Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,6,Mod(1,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.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: | \(71.8519512762\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 14) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 448.1 |
$q$-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 | ||||||||
\(3\) | −8.00000 | −0.513200 | −0.256600 | − | 0.966518i | \(-0.582602\pi\) | ||||
−0.256600 | + | 0.966518i | \(0.582602\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −10.0000 | −0.178885 | −0.0894427 | − | 0.995992i | \(-0.528509\pi\) | ||||
−0.0894427 | + | 0.995992i | \(0.528509\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −179.000 | −0.736626 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 340.000 | 0.847222 | 0.423611 | − | 0.905844i | \(-0.360762\pi\) | ||||
0.423611 | + | 0.905844i | \(0.360762\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 294.000 | 0.482491 | 0.241245 | − | 0.970464i | \(-0.422444\pi\) | ||||
0.241245 | + | 0.970464i | \(0.422444\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 80.0000 | 0.0918040 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1226.00 | 1.02889 | 0.514444 | − | 0.857524i | \(-0.327998\pi\) | ||||
0.514444 | + | 0.857524i | \(0.327998\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2432.00 | −1.54554 | −0.772769 | − | 0.634688i | \(-0.781129\pi\) | ||||
−0.772769 | + | 0.634688i | \(0.781129\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 392.000 | 0.193971 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2000.00 | 0.788334 | 0.394167 | − | 0.919039i | \(-0.371033\pi\) | ||||
0.394167 | + | 0.919039i | \(0.371033\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3025.00 | −0.968000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3376.00 | 0.891237 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6746.00 | 1.48954 | 0.744769 | − | 0.667323i | \(-0.232560\pi\) | ||||
0.744769 | + | 0.667323i | \(0.232560\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8856.00 | 1.65513 | 0.827567 | − | 0.561366i | \(-0.189724\pi\) | ||||
0.827567 | + | 0.561366i | \(0.189724\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2720.00 | −0.434795 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 490.000 | 0.0676123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9182.00 | −1.10264 | −0.551319 | − | 0.834295i | \(-0.685875\pi\) | ||||
−0.551319 | + | 0.834295i | \(0.685875\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2352.00 | −0.247614 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −14574.0 | −1.35400 | −0.677001 | − | 0.735982i | \(-0.736721\pi\) | ||||
−0.677001 | + | 0.735982i | \(0.736721\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8108.00 | −0.668717 | −0.334359 | − | 0.942446i | \(-0.608520\pi\) | ||||
−0.334359 | + | 0.942446i | \(0.608520\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1790.00 | 0.131772 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −312.000 | −0.0206020 | −0.0103010 | − | 0.999947i | \(-0.503279\pi\) | ||||
−0.0103010 | + | 0.999947i | \(0.503279\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9808.00 | −0.528026 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 14634.0 | 0.715605 | 0.357803 | − | 0.933797i | \(-0.383526\pi\) | ||||
0.357803 | + | 0.933797i | \(0.383526\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3400.00 | −0.151556 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 19456.0 | 0.793170 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 27656.0 | 1.03433 | 0.517165 | − | 0.855886i | \(-0.326987\pi\) | ||||
0.517165 | + | 0.855886i | \(0.326987\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −34338.0 | −1.18155 | −0.590773 | − | 0.806838i | \(-0.701177\pi\) | ||||
−0.590773 | + | 0.806838i | \(0.701177\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8771.00 | 0.278418 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2940.00 | −0.0863106 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12316.0 | −0.335184 | −0.167592 | − | 0.985856i | \(-0.553599\pi\) | ||||
−0.167592 | + | 0.985856i | \(0.553599\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −16000.0 | −0.404573 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 36920.0 | 0.869192 | 0.434596 | − | 0.900625i | \(-0.356891\pi\) | ||||
0.434596 | + | 0.900625i | \(0.356891\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −61718.0 | −1.35552 | −0.677758 | − | 0.735285i | \(-0.737048\pi\) | ||||
−0.677758 | + | 0.735285i | \(0.737048\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 24200.0 | 0.496778 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16660.0 | −0.320220 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −64752.0 | −1.16731 | −0.583654 | − | 0.812002i | \(-0.698378\pi\) | ||||
−0.583654 | + | 0.812002i | \(0.698378\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 16489.0 | 0.279243 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 77056.0 | 1.22775 | 0.613877 | − | 0.789402i | \(-0.289609\pi\) | ||||
0.613877 | + | 0.789402i | \(0.289609\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12260.0 | −0.184053 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −53968.0 | −0.764431 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8166.00 | −0.109278 | −0.0546392 | − | 0.998506i | \(-0.517401\pi\) | ||||
−0.0546392 | + | 0.998506i | \(0.517401\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14406.0 | −0.182364 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −70848.0 | −0.849416 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 24320.0 | 0.276474 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 20650.0 | 0.222839 | 0.111419 | − | 0.993773i | \(-0.464460\pi\) | ||||
0.111419 | + | 0.993773i | \(0.464460\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −60860.0 | −0.624085 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −186250. | −1.81674 | −0.908370 | − | 0.418167i | \(-0.862673\pi\) | ||||
−0.908370 | + | 0.418167i | \(0.862673\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −60064.0 | −0.557855 | −0.278927 | − | 0.960312i | \(-0.589979\pi\) | ||||
−0.278927 | + | 0.960312i | \(0.589979\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3920.00 | −0.0346987 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −47892.0 | −0.404393 | −0.202196 | − | 0.979345i | \(-0.564808\pi\) | ||||
−0.202196 | + | 0.979345i | \(0.564808\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −22102.0 | −0.178183 | −0.0890913 | − | 0.996023i | \(-0.528396\pi\) | ||||
−0.0890913 | + | 0.996023i | \(0.528396\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 73456.0 | 0.565874 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −245054. | −1.80537 | −0.902684 | − | 0.430304i | \(-0.858406\pi\) | ||||
−0.902684 | + | 0.430304i | \(0.858406\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −20000.0 | −0.141022 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −52626.0 | −0.355415 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −60074.0 | −0.388883 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −45451.0 | −0.282215 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 116592. | 0.694874 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 61500.0 | 0.352047 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −96696.0 | −0.531985 | −0.265992 | − | 0.963975i | \(-0.585700\pi\) | ||||
−0.265992 | + | 0.963975i | \(0.585700\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 64864.0 | 0.343186 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −134368. | −0.684097 | −0.342048 | − | 0.939682i | \(-0.611121\pi\) | ||||
−0.342048 | + | 0.939682i | \(0.611121\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 119168. | 0.584158 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −33760.0 | −0.159429 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −294662. | −1.34129 | −0.670645 | − | 0.741778i | \(-0.733983\pi\) | ||||
−0.670645 | + | 0.741778i | \(0.733983\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −314944. | −1.38260 | −0.691300 | − | 0.722568i | \(-0.742962\pi\) | ||||
−0.691300 | + | 0.722568i | \(0.742962\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2496.00 | 0.0105730 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 99960.0 | 0.408777 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −67460.0 | −0.266457 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −19208.0 | −0.0733143 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −113622. | −0.419273 | −0.209636 | − | 0.977779i | \(-0.567228\pi\) | ||||
−0.209636 | + | 0.977779i | \(0.567228\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 408208. | 1.45693 | 0.728466 | − | 0.685082i | \(-0.240234\pi\) | ||||
0.728466 | + | 0.685082i | \(0.240234\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −219454. | −0.757905 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −88560.0 | −0.296080 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −293546. | −0.950445 | −0.475223 | − | 0.879866i | \(-0.657632\pi\) | ||||
−0.475223 | + | 0.879866i | \(0.657632\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −117072. | −0.367249 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −98000.0 | −0.297962 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 317116. | 0.934866 | 0.467433 | − | 0.884029i | \(-0.345179\pi\) | ||||
0.467433 | + | 0.884029i | \(0.345179\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 27200.0 | 0.0777784 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 141568. | 0.392802 | 0.196401 | − | 0.980524i | \(-0.437075\pi\) | ||||
0.196401 | + | 0.980524i | \(0.437075\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −284857. | −0.767203 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 435328. | 1.13848 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 71222.0 | 0.180925 | 0.0904626 | − | 0.995900i | \(-0.471165\pi\) | ||||
0.0904626 | + | 0.995900i | \(0.471165\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 148225. | 0.365870 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −221248. | −0.530819 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −485628. | −1.13285 | −0.566423 | − | 0.824114i | \(-0.691673\pi\) | ||||
−0.566423 | + | 0.824114i | \(0.691673\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −657090. | −1.49083 | −0.745416 | − | 0.666600i | \(-0.767749\pi\) | ||||
−0.745416 | + | 0.666600i | \(0.767749\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 274704. | 0.606369 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 91820.0 | 0.197246 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 416840. | 0.871697 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −165424. | −0.336856 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 68304.0 | 0.135476 | 0.0677381 | − | 0.997703i | \(-0.478422\pi\) | ||||
0.0677381 | + | 0.997703i | \(0.478422\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 352754. | 0.681677 | 0.340839 | − | 0.940122i | \(-0.389289\pi\) | ||||
0.340839 | + | 0.940122i | \(0.389289\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 23520.0 | 0.0442946 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −196982. | −0.361627 | −0.180814 | − | 0.983517i | \(-0.557873\pi\) | ||||
−0.180814 | + | 0.983517i | \(0.557873\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.10392e6 | −1.97608 | −0.988041 | − | 0.154192i | \(-0.950723\pi\) | ||||
−0.988041 | + | 0.154192i | \(0.950723\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 98528.0 | 0.172016 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −330554. | −0.562992 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 145740. | 0.242211 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −358000. | −0.580707 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −826880. | −1.30941 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 103444. | 0.159955 | 0.0799777 | − | 0.996797i | \(-0.474515\pi\) | ||||
0.0799777 | + | 0.996797i | \(0.474515\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −295360. | −0.446070 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 81080.0 | 0.119624 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −433944. | −0.625582 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 493744. | 0.695651 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 360444. | 0.496429 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 307328. | 0.413847 | 0.206924 | − | 0.978357i | \(-0.433655\pi\) | ||||
0.206924 | + | 0.978357i | \(0.433655\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 541475. | 0.713053 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 891792. | 1.14868 | 0.574340 | − | 0.818617i | \(-0.305259\pi\) | ||||
0.574340 | + | 0.818617i | \(0.305259\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −276706. | −0.348682 | −0.174341 | − | 0.984685i | \(-0.555780\pi\) | ||||
−0.174341 | + | 0.984685i | \(0.555780\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 133280. | 0.164337 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.47943e6 | 1.78528 | 0.892639 | − | 0.450772i | \(-0.148851\pi\) | ||||
0.892639 | + | 0.450772i | \(0.148851\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3120.00 | 0.00368540 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 518016. | 0.599063 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.00034e6 | 1.13280 | 0.566402 | − | 0.824129i | \(-0.308335\pi\) | ||||
0.566402 | + | 0.824129i | \(0.308335\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.35833e6 | 1.50648 | 0.753239 | − | 0.657747i | \(-0.228490\pi\) | ||||
0.753239 | + | 0.657747i | \(0.228490\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −952280. | −1.03454 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −24010.0 | −0.0255551 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −715008. | −0.745708 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −616448. | −0.630083 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 177408. | 0.177742 | 0.0888708 | − | 0.996043i | \(-0.471674\pi\) | ||||
0.0888708 | + | 0.996043i | \(0.471674\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 680000. | 0.667894 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 98080.0 | 0.0944561 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 326658. | 0.308504 | 0.154252 | − | 0.988032i | \(-0.450703\pi\) | ||||
0.154252 | + | 0.988032i | \(0.450703\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 449918. | 0.416758 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.20753e6 | −1.09723 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −34920.0 | −0.0311304 | −0.0155652 | − | 0.999879i | \(-0.504955\pi\) | ||||
−0.0155652 | + | 0.999879i | \(0.504955\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −146340. | −0.128011 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 65328.0 | 0.0560817 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −716458. | −0.603685 | −0.301842 | − | 0.953358i | \(-0.597602\pi\) | ||||
−0.301842 | + | 0.953358i | \(0.597602\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −953376. | −0.788571 | −0.394286 | − | 0.918988i | \(-0.629008\pi\) | ||||
−0.394286 | + | 0.918988i | \(0.629008\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 115248. | 0.0935894 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.02850e6 | −0.820111 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.84729e6 | 1.44656 | 0.723279 | − | 0.690556i | \(-0.242634\pi\) | ||||
0.723279 | + | 0.690556i | \(0.242634\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.58522e6 | −1.21921 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.99601e6 | −1.50798 | −0.753991 | − | 0.656885i | \(-0.771874\pi\) | ||||
−0.753991 | + | 0.656885i | \(0.771874\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −234088. | −0.173745 | −0.0868726 | − | 0.996219i | \(-0.527687\pi\) | ||||
−0.0868726 | + | 0.996219i | \(0.527687\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −194560. | −0.141887 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 714126. | 0.511764 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 83219.0 | 0.0586108 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −165200. | −0.114361 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.50081e6 | 1.70181 | 0.850905 | − | 0.525320i | \(-0.176054\pi\) | ||||
0.850905 | + | 0.525320i | \(0.176054\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −276560. | −0.185027 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.14784e6 | 0.755075 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 588000. | 0.380364 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 397292. | 0.252751 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.49000e6 | 0.932352 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 343380. | 0.211361 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.34203e6 | −1.41823 | −0.709115 | − | 0.705092i | \(-0.750905\pi\) | ||||
−0.709115 | + | 0.705092i | \(0.750905\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 480512. | 0.286291 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −163064. | −0.0955998 | −0.0477999 | − | 0.998857i | \(-0.515221\pi\) | ||||
−0.0477999 | + | 0.998857i | \(0.515221\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.73965e6 | 1.00369 | 0.501847 | − | 0.864957i | \(-0.332654\pi\) | ||||
0.501847 | + | 0.864957i | \(0.332654\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −87710.0 | −0.0498050 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.79771e6 | 1.00478 | 0.502392 | − | 0.864640i | \(-0.332454\pi\) | ||||
0.502392 | + | 0.864640i | \(0.332454\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.29364e6 | 1.26197 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 383136. | 0.207535 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.98163e6 | −1.59019 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −889350. | −0.467051 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 176816. | 0.0914434 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15288.0 | 0.00778683 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.47541e6 | 1.24187 | 0.620937 | − | 0.783861i | \(-0.286752\pi\) | ||||
0.620937 | + | 0.783861i | \(0.286752\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.64358e6 | 0.812231 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 123160. | 0.0599595 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 89154.0 | 0.0427628 | 0.0213814 | − | 0.999771i | \(-0.493194\pi\) | ||||
0.0213814 | + | 0.999771i | \(0.493194\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.96043e6 | 0.926515 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.01104e6 | 1.40227 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 160000. | 0.0723723 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −938556. | −0.418443 | −0.209222 | − | 0.977868i | \(-0.567093\pi\) | ||||
−0.209222 | + | 0.977868i | \(0.567093\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.34268e6 | −1.46903 | −0.734516 | − | 0.678591i | \(-0.762591\pi\) | ||||
−0.734516 | + | 0.678591i | \(0.762591\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 992544. | 0.430013 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.76606e6 | −1.60861 | −0.804305 | − | 0.594217i | \(-0.797462\pi\) | ||||
−0.804305 | + | 0.594217i | \(0.797462\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −369200. | −0.155486 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 480592. | 0.199575 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.53934e6 | −0.630376 | −0.315188 | − | 0.949029i | \(-0.602068\pi\) | ||||
−0.315188 | + | 0.949029i | \(0.602068\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.43852e6 | 1.38869 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 363608. | 0.144833 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 617180. | 0.242482 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −859312. | −0.333032 | −0.166516 | − | 0.986039i | \(-0.553252\pi\) | ||||
−0.166516 | + | 0.986039i | \(0.553252\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.60875e6 | 0.997392 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −717066. | −0.270473 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 976586. | 0.363445 | 0.181722 | − | 0.983350i | \(-0.441833\pi\) | ||||
0.181722 | + | 0.983350i | \(0.441833\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −492000. | −0.180670 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.98332e6 | 0.718688 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −106444. | −0.0380648 | −0.0190324 | − | 0.999819i | \(-0.506059\pi\) | ||||
−0.0190324 | + | 0.999819i | \(0.506059\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 773568. | 0.273015 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.00634e6 | −0.698889 | −0.349445 | − | 0.936957i | \(-0.613630\pi\) | ||||
−0.349445 | + | 0.936957i | \(0.613630\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 166600. | 0.0572827 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.45133e6 | 0.492594 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 684002. | 0.229184 | 0.114592 | − | 0.993413i | \(-0.463444\pi\) | ||||
0.114592 | + | 0.993413i | \(0.463444\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.45200e6 | 0.811108 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.07494e6 | 0.351079 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 647520. | 0.208814 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 222870. | 0.0709701 | 0.0354850 | − | 0.999370i | \(-0.488702\pi\) | ||||
0.0354850 | + | 0.999370i | \(0.488702\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −953344. | −0.299790 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.90072e6 | 0.590279 | 0.295140 | − | 0.955454i | \(-0.404634\pi\) | ||||
0.295140 | + | 0.955454i | \(0.404634\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.60366e6 | 0.798587 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −164890. | −0.0499524 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.12188e6 | −0.934179 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.77715e6 | 0.525311 | 0.262656 | − | 0.964890i | \(-0.415402\pi\) | ||||
0.262656 | + | 0.964890i | \(0.415402\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.35730e6 | 0.688350 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.35514e6 | −0.390940 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −770560. | −0.219627 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.51955e6 | 0.709550 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28056.0 | −0.00780712 | −0.00390356 | − | 0.999992i | \(-0.501243\pi\) | ||||
−0.00390356 | + | 0.999992i | \(0.501243\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.70897e6 | 0.744902 | 0.372451 | − | 0.928052i | \(-0.378518\pi\) | ||||
0.372451 | + | 0.928052i | \(0.378518\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 55848.0 | 0.0151760 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.70865e6 | −0.995964 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.68256e6 | 0.446582 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −799680. | −0.209784 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.53898e6 | 1.43627 | 0.718136 | − | 0.695902i | \(-0.244995\pi\) | ||||
0.718136 | + | 0.695902i | \(0.244995\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −868294. | −0.222560 | −0.111280 | − | 0.993789i | \(-0.535495\pi\) | ||||
−0.111280 | + | 0.993789i | \(0.535495\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 539680. | 0.136746 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.86400e6 | −1.21840 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.13767e6 | −0.281745 | −0.140872 | − | 0.990028i | \(-0.544991\pi\) | ||||
−0.140872 | + | 0.990028i | \(0.544991\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −429779. | −0.105232 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.75399e6 | −0.424636 | −0.212318 | − | 0.977201i | \(-0.568101\pi\) | ||||
−0.212318 | + | 0.977201i | \(0.568101\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 81660.0 | 0.0195483 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 908976. | 0.215171 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.41674e6 | 0.565736 | 0.282868 | − | 0.959159i | \(-0.408714\pi\) | ||||
0.282868 | + | 0.959159i | \(0.408714\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.95516e6 | −1.14714 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.26566e6 | −0.747698 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 144060. | 0.0326223 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −127430. | −0.0285418 | −0.0142709 | − | 0.999898i | \(-0.504543\pi\) | ||||
−0.0142709 | + | 0.999898i | \(0.504543\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.13898e6 | 0.916983 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 128198. | 0.0280950 | 0.0140475 | − | 0.999901i | \(-0.495528\pi\) | ||||
0.0140475 | + | 0.999901i | \(0.495528\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.01653e6 | −0.870760 | −0.435380 | − | 0.900247i | \(-0.643386\pi\) | ||||
−0.435380 | + | 0.900247i | \(0.643386\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 708480. | 0.151948 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.67246e6 | −1.84014 | −0.920069 | − | 0.391757i | \(-0.871867\pi\) | ||||
−0.920069 | + | 0.391757i | \(0.871867\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 603484. | 0.126687 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.34837e6 | 0.487769 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.75672e6 | −0.566552 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.35680e6 | 1.49608 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.61949e6 | −0.527133 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.28946e6 | 1.65077 | 0.825387 | − | 0.564567i | \(-0.190957\pi\) | ||||
0.825387 | + | 0.564567i | \(0.190957\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.69951e6 | −0.532013 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 784000. | 0.152914 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −206500. | −0.0398626 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.91770e6 | −1.70385 | −0.851923 | − | 0.523667i | \(-0.824563\pi\) | ||||
−0.851923 | + | 0.523667i | \(0.824563\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.53693e6 | −0.479773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.71537e6 | 1.06989 | 0.534947 | − | 0.844886i | \(-0.320332\pi\) | ||||
0.534947 | + | 0.844886i | \(0.320332\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.27060e6 | 1.53257 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 608600. | 0.111640 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.80908e6 | −0.328524 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −125116. | −0.0224937 | −0.0112469 | − | 0.999937i | \(-0.503580\pi\) | ||||
−0.0112469 | + | 0.999937i | \(0.503580\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.13254e6 | −0.201586 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.77116e6 | −0.488362 | −0.244181 | − | 0.969730i | \(-0.578519\pi\) | ||||
−0.244181 | + | 0.969730i | \(0.578519\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.86250e6 | 0.324988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.27886e6 | 0.393729 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 138534. | 0.0237007 | 0.0118504 | − | 0.999930i | \(-0.496228\pi\) | ||||
0.0118504 | + | 0.999930i | \(0.496228\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.02418e6 | 0.512337 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.21043e6 | −1.37744 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 600640. | 0.0997921 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −106080. | −0.0174545 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −569776. | −0.0928508 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.80281e6 | −0.290976 | −0.145488 | − | 0.989360i | \(-0.546475\pi\) | ||||
−0.145488 | + | 0.989360i | \(0.546475\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.77247e6 | −1.56225 | −0.781124 | − | 0.624375i | \(-0.785354\pi\) | ||||
−0.781124 | + | 0.624375i | \(0.785354\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.18580e6 | −0.187764 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.08575e7 | 1.70295 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.43634e6 | −0.378529 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.95042e6 | −0.761914 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.28476e6 | −0.653293 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 478920. | 0.0723400 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.88502e6 | 0.581377 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 816340. | 0.121032 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.45504e6 | −0.360633 | −0.180316 | − | 0.983609i | \(-0.557712\pi\) | ||||
−0.180316 | + | 0.983609i | \(0.557712\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.25672e6 | 0.765095 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 221020. | 0.0318743 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.32081e7 | −1.88744 | −0.943721 | − | 0.330743i | \(-0.892701\pi\) | ||||
−0.943721 | + | 0.330743i | \(0.892701\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.14650e6 | 0.870356 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.64063e7 | −2.30214 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.17285e6 | 0.441201 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −734560. | −0.101227 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.83293e6 | −1.06976 | −0.534880 | − | 0.844928i | \(-0.679643\pi\) | ||||
−0.534880 | + | 0.844928i | \(0.679643\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.38375e6 | −0.322650 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.33472e6 | −0.447355 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.57908e6 | −0.475883 | −0.237942 | − | 0.971279i | \(-0.576473\pi\) | ||||
−0.237942 | + | 0.971279i | \(0.576473\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.45054e6 | 0.322954 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −807961. | −0.105544 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.39581e6 | −0.439707 | −0.219853 | − | 0.975533i | \(-0.570558\pi\) | ||||
−0.219853 | + | 0.975533i | \(0.570558\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.47695e6 | 0.189572 | 0.0947862 | − | 0.995498i | \(-0.469783\pi\) | ||||
0.0947862 | + | 0.995498i | \(0.469783\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −546432. | −0.0695264 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.05000e6 | −0.763108 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.49961e7 | −1.87516 | −0.937580 | − | 0.347771i | \(-0.886939\pi\) | ||||
−0.937580 | + | 0.347771i | \(0.886939\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.82203e6 | −0.349837 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.77574e6 | −0.464047 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.97556e6 | 0.606276 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 526260. | 0.0635786 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.29291e6 | 0.394444 | 0.197222 | − | 0.980359i | \(-0.436808\pi\) | ||||
0.197222 | + | 0.980359i | \(0.436808\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.15378e7 | −2.55807 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.57586e6 | 0.185587 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.17908e7 | −1.37692 | −0.688459 | − | 0.725275i | \(-0.741713\pi\) | ||||
−0.688459 | + | 0.725275i | \(0.741713\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 600740. | 0.0695655 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.83136e6 | 1.01413 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.52642e6 | −0.173823 | −0.0869117 | − | 0.996216i | \(-0.527700\pi\) | ||||
−0.0869117 | + | 0.996216i | \(0.527700\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.00142e7 | −1.13092 | −0.565458 | − | 0.824777i | \(-0.691301\pi\) | ||||
−0.565458 | + | 0.824777i | \(0.691301\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.20456e6 | 0.246905 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 454510. | 0.0504841 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.20660e7 | 1.32920 | 0.664599 | − | 0.747200i | \(-0.268602\pi\) | ||||
0.664599 | + | 0.747200i | \(0.268602\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.64443e6 | 0.288928 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −91728.0 | −0.00994029 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.81950e6 | −0.625511 | −0.312755 | − | 0.949834i | \(-0.601252\pi\) | ||||
−0.312755 | + | 0.949834i | \(0.601252\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.16592e6 | −0.124303 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.16589e6 | −0.440550 | −0.220275 | − | 0.975438i | \(-0.570695\pi\) | ||||
−0.220275 | + | 0.975438i | \(0.570695\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.08090e6 | 0.847683 | 0.423841 | − | 0.905736i | \(-0.360681\pi\) | ||||
0.423841 | + | 0.905736i | \(0.360681\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.75200e6 | 0.702592 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 400134. | 0.0413034 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.83812e6 | 0.905024 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.61504e6 | 0.671991 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.12571e7 | −1.13449 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.40878e6 | −0.840735 | −0.420368 | − | 0.907354i | \(-0.638099\pi\) | ||||
−0.420368 | + | 0.907354i | \(0.638099\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −827552. | −0.0820892 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 966960. | 0.0951643 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 705894. | 0.0689272 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.60868e6 | −0.640269 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.29760e6 | 0.605383 | 0.302691 | − | 0.953089i | \(-0.402115\pi\) | ||||
0.302691 | + | 0.953089i | \(0.402115\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.39762e6 | −0.419460 | −0.209730 | − | 0.977759i | \(-0.567259\pi\) | ||||
−0.209730 | + | 0.977759i | \(0.567259\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −648640. | −0.0613910 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.55397e6 | 0.615522 | 0.307761 | − | 0.951464i | \(-0.400420\pi\) | ||||
0.307761 | + | 0.951464i | \(0.400420\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.40304e6 | 0.876308 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.47155e6 | 0.321049 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.79652e6 | −0.348420 | −0.174210 | − | 0.984709i | \(-0.555737\pi\) | ||||
−0.174210 | + | 0.984709i | \(0.555737\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.34368e6 | 0.122375 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.10475e7 | 0.998508 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.82684e6 | 0.791757 | 0.395879 | − | 0.918303i | \(-0.370440\pi\) | ||||
0.395879 | + | 0.918303i | \(0.370440\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 341270. | 0.0303805 | 0.0151902 | − | 0.999885i | \(-0.495165\pi\) | ||||
0.0151902 | + | 0.999885i | \(0.495165\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.88355e6 | −0.254767 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.19168e6 | −0.104497 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.34920e7 | 1.17425 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.45862e6 | −0.212386 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.16749e7 | −1.00103 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.41807e6 | 0.376006 | 0.188003 | − | 0.982168i | \(-0.439799\pi\) | ||||
0.188003 | + | 0.982168i | \(0.439799\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.02124e7 | −0.862717 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.63858e7 | −1.37403 | −0.687014 | − | 0.726644i | \(-0.741079\pi\) | ||||
−0.687014 | + | 0.726644i | \(0.741079\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.01185e6 | −0.0842251 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.13434e6 | −0.589503 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.75399e7 | 1.43872 | 0.719360 | − | 0.694638i | \(-0.244435\pi\) | ||||
0.719360 | + | 0.694638i | \(0.244435\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.94662e6 | 0.239937 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.21365e6 | 0.178944 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.30240e6 | 0.345273 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.14638e6 | −0.250678 | −0.125339 | − | 0.992114i | \(-0.540002\pi\) | ||||
−0.125339 | + | 0.992114i | \(0.540002\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.98214e6 | 0.235882 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.14944e6 | 0.247327 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.78677e7 | −1.39312 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.18355e7 | −0.916205 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.90919e7 | 1.46742 | 0.733709 | − | 0.679464i | \(-0.237788\pi\) | ||||
0.733709 | + | 0.679464i | \(0.237788\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.23306e7 | 1.70417 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −24960.0 | −0.00189135 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.12625e6 | 0.686663 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −990974. | −0.0740366 | −0.0370183 | − | 0.999315i | \(-0.511786\pi\) | ||||
−0.0370183 | + | 0.999315i | \(0.511786\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.15906e7 | 0.859869 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.77120e7 | 1.30480 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −999600. | −0.0731242 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.00275e6 | −0.581355 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.69014e7 | −1.21928 | −0.609638 | − | 0.792680i | \(-0.708685\pi\) | ||||
−0.609638 | + | 0.792680i | \(0.708685\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.94314e6 | 0.210849 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.08666e7 | −0.773125 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.04066e7 | −1.44187 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.34302e7 | −1.64414 | −0.822071 | − | 0.569384i | \(-0.807182\pi\) | ||||
−0.822071 | + | 0.569384i | \(0.807182\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.61141e6 | 0.251686 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.94041e6 | −0.688035 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −975810. | −0.0670819 | −0.0335409 | − | 0.999437i | \(-0.510678\pi\) | ||||
−0.0335409 | + | 0.999437i | \(0.510678\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 192080. | 0.0131149 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.18744e6 | −0.283975 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.30208e6 | 0.424495 | 0.212247 | − | 0.977216i | \(-0.431922\pi\) | ||||
0.212247 | + | 0.977216i | \(0.431922\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.72006e6 | 0.382697 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.95698e6 | −0.462326 | −0.231163 | − | 0.972915i | \(-0.574253\pi\) | ||||
−0.231163 | + | 0.972915i | \(0.574253\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.13622e6 | 0.0750018 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.37930e7 | −0.904395 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.34671e6 | 0.152846 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.74535e7 | 1.77622 | 0.888112 | − | 0.459628i | \(-0.152017\pi\) | ||||
0.888112 | + | 0.459628i | \(0.152017\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.41926e6 | −0.0912170 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.08208e6 | −0.260624 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.96889e7 | 1.24877 | 0.624384 | − | 0.781118i | \(-0.285350\pi\) | ||||
0.624384 | + | 0.781118i | \(0.285350\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.44000e6 | −0.342763 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.82079e7 | −1.76567 | −0.882835 | − | 0.469684i | \(-0.844368\pi\) | ||||
−0.882835 | + | 0.469684i | \(0.844368\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.08300e6 | 0.0673467 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.19454e6 | 0.135578 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.13086e6 | 0.499055 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.38081e6 | −0.0842009 | −0.0421005 | − | 0.999113i | \(-0.513405\pi\) | ||||
−0.0421005 | + | 0.999113i | \(0.513405\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.61326e6 | −0.158324 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.54347e7 | 0.929074 | 0.464537 | − | 0.885554i | \(-0.346221\pi\) | ||||
0.464537 | + | 0.885554i | \(0.346221\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.67894e7 | −1.60217 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.59934e6 | −0.213880 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.54440e7 | 2.09266 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.25528e7 | 0.736399 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.27745e7 | 1.32753 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.93546e6 | 0.170021 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.10107e6 | 0.408683 | 0.204342 | − | 0.978900i | \(-0.434495\pi\) | ||||
0.204342 | + | 0.978900i | \(0.434495\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 279360. | 0.0159761 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.20076e7 | 0.682365 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.00954e7 | −0.570085 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.17072e6 | 0.0656954 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.48182e6 | −0.361452 | −0.180726 | − | 0.983533i | \(-0.557845\pi\) | ||||
−0.180726 | + | 0.983533i | \(0.557845\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −382512. | −0.0211972 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.46171e6 | 0.0804973 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.09841e7 | −1.14842 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 980000. | 0.0533011 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.73166e6 | 0.309811 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.60578e7 | 0.862610 | 0.431305 | − | 0.902206i | \(-0.358053\pi\) | ||||
0.431305 | + | 0.902206i | \(0.358053\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.84775e6 | −0.258814 | −0.129407 | − | 0.991592i | \(-0.541307\pi\) | ||||
−0.129407 | + | 0.991592i | \(0.541307\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.62701e6 | 0.404695 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.17116e6 | −0.167234 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.97187e7 | 1.03353 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.57867e6 | 0.134334 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.17976e7 | −1.12863 | −0.564314 | − | 0.825560i | \(-0.690859\pi\) | ||||
−0.564314 | + | 0.825560i | \(0.690859\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.20206e7 | 1.64790 | 0.823948 | − | 0.566665i | \(-0.191767\pi\) | ||||
0.823948 | + | 0.566665i | \(0.191767\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.22800e6 | 0.420881 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.19008e7 | −1.11352 | −0.556758 | − | 0.830675i | \(-0.687955\pi\) | ||||
−0.556758 | + | 0.830675i | \(0.687955\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.45999e7 | 0.737844 | 0.368922 | − | 0.929460i | \(-0.379727\pi\) | ||||
0.368922 | + | 0.929460i | \(0.379727\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.47783e7 | −0.742374 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.94363e6 | 0.146984 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.41568e6 | −0.0702666 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.98979e7 | 1.47512 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.60947e6 | 0.226072 | 0.113036 | − | 0.993591i | \(-0.463942\pi\) | ||||
0.113036 | + | 0.993591i | \(0.463942\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.49974e7 | 1.21872 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.59680e7 | 0.773897 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.84857e6 | 0.137241 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.22710e6 | 0.106667 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.87270e6 | 0.0891661 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.83640e7 | −0.869247 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.98437e7 | 0.933793 | 0.466897 | − | 0.884312i | \(-0.345372\pi\) | ||||
0.466897 | + | 0.884312i | \(0.345372\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.35328e6 | −0.203658 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.22960e6 | −0.0571888 | −0.0285944 | − | 0.999591i | \(-0.509103\pi\) | ||||
−0.0285944 | + | 0.999591i | \(0.509103\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.33041e7 | −1.53998 | −0.769989 | − | 0.638058i | \(-0.779738\pi\) | ||||
−0.769989 | + | 0.638058i | \(0.779738\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.71301e6 | −0.262638 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.36616e7 | −1.08148 | −0.540738 | − | 0.841191i | \(-0.681855\pi\) | ||||
−0.540738 | + | 0.841191i | \(0.681855\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −712220. | −0.0323649 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −665752. | −0.0300791 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.20157e7 | −0.988969 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.62090e6 | −0.161723 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.69635e6 | −0.164149 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.01350e6 | −0.133061 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.37812e7 | 1.04408 | 0.522042 | − | 0.852920i | \(-0.325170\pi\) | ||||
0.522042 | + | 0.852920i | \(0.325170\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.00064e7 | −0.873369 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.41871e7 | −0.615818 | −0.307909 | − | 0.951416i | \(-0.599629\pi\) | ||||
−0.307909 | + | 0.951416i | \(0.599629\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.09281e7 | −0.903293 | −0.451647 | − | 0.892197i | \(-0.649163\pi\) | ||||
−0.451647 | + | 0.892197i | \(0.649163\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.21248e6 | 0.0949557 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.98586e6 | −0.340810 | −0.170405 | − | 0.985374i | \(-0.554508\pi\) | ||||
−0.170405 | + | 0.985374i | \(0.554508\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.73810e6 | 0.201071 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.60626e6 | 0.236581 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 758784. | 0.0318412 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.85628e6 | 0.202650 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.70400e6 | −0.195203 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.97426e7 | 2.46538 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.79413e7 | 0.736278 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.17834e6 | −0.129712 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.57090e6 | 0.266688 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.31861e7 | 0.935856 | 0.467928 | − | 0.883767i | \(-0.345001\pi\) | ||||
0.467928 | + | 0.883767i | \(0.345001\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.33388e7 | 1.33826 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.65299e7 | 0.659895 | 0.329948 | − | 0.943999i | \(-0.392969\pi\) | ||||
0.329948 | + | 0.943999i | \(0.392969\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.61990e7 | 1.04018 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.74704e6 | −0.108471 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.58403e6 | 0.258564 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.28087e7 | 0.500283 | 0.250142 | − | 0.968209i | \(-0.419523\pi\) | ||||
0.250142 | + | 0.968209i | \(0.419523\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.87363e7 | 0.727836 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.08545e7 | 0.419377 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.77756e7 | 1.06735 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.07515e7 | 0.410930 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.97319e7 | 1.13027 | 0.565136 | − | 0.824998i | \(-0.308824\pi\) | ||||
0.565136 | + | 0.824998i | \(0.308824\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.83923e6 | −0.220791 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.30451e6 | 0.0490619 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.16840e6 | −0.155934 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.10970e7 | 0.412911 | 0.206456 | − | 0.978456i | \(-0.433807\pi\) | ||||
0.206456 | + | 0.978456i | \(0.433807\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.39172e7 | −0.515096 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.74313e7 | −1.37804 | −0.689019 | − | 0.724743i | \(-0.741958\pi\) | ||||
−0.689019 | + | 0.724743i | \(0.741958\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.91480e7 | −1.06741 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.65424e6 | 0.0602586 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.50907e7 | −0.546808 | −0.273404 | − | 0.961899i | \(-0.588150\pi\) | ||||
−0.273404 | + | 0.961899i | \(0.588150\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.81451e7 | −0.654024 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.43817e7 | −0.515655 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.15741e7 | −0.769484 | −0.384742 | − | 0.923024i | \(-0.625710\pi\) | ||||
−0.384742 | + | 0.923024i | \(0.625710\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −683040. | −0.0242347 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.83491e7 | −0.647643 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.44384e7 | 0.506960 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.97996e7 | 1.73947 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.57267e6 | 0.297886 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.52754e6 | −0.121942 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.29467e7 | −1.13304 | −0.566520 | − | 0.824048i | \(-0.691711\pi\) | ||||
−0.566520 | + | 0.824048i | \(0.691711\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.38531e7 | 0.816083 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.24599e7 | −0.764470 | −0.382235 | − | 0.924065i | \(-0.624846\pi\) | ||||
−0.382235 | + | 0.924065i | \(0.624846\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.54323e7 | 0.522573 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.11480e6 | 0.239691 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.16236e7 | −1.73026 | −0.865132 | − | 0.501545i | \(-0.832765\pi\) | ||||
−0.865132 | + | 0.501545i | \(0.832765\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.77644e6 | −0.0925831 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.95626e6 | 0.131254 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.10202e7 | −0.363751 | −0.181876 | − | 0.983322i | \(-0.558217\pi\) | ||||
−0.181876 | + | 0.983322i | \(0.558217\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.96982e6 | 0.0646898 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −122304. | −0.00399621 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.62160e7 | −0.527173 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.21029e7 | 1.03839 | 0.519194 | − | 0.854656i | \(-0.326232\pi\) | ||||
0.519194 | + | 0.854656i | \(0.326232\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.98033e7 | −0.637330 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.10392e7 | 0.353492 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.81772e7 | −0.897759 | −0.448879 | − | 0.893592i | \(-0.648177\pi\) | ||||
−0.448879 | + | 0.893592i | \(0.648177\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.09984e7 | −0.982711 |
(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 | 448.6.a.f.1.1 | 1 | ||
4.3 | odd | 2 | 448.6.a.k.1.1 | 1 | |||
8.3 | odd | 2 | 112.6.a.d.1.1 | 1 | |||
8.5 | even | 2 | 14.6.a.b.1.1 | ✓ | 1 | ||
24.5 | odd | 2 | 126.6.a.c.1.1 | 1 | |||
24.11 | even | 2 | 1008.6.a.n.1.1 | 1 | |||
40.13 | odd | 4 | 350.6.c.f.99.1 | 2 | |||
40.29 | even | 2 | 350.6.a.b.1.1 | 1 | |||
40.37 | odd | 4 | 350.6.c.f.99.2 | 2 | |||
56.5 | odd | 6 | 98.6.c.b.67.1 | 2 | |||
56.13 | odd | 2 | 98.6.a.b.1.1 | 1 | |||
56.27 | even | 2 | 784.6.a.h.1.1 | 1 | |||
56.37 | even | 6 | 98.6.c.a.67.1 | 2 | |||
56.45 | odd | 6 | 98.6.c.b.79.1 | 2 | |||
56.53 | even | 6 | 98.6.c.a.79.1 | 2 | |||
168.125 | even | 2 | 882.6.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.6.a.b.1.1 | ✓ | 1 | 8.5 | even | 2 | ||
98.6.a.b.1.1 | 1 | 56.13 | odd | 2 | |||
98.6.c.a.67.1 | 2 | 56.37 | even | 6 | |||
98.6.c.a.79.1 | 2 | 56.53 | even | 6 | |||
98.6.c.b.67.1 | 2 | 56.5 | odd | 6 | |||
98.6.c.b.79.1 | 2 | 56.45 | odd | 6 | |||
112.6.a.d.1.1 | 1 | 8.3 | odd | 2 | |||
126.6.a.c.1.1 | 1 | 24.5 | odd | 2 | |||
350.6.a.b.1.1 | 1 | 40.29 | even | 2 | |||
350.6.c.f.99.1 | 2 | 40.13 | odd | 4 | |||
350.6.c.f.99.2 | 2 | 40.37 | odd | 4 | |||
448.6.a.f.1.1 | 1 | 1.1 | even | 1 | trivial | ||
448.6.a.k.1.1 | 1 | 4.3 | odd | 2 | |||
784.6.a.h.1.1 | 1 | 56.27 | even | 2 | |||
882.6.a.g.1.1 | 1 | 168.125 | even | 2 | |||
1008.6.a.n.1.1 | 1 | 24.11 | even | 2 |