Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,6,Mod(1,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("441.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(70.7292645375\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{39}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 39 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 49) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(6.24500\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.353553 | 0.176777 | − | 0.984251i | \(-0.443433\pi\) | ||||
0.176777 | + | 0.984251i | \(0.443433\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −28.0000 | −0.875000 | ||||||||
\(5\) | −74.9400 | −1.34057 | −0.670284 | − | 0.742105i | \(-0.733828\pi\) | ||||
−0.670284 | + | 0.742105i | \(0.733828\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −120.000 | −0.662913 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −149.880 | −0.473962 | ||||||||
\(11\) | 284.000 | 0.707680 | 0.353840 | − | 0.935306i | \(-0.384876\pi\) | ||||
0.353840 | + | 0.935306i | \(0.384876\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 524.580 | 0.860901 | 0.430450 | − | 0.902614i | \(-0.358355\pi\) | ||||
0.430450 | + | 0.902614i | \(0.358355\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 656.000 | 0.640625 | ||||||||
\(17\) | 149.880 | 0.125783 | 0.0628914 | − | 0.998020i | \(-0.479968\pi\) | ||||
0.0628914 | + | 0.998020i | \(0.479968\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2173.26 | 1.38111 | 0.690554 | − | 0.723281i | \(-0.257367\pi\) | ||||
0.690554 | + | 0.723281i | \(0.257367\pi\) | |||||||
\(20\) | 2098.32 | 1.17300 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 568.000 | 0.250202 | ||||||||
\(23\) | −1496.00 | −0.589674 | −0.294837 | − | 0.955548i | \(-0.595265\pi\) | ||||
−0.294837 | + | 0.955548i | \(0.595265\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2491.00 | 0.797120 | ||||||||
\(26\) | 1049.16 | 0.304374 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4366.00 | 0.964026 | 0.482013 | − | 0.876164i | \(-0.339906\pi\) | ||||
0.482013 | + | 0.876164i | \(0.339906\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6444.84 | −1.20450 | −0.602251 | − | 0.798307i | \(-0.705729\pi\) | ||||
−0.602251 | + | 0.798307i | \(0.705729\pi\) | |||||||
\(32\) | 5152.00 | 0.889408 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 299.760 | 0.0444709 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −12630.0 | −1.51670 | −0.758349 | − | 0.651849i | \(-0.773994\pi\) | ||||
−0.758349 | + | 0.651849i | \(0.773994\pi\) | |||||||
\(38\) | 4346.52 | 0.488295 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8992.80 | 0.888679 | ||||||||
\(41\) | 9442.44 | 0.877252 | 0.438626 | − | 0.898670i | \(-0.355465\pi\) | ||||
0.438626 | + | 0.898670i | \(0.355465\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1356.00 | −0.111838 | −0.0559189 | − | 0.998435i | \(-0.517809\pi\) | ||||
−0.0559189 | + | 0.998435i | \(0.517809\pi\) | |||||||
\(44\) | −7952.00 | −0.619220 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2992.00 | −0.208481 | ||||||||
\(47\) | −10042.0 | −0.663092 | −0.331546 | − | 0.943439i | \(-0.607570\pi\) | ||||
−0.331546 | + | 0.943439i | \(0.607570\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4982.00 | 0.281824 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −14688.2 | −0.753288 | ||||||||
\(53\) | −14150.0 | −0.691937 | −0.345969 | − | 0.938246i | \(-0.612450\pi\) | ||||
−0.345969 | + | 0.938246i | \(0.612450\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −21283.0 | −0.948692 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8732.00 | 0.340835 | ||||||||
\(59\) | 37395.0 | 1.39857 | 0.699285 | − | 0.714843i | \(-0.253502\pi\) | ||||
0.699285 | + | 0.714843i | \(0.253502\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −35596.5 | −1.22485 | −0.612425 | − | 0.790529i | \(-0.709806\pi\) | ||||
−0.612425 | + | 0.790529i | \(0.709806\pi\) | |||||||
\(62\) | −12889.7 | −0.425856 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10688.0 | −0.326172 | ||||||||
\(65\) | −39312.0 | −1.15410 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3644.00 | −0.0991725 | −0.0495863 | − | 0.998770i | \(-0.515790\pi\) | ||||
−0.0495863 | + | 0.998770i | \(0.515790\pi\) | |||||||
\(68\) | −4196.64 | −0.110060 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −35632.0 | −0.838869 | −0.419435 | − | 0.907786i | \(-0.637772\pi\) | ||||
−0.419435 | + | 0.907786i | \(0.637772\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 40767.3 | 0.895376 | 0.447688 | − | 0.894190i | \(-0.352248\pi\) | ||||
0.447688 | + | 0.894190i | \(0.352248\pi\) | |||||||
\(74\) | −25260.0 | −0.536234 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −60851.3 | −1.20847 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −54616.0 | −0.984583 | −0.492291 | − | 0.870431i | \(-0.663841\pi\) | ||||
−0.492291 | + | 0.870431i | \(0.663841\pi\) | |||||||
\(80\) | −49160.6 | −0.858801 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 18884.9 | 0.310155 | ||||||||
\(83\) | 524.580 | 0.00835827 | 0.00417913 | − | 0.999991i | \(-0.498670\pi\) | ||||
0.00417913 | + | 0.999991i | \(0.498670\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11232.0 | −0.168620 | ||||||||
\(86\) | −2712.00 | −0.0395406 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −34080.0 | −0.469130 | ||||||||
\(89\) | 20383.7 | 0.272777 | 0.136388 | − | 0.990655i | \(-0.456450\pi\) | ||||
0.136388 | + | 0.990655i | \(0.456450\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 41888.0 | 0.515965 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −20083.9 | −0.234438 | ||||||||
\(95\) | −162864. | −1.85147 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 183603. | 1.98130 | 0.990650 | − | 0.136427i | \(-0.0435619\pi\) | ||||
0.990650 | + | 0.136427i | \(0.0435619\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −69748.0 | −0.697480 | ||||||||
\(101\) | −75914.2 | −0.740491 | −0.370245 | − | 0.928934i | \(-0.620726\pi\) | ||||
−0.370245 | + | 0.928934i | \(0.620726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10941.2 | −0.101619 | −0.0508093 | − | 0.998708i | \(-0.516180\pi\) | ||||
−0.0508093 | + | 0.998708i | \(0.516180\pi\) | |||||||
\(104\) | −62949.6 | −0.570702 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −28300.0 | −0.244637 | ||||||||
\(107\) | −218188. | −1.84235 | −0.921173 | − | 0.389152i | \(-0.872768\pi\) | ||||
−0.921173 | + | 0.389152i | \(0.872768\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −96030.0 | −0.774178 | −0.387089 | − | 0.922042i | \(-0.626519\pi\) | ||||
−0.387089 | + | 0.922042i | \(0.626519\pi\) | |||||||
\(110\) | −42565.9 | −0.335413 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 137422. | 1.01242 | 0.506209 | − | 0.862411i | \(-0.331046\pi\) | ||||
0.506209 | + | 0.862411i | \(0.331046\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 112110. | 0.790498 | ||||||||
\(116\) | −122248. | −0.843523 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 74790.1 | 0.494469 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −80395.0 | −0.499190 | ||||||||
\(122\) | −71193.0 | −0.433050 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 180455. | 1.05394 | ||||||||
\(125\) | 47511.9 | 0.271974 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 170368. | 0.937300 | 0.468650 | − | 0.883384i | \(-0.344741\pi\) | ||||
0.468650 | + | 0.883384i | \(0.344741\pi\) | |||||||
\(128\) | −186240. | −1.00473 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −78624.0 | −0.408034 | ||||||||
\(131\) | 348246. | 1.77300 | 0.886498 | − | 0.462732i | \(-0.153131\pi\) | ||||
0.886498 | + | 0.462732i | \(0.153131\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −7288.00 | −0.0350628 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −17985.6 | −0.0833830 | ||||||||
\(137\) | 75562.0 | 0.343955 | 0.171978 | − | 0.985101i | \(-0.444984\pi\) | ||||
0.171978 | + | 0.985101i | \(0.444984\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 97047.3 | 0.426036 | 0.213018 | − | 0.977048i | \(-0.431671\pi\) | ||||
0.213018 | + | 0.977048i | \(0.431671\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −71264.0 | −0.296585 | ||||||||
\(143\) | 148981. | 0.609242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −327188. | −1.29234 | ||||||||
\(146\) | 81534.7 | 0.316563 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 353640. | 1.32711 | ||||||||
\(149\) | −361030. | −1.33223 | −0.666113 | − | 0.745851i | \(-0.732043\pi\) | ||||
−0.666113 | + | 0.745851i | \(0.732043\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 32280.0 | 0.115210 | 0.0576051 | − | 0.998339i | \(-0.481654\pi\) | ||||
0.0576051 | + | 0.998339i | \(0.481654\pi\) | |||||||
\(152\) | −260791. | −0.915554 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 482976. | 1.61472 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −132869. | −0.430203 | −0.215101 | − | 0.976592i | \(-0.569008\pi\) | ||||
−0.215101 | + | 0.976592i | \(0.569008\pi\) | |||||||
\(158\) | −109232. | −0.348103 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −386091. | −1.19231 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −61364.0 | −0.180903 | −0.0904513 | − | 0.995901i | \(-0.528831\pi\) | ||||
−0.0904513 | + | 0.995901i | \(0.528831\pi\) | |||||||
\(164\) | −264388. | −0.767596 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1049.16 | 0.00295509 | ||||||||
\(167\) | −380845. | −1.05671 | −0.528356 | − | 0.849023i | \(-0.677192\pi\) | ||||
−0.528356 | + | 0.849023i | \(0.677192\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −96109.0 | −0.258849 | ||||||||
\(170\) | −22464.0 | −0.0596163 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 37968.0 | 0.0978581 | ||||||||
\(173\) | −517311. | −1.31412 | −0.657062 | − | 0.753837i | \(-0.728201\pi\) | ||||
−0.657062 | + | 0.753837i | \(0.728201\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 186304. | 0.453357 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 40767.3 | 0.0964412 | ||||||||
\(179\) | −610564. | −1.42429 | −0.712145 | − | 0.702032i | \(-0.752276\pi\) | ||||
−0.712145 | + | 0.702032i | \(0.752276\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −433828. | −0.984285 | −0.492142 | − | 0.870515i | \(-0.663786\pi\) | ||||
−0.492142 | + | 0.870515i | \(0.663786\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 179520. | 0.390902 | ||||||||
\(185\) | 946492. | 2.03324 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 42565.9 | 0.0890139 | ||||||||
\(188\) | 281175. | 0.580205 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −325728. | −0.654593 | ||||||||
\(191\) | −341192. | −0.676730 | −0.338365 | − | 0.941015i | \(-0.609874\pi\) | ||||
−0.338365 | + | 0.941015i | \(0.609874\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −616158. | −1.19069 | −0.595345 | − | 0.803470i | \(-0.702985\pi\) | ||||
−0.595345 | + | 0.803470i | \(0.702985\pi\) | |||||||
\(194\) | 367206. | 0.700495 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −231478. | −0.424956 | −0.212478 | − | 0.977166i | \(-0.568153\pi\) | ||||
−0.212478 | + | 0.977166i | \(0.568153\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −405126. | −0.725199 | −0.362599 | − | 0.931945i | \(-0.618111\pi\) | ||||
−0.362599 | + | 0.931945i | \(0.618111\pi\) | |||||||
\(200\) | −298920. | −0.528421 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −151828. | −0.261803 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −707616. | −1.17602 | ||||||||
\(206\) | −21882.5 | −0.0359276 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 344124. | 0.551515 | ||||||||
\(209\) | 617206. | 0.977382 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 776820. | 1.20120 | 0.600599 | − | 0.799551i | \(-0.294929\pi\) | ||||
0.600599 | + | 0.799551i | \(0.294929\pi\) | |||||||
\(212\) | 396200. | 0.605445 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −436376. | −0.651368 | ||||||||
\(215\) | 101619. | 0.149926 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −192060. | −0.273713 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 595923. | 0.830105 | ||||||||
\(221\) | 78624.0 | 0.108287 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 81834.5 | 0.110198 | 0.0550990 | − | 0.998481i | \(-0.482453\pi\) | ||||
0.0550990 | + | 0.998481i | \(0.482453\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 274844. | 0.357944 | ||||||||
\(227\) | −753671. | −0.970772 | −0.485386 | − | 0.874300i | \(-0.661321\pi\) | ||||
−0.485386 | + | 0.874300i | \(0.661321\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26303.9 | 0.0331461 | 0.0165730 | − | 0.999863i | \(-0.494724\pi\) | ||||
0.0165730 | + | 0.999863i | \(0.494724\pi\) | |||||||
\(230\) | 224220. | 0.279483 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −523920. | −0.639065 | ||||||||
\(233\) | −47542.0 | −0.0573704 | −0.0286852 | − | 0.999588i | \(-0.509132\pi\) | ||||
−0.0286852 | + | 0.999588i | \(0.509132\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 752544. | 0.888919 | ||||||||
\(236\) | −1.04706e6 | −1.22375 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.08899e6 | −1.23319 | −0.616595 | − | 0.787281i | \(-0.711488\pi\) | ||||
−0.616595 | + | 0.787281i | \(0.711488\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.34937e6 | −1.49654 | −0.748270 | − | 0.663395i | \(-0.769115\pi\) | ||||
−0.748270 | + | 0.663395i | \(0.769115\pi\) | |||||||
\(242\) | −160790. | −0.176490 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 996702. | 1.07174 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.14005e6 | 1.18900 | ||||||||
\(248\) | 773381. | 0.798480 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 95023.9 | 0.0961574 | ||||||||
\(251\) | −630020. | −0.631205 | −0.315602 | − | 0.948892i | \(-0.602207\pi\) | ||||
−0.315602 | + | 0.948892i | \(0.602207\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −424864. | −0.417300 | ||||||||
\(254\) | 340736. | 0.331386 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −30464.0 | −0.0290527 | ||||||||
\(257\) | 1.93405e6 | 1.82656 | 0.913282 | − | 0.407327i | \(-0.133539\pi\) | ||||
0.913282 | + | 0.407327i | \(0.133539\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.10074e6 | 1.00983 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 696492. | 0.626849 | ||||||||
\(263\) | 1.11712e6 | 0.995888 | 0.497944 | − | 0.867209i | \(-0.334089\pi\) | ||||
0.497944 | + | 0.867209i | \(0.334089\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.06040e6 | 0.927588 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 102032. | 0.0867760 | ||||||||
\(269\) | −1.52061e6 | −1.28126 | −0.640629 | − | 0.767851i | \(-0.721326\pi\) | ||||
−0.640629 | + | 0.767851i | \(0.721326\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.02038e6 | 0.843995 | 0.421997 | − | 0.906597i | \(-0.361329\pi\) | ||||
0.421997 | + | 0.906597i | \(0.361329\pi\) | |||||||
\(272\) | 98321.2 | 0.0805796 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 151124. | 0.121607 | ||||||||
\(275\) | 707444. | 0.564105 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.89642e6 | 1.48503 | 0.742516 | − | 0.669829i | \(-0.233633\pi\) | ||||
0.742516 | + | 0.669829i | \(0.233633\pi\) | |||||||
\(278\) | 194095. | 0.150626 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.31911e6 | −0.996587 | −0.498293 | − | 0.867008i | \(-0.666040\pi\) | ||||
−0.498293 | + | 0.867008i | \(0.666040\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 478792. | 0.355370 | 0.177685 | − | 0.984087i | \(-0.443139\pi\) | ||||
0.177685 | + | 0.984087i | \(0.443139\pi\) | |||||||
\(284\) | 997696. | 0.734011 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 297961. | 0.215400 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.39739e6 | −0.984179 | ||||||||
\(290\) | −654376. | −0.456912 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.14149e6 | −0.783454 | ||||||||
\(293\) | −1.50187e6 | −1.02203 | −0.511015 | − | 0.859572i | \(-0.670730\pi\) | ||||
−0.511015 | + | 0.859572i | \(0.670730\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.80238e6 | −1.87488 | ||||||||
\(296\) | 1.51560e6 | 1.00544 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −722060. | −0.471013 | ||||||||
\(299\) | −784771. | −0.507651 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 64560.0 | 0.0407330 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.42566e6 | 0.884772 | ||||||||
\(305\) | 2.66760e6 | 1.64199 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.19657e6 | −0.724588 | −0.362294 | − | 0.932064i | \(-0.618006\pi\) | ||||
−0.362294 | + | 0.932064i | \(0.618006\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 965952. | 0.570889 | ||||||||
\(311\) | 1.31475e6 | 0.770799 | 0.385400 | − | 0.922750i | \(-0.374064\pi\) | ||||
0.385400 | + | 0.922750i | \(0.374064\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.65273e6 | −1.53049 | −0.765247 | − | 0.643737i | \(-0.777383\pi\) | ||||
−0.765247 | + | 0.643737i | \(0.777383\pi\) | |||||||
\(314\) | −265737. | −0.152100 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.52925e6 | 0.861510 | ||||||||
\(317\) | 1.59992e6 | 0.894233 | 0.447116 | − | 0.894476i | \(-0.352451\pi\) | ||||
0.447116 | + | 0.894476i | \(0.352451\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.23994e6 | 0.682221 | ||||||||
\(320\) | 800958. | 0.437255 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 325728. | 0.173720 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.30673e6 | 0.686241 | ||||||||
\(326\) | −122728. | −0.0639587 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.13309e6 | −0.581542 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −111708. | −0.0560421 | −0.0280210 | − | 0.999607i | \(-0.508921\pi\) | ||||
−0.0280210 | + | 0.999607i | \(0.508921\pi\) | |||||||
\(332\) | −14688.2 | −0.00731349 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −761690. | −0.373604 | ||||||||
\(335\) | 273081. | 0.132947 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.59301e6 | 0.764087 | 0.382043 | − | 0.924144i | \(-0.375220\pi\) | ||||
0.382043 | + | 0.924144i | \(0.375220\pi\) | |||||||
\(338\) | −192218. | −0.0915171 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 314496. | 0.147543 | ||||||||
\(341\) | −1.83033e6 | −0.852402 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 162720. | 0.0741387 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.03462e6 | −0.464613 | ||||||||
\(347\) | 3.33676e6 | 1.48765 | 0.743827 | − | 0.668372i | \(-0.233009\pi\) | ||||
0.743827 | + | 0.668372i | \(0.233009\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.60259e6 | −0.704303 | −0.352151 | − | 0.935943i | \(-0.614550\pi\) | ||||
−0.352151 | + | 0.935943i | \(0.614550\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.46317e6 | 0.629416 | ||||||||
\(353\) | −1.80965e6 | −0.772962 | −0.386481 | − | 0.922297i | \(-0.626309\pi\) | ||||
−0.386481 | + | 0.922297i | \(0.626309\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.67026e6 | 1.12456 | ||||||||
\(356\) | −570743. | −0.238680 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.22113e6 | −0.503563 | ||||||||
\(359\) | −920792. | −0.377073 | −0.188536 | − | 0.982066i | \(-0.560374\pi\) | ||||
−0.188536 | + | 0.982066i | \(0.560374\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.24696e6 | 0.907458 | ||||||||
\(362\) | −867655. | −0.347997 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.05510e6 | −1.20031 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.34802e6 | 0.522434 | 0.261217 | − | 0.965280i | \(-0.415876\pi\) | ||||
0.261217 | + | 0.965280i | \(0.415876\pi\) | |||||||
\(368\) | −981376. | −0.377760 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.89298e6 | 0.718857 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.13773e6 | 1.16773 | 0.583867 | − | 0.811849i | \(-0.301539\pi\) | ||||
0.583867 | + | 0.811849i | \(0.301539\pi\) | |||||||
\(374\) | 85131.8 | 0.0314712 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.20503e6 | 0.439572 | ||||||||
\(377\) | 2.29032e6 | 0.829931 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.83188e6 | −0.655088 | −0.327544 | − | 0.944836i | \(-0.606221\pi\) | ||||
−0.327544 | + | 0.944836i | \(0.606221\pi\) | |||||||
\(380\) | 4.56019e6 | 1.62003 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −682384. | −0.239260 | ||||||||
\(383\) | 27727.8 | 0.00965869 | 0.00482935 | − | 0.999988i | \(-0.498463\pi\) | ||||
0.00482935 | + | 0.999988i | \(0.498463\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.23232e6 | −0.420973 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.14088e6 | −1.73364 | ||||||||
\(389\) | 548342. | 0.183729 | 0.0918645 | − | 0.995772i | \(-0.470717\pi\) | ||||
0.0918645 | + | 0.995772i | \(0.470717\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −224220. | −0.0741708 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −462956. | −0.150245 | ||||||||
\(395\) | 4.09292e6 | 1.31990 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −403852. | −0.128601 | −0.0643007 | − | 0.997931i | \(-0.520482\pi\) | ||||
−0.0643007 | + | 0.997931i | \(0.520482\pi\) | |||||||
\(398\) | −810251. | −0.256396 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.63410e6 | 0.510655 | ||||||||
\(401\) | 4.16427e6 | 1.29324 | 0.646619 | − | 0.762813i | \(-0.276182\pi\) | ||||
0.646619 | + | 0.762813i | \(0.276182\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.38083e6 | −1.03696 | ||||||||
\(404\) | 2.12560e6 | 0.647929 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.58692e6 | −1.07334 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.54121e6 | −0.751161 | −0.375581 | − | 0.926790i | \(-0.622557\pi\) | ||||
−0.375581 | + | 0.926790i | \(0.622557\pi\) | |||||||
\(410\) | −1.41523e6 | −0.415784 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 306355. | 0.0889163 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −39312.0 | −0.0112048 | ||||||||
\(416\) | 2.70264e6 | 0.765692 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.23441e6 | 0.345557 | ||||||||
\(419\) | 2.30133e6 | 0.640389 | 0.320195 | − | 0.947352i | \(-0.396252\pi\) | ||||
0.320195 | + | 0.947352i | \(0.396252\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.79991e6 | −0.769909 | −0.384955 | − | 0.922936i | \(-0.625783\pi\) | ||||
−0.384955 | + | 0.922936i | \(0.625783\pi\) | |||||||
\(422\) | 1.55364e6 | 0.424687 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.69800e6 | 0.458694 | ||||||||
\(425\) | 373351. | 0.100264 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.10926e6 | 1.61205 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 203237. | 0.0530069 | ||||||||
\(431\) | −954320. | −0.247458 | −0.123729 | − | 0.992316i | \(-0.539485\pi\) | ||||
−0.123729 | + | 0.992316i | \(0.539485\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 519334. | 0.133115 | 0.0665575 | − | 0.997783i | \(-0.478798\pi\) | ||||
0.0665575 | + | 0.997783i | \(0.478798\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.68884e6 | 0.677406 | ||||||||
\(437\) | −3.25120e6 | −0.814403 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.98081e6 | 1.48115 | 0.740574 | − | 0.671974i | \(-0.234554\pi\) | ||||
0.740574 | + | 0.671974i | \(0.234554\pi\) | |||||||
\(440\) | 2.55395e6 | 0.628900 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 157248. | 0.0382851 | ||||||||
\(443\) | −3.74820e6 | −0.907432 | −0.453716 | − | 0.891146i | \(-0.649902\pi\) | ||||
−0.453716 | + | 0.891146i | \(0.649902\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.52755e6 | −0.365676 | ||||||||
\(446\) | 163669. | 0.0389609 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −99458.0 | −0.0232822 | −0.0116411 | − | 0.999932i | \(-0.503706\pi\) | ||||
−0.0116411 | + | 0.999932i | \(0.503706\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.68165e6 | 0.620813 | ||||||||
\(452\) | −3.84782e6 | −0.885866 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.50734e6 | −0.343220 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −161814. | −0.0362431 | −0.0181216 | − | 0.999836i | \(-0.505769\pi\) | ||||
−0.0181216 | + | 0.999836i | \(0.505769\pi\) | |||||||
\(458\) | 52607.9 | 0.0117189 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.13909e6 | −0.691685 | ||||||||
\(461\) | 4.49198e6 | 0.984431 | 0.492215 | − | 0.870473i | \(-0.336187\pi\) | ||||
0.492215 | + | 0.870473i | \(0.336187\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.59382e6 | 0.779118 | 0.389559 | − | 0.921001i | \(-0.372627\pi\) | ||||
0.389559 | + | 0.921001i | \(0.372627\pi\) | |||||||
\(464\) | 2.86410e6 | 0.617579 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −95084.0 | −0.0202835 | ||||||||
\(467\) | −2.05223e6 | −0.435446 | −0.217723 | − | 0.976011i | \(-0.569863\pi\) | ||||
−0.217723 | + | 0.976011i | \(0.569863\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.50509e6 | 0.314280 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.48741e6 | −0.927129 | ||||||||
\(473\) | −385104. | −0.0791453 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.41359e6 | 1.10091 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.17798e6 | −0.435998 | ||||||||
\(479\) | 1.99985e6 | 0.398252 | 0.199126 | − | 0.979974i | \(-0.436190\pi\) | ||||
0.199126 | + | 0.979974i | \(0.436190\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.62544e6 | −1.30573 | ||||||||
\(482\) | −2.69874e6 | −0.529107 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.25106e6 | 0.436791 | ||||||||
\(485\) | −1.37592e7 | −2.65607 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.17126e6 | 0.414848 | 0.207424 | − | 0.978251i | \(-0.433492\pi\) | ||||
0.207424 | + | 0.978251i | \(0.433492\pi\) | |||||||
\(488\) | 4.27158e6 | 0.811968 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.04555e6 | −0.570114 | −0.285057 | − | 0.958511i | \(-0.592013\pi\) | ||||
−0.285057 | + | 0.958511i | \(0.592013\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 654376. | 0.121258 | ||||||||
\(494\) | 2.28010e6 | 0.420374 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.22781e6 | −0.771635 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.99225e6 | −1.43687 | −0.718436 | − | 0.695594i | \(-0.755141\pi\) | ||||
−0.718436 | + | 0.695594i | \(0.755141\pi\) | |||||||
\(500\) | −1.33033e6 | −0.237977 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.26004e6 | −0.223165 | ||||||||
\(503\) | −9.47811e6 | −1.67033 | −0.835164 | − | 0.550001i | \(-0.814627\pi\) | ||||
−0.835164 | + | 0.550001i | \(0.814627\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.68901e6 | 0.992677 | ||||||||
\(506\) | −849728. | −0.147538 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.77030e6 | −0.820138 | ||||||||
\(509\) | −1.01003e7 | −1.72799 | −0.863995 | − | 0.503500i | \(-0.832045\pi\) | ||||
−0.863995 | + | 0.503500i | \(0.832045\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 5.89875e6 | 0.994455 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.86810e6 | 0.645788 | ||||||||
\(515\) | 819936. | 0.136227 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.85192e6 | −0.469257 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.71744e6 | 0.765064 | ||||||||
\(521\) | −5.11975e6 | −0.826332 | −0.413166 | − | 0.910656i | \(-0.635577\pi\) | ||||
−0.413166 | + | 0.910656i | \(0.635577\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.51476e6 | 0.561877 | 0.280939 | − | 0.959726i | \(-0.409354\pi\) | ||||
0.280939 | + | 0.959726i | \(0.409354\pi\) | |||||||
\(524\) | −9.75089e6 | −1.55137 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.23424e6 | 0.352100 | ||||||||
\(527\) | −965952. | −0.151506 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.19833e6 | −0.652285 | ||||||||
\(530\) | 2.12080e6 | 0.327952 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.95331e6 | 0.755227 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.63510e7 | 2.46979 | ||||||||
\(536\) | 437280. | 0.0657427 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.04121e6 | −0.452993 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.47547e6 | −0.510530 | −0.255265 | − | 0.966871i | \(-0.582163\pi\) | ||||
−0.255265 | + | 0.966871i | \(0.582163\pi\) | |||||||
\(542\) | 2.04077e6 | 0.298397 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 772182. | 0.111872 | ||||||||
\(545\) | 7.19649e6 | 1.03784 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.85765e6 | −1.12286 | −0.561429 | − | 0.827525i | \(-0.689748\pi\) | ||||
−0.561429 | + | 0.827525i | \(0.689748\pi\) | |||||||
\(548\) | −2.11574e6 | −0.300961 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.41489e6 | 0.199441 | ||||||||
\(551\) | 9.48845e6 | 1.33142 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.79284e6 | 0.525038 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.71732e6 | −0.372782 | ||||||||
\(557\) | −9.06537e6 | −1.23808 | −0.619039 | − | 0.785361i | \(-0.712478\pi\) | ||||
−0.619039 | + | 0.785361i | \(0.712478\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −711330. | −0.0962813 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.63822e6 | −0.352347 | ||||||||
\(563\) | −5.80957e6 | −0.772455 | −0.386227 | − | 0.922404i | \(-0.626222\pi\) | ||||
−0.386227 | + | 0.922404i | \(0.626222\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.02984e7 | −1.35722 | ||||||||
\(566\) | 957583. | 0.125642 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.27584e6 | 0.556097 | ||||||||
\(569\) | −1.05559e7 | −1.36684 | −0.683418 | − | 0.730027i | \(-0.739507\pi\) | ||||
−0.683418 | + | 0.730027i | \(0.739507\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.99584e6 | 1.02630 | 0.513150 | − | 0.858299i | \(-0.328479\pi\) | ||||
0.513150 | + | 0.858299i | \(0.328479\pi\) | |||||||
\(572\) | −4.17146e6 | −0.533087 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.72654e6 | −0.470041 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.60941e6 | −0.326289 | −0.163145 | − | 0.986602i | \(-0.552164\pi\) | ||||
−0.163145 | + | 0.986602i | \(0.552164\pi\) | |||||||
\(578\) | −2.79479e6 | −0.347960 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.16126e6 | 1.13080 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.01860e6 | −0.489670 | ||||||||
\(584\) | −4.89208e6 | −0.593556 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.00374e6 | −0.361342 | ||||||||
\(587\) | −4.41749e6 | −0.529151 | −0.264576 | − | 0.964365i | \(-0.585232\pi\) | ||||
−0.264576 | + | 0.964365i | \(0.585232\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.40063e7 | −1.66355 | ||||||||
\(590\) | −5.60477e6 | −0.662869 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.28528e6 | −0.971634 | ||||||||
\(593\) | 5.54106e6 | 0.647077 | 0.323539 | − | 0.946215i | \(-0.395127\pi\) | ||||
0.323539 | + | 0.946215i | \(0.395127\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.01088e7 | 1.16570 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.56954e6 | −0.179482 | ||||||||
\(599\) | −5.08611e6 | −0.579187 | −0.289594 | − | 0.957150i | \(-0.593520\pi\) | ||||
−0.289594 | + | 0.957150i | \(0.593520\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.41307e6 | 0.272511 | 0.136255 | − | 0.990674i | \(-0.456493\pi\) | ||||
0.136255 | + | 0.990674i | \(0.456493\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −903840. | −0.100809 | ||||||||
\(605\) | 6.02480e6 | 0.669197 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.62170e6 | 0.839614 | 0.419807 | − | 0.907613i | \(-0.362098\pi\) | ||||
0.419807 | + | 0.907613i | \(0.362098\pi\) | |||||||
\(608\) | 1.11966e7 | 1.22837 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.33520e6 | 0.580532 | ||||||||
\(611\) | −5.26781e6 | −0.570856 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.60126e6 | 0.387082 | 0.193541 | − | 0.981092i | \(-0.438003\pi\) | ||||
0.193541 | + | 0.981092i | \(0.438003\pi\) | |||||||
\(614\) | −2.39313e6 | −0.256180 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.22901e6 | −0.764480 | −0.382240 | − | 0.924063i | \(-0.624847\pi\) | ||||
−0.382240 | + | 0.924063i | \(0.624847\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.25832e7 | −1.31998 | −0.659988 | − | 0.751276i | \(-0.729439\pi\) | ||||
−0.659988 | + | 0.751276i | \(0.729439\pi\) | |||||||
\(620\) | −1.35233e7 | −1.41288 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.62949e6 | 0.272519 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.13449e7 | −1.16172 | ||||||||
\(626\) | −5.30545e6 | −0.541111 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.72032e6 | 0.376427 | ||||||||
\(629\) | −1.89298e6 | −0.190774 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.98350e6 | 0.598249 | 0.299125 | − | 0.954214i | \(-0.403305\pi\) | ||||
0.299125 | + | 0.954214i | \(0.403305\pi\) | |||||||
\(632\) | 6.55392e6 | 0.652692 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.19984e6 | 0.316159 | ||||||||
\(635\) | −1.27674e7 | −1.25651 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.47989e6 | 0.241202 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.39568e7 | 1.34690 | ||||||||
\(641\) | 7.74000e6 | 0.744040 | 0.372020 | − | 0.928225i | \(-0.378665\pi\) | ||||
0.372020 | + | 0.928225i | \(0.378665\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.81377e6 | 0.649920 | 0.324960 | − | 0.945728i | \(-0.394649\pi\) | ||||
0.324960 | + | 0.945728i | \(0.394649\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 651456. | 0.0614191 | ||||||||
\(647\) | 1.07121e7 | 1.00603 | 0.503017 | − | 0.864276i | \(-0.332223\pi\) | ||||
0.503017 | + | 0.864276i | \(0.332223\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.06202e7 | 0.989739 | ||||||||
\(650\) | 2.61346e6 | 0.242623 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.71819e6 | 0.158290 | ||||||||
\(653\) | −1.34167e7 | −1.23129 | −0.615647 | − | 0.788022i | \(-0.711105\pi\) | ||||
−0.615647 | + | 0.788022i | \(0.711105\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.60976e7 | −2.37682 | ||||||||
\(656\) | 6.19424e6 | 0.561990 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.38574e7 | −1.24299 | −0.621494 | − | 0.783419i | \(-0.713474\pi\) | ||||
−0.621494 | + | 0.783419i | \(0.713474\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.20734e7 | −1.07479 | −0.537396 | − | 0.843330i | \(-0.680592\pi\) | ||||
−0.537396 | + | 0.843330i | \(0.680592\pi\) | |||||||
\(662\) | −223416. | −0.0198139 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −62949.6 | −0.00554080 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.53154e6 | −0.568461 | ||||||||
\(668\) | 1.06637e7 | 0.924624 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 546163. | 0.0470040 | ||||||||
\(671\) | −1.01094e7 | −0.866801 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.32490e6 | −0.453183 | −0.226592 | − | 0.973990i | \(-0.572758\pi\) | ||||
−0.226592 | + | 0.973990i | \(0.572758\pi\) | |||||||
\(674\) | 3.18601e6 | 0.270145 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.69105e6 | 0.226493 | ||||||||
\(677\) | 2.34518e7 | 1.96655 | 0.983274 | − | 0.182135i | \(-0.0583008\pi\) | ||||
0.983274 | + | 0.182135i | \(0.0583008\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.34784e6 | 0.111781 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.66067e6 | −0.301370 | ||||||||
\(683\) | −1.82270e7 | −1.49508 | −0.747538 | − | 0.664219i | \(-0.768764\pi\) | ||||
−0.747538 | + | 0.664219i | \(0.768764\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.66261e6 | −0.461095 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −889536. | −0.0716461 | ||||||||
\(689\) | −7.42280e6 | −0.595690 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.60858e6 | 0.606190 | 0.303095 | − | 0.952960i | \(-0.401980\pi\) | ||||
0.303095 | + | 0.952960i | \(0.401980\pi\) | |||||||
\(692\) | 1.44847e7 | 1.14986 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.67353e6 | 0.525965 | ||||||||
\(695\) | −7.27272e6 | −0.571130 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.41523e6 | 0.110343 | ||||||||
\(698\) | −3.20518e6 | −0.249009 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −314162. | −0.0241467 | −0.0120734 | − | 0.999927i | \(-0.503843\pi\) | ||||
−0.0120734 | + | 0.999927i | \(0.503843\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.74483e7 | −2.09472 | ||||||||
\(704\) | −3.03539e6 | −0.230825 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.61930e6 | −0.273283 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.48285e7 | 1.85496 | 0.927482 | − | 0.373869i | \(-0.121969\pi\) | ||||
0.927482 | + | 0.373869i | \(0.121969\pi\) | |||||||
\(710\) | 5.34052e6 | 0.397592 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.44604e6 | −0.180827 | ||||||||
\(713\) | 9.64148e6 | 0.710264 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.11646e7 | −0.816730 | ||||||||
\(716\) | 1.70958e7 | 1.24625 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.84158e6 | −0.133315 | ||||||||
\(719\) | −1.71932e7 | −1.24032 | −0.620160 | − | 0.784475i | \(-0.712932\pi\) | ||||
−0.620160 | + | 0.784475i | \(0.712932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 4.49391e6 | 0.320835 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.21472e7 | 0.861249 | ||||||||
\(725\) | 1.08757e7 | 0.768444 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.12927e7 | −1.49415 | −0.747076 | − | 0.664739i | \(-0.768543\pi\) | ||||
−0.747076 | + | 0.664739i | \(0.768543\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.11021e6 | −0.424374 | ||||||||
\(731\) | −203237. | −0.0140673 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.96024e7 | −1.34757 | −0.673783 | − | 0.738930i | \(-0.735332\pi\) | ||||
−0.673783 | + | 0.738930i | \(0.735332\pi\) | |||||||
\(734\) | 2.69604e6 | 0.184708 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.70739e6 | −0.524461 | ||||||||
\(737\) | −1.03490e6 | −0.0701824 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.44181e7 | 0.971173 | 0.485587 | − | 0.874189i | \(-0.338606\pi\) | ||||
0.485587 | + | 0.874189i | \(0.338606\pi\) | |||||||
\(740\) | −2.65018e7 | −1.77908 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.57521e6 | −0.370501 | −0.185250 | − | 0.982691i | \(-0.559310\pi\) | ||||
−0.185250 | + | 0.982691i | \(0.559310\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.70556e7 | 1.78594 | ||||||||
\(746\) | 6.27547e6 | 0.412856 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.19185e6 | −0.0778872 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 508800. | 0.0329190 | 0.0164595 | − | 0.999865i | \(-0.494761\pi\) | ||||
0.0164595 | + | 0.999865i | \(0.494761\pi\) | |||||||
\(752\) | −6.58752e6 | −0.424793 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.58063e6 | 0.293425 | ||||||||
\(755\) | −2.41906e6 | −0.154447 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.10466e7 | 0.700631 | 0.350316 | − | 0.936632i | \(-0.386074\pi\) | ||||
0.350316 | + | 0.936632i | \(0.386074\pi\) | |||||||
\(758\) | −3.66377e6 | −0.231609 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.95437e7 | 1.22736 | ||||||||
\(761\) | 6.77173e6 | 0.423875 | 0.211937 | − | 0.977283i | \(-0.432023\pi\) | ||||
0.211937 | + | 0.977283i | \(0.432023\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 9.55338e6 | 0.592139 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 55455.6 | 0.00341486 | ||||||||
\(767\) | 1.96167e7 | 1.20403 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.48053e7 | −1.51261 | −0.756307 | − | 0.654216i | \(-0.772999\pi\) | ||||
−0.756307 | + | 0.654216i | \(0.772999\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.72524e7 | 1.04185 | ||||||||
\(773\) | 1.62952e7 | 0.980867 | 0.490434 | − | 0.871479i | \(-0.336838\pi\) | ||||
0.490434 | + | 0.871479i | \(0.336838\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.60541e7 | −0.960133 | ||||||||
\(776\) | −2.20324e7 | −1.31343 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.09668e6 | 0.0649580 | ||||||||
\(779\) | 2.05209e7 | 1.21158 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.01195e7 | −0.593651 | ||||||||
\(782\) | −448441. | −0.0262234 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.95717e6 | 0.576716 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.44214e7 | −0.829984 | −0.414992 | − | 0.909825i | \(-0.636216\pi\) | ||||
−0.414992 | + | 0.909825i | \(0.636216\pi\) | |||||||
\(788\) | 6.48138e6 | 0.371837 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.18584e6 | 0.466655 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.86732e7 | −1.05447 | ||||||||
\(794\) | −807703. | −0.0454674 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.13435e7 | 0.634549 | ||||||||
\(797\) | 1.10109e6 | 0.0614014 | 0.0307007 | − | 0.999529i | \(-0.490226\pi\) | ||||
0.0307007 | + | 0.999529i | \(0.490226\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.50509e6 | −0.0834055 | ||||||||
\(800\) | 1.28336e7 | 0.708965 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.32855e6 | 0.457229 | ||||||||
\(803\) | 1.15779e7 | 0.633639 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.76166e6 | −0.366620 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.10970e6 | 0.490881 | ||||||||
\(809\) | 2.45146e7 | 1.31690 | 0.658450 | − | 0.752625i | \(-0.271213\pi\) | ||||
0.658450 | + | 0.752625i | \(0.271213\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.03580e7 | 1.62077 | 0.810383 | − | 0.585900i | \(-0.199259\pi\) | ||||
0.810383 | + | 0.585900i | \(0.199259\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.17384e6 | −0.379482 | ||||||||
\(815\) | 4.59862e6 | 0.242512 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.94694e6 | −0.154460 | ||||||||
\(818\) | −5.08243e6 | −0.265576 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.98132e7 | 1.02901 | ||||||||
\(821\) | 2.54599e7 | 1.31825 | 0.659126 | − | 0.752032i | \(-0.270926\pi\) | ||||
0.659126 | + | 0.752032i | \(0.270926\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.95232e6 | 0.306328 | 0.153164 | − | 0.988201i | \(-0.451054\pi\) | ||||
0.153164 | + | 0.988201i | \(0.451054\pi\) | |||||||
\(824\) | 1.31295e6 | 0.0673643 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.85900e6 | 0.399580 | 0.199790 | − | 0.979839i | \(-0.435974\pi\) | ||||
0.199790 | + | 0.979839i | \(0.435974\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.12642e7 | 0.569262 | 0.284631 | − | 0.958637i | \(-0.408129\pi\) | ||||
0.284631 | + | 0.958637i | \(0.408129\pi\) | |||||||
\(830\) | −78624.0 | −0.00396150 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.60671e6 | −0.280802 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.85405e7 | 1.41659 | ||||||||
\(836\) | −1.72818e7 | −0.855209 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.60266e6 | 0.226412 | ||||||||
\(839\) | 7.80470e6 | 0.382782 | 0.191391 | − | 0.981514i | \(-0.438700\pi\) | ||||
0.191391 | + | 0.981514i | \(0.438700\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.44919e6 | −0.0706539 | ||||||||
\(842\) | −5.59983e6 | −0.272204 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.17510e7 | −1.05105 | ||||||||
\(845\) | 7.20241e6 | 0.347005 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.28240e6 | −0.443272 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 746702. | 0.0354487 | ||||||||
\(851\) | 1.88945e7 | 0.894357 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.50581e7 | 0.708593 | 0.354296 | − | 0.935133i | \(-0.384720\pi\) | ||||
0.354296 | + | 0.935133i | \(0.384720\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.61826e7 | 1.22132 | ||||||||
\(857\) | −2.28736e7 | −1.06386 | −0.531928 | − | 0.846789i | \(-0.678532\pi\) | ||||
−0.531928 | + | 0.846789i | \(0.678532\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.22863e6 | 0.380491 | 0.190246 | − | 0.981737i | \(-0.439072\pi\) | ||||
0.190246 | + | 0.981737i | \(0.439072\pi\) | |||||||
\(860\) | −2.84532e6 | −0.131185 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.90864e6 | −0.0874895 | ||||||||
\(863\) | −4.09902e6 | −0.187350 | −0.0936748 | − | 0.995603i | \(-0.529861\pi\) | ||||
−0.0936748 | + | 0.995603i | \(0.529861\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.87672e7 | 1.76167 | ||||||||
\(866\) | 1.03867e6 | 0.0470633 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.55109e7 | −0.696769 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.91157e6 | −0.0853777 | ||||||||
\(872\) | 1.15236e7 | 0.513212 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.50239e6 | −0.287935 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 787778. | 0.0345864 | 0.0172932 | − | 0.999850i | \(-0.494495\pi\) | ||||
0.0172932 | + | 0.999850i | \(0.494495\pi\) | |||||||
\(878\) | 1.19616e7 | 0.523665 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.39616e7 | −0.607756 | ||||||||
\(881\) | −1.73321e7 | −0.752336 | −0.376168 | − | 0.926551i | \(-0.622758\pi\) | ||||
−0.376168 | + | 0.926551i | \(0.622758\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.23991e7 | 0.535164 | 0.267582 | − | 0.963535i | \(-0.413775\pi\) | ||||
0.267582 | + | 0.963535i | \(0.413775\pi\) | |||||||
\(884\) | −2.20147e6 | −0.0947507 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.49641e6 | −0.320826 | ||||||||
\(887\) | 1.67555e7 | 0.715071 | 0.357535 | − | 0.933900i | \(-0.383617\pi\) | ||||
0.357535 | + | 0.933900i | \(0.383617\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −3.05510e6 | −0.129286 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.29136e6 | −0.0964233 | ||||||||
\(893\) | −2.18238e7 | −0.915801 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.57557e7 | 1.90936 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −198916. | −0.00823150 | ||||||||
\(899\) | −2.81382e7 | −1.16117 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.12080e6 | −0.0870338 | ||||||||
\(902\) | 5.36330e6 | 0.219491 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.64906e7 | −0.671145 | ||||||||
\(905\) | 3.25110e7 | 1.31950 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.96543e7 | −1.60056 | −0.800280 | − | 0.599627i | \(-0.795316\pi\) | ||||
−0.800280 | + | 0.599627i | \(0.795316\pi\) | |||||||
\(908\) | 2.11028e7 | 0.849426 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.99138e7 | −1.19419 | −0.597097 | − | 0.802169i | \(-0.703679\pi\) | ||||
−0.597097 | + | 0.802169i | \(0.703679\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 148981. | 0.00591498 | ||||||||
\(914\) | −323628. | −0.0128139 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −736510. | −0.0290028 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.98997e7 | 0.777245 | 0.388622 | − | 0.921397i | \(-0.372951\pi\) | ||||
0.388622 | + | 0.921397i | \(0.372951\pi\) | |||||||
\(920\) | −1.34532e7 | −0.524031 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.98395e6 | 0.348049 | ||||||||
\(923\) | −1.86918e7 | −0.722183 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.14613e7 | −1.20899 | ||||||||
\(926\) | 7.18763e6 | 0.275460 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.24936e7 | 0.857412 | ||||||||
\(929\) | −1.19663e7 | −0.454904 | −0.227452 | − | 0.973789i | \(-0.573039\pi\) | ||||
−0.227452 | + | 0.973789i | \(0.573039\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.33118e6 | 0.0501991 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.10446e6 | −0.153953 | ||||||||
\(935\) | −3.18989e6 | −0.119329 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.18165e6 | −0.230015 | −0.115007 | − | 0.993365i | \(-0.536689\pi\) | ||||
−0.115007 | + | 0.993365i | \(0.536689\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.10712e7 | −0.777804 | ||||||||
\(941\) | 2.99426e7 | 1.10234 | 0.551171 | − | 0.834393i | \(-0.314181\pi\) | ||||
0.551171 | + | 0.834393i | \(0.314181\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.41259e7 | −0.517293 | ||||||||
\(944\) | 2.45312e7 | 0.895959 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −770208. | −0.0279821 | ||||||||
\(947\) | 4.84279e7 | 1.75477 | 0.877386 | − | 0.479785i | \(-0.159286\pi\) | ||||
0.877386 | + | 0.479785i | \(0.159286\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.13857e7 | 0.770830 | ||||||||
\(950\) | 1.08272e7 | 0.389230 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.26780e7 | −0.808860 | −0.404430 | − | 0.914569i | \(-0.632530\pi\) | ||||
−0.404430 | + | 0.914569i | \(0.632530\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.55689e7 | 0.907202 | ||||||||
\(956\) | 3.04918e7 | 1.07904 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.99970e6 | 0.140803 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.29068e7 | 0.450827 | ||||||||
\(962\) | −1.32509e7 | −0.461644 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.77823e7 | 1.30947 | ||||||||
\(965\) | 4.61749e7 | 1.59620 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.60431e6 | −0.123953 | −0.0619764 | − | 0.998078i | \(-0.519740\pi\) | ||||
−0.0619764 | + | 0.998078i | \(0.519740\pi\) | |||||||
\(968\) | 9.64740e6 | 0.330919 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.75184e7 | −0.939061 | ||||||||
\(971\) | −2.90807e7 | −0.989821 | −0.494910 | − | 0.868944i | \(-0.664799\pi\) | ||||
−0.494910 | + | 0.868944i | \(0.664799\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 4.34251e6 | 0.146671 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.33513e7 | −0.784669 | ||||||||
\(977\) | 1.81960e7 | 0.609873 | 0.304936 | − | 0.952373i | \(-0.401365\pi\) | ||||
0.304936 | + | 0.952373i | \(0.401365\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.78896e6 | 0.193039 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.09110e6 | −0.201566 | ||||||||
\(983\) | 3.32808e6 | 0.109853 | 0.0549263 | − | 0.998490i | \(-0.482508\pi\) | ||||
0.0549263 | + | 0.998490i | \(0.482508\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.73470e7 | 0.569682 | ||||||||
\(986\) | 1.30875e6 | 0.0428711 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.19213e7 | −1.04037 | ||||||||
\(989\) | 2.02858e6 | 0.0659478 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.25420e7 | 1.69951 | 0.849753 | − | 0.527181i | \(-0.176751\pi\) | ||||
0.849753 | + | 0.527181i | \(0.176751\pi\) | |||||||
\(992\) | −3.32038e7 | −1.07129 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.03601e7 | 0.972177 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.22999e6 | 0.0391889 | 0.0195945 | − | 0.999808i | \(-0.493762\pi\) | ||||
0.0195945 | + | 0.999808i | \(0.493762\pi\) | |||||||
\(998\) | −1.59845e7 | −0.508011 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 441.6.a.u.1.1 | 2 | ||
3.2 | odd | 2 | 49.6.a.c.1.2 | yes | 2 | ||
7.6 | odd | 2 | inner | 441.6.a.u.1.2 | 2 | ||
12.11 | even | 2 | 784.6.a.z.1.1 | 2 | |||
21.2 | odd | 6 | 49.6.c.g.18.1 | 4 | |||
21.5 | even | 6 | 49.6.c.g.18.2 | 4 | |||
21.11 | odd | 6 | 49.6.c.g.30.1 | 4 | |||
21.17 | even | 6 | 49.6.c.g.30.2 | 4 | |||
21.20 | even | 2 | 49.6.a.c.1.1 | ✓ | 2 | ||
84.83 | odd | 2 | 784.6.a.z.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.6.a.c.1.1 | ✓ | 2 | 21.20 | even | 2 | ||
49.6.a.c.1.2 | yes | 2 | 3.2 | odd | 2 | ||
49.6.c.g.18.1 | 4 | 21.2 | odd | 6 | |||
49.6.c.g.18.2 | 4 | 21.5 | even | 6 | |||
49.6.c.g.30.1 | 4 | 21.11 | odd | 6 | |||
49.6.c.g.30.2 | 4 | 21.17 | even | 6 | |||
441.6.a.u.1.1 | 2 | 1.1 | even | 1 | trivial | ||
441.6.a.u.1.2 | 2 | 7.6 | odd | 2 | inner | ||
784.6.a.z.1.1 | 2 | 12.11 | even | 2 | |||
784.6.a.z.1.2 | 2 | 84.83 | odd | 2 |