ||||||||
\(805\) | −3.15949e26 | −0.0784433 | ||||||||
\(806\) | −4.19026e27 | −1.02815 | ||||||||
\(807\) | 4.73819e27 | 1.14898 | ||||||||
\(808\) | −2.24762e27 | −0.538661 | ||||||||
\(809\) | 6.64620e26 | 0.157421 | 0.0787105 | − | 0.996898i | \(-0.474920\pi\) | ||||
0.0787105 | + | 0.996898i | \(0.474920\pi\) | |||||||
\(810\) | −9.40371e26 | −0.220136 | ||||||||
\(811\) | −3.63702e27 | −0.841487 | −0.420743 | − | 0.907180i | \(-0.638231\pi\) | ||||
−0.420743 | + | 0.907180i | \(0.638231\pi\) | |||||||
\(812\) | 1.01833e27 | 0.232866 | ||||||||
\(813\) | −4.83296e27 | −1.09233 | ||||||||
\(814\) | −4.56738e27 | −1.02032 | ||||||||
\(815\) | 1.12562e27 | 0.248539 | ||||||||
\(816\) | −1.72848e27 | −0.377232 | ||||||||
\(817\) | 2.25655e27 | 0.486783 | ||||||||
\(818\) | −5.03964e27 | −1.07459 | ||||||||
\(819\) | −1.53373e27 | −0.323260 | ||||||||
\(820\) | −2.09156e27 | −0.435751 | ||||||||
\(821\) | −4.44788e26 | −0.0915996 | −0.0457998 | − | 0.998951i | \(-0.514584\pi\) | ||||
−0.0457998 | + | 0.998951i | \(0.514584\pi\) | |||||||
\(822\) | 3.16967e27 | 0.645255 | ||||||||
\(823\) | −5.12412e27 | −1.03115 | −0.515574 | − | 0.856845i | \(-0.672421\pi\) | ||||
−0.515574 | + | 0.856845i | \(0.672421\pi\) | |||||||
\(824\) | 5.91631e26 | 0.117691 | ||||||||
\(825\) | 1.73546e27 | 0.341273 | ||||||||
\(826\) | −5.98142e25 | −0.0116277 | ||||||||
\(827\) | −5.00813e27 | −0.962439 | −0.481219 | − | 0.876600i | \(-0.659806\pi\) | ||||
−0.481219 | + | 0.876600i | \(0.659806\pi\) | |||||||
\(828\) | −2.24918e27 | −0.427302 | ||||||||
\(829\) | −3.98409e27 | −0.748275 | −0.374138 | − | 0.927373i | \(-0.622061\pi\) | ||||
−0.374138 | + | 0.927373i | \(0.622061\pi\) | |||||||
\(830\) | −2.77280e27 | −0.514845 | ||||||||
\(831\) | −3.59807e26 | −0.0660481 | ||||||||
\(832\) | −7.00747e26 | −0.127172 | ||||||||
\(833\) | 5.24777e27 | 0.941558 | ||||||||
\(834\) | 5.81797e27 | 1.03203 | ||||||||
\(835\) | 1.34678e27 | 0.236197 | ||||||||
\(836\) | 1.64142e27 | 0.284616 | ||||||||
\(837\) | 3.05004e27 | 0.522893 | ||||||||
\(838\) | 7.15567e26 | 0.121292 | ||||||||
\(839\) | 9.17325e27 | 1.53739 | 0.768696 | − | 0.639615i | \(-0.220906\pi\) | ||||
0.768696 | + | 0.639615i | \(0.220906\pi\) | |||||||
\(840\) | 3.65031e26 | 0.0604890 | ||||||||
\(841\) | 1.41963e28 | 2.32602 | ||||||||
\(842\) | 1.51838e27 | 0.245988 | ||||||||
\(843\) | −5.12047e26 | −0.0820254 | ||||||||
\(844\) | −3.75474e27 | −0.594740 | ||||||||
\(845\) | 1.00068e26 | 0.0156732 | ||||||||
\(846\) | −4.77402e27 | −0.739376 | ||||||||
\(847\) | 4.95936e26 | 0.0759509 | ||||||||
\(848\) | 1.29474e26 | 0.0196075 | ||||||||
\(849\) | −1.08716e28 | −1.62806 | ||||||||
\(850\) | −9.61900e26 | −0.142446 | ||||||||
\(851\) | 5.94167e27 | 0.870118 | ||||||||
\(852\) | 4.93980e27 | 0.715374 | ||||||||
\(853\) | −7.79931e27 | −1.11697 | −0.558484 | − | 0.829516i | \(-0.688617\pi\) | ||||
−0.558484 | + | 0.829516i | \(0.688617\pi\) | |||||||
\(854\) | −1.67353e27 | −0.237019 | ||||||||
\(855\) | 1.98537e27 | 0.278076 | ||||||||
\(856\) | −1.17026e27 | −0.162100 | ||||||||
\(857\) | 5.48738e26 | 0.0751705 | 0.0375852 | − | 0.999293i | \(-0.488033\pi\) | ||||
0.0375852 | + | 0.999293i | \(0.488033\pi\) | |||||||
\(858\) | −9.06079e27 | −1.22754 | ||||||||
\(859\) | 2.88785e27 | 0.386936 | 0.193468 | − | 0.981107i | \(-0.438026\pi\) | ||||
0.193468 | + | 0.981107i | \(0.438026\pi\) | |||||||
\(860\) | 1.64364e27 | 0.217806 | ||||||||
\(861\) | −5.68839e27 | −0.745521 | ||||||||
\(862\) | −8.89559e27 | −1.15307 | ||||||||
\(863\) | −1.27182e27 | −0.163051 | −0.0815257 | − | 0.996671i | \(-0.525979\pi\) | ||||
−0.0815257 | + | 0.996671i | \(0.525979\pi\) | |||||||
\(864\) | 5.10065e26 | 0.0646763 | ||||||||
\(865\) | −8.09071e25 | −0.0101469 | ||||||||
\(866\) | 1.01026e28 | 1.25318 | ||||||||
\(867\) | 1.77566e26 | 0.0217860 | ||||||||
\(868\) | 1.50374e27 | 0.182489 | ||||||||
\(869\) | 4.68111e27 | 0.561903 | ||||||||
\(870\) | 7.27660e27 | 0.863964 | ||||||||
\(871\) | −7.53776e27 | −0.885258 | ||||||||
\(872\) | 5.59841e27 | 0.650367 | ||||||||
\(873\) | −1.40814e27 | −0.161812 | ||||||||
\(874\) | −2.13531e27 | −0.242718 | ||||||||
\(875\) | 2.03140e26 | 0.0228412 | ||||||||
\(876\) | −1.21810e28 | −1.35486 | ||||||||
\(877\) | −7.93254e27 | −0.872803 | −0.436401 | − | 0.899752i | \(-0.643747\pi\) | ||||
−0.436401 | + | 0.899752i | \(0.643747\pi\) | |||||||
\(878\) | 1.21595e28 | 1.32348 | ||||||||
\(879\) | 2.60616e28 | 2.80612 | ||||||||
\(880\) | 1.19558e27 | 0.127349 | ||||||||
\(881\) | −4.65349e27 | −0.490351 | −0.245176 | − | 0.969479i | \(-0.578846\pi\) | ||||
−0.245176 | + | 0.969479i | \(0.578846\pi\) | |||||||
\(882\) | −7.88945e27 | −0.822423 | ||||||||
\(883\) | 1.39322e28 | 1.43678 | 0.718392 | − | 0.695639i | \(-0.244878\pi\) | ||||
0.718392 | + | 0.695639i | \(0.244878\pi\) | |||||||
\(884\) | 5.02206e27 | 0.512372 | ||||||||
\(885\) | −4.27409e26 | −0.0431403 | ||||||||
\(886\) | −5.56353e27 | −0.555559 | ||||||||
\(887\) | −2.98771e27 | −0.295165 | −0.147582 | − | 0.989050i | \(-0.547149\pi\) | ||||
−0.147582 | + | 0.989050i | \(0.547149\pi\) | |||||||
\(888\) | −6.86471e27 | −0.670964 | ||||||||
\(889\) | 1.65569e27 | 0.160107 | ||||||||
\(890\) | −3.88866e26 | −0.0372045 | ||||||||
\(891\) | −8.37662e27 | −0.792922 | ||||||||
\(892\) | 3.68571e27 | 0.345187 | ||||||||
\(893\) | −4.53233e27 | −0.419984 | ||||||||
\(894\) | 9.07092e27 | 0.831658 | ||||||||
\(895\) | 7.13239e27 | 0.647018 | ||||||||
\(896\) | 2.51475e26 | 0.0225719 | ||||||||
\(897\) | 1.17871e28 | 1.04684 | ||||||||
\(898\) | 8.39793e27 | 0.737984 | ||||||||
\(899\) | 2.99759e28 | 2.60649 | ||||||||
\(900\) | 1.44611e27 | 0.124422 | ||||||||
\(901\) | −9.27904e26 | −0.0789982 | ||||||||
\(902\) | −1.86311e28 | −1.56956 | ||||||||
\(903\) | 4.47019e27 | 0.372642 | ||||||||
\(904\) | −1.16849e27 | −0.0963883 | ||||||||
\(905\) | 2.05530e27 | 0.167770 | ||||||||
\(906\) | −2.75101e26 | −0.0222215 | ||||||||
\(907\) | −1.01372e28 | −0.810308 | −0.405154 | − | 0.914248i | \(-0.632782\pi\) | ||||
−0.405154 | + | 0.914248i | \(0.632782\pi\) | |||||||
\(908\) | 8.95068e27 | 0.708011 | ||||||||
\(909\) | −2.42167e28 | −1.89565 | ||||||||
\(910\) | −1.06059e27 | −0.0821587 | ||||||||
\(911\) | 1.01665e28 | 0.779377 | 0.389688 | − | 0.920947i | \(-0.372583\pi\) | ||||
0.389688 | + | 0.920947i | \(0.372583\pi\) | |||||||
\(912\) | 2.46703e27 | 0.187164 | ||||||||
\(913\) | −2.46995e28 | −1.85445 | ||||||||
\(914\) | −9.73448e27 | −0.723309 | ||||||||
\(915\) | −1.19584e28 | −0.879371 | ||||||||
\(916\) | 5.95009e27 | 0.433028 | ||||||||
\(917\) | 5.31207e27 | 0.382609 | ||||||||
\(918\) | −3.65549e27 | −0.260580 | ||||||||
\(919\) | −8.89132e27 | −0.627291 | −0.313645 | − | 0.949540i | \(-0.601550\pi\) | ||||
−0.313645 | + | 0.949540i | \(0.601550\pi\) | |||||||
\(920\) | −1.55533e27 | −0.108602 | ||||||||
\(921\) | −2.25790e28 | −1.56041 | ||||||||
\(922\) | −1.40243e28 | −0.959265 | ||||||||
\(923\) | −1.43524e28 | −0.971650 | ||||||||
\(924\) | 3.25162e27 | 0.217879 | ||||||||
\(925\) | −3.82021e27 | −0.253362 | ||||||||
\(926\) | 1.10592e28 | 0.725968 | ||||||||
\(927\) | 6.37446e27 | 0.414177 | ||||||||
\(928\) | 5.01295e27 | 0.322394 | ||||||||
\(929\) | 7.61744e26 | 0.0484909 | 0.0242454 | − | 0.999706i | \(-0.492282\pi\) | ||||
0.0242454 | + | 0.999706i | \(0.492282\pi\) | |||||||
\(930\) | 1.07452e28 | 0.677058 | ||||||||
\(931\) | −7.49004e27 | −0.467156 | ||||||||
\(932\) | 8.24800e27 | 0.509211 | ||||||||
\(933\) | −1.55746e28 | −0.951791 | ||||||||
\(934\) | 3.36849e27 | 0.203770 | ||||||||
\(935\) | −8.56840e27 | −0.513085 | ||||||||
\(936\) | −7.55012e27 | −0.447541 | ||||||||
\(937\) | −1.46040e28 | −0.856931 | −0.428465 | − | 0.903558i | \(-0.640946\pi\) | ||||
−0.428465 | + | 0.903558i | \(0.640946\pi\) | |||||||
\(938\) | 2.70505e27 | 0.157126 | ||||||||
\(939\) | −3.29191e28 | −1.89289 | ||||||||
\(940\) | −3.30128e27 | −0.187918 | ||||||||
\(941\) | −1.23989e28 | −0.698687 | −0.349344 | − | 0.936995i | \(-0.613595\pi\) | ||||
−0.349344 | + | 0.936995i | \(0.613595\pi\) | |||||||
\(942\) | −8.04642e26 | −0.0448868 | ||||||||
\(943\) | 2.42371e28 | 1.33850 | ||||||||
\(944\) | −2.94448e26 | −0.0160981 | ||||||||
\(945\) | 7.71989e26 | 0.0417839 | ||||||||
\(946\) | 1.46412e28 | 0.784530 | ||||||||
\(947\) | −1.35611e28 | −0.719400 | −0.359700 | − | 0.933068i | \(-0.617121\pi\) | ||||
−0.359700 | + | 0.933068i | \(0.617121\pi\) | |||||||
\(948\) | 7.03565e27 | 0.369509 | ||||||||
\(949\) | 3.53916e28 | 1.84022 | ||||||||
\(950\) | 1.37290e27 | 0.0706749 | ||||||||
\(951\) | 5.24345e28 | 2.67240 | ||||||||
\(952\) | −1.80225e27 | −0.0909419 | ||||||||
\(953\) | −1.00835e28 | −0.503764 | −0.251882 | − | 0.967758i | \(-0.581050\pi\) | ||||
−0.251882 | + | 0.967758i | \(0.581050\pi\) | |||||||
\(954\) | 1.39500e27 | 0.0690026 | ||||||||
\(955\) | −1.29625e28 | −0.634830 | ||||||||
\(956\) | −3.27095e27 | −0.158608 | ||||||||
\(957\) | 6.48183e28 | 3.11196 | ||||||||
\(958\) | 9.43148e27 | 0.448340 | ||||||||
\(959\) | 3.30494e27 | 0.155556 | ||||||||
\(960\) | 1.79694e27 | 0.0837448 | ||||||||
\(961\) | 2.25941e28 | 1.04261 | ||||||||
\(962\) | 1.99452e28 | 0.911331 | ||||||||
\(963\) | −1.26089e28 | −0.570461 | ||||||||
\(964\) | −3.04779e26 | −0.0136538 | ||||||||
\(965\) | −5.18605e27 | −0.230053 | ||||||||
\(966\) | −4.23001e27 | −0.185806 | ||||||||
\(967\) | 1.24965e28 | 0.543547 | 0.271774 | − | 0.962361i | \(-0.412390\pi\) | ||||
0.271774 | + | 0.962361i | \(0.412390\pi\) | |||||||
\(968\) | 2.44135e27 | 0.105151 | ||||||||
\(969\) | −1.76805e28 | −0.754082 | ||||||||
\(970\) | −9.73741e26 | −0.0411256 | ||||||||
\(971\) | −9.87663e27 | −0.413072 | −0.206536 | − | 0.978439i | \(-0.566219\pi\) | ||||
−0.206536 | + | 0.978439i | \(0.566219\pi\) | |||||||
\(972\) | −1.70069e28 | −0.704360 | ||||||||
\(973\) | 6.06627e27 | 0.248800 | ||||||||
\(974\) | −3.00006e28 | −1.21848 | ||||||||
\(975\) | −7.57856e27 | −0.304820 | ||||||||
\(976\) | −8.23829e27 | −0.328144 | ||||||||
\(977\) | −2.84735e27 | −0.112316 | −0.0561581 | − | 0.998422i | \(-0.517885\pi\) | ||||
−0.0561581 | + | 0.998422i | \(0.517885\pi\) | |||||||
\(978\) | 1.50701e28 | 0.588705 | ||||||||
\(979\) | −3.46393e27 | −0.134009 | ||||||||
\(980\) | −5.45562e27 | −0.209024 | ||||||||
\(981\) | 6.03194e28 | 2.28877 | ||||||||
\(982\) | 6.01941e26 | 0.0226201 | ||||||||
\(983\) | −2.10459e28 | −0.783265 | −0.391632 | − | 0.920122i | \(-0.628090\pi\) | ||||
−0.391632 | + | 0.920122i | \(0.628090\pi\) | |||||||
\(984\) | −2.80023e28 | −1.03215 | ||||||||
\(985\) | 1.99913e28 | 0.729789 | ||||||||
\(986\) | −3.59264e28 | −1.29892 | ||||||||
\(987\) | −8.97846e27 | −0.321506 | ||||||||
\(988\) | −7.16789e27 | −0.254214 | ||||||||
\(989\) | −1.90466e28 | −0.669041 | ||||||||
\(990\) | 1.28817e28 | 0.448164 | ||||||||
\(991\) | 5.03784e28 | 1.73598 | 0.867989 | − | 0.496583i | \(-0.165412\pi\) | ||||
0.867989 | + | 0.496583i | \(0.165412\pi\) | |||||||
\(992\) | 7.40251e27 | 0.252649 | ||||||||
\(993\) | 4.28943e28 | 1.45004 | ||||||||
\(994\) | 5.15062e27 | 0.172460 | ||||||||
\(995\) | −4.94301e27 | −0.163935 | ||||||||
\(996\) | −3.71230e28 | −1.21949 | ||||||||
\(997\) | −1.44919e28 | −0.471544 | −0.235772 | − | 0.971808i | \(-0.575762\pi\) | ||||
−0.235772 | + | 0.971808i | \(0.575762\pi\) | |||||||
\(998\) | −8.05144e27 | −0.259498 | ||||||||
\(999\) | −1.45179e28 | −0.463480 |
(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 | 10.20.a.d.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 90.20.a.g.1.1 | 2 | |||
4.3 | odd | 2 | 80.20.a.d.1.1 | 2 | |||
5.2 | odd | 4 | 50.20.b.f.49.3 | 4 | |||
5.3 | odd | 4 | 50.20.b.f.49.2 | 4 | |||
5.4 | even | 2 | 50.20.a.f.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.20.a.d.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.20.a.f.1.1 | 2 | 5.4 | even | 2 | |||
50.20.b.f.49.2 | 4 | 5.3 | odd | 4 | |||
50.20.b.f.49.3 | 4 | 5.2 | odd | 4 | |||
80.20.a.d.1.1 | 2 | 4.3 | odd | 2 | |||
90.20.a.g.1.1 | 2 | 3.2 | odd | 2 |