Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6,10,Mod(1,6)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.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: | \(3.09021501698\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −16.0000 | −0.707107 | ||||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | 256.000 | 0.500000 | ||||||||
\(5\) | 2694.00 | 1.92767 | 0.963835 | − | 0.266501i | \(-0.0858674\pi\) | ||||
0.963835 | + | 0.266501i | \(0.0858674\pi\) | |||||||
\(6\) | −1296.00 | −0.408248 | ||||||||
\(7\) | −3544.00 | −0.557895 | −0.278948 | − | 0.960306i | \(-0.589986\pi\) | ||||
−0.278948 | + | 0.960306i | \(0.589986\pi\) | |||||||
\(8\) | −4096.00 | −0.353553 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | −43104.0 | −1.36307 | ||||||||
\(11\) | 29580.0 | 0.609160 | 0.304580 | − | 0.952487i | \(-0.401484\pi\) | ||||
0.304580 | + | 0.952487i | \(0.401484\pi\) | |||||||
\(12\) | 20736.0 | 0.288675 | ||||||||
\(13\) | −44818.0 | −0.435219 | −0.217609 | − | 0.976036i | \(-0.569826\pi\) | ||||
−0.217609 | + | 0.976036i | \(0.569826\pi\) | |||||||
\(14\) | 56704.0 | 0.394491 | ||||||||
\(15\) | 218214. | 1.11294 | ||||||||
\(16\) | 65536.0 | 0.250000 | ||||||||
\(17\) | −101934. | −0.296005 | −0.148002 | − | 0.988987i | \(-0.547284\pi\) | ||||
−0.148002 | + | 0.988987i | \(0.547284\pi\) | |||||||
\(18\) | −104976. | −0.235702 | ||||||||
\(19\) | −895084. | −1.57570 | −0.787848 | − | 0.615869i | \(-0.788805\pi\) | ||||
−0.787848 | + | 0.615869i | \(0.788805\pi\) | |||||||
\(20\) | 689664. | 0.963835 | ||||||||
\(21\) | −287064. | −0.322101 | ||||||||
\(22\) | −473280. | −0.430741 | ||||||||
\(23\) | −1.11300e6 | −0.829316 | −0.414658 | − | 0.909977i | \(-0.636099\pi\) | ||||
−0.414658 | + | 0.909977i | \(0.636099\pi\) | |||||||
\(24\) | −331776. | −0.204124 | ||||||||
\(25\) | 5.30451e6 | 2.71591 | ||||||||
\(26\) | 717088. | 0.307746 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | −907264. | −0.278948 | ||||||||
\(29\) | −2.35735e6 | −0.618917 | −0.309458 | − | 0.950913i | \(-0.600148\pi\) | ||||
−0.309458 | + | 0.950913i | \(0.600148\pi\) | |||||||
\(30\) | −3.49142e6 | −0.786968 | ||||||||
\(31\) | 175808. | 0.0341909 | 0.0170955 | − | 0.999854i | \(-0.494558\pi\) | ||||
0.0170955 | + | 0.999854i | \(0.494558\pi\) | |||||||
\(32\) | −1.04858e6 | −0.176777 | ||||||||
\(33\) | 2.39598e6 | 0.351698 | ||||||||
\(34\) | 1.63094e6 | 0.209307 | ||||||||
\(35\) | −9.54754e6 | −1.07544 | ||||||||
\(36\) | 1.67962e6 | 0.166667 | ||||||||
\(37\) | −2.91942e6 | −0.256088 | −0.128044 | − | 0.991769i | \(-0.540870\pi\) | ||||
−0.128044 | + | 0.991769i | \(0.540870\pi\) | |||||||
\(38\) | 1.43213e7 | 1.11419 | ||||||||
\(39\) | −3.63026e6 | −0.251274 | ||||||||
\(40\) | −1.10346e7 | −0.681534 | ||||||||
\(41\) | 2.62188e7 | 1.44906 | 0.724528 | − | 0.689245i | \(-0.242058\pi\) | ||||
0.724528 | + | 0.689245i | \(0.242058\pi\) | |||||||
\(42\) | 4.59302e6 | 0.227760 | ||||||||
\(43\) | −1.87630e7 | −0.836938 | −0.418469 | − | 0.908231i | \(-0.637433\pi\) | ||||
−0.418469 | + | 0.908231i | \(0.637433\pi\) | |||||||
\(44\) | 7.57248e6 | 0.304580 | ||||||||
\(45\) | 1.76753e7 | 0.642556 | ||||||||
\(46\) | 1.78080e7 | 0.586415 | ||||||||
\(47\) | −2.09662e7 | −0.626727 | −0.313364 | − | 0.949633i | \(-0.601456\pi\) | ||||
−0.313364 | + | 0.949633i | \(0.601456\pi\) | |||||||
\(48\) | 5.30842e6 | 0.144338 | ||||||||
\(49\) | −2.77937e7 | −0.688753 | ||||||||
\(50\) | −8.48722e7 | −1.92044 | ||||||||
\(51\) | −8.25665e6 | −0.170899 | ||||||||
\(52\) | −1.14734e7 | −0.217609 | ||||||||
\(53\) | 5.72516e7 | 0.996658 | 0.498329 | − | 0.866988i | \(-0.333947\pi\) | ||||
0.498329 | + | 0.866988i | \(0.333947\pi\) | |||||||
\(54\) | −8.50306e6 | −0.136083 | ||||||||
\(55\) | 7.96885e7 | 1.17426 | ||||||||
\(56\) | 1.45162e7 | 0.197246 | ||||||||
\(57\) | −7.25018e7 | −0.909729 | ||||||||
\(58\) | 3.77175e7 | 0.437640 | ||||||||
\(59\) | 3.35876e7 | 0.360865 | 0.180432 | − | 0.983587i | \(-0.442250\pi\) | ||||
0.180432 | + | 0.983587i | \(0.442250\pi\) | |||||||
\(60\) | 5.58628e7 | 0.556470 | ||||||||
\(61\) | 8.22608e7 | 0.760692 | 0.380346 | − | 0.924844i | \(-0.375805\pi\) | ||||
0.380346 | + | 0.924844i | \(0.375805\pi\) | |||||||
\(62\) | −2.81293e6 | −0.0241766 | ||||||||
\(63\) | −2.32522e7 | −0.185965 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | −1.20740e8 | −0.838957 | ||||||||
\(66\) | −3.83357e7 | −0.248688 | ||||||||
\(67\) | −1.88456e8 | −1.14254 | −0.571272 | − | 0.820761i | \(-0.693550\pi\) | ||||
−0.571272 | + | 0.820761i | \(0.693550\pi\) | |||||||
\(68\) | −2.60951e7 | −0.148002 | ||||||||
\(69\) | −9.01530e7 | −0.478806 | ||||||||
\(70\) | 1.52761e8 | 0.760449 | ||||||||
\(71\) | 8.09240e7 | 0.377933 | 0.188967 | − | 0.981984i | \(-0.439486\pi\) | ||||
0.188967 | + | 0.981984i | \(0.439486\pi\) | |||||||
\(72\) | −2.68739e7 | −0.117851 | ||||||||
\(73\) | −2.36141e8 | −0.973236 | −0.486618 | − | 0.873615i | \(-0.661770\pi\) | ||||
−0.486618 | + | 0.873615i | \(0.661770\pi\) | |||||||
\(74\) | 4.67107e7 | 0.181081 | ||||||||
\(75\) | 4.29665e8 | 1.56803 | ||||||||
\(76\) | −2.29142e8 | −0.787848 | ||||||||
\(77\) | −1.04832e8 | −0.339847 | ||||||||
\(78\) | 5.80841e7 | 0.177677 | ||||||||
\(79\) | 5.26910e8 | 1.52200 | 0.761000 | − | 0.648752i | \(-0.224709\pi\) | ||||
0.761000 | + | 0.648752i | \(0.224709\pi\) | |||||||
\(80\) | 1.76554e8 | 0.481917 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | −4.19501e8 | −1.02464 | ||||||||
\(83\) | 1.83465e7 | 0.0424327 | 0.0212164 | − | 0.999775i | \(-0.493246\pi\) | ||||
0.0212164 | + | 0.999775i | \(0.493246\pi\) | |||||||
\(84\) | −7.34884e7 | −0.161050 | ||||||||
\(85\) | −2.74610e8 | −0.570600 | ||||||||
\(86\) | 3.00207e8 | 0.591805 | ||||||||
\(87\) | −1.90945e8 | −0.357332 | ||||||||
\(88\) | −1.21160e8 | −0.215370 | ||||||||
\(89\) | 6.90643e8 | 1.16681 | 0.583403 | − | 0.812183i | \(-0.301721\pi\) | ||||
0.583403 | + | 0.812183i | \(0.301721\pi\) | |||||||
\(90\) | −2.82805e8 | −0.454356 | ||||||||
\(91\) | 1.58835e8 | 0.242806 | ||||||||
\(92\) | −2.84928e8 | −0.414658 | ||||||||
\(93\) | 1.42404e7 | 0.0197401 | ||||||||
\(94\) | 3.35459e8 | 0.443163 | ||||||||
\(95\) | −2.41136e9 | −3.03742 | ||||||||
\(96\) | −8.49347e7 | −0.102062 | ||||||||
\(97\) | −4.38251e8 | −0.502632 | −0.251316 | − | 0.967905i | \(-0.580863\pi\) | ||||
−0.251316 | + | 0.967905i | \(0.580863\pi\) | |||||||
\(98\) | 4.44699e8 | 0.487022 | ||||||||
\(99\) | 1.94074e8 | 0.203053 | ||||||||
\(100\) | 1.35795e9 | 1.35795 | ||||||||
\(101\) | 9.80602e8 | 0.937663 | 0.468831 | − | 0.883288i | \(-0.344675\pi\) | ||||
0.468831 | + | 0.883288i | \(0.344675\pi\) | |||||||
\(102\) | 1.32106e8 | 0.120844 | ||||||||
\(103\) | 1.71909e9 | 1.50498 | 0.752489 | − | 0.658604i | \(-0.228853\pi\) | ||||
0.752489 | + | 0.658604i | \(0.228853\pi\) | |||||||
\(104\) | 1.83575e8 | 0.153873 | ||||||||
\(105\) | −7.73350e8 | −0.620904 | ||||||||
\(106\) | −9.16025e8 | −0.704743 | ||||||||
\(107\) | 4.25005e8 | 0.313449 | 0.156724 | − | 0.987642i | \(-0.449907\pi\) | ||||
0.156724 | + | 0.987642i | \(0.449907\pi\) | |||||||
\(108\) | 1.36049e8 | 0.0962250 | ||||||||
\(109\) | 8.74701e8 | 0.593527 | 0.296763 | − | 0.954951i | \(-0.404093\pi\) | ||||
0.296763 | + | 0.954951i | \(0.404093\pi\) | |||||||
\(110\) | −1.27502e9 | −0.830326 | ||||||||
\(111\) | −2.36473e8 | −0.147852 | ||||||||
\(112\) | −2.32260e8 | −0.139474 | ||||||||
\(113\) | −4.42974e7 | −0.0255579 | −0.0127789 | − | 0.999918i | \(-0.504068\pi\) | ||||
−0.0127789 | + | 0.999918i | \(0.504068\pi\) | |||||||
\(114\) | 1.16003e9 | 0.643275 | ||||||||
\(115\) | −2.99842e9 | −1.59865 | ||||||||
\(116\) | −6.03481e8 | −0.309458 | ||||||||
\(117\) | −2.94051e8 | −0.145073 | ||||||||
\(118\) | −5.37401e8 | −0.255170 | ||||||||
\(119\) | 3.61254e8 | 0.165140 | ||||||||
\(120\) | −8.93805e8 | −0.393484 | ||||||||
\(121\) | −1.48297e9 | −0.628925 | ||||||||
\(122\) | −1.31617e9 | −0.537890 | ||||||||
\(123\) | 2.12372e9 | 0.836613 | ||||||||
\(124\) | 4.50068e7 | 0.0170955 | ||||||||
\(125\) | 9.02863e9 | 3.30771 | ||||||||
\(126\) | 3.72035e8 | 0.131497 | ||||||||
\(127\) | −3.14845e9 | −1.07394 | −0.536970 | − | 0.843601i | \(-0.680431\pi\) | ||||
−0.536970 | + | 0.843601i | \(0.680431\pi\) | |||||||
\(128\) | −2.68435e8 | −0.0883883 | ||||||||
\(129\) | −1.51980e9 | −0.483207 | ||||||||
\(130\) | 1.93184e9 | 0.593233 | ||||||||
\(131\) | −4.16328e9 | −1.23514 | −0.617568 | − | 0.786517i | \(-0.711882\pi\) | ||||
−0.617568 | + | 0.786517i | \(0.711882\pi\) | |||||||
\(132\) | 6.13371e8 | 0.175849 | ||||||||
\(133\) | 3.17218e9 | 0.879073 | ||||||||
\(134\) | 3.01529e9 | 0.807901 | ||||||||
\(135\) | 1.43170e9 | 0.370980 | ||||||||
\(136\) | 4.17522e8 | 0.104654 | ||||||||
\(137\) | −7.36501e9 | −1.78620 | −0.893101 | − | 0.449856i | \(-0.851475\pi\) | ||||
−0.893101 | + | 0.449856i | \(0.851475\pi\) | |||||||
\(138\) | 1.44245e9 | 0.338567 | ||||||||
\(139\) | 4.51143e9 | 1.02506 | 0.512528 | − | 0.858670i | \(-0.328709\pi\) | ||||
0.512528 | + | 0.858670i | \(0.328709\pi\) | |||||||
\(140\) | −2.44417e9 | −0.537719 | ||||||||
\(141\) | −1.69826e9 | −0.361841 | ||||||||
\(142\) | −1.29478e9 | −0.267239 | ||||||||
\(143\) | −1.32572e9 | −0.265118 | ||||||||
\(144\) | 4.29982e8 | 0.0833333 | ||||||||
\(145\) | −6.35069e9 | −1.19307 | ||||||||
\(146\) | 3.77825e9 | 0.688182 | ||||||||
\(147\) | −2.25129e9 | −0.397652 | ||||||||
\(148\) | −7.47371e8 | −0.128044 | ||||||||
\(149\) | −1.10533e9 | −0.183718 | −0.0918591 | − | 0.995772i | \(-0.529281\pi\) | ||||
−0.0918591 | + | 0.995772i | \(0.529281\pi\) | |||||||
\(150\) | −6.87465e9 | −1.10877 | ||||||||
\(151\) | 1.03005e10 | 1.61236 | 0.806181 | − | 0.591668i | \(-0.201531\pi\) | ||||
0.806181 | + | 0.591668i | \(0.201531\pi\) | |||||||
\(152\) | 3.66626e9 | 0.557093 | ||||||||
\(153\) | −6.68789e8 | −0.0986683 | ||||||||
\(154\) | 1.67730e9 | 0.240308 | ||||||||
\(155\) | 4.73627e8 | 0.0659088 | ||||||||
\(156\) | −9.29346e8 | −0.125637 | ||||||||
\(157\) | −7.03726e8 | −0.0924390 | −0.0462195 | − | 0.998931i | \(-0.514717\pi\) | ||||
−0.0462195 | + | 0.998931i | \(0.514717\pi\) | |||||||
\(158\) | −8.43056e9 | −1.07622 | ||||||||
\(159\) | 4.63738e9 | 0.575421 | ||||||||
\(160\) | −2.82486e9 | −0.340767 | ||||||||
\(161\) | 3.94447e9 | 0.462671 | ||||||||
\(162\) | −6.88748e8 | −0.0785674 | ||||||||
\(163\) | 1.10181e10 | 1.22253 | 0.611267 | − | 0.791424i | \(-0.290660\pi\) | ||||
0.611267 | + | 0.791424i | \(0.290660\pi\) | |||||||
\(164\) | 6.71201e9 | 0.724528 | ||||||||
\(165\) | 6.45477e9 | 0.677958 | ||||||||
\(166\) | −2.93543e8 | −0.0300045 | ||||||||
\(167\) | 1.80357e9 | 0.179436 | 0.0897179 | − | 0.995967i | \(-0.471403\pi\) | ||||
0.0897179 | + | 0.995967i | \(0.471403\pi\) | |||||||
\(168\) | 1.17581e9 | 0.113880 | ||||||||
\(169\) | −8.59585e9 | −0.810585 | ||||||||
\(170\) | 4.39376e9 | 0.403475 | ||||||||
\(171\) | −5.87265e9 | −0.525232 | ||||||||
\(172\) | −4.80332e9 | −0.418469 | ||||||||
\(173\) | −8.93250e9 | −0.758168 | −0.379084 | − | 0.925362i | \(-0.623761\pi\) | ||||
−0.379084 | + | 0.925362i | \(0.623761\pi\) | |||||||
\(174\) | 3.05512e9 | 0.252672 | ||||||||
\(175\) | −1.87992e10 | −1.51519 | ||||||||
\(176\) | 1.93855e9 | 0.152290 | ||||||||
\(177\) | 2.72059e9 | 0.208345 | ||||||||
\(178\) | −1.10503e10 | −0.825056 | ||||||||
\(179\) | −4.28652e9 | −0.312080 | −0.156040 | − | 0.987751i | \(-0.549873\pi\) | ||||
−0.156040 | + | 0.987751i | \(0.549873\pi\) | |||||||
\(180\) | 4.52489e9 | 0.321278 | ||||||||
\(181\) | 8.70114e8 | 0.0602591 | 0.0301295 | − | 0.999546i | \(-0.490408\pi\) | ||||
0.0301295 | + | 0.999546i | \(0.490408\pi\) | |||||||
\(182\) | −2.54136e9 | −0.171690 | ||||||||
\(183\) | 6.66313e9 | 0.439186 | ||||||||
\(184\) | 4.55885e9 | 0.293207 | ||||||||
\(185\) | −7.86491e9 | −0.493652 | ||||||||
\(186\) | −2.27847e8 | −0.0139584 | ||||||||
\(187\) | −3.01521e9 | −0.180314 | ||||||||
\(188\) | −5.36734e9 | −0.313364 | ||||||||
\(189\) | −1.88343e9 | −0.107367 | ||||||||
\(190\) | 3.85817e10 | 2.14778 | ||||||||
\(191\) | 3.19445e10 | 1.73678 | 0.868392 | − | 0.495879i | \(-0.165154\pi\) | ||||
0.868392 | + | 0.495879i | \(0.165154\pi\) | |||||||
\(192\) | 1.35895e9 | 0.0721688 | ||||||||
\(193\) | 4.89841e9 | 0.254125 | 0.127063 | − | 0.991895i | \(-0.459445\pi\) | ||||
0.127063 | + | 0.991895i | \(0.459445\pi\) | |||||||
\(194\) | 7.01202e9 | 0.355415 | ||||||||
\(195\) | −9.77992e9 | −0.484372 | ||||||||
\(196\) | −7.11518e9 | −0.344377 | ||||||||
\(197\) | 2.17836e10 | 1.03046 | 0.515230 | − | 0.857052i | \(-0.327707\pi\) | ||||
0.515230 | + | 0.857052i | \(0.327707\pi\) | |||||||
\(198\) | −3.10519e9 | −0.143580 | ||||||||
\(199\) | −3.74165e10 | −1.69131 | −0.845657 | − | 0.533727i | \(-0.820791\pi\) | ||||
−0.845657 | + | 0.533727i | \(0.820791\pi\) | |||||||
\(200\) | −2.17273e10 | −0.960219 | ||||||||
\(201\) | −1.52649e10 | −0.659648 | ||||||||
\(202\) | −1.56896e10 | −0.663028 | ||||||||
\(203\) | 8.35443e9 | 0.345291 | ||||||||
\(204\) | −2.11370e9 | −0.0854493 | ||||||||
\(205\) | 7.06334e10 | 2.79330 | ||||||||
\(206\) | −2.75054e10 | −1.06418 | ||||||||
\(207\) | −7.30239e9 | −0.276439 | ||||||||
\(208\) | −2.93719e9 | −0.108805 | ||||||||
\(209\) | −2.64766e10 | −0.959851 | ||||||||
\(210\) | 1.23736e10 | 0.439045 | ||||||||
\(211\) | 5.74096e9 | 0.199395 | 0.0996973 | − | 0.995018i | \(-0.468213\pi\) | ||||
0.0996973 | + | 0.995018i | \(0.468213\pi\) | |||||||
\(212\) | 1.46564e10 | 0.498329 | ||||||||
\(213\) | 6.55485e9 | 0.218200 | ||||||||
\(214\) | −6.80007e9 | −0.221642 | ||||||||
\(215\) | −5.05474e10 | −1.61334 | ||||||||
\(216\) | −2.17678e9 | −0.0680414 | ||||||||
\(217\) | −6.23064e8 | −0.0190750 | ||||||||
\(218\) | −1.39952e10 | −0.419687 | ||||||||
\(219\) | −1.91274e10 | −0.561898 | ||||||||
\(220\) | 2.04003e10 | 0.587129 | ||||||||
\(221\) | 4.56848e9 | 0.128827 | ||||||||
\(222\) | 3.78357e9 | 0.104547 | ||||||||
\(223\) | 2.21571e10 | 0.599987 | 0.299993 | − | 0.953941i | \(-0.403016\pi\) | ||||
0.299993 | + | 0.953941i | \(0.403016\pi\) | |||||||
\(224\) | 3.71615e9 | 0.0986228 | ||||||||
\(225\) | 3.48029e10 | 0.905303 | ||||||||
\(226\) | 7.08758e8 | 0.0180722 | ||||||||
\(227\) | 7.46127e10 | 1.86508 | 0.932538 | − | 0.361073i | \(-0.117589\pi\) | ||||
0.932538 | + | 0.361073i | \(0.117589\pi\) | |||||||
\(228\) | −1.85605e10 | −0.454864 | ||||||||
\(229\) | −6.44305e10 | −1.54822 | −0.774108 | − | 0.633054i | \(-0.781801\pi\) | ||||
−0.774108 | + | 0.633054i | \(0.781801\pi\) | |||||||
\(230\) | 4.79748e10 | 1.13041 | ||||||||
\(231\) | −8.49135e9 | −0.196211 | ||||||||
\(232\) | 9.65569e9 | 0.218820 | ||||||||
\(233\) | −1.75635e10 | −0.390400 | −0.195200 | − | 0.980763i | \(-0.562536\pi\) | ||||
−0.195200 | + | 0.980763i | \(0.562536\pi\) | |||||||
\(234\) | 4.70481e9 | 0.102582 | ||||||||
\(235\) | −5.64828e10 | −1.20812 | ||||||||
\(236\) | 8.59842e9 | 0.180432 | ||||||||
\(237\) | 4.26797e10 | 0.878727 | ||||||||
\(238\) | −5.78007e9 | −0.116771 | ||||||||
\(239\) | 7.79759e9 | 0.154586 | 0.0772929 | − | 0.997008i | \(-0.475372\pi\) | ||||
0.0772929 | + | 0.997008i | \(0.475372\pi\) | |||||||
\(240\) | 1.43009e10 | 0.278235 | ||||||||
\(241\) | 4.74343e9 | 0.0905765 | 0.0452882 | − | 0.998974i | \(-0.485579\pi\) | ||||
0.0452882 | + | 0.998974i | \(0.485579\pi\) | |||||||
\(242\) | 2.37275e10 | 0.444717 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | 2.10588e10 | 0.380346 | ||||||||
\(245\) | −7.48761e10 | −1.32769 | ||||||||
\(246\) | −3.39796e10 | −0.591575 | ||||||||
\(247\) | 4.01159e10 | 0.685772 | ||||||||
\(248\) | −7.20110e8 | −0.0120883 | ||||||||
\(249\) | 1.48606e9 | 0.0244985 | ||||||||
\(250\) | −1.44458e11 | −2.33890 | ||||||||
\(251\) | −4.72379e10 | −0.751205 | −0.375603 | − | 0.926781i | \(-0.622564\pi\) | ||||
−0.375603 | + | 0.926781i | \(0.622564\pi\) | |||||||
\(252\) | −5.95256e9 | −0.0929825 | ||||||||
\(253\) | −3.29225e10 | −0.505186 | ||||||||
\(254\) | 5.03752e10 | 0.759390 | ||||||||
\(255\) | −2.22434e10 | −0.329436 | ||||||||
\(256\) | 4.29497e9 | 0.0625000 | ||||||||
\(257\) | 7.47016e10 | 1.06815 | 0.534074 | − | 0.845438i | \(-0.320661\pi\) | ||||
0.534074 | + | 0.845438i | \(0.320661\pi\) | |||||||
\(258\) | 2.43168e10 | 0.341679 | ||||||||
\(259\) | 1.03464e10 | 0.142870 | ||||||||
\(260\) | −3.09094e10 | −0.419479 | ||||||||
\(261\) | −1.54665e10 | −0.206306 | ||||||||
\(262\) | 6.66125e10 | 0.873373 | ||||||||
\(263\) | 3.07988e10 | 0.396947 | 0.198474 | − | 0.980106i | \(-0.436402\pi\) | ||||
0.198474 | + | 0.980106i | \(0.436402\pi\) | |||||||
\(264\) | −9.81393e9 | −0.124344 | ||||||||
\(265\) | 1.54236e11 | 1.92123 | ||||||||
\(266\) | −5.07548e10 | −0.621599 | ||||||||
\(267\) | 5.59421e10 | 0.673656 | ||||||||
\(268\) | −4.82447e10 | −0.571272 | ||||||||
\(269\) | −1.49384e11 | −1.73948 | −0.869738 | − | 0.493513i | \(-0.835712\pi\) | ||||
−0.869738 | + | 0.493513i | \(0.835712\pi\) | |||||||
\(270\) | −2.29072e10 | −0.262323 | ||||||||
\(271\) | 1.32111e11 | 1.48791 | 0.743957 | − | 0.668228i | \(-0.232947\pi\) | ||||
0.743957 | + | 0.668228i | \(0.232947\pi\) | |||||||
\(272\) | −6.68035e9 | −0.0740012 | ||||||||
\(273\) | 1.28656e10 | 0.140184 | ||||||||
\(274\) | 1.17840e11 | 1.26304 | ||||||||
\(275\) | 1.56907e11 | 1.65442 | ||||||||
\(276\) | −2.30792e10 | −0.239403 | ||||||||
\(277\) | −9.19219e10 | −0.938123 | −0.469062 | − | 0.883165i | \(-0.655408\pi\) | ||||
−0.469062 | + | 0.883165i | \(0.655408\pi\) | |||||||
\(278\) | −7.21829e10 | −0.724824 | ||||||||
\(279\) | 1.15348e9 | 0.0113970 | ||||||||
\(280\) | 3.91067e10 | 0.380225 | ||||||||
\(281\) | −6.21245e10 | −0.594408 | −0.297204 | − | 0.954814i | \(-0.596054\pi\) | ||||
−0.297204 | + | 0.954814i | \(0.596054\pi\) | |||||||
\(282\) | 2.71721e10 | 0.255860 | ||||||||
\(283\) | −1.46305e11 | −1.35588 | −0.677938 | − | 0.735119i | \(-0.737126\pi\) | ||||
−0.677938 | + | 0.735119i | \(0.737126\pi\) | |||||||
\(284\) | 2.07166e10 | 0.188967 | ||||||||
\(285\) | −1.95320e11 | −1.75366 | ||||||||
\(286\) | 2.12115e10 | 0.187466 | ||||||||
\(287\) | −9.29194e10 | −0.808422 | ||||||||
\(288\) | −6.87971e9 | −0.0589256 | ||||||||
\(289\) | −1.08197e11 | −0.912381 | ||||||||
\(290\) | 1.01611e11 | 0.843626 | ||||||||
\(291\) | −3.54983e10 | −0.290195 | ||||||||
\(292\) | −6.04521e10 | −0.486618 | ||||||||
\(293\) | 9.65207e10 | 0.765096 | 0.382548 | − | 0.923936i | \(-0.375047\pi\) | ||||
0.382548 | + | 0.923936i | \(0.375047\pi\) | |||||||
\(294\) | 3.60206e10 | 0.281182 | ||||||||
\(295\) | 9.04849e10 | 0.695628 | ||||||||
\(296\) | 1.19579e10 | 0.0905406 | ||||||||
\(297\) | 1.57200e10 | 0.117233 | ||||||||
\(298\) | 1.76852e10 | 0.129908 | ||||||||
\(299\) | 4.98824e10 | 0.360934 | ||||||||
\(300\) | 1.09994e11 | 0.784016 | ||||||||
\(301\) | 6.64959e10 | 0.466924 | ||||||||
\(302\) | −1.64808e11 | −1.14011 | ||||||||
\(303\) | 7.94288e10 | 0.541360 | ||||||||
\(304\) | −5.86602e10 | −0.393924 | ||||||||
\(305\) | 2.21611e11 | 1.46636 | ||||||||
\(306\) | 1.07006e10 | 0.0697690 | ||||||||
\(307\) | −2.74874e11 | −1.76608 | −0.883042 | − | 0.469294i | \(-0.844509\pi\) | ||||
−0.883042 | + | 0.469294i | \(0.844509\pi\) | |||||||
\(308\) | −2.68369e10 | −0.169924 | ||||||||
\(309\) | 1.39246e11 | 0.868900 | ||||||||
\(310\) | −7.57803e9 | −0.0466046 | ||||||||
\(311\) | −1.81295e11 | −1.09891 | −0.549457 | − | 0.835522i | \(-0.685165\pi\) | ||||
−0.549457 | + | 0.835522i | \(0.685165\pi\) | |||||||
\(312\) | 1.48695e10 | 0.0888386 | ||||||||
\(313\) | 1.59020e11 | 0.936489 | 0.468245 | − | 0.883599i | \(-0.344887\pi\) | ||||
0.468245 | + | 0.883599i | \(0.344887\pi\) | |||||||
\(314\) | 1.12596e10 | 0.0653642 | ||||||||
\(315\) | −6.26414e10 | −0.358479 | ||||||||
\(316\) | 1.34889e11 | 0.761000 | ||||||||
\(317\) | 1.95485e11 | 1.08730 | 0.543648 | − | 0.839313i | \(-0.317043\pi\) | ||||
0.543648 | + | 0.839313i | \(0.317043\pi\) | |||||||
\(318\) | −7.41980e10 | −0.406884 | ||||||||
\(319\) | −6.97303e10 | −0.377019 | ||||||||
\(320\) | 4.51978e10 | 0.240959 | ||||||||
\(321\) | 3.44254e10 | 0.180970 | ||||||||
\(322\) | −6.31116e10 | −0.327158 | ||||||||
\(323\) | 9.12395e10 | 0.466414 | ||||||||
\(324\) | 1.10200e10 | 0.0555556 | ||||||||
\(325\) | −2.37738e11 | −1.18201 | ||||||||
\(326\) | −1.76289e11 | −0.864463 | ||||||||
\(327\) | 7.08508e10 | 0.342673 | ||||||||
\(328\) | −1.07392e11 | −0.512319 | ||||||||
\(329\) | 7.43041e10 | 0.349648 | ||||||||
\(330\) | −1.03276e11 | −0.479389 | ||||||||
\(331\) | 3.97198e11 | 1.81878 | 0.909391 | − | 0.415942i | \(-0.136548\pi\) | ||||
0.909391 | + | 0.415942i | \(0.136548\pi\) | |||||||
\(332\) | 4.69669e9 | 0.0212164 | ||||||||
\(333\) | −1.91543e10 | −0.0853625 | ||||||||
\(334\) | −2.88571e10 | −0.126880 | ||||||||
\(335\) | −5.07700e11 | −2.20245 | ||||||||
\(336\) | −1.88130e10 | −0.0805252 | ||||||||
\(337\) | −2.59813e11 | −1.09730 | −0.548650 | − | 0.836052i | \(-0.684858\pi\) | ||||
−0.548650 | + | 0.836052i | \(0.684858\pi\) | |||||||
\(338\) | 1.37534e11 | 0.573170 | ||||||||
\(339\) | −3.58809e9 | −0.0147558 | ||||||||
\(340\) | −7.03002e10 | −0.285300 | ||||||||
\(341\) | 5.20040e9 | 0.0208277 | ||||||||
\(342\) | 9.39623e10 | 0.371395 | ||||||||
\(343\) | 2.41514e11 | 0.942147 | ||||||||
\(344\) | 7.68531e10 | 0.295902 | ||||||||
\(345\) | −2.42872e11 | −0.922979 | ||||||||
\(346\) | 1.42920e11 | 0.536106 | ||||||||
\(347\) | −3.26152e11 | −1.20764 | −0.603820 | − | 0.797121i | \(-0.706356\pi\) | ||||
−0.603820 | + | 0.797121i | \(0.706356\pi\) | |||||||
\(348\) | −4.88819e10 | −0.178666 | ||||||||
\(349\) | 1.54936e11 | 0.559032 | 0.279516 | − | 0.960141i | \(-0.409826\pi\) | ||||
0.279516 | + | 0.960141i | \(0.409826\pi\) | |||||||
\(350\) | 3.00787e11 | 1.07140 | ||||||||
\(351\) | −2.38181e10 | −0.0837578 | ||||||||
\(352\) | −3.10169e10 | −0.107685 | ||||||||
\(353\) | 3.48972e11 | 1.19620 | 0.598100 | − | 0.801421i | \(-0.295922\pi\) | ||||
0.598100 | + | 0.801421i | \(0.295922\pi\) | |||||||
\(354\) | −4.35295e10 | −0.147322 | ||||||||
\(355\) | 2.18009e11 | 0.728530 | ||||||||
\(356\) | 1.76805e11 | 0.583403 | ||||||||
\(357\) | 2.92616e10 | 0.0953434 | ||||||||
\(358\) | 6.85843e10 | 0.220674 | ||||||||
\(359\) | 1.21868e11 | 0.387227 | 0.193613 | − | 0.981078i | \(-0.437979\pi\) | ||||
0.193613 | + | 0.981078i | \(0.437979\pi\) | |||||||
\(360\) | −7.23982e10 | −0.227178 | ||||||||
\(361\) | 4.78488e11 | 1.48282 | ||||||||
\(362\) | −1.39218e10 | −0.0426096 | ||||||||
\(363\) | −1.20121e11 | −0.363110 | ||||||||
\(364\) | 4.06618e10 | 0.121403 | ||||||||
\(365\) | −6.36164e11 | −1.87608 | ||||||||
\(366\) | −1.06610e11 | −0.310551 | ||||||||
\(367\) | −5.08451e11 | −1.46303 | −0.731513 | − | 0.681828i | \(-0.761185\pi\) | ||||
−0.731513 | + | 0.681828i | \(0.761185\pi\) | |||||||
\(368\) | −7.29416e10 | −0.207329 | ||||||||
\(369\) | 1.72022e11 | 0.483019 | ||||||||
\(370\) | 1.25839e11 | 0.349065 | ||||||||
\(371\) | −2.02900e11 | −0.556030 | ||||||||
\(372\) | 3.64555e9 | 0.00987007 | ||||||||
\(373\) | −2.56076e11 | −0.684983 | −0.342492 | − | 0.939521i | \(-0.611271\pi\) | ||||
−0.342492 | + | 0.939521i | \(0.611271\pi\) | |||||||
\(374\) | 4.82433e10 | 0.127501 | ||||||||
\(375\) | 7.31319e11 | 1.90971 | ||||||||
\(376\) | 8.58774e10 | 0.221582 | ||||||||
\(377\) | 1.05652e11 | 0.269364 | ||||||||
\(378\) | 3.01348e10 | 0.0759199 | ||||||||
\(379\) | −5.53250e10 | −0.137735 | −0.0688676 | − | 0.997626i | \(-0.521939\pi\) | ||||
−0.0688676 | + | 0.997626i | \(0.521939\pi\) | |||||||
\(380\) | −6.17307e11 | −1.51871 | ||||||||
\(381\) | −2.55025e11 | −0.620040 | ||||||||
\(382\) | −5.11112e11 | −1.22809 | ||||||||
\(383\) | −8.14772e10 | −0.193482 | −0.0967412 | − | 0.995310i | \(-0.530842\pi\) | ||||
−0.0967412 | + | 0.995310i | \(0.530842\pi\) | |||||||
\(384\) | −2.17433e10 | −0.0510310 | ||||||||
\(385\) | −2.82416e11 | −0.655113 | ||||||||
\(386\) | −7.83746e10 | −0.179694 | ||||||||
\(387\) | −1.23104e11 | −0.278979 | ||||||||
\(388\) | −1.12192e11 | −0.251316 | ||||||||
\(389\) | 6.01212e11 | 1.33123 | 0.665617 | − | 0.746293i | \(-0.268168\pi\) | ||||
0.665617 | + | 0.746293i | \(0.268168\pi\) | |||||||
\(390\) | 1.56479e11 | 0.342503 | ||||||||
\(391\) | 1.13453e11 | 0.245482 | ||||||||
\(392\) | 1.13843e11 | 0.243511 | ||||||||
\(393\) | −3.37226e11 | −0.713106 | ||||||||
\(394\) | −3.48537e11 | −0.728645 | ||||||||
\(395\) | 1.41950e12 | 2.93391 | ||||||||
\(396\) | 4.96830e10 | 0.101527 | ||||||||
\(397\) | 1.31066e10 | 0.0264808 | 0.0132404 | − | 0.999912i | \(-0.495785\pi\) | ||||
0.0132404 | + | 0.999912i | \(0.495785\pi\) | |||||||
\(398\) | 5.98664e11 | 1.19594 | ||||||||
\(399\) | 2.56946e11 | 0.507533 | ||||||||
\(400\) | 3.47636e11 | 0.678977 | ||||||||
\(401\) | −5.98151e11 | −1.15521 | −0.577605 | − | 0.816316i | \(-0.696013\pi\) | ||||
−0.577605 | + | 0.816316i | \(0.696013\pi\) | |||||||
\(402\) | 2.44239e11 | 0.466442 | ||||||||
\(403\) | −7.87936e9 | −0.0148805 | ||||||||
\(404\) | 2.51034e11 | 0.468831 | ||||||||
\(405\) | 1.15968e11 | 0.214185 | ||||||||
\(406\) | −1.33671e11 | −0.244157 | ||||||||
\(407\) | −8.63564e10 | −0.155998 | ||||||||
\(408\) | 3.38193e10 | 0.0604218 | ||||||||
\(409\) | −1.97716e11 | −0.349371 | −0.174686 | − | 0.984624i | \(-0.555891\pi\) | ||||
−0.174686 | + | 0.984624i | \(0.555891\pi\) | |||||||
\(410\) | −1.13013e12 | −1.97516 | ||||||||
\(411\) | −5.96565e11 | −1.03126 | ||||||||
\(412\) | 4.40086e11 | 0.752489 | ||||||||
\(413\) | −1.19034e11 | −0.201325 | ||||||||
\(414\) | 1.16838e11 | 0.195472 | ||||||||
\(415\) | 4.94253e10 | 0.0817962 | ||||||||
\(416\) | 4.69951e10 | 0.0769365 | ||||||||
\(417\) | 3.65426e11 | 0.591817 | ||||||||
\(418\) | 4.23625e11 | 0.678717 | ||||||||
\(419\) | 3.37678e11 | 0.535229 | 0.267615 | − | 0.963526i | \(-0.413765\pi\) | ||||
0.267615 | + | 0.963526i | \(0.413765\pi\) | |||||||
\(420\) | −1.97978e11 | −0.310452 | ||||||||
\(421\) | −1.07358e11 | −0.166559 | −0.0832793 | − | 0.996526i | \(-0.526539\pi\) | ||||
−0.0832793 | + | 0.996526i | \(0.526539\pi\) | |||||||
\(422\) | −9.18553e10 | −0.140993 | ||||||||
\(423\) | −1.37559e11 | −0.208909 | ||||||||
\(424\) | −2.34502e11 | −0.352372 | ||||||||
\(425\) | −5.40710e11 | −0.803923 | ||||||||
\(426\) | −1.04878e11 | −0.154291 | ||||||||
\(427\) | −2.91532e11 | −0.424386 | ||||||||
\(428\) | 1.08801e11 | 0.156724 | ||||||||
\(429\) | −1.07383e11 | −0.153066 | ||||||||
\(430\) | 8.08759e11 | 1.14080 | ||||||||
\(431\) | −6.92353e11 | −0.966452 | −0.483226 | − | 0.875496i | \(-0.660535\pi\) | ||||
−0.483226 | + | 0.875496i | \(0.660535\pi\) | |||||||
\(432\) | 3.48285e10 | 0.0481125 | ||||||||
\(433\) | −1.03885e12 | −1.42022 | −0.710110 | − | 0.704091i | \(-0.751355\pi\) | ||||
−0.710110 | + | 0.704091i | \(0.751355\pi\) | |||||||
\(434\) | 9.96902e9 | 0.0134880 | ||||||||
\(435\) | −5.14406e11 | −0.688818 | ||||||||
\(436\) | 2.23923e11 | 0.296763 | ||||||||
\(437\) | 9.96228e11 | 1.30675 | ||||||||
\(438\) | 3.06039e11 | 0.397322 | ||||||||
\(439\) | 9.11781e11 | 1.17166 | 0.585828 | − | 0.810435i | \(-0.300769\pi\) | ||||
0.585828 | + | 0.810435i | \(0.300769\pi\) | |||||||
\(440\) | −3.26404e11 | −0.415163 | ||||||||
\(441\) | −1.82354e11 | −0.229584 | ||||||||
\(442\) | −7.30956e10 | −0.0910943 | ||||||||
\(443\) | −7.88303e11 | −0.972470 | −0.486235 | − | 0.873828i | \(-0.661630\pi\) | ||||
−0.486235 | + | 0.873828i | \(0.661630\pi\) | |||||||
\(444\) | −6.05371e10 | −0.0739261 | ||||||||
\(445\) | 1.86059e12 | 2.24922 | ||||||||
\(446\) | −3.54514e11 | −0.424255 | ||||||||
\(447\) | −8.95314e10 | −0.106070 | ||||||||
\(448\) | −5.94585e10 | −0.0697369 | ||||||||
\(449\) | −7.28687e11 | −0.846121 | −0.423060 | − | 0.906102i | \(-0.639044\pi\) | ||||
−0.423060 | + | 0.906102i | \(0.639044\pi\) | |||||||
\(450\) | −5.56846e11 | −0.640146 | ||||||||
\(451\) | 7.75552e11 | 0.882707 | ||||||||
\(452\) | −1.13401e10 | −0.0127789 | ||||||||
\(453\) | 8.34342e11 | 0.930898 | ||||||||
\(454\) | −1.19380e12 | −1.31881 | ||||||||
\(455\) | 4.27901e11 | 0.468050 | ||||||||
\(456\) | 2.96967e11 | 0.321638 | ||||||||
\(457\) | −1.55747e11 | −0.167031 | −0.0835155 | − | 0.996506i | \(-0.526615\pi\) | ||||
−0.0835155 | + | 0.996506i | \(0.526615\pi\) | |||||||
\(458\) | 1.03089e12 | 1.09475 | ||||||||
\(459\) | −5.41719e10 | −0.0569662 | ||||||||
\(460\) | −7.67596e11 | −0.799323 | ||||||||
\(461\) | 5.84721e11 | 0.602969 | 0.301484 | − | 0.953471i | \(-0.402518\pi\) | ||||
0.301484 | + | 0.953471i | \(0.402518\pi\) | |||||||
\(462\) | 1.35862e11 | 0.138742 | ||||||||
\(463\) | 1.98254e11 | 0.200497 | 0.100249 | − | 0.994962i | \(-0.468036\pi\) | ||||
0.100249 | + | 0.994962i | \(0.468036\pi\) | |||||||
\(464\) | −1.54491e11 | −0.154729 | ||||||||
\(465\) | 3.83638e10 | 0.0380525 | ||||||||
\(466\) | 2.81016e11 | 0.276054 | ||||||||
\(467\) | 1.90984e12 | 1.85810 | 0.929052 | − | 0.369949i | \(-0.120625\pi\) | ||||
0.929052 | + | 0.369949i | \(0.120625\pi\) | |||||||
\(468\) | −7.52770e10 | −0.0725364 | ||||||||
\(469\) | 6.67887e11 | 0.637420 | ||||||||
\(470\) | 9.03725e11 | 0.854272 | ||||||||
\(471\) | −5.70018e10 | −0.0533697 | ||||||||
\(472\) | −1.37575e11 | −0.127585 | ||||||||
\(473\) | −5.55008e11 | −0.509829 | ||||||||
\(474\) | −6.82875e11 | −0.621353 | ||||||||
\(475\) | −4.74798e12 | −4.27945 | ||||||||
\(476\) | 9.24810e10 | 0.0825698 | ||||||||
\(477\) | 3.75628e11 | 0.332219 | ||||||||
\(478\) | −1.24761e11 | −0.109309 | ||||||||
\(479\) | −1.49603e12 | −1.29846 | −0.649232 | − | 0.760590i | \(-0.724910\pi\) | ||||
−0.649232 | + | 0.760590i | \(0.724910\pi\) | |||||||
\(480\) | −2.28814e11 | −0.196742 | ||||||||
\(481\) | 1.30842e11 | 0.111454 | ||||||||
\(482\) | −7.58948e10 | −0.0640472 | ||||||||
\(483\) | 3.19502e11 | 0.267123 | ||||||||
\(484\) | −3.79641e11 | −0.314462 | ||||||||
\(485\) | −1.18065e12 | −0.968908 | ||||||||
\(486\) | −5.57886e10 | −0.0453609 | ||||||||
\(487\) | 3.57916e11 | 0.288337 | 0.144169 | − | 0.989553i | \(-0.453949\pi\) | ||||
0.144169 | + | 0.989553i | \(0.453949\pi\) | |||||||
\(488\) | −3.36940e11 | −0.268945 | ||||||||
\(489\) | 8.92464e11 | 0.705831 | ||||||||
\(490\) | 1.19802e12 | 0.938817 | ||||||||
\(491\) | 7.23262e11 | 0.561603 | 0.280801 | − | 0.959766i | \(-0.409400\pi\) | ||||
0.280801 | + | 0.959766i | \(0.409400\pi\) | |||||||
\(492\) | 5.43673e11 | 0.418307 | ||||||||
\(493\) | 2.40294e11 | 0.183202 | ||||||||
\(494\) | −6.41854e11 | −0.484914 | ||||||||
\(495\) | 5.22836e11 | 0.391419 | ||||||||
\(496\) | 1.15218e10 | 0.00854773 | ||||||||
\(497\) | −2.86795e11 | −0.210847 | ||||||||
\(498\) | −2.37770e10 | −0.0173231 | ||||||||
\(499\) | −6.16113e11 | −0.444844 | −0.222422 | − | 0.974950i | \(-0.571396\pi\) | ||||
−0.222422 | + | 0.974950i | \(0.571396\pi\) | |||||||
\(500\) | 2.31133e12 | 1.65385 | ||||||||
\(501\) | 1.46089e11 | 0.103597 | ||||||||
\(502\) | 7.55806e11 | 0.531182 | ||||||||
\(503\) | −2.17749e12 | −1.51670 | −0.758352 | − | 0.651845i | \(-0.773995\pi\) | ||||
−0.758352 | + | 0.651845i | \(0.773995\pi\) | |||||||
\(504\) | 9.52409e10 | 0.0657486 | ||||||||
\(505\) | 2.64174e12 | 1.80750 | ||||||||
\(506\) | 5.26761e11 | 0.357220 | ||||||||
\(507\) | −6.96264e11 | −0.467991 | ||||||||
\(508\) | −8.06003e11 | −0.536970 | ||||||||
\(509\) | −2.65267e11 | −0.175167 | −0.0875836 | − | 0.996157i | \(-0.527914\pi\) | ||||
−0.0875836 | + | 0.996157i | \(0.527914\pi\) | |||||||
\(510\) | 3.55895e11 | 0.232946 | ||||||||
\(511\) | 8.36883e11 | 0.542964 | ||||||||
\(512\) | −6.87195e10 | −0.0441942 | ||||||||
\(513\) | −4.75684e11 | −0.303243 | ||||||||
\(514\) | −1.19523e12 | −0.755294 | ||||||||
\(515\) | 4.63122e12 | 2.90110 | ||||||||
\(516\) | −3.89069e11 | −0.241603 | ||||||||
\(517\) | −6.20179e11 | −0.381777 | ||||||||
\(518\) | −1.65543e11 | −0.101024 | ||||||||
\(519\) | −7.23533e11 | −0.437729 | ||||||||
\(520\) | 4.94550e11 | 0.296616 | ||||||||
\(521\) | −1.52002e12 | −0.903814 | −0.451907 | − | 0.892065i | \(-0.649256\pi\) | ||||
−0.451907 | + | 0.892065i | \(0.649256\pi\) | |||||||
\(522\) | 2.47465e11 | 0.145880 | ||||||||
\(523\) | 7.54029e11 | 0.440687 | 0.220344 | − | 0.975422i | \(-0.429282\pi\) | ||||
0.220344 | + | 0.975422i | \(0.429282\pi\) | |||||||
\(524\) | −1.06580e12 | −0.617568 | ||||||||
\(525\) | −1.52273e12 | −0.874797 | ||||||||
\(526\) | −4.92781e11 | −0.280684 | ||||||||
\(527\) | −1.79208e10 | −0.0101207 | ||||||||
\(528\) | 1.57023e11 | 0.0879246 | ||||||||
\(529\) | −5.62384e11 | −0.312235 | ||||||||
\(530\) | −2.46777e12 | −1.35851 | ||||||||
\(531\) | 2.20368e11 | 0.120288 | ||||||||
\(532\) | 8.12077e11 | 0.439537 | ||||||||
\(533\) | −1.17507e12 | −0.630656 | ||||||||
\(534\) | −8.95073e11 | −0.476347 | ||||||||
\(535\) | 1.14496e12 | 0.604226 | ||||||||
\(536\) | 7.71915e11 | 0.403950 | ||||||||
\(537\) | −3.47208e11 | −0.180179 | ||||||||
\(538\) | 2.39014e12 | 1.23000 | ||||||||
\(539\) | −8.22137e11 | −0.419561 | ||||||||
\(540\) | 3.66516e11 | 0.185490 | ||||||||
\(541\) | −2.05580e12 | −1.03179 | −0.515896 | − | 0.856651i | \(-0.672541\pi\) | ||||
−0.515896 | + | 0.856651i | \(0.672541\pi\) | |||||||
\(542\) | −2.11378e12 | −1.05211 | ||||||||
\(543\) | 7.04792e10 | 0.0347906 | ||||||||
\(544\) | 1.06886e11 | 0.0523268 | ||||||||
\(545\) | 2.35644e12 | 1.14412 | ||||||||
\(546\) | −2.05850e11 | −0.0991252 | ||||||||
\(547\) | 2.09022e12 | 0.998274 | 0.499137 | − | 0.866523i | \(-0.333650\pi\) | ||||
0.499137 | + | 0.866523i | \(0.333650\pi\) | |||||||
\(548\) | −1.88544e12 | −0.893101 | ||||||||
\(549\) | 5.39713e11 | 0.253564 | ||||||||
\(550\) | −2.51052e12 | −1.16985 | ||||||||
\(551\) | 2.11002e12 | 0.975225 | ||||||||
\(552\) | 3.69267e11 | 0.169283 | ||||||||
\(553\) | −1.86737e12 | −0.849116 | ||||||||
\(554\) | 1.47075e12 | 0.663353 | ||||||||
\(555\) | −6.37058e11 | −0.285010 | ||||||||
\(556\) | 1.15493e12 | 0.512528 | ||||||||
\(557\) | 2.24244e12 | 0.987126 | 0.493563 | − | 0.869710i | \(-0.335694\pi\) | ||||
0.493563 | + | 0.869710i | \(0.335694\pi\) | |||||||
\(558\) | −1.84556e10 | −0.00805888 | ||||||||
\(559\) | 8.40919e11 | 0.364251 | ||||||||
\(560\) | −6.25707e11 | −0.268859 | ||||||||
\(561\) | −2.44232e11 | −0.104104 | ||||||||
\(562\) | 9.93992e11 | 0.420310 | ||||||||
\(563\) | −9.48976e10 | −0.0398077 | −0.0199039 | − | 0.999802i | \(-0.506336\pi\) | ||||
−0.0199039 | + | 0.999802i | \(0.506336\pi\) | |||||||
\(564\) | −4.34754e11 | −0.180921 | ||||||||
\(565\) | −1.19337e11 | −0.0492671 | ||||||||
\(566\) | 2.34088e12 | 0.958750 | ||||||||
\(567\) | −1.52558e11 | −0.0619883 | ||||||||
\(568\) | −3.31465e11 | −0.133620 | ||||||||
\(569\) | 8.02282e10 | 0.0320865 | 0.0160432 | − | 0.999871i | \(-0.494893\pi\) | ||||
0.0160432 | + | 0.999871i | \(0.494893\pi\) | |||||||
\(570\) | 3.12512e12 | 1.24002 | ||||||||
\(571\) | −2.64009e12 | −1.03934 | −0.519668 | − | 0.854368i | \(-0.673944\pi\) | ||||
−0.519668 | + | 0.854368i | \(0.673944\pi\) | |||||||
\(572\) | −3.39383e11 | −0.132559 | ||||||||
\(573\) | 2.58750e12 | 1.00273 | ||||||||
\(574\) | 1.48671e12 | 0.571640 | ||||||||
\(575\) | −5.90392e12 | −2.25235 | ||||||||
\(576\) | 1.10075e11 | 0.0416667 | ||||||||
\(577\) | −2.16306e12 | −0.812414 | −0.406207 | − | 0.913781i | \(-0.633149\pi\) | ||||
−0.406207 | + | 0.913781i | \(0.633149\pi\) | |||||||
\(578\) | 1.73116e12 | 0.645151 | ||||||||
\(579\) | 3.96772e11 | 0.146719 | ||||||||
\(580\) | −1.62578e12 | −0.596534 | ||||||||
\(581\) | −6.50198e10 | −0.0236730 | ||||||||
\(582\) | 5.67973e11 | 0.205199 | ||||||||
\(583\) | 1.69350e12 | 0.607124 | ||||||||
\(584\) | 9.67233e11 | 0.344091 | ||||||||
\(585\) | −7.92173e11 | −0.279652 | ||||||||
\(586\) | −1.54433e12 | −0.541005 | ||||||||
\(587\) | 5.67861e11 | 0.197411 | 0.0987053 | − | 0.995117i | \(-0.468530\pi\) | ||||
0.0987053 | + | 0.995117i | \(0.468530\pi\) | |||||||
\(588\) | −5.76330e11 | −0.198826 | ||||||||
\(589\) | −1.57363e11 | −0.0538745 | ||||||||
\(590\) | −1.44776e12 | −0.491883 | ||||||||
\(591\) | 1.76447e12 | 0.594936 | ||||||||
\(592\) | −1.91327e11 | −0.0640219 | ||||||||
\(593\) | 2.17049e12 | 0.720796 | 0.360398 | − | 0.932799i | \(-0.382641\pi\) | ||||
0.360398 | + | 0.932799i | \(0.382641\pi\) | |||||||
\(594\) | −2.51520e11 | −0.0828961 | ||||||||
\(595\) | 9.73219e11 | 0.318335 | ||||||||
\(596\) | −2.82964e11 | −0.0918591 | ||||||||
\(597\) | −3.03074e12 | −0.976480 | ||||||||
\(598\) | −7.98119e11 | −0.255219 | ||||||||
\(599\) | 2.65417e12 | 0.842379 | 0.421189 | − | 0.906973i | \(-0.361613\pi\) | ||||
0.421189 | + | 0.906973i | \(0.361613\pi\) | |||||||
\(600\) | −1.75991e12 | −0.554383 | ||||||||
\(601\) | −4.55145e12 | −1.42303 | −0.711515 | − | 0.702670i | \(-0.751991\pi\) | ||||
−0.711515 | + | 0.702670i | \(0.751991\pi\) | |||||||
\(602\) | −1.06394e12 | −0.330165 | ||||||||
\(603\) | −1.23646e12 | −0.380848 | ||||||||
\(604\) | 2.63693e12 | 0.806181 | ||||||||
\(605\) | −3.99512e12 | −1.21236 | ||||||||
\(606\) | −1.27086e12 | −0.382799 | ||||||||
\(607\) | −3.34553e12 | −1.00027 | −0.500133 | − | 0.865949i | \(-0.666716\pi\) | ||||
−0.500133 | + | 0.865949i | \(0.666716\pi\) | |||||||
\(608\) | 9.38564e11 | 0.278546 | ||||||||
\(609\) | 6.76709e11 | 0.199354 | ||||||||
\(610\) | −3.54577e12 | −1.03688 | ||||||||
\(611\) | 9.39661e11 | 0.272763 | ||||||||
\(612\) | −1.71210e11 | −0.0493342 | ||||||||
\(613\) | 1.75508e12 | 0.502025 | 0.251012 | − | 0.967984i | \(-0.419236\pi\) | ||||
0.251012 | + | 0.967984i | \(0.419236\pi\) | |||||||
\(614\) | 4.39799e12 | 1.24881 | ||||||||
\(615\) | 5.72131e12 | 1.61271 | ||||||||
\(616\) | 4.29390e11 | 0.120154 | ||||||||
\(617\) | 3.30409e12 | 0.917843 | 0.458922 | − | 0.888477i | \(-0.348236\pi\) | ||||
0.458922 | + | 0.888477i | \(0.348236\pi\) | |||||||
\(618\) | −2.22794e12 | −0.614405 | ||||||||
\(619\) | 1.58035e12 | 0.432658 | 0.216329 | − | 0.976321i | \(-0.430592\pi\) | ||||
0.216329 | + | 0.976321i | \(0.430592\pi\) | |||||||
\(620\) | 1.21248e11 | 0.0329544 | ||||||||
\(621\) | −5.91494e11 | −0.159602 | ||||||||
\(622\) | 2.90072e12 | 0.777050 | ||||||||
\(623\) | −2.44764e12 | −0.650955 | ||||||||
\(624\) | −2.37913e11 | −0.0628184 | ||||||||
\(625\) | 1.39628e13 | 3.66026 | ||||||||
\(626\) | −2.54432e12 | −0.662198 | ||||||||
\(627\) | −2.14460e12 | −0.554170 | ||||||||
\(628\) | −1.80154e11 | −0.0462195 | ||||||||
\(629\) | 2.97588e11 | 0.0758032 | ||||||||
\(630\) | 1.00226e12 | 0.253483 | ||||||||
\(631\) | 3.14102e12 | 0.788748 | 0.394374 | − | 0.918950i | \(-0.370962\pi\) | ||||
0.394374 | + | 0.918950i | \(0.370962\pi\) | |||||||
\(632\) | −2.15822e12 | −0.538108 | ||||||||
\(633\) | 4.65018e11 | 0.115120 | ||||||||
\(634\) | −3.12777e12 | −0.768834 | ||||||||
\(635\) | −8.48193e12 | −2.07020 | ||||||||
\(636\) | 1.18717e12 | 0.287710 | ||||||||
\(637\) | 1.24566e12 | 0.299758 | ||||||||
\(638\) | 1.11568e12 | 0.266593 | ||||||||
\(639\) | 5.30943e11 | 0.125978 | ||||||||
\(640\) | −7.23165e11 | −0.170384 | ||||||||
\(641\) | 3.77817e11 | 0.0883934 | 0.0441967 | − | 0.999023i | \(-0.485927\pi\) | ||||
0.0441967 | + | 0.999023i | \(0.485927\pi\) | |||||||
\(642\) | −5.50806e11 | −0.127965 | ||||||||
\(643\) | 9.78208e11 | 0.225674 | 0.112837 | − | 0.993614i | \(-0.464006\pi\) | ||||
0.112837 | + | 0.993614i | \(0.464006\pi\) | |||||||
\(644\) | 1.00978e12 | 0.231336 | ||||||||
\(645\) | −4.09434e12 | −0.931462 | ||||||||
\(646\) | −1.45983e12 | −0.329804 | ||||||||
\(647\) | −3.41548e12 | −0.766271 | −0.383136 | − | 0.923692i | \(-0.625156\pi\) | ||||
−0.383136 | + | 0.923692i | \(0.625156\pi\) | |||||||
\(648\) | −1.76319e11 | −0.0392837 | ||||||||
\(649\) | 9.93521e11 | 0.219824 | ||||||||
\(650\) | 3.80380e12 | 0.835810 | ||||||||
\(651\) | −5.04681e10 | −0.0110129 | ||||||||
\(652\) | 2.82063e12 | 0.611267 | ||||||||
\(653\) | 1.27409e12 | 0.274215 | 0.137108 | − | 0.990556i | \(-0.456219\pi\) | ||||
0.137108 | + | 0.990556i | \(0.456219\pi\) | |||||||
\(654\) | −1.13361e12 | −0.242306 | ||||||||
\(655\) | −1.12159e13 | −2.38094 | ||||||||
\(656\) | 1.71827e12 | 0.362264 | ||||||||
\(657\) | −1.54932e12 | −0.324412 | ||||||||
\(658\) | −1.18887e12 | −0.247238 | ||||||||
\(659\) | −6.72931e12 | −1.38991 | −0.694954 | − | 0.719054i | \(-0.744575\pi\) | ||||
−0.694954 | + | 0.719054i | \(0.744575\pi\) | |||||||
\(660\) | 1.65242e12 | 0.338979 | ||||||||
\(661\) | −6.58592e12 | −1.34187 | −0.670934 | − | 0.741517i | \(-0.734107\pi\) | ||||
−0.670934 | + | 0.741517i | \(0.734107\pi\) | |||||||
\(662\) | −6.35516e12 | −1.28607 | ||||||||
\(663\) | 3.70047e11 | 0.0743782 | ||||||||
\(664\) | −7.51471e10 | −0.0150022 | ||||||||
\(665\) | 8.54585e12 | 1.69456 | ||||||||
\(666\) | 3.06469e11 | 0.0603604 | ||||||||
\(667\) | 2.62373e12 | 0.513278 | ||||||||
\(668\) | 4.61714e11 | 0.0897179 | ||||||||
\(669\) | 1.79473e12 | 0.346403 | ||||||||
\(670\) | 8.12320e12 | 1.55737 | ||||||||
\(671\) | 2.43328e12 | 0.463383 | ||||||||
\(672\) | 3.01008e11 | 0.0569399 | ||||||||
\(673\) | 2.28085e12 | 0.428577 | 0.214288 | − | 0.976770i | \(-0.431257\pi\) | ||||
0.214288 | + | 0.976770i | \(0.431257\pi\) | |||||||
\(674\) | 4.15700e12 | 0.775909 | ||||||||
\(675\) | 2.81903e12 | 0.522677 | ||||||||
\(676\) | −2.20054e12 | −0.405292 | ||||||||
\(677\) | −1.66591e11 | −0.0304791 | −0.0152396 | − | 0.999884i | \(-0.504851\pi\) | ||||
−0.0152396 | + | 0.999884i | \(0.504851\pi\) | |||||||
\(678\) | 5.74094e10 | 0.0104340 | ||||||||
\(679\) | 1.55316e12 | 0.280416 | ||||||||
\(680\) | 1.12480e12 | 0.201737 | ||||||||
\(681\) | 6.04363e12 | 1.07680 | ||||||||
\(682\) | −8.32064e10 | −0.0147274 | ||||||||
\(683\) | 6.38933e12 | 1.12347 | 0.561736 | − | 0.827317i | \(-0.310134\pi\) | ||||
0.561736 | + | 0.827317i | \(0.310134\pi\) | |||||||
\(684\) | −1.50340e12 | −0.262616 | ||||||||
\(685\) | −1.98413e13 | −3.44321 | ||||||||
\(686\) | −3.86422e12 | −0.666199 | ||||||||
\(687\) | −5.21887e12 | −0.893863 | ||||||||
\(688\) | −1.22965e12 | −0.209235 | ||||||||
\(689\) | −2.56590e12 | −0.433764 | ||||||||
\(690\) | 3.88595e12 | 0.652645 | ||||||||
\(691\) | 7.32350e12 | 1.22199 | 0.610995 | − | 0.791635i | \(-0.290770\pi\) | ||||
0.610995 | + | 0.791635i | \(0.290770\pi\) | |||||||
\(692\) | −2.28672e12 | −0.379084 | ||||||||
\(693\) | −6.87800e11 | −0.113282 | ||||||||
\(694\) | 5.21844e12 | 0.853931 | ||||||||
\(695\) | 1.21538e13 | 1.97597 | ||||||||
\(696\) | 7.82111e11 | 0.126336 | ||||||||
\(697\) | −2.67259e12 | −0.428928 | ||||||||
\(698\) | −2.47897e12 | −0.395295 | ||||||||
\(699\) | −1.42264e12 | −0.225397 | ||||||||
\(700\) | −4.81259e12 | −0.757596 | ||||||||
\(701\) | 8.91596e12 | 1.39456 | 0.697280 | − | 0.716799i | \(-0.254393\pi\) | ||||
0.697280 | + | 0.716799i | \(0.254393\pi\) | |||||||
\(702\) | 3.81090e11 | 0.0592257 | ||||||||
\(703\) | 2.61312e12 | 0.403516 | ||||||||
\(704\) | 4.96270e11 | 0.0761449 | ||||||||
\(705\) | −4.57511e12 | −0.697510 | ||||||||
\(706\) | −5.58355e12 | −0.845842 | ||||||||
\(707\) | −3.47525e12 | −0.523118 | ||||||||
\(708\) | 6.96472e11 | 0.104173 | ||||||||
\(709\) | 1.02284e13 | 1.52020 | 0.760099 | − | 0.649808i | \(-0.225151\pi\) | ||||
0.760099 | + | 0.649808i | \(0.225151\pi\) | |||||||
\(710\) | −3.48815e12 | −0.515149 | ||||||||
\(711\) | 3.45706e12 | 0.507333 | ||||||||
\(712\) | −2.82887e12 | −0.412528 | ||||||||
\(713\) | −1.95674e11 | −0.0283551 | ||||||||
\(714\) | −4.68185e11 | −0.0674180 | ||||||||
\(715\) | −3.57148e12 | −0.511059 | ||||||||
\(716\) | −1.09735e12 | −0.156040 | ||||||||
\(717\) | 6.31605e11 | 0.0892502 | ||||||||
\(718\) | −1.94989e12 | −0.273811 | ||||||||
\(719\) | −8.58812e12 | −1.19845 | −0.599223 | − | 0.800582i | \(-0.704524\pi\) | ||||
−0.599223 | + | 0.800582i | \(0.704524\pi\) | |||||||
\(720\) | 1.15837e12 | 0.160639 | ||||||||
\(721\) | −6.09244e12 | −0.839620 | ||||||||
\(722\) | −7.65580e12 | −1.04851 | ||||||||
\(723\) | 3.84217e11 | 0.0522943 | ||||||||
\(724\) | 2.22749e11 | 0.0301295 | ||||||||
\(725\) | −1.25046e13 | −1.68092 | ||||||||
\(726\) | 1.92193e12 | 0.256757 | ||||||||
\(727\) | 6.40806e12 | 0.850789 | 0.425395 | − | 0.905008i | \(-0.360135\pi\) | ||||
0.425395 | + | 0.905008i | \(0.360135\pi\) | |||||||
\(728\) | −6.50588e11 | −0.0858450 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 1.01786e13 | 1.32659 | ||||||||
\(731\) | 1.91258e12 | 0.247738 | ||||||||
\(732\) | 1.70576e12 | 0.219593 | ||||||||
\(733\) | 7.38425e12 | 0.944797 | 0.472398 | − | 0.881385i | \(-0.343388\pi\) | ||||
0.472398 | + | 0.881385i | \(0.343388\pi\) | |||||||
\(734\) | 8.13522e12 | 1.03452 | ||||||||
\(735\) | −6.06497e12 | −0.766541 | ||||||||
\(736\) | 1.16707e12 | 0.146604 | ||||||||
\(737\) | −5.57452e12 | −0.695992 | ||||||||
\(738\) | −2.75234e12 | −0.341546 | ||||||||
\(739\) | −1.13169e12 | −0.139581 | −0.0697907 | − | 0.997562i | \(-0.522233\pi\) | ||||
−0.0697907 | + | 0.997562i | \(0.522233\pi\) | |||||||
\(740\) | −2.01342e12 | −0.246826 | ||||||||
\(741\) | 3.24939e12 | 0.395931 | ||||||||
\(742\) | 3.24639e12 | 0.393173 | ||||||||
\(743\) | 4.62444e12 | 0.556685 | 0.278343 | − | 0.960482i | \(-0.410215\pi\) | ||||
0.278343 | + | 0.960482i | \(0.410215\pi\) | |||||||
\(744\) | −5.83289e10 | −0.00697920 | ||||||||
\(745\) | −2.97775e12 | −0.354148 | ||||||||
\(746\) | 4.09722e12 | 0.484356 | ||||||||
\(747\) | 1.20371e11 | 0.0141442 | ||||||||
\(748\) | −7.71893e11 | −0.0901571 | ||||||||
\(749\) | −1.50622e12 | −0.174872 | ||||||||
\(750\) | −1.17011e13 | −1.35037 | ||||||||
\(751\) | −3.04009e12 | −0.348744 | −0.174372 | − | 0.984680i | \(-0.555790\pi\) | ||||
−0.174372 | + | 0.984680i | \(0.555790\pi\) | |||||||
\(752\) | −1.37404e12 | −0.156682 | ||||||||
\(753\) | −3.82627e12 | −0.433709 | ||||||||
\(754\) | −1.69042e12 | −0.190469 | ||||||||
\(755\) | 2.77496e13 | 3.10810 | ||||||||
\(756\) | −4.82157e11 | −0.0536835 | ||||||||
\(757\) | 1.21727e13 | 1.34727 | 0.673636 | − | 0.739063i | \(-0.264731\pi\) | ||||
0.673636 | + | 0.739063i | \(0.264731\pi\) | |||||||
\(758\) | 8.85200e11 | 0.0973934 | ||||||||
\(759\) | −2.66673e12 | −0.291669 | ||||||||
\(760\) | 9.87692e12 | 1.07389 | ||||||||
\(761\) | −1.48757e13 | −1.60786 | −0.803928 | − | 0.594727i | \(-0.797260\pi\) | ||||
−0.803928 | + | 0.594727i | \(0.797260\pi\) | |||||||
\(762\) | 4.08039e12 | 0.438434 | ||||||||
\(763\) | −3.09994e12 | −0.331126 | ||||||||
\(764\) | 8.17779e12 | 0.868392 | ||||||||
\(765\) | −1.80172e12 | −0.190200 | ||||||||
\(766\) | 1.30363e12 | 0.136813 | ||||||||
\(767\) | −1.50533e12 | −0.157055 | ||||||||
\(768\) | 3.47892e11 | 0.0360844 | ||||||||
\(769\) | −4.34675e10 | −0.00448225 | −0.00224112 | − | 0.999997i | \(-0.500713\pi\) | ||||
−0.00224112 | + | 0.999997i | \(0.500713\pi\) | |||||||
\(770\) | 4.51866e12 | 0.463235 | ||||||||
\(771\) | 6.05083e12 | 0.616695 | ||||||||
\(772\) | 1.25399e12 | 0.127063 | ||||||||
\(773\) | −6.97640e12 | −0.702787 | −0.351393 | − | 0.936228i | \(-0.614292\pi\) | ||||
−0.351393 | + | 0.936228i | \(0.614292\pi\) | |||||||
\(774\) | 1.96966e12 | 0.197268 | ||||||||
\(775\) | 9.32575e11 | 0.0928595 | ||||||||
\(776\) | 1.79508e12 | 0.177707 | ||||||||
\(777\) | 8.38060e11 | 0.0824860 | ||||||||
\(778\) | −9.61940e12 | −0.941325 | ||||||||
\(779\) | −2.34680e13 | −2.28327 | ||||||||
\(780\) | −2.50366e12 | −0.242186 | ||||||||
\(781\) | 2.39373e12 | 0.230222 | ||||||||
\(782\) | −1.81524e12 | −0.173582 | ||||||||
\(783\) | −1.25279e12 | −0.119111 | ||||||||
\(784\) | −1.82149e12 | −0.172188 | ||||||||
\(785\) | −1.89584e12 | −0.178192 | ||||||||
\(786\) | 5.39561e12 | 0.504242 | ||||||||
\(787\) | −1.28564e13 | −1.19463 | −0.597315 | − | 0.802007i | \(-0.703766\pi\) | ||||
−0.597315 | + | 0.802007i | \(0.703766\pi\) | |||||||
\(788\) | 5.57659e12 | 0.515230 | ||||||||
\(789\) | 2.49470e12 | 0.229178 | ||||||||
\(790\) | −2.27119e13 | −2.07459 | ||||||||
\(791\) | 1.56990e11 | 0.0142586 | ||||||||
\(792\) | −7.94929e11 | −0.0717901 | ||||||||
\(793\) | −3.68677e12 | −0.331067 | ||||||||
\(794\) | −2.09705e11 | −0.0187248 | ||||||||
\(795\) | 1.24931e13 | 1.10922 | ||||||||
\(796\) | −9.57862e12 | −0.845657 | ||||||||
\(797\) | 1.84132e13 | 1.61647 | 0.808233 | − | 0.588862i | \(-0.200424\pi\) | ||||
0.808233 | + | 0.588862i | \(0.200424\pi\) | |||||||
\(798\) | −4.11114e12 | −0.358880 | ||||||||
\(799\) | 2.13716e12 | 0.185514 | ||||||||
\(800\) | −5.56218e12 | −0.480110 | ||||||||
\(801\) | 4.53131e12 | 0.388935 | ||||||||
\(802\) | 9.57041e12 | 0.816857 | ||||||||
\(803\) | −6.98505e12 | −0.592856 | ||||||||
\(804\) | −3.90782e12 | −0.329824 | ||||||||
\(805\) | 1.06264e13 | 0.891877 | ||||||||
\(806\) | 1.26070e11 | 0.0105221 | ||||||||
\(807\) | −1.21001e13 | −1.00429 | ||||||||
\(808\) | −4.01655e12 | −0.331514 | ||||||||
\(809\) | −5.67875e12 | −0.466106 | −0.233053 | − | 0.972464i | \(-0.574872\pi\) | ||||
−0.233053 | + | 0.972464i | \(0.574872\pi\) | |||||||
\(810\) | −1.85549e12 | −0.151452 | ||||||||
\(811\) | −5.49523e12 | −0.446058 | −0.223029 | − | 0.974812i | \(-0.571595\pi\) | ||||
−0.223029 | + | 0.974812i | \(0.571595\pi\) | |||||||
\(812\) | 2.13874e12 | 0.172645 | ||||||||
\(813\) | 1.07010e13 | 0.859047 | ||||||||
\(814\) | 1.38170e12 | 0.110307 | ||||||||
\(815\) | 2.96827e13 | 2.35664 | ||||||||
\(816\) | −5.41108e11 | −0.0427246 | ||||||||
\(817\) | 1.67944e13 | 1.31876 | ||||||||
\(818\) | 3.16346e12 | 0.247043 | ||||||||
\(819\) | 1.04212e12 | 0.0809354 | ||||||||
\(820\) | 1.80822e13 | 1.39665 | ||||||||
\(821\) | 1.56831e12 | 0.120473 | 0.0602363 | − | 0.998184i | \(-0.480815\pi\) | ||||
0.0602363 | + | 0.998184i | \(0.480815\pi\) | |||||||
\(822\) | 9.54505e12 | 0.729214 | ||||||||
\(823\) | −1.46315e13 | −1.11171 | −0.555853 | − | 0.831281i | \(-0.687608\pi\) | ||||
−0.555853 | + | 0.831281i | \(0.687608\pi\) | |||||||
\(824\) | −7.04138e12 | −0.532090 | ||||||||
\(825\) | 1.27095e13 | 0.955181 | ||||||||
\(826\) | 1.90455e12 | 0.142358 | ||||||||
\(827\) | −3.06631e11 | −0.0227951 | −0.0113975 | − | 0.999935i | \(-0.503628\pi\) | ||||
−0.0113975 | + | 0.999935i | \(0.503628\pi\) | |||||||
\(828\) | −1.86941e12 | −0.138219 | ||||||||
\(829\) | −1.41184e13 | −1.03822 | −0.519112 | − | 0.854706i | \(-0.673737\pi\) | ||||
−0.519112 | + | 0.854706i | \(0.673737\pi\) | |||||||
\(830\) | −7.90805e11 | −0.0578387 | ||||||||
\(831\) | −7.44567e12 | −0.541626 | ||||||||
\(832\) | −7.51921e11 | −0.0544023 | ||||||||
\(833\) | 2.83312e12 | 0.203874 | ||||||||
\(834\) | −5.84682e12 | −0.418478 | ||||||||
\(835\) | 4.85882e12 | 0.345893 | ||||||||
\(836\) | −6.77801e12 | −0.479925 | ||||||||
\(837\) | 9.34316e10 | 0.00658005 | ||||||||
\(838\) | −5.40285e12 | −0.378464 | ||||||||
\(839\) | −6.59420e12 | −0.459445 | −0.229722 | − | 0.973256i | \(-0.573782\pi\) | ||||
−0.229722 | + | 0.973256i | \(0.573782\pi\) | |||||||
\(840\) | 3.16764e12 | 0.219523 | ||||||||
\(841\) | −8.95007e12 | −0.616942 | ||||||||
\(842\) | 1.71774e12 | 0.117775 | ||||||||
\(843\) | −5.03208e12 | −0.343181 | ||||||||
\(844\) | 1.46969e12 | 0.0996973 | ||||||||
\(845\) | −2.31572e13 | −1.56254 | ||||||||
\(846\) | 2.20094e12 | 0.147721 | ||||||||
\(847\) | 5.25565e12 | 0.350874 | ||||||||
\(848\) | 3.75204e12 | 0.249164 | ||||||||
\(849\) | −1.18507e13 | −0.782816 | ||||||||
\(850\) | 8.65136e12 | 0.568459 | ||||||||
\(851\) | 3.24931e12 | 0.212377 | ||||||||
\(852\) | 1.67804e12 | 0.109100 | ||||||||
\(853\) | 7.39373e12 | 0.478182 | 0.239091 | − | 0.970997i | \(-0.423151\pi\) | ||||
0.239091 | + | 0.970997i | \(0.423151\pi\) | |||||||
\(854\) | 4.66452e12 | 0.300086 | ||||||||
\(855\) | −1.58209e13 | −1.01247 | ||||||||
\(856\) | −1.74082e12 | −0.110821 | ||||||||
\(857\) | 2.16563e13 | 1.37142 | 0.685710 | − | 0.727875i | \(-0.259492\pi\) | ||||
0.685710 | + | 0.727875i | \(0.259492\pi\) | |||||||
\(858\) | 1.71813e12 | 0.108234 | ||||||||
\(859\) | 1.80961e12 | 0.113401 | 0.0567004 | − | 0.998391i | \(-0.481942\pi\) | ||||
0.0567004 | + | 0.998391i | \(0.481942\pi\) | |||||||
\(860\) | −1.29401e13 | −0.806670 | ||||||||
\(861\) | −7.52647e12 | −0.466742 | ||||||||
\(862\) | 1.10777e13 | 0.683384 | ||||||||
\(863\) | −5.09775e12 | −0.312846 | −0.156423 | − | 0.987690i | \(-0.549996\pi\) | ||||
−0.156423 | + | 0.987690i | \(0.549996\pi\) | |||||||
\(864\) | −5.57256e11 | −0.0340207 | ||||||||
\(865\) | −2.40642e13 | −1.46150 | ||||||||
\(866\) | 1.66215e13 | 1.00425 | ||||||||
\(867\) | −8.76398e12 | −0.526763 | ||||||||
\(868\) | −1.59504e11 | −0.00953748 | ||||||||
\(869\) | 1.55860e13 | 0.927140 | ||||||||
\(870\) | 8.23049e12 | 0.487068 | ||||||||
\(871\) | 8.44621e12 | 0.497256 | ||||||||
\(872\) | −3.58277e12 | −0.209843 | ||||||||
\(873\) | −2.87537e12 | −0.167544 | ||||||||
\(874\) | −1.59397e13 | −0.924012 | ||||||||
\(875\) | −3.19975e13 | −1.84535 | ||||||||
\(876\) | −4.89662e12 | −0.280949 | ||||||||
\(877\) | 2.30219e13 | 1.31415 | 0.657073 | − | 0.753827i | \(-0.271794\pi\) | ||||
0.657073 | + | 0.753827i | \(0.271794\pi\) | |||||||
\(878\) | −1.45885e13 | −0.828486 | ||||||||
\(879\) | 7.81818e12 | 0.441729 | ||||||||
\(880\) | 5.22247e12 | 0.293565 | ||||||||
\(881\) | −2.78088e13 | −1.55522 | −0.777608 | − | 0.628749i | \(-0.783567\pi\) | ||||
−0.777608 | + | 0.628749i | \(0.783567\pi\) | |||||||
\(882\) | 2.91767e12 | 0.162341 | ||||||||
\(883\) | 2.53234e13 | 1.40184 | 0.700922 | − | 0.713238i | \(-0.252772\pi\) | ||||
0.700922 | + | 0.713238i | \(0.252772\pi\) | |||||||
\(884\) | 1.16953e12 | 0.0644134 | ||||||||
\(885\) | 7.32928e12 | 0.401621 | ||||||||
\(886\) | 1.26128e13 | 0.687640 | ||||||||
\(887\) | 2.70530e13 | 1.46744 | 0.733718 | − | 0.679454i | \(-0.237784\pi\) | ||||
0.733718 | + | 0.679454i | \(0.237784\pi\) | |||||||
\(888\) | 9.68593e11 | 0.0522737 | ||||||||
\(889\) | 1.11581e13 | 0.599146 | ||||||||
\(890\) | −2.97695e13 | −1.59044 | ||||||||
\(891\) | 1.27332e12 | 0.0676844 | ||||||||
\(892\) | 5.67223e12 | 0.299993 | ||||||||
\(893\) | 1.87665e13 | 0.987532 | ||||||||
\(894\) | 1.43250e12 | 0.0750027 | ||||||||
\(895\) | −1.15479e13 | −0.601587 | ||||||||
\(896\) | 9.51335e11 | 0.0493114 | ||||||||
\(897\) | 4.04048e12 | 0.208385 | ||||||||
\(898\) | 1.16590e13 | 0.598298 | ||||||||
\(899\) | −4.14440e11 | −0.0211613 | ||||||||
\(900\) | 8.90954e12 | 0.452652 | ||||||||
\(901\) | −5.83588e12 | −0.295016 | ||||||||
\(902\) | −1.24088e13 | −0.624168 | ||||||||
\(903\) | 5.38617e12 | 0.269579 | ||||||||
\(904\) | 1.81442e11 | 0.00903608 | ||||||||
\(905\) | 2.34409e12 | 0.116160 | ||||||||
\(906\) | −1.33495e13 | −0.658244 | ||||||||
\(907\) | −3.10370e13 | −1.52282 | −0.761408 | − | 0.648273i | \(-0.775492\pi\) | ||||
−0.761408 | + | 0.648273i | \(0.775492\pi\) | |||||||
\(908\) | 1.91009e13 | 0.932538 | ||||||||
\(909\) | 6.43373e12 | 0.312554 | ||||||||
\(910\) | −6.84642e12 | −0.330962 | ||||||||
\(911\) | 3.06827e13 | 1.47591 | 0.737956 | − | 0.674849i | \(-0.235791\pi\) | ||||
0.737956 | + | 0.674849i | \(0.235791\pi\) | |||||||
\(912\) | −4.75148e12 | −0.227432 | ||||||||
\(913\) | 5.42688e11 | 0.0258483 | ||||||||
\(914\) | 2.49195e12 | 0.118109 | ||||||||
\(915\) | 1.79505e13 | 0.846605 | ||||||||
\(916\) | −1.64942e13 | −0.774108 | ||||||||
\(917\) | 1.47547e13 | 0.689077 | ||||||||
\(918\) | 8.66751e11 | 0.0402812 | ||||||||
\(919\) | −1.40349e13 | −0.649067 | −0.324534 | − | 0.945874i | \(-0.605207\pi\) | ||||
−0.324534 | + | 0.945874i | \(0.605207\pi\) | |||||||
\(920\) | 1.22815e13 | 0.565207 | ||||||||
\(921\) | −2.22648e13 | −1.01965 | ||||||||
\(922\) | −9.35554e12 | −0.426363 | ||||||||
\(923\) | −3.62685e12 | −0.164484 | ||||||||
\(924\) | −2.17379e12 | −0.0981054 | ||||||||
\(925\) | −1.54861e13 | −0.695511 | ||||||||
\(926\) | −3.17207e12 | −0.141773 | ||||||||
\(927\) | 1.12789e13 | 0.501660 | ||||||||
\(928\) | 2.47186e12 | 0.109410 | ||||||||
\(929\) | −5.44440e12 | −0.239816 | −0.119908 | − | 0.992785i | \(-0.538260\pi\) | ||||
−0.119908 | + | 0.992785i | \(0.538260\pi\) | |||||||
\(930\) | −6.13820e11 | −0.0269072 | ||||||||
\(931\) | 2.48777e13 | 1.08527 | ||||||||
\(932\) | −4.49626e12 | −0.195200 | ||||||||
\(933\) | −1.46849e13 | −0.634458 | ||||||||
\(934\) | −3.05574e13 | −1.31388 | ||||||||
\(935\) | −8.12297e12 | −0.347586 | ||||||||
\(936\) | 1.20443e12 | 0.0512910 | ||||||||
\(937\) | −2.11139e13 | −0.894828 | −0.447414 | − | 0.894327i | \(-0.647655\pi\) | ||||
−0.447414 | + | 0.894327i | \(0.647655\pi\) | |||||||
\(938\) | −1.06862e13 | −0.450724 | ||||||||
\(939\) | 1.28806e13 | 0.540682 | ||||||||
\(940\) | −1.44596e13 | −0.604061 | ||||||||
\(941\) | −1.76055e13 | −0.731975 | −0.365987 | − | 0.930620i | \(-0.619269\pi\) | ||||
−0.365987 | + | 0.930620i | \(0.619269\pi\) | |||||||
\(942\) | 9.12029e11 | 0.0377381 | ||||||||
\(943\) | −2.91815e13 | −1.20173 | ||||||||
\(944\) | 2.20120e12 | 0.0902162 | ||||||||
\(945\) | −5.07395e12 | −0.206968 | ||||||||
\(946\) | 8.88014e12 | 0.360503 | ||||||||
\(947\) | −2.81821e13 | −1.13867 | −0.569336 | − | 0.822105i | \(-0.692800\pi\) | ||||
−0.569336 | + | 0.822105i | \(0.692800\pi\) | |||||||
\(948\) | 1.09260e13 | 0.439363 | ||||||||
\(949\) | 1.05834e13 | 0.423571 | ||||||||
\(950\) | 7.59677e13 | 3.02603 | ||||||||
\(951\) | 1.58343e13 | 0.627751 | ||||||||
\(952\) | −1.47970e12 | −0.0583857 | ||||||||
\(953\) | −4.80527e13 | −1.88712 | −0.943561 | − | 0.331198i | \(-0.892547\pi\) | ||||
−0.943561 | + | 0.331198i | \(0.892547\pi\) | |||||||
\(954\) | −6.01004e12 | −0.234914 | ||||||||
\(955\) | 8.60584e13 | 3.34795 | ||||||||
\(956\) | 1.99618e12 | 0.0772929 | ||||||||
\(957\) | −5.64815e12 | −0.217672 | ||||||||
\(958\) | 2.39365e13 | 0.918153 | ||||||||
\(959\) | 2.61016e13 | 0.996513 | ||||||||
\(960\) | 3.66102e12 | 0.139118 | ||||||||
\(961\) | −2.64087e13 | −0.998831 | ||||||||
\(962\) | −2.09348e12 | −0.0788099 | ||||||||
\(963\) | 2.78846e12 | 0.104483 | ||||||||
\(964\) | 1.21432e12 | 0.0452882 | ||||||||
\(965\) | 1.31963e13 | 0.489869 | ||||||||
\(966\) | −5.11204e12 | −0.188885 | ||||||||
\(967\) | −4.11360e13 | −1.51287 | −0.756437 | − | 0.654066i | \(-0.773062\pi\) | ||||
−0.756437 | + | 0.654066i | \(0.773062\pi\) | |||||||
\(968\) | 6.07425e12 | 0.222358 | ||||||||
\(969\) | 7.39040e12 | 0.269284 | ||||||||
\(970\) | 1.88904e13 | 0.685122 | ||||||||
\(971\) | 1.02331e13 | 0.369419 | 0.184709 | − | 0.982793i | \(-0.440866\pi\) | ||||
0.184709 | + | 0.982793i | \(0.440866\pi\) | |||||||
\(972\) | 8.92617e11 | 0.0320750 | ||||||||
\(973\) | −1.59885e13 | −0.571874 | ||||||||
\(974\) | −5.72666e12 | −0.203885 | ||||||||
\(975\) | −1.92567e13 | −0.682436 | ||||||||
\(976\) | 5.39105e12 | 0.190173 | ||||||||
\(977\) | 3.01369e13 | 1.05821 | 0.529107 | − | 0.848555i | \(-0.322527\pi\) | ||||
0.529107 | + | 0.848555i | \(0.322527\pi\) | |||||||
\(978\) | −1.42794e13 | −0.499098 | ||||||||
\(979\) | 2.04292e13 | 0.710771 | ||||||||
\(980\) | −1.91683e13 | −0.663844 | ||||||||
\(981\) | 5.73891e12 | 0.197842 | ||||||||
\(982\) | −1.15722e13 | −0.397113 | ||||||||
\(983\) | −1.71235e13 | −0.584926 | −0.292463 | − | 0.956277i | \(-0.594475\pi\) | ||||
−0.292463 | + | 0.956277i | \(0.594475\pi\) | |||||||
\(984\) | −8.69877e12 | −0.295787 | ||||||||
\(985\) | 5.86849e13 | 1.98638 | ||||||||
\(986\) | −3.84470e12 | −0.129544 | ||||||||
\(987\) | 6.01863e12 | 0.201869 | ||||||||
\(988\) | 1.02697e13 | 0.342886 | ||||||||
\(989\) | 2.08832e13 | 0.694086 | ||||||||
\(990\) | −8.36538e12 | −0.276775 | ||||||||
\(991\) | 3.26099e13 | 1.07403 | 0.537016 | − | 0.843572i | \(-0.319551\pi\) | ||||
0.537016 | + | 0.843572i | \(0.319551\pi\) | |||||||
\(992\) | −1.84348e11 | −0.00604416 | ||||||||
\(993\) | 3.21730e13 | 1.05007 | ||||||||
\(994\) | 4.58872e12 | 0.149091 | ||||||||
\(995\) | −1.00800e14 | −3.26029 | ||||||||
\(996\) | 3.80432e11 | 0.0122493 | ||||||||
\(997\) | −3.52071e13 | −1.12850 | −0.564251 | − | 0.825603i | \(-0.690835\pi\) | ||||
−0.564251 | + | 0.825603i | \(0.690835\pi\) | |||||||
\(998\) | 9.85781e12 | 0.314552 | ||||||||
\(999\) | −1.55150e12 | −0.0492841 |
(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 | 6.10.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 18.10.a.c.1.1 | 1 | |||
4.3 | odd | 2 | 48.10.a.d.1.1 | 1 | |||
5.2 | odd | 4 | 150.10.c.d.49.1 | 2 | |||
5.3 | odd | 4 | 150.10.c.d.49.2 | 2 | |||
5.4 | even | 2 | 150.10.a.h.1.1 | 1 | |||
7.6 | odd | 2 | 294.10.a.a.1.1 | 1 | |||
8.3 | odd | 2 | 192.10.a.h.1.1 | 1 | |||
8.5 | even | 2 | 192.10.a.a.1.1 | 1 | |||
9.2 | odd | 6 | 162.10.c.e.109.1 | 2 | |||
9.4 | even | 3 | 162.10.c.f.55.1 | 2 | |||
9.5 | odd | 6 | 162.10.c.e.55.1 | 2 | |||
9.7 | even | 3 | 162.10.c.f.109.1 | 2 | |||
12.11 | even | 2 | 144.10.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.10.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
18.10.a.c.1.1 | 1 | 3.2 | odd | 2 | |||
48.10.a.d.1.1 | 1 | 4.3 | odd | 2 | |||
144.10.a.a.1.1 | 1 | 12.11 | even | 2 | |||
150.10.a.h.1.1 | 1 | 5.4 | even | 2 | |||
150.10.c.d.49.1 | 2 | 5.2 | odd | 4 | |||
150.10.c.d.49.2 | 2 | 5.3 | odd | 4 | |||
162.10.c.e.55.1 | 2 | 9.5 | odd | 6 | |||
162.10.c.e.109.1 | 2 | 9.2 | odd | 6 | |||
162.10.c.f.55.1 | 2 | 9.4 | even | 3 | |||
162.10.c.f.109.1 | 2 | 9.7 | even | 3 | |||
192.10.a.a.1.1 | 1 | 8.5 | even | 2 | |||
192.10.a.h.1.1 | 1 | 8.3 | odd | 2 | |||
294.10.a.a.1.1 | 1 | 7.6 | odd | 2 |