Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,5,Mod(296,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.296");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(54.8894503975\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 296.11 | ||
Character | \(\chi\) | \(=\) | 531.296 |
Dual form | 531.5.b.a.296.66 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/531\mathbb{Z}\right)^\times\).
\(n\) | \(119\) | \(415\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 6.38419i | − 1.59605i | −0.602627 | − | 0.798023i | \(-0.705879\pi\) | ||||
0.602627 | − | 0.798023i | \(-0.294121\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −24.7578 | −1.54736 | ||||||||
\(5\) | − 16.4296i | − 0.657185i | −0.944472 | − | 0.328592i | \(-0.893426\pi\) | ||||
0.944472 | − | 0.328592i | \(-0.106574\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 84.4308 | 1.72308 | 0.861538 | − | 0.507693i | \(-0.169501\pi\) | ||||
0.861538 | + | 0.507693i | \(0.169501\pi\) | |||||||
\(8\) | 55.9116i | 0.873618i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −104.890 | −1.04890 | ||||||||
\(11\) | 31.3181i | 0.258827i | 0.991591 | + | 0.129414i | \(0.0413095\pi\) | ||||
−0.991591 | + | 0.129414i | \(0.958691\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 43.8032 | 0.259191 | 0.129595 | − | 0.991567i | \(-0.458632\pi\) | ||||
0.129595 | + | 0.991567i | \(0.458632\pi\) | |||||||
\(14\) | − 539.022i | − 2.75011i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −39.1754 | −0.153029 | ||||||||
\(17\) | 243.216i | 0.841578i | 0.907158 | + | 0.420789i | \(0.138247\pi\) | ||||
−0.907158 | + | 0.420789i | \(0.861753\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 602.103 | 1.66788 | 0.833938 | − | 0.551858i | \(-0.186081\pi\) | ||||
0.833938 | + | 0.551858i | \(0.186081\pi\) | |||||||
\(20\) | 406.761i | 1.01690i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 199.940 | 0.413100 | ||||||||
\(23\) | 401.054i | 0.758135i | 0.925369 | + | 0.379068i | \(0.123755\pi\) | ||||
−0.925369 | + | 0.379068i | \(0.876245\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 355.068 | 0.568108 | ||||||||
\(26\) | − 279.648i | − 0.413680i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2090.32 | −2.66623 | ||||||||
\(29\) | − 1577.03i | − 1.87518i | −0.347742 | − | 0.937590i | \(-0.613051\pi\) | ||||
0.347742 | − | 0.937590i | \(-0.386949\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 306.821 | 0.319273 | 0.159636 | − | 0.987176i | \(-0.448968\pi\) | ||||
0.159636 | + | 0.987176i | \(0.448968\pi\) | |||||||
\(32\) | 1144.69i | 1.11786i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1552.74 | 1.34320 | ||||||||
\(35\) | − 1387.16i | − 1.13238i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2509.88 | 1.83337 | 0.916683 | − | 0.399614i | \(-0.130856\pi\) | ||||
0.916683 | + | 0.399614i | \(0.130856\pi\) | |||||||
\(38\) | − 3843.94i | − 2.66201i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 918.606 | 0.574128 | ||||||||
\(41\) | 1680.84i | 0.999907i | 0.866052 | + | 0.499953i | \(0.166650\pi\) | ||||
−0.866052 | + | 0.499953i | \(0.833350\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2973.39 | 1.60811 | 0.804055 | − | 0.594555i | \(-0.202672\pi\) | ||||
0.804055 | + | 0.594555i | \(0.202672\pi\) | |||||||
\(44\) | − 775.368i | − 0.400500i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2560.40 | 1.21002 | ||||||||
\(47\) | 890.845i | 0.403280i | 0.979460 | + | 0.201640i | \(0.0646271\pi\) | ||||
−0.979460 | + | 0.201640i | \(0.935373\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4727.55 | 1.96899 | ||||||||
\(50\) | − 2266.82i | − 0.906727i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1084.47 | −0.401062 | ||||||||
\(53\) | − 4496.31i | − 1.60068i | −0.599546 | − | 0.800340i | \(-0.704652\pi\) | ||||
0.599546 | − | 0.800340i | \(-0.295348\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 514.544 | 0.170097 | ||||||||
\(56\) | 4720.66i | 1.50531i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −10068.0 | −2.99288 | ||||||||
\(59\) | 453.188i | 0.130189i | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4996.33 | −1.34274 | −0.671369 | − | 0.741124i | \(-0.734293\pi\) | ||||
−0.671369 | + | 0.741124i | \(0.734293\pi\) | |||||||
\(62\) | − 1958.80i | − 0.509574i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6681.09 | 1.63113 | ||||||||
\(65\) | − 719.670i | − 0.170336i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5524.56 | −1.23069 | −0.615344 | − | 0.788259i | \(-0.710983\pi\) | ||||
−0.615344 | + | 0.788259i | \(0.710983\pi\) | |||||||
\(68\) | − 6021.50i | − 1.30223i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8855.92 | −1.80733 | ||||||||
\(71\) | 6512.64i | 1.29193i | 0.763365 | + | 0.645967i | \(0.223546\pi\) | ||||
−0.763365 | + | 0.645967i | \(0.776454\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1300.13 | 0.243973 | 0.121986 | − | 0.992532i | \(-0.461074\pi\) | ||||
0.121986 | + | 0.992532i | \(0.461074\pi\) | |||||||
\(74\) | − 16023.5i | − 2.92614i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14906.8 | −2.58081 | ||||||||
\(77\) | 2644.21i | 0.445979i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7102.80 | −1.13809 | −0.569043 | − | 0.822308i | \(-0.692686\pi\) | ||||
−0.569043 | + | 0.822308i | \(0.692686\pi\) | |||||||
\(80\) | 643.636i | 0.100568i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10730.8 | 1.59590 | ||||||||
\(83\) | − 7734.10i | − 1.12267i | −0.827587 | − | 0.561337i | \(-0.810287\pi\) | ||||
0.827587 | − | 0.561337i | \(-0.189713\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3995.95 | 0.553072 | ||||||||
\(86\) | − 18982.7i | − 2.56662i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1751.04 | −0.226116 | ||||||||
\(89\) | 9381.04i | 1.18433i | 0.805819 | + | 0.592163i | \(0.201726\pi\) | ||||
−0.805819 | + | 0.592163i | \(0.798274\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3698.34 | 0.446606 | ||||||||
\(92\) | − 9929.21i | − 1.17311i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5687.32 | 0.643653 | ||||||||
\(95\) | − 9892.33i | − 1.09610i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16857.7 | −1.79165 | −0.895827 | − | 0.444403i | \(-0.853416\pi\) | ||||
−0.895827 | + | 0.444403i | \(0.853416\pi\) | |||||||
\(98\) | − 30181.6i | − 3.14260i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8790.70 | −0.879070 | ||||||||
\(101\) | 1394.85i | 0.136736i | 0.997660 | + | 0.0683681i | \(0.0217792\pi\) | ||||
−0.997660 | + | 0.0683681i | \(0.978221\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6438.86 | −0.606924 | −0.303462 | − | 0.952843i | \(-0.598143\pi\) | ||||
−0.303462 | + | 0.952843i | \(0.598143\pi\) | |||||||
\(104\) | 2449.11i | 0.226434i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −28705.3 | −2.55476 | ||||||||
\(107\) | − 15170.7i | − 1.32507i | −0.749032 | − | 0.662533i | \(-0.769481\pi\) | ||||
0.749032 | − | 0.662533i | \(-0.230519\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13352.8 | 1.12388 | 0.561938 | − | 0.827179i | \(-0.310056\pi\) | ||||
0.561938 | + | 0.827179i | \(0.310056\pi\) | |||||||
\(110\) | − 3284.94i | − 0.271483i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3307.60 | −0.263680 | ||||||||
\(113\) | 12491.9i | 0.978299i | 0.872200 | + | 0.489150i | \(0.162693\pi\) | ||||
−0.872200 | + | 0.489150i | \(0.837307\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6589.16 | 0.498235 | ||||||||
\(116\) | 39043.8i | 2.90159i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2893.23 | 0.207788 | ||||||||
\(119\) | 20534.9i | 1.45010i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13660.2 | 0.933009 | ||||||||
\(122\) | 31897.5i | 2.14307i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7596.22 | −0.494031 | ||||||||
\(125\) | − 16102.1i | − 1.03054i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6207.75 | 0.384881 | 0.192441 | − | 0.981309i | \(-0.438360\pi\) | ||||
0.192441 | + | 0.981309i | \(0.438360\pi\) | |||||||
\(128\) | − 24338.3i | − 1.48549i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4594.51 | −0.271864 | ||||||||
\(131\) | − 6173.95i | − 0.359766i | −0.983688 | − | 0.179883i | \(-0.942428\pi\) | ||||
0.983688 | − | 0.179883i | \(-0.0575720\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 50836.0 | 2.87388 | ||||||||
\(134\) | 35269.8i | 1.96424i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −13598.6 | −0.735218 | ||||||||
\(137\) | − 17557.9i | − 0.935473i | −0.883868 | − | 0.467736i | \(-0.845070\pi\) | ||||
0.883868 | − | 0.467736i | \(-0.154930\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −34957.5 | −1.80930 | −0.904650 | − | 0.426155i | \(-0.859868\pi\) | ||||
−0.904650 | + | 0.426155i | \(0.859868\pi\) | |||||||
\(140\) | 34343.2i | 1.75220i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 41577.9 | 2.06199 | ||||||||
\(143\) | 1371.83i | 0.0670856i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −25909.9 | −1.23234 | ||||||||
\(146\) | − 8300.28i | − 0.389392i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −62139.1 | −2.83689 | ||||||||
\(149\) | 5530.20i | 0.249097i | 0.992214 | + | 0.124549i | \(0.0397483\pi\) | ||||
−0.992214 | + | 0.124549i | \(0.960252\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −351.339 | −0.0154089 | −0.00770446 | − | 0.999970i | \(-0.502452\pi\) | ||||
−0.00770446 | + | 0.999970i | \(0.502452\pi\) | |||||||
\(152\) | 33664.5i | 1.45709i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 16881.1 | 0.711803 | ||||||||
\(155\) | − 5040.95i | − 0.209821i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14649.0 | 0.594304 | 0.297152 | − | 0.954830i | \(-0.403963\pi\) | ||||
0.297152 | + | 0.954830i | \(0.403963\pi\) | |||||||
\(158\) | 45345.6i | 1.81644i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 18806.8 | 0.734640 | ||||||||
\(161\) | 33861.3i | 1.30633i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14721.4 | −0.554082 | −0.277041 | − | 0.960858i | \(-0.589354\pi\) | ||||
−0.277041 | + | 0.960858i | \(0.589354\pi\) | |||||||
\(164\) | − 41614.0i | − 1.54722i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −49375.9 | −1.79184 | ||||||||
\(167\) | − 1511.22i | − 0.0541870i | −0.999633 | − | 0.0270935i | \(-0.991375\pi\) | ||||
0.999633 | − | 0.0270935i | \(-0.00862518\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −26642.3 | −0.932820 | ||||||||
\(170\) | − 25510.9i | − 0.882729i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −73614.8 | −2.48833 | ||||||||
\(173\) | − 33955.4i | − 1.13453i | −0.823535 | − | 0.567266i | \(-0.808001\pi\) | ||||
0.823535 | − | 0.567266i | \(-0.191999\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 29978.6 | 0.978894 | ||||||||
\(176\) | − 1226.90i | − 0.0396080i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 59890.3 | 1.89024 | ||||||||
\(179\) | 21231.1i | 0.662623i | 0.943522 | + | 0.331311i | \(0.107491\pi\) | ||||
−0.943522 | + | 0.331311i | \(0.892509\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1207.76 | 0.0368657 | 0.0184328 | − | 0.999830i | \(-0.494132\pi\) | ||||
0.0184328 | + | 0.999830i | \(0.494132\pi\) | |||||||
\(182\) | − 23610.9i | − 0.712803i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −22423.5 | −0.662321 | ||||||||
\(185\) | − 41236.3i | − 1.20486i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7617.06 | −0.217823 | ||||||||
\(188\) | − 22055.4i | − 0.624021i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −63154.5 | −1.74943 | ||||||||
\(191\) | 12946.8i | 0.354892i | 0.984131 | + | 0.177446i | \(0.0567836\pi\) | ||||
−0.984131 | + | 0.177446i | \(0.943216\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7860.82 | 0.211034 | 0.105517 | − | 0.994417i | \(-0.466350\pi\) | ||||
0.105517 | + | 0.994417i | \(0.466350\pi\) | |||||||
\(194\) | 107622.i | 2.85956i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −117044. | −3.04675 | ||||||||
\(197\) | 36685.4i | 0.945281i | 0.881255 | + | 0.472640i | \(0.156699\pi\) | ||||
−0.881255 | + | 0.472640i | \(0.843301\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −70653.6 | −1.78414 | −0.892069 | − | 0.451900i | \(-0.850746\pi\) | ||||
−0.892069 | + | 0.451900i | \(0.850746\pi\) | |||||||
\(200\) | 19852.4i | 0.496310i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8904.96 | 0.218237 | ||||||||
\(203\) | − 133150.i | − 3.23108i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 27615.6 | 0.657123 | ||||||||
\(206\) | 41106.9i | 0.968679i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1716.01 | −0.0396636 | ||||||||
\(209\) | 18856.7i | 0.431692i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14850.2 | 0.333555 | 0.166777 | − | 0.985995i | \(-0.446664\pi\) | ||||
0.166777 | + | 0.985995i | \(0.446664\pi\) | |||||||
\(212\) | 111319.i | 2.47683i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −96852.5 | −2.11487 | ||||||||
\(215\) | − 48851.7i | − 1.05682i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 25905.1 | 0.550132 | ||||||||
\(218\) | − 85246.5i | − 1.79376i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −12739.0 | −0.263202 | ||||||||
\(221\) | 10653.7i | 0.218129i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 34364.0 | 0.691026 | 0.345513 | − | 0.938414i | \(-0.387705\pi\) | ||||
0.345513 | + | 0.938414i | \(0.387705\pi\) | |||||||
\(224\) | 96646.9i | 1.92616i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 79750.6 | 1.56141 | ||||||||
\(227\) | − 10950.2i | − 0.212506i | −0.994339 | − | 0.106253i | \(-0.966115\pi\) | ||||
0.994339 | − | 0.106253i | \(-0.0338853\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 29201.6 | 0.556846 | 0.278423 | − | 0.960459i | \(-0.410188\pi\) | ||||
0.278423 | + | 0.960459i | \(0.410188\pi\) | |||||||
\(230\) | − 42066.4i | − 0.795206i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 88174.1 | 1.63819 | ||||||||
\(233\) | 8886.56i | 0.163690i | 0.996645 | + | 0.0818449i | \(0.0260812\pi\) | ||||
−0.996645 | + | 0.0818449i | \(0.973919\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14636.2 | 0.265029 | ||||||||
\(236\) | − 11219.9i | − 0.201450i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 131099. | 2.31443 | ||||||||
\(239\) | − 90627.6i | − 1.58659i | −0.608837 | − | 0.793295i | \(-0.708364\pi\) | ||||
0.608837 | − | 0.793295i | \(-0.291636\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 53499.6 | 0.921120 | 0.460560 | − | 0.887629i | \(-0.347649\pi\) | ||||
0.460560 | + | 0.887629i | \(0.347649\pi\) | |||||||
\(242\) | − 87209.1i | − 1.48912i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 123698. | 2.07770 | ||||||||
\(245\) | − 77671.9i | − 1.29399i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26374.1 | 0.432298 | ||||||||
\(248\) | 17154.9i | 0.278923i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −102799. | −1.64478 | ||||||||
\(251\) | 39389.1i | 0.625214i | 0.949883 | + | 0.312607i | \(0.101202\pi\) | ||||
−0.949883 | + | 0.312607i | \(0.898798\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12560.2 | −0.196226 | ||||||||
\(254\) | − 39631.4i | − 0.614288i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −48482.9 | −0.739791 | ||||||||
\(257\) | 81869.3i | 1.23952i | 0.784790 | + | 0.619762i | \(0.212771\pi\) | ||||
−0.784790 | + | 0.619762i | \(0.787229\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 211911. | 3.15903 | ||||||||
\(260\) | 17817.5i | 0.263572i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −39415.6 | −0.574204 | ||||||||
\(263\) | 71572.4i | 1.03475i | 0.855760 | + | 0.517373i | \(0.173090\pi\) | ||||
−0.855760 | + | 0.517373i | \(0.826910\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −73872.7 | −1.05194 | ||||||||
\(266\) | − 324547.i | − 4.58684i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 136776. | 1.90432 | ||||||||
\(269\) | − 98180.3i | − 1.35681i | −0.734687 | − | 0.678406i | \(-0.762671\pi\) | ||||
0.734687 | − | 0.678406i | \(-0.237329\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2432.69 | −0.0331245 | −0.0165622 | − | 0.999863i | \(-0.505272\pi\) | ||||
−0.0165622 | + | 0.999863i | \(0.505272\pi\) | |||||||
\(272\) | − 9528.08i | − 0.128786i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −112093. | −1.49306 | ||||||||
\(275\) | 11120.0i | 0.147042i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23579.7 | −0.307312 | −0.153656 | − | 0.988124i | \(-0.549105\pi\) | ||||
−0.153656 | + | 0.988124i | \(0.549105\pi\) | |||||||
\(278\) | 223175.i | 2.88773i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 77558.6 | 0.989267 | ||||||||
\(281\) | 45120.5i | 0.571428i | 0.958315 | + | 0.285714i | \(0.0922307\pi\) | ||||
−0.958315 | + | 0.285714i | \(0.907769\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −32901.3 | −0.410809 | −0.205404 | − | 0.978677i | \(-0.565851\pi\) | ||||
−0.205404 | + | 0.978677i | \(0.565851\pi\) | |||||||
\(284\) | − 161239.i | − 1.99909i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8758.04 | 0.107072 | ||||||||
\(287\) | 141915.i | 1.72292i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24366.9 | 0.291746 | ||||||||
\(290\) | 165414.i | 1.96687i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −32188.4 | −0.377515 | ||||||||
\(293\) | − 156217.i | − 1.81968i | −0.414965 | − | 0.909838i | \(-0.636206\pi\) | ||||
0.414965 | − | 0.909838i | \(-0.363794\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7445.70 | 0.0855581 | ||||||||
\(296\) | 140331.i | 1.60166i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 35305.8 | 0.397570 | ||||||||
\(299\) | 17567.4i | 0.196502i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 251046. | 2.77090 | ||||||||
\(302\) | 2243.01i | 0.0245933i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −23587.6 | −0.255233 | ||||||||
\(305\) | 82087.7i | 0.882426i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −144566. | −1.53387 | −0.766936 | − | 0.641723i | \(-0.778220\pi\) | ||||
−0.766936 | + | 0.641723i | \(0.778220\pi\) | |||||||
\(308\) | − 65464.9i | − 0.690092i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −32182.4 | −0.334884 | ||||||||
\(311\) | − 41579.4i | − 0.429890i | −0.976626 | − | 0.214945i | \(-0.931043\pi\) | ||||
0.976626 | − | 0.214945i | \(-0.0689573\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 185290. | 1.89132 | 0.945658 | − | 0.325164i | \(-0.105420\pi\) | ||||
0.945658 | + | 0.325164i | \(0.105420\pi\) | |||||||
\(314\) | − 93521.9i | − 0.948537i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 175850. | 1.76103 | ||||||||
\(317\) | − 125291.i | − 1.24681i | −0.781900 | − | 0.623404i | \(-0.785749\pi\) | ||||
0.781900 | − | 0.623404i | \(-0.214251\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 49389.5 | 0.485348 | ||||||||
\(320\) | − 109768.i | − 1.07195i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 216177. | 2.08496 | ||||||||
\(323\) | 146441.i | 1.40365i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15553.1 | 0.147248 | ||||||||
\(326\) | 93984.1i | 0.884340i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −93978.6 | −0.873537 | ||||||||
\(329\) | 75214.7i | 0.694882i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −157297. | −1.43570 | −0.717851 | − | 0.696197i | \(-0.754874\pi\) | ||||
−0.717851 | + | 0.696197i | \(0.754874\pi\) | |||||||
\(332\) | 191479.i | 1.73718i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9647.92 | −0.0864850 | ||||||||
\(335\) | 90766.4i | 0.808789i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 186500. | 1.64217 | 0.821085 | − | 0.570806i | \(-0.193369\pi\) | ||||
0.821085 | + | 0.570806i | \(0.193369\pi\) | |||||||
\(338\) | 170089.i | 1.48882i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −98931.0 | −0.855804 | ||||||||
\(341\) | 9609.05i | 0.0826365i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 196433. | 1.66965 | ||||||||
\(344\) | 166247.i | 1.40487i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −216778. | −1.81077 | ||||||||
\(347\) | − 137926.i | − 1.14548i | −0.819738 | − | 0.572738i | \(-0.805881\pi\) | ||||
0.819738 | − | 0.572738i | \(-0.194119\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 57501.5 | 0.472094 | 0.236047 | − | 0.971742i | \(-0.424148\pi\) | ||||
0.236047 | + | 0.971742i | \(0.424148\pi\) | |||||||
\(350\) | − 191389.i | − 1.56236i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −35849.4 | −0.289332 | ||||||||
\(353\) | − 130353.i | − 1.04609i | −0.852304 | − | 0.523046i | \(-0.824796\pi\) | ||||
0.852304 | − | 0.523046i | \(-0.175204\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 107000. | 0.849039 | ||||||||
\(356\) | − 232254.i | − 1.83258i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 135543. | 1.05758 | ||||||||
\(359\) | 45021.1i | 0.349323i | 0.984629 | + | 0.174662i | \(0.0558831\pi\) | ||||
−0.984629 | + | 0.174662i | \(0.944117\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 232208. | 1.78181 | ||||||||
\(362\) | − 7710.54i | − 0.0588393i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −91562.9 | −0.691061 | ||||||||
\(365\) | − 21360.7i | − 0.160335i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11975.5 | −0.0889120 | −0.0444560 | − | 0.999011i | \(-0.514155\pi\) | ||||
−0.0444560 | + | 0.999011i | \(0.514155\pi\) | |||||||
\(368\) | − 15711.4i | − 0.116016i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −263260. | −1.92301 | ||||||||
\(371\) | − 379627.i | − 2.75809i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22936.6 | −0.164858 | −0.0824292 | − | 0.996597i | \(-0.526268\pi\) | ||||
−0.0824292 | + | 0.996597i | \(0.526268\pi\) | |||||||
\(374\) | 48628.7i | 0.347656i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −49808.6 | −0.352313 | ||||||||
\(377\) | − 69078.9i | − 0.486030i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 45087.7 | 0.313892 | 0.156946 | − | 0.987607i | \(-0.449835\pi\) | ||||
0.156946 | + | 0.987607i | \(0.449835\pi\) | |||||||
\(380\) | 244912.i | 1.69607i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 82654.9 | 0.566425 | ||||||||
\(383\) | 73353.7i | 0.500063i | 0.968238 | + | 0.250031i | \(0.0804409\pi\) | ||||
−0.968238 | + | 0.250031i | \(0.919559\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 43443.3 | 0.293091 | ||||||||
\(386\) | − 50184.9i | − 0.336821i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 417359. | 2.77234 | ||||||||
\(389\) | 82728.6i | 0.546709i | 0.961913 | + | 0.273354i | \(0.0881332\pi\) | ||||
−0.961913 | + | 0.273354i | \(0.911867\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −97542.7 | −0.638030 | ||||||||
\(392\) | 264325.i | 1.72015i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 234206. | 1.50871 | ||||||||
\(395\) | 116696.i | 0.747933i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 222421. | 1.41122 | 0.705609 | − | 0.708602i | \(-0.250674\pi\) | ||||
0.705609 | + | 0.708602i | \(0.250674\pi\) | |||||||
\(398\) | 451066.i | 2.84757i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13909.9 | −0.0869369 | ||||||||
\(401\) | 76062.6i | 0.473023i | 0.971629 | + | 0.236512i | \(0.0760041\pi\) | ||||
−0.971629 | + | 0.236512i | \(0.923996\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13439.8 | 0.0827526 | ||||||||
\(404\) | − 34533.4i | − 0.211581i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −850052. | −5.15695 | ||||||||
\(407\) | 78604.6i | 0.474525i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −106082. | −0.634153 | −0.317077 | − | 0.948400i | \(-0.602701\pi\) | ||||
−0.317077 | + | 0.948400i | \(0.602701\pi\) | |||||||
\(410\) | − 176303.i | − 1.04880i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 159412. | 0.939133 | ||||||||
\(413\) | 38263.0i | 0.224325i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −127068. | −0.737804 | ||||||||
\(416\) | 50141.0i | 0.289739i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 120385. | 0.689000 | ||||||||
\(419\) | 182880.i | 1.04169i | 0.853652 | + | 0.520844i | \(0.174383\pi\) | ||||
−0.853652 | + | 0.520844i | \(0.825617\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −260085. | −1.46741 | −0.733704 | − | 0.679469i | \(-0.762210\pi\) | ||||
−0.733704 | + | 0.679469i | \(0.762210\pi\) | |||||||
\(422\) | − 94806.4i | − 0.532369i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 251396. | 1.39838 | ||||||||
\(425\) | 86358.2i | 0.478108i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −421844. | −2.31364 | ||||||||
\(428\) | 375593.i | 2.05036i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −311878. | −1.68674 | ||||||||
\(431\) | 13132.3i | 0.0706946i | 0.999375 | + | 0.0353473i | \(0.0112537\pi\) | ||||
−0.999375 | + | 0.0353473i | \(0.988746\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −250937. | −1.33841 | −0.669204 | − | 0.743079i | \(-0.733365\pi\) | ||||
−0.669204 | + | 0.743079i | \(0.733365\pi\) | |||||||
\(434\) | − 165383.i | − 0.878035i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −330585. | −1.73904 | ||||||||
\(437\) | 241476.i | 1.26448i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −151603. | −0.786644 | −0.393322 | − | 0.919401i | \(-0.628674\pi\) | ||||
−0.393322 | + | 0.919401i | \(0.628674\pi\) | |||||||
\(440\) | 28769.0i | 0.148600i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 68014.9 | 0.348145 | ||||||||
\(443\) | 254620.i | 1.29743i | 0.761030 | + | 0.648716i | \(0.224694\pi\) | ||||
−0.761030 | + | 0.648716i | \(0.775306\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 154127. | 0.778320 | ||||||||
\(446\) | − 219386.i | − 1.10291i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 564090. | 2.81056 | ||||||||
\(449\) | − 211564.i | − 1.04942i | −0.851281 | − | 0.524710i | \(-0.824174\pi\) | ||||
0.851281 | − | 0.524710i | \(-0.175826\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −52640.8 | −0.258803 | ||||||||
\(452\) | − 309272.i | − 1.51379i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −69908.2 | −0.339169 | ||||||||
\(455\) | − 60762.3i | − 0.293502i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −108413. | −0.519098 | −0.259549 | − | 0.965730i | \(-0.583574\pi\) | ||||
−0.259549 | + | 0.965730i | \(0.583574\pi\) | |||||||
\(458\) | − 186428.i | − 0.888752i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −163133. | −0.770951 | ||||||||
\(461\) | − 225878.i | − 1.06285i | −0.847105 | − | 0.531426i | \(-0.821656\pi\) | ||||
0.847105 | − | 0.531426i | \(-0.178344\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −146905. | −0.685290 | −0.342645 | − | 0.939465i | \(-0.611323\pi\) | ||||
−0.342645 | + | 0.939465i | \(0.611323\pi\) | |||||||
\(464\) | 61780.6i | 0.286957i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 56733.4 | 0.261257 | ||||||||
\(467\) | 170884.i | 0.783551i | 0.920061 | + | 0.391776i | \(0.128139\pi\) | ||||
−0.920061 | + | 0.391776i | \(0.871861\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −466443. | −2.12057 | ||||||||
\(470\) | − 93440.5i | − 0.422999i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −25338.4 | −0.113735 | ||||||||
\(473\) | 93121.0i | 0.416222i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 213788. | 0.947535 | ||||||||
\(476\) | − 508400.i | − 2.24384i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −578584. | −2.53227 | ||||||||
\(479\) | 338877.i | 1.47697i | 0.674272 | + | 0.738483i | \(0.264457\pi\) | ||||
−0.674272 | + | 0.738483i | \(0.735543\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 109941. | 0.475192 | ||||||||
\(482\) | − 341551.i | − 1.47015i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −338196. | −1.44370 | ||||||||
\(485\) | 276965.i | 1.17745i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 222038. | 0.936202 | 0.468101 | − | 0.883675i | \(-0.344938\pi\) | ||||
0.468101 | + | 0.883675i | \(0.344938\pi\) | |||||||
\(488\) | − 279352.i | − 1.17304i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −495872. | −2.06527 | ||||||||
\(491\) | − 129659.i | − 0.537825i | −0.963165 | − | 0.268912i | \(-0.913336\pi\) | ||||
0.963165 | − | 0.268912i | \(-0.0866642\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 383558. | 1.57811 | ||||||||
\(494\) | − 168377.i | − 0.689968i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12019.8 | −0.0488579 | ||||||||
\(497\) | 549867.i | 2.22610i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 255872. | 1.02759 | 0.513797 | − | 0.857912i | \(-0.328239\pi\) | ||||
0.513797 | + | 0.857912i | \(0.328239\pi\) | |||||||
\(500\) | 398654.i | 1.59462i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 251467. | 0.997870 | ||||||||
\(503\) | − 331218.i | − 1.30912i | −0.756012 | − | 0.654558i | \(-0.772855\pi\) | ||||
0.756012 | − | 0.654558i | \(-0.227145\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22916.8 | 0.0898610 | ||||||||
\(506\) | 80186.8i | 0.313186i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −153690. | −0.595551 | ||||||||
\(509\) | 320646.i | 1.23763i | 0.785538 | + | 0.618814i | \(0.212386\pi\) | ||||
−0.785538 | + | 0.618814i | \(0.787614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 109771. | 0.420384 | ||||||||
\(512\) | − 79889.2i | − 0.304753i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 522669. | 1.97834 | ||||||||
\(515\) | 105788.i | 0.398861i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27899.6 | −0.104380 | ||||||||
\(518\) | − 1.35288e6i | − 5.04196i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 40237.9 | 0.148809 | ||||||||
\(521\) | 99104.2i | 0.365104i | 0.983196 | + | 0.182552i | \(0.0584358\pi\) | ||||
−0.983196 | + | 0.182552i | \(0.941564\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 318725. | 1.16523 | 0.582617 | − | 0.812747i | \(-0.302029\pi\) | ||||
0.582617 | + | 0.812747i | \(0.302029\pi\) | |||||||
\(524\) | 152854.i | 0.556689i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 456931. | 1.65150 | ||||||||
\(527\) | 74623.9i | 0.268693i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 118997. | 0.425231 | ||||||||
\(530\) | 471617.i | 1.67895i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.25859e6 | −4.44694 | ||||||||
\(533\) | 73626.4i | 0.259167i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −249249. | −0.870813 | ||||||||
\(536\) | − 308887.i | − 1.07515i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −626801. | −2.16553 | ||||||||
\(539\) | 148058.i | 0.509629i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −507671. | −1.73455 | −0.867277 | − | 0.497826i | \(-0.834132\pi\) | ||||
−0.867277 | + | 0.497826i | \(0.834132\pi\) | |||||||
\(542\) | 15530.8i | 0.0528682i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −278407. | −0.940766 | ||||||||
\(545\) | − 219381.i | − 0.738594i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −216288. | −0.722865 | −0.361432 | − | 0.932398i | \(-0.617712\pi\) | ||||
−0.361432 | + | 0.932398i | \(0.617712\pi\) | |||||||
\(548\) | 434695.i | 1.44752i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 70992.4 | 0.234686 | ||||||||
\(551\) | − 949533.i | − 3.12757i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −599694. | −1.96101 | ||||||||
\(554\) | 150537.i | 0.490484i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 865471. | 2.79965 | ||||||||
\(557\) | 500929.i | 1.61460i | 0.590139 | + | 0.807302i | \(0.299073\pi\) | ||||
−0.590139 | + | 0.807302i | \(0.700927\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 130244. | 0.416807 | ||||||||
\(560\) | 54342.7i | 0.173287i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 288058. | 0.912025 | ||||||||
\(563\) | 290220.i | 0.915610i | 0.889053 | + | 0.457805i | \(0.151364\pi\) | ||||
−0.889053 | + | 0.457805i | \(0.848636\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 205237. | 0.642923 | ||||||||
\(566\) | 210048.i | 0.655670i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −364132. | −1.12866 | ||||||||
\(569\) | 394021.i | 1.21701i | 0.793549 | + | 0.608506i | \(0.208231\pi\) | ||||
−0.793549 | + | 0.608506i | \(0.791769\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24021.1 | 0.0736750 | 0.0368375 | − | 0.999321i | \(-0.488272\pi\) | ||||
0.0368375 | + | 0.999321i | \(0.488272\pi\) | |||||||
\(572\) | − 33963.6i | − 0.103806i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 906011. | 2.74985 | ||||||||
\(575\) | 142401.i | 0.430703i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21255.5 | 0.0638441 | 0.0319220 | − | 0.999490i | \(-0.489837\pi\) | ||||
0.0319220 | + | 0.999490i | \(0.489837\pi\) | |||||||
\(578\) | − 155563.i | − 0.465640i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 641474. | 1.90688 | ||||||||
\(581\) | − 652996.i | − 1.93445i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 140816. | 0.414299 | ||||||||
\(584\) | 72692.4i | 0.213139i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −997320. | −2.90429 | ||||||||
\(587\) | 67625.0i | 0.196260i | 0.995174 | + | 0.0981298i | \(0.0312860\pi\) | ||||
−0.995174 | + | 0.0981298i | \(0.968714\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 184738. | 0.532508 | ||||||||
\(590\) | − 47534.7i | − 0.136555i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −98325.4 | −0.280558 | ||||||||
\(593\) | − 2627.19i | − 0.00747105i | −0.999993 | − | 0.00373552i | \(-0.998811\pi\) | ||||
0.999993 | − | 0.00373552i | \(-0.00118906\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 337381. | 0.952986 | ||||||||
\(596\) | − 136916.i | − 0.385444i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 112154. | 0.313626 | ||||||||
\(599\) | 114040.i | 0.317836i | 0.987292 | + | 0.158918i | \(0.0508006\pi\) | ||||
−0.987292 | + | 0.158918i | \(0.949199\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −159026. | −0.440270 | −0.220135 | − | 0.975469i | \(-0.570650\pi\) | ||||
−0.220135 | + | 0.975469i | \(0.570650\pi\) | |||||||
\(602\) | − 1.60272e6i | − 4.42248i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8698.38 | 0.0238432 | ||||||||
\(605\) | − 224431.i | − 0.613159i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 225627. | 0.612369 | 0.306185 | − | 0.951972i | \(-0.400948\pi\) | ||||
0.306185 | + | 0.951972i | \(0.400948\pi\) | |||||||
\(608\) | 689220.i | 1.86445i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 524063. | 1.40839 | ||||||||
\(611\) | 39021.9i | 0.104526i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 273471. | 0.727764 | 0.363882 | − | 0.931445i | \(-0.381451\pi\) | ||||
0.363882 | + | 0.931445i | \(0.381451\pi\) | |||||||
\(614\) | 922936.i | 2.44813i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −147842. | −0.389615 | ||||||||
\(617\) | − 493931.i | − 1.29747i | −0.761016 | − | 0.648733i | \(-0.775299\pi\) | ||||
0.761016 | − | 0.648733i | \(-0.224701\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 126364. | 0.329793 | 0.164897 | − | 0.986311i | \(-0.447271\pi\) | ||||
0.164897 | + | 0.986311i | \(0.447271\pi\) | |||||||
\(620\) | 124803.i | 0.324670i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −265451. | −0.686125 | ||||||||
\(623\) | 792048.i | 2.04068i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −42634.5 | −0.109144 | ||||||||
\(626\) | − 1.18293e6i | − 3.01863i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −362677. | −0.919604 | ||||||||
\(629\) | 610443.i | 1.54292i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 60850.8 | 0.152830 | 0.0764148 | − | 0.997076i | \(-0.475653\pi\) | ||||
0.0764148 | + | 0.997076i | \(0.475653\pi\) | |||||||
\(632\) | − 397128.i | − 0.994253i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −799878. | −1.98996 | ||||||||
\(635\) | − 101991.i | − 0.252938i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 207082. | 0.510345 | ||||||||
\(638\) | − 315311.i | − 0.774637i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −399869. | −0.976244 | ||||||||
\(641\) | − 463957.i | − 1.12918i | −0.825373 | − | 0.564588i | \(-0.809035\pi\) | ||||
0.825373 | − | 0.564588i | \(-0.190965\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −118531. | −0.286689 | −0.143345 | − | 0.989673i | \(-0.545786\pi\) | ||||
−0.143345 | + | 0.989673i | \(0.545786\pi\) | |||||||
\(644\) | − 838331.i | − 2.02136i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 934908. | 2.24029 | ||||||||
\(647\) | − 814030.i | − 1.94461i | −0.233722 | − | 0.972304i | \(-0.575090\pi\) | ||||
0.233722 | − | 0.972304i | \(-0.424910\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14193.0 | −0.0336964 | ||||||||
\(650\) | − 99294.0i | − 0.235015i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 364470. | 0.857366 | ||||||||
\(653\) | 671405.i | 1.57456i | 0.616599 | + | 0.787278i | \(0.288510\pi\) | ||||
−0.616599 | + | 0.787278i | \(0.711490\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −101436. | −0.236433 | ||||||||
\(656\) | − 65847.6i | − 0.153014i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 480185. | 1.10906 | ||||||||
\(659\) | 97060.7i | 0.223497i | 0.993737 | + | 0.111749i | \(0.0356452\pi\) | ||||
−0.993737 | + | 0.111749i | \(0.964355\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −332725. | −0.761522 | −0.380761 | − | 0.924673i | \(-0.624338\pi\) | ||||
−0.380761 | + | 0.924673i | \(0.624338\pi\) | |||||||
\(662\) | 1.00421e6i | 2.29145i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 432426. | 0.980788 | ||||||||
\(665\) | − 835217.i | − 1.88867i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 632472. | 1.42164 | ||||||||
\(668\) | 37414.5i | 0.0838470i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 579470. | 1.29087 | ||||||||
\(671\) | − 156475.i | − 0.347537i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −416464. | −0.919491 | −0.459745 | − | 0.888051i | \(-0.652059\pi\) | ||||
−0.459745 | + | 0.888051i | \(0.652059\pi\) | |||||||
\(674\) | − 1.19065e6i | − 2.62098i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 659605. | 1.44341 | ||||||||
\(677\) | − 261128.i | − 0.569739i | −0.958566 | − | 0.284869i | \(-0.908050\pi\) | ||||
0.958566 | − | 0.284869i | \(-0.0919502\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.42331e6 | −3.08716 | ||||||||
\(680\) | 223420.i | 0.483174i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 61346.0 | 0.131892 | ||||||||
\(683\) | 783856.i | 1.68033i | 0.542331 | + | 0.840165i | \(0.317542\pi\) | ||||
−0.542331 | + | 0.840165i | \(0.682458\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −288469. | −0.614778 | ||||||||
\(686\) | − 1.25406e6i | − 2.66484i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −116484. | −0.246087 | ||||||||
\(689\) | − 196953.i | − 0.414882i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 560121. | 1.17307 | 0.586537 | − | 0.809922i | \(-0.300491\pi\) | ||||
0.586537 | + | 0.809922i | \(0.300491\pi\) | |||||||
\(692\) | 840662.i | 1.75553i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −880543. | −1.82823 | ||||||||
\(695\) | 574338.i | 1.18904i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −408808. | −0.841500 | ||||||||
\(698\) | − 367100.i | − 0.753484i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −742206. | −1.51471 | ||||||||
\(701\) | − 6423.80i | − 0.0130724i | −0.999979 | − | 0.00653621i | \(-0.997919\pi\) | ||||
0.999979 | − | 0.00653621i | \(-0.00208056\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.51121e6 | 3.05783 | ||||||||
\(704\) | 209239.i | 0.422180i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −832195. | −1.66961 | ||||||||
\(707\) | 117768.i | 0.235607i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9597.63 | 0.0190929 | 0.00954644 | − | 0.999954i | \(-0.496961\pi\) | ||||
0.00954644 | + | 0.999954i | \(0.496961\pi\) | |||||||
\(710\) | − 683109.i | − 1.35511i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −524509. | −1.03465 | ||||||||
\(713\) | 123052.i | 0.242052i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22538.7 | 0.0440876 | ||||||||
\(716\) | − 525636.i | − 1.02532i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 287423. | 0.557536 | ||||||||
\(719\) | − 244867.i | − 0.473666i | −0.971550 | − | 0.236833i | \(-0.923891\pi\) | ||||
0.971550 | − | 0.236833i | \(-0.0761095\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −543638. | −1.04578 | ||||||||
\(722\) | − 1.48246e6i | − 2.84385i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −29901.4 | −0.0570446 | ||||||||
\(725\) | − 559951.i | − 1.06531i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 398236. | 0.753481 | 0.376740 | − | 0.926319i | \(-0.377045\pi\) | ||||
0.376740 | + | 0.926319i | \(0.377045\pi\) | |||||||
\(728\) | 206780.i | 0.390163i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −136370. | −0.255902 | ||||||||
\(731\) | 723178.i | 1.35335i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 301885. | 0.561866 | 0.280933 | − | 0.959727i | \(-0.409356\pi\) | ||||
0.280933 | + | 0.959727i | \(0.409356\pi\) | |||||||
\(734\) | 76453.6i | 0.141908i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −459081. | −0.847489 | ||||||||
\(737\) | − 173019.i | − 0.318536i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 211672. | 0.387592 | 0.193796 | − | 0.981042i | \(-0.437920\pi\) | ||||
0.193796 | + | 0.981042i | \(0.437920\pi\) | |||||||
\(740\) | 1.02092e6i | 1.86436i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.42361e6 | −4.40205 | ||||||||
\(743\) | 497892.i | 0.901899i | 0.892549 | + | 0.450950i | \(0.148915\pi\) | ||||
−0.892549 | + | 0.450950i | \(0.851085\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 90859.1 | 0.163703 | ||||||||
\(746\) | 146431.i | 0.263122i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 188582. | 0.337052 | ||||||||
\(749\) | − 1.28087e6i | − 2.28319i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −105180. | −0.186489 | −0.0932446 | − | 0.995643i | \(-0.529724\pi\) | ||||
−0.0932446 | + | 0.995643i | \(0.529724\pi\) | |||||||
\(752\) | − 34899.2i | − 0.0617134i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −441012. | −0.775726 | ||||||||
\(755\) | 5772.36i | 0.0101265i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −389680. | −0.680012 | −0.340006 | − | 0.940423i | \(-0.610429\pi\) | ||||
−0.340006 | + | 0.940423i | \(0.610429\pi\) | |||||||
\(758\) | − 287848.i | − 0.500986i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 553096. | 0.957575 | ||||||||
\(761\) | 471821.i | 0.814720i | 0.913268 | + | 0.407360i | \(0.133551\pi\) | ||||
−0.913268 | + | 0.407360i | \(0.866449\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.12738e6 | 1.93652 | ||||||||
\(764\) | − 320535.i | − 0.549148i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 468304. | 0.798123 | ||||||||
\(767\) | 19851.1i | 0.0337438i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −90005.1 | −0.152200 | −0.0761000 | − | 0.997100i | \(-0.524247\pi\) | ||||
−0.0761000 | + | 0.997100i | \(0.524247\pi\) | |||||||
\(770\) | − 277350.i | − 0.467786i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −194617. | −0.326547 | ||||||||
\(773\) | − 344592.i | − 0.576695i | −0.957526 | − | 0.288347i | \(-0.906894\pi\) | ||||
0.957526 | − | 0.288347i | \(-0.0931058\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 108942. | 0.181382 | ||||||||
\(776\) | − 942539.i | − 1.56522i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 528154. | 0.872573 | ||||||||
\(779\) | 1.01204e6i | 1.66772i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −203963. | −0.334388 | ||||||||
\(782\) | 622731.i | 1.01833i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −185204. | −0.301313 | ||||||||
\(785\) | − 240677.i | − 0.390567i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −572667. | −0.924597 | −0.462298 | − | 0.886724i | \(-0.652975\pi\) | ||||
−0.462298 | + | 0.886724i | \(0.652975\pi\) | |||||||
\(788\) | − 908251.i | − 1.46269i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 745010. | 1.19374 | ||||||||
\(791\) | 1.05470e6i | 1.68568i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −218855. | −0.348025 | ||||||||
\(794\) | − 1.41997e6i | − 2.25237i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.74923e6 | 2.76071 | ||||||||
\(797\) | − 996132.i | − 1.56820i | −0.620637 | − | 0.784098i | \(-0.713126\pi\) | ||||
0.620637 | − | 0.784098i | \(-0.286874\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −216668. | −0.339392 | ||||||||
\(800\) | 406442.i | 0.635065i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 485598. | 0.754967 | ||||||||
\(803\) | 40717.6i | 0.0631468i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 556327. | 0.858497 | ||||||||
\(806\) | − 85801.9i | − 0.132077i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −77988.1 | −0.119455 | ||||||||
\(809\) | − 480734.i | − 0.734527i | −0.930117 | − | 0.367263i | \(-0.880295\pi\) | ||||
0.930117 | − | 0.367263i | \(-0.119705\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.03911e6 | −1.57986 | −0.789930 | − | 0.613197i | \(-0.789883\pi\) | ||||
−0.789930 | + | 0.613197i | \(0.789883\pi\) | |||||||
\(812\) | 3.29649e6i | 4.99966i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 501826. | 0.757364 | ||||||||
\(815\) | 241867.i | 0.364134i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.79029e6 | 2.68213 | ||||||||
\(818\) | 677246.i | 1.01214i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −683702. | −1.01681 | ||||||||
\(821\) | 1.16284e6i | 1.72518i | 0.505904 | + | 0.862590i | \(0.331159\pi\) | ||||
−0.505904 | + | 0.862590i | \(0.668841\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −198095. | −0.292465 | −0.146232 | − | 0.989250i | \(-0.546715\pi\) | ||||
−0.146232 | + | 0.989250i | \(0.546715\pi\) | |||||||
\(824\) | − 360007.i | − 0.530220i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 244278. | 0.358034 | ||||||||
\(827\) | 741023.i | 1.08348i | 0.840546 | + | 0.541740i | \(0.182234\pi\) | ||||
−0.840546 | + | 0.541740i | \(0.817766\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −286940. | −0.417524 | −0.208762 | − | 0.977966i | \(-0.566943\pi\) | ||||
−0.208762 | + | 0.977966i | \(0.566943\pi\) | |||||||
\(830\) | 811227.i | 1.17757i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 292654. | 0.422773 | ||||||||
\(833\) | 1.14982e6i | 1.65706i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24828.8 | −0.0356109 | ||||||||
\(836\) | − 466851.i | − 0.667984i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.16754e6 | 1.66258 | ||||||||
\(839\) | 184330.i | 0.261862i | 0.991391 | + | 0.130931i | \(0.0417967\pi\) | ||||
−0.991391 | + | 0.130931i | \(0.958203\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.77973e6 | −2.51630 | ||||||||
\(842\) | 1.66043e6i | 2.34205i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −367659. | −0.516131 | ||||||||
\(845\) | 437722.i | 0.613035i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.15334e6 | 1.60765 | ||||||||
\(848\) | 176145.i | 0.244950i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 551327. | 0.763082 | ||||||||
\(851\) | 1.00660e6i | 1.38994i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.38558e6 | −1.90430 | −0.952149 | − | 0.305635i | \(-0.901131\pi\) | ||||
−0.952149 | + | 0.305635i | \(0.901131\pi\) | |||||||
\(854\) | 2.69313e6i | 3.69268i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 848217. | 1.15760 | ||||||||
\(857\) | 871483.i | 1.18658i | 0.804989 | + | 0.593290i | \(0.202171\pi\) | ||||
−0.804989 | + | 0.593290i | \(0.797829\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −137699. | −0.186614 | −0.0933071 | − | 0.995637i | \(-0.529744\pi\) | ||||
−0.0933071 | + | 0.995637i | \(0.529744\pi\) | |||||||
\(860\) | 1.20946e6i | 1.63529i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 83839.0 | 0.112832 | ||||||||
\(863\) | 42360.1i | 0.0568768i | 0.999596 | + | 0.0284384i | \(0.00905345\pi\) | ||||
−0.999596 | + | 0.0284384i | \(0.990947\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −557874. | −0.745597 | ||||||||
\(866\) | 1.60203e6i | 2.13616i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −641355. | −0.851254 | ||||||||
\(869\) | − 222446.i | − 0.294568i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −241994. | −0.318983 | ||||||||
\(872\) | 746574.i | 0.981838i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.54163e6 | 2.01816 | ||||||||
\(875\) | − 1.35952e6i | − 1.77569i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −745544. | −0.969336 | −0.484668 | − | 0.874698i | \(-0.661060\pi\) | ||||
−0.484668 | + | 0.874698i | \(0.661060\pi\) | |||||||
\(878\) | 967861.i | 1.25552i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −20157.4 | −0.0260298 | ||||||||
\(881\) | 157416.i | 0.202814i | 0.994845 | + | 0.101407i | \(0.0323344\pi\) | ||||
−0.994845 | + | 0.101407i | \(0.967666\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 427912. | 0.548824 | 0.274412 | − | 0.961612i | \(-0.411517\pi\) | ||||
0.274412 | + | 0.961612i | \(0.411517\pi\) | |||||||
\(884\) | − 263761.i | − 0.337526i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.62554e6 | 2.07076 | ||||||||
\(887\) | − 839984.i | − 1.06764i | −0.845599 | − | 0.533819i | \(-0.820756\pi\) | ||||
0.845599 | − | 0.533819i | \(-0.179244\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 524125. | 0.663180 | ||||||||
\(890\) | − 983974.i | − 1.24224i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −850779. | −1.06927 | ||||||||
\(893\) | 536381.i | 0.672621i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 348819. | 0.435465 | ||||||||
\(896\) | − 2.05490e6i | − 2.55962i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.35066e6 | −1.67492 | ||||||||
\(899\) | − 483865.i | − 0.598694i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.09358e6 | 1.34710 | ||||||||
\(902\) | 336069.i | 0.413062i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −698442. | −0.854660 | ||||||||
\(905\) | − 19843.0i | − 0.0242275i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −719458. | −0.874562 | −0.437281 | − | 0.899325i | \(-0.644059\pi\) | ||||
−0.437281 | + | 0.899325i | \(0.644059\pi\) | |||||||
\(908\) | 271103.i | 0.328824i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −387918. | −0.468443 | ||||||||
\(911\) | 24750.9i | 0.0298232i | 0.999889 | + | 0.0149116i | \(0.00474669\pi\) | ||||
−0.999889 | + | 0.0149116i | \(0.995253\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 242217. | 0.290578 | ||||||||
\(914\) | 692130.i | 0.828505i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −722967. | −0.861644 | ||||||||
\(917\) | − 521271.i | − 0.619905i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 655862. | 0.776571 | 0.388286 | − | 0.921539i | \(-0.373067\pi\) | ||||
0.388286 | + | 0.921539i | \(0.373067\pi\) | |||||||
\(920\) | 368410.i | 0.435267i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.44205e6 | −1.69636 | ||||||||
\(923\) | 285275.i | 0.334857i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 891177. | 1.04155 | ||||||||
\(926\) | 937868.i | 1.09375i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.80520e6 | 2.09619 | ||||||||
\(929\) | − 113201.i | − 0.131166i | −0.997847 | − | 0.0655828i | \(-0.979109\pi\) | ||||
0.997847 | − | 0.0655828i | \(-0.0208907\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.84648e6 | 3.28404 | ||||||||
\(932\) | − 220012.i | − 0.253288i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.09095e6 | 1.25058 | ||||||||
\(935\) | 125145.i | 0.143150i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 490926. | 0.559161 | 0.279580 | − | 0.960122i | \(-0.409805\pi\) | ||||
0.279580 | + | 0.960122i | \(0.409805\pi\) | |||||||
\(938\) | 2.97786e6i | 3.38453i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −362362. | −0.410097 | ||||||||
\(941\) | − 1.30667e6i | − 1.47566i | −0.674988 | − | 0.737829i | \(-0.735851\pi\) | ||||
0.674988 | − | 0.737829i | \(-0.264149\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −674108. | −0.758065 | ||||||||
\(944\) | − 17753.8i | − 0.0199226i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 594502. | 0.664310 | ||||||||
\(947\) | 358264.i | 0.399487i | 0.979848 | + | 0.199744i | \(0.0640109\pi\) | ||||
−0.979848 | + | 0.199744i | \(0.935989\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 56950.0 | 0.0632355 | ||||||||
\(950\) | − 1.36486e6i | − 1.51231i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.14814e6 | −1.26684 | ||||||||
\(953\) | 1.20395e6i | 1.32563i | 0.748782 | + | 0.662817i | \(0.230639\pi\) | ||||
−0.748782 | + | 0.662817i | \(0.769361\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 212711. | 0.233230 | ||||||||
\(956\) | 2.24374e6i | 2.45503i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.16345e6 | 2.35731 | ||||||||
\(959\) | − 1.48243e6i | − 1.61189i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −829382. | −0.898065 | ||||||||
\(962\) | − 701883.i | − 0.758428i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.32453e6 | −1.42531 | ||||||||
\(965\) | − 129150.i | − 0.138689i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.14500e6 | −1.22448 | −0.612241 | − | 0.790671i | \(-0.709732\pi\) | ||||
−0.612241 | + | 0.790671i | \(0.709732\pi\) | |||||||
\(968\) | 763762.i | 0.815093i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.76820e6 | 1.87926 | ||||||||
\(971\) | 208959.i | 0.221627i | 0.993841 | + | 0.110813i | \(0.0353456\pi\) | ||||
−0.993841 | + | 0.110813i | \(0.964654\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.95149e6 | −3.11756 | ||||||||
\(974\) | − 1.41753e6i | − 1.49422i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 195733. | 0.205477 | ||||||||
\(977\) | − 245588.i | − 0.257287i | −0.991691 | − | 0.128644i | \(-0.958938\pi\) | ||||
0.991691 | − | 0.128644i | \(-0.0410623\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −293796. | −0.306535 | ||||||||
\(980\) | 1.92299e6i | 2.00228i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −827770. | −0.858394 | ||||||||
\(983\) | − 1.24959e6i | − 1.29318i | −0.762838 | − | 0.646590i | \(-0.776195\pi\) | ||||
0.762838 | − | 0.646590i | \(-0.223805\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 602727. | 0.621224 | ||||||||
\(986\) | − 2.44871e6i | − 2.51874i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −652965. | −0.668923 | ||||||||
\(989\) | 1.19249e6i | 1.21916i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 648193. | 0.660020 | 0.330010 | − | 0.943977i | \(-0.392948\pi\) | ||||
0.330010 | + | 0.943977i | \(0.392948\pi\) | |||||||
\(992\) | 351214.i | 0.356902i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.51045e6 | 3.55296 | ||||||||
\(995\) | 1.16081e6i | 1.17251i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −719032. | −0.723366 | −0.361683 | − | 0.932301i | \(-0.617798\pi\) | ||||
−0.361683 | + | 0.932301i | \(0.617798\pi\) | |||||||
\(998\) | − 1.63353e6i | − 1.64009i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 531.5.b.a.296.11 | ✓ | 76 | |
3.2 | odd | 2 | inner | 531.5.b.a.296.66 | yes | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
531.5.b.a.296.11 | ✓ | 76 | 1.1 | even | 1 | trivial | |
531.5.b.a.296.66 | yes | 76 | 3.2 | odd | 2 | inner |