Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,18,Mod(1,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(53.1344053299\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 29.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 361.094 | 0.997391 | 0.498695 | − | 0.866777i | \(-0.333813\pi\) | ||||
0.498695 | + | 0.866777i | \(0.333813\pi\) | |||||||
\(3\) | −2259.76 | −0.198852 | −0.0994262 | − | 0.995045i | \(-0.531701\pi\) | ||||
−0.0994262 | + | 0.995045i | \(0.531701\pi\) | |||||||
\(4\) | −683.052 | −0.00521127 | ||||||||
\(5\) | −433238. | −0.496000 | −0.248000 | − | 0.968760i | \(-0.579773\pi\) | ||||
−0.248000 | + | 0.968760i | \(0.579773\pi\) | |||||||
\(6\) | −815984. | −0.198334 | ||||||||
\(7\) | −1.41185e7 | −0.925665 | −0.462833 | − | 0.886446i | \(-0.653167\pi\) | ||||
−0.462833 | + | 0.886446i | \(0.653167\pi\) | |||||||
\(8\) | −4.75760e7 | −1.00259 | ||||||||
\(9\) | −1.24034e8 | −0.960458 | ||||||||
\(10\) | −1.56440e8 | −0.494706 | ||||||||
\(11\) | −2.28788e8 | −0.321807 | −0.160903 | − | 0.986970i | \(-0.551441\pi\) | ||||
−0.160903 | + | 0.986970i | \(0.551441\pi\) | |||||||
\(12\) | 1.54353e6 | 0.00103627 | ||||||||
\(13\) | 4.30393e9 | 1.46335 | 0.731673 | − | 0.681656i | \(-0.238740\pi\) | ||||
0.731673 | + | 0.681656i | \(0.238740\pi\) | |||||||
\(14\) | −5.09809e9 | −0.923250 | ||||||||
\(15\) | 9.79012e8 | 0.0986307 | ||||||||
\(16\) | −1.70899e10 | −0.994762 | ||||||||
\(17\) | 3.47755e10 | 1.20909 | 0.604543 | − | 0.796572i | \(-0.293356\pi\) | ||||
0.604543 | + | 0.796572i | \(0.293356\pi\) | |||||||
\(18\) | −4.47878e10 | −0.957952 | ||||||||
\(19\) | 4.54956e10 | 0.614559 | 0.307279 | − | 0.951619i | \(-0.400581\pi\) | ||||
0.307279 | + | 0.951619i | \(0.400581\pi\) | |||||||
\(20\) | 2.95924e8 | 0.00258479 | ||||||||
\(21\) | 3.19043e10 | 0.184071 | ||||||||
\(22\) | −8.26139e10 | −0.320967 | ||||||||
\(23\) | 7.89750e10 | 0.210282 | 0.105141 | − | 0.994457i | \(-0.466471\pi\) | ||||
0.105141 | + | 0.994457i | \(0.466471\pi\) | |||||||
\(24\) | 1.07510e11 | 0.199367 | ||||||||
\(25\) | −5.75244e11 | −0.753984 | ||||||||
\(26\) | 1.55413e12 | 1.45953 | ||||||||
\(27\) | 5.72111e11 | 0.389842 | ||||||||
\(28\) | 9.64364e9 | 0.00482389 | ||||||||
\(29\) | 5.00246e11 | 0.185695 | ||||||||
\(30\) | 3.53515e11 | 0.0983734 | ||||||||
\(31\) | −1.07216e12 | −0.225780 | −0.112890 | − | 0.993607i | \(-0.536011\pi\) | ||||
−0.112890 | + | 0.993607i | \(0.536011\pi\) | |||||||
\(32\) | 6.48253e10 | 0.0104224 | ||||||||
\(33\) | 5.17005e11 | 0.0639920 | ||||||||
\(34\) | 1.25572e13 | 1.20593 | ||||||||
\(35\) | 6.11665e12 | 0.459130 | ||||||||
\(36\) | 8.47215e10 | 0.00500521 | ||||||||
\(37\) | 2.06120e13 | 0.964729 | 0.482364 | − | 0.875971i | \(-0.339778\pi\) | ||||
0.482364 | + | 0.875971i | \(0.339778\pi\) | |||||||
\(38\) | 1.64282e13 | 0.612955 | ||||||||
\(39\) | −9.72584e12 | −0.290990 | ||||||||
\(40\) | 2.06117e13 | 0.497284 | ||||||||
\(41\) | −5.29668e12 | −0.103595 | −0.0517977 | − | 0.998658i | \(-0.516495\pi\) | ||||
−0.0517977 | + | 0.998658i | \(0.516495\pi\) | |||||||
\(42\) | 1.15204e13 | 0.183590 | ||||||||
\(43\) | 4.56833e13 | 0.596040 | 0.298020 | − | 0.954560i | \(-0.403674\pi\) | ||||
0.298020 | + | 0.954560i | \(0.403674\pi\) | |||||||
\(44\) | 1.56274e11 | 0.00167702 | ||||||||
\(45\) | 5.37361e13 | 0.476387 | ||||||||
\(46\) | 2.85174e13 | 0.209734 | ||||||||
\(47\) | −5.43318e13 | −0.332830 | −0.166415 | − | 0.986056i | \(-0.553219\pi\) | ||||
−0.166415 | + | 0.986056i | \(0.553219\pi\) | |||||||
\(48\) | 3.86189e13 | 0.197811 | ||||||||
\(49\) | −3.32996e13 | −0.143144 | ||||||||
\(50\) | −2.07717e14 | −0.752017 | ||||||||
\(51\) | −7.85841e13 | −0.240430 | ||||||||
\(52\) | −2.93981e12 | −0.00762590 | ||||||||
\(53\) | −1.49915e14 | −0.330750 | −0.165375 | − | 0.986231i | \(-0.552883\pi\) | ||||
−0.165375 | + | 0.986231i | \(0.552883\pi\) | |||||||
\(54\) | 2.06586e14 | 0.388824 | ||||||||
\(55\) | 9.91196e13 | 0.159616 | ||||||||
\(56\) | 6.71699e14 | 0.928061 | ||||||||
\(57\) | −1.02809e14 | −0.122206 | ||||||||
\(58\) | 1.80636e14 | 0.185211 | ||||||||
\(59\) | −2.63283e14 | −0.233443 | −0.116722 | − | 0.993165i | \(-0.537239\pi\) | ||||
−0.116722 | + | 0.993165i | \(0.537239\pi\) | |||||||
\(60\) | −6.68716e11 | −0.000513992 0 | ||||||||
\(61\) | 6.02615e14 | 0.402472 | 0.201236 | − | 0.979543i | \(-0.435504\pi\) | ||||
0.201236 | + | 0.979543i | \(0.435504\pi\) | |||||||
\(62\) | −3.87151e14 | −0.225191 | ||||||||
\(63\) | 1.75116e15 | 0.889062 | ||||||||
\(64\) | 2.26341e15 | 1.00516 | ||||||||
\(65\) | −1.86463e15 | −0.725819 | ||||||||
\(66\) | 1.86687e14 | 0.0638251 | ||||||||
\(67\) | 1.53138e15 | 0.460730 | 0.230365 | − | 0.973104i | \(-0.426008\pi\) | ||||
0.230365 | + | 0.973104i | \(0.426008\pi\) | |||||||
\(68\) | −2.37535e13 | −0.00630088 | ||||||||
\(69\) | −1.78464e14 | −0.0418152 | ||||||||
\(70\) | 2.20869e15 | 0.457932 | ||||||||
\(71\) | 9.32986e15 | 1.71466 | 0.857332 | − | 0.514763i | \(-0.172120\pi\) | ||||
0.857332 | + | 0.514763i | \(0.172120\pi\) | |||||||
\(72\) | 5.90102e15 | 0.962944 | ||||||||
\(73\) | −9.89992e14 | −0.143677 | −0.0718385 | − | 0.997416i | \(-0.522887\pi\) | ||||
−0.0718385 | + | 0.997416i | \(0.522887\pi\) | |||||||
\(74\) | 7.44287e15 | 0.962212 | ||||||||
\(75\) | 1.29991e15 | 0.149932 | ||||||||
\(76\) | −3.10758e13 | −0.00320263 | ||||||||
\(77\) | 3.23013e15 | 0.297885 | ||||||||
\(78\) | −3.51194e15 | −0.290231 | ||||||||
\(79\) | 6.42999e15 | 0.476848 | 0.238424 | − | 0.971161i | \(-0.423369\pi\) | ||||
0.238424 | + | 0.971161i | \(0.423369\pi\) | |||||||
\(80\) | 7.40398e15 | 0.493402 | ||||||||
\(81\) | 1.47249e16 | 0.882937 | ||||||||
\(82\) | −1.91260e15 | −0.103325 | ||||||||
\(83\) | 2.58298e16 | 1.25880 | 0.629401 | − | 0.777080i | \(-0.283300\pi\) | ||||
0.629401 | + | 0.777080i | \(0.283300\pi\) | |||||||
\(84\) | −2.17923e13 | −0.000959243 0 | ||||||||
\(85\) | −1.50661e16 | −0.599707 | ||||||||
\(86\) | 1.64960e16 | 0.594485 | ||||||||
\(87\) | −1.13043e15 | −0.0369260 | ||||||||
\(88\) | 1.08848e16 | 0.322640 | ||||||||
\(89\) | −4.98199e16 | −1.34149 | −0.670745 | − | 0.741688i | \(-0.734026\pi\) | ||||
−0.670745 | + | 0.741688i | \(0.734026\pi\) | |||||||
\(90\) | 1.94038e16 | 0.475144 | ||||||||
\(91\) | −6.07649e16 | −1.35457 | ||||||||
\(92\) | −5.39440e13 | −0.00109584 | ||||||||
\(93\) | 2.42282e15 | 0.0448969 | ||||||||
\(94\) | −1.96189e16 | −0.331961 | ||||||||
\(95\) | −1.97104e16 | −0.304821 | ||||||||
\(96\) | −1.46489e14 | −0.00207253 | ||||||||
\(97\) | 4.02028e16 | 0.520831 | 0.260415 | − | 0.965497i | \(-0.416140\pi\) | ||||
0.260415 | + | 0.965497i | \(0.416140\pi\) | |||||||
\(98\) | −1.20243e16 | −0.142770 | ||||||||
\(99\) | 2.83774e16 | 0.309082 | ||||||||
\(100\) | 3.92922e14 | 0.00392922 | ||||||||
\(101\) | −1.37975e17 | −1.26785 | −0.633925 | − | 0.773395i | \(-0.718557\pi\) | ||||
−0.633925 | + | 0.773395i | \(0.718557\pi\) | |||||||
\(102\) | −2.83763e16 | −0.239802 | ||||||||
\(103\) | 4.22562e16 | 0.328681 | 0.164340 | − | 0.986404i | \(-0.447450\pi\) | ||||
0.164340 | + | 0.986404i | \(0.447450\pi\) | |||||||
\(104\) | −2.04764e17 | −1.46713 | ||||||||
\(105\) | −1.38221e16 | −0.0912990 | ||||||||
\(106\) | −5.41334e16 | −0.329887 | ||||||||
\(107\) | −2.50719e17 | −1.41067 | −0.705335 | − | 0.708874i | \(-0.749204\pi\) | ||||
−0.705335 | + | 0.708874i | \(0.749204\pi\) | |||||||
\(108\) | −3.90782e14 | −0.00203157 | ||||||||
\(109\) | −3.12026e16 | −0.149991 | −0.0749956 | − | 0.997184i | \(-0.523894\pi\) | ||||
−0.0749956 | + | 0.997184i | \(0.523894\pi\) | |||||||
\(110\) | 3.57915e16 | 0.159200 | ||||||||
\(111\) | −4.65780e16 | −0.191839 | ||||||||
\(112\) | 2.41283e17 | 0.920816 | ||||||||
\(113\) | 3.91401e17 | 1.38502 | 0.692509 | − | 0.721409i | \(-0.256505\pi\) | ||||
0.692509 | + | 0.721409i | \(0.256505\pi\) | |||||||
\(114\) | −3.71237e16 | −0.121888 | ||||||||
\(115\) | −3.42150e16 | −0.104300 | ||||||||
\(116\) | −3.41694e14 | −0.000967709 0 | ||||||||
\(117\) | −5.33833e17 | −1.40548 | ||||||||
\(118\) | −9.50701e16 | −0.232834 | ||||||||
\(119\) | −4.90976e17 | −1.11921 | ||||||||
\(120\) | −4.65774e16 | −0.0988860 | ||||||||
\(121\) | −4.53103e17 | −0.896440 | ||||||||
\(122\) | 2.17601e17 | 0.401422 | ||||||||
\(123\) | 1.19692e16 | 0.0206002 | ||||||||
\(124\) | 7.32342e14 | 0.00117660 | ||||||||
\(125\) | 5.79752e17 | 0.869976 | ||||||||
\(126\) | 6.32335e17 | 0.886743 | ||||||||
\(127\) | 8.79572e17 | 1.15329 | 0.576647 | − | 0.816994i | \(-0.304361\pi\) | ||||
0.576647 | + | 0.816994i | \(0.304361\pi\) | |||||||
\(128\) | 8.08808e17 | 0.992112 | ||||||||
\(129\) | −1.03233e17 | −0.118524 | ||||||||
\(130\) | −6.73306e17 | −0.723926 | ||||||||
\(131\) | −1.06964e18 | −1.07753 | −0.538767 | − | 0.842455i | \(-0.681110\pi\) | ||||
−0.538767 | + | 0.842455i | \(0.681110\pi\) | |||||||
\(132\) | −3.53141e14 | −0.000333480 0 | ||||||||
\(133\) | −6.42327e17 | −0.568876 | ||||||||
\(134\) | 5.52971e17 | 0.459528 | ||||||||
\(135\) | −2.47860e17 | −0.193361 | ||||||||
\(136\) | −1.65448e18 | −1.21222 | ||||||||
\(137\) | 1.96077e18 | 1.34990 | 0.674949 | − | 0.737864i | \(-0.264166\pi\) | ||||
0.674949 | + | 0.737864i | \(0.264166\pi\) | |||||||
\(138\) | −6.44423e16 | −0.0417061 | ||||||||
\(139\) | −7.92486e17 | −0.482354 | −0.241177 | − | 0.970481i | \(-0.577533\pi\) | ||||
−0.241177 | + | 0.970481i | \(0.577533\pi\) | |||||||
\(140\) | −4.17799e15 | −0.00239265 | ||||||||
\(141\) | 1.22776e17 | 0.0661840 | ||||||||
\(142\) | 3.36896e18 | 1.71019 | ||||||||
\(143\) | −9.84688e17 | −0.470915 | ||||||||
\(144\) | 2.11972e18 | 0.955426 | ||||||||
\(145\) | −2.16726e17 | −0.0921049 | ||||||||
\(146\) | −3.57480e17 | −0.143302 | ||||||||
\(147\) | 7.52490e16 | 0.0284645 | ||||||||
\(148\) | −1.40791e16 | −0.00502747 | ||||||||
\(149\) | −2.70437e18 | −0.911975 | −0.455987 | − | 0.889986i | \(-0.650714\pi\) | ||||
−0.455987 | + | 0.889986i | \(0.650714\pi\) | |||||||
\(150\) | 4.69390e17 | 0.149540 | ||||||||
\(151\) | 9.73683e17 | 0.293166 | 0.146583 | − | 0.989198i | \(-0.453172\pi\) | ||||
0.146583 | + | 0.989198i | \(0.453172\pi\) | |||||||
\(152\) | −2.16450e18 | −0.616150 | ||||||||
\(153\) | −4.31333e18 | −1.16128 | ||||||||
\(154\) | 1.16638e18 | 0.297108 | ||||||||
\(155\) | 4.64501e17 | 0.111987 | ||||||||
\(156\) | 6.64325e15 | 0.00151643 | ||||||||
\(157\) | 6.54835e18 | 1.41574 | 0.707872 | − | 0.706341i | \(-0.249655\pi\) | ||||
0.707872 | + | 0.706341i | \(0.249655\pi\) | |||||||
\(158\) | 2.32183e18 | 0.475604 | ||||||||
\(159\) | 3.38771e17 | 0.0657704 | ||||||||
\(160\) | −2.80848e16 | −0.00516953 | ||||||||
\(161\) | −1.11501e18 | −0.194651 | ||||||||
\(162\) | 5.31707e18 | 0.880633 | ||||||||
\(163\) | 2.56556e18 | 0.403263 | 0.201631 | − | 0.979461i | \(-0.435376\pi\) | ||||
0.201631 | + | 0.979461i | \(0.435376\pi\) | |||||||
\(164\) | 3.61791e15 | 0.000539864 0 | ||||||||
\(165\) | −2.23986e17 | −0.0317400 | ||||||||
\(166\) | 9.32700e18 | 1.25552 | ||||||||
\(167\) | 4.57045e18 | 0.584614 | 0.292307 | − | 0.956325i | \(-0.405577\pi\) | ||||
0.292307 | + | 0.956325i | \(0.405577\pi\) | |||||||
\(168\) | −1.51788e18 | −0.184547 | ||||||||
\(169\) | 9.87343e18 | 1.14138 | ||||||||
\(170\) | −5.44027e18 | −0.598142 | ||||||||
\(171\) | −5.64298e18 | −0.590258 | ||||||||
\(172\) | −3.12040e16 | −0.00310613 | ||||||||
\(173\) | 4.67606e18 | 0.443086 | 0.221543 | − | 0.975151i | \(-0.428891\pi\) | ||||
0.221543 | + | 0.975151i | \(0.428891\pi\) | |||||||
\(174\) | −4.08193e17 | −0.0368296 | ||||||||
\(175\) | 8.12156e18 | 0.697937 | ||||||||
\(176\) | 3.90996e18 | 0.320121 | ||||||||
\(177\) | 5.94956e17 | 0.0464207 | ||||||||
\(178\) | −1.79897e19 | −1.33799 | ||||||||
\(179\) | 1.66722e19 | 1.18234 | 0.591171 | − | 0.806546i | \(-0.298666\pi\) | ||||
0.591171 | + | 0.806546i | \(0.298666\pi\) | |||||||
\(180\) | −3.67046e16 | −0.00248258 | ||||||||
\(181\) | −1.62147e19 | −1.04627 | −0.523133 | − | 0.852251i | \(-0.675237\pi\) | ||||
−0.523133 | + | 0.852251i | \(0.675237\pi\) | |||||||
\(182\) | −2.19419e19 | −1.35103 | ||||||||
\(183\) | −1.36176e18 | −0.0800326 | ||||||||
\(184\) | −3.75731e18 | −0.210827 | ||||||||
\(185\) | −8.92990e18 | −0.478505 | ||||||||
\(186\) | 8.74867e17 | 0.0447798 | ||||||||
\(187\) | −7.95621e18 | −0.389092 | ||||||||
\(188\) | 3.71114e16 | 0.00173447 | ||||||||
\(189\) | −8.07732e18 | −0.360863 | ||||||||
\(190\) | −7.11731e18 | −0.304026 | ||||||||
\(191\) | 1.79651e19 | 0.733916 | 0.366958 | − | 0.930237i | \(-0.380399\pi\) | ||||
0.366958 | + | 0.930237i | \(0.380399\pi\) | |||||||
\(192\) | −5.11476e18 | −0.199878 | ||||||||
\(193\) | −1.49005e19 | −0.557139 | −0.278569 | − | 0.960416i | \(-0.589860\pi\) | ||||
−0.278569 | + | 0.960416i | \(0.589860\pi\) | |||||||
\(194\) | 1.45170e19 | 0.519472 | ||||||||
\(195\) | 4.21360e18 | 0.144331 | ||||||||
\(196\) | 2.27454e16 | 0.000745962 0 | ||||||||
\(197\) | −3.35319e19 | −1.05316 | −0.526581 | − | 0.850125i | \(-0.676526\pi\) | ||||
−0.526581 | + | 0.850125i | \(0.676526\pi\) | |||||||
\(198\) | 1.02469e19 | 0.308275 | ||||||||
\(199\) | −5.61225e19 | −1.61765 | −0.808827 | − | 0.588046i | \(-0.799897\pi\) | ||||
−0.808827 | + | 0.588046i | \(0.799897\pi\) | |||||||
\(200\) | 2.73678e19 | 0.755936 | ||||||||
\(201\) | −3.46054e18 | −0.0916172 | ||||||||
\(202\) | −4.98218e19 | −1.26454 | ||||||||
\(203\) | −7.06271e18 | −0.171892 | ||||||||
\(204\) | 5.36770e16 | 0.00125295 | ||||||||
\(205\) | 2.29472e18 | 0.0513833 | ||||||||
\(206\) | 1.52585e19 | 0.327823 | ||||||||
\(207\) | −9.79556e18 | −0.201967 | ||||||||
\(208\) | −7.35537e19 | −1.45568 | ||||||||
\(209\) | −1.04088e19 | −0.197769 | ||||||||
\(210\) | −4.99109e18 | −0.0910608 | ||||||||
\(211\) | 4.79947e19 | 0.840994 | 0.420497 | − | 0.907294i | \(-0.361856\pi\) | ||||
0.420497 | + | 0.907294i | \(0.361856\pi\) | |||||||
\(212\) | 1.02400e17 | 0.00172363 | ||||||||
\(213\) | −2.10832e19 | −0.340965 | ||||||||
\(214\) | −9.05332e19 | −1.40699 | ||||||||
\(215\) | −1.97917e19 | −0.295636 | ||||||||
\(216\) | −2.72187e19 | −0.390851 | ||||||||
\(217\) | 1.51373e19 | 0.208997 | ||||||||
\(218\) | −1.12671e19 | −0.149600 | ||||||||
\(219\) | 2.23714e18 | 0.0285705 | ||||||||
\(220\) | −6.77038e16 | −0.000831803 0 | ||||||||
\(221\) | 1.49671e20 | 1.76931 | ||||||||
\(222\) | −1.68191e19 | −0.191338 | ||||||||
\(223\) | 1.61706e20 | 1.77066 | 0.885328 | − | 0.464967i | \(-0.153934\pi\) | ||||
0.885328 | + | 0.464967i | \(0.153934\pi\) | |||||||
\(224\) | −9.15233e17 | −0.00964769 | ||||||||
\(225\) | 7.13497e19 | 0.724170 | ||||||||
\(226\) | 1.41333e20 | 1.38140 | ||||||||
\(227\) | 4.30189e19 | 0.404986 | 0.202493 | − | 0.979284i | \(-0.435096\pi\) | ||||
0.202493 | + | 0.979284i | \(0.435096\pi\) | |||||||
\(228\) | 7.02238e16 | 0.000636851 0 | ||||||||
\(229\) | 1.72831e20 | 1.51015 | 0.755075 | − | 0.655638i | \(-0.227600\pi\) | ||||
0.755075 | + | 0.655638i | \(0.227600\pi\) | |||||||
\(230\) | −1.23548e19 | −0.104028 | ||||||||
\(231\) | −7.29931e18 | −0.0592352 | ||||||||
\(232\) | −2.37997e19 | −0.186176 | ||||||||
\(233\) | 2.22248e20 | 1.67615 | 0.838076 | − | 0.545554i | \(-0.183681\pi\) | ||||
0.838076 | + | 0.545554i | \(0.183681\pi\) | |||||||
\(234\) | −1.92764e20 | −1.40182 | ||||||||
\(235\) | 2.35386e19 | 0.165083 | ||||||||
\(236\) | 1.79836e17 | 0.00121654 | ||||||||
\(237\) | −1.45302e19 | −0.0948223 | ||||||||
\(238\) | −1.77289e20 | −1.11629 | ||||||||
\(239\) | 1.44050e20 | 0.875246 | 0.437623 | − | 0.899158i | \(-0.355820\pi\) | ||||
0.437623 | + | 0.899158i | \(0.355820\pi\) | |||||||
\(240\) | −1.67312e19 | −0.0981141 | ||||||||
\(241\) | 3.10781e19 | 0.175917 | 0.0879587 | − | 0.996124i | \(-0.471966\pi\) | ||||
0.0879587 | + | 0.996124i | \(0.471966\pi\) | |||||||
\(242\) | −1.63613e20 | −0.894102 | ||||||||
\(243\) | −1.07157e20 | −0.565416 | ||||||||
\(244\) | −4.11617e17 | −0.00209739 | ||||||||
\(245\) | 1.44267e19 | 0.0709993 | ||||||||
\(246\) | 4.32201e18 | 0.0205465 | ||||||||
\(247\) | 1.95810e20 | 0.899312 | ||||||||
\(248\) | 5.10091e19 | 0.226365 | ||||||||
\(249\) | −5.83691e19 | −0.250316 | ||||||||
\(250\) | 2.09345e20 | 0.867706 | ||||||||
\(251\) | 9.49597e19 | 0.380463 | 0.190232 | − | 0.981739i | \(-0.439076\pi\) | ||||
0.190232 | + | 0.981739i | \(0.439076\pi\) | |||||||
\(252\) | −1.19614e18 | −0.00463315 | ||||||||
\(253\) | −1.80685e19 | −0.0676703 | ||||||||
\(254\) | 3.17608e20 | 1.15028 | ||||||||
\(255\) | 3.40456e19 | 0.119253 | ||||||||
\(256\) | −4.61416e18 | −0.0156334 | ||||||||
\(257\) | 3.95433e20 | 1.29611 | 0.648053 | − | 0.761595i | \(-0.275583\pi\) | ||||
0.648053 | + | 0.761595i | \(0.275583\pi\) | |||||||
\(258\) | −3.72768e19 | −0.118215 | ||||||||
\(259\) | −2.91010e20 | −0.893016 | ||||||||
\(260\) | 1.27364e18 | 0.00378244 | ||||||||
\(261\) | −6.20474e19 | −0.178353 | ||||||||
\(262\) | −3.86240e20 | −1.07472 | ||||||||
\(263\) | −5.83802e20 | −1.57268 | −0.786342 | − | 0.617791i | \(-0.788028\pi\) | ||||
−0.786342 | + | 0.617791i | \(0.788028\pi\) | |||||||
\(264\) | −2.45970e19 | −0.0641577 | ||||||||
\(265\) | 6.49488e19 | 0.164052 | ||||||||
\(266\) | −2.31941e20 | −0.567391 | ||||||||
\(267\) | 1.12581e20 | 0.266758 | ||||||||
\(268\) | −1.04601e18 | −0.00240099 | ||||||||
\(269\) | 1.41736e20 | 0.315200 | 0.157600 | − | 0.987503i | \(-0.449624\pi\) | ||||
0.157600 | + | 0.987503i | \(0.449624\pi\) | |||||||
\(270\) | −8.95008e19 | −0.192857 | ||||||||
\(271\) | −8.28766e20 | −1.73058 | −0.865292 | − | 0.501268i | \(-0.832867\pi\) | ||||
−0.865292 | + | 0.501268i | \(0.832867\pi\) | |||||||
\(272\) | −5.94309e20 | −1.20275 | ||||||||
\(273\) | 1.37314e20 | 0.269359 | ||||||||
\(274\) | 7.08021e20 | 1.34638 | ||||||||
\(275\) | 1.31609e20 | 0.242637 | ||||||||
\(276\) | 1.21900e17 | 0.000217910 0 | ||||||||
\(277\) | 5.35448e20 | 0.928194 | 0.464097 | − | 0.885784i | \(-0.346379\pi\) | ||||
0.464097 | + | 0.885784i | \(0.346379\pi\) | |||||||
\(278\) | −2.86162e20 | −0.481095 | ||||||||
\(279\) | 1.32984e20 | 0.216852 | ||||||||
\(280\) | −2.91006e20 | −0.460318 | ||||||||
\(281\) | −1.64188e20 | −0.251963 | −0.125982 | − | 0.992033i | \(-0.540208\pi\) | ||||
−0.125982 | + | 0.992033i | \(0.540208\pi\) | |||||||
\(282\) | 4.43339e19 | 0.0660113 | ||||||||
\(283\) | 4.18506e18 | 0.00604668 | 0.00302334 | − | 0.999995i | \(-0.499038\pi\) | ||||
0.00302334 | + | 0.999995i | \(0.499038\pi\) | |||||||
\(284\) | −6.37278e18 | −0.00893559 | ||||||||
\(285\) | 4.45407e19 | 0.0606144 | ||||||||
\(286\) | −3.55565e20 | −0.469686 | ||||||||
\(287\) | 7.47809e19 | 0.0958947 | ||||||||
\(288\) | −8.04051e18 | −0.0100103 | ||||||||
\(289\) | 3.82095e20 | 0.461891 | ||||||||
\(290\) | −7.82584e19 | −0.0918645 | ||||||||
\(291\) | −9.08485e19 | −0.103568 | ||||||||
\(292\) | 6.76216e17 | 0.000748740 0 | ||||||||
\(293\) | 5.14492e20 | 0.553355 | 0.276677 | − | 0.960963i | \(-0.410767\pi\) | ||||
0.276677 | + | 0.960963i | \(0.410767\pi\) | |||||||
\(294\) | 2.71720e19 | 0.0283902 | ||||||||
\(295\) | 1.14064e20 | 0.115788 | ||||||||
\(296\) | −9.80635e20 | −0.967226 | ||||||||
\(297\) | −1.30892e20 | −0.125454 | ||||||||
\(298\) | −9.76532e20 | −0.909595 | ||||||||
\(299\) | 3.39903e20 | 0.307716 | ||||||||
\(300\) | −8.87907e17 | −0.000781334 0 | ||||||||
\(301\) | −6.44977e20 | −0.551733 | ||||||||
\(302\) | 3.51591e20 | 0.292401 | ||||||||
\(303\) | 3.11789e20 | 0.252115 | ||||||||
\(304\) | −7.77513e20 | −0.611339 | ||||||||
\(305\) | −2.61076e20 | −0.199626 | ||||||||
\(306\) | −1.55752e21 | −1.15825 | ||||||||
\(307\) | −2.96318e19 | −0.0214330 | −0.0107165 | − | 0.999943i | \(-0.503411\pi\) | ||||
−0.0107165 | + | 0.999943i | \(0.503411\pi\) | |||||||
\(308\) | −2.20635e18 | −0.00155236 | ||||||||
\(309\) | −9.54886e19 | −0.0653589 | ||||||||
\(310\) | 1.67729e20 | 0.111695 | ||||||||
\(311\) | 3.00263e21 | 1.94553 | 0.972767 | − | 0.231786i | \(-0.0744568\pi\) | ||||
0.972767 | + | 0.231786i | \(0.0744568\pi\) | |||||||
\(312\) | 4.62716e20 | 0.291743 | ||||||||
\(313\) | −1.80401e21 | −1.10691 | −0.553454 | − | 0.832880i | \(-0.686691\pi\) | ||||
−0.553454 | + | 0.832880i | \(0.686691\pi\) | |||||||
\(314\) | 2.36457e21 | 1.41205 | ||||||||
\(315\) | −7.58671e20 | −0.440975 | ||||||||
\(316\) | −4.39202e18 | −0.00248498 | ||||||||
\(317\) | 4.23700e20 | 0.233375 | 0.116688 | − | 0.993169i | \(-0.462772\pi\) | ||||
0.116688 | + | 0.993169i | \(0.462772\pi\) | |||||||
\(318\) | 1.22328e20 | 0.0655988 | ||||||||
\(319\) | −1.14450e20 | −0.0597580 | ||||||||
\(320\) | −9.80596e20 | −0.498558 | ||||||||
\(321\) | 5.66564e20 | 0.280515 | ||||||||
\(322\) | −4.02622e20 | −0.194143 | ||||||||
\(323\) | 1.58213e21 | 0.743055 | ||||||||
\(324\) | −1.00579e19 | −0.00460123 | ||||||||
\(325\) | −2.47581e21 | −1.10334 | ||||||||
\(326\) | 9.26409e20 | 0.402210 | ||||||||
\(327\) | 7.05103e19 | 0.0298261 | ||||||||
\(328\) | 2.51995e20 | 0.103864 | ||||||||
\(329\) | 7.67081e20 | 0.308089 | ||||||||
\(330\) | −8.08800e19 | −0.0316572 | ||||||||
\(331\) | 7.74777e20 | 0.295555 | 0.147778 | − | 0.989021i | \(-0.452788\pi\) | ||||
0.147778 | + | 0.989021i | \(0.452788\pi\) | |||||||
\(332\) | −1.76431e19 | −0.00655996 | ||||||||
\(333\) | −2.55658e21 | −0.926581 | ||||||||
\(334\) | 1.65036e21 | 0.583089 | ||||||||
\(335\) | −6.63451e20 | −0.228522 | ||||||||
\(336\) | −5.45240e20 | −0.183106 | ||||||||
\(337\) | −4.66708e21 | −1.52824 | −0.764119 | − | 0.645075i | \(-0.776826\pi\) | ||||
−0.764119 | + | 0.645075i | \(0.776826\pi\) | |||||||
\(338\) | 3.56524e21 | 1.13840 | ||||||||
\(339\) | −8.84471e20 | −0.275414 | ||||||||
\(340\) | 1.02909e19 | 0.00312524 | ||||||||
\(341\) | 2.45298e20 | 0.0726576 | ||||||||
\(342\) | −2.03765e21 | −0.588718 | ||||||||
\(343\) | 3.75452e21 | 1.05817 | ||||||||
\(344\) | −2.17343e21 | −0.597583 | ||||||||
\(345\) | 7.73174e19 | 0.0207403 | ||||||||
\(346\) | 1.68850e21 | 0.441930 | ||||||||
\(347\) | 2.40172e21 | 0.613368 | 0.306684 | − | 0.951811i | \(-0.400781\pi\) | ||||
0.306684 | + | 0.951811i | \(0.400781\pi\) | |||||||
\(348\) | 7.72146e17 | 0.000192431 0 | ||||||||
\(349\) | 3.18348e21 | 0.774257 | 0.387129 | − | 0.922026i | \(-0.373467\pi\) | ||||
0.387129 | + | 0.922026i | \(0.373467\pi\) | |||||||
\(350\) | 2.93265e21 | 0.696116 | ||||||||
\(351\) | 2.46233e21 | 0.570473 | ||||||||
\(352\) | −1.48312e19 | −0.00335401 | ||||||||
\(353\) | 5.75633e21 | 1.27075 | 0.635376 | − | 0.772203i | \(-0.280845\pi\) | ||||
0.635376 | + | 0.772203i | \(0.280845\pi\) | |||||||
\(354\) | 2.14835e20 | 0.0462996 | ||||||||
\(355\) | −4.04205e21 | −0.850473 | ||||||||
\(356\) | 3.40296e19 | 0.00699087 | ||||||||
\(357\) | 1.10949e21 | 0.222557 | ||||||||
\(358\) | 6.02025e21 | 1.17926 | ||||||||
\(359\) | 4.54608e21 | 0.869630 | 0.434815 | − | 0.900520i | \(-0.356814\pi\) | ||||
0.434815 | + | 0.900520i | \(0.356814\pi\) | |||||||
\(360\) | −2.55655e21 | −0.477620 | ||||||||
\(361\) | −3.41054e21 | −0.622318 | ||||||||
\(362\) | −5.85505e21 | −1.04354 | ||||||||
\(363\) | 1.02390e21 | 0.178259 | ||||||||
\(364\) | 4.15056e19 | 0.00705903 | ||||||||
\(365\) | 4.28902e20 | 0.0712638 | ||||||||
\(366\) | −4.91724e20 | −0.0798238 | ||||||||
\(367\) | 9.39502e21 | 1.49017 | 0.745086 | − | 0.666968i | \(-0.232408\pi\) | ||||
0.745086 | + | 0.666968i | \(0.232408\pi\) | |||||||
\(368\) | −1.34967e21 | −0.209181 | ||||||||
\(369\) | 6.56966e20 | 0.0994991 | ||||||||
\(370\) | −3.22453e21 | −0.477257 | ||||||||
\(371\) | 2.11657e21 | 0.306164 | ||||||||
\(372\) | −1.65491e18 | −0.000233970 0 | ||||||||
\(373\) | 4.92376e21 | 0.680412 | 0.340206 | − | 0.940351i | \(-0.389503\pi\) | ||||
0.340206 | + | 0.940351i | \(0.389503\pi\) | |||||||
\(374\) | −2.87294e21 | −0.388077 | ||||||||
\(375\) | −1.31010e21 | −0.172997 | ||||||||
\(376\) | 2.58489e21 | 0.333691 | ||||||||
\(377\) | 2.15303e21 | 0.271737 | ||||||||
\(378\) | −2.91667e21 | −0.359921 | ||||||||
\(379\) | −1.20746e22 | −1.45694 | −0.728468 | − | 0.685079i | \(-0.759767\pi\) | ||||
−0.728468 | + | 0.685079i | \(0.759767\pi\) | |||||||
\(380\) | 1.34632e19 | 0.00158851 | ||||||||
\(381\) | −1.98762e21 | −0.229335 | ||||||||
\(382\) | 6.48710e21 | 0.732002 | ||||||||
\(383\) | 6.75134e21 | 0.745076 | 0.372538 | − | 0.928017i | \(-0.378488\pi\) | ||||
0.372538 | + | 0.928017i | \(0.378488\pi\) | |||||||
\(384\) | −1.82771e21 | −0.197284 | ||||||||
\(385\) | −1.39942e21 | −0.147751 | ||||||||
\(386\) | −5.38048e21 | −0.555685 | ||||||||
\(387\) | −5.66626e21 | −0.572471 | ||||||||
\(388\) | −2.74606e19 | −0.00271419 | ||||||||
\(389\) | −7.82790e21 | −0.756961 | −0.378481 | − | 0.925609i | \(-0.623553\pi\) | ||||
−0.378481 | + | 0.925609i | \(0.623553\pi\) | |||||||
\(390\) | 1.52151e21 | 0.143954 | ||||||||
\(391\) | 2.74639e21 | 0.254250 | ||||||||
\(392\) | 1.58426e21 | 0.143514 | ||||||||
\(393\) | 2.41712e21 | 0.214270 | ||||||||
\(394\) | −1.21082e22 | −1.05041 | ||||||||
\(395\) | −2.78571e21 | −0.236516 | ||||||||
\(396\) | −1.93832e19 | −0.00161071 | ||||||||
\(397\) | 1.23438e20 | 0.0100399 | 0.00501997 | − | 0.999987i | \(-0.498402\pi\) | ||||
0.00501997 | + | 0.999987i | \(0.498402\pi\) | |||||||
\(398\) | −2.02655e22 | −1.61343 | ||||||||
\(399\) | 1.45150e21 | 0.113122 | ||||||||
\(400\) | 9.83085e21 | 0.750034 | ||||||||
\(401\) | −1.62453e22 | −1.21339 | −0.606694 | − | 0.794935i | \(-0.707505\pi\) | ||||
−0.606694 | + | 0.794935i | \(0.707505\pi\) | |||||||
\(402\) | −1.24958e21 | −0.0913782 | ||||||||
\(403\) | −4.61451e21 | −0.330395 | ||||||||
\(404\) | 9.42439e19 | 0.00660711 | ||||||||
\(405\) | −6.37939e21 | −0.437937 | ||||||||
\(406\) | −2.55030e21 | −0.171443 | ||||||||
\(407\) | −4.71577e21 | −0.310456 | ||||||||
\(408\) | 3.73871e21 | 0.241052 | ||||||||
\(409\) | 6.74538e20 | 0.0425950 | 0.0212975 | − | 0.999773i | \(-0.493220\pi\) | ||||
0.0212975 | + | 0.999773i | \(0.493220\pi\) | |||||||
\(410\) | 8.28611e20 | 0.0512493 | ||||||||
\(411\) | −4.43085e21 | −0.268430 | ||||||||
\(412\) | −2.88632e19 | −0.00171284 | ||||||||
\(413\) | 3.71716e21 | 0.216090 | ||||||||
\(414\) | −3.53712e21 | −0.201440 | ||||||||
\(415\) | −1.11905e22 | −0.624366 | ||||||||
\(416\) | 2.79004e20 | 0.0152516 | ||||||||
\(417\) | 1.79082e21 | 0.0959172 | ||||||||
\(418\) | −3.75857e21 | −0.197253 | ||||||||
\(419\) | −2.65087e22 | −1.36323 | −0.681614 | − | 0.731712i | \(-0.738722\pi\) | ||||
−0.681614 | + | 0.731712i | \(0.738722\pi\) | |||||||
\(420\) | 9.44124e18 | 0.000475784 0 | ||||||||
\(421\) | 7.51157e21 | 0.370965 | 0.185483 | − | 0.982648i | \(-0.440615\pi\) | ||||
0.185483 | + | 0.982648i | \(0.440615\pi\) | |||||||
\(422\) | 1.73306e22 | 0.838800 | ||||||||
\(423\) | 6.73897e21 | 0.319669 | ||||||||
\(424\) | 7.13234e21 | 0.331606 | ||||||||
\(425\) | −2.00044e22 | −0.911632 | ||||||||
\(426\) | −7.61302e21 | −0.340075 | ||||||||
\(427\) | −8.50799e21 | −0.372555 | ||||||||
\(428\) | 1.71254e20 | 0.00735139 | ||||||||
\(429\) | 2.22515e21 | 0.0936425 | ||||||||
\(430\) | −7.14667e21 | −0.294864 | ||||||||
\(431\) | 4.21364e22 | 1.70451 | 0.852256 | − | 0.523124i | \(-0.175234\pi\) | ||||
0.852256 | + | 0.523124i | \(0.175234\pi\) | |||||||
\(432\) | −9.77730e21 | −0.387799 | ||||||||
\(433\) | −1.20126e22 | −0.467187 | −0.233594 | − | 0.972334i | \(-0.575049\pi\) | ||||
−0.233594 | + | 0.972334i | \(0.575049\pi\) | |||||||
\(434\) | 5.46598e21 | 0.208452 | ||||||||
\(435\) | 4.89747e20 | 0.0183153 | ||||||||
\(436\) | 2.13130e19 | 0.000781645 0 | ||||||||
\(437\) | 3.59301e21 | 0.129231 | ||||||||
\(438\) | 8.07817e20 | 0.0284960 | ||||||||
\(439\) | 1.85211e22 | 0.640792 | 0.320396 | − | 0.947284i | \(-0.396184\pi\) | ||||
0.320396 | + | 0.947284i | \(0.396184\pi\) | |||||||
\(440\) | −4.71571e21 | −0.160029 | ||||||||
\(441\) | 4.13028e21 | 0.137484 | ||||||||
\(442\) | 5.40455e22 | 1.76470 | ||||||||
\(443\) | −2.08979e22 | −0.669377 | −0.334689 | − | 0.942329i | \(-0.608631\pi\) | ||||
−0.334689 | + | 0.942329i | \(0.608631\pi\) | |||||||
\(444\) | 3.18152e19 | 0.000999723 0 | ||||||||
\(445\) | 2.15839e22 | 0.665379 | ||||||||
\(446\) | 5.83910e22 | 1.76604 | ||||||||
\(447\) | 6.11121e21 | 0.181348 | ||||||||
\(448\) | −3.19559e22 | −0.930439 | ||||||||
\(449\) | −7.53146e21 | −0.215172 | −0.107586 | − | 0.994196i | \(-0.534312\pi\) | ||||
−0.107586 | + | 0.994196i | \(0.534312\pi\) | |||||||
\(450\) | 2.57639e22 | 0.722281 | ||||||||
\(451\) | 1.21182e21 | 0.0333377 | ||||||||
\(452\) | −2.67348e20 | −0.00721771 | ||||||||
\(453\) | −2.20029e21 | −0.0582968 | ||||||||
\(454\) | 1.55339e22 | 0.403929 | ||||||||
\(455\) | 2.63257e22 | 0.671866 | ||||||||
\(456\) | 4.89123e21 | 0.122523 | ||||||||
\(457\) | 6.48078e22 | 1.59345 | 0.796727 | − | 0.604339i | \(-0.206563\pi\) | ||||
0.796727 | + | 0.604339i | \(0.206563\pi\) | |||||||
\(458\) | 6.24083e22 | 1.50621 | ||||||||
\(459\) | 1.98954e22 | 0.471352 | ||||||||
\(460\) | 2.33706e19 | 0.000543536 0 | ||||||||
\(461\) | −5.69183e22 | −1.29955 | −0.649777 | − | 0.760125i | \(-0.725138\pi\) | ||||
−0.649777 | + | 0.760125i | \(0.725138\pi\) | |||||||
\(462\) | −2.63574e21 | −0.0590806 | ||||||||
\(463\) | −3.85663e22 | −0.848730 | −0.424365 | − | 0.905491i | \(-0.639503\pi\) | ||||
−0.424365 | + | 0.905491i | \(0.639503\pi\) | |||||||
\(464\) | −8.54915e21 | −0.184723 | ||||||||
\(465\) | −1.04966e21 | −0.0222689 | ||||||||
\(466\) | 8.02526e22 | 1.67178 | ||||||||
\(467\) | −5.50901e22 | −1.12689 | −0.563443 | − | 0.826155i | \(-0.690524\pi\) | ||||
−0.563443 | + | 0.826155i | \(0.690524\pi\) | |||||||
\(468\) | 3.64636e20 | 0.00732435 | ||||||||
\(469\) | −2.16207e22 | −0.426482 | ||||||||
\(470\) | 8.49964e21 | 0.164653 | ||||||||
\(471\) | −1.47977e22 | −0.281524 | ||||||||
\(472\) | 1.25260e22 | 0.234048 | ||||||||
\(473\) | −1.04518e22 | −0.191810 | ||||||||
\(474\) | −5.24677e21 | −0.0945749 | ||||||||
\(475\) | −2.61711e22 | −0.463368 | ||||||||
\(476\) | 3.35362e20 | 0.00583251 | ||||||||
\(477\) | 1.85945e22 | 0.317671 | ||||||||
\(478\) | 5.20155e22 | 0.872963 | ||||||||
\(479\) | −7.25612e22 | −1.19633 | −0.598167 | − | 0.801371i | \(-0.704104\pi\) | ||||
−0.598167 | + | 0.801371i | \(0.704104\pi\) | |||||||
\(480\) | 6.34647e19 | 0.00102797 | ||||||||
\(481\) | 8.87126e22 | 1.41173 | ||||||||
\(482\) | 1.12221e22 | 0.175458 | ||||||||
\(483\) | 2.51964e21 | 0.0387068 | ||||||||
\(484\) | 3.09493e20 | 0.00467160 | ||||||||
\(485\) | −1.74174e22 | −0.258332 | ||||||||
\(486\) | −3.86938e22 | −0.563940 | ||||||||
\(487\) | −9.08930e22 | −1.30177 | −0.650885 | − | 0.759177i | \(-0.725602\pi\) | ||||
−0.650885 | + | 0.759177i | \(0.725602\pi\) | |||||||
\(488\) | −2.86700e22 | −0.403514 | ||||||||
\(489\) | −5.79754e21 | −0.0801897 | ||||||||
\(490\) | 5.20938e21 | 0.0708141 | ||||||||
\(491\) | −8.39289e22 | −1.12129 | −0.560646 | − | 0.828055i | \(-0.689447\pi\) | ||||
−0.560646 | + | 0.828055i | \(0.689447\pi\) | |||||||
\(492\) | −8.17558e18 | −0.000107353 0 | ||||||||
\(493\) | 1.73963e22 | 0.224522 | ||||||||
\(494\) | 7.07058e22 | 0.896966 | ||||||||
\(495\) | −1.22942e22 | −0.153305 | ||||||||
\(496\) | 1.83231e22 | 0.224598 | ||||||||
\(497\) | −1.31723e23 | −1.58721 | ||||||||
\(498\) | −2.10767e22 | −0.249663 | ||||||||
\(499\) | 3.02223e22 | 0.351943 | 0.175972 | − | 0.984395i | \(-0.443693\pi\) | ||||
0.175972 | + | 0.984395i | \(0.443693\pi\) | |||||||
\(500\) | −3.96001e20 | −0.00453368 | ||||||||
\(501\) | −1.03281e22 | −0.116252 | ||||||||
\(502\) | 3.42894e22 | 0.379471 | ||||||||
\(503\) | 1.25963e22 | 0.137062 | 0.0685308 | − | 0.997649i | \(-0.478169\pi\) | ||||
0.0685308 | + | 0.997649i | \(0.478169\pi\) | |||||||
\(504\) | −8.33133e22 | −0.891364 | ||||||||
\(505\) | 5.97759e22 | 0.628853 | ||||||||
\(506\) | −6.52444e21 | −0.0674937 | ||||||||
\(507\) | −2.23115e22 | −0.226966 | ||||||||
\(508\) | −6.00793e20 | −0.00601013 | ||||||||
\(509\) | −1.27820e23 | −1.25747 | −0.628735 | − | 0.777619i | \(-0.716427\pi\) | ||||
−0.628735 | + | 0.777619i | \(0.716427\pi\) | |||||||
\(510\) | 1.22937e22 | 0.118942 | ||||||||
\(511\) | 1.39772e22 | 0.132997 | ||||||||
\(512\) | −1.07678e23 | −1.00770 | ||||||||
\(513\) | 2.60285e22 | 0.239581 | ||||||||
\(514\) | 1.42788e23 | 1.29273 | ||||||||
\(515\) | −1.83070e22 | −0.163025 | ||||||||
\(516\) | 7.05135e19 | 0.000617660 0 | ||||||||
\(517\) | 1.24304e22 | 0.107107 | ||||||||
\(518\) | −1.05082e23 | −0.890686 | ||||||||
\(519\) | −1.05668e22 | −0.0881088 | ||||||||
\(520\) | 8.87115e22 | 0.727698 | ||||||||
\(521\) | 8.24007e22 | 0.664983 | 0.332491 | − | 0.943106i | \(-0.392111\pi\) | ||||
0.332491 | + | 0.943106i | \(0.392111\pi\) | |||||||
\(522\) | −2.24049e22 | −0.177887 | ||||||||
\(523\) | 1.66840e23 | 1.30327 | 0.651636 | − | 0.758532i | \(-0.274083\pi\) | ||||
0.651636 | + | 0.758532i | \(0.274083\pi\) | |||||||
\(524\) | 7.30619e20 | 0.00561532 | ||||||||
\(525\) | −1.83527e22 | −0.138786 | ||||||||
\(526\) | −2.10807e23 | −1.56858 | ||||||||
\(527\) | −3.72850e22 | −0.272988 | ||||||||
\(528\) | −8.83554e21 | −0.0636568 | ||||||||
\(529\) | −1.34813e23 | −0.955781 | ||||||||
\(530\) | 2.34526e22 | 0.163624 | ||||||||
\(531\) | 3.26560e22 | 0.224212 | ||||||||
\(532\) | 4.38743e20 | 0.00296457 | ||||||||
\(533\) | −2.27965e22 | −0.151596 | ||||||||
\(534\) | 4.06522e22 | 0.266062 | ||||||||
\(535\) | 1.08621e23 | 0.699692 | ||||||||
\(536\) | −7.28568e22 | −0.461923 | ||||||||
\(537\) | −3.76752e22 | −0.235111 | ||||||||
\(538\) | 5.11801e22 | 0.314378 | ||||||||
\(539\) | 7.61855e21 | 0.0460647 | ||||||||
\(540\) | 1.69301e20 | 0.00100766 | ||||||||
\(541\) | 1.28619e23 | 0.753578 | 0.376789 | − | 0.926299i | \(-0.377028\pi\) | ||||
0.376789 | + | 0.926299i | \(0.377028\pi\) | |||||||
\(542\) | −2.99262e23 | −1.72607 | ||||||||
\(543\) | 3.66413e22 | 0.208052 | ||||||||
\(544\) | 2.25433e21 | 0.0126016 | ||||||||
\(545\) | 1.35182e22 | 0.0743956 | ||||||||
\(546\) | 4.95832e22 | 0.268656 | ||||||||
\(547\) | 1.36246e23 | 0.726826 | 0.363413 | − | 0.931628i | \(-0.381611\pi\) | ||||
0.363413 | + | 0.931628i | \(0.381611\pi\) | |||||||
\(548\) | −1.33931e21 | −0.00703469 | ||||||||
\(549\) | −7.47445e22 | −0.386558 | ||||||||
\(550\) | 4.75232e22 | 0.242004 | ||||||||
\(551\) | 2.27590e22 | 0.114121 | ||||||||
\(552\) | 8.49060e21 | 0.0419234 | ||||||||
\(553\) | −9.07815e22 | −0.441401 | ||||||||
\(554\) | 1.93347e23 | 0.925773 | ||||||||
\(555\) | 2.01794e22 | 0.0951519 | ||||||||
\(556\) | 5.41309e20 | 0.00251368 | ||||||||
\(557\) | −1.80838e23 | −0.827031 | −0.413515 | − | 0.910497i | \(-0.635699\pi\) | ||||
−0.413515 | + | 0.910497i | \(0.635699\pi\) | |||||||
\(558\) | 4.80198e22 | 0.216287 | ||||||||
\(559\) | 1.96618e23 | 0.872212 | ||||||||
\(560\) | −1.04533e23 | −0.456725 | ||||||||
\(561\) | 1.79791e22 | 0.0773719 | ||||||||
\(562\) | −5.92872e22 | −0.251306 | ||||||||
\(563\) | 9.08213e22 | 0.379198 | 0.189599 | − | 0.981862i | \(-0.439281\pi\) | ||||
0.189599 | + | 0.981862i | \(0.439281\pi\) | |||||||
\(564\) | −8.38627e19 | −0.000344903 0 | ||||||||
\(565\) | −1.69570e23 | −0.686969 | ||||||||
\(566\) | 1.51120e21 | 0.00603091 | ||||||||
\(567\) | −2.07893e23 | −0.817304 | ||||||||
\(568\) | −4.43877e23 | −1.71910 | ||||||||
\(569\) | 1.95996e23 | 0.747813 | 0.373906 | − | 0.927466i | \(-0.378018\pi\) | ||||
0.373906 | + | 0.927466i | \(0.378018\pi\) | |||||||
\(570\) | 1.60834e22 | 0.0604562 | ||||||||
\(571\) | 3.40549e23 | 1.26117 | 0.630583 | − | 0.776121i | \(-0.282816\pi\) | ||||
0.630583 | + | 0.776121i | \(0.282816\pi\) | |||||||
\(572\) | 6.72593e20 | 0.00245407 | ||||||||
\(573\) | −4.05968e22 | −0.145941 | ||||||||
\(574\) | 2.70030e22 | 0.0956445 | ||||||||
\(575\) | −4.54299e22 | −0.158550 | ||||||||
\(576\) | −2.80739e23 | −0.965411 | ||||||||
\(577\) | 5.07118e23 | 1.71836 | 0.859181 | − | 0.511672i | \(-0.170974\pi\) | ||||
0.859181 | + | 0.511672i | \(0.170974\pi\) | |||||||
\(578\) | 1.37972e23 | 0.460686 | ||||||||
\(579\) | 3.36715e22 | 0.110788 | ||||||||
\(580\) | 1.48035e20 | 0.000479984 0 | ||||||||
\(581\) | −3.64677e23 | −1.16523 | ||||||||
\(582\) | −3.28049e22 | −0.103298 | ||||||||
\(583\) | 3.42987e22 | 0.106438 | ||||||||
\(584\) | 4.70998e22 | 0.144049 | ||||||||
\(585\) | 2.31277e23 | 0.697119 | ||||||||
\(586\) | 1.85780e23 | 0.551911 | ||||||||
\(587\) | 5.19155e23 | 1.52010 | 0.760052 | − | 0.649862i | \(-0.225174\pi\) | ||||
0.760052 | + | 0.649862i | \(0.225174\pi\) | |||||||
\(588\) | −5.13990e19 | −0.000148336 0 | ||||||||
\(589\) | −4.87786e22 | −0.138755 | ||||||||
\(590\) | 4.11880e22 | 0.115486 | ||||||||
\(591\) | 7.57739e22 | 0.209424 | ||||||||
\(592\) | −3.52256e23 | −0.959675 | ||||||||
\(593\) | −1.48323e23 | −0.398332 | −0.199166 | − | 0.979966i | \(-0.563823\pi\) | ||||
−0.199166 | + | 0.979966i | \(0.563823\pi\) | |||||||
\(594\) | −4.72643e22 | −0.125126 | ||||||||
\(595\) | 2.12710e23 | 0.555128 | ||||||||
\(596\) | 1.84723e21 | 0.00475255 | ||||||||
\(597\) | 1.26823e23 | 0.321674 | ||||||||
\(598\) | 1.22737e23 | 0.306913 | ||||||||
\(599\) | −3.86765e23 | −0.953497 | −0.476748 | − | 0.879040i | \(-0.658185\pi\) | ||||
−0.476748 | + | 0.879040i | \(0.658185\pi\) | |||||||
\(600\) | −6.18445e22 | −0.150320 | ||||||||
\(601\) | 4.34922e23 | 1.04227 | 0.521133 | − | 0.853475i | \(-0.325510\pi\) | ||||
0.521133 | + | 0.853475i | \(0.325510\pi\) | |||||||
\(602\) | −2.32897e23 | −0.550294 | ||||||||
\(603\) | −1.89942e23 | −0.442512 | ||||||||
\(604\) | −6.65076e20 | −0.00152777 | ||||||||
\(605\) | 1.96302e23 | 0.444634 | ||||||||
\(606\) | 1.12585e23 | 0.251457 | ||||||||
\(607\) | 1.19494e23 | 0.263175 | 0.131587 | − | 0.991305i | \(-0.457993\pi\) | ||||
0.131587 | + | 0.991305i | \(0.457993\pi\) | |||||||
\(608\) | 2.94926e21 | 0.00640520 | ||||||||
\(609\) | 1.59600e22 | 0.0341811 | ||||||||
\(610\) | −9.42728e22 | −0.199105 | ||||||||
\(611\) | −2.33840e23 | −0.487045 | ||||||||
\(612\) | 2.94623e21 | 0.00605173 | ||||||||
\(613\) | 6.79381e23 | 1.37626 | 0.688128 | − | 0.725589i | \(-0.258433\pi\) | ||||
0.688128 | + | 0.725589i | \(0.258433\pi\) | |||||||
\(614\) | −1.06999e22 | −0.0213771 | ||||||||
\(615\) | −5.18551e21 | −0.0102177 | ||||||||
\(616\) | −1.53677e23 | −0.298656 | ||||||||
\(617\) | 4.92283e22 | 0.0943606 | 0.0471803 | − | 0.998886i | \(-0.484976\pi\) | ||||
0.0471803 | + | 0.998886i | \(0.484976\pi\) | |||||||
\(618\) | −3.44804e22 | −0.0651884 | ||||||||
\(619\) | −4.65769e23 | −0.868560 | −0.434280 | − | 0.900778i | \(-0.642997\pi\) | ||||
−0.434280 | + | 0.900778i | \(0.642997\pi\) | |||||||
\(620\) | −3.17279e20 | −0.000583595 0 | ||||||||
\(621\) | 4.51824e22 | 0.0819768 | ||||||||
\(622\) | 1.08423e24 | 1.94046 | ||||||||
\(623\) | 7.03380e23 | 1.24177 | ||||||||
\(624\) | 1.66213e23 | 0.289465 | ||||||||
\(625\) | 1.87706e23 | 0.322476 | ||||||||
\(626\) | −6.51417e23 | −1.10402 | ||||||||
\(627\) | 2.35214e22 | 0.0393269 | ||||||||
\(628\) | −4.47286e21 | −0.00737783 | ||||||||
\(629\) | 7.16792e23 | 1.16644 | ||||||||
\(630\) | −2.73952e23 | −0.439824 | ||||||||
\(631\) | 6.56020e23 | 1.03912 | 0.519562 | − | 0.854433i | \(-0.326095\pi\) | ||||
0.519562 | + | 0.854433i | \(0.326095\pi\) | |||||||
\(632\) | −3.05913e23 | −0.478082 | ||||||||
\(633\) | −1.08456e23 | −0.167234 | ||||||||
\(634\) | 1.52996e23 | 0.232766 | ||||||||
\(635\) | −3.81064e23 | −0.572033 | ||||||||
\(636\) | −2.31398e20 | −0.000342748 0 | ||||||||
\(637\) | −1.43319e23 | −0.209469 | ||||||||
\(638\) | −4.13273e22 | −0.0596021 | ||||||||
\(639\) | −1.15722e24 | −1.64686 | ||||||||
\(640\) | −3.50406e23 | −0.492087 | ||||||||
\(641\) | −3.45513e23 | −0.478819 | −0.239409 | − | 0.970919i | \(-0.576954\pi\) | ||||
−0.239409 | + | 0.970919i | \(0.576954\pi\) | |||||||
\(642\) | 2.04583e23 | 0.279783 | ||||||||
\(643\) | 1.30958e23 | 0.176742 | 0.0883711 | − | 0.996088i | \(-0.471834\pi\) | ||||
0.0883711 | + | 0.996088i | \(0.471834\pi\) | |||||||
\(644\) | 7.61607e20 | 0.00101438 | ||||||||
\(645\) | 4.47244e22 | 0.0587878 | ||||||||
\(646\) | 5.71298e23 | 0.741116 | ||||||||
\(647\) | −1.84975e23 | −0.236825 | −0.118413 | − | 0.992964i | \(-0.537781\pi\) | ||||
−0.118413 | + | 0.992964i | \(0.537781\pi\) | |||||||
\(648\) | −7.00551e23 | −0.885222 | ||||||||
\(649\) | 6.02361e22 | 0.0751236 | ||||||||
\(650\) | −8.94002e23 | −1.10046 | ||||||||
\(651\) | −3.42065e22 | −0.0415595 | ||||||||
\(652\) | −1.75241e21 | −0.00210151 | ||||||||
\(653\) | 1.66260e23 | 0.196800 | 0.0984002 | − | 0.995147i | \(-0.468627\pi\) | ||||
0.0984002 | + | 0.995147i | \(0.468627\pi\) | |||||||
\(654\) | 2.54608e22 | 0.0297483 | ||||||||
\(655\) | 4.63408e23 | 0.534457 | ||||||||
\(656\) | 9.05196e22 | 0.103053 | ||||||||
\(657\) | 1.22792e23 | 0.137996 | ||||||||
\(658\) | 2.76988e23 | 0.307285 | ||||||||
\(659\) | −4.00812e23 | −0.438949 | −0.219475 | − | 0.975618i | \(-0.570434\pi\) | ||||
−0.219475 | + | 0.975618i | \(0.570434\pi\) | |||||||
\(660\) | 1.52994e20 | 0.000165406 0 | ||||||||
\(661\) | −1.35342e24 | −1.44451 | −0.722256 | − | 0.691626i | \(-0.756895\pi\) | ||||
−0.722256 | + | 0.691626i | \(0.756895\pi\) | |||||||
\(662\) | 2.79767e23 | 0.294784 | ||||||||
\(663\) | −3.38221e23 | −0.351832 | ||||||||
\(664\) | −1.22888e24 | −1.26206 | ||||||||
\(665\) | 2.78281e23 | 0.282162 | ||||||||
\(666\) | −9.23166e23 | −0.924164 | ||||||||
\(667\) | 3.95070e22 | 0.0390485 | ||||||||
\(668\) | −3.12186e21 | −0.00304658 | ||||||||
\(669\) | −3.65415e23 | −0.352099 | ||||||||
\(670\) | −2.39568e23 | −0.227926 | ||||||||
\(671\) | −1.37871e23 | −0.129518 | ||||||||
\(672\) | 2.06820e21 | 0.00191847 | ||||||||
\(673\) | 8.66002e23 | 0.793215 | 0.396608 | − | 0.917988i | \(-0.370187\pi\) | ||||
0.396608 | + | 0.917988i | \(0.370187\pi\) | |||||||
\(674\) | −1.68526e24 | −1.52425 | ||||||||
\(675\) | −3.29103e23 | −0.293934 | ||||||||
\(676\) | −6.74407e21 | −0.00594805 | ||||||||
\(677\) | −4.16997e23 | −0.363186 | −0.181593 | − | 0.983374i | \(-0.558125\pi\) | ||||
−0.181593 | + | 0.983374i | \(0.558125\pi\) | |||||||
\(678\) | −3.19377e23 | −0.274696 | ||||||||
\(679\) | −5.67602e23 | −0.482115 | ||||||||
\(680\) | 7.16783e23 | 0.601259 | ||||||||
\(681\) | −9.72122e22 | −0.0805323 | ||||||||
\(682\) | 8.85755e22 | 0.0724681 | ||||||||
\(683\) | 2.20244e23 | 0.177962 | 0.0889812 | − | 0.996033i | \(-0.471639\pi\) | ||||
0.0889812 | + | 0.996033i | \(0.471639\pi\) | |||||||
\(684\) | 3.85445e21 | 0.00307599 | ||||||||
\(685\) | −8.49478e23 | −0.669549 | ||||||||
\(686\) | 1.35574e24 | 1.05541 | ||||||||
\(687\) | −3.90556e23 | −0.300297 | ||||||||
\(688\) | −7.80721e23 | −0.592917 | ||||||||
\(689\) | −6.45223e23 | −0.484002 | ||||||||
\(690\) | 2.79189e22 | 0.0206862 | ||||||||
\(691\) | 1.77459e24 | 1.29878 | 0.649389 | − | 0.760456i | \(-0.275025\pi\) | ||||
0.649389 | + | 0.760456i | \(0.275025\pi\) | |||||||
\(692\) | −3.19399e21 | −0.00230904 | ||||||||
\(693\) | −4.00645e23 | −0.286106 | ||||||||
\(694\) | 8.67245e23 | 0.611768 | ||||||||
\(695\) | 3.43335e23 | 0.239247 | ||||||||
\(696\) | 5.37815e22 | 0.0370215 | ||||||||
\(697\) | −1.84195e23 | −0.125256 | ||||||||
\(698\) | 1.14953e24 | 0.772237 | ||||||||
\(699\) | −5.02227e23 | −0.333307 | ||||||||
\(700\) | −5.54745e21 | −0.00363714 | ||||||||
\(701\) | −6.81837e23 | −0.441649 | −0.220825 | − | 0.975314i | \(-0.570875\pi\) | ||||
−0.220825 | + | 0.975314i | \(0.570875\pi\) | |||||||
\(702\) | 8.89132e23 | 0.568985 | ||||||||
\(703\) | 9.37754e23 | 0.592882 | ||||||||
\(704\) | −5.17841e23 | −0.323466 | ||||||||
\(705\) | −5.31914e22 | −0.0328272 | ||||||||
\(706\) | 2.07858e24 | 1.26744 | ||||||||
\(707\) | 1.94799e24 | 1.17360 | ||||||||
\(708\) | −4.06386e20 | −0.000241911 0 | ||||||||
\(709\) | −2.52327e24 | −1.48413 | −0.742063 | − | 0.670330i | \(-0.766153\pi\) | ||||
−0.742063 | + | 0.670330i | \(0.766153\pi\) | |||||||
\(710\) | −1.45956e24 | −0.848254 | ||||||||
\(711\) | −7.97535e23 | −0.457992 | ||||||||
\(712\) | 2.37023e24 | 1.34496 | ||||||||
\(713\) | −8.46740e22 | −0.0474776 | ||||||||
\(714\) | 4.00629e23 | 0.221977 | ||||||||
\(715\) | 4.26604e23 | 0.233574 | ||||||||
\(716\) | −1.13880e22 | −0.00616151 | ||||||||
\(717\) | −3.25517e23 | −0.174045 | ||||||||
\(718\) | 1.64156e24 | 0.867361 | ||||||||
\(719\) | −1.14410e24 | −0.597406 | −0.298703 | − | 0.954346i | \(-0.596554\pi\) | ||||
−0.298703 | + | 0.954346i | \(0.596554\pi\) | |||||||
\(720\) | −9.18343e23 | −0.473891 | ||||||||
\(721\) | −5.96592e23 | −0.304248 | ||||||||
\(722\) | −1.23153e24 | −0.620694 | ||||||||
\(723\) | −7.02288e22 | −0.0349816 | ||||||||
\(724\) | 1.10755e22 | 0.00545238 | ||||||||
\(725\) | −2.87764e23 | −0.140011 | ||||||||
\(726\) | 3.69725e23 | 0.177794 | ||||||||
\(727\) | 1.05434e24 | 0.501118 | 0.250559 | − | 0.968101i | \(-0.419386\pi\) | ||||
0.250559 | + | 0.968101i | \(0.419386\pi\) | |||||||
\(728\) | 2.89095e24 | 1.35808 | ||||||||
\(729\) | −1.65943e24 | −0.770503 | ||||||||
\(730\) | 1.54874e23 | 0.0710778 | ||||||||
\(731\) | 1.58866e24 | 0.720664 | ||||||||
\(732\) | 9.30154e20 | 0.000417072 0 | ||||||||
\(733\) | 3.85209e24 | 1.70731 | 0.853656 | − | 0.520838i | \(-0.174380\pi\) | ||||
0.853656 | + | 0.520838i | \(0.174380\pi\) | |||||||
\(734\) | 3.39249e24 | 1.48628 | ||||||||
\(735\) | −3.26007e22 | −0.0141184 | ||||||||
\(736\) | 5.11957e21 | 0.00219166 | ||||||||
\(737\) | −3.50361e23 | −0.148266 | ||||||||
\(738\) | 2.37227e23 | 0.0992395 | ||||||||
\(739\) | −1.44868e24 | −0.599093 | −0.299546 | − | 0.954082i | \(-0.596835\pi\) | ||||
−0.299546 | + | 0.954082i | \(0.596835\pi\) | |||||||
\(740\) | 6.09958e21 | 0.00249362 | ||||||||
\(741\) | −4.42482e23 | −0.178830 | ||||||||
\(742\) | 7.64280e23 | 0.305365 | ||||||||
\(743\) | 3.95298e24 | 1.56142 | 0.780709 | − | 0.624894i | \(-0.214858\pi\) | ||||
0.780709 | + | 0.624894i | \(0.214858\pi\) | |||||||
\(744\) | −1.15268e23 | −0.0450132 | ||||||||
\(745\) | 1.17164e24 | 0.452339 | ||||||||
\(746\) | 1.77794e24 | 0.678637 | ||||||||
\(747\) | −3.20377e24 | −1.20903 | ||||||||
\(748\) | 5.43451e21 | 0.00202767 | ||||||||
\(749\) | 3.53977e24 | 1.30581 | ||||||||
\(750\) | −4.73069e23 | −0.172545 | ||||||||
\(751\) | 3.34972e24 | 1.20800 | 0.604002 | − | 0.796983i | \(-0.293572\pi\) | ||||
0.604002 | + | 0.796983i | \(0.293572\pi\) | |||||||
\(752\) | 9.28523e23 | 0.331086 | ||||||||
\(753\) | −2.14586e23 | −0.0756560 | ||||||||
\(754\) | 7.77445e23 | 0.271028 | ||||||||
\(755\) | −4.21837e23 | −0.145410 | ||||||||
\(756\) | 5.51723e21 | 0.00188055 | ||||||||
\(757\) | −5.40799e24 | −1.82272 | −0.911362 | − | 0.411605i | \(-0.864968\pi\) | ||||
−0.911362 | + | 0.411605i | \(0.864968\pi\) | |||||||
\(758\) | −4.36008e24 | −1.45314 | ||||||||
\(759\) | 4.08304e22 | 0.0134564 | ||||||||
\(760\) | 9.37742e23 | 0.305610 | ||||||||
\(761\) | 4.57639e24 | 1.47487 | 0.737434 | − | 0.675419i | \(-0.236037\pi\) | ||||
0.737434 | + | 0.675419i | \(0.236037\pi\) | |||||||
\(762\) | −7.17717e23 | −0.228737 | ||||||||
\(763\) | 4.40533e23 | 0.138842 | ||||||||
\(764\) | −1.22711e22 | −0.00382464 | ||||||||
\(765\) | 1.86870e24 | 0.575993 | ||||||||
\(766\) | 2.43787e24 | 0.743132 | ||||||||
\(767\) | −1.13315e24 | −0.341608 | ||||||||
\(768\) | 1.04269e22 | 0.00310874 | ||||||||
\(769\) | −4.78476e24 | −1.41087 | −0.705433 | − | 0.708776i | \(-0.749248\pi\) | ||||
−0.705433 | + | 0.708776i | \(0.749248\pi\) | |||||||
\(770\) | −5.05321e23 | −0.147366 | ||||||||
\(771\) | −8.93581e23 | −0.257734 | ||||||||
\(772\) | 1.01778e22 | 0.00290340 | ||||||||
\(773\) | −2.88301e24 | −0.813431 | −0.406715 | − | 0.913555i | \(-0.633326\pi\) | ||||
−0.406715 | + | 0.913555i | \(0.633326\pi\) | |||||||
\(774\) | −2.04605e24 | −0.570977 | ||||||||
\(775\) | 6.16755e23 | 0.170235 | ||||||||
\(776\) | −1.91269e24 | −0.522179 | ||||||||
\(777\) | 6.57610e23 | 0.177578 | ||||||||
\(778\) | −2.82661e24 | −0.754986 | ||||||||
\(779\) | −2.40975e23 | −0.0636655 | ||||||||
\(780\) | −2.87811e21 | −0.000752148 0 | ||||||||
\(781\) | −2.13456e24 | −0.551791 | ||||||||
\(782\) | 9.91707e23 | 0.253586 | ||||||||
\(783\) | 2.86196e23 | 0.0723918 | ||||||||
\(784\) | 5.69087e23 | 0.142394 | ||||||||
\(785\) | −2.83699e24 | −0.702209 | ||||||||
\(786\) | 8.72808e23 | 0.213711 | ||||||||
\(787\) | −5.78719e24 | −1.40179 | −0.700894 | − | 0.713265i | \(-0.747216\pi\) | ||||
−0.700894 | + | 0.713265i | \(0.747216\pi\) | |||||||
\(788\) | 2.29040e22 | 0.00548831 | ||||||||
\(789\) | 1.31925e24 | 0.312732 | ||||||||
\(790\) | −1.00591e24 | −0.235899 | ||||||||
\(791\) | −5.52598e24 | −1.28206 | ||||||||
\(792\) | −1.35008e24 | −0.309882 | ||||||||
\(793\) | 2.59361e24 | 0.588956 | ||||||||
\(794\) | 4.45729e22 | 0.0100137 | ||||||||
\(795\) | −1.46768e23 | −0.0326221 | ||||||||
\(796\) | 3.83346e22 | 0.00843004 | ||||||||
\(797\) | −3.86589e24 | −0.841112 | −0.420556 | − | 0.907267i | \(-0.638165\pi\) | ||||
−0.420556 | + | 0.907267i | \(0.638165\pi\) | |||||||
\(798\) | 5.24129e23 | 0.112827 | ||||||||
\(799\) | −1.88941e24 | −0.402420 | ||||||||
\(800\) | −3.72904e22 | −0.00785836 | ||||||||
\(801\) | 6.17934e24 | 1.28844 | ||||||||
\(802\) | −5.86607e24 | −1.21022 | ||||||||
\(803\) | 2.26498e23 | 0.0462362 | ||||||||
\(804\) | 2.36373e21 | 0.000477442 0 | ||||||||
\(805\) | 4.83063e23 | 0.0965469 | ||||||||
\(806\) | −1.66627e24 | −0.329533 | ||||||||
\(807\) | −3.20289e23 | −0.0626782 | ||||||||
\(808\) | 6.56428e24 | 1.27113 | ||||||||
\(809\) | −7.76614e24 | −1.48814 | −0.744069 | − | 0.668103i | \(-0.767106\pi\) | ||||
−0.744069 | + | 0.668103i | \(0.767106\pi\) | |||||||
\(810\) | −2.30356e24 | −0.436794 | ||||||||
\(811\) | 5.97255e24 | 1.12068 | 0.560341 | − | 0.828262i | \(-0.310670\pi\) | ||||
0.560341 | + | 0.828262i | \(0.310670\pi\) | |||||||
\(812\) | 4.82420e21 | 0.000895775 0 | ||||||||
\(813\) | 1.87281e24 | 0.344131 | ||||||||
\(814\) | −1.70284e24 | −0.309646 | ||||||||
\(815\) | −1.11150e24 | −0.200018 | ||||||||
\(816\) | 1.34299e24 | 0.239170 | ||||||||
\(817\) | 2.07839e24 | 0.366301 | ||||||||
\(818\) | 2.43572e23 | 0.0424838 | ||||||||
\(819\) | 7.53689e24 | 1.30101 | ||||||||
\(820\) | −1.56741e21 | −0.000267773 0 | ||||||||
\(821\) | −3.79757e24 | −0.642080 | −0.321040 | − | 0.947066i | \(-0.604032\pi\) | ||||
−0.321040 | + | 0.947066i | \(0.604032\pi\) | |||||||
\(822\) | −1.59995e24 | −0.267730 | ||||||||
\(823\) | −2.24155e24 | −0.371235 | −0.185618 | − | 0.982622i | \(-0.559429\pi\) | ||||
−0.185618 | + | 0.982622i | \(0.559429\pi\) | |||||||
\(824\) | −2.01038e24 | −0.329531 | ||||||||
\(825\) | −2.97404e23 | −0.0482490 | ||||||||
\(826\) | 1.34224e24 | 0.215527 | ||||||||
\(827\) | 5.49632e24 | 0.873525 | 0.436763 | − | 0.899577i | \(-0.356125\pi\) | ||||
0.436763 | + | 0.899577i | \(0.356125\pi\) | |||||||
\(828\) | 6.69088e21 | 0.00105251 | ||||||||
\(829\) | −3.94938e24 | −0.614916 | −0.307458 | − | 0.951562i | \(-0.599478\pi\) | ||||
−0.307458 | + | 0.951562i | \(0.599478\pi\) | |||||||
\(830\) | −4.04081e24 | −0.622737 | ||||||||
\(831\) | −1.20998e24 | −0.184574 | ||||||||
\(832\) | 9.74157e24 | 1.47089 | ||||||||
\(833\) | −1.15801e24 | −0.173073 | ||||||||
\(834\) | 6.46656e23 | 0.0956669 | ||||||||
\(835\) | −1.98009e24 | −0.289968 | ||||||||
\(836\) | 7.10977e21 | 0.00103063 | ||||||||
\(837\) | −6.13395e23 | −0.0880185 | ||||||||
\(838\) | −9.57212e24 | −1.35967 | ||||||||
\(839\) | −7.15524e24 | −1.00611 | −0.503057 | − | 0.864253i | \(-0.667792\pi\) | ||||
−0.503057 | + | 0.864253i | \(0.667792\pi\) | |||||||
\(840\) | 6.57602e23 | 0.0915354 | ||||||||
\(841\) | 2.50246e23 | 0.0344828 | ||||||||
\(842\) | 2.71238e24 | 0.369997 | ||||||||
\(843\) | 3.71024e23 | 0.0501035 | ||||||||
\(844\) | −3.27829e22 | −0.00438265 | ||||||||
\(845\) | −4.27754e24 | −0.566125 | ||||||||
\(846\) | 2.43340e24 | 0.318835 | ||||||||
\(847\) | 6.39712e24 | 0.829804 | ||||||||
\(848\) | 2.56203e24 | 0.329017 | ||||||||
\(849\) | −9.45721e21 | −0.00120240 | ||||||||
\(850\) | −7.22347e24 | −0.909254 | ||||||||
\(851\) | 1.62783e24 | 0.202866 | ||||||||
\(852\) | 1.44009e22 | 0.00177686 | ||||||||
\(853\) | −3.24126e24 | −0.395956 | −0.197978 | − | 0.980206i | \(-0.563437\pi\) | ||||
−0.197978 | + | 0.980206i | \(0.563437\pi\) | |||||||
\(854\) | −3.07218e24 | −0.371583 | ||||||||
\(855\) | 2.44475e24 | 0.292768 | ||||||||
\(856\) | 1.19282e25 | 1.41432 | ||||||||
\(857\) | 4.49269e24 | 0.527436 | 0.263718 | − | 0.964600i | \(-0.415051\pi\) | ||||
0.263718 | + | 0.964600i | \(0.415051\pi\) | |||||||
\(858\) | 8.03490e23 | 0.0933982 | ||||||||
\(859\) | 6.87241e24 | 0.790983 | 0.395492 | − | 0.918470i | \(-0.370574\pi\) | ||||
0.395492 | + | 0.918470i | \(0.370574\pi\) | |||||||
\(860\) | 1.35188e22 | 0.00154064 | ||||||||
\(861\) | −1.68987e23 | −0.0190689 | ||||||||
\(862\) | 1.52152e25 | 1.70007 | ||||||||
\(863\) | 8.68590e24 | 0.961000 | 0.480500 | − | 0.876995i | \(-0.340455\pi\) | ||||
0.480500 | + | 0.876995i | \(0.340455\pi\) | |||||||
\(864\) | 3.70872e22 | 0.00406310 | ||||||||
\(865\) | −2.02585e24 | −0.219771 | ||||||||
\(866\) | −4.33769e24 | −0.465968 | ||||||||
\(867\) | −8.63440e23 | −0.0918481 | ||||||||
\(868\) | −1.03395e22 | −0.00108914 | ||||||||
\(869\) | −1.47110e24 | −0.153453 | ||||||||
\(870\) | 1.76845e23 | 0.0182675 | ||||||||
\(871\) | 6.59095e24 | 0.674207 | ||||||||
\(872\) | 1.48449e24 | 0.150379 | ||||||||
\(873\) | −4.98650e24 | −0.500236 | ||||||||
\(874\) | 1.29742e24 | 0.128894 | ||||||||
\(875\) | −8.18521e24 | −0.805306 | ||||||||
\(876\) | −1.52808e21 | −0.000148889 0 | ||||||||
\(877\) | 7.40659e24 | 0.714697 | 0.357348 | − | 0.933971i | \(-0.383681\pi\) | ||||
0.357348 | + | 0.933971i | \(0.383681\pi\) | |||||||
\(878\) | 6.68784e24 | 0.639120 | ||||||||
\(879\) | −1.16263e24 | −0.110036 | ||||||||
\(880\) | −1.69394e24 | −0.158780 | ||||||||
\(881\) | −5.91827e24 | −0.549414 | −0.274707 | − | 0.961528i | \(-0.588581\pi\) | ||||
−0.274707 | + | 0.961528i | \(0.588581\pi\) | |||||||
\(882\) | 1.49142e24 | 0.137125 | ||||||||
\(883\) | 1.34375e25 | 1.22364 | 0.611818 | − | 0.790999i | \(-0.290438\pi\) | ||||
0.611818 | + | 0.790999i | \(0.290438\pi\) | |||||||
\(884\) | −1.02233e23 | −0.00922037 | ||||||||
\(885\) | −2.57758e23 | −0.0230247 | ||||||||
\(886\) | −7.54611e24 | −0.667631 | ||||||||
\(887\) | −1.47109e25 | −1.28910 | −0.644552 | − | 0.764561i | \(-0.722956\pi\) | ||||
−0.644552 | + | 0.764561i | \(0.722956\pi\) | |||||||
\(888\) | 2.21600e24 | 0.192335 | ||||||||
\(889\) | −1.24182e25 | −1.06756 | ||||||||
\(890\) | 7.79380e24 | 0.663643 | ||||||||
\(891\) | −3.36888e24 | −0.284135 | ||||||||
\(892\) | −1.10453e23 | −0.00922737 | ||||||||
\(893\) | −2.47185e24 | −0.204543 | ||||||||
\(894\) | 2.20672e24 | 0.180875 | ||||||||
\(895\) | −7.22305e24 | −0.586441 | ||||||||
\(896\) | −1.14191e25 | −0.918363 | ||||||||
\(897\) | −7.68098e23 | −0.0611900 | ||||||||
\(898\) | −2.71957e24 | −0.214610 | ||||||||
\(899\) | −5.36345e23 | −0.0419263 | ||||||||
\(900\) | −4.87355e22 | −0.00377385 | ||||||||
\(901\) | −5.21336e24 | −0.399905 | ||||||||
\(902\) | 4.37579e23 | 0.0332507 | ||||||||
\(903\) | 1.45749e24 | 0.109713 | ||||||||
\(904\) | −1.86213e25 | −1.38860 | ||||||||
\(905\) | 7.02484e24 | 0.518948 | ||||||||
\(906\) | −7.94510e23 | −0.0581447 | ||||||||
\(907\) | 2.49331e25 | 1.80765 | 0.903823 | − | 0.427905i | \(-0.140748\pi\) | ||||
0.903823 | + | 0.427905i | \(0.140748\pi\) | |||||||
\(908\) | −2.93842e22 | −0.00211049 | ||||||||
\(909\) | 1.71135e25 | 1.21772 | ||||||||
\(910\) | 9.50604e24 | 0.670113 | ||||||||
\(911\) | −5.85002e24 | −0.408556 | −0.204278 | − | 0.978913i | \(-0.565485\pi\) | ||||
−0.204278 | + | 0.978913i | \(0.565485\pi\) | |||||||
\(912\) | 1.75699e24 | 0.121566 | ||||||||
\(913\) | −5.90955e24 | −0.405091 | ||||||||
\(914\) | 2.34017e25 | 1.58930 | ||||||||
\(915\) | 5.89967e23 | 0.0396961 | ||||||||
\(916\) | −1.18053e23 | −0.00786981 | ||||||||
\(917\) | 1.51016e25 | 0.997436 | ||||||||
\(918\) | 7.18413e24 | 0.470123 | ||||||||
\(919\) | 7.14568e24 | 0.463299 | 0.231650 | − | 0.972799i | \(-0.425588\pi\) | ||||
0.231650 | + | 0.972799i | \(0.425588\pi\) | |||||||
\(920\) | 1.62781e24 | 0.104570 | ||||||||
\(921\) | 6.69607e22 | 0.00426200 | ||||||||
\(922\) | −2.05529e25 | −1.29616 | ||||||||
\(923\) | 4.01551e25 | 2.50915 | ||||||||
\(924\) | 4.98581e21 | 0.000308691 0 | ||||||||
\(925\) | −1.18569e25 | −0.727390 | ||||||||
\(926\) | −1.39261e25 | −0.846515 | ||||||||
\(927\) | −5.24119e24 | −0.315684 | ||||||||
\(928\) | 3.24286e22 | 0.00193540 | ||||||||
\(929\) | −3.63609e24 | −0.215031 | −0.107516 | − | 0.994203i | \(-0.534290\pi\) | ||||
−0.107516 | + | 0.994203i | \(0.534290\pi\) | |||||||
\(930\) | −3.79026e23 | −0.0222108 | ||||||||
\(931\) | −1.51499e24 | −0.0879703 | ||||||||
\(932\) | −1.51807e23 | −0.00873488 | ||||||||
\(933\) | −6.78521e24 | −0.386874 | ||||||||
\(934\) | −1.98927e25 | −1.12395 | ||||||||
\(935\) | 3.44693e24 | 0.192990 | ||||||||
\(936\) | 2.53976e25 | 1.40912 | ||||||||
\(937\) | −2.73327e25 | −1.50278 | −0.751392 | − | 0.659856i | \(-0.770617\pi\) | ||||
−0.751392 | + | 0.659856i | \(0.770617\pi\) | |||||||
\(938\) | −7.80710e24 | −0.425369 | ||||||||
\(939\) | 4.07662e24 | 0.220111 | ||||||||
\(940\) | −1.60781e22 | −0.000860295 0 | ||||||||
\(941\) | 2.01276e24 | 0.106728 | 0.0533642 | − | 0.998575i | \(-0.483006\pi\) | ||||
0.0533642 | + | 0.998575i | \(0.483006\pi\) | |||||||
\(942\) | −5.34335e24 | −0.280790 | ||||||||
\(943\) | −4.18305e23 | −0.0217843 | ||||||||
\(944\) | 4.49948e24 | 0.232220 | ||||||||
\(945\) | 3.49940e24 | 0.178988 | ||||||||
\(946\) | −3.77407e24 | −0.191309 | ||||||||
\(947\) | 2.29048e25 | 1.15067 | 0.575337 | − | 0.817916i | \(-0.304871\pi\) | ||||
0.575337 | + | 0.817916i | \(0.304871\pi\) | |||||||
\(948\) | 9.92488e21 | 0.000494145 0 | ||||||||
\(949\) | −4.26086e24 | −0.210249 | ||||||||
\(950\) | −9.45021e24 | −0.462159 | ||||||||
\(951\) | −9.57459e23 | −0.0464072 | ||||||||
\(952\) | 2.33587e25 | 1.12211 | ||||||||
\(953\) | 6.92070e23 | 0.0329504 | 0.0164752 | − | 0.999864i | \(-0.494756\pi\) | ||||
0.0164752 | + | 0.999864i | \(0.494756\pi\) | |||||||
\(954\) | 6.71436e24 | 0.316842 | ||||||||
\(955\) | −7.78317e24 | −0.364022 | ||||||||
\(956\) | −9.83935e22 | −0.00456115 | ||||||||
\(957\) | 2.58630e23 | 0.0118830 | ||||||||
\(958\) | −2.62014e25 | −1.19321 | ||||||||
\(959\) | −2.76830e25 | −1.24955 | ||||||||
\(960\) | 2.21591e24 | 0.0991393 | ||||||||
\(961\) | −2.14006e25 | −0.949023 | ||||||||
\(962\) | 3.20336e25 | 1.40805 | ||||||||
\(963\) | 3.10976e25 | 1.35489 | ||||||||
\(964\) | −2.12279e22 | −0.000916754 0 | ||||||||
\(965\) | 6.45546e24 | 0.276341 | ||||||||
\(966\) | 9.09827e23 | 0.0386058 | ||||||||
\(967\) | −4.42650e24 | −0.186181 | −0.0930906 | − | 0.995658i | \(-0.529675\pi\) | ||||
−0.0930906 | + | 0.995658i | \(0.529675\pi\) | |||||||
\(968\) | 2.15568e25 | 0.898761 | ||||||||
\(969\) | −3.57523e24 | −0.147758 | ||||||||
\(970\) | −6.28932e24 | −0.257658 | ||||||||
\(971\) | −2.88845e25 | −1.17301 | −0.586505 | − | 0.809945i | \(-0.699497\pi\) | ||||
−0.586505 | + | 0.809945i | \(0.699497\pi\) | |||||||
\(972\) | 7.31939e22 | 0.00294654 | ||||||||
\(973\) | 1.11887e25 | 0.446498 | ||||||||
\(974\) | −3.28209e25 | −1.29837 | ||||||||
\(975\) | 5.59473e24 | 0.219402 | ||||||||
\(976\) | −1.02986e25 | −0.400364 | ||||||||
\(977\) | −1.35303e25 | −0.521439 | −0.260719 | − | 0.965415i | \(-0.583960\pi\) | ||||
−0.260719 | + | 0.965415i | \(0.583960\pi\) | |||||||
\(978\) | −2.09346e24 | −0.0799805 | ||||||||
\(979\) | 1.13982e25 | 0.431701 | ||||||||
\(980\) | −9.85417e21 | −0.000369997 0 | ||||||||
\(981\) | 3.87017e24 | 0.144060 | ||||||||
\(982\) | −3.03062e25 | −1.11837 | ||||||||
\(983\) | −1.80376e25 | −0.659894 | −0.329947 | − | 0.944000i | \(-0.607031\pi\) | ||||
−0.329947 | + | 0.944000i | \(0.607031\pi\) | |||||||
\(984\) | −5.69446e23 | −0.0206535 | ||||||||
\(985\) | 1.45273e25 | 0.522368 | ||||||||
\(986\) | 6.28171e24 | 0.223936 | ||||||||
\(987\) | −1.73341e24 | −0.0612642 | ||||||||
\(988\) | −1.33748e23 | −0.00468656 | ||||||||
\(989\) | 3.60783e24 | 0.125337 | ||||||||
\(990\) | −4.43935e24 | −0.152905 | ||||||||
\(991\) | 3.71782e25 | 1.26959 | 0.634794 | − | 0.772681i | \(-0.281085\pi\) | ||||
0.634794 | + | 0.772681i | \(0.281085\pi\) | |||||||
\(992\) | −6.95032e22 | −0.00235318 | ||||||||
\(993\) | −1.75081e24 | −0.0587719 | ||||||||
\(994\) | −4.75645e25 | −1.58306 | ||||||||
\(995\) | 2.43144e25 | 0.802356 | ||||||||
\(996\) | 3.98691e22 | 0.00130446 | ||||||||
\(997\) | −1.96631e25 | −0.637886 | −0.318943 | − | 0.947774i | \(-0.603328\pi\) | ||||
−0.318943 | + | 0.947774i | \(0.603328\pi\) | |||||||
\(998\) | 1.09131e25 | 0.351025 | ||||||||
\(999\) | 1.17923e25 | 0.376091 |
(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 | 29.18.a.b.1.16 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.18.a.b.1.16 | ✓ | 21 | 1.1 | even | 1 | trivial |