Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,6,Mod(1,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("560.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.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: | \(89.8149390953\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 463x - 1890 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 280) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(23.3245\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 560.1 |
$q$-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 | ||||||||
\(3\) | 21.3245 | 1.36797 | 0.683983 | − | 0.729498i | \(-0.260246\pi\) | ||||
0.683983 | + | 0.729498i | \(0.260246\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 211.733 | 0.871329 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 381.382 | 0.950338 | 0.475169 | − | 0.879894i | \(-0.342387\pi\) | ||||
0.475169 | + | 0.879894i | \(0.342387\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 372.295 | 0.610982 | 0.305491 | − | 0.952195i | \(-0.401179\pi\) | ||||
0.305491 | + | 0.952195i | \(0.401179\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −533.112 | −0.611773 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1099.55 | −0.922772 | −0.461386 | − | 0.887200i | \(-0.652648\pi\) | ||||
−0.461386 | + | 0.887200i | \(0.652648\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2859.15 | −1.81699 | −0.908497 | − | 0.417892i | \(-0.862769\pi\) | ||||
−0.908497 | + | 0.417892i | \(0.862769\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1044.90 | −0.517042 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2943.73 | −1.16032 | −0.580161 | − | 0.814502i | \(-0.697010\pi\) | ||||
−0.580161 | + | 0.814502i | \(0.697010\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −666.754 | −0.176018 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2410.16 | 0.532171 | 0.266086 | − | 0.963949i | \(-0.414270\pi\) | ||||
0.266086 | + | 0.963949i | \(0.414270\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 463.669 | 0.0866570 | 0.0433285 | − | 0.999061i | \(-0.486204\pi\) | ||||
0.0433285 | + | 0.999061i | \(0.486204\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8132.76 | 1.30003 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1225.00 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1806.73 | 0.216965 | 0.108483 | − | 0.994098i | \(-0.465401\pi\) | ||||
0.108483 | + | 0.994098i | \(0.465401\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7938.99 | 0.835802 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9019.08 | −0.837920 | −0.418960 | − | 0.908005i | \(-0.637605\pi\) | ||||
−0.418960 | + | 0.908005i | \(0.637605\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 33.7132 | 0.00278054 | 0.00139027 | − | 0.999999i | \(-0.499557\pi\) | ||||
0.00139027 | + | 0.999999i | \(0.499557\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5293.32 | −0.389670 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 15132.0 | 0.999199 | 0.499600 | − | 0.866256i | \(-0.333480\pi\) | ||||
0.499600 | + | 0.866256i | \(0.333480\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −23447.4 | −1.26232 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −31344.7 | −1.53276 | −0.766381 | − | 0.642386i | \(-0.777945\pi\) | ||||
−0.766381 | + | 0.642386i | \(0.777945\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9534.55 | −0.425004 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −60969.9 | −2.48558 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 30247.3 | 1.13125 | 0.565623 | − | 0.824664i | \(-0.308636\pi\) | ||||
0.565623 | + | 0.824664i | \(0.308636\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10021.8 | −0.344841 | −0.172421 | − | 0.985023i | \(-0.555159\pi\) | ||||
−0.172421 | + | 0.985023i | \(0.555159\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10374.9 | −0.329331 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9307.37 | −0.273240 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −52832.9 | −1.43786 | −0.718931 | − | 0.695081i | \(-0.755368\pi\) | ||||
−0.718931 | + | 0.695081i | \(0.755368\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −62773.5 | −1.58728 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11610.0 | 0.273330 | 0.136665 | − | 0.990617i | \(-0.456362\pi\) | ||||
0.136665 | + | 0.990617i | \(0.456362\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4765.45 | −0.104664 | −0.0523320 | − | 0.998630i | \(-0.516665\pi\) | ||||
−0.0523320 | + | 0.998630i | \(0.516665\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13327.8 | 0.273593 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −18687.7 | −0.359194 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 28256.2 | 0.509385 | 0.254693 | − | 0.967022i | \(-0.418026\pi\) | ||||
0.254693 | + | 0.967022i | \(0.418026\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −65669.3 | −1.11211 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −36453.8 | −0.580828 | −0.290414 | − | 0.956901i | \(-0.593793\pi\) | ||||
−0.290414 | + | 0.956901i | \(0.593793\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 27488.9 | 0.412676 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 51395.4 | 0.727992 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −132386. | −1.77160 | −0.885802 | − | 0.464063i | \(-0.846391\pi\) | ||||
−0.885802 | + | 0.464063i | \(0.846391\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18242.4 | −0.230930 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9887.49 | 0.118544 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 71478.8 | 0.812584 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −98024.6 | −1.05780 | −0.528902 | − | 0.848683i | \(-0.677396\pi\) | ||||
−0.528902 | + | 0.848683i | \(0.677396\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 80751.1 | 0.828057 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 34873.5 | 0.340167 | 0.170083 | − | 0.985430i | \(-0.445596\pi\) | ||||
0.170083 | + | 0.985430i | \(0.445596\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 93279.1 | 0.866346 | 0.433173 | − | 0.901311i | \(-0.357394\pi\) | ||||
0.433173 | + | 0.901311i | \(0.357394\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 26122.5 | 0.231228 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −193063. | −1.63020 | −0.815098 | − | 0.579324i | \(-0.803317\pi\) | ||||
−0.815098 | + | 0.579324i | \(0.803317\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −34782.7 | −0.280412 | −0.140206 | − | 0.990122i | \(-0.544776\pi\) | ||||
−0.140206 | + | 0.990122i | \(0.544776\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 38527.6 | 0.296801 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 54953.9 | 0.404858 | 0.202429 | − | 0.979297i | \(-0.435116\pi\) | ||||
0.202429 | + | 0.979297i | \(0.435116\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 73593.3 | 0.518912 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 78827.1 | 0.532366 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 53878.1 | 0.348775 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15598.9 | −0.0968568 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −192327. | −1.14625 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −312973. | −1.72186 | −0.860930 | − | 0.508723i | \(-0.830118\pi\) | ||||
−0.860930 | + | 0.508723i | \(0.830118\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 718.916 | 0.00380368 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −112963. | −0.575118 | −0.287559 | − | 0.957763i | \(-0.592844\pi\) | ||||
−0.287559 | + | 0.957763i | \(0.592844\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 140099. | 0.686759 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 16668.8 | 0.0787175 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −41357.4 | −0.188257 | −0.0941287 | − | 0.995560i | \(-0.530007\pi\) | ||||
−0.0941287 | + | 0.995560i | \(0.530007\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 391228. | 1.71749 | 0.858743 | − | 0.512407i | \(-0.171246\pi\) | ||||
0.858743 | + | 0.512407i | \(0.171246\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 322682. | 1.36687 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 141986. | 0.580640 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −60254.1 | −0.237994 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 51200.0 | 0.195424 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −303054. | −1.11829 | −0.559144 | − | 0.829071i | \(-0.688870\pi\) | ||||
−0.559144 | + | 0.829071i | \(0.688870\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 112954. | 0.403144 | 0.201572 | − | 0.979474i | \(-0.435395\pi\) | ||||
0.201572 | + | 0.979474i | \(0.435395\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −232812. | −0.804038 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11591.7 | −0.0387542 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23023.9 | −0.0745470 | −0.0372735 | − | 0.999305i | \(-0.511867\pi\) | ||||
−0.0372735 | + | 0.999305i | \(0.511867\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −668410. | −2.09677 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 144243. | 0.438560 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −212947. | −0.627774 | −0.313887 | − | 0.949460i | \(-0.601631\pi\) | ||||
−0.313887 | + | 0.949460i | \(0.601631\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −203319. | −0.581391 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 509533. | 1.41378 | 0.706889 | − | 0.707325i | \(-0.250098\pi\) | ||||
0.706889 | + | 0.707325i | \(0.250098\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −232690. | −0.626701 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −605377. | −1.58320 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 251973. | 0.640088 | 0.320044 | − | 0.947403i | \(-0.396302\pi\) | ||||
0.320044 | + | 0.947403i | \(0.396302\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −30625.0 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 645008. | 1.54750 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 187246. | 0.436797 | 0.218398 | − | 0.975860i | \(-0.429917\pi\) | ||||
0.218398 | + | 0.975860i | \(0.429917\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −547053. | −1.24117 | −0.620587 | − | 0.784138i | \(-0.713106\pi\) | ||||
−0.620587 | + | 0.784138i | \(0.713106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −213709. | −0.471731 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −45168.3 | −0.0970297 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −419350. | −0.876945 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 32670.9 | 0.0665284 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −82048.2 | −0.162737 | −0.0813684 | − | 0.996684i | \(-0.525929\pi\) | ||||
−0.0813684 | + | 0.996684i | \(0.525929\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 834554. | 1.61273 | 0.806364 | − | 0.591419i | \(-0.201432\pi\) | ||||
0.806364 | + | 0.591419i | \(0.201432\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −198475. | −0.373782 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −801077. | −1.47065 | −0.735324 | − | 0.677716i | \(-0.762970\pi\) | ||||
−0.735324 | + | 0.677716i | \(0.762970\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 728144. | 1.30342 | 0.651710 | − | 0.758468i | \(-0.274052\pi\) | ||||
0.651710 | + | 0.758468i | \(0.274052\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.12663e6 | −1.96695 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −118098. | −0.201142 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 225477. | 0.374729 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −623285. | −1.01102 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.09043e6 | −1.72676 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −737969. | −1.14112 | −0.570561 | − | 0.821255i | \(-0.693274\pi\) | ||||
−0.570561 | + | 0.821255i | \(0.693274\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 247578. | 0.373906 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −842.830 | −0.00124349 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22719.8 | −0.0327533 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −101621. | −0.143177 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −409358. | −0.563797 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 504580. | 0.679466 | 0.339733 | − | 0.940522i | \(-0.389663\pi\) | ||||
0.339733 | + | 0.940522i | \(0.389663\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 132333. | 0.174266 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −793643. | −1.02226 | −0.511129 | − | 0.859504i | \(-0.670772\pi\) | ||||
−0.511129 | + | 0.859504i | \(0.670772\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 533635. | 0.672444 | 0.336222 | − | 0.941783i | \(-0.390851\pi\) | ||||
0.336222 | + | 0.941783i | \(0.390851\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −398505. | −0.491365 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.56974e6 | 1.89425 | 0.947125 | − | 0.320863i | \(-0.103973\pi\) | ||||
0.947125 | + | 0.320863i | \(0.103973\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −378300. | −0.446856 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 602549. | 0.696821 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −318353. | −0.360507 | −0.180253 | − | 0.983620i | \(-0.557692\pi\) | ||||
−0.180253 | + | 0.983620i | \(0.557692\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −719047. | −0.797471 | −0.398736 | − | 0.917066i | \(-0.630551\pi\) | ||||
−0.398736 | + | 0.917066i | \(0.630551\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.23834e6 | −1.34532 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −60025.0 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.06445e6 | −1.11015 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −777358. | −0.794553 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.63688e6 | −1.63995 | −0.819977 | − | 0.572397i | \(-0.806014\pi\) | ||||
−0.819977 | + | 0.572397i | \(0.806014\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.12269e6 | −1.10270 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 586185. | 0.564526 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 713835. | 0.674163 | 0.337082 | − | 0.941475i | \(-0.390560\pi\) | ||||
0.337082 | + | 0.941475i | \(0.390560\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −88530.0 | −0.0820051 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 510311. | 0.463696 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.93481e6 | 1.72484 | 0.862419 | − | 0.506195i | \(-0.168948\pi\) | ||||
0.862419 | + | 0.506195i | \(0.168948\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 783618. | 0.685472 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.82306e6 | −2.42349 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 104742. | 0.0882554 | 0.0441277 | − | 0.999026i | \(-0.485949\pi\) | ||||
0.0441277 | + | 0.999026i | \(0.485949\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.09108e6 | −0.902471 | −0.451235 | − | 0.892405i | \(-0.649017\pi\) | ||||
−0.451235 | + | 0.892405i | \(0.649017\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −389010. | −0.315904 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 238364. | 0.190068 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 328777. | 0.257455 | 0.128728 | − | 0.991680i | \(-0.458911\pi\) | ||||
0.128728 | + | 0.991680i | \(0.458911\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 98174.0 | 0.0755067 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −37359.3 | −0.0282249 | −0.0141125 | − | 0.999900i | \(-0.504492\pi\) | ||||
−0.0141125 | + | 0.999900i | \(0.504492\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.80297e6 | 1.33820 | 0.669101 | − | 0.743172i | \(-0.266679\pi\) | ||||
0.669101 | + | 0.743172i | \(0.266679\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.52425e6 | 1.11159 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 441935. | 0.316704 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −210838. | −0.148492 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.09032e6 | −1.44704 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.56997e6 | −1.06837 | −0.534185 | − | 0.845368i | \(-0.679381\pi\) | ||||
−0.534185 | + | 0.845368i | \(0.679381\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −756183. | −0.505908 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −254288. | −0.167276 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.09594e6 | −0.708936 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1651.95 | −0.00105094 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 743658. | 0.465336 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 250544. | 0.154218 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.27153e6 | 1.37554 | 0.687769 | − | 0.725930i | \(-0.258590\pi\) | ||||
0.687769 | + | 0.725930i | \(0.258590\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.98913e6 | 1.18513 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.71344e6 | 1.59082 | 0.795408 | − | 0.606074i | \(-0.207257\pi\) | ||||
0.795408 | + | 0.606074i | \(0.207257\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.03548e6 | −1.75132 | −0.875661 | − | 0.482926i | \(-0.839574\pi\) | ||||
−0.875661 | + | 0.482926i | \(0.839574\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 259373. | 0.147281 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 655683. | 0.366476 | 0.183238 | − | 0.983069i | \(-0.441342\pi\) | ||||
0.183238 | + | 0.983069i | \(0.441342\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 919192. | 0.505743 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.11697e6 | −2.23005 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.14379e6 | 1.67667 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 232684. | 0.122196 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −741722. | −0.383594 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −741469. | −0.377662 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.77092e6 | 1.89181 | 0.945904 | − | 0.324447i | \(-0.105178\pi\) | ||||
0.945904 | + | 0.324447i | \(0.105178\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 382545. | 0.189048 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.32082e6 | 0.643032 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.44388e6 | −0.692557 | −0.346278 | − | 0.938132i | \(-0.612555\pi\) | ||||
−0.346278 | + | 0.938132i | \(0.612555\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.17186e6 | 0.553831 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 176835. | 0.0823535 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.56934e6 | 0.709853 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.00100e6 | 0.892120 | 0.446060 | − | 0.895003i | \(-0.352827\pi\) | ||||
0.446060 | + | 0.895003i | \(0.352827\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 688692. | 0.302664 | 0.151332 | − | 0.988483i | \(-0.451644\pi\) | ||||
0.151332 | + | 0.988483i | \(0.451644\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −248229. | −0.107544 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 805367. | 0.343999 | 0.172000 | − | 0.985097i | \(-0.444977\pi\) | ||||
0.172000 | + | 0.985097i | \(0.444977\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −290251. | −0.122237 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.14892e6 | 0.477112 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.80310e6 | 0.738386 | 0.369193 | − | 0.929353i | \(-0.379634\pi\) | ||||
0.369193 | + | 0.929353i | \(0.379634\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.69866e6 | 2.30147 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −332638. | −0.132497 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 119136. | 0.0468071 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.17144e6 | −0.841554 | −0.420777 | − | 0.907164i | \(-0.638243\pi\) | ||||
−0.420777 | + | 0.907164i | \(0.638243\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.90964e6 | −0.730104 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.53589e6 | 0.579330 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.31643e6 | 0.862080 | 0.431040 | − | 0.902333i | \(-0.358147\pi\) | ||||
0.431040 | + | 0.902333i | \(0.358147\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −333195. | −0.122355 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 897291. | 0.325147 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.28068e6 | 1.53079 | 0.765393 | − | 0.643563i | \(-0.222545\pi\) | ||||
0.765393 | + | 0.643563i | \(0.222545\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.67399e6 | −2.35544 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.33887e6 | 1.85974 | 0.929871 | − | 0.367886i | \(-0.119918\pi\) | ||||
0.929871 | + | 0.367886i | \(0.119918\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 467193. | 0.160637 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7138.19 | 0.00242276 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.66287e6 | 0.557167 | 0.278584 | − | 0.960412i | \(-0.410135\pi\) | ||||
0.278584 | + | 0.960412i | \(0.410135\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.23679e6 | 1.07071 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.40887e6 | −0.786741 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −706405. | −0.227804 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 274923. | 0.0875458 | 0.0437729 | − | 0.999042i | \(-0.486062\pi\) | ||||
0.0437729 | + | 0.999042i | \(0.486062\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.98753e6 | 0.939462 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.99036e6 | −0.618118 | −0.309059 | − | 0.951043i | \(-0.600014\pi\) | ||||
−0.309059 | + | 0.951043i | \(0.600014\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 172621. | 0.0529459 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.64173e6 | 0.497353 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 689055. | 0.206190 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.80249e6 | 0.828391 | 0.414196 | − | 0.910188i | \(-0.364063\pi\) | ||||
0.414196 | + | 0.910188i | \(0.364063\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −881925. | −0.257530 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.48212e6 | −0.427570 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 911345. | 0.259754 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.34273e6 | 2.34946 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 574142. | 0.159766 | 0.0798830 | − | 0.996804i | \(-0.474545\pi\) | ||||
0.0798830 | + | 0.996804i | \(0.474545\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.80048e6 | −1.04504 | −0.522520 | − | 0.852627i | \(-0.675008\pi\) | ||||
−0.522520 | + | 0.852627i | \(0.675008\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.20395e6 | 0.870631 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −687221. | −0.184554 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 491066. | 0.130338 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.02779e6 | 0.794295 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.21830e6 | −0.575211 | −0.287606 | − | 0.957749i | \(-0.592859\pi\) | ||||
−0.287606 | + | 0.957749i | \(0.592859\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.16997e6 | −0.299886 | −0.149943 | − | 0.988695i | \(-0.547909\pi\) | ||||
−0.149943 | + | 0.988695i | \(0.547909\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.28489e6 | −0.325568 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.41658e6 | 2.10830 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.00014e6 | −0.990636 | −0.495318 | − | 0.868712i | \(-0.664949\pi\) | ||||
−0.495318 | + | 0.868712i | \(0.664949\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 508371. | 0.124476 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.94996e6 | 0.714179 | 0.357089 | − | 0.934070i | \(-0.383769\pi\) | ||||
0.357089 | + | 0.934070i | \(0.383769\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.30965e6 | 0.792286 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.46246e6 | −1.52978 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.44945e6 | −0.807483 | −0.403742 | − | 0.914873i | \(-0.632291\pi\) | ||||
−0.403742 | + | 0.914873i | \(0.632291\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.43971e6 | −0.796307 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.40869e6 | 0.551486 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 456061. | 0.103275 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.94632e6 | −1.55584 | −0.777919 | − | 0.628365i | \(-0.783724\pi\) | ||||
−0.777919 | + | 0.628365i | \(0.783724\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 733132. | 0.162424 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.63913e6 | 0.797527 | 0.398764 | − | 0.917054i | \(-0.369439\pi\) | ||||
0.398764 | + | 0.917054i | \(0.369439\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.29061e6 | −1.14697 | −0.573486 | − | 0.819215i | \(-0.694409\pi\) | ||||
−0.573486 | + | 0.819215i | \(0.694409\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −247187. | −0.0530144 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.01082e6 | −1.48757 | −0.743783 | − | 0.668421i | \(-0.766971\pi\) | ||||
−0.743783 | + | 0.668421i | \(0.766971\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.58881e6 | 0.543461 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −490973. | −0.101978 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12857.6 | 0.00264245 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.78697e6 | −0.363399 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.63671e6 | −1.33554 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.33895e6 | 1.85977 | 0.929885 | − | 0.367850i | \(-0.119906\pi\) | ||||
0.929885 | + | 0.367850i | \(0.119906\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 672638. | 0.132562 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.07590e6 | 0.599935 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.45061e6 | 0.473065 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.02941e6 | −0.578809 | −0.289404 | − | 0.957207i | \(-0.593457\pi\) | ||||
−0.289404 | + | 0.957207i | \(0.593457\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.54099e6 | −0.858773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.58970e6 | 1.04637 | 0.523185 | − | 0.852219i | \(-0.324744\pi\) | ||||
0.523185 | + | 0.852219i | \(0.324744\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.65010e6 | −0.491072 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.01878e6 | −0.370319 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −568892. | −0.103309 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.82995e6 | 0.688561 | 0.344280 | − | 0.938867i | \(-0.388123\pi\) | ||||
0.344280 | + | 0.938867i | \(0.388123\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.08655e7 | 1.93400 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.93999e6 | −1.22304 | −0.611518 | − | 0.791231i | \(-0.709441\pi\) | ||||
−0.611518 | + | 0.791231i | \(0.709441\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −871837. | −0.152127 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.96198e6 | −0.857305 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.13814e6 | −0.707963 | −0.353981 | − | 0.935252i | \(-0.615172\pi\) | ||||
−0.353981 | + | 0.935252i | \(0.615172\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 233507. | 0.0395592 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.90635e6 | 0.319823 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.33198e6 | −0.387442 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.77108e6 | 0.949578 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.37320e6 | 0.875618 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.43012e6 | −0.230823 | −0.115411 | − | 0.993318i | \(-0.536819\pi\) | ||||
−0.115411 | + | 0.993318i | \(0.536819\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.67112e6 | −0.267149 | −0.133574 | − | 0.991039i | \(-0.542646\pi\) | ||||
−0.133574 | + | 0.991039i | \(0.542646\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −653062. | −0.103408 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −509829. | −0.0799646 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.22921e6 | 0.346347 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.40435e6 | 0.985687 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.35776e6 | −0.511954 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.82658e6 | 0.729046 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.99292e6 | 0.597523 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 915698. | 0.135763 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.14416e6 | 0.314966 | 0.157483 | − | 0.987522i | \(-0.449662\pi\) | ||||
0.157483 | + | 0.987522i | \(0.449662\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.16656e7 | −1.69788 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 869566. | 0.125404 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.69979e6 | −0.528700 | −0.264350 | − | 0.964427i | \(-0.585157\pi\) | ||||
−0.264350 | + | 0.964427i | \(0.585157\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.12194e6 | −0.300470 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.89102e6 | −0.966952 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.38455e6 | −0.192529 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −963191. | −0.132733 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.12724e6 | 0.700238 | 0.350119 | − | 0.936705i | \(-0.386141\pi\) | ||||
0.350119 | + | 0.936705i | \(0.386141\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12551.2 | 0.00169886 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.94241e6 | −1.19963 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.94546e6 | 1.05645 | 0.528224 | − | 0.849105i | \(-0.322858\pi\) | ||||
0.528224 | + | 0.849105i | \(0.322858\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.37385e6 | −0.181058 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.21779e6 | 0.420340 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.76137e6 | −0.228071 | −0.114035 | − | 0.993477i | \(-0.536378\pi\) | ||||
−0.114035 | + | 0.993477i | \(0.536378\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 286582. | 0.0367840 | 0.0183920 | − | 0.999831i | \(-0.494145\pi\) | ||||
0.0183920 | + | 0.999831i | \(0.494145\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.74963e6 | −0.222618 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.83983e6 | −0.232064 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.12433e6 | −0.515720 | −0.257860 | − | 0.966182i | \(-0.583017\pi\) | ||||
−0.257860 | + | 0.966182i | \(0.583017\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.77964e7 | 2.20616 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.78624e6 | 0.219532 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.19543e7 | −1.45664 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.97068e6 | −0.238082 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.43423e7 | 1.71800 | 0.859000 | − | 0.511975i | \(-0.171086\pi\) | ||||
0.859000 | + | 0.511975i | \(0.171086\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.32570e6 | −0.157455 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.70825e7 | −2.01180 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.67127e6 | −1.01262 | −0.506309 | − | 0.862352i | \(-0.668991\pi\) | ||||
−0.506309 | + | 0.862352i | \(0.668991\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.34695e6 | −0.155977 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.55273e7 | 1.78303 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.14786e7 | −1.30714 | −0.653571 | − | 0.756866i | \(-0.726730\pi\) | ||||
−0.653571 | + | 0.756866i | \(0.726730\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.21619e7 | 1.37346 | 0.686728 | − | 0.726914i | \(-0.259046\pi\) | ||||
0.686728 | + | 0.726914i | \(0.259046\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.11865e7 | −1.25285 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 389972. | 0.0433157 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.05671e6 | −0.997697 | −0.498849 | − | 0.866689i | \(-0.666244\pi\) | ||||
−0.498849 | + | 0.866689i | \(0.666244\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.51838e6 | −0.275155 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.63357e6 | 0.610493 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.57609e6 | 0.599347 | 0.299673 | − | 0.954042i | \(-0.403122\pi\) | ||||
0.299673 | + | 0.954042i | \(0.403122\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.80818e6 | 0.512616 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.88756e6 | 0.199612 | 0.0998062 | − | 0.995007i | \(-0.468178\pi\) | ||||
0.0998062 | + | 0.995007i | \(0.468178\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 353063. | 0.0370361 | 0.0185181 | − | 0.999829i | \(-0.494105\pi\) | ||||
0.0185181 | + | 0.999829i | \(0.494105\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.96274e6 | 0.204237 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.48691e6 | 0.669604 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.32528e7 | −2.36215 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.98660e6 | −0.200209 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.14879e6 | −0.914724 | −0.457362 | − | 0.889281i | \(-0.651206\pi\) | ||||
−0.457362 | + | 0.889281i | \(0.651206\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.57368e7 | −1.56102 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.82433e6 | 0.770039 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 893880. | 0.0872832 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.45823e6 | 0.238161 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.33065e6 | −0.800818 | −0.400409 | − | 0.916336i | \(-0.631132\pi\) | ||||
−0.400409 | + | 0.916336i | \(0.631132\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.59733e6 | −0.820042 | −0.410021 | − | 0.912076i | \(-0.634479\pi\) | ||||
−0.410021 | + | 0.912076i | \(0.634479\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17972.9 | −0.00170106 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.65094e7 | 1.55050 | 0.775248 | − | 0.631657i | \(-0.217625\pi\) | ||||
0.775248 | + | 0.631657i | \(0.217625\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.15358e7 | 1.07507 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −484487. | −0.0448053 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.65233e6 | 0.702280 | 0.351140 | − | 0.936323i | \(-0.385794\pi\) | ||||
0.351140 | + | 0.936323i | \(0.385794\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.82407e6 | 0.257200 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.00900e6 | −0.0911967 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.28219e7 | 1.15011 | 0.575056 | − | 0.818114i | \(-0.304980\pi\) | ||||
0.575056 | + | 0.818114i | \(0.304980\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.20104e7 | 1.06918 | 0.534592 | − | 0.845110i | \(-0.320465\pi\) | ||||
0.534592 | + | 0.845110i | \(0.320465\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.72935e6 | −0.771255 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.50246e6 | −0.307128 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.09487e6 | −0.617490 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.07599e7 | 0.929486 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.82211e6 | −0.327716 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.31342e6 | −0.537312 | −0.268656 | − | 0.963236i | \(-0.586580\pi\) | ||||
−0.268656 | + | 0.963236i | \(0.586580\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −416721. | −0.0352035 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.43615e6 | 0.120428 | 0.0602142 | − | 0.998185i | \(-0.480822\pi\) | ||||
0.0602142 | + | 0.998185i | \(0.480822\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.80320e6 | 0.399813 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.69240e7 | −1.39841 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.90641e7 | −1.56374 | −0.781871 | − | 0.623441i | \(-0.785734\pi\) | ||||
−0.781871 | + | 0.623441i | \(0.785734\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.03394e6 | 0.0841913 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.13795e7 | 0.919880 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.16695e7 | −0.936491 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.58516e7 | −1.26292 | −0.631462 | − | 0.775407i | \(-0.717545\pi\) | ||||
−0.631462 | + | 0.775407i | \(0.717545\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.95680e6 | −0.312976 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.78070e6 | −0.768083 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.91696e6 | 0.773209 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.34738e7 | 2.59127 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 870113. | 0.0668776 | 0.0334388 | − | 0.999441i | \(-0.489354\pi\) | ||||
0.0334388 | + | 0.999441i | \(0.489354\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.16573e6 | −0.394224 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.06705e6 | −0.611283 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.70880e6 | −0.128571 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.14645e7 | 0.856524 | 0.428262 | − | 0.903655i | \(-0.359126\pi\) | ||||
0.428262 | + | 0.903655i | \(0.359126\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.98277e6 | 0.443842 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.36492e6 | −0.100550 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.54966e6 | −0.259670 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.78870e6 | −0.493161 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.00675e7 | 0.726273 | 0.363137 | − | 0.931736i | \(-0.381706\pi\) | ||||
0.363137 | + | 0.931736i | \(0.381706\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.57068e6 | −0.327448 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.53333e7 | −1.09091 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.50635e6 | 0.106434 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.42656e7 | 1.00104 | 0.500522 | − | 0.865724i | \(-0.333142\pi\) | ||||
0.500522 | + | 0.865724i | \(0.333142\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.04493e7 | −0.728232 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −37069.5 | −0.00256580 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.44090e6 | 0.511524 | 0.255762 | − | 0.966740i | \(-0.417674\pi\) | ||||
0.255762 | + | 0.966740i | \(0.417674\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.28000e6 | −0.0873961 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.01495e7 | −1.36646 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.73511e6 | 0.184231 | 0.0921156 | − | 0.995748i | \(-0.470637\pi\) | ||||
0.0921156 | + | 0.995748i | \(0.470637\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.26988e7 | −1.51865 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.09318e7 | −1.39102 | −0.695511 | − | 0.718515i | \(-0.744822\pi\) | ||||
−0.695511 | + | 0.718515i | \(0.744822\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.57634e6 | 0.500114 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.71847e6 | −0.506093 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.46009e6 | 0.616156 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.73024e7 | 1.76645 | 0.883225 | − | 0.468950i | \(-0.155368\pi\) | ||||
0.883225 | + | 0.468950i | \(0.155368\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.49055e7 | −2.24340 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.82385e6 | −0.180291 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.28294e7 | 0.813703 | 0.406851 | − | 0.913494i | \(-0.366627\pi\) | ||||
0.406851 | + | 0.913494i | \(0.366627\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.39407e7 | −1.50845 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.04401e7 | 1.27945 | 0.639723 | − | 0.768606i | \(-0.279049\pi\) | ||||
0.639723 | + | 0.768606i | \(0.279049\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.70435e6 | 0.105986 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.82029e6 | 0.359577 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.12609e7 | 0.691171 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.17270e7 | −0.715109 | −0.357555 | − | 0.933892i | \(-0.616389\pi\) | ||||
−0.357555 | + | 0.933892i | \(0.616389\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.52221e7 | 0.922232 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.63342e7 | −1.58515 | −0.792576 | − | 0.609773i | \(-0.791260\pi\) | ||||
−0.792576 | + | 0.609773i | \(0.791260\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 289793. | 0.0173314 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.88785e6 | −0.112180 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.57869e7 | 1.52250 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.42786e6 | 0.259756 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.60699e6 | −0.0936715 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 575598. | 0.0333384 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32107.6 | 0.00184787 | 0.000923933 | − | 1.00000i | \(-0.499706\pi\) | ||||
0.000923933 | 1.00000i | \(0.499706\pi\) | ||||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.12587e7 | 2.35952 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.69274e6 | −0.153022 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.73105e6 | −0.210692 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.67102e7 | 0.937702 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.60617e7 | −0.895665 | −0.447832 | − | 0.894118i | \(-0.647804\pi\) | ||||
−0.447832 | + | 0.894118i | \(0.647804\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.66385e7 | −0.922033 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.80305e7 | −1.54365 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.81746e6 | −0.0994662 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.60607e6 | −0.196130 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.23357e6 | 0.120730 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.71020e6 | 0.521623 | 0.260812 | − | 0.965390i | \(-0.416010\pi\) | ||||
0.260812 | + | 0.965390i | \(0.416010\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.95547e7 | 1.57788 | 0.788942 | − | 0.614468i | \(-0.210629\pi\) | ||||
0.788942 | + | 0.614468i | \(0.210629\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.32667e7 | −1.23455 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.32369e6 | 0.280749 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −96391.2 | −0.00505222 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.86253e6 | −0.201216 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.69239e6 | 0.191183 | 0.0955915 | − | 0.995421i | \(-0.469526\pi\) | ||||
0.0955915 | + | 0.995421i | \(0.469526\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.37549e7 | 0.707878 | 0.353939 | − | 0.935268i | \(-0.384842\pi\) | ||||
0.353939 | + | 0.935268i | \(0.384842\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.08298e6 | 0.260006 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.94189e6 | −0.251263 | −0.125632 | − | 0.992077i | \(-0.540096\pi\) | ||||
−0.125632 | + | 0.992077i | \(0.540096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.72295e7 | −1.88149 | −0.940743 | − | 0.339119i | \(-0.889871\pi\) | ||||
−0.940743 | + | 0.339119i | \(0.889871\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.01099e6 | 0.352190 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.64003e6 | −0.131825 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.27383e7 | −0.632260 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −309153. | −0.0152532 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.90655e7 | 0.935066 | 0.467533 | − | 0.883976i | \(-0.345143\pi\) | ||||
0.467533 | + | 0.883976i | \(0.345143\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.47023e7 | −0.716794 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −796667. | −0.0386107 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.81724e6 | 0.280269 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 764345. | 0.0366084 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.84473e7 | 1.83061 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.31854e6 | −0.251749 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.09785e7 | −0.987193 | −0.493596 | − | 0.869691i | \(-0.664318\pi\) | ||||
−0.493596 | + | 0.869691i | \(0.664318\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.51344e7 | 0.708028 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.97938e7 | −1.38571 | −0.692857 | − | 0.721075i | \(-0.743648\pi\) | ||||
−0.692857 | + | 0.721075i | \(0.743648\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.86748e6 | −0.0863520 | −0.0431760 | − | 0.999067i | \(-0.513748\pi\) | ||||
−0.0431760 | + | 0.999067i | \(0.513748\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.42402e6 | 0.433240 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.28328e7 | −1.04359 | −0.521797 | − | 0.853070i | \(-0.674738\pi\) | ||||
−0.521797 | + | 0.853070i | \(0.674738\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.29934e6 | −0.286256 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.49601e6 | −0.203132 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.07764e7 | 0.484088 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.96694e7 | −0.878508 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.07550e7 | −0.921696 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 765625. | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.10654e7 | −1.80292 | −0.901462 | − | 0.432858i | \(-0.857505\pi\) | ||||
−0.901462 | + | 0.432858i | \(0.857505\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.34787e7 | −1.46149 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.94268e7 | −1.71140 | −0.855700 | − | 0.517472i | \(-0.826873\pi\) | ||||
−0.855700 | + | 0.517472i | \(0.826873\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.49358e7 | −0.644654 | −0.322327 | − | 0.946628i | \(-0.604465\pi\) | ||||
−0.322327 | + | 0.946628i | \(0.604465\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.61252e7 | −0.692065 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.44515e7 | 1.04351 | 0.521754 | − | 0.853096i | \(-0.325278\pi\) | ||||
0.521754 | + | 0.853096i | \(0.325278\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.53357e7 | 0.650802 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.50451e7 | −1.05689 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.32647e7 | −1.81554 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.68115e6 | −0.195342 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.33702e7 | −0.969800 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.11752e6 | 0.0461164 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.44652e7 | 1.41439 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −35226.9 | −0.00143766 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.36763e7 | 0.555070 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.77487e7 | −1.12002 | −0.560009 | − | 0.828487i | \(-0.689202\pi\) | ||||
−0.560009 | + | 0.828487i | \(0.689202\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.38386e6 | 0.296397 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.04000e6 | 0.0415181 | 0.0207591 | − | 0.999785i | \(-0.493392\pi\) | ||||
0.0207591 | + | 0.999785i | \(0.493392\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.39028e7 | −0.551984 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.34271e6 | 0.210964 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.53517e6 | 0.217374 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.58322e7 | −1.00896 | −0.504479 | − | 0.863424i | \(-0.668315\pi\) | ||||
−0.504479 | + | 0.863424i | \(0.668315\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.84392e7 | 1.88169 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.32236e6 | 0.167000 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.12921e6 | 0.0433930 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.97503e7 | 0.754872 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.92846e7 | 0.733114 | 0.366557 | − | 0.930396i | \(-0.380536\pi\) | ||||
0.366557 | + | 0.930396i | \(0.380536\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.86483e6 | −0.259571 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.78628e7 | 2.17618 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.04837e7 | 0.392182 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.79237e6 | 0.327158 | 0.163579 | − | 0.986530i | \(-0.447696\pi\) | ||||
0.163579 | + | 0.986530i | \(0.447696\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.47299e7 | −2.39575 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.04584e7 | 1.85763 | 0.928816 | − | 0.370542i | \(-0.120828\pi\) | ||||
0.928816 | + | 0.370542i | \(0.120828\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.65497e7 | 0.972257 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −816773. | −0.0297524 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.48456e6 | 0.234966 | 0.117483 | − | 0.993075i | \(-0.462517\pi\) | ||||
0.117483 | + | 0.993075i | \(0.462517\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.77415e6 | −0.0639478 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.39821e7 | 0.501327 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.67568e7 | −0.597666 | −0.298833 | − | 0.954305i | \(-0.596597\pi\) | ||||
−0.298833 | + | 0.954305i | \(0.596597\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.05121e6 | 0.0727781 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.96013e7 | 0.691838 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.02651e6 | 0.0711546 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.84142e7 | −0.992491 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.08778e7 | −1.42044 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.08639e7 | −0.721234 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.12777e7 | −0.387843 | −0.193921 | − | 0.981017i | \(-0.562121\pi\) | ||||
−0.193921 | + | 0.981017i | \(0.562121\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.70397e7 | 2.29363 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.36109e7 | 0.803644 | 0.401822 | − | 0.915718i | \(-0.368377\pi\) | ||||
0.401822 | + | 0.915718i | \(0.368377\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.91702e7 | −0.649149 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.96187e6 | 0.167160 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.36268e7 | −1.46223 | −0.731117 | − | 0.682252i | \(-0.761001\pi\) | ||||
−0.731117 | + | 0.682252i | \(0.761001\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.04896e7 | −1.68362 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.36463e6 | −0.244331 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.23492e7 | 0.407618 | 0.203809 | − | 0.979011i | \(-0.434668\pi\) | ||||
0.203809 | + | 0.979011i | \(0.434668\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.00269e7 | 0.657694 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.58114e7 | −0.516628 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −99242.6 | −0.00322632 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.32915e7 | −1.72375 | −0.861874 | − | 0.507122i | \(-0.830709\pi\) | ||||
−0.861874 | + | 0.507122i | \(0.830709\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.04128e7 | 2.58793 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.82036e7 | −0.582907 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.43068e6 | 0.204889 | 0.102445 | − | 0.994739i | \(-0.467334\pi\) | ||||
0.102445 | + | 0.994739i | \(0.467334\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.20465e6 | −0.0381897 |
(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 | 560.6.a.s.1.3 | 3 | ||
4.3 | odd | 2 | 280.6.a.e.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.6.a.e.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
560.6.a.s.1.3 | 3 | 1.1 | even | 1 | trivial |