Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,8,Mod(1,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(119.955849786\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 430x^{2} - 2448x + 12138 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.20119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.1 |
$q$-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 | ||||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −170.323 | −0.609367 | −0.304683 | − | 0.952454i | \(-0.598551\pi\) | ||||
−0.304683 | + | 0.952454i | \(0.598551\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −803.427 | −0.885326 | −0.442663 | − | 0.896688i | \(-0.645966\pi\) | ||||
−0.442663 | + | 0.896688i | \(0.645966\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8558.72 | 1.93881 | 0.969404 | − | 0.245472i | \(-0.0789431\pi\) | ||||
0.969404 | + | 0.245472i | \(0.0789431\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1465.98 | 0.185066 | 0.0925332 | − | 0.995710i | \(-0.470504\pi\) | ||||
0.0925332 | + | 0.995710i | \(0.470504\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4598.72 | 0.351818 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 30783.7 | 1.51967 | 0.759836 | − | 0.650115i | \(-0.225279\pi\) | ||||
0.759836 | + | 0.650115i | \(0.225279\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11397.6 | 0.381219 | 0.190610 | − | 0.981666i | \(-0.438954\pi\) | ||||
0.190610 | + | 0.981666i | \(0.438954\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21692.5 | 0.511143 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −116211. | −1.99160 | −0.995799 | − | 0.0915692i | \(-0.970812\pi\) | ||||
−0.995799 | + | 0.0915692i | \(0.970812\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −49115.0 | −0.628672 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −184311. | −1.40332 | −0.701661 | − | 0.712511i | \(-0.747558\pi\) | ||||
−0.701661 | + | 0.712511i | \(0.747558\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 61312.9 | 0.369646 | 0.184823 | − | 0.982772i | \(-0.440829\pi\) | ||||
0.184823 | + | 0.982772i | \(0.440829\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −231086. | −1.11937 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 136842. | 0.539488 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −357060. | −1.15887 | −0.579436 | − | 0.815018i | \(-0.696727\pi\) | ||||
−0.579436 | + | 0.815018i | \(0.696727\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −39581.6 | −0.106848 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 389342. | 0.882243 | 0.441121 | − | 0.897447i | \(-0.354581\pi\) | ||||
0.441121 | + | 0.897447i | \(0.354581\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −939452. | −1.80192 | −0.900959 | − | 0.433904i | \(-0.857136\pi\) | ||||
−0.900959 | + | 0.433904i | \(0.857136\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −124166. | −0.203122 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.13965e6 | 1.60113 | 0.800567 | − | 0.599243i | \(-0.204532\pi\) | ||||
0.800567 | + | 0.599243i | \(0.204532\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −178048. | −0.216198 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −831160. | −0.877383 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −324394. | −0.299300 | −0.149650 | − | 0.988739i | \(-0.547815\pi\) | ||||
−0.149650 | + | 0.988739i | \(0.547815\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.45775e6 | −1.18144 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −307734. | −0.220097 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.86418e6 | 1.18169 | 0.590847 | − | 0.806784i | \(-0.298794\pi\) | ||||
0.590847 | + | 0.806784i | \(0.298794\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.14154e6 | 0.643929 | 0.321965 | − | 0.946752i | \(-0.395657\pi\) | ||||
0.321965 | + | 0.946752i | \(0.395657\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −585698. | −0.295109 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −249691. | −0.112773 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.58844e6 | −0.645223 | −0.322612 | − | 0.946531i | \(-0.604561\pi\) | ||||
−0.322612 | + | 0.946531i | \(0.604561\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.13771e6 | 1.14985 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.98069e6 | 1.31994 | 0.659970 | − | 0.751292i | \(-0.270569\pi\) | ||||
0.659970 | + | 0.751292i | \(0.270569\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.61658e6 | 1.08810 | 0.544050 | − | 0.839053i | \(-0.316890\pi\) | ||||
0.544050 | + | 0.839053i | \(0.316890\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.32611e6 | 0.362964 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.87631e6 | −1.71648 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.26185e6 | 0.972530 | 0.486265 | − | 0.873811i | \(-0.338359\pi\) | ||||
0.486265 | + | 0.873811i | \(0.338359\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 161844. | 0.0310686 | 0.0155343 | − | 0.999879i | \(-0.495055\pi\) | ||||
0.0155343 | + | 0.999879i | \(0.495055\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.24318e6 | −0.926037 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.97639e6 | 0.810209 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.25081e6 | −1.39096 | −0.695480 | − | 0.718545i | \(-0.744808\pi\) | ||||
−0.695480 | + | 0.718545i | \(0.744808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.17781e6 | −0.163844 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.65545e6 | −0.213415 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.94127e6 | −0.232302 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.61098e6 | −0.957969 | −0.478984 | − | 0.877823i | \(-0.658995\pi\) | ||||
−0.478984 | + | 0.877823i | \(0.658995\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.23931e6 | 0.646269 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.60481e6 | 0.444720 | 0.222360 | − | 0.974965i | \(-0.428624\pi\) | ||||
0.222360 | + | 0.974965i | \(0.428624\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.95825e6 | −0.176579 | −0.0882893 | − | 0.996095i | \(-0.528140\pi\) | ||||
−0.0882893 | + | 0.996095i | \(0.528140\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.69474e6 | −0.311474 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −290533. | −0.0229273 | −0.0114636 | − | 0.999934i | \(-0.503649\pi\) | ||||
−0.0114636 | + | 0.999934i | \(0.503649\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.20086e7 | −0.888178 | −0.444089 | − | 0.895983i | \(-0.646473\pi\) | ||||
−0.444089 | + | 0.895983i | \(0.646473\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.64063e6 | 0.669075 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.40975e6 | 0.548288 | 0.274144 | − | 0.961689i | \(-0.411606\pi\) | ||||
0.274144 | + | 0.961689i | \(0.411606\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.97935e7 | 1.21361 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.06870e6 | 0.0616888 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.47325e7 | −1.34541 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.37646e7 | 2.75897 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.05122e7 | −0.509363 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.16719e7 | 0.992458 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.16293e7 | 0.503779 | 0.251890 | − | 0.967756i | \(-0.418948\pi\) | ||||
0.251890 | + | 0.967756i | \(0.418948\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.53652e7 | 1.04034 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.71549e7 | 1.83264 | 0.916320 | − | 0.400448i | \(-0.131145\pi\) | ||||
0.916320 | + | 0.400448i | \(0.131145\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.15711e6 | −0.337503 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.35247e6 | 0.117273 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.51260e7 | −0.502576 | −0.251288 | − | 0.967912i | \(-0.580854\pi\) | ||||
−0.251288 | + | 0.967912i | \(0.580854\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.10238e6 | −0.161146 | −0.0805732 | − | 0.996749i | \(-0.525675\pi\) | ||||
−0.0805732 | + | 0.996749i | \(0.525675\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.07705e7 | −0.924415 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.25470e7 | 0.358808 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.13924e7 | 0.855138 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.80731e6 | 0.124822 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.54568e7 | −1.37342 | −0.686709 | − | 0.726932i | \(-0.740945\pi\) | ||||
−0.686709 | + | 0.726932i | \(0.740945\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.11499e7 | 0.972633 | 0.486317 | − | 0.873783i | \(-0.338340\pi\) | ||||
0.486317 | + | 0.873783i | \(0.338340\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.24413e7 | 0.506557 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.04430e7 | −0.225250 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.41239e7 | 0.497507 | 0.248754 | − | 0.968567i | \(-0.419979\pi\) | ||||
0.248754 | + | 0.968567i | \(0.419979\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.75863e6 | 0.172801 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.33674e7 | 1.76321 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.99050e6 | −0.0540862 | −0.0270431 | − | 0.999634i | \(-0.508609\pi\) | ||||
−0.0270431 | + | 0.999634i | \(0.508609\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.93592e7 | 0.682107 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.25574e7 | 0.873225 | 0.436613 | − | 0.899650i | \(-0.356178\pi\) | ||||
0.436613 | + | 0.899650i | \(0.356178\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.05994e7 | −0.965750 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.30883e6 | 0.127073 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.30414e8 | −1.91498 | −0.957489 | − | 0.288470i | \(-0.906853\pi\) | ||||
−0.957489 | + | 0.288470i | \(0.906853\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.94603e7 | 0.556580 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.03327e7 | −0.682251 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.42930e7 | 0.446910 | 0.223455 | − | 0.974714i | \(-0.428266\pi\) | ||||
0.223455 | + | 0.974714i | \(0.428266\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.04120e6 | −0.0130515 | −0.00652574 | − | 0.999979i | \(-0.502077\pi\) | ||||
−0.00652574 | + | 0.999979i | \(0.502077\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.08217e7 | −0.371773 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.08156e7 | 0.706178 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.63469e8 | 2.94635 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.58138e7 | 0.170381 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.07300e8 | 1.11426 | 0.557128 | − | 0.830427i | \(-0.311903\pi\) | ||||
0.557128 | + | 0.830427i | \(0.311903\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.41745e7 | 0.842810 | 0.421405 | − | 0.906873i | \(-0.361537\pi\) | ||||
0.421405 | + | 0.906873i | \(0.361537\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.74166e6 | 0.0651097 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.24519e8 | −1.16039 | −0.580193 | − | 0.814479i | \(-0.697023\pi\) | ||||
−0.580193 | + | 0.814479i | \(0.697023\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.14773e7 | −0.463053 | −0.231526 | − | 0.972829i | \(-0.574372\pi\) | ||||
−0.231526 | + | 0.972829i | \(0.574372\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.28880e7 | 0.372520 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.48080e8 | 1.24240 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.63140e7 | −0.537609 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.47182e7 | −0.663866 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.75487e7 | 0.739110 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.50525e7 | 0.183596 | 0.0917978 | − | 0.995778i | \(-0.470739\pi\) | ||||
0.0917978 | + | 0.995778i | \(0.470739\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.07479e8 | −0.762068 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.60010e8 | 1.09803 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.92604e7 | −0.327257 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.76478e7 | −0.628215 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.51284e7 | 0.281240 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.69254e8 | 1.62590 | 0.812952 | − | 0.582331i | \(-0.197859\pi\) | ||||
0.812952 | + | 0.582331i | \(0.197859\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.58049e7 | −0.209557 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.89081e7 | 0.561231 | 0.280615 | − | 0.959820i | \(-0.409461\pi\) | ||||
0.280615 | + | 0.959820i | \(0.409461\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.76761e8 | 0.972665 | 0.486333 | − | 0.873774i | \(-0.338334\pi\) | ||||
0.486333 | + | 0.873774i | \(0.338334\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.85660e8 | 0.991008 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.16179e7 | −0.422707 | −0.211354 | − | 0.977410i | \(-0.567787\pi\) | ||||
−0.211354 | + | 0.977410i | \(0.567787\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.94108e8 | −0.975678 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.15070e8 | −0.561491 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.87021e7 | 0.230757 | 0.115379 | − | 0.993322i | \(-0.463192\pi\) | ||||
0.115379 | + | 0.993322i | \(0.463192\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.21691e8 | 1.02021 | 0.510104 | − | 0.860113i | \(-0.329607\pi\) | ||||
0.510104 | + | 0.860113i | \(0.329607\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.03258e7 | 0.131744 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.67087e7 | 0.0705508 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.36977e6 | −0.0179375 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.90667e8 | −0.761059 | −0.380529 | − | 0.924769i | \(-0.624258\pi\) | ||||
−0.380529 | + | 0.924769i | \(0.624258\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.94622e8 | −3.86132 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.41566e8 | 0.534648 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.82788e8 | 0.671711 | 0.335855 | − | 0.941914i | \(-0.390975\pi\) | ||||
0.335855 | + | 0.941914i | \(0.390975\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.86872e8 | 1.02598 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.34362e8 | −0.467774 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.64394e8 | 0.896204 | 0.448102 | − | 0.893982i | \(-0.352100\pi\) | ||||
0.448102 | + | 0.893982i | \(0.352100\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.52518e7 | 0.182384 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.49772e8 | 0.803071 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.76393e6 | −0.0180545 | −0.00902726 | − | 0.999959i | \(-0.502874\pi\) | ||||
−0.00902726 | + | 0.999959i | \(0.502874\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.54148e7 | 0.138613 | 0.0693066 | − | 0.997595i | \(-0.477921\pi\) | ||||
0.0693066 | + | 0.997595i | \(0.477921\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.18009e7 | 0.0945954 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.20362e8 | −1.21887 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.55561e8 | 0.722463 | 0.361231 | − | 0.932476i | \(-0.382356\pi\) | ||||
0.361231 | + | 0.932476i | \(0.382356\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.46971e7 | 0.123215 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.19922e8 | 0.322423 | 0.161211 | − | 0.986920i | \(-0.448460\pi\) | ||||
0.161211 | + | 0.986920i | \(0.448460\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.77072e8 | 0.988943 | 0.494472 | − | 0.869194i | \(-0.335362\pi\) | ||||
0.494472 | + | 0.869194i | \(0.335362\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.24143e7 | 0.134120 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.12808e8 | −0.781073 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.37299e8 | 1.30940 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.32496e8 | 0.553084 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.64702e8 | 1.07929 | 0.539645 | − | 0.841893i | \(-0.318559\pi\) | ||||
0.539645 | + | 0.841893i | \(0.318559\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.17512e8 | −0.720084 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.68461e8 | −0.373124 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.70364e8 | −0.368578 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.54781e8 | 1.59528 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.24330e8 | −0.256759 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.94431e8 | −0.392389 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.92572e8 | −0.577096 | −0.288548 | − | 0.957465i | \(-0.593172\pi\) | ||||
−0.288548 | + | 0.957465i | \(0.593172\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.28728e7 | 0.101948 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.46441e7 | −0.159564 | −0.0797821 | − | 0.996812i | \(-0.525422\pi\) | ||||
−0.0797821 | + | 0.996812i | \(0.525422\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.45028e8 | 0.451660 | 0.225830 | − | 0.974167i | \(-0.427491\pi\) | ||||
0.225830 | + | 0.974167i | \(0.427491\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.97579e7 | 0.179829 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.16827e8 | −1.61652 | −0.808258 | − | 0.588828i | \(-0.799589\pi\) | ||||
−0.808258 | + | 0.588828i | \(0.799589\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.57746e9 | −2.72077 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.84439e6 | 0.0132371 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.50860e8 | 0.579328 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.20019e7 | −0.116346 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.24233e8 | 0.512790 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.15623e8 | −1.41753 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.63201e8 | 1.30832 | 0.654160 | − | 0.756356i | \(-0.273022\pi\) | ||||
0.654160 | + | 0.756356i | \(0.273022\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.60297e8 | −0.386291 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.70549e8 | 0.393177 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.99753e8 | 0.284307 | 0.142154 | − | 0.989845i | \(-0.454597\pi\) | ||||
0.142154 | + | 0.989845i | \(0.454597\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.27063e8 | −0.316554 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.24760e8 | 0.716672 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.04705e8 | 1.07673 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.34425e8 | −0.700680 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.63988e8 | 0.596147 | 0.298073 | − | 0.954543i | \(-0.403656\pi\) | ||||
0.298073 | + | 0.954543i | \(0.403656\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00082e8 | 0.251953 | 0.125976 | − | 0.992033i | \(-0.459794\pi\) | ||||
0.125976 | + | 0.992033i | \(0.459794\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.88550e7 | −0.0356160 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.87624e8 | −0.227026 | −0.113513 | − | 0.993537i | \(-0.536210\pi\) | ||||
−0.113513 | + | 0.993537i | \(0.536210\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.78004e8 | −0.804328 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.67777e8 | 0.776770 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.52437e8 | 0.630162 | 0.315081 | − | 0.949065i | \(-0.397968\pi\) | ||||
0.315081 | + | 0.949065i | \(0.397968\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.63967e8 | −0.854672 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.45164e9 | −1.59289 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.15988e8 | −0.663052 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.84351e8 | 0.511480 | 0.255740 | − | 0.966746i | \(-0.417681\pi\) | ||||
0.255740 | + | 0.966746i | \(0.417681\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.83831e8 | 0.294081 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.60627e8 | 0.264978 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.23031e9 | 1.22753 | 0.613766 | − | 0.789488i | \(-0.289654\pi\) | ||||
0.613766 | + | 0.789488i | \(0.289654\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.85142e8 | −0.572996 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.70196e8 | −0.259708 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.92482e8 | −0.370325 | −0.185162 | − | 0.982708i | \(-0.559281\pi\) | ||||
−0.185162 | + | 0.982708i | \(0.559281\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.13991e8 | −0.290857 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.19343e9 | 1.08543 | 0.542713 | − | 0.839918i | \(-0.317397\pi\) | ||||
0.542713 | + | 0.839918i | \(0.317397\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.17119e9 | 1.04596 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.84860e8 | −0.600639 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.02141e9 | 1.74113 | 0.870566 | − | 0.492052i | \(-0.163753\pi\) | ||||
0.870566 | + | 0.492052i | \(0.163753\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.57742e9 | −3.02658 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.27318e9 | −1.05807 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.25891e8 | −0.592627 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00840e9 | 1.61095 | 0.805477 | − | 0.592627i | \(-0.201909\pi\) | ||||
0.805477 | + | 0.592627i | \(0.201909\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.47242e8 | 0.194858 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.97549e9 | 1.52992 | 0.764961 | − | 0.644077i | \(-0.222758\pi\) | ||||
0.764961 | + | 0.644077i | \(0.222758\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.98837e7 | 0.0684090 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.05167e7 | −0.0677074 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.05598e9 | −2.24683 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.30321e9 | −1.66457 | −0.832285 | − | 0.554348i | \(-0.812968\pi\) | ||||
−0.832285 | + | 0.554348i | \(0.812968\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.08402e8 | 0.290162 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.49773e9 | −1.04618 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.75657e7 | −0.0189322 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.37764e8 | 0.0930379 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.11767e8 | −0.539116 | −0.269558 | − | 0.962984i | \(-0.586878\pi\) | ||||
−0.269558 | + | 0.962984i | \(0.586878\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.79307e9 | 1.17114 | 0.585572 | − | 0.810621i | \(-0.300870\pi\) | ||||
0.585572 | + | 0.810621i | \(0.300870\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.30802e8 | 0.533711 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.51194e9 | −0.955376 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.17147e8 | −0.570087 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.38768e8 | −0.207158 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.25406e9 | −1.35611 | −0.678056 | − | 0.735010i | \(-0.737177\pi\) | ||||
−0.678056 | + | 0.735010i | \(0.737177\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.79170e8 | −0.342846 | −0.171423 | − | 0.985198i | \(-0.554836\pi\) | ||||
−0.171423 | + | 0.985198i | \(0.554836\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.47594e8 | −0.493714 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.32453e9 | −0.759235 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.10809e9 | 1.18922 | 0.594612 | − | 0.804013i | \(-0.297306\pi\) | ||||
0.594612 | + | 0.804013i | \(0.297306\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.29797e8 | −0.0720660 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.30366e9 | −1.80544 | −0.902719 | − | 0.430231i | \(-0.858432\pi\) | ||||
−0.902719 | + | 0.430231i | \(0.858432\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.57563e9 | 0.847605 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.49733e9 | 0.792943 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.97620e9 | −1.03031 | −0.515156 | − | 0.857096i | \(-0.672266\pi\) | ||||
−0.515156 | + | 0.857096i | \(0.672266\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.33227e9 | 1.71050 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.11105e9 | −0.561550 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.00608e8 | 0.0998411 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.00615e9 | 1.47334 | 0.736672 | − | 0.676251i | \(-0.236396\pi\) | ||||
0.736672 | + | 0.676251i | \(0.236396\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.05916e8 | −0.292461 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.10649e9 | −1.00140 | −0.500698 | − | 0.865622i | \(-0.666923\pi\) | ||||
−0.500698 | + | 0.865622i | \(0.666923\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.63797e9 | −1.23520 | −0.617599 | − | 0.786493i | \(-0.711894\pi\) | ||||
−0.617599 | + | 0.786493i | \(0.711894\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.81961e8 | 0.130048 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.52190e9 | −1.60018 | −0.800088 | − | 0.599882i | \(-0.795214\pi\) | ||||
−0.800088 | + | 0.599882i | \(0.795214\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.27620e9 | 0.571233 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.51347e8 | −0.287236 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.04051e9 | −3.49357 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.59792e8 | −0.239662 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.36483e8 | −0.0997667 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.26788e8 | 0.302158 | 0.151079 | − | 0.988522i | \(-0.451725\pi\) | ||||
0.151079 | + | 0.988522i | \(0.451725\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.23445e8 | −0.214468 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.52092e9 | −1.01799 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.46665e9 | 0.583754 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.74369e9 | −1.07643 | −0.538213 | − | 0.842809i | \(-0.680900\pi\) | ||||
−0.538213 | + | 0.842809i | \(0.680900\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.07434e7 | 0.0312267 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.06210e8 | −0.269245 | −0.134623 | − | 0.990897i | \(-0.542982\pi\) | ||||
−0.134623 | + | 0.990897i | \(0.542982\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.67377e9 | −2.13259 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.06270e9 | −0.393815 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.19819e9 | −1.16858 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.00895e8 | 0.180466 | 0.0902329 | − | 0.995921i | \(-0.471239\pi\) | ||||
0.0902329 | + | 0.995921i | \(0.471239\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.41905e9 | −0.504157 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.62878e9 | 0.570658 | 0.285329 | − | 0.958430i | \(-0.407897\pi\) | ||||
0.285329 | + | 0.958430i | \(0.407897\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.84305e8 | −0.270997 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.63618e9 | 0.557576 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.07202e9 | 1.03255 | 0.516277 | − | 0.856422i | \(-0.327318\pi\) | ||||
0.516277 | + | 0.856422i | \(0.327318\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.90566e9 | −0.963323 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.24338e8 | −0.0733656 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.33535e8 | 0.107601 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.75392e9 | 3.10429 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.52119e9 | 1.10561 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.94213e9 | 0.911444 | 0.455722 | − | 0.890122i | \(-0.349381\pi\) | ||||
0.455722 | + | 0.890122i | \(0.349381\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.96275e9 | 0.599942 | 0.299971 | − | 0.953948i | \(-0.403023\pi\) | ||||
0.299971 | + | 0.953948i | \(0.403023\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.06543e9 | −0.321342 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.88744e9 | 0.561741 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.01003e10 | 2.96646 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.35898e9 | 0.393898 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.70770e8 | 0.163273 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.94845e7 | 0.0139711 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.25911e8 | −0.258023 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.52387e9 | −0.419166 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.58836e9 | 0.702804 | 0.351402 | − | 0.936225i | \(-0.385705\pi\) | ||||
0.351402 | + | 0.936225i | \(0.385705\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.81124e7 | 0.00753527 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.04535e9 | 0.541226 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.21608e9 | 0.578936 | 0.289468 | − | 0.957188i | \(-0.406522\pi\) | ||||
0.289468 | + | 0.957188i | \(0.406522\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.32186e8 | 0.214643 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.10069e9 | −0.534973 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.42408e9 | −0.861006 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.64202e9 | −0.407712 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.23234e9 | 0.547353 | 0.273677 | − | 0.961822i | \(-0.411760\pi\) | ||||
0.273677 | + | 0.961822i | \(0.411760\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.37722e9 | −0.333474 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.11367e9 | −1.70108 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.05647e9 | 0.958007 | 0.479004 | − | 0.877813i | \(-0.340998\pi\) | ||||
0.479004 | + | 0.877813i | \(0.340998\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.43237e9 | −0.334108 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.26974e8 | −0.0983695 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.36385e9 | 1.67576 | 0.837881 | − | 0.545854i | \(-0.183795\pi\) | ||||
0.837881 | + | 0.545854i | \(0.183795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.33947e9 | 0.301096 | 0.150548 | − | 0.988603i | \(-0.451896\pi\) | ||||
0.150548 | + | 0.988603i | \(0.451896\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.89711e9 | −0.643316 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.70773e9 | 1.25206 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.99535e9 | 0.649131 | 0.324565 | − | 0.945863i | \(-0.394782\pi\) | ||||
0.324565 | + | 0.945863i | \(0.394782\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.27271e9 | −0.486597 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.30029e8 | −0.0275059 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.77640e9 | −0.580285 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.82025e8 | −0.0375911 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.17790e8 | 0.0240366 | 0.0120183 | − | 0.999928i | \(-0.496174\pi\) | ||||
0.0120183 | + | 0.999928i | \(0.496174\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.98818e8 | 0.140916 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.36200e9 | 0.669949 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.97185e8 | 0.196374 | 0.0981871 | − | 0.995168i | \(-0.468696\pi\) | ||||
0.0981871 | + | 0.995168i | \(0.468696\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.21251e9 | 0.819845 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.38989e9 | 0.267344 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.00115e9 | 0.190328 | 0.0951641 | − | 0.995462i | \(-0.469662\pi\) | ||||
0.0951641 | + | 0.995462i | \(0.469662\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.09863e9 | 0.394343 | 0.197172 | − | 0.980369i | \(-0.436824\pi\) | ||||
0.197172 | + | 0.980369i | \(0.436824\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.15798e9 | −0.215074 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.15735e9 | −1.68123 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.56157e9 | −1.19082 | −0.595411 | − | 0.803421i | \(-0.703011\pi\) | ||||
−0.595411 | + | 0.803421i | \(0.703011\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.99816e9 | −0.717299 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.67070e9 | 0.296316 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.41894e9 | 0.424144 | 0.212072 | − | 0.977254i | \(-0.431979\pi\) | ||||
0.212072 | + | 0.977254i | \(0.431979\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.79048e9 | 0.310389 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.05422e9 | −1.20907 | −0.604534 | − | 0.796579i | \(-0.706641\pi\) | ||||
−0.604534 | + | 0.796579i | \(0.706641\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.23254e9 | 0.886738 | 0.443369 | − | 0.896339i | \(-0.353783\pi\) | ||||
0.443369 | + | 0.896339i | \(0.353783\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.28739e9 | 0.383283 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.43235e9 | 1.23145 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.45882e8 | 0.0239014 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.63381e9 | −0.426726 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.09916e10 | −1.76111 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.89794e9 | −0.776088 | −0.388044 | − | 0.921641i | \(-0.626849\pi\) | ||||
−0.388044 | + | 0.921641i | \(0.626849\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.76417e8 | −0.105999 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.98074e9 | −0.306986 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.61016e8 | −0.0400110 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.90192e9 | 0.439980 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.62626e9 | 1.29366 | 0.646829 | − | 0.762635i | \(-0.276095\pi\) | ||||
0.646829 | + | 0.762635i | \(0.276095\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.94373e9 | −1.32672 | −0.663362 | − | 0.748299i | \(-0.730871\pi\) | ||||
−0.663362 | + | 0.748299i | \(0.730871\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.32028e9 | −0.633947 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.57546e9 | 0.954468 | 0.477234 | − | 0.878776i | \(-0.341639\pi\) | ||||
0.477234 | + | 0.878776i | \(0.341639\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.59550e10 | 2.29108 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.33003e9 | 0.188942 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.14306e9 | 0.301189 | 0.150594 | − | 0.988596i | \(-0.451881\pi\) | ||||
0.150594 | + | 0.988596i | \(0.451881\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.03156e9 | −1.11675 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.63649e9 | 0.362700 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.97182e8 | −0.108507 | −0.0542536 | − | 0.998527i | \(-0.517278\pi\) | ||||
−0.0542536 | + | 0.998527i | \(0.517278\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.11232e9 | −0.419159 | −0.209579 | − | 0.977792i | \(-0.567209\pi\) | ||||
−0.209579 | + | 0.977792i | \(0.567209\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.21847e9 | −0.162374 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.55967e9 | 0.205663 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.14190e10 | 2.79485 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.26985e9 | −0.938716 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.77016e9 | 1.24845 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.27827e9 | 0.288107 | 0.144053 | − | 0.989570i | \(-0.453986\pi\) | ||||
0.144053 | + | 0.989570i | \(0.453986\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.66731e8 | 0.120988 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.55138e9 | −1.18306 | −0.591529 | − | 0.806284i | \(-0.701475\pi\) | ||||
−0.591529 | + | 0.806284i | \(0.701475\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.91829e9 | 0.848115 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.67052e9 | −0.324027 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.27351e10 | 1.52943 | 0.764715 | − | 0.644369i | \(-0.222880\pi\) | ||||
0.764715 | + | 0.644369i | \(0.222880\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.57631e9 | 0.306253 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.77256e9 | −0.561569 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.75556e8 | −0.0553904 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.48449e10 | 1.71161 | 0.855804 | − | 0.517300i | \(-0.173063\pi\) | ||||
0.855804 | + | 0.517300i | \(0.173063\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.01283e9 | −0.572159 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.69053e8 | 0.0981972 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.19854e10 | 1.34072 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.20368e9 | 0.244050 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.56312e8 | 0.0719610 | 0.0359805 | − | 0.999352i | \(-0.488545\pi\) | ||||
0.0359805 | + | 0.999352i | \(0.488545\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.06962e9 | −0.441784 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.24092e9 | 0.563308 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.69963e9 | −0.393722 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.03120e9 | −0.319413 | −0.159706 | − | 0.987165i | \(-0.551055\pi\) | ||||
−0.159706 | + | 0.987165i | \(0.551055\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.10689e9 | 0.324177 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.12526e9 | −0.736186 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.13704e9 | −0.218646 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.31496e9 | −0.133228 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.92132e9 | −0.594111 | −0.297055 | − | 0.954860i | \(-0.596005\pi\) | ||||
−0.297055 | + | 0.954860i | \(0.596005\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.57331e9 | 0.156330 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.98566e9 | −0.589018 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.05242e9 | 0.882230 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.77984e10 | 1.71795 | 0.858975 | − | 0.512017i | \(-0.171102\pi\) | ||||
0.858975 | + | 0.512017i | \(0.171102\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.89198e10 | −2.73832 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.50247e9 | 0.516053 | 0.258026 | − | 0.966138i | \(-0.416928\pi\) | ||||
0.258026 | + | 0.966138i | \(0.416928\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.18795e8 | −0.0760623 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.35950e10 | −1.25096 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.95798e9 | 0.269613 | 0.134806 | − | 0.990872i | \(-0.456959\pi\) | ||||
0.134806 | + | 0.990872i | \(0.456959\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.51134e8 | −0.0407325 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.33970e9 | 0.388150 | 0.194075 | − | 0.980987i | \(-0.437830\pi\) | ||||
0.194075 | + | 0.980987i | \(0.437830\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.44557e9 | 0.836915 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.17984e8 | 0.0103562 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.33422e8 | 0.0202981 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.15573e10 | 0.995675 | 0.497838 | − | 0.867270i | \(-0.334128\pi\) | ||||
0.497838 | + | 0.867270i | \(0.334128\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.14802e9 | 0.439397 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.00877e9 | −0.592690 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.11105e10 | −0.930886 | −0.465443 | − | 0.885078i | \(-0.654105\pi\) | ||||
−0.465443 | + | 0.885078i | \(0.654105\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.68548e10 | 2.22934 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.48974e9 | 0.369297 | 0.184648 | − | 0.982805i | \(-0.440885\pi\) | ||||
0.184648 | + | 0.982805i | \(0.440885\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.64804e9 | 0.786327 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.82228e9 | −0.308679 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.73285e9 | 0.218692 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.08922e10 | −0.863720 | −0.431860 | − | 0.901941i | \(-0.642143\pi\) | ||||
−0.431860 | + | 0.901941i | \(0.642143\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.93528e9 | −0.387813 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.05575e10 | −1.60081 | −0.800407 | − | 0.599456i | \(-0.795383\pi\) | ||||
−0.800407 | + | 0.599456i | \(0.795383\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.01139e9 | −0.232386 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.74554e9 | −0.592350 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.43756e9 | 0.336328 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.40696e10 | 2.55911 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.62779e9 | 0.270070 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.10887e9 | −0.303164 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.87413e9 | 0.575826 | 0.287913 | − | 0.957657i | \(-0.407039\pi\) | ||||
0.287913 | + | 0.957657i | \(0.407039\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.13865e9 | −0.517424 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.75662e9 | −0.485413 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.67349e9 | 0.119170 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.49180e9 | −0.105299 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.81725e10 | −1.27148 | −0.635742 | − | 0.771901i | \(-0.719306\pi\) | ||||
−0.635742 | + | 0.771901i | \(0.719306\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.50826e10 | 2.43320 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.74384e9 | −0.463653 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.09534e10 | 2.10962 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.59026e10 | −1.07444 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.55626e8 | 0.0104238 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.56562e10 | 1.03960 | 0.519801 | − | 0.854288i | \(-0.326006\pi\) | ||||
0.519801 | + | 0.854288i | \(0.326006\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.03230e8 | 0.0462940 | 0.0231470 | − | 0.999732i | \(-0.492631\pi\) | ||||
0.0231470 | + | 0.999732i | \(0.492631\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.22620e9 | −0.0800284 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.09351e8 | 0.0329583 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.07075e10 | −0.686925 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.58624e8 | −0.0546147 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.08592e10 | −0.684850 | −0.342425 | − | 0.939545i | \(-0.611248\pi\) | ||||
−0.342425 | + | 0.939545i | \(0.611248\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.05577e10 | −1.91083 | −0.955414 | − | 0.295271i | \(-0.904590\pi\) | ||||
−0.955414 | + | 0.295271i | \(0.904590\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.13498e10 | 0.703718 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.12107e10 | −0.689229 | −0.344615 | − | 0.938744i | \(-0.611990\pi\) | ||||
−0.344615 | + | 0.938744i | \(0.611990\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.11945e9 | 0.373054 | 0.186527 | − | 0.982450i | \(-0.440277\pi\) | ||||
0.186527 | + | 0.982450i | \(0.440277\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.90015e9 | −0.417114 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.48099e9 | −0.328550 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.95174e9 | −0.532114 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.20682e9 | −0.0711384 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.99122e10 | −1.74856 | −0.874282 | − | 0.485419i | \(-0.838667\pi\) | ||||
−0.874282 | + | 0.485419i | \(0.838667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.67205e10 | 0.969314 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.23789e9 | −0.186151 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.03215e10 | 0.588496 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.31959e10 | −2.44259 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.01809e10 | −0.570967 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.14945e10 | 2.30801 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.07207e10 | 1.14310 | 0.571548 | − | 0.820569i | \(-0.306343\pi\) | ||||
0.571548 | + | 0.820569i | \(0.306343\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.41519e9 | −0.0774341 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.36122e10 | 0.738744 | 0.369372 | − | 0.929282i | \(-0.379573\pi\) | ||||
0.369372 | + | 0.929282i | \(0.379573\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.64286e10 | 0.884351 | 0.442175 | − | 0.896929i | \(-0.354207\pi\) | ||||
0.442175 | + | 0.896929i | \(0.354207\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.44582e9 | 0.450952 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.78780e10 | 0.946849 | 0.473425 | − | 0.880834i | \(-0.343018\pi\) | ||||
0.473425 | + | 0.880834i | \(0.343018\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.22126e10 | 1.16692 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.45071e10 | −0.755984 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.64760e10 | 1.88555 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.32863e9 | −0.119409 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.27740e9 | −0.319323 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.74118e10 | −0.878649 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.42965e9 | −0.472060 | −0.236030 | − | 0.971746i | \(-0.575846\pi\) | ||||
−0.236030 | + | 0.971746i | \(0.575846\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.25470e10 | −0.623128 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.21077e10 | −1.58195 | −0.790977 | − | 0.611845i | \(-0.790428\pi\) | ||||
−0.790977 | + | 0.611845i | \(0.790428\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.75025e10 | −0.855533 | −0.427766 | − | 0.903889i | \(-0.640699\pi\) | ||||
−0.427766 | + | 0.903889i | \(0.640699\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.57283e9 | 0.415741 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.00901e10 | 1.44774 | 0.723870 | − | 0.689937i | \(-0.242362\pi\) | ||||
0.723870 | + | 0.689937i | \(0.242362\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.34328e9 | −0.446009 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.54846e9 | 0.215423 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.29892e10 | 0.610383 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.84089e9 | −0.272332 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.59983e9 | 0.212798 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.13006e10 | −0.518733 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.98605e9 | −0.454838 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.03791e10 | −0.921038 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.77341e8 | 0.00795313 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.55723e10 | −0.692990 | −0.346495 | − | 0.938052i | \(-0.612628\pi\) | ||||
−0.346495 | + | 0.938052i | \(0.612628\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.35690e9 | 0.148240 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.98356e10 | 0.869221 | 0.434610 | − | 0.900619i | \(-0.356886\pi\) | ||||
0.434610 | + | 0.900619i | \(0.356886\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.38517e9 | 0.0602361 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.24965e9 | 0.226546 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.78855e10 | −1.62248 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.00319e10 | −0.426360 | −0.213180 | − | 0.977013i | \(-0.568382\pi\) | ||||
−0.213180 | + | 0.977013i | \(0.568382\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.89944e9 | 0.333186 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.83563e9 | 0.244277 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.75370e10 | 0.728551 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.42756e9 | −0.0588595 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.95372e9 | −0.407315 | −0.203657 | − | 0.979042i | \(-0.565283\pi\) | ||||
−0.203657 | + | 0.979042i | \(0.565283\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.02932e9 | −0.0824188 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.28539e9 | 0.0921244 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.48749e10 | −1.79541 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.47369e10 | −0.982327 | −0.491163 | − | 0.871068i | \(-0.663428\pi\) | ||||
−0.491163 | + | 0.871068i | \(0.663428\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.61577e9 | −0.260766 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.39100e10 | −1.32667 | −0.663337 | − | 0.748321i | \(-0.730860\pi\) | ||||
−0.663337 | + | 0.748321i | \(0.730860\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.52460e10 | −1.75707 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.69346e9 | −0.103825 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.03467e10 | −1.16115 | −0.580573 | − | 0.814208i | \(-0.697172\pi\) | ||||
−0.580573 | + | 0.814208i | \(0.697172\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.30186e9 | 0.201371 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.47543e10 | 0.933296 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.43307e10 | 1.65913 | 0.829564 | − | 0.558412i | \(-0.188589\pi\) | ||||
0.829564 | + | 0.558412i | \(0.188589\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.82758e10 | −0.678990 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.25915e10 | 1.57084 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.21526e10 | 0.444944 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.37533e10 | −0.863362 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.11799e8 | −0.00764242 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.43369e10 | −0.513580 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.65095e10 | 1.29841 | 0.649207 | − | 0.760612i | \(-0.275101\pi\) | ||||
0.649207 | + | 0.760612i | \(0.275101\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.47321e9 | −0.334475 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.35243e10 | −0.824612 | −0.412306 | − | 0.911046i | \(-0.635276\pi\) | ||||
−0.412306 | + | 0.911046i | \(0.635276\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.09939e9 | 0.142667 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.94405e9 | 0.0671725 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.90818e10 | −0.997679 | −0.498840 | − | 0.866694i | \(-0.666240\pi\) | ||||
−0.498840 | + | 0.866694i | \(0.666240\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.91751e10 | −2.69680 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.75428e9 | −0.296059 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.81209e10 | −0.944259 | −0.472130 | − | 0.881529i | \(-0.656515\pi\) | ||||
−0.472130 | + | 0.881529i | \(0.656515\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.12084e10 | 0.707100 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.47218e10 | 0.818409 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.09175e11 | 3.58869 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.76726e10 | 0.576822 | 0.288411 | − | 0.957507i | \(-0.406873\pi\) | ||||
0.288411 | + | 0.957507i | \(0.406873\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.33064e10 | −0.755359 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.76778e9 | 0.282169 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.23958e10 | 1.03528 | 0.517638 | − | 0.855600i | \(-0.326811\pi\) | ||||
0.517638 | + | 0.855600i | \(0.326811\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.02802e9 | 0.223025 |
(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 | 384.8.a.n.1.2 | ✓ | 4 | |
4.3 | odd | 2 | 384.8.a.r.1.2 | yes | 4 | ||
8.3 | odd | 2 | 384.8.a.o.1.3 | yes | 4 | ||
8.5 | even | 2 | 384.8.a.s.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.8.a.n.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
384.8.a.o.1.3 | yes | 4 | 8.3 | odd | 2 | ||
384.8.a.r.1.2 | yes | 4 | 4.3 | odd | 2 | ||
384.8.a.s.1.3 | yes | 4 | 8.5 | even | 2 |