Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,6,Mod(1,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.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: | \(71.8519512762\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{177}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 44 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 56) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-6.15207\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 26.3041 | 1.68741 | 0.843706 | − | 0.536806i | \(-0.180369\pi\) | ||||
0.843706 | + | 0.536806i | \(0.180369\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 97.5207 | 1.74450 | 0.872251 | − | 0.489058i | \(-0.162659\pi\) | ||||
0.872251 | + | 0.489058i | \(0.162659\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 448.908 | 1.84736 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −406.175 | −1.01212 | −0.506060 | − | 0.862498i | \(-0.668898\pi\) | ||||
−0.506060 | + | 0.862498i | \(0.668898\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 905.594 | 1.48619 | 0.743096 | − | 0.669185i | \(-0.233357\pi\) | ||||
0.743096 | + | 0.669185i | \(0.233357\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2565.20 | 2.94369 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 359.825 | 0.301973 | 0.150987 | − | 0.988536i | \(-0.451755\pi\) | ||||
0.150987 | + | 0.988536i | \(0.451755\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1813.25 | −1.15232 | −0.576162 | − | 0.817336i | \(-0.695450\pi\) | ||||
−0.576162 | + | 0.817336i | \(0.695450\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1288.90 | 0.637781 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2163.43 | −0.852751 | −0.426376 | − | 0.904546i | \(-0.640210\pi\) | ||||
−0.426376 | + | 0.904546i | \(0.640210\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6385.28 | 2.04329 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5416.22 | 1.42984 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4090.26 | 0.903141 | 0.451571 | − | 0.892235i | \(-0.350864\pi\) | ||||
0.451571 | + | 0.892235i | \(0.350864\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4451.54 | 0.831966 | 0.415983 | − | 0.909372i | \(-0.363438\pi\) | ||||
0.415983 | + | 0.909372i | \(0.363438\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10684.1 | −1.70786 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4778.51 | 0.659360 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8935.69 | −1.07306 | −0.536530 | − | 0.843882i | \(-0.680265\pi\) | ||||
−0.536530 | + | 0.843882i | \(0.680265\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 23820.9 | 2.50782 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3415.04 | −0.317275 | −0.158637 | − | 0.987337i | \(-0.550710\pi\) | ||||
−0.158637 | + | 0.987337i | \(0.550710\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8694.80 | 0.717114 | 0.358557 | − | 0.933508i | \(-0.383269\pi\) | ||||
0.358557 | + | 0.933508i | \(0.383269\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 43777.8 | 3.22272 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 14204.5 | 0.937955 | 0.468977 | − | 0.883210i | \(-0.344623\pi\) | ||||
0.468977 | + | 0.883210i | \(0.344623\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9464.88 | 0.509553 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 14616.4 | 0.714743 | 0.357371 | − | 0.933962i | \(-0.383673\pi\) | ||||
0.357371 | + | 0.933962i | \(0.383673\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −39610.5 | −1.76564 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −47696.1 | −1.94444 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −21396.8 | −0.800239 | −0.400119 | − | 0.916463i | \(-0.631031\pi\) | ||||
−0.400119 | + | 0.916463i | \(0.631031\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −54081.9 | −1.86092 | −0.930460 | − | 0.366394i | \(-0.880592\pi\) | ||||
−0.930460 | + | 0.366394i | \(0.880592\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 21996.5 | 0.698235 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 88314.1 | 2.59267 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −44973.1 | −1.22396 | −0.611978 | − | 0.790874i | \(-0.709626\pi\) | ||||
−0.611978 | + | 0.790874i | \(0.709626\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −56907.0 | −1.43894 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5700.89 | 0.134214 | 0.0671069 | − | 0.997746i | \(-0.478623\pi\) | ||||
0.0671069 | + | 0.997746i | \(0.478623\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 47650.8 | 1.04656 | 0.523279 | − | 0.852162i | \(-0.324709\pi\) | ||||
0.523279 | + | 0.852162i | \(0.324709\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 167959. | 3.44787 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −19902.6 | −0.382545 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5809.20 | 0.104725 | 0.0523623 | − | 0.998628i | \(-0.483325\pi\) | ||||
0.0523623 | + | 0.998628i | \(0.483325\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 33384.4 | 0.565368 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −27058.2 | −0.431126 | −0.215563 | − | 0.976490i | \(-0.569159\pi\) | ||||
−0.215563 | + | 0.976490i | \(0.569159\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 35090.4 | 0.526794 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 107591. | 1.52397 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −96245.2 | −1.28796 | −0.643982 | − | 0.765040i | \(-0.722719\pi\) | ||||
−0.643982 | + | 0.765040i | \(0.722719\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 44374.1 | 0.561728 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 117094. | 1.40387 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −176830. | −2.01023 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 101968. | 1.10036 | 0.550182 | − | 0.835045i | \(-0.314558\pi\) | ||||
0.550182 | + | 0.835045i | \(0.314558\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −182335. | −1.86974 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 21856.8 | 0.213198 | 0.106599 | − | 0.994302i | \(-0.466004\pi\) | ||||
0.106599 | + | 0.994302i | \(0.466004\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −136106. | −1.26411 | −0.632056 | − | 0.774923i | \(-0.717789\pi\) | ||||
−0.632056 | + | 0.774923i | \(0.717789\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 125695. | 1.11261 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −27394.7 | −0.231317 | −0.115658 | − | 0.993289i | \(-0.536898\pi\) | ||||
−0.115658 | + | 0.993289i | \(0.536898\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −88569.6 | −0.714033 | −0.357016 | − | 0.934098i | \(-0.616206\pi\) | ||||
−0.357016 | + | 0.934098i | \(0.616206\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −235046. | −1.81069 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18947.6 | 0.139591 | 0.0697955 | − | 0.997561i | \(-0.477765\pi\) | ||||
0.0697955 | + | 0.997561i | \(0.477765\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −210979. | −1.48763 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 406528. | 2.74553 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17631.4 | 0.114135 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3927.29 | 0.0243854 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −89829.6 | −0.535373 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 317945. | 1.82002 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −188535. | −1.03725 | −0.518625 | − | 0.855002i | \(-0.673556\pi\) | ||||
−0.518625 | + | 0.855002i | \(0.673556\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 228709. | 1.21007 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 214161. | 1.09034 | 0.545171 | − | 0.838325i | \(-0.316465\pi\) | ||||
0.545171 | + | 0.838325i | \(0.316465\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −88849.4 | −0.435537 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 528193. | 2.49436 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −44903.9 | −0.204401 | −0.102200 | − | 0.994764i | \(-0.532588\pi\) | ||||
−0.102200 | + | 0.994764i | \(0.532588\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −262924. | −1.15423 | −0.577116 | − | 0.816662i | \(-0.695822\pi\) | ||||
−0.577116 | + | 0.816662i | \(0.695822\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 373638. | 1.58272 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −367830. | −1.50420 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 398885. | 1.57553 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 63156.2 | 0.241059 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −209764. | −0.774044 | −0.387022 | − | 0.922070i | \(-0.626496\pi\) | ||||
−0.387022 | + | 0.922070i | \(0.626496\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 330665. | 1.18017 | 0.590087 | − | 0.807340i | \(-0.299093\pi\) | ||||
0.590087 | + | 0.807340i | \(0.299093\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 161528. | 0.557853 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 434117. | 1.45137 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 510079. | 1.65154 | 0.825769 | − | 0.564008i | \(-0.190741\pi\) | ||||
0.825769 | + | 0.564008i | \(0.190741\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 384471. | 1.20606 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −106008. | −0.322310 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −138.797 | −0.000409176 0 | −0.000204588 | − | 1.00000i | \(-0.500065\pi\) | ||||
−0.000204588 | 1.00000i | \(0.500065\pi\) | ||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.04192e6 | −2.97937 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 527469. | 1.46354 | 0.731772 | − | 0.681549i | \(-0.238693\pi\) | ||||
0.731772 | + | 0.681549i | \(0.238693\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 448807. | 1.20877 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −813983. | −2.12875 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 345616. | 0.877968 | 0.438984 | − | 0.898495i | \(-0.355338\pi\) | ||||
0.438984 | + | 0.898495i | \(0.355338\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 312879. | 0.772291 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −562825. | −1.35033 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −349527. | −0.815358 | −0.407679 | − | 0.913125i | \(-0.633662\pi\) | ||||
−0.407679 | + | 0.913125i | \(0.633662\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 469274. | 1.06471 | 0.532353 | − | 0.846522i | \(-0.321308\pi\) | ||||
0.532353 | + | 0.846522i | \(0.321308\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.42258e6 | −3.14014 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −871414. | −1.87195 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −146152. | −0.305633 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 265395. | 0.540428 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 851324. | 1.68854 | 0.844270 | − | 0.535918i | \(-0.180034\pi\) | ||||
0.844270 | + | 0.535918i | \(0.180034\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 122886. | 0.237470 | 0.118735 | − | 0.992926i | \(-0.462116\pi\) | ||||
0.118735 | + | 0.992926i | \(0.462116\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.32303e6 | 4.37489 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −744847. | −1.36742 | −0.683709 | − | 0.729755i | \(-0.739634\pi\) | ||||
−0.683709 | + | 0.729755i | \(0.739634\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 326738. | 0.584880 | 0.292440 | − | 0.956284i | \(-0.405533\pi\) | ||||
0.292440 | + | 0.956284i | \(0.405533\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.18298e6 | −2.06532 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 200423. | 0.341355 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −333037. | −0.553487 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −971178. | −1.57534 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 736498. | 1.16629 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −336421. | −0.520209 | −0.260104 | − | 0.965581i | \(-0.583757\pi\) | ||||
−0.260104 | + | 0.965581i | \(0.583757\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 149957. | 0.226474 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 847923. | 1.25101 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 218125. | 0.314454 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.25341e6 | 1.76597 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 325855. | 0.448791 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 633862. | 0.853556 | 0.426778 | − | 0.904356i | \(-0.359649\pi\) | ||||
0.426778 | + | 0.904356i | \(0.359649\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.86640e6 | 3.77468 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 297408. | 0.383079 | 0.191539 | − | 0.981485i | \(-0.438652\pi\) | ||||
0.191539 | + | 0.981485i | \(0.438652\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −594953. | −0.749711 | −0.374855 | − | 0.927083i | \(-0.622308\pi\) | ||||
−0.374855 | + | 0.927083i | \(0.622308\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −523520. | −0.645511 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 150894. | 0.182088 | 0.0910442 | − | 0.995847i | \(-0.470980\pi\) | ||||
0.0910442 | + | 0.995847i | \(0.470980\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.38523e6 | 1.63626 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 152806. | 0.176713 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −826500. | −0.935941 | −0.467970 | − | 0.883744i | \(-0.655015\pi\) | ||||
−0.467970 | + | 0.883744i | \(0.655015\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.36773e6 | 1.51690 | 0.758450 | − | 0.651731i | \(-0.225957\pi\) | ||||
0.758450 | + | 0.651731i | \(0.225957\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −437993. | −0.475829 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 234147. | 0.249215 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.64207e6 | −1.71257 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −711744. | −0.727487 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.73585e6 | −1.73911 | −0.869557 | − | 0.493832i | \(-0.835596\pi\) | ||||
−0.869557 | + | 0.493832i | \(0.835596\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 878730. | 0.863086 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 923021. | 0.888917 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.04674e6 | −1.93299 | −0.966496 | − | 0.256680i | \(-0.917371\pi\) | ||||
−0.966496 | + | 0.256680i | \(0.917371\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −437849. | −0.405578 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.83615e6 | 1.66842 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −405737. | −0.361705 | −0.180853 | − | 0.983510i | \(-0.557886\pi\) | ||||
−0.180853 | + | 0.983510i | \(0.557886\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.42540e6 | 1.24687 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.53165e6 | −2.17333 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.48037e6 | 1.24736 | 0.623678 | − | 0.781681i | \(-0.285638\pi\) | ||||
0.623678 | + | 0.781681i | \(0.285638\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 457477. | 0.378395 | 0.189198 | − | 0.981939i | \(-0.439411\pi\) | ||||
0.189198 | + | 0.981939i | \(0.439411\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.16722e6 | 0.947866 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.59354e6 | −2.06805 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.45830e6 | −1.14195 | −0.570977 | − | 0.820966i | \(-0.693435\pi\) | ||||
−0.570977 | + | 0.820966i | \(0.693435\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.99833e6 | 1.53694 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.90172e6 | −1.43675 | −0.718373 | − | 0.695658i | \(-0.755113\pi\) | ||||
−0.718373 | + | 0.695658i | \(0.755113\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.01187e6 | −0.751032 | −0.375516 | − | 0.926816i | \(-0.622535\pi\) | ||||
−0.375516 | + | 0.926816i | \(0.622535\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.65135e6 | −3.39209 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −167337. | −0.119919 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.29038e6 | −0.908812 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.68219e6 | 1.85677 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.30915e6 | −0.890882 | −0.445441 | − | 0.895311i | \(-0.646953\pi\) | ||||
−0.445441 | + | 0.895311i | \(0.646953\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.08663e6 | −1.39602 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.19993e6 | −1.44717 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.95918e6 | −1.26735 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 426045. | 0.271044 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 574925. | 0.359753 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.27411e6 | −3.24638 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.83705e6 | 1.11244 | 0.556219 | − | 0.831036i | \(-0.312252\pi\) | ||||
0.556219 | + | 0.831036i | \(0.312252\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.58016e6 | −2.13307 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.41953e6 | 0.832233 | 0.416116 | − | 0.909311i | \(-0.363391\pi\) | ||||
0.416116 | + | 0.909311i | \(0.363391\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.67261e6 | 1.54197 | 0.770983 | − | 0.636855i | \(-0.219765\pi\) | ||||
0.770983 | + | 0.636855i | \(0.219765\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.14511e6 | 1.21807 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −34066.4 | −0.0190405 | −0.00952024 | − | 0.999955i | \(-0.503030\pi\) | ||||
−0.00952024 | + | 0.999955i | \(0.503030\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.66136e6 | −0.914087 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −720595. | −0.390327 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −652453. | −0.347971 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.78247e6 | 3.03672 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.32975e6 | −1.20487 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 696021. | 0.354514 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.55050e6 | −0.777862 | −0.388931 | − | 0.921267i | \(-0.627156\pi\) | ||||
−0.388931 | + | 0.921267i | \(0.627156\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.01130e6 | −1.98232 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.38581e6 | −2.13520 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.49728e6 | −1.67747 | −0.838736 | − | 0.544539i | \(-0.816705\pi\) | ||||
−0.838736 | + | 0.544539i | \(0.816705\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 498399. | 0.235547 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.80810e6 | −0.842049 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.54961e6 | −2.51024 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.25824e6 | −1.45265 | −0.726323 | − | 0.687354i | \(-0.758772\pi\) | ||||
−0.726323 | + | 0.687354i | \(0.758772\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.40547e6 | 0.617672 | 0.308836 | − | 0.951115i | \(-0.400060\pi\) | ||||
0.308836 | + | 0.951115i | \(0.400060\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.90489e6 | 2.12501 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.37361e6 | 1.01385 | 0.506924 | − | 0.861991i | \(-0.330783\pi\) | ||||
0.506924 | + | 0.861991i | \(0.330783\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 555955. | 0.234136 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 463779. | 0.192593 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −785602. | −0.321711 | −0.160856 | − | 0.986978i | \(-0.551425\pi\) | ||||
−0.160856 | + | 0.986978i | \(0.551425\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 811787. | 0.327849 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 103304. | 0.0411481 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.64694e6 | 1.82572 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.62687e6 | −1.01806 | −0.509031 | − | 0.860748i | \(-0.669996\pi\) | ||||
−0.509031 | + | 0.860748i | \(0.669996\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.53304e6 | −0.586120 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 716202. | 0.270147 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.43475e6 | −0.906113 | −0.453056 | − | 0.891482i | \(-0.649666\pi\) | ||||
−0.453056 | + | 0.891482i | \(0.649666\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.36326e6 | 3.07113 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.70411e6 | 1.34224 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −83774.3 | −0.0299580 | −0.0149790 | − | 0.999888i | \(-0.504768\pi\) | ||||
−0.0149790 | + | 0.999888i | \(0.504768\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.95926e6 | −1.75027 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.75410e6 | 0.611021 | 0.305511 | − | 0.952189i | \(-0.401173\pi\) | ||||
0.305511 | + | 0.952189i | \(0.401173\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.94091e6 | −0.667351 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.90316e6 | 1.32477 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.75594e6 | −1.25848 | −0.629238 | − | 0.777213i | \(-0.716633\pi\) | ||||
−0.629238 | + | 0.777213i | \(0.716633\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −778454. | −0.257508 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.63333e6 | 1.83985 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 566517. | 0.182692 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.00266e6 | 0.319286 | 0.159643 | − | 0.987175i | \(-0.448966\pi\) | ||||
0.159643 | + | 0.987175i | \(0.448966\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.33711e6 | −0.734930 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.31342e6 | 1.65011 | 0.825056 | − | 0.565051i | \(-0.191144\pi\) | ||||
0.825056 | + | 0.565051i | \(0.191144\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.03128e6 | 1.23646 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.25567e6 | 0.986286 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.62945e6 | 1.08606 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.58663e6 | −1.35577 | −0.677884 | − | 0.735169i | \(-0.737103\pi\) | ||||
−0.677884 | + | 0.735169i | \(0.737103\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.18116e6 | −0.344908 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.04845e6 | −0.302462 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.63874e6 | −0.752101 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.91599e6 | −1.94767 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.29852e6 | −0.639607 | −0.319803 | − | 0.947484i | \(-0.603617\pi\) | ||||
−0.319803 | + | 0.947484i | \(0.603617\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5554.63 | 0.00152739 | 0.000763695 | − | 1.00000i | \(-0.499757\pi\) | ||||
0.000763695 | 1.00000i | \(0.499757\pi\) | ||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.37652e6 | 1.73274 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.29758e6 | 0.617019 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.65002e6 | −0.703362 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.67544e6 | −2.53821 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.17192e6 | −1.08179 | −0.540895 | − | 0.841090i | \(-0.681915\pi\) | ||||
−0.540895 | + | 0.841090i | \(0.681915\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.68030e6 | 0.430693 | 0.215347 | − | 0.976538i | \(-0.430912\pi\) | ||||
0.215347 | + | 0.976538i | \(0.430912\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.04923e7 | 2.65857 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.92284e6 | 0.982645 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.12899e6 | −0.527245 | −0.263623 | − | 0.964626i | \(-0.584917\pi\) | ||||
−0.263623 | + | 0.964626i | \(0.584917\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.07783e6 | 0.263908 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.46150e6 | 1.32222 | 0.661108 | − | 0.750291i | \(-0.270087\pi\) | ||||
0.661108 | + | 0.750291i | \(0.270087\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.38589e6 | −2.24686 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.51767e6 | −1.30613 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.17382e6 | 0.274779 | 0.137390 | − | 0.990517i | \(-0.456129\pi\) | ||||
0.137390 | + | 0.990517i | \(0.456129\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.38710e6 | 0.321120 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.69786e6 | 1.99144 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.32739e6 | 0.979936 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.88231e6 | 0.869561 | 0.434780 | − | 0.900537i | \(-0.356826\pi\) | ||||
0.434780 | + | 0.900537i | \(0.356826\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.94889e6 | 0.431773 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.13112e6 | 0.247889 | 0.123945 | − | 0.992289i | \(-0.460445\pi\) | ||||
0.123945 | + | 0.992289i | \(0.460445\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.74204e6 | −0.377664 | −0.188832 | − | 0.982009i | \(-0.560470\pi\) | ||||
−0.188832 | + | 0.982009i | \(0.560470\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.14191e7 | 2.44905 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.96811e6 | −1.05414 | −0.527071 | − | 0.849821i | \(-0.676710\pi\) | ||||
−0.527071 | + | 0.849821i | \(0.676710\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.20368e6 | −0.462612 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.34172e7 | 2.78682 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.53161e6 | −0.725805 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.15781e7 | −2.35453 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.56140e6 | 1.32038 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.72949e6 | 0.344412 | 0.172206 | − | 0.985061i | \(-0.444910\pi\) | ||||
0.172206 | + | 0.985061i | \(0.444910\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.09210e6 | −1.59477 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.78844e6 | −0.543869 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.94403e6 | 1.91959 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.90261e6 | −0.745647 | −0.372824 | − | 0.927902i | \(-0.621610\pi\) | ||||
−0.372824 | + | 0.927902i | \(0.621610\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3650.93 | −0.000690448 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.62067e6 | 1.61375 | 0.806877 | − | 0.590720i | \(-0.201156\pi\) | ||||
0.806877 | + | 0.590720i | \(0.201156\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.47178e6 | 0.272725 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.77814e7 | −3.26177 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 279344. | 0.0507280 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.01787e6 | 1.26169 | 0.630846 | − | 0.775908i | \(-0.282708\pi\) | ||||
0.630846 | + | 0.775908i | \(0.282708\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.38746e7 | 2.46960 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.89602e6 | −0.686596 | −0.343298 | − | 0.939226i | \(-0.611544\pi\) | ||||
−0.343298 | + | 0.939226i | \(0.611544\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.13149e6 | 0.371925 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.18055e7 | 2.03969 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.54805e6 | −0.264843 | −0.132422 | − | 0.991193i | \(-0.542275\pi\) | ||||
−0.132422 | + | 0.991193i | \(0.542275\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.33489e6 | 0.395561 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.82097e6 | −1.64764 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.32732e7 | −2.20525 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.76952e6 | −0.949322 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.09113e6 | 1.48149 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.11069e6 | 1.14767 | 0.573836 | − | 0.818970i | \(-0.305455\pi\) | ||||
0.573836 | + | 0.818970i | \(0.305455\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.37329e6 | −0.858986 | −0.429493 | − | 0.903070i | \(-0.641308\pi\) | ||||
−0.429493 | + | 0.903070i | \(0.641308\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.23001e6 | 1.30317 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.60177e6 | 0.251232 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.75593e6 | −0.272815 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.60520e6 | −1.47833 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.09264e6 | −0.471532 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.67155e6 | −0.403533 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.19401e6 | −1.37584 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −975227. | −0.144588 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.26079e6 | −0.772784 | −0.386392 | − | 0.922335i | \(-0.626279\pi\) | ||||
−0.386392 | + | 0.922335i | \(0.626279\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.23438e7 | 1.79660 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.63736e6 | −1.24563 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.26833e6 | −0.609943 | −0.304972 | − | 0.952361i | \(-0.598647\pi\) | ||||
−0.304972 | + | 0.952361i | \(0.598647\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.42778e7 | −3.43778 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.41667e6 | −1.04071 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 284651. | 0.0395822 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.29218e7 | −3.15876 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.28071e6 | 0.721198 | 0.360599 | − | 0.932721i | \(-0.382572\pi\) | ||||
0.360599 | + | 0.932721i | \(0.382572\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.87395e6 | 1.06577 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.84440e6 | −0.515729 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.98229e6 | −1.19431 | −0.597154 | − | 0.802127i | \(-0.703702\pi\) | ||||
−0.597154 | + | 0.802127i | \(0.703702\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.84778e6 | 0.243517 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.63584e6 | 0.213689 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.06571e7 | 1.37993 | 0.689966 | − | 0.723841i | \(-0.257625\pi\) | ||||
0.689966 | + | 0.723841i | \(0.257625\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.52812e6 | 0.452849 | 0.226425 | − | 0.974029i | \(-0.427296\pi\) | ||||
0.226425 | + | 0.974029i | \(0.427296\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.23933e7 | 2.84926 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.38141e7 | −1.74242 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.63312e6 | 0.329254 | 0.164627 | − | 0.986356i | \(-0.447358\pi\) | ||||
0.164627 | + | 0.986356i | \(0.447358\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.23241e6 | 0.400709 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.32585e6 | −0.162950 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.93680e6 | −0.723405 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.96449e7 | 4.78958 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.04984e7 | 1.25755 | 0.628776 | − | 0.777586i | \(-0.283556\pi\) | ||||
0.628776 | + | 0.777586i | \(0.283556\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.07176e6 | −0.958694 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.95925e7 | −2.30740 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.46953e6 | 0.521946 | 0.260973 | − | 0.965346i | \(-0.415957\pi\) | ||||
0.260973 | + | 0.965346i | \(0.415957\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.71943e6 | 0.199109 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.59455e6 | 0.986933 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.44304e6 | 0.961461 | 0.480731 | − | 0.876868i | \(-0.340371\pi\) | ||||
0.480731 | + | 0.876868i | \(0.340371\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.38045e7 | −1.55896 | −0.779481 | − | 0.626426i | \(-0.784517\pi\) | ||||
−0.779481 | + | 0.626426i | \(0.784517\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.01888e7 | −2.26108 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 382992. | 0.0425403 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.43837e6 | −0.709258 | −0.354629 | − | 0.935007i | \(-0.615393\pi\) | ||||
−0.354629 | + | 0.935007i | \(0.615393\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.27194e6 | 0.576007 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.28635e7 | 1.39398 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.29974e6 | 0.139703 | 0.0698513 | − | 0.997557i | \(-0.477748\pi\) | ||||
0.0698513 | + | 0.997557i | \(0.477748\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.76024e6 | −0.933960 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.51795e6 | −0.583532 | −0.291766 | − | 0.956490i | \(-0.594243\pi\) | ||||
−0.291766 | + | 0.956490i | \(0.594243\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.36773e6 | 0.982671 | 0.491335 | − | 0.870971i | \(-0.336509\pi\) | ||||
0.491335 | + | 0.870971i | \(0.336509\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.17176e7 | −1.21930 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.71601e6 | −0.486805 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.10522e7 | 1.13174 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.93730e7 | 1.96801 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.21528e6 | −0.324035 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.50281e6 | 0.750154 | 0.375077 | − | 0.926994i | \(-0.377616\pi\) | ||||
0.375077 | + | 0.926994i | \(0.377616\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.84927e6 | −0.877806 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.83861e7 | −1.80948 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.17433e6 | 0.212313 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.55917e6 | 0.247941 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 112701. | 0.0108338 | 0.00541690 | − | 0.999985i | \(-0.498276\pi\) | ||||
0.00541690 | + | 0.999985i | \(0.498276\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −453508. | −0.0432572 | −0.0216286 | − | 0.999766i | \(-0.506885\pi\) | ||||
−0.0216286 | + | 0.999766i | \(0.506885\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.23039e7 | 2.11096 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.71032e6 | 0.724122 | 0.362061 | − | 0.932154i | \(-0.382073\pi\) | ||||
0.362061 | + | 0.932154i | \(0.382073\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.69087e6 | 0.809937 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.73760e6 | 0.530613 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.98665e6 | 0.549416 | 0.274708 | − | 0.961528i | \(-0.411419\pi\) | ||||
0.274708 | + | 0.961528i | \(0.411419\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.08851e7 | 1.90210 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.13908e7 | 1.93336 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.44274e7 | 1.29412 | 0.647058 | − | 0.762441i | \(-0.275999\pi\) | ||||
0.647058 | + | 0.762441i | \(0.275999\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.80369e7 | 1.60568 | 0.802838 | − | 0.596197i | \(-0.203322\pi\) | ||||
0.802838 | + | 0.596197i | \(0.203322\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.57133e6 | 0.757294 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.66465e6 | −0.759796 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.84897e6 | −0.770155 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.66732e7 | 1.44030 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.19667e7 | 1.88347 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.58113e7 | −1.34564 | −0.672820 | − | 0.739806i | \(-0.734917\pi\) | ||||
−0.672820 | + | 0.739806i | \(0.734917\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.45841e7 | 2.92157 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.27877e7 | 1.07231 | 0.536154 | − | 0.844120i | \(-0.319876\pi\) | ||||
0.536154 | + | 0.844120i | \(0.319876\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.99645e6 | 0.415899 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.82306e6 | 0.646411 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.17491e6 | 0.342448 | 0.171224 | − | 0.985232i | \(-0.445228\pi\) | ||||
0.171224 | + | 0.985232i | \(0.445228\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.37906e6 | −0.356578 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.56497e7 | −1.26507 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.32365e7 | 1.06224 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.31609e6 | 0.662558 | 0.331279 | − | 0.943533i | \(-0.392520\pi\) | ||||
0.331279 | + | 0.943533i | \(0.392520\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.93442e6 | −0.706697 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.56405e7 | −2.01356 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.22882e6 | −0.0958086 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.96914e6 | 0.307258 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.67718e6 | 0.128909 | 0.0644546 | − | 0.997921i | \(-0.479469\pi\) | ||||
0.0644546 | + | 0.997921i | \(0.479469\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.62027e7 | 1.23651 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.64374e7 | 2.76105 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.07099e6 | 0.0805814 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.66093e7 | −1.24090 | −0.620450 | − | 0.784246i | \(-0.713050\pi\) | ||||
−0.620450 | + | 0.784246i | \(0.713050\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.60779e6 | 0.193464 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.63057e6 | −0.709460 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.58710e7 | −2.62409 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.17404e7 | −1.57932 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.32802e7 | −1.67944 | −0.839722 | − | 0.543017i | \(-0.817282\pi\) | ||||
−0.839722 | + | 0.543017i | \(0.817282\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.66921e6 | −0.477789 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.59769e7 | 2.55963 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.61174e7 | 1.84538 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.74527e7 | −1.22469 | −0.612345 | − | 0.790591i | \(-0.709774\pi\) | ||||
−0.612345 | + | 0.790591i | \(0.709774\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.96334e7 | −1.36829 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.12860e6 | 0.216549 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −940675. | −0.0646666 | −0.0323333 | − | 0.999477i | \(-0.510294\pi\) | ||||
−0.0323333 | + | 0.999477i | \(0.510294\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.15904e6 | 0.420528 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.82670e7 | 1.23879 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.13900e7 | −0.767204 | −0.383602 | − | 0.923498i | \(-0.625317\pi\) | ||||
−0.383602 | + | 0.923498i | \(0.625317\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.31932e7 | −2.88982 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 262087. | 0.0174170 | 0.00870851 | − | 0.999962i | \(-0.497228\pi\) | ||||
0.00870851 | + | 0.999962i | \(0.497228\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.04563e7 | −1.35032 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.21466e7 | −0.796443 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.34234e6 | −0.0874296 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.10676e6 | 0.0716069 | 0.0358035 | − | 0.999359i | \(-0.488601\pi\) | ||||
0.0358035 | + | 0.999359i | \(0.488601\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.56601e7 | −2.93460 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.22467e7 | 2.05882 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.07218e7 | −1.94853 | −0.974264 | − | 0.225412i | \(-0.927627\pi\) | ||||
−0.974264 | + | 0.225412i | \(0.927627\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.31142e7 | 1.45638 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.18635e7 | 0.742593 | 0.371297 | − | 0.928514i | \(-0.378913\pi\) | ||||
0.371297 | + | 0.928514i | \(0.378913\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.33991e6 | −0.269879 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.57523e7 | 0.973175 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.93768e7 | −1.18931 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.08006e7 | 1.26841 | 0.634204 | − | 0.773166i | \(-0.281328\pi\) | ||||
0.634204 | + | 0.773166i | \(0.281328\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.38378e7 | −3.26175 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.12633e7 | −0.677980 | −0.338990 | − | 0.940790i | \(-0.610085\pi\) | ||||
−0.338990 | + | 0.940790i | \(0.610085\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.84243e7 | 1.69995 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.15172e7 | −0.684377 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.19233e6 | 0.365603 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.31556e6 | −0.135840 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.21537e7 | 1.29135 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.97433e7 | 2.88111 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.65941e7 | −1.53056 | −0.765278 | − | 0.643700i | \(-0.777399\pi\) | ||||
−0.765278 | + | 0.643700i | \(0.777399\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.06726e7 | −0.610346 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 928431. | 0.0527604 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.89763e7 | −2.76568 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.74938e7 | 2.10398 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.25159e7 | −0.697938 | −0.348969 | − | 0.937134i | \(-0.613468\pi\) | ||||
−0.348969 | + | 0.937134i | \(0.613468\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.11114e6 | 0.283237 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.32052e7 | −2.37933 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.93546e7 | −1.05924 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.03380e7 | −0.562270 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.89399e7 | 2.10480 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.02591e7 | 0.551109 | 0.275555 | − | 0.961285i | \(-0.411139\pi\) | ||||
0.275555 | + | 0.961285i | \(0.411139\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.32031e7 | −0.704892 | −0.352446 | − | 0.935832i | \(-0.614650\pi\) | ||||
−0.352446 | + | 0.935832i | \(0.614650\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.20335e7 | 0.638508 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13535.5 | −0.000713809 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.57659e7 | −0.826348 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.99199e7 | 1.03771 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.88139e7 | −1.49192 | −0.745958 | − | 0.665993i | \(-0.768008\pi\) | ||||
−0.745958 | + | 0.665993i | \(0.768008\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.72097e7 | 1.40031 | 0.700156 | − | 0.713990i | \(-0.253114\pi\) | ||||
0.700156 | + | 0.713990i | \(0.253114\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.82209e7 | −3.48966 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.36307e7 | −1.70991 | −0.854954 | − | 0.518705i | \(-0.826414\pi\) | ||||
−0.854954 | + | 0.518705i | \(0.826414\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.30835e7 | 1.67196 | 0.835978 | − | 0.548763i | \(-0.184901\pi\) | ||||
0.835978 | + | 0.548763i | \(0.184901\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.83594e7 | −1.92695 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 863939. | 0.0431391 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.14392e7 | 2.55316 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.41105e7 | 1.18958 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.85094e7 | 0.907796 | 0.453898 | − | 0.891054i | \(-0.350033\pi\) | ||||
0.453898 | + | 0.891054i | \(0.350033\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.78094e6 | −0.184336 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.00230e7 | −2.42438 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.37679e7 | 2.10870 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 192437. | 0.00921680 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.66164e7 | −1.26730 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.93317e7 | 0.915052 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.52810e7 | −0.719086 | −0.359543 | − | 0.933129i | \(-0.617067\pi\) | ||||
−0.359543 | + | 0.933129i | \(0.617067\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.93802e7 | −3.71361 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.10629e6 | 0.237494 | 0.118747 | − | 0.992925i | \(-0.462112\pi\) | ||||
0.118747 | + | 0.992925i | \(0.462112\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.32935e7 | 1.07709 | 0.538546 | − | 0.842596i | \(-0.318974\pi\) | ||||
0.538546 | + | 0.842596i | \(0.318974\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.40165e6 | −0.202352 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.42566e7 | 1.10867 | 0.554337 | − | 0.832292i | \(-0.312972\pi\) | ||||
0.554337 | + | 0.832292i | \(0.312972\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.37047e7 | 1.53162 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.39424e7 | −1.53354 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.35955e6 | −0.105994 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.07274e7 | −1.81903 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.57744e7 | 2.03276 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.55793e7 | 0.687904 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.81339e7 | 1.23518 | 0.617592 | − | 0.786499i | \(-0.288108\pi\) | ||||
0.617592 | + | 0.786499i | \(0.288108\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.44361e7 | −1.50328 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.51907e6 | −0.369788 | −0.184894 | − | 0.982759i | \(-0.559194\pi\) | ||||
−0.184894 | + | 0.982759i | \(0.559194\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.36512e7 | 0.589210 | 0.294605 | − | 0.955619i | \(-0.404812\pi\) | ||||
0.294605 | + | 0.955619i | \(0.404812\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.48871e7 | −2.35566 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.02750e7 | 0.438502 | 0.219251 | − | 0.975668i | \(-0.429639\pi\) | ||||
0.219251 | + | 0.975668i | \(0.429639\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.23823e6 | −0.392043 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.35599e7 | −0.572220 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.57564e7 | −1.08083 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.40861e7 | −1.42239 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.15346e7 | −2.13854 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.82079e7 | 0.751383 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.25933e6 | 0.215833 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.12067e7 | 0.457362 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.57639e7 | 1.85738 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.08516e7 | −1.24526 | −0.622630 | − | 0.782516i | \(-0.713936\pi\) | ||||
−0.622630 | + | 0.782516i | \(0.713936\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.81170e6 | 0.393853 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.48424e7 | 0.592525 | 0.296263 | − | 0.955107i | \(-0.404260\pi\) | ||||
0.296263 | + | 0.955107i | \(0.404260\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.09904e7 | 0.436351 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.38731e8 | −5.47798 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.04939e7 | 0.412110 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.14065e7 | −1.22668 | −0.613340 | − | 0.789819i | \(-0.710174\pi\) | ||||
−0.613340 | + | 0.789819i | \(0.710174\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.83221e7 | 1.87714 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.16269e6 | 0.199467 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.70569e7 | −2.19257 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.10991e7 | −2.33526 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.75661e6 | −0.294871 | −0.147436 | − | 0.989072i | \(-0.547102\pi\) | ||||
−0.147436 | + | 0.989072i | \(0.547102\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.35362e6 | −0.164618 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.73396e7 | 1.40432 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.42528e7 | −0.533178 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.51058e7 | 0.934167 | 0.467084 | − | 0.884213i | \(-0.345305\pi\) | ||||
0.467084 | + | 0.884213i | \(0.345305\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.03007e7 | 2.60193 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.07777e7 | 1.50123 | 0.750617 | − | 0.660738i | \(-0.229756\pi\) | ||||
0.750617 | + | 0.660738i | \(0.229756\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.38818e6 | 0.270557 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.58815e7 | 0.942778 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.11789e7 | −1.12976 | −0.564879 | − | 0.825174i | \(-0.691077\pi\) | ||||
−0.564879 | + | 0.825174i | \(0.691077\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.31522e7 | 1.55538 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −896086. | −0.0321291 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.49371e7 | −0.889433 | −0.444716 | − | 0.895671i | \(-0.646696\pi\) | ||||
−0.444716 | + | 0.895671i | \(0.646696\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.30217e7 | 2.94566 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.37007e7 | −1.54244 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.20029e6 | −0.0772562 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.81296e6 | −0.307832 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.22977e7 | −0.427325 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.19839e7 | 0.414267 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.62902e6 | −0.331143 | −0.165572 | − | 0.986198i | \(-0.552947\pi\) | ||||
−0.165572 | + | 0.986198i | \(0.552947\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.71622e7 | −0.587170 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.76987e7 | 1.96389 | 0.981946 | − | 0.189161i | \(-0.0605767\pi\) | ||||
0.981946 | + | 0.189161i | \(0.0605767\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.28833e7 | −0.436259 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.52103e8 | 5.12420 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.58334e7 | 1.20102 | 0.600512 | − | 0.799616i | \(-0.294963\pi\) | ||||
0.600512 | + | 0.799616i | \(0.294963\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.90924e7 | 1.30357 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.97595e7 | −1.31907 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.26717e7 | 1.73857 | 0.869287 | − | 0.494307i | \(-0.164578\pi\) | ||||
0.869287 | + | 0.494307i | \(0.164578\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.26380e7 | −2.38547 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.83082e7 | 0.598210 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.88105e7 | −0.611520 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.36827e7 | 0.442577 | 0.221288 | − | 0.975208i | \(-0.428974\pi\) | ||||
0.221288 | + | 0.975208i | \(0.428974\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.07846e7 | −1.31257 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.18637e7 | 1.02032 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.43844e7 | −1.09553 | −0.547763 | − | 0.836633i | \(-0.684521\pi\) | ||||
−0.547763 | + | 0.836633i | \(0.684521\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.83976e7 | −1.53430 |
(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 | 448.6.a.z.1.2 | 2 | ||
4.3 | odd | 2 | 448.6.a.q.1.1 | 2 | |||
8.3 | odd | 2 | 112.6.a.k.1.2 | 2 | |||
8.5 | even | 2 | 56.6.a.c.1.1 | ✓ | 2 | ||
24.5 | odd | 2 | 504.6.a.s.1.2 | 2 | |||
24.11 | even | 2 | 1008.6.a.bt.1.2 | 2 | |||
56.5 | odd | 6 | 392.6.i.g.361.1 | 4 | |||
56.13 | odd | 2 | 392.6.a.f.1.2 | 2 | |||
56.27 | even | 2 | 784.6.a.p.1.1 | 2 | |||
56.37 | even | 6 | 392.6.i.l.361.2 | 4 | |||
56.45 | odd | 6 | 392.6.i.g.177.1 | 4 | |||
56.53 | even | 6 | 392.6.i.l.177.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.6.a.c.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
112.6.a.k.1.2 | 2 | 8.3 | odd | 2 | |||
392.6.a.f.1.2 | 2 | 56.13 | odd | 2 | |||
392.6.i.g.177.1 | 4 | 56.45 | odd | 6 | |||
392.6.i.g.361.1 | 4 | 56.5 | odd | 6 | |||
392.6.i.l.177.2 | 4 | 56.53 | even | 6 | |||
392.6.i.l.361.2 | 4 | 56.37 | even | 6 | |||
448.6.a.q.1.1 | 2 | 4.3 | odd | 2 | |||
448.6.a.z.1.2 | 2 | 1.1 | even | 1 | trivial | ||
504.6.a.s.1.2 | 2 | 24.5 | odd | 2 | |||
784.6.a.p.1.1 | 2 | 56.27 | even | 2 | |||
1008.6.a.bt.1.2 | 2 | 24.11 | even | 2 |