Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,6,Mod(1,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.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: | \(80.8334451857\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 168) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 504.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.00000 | −0.0715542 | −0.0357771 | − | 0.999360i | \(-0.511391\pi\) | ||||
−0.0357771 | + | 0.999360i | \(0.511391\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −370.000 | −0.921977 | −0.460988 | − | 0.887406i | \(-0.652505\pi\) | ||||
−0.460988 | + | 0.887406i | \(0.652505\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 122.000 | 0.200217 | 0.100109 | − | 0.994977i | \(-0.468081\pi\) | ||||
0.100109 | + | 0.994977i | \(0.468081\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1428.00 | 1.19841 | 0.599206 | − | 0.800595i | \(-0.295483\pi\) | ||||
0.599206 | + | 0.800595i | \(0.295483\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1724.00 | 1.09560 | 0.547802 | − | 0.836608i | \(-0.315465\pi\) | ||||
0.547802 | + | 0.836608i | \(0.315465\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2670.00 | 1.05243 | 0.526213 | − | 0.850353i | \(-0.323611\pi\) | ||||
0.526213 | + | 0.850353i | \(0.323611\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3109.00 | −0.994880 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4302.00 | −0.949895 | −0.474947 | − | 0.880014i | \(-0.657533\pi\) | ||||
−0.474947 | + | 0.880014i | \(0.657533\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3104.00 | 0.580120 | 0.290060 | − | 0.957009i | \(-0.406325\pi\) | ||||
0.290060 | + | 0.957009i | \(0.406325\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 196.000 | 0.0270449 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −14318.0 | −1.71940 | −0.859702 | − | 0.510796i | \(-0.829351\pi\) | ||||
−0.859702 | + | 0.510796i | \(0.829351\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12272.0 | 1.14013 | 0.570067 | − | 0.821598i | \(-0.306917\pi\) | ||||
0.570067 | + | 0.821598i | \(0.306917\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −21652.0 | −1.78578 | −0.892888 | − | 0.450279i | \(-0.851324\pi\) | ||||
−0.892888 | + | 0.450279i | \(0.851324\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2644.00 | 0.174589 | 0.0872945 | − | 0.996183i | \(-0.472178\pi\) | ||||
0.0872945 | + | 0.996183i | \(0.472178\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 24342.0 | 1.19033 | 0.595164 | − | 0.803604i | \(-0.297087\pi\) | ||||
0.595164 | + | 0.803604i | \(0.297087\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1480.00 | 0.0659713 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14088.0 | 0.526889 | 0.263445 | − | 0.964675i | \(-0.415141\pi\) | ||||
0.263445 | + | 0.964675i | \(0.415141\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −24474.0 | −0.842132 | −0.421066 | − | 0.907030i | \(-0.638344\pi\) | ||||
−0.421066 | + | 0.907030i | \(0.638344\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −488.000 | −0.0143264 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7208.00 | 0.196168 | 0.0980839 | − | 0.995178i | \(-0.468729\pi\) | ||||
0.0980839 | + | 0.995178i | \(0.468729\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −54302.0 | −1.27841 | −0.639205 | − | 0.769037i | \(-0.720736\pi\) | ||||
−0.639205 | + | 0.769037i | \(0.720736\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −48962.0 | −1.07536 | −0.537678 | − | 0.843150i | \(-0.680698\pi\) | ||||
−0.537678 | + | 0.843150i | \(0.680698\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 18130.0 | 0.348474 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −33332.0 | −0.600888 | −0.300444 | − | 0.953799i | \(-0.597135\pi\) | ||||
−0.300444 | + | 0.953799i | \(0.597135\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4004.00 | 0.0637968 | 0.0318984 | − | 0.999491i | \(-0.489845\pi\) | ||||
0.0318984 | + | 0.999491i | \(0.489845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5712.00 | −0.0857513 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −64752.0 | −0.866519 | −0.433260 | − | 0.901269i | \(-0.642637\pi\) | ||||
−0.433260 | + | 0.901269i | \(0.642637\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5978.00 | −0.0756750 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6896.00 | −0.0783950 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7038.00 | 0.0759486 | 0.0379743 | − | 0.999279i | \(-0.487909\pi\) | ||||
0.0379743 | + | 0.999279i | \(0.487909\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −24784.0 | −0.241751 | −0.120875 | − | 0.992668i | \(-0.538570\pi\) | ||||
−0.120875 | + | 0.992668i | \(0.538570\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 108080. | 1.00381 | 0.501906 | − | 0.864922i | \(-0.332632\pi\) | ||||
0.501906 | + | 0.864922i | \(0.332632\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −108834. | −0.918978 | −0.459489 | − | 0.888183i | \(-0.651967\pi\) | ||||
−0.459489 | + | 0.888183i | \(0.651967\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −202642. | −1.63367 | −0.816833 | − | 0.576874i | \(-0.804272\pi\) | ||||
−0.816833 | + | 0.576874i | \(0.804272\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 50198.0 | 0.369820 | 0.184910 | − | 0.982755i | \(-0.440801\pi\) | ||||
0.184910 | + | 0.982755i | \(0.440801\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10680.0 | −0.0753055 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −69972.0 | −0.452957 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −24151.0 | −0.149959 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 24936.0 | 0.142742 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3052.00 | 0.0167909 | 0.00839547 | − | 0.999965i | \(-0.497328\pi\) | ||||
0.00839547 | + | 0.999965i | \(0.497328\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −218788. | −1.11390 | −0.556949 | − | 0.830547i | \(-0.688028\pi\) | ||||
−0.556949 | + | 0.830547i | \(0.688028\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −84476.0 | −0.414099 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −203070. | −0.924367 | −0.462183 | − | 0.886784i | \(-0.652934\pi\) | ||||
−0.462183 | + | 0.886784i | \(0.652934\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 49540.0 | 0.217480 | 0.108740 | − | 0.994070i | \(-0.465318\pi\) | ||||
0.108740 | + | 0.994070i | \(0.465318\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −45140.0 | −0.184596 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17208.0 | 0.0679689 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −93354.0 | −0.344483 | −0.172241 | − | 0.985055i | \(-0.555101\pi\) | ||||
−0.172241 | + | 0.985055i | \(0.555101\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 70872.0 | 0.252949 | 0.126474 | − | 0.991970i | \(-0.459634\pi\) | ||||
0.126474 | + | 0.991970i | \(0.459634\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12416.0 | −0.0415100 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −374898. | −1.21385 | −0.606924 | − | 0.794760i | \(-0.707597\pi\) | ||||
−0.606924 | + | 0.794760i | \(0.707597\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −130830. | −0.397780 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −125184. | −0.369045 | −0.184523 | − | 0.982828i | \(-0.559074\pi\) | ||||
−0.184523 | + | 0.982828i | \(0.559074\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −444068. | −1.23214 | −0.616068 | − | 0.787693i | \(-0.711275\pi\) | ||||
−0.616068 | + | 0.787693i | \(0.711275\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −356409. | −0.959913 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −544368. | −1.38286 | −0.691429 | − | 0.722445i | \(-0.743018\pi\) | ||||
−0.691429 | + | 0.722445i | \(0.743018\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 152341. | 0.376029 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 616130. | 1.43727 | 0.718637 | − | 0.695385i | \(-0.244766\pi\) | ||||
0.718637 | + | 0.695385i | \(0.244766\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 98266.0 | 0.222950 | 0.111475 | − | 0.993767i | \(-0.464443\pi\) | ||||
0.111475 | + | 0.993767i | \(0.464443\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 57272.0 | 0.123031 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −528360. | −1.10491 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 515138. | 1.02174 | 0.510870 | − | 0.859658i | \(-0.329323\pi\) | ||||
0.510870 | + | 0.859658i | \(0.329323\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −449930. | −0.869464 | −0.434732 | − | 0.900560i | \(-0.643157\pi\) | ||||
−0.434732 | + | 0.900560i | \(0.643157\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 404934. | 0.743393 | 0.371697 | − | 0.928354i | \(-0.378776\pi\) | ||||
0.371697 | + | 0.928354i | \(0.378776\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −342576. | −0.613231 | −0.306616 | − | 0.951833i | \(-0.599197\pi\) | ||||
−0.306616 | + | 0.951833i | \(0.599197\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 210798. | 0.359026 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −49088.0 | −0.0815813 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −637880. | −1.01012 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −812820. | −1.25686 | −0.628432 | − | 0.777865i | \(-0.716303\pi\) | ||||
−0.628432 | + | 0.777865i | \(0.716303\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 86608.0 | 0.127780 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −152096. | −0.219265 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 174216. | 0.239943 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −655320. | −0.882452 | −0.441226 | − | 0.897396i | \(-0.645456\pi\) | ||||
−0.441226 | + | 0.897396i | \(0.645456\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.19258e6 | 1.53611 | 0.768053 | − | 0.640386i | \(-0.221226\pi\) | ||||
0.768053 | + | 0.640386i | \(0.221226\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 374506. | 0.471922 | 0.235961 | − | 0.971763i | \(-0.424176\pi\) | ||||
0.235961 | + | 0.971763i | \(0.424176\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.47249e6 | −1.77690 | −0.888452 | − | 0.458970i | \(-0.848218\pi\) | ||||
−0.888452 | + | 0.458970i | \(0.848218\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10576.0 | −0.0124926 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.28908e6 | 1.45977 | 0.729885 | − | 0.683570i | \(-0.239574\pi\) | ||||
0.729885 | + | 0.683570i | \(0.239574\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 174478. | 0.193508 | 0.0967538 | − | 0.995308i | \(-0.469154\pi\) | ||||
0.0967538 | + | 0.995308i | \(0.469154\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9604.00 | −0.0102220 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 210328. | 0.219359 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 875928. | 0.877575 | 0.438787 | − | 0.898591i | \(-0.355408\pi\) | ||||
0.438787 | + | 0.898591i | \(0.355408\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −987900. | −0.970313 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 674408. | 0.636927 | 0.318464 | − | 0.947935i | \(-0.396833\pi\) | ||||
0.318464 | + | 0.947935i | \(0.396833\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 701582. | 0.649874 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.47155e6 | −1.31186 | −0.655929 | − | 0.754823i | \(-0.727723\pi\) | ||||
−0.655929 | + | 0.754823i | \(0.727723\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −97368.0 | −0.0851729 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.12577e6 | −1.79117 | −0.895583 | − | 0.444894i | \(-0.853241\pi\) | ||||
−0.895583 | + | 0.444894i | \(0.853241\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.10940e6 | 0.917624 | 0.458812 | − | 0.888533i | \(-0.348275\pi\) | ||||
0.458812 | + | 0.888533i | \(0.348275\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.15033e6 | 0.917256 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −229094. | −0.179397 | −0.0896983 | − | 0.995969i | \(-0.528590\pi\) | ||||
−0.0896983 | + | 0.995969i | \(0.528590\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 625962. | 0.472914 | 0.236457 | − | 0.971642i | \(-0.424014\pi\) | ||||
0.236457 | + | 0.971642i | \(0.424014\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.04374e6 | −1.51691 | −0.758455 | − | 0.651726i | \(-0.774045\pi\) | ||||
−0.758455 | + | 0.651726i | \(0.774045\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −601328. | −0.430930 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 619327. | 0.436190 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.96838e6 | −1.33949 | −0.669747 | − | 0.742589i | \(-0.733597\pi\) | ||||
−0.669747 | + | 0.742589i | \(0.733597\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −56352.0 | −0.0377011 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 325740. | 0.210714 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.06095e6 | 0.674960 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 97896.0 | 0.0602581 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.04359e6 | 1.84306 | 0.921531 | − | 0.388305i | \(-0.126939\pi\) | ||||
0.921531 | + | 0.388305i | \(0.126939\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 325724. | 0.190963 | 0.0954814 | − | 0.995431i | \(-0.469561\pi\) | ||||
0.0954814 | + | 0.995431i | \(0.469561\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.28769e6 | 1.31989 | 0.659943 | − | 0.751316i | \(-0.270580\pi\) | ||||
0.659943 | + | 0.751316i | \(0.270580\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −902562. | −0.504463 | −0.252231 | − | 0.967667i | \(-0.581164\pi\) | ||||
−0.252231 | + | 0.967667i | \(0.581164\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.59174e6 | 0.875781 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.46187e6 | 1.31298 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −379298. | −0.199192 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −129556. | −0.0659884 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.56194e6 | 0.783600 | 0.391800 | − | 0.920050i | \(-0.371853\pi\) | ||||
0.391800 | + | 0.920050i | \(0.371853\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −28832.0 | −0.0140366 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −572230. | −0.274471 | −0.137235 | − | 0.990538i | \(-0.543822\pi\) | ||||
−0.137235 | + | 0.990538i | \(0.543822\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.14848e6 | −0.534857 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.88039e6 | 0.838350 | 0.419175 | − | 0.907906i | \(-0.362319\pi\) | ||||
0.419175 | + | 0.907906i | \(0.362319\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.43343e6 | 0.629960 | 0.314980 | − | 0.949098i | \(-0.398002\pi\) | ||||
0.314980 | + | 0.949098i | \(0.398002\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.09802e6 | 1.32327 | 0.661633 | − | 0.749827i | \(-0.269864\pi\) | ||||
0.661633 | + | 0.749827i | \(0.269864\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 217208. | 0.0914755 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −663918. | −0.271881 | −0.135940 | − | 0.990717i | \(-0.543406\pi\) | ||||
−0.135940 | + | 0.990717i | \(0.543406\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 496077. | 0.200346 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 195848. | 0.0769462 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.33787e6 | 1.68117 | 0.840585 | − | 0.541680i | \(-0.182211\pi\) | ||||
0.840585 | + | 0.541680i | \(0.182211\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.19276e6 | −0.449902 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.49537e6 | 1.67299 | 0.836494 | − | 0.547976i | \(-0.184601\pi\) | ||||
0.836494 | + | 0.547976i | \(0.184601\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −524844. | −0.190185 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.44910e6 | −0.518203 | −0.259102 | − | 0.965850i | \(-0.583426\pi\) | ||||
−0.259102 | + | 0.965850i | \(0.583426\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.62465e6 | −1.26261 | −0.631305 | − | 0.775535i | \(-0.717480\pi\) | ||||
−0.631305 | + | 0.775535i | \(0.717480\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −72520.0 | −0.0249348 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 585274. | 0.196103 | 0.0980517 | − | 0.995181i | \(-0.468739\pi\) | ||||
0.0980517 | + | 0.995181i | \(0.468739\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.81276e6 | 1.26124 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 133328. | 0.0429961 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.36239e6 | −1.38915 | −0.694573 | − | 0.719422i | \(-0.744407\pi\) | ||||
−0.694573 | + | 0.719422i | \(0.744407\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.16168e6 | −1.29243 | −0.646216 | − | 0.763155i | \(-0.723649\pi\) | ||||
−0.646216 | + | 0.763155i | \(0.723649\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 378688. | 0.116150 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.29766e6 | 1.58525 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.54131e6 | −1.34237 | −0.671185 | − | 0.741290i | \(-0.734215\pi\) | ||||
−0.671185 | + | 0.741290i | \(0.734215\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −690312. | −0.199145 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16016.0 | −0.00456493 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.93357e6 | 0.538052 | 0.269026 | − | 0.963133i | \(-0.413298\pi\) | ||||
0.269026 | + | 0.963133i | \(0.413298\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.16777e6 | −0.596084 | −0.298042 | − | 0.954553i | \(-0.596333\pi\) | ||||
−0.298042 | + | 0.954553i | \(0.596333\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.43965e6 | −1.19228 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.19923e6 | 0.318296 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.36421e6 | 0.872348 | 0.436174 | − | 0.899862i | \(-0.356333\pi\) | ||||
0.436174 | + | 0.899862i | \(0.356333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.09510e6 | 1.56229 | 0.781144 | − | 0.624351i | \(-0.214637\pi\) | ||||
0.781144 | + | 0.624351i | \(0.214637\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.60308e6 | 1.15304 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.65252e6 | 1.89515 | 0.947574 | − | 0.319536i | \(-0.103527\pi\) | ||||
0.947574 | + | 0.319536i | \(0.103527\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 762570. | 0.184616 | 0.0923082 | − | 0.995730i | \(-0.470575\pi\) | ||||
0.0923082 | + | 0.995730i | \(0.470575\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 259008. | 0.0620031 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.44504e6 | 1.04054 | 0.520271 | − | 0.854001i | \(-0.325831\pi\) | ||||
0.520271 | + | 0.854001i | \(0.325831\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.54064e6 | −1.05118 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 23912.0 | 0.00541486 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.00527e6 | −1.34506 | −0.672531 | − | 0.740069i | \(-0.734793\pi\) | ||||
−0.672531 | + | 0.740069i | \(0.734793\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.86783e6 | 0.628494 | 0.314247 | − | 0.949341i | \(-0.398248\pi\) | ||||
0.314247 | + | 0.949341i | \(0.398248\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.45140e6 | 0.965037 | 0.482518 | − | 0.875886i | \(-0.339722\pi\) | ||||
0.482518 | + | 0.875886i | \(0.339722\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.34522e6 | 0.497613 | 0.248807 | − | 0.968553i | \(-0.419962\pi\) | ||||
0.248807 | + | 0.968553i | \(0.419962\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −353192. | −0.0741445 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.01124e6 | 1.64644 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.35992e6 | −1.08999 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.16154e6 | −0.231311 | −0.115655 | − | 0.993289i | \(-0.536897\pi\) | ||||
−0.115655 | + | 0.993289i | \(0.536897\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.74680e6 | −0.344254 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −28152.0 | −0.00543444 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17776.0 | −0.00339634 | −0.00169817 | − | 0.999999i | \(-0.500541\pi\) | ||||
−0.00169817 | + | 0.999999i | \(0.500541\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.09827e6 | 0.392787 | 0.196393 | − | 0.980525i | \(-0.437077\pi\) | ||||
0.196393 | + | 0.980525i | \(0.437077\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.14326e6 | −1.13836 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.66080e6 | 0.483193 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.44714e6 | −1.51865 | −0.759326 | − | 0.650710i | \(-0.774471\pi\) | ||||
−0.759326 | + | 0.650710i | \(0.774471\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.42743e6 | −1.30894 | −0.654468 | − | 0.756089i | \(-0.727108\pi\) | ||||
−0.654468 | + | 0.756089i | \(0.727108\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 99136.0 | 0.0172983 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.06342e6 | −0.353015 | −0.176508 | − | 0.984299i | \(-0.556480\pi\) | ||||
−0.176508 | + | 0.984299i | \(0.556480\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.39914e6 | 0.406446 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −432320. | −0.0718269 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −978280. | −0.160967 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −233724. | −0.0377232 | −0.0188616 | − | 0.999822i | \(-0.506004\pi\) | ||||
−0.0188616 | + | 0.999822i | \(0.506004\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.15859e7 | 1.85214 | 0.926071 | − | 0.377350i | \(-0.123165\pi\) | ||||
0.926071 | + | 0.377350i | \(0.123165\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.43251e6 | 0.695222 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 692557. | 0.107601 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.49718e6 | 0.228274 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 435336. | 0.0657567 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −888370. | −0.131711 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.75141e6 | 1.28554 | 0.642769 | − | 0.766060i | \(-0.277786\pi\) | ||||
0.642769 | + | 0.766060i | \(0.277786\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 810568. | 0.116896 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.29193e7 | −1.84617 | −0.923084 | − | 0.384598i | \(-0.874340\pi\) | ||||
−0.923084 | + | 0.384598i | \(0.874340\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.41665e6 | −1.04071 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.63327e6 | 0.227114 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.28030e6 | −0.721141 | −0.360571 | − | 0.932732i | \(-0.617418\pi\) | ||||
−0.360571 | + | 0.932732i | \(0.617418\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.64154e6 | −0.357543 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.48097e6 | −1.12765 | −0.563825 | − | 0.825894i | \(-0.690671\pi\) | ||||
−0.563825 | + | 0.825894i | \(0.690671\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −200792. | −0.0264622 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.01798e6 | −0.908723 | −0.454362 | − | 0.890817i | \(-0.650133\pi\) | ||||
−0.454362 | + | 0.890817i | \(0.650133\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.79490e6 | 0.615446 | 0.307723 | − | 0.951476i | \(-0.400433\pi\) | ||||
0.307723 | + | 0.951476i | \(0.400433\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.30103e6 | −1.04704 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.39709e6 | −0.799914 | −0.399957 | − | 0.916534i | \(-0.630975\pi\) | ||||
−0.399957 | + | 0.916534i | \(0.630975\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −196196. | −0.0241129 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.00654e6 | −1.09745 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.49917e6 | 0.658721 | 0.329361 | − | 0.944204i | \(-0.393167\pi\) | ||||
0.329361 | + | 0.944204i | \(0.393167\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.35130e6 | 0.635581 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.34543e7 | 1.57118 | 0.785588 | − | 0.618750i | \(-0.212361\pi\) | ||||
0.785588 | + | 0.618750i | \(0.212361\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 279888. | 0.0324110 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.57493e6 | −0.520976 | −0.260488 | − | 0.965477i | \(-0.583883\pi\) | ||||
−0.260488 | + | 0.965477i | \(0.583883\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.07837e7 | 1.21782 | 0.608910 | − | 0.793240i | \(-0.291607\pi\) | ||||
0.608910 | + | 0.793240i | \(0.291607\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 96604.0 | 0.0107302 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.28728e7 | −1.41808 | −0.709041 | − | 0.705167i | \(-0.750872\pi\) | ||||
−0.709041 | + | 0.705167i | \(0.750872\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 322568. | 0.0349557 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.13805e7 | −1.22323 | −0.611616 | − | 0.791155i | \(-0.709480\pi\) | ||||
−0.611616 | + | 0.791155i | \(0.709480\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.15644e7 | −1.22295 | −0.611477 | − | 0.791263i | \(-0.709424\pi\) | ||||
−0.611477 | + | 0.791263i | \(0.709424\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 641356. | 0.0672779 | 0.0336390 | − | 0.999434i | \(-0.489290\pi\) | ||||
0.0336390 | + | 0.999434i | \(0.489290\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.17285e6 | 0.327513 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.61588e6 | 0.984666 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.04461e7 | −2.06055 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.18685e7 | 1.18665 | 0.593323 | − | 0.804964i | \(-0.297816\pi\) | ||||
0.593323 | + | 0.804964i | \(0.297816\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12208.0 | −0.00120146 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 292922. | 0.0286025 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.80700e6 | −0.269834 | −0.134917 | − | 0.990857i | \(-0.543077\pi\) | ||||
−0.134917 | + | 0.990857i | \(0.543077\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.23109e6 | −0.308192 | −0.154096 | − | 0.988056i | \(-0.549247\pi\) | ||||
−0.154096 | + | 0.988056i | \(0.549247\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.13192e7 | −1.06305 | −0.531527 | − | 0.847041i | \(-0.678382\pi\) | ||||
−0.531527 | + | 0.847041i | \(0.678382\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.21256e6 | −0.485780 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.54002e6 | −0.416653 | −0.208327 | − | 0.978059i | \(-0.566802\pi\) | ||||
−0.208327 | + | 0.978059i | \(0.566802\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 875152. | 0.0797040 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.24941e7 | 1.12070 | 0.560352 | − | 0.828254i | \(-0.310666\pi\) | ||||
0.560352 | + | 0.828254i | \(0.310666\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.61074e7 | −1.43391 | −0.716954 | − | 0.697121i | \(-0.754464\pi\) | ||||
−0.716954 | + | 0.697121i | \(0.754464\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 337904. | 0.0296305 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.14863e7 | −0.999694 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.05538e6 | 0.776427 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.42956e7 | 1.21665 | 0.608326 | − | 0.793688i | \(-0.291841\pi\) | ||||
0.608326 | + | 0.793688i | \(0.291841\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.53658e6 | −0.212705 | −0.106352 | − | 0.994328i | \(-0.533917\pi\) | ||||
−0.106352 | + | 0.994328i | \(0.533917\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −344862. | −0.0287059 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.58174e6 | −0.539870 | −0.269935 | − | 0.962879i | \(-0.587002\pi\) | ||||
−0.269935 | + | 0.962879i | \(0.587002\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 812280. | 0.0661423 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.96972e6 | 0.238324 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.68272e6 | −0.691768 | −0.345884 | − | 0.938277i | \(-0.612421\pi\) | ||||
−0.345884 | + | 0.938277i | \(0.612421\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −198160. | −0.0155616 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.75244e7 | 1.36635 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.22777e6 | −0.324950 | −0.162475 | − | 0.986713i | \(-0.551948\pi\) | ||||
−0.162475 | + | 0.986713i | \(0.551948\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.46842e7 | −1.88378 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.21442e6 | 0.0913732 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.66791e6 | −0.722299 | −0.361150 | − | 0.932508i | \(-0.617616\pi\) | ||||
−0.361150 | + | 0.932508i | \(0.617616\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.28768e6 | 0.610533 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 180560. | 0.0132086 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.23997e7 | −1.61592 | −0.807962 | − | 0.589235i | \(-0.799429\pi\) | ||||
−0.807962 | + | 0.589235i | \(0.799429\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.29592e6 | −0.379405 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.33749e7 | 0.945031 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.06700e7 | −0.748735 | −0.374368 | − | 0.927280i | \(-0.622140\pi\) | ||||
−0.374368 | + | 0.927280i | \(0.622140\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.09191e7 | −2.14009 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.30456e7 | −0.896818 | −0.448409 | − | 0.893828i | \(-0.648009\pi\) | ||||
−0.448409 | + | 0.893828i | \(0.648009\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.66696e6 | −0.180862 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.77150e6 | −0.186683 | −0.0933414 | − | 0.995634i | \(-0.529755\pi\) | ||||
−0.0933414 | + | 0.995634i | \(0.529755\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.37895e7 | 0.916381 | 0.458191 | − | 0.888854i | \(-0.348498\pi\) | ||||
0.458191 | + | 0.888854i | \(0.348498\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 373416. | 0.0246492 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.33287e6 | 0.347341 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.84892e7 | −1.19624 | −0.598118 | − | 0.801408i | \(-0.704085\pi\) | ||||
−0.598118 | + | 0.801408i | \(0.704085\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −283488. | −0.0180995 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.05745e7 | 1.30494 | 0.652469 | − | 0.757816i | \(-0.273733\pi\) | ||||
0.652469 | + | 0.757816i | \(0.273733\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.75512e7 | 1.09862 | 0.549309 | − | 0.835620i | \(-0.314891\pi\) | ||||
0.549309 | + | 0.835620i | \(0.314891\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.92946e6 | 0.617468 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.71874e6 | 0.105492 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.47910e6 | 0.0901947 | 0.0450974 | − | 0.998983i | \(-0.485640\pi\) | ||||
0.0450974 | + | 0.998983i | \(0.485640\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.71423e6 | −0.584736 | −0.292368 | − | 0.956306i | \(-0.594443\pi\) | ||||
−0.292368 | + | 0.956306i | \(0.594443\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.65034e6 | −0.577149 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.11569e7 | 1.24913 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.00917e7 | 1.17866 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.49959e6 | 0.0868558 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.45994e7 | 0.840231 | 0.420115 | − | 0.907471i | \(-0.361990\pi\) | ||||
0.420115 | + | 0.907471i | \(0.361990\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.45970e6 | −0.139779 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.98583e6 | −0.168609 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.46095e7 | 1.37233 | 0.686163 | − | 0.727448i | \(-0.259294\pi\) | ||||
0.686163 | + | 0.727448i | \(0.259294\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.77563e6 | 0.209229 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.81159e7 | 0.991453 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 523320. | 0.0284628 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.00982e7 | 1.07966 | 0.539828 | − | 0.841776i | \(-0.318489\pi\) | ||||
0.539828 | + | 0.841776i | \(0.318489\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.12008e7 | −0.597993 | −0.298996 | − | 0.954254i | \(-0.596652\pi\) | ||||
−0.298996 | + | 0.954254i | \(0.596652\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 500736. | 0.0264067 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.73280e7 | −1.95650 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.38971e7 | −1.23733 | −0.618667 | − | 0.785653i | \(-0.712327\pi\) | ||||
−0.618667 | + | 0.785653i | \(0.712327\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.17972e6 | 0.472422 | 0.236211 | − | 0.971702i | \(-0.424094\pi\) | ||||
0.236211 | + | 0.971702i | \(0.424094\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.82018e7 | −1.43388 | −0.716939 | − | 0.697135i | \(-0.754458\pi\) | ||||
−0.716939 | + | 0.697135i | \(0.754458\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.81930e7 | −0.919429 | −0.459714 | − | 0.888067i | \(-0.652048\pi\) | ||||
−0.459714 | + | 0.888067i | \(0.652048\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.42863e6 | 0.171202 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.77627e6 | 0.0881644 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.97349e6 | 0.145835 | 0.0729175 | − | 0.997338i | \(-0.476769\pi\) | ||||
0.0729175 | + | 0.997338i | \(0.476769\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.00394e6 | −0.0977003 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.42564e6 | 0.0686858 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.18340e6 | 0.0566791 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.82291e7 | −1.80955 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.43801e7 | −0.676690 | −0.338345 | − | 0.941022i | \(-0.609867\pi\) | ||||
−0.338345 | + | 0.941022i | \(0.609867\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.74223e7 | 1.27542 | 0.637708 | − | 0.770278i | \(-0.279883\pi\) | ||||
0.637708 | + | 0.770278i | \(0.279883\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.79786e7 | −1.29373 | −0.646864 | − | 0.762606i | \(-0.723920\pi\) | ||||
−0.646864 | + | 0.762606i | \(0.723920\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.67312e6 | 0.259295 | 0.129648 | − | 0.991560i | \(-0.458615\pi\) | ||||
0.129648 | + | 0.991560i | \(0.458615\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.17747e6 | 0.0989492 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.23328e7 | 0.554005 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 879376. | 0.0392762 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.22186e6 | −0.0539514 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.09211e7 | −0.479478 | −0.239739 | − | 0.970837i | \(-0.577062\pi\) | ||||
−0.239739 | + | 0.970837i | \(0.577062\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.72031e7 | 1.61488 | 0.807438 | − | 0.589952i | \(-0.200854\pi\) | ||||
0.807438 | + | 0.589952i | \(0.200854\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.57619e7 | 1.54355 | 0.771773 | − | 0.635898i | \(-0.219370\pi\) | ||||
0.771773 | + | 0.635898i | \(0.219370\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.25301e7 | 0.961510 | 0.480755 | − | 0.876855i | \(-0.340363\pi\) | ||||
0.480755 | + | 0.876855i | \(0.340363\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −149548. | −0.00634638 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.55826e6 | 0.191280 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.46452e6 | −0.102843 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.33534e7 | −0.551052 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.47604e7 | 1.42650 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −393064. | −0.0159530 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.18871e7 | 1.28705 | 0.643526 | − | 0.765424i | \(-0.277471\pi\) | ||||
0.643526 | + | 0.765424i | \(0.277471\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.21745e7 | −0.885233 | −0.442617 | − | 0.896711i | \(-0.645950\pi\) | ||||
−0.442617 | + | 0.896711i | \(0.645950\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.48148e6 | −0.0588192 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.07206e7 | 0.421014 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.87465e7 | −1.12279 | −0.561393 | − | 0.827549i | \(-0.689734\pi\) | ||||
−0.561393 | + | 0.827549i | \(0.689734\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.62484e6 | −0.255960 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.45147e7 | 1.71060 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.58792e7 | 0.983810 | 0.491905 | − | 0.870649i | \(-0.336301\pi\) | ||||
0.491905 | + | 0.870649i | \(0.336301\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.13932e6 | 0.156515 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.11344e6 | 0.0790607 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.35364e7 | 1.61996 | 0.809979 | − | 0.586459i | \(-0.199478\pi\) | ||||
0.809979 | + | 0.586459i | \(0.199478\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.20702e7 | −1.54882 | −0.774410 | − | 0.632684i | \(-0.781953\pi\) | ||||
−0.774410 | + | 0.632684i | \(0.781953\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.27662e7 | 1.19991 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −505082. | −0.0183015 | −0.00915076 | − | 0.999958i | \(-0.502913\pi\) | ||||
−0.00915076 | + | 0.999958i | \(0.502913\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.97336e6 | −0.215305 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.18755e7 | −0.780234 | −0.390117 | − | 0.920765i | \(-0.627566\pi\) | ||||
−0.390117 | + | 0.920765i | \(0.627566\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.06055e6 | −0.0731097 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.95043e6 | 0.349378 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.89943e7 | −0.663461 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.79972e6 | 0.0622138 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.79738e7 | 0.962024 | 0.481012 | − | 0.876714i | \(-0.340269\pi\) | ||||
0.481012 | + | 0.876714i | \(0.340269\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.37517e7 | −1.48918 | −0.744590 | − | 0.667522i | \(-0.767355\pi\) | ||||
−0.744590 | + | 0.667522i | \(0.767355\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.42746e6 | −0.0821997 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.53190e7 | 1.51895 | 0.759476 | − | 0.650535i | \(-0.225455\pi\) | ||||
0.759476 | + | 0.650535i | \(0.225455\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.39582e7 | 0.798911 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.15059e7 | −1.37002 | −0.685009 | − | 0.728534i | \(-0.740202\pi\) | ||||
−0.685009 | + | 0.728534i | \(0.740202\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.61974e6 | −0.0531929 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.78108e7 | −1.87940 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.40757e7 | 1.10220 | 0.551101 | − | 0.834439i | \(-0.314208\pi\) | ||||
0.551101 | + | 0.834439i | \(0.314208\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.37030e6 | 0.0438793 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.22181e7 | −1.34512 | −0.672560 | − | 0.740042i | \(-0.734805\pi\) | ||||
−0.672560 | + | 0.740042i | \(0.734805\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 504.6.a.d.1.1 | 1 | ||
3.2 | odd | 2 | 168.6.a.b.1.1 | ✓ | 1 | ||
4.3 | odd | 2 | 1008.6.a.q.1.1 | 1 | |||
12.11 | even | 2 | 336.6.a.m.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.6.a.b.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
336.6.a.m.1.1 | 1 | 12.11 | even | 2 | |||
504.6.a.d.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1008.6.a.q.1.1 | 1 | 4.3 | odd | 2 |