Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,34,Mod(1,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 34, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 34);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 34 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(20.6948486643\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5357605x + 842871622 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{6}\cdot 11 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2232.09\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 61269.1 | 0.661069 | 0.330535 | − | 0.943794i | \(-0.392771\pi\) | ||||
0.330535 | + | 0.943794i | \(0.392771\pi\) | |||||||
\(3\) | −4.30467e7 | −0.577350 | ||||||||
\(4\) | −4.83603e9 | −0.562988 | ||||||||
\(5\) | 2.12383e11 | 0.622465 | 0.311232 | − | 0.950334i | \(-0.399258\pi\) | ||||
0.311232 | + | 0.950334i | \(0.399258\pi\) | |||||||
\(6\) | −2.63744e12 | −0.381668 | ||||||||
\(7\) | 1.58203e14 | 1.79927 | 0.899636 | − | 0.436641i | \(-0.143832\pi\) | ||||
0.899636 | + | 0.436641i | \(0.143832\pi\) | |||||||
\(8\) | −8.22597e14 | −1.03324 | ||||||||
\(9\) | 1.85302e15 | 0.333333 | ||||||||
\(10\) | 1.30125e16 | 0.411492 | ||||||||
\(11\) | −2.62906e17 | −1.72513 | −0.862563 | − | 0.505949i | \(-0.831142\pi\) | ||||
−0.862563 | + | 0.505949i | \(0.831142\pi\) | |||||||
\(12\) | 2.08175e17 | 0.325041 | ||||||||
\(13\) | −3.56670e18 | −1.48663 | −0.743313 | − | 0.668944i | \(-0.766747\pi\) | ||||
−0.743313 | + | 0.668944i | \(0.766747\pi\) | |||||||
\(14\) | 9.69295e18 | 1.18944 | ||||||||
\(15\) | −9.14240e18 | −0.359380 | ||||||||
\(16\) | −8.85864e18 | −0.120057 | ||||||||
\(17\) | 1.73081e19 | 0.0862667 | 0.0431334 | − | 0.999069i | \(-0.486266\pi\) | ||||
0.0431334 | + | 0.999069i | \(0.486266\pi\) | |||||||
\(18\) | 1.13533e20 | 0.220356 | ||||||||
\(19\) | −5.11529e20 | −0.406852 | −0.203426 | − | 0.979090i | \(-0.565208\pi\) | ||||
−0.203426 | + | 0.979090i | \(0.565208\pi\) | |||||||
\(20\) | −1.02709e21 | −0.350440 | ||||||||
\(21\) | −6.81012e21 | −1.03881 | ||||||||
\(22\) | −1.61080e22 | −1.14043 | ||||||||
\(23\) | −3.17073e22 | −1.07808 | −0.539039 | − | 0.842281i | \(-0.681212\pi\) | ||||
−0.539039 | + | 0.842281i | \(0.681212\pi\) | |||||||
\(24\) | 3.54101e22 | 0.596543 | ||||||||
\(25\) | −7.13087e22 | −0.612537 | ||||||||
\(26\) | −2.18529e23 | −0.982762 | ||||||||
\(27\) | −7.97664e22 | −0.192450 | ||||||||
\(28\) | −7.65074e23 | −1.01297 | ||||||||
\(29\) | 1.64526e23 | 0.122087 | 0.0610433 | − | 0.998135i | \(-0.480557\pi\) | ||||
0.0610433 | + | 0.998135i | \(0.480557\pi\) | |||||||
\(30\) | −5.60147e23 | −0.237575 | ||||||||
\(31\) | 1.52635e24 | 0.376865 | 0.188433 | − | 0.982086i | \(-0.439659\pi\) | ||||
0.188433 | + | 0.982086i | \(0.439659\pi\) | |||||||
\(32\) | 6.52329e24 | 0.953877 | ||||||||
\(33\) | 1.13172e25 | 0.996002 | ||||||||
\(34\) | 1.06045e24 | 0.0570282 | ||||||||
\(35\) | 3.35996e25 | 1.11998 | ||||||||
\(36\) | −8.96126e24 | −0.187663 | ||||||||
\(37\) | −4.62071e25 | −0.615716 | −0.307858 | − | 0.951432i | \(-0.599612\pi\) | ||||
−0.307858 | + | 0.951432i | \(0.599612\pi\) | |||||||
\(38\) | −3.13410e25 | −0.268957 | ||||||||
\(39\) | 1.53535e26 | 0.858304 | ||||||||
\(40\) | −1.74706e26 | −0.643157 | ||||||||
\(41\) | −3.97631e26 | −0.973972 | −0.486986 | − | 0.873410i | \(-0.661904\pi\) | ||||
−0.486986 | + | 0.873410i | \(0.661904\pi\) | |||||||
\(42\) | −4.17250e26 | −0.686725 | ||||||||
\(43\) | −3.64043e26 | −0.406372 | −0.203186 | − | 0.979140i | \(-0.565130\pi\) | ||||
−0.203186 | + | 0.979140i | \(0.565130\pi\) | |||||||
\(44\) | 1.27142e27 | 0.971225 | ||||||||
\(45\) | 3.93550e26 | 0.207488 | ||||||||
\(46\) | −1.94268e27 | −0.712683 | ||||||||
\(47\) | −2.74215e27 | −0.705467 | −0.352733 | − | 0.935724i | \(-0.614748\pi\) | ||||
−0.352733 | + | 0.935724i | \(0.614748\pi\) | |||||||
\(48\) | 3.81336e26 | 0.0693149 | ||||||||
\(49\) | 1.72972e28 | 2.23738 | ||||||||
\(50\) | −4.36902e27 | −0.404930 | ||||||||
\(51\) | −7.45059e26 | −0.0498061 | ||||||||
\(52\) | 1.72487e28 | 0.836952 | ||||||||
\(53\) | 3.12962e28 | 1.10902 | 0.554511 | − | 0.832177i | \(-0.312906\pi\) | ||||
0.554511 | + | 0.832177i | \(0.312906\pi\) | |||||||
\(54\) | −4.88722e27 | −0.127223 | ||||||||
\(55\) | −5.58368e28 | −1.07383 | ||||||||
\(56\) | −1.30137e29 | −1.85908 | ||||||||
\(57\) | 2.20197e28 | 0.234896 | ||||||||
\(58\) | 1.00804e28 | 0.0807077 | ||||||||
\(59\) | −9.28615e28 | −0.560761 | −0.280380 | − | 0.959889i | \(-0.590461\pi\) | ||||
−0.280380 | + | 0.959889i | \(0.590461\pi\) | |||||||
\(60\) | 4.42129e28 | 0.202327 | ||||||||
\(61\) | −8.67336e28 | −0.302166 | −0.151083 | − | 0.988521i | \(-0.548276\pi\) | ||||
−0.151083 | + | 0.988521i | \(0.548276\pi\) | |||||||
\(62\) | 9.35181e28 | 0.249134 | ||||||||
\(63\) | 2.93153e29 | 0.599757 | ||||||||
\(64\) | 4.75772e29 | 0.750635 | ||||||||
\(65\) | −7.57508e29 | −0.925372 | ||||||||
\(66\) | 6.93397e29 | 0.658426 | ||||||||
\(67\) | 4.18932e29 | 0.310391 | 0.155196 | − | 0.987884i | \(-0.450399\pi\) | ||||
0.155196 | + | 0.987884i | \(0.450399\pi\) | |||||||
\(68\) | −8.37027e28 | −0.0485671 | ||||||||
\(69\) | 1.36489e30 | 0.622428 | ||||||||
\(70\) | 2.05862e30 | 0.740386 | ||||||||
\(71\) | −4.44984e30 | −1.26643 | −0.633216 | − | 0.773975i | \(-0.718266\pi\) | ||||
−0.633216 | + | 0.773975i | \(0.718266\pi\) | |||||||
\(72\) | −1.52429e30 | −0.344414 | ||||||||
\(73\) | 1.71800e30 | 0.309169 | 0.154584 | − | 0.987980i | \(-0.450596\pi\) | ||||
0.154584 | + | 0.987980i | \(0.450596\pi\) | |||||||
\(74\) | −2.83107e30 | −0.407031 | ||||||||
\(75\) | 3.06961e30 | 0.353649 | ||||||||
\(76\) | 2.47377e30 | 0.229053 | ||||||||
\(77\) | −4.15925e31 | −3.10397 | ||||||||
\(78\) | 9.40695e30 | 0.567398 | ||||||||
\(79\) | 2.50450e31 | 1.22426 | 0.612130 | − | 0.790757i | \(-0.290313\pi\) | ||||
0.612130 | + | 0.790757i | \(0.290313\pi\) | |||||||
\(80\) | −1.88143e30 | −0.0747313 | ||||||||
\(81\) | 3.43368e30 | 0.111111 | ||||||||
\(82\) | −2.43625e31 | −0.643863 | ||||||||
\(83\) | 7.18974e31 | 1.55570 | 0.777848 | − | 0.628453i | \(-0.216311\pi\) | ||||
0.777848 | + | 0.628453i | \(0.216311\pi\) | |||||||
\(84\) | 3.29339e31 | 0.584837 | ||||||||
\(85\) | 3.67596e30 | 0.0536980 | ||||||||
\(86\) | −2.23046e31 | −0.268640 | ||||||||
\(87\) | −7.08231e30 | −0.0704868 | ||||||||
\(88\) | 2.16266e32 | 1.78247 | ||||||||
\(89\) | −1.21977e32 | −0.834338 | −0.417169 | − | 0.908829i | \(-0.636978\pi\) | ||||
−0.417169 | + | 0.908829i | \(0.636978\pi\) | |||||||
\(90\) | 2.41125e31 | 0.137164 | ||||||||
\(91\) | −5.64263e32 | −2.67484 | ||||||||
\(92\) | 1.53337e32 | 0.606944 | ||||||||
\(93\) | −6.57043e31 | −0.217583 | ||||||||
\(94\) | −1.68009e32 | −0.466362 | ||||||||
\(95\) | −1.08640e32 | −0.253251 | ||||||||
\(96\) | −2.80806e32 | −0.550721 | ||||||||
\(97\) | 5.67244e32 | 0.937640 | 0.468820 | − | 0.883294i | \(-0.344679\pi\) | ||||
0.468820 | + | 0.883294i | \(0.344679\pi\) | |||||||
\(98\) | 1.05978e33 | 1.47906 | ||||||||
\(99\) | −4.87170e32 | −0.575042 | ||||||||
\(100\) | 3.44851e32 | 0.344851 | ||||||||
\(101\) | −4.34825e32 | −0.368987 | −0.184494 | − | 0.982834i | \(-0.559065\pi\) | ||||
−0.184494 | + | 0.982834i | \(0.559065\pi\) | |||||||
\(102\) | −4.56491e31 | −0.0329253 | ||||||||
\(103\) | −1.39936e33 | −0.859242 | −0.429621 | − | 0.903009i | \(-0.641353\pi\) | ||||
−0.429621 | + | 0.903009i | \(0.641353\pi\) | |||||||
\(104\) | 2.93396e33 | 1.53605 | ||||||||
\(105\) | −1.44635e33 | −0.646623 | ||||||||
\(106\) | 1.91749e33 | 0.733139 | ||||||||
\(107\) | 3.37111e33 | 1.10393 | 0.551965 | − | 0.833868i | \(-0.313878\pi\) | ||||
0.551965 | + | 0.833868i | \(0.313878\pi\) | |||||||
\(108\) | 3.85753e32 | 0.108347 | ||||||||
\(109\) | −4.20805e33 | −1.01518 | −0.507591 | − | 0.861598i | \(-0.669464\pi\) | ||||
−0.507591 | + | 0.861598i | \(0.669464\pi\) | |||||||
\(110\) | −3.42107e33 | −0.709876 | ||||||||
\(111\) | 1.98907e33 | 0.355484 | ||||||||
\(112\) | −1.40146e33 | −0.216015 | ||||||||
\(113\) | −5.11191e33 | −0.680438 | −0.340219 | − | 0.940346i | \(-0.610501\pi\) | ||||
−0.340219 | + | 0.940346i | \(0.610501\pi\) | |||||||
\(114\) | 1.34913e33 | 0.155282 | ||||||||
\(115\) | −6.73409e33 | −0.671065 | ||||||||
\(116\) | −7.95653e32 | −0.0687333 | ||||||||
\(117\) | −6.60917e33 | −0.495542 | ||||||||
\(118\) | −5.68954e33 | −0.370701 | ||||||||
\(119\) | 2.73820e33 | 0.155217 | ||||||||
\(120\) | 7.52051e33 | 0.371327 | ||||||||
\(121\) | 4.58943e34 | 1.97606 | ||||||||
\(122\) | −5.31409e33 | −0.199752 | ||||||||
\(123\) | 1.71167e34 | 0.562323 | ||||||||
\(124\) | −7.38147e33 | −0.212170 | ||||||||
\(125\) | −3.98694e34 | −1.00375 | ||||||||
\(126\) | 1.79612e34 | 0.396481 | ||||||||
\(127\) | 9.75563e34 | 1.89014 | 0.945070 | − | 0.326869i | \(-0.105993\pi\) | ||||
0.945070 | + | 0.326869i | \(0.105993\pi\) | |||||||
\(128\) | −2.68845e34 | −0.457655 | ||||||||
\(129\) | 1.56709e34 | 0.234619 | ||||||||
\(130\) | −4.64118e34 | −0.611735 | ||||||||
\(131\) | −8.73187e34 | −1.01422 | −0.507109 | − | 0.861882i | \(-0.669286\pi\) | ||||
−0.507109 | + | 0.861882i | \(0.669286\pi\) | |||||||
\(132\) | −5.47305e34 | −0.560737 | ||||||||
\(133\) | −8.09254e34 | −0.732037 | ||||||||
\(134\) | 2.56676e34 | 0.205190 | ||||||||
\(135\) | −1.69410e34 | −0.119793 | ||||||||
\(136\) | −1.42376e34 | −0.0891345 | ||||||||
\(137\) | 1.13700e34 | 0.0630770 | 0.0315385 | − | 0.999503i | \(-0.489959\pi\) | ||||
0.0315385 | + | 0.999503i | \(0.489959\pi\) | |||||||
\(138\) | 8.36259e34 | 0.411468 | ||||||||
\(139\) | 7.98052e33 | 0.0348568 | 0.0174284 | − | 0.999848i | \(-0.494452\pi\) | ||||
0.0174284 | + | 0.999848i | \(0.494452\pi\) | |||||||
\(140\) | −1.62489e35 | −0.630537 | ||||||||
\(141\) | 1.18041e35 | 0.407301 | ||||||||
\(142\) | −2.72638e35 | −0.837199 | ||||||||
\(143\) | 9.37707e35 | 2.56462 | ||||||||
\(144\) | −1.64152e34 | −0.0400190 | ||||||||
\(145\) | 3.49426e34 | 0.0759947 | ||||||||
\(146\) | 1.05260e35 | 0.204382 | ||||||||
\(147\) | −7.44586e35 | −1.29175 | ||||||||
\(148\) | 2.23459e35 | 0.346641 | ||||||||
\(149\) | −1.73859e35 | −0.241336 | −0.120668 | − | 0.992693i | \(-0.538504\pi\) | ||||
−0.120668 | + | 0.992693i | \(0.538504\pi\) | |||||||
\(150\) | 1.88072e35 | 0.233786 | ||||||||
\(151\) | 8.75792e35 | 0.975622 | 0.487811 | − | 0.872949i | \(-0.337796\pi\) | ||||
0.487811 | + | 0.872949i | \(0.337796\pi\) | |||||||
\(152\) | 4.20783e35 | 0.420377 | ||||||||
\(153\) | 3.20723e34 | 0.0287556 | ||||||||
\(154\) | −2.54833e36 | −2.05194 | ||||||||
\(155\) | 3.24171e35 | 0.234585 | ||||||||
\(156\) | −7.42499e35 | −0.483215 | ||||||||
\(157\) | 5.38159e35 | 0.315186 | 0.157593 | − | 0.987504i | \(-0.449627\pi\) | ||||
0.157593 | + | 0.987504i | \(0.449627\pi\) | |||||||
\(158\) | 1.53448e36 | 0.809321 | ||||||||
\(159\) | −1.34720e36 | −0.640294 | ||||||||
\(160\) | 1.38544e36 | 0.593755 | ||||||||
\(161\) | −5.01619e36 | −1.93975 | ||||||||
\(162\) | 2.10379e35 | 0.0734521 | ||||||||
\(163\) | −4.22882e36 | −1.33390 | −0.666951 | − | 0.745102i | \(-0.732401\pi\) | ||||
−0.666951 | + | 0.745102i | \(0.732401\pi\) | |||||||
\(164\) | 1.92295e36 | 0.548334 | ||||||||
\(165\) | 2.40359e36 | 0.619977 | ||||||||
\(166\) | 4.40509e36 | 1.02842 | ||||||||
\(167\) | 5.06821e35 | 0.107160 | 0.0535800 | − | 0.998564i | \(-0.482937\pi\) | ||||
0.0535800 | + | 0.998564i | \(0.482937\pi\) | |||||||
\(168\) | 5.60198e36 | 1.07334 | ||||||||
\(169\) | 6.96524e36 | 1.21006 | ||||||||
\(170\) | 2.25223e35 | 0.0354981 | ||||||||
\(171\) | −9.47874e35 | −0.135617 | ||||||||
\(172\) | 1.76052e36 | 0.228782 | ||||||||
\(173\) | −5.77607e36 | −0.682138 | −0.341069 | − | 0.940038i | \(-0.610789\pi\) | ||||
−0.341069 | + | 0.940038i | \(0.610789\pi\) | |||||||
\(174\) | −4.33927e35 | −0.0465966 | ||||||||
\(175\) | −1.12812e37 | −1.10212 | ||||||||
\(176\) | 2.32899e36 | 0.207114 | ||||||||
\(177\) | 3.99738e36 | 0.323755 | ||||||||
\(178\) | −7.47341e36 | −0.551555 | ||||||||
\(179\) | −7.40660e36 | −0.498361 | −0.249180 | − | 0.968457i | \(-0.580161\pi\) | ||||
−0.249180 | + | 0.968457i | \(0.580161\pi\) | |||||||
\(180\) | −1.90322e36 | −0.116813 | ||||||||
\(181\) | 1.00139e37 | 0.560928 | 0.280464 | − | 0.959865i | \(-0.409512\pi\) | ||||
0.280464 | + | 0.959865i | \(0.409512\pi\) | |||||||
\(182\) | −3.45719e37 | −1.76826 | ||||||||
\(183\) | 3.73360e36 | 0.174455 | ||||||||
\(184\) | 2.60823e37 | 1.11392 | ||||||||
\(185\) | −9.81361e36 | −0.383262 | ||||||||
\(186\) | −4.02565e36 | −0.143837 | ||||||||
\(187\) | −4.55041e36 | −0.148821 | ||||||||
\(188\) | 1.32611e37 | 0.397169 | ||||||||
\(189\) | −1.26193e37 | −0.346270 | ||||||||
\(190\) | −6.65629e36 | −0.167416 | ||||||||
\(191\) | 7.94277e37 | 1.83198 | 0.915991 | − | 0.401198i | \(-0.131406\pi\) | ||||
0.915991 | + | 0.401198i | \(0.131406\pi\) | |||||||
\(192\) | −2.04804e37 | −0.433380 | ||||||||
\(193\) | 2.66529e37 | 0.517666 | 0.258833 | − | 0.965922i | \(-0.416662\pi\) | ||||
0.258833 | + | 0.965922i | \(0.416662\pi\) | |||||||
\(194\) | 3.47545e37 | 0.619845 | ||||||||
\(195\) | 3.26082e37 | 0.534264 | ||||||||
\(196\) | −8.36496e37 | −1.25962 | ||||||||
\(197\) | 8.31876e36 | 0.115177 | 0.0575885 | − | 0.998340i | \(-0.481659\pi\) | ||||
0.0575885 | + | 0.998340i | \(0.481659\pi\) | |||||||
\(198\) | −2.98485e37 | −0.380143 | ||||||||
\(199\) | −7.30042e36 | −0.0855603 | −0.0427801 | − | 0.999085i | \(-0.513621\pi\) | ||||
−0.0427801 | + | 0.999085i | \(0.513621\pi\) | |||||||
\(200\) | 5.86584e37 | 0.632900 | ||||||||
\(201\) | −1.80337e37 | −0.179204 | ||||||||
\(202\) | −2.66413e37 | −0.243926 | ||||||||
\(203\) | 2.60285e37 | 0.219667 | ||||||||
\(204\) | 3.60313e36 | 0.0280402 | ||||||||
\(205\) | −8.44501e37 | −0.606263 | ||||||||
\(206\) | −8.57377e37 | −0.568019 | ||||||||
\(207\) | −5.87543e37 | −0.359359 | ||||||||
\(208\) | 3.15962e37 | 0.178480 | ||||||||
\(209\) | 1.34484e38 | 0.701871 | ||||||||
\(210\) | −8.86168e37 | −0.427462 | ||||||||
\(211\) | −2.24819e38 | −1.00270 | −0.501352 | − | 0.865243i | \(-0.667164\pi\) | ||||
−0.501352 | + | 0.865243i | \(0.667164\pi\) | |||||||
\(212\) | −1.51349e38 | −0.624365 | ||||||||
\(213\) | 1.91551e38 | 0.731175 | ||||||||
\(214\) | 2.06545e38 | 0.729773 | ||||||||
\(215\) | −7.73166e37 | −0.252952 | ||||||||
\(216\) | 6.56156e37 | 0.198848 | ||||||||
\(217\) | 2.41473e38 | 0.678083 | ||||||||
\(218\) | −2.57824e38 | −0.671105 | ||||||||
\(219\) | −7.39542e37 | −0.178499 | ||||||||
\(220\) | 2.70028e38 | 0.604554 | ||||||||
\(221\) | −6.17330e37 | −0.128246 | ||||||||
\(222\) | 1.21868e38 | 0.234999 | ||||||||
\(223\) | 9.65044e38 | 1.72789 | 0.863947 | − | 0.503583i | \(-0.167985\pi\) | ||||
0.863947 | + | 0.503583i | \(0.167985\pi\) | |||||||
\(224\) | 1.03200e39 | 1.71628 | ||||||||
\(225\) | −1.32137e38 | −0.204179 | ||||||||
\(226\) | −3.13202e38 | −0.449817 | ||||||||
\(227\) | −1.45369e39 | −1.94109 | −0.970545 | − | 0.240921i | \(-0.922551\pi\) | ||||
−0.970545 | + | 0.240921i | \(0.922551\pi\) | |||||||
\(228\) | −1.06488e38 | −0.132244 | ||||||||
\(229\) | −8.85760e38 | −1.02337 | −0.511683 | − | 0.859174i | \(-0.670978\pi\) | ||||
−0.511683 | + | 0.859174i | \(0.670978\pi\) | |||||||
\(230\) | −4.12592e38 | −0.443620 | ||||||||
\(231\) | 1.79042e39 | 1.79208 | ||||||||
\(232\) | −1.35339e38 | −0.126145 | ||||||||
\(233\) | −1.96369e39 | −1.70491 | −0.852453 | − | 0.522804i | \(-0.824886\pi\) | ||||
−0.852453 | + | 0.522804i | \(0.824886\pi\) | |||||||
\(234\) | −4.04938e38 | −0.327587 | ||||||||
\(235\) | −5.82386e38 | −0.439128 | ||||||||
\(236\) | 4.49081e38 | 0.315701 | ||||||||
\(237\) | −1.07810e39 | −0.706827 | ||||||||
\(238\) | 1.67767e38 | 0.102609 | ||||||||
\(239\) | 1.13364e39 | 0.647008 | 0.323504 | − | 0.946227i | \(-0.395139\pi\) | ||||
0.323504 | + | 0.946227i | \(0.395139\pi\) | |||||||
\(240\) | 8.09892e37 | 0.0431461 | ||||||||
\(241\) | −8.77821e38 | −0.436641 | −0.218321 | − | 0.975877i | \(-0.570058\pi\) | ||||
−0.218321 | + | 0.975877i | \(0.570058\pi\) | |||||||
\(242\) | 2.81191e39 | 1.30631 | ||||||||
\(243\) | −1.47809e38 | −0.0641500 | ||||||||
\(244\) | 4.19446e38 | 0.170115 | ||||||||
\(245\) | 3.67363e39 | 1.39269 | ||||||||
\(246\) | 1.04873e39 | 0.371734 | ||||||||
\(247\) | 1.82447e39 | 0.604836 | ||||||||
\(248\) | −1.25557e39 | −0.389393 | ||||||||
\(249\) | −3.09495e39 | −0.898181 | ||||||||
\(250\) | −2.44276e39 | −0.663547 | ||||||||
\(251\) | −4.39897e39 | −1.11875 | −0.559377 | − | 0.828913i | \(-0.688960\pi\) | ||||
−0.559377 | + | 0.828913i | \(0.688960\pi\) | |||||||
\(252\) | −1.41770e39 | −0.337656 | ||||||||
\(253\) | 8.33603e39 | 1.85982 | ||||||||
\(254\) | 5.97719e39 | 1.24951 | ||||||||
\(255\) | −1.58238e38 | −0.0310026 | ||||||||
\(256\) | −5.73404e39 | −1.05318 | ||||||||
\(257\) | −6.53419e38 | −0.112537 | −0.0562685 | − | 0.998416i | \(-0.517920\pi\) | ||||
−0.0562685 | + | 0.998416i | \(0.517920\pi\) | |||||||
\(258\) | 9.60141e38 | 0.155099 | ||||||||
\(259\) | −7.31010e39 | −1.10784 | ||||||||
\(260\) | 3.66333e39 | 0.520973 | ||||||||
\(261\) | 3.04870e38 | 0.0406955 | ||||||||
\(262\) | −5.34994e39 | −0.670467 | ||||||||
\(263\) | 1.97088e39 | 0.231948 | 0.115974 | − | 0.993252i | \(-0.463001\pi\) | ||||
0.115974 | + | 0.993252i | \(0.463001\pi\) | |||||||
\(264\) | −9.30953e39 | −1.02911 | ||||||||
\(265\) | 6.64678e39 | 0.690327 | ||||||||
\(266\) | −4.95823e39 | −0.483927 | ||||||||
\(267\) | 5.25070e39 | 0.481705 | ||||||||
\(268\) | −2.02597e39 | −0.174746 | ||||||||
\(269\) | −1.40997e40 | −1.14366 | −0.571830 | − | 0.820372i | \(-0.693766\pi\) | ||||
−0.571830 | + | 0.820372i | \(0.693766\pi\) | |||||||
\(270\) | −1.03796e39 | −0.0791917 | ||||||||
\(271\) | 2.95789e39 | 0.212319 | 0.106160 | − | 0.994349i | \(-0.466145\pi\) | ||||
0.106160 | + | 0.994349i | \(0.466145\pi\) | |||||||
\(272\) | −1.53327e38 | −0.0103569 | ||||||||
\(273\) | 2.42897e40 | 1.54432 | ||||||||
\(274\) | 6.96630e38 | 0.0416983 | ||||||||
\(275\) | 1.87475e40 | 1.05670 | ||||||||
\(276\) | −6.60067e39 | −0.350419 | ||||||||
\(277\) | 1.84352e40 | 0.922000 | 0.461000 | − | 0.887400i | \(-0.347491\pi\) | ||||
0.461000 | + | 0.887400i | \(0.347491\pi\) | |||||||
\(278\) | 4.88960e38 | 0.0230427 | ||||||||
\(279\) | 2.82836e39 | 0.125622 | ||||||||
\(280\) | −2.76390e40 | −1.15721 | ||||||||
\(281\) | −3.15556e40 | −1.24572 | −0.622862 | − | 0.782332i | \(-0.714030\pi\) | ||||
−0.622862 | + | 0.782332i | \(0.714030\pi\) | |||||||
\(282\) | 7.23224e39 | 0.269254 | ||||||||
\(283\) | 2.91693e40 | 1.02435 | 0.512176 | − | 0.858880i | \(-0.328840\pi\) | ||||
0.512176 | + | 0.858880i | \(0.328840\pi\) | |||||||
\(284\) | 2.15196e40 | 0.712986 | ||||||||
\(285\) | 4.67660e39 | 0.146214 | ||||||||
\(286\) | 5.74525e40 | 1.69539 | ||||||||
\(287\) | −6.29064e40 | −1.75244 | ||||||||
\(288\) | 1.20878e40 | 0.317959 | ||||||||
\(289\) | −3.99549e40 | −0.992558 | ||||||||
\(290\) | 2.14090e39 | 0.0502377 | ||||||||
\(291\) | −2.44180e40 | −0.541347 | ||||||||
\(292\) | −8.30829e39 | −0.174058 | ||||||||
\(293\) | −7.83490e40 | −1.55138 | −0.775689 | − | 0.631115i | \(-0.782598\pi\) | ||||
−0.775689 | + | 0.631115i | \(0.782598\pi\) | |||||||
\(294\) | −4.56202e40 | −0.853937 | ||||||||
\(295\) | −1.97222e40 | −0.349054 | ||||||||
\(296\) | 3.80098e40 | 0.636184 | ||||||||
\(297\) | 2.09711e40 | 0.332001 | ||||||||
\(298\) | −1.06522e40 | −0.159540 | ||||||||
\(299\) | 1.13091e41 | 1.60270 | ||||||||
\(300\) | −1.48447e40 | −0.199100 | ||||||||
\(301\) | −5.75927e40 | −0.731173 | ||||||||
\(302\) | 5.36590e40 | 0.644953 | ||||||||
\(303\) | 1.87178e40 | 0.213035 | ||||||||
\(304\) | 4.53146e39 | 0.0488454 | ||||||||
\(305\) | −1.84207e40 | −0.188087 | ||||||||
\(306\) | 1.96504e39 | 0.0190094 | ||||||||
\(307\) | 1.14909e41 | 1.05335 | 0.526673 | − | 0.850068i | \(-0.323439\pi\) | ||||
0.526673 | + | 0.850068i | \(0.323439\pi\) | |||||||
\(308\) | 2.01142e41 | 1.74750 | ||||||||
\(309\) | 6.02379e40 | 0.496084 | ||||||||
\(310\) | 1.98617e40 | 0.155077 | ||||||||
\(311\) | −1.32546e41 | −0.981342 | −0.490671 | − | 0.871345i | \(-0.663248\pi\) | ||||
−0.490671 | + | 0.871345i | \(0.663248\pi\) | |||||||
\(312\) | −1.26297e41 | −0.886836 | ||||||||
\(313\) | −1.30815e41 | −0.871319 | −0.435660 | − | 0.900111i | \(-0.643485\pi\) | ||||
−0.435660 | + | 0.900111i | \(0.643485\pi\) | |||||||
\(314\) | 3.29726e40 | 0.208360 | ||||||||
\(315\) | 6.22608e40 | 0.373328 | ||||||||
\(316\) | −1.21118e41 | −0.689244 | ||||||||
\(317\) | 1.44144e41 | 0.778607 | 0.389303 | − | 0.921110i | \(-0.372716\pi\) | ||||
0.389303 | + | 0.921110i | \(0.372716\pi\) | |||||||
\(318\) | −8.25417e40 | −0.423278 | ||||||||
\(319\) | −4.32549e40 | −0.210615 | ||||||||
\(320\) | 1.01046e41 | 0.467244 | ||||||||
\(321\) | −1.45115e41 | −0.637354 | ||||||||
\(322\) | −3.07337e41 | −1.28231 | ||||||||
\(323\) | −8.85362e39 | −0.0350978 | ||||||||
\(324\) | −1.66054e40 | −0.0625542 | ||||||||
\(325\) | 2.54337e41 | 0.910614 | ||||||||
\(326\) | −2.59096e41 | −0.881801 | ||||||||
\(327\) | 1.81143e41 | 0.586115 | ||||||||
\(328\) | 3.27090e41 | 1.00635 | ||||||||
\(329\) | −4.33816e41 | −1.26933 | ||||||||
\(330\) | 1.47266e41 | 0.409847 | ||||||||
\(331\) | 3.16472e41 | 0.837864 | 0.418932 | − | 0.908018i | \(-0.362405\pi\) | ||||
0.418932 | + | 0.908018i | \(0.362405\pi\) | |||||||
\(332\) | −3.47698e41 | −0.875837 | ||||||||
\(333\) | −8.56227e40 | −0.205239 | ||||||||
\(334\) | 3.10525e40 | 0.0708402 | ||||||||
\(335\) | 8.89741e40 | 0.193208 | ||||||||
\(336\) | 6.03284e40 | 0.124716 | ||||||||
\(337\) | −3.75601e41 | −0.739321 | −0.369660 | − | 0.929167i | \(-0.620526\pi\) | ||||
−0.369660 | + | 0.929167i | \(0.620526\pi\) | |||||||
\(338\) | 4.26754e41 | 0.799931 | ||||||||
\(339\) | 2.20051e41 | 0.392851 | ||||||||
\(340\) | −1.77770e40 | −0.0302313 | ||||||||
\(341\) | −4.01286e41 | −0.650140 | ||||||||
\(342\) | −5.80754e40 | −0.0896523 | ||||||||
\(343\) | 1.51340e42 | 2.22638 | ||||||||
\(344\) | 2.99461e41 | 0.419881 | ||||||||
\(345\) | 2.89881e41 | 0.387440 | ||||||||
\(346\) | −3.53895e41 | −0.450940 | ||||||||
\(347\) | −2.69449e41 | −0.327372 | −0.163686 | − | 0.986513i | \(-0.552338\pi\) | ||||
−0.163686 | + | 0.986513i | \(0.552338\pi\) | |||||||
\(348\) | 3.42503e40 | 0.0396832 | ||||||||
\(349\) | 2.33704e41 | 0.258253 | 0.129127 | − | 0.991628i | \(-0.458783\pi\) | ||||
0.129127 | + | 0.991628i | \(0.458783\pi\) | |||||||
\(350\) | −6.91192e41 | −0.728578 | ||||||||
\(351\) | 2.84503e41 | 0.286101 | ||||||||
\(352\) | −1.71501e42 | −1.64556 | ||||||||
\(353\) | 5.73724e41 | 0.525316 | 0.262658 | − | 0.964889i | \(-0.415401\pi\) | ||||
0.262658 | + | 0.964889i | \(0.415401\pi\) | |||||||
\(354\) | 2.44916e41 | 0.214025 | ||||||||
\(355\) | −9.45071e41 | −0.788309 | ||||||||
\(356\) | 5.89883e41 | 0.469722 | ||||||||
\(357\) | −1.17870e41 | −0.0896147 | ||||||||
\(358\) | −4.53796e41 | −0.329451 | ||||||||
\(359\) | −1.52912e42 | −1.06019 | −0.530095 | − | 0.847938i | \(-0.677844\pi\) | ||||
−0.530095 | + | 0.847938i | \(0.677844\pi\) | |||||||
\(360\) | −3.23733e41 | −0.214386 | ||||||||
\(361\) | −1.31911e42 | −0.834472 | ||||||||
\(362\) | 6.13543e41 | 0.370812 | ||||||||
\(363\) | −1.97560e42 | −1.14088 | ||||||||
\(364\) | 2.72879e42 | 1.50590 | ||||||||
\(365\) | 3.64874e41 | 0.192447 | ||||||||
\(366\) | 2.28754e41 | 0.115327 | ||||||||
\(367\) | 2.43178e42 | 1.17202 | 0.586010 | − | 0.810304i | \(-0.300698\pi\) | ||||
0.586010 | + | 0.810304i | \(0.300698\pi\) | |||||||
\(368\) | 2.80884e41 | 0.129431 | ||||||||
\(369\) | −7.36818e41 | −0.324657 | ||||||||
\(370\) | −6.01272e41 | −0.253362 | ||||||||
\(371\) | 4.95115e42 | 1.99543 | ||||||||
\(372\) | 3.17748e41 | 0.122497 | ||||||||
\(373\) | −3.22348e42 | −1.18886 | −0.594428 | − | 0.804149i | \(-0.702621\pi\) | ||||
−0.594428 | + | 0.804149i | \(0.702621\pi\) | |||||||
\(374\) | −2.78800e41 | −0.0983810 | ||||||||
\(375\) | 1.71625e42 | 0.579514 | ||||||||
\(376\) | 2.25568e42 | 0.728918 | ||||||||
\(377\) | −5.86816e41 | −0.181497 | ||||||||
\(378\) | −7.73172e41 | −0.228908 | ||||||||
\(379\) | −5.43594e41 | −0.154073 | −0.0770366 | − | 0.997028i | \(-0.524546\pi\) | ||||
−0.0770366 | + | 0.997028i | \(0.524546\pi\) | |||||||
\(380\) | 5.25387e41 | 0.142577 | ||||||||
\(381\) | −4.19948e42 | −1.09127 | ||||||||
\(382\) | 4.86646e42 | 1.21107 | ||||||||
\(383\) | 5.18860e42 | 1.23672 | 0.618359 | − | 0.785896i | \(-0.287798\pi\) | ||||
0.618359 | + | 0.785896i | \(0.287798\pi\) | |||||||
\(384\) | 1.15729e42 | 0.264227 | ||||||||
\(385\) | −8.83354e42 | −1.93211 | ||||||||
\(386\) | 1.63300e42 | 0.342213 | ||||||||
\(387\) | −6.74580e41 | −0.135457 | ||||||||
\(388\) | −2.74321e42 | −0.527880 | ||||||||
\(389\) | −9.09777e42 | −1.67790 | −0.838951 | − | 0.544207i | \(-0.816831\pi\) | ||||
−0.838951 | + | 0.544207i | \(0.816831\pi\) | |||||||
\(390\) | 1.99788e42 | 0.353185 | ||||||||
\(391\) | −5.48794e41 | −0.0930022 | ||||||||
\(392\) | −1.42286e43 | −2.31176 | ||||||||
\(393\) | 3.75878e42 | 0.585558 | ||||||||
\(394\) | 5.09683e41 | 0.0761400 | ||||||||
\(395\) | 5.31913e42 | 0.762059 | ||||||||
\(396\) | 2.35597e42 | 0.323742 | ||||||||
\(397\) | 9.82606e42 | 1.29520 | 0.647599 | − | 0.761981i | \(-0.275773\pi\) | ||||
0.647599 | + | 0.761981i | \(0.275773\pi\) | |||||||
\(398\) | −4.47291e41 | −0.0565612 | ||||||||
\(399\) | 3.48357e42 | 0.422642 | ||||||||
\(400\) | 6.31699e41 | 0.0735394 | ||||||||
\(401\) | −1.98710e42 | −0.221992 | −0.110996 | − | 0.993821i | \(-0.535404\pi\) | ||||
−0.110996 | + | 0.993821i | \(0.535404\pi\) | |||||||
\(402\) | −1.10491e42 | −0.118467 | ||||||||
\(403\) | −5.44403e42 | −0.560257 | ||||||||
\(404\) | 2.10282e42 | 0.207735 | ||||||||
\(405\) | 7.29256e41 | 0.0691628 | ||||||||
\(406\) | 1.59475e42 | 0.145215 | ||||||||
\(407\) | 1.21481e43 | 1.06219 | ||||||||
\(408\) | 6.12883e41 | 0.0514618 | ||||||||
\(409\) | 3.59927e42 | 0.290255 | 0.145127 | − | 0.989413i | \(-0.453641\pi\) | ||||
0.145127 | + | 0.989413i | \(0.453641\pi\) | |||||||
\(410\) | −5.17418e42 | −0.400782 | ||||||||
\(411\) | −4.89441e41 | −0.0364175 | ||||||||
\(412\) | 6.76735e42 | 0.483743 | ||||||||
\(413\) | −1.46910e43 | −1.00896 | ||||||||
\(414\) | −3.59982e42 | −0.237561 | ||||||||
\(415\) | 1.52698e43 | 0.968366 | ||||||||
\(416\) | −2.32667e43 | −1.41806 | ||||||||
\(417\) | −3.43535e41 | −0.0201246 | ||||||||
\(418\) | 8.23972e42 | 0.463985 | ||||||||
\(419\) | 3.46936e43 | 1.87810 | 0.939049 | − | 0.343783i | \(-0.111708\pi\) | ||||
0.939049 | + | 0.343783i | \(0.111708\pi\) | |||||||
\(420\) | 6.99461e42 | 0.364041 | ||||||||
\(421\) | 2.99185e42 | 0.149722 | 0.0748609 | − | 0.997194i | \(-0.476149\pi\) | ||||
0.0748609 | + | 0.997194i | \(0.476149\pi\) | |||||||
\(422\) | −1.37745e43 | −0.662856 | ||||||||
\(423\) | −5.08126e42 | −0.235156 | ||||||||
\(424\) | −2.57442e43 | −1.14589 | ||||||||
\(425\) | −1.23422e42 | −0.0528416 | ||||||||
\(426\) | 1.17362e43 | 0.483357 | ||||||||
\(427\) | −1.37215e43 | −0.543678 | ||||||||
\(428\) | −1.63028e43 | −0.621499 | ||||||||
\(429\) | −4.03652e43 | −1.48068 | ||||||||
\(430\) | −4.73712e42 | −0.167219 | ||||||||
\(431\) | 4.10600e43 | 1.39490 | 0.697452 | − | 0.716631i | \(-0.254317\pi\) | ||||
0.697452 | + | 0.716631i | \(0.254317\pi\) | |||||||
\(432\) | 7.06622e41 | 0.0231050 | ||||||||
\(433\) | −5.85447e43 | −1.84263 | −0.921313 | − | 0.388822i | \(-0.872882\pi\) | ||||
−0.921313 | + | 0.388822i | \(0.872882\pi\) | |||||||
\(434\) | 1.47948e43 | 0.448260 | ||||||||
\(435\) | −1.50416e42 | −0.0438755 | ||||||||
\(436\) | 2.03502e43 | 0.571535 | ||||||||
\(437\) | 1.62192e43 | 0.438617 | ||||||||
\(438\) | −4.53111e42 | −0.118000 | ||||||||
\(439\) | −1.83589e42 | −0.0460450 | −0.0230225 | − | 0.999735i | \(-0.507329\pi\) | ||||
−0.0230225 | + | 0.999735i | \(0.507329\pi\) | |||||||
\(440\) | 4.59312e43 | 1.10953 | ||||||||
\(441\) | 3.20520e43 | 0.745793 | ||||||||
\(442\) | −3.78233e42 | −0.0847797 | ||||||||
\(443\) | −5.41463e43 | −1.16925 | −0.584625 | − | 0.811303i | \(-0.698758\pi\) | ||||
−0.584625 | + | 0.811303i | \(0.698758\pi\) | |||||||
\(444\) | −9.61918e42 | −0.200133 | ||||||||
\(445\) | −2.59058e43 | −0.519346 | ||||||||
\(446\) | 5.91274e43 | 1.14226 | ||||||||
\(447\) | 7.48404e42 | 0.139336 | ||||||||
\(448\) | 7.52685e43 | 1.35060 | ||||||||
\(449\) | 6.67635e43 | 1.15471 | 0.577357 | − | 0.816492i | \(-0.304084\pi\) | ||||
0.577357 | + | 0.816492i | \(0.304084\pi\) | |||||||
\(450\) | −8.09589e42 | −0.134977 | ||||||||
\(451\) | 1.04539e44 | 1.68022 | ||||||||
\(452\) | 2.47213e43 | 0.383079 | ||||||||
\(453\) | −3.77000e43 | −0.563276 | ||||||||
\(454\) | −8.90664e43 | −1.28319 | ||||||||
\(455\) | −1.19840e44 | −1.66500 | ||||||||
\(456\) | −1.81133e43 | −0.242705 | ||||||||
\(457\) | −6.52277e43 | −0.842975 | −0.421487 | − | 0.906834i | \(-0.638492\pi\) | ||||
−0.421487 | + | 0.906834i | \(0.638492\pi\) | |||||||
\(458\) | −5.42698e43 | −0.676515 | ||||||||
\(459\) | −1.38061e42 | −0.0166020 | ||||||||
\(460\) | 3.25663e43 | 0.377802 | ||||||||
\(461\) | −8.70813e43 | −0.974675 | −0.487337 | − | 0.873214i | \(-0.662032\pi\) | ||||
−0.487337 | + | 0.873214i | \(0.662032\pi\) | |||||||
\(462\) | 1.09697e44 | 1.18469 | ||||||||
\(463\) | 7.08765e43 | 0.738611 | 0.369306 | − | 0.929308i | \(-0.379596\pi\) | ||||
0.369306 | + | 0.929308i | \(0.379596\pi\) | |||||||
\(464\) | −1.45748e42 | −0.0146574 | ||||||||
\(465\) | −1.39545e43 | −0.135438 | ||||||||
\(466\) | −1.20314e44 | −1.12706 | ||||||||
\(467\) | −1.42327e44 | −1.28694 | −0.643469 | − | 0.765473i | \(-0.722505\pi\) | ||||
−0.643469 | + | 0.765473i | \(0.722505\pi\) | |||||||
\(468\) | 3.19621e43 | 0.278984 | ||||||||
\(469\) | 6.62763e43 | 0.558478 | ||||||||
\(470\) | −3.56823e43 | −0.290294 | ||||||||
\(471\) | −2.31660e43 | −0.181973 | ||||||||
\(472\) | 7.63876e43 | 0.579402 | ||||||||
\(473\) | 9.57091e43 | 0.701043 | ||||||||
\(474\) | −6.60545e43 | −0.467261 | ||||||||
\(475\) | 3.64765e43 | 0.249212 | ||||||||
\(476\) | −1.32420e43 | −0.0873854 | ||||||||
\(477\) | 5.79925e43 | 0.369674 | ||||||||
\(478\) | 6.94571e43 | 0.427717 | ||||||||
\(479\) | 3.66112e43 | 0.217810 | 0.108905 | − | 0.994052i | \(-0.465266\pi\) | ||||
0.108905 | + | 0.994052i | \(0.465266\pi\) | |||||||
\(480\) | −5.96385e43 | −0.342805 | ||||||||
\(481\) | 1.64807e44 | 0.915339 | ||||||||
\(482\) | −5.37833e43 | −0.288650 | ||||||||
\(483\) | 2.15930e44 | 1.11992 | ||||||||
\(484\) | −2.21946e44 | −1.11250 | ||||||||
\(485\) | 1.20473e44 | 0.583648 | ||||||||
\(486\) | −9.05612e42 | −0.0424076 | ||||||||
\(487\) | −2.96641e44 | −1.34277 | −0.671387 | − | 0.741107i | \(-0.734301\pi\) | ||||
−0.671387 | + | 0.741107i | \(0.734301\pi\) | |||||||
\(488\) | 7.13468e43 | 0.312210 | ||||||||
\(489\) | 1.82037e44 | 0.770129 | ||||||||
\(490\) | 2.25080e44 | 0.920664 | ||||||||
\(491\) | 9.62405e43 | 0.380639 | 0.190319 | − | 0.981722i | \(-0.439048\pi\) | ||||
0.190319 | + | 0.981722i | \(0.439048\pi\) | |||||||
\(492\) | −8.27769e43 | −0.316581 | ||||||||
\(493\) | 2.84764e42 | 0.0105320 | ||||||||
\(494\) | 1.11784e44 | 0.399838 | ||||||||
\(495\) | −1.03467e44 | −0.357944 | ||||||||
\(496\) | −1.35214e43 | −0.0452453 | ||||||||
\(497\) | −7.03978e44 | −2.27866 | ||||||||
\(498\) | −1.89625e44 | −0.593760 | ||||||||
\(499\) | 2.79044e43 | 0.0845305 | 0.0422652 | − | 0.999106i | \(-0.486543\pi\) | ||||
0.0422652 | + | 0.999106i | \(0.486543\pi\) | |||||||
\(500\) | 1.92810e44 | 0.565098 | ||||||||
\(501\) | −2.18170e43 | −0.0618689 | ||||||||
\(502\) | −2.69521e44 | −0.739573 | ||||||||
\(503\) | 5.95546e44 | 1.58141 | 0.790704 | − | 0.612199i | \(-0.209715\pi\) | ||||
0.790704 | + | 0.612199i | \(0.209715\pi\) | |||||||
\(504\) | −2.41147e44 | −0.619695 | ||||||||
\(505\) | −9.23494e43 | −0.229682 | ||||||||
\(506\) | 5.10742e44 | 1.22947 | ||||||||
\(507\) | −2.99831e44 | −0.698626 | ||||||||
\(508\) | −4.71785e44 | −1.06413 | ||||||||
\(509\) | −9.54525e43 | −0.208422 | −0.104211 | − | 0.994555i | \(-0.533232\pi\) | ||||
−0.104211 | + | 0.994555i | \(0.533232\pi\) | |||||||
\(510\) | −9.69510e42 | −0.0204948 | ||||||||
\(511\) | 2.71792e44 | 0.556279 | ||||||||
\(512\) | −1.20383e44 | −0.238568 | ||||||||
\(513\) | 4.08029e43 | 0.0782986 | ||||||||
\(514\) | −4.00344e43 | −0.0743947 | ||||||||
\(515\) | −2.97201e44 | −0.534848 | ||||||||
\(516\) | −7.57848e43 | −0.132088 | ||||||||
\(517\) | 7.20927e44 | 1.21702 | ||||||||
\(518\) | −4.47884e44 | −0.732359 | ||||||||
\(519\) | 2.48641e44 | 0.393832 | ||||||||
\(520\) | 6.23123e44 | 0.956134 | ||||||||
\(521\) | 4.01987e44 | 0.597571 | 0.298786 | − | 0.954320i | \(-0.403418\pi\) | ||||
0.298786 | + | 0.954320i | \(0.403418\pi\) | |||||||
\(522\) | 1.86791e43 | 0.0269026 | ||||||||
\(523\) | −1.14424e45 | −1.59677 | −0.798383 | − | 0.602150i | \(-0.794311\pi\) | ||||
−0.798383 | + | 0.602150i | \(0.794311\pi\) | |||||||
\(524\) | 4.22276e44 | 0.570992 | ||||||||
\(525\) | 4.85621e44 | 0.636310 | ||||||||
\(526\) | 1.20754e44 | 0.153334 | ||||||||
\(527\) | 2.64183e43 | 0.0325109 | ||||||||
\(528\) | −1.00255e44 | −0.119577 | ||||||||
\(529\) | 1.40347e44 | 0.162250 | ||||||||
\(530\) | 4.07243e44 | 0.456354 | ||||||||
\(531\) | −1.72074e44 | −0.186920 | ||||||||
\(532\) | 3.91358e44 | 0.412128 | ||||||||
\(533\) | 1.41823e45 | 1.44793 | ||||||||
\(534\) | 3.21706e44 | 0.318440 | ||||||||
\(535\) | 7.15968e44 | 0.687157 | ||||||||
\(536\) | −3.44612e44 | −0.320710 | ||||||||
\(537\) | 3.18830e44 | 0.287729 | ||||||||
\(538\) | −8.63876e44 | −0.756039 | ||||||||
\(539\) | −4.54753e45 | −3.85976 | ||||||||
\(540\) | 8.19274e43 | 0.0674422 | ||||||||
\(541\) | −4.23426e44 | −0.338082 | −0.169041 | − | 0.985609i | \(-0.554067\pi\) | ||||
−0.169041 | + | 0.985609i | \(0.554067\pi\) | |||||||
\(542\) | 1.81228e44 | 0.140358 | ||||||||
\(543\) | −4.31066e44 | −0.323852 | ||||||||
\(544\) | 1.12906e44 | 0.0822878 | ||||||||
\(545\) | −8.93719e44 | −0.631915 | ||||||||
\(546\) | 1.48821e45 | 1.02090 | ||||||||
\(547\) | −2.88922e45 | −1.92305 | −0.961523 | − | 0.274724i | \(-0.911414\pi\) | ||||
−0.961523 | + | 0.274724i | \(0.911414\pi\) | |||||||
\(548\) | −5.49857e43 | −0.0355116 | ||||||||
\(549\) | −1.60719e44 | −0.100722 | ||||||||
\(550\) | 1.14864e45 | 0.698555 | ||||||||
\(551\) | −8.41600e43 | −0.0496712 | ||||||||
\(552\) | −1.12276e45 | −0.643119 | ||||||||
\(553\) | 3.96219e45 | 2.20278 | ||||||||
\(554\) | 1.12951e45 | 0.609506 | ||||||||
\(555\) | 4.22444e44 | 0.221276 | ||||||||
\(556\) | −3.85940e43 | −0.0196239 | ||||||||
\(557\) | −3.21957e44 | −0.158923 | −0.0794615 | − | 0.996838i | \(-0.525320\pi\) | ||||
−0.0794615 | + | 0.996838i | \(0.525320\pi\) | |||||||
\(558\) | 1.73291e44 | 0.0830446 | ||||||||
\(559\) | 1.29843e45 | 0.604123 | ||||||||
\(560\) | −2.97647e44 | −0.134462 | ||||||||
\(561\) | 1.95880e44 | 0.0859218 | ||||||||
\(562\) | −1.93338e45 | −0.823510 | ||||||||
\(563\) | 1.66489e45 | 0.688647 | 0.344324 | − | 0.938851i | \(-0.388108\pi\) | ||||
0.344324 | + | 0.938851i | \(0.388108\pi\) | |||||||
\(564\) | −5.70847e44 | −0.229306 | ||||||||
\(565\) | −1.08568e45 | −0.423549 | ||||||||
\(566\) | 1.78718e45 | 0.677168 | ||||||||
\(567\) | 5.43219e44 | 0.199919 | ||||||||
\(568\) | 3.66043e45 | 1.30853 | ||||||||
\(569\) | 1.27473e45 | 0.442656 | 0.221328 | − | 0.975199i | \(-0.428961\pi\) | ||||
0.221328 | + | 0.975199i | \(0.428961\pi\) | |||||||
\(570\) | 2.86531e44 | 0.0966579 | ||||||||
\(571\) | 2.72708e45 | 0.893722 | 0.446861 | − | 0.894603i | \(-0.352542\pi\) | ||||
0.446861 | + | 0.894603i | \(0.352542\pi\) | |||||||
\(572\) | −4.53478e45 | −1.44385 | ||||||||
\(573\) | −3.41910e45 | −1.05770 | ||||||||
\(574\) | −3.85422e45 | −1.15848 | ||||||||
\(575\) | 2.26101e45 | 0.660363 | ||||||||
\(576\) | 8.81615e44 | 0.250212 | ||||||||
\(577\) | −1.55920e45 | −0.430032 | −0.215016 | − | 0.976611i | \(-0.568980\pi\) | ||||
−0.215016 | + | 0.976611i | \(0.568980\pi\) | |||||||
\(578\) | −2.44800e45 | −0.656149 | ||||||||
\(579\) | −1.14732e45 | −0.298874 | ||||||||
\(580\) | −1.68983e44 | −0.0427841 | ||||||||
\(581\) | 1.13744e46 | 2.79912 | ||||||||
\(582\) | −1.49607e45 | −0.357868 | ||||||||
\(583\) | −8.22796e45 | −1.91320 | ||||||||
\(584\) | −1.41322e45 | −0.319446 | ||||||||
\(585\) | −1.40368e45 | −0.308457 | ||||||||
\(586\) | −4.80038e45 | −1.02557 | ||||||||
\(587\) | 4.86237e45 | 1.00999 | 0.504997 | − | 0.863121i | \(-0.331493\pi\) | ||||
0.504997 | + | 0.863121i | \(0.331493\pi\) | |||||||
\(588\) | 3.60084e45 | 0.727240 | ||||||||
\(589\) | −7.80772e44 | −0.153328 | ||||||||
\(590\) | −1.20836e45 | −0.230749 | ||||||||
\(591\) | −3.58095e44 | −0.0664975 | ||||||||
\(592\) | 4.09332e44 | 0.0739210 | ||||||||
\(593\) | −6.11886e45 | −1.07465 | −0.537326 | − | 0.843375i | \(-0.680566\pi\) | ||||
−0.537326 | + | 0.843375i | \(0.680566\pi\) | |||||||
\(594\) | 1.28488e45 | 0.219475 | ||||||||
\(595\) | 5.81547e44 | 0.0966173 | ||||||||
\(596\) | 8.40785e44 | 0.135869 | ||||||||
\(597\) | 3.14259e44 | 0.0493983 | ||||||||
\(598\) | 6.92896e45 | 1.05949 | ||||||||
\(599\) | −7.96637e45 | −1.18500 | −0.592499 | − | 0.805571i | \(-0.701859\pi\) | ||||
−0.592499 | + | 0.805571i | \(0.701859\pi\) | |||||||
\(600\) | −2.52505e45 | −0.365405 | ||||||||
\(601\) | 1.10227e46 | 1.55188 | 0.775942 | − | 0.630805i | \(-0.217275\pi\) | ||||
0.775942 | + | 0.630805i | \(0.217275\pi\) | |||||||
\(602\) | −3.52866e45 | −0.483356 | ||||||||
\(603\) | 7.76290e44 | 0.103464 | ||||||||
\(604\) | −4.23536e45 | −0.549263 | ||||||||
\(605\) | 9.74718e45 | 1.23003 | ||||||||
\(606\) | 1.14682e45 | 0.140831 | ||||||||
\(607\) | 3.64627e45 | 0.435748 | 0.217874 | − | 0.975977i | \(-0.430088\pi\) | ||||
0.217874 | + | 0.975977i | \(0.430088\pi\) | |||||||
\(608\) | −3.33686e45 | −0.388086 | ||||||||
\(609\) | −1.12044e45 | −0.126825 | ||||||||
\(610\) | −1.12862e45 | −0.124339 | ||||||||
\(611\) | 9.78043e45 | 1.04876 | ||||||||
\(612\) | −1.55103e44 | −0.0161890 | ||||||||
\(613\) | −1.42792e46 | −1.45079 | −0.725396 | − | 0.688332i | \(-0.758343\pi\) | ||||
−0.725396 | + | 0.688332i | \(0.758343\pi\) | |||||||
\(614\) | 7.04038e45 | 0.696335 | ||||||||
\(615\) | 3.63530e45 | 0.350026 | ||||||||
\(616\) | 3.42138e46 | 3.20716 | ||||||||
\(617\) | −1.82679e46 | −1.66718 | −0.833592 | − | 0.552381i | \(-0.813720\pi\) | ||||
−0.833592 | + | 0.552381i | \(0.813720\pi\) | |||||||
\(618\) | 3.69073e45 | 0.327946 | ||||||||
\(619\) | −7.53894e45 | −0.652250 | −0.326125 | − | 0.945327i | \(-0.605743\pi\) | ||||
−0.326125 | + | 0.945327i | \(0.605743\pi\) | |||||||
\(620\) | −1.56770e45 | −0.132069 | ||||||||
\(621\) | 2.52918e45 | 0.207476 | ||||||||
\(622\) | −8.12098e45 | −0.648735 | ||||||||
\(623\) | −1.92971e46 | −1.50120 | ||||||||
\(624\) | −1.36011e45 | −0.103045 | ||||||||
\(625\) | −1.66160e44 | −0.0122605 | ||||||||
\(626\) | −8.01495e45 | −0.576002 | ||||||||
\(627\) | −5.78910e45 | −0.405225 | ||||||||
\(628\) | −2.60255e45 | −0.177446 | ||||||||
\(629\) | −7.99759e44 | −0.0531158 | ||||||||
\(630\) | 3.81466e45 | 0.246795 | ||||||||
\(631\) | 1.94441e46 | 1.22547 | 0.612735 | − | 0.790288i | \(-0.290069\pi\) | ||||
0.612735 | + | 0.790288i | \(0.290069\pi\) | |||||||
\(632\) | −2.06019e46 | −1.26496 | ||||||||
\(633\) | 9.67772e45 | 0.578911 | ||||||||
\(634\) | 8.83156e45 | 0.514713 | ||||||||
\(635\) | 2.07193e46 | 1.17655 | ||||||||
\(636\) | 6.51509e45 | 0.360477 | ||||||||
\(637\) | −6.16939e46 | −3.32615 | ||||||||
\(638\) | −2.65019e45 | −0.139231 | ||||||||
\(639\) | −8.24565e45 | −0.422144 | ||||||||
\(640\) | −5.70982e45 | −0.284874 | ||||||||
\(641\) | −6.84441e45 | −0.332796 | −0.166398 | − | 0.986059i | \(-0.553214\pi\) | ||||
−0.166398 | + | 0.986059i | \(0.553214\pi\) | |||||||
\(642\) | −8.89110e45 | −0.421335 | ||||||||
\(643\) | 1.53937e46 | 0.710986 | 0.355493 | − | 0.934679i | \(-0.384313\pi\) | ||||
0.355493 | + | 0.934679i | \(0.384313\pi\) | |||||||
\(644\) | 2.42584e46 | 1.09206 | ||||||||
\(645\) | 3.32823e45 | 0.146042 | ||||||||
\(646\) | −5.42454e44 | −0.0232020 | ||||||||
\(647\) | 3.80872e46 | 1.58803 | 0.794014 | − | 0.607900i | \(-0.207988\pi\) | ||||
0.794014 | + | 0.607900i | \(0.207988\pi\) | |||||||
\(648\) | −2.82454e45 | −0.114805 | ||||||||
\(649\) | 2.44138e46 | 0.967383 | ||||||||
\(650\) | 1.55830e46 | 0.601979 | ||||||||
\(651\) | −1.03946e46 | −0.391491 | ||||||||
\(652\) | 2.04507e46 | 0.750971 | ||||||||
\(653\) | 1.23512e46 | 0.442223 | 0.221111 | − | 0.975249i | \(-0.429032\pi\) | ||||
0.221111 | + | 0.975249i | \(0.429032\pi\) | |||||||
\(654\) | 1.10985e46 | 0.387463 | ||||||||
\(655\) | −1.85450e46 | −0.631315 | ||||||||
\(656\) | 3.52247e45 | 0.116932 | ||||||||
\(657\) | 3.18349e45 | 0.103056 | ||||||||
\(658\) | −2.65795e46 | −0.839112 | ||||||||
\(659\) | −1.48240e46 | −0.456412 | −0.228206 | − | 0.973613i | \(-0.573286\pi\) | ||||
−0.228206 | + | 0.973613i | \(0.573286\pi\) | |||||||
\(660\) | −1.16238e46 | −0.349039 | ||||||||
\(661\) | 4.84462e46 | 1.41885 | 0.709424 | − | 0.704782i | \(-0.248955\pi\) | ||||
0.709424 | + | 0.704782i | \(0.248955\pi\) | |||||||
\(662\) | 1.93900e46 | 0.553886 | ||||||||
\(663\) | 2.65740e45 | 0.0740431 | ||||||||
\(664\) | −5.91426e46 | −1.60741 | ||||||||
\(665\) | −1.71872e46 | −0.455667 | ||||||||
\(666\) | −5.24603e45 | −0.135677 | ||||||||
\(667\) | −5.21668e45 | −0.131619 | ||||||||
\(668\) | −2.45100e45 | −0.0603298 | ||||||||
\(669\) | −4.15420e46 | −0.997600 | ||||||||
\(670\) | 5.45137e45 | 0.127724 | ||||||||
\(671\) | 2.28028e46 | 0.521274 | ||||||||
\(672\) | −4.44244e46 | −0.990897 | ||||||||
\(673\) | −2.12559e45 | −0.0462626 | −0.0231313 | − | 0.999732i | \(-0.507364\pi\) | ||||
−0.0231313 | + | 0.999732i | \(0.507364\pi\) | |||||||
\(674\) | −2.30127e46 | −0.488742 | ||||||||
\(675\) | 5.68804e45 | 0.117883 | ||||||||
\(676\) | −3.36841e46 | −0.681247 | ||||||||
\(677\) | −5.47124e46 | −1.07987 | −0.539937 | − | 0.841705i | \(-0.681552\pi\) | ||||
−0.539937 | + | 0.841705i | \(0.681552\pi\) | |||||||
\(678\) | 1.34823e46 | 0.259702 | ||||||||
\(679\) | 8.97396e46 | 1.68707 | ||||||||
\(680\) | −3.02383e45 | −0.0554831 | ||||||||
\(681\) | 6.25766e46 | 1.12069 | ||||||||
\(682\) | −2.45865e46 | −0.429787 | ||||||||
\(683\) | −6.15868e45 | −0.105086 | −0.0525431 | − | 0.998619i | \(-0.516733\pi\) | ||||
−0.0525431 | + | 0.998619i | \(0.516733\pi\) | |||||||
\(684\) | 4.58395e45 | 0.0763508 | ||||||||
\(685\) | 2.41480e45 | 0.0392632 | ||||||||
\(686\) | 9.27245e46 | 1.47179 | ||||||||
\(687\) | 3.81291e46 | 0.590840 | ||||||||
\(688\) | 3.22493e45 | 0.0487878 | ||||||||
\(689\) | −1.11624e47 | −1.64870 | ||||||||
\(690\) | 1.77607e46 | 0.256124 | ||||||||
\(691\) | −2.57107e46 | −0.362015 | −0.181007 | − | 0.983482i | \(-0.557936\pi\) | ||||
−0.181007 | + | 0.983482i | \(0.557936\pi\) | |||||||
\(692\) | 2.79333e46 | 0.384035 | ||||||||
\(693\) | −7.70717e46 | −1.03466 | ||||||||
\(694\) | −1.65089e46 | −0.216415 | ||||||||
\(695\) | 1.69493e45 | 0.0216971 | ||||||||
\(696\) | 5.82589e45 | 0.0728299 | ||||||||
\(697\) | −6.88225e45 | −0.0840213 | ||||||||
\(698\) | 1.43188e46 | 0.170723 | ||||||||
\(699\) | 8.45304e46 | 0.984328 | ||||||||
\(700\) | 5.45564e46 | 0.620481 | ||||||||
\(701\) | 1.25438e47 | 1.39342 | 0.696709 | − | 0.717354i | \(-0.254647\pi\) | ||||
0.696709 | + | 0.717354i | \(0.254647\pi\) | |||||||
\(702\) | 1.74313e46 | 0.189133 | ||||||||
\(703\) | 2.36363e46 | 0.250505 | ||||||||
\(704\) | −1.25083e47 | −1.29494 | ||||||||
\(705\) | 2.50698e46 | 0.253531 | ||||||||
\(706\) | 3.51516e46 | 0.347270 | ||||||||
\(707\) | −6.87905e46 | −0.663909 | ||||||||
\(708\) | −1.93315e46 | −0.182270 | ||||||||
\(709\) | −4.63194e46 | −0.426678 | −0.213339 | − | 0.976978i | \(-0.568434\pi\) | ||||
−0.213339 | + | 0.976978i | \(0.568434\pi\) | |||||||
\(710\) | −5.79037e46 | −0.521127 | ||||||||
\(711\) | 4.64089e46 | 0.408087 | ||||||||
\(712\) | 1.00338e47 | 0.862073 | ||||||||
\(713\) | −4.83964e46 | −0.406290 | ||||||||
\(714\) | −7.22182e45 | −0.0592415 | ||||||||
\(715\) | 1.99153e47 | 1.59638 | ||||||||
\(716\) | 3.58185e46 | 0.280571 | ||||||||
\(717\) | −4.87995e46 | −0.373550 | ||||||||
\(718\) | −9.36880e46 | −0.700859 | ||||||||
\(719\) | −2.01670e47 | −1.47440 | −0.737200 | − | 0.675675i | \(-0.763852\pi\) | ||||
−0.737200 | + | 0.675675i | \(0.763852\pi\) | |||||||
\(720\) | −3.48632e45 | −0.0249104 | ||||||||
\(721\) | −2.21383e47 | −1.54601 | ||||||||
\(722\) | −8.08206e46 | −0.551643 | ||||||||
\(723\) | 3.77873e46 | 0.252095 | ||||||||
\(724\) | −4.84275e46 | −0.315796 | ||||||||
\(725\) | −1.17322e46 | −0.0747826 | ||||||||
\(726\) | −1.21043e47 | −0.754200 | ||||||||
\(727\) | −1.86775e47 | −1.13763 | −0.568815 | − | 0.822465i | \(-0.692598\pi\) | ||||
−0.568815 | + | 0.822465i | \(0.692598\pi\) | |||||||
\(728\) | 4.64161e47 | 2.76376 | ||||||||
\(729\) | 6.36269e45 | 0.0370370 | ||||||||
\(730\) | 2.23555e46 | 0.127221 | ||||||||
\(731\) | −6.30091e45 | −0.0350564 | ||||||||
\(732\) | −1.80558e46 | −0.0982162 | ||||||||
\(733\) | 2.33399e47 | 1.24132 | 0.620660 | − | 0.784080i | \(-0.286865\pi\) | ||||
0.620660 | + | 0.784080i | \(0.286865\pi\) | |||||||
\(734\) | 1.48993e47 | 0.774786 | ||||||||
\(735\) | −1.58138e47 | −0.804070 | ||||||||
\(736\) | −2.06836e47 | −1.02835 | ||||||||
\(737\) | −1.10140e47 | −0.535464 | ||||||||
\(738\) | −4.51442e46 | −0.214621 | ||||||||
\(739\) | 1.40613e47 | 0.653721 | 0.326861 | − | 0.945073i | \(-0.394009\pi\) | ||||
0.326861 | + | 0.945073i | \(0.394009\pi\) | |||||||
\(740\) | 4.74589e46 | 0.215772 | ||||||||
\(741\) | −7.85376e46 | −0.349202 | ||||||||
\(742\) | 3.03353e47 | 1.31912 | ||||||||
\(743\) | 1.19862e47 | 0.509761 | 0.254881 | − | 0.966973i | \(-0.417964\pi\) | ||||
0.254881 | + | 0.966973i | \(0.417964\pi\) | |||||||
\(744\) | 5.40482e46 | 0.224816 | ||||||||
\(745\) | −3.69246e46 | −0.150223 | ||||||||
\(746\) | −1.97500e47 | −0.785915 | ||||||||
\(747\) | 1.33227e47 | 0.518565 | ||||||||
\(748\) | 2.20059e46 | 0.0837844 | ||||||||
\(749\) | 5.33320e47 | 1.98627 | ||||||||
\(750\) | 1.05153e47 | 0.383099 | ||||||||
\(751\) | −2.14100e47 | −0.763057 | −0.381528 | − | 0.924357i | \(-0.624602\pi\) | ||||
−0.381528 | + | 0.924357i | \(0.624602\pi\) | |||||||
\(752\) | 2.42917e46 | 0.0846962 | ||||||||
\(753\) | 1.89361e47 | 0.645913 | ||||||||
\(754\) | −3.59537e46 | −0.119982 | ||||||||
\(755\) | 1.86004e47 | 0.607290 | ||||||||
\(756\) | 6.10272e46 | 0.194946 | ||||||||
\(757\) | −4.34005e47 | −1.35648 | −0.678239 | − | 0.734842i | \(-0.737256\pi\) | ||||
−0.678239 | + | 0.734842i | \(0.737256\pi\) | |||||||
\(758\) | −3.33055e46 | −0.101853 | ||||||||
\(759\) | −3.58839e47 | −1.07377 | ||||||||
\(760\) | 8.93671e46 | 0.261670 | ||||||||
\(761\) | −7.81557e46 | −0.223931 | −0.111965 | − | 0.993712i | \(-0.535715\pi\) | ||||
−0.111965 | + | 0.993712i | \(0.535715\pi\) | |||||||
\(762\) | −2.57298e47 | −0.721406 | ||||||||
\(763\) | −6.65726e47 | −1.82659 | ||||||||
\(764\) | −3.84114e47 | −1.03138 | ||||||||
\(765\) | 6.81162e45 | 0.0178993 | ||||||||
\(766\) | 3.17901e47 | 0.817556 | ||||||||
\(767\) | 3.31209e47 | 0.833641 | ||||||||
\(768\) | 2.46832e47 | 0.608052 | ||||||||
\(769\) | 5.65995e47 | 1.36467 | 0.682336 | − | 0.731039i | \(-0.260964\pi\) | ||||
0.682336 | + | 0.731039i | \(0.260964\pi\) | |||||||
\(770\) | −5.41223e47 | −1.27726 | ||||||||
\(771\) | 2.81276e46 | 0.0649733 | ||||||||
\(772\) | −1.28894e47 | −0.291439 | ||||||||
\(773\) | −3.30903e47 | −0.732383 | −0.366192 | − | 0.930539i | \(-0.619339\pi\) | ||||
−0.366192 | + | 0.930539i | \(0.619339\pi\) | |||||||
\(774\) | −4.13309e46 | −0.0895466 | ||||||||
\(775\) | −1.08842e47 | −0.230844 | ||||||||
\(776\) | −4.66613e47 | −0.968810 | ||||||||
\(777\) | 3.14676e47 | 0.639612 | ||||||||
\(778\) | −5.57413e47 | −1.10921 | ||||||||
\(779\) | 2.03400e47 | 0.396262 | ||||||||
\(780\) | −1.57694e47 | −0.300784 | ||||||||
\(781\) | 1.16989e48 | 2.18476 | ||||||||
\(782\) | −3.36242e46 | −0.0614809 | ||||||||
\(783\) | −1.31237e46 | −0.0234956 | ||||||||
\(784\) | −1.53229e47 | −0.268613 | ||||||||
\(785\) | 1.14296e47 | 0.196192 | ||||||||
\(786\) | 2.30297e47 | 0.387095 | ||||||||
\(787\) | 8.02705e47 | 1.32121 | 0.660606 | − | 0.750732i | \(-0.270299\pi\) | ||||
0.660606 | + | 0.750732i | \(0.270299\pi\) | |||||||
\(788\) | −4.02298e46 | −0.0648433 | ||||||||
\(789\) | −8.48400e46 | −0.133915 | ||||||||
\(790\) | 3.25899e47 | 0.503774 | ||||||||
\(791\) | −8.08719e47 | −1.22429 | ||||||||
\(792\) | 4.00745e47 | 0.594158 | ||||||||
\(793\) | 3.09353e47 | 0.449207 | ||||||||
\(794\) | 6.02034e47 | 0.856215 | ||||||||
\(795\) | −2.86122e47 | −0.398560 | ||||||||
\(796\) | 3.53050e46 | 0.0481694 | ||||||||
\(797\) | 4.00063e47 | 0.534646 | 0.267323 | − | 0.963607i | \(-0.413861\pi\) | ||||
0.267323 | + | 0.963607i | \(0.413861\pi\) | |||||||
\(798\) | 2.13436e47 | 0.279395 | ||||||||
\(799\) | −4.74615e46 | −0.0608583 | ||||||||
\(800\) | −4.65168e47 | −0.584285 | ||||||||
\(801\) | −2.26025e47 | −0.278113 | ||||||||
\(802\) | −1.21748e47 | −0.146752 | ||||||||
\(803\) | −4.51672e47 | −0.533355 | ||||||||
\(804\) | 8.72113e46 | 0.100890 | ||||||||
\(805\) | −1.06535e48 | −1.20743 | ||||||||
\(806\) | −3.33551e47 | −0.370369 | ||||||||
\(807\) | 6.06946e47 | 0.660293 | ||||||||
\(808\) | 3.57686e47 | 0.381254 | ||||||||
\(809\) | 1.23605e48 | 1.29088 | 0.645438 | − | 0.763813i | \(-0.276675\pi\) | ||||
0.645438 | + | 0.763813i | \(0.276675\pi\) | |||||||
\(810\) | 4.46809e46 | 0.0457214 | ||||||||
\(811\) | −1.79503e48 | −1.79982 | −0.899908 | − | 0.436080i | \(-0.856367\pi\) | ||||
−0.899908 | + | 0.436080i | \(0.856367\pi\) | |||||||
\(812\) | −1.25875e47 | −0.123670 | ||||||||
\(813\) | −1.27328e47 | −0.122583 | ||||||||
\(814\) | 7.44305e47 | 0.702180 | ||||||||
\(815\) | −8.98130e47 | −0.830307 | ||||||||
\(816\) | 6.60021e45 | 0.00597957 | ||||||||
\(817\) | 1.86219e47 | 0.165333 | ||||||||
\(818\) | 2.20524e47 | 0.191879 | ||||||||
\(819\) | −1.04559e48 | −0.891615 | ||||||||
\(820\) | 4.08403e47 | 0.341319 | ||||||||
\(821\) | 1.17790e48 | 0.964816 | 0.482408 | − | 0.875947i | \(-0.339762\pi\) | ||||
0.482408 | + | 0.875947i | \(0.339762\pi\) | |||||||
\(822\) | −2.99876e46 | −0.0240745 | ||||||||
\(823\) | −8.86254e47 | −0.697366 | −0.348683 | − | 0.937241i | \(-0.613371\pi\) | ||||
−0.348683 | + | 0.937241i | \(0.613371\pi\) | |||||||
\(824\) | 1.15111e48 | 0.887806 | ||||||||
\(825\) | −8.07018e47 | −0.610089 | ||||||||
\(826\) | −9.00102e47 | −0.666993 | ||||||||
\(827\) | 1.01884e46 | 0.00740060 | 0.00370030 | − | 0.999993i | \(-0.498822\pi\) | ||||
0.00370030 | + | 0.999993i | \(0.498822\pi\) | |||||||
\(828\) | 2.84137e47 | 0.202315 | ||||||||
\(829\) | −3.40790e47 | −0.237869 | −0.118934 | − | 0.992902i | \(-0.537948\pi\) | ||||
−0.118934 | + | 0.992902i | \(0.537948\pi\) | |||||||
\(830\) | 9.35567e47 | 0.640157 | ||||||||
\(831\) | −7.93574e47 | −0.532317 | ||||||||
\(832\) | −1.69694e48 | −1.11591 | ||||||||
\(833\) | 2.99382e47 | 0.193011 | ||||||||
\(834\) | −2.10481e46 | −0.0133037 | ||||||||
\(835\) | 1.07640e47 | 0.0667034 | ||||||||
\(836\) | −6.50369e47 | −0.395145 | ||||||||
\(837\) | −1.21751e47 | −0.0725277 | ||||||||
\(838\) | 2.12565e48 | 1.24155 | ||||||||
\(839\) | −7.64580e47 | −0.437876 | −0.218938 | − | 0.975739i | \(-0.570259\pi\) | ||||
−0.218938 | + | 0.975739i | \(0.570259\pi\) | |||||||
\(840\) | 1.18977e48 | 0.668118 | ||||||||
\(841\) | −1.78901e48 | −0.985095 | ||||||||
\(842\) | 1.83308e47 | 0.0989765 | ||||||||
\(843\) | 1.35836e48 | 0.719219 | ||||||||
\(844\) | 1.08723e48 | 0.564510 | ||||||||
\(845\) | 1.47930e48 | 0.753218 | ||||||||
\(846\) | −3.11324e47 | −0.155454 | ||||||||
\(847\) | 7.26062e48 | 3.55547 | ||||||||
\(848\) | −2.77242e47 | −0.133146 | ||||||||
\(849\) | −1.25564e48 | −0.591410 | ||||||||
\(850\) | −7.56197e46 | −0.0349319 | ||||||||
\(851\) | 1.46510e48 | 0.663789 | ||||||||
\(852\) | −9.26347e47 | −0.411642 | ||||||||
\(853\) | −1.99182e48 | −0.868142 | −0.434071 | − | 0.900879i | \(-0.642923\pi\) | ||||
−0.434071 | + | 0.900879i | \(0.642923\pi\) | |||||||
\(854\) | −8.40704e47 | −0.359409 | ||||||||
\(855\) | −2.01312e47 | −0.0844170 | ||||||||
\(856\) | −2.77307e48 | −1.14063 | ||||||||
\(857\) | 8.90097e47 | 0.359132 | 0.179566 | − | 0.983746i | \(-0.442531\pi\) | ||||
0.179566 | + | 0.983746i | \(0.442531\pi\) | |||||||
\(858\) | −2.47314e48 | −0.978834 | ||||||||
\(859\) | −1.46621e48 | −0.569259 | −0.284629 | − | 0.958638i | \(-0.591871\pi\) | ||||
−0.284629 | + | 0.958638i | \(0.591871\pi\) | |||||||
\(860\) | 3.73905e47 | 0.142409 | ||||||||
\(861\) | 2.70791e48 | 1.01177 | ||||||||
\(862\) | 2.51571e48 | 0.922128 | ||||||||
\(863\) | −7.60640e47 | −0.273528 | −0.136764 | − | 0.990604i | \(-0.543670\pi\) | ||||
−0.136764 | + | 0.990604i | \(0.543670\pi\) | |||||||
\(864\) | −5.20340e47 | −0.183574 | ||||||||
\(865\) | −1.22674e48 | −0.424607 | ||||||||
\(866\) | −3.58698e48 | −1.21810 | ||||||||
\(867\) | 1.71993e48 | 0.573054 | ||||||||
\(868\) | −1.16777e48 | −0.381752 | ||||||||
\(869\) | −6.58447e48 | −2.11200 | ||||||||
\(870\) | −9.21588e46 | −0.0290048 | ||||||||
\(871\) | −1.49421e48 | −0.461436 | ||||||||
\(872\) | 3.46153e48 | 1.04893 | ||||||||
\(873\) | 1.05111e48 | 0.312547 | ||||||||
\(874\) | 9.93737e47 | 0.289956 | ||||||||
\(875\) | −6.30746e48 | −1.80602 | ||||||||
\(876\) | 3.57645e47 | 0.100493 | ||||||||
\(877\) | 5.90370e47 | 0.162791 | 0.0813956 | − | 0.996682i | \(-0.474062\pi\) | ||||
0.0813956 | + | 0.996682i | \(0.474062\pi\) | |||||||
\(878\) | −1.12483e47 | −0.0304389 | ||||||||
\(879\) | 3.37267e48 | 0.895689 | ||||||||
\(880\) | 4.94638e47 | 0.128921 | ||||||||
\(881\) | 2.55961e48 | 0.654742 | 0.327371 | − | 0.944896i | \(-0.393837\pi\) | ||||
0.327371 | + | 0.944896i | \(0.393837\pi\) | |||||||
\(882\) | 1.96380e48 | 0.493021 | ||||||||
\(883\) | −3.14939e48 | −0.776022 | −0.388011 | − | 0.921655i | \(-0.626838\pi\) | ||||
−0.388011 | + | 0.921655i | \(0.626838\pi\) | |||||||
\(884\) | 2.98543e47 | 0.0722011 | ||||||||
\(885\) | 8.48977e47 | 0.201526 | ||||||||
\(886\) | −3.31750e48 | −0.772955 | ||||||||
\(887\) | 4.83041e48 | 1.10470 | 0.552350 | − | 0.833612i | \(-0.313731\pi\) | ||||
0.552350 | + | 0.833612i | \(0.313731\pi\) | |||||||
\(888\) | −1.63620e48 | −0.367301 | ||||||||
\(889\) | 1.54337e49 | 3.40087 | ||||||||
\(890\) | −1.58723e48 | −0.343324 | ||||||||
\(891\) | −9.02736e47 | −0.191681 | ||||||||
\(892\) | −4.66698e48 | −0.972783 | ||||||||
\(893\) | 1.40269e48 | 0.287020 | ||||||||
\(894\) | 4.58541e47 | 0.0921105 | ||||||||
\(895\) | −1.57304e48 | −0.310212 | ||||||||
\(896\) | −4.25321e48 | −0.823446 | ||||||||
\(897\) | −4.86818e48 | −0.925318 | ||||||||
\(898\) | 4.09054e48 | 0.763346 | ||||||||
\(899\) | 2.51124e47 | 0.0460102 | ||||||||
\(900\) | 6.39016e47 | 0.114950 | ||||||||
\(901\) | 5.41679e47 | 0.0956716 | ||||||||
\(902\) | 6.40504e48 | 1.11074 | ||||||||
\(903\) | 2.47918e48 | 0.422143 | ||||||||
\(904\) | 4.20504e48 | 0.703058 | ||||||||
\(905\) | 2.12678e48 | 0.349158 | ||||||||
\(906\) | −2.30985e48 | −0.372364 | ||||||||
\(907\) | 1.73953e48 | 0.275368 | 0.137684 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137684 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(908\) | 7.03009e48 | 1.09281 | ||||||||
\(909\) | −8.05739e47 | −0.122996 | ||||||||
\(910\) | −7.34249e48 | −1.10068 | ||||||||
\(911\) | −5.97302e48 | −0.879308 | −0.439654 | − | 0.898167i | \(-0.644899\pi\) | ||||
−0.439654 | + | 0.898167i | \(0.644899\pi\) | |||||||
\(912\) | −1.95064e47 | −0.0282009 | ||||||||
\(913\) | −1.89022e49 | −2.68377 | ||||||||
\(914\) | −3.99644e48 | −0.557265 | ||||||||
\(915\) | 7.92953e47 | 0.108592 | ||||||||
\(916\) | 4.28356e48 | 0.576142 | ||||||||
\(917\) | −1.38141e49 | −1.82485 | ||||||||
\(918\) | −8.45887e46 | −0.0109751 | ||||||||
\(919\) | 1.16129e49 | 1.47990 | 0.739952 | − | 0.672660i | \(-0.234848\pi\) | ||||
0.739952 | + | 0.672660i | \(0.234848\pi\) | |||||||
\(920\) | 5.53945e48 | 0.693373 | ||||||||
\(921\) | −4.94646e48 | −0.608150 | ||||||||
\(922\) | −5.33540e48 | −0.644327 | ||||||||
\(923\) | 1.58713e49 | 1.88271 | ||||||||
\(924\) | −8.65852e48 | −1.00892 | ||||||||
\(925\) | 3.29497e48 | 0.377149 | ||||||||
\(926\) | 4.34254e48 | 0.488273 | ||||||||
\(927\) | −2.59304e48 | −0.286414 | ||||||||
\(928\) | 1.07325e48 | 0.116456 | ||||||||
\(929\) | −6.75124e48 | −0.719654 | −0.359827 | − | 0.933019i | \(-0.617164\pi\) | ||||
−0.359827 | + | 0.933019i | \(0.617164\pi\) | |||||||
\(930\) | −8.54979e47 | −0.0895338 | ||||||||
\(931\) | −8.84801e48 | −0.910281 | ||||||||
\(932\) | 9.49646e48 | 0.959841 | ||||||||
\(933\) | 5.70567e48 | 0.566578 | ||||||||
\(934\) | −8.72022e48 | −0.850754 | ||||||||
\(935\) | −9.66431e47 | −0.0926359 | ||||||||
\(936\) | 5.43669e48 | 0.512015 | ||||||||
\(937\) | −5.66941e48 | −0.524607 | −0.262304 | − | 0.964985i | \(-0.584482\pi\) | ||||
−0.262304 | + | 0.964985i | \(0.584482\pi\) | |||||||
\(938\) | 4.06069e48 | 0.369193 | ||||||||
\(939\) | 5.63117e48 | 0.503056 | ||||||||
\(940\) | 2.81644e48 | 0.247224 | ||||||||
\(941\) | −3.24161e48 | −0.279596 | −0.139798 | − | 0.990180i | \(-0.544645\pi\) | ||||
−0.139798 | + | 0.990180i | \(0.544645\pi\) | |||||||
\(942\) | −1.41936e48 | −0.120296 | ||||||||
\(943\) | 1.26078e49 | 1.05002 | ||||||||
\(944\) | 8.22627e47 | 0.0673232 | ||||||||
\(945\) | −2.68012e48 | −0.215541 | ||||||||
\(946\) | 5.86401e48 | 0.463438 | ||||||||
\(947\) | −7.43561e48 | −0.577486 | −0.288743 | − | 0.957407i | \(-0.593237\pi\) | ||||
−0.288743 | + | 0.957407i | \(0.593237\pi\) | |||||||
\(948\) | 5.21374e48 | 0.397935 | ||||||||
\(949\) | −6.12759e48 | −0.459618 | ||||||||
\(950\) | 2.23488e48 | 0.164746 | ||||||||
\(951\) | −6.20492e48 | −0.449529 | ||||||||
\(952\) | −2.25243e48 | −0.160377 | ||||||||
\(953\) | 1.08448e49 | 0.758910 | 0.379455 | − | 0.925210i | \(-0.376111\pi\) | ||||
0.379455 | + | 0.925210i | \(0.376111\pi\) | |||||||
\(954\) | 3.55315e48 | 0.244380 | ||||||||
\(955\) | 1.68691e49 | 1.14034 | ||||||||
\(956\) | −5.48232e48 | −0.364258 | ||||||||
\(957\) | 1.86198e48 | 0.121599 | ||||||||
\(958\) | 2.24313e48 | 0.143987 | ||||||||
\(959\) | 1.79877e48 | 0.113493 | ||||||||
\(960\) | −4.34969e48 | −0.269764 | ||||||||
\(961\) | −1.40737e49 | −0.857973 | ||||||||
\(962\) | 1.00976e49 | 0.605103 | ||||||||
\(963\) | 6.24674e48 | 0.367976 | ||||||||
\(964\) | 4.24517e48 | 0.245824 | ||||||||
\(965\) | 5.66063e48 | 0.322229 | ||||||||
\(966\) | 1.32299e49 | 0.740343 | ||||||||
\(967\) | −8.75090e48 | −0.481411 | −0.240705 | − | 0.970598i | \(-0.577379\pi\) | ||||
−0.240705 | + | 0.970598i | \(0.577379\pi\) | |||||||
\(968\) | −3.77526e49 | −2.04175 | ||||||||
\(969\) | 3.81119e47 | 0.0202637 | ||||||||
\(970\) | 7.38128e48 | 0.385832 | ||||||||
\(971\) | −9.33158e48 | −0.479554 | −0.239777 | − | 0.970828i | \(-0.577074\pi\) | ||||
−0.239777 | + | 0.970828i | \(0.577074\pi\) | |||||||
\(972\) | 7.14808e47 | 0.0361157 | ||||||||
\(973\) | 1.26254e48 | 0.0627168 | ||||||||
\(974\) | −1.81749e49 | −0.887666 | ||||||||
\(975\) | −1.09484e49 | −0.525743 | ||||||||
\(976\) | 7.68342e47 | 0.0362771 | ||||||||
\(977\) | −2.29643e49 | −1.06609 | −0.533044 | − | 0.846087i | \(-0.678952\pi\) | ||||
−0.533044 | + | 0.846087i | \(0.678952\pi\) | |||||||
\(978\) | 1.11532e49 | 0.509108 | ||||||||
\(979\) | 3.20684e49 | 1.43934 | ||||||||
\(980\) | −1.77658e49 | −0.784067 | ||||||||
\(981\) | −7.79760e48 | −0.338394 | ||||||||
\(982\) | 5.89657e48 | 0.251629 | ||||||||
\(983\) | −1.62693e49 | −0.682709 | −0.341355 | − | 0.939935i | \(-0.610886\pi\) | ||||
−0.341355 | + | 0.939935i | \(0.610886\pi\) | |||||||
\(984\) | −1.40801e49 | −0.581016 | ||||||||
\(985\) | 1.76676e48 | 0.0716937 | ||||||||
\(986\) | 1.74473e47 | 0.00696239 | ||||||||
\(987\) | 1.86744e49 | 0.732846 | ||||||||
\(988\) | −8.82320e48 | −0.340515 | ||||||||
\(989\) | 1.15428e49 | 0.438100 | ||||||||
\(990\) | −6.33931e48 | −0.236625 | ||||||||
\(991\) | −2.62407e47 | −0.00963297 | −0.00481649 | − | 0.999988i | \(-0.501533\pi\) | ||||
−0.00481649 | + | 0.999988i | \(0.501533\pi\) | |||||||
\(992\) | 9.95682e48 | 0.359483 | ||||||||
\(993\) | −1.36231e49 | −0.483741 | ||||||||
\(994\) | −4.31321e49 | −1.50635 | ||||||||
\(995\) | −1.55049e48 | −0.0532583 | ||||||||
\(996\) | 1.49672e49 | 0.505665 | ||||||||
\(997\) | −8.00569e47 | −0.0266029 | −0.0133014 | − | 0.999912i | \(-0.504234\pi\) | ||||
−0.0133014 | + | 0.999912i | \(0.504234\pi\) | |||||||
\(998\) | 1.70968e48 | 0.0558805 | ||||||||
\(999\) | 3.68578e48 | 0.118495 |
(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 | 3.34.a.b.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 9.34.a.c.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.34.a.b.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
9.34.a.c.1.2 | 3 | 3.2 | odd | 2 |