Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,6,Mod(1,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, 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("280.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.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: | \(44.9074695476\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 232x^{2} + 60x + 5808 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-5.33412\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 280.1 |
$q$-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 | ||||||||
\(3\) | 13.9563 | 0.895297 | 0.447649 | − | 0.894210i | \(-0.352262\pi\) | ||||
0.447649 | + | 0.894210i | \(0.352262\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −48.2216 | −0.198443 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −473.121 | −1.17894 | −0.589468 | − | 0.807792i | \(-0.700663\pi\) | ||||
−0.589468 | + | 0.807792i | \(0.700663\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 22.8930 | 0.0375703 | 0.0187852 | − | 0.999824i | \(-0.494020\pi\) | ||||
0.0187852 | + | 0.999824i | \(0.494020\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 348.908 | 0.400389 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1781.22 | −1.49484 | −0.747422 | − | 0.664349i | \(-0.768709\pi\) | ||||
−0.747422 | + | 0.664349i | \(0.768709\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2957.77 | −1.87967 | −0.939834 | − | 0.341632i | \(-0.889020\pi\) | ||||
−0.939834 | + | 0.341632i | \(0.889020\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 683.859 | 0.338391 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3336.13 | 1.31499 | 0.657496 | − | 0.753458i | \(-0.271616\pi\) | ||||
0.657496 | + | 0.753458i | \(0.271616\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4064.38 | −1.07296 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4717.44 | −1.04163 | −0.520813 | − | 0.853671i | \(-0.674371\pi\) | ||||
−0.520813 | + | 0.853671i | \(0.674371\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1593.72 | −0.297856 | −0.148928 | − | 0.988848i | \(-0.547582\pi\) | ||||
−0.148928 | + | 0.988848i | \(0.547582\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6603.02 | −1.05550 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1225.00 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7789.36 | 0.935401 | 0.467700 | − | 0.883887i | \(-0.345083\pi\) | ||||
0.467700 | + | 0.883887i | \(0.345083\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 319.502 | 0.0336366 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5784.32 | −0.537394 | −0.268697 | − | 0.963225i | \(-0.586593\pi\) | ||||
−0.268697 | + | 0.963225i | \(0.586593\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4478.15 | −0.369341 | −0.184671 | − | 0.982800i | \(-0.559122\pi\) | ||||
−0.184671 | + | 0.982800i | \(0.559122\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1205.54 | −0.0887462 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 29535.1 | 1.95026 | 0.975132 | − | 0.221627i | \(-0.0711367\pi\) | ||||
0.975132 | + | 0.221627i | \(0.0711367\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −24859.3 | −1.33833 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −24301.3 | −1.18834 | −0.594168 | − | 0.804341i | \(-0.702519\pi\) | ||||
−0.594168 | + | 0.804341i | \(0.702519\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11828.0 | −0.527236 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −41279.6 | −1.68286 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −35855.1 | −1.34098 | −0.670488 | − | 0.741921i | \(-0.733915\pi\) | ||||
−0.670488 | + | 0.741921i | \(0.733915\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12362.5 | 0.425383 | 0.212692 | − | 0.977119i | \(-0.431777\pi\) | ||||
0.212692 | + | 0.977119i | \(0.431777\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2362.86 | −0.0750043 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 572.326 | 0.0168020 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 30370.6 | 0.826543 | 0.413272 | − | 0.910608i | \(-0.364386\pi\) | ||||
0.413272 | + | 0.910608i | \(0.364386\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 46560.0 | 1.17731 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9507.13 | 0.223823 | 0.111911 | − | 0.993718i | \(-0.464303\pi\) | ||||
0.111911 | + | 0.993718i | \(0.464303\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 56604.5 | 1.24321 | 0.621604 | − | 0.783331i | \(-0.286481\pi\) | ||||
0.621604 | + | 0.783331i | \(0.286481\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8722.69 | 0.179059 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −23182.9 | −0.445596 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −75201.1 | −1.35568 | −0.677838 | − | 0.735211i | \(-0.737083\pi\) | ||||
−0.677838 | + | 0.735211i | \(0.737083\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −45005.8 | −0.762178 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 36995.9 | 0.589465 | 0.294733 | − | 0.955580i | \(-0.404769\pi\) | ||||
0.294733 | + | 0.955580i | \(0.404769\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −44530.6 | −0.668515 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −65838.0 | −0.932564 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −77946.0 | −1.04308 | −0.521541 | − | 0.853226i | \(-0.674643\pi\) | ||||
−0.521541 | + | 0.853226i | \(0.674643\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1121.76 | 0.0142002 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −22242.4 | −0.266670 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −73944.4 | −0.840613 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15751.9 | −0.169982 | −0.0849910 | − | 0.996382i | \(-0.527086\pi\) | ||||
−0.0849910 | + | 0.996382i | \(0.527086\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 22814.6 | 0.233951 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −91977.6 | −0.897178 | −0.448589 | − | 0.893738i | \(-0.648073\pi\) | ||||
−0.448589 | + | 0.893738i | \(0.648073\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10835.5 | 0.100637 | 0.0503185 | − | 0.998733i | \(-0.483976\pi\) | ||||
0.0503185 | + | 0.998733i | \(0.483976\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 17096.5 | 0.151333 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −215276. | −1.81776 | −0.908880 | − | 0.417058i | \(-0.863061\pi\) | ||||
−0.908880 | + | 0.417058i | \(0.863061\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20472.3 | 0.165044 | 0.0825222 | − | 0.996589i | \(-0.473702\pi\) | ||||
0.0825222 | + | 0.996589i | \(0.473702\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 108711. | 0.837462 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 72335.2 | 0.532910 | 0.266455 | − | 0.963847i | \(-0.414148\pi\) | ||||
0.266455 | + | 0.963847i | \(0.414148\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 83403.2 | 0.588082 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1103.94 | −0.00745555 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −87279.9 | −0.564998 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 62792.2 | 0.389890 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −80727.8 | −0.481127 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −324470. | −1.78511 | −0.892556 | − | 0.450936i | \(-0.851090\pi\) | ||||
−0.892556 | + | 0.450936i | \(0.851090\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −62498.4 | −0.330670 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −198917. | −1.01273 | −0.506365 | − | 0.862319i | \(-0.669011\pi\) | ||||
−0.506365 | + | 0.862319i | \(0.669011\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −144931. | −0.710448 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −101609. | −0.479843 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 424147. | 1.93070 | 0.965351 | − | 0.260957i | \(-0.0840379\pi\) | ||||
0.965351 | + | 0.260957i | \(0.0840379\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −423775. | −1.86036 | −0.930182 | − | 0.367099i | \(-0.880351\pi\) | ||||
−0.930182 | + | 0.367099i | \(0.880351\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 412200. | 1.74607 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10831.2 | −0.0442930 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −117936. | −0.465829 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 33509.1 | 0.127900 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 357312. | 1.31850 | 0.659252 | − | 0.751922i | \(-0.270873\pi\) | ||||
0.659252 | + | 0.751922i | \(0.270873\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −118548. | −0.423110 | −0.211555 | − | 0.977366i | \(-0.567853\pi\) | ||||
−0.211555 | + | 0.977366i | \(0.567853\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 85893.4 | 0.296641 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −39842.9 | −0.133205 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 218538. | 0.707584 | 0.353792 | − | 0.935324i | \(-0.384892\pi\) | ||||
0.353792 | + | 0.935324i | \(0.384892\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −339156. | −1.06391 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 163470. | 0.497020 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 261352. | 0.770471 | 0.385236 | − | 0.922818i | \(-0.374120\pi\) | ||||
0.385236 | + | 0.922818i | \(0.374120\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −165075. | −0.472033 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 61318.5 | 0.170138 | 0.0850688 | − | 0.996375i | \(-0.472889\pi\) | ||||
0.0850688 | + | 0.996375i | \(0.472889\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −370769. | −0.998588 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 142628. | 0.373006 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 597307. | 1.51734 | 0.758670 | − | 0.651476i | \(-0.225850\pi\) | ||||
0.758670 | + | 0.651476i | \(0.225850\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 30625.0 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −500405. | −1.20057 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 663337. | 1.54740 | 0.773698 | − | 0.633555i | \(-0.218405\pi\) | ||||
0.773698 | + | 0.633555i | \(0.218405\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 651691. | 1.47858 | 0.739291 | − | 0.673386i | \(-0.235161\pi\) | ||||
0.739291 | + | 0.673386i | \(0.235161\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 172534. | 0.380844 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 194734. | 0.418324 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 842734. | 1.76233 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −199154. | −0.405542 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −770455. | −1.52814 | −0.764071 | − | 0.645132i | \(-0.776803\pi\) | ||||
−0.764071 | + | 0.645132i | \(0.776803\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 530263. | 1.02470 | 0.512351 | − | 0.858776i | \(-0.328775\pi\) | ||||
0.512351 | + | 0.858776i | \(0.328775\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7987.55 | 0.0150427 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 237902. | 0.436749 | 0.218374 | − | 0.975865i | \(-0.429925\pi\) | ||||
0.218374 | + | 0.975865i | \(0.429925\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −94676.7 | −0.169477 | −0.0847385 | − | 0.996403i | \(-0.527005\pi\) | ||||
−0.0847385 | + | 0.996403i | \(0.527005\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 423861. | 0.740002 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −231155. | −0.393697 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −144608. | −0.240330 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −160873. | −0.260950 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.39938e6 | 2.21601 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −103131. | −0.159472 | −0.0797358 | − | 0.996816i | \(-0.525408\pi\) | ||||
−0.0797358 | + | 0.996816i | \(0.525408\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 132684. | 0.200388 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −111954. | −0.165174 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −78092.0 | −0.112579 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 789990. | 1.11304 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −40777.6 | −0.0561618 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.35072e6 | 1.81887 | 0.909436 | − | 0.415844i | \(-0.136514\pi\) | ||||
0.909436 | + | 0.415844i | \(0.136514\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −30138.5 | −0.0396885 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.16439e6 | −1.49980 | −0.749899 | − | 0.661553i | \(-0.769898\pi\) | ||||
−0.749899 | + | 0.661553i | \(0.769898\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −367456. | −0.463038 | −0.231519 | − | 0.972830i | \(-0.574369\pi\) | ||||
−0.231519 | + | 0.972830i | \(0.574369\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −323548. | −0.398941 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 336123. | 0.405610 | 0.202805 | − | 0.979219i | \(-0.434994\pi\) | ||||
0.202805 | + | 0.979219i | \(0.434994\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 738376. | 0.872184 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.04953e6 | −1.21373 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −253077. | −0.286588 | −0.143294 | − | 0.989680i | \(-0.545769\pi\) | ||||
−0.143294 | + | 0.989680i | \(0.545769\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 881500. | 0.977641 | 0.488821 | − | 0.872384i | \(-0.337427\pi\) | ||||
0.488821 | + | 0.872384i | \(0.337427\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 359528. | 0.390587 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 60025.0 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −67712.4 | −0.0706197 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 516326. | 0.527747 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.46515e6 | 1.46790 | 0.733952 | − | 0.679202i | \(-0.237674\pi\) | ||||
0.733952 | + | 0.679202i | \(0.237674\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.57839e6 | −1.55029 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −621482. | −0.598520 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.33894e6 | −1.26453 | −0.632265 | − | 0.774752i | \(-0.717875\pi\) | ||||
−0.632265 | + | 0.774752i | \(0.717875\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 381679. | 0.353548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 227482. | 0.206703 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 273438. | 0.243764 | 0.121882 | − | 0.992545i | \(-0.461107\pi\) | ||||
0.121882 | + | 0.992545i | \(0.461107\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −607532. | −0.531440 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.08784e6 | −0.933869 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 958012. | 0.807217 | 0.403608 | − | 0.914932i | \(-0.367756\pi\) | ||||
0.403608 | + | 0.914932i | \(0.367756\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4501.33 | −0.00372321 | −0.00186161 | − | 0.999998i | \(-0.500593\pi\) | ||||
−0.00186161 | + | 0.999998i | \(0.500593\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 15655.6 | 0.0127134 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −295700. | −0.235787 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.73335e6 | 1.35733 | 0.678667 | − | 0.734446i | \(-0.262558\pi\) | ||||
0.678667 | + | 0.734446i | \(0.262558\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 76851.4 | 0.0591073 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.71229e6 | −1.29363 | −0.646817 | − | 0.762645i | \(-0.723900\pi\) | ||||
−0.646817 | + | 0.762645i | \(0.723900\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −769075. | −0.570824 | −0.285412 | − | 0.958405i | \(-0.592130\pi\) | ||||
−0.285412 | + | 0.958405i | \(0.592130\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.03199e6 | −0.752598 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −283432. | −0.203116 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.75290e6 | 1.23456 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −219838. | −0.152185 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.73492e6 | −1.18062 | −0.590309 | − | 0.807177i | \(-0.700994\pi\) | ||||
−0.590309 | + | 0.807177i | \(0.700994\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −896377. | −0.599702 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.92294e6 | 1.26495 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 76374.0 | 0.0494046 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −219429. | −0.139598 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.28367e6 | −0.803241 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 309061. | 0.190237 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.29034e6 | −1.38693 | −0.693465 | − | 0.720490i | \(-0.743917\pi\) | ||||
−0.693465 | + | 0.720490i | \(0.743917\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 151224. | 0.0901001 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.13571e6 | −0.665834 | −0.332917 | − | 0.942956i | \(-0.608033\pi\) | ||||
−0.332917 | + | 0.942956i | \(0.608033\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 231342. | 0.133473 | 0.0667364 | − | 0.997771i | \(-0.478741\pi\) | ||||
0.0667364 | + | 0.997771i | \(0.478741\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −59071.4 | −0.0335429 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.43914e6 | −0.804366 | −0.402183 | − | 0.915559i | \(-0.631749\pi\) | ||||
−0.402183 | + | 0.915559i | \(0.631749\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.23192e6 | 1.22801 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.00446e6 | −1.62744 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.26846e6 | 2.80981 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14308.1 | 0.00751406 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 285718. | 0.147764 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.44722e6 | 0.737130 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −81561.8 | −0.0409182 | −0.0204591 | − | 0.999791i | \(-0.506513\pi\) | ||||
−0.0204591 | + | 0.999791i | \(0.506513\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −375615. | −0.185623 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 759264. | 0.369641 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −880659. | −0.422409 | −0.211204 | − | 0.977442i | \(-0.567739\pi\) | ||||
−0.211204 | + | 0.977442i | \(0.567739\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.00953e6 | 0.477113 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 754020. | 0.351153 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.16400e6 | 0.526508 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.19657e6 | −1.87099 | −0.935493 | − | 0.353346i | \(-0.885044\pi\) | ||||
−0.935493 | + | 0.353346i | \(0.885044\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −456804. | −0.200755 | −0.100377 | − | 0.994949i | \(-0.532005\pi\) | ||||
−0.100377 | + | 0.994949i | \(0.532005\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −93045.9 | −0.0403115 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.40223e6 | −1.88034 | −0.940169 | − | 0.340709i | \(-0.889333\pi\) | ||||
−0.940169 | + | 0.340709i | \(0.889333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 237678. | 0.100096 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.21811e6 | −0.505841 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 276721. | 0.113320 | 0.0566599 | − | 0.998394i | \(-0.481955\pi\) | ||||
0.0566599 | + | 0.998394i | \(0.481955\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.27233e6 | 2.53315 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 876347. | 0.349068 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.41511e6 | 0.555980 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −44862.8 | −0.0173869 | −0.00869344 | − | 0.999962i | \(-0.502767\pi\) | ||||
−0.00869344 | + | 0.999962i | \(0.502767\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 278929. | 0.106642 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.19076e6 | −0.449149 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.03702e6 | −0.385935 | −0.192967 | − | 0.981205i | \(-0.561811\pi\) | ||||
−0.192967 | + | 0.981205i | \(0.561811\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 218067. | 0.0800778 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −107997. | −0.0391342 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −205535. | −0.0735001 | −0.0367500 | − | 0.999324i | \(-0.511701\pi\) | ||||
−0.0367500 | + | 0.999324i | \(0.511701\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.52841e6 | −1.59821 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.43359e6 | 0.499375 | 0.249687 | − | 0.968326i | \(-0.419672\pi\) | ||||
0.249687 | + | 0.968326i | \(0.419672\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −579573. | −0.199277 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 215943. | 0.0732930 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.66566e6 | 0.893163 | 0.446582 | − | 0.894743i | \(-0.352641\pi\) | ||||
0.446582 | + | 0.894743i | \(0.352641\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.94239e6 | −1.96571 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.77615e6 | −0.906695 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.88003e6 | −0.606277 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.94698e6 | −1.57530 | −0.787651 | − | 0.616122i | \(-0.788703\pi\) | ||||
−0.787651 | + | 0.616122i | \(0.788703\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.02270e6 | −0.636062 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 67297.3 | 0.0208995 | 0.0104498 | − | 0.999945i | \(-0.496674\pi\) | ||||
0.0104498 | + | 0.999945i | \(0.496674\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −36485.0 | −0.0111905 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.12515e6 | −0.340856 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.68531e6 | −1.10278 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.30687e6 | 1.27307 | 0.636537 | − | 0.771246i | \(-0.280366\pi\) | ||||
0.636537 | + | 0.771246i | \(0.280366\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.91953e6 | 1.72855 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.75690e6 | −0.506841 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 924897. | 0.263617 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.91433e6 | −1.66558 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.40325e6 | −1.22529 | −0.612645 | − | 0.790358i | \(-0.709894\pi\) | ||||
−0.612645 | + | 0.790358i | \(0.709894\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.49685e6 | 0.411599 | 0.205800 | − | 0.978594i | \(-0.434021\pi\) | ||||
0.205800 | + | 0.978594i | \(0.434021\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.42423e6 | −0.387015 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.11326e6 | −0.298969 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 605761. | 0.160780 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −151163. | −0.0396554 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.10009e6 | 0.803862 | 0.401931 | − | 0.915670i | \(-0.368339\pi\) | ||||
0.401931 | + | 0.915670i | \(0.368339\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −435162. | −0.111540 | −0.0557701 | − | 0.998444i | \(-0.517761\pi\) | ||||
−0.0557701 | + | 0.998444i | \(0.517761\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.64595e6 | −0.417055 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.86751e6 | −2.47175 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.80310e6 | 1.68479 | 0.842395 | − | 0.538860i | \(-0.181145\pi\) | ||||
0.842395 | + | 0.538860i | \(0.181145\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −115780. | −0.0283489 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.49011e6 | 0.602850 | 0.301425 | − | 0.953490i | \(-0.402538\pi\) | ||||
0.301425 | + | 0.953490i | \(0.402538\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.94865e6 | −0.466481 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.98675e6 | 1.18045 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −186239. | −0.0435968 | −0.0217984 | − | 0.999762i | \(-0.506939\pi\) | ||||
−0.0217984 | + | 0.999762i | \(0.506939\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.73668e6 | 0.633553 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.65450e6 | −0.378809 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 28044.0 | 0.00635054 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.11539e6 | 0.473805 | 0.236902 | − | 0.971533i | \(-0.423868\pi\) | ||||
0.236902 | + | 0.971533i | \(0.423868\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.23956e6 | 1.60391 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.86679e6 | −1.28573 | −0.642863 | − | 0.765981i | \(-0.722253\pi\) | ||||
−0.642863 | + | 0.765981i | \(0.722253\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −546789. | −0.118541 | −0.0592704 | − | 0.998242i | \(-0.518877\pi\) | ||||
−0.0592704 | + | 0.998242i | \(0.518877\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −556059. | −0.119258 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.66105e6 | −0.352444 | −0.176222 | − | 0.984350i | \(-0.556388\pi\) | ||||
−0.176222 | + | 0.984350i | \(0.556388\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.48816e6 | 0.312404 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.04998e6 | 0.633498 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.11871e6 | 0.435430 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.84861e6 | −0.375933 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.17184e6 | 0.235816 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −181346. | −0.0361136 | −0.0180568 | − | 0.999837i | \(-0.505748\pi\) | ||||
−0.0180568 | + | 0.999837i | \(0.505748\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 178322. | 0.0351433 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.28144e6 | 0.444981 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −393797. | −0.0760183 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −254424. | −0.0486111 | −0.0243056 | − | 0.999705i | \(-0.507737\pi\) | ||||
−0.0243056 | + | 0.999705i | \(0.507737\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.64750e6 | 0.689801 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.01599e6 | −1.31336 | −0.656682 | − | 0.754168i | \(-0.728041\pi\) | ||||
−0.656682 | + | 0.754168i | \(0.728041\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.40282e6 | 1.55707 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 570365. | 0.104626 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 465850. | 0.0845970 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.72217e6 | −0.489400 | −0.244700 | − | 0.969599i | \(-0.578689\pi\) | ||||
−0.244700 | + | 0.969599i | \(0.578689\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 855780. | 0.152324 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.91147e6 | −0.336859 | −0.168430 | − | 0.985714i | \(-0.553870\pi\) | ||||
−0.168430 | + | 0.985714i | \(0.553870\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.29944e6 | −0.401230 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.17456e6 | −0.894034 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.07515e6 | 0.355022 | 0.177511 | − | 0.984119i | \(-0.443195\pi\) | ||||
0.177511 | + | 0.984119i | \(0.443195\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.77362e6 | 0.469889 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.20215e7 | 2.01681 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 270889. | 0.0450063 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.39736e7 | −2.29924 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.33620e6 | 1.35847 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.09369e6 | −1.14493 | −0.572464 | − | 0.819930i | \(-0.694012\pi\) | ||||
−0.572464 | + | 0.819930i | \(0.694012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.40296e6 | 1.50318 | 0.751589 | − | 0.659631i | \(-0.229288\pi\) | ||||
0.751589 | + | 0.659631i | \(0.229288\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 427412. | 0.0676781 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.83876e6 | 0.445249 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.69340e6 | 0.729202 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.72899e6 | 0.266107 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −132421. | −0.0201901 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.38190e6 | −0.812927 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.25773e6 | 1.38538 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.13596e6 | −0.168419 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.70767e6 | −0.544638 | −0.272319 | − | 0.962207i | \(-0.587791\pi\) | ||||
−0.272319 | + | 0.962207i | \(0.587791\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.09520e6 | 1.32377 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 511808. | 0.0738101 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.60109e6 | −0.371696 | −0.185848 | − | 0.982579i | \(-0.559503\pi\) | ||||
−0.185848 | + | 0.982579i | \(0.559503\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −596137. | −0.0844142 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.39531e7 | 1.95791 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.68485e6 | −0.512398 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.71777e6 | 0.374524 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.23876e7 | 1.69180 | 0.845899 | − | 0.533343i | \(-0.179065\pi\) | ||||
0.845899 | + | 0.533343i | \(0.179065\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −102518. | −0.0138763 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.17614e7 | 1.57781 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.18095e6 | −0.157023 | −0.0785113 | − | 0.996913i | \(-0.525017\pi\) | ||||
−0.0785113 | + | 0.996913i | \(0.525017\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.80838e6 | 0.238324 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.20529e6 | −0.288076 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.06064e6 | 0.525792 | 0.262896 | − | 0.964824i | \(-0.415322\pi\) | ||||
0.262896 | + | 0.964824i | \(0.415322\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 868360. | 0.111458 | 0.0557288 | − | 0.998446i | \(-0.482252\pi\) | ||||
0.0557288 | + | 0.998446i | \(0.482252\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.07527e7 | −1.36814 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.08508e6 | 0.262998 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.42545e6 | −0.428330 | −0.214165 | − | 0.976798i | \(-0.568703\pi\) | ||||
−0.214165 | + | 0.976798i | \(0.568703\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.40051e6 | 0.917414 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.81280e6 | 0.222797 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.14974e7 | 1.40097 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −27598.4 | −0.00333422 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.37523e6 | −0.883446 | −0.441723 | − | 0.897151i | \(-0.645633\pi\) | ||||
−0.441723 | + | 0.897151i | \(0.645633\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.71385e6 | 0.559870 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.32023e6 | 0.391020 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −681768. | −0.0796159 | −0.0398080 | − | 0.999207i | \(-0.512675\pi\) | ||||
−0.0398080 | + | 0.999207i | \(0.512675\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.18200e6 | −0.252675 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.32134e6 | −0.151732 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.65581e7 | −1.88558 | −0.942788 | − | 0.333392i | \(-0.891807\pi\) | ||||
−0.942788 | + | 0.333392i | \(0.891807\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.78009e6 | 0.765684 | 0.382842 | − | 0.923814i | \(-0.374945\pi\) | ||||
0.382842 | + | 0.923814i | \(0.374945\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.46452e6 | −0.164021 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.56981e6 | 0.174364 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.45843e6 | 1.04195 | 0.520975 | − | 0.853572i | \(-0.325568\pi\) | ||||
0.520975 | + | 0.853572i | \(0.325568\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.22606e6 | −0.352476 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 676147. | 0.0732720 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.87909e6 | 0.309460 | 0.154730 | − | 0.987957i | \(-0.450549\pi\) | ||||
0.154730 | + | 0.987957i | \(0.450549\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.01819e6 | −0.215167 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.88639e6 | −0.410992 | −0.205496 | − | 0.978658i | \(-0.565881\pi\) | ||||
−0.205496 | + | 0.978658i | \(0.565881\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.42098e7 | −1.49060 | −0.745302 | − | 0.666727i | \(-0.767695\pi\) | ||||
−0.745302 | + | 0.666727i | \(0.767695\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.35593e7 | −1.41094 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.81935e6 | −0.394248 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.95302e7 | 1.98399 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.38746e7 | −1.39828 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.34544e6 | 0.734419 | 0.367210 | − | 0.930138i | \(-0.380313\pi\) | ||||
0.367210 | + | 0.930138i | \(0.380313\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.43933e6 | −0.142775 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.11176e6 | −0.798327 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 54966.2 | 0.00536719 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −458449. | −0.0444159 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.11128e7 | 1.06826 | 0.534131 | − | 0.845402i | \(-0.320639\pi\) | ||||
0.534131 | + | 0.845402i | \(0.320639\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.31469e6 | 0.411549 | 0.205775 | − | 0.978599i | \(-0.434029\pi\) | ||||
0.205775 | + | 0.978599i | \(0.434029\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.56246e6 | −0.147880 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.97655e6 | 0.279546 | 0.139773 | − | 0.990184i | \(-0.455363\pi\) | ||||
0.139773 | + | 0.990184i | \(0.455363\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.69638e7 | 1.58092 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.08988e6 | −0.100792 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.30910e7 | 1.20141 | 0.600705 | − | 0.799471i | \(-0.294887\pi\) | ||||
0.600705 | + | 0.799471i | \(0.294887\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.97293e6 | −0.452907 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.72956e6 | −0.246706 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.06932e7 | −1.85615 | −0.928076 | − | 0.372390i | \(-0.878538\pi\) | ||||
−0.928076 | + | 0.372390i | \(0.878538\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.52116e7 | 1.35416 | 0.677080 | − | 0.735910i | \(-0.263245\pi\) | ||||
0.677080 | + | 0.735910i | \(0.263245\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −569105. | −0.0502815 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.62327e6 | −0.317722 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.57380e7 | −1.36973 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.88510e7 | 1.62843 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.84894e6 | −0.501500 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.38700e6 | 0.628681 | 0.314340 | − | 0.949310i | \(-0.398217\pi\) | ||||
0.314340 | + | 0.949310i | \(0.398217\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.54024e6 | −0.214593 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.81532e6 | −0.403788 | −0.201894 | − | 0.979407i | \(-0.564710\pi\) | ||||
−0.201894 | + | 0.979407i | \(0.564710\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −771842. | −0.0642472 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.62505e7 | −1.34276 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.65574e6 | 0.135813 | 0.0679063 | − | 0.997692i | \(-0.478368\pi\) | ||||
0.0679063 | + | 0.997692i | \(0.478368\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.06037e7 | 0.863436 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.12832e6 | −0.414556 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −556330. | −0.0446462 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.91133e6 | −0.709982 | −0.354991 | − | 0.934870i | \(-0.615516\pi\) | ||||
−0.354991 | + | 0.934870i | \(0.615516\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.11792e6 | 0.0884252 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.05944e7 | −0.831980 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.03032e7 | 0.803321 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.69103e6 | 0.363141 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.15507e7 | −1.65640 | −0.828201 | − | 0.560432i | \(-0.810635\pi\) | ||||
−0.828201 | + | 0.560432i | \(0.810635\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.30392e7 | −1.75824 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.03050e7 | 0.780864 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.50690e6 | −0.339102 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.59129e6 | −0.268309 | −0.134154 | − | 0.990960i | \(-0.542832\pi\) | ||||
−0.134154 | + | 0.990960i | \(0.542832\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.62631e6 | 0.269024 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.31684e6 | −0.391678 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −270779. | −0.0198084 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.53202e6 | −0.256581 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.19801e7 | −0.864251 | −0.432125 | − | 0.901814i | \(-0.642236\pi\) | ||||
−0.432125 | + | 0.901814i | \(0.642236\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 530942. | 0.0380372 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.23025e7 | 0.875280 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.94840e6 | −0.208325 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.23234e7 | −1.56648 | −0.783238 | − | 0.621722i | \(-0.786433\pi\) | ||||
−0.783238 | + | 0.621722i | \(0.786433\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.59541e7 | 1.11187 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.97659e6 | 0.552108 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.12772e7 | −1.46270 | −0.731349 | − | 0.682003i | \(-0.761109\pi\) | ||||
−0.731349 | + | 0.682003i | \(0.761109\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 837727. | 0.0571985 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.43689e7 | −0.974442 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 683399. | 0.0460324 | 0.0230162 | − | 0.999735i | \(-0.492673\pi\) | ||||
0.0230162 | + | 0.999735i | \(0.492673\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −945015. | −0.0632256 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.89112e6 | −0.590860 | −0.295430 | − | 0.955364i | \(-0.595463\pi\) | ||||
−0.295430 | + | 0.955364i | \(0.595463\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.93280e6 | 0.589653 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.78400e6 | −0.116975 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.05485e7 | −0.687049 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.33218e6 | 0.150891 | 0.0754454 | − | 0.997150i | \(-0.475962\pi\) | ||||
0.0754454 | + | 0.997150i | \(0.475962\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.04481e7 | 1.31421 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.96371e6 | −0.189220 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.09657e6 | 0.132975 | 0.0664875 | − | 0.997787i | \(-0.478821\pi\) | ||||
0.0664875 | + | 0.997787i | \(0.478821\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.20285e7 | −1.38797 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.23202e6 | −0.327497 | −0.163749 | − | 0.986502i | \(-0.552359\pi\) | ||||
−0.163749 | + | 0.986502i | \(0.552359\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.00314e6 | 0.0623809 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.14733e6 | 0.132662 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −820832. | −0.0503809 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.41419e7 | 0.862366 | 0.431183 | − | 0.902265i | \(-0.358096\pi\) | ||||
0.431183 | + | 0.902265i | \(0.358096\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.86867e7 | −1.13213 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.14012e7 | −0.686282 | −0.343141 | − | 0.939284i | \(-0.611491\pi\) | ||||
−0.343141 | + | 0.939284i | \(0.611491\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −996072. | −0.0595712 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.32683e6 | 0.316531 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.71087e7 | 1.01012 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.49802e6 | −0.263872 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.91735e7 | 1.11762 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.46345e6 | 0.316441 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.97329e7 | 1.13568 | 0.567839 | − | 0.823140i | \(-0.307780\pi\) | ||||
0.567839 | + | 0.823140i | \(0.307780\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.81618e6 | 0.218241 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.54443e6 | 0.201421 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 283014. | 0.0159818 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.47890e6 | −0.475797 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.27816e7 | −1.27040 | −0.635198 | − | 0.772349i | \(-0.719082\pi\) | ||||
−0.635198 | + | 0.772349i | \(0.719082\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.26085e7 | −2.91534 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.75868e6 | 0.206992 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.67808e7 | −1.46566 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.08675e6 | 0.222274 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.33703e7 | 0.722699 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.84077e7 | 1.52603 | 0.763017 | − | 0.646378i | \(-0.223717\pi\) | ||||
0.763017 | + | 0.646378i | \(0.223717\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.44008e7 | −0.768838 | −0.384419 | − | 0.923159i | \(-0.625598\pi\) | ||||
−0.384419 | + | 0.923159i | \(0.625598\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −62822.0 | −0.00333338 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.53379e6 | 0.344565 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.32454e7 | 0.694238 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −54092.9 | −0.00281793 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.29199e7 | −0.668961 | −0.334481 | − | 0.942403i | \(-0.608561\pi\) | ||||
−0.334481 | + | 0.942403i | \(0.608561\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.04860e7 | 1.05428 | 0.527142 | − | 0.849777i | \(-0.323263\pi\) | ||||
0.527142 | + | 0.849777i | \(0.323263\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.12689e6 | −0.211100 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.95049e7 | −0.991701 | −0.495851 | − | 0.868408i | \(-0.665144\pi\) | ||||
−0.495851 | + | 0.868408i | \(0.665144\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.30466e7 | −1.16472 | −0.582360 | − | 0.812931i | \(-0.697870\pi\) | ||||
−0.582360 | + | 0.812931i | \(0.697870\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.41912e7 | 1.21522 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.27672e6 | −0.213549 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.53296e6 | 0.0760879 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.47746e6 | 0.319588 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −723933. | −0.0355053 | −0.0177527 | − | 0.999842i | \(-0.505651\pi\) | ||||
−0.0177527 | + | 0.999842i | \(0.505651\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.74310e6 | 0.0849830 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.38972e7 | −1.15819 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.26922e6 | −0.446582 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.07682e6 | 0.147365 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.07334e7 | −0.511057 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.59863e7 | 1.23004 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.46977e6 | 0.304450 | 0.152225 | − | 0.988346i | \(-0.451356\pi\) | ||||
0.152225 | + | 0.988346i | \(0.451356\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.56571e6 | 0.166813 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.07017e7 | 0.497740 | 0.248870 | − | 0.968537i | \(-0.419941\pi\) | ||||
0.248870 | + | 0.968537i | \(0.419941\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.06996e7 | 0.494748 | 0.247374 | − | 0.968920i | \(-0.420432\pi\) | ||||
0.247374 | + | 0.968920i | \(0.420432\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.95566e6 | −0.181849 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.56531e7 | 0.715439 | 0.357720 | − | 0.933829i | \(-0.383554\pi\) | ||||
0.357720 | + | 0.933829i | \(0.383554\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.49327e7 | 0.678575 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.44640e7 | 1.10530 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.55792e7 | 1.59826 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 695274. | 0.0310535 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 759580. | 0.0337317 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 765625. | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.20997e6 | 0.316544 | 0.158272 | − | 0.987396i | \(-0.449408\pi\) | ||||
0.158272 | + | 0.987396i | \(0.449408\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.42130e7 | −1.05700 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.42075e7 | −0.616705 | −0.308352 | − | 0.951272i | \(-0.599778\pi\) | ||||
−0.308352 | + | 0.951272i | \(0.599778\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.79016e7 | −0.772661 | −0.386331 | − | 0.922360i | \(-0.626258\pi\) | ||||
−0.386331 | + | 0.922360i | \(0.626258\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.25101e7 | −0.536912 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.01802e7 | 0.434456 | 0.217228 | − | 0.976121i | \(-0.430299\pi\) | ||||
0.217228 | + | 0.976121i | \(0.430299\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.58990e7 | −0.674709 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.12932e7 | 0.898559 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.73580e7 | −3.66585 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.65834e7 | 0.692017 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.06590e6 | 0.0442319 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.51826e6 | 0.310254 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.32860e7 | 1.77638 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.06242e6 | −0.124982 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.62923e7 | 0.661242 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.28796e7 | 0.519857 | 0.259928 | − | 0.965628i | \(-0.416301\pi\) | ||||
0.259928 | + | 0.965628i | \(0.416301\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.43530e6 | 0.178038 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.33658e7 | −1.33201 | −0.666003 | − | 0.745949i | \(-0.731996\pi\) | ||||
−0.666003 | + | 0.745949i | \(0.731996\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.75035e7 | −0.694942 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.31336e6 | 0.170319 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.74693e6 | −0.382776 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.33616e7 | −1.30304 | −0.651521 | − | 0.758631i | \(-0.725869\pi\) | ||||
−0.651521 | + | 0.758631i | \(0.725869\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.19647e7 | −1.24172 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 217647. | 0.00840908 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.86835e6 | 0.187080 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −522507. | −0.0199707 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.31001e7 | −1.25832 | −0.629159 | − | 0.777276i | \(-0.716601\pi\) | ||||
−0.629159 | + | 0.777276i | \(0.716601\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.10162e6 | −0.268524 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.58503e7 | −0.596119 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.10683e7 | 0.788136 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.64876e7 | 1.35768 | 0.678838 | − | 0.734288i | \(-0.262484\pi\) | ||||
0.678838 | + | 0.734288i | \(0.262484\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.22867e6 | 0.119498 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.90067e7 | −0.699732 | −0.349866 | − | 0.936800i | \(-0.613773\pi\) | ||||
−0.349866 | + | 0.936800i | \(0.613773\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.92972e7 | −0.706669 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.97886e6 | −0.181364 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.04213e7 | −1.46466 | −0.732328 | − | 0.680952i | \(-0.761566\pi\) | ||||
−0.732328 | + | 0.680952i | \(0.761566\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.29585e6 | 0.0467077 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.00850e7 | −0.720147 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.05318e7 | 0.375639 | 0.187820 | − | 0.982204i | \(-0.439858\pi\) | ||||
0.187820 | + | 0.982204i | \(0.439858\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.92614e7 | −0.683406 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.11493e7 | 1.09943 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.07832e7 | 0.729736 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.60892e7 | −0.911282 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.03810e7 | 0.360721 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.32566e7 | 0.458261 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.11101e7 | 1.06988 | 0.534940 | − | 0.844890i | \(-0.320334\pi\) | ||||
0.534940 | + | 0.844890i | \(0.320334\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.35282e7 | 2.51562 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.47706e7 | 0.502747 | 0.251373 | − | 0.967890i | \(-0.419118\pi\) | ||||
0.251373 | + | 0.967890i | \(0.419118\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.07650e7 | −0.703152 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 199689. | 0.00672732 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.13172e7 | 1.38482 | 0.692412 | − | 0.721502i | \(-0.256548\pi\) | ||||
0.692412 | + | 0.721502i | \(0.256548\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.68779e7 | 1.22973 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −987207. | −0.0327518 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.93062e6 | −0.294780 | −0.147390 | − | 0.989078i | \(-0.547087\pi\) | ||||
−0.147390 | + | 0.989078i | \(0.547087\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.94754e6 | 0.195320 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.01978e7 | 0.659951 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.49397e7 | −0.485680 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.58196e7 | 1.48206 | 0.741032 | − | 0.671470i | \(-0.234337\pi\) | ||||
0.741032 | + | 0.671470i | \(0.234337\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.13830e6 | −0.0366340 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.36692e6 | −0.0757924 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.46900e7 | 0.786654 | 0.393327 | − | 0.919399i | \(-0.371324\pi\) | ||||
0.393327 | + | 0.919399i | \(0.371324\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.16589e7 | −1.00365 |
(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 | 280.6.a.g.1.4 | ✓ | 4 | |
4.3 | odd | 2 | 560.6.a.x.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.6.a.g.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
560.6.a.x.1.1 | 4 | 4.3 | odd | 2 |