Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,6,Mod(1,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, 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("800.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.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: | \(128.307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 226x^{3} + 455x^{2} + 9816x + 4656 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(10.4009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 800.1 |
$q$-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 | ||||||||
\(3\) | 19.8018 | 1.27028 | 0.635142 | − | 0.772395i | \(-0.280941\pi\) | ||||
0.635142 | + | 0.772395i | \(0.280941\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 160.939 | 1.24141 | 0.620706 | − | 0.784043i | \(-0.286846\pi\) | ||||
0.620706 | + | 0.784043i | \(0.286846\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 149.111 | 0.613623 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 404.231 | 1.00727 | 0.503637 | − | 0.863915i | \(-0.331995\pi\) | ||||
0.503637 | + | 0.863915i | \(0.331995\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 249.498 | 0.409458 | 0.204729 | − | 0.978819i | \(-0.434369\pi\) | ||||
0.204729 | + | 0.978819i | \(0.434369\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1251.45 | 1.05025 | 0.525125 | − | 0.851025i | \(-0.324019\pi\) | ||||
0.525125 | + | 0.851025i | \(0.324019\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 905.566 | 0.575488 | 0.287744 | − | 0.957707i | \(-0.407095\pi\) | ||||
0.287744 | + | 0.957707i | \(0.407095\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3186.88 | 1.57695 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2150.12 | 0.847507 | 0.423754 | − | 0.905778i | \(-0.360712\pi\) | ||||
0.423754 | + | 0.905778i | \(0.360712\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1859.18 | −0.490808 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2792.21 | −0.616527 | −0.308264 | − | 0.951301i | \(-0.599748\pi\) | ||||
−0.308264 | + | 0.951301i | \(0.599748\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3313.11 | −0.619201 | −0.309600 | − | 0.950867i | \(-0.600195\pi\) | ||||
−0.309600 | + | 0.950867i | \(0.600195\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8004.49 | 1.27952 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13197.0 | 1.58478 | 0.792392 | − | 0.610013i | \(-0.208836\pi\) | ||||
0.792392 | + | 0.610013i | \(0.208836\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4940.51 | 0.520128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5075.65 | −0.471555 | −0.235777 | − | 0.971807i | \(-0.575764\pi\) | ||||
−0.235777 | + | 0.971807i | \(0.575764\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11840.0 | −0.976521 | −0.488261 | − | 0.872698i | \(-0.662368\pi\) | ||||
−0.488261 | + | 0.872698i | \(0.662368\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1615.00 | −0.106642 | −0.0533208 | − | 0.998577i | \(-0.516981\pi\) | ||||
−0.0533208 | + | 0.998577i | \(0.516981\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9094.33 | 0.541104 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 24781.0 | 1.33412 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 33580.6 | 1.64210 | 0.821049 | − | 0.570857i | \(-0.193389\pi\) | ||||
0.821049 | + | 0.570857i | \(0.193389\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17931.8 | 0.731033 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −22150.2 | −0.828413 | −0.414206 | − | 0.910183i | \(-0.635941\pi\) | ||||
−0.414206 | + | 0.910183i | \(0.635941\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −43258.9 | −1.48851 | −0.744254 | − | 0.667896i | \(-0.767195\pi\) | ||||
−0.744254 | + | 0.667896i | \(0.767195\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 23997.7 | 0.761759 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 44075.6 | 1.19953 | 0.599766 | − | 0.800176i | \(-0.295260\pi\) | ||||
0.599766 | + | 0.800176i | \(0.295260\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 42576.2 | 1.07658 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −38109.7 | −0.897200 | −0.448600 | − | 0.893733i | \(-0.648077\pi\) | ||||
−0.448600 | + | 0.893733i | \(0.648077\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −37225.1 | −0.817577 | −0.408788 | − | 0.912629i | \(-0.634049\pi\) | ||||
−0.408788 | + | 0.912629i | \(0.634049\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 65056.4 | 1.25044 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10876.2 | 0.196069 | 0.0980345 | − | 0.995183i | \(-0.468744\pi\) | ||||
0.0980345 | + | 0.995183i | \(0.468744\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −73048.9 | −1.23709 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −75737.5 | −1.20675 | −0.603373 | − | 0.797459i | \(-0.706177\pi\) | ||||
−0.603373 | + | 0.797459i | \(0.706177\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −55290.6 | −0.783165 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 121533. | 1.62637 | 0.813183 | − | 0.582008i | \(-0.197733\pi\) | ||||
0.813183 | + | 0.582008i | \(0.197733\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 40154.0 | 0.508306 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −65605.4 | −0.786561 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 157807. | 1.70293 | 0.851465 | − | 0.524411i | \(-0.175714\pi\) | ||||
0.851465 | + | 0.524411i | \(0.175714\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 60275.0 | 0.618087 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −32558.5 | −0.317586 | −0.158793 | − | 0.987312i | \(-0.550760\pi\) | ||||
−0.158793 | + | 0.987312i | \(0.550760\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1240.18 | 0.0115184 | 0.00575920 | − | 0.999983i | \(-0.498167\pi\) | ||||
0.00575920 | + | 0.999983i | \(0.498167\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 170351. | 1.43842 | 0.719209 | − | 0.694794i | \(-0.244504\pi\) | ||||
0.719209 | + | 0.694794i | \(0.244504\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 127565. | 1.02841 | 0.514204 | − | 0.857668i | \(-0.328088\pi\) | ||||
0.514204 | + | 0.857668i | \(0.328088\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 261323. | 2.01313 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 110843. | 0.816602 | 0.408301 | − | 0.912847i | \(-0.366121\pi\) | ||||
0.408301 | + | 0.912847i | \(0.366121\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 37202.8 | 0.251253 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 201408. | 1.30379 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2351.45 | 0.0146007 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −100507. | −0.599009 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −115536. | −0.635634 | −0.317817 | − | 0.948152i | \(-0.602950\pi\) | ||||
−0.317817 | + | 0.948152i | \(0.602950\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −234454. | −1.24046 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −29750.5 | −0.151466 | −0.0757332 | − | 0.997128i | \(-0.524130\pi\) | ||||
−0.0757332 | + | 0.997128i | \(0.524130\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 145741. | 0.714417 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −238138. | −1.08400 | −0.541998 | − | 0.840380i | \(-0.682332\pi\) | ||||
−0.541998 | + | 0.840380i | \(0.682332\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −406539. | −1.78470 | −0.892351 | − | 0.451342i | \(-0.850945\pi\) | ||||
−0.892351 | + | 0.451342i | \(0.850945\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −31979.8 | −0.135465 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 100855. | 0.412436 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 180084. | 0.687356 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −178599. | −0.659043 | −0.329521 | − | 0.944148i | \(-0.606887\pi\) | ||||
−0.329521 | + | 0.944148i | \(0.606887\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 432317. | 1.54298 | 0.771489 | − | 0.636242i | \(-0.219512\pi\) | ||||
0.771489 | + | 0.636242i | \(0.219512\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 186605. | 0.644458 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 198160. | 0.641603 | 0.320802 | − | 0.947146i | \(-0.396048\pi\) | ||||
0.320802 | + | 0.947146i | \(0.396048\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 664957. | 2.08593 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 346038. | 1.05211 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −450882. | −1.32921 | −0.664605 | − | 0.747195i | \(-0.731400\pi\) | ||||
−0.664605 | + | 0.747195i | \(0.731400\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 519661. | 1.44188 | 0.720940 | − | 0.692998i | \(-0.243710\pi\) | ||||
0.720940 | + | 0.692998i | \(0.243710\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −309044. | −0.832344 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 135029. | 0.353133 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 27351.8 | 0.0694818 | 0.0347409 | − | 0.999396i | \(-0.488939\pi\) | ||||
0.0347409 | + | 0.999396i | \(0.488939\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −438613. | −1.05232 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −100983. | −0.235569 | −0.117784 | − | 0.993039i | \(-0.537579\pi\) | ||||
−0.117784 | + | 0.993039i | \(0.537579\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 124851. | 0.283267 | 0.141633 | − | 0.989919i | \(-0.454765\pi\) | ||||
0.141633 | + | 0.989919i | \(0.454765\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −856604. | −1.89083 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 505876. | 1.05789 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −299214. | −0.609295 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 829467. | 1.64519 | 0.822594 | − | 0.568629i | \(-0.192526\pi\) | ||||
0.822594 | + | 0.568629i | \(0.192526\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −712128. | −1.37615 | −0.688073 | − | 0.725641i | \(-0.741543\pi\) | ||||
−0.688073 | + | 0.725641i | \(0.741543\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −970619. | −1.78190 | −0.890950 | − | 0.454102i | \(-0.849960\pi\) | ||||
−0.890950 | + | 0.454102i | \(0.849960\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 516230. | 0.924082 | 0.462041 | − | 0.886858i | \(-0.347117\pi\) | ||||
0.462041 | + | 0.886858i | \(0.347117\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 872776. | 1.52375 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −449375. | −0.765365 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 320606. | 0.520050 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 366057. | 0.579674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 664118. | 1.02693 | 0.513463 | − | 0.858112i | \(-0.328362\pi\) | ||||
0.513463 | + | 0.858112i | \(0.328362\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −754640. | −1.13970 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −533208. | −0.768683 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −737123. | −1.03856 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 312236. | 0.430033 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 990032. | 1.33317 | 0.666587 | − | 0.745427i | \(-0.267754\pi\) | ||||
0.666587 | + | 0.745427i | \(0.267754\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15566.7 | −0.0200509 | −0.0100254 | − | 0.999950i | \(-0.503191\pi\) | ||||
−0.0100254 | + | 0.999950i | \(0.503191\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 359522. | 0.453040 | 0.226520 | − | 0.974006i | \(-0.427265\pi\) | ||||
0.226520 | + | 0.974006i | \(0.427265\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.28823e6 | 1.58842 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.21546e6 | −1.46673 | −0.733367 | − | 0.679833i | \(-0.762052\pi\) | ||||
−0.733367 | + | 0.679833i | \(0.762052\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 215368. | 0.249064 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.00004e6 | 1.13246 | 0.566231 | − | 0.824247i | \(-0.308401\pi\) | ||||
0.566231 | + | 0.824247i | \(0.308401\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.25841e6 | −1.39566 | −0.697831 | − | 0.716263i | \(-0.745851\pi\) | ||||
−0.697831 | + | 0.716263i | \(0.745851\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −994718. | −1.08065 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 225937. | 0.235638 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.49974e6 | −1.53291 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 990751. | 0.992614 | 0.496307 | − | 0.868147i | \(-0.334689\pi\) | ||||
0.496307 | + | 0.868147i | \(0.334689\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 869145. | 0.853672 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.71639e6 | −1.62100 | −0.810498 | − | 0.585741i | \(-0.800804\pi\) | ||||
−0.810498 | + | 0.585741i | \(0.800804\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.12391e6 | 1.96737 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −416347. | −0.378316 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.59528e6 | −1.42216 | −0.711080 | − | 0.703112i | \(-0.751793\pi\) | ||||
−0.711080 | + | 0.703112i | \(0.751793\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.40657e6 | 2.06595 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 895598. | 0.754627 | 0.377313 | − | 0.926086i | \(-0.376848\pi\) | ||||
0.377313 | + | 0.926086i | \(0.376848\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 648702. | 0.536565 | 0.268282 | − | 0.963340i | \(-0.413544\pi\) | ||||
0.268282 | + | 0.963340i | \(0.413544\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 795120. | 0.645693 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.35736e6 | 1.84597 | 0.922987 | − | 0.384830i | \(-0.125740\pi\) | ||||
0.922987 | + | 0.384830i | \(0.125740\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −494019. | −0.379956 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 586738. | 0.443280 | 0.221640 | − | 0.975129i | \(-0.428859\pi\) | ||||
0.221640 | + | 0.975129i | \(0.428859\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.42618e6 | −1.05855 | −0.529273 | − | 0.848452i | \(-0.677535\pi\) | ||||
−0.529273 | + | 0.848452i | \(0.677535\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −816870. | −0.585394 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 146279. | 0.103024 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.12486e6 | 2.16321 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 931708. | 0.634032 | 0.317016 | − | 0.948420i | \(-0.397319\pi\) | ||||
0.317016 | + | 0.948420i | \(0.397319\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −751537. | −0.494378 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 536451. | 0.347018 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.90552e6 | −1.21227 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −644716. | −0.403424 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.51715e6 | 0.918716 | 0.459358 | − | 0.888251i | \(-0.348079\pi\) | ||||
0.459358 | + | 0.888251i | \(0.348079\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 24557.8 | 0.0146317 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −366257. | −0.214726 | −0.107363 | − | 0.994220i | \(-0.534241\pi\) | ||||
−0.107363 | + | 0.994220i | \(0.534241\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.19487e6 | 0.689381 | 0.344691 | − | 0.938716i | \(-0.387984\pi\) | ||||
0.344691 | + | 0.938716i | \(0.387984\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.14809e6 | 1.20062 | 0.600309 | − | 0.799768i | \(-0.295044\pi\) | ||||
0.600309 | + | 0.799768i | \(0.295044\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.12870e6 | −0.621012 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.37325e6 | 1.82720 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.13327e6 | 0.604406 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.52601e6 | 1.30637 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −259916. | −0.132386 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −442778. | −0.222135 | −0.111067 | − | 0.993813i | \(-0.535427\pi\) | ||||
−0.111067 | + | 0.993813i | \(0.535427\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.96781e6 | 0.972460 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.01258e6 | 1.92464 | 0.962319 | − | 0.271923i | \(-0.0876597\pi\) | ||||
0.962319 | + | 0.271923i | \(0.0876597\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.19488e6 | 1.03732 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.33926e6 | −0.623705 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.24127e6 | −0.569679 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.81191e6 | −0.807816 | −0.403908 | − | 0.914800i | \(-0.632348\pi\) | ||||
−0.403908 | + | 0.914800i | \(0.632348\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.69069e6 | 1.62197 | 0.810987 | − | 0.585065i | \(-0.198931\pi\) | ||||
0.810987 | + | 0.585065i | \(0.198931\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −463862. | −0.200965 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −119137. | −0.0508876 | −0.0254438 | − | 0.999676i | \(-0.508100\pi\) | ||||
−0.0254438 | + | 0.999676i | \(0.508100\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.98823e6 | 1.65619 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.65995e6 | −1.49879 | −0.749393 | − | 0.662126i | \(-0.769654\pi\) | ||||
−0.749393 | + | 0.662126i | \(0.769654\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.65605e6 | −0.668814 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 46563.0 | 0.0185470 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.04946e6 | 0.406726 | 0.203363 | − | 0.979103i | \(-0.434813\pi\) | ||||
0.203363 | + | 0.979103i | \(0.434813\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −756833. | −0.289357 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.40443e6 | 2.03852 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 150748. | 0.0561020 | 0.0280510 | − | 0.999606i | \(-0.491070\pi\) | ||||
0.0280510 | + | 0.999606i | \(0.491070\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −696651. | −0.252442 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 416359. | 0.148892 | 0.0744458 | − | 0.997225i | \(-0.476281\pi\) | ||||
0.0744458 | + | 0.997225i | \(0.476281\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.28781e6 | −0.807436 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.08322e6 | −0.725669 | −0.362834 | − | 0.931854i | \(-0.618191\pi\) | ||||
−0.362834 | + | 0.931854i | \(0.618191\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.76547e6 | −0.599216 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.37343e6 | 0.460186 | 0.230093 | − | 0.973169i | \(-0.426097\pi\) | ||||
0.230093 | + | 0.973169i | \(0.426097\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.69078e6 | 0.890094 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −589113. | −0.192405 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.99424e6 | 0.635040 | 0.317520 | − | 0.948252i | \(-0.397150\pi\) | ||||
0.317520 | + | 0.948252i | \(0.397150\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.88593e6 | 0.907513 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23001.8 | −0.00714333 | −0.00357166 | − | 0.999994i | \(-0.501137\pi\) | ||||
−0.00357166 | + | 0.999994i | \(0.501137\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −826615. | −0.253537 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.33462e6 | 1.59631 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.27406e6 | 0.672193 | 0.336097 | − | 0.941828i | \(-0.390893\pi\) | ||||
0.336097 | + | 0.941828i | \(0.390893\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.71556e6 | −1.37698 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.56482e6 | −1.02840 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.05020e6 | −2.26708 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.94280e6 | 1.09716 | 0.548579 | − | 0.836099i | \(-0.315169\pi\) | ||||
0.548579 | + | 0.836099i | \(0.315169\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.20370e6 | −1.15592 | −0.577958 | − | 0.816067i | \(-0.696150\pi\) | ||||
−0.577958 | + | 0.816067i | \(0.696150\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −240813. | −0.0654378 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.96205e6 | −1.84785 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.99711e6 | 0.523911 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.90469e6 | −1.53110 | −0.765550 | − | 0.643376i | \(-0.777533\pi\) | ||||
−0.765550 | + | 0.643376i | \(0.777533\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.98952e6 | −1.02259 | −0.511294 | − | 0.859406i | \(-0.670834\pi\) | ||||
−0.511294 | + | 0.859406i | \(0.670834\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.94708e6 | 0.487730 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10775.1 | 0.00266846 | 0.00133423 | − | 0.999999i | \(-0.499575\pi\) | ||||
0.00133423 | + | 0.999999i | \(0.499575\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.35606e6 | 0.332034 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.72453e6 | 1.62799 | 0.813996 | − | 0.580870i | \(-0.197288\pi\) | ||||
0.813996 | + | 0.580870i | \(0.197288\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.53658e6 | −0.837172 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.39615e6 | −1.49728 | −0.748640 | − | 0.662977i | \(-0.769293\pi\) | ||||
−0.748640 | + | 0.662977i | \(0.769293\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.05173e6 | −0.474985 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.56065e6 | 1.96002 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.40846e6 | −1.65935 | −0.829674 | − | 0.558248i | \(-0.811474\pi\) | ||||
−0.829674 | + | 0.558248i | \(0.811474\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.32668e6 | −0.515471 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.34835e6 | −0.952954 | −0.476477 | − | 0.879187i | \(-0.658086\pi\) | ||||
−0.476477 | + | 0.879187i | \(0.658086\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.15517e6 | 0.467229 | 0.233614 | − | 0.972329i | \(-0.424945\pi\) | ||||
0.233614 | + | 0.972329i | \(0.424945\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.33954e6 | 0.284226 | 0.142113 | − | 0.989850i | \(-0.454610\pi\) | ||||
0.142113 | + | 0.989850i | \(0.454610\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.09349e6 | 1.48911 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.92392e6 | 0.815019 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.78610e6 | −0.983624 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.00723e6 | 1.00763 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.34745e6 | −1.86146 | −0.930731 | − | 0.365704i | \(-0.880828\pi\) | ||||
−0.930731 | + | 0.365704i | \(0.880828\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.29262e6 | 0.648902 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.85217e6 | 1.33647 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.51352e6 | 0.671305 | 0.335652 | − | 0.941986i | \(-0.391043\pi\) | ||||
0.335652 | + | 0.941986i | \(0.391043\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.92826e6 | −1.68847 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.22485e6 | −0.978070 | −0.489035 | − | 0.872264i | \(-0.662651\pi\) | ||||
−0.489035 | + | 0.872264i | \(0.662651\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.49432e6 | −0.647508 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.13333e6 | −1.11380 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.86243e6 | −0.334834 | −0.167417 | − | 0.985886i | \(-0.553543\pi\) | ||||
−0.167417 | + | 0.985886i | \(0.553543\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.02902e7 | 1.83160 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.06780e6 | −1.06933 | −0.534664 | − | 0.845065i | \(-0.679562\pi\) | ||||
−0.534664 | + | 0.845065i | \(0.679562\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.11961e6 | −1.05731 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.24842e6 | −1.06899 | −0.534497 | − | 0.845170i | \(-0.679499\pi\) | ||||
−0.534497 | + | 0.845170i | \(0.679499\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.99096e6 | −1.01495 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.68361e6 | −0.282454 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −652831. | −0.107417 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 541615. | 0.0882617 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.23593e6 | 1.49069 | 0.745343 | − | 0.666681i | \(-0.232286\pi\) | ||||
0.745343 | + | 0.666681i | \(0.232286\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.05161e6 | 0.168113 | 0.0840566 | − | 0.996461i | \(-0.473212\pi\) | ||||
0.0840566 | + | 0.996461i | \(0.473212\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.14620e6 | −0.650315 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.81332e6 | −0.281732 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.30282e6 | −0.508334 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.26637e6 | −0.193082 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.99965e6 | −0.299239 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.67621e6 | 0.545040 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.34911e6 | 0.638862 | 0.319431 | − | 0.947610i | \(-0.396508\pi\) | ||||
0.319431 | + | 0.947610i | \(0.396508\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.47227e6 | 0.359830 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.98339e6 | 0.426326 | 0.213163 | − | 0.977017i | \(-0.431624\pi\) | ||||
0.213163 | + | 0.977017i | \(0.431624\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.45036e6 | −0.913384 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.52853e6 | −0.354804 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.75040e6 | 0.243402 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.74611e6 | −0.648186 | −0.324093 | − | 0.946025i | \(-0.605059\pi\) | ||||
−0.324093 | + | 0.946025i | \(0.605059\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.95407e6 | −0.399844 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.00172e7 | 1.34382 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.22516e6 | −0.561787 | −0.280894 | − | 0.959739i | \(-0.590631\pi\) | ||||
−0.280894 | + | 0.959739i | \(0.590631\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.17564e7 | −1.53574 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.95043e6 | 0.252551 | 0.126275 | − | 0.991995i | \(-0.459698\pi\) | ||||
0.126275 | + | 0.991995i | \(0.459698\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.24377e7 | −1.59643 | −0.798215 | − | 0.602372i | \(-0.794222\pi\) | ||||
−0.798215 | + | 0.602372i | \(0.794222\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.64249e7 | 2.08986 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.21199e7 | −1.51552 | −0.757758 | − | 0.652536i | \(-0.773705\pi\) | ||||
−0.757758 | + | 0.652536i | \(0.773705\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.41014e7 | −1.74810 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.21891e7 | −1.49807 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.35743e7 | 1.65404 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.40591e6 | −0.168407 | −0.0842036 | − | 0.996449i | \(-0.526835\pi\) | ||||
−0.0842036 | + | 0.996449i | \(0.526835\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.00024e6 | −0.356342 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.92200e7 | −2.26352 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.82785e6 | −1.03090 | −0.515452 | − | 0.856919i | \(-0.672376\pi\) | ||||
−0.515452 | + | 0.856919i | \(0.672376\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.02223e7 | 1.17385 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.21509e6 | 0.479999 | 0.239999 | − | 0.970773i | \(-0.422853\pi\) | ||||
0.239999 | + | 0.970773i | \(0.422853\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.00063e6 | 1.01645 | 0.508226 | − | 0.861224i | \(-0.330302\pi\) | ||||
0.508226 | + | 0.861224i | \(0.330302\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.57214e6 | 0.736061 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.74038e7 | −1.91722 | −0.958611 | − | 0.284721i | \(-0.908099\pi\) | ||||
−0.958611 | + | 0.284721i | \(0.908099\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.89842e6 | −0.972231 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −402939. | −0.0436653 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.31051e6 | −0.785772 | −0.392886 | − | 0.919587i | \(-0.628523\pi\) | ||||
−0.392886 | + | 0.919587i | \(0.628523\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.06016e6 | −0.323617 | −0.161809 | − | 0.986822i | \(-0.551733\pi\) | ||||
−0.161809 | + | 0.986822i | \(0.551733\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.94950e6 | −0.204502 | −0.102251 | − | 0.994759i | \(-0.532604\pi\) | ||||
−0.102251 | + | 0.994759i | \(0.532604\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.99746e6 | −0.415963 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.95593e7 | 2.01899 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.24859e6 | 0.736351 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.65154e7 | 1.66442 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.34043e6 | 0.533953 | 0.266976 | − | 0.963703i | \(-0.413975\pi\) | ||||
0.266976 | + | 0.963703i | \(0.413975\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.31507e7 | 1.30449 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.26902e6 | 0.221559 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.68255e6 | −0.550543 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.70992e7 | −1.64373 | −0.821864 | − | 0.569684i | \(-0.807066\pi\) | ||||
−0.821864 | + | 0.569684i | \(0.807066\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.21597e7 | −1.15983 | −0.579917 | − | 0.814676i | \(-0.696915\pi\) | ||||
−0.579917 | + | 0.814676i | \(0.696915\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.68331e6 | −0.158089 | −0.0790447 | − | 0.996871i | \(-0.525187\pi\) | ||||
−0.0790447 | + | 0.996871i | \(0.525187\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.95377e6 | −0.834439 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.05585e7 | −0.976446 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.29171e7 | −1.18545 | −0.592726 | − | 0.805404i | \(-0.701948\pi\) | ||||
−0.592726 | + | 0.805404i | \(0.701948\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.55065e6 | −0.501684 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.20405e6 | 0.287399 | 0.143700 | − | 0.989621i | \(-0.454100\pi\) | ||||
0.143700 | + | 0.989621i | \(0.454100\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.82464e7 | −1.62433 | −0.812165 | − | 0.583428i | \(-0.801711\pi\) | ||||
−0.812165 | + | 0.583428i | \(0.801711\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.18282e6 | 0.546264 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.00358e6 | −0.522511 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.96044e7 | 1.69351 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.74866e7 | −1.49934 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.17328e7 | −0.998538 | −0.499269 | − | 0.866447i | \(-0.666398\pi\) | ||||
−0.499269 | + | 0.866447i | \(0.666398\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.27923e7 | 1.07270 | 0.536348 | − | 0.843997i | \(-0.319803\pi\) | ||||
0.536348 | + | 0.843997i | \(0.319803\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.53973e7 | 2.11404 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −308249. | −0.0254703 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.34398e7 | 1.10240 | 0.551202 | − | 0.834372i | \(-0.314169\pi\) | ||||
0.551202 | + | 0.834372i | \(0.314169\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.11918e6 | 0.575490 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.37831e6 | 0.672370 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.79328e7 | 1.42874 | 0.714371 | − | 0.699767i | \(-0.246713\pi\) | ||||
0.714371 | + | 0.699767i | \(0.246713\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.70060e6 | 0.767300 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.35194e6 | −0.495250 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.40683e7 | −1.86317 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.36981e6 | 0.182146 | 0.0910728 | − | 0.995844i | \(-0.470970\pi\) | ||||
0.0910728 | + | 0.995844i | \(0.470970\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.19507e7 | 0.912023 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.23993e6 | −0.394255 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.86295e6 | −0.139183 | −0.0695913 | − | 0.997576i | \(-0.522170\pi\) | ||||
−0.0695913 | + | 0.997576i | \(0.522170\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.62175e6 | 0.120313 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.12358e6 | −0.524777 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.98026e7 | 1.43855 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.14819e7 | −0.828308 | −0.414154 | − | 0.910207i | \(-0.635923\pi\) | ||||
−0.414154 | + | 0.910207i | \(0.635923\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 199594. | 0.0142991 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.49188e7 | −1.77289 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.08210e7 | −1.46105 | −0.730524 | − | 0.682887i | \(-0.760724\pi\) | ||||
−0.730524 | + | 0.682887i | \(0.760724\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.94630e6 | −0.135641 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.48172e7 | −1.02559 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.47296e6 | −0.582472 | −0.291236 | − | 0.956651i | \(-0.594066\pi\) | ||||
−0.291236 | + | 0.956651i | \(0.594066\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.78167e7 | 1.20826 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.57784e7 | −1.06280 | −0.531402 | − | 0.847120i | \(-0.678335\pi\) | ||||
−0.531402 | + | 0.847120i | \(0.678335\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.47396e6 | 0.299327 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.54066e7 | −1.02384 | −0.511922 | − | 0.859032i | \(-0.671066\pi\) | ||||
−0.511922 | + | 0.859032i | \(0.671066\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.12933e7 | −0.740487 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.74161e7 | 1.78567 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.60309e7 | −1.03719 | −0.518594 | − | 0.855021i | \(-0.673544\pi\) | ||||
−0.518594 | + | 0.855021i | \(0.673544\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.96186e7 | 1.26090 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.65387e6 | −0.104896 | −0.0524482 | − | 0.998624i | \(-0.516702\pi\) | ||||
−0.0524482 | + | 0.998624i | \(0.516702\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.72106e7 | 1.08441 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.00105e7 | −0.626605 | −0.313302 | − | 0.949653i | \(-0.601435\pi\) | ||||
−0.313302 | + | 0.949653i | \(0.601435\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.05302e7 | 1.27668 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.52643e6 | −0.339200 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.06629e7 | 1.86981 | 0.934906 | − | 0.354895i | \(-0.115483\pi\) | ||||
0.934906 | + | 0.354895i | \(0.115483\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.39875e7 | −2.05913 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.29138e7 | 1.37927 | 0.689633 | − | 0.724159i | \(-0.257772\pi\) | ||||
0.689633 | + | 0.724159i | \(0.257772\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.20571e7 | 2.49912 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.59634e6 | −0.271374 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.54051e7 | −0.903727 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.19121e6 | 0.302597 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.27348e7 | 1.88396 | 0.941982 | − | 0.335663i | \(-0.108960\pi\) | ||||
0.941982 | + | 0.335663i | \(0.108960\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.15894e7 | −1.80655 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.78389e7 | 1.01374 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.07930e7 | −0.609481 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.16718e6 | 0.232379 | 0.116189 | − | 0.993227i | \(-0.462932\pi\) | ||||
0.116189 | + | 0.993227i | \(0.462932\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.02109e6 | −0.112000 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.81218e7 | 0.997976 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.50475e7 | −0.823524 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.77344e7 | 0.958591 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.28521e6 | 0.0690405 | 0.0345202 | − | 0.999404i | \(-0.489010\pi\) | ||||
0.0345202 | + | 0.999404i | \(0.489010\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.16431e6 | 0.329103 | 0.164552 | − | 0.986368i | \(-0.447382\pi\) | ||||
0.164552 | + | 0.986368i | \(0.447382\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.28455e7 | 0.681590 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.07219e7 | −0.561976 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.98738e6 | 0.311908 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.50757e7 | 0.780581 | 0.390291 | − | 0.920692i | \(-0.372375\pi\) | ||||
0.390291 | + | 0.920692i | \(0.372375\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.55088e6 | 0.388596 | 0.194298 | − | 0.980943i | \(-0.437757\pi\) | ||||
0.194298 | + | 0.980943i | \(0.437757\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.02532e6 | −0.204662 | −0.102331 | − | 0.994750i | \(-0.532630\pi\) | ||||
−0.102331 | + | 0.994750i | \(0.532630\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.48566e7 | −0.750813 | −0.375407 | − | 0.926860i | \(-0.622497\pi\) | ||||
−0.375407 | + | 0.926860i | \(0.622497\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.66798e7 | 2.34491 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.13811e7 | 0.568294 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.15966e6 | 0.303909 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.59062e6 | −0.470372 | −0.235186 | − | 0.971950i | \(-0.575570\pi\) | ||||
−0.235186 | + | 0.971950i | \(0.575570\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.27147e7 | −0.619894 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.16185e7 | 0.563092 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 378440. | 0.0181255 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.82410e7 | −1.34465 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.83751e7 | 1.34311 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.24756e6 | 0.293994 | 0.146997 | − | 0.989137i | \(-0.453039\pi\) | ||||
0.146997 | + | 0.989137i | \(0.453039\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.19127e7 | −1.01916 | −0.509581 | − | 0.860423i | \(-0.670200\pi\) | ||||
−0.509581 | + | 0.860423i | \(0.670200\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.90797e6 | 0.411904 | 0.205952 | − | 0.978562i | \(-0.433971\pi\) | ||||
0.205952 | + | 0.978562i | \(0.433971\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.61755e7 | −0.743617 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.28474e7 | −0.587204 | −0.293602 | − | 0.955928i | \(-0.594854\pi\) | ||||
−0.293602 | + | 0.955928i | \(0.594854\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.89659e6 | 0.130870 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.39649e6 | 0.197495 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.09968e7 | 0.491158 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.35307e7 | 1.04496 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.36870e7 | −1.03995 | −0.519973 | − | 0.854183i | \(-0.674058\pi\) | ||||
−0.519973 | + | 0.854183i | \(0.674058\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.84495e7 | 0.805401 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.77488e7 | −0.770423 | −0.385212 | − | 0.922828i | \(-0.625872\pi\) | ||||
−0.385212 | + | 0.922828i | \(0.625872\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 293447. | 0.0126656 | 0.00633282 | − | 0.999980i | \(-0.497984\pi\) | ||||
0.00633282 | + | 0.999980i | \(0.497984\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.50694e7 | 0.643112 | 0.321556 | − | 0.946891i | \(-0.395794\pi\) | ||||
0.321556 | + | 0.946891i | \(0.395794\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.85942e7 | −0.789083 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.95286e7 | −1.24609 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.46249e6 | −0.0613710 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.06227e7 | 0.440812 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.25088e6 | 0.381754 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.20246e7 | 1.72461 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.77327e7 | −1.53992 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.62189e6 | −0.186553 | −0.0932764 | − | 0.995640i | \(-0.529734\pi\) | ||||
−0.0932764 | + | 0.995640i | \(0.529734\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.85481e6 | −0.194878 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.02270e6 | −0.360197 | −0.180099 | − | 0.983649i | \(-0.557642\pi\) | ||||
−0.180099 | + | 0.983649i | \(0.557642\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.06154e7 | −1.21552 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.78801e6 | −0.188032 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.81033e7 | 0.707081 | 0.353540 | − | 0.935419i | \(-0.384978\pi\) | ||||
0.353540 | + | 0.935419i | \(0.384978\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.00422e7 | 1.16703 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.50830e6 | −0.367366 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 184924. | 0.00706797 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.59953e7 | 1.36838 | 0.684190 | − | 0.729304i | \(-0.260156\pi\) | ||||
0.684190 | + | 0.729304i | \(0.260156\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.23551e6 | 0.311398 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.25253e6 | −0.272763 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.79708e7 | −1.04077 | −0.520387 | − | 0.853931i | \(-0.674212\pi\) | ||||
−0.520387 | + | 0.853931i | \(0.674212\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.36605e7 | 0.875710 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.35773e7 | −0.499851 | −0.249926 | − | 0.968265i | \(-0.580406\pi\) | ||||
−0.249926 | + | 0.968265i | \(0.580406\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.09133e7 | −0.399646 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.32801e6 | −0.193059 | −0.0965296 | − | 0.995330i | \(-0.530774\pi\) | ||||
−0.0965296 | + | 0.995330i | \(0.530774\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.28759e6 | −0.334763 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.25360e7 | 1.52513 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.02144e7 | −0.364316 | −0.182158 | − | 0.983269i | \(-0.558308\pi\) | ||||
−0.182158 | + | 0.983269i | \(0.558308\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.23502e7 | −0.788862 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.83257e7 | −1.34569 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.76525e7 | −0.616591 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.54011e7 | 0.882647 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.17005e7 | 0.746285 | 0.373142 | − | 0.927774i | \(-0.378280\pi\) | ||||
0.373142 | + | 0.927774i | \(0.378280\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.24408e7 | 0.767767 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.93228e7 | 1.67880 | 0.839401 | − | 0.543512i | \(-0.182906\pi\) | ||||
0.839401 | + | 0.543512i | \(0.182906\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.54280e7 | −2.21555 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.04782e7 | −0.686366 | −0.343183 | − | 0.939269i | \(-0.611505\pi\) | ||||
−0.343183 | + | 0.939269i | \(0.611505\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.91273e7 | 1.63820 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.90213e7 | 0.631055 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.58306e7 | −0.522533 | −0.261267 | − | 0.965267i | \(-0.584140\pi\) | ||||
−0.261267 | + | 0.965267i | \(0.584140\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.14679e6 | −0.168168 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.54575e7 | −0.827609 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.75681e7 | −0.568250 | −0.284125 | − | 0.958787i | \(-0.591703\pi\) | ||||
−0.284125 | + | 0.958787i | \(0.591703\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.76779e6 | −0.282174 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.21502e7 | −1.34296 | −0.671478 | − | 0.741025i | \(-0.734340\pi\) | ||||
−0.671478 | + | 0.741025i | \(0.734340\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.45355e7 | −0.777825 |
(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 | 800.6.a.t.1.4 | yes | 5 | |
4.3 | odd | 2 | 800.6.a.u.1.2 | yes | 5 | ||
5.2 | odd | 4 | 800.6.c.o.449.3 | 10 | |||
5.3 | odd | 4 | 800.6.c.o.449.8 | 10 | |||
5.4 | even | 2 | 800.6.a.v.1.2 | yes | 5 | ||
20.3 | even | 4 | 800.6.c.n.449.3 | 10 | |||
20.7 | even | 4 | 800.6.c.n.449.8 | 10 | |||
20.19 | odd | 2 | 800.6.a.s.1.4 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
800.6.a.s.1.4 | ✓ | 5 | 20.19 | odd | 2 | ||
800.6.a.t.1.4 | yes | 5 | 1.1 | even | 1 | trivial | |
800.6.a.u.1.2 | yes | 5 | 4.3 | odd | 2 | ||
800.6.a.v.1.2 | yes | 5 | 5.4 | even | 2 | ||
800.6.c.n.449.3 | 10 | 20.3 | even | 4 | |||
800.6.c.n.449.8 | 10 | 20.7 | even | 4 | |||
800.6.c.o.449.3 | 10 | 5.2 | odd | 4 | |||
800.6.c.o.449.8 | 10 | 5.3 | odd | 4 |